LMFDB - Embedded newform 1110.2.e.c.739.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(739,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1110.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.e (of order $2$, degree $1$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 $ x^16 - 2x^15 + 2x^14 + 8x^13 + 138x^12 - 220x^11 + 196x^10 + 744x^9 + 4241x^8 - 3018x^7 + 658x^6 - 1584x^5 + 16372x^4 - 18840x^3 + 10952x^2 - 1184*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.12
Root			$0.623809 + 0.623809i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.c.739.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-0.623809 - 2.14729i) q^{5} -1.00000i q^{6} -5.25373i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-0.623809 - 2.14729i) q^{5} -1.00000i q^{6} -5.25373i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(0.623809 + 2.14729i) q^{10} +1.83033 q^{11} +1.00000i q^{12} -2.67900 q^{13} +5.25373i q^{14} +(2.14729 - 0.623809i) q^{15} +1.00000 q^{16} -2.30522 q^{17} +1.00000 q^{18} -5.44848i q^{19} +(-0.623809 - 2.14729i) q^{20} +5.25373 q^{21} -1.83033 q^{22} -5.33292 q^{23} -1.00000i q^{24} +(-4.22173 + 2.67900i) q^{25} +2.67900 q^{26} -1.00000i q^{27} -5.25373i q^{28} +4.77457i q^{29} +(-2.14729 + 0.623809i) q^{30} +7.06915i q^{31} -1.00000 q^{32} +1.83033i q^{33} +2.30522 q^{34} +(-11.2813 + 3.27732i) q^{35} -1.00000 q^{36} +(6.05032 + 0.627436i) q^{37} +5.44848i q^{38} -2.67900i q^{39} +(0.623809 + 2.14729i) q^{40} +3.37727 q^{41} -5.25373 q^{42} -6.72738 q^{43} +1.83033 q^{44} +(0.623809 + 2.14729i) q^{45} +5.33292 q^{46} +8.67021i q^{47} +1.00000i q^{48} -20.6017 q^{49} +(4.22173 - 2.67900i) q^{50} -2.30522i q^{51} -2.67900 q^{52} +13.4490i q^{53} +1.00000i q^{54} +(-1.14177 - 3.93024i) q^{55} +5.25373i q^{56} +5.44848 q^{57} -4.77457i q^{58} +5.76780i q^{59} +(2.14729 - 0.623809i) q^{60} -8.95036i q^{61} -7.06915i q^{62} +5.25373i q^{63} +1.00000 q^{64} +(1.67118 + 5.75259i) q^{65} -1.83033i q^{66} +1.91054i q^{67} -2.30522 q^{68} -5.33292i q^{69} +(11.2813 - 3.27732i) q^{70} -3.15493 q^{71} +1.00000 q^{72} -15.0257i q^{73} +(-6.05032 - 0.627436i) q^{74} +(-2.67900 - 4.22173i) q^{75} -5.44848i q^{76} -9.61604i q^{77} +2.67900i q^{78} -16.1609i q^{79} +(-0.623809 - 2.14729i) q^{80} +1.00000 q^{81} -3.37727 q^{82} -14.4854i q^{83} +5.25373 q^{84} +(1.43802 + 4.94999i) q^{85} +6.72738 q^{86} -4.77457 q^{87} -1.83033 q^{88} -6.92316i q^{89} +(-0.623809 - 2.14729i) q^{90} +14.0747i q^{91} -5.33292 q^{92} -7.06915 q^{93} -8.67021i q^{94} +(-11.6995 + 3.39881i) q^{95} -1.00000i q^{96} -4.74765 q^{97} +20.6017 q^{98} -1.83033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9	$ 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 + 6 * q^15 + 16 * q^16 - 38 * q^17 + 16 * q^18 - 2 * q^20 + 6 * q^21 - 2 * q^22 - 20 * q^23 - 4 * q^25 - 6 * q^30 - 16 * q^32 + 38 * q^34 - 10 * q^35 - 16 * q^36 - 4 * q^37 + 2 * q^40 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 2 * q^44 + 2 * q^45 + 20 * q^46 - 18 * q^49 + 4 * q^50 + 20 * q^55 + 16 * q^57 + 6 * q^60 + 16 * q^64 + 12 * q^65 - 38 * q^68 + 10 * q^70 - 24 * q^71 + 16 * q^72 + 4 * q^74 - 2 * q^80 + 16 * q^81 + 6 * q^82 + 6 * q^84 + 2 * q^86 + 2 * q^87 - 2 * q^88 - 2 * q^90 - 20 * q^92 + 22 * q^93 - 16 * q^95 + 38 * q^97 + 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	−0.623809	−	2.14729i	−0.278976	−	0.960298i
$5$	−0.623809	−	2.14729i	−0.278976	−	0.960298i
$6$		−	1.00000i		−	0.408248i
$7$		−	5.25373i		−	1.98572i	−0.119270	−	0.992862i	$-0.538055\pi$
$7$		−	5.25373i		−	1.98572i	0.119270	−	0.992862i	$-0.461945\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	0.623809	+	2.14729i	0.197266	+	0.679033i
$11$	1.83033			0.551864			0.275932	−	0.961177i	$-0.411014\pi$
$11$	1.83033			0.551864			0.275932	+	0.961177i	$0.411014\pi$
$12$			1.00000i			0.288675i
$13$	−2.67900			−0.743021			−0.371510	−	0.928429i	$-0.621160\pi$
$13$	−2.67900			−0.743021			−0.371510	+	0.928429i	$0.621160\pi$
$14$			5.25373i			1.40412i
$15$	2.14729	−	0.623809i	0.554428	−	0.161067i
$16$	1.00000			0.250000
$17$	−2.30522			−0.559099			−0.279550	−	0.960131i	$-0.590185\pi$
$17$	−2.30522			−0.559099			−0.279550	+	0.960131i	$0.590185\pi$
$18$	1.00000			0.235702
$19$		−	5.44848i		−	1.24997i	−0.780638	−	0.624984i	$-0.785106\pi$
$19$		−	5.44848i		−	1.24997i	0.780638	−	0.624984i	$-0.214894\pi$
$20$	−0.623809	−	2.14729i	−0.139488	−	0.480149i
$21$	5.25373			1.14646
$22$	−1.83033			−0.390227
$23$	−5.33292			−1.11199			−0.555995	−	0.831185i	$-0.687663\pi$
$23$	−5.33292			−1.11199			−0.555995	+	0.831185i	$0.687663\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−4.22173	+	2.67900i	−0.844345	+	0.535800i
$26$	2.67900			0.525395
$27$		−	1.00000i		−	0.192450i
$28$		−	5.25373i		−	0.992862i
$29$			4.77457i			0.886615i	0.896370	+	0.443307i	$0.146195\pi$
$29$			4.77457i			0.886615i	−0.896370	+	0.443307i	$0.853805\pi$
$30$	−2.14729	+	0.623809i	−0.392040	+	0.113891i
$31$			7.06915i			1.26966i	0.772653	+	0.634829i	$0.218929\pi$
$31$			7.06915i			1.26966i	−0.772653	+	0.634829i	$0.781071\pi$
$32$	−1.00000			−0.176777
$33$			1.83033i			0.318619i
$34$	2.30522			0.395343
$35$	−11.2813	+	3.27732i	−1.90689	+	0.553969i
$36$	−1.00000			−0.166667
$37$	6.05032	+	0.627436i	0.994666	+	0.103150i
$37$	6.05032	+	0.627436i	0.994666	+	0.103150i
$38$			5.44848i			0.883861i
$39$		−	2.67900i		−	0.428983i
$40$	0.623809	+	2.14729i	0.0986328	+	0.339517i
$41$	3.37727			0.527441			0.263720	−	0.964599i	$-0.415050\pi$
$41$	3.37727			0.527441			0.263720	+	0.964599i	$0.415050\pi$
$42$	−5.25373			−0.810668
$43$	−6.72738			−1.02592			−0.512958	−	0.858414i	$-0.671450\pi$
$43$	−6.72738			−1.02592			−0.512958	+	0.858414i	$0.671450\pi$
$44$	1.83033			0.275932
$45$	0.623809	+	2.14729i	0.0929919	+	0.320099i
$46$	5.33292			0.786296
$47$			8.67021i			1.26468i	0.774691	+	0.632340i	$0.217905\pi$
$47$			8.67021i			1.26468i	−0.774691	+	0.632340i	$0.782095\pi$
$48$			1.00000i			0.144338i
$49$	−20.6017			−2.94310
$50$	4.22173	−	2.67900i	0.597042	−	0.378868i
$51$		−	2.30522i		−	0.322796i
$52$	−2.67900			−0.371510
$53$			13.4490i			1.84737i	0.383156	+	0.923684i	$0.374837\pi$
$53$			13.4490i			1.84737i	−0.383156	+	0.923684i	$0.625163\pi$
$54$			1.00000i			0.136083i
$55$	−1.14177	−	3.93024i	−0.153957	−	0.529954i
$56$			5.25373i			0.702059i
$57$	5.44848			0.721669
$58$		−	4.77457i		−	0.626931i
$59$			5.76780i			0.750903i	0.926842	+	0.375452i	$0.122512\pi$
$59$			5.76780i			0.750903i	−0.926842	+	0.375452i	$0.877488\pi$
$60$	2.14729	−	0.623809i	0.277214	−	0.0805334i
$61$		−	8.95036i		−	1.14598i	−0.819564	−	0.572988i	$-0.805784\pi$
$61$		−	8.95036i		−	1.14598i	0.819564	−	0.572988i	$-0.194216\pi$
$62$		−	7.06915i		−	0.897783i
$63$			5.25373i			0.661908i
$64$	1.00000			0.125000
$65$	1.67118	+	5.75259i	0.207285	+	0.713521i
$66$		−	1.83033i		−	0.225297i
$67$			1.91054i			0.233410i	0.993167	+	0.116705i	$0.0372332\pi$
$67$			1.91054i			0.233410i	−0.993167	+	0.116705i	$0.962767\pi$
$68$	−2.30522			−0.279550
$69$		−	5.33292i		−	0.642008i
