LMFDB - Embedded newform 1040.2.q.f.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(81,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, 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("1040.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.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:	$8.30444181021$
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 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1040.81
Dual form			1040.2.q.f.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{19} -5.00000 q^{21} +(1.50000 + 2.59808i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-2.50000 + 4.33013i) q^{33} +(-2.50000 + 4.33013i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(3.50000 - 0.866025i) q^{39} +(2.50000 + 4.33013i) q^{41} +(2.50000 - 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{45} -12.0000 q^{47} +(-9.00000 - 15.5885i) q^{49} -1.00000 q^{51} +2.00000 q^{53} +(2.50000 + 4.33013i) q^{55} +3.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(6.50000 - 11.2583i) q^{61} +(-5.00000 - 8.66025i) q^{63} +(1.00000 - 3.46410i) q^{65} +(1.50000 + 2.59808i) q^{67} +(1.50000 - 2.59808i) q^{69} +(6.50000 - 11.2583i) q^{71} -2.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} -25.0000 q^{77} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +(-0.500000 + 0.866025i) q^{85} +(0.500000 - 0.866025i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(12.5000 + 12.9904i) q^{91} +(1.50000 - 2.59808i) q^{95} +(-5.50000 + 9.52628i) q^{97} -10.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 - 2 * q^5 + 5 * q^7 + 2 * q^9	$ 2 q - q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9} - 5 q^{11} - 2 q^{13} + q^{15} + q^{17} - 3 q^{19} - 10 q^{21} + 3 q^{23} + 2 q^{25} - 10 q^{27} + q^{29} - 5 q^{33} - 5 q^{35} - 7 q^{37} + 7 q^{39} + 5 q^{41} + 5 q^{43} - 2 q^{45} - 24 q^{47} - 18 q^{49} - 2 q^{51} + 4 q^{53} + 5 q^{55} + 6 q^{57} - 11 q^{59} + 13 q^{61} - 10 q^{63} + 2 q^{65} + 3 q^{67} + 3 q^{69} + 13 q^{71} - 4 q^{73} - q^{75} - 50 q^{77} + 8 q^{79} - q^{81} - 24 q^{83} - q^{85} + q^{87} - 7 q^{89} + 25 q^{91} + 3 q^{95} - 11 q^{97} - 20 q^{99}+O(q^{100}) $ 2 * q - q^3 - 2 * q^5 + 5 * q^7 + 2 * q^9 - 5 * q^11 - 2 * q^13 + q^15 + q^17 - 3 * q^19 - 10 * q^21 + 3 * q^23 + 2 * q^25 - 10 * q^27 + q^29 - 5 * q^33 - 5 * q^35 - 7 * q^37 + 7 * q^39 + 5 * q^41 + 5 * q^43 - 2 * q^45 - 24 * q^47 - 18 * q^49 - 2 * q^51 + 4 * q^53 + 5 * q^55 + 6 * q^57 - 11 * q^59 + 13 * q^61 - 10 * q^63 + 2 * q^65 + 3 * q^67 + 3 * q^69 + 13 * q^71 - 4 * q^73 - q^75 - 50 * q^77 + 8 * q^79 - q^81 - 24 * q^83 - q^85 + q^87 - 7 * q^89 + 25 * q^91 + 3 * q^95 - 11 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.755929	−	0.654654i	$-0.227186\pi$
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$		0			0
$21$	−5.00000			−1.09109
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$	−2.50000	+	4.33013i	−0.435194	+	0.753778i
$34$		0			0
$35$	−2.50000	+	4.33013i	−0.422577	+	0.731925i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		0			0
$39$	3.50000	−	0.866025i	0.560449	−	0.138675i
$40$		0			0
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$		0			0
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	0.991241	+	0.132068i	$0.0421616\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$		0			0
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$		0			0
$51$	−1.00000			−0.140028
$52$		0			0
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$		0			0
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$		0			0
$57$	3.00000			0.397360
$58$		0			0
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		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
$63$	−5.00000	−	8.66025i	−0.629941	−	1.09109i
$64$		0			0
$65$	1.00000	−	3.46410i	0.124035	−	0.429669i
$66$		0			0
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	−0.165383	−	0.986229i	$-0.552886\pi$
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	0.936791	−	0.349889i	$-0.113781\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	−25.0000			−2.84901
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−0.500000	+	0.866025i	−0.0542326	+	0.0939336i
$86$		0			0
$87$	0.500000	−	0.866025i	0.0536056	−	0.0928477i
$88$		0			0
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	0.618720	−	0.785611i	$-0.287651\pi$
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	−0.989720	+	0.143022i	$0.954318\pi$
$90$		0			0
$91$	12.5000	+	12.9904i	1.31036	+	1.36176i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	0.439187	+	0.898396i	$0.355267\pi$
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	−0.997627	+	0.0688512i	$0.978067\pi$
$98$		0			0
$99$	−10.0000			−1.00504
$100$		0			0
