LMFDB - Embedded newform 450.2.q.a.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(31,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("450.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.q (of order $15$, degree $8$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			331.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	450.331
Dual form			450.2.q.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(-1.01807 - 1.40126i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.04275 - 0.909491i) q^{5} +(0.704489 + 1.58231i) q^{6} +(0.118034 - 0.204441i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.01807 - 1.40126i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.04275 - 0.909491i) q^{5} +(0.704489 + 1.58231i) q^{6} +(0.118034 - 0.204441i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 + 2.85317i) q^{9} +(1.80902 + 1.31433i) q^{10} +(-1.35177 - 0.287327i) q^{11} +(-0.360114 - 1.69420i) q^{12} +(-2.32991 + 0.495239i) q^{13} +(-0.157960 + 0.175433i) q^{14} +(0.805239 + 3.78835i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.42705 - 1.03681i) q^{17} +(1.50000 - 2.59808i) q^{18} +(3.42705 + 2.48990i) q^{19} +(-1.49622 - 1.66172i) q^{20} +(-0.406642 + 0.0427398i) q^{21} +(1.26249 + 0.562096i) q^{22} +(-1.49622 + 1.66172i) q^{23} +1.73205i q^{24} +(3.34565 + 3.71572i) q^{25} +2.38197 q^{26} +(4.94183 - 1.60570i) q^{27} +(0.190983 - 0.138757i) q^{28} +(0.482716 + 4.59274i) q^{29} -3.87298i q^{30} +(-0.701198 + 6.67146i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.973579 + 2.18669i) q^{33} +(1.18030 + 1.31086i) q^{34} +(-0.427051 + 0.310271i) q^{35} +(-2.00739 + 2.22943i) q^{36} +(1.47214 - 4.53077i) q^{37} +(-2.83448 - 3.14801i) q^{38} +(3.06598 + 2.76062i) q^{39} +(1.11803 + 1.93649i) q^{40} +(-0.373619 + 0.0794152i) q^{41} +(0.406642 + 0.0427398i) q^{42} +(-1.73607 + 3.00696i) q^{43} +(-1.11803 - 0.812299i) q^{44} +(4.48866 - 4.98517i) q^{45} +(1.80902 - 1.31433i) q^{46} +(0.741125 + 7.05133i) q^{47} +(0.360114 - 1.69420i) q^{48} +(3.47214 + 6.01392i) q^{49} +(-2.50000 - 4.33013i) q^{50} +3.05522i q^{51} +(-2.32991 - 0.495239i) q^{52} +(0.0729490 - 0.0530006i) q^{53} +(-5.16769 + 0.543146i) q^{54} +(2.50000 + 1.81636i) q^{55} +(-0.215659 + 0.0960175i) q^{56} -7.33708i q^{57} +(0.482716 - 4.59274i) q^{58} +(-0.461819 + 0.0981626i) q^{59} +(-0.805239 + 3.78835i) q^{60} +(-14.1014 - 2.99734i) q^{61} +(2.07295 - 6.37988i) q^{62} +(0.473881 + 0.526298i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.20985 + 1.10739i) q^{65} +(-0.497665 - 2.34133i) q^{66} +(-0.298335 + 2.83847i) q^{67} +(-0.881966 - 1.52761i) q^{68} +(3.85177 + 0.404837i) q^{69} +(0.482228 - 0.214702i) q^{70} +(-7.09017 + 5.15131i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-1.85410 - 5.70634i) q^{73} +(-2.38197 + 4.12569i) q^{74} +(1.80057 - 8.47101i) q^{75} +(2.11803 + 3.66854i) q^{76} +(-0.218296 + 0.242442i) q^{77} +(-2.42502 - 3.33775i) q^{78} +(0.581419 + 5.53184i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-7.28115 - 5.29007i) q^{81} +0.381966 q^{82} +(-2.65826 + 1.18353i) q^{83} +(-0.388870 - 0.126351i) q^{84} +(1.97214 + 3.41584i) q^{85} +(2.32331 - 2.58030i) q^{86} +(5.94417 - 5.35215i) q^{87} +(0.924716 + 1.02700i) q^{88} +(-2.07295 - 6.37988i) q^{89} +(-5.42705 + 3.94298i) q^{90} +(-0.173762 + 0.534785i) q^{91} +(-2.04275 + 0.909491i) q^{92} +(10.0623 - 5.80948i) q^{93} +(0.741125 - 7.05133i) q^{94} +(-4.73607 - 8.20311i) q^{95} +(-0.704489 + 1.58231i) q^{96} +(0.258409 + 2.45859i) q^{97} +(-2.14590 - 6.60440i) q^{98} +(2.07295 - 3.59045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 5 q^{5} + 3 q^{6} - 8 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q + q^2 + q^4 - 5 * q^5 + 3 * q^6 - 8 * q^7 - 2 * q^8 + 6 * q^9	$ 8 q + q^{2} + q^{4} - 5 q^{5} + 3 q^{6} - 8 q^{7} - 2 q^{8} + 6 q^{9} + 10 q^{10} + 5 q^{11} - 3 q^{12} + 6 q^{13} + 7 q^{14} - 15 q^{15} + q^{16} + 2 q^{17} + 12 q^{18} + 14 q^{19} + 5 q^{20} - 9 q^{21} + 5 q^{23} + 5 q^{25} + 28 q^{26} + 6 q^{28} - 6 q^{29} + 15 q^{31} - 4 q^{32} + 9 q^{34} + 10 q^{35} - 3 q^{36} - 24 q^{37} + 3 q^{38} - 18 q^{39} + 4 q^{41} + 9 q^{42} + 4 q^{43} - 15 q^{45} + 10 q^{46} - 14 q^{47} + 3 q^{48} - 8 q^{49} - 20 q^{50} + 6 q^{52} + 14 q^{53} - 9 q^{54} + 20 q^{55} - 3 q^{56} - 6 q^{58} - 14 q^{59} + 15 q^{60} - 29 q^{61} + 30 q^{62} - 21 q^{63} - 2 q^{64} + 20 q^{65} - 15 q^{66} + 7 q^{67} - 16 q^{68} + 15 q^{69} - 5 q^{70} - 12 q^{71} + 6 q^{72} + 12 q^{73} - 28 q^{74} + 15 q^{75} + 8 q^{76} + 25 q^{77} - 18 q^{79} - 10 q^{80} - 18 q^{81} + 12 q^{82} + 4 q^{83} - 20 q^{85} - 11 q^{86} - 3 q^{87} + 5 q^{88} - 30 q^{89} - 30 q^{90} - 64 q^{91} - 5 q^{92} - 14 q^{94} - 20 q^{95} - 3 q^{96} - 8 q^{97} - 44 q^{98} + 30 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^4 - 5 * q^5 + 3 * q^6 - 8 * q^7 - 2 * q^8 + 6 * q^9 + 10 * q^10 + 5 * q^11 - 3 * q^12 + 6 * q^13 + 7 * q^14 - 15 * q^15 + q^16 + 2 * q^17 + 12 * q^18 + 14 * q^19 + 5 * q^20 - 9 * q^21 + 5 * q^23 + 5 * q^25 + 28 * q^26 + 6 * q^28 - 6 * q^29 + 15 * q^31 - 4 * q^32 + 9 * q^34 + 10 * q^35 - 3 * q^36 - 24 * q^37 + 3 * q^38 - 18 * q^39 + 4 * q^41 + 9 * q^42 + 4 * q^43 - 15 * q^45 + 10 * q^46 - 14 * q^47 + 3 * q^48 - 8 * q^49 - 20 * q^50 + 6 * q^52 + 14 * q^53 - 9 * q^54 + 20 * q^55 - 3 * q^56 - 6 * q^58 - 14 * q^59 + 15 * q^60 - 29 * q^61 + 30 * q^62 - 21 * q^63 - 2 * q^64 + 20 * q^65 - 15 * q^66 + 7 * q^67 - 16 * q^68 + 15 * q^69 - 5 * q^70 - 12 * q^71 + 6 * q^72 + 12 * q^73 - 28 * q^74 + 15 * q^75 + 8 * q^76 + 25 * q^77 - 18 * q^79 - 10 * q^80 - 18 * q^81 + 12 * q^82 + 4 * q^83 - 20 * q^85 - 11 * q^86 - 3 * q^87 + 5 * q^88 - 30 * q^89 - 30 * q^90 - 64 * q^91 - 5 * q^92 - 14 * q^94 - 20 * q^95 - 3 * q^96 - 8 * q^97 - 44 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	−1.01807	−	1.40126i	−0.587785	−	0.809017i
$3$	−1.01807	−	1.40126i	−0.587785	−	0.809017i
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−2.04275	−	0.909491i	−0.913545	−	0.406737i
$5$	−2.04275	−	0.909491i	−0.913545	−	0.406737i
$6$	0.704489	+	1.58231i	0.287606	+	0.645974i
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	−0.842857	−	0.538138i	$-0.819128\pi$
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	0.887469	+	0.460866i	$0.152461\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.927051	+	2.85317i	−0.309017	+	0.951057i
$10$	1.80902	+	1.31433i	0.572061	+	0.415627i
$11$	−1.35177	−	0.287327i	−0.407573	−	0.0866323i	−0.000437096	−	1.00000i	$-0.500139\pi$
$11$	−1.35177	−	0.287327i	−0.407573	−	0.0866323i	−0.407136	+	0.913368i	$0.633472\pi$
$12$	−0.360114	−	1.69420i	−0.103956	−	0.489074i
$13$	−2.32991	+	0.495239i	−0.646202	+	0.137354i	−0.519342	−	0.854566i	$-0.673823\pi$
$13$	−2.32991	+	0.495239i	−0.646202	+	0.137354i	−0.126860	+	0.991921i	$0.540490\pi$
$14$	−0.157960	+	0.175433i	−0.0422167	+	0.0468864i
$15$	0.805239	+	3.78835i	0.207912	+	0.978148i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−1.42705	−	1.03681i	−0.346111	−	0.251464i	0.401125	−	0.916023i	$-0.368619\pi$
$17$	−1.42705	−	1.03681i	−0.346111	−	0.251464i	−0.747236	+	0.664559i	$0.768619\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	3.42705	+	2.48990i	0.786219	+	0.571222i	0.906839	−	0.421477i	$-0.138488\pi$
$19$	3.42705	+	2.48990i	0.786219	+	0.571222i	−0.120620	+	0.992699i	$0.538488\pi$
$20$	−1.49622	−	1.66172i	−0.334565	−	0.371572i
$21$	−0.406642	+	0.0427398i	−0.0887365	+	0.00932658i
$22$	1.26249	+	0.562096i	0.269164	+	0.119839i
$23$	−1.49622	+	1.66172i	−0.311984	+	0.346493i	−0.878660	−	0.477447i	$-0.841562\pi$
$23$	−1.49622	+	1.66172i	−0.311984	+	0.346493i	0.566677	+	0.823940i	$0.308229\pi$
$24$			1.73205i			0.353553i
$25$	3.34565	+	3.71572i	0.669131	+	0.743145i
$26$	2.38197			0.467142
$27$	4.94183	−	1.60570i	0.951057	−	0.309017i
$28$	0.190983	−	0.138757i	0.0360924	−	0.0262227i
$29$	0.482716	+	4.59274i	0.0896381	+	0.852850i	0.943282	+	0.331993i	$0.107721\pi$
$29$	0.482716	+	4.59274i	0.0896381	+	0.852850i	−0.853644	+	0.520857i	$0.825612\pi$
$30$		−	3.87298i		−	0.707107i
$31$	−0.701198	+	6.67146i	−0.125939	+	1.19823i	0.730841	+	0.682547i	$0.239128\pi$
$31$	−0.701198	+	6.67146i	−0.125939	+	1.19823i	−0.856780	+	0.515682i	$0.827539\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.973579	+	2.18669i	0.169478	+	0.380655i
$34$	1.18030	+	1.31086i	0.202420	+	0.224810i
$35$	−0.427051	+	0.310271i	−0.0721848	+	0.0524453i
$36$	−2.00739	+	2.22943i	−0.334565	+	0.371572i
$37$	1.47214	−	4.53077i	0.242018	−	0.744854i	−0.754095	−	0.656765i	$-0.771924\pi$
$37$	1.47214	−	4.53077i	0.242018	−	0.744854i	0.996113	−	0.0880884i	$-0.0280758\pi$
$38$	−2.83448	−	3.14801i	−0.459814	−	0.510675i
$39$	3.06598	+	2.76062i	0.490950	+	0.442053i
$40$	1.11803	+	1.93649i	0.176777	+	0.306186i
$41$	−0.373619	+	0.0794152i	−0.0583495	+	0.0124026i	−0.236994	−	0.971511i	$-0.576162\pi$
$41$	−0.373619	+	0.0794152i	−0.0583495	+	0.0124026i	0.178644	+	0.983914i	$0.442829\pi$
$42$	0.406642	+	0.0427398i	0.0627462	+	0.00659489i
$43$	−1.73607	+	3.00696i	−0.264748	+	0.458557i	−0.967498	−	0.252880i	$-0.918622\pi$
$43$	−1.73607	+	3.00696i	−0.264748	+	0.458557i	0.702750	+	0.711437i	$0.251955\pi$
$44$	−1.11803	−	0.812299i	−0.168550	−	0.122459i
$45$	4.48866	−	4.98517i	0.669131	−	0.743145i
$46$	1.80902	−	1.31433i	0.266725	−	0.193787i
$47$	0.741125	+	7.05133i	0.108104	+	1.02854i	0.905286	+	0.424803i	$0.139657\pi$
$47$	0.741125	+	7.05133i	0.108104	+	1.02854i	−0.797182	+	0.603739i	$0.793677\pi$
$48$	0.360114	−	1.69420i	0.0519779	−	0.244537i
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$			3.05522i			0.427816i
$52$	−2.32991	−	0.495239i	−0.323101	−	0.0686772i
$53$	0.0729490	−	0.0530006i	0.0100203	−	0.00728019i	−0.582764	−	0.812642i	$-0.698029\pi$
$53$	0.0729490	−	0.0530006i	0.0100203	−	0.00728019i	0.592784	+	0.805361i	$0.298029\pi$
$54$	−5.16769	+	0.543146i	−0.703233	+	0.0739128i
