LMFDB - Embedded newform 1064.2.q.n.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, 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:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.2
Root			$-1.19508 + 2.06994i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.n.457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19508 + 2.06994i) q^{3} +(-1.62589 - 2.81613i) q^{5} +(2.05789 + 1.66286i) q^{7} +(-1.35644 - 2.34943i) q^{9} +O(q^{10})$	\(q+(-1.19508 + 2.06994i) q^{3} +(-1.62589 - 2.81613i) q^{5} +(2.05789 + 1.66286i) q^{7} +(-1.35644 - 2.34943i) q^{9} +(0.201447 - 0.348916i) q^{11} -1.63029 q^{13} +7.77230 q^{15} +(-2.21778 + 3.84130i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-5.90137 + 2.27246i) q^{21} +(-0.418614 - 0.725061i) q^{23} +(-2.78706 + 4.82733i) q^{25} -0.686255 q^{27} -5.33215 q^{29} +(-1.58020 + 2.73699i) q^{31} +(0.481491 + 0.833966i) q^{33} +(1.33692 - 8.49891i) q^{35} +(-5.71311 - 9.89540i) q^{37} +(1.94832 - 3.37460i) q^{39} -2.00000 q^{41} +1.93761 q^{43} +(-4.41086 + 7.63983i) q^{45} +(-6.32419 - 10.9538i) q^{47} +(1.46981 + 6.84395i) q^{49} +(-5.30085 - 9.18134i) q^{51} +(5.75320 - 9.96483i) q^{53} -1.31012 q^{55} +2.39016 q^{57} +(-2.58481 + 4.47702i) q^{59} +(-0.0632036 - 0.109472i) q^{61} +(1.11535 - 7.09043i) q^{63} +(2.65067 + 4.59110i) q^{65} +(1.23638 - 2.14148i) q^{67} +2.00111 q^{69} -2.17338 q^{71} +(-6.25982 + 10.8423i) q^{73} +(-6.66153 - 11.5381i) q^{75} +(0.994752 - 0.383053i) q^{77} +(2.20013 + 3.81073i) q^{79} +(4.88946 - 8.46879i) q^{81} -1.87386 q^{83} +14.4235 q^{85} +(6.37236 - 11.0372i) q^{87} +(-7.29262 - 12.6312i) q^{89} +(-3.35495 - 2.71093i) q^{91} +(-3.77694 - 6.54186i) q^{93} +(-1.62589 + 2.81613i) q^{95} -7.50694 q^{97} -1.09300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.19508	+	2.06994i	−0.689981	+	1.19508i	0.281863	+	0.959455i	$0.409048\pi$
$3$	−1.19508	+	2.06994i	−0.689981	+	1.19508i	−0.971844	+	0.235627i	$0.924286\pi$
$4$		0			0
$5$	−1.62589	−	2.81613i	−0.727122	−	1.25941i	−0.958095	−	0.286452i	$-0.907524\pi$
$5$	−1.62589	−	2.81613i	−0.727122	−	1.25941i	0.230973	−	0.972960i	$-0.425809\pi$
$6$		0			0
$7$	2.05789	+	1.66286i	0.777809	+	0.628501i
$7$	2.05789	+	1.66286i	0.777809	+	0.628501i
$8$		0			0
$9$	−1.35644	−	2.34943i	−0.452147	−	0.783142i
$10$		0			0
$11$	0.201447	−	0.348916i	0.0607385	−	0.105202i	−0.834057	−	0.551678i	$-0.813988\pi$
$11$	0.201447	−	0.348916i	0.0607385	−	0.105202i	0.894796	+	0.446476i	$0.147321\pi$
$12$		0			0
$13$	−1.63029			−0.452160			−0.226080	−	0.974109i	$-0.572591\pi$
$13$	−1.63029			−0.452160			−0.226080	+	0.974109i	$0.572591\pi$
$14$		0			0
$15$	7.77230			2.00680
$16$		0			0
$17$	−2.21778	+	3.84130i	−0.537890	+	0.931652i	0.461128	+	0.887334i	$0.347445\pi$
$17$	−2.21778	+	3.84130i	−0.537890	+	0.931652i	−0.999017	+	0.0443186i	$0.985888\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$		0			0
$21$	−5.90137	+	2.27246i	−1.28778	+	0.495892i
$22$		0			0
$23$	−0.418614	−	0.725061i	−0.0872870	−	0.151186i	0.819076	−	0.573684i	$-0.194486\pi$
$23$	−0.418614	−	0.725061i	−0.0872870	−	0.151186i	−0.906363	+	0.422499i	$0.861153\pi$
$24$		0			0
$25$	−2.78706	+	4.82733i	−0.557412	+	0.965466i
$26$		0			0
$27$	−0.686255			−0.132070
$28$		0			0
$29$	−5.33215			−0.990156			−0.495078	−	0.868849i	$-0.664860\pi$
$29$	−5.33215			−0.990156			−0.495078	+	0.868849i	$0.664860\pi$
$30$		0			0
$31$	−1.58020	+	2.73699i	−0.283813	+	0.491578i	−0.972321	−	0.233651i	$-0.924933\pi$
$31$	−1.58020	+	2.73699i	−0.283813	+	0.491578i	0.688508	+	0.725229i	$0.258266\pi$
$32$		0			0
$33$	0.481491	+	0.833966i	0.0838168	+	0.145175i
$34$		0			0
$35$	1.33692	−	8.49891i	0.225980	−	1.43658i
$36$		0			0
$37$	−5.71311	−	9.89540i	−0.939230	−	1.62679i	−0.766912	−	0.641753i	$-0.778208\pi$
$37$	−5.71311	−	9.89540i	−0.939230	−	1.62679i	−0.172318	−	0.985041i	$-0.555126\pi$
$38$		0			0
$39$	1.94832	−	3.37460i	0.311982	−	0.540368i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	1.93761			0.295483			0.147742	−	0.989026i	$-0.452800\pi$
$43$	1.93761			0.295483			0.147742	+	0.989026i	$0.452800\pi$
$44$		0			0
$45$	−4.41086	+	7.63983i	−0.657532	+	1.13888i
$46$		0			0
$47$	−6.32419	−	10.9538i	−0.922479	−	1.59778i	−0.795567	−	0.605866i	$-0.792827\pi$
$47$	−6.32419	−	10.9538i	−0.922479	−	1.59778i	−0.126912	−	0.991914i	$-0.540506\pi$
$48$		0			0
$49$	1.46981	+	6.84395i	0.209973	+	0.977707i
$50$		0			0
$51$	−5.30085	−	9.18134i	−0.742267	−	1.28564i
$52$		0			0
$53$	5.75320	−	9.96483i	0.790263	−	1.36878i	−0.135541	−	0.990772i	$-0.543277\pi$
$53$	5.75320	−	9.96483i	0.790263	−	1.36878i	0.925804	−	0.378004i	$-0.123389\pi$
$54$		0			0
$55$	−1.31012			−0.176657
$56$		0			0
$57$	2.39016			0.316585
$58$		0			0
$59$	−2.58481	+	4.47702i	−0.336514	+	0.582859i	−0.983774	−	0.179410i	$-0.942581\pi$
$59$	−2.58481	+	4.47702i	−0.336514	+	0.582859i	0.647261	+	0.762269i	$0.275914\pi$
$60$		0			0
$61$	−0.0632036	−	0.109472i	−0.00809239	−	0.0140164i	0.861951	−	0.506992i	$-0.169243\pi$
$61$	−0.0632036	−	0.109472i	−0.00809239	−	0.0140164i	−0.870043	+	0.492975i	$0.835909\pi$
$62$		0			0
$63$	1.11535	−	7.09043i	0.140521	−	0.893310i
$64$		0			0
$65$	2.65067	+	4.59110i	0.328775	+	0.569455i
$66$		0			0
$67$	1.23638	−	2.14148i	0.151048	−	0.261623i	−0.780565	−	0.625075i	$-0.785069\pi$
$67$	1.23638	−	2.14148i	0.151048	−	0.261623i	0.931613	+	0.363452i	$0.118402\pi$
$68$		0			0
$69$	2.00111			0.240906
$70$		0			0
$71$	−2.17338			−0.257932			−0.128966	−	0.991649i	$-0.541166\pi$
$71$	−2.17338			−0.257932			−0.128966	+	0.991649i	$0.541166\pi$
$72$		0			0
$73$	−6.25982	+	10.8423i	−0.732657	+	1.26900i	0.223087	+	0.974798i	$0.428387\pi$
$73$	−6.25982	+	10.8423i	−0.732657	+	1.26900i	−0.955744	+	0.294200i	$0.904947\pi$
$74$		0			0
$75$	−6.66153	−	11.5381i	−0.769207	−	1.33231i
$76$		0			0
$77$	0.994752	−	0.383053i	0.113363	−	0.0436529i
$78$		0			0
$79$	2.20013	+	3.81073i	0.247533	+	0.428740i	0.962841	−	0.270069i	$-0.0870467\pi$
$79$	2.20013	+	3.81073i	0.247533	+	0.428740i	−0.715307	+	0.698810i	$0.753713\pi$
$80$		0			0
$81$	4.88946	−	8.46879i	0.543273	−	0.940976i
$82$		0			0
$83$	−1.87386			−0.205683			−0.102841	−	0.994698i	$-0.532793\pi$
$83$	−1.87386			−0.205683			−0.102841	+	0.994698i	$0.532793\pi$
$84$		0			0
