LMFDB - Embedded newform 490.2.e.j.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, not 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.2.e.j.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.292893 + 0.507306i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.585786 q^{6} -1.00000 q^{8} +(1.32843 - 2.30090i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.292893 + 0.507306i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.585786 q^{6} -1.00000 q^{8} +(1.32843 - 2.30090i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.41421 - 4.18154i) q^{11} +(0.292893 - 0.507306i) q^{12} -0.828427 q^{13} +0.585786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.70711 + 4.68885i) q^{17} +(-1.32843 - 2.30090i) q^{18} +(1.70711 - 2.95680i) q^{19} -1.00000 q^{20} -4.82843 q^{22} +(3.41421 - 5.91359i) q^{23} +(-0.292893 - 0.507306i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.414214 + 0.717439i) q^{26} +3.31371 q^{27} +0.828427 q^{29} +(0.292893 - 0.507306i) q^{30} +(1.41421 + 2.44949i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.41421 - 2.44949i) q^{33} +5.41421 q^{34} -2.65685 q^{36} +(-1.82843 + 3.16693i) q^{37} +(-1.70711 - 2.95680i) q^{38} +(-0.242641 - 0.420266i) q^{39} +(-0.500000 + 0.866025i) q^{40} -11.0711 q^{41} -3.17157 q^{43} +(-2.41421 + 4.18154i) q^{44} +(-1.32843 - 2.30090i) q^{45} +(-3.41421 - 5.91359i) q^{46} +(5.41421 - 9.37769i) q^{47} -0.585786 q^{48} -1.00000 q^{50} +(-1.58579 + 2.74666i) q^{51} +(0.414214 + 0.717439i) q^{52} +(5.24264 + 9.08052i) q^{53} +(1.65685 - 2.86976i) q^{54} -4.82843 q^{55} +2.00000 q^{57} +(0.414214 - 0.717439i) q^{58} +(5.70711 + 9.88500i) q^{59} +(-0.292893 - 0.507306i) q^{60} +(-6.65685 + 11.5300i) q^{61} +2.82843 q^{62} +1.00000 q^{64} +(-0.414214 + 0.717439i) q^{65} +(-1.41421 - 2.44949i) q^{66} +(4.82843 + 8.36308i) q^{67} +(2.70711 - 4.68885i) q^{68} +4.00000 q^{69} +12.4853 q^{71} +(-1.32843 + 2.30090i) q^{72} +(-3.29289 - 5.70346i) q^{73} +(1.82843 + 3.16693i) q^{74} +(0.292893 - 0.507306i) q^{75} -3.41421 q^{76} -0.485281 q^{78} +(0.585786 - 1.01461i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.01472 - 5.22165i) q^{81} +(-5.53553 + 9.58783i) q^{82} -6.24264 q^{83} +5.41421 q^{85} +(-1.58579 + 2.74666i) q^{86} +(0.242641 + 0.420266i) q^{87} +(2.41421 + 4.18154i) q^{88} +(-6.36396 + 11.0227i) q^{89} -2.65685 q^{90} -6.82843 q^{92} +(-0.828427 + 1.43488i) q^{93} +(-5.41421 - 9.37769i) q^{94} +(-1.70711 - 2.95680i) q^{95} +(-0.292893 + 0.507306i) q^{96} +16.2426 q^{97} -12.8284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{12} + 8 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} - 4 q^{20} - 8 q^{22} + 8 q^{23} - 4 q^{24} - 2 q^{25} + 4 q^{26} - 32 q^{27} - 8 q^{29} + 4 q^{30} + 2 q^{32} + 16 q^{34} + 12 q^{36} + 4 q^{37} - 4 q^{38} + 16 q^{39} - 2 q^{40} - 16 q^{41} - 24 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} + 16 q^{47} - 8 q^{48} - 4 q^{50} - 12 q^{51} - 4 q^{52} + 4 q^{53} - 16 q^{54} - 8 q^{55} + 8 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 4 q^{64} + 4 q^{65} + 8 q^{67} + 8 q^{68} + 16 q^{69} + 16 q^{71} + 6 q^{72} - 16 q^{73} - 4 q^{74} + 4 q^{75} - 8 q^{76} + 32 q^{78} + 8 q^{79} + 2 q^{80} - 46 q^{81} - 8 q^{82} - 8 q^{83} + 16 q^{85} - 12 q^{86} - 16 q^{87} + 4 q^{88} + 12 q^{90} - 16 q^{92} + 8 q^{93} - 16 q^{94} - 4 q^{95} - 4 q^{96} + 48 q^{97} - 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 4 * q^12 + 8 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 - 4 * q^20 - 8 * q^22 + 8 * q^23 - 4 * q^24 - 2 * q^25 + 4 * q^26 - 32 * q^27 - 8 * q^29 + 4 * q^30 + 2 * q^32 + 16 * q^34 + 12 * q^36 + 4 * q^37 - 4 * q^38 + 16 * q^39 - 2 * q^40 - 16 * q^41 - 24 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 + 16 * q^47 - 8 * q^48 - 4 * q^50 - 12 * q^51 - 4 * q^52 + 4 * q^53 - 16 * q^54 - 8 * q^55 + 8 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 4 * q^64 + 4 * q^65 + 8 * q^67 + 8 * q^68 + 16 * q^69 + 16 * q^71 + 6 * q^72 - 16 * q^73 - 4 * q^74 + 4 * q^75 - 8 * q^76 + 32 * q^78 + 8 * q^79 + 2 * q^80 - 46 * q^81 - 8 * q^82 - 8 * q^83 + 16 * q^85 - 12 * q^86 - 16 * q^87 + 4 * q^88 + 12 * q^90 - 16 * q^92 + 8 * q^93 - 16 * q^94 - 4 * q^95 - 4 * q^96 + 48 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.292893	+	0.507306i	0.169102	+	0.292893i	0.938104	−	0.346353i	$-0.112580\pi$
$3$	0.292893	+	0.507306i	0.169102	+	0.292893i	−0.769002	+	0.639246i	$0.779247\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.585786			0.239146
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.32843	−	2.30090i	0.442809	−	0.766968i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	−0.957764	−	0.287556i	$-0.907157\pi$
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	0.229851	−	0.973226i	$-0.426176\pi$
$12$	0.292893	−	0.507306i	0.0845510	−	0.146447i
$13$	−0.828427			−0.229764			−0.114882	−	0.993379i	$-0.536649\pi$
$13$	−0.828427			−0.229764			−0.114882	+	0.993379i	$0.536649\pi$
$14$		0			0
$15$	0.585786			0.151249
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.70711	+	4.68885i	0.656570	+	1.13721i	0.981498	+	0.191474i	$0.0613266\pi$
$17$	2.70711	+	4.68885i	0.656570	+	1.13721i	−0.324928	+	0.945739i	$0.605340\pi$
$18$	−1.32843	−	2.30090i	−0.313113	−	0.542328i
$19$	1.70711	−	2.95680i	0.391637	−	0.678335i	−0.601028	−	0.799228i	$-0.705242\pi$
$19$	1.70711	−	2.95680i	0.391637	−	0.678335i	0.992666	+	0.120892i	$0.0385755\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−4.82843			−1.02942
$23$	3.41421	−	5.91359i	0.711913	−	1.23307i	−0.252226	−	0.967668i	$-0.581162\pi$
$23$	3.41421	−	5.91359i	0.711913	−	1.23307i	0.964138	−	0.265401i	$-0.0855042\pi$
$24$	−0.292893	−	0.507306i	−0.0597866	−	0.103553i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.414214	+	0.717439i	−0.0812340	+	0.140701i
$27$	3.31371			0.637723
$28$		0			0
$29$	0.828427			0.153835			0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427			0.153835			0.0769175	+	0.997037i	$0.475492\pi$
$30$	0.292893	−	0.507306i	0.0534747	−	0.0926210i
$31$	1.41421	+	2.44949i	0.254000	+	0.439941i	0.964623	−	0.263631i	$-0.0849203\pi$
$31$	1.41421	+	2.44949i	0.254000	+	0.439941i	−0.710623	+	0.703573i	$0.751587\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.41421	−	2.44949i	0.246183	−	0.426401i
$34$	5.41421			0.928530
$35$		0			0
$36$	−2.65685			−0.442809
$37$	−1.82843	+	3.16693i	−0.300592	+	0.520640i	−0.976270	−	0.216557i	$-0.930517\pi$
$37$	−1.82843	+	3.16693i	−0.300592	+	0.520640i	0.675679	+	0.737196i	$0.263851\pi$
$38$	−1.70711	−	2.95680i	−0.276929	−	0.479656i
$39$	−0.242641	−	0.420266i	−0.0388536	−	0.0672964i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−11.0711			−1.72901			−0.864505	−	0.502624i	$-0.832368\pi$
$41$	−11.0711			−1.72901			−0.864505	+	0.502624i	$0.832368\pi$
$42$		0			0
$43$	−3.17157			−0.483660			−0.241830	−	0.970319i	$-0.577748\pi$
$43$	−3.17157			−0.483660			−0.241830	+	0.970319i	$0.577748\pi$
$44$	−2.41421	+	4.18154i	−0.363956	+	0.630391i
$45$	−1.32843	−	2.30090i	−0.198030	−	0.342998i
$46$	−3.41421	−	5.91359i	−0.503398	−	0.871911i
$47$	5.41421	−	9.37769i	0.789744	−	1.36788i	−0.136379	−	0.990657i	$-0.543547\pi$
$47$	5.41421	−	9.37769i	0.789744	−	1.36788i	0.926124	−	0.377220i	$-0.123120\pi$
$48$	−0.585786			−0.0845510
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−1.58579	+	2.74666i	−0.222055	+	0.384610i
$52$	0.414214	+	0.717439i	0.0574411	+	0.0994909i
$53$	5.24264	+	9.08052i	0.720132	+	1.24731i	0.960947	+	0.276734i	$0.0892521\pi$
$53$	5.24264	+	9.08052i	0.720132	+	1.24731i	−0.240814	+	0.970571i	$0.577415\pi$
$54$	1.65685	−	2.86976i	0.225469	−	0.390524i
$55$	−4.82843			−0.651065
$56$		0			0
$57$	2.00000			0.264906
$58$	0.414214	−	0.717439i	0.0543889	−	0.0942043i
$59$	5.70711	+	9.88500i	0.743002	+	1.28692i	0.951122	+	0.308814i	$0.0999321\pi$
$59$	5.70711	+	9.88500i	0.743002	+	1.28692i	−0.208120	+	0.978103i	$0.566735\pi$
$60$	−0.292893	−	0.507306i	−0.0378124	−	0.0654929i
$61$	−6.65685	+	11.5300i	−0.852323	+	1.47627i	0.0267837	+	0.999641i	$0.491473\pi$