$55$	2.50000	+	1.81636i	0.337100	+	0.244917i
$56$	−0.215659	+	0.0960175i	−0.0288186	+	0.0128309i
$57$		−	7.33708i		−	0.971821i
$58$	0.482716	−	4.59274i	0.0633837	−	0.603056i
$59$	−0.461819	+	0.0981626i	−0.0601237	+	0.0127797i	−0.237875	−	0.971296i	$-0.576451\pi$
$59$	−0.461819	+	0.0981626i	−0.0601237	+	0.0127797i	0.177752	+	0.984075i	$0.443118\pi$
$60$	−0.805239	+	3.78835i	−0.103956	+	0.489074i
$61$	−14.1014	−	2.99734i	−1.80550	−	0.383770i	−0.822702	−	0.568473i	$-0.807534\pi$
$61$	−14.1014	−	2.99734i	−1.80550	−	0.383770i	−0.982794	+	0.184703i	$0.940868\pi$
$62$	2.07295	−	6.37988i	0.263265	−	0.810246i
$63$	0.473881	+	0.526298i	0.0597034	+	0.0663073i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.20985	+	1.10739i	0.646202	+	0.137354i
$66$	−0.497665	−	2.34133i	−0.0612583	−	0.288198i
$67$	−0.298335	+	2.83847i	−0.0364474	+	0.346774i	0.961067	+	0.276315i	$0.0891132\pi$
$67$	−0.298335	+	2.83847i	−0.0364474	+	0.346774i	−0.997515	+	0.0704593i	$0.977553\pi$
$68$	−0.881966	−	1.52761i	−0.106954	−	0.185250i
$69$	3.85177	+	0.404837i	0.463698	+	0.0487366i
$70$	0.482228	−	0.214702i	0.0576372	−	0.0256618i
$71$	−7.09017	+	5.15131i	−0.841448	+	0.611348i	−0.922775	−	0.385339i	$-0.874084\pi$
$71$	−7.09017	+	5.15131i	−0.841448	+	0.611348i	0.0813265	+	0.996688i	$0.474084\pi$
$72$	2.42705	−	1.76336i	0.286031	−	0.207813i
$73$	−1.85410	−	5.70634i	−0.217006	−	0.667876i	−0.999005	−	0.0445966i	$-0.985800\pi$
$73$	−1.85410	−	5.70634i	−0.217006	−	0.667876i	0.781999	−	0.623280i	$-0.214200\pi$
$74$	−2.38197	+	4.12569i	−0.276898	+	0.479601i
$75$	1.80057	−	8.47101i	0.207912	−	0.978148i
$76$	2.11803	+	3.66854i	0.242955	+	0.420811i
$77$	−0.218296	+	0.242442i	−0.0248771	+	0.0276288i
$78$	−2.42502	−	3.33775i	−0.274579	−	0.377926i
$79$	0.581419	+	5.53184i	0.0654148	+	0.622380i	0.977289	+	0.211910i	$0.0679685\pi$
$79$	0.581419	+	5.53184i	0.0654148	+	0.622380i	−0.911874	+	0.410470i	$0.865365\pi$
$80$	−0.690983	−	2.12663i	−0.0772542	−	0.237764i
$81$	−7.28115	−	5.29007i	−0.809017	−	0.587785i
$82$	0.381966			0.0421811
$83$	−2.65826	+	1.18353i	−0.291782	+	0.129910i	−0.547408	−	0.836866i	$-0.684385\pi$
$83$	−2.65826	+	1.18353i	−0.291782	+	0.129910i	0.255625	+	0.966776i	$0.417719\pi$
$84$	−0.388870	−	0.126351i	−0.0424292	−	0.0137861i
$85$	1.97214	+	3.41584i	0.213908	+	0.370500i
$86$	2.32331	−	2.58030i	0.250529	−	0.278241i
$87$	5.94417	−	5.35215i	0.637282	−	0.573811i
$88$	0.924716	+	1.02700i	0.0985750	+	0.109479i
$89$	−2.07295	−	6.37988i	−0.219732	−	0.676266i	−0.998784	−	0.0493062i	$-0.984299\pi$
$89$	−2.07295	−	6.37988i	−0.219732	−	0.676266i	0.779052	−	0.626960i	$-0.215701\pi$
$90$	−5.42705	+	3.94298i	−0.572061	+	0.415627i
$91$	−0.173762	+	0.534785i	−0.0182152	+	0.0560607i
$92$	−2.04275	+	0.909491i	−0.212971	+	0.0948210i
$93$	10.0623	−	5.80948i	1.04341	−	0.602414i
$94$	0.741125	−	7.05133i	0.0764412	−	0.727289i
$95$	−4.73607	−	8.20311i	−0.485910	−	0.841621i
$96$	−0.704489	+	1.58231i	−0.0719016	+	0.161494i
$97$	0.258409	+	2.45859i	0.0262374	+	0.249632i	0.999777	+	0.0211142i	$0.00672136\pi$
$97$	0.258409	+	2.45859i	0.0262374	+	0.249632i	−0.973540	+	0.228518i	$0.926612\pi$
$98$	−2.14590	−	6.60440i	−0.216768	−	0.667145i
$99$	2.07295	−	3.59045i	0.208339	−	0.360854i
$100$	1.54508	+	4.75528i	0.154508	+	0.475528i
$101$	2.19098	−	3.79489i	0.218011	−	0.377606i	−0.736189	−	0.676776i	$-0.763376\pi$
$101$	2.19098	−	3.79489i	0.218011	−	0.377606i	0.954200	+	0.299170i	$0.0967098\pi$
$102$	0.635216	−	2.98846i	0.0628957	−	0.295901i
$103$	−18.0043	−	8.01605i	−1.77402	−	0.789845i	−0.984329	−	0.176340i	$-0.943574\pi$
$103$	−18.0043	−	8.01605i	−1.77402	−	0.789845i	−0.789691	−	0.613505i	$-0.789759\pi$
$104$	2.17603	+	0.968833i	0.213378	+	0.0950019i
$105$	0.869539	+	0.282530i	0.0848583	+	0.0275721i
$106$	−0.0823743	+	0.0366754i	−0.00800090	+	0.00356223i
$107$	−9.61803			−0.929810			−0.464905	−	0.885360i	$-0.653912\pi$
$107$	−9.61803			−0.929810			−0.464905	+	0.885360i	$0.653912\pi$
$108$	5.16769	+	0.543146i	0.497261	+	0.0522642i
$109$	6.20820	−	19.1069i	0.594638	−	1.83011i	0.0381187	−	0.999273i	$-0.487863\pi$
$109$	6.20820	−	19.1069i	0.594638	−	1.83011i	0.556519	−	0.830835i	$-0.312137\pi$
$110$	−2.06773	−	2.29644i	−0.197150	−	0.218957i
$111$	−7.84752	+	2.54981i	−0.744854	+	0.242018i
$112$	0.230909	−	0.0490813i	0.0218189	−	0.00463775i
$113$	−10.0124	+	2.12820i	−0.941886	+	0.200204i	−0.653170	−	0.757211i	$-0.726562\pi$
$113$	−10.0124	+	2.12820i	−0.941886	+	0.200204i	−0.288716	+	0.957415i	$0.593228\pi$
$114$	−1.52547	+	7.17675i	−0.142873	+	0.672164i
$115$	4.56773	−	2.03368i	0.425943	−	0.189642i
$116$	−1.42705	+	4.39201i	−0.132498	+	0.407788i
$117$	0.746950	−	7.10675i	0.0690555	−	0.657019i
$118$	0.472136			0.0434636
$119$	−0.380408	+	0.169368i	−0.0348719	+	0.0155260i
$120$	1.57528	−	3.53815i	0.143803	−	0.322987i
$121$	−8.30428	−	3.69731i	−0.754935	−	0.336119i
$122$	13.1700	+	5.86368i	1.19236	+	0.530873i
$123$	0.491653	+	0.442686i	0.0443309	+	0.0399157i
$124$	−3.35410	+	5.80948i	−0.301207	+	0.521706i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−0.354102	−	0.613323i	−0.0315459	−	0.0546391i
$127$	5.42705	+	16.7027i	0.481573	+	1.48213i	0.836884	+	0.547381i	$0.184375\pi$
$127$	5.42705	+	16.7027i	0.481573	+	1.48213i	−0.355311	+	0.934748i	$0.615625\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	5.98097	−	0.628625i	0.526595	−	0.0553474i
$130$	−4.86576	−	2.16638i	−0.426755	−	0.190004i
$131$	1.10989	−	10.5599i	0.0969713	−	0.922620i	−0.832574	−	0.553913i	$-0.813134\pi$
$131$	1.10989	−	10.5599i	0.0969713	−	0.922620i	0.929546	−	0.368707i	$-0.120199\pi$
$132$			2.39364i			0.208339i
$133$	0.913545	−	0.406737i	0.0792144	−	0.0352685i
$134$	0.881966	−	2.71441i	0.0761903	−	0.234490i
$135$	−11.5553	−	1.21451i	−0.994522	−	0.104528i
$136$	0.545085	+	1.67760i	0.0467407	+	0.143853i
$137$	14.2327	+	15.8071i	1.21599	+	1.35049i	0.918330	+	0.395816i	$0.129538\pi$
$137$	14.2327	+	15.8071i	1.21599	+	1.35049i	0.297656	+	0.954673i	$0.403795\pi$
$138$	−3.68343	−	1.19682i	−0.313554	−	0.101880i
$139$	5.15780	−	5.72831i	0.437478	−	0.485869i	−0.483576	−	0.875302i	$-0.660662\pi$
$139$	5.15780	−	5.72831i	0.437478	−	0.485869i	0.921055	+	0.389433i	$0.127329\pi$
$140$	−0.516329	+	0.109749i	−0.0436378	+	0.00927549i
$141$	9.12622	−	8.21728i	0.768566	−	0.692020i
$142$	8.00625	−	3.56461i	0.671870	−	0.299136i
$143$	3.29180			0.275274
$144$	−2.74064	+	1.22021i	−0.228386	+	0.101684i
$145$	3.19098	−	9.82084i	0.264997	−	0.815576i
$146$	0.627171	+	5.96713i	0.0519050	+	0.493843i
$147$	4.89216	−	10.9880i	0.403499	−	0.906273i
$148$	3.18769	−	3.54029i	0.262027	−	0.291010i
$149$	8.42705	+	14.5961i	0.690371	+	1.19576i	0.971716	+	0.236151i	$0.0758860\pi$
$149$	8.42705	+	14.5961i	0.690371	+	1.19576i	−0.281345	+	0.959607i	$0.590781\pi$
$150$	−3.52244	+	7.91154i	−0.287606	+	0.645974i
$151$	−3.59017	+	6.21836i	−0.292164	+	0.506043i	−0.974321	−	0.225163i	$-0.927709\pi$
$151$	−3.59017	+	6.21836i	−0.292164	+	0.506043i	0.682157	+	0.731205i	$0.261042\pi$
$152$	−1.30902	−	4.02874i	−0.106175	−	0.326774i
$153$	4.28115	−	3.11044i	0.346111	−	0.251464i
$154$	0.263932	−	0.191758i	0.0212682	−	0.0154523i
$155$	7.50000	−	12.9904i	0.602414	−	1.04341i
$156$	1.67807	+	3.76900i	0.134353	+	0.301762i
$157$	−9.23607	−	15.9973i	−0.737118	−	1.27673i	−0.953788	−	0.300482i	$-0.902853\pi$
$157$	−9.23607	−	15.9973i	−0.737118	−	1.27673i	0.216669	−	0.976245i	$-0.430481\pi$
$158$	0.581419	−	5.53184i	0.0462552	−	0.440089i
$159$	−0.148535	−	0.0482619i	−0.0117796	−	0.00382742i
$160$	0.233733	+	2.22382i	0.0184782	+	0.175808i
$161$	0.163119	+	0.502029i	0.0128556	+	0.0395654i
$162$	6.02218	+	6.68830i	0.473147	+	0.525483i
$163$	−5.25329	+	16.1680i	−0.411469	+	1.26637i	0.503902	+	0.863761i	$0.331897\pi$
$163$	−5.25329	+	16.1680i	−0.411469	+	1.26637i	−0.915371	+	0.402611i	$0.868103\pi$
$164$	−0.373619	−	0.0794152i	−0.0291748	−	0.00620129i
$165$		−	5.35233i		−	0.416678i
$166$	2.84624	−	0.604988i	0.220911	−	0.0469562i
$167$	−2.18927	+	20.8295i	−0.169411	+	1.61184i	0.498019	+	0.867166i	$0.334061\pi$
$167$	−2.18927	+	20.8295i	−0.169411	+	1.61184i	−0.667430	+	0.744672i	$0.732606\pi$
$168$	0.354102	+	0.204441i	0.0273196	+	0.0157730i
$169$	−6.69285	+	2.97985i	−0.514835	+	0.229219i
$170$	−1.21885	−	3.75123i	−0.0934813	−	0.287706i
$171$	−10.2812	+	7.46969i	−0.786219	+	0.571222i
$172$	−2.80902	+	2.04087i	−0.214186	+	0.155615i
$173$	−5.12165	−	1.08864i	−0.389392	−	0.0827677i	0.00905561	−	0.999959i	$-0.497117\pi$
$173$	−5.12165	−	1.08864i	−0.389392	−	0.0827677i	−0.398447	+	0.917191i	$0.630451\pi$
$174$	−6.92705	+	3.99933i	−0.525138	+	0.303189i
$175$	1.15455	−	0.245406i	0.0872755	−	0.0185510i
$176$	−0.690983	−	1.19682i	−0.0520848	−	0.0902135i
$177$	0.607717	+	0.547191i	0.0456788	+	0.0411294i
$178$	0.701198	+	6.67146i	0.0525570	+	0.500047i
$179$	0.572949	−	0.416272i	0.0428242	−	0.0311136i	−0.566167	−	0.824290i	$-0.691574\pi$
$179$	0.572949	−	0.416272i	0.0428242	−	0.0311136i	0.608991	+	0.793177i	$0.291574\pi$
$180$	6.12825	−	2.72847i	0.456773	−	0.203368i
$181$	−1.85410	−	1.34708i	−0.137814	−	0.100128i	0.516742	−	0.856141i	$-0.327145\pi$
$181$	−1.85410	−	1.34708i	−0.137814	−	0.100128i	−0.654556	+	0.756013i	$0.727145\pi$
$182$	0.281153	−	0.486971i	0.0208404	−	0.0360967i
$183$	10.1562	+	22.8112i	0.750767	+	1.68625i
$184$	2.18720	−	0.464905i	0.161243	−	0.0342732i
$185$	−7.12790	+	7.91633i	−0.524053	+	0.582020i
$186$	−11.0503	+	3.59045i	−0.810246	+	0.263265i
$187$	1.63114	+	1.81156i	0.119280	+	0.132474i
$188$	−2.19098	+	6.74315i	−0.159794	+	0.491795i
$189$	0.255034	−	1.19984i	0.0185510	−	0.0872755i
$190$	2.92705	+	9.00854i	0.212351	+	0.653548i
$191$	5.86422	+	6.51287i	0.424320	+	0.471255i	0.916961	−	0.398978i	$-0.130635\pi$
$191$	5.86422	+	6.51287i	0.424320	+	0.471255i	−0.492641	+	0.870233i	$0.663968\pi$
$192$	1.01807	−	1.40126i	0.0734732	−	0.101127i