$70$	11.2813	−	3.27732i	1.34837	−	0.391715i
$71$	−3.15493			−0.374421			−0.187210	−	0.982320i	$-0.559945\pi$
$71$	−3.15493			−0.374421			−0.187210	+	0.982320i	$0.559945\pi$
$72$	1.00000			0.117851
$73$		−	15.0257i		−	1.75863i	−0.476241	−	0.879315i	$-0.658001\pi$
$73$		−	15.0257i		−	1.75863i	0.476241	−	0.879315i	$-0.341999\pi$
$74$	−6.05032	−	0.627436i	−0.703335	−	0.0729379i
$75$	−2.67900	−	4.22173i	−0.309344	−	0.487483i
$76$		−	5.44848i		−	0.624984i
$77$		−	9.61604i		−	1.09585i
$78$			2.67900i			0.303337i
$79$		−	16.1609i		−	1.81824i	−0.416536	−	0.909119i	$-0.636756\pi$
$79$		−	16.1609i		−	1.81824i	0.416536	−	0.909119i	$-0.363244\pi$
$80$	−0.623809	−	2.14729i	−0.0697439	−	0.240075i
$81$	1.00000			0.111111
$82$	−3.37727			−0.372957
$83$		−	14.4854i		−	1.58997i	−0.606626	−	0.794987i	$-0.707478\pi$
$83$		−	14.4854i		−	1.58997i	0.606626	−	0.794987i	$-0.292522\pi$
$84$	5.25373			0.573229
$85$	1.43802	+	4.94999i	0.155975	+	0.536902i
$86$	6.72738			0.725432
$87$	−4.77457			−0.511887
$88$	−1.83033			−0.195113
$89$		−	6.92316i		−	0.733854i	−0.930250	−	0.366927i	$-0.880410\pi$
$89$		−	6.92316i		−	0.733854i	0.930250	−	0.366927i	$-0.119590\pi$
$90$	−0.623809	−	2.14729i	−0.0657552	−	0.226344i
$91$			14.0747i			1.47543i
$92$	−5.33292			−0.555995
$93$	−7.06915			−0.733037
$94$		−	8.67021i		−	0.894264i
$95$	−11.6995	+	3.39881i	−1.20034	+	0.348711i
$96$		−	1.00000i		−	0.102062i
$97$	−4.74765			−0.482050			−0.241025	−	0.970519i	$-0.577484\pi$
$97$	−4.74765			−0.482050			−0.241025	+	0.970519i	$0.577484\pi$
$98$	20.6017			2.08108
$99$	−1.83033			−0.183955
$100$	−4.22173	+	2.67900i	−0.422173	+	0.267900i
$101$	−11.7467			−1.16884			−0.584418	−	0.811452i	$-0.698677\pi$
$101$	−11.7467			−1.16884			−0.584418	+	0.811452i	$0.698677\pi$
$102$			2.30522i			0.228251i
$103$	14.1230			1.39158			0.695788	−	0.718247i	$-0.255055\pi$
$103$	14.1230			1.39158			0.695788	+	0.718247i	$0.255055\pi$
$104$	2.67900			0.262697
$105$	−3.27732	−	11.2813i	−0.319834	−	1.10094i
$106$		−	13.4490i		−	1.30629i
$107$		−	15.5723i		−	1.50543i	−0.658349	−	0.752713i	$-0.728745\pi$
$107$		−	15.5723i		−	1.50543i	0.658349	−	0.752713i	$-0.271255\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			2.97575i			0.285025i	0.989793	+	0.142513i	$0.0455182\pi$
$109$			2.97575i			0.285025i	−0.989793	+	0.142513i	$0.954482\pi$
$110$	1.14177	+	3.93024i	0.108864	+	0.374734i
$111$	−0.627436	+	6.05032i	−0.0595535	+	0.574271i
$112$		−	5.25373i		−	0.496431i
$113$	0.236199			0.0222197			0.0111099	−	0.999938i	$-0.496464\pi$
$113$	0.236199			0.0222197			0.0111099	+	0.999938i	$0.496464\pi$
$114$	−5.44848			−0.510297
$115$	3.32672	+	11.4513i	0.310219	+	1.06784i
$116$			4.77457i			0.443307i
$117$	2.67900			0.247674
$118$		−	5.76780i		−	0.530969i
$119$			12.1110i			1.11022i
$120$	−2.14729	+	0.623809i	−0.196020	+	0.0569457i
$121$	−7.64991			−0.695446
$122$			8.95036i			0.810327i
$123$			3.37727i			0.304518i
$124$			7.06915i			0.634829i
$125$	8.38614	+	7.39409i	0.750079	+	0.661348i
$126$		−	5.25373i		−	0.468040i
$127$			6.62803i			0.588143i	0.955783	+	0.294071i	$0.0950103\pi$
$127$			6.62803i			0.588143i	−0.955783	+	0.294071i	$0.904990\pi$
$128$	−1.00000			−0.0883883
$129$		−	6.72738i		−	0.592313i
$130$	−1.67118	−	5.75259i	−0.146572	−	0.504536i
$131$			12.3270i			1.07702i	0.842620	+	0.538509i	$0.181012\pi$
$131$			12.3270i			1.07702i	−0.842620	+	0.538509i	$0.818988\pi$
$132$			1.83033i			0.159309i
$133$	−28.6249			−2.48209
$134$		−	1.91054i		−	0.165046i
$135$	−2.14729	+	0.623809i	−0.184809	+	0.0536889i
$136$	2.30522			0.197671
$137$		−	10.3826i		−	0.887049i	−0.896262	−	0.443525i	$-0.853728\pi$
$137$		−	10.3826i		−	0.887049i	0.896262	−	0.443525i	$-0.146272\pi$
$138$			5.33292i			0.453968i
$139$	20.5051			1.73922			0.869611	−	0.493737i	$-0.164369\pi$
$139$	20.5051			1.73922			0.869611	+	0.493737i	$0.164369\pi$
$140$	−11.2813	+	3.27732i	−0.953443	+	0.276984i
$141$	−8.67021			−0.730163
$142$	3.15493			0.264756
$143$	−4.90344			−0.410046
$144$	−1.00000			−0.0833333
$145$	10.2524	−	2.97842i	0.851415	−	0.247344i
$146$			15.0257i			1.24354i
$147$		−	20.6017i		−	1.69920i
$148$	6.05032	+	0.627436i	0.497333	+	0.0515749i
$149$	−13.0910			−1.07246			−0.536228	−	0.844073i	$-0.680151\pi$
$149$	−13.0910			−1.07246			−0.536228	+	0.844073i	$0.680151\pi$
$150$	2.67900	+	4.22173i	0.218739	+	0.344702i
$151$	−3.06560			−0.249475			−0.124738	−	0.992190i	$-0.539809\pi$
$151$	−3.06560			−0.249475			−0.124738	+	0.992190i	$0.539809\pi$
$152$			5.44848i			0.441930i
$153$	2.30522			0.186366
$154$			9.61604i			0.774882i
$155$	15.1795	−	4.40980i	1.21925	−	0.354204i
$156$		−	2.67900i		−	0.214492i
$157$		−	19.5891i		−	1.56338i	−0.623667	−	0.781690i	$-0.714358\pi$
$157$		−	19.5891i		−	1.56338i	0.623667	−	0.781690i	$-0.285642\pi$
$158$			16.1609i			1.28569i
$159$	−13.4490			−1.06658
$160$	0.623809	+	2.14729i	0.0493164	+	0.169758i
$161$			28.0177i			2.20811i
$162$	−1.00000			−0.0785674
$163$	13.6370			1.06813			0.534064	−	0.845444i	$-0.320664\pi$
$163$	13.6370			1.06813			0.534064	+	0.845444i	$0.320664\pi$
$164$	3.37727			0.263720
$165$	3.93024	−	1.14177i	0.305969	−	0.0888869i
$166$			14.4854i			1.12428i
$167$	0.535033			0.0414021			0.0207011	−	0.999786i	$-0.493410\pi$
$167$	0.535033			0.0414021			0.0207011	+	0.999786i	$0.493410\pi$
$168$	−5.25373			−0.405334
$169$	−5.82296			−0.447920
$170$	−1.43802	−	4.94999i	−0.110291	−	0.379647i
$171$			5.44848i			0.416656i
$172$	−6.72738			−0.512958
$173$		−	0.202994i		−	0.0154333i	−0.999970	−	0.00771666i	$-0.997544\pi$
$173$		−	0.202994i		−	0.0154333i	0.999970	−	0.00771666i	$-0.00245631\pi$
$174$	4.77457			0.361959
$175$	14.0747	+	22.1798i	1.06395	+	1.67664i
$176$	1.83033			0.137966
$177$	−5.76780			−0.433534
$178$			6.92316i			0.518913i
$179$		−	8.40329i		−	0.628091i	−0.949408	−	0.314046i	$-0.898316\pi$
$179$		−	8.40329i		−	0.628091i	0.949408	−	0.314046i	$-0.101684\pi$
$180$	0.623809	+	2.14729i	0.0464960	+	0.160050i
$181$	−18.3262			−1.36218			−0.681089	−	0.732201i	$-0.738493\pi$
$181$	−18.3262			−1.36218			−0.681089	+	0.732201i	$0.738493\pi$
$182$		−	14.0747i		−	1.04329i
$183$	8.95036			0.661629
$184$	5.33292			0.393148
$185$	−2.42695	−	13.3832i	−0.178433	−	0.983952i
$186$	7.06915			0.518335
$187$	−4.21931			−0.308547
$188$			8.67021i			0.632340i
$189$	−5.25373			−0.382153
$190$	11.6995	−	3.39881i	0.848770	−	0.246576i
$191$		−	16.1070i		−	1.16546i	−0.812666	−	0.582730i	$-0.801984\pi$
$191$		−	16.1070i		−	1.16546i	0.812666	−	0.582730i	$-0.198016\pi$
$192$			1.00000i			0.0721688i
$193$	1.32351			0.0952686			0.0476343	−	0.998865i	$-0.484832\pi$
$193$	1.32351			0.0952686			0.0476343	+	0.998865i	$0.484832\pi$
$194$	4.74765			0.340861
$195$	−5.75259	+	1.67118i	−0.411952	+	0.119676i
$196$	−20.6017			−1.47155
$197$		−	7.45206i		−	0.530938i	−0.964119	−	0.265469i	$-0.914473\pi$
$197$		−	7.45206i		−	0.530938i	0.964119	−	0.265469i	$-0.0855267\pi$
$198$	1.83033			0.130076
$199$			14.0906i			0.998859i	0.866354	+	0.499430i	$0.166457\pi$
$199$			14.0906i			0.998859i	−0.866354	+	0.499430i	$0.833543\pi$
