LMFDB - Embedded newform 605.2.e.b.362.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.7
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.407176 + 0.407176i) q^{2} +(-0.544295 + 0.544295i) q^{3} +1.66842i q^{4} +(0.752803 + 2.10554i) q^{5} -0.443248i q^{6} +(0.843711 - 0.843711i) q^{7} +(-1.49369 - 1.49369i) q^{8} +2.40749i q^{9} +O(q^{10})$	\(q+(-0.407176 + 0.407176i) q^{2} +(-0.544295 + 0.544295i) q^{3} +1.66842i q^{4} +(0.752803 + 2.10554i) q^{5} -0.443248i q^{6} +(0.843711 - 0.843711i) q^{7} +(-1.49369 - 1.49369i) q^{8} +2.40749i q^{9} +(-1.16385 - 0.550801i) q^{10} +(-0.908110 - 0.908110i) q^{12} +(4.29788 + 4.29788i) q^{13} +0.687078i q^{14} +(-1.55578 - 0.736287i) q^{15} -2.12044 q^{16} +(-0.262219 + 0.262219i) q^{17} +(-0.980271 - 0.980271i) q^{18} +1.37688 q^{19} +(-3.51291 + 1.25599i) q^{20} +0.918455i q^{21} +(3.48057 - 3.48057i) q^{23} +1.62602 q^{24} +(-3.86658 + 3.17011i) q^{25} -3.49999 q^{26} +(-2.94327 - 2.94327i) q^{27} +(1.40766 + 1.40766i) q^{28} -6.12632 q^{29} +(0.933275 - 0.333678i) q^{30} -2.47403 q^{31} +(3.85077 - 3.85077i) q^{32} -0.213539i q^{34} +(2.41161 + 1.14132i) q^{35} -4.01669 q^{36} +(2.10427 + 2.10427i) q^{37} +(-0.560631 + 0.560631i) q^{38} -4.67863 q^{39} +(2.02057 - 4.26948i) q^{40} -6.12549i q^{41} +(-0.373973 - 0.373973i) q^{42} +(-6.75396 - 6.75396i) q^{43} +(-5.06905 + 1.81236i) q^{45} +2.83441i q^{46} +(0.902785 + 0.902785i) q^{47} +(1.15414 - 1.15414i) q^{48} +5.57630i q^{49} +(0.283585 - 2.86517i) q^{50} -0.285449i q^{51} +(-7.17065 + 7.17065i) q^{52} +(-0.288499 + 0.288499i) q^{53} +2.39686 q^{54} -2.52049 q^{56} +(-0.749427 + 0.749427i) q^{57} +(2.49449 - 2.49449i) q^{58} +0.187849i q^{59} +(1.22843 - 2.59569i) q^{60} -0.683312i q^{61} +(1.00736 - 1.00736i) q^{62} +(2.03122 + 2.03122i) q^{63} -1.10499i q^{64} +(-5.81389 + 12.2848i) q^{65} +(7.14016 + 7.14016i) q^{67} +(-0.437491 - 0.437491i) q^{68} +3.78891i q^{69} +(-1.44667 + 0.517234i) q^{70} +1.03406 q^{71} +(3.59604 - 3.59604i) q^{72} +(3.23297 + 3.23297i) q^{73} -1.71362 q^{74} +(0.379084 - 3.83003i) q^{75} +2.29720i q^{76} +(1.90503 - 1.90503i) q^{78} -11.6347 q^{79} +(-1.59627 - 4.46467i) q^{80} -4.01845 q^{81} +(2.49415 + 2.49415i) q^{82} +(8.04790 + 8.04790i) q^{83} -1.53236 q^{84} +(-0.749512 - 0.354713i) q^{85} +5.50010 q^{86} +(3.33452 - 3.33452i) q^{87} +8.04021i q^{89} +(1.32605 - 2.80195i) q^{90} +7.25234 q^{91} +(5.80704 + 5.80704i) q^{92} +(1.34660 - 1.34660i) q^{93} -0.735185 q^{94} +(1.03652 + 2.89906i) q^{95} +4.19191i q^{96} +(5.96870 + 5.96870i) q^{97} +(-2.27054 - 2.27054i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.407176	+	0.407176i	−0.287917	+	0.287917i	−0.836256	−	0.548339i	$-0.815260\pi$
$2$	−0.407176	+	0.407176i	−0.287917	+	0.287917i	0.548339	+	0.836256i	$0.315260\pi$
$3$	−0.544295	+	0.544295i	−0.314249	+	0.314249i	−0.846553	−	0.532304i	$-0.821326\pi$
$3$	−0.544295	+	0.544295i	−0.314249	+	0.314249i	0.532304	+	0.846553i	$0.321326\pi$
$4$			1.66842i			0.834208i
$5$	0.752803	+	2.10554i	0.336664	+	0.941625i
$5$	0.752803	+	2.10554i	0.336664	+	0.941625i
$6$		−	0.443248i		−	0.180955i
$7$	0.843711	−	0.843711i	0.318893	−	0.318893i	−0.529449	−	0.848342i	$-0.677601\pi$
$7$	0.843711	−	0.843711i	0.318893	−	0.318893i	0.848342	+	0.529449i	$0.177601\pi$
$8$	−1.49369	−	1.49369i	−0.528100	−	0.528100i
$9$			2.40749i			0.802495i
$10$	−1.16385	−	0.550801i	−0.368041	−	0.174179i
$11$		0			0
$11$		0			0
$12$	−0.908110	−	0.908110i	−0.262149	−	0.262149i
$13$	4.29788	+	4.29788i	1.19202	+	1.19202i	0.976500	+	0.215518i	$0.0691438\pi$
$13$	4.29788	+	4.29788i	1.19202	+	1.19202i	0.215518	+	0.976500i	$0.430856\pi$
$14$			0.687078i			0.183629i
$15$	−1.55578	−	0.736287i	−0.401701	−	0.190108i
$16$	−2.12044			−0.530110
$17$	−0.262219	+	0.262219i	−0.0635975	+	0.0635975i	−0.738190	−	0.674593i	$-0.764319\pi$
$17$	−0.262219	+	0.262219i	−0.0635975	+	0.0635975i	0.674593	+	0.738190i	$0.264319\pi$
$18$	−0.980271	−	0.980271i	−0.231052	−	0.231052i
$19$	1.37688			0.315877			0.157939	−	0.987449i	$-0.449515\pi$
$19$	1.37688			0.315877			0.157939	+	0.987449i	$0.449515\pi$
$20$	−3.51291	+	1.25599i	−0.785511	+	0.280847i
$21$			0.918455i			0.200423i
$22$		0			0
$23$	3.48057	−	3.48057i	0.725749	−	0.725749i	−0.244021	−	0.969770i	$-0.578467\pi$
$23$	3.48057	−	3.48057i	0.725749	−	0.725749i	0.969770	+	0.244021i	$0.0784665\pi$
$24$	1.62602			0.331909
$25$	−3.86658	+	3.17011i	−0.773315	+	0.634022i
$26$	−3.49999			−0.686404
$27$	−2.94327	−	2.94327i	−0.566432	−	0.566432i
$28$	1.40766	+	1.40766i	0.266023	+	0.266023i
$29$	−6.12632			−1.13763			−0.568814	−	0.822466i	$-0.692598\pi$
$29$	−6.12632			−1.13763			−0.568814	+	0.822466i	$0.692598\pi$
$30$	0.933275	−	0.333678i	0.170392	−	0.0609210i
$31$	−2.47403			−0.444348			−0.222174	−	0.975007i	$-0.571315\pi$
$31$	−2.47403			−0.444348			−0.222174	+	0.975007i	$0.571315\pi$
$32$	3.85077	−	3.85077i	0.680727	−	0.680727i
$33$		0			0
$34$		−	0.213539i		−	0.0366216i
$35$	2.41161	+	1.14132i	0.407637	+	0.192918i
$36$	−4.01669			−0.669448
$37$	2.10427	+	2.10427i	0.345940	+	0.345940i	0.858595	−	0.512655i	$-0.171338\pi$
$37$	2.10427	+	2.10427i	0.345940	+	0.345940i	−0.512655	+	0.858595i	$0.671338\pi$
$38$	−0.560631	+	0.560631i	−0.0909464	+	0.0909464i
$39$	−4.67863			−0.749180
$40$	2.02057	−	4.26948i	0.319480	−	0.675064i
$41$		−	6.12549i		−	0.956641i	−0.878185	−	0.478321i	$-0.841246\pi$
$41$		−	6.12549i		−	0.956641i	0.878185	−	0.478321i	$-0.158754\pi$
$42$	−0.373973	−	0.373973i	−0.0577053	−	0.0577053i
$43$	−6.75396	−	6.75396i	−1.02997	−	1.02997i	−0.999537	−	0.0304328i	$-0.990311\pi$
$43$	−6.75396	−	6.75396i	−1.02997	−	1.02997i	−0.0304328	−	0.999537i	$-0.509689\pi$
$44$		0			0
$45$	−5.06905	+	1.81236i	−0.755650	+	0.270171i
$46$			2.83441i			0.417911i
$47$	0.902785	+	0.902785i	0.131685	+	0.131685i	0.769877	−	0.638192i	$-0.220318\pi$
$47$	0.902785	+	0.902785i	0.131685	+	0.131685i	−0.638192	+	0.769877i	$0.720318\pi$
$48$	1.15414	−	1.15414i	0.166586	−	0.166586i
$49$			5.57630i			0.796615i
$50$	0.283585	−	2.86517i	0.0401050	−	0.405196i
$51$		−	0.285449i		−	0.0399709i
$52$	−7.17065	+	7.17065i	−0.994390	+	0.994390i
$53$	−0.288499	+	0.288499i	−0.0396284	+	0.0396284i	−0.726643	−	0.687015i	$-0.758921\pi$
$53$	−0.288499	+	0.288499i	−0.0396284	+	0.0396284i	0.687015	+	0.726643i	$0.258921\pi$
$54$	2.39686			0.326171
$55$		0			0
$56$	−2.52049			−0.336814
$57$	−0.749427	+	0.749427i	−0.0992640	+	0.0992640i
$58$	2.49449	−	2.49449i	0.327542	−	0.327542i
$59$			0.187849i			0.0244559i	0.999925	+	0.0122279i	$0.00389237\pi$
$59$			0.187849i			0.0244559i	−0.999925	+	0.0122279i	$0.996108\pi$
$60$	1.22843	−	2.59569i	0.158590	−	0.335102i
$61$		−	0.683312i		−	0.0874891i	−0.999043	−	0.0437446i	$-0.986071\pi$
$61$		−	0.683312i		−	0.0874891i	0.999043	−	0.0437446i	$-0.0139288\pi$
$62$	1.00736	−	1.00736i	0.127935	−	0.127935i
$63$	2.03122	+	2.03122i	0.255910	+	0.255910i
$64$		−	1.10499i		−	0.138124i
$65$	−5.81389	+	12.2848i	−0.721125	+	1.52374i
$66$		0			0
$67$	7.14016	+	7.14016i	0.872309	+	0.872309i	0.992724	−	0.120415i	$-0.0384225\pi$
$67$	7.14016	+	7.14016i	0.872309	+	0.872309i	−0.120415	+	0.992724i	$0.538422\pi$
$68$	−0.437491	−	0.437491i	−0.0530536	−	0.0530536i
$69$			3.78891i			0.456132i
$70$	−1.44667	+	0.517234i	−0.172910	+	0.0618213i
$71$	1.03406			0.122721			0.0613604	−	0.998116i	$-0.480456\pi$
$71$	1.03406			0.122721			0.0613604	+	0.998116i	$0.480456\pi$
$72$	3.59604	−	3.59604i	0.423797	−	0.423797i
$73$	3.23297	+	3.23297i	0.378391	+	0.378391i	0.870521	−	0.492131i	$-0.163782\pi$
$73$	3.23297	+	3.23297i	0.378391	+	0.378391i	−0.492131	+	0.870521i	$0.663782\pi$
$74$	−1.71362			−0.199204
$75$	0.379084	−	3.83003i	0.0437729	−	0.442254i
$76$			2.29720i			0.263507i
$77$		0			0
$78$	1.90503	−	1.90503i	0.215702	−	0.215702i
$79$	−11.6347			−1.30900			−0.654500	−	0.756062i	$-0.727121\pi$
$79$	−11.6347			−1.30900			−0.654500	+	0.756062i	$0.727121\pi$
$80$	−1.59627	−	4.46467i	−0.178469	−	0.499165i
$81$	−4.01845			−0.446494
$82$	2.49415	+	2.49415i	0.275433	+	0.275433i