$193$	−6.59017	−	11.4145i	−0.474371	−	0.821634i	0.525199	−	0.850980i	$-0.323991\pi$
$193$	−6.59017	−	11.4145i	−0.474371	−	0.821634i	−0.999569	+	0.0293454i	$0.990658\pi$
$194$	0.258409	−	2.45859i	0.0185527	−	0.176517i
$195$	−3.75227	−	8.42774i	−0.268706	−	0.603523i
$196$	0.725874	+	6.90623i	0.0518481	+	0.493302i
$197$	−11.4721	+	8.33499i	−0.817356	+	0.593844i	−0.915954	−	0.401284i	$-0.868564\pi$
$197$	−11.4721	+	8.33499i	−0.817356	+	0.593844i	0.0985980	+	0.995127i	$0.468564\pi$
$198$	−2.77415	+	3.08100i	−0.197150	+	0.218957i
$199$	26.5623			1.88295			0.941476	−	0.337080i	$-0.109439\pi$
$199$	26.5623			1.88295			0.941476	+	0.337080i	$0.109439\pi$
$200$	−0.522642	−	4.97261i	−0.0369564	−	0.351617i
$201$	4.28115	−	2.47172i	0.301969	−	0.174342i
$202$	−2.93211	+	3.25644i	−0.206302	+	0.229122i
$203$	0.995920	+	0.443412i	0.0698999	+	0.0311214i
$204$	−1.24267	+	2.79108i	−0.0870043	+	0.195415i
$205$	0.835438	+	0.177578i	0.0583495	+	0.0124026i
$206$	15.9443	+	11.5842i	1.11089	+	0.807109i
$207$	−3.35410	−	5.80948i	−0.233126	−	0.403786i
$208$	−1.92705	−	1.40008i	−0.133617	−	0.0970784i
$209$	−3.91716	−	4.35045i	−0.270956	−	0.300927i
$210$	−0.791796	−	0.457144i	−0.0546391	−	0.0315459i
$211$	−14.0375	+	15.5902i	−0.966381	+	1.07328i	0.0308953	+	0.999523i	$0.490164\pi$
$211$	−14.0375	+	15.5902i	−0.966381	+	1.07328i	−0.997277	+	0.0737526i	$0.976502\pi$
$212$	0.0881995	−	0.0187474i	0.00605757	−	0.00128758i
$213$	14.4366	+	4.69075i	0.989182	+	0.321405i
$214$	9.40786	+	1.99970i	0.643108	+	0.136697i
$215$	6.28115	−	4.56352i	0.428371	−	0.311230i
$216$	−4.94183	−	1.60570i	−0.336249	−	0.109254i
$217$	1.28115	+	0.930812i	0.0869703	+	0.0631876i
$218$	−10.0451	+	17.3986i	−0.680339	+	1.17838i
$219$	−6.10844	+	8.40755i	−0.412770	+	0.568130i
$220$	1.54508	+	2.67617i	0.104170	+	0.180427i
$221$	3.83838	+	1.70896i	0.258197	+	0.114957i
$222$	8.20617	−	0.862503i	0.550762	−	0.0578874i
$223$	−18.7067	−	3.97623i	−1.25269	−	0.266268i	−0.466651	−	0.884441i	$-0.654540\pi$
$223$	−18.7067	−	3.97623i	−1.25269	−	0.266268i	−0.786042	+	0.618173i	$0.787873\pi$
$224$	−0.236068			−0.0157730
$225$	−13.7032	+	6.10105i	−0.913545	+	0.406737i
$226$	10.2361			0.680893
$227$	20.7175	+	4.40364i	1.37507	+	0.292280i	0.835421	−	0.549611i	$-0.185224\pi$
$227$	20.7175	+	4.40364i	1.37507	+	0.292280i	0.539648	+	0.841891i	$0.318557\pi$
$228$	2.98426	−	6.70276i	0.197638	−	0.443901i
$229$	3.30524	+	1.47159i	0.218416	+	0.0972452i	0.513028	−	0.858372i	$-0.328524\pi$
$229$	3.30524	+	1.47159i	0.218416	+	0.0972452i	−0.294612	+	0.955617i	$0.595190\pi$
$230$	−4.89074	+	1.03956i	−0.322486	+	0.0685465i
$231$	0.561965	+	0.0590649i	0.0369746	+	0.00388619i
$232$	2.30902	−	3.99933i	0.151594	−	0.262569i
$233$	20.1353	+	14.6291i	1.31910	+	0.958385i	0.999943	+	0.0106851i	$0.00340124\pi$
$233$	20.1353	+	14.6291i	1.31910	+	0.958385i	0.319161	+	0.947700i	$0.396599\pi$
$234$	−2.20820	+	6.79615i	−0.144355	+	0.444278i
$235$	4.89919	−	15.0781i	0.319588	−	0.983590i
$236$	−0.461819	−	0.0981626i	−0.0300618	−	0.00638984i
$237$	7.15960	−	6.44654i	0.465066	−	0.418747i
$238$	0.407308	−	0.0865761i	0.0264019	−	0.00561189i
$239$	−13.8192	+	15.3478i	−0.893890	+	0.992765i	−0.999999	−	0.00158913i	$-0.999494\pi$
$239$	−13.8192	+	15.3478i	−0.893890	+	0.992765i	0.106109	+	0.994355i	$0.466161\pi$
$240$	−2.27648	+	3.13331i	−0.146946	+	0.202254i
$241$	−5.66897	−	6.29602i	−0.365170	−	0.405563i	0.532358	−	0.846519i	$-0.321306\pi$
$241$	−5.66897	−	6.29602i	−0.365170	−	0.405563i	−0.897528	+	0.440957i	$0.854639\pi$
$242$	7.35410	+	5.34307i	0.472740	+	0.343465i
$243$			15.5885i			1.00000i
$244$	−11.6631	−	8.47375i	−0.746655	−	0.542476i
$245$	−1.62310	−	15.4428i	−0.103696	−	0.986604i
$246$	−0.388870	−	0.535233i	−0.0247934	−	0.0341252i
$247$	−9.21783	−	4.10404i	−0.586516	−	0.261134i
$248$	4.48866	−	4.98517i	0.285030	−	0.316558i
$249$	4.36475	+	2.51999i	0.276604	+	0.159698i
$250$	1.16866	+	11.1191i	0.0739128	+	0.703233i
$251$	16.5066			1.04189			0.520943	−	0.853591i	$-0.325580\pi$
$251$	16.5066			1.04189			0.520943	+	0.853591i	$0.325580\pi$
$252$	0.218847	+	0.673542i	0.0137861	+	0.0424292i
$253$	2.50000	−	1.81636i	0.157174	−	0.114193i
$254$	−1.83576	−	17.4661i	−0.115186	−	1.09592i
$255$	2.77869	−	6.24105i	0.174009	−	0.390830i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	3.66312	+	6.34471i	0.228499	+	0.395772i	0.957363	−	0.288886i	$-0.0932849\pi$
$257$	3.66312	+	6.34471i	0.228499	+	0.395772i	−0.728864	+	0.684658i	$0.759952\pi$
$258$	−5.98097	−	0.628625i	−0.372359	−	0.0391365i
$259$	−0.752512	−	0.835749i	−0.0467588	−	0.0519309i
$260$	4.30902	+	3.13068i	0.267234	+	0.194157i
$261$	−13.5514	−	2.88043i	−0.838808	−	0.178294i
$262$	−3.28115	+	10.0984i	−0.202710	+	0.623878i
$263$	−8.50345	−	9.44404i	−0.524345	−	0.582344i	0.421555	−	0.906803i	$-0.361485\pi$
$263$	−8.50345	−	9.44404i	−0.524345	−	0.582344i	−0.945900	+	0.324459i	$0.894818\pi$
$264$	0.497665	−	2.34133i	0.0306291	−	0.144099i
$265$	−0.197220	+	0.0419204i	−0.0121151	+	0.00257515i
$266$	−0.978148	+	0.207912i	−0.0599741	+	0.0127479i
$267$	−6.82945	+	9.39993i	−0.417955	+	0.575266i
$268$	−1.42705	+	2.47172i	−0.0871710	+	0.150985i
$269$	−12.3992	−	9.00854i	−0.755992	−	0.549260i	0.141687	−	0.989912i	$-0.454747\pi$
$269$	−12.3992	−	9.00854i	−0.755992	−	0.549260i	−0.897678	+	0.440651i	$0.854747\pi$
$270$	11.0503	+	3.59045i	0.672499	+	0.218508i
$271$	−12.3713	+	8.98829i	−0.751504	+	0.546000i	−0.896293	−	0.443463i	$-0.853750\pi$
$271$	−12.3713	+	8.98829i	−0.751504	+	0.546000i	0.144788	+	0.989463i	$0.453750\pi$
$272$	−0.184381	−	1.75427i	−0.0111797	−	0.106368i
$273$	0.926274	−	0.300965i	0.0560607	−	0.0182152i
$274$	−10.6353	−	18.4208i	−0.642499	−	1.11284i
$275$	−3.45492	−	5.98409i	−0.208339	−	0.360854i
$276$	3.35410	+	1.93649i	0.201893	+	0.116563i
$277$	−10.7051	−	2.27544i	−0.643208	−	0.136718i	−0.125251	−	0.992125i	$-0.539974\pi$
$277$	−10.7051	−	2.27544i	−0.643208	−	0.136718i	−0.517956	+	0.855407i	$0.673307\pi$
$278$	−6.23607	+	4.53077i	−0.374015	+	0.271737i
$279$	−18.3847	−	8.18542i	−1.10067	−	0.490048i
$280$	0.527864			0.0315459
$281$	28.7512	−	12.8009i	1.71515	−	0.763636i	0.717400	−	0.696662i	$-0.245332\pi$
$281$	28.7512	−	12.8009i	1.71515	−	0.763636i	0.997755	−	0.0669741i	$-0.0213345\pi$
$282$	−10.6353	+	6.14027i	−0.633320	+	0.365648i
$283$	2.98917	−	28.4401i	0.177688	−	1.69059i	−0.435133	−	0.900366i	$-0.643299\pi$
$283$	2.98917	−	28.4401i	0.177688	−	1.69059i	0.612821	−	0.790222i	$-0.290035\pi$
$284$	−8.57242	+	1.82212i	−0.508679	+	0.108123i
$285$	−6.67301	+	14.9878i	−0.395275	+	0.887802i
$286$	−3.21986	−	0.684403i	−0.190394	−	0.0404696i
$287$	−0.0278640	+	0.0857567i	−0.00164476	+	0.00506206i
$288$	2.93444	−	0.623735i	0.172914	−	0.0367539i
$289$	−4.29180	−	13.2088i	−0.252459	−	0.776988i
$290$	−5.16312	+	8.94278i	−0.303189	+	0.525138i
$291$	3.18205	−	2.86513i	0.186535	−	0.167957i
$292$	0.627171	−	5.96713i	0.0367024	−	0.349200i
$293$	10.1803	+	17.6329i	0.594742	+	1.03012i	0.993583	+	0.113103i	$0.0360790\pi$
$293$	10.1803	+	17.6329i	0.594742	+	1.03012i	−0.398841	+	0.917020i	$0.630588\pi$
$294$	−7.06978	+	9.73072i	−0.412318	+	0.567507i
$295$	1.03266	+	0.219498i	0.0601237	+	0.0127797i
$296$	−3.85410	+	2.80017i	−0.224015	+	0.162757i
$297$	−7.14157	+	0.750609i	−0.414396	+	0.0435548i
$298$	−5.20820	−	16.0292i	−0.301703	−	0.928547i
$299$	2.66312	−	4.61266i	0.154012	−	0.266757i
$300$	5.09037	−	7.00629i	0.293893	−	0.404508i
$301$	0.409830	+	0.709846i	0.0236222	+	0.0409149i
$302$	4.80459	−	5.33603i	0.276473	−	0.307054i
$303$	−7.54821	+	0.793349i	−0.433633	+	0.0455767i
$304$	0.442790	+	4.21286i	0.0253957	+	0.241624i
$305$	26.0795	+	18.9479i	1.49331	+	1.08495i
$306$	−4.83430	+	2.15237i	−0.276358	+	0.123043i
$307$	10.5623			0.602823			0.301411	−	0.953494i	$-0.402542\pi$
$307$	10.5623			0.602823			0.301411	+	0.953494i	$0.402542\pi$
$308$	−0.298033	+	0.132693i	−0.0169820	+	0.00756088i
$309$	7.09719	+	33.3897i	0.403745	+	1.89947i
$310$	−10.0370	+	11.1472i	−0.570061	+	0.633117i
$311$	18.3079	−	20.3329i	1.03814	−	1.15298i	0.0501093	−	0.998744i	$-0.484043\pi$
$311$	18.3079	−	20.3329i	1.03814	−	1.15298i	0.988035	−	0.154232i	$-0.0492903\pi$
$312$	−0.857778	−	4.03553i	−0.0485621	−	0.228467i
$313$	17.4808	+	19.4144i	0.988072	+	1.09737i	0.995246	+	0.0973908i	$0.0310497\pi$
$313$	17.4808	+	19.4144i	0.988072	+	1.09737i	−0.00717426	+	0.999974i	$0.502284\pi$
$314$	5.70820	+	17.5680i	0.322133	+	0.991422i
$315$	−0.489357	−	1.50609i	−0.0275721	−	0.0848583i
$316$	−1.71885	+	5.29007i	−0.0966927	+	0.297590i
$317$	−1.44668	+	0.644105i	−0.0812538	+	0.0361765i	−0.446961	−	0.894553i	$-0.647494\pi$
$317$	−1.44668	+	0.644105i	−0.0812538	+	0.0361765i	0.365707	+	0.930730i	$0.380827\pi$
$318$	0.135255	+	0.0780895i	0.00758472	+	0.00437904i
$319$	0.667097	−	6.34700i	0.0373503	−	0.355364i
$320$	0.233733	−	2.22382i	0.0130661	−	0.124315i
$321$	9.79187	+	13.4774i	0.546529	+	0.752232i
$322$	−0.0551768	−	0.524972i	−0.00307488	−	0.0292556i
$323$	−2.30902	−	7.10642i	−0.128477	−	0.395412i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−9.63525	−	7.00042i	−0.534468	−	0.388314i
$326$	8.50000	−	14.7224i	0.470771	−	0.815400i
$327$	−33.0941	+	10.7529i	−1.83011	+	0.594638i
$328$	0.348943	+	0.155360i	0.0192672	+	0.00857830i
$329$	1.52906	+	0.680780i	0.0842997	+	0.0375326i
$330$	−1.11281	+	5.23537i	−0.0612583	+	0.288198i
$331$	29.2140	−	13.0069i	1.60575	−	0.714925i	0.608824	−	0.793306i	$-0.291642\pi$
$331$	29.2140	−	13.0069i	1.60575	−	0.714925i	0.996923	+	0.0783809i	$0.0249750\pi$
$332$	−2.90983			−0.159698
$333$	11.5623	+	8.40051i	0.633610	+	0.460345i
$334$	6.47214	−	19.9192i	0.354140	−	1.08993i
$335$	3.19098	−	5.52694i	0.174342	−	0.301969i
$336$	−0.303858	−	0.273595i	−0.0165768	−	0.0149258i
$337$	−2.04449	+	0.434571i	−0.111371	+	0.0236726i	−0.263260	−	0.964725i	$-0.584798\pi$
$337$	−2.04449	+	0.434571i	−0.111371	+	0.0236726i	0.151889	+	0.988398i	$0.451464\pi$
