LMFDB - Embedded newform 1280.2.o.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(127,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("1280.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.o (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$1$
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:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.127
Dual form			1280.2.o.c.383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000i q^{9} -2.00000 q^{11} +(-3.00000 - 3.00000i) q^{13} +(1.00000 - 3.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +4.00000i q^{19} -6.00000i q^{21} +(-1.00000 - 1.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +10.0000i q^{31} +(2.00000 - 2.00000i) q^{33} +(3.00000 - 9.00000i) q^{35} +(1.00000 - 1.00000i) q^{37} +6.00000 q^{39} +10.0000 q^{41} +(5.00000 - 5.00000i) q^{43} +(-1.00000 - 2.00000i) q^{45} +(3.00000 - 3.00000i) q^{47} -11.0000i q^{49} -2.00000 q^{51} +(-5.00000 - 5.00000i) q^{53} +(4.00000 - 2.00000i) q^{55} +(-4.00000 - 4.00000i) q^{57} +12.0000i q^{59} -2.00000i q^{61} +(-3.00000 - 3.00000i) q^{63} +(9.00000 + 3.00000i) q^{65} +(-1.00000 - 1.00000i) q^{67} +2.00000 q^{69} -2.00000i q^{71} +(-1.00000 + 1.00000i) q^{73} +(1.00000 + 7.00000i) q^{75} +(6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +(-3.00000 - 1.00000i) q^{85} -16.0000i q^{89} +18.0000 q^{91} +(-10.0000 - 10.0000i) q^{93} +(-4.00000 - 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{5} - 6 q^{7}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^5 - 6 * q^7	$ 2 q - 2 q^{3} - 4 q^{5} - 6 q^{7} - 4 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} - 2 q^{23} + 6 q^{25} - 8 q^{27} + 4 q^{33} + 6 q^{35} + 2 q^{37} + 12 q^{39} + 20 q^{41} + 10 q^{43} - 2 q^{45} + 6 q^{47} - 4 q^{51} - 10 q^{53} + 8 q^{55} - 8 q^{57} - 6 q^{63} + 18 q^{65} - 2 q^{67} + 4 q^{69} - 2 q^{73} + 2 q^{75} + 12 q^{77} - 16 q^{79} + 10 q^{81} - 10 q^{83} - 6 q^{85} + 36 q^{91} - 20 q^{93} - 8 q^{95} - 6 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^5 - 6 * q^7 - 4 * q^11 - 6 * q^13 + 2 * q^15 + 2 * q^17 - 2 * q^23 + 6 * q^25 - 8 * q^27 + 4 * q^33 + 6 * q^35 + 2 * q^37 + 12 * q^39 + 20 * q^41 + 10 * q^43 - 2 * q^45 + 6 * q^47 - 4 * q^51 - 10 * q^53 + 8 * q^55 - 8 * q^57 - 6 * q^63 + 18 * q^65 - 2 * q^67 + 4 * q^69 - 2 * q^73 + 2 * q^75 + 12 * q^77 - 16 * q^79 + 10 * q^81 - 10 * q^83 - 6 * q^85 + 36 * q^91 - 20 * q^93 - 8 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		0			0
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		0			0
$15$	1.00000	−	3.00000i	0.258199	−	0.774597i
$16$		0			0
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$		−	6.00000i		−	1.30931i
$22$		0			0
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	3.00000	−	9.00000i	0.507093	−	1.52128i
$36$		0			0
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	−0.620113	−	0.784512i	$-0.712913\pi$
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	0.784512	+	0.620113i	$0.212913\pi$
$38$		0			0
$39$	6.00000			0.960769
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	−0.214280	−	0.976772i	$-0.568740\pi$
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	0.976772	+	0.214280i	$0.0687403\pi$
$44$		0			0
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$		0			0
$47$	3.00000	−	3.00000i	0.437595	−	0.437595i	−0.453607	−	0.891202i	$-0.649863\pi$
$47$	3.00000	−	3.00000i	0.437595	−	0.437595i	0.891202	+	0.453607i	$0.149863\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	0.274721	−	0.961524i	$-0.411414\pi$
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$	4.00000	−	2.00000i	0.539360	−	0.269680i
$56$		0			0
$57$	−4.00000	−	4.00000i	−0.529813	−	0.529813i
$58$		0			0
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$		0			0
$61$		−	2.00000i		−	0.256074i	−0.991769	−	0.128037i	$-0.959132\pi$
$61$		−	2.00000i		−	0.256074i	0.991769	−	0.128037i	$-0.0408676\pi$
$62$		0			0
$63$	−3.00000	−	3.00000i	−0.377964	−	0.377964i
$64$		0			0
$65$	9.00000	+	3.00000i	1.11631	+	0.372104i
$66$		0			0
$67$	−1.00000	−	1.00000i	−0.122169	−	0.122169i	0.643379	−	0.765548i	$-0.277532\pi$
$67$	−1.00000	−	1.00000i	−0.122169	−	0.122169i	−0.765548	+	0.643379i	$0.777532\pi$
$68$		0			0
$69$	2.00000			0.240772
$70$		0			0
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$		0			0
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	−0.763202	−	0.646160i	$-0.776374\pi$
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	0.646160	+	0.763202i	$0.276374\pi$
$74$		0			0
$75$	1.00000	+	7.00000i	0.115470	+	0.808290i
$76$		0			0
$77$	6.00000	−	6.00000i	0.683763	−	0.683763i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$		0			0
$85$	−3.00000	−	1.00000i	−0.325396	−	0.108465i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	16.0000i		−	1.69600i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$		−	16.0000i		−	1.69600i	0.529999	−	0.847998i	$-0.322192\pi$
$90$		0			0
$91$	18.0000			1.88691
$92$		0			0
$93$	−10.0000	−	10.0000i	−1.03695	−	1.03695i
$94$		0			0
$95$	−4.00000	−	8.00000i	−0.410391	−	0.820783i
$96$		0			0
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$		0			0
$99$		−	2.00000i		−	0.201008i
$100$		0			0
$101$			6.00000i			0.597022i	0.954406	+	0.298511i	$0.0964900\pi$
$101$			6.00000i			0.597022i	−0.954406	+	0.298511i	$0.903510\pi$
$102$		0			0
$103$	−9.00000	−	9.00000i	−0.886796	−	0.886796i	0.107418	−	0.994214i	$-0.465742\pi$
$103$	−9.00000	−	9.00000i	−0.886796	−	0.886796i	−0.994214	+	0.107418i	$0.965742\pi$
$104$		0			0
$105$	6.00000	+	12.0000i	0.585540	+	1.17108i
$106$		0			0
$107$	−3.00000	−	3.00000i	−0.290021	−	0.290021i	0.547068	−	0.837088i	$-0.315744\pi$
$107$	−3.00000	−	3.00000i	−0.290021	−	0.290021i	−0.837088	+	0.547068i	$0.815744\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$			2.00000i			0.189832i
