LMFDB - Embedded newform 770.2.bv.a.157.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			157.24
Character	$\chi$	$=$	770.157
Dual form			770.2.bv.a.103.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358368 - 0.933580i) q^{2} +(1.75302 + 2.69941i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(2.03213 + 0.932978i) q^{5} +(1.89189 - 2.60396i) q^{6} +(2.64059 + 0.165124i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.99352 + 6.72356i) q^{9} +O(q^{10})$	\(q+(-0.358368 - 0.933580i) q^{2} +(1.75302 + 2.69941i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(2.03213 + 0.932978i) q^{5} +(1.89189 - 2.60396i) q^{6} +(2.64059 + 0.165124i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.99352 + 6.72356i) q^{9} +(0.142759 - 2.23151i) q^{10} +(-1.08813 - 3.13305i) q^{11} +(-3.10900 - 0.833054i) q^{12} +(2.83979 + 0.449779i) q^{13} +(-0.792148 - 2.52438i) q^{14} +(1.04387 + 7.12107i) q^{15} +(0.104528 - 0.994522i) q^{16} +(1.82100 - 4.74388i) q^{17} +(7.34977 + 0.385185i) q^{18} +(2.30935 - 2.56479i) q^{19} +(-2.13445 + 0.666423i) q^{20} +(4.18326 + 7.41750i) q^{21} +(-2.53500 + 2.13864i) q^{22} +(5.32705 + 1.42738i) q^{23} +(0.336443 + 3.20104i) q^{24} +(3.25911 + 3.79186i) q^{25} +(-0.597786 - 2.81236i) q^{26} +(-13.8602 + 2.19524i) q^{27} +(-2.07283 + 1.64419i) q^{28} +(-6.19603 - 2.01321i) q^{29} +(6.27400 - 3.52650i) q^{30} +(-10.5203 + 1.10573i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(6.54987 - 8.42957i) q^{33} -5.08138 q^{34} +(5.21197 + 2.79917i) q^{35} +(-2.27432 - 6.99964i) q^{36} +(-7.64681 - 4.96589i) q^{37} +(-3.22203 - 1.23682i) q^{38} +(3.76406 + 8.45422i) q^{39} +(1.38708 + 1.75386i) q^{40} +(-6.13033 + 1.99187i) q^{41} +(5.42569 - 6.56361i) q^{42} +(-5.89521 + 5.89521i) q^{43} +(2.90505 + 1.60021i) q^{44} +(-12.3562 + 10.8703i) q^{45} +(-0.576471 - 5.48476i) q^{46} +(-0.189903 - 3.62357i) q^{47} +(2.86786 - 1.46125i) q^{48} +(6.94547 + 0.872051i) q^{49} +(2.37205 - 4.40152i) q^{50} +(15.9979 - 3.40046i) q^{51} +(-2.41134 + 1.56594i) q^{52} +(-2.00001 - 1.61958i) q^{53} +(7.01648 + 12.1529i) q^{54} +(0.711849 - 7.38196i) q^{55} +(2.27782 + 1.34593i) q^{56} +(10.9717 + 1.73775i) q^{57} +(0.340963 + 6.50596i) q^{58} +(-4.09261 - 4.54530i) q^{59} +(-5.54067 - 4.59350i) q^{60} +(-0.185139 - 0.0194589i) q^{61} +(4.80243 + 9.42530i) q^{62} +(-9.01490 + 17.2599i) q^{63} +(0.587785 + 0.809017i) q^{64} +(5.35119 + 3.56347i) q^{65} +(-10.2169 - 3.09394i) q^{66} +(1.55145 - 0.415709i) q^{67} +(1.82100 + 4.74388i) q^{68} +(5.48532 + 16.8821i) q^{69} +(0.745444 - 5.86893i) q^{70} +(2.66137 + 1.93360i) q^{71} +(-5.71968 + 4.63171i) q^{72} +(0.111117 - 2.12024i) q^{73} +(-1.89569 + 8.91853i) q^{74} +(-4.52252 + 15.4448i) q^{75} +3.45127i q^{76} +(-2.35596 - 8.45278i) q^{77} +(6.54378 - 6.54378i) q^{78} +(0.0795894 - 0.178761i) q^{79} +(1.14028 - 1.92348i) q^{80} +(-15.4488 - 17.1577i) q^{81} +(4.05648 + 5.00934i) q^{82} +(0.0426090 + 0.269022i) q^{83} +(-8.07205 - 2.71313i) q^{84} +(8.12645 - 7.94122i) q^{85} +(7.61631 + 3.39100i) q^{86} +(-5.42726 - 20.2548i) q^{87} +(0.452846 - 3.28556i) q^{88} +(-0.977585 - 1.69323i) q^{89} +(14.5763 + 7.63992i) q^{90} +(7.42447 + 1.65660i) q^{91} +(-4.91387 + 2.50374i) q^{92} +(-21.4271 - 26.4602i) q^{93} +(-3.31484 + 1.47586i) q^{94} +(7.08579 - 3.05742i) q^{95} +(-2.39194 - 2.15371i) q^{96} +(-1.65410 + 10.4436i) q^{97} +(-1.67490 - 6.79667i) q^{98} +(24.3226 + 2.06277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$3$	1.75302	+	2.69941i	1.01210	+	1.55850i	0.816109	+	0.577898i	$0.196127\pi$
$3$	1.75302	+	2.69941i	1.01210	+	1.55850i	0.195995	+	0.980605i	$0.437206\pi$
$4$	−0.743145	+	0.669131i	−0.371572	+	0.334565i
$5$	2.03213	+	0.932978i	0.908796	+	0.417240i
$5$	2.03213	+	0.932978i	0.908796	+	0.417240i
$6$	1.89189	−	2.60396i	0.772360	−	1.06306i
$7$	2.64059	+	0.165124i	0.998051	+	0.0624110i
$7$	2.64059	+	0.165124i	0.998051	+	0.0624110i
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	−2.99352	+	6.72356i	−0.997841	+	2.24119i
$10$	0.142759	−	2.23151i	0.0451444	−	0.705664i
$11$	−1.08813	−	3.13305i	−0.328082	−	0.944649i
$11$	−1.08813	−	3.13305i	−0.328082	−	0.944649i
$12$	−3.10900	−	0.833054i	−0.897491	−	0.240482i
$13$	2.83979	+	0.449779i	0.787617	+	0.124746i	0.537270	−	0.843410i	$-0.319455\pi$
$13$	2.83979	+	0.449779i	0.787617	+	0.124746i	0.250346	+	0.968156i	$0.419455\pi$
$14$	−0.792148	−	2.52438i	−0.211710	−	0.674669i
$15$	1.04387	+	7.12107i	0.269526	+	1.83865i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	1.82100	−	4.74388i	0.441658	−	1.15056i	−0.514443	−	0.857524i	$-0.672001\pi$
$17$	1.82100	−	4.74388i	0.441658	−	1.15056i	0.956102	−	0.293035i	$-0.0946652\pi$
$18$	7.34977	+	0.385185i	1.73236	+	0.0907890i
$19$	2.30935	−	2.56479i	0.529801	−	0.588403i	−0.417529	−	0.908664i	$-0.637104\pi$
$19$	2.30935	−	2.56479i	0.529801	−	0.588403i	0.947330	+	0.320260i	$0.103770\pi$
$20$	−2.13445	+	0.666423i	−0.477278	+	0.149017i
$21$	4.18326	+	7.41750i	0.912863	+	1.61863i
$22$	−2.53500	+	2.13864i	−0.540464	+	0.455959i
$23$	5.32705	+	1.42738i	1.11077	+	0.297629i	0.767142	−	0.641478i	$-0.221678\pi$
$23$	5.32705	+	1.42738i	1.11077	+	0.297629i	0.343625	+	0.939107i	$0.388345\pi$
$24$	0.336443	+	3.20104i	0.0686761	+	0.653410i
$25$	3.25911	+	3.79186i	0.651821	+	0.758373i
$26$	−0.597786	−	2.81236i	−0.117235	−	0.551549i
$27$	−13.8602	+	2.19524i	−2.66739	+	0.422474i
$28$	−2.07283	+	1.64419i	−0.391729	+	0.310723i
$29$	−6.19603	−	2.01321i	−1.15057	−	0.373844i	−0.329215	−	0.944255i	$-0.606784\pi$
$29$	−6.19603	−	2.01321i	−1.15057	−	0.373844i	−0.821359	+	0.570411i	$0.806784\pi$
$30$	6.27400	−	3.52650i	1.14547	−	0.643848i
$31$	−10.5203	+	1.10573i	−1.88950	+	0.198595i	−0.977405	−	0.211375i	$-0.932206\pi$
$31$	−10.5203	+	1.10573i	−1.88950	+	0.198595i	−0.912099	+	0.409970i	$0.865539\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	6.54987	−	8.42957i	1.14019	−	1.46740i
$34$	−5.08138			−0.871449
$35$	5.21197	+	2.79917i	0.880984	+	0.473146i
$36$	−2.27432	−	6.99964i	−0.379053	−	1.16661i
$37$	−7.64681	−	4.96589i	−1.25713	−	0.816388i	−0.267996	−	0.963420i	$-0.586361\pi$
$37$	−7.64681	−	4.96589i	−1.25713	−	0.816388i	−0.989132	+	0.147032i	$0.953028\pi$
$38$	−3.22203	−	1.23682i	−0.522683	−	0.200639i
$39$	3.76406	+	8.45422i	0.602732	+	1.35376i
$40$	1.38708	+	1.75386i	0.219316	+	0.277309i
$41$	−6.13033	+	1.99187i	−0.957397	+	0.311077i	−0.745718	−	0.666262i	$-0.767893\pi$
$41$	−6.13033	+	1.99187i	−0.957397	+	0.311077i	−0.211679	+	0.977339i	$0.567893\pi$
$42$	5.42569	−	6.56361i	0.837201	−	1.01279i
$43$	−5.89521	+	5.89521i	−0.899012	+	0.899012i	−0.995349	−	0.0963372i	$-0.969287\pi$
$43$	−5.89521	+	5.89521i	−0.899012	+	0.899012i	0.0963372	+	0.995349i	$0.469287\pi$
$44$	2.90505	+	1.60021i	0.437953	+	0.241241i
$45$	−12.3562	+	10.8703i	−1.84195	+	1.62044i
$46$	−0.576471	−	5.48476i	−0.0849961	−	0.808683i
$47$	−0.189903	−	3.62357i	−0.0277002	−	0.528552i	−0.976876	−	0.213806i	$-0.931414\pi$
$47$	−0.189903	−	3.62357i	−0.0277002	−	0.528552i	0.949176	−	0.314746i	$-0.101919\pi$
$48$	2.86786	−	1.46125i	0.413940	−	0.210913i
$49$	6.94547	+	0.872051i	0.992210	+	0.124579i
$50$	2.37205	−	4.40152i	0.335459	−	0.622469i
$51$	15.9979	−	3.40046i	2.24015	−	0.476159i
$52$	−2.41134	+	1.56594i	−0.334392	+	0.217157i
$53$	−2.00001	−	1.61958i	−0.274723	−	0.222466i	0.482051	−	0.876143i	$-0.339892\pi$
$53$	−2.00001	−	1.61958i	−0.274723	−	0.222466i	−0.756774	+	0.653677i	$0.773225\pi$
$54$	7.01648	+	12.1529i	0.954822	+	1.65380i
$55$	0.711849	−	7.38196i	0.0959857	−	0.995383i
$56$	2.27782	+	1.34593i	0.304387	+	0.179858i
$57$	10.9717	+	1.73775i	1.45324	+	0.230171i
$58$	0.340963	+	6.50596i	0.0447707	+	0.854275i
$59$	−4.09261	−	4.54530i	−0.532812	−	0.591748i	0.415300	−	0.909685i	$-0.363677\pi$
$59$	−4.09261	−	4.54530i	−0.532812	−	0.591748i	−0.948112	+	0.317937i	$0.897010\pi$
$60$	−5.54067	−	4.59350i	−0.715298	−	0.593018i
$61$	−0.185139	−	0.0194589i	−0.0237046	−	0.00249146i	0.0926687	−	0.995697i	$-0.470460\pi$
$61$	−0.185139	−	0.0194589i	−0.0237046	−	0.00249146i	−0.116373	+	0.993206i	$0.537127\pi$
$62$	4.80243	+	9.42530i	0.609909	+	1.19701i
$63$	−9.01490	+	17.2599i	−1.13577	+	2.17454i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	5.35119	+	3.56347i	0.663734	+	0.441994i
$66$	−10.2169	−	3.09394i	−1.25762	−	0.380837i
$67$	1.55145	−	0.415709i	0.189539	−	0.0507869i	−0.162801	−	0.986659i	$-0.552053\pi$
$67$	1.55145	−	0.415709i	0.189539	−	0.0507869i	0.352340	+	0.935872i	$0.385386\pi$
$68$	1.82100	+	4.74388i	0.220829	+	0.575280i
$69$	5.48532	+	16.8821i	0.660356	+	2.03237i
$70$	0.745444	−	5.86893i	0.0890976	−	0.701471i
$71$	2.66137	+	1.93360i	0.315847	+	0.229476i	0.734401	−	0.678716i	$-0.237463\pi$
$71$	2.66137	+	1.93360i	0.315847	+	0.229476i	−0.418554	+	0.908192i	$0.637463\pi$
$72$	−5.71968	+	4.63171i	−0.674071	+	0.545852i
$73$	0.111117	−	2.12024i	0.0130053	−	0.248155i	−0.984389	−	0.176008i	$-0.943682\pi$
$73$	0.111117	−	2.12024i	0.0130053	−	0.248155i	0.997394	−	0.0721471i	$-0.0229851\pi$
$74$	−1.89569	+	8.91853i	−0.220370	+	1.03676i
$75$	−4.52252	+	15.4448i	−0.522216	+	1.78342i
$76$			3.45127i			0.395887i
$77$	−2.35596	−	8.45278i	−0.268486	−	0.963284i
$78$	6.54378	−	6.54378i	0.740937	−	0.740937i
$79$	0.0795894	−	0.178761i	0.00895451	−	0.0201122i	−0.909013	−	0.416768i	$-0.863163\pi$
$79$	0.0795894	−	0.178761i	0.00895451	−	0.0201122i	0.917967	+	0.396656i	$0.129829\pi$
