LMFDB - Embedded newform 770.2.bv.a.3.11

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			3.11
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(-0.647269 + 0.420342i) q^{3} +(0.743145 - 0.669131i) q^{4} +(1.72525 + 1.42250i) q^{5} +(0.453641 - 0.624383i) q^{6} +(-2.58746 - 0.552333i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.977939 + 2.19649i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.647269 + 0.420342i) q^{3} +(0.743145 - 0.669131i) q^{4} +(1.72525 + 1.42250i) q^{5} +(0.453641 - 0.624383i) q^{6} +(-2.58746 - 0.552333i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.977939 + 2.19649i) q^{9} +(-2.12044 - 0.709742i) q^{10} +(-3.05765 - 1.28482i) q^{11} +(-0.199751 + 0.745482i) q^{12} +(1.02884 - 6.49586i) q^{13} +(2.61354 - 0.411614i) q^{14} +(-1.71464 - 0.195545i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-2.69984 - 1.03637i) q^{17} +(0.125834 - 2.40106i) q^{18} +(2.93186 - 3.25616i) q^{19} +(2.23395 - 0.0972963i) q^{20} +(1.90695 - 0.730107i) q^{21} +(3.31500 + 0.103714i) q^{22} +(0.00532186 - 0.0198615i) q^{23} +(-0.0806730 - 0.767552i) q^{24} +(0.952992 + 4.90834i) q^{25} +(1.36740 + 6.43312i) q^{26} +(-0.652484 - 4.11962i) q^{27} +(-2.29244 + 1.32088i) q^{28} +(-1.52145 - 0.494348i) q^{29} +(1.67083 - 0.431915i) q^{30} +(0.795549 - 0.0836156i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.51919 - 0.453637i) q^{33} +2.89192 q^{34} +(-3.67832 - 4.63357i) q^{35} +(0.742987 + 2.28668i) q^{36} +(2.22615 - 3.42798i) q^{37} +(-1.57023 + 4.09058i) q^{38} +(2.06454 + 4.63704i) q^{39} +(-2.05070 + 0.891410i) q^{40} +(1.90459 - 0.618840i) q^{41} +(-1.51864 + 1.36500i) q^{42} +(-5.26196 - 5.26196i) q^{43} +(-3.13199 + 1.09117i) q^{44} +(-4.81169 + 2.39838i) q^{45} +(0.00214932 + 0.0204495i) q^{46} +(-6.84994 + 0.358990i) q^{47} +(0.350381 + 0.687661i) q^{48} +(6.38986 + 2.85827i) q^{49} +(-2.64869 - 4.24081i) q^{50} +(2.18315 - 0.464043i) q^{51} +(-3.58200 - 5.51580i) q^{52} +(2.61051 - 3.22371i) q^{53} +(2.08549 + 3.61217i) q^{54} +(-3.44758 - 6.56614i) q^{55} +(1.66681 - 2.05469i) q^{56} +(-0.529004 + 3.34000i) q^{57} +(1.59755 - 0.0837241i) q^{58} +(-1.05301 - 1.16948i) q^{59} +(-1.40507 + 1.00200i) q^{60} +(4.25970 + 0.447713i) q^{61} +(-0.712744 + 0.363161i) q^{62} +(3.74357 - 5.14317i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(11.0154 - 9.74348i) q^{65} +(-2.18929 + 1.32630i) q^{66} +(-4.05076 - 15.1176i) q^{67} +(-2.69984 + 1.03637i) q^{68} +(0.00490392 + 0.0150927i) q^{69} +(5.09453 + 3.00762i) q^{70} +(5.15987 + 3.74886i) q^{71} +(-1.51311 - 1.86854i) q^{72} +(14.2734 + 0.748037i) q^{73} +(-0.849817 + 3.99808i) q^{74} +(-2.68002 - 2.77644i) q^{75} -4.38160i q^{76} +(7.20190 + 5.01325i) q^{77} +(-3.58918 - 3.58918i) q^{78} +(0.710523 - 1.59586i) q^{79} +(1.59504 - 1.56711i) q^{80} +(-2.67250 - 2.96811i) q^{81} +(-1.55632 + 1.26028i) q^{82} +(-8.67823 + 1.37450i) q^{83} +(0.928602 - 1.81857i) q^{84} +(-3.18367 - 5.62852i) q^{85} +(6.79817 + 3.02674i) q^{86} +(1.19258 - 0.319551i) q^{87} +(2.53293 - 2.14110i) q^{88} +(-3.35933 - 5.81854i) q^{89} +(3.63260 - 3.96344i) q^{90} +(-6.24997 + 16.2395i) q^{91} +(-0.00933500 - 0.0183210i) q^{92} +(-0.479787 + 0.388524i) q^{93} +(6.26632 - 2.78994i) q^{94} +(9.69010 - 1.44713i) q^{95} +(-0.573544 - 0.516422i) q^{96} +(-16.9142 - 2.67895i) q^{97} +(-6.98976 - 0.378510i) q^{98} +(5.81228 - 5.45963i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	−0.647269	+	0.420342i	−0.373701	+	0.242684i	−0.717800	−	0.696249i	$-0.754851\pi$
$3$	−0.647269	+	0.420342i	−0.373701	+	0.242684i	0.344099	+	0.938933i	$0.388184\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	1.72525	+	1.42250i	0.771556	+	0.636161i
$5$	1.72525	+	1.42250i	0.771556	+	0.636161i
$6$	0.453641	−	0.624383i	0.185198	−	0.254903i
$7$	−2.58746	−	0.552333i	−0.977966	−	0.208762i
$7$	−2.58746	−	0.552333i	−0.977966	−	0.208762i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−0.977939	+	2.19649i	−0.325980	+	0.732163i
$10$	−2.12044	−	0.709742i	−0.670542	−	0.224440i
$11$	−3.05765	−	1.28482i	−0.921917	−	0.387387i
$11$	−3.05765	−	1.28482i	−0.921917	−	0.387387i
$12$	−0.199751	+	0.745482i	−0.0576633	+	0.215202i
$13$	1.02884	−	6.49586i	0.285350	−	1.80163i	−0.262371	−	0.964967i	$-0.584504\pi$
$13$	1.02884	−	6.49586i	0.285350	−	1.80163i	0.547720	−	0.836661i	$-0.315496\pi$
$14$	2.61354	−	0.411614i	0.698497	−	0.110008i
$15$	−1.71464	−	0.195545i	−0.442718	−	0.0504894i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−2.69984	−	1.03637i	−0.654807	−	0.251357i	0.00820421	−	0.999966i	$-0.497388\pi$
$17$	−2.69984	−	1.03637i	−0.654807	−	0.251357i	−0.663011	+	0.748610i	$0.730722\pi$
$18$	0.125834	−	2.40106i	0.0296594	−	0.565935i
$19$	2.93186	−	3.25616i	0.672616	−	0.747015i	−0.306153	−	0.951982i	$-0.599042\pi$
$19$	2.93186	−	3.25616i	0.672616	−	0.747015i	0.978769	+	0.204967i	$0.0657087\pi$
$20$	2.23395	−	0.0972963i	0.499526	−	0.0217561i
$21$	1.90695	−	0.730107i	0.416130	−	0.159322i
$22$	3.31500	+	0.103714i	0.706761	+	0.0221119i
$23$	0.00532186	−	0.0198615i	0.00110969	−	0.00414140i	−0.965369	−	0.260889i	$-0.915984\pi$
$23$	0.00532186	−	0.0198615i	0.00110969	−	0.00414140i	0.966478	+	0.256748i	$0.0826510\pi$
$24$	−0.0806730	−	0.767552i	−0.0164673	−	0.156676i
$25$	0.952992	+	4.90834i	0.190598	+	0.981668i
$26$	1.36740	+	6.43312i	0.268169	+	1.26164i
$27$	−0.652484	−	4.11962i	−0.125571	−	0.792822i
$28$	−2.29244	+	1.32088i	−0.433230	+	0.249623i
$29$	−1.52145	−	0.494348i	−0.282525	−	0.0917981i	0.164327	−	0.986406i	$-0.447455\pi$
$29$	−1.52145	−	0.494348i	−0.282525	−	0.0917981i	−0.446852	+	0.894608i	$0.647455\pi$
$30$	1.67083	−	0.431915i	0.305050	−	0.0788565i
$31$	0.795549	−	0.0836156i	0.142885	−	0.0150178i	−0.0328160	−	0.999461i	$-0.510448\pi$
$31$	0.795549	−	0.0836156i	0.142885	−	0.0150178i	0.175701	+	0.984444i	$0.443781\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	2.51919	−	0.453637i	0.438534	−	0.0789681i
$34$	2.89192			0.495960
$35$	−3.67832	−	4.63357i	−0.621750	−	0.783216i
$36$	0.742987	+	2.28668i	0.123831	+	0.381113i
$37$	2.22615	−	3.42798i	0.365978	−	0.563556i	−0.606929	−	0.794756i	$-0.707599\pi$
$37$	2.22615	−	3.42798i	0.365978	−	0.563556i	0.972906	+	0.231200i	$0.0742653\pi$
$38$	−1.57023	+	4.09058i	−0.254724	+	0.663579i
$39$	2.06454	+	4.63704i	0.330591	+	0.742520i
$40$	−2.05070	+	0.891410i	−0.324245	+	0.140944i
$41$	1.90459	−	0.618840i	0.297447	−	0.0966465i	−0.156492	−	0.987679i	$-0.550018\pi$
$41$	1.90459	−	0.618840i	0.297447	−	0.0966465i	0.453939	+	0.891033i	$0.350018\pi$
$42$	−1.51864	+	1.36500i	−0.234332	+	0.210625i
$43$	−5.26196	−	5.26196i	−0.802441	−	0.802441i	0.181036	−	0.983477i	$-0.442055\pi$
$43$	−5.26196	−	5.26196i	−0.802441	−	0.802441i	−0.983477	+	0.181036i	$0.942055\pi$
$44$	−3.13199	+	1.09117i	−0.472165	+	0.164499i
$45$	−4.81169	+	2.39838i	−0.717285	+	0.357529i
$46$	0.00214932	+	0.0204495i	0.000316901	+	0.00301511i
$47$	−6.84994	+	0.358990i	−0.999166	+	0.0523641i	−0.544899	−	0.838501i	$-0.683432\pi$
$47$	−6.84994	+	0.358990i	−0.999166	+	0.0523641i	−0.454267	+	0.890866i	$0.650099\pi$
$48$	0.350381	+	0.687661i	0.0505731	+	0.0992553i
$49$	6.38986	+	2.85827i	0.912837	+	0.408325i
$50$	−2.64869	−	4.24081i	−0.374581	−	0.599741i
$51$	2.18315	−	0.464043i	0.305702	−	0.0649791i
$52$	−3.58200	−	5.51580i	−0.496734	−	0.764904i
$53$	2.61051	−	3.22371i	0.358581	−	0.442810i	−0.565650	−	0.824646i	$-0.691375\pi$
$53$	2.61051	−	3.22371i	0.358581	−	0.442810i	0.924230	+	0.381835i	$0.124708\pi$
$54$	2.08549	+	3.61217i	0.283799	+	0.491554i
$55$	−3.44758	−	6.56614i	−0.464871	−	0.885378i
$56$	1.66681	−	2.05469i	0.222737	−	0.274569i
$57$	−0.529004	+	3.34000i	−0.0700683	+	0.442394i
$58$	1.59755	−	0.0837241i	0.209769	−	0.0109935i
$59$	−1.05301	−	1.16948i	−0.137090	−	0.152254i	0.670690	−	0.741737i	$-0.265998\pi$
$59$	−1.05301	−	1.16948i	−0.137090	−	0.152254i	−0.807780	+	0.589484i	$0.799331\pi$
$60$	−1.40507	+	1.00200i	−0.181394	+	0.129358i
$61$	4.25970	+	0.447713i	0.545399	+	0.0573238i	0.373222	−	0.927742i	$-0.378253\pi$
$61$	4.25970	+	0.447713i	0.545399	+	0.0573238i	0.172178	+	0.985066i	$0.444920\pi$
$62$	−0.712744	+	0.363161i	−0.0905186	+	0.0461215i
$63$	3.74357	−	5.14317i	0.471645	−	0.647978i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	11.0154	−	9.74348i	1.36629	−	1.20853i
$66$	−2.18929	+	1.32630i	−0.269484	+	0.163257i
$67$	−4.05076	−	15.1176i	−0.494879	−	1.84691i	−0.530707	−	0.847555i	$-0.678074\pi$
$67$	−4.05076	−	15.1176i	−0.494879	−	1.84691i	0.0358285	−	0.999358i	$-0.488593\pi$
$68$	−2.69984	+	1.03637i	−0.327403	+	0.125678i
$69$	0.00490392	+	0.0150927i	0.000590363	+	0.00181695i
$70$	5.09453	+	3.00762i	0.608913	+	0.359479i
$71$	5.15987	+	3.74886i	0.612364	+	0.444908i	0.850246	−	0.526386i	$-0.176453\pi$
$71$	5.15987	+	3.74886i	0.612364	+	0.444908i	−0.237882	+	0.971294i	$0.576453\pi$
$72$	−1.51311	−	1.86854i	−0.178322	−	0.220209i
$73$	14.2734	+	0.748037i	1.67058	+	0.0875512i	0.863971	−	0.503541i	$-0.167970\pi$
$73$	14.2734	+	0.748037i	1.67058	+	0.0875512i	0.806604	+	0.591092i	$0.201303\pi$
$74$	−0.849817	+	3.99808i	−0.0987892	+	0.464767i
$75$	−2.68002	−	2.77644i	−0.309462	−	0.320595i
$76$		−	4.38160i		−	0.502604i
$77$	7.20190	+	5.01325i	0.820732	+	0.571313i
$78$	−3.58918	−	3.58918i	−0.406395	−	0.406395i
$79$	0.710523	−	1.59586i	0.0799401	−	0.179548i	−0.869154	−	0.494542i	$-0.835336\pi$
$79$	0.710523	−	1.59586i	0.0799401	−	0.179548i	0.949094	+	0.314994i	$0.102002\pi$
$80$	1.59504	−	1.56711i	0.178331	−	0.175208i
