LMFDB - Embedded newform 1040.2.q.j.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.j.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} -1.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(4.50000 + 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{49} +3.00000 q^{51} -6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} -7.00000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(1.00000 + 1.73205i) q^{63} +(1.00000 + 3.46410i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-1.50000 + 2.59808i) q^{71} +2.00000 q^{73} +(0.500000 + 0.866025i) q^{75} -3.00000 q^{77} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(1.50000 - 2.59808i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(2.00000 + 3.46410i) q^{93} +(-3.50000 + 6.06218i) q^{95} +(3.50000 - 6.06218i) q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 2 * q^5 - q^7 + 2 * q^9	$ 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9} + 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 7 q^{19} - 2 q^{21} - 3 q^{23} + 2 q^{25} + 10 q^{27} - 3 q^{29} + 8 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 5 q^{39} + 9 q^{41} + 11 q^{43} + 2 q^{45} + 6 q^{49} + 6 q^{51} - 12 q^{53} + 3 q^{55} - 14 q^{57} - 3 q^{59} - 11 q^{61} + 2 q^{63} + 2 q^{65} - 7 q^{67} + 3 q^{69} - 3 q^{71} + 4 q^{73} + q^{75} - 6 q^{77} - 16 q^{79} - q^{81} + 24 q^{83} + 3 q^{85} + 3 q^{87} - 15 q^{89} - 7 q^{91} + 4 q^{93} - 7 q^{95} + 7 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + 2 * q^5 - q^7 + 2 * q^9 + 3 * q^11 + 2 * q^13 + q^15 + 3 * q^17 - 7 * q^19 - 2 * q^21 - 3 * q^23 + 2 * q^25 + 10 * q^27 - 3 * q^29 + 8 * q^31 - 3 * q^33 - q^35 + 7 * q^37 - 5 * q^39 + 9 * q^41 + 11 * q^43 + 2 * q^45 + 6 * q^49 + 6 * q^51 - 12 * q^53 + 3 * q^55 - 14 * q^57 - 3 * q^59 - 11 * q^61 + 2 * q^63 + 2 * q^65 - 7 * q^67 + 3 * q^69 - 3 * q^71 + 4 * q^73 + q^75 - 6 * q^77 - 16 * q^79 - q^81 + 24 * q^83 + 3 * q^85 + 3 * q^87 - 15 * q^89 - 7 * q^91 + 4 * q^93 - 7 * q^95 + 7 * q^97 + 12 * 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	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		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
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		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
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	−0.0522047	−	0.998636i	$-0.516625\pi$
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	0.890947	−	0.454108i	$-0.150042\pi$
$44$		0			0
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	3.00000			0.420084
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$		0			0
$57$	−7.00000			−0.927173
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$		0			0
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$		0			0
$65$	1.00000	+	3.46410i	0.124035	+	0.429669i
$66$		0			0
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$	−3.50000	−	0.866025i	−0.366900	−	0.0907841i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	−3.50000	+	6.06218i	−0.359092	+	0.621966i
$96$		0			0
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	−0.631810	−	0.775123i	$-0.717688\pi$
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	0.987181	+	0.159602i	$0.0510211\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	−1.00000			−0.0975900
$106$		0			0
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	0.997298	−	0.0734594i	$-0.0234039\pi$
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	−0.562267	+	0.826956i	$0.690071\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−3.50000	+	6.06218i	−0.332205	+	0.575396i
$112$		0			0
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$	7.00000	+	1.73205i	0.647150	+	0.160128i
$118$		0			0
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.50000	−	16.4545i	−0.842989	−	1.46010i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−9.50000	−	16.4545i	−0.842989	−	1.46010i	0.0443678	−	0.999015i	$-0.485873\pi$
$128$		0			0
$129$	11.0000			0.968496
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−3.50000	−	6.06218i	−0.303488	−	0.525657i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$		0			0
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.50000	+	7.79423i	−0.627182	+	0.651786i