$80$	1.14028	−	1.92348i	0.127487	−	0.215051i
$81$	−15.4488	−	17.1577i	−1.71654	−	1.90641i
$82$	4.05648	+	5.00934i	0.447963	+	0.553189i
$83$	0.0426090	+	0.269022i	0.00467694	+	0.0295290i	0.989916	−	0.141652i	$-0.0452415\pi$
$83$	0.0426090	+	0.269022i	0.00467694	+	0.0295290i	−0.985240	+	0.171182i	$0.945242\pi$
$84$	−8.07205	−	2.71313i	−0.880733	−	0.296026i
$85$	8.12645	−	7.94122i	0.881437	−	0.861346i
$86$	7.61631	+	3.39100i	0.821288	+	0.365661i
$87$	−5.42726	−	20.2548i	−0.581863	−	2.17154i
$88$	0.452846	−	3.28556i	0.0482736	−	0.350242i
$89$	−0.977585	−	1.69323i	−0.103624	−	0.179482i	0.809551	−	0.587049i	$-0.199710\pi$
$89$	−0.977585	−	1.69323i	−0.103624	−	0.179482i	−0.913175	+	0.407567i	$0.866377\pi$
$90$	14.5763	+	7.63992i	1.53648	+	0.805318i
$91$	7.42447	+	1.65660i	0.778296	+	0.173659i
$92$	−4.91387	+	2.50374i	−0.512307	+	0.261033i
$93$	−21.4271	−	26.4602i	−2.22188	−	2.74380i
$94$	−3.31484	+	1.47586i	−0.341900	+	0.152223i
$95$	7.08579	−	3.05742i	0.726986	−	0.313685i
$96$	−2.39194	−	2.15371i	−0.244126	−	0.219812i
$97$	−1.65410	+	10.4436i	−0.167948	+	1.06038i	0.749347	+	0.662177i	$0.230367\pi$
$97$	−1.65410	+	10.4436i	−0.167948	+	1.06038i	−0.917296	+	0.398207i	$0.869633\pi$
$98$	−1.67490	−	6.79667i	−0.169191	−	0.686567i
$99$	24.3226	+	2.06277i	2.44451	+	0.207316i
$100$	−4.95924	−	0.637136i	−0.495924	−	0.0637136i
$101$	−8.06073	+	0.847217i	−0.802072	+	0.0843012i	−0.496689	−	0.867928i	$-0.665451\pi$
$101$	−8.06073	+	0.847217i	−0.802072	+	0.0843012i	−0.305383	+	0.952230i	$0.598785\pi$
$102$	−8.90774	−	13.7167i	−0.881997	−	1.35816i
$103$	8.57961	+	5.57167i	0.845374	+	0.548993i	0.893095	−	0.449868i	$-0.148529\pi$
$103$	8.57961	+	5.57167i	0.845374	+	0.548993i	−0.0477206	+	0.998861i	$0.515196\pi$
$104$	2.32608	+	1.68999i	0.228091	+	0.165718i
$105$	1.58057	+	18.9762i	0.154248	+	1.85189i
$106$	−0.795267	+	2.44758i	−0.0772431	+	0.237730i
$107$	3.69177	−	0.193477i	0.356897	−	0.0187042i	0.126955	−	0.991909i	$-0.459480\pi$
$107$	3.69177	−	0.193477i	0.356897	−	0.0187042i	0.229942	+	0.973204i	$0.426146\pi$
$108$	8.83122	−	10.9057i	0.849785	−	1.04940i
$109$	12.7909	+	7.38481i	1.22514	+	0.707337i	0.966010	−	0.258505i	$-0.0832299\pi$
$109$	12.7909	+	7.38481i	1.22514	+	0.707337i	0.259133	+	0.965842i	$0.416563\pi$
$110$	−7.14675	+	1.98089i	−0.681416	+	0.188870i
$111$		−	29.3471i		−	2.78551i
$112$	0.440237	−	2.60887i	0.0415985	−	0.246515i
$113$	−2.42958	−	1.23793i	−0.228555	−	0.116455i	0.335963	−	0.941875i	$-0.390938\pi$
$113$	−2.42958	−	1.23793i	−0.228555	−	0.116455i	−0.564519	+	0.825420i	$0.690938\pi$
$114$	−2.30959	−	10.8657i	−0.216313	−	1.01767i
$115$	9.49355	+	7.87064i	0.885278	+	0.733941i
$116$	5.95165	−	2.64985i	0.552597	−	0.246032i
$117$	−11.5251	+	17.7471i	−1.06550	+	1.64072i
$118$	−2.77675	+	5.44967i	−0.255620	+	0.501683i
$119$	5.59186	−	12.2260i	0.512605	−	1.12075i
$120$	−2.30280	+	6.81883i	−0.210216	+	0.622471i
$121$	−8.63196	+	6.81830i	−0.784724	+	0.619845i
$122$	0.0481815	+	0.179816i	0.00436214	+	0.0162797i
$123$	−16.1234	−	13.0565i	−1.45380	−	1.17726i
$124$	7.07824	−	7.86118i	0.635645	−	0.705955i
$125$	3.08520	+	10.7462i	0.275949	+	0.961172i
$126$	19.3442	+	2.23074i	1.72331	+	0.198730i
$127$	−3.23254	−	20.4095i	−0.286842	−	1.81105i	−0.537824	−	0.843057i	$-0.680754\pi$
$127$	−3.23254	−	20.4095i	−0.286842	−	1.81105i	0.250982	−	0.967992i	$-0.419246\pi$
$128$	0.544639	−	0.838671i	0.0481397	−	0.0741287i
$129$	−26.2480	−	5.57918i	−2.31101	−	0.491219i
$130$	1.40909	−	6.27280i	0.123585	−	0.550161i
$131$	17.0698	−	9.85527i	1.49140	−	0.861059i	0.491446	−	0.870908i	$-0.336469\pi$
$131$	17.0698	−	9.85527i	1.49140	−	0.861059i	0.999951	+	0.00984937i	$0.00313520\pi$
$132$	0.772986	+	10.6471i	0.0672798	+	0.926712i
$133$	6.52156	−	6.39124i	0.565491	−	0.554191i
$134$	−0.944087	−	1.29942i	−0.0815567	−	0.112253i
$135$	−30.2138	−	8.47023i	−2.60039	−	0.729002i
$136$	3.77620	−	3.40011i	0.323807	−	0.291557i
$137$	0.770734	+	0.295857i	0.0658482	+	0.0252768i	0.391069	−	0.920361i	$-0.372105\pi$
$137$	0.770734	+	0.295857i	0.0658482	+	0.0252768i	−0.325221	+	0.945638i	$0.605439\pi$
$138$	13.7950	−	11.1710i	1.17431	−	0.950938i
$139$	3.05268	−	9.39518i	0.258925	−	0.796888i	−0.734106	−	0.679035i	$-0.762399\pi$
$139$	3.05268	−	9.39518i	0.258925	−	0.796888i	0.993031	−	0.117854i	$-0.0376014\pi$
$140$	−5.74626	+	1.40730i	−0.485648	+	0.118939i
$141$	9.44859	−	6.86480i	0.795715	−	0.578120i
$142$	0.851421	−	3.17754i	0.0714496	−	0.266654i
$143$	−1.68087	−	9.38662i	−0.140562	−	0.784949i
$144$	6.37382	+	3.67993i	0.531152	+	0.306661i
$145$	−10.7129	−	9.87187i	−0.889655	−	0.819814i
$146$	−2.01923	+	0.656089i	−0.167113	+	0.0542983i
$147$	9.82149	+	20.2774i	0.810063	+	1.67245i
$148$	9.00552	−	1.42633i	0.740249	−	0.117244i
$149$	6.99600	+	0.735310i	0.573135	+	0.0602389i	0.386662	−	0.922221i	$-0.373628\pi$
$149$	6.99600	+	0.735310i	0.573135	+	0.0602389i	0.186472	+	0.982460i	$0.440295\pi$
$150$	16.0397	−	1.31280i	1.30964	−	0.107190i
$151$	−4.94331	−	1.05073i	−0.402281	−	0.0855075i	0.00232781	−	0.999997i	$-0.499259\pi$
$151$	−4.94331	−	1.05073i	−0.402281	−	0.0855075i	−0.404609	+	0.914490i	$0.632592\pi$
$152$	3.22203	−	1.23682i	0.261341	−	0.100320i
$153$	26.4445	+	26.4445i	2.13791	+	2.13791i
$154$	−7.04705	+	5.22868i	−0.567867	+	0.421339i
$155$	−22.4103	−	7.56823i	−1.80004	−	0.607895i
$156$	−8.45422	−	3.76406i	−0.676880	−	0.301366i
$157$	−7.18460	+	4.66574i	−0.573394	+	0.372366i	−0.798524	−	0.601962i	$-0.794386\pi$
$157$	−7.18460	+	4.66574i	−0.573394	+	0.372366i	0.225131	+	0.974329i	$0.427719\pi$
$158$	−0.195410	−	0.0102410i	−0.0155460	−	0.000814730i
$159$	0.865848	−	8.23800i	0.0686662	−	0.653316i
$160$	−2.20436	−	0.375233i	−0.174270	−	0.0296648i
$161$	13.8309	+	4.64875i	1.09003	+	0.366373i
$162$	−10.4817	+	20.5715i	−0.823520	+	1.61625i
$163$	−4.43498	+	1.70243i	−0.347374	+	0.133345i	−0.525799	−	0.850609i	$-0.676233\pi$
$163$	−4.43498	+	1.70243i	−0.347374	+	0.133345i	0.178424	+	0.983954i	$0.442900\pi$
$164$	3.22291	−	5.58224i	0.251667	−	0.435900i
$165$	21.1748	−	11.0191i	1.64845	−	0.857837i
$166$	0.235884	−	0.136188i	0.0183082	−	0.0105702i
$167$	0.0918514	−	0.579927i	0.00710767	−	0.0448761i	−0.983880	−	0.178832i	$-0.942768\pi$
$167$	0.0918514	−	0.579927i	0.00710767	−	0.0448761i	0.990987	+	0.133956i	$0.0427681\pi$
$168$	0.359840	+	8.50820i	0.0277623	+	0.656422i
$169$	−4.50161	−	1.46266i	−0.346278	−	0.112513i
$170$	−10.3260	−	4.74081i	−0.791970	−	0.363604i
$171$	10.3314	+	23.2048i	0.790065	+	1.77452i
$172$	0.436330	−	8.32566i	0.0332698	−	0.634826i
$173$	−13.7956	+	0.722994i	−1.04886	+	0.0549683i	−0.568967	−	0.822360i	$-0.692657\pi$
$173$	−13.7956	+	0.722994i	−1.04886	+	0.0549683i	−0.479890	+	0.877329i	$0.659323\pi$
$174$	−16.9645	+	12.3255i	−1.28608	+	0.934390i
$175$	7.97985	+	10.5509i	0.603220	+	0.797575i
$176$	−3.22962	+	0.754672i	−0.243442	+	0.0568856i
$177$	5.09521	−	19.0156i	0.382980	−	1.42930i
$178$	−1.23043	+	1.51945i	−0.0922245	+	0.113888i
$179$	1.38426	−	6.51242i	0.103464	−	0.486761i	−0.895653	−	0.444754i	$-0.853291\pi$
$179$	1.38426	−	6.51242i	0.103464	−	0.486761i	0.999117	−	0.0420077i	$-0.0133754\pi$
$180$	1.90879	−	16.3461i	0.142273	−	1.21836i
$181$	−6.15692	+	8.47427i	−0.457640	+	0.629888i	−0.974017	−	0.226474i	$-0.927280\pi$
$181$	−6.15692	+	8.47427i	−0.457640	+	0.629888i	0.516377	+	0.856361i	$0.327280\pi$
$182$	−1.11412	−	7.52501i	−0.0825841	−	0.557791i
$183$	−0.272024	−	0.533877i	−0.0201086	−	0.0394654i
$184$	4.09842	+	3.69023i	0.302140	+	0.272048i
$185$	−10.9062	−	17.2256i	−0.801843	−	1.26645i
$186$	−17.0240	+	29.4864i	−1.24826	+	2.16205i
$187$	−16.8443	−	0.543355i	−1.23177	−	0.0397341i
$188$	2.56577	+	2.56577i	0.187128	+	0.187128i
$189$	−36.9616	+	3.50808i	−2.68856	+	0.255175i
$190$	−5.39367	−	5.51947i	−0.391298	−	0.400425i
$191$	25.6333	−	5.44853i	1.85476	−	0.394242i	0.861271	−	0.508147i	$-0.169669\pi$
$191$	25.6333	−	5.44853i	1.85476	−	0.394242i	0.993492	+	0.113905i	$0.0363358\pi$
$192$	−1.15347	+	3.00489i	−0.0832445	+	0.216859i
$193$	−9.72461	+	25.3335i	−0.699992	+	1.82354i	−0.149384	+	0.988779i	$0.547729\pi$
$193$	−9.72461	+	25.3335i	−0.699992	+	1.82354i	−0.550609	+	0.834763i	$0.685604\pi$
$194$	10.3427	−	2.19841i	0.742562	−	0.157836i
$195$	−0.238535	+	20.6919i	−0.0170818	+	1.48178i
$196$	−5.74500	+	3.99937i	−0.410357	+	0.285669i
$197$	9.63369	+	9.63369i	0.686372	+	0.686372i	0.961428	−	0.275056i	$-0.0886965\pi$
$197$	9.63369	+	9.63369i	0.686372	+	0.686372i	−0.275056	+	0.961428i	$0.588697\pi$
$198$	−6.79067	−	23.4463i	−0.482592	−	1.66626i
$199$	2.48167	−	4.29837i	0.175921	−	0.304703i	−0.764559	−	0.644554i	$-0.777043\pi$
$199$	2.48167	−	4.29837i	0.175921	−	0.304703i	0.940479	+	0.339850i	$0.110376\pi$
$200$	1.18241	+	4.85818i	0.0836093	+	0.343525i
$201$	3.84188	+	3.45924i	0.270985	+	0.243996i
$202$	3.67965	+	7.22172i	0.258899	+	0.508119i
$203$	−16.0288	−	6.33919i	−1.12500	−	0.444924i
$204$	−9.61341	+	13.2317i	−0.673073	+	0.926405i
$205$	−14.3160	−	1.67173i	−0.999873	−	0.116759i
$206$	2.12694	−	10.0065i	0.148191	−	0.697183i
$207$	−25.5437	+	31.5439i	−1.77541	+	2.19245i
$208$	0.744154	−	2.77722i	0.0515978	−	0.192566i
$209$	−10.5485	−	4.44448i	−0.729653	−	0.307431i
$210$	17.1494	−	8.27606i	1.18342	−	0.571102i
$211$	1.19873	−	0.870925i	0.0825237	−	0.0599569i	−0.545758	−	0.837943i	$-0.683758\pi$
$211$	1.19873	−	0.870925i	0.0825237	−	0.0599569i	0.628282	+	0.777986i	$0.283758\pi$
$212$	2.57001	−	0.134689i	0.176509	−	0.00925045i
