LMFDB - Embedded newform 1520.2.q.b.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, 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:	$12.1372611072$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 760)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1520.961
Dual form			1520.2.q.b.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} -5.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(1.00000 + 1.73205i) q^{15} +(1.00000 - 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +5.00000 q^{31} +(5.00000 - 8.66025i) q^{33} -4.00000 q^{37} -4.00000 q^{39} +(-5.00000 + 8.66025i) q^{41} +(-4.00000 + 6.92820i) q^{43} -1.00000 q^{45} +(-1.00000 - 1.73205i) q^{47} -7.00000 q^{49} +(2.00000 + 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{55} +(-8.00000 - 3.46410i) q^{57} +(3.50000 - 6.06218i) q^{59} +(3.50000 + 6.06218i) q^{61} +2.00000 q^{65} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{69} +(3.50000 - 6.06218i) q^{71} +2.00000 q^{75} +(-0.500000 + 0.866025i) q^{79} +(5.50000 - 9.52628i) q^{81} -4.00000 q^{83} +(-1.00000 - 1.73205i) q^{85} +18.0000 q^{87} +(-4.50000 - 7.79423i) q^{89} +(-5.00000 + 8.66025i) q^{93} +(4.00000 + 1.73205i) q^{95} +(8.00000 - 13.8564i) q^{97} +(2.50000 + 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + q^{5} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + q^5 - q^9	$ 2 q - 2 q^{3} + q^{5} - q^{9} - 10 q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} - 4 q^{23} - q^{25} - 8 q^{27} - 9 q^{29} + 10 q^{31} + 10 q^{33} - 8 q^{37} - 8 q^{39} - 10 q^{41} - 8 q^{43} - 2 q^{45} - 2 q^{47} - 14 q^{49} + 4 q^{51} - 6 q^{53} - 5 q^{55} - 16 q^{57} + 7 q^{59} + 7 q^{61} + 4 q^{65} - 14 q^{67} + 16 q^{69} + 7 q^{71} + 4 q^{75} - q^{79} + 11 q^{81} - 8 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} - 10 q^{93} + 8 q^{95} + 16 q^{97} + 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + q^5 - q^9 - 10 * q^11 + 2 * q^13 + 2 * q^15 + 2 * q^17 + q^19 - 4 * q^23 - q^25 - 8 * q^27 - 9 * q^29 + 10 * q^31 + 10 * q^33 - 8 * q^37 - 8 * q^39 - 10 * q^41 - 8 * q^43 - 2 * q^45 - 2 * q^47 - 14 * q^49 + 4 * q^51 - 6 * q^53 - 5 * q^55 - 16 * q^57 + 7 * q^59 + 7 * q^61 + 4 * q^65 - 14 * q^67 + 16 * q^69 + 7 * q^71 + 4 * q^75 - q^79 + 11 * q^81 - 8 * q^83 - 2 * q^85 + 36 * q^87 - 9 * q^89 - 10 * q^93 + 8 * q^95 + 16 * q^97 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$		0			0
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$		0			0
$33$	5.00000	−	8.66025i	0.870388	−	1.50756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	−4.00000			−0.640513
$40$		0			0
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	0.783830	−	0.620975i	$-0.213263\pi$
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	−0.929695	+	0.368329i	$0.879930\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−2.50000	+	4.33013i	−0.337100	+	0.583874i
$56$		0			0
$57$	−8.00000	−	3.46410i	−1.05963	−	0.458831i
$58$		0			0
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	−0.543065	−	0.839691i	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.00000			0.248069
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	−0.580094	−	0.814550i	$-0.696984\pi$
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	0.995468	+	0.0951014i	$0.0303175\pi$
$72$		0			0
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$		0			0
$75$	2.00000			0.230940
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	−1.00000	−	1.73205i	−0.108465	−	0.187867i
$86$		0			0
$87$	18.0000			1.92980
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.00000	+	8.66025i	−0.518476	+	0.898027i
$94$		0			0
$95$	4.00000	+	1.73205i	0.410391	+	0.177705i
$96$		0			0
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	−0.0989899	−	0.995088i	$-0.531561\pi$
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	0.911267	−	0.411816i	$-0.135106\pi$
$98$		0			0
$99$	2.50000	+	4.33013i	0.251259	+	0.435194i
$100$		0			0
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$		0			0
$103$	−12.0000			−1.18240			−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000			−1.18240			−0.591198	+	0.806527i	$0.701345\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$	4.00000	−	6.92820i	0.379663	−	0.657596i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−4.00000			−0.373002
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$	−10.0000	−	17.3205i	−0.901670	−	1.56174i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.00000	−	15.5885i	−0.798621	−	1.38325i	−0.920514	−	0.390709i	$-0.872230\pi$
$127$	−9.00000	−	15.5885i	−0.798621	−	1.38325i	0.121894	−	0.992543i	$-0.461103\pi$
$128$		0			0
