LMFDB - Embedded newform 340.2.o.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [340,2,Mod(21,340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(340, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("340.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 340 = 2^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	340.o (of order $4$, degree $2$, 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:	$2.71491366872$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6 x^{10} - 16 x^{9} + 9 x^{8} - 72 x^{7} + 114 x^{6} - 144 x^{5} + 391 x^{4} - 484 x^{3} + \cdots + 121 $ x^12 + 6x^10 - 16x^9 + 9x^8 - 72x^7 + 114x^6 - 144x^5 + 391x^4 - 484x^3 + 504x^2 - 396x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.3
Root			$-0.411629 + 1.88205i$ of defining polynomial
Character	$\chi$	$=$	340.81
Dual form			340.2.o.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0789919 - 0.0789919i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(1.97356 - 1.97356i) q^{7} -2.98752i q^{9} +(-0.864802 + 0.864802i) q^{11} -3.40173 q^{13} +0.111711i q^{15} +(3.98802 - 1.04677i) q^{17} -3.42309i q^{19} -0.311790 q^{21} +(6.74584 - 6.74584i) q^{23} +1.00000i q^{25} +(-0.472965 + 0.472965i) q^{27} +(7.08106 + 7.08106i) q^{29} +(-5.64295 - 5.64295i) q^{31} +0.136625 q^{33} -2.79103 q^{35} +(-4.04367 - 4.04367i) q^{37} +(0.268709 + 0.268709i) q^{39} +(-8.23755 + 8.23755i) q^{41} +7.49527i q^{43} +(-2.11250 + 2.11250i) q^{45} +8.61396 q^{47} -0.789873i q^{49} +(-0.397707 - 0.232335i) q^{51} +3.58108i q^{53} +1.22301 q^{55} +(-0.270396 + 0.270396i) q^{57} -4.23376i q^{59} +(-7.67312 + 7.67312i) q^{61} +(-5.89605 - 5.89605i) q^{63} +(2.40539 + 2.40539i) q^{65} +11.1125 q^{67} -1.06573 q^{69} +(0.266369 + 0.266369i) q^{71} +(6.97393 + 6.97393i) q^{73} +(0.0789919 - 0.0789919i) q^{75} +3.41348i q^{77} +(-10.2529 + 10.2529i) q^{79} -8.88784 q^{81} -1.52005i q^{83} +(-3.56013 - 2.07978i) q^{85} -1.11869i q^{87} +4.28461 q^{89} +(-6.71352 + 6.71352i) q^{91} +0.891494i q^{93} +(-2.42049 + 2.42049i) q^{95} +(-1.80991 - 1.80991i) q^{97} +(2.58361 + 2.58361i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{11} + 16 q^{13} - 4 q^{17} + 16 q^{21} + 12 q^{23} - 20 q^{27} + 4 q^{29} - 8 q^{31} - 48 q^{33} - 8 q^{35} - 20 q^{37} + 36 q^{39} + 8 q^{41} + 8 q^{45} - 8 q^{47} + 24 q^{51} + 16 q^{55}+ \cdots - 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^11 + 16 * q^13 - 4 * q^17 + 16 * q^21 + 12 * q^23 - 20 * q^27 + 4 * q^29 - 8 * q^31 - 48 * q^33 - 8 * q^35 - 20 * q^37 + 36 * q^39 + 8 * q^41 + 8 * q^45 - 8 * q^47 + 24 * q^51 + 16 * q^55 - 8 * q^61 + 4 * q^63 + 4 * q^65 + 32 * q^67 - 32 * q^69 + 28 * q^71 - 4 * q^75 - 24 * q^79 - 4 * q^81 - 4 * q^85 - 56 * q^89 - 4 * q^91 + 8 * q^95 - 44 * q^97 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/340\mathbb{Z}\right)^\times$.

$n$	$137$	$171$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.0789919	−	0.0789919i	−0.0456060	−	0.0456060i	0.683936	−	0.729542i	$-0.260267\pi$
$3$	−0.0789919	−	0.0789919i	−0.0456060	−	0.0456060i	−0.729542	+	0.683936i	$0.760267\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$	1.97356	−	1.97356i	0.745935	−	0.745935i	−0.227778	−	0.973713i	$-0.573146\pi$
$7$	1.97356	−	1.97356i	0.745935	−	0.745935i	0.973713	+	0.227778i	$0.0731460\pi$
$8$		0			0
$9$		−	2.98752i		−	0.995840i
$10$		0			0
$11$	−0.864802	+	0.864802i	−0.260748	+	0.260748i	−0.825358	−	0.564610i	$-0.809027\pi$
$11$	−0.864802	+	0.864802i	−0.260748	+	0.260748i	0.564610	+	0.825358i	$0.309027\pi$
$12$		0			0
$13$	−3.40173			−0.943471			−0.471736	−	0.881740i	$-0.656372\pi$
$13$	−3.40173			−0.943471			−0.471736	+	0.881740i	$0.656372\pi$
$14$		0			0
$15$			0.111711i			0.0288437i
$16$		0			0
$17$	3.98802	−	1.04677i	0.967236	−	0.253879i
$17$	3.98802	−	1.04677i	0.967236	−	0.253879i
$18$		0			0
$19$		−	3.42309i		−	0.785311i	−0.919686	−	0.392656i	$-0.871556\pi$
$19$		−	3.42309i		−	0.785311i	0.919686	−	0.392656i	$-0.128444\pi$
$20$		0			0
$21$	−0.311790			−0.0680382
$22$		0			0
$23$	6.74584	−	6.74584i	1.40660	−	1.40660i	0.630047	−	0.776557i	$-0.283036\pi$
$23$	6.74584	−	6.74584i	1.40660	−	1.40660i	0.776557	−	0.630047i	$-0.216964\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−0.472965	+	0.472965i	−0.0910222	+	0.0910222i
$28$		0			0
$29$	7.08106	+	7.08106i	1.31492	+	1.31492i	0.917742	+	0.397178i	$0.130010\pi$
$29$	7.08106	+	7.08106i	1.31492	+	1.31492i	0.397178	+	0.917742i	$0.369990\pi$
$30$		0			0
$31$	−5.64295	−	5.64295i	−1.01350	−	1.01350i	−0.999908	−	0.0135959i	$-0.995672\pi$
$31$	−5.64295	−	5.64295i	−1.01350	−	1.01350i	−0.0135959	−	0.999908i	$-0.504328\pi$
$32$		0			0
$33$	0.136625			0.0237833
$34$		0			0
$35$	−2.79103			−0.471771
$36$		0			0
$37$	−4.04367	−	4.04367i	−0.664776	−	0.664776i	0.291726	−	0.956502i	$-0.405770\pi$
$37$	−4.04367	−	4.04367i	−0.664776	−	0.664776i	−0.956502	+	0.291726i	$0.905770\pi$
$38$		0			0
$39$	0.268709	+	0.268709i	0.0430279	+	0.0430279i
$40$		0			0
$41$	−8.23755	+	8.23755i	−1.28649	+	1.28649i	−0.349584	+	0.936905i	$0.613677\pi$
$41$	−8.23755	+	8.23755i	−1.28649	+	1.28649i	−0.936905	+	0.349584i	$0.886323\pi$
$42$		0			0
$43$			7.49527i			1.14302i	0.820596	+	0.571509i	$0.193642\pi$
$43$			7.49527i			1.14302i	−0.820596	+	0.571509i	$0.806358\pi$
$44$		0			0
$45$	−2.11250	+	2.11250i	−0.314912	+	0.314912i
$46$		0			0
$47$	8.61396			1.25648			0.628238	−	0.778021i	$-0.283777\pi$
$47$	8.61396			1.25648			0.628238	+	0.778021i	$0.283777\pi$
$48$		0			0
$49$		−	0.789873i		−	0.112839i
$50$		0			0
$51$	−0.397707	−	0.232335i	−0.0556901	−	0.0325334i
$52$		0			0
$53$			3.58108i			0.491899i	0.969283	+	0.245949i	$0.0790997\pi$
$53$			3.58108i			0.491899i	−0.969283	+	0.245949i	$0.920900\pi$
$54$		0			0
$55$	1.22301			0.164911
$56$		0			0
$57$	−0.270396	+	0.270396i	−0.0358149	+	0.0358149i
$58$		0			0
$59$		−	4.23376i		−	0.551189i	−0.961274	−	0.275594i	$-0.911125\pi$
$59$		−	4.23376i		−	0.551189i	0.961274	−	0.275594i	$-0.0888747\pi$
$60$		0			0
$61$	−7.67312	+	7.67312i	−0.982443	+	0.982443i	−0.999849	−	0.0174058i	$-0.994459\pi$
$61$	−7.67312	+	7.67312i	−0.982443	+	0.982443i	0.0174058	+	0.999849i	$0.494459\pi$
$62$		0			0
$63$	−5.89605	−	5.89605i	−0.742832	−	0.742832i
$64$		0			0
$65$	2.40539	+	2.40539i	0.298352	+	0.298352i
$66$		0			0
$67$	11.1125			1.35760			0.678802	−	0.734322i	$-0.262500\pi$
