LMFDB - Embedded newform 2006.2.b.a.237.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(237,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2006.237");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.b (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:	$16.0179906455$
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			237.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2006.237
Dual form			2006.2.b.a.237.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -4.00000i q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -4.00000i q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.00000i q^{10} -4.00000i q^{11} +1.00000i q^{12} +1.00000 q^{13} +4.00000i q^{14} +2.00000 q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} -2.00000 q^{18} +2.00000 q^{19} -2.00000i q^{20} +4.00000 q^{21} +4.00000i q^{22} +3.00000i q^{23} -1.00000i q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.00000i q^{27} -4.00000i q^{28} -5.00000i q^{29} -2.00000 q^{30} +7.00000i q^{31} -1.00000 q^{32} +4.00000 q^{33} +(-1.00000 + 4.00000i) q^{34} -8.00000 q^{35} +2.00000 q^{36} -10.0000i q^{37} -2.00000 q^{38} +1.00000i q^{39} +2.00000i q^{40} +2.00000i q^{41} -4.00000 q^{42} -4.00000i q^{44} -4.00000i q^{45} -3.00000i q^{46} -2.00000 q^{47} +1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{50} +(4.00000 + 1.00000i) q^{51} +1.00000 q^{52} -4.00000 q^{53} -5.00000i q^{54} -8.00000 q^{55} +4.00000i q^{56} +2.00000i q^{57} +5.00000i q^{58} -1.00000 q^{59} +2.00000 q^{60} +8.00000i q^{61} -7.00000i q^{62} -8.00000i q^{63} +1.00000 q^{64} -2.00000i q^{65} -4.00000 q^{66} -3.00000 q^{67} +(1.00000 - 4.00000i) q^{68} -3.00000 q^{69} +8.00000 q^{70} -6.00000i q^{71} -2.00000 q^{72} -2.00000i q^{73} +10.0000i q^{74} +1.00000i q^{75} +2.00000 q^{76} -16.0000 q^{77} -1.00000i q^{78} +4.00000i q^{79} -2.00000i q^{80} +1.00000 q^{81} -2.00000i q^{82} +5.00000 q^{83} +4.00000 q^{84} +(-8.00000 - 2.00000i) q^{85} +5.00000 q^{87} +4.00000i q^{88} -6.00000 q^{89} +4.00000i q^{90} -4.00000i q^{91} +3.00000i q^{92} -7.00000 q^{93} +2.00000 q^{94} -4.00000i q^{95} -1.00000i q^{96} -5.00000i q^{97} +9.00000 q^{98} -8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} - 4 q^{18} + 4 q^{19} + 8 q^{21} + 2 q^{25} - 2 q^{26} - 4 q^{30} - 2 q^{32} + 8 q^{33} - 2 q^{34} - 16 q^{35} + 4 q^{36} - 4 q^{38} - 8 q^{42} - 4 q^{47} - 18 q^{49} - 2 q^{50} + 8 q^{51} + 2 q^{52} - 8 q^{53} - 16 q^{55} - 2 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{66} - 6 q^{67} + 2 q^{68} - 6 q^{69} + 16 q^{70} - 4 q^{72} + 4 q^{76} - 32 q^{77} + 2 q^{81} + 10 q^{83} + 8 q^{84} - 16 q^{85} + 10 q^{87} - 12 q^{89} - 14 q^{93} + 4 q^{94} + 18 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 - 4 * q^18 + 4 * q^19 + 8 * q^21 + 2 * q^25 - 2 * q^26 - 4 * q^30 - 2 * q^32 + 8 * q^33 - 2 * q^34 - 16 * q^35 + 4 * q^36 - 4 * q^38 - 8 * q^42 - 4 * q^47 - 18 * q^49 - 2 * q^50 + 8 * q^51 + 2 * q^52 - 8 * q^53 - 16 * q^55 - 2 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^66 - 6 * q^67 + 2 * q^68 - 6 * q^69 + 16 * q^70 - 4 * q^72 + 4 * q^76 - 32 * q^77 + 2 * q^81 + 10 * q^83 + 8 * q^84 - 16 * q^85 + 10 * q^87 - 12 * q^89 - 14 * q^93 + 4 * q^94 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2006\mathbb{Z}\right)^\times$.

$n$	$1123$	$1771$
$\chi(n)$	$1$	$-1$

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	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	1.00000			0.500000
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		−	1.00000i		−	0.408248i
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$	−1.00000			−0.353553
$9$	2.00000			0.666667
$10$			2.00000i			0.632456i
$11$		−	4.00000i		−	1.20605i	−0.797724	−	0.603023i	$-0.793963\pi$
$11$		−	4.00000i		−	1.20605i	0.797724	−	0.603023i	$-0.206037\pi$
$12$			1.00000i			0.288675i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$			4.00000i			1.06904i
$15$	2.00000			0.516398
$16$	1.00000			0.250000
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$18$	−2.00000			−0.471405
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$		−	2.00000i		−	0.447214i
$21$	4.00000			0.872872
$22$			4.00000i			0.852803i
$23$			3.00000i			0.625543i	0.949828	+	0.312772i	$0.101257\pi$
$23$			3.00000i			0.625543i	−0.949828	+	0.312772i	$0.898743\pi$
$24$		−	1.00000i		−	0.204124i
$25$	1.00000			0.200000
$26$	−1.00000			−0.196116
$27$			5.00000i			0.962250i
$28$		−	4.00000i		−	0.755929i
$29$		−	5.00000i		−	0.928477i	−0.885710	−	0.464238i	$-0.846328\pi$
$29$		−	5.00000i		−	0.928477i	0.885710	−	0.464238i	$-0.153672\pi$
$30$	−2.00000			−0.365148
$31$			7.00000i			1.25724i	0.777714	+	0.628619i	$0.216379\pi$
$31$			7.00000i			1.25724i	−0.777714	+	0.628619i	$0.783621\pi$
$32$	−1.00000			−0.176777
$33$	4.00000			0.696311
$34$	−1.00000	+	4.00000i	−0.171499	+	0.685994i
$35$	−8.00000			−1.35225
$36$	2.00000			0.333333
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$	−2.00000			−0.324443
$39$			1.00000i			0.160128i
$40$			2.00000i			0.316228i
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$	−4.00000			−0.617213
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		−	4.00000i		−	0.603023i
$45$		−	4.00000i		−	0.596285i
$46$		−	3.00000i		−	0.442326i
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$			1.00000i			0.144338i
$49$	−9.00000			−1.28571
$50$	−1.00000			−0.141421
$51$	4.00000	+	1.00000i	0.560112	+	0.140028i
$52$	1.00000			0.138675
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		−	5.00000i		−	0.680414i
$55$	−8.00000			−1.07872
$56$			4.00000i			0.534522i
$57$			2.00000i			0.264906i
$58$			5.00000i			0.656532i
$59$	−1.00000			−0.130189
$59$	−1.00000			−0.130189
$60$	2.00000			0.258199
$61$			8.00000i			1.02430i	0.858898	+	0.512148i	$0.171150\pi$
$61$			8.00000i			1.02430i	−0.858898	+	0.512148i	$0.828850\pi$
$62$		−	7.00000i		−	0.889001i
$63$		−	8.00000i		−	1.00791i
$64$	1.00000			0.125000
$65$		−	2.00000i		−	0.248069i
$66$	−4.00000			−0.492366