$129$	−8.00000	−	13.8564i	−0.704361	−	1.21999i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$		0			0
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	4.00000			0.336861
$142$		0			0
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$		0			0
$145$	−9.00000			−0.747409
$146$		0			0
$147$	7.00000	−	12.1244i	0.577350	−	1.00000i
$148$		0			0
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	−0.973028	−	0.230689i	$-0.925902\pi$
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	0.686296	+	0.727322i	$0.259235\pi$
$150$		0			0
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	2.50000	−	4.33013i	0.200805	−	0.347804i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$	12.0000			0.951662
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−14.0000			−1.09656			−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000			−1.09656			−0.548282	+	0.836293i	$0.684718\pi$
$164$		0			0
$165$	−5.00000	−	8.66025i	−0.389249	−	0.674200i
$166$		0			0
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	0.989658	+	0.143448i	$0.0458190\pi$
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	−0.370599	+	0.928793i	$0.620848\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	3.50000	−	2.59808i	0.267652	−	0.198680i
$172$		0			0
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	0.383304	+	0.923622i	$0.374786\pi$
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	−0.991532	+	0.129861i	$0.958547\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.00000	+	12.1244i	0.526152	+	0.911322i
$178$		0			0
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		0			0
$181$	7.00000	+	12.1244i	0.520306	+	0.901196i	0.999721	+	0.0236082i	$0.00751541\pi$
$181$	7.00000	+	12.1244i	0.520306	+	0.901196i	−0.479415	+	0.877588i	$0.659151\pi$
$182$		0			0
$183$	−14.0000			−1.03491
$184$		0			0
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	−5.00000	+	8.66025i	−0.365636	+	0.633300i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.0000			0.940647			0.470323	−	0.882494i	$-0.344137\pi$
$191$	13.0000			0.940647			0.470323	+	0.882494i	$0.344137\pi$
$192$		0			0
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	0.00447566	+	0.999990i	$0.498575\pi$
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	−0.868255	+	0.496119i	$0.834758\pi$
$194$		0			0
$195$	−2.00000	+	3.46410i	−0.143223	+	0.248069i
$196$		0			0
$197$	−14.0000			−0.997459			−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000			−0.997459			−0.498729	+	0.866758i	$0.666200\pi$
$198$		0			0
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	0.999317	+	0.0369532i	$0.0117652\pi$
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	−0.467656	+	0.883911i	$0.654901\pi$
$200$		0			0
$201$	28.0000			1.97497
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$		0			0
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$		0			0
$209$	−2.50000	−	21.6506i	−0.172929	−	1.49761i
$210$		0			0
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	−0.978317	−	0.207114i	$-0.933593\pi$
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	0.668524	+	0.743690i	$0.266926\pi$
$212$		0			0
$213$	7.00000	+	12.1244i	0.479632	+	0.830747i
$214$		0			0
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.00000			0.269069
$222$		0			0
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	−19.0000			−1.25556			−0.627778	−	0.778393i	$-0.716035\pi$
$229$	−19.0000			−1.25556			−0.627778	+	0.778393i	$0.716035\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	−0.896921	−	0.442191i	$-0.854201\pi$
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	0.831409	+	0.555661i	$0.187535\pi$
$234$		0			0
$235$	−2.00000			−0.130466
$236$		0			0
$237$	−1.00000	−	1.73205i	−0.0649570	−	0.112509i
$238$		0			0
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$	1.50000	+	2.59808i	0.0966235	+	0.167357i	0.910285	−	0.413982i	$-0.135862\pi$
$241$	1.50000	+	2.59808i	0.0966235	+	0.167357i	−0.813662	+	0.581339i	$0.802529\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	−3.50000	+	6.06218i	−0.223607	+	0.387298i
$246$		0			0
$247$	−7.00000	+	5.19615i	−0.445399	+	0.330623i
$248$		0			0
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$		0			0
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$		0			0
$253$	10.0000	+	17.3205i	0.628695	+	1.08893i
$254$		0			0
$255$	4.00000			0.250490
$256$		0			0
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	0.978772	−	0.204953i	$-0.0657041\pi$
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	−0.666880	+	0.745165i	$0.732371\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−4.50000	+	7.79423i	−0.278543	+	0.482451i
$262$		0			0