$67$	11.1125			1.35760			0.678802	+	0.734322i	$0.262500\pi$
$68$		0			0
$69$	−1.06573			−0.128299
$70$		0			0
$71$	0.266369	+	0.266369i	0.0316122	+	0.0316122i	0.722736	−	0.691124i	$-0.242884\pi$
$71$	0.266369	+	0.266369i	0.0316122	+	0.0316122i	−0.691124	+	0.722736i	$0.742884\pi$
$72$		0			0
$73$	6.97393	+	6.97393i	0.816237	+	0.816237i	0.985561	−	0.169324i	$-0.0541583\pi$
$73$	6.97393	+	6.97393i	0.816237	+	0.816237i	−0.169324	+	0.985561i	$0.554158\pi$
$74$		0			0
$75$	0.0789919	−	0.0789919i	0.00912119	−	0.00912119i
$76$		0			0
$77$			3.41348i			0.389002i
$78$		0			0
$79$	−10.2529	+	10.2529i	−1.15355	+	1.15355i	−0.167710	+	0.985836i	$0.553637\pi$
$79$	−10.2529	+	10.2529i	−1.15355	+	1.15355i	−0.985836	+	0.167710i	$0.946363\pi$
$80$		0			0
$81$	−8.88784			−0.987538
$82$		0			0
$83$		−	1.52005i		−	0.166848i	−0.996514	−	0.0834238i	$-0.973414\pi$
$83$		−	1.52005i		−	0.166848i	0.996514	−	0.0834238i	$-0.0265855\pi$
$84$		0			0
$85$	−3.56013	−	2.07978i	−0.386150	−	0.225583i
$86$		0			0
$87$		−	1.11869i		−	0.119936i
$88$		0			0
$89$	4.28461			0.454168			0.227084	−	0.973875i	$-0.427081\pi$
$89$	4.28461			0.454168			0.227084	+	0.973875i	$0.427081\pi$
$90$		0			0
$91$	−6.71352	+	6.71352i	−0.703769	+	0.703769i
$92$		0			0
$93$			0.891494i			0.0924436i
$94$		0			0
$95$	−2.42049	+	2.42049i	−0.248337	+	0.248337i
$96$		0			0
$97$	−1.80991	−	1.80991i	−0.183769	−	0.183769i	0.609227	−	0.792996i	$-0.291480\pi$
$97$	−1.80991	−	1.80991i	−0.183769	−	0.183769i	−0.792996	+	0.609227i	$0.791480\pi$
$98$		0			0
$99$	2.58361	+	2.58361i	0.259663	+	0.259663i
$100$		0			0
$101$	2.83260			0.281855			0.140927	−	0.990020i	$-0.454992\pi$
$101$	2.83260			0.281855			0.140927	+	0.990020i	$0.454992\pi$
$102$		0			0
$103$	5.02114			0.494748			0.247374	−	0.968920i	$-0.420432\pi$
$103$	5.02114			0.494748			0.247374	+	0.968920i	$0.420432\pi$
$104$		0			0
$105$	0.220469	+	0.220469i	0.0215156	+	0.0215156i
$106$		0			0
$107$	0.442925	+	0.442925i	0.0428192	+	0.0428192i	0.728192	−	0.685373i	$-0.240361\pi$
$107$	0.442925	+	0.442925i	0.0428192	+	0.0428192i	−0.685373	+	0.728192i	$0.740361\pi$
$108$		0			0
$109$	10.0151	−	10.0151i	0.959274	−	0.959274i	−0.0399281	−	0.999203i	$-0.512713\pi$
$109$	10.0151	−	10.0151i	0.959274	−	0.959274i	0.999203	+	0.0399281i	$0.0127129\pi$
$110$		0			0
$111$			0.638834i			0.0606355i
$112$		0			0
$113$	−7.12246	+	7.12246i	−0.670024	+	0.670024i	−0.957721	−	0.287697i	$-0.907110\pi$
$113$	−7.12246	+	7.12246i	−0.670024	+	0.670024i	0.287697	+	0.957721i	$0.407110\pi$
$114$		0			0
$115$	−9.54005			−0.889614
$116$		0			0
$117$			10.1628i			0.939547i
$118$		0			0
$119$	5.80473	−	9.93645i	0.532119	−	0.910873i
$120$		0			0
$121$			9.50424i			0.864021i
$122$		0			0
$123$	1.30140			0.117343
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$		−	15.7863i		−	1.40081i	−0.713748	−	0.700403i	$-0.753004\pi$
$127$		−	15.7863i		−	1.40081i	0.713748	−	0.700403i	$-0.246996\pi$
$128$		0			0
$129$	0.592065	−	0.592065i	0.0521284	−	0.0521284i
$130$		0			0
$131$	8.21894	+	8.21894i	0.718092	+	0.718092i	0.968214	−	0.250122i	$-0.0804707\pi$
$131$	8.21894	+	8.21894i	0.718092	+	0.718092i	−0.250122	+	0.968214i	$0.580471\pi$
$132$		0			0
$133$	−6.75568	−	6.75568i	−0.585792	−	0.585792i
$134$		0			0
$135$	0.668874			0.0575675
$136$		0			0
$137$	3.40173			0.290630			0.145315	−	0.989385i	$-0.453580\pi$
$137$	3.40173			0.290630			0.145315	+	0.989385i	$0.453580\pi$
$138$		0			0
$139$	−5.46988	−	5.46988i	−0.463950	−	0.463950i	0.435998	−	0.899948i	$-0.356395\pi$
$139$	−5.46988	−	5.46988i	−0.463950	−	0.463950i	−0.899948	+	0.435998i	$0.856395\pi$
$140$		0			0
$141$	−0.680433	−	0.680433i	−0.0573028	−	0.0573028i
$142$		0			0
$143$	2.94183	−	2.94183i	0.246008	−	0.246008i
$144$		0			0
$145$		−	10.0141i		−	0.831628i
$146$		0			0
$147$	−0.0623936	+	0.0623936i	−0.00514613	+	0.00514613i
$148$		0			0
$149$	4.56165			0.373705			0.186853	−	0.982388i	$-0.440171\pi$
$149$	4.56165			0.373705			0.186853	+	0.982388i	$0.440171\pi$
$150$		0			0
$151$		−	12.7622i		−	1.03857i	−0.854601	−	0.519285i	$-0.826198\pi$
$151$		−	12.7622i		−	1.03857i	0.854601	−	0.519285i	$-0.173802\pi$
$152$		0			0
$153$	−3.12724	−	11.9143i	−0.252823	−	0.963213i
$154$		0			0
$155$			7.98033i			0.640996i
$156$		0			0
$157$	22.4488			1.79161			0.895803	−	0.444452i	$-0.146601\pi$
$157$	22.4488			1.79161			0.895803	+	0.444452i	$0.146601\pi$
$158$		0			0
$159$	0.282876	−	0.282876i	0.0224335	−	0.0224335i
$160$		0			0
$161$		−	26.6266i		−	2.09847i
$162$		0			0
$163$	2.02135	−	2.02135i	0.158324	−	0.158324i	−0.623499	−	0.781824i	$-0.714290\pi$
$163$	2.02135	−	2.02135i	0.158324	−	0.158324i	0.781824	+	0.623499i	$0.214290\pi$
$164$		0			0
$165$	−0.0966082	−	0.0966082i	−0.00752094	−	0.00752094i
$166$		0			0
$167$	0.0463087	+	0.0463087i	0.00358347	+	0.00358347i	0.708896	−	0.705313i	$-0.249193\pi$
$167$	0.0463087	+	0.0463087i	0.00358347	+	0.00358347i	−0.705313	+	0.708896i	$0.749193\pi$
$168$		0			0
$169$	−1.42820			−0.109862
$170$		0			0
$171$	−10.2266			−0.782045
$172$		0			0
$173$	−10.2763	−	10.2763i	−0.781294	−	0.781294i	0.198755	−	0.980049i	$-0.436310\pi$
$173$	−10.2763	−	10.2763i	−0.781294	−	0.781294i	−0.980049	+	0.198755i	$0.936310\pi$
$174$		0			0
$175$	1.97356	+	1.97356i	0.149187	+	0.149187i
$176$		0			0
$177$	−0.334433	+	0.334433i	−0.0251375	+	0.0251375i
$178$		0			0
$179$			21.5967i			1.61421i	0.590408	+	0.807105i	$0.298967\pi$
$179$			21.5967i			1.61421i	−0.590408	+	0.807105i	$0.701033\pi$
$180$		0			0
$181$	−2.58484	+	2.58484i	−0.192130	+	0.192130i	−0.796616	−	0.604486i	$-0.793379\pi$
$181$	−2.58484	+	2.58484i	−0.192130	+	0.192130i	0.604486	+	0.796616i	$0.293379\pi$
$182$		0			0
$183$	1.21223			0.0896105
$184$		0			0
$185$			5.71862i			0.420441i
$186$		0			0
$187$	−2.54360	+	4.35409i	−0.186006	+	0.318403i
$188$		0			0
$189$			1.86685i			0.135793i
$190$		0			0
$191$	22.8681			1.65468			0.827340	−	0.561702i	$-0.189853\pi$
$191$	22.8681			1.65468			0.827340	+	0.561702i	$0.189853\pi$
$192$		0			0
$193$	−5.09713	+	5.09713i	−0.366899	+	0.366899i	−0.866345	−	0.499446i	$-0.833537\pi$
$193$	−5.09713	+	5.09713i	−0.366899	+	0.366899i	0.499446	+	0.866345i	$0.333537\pi$
$194$		0			0
$195$		−	0.380012i		−	0.0272132i
$196$		0			0
$197$	11.3698	−	11.3698i	0.810065	−	0.810065i	−0.174578	−	0.984643i	$-0.555856\pi$
$197$	11.3698	−	11.3698i	0.810065	−	0.810065i	0.984643	+	0.174578i	$0.0558562\pi$