$83$	8.04790	+	8.04790i	0.883372	+	0.883372i	0.993876	−	0.110503i	$-0.0352463\pi$
$83$	8.04790	+	8.04790i	0.883372	+	0.883372i	−0.110503	+	0.993876i	$0.535246\pi$
$84$	−1.53236			−0.167195
$85$	−0.749512	−	0.354713i	−0.0812960	−	0.0384741i
$86$	5.50010			0.593091
$87$	3.33452	−	3.33452i	0.357498	−	0.357498i
$88$		0			0
$89$			8.04021i			0.852261i	0.904662	+	0.426130i	$0.140124\pi$
$89$			8.04021i			0.852261i	−0.904662	+	0.426130i	$0.859876\pi$
$90$	1.32605	−	2.80195i	0.139778	−	0.295351i
$91$	7.25234			0.760252
$92$	5.80704	+	5.80704i	0.605425	+	0.605425i
$93$	1.34660	−	1.34660i	0.139636	−	0.139636i
$94$	−0.735185			−0.0758285
$95$	1.03652	+	2.89906i	0.106344	+	0.297438i
$96$			4.19191i			0.427835i
$97$	5.96870	+	5.96870i	0.606030	+	0.606030i	0.941906	−	0.335876i	$-0.109032\pi$
$97$	5.96870	+	5.96870i	0.606030	+	0.606030i	−0.335876	+	0.941906i	$0.609032\pi$
$98$	−2.27054	−	2.27054i	−0.229359	−	0.229359i
$99$		0			0
$100$	−5.28906	−	6.45106i	−0.528906	−	0.645106i
$101$		−	17.3722i		−	1.72860i	−0.502976	−	0.864300i	$-0.667762\pi$
$101$		−	17.3722i		−	1.72860i	0.502976	−	0.864300i	$-0.332238\pi$
$102$	0.116228	+	0.116228i	0.0115083	+	0.0115083i
$103$	12.0395	−	12.0395i	1.18629	−	1.18629i	0.208204	−	0.978085i	$-0.433238\pi$
$103$	12.0395	−	12.0395i	1.18629	−	1.18629i	0.978085	−	0.208204i	$-0.0667618\pi$
$104$		−	12.8394i		−	1.25901i
$105$	−1.93384	+	0.691416i	−0.188724	+	0.0674752i
$106$		−	0.234940i		−	0.0228194i
$107$	10.5999	−	10.5999i	1.02473	−	1.02473i	0.0250455	−	0.999686i	$-0.492027\pi$
$107$	10.5999	−	10.5999i	1.02473	−	1.02473i	0.999686	−	0.0250455i	$-0.00797305\pi$
$108$	4.91059	−	4.91059i	0.472522	−	0.472522i
$109$	10.4970			1.00543			0.502714	−	0.864453i	$-0.332335\pi$
$109$	10.4970			1.00543			0.502714	+	0.864453i	$0.332335\pi$
$110$		0			0
$111$	−2.29069			−0.217422
$112$	−1.78904	+	1.78904i	−0.169048	+	0.169048i
$113$	6.96540	−	6.96540i	0.655250	−	0.655250i	−0.299003	−	0.954252i	$-0.596654\pi$
$113$	6.96540	−	6.96540i	0.655250	−	0.655250i	0.954252	+	0.299003i	$0.0966539\pi$
$114$		−	0.610297i		−	0.0571596i
$115$	9.94865	+	4.70829i	0.927717	+	0.439050i
$116$		−	10.2212i		−	0.949018i
$117$	−10.3471	+	10.3471i	−0.956589	+	0.956589i
$118$	−0.0764876	−	0.0764876i	−0.00704126	−	0.00704126i
$119$			0.442475i			0.0405616i
$120$	1.22407	+	3.42364i	0.111742	+	0.312534i
$121$		0			0
$122$	0.278228	+	0.278228i	0.0251896	+	0.0251896i
$123$	3.33407	+	3.33407i	0.300623	+	0.300623i
$124$		−	4.12770i		−	0.370679i
$125$	−9.58555	−	5.75476i	−0.857358	−	0.514721i
$126$	−1.65413			−0.147362
$127$	−10.3305	+	10.3305i	−0.916680	+	0.916680i	−0.996786	−	0.0801063i	$-0.974474\pi$
$127$	−10.3305	+	10.3305i	−0.916680	+	0.916680i	0.0801063	+	0.996786i	$0.474474\pi$
$128$	8.15148	+	8.15148i	0.720495	+	0.720495i
$129$	7.35229			0.647333
$130$	−2.63480	−	7.36936i	−0.231087	−	0.646335i
$131$			6.23684i			0.544915i	0.962168	+	0.272458i	$0.0878364\pi$
$131$			6.23684i			0.544915i	−0.962168	+	0.272458i	$0.912164\pi$
$132$		0			0
$133$	1.16169	−	1.16169i	0.100731	−	0.100731i
$134$	−5.81460			−0.502305
$135$	3.98146	−	8.41286i	0.342669	−	0.724063i
$136$	0.783349			0.0671717
$137$	−5.65297	−	5.65297i	−0.482966	−	0.482966i	0.423112	−	0.906077i	$-0.360938\pi$
$137$	−5.65297	−	5.65297i	−0.482966	−	0.482966i	−0.906077	+	0.423112i	$0.860938\pi$
$138$	−1.54275	−	1.54275i	−0.131328	−	0.131328i
$139$	10.2351			0.868127			0.434064	−	0.900882i	$-0.357079\pi$
$139$	10.2351			0.868127			0.434064	+	0.900882i	$0.357079\pi$
$140$	−1.90419	+	4.02357i	−0.160934	+	0.340054i
$141$	−0.982762			−0.0827635
$142$	−0.421046	+	0.421046i	−0.0353334	+	0.0353334i
$143$		0			0
$144$		−	5.10493i		−	0.425411i
$145$	−4.61191	−	12.8992i	−0.382998	−	1.07122i
$146$	−2.63278			−0.217890
$147$	−3.03515	−	3.03515i	−0.250335	−	0.250335i
$148$	−3.51080	+	3.51080i	−0.288586	+	0.288586i
$149$	−4.20687			−0.344640			−0.172320	−	0.985041i	$-0.555126\pi$
$149$	−4.20687			−0.344640			−0.172320	+	0.985041i	$0.555126\pi$
$150$	1.40514	+	1.71385i	0.114729	+	0.139935i
$151$			11.1993i			0.911388i	0.890137	+	0.455694i	$0.150609\pi$
$151$			11.1993i			0.911388i	−0.890137	+	0.455694i	$0.849391\pi$
$152$	−2.05663	−	2.05663i	−0.166815	−	0.166815i
$153$	−0.631290	−	0.631290i	−0.0510367	−	0.0510367i
$154$		0			0
$155$	−1.86245	−	5.20916i	−0.149596	−	0.418410i
$156$		−	7.80589i		−	0.624972i
$157$	10.2555	+	10.2555i	0.818478	+	0.818478i	0.985887	−	0.167410i	$-0.0535403\pi$
$157$	10.2555	+	10.2555i	0.818478	+	0.818478i	−0.167410	+	0.985887i	$0.553540\pi$
$158$	4.73735	−	4.73735i	0.376884	−	0.376884i
$159$		−	0.314057i		−	0.0249063i
$160$	11.0068	+	5.20908i	0.870166	+	0.411814i
$161$		−	5.87319i		−	0.462872i
$162$	1.63622	−	1.63622i	0.128553	−	0.128553i
$163$	11.2093	−	11.2093i	0.877981	−	0.877981i	−0.115345	−	0.993326i	$-0.536797\pi$
$163$	11.2093	−	11.2093i	0.877981	−	0.877981i	0.993326	+	0.115345i	$0.0367973\pi$
$164$	10.2199			0.798037
$165$		0			0
$166$	−6.55383			−0.508676
$167$	−1.78383	+	1.78383i	−0.138037	+	0.138037i	−0.772749	−	0.634712i	$-0.781119\pi$
$167$	−1.78383	+	1.78383i	−0.138037	+	0.138037i	0.634712	+	0.772749i	$0.281119\pi$
$168$	1.37189	−	1.37189i	0.105843	−	0.105843i
$169$			23.9436i			1.84181i
$170$	0.449614	−	0.160753i	0.0344838	−	0.0123292i
$171$			3.31481i			0.253490i
$172$	11.2684	−	11.2684i	0.859209	−	0.859209i
$173$	6.30781	+	6.30781i	0.479574	+	0.479574i	0.904995	−	0.425422i	$-0.139874\pi$
$173$	6.30781	+	6.30781i	0.479574	+	0.479574i	−0.425422	+	0.904995i	$0.639874\pi$
$174$			2.71548i			0.205860i
$175$	−0.587618	+	5.93693i	−0.0444198	+	0.448790i
$176$		0			0
$177$	−0.102245	−	0.102245i	−0.00768522	−	0.00768522i
$178$	−3.27378	−	3.27378i	−0.245380	−	0.245380i
$179$			2.74393i			0.205091i	0.994728	+	0.102546i	$0.0326988\pi$
$179$			2.74393i			0.205091i	−0.994728	+	0.102546i	$0.967301\pi$
$180$	−3.02377	−	8.45729i	−0.225379	−	0.630369i
$181$	12.7287			0.946114			0.473057	−	0.881032i	$-0.343150\pi$
$181$	12.7287			0.946114			0.473057	+	0.881032i	$0.343150\pi$
$182$	−2.95298	+	2.95298i	−0.218889	+	0.218889i
$183$	0.371923	+	0.371923i	0.0274934	+	0.0274934i
$184$	−10.3978			−0.766535
$185$	−2.84652	+	6.01472i	−0.209280	+	0.442211i
$186$			1.09661i			0.0804071i
$187$		0			0
$188$	−1.50622	+	1.50622i	−0.109852	+	0.109852i
$189$	−4.96653			−0.361262
$190$	−1.60247	−	0.758385i	−0.116256	−	0.0550190i
$191$	11.2319			0.812710			0.406355	−	0.913715i	$-0.366800\pi$
$191$	11.2319			0.812710			0.406355	+	0.913715i	$0.366800\pi$
$192$	0.601442	+	0.601442i	0.0434054	+	0.0434054i
$193$	−8.22719	−	8.22719i	−0.592206	−	0.592206i	0.346021	−	0.938227i	$-0.387533\pi$
$193$	−8.22719	−	8.22719i	−0.592206	−	0.592206i	−0.938227	+	0.346021i	$0.887533\pi$
$194$	−4.86062			−0.348973
$195$	−3.52208	−	9.85103i	−0.252222	−	0.705447i
$196$	−9.30359			−0.664542
$197$	8.98493	−	8.98493i	0.640150	−	0.640150i	−0.310443	−	0.950592i	$-0.600477\pi$
$197$	8.98493	−	8.98493i	0.640150	−	0.640150i	0.950592	+	0.310443i	$0.100477\pi$
$198$		0			0
$199$			13.9872i			0.991529i	0.868457	+	0.495764i	$0.165112\pi$
$199$			13.9872i			0.991529i	−0.868457	+	0.495764i	$0.834888\pi$
$200$	10.5106	+	1.04031i	0.743214	+	0.0735609i
$201$	−7.77270			−0.548244
$202$	7.07355	+	7.07355i	0.497693	+	0.497693i
$203$	−5.16884	+	5.16884i	−0.362782	+	0.362782i
$204$	0.476248			0.0333440
$205$	12.8975	−	4.61129i	0.900797	−	0.322066i
$206$			9.80441i			0.683106i
$207$	8.37943	+	8.37943i	0.582410	+	0.582410i
$208$	−9.11340	−	9.11340i	−0.631900	−	0.631900i
$209$		0			0
$210$	0.505886	−	1.06894i	0.0349095	−	0.0737640i
$211$			21.2361i			1.46195i	0.682402	+	0.730977i	$0.260935\pi$
$211$			21.2361i			1.46195i	−0.682402	+	0.730977i	$0.739065\pi$
$212$	−0.481336	−	0.481336i	−0.0330583	−	0.0330583i
$213$	−0.562835	+	0.562835i	−0.0385648	+	0.0385648i
$214$			8.63206i			0.590075i
$215$	9.13632	−	19.3051i	0.623092	−	1.31660i
$216$			8.79266i			0.598265i
$217$	−2.08736	+	2.08736i	−0.141700	+	0.141700i
$218$	−4.27412	+	4.27412i	−0.289480	+	0.289480i
$219$	−3.51938			−0.237818
$220$		0			0
$221$	−2.25397			−0.151619
$222$	0.932713	−	0.932713i	0.0625996	−	0.0625996i