$263$	7.00000	−	12.1244i	0.431638	−	0.747620i	−0.565376	−	0.824833i	$-0.691269\pi$
$263$	7.00000	−	12.1244i	0.431638	−	0.747620i	0.997015	+	0.0772134i	$0.0246023\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$		0			0
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$		0			0
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	−0.952531	−	0.304443i	$-0.901530\pi$
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	0.739921	+	0.672694i	$0.234863\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		0			0
$279$	−2.50000	−	4.33013i	−0.149671	−	0.259238i
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	0.464169	+	0.885747i	$0.346353\pi$
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	−0.999164	+	0.0408910i	$0.986980\pi$
$284$		0			0
$285$	−7.00000	+	5.19615i	−0.414644	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	16.0000	+	27.7128i	0.937937	+	1.62455i
$292$		0			0
$293$	−8.00000			−0.467365			−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000			−0.467365			−0.233682	+	0.972313i	$0.575078\pi$
$294$		0			0
$295$	−3.50000	−	6.06218i	−0.203778	−	0.352954i
$296$		0			0
$297$	20.0000			1.16052
$298$		0			0
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−10.0000			−0.574485
$304$		0			0
$305$	7.00000			0.400819
$306$		0			0
$307$	−9.00000	+	15.5885i	−0.513657	+	0.889680i	0.486217	+	0.873838i	$0.338376\pi$
$307$	−9.00000	+	15.5885i	−0.513657	+	0.889680i	−0.999875	+	0.0158424i	$0.994957\pi$
$308$		0			0
$309$	12.0000	−	20.7846i	0.682656	−	1.18240i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$	22.5000	+	38.9711i	1.25976	+	2.18197i
$320$		0			0
$321$	12.0000	−	20.7846i	0.669775	−	1.16008i
$322$		0			0
$323$	8.00000	+	3.46410i	0.445132	+	0.192748i
$324$		0			0
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$		0			0
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$		0			0
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$		0			0
$335$	−14.0000			−0.764902
$336$		0			0
$337$	6.00000	−	10.3923i	0.326841	−	0.566105i	−0.655042	−	0.755592i	$-0.727349\pi$
$337$	6.00000	−	10.3923i	0.326841	−	0.566105i	0.981883	+	0.189487i	$0.0606826\pi$
$338$		0			0
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$		0			0
$341$	−25.0000			−1.35383
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$		0			0
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$		0			0
$351$	−4.00000	−	6.92820i	−0.213504	−	0.369800i
$352$		0			0
$353$	−16.0000			−0.851594			−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−16.0000			−0.851594			−0.425797	+	0.904819i	$0.640006\pi$
$354$		0			0
$355$	−3.50000	−	6.06218i	−0.185761	−	0.321747i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		0			0
$363$	−14.0000	+	24.2487i	−0.734809	+	1.27273i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$		0			0
$369$	10.0000			0.520579
$370$		0			0
$371$		0			0
$372$		0			0
$373$	8.00000			0.414224			0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000			0.414224			0.207112	+	0.978317i	$0.433593\pi$
$374$		0			0
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$		0			0
$377$	9.00000	−	15.5885i	0.463524	−	0.802846i
$378$		0			0
$379$	−21.0000			−1.07870			−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000			−1.07870			−0.539349	+	0.842082i	$0.681330\pi$
$380$		0			0
$381$	36.0000			1.84434
$382$		0			0
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.00000			0.406663
$388$		0			0
$389$	14.5000	+	25.1147i	0.735179	+	1.27337i	0.954645	+	0.297747i	$0.0962353\pi$
$389$	14.5000	+	25.1147i	0.735179	+	1.27337i	−0.219465	+	0.975620i	$0.570431\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$	12.0000	+	20.7846i	0.605320	+	1.04844i
$394$		0			0
$395$	0.500000	+	0.866025i	0.0251577	+	0.0435745i
$396$		0			0
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	−0.811463	−	0.584404i	$-0.801328\pi$
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	0.911840	+	0.410546i	$0.134662\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.5000	−	21.6506i	0.624220	−	1.08118i	−0.364471	−	0.931215i	$-0.618750\pi$
$401$	12.5000	−	21.6506i	0.624220	−	1.08118i	0.988691	−	0.149966i	$-0.0479165\pi$
$402$		0			0
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$		0			0
$405$	−5.50000	−	9.52628i	−0.273297	−	0.473365i
$406$		0			0
$407$	20.0000			0.991363
$408$		0			0
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	0.995968	−	0.0897044i	$-0.0285922\pi$
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	−0.575670	+	0.817682i	$0.695259\pi$
$410$		0			0
$411$	−16.0000			−0.789222