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	0.983889	+	0.178782i	$0.0572157\pi$
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	−0.337115	+	0.941464i	$0.609451\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$	5.00000			0.487950
$106$		0			0
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$		0			0
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$		0			0
$111$	−3.50000	+	6.06218i	−0.332205	+	0.575396i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$	5.00000	+	5.19615i	0.462250	+	0.480384i
$118$		0			0
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	0.978487	−	0.206309i	$-0.0661452\pi$
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	−0.667912	+	0.744240i	$0.732812\pi$
$128$		0			0
$129$	−5.00000			−0.440225
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	7.50000	+	12.9904i	0.650332	+	1.12641i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$		0			0
$141$	6.00000	+	10.3923i	0.505291	+	0.875190i
$142$		0			0
$143$	17.5000	−	4.33013i	1.46342	−	0.362103i
$144$		0			0
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	−5.50000	+	9.52628i	−0.450578	+	0.780423i	−0.998422	−	0.0561570i	$-0.982115\pi$
$149$	−5.50000	+	9.52628i	−0.450578	+	0.780423i	0.547844	+	0.836580i	$0.315449\pi$
$150$		0			0
$151$	24.0000			1.95309			0.976546	−	0.215308i	$-0.0690756\pi$
$151$	24.0000			1.95309			0.976546	+	0.215308i	$0.0690756\pi$
$152$		0			0
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$		0			0
$159$	−1.00000	−	1.73205i	−0.0793052	−	0.137361i
$160$		0			0
$161$	15.0000			1.18217
$162$		0			0
$163$	2.50000	−	4.33013i	0.195815	−	0.339162i	−0.751352	−	0.659901i	$-0.770598\pi$
$163$	2.50000	−	4.33013i	0.195815	−	0.339162i	0.947167	+	0.320740i	$0.103931\pi$
$164$		0			0
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$		0			0
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	−0.999994	−	0.00345033i	$-0.998902\pi$
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	0.497009	−	0.867745i	$-0.334432\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$		0			0
$173$	8.50000	−	14.7224i	0.646243	−	1.11933i	−0.337770	−	0.941229i	$-0.609673\pi$
$173$	8.50000	−	14.7224i	0.646243	−	1.11933i	0.984013	−	0.178097i	$-0.0569941\pi$
$174$		0			0
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$		0			0
$177$	11.0000			0.826811
$178$		0			0
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−13.0000			−0.960988
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	−5.00000			−0.365636
$188$		0			0
$189$	−12.5000	+	21.6506i	−0.909241	+	1.57485i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$		0			0
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	0.0719816	−	0.997406i	$-0.477068\pi$
$194$		0			0
$195$	−3.50000	+	0.866025i	−0.250640	+	0.0620174i
$196$		0			0
$197$	−13.5000	−	23.3827i	−0.961835	−	1.66595i	−0.717888	−	0.696159i	$-0.754891\pi$
$197$	−13.5000	−	23.3827i	−0.961835	−	1.66595i	−0.243947	−	0.969788i	$-0.578442\pi$
$198$		0			0
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	−0.206184	−	0.978513i	$-0.566105\pi$
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	0.950509	−	0.310696i	$-0.100562\pi$
$200$		0			0
$201$	1.50000	−	2.59808i	0.105802	−	0.183254i
$202$		0			0
$203$	5.00000			0.350931
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$		0			0
$213$	−13.0000			−0.890745
$214$		0			0
$215$	−2.50000	+	4.33013i	−0.170499	+	0.295312i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$	2.50000	+	2.59808i	0.168168	+	0.174766i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$		0			0
$227$	8.50000	−	14.7224i	0.564165	−	0.977162i	−0.432962	−	0.901412i	$-0.642532\pi$
$227$	8.50000	−	14.7224i	0.564165	−	0.977162i	0.997127	−	0.0757500i	$-0.0241351\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	12.5000	+	21.6506i	0.822440	+	1.42451i
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$		0			0
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	−0.986996	−	0.160748i	$-0.948609\pi$
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	0.632709	+	0.774389i	$0.281943\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$		0			0
$247$	−7.50000	−	7.79423i	−0.477214	−	0.495935i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$		0			0
$253$	7.50000	−	12.9904i	0.471521	−	0.816698i
$254$		0			0
$255$	1.00000			0.0626224
$256$		0			0
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		0			0
$259$	−35.0000			−2.17479
$260$		0			0
$261$	2.00000			0.123797
$262$		0			0
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	0.984272	−	0.176659i	$-0.0565291\pi$
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	−0.645128	+	0.764075i	$0.723196\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$		0			0
$267$	−3.50000	+	6.06218i	−0.214197	+	0.370999i
$268$		0			0
