LMFDB - Embedded newform 1110.2.e.b.739.2

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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.b.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -3.00000i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -3.00000i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -3.00000 q^{11} +1.00000i q^{12} +4.00000 q^{13} -3.00000i q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} -7.00000 q^{17} -1.00000 q^{18} -4.00000i q^{19} +(-2.00000 - 1.00000i) q^{20} +3.00000 q^{21} -3.00000 q^{22} -6.00000 q^{23} +1.00000i q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} -1.00000i q^{27} -3.00000i q^{28} -9.00000i q^{29} +(1.00000 - 2.00000i) q^{30} -5.00000i q^{31} +1.00000 q^{32} -3.00000i q^{33} -7.00000 q^{34} +(-3.00000 + 6.00000i) q^{35} -1.00000 q^{36} +(-6.00000 + 1.00000i) q^{37} -4.00000i q^{38} +4.00000i q^{39} +(-2.00000 - 1.00000i) q^{40} +7.00000 q^{41} +3.00000 q^{42} -1.00000 q^{43} -3.00000 q^{44} +(2.00000 + 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} +(3.00000 + 4.00000i) q^{50} -7.00000i q^{51} +4.00000 q^{52} -1.00000i q^{53} -1.00000i q^{54} +(6.00000 + 3.00000i) q^{55} -3.00000i q^{56} +4.00000 q^{57} -9.00000i q^{58} +6.00000i q^{59} +(1.00000 - 2.00000i) q^{60} -5.00000i q^{61} -5.00000i q^{62} +3.00000i q^{63} +1.00000 q^{64} +(-8.00000 - 4.00000i) q^{65} -3.00000i q^{66} +2.00000i q^{67} -7.00000 q^{68} -6.00000i q^{69} +(-3.00000 + 6.00000i) q^{70} +12.0000 q^{71} -1.00000 q^{72} +4.00000i q^{73} +(-6.00000 + 1.00000i) q^{74} +(-4.00000 + 3.00000i) q^{75} -4.00000i q^{76} +9.00000i q^{77} +4.00000i q^{78} -4.00000i q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +7.00000 q^{82} +14.0000i q^{83} +3.00000 q^{84} +(14.0000 + 7.00000i) q^{85} -1.00000 q^{86} +9.00000 q^{87} -3.00000 q^{88} +6.00000i q^{89} +(2.00000 + 1.00000i) q^{90} -12.0000i q^{91} -6.00000 q^{92} +5.00000 q^{93} -8.00000i q^{94} +(-4.00000 + 8.00000i) q^{95} +1.00000i q^{96} -7.00000 q^{97} -2.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 8 q^{13} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 2 q^{18} - 4 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{25} + 8 q^{26} + 2 q^{30} + 2 q^{32} - 14 q^{34} - 6 q^{35} - 2 q^{36} - 12 q^{37} - 4 q^{40} + 14 q^{41} + 6 q^{42} - 2 q^{43} - 6 q^{44} + 4 q^{45} - 12 q^{46} - 4 q^{49} + 6 q^{50} + 8 q^{52} + 12 q^{55} + 8 q^{57} + 2 q^{60} + 2 q^{64} - 16 q^{65} - 14 q^{68} - 6 q^{70} + 24 q^{71} - 2 q^{72} - 12 q^{74} - 8 q^{75} - 4 q^{80} + 2 q^{81} + 14 q^{82} + 6 q^{84} + 28 q^{85} - 2 q^{86} + 18 q^{87} - 6 q^{88} + 4 q^{90} - 12 q^{92} + 10 q^{93} - 8 q^{95} - 14 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 8 * q^13 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 2 * q^18 - 4 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^25 + 8 * q^26 + 2 * q^30 + 2 * q^32 - 14 * q^34 - 6 * q^35 - 2 * q^36 - 12 * q^37 - 4 * q^40 + 14 * q^41 + 6 * q^42 - 2 * q^43 - 6 * q^44 + 4 * q^45 - 12 * q^46 - 4 * q^49 + 6 * q^50 + 8 * q^52 + 12 * q^55 + 8 * q^57 + 2 * q^60 + 2 * q^64 - 16 * q^65 - 14 * q^68 - 6 * q^70 + 24 * q^71 - 2 * q^72 - 12 * q^74 - 8 * q^75 - 4 * q^80 + 2 * q^81 + 14 * q^82 + 6 * q^84 + 28 * q^85 - 2 * q^86 + 18 * q^87 - 6 * q^88 + 4 * q^90 - 12 * q^92 + 10 * q^93 - 8 * q^95 - 14 * q^97 - 4 * q^98 + 6 * 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
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$			1.00000i			0.408248i
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	−2.00000	−	1.00000i	−0.632456	−	0.316228i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$			1.00000i			0.288675i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		−	3.00000i		−	0.801784i
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	1.00000			0.250000
$17$	−7.00000			−1.69775			−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000			−1.69775			−0.848875	+	0.528594i	$0.822719\pi$
$18$	−1.00000			−0.235702
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	3.00000			0.654654
$22$	−3.00000			−0.639602
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$			1.00000i			0.204124i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$		−	1.00000i		−	0.192450i
$28$		−	3.00000i		−	0.566947i
$29$		−	9.00000i		−	1.67126i	−0.549294	−	0.835629i	$-0.685103\pi$
$29$		−	9.00000i		−	1.67126i	0.549294	−	0.835629i	$-0.314897\pi$
$30$	1.00000	−	2.00000i	0.182574	−	0.365148i
$31$		−	5.00000i		−	0.898027i	−0.893525	−	0.449013i	$-0.851776\pi$
$31$		−	5.00000i		−	0.898027i	0.893525	−	0.449013i	$-0.148224\pi$
$32$	1.00000			0.176777
$33$		−	3.00000i		−	0.522233i
$34$	−7.00000			−1.20049
$35$	−3.00000	+	6.00000i	−0.507093	+	1.01419i
$36$	−1.00000			−0.166667
$37$	−6.00000	+	1.00000i	−0.986394	+	0.164399i
$37$	−6.00000	+	1.00000i	−0.986394	+	0.164399i
$38$		−	4.00000i		−	0.648886i
$39$			4.00000i			0.640513i
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	3.00000			0.462910
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−3.00000			−0.452267
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	−6.00000			−0.884652
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$			1.00000i			0.144338i
$49$	−2.00000			−0.285714
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$		−	7.00000i		−	0.980196i
$52$	4.00000			0.554700
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$		−	1.00000i		−	0.136083i
$55$	6.00000	+	3.00000i	0.809040	+	0.404520i
$56$		−	3.00000i		−	0.400892i
$57$	4.00000			0.529813
$58$		−	9.00000i		−	1.18176i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$		−	5.00000i		−	0.640184i	−0.947386	−	0.320092i	$-0.896286\pi$
$61$		−	5.00000i		−	0.640184i	0.947386	−	0.320092i	$-0.103714\pi$
$62$		−	5.00000i		−	0.635001i
$63$			3.00000i			0.377964i
$64$	1.00000			0.125000
$65$	−8.00000	−	4.00000i	−0.992278	−	0.496139i
$66$		−	3.00000i		−	0.369274i
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	−7.00000			−0.848875
$69$		−	6.00000i		−	0.722315i
$70$	−3.00000	+	6.00000i	−0.358569	+	0.717137i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.00000			−0.117851
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−6.00000	+	1.00000i	−0.697486	+	0.116248i