$213$	−0.554147	+	10.5738i	−0.0379695	+	0.724502i
$214$	−1.50364	−	3.37723i	−0.102787	−	0.230862i
$215$	−17.4799	+	6.47974i	−1.19212	+	0.441915i
$216$	−13.3461	−	4.33642i	−0.908089	−	0.295056i
$217$	−27.9625	+	1.18263i	−1.89821	+	0.0802819i
$218$	2.31048	−	14.5878i	0.156485	−	0.988009i
$219$	5.91817	−	3.41686i	0.399913	−	0.230890i
$220$	4.41049	+	5.96218i	0.297355	+	0.401970i
$221$	7.30497	−	12.6526i	0.491385	−	0.851105i
$222$	−27.3979	+	10.5171i	−1.83883	+	0.705860i
$223$	−7.69850	+	15.1092i	−0.515530	+	1.01178i	0.475697	+	0.879609i	$0.342196\pi$
$223$	−7.69850	+	15.1092i	−0.515530	+	1.01178i	−0.991226	+	0.132174i	$0.957804\pi$
$224$	−2.59335	+	0.523938i	−0.173276	+	0.0350071i
$225$	−35.2510	+	10.5618i	−2.35007	+	0.704118i
$226$	−0.285026	+	2.71184i	−0.0189596	+	0.180389i
$227$	14.7959	+	0.775420i	0.982038	+	0.0514665i	0.536592	−	0.843842i	$-0.319712\pi$
$227$	14.7959	+	0.775420i	0.982038	+	0.0514665i	0.445447	+	0.895308i	$0.353045\pi$
$228$	−9.31637	+	6.05012i	−0.616992	+	0.400679i
$229$	6.87579	+	3.06130i	0.454365	+	0.202296i	0.621141	−	0.783698i	$-0.286669\pi$
$229$	6.87579	+	3.06130i	0.454365	+	0.202296i	−0.166777	+	0.985995i	$0.553336\pi$
$230$	3.94569	−	11.6836i	0.260171	−	0.770392i
$231$	18.6875	−	21.1775i	1.22954	−	1.39338i
$232$	−4.60672	−	4.60672i	−0.302446	−	0.302446i
$233$	−7.45693	+	2.86245i	−0.488520	+	0.187525i	−0.590145	−	0.807298i	$-0.700929\pi$
$233$	−7.45693	+	2.86245i	−0.488520	+	0.187525i	0.101625	+	0.994823i	$0.467596\pi$
$234$	20.6986	+	4.39962i	1.35311	+	0.287612i
$235$	2.99480	−	7.54074i	0.195359	−	0.491904i
$236$	6.08280	+	0.639328i	0.395957	+	0.0416167i
$237$	0.622069	−	0.0985261i	0.0404077	−	0.00639996i
$238$	−13.4179	−	0.839058i	−0.869751	−	0.0543880i
$239$	6.49504	−	2.11037i	0.420129	−	0.136508i	−0.0913204	−	0.995822i	$-0.529109\pi$
$239$	6.49504	−	2.11037i	0.420129	−	0.136508i	0.511449	+	0.859313i	$0.329109\pi$
$240$	7.19117	−	0.293796i	0.464188	−	0.0189645i
$241$	−1.13878	−	0.657476i	−0.0733553	−	0.0423517i	0.462874	−	0.886424i	$-0.346818\pi$
$241$	−1.13878	−	0.657476i	−0.0733553	−	0.0423517i	−0.536229	+	0.844073i	$0.680152\pi$
$242$	9.45885	+	5.61517i	0.608038	+	0.360957i
$243$	8.33750	−	31.1160i	0.534851	−	1.99609i
$244$	0.150606	−	0.109421i	0.00964154	−	0.00700499i
$245$	13.3005	+	8.25209i	0.849737	+	0.527206i
$246$	−6.41117	+	19.7315i	−0.408761	+	1.25804i
$247$	7.71166	−	6.24478i	0.490681	−	0.397346i
$248$	−9.87566	−	3.79091i	−0.627105	−	0.240723i
$249$	−0.651507	+	0.586619i	−0.0412876	+	0.0371755i
$250$	8.92683	−	6.73139i	0.564583	−	0.425731i
$251$	−3.52460	−	4.85119i	−0.222471	−	0.306205i	0.683163	−	0.730266i	$-0.260604\pi$
$251$	−3.52460	−	4.85119i	−0.222471	−	0.306205i	−0.905633	+	0.424062i	$0.860604\pi$
$252$	−4.84975	−	18.8587i	−0.305505	−	1.18799i
$253$	−1.32446	−	18.2431i	−0.0832679	−	1.14693i
$254$	−17.8955	+	10.3319i	−1.12286	+	0.648284i
$255$	35.6824	+	8.01551i	2.23452	+	0.501950i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	11.5817	−	17.8343i	0.722449	−	1.11247i	−0.266444	−	0.963850i	$-0.585849\pi$
$257$	11.5817	−	17.8343i	0.722449	−	1.11247i	0.988894	−	0.148624i	$-0.0474845\pi$
$258$	4.19782	+	26.5040i	0.261345	+	1.65007i
$259$	−19.3721	−	14.3756i	−1.20373	−	0.893255i
$260$	−6.36114	+	0.932472i	−0.394501	+	0.0578295i
$261$	32.0839	−	35.6328i	1.98595	−	2.20562i
$262$	−15.3180	−	12.4042i	−0.946347	−	0.766337i
$263$	−0.494774	−	1.84652i	−0.0305091	−	0.113861i	0.948992	−	0.315300i	$-0.102105\pi$
$263$	−0.494774	−	1.84652i	−0.0305091	−	0.113861i	−0.979501	+	0.201438i	$0.935438\pi$
$264$	9.66292	−	4.53723i	0.594712	−	0.279247i
$265$	−2.55326	−	5.15716i	−0.156845	−	0.316802i
$266$	−8.30385	−	3.79798i	−0.509142	−	0.232869i
$267$	2.85699	−	5.60715i	0.174845	−	0.343152i
$268$	−0.874786	+	1.34705i	−0.0534361	+	0.0822844i
$269$	17.2477	−	7.67916i	1.05161	−	0.468207i	0.193194	−	0.981161i	$-0.438115\pi$
$269$	17.2477	−	7.67916i	1.05161	−	0.468207i	0.858416	+	0.512954i	$0.171449\pi$
$270$	2.92002	+	31.2425i	0.177707	+	1.90136i
$271$	2.89195	+	13.6056i	0.175674	+	0.826480i	0.974406	+	0.224794i	$0.0721708\pi$
$271$	2.89195	+	13.6056i	0.175674	+	0.826480i	−0.798733	+	0.601686i	$0.794496\pi$
$272$	−4.52754	−	2.30690i	−0.274523	−	0.139876i
$273$	8.54337	+	22.9457i	0.517068	+	1.38874i
$274$		−	0.825568i		−	0.0498744i
$275$	8.33377	−	14.3370i	0.502545	−	0.864551i
$276$	−15.3727	−	8.87544i	−0.925329	−	0.534239i
$277$	2.09096	−	2.58212i	0.125634	−	0.155145i	−0.710448	−	0.703750i	$-0.751508\pi$
$277$	2.09096	−	2.58212i	0.125634	−	0.155145i	0.836082	+	0.548605i	$0.184841\pi$
$278$	−9.86513	+	0.517010i	−0.591671	+	0.0310082i
$279$	24.0584	−	74.0440i	1.44034	−	4.43290i
$280$	3.37311	+	4.86026i	0.201582	+	0.290456i
$281$	−0.446613	−	0.324483i	−0.0266427	−	0.0193570i	0.574384	−	0.818586i	$-0.305242\pi$
$281$	−0.446613	−	0.324483i	−0.0266427	−	0.0193570i	−0.601027	+	0.799229i	$0.705242\pi$
$282$	−9.79491	−	6.36089i	−0.583279	−	0.378786i
$283$	−0.673179	−	1.03660i	−0.0400163	−	0.0616198i	0.818096	−	0.575081i	$-0.195030\pi$
$283$	−0.673179	−	1.03660i	−0.0400163	−	0.0616198i	−0.858113	+	0.513462i	$0.828363\pi$
$284$	−3.27162	+	0.343861i	−0.194135	+	0.0204044i
$285$	20.6747	+	13.7677i	1.22466	+	0.815529i
$286$	−8.16079	+	4.93309i	−0.482558	+	0.291700i
$287$	−16.5166	+	4.24744i	−0.974945	+	0.250719i
$288$	1.15134	−	7.26924i	0.0678431	−	0.428344i
$289$	−6.55485	−	5.90202i	−0.385580	−	0.347177i
$290$	−5.37704	+	13.5391i	−0.315750	+	0.795042i
$291$	−31.0911	+	13.8427i	−1.82259	+	0.811471i
$292$	1.33614	+	1.65000i	0.0781917	+	0.0965587i
$293$	11.9693	−	6.09864i	0.699251	−	0.356286i	−0.0679535	−	0.997688i	$-0.521647\pi$
$293$	11.9693	−	6.09864i	0.699251	−	0.356286i	0.767205	+	0.641402i	$0.221647\pi$
$294$	15.4108	−	16.4359i	0.898778	−	0.958562i
$295$	−4.07605	−	13.0550i	−0.237317	−	0.760089i
$296$	−4.55889	−	7.89622i	−0.264980	−	0.458959i
$297$	21.9594	+	41.0359i	1.27421	+	2.38115i
$298$	−1.82067	−	6.79484i	−0.105469	−	0.393615i
$299$	14.4857	+	6.44946i	0.837731	+	0.372982i
$300$	−6.97373	−	14.5039i	−0.402629	−	0.837384i
$301$	−16.5403	+	14.5934i	−0.953367	+	0.841151i
$302$	0.790581	+	4.99153i	0.0454928	+	0.287230i
$303$	−16.4176	−	20.2740i	−0.943164	−	1.16471i
$304$	−2.30935	−	2.56479i	−0.132450	−	0.147101i
$305$	−0.358072	−	0.212274i	−0.0205031	−	0.0121548i
$306$	15.2112	−	34.1650i	0.869568	−	1.95308i
$307$	4.08952	−	4.08952i	0.233401	−	0.233401i	−0.580709	−	0.814111i	$-0.697225\pi$
$307$	4.08952	−	4.08952i	0.233401	−	0.233401i	0.814111	+	0.580709i	$0.197225\pi$
$308$	7.40683	+	4.70520i	0.422043	+	0.268103i
$309$			32.9271i			1.87316i
$310$	0.965570	+	23.6340i	0.0548407	+	1.34232i
$311$	−1.76777	+	8.31672i	−0.100241	+	0.471598i	0.899180	+	0.437579i	$0.144164\pi$
$311$	−1.76777	+	8.31672i	−0.100241	+	0.471598i	−0.999421	+	0.0340190i	$0.989169\pi$
$312$	−0.484333	+	9.24162i	−0.0274199	+	0.523204i
$313$	−4.46903	+	3.61895i	−0.252605	+	0.204555i	−0.747256	−	0.664536i	$-0.768629\pi$
$313$	−4.46903	+	3.61895i	−0.252605	+	0.204555i	0.494651	+	0.869091i	$0.335296\pi$
$314$	6.93057	+	5.03535i	0.391115	+	0.284161i
$315$	−34.4225	+	26.6637i	−1.93949	+	1.50233i
$316$	0.0604678	+	0.186101i	0.00340158	+	0.0104690i
$317$	4.53743	+	11.8204i	0.254847	+	0.663900i	0.999996	−	0.00299874i	$-0.000954531\pi$
$317$	4.53743	+	11.8204i	0.254847	+	0.663900i	−0.745148	+	0.666899i	$0.767621\pi$
$318$	−8.00113	+	2.14390i	−0.448681	+	0.120224i
$319$	0.434572	+	21.6031i	0.0243314	+	1.20954i
$320$	0.439661	+	2.19242i	0.0245778	+	0.122560i
$321$	6.99400	+	9.62642i	0.390367	+	0.537294i
$322$	−0.616561	−	14.5782i	−0.0343596	−	0.812412i
$323$	−7.96172	−	15.6258i	−0.443002	−	0.869440i
$324$	22.9614	+	2.41334i	1.27564	+	0.134075i
$325$	7.54968	+	12.2340i	0.418781	+	0.678619i
$326$	3.17871	+	3.53031i	0.176052	+	0.195526i
$327$	2.48798	+	47.4734i	0.137585	+	2.62529i
$328$	−6.36645	−	1.00835i	−0.351529	−	0.0556767i
$329$	0.0968811	−	9.59973i	0.00534123	−	0.529251i
$330$	−17.8756	−	15.8195i	−0.984019	−	0.870833i
$331$	10.5716	+	18.3105i	0.581066	+	1.00644i	0.995353	+	0.0962893i	$0.0306974\pi$
$331$	10.5716	+	18.3105i	0.581066	+	1.00644i	−0.414288	+	0.910146i	$0.635969\pi$
$332$	−0.211676	−	0.171412i	−0.0116172	−	0.00940744i
$333$	56.2794	−	36.5483i	3.08409	−	2.00283i
$334$	−0.574325	+	0.122077i	−0.0314257	+	0.00667973i
$335$	3.54059	+	0.602691i	0.193443	+	0.0329285i
$336$	7.81414	−	3.38501i	0.426296	−	0.184667i
$337$	−12.6729	+	6.45714i	−0.690335	+	0.351743i	−0.763708	−	0.645561i	$-0.776623\pi$
$337$	−12.6729	+	6.45714i	−0.690335	+	0.351743i	0.0733737	+	0.997305i	$0.476623\pi$
$338$	0.247721	+	4.72679i	0.0134742	+	0.257103i
$339$	−0.917405	−	8.72852i	−0.0498266	−	0.474068i
$340$	−0.725414	+	11.3391i	−0.0393411	+	0.614951i
$341$	14.9117	+	31.7575i	0.807515	+	1.71976i
$342$	17.9611	−	17.9611i	0.971225	−	0.971225i
$343$	18.1962	+	3.44960i	0.982500	+	0.186261i
$344$	−7.92904	+	2.57630i	−0.427505	+	0.138905i
$345$	−4.60372	+	39.4243i	−0.247856	+	2.12253i
$346$	5.61886	+	12.6202i	0.302072	+	0.678464i
$347$	5.68874	+	2.18370i	0.305388	+	0.117227i	0.506236	−	0.862395i	$-0.331036\pi$
$347$	5.68874	+	2.18370i	0.305388	+	0.117227i	−0.200848	+	0.979622i	$0.564370\pi$
$348$	17.5863	+	11.4207i	0.942727	+	0.612214i
$349$	−2.59476	−	7.98585i	−0.138894	−	0.427473i	0.857281	−	0.514849i	$-0.172152\pi$
$349$	−2.59476	−	7.98585i	−0.138894	−	0.427473i	−0.996175	+	0.0873758i	$0.972152\pi$