$144$		0			0
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$		0			0
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$		0			0
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	−0.0115483	−	0.999933i	$-0.503676\pi$
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	0.871742	−	0.489966i	$-0.162991\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	−0.884943	−	0.465700i	$-0.845802\pi$
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	0.845780	+	0.533533i	$0.179136\pi$
$164$		0			0
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$		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
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	7.00000	+	12.1244i	0.535303	+	0.927173i
$172$		0			0
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$		0			0
$177$	−3.00000			−0.225494
$178$		0			0
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	−0.929114	−	0.369792i	$-0.879429\pi$
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	0.144308	−	0.989533i	$-0.453905\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−11.0000			−0.813143
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$		0			0
$195$	−2.50000	+	2.59808i	−0.179029	+	0.186052i
$196$		0			0
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	−0.948735	−	0.316072i	$-0.897636\pi$
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	0.200641	−	0.979665i	$-0.435697\pi$
$198$		0			0
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$	3.00000			0.210559
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−21.0000			−1.45260
$210$		0			0
$211$	5.50000	+	9.52628i	0.378636	+	0.655816i	0.990864	−	0.134865i	$-0.0430600\pi$
$211$	5.50000	+	9.52628i	0.378636	+	0.655816i	−0.612228	+	0.790681i	$0.709727\pi$
$212$		0			0
$213$	−3.00000			−0.205557
$214$		0			0
$215$	5.50000	−	9.52628i	0.375097	−	0.649687i
$216$		0			0
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$		0			0
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$	10.5000	+	2.59808i	0.706306	+	0.174766i
$222$		0			0
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	−0.986267	−	0.165161i	$-0.947186\pi$
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	0.350100	−	0.936713i	$-0.386148\pi$
$224$		0			0
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$		0			0
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.0634974	−	0.997982i	$-0.479775\pi$
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.832529	−	0.553981i	$-0.186892\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	−1.50000	−	2.59808i	−0.0986928	−	0.170941i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−24.5000	−	6.06218i	−1.55890	−	0.385727i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	−0.317135	−	0.948380i	$-0.602721\pi$
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	0.979889	−	0.199543i	$-0.0639459\pi$
$252$		0			0
$253$	4.50000	−	7.79423i	0.282913	−	0.490019i
$254$		0			0
$255$	3.00000			0.187867
$256$		0			0
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	0.690856	−	0.722993i	$-0.257234\pi$
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$258$		0			0
$259$	−7.00000			−0.434959
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	7.50000	−	12.9904i	0.458993	−	0.794998i
$268$		0			0
$269$	−13.5000	+	23.3827i	−0.823110	+	1.42567i	0.0802460	+	0.996775i	$0.474429\pi$
$269$	−13.5000	+	23.3827i	−0.823110	+	1.42567i	−0.903356	+	0.428892i	$0.858904\pi$
$270$		0			0
$271$	11.5000	+	19.9186i	0.698575	+	1.20997i	0.968960	+	0.247216i	$0.0795156\pi$
$271$	11.5000	+	19.9186i	0.698575	+	1.20997i	−0.270385	+	0.962752i	$0.587151\pi$
$272$		0			0
$273$	−1.00000	−	3.46410i	−0.0605228	−	0.209657i
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$	4.00000	−	6.92820i	0.239474	−	0.414781i
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	0.930714	−	0.365748i	$-0.119187\pi$
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	−0.782104	+	0.623148i	$0.785854\pi$
$284$		0			0
$285$	−7.00000			−0.414644
$286$		0			0
$287$	−9.00000			−0.531253
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	7.00000			0.410347
$292$		0			0