$223$	−1.89010	+	1.89010i	−0.126571	+	0.126571i	−0.767554	−	0.640984i	$-0.778527\pi$
$223$	−1.89010	+	1.89010i	−0.126571	+	0.126571i	0.640984	+	0.767554i	$0.278527\pi$
$224$		−	6.49788i		−	0.434158i
$225$	−7.63199	−	9.30873i	−0.508799	−	0.620582i
$226$			5.67229i			0.377315i
$227$	−15.2410	+	15.2410i	−1.01158	+	1.01158i	−0.0116465	+	0.999932i	$0.503707\pi$
$227$	−15.2410	+	15.2410i	−1.01158	+	1.01158i	−0.999932	+	0.0116465i	$0.996293\pi$
$228$	−1.25035	−	1.25035i	−0.0828068	−	0.0828068i
$229$			0.150832i			0.00996729i	0.999988	+	0.00498365i	$0.00158635\pi$
$229$			0.150832i			0.00996729i	−0.999988	+	0.00498365i	$0.998414\pi$
$230$	−5.96796	+	2.13375i	−0.393515	+	0.140695i
$231$		0			0
$232$	9.15082	+	9.15082i	0.600781	+	0.600781i
$233$	0.869689	+	0.869689i	0.0569752	+	0.0569752i	0.735020	−	0.678045i	$-0.237173\pi$
$233$	0.869689	+	0.869689i	0.0569752	+	0.0569752i	−0.678045	+	0.735020i	$0.737173\pi$
$234$		−	8.42617i		−	0.550836i
$235$	−1.22123	+	2.58047i	−0.0796642	+	0.168331i
$236$	−0.313410			−0.0204013
$237$	6.33268	−	6.33268i	0.411352	−	0.411352i
$238$	−0.180165	−	0.180165i	−0.0116784	−	0.0116784i
$239$	−4.56864			−0.295521			−0.147760	−	0.989023i	$-0.547206\pi$
$239$	−4.56864			−0.295521			−0.147760	+	0.989023i	$0.547206\pi$
$240$	3.29894	+	1.56125i	0.212946	+	0.100778i
$241$			14.4746i			0.932394i	0.884681	+	0.466197i	$0.154376\pi$
$241$			14.4746i			0.932394i	−0.884681	+	0.466197i	$0.845624\pi$
$242$		0			0
$243$	11.0170	−	11.0170i	0.706742	−	0.706742i
$244$	1.14005			0.0729841
$245$	−11.7411	+	4.19786i	−0.750112	+	0.268191i
$246$	−2.71511			−0.173109
$247$	5.91765	+	5.91765i	0.376531	+	0.376531i
$248$	3.69543	+	3.69543i	0.234660	+	0.234660i
$249$	−8.76087			−0.555197
$250$	6.24621	−	1.55981i	0.395045	−	0.0986509i
$251$	−4.19730			−0.264931			−0.132466	−	0.991188i	$-0.542289\pi$
$251$	−4.19730			−0.264931			−0.132466	+	0.991188i	$0.542289\pi$
$252$	−3.38892	+	3.38892i	−0.213482	+	0.213482i
$253$		0			0
$254$		−	8.41263i		−	0.527855i
$255$	0.601024	−	0.214887i	0.0376376	−	0.0134567i
$256$	−4.42818			−0.276762
$257$	−14.7824	−	14.7824i	−0.922100	−	0.922100i	0.0750781	−	0.997178i	$-0.476079\pi$
$257$	−14.7824	−	14.7824i	−0.922100	−	0.922100i	−0.997178	+	0.0750781i	$0.976079\pi$
$258$	−2.99368	+	2.99368i	−0.186378	+	0.186378i
$259$	3.55079			0.220636
$260$	−20.4962	−	9.69999i	−1.27112	−	0.601568i
$261$		−	14.7490i		−	0.912942i
$262$	−2.53949	−	2.53949i	−0.156890	−	0.156890i
$263$	−16.5788	−	16.5788i	−1.02229	−	1.02229i	−0.999746	−	0.0225437i	$-0.992824\pi$
$263$	−16.5788	−	16.5788i	−1.02229	−	1.02229i	−0.0225437	−	0.999746i	$-0.507176\pi$
$264$		0			0
$265$	−0.824628	−	0.390262i	−0.0506565	−	0.0239736i
$266$			0.946022i			0.0580043i
$267$	−4.37625	−	4.37625i	−0.267822	−	0.267822i
$268$	−11.9127	+	11.9127i	−0.727687	+	0.727687i
$269$		−	2.08604i		−	0.127188i	−0.997976	−	0.0635940i	$-0.979744\pi$
$269$		−	2.08604i		−	0.127188i	0.997976	−	0.0635940i	$-0.0202563\pi$
$270$	1.80436	+	5.04667i	0.109810	+	0.307131i
$271$		−	24.9438i		−	1.51523i	−0.652704	−	0.757613i	$-0.726365\pi$
$271$		−	24.9438i		−	1.51523i	0.652704	−	0.757613i	$-0.273635\pi$
$272$	0.556020	−	0.556020i	0.0337137	−	0.0337137i
$273$	−3.94741	+	3.94741i	−0.238908	+	0.238908i
$274$	4.60351			0.278108
$275$		0			0
$276$	−6.32148			−0.380508
$277$	−3.84527	+	3.84527i	−0.231040	+	0.231040i	−0.813127	−	0.582087i	$-0.802236\pi$
$277$	−3.84527	+	3.84527i	−0.231040	+	0.231040i	0.582087	+	0.813127i	$0.302236\pi$
$278$	−4.16748	+	4.16748i	−0.249949	+	0.249949i
$279$		−	5.95619i		−	0.356588i
$280$	−1.89743	−	5.30698i	−0.113393	−	0.317153i
$281$			3.58630i			0.213941i	0.994262	+	0.106970i	$0.0341150\pi$
$281$			3.58630i			0.213941i	−0.994262	+	0.106970i	$0.965885\pi$
$282$	0.400157	−	0.400157i	0.0238290	−	0.0238290i
$283$	−3.68204	−	3.68204i	−0.218874	−	0.218874i	0.589150	−	0.808024i	$-0.299463\pi$
$283$	−3.68204	−	3.68204i	−0.218874	−	0.218874i	−0.808024	+	0.589150i	$0.799463\pi$
$284$			1.72525i			0.102375i
$285$	−2.14212	−	1.01378i	−0.126888	−	0.0600509i
$286$		0			0
$287$	−5.16815	−	5.16815i	−0.305066	−	0.305066i
$288$	9.27069	+	9.27069i	0.546280	+	0.546280i
$289$			16.8625i			0.991911i
$290$	7.13010	+	3.37438i	0.418694	+	0.198151i
$291$	−6.49747			−0.380888
$292$	−5.39394	+	5.39394i	−0.315657	+	0.315657i
$293$	−7.37666	−	7.37666i	−0.430949	−	0.430949i	0.458002	−	0.888951i	$-0.348565\pi$
$293$	−7.37666	−	7.37666i	−0.430949	−	0.430949i	−0.888951	+	0.458002i	$0.848565\pi$
$294$	2.47168			0.144151
$295$	−0.395523	+	0.141413i	−0.0230282	+	0.00823340i
$296$		−	6.28626i		−	0.365381i
$297$		0			0
$298$	1.71293	−	1.71293i	0.0992277	−	0.0992277i
$299$	29.9182			1.73021
$300$	6.39008	+	0.632470i	0.368932	+	0.0365157i
$301$	−11.3968			−0.656900
$302$	−4.56009	−	4.56009i	−0.262404	−	0.262404i
$303$	9.45561	+	9.45561i	0.543211	+	0.543211i
$304$	−2.91958			−0.167450
$305$	1.43874	−	0.514399i	0.0823820	−	0.0294544i
$306$	0.514092			0.0293887
$307$	−0.233432	+	0.233432i	−0.0133227	+	0.0133227i	−0.713737	−	0.700414i	$-0.752999\pi$
$307$	−0.233432	+	0.233432i	−0.0133227	+	0.0133227i	0.700414	+	0.713737i	$0.252999\pi$
$308$		0			0
$309$			13.1061i			0.745580i
$310$	2.87939	+	1.36270i	0.163538	+	0.0773960i
$311$	7.53155			0.427075			0.213538	−	0.976935i	$-0.431501\pi$
$311$	7.53155			0.427075			0.213538	+	0.976935i	$0.431501\pi$
$312$	6.98842	+	6.98842i	0.395642	+	0.395642i
$313$	4.42040	−	4.42040i	0.249856	−	0.249856i	−0.571056	−	0.820911i	$-0.693466\pi$
$313$	4.42040	−	4.42040i	0.249856	−	0.249856i	0.820911	+	0.571056i	$0.193466\pi$
$314$	−8.35158			−0.471307
$315$	−2.74771	+	5.80593i	−0.154816	+	0.327127i
$316$		−	19.4114i		−	1.09198i
$317$	−10.9295	−	10.9295i	−0.613860	−	0.613860i	0.330090	−	0.943950i	$-0.392921\pi$
$317$	−10.9295	−	10.9295i	−0.613860	−	0.613860i	−0.943950	+	0.330090i	$0.892921\pi$
$318$	0.127876	+	0.127876i	0.00717095	+	0.00717095i
$319$		0			0
$320$	2.32661	−	0.831842i	0.130061	−	0.0465014i
$321$			11.5389i			0.644041i
$322$	2.39142	+	2.39142i	0.133269	+	0.133269i
$323$	−0.361044	+	0.361044i	−0.0200890	+	0.0200890i
$324$		−	6.70444i		−	0.372469i
$325$	−30.2428	−	2.99334i	−1.67757	−	0.166040i
$326$			9.12832i			0.505571i
$327$	−5.71345	+	5.71345i	−0.315954	+	0.315954i
$328$	−9.14959	+	9.14959i	−0.505202	+	0.505202i
$329$	1.52338			0.0839866
$330$		0			0
$331$	23.7583			1.30587			0.652937	−	0.757412i	$-0.273537\pi$
$331$	23.7583			1.30587			0.652937	+	0.757412i	$0.273537\pi$
$332$	−13.4272	+	13.4272i	−0.736916	+	0.736916i
$333$	−5.06600	+	5.06600i	−0.277615	+	0.277615i
$334$		−	1.45266i		−	0.0794862i
$335$	−9.65874	+	20.4090i	−0.527713	+	1.11506i
$336$		−	1.94753i		−	0.106246i
$337$	3.11122	−	3.11122i	0.169479	−	0.169479i	−0.617271	−	0.786750i	$-0.711762\pi$
$337$	3.11122	−	3.11122i	0.169479	−	0.169479i	0.786750	+	0.617271i	$0.211762\pi$
$338$	−9.74924	−	9.74924i	−0.530289	−	0.530289i
$339$			7.58246i			0.411823i
$340$	0.591809	−	1.25050i	0.0320954	−	0.0678177i
$341$		0			0
$342$	−1.34971	−	1.34971i	−0.0729840	−	0.0729840i
$343$	10.6108	+	10.6108i	0.572928	+	0.572928i
$344$			20.1767i			1.08785i
$345$	−7.97770	+	2.85230i	−0.429505	+	0.153563i
$346$	−5.13678			−0.276155
$347$	1.67037	−	1.67037i	0.0896702	−	0.0896702i	−0.660849	−	0.750519i	$-0.729804\pi$
$347$	1.67037	−	1.67037i	0.0896702	−	0.0896702i	0.750519	+	0.660849i	$0.229804\pi$
$348$	5.56337	+	5.56337i	0.298228	+	0.298228i
$349$	−17.0546			−0.912912			−0.456456	−	0.889746i	$-0.650881\pi$
$349$	−17.0546			−0.912912			−0.456456	+	0.889746i	$0.650881\pi$
$350$	−2.17811	−	2.65664i	−0.116425	−	0.142003i
$351$		−	25.2996i		−	1.35039i
$352$		0			0
$353$	−7.79889	+	7.79889i	−0.415093	+	0.415093i	−0.883508	−	0.468415i	$-0.844825\pi$
$353$	−7.79889	+	7.79889i	−0.415093	+	0.415093i	0.468415	+	0.883508i	$0.344825\pi$
$354$	0.0832636			0.00442541
$355$	0.778446	+	2.17726i	0.0413156	+	0.115557i
$356$	−13.4144			−0.710962
$357$	−0.240837	−	0.240837i	−0.0127464	−	0.0127464i
$358$	−1.11726	−	1.11726i	−0.0590492	−	0.0590492i
$359$	16.3888			0.864968			0.432484	−	0.901642i	$-0.357637\pi$