$85$	14.4235			1.56445
$86$		0			0
$87$	6.37236	−	11.0372i	0.683189	−	1.18332i
$88$		0			0
$89$	−7.29262	−	12.6312i	−0.773016	−	1.33890i	−0.935903	−	0.352259i	$-0.885414\pi$
$89$	−7.29262	−	12.6312i	−0.773016	−	1.33890i	0.162886	−	0.986645i	$-0.447920\pi$
$90$		0			0
$91$	−3.35495	−	2.71093i	−0.351694	−	0.284183i
$92$		0			0
$93$	−3.77694	−	6.54186i	−0.391651	−	0.678359i
$94$		0			0
$95$	−1.62589	+	2.81613i	−0.166813	+	0.288929i
$96$		0			0
$97$	−7.50694			−0.762215			−0.381107	−	0.924531i	$-0.624457\pi$
$97$	−7.50694			−0.762215			−0.381107	+	0.924531i	$0.624457\pi$
$98$		0			0
$99$	−1.09300			−0.109851
$100$		0			0
$101$	1.60230	−	2.77526i	0.159435	−	0.276149i	−0.775230	−	0.631679i	$-0.782366\pi$
$101$	1.60230	−	2.77526i	0.159435	−	0.276149i	0.934665	+	0.355530i	$0.115700\pi$
$102$		0			0
$103$	−2.91848	−	5.05495i	−0.287566	−	0.498079i	0.685662	−	0.727920i	$-0.259513\pi$
$103$	−2.91848	−	5.05495i	−0.287566	−	0.498079i	−0.973228	+	0.229841i	$0.926179\pi$
$104$		0			0
$105$	15.9945	+	12.9242i	1.56091	+	1.26128i
$106$		0			0
$107$	−7.67630	−	13.2957i	−0.742096	−	1.28535i	−0.951539	−	0.307527i	$-0.900498\pi$
$107$	−7.67630	−	13.2957i	−0.742096	−	1.28535i	0.209443	−	0.977821i	$-0.432835\pi$
$108$		0			0
$109$	−5.96190	+	10.3263i	−0.571046	+	0.989081i	0.425413	+	0.904999i	$0.360129\pi$
$109$	−5.96190	+	10.3263i	−0.571046	+	0.989081i	−0.996459	+	0.0840813i	$0.973204\pi$
$110$		0			0
$111$	27.3106			2.59220
$112$		0			0
$113$	−19.0112			−1.78842			−0.894210	−	0.447648i	$-0.852262\pi$
$113$	−19.0112			−1.78842			−0.894210	+	0.447648i	$0.852262\pi$
$114$		0			0
$115$	−1.36124	+	2.35774i	−0.126937	+	0.219861i
$116$		0			0
$117$	2.21139	+	3.83023i	0.204443	+	0.354105i
$118$		0			0
$119$	−10.9515	+	4.21712i	−1.00392	+	0.386583i
$120$		0			0
$121$	5.41884	+	9.38570i	0.492622	+	0.853246i
$122$		0			0
$123$	2.39016	−	4.13989i	0.215514	−	0.373281i
$124$		0			0
$125$	1.86692			0.166982
$126$		0			0
$127$	7.16086			0.635424			0.317712	−	0.948187i	$-0.397086\pi$
$127$	7.16086			0.635424			0.317712	+	0.948187i	$0.397086\pi$
$128$		0			0
$129$	−2.31561	+	4.01075i	−0.203878	+	0.353127i
$130$		0			0
$131$	0.980160	+	1.69769i	0.0856370	+	0.148328i	0.905662	−	0.423999i	$-0.139374\pi$
$131$	0.980160	+	1.69769i	0.0856370	+	0.148328i	−0.820026	+	0.572327i	$0.806041\pi$
$132$		0			0
$133$	0.411132	−	2.61361i	0.0356497	−	0.226629i
$134$		0			0
$135$	1.11578	+	1.93258i	0.0960308	+	0.166330i
$136$		0			0
$137$	8.05386	−	13.9497i	0.688088	−	1.19180i	−0.284368	−	0.958715i	$-0.591784\pi$
$137$	8.05386	−	13.9497i	0.688088	−	1.19180i	0.972456	−	0.233088i	$-0.0748830\pi$
$138$		0			0
$139$	−2.58462			−0.219224			−0.109612	−	0.993974i	$-0.534961\pi$
$139$	−2.58462			−0.219224			−0.109612	+	0.993974i	$0.534961\pi$
$140$		0			0
$141$	30.2317			2.54597
$142$		0			0
$143$	−0.328416	+	0.568832i	−0.0274635	+	0.0475682i
$144$		0			0
$145$	8.66951	+	15.0160i	0.719964	+	1.24701i
$146$		0			0
$147$	−15.9231	−	5.13666i	−1.31332	−	0.423664i
$148$		0			0
$149$	4.84038	+	8.38379i	0.396540	+	0.686827i	0.993296	−	0.115595i	$-0.0368776\pi$
$149$	4.84038	+	8.38379i	0.396540	+	0.686827i	−0.596757	+	0.802422i	$0.703544\pi$
$150$		0			0
$151$	−1.95220	+	3.38131i	−0.158868	+	0.275167i	−0.934461	−	0.356066i	$-0.884118\pi$
$151$	−1.95220	+	3.38131i	−0.158868	+	0.275167i	0.775593	+	0.631233i	$0.217451\pi$
$152$		0			0
$153$	12.0331			0.972822
$154$		0			0
$155$	10.2770			0.825466
$156$		0			0
$157$	−7.51743	+	13.0206i	−0.599956	+	1.03915i	0.392871	+	0.919594i	$0.371482\pi$
$157$	−7.51743	+	13.0206i	−0.599956	+	1.03915i	−0.992827	+	0.119561i	$0.961851\pi$
$158$		0			0
$159$	13.7511	+	23.8176i	1.09053	+	1.88886i
$160$		0			0
$161$	0.344211	−	2.18819i	0.0271277	−	0.172453i
$162$		0			0
$163$	8.55353	+	14.8151i	0.669964	+	1.16041i	0.977914	+	0.209009i	$0.0670238\pi$
$163$	8.55353	+	14.8151i	0.669964	+	1.16041i	−0.307950	+	0.951403i	$0.599643\pi$
$164$		0			0
$165$	1.56570	−	2.71188i	0.121890	−	0.211120i
$166$		0			0
$167$	9.06642			0.701580			0.350790	−	0.936454i	$-0.385913\pi$
$167$	9.06642			0.701580			0.350790	+	0.936454i	$0.385913\pi$
$168$		0			0
$169$	−10.3422			−0.795552
$170$		0			0
$171$	−1.35644	+	2.34943i	−0.103730	+	0.179665i
$172$		0			0
$173$	−5.64278	−	9.77358i	−0.429013	−	0.743072i	0.567773	−	0.823185i	$-0.307805\pi$
$173$	−5.64278	−	9.77358i	−0.429013	−	0.743072i	−0.996786	+	0.0801135i	$0.974472\pi$
$174$		0			0
$175$	−13.7626	+	5.29962i	−1.04036	+	0.400614i
$176$		0			0
$177$	−6.17812	−	10.7008i	−0.464376	−	0.804323i
$178$		0			0
$179$	−11.7296	+	20.3162i	−0.876709	+	1.51850i	−0.0217770	+	0.999763i	$0.506932\pi$
$179$	−11.7296	+	20.3162i	−0.876709	+	1.51850i	−0.854932	+	0.518741i	$0.826401\pi$
$180$		0			0
$181$	−5.24897			−0.390153			−0.195076	−	0.980788i	$-0.562495\pi$
$181$	−5.24897			−0.390153			−0.195076	+	0.980788i	$0.562495\pi$
$182$		0			0
$183$	0.302134			0.0223344
$184$		0			0
$185$	−18.5778	+	32.1777i	−1.36587	+	2.36575i
$186$		0			0
$187$	0.893527	+	1.54763i	0.0653412	+	0.113174i
$188$		0			0
$189$	−1.41224	−	1.14114i	−0.102725	−	0.0830060i
$190$		0			0
$191$	9.71067	+	16.8194i	0.702640	+	1.21701i	0.967537	+	0.252731i	$0.0813287\pi$
$191$	9.71067	+	16.8194i	0.702640	+	1.21701i	−0.264897	+	0.964277i	$0.585338\pi$
$192$		0			0
$193$	2.94528	−	5.10137i	0.212006	−	0.367205i	−0.740336	−	0.672237i	$-0.765334\pi$
$193$	2.94528	−	5.10137i	0.212006	−	0.367205i	0.952342	+	0.305032i	$0.0986671\pi$
$194$		0			0
$195$	−12.6711			−0.907394
$196$		0			0
$197$	0.994596			0.0708620			0.0354310	−	0.999372i	$-0.488720\pi$
$197$	0.994596			0.0708620			0.0354310	+	0.999372i	$0.488720\pi$
$198$		0			0
$199$	−0.298176	+	0.516455i	−0.0211371	+	0.0366106i	−0.876400	−	0.481583i	$-0.840062\pi$
$199$	−0.298176	+	0.516455i	−0.0211371	+	0.0366106i	0.855263	+	0.518194i	$0.173395\pi$
$200$		0			0
$201$	2.95515	+	5.11848i	0.208441	+	0.361030i
$202$		0			0
$203$	−10.9730	−	8.86661i	−0.770152	−	0.622314i
$204$		0			0
$205$	3.25179	+	5.63226i	0.227115	+	0.393374i
$206$		0			0
$207$	−1.13565	+	1.96701i	−0.0789332	+	0.136716i
$208$		0			0
$209$	−0.402893			−0.0278687
$210$		0			0
$211$	12.2877			0.845921			0.422960	−	0.906148i	$-0.360991\pi$
$211$	12.2877			0.845921			0.422960	+	0.906148i	$0.360991\pi$