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$		−	4.00000i		−	0.458831i
$77$			9.00000i			1.02565i
$78$			4.00000i			0.452911i
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$	7.00000			0.773021
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$	3.00000			0.327327
$85$	14.0000	+	7.00000i	1.51851	+	0.759257i
$86$	−1.00000			−0.107833
$87$	9.00000			0.964901
$88$	−3.00000			−0.319801
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$	2.00000	+	1.00000i	0.210819	+	0.105409i
$91$		−	12.0000i		−	1.25794i
$92$	−6.00000			−0.625543
$93$	5.00000			0.518476
$94$		−	8.00000i		−	0.825137i
$95$	−4.00000	+	8.00000i	−0.410391	+	0.820783i
$96$			1.00000i			0.102062i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−2.00000			−0.202031
$99$	3.00000			0.301511
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$		−	7.00000i		−	0.693103i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	4.00000			0.392232
$105$	−6.00000	−	3.00000i	−0.585540	−	0.292770i
$106$		−	1.00000i		−	0.0971286i
$107$		−	18.0000i		−	1.74013i	−0.492941	−	0.870063i	$-0.664078\pi$
$107$		−	18.0000i		−	1.74013i	0.492941	−	0.870063i	$-0.335922\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			11.0000i			1.05361i	0.849987	+	0.526804i	$0.176610\pi$
$109$			11.0000i			1.05361i	−0.849987	+	0.526804i	$0.823390\pi$
$110$	6.00000	+	3.00000i	0.572078	+	0.286039i
$111$	−1.00000	−	6.00000i	−0.0949158	−	0.569495i
$112$		−	3.00000i		−	0.283473i
$113$	−1.00000			−0.0940721			−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000			−0.0940721			−0.0470360	+	0.998893i	$0.514978\pi$
$114$	4.00000			0.374634
$115$	12.0000	+	6.00000i	1.11901	+	0.559503i
$116$		−	9.00000i		−	0.835629i
$117$	−4.00000			−0.369800
$118$			6.00000i			0.552345i
$119$			21.0000i			1.92507i
$120$	1.00000	−	2.00000i	0.0912871	−	0.182574i
$121$	−2.00000			−0.181818
$122$		−	5.00000i		−	0.452679i
$123$			7.00000i			0.631169i
$124$		−	5.00000i		−	0.449013i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$			3.00000i			0.267261i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	1.00000			0.0883883
$129$		−	1.00000i		−	0.0880451i
$130$	−8.00000	−	4.00000i	−0.701646	−	0.350823i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		−	3.00000i		−	0.261116i
$133$	−12.0000			−1.04053
$134$			2.00000i			0.172774i
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$	−7.00000			−0.600245
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−15.0000			−1.27228			−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000			−1.27228			−0.636142	+	0.771572i	$0.719471\pi$
$140$	−3.00000	+	6.00000i	−0.253546	+	0.507093i
$141$	8.00000			0.673722
$142$	12.0000			1.00702
$143$	−12.0000			−1.00349
$144$	−1.00000			−0.0833333
$145$	−9.00000	+	18.0000i	−0.747409	+	1.49482i
$146$			4.00000i			0.331042i
$147$		−	2.00000i		−	0.164957i
$148$	−6.00000	+	1.00000i	−0.493197	+	0.0821995i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	−4.00000	+	3.00000i	−0.326599	+	0.244949i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		−	4.00000i		−	0.324443i
$153$	7.00000			0.565916
$154$			9.00000i			0.725241i
$155$	−5.00000	+	10.0000i	−0.401610	+	0.803219i
$156$			4.00000i			0.320256i
$157$			7.00000i			0.558661i	0.960195	+	0.279330i	$0.0901125\pi$
$157$			7.00000i			0.558661i	−0.960195	+	0.279330i	$0.909888\pi$
$158$		−	4.00000i		−	0.318223i
$159$	1.00000			0.0793052
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$			18.0000i			1.41860i
$162$	1.00000			0.0785674
$163$	9.00000			0.704934			0.352467	−	0.935824i	$-0.385343\pi$
$163$	9.00000			0.704934			0.352467	+	0.935824i	$0.385343\pi$
$164$	7.00000			0.546608
$165$	−3.00000	+	6.00000i	−0.233550	+	0.467099i
$166$			14.0000i			1.08661i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	3.00000			0.231455
$169$	3.00000			0.230769
$170$	14.0000	+	7.00000i	1.07375	+	0.536875i
$171$			4.00000i			0.305888i
$172$	−1.00000			−0.0762493
$173$			9.00000i			0.684257i	0.939653	+	0.342129i	$0.111148\pi$
$173$			9.00000i			0.684257i	−0.939653	+	0.342129i	$0.888852\pi$
$174$	9.00000			0.682288
$175$	12.0000	−	9.00000i	0.907115	−	0.680336i
$176$	−3.00000			−0.226134
$177$	−6.00000			−0.450988
$178$			6.00000i			0.449719i
$179$		−	4.00000i		−	0.298974i	−0.988764	−	0.149487i	$-0.952238\pi$
$179$		−	4.00000i		−	0.298974i	0.988764	−	0.149487i	$-0.0477622\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		−	12.0000i		−	0.889499i
$183$	5.00000			0.369611
$184$	−6.00000			−0.442326
$185$	13.0000	+	4.00000i	0.955779	+	0.294086i
$186$	5.00000			0.366618
$187$	21.0000			1.53567
$188$		−	8.00000i		−	0.583460i
$189$	−3.00000			−0.218218
$190$	−4.00000	+	8.00000i	−0.290191	+	0.580381i
$191$		−	15.0000i		−	1.08536i	−0.839939	−	0.542681i	$-0.817409\pi$
$191$		−	15.0000i		−	1.08536i	0.839939	−	0.542681i	$-0.182591\pi$
$192$			1.00000i			0.0721688i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−7.00000			−0.502571
$195$	4.00000	−	8.00000i	0.286446	−	0.572892i
$196$	−2.00000			−0.142857
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	3.00000			0.213201
$199$			16.0000i			1.13421i	0.823646	+	0.567105i	$0.191937\pi$
$199$			16.0000i			1.13421i	−0.823646	+	0.567105i	$0.808063\pi$
$200$	3.00000	+	4.00000i	0.212132	+	0.282843i
$201$	−2.00000			−0.141069
$202$	2.00000			0.140720
$203$	−27.0000			−1.89503
$204$		−	7.00000i		−	0.490098i
$205$	−14.0000	−	7.00000i	−0.977802	−	0.488901i
$206$	14.0000			0.975426
$207$	6.00000			0.417029
$208$	4.00000			0.277350
$209$			12.0000i			0.830057i
$210$	−6.00000	−	3.00000i	−0.414039	−	0.207020i
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		−	1.00000i		−	0.0686803i
$213$			12.0000i			0.822226i
$214$		−	18.0000i		−	1.23045i
$215$	2.00000	+	1.00000i	0.136399	+	0.0681994i
$216$		−	1.00000i		−	0.0680414i
$217$	−15.0000			−1.01827
$218$			11.0000i			0.745014i
$219$	−4.00000			−0.270295
$220$	6.00000	+	3.00000i	0.404520	+	0.202260i
$221$	−28.0000			−1.88348
$222$	−1.00000	−	6.00000i	−0.0671156	−	0.402694i
$223$		−	11.0000i		−	0.736614i	−0.929704	−	0.368307i	$-0.879937\pi$
$223$		−	11.0000i		−	0.736614i	0.929704	−	0.368307i	$-0.120063\pi$