$81$	−2.67250	−	2.96811i	−0.296945	−	0.329791i
$82$	−1.55632	+	1.26028i	−0.171867	+	0.139175i
$83$	−8.67823	+	1.37450i	−0.952560	+	0.150871i	−0.613325	−	0.789831i	$-0.710168\pi$
$83$	−8.67823	+	1.37450i	−0.952560	+	0.150871i	−0.339235	+	0.940702i	$0.610168\pi$
$84$	0.928602	−	1.81857i	0.101319	−	0.198423i
$85$	−3.18367	−	5.62852i	−0.345317	−	0.610499i
$86$	6.79817	+	3.02674i	0.733066	+	0.326382i
$87$	1.19258	−	0.319551i	0.127858	−	0.0342594i
$88$	2.53293	−	2.14110i	0.270011	−	0.228242i
$89$	−3.35933	−	5.81854i	−0.356089	−	0.616764i	0.631215	−	0.775608i	$-0.282557\pi$
$89$	−3.35933	−	5.81854i	−0.356089	−	0.616764i	−0.987304	+	0.158844i	$0.949223\pi$
$90$	3.63260	−	3.96344i	0.382910	−	0.417783i
$91$	−6.24997	+	16.2395i	−0.655175	+	1.70236i
$92$	−0.00933500	−	0.0183210i	−0.000973241	−	0.00191009i
$93$	−0.479787	+	0.388524i	−0.0497516	+	0.0402881i
$94$	6.26632	−	2.78994i	0.646321	−	0.287761i
$95$	9.69010	−	1.44713i	0.994183	−	0.148473i
$96$	−0.573544	−	0.516422i	−0.0585371	−	0.0527071i
$97$	−16.9142	−	2.67895i	−1.71738	−	0.272006i	−0.781393	−	0.624039i	$-0.785490\pi$
$97$	−16.9142	−	2.67895i	−1.71738	−	0.272006i	−0.935988	+	0.352033i	$0.885490\pi$
$98$	−6.98976	−	0.378510i	−0.706072	−	0.0382353i
$99$	5.81228	−	5.45963i	0.584156	−	0.548713i
$100$	3.99253	+	3.00993i	0.399253	+	0.300993i
$101$	4.60006	−	0.483486i	0.457723	−	0.0481086i	0.127138	−	0.991885i	$-0.459421\pi$
$101$	4.60006	−	0.483486i	0.457723	−	0.0481086i	0.330585	+	0.943776i	$0.392754\pi$
$102$	−1.87185	+	1.21559i	−0.185341	+	0.120362i
$103$	−0.201018	+	0.309541i	−0.0198069	+	0.0305000i	−0.848435	−	0.529299i	$-0.822455\pi$
$103$	−0.201018	+	0.309541i	−0.0198069	+	0.0305000i	0.828628	+	0.559799i	$0.189122\pi$
$104$	5.32077	+	3.86577i	0.521745	+	0.379070i
$105$	4.32855	+	1.45301i	0.422423	+	0.141800i
$106$	−1.28184	+	3.94511i	−0.124504	+	0.383183i
$107$	−0.950548	−	18.1375i	−0.0918929	−	1.75342i	−0.524109	−	0.851651i	$-0.675602\pi$
$107$	−0.950548	−	18.1375i	−0.0918929	−	1.75342i	0.432216	−	0.901770i	$-0.357732\pi$
$108$	−3.24146	−	2.62488i	−0.311909	−	0.252579i
$109$	−14.0007	−	8.08331i	−1.34102	−	0.774240i	−0.354066	−	0.935220i	$-0.615201\pi$
$109$	−14.0007	−	8.08331i	−1.34102	−	0.774240i	−0.986958	+	0.160980i	$0.948535\pi$
$110$	5.57168	+	4.89452i	0.531239	+	0.466674i
$111$			3.15457i			0.299419i
$112$	−0.819770	+	2.51555i	−0.0774610	+	0.237697i
$113$	−1.34482	+	2.63936i	−0.126510	+	0.248290i	−0.945571	−	0.325417i	$-0.894495\pi$
$113$	−1.34482	+	2.63936i	−0.126510	+	0.248290i	0.819060	+	0.573707i	$0.194495\pi$
$114$	−0.703081	−	3.30774i	−0.0658496	−	0.309798i
$115$	0.0374345	−	0.0266957i	0.00349078	−	0.00248939i
$116$	−1.46144	+	0.650674i	−0.135691	+	0.0604136i
$117$	13.2619	+	8.61241i	1.22607	+	0.796217i
$118$	1.40217	+	0.714442i	0.129080	+	0.0657697i
$119$	6.41329	+	4.17277i	0.587905	+	0.382518i
$120$	0.952661	−	1.43898i	0.0869657	−	0.131360i
$121$	7.69850	+	7.85705i	0.699863	+	0.714277i
$122$	−4.13722	+	1.10857i	−0.374567	+	0.100365i
$123$	−0.972660	+	1.20114i	−0.0877018	+	0.108303i
$124$	0.535259	−	0.594465i	0.0480676	−	0.0533845i
$125$	−5.33796	+	9.82376i	−0.477441	+	0.878664i
$126$	−1.65178	+	6.14314i	−0.147152	+	0.547274i
$127$	−13.9312	+	2.20649i	−1.23619	+	0.195794i	−0.740113	−	0.672482i	$-0.765228\pi$
$127$	−13.9312	+	2.20649i	−1.23619	+	0.195794i	−0.496081	+	0.868276i	$0.665228\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	5.61772	+	1.19408i	0.494613	+	0.105133i
$130$	−6.79199	+	13.0439i	−0.595697	+	1.14402i
$131$	−16.0783	+	9.28281i	−1.40477	+	0.811043i	−0.994877	−	0.101092i	$-0.967766\pi$
$131$	−16.0783	+	9.28281i	−1.40477	+	0.811043i	−0.409890	+	0.912135i	$0.634433\pi$
$132$	1.56858	−	2.02278i	0.136527	−	0.176061i
$133$	−9.38456	+	6.80582i	−0.813744	+	0.590139i
$134$	9.19938	+	12.6619i	0.794706	+	1.09382i
$135$	4.73446	−	8.03555i	0.407477	−	0.691590i
$136$	2.14911	−	1.93507i	0.184285	−	0.165931i
$137$	−3.39559	+	8.84581i	−0.290105	+	0.755749i	0.708636	+	0.705574i	$0.249311\pi$
$137$	−3.39559	+	8.84581i	−0.290105	+	0.755749i	−0.998740	+	0.0501741i	$0.984022\pi$
$138$	−0.00998695	−	0.0123329i	−0.000850146	−	0.00104984i
$139$	−1.35790	+	4.17917i	−0.115175	+	0.354473i	−0.991984	−	0.126367i	$-0.959668\pi$
$139$	−1.35790	+	4.17917i	−0.115175	+	0.354473i	0.876808	+	0.480840i	$0.159668\pi$
$140$	−5.83399	−	0.982135i	−0.493062	−	0.0830055i
$141$	4.28286	−	3.11168i	0.360682	−	0.262051i
$142$	−6.16063	−	1.65073i	−0.516988	−	0.138527i
$143$	−11.4918	+	18.5402i	−0.960996	+	1.55041i
$144$	2.08223	+	1.20218i	0.173519	+	0.100181i
$145$	−1.92167	−	3.01713i	−0.159586	−	0.250559i
$146$	−13.5934	+	4.41678i	−1.12500	+	0.365535i
$147$	−5.33741	+	0.835849i	−0.440222	+	0.0689396i
$148$	−0.639409	−	4.03707i	−0.0525591	−	0.331845i
$149$	9.83565	+	1.03377i	0.805768	+	0.0846896i	0.498451	−	0.866918i	$-0.333902\pi$
$149$	9.83565	+	1.03377i	0.805768	+	0.0846896i	0.307317	+	0.951607i	$0.400569\pi$
$150$	3.49700	+	1.63159i	0.285529	+	0.133219i
$151$	−10.7896	−	2.29339i	−0.878042	−	0.186634i	−0.253227	−	0.967407i	$-0.581492\pi$
$151$	−10.7896	−	2.29339i	−0.878042	−	0.186634i	−0.624814	+	0.780773i	$0.714825\pi$
$152$	1.57023	+	4.09058i	0.127362	+	0.331790i
$153$	4.91665	−	4.91665i	0.397488	−	0.397488i
$154$	−8.52014	−	2.09934i	−0.686572	−	0.169170i
$155$	1.49147	+	0.987410i	0.119797	+	0.0793107i
$156$	4.63704	+	2.06454i	0.371260	+	0.165296i
$157$	−2.99691	−	4.61484i	−0.239180	−	0.368304i	0.698613	−	0.715499i	$-0.253801\pi$
$157$	−2.99691	−	4.61484i	−0.239180	−	0.368304i	−0.937793	+	0.347195i	$0.887134\pi$
$158$	−0.0914250	+	1.74449i	−0.00727338	+	0.138784i
$159$	−0.334643	+	3.18391i	−0.0265389	+	0.252501i
$160$	−0.927500	+	2.03464i	−0.0733254	+	0.160852i
$161$	−0.0247402	+	0.0484512i	−0.00194980	+	0.00381849i
$162$	3.55867	+	1.81323i	0.279596	+	0.142461i
$163$	6.79053	+	17.6899i	0.531876	+	1.38558i	0.891727	+	0.452574i	$0.149494\pi$
$163$	6.79053	+	17.6899i	0.531876	+	1.38558i	−0.359852	+	0.933010i	$0.617173\pi$
$164$	1.00130	−	1.73431i	0.0781887	−	0.135427i
$165$	4.99153	+	2.80090i	0.388590	+	0.218050i
$166$	7.60925	−	4.39320i	0.590593	−	0.340979i
$167$	24.6534	+	3.90472i	1.90774	+	0.302156i	0.994455	−	0.105162i	$-0.0335362\pi$
$167$	24.6534	+	3.90472i	1.90774	+	0.302156i	0.913286	+	0.407319i	$0.133536\pi$
$168$	−0.215207	+	2.03057i	−0.0166036	+	0.156662i
$169$	−28.7740	−	9.34924i	−2.21338	−	0.719172i
$170$	4.98929	+	4.11375i	0.382661	+	0.315510i
$171$	4.28494	+	9.62414i	0.327678	+	0.735976i
$172$	−7.43133	−	0.389460i	−0.566634	−	0.0296960i
$173$	0.839693	+	16.0223i	0.0638407	+	1.21815i	0.823303	+	0.567602i	$0.192129\pi$
$173$	0.839693	+	16.0223i	0.0638407	+	1.21815i	−0.759463	+	0.650551i	$0.774538\pi$
$174$	−0.998853	+	0.725709i	−0.0757228	+	0.0550158i
$175$	0.245213	−	13.2265i	0.0185364	−	0.999828i
$176$	−1.59739	+	2.90660i	−0.120408	+	0.219094i
$177$	1.17316	+	0.314347i	0.0881801	+	0.0236278i
$178$	5.22138	+	4.22819i	0.391359	+	0.316917i
$179$	4.54182	−	21.3676i	0.339471	−	1.59709i	−0.395155	−	0.918614i	$-0.629309\pi$
$179$	4.54182	−	21.3676i	0.339471	−	1.59709i	0.734626	−	0.678472i	$-0.237358\pi$
$180$	−1.97096	+	5.00199i	−0.146907	+	0.372827i
$181$	−5.23613	+	7.20692i	−0.389199	+	0.535686i	−0.957992	−	0.286794i	$-0.907410\pi$
$181$	−5.23613	+	7.20692i	−0.389199	+	0.535686i	0.568794	+	0.822480i	$0.307410\pi$
$182$	0.0151327	−	17.4007i	0.00112171	−	1.28982i
$183$	−2.94537	+	1.50074i	−0.217728	+	0.110938i
$184$	0.0152806	+	0.0137587i	0.00112650	+	0.00101431i
$185$	8.71697	−	2.74742i	0.640885	−	0.201995i
$186$	0.308686	−	0.534659i	0.0226339	−	0.0392031i
$187$	6.92363	+	6.63766i	0.506306	+	0.485394i
$188$	−4.85029	+	4.85029i	−0.353743	+	0.353743i
$189$	−0.587130	+	11.0197i	−0.0427074	+	0.801567i
$190$	−8.52788	+	4.82363i	−0.618677	+	0.349943i
$191$	4.98117	−	1.05878i	0.360425	−	0.0766107i	−0.0241400	−	0.999709i	$-0.507685\pi$
$191$	4.98117	−	1.05878i	0.360425	−	0.0766107i	0.384565	+	0.923098i	$0.374351\pi$
$192$	0.720519	+	0.276581i	0.0519990	+	0.0199605i
$193$	−1.88584	−	0.723908i	−0.135746	−	0.0521080i	0.289547	−	0.957164i	$-0.406495\pi$
$193$	−1.88584	−	0.723908i	−0.135746	−	0.0521080i	−0.425293	+	0.905056i	$0.639829\pi$
$194$	16.7509	−	3.56050i	1.20264	−	0.255629i
$195$	−3.03433	+	10.9369i	−0.217293	+	0.783206i
$196$	6.66115	−	2.15154i	0.475796	−	0.153681i
$197$	−8.01150	+	8.01150i	−0.570796	+	0.570796i	−0.932351	−	0.361555i	$-0.882246\pi$
$197$	−8.01150	+	8.01150i	−0.570796	+	0.570796i	0.361555	+	0.932351i	$0.382246\pi$
$198$	−3.46968	+	7.17994i	−0.246579	+	0.510256i
$199$	4.70394	−	8.14747i	0.333454	−	0.577559i	−0.649733	−	0.760163i	$-0.725119\pi$
$199$	4.70394	−	8.14747i	0.333454	−	0.577559i	0.983187	+	0.182604i	$0.0584525\pi$
$200$	−4.80601	−	1.37922i	−0.339836	−	0.0975254i
$201$	8.97650	+	8.08248i	0.633154	+	0.570094i
$202$	−4.12126	+	2.09989i	−0.289971	+	0.147748i
$203$	3.66363	+	2.11945i	0.257136	+	0.148756i
$204$	1.31189	−	1.80567i	0.0918508	−	0.126422i
$205$	4.16620	+	1.64163i	0.290980	+	0.114656i
$206$	0.0767371	−	0.361020i	0.00534653	−	0.0251534i
$207$	0.0384210	+	0.0311127i	0.00267044	+	0.00216248i
$208$	−6.35274	−	1.70221i	−0.440483	−	0.118027i
$209$	−13.1482	+	6.18932i	−0.909480	+	0.428124i
$210$	−4.56176	+	0.194706i	−0.314791	+	0.0134360i
$211$	11.0341	−	8.01671i	0.759616	−	0.551893i	−0.139177	−	0.990268i	$-0.544446\pi$
$211$	11.0341	−	8.01671i	0.759616	−	0.551893i	0.898792	+	0.438374i	$0.144446\pi$
$212$	−0.217097	−	4.14245i	−0.0149103	−	0.284505i
$213$	−4.91563	−	0.257617i	−0.336813	−	0.0176516i