$61$	−6.65685	+	11.5300i	−0.852323	+	1.47627i	−0.879107	+	0.476625i	$0.841860\pi$
$62$	2.82843			0.359211
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.414214	+	0.717439i	−0.0513769	+	0.0889873i
$66$	−1.41421	−	2.44949i	−0.174078	−	0.301511i
$67$	4.82843	+	8.36308i	0.589886	+	1.02171i	0.994247	+	0.107113i	$0.0341608\pi$
$67$	4.82843	+	8.36308i	0.589886	+	1.02171i	−0.404361	+	0.914600i	$0.632506\pi$
$68$	2.70711	−	4.68885i	0.328285	−	0.568606i
$69$	4.00000			0.481543
$70$		0			0
$71$	12.4853			1.48173			0.740865	−	0.671654i	$-0.234416\pi$
$71$	12.4853			1.48173			0.740865	+	0.671654i	$0.234416\pi$
$72$	−1.32843	+	2.30090i	−0.156557	+	0.271164i
$73$	−3.29289	−	5.70346i	−0.385404	−	0.667539i	0.606421	−	0.795144i	$-0.292605\pi$
$73$	−3.29289	−	5.70346i	−0.385404	−	0.667539i	−0.991825	+	0.127604i	$0.959271\pi$
$74$	1.82843	+	3.16693i	0.212550	+	0.368148i
$75$	0.292893	−	0.507306i	0.0338204	−	0.0585786i
$76$	−3.41421			−0.391637
$77$		0			0
$78$	−0.485281			−0.0549473
$79$	0.585786	−	1.01461i	0.0659061	−	0.114153i	−0.831189	−	0.555989i	$-0.812340\pi$
$79$	0.585786	−	1.01461i	0.0659061	−	0.114153i	0.897096	+	0.441837i	$0.145673\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.01472	−	5.22165i	−0.334969	−	0.580183i
$82$	−5.53553	+	9.58783i	−0.611297	+	1.05880i
$83$	−6.24264			−0.685219			−0.342609	−	0.939478i	$-0.611311\pi$
$83$	−6.24264			−0.685219			−0.342609	+	0.939478i	$0.611311\pi$
$84$		0			0
$85$	5.41421			0.587254
$86$	−1.58579	+	2.74666i	−0.171000	+	0.296180i
$87$	0.242641	+	0.420266i	0.0260138	+	0.0450572i
$88$	2.41421	+	4.18154i	0.257356	+	0.445754i
$89$	−6.36396	+	11.0227i	−0.674579	+	1.16840i	0.302013	+	0.953304i	$0.402341\pi$
$89$	−6.36396	+	11.0227i	−0.674579	+	1.16840i	−0.976592	+	0.215101i	$0.930992\pi$
$90$	−2.65685			−0.280057
$91$		0			0
$92$	−6.82843			−0.711913
$93$	−0.828427	+	1.43488i	−0.0859039	+	0.148790i
$94$	−5.41421	−	9.37769i	−0.558433	−	0.967235i
$95$	−1.70711	−	2.95680i	−0.175145	−	0.303361i
$96$	−0.292893	+	0.507306i	−0.0298933	+	0.0517767i
$97$	16.2426			1.64919			0.824595	−	0.565723i	$-0.191403\pi$
$97$	16.2426			1.64919			0.824595	+	0.565723i	$0.191403\pi$
$98$		0			0
$99$	−12.8284			−1.28931
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−4.65685	−	8.06591i	−0.463374	−	0.802588i	0.535752	−	0.844375i	$-0.320028\pi$
$101$	−4.65685	−	8.06591i	−0.463374	−	0.802588i	−0.999127	+	0.0417874i	$0.986695\pi$
$102$	1.58579	+	2.74666i	0.157016	+	0.271960i
$103$	−4.58579	+	7.94282i	−0.451851	+	0.782629i	−0.998501	−	0.0547323i	$-0.982569\pi$
$103$	−4.58579	+	7.94282i	−0.451851	+	0.782629i	0.546650	+	0.837361i	$0.315903\pi$
$104$	0.828427			0.0812340
$105$		0			0
$106$	10.4853			1.01842
$107$	0.828427	−	1.43488i	0.0800871	−	0.138715i	−0.823200	−	0.567751i	$-0.807813\pi$
$107$	0.828427	−	1.43488i	0.0800871	−	0.138715i	0.903287	+	0.429036i	$0.141147\pi$
$108$	−1.65685	−	2.86976i	−0.159431	−	0.276142i
$109$	7.24264	+	12.5446i	0.693719	+	1.20156i	0.970611	+	0.240656i	$0.0773624\pi$
$109$	7.24264	+	12.5446i	0.693719	+	1.20156i	−0.276891	+	0.960901i	$0.589304\pi$
$110$	−2.41421	+	4.18154i	−0.230186	+	0.398694i
$111$	−2.14214			−0.203323
$112$		0			0
$113$	7.31371			0.688016			0.344008	−	0.938967i	$-0.388215\pi$
$113$	7.31371			0.688016			0.344008	+	0.938967i	$0.388215\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	−3.41421	−	5.91359i	−0.318377	−	0.551445i
$116$	−0.414214	−	0.717439i	−0.0384588	−	0.0666125i
$117$	−1.10051	+	1.90613i	−0.101742	+	0.176222i
$118$	11.4142			1.05076
$119$		0			0
$120$	−0.585786			−0.0534747
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$	6.65685	+	11.5300i	0.602683	+	1.04388i
$123$	−3.24264	−	5.61642i	−0.292379	−	0.506415i
$124$	1.41421	−	2.44949i	0.127000	−	0.219971i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.82843			−0.250982			−0.125491	−	0.992095i	$-0.540051\pi$
$127$	−2.82843			−0.250982			−0.125491	+	0.992095i	$0.540051\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.928932	−	1.60896i	−0.0817879	−	0.141661i
$130$	0.414214	+	0.717439i	0.0363289	+	0.0629236i
$131$	1.12132	−	1.94218i	0.0979702	−	0.169689i	−0.812874	−	0.582439i	$-0.802098\pi$
$131$	1.12132	−	1.94218i	0.0979702	−	0.169689i	0.910844	+	0.412750i	$0.135432\pi$
$132$	−2.82843			−0.246183
$133$		0			0
$134$	9.65685			0.834225
$135$	1.65685	−	2.86976i	0.142599	−	0.246989i
$136$	−2.70711	−	4.68885i	−0.232132	−	0.402065i
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	0.973910	+	0.226935i	$0.0728704\pi$
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	−0.290424	+	0.956898i	$0.593796\pi$
$138$	2.00000	−	3.46410i	0.170251	−	0.294884i
$139$	−0.100505			−0.00852473			−0.00426236	−	0.999991i	$-0.501357\pi$
$139$	−0.100505			−0.00852473			−0.00426236	+	0.999991i	$0.501357\pi$
$140$		0			0
$141$	6.34315			0.534189
$142$	6.24264	−	10.8126i	0.523871	−	0.907371i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	1.32843	+	2.30090i	0.110702	+	0.191742i
$145$	0.414214	−	0.717439i	0.0343986	−	0.0595801i
$146$	−6.58579			−0.545044
$147$		0			0
$148$	3.65685			0.300592
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−0.292893	−	0.507306i	−0.0239146	−	0.0414214i
$151$	−5.65685	−	9.79796i	−0.460348	−	0.797347i	0.538630	−	0.842542i	$-0.318942\pi$
$151$	−5.65685	−	9.79796i	−0.460348	−	0.797347i	−0.998978	+	0.0451959i	$0.985609\pi$
$152$	−1.70711	+	2.95680i	−0.138465	+	0.239828i
$153$	14.3848			1.16294
$154$		0			0
$155$	2.82843			0.227185
$156$	−0.242641	+	0.420266i	−0.0194268	+	0.0336482i
$157$	−5.24264	−	9.08052i	−0.418408	−	0.724704i	0.577371	−	0.816482i	$-0.304079\pi$
$157$	−5.24264	−	9.08052i	−0.418408	−	0.724704i	−0.995780	+	0.0917773i	$0.970745\pi$
$158$	−0.585786	−	1.01461i	−0.0466027	−	0.0807182i
$159$	−3.07107	+	5.31925i	−0.243552	+	0.421844i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−6.02944			−0.473717
$163$	−4.07107	+	7.05130i	−0.318871	+	0.552300i	−0.980253	−	0.197749i	$-0.936637\pi$
$163$	−4.07107	+	7.05130i	−0.318871	+	0.552300i	0.661382	+	0.750049i	$0.269970\pi$
$164$	5.53553	+	9.58783i	0.432253	+	0.748683i
$165$	−1.41421	−	2.44949i	−0.110096	−	0.190693i
$166$	−3.12132	+	5.40629i	−0.242261	+	0.419609i
$167$	23.7990			1.84162			0.920811	−	0.390010i	$-0.127529\pi$
$167$	23.7990			1.84162			0.920811	+	0.390010i	$0.127529\pi$
$168$		0			0
$169$	−12.3137			−0.947208
$170$	2.70711	−	4.68885i	0.207626	−	0.359618i
$171$	−4.53553	−	7.85578i	−0.346841	−	0.600746i
$172$	1.58579	+	2.74666i	0.120915	+	0.209431i
$173$	−1.58579	+	2.74666i	−0.120565	+	0.208825i	−0.919991	−	0.391940i	$-0.871804\pi$
$173$	−1.58579	+	2.74666i	−0.120565	+	0.208825i	0.799426	+	0.600765i	$0.205137\pi$
$174$	0.485281			0.0367891
$175$		0			0
$176$	4.82843			0.363956
$177$	−3.34315	+	5.79050i	−0.251286	+	0.435241i
$178$	6.36396	+	11.0227i	0.476999	+	0.826187i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	−1.32843	+	2.30090i	−0.0990151	+	0.171499i
$181$	−14.4853			−1.07668			−0.538341	−	0.842727i	$-0.680949\pi$
$181$	−14.4853			−1.07668			−0.538341	+	0.842727i	$0.680949\pi$
$182$		0			0
$183$	−7.79899			−0.576518
$184$	−3.41421	+	5.91359i	−0.251699	+	0.435956i
$185$	1.82843	+	3.16693i	0.134429	+	0.232837i
$186$	0.828427	+	1.43488i	0.0607432	+	0.105210i
$187$	13.0711	−	22.6398i	0.955851	−	1.65558i
$188$	−10.8284			−0.789744
$189$		0			0
$190$	−3.41421			−0.247693
$191$	9.07107	−	15.7116i	0.656359	−	1.13685i	−0.325192	−	0.945648i	$-0.605429\pi$
$191$	9.07107	−	15.7116i	0.656359	−	1.13685i	0.981551	−	0.191200i	$-0.0612378\pi$
$192$	0.292893	+	0.507306i	0.0211377	+	0.0366117i
$193$	2.82843	+	4.89898i	0.203595	+	0.352636i	0.949684	−	0.313210i	$-0.101404\pi$
$193$	2.82843	+	4.89898i	0.203595	+	0.352636i	−0.746089	+	0.665846i	$0.768071\pi$
$194$	8.12132	−	14.0665i	0.583077	−	1.00992i
$195$	−0.485281			−0.0347517
$196$		0			0
$197$	13.7990			0.983137			0.491569	−	0.870839i	$-0.336424\pi$
$197$	13.7990			0.983137			0.491569	+	0.870839i	$0.336424\pi$
$198$	−6.41421	+	11.1097i	−0.455838	+	0.789535i
$199$	−0.242641	−	0.420266i	−0.0172003	−	0.0297919i	0.857297	−	0.514822i	$-0.172142\pi$