$359$	16.3888			0.864968			0.432484	+	0.901642i	$0.357637\pi$
$360$	10.2787	+	4.86449i	0.541735	+	0.256381i
$361$	−17.1042			−0.900222
$362$	−5.18281	+	5.18281i	−0.272402	+	0.272402i
$363$		0			0
$364$			12.0999i			0.634208i
$365$	−4.37336	+	9.24094i	−0.228912	+	0.483693i
$366$	−0.302876			−0.0158316
$367$	12.2685	+	12.2685i	0.640412	+	0.640412i	0.950657	−	0.310245i	$-0.100411\pi$
$367$	12.2685	+	12.2685i	0.640412	+	0.640412i	−0.310245	+	0.950657i	$0.600411\pi$
$368$	−7.38034	+	7.38034i	−0.384727	+	0.384727i
$369$	14.7470			0.767700
$370$	−1.29002	−	3.60809i	−0.0670647	−	0.187575i
$371$			0.486819i			0.0252744i
$372$	2.24669	+	2.24669i	0.116485	+	0.116485i
$373$	20.0262	+	20.0262i	1.03692	+	1.03692i	0.999292	+	0.0376235i	$0.0119787\pi$
$373$	20.0262	+	20.0262i	1.03692	+	1.03692i	0.0376235	+	0.999292i	$0.488021\pi$
$374$		0			0
$375$	8.34965	−	2.08508i	0.431174	−	0.107673i
$376$		−	2.69696i		−	0.139085i
$377$	−26.3302	−	26.3302i	−1.35607	−	1.35607i
$378$	2.02225	−	2.02225i	0.104014	−	0.104014i
$379$		−	8.59089i		−	0.441284i	−0.975355	−	0.220642i	$-0.929185\pi$
$379$		−	8.59089i		−	0.441284i	0.975355	−	0.220642i	$-0.0708153\pi$
$380$	−4.83684	+	1.72934i	−0.248125	+	0.0887132i
$381$		−	11.2456i		−	0.576131i
$382$	−4.57335	+	4.57335i	−0.233993	+	0.233993i
$383$	1.01758	−	1.01758i	0.0519961	−	0.0519961i	−0.680631	−	0.732627i	$-0.738294\pi$
$383$	1.01758	−	1.01758i	0.0519961	−	0.0519961i	0.732627	+	0.680631i	$0.238294\pi$
$384$	−8.87361			−0.452830
$385$		0			0
$386$	6.69983			0.341012
$387$	16.2601	−	16.2601i	0.826546	−	0.826546i
$388$	−9.95827	+	9.95827i	−0.505555	+	0.505555i
$389$			8.71180i			0.441706i	0.975307	+	0.220853i	$0.0708840\pi$
$389$			8.71180i			0.441706i	−0.975307	+	0.220853i	$0.929116\pi$
$390$	5.44521	+	2.57699i	0.275729	+	0.130491i
$391$			1.82535i			0.0923117i
$392$	8.32927	−	8.32927i	0.420692	−	0.420692i
$393$	−3.39468	−	3.39468i	−0.171239	−	0.171239i
$394$			7.31690i			0.368620i
$395$	−8.75860	−	24.4972i	−0.440693	−	1.23259i
$396$		0			0
$397$	−23.6145	−	23.6145i	−1.18518	−	1.18518i	−0.978384	−	0.206796i	$-0.933696\pi$
$397$	−23.6145	−	23.6145i	−1.18518	−	1.18518i	−0.206796	−	0.978384i	$-0.566304\pi$
$398$	−5.69527	−	5.69527i	−0.285478	−	0.285478i
$399$			1.26460i			0.0633092i
$400$	8.19884	−	6.72202i	0.409942	−	0.336101i
$401$	11.2634			0.562469			0.281235	−	0.959639i	$-0.409256\pi$
$401$	11.2634			0.562469			0.281235	+	0.959639i	$0.409256\pi$
$402$	3.16486	−	3.16486i	0.157849	−	0.157849i
$403$	−10.6331	−	10.6331i	−0.529671	−	0.529671i
$404$	28.9841			1.44201
$405$	−3.02510	−	8.46100i	−0.150318	−	0.420430i
$406$		−	4.20926i		−	0.208902i
$407$		0			0
$408$	−0.426373	+	0.426373i	−0.0211086	+	0.0211086i
$409$	−11.8274			−0.584828			−0.292414	−	0.956292i	$-0.594458\pi$
$409$	−11.8274			−0.584828			−0.292414	+	0.956292i	$0.594458\pi$
$410$	−3.37393	+	7.12914i	−0.166627	+	0.352083i
$411$	6.15376			0.303543
$412$	20.0869	+	20.0869i	0.989612	+	0.989612i
$413$	0.158490	+	0.158490i	0.00779880	+	0.00779880i
$414$	−6.82380			−0.335372
$415$	−10.8867	+	23.0036i	−0.534406	+	1.12920i
$416$	33.1003			1.62288
$417$	−5.57090	+	5.57090i	−0.272808	+	0.272808i
$418$		0			0
$419$		−	38.2403i		−	1.86816i	−0.357062	−	0.934081i	$-0.616222\pi$
$419$		−	38.2403i		−	1.86816i	0.357062	−	0.934081i	$-0.383778\pi$
$420$	−1.15357	−	3.22645i	−0.0562884	−	0.157435i
$421$	−2.62381			−0.127877			−0.0639384	−	0.997954i	$-0.520366\pi$
$421$	−2.62381			−0.127877			−0.0639384	+	0.997954i	$0.520366\pi$
$422$	−8.64684	−	8.64684i	−0.420922	−	0.420922i
$423$	−2.17344	+	2.17344i	−0.105676	+	0.105676i
$424$	0.861856			0.0418554
$425$	0.182627	−	1.84515i	0.00885873	−	0.0895032i
$426$		−	0.458346i		−	0.0222069i
$427$	−0.576518	−	0.576518i	−0.0278997	−	0.0278997i
$428$	17.6850	+	17.6850i	0.854839	+	0.854839i
$429$		0			0
$430$	4.14049	+	11.5807i	0.199672	+	0.558470i
$431$		−	1.07657i		−	0.0518565i	−0.999664	−	0.0259283i	$-0.991746\pi$
$431$		−	1.07657i		−	0.0518565i	0.999664	−	0.0259283i	$-0.00825415\pi$
$432$	6.24102	+	6.24102i	0.300271	+	0.300271i
$433$	−0.702105	+	0.702105i	−0.0337410	+	0.0337410i	−0.723776	−	0.690035i	$-0.757595\pi$
$433$	−0.702105	+	0.702105i	−0.0337410	+	0.0337410i	0.690035	+	0.723776i	$0.257595\pi$
$434$		−	1.69985i		−	0.0815954i
$435$	9.53120	+	4.51072i	0.456986	+	0.216273i
$436$			17.5133i			0.838735i
$437$	4.79231	−	4.79231i	0.229248	−	0.229248i
$438$	1.43301	−	1.43301i	0.0684718	−	0.0684718i
$439$	−20.9374			−0.999287			−0.499644	−	0.866231i	$-0.666536\pi$
$439$	−20.9374			−0.999287			−0.499644	+	0.866231i	$0.666536\pi$
$440$		0			0
$441$	−13.4249			−0.639280
$442$	0.917765	−	0.917765i	0.0436536	−	0.0436536i
$443$	19.6295	−	19.6295i	0.932627	−	0.932627i	−0.0652425	−	0.997869i	$-0.520782\pi$
$443$	19.6295	−	19.6295i	0.932627	−	0.932627i	0.997869	+	0.0652425i	$0.0207821\pi$
$444$		−	3.82182i		−	0.181375i
$445$	−16.9290	+	6.05269i	−0.802510	+	0.286925i
$446$		−	1.53921i		−	0.0728837i
$447$	2.28977	−	2.28977i	0.108303	−	0.108303i
$448$	−0.932295	−	0.932295i	−0.0440468	−	0.0440468i
$449$			8.17071i			0.385599i	0.981238	+	0.192800i	$0.0617568\pi$
$449$			8.17071i			0.385599i	−0.981238	+	0.192800i	$0.938243\pi$
$450$	6.89786	+	0.682728i	0.325168	+	0.0321841i
$451$		0			0
$452$	11.6212	+	11.6212i	0.546614	+	0.546614i
$453$	−6.09573	−	6.09573i	−0.286402	−	0.286402i
$454$		−	12.4115i		−	0.582501i
$455$	5.45958	+	15.2701i	0.255949	+	0.715872i
$456$	2.23882			0.104843
$457$	18.5963	−	18.5963i	0.869899	−	0.869899i	−0.122562	−	0.992461i	$-0.539111\pi$
$457$	18.5963	−	18.5963i	0.869899	−	0.869899i	0.992461	+	0.122562i	$0.0391110\pi$
$458$	−0.0614154	−	0.0614154i	−0.00286975	−	0.00286975i
$459$	1.54356			0.0720474
$460$	−7.85538	+	16.5985i	−0.366259	+	0.773908i
$461$			17.9953i			0.838126i	0.907957	+	0.419063i	$0.137641\pi$
$461$			17.9953i			0.838126i	−0.907957	+	0.419063i	$0.862359\pi$
$462$		0			0
$463$	0.607001	−	0.607001i	0.0282097	−	0.0282097i	−0.692861	−	0.721071i	$-0.743650\pi$
$463$	0.607001	−	0.607001i	0.0282097	−	0.0282097i	0.721071	+	0.692861i	$0.243650\pi$
$464$	12.9905			0.603068
$465$	3.84904	+	1.82159i	0.178495	+	0.0844744i
$466$	−0.708233			−0.0328083
$467$	−24.4594	−	24.4594i	−1.13185	−	1.13185i	−0.989870	−	0.141977i	$-0.954654\pi$
$467$	−24.4594	−	24.4594i	−1.13185	−	1.13185i	−0.141977	−	0.989870i	$-0.545346\pi$
$468$	−17.2632	−	17.2632i	−0.797994	−	0.797994i
$469$	12.0485			0.556346
$470$	−0.553449	−	1.54796i	−0.0255287	−	0.0714020i
$471$	−11.1640			−0.514411
$472$	0.280588	−	0.280588i	0.0129151	−	0.0129151i
$473$		0			0
$474$			5.15703i			0.236870i
$475$	−5.32380	+	4.36485i	−0.244273	+	0.200273i
$476$	−0.738232			−0.0338368
$477$	−0.694557	−	0.694557i	−0.0318016	−	0.0318016i
$478$	1.86024	−	1.86024i	0.0850855	−	0.0850855i
$479$	4.22564			0.193075			0.0965373	−	0.995329i	$-0.469223\pi$
$479$	4.22564			0.193075			0.0965373	+	0.995329i	$0.469223\pi$
$480$	−8.82623	+	3.15568i	−0.402860	+	0.144037i
$481$			18.0878i			0.824733i
$482$	−5.89373	−	5.89373i	−0.268452	−	0.268452i
$483$	3.19675	+	3.19675i	0.145457	+	0.145457i
$484$		0			0
$485$	−8.07407	+	17.0606i	−0.366625	+	0.774681i
$486$			8.97174i			0.406966i
$487$	2.00003	+	2.00003i	0.0906300	+	0.0906300i	0.750968	−	0.660338i	$-0.229587\pi$
$487$	2.00003	+	2.00003i	0.0906300	+	0.0906300i	−0.660338	+	0.750968i	$0.729587\pi$
$488$	−1.02066	+	1.02066i	−0.0462030	+	0.0462030i
$489$			12.2023i			0.551809i
$490$	3.07143	−	6.48997i	0.138753	−	0.293187i
$491$			39.7844i			1.79544i	0.440563	+	0.897722i	$0.354779\pi$
$491$			39.7844i			1.79544i	−0.440563	+	0.897722i	$0.645221\pi$
$492$	−5.56262	+	5.56262i	−0.250782	+	0.250782i
$493$	1.60644	−	1.60644i	0.0723504	−	0.0723504i
$494$	−4.81905			−0.216819
$495$		0			0
$496$	5.24603			0.235554
$497$	0.872451	−	0.872451i	0.0391348	−	0.0391348i
$498$	3.56721	−	3.56721i	0.159851	−	0.159851i
$499$		−	29.9550i		−	1.34097i	−0.741923	−	0.670485i	$-0.766086\pi$
$499$		−	29.9550i		−	1.34097i	0.741923	−	0.670485i	$-0.233914\pi$
$500$	9.60132	−	15.9927i	0.429384	−	0.715214i