$350$	6.99042	−	11.2309i	0.373654	−	0.600319i
$351$	−40.3474			−2.15359
$352$	1.86194	+	2.74466i	0.0992418	+	0.146291i
$353$	3.61474	−	0.968568i	0.192393	−	0.0515517i	−0.161336	−	0.986900i	$-0.551580\pi$
$353$	3.61474	−	0.968568i	0.192393	−	0.0515517i	0.353729	+	0.935348i	$0.384913\pi$
$354$	−19.5786	+	2.05779i	−1.04059	+	0.109370i
$355$	3.60425	+	6.41233i	0.191294	+	0.340331i
$356$	1.85948	+	0.604181i	0.0985521	+	0.0320215i
$357$	42.8054	−	6.33759i	2.26550	−	0.335421i
$358$	−6.57594	+	1.04153i	−0.347549	+	0.0550464i
$359$	3.71125	+	17.4601i	0.195873	+	0.921508i	0.960768	+	0.277353i	$0.0894573\pi$
$359$	3.71125	+	17.4601i	0.195873	+	0.921508i	−0.764895	+	0.644154i	$0.777209\pi$
$360$	−15.9444	+	4.07590i	−0.840345	+	0.214819i
$361$	0.740978	+	7.04993i	0.0389988	+	0.371049i
$362$	10.1179	+	2.71107i	0.531783	+	0.142491i
$363$	−33.5373	−	11.3486i	−1.76025	−	0.595647i
$364$	−6.62594	+	3.73684i	−0.347294	+	0.195864i
$365$	2.20394	−	4.20493i	0.115359	−	0.220096i
$366$	−0.400933	+	0.445281i	−0.0209571	+	0.0232752i
$367$	15.0837	+	0.790502i	0.787362	+	0.0412639i	0.441778	−	0.897124i	$-0.354348\pi$
$367$	15.0837	+	0.790502i	0.787362	+	0.0412639i	0.345583	+	0.938388i	$0.387681\pi$
$368$	1.97639	−	5.14867i	0.103026	−	0.268393i
$369$	4.95886	−	47.1804i	0.258148	−	2.45611i
$370$	−12.1731	+	16.3550i	−0.632848	+	0.850254i
$371$	−5.01379	−	4.60690i	−0.260303	−	0.239178i
$372$	33.6288	+	5.32628i	1.74357	+	0.276155i
$373$	−14.6746	−	3.93204i	−0.759820	−	0.203593i	−0.141951	−	0.989874i	$-0.545337\pi$
$373$	−14.6746	−	3.93204i	−0.759820	−	0.203593i	−0.617870	+	0.786280i	$0.712004\pi$
$374$	5.52918	+	15.9202i	0.285907	+	0.823214i
$375$	−23.6000	+	27.1665i	−1.21870	+	1.40287i
$376$	1.47586	−	3.31484i	0.0761117	−	0.170950i
$377$	−16.6899	−	8.50395i	−0.859576	−	0.437976i
$378$	16.5209	+	33.2494i	0.849745	+	1.71017i
$379$	−19.7770	+	27.2208i	−1.01588	+	1.39824i	−0.100825	+	0.994904i	$0.532148\pi$
$379$	−19.7770	+	27.2208i	−1.01588	+	1.39824i	−0.915053	+	0.403333i	$0.867852\pi$
$380$	−3.21995	+	7.01342i	−0.165180	+	0.359781i
$381$	49.4268	−	44.5041i	2.53221	−	2.28001i
$382$	−14.2728	−	21.9782i	−0.730260	−	1.12450i
$383$	−10.6656	−	27.7849i	−0.544989	−	1.41974i	−0.878839	−	0.477118i	$-0.841681\pi$
$383$	−10.6656	−	27.7849i	−0.544989	−	1.41974i	0.333851	−	0.942626i	$-0.391652\pi$
$384$	3.21867			0.164252
$385$	3.09864	−	19.3752i	0.157921	−	0.987452i
$386$	27.1358			1.38118
$387$	−21.9894	−	57.2843i	−1.11778	−	2.91192i
$388$	−5.75888	−	8.86790i	−0.292363	−	0.450199i
$389$	21.6050	−	19.4532i	1.09542	−	0.986318i	0.0954583	−	0.995433i	$-0.469568\pi$
$389$	21.6050	−	19.4532i	1.09542	−	0.986318i	0.999958	+	0.00911575i	$0.00290167\pi$
$390$	19.4030	−	7.19261i	0.982509	−	0.364212i
$391$	16.4719	−	22.6716i	0.833019	−	1.14655i
$392$	5.79255	+	3.93018i	0.292568	+	0.198504i
$393$	56.5270	+	28.8020i	2.85141	+	1.45287i
$394$	5.54142	−	12.4462i	0.279173	−	0.627032i
$395$	0.328516	−	0.289010i	0.0165294	−	0.0145417i
$396$	−19.4555	+	14.7420i	−0.977673	+	0.740815i
$397$	14.4365	+	3.86826i	0.724549	+	0.194142i	0.602201	−	0.798345i	$-0.294291\pi$
$397$	14.4365	+	3.86826i	0.724549	+	0.194142i	0.122349	+	0.992487i	$0.460957\pi$
$398$	−4.90222	−	0.776436i	−0.245726	−	0.0389192i
$399$	28.6849	+	6.40039i	1.43604	+	0.320420i
$400$	4.11176	−	2.84489i	0.205588	−	0.142245i
$401$	−3.31049	+	31.4972i	−0.165318	+	1.57289i	0.526089	+	0.850429i	$0.323658\pi$
$401$	−3.31049	+	31.4972i	−0.165318	+	1.57289i	−0.691407	+	0.722465i	$0.743009\pi$
$402$	1.85268	−	4.82638i	0.0924030	−	0.240718i
$403$	−30.3728	−	1.59177i	−1.51298	−	0.0792919i
$404$	5.42339	−	6.02328i	0.269824	−	0.299670i
$405$	−15.3863	−	49.2800i	−0.764553	−	2.44874i
$406$	−0.173946	+	17.2359i	−0.00863279	+	0.855404i
$407$	−7.23769	+	29.3613i	−0.358759	+	1.45539i
$408$	15.7980	+	4.23306i	0.782118	+	0.209568i
$409$	3.60204	+	34.2712i	0.178110	+	1.69460i	0.609782	+	0.792569i	$0.291257\pi$
$409$	3.60204	+	34.2712i	0.178110	+	1.69460i	−0.431673	+	0.902030i	$0.642076\pi$
$410$	3.56970	+	13.9642i	0.176295	+	0.689644i
$411$	0.552470	+	2.59917i	0.0272513	+	0.128207i
$412$	−10.1041	+	1.60033i	−0.497792	+	0.0788425i
$413$	−10.0564	−	12.6781i	−0.494842	−	0.623848i
$414$	38.6028	+	12.5428i	1.89722	+	0.616445i
$415$	−0.164405	+	0.586442i	−0.00807032	+	0.0287873i
$416$	−2.85944	+	0.300539i	−0.140196	+	0.0147352i
$417$	30.7128	−	8.22947i	1.50401	−	0.402999i
$418$	−0.369046	+	11.4406i	−0.0180506	+	0.559578i
$419$	−21.0651			−1.02910			−0.514549	−	0.857461i	$-0.672041\pi$
$419$	−21.0651			−1.02910			−0.514549	+	0.857461i	$0.672041\pi$
$420$	−13.8722	−	13.0445i	−0.676892	−	0.636505i
$421$	6.53984	+	20.1275i	0.318732	+	0.980957i	0.974191	+	0.225726i	$0.0724753\pi$
$421$	6.53984	+	20.1275i	0.318732	+	0.980957i	−0.655459	+	0.755231i	$0.727525\pi$
$422$	−1.24266	−	0.806995i	−0.0604919	−	0.0392839i
$423$	24.9318	+	9.57042i	1.21223	+	0.465330i
$424$	−1.04675	−	2.35104i	−0.0508348	−	0.114177i
$425$	23.9230	−	8.55580i	1.16043	−	0.415017i
$426$	10.0700	−	3.27195i	0.487895	−	0.158527i
$427$	−0.485664	−	0.0819540i	−0.0235029	−	0.00396603i
$428$	−2.61406	+	2.61406i	−0.126355	+	0.126355i
$429$	22.3917	−	20.9922i	1.08108	−	1.01352i
$430$	12.3136	+	13.9968i	0.593815	+	0.674986i
$431$	0.920396	+	8.75699i	0.0443339	+	0.421809i	0.994069	+	0.108754i	$0.0346859\pi$
$431$	0.920396	+	8.75699i	0.0443339	+	0.421809i	−0.949735	+	0.313056i	$0.898647\pi$
$432$	0.734428	+	14.0137i	0.0353352	+	0.674236i
$433$	−27.6036	+	14.0647i	−1.32654	+	0.675907i	−0.966413	−	0.256995i	$-0.917268\pi$
$433$	−27.6036	+	14.0647i	−1.32654	+	0.675907i	−0.360130	+	0.932902i	$0.617268\pi$
$434$	11.1249	+	25.6814i	0.534013	+	1.23275i
$435$	7.86838	−	46.2239i	0.377260	−	2.21627i
$436$	−14.4469	+	3.07078i	−0.691880	+	0.147064i
$437$	15.9629	−	10.3665i	0.763611	−	0.495895i
$438$	−5.31080	−	4.30060i	−0.253760	−	0.205490i
$439$	0.438843	+	0.760098i	0.0209448	+	0.0362775i	0.876308	−	0.481752i	$-0.159999\pi$
$439$	0.438843	+	0.760098i	0.0209448	+	0.0362775i	−0.855363	+	0.518029i	$0.826666\pi$
$440$	3.98560	−	6.25420i	0.190006	−	0.298157i
$441$	−26.6547	+	44.0878i	−1.26927	+	2.09942i
$442$	−14.4301	−	2.28550i	−0.686368	−	0.108710i
$443$	−1.12270	−	21.4225i	−0.0533413	−	1.01781i	−0.885900	−	0.463876i	$-0.846458\pi$
$443$	−1.12270	−	21.4225i	−0.0533413	−	1.01781i	0.832559	−	0.553937i	$-0.186875\pi$
$444$	19.6371	+	21.8092i	0.931934	+	1.03502i
$445$	−0.406837	−	4.35292i	−0.0192859	−	0.206348i
$446$	16.8645	+	1.77253i	0.798557	+	0.0839318i
$447$	10.2792	+	20.1741i	0.486189	+	0.954200i
$448$	1.41851	+	2.23334i	0.0670185	+	0.105516i
$449$	5.04105	+	6.93841i	0.237902	+	0.327444i	0.911228	−	0.411901i	$-0.135135\pi$
$449$	5.04105	+	6.93841i	0.237902	+	0.327444i	−0.673327	+	0.739345i	$0.735135\pi$
$450$	22.4931	+	29.1247i	1.06034	+	1.37295i
$451$	12.9112	+	17.0392i	0.607964	+	0.802345i
$452$	2.63386	−	0.705742i	0.123887	−	0.0331953i
$453$	−5.82935	−	15.1860i	−0.273887	−	0.713499i
$454$	−4.57846	−	14.0911i	−0.214878	−	0.661326i
$455$	13.5419	+	10.2933i	0.634855	+	0.482557i
$456$	8.98696	+	6.52941i	0.420853	+	0.305768i
$457$	15.3677	−	12.4445i	0.718870	−	0.582130i	−0.198530	−	0.980095i	$-0.563617\pi$
$457$	15.3677	−	12.4445i	0.718870	−	0.582130i	0.917401	+	0.397965i	$0.130283\pi$
$458$	0.393906	−	7.51617i	0.0184060	−	0.351208i
$459$	−14.8255	+	69.7485i	−0.691996	+	3.25558i
$460$	−12.3216	+	0.503399i	−0.574496	+	0.0234711i
$461$		−	17.0570i		−	0.794422i	−0.917727	−	0.397211i	$-0.869978\pi$
$461$		−	17.0570i		−	0.794422i	0.917727	−	0.397211i	$-0.130022\pi$
$462$	−26.4679	−	9.85690i	−1.23140	−	0.458584i
$463$	6.29539	−	6.29539i	0.292571	−	0.292571i	−0.545524	−	0.838095i	$-0.683669\pi$
$463$	6.29539	−	6.29539i	0.292571	−	0.292571i	0.838095	+	0.545524i	$0.183669\pi$
$464$	−2.64985	+	5.95165i	−0.123016	+	0.276298i
$465$	−18.8558	−	73.7616i	−0.874417	−	3.42061i
$466$	5.34465	+	5.93584i	0.247586	+	0.274972i
$467$	−14.3471	−	17.7172i	−0.663905	−	0.819855i	0.328286	−	0.944578i	$-0.393529\pi$
$467$	−14.3471	−	17.7172i	−0.663905	−	0.819855i	−0.992192	+	0.124723i	$0.960196\pi$
$468$	−3.31031	−	20.9005i	−0.153019	−	0.966124i
$469$	4.16539	−	0.841537i	0.192340	−	0.0388586i
$470$	−8.11313	−	0.0935278i	−0.374231	−	0.00431411i
$471$	−25.1894	−	11.2151i	−1.16067	−	0.516763i
$472$	−1.58302	−	5.90790i	−0.0728643	−	0.271933i
$473$	24.8847	+	12.0552i	1.14420	+	0.554301i
$474$	−0.314912	−	0.545443i	−0.0144644	−	0.0250530i
$475$	17.2517	+	0.397807i	0.791564	+	0.0182527i
$476$	4.02520	+	12.8273i	0.184495	+	0.587940i
$477$	16.8764	−	8.59897i	0.772719	−	0.393720i
$478$	−4.29781	−	5.30735i	−0.196577	−	0.242753i
$479$	−15.5948	+	6.94324i	−0.712543	+	0.317245i	−0.730803	−	0.682589i	$-0.760854\pi$
$479$	−15.5948	+	6.94324i	−0.712543	+	0.317245i	0.0182595	+	0.999833i	$0.494187\pi$
$480$	−2.85137	−	6.60825i	−0.130147	−	0.301624i
$481$	−19.4818	−	17.5415i	−0.888293	−	0.799823i
$482$	−0.205704	+	1.29876i	−0.00936955	+	0.0591570i
$483$	11.6969	+	45.4845i	0.532226	+	2.06962i
$484$	1.85247	−	10.8429i	0.0842031	−	0.492859i
$485$	−13.1050	+	19.6795i	−0.595066	+	0.893598i
$486$	−32.0371	+	3.36724i	−1.45323	+	0.152741i
$487$	−15.7954	−	24.3227i	−0.715756	−	1.10217i	−0.990077	−	0.140529i	$-0.955120\pi$
$487$	−15.7954	−	24.3227i	−0.715756	−	1.10217i	0.274320	−	0.961638i	$-0.411547\pi$
$488$	−0.156126	−	0.101389i	−0.00706749	−	0.00458968i
$489$	−12.3701	−	8.98743i	−0.559397	−	0.406426i
