LMFDB - Embedded newform 1040.2.q.o.321.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.2
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	1040.321
Dual form			1040.2.q.o.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(0.802776 - 1.39045i) q^{11} -3.60555 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-3.80278 - 6.58660i) q^{17} +(-2.80278 - 4.85455i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(3.10555 - 5.37897i) q^{29} +4.00000 q^{31} +(-0.802776 - 1.39045i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-1.80278 + 3.12250i) q^{37} +(-1.80278 + 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-5.10555 - 8.84307i) q^{43} +(-1.00000 - 1.73205i) q^{45} -9.21110 q^{47} +(3.00000 - 5.19615i) q^{49} -7.60555 q^{51} -3.21110 q^{53} +(-0.802776 + 1.39045i) q^{55} -5.60555 q^{57} +(-5.40833 - 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} +3.60555 q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(2.40833 + 4.17134i) q^{71} -0.788897 q^{73} +(0.500000 - 0.866025i) q^{75} -1.60555 q^{77} -5.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.21110 q^{83} +(3.80278 + 6.58660i) q^{85} +(-3.10555 - 5.37897i) q^{87} +(3.10555 - 5.37897i) q^{89} +(1.80278 + 3.12250i) q^{91} +(2.00000 - 3.46410i) q^{93} +(2.80278 + 4.85455i) q^{95} +(4.19722 + 7.26981i) q^{97} +3.21110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 4 q^{9} - 4 q^{11} - 2 q^{15} - 8 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 4 q^{25} + 20 q^{27} - 2 q^{29} + 16 q^{31} + 4 q^{33} + 2 q^{35} - 6 q^{41} - 6 q^{43} - 4 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 4 * q^9 - 4 * q^11 - 2 * q^15 - 8 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 4 * q^25 + 20 * q^27 - 2 * q^29 + 16 * q^31 + 4 * q^33 + 2 * q^35 - 6 * q^41 - 6 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 16 * q^51 + 16 * q^53 + 4 * q^55 - 8 * q^57 + 2 * q^61 + 4 * q^63 - 14 * q^67 + 6 * q^69 - 12 * q^71 - 32 * q^73 + 2 * q^75 + 8 * q^77 + 8 * q^79 - 2 * q^81 + 8 * q^83 + 8 * q^85 + 2 * q^87 - 2 * q^89 + 8 * q^93 + 4 * q^95 + 24 * q^97 - 16 * q^99

Character values

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

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	0.802776	−	1.39045i	0.242046	−	0.419236i	−0.719251	−	0.694750i	$-0.755515\pi$
$11$	0.802776	−	1.39045i	0.242046	−	0.419236i	0.961297	+	0.275514i	$0.0888482\pi$
$12$		0			0
$13$	−3.60555			−1.00000
$13$	−3.60555			−1.00000
$14$		0			0
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$		0			0
$17$	−3.80278	−	6.58660i	−0.922309	−	1.59749i	−0.795834	−	0.605516i	$-0.792967\pi$
$17$	−3.80278	−	6.58660i	−0.922309	−	1.59749i	−0.126475	−	0.991970i	$-0.540366\pi$
$18$		0			0
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	−0.984759	−	0.173922i	$-0.944356\pi$
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	0.341759	−	0.939788i	$-0.388977\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	3.10555	−	5.37897i	0.576686	−	0.998850i	−0.419170	−	0.907908i	$-0.637679\pi$
$29$	3.10555	−	5.37897i	0.576686	−	0.998850i	0.995856	−	0.0909423i	$-0.0289879\pi$
$30$		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
$33$	−0.802776	−	1.39045i	−0.139745	−	0.242046i
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	−1.80278	+	3.12250i	−0.296374	+	0.513336i	−0.975304	−	0.220868i	$-0.929111\pi$
$37$	−1.80278	+	3.12250i	−0.296374	+	0.513336i	0.678929	+	0.734204i	$0.262444\pi$
$38$		0			0
$39$	−1.80278	+	3.12250i	−0.288675	+	0.500000i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−5.10555	−	8.84307i	−0.778589	−	1.34856i	−0.932755	−	0.360511i	$-0.882602\pi$
$43$	−5.10555	−	8.84307i	−0.778589	−	1.34856i	0.154166	−	0.988045i	$-0.450731\pi$
$44$		0			0
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$		0			0
$47$	−9.21110			−1.34358			−0.671789	−	0.740743i	$-0.734474\pi$
$47$	−9.21110			−1.34358			−0.671789	+	0.740743i	$0.734474\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	−7.60555			−1.06499
$52$		0			0
$53$	−3.21110			−0.441079			−0.220539	−	0.975378i	$-0.570782\pi$
$53$	−3.21110			−0.441079			−0.220539	+	0.975378i	$0.570782\pi$
$54$		0			0
$55$	−0.802776	+	1.39045i	−0.108246	+	0.187488i
$56$		0			0
$57$	−5.60555			−0.742473
$58$		0			0
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	−0.967014	−	0.254724i	$-0.918015\pi$
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	0.262910	−	0.964820i	$-0.415318\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$		0			0
$65$	3.60555			0.447214
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	2.40833	+	4.17134i	0.285816	+	0.495048i	0.972807	−	0.231619i	$-0.0744021\pi$
$71$	2.40833	+	4.17134i	0.285816	+	0.495048i	−0.686991	+	0.726666i	$0.741069\pi$
$72$		0			0
$73$	−0.788897			−0.0923335			−0.0461667	−	0.998934i	$-0.514701\pi$
$73$	−0.788897			−0.0923335			−0.0461667	+	0.998934i	$0.514701\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	−1.60555			−0.182970
$78$		0			0
$79$	−5.21110			−0.586295			−0.293147	−	0.956067i	$-0.594703\pi$
$79$	−5.21110			−0.586295			−0.293147	+	0.956067i	$0.594703\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.21110			1.01105			0.505525	−	0.862812i	$-0.331299\pi$
$83$	9.21110			1.01105			0.505525	+	0.862812i	$0.331299\pi$
$84$		0			0
$85$	3.80278	+	6.58660i	0.412469	+	0.714417i
$86$		0			0
$87$	−3.10555	−	5.37897i	−0.332950	−	0.576686i
$88$		0			0
$89$	3.10555	−	5.37897i	0.329188	−	0.570170i	−0.653163	−	0.757217i	$-0.726558\pi$
$89$	3.10555	−	5.37897i	0.329188	−	0.570170i	0.982351	+	0.187047i	$0.0598918\pi$
$90$		0			0
$91$	1.80278	+	3.12250i	0.188982	+	0.327327i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$	2.80278	+	4.85455i	0.287559	+	0.498066i
$96$		0			0
$97$	4.19722	+	7.26981i	0.426164	+	0.738137i	0.996528	−	0.0832546i	$-0.0265315\pi$
$97$	4.19722	+	7.26981i	0.426164	+	0.738137i	−0.570365	+	0.821392i	$0.693198\pi$
$98$		0			0
