LMFDB - Embedded newform 720.2.q.b.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.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:	$5.74922894553$
Analytic rank:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	720.241
Dual form			720.2.q.b.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-1.50000 - 0.866025i) q^{15} +4.00000 q^{19} -1.73205i q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 - 3.46410i) q^{31} +10.3923i q^{33} -1.00000 q^{35} +8.00000 q^{37} +(3.00000 + 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{43} +3.00000 q^{45} +(-1.50000 + 2.59808i) q^{47} +(3.00000 + 5.19615i) q^{49} +6.00000 q^{53} +6.00000 q^{55} +(-6.00000 + 3.46410i) q^{57} +(3.00000 + 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{63} +(1.00000 - 1.73205i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-13.5000 - 7.79423i) q^{69} +6.00000 q^{71} -4.00000 q^{73} -1.73205i q^{75} +(3.00000 + 5.19615i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} -5.19615i q^{87} +9.00000 q^{89} +2.00000 q^{91} +(6.00000 + 3.46410i) q^{93} +(2.00000 + 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + q^{5} - q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + q^5 - q^7 + 3 * q^9	$ 2 q - 3 q^{3} + q^{5} - q^{7} + 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} + 8 q^{19} + 9 q^{23} - q^{25} - 3 q^{29} - 4 q^{31} - 2 q^{35} + 16 q^{37} + 6 q^{39} + 3 q^{41} + 8 q^{43} + 6 q^{45} - 3 q^{47} + 6 q^{49} + 12 q^{53} + 12 q^{55} - 12 q^{57} + 6 q^{59} + 13 q^{61} + 3 q^{63} + 2 q^{65} - 13 q^{67} - 27 q^{69} + 12 q^{71} - 8 q^{73} + 6 q^{77} - 10 q^{79} - 9 q^{81} - 9 q^{83} + 18 q^{89} + 4 q^{91} + 12 q^{93} + 4 q^{95} - 2 q^{97} - 18 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + q^5 - q^7 + 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 + 8 * q^19 + 9 * q^23 - q^25 - 3 * q^29 - 4 * q^31 - 2 * q^35 + 16 * q^37 + 6 * q^39 + 3 * q^41 + 8 * q^43 + 6 * q^45 - 3 * q^47 + 6 * q^49 + 12 * q^53 + 12 * q^55 - 12 * q^57 + 6 * q^59 + 13 * q^61 + 3 * q^63 + 2 * q^65 - 13 * q^67 - 27 * q^69 + 12 * q^71 - 8 * q^73 + 6 * q^77 - 10 * q^79 - 9 * q^81 - 9 * q^83 + 18 * q^89 + 4 * q^91 + 12 * q^93 + 4 * q^95 - 2 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		−	1.73205i		−	0.377964i
$22$		0			0
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.768613	+	0.639713i	$0.220947\pi$
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.169701	+	0.985496i	$0.445720\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$			10.3923i			1.80907i
$34$		0			0
$35$	−1.00000			−0.169031
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$	3.00000	+	1.73205i	0.480384	+	0.277350i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$	3.00000			0.447214
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$	−6.00000	+	3.46410i	−0.794719	+	0.458831i
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$		0			0
$69$	−13.5000	−	7.79423i	−1.62521	−	0.938315i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		0			0
$75$		−	1.73205i		−	0.200000i
$76$		0			0
$77$	3.00000	+	5.19615i	0.341882	+	0.592157i
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	5.19615i		−	0.557086i
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$		0			0
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$		0			0
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	−9.00000	−	15.5885i	−0.904534	−	1.56670i
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$		0			0
$105$	1.50000	−	0.866025i	0.146385	−	0.0845154i
$106$		0			0
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$	−12.0000	+	6.92820i	−1.13899	+	0.657596i
$112$		0			0
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$	−6.00000			−0.554700
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.00000			0.621150			0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000			0.621150			0.310575	+	0.950549i	$0.399478\pi$
$128$		0			0
$129$			13.8564i			1.21999i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$		0			0