$199$	−0.242641	−	0.420266i	−0.0172003	−	0.0297919i	−0.874497	+	0.485030i	$0.838809\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−2.82843	+	4.89898i	−0.199502	+	0.345547i
$202$	−9.31371			−0.655310
$203$		0			0
$204$	3.17157			0.222055
$205$	−5.53553	+	9.58783i	−0.386618	+	0.669643i
$206$	4.58579	+	7.94282i	0.319507	+	0.553402i
$207$	−9.07107	−	15.7116i	−0.630483	−	1.09203i
$208$	0.414214	−	0.717439i	0.0287205	−	0.0497454i
$209$	−16.4853			−1.14031
$210$		0			0
$211$	−26.6274			−1.83311			−0.916553	−	0.399912i	$-0.869041\pi$
$211$	−26.6274			−1.83311			−0.916553	+	0.399912i	$0.869041\pi$
$212$	5.24264	−	9.08052i	0.360066	−	0.623653i
$213$	3.65685	+	6.33386i	0.250564	+	0.433989i
$214$	−0.828427	−	1.43488i	−0.0566301	−	0.0980862i
$215$	−1.58579	+	2.74666i	−0.108150	+	0.187321i
$216$	−3.31371			−0.225469
$217$		0			0
$218$	14.4853			0.981067
$219$	1.92893	−	3.34101i	0.130345	−	0.225764i
$220$	2.41421	+	4.18154i	0.162766	+	0.281919i
$221$	−2.24264	−	3.88437i	−0.150856	−	0.261291i
$222$	−1.07107	+	1.85514i	−0.0718854	+	0.124509i
$223$	−15.3137			−1.02548			−0.512741	−	0.858543i	$-0.671370\pi$
$223$	−15.3137			−1.02548			−0.512741	+	0.858543i	$0.671370\pi$
$224$		0			0
$225$	−2.65685			−0.177124
$226$	3.65685	−	6.33386i	0.243250	−	0.421322i
$227$	4.87868	+	8.45012i	0.323809	+	0.560854i	0.981271	−	0.192634i	$-0.0617030\pi$
$227$	4.87868	+	8.45012i	0.323809	+	0.560854i	−0.657461	+	0.753488i	$0.728370\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	6.07107	−	10.5154i	0.401187	−	0.694877i	−0.592682	−	0.805437i	$-0.701931\pi$
$229$	6.07107	−	10.5154i	0.401187	−	0.694877i	0.993870	+	0.110559i	$0.0352643\pi$
$230$	−6.82843			−0.450253
$231$		0			0
$232$	−0.828427			−0.0543889
$233$	−0.343146	+	0.594346i	−0.0224802	+	0.0389369i	−0.877047	−	0.480405i	$-0.840490\pi$
$233$	−0.343146	+	0.594346i	−0.0224802	+	0.0389369i	0.854566	+	0.519342i	$0.173823\pi$
$234$	1.10051	+	1.90613i	0.0719423	+	0.124608i
$235$	−5.41421	−	9.37769i	−0.353184	−	0.611733i
$236$	5.70711	−	9.88500i	0.371501	−	0.643459i
$237$	0.686292			0.0445794
$238$		0			0
$239$	−9.65685			−0.624650			−0.312325	−	0.949975i	$-0.601108\pi$
$239$	−9.65685			−0.624650			−0.312325	+	0.949975i	$0.601108\pi$
$240$	−0.292893	+	0.507306i	−0.0189062	+	0.0327465i
$241$	−5.29289	−	9.16756i	−0.340945	−	0.590534i	0.643663	−	0.765309i	$-0.277414\pi$
$241$	−5.29289	−	9.16756i	−0.340945	−	0.590534i	−0.984609	+	0.174774i	$0.944080\pi$
$242$	6.15685	+	10.6640i	0.395778	+	0.685507i
$243$	6.73654	−	11.6680i	0.432150	−	0.748505i
$244$	13.3137			0.852323
$245$		0			0
$246$	−6.48528			−0.413486
$247$	−1.41421	+	2.44949i	−0.0899843	+	0.155857i
$248$	−1.41421	−	2.44949i	−0.0898027	−	0.155543i
$249$	−1.82843	−	3.16693i	−0.115872	−	0.200696i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−3.41421			−0.215503			−0.107752	−	0.994178i	$-0.534365\pi$
$251$	−3.41421			−0.215503			−0.107752	+	0.994178i	$0.534365\pi$
$252$		0			0
$253$	−32.9706			−2.07284
$254$	−1.41421	+	2.44949i	−0.0887357	+	0.153695i
$255$	1.58579	+	2.74666i	0.0993058	+	0.172003i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.94975	−	8.57321i	0.308757	−	0.534782i	−0.669334	−	0.742962i	$-0.733420\pi$
$257$	4.94975	−	8.57321i	0.308757	−	0.534782i	0.978091	+	0.208179i	$0.0667538\pi$
$258$	−1.85786			−0.115666
$259$		0			0
$260$	0.828427			0.0513769
$261$	1.10051	−	1.90613i	0.0681196	−	0.117987i
$262$	−1.12132	−	1.94218i	−0.0692754	−	0.119989i
$263$	−14.0000	−	24.2487i	−0.863277	−	1.49524i	−0.868748	−	0.495255i	$-0.835075\pi$
$263$	−14.0000	−	24.2487i	−0.863277	−	1.49524i	0.00547092	−	0.999985i	$-0.498259\pi$
$264$	−1.41421	+	2.44949i	−0.0870388	+	0.150756i
$265$	10.4853			0.644106
$266$		0			0
$267$	−7.45584			−0.456290
$268$	4.82843	−	8.36308i	0.294943	−	0.510856i
$269$	0.757359	+	1.31178i	0.0461770	+	0.0799809i	0.888190	−	0.459476i	$-0.151963\pi$
$269$	0.757359	+	1.31178i	0.0461770	+	0.0799809i	−0.842013	+	0.539457i	$0.818630\pi$
$270$	−1.65685	−	2.86976i	−0.100833	−	0.174648i
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$	−5.41421			−0.328285
$273$		0			0
$274$	16.0000			0.966595
$275$	−2.41421	+	4.18154i	−0.145583	+	0.252156i
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−10.0711	−	17.4436i	−0.605112	−	1.04808i	−0.992034	−	0.125972i	$-0.959795\pi$
$277$	−10.0711	−	17.4436i	−0.605112	−	1.04808i	0.386922	−	0.922112i	$-0.373538\pi$
$278$	−0.0502525	+	0.0870399i	−0.00301395	+	0.00522031i
$279$	7.51472			0.449894
$280$		0			0
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$	3.17157	−	5.49333i	0.188864	−	0.327123i
$283$	3.12132	+	5.40629i	0.185543	+	0.321370i	0.943759	−	0.330633i	$-0.107262\pi$
$283$	3.12132	+	5.40629i	0.185543	+	0.321370i	−0.758216	+	0.652003i	$0.773929\pi$
$284$	−6.24264	−	10.8126i	−0.370433	−	0.641608i
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$	4.00000			0.236525
$287$		0			0
$288$	2.65685			0.156557
$289$	−6.15685	+	10.6640i	−0.362168	+	0.627293i
$290$	−0.414214	−	0.717439i	−0.0243235	−	0.0421295i
$291$	4.75736	+	8.23999i	0.278881	+	0.483037i
$292$	−3.29289	+	5.70346i	−0.192702	+	0.333770i
$293$	19.6569			1.14837			0.574183	−	0.818727i	$-0.305320\pi$
$293$	19.6569			1.14837			0.574183	+	0.818727i	$0.305320\pi$
$294$		0			0
$295$	11.4142			0.664561
$296$	1.82843	−	3.16693i	0.106275	−	0.184074i
$297$	−8.00000	−	13.8564i	−0.464207	−	0.804030i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−2.82843	+	4.89898i	−0.163572	+	0.283315i
$300$	−0.585786			−0.0338204
$301$		0			0
$302$	−11.3137			−0.651031
$303$	2.72792	−	4.72490i	0.156715	−	0.271438i
$304$	1.70711	+	2.95680i	0.0979093	+	0.169584i
$305$	6.65685	+	11.5300i	0.381170	+	0.660206i
$306$	7.19239	−	12.4576i	0.411161	−	0.712153i
$307$	−29.0711			−1.65917			−0.829587	−	0.558378i	$-0.811424\pi$
$307$	−29.0711			−1.65917			−0.829587	+	0.558378i	$0.811424\pi$
$308$		0			0
$309$	−5.37258			−0.305636
$310$	1.41421	−	2.44949i	0.0803219	−	0.139122i
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	0.917143	−	0.398559i	$-0.130489\pi$
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	−0.803733	+	0.594990i	$0.797156\pi$
$312$	0.242641	+	0.420266i	0.0137368	+	0.0237929i
$313$	−11.1924	+	19.3858i	−0.632631	+	1.09575i	0.354381	+	0.935101i	$0.384692\pi$
$313$	−11.1924	+	19.3858i	−0.632631	+	1.09575i	−0.987012	+	0.160648i	$0.948642\pi$
$314$	−10.4853			−0.591719
$315$		0			0
$316$	−1.17157			−0.0659061
$317$	3.24264	−	5.61642i	0.182125	−	0.315449i	−0.760479	−	0.649362i	$-0.775036\pi$
$317$	3.24264	−	5.61642i	0.182125	−	0.315449i	0.942604	+	0.333913i	$0.108369\pi$
$318$	3.07107	+	5.31925i	0.172217	+	0.298288i
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	0.970563			0.0541715
$322$		0			0
$323$	18.4853			1.02855
$324$	−3.01472	+	5.22165i	−0.167484	+	0.290091i
$325$	0.414214	+	0.717439i	0.0229764	+	0.0397964i
$326$	4.07107	+	7.05130i	0.225476	+	0.390535i
$327$	−4.24264	+	7.34847i	−0.234619	+	0.406371i
$328$	11.0711			0.611297
$329$		0			0
$330$	−2.82843			−0.155700
$331$	2.89949	−	5.02207i	0.159371	−	0.276038i	−0.775271	−	0.631628i	$-0.782387\pi$
$331$	2.89949	−	5.02207i	0.159371	−	0.276038i	0.934642	+	0.355590i	$0.115720\pi$
$332$	3.12132	+	5.40629i	0.171305	+	0.296708i
$333$	4.85786	+	8.41407i	0.266209	+	0.461088i
$334$	11.8995	−	20.6105i	0.651111	−	1.12776i
$335$	9.65685			0.527610
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	−6.15685	+	10.6640i	−0.334889	+	0.580044i
$339$	2.14214	+	3.71029i	0.116345	+	0.201515i
$340$	−2.70711	−	4.68885i	−0.146813	−	0.254288i
$341$	6.82843	−	11.8272i	0.369780	−	0.640478i
$342$	−9.07107			−0.490507
$343$		0			0
$344$	3.17157			0.171000
$345$	2.00000	−	3.46410i	0.107676	−	0.186501i
$346$	1.58579	+	2.74666i	0.0852524	+	0.147662i
$347$	4.41421	+	7.64564i	0.236967	+	0.410440i	0.959843	−	0.280539i	$-0.0905132\pi$
$347$	4.41421	+	7.64564i	0.236967	+	0.410440i	−0.722875	+	0.690979i	$0.757180\pi$
$348$	0.242641	−	0.420266i	0.0130069	−	0.0225286i
$349$	14.4853			0.775379			0.387690	−	0.921790i	$-0.373273\pi$
$349$	14.4853			0.775379			0.387690	+	0.921790i	$0.373273\pi$
$350$		0			0
$351$	−2.74517			−0.146526
$352$	2.41421	−	4.18154i	0.128678	−	0.222877i