$293$	13.5000	−	23.3827i	0.788678	−	1.36603i	−0.138098	−	0.990419i	$-0.544099\pi$
$293$	13.5000	−	23.3827i	0.788678	−	1.36603i	0.926777	−	0.375613i	$-0.122568\pi$
$294$		0			0
$295$	−1.50000	+	2.59808i	−0.0873334	+	0.151266i
$296$		0			0
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$		0			0
$299$	7.50000	−	7.79423i	0.433736	−	0.450752i
$300$		0			0
$301$	5.50000	+	9.52628i	0.317015	+	0.549086i
$302$		0			0
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$		0			0
$305$	−5.50000	+	9.52628i	−0.314929	+	0.545473i
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$		0			0
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$		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
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$		0			0
$323$	10.5000	+	18.1865i	0.584236	+	1.01193i
$324$		0			0
$325$	1.00000	+	3.46410i	0.0554700	+	0.192154i
$326$		0			0
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	0.477500	+	0.878632i	$0.341543\pi$
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	−0.999667	+	0.0257885i	$0.991790\pi$
$332$		0			0
$333$	14.0000			0.767195
$334$		0			0
$335$	−3.50000	−	6.06218i	−0.191225	−	0.331212i
$336$		0			0
$337$	−34.0000			−1.85210			−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000			−1.85210			−0.926049	+	0.377403i	$0.876817\pi$
$338$		0			0
$339$	−9.00000			−0.488813
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	1.50000	−	2.59808i	0.0807573	−	0.139876i
$346$		0			0
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$		0			0
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	0.879097	−	0.476642i	$-0.158146\pi$
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	−0.852333	+	0.523000i	$0.824813\pi$
$350$		0			0
$351$	5.00000	+	17.3205i	0.266880	+	0.924500i
$352$		0			0
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$	−1.50000	+	2.59808i	−0.0796117	+	0.137892i
$356$		0			0
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$		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
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	2.00000			0.104685
$366$		0			0
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	0.923869	−	0.382709i	$-0.125009\pi$
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	−0.793370	+	0.608740i	$0.791675\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	7.50000	−	7.79423i	0.386270	−	0.401423i
$378$		0			0
$379$	−0.500000	−	0.866025i	−0.0256833	−	0.0444847i	0.852898	−	0.522077i	$-0.174843\pi$
$379$	−0.500000	−	0.866025i	−0.0256833	−	0.0444847i	−0.878581	+	0.477593i	$0.841509\pi$
$380$		0			0
$381$	9.50000	−	16.4545i	0.486700	−	0.842989i
$382$		0			0
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$		0			0
$385$	−3.00000			−0.152894
$386$		0			0
$387$	−11.0000	−	19.0526i	−0.559161	−	0.968496i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$	−8.00000			−0.402524
$396$		0			0
$397$	−2.50000	+	4.33013i	−0.125471	+	0.217323i	−0.921917	−	0.387387i	$-0.873378\pi$
$397$	−2.50000	+	4.33013i	−0.125471	+	0.217323i	0.796446	+	0.604710i	$0.206711\pi$
$398$		0			0
$399$	3.50000	−	6.06218i	0.175219	−	0.303488i
$400$		0			0
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	0.902703	+	0.430263i	$0.141579\pi$
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	−0.0787327	+	0.996896i	$0.525087\pi$
$402$		0			0
$403$	4.00000	+	13.8564i	0.199254	+	0.690237i
$404$		0			0
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		0			0
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	15.0000			0.739895
$412$		0			0
$413$	−1.50000	−	2.59808i	−0.0738102	−	0.127843i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$	5.00000			0.244851
$418$		0			0
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$		0			0
$427$	−5.50000	−	9.52628i	−0.266164	−	0.461009i
$428$		0			0
$429$	−10.5000	−	2.59808i	−0.506945	−	0.125436i
$430$		0			0
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$		0			0
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	0.272736	+	0.962089i	$0.412071\pi$
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	−0.969561	+	0.244848i	$0.921262\pi$
$434$		0			0
$435$	1.50000	−	2.59808i	0.0719195	−	0.124568i
$436$		0			0
$437$	21.0000			1.00457
$438$		0			0