$112$		0			0
$113$	−3.00000	+	3.00000i	−0.282216	+	0.282216i	−0.833992	−	0.551776i	$-0.813950\pi$
$113$	−3.00000	+	3.00000i	−0.282216	+	0.282216i	0.551776	+	0.833992i	$0.313950\pi$
$114$		0			0
$115$	3.00000	+	1.00000i	0.279751	+	0.0932505i
$116$		0			0
$117$	3.00000	−	3.00000i	0.277350	−	0.277350i
$118$		0			0
$119$	−6.00000			−0.550019
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$	−10.0000	+	10.0000i	−0.901670	+	0.901670i
$124$		0			0
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$		0			0
$129$			10.0000i			0.880451i
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$		0			0
$133$	−12.0000	−	12.0000i	−1.04053	−	1.04053i
$134$		0			0
$135$	12.0000	+	4.00000i	1.03280	+	0.344265i
$136$		0			0
$137$	11.0000	+	11.0000i	0.939793	+	0.939793i	0.998288	−	0.0584943i	$-0.0186300\pi$
$137$	11.0000	+	11.0000i	0.939793	+	0.939793i	−0.0584943	+	0.998288i	$0.518630\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$			6.00000i			0.505291i
$142$		0			0
$143$	6.00000	+	6.00000i	0.501745	+	0.501745i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11.0000	+	11.0000i	0.907265	+	0.907265i
$148$		0			0
$149$	4.00000			0.327693			0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000			0.327693			0.163846	+	0.986486i	$0.447610\pi$
$150$		0			0
$151$			6.00000i			0.488273i	0.969741	+	0.244137i	$0.0785045\pi$
$151$			6.00000i			0.488273i	−0.969741	+	0.244137i	$0.921495\pi$
$152$		0			0
$153$	−1.00000	+	1.00000i	−0.0808452	+	0.0808452i
$154$		0			0
$155$	−10.0000	−	20.0000i	−0.803219	−	1.60644i
$156$		0			0
$157$	−1.00000	+	1.00000i	−0.0798087	+	0.0798087i	−0.745884	−	0.666076i	$-0.767973\pi$
$157$	−1.00000	+	1.00000i	−0.0798087	+	0.0798087i	0.666076	+	0.745884i	$0.267973\pi$
$158$		0			0
$159$	10.0000			0.793052
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	−0.745184	−	0.666858i	$-0.767639\pi$
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	0.666858	+	0.745184i	$0.267639\pi$
$164$		0			0
$165$	−2.00000	+	6.00000i	−0.155700	+	0.467099i
$166$		0			0
$167$	1.00000	−	1.00000i	0.0773823	−	0.0773823i	−0.667356	−	0.744739i	$-0.732574\pi$
$167$	1.00000	−	1.00000i	0.0773823	−	0.0773823i	0.744739	+	0.667356i	$0.232574\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−4.00000			−0.305888
$172$		0			0
$173$	5.00000	+	5.00000i	0.380143	+	0.380143i	0.871154	−	0.491011i	$-0.163372\pi$
$173$	5.00000	+	5.00000i	0.380143	+	0.380143i	−0.491011	+	0.871154i	$0.663372\pi$
$174$		0			0
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$		0			0
$177$	−12.0000	−	12.0000i	−0.901975	−	0.901975i
$178$		0			0
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$		0			0
$181$			22.0000i			1.63525i	0.575753	+	0.817624i	$0.304709\pi$
$181$			22.0000i			1.63525i	−0.575753	+	0.817624i	$0.695291\pi$
$182$		0			0
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$		0			0
$185$	−1.00000	+	3.00000i	−0.0735215	+	0.220564i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$	24.0000			1.74574
$190$		0			0
$191$		−	14.0000i		−	1.01300i	−0.862239	−	0.506502i	$-0.830938\pi$
$191$		−	14.0000i		−	1.01300i	0.862239	−	0.506502i	$-0.169062\pi$
$192$		0			0
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$		0			0
$195$	−12.0000	+	6.00000i	−0.859338	+	0.429669i
$196$		0			0
$197$	13.0000	−	13.0000i	0.926212	−	0.926212i	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	13.0000	−	13.0000i	0.926212	−	0.926212i	0.997459	+	0.0712470i	$0.0226979\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$	2.00000			0.141069
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−20.0000	+	10.0000i	−1.39686	+	0.698430i
$206$		0			0
$207$	1.00000	−	1.00000i	0.0695048	−	0.0695048i
$208$		0			0
$209$		−	8.00000i		−	0.553372i
$210$		0			0
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$		0			0
$213$	2.00000	+	2.00000i	0.137038	+	0.137038i
$214$		0			0
$215$	−5.00000	+	15.0000i	−0.340997	+	1.02299i
$216$		0			0
$217$	−30.0000	−	30.0000i	−2.03653	−	2.03653i
$218$		0			0
$219$		−	2.00000i		−	0.135147i
$220$		0			0
$221$		−	6.00000i		−	0.403604i
$222$		0			0
$223$	1.00000	+	1.00000i	0.0669650	+	0.0669650i	0.739796	−	0.672831i	$-0.234922\pi$
$223$	1.00000	+	1.00000i	0.0669650	+	0.0669650i	−0.672831	+	0.739796i	$0.734922\pi$
$224$		0			0
$225$	4.00000	+	3.00000i	0.266667	+	0.200000i
$226$		0			0
$227$	−5.00000	−	5.00000i	−0.331862	−	0.331862i	0.521431	−	0.853293i	$-0.325398\pi$
$227$	−5.00000	−	5.00000i	−0.331862	−	0.331862i	−0.853293	+	0.521431i	$0.825398\pi$
$228$		0			0
$229$	8.00000			0.528655			0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000			0.528655			0.264327	+	0.964433i	$0.414850\pi$
$230$		0			0
$231$			12.0000i			0.789542i
$232$		0			0
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.524097	+	0.851658i	$0.675597\pi$
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−3.00000	+	9.00000i	−0.195698	+	0.587095i
$236$		0			0
$237$	8.00000	−	8.00000i	0.519656	−	0.519656i
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	11.0000	+	22.0000i	0.702764	+	1.40553i
$246$		0			0
$247$	12.0000	−	12.0000i	0.763542	−	0.763542i
$248$		0			0
$249$		−	10.0000i		−	0.633724i
$250$		0			0
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		0			0
$253$	2.00000	+	2.00000i	0.125739	+	0.125739i
$254$		0			0
$255$	4.00000	−	2.00000i	0.250490	−	0.125245i
$256$		0			0
$257$	5.00000	+	5.00000i	0.311891	+	0.311891i	0.845642	−	0.533751i	$-0.179218\pi$
$257$	5.00000	+	5.00000i	0.311891	+	0.311891i	−0.533751	+	0.845642i	$0.679218\pi$
$258$		0			0
$259$			6.00000i			0.372822i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	0.959613	−	0.281324i	$-0.0907735\pi$
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	−0.281324	+	0.959613i	$0.590774\pi$
