LMFDB - Embedded newform 770.2.bv.a.257.5

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			257.5
Character	$\chi$	$=$	770.257
Dual form			770.2.bv.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 - 0.358368i) q^{2} +(-1.55619 - 1.01060i) q^{3} +(0.743145 + 0.669131i) q^{4} +(0.808226 + 2.08489i) q^{5} +(1.09066 + 1.50116i) q^{6} +(2.61764 + 0.384675i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.180196 + 0.404728i) q^{9} +O(q^{10})$	\(q+(-0.933580 - 0.358368i) q^{2} +(-1.55619 - 1.01060i) q^{3} +(0.743145 + 0.669131i) q^{4} +(0.808226 + 2.08489i) q^{5} +(1.09066 + 1.50116i) q^{6} +(2.61764 + 0.384675i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.180196 + 0.404728i) q^{9} +(-0.00738565 - 2.23606i) q^{10} +(1.05151 - 3.14553i) q^{11} +(-0.480249 - 1.79231i) q^{12} +(0.269983 + 1.70461i) q^{13} +(-2.30592 - 1.29720i) q^{14} +(0.849240 - 4.06127i) q^{15} +(0.104528 + 0.994522i) q^{16} +(-3.65329 + 1.40237i) q^{17} +(-0.0231864 - 0.442422i) q^{18} +(1.85643 + 2.06177i) q^{19} +(-0.794436 + 2.09018i) q^{20} +(-3.68478 - 3.24401i) q^{21} +(-2.10892 + 2.55977i) q^{22} +(0.520545 + 1.94270i) q^{23} +(-0.193957 + 1.84538i) q^{24} +(-3.69354 + 3.37013i) q^{25} +(0.358825 - 1.68814i) q^{26} +(-0.742213 + 4.68615i) q^{27} +(1.68789 + 2.03741i) q^{28} +(6.75599 - 2.19515i) q^{29} +(-2.24826 + 3.48718i) q^{30} +(4.86065 + 0.510875i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.81521 + 3.83237i) q^{33} +3.91321 q^{34} +(1.31364 + 5.76839i) q^{35} +(-0.136904 + 0.421346i) q^{36} +(1.67913 + 2.58563i) q^{37} +(-0.994252 - 2.59012i) q^{38} +(1.30253 - 2.92553i) q^{39} +(1.49072 - 1.66666i) q^{40} +(-2.00363 - 0.651020i) q^{41} +(2.27749 + 4.34905i) q^{42} +(0.687996 - 0.687996i) q^{43} +(2.88619 - 1.63398i) q^{44} +(-0.698174 + 0.702801i) q^{45} +(0.210231 - 2.00021i) q^{46} +(3.96165 + 0.207621i) q^{47} +(0.842398 - 1.65330i) q^{48} +(6.70405 + 2.01388i) q^{49} +(4.65596 - 1.82264i) q^{50} +(7.10244 + 1.50967i) q^{51} +(-0.939967 + 1.44742i) q^{52} +(-5.08396 - 6.27817i) q^{53} +(2.37228 - 4.10891i) q^{54} +(7.40793 - 0.350012i) q^{55} +(-0.845635 - 2.50697i) q^{56} +(-0.805323 - 5.08461i) q^{57} +(-7.09393 - 0.371777i) q^{58} +(3.08976 - 3.43153i) q^{59} +(3.34863 - 2.44986i) q^{60} +(-0.102327 + 0.0107550i) q^{61} +(-4.35473 - 2.21885i) q^{62} +(0.316000 + 1.12875i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-3.33571 + 1.94059i) q^{65} +(5.86879 - 1.85221i) q^{66} +(-0.700150 + 2.61300i) q^{67} +(-3.65329 - 1.40237i) q^{68} +(1.15323 - 3.54927i) q^{69} +(0.840821 - 5.85602i) q^{70} +(11.5314 - 8.37805i) q^{71} +(0.278807 - 0.344299i) q^{72} +(12.0324 - 0.630590i) q^{73} +(-0.640994 - 3.01564i) q^{74} +(9.15369 - 1.51185i) q^{75} +2.77439i q^{76} +(3.96247 - 7.82936i) q^{77} +(-2.26443 + 2.26443i) q^{78} +(5.47501 + 12.2971i) q^{79} +(-1.98899 + 1.02173i) q^{80} +(6.78018 - 7.53015i) q^{81} +(1.63725 + 1.32582i) q^{82} +(6.31111 + 0.999581i) q^{83} +(-0.567660 - 4.87637i) q^{84} +(-5.87647 - 6.48329i) q^{85} +(-0.888855 + 0.395744i) q^{86} +(-12.7320 - 3.41153i) q^{87} +(-3.28006 + 0.491137i) q^{88} +(-4.69912 + 8.13911i) q^{89} +(0.903662 - 0.405918i) q^{90} +(0.0509992 + 4.56590i) q^{91} +(-0.913080 + 1.79202i) q^{92} +(-7.04779 - 5.70719i) q^{93} +(-3.62412 - 1.61356i) q^{94} +(-2.79816 + 5.53683i) q^{95} +(-1.37894 + 1.24160i) q^{96} +(-5.78741 + 0.916635i) q^{97} +(-5.53706 - 4.28263i) q^{98} +(1.46256 - 0.141237i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

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
$3$	−1.55619	−	1.01060i	−0.898465	−	0.583470i	0.0106831	−	0.999943i	$-0.496599\pi$
$3$	−1.55619	−	1.01060i	−0.898465	−	0.583470i	−0.909148	+	0.416473i	$0.863266\pi$
$4$	0.743145	+	0.669131i	0.371572	+	0.334565i
$5$	0.808226	+	2.08489i	0.361450	+	0.932392i
$5$	0.808226	+	2.08489i	0.361450	+	0.932392i
$6$	1.09066	+	1.50116i	0.445260	+	0.612847i
$7$	2.61764	+	0.384675i	0.989374	+	0.145393i
$7$	2.61764	+	0.384675i	0.989374	+	0.145393i
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	0.180196	+	0.404728i	0.0600654	+	0.134909i
$10$	−0.00738565	−	2.23606i	−0.00233555	−	0.707103i
$11$	1.05151	−	3.14553i	0.317042	−	0.948411i
$11$	1.05151	−	3.14553i	0.317042	−	0.948411i
$12$	−0.480249	−	1.79231i	−0.138636	−	0.517397i
$13$	0.269983	+	1.70461i	0.0748798	+	0.472773i	0.996424	+	0.0844982i	$0.0269287\pi$
$13$	0.269983	+	1.70461i	0.0748798	+	0.472773i	−0.921544	+	0.388274i	$0.873071\pi$
$14$	−2.30592	−	1.29720i	−0.616283	−	0.346692i
$15$	0.849240	−	4.06127i	0.219273	−	1.04862i
$16$	0.104528	+	0.994522i	0.0261321	+	0.248630i
$17$	−3.65329	+	1.40237i	−0.886054	+	0.340124i	−0.758473	−	0.651704i	$-0.774054\pi$
$17$	−3.65329	+	1.40237i	−0.886054	+	0.340124i	−0.127580	+	0.991828i	$0.540721\pi$
$18$	−0.0231864	−	0.442422i	−0.00546508	−	0.104280i
$19$	1.85643	+	2.06177i	0.425894	+	0.473003i	0.917455	−	0.397840i	$-0.130240\pi$
$19$	1.85643	+	2.06177i	0.425894	+	0.473003i	−0.491561	+	0.870843i	$0.663573\pi$
$20$	−0.794436	+	2.09018i	−0.177641	+	0.467380i
$21$	−3.68478	−	3.24401i	−0.804085	−	0.707901i
$22$	−2.10892	+	2.55977i	−0.449624	+	0.545746i
$23$	0.520545	+	1.94270i	0.108541	+	0.405081i	0.998723	−	0.0505248i	$-0.0160894\pi$
$23$	0.520545	+	1.94270i	0.108541	+	0.405081i	−0.890182	+	0.455606i	$0.849423\pi$
$24$	−0.193957	+	1.84538i	−0.0395913	+	0.376686i
$25$	−3.69354	+	3.37013i	−0.738708	+	0.674025i
$26$	0.358825	−	1.68814i	0.0703714	−	0.331071i
$27$	−0.742213	+	4.68615i	−0.142839	+	0.901850i
$28$	1.68789	+	2.03741i	0.318981	+	0.385034i
$29$	6.75599	−	2.19515i	1.25456	−	0.407630i	0.395004	−	0.918679i	$-0.370743\pi$
$29$	6.75599	−	2.19515i	1.25456	−	0.407630i	0.859551	+	0.511050i	$0.170743\pi$
$30$	−2.24826	+	3.48718i	−0.410475	+	0.636670i
$31$	4.86065	+	0.510875i	0.872999	+	0.0917559i	0.530422	−	0.847734i	$-0.322034\pi$
$31$	4.86065	+	0.510875i	0.872999	+	0.0917559i	0.342577	+	0.939490i	$0.388700\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−4.81521	+	3.83237i	−0.838221	+	0.667130i
$34$	3.91321			0.671109
$35$	1.31364	+	5.76839i	0.222045	+	0.975036i
$36$	−0.136904	+	0.421346i	−0.0228173	+	0.0702243i
$37$	1.67913	+	2.58563i	0.276047	+	0.425075i	0.949316	−	0.314322i	$-0.101777\pi$
$37$	1.67913	+	2.58563i	0.276047	+	0.425075i	−0.673269	+	0.739397i	$0.735111\pi$
$38$	−0.994252	−	2.59012i	−0.161289	−	0.420172i
$39$	1.30253	−	2.92553i	0.208572	−	0.468460i
$40$	1.49072	−	1.66666i	0.235704	−	0.263521i
$41$	−2.00363	−	0.651020i	−0.312915	−	0.101672i	0.148349	−	0.988935i	$-0.452604\pi$
$41$	−2.00363	−	0.651020i	−0.312915	−	0.101672i	−0.461264	+	0.887263i	$0.652604\pi$
$42$	2.27749	+	4.34905i	0.351424	+	0.671073i
$43$	0.687996	−	0.687996i	0.104918	−	0.104918i	−0.652699	−	0.757617i	$-0.726363\pi$
$43$	0.687996	−	0.687996i	0.104918	−	0.104918i	0.757617	+	0.652699i	$0.226363\pi$
$44$	2.88619	−	1.63398i	0.435110	−	0.246332i
$45$	−0.698174	+	0.702801i	−0.104078	+	0.104767i
$46$	0.210231	−	2.00021i	0.0309969	−	0.294915i
$47$	3.96165	+	0.207621i	0.577867	+	0.0302847i	0.339031	−	0.940775i	$-0.389901\pi$
$47$	3.96165	+	0.207621i	0.577867	+	0.0302847i	0.238836	+	0.971060i	$0.423234\pi$
$48$	0.842398	−	1.65330i	0.121590	−	0.238633i
$49$	6.70405	+	2.01388i	0.957722	+	0.287697i
$50$	4.65596	−	1.82264i	0.658453	−	0.257760i
$51$	7.10244	+	1.50967i	0.994541	+	0.211396i
$52$	−0.939967	+	1.44742i	−0.130350	+	0.200721i
$53$	−5.08396	−	6.27817i	−0.698336	−	0.862373i	0.297388	−	0.954757i	$-0.403885\pi$
$53$	−5.08396	−	6.27817i	−0.698336	−	0.862373i	−0.995723	+	0.0923840i	$0.970551\pi$
$54$	2.37228	−	4.10891i	0.322827	−	0.559152i
$55$	7.40793	−	0.350012i	0.998886	−	0.0471956i
$56$	−0.845635	−	2.50697i	−0.113003	−	0.335008i
$57$	−0.805323	−	5.08461i	−0.106668	−	0.673473i
$58$	−7.09393	−	0.371777i	−0.931479	−	0.0488167i
$59$	3.08976	−	3.43153i	0.402253	−	0.446747i	−0.507653	−	0.861561i	$-0.669487\pi$
$59$	3.08976	−	3.43153i	0.402253	−	0.446747i	0.909906	+	0.414815i	$0.136154\pi$
$60$	3.34863	−	2.44986i	0.432306	−	0.316276i
$61$	−0.102327	+	0.0107550i	−0.0131017	+	0.00137704i	−0.111077	−	0.993812i	$-0.535430\pi$
$61$	−0.102327	+	0.0107550i	−0.0131017	+	0.00137704i	0.0979754	+	0.995189i	$0.468763\pi$
$62$	−4.35473	−	2.21885i	−0.553051	−	0.281794i
$63$	0.316000	+	1.12875i	0.0398123	+	0.142209i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−3.33571	+	1.94059i	−0.413744	+	0.240701i
$66$	5.86879	−	1.85221i	0.722398	−	0.227991i
$67$	−0.700150	+	2.61300i	−0.0855370	+	0.319228i	−0.995415	−	0.0956468i	$-0.969508\pi$
$67$	−0.700150	+	2.61300i	−0.0855370	+	0.319228i	0.909878	+	0.414875i	$0.136175\pi$
$68$	−3.65329	−	1.40237i	−0.443027	−	0.170062i
$69$	1.15323	−	3.54927i	0.138832	−	0.427281i
$70$	0.840821	−	5.85602i	0.100497	−	0.699929i
$71$	11.5314	−	8.37805i	1.36852	−	0.994292i	0.370674	−	0.928763i	$-0.379127\pi$
$71$	11.5314	−	8.37805i	1.36852	−	0.994292i	0.997851	−	0.0655287i	$-0.0208734\pi$
$72$	0.278807	−	0.344299i	0.0328578	−	0.0405760i
$73$	12.0324	−	0.630590i	1.40828	−	0.0738049i	0.667030	−	0.745031i	$-0.267565\pi$
$73$	12.0324	−	0.630590i	1.40828	−	0.0738049i	0.741252	+	0.671226i	$0.234232\pi$
$74$	−0.640994	−	3.01564i	−0.0745140	−	0.350561i
$75$	9.15369	−	1.51185i	1.05698	−	0.174574i
$76$			2.77439i			0.318244i
$77$	3.96247	−	7.82936i	0.451566	−	0.892238i
$78$	−2.26443	+	2.26443i	−0.256397	+	0.256397i
$79$	5.47501	+	12.2971i	0.615987	+	1.38353i	0.904674	+	0.426105i	$0.140115\pi$
$79$	5.47501	+	12.2971i	0.615987	+	1.38353i	−0.288687	+	0.957423i	$0.593219\pi$