$212$		0			0
$213$	2.59736	−	4.49876i	0.177968	−	0.308250i
$214$		0			0
$215$	−3.15035	−	5.45657i	−0.214852	−	0.372135i
$216$		0			0
$217$	−7.80311	+	3.00477i	−0.529709	+	0.203977i
$218$		0			0
$219$	−14.9620	−	25.9149i	−1.01104	−	1.75117i
$220$		0			0
$221$	3.61561	−	6.26242i	0.243212	−	0.421256i
$222$		0			0
$223$	−9.41919			−0.630755			−0.315378	−	0.948966i	$-0.602131\pi$
$223$	−9.41919			−0.630755			−0.315378	+	0.948966i	$0.602131\pi$
$224$		0			0
$225$	15.1219			1.00813
$226$		0			0
$227$	−3.61222	+	6.25656i	−0.239752	+	0.415262i	−0.960643	−	0.277786i	$-0.910399\pi$
$227$	−3.61222	+	6.25656i	−0.239752	+	0.415262i	0.720891	+	0.693048i	$0.243733\pi$
$228$		0			0
$229$	−2.77916	−	4.81365i	−0.183652	−	0.318095i	0.759469	−	0.650543i	$-0.225459\pi$
$229$	−2.77916	−	4.81365i	−0.183652	−	0.318095i	−0.943121	+	0.332448i	$0.892125\pi$
$230$		0			0
$231$	−0.395913	+	2.51686i	−0.0260491	+	0.165597i
$232$		0			0
$233$	−5.76784	−	9.99020i	−0.377864	−	0.654480i	0.612887	−	0.790170i	$-0.290008\pi$
$233$	−5.76784	−	9.99020i	−0.377864	−	0.654480i	−0.990751	+	0.135691i	$0.956675\pi$
$234$		0			0
$235$	−20.5649	+	35.6195i	−1.34151	+	2.32356i
$236$		0			0
$237$	−10.5173			−0.683173
$238$		0			0
$239$	28.9484			1.87252			0.936259	−	0.351309i	$-0.114263\pi$
$239$	28.9484			1.87252			0.936259	+	0.351309i	$0.114263\pi$
$240$		0			0
$241$	−11.1396	+	19.2944i	−0.717566	+	1.24286i	0.244396	+	0.969676i	$0.421410\pi$
$241$	−11.1396	+	19.2944i	−0.717566	+	1.24286i	−0.961962	+	0.273185i	$0.911923\pi$
$242$		0			0
$243$	10.6572	+	18.4588i	0.683661	+	1.18414i
$244$		0			0
$245$	16.8837	−	15.2667i	1.07866	−	0.975355i
$246$		0			0
$247$	0.815143	+	1.41187i	0.0518663	+	0.0898350i
$248$		0			0
$249$	2.23942	−	3.87878i	0.141917	−	0.245808i
$250$		0			0
$251$	−6.67790			−0.421505			−0.210753	−	0.977539i	$-0.567591\pi$
$251$	−6.67790			−0.421505			−0.210753	+	0.977539i	$0.567591\pi$
$252$		0			0
$253$	−0.337314			−0.0212067
$254$		0			0
$255$	−17.2372	+	29.8558i	−1.07944	+	1.86964i
$256$		0			0
$257$	13.9189	+	24.1082i	0.868236	+	1.50383i	0.863798	+	0.503839i	$0.168080\pi$
$257$	13.9189	+	24.1082i	0.868236	+	1.50383i	0.00443863	+	0.999990i	$0.498587\pi$
$258$		0			0
$259$	4.69769	−	29.8637i	0.291900	−	1.85564i
$260$		0			0
$261$	7.23275	+	12.5275i	0.447696	+	0.775433i
$262$		0			0
$263$	1.42613	−	2.47013i	0.0879388	−	0.152315i	−0.818701	−	0.574220i	$-0.805305\pi$
$263$	1.42613	−	2.47013i	0.0879388	−	0.152315i	0.906640	+	0.421906i	$0.138639\pi$
$264$		0			0
$265$	−37.4164			−2.29847
$266$		0			0
$267$	34.8611			2.13347
$268$		0			0
$269$	−4.19250	+	7.26162i	−0.255621	+	0.442749i	−0.965064	−	0.262014i	$-0.915613\pi$
$269$	−4.19250	+	7.26162i	−0.255621	+	0.442749i	0.709443	+	0.704763i	$0.248947\pi$
$270$		0			0
$271$	7.12836	+	12.3467i	0.433017	+	0.750008i	0.997131	−	0.0756888i	$-0.0241156\pi$
$271$	7.12836	+	12.3467i	0.433017	+	0.750008i	−0.564114	+	0.825697i	$0.690782\pi$
$272$		0			0
$273$	9.62091	−	3.70476i	0.582284	−	0.224222i
$274$		0			0
$275$	1.12289	+	1.94490i	0.0677127	+	0.117282i
$276$		0			0
$277$	12.6694	−	21.9441i	0.761233	−	1.31849i	−0.180983	−	0.983486i	$-0.557928\pi$
$277$	12.6694	−	21.9441i	0.761233	−	1.31849i	0.942215	−	0.335008i	$-0.108739\pi$
$278$		0			0
$279$	8.57381			0.513301
$280$		0			0
$281$	19.0107			1.13408			0.567041	−	0.823689i	$-0.308088\pi$
$281$	19.0107			1.13408			0.567041	+	0.823689i	$0.308088\pi$
$282$		0			0
$283$	11.7665	−	20.3802i	0.699447	−	1.21148i	−0.269211	−	0.963081i	$-0.586763\pi$
$283$	11.7665	−	20.3802i	0.699447	−	1.21148i	0.968658	−	0.248397i	$-0.0799038\pi$
$284$		0			0
$285$	−3.88615	−	6.73101i	−0.230196	−	0.398711i
$286$		0			0
$287$	−4.11578	−	3.32571i	−0.242947	−	0.196311i
$288$		0			0
$289$	−1.33706	−	2.31586i	−0.0786507	−	0.136227i
$290$		0			0
$291$	8.97141	−	15.5389i	0.525913	−	0.910909i
$292$		0			0
$293$	−11.1260			−0.649989			−0.324995	−	0.945716i	$-0.605362\pi$
$293$	−11.1260			−0.649989			−0.324995	+	0.945716i	$0.605362\pi$
$294$		0			0
$295$	16.8105			0.978746
$296$		0			0
$297$	−0.138244	+	0.239445i	−0.00802171	+	0.0138940i
$298$		0			0
$299$	0.682460	+	1.18206i	0.0394677	+	0.0683600i
$300$		0			0
$301$	3.98739	+	3.22198i	0.229830	+	0.185712i
$302$		0			0
$303$	3.82976	+	6.63333i	0.220014	+	0.381075i
$304$		0			0
$305$	−0.205525	+	0.355979i	−0.0117683	+	0.0203833i
$306$		0			0
$307$	26.8920			1.53481			0.767404	−	0.641164i	$-0.221548\pi$
$307$	26.8920			1.53481			0.767404	+	0.641164i	$0.221548\pi$
$308$		0			0
$309$	13.9513			0.793660
$310$		0			0
$311$	12.5216	−	21.6881i	0.710036	−	1.22982i	−0.254807	−	0.966992i	$-0.582012\pi$
$311$	12.5216	−	21.6881i	0.710036	−	1.22982i	0.964843	−	0.262827i	$-0.0846549\pi$
$312$		0			0
$313$	6.41896	+	11.1180i	0.362821	+	0.628424i	0.988424	−	0.151717i	$-0.0484803\pi$
$313$	6.41896	+	11.1180i	0.362821	+	0.628424i	−0.625603	+	0.780142i	$0.715147\pi$
$314$		0			0
$315$	−21.7810	+	8.38730i	−1.22722	+	0.472571i
$316$		0			0
$317$	6.24249	+	10.8123i	0.350613	+	0.607280i	0.986357	−	0.164620i	$-0.0526399\pi$
$317$	6.24249	+	10.8123i	0.350613	+	0.607280i	−0.635744	+	0.771900i	$0.719307\pi$
$318$		0			0
$319$	−1.07414	+	1.86047i	−0.0601405	+	0.104166i
$320$		0			0
$321$	36.6952			2.04813
$322$		0			0
$323$	4.43555			0.246801
$324$		0			0
$325$	4.54370	−	7.86992i	0.252039	−	0.436545i
$326$		0			0
$327$	−14.2499	−	24.6816i	−0.788022	−	1.36489i
$328$		0			0
$329$	5.20016	−	33.0580i	0.286694	−	1.82255i
$330$		0			0
$331$	−3.11482	−	5.39502i	−0.171206	−	0.296537i	0.767636	−	0.640886i	$-0.221433\pi$
$331$	−3.11482	−	5.39502i	−0.171206	−	0.296537i	−0.938842	+	0.344349i	$0.888100\pi$
$332$		0			0
$333$	−15.4990	+	26.8451i	−0.849341	+	1.47110i
$334$		0			0
$335$	−8.04090			−0.439321
$336$		0			0
$337$	−26.0259			−1.41772			−0.708860	−	0.705349i	$-0.750790\pi$
$337$	−26.0259			−1.41772			−0.708860	+	0.705349i	$0.750790\pi$
$338$		0			0
$339$	22.7199	−	39.3520i	1.23398	−	2.13731i
$340$		0			0
$341$	0.636653	+	1.10272i	0.0344767	+	0.0597154i
$342$		0			0
$343$	−8.35581	+	16.5282i	−0.451171	+	0.892437i
$344$		0			0
$345$	−3.25359	−	5.63539i	−0.175168	−	0.303399i
$346$		0			0
$347$	−4.60355	+	7.97359i	−0.247132	+	0.428045i	−0.962729	−	0.270469i	$-0.912821\pi$