$224$		−	3.00000i		−	0.200446i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−1.00000			−0.0665190
$227$	13.0000			0.862840			0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000			0.862840			0.431420	+	0.902151i	$0.358013\pi$
$228$	4.00000			0.264906
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	12.0000	+	6.00000i	0.791257	+	0.395628i
$231$	−9.00000			−0.592157
$232$		−	9.00000i		−	0.590879i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	−4.00000			−0.261488
$235$	−8.00000	+	16.0000i	−0.521862	+	1.04372i
$236$			6.00000i			0.390567i
$237$	4.00000			0.259828
$238$			21.0000i			1.36123i
$239$		−	9.00000i		−	0.582162i	−0.956698	−	0.291081i	$-0.905985\pi$
$239$		−	9.00000i		−	0.582162i	0.956698	−	0.291081i	$-0.0940149\pi$
$240$	1.00000	−	2.00000i	0.0645497	−	0.129099i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−2.00000			−0.128565
$243$			1.00000i			0.0641500i
$244$		−	5.00000i		−	0.320092i
$245$	4.00000	+	2.00000i	0.255551	+	0.127775i
$246$			7.00000i			0.446304i
$247$		−	16.0000i		−	1.01806i
$248$		−	5.00000i		−	0.317500i
$249$	−14.0000			−0.887214
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$			20.0000i			1.26239i	0.775625	+	0.631194i	$0.217435\pi$
$251$			20.0000i			1.26239i	−0.775625	+	0.631194i	$0.782565\pi$
$252$			3.00000i			0.188982i
$253$	18.0000			1.13165
$254$		−	8.00000i		−	0.501965i
$255$	−7.00000	+	14.0000i	−0.438357	+	0.876714i
$256$	1.00000			0.0625000
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		−	1.00000i		−	0.0622573i
$259$	3.00000	+	18.0000i	0.186411	+	1.11847i
$260$	−8.00000	−	4.00000i	−0.496139	−	0.248069i
$261$			9.00000i			0.557086i
$262$		0			0
$263$		−	31.0000i		−	1.91154i	−0.294112	−	0.955771i	$-0.595024\pi$
$263$		−	31.0000i		−	1.91154i	0.294112	−	0.955771i	$-0.404976\pi$
$264$		−	3.00000i		−	0.184637i
$265$	−1.00000	+	2.00000i	−0.0614295	+	0.122859i
$266$	−12.0000			−0.735767
$267$	−6.00000			−0.367194
$268$			2.00000i			0.122169i
$269$	20.0000			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$269$	20.0000			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$270$	−1.00000	+	2.00000i	−0.0608581	+	0.121716i
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	−7.00000			−0.424437
$273$	12.0000			0.726273
$274$			12.0000i			0.724947i
$275$	−9.00000	−	12.0000i	−0.542720	−	0.723627i
$276$		−	6.00000i		−	0.361158i
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$	−15.0000			−0.899640
$279$			5.00000i			0.299342i
$280$	−3.00000	+	6.00000i	−0.179284	+	0.358569i
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	8.00000			0.476393
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$	12.0000			0.712069
$285$	−8.00000	−	4.00000i	−0.473879	−	0.236940i
$286$	−12.0000			−0.709575
$287$		−	21.0000i		−	1.23959i
$288$	−1.00000			−0.0589256
$289$	32.0000			1.88235
$290$	−9.00000	+	18.0000i	−0.528498	+	1.05700i
$291$		−	7.00000i		−	0.410347i
$292$			4.00000i			0.234082i
$293$			29.0000i			1.69420i	0.531435	+	0.847099i	$0.321653\pi$
$293$			29.0000i			1.69420i	−0.531435	+	0.847099i	$0.678347\pi$
$294$		−	2.00000i		−	0.116642i
$295$	6.00000	−	12.0000i	0.349334	−	0.698667i
$296$	−6.00000	+	1.00000i	−0.348743	+	0.0581238i
$297$			3.00000i			0.174078i
$298$		0			0
$299$	−24.0000			−1.38796
$300$	−4.00000	+	3.00000i	−0.230940	+	0.173205i
$301$			3.00000i			0.172917i
$302$	2.00000			0.115087
$303$			2.00000i			0.114897i
$304$		−	4.00000i		−	0.229416i
$305$	−5.00000	+	10.0000i	−0.286299	+	0.572598i
$306$	7.00000			0.400163
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$			9.00000i			0.512823i
$309$			14.0000i			0.796432i
$310$	−5.00000	+	10.0000i	−0.283981	+	0.567962i
$311$			15.0000i			0.850572i	0.905059	+	0.425286i	$0.139826\pi$
$311$			15.0000i			0.850572i	−0.905059	+	0.425286i	$0.860174\pi$
$312$			4.00000i			0.226455i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$			7.00000i			0.395033i
$315$	3.00000	−	6.00000i	0.169031	−	0.338062i
$316$		−	4.00000i		−	0.225018i
$317$			27.0000i			1.51647i	0.651981	+	0.758236i	$0.273938\pi$
$317$			27.0000i			1.51647i	−0.651981	+	0.758236i	$0.726062\pi$
$318$	1.00000			0.0560772
$319$			27.0000i			1.51171i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	18.0000			1.00466
$322$			18.0000i			1.00310i
$323$			28.0000i			1.55796i
$324$	1.00000			0.0555556
$325$	12.0000	+	16.0000i	0.665640	+	0.887520i
$326$	9.00000			0.498464
$327$	−11.0000			−0.608301
$328$	7.00000			0.386510
$329$	−24.0000			−1.32316
$330$	−3.00000	+	6.00000i	−0.165145	+	0.330289i
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$			14.0000i			0.768350i
$333$	6.00000	−	1.00000i	0.328798	−	0.0547997i
$334$	−12.0000			−0.656611
$335$	2.00000	−	4.00000i	0.109272	−	0.218543i
$336$	3.00000			0.163663
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$	3.00000			0.163178
$339$		−	1.00000i		−	0.0543125i
$340$	14.0000	+	7.00000i	0.759257	+	0.379628i
$341$			15.0000i			0.812296i
$342$			4.00000i			0.216295i
$343$		−	15.0000i		−	0.809924i
$344$	−1.00000			−0.0539164
$345$	−6.00000	+	12.0000i	−0.323029	+	0.646058i
$346$			9.00000i			0.483843i
$347$	28.0000			1.50312			0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000			1.50312			0.751559	+	0.659665i	$0.229302\pi$
$348$	9.00000			0.482451
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	12.0000	−	9.00000i	0.641427	−	0.481070i
$351$		−	4.00000i		−	0.213504i
$352$	−3.00000			−0.159901
$353$	−31.0000			−1.64996			−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000			−1.64996			−0.824982	+	0.565159i	$0.808815\pi$
$354$	−6.00000			−0.318896
$355$	−24.0000	−	12.0000i	−1.27379	−	0.636894i
$356$			6.00000i			0.317999i
$357$	−21.0000			−1.11144
$358$		−	4.00000i		−	0.211407i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	2.00000	+	1.00000i	0.105409	+	0.0527046i
$361$	3.00000			0.157895
$362$	−18.0000			−0.946059
$363$		−	2.00000i		−	0.104973i
$364$		−	12.0000i		−	0.628971i
$365$	4.00000	−	8.00000i	0.209370	−	0.418739i
$366$	5.00000			0.261354
$367$		−	23.0000i		−	1.20059i	−0.799779	−	0.600295i	$-0.795050\pi$
$367$		−	23.0000i		−	1.20059i	0.799779	−	0.600295i	$-0.204950\pi$
$368$	−6.00000			−0.312772