$338$	7.16614	−	1.52321i	0.389787	−	0.0828517i
$339$	13.1755	+	11.8633i	0.715595	+	0.644325i
$340$	0.412289	+	3.92266i	0.0223595	+	0.212736i
$341$	2.86475	−	8.81678i	0.155135	−	0.477455i
$342$	11.6095	−	5.16889i	0.627771	−	0.279502i
$343$	3.29180			0.177740
$344$	3.17195	−	1.41224i	0.171020	−	0.0761431i
$345$	−7.50000	−	4.33013i	−0.403786	−	0.233126i
$346$	4.78339	+	2.12970i	0.257156	+	0.114493i
$347$	−10.4803	−	4.66614i	−0.562613	−	0.250491i	0.105667	−	0.994402i	$-0.466302\pi$
$347$	−10.4803	−	4.66614i	−0.562613	−	0.250491i	−0.668280	+	0.743910i	$0.732969\pi$
$348$	7.60719	−	2.47172i	0.407788	−	0.132498i
$349$	−1.21885	+	2.11111i	−0.0652434	+	0.113005i	−0.896802	−	0.442432i	$-0.854116\pi$
$349$	−1.21885	+	2.11111i	−0.0652434	+	0.113005i	0.831559	+	0.555437i	$0.187449\pi$
$350$	−1.18034			−0.0630918
$351$	−10.7188	+	6.18853i	−0.572130	+	0.330319i
$352$	0.427051	+	1.31433i	0.0227619	+	0.0700539i
$353$	0.722274	+	6.87198i	0.0384428	+	0.365758i	0.996784	+	0.0801332i	$0.0255346\pi$
$353$	0.722274	+	6.87198i	0.0384428	+	0.365758i	−0.958341	+	0.285625i	$0.907799\pi$
$354$	−0.480669	−	0.661585i	−0.0255473	−	0.0351628i
$355$	19.1685	−	4.07439i	1.01736	−	0.216246i
$356$	0.701198	−	6.67146i	0.0371634	−	0.353586i
$357$	0.624612	+	0.360620i	0.0330580	+	0.0190860i
$358$	−0.646976	+	0.288052i	−0.0341938	+	0.0152240i
$359$	−2.04508	+	6.29412i	−0.107935	+	0.332191i	−0.990408	−	0.138172i	$-0.955877\pi$
$359$	−2.04508	+	6.29412i	−0.107935	+	0.332191i	0.882473	+	0.470364i	$0.155877\pi$
$360$	−6.56161	+	1.39471i	−0.345827	+	0.0735079i
$361$	−0.326238	−	1.00406i	−0.0171704	−	0.0528451i
$362$	1.53351	+	1.70314i	0.0805995	+	0.0895149i
$363$	3.27349	+	15.4006i	0.171814	+	0.808321i
$364$	−0.376256	+	0.417875i	−0.0197212	+	0.0219026i
$365$	−1.40240	+	13.3429i	−0.0734048	+	0.698400i
$366$	−5.19154	−	24.4243i	−0.271366	−	1.27668i
$367$	−12.2565	+	5.45694i	−0.639784	+	0.284850i	−0.700877	−	0.713282i	$-0.747208\pi$
$367$	−12.2565	+	5.45694i	−0.639784	+	0.284850i	0.0610933	+	0.998132i	$0.480541\pi$
$368$	−2.23607			−0.116563
$369$	0.119779	−	1.13962i	0.00623544	−	0.0593263i
$370$	8.61803	−	6.26137i	0.448030	−	0.325513i
$371$	−0.00222502	−	0.0211696i	−0.000115517	−	0.00109907i
$372$	11.5553	−	1.21451i	0.599114	−	0.0629695i
$373$	22.4576	−	24.9417i	1.16281	−	1.29143i	0.213551	−	0.976932i	$-0.431497\pi$
$373$	22.4576	−	24.9417i	1.16281	−	1.29143i	0.949258	−	0.314498i	$-0.101836\pi$
$374$	−1.21885	−	2.11111i	−0.0630251	−	0.109163i
$375$	−11.3824	+	15.6665i	−0.587785	+	0.809017i
$376$	3.54508	−	6.14027i	0.182824	−	0.316660i
$377$	−3.39919	−	10.4616i	−0.175067	−	0.538801i
$378$	−0.498922	+	1.12060i	−0.0256618	+	0.0576372i
$379$	−16.1803	+	11.7557i	−0.831128	+	0.603850i	−0.919878	−	0.392204i	$-0.871713\pi$
$379$	−16.1803	+	11.7557i	−0.831128	+	0.603850i	0.0887501	+	0.996054i	$0.471713\pi$
$380$	−0.990108	−	9.42025i	−0.0507915	−	0.483248i
$381$	17.8797	−	24.6093i	0.916006	−	1.26077i
$382$	−4.38197	−	7.58979i	−0.224201	−	0.388327i
$383$	2.17402	−	20.6844i	0.111087	−	1.05693i	−0.786953	−	0.617013i	$-0.788343\pi$
$383$	2.17402	−	20.6844i	0.111087	−	1.05693i	0.898041	−	0.439913i	$-0.144991\pi$
$384$	−1.28716	+	1.15897i	−0.0656853	+	0.0591433i
$385$	0.666422	−	0.296710i	0.0339640	−	0.0151218i
$386$	4.07295	+	12.5352i	0.207308	+	0.638027i
$387$	−6.96994	−	7.74090i	−0.354302	−	0.393492i
$388$	−0.763932	+	2.35114i	−0.0387828	+	0.119361i
$389$	−32.6317	−	6.93608i	−1.65449	−	0.351673i	−0.716301	−	0.697792i	$-0.754166\pi$
$389$	−32.6317	−	6.93608i	−1.65449	−	0.351673i	−0.938191	+	0.346119i	$0.887499\pi$
$390$	1.91805	+	9.02372i	0.0971243	+	0.456934i
$391$	3.85808	−	0.820060i	0.195111	−	0.0414722i
$392$	0.725874	−	6.90623i	0.0366622	−	0.348817i
$393$	−15.9271	+	9.19549i	−0.803413	+	0.463851i
$394$	12.9544	−	5.76766i	0.652632	−	0.290571i
$395$	3.84346	−	11.8290i	0.193385	−	0.595179i
$396$	3.35410	−	2.43690i	0.168550	−	0.122459i
$397$	−18.8713	+	13.7108i	−0.947125	+	0.688126i	−0.950125	−	0.311869i	$-0.899045\pi$
$397$	−18.8713	+	13.7108i	−0.947125	+	0.688126i	0.00300049	+	0.999995i	$0.499045\pi$
$398$	−25.9819	−	5.52261i	−1.30235	−	0.276824i
$399$	−1.50000	−	0.866025i	−0.0750939	−	0.0433555i
$400$	−0.522642	+	4.97261i	−0.0261321	+	0.248630i
$401$	−5.97214	−	10.3440i	−0.298234	−	0.516557i	0.677498	−	0.735525i	$-0.263064\pi$
$401$	−5.97214	−	10.3440i	−0.298234	−	0.516557i	−0.975732	+	0.218968i	$0.929731\pi$
$402$	−4.70150	+	1.52761i	−0.234490	+	0.0761903i
$403$	−1.67023	−	15.8912i	−0.0832001	−	0.791596i
$404$	3.54508	−	2.57565i	0.176375	−	0.128144i
$405$	10.0623	+	17.4284i	0.500000	+	0.866025i
$406$	−0.881966	−	0.640786i	−0.0437712	−	0.0318017i
$407$	−3.29180	+	5.70156i	−0.163168	+	0.282616i
$408$	1.79581	−	2.47172i	0.0889060	−	0.122369i
$409$	23.0474	−	4.89888i	1.13962	−	0.242234i	0.400820	−	0.916157i	$-0.368725\pi$
$409$	23.0474	−	4.89888i	1.13962	−	0.242234i	0.738802	+	0.673923i	$0.235392\pi$
$410$	−0.780261	−	0.347395i	−0.0385343	−	0.0171566i
$411$	7.65980	−	36.0365i	0.377830	−	1.77755i
$412$	−13.1874	−	14.6460i	−0.649695	−	0.721559i
$413$	−0.0344419	+	0.106001i	−0.00169477	+	0.00521597i
$414$	2.07295	+	6.37988i	0.101880	+	0.313554i
$415$	6.50658			0.319395
$416$	1.59385	+	1.77015i	0.0781447	+	0.0867885i
$417$	−13.2779	−	1.39556i	−0.650220	−	0.0683408i
$418$	2.92705	+	5.06980i	0.143167	+	0.247972i
$419$	2.09999	−	19.9801i	0.102591	−	0.976092i	−0.815240	−	0.579123i	$-0.803395\pi$
$419$	2.09999	−	19.9801i	0.102591	−	0.976092i	0.917832	−	0.396970i	$-0.129938\pi$
$420$	0.679448	+	0.611778i	0.0331537	+	0.0298517i
$421$	1.40240	+	13.3429i	0.0683486	+	0.650294i	0.974043	+	0.226363i	$0.0726834\pi$
$421$	1.40240	+	13.3429i	0.0683486	+	0.650294i	−0.905694	+	0.423931i	$0.860650\pi$
$422$	16.9721	−	12.3310i	0.826191	−	0.600263i
$423$	−20.8057	−	4.42239i	−1.01161	−	0.215024i
$424$	−0.0901699			−0.00437904
$425$	−0.921906	−	8.77135i	−0.0447190	−	0.425473i
$426$	−13.1459	−	7.58979i	−0.636921	−	0.367726i
$427$	−2.27722	+	2.52911i	−0.110202	+	0.122392i
$428$	−8.78651	−	3.91201i	−0.424712	−	0.189094i
$429$	−3.35129	−	4.61266i	−0.161802	−	0.222701i
$430$	−7.09270	+	3.15788i	−0.342041	+	0.152286i
$431$	5.20820	+	3.78398i	0.250870	+	0.182268i	0.706112	−	0.708100i	$-0.250447\pi$
$431$	5.20820	+	3.78398i	0.250870	+	0.182268i	−0.455242	+	0.890368i	$0.650447\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−12.3713	−	8.98829i	−0.594528	−	0.431950i	0.249404	−	0.968399i	$-0.419765\pi$
$433$	−12.3713	−	8.98829i	−0.594528	−	0.431950i	−0.843932	+	0.536450i	$0.819765\pi$
$434$	−1.05963	−	1.17684i	−0.0508639	−	0.0564900i
$435$	−17.0102	+	5.52694i	−0.815576	+	0.264997i
$436$	13.4429	−	14.9299i	0.643800	−	0.715013i
$437$	−9.26515	+	1.96937i	−0.443212	+	0.0942076i
$438$	7.72299	−	6.95381i	0.369019	−	0.332266i
$439$	7.25434	+	1.54196i	0.346231	+	0.0735936i	0.377745	−	0.925910i	$-0.376700\pi$
$439$	7.25434	+	1.54196i	0.346231	+	0.0735936i	−0.0315142	+	0.999503i	$0.510033\pi$
$440$	−0.954915	−	2.93893i	−0.0455238	−	0.140108i
$441$	−20.3776	+	4.33139i	−0.970360	+	0.206256i
$442$	−3.39919	−	2.46965i	−0.161683	−	0.117469i
$443$	−18.2254	+	31.5674i	−0.865916	+	1.49981i	0.000218632		1.00000i	$0.499930\pi$
$443$	−18.2254	+	31.5674i	−0.865916	+	1.49981i	−0.866135	+	0.499811i	$0.833403\pi$
$444$	−8.20617	−	0.862503i	−0.389448	−	0.0409326i
$445$	−1.56793	+	14.9178i	−0.0743269	+	0.707173i
$446$	17.4712	+	7.77868i	0.827285	+	0.368331i
$447$	11.8735	−	26.6684i	0.561598	−	1.26137i
$448$	0.230909	+	0.0490813i	0.0109094	+	0.00231887i
$449$	−19.1459			−0.903551			−0.451775	−	0.892132i	$-0.649209\pi$
$449$	−19.1459			−0.903551			−0.451775	+	0.892132i	$0.649209\pi$
$450$	14.6722	−	3.11868i	0.691655	−	0.147016i
$451$	0.527864			0.0248561
$452$	−10.0124	−	2.12820i	−0.470943	−	0.100102i
$453$	12.3686	−	1.29999i	0.581127	−	0.0610789i
$454$	−19.3492	−	8.61482i	−0.908103	−	0.404314i
$455$	0.841334	−	0.934396i	0.0394424	−	0.0438052i
$456$	−4.31263	+	5.93583i	−0.201957	+	0.277971i
$457$	6.63525	−	11.4926i	0.310384	−	0.537601i	−0.668061	−	0.744106i	$-0.732876\pi$
$457$	6.63525	−	11.4926i	0.310384	−	0.537601i	0.978446	+	0.206505i	$0.0662090\pi$
$458$	−2.92705	−	2.12663i	−0.136772	−	0.0993708i
$459$	−8.71706	−	2.83234i	−0.406878	−	0.132203i
$460$	5.00000			0.233126
$461$	−26.7836	−	5.69303i	−1.24744	−	0.265151i	−0.463559	−	0.886066i	$-0.653428\pi$
$461$	−26.7836	−	5.69303i	−1.24744	−	0.265151i	−0.783878	+	0.620915i	$0.786761\pi$
$462$	−0.537405	−	0.174613i	−0.0250023	−	0.00812375i
$463$	−4.31990	+	0.918223i	−0.200763	+	0.0426734i	−0.307195	−	0.951646i	$-0.599390\pi$
$463$	−4.31990	+	0.918223i	−0.200763	+	0.0426734i	0.106433	+	0.994320i	$0.466057\pi$
$464$	−3.09007	+	3.43187i	−0.143453	+	0.159320i
$465$	−25.8384	+	2.71573i	−1.19823	+	0.125939i
$466$	−16.6537	−	18.4958i	−0.771467	−	0.856801i
$467$	−7.66312	−	5.56758i	−0.354607	−	0.257637i	0.396192	−	0.918168i	$-0.370331\pi$
$467$	−7.66312	−	5.56758i	−0.354607	−	0.257637i	−0.750799	+	0.660531i	$0.770331\pi$
$468$	3.57295	−	6.18853i	0.165160	−	0.286065i
$469$	0.545085	+	0.396027i	0.0251697	+	0.0182868i
$470$	−7.92705	+	13.7301i	−0.365648	+	0.633320i
$471$	−13.0134	+	29.2286i	−0.599626	+	1.34678i
$472$	0.431318	+	0.192035i	0.0198530	+	0.00883913i
$473$	3.21074	−	3.56589i	0.147630	−	0.163960i
$474$	−8.34346	+	4.81710i	−0.383228	+	0.221257i
$475$	2.21395	+	21.0643i	0.101583	+	0.966497i
$476$	−0.416408			−0.0190860
$477$	0.0835921	+	0.257270i	0.00382742	+	0.0117796i
$478$	16.7082	−	12.1392i	0.764215	−	0.555235i
$479$	−2.96450	−	28.2053i	−0.135451	−	1.28873i	−0.825265	−	0.564746i	$-0.808974\pi$
$479$	−2.96450	−	28.2053i	−0.135451	−	1.28873i	0.689813	−	0.723987i	$-0.257693\pi$
$480$	2.87819	−	2.59153i	0.131371	−	0.118287i
$481$	−1.18614	+	11.2854i	−0.0540833	+	0.514568i
$482$	4.23607	+	7.33708i	0.192948	+	0.334195i
$483$	0.537405	−	0.739674i	0.0244528	−	0.0336563i