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$		−	5.19615i		−	0.437595i
$142$		0			0
$143$	−12.0000			−1.00349
$144$		0			0
$145$	−3.00000			−0.249136
$146$		0			0
$147$	−9.00000	−	5.19615i	−0.742307	−	0.428571i
$148$		0			0
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	−0.426948	−	0.904276i	$-0.640411\pi$
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	0.996600	−	0.0823900i	$-0.0262553\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$	−9.00000	+	5.19615i	−0.713746	+	0.412082i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	−9.00000	+	5.19615i	−0.700649	+	0.404520i
$166$		0			0
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$		0			0
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.101598	+	0.994826i	$0.532395\pi$
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.810745	+	0.585399i	$0.800938\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$		0			0
$177$	−9.00000	−	5.19615i	−0.676481	−	0.390567i
$178$		0			0
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$			22.5167i			1.66448i
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$			3.46410i			0.248069i
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	19.5000	+	11.2583i	1.37542	+	0.794101i
$202$		0			0
$203$	−1.50000	−	2.59808i	−0.105279	−	0.182349i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	27.0000			1.87663
$208$		0			0
$209$	12.0000	−	20.7846i	0.830057	−	1.43770i
$210$		0			0
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	0.898392	−	0.439194i	$-0.144736\pi$
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	−0.829549	+	0.558433i	$0.811403\pi$
$212$		0			0
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	4.00000			0.271538
$218$		0			0
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$		0			0
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$	−9.00000	−	5.19615i	−0.592157	−	0.341882i
$232$		0			0
$233$	−12.0000			−0.786146			−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000			−0.786146			−0.393073	+	0.919507i	$0.628588\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$		0			0
$237$		−	17.3205i		−	1.12509i
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−14.5000	+	25.1147i	−0.934027	+	1.61778i	−0.157667	+	0.987492i	$0.550397\pi$
$241$	−14.5000	+	25.1147i	−0.934027	+	1.61778i	−0.776360	+	0.630290i	$0.782936\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$		0			0
$249$		−	15.5885i		−	0.987878i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	54.0000			3.39495
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	−4.00000	+	6.92820i	−0.248548	+	0.430498i
$260$		0			0
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	3.00000	+	5.19615i	0.184289	+	0.319197i
$266$		0			0
$267$	−13.5000	+	7.79423i	−0.826187	+	0.476999i
$268$		0			0
$269$	21.0000			1.28039			0.640196	−	0.768211i	$-0.278853\pi$
$269$	21.0000			1.28039			0.640196	+	0.768211i	$0.278853\pi$
$270$		0			0
$271$	4.00000			0.242983			0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000			0.242983			0.121491	+	0.992592i	$0.461232\pi$
$272$		0			0
$273$	−3.00000	+	1.73205i	−0.181568	+	0.104828i
$274$		0			0
$275$	3.00000	+	5.19615i	0.180907	+	0.313340i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		0			0
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	0.605575	−	0.795788i	$-0.292943\pi$
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	−0.991960	+	0.126550i	$0.959610\pi$
$284$		0			0
$285$	−6.00000	−	3.46410i	−0.355409	−	0.205196i
$286$		0			0
$287$	−3.00000			−0.177084
$288$		0			0
$289$	−17.0000			−1.00000
$290$		0			0
$291$		−	3.46410i		−	0.203069i
$292$		0			0
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$		0			0
$297$	27.0000	+	15.5885i	1.56670	+	0.904534i
$298$		0			0
$299$	9.00000	−	15.5885i	0.520483	−	0.901504i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$		0			0
$303$		−	10.3923i		−	0.597022i
$304$		0			0
$305$	13.0000			0.744378