$369$	−7.00000			−0.364405
$370$	13.0000	+	4.00000i	0.675838	+	0.207950i
$371$	−3.00000			−0.155752
$372$	5.00000			0.259238
$373$			14.0000i			0.724893i	0.932005	+	0.362446i	$0.118058\pi$
$373$			14.0000i			0.724893i	−0.932005	+	0.362446i	$0.881942\pi$
$374$	21.0000			1.08588
$375$	11.0000	−	2.00000i	0.568038	−	0.103280i
$376$		−	8.00000i		−	0.412568i
$377$		−	36.0000i		−	1.85409i
$378$	−3.00000			−0.154303
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−4.00000	+	8.00000i	−0.205196	+	0.410391i
$381$	8.00000			0.409852
$382$		−	15.0000i		−	0.767467i
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$			1.00000i			0.0510310i
$385$	9.00000	−	18.0000i	0.458682	−	0.917365i
$386$	14.0000			0.712581
$387$	1.00000			0.0508329
$388$	−7.00000			−0.355371
$389$			31.0000i			1.57176i	0.618378	+	0.785881i	$0.287790\pi$
$389$			31.0000i			1.57176i	−0.618378	+	0.785881i	$0.712210\pi$
$390$	4.00000	−	8.00000i	0.202548	−	0.405096i
$391$	42.0000			2.12403
$392$	−2.00000			−0.101015
$393$		0			0
$394$		−	18.0000i		−	0.906827i
$395$	−4.00000	+	8.00000i	−0.201262	+	0.402524i
$396$	3.00000			0.150756
$397$		−	38.0000i		−	1.90717i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$		−	38.0000i		−	1.90717i	0.301131	−	0.953583i	$-0.402636\pi$
$398$			16.0000i			0.802008i
$399$		−	12.0000i		−	0.600751i
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$		−	10.0000i		−	0.499376i	−0.968326	−	0.249688i	$-0.919672\pi$
$401$		−	10.0000i		−	0.499376i	0.968326	−	0.249688i	$-0.0803281\pi$
$402$	−2.00000			−0.0997509
$403$		−	20.0000i		−	0.996271i
$404$	2.00000			0.0995037
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$	−27.0000			−1.33999
$407$	18.0000	−	3.00000i	0.892227	−	0.148704i
$408$		−	7.00000i		−	0.346552i
$409$		−	14.0000i		−	0.692255i	−0.938187	−	0.346128i	$-0.887496\pi$
$409$		−	14.0000i		−	0.692255i	0.938187	−	0.346128i	$-0.112504\pi$
$410$	−14.0000	−	7.00000i	−0.691411	−	0.345705i
$411$	−12.0000			−0.591916
$412$	14.0000			0.689730
$413$	18.0000			0.885722
$414$	6.00000			0.294884
$415$	14.0000	−	28.0000i	0.687233	−	1.37447i
$416$	4.00000			0.196116
$417$		−	15.0000i		−	0.734553i
$418$			12.0000i			0.586939i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−6.00000	−	3.00000i	−0.292770	−	0.146385i
$421$			30.0000i			1.46211i	0.682318	+	0.731055i	$0.260972\pi$
$421$			30.0000i			1.46211i	−0.682318	+	0.731055i	$0.739028\pi$
$422$	−13.0000			−0.632830
$423$			8.00000i			0.388973i
$424$		−	1.00000i		−	0.0485643i
$425$	−21.0000	−	28.0000i	−1.01865	−	1.35820i
$426$			12.0000i			0.581402i
$427$	−15.0000			−0.725901
$428$		−	18.0000i		−	0.870063i
$429$		−	12.0000i		−	0.579365i
$430$	2.00000	+	1.00000i	0.0964486	+	0.0482243i
$431$		−	25.0000i		−	1.20421i	−0.798418	−	0.602104i	$-0.794329\pi$
$431$		−	25.0000i		−	1.20421i	0.798418	−	0.602104i	$-0.205671\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			34.0000i			1.63394i	0.576683	+	0.816968i	$0.304347\pi$
$433$			34.0000i			1.63394i	−0.576683	+	0.816968i	$0.695653\pi$
$434$	−15.0000			−0.720023
$435$	−18.0000	−	9.00000i	−0.863034	−	0.431517i
$436$			11.0000i			0.526804i
$437$			24.0000i			1.14808i
$438$	−4.00000			−0.191127
$439$		−	9.00000i		−	0.429547i	−0.976664	−	0.214773i	$-0.931099\pi$
$439$		−	9.00000i		−	0.429547i	0.976664	−	0.214773i	$-0.0689013\pi$
$440$	6.00000	+	3.00000i	0.286039	+	0.143019i
$441$	2.00000			0.0952381
$442$	−28.0000			−1.33182
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	−1.00000	−	6.00000i	−0.0474579	−	0.284747i
$445$	6.00000	−	12.0000i	0.284427	−	0.568855i
$446$		−	11.0000i		−	0.520865i
$447$		0			0
$448$		−	3.00000i		−	0.141737i
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$	−3.00000	−	4.00000i	−0.141421	−	0.188562i
$451$	−21.0000			−0.988851
$452$	−1.00000			−0.0470360
$453$			2.00000i			0.0939682i
$454$	13.0000			0.610120
$455$	−12.0000	+	24.0000i	−0.562569	+	1.12514i
$456$	4.00000			0.187317
$457$	13.0000			0.608114			0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000			0.608114			0.304057	+	0.952654i	$0.401659\pi$
$458$	10.0000			0.467269
$459$			7.00000i			0.326732i
$460$	12.0000	+	6.00000i	0.559503	+	0.279751i
$461$			25.0000i			1.16437i	0.813058	+	0.582183i	$0.197801\pi$
$461$			25.0000i			1.16437i	−0.813058	+	0.582183i	$0.802199\pi$
$462$	−9.00000			−0.418718
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$		−	9.00000i		−	0.417815i
$465$	−10.0000	−	5.00000i	−0.463739	−	0.231869i
$466$		−	6.00000i		−	0.277945i
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$	−4.00000			−0.184900
$469$	6.00000			0.277054
$470$	−8.00000	+	16.0000i	−0.369012	+	0.738025i
$471$	−7.00000			−0.322543
$472$			6.00000i			0.276172i
$473$	3.00000			0.137940
$474$	4.00000			0.183726
$475$	16.0000	−	12.0000i	0.734130	−	0.550598i
$476$			21.0000i			0.962533i
$477$			1.00000i			0.0457869i
$478$		−	9.00000i		−	0.411650i
$479$		−	24.0000i		−	1.09659i	−0.836286	−	0.548294i	$-0.815277\pi$
$479$		−	24.0000i		−	1.09659i	0.836286	−	0.548294i	$-0.184723\pi$
$480$	1.00000	−	2.00000i	0.0456435	−	0.0912871i
$481$	−24.0000	+	4.00000i	−1.09431	+	0.182384i
$482$		0			0
$483$	−18.0000			−0.819028
$484$	−2.00000			−0.0909091
$485$	14.0000	+	7.00000i	0.635707	+	0.317854i
$486$			1.00000i			0.0453609i
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$		−	5.00000i		−	0.226339i
$489$			9.00000i			0.406994i
$490$	4.00000	+	2.00000i	0.180702	+	0.0903508i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$			7.00000i			0.315584i
$493$			63.0000i			2.83738i
$494$		−	16.0000i		−	0.719874i
$495$	−6.00000	−	3.00000i	−0.269680	−	0.134840i
$496$		−	5.00000i		−	0.224507i
$497$		−	36.0000i		−	1.61482i
$498$	−14.0000			−0.627355
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$		−	12.0000i		−	0.536120i
$502$			20.0000i			0.892644i
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$			3.00000i			0.133631i
$505$	−4.00000	−	2.00000i	−0.177998	−	0.0889988i
$506$	18.0000			0.800198
$507$			3.00000i			0.133235i
$508$		−	8.00000i		−	0.354943i
$509$	−10.0000			−0.443242			−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000			−0.443242			−0.221621	+	0.975133i	$0.571135\pi$