$353$	17.1924	+	29.7781i	0.915058	+	1.58493i	0.806816	+	0.590803i	$0.201189\pi$
$353$	17.1924	+	29.7781i	0.915058	+	1.58493i	0.108243	+	0.994124i	$0.465478\pi$
$354$	3.34315	+	5.79050i	0.177686	+	0.307762i
$355$	6.24264	−	10.8126i	0.331325	−	0.573872i
$356$	12.7279			0.674579
$357$		0			0
$358$	−4.00000			−0.211407
$359$	14.1421	−	24.4949i	0.746393	−	1.29279i	−0.203148	−	0.979148i	$-0.565117\pi$
$359$	14.1421	−	24.4949i	0.746393	−	1.29279i	0.949541	−	0.313643i	$-0.101550\pi$
$360$	1.32843	+	2.30090i	0.0700143	+	0.121268i
$361$	3.67157	+	6.35935i	0.193241	+	0.334703i
$362$	−7.24264	+	12.5446i	−0.380665	+	0.659331i
$363$	−7.21320			−0.378595
$364$		0			0
$365$	−6.58579			−0.344716
$366$	−3.89949	+	6.75412i	−0.203830	+	0.353044i
$367$	−4.48528	−	7.76874i	−0.234130	−	0.405525i	0.724890	−	0.688865i	$-0.241891\pi$
$367$	−4.48528	−	7.76874i	−0.234130	−	0.405525i	−0.959019	+	0.283340i	$0.908557\pi$
$368$	3.41421	+	5.91359i	0.177978	+	0.308267i
$369$	−14.7071	+	25.4735i	−0.765621	+	1.32610i
$370$	3.65685			0.190111
$371$		0			0
$372$	1.65685			0.0859039
$373$	6.75736	−	11.7041i	0.349883	−	0.606015i	−0.636346	−	0.771404i	$-0.719555\pi$
$373$	6.75736	−	11.7041i	0.349883	−	0.606015i	0.986228	+	0.165389i	$0.0528881\pi$
$374$	−13.0711	−	22.6398i	−0.675889	−	1.17067i
$375$	−0.292893	−	0.507306i	−0.0151249	−	0.0261972i
$376$	−5.41421	+	9.37769i	−0.279217	+	0.483618i
$377$	−0.686292			−0.0353458
$378$		0			0
$379$	17.5147			0.899671			0.449835	−	0.893112i	$-0.351483\pi$
$379$	17.5147			0.899671			0.449835	+	0.893112i	$0.351483\pi$
$380$	−1.70711	+	2.95680i	−0.0875727	+	0.151680i
$381$	−0.828427	−	1.43488i	−0.0424416	−	0.0735110i
$382$	−9.07107	−	15.7116i	−0.464116	−	0.803873i
$383$	−7.75736	+	13.4361i	−0.396383	+	0.686555i	−0.993277	−	0.115765i	$-0.963068\pi$
$383$	−7.75736	+	13.4361i	−0.396383	+	0.686555i	0.596894	+	0.802320i	$0.296401\pi$
$384$	0.585786			0.0298933
$385$		0			0
$386$	5.65685			0.287926
$387$	−4.21320	+	7.29748i	−0.214169	+	0.370952i
$388$	−8.12132	−	14.0665i	−0.412298	−	0.714120i
$389$	0.0710678	+	0.123093i	0.00360328	+	0.00624107i	0.867821	−	0.496876i	$-0.165520\pi$
$389$	0.0710678	+	0.123093i	0.00360328	+	0.00624107i	−0.864218	+	0.503117i	$0.832186\pi$
$390$	−0.242641	+	0.420266i	−0.0122866	+	0.0212810i
$391$	36.9706			1.86968
$392$		0			0
$393$	1.31371			0.0662678
$394$	6.89949	−	11.9503i	0.347592	−	0.602046i
$395$	−0.585786	−	1.01461i	−0.0294741	−	0.0510507i
$396$	6.41421	+	11.1097i	0.322326	+	0.558286i
$397$	−2.89949	+	5.02207i	−0.145521	+	0.252051i	−0.929567	−	0.368652i	$-0.879819\pi$
$397$	−2.89949	+	5.02207i	−0.145521	+	0.252051i	0.784046	+	0.620703i	$0.213153\pi$
$398$	−0.485281			−0.0243250
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	2.82843	+	4.89898i	0.141069	+	0.244339i
$403$	−1.17157	−	2.02922i	−0.0583602	−	0.101083i
$404$	−4.65685	+	8.06591i	−0.231687	+	0.401294i
$405$	−6.02944			−0.299605
$406$		0			0
$407$	17.6569			0.875218
$408$	1.58579	−	2.74666i	0.0785081	−	0.135980i
$409$	−6.70711	−	11.6170i	−0.331645	−	0.574426i	0.651189	−	0.758915i	$-0.274270\pi$
$409$	−6.70711	−	11.6170i	−0.331645	−	0.574426i	−0.982835	+	0.184489i	$0.940937\pi$
$410$	5.53553	+	9.58783i	0.273381	+	0.473509i
$411$	−4.68629	+	8.11689i	−0.231158	+	0.400377i
$412$	9.17157			0.451851
$413$		0			0
$414$	−18.1421			−0.891637
$415$	−3.12132	+	5.40629i	−0.153220	+	0.265384i
$416$	−0.414214	−	0.717439i	−0.0203085	−	0.0351753i
$417$	−0.0294373	−	0.0509868i	−0.00144155	−	0.00249684i
$418$	−8.24264	+	14.2767i	−0.403161	+	0.698295i
$419$	−32.8701			−1.60581			−0.802904	−	0.596109i	$-0.796713\pi$
$419$	−32.8701			−1.60581			−0.802904	+	0.596109i	$0.796713\pi$
$420$		0			0
$421$	−5.31371			−0.258974			−0.129487	−	0.991581i	$-0.541333\pi$
$421$	−5.31371			−0.258974			−0.129487	+	0.991581i	$0.541333\pi$
$422$	−13.3137	+	23.0600i	−0.648101	+	1.12254i
$423$	−14.3848	−	24.9152i	−0.699412	−	1.21142i
$424$	−5.24264	−	9.08052i	−0.254605	−	0.440989i
$425$	2.70711	−	4.68885i	0.131314	−	0.227442i
$426$	7.31371			0.354350
$427$		0			0
$428$	−1.65685			−0.0800871
$429$	−1.17157	+	2.02922i	−0.0565641	+	0.0979718i
$430$	1.58579	+	2.74666i	0.0764734	+	0.132456i
$431$	16.8284	+	29.1477i	0.810597	+	1.40399i	0.912447	+	0.409195i	$0.134190\pi$
$431$	16.8284	+	29.1477i	0.810597	+	1.40399i	−0.101850	+	0.994800i	$0.532476\pi$
$432$	−1.65685	+	2.86976i	−0.0797154	+	0.138071i
$433$	−13.4142			−0.644646			−0.322323	−	0.946630i	$-0.604464\pi$
$433$	−13.4142			−0.644646			−0.322323	+	0.946630i	$0.604464\pi$
$434$		0			0
$435$	0.485281			0.0232675
$436$	7.24264	−	12.5446i	0.346860	−	0.600778i
$437$	−11.6569	−	20.1903i	−0.557623	−	0.965831i
$438$	−1.92893	−	3.34101i	−0.0921679	−	0.159640i
$439$	4.48528	−	7.76874i	0.214071	−	0.370782i	−0.738914	−	0.673800i	$-0.764661\pi$
$439$	4.48528	−	7.76874i	0.214071	−	0.370782i	0.952985	+	0.303018i	$0.0979943\pi$
$440$	4.82843			0.230186
$441$		0			0
$442$	−4.48528			−0.213343
$443$	−18.4853	+	32.0174i	−0.878262	+	1.52119i	−0.0250157	+	0.999687i	$0.507964\pi$
$443$	−18.4853	+	32.0174i	−0.878262	+	1.52119i	−0.853247	+	0.521508i	$0.825370\pi$
$444$	1.07107	+	1.85514i	0.0508306	+	0.0880412i
$445$	6.36396	+	11.0227i	0.301681	+	0.522526i
$446$	−7.65685	+	13.2621i	−0.362563	+	0.627977i
$447$	3.51472			0.166240
$448$		0			0
$449$	28.6274			1.35101			0.675506	−	0.737355i	$-0.263925\pi$
$449$	28.6274			1.35101			0.675506	+	0.737355i	$0.263925\pi$
$450$	−1.32843	+	2.30090i	−0.0626227	+	0.108466i
$451$	26.7279	+	46.2941i	1.25857	+	2.17990i
$452$	−3.65685	−	6.33386i	−0.172004	−	0.297920i
$453$	3.31371	−	5.73951i	0.155692	−	0.269666i
$454$	9.75736			0.457936
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−5.17157	+	8.95743i	−0.241916	+	0.419011i	−0.961260	−	0.275643i	$-0.911109\pi$
$457$	−5.17157	+	8.95743i	−0.241916	+	0.419011i	0.719344	+	0.694654i	$0.244443\pi$
$458$	−6.07107	−	10.5154i	−0.283682	−	0.491352i
$459$	8.97056	+	15.5375i	0.418710	+	0.725227i
$460$	−3.41421	+	5.91359i	−0.159189	+	0.275723i
$461$	7.17157			0.334013			0.167007	−	0.985956i	$-0.446590\pi$
$461$	7.17157			0.334013			0.167007	+	0.985956i	$0.446590\pi$
$462$		0			0
$463$	16.9706			0.788689			0.394344	−	0.918963i	$-0.370972\pi$
$463$	16.9706			0.788689			0.394344	+	0.918963i	$0.370972\pi$
$464$	−0.414214	+	0.717439i	−0.0192294	+	0.0333063i
$465$	0.828427	+	1.43488i	0.0384174	+	0.0665409i
$466$	0.343146	+	0.594346i	0.0158959	+	0.0275325i
$467$	1.94975	−	3.37706i	0.0902236	−	0.156272i	−0.817382	−	0.576097i	$-0.804575\pi$
$467$	1.94975	−	3.37706i	0.0902236	−	0.156272i	0.907605	+	0.419825i	$0.137909\pi$
$468$	2.20101			0.101742
$469$		0			0
$470$	−10.8284			−0.499478
$471$	3.07107	−	5.31925i	0.141507	−	0.245098i
$472$	−5.70711	−	9.88500i	−0.262691	−	0.454994i
$473$	7.65685	+	13.2621i	0.352063	+	0.609790i
$474$	0.343146	−	0.594346i	0.0157612	−	0.0272992i
$475$	−3.41421			−0.156655
$476$		0			0
$477$	27.8579			1.27552
$478$	−4.82843	+	8.36308i	−0.220847	+	0.382518i
$479$	−11.4142	−	19.7700i	−0.521529	−	0.903314i	−0.999686	−	0.0250403i	$-0.992029\pi$
$479$	−11.4142	−	19.7700i	−0.521529	−	0.903314i	0.478158	−	0.878274i	$-0.341305\pi$
$480$	0.292893	+	0.507306i	0.0133687	+	0.0231552i
$481$	1.51472	−	2.62357i	0.0690652	−	0.119624i
$482$	−10.5858			−0.482169
$483$		0			0
$484$	12.3137			0.559714
$485$	8.12132	−	14.0665i	0.368770	−	0.638729i
$486$	−6.73654	−	11.6680i	−0.305576	−	0.529273i
$487$	3.89949	+	6.75412i	0.176703	+	0.306059i	0.940749	−	0.339103i	$-0.110123\pi$
$487$	3.89949	+	6.75412i	0.176703	+	0.306059i	−0.764046	+	0.645161i	$0.776790\pi$
$488$	6.65685	−	11.5300i	0.301342	−	0.521939i
$489$	−4.76955			−0.215687
$490$		0			0
$491$	−24.2843			−1.09593			−0.547967	−	0.836500i	$-0.684598\pi$
$491$	−24.2843			−1.09593			−0.547967	+	0.836500i	$0.684598\pi$
$492$	−3.24264	+	5.61642i	−0.146190	+	0.253208i
$493$	2.24264	+	3.88437i	0.101003	+	0.174943i
$494$	1.41421	+	2.44949i	0.0636285	+	0.110208i
$495$	−6.41421	+	11.1097i	−0.288297	+	0.499346i
$496$	−2.82843			−0.127000
$497$		0			0
$498$	−3.65685			−0.163868
$499$	−20.8284	+	36.0759i	−0.932408	+	1.61498i	−0.153217	+	0.988193i	$0.548963\pi$