$306$		0			0
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$		0			0
$309$	−12.0000	−	6.92820i	−0.682656	−	0.394132i
$310$		0			0
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	−0.892903	−	0.450250i	$-0.851335\pi$
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	0.836379	+	0.548151i	$0.184668\pi$
$314$		0			0
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$		0			0
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	2.00000			0.110940
$326$		0			0
$327$	10.5000	−	6.06218i	0.580651	−	0.335239i
$328$		0			0
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$		0			0
$333$	12.0000	−	20.7846i	0.657596	−	1.13899i
$334$		0			0
$335$	6.50000	−	11.2583i	0.355133	−	0.615108i
$336$		0			0
$337$	−4.00000	−	6.92820i	−0.217894	−	0.377403i	0.736270	−	0.676688i	$-0.236585\pi$
$337$	−4.00000	−	6.92820i	−0.217894	−	0.377403i	−0.954164	+	0.299285i	$0.903252\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		−	15.5885i		−	0.839254i
$346$		0			0
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	0.374701	+	0.927146i	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$	9.00000	−	5.19615i	0.480384	−	0.277350i
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$	37.5000	+	21.6506i	1.96824	+	1.13636i
$364$		0			0
$365$	−2.00000	−	3.46410i	−0.104685	−	0.181319i
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	9.00000			0.468521
$370$		0			0
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$		0			0
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	6.00000			0.309016
$378$		0			0
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$	−10.5000	+	6.06218i	−0.537931	+	0.310575i
$382$		0			0
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	−3.00000	+	5.19615i	−0.152894	+	0.264820i
$386$		0			0
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$		0			0
$389$	−10.5000	+	18.1865i	−0.532371	+	0.922094i	0.466915	+	0.884302i	$0.345366\pi$
$389$	−10.5000	+	18.1865i	−0.532371	+	0.922094i	−0.999286	+	0.0377914i	$0.987968\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	27.0000	+	15.5885i	1.36197	+	0.786334i
$394$		0			0
$395$	−10.0000			−0.503155
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$		−	6.92820i		−	0.346844i
$400$		0			0
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$		0			0
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$		0			0
$407$	24.0000	−	41.5692i	1.18964	−	2.06051i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$		0			0
$413$	−6.00000			−0.295241
$414$		0			0
$415$	−9.00000			−0.441793
$416$		0			0
$417$	24.0000	+	13.8564i	1.17529	+	0.678551i
$418$		0			0
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$		0			0
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$		0			0
$423$	4.50000	+	7.79423i	0.218797	+	0.378968i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.50000	+	11.2583i	0.314557	+	0.544829i
$428$		0			0
$429$	18.0000	−	10.3923i	0.869048	−	0.501745i
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	4.50000	−	2.59808i	0.215758	−	0.124568i
$436$		0			0
$437$	18.0000	+	31.1769i	0.861057	+	1.49139i
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$		0			0
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$		0			0
$447$	−4.50000	−	2.59808i	−0.212843	−	0.122885i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	18.0000			0.847587
$452$		0			0
$453$			24.2487i			1.13930i
$454$		0			0
$455$	1.00000	+	1.73205i	0.0468807	+	0.0811998i
$456$		0			0
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.5000	−	23.3827i	0.628758	−	1.08904i	−0.359044	−	0.933321i	$-0.616897\pi$
$461$	13.5000	−	23.3827i	0.628758	−	1.08904i	0.987801	−	0.155719i	$-0.0497696\pi$
$462$		0			0
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	0.815802	−	0.578331i	$-0.196296\pi$
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	−0.908750	+	0.417340i	$0.862962\pi$
$464$		0			0
$465$			6.92820i			0.321288i
$466$		0			0
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$	13.0000			0.600284