$198$		0			0
$199$	−7.48293	−	7.48293i	−0.530451	−	0.530451i	0.390255	−	0.920707i	$-0.372387\pi$
$199$	−7.48293	−	7.48293i	−0.530451	−	0.530451i	−0.920707	+	0.390255i	$0.872387\pi$
$200$		0			0
$201$	−0.877794	−	0.877794i	−0.0619148	−	0.0619148i
$202$		0			0
$203$	27.9498			1.96169
$204$		0			0
$205$	11.6497			0.813647
$206$		0			0
$207$	−20.1533	−	20.1533i	−1.40075	−	1.40075i
$208$		0			0
$209$	2.96030	+	2.96030i	0.204768	+	0.204768i
$210$		0			0
$211$	−3.45096	+	3.45096i	−0.237574	+	0.237574i	−0.815845	−	0.578271i	$-0.803728\pi$
$211$	−3.45096	+	3.45096i	−0.237574	+	0.237574i	0.578271	+	0.815845i	$0.303728\pi$
$212$		0			0
$213$		−	0.0420820i		−	0.00288341i
$214$		0			0
$215$	5.29996	−	5.29996i	0.361454	−	0.361454i
$216$		0			0
$217$	−22.2734			−1.51202
$218$		0			0
$219$		−	1.10177i		−	0.0744505i
$220$		0			0
$221$	−13.5662	+	3.56083i	−0.912559	+	0.239527i
$222$		0			0
$223$		−	8.91984i		−	0.597317i	−0.954360	−	0.298658i	$-0.903461\pi$
$223$		−	8.91984i		−	0.597317i	0.954360	−	0.298658i	$-0.0965391\pi$
$224$		0			0
$225$	2.98752			0.199168
$226$		0			0
$227$	−9.14513	+	9.14513i	−0.606984	+	0.606984i	−0.942157	−	0.335173i	$-0.891205\pi$
$227$	−9.14513	+	9.14513i	−0.606984	+	0.606984i	0.335173	+	0.942157i	$0.391205\pi$
$228$		0			0
$229$		−	13.9331i		−	0.920726i	−0.887731	−	0.460363i	$-0.847719\pi$
$229$		−	13.9331i		−	0.920726i	0.887731	−	0.460363i	$-0.152281\pi$
$230$		0			0
$231$	0.269637	−	0.269637i	0.0177408	−	0.0177408i
$232$		0			0
$233$	11.0316	+	11.0316i	0.722702	+	0.722702i	0.969155	−	0.246452i	$-0.0792649\pi$
$233$	11.0316	+	11.0316i	0.722702	+	0.722702i	−0.246452	+	0.969155i	$0.579265\pi$
$234$		0			0
$235$	−6.09099	−	6.09099i	−0.397332	−	0.397332i
$236$		0			0
$237$	1.61980			0.105217
$238$		0			0
$239$	14.8296			0.959246			0.479623	−	0.877475i	$-0.340773\pi$
$239$	14.8296			0.959246			0.479623	+	0.877475i	$0.340773\pi$
$240$		0			0
$241$	0.224326	+	0.224326i	0.0144501	+	0.0144501i	0.714295	−	0.699845i	$-0.246748\pi$
$241$	0.224326	+	0.224326i	0.0144501	+	0.0144501i	−0.699845	+	0.714295i	$0.746748\pi$
$242$		0			0
$243$	2.12096	+	2.12096i	0.136060	+	0.136060i
$244$		0			0
$245$	−0.558525	+	0.558525i	−0.0356828	+	0.0356828i
$246$		0			0
$247$			11.6445i			0.740919i
$248$		0			0
$249$	−0.120072	+	0.120072i	−0.00760925	+	0.00760925i
$250$		0			0
$251$	−6.74154			−0.425522			−0.212761	−	0.977104i	$-0.568246\pi$
$251$	−6.74154			−0.425522			−0.212761	+	0.977104i	$0.568246\pi$
$252$		0			0
$253$			11.6676i			0.733537i
$254$		0			0
$255$	0.116936	+	0.445507i	0.00732281	+	0.0278987i
$256$		0			0
$257$			4.80913i			0.299985i	0.988687	+	0.149993i	$0.0479250\pi$
$257$			4.80913i			0.299985i	−0.988687	+	0.149993i	$0.952075\pi$
$258$		0			0
$259$	−15.9609			−0.991759
$260$		0			0
$261$	21.1548	−	21.1548i	1.30945	−	1.30945i
$262$		0			0
$263$			6.06324i			0.373876i	0.982372	+	0.186938i	$0.0598563\pi$
$263$			6.06324i			0.373876i	−0.982372	+	0.186938i	$0.940144\pi$
$264$		0			0
$265$	2.53220	−	2.53220i	0.155552	−	0.155552i
$266$		0			0
$267$	−0.338449	−	0.338449i	−0.0207128	−	0.0207128i
$268$		0			0
$269$	−12.1126	−	12.1126i	−0.738517	−	0.738517i	0.233774	−	0.972291i	$-0.424892\pi$
$269$	−12.1126	−	12.1126i	−0.738517	−	0.738517i	−0.972291	+	0.233774i	$0.924892\pi$
$270$		0			0
$271$	26.0008			1.57944			0.789719	−	0.613468i	$-0.210226\pi$
$271$	26.0008			1.57944			0.789719	+	0.613468i	$0.210226\pi$
$272$		0			0
$273$	1.06063			0.0641921
$274$		0			0
$275$	−0.864802	−	0.864802i	−0.0521495	−	0.0521495i
$276$		0			0
$277$	−4.51774	−	4.51774i	−0.271445	−	0.271445i	0.558237	−	0.829682i	$-0.311478\pi$
$277$	−4.51774	−	4.51774i	−0.271445	−	0.271445i	−0.829682	+	0.558237i	$0.811478\pi$
$278$		0			0
$279$	−16.8584	+	16.8584i	−1.00929	+	1.00929i
$280$		0			0
$281$			1.36275i			0.0812946i	0.999174	+	0.0406473i	$0.0129420\pi$
$281$			1.36275i			0.0812946i	−0.999174	+	0.0406473i	$0.987058\pi$
$282$		0			0
$283$	−17.6020	+	17.6020i	−1.04633	+	1.04633i	−0.0474589	+	0.998873i	$0.515112\pi$
$283$	−17.6020	+	17.6020i	−1.04633	+	1.04633i	−0.998873	+	0.0474589i	$0.984888\pi$
$284$		0			0
$285$	0.382398			0.0226513
$286$		0			0
$287$			32.5146i			1.91928i
$288$		0			0
$289$	14.8086	−	8.34906i	0.871091	−	0.491121i
$290$		0			0
$291$			0.285936i			0.0167619i
$292$		0			0
$293$	−13.2673			−0.775081			−0.387541	−	0.921853i	$-0.626675\pi$
$293$	−13.2673			−0.775081			−0.387541	+	0.921853i	$0.626675\pi$
$294$		0			0
$295$	−2.99372	+	2.99372i	−0.174301	+	0.174301i
$296$		0			0
$297$		−	0.818043i		−	0.0474676i
$298$		0			0
$299$	−22.9475	+	22.9475i	−1.32709	+	1.32709i
$300$		0			0
$301$	14.7924	+	14.7924i	0.852618	+	0.852618i
$302$		0			0
$303$	−0.223753	−	0.223753i	−0.0128543	−	0.0128543i
$304$		0			0
$305$	10.8514			0.621351
$306$		0			0
$307$	−20.9807			−1.19743			−0.598717	−	0.800960i	$-0.704323\pi$
$307$	−20.9807			−1.19743			−0.598717	+	0.800960i	$0.704323\pi$
$308$		0			0
$309$	−0.396629	−	0.396629i	−0.0225635	−	0.0225635i
$310$		0			0
$311$	−0.507265	−	0.507265i	−0.0287644	−	0.0287644i	0.692578	−	0.721343i	$-0.256475\pi$
$311$	−0.507265	−	0.507265i	−0.0287644	−	0.0287644i	−0.721343	+	0.692578i	$0.756475\pi$
$312$		0			0
$313$	7.50076	−	7.50076i	0.423968	−	0.423968i	−0.462599	−	0.886567i	$-0.653083\pi$
$313$	7.50076	−	7.50076i	0.423968	−	0.423968i	0.886567	+	0.462599i	$0.153083\pi$
$314$		0			0
$315$			8.33827i			0.469808i
$316$		0			0
$317$	−15.0951	+	15.0951i	−0.847823	+	0.847823i	−0.989861	−	0.142038i	$-0.954635\pi$
$317$	−15.0951	+	15.0951i	−0.847823	+	0.847823i	0.142038	+	0.989861i	$0.454635\pi$
$318$		0			0
$319$	−12.2474			−0.685724
$320$		0			0
$321$		−	0.0699749i		−	0.00390562i
$322$		0			0
$323$	−3.58319	−	13.6514i	−0.199374	−	0.759582i
$324$		0			0
$325$		−	3.40173i		−	0.188694i
$326$		0			0
$327$	−1.58223			−0.0874973
$328$		0			0
$329$	17.0002	−	17.0002i	0.937250	−	0.937250i
$330$		0			0
$331$			12.4420i			0.683872i	0.939723	+	0.341936i	$0.111083\pi$
$331$			12.4420i			0.683872i	−0.939723	+	0.341936i	$0.888917\pi$
$332$		0			0
$333$	−12.0806	+	12.0806i	−0.662010	+	0.662010i
$334$		0			0
$335$	−7.85770	−	7.85770i	−0.429312	−	0.429312i
$336$		0			0
$337$	7.22692	+	7.22692i	0.393675	+	0.393675i	0.875995	−	0.482320i	$-0.160206\pi$
$337$	7.22692	+	7.22692i	0.393675	+	0.393675i	−0.482320	+	0.875995i	$0.660206\pi$
$338$		0			0
$339$	1.12523			0.0611142