$214$	7.38732	+	16.5922i	0.504987	+	1.13422i
$215$	−1.59307	−	16.5633i	−0.108647	−	1.12961i
$216$	3.96683	+	1.28890i	0.269909	+	0.0876987i
$217$	−2.10463	−	0.223056i	−0.142872	−	0.0151421i
$218$	15.9676	+	2.52902i	1.08146	+	0.171287i
$219$	−9.55317	+	5.51552i	−0.645543	+	0.372705i
$220$	−6.95565	−	2.57272i	−0.468950	−	0.173453i
$221$	−9.50984	+	16.4715i	−0.639701	+	1.10799i
$222$	−1.13050	−	2.94504i	−0.0758740	−	0.197658i
$223$	−10.7033	−	5.45363i	−0.716749	−	0.365202i	0.0572745	−	0.998358i	$-0.481759\pi$
$223$	−10.7033	−	5.45363i	−0.716749	−	0.365202i	−0.774024	+	0.633156i	$0.781759\pi$
$224$	−0.136170	−	2.64224i	−0.00909825	−	0.176542i
$225$	−11.7131	−	2.70682i	−0.780872	−	0.180455i
$226$	0.309637	−	2.94600i	0.0205967	−	0.195965i
$227$	−0.0397126	+	0.757761i	−0.00263582	+	0.0502944i	−0.999631	−	0.0271722i	$-0.991350\pi$
$227$	−0.0397126	+	0.757761i	−0.00263582	+	0.0502944i	0.996995	+	0.0774666i	$0.0246831\pi$
$228$	1.84177	+	2.83608i	0.121974	+	0.187824i
$229$	−2.20894	−	0.983481i	−0.145971	−	0.0649903i	0.332451	−	0.943120i	$-0.392124\pi$
$229$	−2.20894	−	0.983481i	−0.145971	−	0.0649903i	−0.478422	+	0.878130i	$0.658791\pi$
$230$	−0.0253812	+	0.0383379i	−0.00167359	+	0.00252793i
$231$	−6.76884	−	0.217664i	−0.445357	−	0.0143213i
$232$	1.13119	−	1.13119i	0.0742662	−	0.0742662i
$233$	10.8550	+	28.2783i	0.711137	+	1.85257i	0.472035	+	0.881580i	$0.343520\pi$
$233$	10.8550	+	28.2783i	0.711137	+	1.85257i	0.239102	+	0.970994i	$0.423147\pi$
$234$	−15.4675	−	3.28772i	−1.01114	−	0.214925i
$235$	−12.3285	−	9.12468i	−0.804225	−	0.595229i
$236$	−1.56507	−	0.164496i	−0.101878	−	0.0107078i
$237$	0.210907	+	1.33161i	0.0136999	+	0.0864976i
$238$	−7.48271	−	1.59730i	−0.485032	−	0.103538i
$239$	0.0279272	−	0.00907408i	0.00180646	−	0.000586954i	−0.308114	−	0.951350i	$-0.599698\pi$
$239$	0.0279272	−	0.00907408i	0.00180646	−	0.000586954i	0.309920	+	0.950763i	$0.399698\pi$
$240$	−0.373702	+	1.68481i	−0.0241224	+	0.108754i
$241$	−17.8525	−	10.3071i	−1.14998	−	0.663942i	−0.201098	−	0.979571i	$-0.564451\pi$
$241$	−17.8525	−	10.3071i	−1.14998	−	0.663942i	−0.948882	+	0.315630i	$0.897784\pi$
$242$	−10.0029	−	4.57629i	−0.643009	−	0.294175i
$243$	15.0640	+	4.03639i	0.966356	+	0.258934i
$244$	3.46516	−	2.51758i	0.221834	−	0.161172i
$245$	6.95822	+	14.0208i	0.444544	+	0.895757i
$246$	0.477608	−	1.46993i	0.0304512	−	0.0937191i
$247$	−18.1352	−	22.3951i	−1.15391	−	1.42496i
$248$	−0.286670	+	0.746800i	−0.0182035	+	0.0474219i
$249$	5.03940	−	4.53749i	0.319359	−	0.287552i
$250$	1.46289	−	11.0842i	0.0925215	−	0.701028i
$251$	1.51451	+	2.08454i	0.0955947	+	0.131575i	0.854135	−	0.520051i	$-0.174087\pi$
$251$	1.51451	+	2.08454i	0.0955947	+	0.131575i	−0.758540	+	0.651626i	$0.774087\pi$
$252$	−0.659438	−	6.32705i	−0.0415407	−	0.398567i
$253$	−0.0417907	+	0.0538919i	−0.00262736	+	0.00338815i
$254$	12.2152	−	7.05243i	0.766448	−	0.442509i
$255$	4.42659	+	2.30494i	0.277204	+	0.144341i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	23.9182	+	15.5327i	1.49198	+	0.968903i	0.994864	+	0.101218i	$0.0322739\pi$
$257$	23.9182	+	15.5327i	1.49198	+	0.968903i	0.497115	+	0.867685i	$0.334393\pi$
$258$	−5.67251	+	0.898438i	−0.353155	+	0.0559343i
$259$	−7.65346	+	7.64016i	−0.475563	+	0.474737i
$260$	1.66636	−	14.6115i	0.103343	−	0.906169i
$261$	2.57371	−	2.85840i	0.159309	−	0.176930i
$262$	11.6837	−	14.4282i	0.721823	−	0.891377i
$263$	−15.6118	+	4.18316i	−0.962663	+	0.257945i	−0.705727	−	0.708484i	$-0.749380\pi$
$263$	−15.6118	+	4.18316i	−0.962663	+	0.257945i	−0.256936	+	0.966428i	$0.582713\pi$
$264$	−0.739493	+	2.45056i	−0.0455127	+	0.150821i
$265$	9.08950	−	1.84827i	0.558364	−	0.113538i
$266$	6.32225	−	9.71690i	0.387642	−	0.595781i
$267$	4.62017	+	2.35409i	0.282750	+	0.144068i
$268$	−13.1260	−	8.52411i	−0.801796	−	0.520693i
$269$	11.5577	−	5.14580i	0.704682	−	0.313745i	−0.0229264	−	0.999737i	$-0.507298\pi$
$269$	11.5577	−	5.14580i	0.704682	−	0.313745i	0.727609	+	0.685992i	$0.240632\pi$
$270$	−1.54032	+	9.19851i	−0.0937407	+	0.559803i
$271$	3.88258	+	18.2661i	0.235850	+	1.10959i	0.923516	+	0.383559i	$0.125302\pi$
$271$	3.88258	+	18.2661i	0.235850	+	1.10959i	−0.687667	+	0.726027i	$0.741365\pi$
$272$	−1.31290	+	2.57672i	−0.0796065	+	0.156236i
$273$	−2.78072	−	13.1384i	−0.168297	−	0.795175i
$274$		−	9.47514i		−	0.572414i
$275$	3.39239	−	16.2324i	0.204569	−	0.978852i
$276$	0.0137433	+	0.00793471i	0.000827251	+	0.000477613i
$277$	−13.1805	−	10.6734i	−0.791939	−	0.641300i	0.145535	−	0.989353i	$-0.453510\pi$
$277$	−13.1805	−	10.6734i	−0.791939	−	0.641300i	−0.937475	+	0.348053i	$0.886843\pi$
$278$	−0.229977	−	4.38822i	−0.0137931	−	0.263188i
$279$	−0.594338	+	1.82919i	−0.0355821	+	0.109510i
$280$	5.79846	−	1.17381i	0.346524	−	0.0701487i
$281$	−1.37324	−	0.997716i	−0.0819205	−	0.0595188i	0.546071	−	0.837739i	$-0.316123\pi$
$281$	−1.37324	−	0.997716i	−0.0819205	−	0.0595188i	−0.627992	+	0.778220i	$0.716123\pi$
$282$	−2.88327	+	4.43984i	−0.171696	+	0.264389i
$283$	15.4560	−	10.0373i	0.918766	−	0.596654i	0.00371555	−	0.999993i	$-0.498817\pi$
$283$	15.4560	−	10.0373i	0.918766	−	0.596654i	0.915050	+	0.403340i	$0.132151\pi$
$284$	6.34301	−	0.666677i	0.376388	−	0.0395600i
$285$	−5.66381	+	5.00983i	−0.335495	+	0.296757i
$286$	4.08433	−	21.4271i	0.241512	−	1.26701i
$287$	−5.26986	+	0.549251i	−0.311070	+	0.0324213i
$288$	−2.37475	−	0.376124i	−0.139934	−	0.0221633i
$289$	−6.41840	−	5.77915i	−0.377553	−	0.339950i
$290$	2.87528	+	2.12807i	0.168842	+	0.124965i
$291$	12.0741	−	5.37575i	0.707799	−	0.315132i
$292$	11.1077	−	8.99487i	0.650031	−	0.526385i
$293$	−10.5416	−	20.6890i	−0.615844	−	1.20866i	−0.962656	−	0.270727i	$-0.912736\pi$
$293$	−10.5416	−	20.6890i	−0.615844	−	1.20866i	0.346812	−	0.937935i	$-0.387264\pi$
$294$	4.68336	−	2.69309i	0.273139	−	0.157064i
$295$	−0.153115	−	3.51555i	−0.00891468	−	0.204683i
$296$	2.04370	+	3.53979i	0.118787	+	0.205746i
$297$	−3.29789	+	13.4347i	−0.191363	+	0.779560i
$298$	−9.55284	+	2.55968i	−0.553381	+	0.148278i
$299$	−0.123542	−	0.0550045i	−0.00714462	−	0.00318099i
$300$	−3.84944	−	0.270009i	−0.222248	−	0.0155890i
$301$	10.7087	+	16.5214i	0.617241	+	0.952279i
$302$	10.8948	−	1.72557i	0.626925	−	0.0992952i
$303$	−2.77425	+	2.24654i	−0.159376	+	0.129060i
$304$	−2.93186	−	3.25616i	−0.168154	−	0.186754i
$305$	6.71220	+	6.83184i	0.384339	+	0.391190i
$306$	−2.82812	+	6.35206i	−0.161673	+	0.363123i
$307$	3.94042	+	3.94042i	0.224892	+	0.224892i	0.810555	−	0.585663i	$-0.199166\pi$
$307$	3.94042	+	3.94042i	0.224892	+	0.224892i	−0.585663	+	0.810555i	$0.699166\pi$
$308$	8.70657	−	1.09344i	0.496103	−	0.0623046i
$309$		−	0.284853i		−	0.0162047i
$310$	−1.74626	−	0.387333i	−0.0991809	−	0.0219990i
$311$	−3.26217	+	15.3473i	−0.184981	+	0.870266i	0.783542	+	0.621339i	$0.213411\pi$
$311$	−3.26217	+	15.3473i	−0.184981	+	0.870266i	−0.968522	+	0.248927i	$0.919922\pi$
$312$	−5.06891	−	0.265651i	−0.286971	−	0.0150395i
$313$	13.0993	+	16.1763i	0.740417	+	0.914339i	0.998661	−	0.0517410i	$-0.0164770\pi$
$313$	13.0993	+	16.1763i	0.740417	+	0.914339i	−0.258243	+	0.966080i	$0.583144\pi$
$314$	4.45167	+	3.23433i	0.251222	+	0.182524i
$315$	13.7748	−	3.54804i	0.776119	−	0.199909i
$316$	−0.539818	−	1.66139i	−0.0303671	−	0.0934604i
$317$	−2.51072	+	0.963775i	−0.141016	+	0.0541310i	−0.427852	−	0.903849i	$-0.640730\pi$
$317$	−2.51072	+	0.963775i	−0.141016	+	0.0541310i	0.286836	+	0.957980i	$0.407396\pi$
$318$	−0.828596	−	3.09236i	−0.0464654	−	0.173411i
$319$	4.01691	+	3.46632i	0.224904	+	0.194077i
$320$	0.136748	−	2.23188i	0.00764445	−	0.124766i
$321$	8.23922	+	11.3403i	0.459868	+	0.632954i
$322$	0.00573363	−	0.0540992i	0.000319523	−	0.00301483i
$323$	−11.2902	+	5.75262i	−0.628201	+	0.320084i
$324$	−3.97211	−	0.417486i	−0.220673	−	0.0231937i
$325$	32.8644	−	1.14059i	1.82299	−	0.0632687i
$326$	−12.6790	−	14.0815i	−0.702226	−	0.779901i
$327$	12.4600	−	0.652999i	0.689038	−	0.0361110i
$328$	−0.313277	+	1.97795i	−0.0172978	+	0.109214i
$329$	17.9222	+	2.85458i	0.988083	+	0.157378i
$330$	−5.66375	−	0.826063i	−0.311779	−	0.0454733i
$331$	9.48243	+	16.4240i	0.521201	+	0.902747i	0.999696	+	0.0246567i	$0.00784928\pi$
$331$	9.48243	+	16.4240i	0.521201	+	0.902747i	−0.478495	+	0.878090i	$0.658817\pi$
$332$	−5.52947	+	6.82832i	−0.303469	+	0.374753i
$333$	5.35247	+	8.24208i	0.293313	+	0.451663i
$334$	−24.4153	+	5.18963i	−1.33595	+	0.283964i
$335$	14.5162	−	31.8439i	0.793107	−	1.73982i
$336$	−0.526777	−	1.97282i	−0.0287380	−	0.107626i
$337$	−14.4169	−	28.2949i	−0.785341	−	1.54132i	−0.839858	−	0.542806i	$-0.817362\pi$
$337$	−14.4169	−	28.2949i	−0.785341	−	1.54132i	0.0545169	−	0.998513i	$-0.482638\pi$
$338$	30.2133	−	1.58341i	1.64339	−	0.0861263i
$339$	−0.238972	−	2.27366i	−0.0129792	−	0.123488i
$340$	−6.13214	−	2.05252i	−0.332562	−	0.111313i
$341$	−2.53994	−	0.766467i	−0.137546	−	0.0415065i
$342$	−7.44932	−	7.44932i	−0.402813	−	0.402813i
$343$	−14.9548	−	10.9250i	−0.807481	−	0.589894i
$344$	7.07731	−	2.29956i	0.381583	−	0.123984i
$345$	−0.0130089	+	0.0330146i	−0.000700374	+	0.00177744i
$346$	−6.52580	−	14.6572i	−0.350829	−	0.787975i
$347$	−7.96405	+	20.7471i	−0.427533	+	1.11376i	0.535538	+	0.844511i	$0.320109\pi$
$347$	−7.96405	+	20.7471i	−0.427533	+	1.11376i	−0.963071	+	0.269249i	$0.913224\pi$
$348$	0.672438	−	1.03546i	0.0360465	−	0.0555067i
$349$	4.12778	+	12.7040i	0.220955	+	0.680029i	0.998677	+	0.0514211i	$0.0163751\pi$
$349$	4.12778	+	12.7040i	0.220955	+	0.680029i	−0.777722	+	0.628608i	$0.783625\pi$
$350$	4.51102	+	12.4359i	0.241124	+	0.664725i
$351$	−27.4318			−1.46420