$499$	−20.8284	+	36.0759i	−0.932408	+	1.61498i	−0.779191	+	0.626786i	$0.784370\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	6.97056	+	12.0734i	0.311422	+	0.539398i
$502$	−1.70711	+	2.95680i	−0.0761919	+	0.131968i
$503$	−6.34315			−0.282827			−0.141413	−	0.989951i	$-0.545165\pi$
$503$	−6.34315			−0.282827			−0.141413	+	0.989951i	$0.545165\pi$
$504$		0			0
$505$	−9.31371			−0.414455
$506$	−16.4853	+	28.5533i	−0.732860	+	1.26935i
$507$	−3.60660	−	6.24682i	−0.160175	−	0.277431i
$508$	1.41421	+	2.44949i	0.0627456	+	0.108679i
$509$	−16.8995	+	29.2708i	−0.749057	+	1.29740i	0.199218	+	0.979955i	$0.436160\pi$
$509$	−16.8995	+	29.2708i	−0.749057	+	1.29740i	−0.948275	+	0.317450i	$0.897174\pi$
$510$	3.17157			0.140440
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.65685	−	9.79796i	0.249756	−	0.432590i
$514$	−4.94975	−	8.57321i	−0.218324	−	0.378148i
$515$	4.58579	+	7.94282i	0.202074	+	0.350002i
$516$	−0.928932	+	1.60896i	−0.0408940	+	0.0708304i
$517$	−52.2843			−2.29946
$518$		0			0
$519$	−1.85786			−0.0815512
$520$	0.414214	−	0.717439i	0.0181645	−	0.0314618i
$521$	2.46447	+	4.26858i	0.107970	+	0.187010i	0.914948	−	0.403572i	$-0.132232\pi$
$521$	2.46447	+	4.26858i	0.107970	+	0.187010i	−0.806978	+	0.590582i	$0.798898\pi$
$522$	−1.10051	−	1.90613i	−0.0481678	−	0.0834291i
$523$	2.05025	−	3.55114i	0.0896513	−	0.155281i	−0.817712	−	0.575627i	$-0.804758\pi$
$523$	2.05025	−	3.55114i	0.0896513	−	0.155281i	0.907364	+	0.420346i	$0.138091\pi$
$524$	−2.24264			−0.0979702
$525$		0			0
$526$	−28.0000			−1.22086
$527$	−7.65685	+	13.2621i	−0.333538	+	0.577704i
$528$	1.41421	+	2.44949i	0.0615457	+	0.106600i
$529$	−11.8137	−	20.4619i	−0.513639	−	0.889650i
$530$	5.24264	−	9.08052i	0.227726	−	0.394433i
$531$	30.3259			1.31603
$532$		0			0
$533$	9.17157			0.397265
$534$	−3.72792	+	6.45695i	−0.161323	+	0.279420i
$535$	−0.828427	−	1.43488i	−0.0358160	−	0.0620352i
$536$	−4.82843	−	8.36308i	−0.208556	−	0.361230i
$537$	1.17157	−	2.02922i	0.0505571	−	0.0875675i
$538$	1.51472			0.0653042
$539$		0			0
$540$	−3.31371			−0.142599
$541$	−9.48528	+	16.4290i	−0.407804	+	0.706337i	−0.994643	−	0.103366i	$-0.967039\pi$
$541$	−9.48528	+	16.4290i	−0.407804	+	0.706337i	0.586839	+	0.809703i	$0.300372\pi$
$542$	−6.00000	−	10.3923i	−0.257722	−	0.446388i
$543$	−4.24264	−	7.34847i	−0.182069	−	0.315353i
$544$	−2.70711	+	4.68885i	−0.116066	+	0.201033i
$545$	14.4853			0.620481
$546$		0			0
$547$	6.48528			0.277291			0.138645	−	0.990342i	$-0.455725\pi$
$547$	6.48528			0.277291			0.138645	+	0.990342i	$0.455725\pi$
$548$	8.00000	−	13.8564i	0.341743	−	0.591916i
$549$	17.6863	+	30.6336i	0.754833	+	1.30741i
$550$	2.41421	+	4.18154i	0.102942	+	0.178301i
$551$	1.41421	−	2.44949i	0.0602475	−	0.104352i
$552$	−4.00000			−0.170251
$553$		0			0
$554$	−20.1421			−0.855757
$555$	−1.07107	+	1.85514i	−0.0454643	+	0.0787465i
$556$	0.0502525	+	0.0870399i	0.00213118	+	0.00369132i
$557$	−10.4142	−	18.0379i	−0.441264	−	0.764292i	0.556519	−	0.830835i	$-0.312137\pi$
$557$	−10.4142	−	18.0379i	−0.441264	−	0.764292i	−0.997784	+	0.0665424i	$0.978803\pi$
$558$	3.75736	−	6.50794i	0.159062	−	0.275503i
$559$	2.62742			0.111128
$560$		0			0
$561$	15.3137			0.646545
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	−19.7071	−	34.1337i	−0.830556	−	1.43856i	−0.897598	−	0.440814i	$-0.854690\pi$
$563$	−19.7071	−	34.1337i	−0.830556	−	1.43856i	0.0670428	−	0.997750i	$-0.478644\pi$
$564$	−3.17157	−	5.49333i	−0.133547	−	0.231311i
$565$	3.65685	−	6.33386i	0.153845	−	0.266467i
$566$	6.24264			0.262398
$567$		0			0
$568$	−12.4853			−0.523871
$569$	3.34315	−	5.79050i	0.140152	−	0.242750i	−0.787402	−	0.616440i	$-0.788574\pi$
$569$	3.34315	−	5.79050i	0.140152	−	0.242750i	0.927554	+	0.373690i	$0.121908\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	20.8995	+	36.1990i	0.874617	+	1.51488i	0.857171	+	0.515033i	$0.172220\pi$
$571$	20.8995	+	36.1990i	0.874617	+	1.51488i	0.0174461	+	0.999848i	$0.494446\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	10.6274			0.443967
$574$		0			0
$575$	−6.82843			−0.284765
$576$	1.32843	−	2.30090i	0.0553511	−	0.0958710i
$577$	12.9497	+	22.4296i	0.539105	+	0.933757i	0.998952	+	0.0457594i	$0.0145708\pi$
$577$	12.9497	+	22.4296i	0.539105	+	0.933757i	−0.459847	+	0.887998i	$0.652096\pi$
$578$	6.15685	+	10.6640i	0.256091	+	0.443563i
$579$	−1.65685	+	2.86976i	−0.0688565	+	0.119263i
$580$	−0.828427			−0.0343986
$581$		0			0
$582$	9.51472			0.394398
$583$	25.3137	−	43.8446i	1.04839	−	1.81586i
$584$	3.29289	+	5.70346i	0.136261	+	0.236011i
$585$	1.10051	+	1.90613i	0.0455003	+	0.0788088i
$586$	9.82843	−	17.0233i	0.406009	−	0.703227i
$587$	−2.92893			−0.120890			−0.0604450	−	0.998172i	$-0.519252\pi$
$587$	−2.92893			−0.120890			−0.0604450	+	0.998172i	$0.519252\pi$
$588$		0			0
$589$	9.65685			0.397904
$590$	5.70711	−	9.88500i	0.234958	−	0.406959i
$591$	4.04163	+	7.00031i	0.166250	+	0.287954i
$592$	−1.82843	−	3.16693i	−0.0751479	−	0.130160i
$593$	14.3640	−	24.8791i	0.589857	−	1.02166i	−0.404393	−	0.914585i	$-0.632517\pi$
$593$	14.3640	−	24.8791i	0.589857	−	1.02166i	0.994251	−	0.107078i	$-0.0341493\pi$
$594$	−16.0000			−0.656488
$595$		0			0
$596$	−6.00000			−0.245770
$597$	0.142136	−	0.246186i	0.00581722	−	0.0100757i
$598$	2.82843	+	4.89898i	0.115663	+	0.200334i
$599$	2.58579	+	4.47871i	0.105652	+	0.182995i	0.914005	−	0.405704i	$-0.132974\pi$
$599$	2.58579	+	4.47871i	0.105652	+	0.182995i	−0.808352	+	0.588699i	$0.799640\pi$
$600$	−0.292893	+	0.507306i	−0.0119573	+	0.0207107i
$601$	−9.41421			−0.384014			−0.192007	−	0.981394i	$-0.561500\pi$
$601$	−9.41421			−0.384014			−0.192007	+	0.981394i	$0.561500\pi$
$602$		0			0
$603$	25.6569			1.04483
$604$	−5.65685	+	9.79796i	−0.230174	+	0.398673i
$605$	6.15685	+	10.6640i	0.250312	+	0.433553i
$606$	−2.72792	−	4.72490i	−0.110814	−	0.191936i
$607$	−20.1421	+	34.8872i	−0.817544	+	1.41603i	0.0899426	+	0.995947i	$0.471332\pi$
$607$	−20.1421	+	34.8872i	−0.817544	+	1.41603i	−0.907487	+	0.420081i	$0.862002\pi$
$608$	3.41421			0.138465
$609$		0			0
$610$	13.3137			0.539056
$611$	−4.48528	+	7.76874i	−0.181455	+	0.314289i
$612$	−7.19239	−	12.4576i	−0.290735	−	0.503568i
$613$	11.8284	+	20.4874i	0.477746	+	0.827480i	0.999675	−	0.0255092i	$-0.00812071\pi$
$613$	11.8284	+	20.4874i	0.477746	+	0.827480i	−0.521929	+	0.852989i	$0.674787\pi$
$614$	−14.5355	+	25.1763i	−0.586606	+	1.01603i
$615$	−6.48528			−0.261512
$616$		0			0
$617$	−10.6863			−0.430214			−0.215107	−	0.976590i	$-0.569010\pi$
$617$	−10.6863			−0.430214			−0.215107	+	0.976590i	$0.569010\pi$
$618$	−2.68629	+	4.65279i	−0.108058	+	0.187163i
$619$	7.46447	+	12.9288i	0.300022	+	0.519654i	0.976141	−	0.217139i	$-0.0696726\pi$
$619$	7.46447	+	12.9288i	0.300022	+	0.519654i	−0.676118	+	0.736793i	$0.736339\pi$
$620$	−1.41421	−	2.44949i	−0.0567962	−	0.0983739i
$621$	11.3137	−	19.5959i	0.454003	−	0.786357i
$622$	4.00000			0.160385
$623$		0			0
$624$	0.485281			0.0194268
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.1924	+	19.3858i	0.447338	+	0.774812i
$627$	−4.82843	−	8.36308i	−0.192829	−	0.333989i
$628$	−5.24264	+	9.08052i	−0.209204	+	0.362352i
$629$	−19.7990			−0.789437
$630$		0			0
$631$	4.48528			0.178556			0.0892781	−	0.996007i	$-0.471544\pi$
$631$	4.48528			0.178556			0.0892781	+	0.996007i	$0.471544\pi$
$632$	−0.585786	+	1.01461i	−0.0233013	+	0.0403591i
$633$	−7.79899	−	13.5082i	−0.309982	−	0.536905i
$634$	−3.24264	−	5.61642i	−0.128782	−	0.223056i
$635$	−1.41421	+	2.44949i	−0.0561214	+	0.0972050i
$636$	6.14214			0.243552
$637$		0			0
$638$	−4.00000			−0.158362
$639$	16.5858	−	28.7274i	0.656124	−	1.13644i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−10.3137	−	17.8639i	−0.407367	−	0.705580i	0.587227	−	0.809422i	$-0.300220\pi$
$641$	−10.3137	−	17.8639i	−0.407367	−	0.705580i	−0.994594	+	0.103842i	$0.966886\pi$
$642$	0.485281	−	0.840532i	0.0191525	−	0.0331732i
$643$	−47.2132			−1.86191			−0.930953	−	0.365138i	$-0.881022\pi$
$643$	−47.2132			−1.86191			−0.930953	+	0.365138i	$0.881022\pi$
$644$		0			0
$645$	−1.85786			−0.0731533
$646$	9.24264	−	16.0087i	0.363647	−	0.629855i