$510$	−7.00000	+	14.0000i	−0.309965	+	0.619930i
$511$	12.0000			0.530849
$512$	1.00000			0.0441942
$513$	−4.00000			−0.176604
$514$	18.0000			0.793946
$515$	−28.0000	−	14.0000i	−1.23383	−	0.616914i
$516$		−	1.00000i		−	0.0440225i
$517$			24.0000i			1.05552i
$518$	3.00000	+	18.0000i	0.131812	+	0.790875i
$519$	−9.00000			−0.395056
$520$	−8.00000	−	4.00000i	−0.350823	−	0.175412i
$521$	37.0000			1.62100			0.810500	−	0.585739i	$-0.199196\pi$
$521$	37.0000			1.62100			0.810500	+	0.585739i	$0.199196\pi$
$522$			9.00000i			0.393919i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$		0			0
$525$	9.00000	+	12.0000i	0.392792	+	0.523723i
$526$		−	31.0000i		−	1.35166i
$527$			35.0000i			1.52462i
$528$		−	3.00000i		−	0.130558i
$529$	13.0000			0.565217
$530$	−1.00000	+	2.00000i	−0.0434372	+	0.0868744i
$531$		−	6.00000i		−	0.260378i
$532$	−12.0000			−0.520266
$533$	28.0000			1.21281
$534$	−6.00000			−0.259645
$535$	−18.0000	+	36.0000i	−0.778208	+	1.55642i
$536$			2.00000i			0.0863868i
$537$	4.00000			0.172613
$538$	20.0000			0.862261
$539$	6.00000			0.258438
$540$	−1.00000	+	2.00000i	−0.0430331	+	0.0860663i
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$	22.0000			0.944981
$543$		−	18.0000i		−	0.772454i
$544$	−7.00000			−0.300123
$545$	11.0000	−	22.0000i	0.471188	−	0.942376i
$546$	12.0000			0.513553
$547$	23.0000			0.983409			0.491704	−	0.870762i	$-0.336374\pi$
$547$	23.0000			0.983409			0.491704	+	0.870762i	$0.336374\pi$
$548$			12.0000i			0.512615i
$549$			5.00000i			0.213395i
$550$	−9.00000	−	12.0000i	−0.383761	−	0.511682i
$551$	−36.0000			−1.53365
$552$		−	6.00000i		−	0.255377i
$553$	−12.0000			−0.510292
$554$	28.0000			1.18961
$555$	−4.00000	+	13.0000i	−0.169791	+	0.551819i
$556$	−15.0000			−0.636142
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$			5.00000i			0.211667i
$559$	−4.00000			−0.169182
$560$	−3.00000	+	6.00000i	−0.126773	+	0.253546i
$561$			21.0000i			0.886621i
$562$		−	30.0000i		−	1.26547i
$563$	−21.0000			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$564$	8.00000			0.336861
$565$	2.00000	+	1.00000i	0.0841406	+	0.0420703i
$566$	4.00000			0.168133
$567$		−	3.00000i		−	0.125988i
$568$	12.0000			0.503509
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$	−8.00000	−	4.00000i	−0.335083	−	0.167542i
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	−12.0000			−0.501745
$573$	15.0000			0.626634
$574$		−	21.0000i		−	0.876523i
$575$	−18.0000	−	24.0000i	−0.750652	−	1.00087i
$576$	−1.00000			−0.0416667
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$	32.0000			1.33102
$579$			14.0000i			0.581820i
$580$	−9.00000	+	18.0000i	−0.373705	+	0.747409i
$581$	42.0000			1.74245
$582$		−	7.00000i		−	0.290159i
$583$			3.00000i			0.124247i
$584$			4.00000i			0.165521i
$585$	8.00000	+	4.00000i	0.330759	+	0.165380i
$586$			29.0000i			1.19798i
$587$	−47.0000			−1.93990			−0.969949	−	0.243309i	$-0.921767\pi$
$587$	−47.0000			−1.93990			−0.969949	+	0.243309i	$0.921767\pi$
$588$		−	2.00000i		−	0.0824786i
$589$	−20.0000			−0.824086
$590$	6.00000	−	12.0000i	0.247016	−	0.494032i
$591$	18.0000			0.740421
$592$	−6.00000	+	1.00000i	−0.246598	+	0.0410997i
$593$		−	46.0000i		−	1.88899i	−0.328521	−	0.944497i	$-0.606550\pi$
$593$		−	46.0000i		−	1.88899i	0.328521	−	0.944497i	$-0.393450\pi$
$594$			3.00000i			0.123091i
$595$	21.0000	−	42.0000i	0.860916	−	1.72183i
$596$		0			0
$597$	−16.0000			−0.654836
$598$	−24.0000			−0.981433
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	−4.00000	+	3.00000i	−0.163299	+	0.122474i
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$			3.00000i			0.122271i
$603$		−	2.00000i		−	0.0814463i
$604$	2.00000			0.0813788
$605$	4.00000	+	2.00000i	0.162623	+	0.0813116i
$606$			2.00000i			0.0812444i
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$		−	4.00000i		−	0.162221i
$609$		−	27.0000i		−	1.09410i
$610$	−5.00000	+	10.0000i	−0.202444	+	0.404888i
$611$		−	32.0000i		−	1.29458i
$612$	7.00000			0.282958
$613$		−	31.0000i		−	1.25208i	−0.779792	−	0.626039i	$-0.784675\pi$
$613$		−	31.0000i		−	1.25208i	0.779792	−	0.626039i	$-0.215325\pi$
$614$		−	18.0000i		−	0.726421i
$615$	7.00000	−	14.0000i	0.282267	−	0.564534i
$616$			9.00000i			0.362620i
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$			14.0000i			0.563163i
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$	−5.00000	+	10.0000i	−0.200805	+	0.401610i
$621$			6.00000i			0.240772i
$622$			15.0000i			0.601445i
$623$	18.0000			0.721155
$624$			4.00000i			0.160128i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−6.00000			−0.239808
$627$	−12.0000			−0.479234
$628$			7.00000i			0.279330i
$629$	42.0000	−	7.00000i	1.67465	−	0.279108i
$630$	3.00000	−	6.00000i	0.119523	−	0.239046i
$631$		−	25.0000i		−	0.995234i	−0.867397	−	0.497617i	$-0.834208\pi$
$631$		−	25.0000i		−	0.995234i	0.867397	−	0.497617i	$-0.165792\pi$
$632$		−	4.00000i		−	0.159111i
$633$		−	13.0000i		−	0.516704i
$634$			27.0000i			1.07231i
$635$	−8.00000	+	16.0000i	−0.317470	+	0.634941i
$636$	1.00000			0.0396526
$637$	−8.00000			−0.316972
$638$			27.0000i			1.06894i
$639$	−12.0000			−0.474713
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	17.0000			0.671460			0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000			0.671460			0.335730	+	0.941958i	$0.391017\pi$
$642$	18.0000			0.710403
$643$	−31.0000			−1.22252			−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000			−1.22252			−0.611260	+	0.791430i	$0.709337\pi$
$644$			18.0000i			0.709299i
$645$	−1.00000	+	2.00000i	−0.0393750	+	0.0787499i
$646$			28.0000i			1.10165i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$	1.00000			0.0392837
$649$		−	18.0000i		−	0.706562i
$650$	12.0000	+	16.0000i	0.470679	+	0.627572i
$651$		−	15.0000i		−	0.587896i
$652$	9.00000			0.352467
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$	−11.0000			−0.430134
$655$		0			0
$656$	7.00000			0.273304
$657$		−	4.00000i		−	0.156055i
$658$	−24.0000			−0.935617
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$	−3.00000	+	6.00000i	−0.116775	+	0.233550i
$661$		−	35.0000i		−	1.36134i	−0.732589	−	0.680671i	$-0.761688\pi$
$661$		−	35.0000i		−	1.36134i	0.732589	−	0.680671i	$-0.238312\pi$
