LMFDB - Embedded newform 1110.2.d.c.889.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(889,1110)]

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, 0]))

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

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

chi := DirichletCharacter("1110.889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.d (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			889.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.c.889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} +5.00000 q^{11} +1.00000i q^{12} -1.00000 q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -1.00000i q^{18} +(-1.00000 + 2.00000i) q^{20} +1.00000 q^{21} +5.00000i q^{22} -4.00000i q^{23} -1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +1.00000i q^{27} -1.00000i q^{28} +3.00000 q^{29} +(1.00000 - 2.00000i) q^{30} +1.00000 q^{31} +1.00000i q^{32} -5.00000i q^{33} -1.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +(-2.00000 - 1.00000i) q^{40} -1.00000 q^{41} +1.00000i q^{42} -7.00000i q^{43} -5.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} +4.00000 q^{46} -4.00000i q^{47} -1.00000i q^{48} +6.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +1.00000 q^{51} -3.00000i q^{53} -1.00000 q^{54} +(5.00000 - 10.0000i) q^{55} +1.00000 q^{56} +3.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} +5.00000 q^{61} +1.00000i q^{62} -1.00000i q^{63} -1.00000 q^{64} +5.00000 q^{66} -4.00000i q^{67} -1.00000i q^{68} -4.00000 q^{69} +(-1.00000 + 2.00000i) q^{70} -6.00000 q^{71} +1.00000i q^{72} -10.0000i q^{73} +1.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +5.00000i q^{77} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -1.00000i q^{82} +8.00000i q^{83} -1.00000 q^{84} +(2.00000 + 1.00000i) q^{85} +7.00000 q^{86} -3.00000i q^{87} -5.00000i q^{88} -8.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +4.00000i q^{92} -1.00000i q^{93} +4.00000 q^{94} +1.00000 q^{96} -1.00000i q^{97} +6.00000i q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} + 10 q^{11} - 2 q^{14} - 4 q^{15} + 2 q^{16} - 2 q^{20} + 2 q^{21} - 2 q^{24} - 6 q^{25} + 6 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{40} - 2 q^{41} - 10 q^{44} - 2 q^{45} + 8 q^{46} + 12 q^{49} + 8 q^{50} + 2 q^{51} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 16 q^{59} + 4 q^{60} + 10 q^{61} - 2 q^{64} + 10 q^{66} - 8 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{74} - 8 q^{75} + 2 q^{80} + 2 q^{81} - 2 q^{84} + 4 q^{85} + 14 q^{86} - 16 q^{89} - 4 q^{90} + 8 q^{94} + 2 q^{96} - 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 + 10 * q^11 - 2 * q^14 - 4 * q^15 + 2 * q^16 - 2 * q^20 + 2 * q^21 - 2 * q^24 - 6 * q^25 + 6 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^40 - 2 * q^41 - 10 * q^44 - 2 * q^45 + 8 * q^46 + 12 * q^49 + 8 * q^50 + 2 * q^51 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 16 * q^59 + 4 * q^60 + 10 * q^61 - 2 * q^64 + 10 * q^66 - 8 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^74 - 8 * q^75 + 2 * q^80 + 2 * q^81 - 2 * q^84 + 4 * q^85 + 14 * q^86 - 16 * q^89 - 4 * q^90 + 8 * q^94 + 2 * q^96 - 10 * 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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	1.00000			0.408248
$7$			1.00000i			0.377964i	0.981981	+	0.188982i	$0.0605189\pi$
$7$			1.00000i			0.377964i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$			1.00000i			0.288675i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−1.00000			−0.267261
$15$	−2.00000	−	1.00000i	−0.516398	−	0.258199i
$16$	1.00000			0.250000
$17$			1.00000i			0.242536i	0.992620	+	0.121268i	$0.0386960\pi$
$17$			1.00000i			0.242536i	−0.992620	+	0.121268i	$0.961304\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$	1.00000			0.218218
$22$			5.00000i			1.06600i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−1.00000			−0.204124
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		−	1.00000i		−	0.188982i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	1.00000	−	2.00000i	0.182574	−	0.365148i
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$			1.00000i			0.176777i
$33$		−	5.00000i		−	0.870388i
$34$	−1.00000			−0.171499
$35$	2.00000	+	1.00000i	0.338062	+	0.169031i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		0			0
$39$		0			0
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$	−1.00000			−0.156174			−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000			−0.156174			−0.0780869	+	0.996947i	$0.524881\pi$
$42$			1.00000i			0.154303i
$43$		−	7.00000i		−	1.06749i	−0.845645	−	0.533745i	$-0.820784\pi$
$43$		−	7.00000i		−	1.06749i	0.845645	−	0.533745i	$-0.179216\pi$
$44$	−5.00000			−0.753778
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	4.00000			0.589768
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.00000			0.857143
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	1.00000			0.140028
$52$		0			0
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	−1.00000			−0.136083
$55$	5.00000	−	10.0000i	0.674200	−	1.34840i
$56$	1.00000			0.133631
$57$		0			0
$58$			3.00000i			0.393919i
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$	2.00000	+	1.00000i	0.258199	+	0.129099i
$61$	5.00000			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$62$			1.00000i			0.127000i
$63$		−	1.00000i		−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.00000			0.615457
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$		−	1.00000i		−	0.121268i
$69$	−4.00000			−0.481543
$70$	−1.00000	+	2.00000i	−0.119523	+	0.239046i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$			1.00000i			0.117851i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	1.00000			0.116248
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$		0			0
$77$			5.00000i			0.569803i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.00000	−	2.00000i	0.111803	−	0.223607i