$352$	0.449658	−	3.28600i	0.0239668	−	0.175144i
$353$	−7.10736	−	26.5250i	−0.378287	−	1.41179i	−0.848483	−	0.529223i	$-0.822483\pi$
$353$	−7.10736	−	26.5250i	−0.378287	−	1.41179i	0.470196	−	0.882562i	$-0.344183\pi$
$354$	−1.20789	+	0.126955i	−0.0641987	+	0.00674756i
$355$	3.56932	+	13.8076i	0.189440	+	0.732834i
$356$	−6.38983	−	2.07618i	−0.338660	−	0.110037i
$357$	−5.90512	−	0.00513545i	−0.312532	−	0.000271797i
$358$	3.41730	+	21.5760i	0.180610	+	1.14033i
$359$	−0.349131	−	1.64253i	−0.0184264	−	0.0866894i	0.967974	−	0.251052i	$-0.0807766\pi$
$359$	−0.349131	−	1.64253i	−0.0184264	−	0.0866894i	−0.986400	+	0.164363i	$0.947443\pi$
$360$	0.0474931	−	5.37609i	0.00250310	−	0.283345i
$361$	−0.0207419	−	0.197346i	−0.00109168	−	0.0103866i
$362$	2.30562	−	8.60470i	0.121181	−	0.452253i
$363$	−8.28564	−	1.84963i	−0.434883	−	0.0970802i
$364$	6.22171	+	16.2503i	0.326106	+	0.851749i
$365$	23.5611	+	21.5945i	1.23325	+	1.13031i
$366$	2.21192	−	2.45659i	0.115619	−	0.128408i
$367$	−1.52275	+	29.0558i	−0.0794869	+	1.51670i	0.610000	+	0.792402i	$0.291170\pi$
$367$	−1.52275	+	29.0558i	−0.0794869	+	1.51670i	−0.689487	+	0.724298i	$0.742164\pi$
$368$	−0.0191964	−	0.00736880i	−0.00100068	−	0.000384125i
$369$	−0.503303	+	4.78860i	−0.0262009	+	0.249285i
$370$	−7.15341	+	5.68883i	−0.371888	+	0.295748i
$371$	−8.53513	+	6.89933i	−0.443122	+	0.358195i
$372$	−0.0965781	+	0.609770i	−0.00500734	+	0.0316151i
$373$	8.39721	−	31.3388i	0.434791	−	1.62266i	−0.306774	−	0.951782i	$-0.599250\pi$
$373$	8.39721	−	31.3388i	0.434791	−	1.62266i	0.741565	−	0.670881i	$-0.234084\pi$
$374$	−8.84249	−	3.71558i	−0.457234	−	0.192128i
$375$	−0.674237	−	8.60238i	−0.0348175	−	0.444225i
$376$	2.78994	−	6.26632i	0.143880	−	0.323161i
$377$	−4.77655	+	9.37450i	−0.246005	+	0.482811i
$378$	−3.40099	−	10.4982i	−0.174928	−	0.539970i
$379$	2.88812	−	3.97515i	0.148353	−	0.204190i	−0.728373	−	0.685181i	$-0.759723\pi$
$379$	2.88812	−	3.97515i	0.148353	−	0.204190i	0.876725	+	0.480991i	$0.159723\pi$
$380$	6.23282	−	7.55937i	0.319737	−	0.387787i
$381$	8.08976	−	7.28405i	0.414451	−	0.373173i
$382$	−4.27089	+	2.77355i	−0.218518	+	0.141907i
$383$	5.81107	−	2.23066i	0.296932	−	0.113981i	−0.205341	−	0.978690i	$-0.565830\pi$
$383$	5.81107	−	2.23066i	0.296932	−	0.113981i	0.502273	+	0.864709i	$0.332497\pi$
$384$	−0.771780			−0.0393847
$385$	5.29375	+	18.8938i	0.269795	+	0.962918i
$386$	2.02001			0.102816
$387$	16.7037	−	6.41195i	0.849097	−	0.325938i
$388$	−14.3623	+	9.32698i	−0.729135	+	0.473506i
$389$	16.2074	−	14.5932i	0.821749	−	0.739906i	−0.146683	−	0.989184i	$-0.546860\pi$
$389$	16.2074	−	14.5932i	0.821749	−	0.739906i	0.968432	+	0.249277i	$0.0801930\pi$
$390$	−1.08664	−	11.2979i	−0.0550240	−	0.572089i
$391$	−0.0349520	+	0.0481073i	−0.00176760	+	0.00243289i
$392$	−5.44768	+	4.39577i	−0.275149	+	0.222020i
$393$	6.50504	−	12.7669i	0.328136	−	0.644003i
$394$	4.60831	−	10.3504i	0.232163	−	0.521448i
$395$	3.49594	−	1.74254i	0.175900	−	0.0876769i
$396$	0.666164	−	7.94647i	0.0334760	−	0.399325i
$397$	1.61509	−	6.02760i	0.0810591	−	0.302517i	−0.913480	−	0.406884i	$-0.866615\pi$
$397$	1.61509	−	6.02760i	0.0810591	−	0.302517i	0.994539	+	0.104368i	$0.0332819\pi$
$398$	−1.47172	+	9.29206i	−0.0737706	+	0.465769i
$399$	3.21357	−	8.34991i	0.160880	−	0.418019i
$400$	4.98107	−	0.434710i	0.249053	−	0.0217355i
$401$	2.91803	−	27.7632i	0.145719	−	1.38643i	−0.640252	−	0.768165i	$-0.721170\pi$
$401$	2.91803	−	27.7632i	0.145719	−	1.38643i	0.785972	−	0.618262i	$-0.212163\pi$
$402$	−11.2768	−	4.32875i	−0.562435	−	0.215899i
$403$	0.275340	−	5.25381i	0.0137157	−	0.261711i
$404$	3.09500	−	3.43734i	0.153982	−	0.171014i
$405$	−0.388601	−	8.92238i	−0.0193097	−	0.443357i
$406$	−4.17983	−	0.665748i	−0.207442	−	0.0330405i
$407$	−11.2111	+	7.62137i	−0.555715	+	0.377777i
$408$	−0.577665	+	2.15587i	−0.0285987	+	0.106732i
$409$	−0.403453	−	3.83860i	−0.0199495	−	0.189807i	0.980009	−	0.198955i	$-0.0637547\pi$
$409$	−0.403453	−	3.83860i	−0.0199495	−	0.189807i	−0.999958	+	0.00914816i	$0.997088\pi$
$410$	−4.47779	−	0.0395574i	−0.221142	−	0.00195360i
$411$	−1.52040	−	7.15293i	−0.0749959	−	0.352828i
$412$	0.0577376	+	0.364541i	0.00284453	+	0.0179597i
$413$	2.07866	+	3.60759i	0.102284	+	0.177518i
$414$	−0.0470189	−	0.0152774i	−0.00231085	−	0.000750842i
$415$	−16.9274	−	9.97343i	−0.830932	−	0.489576i
$416$	6.54081	−	0.687467i	0.320689	−	0.0337058i
$417$	−0.877756	−	3.27583i	−0.0429839	−	0.160418i
$418$	10.0568	−	10.4901i	0.491896	−	0.513089i
$419$	−7.00220			−0.342080			−0.171040	−	0.985264i	$-0.554713\pi$
$419$	−7.00220			−0.342080			−0.171040	+	0.985264i	$0.554713\pi$
$420$	4.18899	−	1.81656i	0.204402	−	0.0886391i
$421$	−0.184965	−	0.569263i	−0.00901463	−	0.0277442i	0.946448	−	0.322856i	$-0.104643\pi$
$421$	−0.184965	−	0.569263i	−0.00901463	−	0.0277442i	−0.955463	+	0.295112i	$0.904643\pi$
$422$	−7.42825	+	11.4385i	−0.361601	+	0.556817i
$423$	5.91031	−	15.3969i	0.287369	−	0.748622i
$424$	1.68720	+	3.78951i	0.0819376	+	0.184035i
$425$	2.51394	−	14.2394i	0.121944	−	0.690711i
$426$	4.68146	−	1.52110i	0.226817	−	0.0736974i
$427$	−10.7745	−	3.51121i	−0.521415	−	0.169920i
$428$	−12.8428	−	12.8428i	−0.620779	−	0.620779i
$429$	−0.354915	−	16.8310i	−0.0171355	−	0.812609i
$430$	7.42303	+	14.8923i	0.357970	+	0.718170i
$431$	−3.50301	−	33.3290i	−0.168734	−	1.60540i	−0.671519	−	0.740988i	$-0.734358\pi$
$431$	−3.50301	−	33.3290i	−0.168734	−	1.60540i	0.502784	−	0.864412i	$-0.332309\pi$
$432$	−4.16526	+	0.218292i	−0.200401	+	0.0105026i
$433$	0.735552	+	1.44360i	0.0353484	+	0.0693751i	0.908005	−	0.418959i	$-0.137605\pi$
$433$	0.735552	+	1.44360i	0.0353484	+	0.0693751i	−0.872657	+	0.488334i	$0.837605\pi$
$434$	2.04478	−	0.545992i	0.0981526	−	0.0262084i
$435$	2.51206	+	1.14514i	0.120444	+	0.0549052i
$436$	−15.8133	+	3.36123i	−0.757321	+	0.160974i
$437$	−0.0490692	−	0.0755600i	−0.00234730	−	0.00361452i
$438$	6.94206	−	8.57273i	0.331705	−	0.409621i
$439$	−16.5718	−	28.7033i	−0.790931	−	1.36993i	−0.925391	−	0.379014i	$-0.876263\pi$
$439$	−16.5718	−	28.7033i	−0.790931	−	1.36993i	0.134460	−	0.990919i	$-0.457070\pi$
$440$	7.41564	−	0.0908458i	0.353527	−	0.00433090i
$441$	−12.5271	+	11.2400i	−0.596527	+	0.535239i
$442$	2.97533	−	18.7855i	0.141522	−	0.893536i
$443$	−9.16966	+	0.480561i	−0.435664	+	0.0228322i	−0.268907	−	0.963166i	$-0.586663\pi$
$443$	−9.16966	+	0.480561i	−0.435664	+	0.0228322i	−0.166756	+	0.985998i	$0.553329\pi$
$444$	2.11082	+	2.34430i	0.100175	+	0.111256i
$445$	2.48116	−	14.8171i	0.117618	−	0.702398i
$446$	11.9468	+	1.25566i	0.565699	+	0.0594574i
$447$	−6.80085	+	3.46521i	−0.321669	+	0.163899i
$448$	1.07402	+	2.41795i	0.0507428	+	0.114237i
$449$	0.630596	+	0.867941i	0.0297597	+	0.0409607i	0.823638	−	0.567117i	$-0.191941\pi$
$449$	0.630596	+	0.867941i	0.0297597	+	0.0409607i	−0.793878	+	0.608077i	$0.791941\pi$
$450$	11.9051	−	1.67055i	0.561214	−	0.0787507i
$451$	−6.61868	−	0.554854i	−0.311662	−	0.0261270i
$452$	0.766680	+	2.86129i	0.0360616	+	0.134584i
$453$	7.94776	−	3.05086i	0.373418	−	0.143342i
$454$	−0.234483	−	0.721663i	−0.0110048	−	0.0338693i
$455$	−33.8834	+	19.1267i	−1.58848	+	0.896672i
$456$	−2.73580	−	1.98767i	−0.128115	−	0.0930814i
$457$	−2.88964	−	3.56841i	−0.135172	−	0.166923i	0.705065	−	0.709142i	$-0.250918\pi$
$457$	−2.88964	−	3.56841i	−0.135172	−	0.166923i	−0.840237	+	0.542219i	$0.817584\pi$
$458$	2.41467	+	0.126547i	0.112830	+	0.00591317i
$459$	−2.50785	+	11.7985i	−0.117057	+	0.550708i
$460$	0.00995633	−	0.0448873i	0.000464216	−	0.00209288i
$461$		−	36.1594i		−	1.68411i	−0.539391	−	0.842055i	$-0.681346\pi$
$461$		−	36.1594i		−	1.68411i	0.539391	−	0.842055i	$-0.318654\pi$
$462$	6.39726	−	2.22253i	0.297628	−	0.103401i
$463$	25.5466	+	25.5466i	1.18725	+	1.18725i	0.977824	+	0.209428i	$0.0671603\pi$
$463$	25.5466	+	25.5466i	1.18725	+	1.18725i	0.209428	+	0.977824i	$0.432840\pi$
$464$	−0.650674	+	1.46144i	−0.0302068	+	0.0678455i
$465$	−1.38043	−	0.0121949i	−0.0640159	−	0.000565524i
$466$	−20.2681	−	22.5100i	−0.938901	−	1.04276i
$467$	−12.4699	+	10.0979i	−0.577036	+	0.467274i	−0.872862	−	0.487967i	$-0.837738\pi$
$467$	−12.4699	+	10.0979i	−0.577036	+	0.467274i	0.295826	+	0.955242i	$0.404405\pi$
$468$	15.6184	−	2.47371i	0.721959	−	0.114347i
$469$	2.13119	+	41.3536i	0.0984092	+	1.90953i
$470$	14.7797	+	4.10047i	0.681736	+	0.189141i
$471$	3.87962	+	1.72732i	0.178763	+	0.0795906i
$472$	1.52007	−	0.407302i	0.0699669	−	0.0187476i
$473$	9.32859	+	22.8499i	0.428929	+	1.05064i
$474$	−0.674106	−	1.16759i	−0.0309627	−	0.0536290i
$475$	18.7764	+	11.2875i	0.861521	+	0.517905i
$476$	7.55813	−	1.19035i	0.346427	−	0.0545598i
$477$	4.52792	+	8.88654i	0.207319	+	0.406887i
$478$	−0.0228204	+	0.0184796i	−0.00104378	+	0.000845236i
$479$	−12.2839	+	5.46914i	−0.561265	+	0.249891i	−0.667703	−	0.744428i	$-0.732722\pi$
$479$	−12.2839	+	5.46914i	−0.561265	+	0.249891i	0.106437	+	0.994319i	$0.466056\pi$
$480$	−0.254899	−	1.70682i	−0.0116345	−	0.0779055i
$481$	−19.9773	−	17.9877i	−0.910887	−	0.820166i
$482$	20.3605	+	3.22479i	0.927395	+	0.146885i
$483$	−0.00435247	−	0.0417603i	−0.000198044	−	0.00190016i
$484$	10.9785	+	0.687624i	0.499022	+	0.0312556i
$485$	−25.3705	−	28.6824i	−1.15202	−	1.30240i
$486$	−15.5100	+	1.63016i	−0.703547	+	0.0739457i
$487$	11.8820	−	7.71626i	0.538425	−	0.349657i	−0.246604	−	0.969116i	$-0.579315\pi$
$487$	11.8820	−	7.71626i	0.538425	−	0.349657i	0.785029	+	0.619459i	$0.212648\pi$
$488$	−2.33278	+	3.59217i	−0.105600	+	0.162610i
$489$	−11.8311	−	8.59581i	−0.535022	−	0.388716i
$490$	−11.5207	−	10.5960i	−0.520451	−	0.478676i