$347$	−4.60355	+	7.97359i	−0.247132	+	0.428045i	0.715597	+	0.698513i	$0.246155\pi$
$348$		0			0
$349$	−26.8773			−1.43871			−0.719354	−	0.694643i	$-0.755562\pi$
$349$	−26.8773			−1.43871			−0.719354	+	0.694643i	$0.755562\pi$
$350$		0			0
$351$	1.11879			0.0597166
$352$		0			0
$353$	10.3602	−	17.9443i	0.551416	−	0.955080i	−0.446757	−	0.894655i	$-0.647421\pi$
$353$	10.3602	−	17.9443i	0.551416	−	0.955080i	0.998173	−	0.0604245i	$-0.0192454\pi$
$354$		0			0
$355$	3.53368	+	6.12051i	0.187548	+	0.324843i
$356$		0			0
$357$	4.35870	−	27.7087i	0.230687	−	1.46650i
$358$		0			0
$359$	10.3347	+	17.9001i	0.545442	+	0.944733i	0.998579	+	0.0532924i	$0.0169715\pi$
$359$	10.3347	+	17.9001i	0.545442	+	0.944733i	−0.453137	+	0.891441i	$0.649695\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	−25.9038			−1.35960
$364$		0			0
$365$	40.7112			2.13092
$366$		0			0
$367$	16.9463	−	29.3519i	0.884590	−	1.53216i	0.0384082	−	0.999262i	$-0.487771\pi$
$367$	16.9463	−	29.3519i	0.884590	−	1.53216i	0.846182	−	0.532894i	$-0.178895\pi$
$368$		0			0
$369$	2.71288	+	4.69885i	0.141227	+	0.244612i
$370$		0			0
$371$	28.4095	−	10.9398i	1.47495	−	0.567964i
$372$		0			0
$373$	−13.5085	−	23.3974i	−0.699444	−	1.21147i	−0.968659	−	0.248393i	$-0.920098\pi$
$373$	−13.5085	−	23.3974i	−0.699444	−	1.21147i	0.269215	−	0.963080i	$-0.413236\pi$
$374$		0			0
$375$	−2.23112	+	3.86441i	−0.115215	+	0.199557i
$376$		0			0
$377$	8.69293			0.447709
$378$		0			0
$379$	−16.8406			−0.865041			−0.432521	−	0.901624i	$-0.642376\pi$
$379$	−16.8406			−0.865041			−0.432521	+	0.901624i	$0.642376\pi$
$380$		0			0
$381$	−8.55782	+	14.8226i	−0.438430	+	0.759383i
$382$		0			0
$383$	16.9859	+	29.4205i	0.867940	+	1.50332i	0.864098	+	0.503323i	$0.167889\pi$
$383$	16.9859	+	29.4205i	0.867940	+	1.50332i	0.00384112	+	0.999993i	$0.498777\pi$
$384$		0			0
$385$	−2.69609	−	2.17855i	−0.137405	−	0.111029i
$386$		0			0
$387$	−2.62826	−	4.55228i	−0.133602	−	0.231405i
$388$		0			0
$389$	5.84231	−	10.1192i	0.296217	−	0.513062i	−0.679051	−	0.734092i	$-0.737608\pi$
$389$	5.84231	−	10.1192i	0.296217	−	0.513062i	0.975267	+	0.221029i	$0.0709416\pi$
$390$		0			0
$391$	3.71357			0.187803
$392$		0			0
$393$	−4.68549			−0.236351
$394$		0			0
$395$	7.15434	−	12.3917i	0.359974	−	0.623493i
$396$		0			0
$397$	5.00887	+	8.67562i	0.251388	+	0.435417i	0.963908	−	0.266235i	$-0.0857796\pi$
$397$	5.00887	+	8.67562i	0.251388	+	0.435417i	−0.712520	+	0.701652i	$0.752446\pi$
$398$		0			0
$399$	4.91869	+	3.97450i	0.246243	+	0.198974i
$400$		0			0
$401$	−5.23488	−	9.06707i	−0.261417	−	0.452788i	0.705202	−	0.709007i	$-0.250857\pi$
$401$	−5.23488	−	9.06707i	−0.261417	−	0.452788i	−0.966619	+	0.256219i	$0.917523\pi$
$402$		0			0
$403$	2.57618	−	4.46208i	0.128329	−	0.222272i
$404$		0			0
$405$	−31.7989			−1.58010
$406$		0			0
$407$	−4.60355			−0.228190
$408$		0			0
$409$	12.0047	−	20.7927i	0.593593	−	1.02813i	−0.400151	−	0.916449i	$-0.631042\pi$
$409$	12.0047	−	20.7927i	0.593593	−	1.02813i	0.993744	−	0.111684i	$-0.0356243\pi$
$410$		0			0
$411$	19.2501	+	33.3421i	0.949535	+	1.64464i
$412$		0			0
$413$	−12.7639	+	4.91504i	−0.628071	+	0.241853i
$414$		0			0
$415$	3.04670	+	5.27703i	0.149556	+	0.259039i
$416$		0			0
$417$	3.08883	−	5.35001i	0.151261	−	0.261991i
$418$		0			0
$419$	−15.1723			−0.741216			−0.370608	−	0.928789i	$-0.620851\pi$
$419$	−15.1723			−0.741216			−0.370608	+	0.928789i	$0.620851\pi$
$420$		0			0
$421$	1.77965			0.0867348			0.0433674	−	0.999059i	$-0.486191\pi$
$421$	1.77965			0.0867348			0.0433674	+	0.999059i	$0.486191\pi$
$422$		0			0
$423$	−17.1568	+	29.7165i	−0.834192	+	1.44486i
$424$		0			0
$425$	−12.3622	−	21.4119i	−0.599652	−	1.03863i
$426$		0			0
$427$	0.0519701	−	0.330379i	0.00251501	−	0.0159882i
$428$		0			0
$429$	−0.784967	−	1.35960i	−0.0378986	−	0.0656422i
$430$		0			0
$431$	−16.3674	+	28.3493i	−0.788392	+	1.36554i	0.138559	+	0.990354i	$0.455753\pi$
$431$	−16.3674	+	28.3493i	−0.788392	+	1.36554i	−0.926951	+	0.375181i	$0.877580\pi$
$432$		0			0
$433$	−4.83058			−0.232143			−0.116071	−	0.993241i	$-0.537030\pi$
$433$	−4.83058			−0.232143			−0.116071	+	0.993241i	$0.537030\pi$
$434$		0			0
$435$	−41.4431			−1.98705
$436$		0			0
$437$	−0.418614	+	0.725061i	−0.0200250	+	0.0346844i
$438$		0			0
$439$	−14.1797	−	24.5600i	−0.676762	−	1.17219i	−0.975950	−	0.217992i	$-0.930049\pi$
$439$	−14.1797	−	24.5600i	−0.676762	−	1.17219i	0.299188	−	0.954194i	$-0.403284\pi$
$440$		0			0
$441$	14.0856	−	12.7366i	0.670745	−	0.606506i
$442$		0			0
$443$	−9.64006	−	16.6971i	−0.458013	−	0.793302i	0.540843	−	0.841124i	$-0.318105\pi$
$443$	−9.64006	−	16.6971i	−0.458013	−	0.793302i	−0.998856	+	0.0478218i	$0.984772\pi$
$444$		0			0
$445$	−23.7141	+	41.0739i	−1.12415	+	1.94709i
$446$		0			0
$447$	−23.1386			−1.09442
$448$		0			0
$449$	−16.0035			−0.755254			−0.377627	−	0.925958i	$-0.623260\pi$
$449$	−16.0035			−0.755254			−0.377627	+	0.925958i	$0.623260\pi$
$450$		0			0
$451$	−0.402893	+	0.697832i	−0.0189715	+	0.0328596i
$452$		0			0
$453$	−4.66608	−	8.08188i	−0.219231	−	0.379720i
$454$		0			0
$455$	−2.17955	+	13.8556i	−0.102179	+	0.649563i
$456$		0			0
$457$	−12.0173	−	20.8147i	−0.562148	−	0.973669i	−0.997309	−	0.0733158i	$-0.976642\pi$
$457$	−12.0173	−	20.8147i	−0.562148	−	0.973669i	0.435161	−	0.900353i	$-0.356691\pi$
$458$		0			0
$459$	1.52196	−	2.63611i	0.0710390	−	0.123043i
$460$		0			0
$461$	27.2907			1.27106			0.635528	−	0.772078i	$-0.280782\pi$
$461$	27.2907			1.27106			0.635528	+	0.772078i	$0.280782\pi$
$462$		0			0
$463$	−25.5689			−1.18829			−0.594143	−	0.804359i	$-0.702509\pi$
$463$	−25.5689			−1.18829			−0.594143	+	0.804359i	$0.702509\pi$
$464$		0			0
$465$	−12.2818	+	21.2727i	−0.569556	+	0.986499i
$466$		0			0
$467$	4.85142	+	8.40291i	0.224497	+	0.388840i	0.956168	−	0.292817i	$-0.0945927\pi$
$467$	4.85142	+	8.40291i	0.224497	+	0.388840i	−0.731671	+	0.681658i	$0.761259\pi$
$468$		0			0
$469$	6.10530	−	2.35099i	0.281917	−	0.108559i
$470$		0			0
$471$	−17.9679	−	31.1213i	−0.827916	−	1.43399i
$472$		0			0
$473$	0.390326	−	0.676064i	0.0179472	−	0.0310855i
$474$		0			0
$475$	5.57412			0.255758
$476$		0			0
$477$	−31.2155			−1.42926
$478$		0			0
$479$	−13.7515	+	23.8183i	−0.628323	+	1.08829i	0.359565	+	0.933120i	$0.382925\pi$