$81$	1.00000			0.111111
$82$		−	1.00000i		−	0.110432i
$83$			8.00000i			0.878114i	0.898459	+	0.439057i	$0.144687\pi$
$83$			8.00000i			0.878114i	−0.898459	+	0.439057i	$0.855313\pi$
$84$	−1.00000			−0.109109
$85$	2.00000	+	1.00000i	0.216930	+	0.108465i
$86$	7.00000			0.754829
$87$		−	3.00000i		−	0.321634i
$88$		−	5.00000i		−	0.533002i
$89$	−8.00000			−0.847998			−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000			−0.847998			−0.423999	+	0.905663i	$0.639374\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$		0			0
$92$			4.00000i			0.417029i
$93$		−	1.00000i		−	0.103695i
$94$	4.00000			0.412568
$95$		0			0
$96$	1.00000			0.102062
$97$		−	1.00000i		−	0.101535i	−0.998711	−	0.0507673i	$-0.983833\pi$
$97$		−	1.00000i		−	0.101535i	0.998711	−	0.0507673i	$-0.0161667\pi$
$98$			6.00000i			0.606092i
$99$	−5.00000			−0.502519
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$			1.00000i			0.0990148i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$		0			0
$105$	1.00000	−	2.00000i	0.0975900	−	0.195180i
$106$	3.00000			0.291386
$107$			6.00000i			0.580042i	0.957020	+	0.290021i	$0.0936623\pi$
$107$			6.00000i			0.580042i	−0.957020	+	0.290021i	$0.906338\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	10.0000	+	5.00000i	0.953463	+	0.476731i
$111$	−1.00000			−0.0949158
$112$			1.00000i			0.0944911i
$113$			21.0000i			1.97551i	0.156001	+	0.987757i	$0.450140\pi$
$113$			21.0000i			1.97551i	−0.156001	+	0.987757i	$0.549860\pi$
$114$		0			0
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$	−3.00000			−0.278543
$117$		0			0
$118$			8.00000i			0.736460i
$119$	−1.00000			−0.0916698
$120$	−1.00000	+	2.00000i	−0.0912871	+	0.182574i
$121$	14.0000			1.27273
$122$			5.00000i			0.452679i
$123$			1.00000i			0.0901670i
$124$	−1.00000			−0.0898027
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	1.00000			0.0890871
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.00000			−0.616316
$130$		0			0
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$			5.00000i			0.435194i
$133$		0			0
$134$	4.00000			0.345547
$135$	2.00000	+	1.00000i	0.172133	+	0.0860663i
$136$	1.00000			0.0857493
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$		−	4.00000i		−	0.340503i
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$	−2.00000	−	1.00000i	−0.169031	−	0.0845154i
$141$	−4.00000			−0.336861
$142$		−	6.00000i		−	0.503509i
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	3.00000	−	6.00000i	0.249136	−	0.498273i
$146$	10.0000			0.827606
$147$		−	6.00000i		−	0.494872i
$148$			1.00000i			0.0821995i
$149$	−4.00000			−0.327693			−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000			−0.327693			−0.163846	+	0.986486i	$0.552390\pi$
$150$	−3.00000	−	4.00000i	−0.244949	−	0.326599i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$		−	1.00000i		−	0.0808452i
$154$	−5.00000			−0.402911
$155$	1.00000	−	2.00000i	0.0803219	−	0.160644i
$156$		0			0
$157$			23.0000i			1.83560i	0.397043	+	0.917800i	$0.370036\pi$
$157$			23.0000i			1.83560i	−0.397043	+	0.917800i	$0.629964\pi$
$158$		0			0
$159$	−3.00000			−0.237915
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$	4.00000			0.315244
$162$			1.00000i			0.0785674i
$163$			1.00000i			0.0783260i	0.999233	+	0.0391630i	$0.0124692\pi$
$163$			1.00000i			0.0783260i	−0.999233	+	0.0391630i	$0.987531\pi$
$164$	1.00000			0.0780869
$165$	−10.0000	−	5.00000i	−0.778499	−	0.389249i
$166$	−8.00000			−0.620920
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$		−	1.00000i		−	0.0771517i
$169$	13.0000			1.00000
$170$	−1.00000	+	2.00000i	−0.0766965	+	0.153393i
$171$		0			0
$172$			7.00000i			0.533745i
$173$			13.0000i			0.988372i	0.869356	+	0.494186i	$0.164534\pi$
$173$			13.0000i			0.988372i	−0.869356	+	0.494186i	$0.835466\pi$
$174$	3.00000			0.227429
$175$	4.00000	−	3.00000i	0.302372	−	0.226779i
$176$	5.00000			0.376889
$177$		−	8.00000i		−	0.601317i
$178$		−	8.00000i		−	0.599625i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	1.00000	−	2.00000i	0.0745356	−	0.149071i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$		0			0
$183$		−	5.00000i		−	0.369611i
$184$	−4.00000			−0.294884
$185$	−2.00000	−	1.00000i	−0.147043	−	0.0735215i
$186$	1.00000			0.0733236
$187$			5.00000i			0.365636i
$188$			4.00000i			0.291730i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$			1.00000i			0.0721688i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	1.00000			0.0717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$			26.0000i			1.85242i	0.377004	+	0.926212i	$0.376954\pi$
$197$			26.0000i			1.85242i	−0.377004	+	0.926212i	$0.623046\pi$
$198$		−	5.00000i		−	0.355335i
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	−4.00000			−0.282138
$202$			10.0000i			0.703598i
$203$			3.00000i			0.210559i
$204$	−1.00000			−0.0700140
$205$	−1.00000	+	2.00000i	−0.0698430	+	0.139686i
$206$	8.00000			0.557386
$207$			4.00000i			0.278019i
$208$		0			0
$209$		0			0
$210$	2.00000	+	1.00000i	0.138013	+	0.0690066i
$211$	−21.0000			−1.44570			−0.722850	−	0.691005i	$-0.757168\pi$
$211$	−21.0000			−1.44570			−0.722850	+	0.691005i	$0.757168\pi$
$212$			3.00000i			0.206041i
$213$			6.00000i			0.411113i
$214$	−6.00000			−0.410152
$215$	−14.0000	−	7.00000i	−0.954792	−	0.477396i
$216$	1.00000			0.0680414
$217$			1.00000i			0.0678844i
$218$		−	1.00000i		−	0.0677285i
$219$	−10.0000			−0.675737
$220$	−5.00000	+	10.0000i	−0.337100	+	0.674200i
$221$		0			0
$222$		−	1.00000i		−	0.0671156i
$223$			5.00000i			0.334825i	0.985887	+	0.167412i	$0.0535411\pi$
$223$			5.00000i			0.334825i	−0.985887	+	0.167412i	$0.946459\pi$
$224$	−1.00000			−0.0668153
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$	−21.0000			−1.39690
$227$			1.00000i			0.0663723i	0.999449	+	0.0331862i	$0.0105654\pi$
$227$			1.00000i			0.0663723i	−0.999449	+	0.0331862i	$0.989435\pi$
$228$		0			0