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	1.00000	−	4.00000i	0.121268	−	0.485071i
$69$	−3.00000			−0.361158
$70$	8.00000			0.956183
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	−2.00000			−0.235702
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$			10.0000i			1.16248i
$75$			1.00000i			0.115470i
$76$	2.00000			0.229416
$77$	−16.0000			−1.82337
$78$		−	1.00000i		−	0.113228i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$		−	2.00000i		−	0.223607i
$81$	1.00000			0.111111
$82$		−	2.00000i		−	0.220863i
$83$	5.00000			0.548821			0.274411	−	0.961613i	$-0.411517\pi$
$83$	5.00000			0.548821			0.274411	+	0.961613i	$0.411517\pi$
$84$	4.00000			0.436436
$85$	−8.00000	−	2.00000i	−0.867722	−	0.216930i
$86$		0			0
$87$	5.00000			0.536056
$88$			4.00000i			0.426401i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$			4.00000i			0.421637i
$91$		−	4.00000i		−	0.419314i
$92$			3.00000i			0.312772i
$93$	−7.00000			−0.725866
$94$	2.00000			0.206284
$95$		−	4.00000i		−	0.410391i
$96$		−	1.00000i		−	0.102062i
$97$		−	5.00000i		−	0.507673i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$		−	5.00000i		−	0.507673i	0.967247	−	0.253837i	$-0.0816925\pi$
$98$	9.00000			0.909137
$99$		−	8.00000i		−	0.804030i
$100$	1.00000			0.100000
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$	−4.00000	−	1.00000i	−0.396059	−	0.0990148i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	−1.00000			−0.0980581
$105$		−	8.00000i		−	0.780720i
$106$	4.00000			0.388514
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$			5.00000i			0.481125i
$109$			20.0000i			1.91565i	0.287348	+	0.957826i	$0.407226\pi$
$109$			20.0000i			1.91565i	−0.287348	+	0.957826i	$0.592774\pi$
$110$	8.00000			0.762770
$111$	10.0000			0.949158
$112$		−	4.00000i		−	0.377964i
$113$			2.00000i			0.188144i	0.995565	+	0.0940721i	$0.0299884\pi$
$113$			2.00000i			0.188144i	−0.995565	+	0.0940721i	$0.970012\pi$
$114$		−	2.00000i		−	0.187317i
$115$	6.00000			0.559503
$116$		−	5.00000i		−	0.464238i
$117$	2.00000			0.184900
$118$	1.00000			0.0920575
$119$	−16.0000	−	4.00000i	−1.46672	−	0.366679i
$120$	−2.00000			−0.182574
$121$	−5.00000			−0.454545
$122$		−	8.00000i		−	0.724286i
$123$	−2.00000			−0.180334
$124$			7.00000i			0.628619i
$125$		−	12.0000i		−	1.07331i
$126$			8.00000i			0.712697i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$			2.00000i			0.175412i
$131$		−	6.00000i		−	0.524222i	−0.965038	−	0.262111i	$-0.915581\pi$
$131$		−	6.00000i		−	0.524222i	0.965038	−	0.262111i	$-0.0844187\pi$
$132$	4.00000			0.348155
$133$		−	8.00000i		−	0.693688i
$134$	3.00000			0.259161
$135$	10.0000			0.860663
$136$	−1.00000	+	4.00000i	−0.0857493	+	0.342997i
$137$	23.0000			1.96502			0.982511	−	0.186203i	$-0.0596182\pi$
$137$	23.0000			1.96502			0.982511	+	0.186203i	$0.0596182\pi$
$138$	3.00000			0.255377
$139$		−	9.00000i		−	0.763370i	−0.924292	−	0.381685i	$-0.875344\pi$
$139$		−	9.00000i		−	0.763370i	0.924292	−	0.381685i	$-0.124656\pi$
$140$	−8.00000			−0.676123
$141$		−	2.00000i		−	0.168430i
$142$			6.00000i			0.503509i
$143$		−	4.00000i		−	0.334497i
$144$	2.00000			0.166667
$145$	−10.0000			−0.830455
$146$			2.00000i			0.165521i
$147$		−	9.00000i		−	0.742307i
$148$		−	10.0000i		−	0.821995i
$149$	−3.00000			−0.245770			−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000			−0.245770			−0.122885	+	0.992421i	$0.539215\pi$
$150$		−	1.00000i		−	0.0816497i
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−2.00000			−0.162221
$153$	2.00000	−	8.00000i	0.161690	−	0.646762i
$154$	16.0000			1.28932
$155$	14.0000			1.12451
$156$			1.00000i			0.0800641i
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$		−	4.00000i		−	0.318223i
$159$		−	4.00000i		−	0.317221i
$160$			2.00000i			0.158114i
$161$	12.0000			0.945732
$162$	−1.00000			−0.0785674
$163$		−	3.00000i		−	0.234978i	−0.993074	−	0.117489i	$-0.962515\pi$
$163$		−	3.00000i		−	0.234978i	0.993074	−	0.117489i	$-0.0374845\pi$
$164$			2.00000i			0.156174i
$165$		−	8.00000i		−	0.622799i
$166$	−5.00000			−0.388075
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$	−4.00000			−0.308607
$169$	−12.0000			−0.923077
$170$	8.00000	+	2.00000i	0.613572	+	0.153393i
$171$	4.00000			0.305888
$172$		0			0
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$	−5.00000			−0.379049
$175$		−	4.00000i		−	0.302372i
$176$		−	4.00000i		−	0.301511i
$177$		−	1.00000i		−	0.0751646i
$178$	6.00000			0.449719
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		−	4.00000i		−	0.298142i
$181$			7.00000i			0.520306i	0.965567	+	0.260153i	$0.0837730\pi$
$181$			7.00000i			0.520306i	−0.965567	+	0.260153i	$0.916227\pi$
$182$			4.00000i			0.296500i
$183$	−8.00000			−0.591377
$184$		−	3.00000i		−	0.221163i
$185$	−20.0000			−1.47043
$186$	7.00000			0.513265
$187$	−16.0000	−	4.00000i	−1.17004	−	0.292509i
$188$	−2.00000			−0.145865
$189$	20.0000			1.45479
$190$			4.00000i			0.290191i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$			1.00000i			0.0721688i
$193$		−	20.0000i		−	1.43963i	−0.694165	−	0.719816i	$-0.744226\pi$
$193$		−	20.0000i		−	1.43963i	0.694165	−	0.719816i	$-0.255774\pi$
$194$			5.00000i			0.358979i
$195$	2.00000			0.143223
$196$	−9.00000			−0.642857
$197$		−	21.0000i		−	1.49619i	−0.663593	−	0.748094i	$-0.730969\pi$
$197$		−	21.0000i		−	1.49619i	0.663593	−	0.748094i	$-0.269031\pi$
$198$			8.00000i			0.568535i
$199$			20.0000i			1.41776i	0.705328	+	0.708881i	$0.250800\pi$
$199$			20.0000i			1.41776i	−0.705328	+	0.708881i	$0.749200\pi$
$200$	−1.00000			−0.0707107
$201$		−	3.00000i		−	0.211604i
$202$	9.00000			0.633238
$203$	−20.0000			−1.40372
$204$	4.00000	+	1.00000i	0.280056	+	0.0700140i
$205$	4.00000			0.279372
$206$	10.0000			0.696733
$207$			6.00000i			0.417029i
$208$	1.00000			0.0693375
$209$		−	8.00000i		−	0.553372i
$210$			8.00000i			0.552052i
$211$			14.0000i			0.963800i	0.876226	+	0.481900i	$0.160053\pi$
$211$			14.0000i			0.963800i	−0.876226	+	0.481900i	$0.839947\pi$
$212$	−4.00000			−0.274721
$213$	6.00000			0.411113
$214$		−	3.00000i		−	0.205076i
$215$		0			0