$99$	3.21110			0.322728
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$		0			0
$107$	3.10555	−	5.37897i	0.300225	−	0.520005i	−0.675962	−	0.736937i	$-0.736272\pi$
$107$	3.10555	−	5.37897i	0.300225	−	0.520005i	0.976187	+	0.216932i	$0.0696049\pi$
$108$		0			0
$109$	−19.2111			−1.84009			−0.920045	−	0.391813i	$-0.871848\pi$
$109$	−19.2111			−1.84009			−0.920045	+	0.391813i	$0.871848\pi$
$110$		0			0
$111$	1.80278	+	3.12250i	0.171112	+	0.296374i
$112$		0			0
$113$	0.802776	+	1.39045i	0.0755188	+	0.130802i	0.901312	−	0.433171i	$-0.142605\pi$
$113$	0.802776	+	1.39045i	0.0755188	+	0.130802i	−0.825793	+	0.563973i	$0.809272\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$		0			0
$117$	−3.60555	−	6.24500i	−0.333333	−	0.577350i
$118$		0			0
$119$	−3.80278	+	6.58660i	−0.348600	+	0.603793i
$120$		0			0
$121$	4.21110	+	7.29384i	0.382828	+	0.663077i
$122$		0			0
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.10555	+	3.64692i	−0.186837	+	0.323612i	−0.944194	−	0.329389i	$-0.893157\pi$
$127$	−2.10555	+	3.64692i	−0.186837	+	0.323612i	0.757357	+	0.653001i	$0.226490\pi$
$128$		0			0
$129$	−10.2111			−0.899037
$130$		0			0
$131$	21.2111			1.85322			0.926611	−	0.376021i	$-0.122708\pi$
$131$	21.2111			1.85322			0.926611	+	0.376021i	$0.122708\pi$
$132$		0			0
$133$	−2.80278	+	4.85455i	−0.243031	+	0.420943i
$134$		0			0
$135$	−5.00000			−0.430331
$136$		0			0
$137$	0.802776	+	1.39045i	0.0685858	+	0.118794i	0.898279	−	0.439426i	$-0.144818\pi$
$137$	0.802776	+	1.39045i	0.0685858	+	0.118794i	−0.829693	+	0.558220i	$0.811485\pi$
$138$		0			0
$139$	3.19722	+	5.53776i	0.271185	+	0.469706i	0.969166	−	0.246410i	$-0.0792511\pi$
$139$	3.19722	+	5.53776i	0.271185	+	0.469706i	−0.697981	+	0.716117i	$0.745918\pi$
$140$		0			0
$141$	−4.60555	+	7.97705i	−0.387857	+	0.671789i
$142$		0			0
$143$	−2.89445	+	5.01333i	−0.242046	+	0.419236i
$144$		0			0
$145$	−3.10555	+	5.37897i	−0.257902	+	0.446699i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	1.21110			0.0985581			0.0492791	−	0.998785i	$-0.484308\pi$
$151$	1.21110			0.0985581			0.0492791	+	0.998785i	$0.484308\pi$
$152$		0			0
$153$	7.60555	−	13.1732i	0.614872	−	1.06499i
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	11.2111			0.894743			0.447372	−	0.894348i	$-0.352360\pi$
$157$	11.2111			0.894743			0.447372	+	0.894348i	$0.352360\pi$
$158$		0			0
$159$	−1.60555	+	2.78090i	−0.127328	+	0.220539i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−1.89445	−	3.28128i	−0.148385	−	0.257010i	0.782246	−	0.622970i	$-0.214074\pi$
$163$	−1.89445	−	3.28128i	−0.148385	−	0.257010i	−0.930631	+	0.365960i	$0.880741\pi$
$164$		0			0
$165$	0.802776	+	1.39045i	0.0624960	+	0.108246i
$166$		0			0
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	5.60555	−	9.70910i	0.428667	−	0.742473i
$172$		0			0
$173$	−2.40833	−	4.17134i	−0.183102	−	0.317141i	0.759834	−	0.650118i	$-0.225280\pi$
$173$	−2.40833	−	4.17134i	−0.183102	−	0.317141i	−0.942935	+	0.332976i	$0.891947\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$		0			0
$177$	−10.8167			−0.813029
$178$		0			0
$179$	11.4083	−	19.7598i	0.852698	−	1.47692i	−0.0260655	−	0.999660i	$-0.508298\pi$
$179$	11.4083	−	19.7598i	0.852698	−	1.47692i	0.878764	−	0.477257i	$-0.158369\pi$
$180$		0			0
$181$	17.6333			1.31067			0.655337	−	0.755337i	$-0.272527\pi$
$181$	17.6333			1.31067			0.655337	+	0.755337i	$0.272527\pi$
$182$		0			0
$183$	1.00000			0.0739221
$184$		0			0
$185$	1.80278	−	3.12250i	0.132543	−	0.229571i
$186$		0			0
$187$	−12.2111			−0.892964
$188$		0			0
$189$	−2.50000	−	4.33013i	−0.181848	−	0.314970i
$190$		0			0
$191$	8.40833	+	14.5636i	0.608405	+	1.05379i	0.991503	+	0.130081i	$0.0415238\pi$
$191$	8.40833	+	14.5636i	0.608405	+	1.05379i	−0.383098	+	0.923708i	$0.625143\pi$
$192$		0			0
$193$	−7.80278	+	13.5148i	−0.561656	+	0.972817i	0.435696	+	0.900094i	$0.356502\pi$
$193$	−7.80278	+	13.5148i	−0.561656	+	0.972817i	−0.997352	+	0.0727230i	$0.976831\pi$
$194$		0			0
$195$	1.80278	−	3.12250i	0.129099	−	0.223607i
$196$		0			0
$197$	−0.591673	+	1.02481i	−0.0421550	+	0.0730145i	−0.886333	−	0.463048i	$-0.846756\pi$
$197$	−0.591673	+	1.02481i	−0.0421550	+	0.0730145i	0.844178	+	0.536063i	$0.180089\pi$
$198$		0			0
$199$	6.40833	+	11.0995i	0.454274	+	0.786826i	0.998646	−	0.0520179i	$-0.0165653\pi$
$199$	6.40833	+	11.0995i	0.454274	+	0.786826i	−0.544372	+	0.838844i	$0.683232\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$	−6.21110			−0.435934
$204$		0			0
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$		0			0
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−11.8028	+	20.4430i	−0.812537	+	1.40735i	0.0985467	+	0.995132i	$0.468581\pi$
$211$	−11.8028	+	20.4430i	−0.812537	+	1.40735i	−0.911083	+	0.412222i	$0.864753\pi$
$212$		0			0
$213$	4.81665			0.330032
$214$		0			0
$215$	5.10555	+	8.84307i	0.348196	+	0.603093i
$216$		0			0
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$		0			0
$219$	−0.394449	+	0.683205i	−0.0266544	+	0.0461667i
$220$		0			0
$221$	13.7111	+	23.7483i	0.922309	+	1.59749i
$222$		0			0
$223$	−2.10555	+	3.64692i	−0.140998	+	0.244216i	−0.927873	−	0.372897i	$-0.878364\pi$
$223$	−2.10555	+	3.64692i	−0.140998	+	0.244216i	0.786875	+	0.617113i	$0.211698\pi$
$224$		0			0
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$		0			0
$227$	−13.7111	−	23.7483i	−0.910038	−	1.57623i	−0.814008	−	0.580853i	$-0.802719\pi$
$227$	−13.7111	−	23.7483i	−0.910038	−	1.57623i	−0.0960296	−	0.995378i	$-0.530614\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$	−0.802776	+	1.39045i	−0.0528188	+	0.0914848i
$232$		0			0
$233$	15.2111			0.996512			0.498256	−	0.867030i	$-0.333974\pi$
$233$	15.2111			0.996512			0.498256	+	0.867030i	$0.333974\pi$
$234$		0			0
$235$	9.21110			0.600866
$236$		0			0
$237$	−2.60555	+	4.51295i	−0.169249	+	0.293147i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−0.894449	−	1.54923i	−0.0576165	−	0.0997947i	0.835778	−	0.549067i	$-0.185017\pi$