$491$	−0.932254	+	2.86918i	−0.0420720	+	0.129484i	−0.969886	−	0.243558i	$-0.921685\pi$
$491$	−0.932254	+	2.86918i	−0.0420720	+	0.129484i	0.927814	+	0.373042i	$0.121685\pi$
$492$	0.0808890	+	1.54345i	0.00364676	+	0.0695843i
$493$	3.59533	+	2.91144i	0.161926	+	0.131125i
$494$	24.9563	+	14.4085i	1.12284	+	0.648271i
$495$	17.7940	−	1.15127i	0.799780	−	0.0517456i
$496$		−	0.799931i		−	0.0359180i
$497$	−11.2803	−	12.5500i	−0.505991	−	0.562944i
$498$	−3.07859	+	6.04207i	−0.137955	+	0.270752i
$499$	1.90640	+	8.96891i	0.0853422	+	0.401503i	0.999996	−	0.00273407i	$-0.000870282\pi$
$499$	1.90640	+	8.96891i	0.0853422	+	0.401503i	−0.914654	+	0.404237i	$0.867537\pi$
$500$	2.60650	+	10.8723i	0.116566	+	0.486222i
$501$	−17.5987	+	7.83546i	−0.786253	+	0.350063i
$502$	−2.16094	−	1.40333i	−0.0964477	−	0.0626338i
$503$	−5.12947	−	2.61360i	−0.228712	−	0.116535i	0.335880	−	0.941905i	$-0.390966\pi$
$503$	−5.12947	−	2.61360i	−0.228712	−	0.116535i	−0.564592	+	0.825370i	$0.690966\pi$
$504$	2.88305	+	5.67049i	0.128421	+	0.252584i
$505$	8.62402	+	5.70945i	0.383764	+	0.254067i
$506$	0.0197019	−	0.0652889i	0.000875856	−	0.00290244i
$507$	22.5544	−	6.04343i	1.00168	−	0.268398i
$508$	−8.87647	+	10.9615i	−0.393830	+	0.486339i
$509$	−21.3257	+	23.6846i	−0.945245	+	1.04980i	0.0534416	+	0.998571i	$0.482981\pi$
$509$	−21.3257	+	23.6846i	−0.945245	+	1.04980i	−0.998687	+	0.0512303i	$0.983686\pi$
$510$	−4.95859	−	0.565499i	−0.219570	−	0.0250407i
$511$	−36.5186	−	9.81919i	−1.61549	−	0.434375i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−15.3272	−	9.95358i	−0.676711	−	0.439461i
$514$	−27.8960	−	5.92948i	−1.23044	−	0.261538i
$515$	−0.787129	+	0.248088i	−0.0346850	+	0.0109321i
$516$	4.97378	−	2.87161i	0.218958	−	0.126416i
$517$	21.4060	+	7.70324i	0.941434	+	0.338788i
$518$	4.40713	−	9.87546i	0.193638	−	0.433903i
$519$	−7.27834	−	10.0178i	−0.319484	−	0.439732i
$520$	3.68062	+	14.2382i	0.161406	+	0.624387i
$521$	−7.32691	+	6.59718i	−0.320998	+	0.289028i	−0.813838	−	0.581092i	$-0.802626\pi$
$521$	−7.32691	+	6.59718i	−0.320998	+	0.289028i	0.492840	+	0.870120i	$0.335959\pi$
$522$	−1.37841	+	3.59088i	−0.0603313	+	0.157168i
$523$	9.70278	+	11.9819i	0.424273	+	0.523933i	0.943798	−	0.330521i	$-0.107225\pi$
$523$	9.70278	+	11.9819i	0.424273	+	0.523933i	−0.519526	+	0.854455i	$0.673891\pi$
$524$	−5.73709	+	17.6570i	−0.250626	+	0.771348i
$525$	5.40092	+	8.66417i	0.235716	+	0.378135i
$526$	13.0757	−	9.50008i	0.570129	−	0.414223i
$527$	−2.23451	−	0.598735i	−0.0973368	−	0.0260813i
$528$	−0.187825	−	2.55280i	−0.00817405	−	0.111097i
$529$	19.9182	+	11.4998i	0.866009	+	0.499991i
$530$	−7.82342	+	4.98289i	−0.339828	+	0.216443i
$531$	3.59853	−	1.16923i	0.156163	−	0.0507404i
$532$	−2.42010	+	11.3372i	−0.104925	+	0.491530i
$533$	−2.06037	−	13.0087i	−0.0892446	−	0.563468i
$534$	−5.15693	−	0.542015i	−0.223162	−	0.0234553i
$535$	24.1607	−	32.6440i	1.04456	−	1.41132i
$536$	15.3089	+	3.25401i	0.661245	+	0.140552i
$537$	6.04190	+	15.7397i	0.260727	+	0.679217i
$538$	−8.94591	+	8.94591i	−0.385685	+	0.385685i
$539$	−15.8656	−	16.9494i	−0.683380	−	0.730063i
$540$	−1.85844	−	9.13955i	−0.0799746	−	0.393303i
$541$	3.66532	+	1.63191i	0.157585	+	0.0701612i	0.484013	−	0.875061i	$-0.339179\pi$
$541$	3.66532	+	1.63191i	0.157585	+	0.0701612i	−0.326429	+	0.945222i	$0.605845\pi$
$542$	−10.1707	−	15.6615i	−0.436868	−	0.672718i
$543$	0.359820	−	6.86578i	0.0154414	−	0.294639i
$544$	0.302288	−	2.87608i	0.0129605	−	0.123311i
$545$	−12.6562	−	33.8617i	−0.542134	−	1.45048i
$546$	7.30443	+	11.2693i	0.312601	+	0.482281i
$547$	6.65770	+	3.39227i	0.284663	+	0.145043i	0.590492	−	0.807043i	$-0.298934\pi$
$547$	6.65770	+	3.39227i	0.284663	+	0.145043i	−0.305829	+	0.952086i	$0.598934\pi$
$548$	3.39559	+	8.84581i	0.145052	+	0.377874i
$549$	−5.14913	+	8.91855i	−0.219760	+	0.380635i
$550$	2.65011	+	16.3700i	0.113001	+	0.698019i
$551$	−6.07035	+	3.50472i	−0.258606	+	0.149306i
$552$	−0.0156740	−	0.00248252i	−0.000667132	−	0.000105663i
$553$	−2.71989	+	3.73677i	−0.115662	+	0.158904i
$554$	16.1300	+	5.24097i	0.685300	+	0.222667i
$555$	−4.48737	+	5.44243i	−0.190478	+	0.231018i
$556$	1.78730	+	4.01434i	0.0757984	+	0.170246i
$557$	18.6283	+	0.976269i	0.789307	+	0.0413658i	0.442729	−	0.896655i	$-0.354010\pi$
$557$	18.6283	+	0.976269i	0.789307	+	0.0413658i	0.346578	+	0.938021i	$0.387344\pi$
$558$	−0.100659	−	1.92068i	−0.00426122	−	0.0813090i
$559$	−39.5947	+	28.7672i	−1.67468	+	1.21672i
$560$	−4.99267	+	3.17383i	−0.210979	+	0.134119i
$561$	−7.27153	−	1.38606i	−0.307004	−	0.0585197i
$562$	1.63958	+	0.439324i	0.0691614	+	0.0185318i
$563$	−1.20201	−	0.973370i	−0.0506588	−	0.0410227i	0.603657	−	0.797244i	$-0.293710\pi$
$563$	−1.20201	−	0.973370i	−0.0506588	−	0.0410227i	−0.654315	+	0.756222i	$0.727043\pi$
$564$	1.10066	−	5.17822i	0.0463463	−	0.218042i
$565$	−6.07465	+	2.64056i	−0.255562	+	0.111089i
$566$	−10.8324	+	14.9095i	−0.455320	+	0.626695i
$567$	5.27559	+	9.15598i	0.221554	+	0.384515i
$568$	−5.68279	+	2.89553i	−0.238445	+	0.121494i
$569$	−10.8405	−	9.76083i	−0.454457	−	0.409195i	0.409855	−	0.912151i	$-0.365579\pi$
$569$	−10.8405	−	9.76083i	−0.454457	−	0.409195i	−0.864312	+	0.502956i	$0.832246\pi$
$570$	3.49226	−	6.70681i	0.146275	−	0.280917i
$571$	16.4454	−	28.4842i	0.688218	−	1.19203i	−0.284196	−	0.958766i	$-0.591727\pi$
$571$	16.4454	−	28.4842i	0.688218	−	1.19203i	0.972414	−	0.233262i	$-0.0749399\pi$
$572$	3.86573	+	21.4676i	0.161634	+	0.897606i
$573$	−2.77911	+	2.77911i	−0.116099	+	0.116099i
$574$	4.72300	−	2.40132i	0.197134	−	0.100229i
$575$	0.102559	+	0.00719370i	0.00427699	+	0.000299998i
$576$	2.35181	−	0.499894i	0.0979923	−	0.0208289i
$577$	30.2400	+	11.6080i	1.25891	+	0.483249i	0.894114	−	0.447840i	$-0.147807\pi$
$577$	30.2400	+	11.6080i	1.25891	+	0.483249i	0.364792	+	0.931089i	$0.381140\pi$
$578$	8.06316	+	3.09516i	0.335383	+	0.128741i
$579$	1.52494	−	0.324136i	0.0633743	−	0.0134706i
$580$	−3.44693	−	0.956317i	−0.143126	−	0.0397089i
$581$	23.2137	+	1.23682i	0.963068	+	0.0513121i
$582$	−9.34568	+	9.34568i	−0.387391	+	0.387391i
$583$	−12.1239	+	6.50296i	−0.502121	+	0.269325i
$584$	−7.14650	+	12.3781i	−0.295724	+	0.512209i
$585$	10.6291	+	33.7237i	0.439457	+	1.39430i
$586$	17.2556	+	15.5371i	0.712824	+	0.641830i
$587$	40.6427	−	20.7085i	1.67750	−	0.854731i	0.685566	−	0.728011i	$-0.259555\pi$
$587$	40.6427	−	20.7085i	1.67750	−	0.854731i	0.991938	−	0.126720i	$-0.0404451\pi$
$588$	−3.40718	+	4.19258i	−0.140510	+	0.172899i
$589$	2.06018	−	2.83559i	0.0848881	−	0.116838i
$590$	1.40281	+	3.22718i	0.0577526	+	0.132861i
$591$	1.81803	−	8.55316i	0.0747838	−	0.351830i
$592$	−3.17650	−	2.57228i	−0.130553	−	0.105720i
$593$	6.50889	+	1.74405i	0.267288	+	0.0716196i	0.389974	−	0.920826i	$-0.372484\pi$
$593$	6.50889	+	1.74405i	0.267288	+	0.0716196i	−0.122686	+	0.992446i	$0.539151\pi$
$594$	−1.73572	−	13.7242i	−0.0712176	−	0.563112i
$595$	5.12878	+	16.3220i	0.210259	+	0.669136i
$596$	8.00104	−	5.81310i	0.327735	−	0.238114i
$597$	0.380002	+	7.25087i	0.0155524	+	0.296758i
$598$	0.135048	+	0.00707758i	0.00552253	+	0.000289424i
$599$	−1.65296	−	3.71261i	−0.0675380	−	0.151693i	0.876622	−	0.481179i	$-0.159791\pi$
$599$	−1.65296	−	3.71261i	−0.0675380	−	0.151693i	−0.944160	+	0.329486i	$0.893125\pi$
$600$	3.69053	−	1.12744i	0.150665	−	0.0460276i
$601$	44.9786	+	14.6144i	1.83471	+	0.596135i	0.998888	+	0.0471395i	$0.0150105\pi$
$601$	44.9786	+	14.6144i	1.83471	+	0.596135i	0.835826	+	0.548995i	$0.184989\pi$
$602$	−15.9182	−	11.5864i	−0.648778	−	0.472227i
$603$	37.1671	+	5.88669i	1.51356	+	0.239725i
$604$	−9.55278	+	5.51530i	−0.388697	+	0.224414i
$605$	2.10521	+	24.5065i	0.0855888	+	0.996331i
$606$	1.78489	−	3.09153i	0.0725064	−	0.125585i
$607$	11.6954	+	30.4676i	0.474702	+	1.23664i	0.936816	+	0.349821i	$0.113758\pi$
$607$	11.6954	+	30.4676i	0.474702	+	1.23664i	−0.462114	+	0.886821i	$0.652909\pi$
$608$	3.90404	+	1.98921i	0.158330	+	0.0806729i
$609$	−3.26225	+	0.168122i	−0.132193	+	0.00681266i
$610$	−8.71469	−	3.97264i	−0.352847	−	0.160848i
$611$	−4.71557	+	44.8656i	−0.190771	+	1.81507i
$612$	0.363902	−	6.94367i	0.0147099	−	0.280681i
$613$	−6.97988	−	10.7481i	−0.281915	−	0.434110i	0.669139	−	0.743138i	$-0.266663\pi$
$613$	−6.97988	−	10.7481i	−0.281915	−	0.434110i	−0.951053	+	0.309027i	$0.899997\pi$
$614$	−5.09082	−	2.26658i	−0.205449	−	0.0914716i
$615$	−3.38670	+	0.688653i	−0.136565	+	0.0277692i
$616$	−7.73643	+	4.14097i	−0.311710	+	0.166844i
$617$	31.1739	−	31.1739i	1.25502	−	1.25502i	0.301572	−	0.953443i	$-0.402489\pi$
$617$	31.1739	−	31.1739i	1.25502	−	1.25502i	0.953443	−	0.301572i	$-0.0975114\pi$
$618$	0.102082	+	0.265933i	0.00410634	+	0.0106974i
$619$	3.93025	+	0.835401i	0.157970	+	0.0335776i	0.286218	−	0.958165i	$-0.407602\pi$
$619$	3.93025	+	0.835401i	0.157970	+	0.0335776i	−0.128248	+	0.991742i	$0.540935\pi$
$620$	1.76908	−	0.264197i	0.0710480	−	0.0106104i
$621$	−0.0852942	−	0.00896478i	−0.00342274	−	0.000359744i
$622$	−2.45448	−	15.4970i	−0.0984159	−	0.621373i
$623$	5.47836	+	16.9107i	0.219486	+	0.677512i
$624$	4.82744	−	1.56853i	0.193252	−	0.0627915i
$625$	−23.1836	+	9.35522i	−0.927344	+	0.374209i
$626$	−18.0263	−	10.4075i	−0.720477	−	0.415968i
$627$	5.90880	−	9.53289i	0.235975	−	0.380707i
$628$	−5.31507	−	1.42417i	−0.212094	−	0.0568305i
$629$	−9.56291	+	6.94786i	−0.381298	+	0.277029i
$630$	−11.5883	+	8.24881i	−0.461690	+	0.328640i
$631$	6.06499	−	18.6661i	0.241443	−	0.743087i	−0.754758	−	0.656004i	$-0.772246\pi$
$631$	6.06499	−	18.6661i	0.241443	−	0.743087i	0.996201	−	0.0870828i	$-0.0277545\pi$