$216$		−	5.00000i		−	0.340207i
$217$	28.0000			1.90076
$218$		−	20.0000i		−	1.35457i
$219$	2.00000			0.135147
$220$	−8.00000			−0.539360
$221$	1.00000	−	4.00000i	0.0672673	−	0.269069i
$222$	−10.0000			−0.671156
$223$	−9.00000			−0.602685			−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000			−0.602685			−0.301342	+	0.953516i	$0.597435\pi$
$224$			4.00000i			0.267261i
$225$	2.00000			0.133333
$226$		−	2.00000i		−	0.133038i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$			2.00000i			0.132453i
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$	−6.00000			−0.395628
$231$		−	16.0000i		−	1.05272i
$232$			5.00000i			0.328266i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	−2.00000			−0.130744
$235$			4.00000i			0.260931i
$236$	−1.00000			−0.0650945
$237$	−4.00000			−0.259828
$238$	16.0000	+	4.00000i	1.03713	+	0.259281i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	2.00000			0.129099
$241$		−	20.0000i		−	1.28831i	−0.764894	−	0.644157i	$-0.777208\pi$
$241$		−	20.0000i		−	1.28831i	0.764894	−	0.644157i	$-0.222792\pi$
$242$	5.00000			0.321412
$243$			16.0000i			1.02640i
$244$			8.00000i			0.512148i
$245$			18.0000i			1.14998i
$246$	2.00000			0.127515
$247$	2.00000			0.127257
$248$		−	7.00000i		−	0.444500i
$249$			5.00000i			0.316862i
$250$			12.0000i			0.758947i
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$		−	8.00000i		−	0.503953i
$253$	12.0000			0.754434
$254$	−11.0000			−0.690201
$255$	2.00000	−	8.00000i	0.125245	−	0.500979i
$256$	1.00000			0.0625000
$257$	−1.00000			−0.0623783			−0.0311891	−	0.999514i	$-0.509929\pi$
$257$	−1.00000			−0.0623783			−0.0311891	+	0.999514i	$0.509929\pi$
$258$		0			0
$259$	−40.0000			−2.48548
$260$		−	2.00000i		−	0.124035i
$261$		−	10.0000i		−	0.618984i
$262$			6.00000i			0.370681i
$263$	−27.0000			−1.66489			−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000			−1.66489			−0.832446	+	0.554107i	$0.813060\pi$
$264$	−4.00000			−0.246183
$265$			8.00000i			0.491436i
$266$			8.00000i			0.490511i
$267$		−	6.00000i		−	0.367194i
$268$	−3.00000			−0.183254
$269$		−	18.0000i		−	1.09748i	−0.835993	−	0.548740i	$-0.815108\pi$
$269$		−	18.0000i		−	1.09748i	0.835993	−	0.548740i	$-0.184892\pi$
$270$	−10.0000			−0.608581
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	1.00000	−	4.00000i	0.0606339	−	0.242536i
$273$	4.00000			0.242091
$274$	−23.0000			−1.38948
$275$		−	4.00000i		−	0.241209i
$276$	−3.00000			−0.180579
$277$			9.00000i			0.540758i	0.962754	+	0.270379i	$0.0871489\pi$
$277$			9.00000i			0.540758i	−0.962754	+	0.270379i	$0.912851\pi$
$278$			9.00000i			0.539784i
$279$			14.0000i			0.838158i
$280$	8.00000			0.478091
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$			2.00000i			0.119098i
$283$			14.0000i			0.832214i	0.909316	+	0.416107i	$0.136606\pi$
$283$			14.0000i			0.832214i	−0.909316	+	0.416107i	$0.863394\pi$
$284$		−	6.00000i		−	0.356034i
$285$	4.00000			0.236940
$286$			4.00000i			0.236525i
$287$	8.00000			0.472225
$288$	−2.00000			−0.117851
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	10.0000			0.587220
$291$	5.00000			0.293105
$292$		−	2.00000i		−	0.117041i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$			9.00000i			0.524891i
$295$			2.00000i			0.116445i
$296$			10.0000i			0.581238i
$297$	20.0000			1.16052
$298$	3.00000			0.173785
$299$			3.00000i			0.173494i
$300$			1.00000i			0.0577350i
$301$		0			0
$302$	−12.0000			−0.690522
$303$		−	9.00000i		−	0.517036i
$304$	2.00000			0.114708
$305$	16.0000			0.916157
$306$	−2.00000	+	8.00000i	−0.114332	+	0.457330i
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$	−16.0000			−0.911685
$309$		−	10.0000i		−	0.568880i
$310$	−14.0000			−0.795147
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		−	1.00000i		−	0.0566139i
$313$			13.0000i			0.734803i	0.930062	+	0.367402i	$0.119753\pi$
$313$			13.0000i			0.734803i	−0.930062	+	0.367402i	$0.880247\pi$
$314$	−5.00000			−0.282166
$315$	−16.0000			−0.901498
$316$			4.00000i			0.225018i
$317$		−	29.0000i		−	1.62880i	−0.580302	−	0.814401i	$-0.697066\pi$
$317$		−	29.0000i		−	1.62880i	0.580302	−	0.814401i	$-0.302934\pi$
$318$			4.00000i			0.224309i
$319$	−20.0000			−1.11979
$320$		−	2.00000i		−	0.111803i
$321$	−3.00000			−0.167444
$322$	−12.0000			−0.668734
$323$	2.00000	−	8.00000i	0.111283	−	0.445132i
$324$	1.00000			0.0555556
$325$	1.00000			0.0554700
$326$			3.00000i			0.166155i
$327$	−20.0000			−1.10600
$328$		−	2.00000i		−	0.110432i
$329$			8.00000i			0.441054i
$330$			8.00000i			0.440386i
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$	5.00000			0.274411
$333$		−	20.0000i		−	1.09599i
$334$		−	12.0000i		−	0.656611i
$335$			6.00000i			0.327815i
$336$	4.00000			0.218218
$337$			33.0000i			1.79762i	0.438334	+	0.898812i	$0.355569\pi$
$337$			33.0000i			1.79762i	−0.438334	+	0.898812i	$0.644431\pi$
$338$	12.0000			0.652714
$339$	−2.00000			−0.108625
$340$	−8.00000	−	2.00000i	−0.433861	−	0.108465i
$341$	28.0000			1.51629
$342$	−4.00000			−0.216295
$343$			8.00000i			0.431959i
$344$		0			0
$345$			6.00000i			0.323029i
$346$			6.00000i			0.322562i
$347$		−	2.00000i		−	0.107366i	−0.998558	−	0.0536828i	$-0.982904\pi$
$347$		−	2.00000i		−	0.107366i	0.998558	−	0.0536828i	$-0.0170960\pi$
$348$	5.00000			0.268028
$349$	19.0000			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$350$			4.00000i			0.213809i
$351$			5.00000i			0.266880i
$352$			4.00000i			0.213201i
$353$	−36.0000			−1.91609			−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000			−1.91609			−0.958043	+	0.286623i	$0.907467\pi$
$354$			1.00000i			0.0531494i
$355$	−12.0000			−0.636894
$356$	−6.00000			−0.317999
$357$	4.00000	−	16.0000i	0.211702	−	0.846810i
$358$	−9.00000			−0.475665
$359$	11.0000			0.580558			0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000			0.580558			0.290279	+	0.956942i	$0.406252\pi$
$360$			4.00000i			0.210819i
$361$	−15.0000			−0.789474
$362$		−	7.00000i		−	0.367912i
$363$		−	5.00000i		−	0.262432i
$364$		−	4.00000i		−	0.209657i
$365$	−4.00000			−0.209370