$484$	−6.08251	−	6.75531i	−0.276478	−	0.307060i
$485$	1.70820	−	5.25731i	0.0775655	−	0.238722i
$486$	3.24102	−	15.2478i	0.147016	−	0.691655i
$487$	1.51064	−	4.64928i	0.0684538	−	0.210679i	−0.910978	−	0.412455i	$-0.864671\pi$
$487$	1.51064	−	4.64928i	0.0684538	−	0.210679i	0.979432	+	0.201776i	$0.0646713\pi$
$488$	9.64646	+	10.7135i	0.436675	+	0.484976i
$489$	28.0037	−	9.09896i	1.26637	−	0.411469i
$490$	−1.62310	+	15.4428i	−0.0733244	+	0.697635i
$491$	30.7299	−	6.53184i	1.38682	−	0.294778i	0.546768	−	0.837284i	$-0.315858\pi$
$491$	30.7299	−	6.53184i	1.38682	−	0.294778i	0.840052	+	0.542506i	$0.182524\pi$
$492$	0.269091	+	0.604388i	0.0121315	+	0.0272479i
$493$	4.07295	−	7.05455i	0.183436	−	0.317721i
$494$	8.16312	+	5.93085i	0.367276	+	0.266842i
$495$	−7.50000	+	5.44907i	−0.337100	+	0.244917i
$496$	−5.42705	+	3.94298i	−0.243682	+	0.177045i
$497$	0.216257	+	2.05755i	0.00970046	+	0.0922937i
$498$	−3.74543	−	3.37240i	−0.167837	−	0.151121i
$499$	−1.71885	−	2.97713i	−0.0769462	−	0.133275i	0.824985	−	0.565155i	$-0.191184\pi$
$499$	−1.71885	−	2.97713i	−0.0769462	−	0.133275i	−0.901931	+	0.431880i	$0.857850\pi$
$500$	1.16866	−	11.1191i	0.0522642	−	0.497261i
$501$	31.4164	−	18.1383i	1.40358	−	0.810358i
$502$	−16.1459	−	3.43191i	−0.720625	−	0.153174i
$503$	10.4443	−	7.58821i	0.465687	−	0.338341i	−0.330071	−	0.943956i	$-0.607073\pi$
$503$	10.4443	−	7.58821i	0.465687	−	0.338341i	0.795758	+	0.605615i	$0.207073\pi$
$504$	−0.0740275	−	0.704324i	−0.00329745	−	0.0313731i
$505$	−7.92705	+	5.75934i	−0.352749	+	0.256287i
$506$	−2.82301	+	1.25689i	−0.125498	+	0.0558754i
$507$	10.9894	+	6.34471i	0.488054	+	0.281778i
$508$	−1.83576	+	17.4661i	−0.0814487	+	0.774933i
$509$	−10.6714	+	2.26828i	−0.473003	+	0.100540i	−0.438244	−	0.898856i	$-0.644399\pi$
$509$	−10.6714	+	2.26828i	−0.473003	+	0.100540i	−0.0347584	+	0.999396i	$0.511066\pi$
$510$	−4.01556	+	5.52694i	−0.177812	+	0.244737i
$511$	−1.38546	−	0.294488i	−0.0612890	−	0.0130274i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	20.9339	+	6.80185i	0.924256	+	0.300309i
$514$	−2.26393	−	6.96767i	−0.0998578	−	0.307331i
$515$	29.4878	+	32.7496i	1.29939	+	1.44312i
$516$	5.71957	+	1.85840i	0.251790	+	0.0818116i
$517$	1.02421	−	9.74470i	0.0450447	−	0.428571i
$518$	0.562306	+	0.973942i	0.0247063	+	0.0427926i
$519$	3.68875	+	8.28507i	0.161918	+	0.363674i
$520$	−3.56395	−	3.95817i	−0.156289	−	0.173577i
$521$	−15.1803	+	11.0292i	−0.665063	+	0.483196i	−0.868369	−	0.495919i	$-0.834831\pi$
$521$	−15.1803	+	11.0292i	−0.665063	+	0.483196i	0.203306	+	0.979115i	$0.434831\pi$
$522$	12.6564	+	5.63497i	0.553953	+	0.246636i
$523$	5.50658	+	16.9475i	0.240786	+	0.741063i	0.996301	+	0.0859315i	$0.0273866\pi$
$523$	5.50658	+	16.9475i	0.240786	+	0.741063i	−0.755515	+	0.655131i	$0.772613\pi$
$524$	5.30902	−	9.19549i	0.231925	−	0.401707i
$525$	−1.51929	−	1.36798i	−0.0663073	−	0.0597034i
$526$	6.35410	+	11.0056i	0.277052	+	0.479868i
$527$	7.91770	−	8.79350i	0.344900	−	0.383051i
$528$	−0.973579	+	2.18669i	−0.0423696	+	0.0951637i
$529$	1.88151	+	17.9014i	0.0818049	+	0.778321i
$530$	0.201626			0.00875808
$531$	0.148055	−	1.40865i	0.00642504	−	0.0611301i
$532$	1.00000			0.0433555
$533$	0.831171	−	0.370061i	0.0360020	−	0.0160291i
$534$	8.63456	−	7.77460i	0.373654	−	0.336440i
$535$	19.6472	+	8.74751i	0.849424	+	0.378188i
$536$	1.90977	−	2.12101i	0.0824894	−	0.0916137i
$537$	−1.16661	−	0.379054i	−0.0503429	−	0.0163574i
$538$	10.2553	+	11.3896i	0.442135	+	0.491041i
$539$	−2.96556	−	9.12705i	−0.127736	−	0.393130i
$540$	−10.0623	−	5.80948i	−0.433013	−	0.250000i
$541$	−5.86475	+	18.0498i	−0.252145	+	0.776023i	0.742234	+	0.670141i	$0.233766\pi$
$541$	−5.86475	+	18.0498i	−0.252145	+	0.776023i	−0.994379	+	0.105882i	$0.966234\pi$
$542$	13.9698	−	6.21973i	0.600052	−	0.267160i
$543$			3.96951i			0.170348i
$544$	−0.184381	+	1.75427i	−0.00790527	+	0.0752137i
$545$	−30.0593	+	33.3843i	−1.28760	+	1.43003i
$546$	−0.968607	+	0.101805i	−0.0414526	+	0.00435684i
$547$	0.866729	+	8.24637i	0.0370586	+	0.352589i	0.997301	+	0.0734217i	$0.0233919\pi$
$547$	0.866729	+	8.24637i	0.0370586	+	0.352589i	−0.960242	+	0.279168i	$0.909941\pi$
$548$	6.57295	+	20.2295i	0.280782	+	0.864160i
$549$	21.6246	−	37.4549i	0.922916	−	1.59854i
$550$	2.13525	+	6.57164i	0.0910476	+	0.280216i
$551$	−9.78115	+	16.9415i	−0.416691	+	0.721730i
$552$	−2.87819	−	2.59153i	−0.122504	−	0.110303i
$553$	1.19956	+	0.534079i	0.0510105	+	0.0227113i
$554$	9.99809	+	4.45144i	0.424778	+	0.189123i
$555$	18.3496	+	1.92862i	0.778895	+	0.0818652i
$556$	7.04179	−	3.13521i	0.298639	−	0.132962i
$557$	−16.5967			−0.703227			−0.351613	−	0.936145i	$-0.614367\pi$
$557$	−16.5967			−0.703227			−0.351613	+	0.936145i	$0.614367\pi$
$558$	16.2812	+	11.8290i	0.689236	+	0.500759i
$559$	2.55573	−	7.86572i	0.108096	−	0.332685i
$560$	−0.516329	−	0.109749i	−0.0218189	−	0.00463775i
$561$	0.877847	−	4.12994i	0.0370627	−	0.174366i
$562$	−30.7844	+	6.54343i	−1.29856	+	0.276018i
$563$	−1.01184	+	0.215073i	−0.0426438	+	0.00906423i	−0.229184	−	0.973383i	$-0.573606\pi$
$563$	−1.01184	+	0.215073i	−0.0426438	+	0.00906423i	0.186540	+	0.982447i	$0.440272\pi$
$564$	11.6795	−	3.79489i	0.491795	−	0.159794i
$565$	22.3884	+	4.75880i	0.941886	+	0.200204i
$566$	−8.83688	+	27.1971i	−0.371442	+	1.14318i
$567$	−1.94093	+	0.864157i	−0.0815114	+	0.0362912i
$568$	8.76393			0.367726
$569$	27.6220	−	12.2981i	1.15798	−	0.515564i	0.264372	−	0.964421i	$-0.414835\pi$
$569$	27.6220	−	12.2981i	1.15798	−	0.515564i	0.893604	+	0.448857i	$0.148169\pi$
$570$	9.64333	−	13.2729i	0.403915	−	0.555941i
$571$	−2.22694	−	0.991500i	−0.0931947	−	0.0414930i	0.359610	−	0.933103i	$-0.382910\pi$
$571$	−2.22694	−	0.991500i	−0.0931947	−	0.0414930i	−0.452805	+	0.891610i	$0.649576\pi$
$572$	3.00721	+	1.33889i	0.125738	+	0.0559820i
$573$	3.15601	−	14.8479i	0.131844	−	0.620278i
$574$	0.0450850	−	0.0780895i	0.00188181	−	0.00325939i
$575$	−11.1803			−0.466252
$576$	−3.00000			−0.125000
$577$	0.854102	+	2.62866i	0.0355567	+	0.109432i	0.967260	−	0.253789i	$-0.0816769\pi$
$577$	0.854102	+	2.62866i	0.0355567	+	0.109432i	−0.931703	+	0.363221i	$0.881677\pi$
$578$	1.45175	+	13.8125i	0.0603848	+	0.574523i
$579$	−9.28540	+	20.8553i	−0.385888	+	0.866719i
$580$	6.90960	−	7.67389i	0.286906	−	0.318641i
$581$	−0.0718025	+	0.683155i	−0.00297887	+	0.0283420i
$582$	−3.70820	+	2.14093i	−0.153710	+	0.0887445i
$583$	−0.113839	+	0.0506842i	−0.00471471	+	0.00209912i
$584$	−1.85410	+	5.70634i	−0.0767233	+	0.236130i
$585$	−7.98936	+	13.8380i	−0.330319	+	0.572130i
$586$	−6.29180	−	19.3642i	−0.259912	−	0.799926i
$587$	2.16535	+	2.40487i	0.0893736	+	0.0992595i	0.786173	−	0.618007i	$-0.212060\pi$
$587$	2.16535	+	2.40487i	0.0893736	+	0.0992595i	−0.696799	+	0.717267i	$0.745393\pi$
$588$	8.93842	−	8.04819i	0.368614	−	0.331902i
$589$	−19.0143	+	21.1175i	−0.783470	+	0.870132i
$590$	−0.964456	−	0.429403i	−0.0397060	−	0.0176783i
$591$	23.3590	+	7.58979i	0.960859	+	0.312202i
$592$	4.35207	−	1.93767i	0.178869	−	0.0796376i
$593$	1.52786			0.0627419			0.0313709	−	0.999508i	$-0.490013\pi$
$593$	1.52786			0.0627419			0.0313709	+	0.999508i	$0.490013\pi$
$594$	7.14157	+	0.750609i	0.293022	+	0.0307979i
$595$	0.931116			0.0381720
$596$	1.76173	+	16.7618i	0.0721634	+	0.686589i
$597$	−27.0424	−	37.2207i	−1.10677	−	1.52334i
$598$	−3.56395	+	3.95817i	−0.145741	+	0.161861i
$599$	3.02786	+	5.24441i	0.123715	+	0.214281i	0.921230	−	0.389018i	$-0.127186\pi$
$599$	3.02786	+	5.24441i	0.123715	+	0.214281i	−0.797515	+	0.603299i	$0.793852\pi$
$600$	−6.43582	+	5.79484i	−0.262741	+	0.236573i
$601$	0.527864	−	0.914287i	0.0215320	−	0.0372946i	−0.855059	−	0.518531i	$-0.826479\pi$
$601$	0.527864	−	0.914287i	0.0215320	−	0.0372946i	0.876591	+	0.481237i	$0.159812\pi$
$602$	−0.253289	−	0.779543i	−0.0103233	−	0.0317718i
$603$	−7.82206	−	3.48260i	−0.318539	−	0.141823i
$604$	−5.80902	+	4.22050i	−0.236366	+	0.171730i
$605$	13.6009	+	15.1053i	0.552956	+	0.614119i
$606$	7.54821	+	0.793349i	0.306625	+	0.0322276i
$607$	16.1803	+	28.0252i	0.656740	+	1.13751i	0.981455	+	0.191695i	$0.0613983\pi$
$607$	16.1803	+	28.0252i	0.656740	+	1.13751i	−0.324715	+	0.945812i	$0.605268\pi$
$608$	0.442790	−	4.21286i	0.0179575	−	0.170854i
$609$	−0.392585	−	1.84697i	−0.0159083	−	0.0748429i
$610$	−21.5701	−	23.9561i	−0.873349	−	0.969953i
$611$	−5.21885	−	16.0620i	−0.211132	−	0.649797i
$612$	5.17616	−	1.10023i	0.209234	−	0.0444740i
$613$	−8.70163	+	26.7809i	−0.351455	+	1.08167i	0.606581	+	0.795022i	$0.292541\pi$
$613$	−8.70163	+	26.7809i	−0.351455	+	1.08167i	−0.958036	+	0.286647i	$0.907459\pi$
$614$	−10.3315	−	2.19603i	−0.416945	−	0.0886244i
$615$	−0.601705	−	1.35145i	−0.0242631	−	0.0544958i
$616$	0.319109	−	0.0678287i	0.0128573	−	0.00273290i
$617$	−3.48714	+	33.1779i	−0.140387	+	1.33569i	0.666729	+	0.745300i	$0.267694\pi$
$617$	−3.48714	+	33.1779i	−0.140387	+	1.33569i	−0.807116	+	0.590393i	$0.798973\pi$
$618$		−	34.1356i		−	1.37314i
$619$	29.4806	−	13.1256i	1.18492	−	0.527562i	0.282859	−	0.959162i	$-0.408717\pi$
$619$	29.4806	−	13.1256i	1.18492	−	0.527562i	0.902066	+	0.431599i	$0.142050\pi$
$620$	12.1353	−	8.81678i	0.487364	−	0.354090i
$621$	−4.72585	+	10.6144i	−0.189642	+	0.425943i
$622$	−22.1353	+	16.0822i	−0.887543	+	0.644838i
$623$	−1.54899	−	0.329247i	−0.0620588	−	0.0131910i
$624$			4.12569i			0.165160i
$625$	−2.61321	+	24.8630i	−0.104528	+	0.994522i
$626$	−13.0623	−	22.6246i	−0.522075	−	0.904260i
$627$	−2.10814	+	9.91803i	−0.0841911	+	0.396088i
$628$	−1.93086	−	18.3709i	−0.0770499	−	0.733080i
$629$	−6.79837	+	4.93931i	−0.271069	+	0.196943i
$630$	0.165530	+	1.57492i	0.00659489	+	0.0627462i
$631$	26.9894	+	19.6089i	1.07443	+	0.780619i	0.976703	−	0.214595i	$-0.0688431\pi$
$631$	26.9894	+	19.6089i	1.07443	+	0.780619i	0.0977262	+	0.995213i	$0.468843\pi$
$632$	2.78115	−	4.81710i	0.110628	−	0.191614i
$633$	36.1371	+	3.79817i	1.43632	+	0.150964i
$634$	1.54899	−	0.329247i	0.0615181	−	0.0130761i