$200$	4.22173	−	2.67900i	0.298521	−	0.189434i
$201$	−1.91054			−0.134759
$202$	11.7467			0.826492
$203$	25.0843			1.76057
$204$		−	2.30522i		−	0.161398i
$205$	−2.10677	−	7.25198i	−0.147143	−	0.506500i
$206$	−14.1230			−0.983993
$207$	5.33292			0.370664
$208$	−2.67900			−0.185755
$209$		−	9.97250i		−	0.689812i
$210$	3.27732	+	11.2813i	0.226157	+	0.778483i
$211$	−5.60670			−0.385981			−0.192990	−	0.981201i	$-0.561819\pi$
$211$	−5.60670			−0.385981			−0.192990	+	0.981201i	$0.561819\pi$
$212$			13.4490i			0.923684i
$213$		−	3.15493i		−	0.216172i
$214$			15.5723i			1.06450i
$215$	4.19660	+	14.4457i	0.286206	+	0.985186i
$216$			1.00000i			0.0680414i
$217$	37.1394			2.52119
$218$		−	2.97575i		−	0.201543i
$219$	15.0257			1.01535
$220$	−1.14177	−	3.93024i	−0.0769783	−	0.264977i
$221$	6.17569			0.415422
$222$	0.627436	−	6.05032i	0.0421107	−	0.406071i
$223$			14.0077i			0.938027i	0.883191	+	0.469013i	$0.155390\pi$
$223$			14.0077i			0.938027i	−0.883191	+	0.469013i	$0.844610\pi$
$224$			5.25373i			0.351030i
$225$	4.22173	−	2.67900i	0.281448	−	0.178600i
$226$	−0.236199			−0.0157117
$227$	−22.6905			−1.50602			−0.753011	−	0.658008i	$-0.771399\pi$
$227$	−22.6905			−1.50602			−0.753011	+	0.658008i	$0.771399\pi$
$228$	5.44848			0.360835
$229$	3.84170			0.253867			0.126933	−	0.991911i	$-0.459487\pi$
$229$	3.84170			0.253867			0.126933	+	0.991911i	$0.459487\pi$
$230$	−3.32672	−	11.4513i	−0.219358	−	0.755079i
$231$	9.61604			0.632689
$232$		−	4.77457i		−	0.313466i
$233$			10.9135i			0.714969i	0.933919	+	0.357484i	$0.116365\pi$
$233$			10.9135i			0.714969i	−0.933919	+	0.357484i	$0.883635\pi$
$234$	−2.67900			−0.175132
$235$	18.6175	−	5.40855i	1.21447	−	0.352815i
$236$			5.76780i			0.375452i
$237$	16.1609			1.04976
$238$		−	12.1110i		−	0.785042i
$239$			2.52279i			0.163186i	0.996666	+	0.0815928i	$0.0260007\pi$
$239$			2.52279i			0.163186i	−0.996666	+	0.0815928i	$0.973999\pi$
$240$	2.14729	−	0.623809i	0.138607	−	0.0402667i
$241$		−	6.04670i		−	0.389502i	−0.980853	−	0.194751i	$-0.937610\pi$
$241$		−	6.04670i		−	0.389502i	0.980853	−	0.194751i	$-0.0623899\pi$
$242$	7.64991			0.491755
$243$			1.00000i			0.0641500i
$244$		−	8.95036i		−	0.572988i
$245$	12.8515	+	44.2378i	0.821053	+	2.82625i
$246$		−	3.37727i		−	0.215327i
$247$			14.5965i			0.928752i
$248$		−	7.06915i		−	0.448892i
$249$	14.4854			0.917972
$250$	−8.38614	−	7.39409i	−0.530386	−	0.467644i
$251$		−	16.4821i		−	1.04034i	−0.854062	−	0.520171i	$-0.825868\pi$
$251$		−	16.4821i		−	1.04034i	0.854062	−	0.520171i	$-0.174132\pi$
$252$			5.25373i			0.330954i
$253$	−9.76098			−0.613668
$254$		−	6.62803i		−	0.415880i
$255$	−4.94999	+	1.43802i	−0.309980	+	0.0900523i
$256$	1.00000			0.0625000
$257$	4.09511			0.255446			0.127723	−	0.991810i	$-0.459233\pi$
$257$	4.09511			0.255446			0.127723	+	0.991810i	$0.459233\pi$
$258$			6.72738i			0.418829i
$259$	3.29638	−	31.7867i	0.204827	−	1.97513i
$260$	1.67118	+	5.75259i	0.103642	+	0.356761i
$261$		−	4.77457i		−	0.295538i
$262$		−	12.3270i		−	0.761567i
$263$			18.6780i			1.15174i	0.817542	+	0.575868i	$0.195336\pi$
$263$			18.6780i			1.15174i	−0.817542	+	0.575868i	$0.804664\pi$
$264$		−	1.83033i		−	0.112649i
$265$	28.8790	−	8.38963i	1.77402	−	0.515371i
$266$	28.6249			1.75510
$267$	6.92316			0.423691
$268$			1.91054i			0.116705i
$269$	−2.14866			−0.131006			−0.0655031	−	0.997852i	$-0.520865\pi$
$269$	−2.14866			−0.131006			−0.0655031	+	0.997852i	$0.520865\pi$
$270$	2.14729	−	0.623809i	0.130680	−	0.0379638i
$271$	5.65331			0.343414			0.171707	−	0.985148i	$-0.445072\pi$
$271$	5.65331			0.343414			0.171707	+	0.985148i	$0.445072\pi$
$272$	−2.30522			−0.139775
$273$	−14.0747			−0.851842
$274$			10.3826i			0.627238i
$275$	−7.72713	+	4.90344i	−0.465964	+	0.295689i
$276$		−	5.33292i		−	0.321004i
$277$	−19.6183			−1.17875			−0.589375	−	0.807860i	$-0.700626\pi$
$277$	−19.6183			−1.17875			−0.589375	+	0.807860i	$0.700626\pi$
$278$	−20.5051			−1.22982
$279$		−	7.06915i		−	0.423219i
$280$	11.2813	−	3.27732i	0.674186	−	0.195858i
$281$		−	10.7651i		−	0.642195i	−0.947046	−	0.321097i	$-0.895948\pi$
$281$		−	10.7651i		−	0.642195i	0.947046	−	0.321097i	$-0.104052\pi$
$282$	8.67021			0.516303
$283$	12.3991			0.737048			0.368524	−	0.929618i	$-0.379863\pi$
$283$	12.3991			0.737048			0.368524	+	0.929618i	$0.379863\pi$
$284$	−3.15493			−0.187210
$285$	−3.39881	−	11.6995i	−0.201328	−	0.693017i
$286$	4.90344			0.289946
$287$		−	17.7433i		−	1.04735i
$288$	1.00000			0.0589256
$289$	−11.6859			−0.687408
$290$	−10.2524	+	2.97842i	−0.602041	+	0.174899i
$291$		−	4.74765i		−	0.278312i
$292$		−	15.0257i		−	0.879315i
$293$		−	16.3278i		−	0.953878i	−0.878937	−	0.476939i	$-0.841746\pi$
$293$		−	16.3278i		−	0.953878i	0.878937	−	0.476939i	$-0.158254\pi$
$294$			20.6017i			1.20151i
$295$	12.3851	−	3.59800i	0.721091	−	0.209484i
$296$	−6.05032	−	0.627436i	−0.351667	−	0.0364690i
$297$		−	1.83033i		−	0.106206i
$298$	13.0910			0.758341
$299$	14.2869			0.826232
$300$	−2.67900	−	4.22173i	−0.154672	−	0.243741i
$301$			35.3439i			2.03719i
$302$	3.06560			0.176406
$303$		−	11.7467i		−	0.674828i
$304$		−	5.44848i		−	0.312492i
$305$	−19.2190	+	5.58331i	−1.10048	+	0.319699i
$306$	−2.30522			−0.131781
$307$		−	3.93189i		−	0.224405i	−0.993685	−	0.112203i	$-0.964209\pi$
$307$		−	3.93189i		−	0.224405i	0.993685	−	0.112203i	$-0.0357905\pi$
$308$		−	9.61604i		−	0.547925i
$309$			14.1230i			0.803427i
$310$	−15.1795	+	4.40980i	−0.862139	+	0.250460i
$311$			11.0216i			0.624980i	0.949921	+	0.312490i	$0.101163\pi$
$311$			11.0216i			0.624980i	−0.949921	+	0.312490i	$0.898837\pi$
$312$			2.67900i			0.151668i
$313$	14.8364			0.838602			0.419301	−	0.907847i	$-0.362275\pi$
$313$	14.8364			0.838602			0.419301	+	0.907847i	$0.362275\pi$
$314$			19.5891i			1.10548i
$315$	11.2813	−	3.27732i	0.635629	−	0.184656i
$316$		−	16.1609i		−	0.909119i
$317$		−	17.1800i		−	0.964926i	−0.875916	−	0.482463i	$-0.839742\pi$
$317$		−	17.1800i		−	0.964926i	0.875916	−	0.482463i	$-0.160258\pi$
$318$	13.4490			0.754185
$319$			8.73901i			0.489291i
$320$	−0.623809	−	2.14729i	−0.0348720	−	0.120037i
$321$	15.5723			0.869158
$322$		−	28.0177i		−	1.56137i
$323$			12.5600i			0.698856i
$324$	1.00000			0.0555556
$325$	11.3100	−	7.17704i	0.627366	−	0.398110i
$326$	−13.6370			−0.755281
$327$	−2.97575			−0.164559
$328$	−3.37727			−0.186478
$329$	45.5509			2.51130
$330$	−3.93024	+	1.14177i	−0.216353	+	0.0628525i
$331$		−	2.90130i		−	0.159470i	−0.996816	−	0.0797349i	$-0.974593\pi$
$331$		−	2.90130i		−	0.159470i	0.996816	−	0.0797349i	$-0.0254074\pi$
$332$		−	14.4854i		−	0.794987i
$333$	−6.05032	−	0.627436i	−0.331555	−	0.0343833i
$334$	−0.535033			−0.0292757
$335$	4.10250	−	1.19181i	0.224143	−	0.0651158i
$336$	5.25373			0.286615
$337$		−	6.33337i		−	0.345001i	−0.985009	−	0.172500i	$-0.944815\pi$
$337$		−	6.33337i		−	0.345001i	0.985009	−	0.172500i	$-0.0551846\pi$
$338$	5.82296			0.316728
$339$			0.236199i			0.0128286i
$340$	1.43802	+	4.94999i	0.0779875	+	0.268451i
$341$			12.9388i			0.700678i
$342$		−	5.44848i		−	0.294620i
$343$			71.4596i			3.85846i
$344$	6.72738			0.362716