$241$	−0.894449	−	1.54923i	−0.0576165	−	0.0997947i	−0.893395	+	0.449272i	$0.851683\pi$
$242$		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
$247$	10.1056	+	17.5033i	0.643001	+	1.11371i
$248$		0			0
$249$	4.60555	−	7.97705i	0.291865	−	0.505525i
$250$		0			0
$251$	−3.59167	−	6.22096i	−0.226704	−	0.392664i	0.730125	−	0.683314i	$-0.239462\pi$
$251$	−3.59167	−	6.22096i	−0.226704	−	0.392664i	−0.956829	+	0.290650i	$0.906128\pi$
$252$		0			0
$253$	2.40833	+	4.17134i	0.151410	+	0.262250i
$254$		0			0
$255$	7.60555			0.476278
$256$		0			0
$257$	8.19722	−	14.1980i	0.511329	−	0.885647i	−0.488585	−	0.872516i	$-0.662487\pi$
$257$	8.19722	−	14.1980i	0.511329	−	0.885647i	0.999914	−	0.0131312i	$-0.00417990\pi$
$258$		0			0
$259$	3.60555			0.224038
$260$		0			0
$261$	12.4222			0.768915
$262$		0			0
$263$	5.89445	−	10.2095i	0.363467	−	0.629544i	−0.625062	−	0.780575i	$-0.714926\pi$
$263$	5.89445	−	10.2095i	0.363467	−	0.629544i	0.988529	+	0.151032i	$0.0482595\pi$
$264$		0			0
$265$	3.21110			0.197256
$266$		0			0
$267$	−3.10555	−	5.37897i	−0.190057	−	0.329188i
$268$		0			0
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$		0			0
$271$	−10.4083	+	18.0278i	−0.632261	+	1.09511i	0.354828	+	0.934932i	$0.384540\pi$
$271$	−10.4083	+	18.0278i	−0.632261	+	1.09511i	−0.987088	+	0.160176i	$0.948794\pi$
$272$		0			0
$273$	3.60555			0.218218
$274$		0			0
$275$	0.802776	−	1.39045i	0.0484092	−	0.0838472i
$276$		0			0
$277$	−13.8028	−	23.9071i	−0.829328	−	1.43644i	−0.898566	−	0.438839i	$-0.855390\pi$
$277$	−13.8028	−	23.9071i	−0.829328	−	1.43644i	0.0692374	−	0.997600i	$-0.477943\pi$
$278$		0			0
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$		0			0
$285$	5.60555			0.332044
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	−20.4222	+	35.3723i	−1.20131	+	2.08072i
$290$		0			0
$291$	8.39445			0.492091
$292$		0			0
$293$	−5.19722	−	9.00186i	−0.303625	−	0.525894i	0.673329	−	0.739343i	$-0.264864\pi$
$293$	−5.19722	−	9.00186i	−0.303625	−	0.525894i	−0.976954	+	0.213449i	$0.931530\pi$
$294$		0			0
$295$	5.40833	+	9.36750i	0.314885	+	0.545397i
$296$		0			0
$297$	4.01388	−	6.95224i	0.232909	−	0.403410i
$298$		0			0
$299$	5.40833	−	9.36750i	0.312772	−	0.541736i
$300$		0			0
$301$	−5.10555	+	8.84307i	−0.294279	+	0.509706i
$302$		0			0
$303$	−4.50000	−	7.79423i	−0.258518	−	0.447767i
$304$		0			0
$305$	−0.500000	−	0.866025i	−0.0286299	−	0.0495885i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$		0			0
$311$	9.21110			0.522314			0.261157	−	0.965296i	$-0.415896\pi$
$311$	9.21110			0.522314			0.261157	+	0.965296i	$0.415896\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$		0			0
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	−4.98612	−	8.63622i	−0.279169	−	0.483535i
$320$		0			0
$321$	−3.10555	−	5.37897i	−0.173335	−	0.300225i
$322$		0			0
$323$	−21.3167	+	36.9215i	−1.18609	+	2.05437i
$324$		0			0
$325$	−3.60555			−0.200000
$326$		0			0
$327$	−9.60555	+	16.6373i	−0.531188	+	0.920045i
$328$		0			0
$329$	4.60555	+	7.97705i	0.253912	+	0.439789i
$330$		0			0
$331$	5.01388	+	8.68429i	0.275588	+	0.477332i	0.970283	−	0.241972i	$-0.0777942\pi$
$331$	5.01388	+	8.68429i	0.275588	+	0.477332i	−0.694696	+	0.719304i	$0.744461\pi$
$332$		0			0
$333$	−7.21110			−0.395166
$334$		0			0
$335$	3.50000	−	6.06218i	0.191225	−	0.331212i
$336$		0			0
$337$	−25.6333			−1.39634			−0.698168	−	0.715934i	$-0.746001\pi$
$337$	−25.6333			−1.39634			−0.698168	+	0.715934i	$0.746001\pi$
$338$		0			0
$339$	1.60555			0.0872016
$340$		0			0
$341$	3.21110	−	5.56179i	0.173891	−	0.301188i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$		0			0
$347$	2.89445	+	5.01333i	0.155382	+	0.269130i	0.933198	−	0.359362i	$-0.117006\pi$
$347$	2.89445	+	5.01333i	0.155382	+	0.269130i	−0.777816	+	0.628492i	$0.783672\pi$
$348$		0			0
$349$	1.89445	−	3.28128i	0.101408	−	0.175643i	−0.810857	−	0.585244i	$-0.800999\pi$
$349$	1.89445	−	3.28128i	0.101408	−	0.175643i	0.912265	+	0.409601i	$0.134332\pi$
$350$		0			0
$351$	−18.0278			−0.962250
$352$		0			0
$353$	−8.40833	+	14.5636i	−0.447530	+	0.775145i	−0.998225	−	0.0595620i	$-0.981030\pi$
$353$	−8.40833	+	14.5636i	−0.447530	+	0.775145i	0.550695	+	0.834707i	$0.314363\pi$
$354$		0			0
$355$	−2.40833	−	4.17134i	−0.127821	−	0.221392i
$356$		0			0
$357$	3.80278	+	6.58660i	0.201264	+	0.348600i
$358$		0			0
$359$	−18.4222			−0.972287			−0.486143	−	0.873879i	$-0.661597\pi$
$359$	−18.4222			−0.972287			−0.486143	+	0.873879i	$0.661597\pi$
$360$		0			0
$361$	−6.21110	+	10.7579i	−0.326900	+	0.566208i
$362$		0			0
$363$	8.42221			0.442051
$364$		0			0
$365$	0.788897			0.0412928
$366$		0			0
$367$	5.71110	−	9.89192i	0.298117	−	0.516354i	−0.677588	−	0.735442i	$-0.736975\pi$
$367$	5.71110	−	9.89192i	0.298117	−	0.516354i	0.975705	+	0.219088i	$0.0703081\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	1.60555	+	2.78090i	0.0833561	+	0.144377i
$372$		0			0
$373$	10.1972	+	17.6621i	0.527992	+	0.914509i	0.999467	+	0.0326301i	$0.0103883\pi$
$373$	10.1972	+	17.6621i	0.527992	+	0.914509i	−0.471475	+	0.881879i	$0.656278\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−11.1972	+	19.3942i	−0.576686	+	0.998850i
$378$		0			0
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	−0.715907	−	0.698196i	$-0.753986\pi$
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	0.962609	+	0.270895i	$0.0873198\pi$
$380$		0			0
$381$	2.10555	+	3.64692i	0.107871	+	0.186837i
$382$		0			0
$383$	−12.3167	−	21.3331i	−0.629352	−	1.09007i	−0.987682	−	0.156474i	$-0.949987\pi$
$383$	−12.3167	−	21.3331i	−0.629352	−	1.09007i	0.358330	−	0.933595i	$-0.383346\pi$
$384$		0			0
$385$	1.60555			0.0818265
$386$		0			0
$387$	10.2111	−	17.6861i	0.519060	−	0.899037i
$388$		0			0
$389$	−15.2111			−0.771234			−0.385617	−	0.922659i	$-0.626011\pi$
$389$	−15.2111			−0.771234			−0.385617	+	0.922659i	$0.626011\pi$
$390$		0			0
$391$	22.8167			1.15389
$392$		0			0
$393$	10.6056	−	18.3694i	0.534979	−	0.926611i