$635$	4.10489	−	39.0554i	0.162897	−	1.54987i
$636$	−0.116064	−	0.104504i	−0.00460222	−	0.00414386i
$637$	−11.0681	−	12.2924i	−0.438534	−	0.487042i
$638$	−1.97214	+	6.06961i	−0.0780776	+	0.240298i
$639$	−8.12461	−	25.0050i	−0.321405	−	0.989182i
$640$	−0.690983	+	2.12663i	−0.0273135	+	0.0840623i
$641$	−31.3142	−	34.7780i	−1.23684	−	1.37365i	−0.902210	−	0.431297i	$-0.858056\pi$
$641$	−31.3142	−	34.7780i	−1.23684	−	1.37365i	−0.334627	−	0.942351i	$-0.608610\pi$
$642$	−6.77579	−	15.2187i	−0.267419	−	0.600634i
$643$	9.79180	+	16.9599i	0.386151	+	0.668833i	0.991928	−	0.126801i	$-0.0404711\pi$
$643$	9.79180	+	16.9599i	0.386151	+	0.668833i	−0.605777	+	0.795634i	$0.707138\pi$
$644$	−0.0551768	+	0.524972i	−0.00217427	+	0.0206868i
$645$	−12.7894	−	4.15551i	−0.503580	−	0.163623i
$646$	0.781051	+	7.43120i	0.0307300	+	0.292377i
$647$	−8.42705	+	6.12261i	−0.331302	+	0.240705i	−0.740983	−	0.671524i	$-0.765640\pi$
$647$	−8.42705	+	6.12261i	−0.331302	+	0.240705i	0.409681	+	0.912229i	$0.365640\pi$
$648$	2.78115	+	8.55951i	0.109254	+	0.336249i
$649$	0.652476			0.0256119
$650$	7.96923	+	8.85073i	0.312579	+	0.347154i
$651$		−	2.74286i		−	0.107501i
$652$	−11.3752	+	12.6335i	−0.445488	+	0.494765i
$653$	28.2375	+	12.5722i	1.10502	+	0.491987i	0.876427	−	0.481535i	$-0.159921\pi$
$653$	28.2375	+	12.5722i	1.10502	+	0.491987i	0.228593	+	0.973522i	$0.426587\pi$
$654$	34.6066	−	3.63730i	1.35322	−	0.142230i
$655$	−11.8713	+	20.5617i	−0.463851	+	0.803413i
$656$	−0.309017	−	0.224514i	−0.0120651	−	0.00876580i
$657$	18.0000			0.702247
$658$	−1.35410	−	0.983813i	−0.0527884	−	0.0383530i
$659$	−5.91031	−	6.56406i	−0.230233	−	0.255700i	0.616948	−	0.787004i	$-0.288369\pi$
$659$	−5.91031	−	6.56406i	−0.230233	−	0.255700i	−0.847181	+	0.531304i	$0.821702\pi$
$660$	2.17699	−	4.88960i	0.0847392	−	0.190327i
$661$	−30.2688	+	33.6169i	−1.17732	+	1.30755i	−0.235328	+	0.971916i	$0.575616\pi$
$661$	−30.2688	+	33.6169i	−1.17732	+	1.30755i	−0.941993	+	0.335632i	$0.891050\pi$
$662$	−31.2799	+	6.64875i	−1.21573	+	0.258411i
$663$	−1.51306	−	7.11840i	−0.0587625	−	0.276456i
$664$	2.84624	+	0.604988i	0.110456	+	0.0234781i
$665$	−2.23607			−0.0867110
$666$	−9.56308	−	10.6209i	−0.370562	−	0.411551i
$667$	−8.35410	−	6.06961i	−0.323472	−	0.235016i
$668$	−10.4721	+	18.1383i	−0.405179	+	0.701791i
$669$	13.4731	+	30.2610i	0.520899	+	1.16996i
$670$	−4.27037	+	4.74273i	−0.164979	+	0.183227i
$671$	18.2006	+	8.10341i	0.702625	+	0.312829i
$672$	0.240335	+	0.330792i	0.00927111	+	0.0127606i
$673$	−16.6285	−	3.53450i	−0.640982	−	0.136245i	−0.124056	−	0.992275i	$-0.539590\pi$
$673$	−16.6285	−	3.53450i	−0.640982	−	0.136245i	−0.516926	+	0.856030i	$0.672924\pi$
$674$	2.09017			0.0805103
$675$	22.5000	+	12.9904i	0.866025	+	0.500000i
$676$	−7.32624			−0.281778
$677$	18.9376	+	4.02531i	0.727831	+	0.154705i	0.556902	−	0.830578i	$-0.311990\pi$
$677$	18.9376	+	4.02531i	0.727831	+	0.154705i	0.170929	+	0.985283i	$0.445323\pi$
$678$	−10.4211	−	14.3434i	−0.400219	−	0.550854i
$679$	0.533138	+	0.237368i	0.0204600	+	0.00910936i
$680$	0.412289	−	3.92266i	0.0158105	−	0.150427i
$681$	−14.9213	−	33.5138i	−0.571786	−	1.28425i
$682$	−4.63525	+	8.02850i	−0.177493	+	0.307427i
$683$	16.6353	+	12.0862i	0.636530	+	0.462466i	0.858656	−	0.512552i	$-0.171300\pi$
$683$	16.6353	+	12.0862i	0.636530	+	0.462466i	−0.222126	+	0.975018i	$0.571300\pi$
$684$	−12.4305	+	2.64218i	−0.475292	+	0.101026i
$685$	−14.6976	−	45.2344i	−0.561565	−	1.72832i
$686$	−3.21986	−	0.684403i	−0.122935	−	0.0261306i
$687$	−1.30290	−	6.12968i	−0.0497089	−	0.233862i
$688$	−3.39626	+	0.721898i	−0.129481	+	0.0275221i
$689$	−0.143717	+	0.159614i	−0.00547518	+	0.00608081i
$690$	6.43582	+	5.79484i	0.245008	+	0.220606i
$691$	8.40582	+	9.33561i	0.319773	+	0.355143i	0.881504	−	0.472176i	$-0.156531\pi$
$691$	8.40582	+	9.33561i	0.319773	+	0.355143i	−0.561732	+	0.827319i	$0.689865\pi$
$692$	−4.23607	−	3.07768i	−0.161031	−	0.116996i
$693$	−0.489357	−	0.847591i	−0.0185891	−	0.0321973i
$694$	9.28115	+	6.74315i	0.352308	+	0.255967i
$695$	−15.7459	+	7.01054i	−0.597277	+	0.265925i
$696$	−7.95485	+	0.836089i	−0.301528	+	0.0316919i
$697$	0.615512	+	0.274044i	0.0233142	+	0.0103801i
$698$	1.63114	−	1.81156i	0.0617394	−	0.0685685i
$699$		−	43.1082i		−	1.63050i
$700$	1.15455	+	0.245406i	0.0436378	+	0.00927549i
$701$	−21.8197			−0.824117			−0.412059	−	0.911157i	$-0.635190\pi$
$701$	−21.8197			−0.824117			−0.412059	+	0.911157i	$0.635190\pi$
$702$	11.7713	−	3.82472i	0.444278	−	0.144355i
$703$	16.3262	−	11.8617i	0.615756	−	0.447373i
$704$	−0.144455	−	1.37440i	−0.00544434	−	0.0517995i
$705$	−26.1161	+	8.48564i	−0.983590	+	0.319588i
$706$	0.722274	−	6.87198i	0.0271831	−	0.258630i
$707$	−0.517221	−	0.895853i	−0.0194521	−	0.0336920i
$708$	0.332614	+	0.747064i	0.0125004	+	0.0280764i
$709$	−8.69870	−	9.66088i	−0.326686	−	0.362822i	0.557319	−	0.830298i	$-0.311830\pi$
$709$	−8.69870	−	9.66088i	−0.326686	−	0.362822i	−0.884006	+	0.467476i	$0.845163\pi$
$710$	−19.5967			−0.735453
$711$	−16.3223	−	3.46941i	−0.612133	−	0.130113i
$712$	−2.07295	+	6.37988i	−0.0776870	+	0.239096i
$713$	−10.0370	−	11.1472i	−0.375887	−	0.417465i
$714$	−0.535985	−	0.482603i	−0.0200588	−	0.0180610i
$715$	−6.72432	−	2.99386i	−0.251475	−	0.111964i
$716$	0.692728	−	0.147244i	0.0258885	−	0.00550276i
$717$	35.5752	+	3.73910i	1.32858	+	0.139639i
$718$	3.30902	−	5.73139i	0.123491	−	0.213893i
$719$	−32.6525	−	23.7234i	−1.21773	−	0.884734i	−0.221822	−	0.975087i	$-0.571200\pi$
$719$	−32.6525	−	23.7234i	−1.21773	−	0.884734i	−0.995910	+	0.0903532i	$0.971200\pi$
$720$	6.70820			0.250000
$721$	−3.76393	+	2.73466i	−0.140176	+	0.101844i
$722$	0.110354	+	1.04994i	0.00410694	+	0.0390749i
$723$	−3.05093	+	14.3535i	−0.113465	+	0.533813i
$724$	−1.14590	−	1.98475i	−0.0425870	−	0.0737628i
$725$	−15.4503	+	17.1593i	−0.573811	+	0.637282i
$726$		−	15.7446i		−	0.584338i
$727$	8.11060	+	1.72396i	0.300806	+	0.0639382i	0.355842	−	0.934546i	$-0.384194\pi$
$727$	8.11060	+	1.72396i	0.300806	+	0.0639382i	−0.0550364	+	0.998484i	$0.517527\pi$
$728$	0.454915	−	0.330515i	0.0168603	−	0.0122497i
$729$	21.8435	−	15.8702i	0.809017	−	0.587785i
$730$	4.14590	−	12.7598i	0.153447	−	0.472260i
$731$	5.59511	−	2.49110i	0.206943	−	0.0921368i
$732$			24.9700i			0.922916i
$733$	1.87929	−	17.8802i	0.0694131	−	0.660421i	−0.903395	−	0.428809i	$-0.858933\pi$
$733$	1.87929	−	17.8802i	0.0694131	−	0.660421i	0.972808	−	0.231612i	$-0.0744000\pi$
$734$	13.1232	−	2.78943i	0.484387	−	0.102960i
$735$	−19.9869	+	17.9963i	−0.737229	+	0.663804i
$736$	2.18720	+	0.464905i	0.0806214	+	0.0171366i
$737$	1.21885	−	3.75123i	0.0448968	−	0.138178i
$738$	−0.354102	+	1.08981i	−0.0130347	+	0.0401166i
$739$	6.77051	+	20.8375i	0.249057	+	0.766519i	0.994943	+	0.100445i	$0.0320267\pi$
$739$	6.77051	+	20.8375i	0.249057	+	0.766519i	−0.745885	+	0.666074i	$0.767973\pi$
$740$	−9.73152	+	4.33275i	−0.357738	+	0.159275i
$741$	3.63361	+	17.0948i	0.133484	+	0.627992i
$742$	−0.00222502	+	0.0211696i	−8.16830e−5	+	0.000777161i
$743$	1.93769	+	3.35618i	0.0710871	+	0.123126i	0.899378	−	0.437172i	$-0.144020\pi$
$743$	1.93769	+	3.35618i	0.0710871	+	0.123126i	−0.828291	+	0.560298i	$0.810687\pi$
$744$	−11.5553	−	1.21451i	−0.423638	−	0.0445261i
$745$	−3.93936	−	37.4805i	−0.144327	−	1.37318i
$746$	−27.1525	+	19.7274i	−0.994123	+	0.722272i
$747$	−0.912480	−	8.68167i	−0.0333859	−	0.317646i
$748$	0.753289	+	2.31838i	0.0275430	+	0.0847685i
$749$	−1.13525	+	1.96632i	−0.0414813	+	0.0718477i
$750$	14.3909	−	12.9577i	0.525483	−	0.473147i
$751$	−0.663119	−	1.14856i	−0.0241976	−	0.0419114i	0.853673	−	0.520809i	$-0.174370\pi$
$751$	−0.663119	−	1.14856i	−0.0241976	−	0.0419114i	−0.877871	+	0.478898i	$0.841036\pi$
$752$	−4.74425	+	5.26902i	−0.173005	+	0.192142i
$753$	−16.8049	−	23.1300i	−0.612405	−	0.842903i
$754$	1.14981	+	10.9397i	0.0418737	+	0.398402i
$755$	12.9894	−	9.43732i	0.472731	−	0.343459i
$756$	0.721004	−	0.992377i	0.0262227	−	0.0360924i
$757$	18.6180			0.676684			0.338342	−	0.941023i	$-0.390134\pi$
$757$	18.6180			0.676684			0.338342	+	0.941023i	$0.390134\pi$
$758$	18.2709	−	8.13473i	0.663629	−	0.295467i
$759$	−5.09037	−	1.65396i	−0.184769	−	0.0600350i
$760$	−0.990108	+	9.42025i	−0.0359150	+	0.341708i
$761$	2.65348	−	2.94698i	0.0961884	−	0.106828i	−0.693129	−	0.720814i	$-0.743768\pi$
$761$	2.65348	−	2.94698i	0.0961884	−	0.106828i	0.789317	+	0.613986i	$0.210435\pi$
$762$	−22.6056	+	20.3542i	−0.818914	+	0.737353i
$763$	−3.17345	−	3.52447i	−0.114887	−	0.127594i
$764$	2.70820	+	8.33499i	0.0979794	+	0.301550i
$765$	−11.5742	+	2.46018i	−0.418468	+	0.0889480i
$766$	−6.42705	+	19.7804i	−0.232219	+	0.714696i
$767$	1.02738	−	0.457421i	0.0370967	−	0.0165165i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	−2.98335	+	28.3847i	−0.107582	+	1.02358i	0.798937	+	0.601414i	$0.205396\pi$
$769$	−2.98335	+	28.3847i	−0.107582	+	1.02358i	−0.906520	+	0.422163i	$0.861271\pi$
$770$	−0.713549	+	0.151670i	−0.0257145	+	0.00546579i
$771$	5.16125	−	11.5924i	0.185878	−	0.417489i
$772$	−1.37772	−	13.1081i	−0.0495853	−	0.471772i
$773$	−5.70820	−	17.5680i	−0.205310	−	0.631879i	−0.999701	−	0.0244715i	$-0.992210\pi$
$773$	−5.70820	−	17.5680i	−0.205310	−	0.631879i	0.794391	−	0.607407i	$-0.207790\pi$
$774$	5.20820	+	9.02087i	0.187205	+	0.324249i
$775$	−27.1353	+	19.7149i	−0.974727	+	0.708181i
$776$	1.23607	−	2.14093i	0.0443723	−	0.0768550i
$777$	−0.404988	+	1.90532i	−0.0145289	+	0.0683529i
$778$	30.4765	+	13.5690i	1.09264	+	0.486473i
$779$	−1.47815	−	0.658114i	−0.0529601	−	0.0235794i
$780$		−	9.22531i		−	0.330319i
$781$	11.0644	−	4.92617i	0.395914	−	0.176272i
$782$	−3.94427			−0.141047
$783$	9.76006	+	21.9214i	0.348796	+	0.783409i
$784$	−2.14590	+	6.60440i	−0.0766392	+	0.235871i
$785$	4.31754	+	41.0787i	0.154100	+	1.46616i
$786$	17.4909	−	5.68312i	0.623878	−	0.202710i
$787$	30.4990	−	6.48276i	1.08717	−	0.231085i	0.370735	−	0.928739i	$-0.379106\pi$