$80$	−1.98899	+	1.02173i	−0.222376	+	0.114233i
$81$	6.78018	−	7.53015i	0.753353	−	0.836683i
$82$	1.63725	+	1.32582i	0.180804	+	0.146412i
$83$	6.31111	+	0.999581i	0.692734	+	0.109718i	0.492867	−	0.870105i	$-0.335949\pi$
$83$	6.31111	+	0.999581i	0.692734	+	0.109718i	0.199867	+	0.979823i	$0.435949\pi$
$84$	−0.567660	−	4.87637i	−0.0619368	−	0.532055i
$85$	−5.87647	−	6.48329i	−0.637393	−	0.703211i
$86$	−0.888855	+	0.395744i	−0.0958477	+	0.0426741i
$87$	−12.7320	−	3.41153i	−1.36501	−	0.365754i
$88$	−3.28006	+	0.491137i	−0.349655	+	0.0523554i
$89$	−4.69912	+	8.13911i	−0.498105	+	0.862744i	−0.999998	−	0.00218630i	$-0.999304\pi$
$89$	−4.69912	+	8.13911i	−0.498105	+	0.862744i	0.501892	+	0.864930i	$0.332637\pi$
$90$	0.903662	−	0.405918i	0.0952544	−	0.0427875i
$91$	0.0509992	+	4.56590i	0.00534617	+	0.478636i
$92$	−0.913080	+	1.79202i	−0.0951951	+	0.186831i
$93$	−7.04779	−	5.70719i	−0.730822	−	0.591808i
$94$	−3.62412	−	1.61356i	−0.373799	−	0.166426i
$95$	−2.79816	+	5.53683i	−0.287085	+	0.568067i
$96$	−1.37894	+	1.24160i	−0.140737	+	0.126720i
$97$	−5.78741	+	0.916635i	−0.587622	+	0.0930702i	−0.443164	−	0.896441i	$-0.646144\pi$
$97$	−5.78741	+	0.916635i	−0.587622	+	0.0930702i	−0.144458	+	0.989511i	$0.546144\pi$
$98$	−5.53706	−	4.28263i	−0.559328	−	0.432611i
$99$	1.46256	−	0.141237i	0.146993	−	0.0141949i
$100$	−4.99989	+	0.0330295i	−0.499989	+	0.00330295i
$101$	16.4458	+	1.72852i	1.63642	+	0.171994i	0.877629	−	0.479341i	$-0.159124\pi$
$101$	16.4458	+	1.72852i	1.63642	+	0.171994i	0.758790	+	0.651336i	$0.225791\pi$
$102$	−6.08968	−	3.95469i	−0.602968	−	0.391572i
$103$	5.35959	+	8.25304i	0.528096	+	0.813196i	0.997564	−	0.0697529i	$-0.0222211\pi$
$103$	5.35959	+	8.25304i	0.528096	+	0.813196i	−0.469468	+	0.882949i	$0.655554\pi$
$104$	1.39625	−	1.01443i	0.136913	−	0.0994732i
$105$	3.78527	−	10.3043i	0.369405	−	1.00559i
$106$	2.49639	+	7.68310i	0.242471	+	0.746249i
$107$	−0.810729	+	15.4696i	−0.0783761	+	1.49550i	0.622724	+	0.782442i	$0.286026\pi$
$107$	−0.810729	+	15.4696i	−0.0783761	+	1.49550i	−0.701100	+	0.713063i	$0.747307\pi$
$108$	−3.68722	+	2.98585i	−0.354803	+	0.287313i
$109$	−1.74617	+	1.00815i	−0.167253	+	0.0965633i	−0.581290	−	0.813697i	$-0.697452\pi$
$109$	−1.74617	+	1.00815i	−0.167253	+	0.0965633i	0.414037	+	0.910260i	$0.364118\pi$
$110$	−7.04134	−	2.32800i	−0.671365	−	0.221966i
$111$		−	5.72065i		−	0.542980i
$112$	−0.108950	+	2.64351i	−0.0102948	+	0.249788i
$113$	−1.95365	−	3.83425i	−0.183784	−	0.360696i	0.780672	−	0.624941i	$-0.214877\pi$
$113$	−1.95365	−	3.83425i	−0.183784	−	0.360696i	−0.964455	+	0.264245i	$0.914877\pi$
$114$	−1.07033	+	5.03549i	−0.100245	+	0.471617i
$115$	−3.62960	+	2.65542i	−0.338462	+	0.247619i
$116$	6.48952	+	2.88932i	0.602537	+	0.268267i
$117$	−0.641251	+	0.416433i	−0.0592837	+	0.0384993i
$118$	−4.11429	+	2.09634i	−0.378751	+	0.192983i
$119$	−10.1025	+	2.26556i	−0.926090	+	0.207684i
$120$	−4.00417	+	1.08710i	−0.365529	+	0.0992383i
$121$	−8.78866	−	6.61510i	−0.798969	−	0.601373i
$122$	0.0993849	+	0.0266301i	0.00899789	+	0.00241098i
$123$	2.46011	+	3.03798i	0.221820	+	0.273925i
$124$	3.27033	+	3.63207i	0.293684	+	0.326169i
$125$	−10.0116	−	4.97681i	−0.895461	−	0.445139i
$126$	0.109495	−	1.16702i	0.00975460	−	0.103966i
$127$	−2.15455	−	0.341247i	−0.191185	−	0.0302807i	0.0601075	−	0.998192i	$-0.480856\pi$
$127$	−2.15455	−	0.341247i	−0.191185	−	0.0302807i	−0.251293	+	0.967911i	$0.580856\pi$
$128$	0.838671	−	0.544639i	0.0741287	−	0.0481397i
$129$	−1.76594	+	0.375362i	−0.155482	+	0.0330488i
$130$	3.80960	−	0.616287i	0.334124	−	0.0540519i
$131$	3.23637	+	1.86852i	0.282763	+	0.163253i	0.634674	−	0.772780i	$-0.281135\pi$
$131$	3.23637	+	1.86852i	0.282763	+	0.163253i	−0.351910	+	0.936034i	$0.614468\pi$
$132$	−6.14276	−	0.374000i	−0.534658	−	0.0325525i
$133$	4.06635	+	6.11109i	0.352597	+	0.529899i
$134$	1.59006	−	2.18853i	0.137360	−	0.189060i
$135$	−10.3700	+	2.24003i	−0.892506	+	0.192791i
$136$	2.90808	+	2.61845i	0.249366	+	0.224530i
$137$	2.11811	+	5.51786i	0.180962	+	0.471423i	0.993815	−	0.111046i	$-0.0354201\pi$
$137$	2.11811	+	5.51786i	0.180962	+	0.471423i	−0.812853	+	0.582469i	$0.802087\pi$
$138$	−2.34857	+	2.90025i	−0.199924	+	0.246885i
$139$	2.70239	+	8.31712i	0.229214	+	0.705449i	0.997836	+	0.0657457i	$0.0209426\pi$
$139$	2.70239	+	8.31712i	0.229214	+	0.705449i	−0.768622	+	0.639703i	$0.779057\pi$
$140$	−2.88359	+	5.16575i	−0.243707	+	0.436585i
$141$	−5.95525	−	4.32674i	−0.501523	−	0.364378i
$142$	−13.7679	+	3.68910i	−1.15538	+	0.309582i
$143$	5.64577	+	0.943171i	0.472123	+	0.0788719i
$144$	−0.383675	+	0.221515i	−0.0319729	+	0.0184596i
$145$	10.0370	+	12.3113i	0.833529	+	1.02240i
$146$	−11.4592	−	3.72331i	−0.948367	−	0.308143i
$147$	−8.39753	−	9.90908i	−0.692617	−	0.817287i
$148$	−0.482289	+	3.04505i	−0.0396439	+	0.250302i
$149$	−13.1396	+	1.38103i	−1.07644	+	0.113138i	−0.626117	−	0.779729i	$-0.715357\pi$
$149$	−13.1396	+	1.38103i	−1.07644	+	0.113138i	−0.450320	+	0.892867i	$0.648690\pi$
$150$	−9.08751	−	1.86895i	−0.741992	−	0.152599i
$151$	−1.83875	+	0.390839i	−0.149636	+	0.0318061i	−0.282120	−	0.959379i	$-0.591038\pi$
$151$	−1.83875	+	0.390839i	−0.149636	+	0.0318061i	0.132485	+	0.991185i	$0.457704\pi$
$152$	0.994252	−	2.59012i	0.0806445	−	0.210086i
$153$	−1.22589	−	1.22589i	−0.0991071	−	0.0991071i
$154$	−6.50508	+	5.88931i	−0.524194	+	0.474574i
$155$	2.86339	+	10.5468i	0.229993	+	0.847142i
$156$	2.92553	−	1.30253i	0.234230	−	0.104286i
$157$	7.55327	−	11.6310i	0.602817	−	0.928256i	−0.397128	−	0.917763i	$-0.629993\pi$
$157$	7.55327	−	11.6310i	0.602817	−	0.928256i	0.999945	−	0.0104933i	$-0.00334018\pi$
$158$	−0.704485	−	13.4424i	−0.0560458	−	1.06942i
$159$	1.56688	+	14.9079i	0.124262	+	1.18227i
$160$	2.22303	−	0.241077i	0.175746	−	0.0190588i
$161$	0.615290	+	5.28552i	0.0484917	+	0.416558i
$162$	−9.02840	+	4.60020i	−0.709338	+	0.361426i
$163$	6.43336	−	16.7595i	0.503900	−	1.31270i	−0.411959	−	0.911202i	$-0.635155\pi$
$163$	6.43336	−	16.7595i	0.503900	−	1.31270i	0.915859	−	0.401501i	$-0.131511\pi$
$164$	−1.05337	−	1.82449i	−0.0822545	−	0.142469i
$165$	−11.8819	−	6.94177i	−0.925001	−	0.540416i
$166$	−5.53371	−	3.19489i	−0.429499	−	0.247971i
$167$	−24.0466	+	3.80860i	−1.86078	+	0.294718i	−0.982896	−	0.184159i	$-0.941044\pi$
$167$	−24.0466	+	3.80860i	−1.86078	+	0.294718i	−0.877882	+	0.478877i	$0.841044\pi$
$168$	−1.21758	+	4.75591i	−0.0939381	+	0.366927i
$169$	9.53094	−	3.09679i	0.733150	−	0.238215i
$170$	3.16275	+	8.15861i	0.242572	+	0.625737i
$171$	−0.499935	+	1.12287i	−0.0382310	+	0.0858681i
$172$	0.971639	−	0.0509215i	0.0740868	−	0.00388272i
$173$	0.261984	−	4.99896i	0.0199183	−	0.380064i	−0.970423	−	0.241412i	$-0.922390\pi$
$173$	0.261984	−	4.99896i	0.0199183	−	0.380064i	0.990341	−	0.138652i	$-0.0442770\pi$
$174$	10.6638	+	7.74768i	0.808418	+	0.587350i
$175$	−10.9648	+	7.40096i	−0.828858	+	0.559460i
$176$	3.23821	+	0.716952i	0.244089	+	0.0540423i
$177$	−8.27615	+	2.21759i	−0.622073	+	0.166684i
$178$	7.30380	−	5.91450i	0.547443	−	0.443311i
$179$	−5.22223	−	24.5686i	−0.390327	−	1.83635i	−0.532404	−	0.846491i	$-0.678711\pi$
$179$	−5.22223	−	24.5686i	−0.390327	−	1.83635i	0.142076	−	0.989856i	$-0.454622\pi$
$180$	−0.989110	+	0.0551136i	−0.0737239	+	0.00410792i
$181$	−7.32503	−	10.0820i	−0.544465	−	0.749392i	0.444783	−	0.895638i	$-0.353281\pi$
$181$	−7.32503	−	10.0820i	−0.544465	−	0.749392i	−0.989248	+	0.146247i	$0.953281\pi$
$182$	1.58866	−	4.28091i	0.117759	−	0.317322i
$183$	0.170109	+	0.0866750i	0.0125748	+	0.00640720i
$184$	1.49464	−	1.34578i	0.110186	−	0.0992119i
$185$	−4.03364	+	5.59057i	−0.296559	+	0.411027i
$186$	4.53441	+	7.85383i	0.332479	+	0.575870i
$187$	0.569711	+	12.9661i	0.0416614	+	0.948177i
$188$	2.80516	+	2.80516i	0.204587	+	0.204587i
$189$	−3.74549	+	11.9811i	−0.272444	+	0.871499i
$190$	4.59653	−	4.16631i	0.333467	−	0.302256i
$191$	−7.87873	−	1.67468i	−0.570085	−	0.121175i	−0.0861546	−	0.996282i	$-0.527458\pi$
$191$	−7.87873	−	1.67468i	−0.570085	−	0.121175i	−0.483930	+	0.875106i	$0.660791\pi$
$192$	1.73230	−	0.664966i	0.125018	−	0.0479898i
$193$	−8.84518	+	3.39535i	−0.636690	+	0.244402i	−0.655234	−	0.755426i	$-0.727430\pi$
$193$	−8.84518	+	3.39535i	−0.636690	+	0.244402i	0.0185445	+	0.999828i	$0.494097\pi$
$194$	5.73150	+	1.21827i	0.411498	+	0.0874666i
$195$	7.15215	+	0.351144i	0.512176	+	0.0251460i
$196$	3.63453	+	5.98249i	0.259610	+	0.427321i
$197$	−12.7709	−	12.7709i	−0.909888	−	0.909888i	0.0863745	−	0.996263i	$-0.472472\pi$
$197$	−12.7709	−	12.7709i	−0.909888	−	0.909888i	−0.996263	+	0.0863745i	$0.972472\pi$
$198$	−1.41603	−	0.392278i	−0.100633	−	0.0278780i
$199$	11.1994	+	19.3980i	0.793908	+	1.37509i	0.923530	+	0.383525i	$0.125290\pi$
$199$	11.1994	+	19.3980i	0.793908	+	1.37509i	−0.129623	+	0.991563i	$0.541377\pi$
$200$	4.67964	+	1.76096i	0.330900	+	0.124519i
$201$	3.73026	−	3.35874i	0.263112	−	0.236907i
$202$	−14.7340	−	7.50736i	−1.03668	−	0.528216i
$203$	18.5291	−	3.14726i	1.30049	−	0.220894i
$204$	4.26798	+	5.87436i	0.298818	+	0.411288i
$205$	−0.262082	−	4.70353i	−0.0183046	−	0.328508i
$206$	−2.04598	−	9.62558i	−0.142550	−	0.670646i
$207$	−0.692464	+	0.560746i	−0.0481296	+	0.0389746i
$208$	−1.66705	+	0.446684i	−0.115589	+	0.0309720i
$209$	8.43741	−	3.67147i	0.583628	−	0.253961i
$210$	−7.22657	+	8.26334i	−0.498681	+	0.570224i
$211$	−3.92271	−	2.85002i	−0.270051	−	0.196203i	0.444515	−	0.895771i	$-0.353376\pi$
$211$	−3.92271	−	2.85002i	−0.270051	−	0.196203i	−0.714566	+	0.699568i	$0.753376\pi$