$501$		−	1.94186i		−	0.0867557i
$502$	1.70904	−	1.70904i	0.0762782	−	0.0762782i
$503$	13.9805	+	13.9805i	0.623360	+	0.623360i	0.946389	−	0.323029i	$-0.104701\pi$
$503$	13.9805	+	13.9805i	0.623360	+	0.623360i	−0.323029	+	0.946389i	$0.604701\pi$
$504$		−	6.06804i		−	0.270292i
$505$	36.5779	−	13.0779i	1.62769	−	0.581957i
$506$		0			0
$507$	−13.0324	−	13.0324i	−0.578787	−	0.578787i
$508$	−17.2355	−	17.2355i	−0.764701	−	0.764701i
$509$		−	28.6869i		−	1.27153i	−0.771885	−	0.635763i	$-0.780686\pi$
$509$		−	28.6869i		−	1.27153i	0.771885	−	0.635763i	$-0.219314\pi$
$510$	−0.157226	+	0.332219i	−0.00696208	+	0.0147109i
$511$	5.45539			0.241332
$512$	−14.4999	+	14.4999i	−0.640811	+	0.640811i
$513$	−4.05251	−	4.05251i	−0.178923	−	0.178923i
$514$	12.0381			0.530976
$515$	34.4131	+	16.2863i	1.51642	+	0.717659i
$516$			12.2667i			0.540010i
$517$		0			0
$518$	−1.44580	+	1.44580i	−0.0635247	+	0.0635247i
$519$	−6.86661			−0.301411
$520$	27.0339	−	9.66554i	1.18551	−	0.423862i
$521$	24.2035			1.06037			0.530186	−	0.847881i	$-0.322122\pi$
$521$	24.2035			1.06037			0.530186	+	0.847881i	$0.322122\pi$
$522$	6.00545	+	6.00545i	0.262851	+	0.262851i
$523$	−0.0658798	−	0.0658798i	−0.00288072	−	0.00288072i	0.705665	−	0.708546i	$-0.250648\pi$
$523$	−0.0658798	−	0.0658798i	−0.00288072	−	0.00288072i	−0.708546	+	0.705665i	$0.750648\pi$
$524$	−10.4056			−0.454572
$525$	−2.91160	−	3.55128i	−0.127073	−	0.154990i
$526$	13.5009			0.588669
$527$	0.648738	−	0.648738i	0.0282595	−	0.0282595i
$528$		0			0
$529$		−	1.22874i		−	0.0534235i
$530$	0.494674	−	0.176863i	0.0214873	−	0.00768244i
$531$	−0.452244			−0.0196257
$532$	1.93817	+	1.93817i	0.0840305	+	0.0840305i
$533$	26.3266	−	26.3266i	1.14033	−	1.14033i
$534$	3.56380			0.154221
$535$	30.2981	+	14.3389i	1.30990	+	0.619923i
$536$		−	21.3304i		−	0.921332i
$537$	−1.49351	−	1.49351i	−0.0644496	−	0.0644496i
$538$	0.849385	+	0.849385i	0.0366196	+	0.0366196i
$539$		0			0
$540$	14.0361	+	6.64273i	0.604019	+	0.285858i
$541$		−	20.3922i		−	0.876731i	−0.898797	−	0.438366i	$-0.855558\pi$
$541$		−	20.3922i		−	0.876731i	0.898797	−	0.438366i	$-0.144442\pi$
$542$	10.1565	+	10.1565i	0.436260	+	0.436260i
$543$	−6.92815	+	6.92815i	−0.297315	+	0.297315i
$544$			2.01950i			0.0865851i
$545$	7.90215	+	22.1018i	0.338491	+	0.946736i
$546$		−	3.21458i		−	0.137571i
$547$	4.52745	−	4.52745i	0.193580	−	0.193580i	−0.603661	−	0.797241i	$-0.706292\pi$
$547$	4.52745	−	4.52745i	0.193580	−	0.193580i	0.797241	+	0.603661i	$0.206292\pi$
$548$	9.43150	−	9.43150i	0.402894	−	0.402894i
$549$	1.64506			0.0702096
$550$		0			0
$551$	−8.43518			−0.359351
$552$	5.65946	−	5.65946i	0.240883	−	0.240883i
$553$	−9.81629	+	9.81629i	−0.417431	+	0.417431i
$554$		−	3.13140i		−	0.133040i
$555$	−1.72444	−	4.82313i	−0.0731982	−	0.204730i
$556$			17.0764i			0.724199i
$557$	12.6630	−	12.6630i	0.536550	−	0.536550i	−0.385964	−	0.922514i	$-0.626131\pi$
$557$	12.6630	−	12.6630i	0.536550	−	0.536550i	0.922514	+	0.385964i	$0.126131\pi$
$558$	2.42522	+	2.42522i	0.102668	+	0.102668i
$559$		−	58.0554i		−	2.45548i
$560$	−5.11368	−	2.42010i	−0.216093	−	0.102268i
$561$		0			0
$562$	−1.46026	−	1.46026i	−0.0615972	−	0.0615972i
$563$	−26.7977	−	26.7977i	−1.12939	−	1.12939i	−0.990276	−	0.139114i	$-0.955575\pi$
$563$	−26.7977	−	26.7977i	−1.12939	−	1.12939i	−0.139114	−	0.990276i	$-0.544425\pi$
$564$		−	1.63966i		−	0.0690419i
$565$	19.9095	+	9.42234i	0.837598	+	0.396401i
$566$	2.99847			0.126035
$567$	−3.39041	+	3.39041i	−0.142384	+	0.142384i
$568$	−1.54457	−	1.54457i	−0.0648088	−	0.0648088i
$569$	−28.2667			−1.18500			−0.592501	−	0.805569i	$-0.701860\pi$
$569$	−28.2667			−1.18500			−0.592501	+	0.805569i	$0.701860\pi$
$570$	1.28500	−	0.459433i	0.0538229	−	0.0192435i
$571$		−	17.8465i		−	0.746854i	−0.927660	−	0.373427i	$-0.878183\pi$
$571$		−	17.8465i		−	0.746854i	0.927660	−	0.373427i	$-0.121817\pi$
$572$		0			0
$573$	−6.11345	+	6.11345i	−0.255393	+	0.255393i
$574$	4.20869			0.175667
$575$	−2.42411	+	24.4917i	−0.101092	+	1.02137i
$576$	2.66026			0.110844
$577$	3.27014	+	3.27014i	0.136138	+	0.136138i	0.771892	−	0.635754i	$-0.219311\pi$
$577$	3.27014	+	3.27014i	0.136138	+	0.136138i	−0.635754	+	0.771892i	$0.719311\pi$
$578$	−6.86600	−	6.86600i	−0.285588	−	0.285588i
$579$	8.95603			0.372200
$580$	21.5212	−	7.69458i	0.893619	−	0.319500i
$581$	13.5802			0.563402
$582$	2.64561	−	2.64561i	0.109664	−	0.109664i
$583$		0			0
$584$		−	9.65813i		−	0.399656i
$585$	−29.5755	−	13.9969i	−1.22280	−	0.578699i
$586$	6.00720			0.248155
$587$	−26.9761	−	26.9761i	−1.11342	−	1.11342i	−0.992684	−	0.120741i	$-0.961473\pi$
$587$	−26.9761	−	26.9761i	−1.11342	−	1.11342i	−0.120741	−	0.992684i	$-0.538527\pi$
$588$	5.06389	−	5.06389i	0.208832	−	0.208832i
$589$	−3.40643			−0.140359
$590$	0.103467	−	0.218628i	0.00425969	−	0.00900076i
$591$			9.78090i			0.402332i
$592$	−4.46198	−	4.46198i	−0.183386	−	0.183386i
$593$	23.5327	+	23.5327i	0.966374	+	0.966374i	0.999453	−	0.0330786i	$-0.0105312\pi$
$593$	23.5327	+	23.5327i	0.966374	+	0.966374i	−0.0330786	+	0.999453i	$0.510531\pi$
$594$		0			0
$595$	−0.931647	+	0.333096i	−0.0381938	+	0.0136556i
$596$		−	7.01880i		−	0.287501i
$597$	−7.61318	−	7.61318i	−0.311587	−	0.311587i
$598$	−12.1820	+	12.1820i	−0.498157	+	0.498157i
$599$			11.8751i			0.485205i	0.970126	+	0.242602i	$0.0780011\pi$
$599$			11.8751i			0.485205i	−0.970126	+	0.242602i	$0.921999\pi$
$600$	−6.28712	+	5.15465i	−0.256670	+	0.210438i
$601$			0.206833i			0.00843690i	0.999991	+	0.00421845i	$0.00134278\pi$
$601$			0.206833i			0.00843690i	−0.999991	+	0.00421845i	$0.998657\pi$
$602$	4.64050	−	4.64050i	0.189133	−	0.189133i
$603$	−17.1898	+	17.1898i	−0.700024	+	0.700024i
$604$	−18.6851			−0.760287
$605$		0			0
$606$	−7.70020			−0.312799
$607$	15.5576	−	15.5576i	0.631464	−	0.631464i	−0.316971	−	0.948435i	$-0.602666\pi$
$607$	15.5576	−	15.5576i	0.631464	−	0.631464i	0.948435	+	0.316971i	$0.102666\pi$
$608$	5.30204	−	5.30204i	0.215026	−	0.215026i
$609$		−	5.62675i		−	0.228007i
$610$	−0.376369	+	0.795271i	−0.0152387	+	0.0321996i
$611$			7.76012i			0.313941i
$612$	1.05325	−	1.05325i	0.0425752	−	0.0425752i
$613$	12.6022	+	12.6022i	0.508998	+	0.508998i	0.914219	−	0.405221i	$-0.132805\pi$
$613$	12.6022	+	12.6022i	0.508998	+	0.508998i	−0.405221	+	0.914219i	$0.632805\pi$
$614$		−	0.190096i		−	0.00767166i
$615$	−4.51012	+	9.52992i	−0.181866	+	0.384283i
$616$		0			0
$617$	16.9031	+	16.9031i	0.680493	+	0.680493i	0.960111	−	0.279619i	$-0.0902080\pi$
$617$	16.9031	+	16.9031i	0.680493	+	0.680493i	−0.279619	+	0.960111i	$0.590208\pi$
$618$	−5.33649	−	5.33649i	−0.214665	−	0.214665i
$619$		−	27.8928i		−	1.12111i	−0.828118	−	0.560553i	$-0.810589\pi$
$619$		−	27.8928i		−	1.12111i	0.828118	−	0.560553i	$-0.189411\pi$
$620$	8.69104	−	3.10735i	0.349040	−	0.124794i
$621$	−20.4885			−0.822175
$622$	−3.06667	+	3.06667i	−0.122962	+	0.122962i
$623$	6.78362	+	6.78362i	0.271780	+	0.271780i
$624$	9.92075			0.397148
$625$	4.90083	−	24.5149i	0.196033	−	0.980597i
$626$			3.59976i			0.143875i
$627$		0			0
$628$	−17.1104	+	17.1104i	−0.682780	+	0.682780i
$629$	−1.10356			−0.0440019
$630$	−1.24523	−	3.48284i	−0.0496113	−	0.138759i
$631$	29.4839			1.17374			0.586868	−	0.809683i	$-0.300361\pi$
$631$	29.4839			1.17374			0.586868	+	0.809683i	$0.300361\pi$
$632$	17.3786	+	17.3786i	0.691283	+	0.691283i
$633$	−11.5587	−	11.5587i	−0.459417	−	0.459417i
$634$	8.90043			0.353481
$635$	−29.5280	−	13.9744i	−1.17178	−	0.554556i
$636$	0.523977			0.0207770
$637$	−23.9663	+	23.9663i	−0.949579	+	0.949579i
$638$		0			0
$639$			2.48949i			0.0984828i
$640$	−11.0268	+	23.2997i	−0.435872	+	0.921001i
$641$	45.5491			1.79908			0.899540	−	0.436839i	$-0.143902\pi$
$641$	45.5491			1.79908			0.899540	+	0.436839i	$0.143902\pi$
$642$	−4.69838	−	4.69838i	−0.185430	−	0.185430i
$643$	13.6654	−	13.6654i	0.538911	−	0.538911i	−0.384298	−	0.923209i	$-0.625556\pi$
$643$	13.6654	−	13.6654i	0.538911	−	0.538911i	0.923209	+	0.384298i	$0.125556\pi$
$644$	9.79892			0.386132
$645$	5.53483	+	15.4805i	0.217934	+	0.609545i
$646$		−	0.294017i		−	0.0115679i