$345$	−11.4513	+	3.32672i	−0.616519	+	0.179105i
$346$			0.202994i			0.0109130i
$347$	−23.9733			−1.28696			−0.643478	−	0.765464i	$-0.722509\pi$
$347$	−23.9733			−1.28696			−0.643478	+	0.765464i	$0.722509\pi$
$348$	−4.77457			−0.255944
$349$	−6.41043			−0.343142			−0.171571	−	0.985172i	$-0.554884\pi$
$349$	−6.41043			−0.343142			−0.171571	+	0.985172i	$0.554884\pi$
$350$	−14.0747	−	22.1798i	−0.752326	−	1.18556i
$351$			2.67900i			0.142994i
$352$	−1.83033			−0.0975567
$353$	10.7349			0.571364			0.285682	−	0.958325i	$-0.407780\pi$
$353$	10.7349			0.571364			0.285682	+	0.958325i	$0.407780\pi$
$354$	5.76780			0.306555
$355$	1.96807	+	6.77455i	0.104454	+	0.359556i
$356$		−	6.92316i		−	0.366927i
$357$	−12.1110			−0.640984
$358$			8.40329i			0.444127i
$359$	−10.5719			−0.557964			−0.278982	−	0.960296i	$-0.589997\pi$
$359$	−10.5719			−0.557964			−0.278982	+	0.960296i	$0.589997\pi$
$360$	−0.623809	−	2.14729i	−0.0328776	−	0.113172i
$361$	−10.6860			−0.562419
$362$	18.3262			0.963205
$363$		−	7.64991i		−	0.401516i
$364$			14.0747i			0.737717i
$365$	−32.2647	+	9.37319i	−1.68881	+	0.490615i
$366$	−8.95036			−0.467843
$367$			12.7249i			0.664234i	0.943238	+	0.332117i	$0.107763\pi$
$367$			12.7249i			0.664234i	−0.943238	+	0.332117i	$0.892237\pi$
$368$	−5.33292			−0.277998
$369$	−3.37727			−0.175814
$370$	2.42695	+	13.3832i	0.126171	+	0.695759i
$371$	70.6576			3.66836
$372$	−7.06915			−0.366518
$373$			20.8664i			1.08042i	0.841530	+	0.540211i	$0.181656\pi$
$373$			20.8664i			1.08042i	−0.841530	+	0.540211i	$0.818344\pi$
$374$	4.21931			0.218175
$375$	−7.39409	+	8.38614i	−0.381829	+	0.433059i
$376$		−	8.67021i		−	0.447132i
$377$		−	12.7911i		−	0.658773i
$378$	5.25373			0.270223
$379$	−3.99708			−0.205316			−0.102658	−	0.994717i	$-0.532735\pi$
$379$	−3.99708			−0.205316			−0.102658	+	0.994717i	$0.532735\pi$
$380$	−11.6995	+	3.39881i	−0.600171	+	0.174355i
$381$	−6.62803			−0.339564
$382$			16.1070i			0.824105i
$383$	28.8603			1.47469			0.737347	−	0.675514i	$-0.236078\pi$
$383$	28.8603			1.47469			0.737347	+	0.675514i	$0.236078\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−20.6484	+	5.99857i	−1.05234	+	0.305715i
$386$	−1.32351			−0.0673651
$387$	6.72738			0.341972
$388$	−4.74765			−0.241025
$389$		−	2.05542i		−	0.104214i	−0.998642	−	0.0521069i	$-0.983406\pi$
$389$		−	2.05542i		−	0.104214i	0.998642	−	0.0521069i	$-0.0165936\pi$
$390$	5.75259	−	1.67118i	0.291294	−	0.0846236i
$391$	12.2936			0.621713
$392$	20.6017			1.04054
$393$	−12.3270			−0.621817
$394$			7.45206i			0.375430i
$395$	−34.7021	+	10.0813i	−1.74605	+	0.507245i
$396$	−1.83033			−0.0919773
$397$		−	24.9457i		−	1.25199i	−0.779828	−	0.625994i	$-0.784694\pi$
$397$		−	24.9457i		−	1.25199i	0.779828	−	0.625994i	$-0.215306\pi$
$398$		−	14.0906i		−	0.706300i
$399$		−	28.6249i		−	1.43304i
$400$	−4.22173	+	2.67900i	−0.211086	+	0.133950i
$401$		−	17.0242i		−	0.850150i	−0.905158	−	0.425075i	$-0.860248\pi$
$401$		−	17.0242i		−	0.850150i	0.905158	−	0.425075i	$-0.139752\pi$
$402$	1.91054			0.0952893
$403$		−	18.9382i		−	0.943381i
$404$	−11.7467			−0.584418
$405$	−0.623809	−	2.14729i	−0.0309973	−	0.106700i
$406$	−25.0843			−1.24491
$407$	11.0740	+	1.14841i	0.548920	+	0.0569246i
$408$			2.30522i			0.114126i
$409$		−	6.52138i		−	0.322461i	−0.986917	−	0.161231i	$-0.948454\pi$
$409$		−	6.52138i		−	0.322461i	0.986917	−	0.161231i	$-0.0515463\pi$
$410$	2.10677	+	7.25198i	0.104046	+	0.358150i
$411$	10.3826			0.512138
$412$	14.1230			0.695788
$413$	30.3025			1.49109
$414$	−5.33292			−0.262099
$415$	−31.1043	+	9.03609i	−1.52685	+	0.443564i
$416$	2.67900			0.131349
$417$			20.5051i			1.00414i
$418$			9.97250i			0.487771i
$419$	−8.70864			−0.425445			−0.212722	−	0.977113i	$-0.568233\pi$
$419$	−8.70864			−0.425445			−0.212722	+	0.977113i	$0.568233\pi$
$420$	−3.27732	−	11.2813i	−0.159917	−	0.550471i
$421$		−	30.1490i		−	1.46937i	−0.678408	−	0.734686i	$-0.737330\pi$
$421$		−	30.1490i		−	1.46937i	0.678408	−	0.734686i	$-0.262670\pi$
$422$	5.60670			0.272930
$423$		−	8.67021i		−	0.421560i
$424$		−	13.4490i		−	0.653143i
$425$	9.73203	−	6.17569i	0.472073	−	0.299565i
$426$			3.15493i			0.152857i
$427$	−47.0228			−2.27559
$428$		−	15.5723i		−	0.752713i
$429$		−	4.90344i		−	0.236740i
$430$	−4.19660	−	14.4457i	−0.202378	−	0.696631i
$431$			13.4931i			0.649938i	0.945725	+	0.324969i	$0.105354\pi$
$431$			13.4931i			0.649938i	−0.945725	+	0.324969i	$0.894646\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			16.6005i			0.797769i	0.917001	+	0.398884i	$0.130603\pi$
$433$			16.6005i			0.797769i	−0.917001	+	0.398884i	$0.869397\pi$
$434$	−37.1394			−1.78275
$435$	2.97842	+	10.2524i	0.142804	+	0.491564i
$436$			2.97575i			0.142513i
$437$			29.0563i			1.38995i
$438$	−15.0257			−0.717958
$439$		−	5.27040i		−	0.251543i	−0.992059	−	0.125771i	$-0.959859\pi$
$439$		−	5.27040i		−	0.251543i	0.992059	−	0.125771i	$-0.0401406\pi$
$440$	1.14177	+	3.93024i	0.0544319	+	0.187367i
$441$	20.6017			0.981033
$442$	−6.17569			−0.293748
$443$		−	28.9960i		−	1.37764i	−0.724931	−	0.688822i	$-0.758128\pi$
$443$		−	28.9960i		−	1.37764i	0.724931	−	0.688822i	$-0.241872\pi$
$444$	−0.627436	+	6.05032i	−0.0297768	+	0.287135i
$445$	−14.8661	+	4.31873i	−0.704718	+	0.204727i
$446$		−	14.0077i		−	0.663285i
$447$		−	13.0910i		−	0.619183i
$448$		−	5.25373i		−	0.248215i
$449$			8.02620i			0.378780i	0.981902	+	0.189390i	$0.0606510\pi$
$449$			8.02620i			0.378780i	−0.981902	+	0.189390i	$0.939349\pi$
$450$	−4.22173	+	2.67900i	−0.199014	+	0.126289i
$451$	6.18150			0.291075
$452$	0.236199			0.0111099
$453$		−	3.06560i		−	0.144035i
$454$	22.6905			1.06492
$455$	30.2226	−	8.77995i	1.41686	−	0.411610i
$456$	−5.44848			−0.255149
$457$	−12.5165			−0.585498			−0.292749	−	0.956189i	$-0.594570\pi$
$457$	−12.5165			−0.585498			−0.292749	+	0.956189i	$0.594570\pi$
$458$	−3.84170			−0.179511
$459$			2.30522i			0.107599i
$460$	3.32672	+	11.4513i	0.155109	+	0.533921i
$461$		−	36.1735i		−	1.68477i	−0.538877	−	0.842385i	$-0.681151\pi$
$461$		−	36.1735i		−	1.68477i	0.538877	−	0.842385i	$-0.318849\pi$
$462$	−9.61604			−0.447379
$463$	11.4033			0.529955			0.264977	−	0.964255i	$-0.414635\pi$
$463$	11.4033			0.529955			0.264977	+	0.964255i	$0.414635\pi$
$464$			4.77457i			0.221654i
$465$	4.40980	+	15.1795i	0.204500	+	0.703934i
$466$		−	10.9135i		−	0.505559i
$467$	−14.8992			−0.689451			−0.344726	−	0.938703i	$-0.612028\pi$
$467$	−14.8992			−0.689451			−0.344726	+	0.938703i	$0.612028\pi$
$468$	2.67900			0.123837
$469$	10.0375			0.463488
$470$	−18.6175	+	5.40855i	−0.858760	+	0.249478i
$471$	19.5891			0.902618
$472$		−	5.76780i		−	0.265484i
$473$	−12.3133			−0.566166
$474$	−16.1609			−0.742293
$475$	14.5965	+	23.0020i	0.669732	+	1.05540i
$476$			12.1110i			0.555108i
$477$		−	13.4490i		−	0.615789i
$478$		−	2.52279i		−	0.115390i
$479$		−	13.8137i		−	0.631164i	−0.948898	−	0.315582i	$-0.897800\pi$
$479$		−	13.8137i		−	0.631164i	0.948898	−	0.315582i	$-0.102200\pi$
$480$	−2.14729	+	0.623809i	−0.0980100	+	0.0284728i
$481$	−16.2088	−	1.68090i	−0.739057	−	0.0766424i
$482$			6.04670i			0.275419i