$212$	0.422796	−	8.06742i	0.0290377	−	0.554073i
$213$	−26.4119	+	1.38419i	−1.80971	+	0.0948429i
$214$	6.30070	−	14.1516i	0.430707	−	0.967383i
$215$	1.99045	+	0.878340i	0.135748	+	0.0599023i
$216$	4.51235	−	1.46615i	0.307026	−	0.0997589i
$217$	12.5269	+	3.20706i	0.850382	+	0.217709i
$218$	1.99148	−	0.315419i	0.134880	−	0.0213629i
$219$	−19.3619	−	11.1786i	−1.30836	−	0.755379i
$220$	5.73937	+	4.69677i	0.386948	+	0.316656i
$221$	−3.37681	−	5.84881i	−0.227149	−	0.393434i
$222$	−2.05010	+	5.34069i	−0.137594	+	0.358443i
$223$	22.5547	−	11.4922i	1.51038	−	0.769575i	0.514260	−	0.857634i	$-0.328067\pi$
$223$	22.5547	−	11.4922i	1.51038	−	0.769575i	0.996115	+	0.0880598i	$0.0280667\pi$
$224$	1.04906	−	2.42888i	0.0700934	−	0.162287i
$225$	−2.02955	−	0.887594i	−0.135303	−	0.0591729i
$226$	0.449815	+	4.27971i	0.0299213	+	0.284682i
$227$	−0.436443	−	8.32782i	−0.0289677	−	0.552737i	−0.974110	−	0.226077i	$-0.927410\pi$
$227$	−0.436443	−	8.32782i	−0.0289677	−	0.552737i	0.945142	−	0.326660i	$-0.105923\pi$
$228$	2.80380	−	4.31747i	0.185686	−	0.285931i
$229$	−3.92484	+	1.74745i	−0.259361	+	0.115475i	−0.532298	−	0.846557i	$-0.678672\pi$
$229$	−3.92484	+	1.74745i	−0.259361	+	0.115475i	0.272937	+	0.962032i	$0.412005\pi$
$230$	4.34014	−	1.17832i	0.286180	−	0.0776958i
$231$	−14.0787	+	8.17947i	−0.926310	+	0.538169i
$232$	−5.02305	−	5.02305i	−0.329779	−	0.329779i
$233$	−2.30419	+	6.00262i	−0.150953	+	0.393245i	−0.988116	−	0.153707i	$-0.950879\pi$
$233$	−2.30419	+	6.00262i	−0.150953	+	0.393245i	0.837164	+	0.546952i	$0.184212\pi$
$234$	0.747896	−	0.158970i	0.0488915	−	0.0103922i
$235$	2.76904	+	8.42742i	0.180632	+	0.549744i
$236$	4.59228	−	0.482668i	0.298932	−	0.0314190i
$237$	3.90728	−	24.6696i	0.253805	−	1.60246i
$238$	10.2434	+	1.50531i	0.663978	+	0.0975748i
$239$	−25.5293	−	8.29498i	−1.65135	−	0.536557i	−0.672321	−	0.740260i	$-0.734703\pi$
$239$	−25.5293	−	8.29498i	−1.65135	−	0.536557i	−0.979033	+	0.203702i	$0.934703\pi$
$240$	4.12779	+	0.420069i	0.266448	+	0.0271153i
$241$	−20.9497	+	12.0953i	−1.34949	+	0.779128i	−0.988177	−	0.153317i	$-0.951005\pi$
$241$	−20.9497	+	12.0953i	−1.34949	+	0.779128i	−0.361312	+	0.932445i	$0.617671\pi$
$242$	5.83428	+	9.32530i	0.375042	+	0.599453i
$243$	−4.41250	+	1.18233i	−0.283062	+	0.0758463i
$244$	−0.0832405	−	0.0604777i	−0.00532892	−	0.00387169i
$245$	1.21967	+	15.6049i	0.0779220	+	0.996959i
$246$	−1.20799	−	3.71782i	−0.0770188	−	0.237040i
$247$	−3.01331	+	3.72112i	−0.191732	+	0.236769i
$248$	−1.75150	−	4.56281i	−0.111220	−	0.289738i
$249$	−8.81109	−	7.93354i	−0.558380	−	0.502768i
$250$	7.56307	+	8.23408i	0.478330	+	0.520769i
$251$	14.2304	−	19.5865i	0.898217	−	1.23629i	−0.0728158	−	0.997345i	$-0.523199\pi$
$251$	14.2304	−	19.5865i	0.898217	−	1.23629i	0.971033	−	0.238945i	$-0.0768015\pi$
$252$	−0.520445	+	1.05027i	−0.0327850	+	0.0661607i
$253$	6.65817	+	0.405380i	0.418595	+	0.0254860i
$254$	1.88915	+	1.09070i	0.118536	+	0.0684367i
$255$	2.59288	+	16.0280i	0.162372	+	1.00371i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−7.96688	+	5.17375i	−0.496960	+	0.322730i	−0.768666	−	0.639651i	$-0.779079\pi$
$257$	−7.96688	+	5.17375i	−0.496960	+	0.322730i	0.271705	+	0.962380i	$0.412412\pi$
$258$	1.78316	+	0.282425i	0.111015	+	0.0175830i
$259$	3.40072	+	7.41416i	0.211311	+	0.460694i
$260$	−3.77743	−	0.789885i	−0.234266	−	0.0489866i
$261$	2.10584	+	2.33878i	0.130348	+	0.144767i
$262$	−2.35180	−	2.90423i	−0.145294	−	0.179424i
$263$	−0.684492	−	0.183409i	−0.0422076	−	0.0113095i	0.237653	−	0.971350i	$-0.423622\pi$
$263$	−0.684492	−	0.183409i	−0.0422076	−	0.0113095i	−0.279861	+	0.960041i	$0.590288\pi$
$264$	5.60073	+	2.55053i	0.344701	+	0.156974i
$265$	8.98031	−	15.6737i	0.551656	−	0.962827i
$266$	−1.60624	−	7.16245i	−0.0984849	−	0.439158i
$267$	15.5381	−	7.91705i	0.950915	−	0.484516i
$268$	−2.26875	+	1.47334i	−0.138586	+	0.0899987i
$269$	−28.5296	−	12.7022i	−1.73948	−	0.774467i	−0.994179	−	0.107739i	$-0.965639\pi$
$269$	−28.5296	−	12.7022i	−1.73948	−	0.774467i	−0.745301	−	0.666728i	$-0.767694\pi$
$270$	10.4840	+	1.62502i	0.638034	+	0.0988955i
$271$	−2.46081	+	11.5772i	−0.149484	+	0.703265i	0.838016	+	0.545645i	$0.183715\pi$
$271$	−2.46081	+	11.5772i	−0.149484	+	0.703265i	−0.987500	+	0.157620i	$0.949618\pi$
$272$	−1.77656	−	3.48669i	−0.107720	−	0.211412i
$273$	4.53493	−	7.15693i	0.274466	−	0.433157i
$274$		−	5.91043i		−	0.357062i
$275$	6.71702	+	15.1618i	0.405052	+	0.914294i
$276$	3.23194	−	1.86596i	0.194540	−	0.112318i
$277$	2.88486	−	2.33611i	0.173334	−	0.140363i	−0.538728	−	0.842480i	$-0.681095\pi$
$277$	2.88486	−	2.33611i	0.173334	−	0.140363i	0.712062	+	0.702117i	$0.247761\pi$
$278$	0.457685	−	8.73315i	0.0274501	−	0.523779i
$279$	0.669106	+	2.05930i	0.0400584	+	0.123287i
$280$	4.54330	−	3.78926i	0.271514	−	0.226451i
$281$	−16.1699	+	11.7481i	−0.964617	+	0.700835i	−0.954218	−	0.299110i	$-0.903310\pi$
$281$	−16.1699	+	11.7481i	−0.964617	+	0.700835i	−0.0103988	+	0.999946i	$0.503310\pi$
$282$	4.00914	+	6.17353i	0.238741	+	0.367629i
$283$	8.23530	+	5.34807i	0.489538	+	0.317909i	0.765696	−	0.643203i	$-0.222395\pi$
$283$	8.23530	+	5.34807i	0.489538	+	0.317909i	−0.276158	+	0.961112i	$0.589061\pi$
$284$	14.1755	+	1.48991i	0.841162	+	0.0884096i
$285$	9.94998	−	5.78852i	0.589386	−	0.342883i
$286$	−4.93278	−	2.90379i	−0.291681	−	0.171705i
$287$	−4.99435	−	2.47488i	−0.294807	−	0.146088i
$288$	0.437575	−	0.0693051i	0.0257844	−	0.00408384i
$289$	−1.25355	+	1.12870i	−0.0737379	+	0.0663939i
$290$	−4.95838	−	15.0906i	−0.291166	−	0.886148i
$291$	9.93264	+	4.42230i	0.582262	+	0.259240i
$292$	9.36374	+	7.58261i	0.547971	+	0.443738i
$293$	4.32147	−	8.48136i	0.252463	−	0.495487i	−0.729640	−	0.683832i	$-0.760312\pi$
$293$	4.32147	−	8.48136i	0.252463	−	0.495487i	0.982103	+	0.188345i	$0.0603123\pi$
$294$	4.28868	+	12.2603i	0.250121	+	0.715037i
$295$	9.65159	+	3.66837i	0.561937	+	0.213581i
$296$	1.54151	−	2.66997i	0.0895982	−	0.155189i
$297$	13.9600	+	7.26218i	0.810039	+	0.421394i
$298$	12.7618	+	3.41951i	0.739270	+	0.198087i
$299$	−3.17100	+	1.41182i	−0.183384	+	0.0816476i
$300$	7.81414	+	5.00149i	0.451150	+	0.288761i
$301$	2.06558	−	1.53627i	0.119058	−	0.0885490i
$302$	1.85669	+	0.294071i	0.106840	+	0.0169219i
$303$	−23.8459	−	19.3100i	−1.36991	−	1.10933i
$304$	−1.85643	+	2.06177i	−0.106473	+	0.118251i
$305$	−0.105127	−	0.204649i	−0.00601953	−	0.0117181i
$306$	0.705145	+	1.58378i	0.0403105	+	0.0905388i
$307$	−13.7936	+	13.7936i	−0.787241	+	0.787241i	−0.981041	−	0.193800i	$-0.937919\pi$
$307$	−13.7936	+	13.7936i	−0.787241	+	0.787241i	0.193800	+	0.981041i	$0.437919\pi$
$308$	8.18355	−	3.16693i	0.466301	−	0.180453i
$309$		−	18.2597i		−	1.03876i
$310$	1.10645	−	10.8725i	0.0628419	−	0.617514i
$311$	−0.738549	−	3.47460i	−0.0418793	−	0.197027i	0.952234	−	0.305368i	$-0.0987794\pi$
$311$	−0.738549	−	3.47460i	−0.0418793	−	0.197027i	−0.994114	+	0.108341i	$0.965446\pi$
$312$	−3.19800	+	0.167600i	−0.181051	+	0.00948849i
$313$	−16.5187	+	20.3988i	−0.933690	+	1.15301i	0.0543051	+	0.998524i	$0.482706\pi$
$313$	−16.5187	+	20.3988i	−0.933690	+	1.15301i	−0.987995	+	0.154487i	$0.950628\pi$
$314$	−11.2198	+	8.15164i	−0.633168	+	0.460024i
$315$	−2.09791	+	1.57111i	−0.118204	+	0.0885219i
$316$	−4.15962	+	12.8020i	−0.233997	+	0.720169i
$317$	25.7020	+	9.86607i	1.44357	+	0.554134i	0.949076	−	0.315049i	$-0.102021\pi$
$317$	25.7020	+	9.86607i	1.44357	+	0.554134i	0.494492	+	0.869182i	$0.335354\pi$
$318$	3.87969	−	14.4792i	0.217562	−	0.811953i
$319$	0.199074	−	23.5594i	0.0111460	−	1.31907i
$320$	−2.16178	−	0.571600i	−0.120847	−	0.0319534i
$321$	16.8952	−	23.2543i	0.943000	−	1.29793i
$322$	1.31974	−	5.15496i	0.0735462	−	0.287275i
$323$	−9.67344	−	4.92887i	−0.538245	−	0.274249i
$324$	10.0773	−	1.05917i	0.559850	−	0.0588426i
$325$	−6.74193	−	5.38616i	−0.373975	−	0.298770i
$326$	−12.0121	+	13.3408i	−0.665290	+	0.738879i
$327$	3.73620	+	0.195806i	0.206612	+	0.0108281i
$328$	0.329567	+	2.08081i	0.0181973	+	0.114893i
$329$	10.2903	+	2.06742i	0.567323	+	0.113981i
$330$	8.60496	+	10.7388i	0.473687	+	0.591150i
$331$	7.81544	−	13.5367i	0.429575	−	0.744047i	−0.567260	−	0.823539i	$-0.691997\pi$
$331$	7.81544	−	13.5367i	0.429575	−	0.744047i	0.996835	+	0.0794922i	$0.0253299\pi$
$332$	4.02122	+	4.96579i	0.220693	+	0.272533i
$333$	−0.743903	+	1.14551i	−0.0407656	+	0.0627736i
$334$	23.8143	+	5.06188i	1.30306	+	0.276974i
$335$	−6.01369	+	0.652154i	−0.328563	+	0.0356310i
$336$	2.84107	−	4.00369i	0.154993	−	0.218419i
$337$	−9.27371	+	18.2007i	−0.505171	+	0.991454i	0.487784	+	0.872964i	$0.337805\pi$
$337$	−9.27371	+	18.2007i	−0.505171	+	0.991454i	−0.992955	+	0.118490i	$0.962195\pi$
$338$	−10.0077	−	0.524481i	−0.544347	−	0.0285280i
$339$	−0.834651	+	7.94117i	−0.0453320	+	0.431305i
$340$	−0.0289016	−	8.75015i	−0.00156741	−	0.474543i
$341$	6.71799	−	14.7521i	0.363800	−	0.798872i
$342$	0.869130	−	0.869130i	0.0469972	−	0.0469972i
$343$	16.7741	+	7.85048i	0.905716	+	0.423886i
$344$	−0.925352	−	0.300665i	−0.0498916	−	0.0162108i
$345$	8.33190	−	0.464257i	0.448575	−	0.0249948i
$346$	−2.03605	+	4.57304i	−0.109459	+	0.245848i
$347$	1.72345	+	4.48975i	0.0925199	+	0.241023i	0.972030	−	0.234858i	$-0.0754626\pi$
$347$	1.72345	+	4.48975i	0.0925199	+	0.241023i	−0.879510	+	0.475881i	$0.842129\pi$
$348$	−7.17896	−	11.0546i	−0.384833	−	0.592590i
$349$	−4.37694	+	13.4708i	−0.234292	+	0.721078i	0.762922	+	0.646490i	$0.223764\pi$
$349$	−4.37694	+	13.4708i	−0.234292	+	0.721078i	−0.997214	+	0.0745873i	$0.976236\pi$