$366$	8.00000			0.418167
$367$			21.0000i			1.09619i	0.836416	+	0.548096i	$0.184647\pi$
$367$			21.0000i			1.09619i	−0.836416	+	0.548096i	$0.815353\pi$
$368$			3.00000i			0.156386i
$369$			4.00000i			0.208232i
$370$	20.0000			1.03975
$371$			16.0000i			0.830679i
$372$	−7.00000			−0.362933
$373$	28.0000			1.44979			0.724893	−	0.688862i	$-0.241889\pi$
$373$	28.0000			1.44979			0.724893	+	0.688862i	$0.241889\pi$
$374$	16.0000	+	4.00000i	0.827340	+	0.206835i
$375$	12.0000			0.619677
$376$	2.00000			0.103142
$377$		−	5.00000i		−	0.257513i
$378$	−20.0000			−1.02869
$379$			36.0000i			1.84920i	0.380945	+	0.924598i	$0.375599\pi$
$379$			36.0000i			1.84920i	−0.380945	+	0.924598i	$0.624401\pi$
$380$		−	4.00000i		−	0.205196i
$381$			11.0000i			0.563547i
$382$	−16.0000			−0.818631
$383$	−24.0000			−1.22634			−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000			−1.22634			−0.613171	+	0.789950i	$0.710106\pi$
$384$		−	1.00000i		−	0.0510310i
$385$			32.0000i			1.63087i
$386$			20.0000i			1.01797i
$387$		0			0
$388$		−	5.00000i		−	0.253837i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$	−2.00000			−0.101274
$391$	12.0000	+	3.00000i	0.606866	+	0.151717i
$392$	9.00000			0.454569
$393$	6.00000			0.302660
$394$			21.0000i			1.05796i
$395$	8.00000			0.402524
$396$		−	8.00000i		−	0.402015i
$397$		−	28.0000i		−	1.40528i	−0.711546	−	0.702640i	$-0.752005\pi$
$397$		−	28.0000i		−	1.40528i	0.711546	−	0.702640i	$-0.247995\pi$
$398$		−	20.0000i		−	1.00251i
$399$	8.00000			0.400501
$400$	1.00000			0.0500000
$401$			3.00000i			0.149813i	0.997191	+	0.0749064i	$0.0238658\pi$
$401$			3.00000i			0.149813i	−0.997191	+	0.0749064i	$0.976134\pi$
$402$			3.00000i			0.149626i
$403$			7.00000i			0.348695i
$404$	−9.00000			−0.447767
$405$		−	2.00000i		−	0.0993808i
$406$	20.0000			0.992583
$407$	−40.0000			−1.98273
$408$	−4.00000	−	1.00000i	−0.198030	−	0.0495074i
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$	−4.00000			−0.197546
$411$			23.0000i			1.13451i
$412$	−10.0000			−0.492665
$413$			4.00000i			0.196827i
$414$		−	6.00000i		−	0.294884i
$415$		−	10.0000i		−	0.490881i
$416$	−1.00000			−0.0490290
$417$	9.00000			0.440732
$418$			8.00000i			0.391293i
$419$		−	6.00000i		−	0.293119i	−0.989202	−	0.146560i	$-0.953180\pi$
$419$		−	6.00000i		−	0.293119i	0.989202	−	0.146560i	$-0.0468200\pi$
$420$		−	8.00000i		−	0.390360i
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$		−	14.0000i		−	0.681509i
$423$	−4.00000			−0.194487
$424$	4.00000			0.194257
$425$	1.00000	−	4.00000i	0.0485071	−	0.194029i
$426$	−6.00000			−0.290701
$427$	32.0000			1.54859
$428$			3.00000i			0.145010i
$429$	4.00000			0.193122
$430$		0			0
$431$			40.0000i			1.92673i	0.268190	+	0.963366i	$0.413575\pi$
$431$			40.0000i			1.92673i	−0.268190	+	0.963366i	$0.586425\pi$
$432$			5.00000i			0.240563i
$433$	19.0000			0.913082			0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000			0.913082			0.456541	+	0.889702i	$0.349088\pi$
$434$	−28.0000			−1.34404
$435$		−	10.0000i		−	0.479463i
$436$			20.0000i			0.957826i
$437$			6.00000i			0.287019i
$438$	−2.00000			−0.0955637
$439$			4.00000i			0.190910i	0.995434	+	0.0954548i	$0.0304305\pi$
$439$			4.00000i			0.190910i	−0.995434	+	0.0954548i	$0.969569\pi$
$440$	8.00000			0.381385
$441$	−18.0000			−0.857143
$442$	−1.00000	+	4.00000i	−0.0475651	+	0.190261i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	10.0000			0.474579
$445$			12.0000i			0.568855i
$446$	9.00000			0.426162
$447$		−	3.00000i		−	0.141895i
$448$		−	4.00000i		−	0.188982i
$449$			22.0000i			1.03824i	0.854700	+	0.519122i	$0.173741\pi$
$449$			22.0000i			1.03824i	−0.854700	+	0.519122i	$0.826259\pi$
$450$	−2.00000			−0.0942809
$451$	8.00000			0.376705
$452$			2.00000i			0.0940721i
$453$			12.0000i			0.563809i
$454$			12.0000i			0.563188i
$455$	−8.00000			−0.375046
$456$		−	2.00000i		−	0.0936586i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	13.0000			0.607450
$459$	20.0000	+	5.00000i	0.933520	+	0.233380i
$460$	6.00000			0.279751
$461$	26.0000			1.21094			0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000			1.21094			0.605470	+	0.795868i	$0.292985\pi$
$462$			16.0000i			0.744387i
$463$	2.00000			0.0929479			0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000			0.0929479			0.0464739	+	0.998920i	$0.485202\pi$
$464$		−	5.00000i		−	0.232119i
$465$			14.0000i			0.649234i
$466$			6.00000i			0.277945i
$467$	−11.0000			−0.509019			−0.254510	−	0.967070i	$-0.581914\pi$
$467$	−11.0000			−0.509019			−0.254510	+	0.967070i	$0.581914\pi$
$468$	2.00000			0.0924500
$469$			12.0000i			0.554109i
$470$		−	4.00000i		−	0.184506i
$471$			5.00000i			0.230388i
$472$	1.00000			0.0460287
$473$		0			0
$474$	4.00000			0.183726
$475$	2.00000			0.0917663
$476$	−16.0000	−	4.00000i	−0.733359	−	0.183340i
$477$	−8.00000			−0.366295
$478$	16.0000			0.731823
$479$		−	4.00000i		−	0.182765i	−0.995816	−	0.0913823i	$-0.970871\pi$
$479$		−	4.00000i		−	0.182765i	0.995816	−	0.0913823i	$-0.0291285\pi$
$480$	−2.00000			−0.0912871
$481$		−	10.0000i		−	0.455961i
$482$			20.0000i			0.910975i
$483$			12.0000i			0.546019i
$484$	−5.00000			−0.227273
$485$	−10.0000			−0.454077
$486$		−	16.0000i		−	0.725775i
$487$		−	4.00000i		−	0.181257i	−0.995885	−	0.0906287i	$-0.971112\pi$
$487$		−	4.00000i		−	0.181257i	0.995885	−	0.0906287i	$-0.0288876\pi$
$488$		−	8.00000i		−	0.362143i
$489$	3.00000			0.135665
$490$		−	18.0000i		−	0.813157i
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	−2.00000			−0.0901670
$493$	−20.0000	−	5.00000i	−0.900755	−	0.225189i
$494$	−2.00000			−0.0899843
$495$	−16.0000			−0.719147
$496$			7.00000i			0.314309i
$497$	−24.0000			−1.07655
$498$		−	5.00000i		−	0.224055i
$499$		−	31.0000i		−	1.38775i	−0.720095	−	0.693875i	$-0.755902\pi$
$499$		−	31.0000i		−	1.38775i	0.720095	−	0.693875i	$-0.244098\pi$
$500$		−	12.0000i		−	0.536656i
$501$	−12.0000			−0.536120
$502$	10.0000			0.446322
$503$			21.0000i			0.936344i	0.883637	+	0.468172i	$0.155087\pi$
$503$			21.0000i			0.936344i	−0.883637	+	0.468172i	$0.844913\pi$