$490$	2.93752	−	15.3744i	0.132703	−	0.694543i
$491$	7.27128	−	22.3787i	0.328148	−	1.00994i	−0.641851	−	0.766829i	$-0.721833\pi$
$491$	7.27128	−	22.3787i	0.328148	−	1.00994i	0.969999	−	0.243107i	$-0.0781667\pi$
$492$	20.7185	−	1.08581i	0.934064	−	0.0489522i
$493$	−20.8334	+	25.7271i	−0.938290	+	1.15869i
$494$	−8.59361	−	4.96152i	−0.386645	−	0.223230i
$495$	47.5021	+	26.8842i	2.13506	+	1.20836i
$496$			10.5783i			0.474978i
$497$	6.70832	+	5.54531i	0.300909	+	0.248741i
$498$	0.781135	+	0.398008i	0.0350035	+	0.0178352i
$499$	−4.90141	−	23.0593i	−0.219417	−	1.03228i	−0.940596	−	0.339528i	$-0.889733\pi$
$499$	−4.90141	−	23.0593i	−0.219417	−	1.03228i	0.721178	−	0.692749i	$-0.243601\pi$
$500$	−9.48339	−	5.92160i	−0.424110	−	0.264822i
$501$	1.72648	−	0.768676i	0.0771332	−	0.0343419i
$502$	−3.26588	+	5.02901i	−0.145763	+	0.224456i
$503$	6.39170	−	12.5444i	0.284992	−	0.559328i	−0.703483	−	0.710712i	$-0.748373\pi$
$503$	6.39170	−	12.5444i	0.284992	−	0.559328i	0.988475	+	0.151384i	$0.0483729\pi$
$504$	−15.8682	+	11.2860i	−0.706824	+	0.502718i
$505$	−17.1709	−	5.79882i	−0.764094	−	0.258044i
$506$	−16.5567	+	7.77422i	−0.736036	+	0.345606i
$507$	−3.94307	−	14.7158i	−0.175118	−	0.653550i
$508$	16.0589	+	13.0042i	0.712497	+	0.576968i
$509$	−2.17307	+	2.41344i	−0.0963196	+	0.106974i	−0.789377	−	0.613908i	$-0.789596\pi$
$509$	−2.17307	+	2.41344i	−0.0963196	+	0.106974i	0.693058	+	0.720882i	$0.256263\pi$
$510$	−5.30430	−	36.1849i	−0.234878	−	1.60229i
$511$	0.643517	−	5.58034i	0.0284675	−	0.246860i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−26.3777	+	40.6180i	−1.16460	+	1.79333i
$514$	−20.8003	−	4.42124i	−0.917462	−	0.195013i
$515$	12.2367	+	19.3269i	0.539211	+	0.851647i
$516$	23.2392	−	13.4172i	1.02305	−	0.590659i
$517$	−11.1462	+	4.53788i	−0.490208	+	0.199576i
$518$	−6.47841	+	23.2372i	−0.284645	+	1.02098i
$519$	−26.1355	−	35.9724i	−1.14722	−	1.57901i
$520$	3.15017	+	5.60447i	0.138144	+	0.245772i
$521$	−16.8623	+	15.1829i	−0.738751	+	0.665174i	−0.949997	−	0.312259i	$-0.898914\pi$
$521$	−16.8623	+	15.1829i	−0.738751	+	0.665174i	0.211246	+	0.977433i	$0.432248\pi$
$522$	−44.7639	−	17.1833i	−1.95926	−	0.752091i
$523$	29.1932	−	23.6402i	1.27653	−	1.03371i	0.279236	−	0.960223i	$-0.409919\pi$
$523$	29.1932	−	23.6402i	1.27653	−	1.03371i	0.997296	−	0.0734923i	$-0.0234144\pi$
$524$	−6.09089	+	18.7458i	−0.266082	+	0.818915i
$525$	−14.4924	+	40.0368i	−0.632502	+	1.74735i
$526$	−1.54657	+	1.12365i	−0.0674335	+	0.0489933i
$527$	−13.9121	+	51.9206i	−0.606020	+	2.26170i
$528$	−7.69875	−	7.39512i	−0.335045	−	0.321831i
$529$	6.42148	+	3.70744i	0.279195	+	0.161193i
$530$	−3.89962	+	4.23183i	−0.169389	+	0.183819i
$531$	42.8120	−	13.9104i	1.85788	−	0.603662i
$532$	−0.569887	+	9.11339i	−0.0247077	+	0.395116i
$533$	−18.3048	+	2.89919i	−0.792868	+	0.125578i
$534$	−6.25858	−	0.657803i	−0.270835	−	0.0284659i
$535$	7.68266	+	3.05117i	0.332151	+	0.131913i
$536$	1.57108	+	0.333943i	0.0678602	+	0.0144241i
$537$	20.0063	−	7.67970i	0.863335	−	0.331403i
$538$	−13.3501	−	13.3501i	−0.575565	−	0.575565i
$539$	−4.82537	−	22.7094i	−0.207843	−	0.978162i
$540$	28.1209	−	13.9224i	1.21013	−	0.599124i
$541$	−9.39411	−	4.18253i	−0.403885	−	0.179821i	0.194732	−	0.980856i	$-0.437616\pi$
$541$	−9.39411	−	4.18253i	−0.403885	−	0.179821i	−0.598617	+	0.801035i	$0.704283\pi$
$542$	11.6655	−	7.57567i	0.501077	−	0.325403i
$543$	−33.6687	−	1.76450i	−1.44486	−	0.0757220i
$544$	−0.531149	+	5.05354i	−0.0227728	+	0.216669i
$545$	19.1028	+	26.9405i	0.818276	+	1.15400i
$546$	18.3600	−	16.1989i	0.785735	−	0.693250i
$547$	6.06915	−	11.9114i	0.259498	−	0.509293i	−0.724094	−	0.689701i	$-0.757742\pi$
$547$	6.06915	−	11.9114i	0.259498	−	0.509293i	0.983592	+	0.180408i	$0.0577418\pi$
$548$	−0.770734	+	0.295857i	−0.0329241	+	0.0126384i
$549$	0.685051	−	1.18654i	0.0292373	−	0.0506405i
$550$	−16.3713	−	2.64234i	−0.698073	−	0.112670i
$551$	−19.4723	+	11.2423i	−0.829546	+	0.478939i
$552$	−2.77685	+	17.5323i	−0.118191	+	0.746226i
$553$	0.239681	−	0.458892i	0.0101923	−	0.0195141i
$554$	−3.15996	−	1.02673i	−0.134254	−	0.0436216i
$555$	27.3802	−	59.6372i	1.16223	−	2.53146i
$556$	4.01802	+	9.02462i	0.170402	+	0.382729i
$557$	0.200108	−	3.81828i	0.00847883	−	0.161786i	−0.991108	−	0.133057i	$-0.957521\pi$
$557$	0.200108	−	3.81828i	0.00847883	−	0.161786i	0.999587	−	0.0287289i	$-0.00914596\pi$
$558$	−77.7478	+	4.07459i	−3.29133	+	0.172491i
$559$	−19.3927	+	14.0896i	−0.820225	+	0.595928i
$560$	3.32863	−	4.89083i	0.140660	−	0.206675i
$561$	−28.0615	−	46.4220i	−1.18476	−	1.95994i
$562$	−0.142879	+	0.533233i	−0.00602700	+	0.0224931i
$563$	−0.385490	+	0.476040i	−0.0162464	+	0.0200627i	−0.785204	−	0.619237i	$-0.787442\pi$
$563$	−0.385490	+	0.476040i	−0.0162464	+	0.0200627i	0.768958	+	0.639299i	$0.220776\pi$
$564$	−2.42822	+	11.4239i	−0.102247	+	0.481032i
$565$	−3.78225	−	4.78237i	−0.159121	−	0.201196i
$566$	−0.726508	+	0.999953i	−0.0305374	+	0.0420311i
$567$	−37.9609	−	47.8574i	−1.59421	−	2.00982i
$568$	1.49346	+	2.93109i	0.0626643	+	0.122986i
$569$	−25.1220	−	22.6200i	−1.05317	−	0.948278i	−0.0544319	−	0.998517i	$-0.517335\pi$
$569$	−25.1220	−	22.6200i	−1.05317	−	0.948278i	−0.998737	+	0.0502398i	$0.984001\pi$
$570$	5.44412	−	24.2354i	0.228029	−	1.01511i
$571$	16.2487	−	28.1435i	0.679986	−	1.17777i	−0.294999	−	0.955498i	$-0.595319\pi$
$571$	16.2487	−	28.1435i	0.679986	−	1.17777i	0.974985	−	0.222272i	$-0.0713473\pi$
$572$	7.53001	+	5.85089i	0.314845	+	0.244638i
$573$	59.6434	+	59.6434i	2.49164	+	2.49164i
$574$	9.88436	+	13.8974i	0.412565	+	0.580068i
$575$	11.9490	+	24.8514i	0.498308	+	1.03638i
$576$	−7.19903	+	1.53020i	−0.299959	+	0.0637583i
$577$	−16.8641	+	43.9326i	−0.702064	+	1.82894i	−0.163099	+	0.986610i	$0.552149\pi$
$577$	−16.8641	+	43.9326i	−0.702064	+	1.82894i	−0.538964	+	0.842329i	$0.681184\pi$
$578$	−3.16096	+	8.23457i	−0.131478	+	0.342513i
$579$	−85.4327	+	18.1593i	−3.55046	+	0.754674i
$580$	14.5668	+	0.167925i	0.604852	+	0.00697271i
$581$	0.0680909	+	0.717415i	0.00282489	+	0.0297634i
$582$	24.0653	+	24.0653i	0.997538	+	0.997538i
$583$	−2.89795	+	8.02844i	−0.120021	+	0.332504i
$584$	1.06157	−	1.83870i	0.0439282	−	0.0760859i
$585$	−39.9782	+	25.3118i	−1.65289	+	1.04651i
$586$	−9.98297	−	8.98870i	−0.412393	−	0.371320i
$587$	15.8690	+	31.1447i	0.654984	+	1.28548i	0.944565	+	0.328325i	$0.106484\pi$
$587$	15.8690	+	31.1447i	0.654984	+	1.28548i	−0.289581	+	0.957154i	$0.593516\pi$
$588$	−20.8670	−	8.49715i	−0.860540	−	0.350417i
$589$	−21.4591	+	29.5359i	−0.884207	+	1.21701i
$590$	−10.7271	+	8.48380i	−0.441629	+	0.349272i
$591$	−9.11724	+	42.8932i	−0.375033	+	1.76439i
$592$	−5.73800	+	7.08584i	−0.235830	+	0.291226i
$593$	−5.84611	+	21.8180i	−0.240071	+	0.895957i	0.735726	+	0.677279i	$0.236841\pi$
$593$	−5.84611	+	21.8180i	−0.240071	+	0.895957i	−0.975797	+	0.218678i	$0.929826\pi$
$594$	30.4408	−	35.2068i	1.24900	−	1.44455i
$595$	22.7699	−	19.6277i	0.933476	−	0.804656i
$596$	−5.69106	+	4.13480i	−0.233115	+	0.169368i
$597$	15.9534	−	0.836085i	0.652931	−	0.0342187i
$598$	0.829870	−	15.8349i	0.0339359	−	0.647536i
$599$	13.8238	+	31.0488i	0.564826	+	1.26862i	0.939844	+	0.341603i	$0.110970\pi$
$599$	13.8238	+	31.0488i	0.564826	+	1.26862i	−0.375018	+	0.927017i	$0.622364\pi$
$600$	−11.0414	+	11.7083i	−0.450764	+	0.477988i
$601$	−9.53234	−	3.09725i	−0.388832	−	0.126339i	0.108075	−	0.994143i	$-0.465531\pi$
$601$	−9.53234	−	3.09725i	−0.388832	−	0.126339i	−0.496908	+	0.867803i	$0.665531\pi$
$602$	19.5516	+	10.2119i	0.796866	+	0.416205i
$603$	−1.84925	+	11.6757i	−0.0753072	+	0.475471i
$604$	4.37668	−	2.52688i	0.178084	−	0.102817i
$605$	−23.9026	+	5.80224i	−0.971779	+	0.235895i
$606$	−13.0439	+	22.5927i	−0.529871	+	0.917764i
$607$	42.2811	−	16.2302i	1.71614	−	0.658763i	0.716875	−	0.697202i	$-0.245572\pi$
$607$	42.2811	−	16.2302i	1.71614	−	0.658763i	0.999261	+	0.0384389i	$0.0122385\pi$
$608$	−1.56684	+	3.07510i	−0.0635438	+	0.124712i
$609$	−10.9866	−	54.3809i	−0.445201	−	2.20362i
$610$	−0.0698530	+	0.410361i	−0.00282826	+	0.0166150i
$611$	1.09052	−	10.3756i	0.0441177	−	0.419752i
$612$	−37.3470	−	1.95727i	−1.50966	−	0.0791180i
$613$	20.5056	−	13.3165i	0.828213	−	0.537848i	−0.0595090	−	0.998228i	$-0.518954\pi$
$613$	20.5056	−	13.3165i	0.828213	−	0.537848i	0.887722	+	0.460380i	$0.152287\pi$
$614$	−5.28345	−	2.35234i	−0.213223	−	0.0949329i
$615$	−20.5835	−	41.5753i	−0.830006	−	1.67648i
$616$	1.73831	−	8.60106i	0.0700384	−	0.346547i
$617$	−16.3626	−	16.3626i	−0.658734	−	0.658734i	0.296347	−	0.955080i	$-0.404232\pi$
$617$	−16.3626	−	16.3626i	−0.658734	−	0.658734i	−0.955080	+	0.296347i	$0.904232\pi$
$618$	30.7401	−	11.8000i	1.23655	−	0.474666i
$619$	−3.04100	−	0.646384i	−0.122228	−	0.0259804i	0.146391	−	0.989227i	$-0.453234\pi$
$619$	−3.04100	−	0.646384i	−0.122228	−	0.0259804i	−0.268620	+	0.963246i	$0.586567\pi$
$620$	21.7182	−	9.37110i	0.872224	−	0.376353i
$621$	−76.9674	−	8.08960i	−3.08859	−	0.324624i
$622$	8.39784	−	1.33009i	0.336723	−	0.0533317i
$623$	−2.30181	−	4.63255i	−0.0922202	−	0.185599i
$624$	8.80136	−	2.85974i	0.352336	−	0.114481i
$625$	−3.75646	+	24.7162i	−0.150258	+	0.988647i
$626$	4.98014	+	2.87528i	0.199046	+	0.114919i
$627$	−6.49417	−	36.2658i	−0.259352	−	1.44832i
$628$	2.21721	−	8.27475i	0.0884765	−	0.330199i
$629$	−37.4825	+	27.2326i	−1.49452	+	1.08583i
$630$	37.2286	+	22.5808i	1.48322	+	0.899641i
$631$	−0.989734	+	3.04609i	−0.0394007	+	0.121263i	−0.968822	−	0.247757i	$-0.920307\pi$