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$		0			0
$273$	5.00000	−	17.3205i	0.302614	−	1.04828i
$274$		0			0
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$		0			0
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	−0.601975	−	0.798515i	$-0.705619\pi$
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	0.992522	+	0.122068i	$0.0389525\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	11.5000	+	19.9186i	0.683604	+	1.18404i	0.973873	+	0.227092i	$0.0729218\pi$
$283$	11.5000	+	19.9186i	0.683604	+	1.18404i	−0.290269	+	0.956945i	$0.593745\pi$
$284$		0			0
$285$	−3.00000			−0.177705
$286$		0			0
$287$	25.0000			1.47570
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$	11.0000			0.644831
$292$		0			0
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	−0.949964	−	0.312358i	$-0.898881\pi$
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	0.745492	+	0.666514i	$0.232214\pi$
$294$		0			0
$295$	5.50000	−	9.52628i	0.320222	−	0.554641i
$296$		0			0
$297$	12.5000	+	21.6506i	0.725324	+	1.25630i
$298$		0			0
$299$	−10.5000	+	2.59808i	−0.607231	+	0.150251i
$300$		0			0
$301$	−12.5000	−	21.6506i	−0.720488	−	1.24792i
$302$		0			0
$303$	6.50000	−	11.2583i	0.373415	−	0.646774i
$304$		0			0
$305$	−6.50000	+	11.2583i	−0.372189	+	0.644650i
$306$		0			0
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$	5.00000	+	8.66025i	0.281718	+	0.487950i
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$		0			0
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$		0			0
$323$	1.50000	+	2.59808i	0.0834622	+	0.144561i
$324$		0			0
$325$	−1.00000	+	3.46410i	−0.0554700	+	0.192154i
$326$		0			0
$327$	−9.00000	−	15.5885i	−0.497701	−	0.862044i
$328$		0			0
$329$	−30.0000	+	51.9615i	−1.65395	+	2.86473i
$330$		0			0
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$		0			0
$333$	−14.0000			−0.767195
$334$		0			0
$335$	−1.50000	−	2.59808i	−0.0819538	−	0.141948i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	−1.00000			−0.0543125
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−55.0000			−2.96972
$344$		0			0
$345$	−1.50000	+	2.59808i	−0.0807573	+	0.139876i
$346$		0			0
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	0.234372	+	0.972147i	$0.424697\pi$
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	−0.959090	+	0.283101i	$0.908637\pi$
$348$		0			0
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.771477	−	0.636257i	$-0.780482\pi$
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.165277	−	0.986247i	$-0.552852\pi$
$350$		0			0
$351$	5.00000	−	17.3205i	0.266880	−	0.924500i
$352$		0			0
$353$	2.50000	+	4.33013i	0.133062	+	0.230469i	0.924855	−	0.380319i	$-0.124186\pi$
$353$	2.50000	+	4.33013i	0.133062	+	0.230469i	−0.791794	+	0.610789i	$0.790853\pi$
$354$		0			0
$355$	−6.50000	+	11.2583i	−0.344984	+	0.597530i
$356$		0			0
$357$	−2.50000	+	4.33013i	−0.132314	+	0.229175i
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$	2.00000			0.104685
$366$		0			0
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$		0			0
$369$	10.0000			0.520579
$370$		0			0
$371$	5.00000	−	8.66025i	0.259587	−	0.449618i
$372$		0			0
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−3.50000	+	0.866025i	−0.180259	+	0.0446026i
$378$		0			0
$379$	−10.5000	−	18.1865i	−0.539349	−	0.934179i	−0.998939	−	0.0460485i	$-0.985337\pi$
$379$	−10.5000	−	18.1865i	−0.539349	−	0.934179i	0.459590	−	0.888131i	$-0.347996\pi$
$380$		0			0
$381$	3.50000	−	6.06218i	0.179310	−	0.310575i
$382$		0			0
$383$	−1.50000	+	2.59808i	−0.0766464	+	0.132755i	−0.901801	−	0.432151i	$-0.857755\pi$
$383$	−1.50000	+	2.59808i	−0.0766464	+	0.132755i	0.825155	+	0.564907i	$0.191088\pi$
$384$		0			0
$385$	25.0000			1.27412
$386$		0			0
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$		0			0
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	3.00000			0.151717
$392$		0			0
$393$	2.00000	+	3.46410i	0.100887	+	0.174741i
$394$		0			0
$395$	−4.00000			−0.201262
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$		0			0
$399$	7.50000	−	12.9904i	0.375470	−	0.650332i
$400$		0			0
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$		0			0
$407$	−17.5000	+	30.3109i	−0.867443	+	1.50245i
$408$		0			0
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$		0			0
$411$	3.00000			0.147979
$412$		0			0
$413$	27.5000	+	47.6314i	1.35319	+	2.34379i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$	−13.0000			−0.636613
$418$		0			0
$419$	−8.50000	−	14.7224i	−0.415252	−	0.719238i	0.580203	−	0.814472i	$-0.302973\pi$
$419$	−8.50000	−	14.7224i	−0.415252	−	0.719238i	−0.995455	+	0.0952342i	$0.969640\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	−12.0000	+	20.7846i	−0.583460	+	1.01058i
$424$		0			0
$425$	0.500000	−	0.866025i	0.0242536	−	0.0420084i