$439$	5.50000	+	9.52628i	0.262501	+	0.454665i	0.966906	−	0.255134i	$-0.0821195\pi$
$439$	5.50000	+	9.52628i	0.262501	+	0.454665i	−0.704405	+	0.709798i	$0.748786\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$		0			0
$447$	21.0000			0.993266
$448$		0			0
$449$	−1.50000	+	2.59808i	−0.0707894	+	0.122611i	−0.899247	−	0.437440i	$-0.855885\pi$
$449$	−1.50000	+	2.59808i	−0.0707894	+	0.122611i	0.828458	+	0.560051i	$0.189218\pi$
$450$		0			0
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$		0			0
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$		0			0
$455$	−3.50000	−	0.866025i	−0.164083	−	0.0405999i
$456$		0			0
$457$	−2.50000	−	4.33013i	−0.116945	−	0.202555i	0.801611	−	0.597847i	$-0.203977\pi$
$457$	−2.50000	−	4.33013i	−0.116945	−	0.202555i	−0.918556	+	0.395292i	$0.870643\pi$
$458$		0			0
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$		0			0
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	0.359044	+	0.933321i	$0.383103\pi$
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	−0.987801	+	0.155719i	$0.950230\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$		0			0
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$		0			0
$473$	33.0000			1.51734
$474$		0			0
$475$	−3.50000	+	6.06218i	−0.160591	+	0.278152i
$476$		0			0
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$		0			0
$479$	19.5000	+	33.7750i	0.890978	+	1.54322i	0.838705	+	0.544586i	$0.183313\pi$
$479$	19.5000	+	33.7750i	0.890978	+	1.54322i	0.0522726	+	0.998633i	$0.483354\pi$
$480$		0			0
$481$	−17.5000	+	18.1865i	−0.797931	+	0.829235i
$482$		0			0
$483$	1.50000	+	2.59808i	0.0682524	+	0.118217i
$484$		0			0
$485$	3.50000	−	6.06218i	0.158927	−	0.275269i
$486$		0			0
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	−0.714083	−	0.700061i	$-0.753156\pi$
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	0.963312	+	0.268384i	$0.0864896\pi$
$488$		0			0
$489$	−1.00000			−0.0452216
$490$		0			0
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$		0			0
$495$	6.00000			0.269680
$496$		0			0
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$		0			0
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	7.50000	−	12.9904i	0.334408	−	0.579212i	−0.648963	−	0.760820i	$-0.724797\pi$
$503$	7.50000	−	12.9904i	0.334408	−	0.579212i	0.983371	+	0.181608i	$0.0581302\pi$
$504$		0			0
$505$	4.50000	+	7.79423i	0.200247	+	0.346839i
$506$		0			0
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$		0			0
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	0.948353	−	0.317217i	$-0.102748\pi$
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	−0.748894	+	0.662690i	$0.769415\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$		0			0
$513$	−17.5000	+	30.3109i	−0.772644	+	1.33826i
$514$		0			0
$515$	−8.00000			−0.352522
$516$		0			0
$517$		0			0
$518$		0			0
$519$	3.00000			0.131685
$520$		0			0
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	0.986718	+	0.162446i	$0.0519382\pi$
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	−0.352677	+	0.935745i	$0.614728\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$		0			0
$533$	−22.5000	+	23.3827i	−0.974583	+	1.01282i
$534$		0			0
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$		0			0
$537$	10.5000	−	18.1865i	0.453108	−	0.784807i
$538$		0			0
$539$	−9.00000	+	15.5885i	−0.387657	+	0.671442i
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$		0			0
$543$	1.00000	+	1.73205i	0.0429141	+	0.0743294i
$544$		0			0
$545$	2.00000			0.0856706
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$		0			0
$549$	11.0000	+	19.0526i	0.469469	+	0.813143i
$550$		0			0
$551$	21.0000			0.894630
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$		0			0
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	0.900967	+	0.433888i	$0.142859\pi$
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	−0.0747252	+	0.997204i	$0.523808\pi$
$558$		0			0
$559$	38.5000	+	9.52628i	1.62838	+	0.402919i
$560$		0			0
$561$	4.50000	+	7.79423i	0.189990	+	0.329073i
$562$		0			0
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$		0			0
$565$	−4.50000	+	7.79423i	−0.189316	+	0.327906i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$		0			0