$631$	−0.989734	+	3.04609i	−0.0394007	+	0.121263i	0.929422	+	0.369020i	$0.120307\pi$
$632$	0.152070	−	0.123144i	0.00604903	−	0.00489841i
$633$	4.45236	+	1.70910i	0.176966	+	0.0679307i
$634$	9.40923	−	8.47211i	0.373688	−	0.336471i
$635$	12.4726	−	44.4906i	0.494962	−	1.76556i
$636$	4.86885	+	6.70139i	0.193062	+	0.265727i
$637$	19.3315	+	5.60037i	0.765940	+	0.221895i
$638$	20.0125	−	8.14756i	0.792302	−	0.322565i
$639$	−20.9676	+	12.1056i	−0.829464	+	0.478891i
$640$	1.88924	−	1.19615i	0.0746787	−	0.0472821i
$641$	−15.7535	−	3.34852i	−0.622228	−	0.132259i	−0.113999	−	0.993481i	$-0.536366\pi$
$641$	−15.7535	−	3.34852i	−0.622228	−	0.132259i	−0.508229	+	0.861222i	$0.669699\pi$
$642$	6.48061	−	9.97926i	0.255769	−	0.393850i
$643$	3.21435	+	20.2946i	0.126762	+	0.800342i	0.966371	+	0.257151i	$0.0827838\pi$
$643$	3.21435	+	20.2946i	0.126762	+	0.800342i	−0.839610	+	0.543190i	$0.817216\pi$
$644$	−13.3890	+	5.79997i	−0.527599	+	0.228551i
$645$	−48.1340	−	35.8264i	−1.89528	−	1.41066i
$646$	−11.7347	+	13.0327i	−0.461695	+	0.512764i
$647$	−8.49845	−	6.88191i	−0.334109	−	0.270556i	0.447555	−	0.894257i	$-0.352295\pi$
$647$	−8.49845	−	6.88191i	−0.334109	−	0.270556i	−0.781663	+	0.623701i	$0.785628\pi$
$648$	−5.97559	−	22.3012i	−0.234743	−	0.876075i
$649$	−9.78737	+	17.7682i	−0.384188	+	0.697463i
$650$	8.71584	−	11.4325i	0.341863	−	0.448420i
$651$	−52.2110	−	73.4089i	−2.04631	−	2.87712i
$652$	2.15668	−	4.23273i	0.0844623	−	0.165767i
$653$	13.4466	−	20.7060i	0.526208	−	0.810289i	−0.471216	−	0.882018i	$-0.656185\pi$
$653$	13.4466	−	20.7060i	0.526208	−	0.810289i	0.997424	+	0.0717285i	$0.0228515\pi$
$654$	43.4287	−	19.3357i	1.69819	−	0.756085i
$655$	43.8828	−	4.10142i	1.71464	−	0.160256i
$656$	1.34016	+	6.30496i	0.0523245	+	0.246167i
$657$	13.9229	+	7.09408i	0.543185	+	0.276767i
$658$	−8.99684	+	3.34979i	−0.350733	+	0.130588i
$659$			1.99542i			0.0777306i	0.999244	+	0.0388653i	$0.0123743\pi$
$659$			1.99542i			0.0777306i	−0.999244	+	0.0388653i	$0.987626\pi$
$660$	−8.36271	+	22.3575i	−0.325518	+	0.870264i
$661$	−4.59982	−	2.65570i	−0.178912	−	0.103295i	0.407869	−	0.913040i	$-0.366272\pi$
$661$	−4.59982	−	2.65570i	−0.178912	−	0.103295i	−0.586781	+	0.809745i	$0.699605\pi$
$662$	13.3058	−	16.4313i	0.517145	−	0.638620i
$663$	46.9602	−	2.46108i	1.82378	−	0.0955804i
$664$	−0.0841688	+	0.259045i	−0.00326638	+	0.0100529i
$665$	19.2155	−	6.90337i	0.745147	−	0.267701i
$666$	−54.2895	−	39.4436i	−2.10367	−	1.52841i
$667$	−30.1330	−	19.5686i	−1.16675	−	0.757698i
$668$	0.319788	+	0.492430i	0.0123730	+	0.0190527i
$669$	−54.2813	+	5.70520i	−2.09864	+	0.220576i
$670$	−0.706174	−	3.52141i	−0.0272819	−	0.136044i
$671$	0.140489	+	0.601223i	0.00542352	+	0.0232100i
$672$	−5.96051	−	6.08205i	−0.229932	−	0.234620i
$673$	3.66070	−	23.1127i	0.141110	−	0.890931i	−0.810972	−	0.585086i	$-0.801061\pi$
$673$	3.66070	−	23.1127i	0.141110	−	0.890931i	0.952081	−	0.305845i	$-0.0989391\pi$
$674$	10.5698	+	9.51710i	0.407134	+	0.366585i
$675$	−53.4959	−	45.4014i	−2.05906	−	1.74750i
$676$	4.32406	−	1.92520i	0.166310	−	0.0740460i
$677$	10.0051	+	12.3553i	0.384529	+	0.474854i	0.932254	−	0.361805i	$-0.117839\pi$
$677$	10.0051	+	12.3553i	0.384529	+	0.474854i	−0.547725	+	0.836658i	$0.684506\pi$
$678$	−7.82001	+	3.98449i	−0.300326	+	0.153024i
$679$	−6.09229	+	27.3041i	−0.233801	+	1.04784i
$680$	10.8460	−	3.38635i	0.415923	−	0.129861i
$681$	23.8443	+	41.2995i	0.913714	+	1.58260i
$682$	24.3043	−	25.3022i	0.930658	−	0.968869i
$683$	3.18155	+	11.8737i	0.121739	+	0.454335i	0.999702	−	0.0243920i	$-0.00776497\pi$
$683$	3.18155	+	11.8737i	0.121739	+	0.454335i	−0.877964	+	0.478727i	$0.841098\pi$
$684$	−23.2048	−	10.3314i	−0.887258	−	0.395033i
$685$	1.29020	+	1.32030i	0.0492961	+	0.0504460i
$686$	−3.30045	−	18.2238i	−0.126012	−	0.695788i
$687$	3.78967	+	23.9270i	0.144585	+	0.912874i
$688$	5.24670	+	6.47914i	0.200029	+	0.247015i
$689$	−4.95117	−	5.49883i	−0.188625	−	0.209489i
$690$	38.4556	−	9.83046i	1.46398	−	0.374239i
$691$	−4.44860	+	9.99172i	−0.169233	+	0.380103i	−0.978174	−	0.207786i	$-0.933374\pi$
$691$	−4.44860	+	9.99172i	−0.169233	+	0.380103i	0.808942	+	0.587889i	$0.200041\pi$
$692$	9.76832	−	9.76832i	0.371336	−	0.371336i
$693$	63.8854	+	9.46317i	2.42681	+	0.359476i
$694$		−	6.09347i		−	0.231305i
$695$	14.9689	−	16.2441i	0.567804	−	0.616175i
$696$	4.35976	−	20.5111i	0.165256	−	0.777470i
$697$	−1.71419	+	32.7087i	−0.0649297	+	1.23893i
$698$	−6.52556	+	5.28429i	−0.246996	+	0.200013i
$699$	−20.7990	−	15.1114i	−0.786691	−	0.571565i
$700$	−12.9901	−	2.50131i	−0.490981	−	0.0945405i
$701$	−0.100111	−	0.308109i	−0.00378113	−	0.0116371i	0.949148	−	0.314830i	$-0.101947\pi$
$701$	−0.100111	−	0.308109i	−0.00378113	−	0.0116371i	−0.952929	+	0.303193i	$0.901947\pi$
$702$	14.4592	+	37.6676i	0.545728	+	1.42167i
$703$	−30.3956	+	8.14448i	−1.14639	+	0.307175i
$704$	1.89510	−	2.72187i	0.0714244	−	0.102584i
$705$	25.6055	−	5.13485i	0.964357	−	0.193390i
$706$	−2.19964	−	3.02755i	−0.0827847	−	0.113943i
$707$	−21.4250	+	0.906135i	−0.805770	+	0.0340787i
$708$	8.93744	+	17.5407i	0.335889	+	0.659220i
$709$	34.9403	+	3.67237i	1.31221	+	0.137919i	0.734659	−	0.678436i	$-0.237342\pi$
$709$	34.9403	+	3.67237i	1.31221	+	0.137919i	0.577551	+	0.816355i	$0.304009\pi$
$710$	4.69478	−	5.66283i	0.176192	−	0.212522i
$711$	0.963656	+	1.07025i	0.0361399	+	0.0401375i
$712$	−0.102326	−	1.95249i	−0.00383482	−	0.0731727i
$713$	−57.6205	−	9.12620i	−2.15791	−	0.341779i
$714$	−21.2568	−	37.6911i	−0.795514	−	1.41056i
$715$	5.34175	−	20.6430i	0.199770	−	0.772006i
$716$	3.32896	+	5.76592i	0.124409	+	0.215483i
$717$	17.0826	+	13.8332i	0.637963	+	0.516612i
$718$	14.9704	−	9.72189i	0.558690	−	0.362818i
$719$	4.87830	−	1.03692i	0.181930	−	0.0386704i	−0.116046	−	0.993244i	$-0.537022\pi$
$719$	4.87830	−	1.03692i	0.181930	−	0.0386704i	0.297976	+	0.954573i	$0.403689\pi$
$720$	9.51915	+	13.4247i	0.354758	+	0.500310i
$721$	21.7353	+	16.1292i	0.809463	+	0.600683i
$722$	6.31613	−	3.21823i	0.235062	−	0.119770i
$723$	−0.221507	−	4.22660i	−0.00823792	−	0.157189i
$724$	−1.09491	−	10.4174i	−0.0406921	−	0.387159i
$725$	−12.5597	−	30.0558i	−0.466455	−	1.11624i
$726$	1.42387	+	35.3768i	0.0528447	+	1.31295i
$727$	−34.6791	+	34.6791i	−1.28618	+	1.28618i	−0.349089	+	0.937090i	$0.613509\pi$
$727$	−34.6791	+	34.6791i	−1.28618	+	1.28618i	−0.937090	+	0.349089i	$0.886491\pi$
$728$	5.86317	+	4.84668i	0.217303	+	0.179630i
$729$	32.7366	−	10.6368i	1.21247	−	0.393955i
$730$	−4.71546	−	0.550642i	−0.174527	−	0.0203802i
$731$	17.2310	+	38.7014i	0.637310	+	1.43142i
$732$	0.559387	+	0.214729i	0.0206755	+	0.00793660i
$733$	6.16733	+	4.00511i	0.227796	+	0.147932i	0.653491	−	0.756934i	$-0.273304\pi$
$733$	6.16733	+	4.00511i	0.227796	+	0.147932i	−0.425695	+	0.904867i	$0.639970\pi$
$734$	−4.66751	−	14.3651i	−0.172281	−	0.530226i
$735$	1.04023	+	50.3695i	0.0383693	+	1.85791i
$736$	−5.51497			−0.203284
$737$	−2.99061	−	4.40841i	−0.110160	−	0.162386i
$738$	−45.8238	+	12.2784i	−1.68680	+	0.451976i
$739$	21.6274	−	2.27313i	0.795576	−	0.0836184i	0.301985	−	0.953313i	$-0.402351\pi$
$739$	21.6274	−	2.27313i	0.795576	−	0.0836184i	0.493591	+	0.869694i	$0.335684\pi$
$740$	19.6311	+	5.50345i	0.721654	+	0.202311i
$741$	30.3758	+	9.86971i	1.11588	+	0.362573i
$742$	−2.50413	+	6.33174i	−0.0919295	+	0.232446i
$743$	26.6451	−	4.22017i	0.977513	−	0.154823i	0.352818	−	0.935692i	$-0.385223\pi$
$743$	26.6451	−	4.22017i	0.977513	−	0.154823i	0.624695	+	0.780869i	$0.285223\pi$
$744$	−7.07897	−	33.3039i	−0.259528	−	1.22098i
$745$	13.5308	+	8.02136i	0.495729	+	0.293880i
$746$	1.58802	+	15.1090i	0.0581416	+	0.553180i
$747$	−1.93634	−	0.518841i	−0.0708470	−	0.0189834i
$748$	12.8813	−	10.8672i	0.470987	−	0.397345i
$749$	9.78041	+	0.0987045i	0.357368	+	0.00360658i
$750$	33.8196	+	12.2969i	1.23492	+	0.449020i
$751$	26.2054	−	29.1041i	0.956249	−	1.06202i	−0.0417709	−	0.999127i	$-0.513300\pi$
$751$	26.2054	−	29.1041i	0.956249	−	1.06202i	0.998020	−	0.0628952i	$-0.0200334\pi$
$752$	−3.62357	−	0.189903i	−0.132138	−	0.00692506i
$753$	6.91667	−	18.0185i	0.252057	−	0.656632i
$754$	−1.95798	+	18.6289i	−0.0713055	+	0.678426i
$755$	−9.06515	−	6.74723i	−0.329914	−	0.245557i
$756$	25.1205	−	27.3392i	0.913622	−	0.994315i
$757$	−35.6844	−	5.65185i	−1.29697	−	0.205420i	−0.530492	−	0.847690i	$-0.677993\pi$
$757$	−35.6844	−	5.65185i	−1.29697	−	0.205420i	−0.766479	+	0.642270i	$0.777993\pi$
$758$	32.5002	+	8.70841i	1.18046	+	0.316304i
$759$	46.9237	−	35.5556i	1.70322	−	1.29059i
$760$	7.70152	+	0.492700i	0.279364	+	0.0178721i
$761$	−18.4381	+	41.4126i	−0.668380	+	1.50121i	0.186541	+	0.982447i	$0.440272\pi$
$761$	−18.4381	+	41.4126i	−0.668380	+	1.50121i	−0.854921	+	0.518759i	$0.826394\pi$
$762$	−59.2611	−	30.1950i	−2.14680	−	1.09385i
$763$	32.5561	+	21.6124i	1.17861	+	0.782420i
$764$	−15.4035	+	21.2011i	−0.557279	+	0.767029i
$765$	29.0666	+	78.4109i	1.05090	+	2.83495i
$766$	−22.1173	+	19.9145i	−0.799129	+	0.719539i
$767$	−9.57778	−	14.7485i	−0.345834	−	0.532537i
$768$	−1.15347	−	3.00489i	−0.0416222	−	0.108430i
$769$	2.49217			0.0898701			0.0449350	−	0.998990i	$-0.485692\pi$
$769$	2.49217			0.0898701			0.0449350	+	0.998990i	$0.485692\pi$
$770$	−19.1988	+	4.05062i	−0.691875	+	0.145974i
$771$	68.4451			2.46499
$772$	−9.72461	−	25.3335i	−0.349996	−	0.911771i
$773$	18.8039	+	28.9554i	0.676329	+	1.04145i	0.995592	+	0.0937886i	$0.0298978\pi$