$229$	16.0000			1.05731			0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000			1.05731			0.528655	+	0.848837i	$0.322697\pi$
$230$	4.00000	−	8.00000i	0.263752	−	0.527504i
$231$	5.00000			0.328976
$232$		−	3.00000i		−	0.196960i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$		0			0
$235$	−8.00000	−	4.00000i	−0.521862	−	0.260931i
$236$	−8.00000			−0.520756
$237$		0			0
$238$		−	1.00000i		−	0.0648204i
$239$	−11.0000			−0.711531			−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000			−0.711531			−0.355765	+	0.934575i	$0.615780\pi$
$240$	−2.00000	−	1.00000i	−0.129099	−	0.0645497i
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$			14.0000i			0.899954i
$243$		−	1.00000i		−	0.0641500i
$244$	−5.00000			−0.320092
$245$	6.00000	−	12.0000i	0.383326	−	0.766652i
$246$	−1.00000			−0.0637577
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$	8.00000			0.506979
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$			1.00000i			0.0629941i
$253$		−	20.0000i		−	1.25739i
$254$	8.00000			0.501965
$255$	1.00000	−	2.00000i	0.0626224	−	0.125245i
$256$	1.00000			0.0625000
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$		−	7.00000i		−	0.435801i
$259$	1.00000			0.0621370
$260$		0			0
$261$	−3.00000			−0.185695
$262$		−	6.00000i		−	0.370681i
$263$		−	19.0000i		−	1.17159i	−0.810459	−	0.585795i	$-0.800782\pi$
$263$		−	19.0000i		−	1.17159i	0.810459	−	0.585795i	$-0.199218\pi$
$264$	−5.00000			−0.307729
$265$	−6.00000	−	3.00000i	−0.368577	−	0.184289i
$266$		0			0
$267$			8.00000i			0.489592i
$268$			4.00000i			0.244339i
$269$	12.0000			0.731653			0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000			0.731653			0.365826	+	0.930683i	$0.380786\pi$
$270$	−1.00000	+	2.00000i	−0.0608581	+	0.121716i
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$			1.00000i			0.0606339i
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−15.0000	−	20.0000i	−0.904534	−	1.20605i
$276$	4.00000			0.240772
$277$		−	8.00000i		−	0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$		−	8.00000i		−	0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$			11.0000i			0.659736i
$279$	−1.00000			−0.0598684
$280$	1.00000	−	2.00000i	0.0597614	−	0.119523i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		−	4.00000i		−	0.238197i
$283$			16.0000i			0.951101i	0.879688	+	0.475551i	$0.157751\pi$
$283$			16.0000i			0.951101i	−0.879688	+	0.475551i	$0.842249\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$		0			0
$287$		−	1.00000i		−	0.0590281i
$288$		−	1.00000i		−	0.0589256i
$289$	16.0000			0.941176
$290$	6.00000	+	3.00000i	0.352332	+	0.176166i
$291$	−1.00000			−0.0586210
$292$			10.0000i			0.585206i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$	6.00000			0.349927
$295$	8.00000	−	16.0000i	0.465778	−	0.931556i
$296$	−1.00000			−0.0581238
$297$			5.00000i			0.290129i
$298$		−	4.00000i		−	0.231714i
$299$		0			0
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	7.00000			0.403473
$302$		−	2.00000i		−	0.115087i
$303$		−	10.0000i		−	0.574485i
$304$		0			0
$305$	5.00000	−	10.0000i	0.286299	−	0.572598i
$306$	1.00000			0.0571662
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		−	5.00000i		−	0.284901i
$309$	−8.00000			−0.455104
$310$	2.00000	+	1.00000i	0.113592	+	0.0567962i
$311$	15.0000			0.850572			0.425286	−	0.905059i	$-0.360174\pi$
$311$	15.0000			0.850572			0.425286	+	0.905059i	$0.360174\pi$
$312$		0			0
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	−23.0000			−1.29797
$315$	−2.00000	−	1.00000i	−0.112687	−	0.0563436i
$316$		0			0
$317$		−	5.00000i		−	0.280828i	−0.990093	−	0.140414i	$-0.955157\pi$
$317$		−	5.00000i		−	0.280828i	0.990093	−	0.140414i	$-0.0448433\pi$
$318$		−	3.00000i		−	0.168232i
$319$	15.0000			0.839839
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$	6.00000			0.334887
$322$			4.00000i			0.222911i
$323$		0			0
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−1.00000			−0.0553849
$327$			1.00000i			0.0553001i
$328$			1.00000i			0.0552158i
$329$	4.00000			0.220527
$330$	5.00000	−	10.0000i	0.275241	−	0.550482i
$331$	−26.0000			−1.42909			−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000			−1.42909			−0.714545	+	0.699590i	$0.753366\pi$
$332$		−	8.00000i		−	0.439057i
$333$			1.00000i			0.0547997i
$334$	6.00000			0.328305
$335$	−8.00000	−	4.00000i	−0.437087	−	0.218543i
$336$	1.00000			0.0545545
$337$			16.0000i			0.871576i	0.900049	+	0.435788i	$0.143530\pi$
$337$			16.0000i			0.871576i	−0.900049	+	0.435788i	$0.856470\pi$
$338$			13.0000i			0.707107i
$339$	21.0000			1.14056
$340$	−2.00000	−	1.00000i	−0.108465	−	0.0542326i
$341$	5.00000			0.270765
$342$		0			0
$343$			13.0000i			0.701934i
$344$	−7.00000			−0.377415
$345$	−4.00000	+	8.00000i	−0.215353	+	0.430706i
$346$	−13.0000			−0.698884
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$			3.00000i			0.160817i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	3.00000	+	4.00000i	0.160357	+	0.213809i
$351$		0			0
$352$			5.00000i			0.266501i
$353$			31.0000i			1.64996i	0.565159	+	0.824982i	$0.308815\pi$
$353$			31.0000i			1.64996i	−0.565159	+	0.824982i	$0.691185\pi$
$354$	8.00000			0.425195
$355$	−6.00000	+	12.0000i	−0.318447	+	0.636894i
$356$	8.00000			0.423999
$357$			1.00000i			0.0529256i
$358$		−	10.0000i		−	0.528516i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$	2.00000	+	1.00000i	0.105409	+	0.0527046i
$361$	−19.0000			−1.00000
$362$		−	16.0000i		−	0.840941i
$363$		−	14.0000i		−	0.734809i
$364$		0			0
$365$	−20.0000	−	10.0000i	−1.04685	−	0.523424i
$366$	5.00000			0.261354
$367$			13.0000i			0.678594i	0.940679	+	0.339297i	$0.110189\pi$
$367$			13.0000i			0.678594i	−0.940679	+	0.339297i	$0.889811\pi$
$368$		−	4.00000i		−	0.208514i
$369$	1.00000			0.0520579
$370$	1.00000	−	2.00000i	0.0519875	−	0.103975i
$371$	3.00000			0.155752
$372$			1.00000i			0.0518476i
$373$		−	6.00000i		−	0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$		−	6.00000i		−	0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	−5.00000			−0.258544