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$		0			0
$573$	−3.00000			−0.125327
$574$		0			0
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	2.50000	−	4.33013i	0.103896	−	0.179954i
$580$		0			0
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$		0			0
$585$	7.00000	+	1.73205i	0.289414	+	0.0716115i
$586$		0			0
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$		0			0
$589$	−14.0000	+	24.2487i	−0.576860	+	0.999151i
$590$		0			0
$591$	10.5000	−	18.1865i	0.431912	−	0.748094i
$592$		0			0
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$	1.50000	+	2.59808i	0.0614940	+	0.106511i
$596$		0			0
$597$	17.0000			0.695764
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$	−14.0000			−0.570124
$604$		0			0
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$		0			0
$609$	1.50000	+	2.59808i	0.0607831	+	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.863655	+	0.504084i	$0.168170\pi$
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.00472215	+	0.999989i	$0.498497\pi$
$614$		0			0
$615$	−4.50000	+	7.79423i	−0.181458	+	0.314294i
$616$		0			0
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	0.315219	+	0.949019i	$0.397922\pi$
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	−0.979484	+	0.201522i	$0.935411\pi$
$618$		0			0
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$		0			0
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$		0			0
$623$	15.0000			0.600962
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−10.5000	−	18.1865i	−0.419330	−	0.726300i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	−0.645748	−	0.763550i	$-0.723455\pi$
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	0.984128	+	0.177459i	$0.0567879\pi$
$632$		0			0
$633$	−5.50000	+	9.52628i	−0.218605	+	0.378636i
$634$		0			0
$635$	−9.50000	−	16.4545i	−0.376996	−	0.652976i
$636$		0			0
$637$	−15.0000	+	15.5885i	−0.594322	+	0.617637i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		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
$643$	5.50000	−	9.52628i	0.216899	−	0.375680i	−0.736959	−	0.675937i	$-0.763739\pi$
$643$	5.50000	−	9.52628i	0.216899	−	0.375680i	0.953858	+	0.300257i	$0.0970725\pi$
$644$		0			0
$645$	11.0000			0.433125
$646$		0			0
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.846210	+	0.532850i	$0.178879\pi$
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.0383563	+	0.999264i	$0.487788\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$	−4.00000			−0.156772
$652$		0			0
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	12.0000			0.468879
$656$		0			0
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$		0			0
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$		0			0
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	0.875585	−	0.483063i	$-0.160476\pi$
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	−0.856138	+	0.516748i	$0.827143\pi$
$662$		0			0
$663$	3.00000	+	10.3923i	0.116510	+	0.403604i
$664$		0			0
$665$	−3.50000	−	6.06218i	−0.135724	−	0.235081i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$		0			0
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	−33.0000			−1.27395
$672$		0			0
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	0.654394	−	0.756153i	$-0.272924\pi$
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	−0.982045	+	0.188645i	$0.939590\pi$
$674$		0			0
$675$	5.00000			0.192450
$676$		0			0
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$		0			0
$679$	3.50000	+	6.06218i	0.134318	+	0.232645i
$680$		0			0
$681$	27.0000			1.03464
$682$		0			0
$683$	25.5000	−	44.1673i	0.975730	−	1.69001i	0.298227	−	0.954495i	$-0.403605\pi$
$683$	25.5000	−	44.1673i	0.975730	−	1.69001i	0.677503	−	0.735520i	$-0.263062\pi$
$684$		0			0
$685$	7.50000	−	12.9904i	0.286560	−	0.496337i
$686$		0			0
$687$	−11.0000	−	19.0526i	−0.419676	−	0.726900i
$688$		0			0
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$		0			0
$691$	11.5000	+	19.9186i	0.437481	+	0.757739i	0.997494	−	0.0707446i	$-0.0225375\pi$
$691$	11.5000	+	19.9186i	0.437481	+	0.757739i	−0.560014	+	0.828483i	$0.689204\pi$
$692$		0			0
$693$	−3.00000	+	5.19615i	−0.113961	+	0.197386i