$394$		0			0
$395$	5.21110			0.262199
$396$		0			0
$397$	−11.0139	−	19.0766i	−0.552771	−	0.957427i	−0.998073	−	0.0620468i	$-0.980237\pi$
$397$	−11.0139	−	19.0766i	−0.552771	−	0.957427i	0.445303	−	0.895380i	$-0.353096\pi$
$398$		0			0
$399$	2.80278	+	4.85455i	0.140314	+	0.243031i
$400$		0			0
$401$	−6.10555	+	10.5751i	−0.304897	+	0.528097i	−0.977238	−	0.212144i	$-0.931955\pi$
$401$	−6.10555	+	10.5751i	−0.304897	+	0.528097i	0.672342	+	0.740241i	$0.265289\pi$
$402$		0			0
$403$	−14.4222			−0.718421
$404$		0			0
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	2.89445	+	5.01333i	0.143472	+	0.248502i
$408$		0			0
$409$	−4.10555	−	7.11102i	−0.203006	−	0.351617i	0.746489	−	0.665397i	$-0.231738\pi$
$409$	−4.10555	−	7.11102i	−0.203006	−	0.351617i	−0.949496	+	0.313780i	$0.898405\pi$
$410$		0			0
$411$	1.60555			0.0791960
$412$		0			0
$413$	−5.40833	+	9.36750i	−0.266126	+	0.460944i
$414$		0			0
$415$	−9.21110			−0.452155
$416$		0			0
$417$	6.39445			0.313138
$418$		0			0
$419$	8.61943	−	14.9293i	0.421087	−	0.729344i	−0.574959	−	0.818182i	$-0.694982\pi$
$419$	8.61943	−	14.9293i	0.421087	−	0.729344i	0.996046	+	0.0888384i	$0.0283155\pi$
$420$		0			0
$421$	32.4222			1.58016			0.790081	−	0.613003i	$-0.210039\pi$
$421$	32.4222			1.58016			0.790081	+	0.613003i	$0.210039\pi$
$422$		0			0
$423$	−9.21110	−	15.9541i	−0.447859	−	0.775715i
$424$		0			0
$425$	−3.80278	−	6.58660i	−0.184462	−	0.319497i
$426$		0			0
$427$	0.500000	−	0.866025i	0.0241967	−	0.0419099i
$428$		0			0
$429$	2.89445	+	5.01333i	0.139745	+	0.242046i
$430$		0			0
$431$	14.6194	−	25.3216i	0.704193	−	1.21970i	−0.262789	−	0.964853i	$-0.584642\pi$
$431$	14.6194	−	25.3216i	0.704193	−	1.21970i	0.966982	−	0.254845i	$-0.0820244\pi$
$432$		0			0
$433$	−1.80278	−	3.12250i	−0.0866359	−	0.150058i	0.819451	−	0.573149i	$-0.194278\pi$
$433$	−1.80278	−	3.12250i	−0.0866359	−	0.150058i	−0.906087	+	0.423091i	$0.860945\pi$
$434$		0			0
$435$	3.10555	+	5.37897i	0.148900	+	0.257902i
$436$		0			0
$437$	16.8167			0.804450
$438$		0			0
$439$	−13.6194	+	23.5895i	−0.650020	+	1.12587i	0.333098	+	0.942892i	$0.391906\pi$
$439$	−13.6194	+	23.5895i	−0.650020	+	1.12587i	−0.983118	+	0.182975i	$0.941427\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$	−6.42221			−0.305128			−0.152564	−	0.988294i	$-0.548753\pi$
$443$	−6.42221			−0.305128			−0.152564	+	0.988294i	$0.548753\pi$
$444$		0			0
$445$	−3.10555	+	5.37897i	−0.147217	+	0.254988i
$446$		0			0
$447$	−3.00000			−0.141895
$448$		0			0
$449$	−15.3167	−	26.5292i	−0.722838	−	1.25199i	−0.959858	−	0.280487i	$-0.909504\pi$
$449$	−15.3167	−	26.5292i	−0.722838	−	1.25199i	0.237020	−	0.971505i	$-0.423829\pi$
$450$		0			0
$451$	2.40833	+	4.17134i	0.113404	+	0.196421i
$452$		0			0
$453$	0.605551	−	1.04885i	0.0284513	−	0.0492791i
$454$		0			0
$455$	−1.80278	−	3.12250i	−0.0845154	−	0.146385i
$456$		0			0
$457$	13.4083	−	23.2239i	0.627215	−	1.08637i	−0.360893	−	0.932607i	$-0.617528\pi$
$457$	13.4083	−	23.2239i	0.627215	−	1.08637i	0.988108	−	0.153761i	$-0.0491386\pi$
$458$		0			0
$459$	−19.0139	−	32.9330i	−0.887492	−	1.53718i
$460$		0			0
$461$	−18.1056	−	31.3597i	−0.843260	−	1.46057i	−0.887124	−	0.461531i	$-0.847300\pi$
$461$	−18.1056	−	31.3597i	−0.843260	−	1.46057i	0.0438645	−	0.999037i	$-0.486033\pi$
$462$		0			0
$463$	34.4222			1.59974			0.799868	−	0.600176i	$-0.204903\pi$
$463$	34.4222			1.59974			0.799868	+	0.600176i	$0.204903\pi$
$464$		0			0
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$		0			0
$467$	−2.78890			−0.129055			−0.0645274	−	0.997916i	$-0.520554\pi$
$467$	−2.78890			−0.129055			−0.0645274	+	0.997916i	$0.520554\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	5.60555	−	9.70910i	0.258290	−	0.447372i
$472$		0			0
$473$	−16.3944			−0.753818
$474$		0			0
$475$	−2.80278	−	4.85455i	−0.128600	−	0.222742i
$476$		0			0
$477$	−3.21110	−	5.56179i	−0.147026	−	0.254657i
$478$		0			0
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	0.322714	+	0.946497i	$0.395405\pi$
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	−0.981047	+	0.193770i	$0.937928\pi$
$480$		0			0
$481$	6.50000	−	11.2583i	0.296374	−	0.513336i
$482$		0			0
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$		0			0
$485$	−4.19722	−	7.26981i	−0.190586	−	0.330105i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$		0			0
$489$	−3.78890			−0.171340
$490$		0			0
$491$	−8.40833	+	14.5636i	−0.379462	+	0.657248i	−0.990984	−	0.133979i	$-0.957224\pi$
$491$	−8.40833	+	14.5636i	−0.379462	+	0.657248i	0.611522	+	0.791228i	$0.290558\pi$
$492$		0			0
$493$	−47.2389			−2.12753
$494$		0			0
$495$	−3.21110			−0.144328
$496$		0			0
$497$	2.40833	−	4.17134i	0.108028	−	0.187110i
$498$		0			0
$499$	−2.42221			−0.108433			−0.0542164	−	0.998529i	$-0.517266\pi$
$499$	−2.42221			−0.108433			−0.0542164	+	0.998529i	$0.517266\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$		0			0
$503$	1.50000	+	2.59808i	0.0668817	+	0.115842i	0.897527	−	0.440959i	$-0.145362\pi$
$503$	1.50000	+	2.59808i	0.0668817	+	0.115842i	−0.830645	+	0.556802i	$0.812028\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$		0			0
$507$	6.50000	−	11.2583i	0.288675	−	0.500000i
$508$		0			0
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$		0			0
$511$	0.394449	+	0.683205i	0.0174494	+	0.0302232i
$512$		0			0
$513$	−14.0139	−	24.2727i	−0.618728	−	1.07167i
$514$		0			0
$515$	−4.00000			−0.176261
$516$		0			0
$517$	−7.39445	+	12.8076i	−0.325207	+	0.563276i
$518$		0			0
$519$	−4.81665			−0.211428
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	−0.711103	+	1.23167i	−0.0310943	+	0.0538570i	−0.881154	−	0.472830i	$-0.843233\pi$
$523$	−0.711103	+	1.23167i	−0.0310943	+	0.0538570i	0.850059	+	0.526687i	$0.176566\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$	−15.2111	−	26.3464i	−0.662606	−	1.14767i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	10.8167	−	18.7350i	0.469403	−	0.813029i
$532$		0			0