$483$	−28.0177			−1.27485
$484$	−7.64991			−0.347723
$485$	2.96162	+	10.1946i	0.134480	+	0.462912i
$486$		−	1.00000i		−	0.0453609i
$487$	11.7541			0.532630			0.266315	−	0.963886i	$-0.414194\pi$
$487$	11.7541			0.532630			0.266315	+	0.963886i	$0.414194\pi$
$488$			8.95036i			0.405164i
$489$			13.6370i			0.616684i
$490$	−12.8515	−	44.2378i	−0.580572	−	1.99846i
$491$	12.6999			0.573139			0.286569	−	0.958059i	$-0.407485\pi$
$491$	12.6999			0.573139			0.286569	+	0.958059i	$0.407485\pi$
$492$			3.37727i			0.152259i
$493$		−	11.0065i		−	0.495706i
$494$		−	14.5965i		−	0.656727i
$495$	1.14177	+	3.93024i	0.0513189	+	0.176651i
$496$			7.06915i			0.317414i
$497$			16.5751i			0.743497i
$498$	−14.4854			−0.649104
$499$		−	33.2927i		−	1.49038i	−0.666850	−	0.745192i	$-0.732358\pi$
$499$		−	33.2927i		−	1.49038i	0.666850	−	0.745192i	$-0.267642\pi$
$500$	8.38614	+	7.39409i	0.375040	+	0.330674i
$501$			0.535033i			0.0239035i
$502$			16.4821i			0.735633i
$503$	19.4476			0.867125			0.433563	−	0.901123i	$-0.357256\pi$
$503$	19.4476			0.867125			0.433563	+	0.901123i	$0.357256\pi$
$504$		−	5.25373i		−	0.234020i
$505$	7.32767	+	25.2235i	0.326077	+	1.12243i
$506$	9.76098			0.433929
$507$		−	5.82296i		−	0.258607i
$508$			6.62803i			0.294071i
$509$	−23.2805			−1.03189			−0.515946	−	0.856621i	$-0.672559\pi$
$509$	−23.2805			−1.03189			−0.515946	+	0.856621i	$0.672559\pi$
$510$	4.94999	−	1.43802i	0.219189	−	0.0636766i
$511$	−78.9412			−3.49215
$512$	−1.00000			−0.0441942
$513$	−5.44848			−0.240556
$514$	−4.09511			−0.180628
$515$	−8.81002	−	30.3261i	−0.388216	−	1.33633i
$516$		−	6.72738i		−	0.296157i
$517$			15.8693i			0.697931i
$518$	−3.29638	+	31.7867i	−0.144835	+	1.39663i
$519$	0.202994			0.00891043
$520$	−1.67118	−	5.75259i	−0.0732862	−	0.252268i
$521$	20.5096			0.898544			0.449272	−	0.893395i	$-0.351683\pi$
$521$	20.5096			0.898544			0.449272	+	0.893395i	$0.351683\pi$
$522$			4.77457i			0.208977i
$523$	−30.0162			−1.31252			−0.656259	−	0.754535i	$-0.727862\pi$
$523$	−30.0162			−1.31252			−0.656259	+	0.754535i	$0.727862\pi$
$524$			12.3270i			0.538509i
$525$	−22.1798	+	14.0747i	−0.968006	+	0.614272i
$526$		−	18.6780i		−	0.814401i
$527$		−	16.2960i		−	0.709864i
$528$			1.83033i			0.0796547i
$529$	5.44005			0.236524
$530$	−28.8790	+	8.38963i	−1.25442	+	0.364422i
$531$		−	5.76780i		−	0.250301i
$532$	−28.6249			−1.24105
$533$	−9.04770			−0.391899
$534$	−6.92316			−0.299595
$535$	−33.4382	+	9.71411i	−1.44566	+	0.419977i
$536$		−	1.91054i		−	0.0825230i
$537$	8.40329			0.362629
$538$	2.14866			0.0926354
$539$	−37.7078			−1.62419
$540$	−2.14729	+	0.623809i	−0.0924047	+	0.0268445i
$541$			34.9432i			1.50232i	0.660118	+	0.751162i	$0.270506\pi$
$541$			34.9432i			1.50232i	−0.660118	+	0.751162i	$0.729494\pi$
$542$	−5.65331			−0.242831
$543$		−	18.3262i		−	0.786454i
$544$	2.30522			0.0988357
$545$	6.38981	−	1.85630i	0.273709	−	0.0795152i
$546$	14.0747			0.602343
$547$	35.4031			1.51373			0.756864	−	0.653572i	$-0.226731\pi$
$547$	35.4031			1.51373			0.756864	+	0.653572i	$0.226731\pi$
$548$		−	10.3826i		−	0.443525i
$549$			8.95036i			0.381992i
$550$	7.72713	−	4.90344i	0.329486	−	0.209083i
$551$	26.0141			1.10824
$552$			5.33292i			0.226984i
$553$	−84.9048			−3.61052
$554$	19.6183			0.833502
$555$	13.3832	−	2.42695i	0.568085	−	0.103018i
$556$	20.5051			0.869611
$557$	−25.8595			−1.09570			−0.547851	−	0.836576i	$-0.684554\pi$
$557$	−25.8595			−1.09570			−0.547851	+	0.836576i	$0.684554\pi$
$558$			7.06915i			0.299261i
$559$	18.0227			0.762277
$560$	−11.2813	+	3.27732i	−0.476722	+	0.138492i
$561$		−	4.21931i		−	0.178139i
$562$			10.7651i			0.454100i
$563$	−0.109349			−0.00460850			−0.00230425	−	0.999997i	$-0.500733\pi$
$563$	−0.109349			−0.00460850			−0.00230425	+	0.999997i	$0.500733\pi$
$564$	−8.67021			−0.365082
$565$	−0.147343	−	0.507188i	−0.00619876	−	0.0213376i
$566$	−12.3991			−0.521171
$567$		−	5.25373i		−	0.220636i
$568$	3.15493			0.132378
$569$		−	17.8480i		−	0.748228i	−0.927383	−	0.374114i	$-0.877947\pi$
$569$		−	17.8480i		−	0.748228i	0.927383	−	0.374114i	$-0.122053\pi$
$570$	3.39881	+	11.6995i	0.142361	+	0.490037i
$571$	−33.1409			−1.38690			−0.693451	−	0.720503i	$-0.743911\pi$
$571$	−33.1409			−1.38690			−0.693451	+	0.720503i	$0.743911\pi$
$572$	−4.90344			−0.205023
$573$	16.1070			0.672879
$574$			17.7433i			0.740589i
$575$	22.5141	−	14.2869i	0.938904	−	0.595805i
$576$	−1.00000			−0.0416667
$577$	−0.421635			−0.0175529			−0.00877645	−	0.999961i	$-0.502794\pi$
$577$	−0.421635			−0.0175529			−0.00877645	+	0.999961i	$0.502794\pi$
$578$	11.6859			0.486071
$579$			1.32351i			0.0550034i
$580$	10.2524	−	2.97842i	0.425707	−	0.123672i
$581$	−76.1022			−3.15725
$582$			4.74765i			0.196796i
$583$			24.6161i			1.01950i
$584$			15.0257i			0.621770i
$585$	−1.67118	−	5.75259i	−0.0690949	−	0.237840i
$586$			16.3278i			0.674493i
$587$	−21.3478			−0.881120			−0.440560	−	0.897723i	$-0.645220\pi$
$587$	−21.3478			−0.881120			−0.440560	+	0.897723i	$0.645220\pi$
$588$		−	20.6017i		−	0.849599i
$589$	38.5161			1.58703
$590$	−12.3851	+	3.59800i	−0.509888	+	0.148127i
$591$	7.45206			0.306537
$592$	6.05032	+	0.627436i	0.248666	+	0.0257874i
$593$		−	22.5618i		−	0.926502i	−0.886227	−	0.463251i	$-0.846683\pi$
$593$		−	22.5618i		−	0.926502i	0.886227	−	0.463251i	$-0.153317\pi$
$594$			1.83033i			0.0750992i
$595$	26.0059	−	7.55497i	1.06614	−	0.309723i
$596$	−13.0910			−0.536228
$597$	−14.0906			−0.576692
$598$	−14.2869			−0.584234
$599$	34.7378			1.41935			0.709675	−	0.704530i	$-0.248842\pi$
$599$	34.7378			1.41935			0.709675	+	0.704530i	$0.248842\pi$
$600$	2.67900	+	4.22173i	0.109370	+	0.172351i
$601$	−1.49609			−0.0610270			−0.0305135	−	0.999534i	$-0.509714\pi$
$601$	−1.49609			−0.0610270			−0.0305135	+	0.999534i	$0.509714\pi$
$602$		−	35.3439i		−	1.44051i
$603$		−	1.91054i		−	0.0778034i
$604$	−3.06560			−0.124738
$605$	4.77208	+	16.4266i	0.194013	+	0.667836i
$606$			11.7467i			0.477176i
$607$	17.2029			0.698246			0.349123	−	0.937077i	$-0.386480\pi$
$607$	17.2029			0.698246			0.349123	+	0.937077i	$0.386480\pi$
$608$			5.44848i			0.220965i
$609$			25.0843i			1.01647i
$610$	19.2190	−	5.58331i	0.778156	−	0.226062i
$611$		−	23.2275i		−	0.939683i
$612$	2.30522			0.0931832
$613$			23.3615i			0.943563i	0.881716	+	0.471781i	$0.156389\pi$
$613$			23.3615i			0.943563i	−0.881716	+	0.471781i	$0.843611\pi$
$614$			3.93189i			0.158678i
$615$	7.25198	−	2.10677i	0.292428	−	0.0849531i
$616$			9.61604i			0.387441i
$617$			11.9196i			0.479863i	0.970790	+	0.239932i	$0.0771250\pi$
$617$			11.9196i			0.479863i	−0.970790	+	0.239932i	$0.922875\pi$
$618$		−	14.1230i		−	0.568109i
$619$	17.2127			0.691836			0.345918	−	0.938265i	$-0.387568\pi$
$619$	17.2127			0.691836			0.345918	+	0.938265i	$0.387568\pi$
$620$	15.1795	−	4.40980i	0.609625	−	0.177102i
$621$			5.33292i			0.214003i
$622$		−	11.0216i		−	0.441928i
$623$	−36.3724			−1.45723
$624$		−	2.67900i		−	0.107246i
$625$	10.6459	−	22.6200i	0.425837	−	0.904800i
$626$	−14.8364			−0.592981
$627$	9.97250			0.398263
$628$		−	19.5891i		−	0.781690i
$629$	−13.9473	−	1.44638i	−0.556117	−	0.0576709i