$375$	2.00000	+	11.0000i	0.103280	+	0.568038i
$376$	−4.00000			−0.206284
$377$		0			0
$378$		−	1.00000i		−	0.0514344i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	−8.00000			−0.409852
$382$			3.00000i			0.153493i
$383$		−	8.00000i		−	0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$		−	8.00000i		−	0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$	−1.00000			−0.0510310
$385$	10.0000	+	5.00000i	0.509647	+	0.254824i
$386$	10.0000			0.508987
$387$			7.00000i			0.355830i
$388$			1.00000i			0.0507673i
$389$	−23.0000			−1.16615			−0.583073	−	0.812420i	$-0.698150\pi$
$389$	−23.0000			−1.16615			−0.583073	+	0.812420i	$0.698150\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		−	6.00000i		−	0.303046i
$393$			6.00000i			0.302660i
$394$	−26.0000			−1.30986
$395$		0			0
$396$	5.00000			0.251259
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$		−	24.0000i		−	1.20301i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$		−	4.00000i		−	0.199502i
$403$		0			0
$404$	−10.0000			−0.497519
$405$	1.00000	−	2.00000i	0.0496904	−	0.0993808i
$406$	−3.00000			−0.148888
$407$		−	5.00000i		−	0.247841i
$408$		−	1.00000i		−	0.0495074i
$409$	40.0000			1.97787			0.988936	−	0.148340i	$-0.0473931\pi$
$409$	40.0000			1.97787			0.988936	+	0.148340i	$0.0473931\pi$
$410$	−2.00000	−	1.00000i	−0.0987730	−	0.0493865i
$411$	18.0000			0.887875
$412$			8.00000i			0.394132i
$413$			8.00000i			0.393654i
$414$	−4.00000			−0.196589
$415$	16.0000	+	8.00000i	0.785409	+	0.392705i
$416$		0			0
$417$		−	11.0000i		−	0.538672i
$418$		0			0
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$	−1.00000	+	2.00000i	−0.0487950	+	0.0975900i
$421$	−38.0000			−1.85201			−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−38.0000			−1.85201			−0.926003	+	0.377515i	$0.876779\pi$
$422$		−	21.0000i		−	1.02226i
$423$			4.00000i			0.194487i
$424$	−3.00000			−0.145693
$425$	4.00000	−	3.00000i	0.194029	−	0.145521i
$426$	−6.00000			−0.290701
$427$			5.00000i			0.241967i
$428$		−	6.00000i		−	0.290021i
$429$		0			0
$430$	7.00000	−	14.0000i	0.337570	−	0.675140i
$431$	−13.0000			−0.626188			−0.313094	−	0.949722i	$-0.601365\pi$
$431$	−13.0000			−0.626188			−0.313094	+	0.949722i	$0.601365\pi$
$432$			1.00000i			0.0481125i
$433$			20.0000i			0.961139i	0.876957	+	0.480569i	$0.159570\pi$
$433$			20.0000i			0.961139i	−0.876957	+	0.480569i	$0.840430\pi$
$434$	−1.00000			−0.0480015
$435$	−6.00000	−	3.00000i	−0.287678	−	0.143839i
$436$	1.00000			0.0478913
$437$		0			0
$438$		−	10.0000i		−	0.477818i
$439$	33.0000			1.57500			0.787502	−	0.616312i	$-0.211374\pi$
$439$	33.0000			1.57500			0.787502	+	0.616312i	$0.211374\pi$
$440$	−10.0000	−	5.00000i	−0.476731	−	0.238366i
$441$	−6.00000			−0.285714
$442$		0			0
$443$			6.00000i			0.285069i	0.989790	+	0.142534i	$0.0455251\pi$
$443$			6.00000i			0.285069i	−0.989790	+	0.142534i	$0.954475\pi$
$444$	1.00000			0.0474579
$445$	−8.00000	+	16.0000i	−0.379236	+	0.758473i
$446$	−5.00000			−0.236757
$447$			4.00000i			0.189194i
$448$		−	1.00000i		−	0.0472456i
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−5.00000			−0.235441
$452$		−	21.0000i		−	0.987757i
$453$			2.00000i			0.0939682i
$454$	−1.00000			−0.0469323
$455$		0			0
$456$		0			0
$457$			19.0000i			0.888783i	0.895833	+	0.444391i	$0.146580\pi$
$457$			19.0000i			0.888783i	−0.895833	+	0.444391i	$0.853420\pi$
$458$			16.0000i			0.747631i
$459$	−1.00000			−0.0466760
$460$	8.00000	+	4.00000i	0.373002	+	0.186501i
$461$	3.00000			0.139724			0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000			0.139724			0.0698620	+	0.997557i	$0.477744\pi$
$462$			5.00000i			0.232621i
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	3.00000			0.139272
$465$	−2.00000	−	1.00000i	−0.0927478	−	0.0463739i
$466$	−10.0000			−0.463241
$467$			27.0000i			1.24941i	0.780860	+	0.624705i	$0.214781\pi$
$467$			27.0000i			1.24941i	−0.780860	+	0.624705i	$0.785219\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$	4.00000	−	8.00000i	0.184506	−	0.369012i
$471$	23.0000			1.05978
$472$		−	8.00000i		−	0.368230i
$473$		−	35.0000i		−	1.60930i
$474$		0			0
$475$		0			0
$476$	1.00000			0.0458349
$477$			3.00000i			0.137361i
$478$		−	11.0000i		−	0.503128i
$479$	28.0000			1.27935			0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000			1.27935			0.639676	+	0.768644i	$0.279068\pi$
$480$	1.00000	−	2.00000i	0.0456435	−	0.0912871i
$481$		0			0
$482$		−	2.00000i		−	0.0910975i
$483$		−	4.00000i		−	0.182006i
$484$	−14.0000			−0.636364
$485$	−2.00000	−	1.00000i	−0.0908153	−	0.0454077i
$486$	1.00000			0.0453609
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$		−	5.00000i		−	0.226339i
$489$	1.00000			0.0452216
$490$	12.0000	+	6.00000i	0.542105	+	0.271052i
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		−	1.00000i		−	0.0450835i
$493$			3.00000i			0.135113i
$494$		0			0
$495$	−5.00000	+	10.0000i	−0.224733	+	0.449467i
$496$	1.00000			0.0449013
$497$		−	6.00000i		−	0.269137i
$498$			8.00000i			0.358489i
$499$	30.0000			1.34298			0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000			1.34298			0.671492	+	0.741012i	$0.265654\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$	−6.00000			−0.268060
$502$		0			0
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$	−1.00000			−0.0445435
$505$	10.0000	−	20.0000i	0.444994	−	0.889988i
$506$	20.0000			0.889108
$507$		−	13.0000i		−	0.577350i
$508$			8.00000i			0.354943i
$509$	42.0000			1.86162			0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000			1.86162			0.930809	+	0.365507i	$0.119104\pi$
$510$	2.00000	+	1.00000i	0.0885615	+	0.0442807i
$511$	10.0000			0.442374
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−6.00000			−0.264649
$515$	−16.0000	−	8.00000i	−0.705044	−	0.352522i
$516$	7.00000			0.308158
$517$		−	20.0000i		−	0.879599i
$518$			1.00000i			0.0439375i