$787$	30.4990	−	6.48276i	1.08717	−	0.231085i	0.716436	+	0.697653i	$0.245772\pi$
$788$	−13.8705	+	2.94826i	−0.494115	+	0.105027i
$789$	−4.57640	+	21.5303i	−0.162924	+	0.766497i
$790$	−6.21885	+	10.7714i	−0.221257	+	0.383228i
$791$	−0.746711	+	2.29814i	−0.0265500	+	0.0817125i
$792$	−3.78747	+	1.68629i	−0.134582	+	0.0599197i
$793$	34.3394			1.21943
$794$	21.3096	−	9.48764i	0.756249	−	0.336704i
$795$	0.259526	+	0.233678i	0.00920444	+	0.00828771i
$796$	24.2659	+	10.8039i	0.860081	+	0.382933i
$797$	−0.545156	−	0.242719i	−0.0193104	−	0.00859755i	0.397059	−	0.917793i	$-0.370031\pi$
$797$	−0.545156	−	0.242719i	−0.0193104	−	0.00859755i	−0.416369	+	0.909196i	$0.636698\pi$
$798$	1.28716	+	1.15897i	0.0455651	+	0.0410270i
$799$	6.25329	−	10.8310i	0.221225	−	0.383174i
$800$	1.54508	−	4.75528i	0.0546270	−	0.168125i
$801$	20.1246			0.711068
$802$	3.69098	+	11.3597i	0.130333	+	0.401124i
$803$	0.866729	+	8.24637i	0.0305862	+	0.291008i
$804$	4.91637	−	0.516731i	0.173387	−	0.0182237i
$805$	0.123379	−	1.17387i	0.00434854	−	0.0413736i
$806$	−1.67023	+	15.8912i	−0.0588314	+	0.559743i
$807$			26.5458i			0.934457i
$808$	−4.00313	+	1.78231i	−0.140829	+	0.0627013i
$809$	−0.506578	+	1.55909i	−0.0178103	+	0.0548146i	−0.959567	−	0.281481i	$-0.909174\pi$
$809$	−0.506578	+	1.55909i	−0.0178103	+	0.0548146i	0.941756	+	0.336296i	$0.109174\pi$
$810$	−6.21885	−	19.1396i	−0.218508	−	0.672499i
$811$	−2.92705	−	9.00854i	−0.102783	−	0.316333i	0.886421	−	0.462880i	$-0.153184\pi$
$811$	−2.92705	−	9.00854i	−0.102783	−	0.316333i	−0.989204	+	0.146547i	$0.953184\pi$
$812$	0.729466	+	0.810154i	0.0255992	+	0.0284308i
$813$	25.1898	+	8.18468i	0.883446	+	0.287049i
$814$	4.40528	−	4.89256i	0.154405	−	0.171484i
$815$	25.4358	−	28.2493i	0.890976	−	0.989529i
$816$	−2.27047	+	2.04434i	−0.0794824	+	0.0715663i
$817$	−13.4366	+	5.98237i	−0.470088	+	0.209296i
$818$	−23.5623			−0.823837
$819$	−1.36475	−	0.991545i	−0.0476881	−	0.0346474i
$820$	0.690983	+	0.502029i	0.0241302	+	0.0175316i
$821$	−1.17089	−	11.1403i	−0.0408643	−	0.388798i	−0.995769	−	0.0918868i	$-0.970710\pi$
$821$	−1.17089	−	11.1403i	−0.0408643	−	0.388798i	0.954905	−	0.296911i	$-0.0959565\pi$
$822$	−14.9848	+	33.6565i	−0.522656	+	1.17390i
$823$	−7.84856	+	8.71671i	−0.273584	+	0.303845i	−0.864242	−	0.503076i	$-0.832201\pi$
$823$	−7.84856	+	8.71671i	−0.273584	+	0.303845i	0.590658	+	0.806922i	$0.298868\pi$
$824$	9.85410	+	17.0678i	0.343284	+	0.594585i
$825$	−4.86790	+	10.9335i	−0.169478	+	0.380655i
$826$	0.0557281	−	0.0965239i	0.00193903	−	0.00335850i
$827$	−2.81559	−	8.66551i	−0.0979078	−	0.301329i	0.890093	−	0.455779i	$-0.150639\pi$
$827$	−2.81559	−	8.66551i	−0.0979078	−	0.301329i	−0.988001	+	0.154450i	$0.950639\pi$
$828$	−0.701198	−	6.67146i	−0.0243683	−	0.231849i
$829$	−37.3328	+	27.1239i	−1.29662	+	0.942051i	−0.999917	−	0.0129177i	$-0.995888\pi$
$829$	−37.3328	+	27.1239i	−1.29662	+	0.942051i	−0.296706	+	0.954969i	$0.595888\pi$
$830$	−6.36439	−	1.35279i	−0.220911	−	0.0469562i
$831$	7.71011	+	17.3172i	0.267461	+	0.600727i
$832$	−1.19098	−	2.06284i	−0.0412899	−	0.0715162i
$833$	1.28039	−	12.1821i	0.0443630	−	0.422085i
$834$	12.6976	+	4.12569i	0.439680	+	0.142861i
$835$	23.4164	−	40.5584i	0.810358	−	1.40358i
$836$	−1.80902	−	5.56758i	−0.0625662	−	0.192559i
$837$	7.24715	+	34.0951i	0.250498	+	1.17850i
$838$	−6.20820	+	19.1069i	−0.214459	+	0.660036i
$839$	−19.1556	−	4.07166i	−0.661326	−	0.140569i	−0.134992	−	0.990847i	$-0.543101\pi$
$839$	−19.1556	−	4.07166i	−0.661326	−	0.140569i	−0.526335	+	0.850278i	$0.676434\pi$
$840$	−0.537405	−	0.739674i	−0.0185422	−	0.0255212i
$841$	7.50607	−	1.59546i	0.258830	−	0.0550160i
$842$	1.40240	−	13.3429i	0.0483298	−	0.459827i
$843$	−47.2082	−	27.2557i	−1.62594	−	0.938735i
$844$	−19.1650	+	8.53281i	−0.659687	+	0.293711i
$845$	16.3820			0.563557
$846$	19.4316	+	8.65150i	0.668071	+	0.297445i
$847$	−1.73607	+	1.26133i	−0.0596520	+	0.0433397i
$848$	0.0881995	+	0.0187474i	0.00302878	+	0.000643788i
$849$	−42.8951	+	24.7655i	−1.47216	+	0.849950i
$850$	−0.921906	+	8.77135i	−0.0316211	+	0.300855i
$851$	5.32624	+	9.22531i	0.182581	+	0.316240i
$852$	11.2806	+	10.1571i	0.386468	+	0.347977i
$853$	−0.165530	−	1.57492i	−0.00566765	−	0.0539241i	0.991323	−	0.131452i	$-0.0419640\pi$
$853$	−0.165530	−	1.57492i	−0.00566765	−	0.0539241i	−0.996990	+	0.0775280i	$0.975297\pi$
$854$	2.75329	−	2.00038i	0.0942156	−	0.0684516i
$855$	27.7954	−	5.90810i	0.950584	−	0.202053i
$856$	7.78115	+	5.65334i	0.265954	+	0.193227i
$857$	26.8607	−	46.5241i	0.917543	−	1.58923i	0.114409	−	0.993434i	$-0.463503\pi$
$857$	26.8607	−	46.5241i	0.917543	−	1.58923i	0.803134	−	0.595798i	$-0.203164\pi$
$858$	2.31903	+	5.20863i	0.0791705	+	0.177820i
$859$	5.03345	−	1.06989i	0.171739	−	0.0365043i	−0.121239	−	0.992623i	$-0.538687\pi$
$859$	5.03345	−	1.06989i	0.171739	−	0.0365043i	0.292978	+	0.956119i	$0.405354\pi$
$860$	7.59427	−	1.61421i	0.258963	−	0.0550442i
$861$	0.148535	−	0.0482619i	0.00506206	−	0.00164476i
$862$	−4.30766	−	4.78414i	−0.146719	−	0.162948i
$863$	15.4549	−	47.5653i	0.526091	−	1.61914i	−0.236056	−	0.971739i	$-0.575855\pi$
$863$	15.4549	−	47.5653i	0.526091	−	1.61914i	0.762147	−	0.647403i	$-0.224145\pi$
$864$	−3.86149	−	3.47690i	−0.131371	−	0.118287i
$865$	9.47214	+	6.88191i	0.322062	+	0.233992i
$866$	10.2322	+	11.3640i	0.347705	+	0.386165i
$867$	−14.1396	+	19.4614i	−0.480205	+	0.660945i
$868$	0.791796	+	1.37143i	0.0268753	+	0.0465494i
$869$	0.803502	−	7.64481i	0.0272569	−	0.259332i
$870$	17.7876	−	1.86955i	0.603056	−	0.0633837i
$871$	−0.710624	−	6.76113i	−0.0240786	−	0.229092i
$872$	−16.2533	+	11.8087i	−0.550406	+	0.399893i
$873$	−7.25434	−	1.54196i	−0.245522	−	0.0521874i
$874$	9.47214			0.320400
$875$	−2.58164	−	0.548746i	−0.0872755	−	0.0185510i
$876$	−9.00000	+	5.19615i	−0.304082	+	0.175562i
$877$	30.4641	−	33.8338i	1.02870	−	1.14249i	0.0390122	−	0.999239i	$-0.487579\pi$
$877$	30.4641	−	33.8338i	1.02870	−	1.14249i	0.989687	−	0.143247i	$-0.0457545\pi$
$878$	−6.77523	−	3.01652i	−0.228653	−	0.101803i
$879$	14.3439	−	32.2168i	0.483807	−	1.08665i
$880$	0.323011	+	3.07324i	0.0108887	+	0.103599i
$881$	−9.20820	−	6.69015i	−0.310232	−	0.225397i	0.421764	−	0.906706i	$-0.361411\pi$
$881$	−9.20820	−	6.69015i	−0.310232	−	0.225397i	−0.731996	+	0.681309i	$0.761411\pi$
$882$	20.8328			0.701477
$883$	−30.9787	−	22.5074i	−1.04252	−	0.757433i	−0.0717415	−	0.997423i	$-0.522856\pi$
$883$	−30.9787	−	22.5074i	−1.04252	−	0.757433i	−0.970775	+	0.239991i	$0.922856\pi$
$884$	2.81144	+	3.12242i	0.0945588	+	0.105018i
$885$	−0.743748	−	1.67049i	−0.0250008	−	0.0561528i
$886$	24.3904	−	27.0883i	0.819411	−	0.910048i
$887$	−27.1027	+	5.76086i	−0.910020	+	0.193431i	−0.639057	−	0.769159i	$-0.720675\pi$
$887$	−27.1027	+	5.76086i	−0.910020	+	0.193431i	−0.270963	+	0.962590i	$0.587342\pi$
$888$	7.84752	+	2.54981i	0.263346	+	0.0855662i
$889$	4.05530	+	0.861981i	0.136010	+	0.0289099i
$890$	4.63525	−	14.2658i	0.155374	−	0.478192i
$891$	8.32244	+	9.24301i	0.278812	+	0.309652i
$892$	−15.4721	−	11.2412i	−0.518045	−	0.376382i
$893$	−15.0172	+	26.0106i	−0.502532	+	0.870411i
$894$	−17.1587	+	23.6170i	−0.573873	+	0.789869i
$895$	−1.54899	+	0.329247i	−0.0517769	+	0.0110055i
$896$	−0.215659	−	0.0960175i	−0.00720466	−	0.00320772i
$897$	−9.17478	+	0.964308i	−0.306337	+	0.0321973i
$898$	18.7275	+	3.98066i	0.624945	+	0.132836i
$899$	−30.9787			−1.03320
$900$	−15.0000			−0.500000
$901$	−0.159054			−0.00529885
$902$	−0.516329	−	0.109749i	−0.0171919	−	0.00365425i
$903$	0.577441	−	1.29695i	0.0192160	−	0.0431599i
$904$	9.35111	+	4.16338i	0.311013	+	0.138472i
$905$	2.56231	+	4.43804i	0.0851739	+	0.147526i
$906$	−12.3686	−	1.29999i	−0.410919	−	0.0431893i
$907$	−15.4443	+	26.7503i	−0.512819	+	0.888228i	0.487071	+	0.873362i	$0.338065\pi$
$907$	−15.4443	+	26.7503i	−0.512819	+	0.888228i	−0.999890	+	0.0148655i	$0.995268\pi$
$908$	17.1353	+	12.4495i	0.568653	+	0.413151i
$909$	8.79632	+	9.76931i	0.291756	+	0.324027i
$910$	−1.01722	+	0.739054i	−0.0337205	+	0.0244994i
$911$	−39.5332	−	8.40304i	−1.30979	−	0.278405i	−0.500463	−	0.865758i	$-0.666837\pi$
$911$	−39.5332	−	8.40304i	−1.30979	−	0.278405i	−0.809331	+	0.587353i	$0.800170\pi$
$912$	5.45252	−	4.90947i	0.180551	−	0.162569i
$913$	3.93341	−	0.836072i	0.130177	−	0.0276700i
$914$	−8.87970	+	9.86191i	−0.293715	+	0.326203i
$915$		−	55.8345i		−	1.84583i
$916$	2.42094	+	2.68872i	0.0799900	+	0.0888379i
$917$	−2.02786	−	1.47333i	−0.0669660	−	0.0486536i
$918$	7.93769	+	4.58283i	0.261983	+	0.151256i
$919$	4.28115	+	3.11044i	0.141222	+	0.102604i	0.656153	−	0.754628i	$-0.272182\pi$
$919$	4.28115	+	3.11044i	0.141222	+	0.102604i	−0.514931	+	0.857232i	$0.672182\pi$
$920$	−4.89074	−	1.03956i	−0.161243	−	0.0342732i
$921$	−10.7532	−	14.8005i	−0.354330	−	0.487694i
$922$	25.0147	+	11.1372i	0.823814	+	0.366786i
$923$	13.9684	−	15.5134i	0.459774	−	0.510631i
$924$	0.489357	+	0.282530i	0.0160987	+	0.00929457i
$925$	21.7603	−	9.68833i	0.715476	−	0.318550i
$926$	4.41641			0.145132
$927$	39.5621	−	43.9381i	1.29939	−	1.44312i
$928$	3.73607	−	2.71441i	0.122642	−	0.0891049i
$929$	−2.29740	−	21.8583i	−0.0753753	−	0.717148i	−0.965318	−	0.261076i	$-0.915923\pi$
$929$	−2.29740	−	21.8583i	−0.0753753	−	0.717148i	0.889943	−	0.456072i	$-0.150744\pi$
$930$	25.8384	+	2.71573i	0.847276	+	0.0890523i
$931$	−3.07485	+	29.2553i	−0.100774	+	0.958802i
$932$	12.4443	+	21.5541i	0.407626	+	0.706028i
$933$	−47.1305	−	4.95361i	−1.54298	−	0.162174i
$934$	6.33810	+	7.03917i	0.207389	+	0.230329i
$935$	−1.68441	−	5.18407i	−0.0550859	−	0.169537i
$936$	−4.78154	+	5.31044i	−0.156289	+	0.173577i
$937$	9.28115	−	28.5645i	0.303202	−	0.933160i	−0.677140	−	0.735854i	$-0.736781\pi$
$937$	9.28115	−	28.5645i	0.303202	−	0.933160i	0.980342	−	0.197306i	$-0.0632192\pi$
$938$	−0.450835	−	0.500703i	−0.0147203	−	0.0163485i
$939$	9.40783	−	44.2604i	0.307013	−	1.44438i
$940$	10.6085	−	11.7819i	0.346010	−	0.384283i