$630$	−11.2813	+	3.27732i	−0.449458	+	0.130572i
$631$			13.4504i			0.535453i	0.963495	+	0.267727i	$0.0862724\pi$
$631$			13.4504i			0.535453i	−0.963495	+	0.267727i	$0.913728\pi$
$632$			16.1609i			0.642844i
$633$		−	5.60670i		−	0.222846i
$634$			17.1800i			0.682306i
$635$	14.2323	−	4.13462i	0.564792	−	0.164078i
$636$	−13.4490			−0.533289
$637$	55.1919			2.18678
$638$		−	8.73901i		−	0.345981i
$639$	3.15493			0.124807
$640$	0.623809	+	2.14729i	0.0246582	+	0.0848792i
$641$	13.3453			0.527107			0.263554	−	0.964645i	$-0.415105\pi$
$641$	13.3453			0.527107			0.263554	+	0.964645i	$0.415105\pi$
$642$	−15.5723			−0.614588
$643$	31.9155			1.25862			0.629312	−	0.777152i	$-0.283337\pi$
$643$	31.9155			1.25862			0.629312	+	0.777152i	$0.283337\pi$
$644$			28.0177i			1.10405i
$645$	−14.4457	+	4.19660i	−0.568797	+	0.165241i
$646$		−	12.5600i		−	0.494166i
$647$	−21.6426			−0.850858			−0.425429	−	0.904992i	$-0.639877\pi$
$647$	−21.6426			−0.850858			−0.425429	+	0.904992i	$0.639877\pi$
$648$	−1.00000			−0.0392837
$649$			10.5569i			0.414396i
$650$	−11.3100	+	7.17704i	−0.443615	+	0.281506i
$651$			37.1394i			1.45561i
$652$	13.6370			0.534064
$653$	−17.8603			−0.698929			−0.349464	−	0.936950i	$-0.613636\pi$
$653$	−17.8603			−0.698929			−0.349464	+	0.936950i	$0.613636\pi$
$654$	2.97575			0.116361
$655$	26.4698	−	7.68972i	1.03426	−	0.300462i
$656$	3.37727			0.131860
$657$			15.0257i			0.586210i
$658$	−45.5509			−1.77576
$659$	24.2533			0.944776			0.472388	−	0.881391i	$-0.343392\pi$
$659$	24.2533			0.944776			0.472388	+	0.881391i	$0.343392\pi$
$660$	3.93024	−	1.14177i	0.152985	−	0.0444435i
$661$			18.8886i			0.734682i	0.930086	+	0.367341i	$0.119732\pi$
$661$			18.8886i			0.734682i	−0.930086	+	0.367341i	$0.880268\pi$
$662$			2.90130i			0.112762i
$663$			6.17569i			0.239844i
$664$			14.4854i			0.562141i
$665$	17.8564	+	61.4659i	0.692443	+	2.38355i
$666$	6.05032	+	0.627436i	0.234445	+	0.0243126i
$667$		−	25.4624i		−	0.985908i
$668$	0.535033			0.0207011
$669$	−14.0077			−0.541570
$670$	−4.10250	+	1.19181i	−0.158493	+	0.0460438i
$671$		−	16.3821i		−	0.632423i
$672$	−5.25373			−0.202667
$673$			1.74070i			0.0670989i	0.999437	+	0.0335495i	$0.0106811\pi$
$673$			1.74070i			0.0670989i	−0.999437	+	0.0335495i	$0.989319\pi$
$674$			6.33337i			0.243952i
$675$	2.67900	+	4.22173i	0.103115	+	0.162494i
$676$	−5.82296			−0.223960
$677$		−	13.8474i		−	0.532200i	−0.963945	−	0.266100i	$-0.914265\pi$
$677$		−	13.8474i		−	0.532200i	0.963945	−	0.266100i	$-0.0857351\pi$
$678$		−	0.236199i		−	0.00907116i
$679$			24.9429i			0.957219i
$680$	−1.43802	−	4.94999i	−0.0551455	−	0.189823i
$681$		−	22.6905i		−	0.869502i
$682$		−	12.9388i		−	0.495454i
$683$	−1.14412			−0.0437784			−0.0218892	−	0.999760i	$-0.506968\pi$
$683$	−1.14412			−0.0437784			−0.0218892	+	0.999760i	$0.506968\pi$
$684$			5.44848i			0.208328i
$685$	−22.2946	+	6.47678i	−0.851832	+	0.247465i
$686$		−	71.4596i		−	2.72834i
$687$			3.84170i			0.146570i
$688$	−6.72738			−0.256479
$689$		−	36.0300i		−	1.37263i
$690$	11.4513	−	3.32672i	0.435945	−	0.126646i
$691$	44.8384			1.70573			0.852867	−	0.522128i	$-0.174862\pi$
$691$	44.8384			1.70573			0.852867	+	0.522128i	$0.174862\pi$
$692$		−	0.202994i		−	0.00771666i
$693$			9.61604i			0.365283i
$694$	23.9733			0.910016
$695$	−12.7913	−	44.0305i	−0.485201	−	1.67017i
$696$	4.77457			0.180980
$697$	−7.78536			−0.294892
$698$	6.41043			0.242638
$699$	−10.9135			−0.412787
$700$	14.0747	+	22.1798i	0.531975	+	0.838318i
$701$		−	19.3674i		−	0.731498i	−0.930713	−	0.365749i	$-0.880813\pi$
$701$		−	19.3674i		−	0.731498i	0.930713	−	0.365749i	$-0.119187\pi$
$702$		−	2.67900i		−	0.101112i
$703$	3.41857	−	32.9650i	0.128934	−	1.24330i
$704$	1.83033			0.0689830
$705$	5.40855	+	18.6175i	0.203698	+	0.701174i
$706$	−10.7349			−0.404015
$707$			61.7138i			2.32099i
$708$	−5.76780			−0.216767
$709$		−	39.0731i		−	1.46742i	−0.679463	−	0.733710i	$-0.737787\pi$
$709$		−	39.0731i		−	1.46742i	0.679463	−	0.733710i	$-0.262213\pi$
$710$	−1.96807	−	6.77455i	−0.0738604	−	0.254244i
$711$			16.1609i			0.606080i
$712$			6.92316i			0.259457i
$713$		−	37.6992i		−	1.41185i
$714$	12.1110			0.453244
$715$	3.05881	+	10.5291i	0.114393	+	0.393767i
$716$		−	8.40329i		−	0.314046i
$717$	−2.52279			−0.0942153
$718$	10.5719			0.394540
$719$	37.5421			1.40009			0.700043	−	0.714101i	$-0.253164\pi$
$719$	37.5421			1.40009			0.700043	+	0.714101i	$0.253164\pi$
$720$	0.623809	+	2.14729i	0.0232480	+	0.0800248i
$721$		−	74.1982i		−	2.76329i
$722$	10.6860			0.397690
$723$	6.04670			0.224879
$724$	−18.3262			−0.681089
$725$	−12.7911	−	20.1569i	−0.475048	−	0.748609i
$726$			7.64991i			0.283915i
$727$	8.90095			0.330118			0.165059	−	0.986284i	$-0.447219\pi$
$727$	8.90095			0.330118			0.165059	+	0.986284i	$0.447219\pi$
$728$		−	14.0747i		−	0.521645i
$729$	−1.00000			−0.0370370
$730$	32.2647	−	9.37319i	1.19417	−	0.346917i
$731$	15.5081			0.573589
$732$	8.95036			0.330815
$733$		−	0.304740i		−	0.0112558i	−0.999984	−	0.00562791i	$-0.998209\pi$
$733$		−	0.304740i		−	0.0112558i	0.999984	−	0.00562791i	$-0.00179143\pi$
$734$		−	12.7249i		−	0.469684i
$735$	−44.2378	+	12.8515i	−1.63174	+	0.474035i
$736$	5.33292			0.196574
$737$			3.49692i			0.128811i
$738$	3.37727			0.124319
$739$	15.8529			0.583158			0.291579	−	0.956547i	$-0.405819\pi$
$739$	15.8529			0.583158			0.291579	+	0.956547i	$0.405819\pi$
$740$	−2.42695	−	13.3832i	−0.0892166	−	0.491976i
$741$	−14.5965			−0.536215
$742$	−70.6576			−2.59392
$743$		−	31.5330i		−	1.15683i	−0.815742	−	0.578417i	$-0.803671\pi$
$743$		−	31.5330i		−	1.15683i	0.815742	−	0.578417i	$-0.196329\pi$
$744$	7.06915			0.259168
$745$	8.16627	+	28.1102i	0.299189	+	1.02988i
$746$		−	20.8664i		−	0.763974i
$747$			14.4854i			0.529991i
$748$	−4.21931			−0.154273
$749$	−81.8124			−2.98936
$750$	7.39409	−	8.38614i	0.269994	−	0.306219i
$751$	−25.2434			−0.921146			−0.460573	−	0.887622i	$-0.652356\pi$
$751$	−25.2434			−0.921146			−0.460573	+	0.887622i	$0.652356\pi$
$752$			8.67021i			0.316170i
$753$	16.4821			0.600642
$754$			12.7911i			0.465823i
$755$	1.91235	+	6.58275i	0.0695976	+	0.239571i
$756$	−5.25373			−0.191076
$757$	2.73559			0.0994266			0.0497133	−	0.998764i	$-0.484169\pi$
$757$	2.73559			0.0994266			0.0497133	+	0.998764i	$0.484169\pi$
$758$	3.99708			0.145181
$759$		−	9.76098i		−	0.354301i
$760$	11.6995	−	3.39881i	0.424385	−	0.123288i
$761$	−37.2963			−1.35199			−0.675994	−	0.736907i	$-0.736286\pi$
$761$	−37.2963			−1.35199			−0.675994	+	0.736907i	$0.736286\pi$
$762$	6.62803			0.240108
$763$	15.6338			0.565982
$764$		−	16.1070i		−	0.582730i
$765$	−1.43802	−	4.94999i	−0.0519917	−	0.178967i
$766$	−28.8603			−1.04277
$767$		−	15.4519i		−	0.557937i
$768$			1.00000i			0.0360844i
$769$			11.2871i			0.407024i	0.979072	+	0.203512i	$0.0652357\pi$
$769$			11.2871i			0.407024i	−0.979072	+	0.203512i	$0.934764\pi$
$770$	20.6484	−	5.99857i	0.744118	−	0.216173i
$771$			4.09511i			0.147482i
$772$	1.32351			0.0476343
$773$			53.7111i			1.93186i	0.258812	+	0.965928i	$0.416669\pi$