$340$		0			0
$341$	9.76006			0.528537
$342$		0			0
$343$	12.2561	+	12.2561i	0.661765	+	0.661765i
$344$		0			0
$345$	0.753586	+	0.753586i	0.0405717	+	0.0405717i
$346$		0			0
$347$	12.3917	−	12.3917i	0.665223	−	0.665223i	−0.291383	−	0.956606i	$-0.594115\pi$
$347$	12.3917	−	12.3917i	0.665223	−	0.665223i	0.956606	+	0.291383i	$0.0941155\pi$
$348$		0			0
$349$			20.4572i			1.09505i	0.836789	+	0.547525i	$0.184430\pi$
$349$			20.4572i			1.09505i	−0.836789	+	0.547525i	$0.815570\pi$
$350$		0			0
$351$	1.60890	−	1.60890i	0.0858769	−	0.0858769i
$352$		0			0
$353$	−20.0292			−1.06605			−0.533023	−	0.846101i	$-0.678944\pi$
$353$	−20.0292			−1.06605			−0.533023	+	0.846101i	$0.678944\pi$
$354$		0			0
$355$		−	0.376703i		−	0.0199933i
$356$		0			0
$357$	−1.24342	+	0.326372i	−0.0658090	+	0.0172734i
$358$		0			0
$359$			19.4670i			1.02743i	0.857961	+	0.513715i	$0.171731\pi$
$359$			19.4670i			1.02743i	−0.857961	+	0.513715i	$0.828269\pi$
$360$		0			0
$361$	7.28243			0.383286
$362$		0			0
$363$	0.750757	−	0.750757i	0.0394045	−	0.0394045i
$364$		0			0
$365$		−	9.86263i		−	0.516234i
$366$		0			0
$367$	−16.4806	+	16.4806i	−0.860278	+	0.860278i	−0.991370	−	0.131092i	$-0.958152\pi$
$367$	−16.4806	+	16.4806i	−0.860278	+	0.860278i	0.131092	+	0.991370i	$0.458152\pi$
$368$		0			0
$369$	24.6098	+	24.6098i	1.28114	+	1.28114i
$370$		0			0
$371$	7.06747	+	7.06747i	0.366925	+	0.366925i
$372$		0			0
$373$	−15.4630			−0.800642			−0.400321	−	0.916375i	$-0.631101\pi$
$373$	−15.4630			−0.800642			−0.400321	+	0.916375i	$0.631101\pi$
$374$		0			0
$375$	−0.111711			−0.00576875
$376$		0			0
$377$	−24.0879	−	24.0879i	−1.24059	−	1.24059i
$378$		0			0
$379$	−5.34520	−	5.34520i	−0.274564	−	0.274564i	0.556370	−	0.830935i	$-0.312194\pi$
$379$	−5.34520	−	5.34520i	−0.274564	−	0.274564i	−0.830935	+	0.556370i	$0.812194\pi$
$380$		0			0
$381$	−1.24699	+	1.24699i	−0.0638851	+	0.0638851i
$382$		0			0
$383$		−	10.1244i		−	0.517333i	−0.965967	−	0.258666i	$-0.916717\pi$
$383$		−	10.1244i		−	0.517333i	0.965967	−	0.258666i	$-0.0832830\pi$
$384$		0			0
$385$	2.41369	−	2.41369i	0.123013	−	0.123013i
$386$		0			0
$387$	22.3923			1.13826
$388$		0			0
$389$		−	12.6889i		−	0.643355i	−0.946849	−	0.321677i	$-0.895753\pi$
$389$		−	12.6889i		−	0.643355i	0.946849	−	0.321677i	$-0.104247\pi$
$390$		0			0
$391$	19.8412	−	33.9638i	1.00341	−	1.71762i
$392$		0			0
$393$		−	1.29846i		−	0.0654986i
$394$		0			0
$395$	14.4999			0.729567
$396$		0			0
$397$	−16.5441	+	16.5441i	−0.830323	+	0.830323i	−0.987561	−	0.157238i	$-0.949741\pi$
$397$	−16.5441	+	16.5441i	−0.830323	+	0.830323i	0.157238	+	0.987561i	$0.449741\pi$
$398$		0			0
$399$			1.06729i			0.0534312i
$400$		0			0
$401$	7.99397	−	7.99397i	0.399200	−	0.399200i	−0.478751	−	0.877951i	$-0.658910\pi$
$401$	7.99397	−	7.99397i	0.399200	−	0.399200i	0.877951	+	0.478751i	$0.158910\pi$
$402$		0			0
$403$	19.1958	+	19.1958i	0.956211	+	0.956211i
$404$		0			0
$405$	6.28465	+	6.28465i	0.312287	+	0.312287i
$406$		0			0
$407$	6.99395			0.346677
$408$		0			0
$409$	−21.1081			−1.04373			−0.521864	−	0.853029i	$-0.674763\pi$
$409$	−21.1081			−1.04373			−0.521864	+	0.853029i	$0.674763\pi$
$410$		0			0
$411$	−0.268709	−	0.268709i	−0.0132545	−	0.0132545i
$412$		0			0
$413$	−8.35558	−	8.35558i	−0.411151	−	0.411151i
$414$		0			0
$415$	−1.07484	+	1.07484i	−0.0527619	+	0.0527619i
$416$		0			0
$417$			0.864153i			0.0423177i
$418$		0			0
$419$	−14.2384	+	14.2384i	−0.695589	+	0.695589i	−0.963456	−	0.267867i	$-0.913681\pi$
$419$	−14.2384	+	14.2384i	−0.695589	+	0.695589i	0.267867	+	0.963456i	$0.413681\pi$
$420$		0			0
$421$	11.6969			0.570072			0.285036	−	0.958517i	$-0.407995\pi$
$421$	11.6969			0.570072			0.285036	+	0.958517i	$0.407995\pi$
$422$		0			0
$423$		−	25.7344i		−	1.25125i
$424$		0			0
$425$	1.04677	+	3.98802i	0.0507757	+	0.193447i
$426$		0			0
$427$			30.2867i			1.46568i
$428$		0			0
$429$	−0.464761			−0.0224388
$430$		0			0
$431$	2.04736	−	2.04736i	0.0986177	−	0.0986177i	−0.656077	−	0.754694i	$-0.727785\pi$
$431$	2.04736	−	2.04736i	0.0986177	−	0.0986177i	0.754694	+	0.656077i	$0.227785\pi$
$432$		0			0
$433$		−	19.7898i		−	0.951038i	−0.879705	−	0.475519i	$-0.842260\pi$
$433$		−	19.7898i		−	0.951038i	0.879705	−	0.475519i	$-0.157740\pi$
$434$		0			0
$435$	−0.791034	+	0.791034i	−0.0379272	+	0.0379272i
$436$		0			0
$437$	−23.0916	−	23.0916i	−1.10462	−	1.10462i
$438$		0			0
$439$	−25.0903	−	25.0903i	−1.19749	−	1.19749i	−0.974914	−	0.222580i	$-0.928552\pi$
$439$	−25.0903	−	25.0903i	−1.19749	−	1.19749i	−0.222580	−	0.974914i	$-0.571448\pi$
$440$		0			0
$441$	−2.35976			−0.112370
$442$		0			0
$443$	−14.7915			−0.702763			−0.351382	−	0.936232i	$-0.614288\pi$
$443$	−14.7915			−0.702763			−0.351382	+	0.936232i	$0.614288\pi$
$444$		0			0
$445$	−3.02968	−	3.02968i	−0.143621	−	0.143621i
$446$		0			0
$447$	−0.360333	−	0.360333i	−0.0170432	−	0.0170432i
$448$		0			0
$449$	−12.2258	+	12.2258i	−0.576973	+	0.576973i	−0.934068	−	0.357095i	$-0.883767\pi$
$449$	−12.2258	+	12.2258i	−0.576973	+	0.576973i	0.357095	+	0.934068i	$0.383767\pi$
$450$		0			0
$451$		−	14.2477i		−	0.670898i
$452$		0			0
$453$	−1.00811	+	1.00811i	−0.0473650	+	0.0473650i
$454$		0			0
$455$	9.49436			0.445102
$456$		0			0
$457$		−	4.94745i		−	0.231432i	−0.993282	−	0.115716i	$-0.963084\pi$
$457$		−	4.94745i		−	0.231432i	0.993282	−	0.115716i	$-0.0369163\pi$
$458$		0			0
$459$	−1.39111	+	2.38128i	−0.0649314	+	0.111149i
$460$		0			0
$461$		−	9.14971i		−	0.426145i	−0.977036	−	0.213072i	$-0.931653\pi$
$461$		−	9.14971i		−	0.426145i	0.977036	−	0.213072i	$-0.0683470\pi$
$462$		0			0
$463$	9.60773			0.446509			0.223255	−	0.974760i	$-0.428332\pi$
$463$	9.60773			0.446509			0.223255	+	0.974760i	$0.428332\pi$
$464$		0			0
$465$	0.630381	−	0.630381i	0.0292332	−	0.0292332i
$466$		0			0
$467$		−	15.2164i		−	0.704132i	−0.935975	−	0.352066i	$-0.885479\pi$
$467$		−	15.2164i		−	0.704132i	0.935975	−	0.352066i	$-0.114521\pi$
$468$		0			0
$469$	21.9311	−	21.9311i	1.01268	−	1.01268i
$470$		0			0
$471$	−1.77327	−	1.77327i	−0.0817079	−	0.0817079i
$472$		0			0
$473$	−6.48192	−	6.48192i	−0.298039	−	0.298039i
$474$		0			0
$475$	3.42309			0.157062
$476$		0			0
$477$	10.6985			0.489853
$478$		0			0
$479$	11.1721	+	11.1721i	0.510466	+	0.510466i	0.914669	−	0.404203i	$-0.132451\pi$
$479$	11.1721	+	11.1721i	0.510466	+	0.510466i	−0.404203	+	0.914669i	$0.632451\pi$
$480$		0			0