$632$	1.09935	+	1.35759i	0.0437299	+	0.0540019i
$633$	−3.77225	+	9.82704i	−0.149933	+	0.390590i
$634$	1.99857	−	1.79952i	0.0793734	−	0.0714682i
$635$	−27.1736	−	16.0104i	−1.07835	−	0.635353i
$636$	1.88176	+	2.59003i	0.0746168	+	0.102701i
$637$	25.1411	−	38.5669i	0.996128	−	1.52808i
$638$	−4.99233	−	1.79656i	−0.197648	−	0.0711265i
$639$	−13.2804	+	7.66743i	−0.525364	+	0.303319i
$640$	0.672170	+	2.13265i	0.0265698	+	0.0843003i
$641$	24.2286	+	5.14995i	0.956973	+	0.203411i	0.659824	−	0.751420i	$-0.270631\pi$
$641$	24.2286	+	5.14995i	0.956973	+	0.203411i	0.297149	+	0.954831i	$0.403964\pi$
$642$	−11.7560	−	7.63442i	−0.463971	−	0.301307i
$643$	9.07741	−	1.43772i	0.357978	−	0.0566982i	0.0251448	−	0.999684i	$-0.491995\pi$
$643$	9.07741	−	1.43772i	0.357978	−	0.0566982i	0.332833	+	0.942986i	$0.391995\pi$
$644$	0.0140346	+	0.0525607i	0.000553042	+	0.00207118i
$645$	7.99340	+	10.0513i	0.314740	+	0.395769i
$646$	8.47871	−	9.41656i	0.333590	−	0.370490i
$647$	−10.4367	+	12.8882i	−0.410307	+	0.506687i	−0.939846	−	0.341598i	$-0.889032\pi$
$647$	−10.4367	+	12.8882i	−0.410307	+	0.506687i	0.529539	+	0.848286i	$0.322365\pi$
$648$	3.85790	−	1.03372i	0.151553	−	0.0406084i
$649$	1.71716	+	4.92879i	0.0674044	+	0.193472i
$650$	−30.2728	+	12.8424i	−1.18740	+	0.503720i
$651$	1.45602	−	0.740287i	0.0570661	−	0.0290141i
$652$	16.8832	+	8.60244i	0.661198	+	0.336897i
$653$	−23.2787	−	15.1174i	−0.910965	−	0.591588i	0.00183317	−	0.999998i	$-0.499416\pi$
$653$	−23.2787	−	15.1174i	−0.910965	−	0.591588i	−0.912798	+	0.408411i	$0.866083\pi$
$654$	−11.3984	+	5.07488i	−0.445712	+	0.198444i
$655$	−40.9439	−	6.85618i	−1.59981	−	0.267893i
$656$	−0.416366	−	1.95885i	−0.0162563	−	0.0764801i
$657$	−15.6016	+	30.6198i	−0.608676	+	1.19459i
$658$	−17.7548	+	3.75776i	−0.692154	+	0.146493i
$659$			11.6821i			0.455071i	0.973770	+	0.227535i	$0.0730667\pi$
$659$			11.6821i			0.455071i	−0.973770	+	0.227535i	$0.926933\pi$
$660$	5.58360	−	1.25851i	0.217341	−	0.0489874i
$661$	−24.3255	−	14.0444i	−0.946154	−	0.546262i	−0.0542697	−	0.998526i	$-0.517283\pi$
$661$	−24.3255	−	14.0444i	−0.946154	−	0.546262i	−0.891884	+	0.452264i	$0.850616\pi$
$662$	−14.7385	−	11.9350i	−0.572827	−	0.463866i
$663$	−0.768240	−	14.6589i	−0.0298360	−	0.569304i
$664$	2.71515	−	8.35637i	0.105368	−	0.324290i
$665$	−25.8720	−	1.60777i	−1.00327	−	0.0623466i
$666$	−7.95065	−	5.77649i	−0.308082	−	0.223834i
$667$	−0.0179154	+	0.0275873i	−0.000693687	+	0.00106818i
$668$	20.9339	−	13.5946i	0.809955	−	0.525991i
$669$	9.22034	−	0.969096i	0.356479	−	0.0374674i
$670$	−2.14023	+	34.9310i	−0.0826844	+	1.34950i
$671$	−12.4495	−	6.84189i	−0.480607	−	0.264128i
$672$	1.19878	+	1.65301i	0.0462441	+	0.0637661i
$673$	7.62582	+	1.20781i	0.293954	+	0.0465577i	0.301670	−	0.953413i	$-0.402456\pi$
$673$	7.62582	+	1.20781i	0.293954	+	0.0465577i	−0.00771584	+	0.999970i	$0.502456\pi$
$674$	23.5993	+	21.2489i	0.909013	+	0.818479i
$675$	19.5987	−	7.12858i	0.754354	−	0.274379i
$676$	−27.6391	+	12.3057i	−1.06304	+	0.473297i
$677$	−26.7192	+	21.6368i	−1.02690	+	0.831569i	−0.985857	−	0.167588i	$-0.946402\pi$
$677$	−26.7192	+	21.6368i	−1.02690	+	0.831569i	−0.0410453	+	0.999157i	$0.513069\pi$
$678$	1.03791	+	2.03701i	0.0398606	+	0.0782308i
$679$	42.2852	+	16.2740i	1.62276	+	0.624537i
$680$	6.46040	−	0.281373i	0.247745	−	0.0107902i
$681$	−0.292814	−	0.507169i	−0.0112207	−	0.0194347i
$682$	2.64592	−	0.194676i	0.101318	−	0.00745454i
$683$	−17.0006	+	4.55529i	−0.650508	+	0.174303i	−0.568959	−	0.822366i	$-0.692654\pi$
$683$	−17.0006	+	4.55529i	−0.650508	+	0.174303i	−0.0815496	+	0.996669i	$0.525987\pi$
$684$	9.62414	+	4.28494i	0.367988	+	0.163839i
$685$	−18.4414	+	10.4310i	−0.704610	+	0.398549i
$686$	17.8766	+	4.84005i	0.682533	+	0.184794i
$687$	1.84317	−	0.291930i	0.0703215	−	0.0111378i
$688$	−5.78315	+	4.68311i	−0.220481	+	0.178542i
$689$	−18.2550	−	20.2742i	−0.695459	−	0.772385i
$690$	0.000313467	−	0.0354837i	1.19335e−5	−	0.00135084i
$691$	6.65468	−	14.9467i	0.253156	−	0.568597i	−0.741604	−	0.670838i	$-0.765935\pi$
$691$	6.65468	−	14.9467i	0.253156	−	0.568597i	0.994760	+	0.102241i	$0.0326012\pi$
$692$	11.3450	+	11.3450i	0.431273	+	0.431273i
$693$	−18.0546	+	10.9162i	−0.685836	+	0.414673i
$694$		−	22.2231i		−	0.843578i
$695$	−8.28758	+	5.27852i	−0.314366	+	0.200226i
$696$	−0.256698	+	1.20767i	−0.00973012	+	0.0457766i
$697$	−5.78344	−	0.303097i	−0.219063	−	0.0114806i
$698$	−8.40632	−	10.3809i	−0.318184	−	0.392924i
$699$	−18.9127	−	13.7409i	−0.715343	−	0.519727i
$700$	−8.66802	−	9.99327i	−0.327620	−	0.377710i
$701$	7.16544	+	22.0529i	0.270635	+	0.832928i	0.990341	+	0.138650i	$0.0442763\pi$
$701$	7.16544	+	22.0529i	0.270635	+	0.832928i	−0.719707	+	0.694278i	$0.755724\pi$
$702$	25.6098	−	9.83068i	0.966580	−	0.371035i
$703$	−4.63528	−	17.2991i	−0.174823	−	0.652448i
$704$	0.757806	+	3.22889i	0.0285609	+	0.121693i
$705$	11.8154	+	0.723931i	0.444992	+	0.0272648i
$706$	16.1410	+	22.2162i	0.607475	+	0.836118i
$707$	−12.1695	−	1.28977i	−0.457681	−	0.0485067i
$708$	1.08217	−	0.551392i	0.0406704	−	0.0207226i
$709$	−3.08451	−	0.324195i	−0.115841	−	0.0121754i	0.0464304	−	0.998922i	$-0.485215\pi$
$709$	−3.08451	−	0.324195i	−0.115841	−	0.0121754i	−0.162272	+	0.986746i	$0.551882\pi$
$710$	−8.28047	−	11.6114i	−0.310760	−	0.435769i
$711$	2.81044	+	3.12131i	0.105400	+	0.117058i
$712$	6.70946	−	0.351628i	0.251448	−	0.0131778i
$713$	0.00257308	−	0.0162458i	9.63625e−5	−	0.000608409i
$714$	5.51474	−	2.11141i	0.206384	−	0.0790175i
$715$	−46.1998	+	15.6394i	−1.72777	+	0.584882i
$716$	−10.9225	−	18.9183i	−0.408192	−	0.707009i
$717$	−0.0142622	+	0.0176123i	−0.000532631	+	0.000657744i
$718$	0.914572	+	1.40832i	0.0341315	+	0.0525579i
$719$	−19.5629	+	4.15821i	−0.729571	+	0.155075i	−0.557698	−	0.830044i	$-0.688315\pi$
$719$	−19.5629	+	4.15821i	−0.729571	+	0.155075i	−0.171873	+	0.985119i	$0.554982\pi$
$720$	1.88228	+	5.03603i	0.0701485	+	0.187682i
$721$	0.691095	−	0.689894i	0.0257377	−	0.0256930i
$722$	0.0900868	+	0.176805i	0.00335268	+	0.00658001i
$723$	15.8879	−	0.832649i	0.590877	−	0.0309666i
$724$	0.931165	+	8.85944i	0.0346065	+	0.329259i
$725$	0.976501	−	7.93888i	0.0362663	−	0.294843i
$726$	8.39816	−	1.24253i	0.311685	−	0.0461147i
$727$	22.6346	+	22.6346i	0.839469	+	0.839469i	0.988789	−	0.149320i	$-0.0477083\pi$
$727$	22.6346	+	22.6346i	0.839469	+	0.839469i	−0.149320	+	0.988789i	$0.547708\pi$
$728$	−11.6321	−	12.9413i	−0.431113	−	0.479638i
$729$	−0.0515915	+	0.0167631i	−0.00191080	+	0.000620856i
$730$	−29.7350	−	11.7166i	−1.10054	−	0.433651i
$731$	8.75309	+	19.6598i	0.323745	+	0.727143i
$732$	−1.18464	+	3.08610i	−0.0437857	+	0.114066i
$733$	−13.1199	+	20.2029i	−0.484596	+	0.746212i	−0.993404	−	0.114668i	$-0.963420\pi$
$733$	−13.1199	+	20.2029i	−0.484596	+	0.746212i	0.508808	+	0.860880i	$0.330086\pi$
$734$	−8.99106	−	27.6716i	−0.331866	−	1.02138i
$735$	−10.3974	−	6.15041i	−0.383513	−	0.226861i
$736$	0.0205621			0.000757929
$737$	−7.03756	+	51.4290i	−0.259232	+	1.89441i
$738$	−1.24621	−	4.65091i	−0.0458736	−	0.171203i
$739$	3.80798	−	0.400235i	0.140079	−	0.0147229i	−0.0342295	−	0.999414i	$-0.510898\pi$
$739$	3.80798	−	0.400235i	0.140079	−	0.0147229i	0.174308	+	0.984691i	$0.444231\pi$
$740$	4.63959	−	7.87453i	0.170555	−	0.289473i
$741$	21.1519	+	6.87268i	0.777035	+	0.252474i
$742$	5.49573	−	9.49980i	0.201755	−	0.348749i
$743$	−2.83071	−	17.8724i	−0.103849	−	0.655674i	−0.983617	−	0.180271i	$-0.942302\pi$
$743$	−2.83071	−	17.8724i	−0.103849	−	0.655674i	0.879768	−	0.475403i	$-0.157698\pi$
$744$	−0.128359	−	0.603880i	−0.00470586	−	0.0221393i
$745$	15.4984	+	15.7747i	0.567819	+	0.577941i
$746$	3.39136	+	32.2666i	0.124166	+	1.18136i
$747$	5.46772	−	20.4058i	0.200053	−	0.746610i
$748$	9.58672	+	0.299932i	0.350525	+	0.0109666i
$749$	−7.55846	+	47.4551i	−0.276180	+	1.73397i
$750$	3.71227	+	7.78939i	0.135553	+	0.284428i
$751$	7.85657	−	8.72561i	0.286690	−	0.318402i	−0.582547	−	0.812797i	$-0.697944\pi$
$751$	7.85657	−	8.72561i	0.286690	−	0.318402i	0.869237	+	0.494395i	$0.164610\pi$
$752$	−0.358990	+	6.84994i	−0.0130910	+	0.249792i
$753$	−1.85651	−	0.712648i	−0.0676550	−	0.0259703i
$754$	1.09977	−	10.4636i	0.0400512	−	0.381062i
$755$	−15.3524	−	19.3048i	−0.558730	−	0.702574i
$756$	6.93732	+	8.58212i	0.252308	+	0.312129i
$757$	1.35177	−	8.53477i	0.0491311	−	0.310201i	−0.950869	−	0.309594i	$-0.899807\pi$
$757$	1.35177	−	8.53477i	0.0491311	−	0.310201i	1.00000		0.000607089i	$-0.000193242\pi$
$758$	−1.27172	+	4.74613i	−0.0461910	+	0.172387i
$759$	0.00439687	−	0.0524489i	0.000159596	−	0.00190378i
$760$	−3.10981	+	9.29092i	−0.112805	+	0.337017i
$761$	13.6749	−	30.7143i	0.495714	−	1.11339i	−0.476474	−	0.879189i	$-0.658085\pi$
$761$	13.6749	−	30.7143i	0.495714	−	1.11339i	0.972188	−	0.234203i	$-0.0752480\pi$
$762$	−4.94207	+	9.69936i	−0.179032	+	0.351371i
$763$	31.7615	+	28.6483i	1.14984	+	1.03714i
$764$	2.99327	−	4.11988i	0.108293	−	0.149052i
$765$	15.4764	−	1.48853i	0.559551	−	0.0538180i
$766$	−4.62571	+	4.16500i	−0.167134	+	0.150488i
$767$	−8.68018	+	5.63697i	−0.313423	+	0.203539i
$768$	0.720519	−	0.276581i	0.0259995	−	0.00998027i
$769$	−10.1560			−0.366236			−0.183118	−	0.983091i	$-0.558619\pi$
$769$	−10.1560			−0.366236			−0.183118	+	0.983091i	$0.558619\pi$
$770$	−11.7131	−	15.7418i	−0.422110	−	0.567295i
$771$	−22.0106			−0.792692
$772$	−1.88584	+	0.723908i	−0.0678730	+	0.0260540i
$773$	−18.6317	+	12.0996i	−0.670135	+	0.435191i	−0.834351	−	0.551234i	$-0.814157\pi$
$773$	−18.6317	+	12.0996i	−0.670135	+	0.435191i	0.164216	+	0.986424i	$0.447491\pi$