$264$		0			0
$265$	15.0000	+	5.00000i	0.921443	+	0.307148i
$266$		0			0
$267$	16.0000	+	16.0000i	0.979184	+	0.979184i
$268$		0			0
$269$	20.0000			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$269$	20.0000			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$270$		0			0
$271$		−	14.0000i		−	0.850439i	−0.905090	−	0.425220i	$-0.860197\pi$
$271$		−	14.0000i		−	0.850439i	0.905090	−	0.425220i	$-0.139803\pi$
$272$		0			0
$273$	−18.0000	+	18.0000i	−1.08941	+	1.08941i
$274$		0			0
$275$	−6.00000	+	8.00000i	−0.361814	+	0.482418i
$276$		0			0
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	−0.955598	−	0.294672i	$-0.904789\pi$
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	0.294672	+	0.955598i	$0.404789\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−7.00000	+	7.00000i	−0.416107	+	0.416107i	−0.883859	−	0.467753i	$-0.845064\pi$
$283$	−7.00000	+	7.00000i	−0.416107	+	0.416107i	0.467753	+	0.883859i	$0.345064\pi$
$284$		0			0
$285$	12.0000	+	4.00000i	0.710819	+	0.236940i
$286$		0			0
$287$	−30.0000	+	30.0000i	−1.77084	+	1.77084i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	6.00000			0.351726
$292$		0			0
$293$	11.0000	+	11.0000i	0.642627	+	0.642627i	0.951200	−	0.308574i	$-0.0998516\pi$
$293$	11.0000	+	11.0000i	0.642627	+	0.642627i	−0.308574	+	0.951200i	$0.599852\pi$
$294$		0			0
$295$	−12.0000	−	24.0000i	−0.698667	−	1.39733i
$296$		0			0
$297$	8.00000	+	8.00000i	0.464207	+	0.464207i
$298$		0			0
$299$			6.00000i			0.346989i
$300$		0			0
$301$			30.0000i			1.72917i
$302$		0			0
$303$	−6.00000	−	6.00000i	−0.344691	−	0.344691i
$304$		0			0
$305$	2.00000	+	4.00000i	0.114520	+	0.229039i
$306$		0			0
$307$	−17.0000	−	17.0000i	−0.970241	−	0.970241i	0.0293286	−	0.999570i	$-0.490663\pi$
$307$	−17.0000	−	17.0000i	−0.970241	−	0.970241i	−0.999570	+	0.0293286i	$0.990663\pi$
$308$		0			0
$309$	18.0000			1.02398
$310$		0			0
$311$		−	18.0000i		−	1.02069i	−0.859971	−	0.510343i	$-0.829518\pi$
$311$		−	18.0000i		−	1.02069i	0.859971	−	0.510343i	$-0.170482\pi$
$312$		0			0
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	−0.914130	−	0.405420i	$-0.867125\pi$
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	0.405420	+	0.914130i	$0.367125\pi$
$314$		0			0
$315$	9.00000	+	3.00000i	0.507093	+	0.169031i
$316$		0			0
$317$	−13.0000	+	13.0000i	−0.730153	+	0.730153i	−0.970650	−	0.240497i	$-0.922690\pi$
$317$	−13.0000	+	13.0000i	−0.730153	+	0.730153i	0.240497	+	0.970650i	$0.422690\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	−4.00000	+	4.00000i	−0.222566	+	0.222566i
$324$		0			0
$325$	−21.0000	+	3.00000i	−1.16487	+	0.166410i
$326$		0			0
$327$	4.00000	−	4.00000i	0.221201	−	0.221201i
$328$		0			0
$329$			18.0000i			0.992372i
$330$		0			0
$331$	−26.0000			−1.42909			−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000			−1.42909			−0.714545	+	0.699590i	$0.753366\pi$
$332$		0			0
$333$	1.00000	+	1.00000i	0.0547997	+	0.0547997i
$334$		0			0
$335$	3.00000	+	1.00000i	0.163908	+	0.0546358i
$336$		0			0
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	0.168585	−	0.985687i	$-0.446080\pi$
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	−0.985687	+	0.168585i	$0.946080\pi$
$338$		0			0
$339$		−	6.00000i		−	0.325875i
$340$		0			0
$341$		−	20.0000i		−	1.08306i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$		0			0
$345$	−4.00000	+	2.00000i	−0.215353	+	0.107676i
$346$		0			0
$347$	9.00000	+	9.00000i	0.483145	+	0.483145i	0.906135	−	0.422989i	$-0.139019\pi$
$347$	9.00000	+	9.00000i	0.483145	+	0.483145i	−0.422989	+	0.906135i	$0.639019\pi$
$348$		0			0
$349$	−8.00000			−0.428230			−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000			−0.428230			−0.214115	+	0.976808i	$0.568687\pi$
$350$		0			0
$351$			24.0000i			1.28103i
$352$		0			0
$353$	−15.0000	+	15.0000i	−0.798369	+	0.798369i	−0.982838	−	0.184469i	$-0.940943\pi$
$353$	−15.0000	+	15.0000i	−0.798369	+	0.798369i	0.184469	+	0.982838i	$0.440943\pi$
$354$		0			0
$355$	2.00000	+	4.00000i	0.106149	+	0.212298i
$356$		0			0
$357$	6.00000	−	6.00000i	0.317554	−	0.317554i
$358$		0			0
$359$	32.0000			1.68890			0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000			1.68890			0.844448	+	0.535638i	$0.179929\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$	7.00000	−	7.00000i	0.367405	−	0.367405i
$364$		0			0
$365$	1.00000	−	3.00000i	0.0523424	−	0.157027i
$366$		0			0
$367$	15.0000	−	15.0000i	0.782994	−	0.782994i	−0.197341	−	0.980335i	$-0.563231\pi$
$367$	15.0000	−	15.0000i	0.782994	−	0.782994i	0.980335	+	0.197341i	$0.0632307\pi$
$368$		0			0
$369$			10.0000i			0.520579i
$370$		0			0
$371$	30.0000			1.55752
$372$		0			0
$373$	−9.00000	−	9.00000i	−0.466002	−	0.466002i	0.434614	−	0.900617i	$-0.356885\pi$
$373$	−9.00000	−	9.00000i	−0.466002	−	0.466002i	−0.900617	+	0.434614i	$0.856885\pi$
$374$		0			0
$375$	−9.00000	−	13.0000i	−0.464758	−	0.671317i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	20.0000i		−	1.02733i	−0.857991	−	0.513665i	$-0.828287\pi$
$379$		−	20.0000i		−	1.02733i	0.857991	−	0.513665i	$-0.171713\pi$
$380$		0			0
$381$			14.0000i			0.717242i
$382$		0			0
$383$	1.00000	+	1.00000i	0.0510976	+	0.0510976i	0.732194	−	0.681096i	$-0.238496\pi$
$383$	1.00000	+	1.00000i	0.0510976	+	0.0510976i	−0.681096	+	0.732194i	$0.738496\pi$
$384$		0			0
$385$	−6.00000	+	18.0000i	−0.305788	+	0.917365i
$386$		0			0
$387$	5.00000	+	5.00000i	0.254164	+	0.254164i
$388$		0			0
$389$	4.00000			0.202808			0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000			0.202808			0.101404	+	0.994845i	$0.467667\pi$
$390$		0			0
$391$		−	2.00000i		−	0.101144i
$392$		0			0
$393$	−10.0000	+	10.0000i	−0.504433	+	0.504433i
$394$		0			0
$395$	16.0000	−	8.00000i	0.805047	−	0.402524i
$396$		0			0