$694$		0			0
$695$	2.50000	−	4.33013i	0.0948304	−	0.164251i
$696$		0			0
$697$	27.0000			1.02270
$698$		0			0
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−49.0000			−1.84807
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.00000			−0.338480
$708$		0			0
$709$	18.5000	−	32.0429i	0.694782	−	1.20340i	−0.275472	−	0.961309i	$-0.588834\pi$
$709$	18.5000	−	32.0429i	0.694782	−	1.20340i	0.970254	−	0.242089i	$-0.0778325\pi$
$710$		0			0
$711$	−8.00000	+	13.8564i	−0.300023	+	0.519656i
$712$		0			0
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$		0			0
$715$	−7.50000	+	7.79423i	−0.280484	+	0.291488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$		0			0
$723$	1.00000			0.0371904
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	52.0000			1.92857			0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000			1.92857			0.964287	+	0.264861i	$0.0853260\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−16.5000	−	28.5788i	−0.610275	−	1.05703i
$732$		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
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$		0			0
$737$	10.5000	−	18.1865i	0.386772	−	0.669910i
$738$		0			0
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	0.867581	+	0.497296i	$0.165674\pi$
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	−0.00311943	+	0.999995i	$0.500993\pi$
$740$		0			0
$741$	−7.00000	−	24.2487i	−0.257151	−	0.890799i
$742$		0			0
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$		0			0
$745$	10.5000	−	18.1865i	0.384690	−	0.666303i
$746$		0			0
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$		0			0
$749$	−9.00000			−0.328853
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$		0			0
$753$	21.0000			0.765283
$754$		0			0
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−14.5000	−	25.1147i	−0.527011	−	0.912811i	−0.999505	−	0.0314762i	$-0.989979\pi$
$757$	−14.5000	−	25.1147i	−0.527011	−	0.912811i	0.472493	−	0.881334i	$-0.343354\pi$
$758$		0			0
$759$	9.00000			0.326679
$760$		0			0
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		0			0
$763$	−1.00000	+	1.73205i	−0.0362024	+	0.0627044i
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$	−10.5000	−	2.59808i	−0.379133	−	0.0938111i
$768$		0			0
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	0.959097	−	0.283078i	$-0.0913554\pi$
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	−0.724701	+	0.689063i	$0.758022\pi$
$770$		0			0
$771$	4.50000	−	7.79423i	0.162064	−	0.280702i
$772$		0			0
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	−0.514301	−	0.857610i	$-0.671949\pi$
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	0.999862	+	0.0165929i	$0.00528194\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$	−3.50000	−	6.06218i	−0.125562	−	0.217479i
$778$		0			0
$779$	−63.0000			−2.25721
$780$		0			0
$781$	−9.00000			−0.322045
$782$		0			0
$783$	−7.50000	−	12.9904i	−0.268028	−	0.464238i
$784$		0			0
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−18.5000	+	32.0429i	−0.659454	+	1.14221i	0.321303	+	0.946976i	$0.395879\pi$
$787$	−18.5000	+	32.0429i	−0.659454	+	1.14221i	−0.980757	+	0.195231i	$0.937454\pi$
$788$		0			0
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$		0			0
$791$	−4.50000	−	7.79423i	−0.160002	−	0.277131i
$792$		0			0
$793$	−38.5000	−	9.52628i	−1.36718	−	0.338288i
$794$		0			0
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$		0			0
$797$	25.5000	−	44.1673i	0.903256	−	1.56449i	0.0800155	−	0.996794i	$-0.474503\pi$
$797$	25.5000	−	44.1673i	0.903256	−	1.56449i	0.823241	−	0.567692i	$-0.192164\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−30.0000			−1.06000
$802$		0			0
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$	3.00000			0.105736
$806$		0			0
$807$	−27.0000			−0.950445
$808$		0			0
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	0.703533	−	0.710663i	$-0.251605\pi$
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	−0.967219	+	0.253946i	$0.918272\pi$
$810$		0			0
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$	−11.5000	+	19.9186i	−0.403323	+	0.698575i
$814$		0			0
$815$	−0.500000	+	0.866025i	−0.0175142	+	0.0303355i
$816$		0			0
$817$	38.5000	+	66.6840i	1.34694	+	2.33298i