$504$			8.00000i			0.356348i
$505$			18.0000i			0.800989i
$506$	−12.0000			−0.533465
$507$		−	12.0000i		−	0.532939i
$508$	11.0000			0.488046
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$	−2.00000	+	8.00000i	−0.0885615	+	0.354246i
$511$	−8.00000			−0.353899
$512$	−1.00000			−0.0441942
$513$			10.0000i			0.441511i
$514$	1.00000			0.0441081
$515$			20.0000i			0.881305i
$516$		0			0
$517$			8.00000i			0.351840i
$518$	40.0000			1.75750
$519$	6.00000			0.263371
$520$			2.00000i			0.0877058i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$			10.0000i			0.437688i
$523$	34.0000			1.48672			0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000			1.48672			0.743358	+	0.668894i	$0.233232\pi$
$524$		−	6.00000i		−	0.262111i
$525$	4.00000			0.174574
$526$	27.0000			1.17726
$527$	28.0000	+	7.00000i	1.21970	+	0.304925i
$528$	4.00000			0.174078
$529$	14.0000			0.608696
$530$		−	8.00000i		−	0.347498i
$531$	−2.00000			−0.0867926
$532$		−	8.00000i		−	0.346844i
$533$			2.00000i			0.0866296i
$534$			6.00000i			0.259645i
$535$	6.00000			0.259403
$536$	3.00000			0.129580
$537$			9.00000i			0.388379i
$538$			18.0000i			0.776035i
$539$			36.0000i			1.55063i
$540$	10.0000			0.430331
$541$			22.0000i			0.945854i	0.881102	+	0.472927i	$0.156803\pi$
$541$			22.0000i			0.945854i	−0.881102	+	0.472927i	$0.843197\pi$
$542$	8.00000			0.343629
$543$	−7.00000			−0.300399
$544$	−1.00000	+	4.00000i	−0.0428746	+	0.171499i
$545$	40.0000			1.71341
$546$	−4.00000			−0.171184
$547$			4.00000i			0.171028i	0.996337	+	0.0855138i	$0.0272532\pi$
$547$			4.00000i			0.171028i	−0.996337	+	0.0855138i	$0.972747\pi$
$548$	23.0000			0.982511
$549$			16.0000i			0.682863i
$550$			4.00000i			0.170561i
$551$		−	10.0000i		−	0.426014i
$552$	3.00000			0.127688
$553$	16.0000			0.680389
$554$		−	9.00000i		−	0.382373i
$555$		−	20.0000i		−	0.848953i
$556$		−	9.00000i		−	0.381685i
$557$	20.0000			0.847427			0.423714	−	0.905796i	$-0.360726\pi$
$557$	20.0000			0.847427			0.423714	+	0.905796i	$0.360726\pi$
$558$		−	14.0000i		−	0.592667i
$559$		0			0
$560$	−8.00000			−0.338062
$561$	4.00000	−	16.0000i	0.168880	−	0.675521i
$562$	−27.0000			−1.13893
$563$	7.00000			0.295015			0.147507	−	0.989061i	$-0.452875\pi$
$563$	7.00000			0.295015			0.147507	+	0.989061i	$0.452875\pi$
$564$		−	2.00000i		−	0.0842152i
$565$	4.00000			0.168281
$566$		−	14.0000i		−	0.588464i
$567$		−	4.00000i		−	0.167984i
$568$			6.00000i			0.251754i
$569$	26.0000			1.08998			0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000			1.08998			0.544988	+	0.838444i	$0.316534\pi$
$570$	−4.00000			−0.167542
$571$		−	4.00000i		−	0.167395i	−0.996491	−	0.0836974i	$-0.973327\pi$
$571$		−	4.00000i		−	0.167395i	0.996491	−	0.0836974i	$-0.0266729\pi$
$572$		−	4.00000i		−	0.167248i
$573$			16.0000i			0.668410i
$574$	−8.00000			−0.333914
$575$			3.00000i			0.125109i
$576$	2.00000			0.0833333
$577$	3.00000			0.124892			0.0624458	−	0.998048i	$-0.480110\pi$
$577$	3.00000			0.124892			0.0624458	+	0.998048i	$0.480110\pi$
$578$	15.0000	+	8.00000i	0.623918	+	0.332756i
$579$	20.0000			0.831172
$580$	−10.0000			−0.415227
$581$		−	20.0000i		−	0.829740i
$582$	−5.00000			−0.207257
$583$			16.0000i			0.662652i
$584$			2.00000i			0.0827606i
$585$		−	4.00000i		−	0.165380i
$586$	12.0000			0.495715
$587$	−15.0000			−0.619116			−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000			−0.619116			−0.309558	+	0.950881i	$0.600181\pi$
$588$		−	9.00000i		−	0.371154i
$589$			14.0000i			0.576860i
$590$		−	2.00000i		−	0.0823387i
$591$	21.0000			0.863825
$592$		−	10.0000i		−	0.410997i
$593$	33.0000			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$594$	−20.0000			−0.820610
$595$	−8.00000	+	32.0000i	−0.327968	+	1.31187i
$596$	−3.00000			−0.122885
$597$	−20.0000			−0.818546
$598$		−	3.00000i		−	0.122679i
$599$	−45.0000			−1.83865			−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000			−1.83865			−0.919325	+	0.393499i	$0.871265\pi$
$600$		−	1.00000i		−	0.0408248i
$601$		−	17.0000i		−	0.693444i	−0.937968	−	0.346722i	$-0.887295\pi$
$601$		−	17.0000i		−	0.693444i	0.937968	−	0.346722i	$-0.112705\pi$
$602$		0			0
$603$	−6.00000			−0.244339
$604$	12.0000			0.488273
$605$			10.0000i			0.406558i
$606$			9.00000i			0.365600i
$607$		−	4.00000i		−	0.162355i	−0.996700	−	0.0811775i	$-0.974132\pi$
$607$		−	4.00000i		−	0.162355i	0.996700	−	0.0811775i	$-0.0258681\pi$
$608$	−2.00000			−0.0811107
$609$		−	20.0000i		−	0.810441i
$610$	−16.0000			−0.647821
$611$	−2.00000			−0.0809113
$612$	2.00000	−	8.00000i	0.0808452	−	0.323381i
$613$	−21.0000			−0.848182			−0.424091	−	0.905620i	$-0.639406\pi$
$613$	−21.0000			−0.848182			−0.424091	+	0.905620i	$0.639406\pi$
$614$	−32.0000			−1.29141
$615$			4.00000i			0.161296i
$616$	16.0000			0.644658
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$			10.0000i			0.402259i
$619$		−	4.00000i		−	0.160774i	−0.996764	−	0.0803868i	$-0.974384\pi$
$619$		−	4.00000i		−	0.160774i	0.996764	−	0.0803868i	$-0.0256155\pi$
$620$	14.0000			0.562254
$621$	−15.0000			−0.601929
$622$		−	6.00000i		−	0.240578i
$623$			24.0000i			0.961540i
$624$			1.00000i			0.0400320i
$625$	−19.0000			−0.760000
$626$		−	13.0000i		−	0.519584i
$627$	8.00000			0.319489
$628$	5.00000			0.199522
$629$	−40.0000	−	10.0000i	−1.59490	−	0.398726i
$630$	16.0000			0.637455
$631$	−5.00000			−0.199047			−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000			−0.199047			−0.0995234	+	0.995035i	$0.531732\pi$
$632$		−	4.00000i		−	0.159111i
$633$	−14.0000			−0.556450
$634$			29.0000i			1.15174i
$635$		−	22.0000i		−	0.873043i
$636$		−	4.00000i		−	0.158610i
$637$	−9.00000			−0.356593
$638$	20.0000			0.791808
$639$		−	12.0000i		−	0.474713i
$640$			2.00000i			0.0790569i
$641$		−	20.0000i		−	0.789953i	−0.918691	−	0.394976i	$-0.870753\pi$
$641$		−	20.0000i		−	0.789953i	0.918691	−	0.394976i	$-0.129247\pi$
$642$	3.00000			0.118401
$643$			49.0000i			1.93237i	0.257847	+	0.966186i	$0.416987\pi$
$643$			49.0000i			1.93237i	−0.257847	+	0.966186i	$0.583013\pi$
