LMFDB - Embedded newform 126.2.k.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(17,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("126.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.k (of order $6$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	126.17
Dual form			126.2.k.a.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 3.62132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 3.62132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +(3.62132 + 2.09077i) q^{10} +(2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.507306 - 0.878680i) q^{17} +(-0.878680 + 0.507306i) q^{19} -4.18154 q^{20} -3.00000 q^{22} +(3.67423 - 2.12132i) q^{23} +(-6.24264 + 10.8126i) q^{25} +(1.22474 + 2.12132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +1.24264i q^{29} +(4.86396 + 2.80821i) q^{31} +(0.866025 + 0.500000i) q^{32} +1.01461i q^{34} +(-4.18154 + 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} +(0.507306 - 0.878680i) q^{38} +(3.62132 - 2.09077i) q^{40} -2.02922 q^{41} +8.24264 q^{43} +(2.59808 - 1.50000i) q^{44} +(-2.12132 + 3.67423i) q^{46} +(0.507306 + 0.878680i) q^{47} +(-1.74264 + 6.77962i) q^{49} -12.4853i q^{50} +(-2.12132 - 1.22474i) q^{52} +(-1.07616 - 0.621320i) q^{53} -12.5446i q^{55} +(2.09077 - 1.62132i) q^{56} +(-0.621320 - 1.07616i) q^{58} +(5.76500 - 9.98528i) q^{59} +(5.12132 - 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-8.87039 + 5.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} +(-0.507306 - 0.878680i) q^{68} +(-1.50000 - 10.9612i) q^{70} +10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(7.13834 + 4.12132i) q^{74} +1.01461i q^{76} +(-1.07616 - 7.86396i) q^{77} +(5.62132 + 9.73641i) q^{79} +(-2.09077 + 3.62132i) q^{80} +(1.75736 - 1.01461i) q^{82} +3.16693 q^{83} -4.24264 q^{85} +(-7.13834 + 4.12132i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-5.12132 + 3.97141i) q^{91} -4.24264i q^{92} +(-0.878680 - 0.507306i) q^{94} +(3.67423 + 2.12132i) q^{95} -3.76127i q^{97} +(-1.88064 - 6.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^7	$ 8 q + 4 q^{4} + 4 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} - 24 q^{22} - 16 q^{25} - 4 q^{28} - 12 q^{31} - 16 q^{37} + 12 q^{40} + 32 q^{43} + 20 q^{49} + 12 q^{58} + 24 q^{61} - 8 q^{64} + 40 q^{67} - 12 q^{70} + 24 q^{73} + 28 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 - 24 * q^22 - 16 * q^25 - 4 * q^28 - 12 * q^31 - 16 * q^37 + 12 * q^40 + 32 * q^43 + 20 * q^49 + 12 * q^58 + 24 * q^61 - 8 * q^64 + 40 * q^67 - 12 * q^70 + 24 * q^73 + 28 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.09077	−	3.62132i	−0.935021	−	1.61950i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$	−2.09077	−	3.62132i	−0.935021	−	1.61950i	−0.160424	−	0.987048i	$-0.551286\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.62132	+	2.09077i	1.14516	+	0.661160i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	2.44949	+	1.00000i	0.654654	+	0.267261i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.507306	−	0.878680i	0.123040	−	0.213111i	−0.797925	−	0.602756i	$-0.794069\pi$
$17$	0.507306	−	0.878680i	0.123040	−	0.213111i	0.920965	+	0.389645i	$0.127402\pi$
$18$		0			0
$19$	−0.878680	+	0.507306i	−0.201583	+	0.116384i	−0.597394	−	0.801948i	$-0.703797\pi$
$19$	−0.878680	+	0.507306i	−0.201583	+	0.116384i	0.395811	+	0.918332i	$0.370464\pi$
$20$	−4.18154			−0.935021
$21$		0			0
$22$	−3.00000			−0.639602