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.00000	+	3.46410i	−0.0981761	+	0.170046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	21.0000			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$420$		0			0
$421$	−0.500000	+	0.866025i	−0.0243685	+	0.0422075i	−0.877952	−	0.478748i	$-0.841091\pi$
$421$	−0.500000	+	0.866025i	−0.0243685	+	0.0422075i	0.853584	+	0.520955i	$0.174424\pi$
$422$		0			0
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$		0			0
$425$	−2.00000			−0.0970143
$426$		0			0
$427$		0			0
$428$		0			0
$429$	20.0000			0.965609
$430$		0			0
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	0.983057	+	0.183301i	$0.0586785\pi$
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	−0.332785	+	0.943003i	$0.607988\pi$
$432$		0			0
$433$	−10.0000	−	17.3205i	−0.480569	−	0.832370i	0.519182	−	0.854664i	$-0.326237\pi$
$433$	−10.0000	−	17.3205i	−0.480569	−	0.832370i	−0.999751	+	0.0222931i	$0.992903\pi$
$434$		0			0
$435$	9.00000	−	15.5885i	0.431517	−	0.747409i
$436$		0			0
$437$	14.0000	−	10.3923i	0.669711	−	0.497131i
$438$		0			0
$439$	−15.5000	+	26.8468i	−0.739775	+	1.28133i	0.212822	+	0.977091i	$0.431735\pi$
$439$	−15.5000	+	26.8468i	−0.739775	+	1.28133i	−0.952597	+	0.304236i	$0.901599\pi$
$440$		0			0
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	−9.00000			−0.426641
$446$		0			0
$447$	−7.00000	−	12.1244i	−0.331089	−	0.573462i
$448$		0			0
$449$	−41.0000			−1.93491			−0.967455	−	0.253044i	$-0.918568\pi$
$449$	−41.0000			−1.93491			−0.967455	+	0.253044i	$0.918568\pi$
$450$		0			0
$451$	25.0000	−	43.3013i	1.17720	−	2.03898i
$452$		0			0
$453$	−5.00000	+	8.66025i	−0.234920	+	0.406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	34.0000			1.59045			0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000			1.59045			0.795226	+	0.606313i	$0.207352\pi$
$458$		0			0
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$		0			0
$461$	18.5000	−	32.0429i	0.861631	−	1.49239i	−0.00872311	−	0.999962i	$-0.502777\pi$
$461$	18.5000	−	32.0429i	0.861631	−	1.49239i	0.870354	−	0.492427i	$-0.163890\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$	5.00000	+	8.66025i	0.231869	+	0.401610i
$466$		0			0
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.00000	−	3.46410i	−0.0921551	−	0.159617i
$472$		0			0
$473$	20.0000	−	34.6410i	0.919601	−	1.59280i
$474$		0			0
$475$	3.50000	−	2.59808i	0.160591	−	0.119208i
$476$		0			0
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$		0			0
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.00000	−	13.8564i	−0.363261	−	0.629187i
$486$		0			0
$487$	−38.0000			−1.72194			−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000			−1.72194			−0.860972	+	0.508652i	$0.830144\pi$
$488$		0			0
$489$	14.0000	−	24.2487i	0.633102	−	1.09656i
$490$		0			0
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$	−18.0000			−0.810679
$494$		0			0
$495$	5.00000			0.224733
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$	−32.0000			−1.42965
$502$		0			0
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	0.791361	−	0.611349i	$-0.209373\pi$
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	−0.925124	+	0.379664i	$0.876040\pi$
$504$		0			0
$505$	5.00000			0.222497
$506$		0			0
$507$	9.00000	+	15.5885i	0.399704	+	0.692308i
$508$		0			0
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	0.512331	−	0.858788i	$-0.328782\pi$
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	−0.999898	+	0.0142980i	$0.995449\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.00000	−	17.3205i	−0.0883022	−	0.764719i
$514$		0			0
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$		0			0
$517$	5.00000	+	8.66025i	0.219900	+	0.380878i
$518$		0			0
$519$	−16.0000	−	27.7128i	−0.702322	−	1.21646i
$520$		0			0
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	0.954391	−	0.298560i	$-0.0965063\pi$
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	−0.735756	+	0.677247i	$0.763173\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−7.00000			−0.303774
$532$		0			0
$533$	−20.0000			−0.866296
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$	−15.0000	+	25.9808i	−0.647298	+	1.12115i
$538$		0			0
$539$	35.0000			1.50756
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−28.0000			−1.20160
$544$		0			0
$545$	3.50000	+	6.06218i	0.149924	+	0.259675i
$546$		0			0
$547$	8.00000	+	13.8564i	0.342055	+	0.592457i	0.984814	−	0.173611i	$-0.0555436\pi$
$547$	8.00000	+	13.8564i	0.342055	+	0.592457i	−0.642759	+	0.766068i	$0.722210\pi$
$548$		0			0
$549$	3.50000	−	6.06218i	0.149376	−	0.258727i
$550$		0			0
$551$	31.5000	−	23.3827i	1.34195	−	0.996136i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.00000	−	6.92820i	−0.169791	−	0.294086i
$556$		0			0