$644$	12.0000			0.472866
$645$		0			0
$646$	−2.00000	+	8.00000i	−0.0786889	+	0.314756i
$647$	−13.0000			−0.511083			−0.255541	−	0.966798i	$-0.582254\pi$
$647$	−13.0000			−0.511083			−0.255541	+	0.966798i	$0.582254\pi$
$648$	−1.00000			−0.0392837
$649$			4.00000i			0.157014i
$650$	−1.00000			−0.0392232
$651$			28.0000i			1.09741i
$652$		−	3.00000i		−	0.117489i
$653$		−	22.0000i		−	0.860927i	−0.902608	−	0.430463i	$-0.858350\pi$
$653$		−	22.0000i		−	0.860927i	0.902608	−	0.430463i	$-0.141650\pi$
$654$	20.0000			0.782062
$655$	−12.0000			−0.468879
$656$			2.00000i			0.0780869i
$657$		−	4.00000i		−	0.156055i
$658$		−	8.00000i		−	0.311872i
$659$	−19.0000			−0.740135			−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000			−0.740135			−0.370067	+	0.929005i	$0.620665\pi$
$660$		−	8.00000i		−	0.311400i
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	−28.0000			−1.08825
$663$	4.00000	+	1.00000i	0.155347	+	0.0388368i
$664$	−5.00000			−0.194038
$665$	−16.0000			−0.620453
$666$			20.0000i			0.774984i
$667$	15.0000			0.580802
$668$			12.0000i			0.464294i
$669$		−	9.00000i		−	0.347960i
$670$		−	6.00000i		−	0.231800i
$671$	32.0000			1.23535
$672$	−4.00000			−0.154303
$673$		−	17.0000i		−	0.655302i	−0.944799	−	0.327651i	$-0.893743\pi$
$673$		−	17.0000i		−	0.655302i	0.944799	−	0.327651i	$-0.106257\pi$
$674$		−	33.0000i		−	1.27111i
$675$			5.00000i			0.192450i
$676$	−12.0000			−0.461538
$677$		−	7.00000i		−	0.269032i	−0.990911	−	0.134516i	$-0.957052\pi$
$677$		−	7.00000i		−	0.269032i	0.990911	−	0.134516i	$-0.0429479\pi$
$678$	2.00000			0.0768095
$679$	−20.0000			−0.767530
$680$	8.00000	+	2.00000i	0.306786	+	0.0766965i
$681$	12.0000			0.459841
$682$	−28.0000			−1.07218
$683$		−	46.0000i		−	1.76014i	−0.474843	−	0.880071i	$-0.657495\pi$
$683$		−	46.0000i		−	1.76014i	0.474843	−	0.880071i	$-0.342505\pi$
$684$	4.00000			0.152944
$685$		−	46.0000i		−	1.75757i
$686$		−	8.00000i		−	0.305441i
$687$		−	13.0000i		−	0.495981i
$688$		0			0
$689$	−4.00000			−0.152388
$690$		−	6.00000i		−	0.228416i
$691$		−	2.00000i		−	0.0760836i	−0.999276	−	0.0380418i	$-0.987888\pi$
$691$		−	2.00000i		−	0.0760836i	0.999276	−	0.0380418i	$-0.0121120\pi$
$692$		−	6.00000i		−	0.228086i
$693$	−32.0000			−1.21558
$694$			2.00000i			0.0759190i
$695$	−18.0000			−0.682779
$696$	−5.00000			−0.189525
$697$	8.00000	+	2.00000i	0.303022	+	0.0757554i
$698$	−19.0000			−0.719161
$699$	6.00000			0.226941
$700$		−	4.00000i		−	0.151186i
$701$	−37.0000			−1.39747			−0.698735	−	0.715380i	$-0.746253\pi$
$701$	−37.0000			−1.39747			−0.698735	+	0.715380i	$0.746253\pi$
$702$		−	5.00000i		−	0.188713i
$703$		−	20.0000i		−	0.754314i
$704$		−	4.00000i		−	0.150756i
$705$	−4.00000			−0.150649
$706$	36.0000			1.35488
$707$			36.0000i			1.35392i
$708$		−	1.00000i		−	0.0375823i
$709$			15.0000i			0.563337i	0.959512	+	0.281668i	$0.0908878\pi$
$709$			15.0000i			0.563337i	−0.959512	+	0.281668i	$0.909112\pi$
$710$	12.0000			0.450352
$711$			8.00000i			0.300023i
$712$	6.00000			0.224860
$713$	−21.0000			−0.786456
$714$	−4.00000	+	16.0000i	−0.149696	+	0.598785i
$715$	−8.00000			−0.299183
$716$	9.00000			0.336346
$717$		−	16.0000i		−	0.597531i
$718$	−11.0000			−0.410516
$719$			24.0000i			0.895049i	0.894272	+	0.447524i	$0.147694\pi$
$719$			24.0000i			0.895049i	−0.894272	+	0.447524i	$0.852306\pi$
$720$		−	4.00000i		−	0.149071i
$721$			40.0000i			1.48968i
$722$	15.0000			0.558242
$723$	20.0000			0.743808
$724$			7.00000i			0.260153i
$725$		−	5.00000i		−	0.185695i
$726$			5.00000i			0.185567i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$			4.00000i			0.148250i
$729$	−13.0000			−0.481481
$730$	4.00000			0.148047
$731$		0			0
$732$	−8.00000			−0.295689
$733$	−14.0000			−0.517102			−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000			−0.517102			−0.258551	+	0.965998i	$0.583245\pi$
$734$		−	21.0000i		−	0.775124i
$735$	−18.0000			−0.663940
$736$		−	3.00000i		−	0.110581i
$737$			12.0000i			0.442026i
$738$		−	4.00000i		−	0.147242i
$739$	7.00000			0.257499			0.128750	−	0.991677i	$-0.458904\pi$
$739$	7.00000			0.257499			0.128750	+	0.991677i	$0.458904\pi$
$740$	−20.0000			−0.735215
$741$			2.00000i			0.0734718i
$742$		−	16.0000i		−	0.587378i
$743$			2.00000i			0.0733729i	0.999327	+	0.0366864i	$0.0116803\pi$
$743$			2.00000i			0.0733729i	−0.999327	+	0.0366864i	$0.988320\pi$
$744$	7.00000			0.256632
$745$			6.00000i			0.219823i
$746$	−28.0000			−1.02515
$747$	10.0000			0.365881
$748$	−16.0000	−	4.00000i	−0.585018	−	0.146254i
$749$	12.0000			0.438470
$750$	−12.0000			−0.438178
$751$			35.0000i			1.27717i	0.769552	+	0.638584i	$0.220480\pi$
$751$			35.0000i			1.27717i	−0.769552	+	0.638584i	$0.779520\pi$
$752$	−2.00000			−0.0729325
$753$		−	10.0000i		−	0.364420i
$754$			5.00000i			0.182089i
$755$		−	24.0000i		−	0.873449i
$756$	20.0000			0.727393
$757$	−52.0000			−1.88997			−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000			−1.88997			−0.944986	+	0.327111i	$0.893925\pi$
$758$		−	36.0000i		−	1.30758i
$759$			12.0000i			0.435572i
$760$			4.00000i			0.145095i
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$		−	11.0000i		−	0.398488i
$763$	80.0000			2.89619
$764$	16.0000			0.578860
$765$	−16.0000	−	4.00000i	−0.578481	−	0.144620i
$766$	24.0000			0.867155
$767$	−1.00000			−0.0361079
$768$			1.00000i			0.0360844i
$769$	44.0000			1.58668			0.793340	−	0.608778i	$-0.208340\pi$
$769$	44.0000			1.58668			0.793340	+	0.608778i	$0.208340\pi$
$770$		−	32.0000i		−	1.15320i
$771$		−	1.00000i		−	0.0360141i
$772$		−	20.0000i		−	0.719816i
$773$	35.0000			1.25886			0.629431	−	0.777056i	$-0.283288\pi$
$773$	35.0000			1.25886			0.629431	+	0.777056i	$0.283288\pi$
$774$		0			0
$775$			7.00000i			0.251447i
$776$			5.00000i			0.179490i
$777$		−	40.0000i		−	1.43499i
$778$	18.0000			0.645331
$779$			4.00000i			0.143315i
$780$	2.00000			0.0716115
$781$	−24.0000			−0.858788
$782$	−12.0000	−	3.00000i	−0.429119	−	0.107280i
$783$	25.0000			0.893427
$784$	−9.00000			−0.321429
$785$		−	10.0000i		−	0.356915i
$786$	−6.00000			−0.214013