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	−0.222178	−	0.975006i	$-0.571317\pi$
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	0.975006	+	0.222178i	$0.0713165\pi$
$398$		0			0
$399$	24.0000			1.20150
$400$		0			0
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$		0			0
$403$	30.0000	−	30.0000i	1.49441	−	1.49441i
$404$		0			0
$405$	−10.0000	+	5.00000i	−0.496904	+	0.248452i
$406$		0			0
$407$	−2.00000	+	2.00000i	−0.0991363	+	0.0991363i
$408$		0			0
$409$		−	20.0000i		−	0.988936i	−0.869196	−	0.494468i	$-0.835363\pi$
$409$		−	20.0000i		−	0.988936i	0.869196	−	0.494468i	$-0.164637\pi$
$410$		0			0
$411$	−22.0000			−1.08518
$412$		0			0
$413$	−36.0000	−	36.0000i	−1.77144	−	1.77144i
$414$		0			0
$415$	5.00000	−	15.0000i	0.245440	−	0.736321i
$416$		0			0
$417$	12.0000	+	12.0000i	0.587643	+	0.587643i
$418$		0			0
$419$			28.0000i			1.36789i	0.729534	+	0.683945i	$0.239737\pi$
$419$			28.0000i			1.36789i	−0.729534	+	0.683945i	$0.760263\pi$
$420$		0			0
$421$			34.0000i			1.65706i	0.559946	+	0.828529i	$0.310822\pi$
$421$			34.0000i			1.65706i	−0.559946	+	0.828529i	$0.689178\pi$
$422$		0			0
$423$	3.00000	+	3.00000i	0.145865	+	0.145865i
$424$		0			0
$425$	7.00000	−	1.00000i	0.339550	−	0.0485071i
$426$		0			0
$427$	6.00000	+	6.00000i	0.290360	+	0.290360i
$428$		0			0
$429$	−12.0000			−0.579365
$430$		0			0
$431$		−	30.0000i		−	1.44505i	−0.691345	−	0.722525i	$-0.742982\pi$
$431$		−	30.0000i		−	1.44505i	0.691345	−	0.722525i	$-0.257018\pi$
$432$		0			0
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.00923827	−	0.999957i	$-0.497059\pi$
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.999957	−	0.00923827i	$-0.00294067\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.00000	−	4.00000i	0.191346	−	0.191346i
$438$		0			0
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	11.0000			0.523810
$442$		0			0
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.210108	−	0.977678i	$-0.432619\pi$
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.977678	−	0.210108i	$-0.0673814\pi$
$444$		0			0
$445$	16.0000	+	32.0000i	0.758473	+	1.51695i
$446$		0			0
$447$	−4.00000	+	4.00000i	−0.189194	+	0.189194i
$448$		0			0
$449$		−	12.0000i		−	0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$		0			0
$451$	−20.0000			−0.941763
$452$		0			0
$453$	−6.00000	−	6.00000i	−0.281905	−	0.281905i
$454$		0			0
$455$	−36.0000	+	18.0000i	−1.68771	+	0.843853i
$456$		0			0
$457$	−9.00000	−	9.00000i	−0.421002	−	0.421002i	0.464546	−	0.885549i	$-0.346217\pi$
$457$	−9.00000	−	9.00000i	−0.421002	−	0.421002i	−0.885549	+	0.464546i	$0.846217\pi$
$458$		0			0
$459$		−	8.00000i		−	0.373408i
$460$		0			0
$461$			2.00000i			0.0931493i	0.998915	+	0.0465746i	$0.0148305\pi$
$461$			2.00000i			0.0931493i	−0.998915	+	0.0465746i	$0.985169\pi$
$462$		0			0
$463$	−11.0000	−	11.0000i	−0.511213	−	0.511213i	0.403685	−	0.914898i	$-0.367729\pi$
$463$	−11.0000	−	11.0000i	−0.511213	−	0.511213i	−0.914898	+	0.403685i	$0.867729\pi$
$464$		0			0
$465$	30.0000	+	10.0000i	1.39122	+	0.463739i
$466$		0			0
$467$	−13.0000	−	13.0000i	−0.601568	−	0.601568i	0.339160	−	0.940729i	$-0.389857\pi$
$467$	−13.0000	−	13.0000i	−0.601568	−	0.601568i	−0.940729	+	0.339160i	$0.889857\pi$
$468$		0			0
$469$	6.00000			0.277054
$470$		0			0
$471$		−	2.00000i		−	0.0921551i
$472$		0			0
$473$	−10.0000	+	10.0000i	−0.459800	+	0.459800i
$474$		0			0
$475$	16.0000	+	12.0000i	0.734130	+	0.550598i
$476$		0			0
$477$	5.00000	−	5.00000i	0.228934	−	0.228934i
$478$		0			0
$479$	40.0000			1.82765			0.913823	−	0.406112i	$-0.133116\pi$
$479$	40.0000			1.82765			0.913823	+	0.406112i	$0.133116\pi$
$480$		0			0
$481$	−6.00000			−0.273576
$482$		0			0
$483$	−6.00000	+	6.00000i	−0.273009	+	0.273009i
$484$		0			0
$485$	9.00000	+	3.00000i	0.408669	+	0.136223i
$486$		0			0
$487$	−19.0000	+	19.0000i	−0.860972	+	0.860972i	−0.991451	−	0.130479i	$-0.958349\pi$
$487$	−19.0000	+	19.0000i	−0.860972	+	0.860972i	0.130479	+	0.991451i	$0.458349\pi$
$488$		0			0
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	−10.0000			−0.451294			−0.225647	−	0.974209i	$-0.572450\pi$
$491$	−10.0000			−0.451294			−0.225647	+	0.974209i	$0.572450\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	2.00000	+	4.00000i	0.0898933	+	0.179787i
$496$		0			0
$497$	6.00000	+	6.00000i	0.269137	+	0.269137i
$498$		0			0
$499$			28.0000i			1.25345i	0.779240	+	0.626726i	$0.215605\pi$
$499$			28.0000i			1.25345i	−0.779240	+	0.626726i	$0.784395\pi$
$500$		0			0
$501$			2.00000i			0.0893534i
$502$		0			0
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	0.217964	−	0.975957i	$-0.430058\pi$
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	−0.975957	+	0.217964i	$0.930058\pi$
$504$		0			0
$505$	−6.00000	−	12.0000i	−0.266996	−	0.533993i
$506$		0			0
$507$	−5.00000	−	5.00000i	−0.222058	−	0.222058i
$508$		0			0
$509$	24.0000			1.06378			0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000			1.06378			0.531891	+	0.846813i	$0.321482\pi$
$510$		0			0
$511$		−	6.00000i		−	0.265424i
$512$		0			0
$513$	16.0000	−	16.0000i	0.706417	−	0.706417i
$514$		0			0
$515$	27.0000	+	9.00000i	1.18976	+	0.396587i
$516$		0			0
$517$	−6.00000	+	6.00000i	−0.263880	+	0.263880i
$518$		0			0
$519$	−10.0000			−0.438951
$520$		0			0
$521$	14.0000			0.613351			0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	−15.0000	+	15.0000i	−0.655904	+	0.655904i	−0.954408	−	0.298504i	$-0.903512\pi$
$523$	−15.0000	+	15.0000i	−0.655904	+	0.655904i	0.298504	+	0.954408i	$0.403512\pi$
$524$		0			0
$525$	−24.0000	−	18.0000i	−1.04745	−	0.785584i
$526$		0			0
$527$	−10.0000	+	10.0000i	−0.435607	+	0.435607i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−30.0000	−	30.0000i	−1.29944	−	1.29944i
$534$		0			0
$535$	9.00000	+	3.00000i	0.389104	+	0.129701i