$350$	12.8887	−	2.97997i	0.688932	−	0.159286i
$351$	−8.18842			−0.437066
$352$	−2.76619	−	1.82980i	−0.147439	−	0.0975288i
$353$	−0.730726	+	2.72711i	−0.0388926	+	0.145149i	−0.982642	−	0.185513i	$-0.940605\pi$
$353$	−0.730726	+	2.72711i	−0.0388926	+	0.145149i	0.943749	+	0.330662i	$0.107272\pi$
$354$	8.52116	+	0.895610i	0.452895	+	0.0476011i
$355$	26.7873	+	17.2703i	1.42172	+	0.916615i
$356$	−8.93825	+	2.90421i	−0.473726	+	0.153923i
$357$	18.0109	+	6.68390i	0.953237	+	0.353749i
$358$	−3.92925	+	24.8083i	−0.207667	+	1.31116i
$359$	−6.54467	+	30.7903i	−0.345415	+	1.62505i	0.371882	+	0.928280i	$0.378713\pi$
$359$	−6.54467	+	30.7903i	−0.345415	+	1.62505i	−0.717297	+	0.696768i	$0.754621\pi$
$360$	0.943164	+	0.303012i	0.0497091	+	0.0159701i
$361$	1.18146	−	11.2408i	0.0621821	−	0.591624i
$362$	3.22542	+	12.0374i	0.169524	+	0.632674i
$363$	6.99158	+	19.1761i	0.366963	+	1.00649i
$364$	−3.01728	+	3.42725i	−0.158148	+	0.179637i
$365$	11.0396	+	24.5765i	0.577838	+	1.28639i
$366$	−0.127749	−	0.141880i	−0.00667756	−	0.00741618i
$367$	0.0740417	+	1.41280i	0.00386495	+	0.0737476i	0.999881	−	0.0154265i	$-0.00491059\pi$
$367$	0.0740417	+	1.41280i	0.00386495	+	0.0737476i	−0.996016	+	0.0891741i	$0.971577\pi$
$368$	−1.87765	+	0.720761i	−0.0978791	+	0.0375722i
$369$	−0.0975616	−	0.928236i	−0.00507885	−	0.0483221i
$370$	5.76921	−	3.77372i	0.299927	−	0.196186i
$371$	−10.8929	−	18.3896i	−0.565532	−	0.954743i
$372$	−1.41868	−	8.95716i	−0.0735549	−	0.464407i
$373$	−9.95579	−	37.1555i	−0.515491	−	1.92384i	−0.345622	−	0.938374i	$-0.612332\pi$
$373$	−9.95579	−	37.1555i	−0.515491	−	1.92384i	−0.169869	−	0.985467i	$-0.554335\pi$
$374$	4.11477	−	12.3091i	0.212770	−	0.636488i
$375$	10.5503	+	17.8625i	0.544815	+	0.922417i
$376$	−1.61356	−	3.62412i	−0.0832130	−	0.186900i
$377$	5.56587	+	10.9236i	0.286657	+	0.562596i
$378$	7.79036	−	9.84308i	0.400693	−	0.506274i
$379$	−9.97983	−	13.7361i	−0.512630	−	0.705574i	0.471730	−	0.881743i	$-0.343630\pi$
$379$	−9.97983	−	13.7361i	−0.512630	−	0.705574i	−0.984360	+	0.176169i	$0.943630\pi$
$380$	−5.78430	+	2.24233i	−0.296728	+	0.115029i
$381$	3.00801	+	2.70843i	0.154105	+	0.138757i
$382$	6.75528	+	4.38693i	0.345630	+	0.224455i
$383$	−21.0293	−	8.07239i	−1.07455	−	0.412480i	−0.244199	−	0.969725i	$-0.578525\pi$
$383$	−21.0293	−	8.07239i	−1.07455	−	0.412480i	−0.830348	+	0.557245i	$0.811858\pi$
$384$	−1.85554			−0.0946901
$385$	19.5259	+	1.93344i	0.995133	+	0.0985372i
$386$	9.47447			0.482238
$387$	0.402425	+	0.154476i	0.0204564	+	0.00785248i
$388$	−4.91423	−	3.19134i	−0.249482	−	0.162016i
$389$	17.7343	+	15.9681i	0.899166	+	0.809613i	0.982375	−	0.186919i	$-0.0598502\pi$
$389$	17.7343	+	15.9681i	0.899166	+	0.809613i	−0.0832089	+	0.996532i	$0.526517\pi$
$390$	−6.55127	−	2.89092i	−0.331736	−	0.146388i
$391$	−4.62608	−	6.36726i	−0.233951	−	0.322006i
$392$	−1.24920	−	6.88763i	−0.0630940	−	0.347878i
$393$	−3.14807	−	6.17844i	−0.158799	−	0.311661i
$394$	7.34598	+	16.4993i	0.370085	+	0.831224i
$395$	−21.2130	+	21.3536i	−1.06734	+	1.07442i
$396$	1.18140	+	0.873683i	0.0593675	+	0.0439042i
$397$	−7.67053	−	28.6268i	−0.384973	−	1.43674i	−0.838210	−	0.545348i	$-0.816398\pi$
$397$	−7.67053	−	28.6268i	−0.384973	−	1.43674i	0.453237	−	0.891390i	$-0.350269\pi$
$398$	−3.50396	−	22.1231i	−0.175638	−	1.10893i
$399$	−0.152124	−	13.6195i	−0.00761572	−	0.681825i
$400$	−3.73774	−	3.32103i	−0.186887	−	0.166052i
$401$	1.88778	+	17.9611i	0.0942714	+	0.896932i	0.934802	+	0.355169i	$0.115577\pi$
$401$	1.88778	+	17.9611i	0.0942714	+	0.896932i	−0.840531	+	0.541764i	$0.817757\pi$
$402$	−4.68616	+	1.79885i	−0.233724	+	0.0897184i
$403$	0.441453	+	8.42342i	0.0219903	+	0.419601i
$404$	11.0650	+	12.2889i	0.550505	+	0.611397i
$405$	21.1795	+	8.04987i	1.05242	+	0.400001i
$406$	−18.4263	−	3.70203i	−0.914483	−	0.183729i
$407$	9.89878	−	2.56292i	0.490665	−	0.127039i
$408$	−1.87931	−	7.01370i	−0.0930399	−	0.347230i
$409$	−1.22800	+	11.6836i	−0.0607206	+	0.577718i	0.921288	+	0.388881i	$0.127138\pi$
$409$	−1.22800	+	11.6836i	−0.0607206	+	0.577718i	−0.982009	+	0.188837i	$0.939528\pi$
$410$	−1.44092	+	4.48504i	−0.0711619	+	0.221500i
$411$	2.28018	−	10.7274i	0.112473	−	0.529143i
$412$	−1.53941	+	9.71947i	−0.0758414	+	0.478844i
$413$	9.40790	−	7.79394i	0.462932	−	0.383515i
$414$	0.847424	−	0.275345i	0.0416486	−	0.0135325i
$415$	3.01678	+	13.9659i	0.148088	+	0.685557i
$416$	1.71640	+	0.180401i	0.0841534	+	0.00884488i
$417$	4.19984	−	15.6740i	0.205667	−	0.767560i
$418$	−9.19274	+	0.403914i	−0.449631	+	0.0197561i
$419$	−28.1072			−1.37313			−0.686563	−	0.727070i	$-0.740882\pi$
$419$	−28.1072			−1.37313			−0.686563	+	0.727070i	$0.740882\pi$
$420$	9.70790	−	5.12472i	0.473697	−	0.250061i
$421$	3.32754	−	10.2411i	0.162174	−	0.499121i	−0.836643	−	0.547749i	$-0.815485\pi$
$421$	3.32754	−	10.2411i	0.162174	−	0.499121i	0.998817	+	0.0486277i	$0.0154848\pi$
$422$	2.64081	+	4.06650i	0.128553	+	0.197954i
$423$	0.629845	+	1.64080i	0.0306241	+	0.0797786i
$424$	−3.28582	+	7.38007i	−0.159573	+	0.358408i
$425$	8.76744	−	17.4918i	0.425283	−	0.848475i
$426$	25.1536	+	8.17292i	1.21870	+	0.395979i
$427$	−0.271993	−	0.0112099i	−0.0131627	−	0.000542486i
$428$	−10.9537	+	10.9537i	−0.529466	+	0.529466i
$429$	−7.83271	−	7.17336i	−0.378167	−	0.346333i
$430$	−1.54348	−	1.53332i	−0.0744331	−	0.0739430i
$431$	3.91041	−	37.2050i	0.188358	−	1.79210i	−0.337289	−	0.941401i	$-0.609510\pi$
$431$	3.91041	−	37.2050i	0.188358	−	1.79210i	0.525647	−	0.850703i	$-0.323823\pi$
$432$	−4.73806	−	0.248311i	−0.227960	−	0.0119469i
$433$	−1.54363	+	3.02954i	−0.0741819	+	0.145590i	−0.925119	−	0.379678i	$-0.876035\pi$
$433$	−1.54363	+	3.02954i	−0.0741819	+	0.145590i	0.850937	+	0.525268i	$0.176035\pi$
$434$	−10.5456	−	7.48329i	−0.506203	−	0.359209i
$435$	−3.17766	−	29.3021i	−0.152357	−	1.40493i
$436$	−1.97224	−	0.419213i	−0.0944532	−	0.0200766i
$437$	−3.03905	+	4.67973i	−0.145378	+	0.223862i
$438$	14.0698	+	17.3748i	0.672282	+	0.830200i
$439$	1.58493	−	2.74519i	0.0756448	−	0.131021i	−0.825722	−	0.564078i	$-0.809232\pi$
$439$	1.58493	−	2.74519i	0.0756448	−	0.131021i	0.901366	+	0.433057i	$0.142565\pi$
$440$	−3.67499	−	6.44162i	−0.175199	−	0.307092i
$441$	0.392974	+	3.07621i	0.0187130	+	0.146486i
$442$	1.05650	+	6.67048i	0.0502526	+	0.317282i
$443$	10.9509	+	0.573914i	0.520294	+	0.0272675i	0.310676	−	0.950516i	$-0.399445\pi$
$443$	10.9509	+	0.573914i	0.520294	+	0.0272675i	0.209618	+	0.977783i	$0.432778\pi$
$444$	3.82786	−	4.25127i	0.181662	−	0.201756i
$445$	−20.7671	−	3.21891i	−0.984455	−	0.152591i
$446$	−25.1751	+	2.64601i	−1.19207	+	0.125292i
$447$	21.8433	+	11.1297i	1.03315	+	0.526418i
$448$	−1.84982	+	1.89161i	−0.0873956	+	0.0893700i
$449$	1.47825	−	2.03464i	0.0697630	−	0.0960205i	−0.772710	−	0.634760i	$-0.781099\pi$
$449$	1.47825	−	2.03464i	0.0697630	−	0.0960205i	0.842473	+	0.538739i	$0.181099\pi$
$450$	1.57666	+	1.55596i	0.0743244	+	0.0733489i
$451$	−4.15464	+	5.61792i	−0.195634	+	0.264538i
$452$	1.11377	−	4.15665i	0.0523874	−	0.195512i
$453$	3.25643	+	1.25003i	0.153000	+	0.0587313i
$454$	−2.57697	+	7.93110i	−0.120943	+	0.372225i
$455$	−9.47818	+	3.79660i	−0.444344	+	0.177987i
$456$	−4.16481	+	3.02591i	−0.195035	+	0.141701i
$457$	14.8112	−	18.2903i	0.692837	−	0.855583i	−0.302388	−	0.953185i	$-0.597784\pi$
$457$	14.8112	−	18.2903i	0.692837	−	0.855583i	0.995226	+	0.0976020i	$0.0311172\pi$
$458$	4.29039	−	0.224850i	0.200477	−	0.0105065i
$459$	−3.86018	−	18.1607i	−0.180178	−	0.847670i
$460$	−4.47414	−	0.455315i	−0.208608	−	0.0212292i
$461$			18.7113i			0.871470i	0.900075	+	0.435735i	$0.143512\pi$
$461$			18.7113i			0.871470i	−0.900075	+	0.435735i	$0.856488\pi$
$462$	16.0749	−	2.59084i	0.747870	−	0.120537i
$463$	20.8341	−	20.8341i	0.968241	−	0.968241i	−0.0312701	−	0.999511i	$-0.509955\pi$
$463$	20.8341	−	20.8341i	0.968241	−	0.968241i	0.999511	+	0.0312701i	$0.00995519\pi$
$464$	2.88932	+	6.48952i	0.134133	+	0.301268i
$465$	6.20266	−	19.3066i	0.287642	−	0.895321i
$466$	4.30229	−	4.77818i	0.199300	−	0.221345i
$467$	−12.0761	−	9.77902i	−0.558815	−	0.452519i	0.307833	−	0.951440i	$-0.400396\pi$
$467$	−12.0761	−	9.77902i	−0.558815	−	0.452519i	−0.866647	+	0.498921i	$0.833730\pi$
$468$	−0.755191	−	0.119610i	−0.0349087	−	0.00552899i
$469$	−2.83789	+	6.57055i	−0.131042	+	0.303400i
$470$	0.434994	−	8.86001i	0.0200648	−	0.408682i
$471$	−23.5086	+	10.4667i	−1.08322	+	0.482280i
$472$	−4.46024	−	1.19512i	−0.205299	−	0.0550097i
$473$	−1.44067	−	2.88754i	−0.0662422	−	0.132769i
$474$	−12.4885	+	21.6308i	−0.573618	+	0.993535i
$475$	−13.8052	−	1.35885i	−0.633427	−	0.0623482i
$476$	−9.02354	−	5.07622i	−0.413593	−	0.232668i
$477$	1.62484	−	3.18892i	0.0743962	−	0.146011i
$478$	20.8610	+	16.8929i	0.954161	+	0.772664i
$479$	34.7301	+	15.4628i	1.58686	+	0.706514i	0.995032	−	0.0995523i	$-0.0317411\pi$
$479$	34.7301	+	15.4628i	1.58686	+	0.706514i	0.591825	+	0.806067i	$0.298408\pi$
$480$	−3.70309	−	1.87144i	−0.169022	−	0.0854190i
$481$	−3.95414	+	3.56033i	−0.180293	+	0.162337i
$482$	23.8928	−	3.78425i	1.08829	−	0.172368i
$483$	4.38404	−	8.84708i	0.199481	−	0.402556i
$484$	−2.10488	−	10.7967i	−0.0956763	−	0.490761i
$485$	−6.58862	−	11.3253i	−0.299174	−	0.514254i
$486$	4.54313	+	0.477502i	0.206081	+	0.0216600i
$487$	−15.8996	−	10.3253i	−0.720480	−	0.467885i	0.131596	−	0.991303i	$-0.457990\pi$
$487$	−15.8996	−	10.3253i	−0.720480	−	0.467885i	−0.852076	+	0.523418i	$0.824657\pi$
$488$	0.0560384	+	0.0862915i	0.00253674	+	0.00390623i
$489$	−26.9486	+	19.5793i	−1.21866	+	0.885408i