$481$	13.7555	+	13.7555i	0.627197	+	0.627197i
$482$		0			0
$483$	−2.10329	+	2.10329i	−0.0957028	+	0.0957028i
$484$		0			0
$485$			2.55960i			0.116225i
$486$		0			0
$487$	8.29075	−	8.29075i	0.375690	−	0.375690i	−0.493855	−	0.869545i	$-0.664412\pi$
$487$	8.29075	−	8.29075i	0.375690	−	0.375690i	0.869545	+	0.493855i	$0.164412\pi$
$488$		0			0
$489$	−0.319340			−0.0144411
$490$		0			0
$491$		−	6.73370i		−	0.303888i	−0.988389	−	0.151944i	$-0.951447\pi$
$491$		−	6.73370i		−	0.303888i	0.988389	−	0.151944i	$-0.0485533\pi$
$492$		0			0
$493$	35.6516	+	20.8271i	1.60567	+	0.938008i
$494$		0			0
$495$		−	3.65378i		−	0.164225i
$496$		0			0
$497$	1.05139			0.0471613
$498$		0			0
$499$	19.5901	−	19.5901i	0.876972	−	0.876972i	−0.116248	−	0.993220i	$-0.537087\pi$
$499$	19.5901	−	19.5901i	0.876972	−	0.876972i	0.993220	+	0.116248i	$0.0370868\pi$
$500$		0			0
$501$		−	0.00731601i		−	0.000326855i
$502$		0			0
$503$	−7.00563	+	7.00563i	−0.312366	+	0.312366i	−0.845825	−	0.533460i	$-0.820892\pi$
$503$	−7.00563	+	7.00563i	−0.312366	+	0.312366i	0.533460	+	0.845825i	$0.320892\pi$
$504$		0			0
$505$	−2.00295	−	2.00295i	−0.0891303	−	0.0891303i
$506$		0			0
$507$	0.112817	+	0.112817i	0.00501036	+	0.00501036i
$508$		0			0
$509$	10.2748			0.455423			0.227712	−	0.973729i	$-0.426876\pi$
$509$	10.2748			0.455423			0.227712	+	0.973729i	$0.426876\pi$
$510$		0			0
$511$	27.5269			1.21772
$512$		0			0
$513$	1.61900	+	1.61900i	0.0714808	+	0.0714808i
$514$		0			0
$515$	−3.55049	−	3.55049i	−0.156453	−	0.156453i
$516$		0			0
$517$	−7.44937	+	7.44937i	−0.327623	+	0.327623i
$518$		0			0
$519$			1.62349i			0.0712633i
$520$		0			0
$521$	−6.83069	+	6.83069i	−0.299258	+	0.299258i	−0.840723	−	0.541465i	$-0.817870\pi$
$521$	−6.83069	+	6.83069i	−0.299258	+	0.299258i	0.541465	+	0.840723i	$0.317870\pi$
$522$		0			0
$523$	8.21602			0.359262			0.179631	−	0.983734i	$-0.442510\pi$
$523$	8.21602			0.359262			0.179631	+	0.983734i	$0.442510\pi$
$524$		0			0
$525$		−	0.311790i		−	0.0136076i
$526$		0			0
$527$	−28.4110	−	16.5973i	−1.23760	−	0.722990i
$528$		0			0
$529$		−	68.0126i		−	2.95707i
$530$		0			0
$531$	−12.6484			−0.548896
$532$		0			0
$533$	28.0220	−	28.0220i	1.21377	−	1.21377i
$534$		0			0
$535$		−	0.626391i		−	0.0270812i
$536$		0			0
$537$	1.70596	−	1.70596i	0.0736176	−	0.0736176i
$538$		0			0
$539$	0.683084	+	0.683084i	0.0294225	+	0.0294225i
$540$		0			0
$541$	−24.1876	−	24.1876i	−1.03991	−	1.03991i	−0.999170	−	0.0407372i	$-0.987029\pi$
$541$	−24.1876	−	24.1876i	−1.03991	−	1.03991i	−0.0407372	−	0.999170i	$-0.512971\pi$
$542$		0			0
$543$	0.408363			0.0175245
$544$		0			0
$545$	−14.1635			−0.606698
$546$		0			0
$547$	15.8269	+	15.8269i	0.676711	+	0.676711i	0.959254	−	0.282544i	$-0.0911782\pi$
$547$	15.8269	+	15.8269i	0.676711	+	0.676711i	−0.282544	+	0.959254i	$0.591178\pi$
$548$		0			0
$549$	22.9236	+	22.9236i	0.978356	+	0.978356i
$550$		0			0
$551$	24.2391	−	24.2391i	1.03262	−	1.03262i
$552$		0			0
$553$			40.4696i			1.72094i
$554$		0			0
$555$	0.451724	−	0.451724i	0.0191746	−	0.0191746i
$556$		0			0
$557$	−26.3875			−1.11807			−0.559036	−	0.829143i	$-0.688829\pi$
$557$	−26.3875			−1.11807			−0.559036	+	0.829143i	$0.688829\pi$
$558$		0			0
$559$		−	25.4969i		−	1.07840i
$560$		0			0
$561$	0.544861	−	0.143014i	0.0230041	−	0.00603807i
$562$		0			0
$563$		−	3.35687i		−	0.141475i	−0.997495	−	0.0707376i	$-0.977465\pi$
$563$		−	3.35687i		−	0.141475i	0.997495	−	0.0707376i	$-0.0225353\pi$
$564$		0			0
$565$	10.0727			0.423761
$566$		0			0
$567$	−17.5407	+	17.5407i	−0.736639	+	0.736639i
$568$		0			0
$569$			42.4229i			1.77846i	0.457458	+	0.889231i	$0.348760\pi$
$569$			42.4229i			1.77846i	−0.457458	+	0.889231i	$0.651240\pi$
$570$		0			0
$571$	−9.57415	+	9.57415i	−0.400666	+	0.400666i	−0.878468	−	0.477802i	$-0.841434\pi$
$571$	−9.57415	+	9.57415i	−0.400666	+	0.400666i	0.477802	+	0.878468i	$0.341434\pi$
$572$		0			0
$573$	−1.80640	−	1.80640i	−0.0754632	−	0.0754632i
$574$		0			0
$575$	6.74584	+	6.74584i	0.281321	+	0.281321i
$576$		0			0
$577$	20.7010			0.861792			0.430896	−	0.902402i	$-0.358198\pi$
$577$	20.7010			0.861792			0.430896	+	0.902402i	$0.358198\pi$
$578$		0			0
$579$	0.805263			0.0334656
$580$		0			0
$581$	−2.99992	−	2.99992i	−0.124458	−	0.124458i
$582$		0			0
$583$	−3.09692	−	3.09692i	−0.128261	−	0.128261i
$584$		0			0
$585$	7.18615	−	7.18615i	0.297111	−	0.297111i
$586$		0			0
$587$		−	33.1051i		−	1.36639i	−0.730235	−	0.683197i	$-0.760589\pi$
$587$		−	33.1051i		−	1.36639i	0.730235	−	0.683197i	$-0.239411\pi$
$588$		0			0
$589$	−19.3163	+	19.3163i	−0.795916	+	0.795916i
$590$		0			0
$591$	−1.79624			−0.0738876
$592$		0			0
$593$			11.1110i			0.456276i	0.973629	+	0.228138i	$0.0732637\pi$
$593$			11.1110i			0.456276i	−0.973629	+	0.228138i	$0.926736\pi$
$594$		0			0
$595$	−11.1307	+	2.92157i	−0.456314	+	0.119773i
$596$		0			0
$597$			1.18218i			0.0483835i
$598$		0			0
$599$	−38.6224			−1.57807			−0.789034	−	0.614349i	$-0.789419\pi$
$599$	−38.6224			−1.57807			−0.789034	+	0.614349i	$0.789419\pi$
$600$		0			0
$601$	−10.5195	+	10.5195i	−0.429099	+	0.429099i	−0.888321	−	0.459223i	$-0.848128\pi$
$601$	−10.5195	+	10.5195i	−0.429099	+	0.429099i	0.459223	+	0.888321i	$0.348128\pi$
$602$		0			0
$603$		−	33.1987i		−	1.35196i
$604$		0			0
$605$	6.72051	−	6.72051i	0.273228	−	0.273228i
$606$		0			0
$607$	−22.2976	−	22.2976i	−0.905031	−	0.905031i	0.0908348	−	0.995866i	$-0.471046\pi$
$607$	−22.2976	−	22.2976i	−0.905031	−	0.905031i	−0.995866	+	0.0908348i	$0.971046\pi$
$608$		0			0
$609$	−2.20780	−	2.20780i	−0.0894648	−	0.0894648i
$610$		0			0
$611$	−29.3024			−1.18545
$612$		0			0
$613$	4.65730			0.188107			0.0940533	−	0.995567i	$-0.470018\pi$
$613$	4.65730			0.188107			0.0940533	+	0.995567i	$0.470018\pi$
$614$		0			0
$615$	−0.920228	−	0.920228i	−0.0371072	−	0.0371072i
$616$		0			0
$617$	29.1461	+	29.1461i	1.17338	+	1.17338i	0.981399	+	0.191978i	$0.0614902\pi$
$617$	29.1461	+	29.1461i	1.17338	+	1.17338i	0.191978	+	0.981399i	$0.438510\pi$
$618$		0			0
$619$	6.07033	−	6.07033i	0.243987	−	0.243987i	−0.574510	−	0.818497i	$-0.694807\pi$
$619$	6.07033	−	6.07033i	0.243987	−	0.243987i	0.818497	+	0.574510i	$0.194807\pi$
$620$		0			0
$621$			6.38109i			0.256064i
$622$		0			0
$623$	8.45594	−	8.45594i	0.338780	−	0.338780i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		−	0.467679i		−	0.0186773i
$628$		0			0
$629$	−20.3590	−	11.8934i	−0.811767	−	0.474223i