$536$		0			0
$537$	12.0000	+	12.0000i	0.517838	+	0.517838i
$538$		0			0
$539$			22.0000i			0.947607i
$540$		0			0
$541$		−	30.0000i		−	1.28980i	−0.764267	−	0.644900i	$-0.776899\pi$
$541$		−	30.0000i		−	1.28980i	0.764267	−	0.644900i	$-0.223101\pi$
$542$		0			0
$543$	−22.0000	−	22.0000i	−0.944110	−	0.944110i
$544$		0			0
$545$	8.00000	−	4.00000i	0.342682	−	0.171341i
$546$		0			0
$547$	11.0000	+	11.0000i	0.470326	+	0.470326i	0.902020	−	0.431694i	$-0.142084\pi$
$547$	11.0000	+	11.0000i	0.470326	+	0.470326i	−0.431694	+	0.902020i	$0.642084\pi$
$548$		0			0
$549$	2.00000			0.0853579
$550$		0			0
$551$		0			0
$552$		0			0
$553$	24.0000	−	24.0000i	1.02058	−	1.02058i
$554$		0			0
$555$	−2.00000	−	4.00000i	−0.0848953	−	0.169791i
$556$		0			0
$557$	27.0000	−	27.0000i	1.14403	−	1.14403i	0.156320	−	0.987706i	$-0.450037\pi$
$557$	27.0000	−	27.0000i	1.14403	−	1.14403i	0.987706	−	0.156320i	$-0.0499632\pi$
$558$		0			0
$559$	−30.0000			−1.26886
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−33.0000	+	33.0000i	−1.39078	+	1.39078i	−0.567213	+	0.823571i	$0.691978\pi$
$563$	−33.0000	+	33.0000i	−1.39078	+	1.39078i	−0.823571	+	0.567213i	$0.808022\pi$
$564$		0			0
$565$	3.00000	−	9.00000i	0.126211	−	0.378633i
$566$		0			0
$567$	−15.0000	+	15.0000i	−0.629941	+	0.629941i
$568$		0			0
$569$		−	12.0000i		−	0.503066i	−0.967849	−	0.251533i	$-0.919065\pi$
$569$		−	12.0000i		−	0.503066i	0.967849	−	0.251533i	$-0.0809347\pi$
$570$		0			0
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$		0			0
$573$	14.0000	+	14.0000i	0.584858	+	0.584858i
$574$		0			0
$575$	−7.00000	+	1.00000i	−0.291920	+	0.0417029i
$576$		0			0
$577$	−19.0000	−	19.0000i	−0.790980	−	0.790980i	0.190673	−	0.981654i	$-0.438933\pi$
$577$	−19.0000	−	19.0000i	−0.790980	−	0.790980i	−0.981654	+	0.190673i	$0.938933\pi$
$578$		0			0
$579$		−	30.0000i		−	1.24676i
$580$		0			0
$581$		−	30.0000i		−	1.24461i
$582$		0			0
$583$	10.0000	+	10.0000i	0.414158	+	0.414158i
$584$		0			0
$585$	−3.00000	+	9.00000i	−0.124035	+	0.372104i
$586$		0			0
$587$	−23.0000	−	23.0000i	−0.949312	−	0.949312i	0.0494643	−	0.998776i	$-0.484249\pi$
$587$	−23.0000	−	23.0000i	−0.949312	−	0.949312i	−0.998776	+	0.0494643i	$0.984249\pi$
$588$		0			0
$589$	−40.0000			−1.64817
$590$		0			0
$591$			26.0000i			1.06950i
$592$		0			0
$593$	−7.00000	+	7.00000i	−0.287456	+	0.287456i	−0.836073	−	0.548618i	$-0.815154\pi$
$593$	−7.00000	+	7.00000i	−0.287456	+	0.287456i	0.548618	+	0.836073i	$0.315154\pi$
$594$		0			0
$595$	12.0000	−	6.00000i	0.491952	−	0.245976i
$596$		0			0
$597$	16.0000	−	16.0000i	0.654836	−	0.654836i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	1.00000	−	1.00000i	0.0407231	−	0.0407231i
$604$		0			0
$605$	14.0000	−	7.00000i	0.569181	−	0.284590i
$606$		0			0
$607$	−5.00000	+	5.00000i	−0.202944	+	0.202944i	−0.801260	−	0.598316i	$-0.795837\pi$
$607$	−5.00000	+	5.00000i	−0.202944	+	0.202944i	0.598316	+	0.801260i	$0.295837\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−18.0000			−0.728202
$612$		0			0
$613$	15.0000	+	15.0000i	0.605844	+	0.605844i	0.941857	−	0.336013i	$-0.109079\pi$
$613$	15.0000	+	15.0000i	0.605844	+	0.605844i	−0.336013	+	0.941857i	$0.609079\pi$
$614$		0			0
$615$	10.0000	−	30.0000i	0.403239	−	1.20972i
$616$		0			0
$617$	−13.0000	−	13.0000i	−0.523360	−	0.523360i	0.395224	−	0.918585i	$-0.370667\pi$
$617$	−13.0000	−	13.0000i	−0.523360	−	0.523360i	−0.918585	+	0.395224i	$0.870667\pi$
$618$		0			0
$619$			12.0000i			0.482321i	0.970485	+	0.241160i	$0.0775280\pi$
$619$			12.0000i			0.482321i	−0.970485	+	0.241160i	$0.922472\pi$
$620$		0			0
$621$			8.00000i			0.321029i
$622$		0			0
$623$	48.0000	+	48.0000i	1.92308	+	1.92308i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	8.00000	+	8.00000i	0.319489	+	0.319489i
$628$		0			0
$629$	2.00000			0.0797452
$630$		0			0
$631$			14.0000i			0.557331i	0.960388	+	0.278666i	$0.0898921\pi$
$631$			14.0000i			0.557331i	−0.960388	+	0.278666i	$0.910108\pi$
$632$		0			0
$633$	14.0000	−	14.0000i	0.556450	−	0.556450i
$634$		0			0
$635$	−7.00000	+	21.0000i	−0.277787	+	0.833360i
$636$		0			0
$637$	−33.0000	+	33.0000i	−1.30751	+	1.30751i
$638$		0			0
$639$	2.00000			0.0791188
$640$		0			0
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	27.0000	−	27.0000i	1.06478	−	1.06478i	0.0670247	−	0.997751i	$-0.478649\pi$
$643$	27.0000	−	27.0000i	1.06478	−	1.06478i	0.997751	−	0.0670247i	$-0.0213506\pi$
$644$		0			0
$645$	−10.0000	−	20.0000i	−0.393750	−	0.787499i
$646$		0			0
$647$	29.0000	−	29.0000i	1.14011	−	1.14011i	0.151678	−	0.988430i	$-0.451532\pi$
$647$	29.0000	−	29.0000i	1.14011	−	1.14011i	0.988430	−	0.151678i	$-0.0484676\pi$
$648$		0			0
$649$		−	24.0000i		−	0.942082i
$650$		0			0
$651$	60.0000			2.35159
$652$		0			0
$653$	1.00000	+	1.00000i	0.0391330	+	0.0391330i	0.726403	−	0.687270i	$-0.241191\pi$
$653$	1.00000	+	1.00000i	0.0391330	+	0.0391330i	−0.687270	+	0.726403i	$0.741191\pi$
$654$		0			0
$655$	−20.0000	+	10.0000i	−0.781465	+	0.390732i
$656$		0			0
$657$	−1.00000	−	1.00000i	−0.0390137	−	0.0390137i
$658$		0			0
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$		0			0
$661$		−	30.0000i		−	1.16686i	−0.812162	−	0.583432i	$-0.801709\pi$
$661$		−	30.0000i		−	1.16686i	0.812162	−	0.583432i	$-0.198291\pi$
$662$		0			0
$663$	6.00000	+	6.00000i	0.233021	+	0.233021i
$664$		0			0
$665$	36.0000	+	12.0000i	1.39602	+	0.465340i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−2.00000			−0.0773245
$670$		0			0
$671$			4.00000i			0.154418i
$672$		0			0
$673$	−3.00000	+	3.00000i	−0.115642	+	0.115642i	−0.762560	−	0.646918i	$-0.776058\pi$
$673$	−3.00000	+	3.00000i	−0.115642	+	0.115642i	0.646918	+	0.762560i	$0.276058\pi$
$674$		0			0
$675$	−28.0000	+	4.00000i	−1.07772	+	0.153960i
$676$		0			0