$490$	4.45363	−	15.0055i	0.201194	−	0.677880i
$491$	5.97651	+	18.3938i	0.269716	+	0.830101i	0.990569	+	0.137013i	$0.0437502\pi$
$491$	5.97651	+	18.3938i	0.269716	+	0.830101i	−0.720853	+	0.693088i	$0.756250\pi$
$492$	−0.204589	+	3.90379i	−0.00922358	+	0.175996i
$493$	−21.6032	+	17.4939i	−0.972959	+	0.787887i
$494$	4.14669	−	2.39410i	0.186569	−	0.107715i
$495$	1.47654	+	2.93512i	0.0663656	+	0.131924i
$496$			4.88743i			0.219452i
$497$	33.4078	−	17.4949i	1.49855	−	0.784752i
$498$	5.38273	+	10.5642i	0.241206	+	0.473394i
$499$	7.65189	−	35.9993i	0.342546	−	1.61155i	−0.383252	−	0.923644i	$-0.625196\pi$
$499$	7.65189	−	35.9993i	0.342546	−	1.61155i	0.725798	−	0.687908i	$-0.241471\pi$
$500$	−4.10990	−	10.3975i	−0.183800	−	0.464992i
$501$	41.2699	+	18.3745i	1.84380	+	0.820914i
$502$	−20.3044	+	13.1859i	−0.906232	+	0.588514i
$503$	7.72665	−	3.93692i	0.344514	−	0.175539i	−0.273168	−	0.961966i	$-0.588072\pi$
$503$	7.72665	−	3.93692i	0.344514	−	0.175539i	0.617683	+	0.786427i	$0.288072\pi$
$504$	0.862260	−	0.793999i	0.0384081	−	0.0353675i
$505$	9.68814	+	35.6847i	0.431116	+	1.58795i
$506$	−6.07066	−	2.76453i	−0.269874	−	0.122898i
$507$	−17.9615	−	4.81278i	−0.797700	−	0.213743i
$508$	−1.37280	−	1.69527i	−0.0609082	−	0.0752154i
$509$	−12.7088	−	14.1146i	−0.563308	−	0.625617i	0.392449	−	0.919774i	$-0.371628\pi$
$509$	−12.7088	−	14.1146i	−0.563308	−	0.625617i	−0.955757	+	0.294157i	$0.904961\pi$
$510$	3.32325	−	15.8926i	0.147156	−	0.703736i
$511$	31.7389	+	2.97789i	1.40405	+	0.131734i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	−11.0396	+	7.16922i	−0.487412	+	0.316529i
$514$	9.29183	−	1.97504i	0.409845	−	0.0871153i
$515$	−12.8749	+	17.8445i	−0.567338	+	0.786322i
$516$	−1.56351	−	0.902695i	−0.0688298	−	0.0397389i
$517$	4.81879	−	12.2432i	0.211930	−	0.538454i
$518$	−0.517850	−	8.14043i	−0.0227530	−	0.357670i
$519$	−5.45964	+	7.51455i	−0.239652	+	0.329852i
$520$	3.24346	+	2.09113i	0.142235	+	0.0917021i
$521$	4.66806	+	4.20314i	0.204511	+	0.184143i	0.765022	−	0.644005i	$-0.222728\pi$
$521$	4.66806	+	4.20314i	0.204511	+	0.184143i	−0.560510	+	0.828148i	$0.689395\pi$
$522$	−1.12783	−	2.93810i	−0.0493638	−	0.128597i
$523$	−0.0146199	+	0.0180541i	−0.000639285	+	0.000789451i	−0.777466	−	0.628926i	$-0.783495\pi$
$523$	−0.0146199	+	0.0180541i	−0.000639285	+	0.000789451i	0.776826	+	0.629715i	$0.216828\pi$
$524$	1.15481	+	3.55414i	0.0504481	+	0.155263i
$525$	24.5426	−	0.436293i	1.07113	−	0.0190414i
$526$	0.573300	+	0.416527i	0.0249971	+	0.0181614i
$527$	−18.4738	+	4.95005i	−0.804732	+	0.215627i
$528$	−4.31470	−	4.38824i	−0.187773	−	0.190974i
$529$	16.4155	−	9.47748i	0.713716	−	0.412064i
$530$	−14.0008	+	11.4144i	−0.608155	+	0.495809i
$531$	1.94560	+	0.632163i	0.0844317	+	0.0274335i
$532$	−1.06724	+	7.26234i	−0.0462706	+	0.314863i
$533$	0.568785	−	3.59117i	0.0246368	−	0.155551i
$534$	−17.3433	+	1.82285i	−0.750517	+	0.0788825i
$535$	−32.9077	+	10.8127i	−1.42273	+	0.467472i
$536$	2.64606	−	0.562437i	0.114292	−	0.0242936i
$537$	−16.7023	+	43.5110i	−0.720757	+	1.87764i
$538$	22.0826	+	22.0826i	0.952049	+	0.952049i
$539$	13.3841	−	18.9701i	0.576493	−	0.817102i
$540$	−9.20527	−	5.27421i	−0.396132	−	0.226966i
$541$	−24.5660	+	10.9375i	−1.05618	+	0.470240i	−0.859982	−	0.510325i	$-0.829525\pi$
$541$	−24.5660	+	10.9375i	−1.05618	+	0.470240i	−0.196195	+	0.980565i	$0.562859\pi$
$542$	6.44626	−	9.92637i	0.276891	−	0.426374i
$543$	1.21021	+	23.0922i	0.0519351	+	0.990981i
$544$	0.409042	+	3.89177i	0.0175375	+	0.166858i
$545$	−3.51318	−	2.82576i	−0.150488	−	0.121042i
$546$	−6.79853	+	5.05639i	−0.290950	+	0.216394i
$547$	−16.0739	+	8.19007i	−0.687271	+	0.350182i	−0.762504	−	0.646984i	$-0.776030\pi$
$547$	−16.0739	+	8.19007i	−0.687271	+	0.350182i	0.0752326	+	0.997166i	$0.476030\pi$
$548$	−2.11811	+	5.51786i	−0.0904811	+	0.235711i
$549$	−0.0227918	−	0.0394766i	−0.000972732	−	0.00168482i
$550$	−0.837359	−	16.5620i	−0.0357051	−	0.706205i
$551$	17.0679	+	9.85417i	0.727118	+	0.419802i
$552$	−3.68597	+	0.583801i	−0.156885	+	0.0248482i
$553$	9.60122	+	34.2954i	0.408285	+	1.45839i
$554$	−3.53044	+	1.14711i	−0.149994	+	0.0487360i
$555$	11.9269	−	4.62358i	0.506270	−	0.196260i
$556$	−3.55697	+	7.98908i	−0.150849	+	0.338812i
$557$	40.0167	−	2.09719i	1.69556	−	0.0888607i	0.820123	−	0.572187i	$-0.193905\pi$
$557$	40.0167	−	2.09719i	1.69556	−	0.0888607i	0.875440	+	0.483327i	$0.160572\pi$
$558$	0.113322	−	2.16231i	0.00479729	−	0.0915377i
$559$	1.35851	+	0.987014i	0.0574588	+	0.0417462i
$560$	−5.59948	+	1.90940i	−0.236621	+	0.0806870i
$561$	12.2170	−	20.7535i	0.515802	−	0.876212i
$562$	19.3061	−	5.17305i	0.814378	−	0.218212i
$563$	24.4963	−	19.8367i	1.03240	−	0.836018i	0.0457595	−	0.998952i	$-0.485429\pi$
$563$	24.4963	−	19.8367i	1.03240	−	0.836018i	0.986637	+	0.162934i	$0.0520959\pi$
$564$	−1.53046	−	7.20024i	−0.0644439	−	0.303185i
$565$	6.41501	−	7.17209i	0.269881	−	0.301732i
$566$	−5.77174	−	7.94412i	−0.242604	−	0.333916i
$567$	20.6447	−	17.1030i	0.866996	−	0.718260i
$568$	−12.7000	−	6.47099i	−0.532882	−	0.271517i
$569$	28.9289	−	26.0477i	1.21276	−	1.09198i	0.219557	−	0.975600i	$-0.429539\pi$
$569$	28.9289	−	26.0477i	1.21276	−	1.09198i	0.993205	−	0.116376i	$-0.0371278\pi$
$570$	−11.3635	+	1.83830i	−0.475966	+	0.0769979i
$571$	1.18106	+	2.04565i	0.0494256	+	0.0856077i	0.889680	−	0.456585i	$-0.150928\pi$
$571$	1.18106	+	2.04565i	0.0494256	+	0.0856077i	−0.840254	+	0.542193i	$0.817594\pi$
$572$	3.56452	+	4.47867i	0.149040	+	0.187263i
$573$	10.5684	+	10.5684i	0.441499	+	0.441499i
$574$	3.77571	+	4.10031i	0.157595	+	0.171144i
$575$	−8.46980	−	5.42114i	−0.353215	−	0.226077i
$576$	−0.433348	−	0.0921110i	−0.0180562	−	0.00383796i
$577$	−30.5614	+	11.7314i	−1.27229	+	0.488386i	−0.898437	−	0.439102i	$-0.855297\pi$
$577$	−30.5614	+	11.7314i	−1.27229	+	0.488386i	−0.373852	+	0.927488i	$0.621963\pi$
$578$	1.57477	−	0.604499i	0.0655020	−	0.0251438i
$579$	17.1961	+	3.65514i	0.714645	+	0.151902i
$580$	−0.778921	+	15.8652i	−0.0323429	+	0.658765i
$581$	16.1357	+	5.04426i	0.669421	+	0.209271i
$582$	−7.68811	−	7.68811i	−0.318682	−	0.318682i
$583$	−25.0940	+	9.39017i	−1.03929	+	0.388901i
$584$	−6.02444	−	10.4346i	−0.249293	−	0.431788i
$585$	−1.38649	−	1.00037i	−0.0573245	−	0.0413601i
$586$	−7.07389	+	6.36936i	−0.292220	+	0.263116i
$587$	−15.9219	−	8.11261i	−0.657167	−	0.334843i	0.0934086	−	0.995628i	$-0.470224\pi$
$587$	−15.9219	−	8.11261i	−0.657167	−	0.334843i	−0.750576	+	0.660785i	$0.770224\pi$
$588$	0.389886	−	12.9829i	0.0160786	−	0.535407i
$589$	7.97015	+	10.9700i	0.328404	+	0.452010i
$590$	−7.69591	−	6.88354i	−0.316836	−	0.283391i
$591$	6.96764	+	32.7801i	0.286610	+	1.34840i
$592$	−2.39595	+	1.94020i	−0.0984729	+	0.0797418i
$593$	−6.82813	+	1.82959i	−0.280398	+	0.0751324i	−0.396277	−	0.918131i	$-0.629698\pi$
$593$	−6.82813	+	1.82959i	−0.280398	+	0.0751324i	0.115879	+	0.993263i	$0.463031\pi$
$594$	−10.4302	−	11.7826i	−0.427957	−	0.483447i
$595$	−12.8885	−	19.2314i	−0.528378	−	0.788412i
$596$	−10.6887	−	7.76580i	−0.437827	−	0.318100i
$597$	2.17519	−	41.5051i	0.0890246	−	1.69869i
$598$	3.46633	−	0.181663i	0.141749	−	0.00742875i
$599$	8.10344	−	18.2006i	0.331097	−	0.743657i	−0.668903	−	0.743350i	$-0.733236\pi$
$599$	8.10344	−	18.2006i	0.331097	−	0.743657i	1.00000		0.000306878i	$-9.76822e-5\pi$
$600$	−5.50276	−	7.46963i	−0.224649	−	0.304946i
$601$	−12.8111	+	4.16257i	−0.522575	+	0.169795i	−0.558413	−	0.829563i	$-0.688590\pi$
$601$	−12.8111	+	4.16257i	−0.522575	+	0.169795i	0.0358389	+	0.999358i	$0.488590\pi$
$602$	−2.47893	+	0.693993i	−0.101034	+	0.0282851i
$603$	−1.18372	+	0.187482i	−0.0482046	+	0.00763487i
$604$	−1.62798	−	0.939917i	−0.0662417	−	0.0382447i
$605$	6.68854	−	23.6699i	0.271928	−	0.962318i
$606$	15.3420	+	26.5731i	0.623225	+	1.07946i
$607$	14.9166	−	38.8590i	0.605445	−	1.57724i	−0.196930	−	0.980418i	$-0.563097\pi$
$607$	14.9166	−	38.8590i	0.605445	−	1.57724i	0.802375	−	0.596821i	$-0.203570\pi$
$608$	2.47200	−	1.25955i	0.100253	−	0.0510813i
$609$	−32.0154	−	13.8278i	−1.29733	−	0.560332i
$610$	0.0248046	+	0.228730i	0.00100431	+	0.00926100i
$611$	0.715666	+	6.80911i	0.0289528	+	0.275467i
$612$	−0.0907331	−	1.73129i	−0.00366767	−	0.0699832i
$613$	−15.2201	+	23.4369i	−0.614734	+	0.946608i	0.384985	+	0.922923i	$0.374207\pi$
$613$	−15.2201	+	23.4369i	−0.614734	+	0.946608i	−0.999719	+	0.0236850i	$0.992460\pi$
$614$	17.8206	−	7.93424i	0.719181	−	0.320200i
$615$	−4.34553	+	7.58443i	−0.175229	+	0.305834i
$616$	−8.77493	+	0.0238628i	−0.353552	+	0.000961461i
$617$	−23.5013	−	23.5013i	−0.946126	−	0.946126i	0.0524947	−	0.998621i	$-0.483283\pi$
$617$	−23.5013	−	23.5013i	−0.946126	−	0.946126i	−0.998621	+	0.0524947i	$0.983283\pi$
$618$	−6.54368	+	17.0469i	−0.263226	+	0.685726i
$619$	47.1681	−	10.0259i	1.89585	−	0.402975i	0.896640	−	0.442761i	$-0.146001\pi$
$619$	47.1681	−	10.0259i	1.89585	−	0.402975i	0.999208	+	0.0397860i	$0.0126676\pi$
$620$	−4.92930	+	9.75380i	−0.197965	+	0.391722i
$621$	−9.49013	+	0.997453i	−0.380826	+	0.0400264i
$622$	−0.555690	+	3.50849i	−0.0222812	+	0.140678i
$623$	−15.4315	+	19.4976i	−0.618250	+	0.781155i
$624$	3.04566	+	0.989593i	0.121924	+	0.0396154i
$625$	2.28451	−	24.8954i	0.0913802	−	0.995816i
$626$	22.7318	−	13.1242i	0.908545	−	0.524549i
$627$	−16.8406	−	2.81335i	−0.672548	−	0.112354i
$628$	13.3958	−	3.58941i	0.534552	−	0.143233i
$629$	−9.76035	−	7.09131i	−0.389171	−	0.282749i
$630$	2.52161	−	0.714931i	0.100463	−	0.0284835i
$631$	1.24986	+	3.84667i	0.0497561	+	0.153133i	0.972847	−	0.231447i	$-0.0743461\pi$