$773$			53.7111i			1.93186i	−0.258812	+	0.965928i	$0.583331\pi$
$774$	−6.72738			−0.241811
$775$	−18.9382	−	29.8440i	−0.680282	−	1.07203i
$776$	4.74765			0.170431
$777$	31.7867	+	3.29638i	1.14034	+	0.118257i
$778$			2.05542i			0.0736903i
$779$		−	18.4010i		−	0.659284i
$780$	−5.75259	+	1.67118i	−0.205976	+	0.0598379i
$781$	−5.77454			−0.206629
$782$	−12.2936			−0.439618
$783$	4.77457			0.170629
$784$	−20.6017			−0.735775
$785$	−42.0635	+	12.2198i	−1.50131	+	0.436145i
$786$	12.3270			0.439691
$787$		−	31.5272i		−	1.12382i	−0.827197	−	0.561912i	$-0.810066\pi$
$787$		−	31.5272i		−	1.12382i	0.827197	−	0.561912i	$-0.189934\pi$
$788$		−	7.45206i		−	0.265469i
$789$	−18.6780			−0.664956
$790$	34.7021	−	10.0813i	1.23464	−	0.358676i
$791$		−	1.24093i		−	0.0441222i
$792$	1.83033			0.0650378
$793$			23.9780i			0.851484i
$794$			24.9457i			0.885289i
$795$	8.38963	+	28.8790i	0.297549	+	1.02423i
$796$			14.0906i			0.499430i
$797$	−45.7575			−1.62082			−0.810408	−	0.585866i	$-0.800754\pi$
$797$	−45.7575			−1.62082			−0.810408	+	0.585866i	$0.800754\pi$
$798$			28.6249i			1.01331i
$799$		−	19.9868i		−	0.707081i
$800$	4.22173	−	2.67900i	0.149261	−	0.0947169i
$801$			6.92316i			0.244618i
$802$			17.0242i			0.601147i
$803$		−	27.5020i		−	0.970524i
$804$	−1.91054			−0.0673797
$805$	60.1623	−	17.4777i	2.12044	−	0.616008i
$806$			18.9382i			0.667071i
$807$		−	2.14866i		−	0.0756365i
$808$	11.7467			0.413246
$809$		−	48.5715i		−	1.70768i	−0.520534	−	0.853841i	$-0.674267\pi$
$809$		−	48.5715i		−	1.70768i	0.520534	−	0.853841i	$-0.325733\pi$
$810$	0.623809	+	2.14729i	0.0219184	+	0.0754481i
$811$	−21.1057			−0.741123			−0.370562	−	0.928808i	$-0.620835\pi$
$811$	−21.1057			−0.741123			−0.370562	+	0.928808i	$0.620835\pi$
$812$	25.0843			0.880286
$813$			5.65331i			0.198270i
$814$	−11.0740	−	1.14841i	−0.388145	−	0.0402518i
$815$	−8.50685	−	29.2825i	−0.297982	−	1.02572i
$816$		−	2.30522i		−	0.0806990i
$817$			36.6540i			1.28236i
$818$			6.52138i			0.228015i
$819$		−	14.0747i		−	0.491811i
$820$	−2.10677	−	7.25198i	−0.0735716	−	0.253250i
$821$	13.1695			0.459620			0.229810	−	0.973236i	$-0.426190\pi$
$821$	13.1695			0.459620			0.229810	+	0.973236i	$0.426190\pi$
$822$	−10.3826			−0.362136
$823$		−	2.65133i		−	0.0924196i	−0.998932	−	0.0462098i	$-0.985286\pi$
$823$		−	2.65133i		−	0.0924196i	0.998932	−	0.0462098i	$-0.0147143\pi$
$824$	−14.1230			−0.491996
$825$	−4.90344	−	7.72713i	−0.170716	−	0.269024i
$826$	−30.3025			−1.05436
$827$	−24.0275			−0.835519			−0.417760	−	0.908558i	$-0.637185\pi$
$827$	−24.0275			−0.835519			−0.417760	+	0.908558i	$0.637185\pi$
$828$	5.33292			0.185332
$829$			24.7297i			0.858899i	0.903091	+	0.429449i	$0.141292\pi$
$829$			24.7297i			0.858899i	−0.903091	+	0.429449i	$0.858708\pi$
$830$	31.1043	−	9.03609i	1.07965	−	0.313647i
$831$		−	19.6183i		−	0.680551i
$832$	−2.67900			−0.0928776
$833$	47.4915			1.64548
$834$		−	20.5051i		−	0.710035i
$835$	−0.333758	−	1.14887i	−0.0115502	−	0.0397584i
$836$		−	9.97250i		−	0.344906i
$837$	7.06915			0.244346
$838$	8.70864			0.300835
$839$	23.1044			0.797651			0.398826	−	0.917027i	$-0.369418\pi$
$839$	23.1044			0.797651			0.398826	+	0.917027i	$0.369418\pi$
$840$	3.27732	+	11.2813i	0.113078	+	0.389242i
$841$	6.20350			0.213914
$842$			30.1490i			1.03900i
$843$	10.7651			0.370771
$844$	−5.60670			−0.192990
$845$	3.63242	+	12.5036i	0.124959	+	0.430137i
$846$			8.67021i			0.298088i
$847$			40.1906i			1.38096i
$848$			13.4490i			0.461842i
$849$			12.3991i			0.425535i
$850$	−9.73203	+	6.17569i	−0.333806	+	0.211825i
$851$	−32.2659	−	3.34606i	−1.10606	−	0.114702i
$852$		−	3.15493i		−	0.108086i
$853$	48.8594			1.67291			0.836457	−	0.548033i	$-0.184623\pi$
$853$	48.8594			1.67291			0.836457	+	0.548033i	$0.184623\pi$
$854$	47.0228			1.60909
$855$	11.6995	−	3.39881i	0.400114	−	0.116237i
$856$			15.5723i			0.532249i
$857$	23.3468			0.797512			0.398756	−	0.917057i	$-0.369442\pi$
$857$	23.3468			0.797512			0.398756	+	0.917057i	$0.369442\pi$
$858$			4.90344i			0.167401i
$859$			44.2168i			1.50866i	0.656496	+	0.754330i	$0.272038\pi$
$859$			44.2168i			1.50866i	−0.656496	+	0.754330i	$0.727962\pi$
$860$	4.19660	+	14.4457i	0.143103	+	0.492593i
$861$	17.7433			0.604689
$862$		−	13.4931i		−	0.459575i
$863$			20.4371i			0.695686i	0.937553	+	0.347843i	$0.113086\pi$
$863$			20.4371i			0.695686i	−0.937553	+	0.347843i	$0.886914\pi$
$864$			1.00000i			0.0340207i
$865$	−0.435887	+	0.126629i	−0.0148206	+	0.00430552i
$866$		−	16.6005i		−	0.564108i
$867$		−	11.6859i		−	0.396875i
$868$	37.1394			1.26059
$869$		−	29.5796i		−	1.00342i
$870$	−2.97842	−	10.2524i	−0.100978	−	0.347589i
$871$		−	5.11835i		−	0.173429i
$872$		−	2.97575i		−	0.100772i
$873$	4.74765			0.160683
$874$		−	29.0563i		−	0.982845i
$875$	38.8466	−	44.0585i	1.31325	−	1.48945i
$876$	15.0257			0.507673
$877$		−	14.7403i		−	0.497744i	−0.968536	−	0.248872i	$-0.919940\pi$
$877$		−	14.7403i		−	0.497744i	0.968536	−	0.248872i	$-0.0800598\pi$
$878$			5.27040i			0.177868i
$879$	16.3278			0.550721
$880$	−1.14177	−	3.93024i	−0.0384892	−	0.132488i
$881$	34.7196			1.16973			0.584866	−	0.811130i	$-0.301147\pi$
$881$	34.7196			1.16973			0.584866	+	0.811130i	$0.301147\pi$
$882$	−20.6017			−0.693695
$883$	−19.6446			−0.661094			−0.330547	−	0.943790i	$-0.607233\pi$
$883$	−19.6446			−0.661094			−0.330547	+	0.943790i	$0.607233\pi$
$884$	6.17569			0.207711
$885$	3.59800	+	12.3851i	0.120946	+	0.416322i
$886$			28.9960i			0.974141i
$887$			33.7956i			1.13474i	0.823461	+	0.567372i	$0.192040\pi$
$887$			33.7956i			1.13474i	−0.823461	+	0.567372i	$0.807960\pi$
$888$	0.627436	−	6.05032i	0.0210554	−	0.203035i
$889$	34.8219			1.16789
$890$	14.8661	−	4.31873i	0.498311	−	0.144764i
$891$	1.83033			0.0613182
$892$			14.0077i			0.469013i
$893$	47.2395			1.58081
$894$			13.0910i			0.437828i
$895$	−18.0443	+	5.24204i	−0.603155	+	0.175222i
$896$			5.25373i			0.175515i
$897$			14.2869i			0.477025i
$898$		−	8.02620i		−	0.267838i
$899$	−33.7521			−1.12570
$900$	4.22173	−	2.67900i	0.140724	−	0.0893000i
$901$		−	31.0031i		−	1.03286i
$902$	−6.18150			−0.205821
$903$	−35.3439			−1.17617
$904$	−0.236199			−0.00785586
$905$	11.4321	+	39.3518i	0.380015	+	1.30810i
$906$			3.06560i			0.101848i
$907$	−6.13225			−0.203618			−0.101809	−	0.994804i	$-0.532463\pi$
$907$	−6.13225			−0.203618			−0.101809	+	0.994804i	$0.532463\pi$
$908$	−22.6905			−0.753011
$909$	11.7467			0.389612
$910$	−30.2226	+	8.77995i	−1.00187	+	0.291052i
$911$			7.19615i			0.238419i	0.992869	+	0.119210i	$0.0380360\pi$
$911$			7.19615i			0.238419i	−0.992869	+	0.119210i	$0.961964\pi$
$912$	5.44848			0.180417
$913$		−	26.5129i		−	0.877449i
$914$	12.5165			0.414010
$915$	−5.58331	−	19.2190i	−0.184579	−	0.635361i
$916$	3.84170			0.126933
$917$	64.7630			2.13866
$918$		−	2.30522i		−	0.0760838i
$919$		−	17.7546i		−	0.585669i	−0.956163	−	0.292835i	$-0.905401\pi$
$919$		−	17.7546i		−	0.585669i	0.956163	−	0.292835i	$-0.0945986\pi$
$920$	−3.32672	−	11.4513i	−0.109679	−	0.377539i
$921$	3.93189			0.129560
$922$			36.1735i			1.19131i
$923$	8.45205			0.278203
$924$	9.61604			0.316344