$470$		0			0
$471$	21.0000	+	12.1244i	0.967629	+	0.558661i
$472$		0			0
$473$	−24.0000	−	41.5692i	−1.10352	−	1.91135i
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$		0			0
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		0			0
$483$	13.5000	−	7.79423i	0.614271	−	0.354650i
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	−8.00000			−0.362515			−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000			−0.362515			−0.181257	+	0.983436i	$0.558017\pi$
$488$		0			0
$489$	−6.00000	+	3.46410i	−0.271329	+	0.156652i
$490$		0			0
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	9.00000	−	15.5885i	0.404520	−	0.700649i
$496$		0			0
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$		0			0
$501$	4.50000	+	2.59808i	0.201045	+	0.116073i
$502$		0			0
$503$	−27.0000			−1.20387			−0.601935	−	0.798545i	$-0.705603\pi$
$503$	−27.0000			−1.20387			−0.601935	+	0.798545i	$0.705603\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$			15.5885i			0.692308i
$508$		0			0
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$		0			0
$513$			20.7846i			0.917663i
$514$		0			0
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$		0			0
$519$		−	41.5692i		−	1.82469i
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	19.0000			0.830812			0.415406	−	0.909636i	$-0.363640\pi$
$523$	19.0000			0.830812			0.415406	+	0.909636i	$0.363640\pi$
$524$		0			0
$525$	1.50000	+	0.866025i	0.0654654	+	0.0377964i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$		0			0
$537$	−27.0000	+	15.5885i	−1.16514	+	0.672692i
$538$		0			0
$539$	36.0000			1.55063
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$	−7.50000	+	4.33013i	−0.321856	+	0.185824i
$544$		0			0
$545$	−3.50000	−	6.06218i	−0.149924	−	0.259675i
$546$		0			0
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.118753	+	0.992924i	$0.537890\pi$
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.800521	+	0.599305i	$0.795444\pi$
$548$		0			0
$549$	−19.5000	−	33.7750i	−0.832240	−	1.44148i
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	−5.00000	−	8.66025i	−0.212622	−	0.368271i
$554$		0			0
$555$	−12.0000	−	6.92820i	−0.509372	−	0.294086i
$556$		0			0
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	9.00000			0.377964
$568$		0			0
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	−0.892413	−	0.451219i	$-0.850989\pi$
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	0.0554391	−	0.998462i	$-0.482344\pi$
$572$		0			0
$573$		−	20.7846i		−	0.868290i
$574$		0			0
$575$	−9.00000			−0.375326
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$	3.00000	+	1.73205i	0.124676	+	0.0719816i
$580$		0			0
$581$	−4.50000	−	7.79423i	−0.186691	−	0.323359i
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$		0			0
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$		0			0
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	−0.978266	−	0.207355i	$-0.933514\pi$
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	0.668708	+	0.743525i	$0.266848\pi$
$588$		0			0
$589$	−8.00000	−	13.8564i	−0.329634	−	0.570943i
$590$		0			0
$591$	18.0000	−	10.3923i	0.740421	−	0.427482i
$592$		0			0
$593$	24.0000			0.985562			0.492781	−	0.870153i	$-0.335980\pi$
$593$	24.0000			0.985562			0.492781	+	0.870153i	$0.335980\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	12.0000	−	6.92820i	0.491127	−	0.283552i
$598$		0			0
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$		0			0
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−39.0000			−1.58820
$604$		0			0
$605$	12.5000	−	21.6506i	0.508197	−	0.880223i
$606$		0			0
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	0.994424	+	0.105453i	$0.0336291\pi$
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$	4.50000	+	2.59808i	0.182349	+	0.105279i
$610$		0			0
$611$	6.00000			0.242734
$612$		0			0
$613$	−40.0000			−1.61558			−0.807792	−	0.589467i	$-0.799338\pi$
$613$	−40.0000			−1.61558			−0.807792	+	0.589467i	$0.799338\pi$