$426$		0			0
$427$	−32.5000	−	56.2917i	−1.57279	−	2.72414i
$428$		0			0
$429$	−12.5000	−	12.9904i	−0.603506	−	0.627182i
$430$		0			0
$431$	−10.5000	−	18.1865i	−0.505767	−	0.876014i	−0.999978	−	0.00667224i	$-0.997876\pi$
$431$	−10.5000	−	18.1865i	−0.505767	−	0.876014i	0.494211	−	0.869342i	$-0.335457\pi$
$432$		0			0
$433$	−3.50000	+	6.06218i	−0.168199	+	0.291330i	−0.937787	−	0.347212i	$-0.887129\pi$
$433$	−3.50000	+	6.06218i	−0.168199	+	0.291330i	0.769588	+	0.638541i	$0.220462\pi$
$434$		0			0
$435$	−0.500000	+	0.866025i	−0.0239732	+	0.0415227i
$436$		0			0
$437$	−9.00000			−0.430528
$438$		0			0
$439$	−14.5000	−	25.1147i	−0.692047	−	1.19866i	−0.971166	−	0.238404i	$-0.923376\pi$
$439$	−14.5000	−	25.1147i	−0.692047	−	1.19866i	0.279119	−	0.960257i	$-0.409958\pi$
$440$		0			0
$441$	−36.0000			−1.71429
$442$		0			0
$443$	20.0000			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$444$		0			0
$445$	3.50000	+	6.06218i	0.165916	+	0.287375i
$446$		0			0
$447$	11.0000			0.520282
$448$		0			0
$449$	10.5000	−	18.1865i	0.495526	−	0.858276i	−0.504461	−	0.863434i	$-0.668309\pi$
$449$	10.5000	−	18.1865i	0.495526	−	0.858276i	0.999987	+	0.00515887i	$0.00164213\pi$
$450$		0			0
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$		0			0
$453$	−12.0000	−	20.7846i	−0.563809	−	0.976546i
$454$		0			0
$455$	−12.5000	−	12.9904i	−0.586009	−	0.608998i
$456$		0			0
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$		0			0
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$		0			0
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		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
$465$		0			0
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	15.0000			0.692636
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$		0			0
$473$	−25.0000			−1.14950
$474$		0			0
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$		0			0
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$		0			0
$479$	5.50000	+	9.52628i	0.251301	+	0.435267i	0.963884	−	0.266321i	$-0.0858081\pi$
$479$	5.50000	+	9.52628i	0.251301	+	0.435267i	−0.712583	+	0.701588i	$0.752475\pi$
$480$		0			0
$481$	24.5000	−	6.06218i	1.11710	−	0.276412i
$482$		0			0
$483$	−7.50000	−	12.9904i	−0.341262	−	0.591083i
$484$		0			0
$485$	5.50000	−	9.52628i	0.249742	−	0.432566i
$486$		0			0
$487$	8.50000	−	14.7224i	0.385172	−	0.667137i	−0.606621	−	0.794991i	$-0.707476\pi$
$487$	8.50000	−	14.7224i	0.385172	−	0.667137i	0.991793	+	0.127854i	$0.0408089\pi$
$488$		0			0
$489$	−5.00000			−0.226108
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$		0			0
$493$	1.00000			0.0450377
$494$		0			0
$495$	10.0000			0.449467
$496$		0			0
$497$	−32.5000	−	56.2917i	−1.45782	−	2.52503i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	−6.50000	+	11.2583i	−0.290399	+	0.502985i
$502$		0			0
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	−0.962197	−	0.272354i	$-0.912198\pi$
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	0.716964	+	0.697110i	$0.245531\pi$
$504$		0			0
$505$	−6.50000	−	11.2583i	−0.289246	−	0.500989i
$506$		0			0
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$		0			0
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$		0			0
$513$	7.50000	−	12.9904i	0.331133	−	0.573539i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	30.0000	+	51.9615i	1.31940	+	2.28527i
$518$		0			0
$519$	−17.0000			−0.746217
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	0.539782	−	0.841805i	$-0.318507\pi$
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	−0.998915	+	0.0465630i	$0.985173\pi$
$524$		0			0
$525$	−5.00000			−0.218218
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	11.0000	+	19.0526i	0.477359	+	0.826811i
$532$		0			0
$533$	−17.5000	+	4.33013i	−0.758009	+	0.187559i
$534$		0			0
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$		0			0
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$		0			0
$539$	−45.0000	+	77.9423i	−1.93829	+	3.35721i
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	−18.0000			−0.771035
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		0			0
$549$	−13.0000	−	22.5167i	−0.554826	−	0.960988i
$550$		0			0
$551$	−3.00000			−0.127804
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$		0			0
$555$	3.50000	−	6.06218i	0.148567	−	0.257325i
$556$		0			0
$557$	6.50000	+	11.2583i	0.275414	+	0.477031i	0.970239	−	0.242147i	$-0.0778518\pi$
$557$	6.50000	+	11.2583i	0.275414	+	0.477031i	−0.694826	+	0.719178i	$0.744518\pi$
$558$		0			0
$559$	12.5000	+	12.9904i	0.528694	+	0.549435i
$560$		0			0
$561$	2.50000	+	4.33013i	0.105550	+	0.182818i
$562$		0			0
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	−0.755482	−	0.655169i	$-0.772597\pi$