$925$	−27.2237	+	13.5599i	−0.895109	+	0.445848i
$926$	−11.4033			−0.374735
$927$	−14.1230			−0.463859
$928$		−	4.77457i		−	0.156733i
$929$	−25.6404			−0.841233			−0.420616	−	0.907239i	$-0.638186\pi$
$929$	−25.6404			−0.841233			−0.420616	+	0.907239i	$0.638186\pi$
$930$	−4.40980	−	15.1795i	−0.144603	−	0.497756i
$931$			112.248i			3.67878i
$932$			10.9135i			0.357484i
$933$	−11.0216			−0.360833
$934$	14.8992			0.487516
$935$	2.63204	+	9.06009i	0.0860770	+	0.296297i
$936$	−2.67900			−0.0875658
$937$		−	56.6550i		−	1.85084i	−0.378946	−	0.925419i	$-0.623713\pi$
$937$		−	56.6550i		−	1.85084i	0.378946	−	0.925419i	$-0.376287\pi$
$938$	−10.0375			−0.327736
$939$			14.8364i			0.484167i
$940$	18.6175	−	5.40855i	0.607235	−	0.176407i
$941$	24.5485			0.800258			0.400129	−	0.916459i	$-0.368965\pi$
$941$	24.5485			0.800258			0.400129	+	0.916459i	$0.368965\pi$
$942$	−19.5891			−0.638247
$943$	−18.0107			−0.586509
$944$			5.76780i			0.187726i
$945$	3.27732	+	11.2813i	0.106611	+	0.366981i
$946$	12.3133			0.400340
$947$	−40.7070			−1.32280			−0.661400	−	0.750033i	$-0.730037\pi$
$947$	−40.7070			−1.32280			−0.661400	+	0.750033i	$0.730037\pi$
$948$	16.1609			0.524880
$949$			40.2539i			1.30670i
$950$	−14.5965	−	23.0020i	−0.473572	−	0.746283i
$951$	17.1800			0.557101
$952$		−	12.1110i		−	0.392521i
$953$			5.64283i			0.182789i	0.995815	+	0.0913946i	$0.0291325\pi$
$953$			5.64283i			0.182789i	−0.995815	+	0.0913946i	$0.970868\pi$
$954$			13.4490i			0.435429i
$955$	−34.5864	+	10.0477i	−1.11919	+	0.325135i
$956$			2.52279i			0.0815928i
$957$	−8.73901			−0.282492
$958$			13.8137i			0.446300i
$959$	−54.5476			−1.76143
$960$	2.14729	−	0.623809i	0.0693035	−	0.0201333i
$961$	−18.9729			−0.612029
$962$	16.2088	+	1.68090i	0.522592	+	0.0541944i
$963$			15.5723i			0.501809i
$964$		−	6.04670i		−	0.194751i
$965$	−0.825620	−	2.84197i	−0.0265776	−	0.0914863i
$966$	28.0177			0.901456
$967$	−13.0557			−0.419844			−0.209922	−	0.977718i	$-0.567321\pi$
$967$	−13.0557			−0.419844			−0.209922	+	0.977718i	$0.567321\pi$
$968$	7.64991			0.245877
$969$	−12.5600			−0.403485
$970$	−2.96162	−	10.1946i	−0.0950920	−	0.327328i
$971$	1.64483			0.0527851			0.0263925	−	0.999652i	$-0.491598\pi$
$971$	1.64483			0.0527851			0.0263925	+	0.999652i	$0.491598\pi$
$972$			1.00000i			0.0320750i
$973$		−	107.728i		−	3.45362i
$974$	−11.7541			−0.376626
$975$	7.17704	+	11.3100i	0.229849	+	0.362210i
$976$		−	8.95036i		−	0.286494i
$977$	47.4708			1.51872			0.759362	−	0.650668i	$-0.225511\pi$
$977$	47.4708			1.51872			0.759362	+	0.650668i	$0.225511\pi$
$978$		−	13.6370i		−	0.436062i
$979$		−	12.6716i		−	0.404987i
$980$	12.8515	+	44.2378i	0.410527	+	1.41313i
$981$		−	2.97575i		−	0.0950084i
$982$	−12.6999			−0.405270
$983$		−	32.8789i		−	1.04867i	−0.851511	−	0.524337i	$-0.824313\pi$
$983$		−	32.8789i		−	1.04867i	0.851511	−	0.524337i	$-0.175687\pi$
$984$		−	3.37727i		−	0.107663i
$985$	−16.0018	+	4.64866i	−0.509858	+	0.148119i
$986$			11.0065i			0.350517i
$987$			45.5509i			1.44990i
$988$			14.5965i			0.464376i
$989$	35.8766			1.14081
$990$	−1.14177	−	3.93024i	−0.0362879	−	0.124911i
$991$			29.0413i			0.922526i	0.887263	+	0.461263i	$0.152604\pi$
$991$			29.0413i			0.922526i	−0.887263	+	0.461263i	$0.847396\pi$
$992$		−	7.06915i		−	0.224446i
$993$	2.90130			0.0920699
$994$		−	16.5751i		−	0.525732i
$995$	30.2567	−	8.78987i	0.959203	−	0.278658i
$996$	14.4854			0.458986
$997$	32.2039			1.01991			0.509953	−	0.860202i	$-0.329663\pi$
$997$	32.2039			1.01991			0.509953	+	0.860202i	$0.329663\pi$
$998$			33.2927i			1.05386i
$999$	0.627436	−	6.05032i	0.0198512	−	0.191424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.c.739.12	yes	16
3.2	odd	2		3330.2.e.f.739.10		16
5.4	even	2		1110.2.e.d.739.5	yes	16
15.14	odd	2		3330.2.e.e.739.8		16
37.36	even	2		1110.2.e.d.739.13	yes	16
111.110	odd	2		3330.2.e.e.739.7		16
185.184	even	2	inner	1110.2.e.c.739.4	✓	16
555.554	odd	2		3330.2.e.f.739.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.4	✓	16	185.184	even	2	inner
1110.2.e.c.739.12	yes	16	1.1	even	1	trivial
1110.2.e.d.739.5	yes	16	5.4	even	2
1110.2.e.d.739.13	yes	16	37.36	even	2
3330.2.e.e.739.7		16	111.110	odd	2
3330.2.e.e.739.8		16	15.14	odd	2
3330.2.e.f.739.9		16	555.554	odd	2
3330.2.e.f.739.10		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-0.623809 - 2.14729i) q^{5} -1.00000i q^{6} -5.25373i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-0.623809 - 2.14729i) q^{5} -1.00000i q^{6} -5.25373i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(0.623809 + 2.14729i) q^{10} +1.83033 q^{11} +1.00000i q^{12} -2.67900 q^{13} +5.25373i q^{14} +(2.14729 - 0.623809i) q^{15} +1.00000 q^{16} -2.30522 q^{17} +1.00000 q^{18} -5.44848i q^{19} +(-0.623809 - 2.14729i) q^{20} +5.25373 q^{21} -1.83033 q^{22} -5.33292 q^{23} -1.00000i q^{24} +(-4.22173 + 2.67900i) q^{25} +2.67900 q^{26} -1.00000i q^{27} -5.25373i q^{28} +4.77457i q^{29} +(-2.14729 + 0.623809i) q^{30} +7.06915i q^{31} -1.00000 q^{32} +1.83033i q^{33} +2.30522 q^{34} +(-11.2813 + 3.27732i) q^{35} -1.00000 q^{36} +(6.05032 + 0.627436i) q^{37} +5.44848i q^{38} -2.67900i q^{39} +(0.623809 + 2.14729i) q^{40} +3.37727 q^{41} -5.25373 q^{42} -6.72738 q^{43} +1.83033 q^{44} +(0.623809 + 2.14729i) q^{45} +5.33292 q^{46} +8.67021i q^{47} +1.00000i q^{48} -20.6017 q^{49} +(4.22173 - 2.67900i) q^{50} -2.30522i q^{51} -2.67900 q^{52} +13.4490i q^{53} +1.00000i q^{54} +(-1.14177 - 3.93024i) q^{55} +5.25373i q^{56} +5.44848 q^{57} -4.77457i q^{58} +5.76780i q^{59} +(2.14729 - 0.623809i) q^{60} -8.95036i q^{61} -7.06915i q^{62} +5.25373i q^{63} +1.00000 q^{64} +(1.67118 + 5.75259i) q^{65} -1.83033i q^{66} +1.91054i q^{67} -2.30522 q^{68} -5.33292i q^{69} +(11.2813 - 3.27732i) q^{70} -3.15493 q^{71} +1.00000 q^{72} -15.0257i q^{73} +(-6.05032 - 0.627436i) q^{74} +(-2.67900 - 4.22173i) q^{75} -5.44848i q^{76} -9.61604i q^{77} +2.67900i q^{78} -16.1609i q^{79} +(-0.623809 - 2.14729i) q^{80} +1.00000 q^{81} -3.37727 q^{82} -14.4854i q^{83} +5.25373 q^{84} +(1.43802 + 4.94999i) q^{85} +6.72738 q^{86} -4.77457 q^{87} -1.83033 q^{88} -6.92316i q^{89} +(-0.623809 - 2.14729i) q^{90} +14.0747i q^{91} -5.33292 q^{92} -7.06915 q^{93} -8.67021i q^{94} +(-11.6995 + 3.39881i) q^{95} -1.00000i q^{96} -4.74765 q^{97} +20.6017 q^{98} -1.83033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9	\( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 + 6 * q^15 + 16 * q^16 - 38 * q^17 + 16 * q^18 - 2 * q^20 + 6 * q^21 - 2 * q^22 - 20 * q^23 - 4 * q^25 - 6 * q^30 - 16 * q^32 + 38 * q^34 - 10 * q^35 - 16 * q^36 - 4 * q^37 + 2 * q^40 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 2 * q^44 + 2 * q^45 + 20 * q^46 - 18 * q^49 + 4 * q^50 + 20 * q^55 + 16 * q^57 + 6 * q^60 + 16 * q^64 + 12 * q^65 - 38 * q^68 + 10 * q^70 - 24 * q^71 + 16 * q^72 + 4 * q^74 - 2 * q^80 + 16 * q^81 + 6 * q^82 + 6 * q^84 + 2 * q^86 + 2 * q^87 - 2 * q^88 - 2 * q^90 - 20 * q^92 + 22 * q^93 - 16 * q^95 + 38 * q^97 + 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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