$614$		0			0
$615$		−	5.19615i		−	0.209529i
$616$		0			0
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	0.719605	−	0.694383i	$-0.244323\pi$
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	−0.961156	+	0.276005i	$0.910989\pi$
$618$		0			0
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	0.113185	+	0.993574i	$0.463895\pi$
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	−0.917053	+	0.398766i	$0.869439\pi$
$620$		0			0
$621$	−40.5000	+	23.3827i	−1.62521	+	0.938315i
$622$		0			0
$623$	−4.50000	+	7.79423i	−0.180289	+	0.312269i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$			41.5692i			1.66011i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$	−3.00000	−	1.73205i	−0.119239	−	0.0688428i
$634$		0			0
$635$	3.50000	+	6.06218i	0.138893	+	0.240570i
$636$		0			0
$637$	6.00000	−	10.3923i	0.237729	−	0.411758i
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$	−15.5000	−	26.8468i	−0.611260	−	1.05873i	−0.991028	−	0.133652i	$-0.957330\pi$
$643$	−15.5000	−	26.8468i	−0.611260	−	1.05873i	0.379768	−	0.925082i	$-0.376004\pi$
$644$		0			0
$645$	−12.0000	+	6.92820i	−0.472500	+	0.272798i
$646$		0			0
$647$	3.00000			0.117942			0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000			0.117942			0.0589711	+	0.998260i	$0.481218\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$		0			0
$651$	−6.00000	+	3.46410i	−0.235159	+	0.135769i
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$		0			0
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	23.0000	+	39.8372i	0.894596	+	1.54949i	0.834303	+	0.551306i	$0.185870\pi$
$661$	23.0000	+	39.8372i	0.894596	+	1.54949i	0.0602929	+	0.998181i	$0.480797\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.00000			−0.155113
$666$		0			0
$667$	−27.0000			−1.04544
$668$		0			0
$669$		−	1.73205i		−	0.0669650i
$670$		0			0
$671$	−39.0000	−	67.5500i	−1.50558	−	2.60774i
$672$		0			0
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.0426985	−	0.999088i	$-0.486405\pi$
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.843886	−	0.536522i	$-0.180262\pi$
$674$		0			0
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$		0			0
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$		0			0
$681$		−	20.7846i		−	0.796468i
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	−19.5000	−	11.2583i	−0.743971	−	0.429532i
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$		0			0
$693$	18.0000			0.683763
$694$		0			0
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	18.0000	−	10.3923i	0.680823	−	0.393073i
$700$		0			0
$701$	−45.0000			−1.69963			−0.849813	−	0.527084i	$-0.823285\pi$
$701$	−45.0000			−1.69963			−0.849813	+	0.527084i	$0.823285\pi$
$702$		0			0
$703$	32.0000			1.20690
$704$		0			0
$705$	4.50000	−	2.59808i	0.169480	−	0.0978492i
$706$		0			0
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		0			0
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$		0			0
$713$	18.0000	−	31.1769i	0.674105	−	1.16758i
$714$		0			0
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		0			0
$723$		−	50.2295i		−	1.86805i
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	26.5000	−	45.8993i	0.982831	−	1.70231i	0.331625	−	0.943411i	$-0.392403\pi$
$727$	26.5000	−	45.8993i	0.982831	−	1.70231i	0.651206	−	0.758901i	$-0.274263\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$		−	10.3923i		−	0.383326i
$736$		0			0
$737$	−78.0000			−2.87317
$738$		0			0
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$		0			0
$741$	12.0000	+	6.92820i	0.440831	+	0.254514i
$742$		0			0
$743$	−7.50000	−	12.9904i	−0.275148	−	0.476571i	0.695024	−	0.718986i	$-0.255394\pi$
$743$	−7.50000	−	12.9904i	−0.275148	−	0.476571i	−0.970173	+	0.242415i	$0.922060\pi$
$744$		0			0
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$		0			0
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$		0			0
$749$	−1.50000	+	2.59808i	−0.0548088	+	0.0949316i
$750$		0			0