$662$		−	20.0000i		−	0.777322i
$663$		−	28.0000i		−	1.08743i
$664$			14.0000i			0.543305i
$665$	24.0000	+	12.0000i	0.930680	+	0.465340i
$666$	6.00000	−	1.00000i	0.232495	−	0.0387492i
$667$			54.0000i			2.09089i
$668$	−12.0000			−0.464294
$669$	11.0000			0.425285
$670$	2.00000	−	4.00000i	0.0772667	−	0.154533i
$671$			15.0000i			0.579069i
$672$	3.00000			0.115728
$673$		−	26.0000i		−	1.00223i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$		−	26.0000i		−	1.00223i	0.865382	−	0.501113i	$-0.167076\pi$
$674$		−	18.0000i		−	0.693334i
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	3.00000			0.115385
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		−	1.00000i		−	0.0384048i
$679$			21.0000i			0.805906i
$680$	14.0000	+	7.00000i	0.536875	+	0.268438i
$681$			13.0000i			0.498161i
$682$			15.0000i			0.574380i
$683$	−1.00000			−0.0382639			−0.0191320	−	0.999817i	$-0.506090\pi$
$683$	−1.00000			−0.0382639			−0.0191320	+	0.999817i	$0.506090\pi$
$684$			4.00000i			0.152944i
$685$	12.0000	−	24.0000i	0.458496	−	0.916993i
$686$		−	15.0000i		−	0.572703i
$687$			10.0000i			0.381524i
$688$	−1.00000			−0.0381246
$689$		−	4.00000i		−	0.152388i
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	−43.0000			−1.63580			−0.817899	−	0.575362i	$-0.804861\pi$
$691$	−43.0000			−1.63580			−0.817899	+	0.575362i	$0.804861\pi$
$692$			9.00000i			0.342129i
$693$		−	9.00000i		−	0.341882i
$694$	28.0000			1.06287
$695$	30.0000	+	15.0000i	1.13796	+	0.568982i
$696$	9.00000			0.341144
$697$	−49.0000			−1.85601
$698$		0			0
$699$	6.00000			0.226941
$700$	12.0000	−	9.00000i	0.453557	−	0.340168i
$701$		−	10.0000i		−	0.377695i	−0.982006	−	0.188847i	$-0.939525\pi$
$701$		−	10.0000i		−	0.377695i	0.982006	−	0.188847i	$-0.0604752\pi$
$702$		−	4.00000i		−	0.150970i
$703$	4.00000	+	24.0000i	0.150863	+	0.905177i
$704$	−3.00000			−0.113067
$705$	−16.0000	−	8.00000i	−0.602595	−	0.301297i
$706$	−31.0000			−1.16670
$707$		−	6.00000i		−	0.225653i
$708$	−6.00000			−0.225494
$709$			11.0000i			0.413114i	0.978435	+	0.206557i	$0.0662258\pi$
$709$			11.0000i			0.413114i	−0.978435	+	0.206557i	$0.933774\pi$
$710$	−24.0000	−	12.0000i	−0.900704	−	0.450352i
$711$			4.00000i			0.150012i
$712$			6.00000i			0.224860i
$713$			30.0000i			1.12351i
$714$	−21.0000			−0.785905
$715$	24.0000	+	12.0000i	0.897549	+	0.448775i
$716$		−	4.00000i		−	0.149487i
$717$	9.00000			0.336111
$718$		0			0
$719$	50.0000			1.86469			0.932343	−	0.361576i	$-0.117761\pi$
$719$	50.0000			1.86469			0.932343	+	0.361576i	$0.117761\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$		−	42.0000i		−	1.56416i
$722$	3.00000			0.111648
$723$		0			0
$724$	−18.0000			−0.668965
$725$	36.0000	−	27.0000i	1.33701	−	1.00275i
$726$		−	2.00000i		−	0.0742270i
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$		−	12.0000i		−	0.444750i
$729$	−1.00000			−0.0370370
$730$	4.00000	−	8.00000i	0.148047	−	0.296093i
$731$	7.00000			0.258904
$732$	5.00000			0.184805
$733$		−	11.0000i		−	0.406294i	−0.979148	−	0.203147i	$-0.934883\pi$
$733$		−	11.0000i		−	0.406294i	0.979148	−	0.203147i	$-0.0651170\pi$
$734$		−	23.0000i		−	0.848945i
$735$	−2.00000	+	4.00000i	−0.0737711	+	0.147542i
$736$	−6.00000			−0.221163
$737$		−	6.00000i		−	0.221013i
$738$	−7.00000			−0.257674
$739$	5.00000			0.183928			0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000			0.183928			0.0919640	+	0.995762i	$0.470686\pi$
$740$	13.0000	+	4.00000i	0.477890	+	0.147043i
$741$	16.0000			0.587775
$742$	−3.00000			−0.110133
$743$		−	51.0000i		−	1.87101i	−0.353315	−	0.935504i	$-0.614946\pi$
$743$		−	51.0000i		−	1.87101i	0.353315	−	0.935504i	$-0.385054\pi$
$744$	5.00000			0.183309
$745$		0			0
$746$			14.0000i			0.512576i
$747$		−	14.0000i		−	0.512233i
$748$	21.0000			0.767836
$749$	−54.0000			−1.97312
$750$	11.0000	−	2.00000i	0.401663	−	0.0730297i
$751$	−18.0000			−0.656829			−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000			−0.656829			−0.328415	+	0.944534i	$0.606514\pi$
$752$		−	8.00000i		−	0.291730i
$753$	−20.0000			−0.728841
$754$		−	36.0000i		−	1.31104i
$755$	−4.00000	−	2.00000i	−0.145575	−	0.0727875i
$756$	−3.00000			−0.109109
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	20.0000			0.726433
$759$			18.0000i			0.653359i
$760$	−4.00000	+	8.00000i	−0.145095	+	0.290191i
$761$	−13.0000			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$762$	8.00000			0.289809
$763$	33.0000			1.19468
$764$		−	15.0000i		−	0.542681i
$765$	−14.0000	−	7.00000i	−0.506171	−	0.253086i
$766$	−6.00000			−0.216789
$767$			24.0000i			0.866590i
$768$			1.00000i			0.0360844i
$769$			26.0000i			0.937584i	0.883309	+	0.468792i	$0.155311\pi$
$769$			26.0000i			0.937584i	−0.883309	+	0.468792i	$0.844689\pi$
$770$	9.00000	−	18.0000i	0.324337	−	0.648675i
$771$			18.0000i			0.648254i
$772$	14.0000			0.503871
$773$		−	11.0000i		−	0.395643i	−0.980238	−	0.197821i	$-0.936613\pi$
$773$		−	11.0000i		−	0.395643i	0.980238	−	0.197821i	$-0.0633866\pi$
$774$	1.00000			0.0359443
$775$	20.0000	−	15.0000i	0.718421	−	0.538816i
$776$	−7.00000			−0.251285
$777$	−18.0000	+	3.00000i	−0.645746	+	0.107624i
$778$			31.0000i			1.11140i
$779$		−	28.0000i		−	1.00320i
$780$	4.00000	−	8.00000i	0.143223	−	0.286446i
$781$	−36.0000			−1.28818
$782$	42.0000			1.50192
$783$	−9.00000			−0.321634
$784$	−2.00000			−0.0714286
$785$	7.00000	−	14.0000i	0.249841	−	0.499681i
$786$		0			0
$787$		−	28.0000i		−	0.998092i	−0.866575	−	0.499046i	$-0.833684\pi$
$787$		−	28.0000i		−	0.998092i	0.866575	−	0.499046i	$-0.166316\pi$
$788$		−	18.0000i		−	0.641223i
$789$	31.0000			1.10363
$790$	−4.00000	+	8.00000i	−0.142314	+	0.284627i
$791$			3.00000i			0.106668i
$792$	3.00000			0.106600
$793$		−	20.0000i		−	0.710221i
$794$		−	38.0000i		−	1.34857i
$795$	−2.00000	−	1.00000i	−0.0709327	−	0.0354663i
$796$			16.0000i			0.567105i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$		−	12.0000i		−	0.424795i
$799$			56.0000i			1.98114i
$800$	3.00000	+	4.00000i	0.106066	+	0.141421i
$801$		−	6.00000i		−	0.212000i
$802$		−	10.0000i		−	0.353112i
$803$		−	12.0000i		−	0.423471i
$804$	−2.00000			−0.0705346
$805$	18.0000	−	36.0000i	0.634417	−	1.26883i
$806$		−	20.0000i		−	0.704470i