$773$	18.8039	+	28.9554i	0.676329	+	1.04145i	−0.319264	+	0.947666i	$0.603436\pi$
$774$	−45.5992	+	41.0577i	−1.63903	+	1.47579i
$775$	−38.4796	−	36.2879i	−1.38223	−	1.30350i
$776$	−6.21510	+	8.55435i	−0.223109	+	0.307083i
$777$	4.84592	−	77.4938i	0.173846	−	2.78008i
$778$	−25.9037	−	13.1986i	−0.928692	−	0.473192i
$779$	−9.04835	+	20.3229i	−0.324191	+	0.728145i
$780$	−13.6683	−	15.5367i	−0.489404	−	0.556302i
$781$	3.16215	−	10.4422i	0.113151	−	0.373651i
$782$	−27.0688	−	7.25306i	−0.967977	−	0.259369i
$783$	90.2976	+	14.3017i	3.22697	+	0.511102i
$784$	1.59327	−	6.81627i	0.0569026	−	0.243438i
$785$	−18.9531	+	2.77831i	−0.676464	+	0.0991621i
$786$	6.63147	−	63.0942i	0.236537	−	2.25050i
$787$	−12.9158	+	33.6467i	−0.460397	+	1.19938i	0.485306	+	0.874345i	$0.338708\pi$
$787$	−12.9158	+	33.6467i	−0.460397	+	1.19938i	−0.945703	+	0.325032i	$0.894625\pi$
$788$	−13.6054	−	0.713030i	−0.484673	−	0.0254006i
$789$	4.11717	−	4.57258i	0.146575	−	0.162788i
$790$	−0.387544	−	0.203124i	−0.0137882	−	0.00722683i
$791$	−6.21111	−	3.67005i	−0.220842	−	0.130492i
$792$	20.7351	+	12.8802i	0.736789	+	0.457676i
$793$	−0.517004	−	0.138531i	−0.0183594	−	0.00491938i
$794$	−1.56226	−	14.8639i	−0.0554426	−	0.527501i
$795$	9.44538	−	15.9329i	0.334993	−	0.565081i
$796$	1.03193	+	4.85487i	0.0365760	+	0.172076i
$797$	−24.7654	+	3.92245i	−0.877235	+	0.138940i	−0.578781	−	0.815483i	$-0.696471\pi$
$797$	−24.7654	+	3.92245i	−0.877235	+	0.138940i	−0.298455	+	0.954424i	$0.596471\pi$
$798$	−4.30448	−	29.0734i	−0.152377	−	1.02919i
$799$	−17.5356	−	5.69766i	−0.620365	−	0.201569i
$800$	−4.12946	−	2.81914i	−0.145998	−	0.0996717i
$801$	14.3109	−	1.50414i	0.505652	−	0.0531462i
$802$	30.5915	−	8.19698i	1.08022	−	0.289445i
$803$	−6.76371	+	1.95895i	−0.238686	+	0.0691299i
$804$	−5.16976			−0.182323
$805$	23.7690	+	22.3508i	0.837746	+	0.787761i
$806$	9.39860	+	28.9259i	0.331052	+	1.01887i
$807$	50.9646	+	33.0968i	1.79404	+	1.16506i
$808$	−7.56679	−	2.90462i	−0.266199	−	0.102184i
$809$	−13.6121	−	30.5732i	−0.478575	−	1.07490i	−0.978012	−	0.208548i	$-0.933126\pi$
$809$	−13.6121	−	30.5732i	−0.478575	−	1.07490i	0.499437	−	0.866350i	$-0.333540\pi$
$810$	−40.4929	+	32.0248i	−1.42278	+	1.12524i
$811$	−3.36794	+	1.09431i	−0.118264	+	0.0384264i	−0.367551	−	0.930003i	$-0.619804\pi$
$811$	−3.36794	+	1.09431i	−0.118264	+	0.0384264i	0.249287	+	0.968430i	$0.419804\pi$
$812$	16.1534	−	6.01440i	0.566875	−	0.211064i
$813$	−31.6573	+	31.6573i	−1.11027	+	1.11027i
$814$	30.0049	−	3.76519i	1.05167	−	0.131970i
$815$	−10.6008	−	0.678179i	−0.371329	−	0.0237556i
$816$	−1.70959	−	16.2657i	−0.0598478	−	0.569414i
$817$	1.50589	+	28.7341i	0.0526844	+	1.00528i
$818$	30.7040	−	15.6445i	1.07354	−	0.546996i
$819$	−33.3636	+	44.9598i	−1.16582	+	1.57102i
$820$	11.7575	−	8.33694i	0.410589	−	0.291138i
$821$	−51.7226	+	10.9940i	−1.80513	+	0.383693i	−0.982705	−	0.185178i	$-0.940714\pi$
$821$	−51.7226	+	10.9940i	−1.80513	+	0.383693i	−0.822427	+	0.568871i	$0.807380\pi$
$822$	2.22854	−	1.44723i	0.0777293	−	0.0504780i
$823$	15.0420	+	12.1808i	0.524330	+	0.424594i	0.854596	−	0.519294i	$-0.173805\pi$
$823$	15.0420	+	12.1808i	0.524330	+	0.424594i	−0.330266	+	0.943888i	$0.607138\pi$
$824$	5.11501	+	8.85945i	0.178190	+	0.308634i
$825$	53.3105	−	2.63667i	1.85603	−	0.0917971i
$826$	−8.23213	+	13.9319i	−0.286432	+	0.484751i
$827$	−13.9353	−	2.20713i	−0.484576	−	0.0767494i	−0.0906336	−	0.995884i	$-0.528889\pi$
$827$	−13.9353	−	2.20713i	−0.484576	−	0.0767494i	−0.393943	+	0.919135i	$0.628889\pi$
$828$	−2.12428	−	40.5338i	−0.0738240	−	1.40865i
$829$	27.6883	+	30.7509i	0.961653	+	1.06802i	0.997639	+	0.0686714i	$0.0218760\pi$
$829$	27.6883	+	30.7509i	0.961653	+	1.06802i	−0.0359865	+	0.999352i	$0.511457\pi$
$830$	0.606408	−	0.0566767i	0.0210487	−	0.00196728i
$831$	10.6357	+	1.11786i	0.368948	+	0.0387780i
$832$	1.30531	+	2.56181i	0.0452535	+	0.0888149i
$833$	16.7846	−	31.3604i	0.581553	−	1.08657i
$834$	−18.6893	−	25.7237i	−0.647159	−	0.890738i
$835$	0.727713	−	1.09279i	0.0251835	−	0.0378176i
$836$	10.8130	−	3.75541i	0.373975	−	0.129884i
$837$	143.386	−	38.4202i	4.95615	−	1.32800i
$838$	7.54907	+	19.6660i	0.260778	+	0.679350i
$839$	9.55790	+	29.4162i	0.329975	+	1.01556i	0.969144	+	0.246493i	$0.0792784\pi$
$839$	9.55790	+	29.4162i	0.329975	+	1.01556i	−0.639169	+	0.769066i	$0.720722\pi$
$840$	−7.20672	+	17.6255i	−0.248655	+	0.608137i
$841$	10.8763	+	7.90208i	0.375044	+	0.272486i
$842$	16.4470	−	13.3185i	0.566802	−	0.458987i
$843$	0.0929930	−	1.77441i	0.00320285	−	0.0611140i
$844$	−0.308064	+	1.44933i	−0.0106040	+	0.0498879i
$845$	−7.78323	−	7.17222i	−0.267751	−	0.246732i
$846$		−	26.7056i		−	0.918156i
$847$	−23.9194	+	16.5790i	−0.821879	+	0.569661i
$848$	−1.81977	+	1.81977i	−0.0624910	+	0.0624910i
$849$	1.61812	−	3.63437i	0.0555339	−	0.124731i
$850$	−16.5608	−	19.2679i	−0.568029	−	0.660884i
$851$	−33.6467	−	37.3685i	−1.15339	−	1.28097i
$852$	−6.66341	−	8.22863i	−0.228285	−	0.281908i
$853$	−0.696389	−	4.39683i	−0.0238439	−	0.150545i	0.972894	−	0.231252i	$-0.0742821\pi$
$853$	−0.696389	−	4.39683i	−0.0238439	−	0.150545i	−0.996738	+	0.0807073i	$0.974282\pi$
$854$	0.0975358	+	0.482776i	0.00333761	+	0.0165203i
$855$	−0.654721	+	56.7942i	−0.0223910	+	1.94232i
$856$	3.37723	+	1.50364i	0.115431	+	0.0513933i
$857$	−5.90540	−	22.0393i	−0.201725	−	0.752847i	−0.990423	−	0.138066i	$-0.955911\pi$
$857$	−5.90540	−	22.0393i	−0.201725	−	0.752847i	0.788698	−	0.614781i	$-0.210755\pi$
$858$	−27.6224	−	13.3815i	−0.943014	−	0.456837i
$859$	6.96173	+	12.0581i	0.237531	+	0.411416i	0.960005	−	0.279982i	$-0.0903285\pi$
$859$	6.96173	+	12.0581i	0.237531	+	0.411416i	−0.722474	+	0.691398i	$0.756995\pi$
$860$	8.65434	−	16.5117i	0.295110	−	0.563046i
$861$	−40.4195	−	37.1392i	−1.37749	−	1.26570i
$862$	7.84551	−	3.99749i	0.267219	−	0.136155i
$863$	−2.46209	−	3.04042i	−0.0838104	−	0.103497i	0.733516	−	0.679672i	$-0.237878\pi$
$863$	−2.46209	−	3.04042i	−0.0838104	−	0.103497i	−0.817326	+	0.576175i	$0.804545\pi$
$864$	12.8197	−	5.70772i	0.436136	−	0.194180i
$865$	−28.7089	−	11.4017i	−0.976132	−	0.387670i
$866$	23.0228	+	20.7298i	0.782346	+	0.704428i
$867$	4.44118	−	28.0405i	0.150831	−	0.952306i
$868$	19.9888	−	19.5894i	0.678465	−	0.664907i
$869$	−0.646669	−	0.0548432i	−0.0219367	−	0.00186043i
$870$	−45.9735	+	9.21940i	−1.55865	+	0.312567i
$871$	4.59277	−	0.482719i	0.155620	−	0.0163563i
$872$	8.04411	+	12.3868i	0.272408	+	0.419472i
$873$	−65.2664	−	42.3845i	−2.20893	−	1.43450i
$874$	−15.3985	−	11.1877i	−0.520863	−	0.378429i
$875$	6.37231	+	28.8859i	0.215423	+	0.976521i
$876$	−2.11173	+	6.49925i	−0.0713489	+	0.219589i
$877$	46.9539	−	2.46075i	1.58552	−	0.0830935i	0.760933	−	0.648830i	$-0.224741\pi$
$877$	46.9539	−	2.46075i	1.58552	−	0.0830935i	0.824586	+	0.565737i	$0.191408\pi$
$878$	0.552346	−	0.682090i	0.0186408	−	0.0230194i
$879$	37.4450	+	21.6189i	1.26299	+	0.729187i
$880$	−7.26711	−	1.47957i	−0.244974	−	0.0498764i
$881$		−	25.7685i		−	0.868164i	−0.900873	−	0.434082i	$-0.857073\pi$
$881$		−	25.7685i		−	0.868164i	0.900873	−	0.434082i	$-0.142927\pi$
$882$	50.7117	+	9.08466i	1.70755	+	0.305897i
$883$	−44.3735	−	22.6094i	−1.49329	−	0.760867i	−0.498898	−	0.866661i	$-0.666262\pi$
$883$	−44.3735	−	22.6094i	−1.49329	−	0.760867i	−0.994388	+	0.105793i	$0.966262\pi$
$884$	3.03758	+	14.2907i	0.102165	+	0.480647i
$885$	28.0953	−	33.8885i	0.944412	−	1.13915i
$886$	−19.5973	+	8.72527i	−0.658383	+	0.293131i
$887$	17.4480	−	26.8676i	0.585846	−	0.902124i	−0.414121	−	0.910222i	$-0.635911\pi$
$887$	17.4480	−	26.8676i	0.585846	−	0.902124i	0.999967	+	0.00809776i	$0.00257763\pi$
$888$	13.3233	−	26.1485i	0.447101	−	0.877486i
$889$	−5.16574	−	54.4269i	−0.173253	−	1.82542i
$890$	−3.91801	+	1.93976i	−0.131332	+	0.0650210i
$891$	−36.9455	+	67.0716i	−1.23772	+	2.24698i
$892$	−4.38890	−	16.3796i	−0.146951	−	0.548429i
$893$	−9.73225	−	7.88102i	−0.325677	−	0.263728i
$894$	15.1504	−	16.8262i	0.506704	−	0.562752i
$895$	8.88893	−	11.9426i	0.297124	−	0.399197i
$896$	1.57665	−	2.12466i	0.0526723	−	0.0709797i
$897$	7.98397	+	50.4088i	0.266577	+	1.68310i
$898$	4.67101	−	7.19273i	0.155874	−	0.240025i
$899$	67.4103	+	14.3285i	2.24826	+	0.477882i
$900$	19.1294	−	31.4365i	0.637648	−	1.04788i
$901$	−11.3251	+	6.53856i	−0.377294	+	0.217831i
$902$	11.2805	−	18.1599i	0.375600	−	0.604660i
$903$	−68.3890	−	19.0665i	−2.27584	−	0.634494i
$904$	−1.60276	−	2.20601i	−0.0533070	−	0.0733707i
$905$	−20.4180	+	11.4766i	−0.678716	+	0.381494i
$906$	−12.0883	+	10.8843i	−0.401606	+	0.361608i
$907$	21.6124	+	8.29621i	0.717627	+	0.275471i	0.689655	−	0.724138i	$-0.257762\pi$
$907$	21.6124	+	8.29621i	0.717627	+	0.275471i	0.0279712	+	0.999609i	$0.491095\pi$
$908$	−11.5144	+	9.32414i	−0.382117	+	0.309432i
$909$	18.4337	−	56.7330i	0.611406	−	1.88171i
$910$	4.75663	−	16.3313i	0.157681	−	0.541376i
$911$	−15.4873	+	11.2522i	−0.513119	+	0.372802i	−0.814005	−	0.580857i	$-0.802717\pi$
$911$	−15.4873	+	11.2522i	−0.513119	+	0.372802i	0.300887	+	0.953660i	$0.402717\pi$
$912$	2.87509	−	10.7300i	0.0952038	−	0.355305i
$913$	0.796496	−	0.426226i	0.0263602	−	0.0141060i
$914$	−17.1252	−	9.88726i	−0.566453	−	0.327042i
$915$	−0.0546928	−	1.33870i	−0.00180809	−	0.0442561i
$916$	−7.15811	+	2.32581i	−0.236511	+	0.0768470i
$917$	46.7018	−	23.2051i	1.54223	−	0.766300i
$918$	70.4289	−	11.1548i	2.32450	−	0.368164i
$919$	−4.23682	−	0.445308i	−0.139760	−	0.0146893i	0.0343902	−	0.999408i	$-0.489051\pi$
$919$	−4.23682	−	0.445308i	−0.139760	−	0.0146893i	−0.174150	+	0.984719i	$0.555718\pi$