$647$	−10.2871	−	10.2871i	−0.404427	−	0.404427i	0.475363	−	0.879790i	$-0.342317\pi$
$647$	−10.2871	−	10.2871i	−0.404427	−	0.404427i	−0.879790	+	0.475363i	$0.842317\pi$
$648$	6.00232	+	6.00232i	0.235793	+	0.235793i
$649$		0			0
$650$	13.5330	−	11.0953i	0.530807	−	0.435195i
$651$		−	2.27228i		−	0.0890578i
$652$	18.7018	+	18.7018i	0.732418	+	0.732418i
$653$	−12.7016	+	12.7016i	−0.497053	+	0.497053i	−0.910519	−	0.413466i	$-0.864318\pi$
$653$	−12.7016	+	12.7016i	−0.497053	+	0.497053i	0.413466	+	0.910519i	$0.364318\pi$
$654$		−	4.65276i		−	0.181937i
$655$	−13.1319	+	4.69511i	−0.513106	+	0.183453i
$656$			12.9887i			0.507125i
$657$	−7.78334	+	7.78334i	−0.303657	+	0.303657i
$658$	−0.620284	+	0.620284i	−0.0241812	+	0.0241812i
$659$	15.1631			0.590672			0.295336	−	0.955393i	$-0.404568\pi$
$659$	15.1631			0.590672			0.295336	+	0.955393i	$0.404568\pi$
$660$		0			0
$661$	20.7843			0.808416			0.404208	−	0.914667i	$-0.367547\pi$
$661$	20.7843			0.808416			0.404208	+	0.914667i	$0.367547\pi$
$662$	−9.67381	+	9.67381i	−0.375983	+	0.375983i
$663$	1.22683	−	1.22683i	0.0476460	−	0.0476460i
$664$		−	24.0422i		−	0.933017i
$665$	3.32049	+	1.57145i	0.128763	+	0.0609383i
$666$		−	4.12551i		−	0.159860i
$667$	−21.3231	+	21.3231i	−0.825633	+	0.825633i
$668$	−2.97616	−	2.97616i	−0.115151	−	0.115151i
$669$		−	2.05755i		−	0.0795494i
$670$	−4.37725	−	12.2429i	−0.169108	−	0.472983i
$671$		0			0
$672$	3.53676	+	3.53676i	0.136434	+	0.136434i
$673$	1.77047	+	1.77047i	0.0682466	+	0.0682466i	0.740406	−	0.672160i	$-0.234633\pi$
$673$	1.77047	+	1.77047i	0.0682466	+	0.0682466i	−0.672160	+	0.740406i	$0.734633\pi$
$674$			2.53363i			0.0975918i
$675$	20.7108	+	2.04989i	0.797161	+	0.0789004i
$676$	−39.9478			−1.53645
$677$	13.8715	−	13.8715i	0.533127	−	0.533127i	−0.388375	−	0.921502i	$-0.626963\pi$
$677$	13.8715	−	13.8715i	0.533127	−	0.533127i	0.921502	+	0.388375i	$0.126963\pi$
$678$	−3.08740	−	3.08740i	−0.118571	−	0.118571i
$679$	10.0717			0.386517
$680$	0.589707	+	1.64937i	0.0226142	+	0.0632505i
$681$		−	16.5912i		−	0.635775i
$682$		0			0
$683$	−28.4186	+	28.4186i	−1.08741	+	1.08741i	−0.0916116	+	0.995795i	$0.529202\pi$
$683$	−28.4186	+	28.4186i	−1.08741	+	1.08741i	−0.995795	+	0.0916116i	$0.970798\pi$
$684$	−5.53048			−0.211463
$685$	7.64696	−	16.1581i	0.292176	−	0.617369i
$686$	−8.64090			−0.329911
$687$	−0.0820973	−	0.0820973i	−0.00313221	−	0.00313221i
$688$	14.3214	+	14.3214i	0.545997	+	0.545997i
$689$	−2.47987			−0.0944754
$690$	2.08694	−	4.40972i	0.0794484	−	0.167875i
$691$	19.9967			0.760712			0.380356	−	0.924840i	$-0.375802\pi$
$691$	19.9967			0.760712			0.380356	+	0.924840i	$0.375802\pi$
$692$	−10.5240	+	10.5240i	−0.400064	+	0.400064i
$693$		0			0
$694$			1.36027i			0.0516352i
$695$	7.70499	+	21.5503i	0.292267	+	0.817451i
$696$	−9.96149			−0.377589
$697$	1.60622	+	1.60622i	0.0608400	+	0.0608400i
$698$	6.94423	−	6.94423i	0.262843	−	0.262843i
$699$	−0.946734			−0.0358088
$700$	−9.90526	−	0.980391i	−0.374384	−	0.0370553i
$701$			46.7671i			1.76637i	0.469025	+	0.883185i	$0.344606\pi$
$701$			46.7671i			1.76637i	−0.469025	+	0.883185i	$0.655394\pi$
$702$	10.3014	+	10.3014i	0.388801	+	0.388801i
$703$	2.89732	+	2.89732i	0.109275	+	0.109275i
$704$		0			0
$705$	−0.739826	−	2.06924i	−0.0278635	−	0.0779322i
$706$		−	6.35104i		−	0.239025i
$707$	−14.6571	−	14.6571i	−0.551238	−	0.551238i
$708$	0.170588	−	0.170588i	0.00641107	−	0.00641107i
$709$		−	18.3465i		−	0.689017i	−0.938783	−	0.344508i	$-0.888046\pi$
$709$		−	18.3465i		−	0.689017i	0.938783	−	0.344508i	$-0.111954\pi$
$710$	−1.20349	−	0.569563i	−0.0451663	−	0.0213753i
$711$		−	28.0103i		−	1.05047i
$712$	12.0096	−	12.0096i	0.450078	−	0.450078i
$713$	−8.61103	+	8.61103i	−0.322485	+	0.322485i
$714$	0.196126			0.00733983
$715$		0			0
$716$	−4.57802			−0.171089
$717$	2.48669	−	2.48669i	0.0928671	−	0.0928671i
$718$	−6.67313	+	6.67313i	−0.249039	+	0.249039i
$719$			8.21075i			0.306209i	0.988210	+	0.153105i	$0.0489272\pi$
$719$			8.21075i			0.306209i	−0.988210	+	0.153105i	$0.951073\pi$
$720$	10.7486	−	3.84300i	0.400578	−	0.143220i
$721$		−	20.3158i		−	0.756599i
$722$	6.96443	−	6.96443i	0.259189	−	0.259189i
$723$	−7.87847	−	7.87847i	−0.293004	−	0.293004i
$724$			21.2367i			0.789256i
$725$	23.6879	−	19.4211i	0.879745	−	0.721281i
$726$		0			0
$727$	−14.7234	−	14.7234i	−0.546062	−	0.546062i	0.379238	−	0.925299i	$-0.376186\pi$
$727$	−14.7234	−	14.7234i	−0.546062	−	0.546062i	−0.925299	+	0.379238i	$0.876186\pi$
$728$	−10.8328	−	10.8328i	−0.401489	−	0.401489i
$729$		−	0.0623328i		−	0.00230862i
$730$	−1.98196	−	5.54341i	−0.0733557	−	0.205171i
$731$	3.54204			0.131007
$732$	−0.620522	+	0.620522i	−0.0229352	+	0.0229352i
$733$	−26.6017	−	26.6017i	−0.982555	−	0.982555i	0.0172958	−	0.999850i	$-0.494494\pi$
$733$	−26.6017	−	26.6017i	−0.982555	−	0.982555i	−0.999850	+	0.0172958i	$0.994494\pi$
$734$	−9.99091			−0.368771
$735$	4.10576	−	8.67550i	0.151443	−	0.320001i
$736$		−	26.8058i		−	0.988074i
$737$		0			0
$738$	−6.00464	+	6.00464i	−0.221034	+	0.221034i
$739$	8.83972			0.325174			0.162587	−	0.986694i	$-0.448016\pi$
$739$	8.83972			0.325174			0.162587	+	0.986694i	$0.448016\pi$
$740$	−10.0351	−	4.74918i	−0.368896	−	0.174583i
$741$	−6.44189			−0.236649
$742$	−0.198221	−	0.198221i	−0.00727693	−	0.00727693i
$743$	7.33161	+	7.33161i	0.268971	+	0.268971i	0.828685	−	0.559715i	$-0.189089\pi$
$743$	7.33161	+	7.33161i	0.268971	+	0.268971i	−0.559715	+	0.828685i	$0.689089\pi$
$744$	−4.02281			−0.147483
$745$	−3.16694	−	8.85771i	−0.116028	−	0.324521i
$746$	−16.3083			−0.597091
$747$	−19.3752	+	19.3752i	−0.708902	+	0.708902i
$748$		0			0
$749$		−	17.8865i		−	0.653559i
$750$	−2.55078	+	4.24877i	−0.0931414	+	0.155143i
$751$	−35.6551			−1.30107			−0.650536	−	0.759475i	$-0.725456\pi$
$751$	−35.6551			−1.30107			−0.650536	+	0.759475i	$0.725456\pi$
$752$	−1.91430	−	1.91430i	−0.0698074	−	0.0698074i
$753$	2.28457	−	2.28457i	0.0832543	−	0.0832543i
$754$	21.4420			0.780873
$755$	−23.5806	+	8.43088i	−0.858185	+	0.306831i
$756$		−	8.28624i		−	0.301368i
$757$	27.6795	+	27.6795i	1.00603	+	1.00603i	0.999982	+	0.00604557i	$0.00192438\pi$
$757$	27.6795	+	27.6795i	1.00603	+	1.00603i	0.00604557	+	0.999982i	$0.498076\pi$
$758$	3.49801	+	3.49801i	0.127053	+	0.127053i
$759$		0			0
$760$	2.78207	−	5.87854i	0.100916	−	0.213237i
$761$			1.69771i			0.0615419i	0.999526	+	0.0307709i	$0.00979624\pi$
$761$			1.69771i			0.0615419i	−0.999526	+	0.0307709i	$0.990204\pi$
$762$	4.57895	+	4.57895i	0.165878	+	0.165878i
$763$	8.85641	−	8.85641i	0.320624	−	0.320624i
$764$			18.7394i			0.677969i
$765$	0.853967	−	1.80444i	0.0308753	−	0.0652397i
$766$			0.828672i			0.0299411i
$767$	−0.807352	+	0.807352i	−0.0291518	+	0.0291518i
$768$	2.41024	−	2.41024i	0.0869720	−	0.0869720i
$769$	−31.3444			−1.13031			−0.565155	−	0.824985i	$-0.691184\pi$
$769$	−31.3444			−1.13031			−0.565155	+	0.824985i	$0.691184\pi$
$770$		0			0
$771$	16.0919			0.579537
$772$	13.7264	−	13.7264i	0.494023	−	0.494023i
$773$	−34.7748	+	34.7748i	−1.25076	+	1.25076i	−0.295383	+	0.955379i	$0.595447\pi$
$773$	−34.7748	+	34.7748i	−1.25076	+	1.25076i	−0.955379	+	0.295383i	$0.904553\pi$
$774$			13.2414i			0.475953i
$775$	9.56602	−	7.84293i	0.343621	−	0.281727i
$776$		−	17.8308i		−	0.640088i
$777$	−1.93268	+	1.93268i	−0.0693345	+	0.0693345i
$778$	−3.54724	−	3.54724i	−0.127175	−	0.127175i
$779$		−	8.43405i		−	0.302181i
$780$	16.4356	−	5.87630i	0.588489	−	0.210405i
$781$		0			0
$782$	−0.743237	−	0.743237i	−0.0265781	−	0.0265781i
$783$	18.0314	+	18.0314i	0.644389	+	0.644389i
$784$		−	11.8242i		−	0.422293i
$785$	−13.8730	+	29.3137i	−0.495147	+	1.04625i
$786$	2.76446			0.0986052
$787$	18.1131	−	18.1131i	0.645661	−	0.645661i	−0.306280	−	0.951941i	$-0.599084\pi$
$787$	18.1131	−	18.1131i	0.645661	−	0.645661i	0.951941	+	0.306280i	$0.0990845\pi$
$788$	14.9906	+	14.9906i	0.534018	+	0.534018i
$789$	18.0475			0.642506
$790$	13.5410	+	6.40838i	0.481766	+	0.228000i
$791$		−	11.7536i		−	0.417909i
$792$		0			0
$793$	2.93679	−	2.93679i	0.104289	−	0.104289i
$794$	19.2306			0.682467
$795$	0.661258	−	0.236423i	0.0234524	−	0.00838505i