$807$			20.0000i			0.704033i
$808$	2.00000			0.0703598
$809$			6.00000i			0.210949i	0.994422	+	0.105474i	$0.0336361\pi$
$809$			6.00000i			0.210949i	−0.994422	+	0.105474i	$0.966364\pi$
$810$	−2.00000	−	1.00000i	−0.0702728	−	0.0351364i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−27.0000			−0.947514
$813$			22.0000i			0.771574i
$814$	18.0000	−	3.00000i	0.630900	−	0.105150i
$815$	−18.0000	−	9.00000i	−0.630512	−	0.315256i
$816$		−	7.00000i		−	0.245049i
$817$			4.00000i			0.139942i
$818$		−	14.0000i		−	0.489499i
$819$			12.0000i			0.419314i
$820$	−14.0000	−	7.00000i	−0.488901	−	0.244451i
$821$	52.0000			1.81481			0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000			1.81481			0.907406	+	0.420255i	$0.138059\pi$
$822$	−12.0000			−0.418548
$823$		−	16.0000i		−	0.557725i	−0.960331	−	0.278862i	$-0.910043\pi$
$823$		−	16.0000i		−	0.557725i	0.960331	−	0.278862i	$-0.0899574\pi$
$824$	14.0000			0.487713
$825$	12.0000	−	9.00000i	0.417786	−	0.313340i
$826$	18.0000			0.626300
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$	6.00000			0.208514
$829$		−	19.0000i		−	0.659897i	−0.943999	−	0.329949i	$-0.892969\pi$
$829$		−	19.0000i		−	0.659897i	0.943999	−	0.329949i	$-0.107031\pi$
$830$	14.0000	−	28.0000i	0.485947	−	0.971894i
$831$			28.0000i			0.971309i
$832$	4.00000			0.138675
$833$	14.0000			0.485071
$834$		−	15.0000i		−	0.519408i
$835$	24.0000	+	12.0000i	0.830554	+	0.415277i
$836$			12.0000i			0.415029i
$837$	−5.00000			−0.172825
$838$		0			0
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	−6.00000	−	3.00000i	−0.207020	−	0.103510i
$841$	−52.0000			−1.79310
$842$			30.0000i			1.03387i
$843$	30.0000			1.03325
$844$	−13.0000			−0.447478
$845$	−6.00000	−	3.00000i	−0.206406	−	0.103203i
$846$			8.00000i			0.275046i
$847$			6.00000i			0.206162i
$848$		−	1.00000i		−	0.0343401i
$849$			4.00000i			0.137280i
$850$	−21.0000	−	28.0000i	−0.720294	−	0.960392i
$851$	36.0000	−	6.00000i	1.23406	−	0.205677i
$852$			12.0000i			0.411113i
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	−15.0000			−0.513289
$855$	4.00000	−	8.00000i	0.136797	−	0.273594i
$856$		−	18.0000i		−	0.615227i
$857$	43.0000			1.46885			0.734426	−	0.678689i	$-0.237451\pi$
$857$	43.0000			1.46885			0.734426	+	0.678689i	$0.237451\pi$
$858$		−	12.0000i		−	0.409673i
$859$			36.0000i			1.22830i	0.789188	+	0.614152i	$0.210502\pi$
$859$			36.0000i			1.22830i	−0.789188	+	0.614152i	$0.789498\pi$
$860$	2.00000	+	1.00000i	0.0681994	+	0.0340997i
$861$	21.0000			0.715678
$862$		−	25.0000i		−	0.851503i
$863$			49.0000i			1.66798i	0.551780	+	0.833990i	$0.313949\pi$
$863$			49.0000i			1.66798i	−0.551780	+	0.833990i	$0.686051\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	9.00000	−	18.0000i	0.306009	−	0.612018i
$866$			34.0000i			1.15537i
$867$			32.0000i			1.08678i
$868$	−15.0000			−0.509133
$869$			12.0000i			0.407072i
$870$	−18.0000	−	9.00000i	−0.610257	−	0.305129i
$871$			8.00000i			0.271070i
$872$			11.0000i			0.372507i
$873$	7.00000			0.236914
$874$			24.0000i			0.811812i
$875$	−33.0000	+	6.00000i	−1.11560	+	0.202837i
$876$	−4.00000			−0.135147
$877$			27.0000i			0.911725i	0.890050	+	0.455863i	$0.150669\pi$
$877$			27.0000i			0.911725i	−0.890050	+	0.455863i	$0.849331\pi$
$878$		−	9.00000i		−	0.303735i
$879$	−29.0000			−0.978146
$880$	6.00000	+	3.00000i	0.202260	+	0.101130i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$	2.00000			0.0673435
$883$	19.0000			0.639401			0.319700	−	0.947519i	$-0.396418\pi$
$883$	19.0000			0.639401			0.319700	+	0.947519i	$0.396418\pi$
$884$	−28.0000			−0.941742
$885$	12.0000	+	6.00000i	0.403376	+	0.201688i
$886$		−	36.0000i		−	1.20944i
$887$			27.0000i			0.906571i	0.891365	+	0.453286i	$0.149748\pi$
$887$			27.0000i			0.906571i	−0.891365	+	0.453286i	$0.850252\pi$
$888$	−1.00000	−	6.00000i	−0.0335578	−	0.201347i
$889$	−24.0000			−0.804934
$890$	6.00000	−	12.0000i	0.201120	−	0.402241i
$891$	−3.00000			−0.100504
$892$		−	11.0000i		−	0.368307i
$893$	−32.0000			−1.07084
$894$		0			0
$895$	−4.00000	+	8.00000i	−0.133705	+	0.267411i
$896$		−	3.00000i		−	0.100223i
$897$		−	24.0000i		−	0.801337i
$898$			6.00000i			0.200223i
$899$	−45.0000			−1.50083
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$			7.00000i			0.233204i
$902$	−21.0000			−0.699224
$903$	−3.00000			−0.0998337
$904$	−1.00000			−0.0332595
$905$	36.0000	+	18.0000i	1.19668	+	0.598340i
$906$			2.00000i			0.0664455i
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$	13.0000			0.431420
$909$	−2.00000			−0.0663358
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	4.00000			0.132453
$913$		−	42.0000i		−	1.39000i
$914$	13.0000			0.430002
$915$	−10.0000	−	5.00000i	−0.330590	−	0.165295i
$916$	10.0000			0.330409
$917$		0			0
$918$			7.00000i			0.231034i
$919$		−	24.0000i		−	0.791687i	−0.918318	−	0.395843i	$-0.870452\pi$
$919$		−	24.0000i		−	0.791687i	0.918318	−	0.395843i	$-0.129548\pi$
$920$	12.0000	+	6.00000i	0.395628	+	0.197814i
$921$	18.0000			0.593120
$922$			25.0000i			0.823331i
$923$	48.0000			1.57994
$924$	−9.00000			−0.296078
$925$	−22.0000	−	21.0000i	−0.723356	−	0.690476i
$926$	−26.0000			−0.854413
$927$	−14.0000			−0.459820
$928$		−	9.00000i		−	0.295439i
$929$	−5.00000			−0.164045			−0.0820223	−	0.996630i	$-0.526138\pi$
$929$	−5.00000			−0.164045			−0.0820223	+	0.996630i	$0.526138\pi$
$930$	−10.0000	−	5.00000i	−0.327913	−	0.163956i
$931$			8.00000i			0.262189i
$932$		−	6.00000i		−	0.196537i
$933$	−15.0000			−0.491078
$934$	23.0000			0.752583
$935$	−42.0000	−	21.0000i	−1.37355	−	0.686773i
$936$	−4.00000			−0.130744
$937$			12.0000i			0.392023i	0.980602	+	0.196011i	$0.0627990\pi$
$937$			12.0000i			0.392023i	−0.980602	+	0.196011i	$0.937201\pi$
$938$	6.00000			0.195907
$939$		−	6.00000i		−	0.195803i
$940$	−8.00000	+	16.0000i	−0.260931	+	0.521862i
$941$	12.0000			0.391189			0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000			0.391189			0.195594	+	0.980685i	$0.437336\pi$
$942$	−7.00000			−0.228072
$943$	−42.0000			−1.36771
$944$			6.00000i			0.195283i
$945$	6.00000	+	3.00000i	0.195180	+	0.0975900i
$946$	3.00000			0.0975384
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$	4.00000			0.129914