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$	−10.0000	−	17.3205i	−0.422200	−	0.731272i
$562$		0			0
$563$	14.0000			0.590030			0.295015	−	0.955493i	$-0.404675\pi$
$563$	14.0000			0.590030			0.295015	+	0.955493i	$0.404675\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000			−0.377300			−0.188650	−	0.982044i	$-0.560411\pi$
$569$	−9.00000			−0.377300			−0.188650	+	0.982044i	$0.560411\pi$
$570$		0			0
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$		0			0
$573$	−13.0000	+	22.5167i	−0.543083	+	0.940647i
$574$		0			0
$575$	−2.00000	+	3.46410i	−0.0834058	+	0.144463i
$576$		0			0
$577$	−44.0000			−1.83174			−0.915872	−	0.401470i	$-0.868499\pi$
$577$	−44.0000			−1.83174			−0.915872	+	0.401470i	$0.868499\pi$
$578$		0			0
$579$	−24.0000	−	41.5692i	−0.997406	−	1.72756i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	15.0000	+	25.9808i	0.621237	+	1.07601i
$584$		0			0
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$		0			0
$587$	20.0000	−	34.6410i	0.825488	−	1.42979i	−0.0760572	−	0.997103i	$-0.524233\pi$
$587$	20.0000	−	34.6410i	0.825488	−	1.42979i	0.901546	−	0.432684i	$-0.142434\pi$
$588$		0			0
$589$	2.50000	+	21.6506i	0.103011	+	0.892099i
$590$		0			0
$591$	14.0000	−	24.2487i	0.575883	−	0.997459i
$592$		0			0
$593$	2.00000	+	3.46410i	0.0821302	+	0.142254i	0.904165	−	0.427184i	$-0.140494\pi$
$593$	2.00000	+	3.46410i	0.0821302	+	0.142254i	−0.822035	+	0.569438i	$0.807161\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−30.0000			−1.22782
$598$		0			0
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	0.936099	−	0.351738i	$-0.114409\pi$
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	−0.772663	+	0.634816i	$0.781076\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$		0			0
$603$	−7.00000	+	12.1244i	−0.285062	+	0.493742i
$604$		0			0
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	6.00000			0.243532			0.121766	−	0.992559i	$-0.461144\pi$
$607$	6.00000			0.243532			0.121766	+	0.992559i	$0.461144\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.00000	−	3.46410i	0.0809113	−	0.140143i
$612$		0			0
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$		0			0
$615$	−20.0000			−0.806478
$616$		0			0
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.706346	+	0.707867i	$0.250342\pi$
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.259858	+	0.965647i	$0.416324\pi$
$618$		0			0
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$		0			0
$621$	8.00000	+	13.8564i	0.321029	+	0.556038i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	40.0000	+	17.3205i	1.59745	+	0.691714i
$628$		0			0
$629$	−4.00000	+	6.92820i	−0.159490	+	0.276246i
$630$		0			0
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	0.645748	−	0.763550i	$-0.276545\pi$
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	−0.984128	+	0.177459i	$0.943212\pi$
$632$		0			0
$633$	−9.00000	−	15.5885i	−0.357718	−	0.619586i
$634$		0			0
$635$	−18.0000			−0.714308
$636$		0			0
$637$	−7.00000	−	12.1244i	−0.277350	−	0.480384i
$638$		0			0
$639$	−7.00000			−0.276916
$640$		0			0
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$		0			0
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	0.307372	+	0.951589i	$0.400550\pi$
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	−0.977787	+	0.209603i	$0.932783\pi$
$644$		0			0
$645$	−16.0000			−0.629999
$646$		0			0
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$	−17.5000	+	30.3109i	−0.686935	+	1.18981i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.0000	−	38.1051i	−0.856998	−	1.48436i	−0.874779	−	0.484523i	$-0.838993\pi$
$659$	−22.0000	−	38.1051i	−0.856998	−	1.48436i	0.0177803	−	0.999842i	$-0.494340\pi$
$660$		0			0
$661$	−0.500000	−	0.866025i	−0.0194477	−	0.0336845i	0.856138	−	0.516748i	$-0.172857\pi$
$661$	−0.500000	−	0.866025i	−0.0194477	−	0.0336845i	−0.875585	+	0.483063i	$0.839524\pi$
$662$		0			0
$663$	−4.00000	+	6.92820i	−0.155347	+	0.269069i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−18.0000	+	31.1769i	−0.696963	+	1.20717i
$668$		0			0
$669$	28.0000	+	48.4974i	1.08254	+	1.87502i
$670$		0			0
$671$	−17.5000	−	30.3109i	−0.675580	−	1.17014i
$672$		0			0
$673$	−24.0000			−0.925132			−0.462566	−	0.886585i	$-0.653071\pi$
$673$	−24.0000			−0.925132			−0.462566	+	0.886585i	$0.653071\pi$
$674$		0			0
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$		0			0
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−12.0000	+	20.7846i	−0.459841	+	0.796468i
$682$		0			0
$683$	−18.0000			−0.688751			−0.344375	−	0.938832i	$-0.611909\pi$
$683$	−18.0000			−0.688751			−0.344375	+	0.938832i	$0.611909\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$		0			0