$519$	13.0000			0.570637
$520$		0			0
$521$	−35.0000			−1.53338			−0.766689	−	0.642019i	$-0.778097\pi$
$521$	−35.0000			−1.53338			−0.766689	+	0.642019i	$0.778097\pi$
$522$		−	3.00000i		−	0.131306i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	6.00000			0.262111
$525$	−3.00000	−	4.00000i	−0.130931	−	0.174574i
$526$	19.0000			0.828439
$527$			1.00000i			0.0435607i
$528$		−	5.00000i		−	0.217597i
$529$	7.00000			0.304348
$530$	3.00000	−	6.00000i	0.130312	−	0.260623i
$531$	−8.00000			−0.347170
$532$		0			0
$533$		0			0
$534$	−8.00000			−0.346194
$535$	12.0000	+	6.00000i	0.518805	+	0.259403i
$536$	−4.00000			−0.172774
$537$			10.0000i			0.431532i
$538$			12.0000i			0.517357i
$539$	30.0000			1.29219
$540$	−2.00000	−	1.00000i	−0.0860663	−	0.0430331i
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$		−	14.0000i		−	0.601351i
$543$			16.0000i			0.686626i
$544$	−1.00000			−0.0428746
$545$	−1.00000	+	2.00000i	−0.0428353	+	0.0856706i
$546$		0			0
$547$		−	41.0000i		−	1.75303i	−0.481371	−	0.876517i	$-0.659861\pi$
$547$		−	41.0000i		−	1.75303i	0.481371	−	0.876517i	$-0.340139\pi$
$548$		−	18.0000i		−	0.768922i
$549$	−5.00000			−0.213395
$550$	20.0000	−	15.0000i	0.852803	−	0.639602i
$551$		0			0
$552$			4.00000i			0.170251i
$553$		0			0
$554$	8.00000			0.339887
$555$	−1.00000	+	2.00000i	−0.0424476	+	0.0848953i
$556$	−11.0000			−0.466504
$557$			6.00000i			0.254228i	0.991888	+	0.127114i	$0.0405714\pi$
$557$			6.00000i			0.254228i	−0.991888	+	0.127114i	$0.959429\pi$
$558$		−	1.00000i		−	0.0423334i
$559$		0			0
$560$	2.00000	+	1.00000i	0.0845154	+	0.0422577i
$561$	5.00000			0.211100
$562$			18.0000i			0.759284i
$563$			19.0000i			0.800755i	0.916350	+	0.400377i	$0.131121\pi$
$563$			19.0000i			0.800755i	−0.916350	+	0.400377i	$0.868879\pi$
$564$	4.00000			0.168430
$565$	42.0000	+	21.0000i	1.76695	+	0.883477i
$566$	−16.0000			−0.672530
$567$			1.00000i			0.0419961i
$568$			6.00000i			0.251754i
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$		0			0
$571$	−29.0000			−1.21361			−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000			−1.21361			−0.606806	+	0.794850i	$0.707550\pi$
$572$		0			0
$573$		−	3.00000i		−	0.125327i
$574$	1.00000			0.0417392
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$	1.00000			0.0416667
$577$			22.0000i			0.915872i	0.888985	+	0.457936i	$0.151411\pi$
$577$			22.0000i			0.915872i	−0.888985	+	0.457936i	$0.848589\pi$
$578$			16.0000i			0.665512i
$579$	−10.0000			−0.415586
$580$	−3.00000	+	6.00000i	−0.124568	+	0.249136i
$581$	−8.00000			−0.331896
$582$		−	1.00000i		−	0.0414513i
$583$		−	15.0000i		−	0.621237i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	9.00000			0.371787
$587$		−	33.0000i		−	1.36206i	−0.732257	−	0.681028i	$-0.761533\pi$
$587$		−	33.0000i		−	1.36206i	0.732257	−	0.681028i	$-0.238467\pi$
$588$			6.00000i			0.247436i
$589$		0			0
$590$	16.0000	+	8.00000i	0.658710	+	0.329355i
$591$	26.0000			1.06950
$592$		−	1.00000i		−	0.0410997i
$593$			24.0000i			0.985562i	0.870153	+	0.492781i	$0.164020\pi$
$593$			24.0000i			0.985562i	−0.870153	+	0.492781i	$0.835980\pi$
$594$	−5.00000			−0.205152
$595$	−1.00000	+	2.00000i	−0.0409960	+	0.0819920i
$596$	4.00000			0.163846
$597$			24.0000i			0.982255i
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	3.00000	+	4.00000i	0.122474	+	0.163299i
$601$	−7.00000			−0.285536			−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000			−0.285536			−0.142768	+	0.989756i	$0.545600\pi$
$602$			7.00000i			0.285299i
$603$			4.00000i			0.162893i
$604$	2.00000			0.0813788
$605$	14.0000	−	28.0000i	0.569181	−	1.13836i
$606$	10.0000			0.406222
$607$		−	10.0000i		−	0.405887i	−0.979190	−	0.202944i	$-0.934949\pi$
$607$		−	10.0000i		−	0.405887i	0.979190	−	0.202944i	$-0.0650509\pi$
$608$		0			0
$609$	3.00000			0.121566
$610$	10.0000	+	5.00000i	0.404888	+	0.202444i
$611$		0			0
$612$			1.00000i			0.0404226i
$613$		−	37.0000i		−	1.49442i	−0.664590	−	0.747208i	$-0.731394\pi$
$613$		−	37.0000i		−	1.49442i	0.664590	−	0.747208i	$-0.268606\pi$
$614$		0			0
$615$	2.00000	+	1.00000i	0.0806478	+	0.0403239i
$616$	5.00000			0.201456
$617$			34.0000i			1.36879i	0.729112	+	0.684394i	$0.239933\pi$
$617$			34.0000i			1.36879i	−0.729112	+	0.684394i	$0.760067\pi$
$618$		−	8.00000i		−	0.321807i
$619$	31.0000			1.24600			0.622998	−	0.782224i	$-0.285915\pi$
$619$	31.0000			1.24600			0.622998	+	0.782224i	$0.285915\pi$
$620$	−1.00000	+	2.00000i	−0.0401610	+	0.0803219i
$621$	4.00000			0.160514
$622$			15.0000i			0.601445i
$623$		−	8.00000i		−	0.320513i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	10.0000			0.399680
$627$		0			0
$628$		−	23.0000i		−	0.917800i
$629$	1.00000			0.0398726
$630$	1.00000	−	2.00000i	0.0398410	−	0.0796819i
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$		0			0
$633$			21.0000i			0.834675i
$634$	5.00000			0.198575
$635$	−16.0000	−	8.00000i	−0.634941	−	0.317470i
$636$	3.00000			0.118958
$637$		0			0
$638$			15.0000i			0.593856i
$639$	6.00000			0.237356
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	−37.0000			−1.46141			−0.730706	−	0.682692i	$-0.760809\pi$
$641$	−37.0000			−1.46141			−0.730706	+	0.682692i	$0.760809\pi$
$642$			6.00000i			0.236801i
$643$			21.0000i			0.828159i	0.910241	+	0.414080i	$0.135896\pi$
$643$			21.0000i			0.828159i	−0.910241	+	0.414080i	$0.864104\pi$
$644$	−4.00000			−0.157622
$645$	−7.00000	+	14.0000i	−0.275625	+	0.551249i
$646$		0			0
$647$			42.0000i			1.65119i	0.564263	+	0.825595i	$0.309160\pi$
$647$			42.0000i			1.65119i	−0.564263	+	0.825595i	$0.690840\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	40.0000			1.57014
$650$		0			0
$651$	1.00000			0.0391931
$652$		−	1.00000i		−	0.0391630i
$653$		−	10.0000i		−	0.391330i	−0.980671	−	0.195665i	$-0.937313\pi$
$653$		−	10.0000i		−	0.391330i	0.980671	−	0.195665i	$-0.0626866\pi$
$654$	−1.00000			−0.0391031
$655$	−6.00000	+	12.0000i	−0.234439	+	0.468879i