$631$	1.24986	+	3.84667i	0.0497561	+	0.153133i	−0.923091	+	0.384581i	$0.874346\pi$
$632$	8.47117	−	10.4610i	0.336965	−	0.416117i
$633$	3.22425	+	8.39945i	0.128152	+	0.333848i
$634$	−20.4592	−	18.4215i	−0.812538	−	0.731613i
$635$	−1.02990	−	4.76780i	−0.0408703	−	0.189204i
$636$	−8.81088	+	12.1271i	−0.349374	+	0.480872i
$637$	−1.62289	+	11.9715i	−0.0643011	+	0.474327i
$638$	−8.62877	+	21.9232i	−0.341616	+	0.867948i
$639$	5.46874	+	3.15738i	0.216340	+	0.124904i
$640$	1.81335	+	1.30835i	0.0716789	+	0.0517169i
$641$	−41.3107	+	8.78085i	−1.63167	+	0.346823i	−0.930535	−	0.366203i	$-0.880658\pi$
$641$	−41.3107	+	8.78085i	−1.63167	+	0.346823i	−0.701138	+	0.713026i	$0.747324\pi$
$642$	−24.1067	+	15.6550i	−0.951414	+	0.617855i
$643$	−14.5862	−	2.31022i	−0.575222	−	0.0911062i	−0.137956	−	0.990438i	$-0.544053\pi$
$643$	−14.5862	−	2.31022i	−0.575222	−	0.0911062i	−0.437266	+	0.899332i	$0.644053\pi$
$644$	−3.07946	+	4.33962i	−0.121348	+	0.171005i
$645$	−2.20986	−	3.37841i	−0.0870133	−	0.133025i
$646$	7.26459	+	8.06814i	0.285821	+	0.317437i
$647$	7.98759	+	9.86385i	0.314024	+	0.387788i	0.909582	−	0.415525i	$-0.136402\pi$
$647$	7.98759	+	9.86385i	0.314024	+	0.387788i	−0.595557	+	0.803313i	$0.703069\pi$
$648$	−9.78755	−	2.62257i	−0.384491	−	0.103024i
$649$	−7.54504	−	13.3272i	−0.296169	−	0.523139i
$650$	4.36391	+	7.44450i	0.171167	+	0.291997i
$651$	−16.2532	−	17.6505i	−0.637011	−	0.691776i
$652$	15.9952	−	8.14996i	0.626420	−	0.319177i
$653$	−17.2314	+	11.1902i	−0.674316	+	0.437906i	−0.835847	−	0.548962i	$-0.815023\pi$
$653$	−17.2314	+	11.1902i	−0.674316	+	0.437906i	0.161532	+	0.986868i	$0.448357\pi$
$654$	−3.41787	−	1.52174i	−0.133649	−	0.0595046i
$655$	−1.27994	+	8.25767i	−0.0500115	+	0.322654i
$656$	0.438017	−	2.06071i	0.0171017	−	0.0804571i
$657$	2.42341	+	4.75620i	0.0945460	+	0.185557i
$658$	−8.86593	−	5.61782i	−0.345630	−	0.219006i
$659$			20.1243i			0.783931i	0.919980	+	0.391966i	$0.128205\pi$
$659$			20.1243i			0.783931i	−0.919980	+	0.391966i	$0.871795\pi$
$660$	−4.18499	−	13.1093i	−0.162900	−	0.510277i
$661$	−12.8238	+	7.40380i	−0.498786	+	0.287974i	−0.728212	−	0.685352i	$-0.759648\pi$
$661$	−12.8238	+	7.40380i	−0.498786	+	0.287974i	0.229426	+	0.973326i	$0.426315\pi$
$662$	−12.1475	+	9.83683i	−0.472125	+	0.382319i
$663$	−0.655854	+	12.5144i	−0.0254713	+	0.486021i
$664$	−1.97455	−	6.07704i	−0.0766274	−	0.235835i
$665$	−9.45444	+	13.4170i	−0.366627	+	0.520290i
$666$	1.10501	−	0.802835i	0.0428182	−	0.0311092i
$667$	7.78132	+	11.9822i	0.301294	+	0.463952i
$668$	−20.4185	−	13.2599i	−0.790016	−	0.513043i
$669$	−46.7134	−	4.90977i	−1.80604	−	0.189823i
$670$	5.84798	+	1.54628i	0.225927	+	0.0597379i
$671$	−0.0737678	+	0.333182i	−0.00284778	+	0.0128623i
$672$	−4.08716	+	2.71961i	−0.157666	+	0.104911i
$673$	22.0992	−	3.50017i	0.851863	−	0.134922i	0.284790	−	0.958590i	$-0.408076\pi$
$673$	22.0992	−	3.50017i	0.851863	−	0.134922i	0.567072	+	0.823668i	$0.308076\pi$
$674$	15.1803	−	13.6684i	0.584723	−	0.526487i
$675$	−13.0515	−	19.8098i	−0.502353	−	0.762481i
$676$	9.15503	+	4.07608i	0.352117	+	0.156772i
$677$	−13.7958	−	11.1716i	−0.530216	−	0.429360i	0.326464	−	0.945210i	$-0.394143\pi$
$677$	−13.7958	−	11.1716i	−0.530216	−	0.429360i	−0.856679	+	0.515850i	$0.827476\pi$
$678$	3.62507	−	7.11461i	0.139220	−	0.273235i
$679$	−15.5019	+	0.173150i	−0.594910	+	0.00664490i
$680$	−3.10879	+	8.17933i	−0.119217	+	0.313663i
$681$	−7.73691	+	13.4007i	−0.296479	+	0.513517i
$682$	−11.5585	+	11.3648i	−0.442597	+	0.435180i
$683$	−17.8393	−	4.78002i	−0.682601	−	0.182902i	−0.0991768	−	0.995070i	$-0.531621\pi$
$683$	−17.8393	−	4.78002i	−0.682601	−	0.182902i	−0.583425	+	0.812167i	$0.698288\pi$
$684$	−1.12287	+	0.499935i	−0.0429341	+	0.0191155i
$685$	−9.79223	+	8.87571i	−0.374142	+	0.339123i
$686$	−12.8466	−	13.3403i	−0.490485	−	0.509337i
$687$	7.87377	+	1.24708i	0.300403	+	0.0475792i
$688$	0.756142	+	0.612312i	0.0288276	+	0.0233442i
$689$	9.32922	−	10.3611i	0.355415	−	0.394728i
$690$	−7.94488	−	2.55247i	−0.302456	−	0.0971707i
$691$	10.6449	+	23.9089i	0.404951	+	0.909536i	0.994783	+	0.102010i	$0.0325273\pi$
$691$	10.6449	+	23.9089i	0.404951	+	0.909536i	−0.589832	+	0.807526i	$0.700806\pi$
$692$	3.53965	−	3.53965i	0.134557	−	0.134557i
$693$	3.88278	+	0.192901i	0.147495	+	0.00732772i
$694$		−	4.80918i		−	0.182554i
$695$	−15.1561	+	12.3563i	−0.574905	+	0.468701i
$696$	2.74051	+	12.8931i	0.103879	+	0.488712i
$697$	8.23283	−	0.431464i	0.311840	−	0.0163429i
$698$	8.91375	−	11.0076i	0.337390	−	0.416642i
$699$	9.65200	−	7.01259i	0.365072	−	0.265240i
$700$	−13.1006	−	1.83687i	−0.495156	−	0.0694272i
$701$	−12.7765	+	39.3220i	−0.482562	+	1.48517i	0.352920	+	0.935653i	$0.385189\pi$
$701$	−12.7765	+	39.3220i	−0.482562	+	1.48517i	−0.835482	+	0.549518i	$0.814811\pi$
$702$	7.64455	+	2.93447i	0.288525	+	0.110754i
$703$	−2.21380	+	8.26202i	−0.0834951	+	0.311608i
$704$	1.92672	+	2.69958i	0.0726160	+	0.101744i
$705$	4.20760	−	15.9130i	0.158467	−	0.599320i
$706$	1.65950	−	2.28410i	0.0624560	−	0.0859634i
$707$	42.3842	+	10.8509i	1.59402	+	0.408091i
$708$	−7.63423	−	3.88984i	−0.286912	−	0.146189i
$709$	−17.2843	+	1.81665i	−0.649126	+	0.0682259i	−0.423368	−	0.905958i	$-0.639152\pi$
$709$	−17.2843	+	1.81665i	−0.649126	+	0.0682259i	−0.225758	+	0.974184i	$0.572486\pi$
$710$	−18.8190	−	25.7230i	−0.706263	−	0.965366i
$711$	−3.99039	+	4.43177i	−0.149651	+	0.166204i
$712$	9.38535	+	0.491866i	0.351731	+	0.0184334i
$713$	1.53771	+	9.70872i	0.0575877	+	0.363595i
$714$	−14.4193	−	12.6945i	−0.539629	−	0.475079i
$715$	2.59665	+	12.5331i	0.0971092	+	0.468712i
$716$	12.5588	−	21.7524i	0.469343	−	0.812926i
$717$	31.3455	+	38.7084i	1.17062	+	1.44559i
$718$	17.1442	−	26.3998i	0.639817	−	0.985231i
$719$	37.5055	+	7.97205i	1.39872	+	0.297307i	0.844720	−	0.535209i	$-0.179767\pi$
$719$	37.5055	+	7.97205i	1.39872	+	0.297307i	0.554001	+	0.832516i	$0.313100\pi$
$720$	−0.771930	−	0.620886i	−0.0287681	−	0.0231391i
$721$	10.8547	+	23.6652i	0.404251	+	0.881337i
$722$	−5.13135	+	10.0708i	−0.190969	+	0.374798i
$723$	44.8252	+	2.34919i	1.66707	+	0.0873673i
$724$	1.30264	−	12.3938i	0.0484123	−	0.460612i
$725$	−17.5556	+	30.8764i	−0.651998	+	1.14672i
$726$	0.344917	−	20.4080i	0.0128011	−	0.757413i
$727$	−19.5408	+	19.5408i	−0.724730	+	0.724730i	−0.969565	−	0.244835i	$-0.921266\pi$
$727$	−19.5408	+	19.5408i	−0.724730	+	0.724730i	0.244835	+	0.969565i	$0.421266\pi$
$728$	4.04509	−	2.11831i	0.149921	−	0.0785099i
$729$	−20.8491	−	6.77428i	−0.772189	−	0.250899i
$730$	−1.49890	−	26.9004i	−0.0554768	−	0.995628i
$731$	−1.54863	+	3.47827i	−0.0572780	+	0.128649i
$732$	0.0684189	+	0.178237i	0.00252884	+	0.00658785i
$733$	−26.5965	−	40.9551i	−0.982365	−	1.51271i	−0.853530	−	0.521044i	$-0.825543\pi$
$733$	−26.5965	−	40.9551i	−0.982365	−	1.51271i	−0.128835	−	0.991666i	$-0.541124\pi$
$734$	0.437178	−	1.34550i	0.0161366	−	0.0496632i
$735$	13.8723	−	25.5167i	0.511686	−	0.941198i
$736$	2.01123			0.0741350
$737$	7.48303	+	4.94993i	0.275641	+	0.182333i
$738$	−0.241569	+	0.901546i	−0.00889226	+	0.0331864i
$739$	−39.4553	−	4.14692i	−1.45139	−	0.152547i	−0.654220	−	0.756304i	$-0.727003\pi$
$739$	−39.4553	−	4.14692i	−1.45139	−	0.152547i	−0.797168	+	0.603757i	$0.793670\pi$
$740$	−6.73840	+	1.45557i	−0.247709	+	0.0535078i
$741$	8.44983	−	2.74552i	0.310412	−	0.100859i
$742$	3.57915	+	21.0719i	0.131395	+	0.773573i
$743$	−4.79630	+	30.2827i	−0.175959	+	1.11096i	0.728702	+	0.684831i	$0.240124\pi$
$743$	−4.79630	+	30.2827i	−0.175959	+	1.11096i	−0.904661	+	0.426132i	$0.859876\pi$
$744$	−1.88551	+	8.87064i	−0.0691263	+	0.325213i
$745$	−13.4991	−	26.2784i	−0.494567	−	0.962768i
$746$	−4.02082	+	38.2555i	−0.147213	+	1.40063i
$747$	0.732680	+	2.73440i	0.0268074	+	0.100046i
$748$	−8.25266	+	10.0169i	−0.301747	+	0.366255i
$749$	−8.07296	+	40.1820i	−0.294980	+	1.46822i
$750$	−3.44819	−	20.4570i	−0.125910	−	0.746984i
$751$	−9.69052	−	10.7624i	−0.353612	−	0.392726i	0.539927	−	0.841712i	$-0.318452\pi$
$751$	−9.69052	−	10.7624i	−0.353612	−	0.392726i	−0.893539	+	0.448986i	$0.851785\pi$
$752$	0.207621	+	3.96165i	0.00757118	+	0.144467i
$753$	−41.9394	+	16.0990i	−1.52835	+	0.586681i
$754$	−1.28151	−	12.1927i	−0.0466697	−	0.444033i
$755$	−2.30099	−	3.51772i	−0.0837415	−	0.128023i
$756$	−10.8004	+	6.39749i	−0.392806	+	0.232675i
$757$	6.17640	+	38.9962i	0.224485	+	1.41734i	0.800220	+	0.599706i	$0.204716\pi$
$757$	6.17640	+	38.9962i	0.224485	+	1.41734i	−0.575736	+	0.817636i	$0.695284\pi$
$758$	4.39441	+	16.4002i	0.159612	+	0.595681i
$759$	−9.95168	−	7.35959i	−0.361223	−	0.267136i
$760$	6.20369	−	0.0204907i	0.225031	−	0.000743275i
$761$	−2.54296	−	5.71157i	−0.0921821	−	0.207044i	0.861570	−	0.507639i	$-0.169482\pi$
$761$	−2.54296	−	5.71157i	−0.0921821	−	0.207044i	−0.953752	+	0.300595i	$0.902815\pi$
$762$	−1.83761	−	3.60651i	−0.0665695	−	0.130650i
$763$	−4.95864	+	1.96727i	−0.179515	+	0.0712198i
$764$	−4.73446	−	6.51643i	−0.171287	−	0.235756i
$765$	1.56505	−	3.54663i	0.0565844	−	0.128229i
$766$	16.7397	+	15.0725i	0.604829	+	0.544590i
$767$	6.68359	+	4.34037i	0.241330	+	0.156722i
$768$	1.73230	+	0.664966i	0.0625088	+	0.0239949i
$769$	−5.37962			−0.193994			−0.0969971	−	0.995285i	$-0.530924\pi$
$769$	−5.37962			−0.193994			−0.0969971	+	0.995285i	$0.530924\pi$
$770$	−17.5361	−	8.80249i	−0.631959	−	0.317220i
$771$	17.6266			0.634805
$772$	−8.84518	−	3.39535i	−0.318345	−	0.122201i
$773$	−27.6039	−	17.9262i	−0.992843	−	0.644760i	−0.0574421	−	0.998349i	$-0.518294\pi$