$796$	−23.3365			−0.827141
$797$	−5.66431	−	5.66431i	−0.200640	−	0.200640i	0.599634	−	0.800274i	$-0.295313\pi$
$797$	−5.66431	−	5.66431i	−0.200640	−	0.200640i	−0.800274	+	0.599634i	$0.795313\pi$
$798$	−0.514915	−	0.514915i	−0.0182278	−	0.0182278i
$799$	−0.473455			−0.0167496
$800$	−2.68194	+	27.0967i	−0.0948210	+	0.958013i
$801$	−19.3567			−0.683935
$802$	−4.58620	+	4.58620i	−0.161944	+	0.161944i
$803$		0			0
$804$		−	12.9681i		−	0.457349i
$805$	12.3662	−	4.42135i	0.435852	−	0.155832i
$806$	8.65907			0.305003
$807$	1.13542	+	1.13542i	0.0399687	+	0.0399687i
$808$	−25.9487	+	25.9487i	−0.912873	+	0.912873i
$809$	3.65583			0.128532			0.0642661	−	0.997933i	$-0.479529\pi$
$809$	3.65583			0.128532			0.0642661	+	0.997933i	$0.479529\pi$
$810$	4.67686	+	2.21337i	0.164328	+	0.0777698i
$811$		−	20.2295i		−	0.710353i	−0.934799	−	0.355177i	$-0.884421\pi$
$811$		−	20.2295i		−	0.710353i	0.934799	−	0.355177i	$-0.115579\pi$
$812$	−8.62377	−	8.62377i	−0.302635	−	0.302635i
$813$	13.5768	+	13.5768i	0.476158	+	0.476158i
$814$		0			0
$815$	32.0400	+	15.1632i	1.12231	+	0.531144i
$816$			0.605278i			0.0211890i
$817$	−9.29937	−	9.29937i	−0.325344	−	0.325344i
$818$	4.81584	−	4.81584i	0.168382	−	0.168382i
$819$			17.4599i			0.610099i
$820$	7.69354	+	21.5183i	0.268670	+	0.751452i
$821$		−	32.5960i		−	1.13761i	−0.822474	−	0.568803i	$-0.807407\pi$
$821$		−	32.5960i		−	1.13761i	0.822474	−	0.568803i	$-0.192593\pi$
$822$	−2.50566	+	2.50566i	−0.0873951	+	0.0873951i
$823$	−24.9371	+	24.9371i	−0.869251	+	0.869251i	−0.992390	−	0.123138i	$-0.960704\pi$
$823$	−24.9371	+	24.9371i	−0.869251	+	0.869251i	0.123138	+	0.992390i	$0.460704\pi$
$824$	−35.9667			−1.25296
$825$		0			0
$826$	−0.129067			−0.00449081
$827$	−21.1230	+	21.1230i	−0.734518	+	0.734518i	−0.971511	−	0.236993i	$-0.923838\pi$
$827$	−21.1230	+	21.1230i	−0.734518	+	0.734518i	0.236993	+	0.971511i	$0.423838\pi$
$828$	−13.9804	+	13.9804i	−0.485851	+	0.485851i
$829$		−	7.75179i		−	0.269231i	−0.990898	−	0.134615i	$-0.957020\pi$
$829$		−	7.75179i		−	0.269231i	0.990898	−	0.134615i	$-0.0429799\pi$
$830$	−4.93374	−	13.7993i	−0.171253	−	0.478982i
$831$		−	4.18592i		−	0.145208i
$832$	4.74913	−	4.74913i	0.164646	−	0.164646i
$833$	−1.46221	−	1.46221i	−0.0506627	−	0.0506627i
$834$		−	4.53667i		−	0.157092i
$835$	−5.09878	−	2.41304i	−0.176451	−	0.0835068i
$836$		0			0
$837$	7.28172	+	7.28172i	0.251693	+	0.251693i
$838$	15.5705	+	15.5705i	0.537875	+	0.537875i
$839$			21.3137i			0.735829i	0.929860	+	0.367915i	$0.119928\pi$
$839$			21.3137i			0.735829i	−0.929860	+	0.367915i	$0.880072\pi$
$840$	3.92132	+	1.85580i	0.135299	+	0.0640312i
$841$	8.53175			0.294198
$842$	1.06835	−	1.06835i	0.0368179	−	0.0368179i
$843$	−1.95201	−	1.95201i	−0.0672306	−	0.0672306i
$844$	−35.4307			−1.21957
$845$	−50.4140	+	18.0248i	−1.73430	+	0.620071i
$846$		−	1.76995i		−	0.0608520i
$847$		0			0
$848$	0.611744	−	0.611744i	0.0210074	−	0.0210074i
$849$	4.00823			0.137562
$850$	0.676941	+	0.825665i	0.0232189	+	0.0283201i
$851$	14.6481			0.502131
$852$	−0.939043	−	0.939043i	−0.0321711	−	0.0321711i
$853$	−23.8130	−	23.8130i	−0.815343	−	0.815343i	0.170086	−	0.985429i	$-0.445595\pi$
$853$	−23.8130	−	23.8130i	−0.815343	−	0.815343i	−0.985429	+	0.170086i	$0.945595\pi$
$854$	0.469489			0.0160656
$855$	−6.97946	+	2.49540i	−0.238692	+	0.0853408i
$856$	−31.6660			−1.08232
$857$	14.1050	−	14.1050i	0.481819	−	0.481819i	−0.423893	−	0.905712i	$-0.639337\pi$
$857$	14.1050	−	14.1050i	0.481819	−	0.481819i	0.905712	+	0.423893i	$0.139337\pi$
$858$		0			0
$859$		−	43.5337i		−	1.48535i	−0.669652	−	0.742675i	$-0.733557\pi$
$859$		−	43.5337i		−	1.48535i	0.669652	−	0.742675i	$-0.266443\pi$
$860$	32.2090	+	15.2432i	1.09832	+	0.519788i
$861$	5.62599			0.191733
$862$	0.438353	+	0.438353i	0.0149304	+	0.0149304i
$863$	−34.4450	+	34.4450i	−1.17252	+	1.17252i	−0.190915	+	0.981607i	$0.561145\pi$
$863$	−34.4450	+	34.4450i	−1.17252	+	1.17252i	−0.981607	+	0.190915i	$0.938855\pi$
$864$	−22.6677			−0.771171
$865$	−8.53279	+	18.0299i	−0.290124	+	0.613034i
$866$		−	0.571760i		−	0.0194292i
$867$	−9.17816	−	9.17816i	−0.311707	−	0.311707i
$868$	−3.48259	−	3.48259i	−0.118207	−	0.118207i
$869$		0			0
$870$	−5.71753	+	2.04422i	−0.193843	+	0.0693054i
$871$			61.3751i			2.07961i
$872$	−15.6792	−	15.6792i	−0.530966	−	0.530966i
$873$	−14.3696	+	14.3696i	−0.486336	+	0.486336i
$874$			3.90263i			0.132008i
$875$	−12.9428	+	3.23208i	−0.437546	+	0.109264i
$876$		−	5.87179i		−	0.198389i
$877$	16.7469	−	16.7469i	0.565503	−	0.565503i	−0.365362	−	0.930866i	$-0.619055\pi$
$877$	16.7469	−	16.7469i	0.565503	−	0.565503i	0.930866	+	0.365362i	$0.119055\pi$
$878$	8.52521	−	8.52521i	0.287712	−	0.287712i
$879$	8.03015			0.270850
$880$		0			0
$881$	−30.2702			−1.01983			−0.509914	−	0.860225i	$-0.670323\pi$
$881$	−30.2702			−1.01983			−0.509914	+	0.860225i	$0.670323\pi$
$882$	5.46629	−	5.46629i	0.184059	−	0.184059i
$883$	6.62228	−	6.62228i	0.222858	−	0.222858i	−0.586843	−	0.809701i	$-0.699629\pi$
$883$	6.62228	−	6.62228i	0.222858	−	0.222858i	0.809701	+	0.586843i	$0.199629\pi$
$884$		−	3.76057i		−	0.126482i
$885$	0.138311	−	0.292252i	0.00464926	−	0.00982393i
$886$			15.9853i			0.537038i
$887$	23.9251	−	23.9251i	0.803326	−	0.803326i	−0.180288	−	0.983614i	$-0.557703\pi$
$887$	23.9251	−	23.9251i	0.803326	−	0.803326i	0.983614	+	0.180288i	$0.0577028\pi$
$888$	3.42158	+	3.42158i	0.114821	+	0.114821i
$889$			17.4318i			0.584645i
$890$	4.42856	−	9.35758i	0.148446	−	0.313667i
$891$		0			0
$892$	−3.15348	−	3.15348i	−0.105586	−	0.105586i
$893$	1.24302	+	1.24302i	0.0415962	+	0.0415962i
$894$			1.86468i			0.0623643i
$895$	−5.77745	+	2.06564i	−0.193119	+	0.0690467i
$896$	13.7550			0.459522
$897$	−16.2843	+	16.2843i	−0.543717	+	0.543717i
$898$	−3.32692	−	3.32692i	−0.111021	−	0.111021i
$899$	15.1567			0.505503
$900$	15.5308	−	12.7333i	0.517694	−	0.424444i
$901$		−	0.151300i		−	0.00504053i
$902$		0			0
$903$	6.20321	−	6.20321i	0.206430	−	0.206430i
$904$	−20.8083			−0.692074
$905$	9.58217	+	26.8007i	0.318522	+	0.890885i
$906$	4.96407			0.164920
$907$	−20.9808	−	20.9808i	−0.696655	−	0.696655i	0.267032	−	0.963688i	$-0.413957\pi$
$907$	−20.9808	−	20.9808i	−0.696655	−	0.696655i	−0.963688	+	0.267032i	$0.913957\pi$
$908$	−25.4283	−	25.4283i	−0.843867	−	0.843867i
$909$	41.8234			1.38719
$910$	−8.44062	−	3.99460i	−0.279804	−	0.132420i
$911$	24.6094			0.815344			0.407672	−	0.913128i	$-0.366341\pi$
$911$	24.6094			0.815344			0.407672	+	0.913128i	$0.366341\pi$
$912$	1.58911	−	1.58911i	0.0526208	−	0.0526208i
$913$		0			0
$914$			15.1439i			0.500917i
$915$	−0.503113	+	1.06308i	−0.0166324	+	0.0351444i
$916$	−0.251651			−0.00831479
$917$	5.26209	+	5.26209i	0.173770	+	0.173770i
$918$	−0.628502	+	0.628502i	−0.0207437	+	0.0207437i
$919$	−24.2408			−0.799630			−0.399815	−	0.916596i	$-0.630926\pi$
$919$	−24.2408			−0.799630			−0.399815	+	0.916596i	$0.630926\pi$
$920$	−7.82749	−	21.8929i	−0.258065	−	0.721789i
$921$		−	0.254112i		−	0.00837328i
$922$	−7.32726	−	7.32726i	−0.241311	−	0.241311i
$923$	4.44428	+	4.44428i	0.146285	+	0.146285i
$924$		0			0
$925$	−14.8071	−	1.46556i	−0.486854	−	0.0481872i
$926$			0.494313i			0.0162441i
$927$	28.9850	+	28.9850i	0.951992	+	0.951992i
$928$	−23.5911	+	23.5911i	−0.774414	+	0.774414i
$929$			46.9432i			1.54016i	0.637949	+	0.770078i	$0.279783\pi$
$929$			46.9432i			1.54016i	−0.637949	+	0.770078i	$0.720217\pi$
$930$	−2.30895	+	0.825528i	−0.0757133	+	0.0270701i
$931$			7.67788i			0.251632i
$932$	−1.45100	+	1.45100i	−0.0475292	+	0.0475292i
$933$	−4.09939	+	4.09939i	−0.134208	+	0.134208i
$934$	19.9186			0.651756
$935$		0			0
$936$	30.9107			1.01035
$937$	31.0116	−	31.0116i	1.01311	−	1.01311i	0.0131926	−	0.999913i	$-0.495801\pi$
$937$	31.0116	−	31.0116i	1.01311	−	1.01311i	0.999913	−	0.0131926i	$-0.00419947\pi$
$938$	−4.90584	+	4.90584i	−0.160182	+	0.160182i
$939$			4.81200i			0.157034i
$940$	−4.30529	−	2.03752i	−0.140423	−	0.0664564i
$941$			56.3356i			1.83649i	0.396014	+	0.918245i	$0.370393\pi$
$941$			56.3356i			1.83649i	−0.396014	+	0.918245i	$0.629607\pi$
$942$	4.54572	−	4.54572i	0.148108	−	0.148108i