$656$	−1.00000			−0.0390434
$657$			10.0000i			0.390137i
$658$			4.00000i			0.155936i
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$	10.0000	+	5.00000i	0.389249	+	0.194625i
$661$	−13.0000			−0.505641			−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000			−0.505641			−0.252821	+	0.967513i	$0.581358\pi$
$662$		−	26.0000i		−	1.01052i
$663$		0			0
$664$	8.00000			0.310460
$665$		0			0
$666$	−1.00000			−0.0387492
$667$		−	12.0000i		−	0.464642i
$668$			6.00000i			0.232147i
$669$	5.00000			0.193311
$670$	4.00000	−	8.00000i	0.154533	−	0.309067i
$671$	25.0000			0.965114
$672$			1.00000i			0.0385758i
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	−16.0000			−0.616297
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	−13.0000			−0.500000
$677$		−	2.00000i		−	0.0768662i	−0.999261	−	0.0384331i	$-0.987763\pi$
$677$		−	2.00000i		−	0.0768662i	0.999261	−	0.0384331i	$-0.0122367\pi$
$678$			21.0000i			0.806500i
$679$	1.00000			0.0383765
$680$	1.00000	−	2.00000i	0.0383482	−	0.0766965i
$681$	1.00000			0.0383201
$682$			5.00000i			0.191460i
$683$		−	37.0000i		−	1.41577i	−0.706330	−	0.707883i	$-0.749650\pi$
$683$		−	37.0000i		−	1.41577i	0.706330	−	0.707883i	$-0.250350\pi$
$684$		0			0
$685$	36.0000	+	18.0000i	1.37549	+	0.687745i
$686$	−13.0000			−0.496342
$687$		−	16.0000i		−	0.610438i
$688$		−	7.00000i		−	0.266872i
$689$		0			0
$690$	−8.00000	−	4.00000i	−0.304555	−	0.152277i
$691$	−5.00000			−0.190209			−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000			−0.190209			−0.0951045	+	0.995467i	$0.530319\pi$
$692$		−	13.0000i		−	0.494186i
$693$		−	5.00000i		−	0.189934i
$694$	−12.0000			−0.455514
$695$	11.0000	−	22.0000i	0.417254	−	0.834508i
$696$	−3.00000			−0.113715
$697$		−	1.00000i		−	0.0378777i
$698$			2.00000i			0.0757011i
$699$	10.0000			0.378235
$700$	−4.00000	+	3.00000i	−0.151186	+	0.113389i
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$		0			0
$704$	−5.00000			−0.188445
$705$	−4.00000	+	8.00000i	−0.150649	+	0.301297i
$706$	−31.0000			−1.16670
$707$			10.0000i			0.376089i
$708$			8.00000i			0.300658i
$709$	−9.00000			−0.338002			−0.169001	−	0.985616i	$-0.554054\pi$
$709$	−9.00000			−0.338002			−0.169001	+	0.985616i	$0.554054\pi$
$710$	−12.0000	−	6.00000i	−0.450352	−	0.225176i
$711$		0			0
$712$			8.00000i			0.299813i
$713$		−	4.00000i		−	0.149801i
$714$	−1.00000			−0.0374241
$715$		0			0
$716$	10.0000			0.373718
$717$			11.0000i			0.410803i
$718$		−	6.00000i		−	0.223918i
$719$	28.0000			1.04422			0.522112	−	0.852877i	$-0.325144\pi$
$719$	28.0000			1.04422			0.522112	+	0.852877i	$0.325144\pi$
$720$	−1.00000	+	2.00000i	−0.0372678	+	0.0745356i
$721$	8.00000			0.297936
$722$		−	19.0000i		−	0.707107i
$723$			2.00000i			0.0743808i
$724$	16.0000			0.594635
$725$	−9.00000	−	12.0000i	−0.334252	−	0.445669i
$726$	14.0000			0.519589
$727$		−	42.0000i		−	1.55769i	−0.627214	−	0.778847i	$-0.715805\pi$
$727$		−	42.0000i		−	1.55769i	0.627214	−	0.778847i	$-0.284195\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	10.0000	−	20.0000i	0.370117	−	0.740233i
$731$	7.00000			0.258904
$732$			5.00000i			0.184805i
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$	−13.0000			−0.479839
$735$	−12.0000	−	6.00000i	−0.442627	−	0.221313i
$736$	4.00000			0.147442
$737$		−	20.0000i		−	0.736709i
$738$			1.00000i			0.0368105i
$739$	−37.0000			−1.36107			−0.680534	−	0.732717i	$-0.738252\pi$
$739$	−37.0000			−1.36107			−0.680534	+	0.732717i	$0.738252\pi$
$740$	2.00000	+	1.00000i	0.0735215	+	0.0367607i
$741$		0			0
$742$			3.00000i			0.110133i
$743$		−	15.0000i		−	0.550297i	−0.961402	−	0.275148i	$-0.911273\pi$
$743$		−	15.0000i		−	0.550297i	0.961402	−	0.275148i	$-0.0887270\pi$
$744$	−1.00000			−0.0366618
$745$	−4.00000	+	8.00000i	−0.146549	+	0.293097i
$746$	6.00000			0.219676
$747$		−	8.00000i		−	0.292705i
$748$		−	5.00000i		−	0.182818i
$749$	−6.00000			−0.219235
$750$	−11.0000	+	2.00000i	−0.401663	+	0.0730297i
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		−	4.00000i		−	0.145865i
$753$		0			0
$754$		0			0
$755$	−2.00000	+	4.00000i	−0.0727875	+	0.145575i
$756$	1.00000			0.0363696
$757$		−	20.0000i		−	0.726912i	−0.931611	−	0.363456i	$-0.881597\pi$
$757$		−	20.0000i		−	0.726912i	0.931611	−	0.363456i	$-0.118403\pi$
$758$		−	20.0000i		−	0.726433i
$759$	−20.0000			−0.725954
$760$		0			0
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$		−	8.00000i		−	0.289809i
$763$		−	1.00000i		−	0.0362024i
$764$	−3.00000			−0.108536
$765$	−2.00000	−	1.00000i	−0.0723102	−	0.0361551i
$766$	8.00000			0.289052
$767$		0			0
$768$		−	1.00000i		−	0.0360844i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$	−5.00000	+	10.0000i	−0.180187	+	0.360375i
$771$	6.00000			0.216085
$772$			10.0000i			0.359908i
$773$			27.0000i			0.971123i	0.874203	+	0.485561i	$0.161385\pi$
$773$			27.0000i			0.971123i	−0.874203	+	0.485561i	$0.838615\pi$
$774$	−7.00000			−0.251610
$775$	−3.00000	−	4.00000i	−0.107763	−	0.143684i
$776$	−1.00000			−0.0358979
$777$		−	1.00000i		−	0.0358748i
$778$		−	23.0000i		−	0.824590i
$779$		0			0
$780$		0			0
$781$	−30.0000			−1.07348
$782$			4.00000i			0.143040i
$783$			3.00000i			0.107211i
$784$	6.00000			0.214286
$785$	46.0000	+	23.0000i	1.64181	+	0.820905i
$786$	−6.00000			−0.214013
$787$			10.0000i			0.356462i	0.983989	+	0.178231i	$0.0570374\pi$
$787$			10.0000i			0.356462i	−0.983989	+	0.178231i	$0.942963\pi$
$788$		−	26.0000i		−	0.926212i
$789$	−19.0000			−0.676418
$790$		0			0
$791$	−21.0000			−0.746674
$792$			5.00000i			0.177667i
$793$		0			0
$794$	−22.0000			−0.780751
$795$	−3.00000	+	6.00000i	−0.106399	+	0.212798i
$796$	24.0000			0.850657
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$	8.00000			0.282666
$802$			10.0000i			0.353112i
$803$		−	50.0000i		−	1.76446i
$804$	4.00000			0.141069
$805$	4.00000	−	8.00000i	0.140981	−	0.281963i
$806$		0			0
$807$		−	12.0000i		−	0.422420i