$818$		0			0
$819$	−5.00000	+	5.19615i	−0.174714	+	0.181568i
$820$		0			0
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$		0			0
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	−0.956791	−	0.290776i	$-0.906086\pi$
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	0.730215	+	0.683217i	$0.239420\pi$
$824$		0			0
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	19.0000			0.659103
$832$		0			0
$833$	18.0000			0.623663
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$	20.0000			0.691301
$838$		0			0
$839$	10.5000	−	18.1865i	0.362500	−	0.627869i	−0.625871	−	0.779926i	$-0.715257\pi$
$839$	10.5000	−	18.1865i	0.362500	−	0.627869i	0.988372	+	0.152057i	$0.0485899\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$		0			0
$845$	−11.0000	+	6.92820i	−0.378412	+	0.238337i
$846$		0			0
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$		0			0
$849$	−2.50000	+	4.33013i	−0.0857998	+	0.148610i
$850$		0			0
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$	7.00000	+	12.1244i	0.239395	+	0.414644i
$856$		0			0
$857$	−30.0000			−1.02478			−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000			−1.02478			−0.512390	+	0.858753i	$0.671240\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$		0			0
$861$	−4.50000	−	7.79423i	−0.153360	−	0.265627i
$862$		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
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$		0			0
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	17.5000	−	18.1865i	0.592965	−	0.616227i
$872$		0			0
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$		0			0
$877$	−20.5000	+	35.5070i	−0.692236	+	1.19899i	0.278868	+	0.960329i	$0.410041\pi$
$877$	−20.5000	+	35.5070i	−0.692236	+	1.19899i	−0.971104	+	0.238658i	$0.923292\pi$
$878$		0			0
$879$	27.0000			0.910687
$880$		0			0
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	0.543852	−	0.839181i	$-0.316965\pi$
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	−0.998678	+	0.0513987i	$0.983632\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$	−3.00000			−0.100844
$886$		0			0
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	0.931630	−	0.363407i	$-0.118387\pi$
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	−0.780535	+	0.625112i	$0.785053\pi$
$888$		0			0
$889$	19.0000			0.637240
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−10.5000	−	18.1865i	−0.350976	−	0.607909i
$896$		0			0
$897$	10.5000	+	2.59808i	0.350585	+	0.0867472i
$898$		0			0
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$		0			0
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	−5.50000	+	9.52628i	−0.183029	+	0.317015i
$904$		0			0
$905$	2.00000			0.0664822
$906$		0			0
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$		0			0
$915$	−11.0000			−0.363649
$916$		0			0
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$		0			0
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	−0.521380	−	0.853325i	$-0.674583\pi$
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	0.999691	+	0.0248659i	$0.00791589\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$		0			0
$923$	−10.5000	−	2.59808i	−0.345612	−	0.0855167i
$924$		0			0
$925$	3.50000	+	6.06218i	0.115079	+	0.199323i
$926$		0			0
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$		0			0
$929$	−25.5000	+	44.1673i	−0.836628	+	1.44908i	0.0560703	+	0.998427i	$0.482143\pi$
$929$	−25.5000	+	44.1673i	−0.836628	+	1.44908i	−0.892698	+	0.450655i	$0.851190\pi$
$930$		0			0
$931$	−42.0000			−1.37649
$932$		0			0
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$		0			0
$935$	9.00000			0.294331
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	−11.0000	−	19.0526i	−0.358971	−	0.621757i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$	−2.50000	+	4.33013i	−0.0813250	+	0.140859i
$946$		0			0
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	0.984657	−	0.174503i	$-0.0558319\pi$
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	−0.643452	+	0.765486i	$0.722499\pi$
$948$		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
$953$	25.5000	−	44.1673i	0.826026	−	1.43072i	−0.0751066	−	0.997176i	$-0.523930\pi$