$687$	19.0000	−	32.9090i	0.724895	−	1.25556i
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	27.0000			1.02713			0.513564	−	0.858051i	$-0.328325\pi$
$691$	27.0000			1.02713			0.513564	+	0.858051i	$0.328325\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.0000	+	17.3205i	0.378777	+	0.656061i
$698$		0			0
$699$	−2.00000	−	3.46410i	−0.0756469	−	0.131024i
$700$		0			0
$701$	17.0000	−	29.4449i	0.642081	−	1.11212i	−0.342886	−	0.939377i	$-0.611405\pi$
$701$	17.0000	−	29.4449i	0.642081	−	1.11212i	0.984967	−	0.172740i	$-0.0552621\pi$
$702$		0			0
$703$	−2.00000	−	17.3205i	−0.0754314	−	0.653255i
$704$		0			0
$705$	2.00000	−	3.46410i	0.0753244	−	0.130466i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	0.981331	+	0.192328i	$0.0616038\pi$
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	−0.324104	+	0.946021i	$0.605063\pi$
$710$		0			0
$711$	1.00000			0.0375029
$712$		0			0
$713$	−10.0000	−	17.3205i	−0.374503	−	0.648658i
$714$		0			0
$715$	−10.0000			−0.373979
$716$		0			0
$717$	15.0000	−	25.9808i	0.560185	−	0.970269i
$718$		0			0
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	−0.0515326	−	0.998671i	$-0.516411\pi$
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	0.890641	−	0.454707i	$-0.150256\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−6.00000			−0.223142
$724$		0			0
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$		0			0
$727$	−19.0000	+	32.9090i	−0.704671	+	1.22053i	0.262139	+	0.965030i	$0.415572\pi$
$727$	−19.0000	+	32.9090i	−0.704671	+	1.22053i	−0.966810	+	0.255496i	$0.917761\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$		0			0
$733$	24.0000			0.886460			0.443230	−	0.896408i	$-0.353832\pi$
$733$	24.0000			0.886460			0.443230	+	0.896408i	$0.353832\pi$
$734$		0			0
$735$	−7.00000	−	12.1244i	−0.258199	−	0.447214i
$736$		0			0
$737$	35.0000	+	60.6218i	1.28924	+	2.23303i
$738$		0			0
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	0.340841	+	0.940121i	$0.389288\pi$
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	−0.984589	+	0.174883i	$0.944045\pi$
$740$		0			0
$741$	−2.00000	−	17.3205i	−0.0734718	−	0.636285i
$742$		0			0
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	−0.974633	−	0.223810i	$-0.928151\pi$
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	0.681141	+	0.732152i	$0.261484\pi$
$744$		0			0
$745$	3.50000	+	6.06218i	0.128230	+	0.222101i
$746$		0			0
$747$	2.00000	+	3.46410i	0.0731762	+	0.126745i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	0.929270	+	0.369402i	$0.120437\pi$
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	−0.144724	+	0.989472i	$0.546229\pi$
$752$		0			0
$753$	−30.0000			−1.09326
$754$		0			0
$755$	2.50000	−	4.33013i	0.0909843	−	0.157589i
$756$		0			0
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	−0.0573060	−	0.998357i	$-0.518251\pi$
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	0.893255	−	0.449550i	$-0.148416\pi$
$758$		0			0
$759$	−40.0000			−1.45191
$760$		0			0
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$		0			0
$767$	14.0000			0.505511
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$	−20.0000			−0.720282
$772$		0			0
$773$	−19.0000	−	32.9090i	−0.683383	−	1.18365i	−0.973942	−	0.226796i	$-0.927175\pi$
$773$	−19.0000	−	32.9090i	−0.683383	−	1.18365i	0.290560	−	0.956857i	$-0.406159\pi$
$774$		0			0
$775$	−2.50000	−	4.33013i	−0.0898027	−	0.155543i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−40.0000	−	17.3205i	−1.43315	−	0.620572i
$780$		0			0
$781$	−17.5000	+	30.3109i	−0.626199	+	1.08461i
$782$		0			0
$783$	18.0000	+	31.1769i	0.643268	+	1.11417i
$784$		0			0
$785$	1.00000	+	1.73205i	0.0356915	+	0.0618195i
$786$		0			0
$787$	−2.00000			−0.0712923			−0.0356462	−	0.999364i	$-0.511349\pi$
$787$	−2.00000			−0.0712923			−0.0356462	+	0.999364i	$0.511349\pi$
$788$		0			0
$789$	14.0000	+	24.2487i	0.498413	+	0.863277i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7.00000	+	12.1244i	−0.248577	+	0.430548i
$794$		0			0
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$		0			0
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	−4.00000			−0.141510
$800$		0			0
$801$	−4.50000	+	7.79423i	−0.159000	+	0.275396i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−31.0000	−	53.6936i	−1.09125	−	1.89010i
$808$		0			0
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	−22.5000	−	38.9711i	−0.790082	−	1.36846i	−0.925916	−	0.377730i	$-0.876705\pi$
$811$	−22.5000	−	38.9711i	−0.790082	−	1.36846i	0.135834	−	0.990732i	$-0.456629\pi$
$812$		0			0
$813$	−7.00000	−	12.1244i	−0.245501	−	0.425220i
$814$		0			0
$815$	−7.00000	+	12.1244i	−0.245199	+	0.424698i