$774$	−13.2964	+	11.9721i	−0.477929	+	0.430330i
$775$	1.16857	+	3.82514i	0.0419761	+	0.137403i
$776$	10.0659	−	13.8545i	0.361344	−	0.497347i
$777$	1.74237	−	8.16231i	0.0625073	−	0.292821i
$778$	−9.90119	+	19.4322i	−0.354975	+	0.696677i
$779$	3.56896	−	8.01602i	0.127871	−	0.287204i
$780$	5.06325	+	10.1580i	0.181294	+	0.363716i
$781$	−10.9605	−	18.0922i	−0.392197	−	0.647390i
$782$	0.0153904	−	0.0574377i	0.000550359	−	0.00205397i
$783$	−1.04381	+	6.59034i	−0.0373026	+	0.235519i
$784$	3.51054	−	6.05608i	0.125376	−	0.216289i
$785$	1.39418	−	12.2249i	0.0497603	−	0.436324i
$786$	−1.49774	+	14.2501i	−0.0534228	+	0.508284i
$787$	17.8543	+	6.85362i	0.636436	+	0.244305i	0.655125	−	0.755520i	$-0.272616\pi$
$787$	17.8543	+	6.85362i	0.636436	+	0.244305i	−0.0186889	+	0.999825i	$0.505949\pi$
$788$	−0.592965	+	11.3144i	−0.0211235	+	0.403060i
$789$	8.34667	−	9.26991i	0.297149	−	0.330018i
$790$	−2.63927	+	2.87964i	−0.0939011	+	0.102453i
$791$	4.93747	−	6.08644i	0.175556	−	0.216409i
$792$	2.22584	+	7.65740i	0.0790919	+	0.272094i
$793$	7.29085	−	27.2098i	0.258906	−	0.966250i
$794$	0.652282	+	6.20605i	0.0231486	+	0.220244i
$795$	−5.10645	+	5.01702i	−0.181107	+	0.177935i
$796$	−1.95601	−	9.20230i	−0.0693289	−	0.326167i
$797$	7.28429	+	45.9912i	0.258023	+	1.62909i	0.687620	+	0.726070i	$0.258655\pi$
$797$	7.28429	+	45.9912i	0.258023	+	1.62909i	−0.429598	+	0.903020i	$0.641345\pi$
$798$	−0.00778082	+	8.94696i	−0.000275438	+	0.316719i
$799$	18.8658	+	6.12986i	0.667423	+	0.216859i
$800$	−4.49444	+	2.19089i	−0.158902	+	0.0774597i
$801$	16.0656	−	1.68856i	0.567649	−	0.0596623i
$802$	7.22522	+	26.9649i	0.255131	+	0.952163i
$803$	−42.6820	−	20.6259i	−1.50622	−	0.727874i
$804$	12.0791			0.425996
$805$	−0.111605	+	0.0483976i	−0.00393356	+	0.00170579i
$806$	1.62574	+	5.00352i	0.0572644	+	0.176242i
$807$	−5.31792	+	8.18888i	−0.187200	+	0.288262i
$808$	−1.65759	+	4.31818i	−0.0583140	+	0.151913i
$809$	−15.4173	−	34.6279i	−0.542045	−	1.21745i	−0.952211	−	0.305441i	$-0.901196\pi$
$809$	−15.4173	−	34.6279i	−0.542045	−	1.21745i	0.410166	−	0.912011i	$-0.365471\pi$
$810$	3.56028	+	8.19050i	0.125096	+	0.287785i
$811$	22.5193	−	7.31695i	0.790758	−	0.256933i	0.114331	−	0.993443i	$-0.463527\pi$
$811$	22.5193	−	7.31695i	0.790758	−	0.256933i	0.676427	+	0.736510i	$0.263527\pi$
$812$	4.14079	−	0.876390i	0.145313	−	0.0307553i
$813$	−10.1911	−	10.1911i	−0.357416	−	0.357416i
$814$	7.73524	−	11.1329i	0.271120	−	0.390207i
$815$	−13.4485	+	40.1791i	−0.471082	+	1.40741i
$816$	−0.233300	−	2.21970i	−0.00816712	−	0.0777050i
$817$	−32.5611	+	1.70646i	−1.13917	+	0.0597014i
$818$	1.75229	+	3.43906i	0.0612673	+	0.120244i
$819$	−29.5578	−	29.6092i	−1.03283	−	1.03463i
$820$	4.19456	−	1.56777i	0.146480	−	0.0547488i
$821$	41.2579	−	8.76964i	1.43991	−	0.306063i	0.579213	−	0.815177i	$-0.303360\pi$
$821$	41.2579	−	8.76964i	1.43991	−	0.306063i	0.860699	+	0.509114i	$0.170027\pi$
$822$	3.98280	+	6.13297i	0.138916	+	0.213912i
$823$	25.7451	−	31.7926i	0.897418	−	1.10822i	−0.0961933	−	0.995363i	$-0.530667\pi$
$823$	25.7451	−	31.7926i	0.897418	−	1.10822i	0.993611	−	0.112856i	$-0.0360000\pi$
$824$	−0.184543	−	0.319637i	−0.00642885	−	0.0111351i
$825$	4.62737	+	11.9327i	0.161104	+	0.415444i
$826$	−3.23345	−	2.62305i	−0.112506	−	0.0912677i
$827$	6.81722	−	43.0422i	0.237058	−	1.49672i	−0.526050	−	0.850454i	$-0.676328\pi$
$827$	6.81722	−	43.0422i	0.237058	−	1.49672i	0.763108	−	0.646271i	$-0.223672\pi$
$828$	0.0493709	−	0.00258742i	0.00171576	−	8.99189e-5i
$829$	−7.34065	−	8.15262i	−0.254951	−	0.283152i	0.602059	−	0.798452i	$-0.294347\pi$
$829$	−7.34065	−	8.15262i	−0.254951	−	0.283152i	−0.857010	+	0.515300i	$0.827681\pi$
$830$	19.3772	+	3.24477i	0.672593	+	0.112628i
$831$	13.0178	+	1.36822i	0.451582	+	0.0474632i
$832$	−5.86000	+	2.98582i	−0.203159	+	0.103515i
$833$	−14.2893	−	14.3391i	−0.495096	−	0.496822i
$834$	1.99341	+	2.74369i	0.0690261	+	0.0950062i
$835$	36.9790	+	41.8061i	1.27971	+	1.44676i
$836$	−5.62955	+	13.3974i	−0.194702	+	0.463360i
$837$	−0.863548	−	3.22280i	−0.0298486	−	0.111396i
$838$	6.53712	−	2.50937i	0.225821	−	0.0866846i
$839$	13.9634	+	42.9748i	0.482069	+	1.48366i	0.836181	+	0.548453i	$0.184783\pi$
$839$	13.9634	+	42.9748i	0.482069	+	1.48366i	−0.354112	+	0.935203i	$0.615217\pi$
$840$	−3.25976	+	3.19711i	−0.112473	+	0.110311i
$841$	−21.3911	−	15.5415i	−0.737623	−	0.535915i
$842$	0.376685	+	0.465167i	0.0129814	+	0.0160307i
$843$	1.30824	+	0.0685618i	0.0450581	+	0.00236139i
$844$	2.83568	−	13.3408i	0.0976080	−	0.459209i
$845$	−36.3431	−	57.0608i	−1.25024	−	1.96295i
$846$			16.4923i			0.567017i
$847$	−15.5798	−	24.5819i	−0.535329	−	0.844644i
$848$	−2.93318	−	2.93318i	−0.100726	−	0.100726i
$849$	−5.78514	+	12.9936i	−0.198545	+	0.445940i
$850$	2.75598	+	14.1945i	0.0945292	+	0.486868i
$851$	−0.0562374	−	0.0624579i	−0.00192779	−	0.00214103i
$852$	−3.82540	+	3.09775i	−0.131056	+	0.106127i
$853$	18.0057	−	2.85182i	0.616503	−	0.0976445i	0.159631	−	0.987177i	$-0.448970\pi$
$853$	18.0057	−	2.85182i	0.616503	−	0.0976445i	0.456872	+	0.889532i	$0.348970\pi$
$854$	11.3172	−	0.583240i	0.387266	−	0.0199580i
$855$	−6.29772	+	22.6994i	−0.215377	+	0.776303i
$856$	16.5922	+	7.38732i	0.567110	+	0.252493i
$857$	−16.0260	+	4.29415i	−0.547438	+	0.146686i	−0.521929	−	0.852989i	$-0.674787\pi$
$857$	−16.0260	+	4.29415i	−0.547438	+	0.146686i	−0.0255091	+	0.999675i	$0.508121\pi$
$858$	6.36304	+	15.5859i	0.217231	+	0.532094i
$859$	−3.66096	−	6.34097i	−0.124910	−	0.216351i	0.796787	−	0.604260i	$-0.206531\pi$
$859$	−3.66096	−	6.34097i	−0.124910	−	0.216351i	−0.921698	+	0.387908i	$0.873198\pi$
$860$	−12.2669	−	11.2430i	−0.418298	−	0.383382i
$861$	3.18014	−	2.57065i	0.108379	−	0.0876076i
$862$	15.2144	+	29.8599i	0.518204	+	1.01703i
$863$	20.6603	−	16.7303i	0.703283	−	0.569508i	−0.209571	−	0.977793i	$-0.567207\pi$
$863$	20.6603	−	16.7303i	0.703283	−	0.569508i	0.912854	+	0.408286i	$0.133873\pi$
$864$	3.81037	−	1.69649i	0.129632	−	0.0577157i
$865$	−21.3430	+	28.8370i	−0.725685	+	0.980486i
$866$	−1.20404	−	1.08412i	−0.0409149	−	0.0368399i
$867$	6.58365	+	1.04275i	0.223593	+	0.0354136i
$868$	−1.71330	+	1.24251i	−0.0581532	+	0.0421736i
$869$	−4.22292	+	3.96670i	−0.143253	+	0.134561i
$870$	−2.75559	−	0.168836i	−0.0934234	−	0.00572407i
$871$	−102.370	+	10.7595i	−3.46867	+	0.364571i
$872$	13.5585	−	8.80497i	0.459148	−	0.298174i
$873$	22.4254	−	34.5321i	0.758984	−	1.16873i
$874$	0.0728883	+	0.0529565i	0.00246548	+	0.00179128i
$875$	19.2377	−	22.4702i	0.650354	−	0.759632i
$876$	−3.40878	+	10.4911i	−0.115172	+	0.354463i
$877$	−1.33570	−	25.4868i	−0.0451035	−	0.860626i	−0.923713	−	0.383085i	$-0.874862\pi$
$877$	−1.33570	−	25.4868i	−0.0451035	−	0.860626i	0.878609	−	0.477541i	$-0.158472\pi$
$878$	25.7575	+	20.8580i	0.869273	+	0.703924i
$879$	15.5197	+	8.96027i	0.523465	+	0.302223i
$880$	−6.89054	+	2.74234i	−0.232280	+	0.0924443i
$881$			20.5550i			0.692516i	0.938139	+	0.346258i	$0.112548\pi$
$881$			20.5550i			0.692516i	−0.938139	+	0.346258i	$0.887452\pi$
$882$	7.66695	−	14.9828i	0.258160	−	0.504496i
$883$	3.89076	−	7.63604i	0.130934	−	0.256973i	−0.816227	−	0.577732i	$-0.803938\pi$
$883$	3.89076	−	7.63604i	0.130934	−	0.256973i	0.947161	+	0.320759i	$0.103938\pi$
$884$	3.95441	+	18.6040i	0.133001	+	0.625722i
$885$	1.57684	+	2.21115i	0.0530049	+	0.0743269i
$886$	8.38839	−	3.73475i	0.281814	−	0.125472i
$887$	−37.7780	−	24.5333i	−1.26846	−	0.823748i	−0.277871	−	0.960618i	$-0.589629\pi$
$887$	−37.7780	−	24.5333i	−1.26846	−	0.823748i	−0.990589	+	0.136871i	$0.956296\pi$
$888$	−2.81074	−	1.43214i	−0.0943223	−	0.0480596i
$889$	37.2651	+	1.98548i	1.24983	+	0.0665908i
$890$	2.99360	+	14.7221i	0.100346	+	0.493486i
$891$	4.35811	+	12.5091i	0.146002	+	0.419072i
$892$	−11.6033	+	3.10910i	−0.388508	+	0.104100i
$893$	−18.9142	+	23.3570i	−0.632938	+	0.781614i
$894$	5.10732	−	5.67226i	0.170814	−	0.189709i
$895$	38.2311	−	30.4037i	1.27793	−	1.01628i
$896$	−1.86920	−	1.87245i	−0.0624456	−	0.0625543i
$897$	0.103086	−	0.0163272i	0.00344193	−	0.000545148i
$898$	−0.899754	−	0.584307i	−0.0300252	−	0.0194986i
$899$	−1.25172	−	0.266061i	−0.0417472	−	0.00887364i
$900$	−10.5157	+	5.82602i	−0.350524	+	0.194201i
$901$	−10.3889	+	5.99804i	−0.346105	+	0.199824i
$902$	6.37791	−	1.85392i	0.212361	−	0.0617289i
$903$	−13.8761	−	6.19249i	−0.461767	−	0.206073i
$904$	−1.74115	−	2.39649i	−0.0579099	−	0.0797061i
$905$	−19.2855	+	4.98536i	−0.641071	+	0.165719i
$906$	−6.32654	+	5.69644i	−0.210185	+	0.189252i
$907$	9.08726	−	23.6731i	0.301738	−	0.786053i	−0.695950	−	0.718090i	$-0.745017\pi$
$907$	9.08726	−	23.6731i	0.301738	−	0.786053i	0.997688	−	0.0679634i	$-0.0216501\pi$
$908$	0.477529	+	0.589699i	0.0158474	+	0.0195699i
$909$	−3.43661	+	10.5768i	−0.113985	+	0.350810i
$910$	24.7785	−	29.9990i	0.821401	−	0.994458i
$911$	−34.5493	+	25.1016i	−1.14467	+	0.831652i	−0.987763	−	0.155961i	$-0.950152\pi$
$911$	−34.5493	+	25.1016i	−1.14467	+	0.831652i	−0.156908	+	0.987613i	$0.550152\pi$
$912$	3.26641	+	0.875231i	0.108162	+	0.0289818i
$913$	28.3010	+	6.94720i	0.936627	+	0.229919i
$914$	3.97652	+	2.29584i	0.131531	+	0.0759397i
$915$	−7.21631	−	1.60063i	−0.238564	−	0.0529151i
$916$	−2.29964	+	0.747197i	−0.0759821	+	0.0246881i
$917$	46.7291	−	15.1383i	1.54313	−	0.499910i
$918$	−1.88693	−	11.9136i	−0.0622780	−	0.393208i
$919$	11.9188	+	1.25272i	0.393165	+	0.0413233i	0.299049	−	0.954238i	$-0.403331\pi$
$919$	11.9188	+	1.25272i	0.393165	+	0.0413233i	0.0941165	+	0.995561i	$0.469997\pi$
$920$	0.00679114	+	0.0454740i	0.000223897	+	0.00149923i