$808$		−	10.0000i		−	0.351799i
$809$	−48.0000			−1.68759			−0.843795	−	0.536666i	$-0.819684\pi$
$809$	−48.0000			−1.68759			−0.843795	+	0.536666i	$0.819684\pi$
$810$	2.00000	+	1.00000i	0.0702728	+	0.0351364i
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		−	3.00000i		−	0.105279i
$813$			14.0000i			0.491001i
$814$	5.00000			0.175250
$815$	2.00000	+	1.00000i	0.0700569	+	0.0350285i
$816$	1.00000			0.0350070
$817$		0			0
$818$			40.0000i			1.39857i
$819$		0			0
$820$	1.00000	−	2.00000i	0.0349215	−	0.0698430i
$821$	−50.0000			−1.74501			−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000			−1.74501			−0.872506	+	0.488603i	$0.837507\pi$
$822$			18.0000i			0.627822i
$823$			24.0000i			0.836587i	0.908312	+	0.418294i	$0.137372\pi$
$823$			24.0000i			0.836587i	−0.908312	+	0.418294i	$0.862628\pi$
$824$	−8.00000			−0.278693
$825$	−20.0000	+	15.0000i	−0.696311	+	0.522233i
$826$	−8.00000			−0.278356
$827$		−	35.0000i		−	1.21707i	−0.793527	−	0.608535i	$-0.791758\pi$
$827$		−	35.0000i		−	1.21707i	0.793527	−	0.608535i	$-0.208242\pi$
$828$		−	4.00000i		−	0.139010i
$829$	−21.0000			−0.729360			−0.364680	−	0.931133i	$-0.618822\pi$
$829$	−21.0000			−0.729360			−0.364680	+	0.931133i	$0.618822\pi$
$830$	−8.00000	+	16.0000i	−0.277684	+	0.555368i
$831$	−8.00000			−0.277517
$832$		0			0
$833$			6.00000i			0.207888i
$834$	11.0000			0.380899
$835$	−12.0000	−	6.00000i	−0.415277	−	0.207639i
$836$		0			0
$837$			1.00000i			0.0345651i
$838$		−	20.0000i		−	0.690889i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	−2.00000	−	1.00000i	−0.0690066	−	0.0345033i
$841$	−20.0000			−0.689655
$842$		−	38.0000i		−	1.30957i
$843$		−	18.0000i		−	0.619953i
$844$	21.0000			0.722850
$845$	13.0000	−	26.0000i	0.447214	−	0.894427i
$846$	−4.00000			−0.137523
$847$			14.0000i			0.481046i
$848$		−	3.00000i		−	0.103020i
$849$	16.0000			0.549119
$850$	3.00000	+	4.00000i	0.102899	+	0.137199i
$851$	−4.00000			−0.137118
$852$		−	6.00000i		−	0.205557i
$853$		−	2.00000i		−	0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$		−	2.00000i		−	0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$	−5.00000			−0.171096
$855$		0			0
$856$	6.00000			0.205076
$857$			27.0000i			0.922302i	0.887322	+	0.461151i	$0.152563\pi$
$857$			27.0000i			0.922302i	−0.887322	+	0.461151i	$0.847437\pi$
$858$		0			0
$859$	−8.00000			−0.272956			−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000			−0.272956			−0.136478	+	0.990643i	$0.543578\pi$
$860$	14.0000	+	7.00000i	0.477396	+	0.238698i
$861$	−1.00000			−0.0340799
$862$		−	13.0000i		−	0.442782i
$863$		−	21.0000i		−	0.714848i	−0.933942	−	0.357424i	$-0.883655\pi$
$863$		−	21.0000i		−	0.714848i	0.933942	−	0.357424i	$-0.116345\pi$
$864$	−1.00000			−0.0340207
$865$	26.0000	+	13.0000i	0.884027	+	0.442013i
$866$	−20.0000			−0.679628
$867$		−	16.0000i		−	0.543388i
$868$		−	1.00000i		−	0.0339422i
$869$		0			0
$870$	3.00000	−	6.00000i	0.101710	−	0.203419i
$871$		0			0
$872$			1.00000i			0.0338643i
$873$			1.00000i			0.0338449i
$874$		0			0
$875$	−2.00000	−	11.0000i	−0.0676123	−	0.371868i
$876$	10.0000			0.337869
$877$		−	13.0000i		−	0.438979i	−0.975615	−	0.219489i	$-0.929561\pi$
$877$		−	13.0000i		−	0.438979i	0.975615	−	0.219489i	$-0.0704391\pi$
$878$			33.0000i			1.11370i
$879$	−9.00000			−0.303562
$880$	5.00000	−	10.0000i	0.168550	−	0.337100i
$881$	−45.0000			−1.51609			−0.758044	−	0.652203i	$-0.773845\pi$
$881$	−45.0000			−1.51609			−0.758044	+	0.652203i	$0.773845\pi$
$882$		−	6.00000i		−	0.202031i
$883$		−	33.0000i		−	1.11054i	−0.831671	−	0.555269i	$-0.812615\pi$
$883$		−	33.0000i		−	1.11054i	0.831671	−	0.555269i	$-0.187385\pi$
$884$		0			0
$885$	−16.0000	−	8.00000i	−0.537834	−	0.268917i
$886$	−6.00000			−0.201574
$887$		−	45.0000i		−	1.51095i	−0.655176	−	0.755476i	$-0.727406\pi$
$887$		−	45.0000i		−	1.51095i	0.655176	−	0.755476i	$-0.272594\pi$
$888$			1.00000i			0.0335578i
$889$	8.00000			0.268311
$890$	−16.0000	−	8.00000i	−0.536321	−	0.268161i
$891$	5.00000			0.167506
$892$		−	5.00000i		−	0.167412i
$893$		0			0
$894$	−4.00000			−0.133780
$895$	−10.0000	+	20.0000i	−0.334263	+	0.668526i
$896$	1.00000			0.0334077
$897$		0			0
$898$			24.0000i			0.800890i
$899$	3.00000			0.100056
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$	3.00000			0.0999445
$902$		−	5.00000i		−	0.166482i
$903$		−	7.00000i		−	0.232945i
$904$	21.0000			0.698450
$905$	−16.0000	+	32.0000i	−0.531858	+	1.06372i
$906$	−2.00000			−0.0664455
$907$			36.0000i			1.19536i	0.801735	+	0.597680i	$0.203911\pi$
$907$			36.0000i			1.19536i	−0.801735	+	0.597680i	$0.796089\pi$
$908$		−	1.00000i		−	0.0331862i
$909$	−10.0000			−0.331679
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$			40.0000i			1.32381i
$914$	−19.0000			−0.628464
$915$	−10.0000	−	5.00000i	−0.330590	−	0.165295i
$916$	−16.0000			−0.528655
$917$		−	6.00000i		−	0.198137i
$918$		−	1.00000i		−	0.0330049i
$919$	−48.0000			−1.58337			−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000			−1.58337			−0.791687	+	0.610927i	$0.790797\pi$
$920$	−4.00000	+	8.00000i	−0.131876	+	0.263752i
$921$		0			0
$922$			3.00000i			0.0987997i
$923$		0			0
$924$	−5.00000			−0.164488
$925$	−4.00000	+	3.00000i	−0.131519	+	0.0986394i
$926$	−24.0000			−0.788689
$927$			8.00000i			0.262754i
$928$			3.00000i			0.0984798i
$929$	3.00000			0.0984268			0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000			0.0984268			0.0492134	+	0.998788i	$0.484329\pi$
$930$	1.00000	−	2.00000i	0.0327913	−	0.0655826i
$931$		0			0
$932$		−	10.0000i		−	0.327561i
$933$		−	15.0000i		−	0.491078i
$934$	−27.0000			−0.883467
$935$	10.0000	+	5.00000i	0.327035	+	0.163517i
$936$		0			0
$937$		−	16.0000i		−	0.522697i	−0.965244	−	0.261349i	$-0.915833\pi$
$937$		−	16.0000i		−	0.522697i	0.965244	−	0.261349i	$-0.0841672\pi$
$938$			4.00000i			0.130605i
$939$	−10.0000			−0.326338
$940$	8.00000	+	4.00000i	0.260931	+	0.130466i