$773$	−27.6039	−	17.9262i	−0.992843	−	0.644760i	−0.935401	+	0.353589i	$0.884961\pi$
$774$	−0.320337	−	0.288432i	−0.0115143	−	0.0103675i
$775$	−19.6747	+	14.4941i	−0.706737	+	0.520642i
$776$	3.44416	+	4.74047i	0.123638	+	0.170173i
$777$	2.20059	−	14.9746i	0.0789457	−	0.537210i
$778$	−10.8340	−	21.2629i	−0.388417	−	0.762312i
$779$	−2.37735	−	5.33961i	−0.0851772	−	0.191311i
$780$	5.08012	+	5.04667i	0.181898	+	0.180700i
$781$	−14.2280	−	45.0819i	−0.509118	−	1.61316i
$782$	2.03700	+	7.60219i	0.0728430	+	0.271854i
$783$	5.27243	+	33.2888i	0.188421	+	1.18965i
$784$	−1.30208	+	6.87783i	−0.0465029	+	0.245637i
$785$	30.3542	+	6.34726i	1.08339	+	0.226543i
$786$	0.724824	+	6.89624i	0.0258536	+	0.245981i
$787$	8.12106	−	3.11738i	0.289484	−	0.111123i	−0.209292	−	0.977853i	$-0.567116\pi$
$787$	8.12106	−	3.11738i	0.289484	−	0.111123i	0.498777	+	0.866730i	$0.333783\pi$
$788$	−0.945227	−	18.0360i	−0.0336723	−	0.642506i
$789$	0.879844	+	0.977166i	0.0313233	+	0.0347880i
$790$	27.4565	−	12.3332i	0.976858	−	0.438797i
$791$	−3.63901	−	10.7882i	−0.129388	−	0.383584i
$792$	−0.789831	−	1.23903i	−0.0280654	−	0.0440270i
$793$	−0.0459597	−	0.171524i	−0.00163208	−	0.00609099i
$794$	−3.09787	+	29.4743i	−0.109939	+	1.04600i
$795$	−29.8149	+	15.3157i	−1.05742	+	0.543191i
$796$	−4.65699	+	21.9094i	−0.165063	+	0.776559i
$797$	−1.27232	+	8.03312i	−0.0450680	+	0.284548i	−0.999922	−	0.0125290i	$-0.996012\pi$
$797$	−1.27232	+	8.03312i	−0.0450680	+	0.284548i	0.954854	+	0.297077i	$0.0960118\pi$
$798$	−4.73876	+	12.7694i	−0.167750	+	0.452031i
$799$	−14.7642	+	4.79719i	−0.522321	+	0.169713i
$800$	2.29933	+	4.43994i	0.0812937	+	0.156976i
$801$	−4.14089	−	0.435225i	−0.146311	−	0.0153779i
$802$	4.67427	−	17.4446i	0.165054	−	0.615990i
$803$	10.6686	−	38.5112i	0.376487	−	1.35903i
$804$	5.01956			0.177026
$805$	−10.5224	+	5.55471i	−0.370868	+	0.195778i
$806$	2.60655	−	8.02215i	0.0918119	−	0.282568i
$807$	31.5606	+	48.5990i	1.11098	+	1.71077i
$808$	−5.92611	−	15.4380i	−0.208480	−	0.543109i
$809$	−1.81193	+	4.06967i	−0.0637042	+	0.143082i	−0.942592	−	0.333947i	$-0.891619\pi$
$809$	−1.81193	+	4.06967i	−0.0637042	+	0.143082i	0.878888	+	0.477028i	$0.158286\pi$
$810$	−16.8879	−	15.1052i	−0.593381	−	0.530744i
$811$	−47.0279	−	15.2803i	−1.65137	−	0.536563i	−0.672335	−	0.740247i	$-0.734708\pi$
$811$	−47.0279	−	15.2803i	−1.65137	−	0.536563i	−0.979037	+	0.203684i	$0.934708\pi$
$812$	15.8758	+	10.0595i	0.557130	+	0.353021i
$813$	15.5294	−	15.5294i	0.544640	−	0.544640i
$814$	−10.1598	−	1.15471i	−0.356100	−	0.0404726i
$815$	40.1413	−	0.132586i	1.40609	−	0.00464428i
$816$	−0.758993	+	7.22134i	−0.0265701	+	0.252797i
$817$	2.69571	+	0.141276i	0.0943108	+	0.00494262i
$818$	5.33347	−	10.4675i	0.186480	−	0.365988i
$819$	−1.83875	+	0.843398i	−0.0642513	+	0.0294707i
$820$	2.95251	−	3.67077i	0.103106	−	0.128189i
$821$	−23.1453	−	4.91969i	−0.807777	−	0.171698i	−0.214528	−	0.976718i	$-0.568821\pi$
$821$	−23.1453	−	4.91969i	−0.807777	−	0.171698i	−0.593248	+	0.805019i	$0.702155\pi$
$822$	−5.97308	+	9.19774i	−0.208335	+	0.320808i
$823$	−14.2066	−	17.5437i	−0.495212	−	0.611535i	0.466860	−	0.884331i	$-0.345385\pi$
$823$	−14.2066	−	17.5437i	−0.495212	−	0.611535i	−0.962072	+	0.272796i	$0.912052\pi$
$824$	4.92031	−	8.52223i	0.171407	−	0.296886i
$825$	4.86962	−	30.3829i	0.169538	−	1.05780i
$826$	−11.5761	+	3.90478i	−0.402785	+	0.135865i
$827$	−6.15828	−	38.8818i	−0.214144	−	1.35205i	−0.827153	−	0.561977i	$-0.810041\pi$
$827$	−6.15828	−	38.8818i	−0.214144	−	1.35205i	0.613008	−	0.790076i	$-0.289959\pi$
$828$	−0.889813	−	0.0466331i	−0.0309232	−	0.00162061i
$829$	25.5097	−	28.3314i	0.885990	−	0.983991i	−0.113965	−	0.993485i	$-0.536355\pi$
$829$	25.5097	−	28.3314i	0.885990	−	0.983991i	0.999955	+	0.00949349i	$0.00302192\pi$
$830$	2.18851	−	14.1194i	0.0759642	−	0.490091i
$831$	−6.85026	+	0.719991i	−0.237633	+	0.0249762i
$832$	−1.53775	−	0.783521i	−0.0533118	−	0.0271637i
$833$	−27.3161	+	2.04426i	−0.946445	+	0.0708295i
$834$	−9.53796	+	13.1279i	−0.330273	+	0.454581i
$835$	−27.3756	−	47.0562i	−0.947370	−	1.62845i
$836$	8.72691	+	2.91730i	0.301826	+	0.100897i
$837$	−6.00168	+	22.3986i	−0.207448	+	0.774208i
$838$	26.2403	+	10.0727i	0.906457	+	0.347956i
$839$	−12.0059	+	36.9503i	−0.414489	+	1.27567i	0.498218	+	0.867052i	$0.333988\pi$
$839$	−12.0059	+	36.9503i	−0.414489	+	1.27567i	−0.912707	+	0.408614i	$0.866012\pi$
$840$	−10.8996	+	1.30534i	−0.376073	+	0.0450384i
$841$	17.3632	−	12.6151i	0.598730	−	0.435003i
$842$	−6.77661	+	8.36842i	−0.233538	+	0.288395i
$843$	37.0361	−	1.94098i	1.27559	−	0.0668509i
$844$	−1.00811	−	4.74278i	−0.0347006	−	0.163253i
$845$	14.1596	+	17.3681i	0.487106	+	0.597480i
$846$		−	1.75754i		−	0.0604254i
$847$	−20.4609	−	20.6967i	−0.703043	−	0.711147i
$848$	5.71236	−	5.71236i	0.196163	−	0.196163i
$849$	−7.41091	−	16.6452i	−0.254342	−	0.571261i
$850$	−14.4536	+	13.1880i	−0.495754	+	0.452345i
$851$	−4.14904	+	4.60798i	−0.142227	+	0.157959i
$852$	−20.5540	−	16.6443i	−0.704170	−	0.570226i
$853$	46.4971	+	7.36442i	1.59203	+	0.252153i	0.888625	−	0.458634i	$-0.151661\pi$
$853$	46.4971	+	7.36442i	1.59203	+	0.252153i	0.703407	+	0.710787i	$0.251661\pi$
$854$	0.249910	+	0.107939i	0.00855174	+	0.00369359i
$855$	−2.74513	−	0.134775i	−0.0938813	−	0.00460922i
$856$	14.1516	−	6.30070i	0.483692	−	0.215353i
$857$	10.0713	+	2.69859i	0.344028	+	0.0921820i	0.426696	−	0.904395i	$-0.359677\pi$
$857$	10.0713	+	2.69859i	0.344028	+	0.0921820i	−0.0826680	+	0.996577i	$0.526344\pi$
$858$	4.74176	+	9.50390i	0.161881	+	0.324458i
$859$	14.0919	−	24.4080i	0.480811	−	0.832789i	−0.518947	−	0.854807i	$-0.673676\pi$
$859$	14.0919	−	24.4080i	0.480811	−	0.832789i	0.999758	+	0.0220178i	$0.00700905\pi$
$860$	0.891470	+	1.98461i	0.0303989	+	0.0676745i
$861$	5.27103	+	8.89867i	0.179636	+	0.303266i
$862$	−16.9838	+	33.3325i	−0.578470	+	1.13531i
$863$	31.8051	+	25.7553i	1.08266	+	0.876719i	0.992865	−	0.119241i	$-0.0380462\pi$
$863$	31.8051	+	25.7553i	1.08266	+	0.876719i	0.0897927	+	0.995960i	$0.471380\pi$
$864$	4.33437	+	1.92979i	0.147458	+	0.0656527i
$865$	10.6340	−	3.49408i	0.361568	−	0.118802i
$866$	2.52679	−	2.27513i	0.0858637	−	0.0773120i
$867$	3.09141	−	0.489631i	0.104990	−	0.0166288i
$868$	7.16337	+	10.7654i	0.243140	+	0.365403i
$869$	44.4378	−	4.29129i	1.50745	−	0.145572i
$870$	−7.53434	+	28.4947i	−0.255438	+	0.966060i
$871$	−4.64316	−	0.488016i	−0.157327	−	0.0165358i
$872$	1.69101	+	1.09816i	0.0572649	+	0.0371883i
$873$	−1.41386	−	2.17715i	−0.0478518	−	0.0736853i
$874$	4.51426	−	3.27980i	0.152697	−	0.110941i
$875$	−24.2922	−	16.8787i	−0.821226	−	0.570603i
$876$	−6.90875	−	21.2629i	−0.233425	−	0.718408i
$877$	1.97424	−	37.6707i	0.0666652	−	1.27205i	−0.736560	−	0.676373i	$-0.763551\pi$
$877$	1.97424	−	37.6707i	0.0666652	−	1.27205i	0.803225	−	0.595676i	$-0.203116\pi$
$878$	−2.46345	+	1.99486i	−0.0831374	+	0.0673233i
$879$	−15.2963	+	8.83131i	−0.515931	+	0.297873i
$880$	1.12243	+	7.33077i	0.0378373	+	0.247120i
$881$			41.5803i			1.40088i	0.713714	+	0.700438i	$0.247012\pi$
$881$			41.5803i			1.40088i	−0.713714	+	0.700438i	$0.752988\pi$
$882$	0.735541	−	3.01272i	0.0247670	−	0.101443i
$883$	4.36979	+	8.57620i	0.147055	+	0.288612i	0.952771	−	0.303691i	$-0.0982190\pi$
$883$	4.36979	+	8.57620i	0.147055	+	0.288612i	−0.805715	+	0.592303i	$0.798219\pi$
$884$	1.40416	−	6.60604i	0.0472269	−	0.222185i
$885$	−11.3124	−	15.4626i	−0.380263	−	0.519768i
$886$	−10.0179	−	4.46026i	−0.336558	−	0.149845i
$887$	2.65550	−	1.72450i	0.0891629	−	0.0579031i	−0.499288	−	0.866436i	$-0.666405\pi$
$887$	2.65550	−	1.72450i	0.0891629	−	0.0579031i	0.588450	+	0.808533i	$0.299738\pi$
$888$	−5.09714	+	2.59712i	−0.171049	+	0.0871537i
$889$	−5.50855	−	1.72206i	−0.184751	−	0.0577560i
$890$	18.2342	+	10.4474i	0.611212	+	0.350197i
$891$	−16.5569	−	29.2452i	−0.554675	−	0.979752i
$892$	24.4512	+	6.55168i	0.818687	+	0.219366i
$893$	6.92646	+	8.55346i	0.231785	+	0.286231i
$894$	−16.4040	−	18.2185i	−0.548631	−	0.609316i
$895$	47.0022	−	30.7448i	1.57111	−	1.02768i
$896$	2.40484	−	1.10305i	0.0803402	−	0.0368504i
$897$	6.36145	+	1.00756i	0.212403	+	0.0336413i
$898$	−2.10921	+	1.36974i	−0.0703854	+	0.0457088i
$899$	33.9600	−	7.21841i	1.13263	−	0.240748i
$900$	−0.914330	−	2.01764i	−0.0304777	−	0.0672547i
$901$	27.3775	+	15.8064i	0.912077	+	0.526588i
$902$	5.89197	−	3.75589i	0.196181	−	0.125058i
$903$	−4.76698	+	0.303249i	−0.158635	+	0.0100915i
$904$	−2.52941	+	3.48143i	−0.0841268	+	0.115791i
$905$	15.0997	−	23.4204i	0.501930	−	0.778522i
$906$	−2.59217	−	2.33400i	−0.0861190	−	0.0775419i
$907$	−3.99528	−	10.4081i	−0.132661	−	0.345594i	0.851119	−	0.524973i	$-0.175924\pi$
$907$	−3.99528	−	10.4081i	−0.132661	−	0.345594i	−0.983780	+	0.179379i	$0.942591\pi$
$908$	5.24806	−	6.48082i	0.174163	−	0.215073i
$909$	2.26389	+	6.96754i	0.0750885	+	0.231099i
$910$	10.2092	−	0.147759i	0.338432	−	0.00489817i
$911$	1.25441	+	0.911380i	0.0415604	+	0.0301954i	0.608371	−	0.793652i	$-0.291823\pi$
$911$	1.25441	+	0.911380i	0.0415604	+	0.0301954i	−0.566811	+	0.823848i	$0.691823\pi$
$912$	4.97258	−	1.33240i	0.164658	−	0.0441201i
$913$	9.78040	−	18.8007i	0.323684	−	0.622212i
$914$	−20.3821	+	11.7676i	−0.674179	+	0.389237i
$915$	−0.0432212	+	0.424712i	−0.00142885	+	0.0140406i
$916$	−4.08600	−	1.32762i	−0.135005	−	0.0438659i
$917$	7.75288	+	6.13606i	0.256023	+	0.202631i
$918$	−2.90443	+	18.3379i	−0.0958606	+	0.605240i
$919$	22.4850	−	2.36327i	0.741711	−	0.0779569i	0.273866	−	0.961768i	$-0.411697\pi$
$919$	22.4850	−	2.36327i	0.741711	−	0.0779569i	0.467844	+	0.883811i	$0.345031\pi$