$630$		0			0
$631$			17.3123i			0.689192i	0.938751	+	0.344596i	$0.111984\pi$
$631$			17.3123i			0.689192i	−0.938751	+	0.344596i	$0.888016\pi$
$632$		0			0
$633$	0.545195			0.0216696
$634$		0			0
$635$	−11.1626	+	11.1626i	−0.442974	+	0.442974i
$636$		0			0
$637$			2.68694i			0.106460i
$638$		0			0
$639$	0.795784	−	0.795784i	0.0314807	−	0.0314807i
$640$		0			0
$641$	−11.0134	−	11.0134i	−0.435002	−	0.435002i	0.455324	−	0.890326i	$-0.349524\pi$
$641$	−11.0134	−	11.0134i	−0.435002	−	0.435002i	−0.890326	+	0.455324i	$0.849524\pi$
$642$		0			0
$643$	7.87307	+	7.87307i	0.310484	+	0.310484i	0.845097	−	0.534613i	$-0.179543\pi$
$643$	7.87307	+	7.87307i	0.310484	+	0.310484i	−0.534613	+	0.845097i	$0.679543\pi$
$644$		0			0
$645$	−0.837307			−0.0329689
$646$		0			0
$647$	15.7228			0.618129			0.309064	−	0.951041i	$-0.399984\pi$
$647$	15.7228			0.618129			0.309064	+	0.951041i	$0.399984\pi$
$648$		0			0
$649$	3.66136	+	3.66136i	0.143721	+	0.143721i
$650$		0			0
$651$	1.75942	+	1.75942i	0.0689570	+	0.0689570i
$652$		0			0
$653$	−18.7020	+	18.7020i	−0.731866	+	0.731866i	−0.970989	−	0.239123i	$-0.923140\pi$
$653$	−18.7020	+	18.7020i	−0.731866	+	0.731866i	0.239123	+	0.970989i	$0.423140\pi$
$654$		0			0
$655$		−	11.6233i		−	0.454161i
$656$		0			0
$657$	20.8348	−	20.8348i	0.812842	−	0.812842i
$658$		0			0
$659$	31.7204			1.23565			0.617826	−	0.786315i	$-0.288014\pi$
$659$	31.7204			1.23565			0.617826	+	0.786315i	$0.288014\pi$
$660$		0			0
$661$			41.6769i			1.62105i	0.585707	+	0.810523i	$0.300817\pi$
$661$			41.6769i			1.62105i	−0.585707	+	0.810523i	$0.699183\pi$
$662$		0			0
$663$	1.35289	+	0.790341i	0.0525420	+	0.0306943i
$664$		0			0
$665$			9.55397i			0.370487i
$666$		0			0
$667$	95.5353			3.69914
$668$		0			0
$669$	−0.704595	+	0.704595i	−0.0272412	+	0.0272412i
$670$		0			0
$671$		−	13.2715i		−	0.512339i
$672$		0			0
$673$	−1.85204	+	1.85204i	−0.0713907	+	0.0713907i	−0.741901	−	0.670510i	$-0.766075\pi$
$673$	−1.85204	+	1.85204i	−0.0713907	+	0.0713907i	0.670510	+	0.741901i	$0.266075\pi$
$674$		0			0
$675$	−0.472965	−	0.472965i	−0.0182044	−	0.0182044i
$676$		0			0
$677$	8.46007	+	8.46007i	0.325147	+	0.325147i	0.850738	−	0.525591i	$-0.176156\pi$
$677$	8.46007	+	8.46007i	0.325147	+	0.325147i	−0.525591	+	0.850738i	$0.676156\pi$
$678$		0			0
$679$	−7.14393			−0.274159
$680$		0			0
$681$	1.44478			0.0553642
$682$		0			0
$683$	−14.2066	−	14.2066i	−0.543599	−	0.543599i	0.380983	−	0.924582i	$-0.375586\pi$
$683$	−14.2066	−	14.2066i	−0.543599	−	0.543599i	−0.924582	+	0.380983i	$0.875586\pi$
$684$		0			0
$685$	−2.40539	−	2.40539i	−0.0919052	−	0.0919052i
$686$		0			0
$687$	−1.10060	+	1.10060i	−0.0419906	+	0.0419906i
$688$		0			0
$689$		−	12.1819i		−	0.464092i
$690$		0			0
$691$	−14.9314	+	14.9314i	−0.568017	+	0.568017i	−0.931572	−	0.363556i	$-0.881563\pi$
$691$	−14.9314	+	14.9314i	−0.568017	+	0.568017i	0.363556	+	0.931572i	$0.381563\pi$
$692$		0			0
$693$	10.1978			0.387383
$694$		0			0
$695$			7.73558i			0.293427i
$696$		0			0
$697$	−24.2287	+	41.4743i	−0.917727	+	1.57095i
$698$		0			0
$699$		−	1.74281i		−	0.0659191i
$700$		0			0
$701$	−35.6241			−1.34551			−0.672753	−	0.739868i	$-0.734888\pi$
$701$	−35.6241			−1.34551			−0.672753	+	0.739868i	$0.734888\pi$
$702$		0			0
$703$	−13.8419	+	13.8419i	−0.522056	+	0.522056i
$704$		0			0
$705$			0.962277i			0.0362415i
$706$		0			0
$707$	5.59031	−	5.59031i	0.210245	−	0.210245i
$708$		0			0
$709$	27.4579	+	27.4579i	1.03120	+	1.03120i	0.999497	+	0.0317069i	$0.0100943\pi$
$709$	27.4579	+	27.4579i	1.03120	+	1.03120i	0.0317069	+	0.999497i	$0.489906\pi$
$710$		0			0
$711$	30.6309	+	30.6309i	1.14875	+	1.14875i
$712$		0			0
$713$	−76.1328			−2.85120
$714$		0			0
$715$	−4.16037			−0.155589
$716$		0			0
$717$	−1.17142	−	1.17142i	−0.0437473	−	0.0437473i
$718$		0			0
$719$	−7.29926	−	7.29926i	−0.272217	−	0.272217i	0.557775	−	0.829992i	$-0.311655\pi$
$719$	−7.29926	−	7.29926i	−0.272217	−	0.272217i	−0.829992	+	0.557775i	$0.811655\pi$
$720$		0			0
$721$	9.90953	−	9.90953i	0.369050	−	0.369050i
$722$		0			0
$723$		−	0.0354399i		−	0.00131802i
$724$		0			0
$725$	−7.08106	+	7.08106i	−0.262984	+	0.262984i
$726$		0			0
$727$	−36.4252			−1.35094			−0.675468	−	0.737389i	$-0.736059\pi$
$727$	−36.4252			−1.35094			−0.675468	+	0.737389i	$0.736059\pi$
$728$		0			0
$729$			26.3284i			0.975128i
$730$		0			0
$731$	7.84581	+	29.8913i	0.290188	+	1.10557i
$732$		0			0
$733$			33.2356i			1.22759i	0.789467	+	0.613793i	$0.210357\pi$
$733$			33.2356i			1.22759i	−0.789467	+	0.613793i	$0.789643\pi$
$734$		0			0
$735$	0.0882378			0.00325470
$736$		0			0
$737$	−9.61008	+	9.61008i	−0.353992	+	0.353992i
$738$		0			0
$739$			11.8455i			0.435745i	0.975977	+	0.217872i	$0.0699116\pi$
$739$			11.8455i			0.435745i	−0.975977	+	0.217872i	$0.930088\pi$
$740$		0			0
$741$	0.919817	−	0.919817i	0.0337903	−	0.0337903i
$742$		0			0
$743$	12.4200	+	12.4200i	0.455645	+	0.455645i	0.897223	−	0.441578i	$-0.145581\pi$
$743$	12.4200	+	12.4200i	0.455645	+	0.455645i	−0.441578	+	0.897223i	$0.645581\pi$
$744$		0			0
$745$	−3.22558	−	3.22558i	−0.118176	−	0.118176i
$746$		0			0
$747$	−4.54119			−0.166154
$748$		0			0
$749$	1.74828			0.0638807
$750$		0			0
$751$	−11.8641	−	11.8641i	−0.432927	−	0.432927i	0.456696	−	0.889623i	$-0.349033\pi$
$751$	−11.8641	−	11.8641i	−0.432927	−	0.432927i	−0.889623	+	0.456696i	$0.849033\pi$
$752$		0			0
$753$	0.532527	+	0.532527i	0.0194064	+	0.0194064i
$754$		0			0
$755$	−9.02420	+	9.02420i	−0.328424	+	0.328424i
$756$		0			0
$757$		−	45.4038i		−	1.65023i	−0.564966	−	0.825114i	$-0.691111\pi$
$757$		−	45.4038i		−	1.65023i	0.564966	−	0.825114i	$-0.308889\pi$
$758$		0			0
$759$	0.921647	−	0.921647i	0.0334537	−	0.0334537i
$760$		0			0
$761$	−8.72830			−0.316401			−0.158200	−	0.987407i	$-0.550569\pi$
$761$	−8.72830			−0.316401			−0.158200	+	0.987407i	$0.550569\pi$
$762$		0			0
$763$		−	39.5309i		−	1.43111i
$764$		0			0
$765$	−6.21338	+	10.6360i	−0.224645	+	0.384544i
$766$		0			0
$767$			14.4021i			0.520031i
$768$		0			0
$769$	−0.280789			−0.0101255			−0.00506276	−	0.999987i	$-0.501612\pi$
$769$	−0.280789			−0.0101255			−0.00506276	+	0.999987i	$0.501612\pi$
$770$		0			0
$771$	0.379882	−	0.379882i	0.0136811	−	0.0136811i
$772$		0			0
$773$		−	14.6221i		−	0.525922i	−0.964807	−	0.262961i	$-0.915301\pi$
$773$		−	14.6221i		−	0.525922i	0.964807	−	0.262961i	$-0.0846990\pi$