$949$			16.0000i			0.519382i
$950$	16.0000	−	12.0000i	0.519109	−	0.389331i
$951$	−27.0000			−0.875535
$952$			21.0000i			0.680614i
$953$		−	16.0000i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$953$		−	16.0000i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$954$			1.00000i			0.0323762i
$955$	−15.0000	+	30.0000i	−0.485389	+	0.970777i
$956$		−	9.00000i		−	0.291081i
$957$	−27.0000			−0.872786
$958$		−	24.0000i		−	0.775405i
$959$	36.0000			1.16250
$960$	1.00000	−	2.00000i	0.0322749	−	0.0645497i
$961$	6.00000			0.193548
$962$	−24.0000	+	4.00000i	−0.773791	+	0.128965i
$963$			18.0000i			0.580042i
$964$		0			0
$965$	−28.0000	−	14.0000i	−0.901352	−	0.450676i
$966$	−18.0000			−0.579141
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−2.00000			−0.0642824
$969$	−28.0000			−0.899490
$970$	14.0000	+	7.00000i	0.449513	+	0.224756i
$971$	57.0000			1.82922			0.914609	−	0.404341i	$-0.132499\pi$
$971$	57.0000			1.82922			0.914609	+	0.404341i	$0.132499\pi$
$972$			1.00000i			0.0320750i
$973$			45.0000i			1.44263i
$974$	−22.0000			−0.704925
$975$	−16.0000	+	12.0000i	−0.512410	+	0.384308i
$976$		−	5.00000i		−	0.160046i
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$			9.00000i			0.287788i
$979$		−	18.0000i		−	0.575282i
$980$	4.00000	+	2.00000i	0.127775	+	0.0638877i
$981$		−	11.0000i		−	0.351203i
$982$	−8.00000			−0.255290
$983$			19.0000i			0.606006i	0.952990	+	0.303003i	$0.0979892\pi$
$983$			19.0000i			0.606006i	−0.952990	+	0.303003i	$0.902011\pi$
$984$			7.00000i			0.223152i
$985$	−18.0000	+	36.0000i	−0.573528	+	1.14706i
$986$			63.0000i			2.00633i
$987$		−	24.0000i		−	0.763928i
$988$		−	16.0000i		−	0.509028i
$989$	6.00000			0.190789
$990$	−6.00000	−	3.00000i	−0.190693	−	0.0953463i
$991$			25.0000i			0.794151i	0.917786	+	0.397076i	$0.129975\pi$
$991$			25.0000i			0.794151i	−0.917786	+	0.397076i	$0.870025\pi$
$992$		−	5.00000i		−	0.158750i
$993$	20.0000			0.634681
$994$		−	36.0000i		−	1.14185i
$995$	16.0000	−	32.0000i	0.507234	−	1.01447i
$996$	−14.0000			−0.443607
$997$	−42.0000			−1.33015			−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000			−1.33015			−0.665077	+	0.746775i	$0.731601\pi$
$998$		−	24.0000i		−	0.759707i
$999$	1.00000	+	6.00000i	0.0316386	+	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.b.739.2	yes	2
3.2	odd	2		3330.2.e.a.739.2		2
5.4	even	2		1110.2.e.a.739.1	✓	2
15.14	odd	2		3330.2.e.b.739.2		2
37.36	even	2		1110.2.e.a.739.2	yes	2
111.110	odd	2		3330.2.e.b.739.1		2
185.184	even	2	inner	1110.2.e.b.739.1	yes	2
555.554	odd	2		3330.2.e.a.739.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.a.739.1	✓	2	5.4	even	2
1110.2.e.a.739.2	yes	2	37.36	even	2
1110.2.e.b.739.1	yes	2	185.184	even	2	inner
1110.2.e.b.739.2	yes	2	1.1	even	1	trivial
3330.2.e.a.739.1		2	555.554	odd	2
3330.2.e.a.739.2		2	3.2	odd	2
3330.2.e.b.739.1		2	111.110	odd	2
3330.2.e.b.739.2		2	15.14	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -3.00000i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -3.00000i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -3.00000 q^{11} +1.00000i q^{12} +4.00000 q^{13} -3.00000i q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} -7.00000 q^{17} -1.00000 q^{18} -4.00000i q^{19} +(-2.00000 - 1.00000i) q^{20} +3.00000 q^{21} -3.00000 q^{22} -6.00000 q^{23} +1.00000i q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} -1.00000i q^{27} -3.00000i q^{28} -9.00000i q^{29} +(1.00000 - 2.00000i) q^{30} -5.00000i q^{31} +1.00000 q^{32} -3.00000i q^{33} -7.00000 q^{34} +(-3.00000 + 6.00000i) q^{35} -1.00000 q^{36} +(-6.00000 + 1.00000i) q^{37} -4.00000i q^{38} +4.00000i q^{39} +(-2.00000 - 1.00000i) q^{40} +7.00000 q^{41} +3.00000 q^{42} -1.00000 q^{43} -3.00000 q^{44} +(2.00000 + 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} +(3.00000 + 4.00000i) q^{50} -7.00000i q^{51} +4.00000 q^{52} -1.00000i q^{53} -1.00000i q^{54} +(6.00000 + 3.00000i) q^{55} -3.00000i q^{56} +4.00000 q^{57} -9.00000i q^{58} +6.00000i q^{59} +(1.00000 - 2.00000i) q^{60} -5.00000i q^{61} -5.00000i q^{62} +3.00000i q^{63} +1.00000 q^{64} +(-8.00000 - 4.00000i) q^{65} -3.00000i q^{66} +2.00000i q^{67} -7.00000 q^{68} -6.00000i q^{69} +(-3.00000 + 6.00000i) q^{70} +12.0000 q^{71} -1.00000 q^{72} +4.00000i q^{73} +(-6.00000 + 1.00000i) q^{74} +(-4.00000 + 3.00000i) q^{75} -4.00000i q^{76} +9.00000i q^{77} +4.00000i q^{78} -4.00000i q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +7.00000 q^{82} +14.0000i q^{83} +3.00000 q^{84} +(14.0000 + 7.00000i) q^{85} -1.00000 q^{86} +9.00000 q^{87} -3.00000 q^{88} +6.00000i q^{89} +(2.00000 + 1.00000i) q^{90} -12.0000i q^{91} -6.00000 q^{92} +5.00000 q^{93} -8.00000i q^{94} +(-4.00000 + 8.00000i) q^{95} +1.00000i q^{96} -7.00000 q^{97} -2.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 8 q^{13} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 2 q^{18} - 4 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{25} + 8 q^{26} + 2 q^{30} + 2 q^{32} - 14 q^{34} - 6 q^{35} - 2 q^{36} - 12 q^{37} - 4 q^{40} + 14 q^{41} + 6 q^{42} - 2 q^{43} - 6 q^{44} + 4 q^{45} - 12 q^{46} - 4 q^{49} + 6 q^{50} + 8 q^{52} + 12 q^{55} + 8 q^{57} + 2 q^{60} + 2 q^{64} - 16 q^{65} - 14 q^{68} - 6 q^{70} + 24 q^{71} - 2 q^{72} - 12 q^{74} - 8 q^{75} - 4 q^{80} + 2 q^{81} + 14 q^{82} + 6 q^{84} + 28 q^{85} - 2 q^{86} + 18 q^{87} - 6 q^{88} + 4 q^{90} - 12 q^{92} + 10 q^{93} - 8 q^{95} - 14 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 8 * q^13 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 2 * q^18 - 4 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^25 + 8 * q^26 + 2 * q^30 + 2 * q^32 - 14 * q^34 - 6 * q^35 - 2 * q^36 - 12 * q^37 - 4 * q^40 + 14 * q^41 + 6 * q^42 - 2 * q^43 - 6 * q^44 + 4 * q^45 - 12 * q^46 - 4 * q^49 + 6 * q^50 + 8 * q^52 + 12 * q^55 + 8 * q^57 + 2 * q^60 + 2 * q^64 - 16 * q^65 - 14 * q^68 - 6 * q^70 + 24 * q^71 - 2 * q^72 - 12 * q^74 - 8 * q^75 - 4 * q^80 + 2 * q^81 + 14 * q^82 + 6 * q^84 + 28 * q^85 - 2 * q^86 + 18 * q^87 - 6 * q^88 + 4 * q^90 - 12 * q^92 + 10 * q^93 - 8 * q^95 - 14 * q^97 - 4 * q^98 + 6 * q^99

Introduction

L-functions

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