$677$	−3.00000	+	3.00000i	−0.115299	+	0.115299i	−0.762402	−	0.647103i	$-0.775980\pi$
$677$	−3.00000	+	3.00000i	−0.115299	+	0.115299i	0.647103	+	0.762402i	$0.275980\pi$
$678$		0			0
$679$	18.0000			0.690777
$680$		0			0
$681$	10.0000			0.383201
$682$		0			0
$683$	−11.0000	+	11.0000i	−0.420903	+	0.420903i	−0.885515	−	0.464611i	$-0.846194\pi$
$683$	−11.0000	+	11.0000i	−0.420903	+	0.420903i	0.464611	+	0.885515i	$0.346194\pi$
$684$		0			0
$685$	−33.0000	−	11.0000i	−1.26087	−	0.420288i
$686$		0			0
$687$	−8.00000	+	8.00000i	−0.305219	+	0.305219i
$688$		0			0
$689$			30.0000i			1.14291i
$690$		0			0
$691$	−14.0000			−0.532585			−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000			−0.532585			−0.266293	+	0.963892i	$0.585799\pi$
$692$		0			0
$693$	6.00000	+	6.00000i	0.227921	+	0.227921i
$694$		0			0
$695$	12.0000	+	24.0000i	0.455186	+	0.910372i
$696$		0			0
$697$	10.0000	+	10.0000i	0.378777	+	0.378777i
$698$		0			0
$699$		−	42.0000i		−	1.58859i
$700$		0			0
$701$		−	34.0000i		−	1.28416i	−0.766637	−	0.642081i	$-0.778071\pi$
$701$		−	34.0000i		−	1.28416i	0.766637	−	0.642081i	$-0.221929\pi$
$702$		0			0
$703$	4.00000	+	4.00000i	0.150863	+	0.150863i
$704$		0			0
$705$	−6.00000	−	12.0000i	−0.225973	−	0.451946i
$706$		0			0
$707$	−18.0000	−	18.0000i	−0.676960	−	0.676960i
$708$		0			0
$709$	−48.0000			−1.80268			−0.901339	−	0.433114i	$-0.857415\pi$
$709$	−48.0000			−1.80268			−0.901339	+	0.433114i	$0.857415\pi$
$710$		0			0
$711$		−	8.00000i		−	0.300023i
$712$		0			0
$713$	10.0000	−	10.0000i	0.374503	−	0.374503i
$714$		0			0
$715$	−18.0000	−	6.00000i	−0.673162	−	0.224387i
$716$		0			0
$717$	16.0000	−	16.0000i	0.597531	−	0.597531i
$718$		0			0
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$		0			0
$721$	54.0000			2.01107
$722$		0			0
$723$	2.00000	−	2.00000i	0.0743808	−	0.0743808i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.00000	+	3.00000i	−0.111264	+	0.111264i	−0.760547	−	0.649283i	$-0.775069\pi$
$727$	−3.00000	+	3.00000i	−0.111264	+	0.111264i	0.649283	+	0.760547i	$0.275069\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	10.0000			0.369863
$732$		0			0
$733$	−27.0000	−	27.0000i	−0.997268	−	0.997268i	0.00272852	−	0.999996i	$-0.499131\pi$
$733$	−27.0000	−	27.0000i	−0.997268	−	0.997268i	−0.999996	+	0.00272852i	$0.999131\pi$
$734$		0			0
$735$	−33.0000	−	11.0000i	−1.21722	−	0.405741i
$736$		0			0
$737$	2.00000	+	2.00000i	0.0736709	+	0.0736709i
$738$		0			0
$739$		−	28.0000i		−	1.03000i	−0.857191	−	0.514998i	$-0.827793\pi$
$739$		−	28.0000i		−	1.03000i	0.857191	−	0.514998i	$-0.172207\pi$
$740$		0			0
$741$			24.0000i			0.881662i
$742$		0			0
$743$	−21.0000	−	21.0000i	−0.770415	−	0.770415i	0.207764	−	0.978179i	$-0.433381\pi$
$743$	−21.0000	−	21.0000i	−0.770415	−	0.770415i	−0.978179	+	0.207764i	$0.933381\pi$
$744$		0			0
$745$	−8.00000	+	4.00000i	−0.293097	+	0.146549i
$746$		0			0
$747$	−5.00000	−	5.00000i	−0.182940	−	0.182940i
$748$		0			0
$749$	18.0000			0.657706
$750$		0			0
$751$			2.00000i			0.0729810i	0.999334	+	0.0364905i	$0.0116179\pi$
$751$			2.00000i			0.0729810i	−0.999334	+	0.0364905i	$0.988382\pi$
$752$		0			0
$753$	−6.00000	+	6.00000i	−0.218652	+	0.218652i
$754$		0			0
$755$	−6.00000	−	12.0000i	−0.218362	−	0.436725i
$756$		0			0
$757$	−19.0000	+	19.0000i	−0.690567	+	0.690567i	−0.962357	−	0.271790i	$-0.912384\pi$
$757$	−19.0000	+	19.0000i	−0.690567	+	0.690567i	0.271790	+	0.962357i	$0.412384\pi$
$758$		0			0
$759$	−4.00000			−0.145191
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		0			0
$763$	12.0000	−	12.0000i	0.434429	−	0.434429i
$764$		0			0
$765$	1.00000	−	3.00000i	0.0361551	−	0.108465i
$766$		0			0
$767$	36.0000	−	36.0000i	1.29988	−	1.29988i
$768$		0			0
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$		0			0
$771$	−10.0000			−0.360141
$772$		0			0
$773$	−17.0000	−	17.0000i	−0.611448	−	0.611448i	0.331876	−	0.943323i	$-0.392319\pi$
$773$	−17.0000	−	17.0000i	−0.611448	−	0.611448i	−0.943323	+	0.331876i	$0.892319\pi$
$774$		0			0
$775$	40.0000	+	30.0000i	1.43684	+	1.07763i
$776$		0			0
$777$	−6.00000	−	6.00000i	−0.215249	−	0.215249i
$778$		0			0
$779$			40.0000i			1.43315i
$780$		0			0
$781$			4.00000i			0.143131i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.00000	−	3.00000i	0.0356915	−	0.107075i
$786$		0			0
$787$	31.0000	+	31.0000i	1.10503	+	1.10503i	0.993794	+	0.111237i	$0.0354812\pi$
$787$	31.0000	+	31.0000i	1.10503	+	1.10503i	0.111237	+	0.993794i	$0.464519\pi$
$788$		0			0
$789$	−22.0000			−0.783221
$790$		0			0
$791$		−	18.0000i		−	0.640006i
$792$		0			0
$793$	−6.00000	+	6.00000i	−0.213066	+	0.213066i
$794$		0			0
$795$	−20.0000	+	10.0000i	−0.709327	+	0.354663i
$796$		0			0
$797$	−37.0000	+	37.0000i	−1.31061	+	1.31061i	−0.389640	+	0.920967i	$0.627401\pi$
$797$	−37.0000	+	37.0000i	−1.31061	+	1.31061i	−0.920967	+	0.389640i	$0.872599\pi$
$798$		0			0
$799$	6.00000			0.212265
$800$		0			0
$801$	16.0000			0.565332
$802$		0			0
$803$	2.00000	−	2.00000i	0.0705785	−	0.0705785i
$804$		0			0
$805$	−12.0000	+	6.00000i	−0.422944	+	0.211472i
$806$		0			0
$807$	−20.0000	+	20.0000i	−0.704033	+	0.704033i
$808$		0			0
$809$		−	16.0000i		−	0.562530i	−0.959630	−	0.281265i	$-0.909246\pi$
$809$		−	16.0000i		−	0.562530i	0.959630	−	0.281265i	$-0.0907540\pi$
$810$		0			0
$811$	54.0000			1.89620			0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000			1.89620			0.948098	+	0.317978i	$0.103004\pi$
$812$		0			0
$813$	14.0000	+	14.0000i	0.491001	+	0.491001i
$814$		0			0
$815$	1.00000	−	3.00000i	0.0350285	−	0.105085i
$816$		0			0
$817$	20.0000	+	20.0000i	0.699711	+	0.699711i
$818$		0			0
$819$			18.0000i			0.628971i
$820$		0			0
$821$			10.0000i			0.349002i	0.984657	+	0.174501i	$0.0558313\pi$
$821$			10.0000i			0.349002i	−0.984657	+	0.174501i	$0.944169\pi$
$822$		0			0