$921$	−4.20683	−	0.894190i	−0.138620	−	0.0294646i
$922$	12.9584	+	33.7577i	0.426761	+	1.11175i
$923$	29.6608	−	29.6608i	0.976298	−	0.976298i
$924$	−5.17588	+	4.36748i	−0.170274	+	0.143680i
$925$	18.9472	+	7.65989i	0.622980	+	0.251856i
$926$	−33.0049	−	14.6947i	−1.08461	−	0.482899i
$927$	−0.483319	−	0.744246i	−0.0158743	−	0.0244443i
$928$	0.0837241	−	1.59755i	0.00274838	−	0.0524422i
$929$	3.95328	−	37.6129i	0.129703	−	1.23404i	−0.715123	−	0.698999i	$-0.753629\pi$
$929$	3.95328	−	37.6129i	0.129703	−	1.23404i	0.844826	−	0.535042i	$-0.179704\pi$
$930$	1.29311	−	0.483317i	0.0424028	−	0.0158486i
$931$	28.0412	−	12.4264i	0.919013	−	0.407257i
$932$	26.9888	+	13.7515i	0.884046	+	0.450444i
$933$	−4.33961	−	11.3051i	−0.142072	−	0.370111i
$934$	8.02285	−	13.8960i	0.262516	−	0.454690i
$935$	2.50294	+	21.3005i	0.0818548	+	0.696600i
$936$	−13.6945	+	7.90653i	−0.447619	+	0.258433i
$937$	−13.2142	−	2.09292i	−0.431688	−	0.0683726i	−0.0631906	−	0.998001i	$-0.520128\pi$
$937$	−13.2142	−	2.09292i	−0.431688	−	0.0683726i	−0.368497	+	0.929629i	$0.620128\pi$
$938$	−16.8094	−	37.8431i	−0.548847	−	1.23562i
$939$	−15.2784	−	4.96424i	−0.498590	−	0.162002i
$940$	−15.2675	+	1.46844i	−0.497971	+	0.0478952i
$941$	−4.86607	−	10.9294i	−0.158629	−	0.356287i	0.816693	−	0.577072i	$-0.195805\pi$
$941$	−4.86607	−	10.9294i	−0.158629	−	0.356287i	−0.975323	+	0.220785i	$0.929138\pi$
$942$	−4.24095	−	0.222259i	−0.138178	−	0.00724158i
$943$	−0.00215508	−	0.0411214i	−7.01791e−5	−	0.00133910i
$944$	−1.27314	+	0.924994i	−0.0414373	+	0.0301060i
$945$	−16.6885	+	18.1766i	−0.542877	+	0.591286i
$946$	−16.8977	−	17.9891i	−0.549390	−	0.584877i
$947$	15.2940	+	4.09803i	0.496990	+	0.133168i	0.498603	−	0.866831i	$-0.333847\pi$
$947$	15.2940	+	4.09803i	0.496990	+	0.133168i	−0.00161285	+	0.999999i	$0.500513\pi$
$948$	1.04776	+	0.848458i	0.0340296	+	0.0275566i
$949$	19.5443	−	91.9485i	0.634433	−	2.98477i
$950$	−21.5744	−	3.80891i	−0.699965	−	0.123577i
$951$	1.22000	−	1.67918i	0.0395611	−	0.0544512i
$952$	−6.62954	+	3.81988i	−0.214865	+	0.123803i
$953$	−27.2803	+	13.9000i	−0.883696	+	0.450266i	−0.836085	−	0.548600i	$-0.815161\pi$
$953$	−27.2803	+	13.9000i	−0.883696	+	0.450266i	−0.0476115	+	0.998866i	$0.515161\pi$
$954$	−7.41183	−	6.67364i	−0.239967	−	0.216067i
$955$	10.0999	+	5.25905i	0.326825	+	0.170179i
$956$	0.0146822	−	0.0254303i	0.000474855	−	0.000822474i
$957$	−4.05706	−	0.555170i	−0.131146	−	0.0179461i
$958$	9.50804	−	9.50804i	0.307191	−	0.307191i
$959$	13.6718	−	21.0126i	0.441484	−	0.678534i
$960$	0.849640	+	1.50211i	0.0274220	+	0.0484804i
$961$	−29.6967	+	6.31222i	−0.957957	+	0.203620i
$962$	25.0966	+	9.63369i	0.809148	+	0.310603i
$963$	40.7684	+	15.6495i	1.31374	+	0.504299i
$964$	−20.1638	+	4.28595i	−0.649433	+	0.138041i
$965$	−2.22380	−	3.93154i	−0.0715867	−	0.126561i
$966$	0.0190289	+	0.0374268i	0.000612246	+	0.00120419i
$967$	−39.2624	+	39.2624i	−1.26259	+	1.26259i	−0.312761	+	0.949832i	$0.601254\pi$
$967$	−39.2624	+	39.2624i	−1.26259	+	1.26259i	−0.949832	+	0.312761i	$0.898746\pi$
$968$	−10.4957	+	3.29239i	−0.337345	+	0.105821i
$969$	4.88970	−	8.46921i	0.157080	−	0.272070i
$970$	33.9643	+	17.6853i	1.09053	+	0.567841i
$971$	30.5210	+	27.4812i	0.979466	+	0.881915i	0.993014	−	0.117993i	$-0.0376461\pi$
$971$	30.5210	+	27.4812i	0.979466	+	0.881915i	−0.0135484	+	0.999908i	$0.504313\pi$
$972$	13.8956	−	7.08017i	0.445702	−	0.227096i
$973$	5.82179	−	10.0634i	0.186638	−	0.322618i
$974$	−8.32754	+	11.4619i	−0.266832	+	0.367262i
$975$	−20.7927	+	14.5525i	−0.665898	+	0.466054i
$976$	0.890521	−	4.18957i	0.0285049	−	0.134105i
$977$	−6.88458	−	5.57502i	−0.220257	−	0.178361i	0.512841	−	0.858484i	$-0.328593\pi$
$977$	−6.88458	−	5.57502i	−0.220257	−	0.178361i	−0.733098	+	0.680123i	$0.761926\pi$
$978$	14.1258	+	3.78499i	0.451692	+	0.121031i
$979$	2.79593	+	22.1072i	0.0893583	+	0.706549i
$980$	14.5527	+	5.76353i	0.464870	+	0.184109i
$981$	31.4467	−	22.8474i	1.00402	−	0.729461i
$982$	−0.157889	−	3.01270i	−0.00503844	−	0.0961392i
$983$	53.4990	+	2.80376i	1.70635	+	0.0894262i	0.880375	−	0.474277i	$-0.157291\pi$
$983$	53.4990	+	2.80376i	1.70635	+	0.0894262i	0.825977	+	0.563704i	$0.190624\pi$
$984$	−0.628641	−	1.41195i	−0.0200403	−	0.0450114i
$985$	−25.2182	+	2.42551i	−0.803519	+	0.0772831i
$986$	−4.39990	−	1.42961i	−0.140121	−	0.0455282i
$987$	−12.8004	+	5.68577i	−0.407441	+	0.180980i
$988$	−28.4623	−	4.50798i	−0.905506	−	0.143418i
$989$	−0.132514	+	0.0765067i	−0.00421369	+	0.00243277i
$990$	−16.1995	+	7.45159i	−0.514855	+	0.236827i
$991$	9.40887	−	16.2966i	0.298883	−	0.517680i	−0.676998	−	0.735985i	$-0.736719\pi$
$991$	9.40887	−	16.2966i	0.298883	−	0.517680i	0.975881	+	0.218305i	$0.0700527\pi$
$992$	0.286670	+	0.746800i	0.00910177	+	0.0237109i
$993$	−13.0414	−	6.64492i	−0.413856	−	0.210870i
$994$	15.0286	+	7.67392i	0.476678	+	0.243402i
$995$	19.7053	−	7.36509i	0.624699	−	0.233489i
$996$	0.708826	−	6.74403i	0.0224600	−	0.213693i
$997$	0.538621	−	10.2775i	0.0170583	−	0.325492i	−0.976750	−	0.214382i	$-0.931226\pi$
$997$	0.538621	−	10.2775i	0.0170583	−	0.325492i	0.993808	−	0.111110i	$-0.0354405\pi$
$998$	−4.99395	−	7.69000i	−0.158081	−	0.243423i
$999$	−15.5745	−	6.93422i	−0.492755	−	0.219389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.11	✓	768
5.2	odd	4	inner	770.2.bv.a.157.14	yes	768
7.5	odd	6	inner	770.2.bv.a.663.38	yes	768
11.4	even	5	inner	770.2.bv.a.213.14	yes	768
35.12	even	12	inner	770.2.bv.a.47.14	yes	768
55.37	odd	20	inner	770.2.bv.a.367.38	yes	768
77.26	odd	30	inner	770.2.bv.a.103.14	yes	768
385.257	even	60	inner	770.2.bv.a.257.11	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.11	✓	768	1.1	even	1	trivial
770.2.bv.a.47.14	yes	768	35.12	even	12	inner
770.2.bv.a.103.14	yes	768	77.26	odd	30	inner
770.2.bv.a.157.14	yes	768	5.2	odd	4	inner
770.2.bv.a.213.14	yes	768	11.4	even	5	inner
770.2.bv.a.257.11	yes	768	385.257	even	60	inner
770.2.bv.a.367.38	yes	768	55.37	odd	20	inner
770.2.bv.a.663.38	yes	768	7.5	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.647269 + 0.420342i) q^{3} +(0.743145 - 0.669131i) q^{4} +(1.72525 + 1.42250i) q^{5} +(0.453641 - 0.624383i) q^{6} +(-2.58746 - 0.552333i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.977939 + 2.19649i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.647269 + 0.420342i) q^{3} +(0.743145 - 0.669131i) q^{4} +(1.72525 + 1.42250i) q^{5} +(0.453641 - 0.624383i) q^{6} +(-2.58746 - 0.552333i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.977939 + 2.19649i) q^{9} +(-2.12044 - 0.709742i) q^{10} +(-3.05765 - 1.28482i) q^{11} +(-0.199751 + 0.745482i) q^{12} +(1.02884 - 6.49586i) q^{13} +(2.61354 - 0.411614i) q^{14} +(-1.71464 - 0.195545i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-2.69984 - 1.03637i) q^{17} +(0.125834 - 2.40106i) q^{18} +(2.93186 - 3.25616i) q^{19} +(2.23395 - 0.0972963i) q^{20} +(1.90695 - 0.730107i) q^{21} +(3.31500 + 0.103714i) q^{22} +(0.00532186 - 0.0198615i) q^{23} +(-0.0806730 - 0.767552i) q^{24} +(0.952992 + 4.90834i) q^{25} +(1.36740 + 6.43312i) q^{26} +(-0.652484 - 4.11962i) q^{27} +(-2.29244 + 1.32088i) q^{28} +(-1.52145 - 0.494348i) q^{29} +(1.67083 - 0.431915i) q^{30} +(0.795549 - 0.0836156i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.51919 - 0.453637i) q^{33} +2.89192 q^{34} +(-3.67832 - 4.63357i) q^{35} +(0.742987 + 2.28668i) q^{36} +(2.22615 - 3.42798i) q^{37} +(-1.57023 + 4.09058i) q^{38} +(2.06454 + 4.63704i) q^{39} +(-2.05070 + 0.891410i) q^{40} +(1.90459 - 0.618840i) q^{41} +(-1.51864 + 1.36500i) q^{42} +(-5.26196 - 5.26196i) q^{43} +(-3.13199 + 1.09117i) q^{44} +(-4.81169 + 2.39838i) q^{45} +(0.00214932 + 0.0204495i) q^{46} +(-6.84994 + 0.358990i) q^{47} +(0.350381 + 0.687661i) q^{48} +(6.38986 + 2.85827i) q^{49} +(-2.64869 - 4.24081i) q^{50} +(2.18315 - 0.464043i) q^{51} +(-3.58200 - 5.51580i) q^{52} +(2.61051 - 3.22371i) q^{53} +(2.08549 + 3.61217i) q^{54} +(-3.44758 - 6.56614i) q^{55} +(1.66681 - 2.05469i) q^{56} +(-0.529004 + 3.34000i) q^{57} +(1.59755 - 0.0837241i) q^{58} +(-1.05301 - 1.16948i) q^{59} +(-1.40507 + 1.00200i) q^{60} +(4.25970 + 0.447713i) q^{61} +(-0.712744 + 0.363161i) q^{62} +(3.74357 - 5.14317i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(11.0154 - 9.74348i) q^{65} +(-2.18929 + 1.32630i) q^{66} +(-4.05076 - 15.1176i) q^{67} +(-2.69984 + 1.03637i) q^{68} +(0.00490392 + 0.0150927i) q^{69} +(5.09453 + 3.00762i) q^{70} +(5.15987 + 3.74886i) q^{71} +(-1.51311 - 1.86854i) q^{72} +(14.2734 + 0.748037i) q^{73} +(-0.849817 + 3.99808i) q^{74} +(-2.68002 - 2.77644i) q^{75} -4.38160i q^{76} +(7.20190 + 5.01325i) q^{77} +(-3.58918 - 3.58918i) q^{78} +(0.710523 - 1.59586i) q^{79} +(1.59504 - 1.56711i) q^{80} +(-2.67250 - 2.96811i) q^{81} +(-1.55632 + 1.26028i) q^{82} +(-8.67823 + 1.37450i) q^{83} +(0.928602 - 1.81857i) q^{84} +(-3.18367 - 5.62852i) q^{85} +(6.79817 + 3.02674i) q^{86} +(1.19258 - 0.319551i) q^{87} +(2.53293 - 2.14110i) q^{88} +(-3.35933 - 5.81854i) q^{89} +(3.63260 - 3.96344i) q^{90} +(-6.24997 + 16.2395i) q^{91} +(-0.00933500 - 0.0183210i) q^{92} +(-0.479787 + 0.388524i) q^{93} +(6.26632 - 2.78994i) q^{94} +(9.69010 - 1.44713i) q^{95} +(-0.573544 - 0.516422i) q^{96} +(-16.9142 - 2.67895i) q^{97} +(-6.98976 - 0.378510i) q^{98} +(5.81228 - 5.45963i) 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

Varieties

Fields

Representations

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Database

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