$941$	−43.2486	+	9.19277i	−1.40986	+	0.299676i	−0.849070	−	0.528280i	$-0.822837\pi$
$941$	−43.2486	+	9.19277i	−1.40986	+	0.299676i	−0.560793	+	0.827956i	$0.689504\pi$
$942$	18.8060	−	25.8842i	0.612733	−	0.843354i
$943$	0.427051	−	0.739674i	0.0139067	−	0.0240871i
$944$	−0.381966	−	0.277515i	−0.0124319	−	0.00903233i
$945$	−1.61221	+	2.21902i	−0.0524453	+	0.0721848i
$946$	−3.88197	+	2.82041i	−0.126214	+	0.0916995i
$947$	−0.142230	−	1.35323i	−0.00462185	−	0.0439739i	0.991968	−	0.126490i	$-0.0403711\pi$
$947$	−0.142230	−	1.35323i	−0.00462185	−	0.0439739i	−0.996590	+	0.0825159i	$0.973704\pi$
$948$	9.16267	−	2.97713i	0.297590	−	0.0966927i
$949$	7.14590	+	12.3771i	0.231966	+	0.401776i
$950$	2.21395	−	21.0643i	0.0718300	−	0.683417i
$951$	2.37539	+	1.37143i	0.0770272	+	0.0444717i
$952$	0.407308	+	0.0865761i	0.0132009	+	0.00280595i
$953$	−7.66312	+	5.56758i	−0.248233	+	0.180352i	−0.704943	−	0.709264i	$-0.749028\pi$
$953$	−7.66312	+	5.56758i	−0.248233	+	0.180352i	0.456710	+	0.889615i	$0.349028\pi$
$954$	−0.0282760	−	0.269028i	−0.000915469	−	0.00871010i
$955$	−6.05573	−	18.6376i	−0.195959	−	0.603099i
$956$	−18.8670	+	8.40012i	−0.610202	+	0.271679i
$957$	−9.57295	+	5.52694i	−0.309449	+	0.178661i
$958$	−2.96450	+	28.2053i	−0.0957786	+	0.911272i
$959$	4.91156	−	1.04398i	0.158603	−	0.0337120i
$960$	−3.35410	+	1.93649i	−0.108253	+	0.0625000i
$961$	−13.6941	−	2.91076i	−0.441744	−	0.0938956i
$962$	3.50658	−	10.7921i	0.113057	−	0.347952i
$963$	8.91641	−	27.4419i	0.287327	−	0.884302i
$964$	−2.61803	−	8.05748i	−0.0843212	−	0.259514i
$965$	3.08068	+	29.3107i	0.0991705	+	0.943544i
$966$	−0.679448	+	0.611778i	−0.0218609	+	0.0196836i
$967$	−0.123379	+	1.17387i	−0.00396760	+	0.0377492i	−0.996327	−	0.0856350i	$-0.972708\pi$
$967$	−0.123379	+	1.17387i	−0.00396760	+	0.0377492i	0.992359	+	0.123384i	$0.0393748\pi$
$968$	4.54508	+	7.87232i	0.146085	+	0.253026i
$969$	−7.60719	+	10.4704i	−0.244378	+	0.336358i
$970$	−2.76393	+	4.78727i	−0.0887445	+	0.153710i
$971$	26.0344	−	18.9151i	0.835485	−	0.607015i	−0.0856208	−	0.996328i	$-0.527287\pi$
$971$	26.0344	−	18.9151i	0.835485	−	0.607015i	0.921106	+	0.389312i	$0.127287\pi$
$972$	−6.34040	+	14.2408i	−0.203368	+	0.456773i
$973$	−0.562306	−	1.73060i	−0.0180267	−	0.0554805i
$974$	−2.44427	+	4.23360i	−0.0783195	+	0.135653i
$975$			20.6284i			0.660639i
$976$	−7.20820	−	12.4850i	−0.230729	−	0.399634i
$977$	22.3084	−	24.7760i	0.713709	−	0.792654i	−0.271786	−	0.962358i	$-0.587614\pi$
$977$	22.3084	−	24.7760i	0.713709	−	0.792654i	0.985495	+	0.169703i	$0.0542809\pi$
$978$	−29.2836	+	3.07783i	−0.936385	+	0.0984180i
$979$	0.969032	+	9.21973i	0.0309704	+	0.294664i
$980$	4.79837	−	14.7679i	0.153278	−	0.471743i
$981$	48.7599	+	35.4261i	1.55678	+	1.13107i
$982$	−31.4164			−1.00254
$983$	14.0012	−	6.23374i	0.446569	−	0.198826i	−0.171116	−	0.985251i	$-0.554737\pi$
$983$	14.0012	−	6.23374i	0.446569	−	0.198826i	0.617685	+	0.786425i	$0.288071\pi$
$984$	−0.137551	−	0.647127i	−0.00438497	−	0.0206297i
$985$	31.0153	−	6.59251i	0.988230	−	0.210055i
$986$	−5.45067	+	6.05358i	−0.173585	+	0.192785i
$987$	−0.602745	−	2.83569i	−0.0191856	−	0.0902610i
$988$	−6.75164	−	7.49846i	−0.214798	−	0.238558i
$989$	−2.39919	−	7.38394i	−0.0762897	−	0.234796i
$990$	8.46903	−	3.77066i	0.269164	−	0.119839i
$991$	10.3197	−	31.7606i	0.327815	−	1.00891i	−0.642339	−	0.766421i	$-0.722036\pi$
$991$	10.3197	−	31.7606i	0.327815	−	1.00891i	0.970154	−	0.242490i	$-0.0779641\pi$
$992$	6.12825	−	2.72847i	0.194572	−	0.0866291i
$993$	−47.9681	−	27.6944i	−1.52222	−	0.878855i
$994$	0.216257	−	2.05755i	0.00685926	−	0.0652615i
$995$	−54.2601	−	24.1582i	−1.72016	−	0.765866i
$996$	2.96242	+	4.07742i	0.0938679	+	0.129198i
$997$	−2.69889	−	25.6782i	−0.0854747	−	0.813237i	−0.950336	−	0.311226i	$-0.899260\pi$
$997$	−2.69889	−	25.6782i	−0.0854747	−	0.813237i	0.864861	−	0.502011i	$-0.167406\pi$
$998$	1.06231	+	3.26944i	0.0336267	+	0.103492i
$999$		−	24.7541i		−	0.783186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.q.a.331.1	yes	8
9.4	even	3	inner	450.2.q.a.31.1	✓	8
25.21	even	5	inner	450.2.q.a.421.1	yes	8
225.121	even	15	inner	450.2.q.a.121.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.q.a.31.1	✓	8	9.4	even	3	inner
450.2.q.a.121.1	yes	8	225.121	even	15	inner
450.2.q.a.331.1	yes	8	1.1	even	1	trivial
450.2.q.a.421.1	yes	8	25.21	even	5	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.01807 - 1.40126i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.04275 - 0.909491i) q^{5} +(0.704489 + 1.58231i) q^{6} +(0.118034 - 0.204441i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.01807 - 1.40126i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.04275 - 0.909491i) q^{5} +(0.704489 + 1.58231i) q^{6} +(0.118034 - 0.204441i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 + 2.85317i) q^{9} +(1.80902 + 1.31433i) q^{10} +(-1.35177 - 0.287327i) q^{11} +(-0.360114 - 1.69420i) q^{12} +(-2.32991 + 0.495239i) q^{13} +(-0.157960 + 0.175433i) q^{14} +(0.805239 + 3.78835i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.42705 - 1.03681i) q^{17} +(1.50000 - 2.59808i) q^{18} +(3.42705 + 2.48990i) q^{19} +(-1.49622 - 1.66172i) q^{20} +(-0.406642 + 0.0427398i) q^{21} +(1.26249 + 0.562096i) q^{22} +(-1.49622 + 1.66172i) q^{23} +1.73205i q^{24} +(3.34565 + 3.71572i) q^{25} +2.38197 q^{26} +(4.94183 - 1.60570i) q^{27} +(0.190983 - 0.138757i) q^{28} +(0.482716 + 4.59274i) q^{29} -3.87298i q^{30} +(-0.701198 + 6.67146i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.973579 + 2.18669i) q^{33} +(1.18030 + 1.31086i) q^{34} +(-0.427051 + 0.310271i) q^{35} +(-2.00739 + 2.22943i) q^{36} +(1.47214 - 4.53077i) q^{37} +(-2.83448 - 3.14801i) q^{38} +(3.06598 + 2.76062i) q^{39} +(1.11803 + 1.93649i) q^{40} +(-0.373619 + 0.0794152i) q^{41} +(0.406642 + 0.0427398i) q^{42} +(-1.73607 + 3.00696i) q^{43} +(-1.11803 - 0.812299i) q^{44} +(4.48866 - 4.98517i) q^{45} +(1.80902 - 1.31433i) q^{46} +(0.741125 + 7.05133i) q^{47} +(0.360114 - 1.69420i) q^{48} +(3.47214 + 6.01392i) q^{49} +(-2.50000 - 4.33013i) q^{50} +3.05522i q^{51} +(-2.32991 - 0.495239i) q^{52} +(0.0729490 - 0.0530006i) q^{53} +(-5.16769 + 0.543146i) q^{54} +(2.50000 + 1.81636i) q^{55} +(-0.215659 + 0.0960175i) q^{56} -7.33708i q^{57} +(0.482716 - 4.59274i) q^{58} +(-0.461819 + 0.0981626i) q^{59} +(-0.805239 + 3.78835i) q^{60} +(-14.1014 - 2.99734i) q^{61} +(2.07295 - 6.37988i) q^{62} +(0.473881 + 0.526298i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.20985 + 1.10739i) q^{65} +(-0.497665 - 2.34133i) q^{66} +(-0.298335 + 2.83847i) q^{67} +(-0.881966 - 1.52761i) q^{68} +(3.85177 + 0.404837i) q^{69} +(0.482228 - 0.214702i) q^{70} +(-7.09017 + 5.15131i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-1.85410 - 5.70634i) q^{73} +(-2.38197 + 4.12569i) q^{74} +(1.80057 - 8.47101i) q^{75} +(2.11803 + 3.66854i) q^{76} +(-0.218296 + 0.242442i) q^{77} +(-2.42502 - 3.33775i) q^{78} +(0.581419 + 5.53184i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-7.28115 - 5.29007i) q^{81} +0.381966 q^{82} +(-2.65826 + 1.18353i) q^{83} +(-0.388870 - 0.126351i) q^{84} +(1.97214 + 3.41584i) q^{85} +(2.32331 - 2.58030i) q^{86} +(5.94417 - 5.35215i) q^{87} +(0.924716 + 1.02700i) q^{88} +(-2.07295 - 6.37988i) q^{89} +(-5.42705 + 3.94298i) q^{90} +(-0.173762 + 0.534785i) q^{91} +(-2.04275 + 0.909491i) q^{92} +(10.0623 - 5.80948i) q^{93} +(0.741125 - 7.05133i) q^{94} +(-4.73607 - 8.20311i) q^{95} +(-0.704489 + 1.58231i) q^{96} +(0.258409 + 2.45859i) q^{97} +(-2.14590 - 6.60440i) q^{98} +(2.07295 - 3.59045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 5 q^{5} + 3 q^{6} - 8 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q + q^2 + q^4 - 5 * q^5 + 3 * q^6 - 8 * q^7 - 2 * q^8 + 6 * q^9	\( 8 q + q^{2} + q^{4} - 5 q^{5} + 3 q^{6} - 8 q^{7} - 2 q^{8} + 6 q^{9} + 10 q^{10} + 5 q^{11} - 3 q^{12} + 6 q^{13} + 7 q^{14} - 15 q^{15} + q^{16} + 2 q^{17} + 12 q^{18} + 14 q^{19} + 5 q^{20} - 9 q^{21} + 5 q^{23} + 5 q^{25} + 28 q^{26} + 6 q^{28} - 6 q^{29} + 15 q^{31} - 4 q^{32} + 9 q^{34} + 10 q^{35} - 3 q^{36} - 24 q^{37} + 3 q^{38} - 18 q^{39} + 4 q^{41} + 9 q^{42} + 4 q^{43} - 15 q^{45} + 10 q^{46} - 14 q^{47} + 3 q^{48} - 8 q^{49} - 20 q^{50} + 6 q^{52} + 14 q^{53} - 9 q^{54} + 20 q^{55} - 3 q^{56} - 6 q^{58} - 14 q^{59} + 15 q^{60} - 29 q^{61} + 30 q^{62} - 21 q^{63} - 2 q^{64} + 20 q^{65} - 15 q^{66} + 7 q^{67} - 16 q^{68} + 15 q^{69} - 5 q^{70} - 12 q^{71} + 6 q^{72} + 12 q^{73} - 28 q^{74} + 15 q^{75} + 8 q^{76} + 25 q^{77} - 18 q^{79} - 10 q^{80} - 18 q^{81} + 12 q^{82} + 4 q^{83} - 20 q^{85} - 11 q^{86} - 3 q^{87} + 5 q^{88} - 30 q^{89} - 30 q^{90} - 64 q^{91} - 5 q^{92} - 14 q^{94} - 20 q^{95} - 3 q^{96} - 8 q^{97} - 44 q^{98} + 30 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^4 - 5 * q^5 + 3 * q^6 - 8 * q^7 - 2 * q^8 + 6 * q^9 + 10 * q^10 + 5 * q^11 - 3 * q^12 + 6 * q^13 + 7 * q^14 - 15 * q^15 + q^16 + 2 * q^17 + 12 * q^18 + 14 * q^19 + 5 * q^20 - 9 * q^21 + 5 * q^23 + 5 * q^25 + 28 * q^26 + 6 * q^28 - 6 * q^29 + 15 * q^31 - 4 * q^32 + 9 * q^34 + 10 * q^35 - 3 * q^36 - 24 * q^37 + 3 * q^38 - 18 * q^39 + 4 * q^41 + 9 * q^42 + 4 * q^43 - 15 * q^45 + 10 * q^46 - 14 * q^47 + 3 * q^48 - 8 * q^49 - 20 * q^50 + 6 * q^52 + 14 * q^53 - 9 * q^54 + 20 * q^55 - 3 * q^56 - 6 * q^58 - 14 * q^59 + 15 * q^60 - 29 * q^61 + 30 * q^62 - 21 * q^63 - 2 * q^64 + 20 * q^65 - 15 * q^66 + 7 * q^67 - 16 * q^68 + 15 * q^69 - 5 * q^70 - 12 * q^71 + 6 * q^72 + 12 * q^73 - 28 * q^74 + 15 * q^75 + 8 * q^76 + 25 * q^77 - 18 * q^79 - 10 * q^80 - 18 * q^81 + 12 * q^82 + 4 * q^83 - 20 * q^85 - 11 * q^86 - 3 * q^87 + 5 * q^88 - 30 * q^89 - 30 * q^90 - 64 * q^91 - 5 * q^92 - 14 * q^94 - 20 * q^95 - 3 * q^96 - 8 * q^97 - 44 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

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