$787$		−	8.00000i		−	0.285169i	−0.989783	−	0.142585i	$-0.954459\pi$
$787$		−	8.00000i		−	0.285169i	0.989783	−	0.142585i	$-0.0455413\pi$
$788$		−	21.0000i		−	0.748094i
$789$		−	27.0000i		−	0.961225i
$790$	−8.00000			−0.284627
$791$	8.00000			0.284447
$792$			8.00000i			0.284268i
$793$			8.00000i			0.284088i
$794$			28.0000i			0.993683i
$795$	−8.00000			−0.283731
$796$			20.0000i			0.708881i
$797$	37.0000			1.31061			0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000			1.31061			0.655304	+	0.755366i	$0.272541\pi$
$798$	−8.00000			−0.283197
$799$	−2.00000	+	8.00000i	−0.0707549	+	0.283020i
$800$	−1.00000			−0.0353553
$801$	−12.0000			−0.423999
$802$		−	3.00000i		−	0.105934i
$803$	−8.00000			−0.282314
$804$		−	3.00000i		−	0.105802i
$805$		−	24.0000i		−	0.845889i
$806$		−	7.00000i		−	0.246564i
$807$	18.0000			0.633630
$808$	9.00000			0.316619
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$			2.00000i			0.0702728i
$811$			48.0000i			1.68551i	0.538299	+	0.842754i	$0.319067\pi$
$811$			48.0000i			1.68551i	−0.538299	+	0.842754i	$0.680933\pi$
$812$	−20.0000			−0.701862
$813$		−	8.00000i		−	0.280572i
$814$	40.0000			1.40200
$815$	−6.00000			−0.210171
$816$	4.00000	+	1.00000i	0.140028	+	0.0350070i
$817$		0			0
$818$		0			0
$819$		−	8.00000i		−	0.279543i
$820$	4.00000			0.139686
$821$		−	24.0000i		−	0.837606i	−0.908077	−	0.418803i	$-0.862450\pi$
$821$		−	24.0000i		−	0.837606i	0.908077	−	0.418803i	$-0.137550\pi$
$822$		−	23.0000i		−	0.802217i
$823$		−	20.0000i		−	0.697156i	−0.937280	−	0.348578i	$-0.886665\pi$
$823$		−	20.0000i		−	0.697156i	0.937280	−	0.348578i	$-0.113335\pi$
$824$	10.0000			0.348367
$825$	4.00000			0.139262
$826$		−	4.00000i		−	0.139178i
$827$		−	37.0000i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$827$		−	37.0000i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$828$			6.00000i			0.208514i
$829$	−16.0000			−0.555703			−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000			−0.555703			−0.277851	+	0.960624i	$0.589622\pi$
$830$			10.0000i			0.347105i
$831$	−9.00000			−0.312207
$832$	1.00000			0.0346688
$833$	−9.00000	+	36.0000i	−0.311832	+	1.24733i
$834$	−9.00000			−0.311645
$835$	24.0000			0.830554
$836$		−	8.00000i		−	0.276686i
$837$	−35.0000			−1.20978
$838$			6.00000i			0.207267i
$839$			13.0000i			0.448810i	0.974496	+	0.224405i	$0.0720438\pi$
$839$			13.0000i			0.448810i	−0.974496	+	0.224405i	$0.927956\pi$
$840$			8.00000i			0.276026i
$841$	4.00000			0.137931
$842$	6.00000			0.206774
$843$			27.0000i			0.929929i
$844$			14.0000i			0.481900i
$845$			24.0000i			0.825625i
$846$	4.00000			0.137523
$847$			20.0000i			0.687208i
$848$	−4.00000			−0.137361
$849$	−14.0000			−0.480479
$850$	−1.00000	+	4.00000i	−0.0342997	+	0.137199i
$851$	30.0000			1.02839
$852$	6.00000			0.205557
$853$			22.0000i			0.753266i	0.926363	+	0.376633i	$0.122918\pi$
$853$			22.0000i			0.753266i	−0.926363	+	0.376633i	$0.877082\pi$
$854$	−32.0000			−1.09502
$855$		−	8.00000i		−	0.273594i
$856$		−	3.00000i		−	0.102538i
$857$			25.0000i			0.853984i	0.904255	+	0.426992i	$0.140427\pi$
$857$			25.0000i			0.853984i	−0.904255	+	0.426992i	$0.859573\pi$
$858$	−4.00000			−0.136558
$859$	−15.0000			−0.511793			−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000			−0.511793			−0.255897	+	0.966704i	$0.582371\pi$
$860$		0			0
$861$			8.00000i			0.272639i
$862$		−	40.0000i		−	1.36241i
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$		−	5.00000i		−	0.170103i
$865$	−12.0000			−0.408012
$866$	−19.0000			−0.645646
$867$	8.00000	−	15.0000i	0.271694	−	0.509427i
$868$	28.0000			0.950382
$869$	16.0000			0.542763
$870$			10.0000i			0.339032i
$871$	−3.00000			−0.101651
$872$		−	20.0000i		−	0.677285i
$873$		−	10.0000i		−	0.338449i
$874$		−	6.00000i		−	0.202953i
$875$	−48.0000			−1.62270
$876$	2.00000			0.0675737
$877$		−	15.0000i		−	0.506514i	−0.967399	−	0.253257i	$-0.918498\pi$
$877$		−	15.0000i		−	0.506514i	0.967399	−	0.253257i	$-0.0815018\pi$
$878$		−	4.00000i		−	0.134993i
$879$		−	12.0000i		−	0.404750i
$880$	−8.00000			−0.269680
$881$		−	35.0000i		−	1.17918i	−0.807703	−	0.589590i	$-0.799289\pi$
$881$		−	35.0000i		−	1.17918i	0.807703	−	0.589590i	$-0.200711\pi$
$882$	18.0000			0.606092
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	1.00000	−	4.00000i	0.0336336	−	0.134535i
$885$	−2.00000			−0.0672293
$886$	4.00000			0.134383
$887$			37.0000i			1.24234i	0.783676	+	0.621169i	$0.213342\pi$
$887$			37.0000i			1.24234i	−0.783676	+	0.621169i	$0.786658\pi$
$888$	−10.0000			−0.335578
$889$		−	44.0000i		−	1.47571i
$890$		−	12.0000i		−	0.402241i
$891$		−	4.00000i		−	0.134005i
$892$	−9.00000			−0.301342
$893$	−4.00000			−0.133855
$894$			3.00000i			0.100335i
$895$		−	18.0000i		−	0.601674i
$896$			4.00000i			0.133631i
$897$	−3.00000			−0.100167
$898$		−	22.0000i		−	0.734150i
$899$	35.0000			1.16732
$900$	2.00000			0.0666667
$901$	−4.00000	+	16.0000i	−0.133259	+	0.533037i
$902$	−8.00000			−0.266371
$903$		0			0
$904$		−	2.00000i		−	0.0665190i
$905$	14.0000			0.465376
$906$		−	12.0000i		−	0.398673i
$907$		−	25.0000i		−	0.830111i	−0.909796	−	0.415056i	$-0.863762\pi$
$907$		−	25.0000i		−	0.830111i	0.909796	−	0.415056i	$-0.136238\pi$
$908$		−	12.0000i		−	0.398234i
$909$	−18.0000			−0.597022
$910$	8.00000			0.265197
$911$			12.0000i			0.397578i	0.980042	+	0.198789i	$0.0637008\pi$
$911$			12.0000i			0.397578i	−0.980042	+	0.198789i	$0.936299\pi$
$912$			2.00000i			0.0662266i
$913$		−	20.0000i		−	0.661903i
$914$	10.0000			0.330771
$915$			16.0000i			0.528944i
$916$	−13.0000			−0.429532
$917$	−24.0000			−0.792550
$918$	−20.0000	−	5.00000i	−0.660098	−	0.165025i
$919$	26.0000			0.857661			0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000			0.857661			0.428830	+	0.903385i	$0.358926\pi$
$920$	−6.00000			−0.197814
$921$			32.0000i			1.05444i
$922$	−26.0000			−0.856264
$923$		−	6.00000i		−	0.197492i
$924$		−	16.0000i		−	0.526361i
$925$		−	10.0000i		−	0.328798i
$926$	−2.00000			−0.0657241
$927$	−20.0000			−0.656886
$928$			5.00000i			0.164133i