$479$	−13.7515	+	23.8183i	−0.628323	+	1.08829i	−0.987888	+	0.155167i	$0.950408\pi$
$480$		0			0
$481$	9.31400	+	16.1323i	0.424682	+	0.735571i
$482$		0			0
$483$	4.11807	+	3.32756i	0.187378	+	0.151409i
$484$		0			0
$485$	12.2055	+	21.1405i	0.554223	+	0.959942i
$486$		0			0
$487$	−3.38738	+	5.86711i	−0.153497	+	0.265864i	−0.932511	−	0.361142i	$-0.882387\pi$
$487$	−3.38738	+	5.86711i	−0.153497	+	0.265864i	0.779014	+	0.627007i	$0.215720\pi$
$488$		0			0
$489$	−40.8887			−1.84905
$490$		0			0
$491$	−41.5603			−1.87559			−0.937796	−	0.347188i	$-0.887137\pi$
$491$	−41.5603			−1.87559			−0.937796	+	0.347188i	$0.887137\pi$
$492$		0			0
$493$	11.8255	−	20.4824i	0.532595	−	0.922481i
$494$		0			0
$495$	1.77711	+	3.07804i	0.0798750	+	0.138348i
$496$		0			0
$497$	−4.47256	−	3.61401i	−0.200622	−	0.162111i
$498$		0			0
$499$	7.86140	+	13.6163i	0.351924	+	0.609551i	0.986587	−	0.163239i	$-0.0521941\pi$
$499$	7.86140	+	13.6163i	0.351924	+	0.609551i	−0.634662	+	0.772790i	$0.718861\pi$
$500$		0			0
$501$	−10.8351	+	18.7670i	−0.484077	+	0.838446i
$502$		0			0
$503$	14.0804			0.627813			0.313906	−	0.949454i	$-0.398362\pi$
$503$	14.0804			0.627813			0.313906	+	0.949454i	$0.398362\pi$
$504$		0			0
$505$	−10.4207			−0.463714
$506$		0			0
$507$	12.3597	−	21.4077i	0.548915	−	0.950749i
$508$		0			0
$509$	−16.7164	−	28.9536i	−0.740939	−	1.28334i	−0.952068	−	0.305886i	$-0.901047\pi$
$509$	−16.7164	−	28.9536i	−0.740939	−	1.28334i	0.211129	−	0.977458i	$-0.432286\pi$
$510$		0			0
$511$	−30.9113	+	11.9031i	−1.36743	+	0.526563i
$512$		0			0
$513$	0.343127	+	0.594314i	0.0151494	+	0.0262396i
$514$		0			0
$515$	−9.49027	+	16.4376i	−0.418191	+	0.724328i
$516$		0			0
$517$	−5.09595			−0.224120
$518$		0			0
$519$	26.9743			1.18404
$520$		0			0
$521$	12.4194	−	21.5111i	0.544106	−	0.942419i	−0.454557	−	0.890718i	$-0.650202\pi$
$521$	12.4194	−	21.5111i	0.544106	−	0.942419i	0.998663	−	0.0517012i	$-0.0164644\pi$
$522$		0			0
$523$	9.31887	+	16.1407i	0.407486	+	0.705786i	0.994607	−	0.103713i	$-0.0330723\pi$
$523$	9.31887	+	16.1407i	0.407486	+	0.705786i	−0.587122	+	0.809499i	$0.699739\pi$
$524$		0			0
$525$	5.47754	−	34.8213i	0.239060	−	1.51973i
$526$		0			0
$527$	−7.00907	−	12.1401i	−0.305320	−	0.528830i
$528$		0			0
$529$	11.1495	−	19.3115i	0.484762	−	0.839632i
$530$		0			0
$531$	14.0246			0.608615
$532$		0			0
$533$	3.26057			0.141231
$534$		0			0
$535$	−24.9617	+	43.2349i	−1.07919	+	1.86921i
$536$		0			0
$537$	−28.0356	−	48.5590i	−1.20982	−	2.09548i
$538$		0			0
$539$	2.68405	+	0.865851i	0.115610	+	0.0372948i
$540$		0			0
$541$	12.6806	+	21.9634i	0.545181	+	0.944281i	0.998596	+	0.0529813i	$0.0168724\pi$
$541$	12.6806	+	21.9634i	0.545181	+	0.944281i	−0.453415	+	0.891300i	$0.649794\pi$
$542$		0			0
$543$	6.27295	−	10.8651i	0.269198	−	0.466265i
$544$		0			0
$545$	38.7736			1.66088
$546$		0			0
$547$	30.1315			1.28833			0.644165	−	0.764886i	$-0.277205\pi$
$547$	30.1315			1.28833			0.644165	+	0.764886i	$0.277205\pi$
$548$		0			0
$549$	−0.171464	+	0.296984i	−0.00731791	+	0.0126750i
$550$		0			0
$551$	2.66608	+	4.61778i	0.113579	+	0.196724i
$552$		0			0
$553$	−1.80909	+	11.5005i	−0.0769301	+	0.489053i
$554$		0			0
$555$	−44.4041	−	76.9101i	−1.88485	−	3.26465i
$556$		0			0
$557$	−17.2661	+	29.9058i	−0.731589	+	1.26715i	0.224614	+	0.974448i	$0.427888\pi$
$557$	−17.2661	+	29.9058i	−0.731589	+	1.26715i	−0.956204	+	0.292702i	$0.905446\pi$
$558$		0			0
$559$	−3.15886			−0.133606
$560$		0			0
$561$	−4.27135			−0.180337
$562$		0			0
$563$	3.96025	−	6.85935i	0.166905	−	0.289087i	−0.770425	−	0.637530i	$-0.779956\pi$
$563$	3.96025	−	6.85935i	0.166905	−	0.289087i	0.937330	+	0.348443i	$0.113289\pi$
$564$		0			0
$565$	30.9101	+	53.5379i	1.30040	+	2.25236i
$566$		0			0
$567$	24.1443	−	9.29735i	1.01397	−	0.390452i
$568$		0			0
$569$	−3.66672	−	6.35095i	−0.153717	−	0.266245i	0.778874	−	0.627180i	$-0.215791\pi$
$569$	−3.66672	−	6.35095i	−0.153717	−	0.266245i	−0.932591	+	0.360935i	$0.882458\pi$
$570$		0			0
$571$	11.8922	−	20.5979i	0.497673	−	0.861995i	−0.502323	−	0.864680i	$-0.667521\pi$
$571$	11.8922	−	20.5979i	0.497673	−	0.861995i	0.999996	+	0.00268474i	$0.000854579\pi$
$572$		0			0
$573$	−46.4202			−1.93923
$574$		0			0
$575$	4.66681			0.194619
$576$		0			0
$577$	−0.898612	+	1.55644i	−0.0374097	+	0.0647955i	−0.884124	−	0.467252i	$-0.845244\pi$
$577$	−0.898612	+	1.55644i	−0.0374097	+	0.0647955i	0.846714	+	0.532048i	$0.178577\pi$
$578$		0			0
$579$	7.03970	+	12.1931i	0.292560	+	0.506729i
$580$		0			0
$581$	−3.85620	−	3.11596i	−0.159982	−	0.129272i
$582$		0			0
$583$	−2.31793	−	4.01477i	−0.0959987	−	0.166275i
$584$		0			0
$585$	7.19096	−	12.4551i	0.297310	−	0.514955i
$586$		0			0
$587$	−40.2209			−1.66009			−0.830046	−	0.557695i	$-0.811686\pi$
$587$	−40.2209			−1.66009			−0.830046	+	0.557695i	$0.811686\pi$
$588$		0			0
$589$	3.16041			0.130222
$590$		0			0
$591$	−1.18862	+	2.05876i	−0.0488934	+	0.0846859i
$592$		0			0
$593$	−4.94620	−	8.56707i	−0.203116	−	0.351807i	0.746415	−	0.665481i	$-0.231774\pi$
$593$	−4.94620	−	8.56707i	−0.203116	−	0.351807i	−0.949531	+	0.313674i	$0.898440\pi$
$594$		0			0
$595$	29.6819	+	23.9842i	1.21684	+	0.983255i
$596$		0			0
$597$	−0.712689	−	1.23441i	−0.0291684	−	0.0505212i
$598$		0			0
$599$	−12.8152	+	22.1965i	−0.523613	+	0.906925i	0.476009	+	0.879440i	$0.342083\pi$
$599$	−12.8152	+	22.1965i	−0.523613	+	0.906925i	−0.999622	+	0.0274844i	$0.991250\pi$
$600$		0			0
$601$	31.9887			1.30485			0.652423	−	0.757855i	$-0.273753\pi$
$601$	31.9887			1.30485			0.652423	+	0.757855i	$0.273753\pi$
$602$		0			0
$603$	−6.70832			−0.273184
$604$		0			0
$605$	17.6209	−	30.5203i	0.716392	−	1.24083i
$606$		0			0
$607$	20.7386	+	35.9202i	0.841752	+	1.45796i	0.888412	+	0.459047i	$0.151809\pi$
$607$	20.7386	+	35.9202i	0.841752	+	1.45796i	−0.0466596	+	0.998911i	$0.514858\pi$
$608$		0			0
$609$	31.4670	−	12.1171i	1.27511	−	0.491010i
$610$		0			0
$611$	10.3102	+	17.8579i	0.417108	+	0.722452i
$612$		0			0
$613$	−1.66801	+	2.88908i	−0.0673703	+	0.116689i	−0.897743	−	0.440520i	$-0.854794\pi$
$613$	−1.66801	+	2.88908i	−0.0673703	+	0.116689i	0.830373	+	0.557208i	$0.188128\pi$
$614$		0			0
$615$	−15.5446			−0.626819
$616$		0			0
$617$	1.45553			0.0585976			0.0292988	−	0.999571i	$-0.490673\pi$
$617$	1.45553			0.0585976			0.0292988	+	0.999571i	$0.490673\pi$