$816$		0			0
$817$	−32.0000	−	13.8564i	−1.11954	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.50000	+	6.06218i	0.122151	+	0.211571i	0.920616	−	0.390470i	$-0.127687\pi$
$821$	3.50000	+	6.06218i	0.122151	+	0.211571i	−0.798465	+	0.602042i	$0.794354\pi$
$822$		0			0
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	0.848070	−	0.529884i	$-0.177765\pi$
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	−0.882928	+	0.469508i	$0.844431\pi$
$824$		0			0
$825$	−10.0000			−0.348155
$826$		0			0
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	−0.956780	−	0.290813i	$-0.906074\pi$
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	0.226538	−	0.974002i	$-0.427259\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.00000	+	12.1244i	−0.242536	+	0.420084i
$834$		0			0
$835$	16.0000			0.553703
$836$		0			0
$837$	−20.0000			−0.691301
$838$		0			0
$839$	−4.00000	+	6.92820i	−0.138095	+	0.239188i	−0.926776	−	0.375615i	$-0.877431\pi$
$839$	−4.00000	+	6.92820i	−0.138095	+	0.239188i	0.788680	+	0.614804i	$0.210765\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	12.0000			0.413302
$844$		0			0
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−18.0000	−	31.1769i	−0.617758	−	1.06999i
$850$		0			0
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$		0			0
$853$	−3.00000	+	5.19615i	−0.102718	+	0.177913i	−0.912804	−	0.408399i	$-0.866087\pi$
$853$	−3.00000	+	5.19615i	−0.102718	+	0.177913i	0.810086	+	0.586312i	$0.199421\pi$
$854$		0			0
$855$	−0.500000	−	4.33013i	−0.0170996	−	0.148087i
$856$		0			0
$857$	22.0000	−	38.1051i	0.751506	−	1.30165i	−0.195587	−	0.980686i	$-0.562661\pi$
$857$	22.0000	−	38.1051i	0.751506	−	1.30165i	0.947093	−	0.320960i	$-0.104005\pi$
$858$		0			0
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	0.570064	−	0.821600i	$-0.306918\pi$
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	−0.996559	+	0.0828900i	$0.973585\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$		0			0
$865$	8.00000	+	13.8564i	0.272008	+	0.471132i
$866$		0			0
$867$	−26.0000			−0.883006
$868$		0			0
$869$	2.50000	−	4.33013i	0.0848067	−	0.146889i
$870$		0			0
$871$	14.0000	−	24.2487i	0.474372	−	0.821636i
$872$		0			0
$873$	−16.0000			−0.541518
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	−0.526767	−	0.850010i	$-0.676596\pi$
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	0.999514	+	0.0311889i	$0.00992933\pi$
$878$		0			0
$879$	8.00000	−	13.8564i	0.269833	−	0.467365i
$880$		0			0
$881$	41.0000			1.38133			0.690663	−	0.723177i	$-0.257319\pi$
$881$	41.0000			1.38133			0.690663	+	0.723177i	$0.257319\pi$
$882$		0			0
$883$	2.00000	+	3.46410i	0.0673054	+	0.116576i	0.897714	−	0.440578i	$-0.145226\pi$
$883$	2.00000	+	3.46410i	0.0673054	+	0.116576i	−0.830409	+	0.557154i	$0.811893\pi$
$884$		0			0
$885$	14.0000			0.470605
$886$		0			0
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−27.5000	+	47.6314i	−0.921285	+	1.59571i
$892$		0			0
$893$	7.00000	−	5.19615i	0.234246	−	0.173883i
$894$		0			0
$895$	7.50000	−	12.9904i	0.250697	−	0.434221i
$896$		0			0
$897$	8.00000	+	13.8564i	0.267112	+	0.462652i
$898$		0			0
$899$	−22.5000	−	38.9711i	−0.750417	−	1.29976i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.0000			0.465376
$906$		0			0
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	−0.702094	−	0.712084i	$-0.747752\pi$
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	0.967730	+	0.251990i	$0.0810849\pi$
$908$		0			0
$909$	2.50000	−	4.33013i	0.0829198	−	0.143621i
$910$		0			0
$911$	17.0000			0.563235			0.281618	−	0.959527i	$-0.409129\pi$
$911$	17.0000			0.563235			0.281618	+	0.959527i	$0.409129\pi$
$912$		0			0
$913$	20.0000			0.661903
$914$		0			0
$915$	−7.00000	+	12.1244i	−0.231413	+	0.400819i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$	−18.0000	−	31.1769i	−0.593120	−	1.02731i
$922$		0			0
$923$	14.0000			0.460816
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$	6.00000	+	10.3923i	0.197066	+	0.341328i
$928$		0			0
$929$	−21.5000	+	37.2391i	−0.705392	+	1.22177i	0.261158	+	0.965296i	$0.415896\pi$
$929$	−21.5000	+	37.2391i	−0.705392	+	1.22177i	−0.966550	+	0.256479i	$0.917438\pi$
$930$		0			0
$931$	−3.50000	−	30.3109i	−0.114708	−	0.993399i
$932$		0			0
$933$	24.0000	−	41.5692i	0.785725	−	1.36092i
$934$		0			0
$935$	5.00000	+	8.66025i	0.163517	+	0.283221i
$936$		0			0
$937$	−5.00000	−	8.66025i	−0.163343	−	0.282918i	0.772723	−	0.634744i	$-0.218894\pi$
$937$	−5.00000	−	8.66025i	−0.163343	−	0.282918i	−0.936066	+	0.351826i	$0.885561\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$		0			0
$941$	−25.5000	−	44.1673i	−0.831276	−	1.43981i	−0.897027	−	0.441977i	$-0.854277\pi$