$953$	25.5000	−	44.1673i	0.826026	−	1.43072i	0.901133	−	0.433544i	$-0.142737\pi$
$954$		0			0
$955$	−1.50000	+	2.59808i	−0.0485389	+	0.0840718i
$956$		0			0
$957$	9.00000			0.290929
$958$		0			0
$959$	7.50000	+	12.9904i	0.242188	+	0.419481i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	18.0000			0.580042
$964$		0			0
$965$	−2.50000	−	4.33013i	−0.0804778	−	0.139392i
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$		0			0
$969$	−10.5000	+	18.1865i	−0.337309	+	0.584236i
$970$		0			0
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	−0.646899	−	0.762576i	$-0.723934\pi$
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	0.983860	+	0.178942i	$0.0572676\pi$
$972$		0			0
$973$	2.50000	+	4.33013i	0.0801463	+	0.138817i
$974$		0			0
$975$	−2.50000	+	2.59808i	−0.0800641	+	0.0832050i
$976$		0			0
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$		0			0
$981$	2.00000	−	3.46410i	0.0638551	−	0.110600i
$982$		0			0
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	−10.5000	−	18.1865i	−0.334558	−	0.579471i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−33.0000			−1.04934
$990$		0			0
$991$	−30.5000	−	52.8275i	−0.968864	−	1.67812i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−30.5000	−	52.8275i	−0.968864	−	1.67812i	−0.270011	−	0.962857i	$-0.587027\pi$
$992$		0			0
$993$	−19.0000			−0.602947
$994$		0			0
$995$	8.50000	−	14.7224i	0.269468	−	0.466732i
$996$		0			0
$997$	15.5000	−	26.8468i	0.490890	−	0.850246i	−0.509055	−	0.860734i	$-0.670005\pi$
$997$	15.5000	−	26.8468i	0.490890	−	0.850246i	0.999945	+	0.0104877i	$0.00333839\pi$
$998$		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.j.81.1		2
4.3	odd	2		260.2.i.b.81.1	yes	2
12.11	even	2		2340.2.q.b.2161.1		2
13.9	even	3	inner	1040.2.q.j.321.1		2
20.3	even	4		1300.2.bb.a.549.2		4
20.7	even	4		1300.2.bb.a.549.1		4
20.19	odd	2		1300.2.i.e.601.1		2
52.3	odd	6		3380.2.a.h.1.1		1
52.11	even	12		3380.2.f.e.3041.2		2
52.15	even	12		3380.2.f.e.3041.1		2
52.23	odd	6		3380.2.a.g.1.1		1
52.35	odd	6		260.2.i.b.61.1	✓	2
156.35	even	6		2340.2.q.b.1621.1		2
260.87	even	12		1300.2.bb.a.1049.2		4
260.139	odd	6		1300.2.i.e.1101.1		2
260.243	even	12		1300.2.bb.a.1049.1		4

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} -1.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(4.50000 + 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{49} +3.00000 q^{51} -6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} -7.00000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(1.00000 + 1.73205i) q^{63} +(1.00000 + 3.46410i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-1.50000 + 2.59808i) q^{71} +2.00000 q^{73} +(0.500000 + 0.866025i) q^{75} -3.00000 q^{77} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(1.50000 - 2.59808i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(2.00000 + 3.46410i) q^{93} +(-3.50000 + 6.06218i) q^{95} +(3.50000 - 6.06218i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 2 * q^5 - q^7 + 2 * q^9	\( 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9} + 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 7 q^{19} - 2 q^{21} - 3 q^{23} + 2 q^{25} + 10 q^{27} - 3 q^{29} + 8 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 5 q^{39} + 9 q^{41} + 11 q^{43} + 2 q^{45} + 6 q^{49} + 6 q^{51} - 12 q^{53} + 3 q^{55} - 14 q^{57} - 3 q^{59} - 11 q^{61} + 2 q^{63} + 2 q^{65} - 7 q^{67} + 3 q^{69} - 3 q^{71} + 4 q^{73} + q^{75} - 6 q^{77} - 16 q^{79} - q^{81} + 24 q^{83} + 3 q^{85} + 3 q^{87} - 15 q^{89} - 7 q^{91} + 4 q^{93} - 7 q^{95} + 7 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + 2 * q^5 - q^7 + 2 * q^9 + 3 * q^11 + 2 * q^13 + q^15 + 3 * q^17 - 7 * q^19 - 2 * q^21 - 3 * q^23 + 2 * q^25 + 10 * q^27 - 3 * q^29 + 8 * q^31 - 3 * q^33 - q^35 + 7 * q^37 - 5 * q^39 + 9 * q^41 + 11 * q^43 + 2 * q^45 + 6 * q^49 + 6 * q^51 - 12 * q^53 + 3 * q^55 - 14 * q^57 - 3 * q^59 - 11 * q^61 + 2 * q^63 + 2 * q^65 - 7 * q^67 + 3 * q^69 - 3 * q^71 + 4 * q^73 + q^75 - 6 * q^77 - 16 * q^79 - q^81 + 24 * q^83 + 3 * q^85 + 3 * q^87 - 15 * q^89 - 7 * q^91 + 4 * q^93 - 7 * q^95 + 7 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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