$533$	5.40833	−	9.36750i	0.234261	−	0.405751i
$534$		0			0
$535$	−3.10555	+	5.37897i	−0.134265	+	0.232553i
$536$		0			0
$537$	−11.4083	−	19.7598i	−0.492306	−	0.852698i
$538$		0			0
$539$	−4.81665	−	8.34269i	−0.207468	−	0.359345i
$540$		0			0
$541$	−25.6333			−1.10206			−0.551031	−	0.834485i	$-0.685765\pi$
$541$	−25.6333			−1.10206			−0.551031	+	0.834485i	$0.685765\pi$
$542$		0			0
$543$	8.81665	−	15.2709i	0.378359	−	0.655337i
$544$		0			0
$545$	19.2111			0.822913
$546$		0			0
$547$	−32.8444			−1.40433			−0.702163	−	0.712016i	$-0.747782\pi$
$547$	−32.8444			−1.40433			−0.702163	+	0.712016i	$0.747782\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−34.8167			−1.48324
$552$		0			0
$553$	2.60555	+	4.51295i	0.110799	+	0.191910i
$554$		0			0
$555$	−1.80278	−	3.12250i	−0.0765236	−	0.132543i
$556$		0			0
$557$	0.802776	−	1.39045i	0.0340147	−	0.0589152i	−0.848517	−	0.529168i	$-0.822504\pi$
$557$	0.802776	−	1.39045i	0.0340147	−	0.0589152i	0.882532	+	0.470253i	$0.155837\pi$
$558$		0			0
$559$	18.4083	+	31.8842i	0.778589	+	1.34856i
$560$		0			0
$561$	−6.10555	+	10.5751i	−0.257777	+	0.446482i
$562$		0			0
$563$	4.71110	+	8.15987i	0.198549	+	0.343897i	0.948058	−	0.318097i	$-0.103044\pi$
$563$	4.71110	+	8.15987i	0.198549	+	0.343897i	−0.749509	+	0.661994i	$0.769710\pi$
$564$		0			0
$565$	−0.802776	−	1.39045i	−0.0337730	−	0.0584966i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	13.7111	−	23.7483i	0.574799	−	0.995582i	−0.421264	−	0.906938i	$-0.638413\pi$
$569$	13.7111	−	23.7483i	0.574799	−	0.995582i	0.996063	−	0.0886436i	$-0.0282532\pi$
$570$		0			0
$571$	−20.8444			−0.872311			−0.436156	−	0.899871i	$-0.643660\pi$
$571$	−20.8444			−0.872311			−0.436156	+	0.899871i	$0.643660\pi$
$572$		0			0
$573$	16.8167			0.702526
$574$		0			0
$575$	−1.50000	+	2.59808i	−0.0625543	+	0.108347i
$576$		0			0
$577$	−13.6333			−0.567562			−0.283781	−	0.958889i	$-0.591589\pi$
$577$	−13.6333			−0.567562			−0.283781	+	0.958889i	$0.591589\pi$
$578$		0			0
$579$	7.80278	+	13.5148i	0.324272	+	0.561656i
$580$		0			0
$581$	−4.60555	−	7.97705i	−0.191070	−	0.330944i
$582$		0			0
$583$	−2.57779	+	4.46487i	−0.106761	+	0.184916i
$584$		0			0
$585$	3.60555	+	6.24500i	0.149071	+	0.258199i
$586$		0			0
$587$	−16.7111	+	28.9445i	−0.689741	+	1.19467i	0.282181	+	0.959361i	$0.408942\pi$
$587$	−16.7111	+	28.9445i	−0.689741	+	1.19467i	−0.971922	+	0.235305i	$0.924391\pi$
$588$		0			0
$589$	−11.2111	−	19.4182i	−0.461945	−	0.800113i
$590$		0			0
$591$	0.591673	+	1.02481i	0.0243382	+	0.0421550i
$592$		0			0
$593$	20.7889			0.853698			0.426849	−	0.904323i	$-0.359624\pi$
$593$	20.7889			0.853698			0.426849	+	0.904323i	$0.359624\pi$
$594$		0			0
$595$	3.80278	−	6.58660i	0.155899	−	0.270024i
$596$		0			0
$597$	12.8167			0.524551
$598$		0			0
$599$	21.2111			0.866662			0.433331	−	0.901235i	$-0.357338\pi$
$599$	21.2111			0.866662			0.433331	+	0.901235i	$0.357338\pi$
$600$		0			0
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	−0.971688	−	0.236267i	$-0.924076\pi$
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	0.690458	+	0.723373i	$0.257409\pi$
$602$		0			0
$603$	−14.0000			−0.570124
$604$		0			0
$605$	−4.21110	−	7.29384i	−0.171206	−	0.296537i
$606$		0			0
$607$	−17.1056	−	29.6277i	−0.694293	−	1.20255i	−0.970418	−	0.241429i	$-0.922384\pi$
$607$	−17.1056	−	29.6277i	−0.694293	−	1.20255i	0.276126	−	0.961122i	$-0.410949\pi$
$608$		0			0
$609$	−3.10555	+	5.37897i	−0.125843	+	0.217967i
$610$		0			0
$611$	33.2111			1.34358
$612$		0			0
$613$	2.80278	−	4.85455i	0.113203	−	0.196073i	−0.803857	−	0.594823i	$-0.797222\pi$
$613$	2.80278	−	4.85455i	0.113203	−	0.196073i	0.917060	+	0.398749i	$0.130556\pi$
$614$		0			0
$615$	−1.50000	−	2.59808i	−0.0604858	−	0.104765i
$616$		0			0
$617$	19.2250	+	33.2986i	0.773969	+	1.34055i	0.935372	+	0.353664i	$0.115065\pi$
$617$	19.2250	+	33.2986i	0.773969	+	1.34055i	−0.161404	+	0.986888i	$0.551602\pi$
$618$		0			0
$619$	−14.4222			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$619$	−14.4222			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$620$		0			0
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$		0			0
$623$	−6.21110			−0.248843
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$		0			0
$629$	27.4222			1.09339
$630$		0			0
$631$	−18.0139	−	31.2010i	−0.717121	−	1.24209i	−0.962136	−	0.272571i	$-0.912126\pi$
$631$	−18.0139	−	31.2010i	−0.717121	−	1.24209i	0.245015	−	0.969519i	$-0.421207\pi$
$632$		0			0
$633$	11.8028	+	20.4430i	0.469118	+	0.812537i
$634$		0			0
$635$	2.10555	−	3.64692i	0.0835563	−	0.144724i
$636$		0			0
$637$	−10.8167	+	18.7350i	−0.428571	+	0.742307i
$638$		0			0
$639$	−4.81665	+	8.34269i	−0.190544	+	0.330032i
$640$		0			0
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	0.757862	−	0.652415i	$-0.226244\pi$
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	−0.943939	+	0.330120i	$0.892911\pi$
$642$		0			0
$643$	1.31665	+	2.28051i	0.0519238	+	0.0899346i	0.890819	−	0.454358i	$-0.150131\pi$
$643$	1.31665	+	2.28051i	0.0519238	+	0.0899346i	−0.838895	+	0.544293i	$0.816798\pi$
$644$		0			0
$645$	10.2111			0.402062
$646$		0			0
$647$	19.7111	−	34.1406i	0.774923	−	1.34221i	−0.159914	−	0.987131i	$-0.551122\pi$
$647$	19.7111	−	34.1406i	0.774923	−	1.34221i	0.934838	−	0.355076i	$-0.115545\pi$
$648$		0			0
$649$	−17.3667			−0.681702
$650$		0			0
$651$	−4.00000			−0.156772
$652$		0			0
$653$	3.59167	−	6.22096i	0.140553	−	0.243445i	−0.787152	−	0.616759i	$-0.788445\pi$
$653$	3.59167	−	6.22096i	0.140553	−	0.243445i	0.927705	+	0.373314i	$0.121779\pi$
$654$		0			0
$655$	−21.2111			−0.828786
$656$		0			0
$657$	−0.788897	−	1.36641i	−0.0307778	−	0.0533087i
$658$		0			0
$659$	−17.4083	−	30.1521i	−0.678132	−	1.17456i	−0.975543	−	0.219810i	$-0.929456\pi$
$659$	−17.4083	−	30.1521i	−0.678132	−	1.17456i	0.297411	−	0.954750i	$-0.403877\pi$
$660$		0			0
$661$	2.31665	−	4.01256i	0.0901074	−	0.156071i	−0.817449	−	0.576001i	$-0.804612\pi$