$647$	19.5563	+	33.8726i	0.768839	+	1.33167i	0.938193	+	0.346114i	$0.112499\pi$
$647$	19.5563	+	33.8726i	0.768839	+	1.33167i	−0.169353	+	0.985555i	$0.554168\pi$
$648$	3.01472	+	5.22165i	0.118429	+	0.205126i
$649$	27.5563	−	47.7290i	1.08168	−	1.87353i
$650$	0.828427			0.0324936
$651$		0			0
$652$	8.14214			0.318871
$653$	−7.82843	+	13.5592i	−0.306350	+	0.530614i	−0.977561	−	0.210653i	$-0.932441\pi$
$653$	−7.82843	+	13.5592i	−0.306350	+	0.530614i	0.671211	+	0.741266i	$0.265774\pi$
$654$	4.24264	+	7.34847i	0.165900	+	0.287348i
$655$	−1.12132	−	1.94218i	−0.0438136	−	0.0758874i
$656$	5.53553	−	9.58783i	0.216126	−	0.374342i
$657$	−17.4975			−0.682642
$658$		0			0
$659$	−32.8284			−1.27881			−0.639407	−	0.768868i	$-0.720820\pi$
$659$	−32.8284			−1.27881			−0.639407	+	0.768868i	$0.720820\pi$
$660$	−1.41421	+	2.44949i	−0.0550482	+	0.0953463i
$661$	9.14214	+	15.8346i	0.355588	+	0.615896i	0.987218	−	0.159373i	$-0.0509473\pi$
$661$	9.14214	+	15.8346i	0.355588	+	0.615896i	−0.631631	+	0.775270i	$0.717614\pi$
$662$	−2.89949	−	5.02207i	−0.112692	−	0.195188i
$663$	1.31371	−	2.27541i	0.0510202	−	0.0883696i
$664$	6.24264			0.242261
$665$		0			0
$666$	9.71573			0.376477
$667$	2.82843	−	4.89898i	0.109517	−	0.189689i
$668$	−11.8995	−	20.6105i	−0.460405	−	0.797445i
$669$	−4.48528	−	7.76874i	−0.173411	−	0.300357i
$670$	4.82843	−	8.36308i	0.186538	−	0.323094i
$671$	64.2843			2.48167
$672$		0			0
$673$	−48.0000			−1.85026			−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000			−1.85026			−0.925132	+	0.379646i	$0.876046\pi$
$674$	3.00000	−	5.19615i	0.115556	−	0.200148i
$675$	−1.65685	−	2.86976i	−0.0637723	−	0.110457i
$676$	6.15685	+	10.6640i	0.236802	+	0.410153i
$677$	−5.72792	+	9.92105i	−0.220142	+	0.381297i	−0.954851	−	0.297085i	$-0.903985\pi$
$677$	−5.72792	+	9.92105i	−0.220142	+	0.381297i	0.734709	+	0.678382i	$0.237319\pi$
$678$	4.28427			0.164536
$679$		0			0
$680$	−5.41421			−0.207626
$681$	−2.85786	+	4.94997i	−0.109514	+	0.189683i
$682$	−6.82843	−	11.8272i	−0.261474	−	0.452886i
$683$	−11.1716	−	19.3497i	−0.427468	−	0.740397i	0.569179	−	0.822214i	$-0.307261\pi$
$683$	−11.1716	−	19.3497i	−0.427468	−	0.740397i	−0.996647	+	0.0818167i	$0.973928\pi$
$684$	−4.53553	+	7.85578i	−0.173420	+	0.300373i
$685$	16.0000			0.611329
$686$		0			0
$687$	7.11270			0.271366
$688$	1.58579	−	2.74666i	0.0604575	−	0.104716i
$689$	−4.34315	−	7.52255i	−0.165461	−	0.286586i
$690$	−2.00000	−	3.46410i	−0.0761387	−	0.131876i
$691$	5.12132	−	8.87039i	0.194824	−	0.337445i	−0.752019	−	0.659142i	$-0.770920\pi$
$691$	5.12132	−	8.87039i	0.194824	−	0.337445i	0.946843	+	0.321696i	$0.104253\pi$
$692$	3.17157			0.120565
$693$		0			0
$694$	8.82843			0.335123
$695$	−0.0502525	+	0.0870399i	−0.00190619	+	0.00330161i
$696$	−0.242641	−	0.420266i	−0.00919727	−	0.0159301i
$697$	−29.9706	−	51.9105i	−1.13522	−	1.96625i
$698$	7.24264	−	12.5446i	0.274138	−	0.474821i
$699$	−0.402020			−0.0152058
$700$		0			0
$701$	−14.4853			−0.547102			−0.273551	−	0.961858i	$-0.588198\pi$
$701$	−14.4853			−0.547102			−0.273551	+	0.961858i	$0.588198\pi$
$702$	−1.37258	+	2.37738i	−0.0518048	+	0.0897286i
$703$	6.24264	+	10.8126i	0.235446	+	0.407804i
$704$	−2.41421	−	4.18154i	−0.0909891	−	0.157598i
$705$	3.17157	−	5.49333i	0.119448	−	0.206891i
$706$	34.3848			1.29409
$707$		0			0
$708$	6.68629			0.251286
$709$	8.55635	−	14.8200i	0.321340	−	0.556578i	−0.659424	−	0.751771i	$-0.729200\pi$
$709$	8.55635	−	14.8200i	0.321340	−	0.556578i	0.980765	+	0.195193i	$0.0625333\pi$
$710$	−6.24264	−	10.8126i	−0.234282	−	0.405789i
$711$	−1.55635	−	2.69568i	−0.0583677	−	0.101096i
$712$	6.36396	−	11.0227i	0.238500	−	0.413093i
$713$	19.3137			0.723304
$714$		0			0
$715$	4.00000			0.149592
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$	−2.82843	−	4.89898i	−0.105630	−	0.182956i
$718$	−14.1421	−	24.4949i	−0.527780	−	0.914141i
$719$	−4.72792	+	8.18900i	−0.176322	+	0.305398i	−0.940618	−	0.339467i	$-0.889753\pi$
$719$	−4.72792	+	8.18900i	−0.176322	+	0.305398i	0.764296	+	0.644865i	$0.223087\pi$
$720$	2.65685			0.0990151
$721$		0			0
$722$	7.34315			0.273284
$723$	3.10051	−	5.37023i	0.115309	−	0.199721i
$724$	7.24264	+	12.5446i	0.269171	+	0.466217i
$725$	−0.414214	−	0.717439i	−0.0153835	−	0.0266450i
$726$	−3.60660	+	6.24682i	−0.133854	+	0.231841i
$727$	20.4853			0.759757			0.379879	−	0.925036i	$-0.375966\pi$
$727$	20.4853			0.759757			0.379879	+	0.925036i	$0.375966\pi$
$728$		0			0
$729$	−10.1960			−0.377628
$730$	−3.29289	+	5.70346i	−0.121875	+	0.211094i
$731$	−8.58579	−	14.8710i	−0.317557	−	0.550024i
$732$	3.89949	+	6.75412i	0.144129	+	0.249640i
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	−0.360061	−	0.932929i	$-0.617244\pi$
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	0.987971	−	0.154642i	$-0.0494225\pi$
$734$	−8.97056			−0.331110
$735$		0			0
$736$	6.82843			0.251699
$737$	23.3137	−	40.3805i	0.858771	−	1.48744i
$738$	14.7071	+	25.4735i	0.541376	+	0.937691i
$739$	−4.41421	−	7.64564i	−0.162379	−	0.281249i	0.773342	−	0.633989i	$-0.218584\pi$
$739$	−4.41421	−	7.64564i	−0.162379	−	0.281249i	−0.935722	+	0.352739i	$0.885250\pi$
$740$	1.82843	−	3.16693i	0.0672143	−	0.116419i
$741$	−1.65685			−0.0608661
$742$		0			0
$743$	12.2010			0.447612			0.223806	−	0.974634i	$-0.428152\pi$
$743$	12.2010			0.447612			0.223806	+	0.974634i	$0.428152\pi$
$744$	0.828427	−	1.43488i	0.0303716	−	0.0526052i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	−6.75736	−	11.7041i	−0.247405	−	0.428517i
$747$	−8.29289	+	14.3637i	−0.303421	+	0.525541i
$748$	−26.1421			−0.955851
$749$		0			0
$750$	−0.585786			−0.0213899
$751$	8.34315	−	14.4508i	0.304446	−	0.527315i	−0.672692	−	0.739923i	$-0.734862\pi$
$751$	8.34315	−	14.4508i	0.304446	−	0.527315i	0.977138	+	0.212607i	$0.0681954\pi$
$752$	5.41421	+	9.37769i	0.197436	+	0.341969i
$753$	−1.00000	−	1.73205i	−0.0364420	−	0.0631194i
$754$	−0.343146	+	0.594346i	−0.0124966	+	0.0216448i
$755$	−11.3137			−0.411748
$756$		0			0
$757$	−7.65685			−0.278293			−0.139147	−	0.990272i	$-0.544436\pi$
$757$	−7.65685			−0.278293			−0.139147	+	0.990272i	$0.544436\pi$
$758$	8.75736	−	15.1682i	0.318082	−	0.550934i
$759$	−9.65685	−	16.7262i	−0.350522	−	0.607121i
$760$	1.70711	+	2.95680i	0.0619233	+	0.107254i
$761$	−7.19239	+	12.4576i	−0.260724	+	0.451587i	−0.966434	−	0.256913i	$-0.917295\pi$
$761$	−7.19239	+	12.4576i	−0.260724	+	0.451587i	0.705711	+	0.708500i	$0.250628\pi$
$762$	−1.65685			−0.0600215
$763$		0			0
$764$	−18.1421			−0.656359
$765$	7.19239	−	12.4576i	0.260041	−	0.450405i
$766$	7.75736	+	13.4361i	0.280285	+	0.485467i
$767$	−4.72792	−	8.18900i	−0.170715	−	0.295688i
$768$	0.292893	−	0.507306i	0.0105689	−	0.0183058i
$769$	11.5563			0.416733			0.208366	−	0.978051i	$-0.433185\pi$
$769$	11.5563			0.416733			0.208366	+	0.978051i	$0.433185\pi$
$770$		0			0
$771$	5.79899			0.208846
$772$	2.82843	−	4.89898i	0.101797	−	0.176318i
$773$	−1.00000	−	1.73205i	−0.0359675	−	0.0622975i	0.847481	−	0.530825i	$-0.178118\pi$
$773$	−1.00000	−	1.73205i	−0.0359675	−	0.0622975i	−0.883449	+	0.468528i	$0.844785\pi$
$774$	4.21320	+	7.29748i	0.151440	+	0.262303i
$775$	1.41421	−	2.44949i	0.0508001	−	0.0879883i
$776$	−16.2426			−0.583077
$777$		0			0
$778$	0.142136			0.00509581
$779$	−18.8995	+	32.7349i	−0.677145	+	1.17285i
$780$	0.242641	+	0.420266i	0.00868793	+	0.0150479i
$781$	−30.1421	−	52.2077i	−1.07857	−	1.86814i
$782$	18.4853	−	32.0174i	0.661032	−	1.14494i
$783$	2.74517			0.0981042
$784$		0			0
$785$	−10.4853			−0.374236
$786$	0.656854	−	1.13770i	0.0234292	−	0.0405806i
$787$	−13.3640	−	23.1471i	−0.476374	−	0.825104i	0.523260	−	0.852173i	$-0.324716\pi$
$787$	−13.3640	−	23.1471i	−0.476374	−	0.825104i	−0.999634	+	0.0270697i	$0.991382\pi$
$788$	−6.89949	−	11.9503i	−0.245784	−	0.425711i
$789$	8.20101	−	14.2046i	0.291964	−	0.505696i
$790$	−1.17157			−0.0416827
$791$		0			0
$792$	12.8284			0.455838
$793$	5.51472	−	9.55177i	0.195833	−	0.339193i
$794$	2.89949	+	5.02207i	0.102899	+	0.178227i
$795$	3.07107	+	5.31925i	0.108920	+	0.188654i
$796$	−0.242641	+	0.420266i	−0.00860017	+	0.0148959i
$797$	2.20101			0.0779638			0.0389819	−	0.999240i	$-0.487589\pi$