$774$		0			0
$775$	5.64295	−	5.64295i	0.202701	−	0.202701i
$776$		0			0
$777$	1.26078	+	1.26078i	0.0452301	+	0.0452301i
$778$		0			0
$779$	28.1979	+	28.1979i	1.01029	+	1.01029i
$780$		0			0
$781$	−0.460713			−0.0164856
$782$		0			0
$783$	−6.69819			−0.239374
$784$		0			0
$785$	−15.8737	−	15.8737i	−0.566556	−	0.566556i
$786$		0			0
$787$	−30.0405	−	30.0405i	−1.07083	−	1.07083i	−0.997293	−	0.0735341i	$-0.976572\pi$
$787$	−30.0405	−	30.0405i	−1.07083	−	1.07083i	−0.0735341	−	0.997293i	$-0.523428\pi$
$788$		0			0
$789$	0.478947	−	0.478947i	0.0170510	−	0.0170510i
$790$		0			0
$791$			28.1132i			0.999590i
$792$		0			0
$793$	26.1019	−	26.1019i	0.926906	−	0.926906i
$794$		0			0
$795$	−0.400047			−0.0141882
$796$		0			0
$797$			39.4840i			1.39860i	0.714831	+	0.699298i	$0.246504\pi$
$797$			39.4840i			1.39860i	−0.714831	+	0.699298i	$0.753496\pi$
$798$		0			0
$799$	34.3526	−	9.01682i	1.21531	−	0.318992i
$800$		0			0
$801$		−	12.8004i		−	0.452279i
$802$		0			0
$803$	−12.0621			−0.425664
$804$		0			0
$805$	−18.8279	+	18.8279i	−0.663595	+	0.663595i
$806$		0			0
$807$			1.91359i			0.0673616i
$808$		0			0
$809$	−22.5276	+	22.5276i	−0.792030	+	0.792030i	−0.981824	−	0.189794i	$-0.939218\pi$
$809$	−22.5276	+	22.5276i	−0.792030	+	0.792030i	0.189794	+	0.981824i	$0.439218\pi$
$810$		0			0
$811$	−30.7078	−	30.7078i	−1.07830	−	1.07830i	−0.996662	−	0.0816334i	$-0.973986\pi$
$811$	−30.7078	−	30.7078i	−1.07830	−	1.07830i	−0.0816334	−	0.996662i	$-0.526014\pi$
$812$		0			0
$813$	−2.05385	−	2.05385i	−0.0720318	−	0.0720318i
$814$		0			0
$815$	−2.85862			−0.100133
$816$		0			0
$817$	25.6570			0.897625
$818$		0			0
$819$	20.0568	+	20.0568i	0.700841	+	0.700841i
$820$		0			0
$821$	−6.72368	−	6.72368i	−0.234658	−	0.234658i	0.579976	−	0.814634i	$-0.303062\pi$
$821$	−6.72368	−	6.72368i	−0.234658	−	0.234658i	−0.814634	+	0.579976i	$0.803062\pi$
$822$		0			0
$823$	−15.5249	+	15.5249i	−0.541165	+	0.541165i	−0.923870	−	0.382706i	$-0.874992\pi$
$823$	−15.5249	+	15.5249i	−0.541165	+	0.541165i	0.382706	+	0.923870i	$0.374992\pi$
$824$		0			0
$825$			0.136625i			0.00475666i
$826$		0			0
$827$	27.8026	−	27.8026i	0.966791	−	0.966791i	−0.0326746	−	0.999466i	$-0.510402\pi$
$827$	27.8026	−	27.8026i	0.966791	−	0.966791i	0.999466	+	0.0326746i	$0.0104025\pi$
$828$		0			0
$829$	−7.75039			−0.269182			−0.134591	−	0.990901i	$-0.542972\pi$
$829$	−7.75039			−0.269182			−0.134591	+	0.990901i	$0.542972\pi$
$830$		0			0
$831$			0.713729i			0.0247590i
$832$		0			0
$833$	−0.826814	−	3.15003i	−0.0286474	−	0.109142i
$834$		0			0
$835$		−	0.0654903i		−	0.00226639i
$836$		0			0
$837$	5.33784			0.184503
$838$		0			0
$839$	8.10722	−	8.10722i	0.279892	−	0.279892i	−0.553174	−	0.833066i	$-0.686583\pi$
$839$	8.10722	−	8.10722i	0.279892	−	0.279892i	0.833066	+	0.553174i	$0.186583\pi$
$840$		0			0
$841$			71.2827i			2.45803i
$842$		0			0
$843$	0.107646	−	0.107646i	0.00370752	−	0.00370752i
$844$		0			0
$845$	1.00989	+	1.00989i	0.0347414	+	0.0347414i
$846$		0			0
$847$	18.7572	+	18.7572i	0.644504	+	0.644504i
$848$		0			0
$849$	2.78083			0.0954380
$850$		0			0
$851$	−54.5559			−1.87015
$852$		0			0
$853$	19.5663	+	19.5663i	0.669936	+	0.669936i	0.957701	−	0.287765i	$-0.0929123\pi$
$853$	19.5663	+	19.5663i	0.669936	+	0.669936i	−0.287765	+	0.957701i	$0.592912\pi$
$854$		0			0
$855$	7.23127	+	7.23127i	0.247304	+	0.247304i
$856$		0			0
$857$	3.79301	−	3.79301i	0.129567	−	0.129567i	−0.639349	−	0.768916i	$-0.720796\pi$
$857$	3.79301	−	3.79301i	0.129567	−	0.129567i	0.768916	+	0.639349i	$0.220796\pi$
$858$		0			0
$859$		−	8.60568i		−	0.293622i	−0.989165	−	0.146811i	$-0.953099\pi$
$859$		−	8.60568i		−	0.293622i	0.989165	−	0.146811i	$-0.0469009\pi$
$860$		0			0
$861$	2.56839	−	2.56839i	0.0875304	−	0.0875304i
$862$		0			0
$863$	54.1029			1.84168			0.920841	−	0.389937i	$-0.127503\pi$
$863$	54.1029			1.84168			0.920841	+	0.389937i	$0.127503\pi$
$864$		0			0
$865$			14.5329i			0.494134i
$866$		0			0
$867$	−1.82926	−	0.510247i	−0.0621250	−	0.0173289i
$868$		0			0
$869$		−	17.7335i		−	0.601569i
$870$		0			0
$871$	−37.8016			−1.28086
$872$		0			0
$873$	−5.40715	+	5.40715i	−0.183004	+	0.183004i
$874$		0			0
$875$		−	2.79103i		−	0.0943542i
$876$		0			0
$877$	37.1480	−	37.1480i	1.25440	−	1.25440i	0.300671	−	0.953728i	$-0.402789\pi$
$877$	37.1480	−	37.1480i	1.25440	−	1.25440i	0.953728	−	0.300671i	$-0.0972107\pi$
$878$		0			0
$879$	1.04801	+	1.04801i	0.0353483	+	0.0353483i
$880$		0			0
$881$	−21.8952	−	21.8952i	−0.737667	−	0.737667i	0.234459	−	0.972126i	$-0.424668\pi$
$881$	−21.8952	−	21.8952i	−0.737667	−	0.737667i	−0.972126	+	0.234459i	$0.924668\pi$
$882$		0			0
$883$	38.5522			1.29739			0.648693	−	0.761051i	$-0.275316\pi$
$883$	38.5522			1.29739			0.648693	+	0.761051i	$0.275316\pi$
$884$		0			0
$885$	0.472959			0.0158983
$886$		0			0
$887$	14.4598	+	14.4598i	0.485512	+	0.485512i	0.906887	−	0.421375i	$-0.138452\pi$
$887$	14.4598	+	14.4598i	0.485512	+	0.485512i	−0.421375	+	0.906887i	$0.638452\pi$
$888$		0			0
$889$	−31.1552	−	31.1552i	−1.04491	−	1.04491i
$890$		0			0
$891$	7.68622	−	7.68622i	0.257498	−	0.257498i
$892$		0			0
$893$		−	29.4864i		−	0.986725i
$894$		0			0
$895$	15.2711	−	15.2711i	0.510458	−	0.510458i
$896$		0			0
$897$	3.62534			0.121046
$898$		0			0
$899$		−	79.9161i		−	2.66535i
$900$		0			0
$901$	3.74856	+	14.2814i	0.124883	+	0.475782i
$902$		0			0
$903$		−	2.33695i		−	0.0777689i
$904$		0			0
$905$	3.65552			0.121514
$906$		0			0
$907$	2.10137	−	2.10137i	0.0697748	−	0.0697748i	−0.671358	−	0.741133i	$-0.734289\pi$
$907$	2.10137	−	2.10137i	0.0697748	−	0.0697748i	0.741133	+	0.671358i	$0.234289\pi$
$908$		0			0
$909$		−	8.46246i		−	0.280682i
$910$		0			0
$911$	−18.3384	+	18.3384i	−0.607579	+	0.607579i	−0.942313	−	0.334733i	$-0.891354\pi$
$911$	−18.3384	+	18.3384i	−0.607579	+	0.607579i	0.334733	+	0.942313i	$0.391354\pi$
$912$		0			0
$913$	1.31455	+	1.31455i	0.0435051	+	0.0435051i
$914$		0			0
$915$	−0.857175	−	0.857175i	−0.0283373	−	0.0283373i
$916$		0			0
$917$	32.4411			1.07130
$918$		0			0
$919$	−13.2875			−0.438313			−0.219157	−	0.975690i	$-0.570331\pi$
$919$	−13.2875			−0.438313			−0.219157	+	0.975690i	$0.570331\pi$
$920$		0			0
$921$	1.65731	+	1.65731i	0.0546102	+	0.0546102i
$922$		0			0
$923$	−0.906118	−	0.906118i	−0.0298252	−	0.0298252i
$924$		0			0
$925$	4.04367	−	4.04367i	0.132955	−	0.132955i
$926$		0			0
$927$		−	15.0008i		−	0.492690i