$618$		0			0
$619$	−20.0016	+	34.6437i	−0.803931	+	1.39245i	0.113079	+	0.993586i	$0.463929\pi$
$619$	−20.0016	+	34.6437i	−0.803931	+	1.39245i	−0.917010	+	0.398863i	$0.869405\pi$
$620$		0			0
$621$	0.287276	+	0.497576i	0.0115280	+	0.0199670i
$622$		0			0
$623$	5.99647	−	38.1202i	0.240243	−	1.52725i
$624$		0			0
$625$	10.8999	+	18.8792i	0.435996	+	0.755167i
$626$		0			0
$627$	0.481491	−	0.833966i	0.0192289	−	0.0333054i
$628$		0			0
$629$	50.6816			2.02081
$630$		0			0
$631$	29.6609			1.18078			0.590390	−	0.807118i	$-0.298974\pi$
$631$	29.6609			1.18078			0.590390	+	0.807118i	$0.298974\pi$
$632$		0			0
$633$	−14.6848	+	25.4348i	−0.583669	+	1.01094i
$634$		0			0
$635$	−11.6428	−	20.1659i	−0.462030	−	0.800260i
$636$		0			0
$637$	−2.39621	−	11.1576i	−0.0949413	−	0.442080i
$638$		0			0
$639$	2.94806	+	5.10618i	0.116623	+	0.201998i
$640$		0			0
$641$	15.9911	−	27.6975i	0.631612	−	1.09398i	−0.355610	−	0.934634i	$-0.615727\pi$
$641$	15.9911	−	27.6975i	0.631612	−	1.09398i	0.987222	−	0.159350i	$-0.0509398\pi$
$642$		0			0
$643$	−19.8251			−0.781825			−0.390912	−	0.920428i	$-0.627840\pi$
$643$	−19.8251			−0.781825			−0.390912	+	0.920428i	$0.627840\pi$
$644$		0			0
$645$	15.0597			0.592976
$646$		0			0
$647$	9.43764	−	16.3465i	0.371032	−	0.642646i	−0.618692	−	0.785633i	$-0.712337\pi$
$647$	9.43764	−	16.3465i	0.371032	−	0.642646i	0.989725	+	0.142987i	$0.0456706\pi$
$648$		0			0
$649$	1.04140	+	1.80376i	0.0408786	+	0.0708039i
$650$		0			0
$651$	3.10565	−	19.7429i	0.121720	−	0.773787i
$652$		0			0
$653$	1.04816	+	1.81547i	0.0410178	+	0.0710449i	0.885805	−	0.464057i	$-0.153607\pi$
$653$	1.04816	+	1.81547i	0.0410178	+	0.0710449i	−0.844788	+	0.535102i	$0.820273\pi$
$654$		0			0
$655$	3.18727	−	5.52052i	0.124537	−	0.215704i
$656$		0			0
$657$	33.9643			1.32507
$658$		0			0
$659$	−37.1279			−1.44630			−0.723148	−	0.690693i	$-0.757306\pi$
$659$	−37.1279			−1.44630			−0.723148	+	0.690693i	$0.757306\pi$
$660$		0			0
$661$	13.4324	−	23.2656i	0.522461	−	0.904929i	−0.477198	−	0.878796i	$-0.658347\pi$
$661$	13.4324	−	23.2656i	0.522461	−	0.904929i	0.999658	−	0.0261328i	$-0.00831928\pi$
$662$		0			0
$663$	8.64189	+	14.9682i	0.335623	+	0.581317i
$664$		0			0
$665$	−8.02873	+	3.09165i	−0.311341	+	0.119889i
$666$		0			0
$667$	2.23211	+	3.86613i	0.0864278	+	0.149697i
$668$		0			0
$669$	11.2567	−	19.4972i	0.435209	−	0.753804i
$670$		0			0
$671$	−0.0509286			−0.00196608
$672$		0			0
$673$	4.79647			0.184890			0.0924452	−	0.995718i	$-0.470532\pi$
$673$	4.79647			0.184890			0.0924452	+	0.995718i	$0.470532\pi$
$674$		0			0
$675$	1.91263	−	3.31278i	0.0736173	−	0.127509i
$676$		0			0
$677$	22.6597	+	39.2477i	0.870882	+	1.50841i	0.861086	+	0.508459i	$0.169785\pi$
$677$	22.6597	+	39.2477i	0.870882	+	1.50841i	0.00979576	+	0.999952i	$0.496882\pi$
$678$		0			0
$679$	−15.4485	−	12.4830i	−0.592857	−	0.479053i
$680$		0			0
$681$	−8.63381	−	14.9542i	−0.330848	−	0.573046i
$682$		0			0
$683$	−6.82929	+	11.8287i	−0.261316	+	0.452612i	−0.966592	−	0.256321i	$-0.917490\pi$
$683$	−6.82929	+	11.8287i	−0.261316	+	0.452612i	0.705276	+	0.708933i	$0.250823\pi$
$684$		0			0
$685$	−52.3789			−2.00129
$686$		0			0
$687$	13.2853			0.506866
$688$		0			0
$689$	−9.37936	+	16.2455i	−0.357325	+	0.618905i
$690$		0			0
$691$	4.68144	+	8.10850i	0.178090	+	0.308462i	0.941226	−	0.337776i	$-0.109675\pi$
$691$	4.68144	+	8.10850i	0.178090	+	0.308462i	−0.763136	+	0.646238i	$0.776341\pi$
$692$		0			0
$693$	−2.24928	−	1.81751i	−0.0854430	−	0.0690414i
$694$		0			0
$695$	4.20231	+	7.27862i	0.159403	+	0.276094i
$696$		0			0
$697$	4.43555	−	7.68260i	0.168009	−	0.290999i
$698$		0			0
$699$	27.5722			1.04288
$700$		0			0
$701$	−16.3095			−0.616003			−0.308001	−	0.951386i	$-0.599660\pi$
$701$	−16.3095			−0.616003			−0.308001	+	0.951386i	$0.599660\pi$
$702$		0			0
$703$	−5.71311	+	9.89540i	−0.215474	+	0.373212i
$704$		0			0
$705$	−49.1536	−	85.1365i	−1.85123	−	3.20643i
$706$		0			0
$707$	7.91222	−	3.04679i	0.297570	−	0.114586i
$708$		0			0
$709$	−17.6708	−	30.6068i	−0.663642	−	1.14946i	−0.979652	−	0.200705i	$-0.935677\pi$
$709$	−17.6708	−	30.6068i	−0.663642	−	1.14946i	0.316010	−	0.948756i	$-0.397657\pi$
$710$		0			0
$711$	5.96868	−	10.3381i	0.223843	−	0.387708i
$712$		0			0
$713$	2.64598			0.0990927
$714$		0			0
$715$	2.13587			0.0798772
$716$		0			0
$717$	−34.5958	+	59.9216i	−1.29200	+	2.23781i
$718$		0			0
$719$	−16.2748	−	28.1887i	−0.606946	−	1.05126i	−0.991741	−	0.128260i	$-0.959061\pi$
$719$	−16.2748	−	28.1887i	−0.606946	−	1.05126i	0.384794	−	0.923002i	$-0.374272\pi$
$720$		0			0
$721$	2.39976	−	15.2555i	0.0893718	−	0.568146i
$722$		0			0
$723$	−26.6255	−	46.1167i	−0.990213	−	1.71510i
$724$		0			0
$725$	14.8610	−	25.7401i	0.551925	−	0.955962i
$726$		0			0
$727$	−12.5070			−0.463859			−0.231929	−	0.972733i	$-0.574504\pi$
$727$	−12.5070			−0.463859			−0.231929	+	0.972733i	$0.574504\pi$
$728$		0			0
$729$	−21.6083			−0.800306
$730$		0			0
$731$	−4.29719	+	7.44296i	−0.158937	+	0.275288i
$732$		0			0
$733$	−8.41623	−	14.5773i	−0.310861	−	0.538426i	0.667688	−	0.744441i	$-0.267284\pi$
$733$	−8.41623	−	14.5773i	−0.310861	−	0.538426i	−0.978549	+	0.206015i	$0.933951\pi$
$734$		0			0
$735$	11.4238	+	53.1933i	0.421374	+	1.96206i
$736$		0			0
$737$	−0.498130	−	0.862786i	−0.0183488	−	0.0317811i
$738$		0			0
$739$	−23.6385	+	40.9431i	−0.869556	+	1.50611i	−0.00710414	+	0.999975i	$0.502261\pi$
$739$	−23.6385	+	40.9431i	−0.869556	+	1.50611i	−0.862451	+	0.506140i	$0.831072\pi$
$740$		0			0
$741$	−3.89665			−0.143147
$742$		0			0
$743$	29.4769			1.08140			0.540701	−	0.841215i	$-0.318159\pi$
$743$	29.4769			1.08140			0.540701	+	0.841215i	$0.318159\pi$
$744$		0			0
$745$	15.7399	−	27.2623i	0.576665	−	0.998813i
$746$		0			0
$747$	2.54178	+	4.40250i	0.0929990	+	0.161079i
$748$		0			0
$749$	6.31195	−	40.1258i	0.230634	−	1.46616i
$750$		0			0
$751$	−16.0079	−	27.7266i	−0.584138	−	1.01176i	−0.994982	−	0.100052i	$-0.968099\pi$
$751$	−16.0079	−	27.7266i	−0.584138	−	1.01176i	0.410844	−	0.911706i	$-0.365234\pi$
$752$		0			0
$753$	7.98064	−	13.8229i	0.290831	−	0.503733i
$754$		0			0
$755$	12.6963			0.462065
$756$		0			0
$757$	−44.8062			−1.62851			−0.814254	−	0.580509i	$-0.802854\pi$