$797$	2.20101			0.0779638			0.0389819	+	0.999240i	$0.487589\pi$
$798$		0			0
$799$	58.6274			2.07409
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	16.9081	+	29.2857i	0.597419	+	1.03476i
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$	−15.8995	+	27.5387i	−0.561081	+	0.971821i
$804$	5.65685			0.199502
$805$		0			0
$806$	−2.34315			−0.0825338
$807$	−0.443651	+	0.768426i	−0.0156172	+	0.0270499i
$808$	4.65685	+	8.06591i	0.163828	+	0.283758i
$809$	−18.4853	−	32.0174i	−0.649908	−	1.12567i	−0.983144	−	0.182830i	$-0.941474\pi$
$809$	−18.4853	−	32.0174i	−0.649908	−	1.12567i	0.333237	−	0.942843i	$-0.391859\pi$
$810$	−3.01472	+	5.22165i	−0.105926	+	0.183470i
$811$	−35.4142			−1.24356			−0.621781	−	0.783191i	$-0.713590\pi$
$811$	−35.4142			−1.24356			−0.621781	+	0.783191i	$0.713590\pi$
$812$		0			0
$813$	7.02944			0.246533
$814$	8.82843	−	15.2913i	0.309436	−	0.535959i
$815$	4.07107	+	7.05130i	0.142603	+	0.246996i
$816$	−1.58579	−	2.74666i	−0.0555136	−	0.0961524i
$817$	−5.41421	+	9.37769i	−0.189419	+	0.328084i
$818$	−13.4142			−0.469017
$819$		0			0
$820$	11.0711			0.386618
$821$	2.65685	−	4.60181i	0.0927249	−	0.160604i	−0.815932	−	0.578148i	$-0.803776\pi$
$821$	2.65685	−	4.60181i	0.0927249	−	0.160604i	0.908657	+	0.417544i	$0.137109\pi$
$822$	4.68629	+	8.11689i	0.163453	+	0.283109i
$823$	18.1421	+	31.4231i	0.632395	+	1.09534i	0.987061	+	0.160347i	$0.0512614\pi$
$823$	18.1421	+	31.4231i	0.632395	+	1.09534i	−0.354666	+	0.934993i	$0.615405\pi$
$824$	4.58579	−	7.94282i	0.159753	−	0.276701i
$825$	−2.82843			−0.0984732
$826$		0			0
$827$	−50.6274			−1.76049			−0.880244	−	0.474522i	$-0.842621\pi$
$827$	−50.6274			−1.76049			−0.880244	+	0.474522i	$0.842621\pi$
$828$	−9.07107	+	15.7116i	−0.315241	+	0.546014i
$829$	−19.4853	−	33.7495i	−0.676752	−	1.17217i	−0.975954	−	0.217979i	$-0.930054\pi$
$829$	−19.4853	−	33.7495i	−0.676752	−	1.17217i	0.299202	−	0.954190i	$-0.403280\pi$
$830$	3.12132	+	5.40629i	0.108343	+	0.187655i
$831$	5.89949	−	10.2182i	0.204651	−	0.354466i
$832$	−0.828427			−0.0287205
$833$		0			0
$834$	−0.0588745			−0.00203866
$835$	11.8995	−	20.6105i	0.411799	−	0.713257i
$836$	8.24264	+	14.2767i	0.285078	+	0.493769i
$837$	4.68629	+	8.11689i	0.161982	+	0.280561i
$838$	−16.4350	+	28.4663i	−0.567739	+	0.983352i
$839$	13.8579			0.478427			0.239213	−	0.970967i	$-0.423110\pi$
$839$	13.8579			0.478427			0.239213	+	0.970967i	$0.423110\pi$
$840$		0			0
$841$	−28.3137			−0.976335
$842$	−2.65685	+	4.60181i	−0.0915612	+	0.158589i
$843$	2.34315	+	4.05845i	0.0807022	+	0.139780i
$844$	13.3137	+	23.0600i	0.458277	+	0.793759i
$845$	−6.15685	+	10.6640i	−0.211802	+	0.366852i
$846$	−28.7696			−0.989118
$847$		0			0
$848$	−10.4853			−0.360066
$849$	−1.82843	+	3.16693i	−0.0627515	+	0.108689i
$850$	−2.70711	−	4.68885i	−0.0928530	−	0.160826i
$851$	12.4853	+	21.6251i	0.427990	+	0.741300i
$852$	3.65685	−	6.33386i	0.125282	−	0.216994i
$853$	48.8284			1.67185			0.835927	−	0.548841i	$-0.184931\pi$
$853$	48.8284			1.67185			0.835927	+	0.548841i	$0.184931\pi$
$854$		0			0
$855$	−9.07107			−0.310224
$856$	−0.828427	+	1.43488i	−0.0283151	+	0.0490431i
$857$	−9.53553	−	16.5160i	−0.325728	−	0.564177i	0.655932	−	0.754820i	$-0.272276\pi$
$857$	−9.53553	−	16.5160i	−0.325728	−	0.564177i	−0.981659	+	0.190643i	$0.938943\pi$
$858$	1.17157	+	2.02922i	0.0399968	+	0.0692766i
$859$	17.6066	−	30.4955i	0.600729	−	1.04049i	−0.391981	−	0.919973i	$-0.628210\pi$
$859$	17.6066	−	30.4955i	0.600729	−	1.04049i	0.992711	−	0.120521i	$-0.0384565\pi$
$860$	3.17157			0.108150
$861$		0			0
$862$	33.6569			1.14636
$863$	−14.4853	+	25.0892i	−0.493085	+	0.854048i	−0.999968	−	0.00796676i	$-0.997464\pi$
$863$	−14.4853	+	25.0892i	−0.493085	+	0.854048i	0.506884	+	0.862015i	$0.330797\pi$
$864$	1.65685	+	2.86976i	0.0563673	+	0.0976311i
$865$	1.58579	+	2.74666i	0.0539184	+	0.0933893i
$866$	−6.70711	+	11.6170i	−0.227917	+	0.394763i
$867$	−7.21320			−0.244973
$868$		0			0
$869$	−5.65685			−0.191896
$870$	0.242641	−	0.420266i	0.00822629	−	0.0142484i
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$	−7.24264	−	12.5446i	−0.245267	−	0.424814i
$873$	21.5772	−	37.3727i	0.730276	−	1.26488i
$874$	−23.3137			−0.788598
$875$		0			0
$876$	−3.85786			−0.130345
$877$	−13.1421	+	22.7628i	−0.443778	+	0.768647i	−0.997966	−	0.0637449i	$-0.979696\pi$
$877$	−13.1421	+	22.7628i	−0.443778	+	0.768647i	0.554188	+	0.832392i	$0.313029\pi$
$878$	−4.48528	−	7.76874i	−0.151371	−	0.262182i
$879$	5.75736	+	9.97204i	0.194191	+	0.336349i
$880$	2.41421	−	4.18154i	0.0813831	−	0.140960i
$881$	−34.3848			−1.15845			−0.579226	−	0.815167i	$-0.696645\pi$
$881$	−34.3848			−1.15845			−0.579226	+	0.815167i	$0.696645\pi$
$882$		0			0
$883$	−30.3431			−1.02113			−0.510564	−	0.859840i	$-0.670563\pi$
$883$	−30.3431			−1.02113			−0.510564	+	0.859840i	$0.670563\pi$
$884$	−2.24264	+	3.88437i	−0.0754282	+	0.130645i
$885$	3.34315	+	5.79050i	0.112379	+	0.194645i
$886$	18.4853	+	32.0174i	0.621025	+	1.07565i
$887$	3.55635	−	6.15978i	0.119411	−	0.206825i	−0.800124	−	0.599835i	$-0.795233\pi$
$887$	3.55635	−	6.15978i	0.119411	−	0.206825i	0.919534	+	0.393010i	$0.128566\pi$
$888$	2.14214			0.0718854
$889$		0			0
$890$	12.7279			0.426641
$891$	−14.5563	+	25.2123i	−0.487656	+	0.844645i
$892$	7.65685	+	13.2621i	0.256370	+	0.444047i
$893$	−18.4853	−	32.0174i	−0.618586	−	1.07142i
$894$	1.75736	−	3.04384i	0.0587749	−	0.101801i
$895$	−4.00000			−0.133705
$896$		0			0
$897$	−3.31371			−0.110642
$898$	14.3137	−	24.7921i	0.477655	−	0.827322i
$899$	1.17157	+	2.02922i	0.0390741	+	0.0676784i
$900$	1.32843	+	2.30090i	0.0442809	+	0.0766968i
$901$	−28.3848	+	49.1639i	−0.945634	+	1.63789i
$902$	53.4558			1.77988
$903$		0			0
$904$	−7.31371			−0.243250
$905$	−7.24264	+	12.5446i	−0.240754	+	0.416997i
$906$	−3.31371	−	5.73951i	−0.110091	−	0.190682i
$907$	28.1421	+	48.7436i	0.934444	+	1.61850i	0.775622	+	0.631198i	$0.217436\pi$
$907$	28.1421	+	48.7436i	0.934444	+	1.61850i	0.158822	+	0.987307i	$0.449230\pi$
$908$	4.87868	−	8.45012i	0.161905	−	0.280427i
$909$	−24.7452			−0.820745
$910$		0			0
$911$	−20.2843			−0.672048			−0.336024	−	0.941853i	$-0.609082\pi$
$911$	−20.2843			−0.672048			−0.336024	+	0.941853i	$0.609082\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	15.0711	+	26.1039i	0.498780	+	0.863912i
$914$	5.17157	+	8.95743i	0.171060	+	0.296285i
$915$	−3.89949	+	6.75412i	−0.128913	+	0.223284i
$916$	−12.1421			−0.401187
$917$		0			0
$918$	17.9411			0.592145
$919$	−16.2426	+	28.1331i	−0.535795	+	0.928025i	0.463329	+	0.886186i	$0.346655\pi$
$919$	−16.2426	+	28.1331i	−0.535795	+	0.928025i	−0.999124	+	0.0418384i	$0.986679\pi$
$920$	3.41421	+	5.91359i	0.112563	+	0.194965i
$921$	−8.51472	−	14.7479i	−0.280570	−	0.485961i
$922$	3.58579	−	6.21076i	0.118092	−	0.204541i
$923$	−10.3431			−0.340449
$924$		0			0
$925$	3.65685			0.120237
$926$	8.48528	−	14.6969i	0.278844	−	0.482971i
$927$	12.1838	+	21.1029i	0.400167	+	0.693110i
$928$	0.414214	+	0.717439i	0.0135972	+	0.0235511i
$929$	12.6066	−	21.8353i	0.413609	−	0.716392i	−0.581672	−	0.813423i	$-0.697601\pi$
$929$	12.6066	−	21.8353i	0.413609	−	0.716392i	0.995281	+	0.0970312i	$0.0309347\pi$
$930$	1.65685			0.0543304
$931$		0			0
$932$	0.686292			0.0224802
$933$	−1.17157	+	2.02922i	−0.0383556	+	0.0664338i
$934$	−1.94975	−	3.37706i	−0.0637977	−	0.110501i
$935$	−13.0711	−	22.6398i	−0.427470	−	0.740399i
$936$	1.10051	−	1.90613i	0.0359711	−	0.0623038i
$937$	−11.7574			−0.384096			−0.192048	−	0.981386i	$-0.561513\pi$
$937$	−11.7574			−0.384096			−0.192048	+	0.981386i	$0.561513\pi$
$938$		0			0
$939$	−13.1127			−0.427917
$940$	−5.41421	+	9.37769i	−0.176592	+	0.305867i
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	−0.909345	−	0.416044i	$-0.863416\pi$
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	0.0943679	−	0.995537i	$-0.469917\pi$
$942$	−3.07107	−	5.31925i	−0.100061	−	0.173310i
$943$	−37.7990	+	65.4698i	−1.23090	+	2.13199i
$944$	−11.4142			−0.371501
$945$		0			0
$946$	15.3137			0.497892
$947$	−0.414214	+	0.717439i	−0.0134601	+	0.0233136i	−0.872677	−	0.488298i	$-0.837618\pi$