$823$	7.00000	+	7.00000i	0.244005	+	0.244005i	0.818505	−	0.574500i	$-0.194803\pi$
$823$	7.00000	+	7.00000i	0.244005	+	0.244005i	−0.574500	+	0.818505i	$0.694803\pi$
$824$		0			0
$825$	−2.00000	−	14.0000i	−0.0696311	−	0.487417i
$826$		0			0
$827$	25.0000	+	25.0000i	0.869335	+	0.869335i	0.992399	−	0.123064i	$-0.0392719\pi$
$827$	25.0000	+	25.0000i	0.869335	+	0.869335i	−0.123064	+	0.992399i	$0.539272\pi$
$828$		0			0
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		−	22.0000i		−	0.763172i
$832$		0			0
$833$	11.0000	−	11.0000i	0.381127	−	0.381127i
$834$		0			0
$835$	−1.00000	+	3.00000i	−0.0346064	+	0.103819i
$836$		0			0
$837$	40.0000	−	40.0000i	1.38260	−	1.38260i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$	6.00000	−	6.00000i	0.206651	−	0.206651i
$844$		0			0
$845$	−5.00000	−	10.0000i	−0.172005	−	0.344010i
$846$		0			0
$847$	21.0000	−	21.0000i	0.721569	−	0.721569i
$848$		0			0
$849$		−	14.0000i		−	0.480479i
$850$		0			0
$851$	−2.00000			−0.0685591
$852$		0			0
$853$	−9.00000	−	9.00000i	−0.308154	−	0.308154i	0.536039	−	0.844193i	$-0.319920\pi$
$853$	−9.00000	−	9.00000i	−0.308154	−	0.308154i	−0.844193	+	0.536039i	$0.819920\pi$
$854$		0			0
$855$	8.00000	−	4.00000i	0.273594	−	0.136797i
$856$		0			0
$857$	35.0000	+	35.0000i	1.19558	+	1.19558i	0.975477	+	0.220100i	$0.0706383\pi$
$857$	35.0000	+	35.0000i	1.19558	+	1.19558i	0.220100	+	0.975477i	$0.429362\pi$
$858$		0			0
$859$			28.0000i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$859$			28.0000i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$860$		0			0
$861$		−	60.0000i		−	2.04479i
$862$		0			0
$863$	13.0000	+	13.0000i	0.442525	+	0.442525i	0.892860	−	0.450335i	$-0.148695\pi$
$863$	13.0000	+	13.0000i	0.442525	+	0.442525i	−0.450335	+	0.892860i	$0.648695\pi$
$864$		0			0
$865$	−15.0000	−	5.00000i	−0.510015	−	0.170005i
$866$		0			0
$867$	15.0000	+	15.0000i	0.509427	+	0.509427i
$868$		0			0
$869$	16.0000			0.542763
$870$		0			0
$871$			6.00000i			0.203302i
$872$		0			0
$873$	3.00000	−	3.00000i	0.101535	−	0.101535i
$874$		0			0
$875$	−27.0000	−	39.0000i	−0.912767	−	1.31844i
$876$		0			0
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	−0.578973	−	0.815347i	$-0.696546\pi$
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	0.815347	+	0.578973i	$0.196546\pi$
$878$		0			0
$879$	−22.0000			−0.742042
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−33.0000	+	33.0000i	−1.11054	+	1.11054i	−0.117461	+	0.993078i	$0.537475\pi$
$883$	−33.0000	+	33.0000i	−1.11054	+	1.11054i	−0.993078	+	0.117461i	$0.962525\pi$
$884$		0			0
$885$	36.0000	+	12.0000i	1.21013	+	0.403376i
$886$		0			0
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	−0.618165	−	0.786048i	$-0.712124\pi$
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	0.786048	+	0.618165i	$0.212124\pi$
$888$		0			0
$889$			42.0000i			1.40863i
$890$		0			0
$891$	−10.0000			−0.335013
$892$		0			0
$893$	12.0000	+	12.0000i	0.401565	+	0.401565i
$894$		0			0
$895$	12.0000	+	24.0000i	0.401116	+	0.802232i
$896$		0			0
$897$	−6.00000	−	6.00000i	−0.200334	−	0.200334i
$898$		0			0
$899$		0			0
$900$		0			0
$901$		−	10.0000i		−	0.333148i
$902$		0			0
$903$	−30.0000	−	30.0000i	−0.998337	−	0.998337i
$904$		0			0
$905$	−22.0000	−	44.0000i	−0.731305	−	1.46261i
$906$		0			0
$907$	−27.0000	−	27.0000i	−0.896520	−	0.896520i	0.0986062	−	0.995127i	$-0.468562\pi$
$907$	−27.0000	−	27.0000i	−0.896520	−	0.896520i	−0.995127	+	0.0986062i	$0.968562\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$		−	6.00000i		−	0.198789i	−0.995048	−	0.0993944i	$-0.968309\pi$
$911$		−	6.00000i		−	0.198789i	0.995048	−	0.0993944i	$-0.0316906\pi$
$912$		0			0
$913$	10.0000	−	10.0000i	0.330952	−	0.330952i
$914$		0			0
$915$	−6.00000	−	2.00000i	−0.198354	−	0.0661180i
$916$		0			0
$917$	−30.0000	+	30.0000i	−0.990687	+	0.990687i
$918$		0			0
$919$	−48.0000			−1.58337			−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000			−1.58337			−0.791687	+	0.610927i	$0.790797\pi$
$920$		0			0
$921$	34.0000			1.12034
$922$		0			0
$923$	−6.00000	+	6.00000i	−0.197492	+	0.197492i
$924$		0			0
$925$	−1.00000	−	7.00000i	−0.0328798	−	0.230159i
$926$		0			0
$927$	9.00000	−	9.00000i	0.295599	−	0.295599i
$928$		0			0
$929$			28.0000i			0.918650i	0.888268	+	0.459325i	$0.151909\pi$
$929$			28.0000i			0.918650i	−0.888268	+	0.459325i	$0.848091\pi$
$930$		0			0
$931$	44.0000			1.44204
$932$		0			0
$933$	18.0000	+	18.0000i	0.589294	+	0.589294i
$934$		0			0
$935$	6.00000	+	2.00000i	0.196221	+	0.0654070i
$936$		0			0
$937$	−21.0000	−	21.0000i	−0.686040	−	0.686040i	0.275314	−	0.961354i	$-0.411218\pi$
$937$	−21.0000	−	21.0000i	−0.686040	−	0.686040i	−0.961354	+	0.275314i	$0.911218\pi$
$938$		0			0
$939$		−	18.0000i		−	0.587408i
$940$		0			0
$941$			34.0000i			1.10837i	0.832394	+	0.554184i	$0.186970\pi$
$941$			34.0000i			1.10837i	−0.832394	+	0.554184i	$0.813030\pi$
$942$		0			0
$943$	−10.0000	−	10.0000i	−0.325645	−	0.325645i
$944$		0			0
$945$	−48.0000	+	24.0000i	−1.56144	+	0.780720i
$946$		0			0
$947$	31.0000	+	31.0000i	1.00736	+	1.00736i	0.999973	+	0.00739197i	$0.00235296\pi$
$947$	31.0000	+	31.0000i	1.00736	+	1.00736i	0.00739197	+	0.999973i	$0.497647\pi$
$948$		0			0
$949$	6.00000			0.194768
$950$		0			0
$951$		−	26.0000i		−	0.843108i
$952$		0			0
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.00419731	−	0.999991i	$-0.498664\pi$
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.999991	−	0.00419731i	$-0.00133605\pi$
$954$		0			0
$955$	14.0000	+	28.0000i	0.453029	+	0.906059i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−66.0000			−2.13125
$960$		0			0
$961$	−69.0000			−2.22581
$962$		0			0
$963$	3.00000	−	3.00000i	0.0966736	−	0.0966736i
$964$		0			0
$965$	15.0000	−	45.0000i	0.482867	−	1.44860i
$966$		0			0