$757$	−44.8062			−1.62851			−0.814254	+	0.580509i	$0.802854\pi$
$758$		0			0
$759$	0.403117	−	0.698220i	0.0146322	−	0.0253438i
$760$		0			0
$761$	8.73474	+	15.1290i	0.316634	+	0.548426i	0.979783	−	0.200061i	$-0.0641140\pi$
$761$	8.73474	+	15.1290i	0.316634	+	0.548426i	−0.663149	+	0.748487i	$0.730781\pi$
$762$		0			0
$763$	−29.4401	+	11.3366i	−1.06580	+	0.410413i
$764$		0			0
$765$	−19.5646	−	33.8869i	−0.707360	−	1.22518i
$766$		0			0
$767$	4.21398	−	7.29882i	0.152158	−	0.263545i
$768$		0			0
$769$	18.1746			0.655392			0.327696	−	0.944783i	$-0.393728\pi$
$769$	18.1746			0.655392			0.327696	+	0.944783i	$0.393728\pi$
$770$		0			0
$771$	−66.5368			−2.39627
$772$		0			0
$773$	−13.3940	+	23.1992i	−0.481750	+	0.834416i	−0.999781	−	0.0209465i	$-0.993332\pi$
$773$	−13.3940	+	23.1992i	−0.481750	+	0.834416i	0.518030	+	0.855362i	$0.326665\pi$
$774$		0			0
$775$	−8.80824	−	15.2563i	−0.316401	−	0.548023i
$776$		0			0
$777$	56.2021	+	45.4136i	2.01624	+	1.62920i
$778$		0			0
$779$	1.00000	+	1.73205i	0.0358287	+	0.0620572i
$780$		0			0
$781$	−0.437819	+	0.758325i	−0.0156664	+	0.0271350i
$782$		0			0
$783$	3.65921			0.130770
$784$		0			0
$785$	48.8902			1.74496
$786$		0			0
$787$	−16.0439	+	27.7889i	−0.571904	+	0.990567i	0.424466	+	0.905444i	$0.360462\pi$
$787$	−16.0439	+	27.7889i	−0.571904	+	0.990567i	−0.996370	+	0.0851233i	$0.972872\pi$
$788$		0			0
$789$	3.40868	+	5.90401i	0.121352	+	0.210188i
$790$		0			0
$791$	−39.1229	−	31.6129i	−1.39105	−	1.12402i
$792$		0			0
$793$	0.103040	+	0.178470i	0.00365905	+	0.00633767i
$794$		0			0
$795$	44.7156	−	77.4497i	1.58590	−	2.74686i
$796$		0			0
$797$	−15.2145			−0.538925			−0.269462	−	0.963011i	$-0.586846\pi$
$797$	−15.2145			−0.538925			−0.269462	+	0.963011i	$0.586846\pi$
$798$		0			0
$799$	56.1026			1.98477
$800$		0			0
$801$	−19.7840	+	34.2670i	−0.699035	+	1.21076i
$802$		0			0
$803$	2.52204	+	4.36830i	0.0890009	+	0.154154i
$804$		0			0
$805$	−6.72188	+	2.58842i	−0.236915	+	0.0912298i
$806$		0			0
$807$	−10.0208	−	17.3565i	−0.352747	−	0.610977i
$808$		0			0
$809$	12.8710	−	22.2933i	0.452521	−	0.783790i	−0.546021	−	0.837772i	$-0.683858\pi$
$809$	12.8710	−	22.2933i	0.452521	−	0.783790i	0.998542	+	0.0539818i	$0.0171913\pi$
$810$		0			0
$811$	31.6453			1.11122			0.555608	−	0.831444i	$-0.312486\pi$
$811$	31.6453			1.11122			0.555608	+	0.831444i	$0.312486\pi$
$812$		0			0
$813$	−34.0759			−1.19509
$814$		0			0
$815$	27.8143	−	48.1757i	0.974291	−	1.68752i
$816$		0			0
$817$	−0.968807	−	1.67802i	−0.0338943	−	0.0587066i
$818$		0			0
$819$	−1.81835	+	11.5594i	−0.0635381	+	0.403919i
$820$		0			0
$821$	23.5147	+	40.7287i	0.820669	+	1.42144i	0.905185	+	0.425018i	$0.139732\pi$
$821$	23.5147	+	40.7287i	0.820669	+	1.42144i	−0.0845165	+	0.996422i	$0.526935\pi$
$822$		0			0
$823$	−3.15946	+	5.47234i	−0.110132	+	0.190754i	−0.915823	−	0.401582i	$-0.868461\pi$
$823$	−3.15946	+	5.47234i	−0.110132	+	0.190754i	0.805691	+	0.592335i	$0.201794\pi$
$824$		0			0
$825$	−5.36777			−0.186882
$826$		0			0
$827$	−46.8959			−1.63073			−0.815364	−	0.578948i	$-0.803463\pi$
$827$	−46.8959			−1.63073			−0.815364	+	0.578948i	$0.803463\pi$
$828$		0			0
$829$	7.18757	−	12.4492i	0.249635	−	0.432380i	−0.713790	−	0.700360i	$-0.753023\pi$
$829$	7.18757	−	12.4492i	0.249635	−	0.432380i	0.963424	+	0.267980i	$0.0863561\pi$
$830$		0			0
$831$	30.2820	+	52.4500i	1.05047	+	1.81947i
$832$		0			0
$833$	−29.5494	−	9.53236i	−1.02383	−	0.330277i
$834$		0			0
$835$	−14.7410	−	25.5322i	−0.510134	−	0.883579i
$836$		0			0
$837$	1.08442	−	1.87827i	0.0374831	−	0.0649226i
$838$		0			0
$839$	33.5325			1.15767			0.578835	−	0.815445i	$-0.303507\pi$
$839$	33.5325			1.15767			0.578835	+	0.815445i	$0.303507\pi$
$840$		0			0
$841$	−0.568151			−0.0195914
$842$		0			0
$843$	−22.7193	+	39.3510i	−0.782495	+	1.35532i
$844$		0			0
$845$	16.8153	+	29.1249i	0.578463	+	1.00193i
$846$		0			0
$847$	−4.45572	+	28.3255i	−0.153100	+	0.973275i
$848$		0			0
$849$	28.1239	+	48.7121i	0.965211	+	1.67179i
$850$		0			0
$851$	−4.78318	+	8.28471i	−0.163965	+	0.283996i
$852$		0			0
$853$	3.37139			0.115434			0.0577171	−	0.998333i	$-0.481618\pi$
$853$	3.37139			0.115434			0.0577171	+	0.998333i	$0.481618\pi$
$854$		0			0
$855$	8.82172			0.301696
$856$		0			0
$857$	19.0314	−	32.9634i	0.650101	−	1.12601i	−0.332998	−	0.942928i	$-0.608060\pi$
$857$	19.0314	−	32.9634i	0.650101	−	1.12601i	0.983098	−	0.183080i	$-0.0586066\pi$
$858$		0			0
$859$	14.3389	+	24.8357i	0.489237	+	0.847384i	0.999923	−	0.0123833i	$-0.00394182\pi$
$859$	14.3389	+	24.8357i	0.489237	+	0.847384i	−0.510686	+	0.859767i	$0.670608\pi$
$860$		0			0
$861$	11.8027	−	4.54492i	0.402236	−	0.154891i
$862$		0			0
$863$	−22.9344	−	39.7236i	−0.780697	−	1.35221i	−0.931536	−	0.363649i	$-0.881531\pi$
$863$	−22.9344	−	39.7236i	−0.780697	−	1.35221i	0.150839	−	0.988558i	$-0.451802\pi$
$864$		0			0
$865$	−18.3491	+	31.7816i	−0.623889	+	1.08061i
$866$		0			0
$867$	6.39159			0.217070
$868$		0			0
$869$	1.77283			0.0601392
$870$		0			0
$871$	−2.01565	+	3.49122i	−0.0682978	+	0.118295i
$872$		0			0
$873$	10.1827	+	17.6370i	0.344633	+	0.596922i
$874$		0			0
$875$	3.84191	+	3.10442i	0.129880	+	0.104948i
$876$		0			0
$877$	6.00705	+	10.4045i	0.202844	+	0.351335i	0.949444	−	0.313938i	$-0.101648\pi$
$877$	6.00705	+	10.4045i	0.202844	+	0.351335i	−0.746600	+	0.665273i	$0.768315\pi$
$878$		0			0
$879$	13.2965	−	23.0302i	0.448480	−	0.776790i
$880$		0			0
$881$	3.35650			0.113083			0.0565417	−	0.998400i	$-0.481993\pi$
$881$	3.35650			0.113083			0.0565417	+	0.998400i	$0.481993\pi$
$882$		0			0
$883$	6.45095			0.217092			0.108546	−	0.994091i	$-0.465381\pi$
$883$	6.45095			0.217092			0.108546	+	0.994091i	$0.465381\pi$
$884$		0			0
$885$	−20.0899	+	34.7968i	−0.675316	+	1.16968i
$886$		0			0
$887$	−17.1837	−	29.7630i	−0.576971	−	0.999344i	−0.995824	−	0.0912898i	$-0.970901\pi$
$887$	−17.1837	−	29.7630i	−0.576971	−	0.999344i	0.418853	−	0.908054i	$-0.362432\pi$
$888$		0			0
$889$	14.7363	+	11.9075i	0.494238	+	0.399364i
$890$		0			0
$891$	−1.96993	−	3.41202i	−0.0659951	−	0.114307i
$892$		0			0
$893$	−6.32419	+	10.9538i	−0.211631	+	0.366556i
$894$		0			0
$895$	76.2841			2.54990
$896$		0			0
$897$	−3.26238			−0.108928
$898$		0			0
$899$	8.42588	−	14.5941i	0.281019	−	0.486739i
$900$		0			0