$929$			30.0000i			0.984268i	0.870519	+	0.492134i	$0.163783\pi$
$929$			30.0000i			0.984268i	−0.870519	+	0.492134i	$0.836217\pi$
$930$		−	14.0000i		−	0.459078i
$931$	−18.0000			−0.589926
$932$		−	6.00000i		−	0.196537i
$933$	−6.00000			−0.196431
$934$	11.0000			0.359931
$935$	−8.00000	+	32.0000i	−0.261628	+	1.04651i
$936$	−2.00000			−0.0653720
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		−	12.0000i		−	0.391814i
$939$	−13.0000			−0.424239
$940$			4.00000i			0.130466i
$941$			20.0000i			0.651981i	0.945373	+	0.325991i	$0.105698\pi$
$941$			20.0000i			0.651981i	−0.945373	+	0.325991i	$0.894302\pi$
$942$		−	5.00000i		−	0.162909i
$943$	−6.00000			−0.195387
$944$	−1.00000			−0.0325472
$945$		−	40.0000i		−	1.30120i
$946$		0			0
$947$		−	57.0000i		−	1.85225i	−0.377215	−	0.926126i	$-0.623118\pi$
$947$		−	57.0000i		−	1.85225i	0.377215	−	0.926126i	$-0.376882\pi$
$948$	−4.00000			−0.129914
$949$		−	2.00000i		−	0.0649227i
$950$	−2.00000			−0.0648886
$951$	29.0000			0.940389
$952$	16.0000	+	4.00000i	0.518563	+	0.129641i
$953$	37.0000			1.19855			0.599274	−	0.800544i	$-0.295456\pi$
$953$	37.0000			1.19855			0.599274	+	0.800544i	$0.295456\pi$
$954$	8.00000			0.259010
$955$		−	32.0000i		−	1.03550i
$956$	−16.0000			−0.517477
$957$		−	20.0000i		−	0.646508i
$958$			4.00000i			0.129234i
$959$		−	92.0000i		−	2.97083i
$960$	2.00000			0.0645497
$961$	−18.0000			−0.580645
$962$			10.0000i			0.322413i
$963$			6.00000i			0.193347i
$964$		−	20.0000i		−	0.644157i
$965$	−40.0000			−1.28765
$966$		−	12.0000i		−	0.386094i
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$	5.00000			0.160706
$969$	8.00000	+	2.00000i	0.256997	+	0.0642493i
$970$	10.0000			0.321081
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$			16.0000i			0.513200i
$973$	−36.0000			−1.15411
$974$			4.00000i			0.128168i
$975$			1.00000i			0.0320256i
$976$			8.00000i			0.256074i
$977$	36.0000			1.15174			0.575871	−	0.817541i	$-0.304663\pi$
$977$	36.0000			1.15174			0.575871	+	0.817541i	$0.304663\pi$
$978$	−3.00000			−0.0959294
$979$			24.0000i			0.767043i
$980$			18.0000i			0.574989i
$981$			40.0000i			1.27710i
$982$	−24.0000			−0.765871
$983$		−	56.0000i		−	1.78612i	−0.449935	−	0.893061i	$-0.648553\pi$
$983$		−	56.0000i		−	1.78612i	0.449935	−	0.893061i	$-0.351447\pi$
$984$	2.00000			0.0637577
$985$	−42.0000			−1.33823
$986$	20.0000	+	5.00000i	0.636930	+	0.159232i
$987$	−8.00000			−0.254643
$988$	2.00000			0.0636285
$989$		0			0
$990$	16.0000			0.508513
$991$		−	20.0000i		−	0.635321i	−0.948205	−	0.317660i	$-0.897103\pi$
$991$		−	20.0000i		−	0.635321i	0.948205	−	0.317660i	$-0.102897\pi$
$992$		−	7.00000i		−	0.222250i
$993$			28.0000i			0.888553i
$994$	24.0000			0.761234
$995$	40.0000			1.26809
$996$			5.00000i			0.158431i
$997$		−	53.0000i		−	1.67853i	−0.543725	−	0.839263i	$-0.682987\pi$
$997$		−	53.0000i		−	1.67853i	0.543725	−	0.839263i	$-0.317013\pi$
$998$			31.0000i			0.981288i
$999$	50.0000			1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.b.a.237.2	yes	2
17.16	even	2	inner	2006.2.b.a.237.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.b.a.237.1	✓	2	17.16	even	2	inner
2006.2.b.a.237.2	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -4.00000i q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -4.00000i q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.00000i q^{10} -4.00000i q^{11} +1.00000i q^{12} +1.00000 q^{13} +4.00000i q^{14} +2.00000 q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} -2.00000 q^{18} +2.00000 q^{19} -2.00000i q^{20} +4.00000 q^{21} +4.00000i q^{22} +3.00000i q^{23} -1.00000i q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.00000i q^{27} -4.00000i q^{28} -5.00000i q^{29} -2.00000 q^{30} +7.00000i q^{31} -1.00000 q^{32} +4.00000 q^{33} +(-1.00000 + 4.00000i) q^{34} -8.00000 q^{35} +2.00000 q^{36} -10.0000i q^{37} -2.00000 q^{38} +1.00000i q^{39} +2.00000i q^{40} +2.00000i q^{41} -4.00000 q^{42} -4.00000i q^{44} -4.00000i q^{45} -3.00000i q^{46} -2.00000 q^{47} +1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{50} +(4.00000 + 1.00000i) q^{51} +1.00000 q^{52} -4.00000 q^{53} -5.00000i q^{54} -8.00000 q^{55} +4.00000i q^{56} +2.00000i q^{57} +5.00000i q^{58} -1.00000 q^{59} +2.00000 q^{60} +8.00000i q^{61} -7.00000i q^{62} -8.00000i q^{63} +1.00000 q^{64} -2.00000i q^{65} -4.00000 q^{66} -3.00000 q^{67} +(1.00000 - 4.00000i) q^{68} -3.00000 q^{69} +8.00000 q^{70} -6.00000i q^{71} -2.00000 q^{72} -2.00000i q^{73} +10.0000i q^{74} +1.00000i q^{75} +2.00000 q^{76} -16.0000 q^{77} -1.00000i q^{78} +4.00000i q^{79} -2.00000i q^{80} +1.00000 q^{81} -2.00000i q^{82} +5.00000 q^{83} +4.00000 q^{84} +(-8.00000 - 2.00000i) q^{85} +5.00000 q^{87} +4.00000i q^{88} -6.00000 q^{89} +4.00000i q^{90} -4.00000i q^{91} +3.00000i q^{92} -7.00000 q^{93} +2.00000 q^{94} -4.00000i q^{95} -1.00000i q^{96} -5.00000i q^{97} +9.00000 q^{98} -8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} - 4 q^{18} + 4 q^{19} + 8 q^{21} + 2 q^{25} - 2 q^{26} - 4 q^{30} - 2 q^{32} + 8 q^{33} - 2 q^{34} - 16 q^{35} + 4 q^{36} - 4 q^{38} - 8 q^{42} - 4 q^{47} - 18 q^{49} - 2 q^{50} + 8 q^{51} + 2 q^{52} - 8 q^{53} - 16 q^{55} - 2 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{66} - 6 q^{67} + 2 q^{68} - 6 q^{69} + 16 q^{70} - 4 q^{72} + 4 q^{76} - 32 q^{77} + 2 q^{81} + 10 q^{83} + 8 q^{84} - 16 q^{85} + 10 q^{87} - 12 q^{89} - 14 q^{93} + 4 q^{94} + 18 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 - 4 * q^18 + 4 * q^19 + 8 * q^21 + 2 * q^25 - 2 * q^26 - 4 * q^30 - 2 * q^32 + 8 * q^33 - 2 * q^34 - 16 * q^35 + 4 * q^36 - 4 * q^38 - 8 * q^42 - 4 * q^47 - 18 * q^49 - 2 * q^50 + 8 * q^51 + 2 * q^52 - 8 * q^53 - 16 * q^55 - 2 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^66 - 6 * q^67 + 2 * q^68 - 6 * q^69 + 16 * q^70 - 4 * q^72 + 4 * q^76 - 32 * q^77 + 2 * q^81 + 10 * q^83 + 8 * q^84 - 16 * q^85 + 10 * q^87 - 12 * q^89 - 14 * q^93 + 4 * q^94 + 18 * q^98

Introduction

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