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	0.945134	+	0.326682i	$0.105931\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$		0			0
$567$	−5.00000			−0.209980
$568$		0			0
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	15.0000			0.626634
$574$		0			0
$575$	1.50000	+	2.59808i	0.0625543	+	0.108347i
$576$		0			0
$577$	−42.0000			−1.74848			−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000			−1.74848			−0.874241	+	0.485491i	$0.838641\pi$
$578$		0			0
$579$	−11.5000	+	19.9186i	−0.477924	+	0.827788i
$580$		0			0
$581$	−30.0000	+	51.9615i	−1.24461	+	2.15573i
$582$		0			0
$583$	−5.00000	−	8.66025i	−0.207079	−	0.358671i
$584$		0			0
$585$	−5.00000	−	5.19615i	−0.206725	−	0.214834i
$586$		0			0
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−13.5000	+	23.3827i	−0.555316	+	0.961835i
$592$		0			0
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$		0			0
$595$	2.50000	+	4.33013i	0.102490	+	0.177518i
$596$		0			0
$597$	−21.0000			−0.859473
$598$		0			0
$599$	36.0000			1.47092			0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000			1.47092			0.735460	+	0.677568i	$0.236966\pi$
$600$		0			0
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$		0			0
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	−15.5000	+	26.8468i	−0.629126	+	1.08968i	0.358602	+	0.933491i	$0.383254\pi$
$607$	−15.5000	+	26.8468i	−0.629126	+	1.08968i	−0.987728	+	0.156187i	$0.950080\pi$
$608$		0			0
$609$	−2.50000	−	4.33013i	−0.101305	−	0.175466i
$610$		0			0
$611$	12.0000	−	41.5692i	0.485468	−	1.68171i
$612$		0			0
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$		0			0
$615$	−2.50000	+	4.33013i	−0.100810	+	0.174608i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$		0			0
$623$	−35.0000			−1.40225
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.50000	−	12.9904i	−0.299521	−	0.518786i
$628$		0			0
$629$	−7.00000			−0.279108
$630$		0			0
$631$	−13.5000	+	23.3827i	−0.537427	+	0.930850i	0.461615	+	0.887080i	$0.347270\pi$
$631$	−13.5000	+	23.3827i	−0.537427	+	0.930850i	−0.999042	+	0.0437697i	$0.986063\pi$
$632$		0			0
$633$	−2.50000	+	4.33013i	−0.0993661	+	0.172107i
$634$		0			0
$635$	−3.50000	−	6.06218i	−0.138893	−	0.240570i
$636$		0			0
$637$	63.0000	−	15.5885i	2.49615	−	0.617637i
$638$		0			0
$639$	−13.0000	−	22.5167i	−0.514272	−	0.890745i
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$		0			0
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	−0.812511	−	0.582946i	$-0.801900\pi$
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	0.911101	+	0.412182i	$0.135233\pi$
$644$		0			0
$645$	5.00000			0.196875
$646$		0			0
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$	55.0000			2.15894
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$		0			0
$655$	4.00000			0.156293
$656$		0			0
$657$	−2.00000	+	3.46410i	−0.0780274	+	0.135147i
$658$		0			0
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	−0.651617	−	0.758548i	$-0.725909\pi$
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	0.982730	+	0.185043i	$0.0592425\pi$
$660$		0			0
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	0.835379	−	0.549675i	$-0.185248\pi$
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	−0.893722	+	0.448622i	$0.851915\pi$
$662$		0			0
$663$	1.00000	−	3.46410i	0.0388368	−	0.134535i
$664$		0			0
$665$	−7.50000	−	12.9904i	−0.290838	−	0.503745i
$666$		0			0
$667$	−1.50000	+	2.59808i	−0.0580802	+	0.100598i
$668$		0			0
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	−65.0000			−2.50930
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$		0			0
$675$	−5.00000			−0.192450
$676$		0			0
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$	27.5000	+	47.6314i	1.05535	+	1.82793i
$680$		0			0
$681$	−17.0000			−0.651441
$682$		0			0
$683$	24.5000	−	42.4352i	0.937466	−	1.62374i	0.167291	−	0.985908i	$-0.446498\pi$
$683$	24.5000	−	42.4352i	0.937466	−	1.62374i	0.770176	−	0.637832i	$-0.220169\pi$
$684$		0			0
$685$	1.50000	−	2.59808i	0.0573121	−	0.0992674i
$686$		0			0
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$		0			0
$689$	−2.00000	+	6.92820i	−0.0761939	+	0.263944i
$690$		0			0
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	0.814548	−	0.580097i	$-0.196985\pi$
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	−0.909652	+	0.415371i	$0.863652\pi$
$692$		0			0
$693$	−25.0000	+	43.3013i	−0.949671	+	1.64488i
$694$		0			0
$695$	−6.50000	+	11.2583i	−0.246559	+	0.427053i
$696$		0			0
$697$	5.00000			0.189389
$698$		0			0
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	21.0000			0.792030
$704$		0			0
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$		0			0
$707$	65.0000			2.44458
$708$		0			0
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	−0.997036	−	0.0769337i	$-0.975487\pi$
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	0.565145	+	0.824992i	$0.308820\pi$