$928$		0			0
$929$	3.35997	−	3.35997i	0.110237	−	0.110237i	−0.649837	−	0.760074i	$-0.725163\pi$
$929$	3.35997	−	3.35997i	0.110237	−	0.110237i	0.760074	+	0.649837i	$0.225163\pi$
$930$		0			0
$931$	−2.70381			−0.0886138
$932$		0			0
$933$			0.0801396i			0.00262365i
$934$		0			0
$935$	4.87740	−	1.28021i	0.159508	−	0.0418674i
$936$		0			0
$937$			13.3082i			0.434759i	0.976087	+	0.217380i	$0.0697509\pi$
$937$			13.3082i			0.434759i	−0.976087	+	0.217380i	$0.930249\pi$
$938$		0			0
$939$	−1.18500			−0.0386710
$940$		0			0
$941$	−3.04861	+	3.04861i	−0.0993817	+	0.0993817i	−0.755050	−	0.655668i	$-0.772387\pi$
$941$	−3.04861	+	3.04861i	−0.0993817	+	0.0993817i	0.655668	+	0.755050i	$0.272387\pi$
$942$		0			0
$943$			111.138i			3.61916i
$944$		0			0
$945$	1.32006	−	1.32006i	0.0429416	−	0.0429416i
$946$		0			0
$947$	−38.5353	−	38.5353i	−1.25223	−	1.25223i	−0.954719	−	0.297510i	$-0.903844\pi$
$947$	−38.5353	−	38.5353i	−1.25223	−	1.25223i	−0.297510	−	0.954719i	$-0.596156\pi$
$948$		0			0
$949$	−23.7235	−	23.7235i	−0.770096	−	0.770096i
$950$		0			0
$951$	2.38477			0.0773316
$952$		0			0
$953$	31.4405			1.01846			0.509229	−	0.860631i	$-0.329931\pi$
$953$	31.4405			1.01846			0.509229	+	0.860631i	$0.329931\pi$
$954$		0			0
$955$	−16.1702	−	16.1702i	−0.523256	−	0.523256i
$956$		0			0
$957$	0.967447	+	0.967447i	0.0312731	+	0.0312731i
$958$		0			0
$959$	6.71352	−	6.71352i	0.216791	−	0.216791i
$960$		0			0
$961$			32.6857i			1.05438i
$962$		0			0
$963$	1.32325	−	1.32325i	0.0426411	−	0.0426411i
$964$		0			0
$965$	7.20843			0.232048
$966$		0			0
$967$			28.4642i			0.915347i	0.889120	+	0.457674i	$0.151317\pi$
$967$			28.4642i			0.915347i	−0.889120	+	0.457674i	$0.848683\pi$
$968$		0			0
$969$	−0.795303	+	1.36139i	−0.0255488	+	0.0437341i
$970$		0			0
$971$		−	44.9224i		−	1.44163i	−0.693128	−	0.720815i	$-0.743768\pi$
$971$		−	44.9224i		−	1.44163i	0.693128	−	0.720815i	$-0.256232\pi$
$972$		0			0
$973$	−21.5903			−0.692153
$974$		0			0
$975$	−0.268709	+	0.268709i	−0.00860558	+	0.00860558i
$976$		0			0
$977$		−	37.8272i		−	1.21020i	−0.796150	−	0.605100i	$-0.793133\pi$
$977$		−	37.8272i		−	1.21020i	0.796150	−	0.605100i	$-0.206867\pi$
$978$		0			0
$979$	−3.70534	+	3.70534i	−0.118423	+	0.118423i
$980$		0			0
$981$	−29.9204	−	29.9204i	−0.955284	−	0.955284i
$982$		0			0
$983$	−26.7685	−	26.7685i	−0.853783	−	0.853783i	0.136814	−	0.990597i	$-0.456314\pi$
$983$	−26.7685	−	26.7685i	−0.853783	−	0.853783i	−0.990597	+	0.136814i	$0.956314\pi$
$984$		0			0
$985$	−16.0793			−0.512330
$986$		0			0
$987$	−2.68575			−0.0854883
$988$		0			0
$989$	50.5619	+	50.5619i	1.60777	+	1.60777i
$990$		0			0
$991$	−12.6185	−	12.6185i	−0.400838	−	0.400838i	0.477690	−	0.878528i	$-0.341474\pi$
$991$	−12.6185	−	12.6185i	−0.400838	−	0.400838i	−0.878528	+	0.477690i	$0.841474\pi$
$992$		0			0
$993$	0.982814	−	0.982814i	0.0311887	−	0.0311887i
$994$		0			0
$995$			10.5825i			0.335487i
$996$		0			0
$997$	36.3754	−	36.3754i	1.15202	−	1.15202i	0.165872	−	0.986147i	$-0.446956\pi$
$997$	36.3754	−	36.3754i	1.15202	−	1.15202i	0.986147	−	0.165872i	$-0.0530440\pi$
$998$		0			0
$999$	3.82503			0.121019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	340.2.o.a.81.3	yes	12
3.2	odd	2		3060.2.be.b.1441.6		12
4.3	odd	2		1360.2.bt.c.81.4		12
5.2	odd	4		1700.2.m.f.149.3		12
5.3	odd	4		1700.2.m.c.149.4		12
5.4	even	2		1700.2.o.d.1101.4		12
17.2	even	8		5780.2.a.n.1.4		6
17.4	even	4	inner	340.2.o.a.21.3	✓	12
17.8	even	8		5780.2.c.h.5201.7		12
17.9	even	8		5780.2.c.h.5201.6		12
17.15	even	8		5780.2.a.m.1.3		6
51.38	odd	4		3060.2.be.b.361.6		12
68.55	odd	4		1360.2.bt.c.1041.4		12
85.4	even	4		1700.2.o.d.701.4		12
85.38	odd	4		1700.2.m.f.1449.3		12
85.72	odd	4		1700.2.m.c.1449.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.o.a.21.3	✓	12	17.4	even	4	inner
340.2.o.a.81.3	yes	12	1.1	even	1	trivial
1360.2.bt.c.81.4		12	4.3	odd	2
1360.2.bt.c.1041.4		12	68.55	odd	4
1700.2.m.c.149.4		12	5.3	odd	4
1700.2.m.c.1449.4		12	85.72	odd	4
1700.2.m.f.149.3		12	5.2	odd	4
1700.2.m.f.1449.3		12	85.38	odd	4
1700.2.o.d.701.4		12	85.4	even	4
1700.2.o.d.1101.4		12	5.4	even	2
3060.2.be.b.361.6		12	51.38	odd	4
3060.2.be.b.1441.6		12	3.2	odd	2
5780.2.a.m.1.3		6	17.15	even	8
5780.2.a.n.1.4		6	17.2	even	8
5780.2.c.h.5201.6		12	17.9	even	8
5780.2.c.h.5201.7		12	17.8	even	8

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:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0789919 - 0.0789919i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(1.97356 - 1.97356i) q^{7} -2.98752i q^{9} +(-0.864802 + 0.864802i) q^{11} -3.40173 q^{13} +0.111711i q^{15} +(3.98802 - 1.04677i) q^{17} -3.42309i q^{19} -0.311790 q^{21} +(6.74584 - 6.74584i) q^{23} +1.00000i q^{25} +(-0.472965 + 0.472965i) q^{27} +(7.08106 + 7.08106i) q^{29} +(-5.64295 - 5.64295i) q^{31} +0.136625 q^{33} -2.79103 q^{35} +(-4.04367 - 4.04367i) q^{37} +(0.268709 + 0.268709i) q^{39} +(-8.23755 + 8.23755i) q^{41} +7.49527i q^{43} +(-2.11250 + 2.11250i) q^{45} +8.61396 q^{47} -0.789873i q^{49} +(-0.397707 - 0.232335i) q^{51} +3.58108i q^{53} +1.22301 q^{55} +(-0.270396 + 0.270396i) q^{57} -4.23376i q^{59} +(-7.67312 + 7.67312i) q^{61} +(-5.89605 - 5.89605i) q^{63} +(2.40539 + 2.40539i) q^{65} +11.1125 q^{67} -1.06573 q^{69} +(0.266369 + 0.266369i) q^{71} +(6.97393 + 6.97393i) q^{73} +(0.0789919 - 0.0789919i) q^{75} +3.41348i q^{77} +(-10.2529 + 10.2529i) q^{79} -8.88784 q^{81} -1.52005i q^{83} +(-3.56013 - 2.07978i) q^{85} -1.11869i q^{87} +4.28461 q^{89} +(-6.71352 + 6.71352i) q^{91} +0.891494i q^{93} +(-2.42049 + 2.42049i) q^{95} +(-1.80991 - 1.80991i) q^{97} +(2.58361 + 2.58361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{11} + 16 q^{13} - 4 q^{17} + 16 q^{21} + 12 q^{23} - 20 q^{27} + 4 q^{29} - 8 q^{31} - 48 q^{33} - 8 q^{35} - 20 q^{37} + 36 q^{39} + 8 q^{41} + 8 q^{45} - 8 q^{47} + 24 q^{51} + 16 q^{55}+ \cdots - 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^11 + 16 * q^13 - 4 * q^17 + 16 * q^21 + 12 * q^23 - 20 * q^27 + 4 * q^29 - 8 * q^31 - 48 * q^33 - 8 * q^35 - 20 * q^37 + 36 * q^39 + 8 * q^41 + 8 * q^45 - 8 * q^47 + 24 * q^51 + 16 * q^55 - 8 * q^61 + 4 * q^63 + 4 * q^65 + 32 * q^67 - 32 * q^69 + 28 * q^71 - 4 * q^75 - 24 * q^79 - 4 * q^81 - 4 * q^85 - 56 * q^89 - 4 * q^91 + 8 * q^95 - 44 * q^97 - 40 * q^99

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