$967$	1.00000	−	1.00000i	0.0321578	−	0.0321578i	−0.690845	−	0.723003i	$-0.742761\pi$
$967$	1.00000	−	1.00000i	0.0321578	−	0.0321578i	0.723003	+	0.690845i	$0.242761\pi$
$968$		0			0
$969$		−	8.00000i		−	0.256997i
$970$		0			0
$971$	−2.00000			−0.0641831			−0.0320915	−	0.999485i	$-0.510217\pi$
$971$	−2.00000			−0.0641831			−0.0320915	+	0.999485i	$0.510217\pi$
$972$		0			0
$973$	36.0000	+	36.0000i	1.15411	+	1.15411i
$974$		0			0
$975$	18.0000	−	24.0000i	0.576461	−	0.768615i
$976$		0			0
$977$	21.0000	+	21.0000i	0.671850	+	0.671850i	0.958142	−	0.286293i	$-0.0924230\pi$
$977$	21.0000	+	21.0000i	0.671850	+	0.671850i	−0.286293	+	0.958142i	$0.592423\pi$
$978$		0			0
$979$			32.0000i			1.02272i
$980$		0			0
$981$		−	4.00000i		−	0.127710i
$982$		0			0
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	0.622859	−	0.782334i	$-0.285971\pi$
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	−0.782334	+	0.622859i	$0.785971\pi$
$984$		0			0
$985$	−13.0000	+	39.0000i	−0.414214	+	1.24264i
$986$		0			0
$987$	−18.0000	−	18.0000i	−0.572946	−	0.572946i
$988$		0			0
$989$	−10.0000			−0.317982
$990$		0			0
$991$			10.0000i			0.317660i	0.987306	+	0.158830i	$0.0507723\pi$
$991$			10.0000i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$992$		0			0
$993$	26.0000	−	26.0000i	0.825085	−	0.825085i
$994$		0			0
$995$	32.0000	−	16.0000i	1.01447	−	0.507234i
$996$		0			0
$997$	17.0000	−	17.0000i	0.538395	−	0.538395i	−0.384662	−	0.923057i	$-0.625682\pi$
$997$	17.0000	−	17.0000i	0.538395	−	0.538395i	0.923057	+	0.384662i	$0.125682\pi$
$998$		0			0
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.o.c.127.1		2
4.3	odd	2		1280.2.o.l.127.1		2
5.3	odd	4		1280.2.o.f.383.1		2
8.3	odd	2		1280.2.o.f.127.1		2
8.5	even	2		1280.2.o.m.127.1		2
16.3	odd	4		160.2.n.d.127.1	yes	2
16.5	even	4		320.2.n.g.127.1		2
16.11	odd	4		320.2.n.b.127.1		2
16.13	even	4		160.2.n.c.127.1	yes	2
20.3	even	4		1280.2.o.m.383.1		2
40.3	even	4	inner	1280.2.o.c.383.1		2
40.13	odd	4		1280.2.o.l.383.1		2
48.29	odd	4		1440.2.x.f.127.1		2
48.35	even	4		1440.2.x.a.127.1		2
80.3	even	4		160.2.n.c.63.1	✓	2
80.13	odd	4		160.2.n.d.63.1	yes	2
80.19	odd	4		800.2.n.e.607.1		2
80.27	even	4		1600.2.n.c.1343.1		2
80.29	even	4		800.2.n.f.607.1		2
80.37	odd	4		1600.2.n.m.1343.1		2
80.43	even	4		320.2.n.g.63.1		2
80.53	odd	4		320.2.n.b.63.1		2
80.59	odd	4		1600.2.n.m.1407.1		2
80.67	even	4		800.2.n.f.543.1		2
80.69	even	4		1600.2.n.c.1407.1		2
80.77	odd	4		800.2.n.e.543.1		2
240.83	odd	4		1440.2.x.f.703.1		2
240.173	even	4		1440.2.x.a.703.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.n.c.63.1	✓	2	80.3	even	4
160.2.n.c.127.1	yes	2	16.13	even	4
160.2.n.d.63.1	yes	2	80.13	odd	4
160.2.n.d.127.1	yes	2	16.3	odd	4
320.2.n.b.63.1		2	80.53	odd	4
320.2.n.b.127.1		2	16.11	odd	4
320.2.n.g.63.1		2	80.43	even	4
320.2.n.g.127.1		2	16.5	even	4
800.2.n.e.543.1		2	80.77	odd	4
800.2.n.e.607.1		2	80.19	odd	4
800.2.n.f.543.1		2	80.67	even	4
800.2.n.f.607.1		2	80.29	even	4
1280.2.o.c.127.1		2	1.1	even	1	trivial
1280.2.o.c.383.1		2	40.3	even	4	inner
1280.2.o.f.127.1		2	8.3	odd	2
1280.2.o.f.383.1		2	5.3	odd	4
1280.2.o.l.127.1		2	4.3	odd	2
1280.2.o.l.383.1		2	40.13	odd	4
1280.2.o.m.127.1		2	8.5	even	2
1280.2.o.m.383.1		2	20.3	even	4
1440.2.x.a.127.1		2	48.35	even	4
1440.2.x.a.703.1		2	240.173	even	4
1440.2.x.f.127.1		2	48.29	odd	4
1440.2.x.f.703.1		2	240.83	odd	4
1600.2.n.c.1343.1		2	80.27	even	4
1600.2.n.c.1407.1		2	80.69	even	4
1600.2.n.m.1343.1		2	80.37	odd	4
1600.2.n.m.1407.1		2	80.59	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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000i q^{9} -2.00000 q^{11} +(-3.00000 - 3.00000i) q^{13} +(1.00000 - 3.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +4.00000i q^{19} -6.00000i q^{21} +(-1.00000 - 1.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +10.0000i q^{31} +(2.00000 - 2.00000i) q^{33} +(3.00000 - 9.00000i) q^{35} +(1.00000 - 1.00000i) q^{37} +6.00000 q^{39} +10.0000 q^{41} +(5.00000 - 5.00000i) q^{43} +(-1.00000 - 2.00000i) q^{45} +(3.00000 - 3.00000i) q^{47} -11.0000i q^{49} -2.00000 q^{51} +(-5.00000 - 5.00000i) q^{53} +(4.00000 - 2.00000i) q^{55} +(-4.00000 - 4.00000i) q^{57} +12.0000i q^{59} -2.00000i q^{61} +(-3.00000 - 3.00000i) q^{63} +(9.00000 + 3.00000i) q^{65} +(-1.00000 - 1.00000i) q^{67} +2.00000 q^{69} -2.00000i q^{71} +(-1.00000 + 1.00000i) q^{73} +(1.00000 + 7.00000i) q^{75} +(6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +(-3.00000 - 1.00000i) q^{85} -16.0000i q^{89} +18.0000 q^{91} +(-10.0000 - 10.0000i) q^{93} +(-4.00000 - 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{5} - 6 q^{7}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^5 - 6 * q^7	\( 2 q - 2 q^{3} - 4 q^{5} - 6 q^{7} - 4 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} - 2 q^{23} + 6 q^{25} - 8 q^{27} + 4 q^{33} + 6 q^{35} + 2 q^{37} + 12 q^{39} + 20 q^{41} + 10 q^{43} - 2 q^{45} + 6 q^{47} - 4 q^{51} - 10 q^{53} + 8 q^{55} - 8 q^{57} - 6 q^{63} + 18 q^{65} - 2 q^{67} + 4 q^{69} - 2 q^{73} + 2 q^{75} + 12 q^{77} - 16 q^{79} + 10 q^{81} - 10 q^{83} - 6 q^{85} + 36 q^{91} - 20 q^{93} - 8 q^{95} - 6 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^5 - 6 * q^7 - 4 * q^11 - 6 * q^13 + 2 * q^15 + 2 * q^17 - 2 * q^23 + 6 * q^25 - 8 * q^27 + 4 * q^33 + 6 * q^35 + 2 * q^37 + 12 * q^39 + 20 * q^41 + 10 * q^43 - 2 * q^45 + 6 * q^47 - 4 * q^51 - 10 * q^53 + 8 * q^55 - 8 * q^57 - 6 * q^63 + 18 * q^65 - 2 * q^67 + 4 * q^69 - 2 * q^73 + 2 * q^75 + 12 * q^77 - 16 * q^79 + 10 * q^81 - 10 * q^83 - 6 * q^85 + 36 * q^91 - 20 * q^93 - 8 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

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Database

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