$943$	−21.3202	−	21.3202i	−0.694282	−	0.694282i
$944$		−	0.398323i		−	0.0129643i
$945$	−3.73882	−	10.4572i	−0.121624	−	0.340174i
$946$		0			0
$947$	−8.42915	−	8.42915i	−0.273910	−	0.273910i	0.556762	−	0.830672i	$-0.312044\pi$
$947$	−8.42915	−	8.42915i	−0.273910	−	0.273910i	−0.830672	+	0.556762i	$0.812044\pi$
$948$	10.5655	+	10.5655i	0.343153	+	0.343153i
$949$			27.7899i			0.902097i
$950$	0.390462	−	3.94498i	0.0126683	−	0.127992i
$951$	11.8977			0.385809
$952$	0.660921	−	0.660921i	0.0214206	−	0.0214206i
$953$	−14.1367	−	14.1367i	−0.457932	−	0.457932i	0.440044	−	0.897976i	$-0.354963\pi$
$953$	−14.1367	−	14.1367i	−0.457932	−	0.457932i	−0.897976	+	0.440044i	$0.854963\pi$
$954$	0.565614			0.0183124
$955$	8.45538	+	23.6491i	0.273610	+	0.765268i
$956$		−	7.62239i		−	0.246526i
$957$		0			0
$958$	−1.72058	+	1.72058i	−0.0555894	+	0.0555894i
$959$	−9.53894			−0.308029
$960$	−0.813592	+	1.71913i	−0.0262586	+	0.0554846i
$961$	−24.8792			−0.802555
$962$	−7.36492	−	7.36492i	−0.237455	−	0.237455i
$963$	25.5191	+	25.5191i	0.822343	+	0.822343i
$964$	−24.1497			−0.777810
$965$	11.1292	−	23.5161i	0.358262	−	0.757010i
$966$	−2.60328			−0.0837591
$967$	30.1366	−	30.1366i	0.969127	−	0.969127i	−0.0304105	−	0.999537i	$-0.509681\pi$
$967$	30.1366	−	30.1366i	0.969127	−	0.969127i	0.999537	+	0.0304105i	$0.00968144\pi$
$968$		0			0
$969$		−	0.393028i		−	0.0126259i
$970$	−3.65909	−	10.2342i	−0.117486	−	0.328601i
$971$	−21.4445			−0.688188			−0.344094	−	0.938935i	$-0.611814\pi$
$971$	−21.4445			−0.688188			−0.344094	+	0.938935i	$0.611814\pi$
$972$	18.3810	+	18.3810i	0.589570	+	0.589570i
$973$	8.63545	−	8.63545i	0.276840	−	0.276840i
$974$	−1.62873			−0.0521878
$975$	18.0903	−	14.8318i	0.579352	−	0.474996i
$976$			1.44892i			0.0463789i
$977$	−1.27524	−	1.27524i	−0.0407986	−	0.0407986i	0.686413	−	0.727212i	$-0.259184\pi$
$977$	−1.27524	−	1.27524i	−0.0407986	−	0.0407986i	−0.727212	+	0.686413i	$0.759184\pi$
$978$	−4.96850	−	4.96850i	−0.158875	−	0.158875i
$979$		0			0
$980$	−7.00377	−	19.5891i	−0.223727	−	0.625749i
$981$			25.2713i			0.806851i
$982$	−16.1992	−	16.1992i	−0.516939	−	0.516939i
$983$	−16.5299	+	16.5299i	−0.527221	+	0.527221i	−0.919743	−	0.392521i	$-0.871603\pi$
$983$	−16.5299	+	16.5299i	−0.527221	+	0.527221i	0.392521	+	0.919743i	$0.371603\pi$
$984$		−	9.96015i		−	0.317518i
$985$	25.6820	+	12.1542i	0.818296	+	0.387266i
$986$			1.30821i			0.0416618i
$987$	−0.829167	+	0.829167i	−0.0263927	+	0.0263927i
$988$	−9.87310	+	9.87310i	−0.314105	+	0.314105i
$989$	−47.0153			−1.49500
$990$		0			0
$991$	45.9530			1.45974			0.729872	−	0.683584i	$-0.239580\pi$
$991$	45.9530			1.45974			0.729872	+	0.683584i	$0.239580\pi$
$992$	−9.52692	+	9.52692i	−0.302480	+	0.302480i
$993$	−12.9315	+	12.9315i	−0.410369	+	0.410369i
$994$			0.710482i			0.0225351i
$995$	−29.4507	+	10.5296i	−0.933648	+	0.333812i
$996$		−	14.6168i		−	0.463150i
$997$	−42.5630	+	42.5630i	−1.34798	+	1.34798i	−0.460134	+	0.887849i	$0.652199\pi$
$997$	−42.5630	+	42.5630i	−1.34798	+	1.34798i	−0.887849	+	0.460134i	$0.847801\pi$
$998$	12.1970	+	12.1970i	0.386088	+	0.386088i
$999$		−	12.3869i		−	0.391903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.362.7		32
5.3	odd	4	inner	605.2.e.b.483.10		32
11.2	odd	10		605.2.m.d.282.3		32
11.3	even	5		605.2.m.e.112.2		32
11.4	even	5		55.2.l.a.17.3	yes	32
11.5	even	5		605.2.m.d.602.2		32
11.6	odd	10		605.2.m.c.602.3		32
11.7	odd	10		605.2.m.e.457.2		32
11.8	odd	10		55.2.l.a.2.3	✓	32
11.9	even	5		605.2.m.c.282.2		32
11.10	odd	2	inner	605.2.e.b.362.10		32
33.8	even	10		495.2.bj.a.442.2		32
33.26	odd	10		495.2.bj.a.127.2		32
44.15	odd	10		880.2.cm.a.17.2		32
44.19	even	10		880.2.cm.a.497.2		32
55.3	odd	20		605.2.m.e.233.2		32
55.4	even	10		275.2.bm.b.182.2		32
55.8	even	20		55.2.l.a.13.3	yes	32
55.13	even	20		605.2.m.d.403.2		32
55.18	even	20		605.2.m.e.578.2		32
55.19	odd	10		275.2.bm.b.57.2		32
55.28	even	20		605.2.m.c.118.2		32
55.37	odd	20		275.2.bm.b.193.2		32
55.38	odd	20		605.2.m.d.118.3		32
55.43	even	4	inner	605.2.e.b.483.7		32
55.48	odd	20		55.2.l.a.28.3	yes	32
55.52	even	20		275.2.bm.b.68.2		32
55.53	odd	20		605.2.m.c.403.3		32
165.8	odd	20		495.2.bj.a.343.2		32
165.158	even	20		495.2.bj.a.28.2		32
220.63	odd	20		880.2.cm.a.673.2		32
220.103	even	20		880.2.cm.a.193.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.3	✓	32	11.8	odd	10
55.2.l.a.13.3	yes	32	55.8	even	20
55.2.l.a.17.3	yes	32	11.4	even	5
55.2.l.a.28.3	yes	32	55.48	odd	20
275.2.bm.b.57.2		32	55.19	odd	10
275.2.bm.b.68.2		32	55.52	even	20
275.2.bm.b.182.2		32	55.4	even	10
275.2.bm.b.193.2		32	55.37	odd	20
495.2.bj.a.28.2		32	165.158	even	20
495.2.bj.a.127.2		32	33.26	odd	10
495.2.bj.a.343.2		32	165.8	odd	20
495.2.bj.a.442.2		32	33.8	even	10
605.2.e.b.362.7		32	1.1	even	1	trivial
605.2.e.b.362.10		32	11.10	odd	2	inner
605.2.e.b.483.7		32	55.43	even	4	inner
605.2.e.b.483.10		32	5.3	odd	4	inner
605.2.m.c.118.2		32	55.28	even	20
605.2.m.c.282.2		32	11.9	even	5
605.2.m.c.403.3		32	55.53	odd	20
605.2.m.c.602.3		32	11.6	odd	10
605.2.m.d.118.3		32	55.38	odd	20
605.2.m.d.282.3		32	11.2	odd	10
605.2.m.d.403.2		32	55.13	even	20
605.2.m.d.602.2		32	11.5	even	5
605.2.m.e.112.2		32	11.3	even	5
605.2.m.e.233.2		32	55.3	odd	20
605.2.m.e.457.2		32	11.7	odd	10
605.2.m.e.578.2		32	55.18	even	20
880.2.cm.a.17.2		32	44.15	odd	10
880.2.cm.a.193.2		32	220.103	even	20
880.2.cm.a.497.2		32	44.19	even	10
880.2.cm.a.673.2		32	220.63	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.407176 + 0.407176i) q^{2} +(-0.544295 + 0.544295i) q^{3} +1.66842i q^{4} +(0.752803 + 2.10554i) q^{5} -0.443248i q^{6} +(0.843711 - 0.843711i) q^{7} +(-1.49369 - 1.49369i) q^{8} +2.40749i q^{9} +O(q^{10})\)	\(q+(-0.407176 + 0.407176i) q^{2} +(-0.544295 + 0.544295i) q^{3} +1.66842i q^{4} +(0.752803 + 2.10554i) q^{5} -0.443248i q^{6} +(0.843711 - 0.843711i) q^{7} +(-1.49369 - 1.49369i) q^{8} +2.40749i q^{9} +(-1.16385 - 0.550801i) q^{10} +(-0.908110 - 0.908110i) q^{12} +(4.29788 + 4.29788i) q^{13} +0.687078i q^{14} +(-1.55578 - 0.736287i) q^{15} -2.12044 q^{16} +(-0.262219 + 0.262219i) q^{17} +(-0.980271 - 0.980271i) q^{18} +1.37688 q^{19} +(-3.51291 + 1.25599i) q^{20} +0.918455i q^{21} +(3.48057 - 3.48057i) q^{23} +1.62602 q^{24} +(-3.86658 + 3.17011i) q^{25} -3.49999 q^{26} +(-2.94327 - 2.94327i) q^{27} +(1.40766 + 1.40766i) q^{28} -6.12632 q^{29} +(0.933275 - 0.333678i) q^{30} -2.47403 q^{31} +(3.85077 - 3.85077i) q^{32} -0.213539i q^{34} +(2.41161 + 1.14132i) q^{35} -4.01669 q^{36} +(2.10427 + 2.10427i) q^{37} +(-0.560631 + 0.560631i) q^{38} -4.67863 q^{39} +(2.02057 - 4.26948i) q^{40} -6.12549i q^{41} +(-0.373973 - 0.373973i) q^{42} +(-6.75396 - 6.75396i) q^{43} +(-5.06905 + 1.81236i) q^{45} +2.83441i q^{46} +(0.902785 + 0.902785i) q^{47} +(1.15414 - 1.15414i) q^{48} +5.57630i q^{49} +(0.283585 - 2.86517i) q^{50} -0.285449i q^{51} +(-7.17065 + 7.17065i) q^{52} +(-0.288499 + 0.288499i) q^{53} +2.39686 q^{54} -2.52049 q^{56} +(-0.749427 + 0.749427i) q^{57} +(2.49449 - 2.49449i) q^{58} +0.187849i q^{59} +(1.22843 - 2.59569i) q^{60} -0.683312i q^{61} +(1.00736 - 1.00736i) q^{62} +(2.03122 + 2.03122i) q^{63} -1.10499i q^{64} +(-5.81389 + 12.2848i) q^{65} +(7.14016 + 7.14016i) q^{67} +(-0.437491 - 0.437491i) q^{68} +3.78891i q^{69} +(-1.44667 + 0.517234i) q^{70} +1.03406 q^{71} +(3.59604 - 3.59604i) q^{72} +(3.23297 + 3.23297i) q^{73} -1.71362 q^{74} +(0.379084 - 3.83003i) q^{75} +2.29720i q^{76} +(1.90503 - 1.90503i) q^{78} -11.6347 q^{79} +(-1.59627 - 4.46467i) q^{80} -4.01845 q^{81} +(2.49415 + 2.49415i) q^{82} +(8.04790 + 8.04790i) q^{83} -1.53236 q^{84} +(-0.749512 - 0.354713i) q^{85} +5.50010 q^{86} +(3.33452 - 3.33452i) q^{87} +8.04021i q^{89} +(1.32605 - 2.80195i) q^{90} +7.25234 q^{91} +(5.80704 + 5.80704i) q^{92} +(1.34660 - 1.34660i) q^{93} -0.735185 q^{94} +(1.03652 + 2.89906i) q^{95} +4.19191i q^{96} +(5.96870 + 5.96870i) q^{97} +(-2.27054 - 2.27054i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

L-functions

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