$941$	−22.0000			−0.717180			−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000			−0.717180			−0.358590	+	0.933495i	$0.616742\pi$
$942$			23.0000i			0.749380i
$943$			4.00000i			0.130258i
$944$	8.00000			0.260378
$945$	−1.00000	+	2.00000i	−0.0325300	+	0.0650600i
$946$	35.0000			1.13795
$947$		−	27.0000i		−	0.877382i	−0.898638	−	0.438691i	$-0.855442\pi$
$947$		−	27.0000i		−	0.877382i	0.898638	−	0.438691i	$-0.144558\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−5.00000			−0.162136
$952$			1.00000i			0.0324102i
$953$		−	14.0000i		−	0.453504i	−0.973952	−	0.226752i	$-0.927189\pi$
$953$		−	14.0000i		−	0.453504i	0.973952	−	0.226752i	$-0.0728108\pi$
$954$	−3.00000			−0.0971286
$955$	3.00000	−	6.00000i	0.0970777	−	0.194155i
$956$	11.0000			0.355765
$957$		−	15.0000i		−	0.484881i
$958$			28.0000i			0.904639i
$959$	−18.0000			−0.581250
$960$	2.00000	+	1.00000i	0.0645497	+	0.0322749i
$961$	−30.0000			−0.967742
$962$		0			0
$963$		−	6.00000i		−	0.193347i
$964$	2.00000			0.0644157
$965$	−20.0000	−	10.0000i	−0.643823	−	0.321911i
$966$	4.00000			0.128698
$967$		−	10.0000i		−	0.321578i	−0.986989	−	0.160789i	$-0.948596\pi$
$967$		−	10.0000i		−	0.321578i	0.986989	−	0.160789i	$-0.0514039\pi$
$968$		−	14.0000i		−	0.449977i
$969$		0			0
$970$	1.00000	−	2.00000i	0.0321081	−	0.0642161i
$971$	39.0000			1.25157			0.625785	−	0.779996i	$-0.284779\pi$
$971$	39.0000			1.25157			0.625785	+	0.779996i	$0.284779\pi$
$972$			1.00000i			0.0320750i
$973$			11.0000i			0.352644i
$974$	12.0000			0.384505
$975$		0			0
$976$	5.00000			0.160046
$977$		−	3.00000i		−	0.0959785i	−0.998848	−	0.0479893i	$-0.984719\pi$
$977$		−	3.00000i		−	0.0959785i	0.998848	−	0.0479893i	$-0.0152813\pi$
$978$			1.00000i			0.0319765i
$979$	−40.0000			−1.27841
$980$	−6.00000	+	12.0000i	−0.191663	+	0.383326i
$981$	1.00000			0.0319275
$982$			12.0000i			0.382935i
$983$			7.00000i			0.223265i	0.993750	+	0.111633i	$0.0356080\pi$
$983$			7.00000i			0.223265i	−0.993750	+	0.111633i	$0.964392\pi$
$984$	1.00000			0.0318788
$985$	52.0000	+	26.0000i	1.65686	+	0.828429i
$986$	−3.00000			−0.0955395
$987$		−	4.00000i		−	0.127321i
$988$		0			0
$989$	−28.0000			−0.890348
$990$	−10.0000	−	5.00000i	−0.317821	−	0.158910i
$991$	−5.00000			−0.158830			−0.0794151	−	0.996842i	$-0.525305\pi$
$991$	−5.00000			−0.158830			−0.0794151	+	0.996842i	$0.525305\pi$
$992$			1.00000i			0.0317500i
$993$			26.0000i			0.825085i
$994$	6.00000			0.190308
$995$	−24.0000	+	48.0000i	−0.760851	+	1.52170i
$996$	−8.00000			−0.253490
$997$		−	24.0000i		−	0.760088i	−0.924968	−	0.380044i	$-0.875909\pi$
$997$		−	24.0000i		−	0.760088i	0.924968	−	0.380044i	$-0.124091\pi$
$998$			30.0000i			0.949633i
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.d.c.889.2	yes	2
3.2	odd	2		3330.2.d.d.1999.1		2
5.2	odd	4		5550.2.a.d.1.1		1
5.3	odd	4		5550.2.a.bo.1.1		1
5.4	even	2	inner	1110.2.d.c.889.1	✓	2
15.14	odd	2		3330.2.d.d.1999.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.c.889.1	✓	2	5.4	even	2	inner
1110.2.d.c.889.2	yes	2	1.1	even	1	trivial
3330.2.d.d.1999.1		2	3.2	odd	2
3330.2.d.d.1999.2		2	15.14	odd	2
5550.2.a.d.1.1		1	5.2	odd	4
5550.2.a.bo.1.1		1	5.3	odd	4

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} +5.00000 q^{11} +1.00000i q^{12} -1.00000 q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -1.00000i q^{18} +(-1.00000 + 2.00000i) q^{20} +1.00000 q^{21} +5.00000i q^{22} -4.00000i q^{23} -1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +1.00000i q^{27} -1.00000i q^{28} +3.00000 q^{29} +(1.00000 - 2.00000i) q^{30} +1.00000 q^{31} +1.00000i q^{32} -5.00000i q^{33} -1.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +(-2.00000 - 1.00000i) q^{40} -1.00000 q^{41} +1.00000i q^{42} -7.00000i q^{43} -5.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} +4.00000 q^{46} -4.00000i q^{47} -1.00000i q^{48} +6.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +1.00000 q^{51} -3.00000i q^{53} -1.00000 q^{54} +(5.00000 - 10.0000i) q^{55} +1.00000 q^{56} +3.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} +5.00000 q^{61} +1.00000i q^{62} -1.00000i q^{63} -1.00000 q^{64} +5.00000 q^{66} -4.00000i q^{67} -1.00000i q^{68} -4.00000 q^{69} +(-1.00000 + 2.00000i) q^{70} -6.00000 q^{71} +1.00000i q^{72} -10.0000i q^{73} +1.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +5.00000i q^{77} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -1.00000i q^{82} +8.00000i q^{83} -1.00000 q^{84} +(2.00000 + 1.00000i) q^{85} +7.00000 q^{86} -3.00000i q^{87} -5.00000i q^{88} -8.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +4.00000i q^{92} -1.00000i q^{93} +4.00000 q^{94} +1.00000 q^{96} -1.00000i q^{97} +6.00000i q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} + 10 q^{11} - 2 q^{14} - 4 q^{15} + 2 q^{16} - 2 q^{20} + 2 q^{21} - 2 q^{24} - 6 q^{25} + 6 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{40} - 2 q^{41} - 10 q^{44} - 2 q^{45} + 8 q^{46} + 12 q^{49} + 8 q^{50} + 2 q^{51} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 16 q^{59} + 4 q^{60} + 10 q^{61} - 2 q^{64} + 10 q^{66} - 8 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{74} - 8 q^{75} + 2 q^{80} + 2 q^{81} - 2 q^{84} + 4 q^{85} + 14 q^{86} - 16 q^{89} - 4 q^{90} + 8 q^{94} + 2 q^{96} - 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 + 10 * q^11 - 2 * q^14 - 4 * q^15 + 2 * q^16 - 2 * q^20 + 2 * q^21 - 2 * q^24 - 6 * q^25 + 6 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^40 - 2 * q^41 - 10 * q^44 - 2 * q^45 + 8 * q^46 + 12 * q^49 + 8 * q^50 + 2 * q^51 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 16 * q^59 + 4 * q^60 + 10 * q^61 - 2 * q^64 + 10 * q^66 - 8 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^74 - 8 * q^75 + 2 * q^80 + 2 * q^81 - 2 * q^84 + 4 * q^85 + 14 * q^86 - 16 * q^89 - 4 * q^90 + 8 * q^94 + 2 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

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