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	0.883694	−	0.468065i	$-0.155049\pi$
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	−0.847203	+	0.531269i	$0.821715\pi$
$752$		0			0
$753$	18.0000	−	10.3923i	0.655956	−	0.378717i
$754$		0			0
$755$	14.0000			0.509512
$756$		0			0
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$		0			0
$759$	−81.0000	+	46.7654i	−2.94011	+	1.69748i
$760$		0			0
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	0.993098	+	0.117289i	$0.0374205\pi$
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	−0.394973	+	0.918693i	$0.629246\pi$
$762$		0			0
$763$	3.50000	−	6.06218i	0.126709	−	0.219466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		0			0
$769$	−14.5000	−	25.1147i	−0.522883	−	0.905661i	−0.999645	−	0.0266282i	$-0.991523\pi$
$769$	−14.5000	−	25.1147i	−0.522883	−	0.905661i	0.476762	−	0.879032i	$-0.341810\pi$
$770$		0			0
$771$	27.0000	+	15.5885i	0.972381	+	0.561405i
$772$		0			0
$773$	−48.0000			−1.72644			−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000			−1.72644			−0.863220	+	0.504828i	$0.831556\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$		−	13.8564i		−	0.497096i
$778$		0			0
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$		0			0
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$		0			0
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−26.0000			−0.923287
$794$		0			0
$795$	−9.00000	−	5.19615i	−0.319197	−	0.184289i
$796$		0			0
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	0.950726	+	0.310031i	$0.100340\pi$
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	−0.206868	+	0.978369i	$0.566327\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	13.5000	−	23.3827i	0.476999	−	0.826187i
$802$		0			0
$803$	−12.0000	+	20.7846i	−0.423471	+	0.733473i
$804$		0			0
$805$	−4.50000	−	7.79423i	−0.158604	−	0.274710i
$806$		0			0
$807$	−31.5000	+	18.1865i	−1.10885	+	0.640196i
$808$		0			0
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	−6.00000	+	3.46410i	−0.210429	+	0.121491i
$814$		0			0
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$		0			0
$819$	3.00000	−	5.19615i	0.104828	−	0.181568i
$820$		0			0
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	−0.999456	−	0.0329950i	$-0.989495\pi$
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	0.528302	+	0.849056i	$0.322829\pi$
$822$		0			0
$823$	−12.5000	−	21.6506i	−0.435723	−	0.754694i	0.561632	−	0.827387i	$-0.310174\pi$
$823$	−12.5000	−	21.6506i	−0.435723	−	0.754694i	−0.997354	+	0.0726937i	$0.976840\pi$
$824$		0			0
$825$	−9.00000	−	5.19615i	−0.313340	−	0.180907i
$826$		0			0
$827$	−3.00000			−0.104320			−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000			−0.104320			−0.0521601	+	0.998639i	$0.516611\pi$
$828$		0			0
$829$	−7.00000			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$830$		0			0
$831$		−	13.8564i		−	0.480673i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$		0			0
$837$	18.0000	−	10.3923i	0.622171	−	0.359211i
$838$		0			0
$839$	18.0000	−	31.1769i	0.621429	−	1.07635i	−0.367791	−	0.929909i	$-0.619886\pi$
$839$	18.0000	−	31.1769i	0.621429	−	1.07635i	0.989220	−	0.146438i	$-0.0467809\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$			25.9808i			0.894825i
$844$		0			0
$845$	9.00000			0.309609
$846$		0			0
$847$	25.0000			0.859010
$848$		0			0
$849$	19.5000	+	11.2583i	0.669238	+	0.386385i
$850$		0			0
$851$	36.0000	+	62.3538i	1.23406	+	2.13746i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$		0			0
$855$	12.0000			0.410391
$856$		0			0
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$		0			0
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	−0.995475	−	0.0950262i	$-0.969707\pi$
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	0.415442	−	0.909620i	$-0.363627\pi$
$860$		0			0
$861$	4.50000	−	2.59808i	0.153360	−	0.0885422i
$862$		0			0
$863$	−3.00000			−0.102121			−0.0510606	−	0.998696i	$-0.516260\pi$
$863$	−3.00000			−0.102121			−0.0510606	+	0.998696i	$0.516260\pi$