$941$	−25.5000	−	44.1673i	−0.831276	−	1.43981i	0.0657503	−	0.997836i	$-0.479056\pi$
$942$		0			0
$943$	40.0000			1.30258
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.0000	+	32.9090i	−0.617417	+	1.06940i	0.372538	+	0.928017i	$0.378488\pi$
$947$	−19.0000	+	32.9090i	−0.617417	+	1.06940i	−0.989955	+	0.141381i	$0.954846\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	24.0000	−	41.5692i	0.777436	−	1.34656i	−0.155979	−	0.987760i	$-0.549853\pi$
$953$	24.0000	−	41.5692i	0.777436	−	1.34656i	0.933415	−	0.358799i	$-0.116814\pi$
$954$		0			0
$955$	6.50000	−	11.2583i	0.210335	−	0.364311i
$956$		0			0
$957$	−90.0000			−2.90929
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.00000			−0.193548
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$		0			0
$965$	12.0000	+	20.7846i	0.386294	+	0.669080i
$966$		0			0
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	−0.341567	−	0.939857i	$-0.610958\pi$
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	0.984724	−	0.174123i	$-0.0557089\pi$
$968$		0			0
$969$	−14.0000	+	10.3923i	−0.449745	+	0.333849i
$970$		0			0
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.247193	+	0.968966i	$0.579508\pi$
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.715553	+	0.698558i	$0.753825\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$		0			0
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$	22.5000	+	38.9711i	0.719103	+	1.24552i
$980$		0			0
$981$	7.00000			0.223493
$982$		0			0
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	−0.551627	−	0.834091i	$-0.685993\pi$
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	0.998157	+	0.0606773i	$0.0193260\pi$
$984$		0			0
$985$	−7.00000	+	12.1244i	−0.223039	+	0.386314i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	32.0000			1.01754
$990$		0			0
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$		0			0
$993$	−4.00000	+	6.92820i	−0.126936	+	0.219860i
$994$		0			0
$995$	15.0000			0.475532
$996$		0			0
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$		0			0
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.b.961.1		2
4.3	odd	2		760.2.q.c.201.1	yes	2
19.7	even	3	inner	1520.2.q.b.881.1		2
76.7	odd	6		760.2.q.c.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.q.c.121.1	✓	2	76.7	odd	6
760.2.q.c.201.1	yes	2	4.3	odd	2
1520.2.q.b.881.1		2	19.7	even	3	inner
1520.2.q.b.961.1		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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} -5.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(1.00000 + 1.73205i) q^{15} +(1.00000 - 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +5.00000 q^{31} +(5.00000 - 8.66025i) q^{33} -4.00000 q^{37} -4.00000 q^{39} +(-5.00000 + 8.66025i) q^{41} +(-4.00000 + 6.92820i) q^{43} -1.00000 q^{45} +(-1.00000 - 1.73205i) q^{47} -7.00000 q^{49} +(2.00000 + 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{55} +(-8.00000 - 3.46410i) q^{57} +(3.50000 - 6.06218i) q^{59} +(3.50000 + 6.06218i) q^{61} +2.00000 q^{65} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{69} +(3.50000 - 6.06218i) q^{71} +2.00000 q^{75} +(-0.500000 + 0.866025i) q^{79} +(5.50000 - 9.52628i) q^{81} -4.00000 q^{83} +(-1.00000 - 1.73205i) q^{85} +18.0000 q^{87} +(-4.50000 - 7.79423i) q^{89} +(-5.00000 + 8.66025i) q^{93} +(4.00000 + 1.73205i) q^{95} +(8.00000 - 13.8564i) q^{97} +(2.50000 + 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + q^{5} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + q^5 - q^9	\( 2 q - 2 q^{3} + q^{5} - q^{9} - 10 q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} - 4 q^{23} - q^{25} - 8 q^{27} - 9 q^{29} + 10 q^{31} + 10 q^{33} - 8 q^{37} - 8 q^{39} - 10 q^{41} - 8 q^{43} - 2 q^{45} - 2 q^{47} - 14 q^{49} + 4 q^{51} - 6 q^{53} - 5 q^{55} - 16 q^{57} + 7 q^{59} + 7 q^{61} + 4 q^{65} - 14 q^{67} + 16 q^{69} + 7 q^{71} + 4 q^{75} - q^{79} + 11 q^{81} - 8 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} - 10 q^{93} + 8 q^{95} + 16 q^{97} + 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + q^5 - q^9 - 10 * q^11 + 2 * q^13 + 2 * q^15 + 2 * q^17 + q^19 - 4 * q^23 - q^25 - 8 * q^27 - 9 * q^29 + 10 * q^31 + 10 * q^33 - 8 * q^37 - 8 * q^39 - 10 * q^41 - 8 * q^43 - 2 * q^45 - 2 * q^47 - 14 * q^49 + 4 * q^51 - 6 * q^53 - 5 * q^55 - 16 * q^57 + 7 * q^59 + 7 * q^61 + 4 * q^65 - 14 * q^67 + 16 * q^69 + 7 * q^71 + 4 * q^75 - q^79 + 11 * q^81 - 8 * q^83 - 2 * q^85 + 36 * q^87 - 9 * q^89 - 10 * q^93 + 8 * q^95 + 16 * q^97 + 5 * q^99

Introduction

L-functions

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Database

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