$920$	4.88562	+	11.3228i	0.161074	+	0.373301i
$921$	18.2083	+	3.87029i	0.599983	+	0.127530i
$922$	−15.9240	+	6.11267i	−0.524430	+	0.201310i
$923$	6.68805	+	6.68805i	0.220140	+	0.220140i
$924$	0.283048	+	28.2423i	0.00931159	+	0.929104i
$925$	−6.09176	−	45.1800i	−0.200296	−	1.48551i
$926$	−8.13331	−	3.62118i	−0.267277	−	0.118999i
$927$	−63.1447	+	41.0067i	−2.07394	+	1.34684i
$928$	6.50596	+	0.340963i	0.213569	+	0.0111927i
$929$	−3.31936	+	31.5816i	−0.108905	+	1.03616i	0.794469	+	0.607305i	$0.207749\pi$
$929$	−3.31936	+	31.5816i	−0.108905	+	1.03616i	−0.903373	+	0.428855i	$0.858917\pi$
$930$	−62.1051	+	44.0372i	−2.03651	+	1.44404i
$931$	18.2761	−	15.7998i	0.598976	−	0.517818i
$932$	3.62623	−	7.11688i	0.118781	−	0.233121i
$933$	−25.5492	+	9.80740i	−0.836442	+	0.321080i
$934$	−11.3989	+	19.7435i	−0.372983	+	0.646026i
$935$	−33.7228	−	16.8195i	−1.10285	−	0.550056i
$936$	−18.3260	+	10.5805i	−0.599003	+	0.345834i
$937$	4.44209	−	28.0462i	0.145117	−	0.916230i	−0.802461	−	0.596705i	$-0.796476\pi$
$937$	4.44209	−	28.0462i	0.145117	−	0.916230i	0.947578	−	0.319526i	$-0.103524\pi$
$938$	−2.27838	−	3.58714i	−0.0743919	−	0.117124i
$939$	−17.6033	−	5.71966i	−0.574462	−	0.186654i
$940$	2.82017	+	7.60778i	0.0919838	+	0.248138i
$941$	−12.3388	−	27.7135i	−0.402235	−	0.903434i	−0.995168	−	0.0981826i	$-0.968697\pi$
$941$	−12.3388	−	27.7135i	−0.402235	−	0.903434i	0.592934	−	0.805251i	$-0.297970\pi$
$942$	−1.44307	+	27.5355i	−0.0470179	+	0.897154i
$943$	−35.4997	+	1.86046i	−1.15603	+	0.0605850i
$944$	−4.94820	+	3.59508i	−0.161050	+	0.117010i
$945$	−78.3837	−	27.3555i	−2.54982	−	0.889873i
$946$	2.33666	−	27.5521i	0.0759713	−	0.895796i
$947$	5.76922	−	21.5310i	0.187474	−	0.699664i	−0.806613	−	0.591080i	$-0.798702\pi$
$947$	5.76922	−	21.5310i	0.187474	−	0.699664i	0.994087	−	0.108584i	$-0.0346316\pi$
$948$	−0.396361	+	0.489465i	−0.0128732	+	0.0158971i
$949$	1.26919	−	5.97106i	0.0411996	−	0.193829i
$950$	−5.81109	−	16.2485i	−0.188537	−	0.527169i
$951$	−23.9539	+	32.9697i	−0.776759	+	1.06912i
$952$	10.5329	−	8.35476i	0.341372	−	0.270779i
$953$	4.63783	+	9.10226i	0.150234	+	0.294851i	0.953842	−	0.300307i	$-0.0970892\pi$
$953$	4.63783	+	9.10226i	0.150234	+	0.294851i	−0.803608	+	0.595159i	$0.797089\pi$
$954$	−14.0758	−	12.6739i	−0.455721	−	0.410333i
$955$	57.1736	+	12.8432i	1.85009	+	0.415596i
$956$	−3.41464	+	5.91434i	−0.110437	+	0.191283i
$957$	−57.5537	+	39.0436i	−1.86045	+	1.26210i
$958$	12.0707	+	12.0707i	0.389988	+	0.389988i
$959$	1.98634	+	0.908505i	0.0641423	+	0.0293371i
$960$	−5.14749	+	5.03017i	−0.166135	+	0.162348i
$961$	79.1318	−	16.8200i	2.55264	−	0.542580i
$962$	−9.39474	+	24.4741i	−0.302898	+	0.789077i
$963$	−9.75054	+	25.4010i	−0.314207	+	0.818537i
$964$	1.28622	−	0.273394i	0.0414262	−	0.00880542i
$965$	−43.3972	+	42.4081i	−1.39701	+	1.36516i
$966$	38.2717	−	27.2202i	1.23137	−	0.875794i
$967$	−32.7964	−	32.7964i	−1.05466	−	1.05466i	−0.998417	−	0.0562427i	$-0.982088\pi$
$967$	−32.7964	−	32.7964i	−1.05466	−	1.05466i	−0.0562427	−	0.998417i	$-0.517912\pi$
$968$	−10.7866	+	2.15632i	−0.346694	+	0.0693067i
$969$	28.2232	−	48.8841i	0.906661	−	1.57038i
$970$	23.0688	+	5.18205i	0.740693	+	0.166386i
$971$	−40.2042	−	36.2000i	−1.29021	−	1.16171i	−0.977283	−	0.211938i	$-0.932023\pi$
$971$	−40.2042	−	36.2000i	−1.29021	−	1.16171i	−0.312931	−	0.949776i	$-0.601311\pi$
$972$	14.6247	+	28.7025i	0.469087	+	0.920634i
$973$	9.61225	−	24.3048i	0.308155	−	0.779175i
$974$	−17.0467	+	23.4627i	−0.546210	+	0.751794i
$975$	−19.7898	+	41.8260i	−0.633780	+	1.33950i
$976$	−0.0387046	+	0.182091i	−0.00123890	+	0.00582859i
$977$	−11.3959	+	14.0727i	−0.364586	+	0.450226i	−0.926121	−	0.377227i	$-0.876878\pi$
$977$	−11.3959	+	14.0727i	−0.364586	+	0.450226i	0.561535	+	0.827453i	$0.310211\pi$
$978$	−3.95743	+	14.7693i	−0.126545	+	0.472271i
$979$	−4.24122	+	4.90526i	−0.135550	+	0.156773i
$980$	−15.4059	+	2.76727i	−0.492124	+	0.0883972i
$981$	−87.9420	+	63.8936i	−2.80777	+	2.03997i
$982$	−23.4981	+	1.23148i	−0.749855	+	0.0392982i
$983$	1.01892	−	19.4421i	0.0324984	−	0.620107i	−0.933028	−	0.359803i	$-0.882844\pi$
$983$	1.01892	−	19.4421i	0.0324984	−	0.620107i	0.965527	−	0.260304i	$-0.0838228\pi$
$984$	−8.43855	−	18.9533i	−0.269011	−	0.604209i
$985$	10.5889	+	28.5649i	0.337390	+	0.910154i
$986$	31.4844	+	10.2299i	1.00267	+	0.325786i
$987$	26.0834	−	16.5670i	0.830244	−	0.527332i
$988$	−1.55231	+	9.80088i	−0.0493855	+	0.311808i
$989$	−39.8188	+	22.9894i	−1.26616	+	0.731020i
$990$	8.07535	−	53.9815i	0.256651	−	1.71564i
$991$	5.47333	−	9.48008i	0.173866	−	0.301145i	−0.765902	−	0.642957i	$-0.777707\pi$
$991$	5.47333	−	9.48008i	0.173866	−	0.301145i	0.939768	+	0.341812i	$0.111041\pi$
$992$	9.87566	−	3.79091i	0.313552	−	0.120362i
$993$	−30.8953	+	60.6355i	−0.980434	+	1.92421i
$994$	2.77294	−	8.25001i	0.0879525	−	0.261675i
$995$	9.05335	−	6.41951i	0.287011	−	0.203512i
$996$	0.0916389	−	0.871886i	0.00290369	−	0.0276268i
$997$	−19.7254	−	1.03376i	−0.624708	−	0.0327396i	−0.262644	−	0.964893i	$-0.584595\pi$
$997$	−19.7254	−	1.03376i	−0.624708	−	0.0327396i	−0.362064	+	0.932153i	$0.617928\pi$
$998$	−19.7712	+	12.8396i	−0.625848	+	0.406430i
$999$	116.887	+	52.0417i	3.69816	+	1.64653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.157.24	yes	768
5.3	odd	4	inner	770.2.bv.a.3.1	✓	768
7.5	odd	6	inner	770.2.bv.a.47.24	yes	768
11.4	even	5	inner	770.2.bv.a.367.48	yes	768
35.33	even	12	inner	770.2.bv.a.663.48	yes	768
55.48	odd	20	inner	770.2.bv.a.213.24	yes	768
77.26	odd	30	inner	770.2.bv.a.257.1	yes	768
385.103	even	60	inner	770.2.bv.a.103.24	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.1	✓	768	5.3	odd	4	inner
770.2.bv.a.47.24	yes	768	7.5	odd	6	inner
770.2.bv.a.103.24	yes	768	385.103	even	60	inner
770.2.bv.a.157.24	yes	768	1.1	even	1	trivial
770.2.bv.a.213.24	yes	768	55.48	odd	20	inner
770.2.bv.a.257.1	yes	768	77.26	odd	30	inner
770.2.bv.a.367.48	yes	768	11.4	even	5	inner
770.2.bv.a.663.48	yes	768	35.33	even	12	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358368 - 0.933580i) q^{2} +(1.75302 + 2.69941i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(2.03213 + 0.932978i) q^{5} +(1.89189 - 2.60396i) q^{6} +(2.64059 + 0.165124i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.99352 + 6.72356i) q^{9} +O(q^{10})\)	\(q+(-0.358368 - 0.933580i) q^{2} +(1.75302 + 2.69941i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(2.03213 + 0.932978i) q^{5} +(1.89189 - 2.60396i) q^{6} +(2.64059 + 0.165124i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.99352 + 6.72356i) q^{9} +(0.142759 - 2.23151i) q^{10} +(-1.08813 - 3.13305i) q^{11} +(-3.10900 - 0.833054i) q^{12} +(2.83979 + 0.449779i) q^{13} +(-0.792148 - 2.52438i) q^{14} +(1.04387 + 7.12107i) q^{15} +(0.104528 - 0.994522i) q^{16} +(1.82100 - 4.74388i) q^{17} +(7.34977 + 0.385185i) q^{18} +(2.30935 - 2.56479i) q^{19} +(-2.13445 + 0.666423i) q^{20} +(4.18326 + 7.41750i) q^{21} +(-2.53500 + 2.13864i) q^{22} +(5.32705 + 1.42738i) q^{23} +(0.336443 + 3.20104i) q^{24} +(3.25911 + 3.79186i) q^{25} +(-0.597786 - 2.81236i) q^{26} +(-13.8602 + 2.19524i) q^{27} +(-2.07283 + 1.64419i) q^{28} +(-6.19603 - 2.01321i) q^{29} +(6.27400 - 3.52650i) q^{30} +(-10.5203 + 1.10573i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(6.54987 - 8.42957i) q^{33} -5.08138 q^{34} +(5.21197 + 2.79917i) q^{35} +(-2.27432 - 6.99964i) q^{36} +(-7.64681 - 4.96589i) q^{37} +(-3.22203 - 1.23682i) q^{38} +(3.76406 + 8.45422i) q^{39} +(1.38708 + 1.75386i) q^{40} +(-6.13033 + 1.99187i) q^{41} +(5.42569 - 6.56361i) q^{42} +(-5.89521 + 5.89521i) q^{43} +(2.90505 + 1.60021i) q^{44} +(-12.3562 + 10.8703i) q^{45} +(-0.576471 - 5.48476i) q^{46} +(-0.189903 - 3.62357i) q^{47} +(2.86786 - 1.46125i) q^{48} +(6.94547 + 0.872051i) q^{49} +(2.37205 - 4.40152i) q^{50} +(15.9979 - 3.40046i) q^{51} +(-2.41134 + 1.56594i) q^{52} +(-2.00001 - 1.61958i) q^{53} +(7.01648 + 12.1529i) q^{54} +(0.711849 - 7.38196i) q^{55} +(2.27782 + 1.34593i) q^{56} +(10.9717 + 1.73775i) q^{57} +(0.340963 + 6.50596i) q^{58} +(-4.09261 - 4.54530i) q^{59} +(-5.54067 - 4.59350i) q^{60} +(-0.185139 - 0.0194589i) q^{61} +(4.80243 + 9.42530i) q^{62} +(-9.01490 + 17.2599i) q^{63} +(0.587785 + 0.809017i) q^{64} +(5.35119 + 3.56347i) q^{65} +(-10.2169 - 3.09394i) q^{66} +(1.55145 - 0.415709i) q^{67} +(1.82100 + 4.74388i) q^{68} +(5.48532 + 16.8821i) q^{69} +(0.745444 - 5.86893i) q^{70} +(2.66137 + 1.93360i) q^{71} +(-5.71968 + 4.63171i) q^{72} +(0.111117 - 2.12024i) q^{73} +(-1.89569 + 8.91853i) q^{74} +(-4.52252 + 15.4448i) q^{75} +3.45127i q^{76} +(-2.35596 - 8.45278i) q^{77} +(6.54378 - 6.54378i) q^{78} +(0.0795894 - 0.178761i) q^{79} +(1.14028 - 1.92348i) q^{80} +(-15.4488 - 17.1577i) q^{81} +(4.05648 + 5.00934i) q^{82} +(0.0426090 + 0.269022i) q^{83} +(-8.07205 - 2.71313i) q^{84} +(8.12645 - 7.94122i) q^{85} +(7.61631 + 3.39100i) q^{86} +(-5.42726 - 20.2548i) q^{87} +(0.452846 - 3.28556i) q^{88} +(-0.977585 - 1.69323i) q^{89} +(14.5763 + 7.63992i) q^{90} +(7.42447 + 1.65660i) q^{91} +(-4.91387 + 2.50374i) q^{92} +(-21.4271 - 26.4602i) q^{93} +(-3.31484 + 1.47586i) q^{94} +(7.08579 - 3.05742i) q^{95} +(-2.39194 - 2.15371i) q^{96} +(-1.65410 + 10.4436i) q^{97} +(-1.67490 - 6.79667i) q^{98} +(24.3226 + 2.06277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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