$661$	2.31665	−	4.01256i	0.0901074	−	0.156071i	0.907556	+	0.419931i	$0.137946\pi$
$662$		0			0
$663$	27.4222			1.06499
$664$		0			0
$665$	2.80278	−	4.85455i	0.108687	−	0.188251i
$666$		0			0
$667$	9.31665	+	16.1369i	0.360742	+	0.624824i
$668$		0			0
$669$	2.10555	+	3.64692i	0.0814053	+	0.140998i
$670$		0			0
$671$	1.60555			0.0619816
$672$		0			0
$673$	8.80278	−	15.2469i	0.339322	−	0.587723i	−0.644983	−	0.764197i	$-0.723136\pi$
$673$	8.80278	−	15.2469i	0.339322	−	0.587723i	0.984305	+	0.176474i	$0.0564690\pi$
$674$		0			0
$675$	5.00000			0.192450
$676$		0			0
$677$	−9.63331			−0.370238			−0.185119	−	0.982716i	$-0.559267\pi$
$677$	−9.63331			−0.370238			−0.185119	+	0.982716i	$0.559267\pi$
$678$		0			0
$679$	4.19722	−	7.26981i	0.161075	−	0.278990i
$680$		0			0
$681$	−27.4222			−1.05082
$682$		0			0
$683$	18.1056	+	31.3597i	0.692790	+	1.19995i	0.970920	+	0.239404i	$0.0769519\pi$
$683$	18.1056	+	31.3597i	0.692790	+	1.19995i	−0.278130	+	0.960543i	$0.589715\pi$
$684$		0			0
$685$	−0.802776	−	1.39045i	−0.0306725	−	0.0531263i
$686$		0			0
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$		0			0
$689$	11.5778			0.441079
$690$		0			0
$691$	−15.0139	+	26.0048i	−0.571155	+	0.989269i	0.425293	+	0.905056i	$0.360171\pi$
$691$	−15.0139	+	26.0048i	−0.571155	+	0.989269i	−0.996448	+	0.0842134i	$0.973162\pi$
$692$		0			0
$693$	−1.60555	−	2.78090i	−0.0609898	−	0.105638i
$694$		0			0
$695$	−3.19722	−	5.53776i	−0.121278	−	0.210059i
$696$		0			0
$697$	22.8167			0.864242
$698$		0			0
$699$	7.60555	−	13.1732i	0.287668	−	0.498256i
$700$		0			0
$701$	−36.4222			−1.37565			−0.687824	−	0.725878i	$-0.741434\pi$
$701$	−36.4222			−1.37565			−0.687824	+	0.725878i	$0.741434\pi$
$702$		0			0
$703$	20.2111			0.762276
$704$		0			0
$705$	4.60555	−	7.97705i	0.173455	−	0.300433i
$706$		0			0
$707$	−9.00000			−0.338480
$708$		0			0
$709$	6.92221	+	11.9896i	0.259969	+	0.450279i	0.966233	−	0.257669i	$-0.0829544\pi$
$709$	6.92221	+	11.9896i	0.259969	+	0.450279i	−0.706264	+	0.707948i	$0.749621\pi$
$710$		0			0
$711$	−5.21110	−	9.02589i	−0.195432	−	0.338497i
$712$		0			0
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	2.89445	−	5.01333i	0.108246	−	0.187488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.8028	−	22.1751i	−0.477463	−	0.826990i	0.522203	−	0.852821i	$-0.325110\pi$
$719$	−12.8028	−	22.1751i	−0.477463	−	0.826990i	−0.999666	+	0.0258309i	$0.991777\pi$
$720$		0			0
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$		0			0
$723$	−1.78890			−0.0665298
$724$		0			0
$725$	3.10555	−	5.37897i	0.115337	−	0.199770i
$726$		0			0
$727$	−13.5778			−0.503573			−0.251786	−	0.967783i	$-0.581018\pi$
$727$	−13.5778			−0.503573			−0.251786	+	0.967783i	$0.581018\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−38.8305	+	67.2565i	−1.43620	+	2.48757i
$732$		0			0
$733$	−46.8444			−1.73024			−0.865119	−	0.501567i	$-0.832757\pi$
$733$	−46.8444			−1.73024			−0.865119	+	0.501567i	$0.832757\pi$
$734$		0			0
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$		0			0
$737$	5.61943	+	9.73314i	0.206994	+	0.358525i
$738$		0			0
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	0.327037	+	0.945012i	$0.393950\pi$
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	−0.981922	+	0.189284i	$0.939383\pi$
$740$		0			0
$741$	20.2111			0.742473
$742$		0			0
$743$	18.3167	−	31.7254i	0.671973	−	1.16389i	−0.305371	−	0.952233i	$-0.598780\pi$
$743$	18.3167	−	31.7254i	0.671973	−	1.16389i	0.977344	−	0.211658i	$-0.0678862\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$		0			0
$747$	9.21110	+	15.9541i	0.337017	+	0.583730i
$748$		0			0
$749$	−6.21110			−0.226949
$750$		0			0
$751$	23.2250	−	40.2268i	0.847492	−	1.46790i	−0.0359481	−	0.999354i	$-0.511445\pi$
$751$	23.2250	−	40.2268i	0.847492	−	1.46790i	0.883440	−	0.468545i	$-0.155222\pi$
$752$		0			0
$753$	−7.18335			−0.261776
$754$		0			0
$755$	−1.21110			−0.0440765
$756$		0			0
$757$	−0.408327	+	0.707243i	−0.0148409	+	0.0257052i	−0.873350	−	0.487092i	$-0.838058\pi$
$757$	−0.408327	+	0.707243i	−0.0148409	+	0.0257052i	0.858510	+	0.512798i	$0.171391\pi$
$758$		0			0
$759$	4.81665			0.174833
$760$		0			0
$761$	−9.31665	−	16.1369i	−0.337728	−	0.584963i	0.646277	−	0.763103i	$-0.276325\pi$
$761$	−9.31665	−	16.1369i	−0.337728	−	0.584963i	−0.984005	+	0.178140i	$0.942992\pi$
$762$		0			0
$763$	9.60555	+	16.6373i	0.347744	+	0.602311i
$764$		0			0
$765$	−7.60555	+	13.1732i	−0.274979	+	0.476278i
$766$		0			0
$767$	19.5000	+	33.7750i	0.704104	+	1.21954i
$768$		0			0
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$770$		0			0
$771$	−8.19722	−	14.1980i	−0.295216	−	0.511329i
$772$		0			0
$773$	−11.1972	−	19.3942i	−0.402736	−	0.697560i	0.591319	−	0.806438i	$-0.298607\pi$
$773$	−11.1972	−	19.3942i	−0.402736	−	0.697560i	−0.994055	+	0.108878i	$0.965274\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$	1.80278	−	3.12250i	0.0646742	−	0.112019i
$778$		0			0
$779$	16.8167			0.602519
$780$		0			0
$781$	7.73338			0.276722
$782$		0			0
$783$	15.5278	−	26.8949i	0.554917	−	0.961144i
$784$		0			0
$785$	−11.2111			−0.400141
$786$		0			0
$787$	7.31665	+	12.6728i	0.260811	+	0.451737i	0.966458	−	0.256826i	$-0.0826769\pi$
$787$	7.31665	+	12.6728i	0.260811	+	0.451737i	−0.705647	+	0.708564i	$0.749344\pi$
$788$		0			0
$789$	−5.89445	−	10.2095i	−0.209848	−	0.363467i
$790$		0			0
$791$	0.802776	−	1.39045i	0.0285434	−	0.0494386i
$792$		0			0
$793$	−1.80278	−	3.12250i	−0.0640184	−	0.110883i
$794$		0			0
$795$	1.60555	−	2.78090i	0.0569430	−	0.0986282i
$796$		0			0
$797$	7.22498	+	12.5140i	0.255922	+	0.443270i	0.965146	−	0.261714i	$-0.0842877\pi$
$797$	7.22498	+	12.5140i	0.255922	+	0.443270i	−0.709224	+	0.704984i	$0.750954\pi$
$798$		0			0
$799$	35.0278	+	60.6699i	1.23919	+	2.14635i
$800$		0			0
$801$	12.4222			0.438917
$802$		0			0
$803$	−0.633308	+	1.09692i	−0.0223489	+	0.0387095i
$804$		0			0
$805$	−3.00000			−0.105736
$806$		0			0
$807$	9.00000			0.316815