$710$		0			0
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−17.5000	+	4.33013i	−0.654463	+	0.161938i
$716$		0			0
$717$	−4.00000	−	6.92820i	−0.149383	−	0.258738i
$718$		0			0
$719$	16.5000	−	28.5788i	0.615346	−	1.06581i	−0.374978	−	0.927034i	$-0.622350\pi$
$719$	16.5000	−	28.5788i	0.615346	−	1.06581i	0.990324	−	0.138777i	$-0.0443171\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	11.0000			0.409094
$724$		0			0
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−2.50000	−	4.33013i	−0.0924658	−	0.160156i
$732$		0			0
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$		0			0
$735$	9.00000	−	15.5885i	0.331970	−	0.574989i
$736$		0			0
$737$	7.50000	−	12.9904i	0.276266	−	0.478507i
$738$		0			0
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	0.970360	−	0.241665i	$-0.0776935\pi$
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	−0.694468	+	0.719524i	$0.744360\pi$
$740$		0			0
$741$	−3.00000	+	10.3923i	−0.110208	+	0.381771i
$742$		0			0
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	0.771598	−	0.636111i	$-0.219458\pi$
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	−0.936687	+	0.350168i	$0.886124\pi$
$744$		0			0
$745$	5.50000	−	9.52628i	0.201504	−	0.349016i
$746$		0			0
$747$	−12.0000	+	20.7846i	−0.439057	+	0.760469i
$748$		0			0
$749$	−45.0000			−1.64426
$750$		0			0
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	0.542621	−	0.839978i	$-0.317432\pi$
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	−0.998752	+	0.0499348i	$0.984099\pi$
$752$		0			0
$753$	15.0000			0.546630
$754$		0			0
$755$	−24.0000			−0.873449
$756$		0			0
$757$	4.50000	+	7.79423i	0.163555	+	0.283286i	0.936141	−	0.351624i	$-0.114370\pi$
$757$	4.50000	+	7.79423i	0.163555	+	0.283286i	−0.772586	+	0.634910i	$0.781037\pi$
$758$		0			0
$759$	−15.0000			−0.544466
$760$		0			0
$761$	−9.50000	+	16.4545i	−0.344375	+	0.596475i	−0.985240	−	0.171179i	$-0.945242\pi$
$761$	−9.50000	+	16.4545i	−0.344375	+	0.596475i	0.640865	+	0.767653i	$0.278576\pi$
$762$		0			0
$763$	45.0000	−	77.9423i	1.62911	−	2.82170i
$764$		0			0
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$		0			0
$767$	−27.5000	−	28.5788i	−0.992967	−	1.03192i
$768$		0			0
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	0.642332	−	0.766426i	$-0.277967\pi$
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	−0.984911	+	0.173063i	$0.944634\pi$
$770$		0			0
$771$	−7.50000	+	12.9904i	−0.270106	+	0.467837i
$772$		0			0
$773$	18.5000	−	32.0429i	0.665399	−	1.15250i	−0.313778	−	0.949496i	$-0.601595\pi$
$773$	18.5000	−	32.0429i	0.665399	−	1.15250i	0.979177	−	0.203008i	$-0.0650718\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	17.5000	+	30.3109i	0.627809	+	1.08740i
$778$		0			0
$779$	−15.0000			−0.537431
$780$		0			0
$781$	−65.0000			−2.32588
$782$		0			0
$783$	−2.50000	−	4.33013i	−0.0893427	−	0.154746i
$784$		0			0
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−5.50000	+	9.52628i	−0.196054	+	0.339575i	−0.947245	−	0.320509i	$-0.896146\pi$
$787$	−5.50000	+	9.52628i	−0.196054	+	0.339575i	0.751192	+	0.660084i	$0.229479\pi$
$788$		0			0
$789$	5.50000	−	9.52628i	0.195805	−	0.339145i
$790$		0			0
$791$	−2.50000	−	4.33013i	−0.0888898	−	0.153962i
$792$		0			0
$793$	32.5000	+	33.7750i	1.15411	+	1.19939i
$794$		0			0
$795$	1.00000	+	1.73205i	0.0354663	+	0.0614295i
$796$		0			0
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$		0			0
$801$	−14.0000			−0.494666
$802$		0			0
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$		0			0
$805$	−15.0000			−0.528681
$806$		0			0
$807$	−9.00000			−0.316815
$808$		0			0
$809$	18.5000	+	32.0429i	0.650425	+	1.12657i	0.983020	+	0.183500i	$0.0587427\pi$
$809$	18.5000	+	32.0429i	0.650425	+	1.12657i	−0.332594	+	0.943070i	$0.607924\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		0			0
$813$	3.50000	−	6.06218i	0.122750	−	0.212610i
$814$		0			0
$815$	−2.50000	+	4.33013i	−0.0875712	+	0.151678i
$816$		0			0
$817$	7.50000	+	12.9904i	0.262392	+	0.454476i
$818$		0			0
$819$	35.0000	−	8.66025i	1.22300	−	0.302614i
$820$		0			0
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	0.997397	−	0.0721058i	$-0.0229719\pi$
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	−0.561144	+	0.827718i	$0.689639\pi$
$822$		0			0
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	0.458591	+	0.888648i	$0.348354\pi$
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	−0.998887	+	0.0471726i	$0.984979\pi$
$824$		0			0
$825$	−2.50000	+	4.33013i	−0.0870388	+	0.150756i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	−13.0000			−0.450965
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	6.50000	+	11.2583i	0.224942	+	0.389611i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	0.209200	+	0.977873i	$0.432914\pi$