$947$	−0.414214	+	0.717439i	−0.0134601	+	0.0233136i	0.859217	+	0.511612i	$0.170951\pi$
$948$	−0.343146	−	0.594346i	−0.0111449	−	0.0193035i
$949$	2.72792	+	4.72490i	0.0885521	+	0.153377i
$950$	−1.70711	+	2.95680i	−0.0553859	+	0.0959311i
$951$	3.79899			0.123191
$952$		0			0
$953$	11.6569			0.377603			0.188801	−	0.982015i	$-0.439540\pi$
$953$	11.6569			0.377603			0.188801	+	0.982015i	$0.439540\pi$
$954$	13.9289	−	24.1256i	0.450966	−	0.781096i
$955$	−9.07107	−	15.7116i	−0.293533	−	0.508414i
$956$	4.82843	+	8.36308i	0.156162	+	0.270481i
$957$	1.17157	−	2.02922i	0.0378716	−	0.0655955i
$958$	−22.8284			−0.737553
$959$		0			0
$960$	0.585786			0.0189062
$961$	11.5000	−	19.9186i	0.370968	−	0.642535i
$962$	−1.51472	−	2.62357i	−0.0488365	−	0.0845873i
$963$	−2.20101	−	3.81226i	−0.0709266	−	0.122848i
$964$	−5.29289	+	9.16756i	−0.170473	+	0.295267i
$965$	5.65685			0.182101
$966$		0			0
$967$	13.4558			0.432711			0.216355	−	0.976315i	$-0.430583\pi$
$967$	13.4558			0.432711			0.216355	+	0.976315i	$0.430583\pi$
$968$	6.15685	−	10.6640i	0.197889	−	0.342753i
$969$	5.41421	+	9.37769i	0.173930	+	0.301255i
$970$	−8.12132	−	14.0665i	−0.260760	−	0.451649i
$971$	18.6777	−	32.3507i	0.599395	−	1.03818i	−0.393516	−	0.919318i	$-0.628741\pi$
$971$	18.6777	−	32.3507i	0.599395	−	1.03818i	0.992910	−	0.118865i	$-0.0379254\pi$
$972$	−13.4731			−0.432150
$973$		0			0
$974$	7.79899			0.249896
$975$	−0.242641	+	0.420266i	−0.00777072	+	0.0134593i
$976$	−6.65685	−	11.5300i	−0.213081	−	0.369067i
$977$	17.6569	+	30.5826i	0.564893	+	0.978423i	0.997060	+	0.0766294i	$0.0244158\pi$
$977$	17.6569	+	30.5826i	0.564893	+	0.978423i	−0.432167	+	0.901794i	$0.642251\pi$
$978$	−2.38478	+	4.13055i	−0.0762567	+	0.132081i
$979$	61.4558			1.96414
$980$		0			0
$981$	38.4853			1.22874
$982$	−12.1421	+	21.0308i	−0.387471	+	0.671120i
$983$	−25.8995	−	44.8592i	−0.826066	−	1.43079i	−0.901102	−	0.433607i	$-0.857241\pi$
$983$	−25.8995	−	44.8592i	−0.826066	−	1.43079i	0.0750366	−	0.997181i	$-0.476093\pi$
$984$	3.24264	+	5.61642i	0.103372	+	0.179045i
$985$	6.89949	−	11.9503i	0.219836	−	0.380767i
$986$	4.48528			0.142840
$987$		0			0
$988$	2.82843			0.0899843
$989$	−10.8284	+	18.7554i	−0.344324	+	0.596387i
$990$	6.41421	+	11.1097i	0.203857	+	0.353091i
$991$	14.3848	+	24.9152i	0.456947	+	0.791456i	0.998798	−	0.0490187i	$-0.0156094\pi$
$991$	14.3848	+	24.9152i	0.456947	+	0.791456i	−0.541850	+	0.840475i	$0.682276\pi$
$992$	−1.41421	+	2.44949i	−0.0449013	+	0.0777714i
$993$	3.39697			0.107800
$994$		0			0
$995$	−0.485281			−0.0153845
$996$	−1.82843	+	3.16693i	−0.0579359	+	0.100348i
$997$	19.1421	+	33.1552i	0.606238	+	1.05003i	0.991855	+	0.127375i	$0.0406553\pi$
$997$	19.1421	+	33.1552i	0.606238	+	1.05003i	−0.385617	+	0.922659i	$0.626011\pi$
$998$	20.8284	+	36.0759i	0.659312	+	1.14196i
$999$	−6.05887	+	10.4943i	−0.191694	+	0.332024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.j.471.1		4
7.2	even	3		490.2.a.l.1.2	✓	2
7.3	odd	6		490.2.e.i.361.2		4
7.4	even	3	inner	490.2.e.j.361.1		4
7.5	odd	6		490.2.a.m.1.1	yes	2
7.6	odd	2		490.2.e.i.471.2		4
21.2	odd	6		4410.2.a.by.1.1		2
21.5	even	6		4410.2.a.bt.1.1		2
28.19	even	6		3920.2.a.bm.1.2		2
28.23	odd	6		3920.2.a.ca.1.1		2
35.2	odd	12		2450.2.c.w.99.1		4
35.9	even	6		2450.2.a.bs.1.1		2
35.12	even	12		2450.2.c.t.99.2		4
35.19	odd	6		2450.2.a.bn.1.2		2
35.23	odd	12		2450.2.c.w.99.4		4
35.33	even	12		2450.2.c.t.99.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.a.l.1.2	✓	2	7.2	even	3
490.2.a.m.1.1	yes	2	7.5	odd	6
490.2.e.i.361.2		4	7.3	odd	6
490.2.e.i.471.2		4	7.6	odd	2
490.2.e.j.361.1		4	7.4	even	3	inner
490.2.e.j.471.1		4	1.1	even	1	trivial
2450.2.a.bn.1.2		2	35.19	odd	6
2450.2.a.bs.1.1		2	35.9	even	6
2450.2.c.t.99.2		4	35.12	even	12
2450.2.c.t.99.3		4	35.33	even	12
2450.2.c.w.99.1		4	35.2	odd	12
2450.2.c.w.99.4		4	35.23	odd	12
3920.2.a.bm.1.2		2	28.19	even	6
3920.2.a.ca.1.1		2	28.23	odd	6
4410.2.a.bt.1.1		2	21.5	even	6
4410.2.a.by.1.1		2	21.2	odd	6

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.292893 + 0.507306i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.585786 q^{6} -1.00000 q^{8} +(1.32843 - 2.30090i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.292893 + 0.507306i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.585786 q^{6} -1.00000 q^{8} +(1.32843 - 2.30090i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.41421 - 4.18154i) q^{11} +(0.292893 - 0.507306i) q^{12} -0.828427 q^{13} +0.585786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.70711 + 4.68885i) q^{17} +(-1.32843 - 2.30090i) q^{18} +(1.70711 - 2.95680i) q^{19} -1.00000 q^{20} -4.82843 q^{22} +(3.41421 - 5.91359i) q^{23} +(-0.292893 - 0.507306i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.414214 + 0.717439i) q^{26} +3.31371 q^{27} +0.828427 q^{29} +(0.292893 - 0.507306i) q^{30} +(1.41421 + 2.44949i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.41421 - 2.44949i) q^{33} +5.41421 q^{34} -2.65685 q^{36} +(-1.82843 + 3.16693i) q^{37} +(-1.70711 - 2.95680i) q^{38} +(-0.242641 - 0.420266i) q^{39} +(-0.500000 + 0.866025i) q^{40} -11.0711 q^{41} -3.17157 q^{43} +(-2.41421 + 4.18154i) q^{44} +(-1.32843 - 2.30090i) q^{45} +(-3.41421 - 5.91359i) q^{46} +(5.41421 - 9.37769i) q^{47} -0.585786 q^{48} -1.00000 q^{50} +(-1.58579 + 2.74666i) q^{51} +(0.414214 + 0.717439i) q^{52} +(5.24264 + 9.08052i) q^{53} +(1.65685 - 2.86976i) q^{54} -4.82843 q^{55} +2.00000 q^{57} +(0.414214 - 0.717439i) q^{58} +(5.70711 + 9.88500i) q^{59} +(-0.292893 - 0.507306i) q^{60} +(-6.65685 + 11.5300i) q^{61} +2.82843 q^{62} +1.00000 q^{64} +(-0.414214 + 0.717439i) q^{65} +(-1.41421 - 2.44949i) q^{66} +(4.82843 + 8.36308i) q^{67} +(2.70711 - 4.68885i) q^{68} +4.00000 q^{69} +12.4853 q^{71} +(-1.32843 + 2.30090i) q^{72} +(-3.29289 - 5.70346i) q^{73} +(1.82843 + 3.16693i) q^{74} +(0.292893 - 0.507306i) q^{75} -3.41421 q^{76} -0.485281 q^{78} +(0.585786 - 1.01461i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.01472 - 5.22165i) q^{81} +(-5.53553 + 9.58783i) q^{82} -6.24264 q^{83} +5.41421 q^{85} +(-1.58579 + 2.74666i) q^{86} +(0.242641 + 0.420266i) q^{87} +(2.41421 + 4.18154i) q^{88} +(-6.36396 + 11.0227i) q^{89} -2.65685 q^{90} -6.82843 q^{92} +(-0.828427 + 1.43488i) q^{93} +(-5.41421 - 9.37769i) q^{94} +(-1.70711 - 2.95680i) q^{95} +(-0.292893 + 0.507306i) q^{96} +16.2426 q^{97} -12.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{12} + 8 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} - 4 q^{20} - 8 q^{22} + 8 q^{23} - 4 q^{24} - 2 q^{25} + 4 q^{26} - 32 q^{27} - 8 q^{29} + 4 q^{30} + 2 q^{32} + 16 q^{34} + 12 q^{36} + 4 q^{37} - 4 q^{38} + 16 q^{39} - 2 q^{40} - 16 q^{41} - 24 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} + 16 q^{47} - 8 q^{48} - 4 q^{50} - 12 q^{51} - 4 q^{52} + 4 q^{53} - 16 q^{54} - 8 q^{55} + 8 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 4 q^{64} + 4 q^{65} + 8 q^{67} + 8 q^{68} + 16 q^{69} + 16 q^{71} + 6 q^{72} - 16 q^{73} - 4 q^{74} + 4 q^{75} - 8 q^{76} + 32 q^{78} + 8 q^{79} + 2 q^{80} - 46 q^{81} - 8 q^{82} - 8 q^{83} + 16 q^{85} - 12 q^{86} - 16 q^{87} + 4 q^{88} + 12 q^{90} - 16 q^{92} + 8 q^{93} - 16 q^{94} - 4 q^{95} - 4 q^{96} + 48 q^{97} - 40 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 4 * q^12 + 8 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 - 4 * q^20 - 8 * q^22 + 8 * q^23 - 4 * q^24 - 2 * q^25 + 4 * q^26 - 32 * q^27 - 8 * q^29 + 4 * q^30 + 2 * q^32 + 16 * q^34 + 12 * q^36 + 4 * q^37 - 4 * q^38 + 16 * q^39 - 2 * q^40 - 16 * q^41 - 24 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 + 16 * q^47 - 8 * q^48 - 4 * q^50 - 12 * q^51 - 4 * q^52 + 4 * q^53 - 16 * q^54 - 8 * q^55 + 8 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 4 * q^64 + 4 * q^65 + 8 * q^67 + 8 * q^68 + 16 * q^69 + 16 * q^71 + 6 * q^72 - 16 * q^73 - 4 * q^74 + 4 * q^75 - 8 * q^76 + 32 * q^78 + 8 * q^79 + 2 * q^80 - 46 * q^81 - 8 * q^82 - 8 * q^83 + 16 * q^85 - 12 * q^86 - 16 * q^87 + 4 * q^88 + 12 * q^90 - 16 * q^92 + 8 * q^93 - 16 * q^94 - 4 * q^95 - 4 * q^96 + 48 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more