$808$		0			0
$809$	27.5278	−	47.6795i	0.967824	−	1.67632i	0.265997	−	0.963974i	$-0.414299\pi$
$809$	27.5278	−	47.6795i	0.967824	−	1.67632i	0.701827	−	0.712347i	$-0.252368\pi$
$810$		0			0
$811$	46.4222			1.63010			0.815052	−	0.579388i	$-0.196708\pi$
$811$	46.4222			1.63010			0.815052	+	0.579388i	$0.196708\pi$
$812$		0			0
$813$	10.4083	+	18.0278i	0.365036	+	0.632261i
$814$		0			0
$815$	1.89445	+	3.28128i	0.0663596	+	0.114938i
$816$		0			0
$817$	−28.6194	+	49.5703i	−1.00127	+	1.73425i
$818$		0			0
$819$	−3.60555	+	6.24500i	−0.125988	+	0.218218i
$820$		0			0
$821$	−10.7111	+	18.5522i	−0.373820	+	0.647475i	−0.990150	−	0.140013i	$-0.955286\pi$
$821$	−10.7111	+	18.5522i	−0.373820	+	0.647475i	0.616330	+	0.787488i	$0.288619\pi$
$822$		0			0
$823$	−8.31665	−	14.4049i	−0.289900	−	0.502122i	0.683885	−	0.729589i	$-0.260289\pi$
$823$	−8.31665	−	14.4049i	−0.289900	−	0.502122i	−0.973786	+	0.227467i	$0.926955\pi$
$824$		0			0
$825$	−0.802776	−	1.39045i	−0.0279491	−	0.0484092i
$826$		0			0
$827$	42.4222			1.47516			0.737582	−	0.675257i	$-0.235967\pi$
$827$	42.4222			1.47516			0.737582	+	0.675257i	$0.235967\pi$
$828$		0			0
$829$	−14.7111	+	25.4804i	−0.510938	+	0.884970i	0.488982	+	0.872294i	$0.337368\pi$
$829$	−14.7111	+	25.4804i	−0.510938	+	0.884970i	−0.999920	+	0.0126762i	$0.995965\pi$
$830$		0			0
$831$	−27.6056			−0.957626
$832$		0			0
$833$	−45.6333			−1.58110
$834$		0			0
$835$	−4.50000	+	7.79423i	−0.155729	+	0.269730i
$836$		0			0
$837$	20.0000			0.691301
$838$		0			0
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	0.639766	−	0.768569i	$-0.279031\pi$
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	−0.985484	+	0.169769i	$0.945698\pi$
$840$		0			0
$841$	−4.78890	−	8.29461i	−0.165134	−	0.286021i
$842$		0			0
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$		0			0
$845$	−13.0000			−0.447214
$846$		0			0
$847$	4.21110	−	7.29384i	0.144695	−	0.250619i
$848$		0			0
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$		0			0
$851$	−5.40833	−	9.36750i	−0.185395	−	0.321114i
$852$		0			0
$853$	47.2111			1.61648			0.808239	−	0.588855i	$-0.200421\pi$
$853$	47.2111			1.61648			0.808239	+	0.588855i	$0.200421\pi$
$854$		0			0
$855$	−5.60555	+	9.70910i	−0.191706	+	0.332044i
$856$		0			0
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	−10.7889			−0.368112			−0.184056	−	0.982916i	$-0.558923\pi$
$859$	−10.7889			−0.368112			−0.184056	+	0.982916i	$0.558923\pi$
$860$		0			0
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	2.40833	+	4.17134i	0.0818856	+	0.141830i
$866$		0			0
$867$	20.4222	+	35.3723i	0.693574	+	1.20131i
$868$		0			0
$869$	−4.18335	+	7.24577i	−0.141910	+	0.245796i
$870$		0			0
$871$	12.6194	−	21.8575i	0.427593	−	0.740613i
$872$		0			0
$873$	−8.39445	+	14.5396i	−0.284109	+	0.492091i
$874$		0			0
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	0.986122	+	1.70801i	0.0332990	+	0.0576755i	0.882195	−	0.470885i	$-0.156065\pi$
$877$	0.986122	+	1.70801i	0.0332990	+	0.0576755i	−0.848896	+	0.528560i	$0.822732\pi$
$878$		0			0
$879$	−10.3944			−0.350596
$880$		0			0
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	−0.621271	−	0.783596i	$-0.713383\pi$
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	0.989249	+	0.146238i	$0.0467167\pi$
$882$		0			0
$883$	−11.6333			−0.391492			−0.195746	−	0.980655i	$-0.562713\pi$
$883$	−11.6333			−0.391492			−0.195746	+	0.980655i	$0.562713\pi$
$884$		0			0
$885$	10.8167			0.363598
$886$		0			0
$887$	−18.5278	+	32.0910i	−0.622101	+	1.07751i	0.366993	+	0.930224i	$0.380387\pi$
$887$	−18.5278	+	32.0910i	−0.622101	+	1.07751i	−0.989094	+	0.147287i	$0.952946\pi$
$888$		0			0
$889$	4.21110			0.141236
$890$		0			0
$891$	0.802776	+	1.39045i	0.0268940	+	0.0465818i
$892$		0			0
$893$	25.8167	+	44.7158i	0.863921	+	1.49636i
$894$		0			0
$895$	−11.4083	+	19.7598i	−0.381338	+	0.660497i
$896$		0			0
$897$	−5.40833	−	9.36750i	−0.180579	−	0.312772i
$898$		0			0
$899$	12.4222	−	21.5159i	0.414304	−	0.717595i
$900$		0			0
$901$	12.2111	+	21.1503i	0.406811	+	0.704617i
$902$		0			0
$903$	5.10555	+	8.84307i	0.169902	+	0.294279i
$904$		0			0
$905$	−17.6333			−0.586151
$906$		0			0
$907$	−19.1333	+	33.1399i	−0.635311	+	1.10039i	0.351138	+	0.936324i	$0.385795\pi$
$907$	−19.1333	+	33.1399i	−0.635311	+	1.10039i	−0.986449	+	0.164067i	$0.947539\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	7.39445	−	12.8076i	0.244721	−	0.423868i
$914$		0			0
$915$	−1.00000			−0.0330590
$916$		0			0
$917$	−10.6056	−	18.3694i	−0.350226	−	0.606610i
$918$		0			0
$919$	−19.4083	−	33.6162i	−0.640222	−	1.10890i	−0.985383	−	0.170353i	$-0.945509\pi$
$919$	−19.4083	−	33.6162i	−0.640222	−	1.10890i	0.345161	−	0.938543i	$-0.387824\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$		0			0
$923$	−8.68335	−	15.0400i	−0.285816	−	0.495048i
$924$		0			0
$925$	−1.80278	+	3.12250i	−0.0592749	+	0.102667i
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	7.71110	+	13.3560i	0.252993	+	0.438197i	0.964348	−	0.264636i	$-0.0852517\pi$
$929$	7.71110	+	13.3560i	0.252993	+	0.438197i	−0.711355	+	0.702832i	$0.751918\pi$
$930$		0			0
$931$	−33.6333			−1.10229
$932$		0			0
$933$	4.60555	−	7.97705i	0.150779	−	0.261157i
$934$		0			0
$935$	12.2111			0.399346
$936$		0			0
$937$	54.4777			1.77971			0.889855	−	0.456244i	$-0.150806\pi$
$937$	54.4777			1.77971			0.889855	+	0.456244i	$0.150806\pi$
$938$		0			0
$939$	7.00000	−	12.1244i	0.228436	−	0.395663i
$940$		0			0
$941$	−9.63331			−0.314037			−0.157018	−	0.987596i	$-0.550188\pi$
$941$	−9.63331			−0.314037			−0.157018	+	0.987596i	$0.550188\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$		0			0
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$		0			0
$947$	−9.31665	+	16.1369i	−0.302751	+	0.524379i	−0.976758	−	0.214345i	$-0.931238\pi$
$947$	−9.31665	+	16.1369i	−0.302751	+	0.524379i	0.674007	+	0.738725i	$0.264572\pi$
$948$		0			0
$949$	2.84441			0.0923335
$950$		0			0