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	−0.951463	+	0.307763i	$0.900419\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	−15.0000	−	25.9808i	−0.516627	−	0.894825i
$844$		0			0
$845$	11.0000	+	6.92820i	0.378412	+	0.238337i
$846$		0			0
$847$	35.0000	+	60.6218i	1.20261	+	2.08299i
$848$		0			0
$849$	11.5000	−	19.9186i	0.394679	−	0.683604i
$850$		0			0
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$	34.0000			1.16414			0.582069	−	0.813139i	$-0.302243\pi$
$853$	34.0000			1.16414			0.582069	+	0.813139i	$0.302243\pi$
$854$		0			0
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$		0			0
$857$	−26.0000			−0.888143			−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000			−0.888143			−0.444072	+	0.895991i	$0.646466\pi$
$858$		0			0
$859$	36.0000			1.22830			0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000			1.22830			0.614152	+	0.789188i	$0.289498\pi$
$860$		0			0
$861$	−12.5000	−	21.6506i	−0.425999	−	0.737852i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	−8.50000	+	14.7224i	−0.289009	+	0.500578i
$866$		0			0
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$		0			0
$869$	−10.0000	−	17.3205i	−0.339227	−	0.587558i
$870$		0			0
$871$	−10.5000	+	2.59808i	−0.355779	+	0.0880325i
$872$		0			0
$873$	11.0000	+	19.0526i	0.372294	+	0.644831i
$874$		0			0
$875$	−2.50000	+	4.33013i	−0.0845154	+	0.146385i
$876$		0			0
$877$	−15.5000	+	26.8468i	−0.523398	+	0.906552i	0.476231	+	0.879320i	$0.342002\pi$
$877$	−15.5000	+	26.8468i	−0.523398	+	0.906552i	−0.999629	+	0.0272316i	$0.991331\pi$
$878$		0			0
$879$	7.00000			0.236104
$880$		0			0
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	0.943847	+	0.330384i	$0.107178\pi$
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	−0.185802	+	0.982587i	$0.559488\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	−11.0000			−0.369761
$886$		0			0
$887$	15.5000	+	26.8468i	0.520439	+	0.901427i	0.999718	+	0.0237640i	$0.00756504\pi$
$887$	15.5000	+	26.8468i	0.520439	+	0.901427i	−0.479279	+	0.877663i	$0.659102\pi$
$888$		0			0
$889$	35.0000			1.17386
$890$		0			0
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$		0			0
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$		0			0
$895$	−5.50000	−	9.52628i	−0.183845	−	0.318428i
$896$		0			0
$897$	7.50000	+	7.79423i	0.250418	+	0.260242i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	1.00000	−	1.73205i	0.0333148	−	0.0577030i
$902$		0			0
$903$	−12.5000	+	21.6506i	−0.415974	+	0.720488i
$904$		0			0
$905$	−10.0000			−0.332411
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$		0			0
$909$	26.0000			0.862366
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	30.0000	+	51.9615i	0.992855	+	1.71968i
$914$		0			0
$915$	13.0000			0.429767
$916$		0			0
$917$	−10.0000	+	17.3205i	−0.330229	+	0.571974i
$918$		0			0
$919$	24.5000	−	42.4352i	0.808180	−	1.39981i	−0.105942	−	0.994372i	$-0.533786\pi$
$919$	24.5000	−	42.4352i	0.808180	−	1.39981i	0.914123	−	0.405437i	$-0.132881\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$		0			0
$923$	32.5000	+	33.7750i	1.06975	+	1.11172i
$924$		0			0
$925$	−3.50000	−	6.06218i	−0.115079	−	0.199323i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	22.5000	−	38.9711i	0.738201	−	1.27860i	−0.215104	−	0.976591i	$-0.569009\pi$
$929$	22.5000	−	38.9711i	0.738201	−	1.27860i	0.953305	−	0.302010i	$-0.0976578\pi$
$930$		0			0
$931$	54.0000			1.76978
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.00000			0.163517
$936$		0			0
$937$	−18.0000			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$938$		0			0
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$	−7.50000	+	12.9904i	−0.244234	+	0.423025i
$944$		0			0
$945$	12.5000	−	21.6506i	0.406625	−	0.704295i
$946$		0			0
$947$	15.5000	+	26.8468i	0.503682	+	0.872403i	0.999991	+	0.00425721i	$0.00135512\pi$
$947$	15.5000	+	26.8468i	0.503682	+	0.872403i	−0.496309	+	0.868146i	$0.665312\pi$
$948$		0			0
$949$	2.00000	−	6.92820i	0.0649227	−	0.224899i
$950$		0			0
$951$	9.00000	+	15.5885i	0.291845	+	0.505490i
$952$		0			0
$953$	−1.50000	+	2.59808i	−0.0485898	+	0.0841599i	−0.889297	−	0.457329i	$-0.848806\pi$
$953$	−1.50000	+	2.59808i	−0.0485898	+	0.0841599i	0.840708	+	0.541489i	$0.182139\pi$
$954$		0			0
$955$	7.50000	−	12.9904i	0.242694	−	0.420359i
$956$		0			0
$957$	−5.00000			−0.161627
$958$		0			0
$959$	7.50000	+	12.9904i	0.242188	+	0.419481i
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−18.0000			−0.580042
$964$		0			0
$965$	11.5000	+	19.9186i	0.370198	+	0.641202i
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$		0			0
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$		0			0
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	−0.916705	−	0.399564i	$-0.869162\pi$