$920$	4.01380	+	2.02846i	0.132331	+	0.0668764i
$921$	35.4052	−	7.52560i	1.16664	−	0.247977i
$922$	6.70552	−	17.4685i	0.220834	−	0.575293i
$923$	17.3946	+	17.3946i	0.572549	+	0.572549i
$924$	−15.9356	−	3.34196i	−0.524244	−	0.109942i
$925$	−14.9158	−	3.89126i	−0.490429	−	0.127944i
$926$	−26.9165	+	11.9840i	−0.884532	+	0.393819i
$927$	−2.37446	+	3.65634i	−0.0779873	+	0.120090i
$928$	−0.371777	−	7.09393i	−0.0122042	−	0.232870i
$929$	−0.178608	−	1.69934i	−0.00585993	−	0.0557535i	0.991201	−	0.132364i	$-0.0422568\pi$
$929$	−0.178608	−	1.69934i	−0.00585993	−	0.0557535i	−0.997061	+	0.0766107i	$0.975590\pi$
$930$	−12.7095	+	15.8014i	−0.416762	+	0.518149i
$931$	8.29343	+	17.5608i	0.271806	+	0.575534i
$932$	−5.72888	+	2.91901i	−0.187656	+	0.0956154i
$933$	−2.36211	+	6.15351i	−0.0773320	+	0.201457i
$934$	7.76951	+	13.4572i	0.254226	+	0.440332i
$935$	−26.5725	+	11.6673i	−0.869014	+	0.381563i
$936$	0.662167	+	0.382302i	0.0216436	+	0.0124959i
$937$	−11.8300	+	1.87370i	−0.386471	+	0.0612109i	−0.346647	−	0.937996i	$-0.612680\pi$
$937$	−11.8300	+	1.87370i	−0.386471	+	0.0612109i	−0.0398240	+	0.999207i	$0.512680\pi$
$938$	5.00408	−	5.11712i	0.163389	−	0.167080i
$939$	46.3212	−	15.0507i	1.51163	−	0.491160i
$940$	−3.58125	+	8.11565i	−0.116807	+	0.264703i
$941$	−18.2828	+	41.0638i	−0.596002	+	1.33864i	0.323750	+	0.946143i	$0.395056\pi$
$941$	−18.2828	+	41.0638i	−0.596002	+	1.33864i	−0.919752	+	0.392500i	$0.871610\pi$
$942$	25.6981	−	1.34678i	0.837290	−	0.0438805i
$943$	0.221755	−	4.23134i	0.00722134	−	0.137791i
$944$	3.73570	+	2.71414i	0.121587	+	0.0883378i
$945$	−28.0065	+	1.87452i	−0.911053	+	0.0609783i
$946$	0.310182	+	3.21204i	0.0100849	+	0.104433i
$947$	50.3955	−	13.5034i	1.63763	−	0.438802i	0.681519	−	0.731800i	$-0.261320\pi$
$947$	50.3955	−	13.5034i	1.63763	−	0.438802i	0.956113	+	0.292998i	$0.0946529\pi$
$948$	19.4108	−	15.7186i	0.630435	−	0.510516i
$949$	4.32344	+	20.3402i	0.140345	+	0.660271i
$950$	12.4013	+	6.21594i	0.402352	+	0.201672i
$951$	−30.0265	−	41.3279i	−0.973674	−	1.34015i
$952$	6.60505	+	7.97281i	0.214071	+	0.258400i
$953$	4.27323	+	2.17732i	0.138423	+	0.0705303i	0.521830	−	0.853049i	$-0.325249\pi$
$953$	4.27323	+	2.17732i	0.138423	+	0.0705303i	−0.383407	+	0.923579i	$0.625249\pi$
$954$	−2.65972	+	2.39483i	−0.0861117	+	0.0775353i
$955$	−2.87628	−	17.7798i	−0.0930741	−	0.575341i
$956$	−13.4216	−	23.2468i	−0.434084	−	0.751856i
$957$	−24.1189	+	36.4616i	−0.779652	+	1.17864i
$958$	−26.8819	−	26.8819i	−0.868516	−	0.868516i
$959$	3.42186	+	15.2585i	0.110498	+	0.492724i
$960$	2.78647	+	3.07421i	0.0899329	+	0.0992196i
$961$	−6.95762	−	1.47889i	−0.224439	−	0.0477061i
$962$	4.96742	−	1.90681i	0.160156	−	0.0614781i
$963$	−6.40707	+	2.45944i	−0.206465	+	0.0792545i
$964$	−23.6620	−	5.02952i	−0.762102	−	0.161990i
$965$	−14.2278	−	15.6970i	−0.458010	−	0.505305i
$966$	−7.26336	+	6.68836i	−0.233695	+	0.215194i
$967$	22.6662	+	22.6662i	0.728895	+	0.728895i	0.970400	−	0.241504i	$-0.0776408\pi$
$967$	22.6662	+	22.6662i	0.728895	+	0.728895i	−0.241504	+	0.970400i	$0.577641\pi$
$968$	−1.90413	+	10.8339i	−0.0612010	+	0.348216i
$969$	10.0726	+	17.4462i	0.323578	+	0.560453i
$970$	2.09239	+	12.9342i	0.0671826	+	0.415292i
$971$	11.4673	−	10.3252i	0.368004	−	0.331352i	−0.464294	−	0.885681i	$-0.653692\pi$
$971$	11.4673	−	10.3252i	0.368004	−	0.331352i	0.832298	+	0.554329i	$0.187025\pi$
$972$	−4.07026	−	2.07390i	−0.130554	−	0.0665204i
$973$	3.87451	+	22.8107i	0.124211	+	0.731279i
$974$	11.1433	+	15.3374i	0.357054	+	0.491443i
$975$	5.04846	+	15.1953i	0.161680	+	0.486638i
$976$	−0.0213922	−	0.100642i	−0.000684748	−	0.00322149i
$977$	34.2896	−	27.7672i	1.09702	−	0.888351i	0.102694	−	0.994713i	$-0.467254\pi$
$977$	34.2896	−	27.7672i	1.09702	−	0.888351i	0.994327	+	0.106362i	$0.0339203\pi$
$978$	32.1753	−	8.62135i	1.02885	−	0.275680i
$979$	20.6606	+	23.3395i	0.660316	+	0.745935i
$980$	−9.53531	+	12.4128i	−0.304594	+	0.396513i
$981$	−0.722679	−	0.525057i	−0.0230734	−	0.0167638i
$982$	1.01220	−	19.3139i	0.0323005	−	0.616331i
$983$	−34.9749	+	1.83296i	−1.11552	+	0.0584622i	−0.601174	−	0.799118i	$-0.705300\pi$
$983$	−34.9749	+	1.83296i	−1.11552	+	0.0584622i	−0.514351	+	0.857580i	$0.671967\pi$
$984$	1.58999	−	3.57118i	0.0506871	−	0.113845i
$985$	16.3042	−	36.9477i	0.519493	−	1.17725i
$986$	26.4376	−	8.59009i	0.841944	−	0.273564i
$987$	−13.9243	−	13.6167i	−0.443215	−	0.433424i
$988$	−4.72924	+	0.749038i	−0.150457	+	0.0238301i
$989$	1.69470	+	0.978436i	0.0538884	+	0.0311125i
$990$	−0.326616	−	3.26932i	−0.0103805	−	0.103906i
$991$	−5.53211	−	9.58190i	−0.175733	−	0.304379i	0.764681	−	0.644408i	$-0.222896\pi$
$991$	−5.53211	−	9.58190i	−0.175733	−	0.304379i	−0.940415	+	0.340029i	$0.889563\pi$
$992$	1.75150	−	4.56281i	0.0556101	−	0.144869i
$993$	−25.8425	+	13.1674i	−0.820087	+	0.417855i
$994$	−37.4585	+	4.36056i	−1.18811	+	0.138309i
$995$	−31.3911	+	39.0276i	−0.995164	+	1.23726i
$996$	−1.23934	−	11.7915i	−0.0392700	−	0.373629i
$997$	−2.92273	−	55.7691i	−0.0925639	−	1.76622i	−0.512516	−	0.858678i	$-0.671286\pi$
$997$	−2.92273	−	55.7691i	−0.0925639	−	1.76622i	0.419952	−	0.907546i	$-0.362047\pi$
$998$	−20.0447	+	30.8661i	−0.634503	+	0.977049i
$999$	−13.3629	+	5.94955i	−0.422784	+	0.188236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.257.5	yes	768
5.3	odd	4	inner	770.2.bv.a.103.20	yes	768
7.3	odd	6	inner	770.2.bv.a.367.44	yes	768
11.3	even	5	inner	770.2.bv.a.47.20	yes	768
35.3	even	12	inner	770.2.bv.a.213.20	yes	768
55.3	odd	20	inner	770.2.bv.a.663.44	yes	768
77.3	odd	30	inner	770.2.bv.a.157.20	yes	768
385.3	even	60	inner	770.2.bv.a.3.5	✓	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.5	✓	768	385.3	even	60	inner
770.2.bv.a.47.20	yes	768	11.3	even	5	inner
770.2.bv.a.103.20	yes	768	5.3	odd	4	inner
770.2.bv.a.157.20	yes	768	77.3	odd	30	inner
770.2.bv.a.213.20	yes	768	35.3	even	12	inner
770.2.bv.a.257.5	yes	768	1.1	even	1	trivial
770.2.bv.a.367.44	yes	768	7.3	odd	6	inner
770.2.bv.a.663.44	yes	768	55.3	odd	20	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)

\(f(q)\)	\(=\)	\(q+(-0.933580 - 0.358368i) q^{2} +(-1.55619 - 1.01060i) q^{3} +(0.743145 + 0.669131i) q^{4} +(0.808226 + 2.08489i) q^{5} +(1.09066 + 1.50116i) q^{6} +(2.61764 + 0.384675i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.180196 + 0.404728i) q^{9} +O(q^{10})\)	\(q+(-0.933580 - 0.358368i) q^{2} +(-1.55619 - 1.01060i) q^{3} +(0.743145 + 0.669131i) q^{4} +(0.808226 + 2.08489i) q^{5} +(1.09066 + 1.50116i) q^{6} +(2.61764 + 0.384675i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(0.180196 + 0.404728i) q^{9} +(-0.00738565 - 2.23606i) q^{10} +(1.05151 - 3.14553i) q^{11} +(-0.480249 - 1.79231i) q^{12} +(0.269983 + 1.70461i) q^{13} +(-2.30592 - 1.29720i) q^{14} +(0.849240 - 4.06127i) q^{15} +(0.104528 + 0.994522i) q^{16} +(-3.65329 + 1.40237i) q^{17} +(-0.0231864 - 0.442422i) q^{18} +(1.85643 + 2.06177i) q^{19} +(-0.794436 + 2.09018i) q^{20} +(-3.68478 - 3.24401i) q^{21} +(-2.10892 + 2.55977i) q^{22} +(0.520545 + 1.94270i) q^{23} +(-0.193957 + 1.84538i) q^{24} +(-3.69354 + 3.37013i) q^{25} +(0.358825 - 1.68814i) q^{26} +(-0.742213 + 4.68615i) q^{27} +(1.68789 + 2.03741i) q^{28} +(6.75599 - 2.19515i) q^{29} +(-2.24826 + 3.48718i) q^{30} +(4.86065 + 0.510875i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.81521 + 3.83237i) q^{33} +3.91321 q^{34} +(1.31364 + 5.76839i) q^{35} +(-0.136904 + 0.421346i) q^{36} +(1.67913 + 2.58563i) q^{37} +(-0.994252 - 2.59012i) q^{38} +(1.30253 - 2.92553i) q^{39} +(1.49072 - 1.66666i) q^{40} +(-2.00363 - 0.651020i) q^{41} +(2.27749 + 4.34905i) q^{42} +(0.687996 - 0.687996i) q^{43} +(2.88619 - 1.63398i) q^{44} +(-0.698174 + 0.702801i) q^{45} +(0.210231 - 2.00021i) q^{46} +(3.96165 + 0.207621i) q^{47} +(0.842398 - 1.65330i) q^{48} +(6.70405 + 2.01388i) q^{49} +(4.65596 - 1.82264i) q^{50} +(7.10244 + 1.50967i) q^{51} +(-0.939967 + 1.44742i) q^{52} +(-5.08396 - 6.27817i) q^{53} +(2.37228 - 4.10891i) q^{54} +(7.40793 - 0.350012i) q^{55} +(-0.845635 - 2.50697i) q^{56} +(-0.805323 - 5.08461i) q^{57} +(-7.09393 - 0.371777i) q^{58} +(3.08976 - 3.43153i) q^{59} +(3.34863 - 2.44986i) q^{60} +(-0.102327 + 0.0107550i) q^{61} +(-4.35473 - 2.21885i) q^{62} +(0.316000 + 1.12875i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-3.33571 + 1.94059i) q^{65} +(5.86879 - 1.85221i) q^{66} +(-0.700150 + 2.61300i) q^{67} +(-3.65329 - 1.40237i) q^{68} +(1.15323 - 3.54927i) q^{69} +(0.840821 - 5.85602i) q^{70} +(11.5314 - 8.37805i) q^{71} +(0.278807 - 0.344299i) q^{72} +(12.0324 - 0.630590i) q^{73} +(-0.640994 - 3.01564i) q^{74} +(9.15369 - 1.51185i) q^{75} +2.77439i q^{76} +(3.96247 - 7.82936i) q^{77} +(-2.26443 + 2.26443i) q^{78} +(5.47501 + 12.2971i) q^{79} +(-1.98899 + 1.02173i) q^{80} +(6.78018 - 7.53015i) q^{81} +(1.63725 + 1.32582i) q^{82} +(6.31111 + 0.999581i) q^{83} +(-0.567660 - 4.87637i) q^{84} +(-5.87647 - 6.48329i) q^{85} +(-0.888855 + 0.395744i) q^{86} +(-12.7320 - 3.41153i) q^{87} +(-3.28006 + 0.491137i) q^{88} +(-4.69912 + 8.13911i) q^{89} +(0.903662 - 0.405918i) q^{90} +(0.0509992 + 4.56590i) q^{91} +(-0.913080 + 1.79202i) q^{92} +(-7.04779 - 5.70719i) q^{93} +(-3.62412 - 1.61356i) q^{94} +(-2.79816 + 5.53683i) q^{95} +(-1.37894 + 1.24160i) q^{96} +(-5.78741 + 0.916635i) q^{97} +(-5.53706 - 4.28263i) q^{98} +(1.46256 - 0.141237i) 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

Groups

Database

Properties

Related objects

Downloads

Learn more