$951$	3.00000	−	5.19615i	0.0972817	−	0.168497i
$952$		0			0
$953$	7.22498	+	12.5140i	0.234040	+	0.405369i	0.958993	−	0.283429i	$-0.0914720\pi$
$953$	7.22498	+	12.5140i	0.234040	+	0.405369i	−0.724953	+	0.688798i	$0.758139\pi$
$954$		0			0
$955$	−8.40833	−	14.5636i	−0.272087	−	0.471269i
$956$		0			0
$957$	−9.97224			−0.322357
$958$		0			0
$959$	0.802776	−	1.39045i	0.0259230	−	0.0448999i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	12.4222			0.400300
$964$		0			0
$965$	7.80278	−	13.5148i	0.251180	−	0.435057i
$966$		0			0
$967$	44.4777			1.43031			0.715153	−	0.698967i	$-0.246357\pi$
$967$	44.4777			1.43031			0.715153	+	0.698967i	$0.246357\pi$
$968$		0			0
$969$	21.3167	+	36.9215i	0.684790	+	1.18609i
$970$		0			0
$971$	−22.0139	−	38.1292i	−0.706459	−	1.22362i	−0.966162	−	0.257934i	$-0.916958\pi$
$971$	−22.0139	−	38.1292i	−0.706459	−	1.22362i	0.259703	−	0.965688i	$-0.416375\pi$
$972$		0			0
$973$	3.19722	−	5.53776i	0.102498	−	0.177532i
$974$		0			0
$975$	−1.80278	+	3.12250i	−0.0577350	+	0.100000i
$976$		0			0
$977$	−14.4083	+	24.9560i	−0.460963	+	0.798412i	−0.999009	−	0.0445038i	$-0.985829\pi$
$977$	−14.4083	+	24.9560i	−0.460963	+	0.798412i	0.538046	+	0.842915i	$0.319163\pi$
$978$		0			0
$979$	−4.98612	−	8.63622i	−0.159357	−	0.276015i
$980$		0			0
$981$	−19.2111	−	33.2746i	−0.613363	−	1.06238i
$982$		0			0
$983$	−18.4222			−0.587577			−0.293789	−	0.955870i	$-0.594916\pi$
$983$	−18.4222			−0.587577			−0.293789	+	0.955870i	$0.594916\pi$
$984$		0			0
$985$	0.591673	−	1.02481i	0.0188523	−	0.0326531i
$986$		0			0
$987$	9.21110			0.293193
$988$		0			0
$989$	30.6333			0.974083
$990$		0			0
$991$	20.0139	−	34.6651i	0.635762	−	1.10117i	−0.350591	−	0.936529i	$-0.614019\pi$
$991$	20.0139	−	34.6651i	0.635762	−	1.10117i	0.986353	−	0.164643i	$-0.0526473\pi$
$992$		0			0
$993$	10.0278			0.318221
$994$		0			0
$995$	−6.40833	−	11.0995i	−0.203158	−	0.351879i
$996$		0			0
$997$	9.22498	+	15.9781i	0.292158	+	0.506033i	0.974320	−	0.225169i	$-0.0722933\pi$
$997$	9.22498	+	15.9781i	0.292158	+	0.506033i	−0.682162	+	0.731201i	$0.738960\pi$
$998$		0			0
$999$	−9.01388	+	15.6125i	−0.285186	+	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.o.321.2		4
4.3	odd	2		65.2.e.b.61.2	yes	4
12.11	even	2		585.2.j.d.451.1		4
13.3	even	3	inner	1040.2.q.o.81.2		4
20.3	even	4		325.2.o.b.74.1		8
20.7	even	4		325.2.o.b.74.4		8
20.19	odd	2		325.2.e.a.126.1		4
52.3	odd	6		65.2.e.b.16.2	✓	4
52.7	even	12		845.2.c.d.506.1		4
52.11	even	12		845.2.m.d.361.1		8
52.15	even	12		845.2.m.d.361.4		8
52.19	even	12		845.2.c.d.506.4		4
52.23	odd	6		845.2.e.d.146.1		4
52.31	even	4		845.2.m.d.316.1		8
52.35	odd	6		845.2.a.c.1.1		2
52.43	odd	6		845.2.a.f.1.2		2
52.47	even	4		845.2.m.d.316.4		8
52.51	odd	2		845.2.e.d.191.1		4
156.35	even	6		7605.2.a.bg.1.2		2
156.95	even	6		7605.2.a.bb.1.1		2
156.107	even	6		585.2.j.d.406.1		4
260.3	even	12		325.2.o.b.224.4		8
260.107	even	12		325.2.o.b.224.1		8
260.139	odd	6		4225.2.a.x.1.2		2
260.159	odd	6		325.2.e.a.276.1		4
260.199	odd	6		4225.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.2	✓	4	52.3	odd	6
65.2.e.b.61.2	yes	4	4.3	odd	2
325.2.e.a.126.1		4	20.19	odd	2
325.2.e.a.276.1		4	260.159	odd	6
325.2.o.b.74.1		8	20.3	even	4
325.2.o.b.74.4		8	20.7	even	4
325.2.o.b.224.1		8	260.107	even	12
325.2.o.b.224.4		8	260.3	even	12
585.2.j.d.406.1		4	156.107	even	6
585.2.j.d.451.1		4	12.11	even	2
845.2.a.c.1.1		2	52.35	odd	6
845.2.a.f.1.2		2	52.43	odd	6
845.2.c.d.506.1		4	52.7	even	12
845.2.c.d.506.4		4	52.19	even	12
845.2.e.d.146.1		4	52.23	odd	6
845.2.e.d.191.1		4	52.51	odd	2
845.2.m.d.316.1		8	52.31	even	4
845.2.m.d.316.4		8	52.47	even	4
845.2.m.d.361.1		8	52.11	even	12
845.2.m.d.361.4		8	52.15	even	12
1040.2.q.o.81.2		4	13.3	even	3	inner
1040.2.q.o.321.2		4	1.1	even	1	trivial
4225.2.a.t.1.1		2	260.199	odd	6
4225.2.a.x.1.2		2	260.139	odd	6
7605.2.a.bb.1.1		2	156.95	even	6
7605.2.a.bg.1.2		2	156.35	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(0.802776 - 1.39045i) q^{11} -3.60555 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-3.80278 - 6.58660i) q^{17} +(-2.80278 - 4.85455i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(3.10555 - 5.37897i) q^{29} +4.00000 q^{31} +(-0.802776 - 1.39045i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-1.80278 + 3.12250i) q^{37} +(-1.80278 + 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-5.10555 - 8.84307i) q^{43} +(-1.00000 - 1.73205i) q^{45} -9.21110 q^{47} +(3.00000 - 5.19615i) q^{49} -7.60555 q^{51} -3.21110 q^{53} +(-0.802776 + 1.39045i) q^{55} -5.60555 q^{57} +(-5.40833 - 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} +3.60555 q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(2.40833 + 4.17134i) q^{71} -0.788897 q^{73} +(0.500000 - 0.866025i) q^{75} -1.60555 q^{77} -5.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.21110 q^{83} +(3.80278 + 6.58660i) q^{85} +(-3.10555 - 5.37897i) q^{87} +(3.10555 - 5.37897i) q^{89} +(1.80278 + 3.12250i) q^{91} +(2.00000 - 3.46410i) q^{93} +(2.80278 + 4.85455i) q^{95} +(4.19722 + 7.26981i) q^{97} +3.21110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 4 q^{9} - 4 q^{11} - 2 q^{15} - 8 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 4 q^{25} + 20 q^{27} - 2 q^{29} + 16 q^{31} + 4 q^{33} + 2 q^{35} - 6 q^{41} - 6 q^{43} - 4 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 4 * q^9 - 4 * q^11 - 2 * q^15 - 8 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 4 * q^25 + 20 * q^27 - 2 * q^29 + 16 * q^31 + 4 * q^33 + 2 * q^35 - 6 * q^41 - 6 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 16 * q^51 + 16 * q^53 + 4 * q^55 - 8 * q^57 + 2 * q^61 + 4 * q^63 - 14 * q^67 + 6 * q^69 - 12 * q^71 - 32 * q^73 + 2 * q^75 + 8 * q^77 + 8 * q^79 - 2 * q^81 + 8 * q^83 + 8 * q^85 + 2 * q^87 - 2 * q^89 + 8 * q^93 + 4 * q^95 + 24 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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