$864$		0			0
$865$	−24.0000			−0.816024
$866$		0			0
$867$	25.5000	−	14.7224i	0.866025	−	0.500000i
$868$		0			0
$869$	30.0000	+	51.9615i	1.01768	+	1.76267i
$870$		0			0
$871$	−13.0000	+	22.5167i	−0.440488	+	0.762948i
$872$		0			0
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	31.0000			1.04323			0.521617	−	0.853180i	$-0.325329\pi$
$883$	31.0000			1.04323			0.521617	+	0.853180i	$0.325329\pi$
$884$		0			0
$885$		−	10.3923i		−	0.349334i
$886$		0			0
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	−3.50000	+	6.06218i	−0.117386	+	0.203319i
$890$		0			0
$891$	−54.0000			−1.80907
$892$		0			0
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$		0			0
$897$			31.1769i			1.04097i
$898$		0			0
$899$	12.0000			0.400222
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−12.0000	−	6.92820i	−0.399335	−	0.230556i
$904$		0			0
$905$	2.50000	+	4.33013i	0.0831028	+	0.143938i
$906$		0			0
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	0.376228	+	0.926527i	$0.377221\pi$
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	−0.990510	+	0.137441i	$0.956112\pi$
$908$		0			0
$909$	9.00000	+	15.5885i	0.298511	+	0.517036i
$910$		0			0
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	−0.999994	−	0.00349271i	$-0.998888\pi$
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	0.503022	+	0.864274i	$0.332222\pi$
$912$		0			0
$913$	27.0000	+	46.7654i	0.893570	+	1.54771i
$914$		0			0
$915$	−19.5000	+	11.2583i	−0.644650	+	0.372189i
$916$		0			0
$917$	18.0000			0.594412
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$	−10.5000	+	6.06218i	−0.345987	+	0.199756i
$922$		0			0
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$		0			0
$927$	24.0000			0.788263
$928$		0			0
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$		0			0
$931$	12.0000	+	20.7846i	0.393284	+	0.681188i
$932$		0			0
$933$	−18.0000	−	10.3923i	−0.589294	−	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	56.0000			1.82944			0.914720	−	0.404088i	$-0.132411\pi$
$937$	56.0000			1.82944			0.914720	+	0.404088i	$0.132411\pi$
$938$		0			0
$939$		−	3.46410i		−	0.113047i
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$		0			0
$945$		−	5.19615i		−	0.169031i
$946$		0			0
$947$	19.5000	−	33.7750i	0.633665	−	1.09754i	−0.353131	−	0.935574i	$-0.614883\pi$
$947$	19.5000	−	33.7750i	0.633665	−	1.09754i	0.986796	−	0.161966i	$-0.0517835\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$			10.3923i			0.336994i
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	−12.0000			−0.388311
$956$		0			0
$957$	−27.0000	−	15.5885i	−0.872786	−	0.503903i
$958$		0			0
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$		0			0
$965$	1.00000	−	1.73205i	0.0321911	−	0.0557567i
$966$		0			0
$967$	−18.5000	−	32.0429i	−0.594920	−	1.03043i	−0.993558	−	0.113323i	$-0.963850\pi$
$967$	−18.5000	−	32.0429i	−0.594920	−	1.03043i	0.398638	−	0.917108i	$-0.369483\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.0000			0.770197			0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000			0.770197			0.385098	+	0.922876i	$0.374168\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$		0			0
$975$	−3.00000	+	1.73205i	−0.0960769	+	0.0554700i
$976$		0			0
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$		0			0
$979$	27.0000	−	46.7654i	0.862924	−	1.49463i
$980$		0			0
$981$	−10.5000	+	18.1865i	−0.335239	+	0.580651i
$982$		0			0
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$	4.50000	+	2.59808i	0.143237	+	0.0826977i
$988$		0			0
$989$	72.0000			2.28947
$990$		0			0
$991$	10.0000			0.317660			0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000			0.317660			0.158830	+	0.987306i	$0.449228\pi$
$992$		0			0
$993$		−	17.3205i		−	0.549650i
$994$		0			0
$995$	−4.00000	−	6.92820i	−0.126809	−	0.219639i
$996$		0			0
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$		0			0
$999$			41.5692i			1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.b.241.1		2
3.2	odd	2		2160.2.q.b.721.1		2