$901$	25.5186	+	44.1995i	0.850148	+	1.47250i
$902$		0			0
$903$	−11.4346	+	4.40315i	−0.380519	+	0.146528i
$904$		0			0
$905$	8.53426	+	14.7818i	0.283689	+	0.491363i
$906$		0			0
$907$	−0.161426	+	0.279598i	−0.00536005	+	0.00928389i	−0.868693	−	0.495351i	$-0.835039\pi$
$907$	−0.161426	+	0.279598i	−0.00536005	+	0.00928389i	0.863333	+	0.504635i	$0.168373\pi$
$908$		0			0
$909$	−8.69370			−0.288352
$910$		0			0
$911$	19.3296			0.640419			0.320209	−	0.947347i	$-0.396247\pi$
$911$	19.3296			0.640419			0.320209	+	0.947347i	$0.396247\pi$
$912$		0			0
$913$	−0.377483	+	0.653820i	−0.0124929	+	0.0216383i
$914$		0			0
$915$	−0.491238	−	0.850848i	−0.0162398	−	0.0281282i
$916$		0			0
$917$	−0.805951	+	5.12352i	−0.0266148	+	0.169193i
$918$		0			0
$919$	−5.82201	−	10.0840i	−0.192050	−	0.332641i	0.753879	−	0.657013i	$-0.228180\pi$
$919$	−5.82201	−	10.0840i	−0.192050	−	0.332641i	−0.945930	+	0.324372i	$0.894847\pi$
$920$		0			0
$921$	−32.1382	+	55.6649i	−1.05899	+	1.83422i
$922$		0			0
$923$	3.54322			0.116627
$924$		0			0
$925$	63.6912			2.09415
$926$		0			0
$927$	−7.91749	+	13.7135i	−0.260044	+	0.450410i
$928$		0			0
$929$	5.41199	+	9.37384i	0.177562	+	0.307546i	0.941045	−	0.338282i	$-0.109846\pi$
$929$	5.41199	+	9.37384i	0.177562	+	0.307546i	−0.763483	+	0.645828i	$0.776512\pi$
$930$		0			0
$931$	5.19213	−	4.69487i	0.170165	−	0.153868i
$932$		0			0
$933$	29.9287	+	51.8381i	0.979823	+	1.69710i
$934$		0			0
$935$	2.90556	−	5.03258i	0.0950220	−	0.164583i
$936$		0			0
$937$	−18.0113			−0.588402			−0.294201	−	0.955744i	$-0.595054\pi$
$937$	−18.0113			−0.588402			−0.294201	+	0.955744i	$0.595054\pi$
$938$		0			0
$939$	−30.6847			−1.00136
$940$		0			0
$941$	3.67628	−	6.36751i	0.119843	−	0.207575i	−0.799862	−	0.600184i	$-0.795094\pi$
$941$	3.67628	−	6.36751i	0.119843	−	0.207575i	0.919705	+	0.392609i	$0.128427\pi$
$942$		0			0
$943$	0.837228	+	1.45012i	0.0272639	+	0.0472224i
$944$		0			0
$945$	−0.917464	+	5.83242i	−0.0298451	+	0.189729i
$946$		0			0
$947$	−2.65037	−	4.59057i	−0.0861253	−	0.149173i	0.819745	−	0.572729i	$-0.194115\pi$
$947$	−2.65037	−	4.59057i	−0.0861253	−	0.149173i	−0.905870	+	0.423555i	$0.860782\pi$
$948$		0			0
$949$	10.2053	−	17.6761i	0.331278	−	0.573790i
$950$		0			0
$951$	−29.8411			−0.967666
$952$		0			0
$953$	−46.1846			−1.49607			−0.748033	−	0.663661i	$-0.769002\pi$
$953$	−46.1846			−1.49607			−0.748033	+	0.663661i	$0.769002\pi$
$954$		0			0
$955$	31.5770	−	54.6930i	1.02181	−	1.76983i
$956$		0			0
$957$	−2.56738	−	4.44683i	−0.0829916	−	0.143746i
$958$		0			0
$959$	39.7703	−	15.3145i	1.28425	−	0.494531i
$960$		0			0
$961$	10.5059	+	18.1968i	0.338901	+	0.586993i
$962$		0			0
$963$	−20.8249	+	36.0698i	−0.671073	+	1.16233i
$964$		0			0
$965$	−19.1548			−0.616616
$966$		0			0
$967$	9.76088			0.313889			0.156944	−	0.987607i	$-0.449836\pi$
$967$	9.76088			0.313889			0.156944	+	0.987607i	$0.449836\pi$
$968$		0			0
$969$	−5.30085	+	9.18134i	−0.170288	+	0.294947i
$970$		0			0
$971$	−10.6313	−	18.4139i	−0.341174	−	0.590930i	0.643477	−	0.765465i	$-0.277491\pi$
$971$	−10.6313	−	18.4139i	−0.341174	−	0.590930i	−0.984651	+	0.174535i	$0.944158\pi$
$972$		0			0
$973$	−5.31885	−	4.29785i	−0.170515	−	0.137783i
$974$		0			0
$975$	10.8602	+	18.8104i	0.347805	+	0.602415i
$976$		0			0
$977$	0.944275	−	1.63553i	0.0302100	−	0.0523253i	−0.850525	−	0.525934i	$-0.823716\pi$
$977$	0.944275	−	1.63553i	0.0302100	−	0.0523253i	0.880735	+	0.473609i	$0.157049\pi$
$978$		0			0
$979$	−5.87630			−0.187807
$980$		0			0
$981$	32.3479			1.03279
$982$		0			0
$983$	−12.9245	+	22.3858i	−0.412226	+	0.713997i	−0.995133	−	0.0985422i	$-0.968582\pi$
$983$	−12.9245	+	22.3858i	−0.412226	+	0.713997i	0.582906	+	0.812539i	$0.301915\pi$
$984$		0			0
$985$	−1.61711	−	2.80091i	−0.0515253	−	0.0892444i
$986$		0			0
$987$	62.2135	+	50.2710i	1.98028	+	1.60014i
$988$		0			0
$989$	−0.811112	−	1.40489i	−0.0257919	−	0.0446728i
$990$		0			0
$991$	8.49262	−	14.7097i	0.269777	−	0.467267i	−0.699027	−	0.715095i	$-0.746383\pi$
$991$	8.49262	−	14.7097i	0.269777	−	0.467267i	0.968804	+	0.247828i	$0.0797167\pi$
$992$		0			0
$993$	14.8898			0.472515
$994$		0			0
$995$	1.93921			0.0614770
$996$		0			0
$997$	5.90432	−	10.2266i	0.186992	−	0.323879i	−0.757254	−	0.653120i	$-0.773460\pi$
$997$	5.90432	−	10.2266i	0.186992	−	0.323879i	0.944246	+	0.329241i	$0.106793\pi$
$998$		0			0
$999$	3.92065	+	6.79077i	0.124044	+	0.214850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.305.2	✓	16
7.2	even	3	inner	1064.2.q.n.457.2	yes	16
7.3	odd	6		7448.2.a.br.1.2		8
7.4	even	3		7448.2.a.bq.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.2	✓	16	1.1	even	1	trivial
1064.2.q.n.457.2	yes	16	7.2	even	3	inner
7448.2.a.bq.1.7		8	7.4	even	3
7448.2.a.br.1.2		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19508 + 2.06994i) q^{3} +(-1.62589 - 2.81613i) q^{5} +(2.05789 + 1.66286i) q^{7} +(-1.35644 - 2.34943i) q^{9} +O(q^{10})\)	\(q+(-1.19508 + 2.06994i) q^{3} +(-1.62589 - 2.81613i) q^{5} +(2.05789 + 1.66286i) q^{7} +(-1.35644 - 2.34943i) q^{9} +(0.201447 - 0.348916i) q^{11} -1.63029 q^{13} +7.77230 q^{15} +(-2.21778 + 3.84130i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-5.90137 + 2.27246i) q^{21} +(-0.418614 - 0.725061i) q^{23} +(-2.78706 + 4.82733i) q^{25} -0.686255 q^{27} -5.33215 q^{29} +(-1.58020 + 2.73699i) q^{31} +(0.481491 + 0.833966i) q^{33} +(1.33692 - 8.49891i) q^{35} +(-5.71311 - 9.89540i) q^{37} +(1.94832 - 3.37460i) q^{39} -2.00000 q^{41} +1.93761 q^{43} +(-4.41086 + 7.63983i) q^{45} +(-6.32419 - 10.9538i) q^{47} +(1.46981 + 6.84395i) q^{49} +(-5.30085 - 9.18134i) q^{51} +(5.75320 - 9.96483i) q^{53} -1.31012 q^{55} +2.39016 q^{57} +(-2.58481 + 4.47702i) q^{59} +(-0.0632036 - 0.109472i) q^{61} +(1.11535 - 7.09043i) q^{63} +(2.65067 + 4.59110i) q^{65} +(1.23638 - 2.14148i) q^{67} +2.00111 q^{69} -2.17338 q^{71} +(-6.25982 + 10.8423i) q^{73} +(-6.66153 - 11.5381i) q^{75} +(0.994752 - 0.383053i) q^{77} +(2.20013 + 3.81073i) q^{79} +(4.88946 - 8.46879i) q^{81} -1.87386 q^{83} +14.4235 q^{85} +(6.37236 - 11.0372i) q^{87} +(-7.29262 - 12.6312i) q^{89} +(-3.35495 - 2.71093i) q^{91} +(-3.77694 - 6.54186i) q^{93} +(-1.62589 + 2.81613i) q^{95} -7.50694 q^{97} -1.09300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more