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	0.804385	+	0.594108i	$0.202495\pi$
$972$		0			0
$973$	−32.5000	−	56.2917i	−1.04190	−	1.80463i
$974$		0			0
$975$	3.50000	−	0.866025i	0.112090	−	0.0277350i
$976$		0			0
$977$	22.5000	+	38.9711i	0.719839	+	1.24680i	0.961063	+	0.276328i	$0.0891176\pi$
$977$	22.5000	+	38.9711i	0.719839	+	1.24680i	−0.241225	+	0.970469i	$0.577549\pi$
$978$		0			0
$979$	−17.5000	+	30.3109i	−0.559302	+	0.968740i
$980$		0			0
$981$	18.0000	−	31.1769i	0.574696	−	0.995402i
$982$		0			0
$983$	16.0000			0.510321			0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000			0.510321			0.255160	+	0.966899i	$0.417872\pi$
$984$		0			0
$985$	13.5000	+	23.3827i	0.430146	+	0.745034i
$986$		0			0
$987$	60.0000			1.90982
$988$		0			0
$989$	15.0000			0.476972
$990$		0			0
$991$	1.50000	+	2.59808i	0.0476491	+	0.0825306i	0.888866	−	0.458167i	$-0.151494\pi$
$991$	1.50000	+	2.59808i	0.0476491	+	0.0825306i	−0.841217	+	0.540697i	$0.818160\pi$
$992$		0			0
$993$	−1.00000			−0.0317340
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		0			0
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	−0.916112	−	0.400923i	$-0.868689\pi$
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	0.805266	+	0.592914i	$0.202023\pi$
$998$		0			0
$999$	17.5000	+	30.3109i	0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.f.81.1		2
4.3	odd	2		260.2.i.c.81.1	yes	2
12.11	even	2		2340.2.q.c.2161.1		2
13.9	even	3	inner	1040.2.q.f.321.1		2
20.3	even	4		1300.2.bb.c.549.1		4
20.7	even	4		1300.2.bb.c.549.2		4
20.19	odd	2		1300.2.i.c.601.1		2
52.3	odd	6		3380.2.a.d.1.1		1
52.11	even	12		3380.2.f.c.3041.1		2
52.15	even	12		3380.2.f.c.3041.2		2
52.23	odd	6		3380.2.a.e.1.1		1
52.35	odd	6		260.2.i.c.61.1	✓	2
156.35	even	6		2340.2.q.c.1621.1		2
260.87	even	12		1300.2.bb.c.1049.1		4
260.139	odd	6		1300.2.i.c.1101.1		2
260.243	even	12		1300.2.bb.c.1049.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.c.61.1	✓	2	52.35	odd	6
260.2.i.c.81.1	yes	2	4.3	odd	2
1040.2.q.f.81.1		2	1.1	even	1	trivial
1040.2.q.f.321.1		2	13.9	even	3	inner
1300.2.i.c.601.1		2	20.19	odd	2
1300.2.i.c.1101.1		2	260.139	odd	6
1300.2.bb.c.549.1		4	20.3	even	4
1300.2.bb.c.549.2		4	20.7	even	4
1300.2.bb.c.1049.1		4	260.87	even	12
1300.2.bb.c.1049.2		4	260.243	even	12
2340.2.q.c.1621.1		2	156.35	even	6
2340.2.q.c.2161.1		2	12.11	even	2
3380.2.a.d.1.1		1	52.3	odd	6
3380.2.a.e.1.1		1	52.23	odd	6
3380.2.f.c.3041.1		2	52.11	even	12
3380.2.f.c.3041.2		2	52.15	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{19} -5.00000 q^{21} +(1.50000 + 2.59808i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-2.50000 + 4.33013i) q^{33} +(-2.50000 + 4.33013i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(3.50000 - 0.866025i) q^{39} +(2.50000 + 4.33013i) q^{41} +(2.50000 - 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{45} -12.0000 q^{47} +(-9.00000 - 15.5885i) q^{49} -1.00000 q^{51} +2.00000 q^{53} +(2.50000 + 4.33013i) q^{55} +3.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(6.50000 - 11.2583i) q^{61} +(-5.00000 - 8.66025i) q^{63} +(1.00000 - 3.46410i) q^{65} +(1.50000 + 2.59808i) q^{67} +(1.50000 - 2.59808i) q^{69} +(6.50000 - 11.2583i) q^{71} -2.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} -25.0000 q^{77} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +(-0.500000 + 0.866025i) q^{85} +(0.500000 - 0.866025i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(12.5000 + 12.9904i) q^{91} +(1.50000 - 2.59808i) q^{95} +(-5.50000 + 9.52628i) q^{97} -10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 - 2 * q^5 + 5 * q^7 + 2 * q^9	\( 2 q - q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9} - 5 q^{11} - 2 q^{13} + q^{15} + q^{17} - 3 q^{19} - 10 q^{21} + 3 q^{23} + 2 q^{25} - 10 q^{27} + q^{29} - 5 q^{33} - 5 q^{35} - 7 q^{37} + 7 q^{39} + 5 q^{41} + 5 q^{43} - 2 q^{45} - 24 q^{47} - 18 q^{49} - 2 q^{51} + 4 q^{53} + 5 q^{55} + 6 q^{57} - 11 q^{59} + 13 q^{61} - 10 q^{63} + 2 q^{65} + 3 q^{67} + 3 q^{69} + 13 q^{71} - 4 q^{73} - q^{75} - 50 q^{77} + 8 q^{79} - q^{81} - 24 q^{83} - q^{85} + q^{87} - 7 q^{89} + 25 q^{91} + 3 q^{95} - 11 q^{97} - 20 q^{99}+O(q^{100}) \) 2 * q - q^3 - 2 * q^5 + 5 * q^7 + 2 * q^9 - 5 * q^11 - 2 * q^13 + q^15 + q^17 - 3 * q^19 - 10 * q^21 + 3 * q^23 + 2 * q^25 - 10 * q^27 + q^29 - 5 * q^33 - 5 * q^35 - 7 * q^37 + 7 * q^39 + 5 * q^41 + 5 * q^43 - 2 * q^45 - 24 * q^47 - 18 * q^49 - 2 * q^51 + 4 * q^53 + 5 * q^55 + 6 * q^57 - 11 * q^59 + 13 * q^61 - 10 * q^63 + 2 * q^65 + 3 * q^67 + 3 * q^69 + 13 * q^71 - 4 * q^73 - q^75 - 50 * q^77 + 8 * q^79 - q^81 - 24 * q^83 - q^85 + q^87 - 7 * q^89 + 25 * q^91 + 3 * q^95 - 11 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more