4.3	odd	2		90.2.e.a.61.1	yes	2
9.2	odd	6		6480.2.a.v.1.1		1
9.4	even	3	inner	720.2.q.b.481.1		2
9.5	odd	6		2160.2.q.b.1441.1		2
9.7	even	3		6480.2.a.g.1.1		1
12.11	even	2		270.2.e.b.181.1		2
20.3	even	4		450.2.j.c.349.2		4
20.7	even	4		450.2.j.c.349.1		4
20.19	odd	2		450.2.e.e.151.1		2
36.7	odd	6		810.2.a.g.1.1		1
36.11	even	6		810.2.a.b.1.1		1
36.23	even	6		270.2.e.b.91.1		2
36.31	odd	6		90.2.e.a.31.1	✓	2
60.23	odd	4		1350.2.j.e.1099.1		4
60.47	odd	4		1350.2.j.e.1099.2		4
60.59	even	2		1350.2.e.b.451.1		2
180.7	even	12		4050.2.c.t.649.2		2
180.23	odd	12		1350.2.j.e.199.2		4
180.43	even	12		4050.2.c.t.649.1		2
180.47	odd	12		4050.2.c.a.649.1		2
180.59	even	6		1350.2.e.b.901.1		2
180.67	even	12		450.2.j.c.49.2		4
180.79	odd	6		4050.2.a.n.1.1		1
180.83	odd	12		4050.2.c.a.649.2		2
180.103	even	12		450.2.j.c.49.1		4
180.119	even	6		4050.2.a.ba.1.1		1
180.139	odd	6		450.2.e.e.301.1		2
180.167	odd	12		1350.2.j.e.199.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.a.31.1	✓	2	36.31	odd	6
90.2.e.a.61.1	yes	2	4.3	odd	2
270.2.e.b.91.1		2	36.23	even	6
270.2.e.b.181.1		2	12.11	even	2
450.2.e.e.151.1		2	20.19	odd	2
450.2.e.e.301.1		2	180.139	odd	6
450.2.j.c.49.1		4	180.103	even	12
450.2.j.c.49.2		4	180.67	even	12
450.2.j.c.349.1		4	20.7	even	4
450.2.j.c.349.2		4	20.3	even	4
720.2.q.b.241.1		2	1.1	even	1	trivial
720.2.q.b.481.1		2	9.4	even	3	inner
810.2.a.b.1.1		1	36.11	even	6
810.2.a.g.1.1		1	36.7	odd	6
1350.2.e.b.451.1		2	60.59	even	2
1350.2.e.b.901.1		2	180.59	even	6
1350.2.j.e.199.1		4	180.167	odd	12
1350.2.j.e.199.2		4	180.23	odd	12
1350.2.j.e.1099.1		4	60.23	odd	4
1350.2.j.e.1099.2		4	60.47	odd	4
2160.2.q.b.721.1		2	3.2	odd	2
2160.2.q.b.1441.1		2	9.5	odd	6
4050.2.a.n.1.1		1	180.79	odd	6
4050.2.a.ba.1.1		1	180.119	even	6
4050.2.c.a.649.1		2	180.47	odd	12
4050.2.c.a.649.2		2	180.83	odd	12
4050.2.c.t.649.1		2	180.43	even	12
4050.2.c.t.649.2		2	180.7	even	12
6480.2.a.g.1.1		1	9.7	even	3
6480.2.a.v.1.1		1	9.2	odd	6

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-1.50000 - 0.866025i) q^{15} +4.00000 q^{19} -1.73205i q^{21} +(4.50000 + 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 - 3.46410i) q^{31} +10.3923i q^{33} -1.00000 q^{35} +8.00000 q^{37} +(3.00000 + 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{43} +3.00000 q^{45} +(-1.50000 + 2.59808i) q^{47} +(3.00000 + 5.19615i) q^{49} +6.00000 q^{53} +6.00000 q^{55} +(-6.00000 + 3.46410i) q^{57} +(3.00000 + 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{63} +(1.00000 - 1.73205i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-13.5000 - 7.79423i) q^{69} +6.00000 q^{71} -4.00000 q^{73} -1.73205i q^{75} +(3.00000 + 5.19615i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} -5.19615i q^{87} +9.00000 q^{89} +2.00000 q^{91} +(6.00000 + 3.46410i) q^{93} +(2.00000 + 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + q^5 - q^7 + 3 * q^9	\( 2 q - 3 q^{3} + q^{5} - q^{7} + 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} + 8 q^{19} + 9 q^{23} - q^{25} - 3 q^{29} - 4 q^{31} - 2 q^{35} + 16 q^{37} + 6 q^{39} + 3 q^{41} + 8 q^{43} + 6 q^{45} - 3 q^{47} + 6 q^{49} + 12 q^{53} + 12 q^{55} - 12 q^{57} + 6 q^{59} + 13 q^{61} + 3 q^{63} + 2 q^{65} - 13 q^{67} - 27 q^{69} + 12 q^{71} - 8 q^{73} + 6 q^{77} - 10 q^{79} - 9 q^{81} - 9 q^{83} + 18 q^{89} + 4 q^{91} + 12 q^{93} + 4 q^{95} - 2 q^{97} - 18 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + q^5 - q^7 + 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 + 8 * q^19 + 9 * q^23 - q^25 - 3 * q^29 - 4 * q^31 - 2 * q^35 + 16 * q^37 + 6 * q^39 + 3 * q^41 + 8 * q^43 + 6 * q^45 - 3 * q^47 + 6 * q^49 + 12 * q^53 + 12 * q^55 - 12 * q^57 + 6 * q^59 + 13 * q^61 + 3 * q^63 + 2 * q^65 - 13 * q^67 - 27 * q^69 + 12 * q^71 - 8 * q^73 + 6 * q^77 - 10 * q^79 - 9 * q^81 - 9 * q^83 + 18 * q^89 + 4 * q^91 + 12 * q^93 + 4 * q^95 - 2 * q^97 - 18 * q^99

Introduction

L-functions

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