$23$	3.67423	−	2.12132i	0.766131	−	0.442326i	−0.0653618	−	0.997862i	$-0.520820\pi$
$23$	3.67423	−	2.12132i	0.766131	−	0.442326i	0.831493	+	0.555536i	$0.187487\pi$
$24$		0			0
$25$	−6.24264	+	10.8126i	−1.24853	+	2.16251i
$26$	1.22474	+	2.12132i	0.240192	+	0.416025i
$27$		0			0
$28$	−2.62132	+	0.358719i	−0.495383	+	0.0677916i
$29$			1.24264i			0.230753i	0.993322	+	0.115376i	$0.0368074\pi$
$29$			1.24264i			0.230753i	−0.993322	+	0.115376i	$0.963193\pi$
$30$		0			0
$31$	4.86396	+	2.80821i	0.873593	+	0.504369i	0.868541	−	0.495618i	$-0.165058\pi$
$31$	4.86396	+	2.80821i	0.873593	+	0.504369i	0.00505256	+	0.999987i	$0.498392\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			1.01461i			0.174005i
$35$	−4.18154	+	10.2426i	−0.706809	+	1.73132i
$36$		0			0
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	−0.975719	−	0.219025i	$-0.929712\pi$
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	0.298178	−	0.954510i	$-0.403621\pi$
$38$	0.507306	−	0.878680i	0.0822959	−	0.142541i
$39$		0			0
$40$	3.62132	−	2.09077i	0.572581	−	0.330580i
$41$	−2.02922			−0.316912			−0.158456	−	0.987366i	$-0.550652\pi$
$41$	−2.02922			−0.316912			−0.158456	+	0.987366i	$0.550652\pi$
$42$		0			0
$43$	8.24264			1.25699			0.628495	−	0.777813i	$-0.283671\pi$
$43$	8.24264			1.25699			0.628495	+	0.777813i	$0.283671\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$	−2.12132	+	3.67423i	−0.312772	+	0.541736i
$47$	0.507306	+	0.878680i	0.0739982	+	0.128169i	0.900650	−	0.434545i	$-0.143091\pi$
$47$	0.507306	+	0.878680i	0.0739982	+	0.128169i	−0.826652	+	0.562713i	$0.809757\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		−	12.4853i		−	1.76569i
$51$		0			0
$52$	−2.12132	−	1.22474i	−0.294174	−	0.169842i
$53$	−1.07616	−	0.621320i	−0.147822	−	0.0853449i	0.424265	−	0.905538i	$-0.360533\pi$
$53$	−1.07616	−	0.621320i	−0.147822	−	0.0853449i	−0.572087	+	0.820193i	$0.693866\pi$
$54$		0			0
$55$		−	12.5446i		−	1.69152i
$56$	2.09077	−	1.62132i	0.279391	−	0.216658i
$57$		0			0
$58$	−0.621320	−	1.07616i	−0.0815834	−	0.141307i
$59$	5.76500	−	9.98528i	0.750540	−	1.29997i	−0.197022	−	0.980399i	$-0.563127\pi$
$59$	5.76500	−	9.98528i	0.750540	−	1.29997i	0.947561	−	0.319574i	$-0.103540\pi$
$60$		0			0
$61$	5.12132	−	2.95680i	0.655718	−	0.378579i	−0.134926	−	0.990856i	$-0.543080\pi$
$61$	5.12132	−	2.95680i	0.655718	−	0.378579i	0.790643	+	0.612277i	$0.209746\pi$
$62$	−5.61642			−0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.87039	+	5.12132i	−1.10024	+	0.635222i
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	−0.507306	−	0.878680i	−0.0615199	−	0.106556i
$69$		0			0
$70$	−1.50000	−	10.9612i	−0.179284	−	1.31011i
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$		0			0
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	0.859870	−	0.510513i	$-0.170545\pi$
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	−0.0121828	+	0.999926i	$0.503878\pi$
$74$	7.13834	+	4.12132i	0.829815	+	0.479094i
$75$		0			0
$76$			1.01461i			0.116384i
$77$	−1.07616	−	7.86396i	−0.122640	−	0.896182i
$78$		0			0
$79$	5.62132	+	9.73641i	0.632448	+	1.09543i	0.987050	+	0.160415i	$0.0512831\pi$
$79$	5.62132	+	9.73641i	0.632448	+	1.09543i	−0.354602	+	0.935017i	$0.615384\pi$
$80$	−2.09077	+	3.62132i	−0.233755	+	0.404876i
$81$		0			0
$82$	1.75736	−	1.01461i	0.194068	−	0.112045i
$83$	3.16693			0.347616			0.173808	−	0.984780i	$-0.444393\pi$
$83$	3.16693			0.347616			0.173808	+	0.984780i	$0.444393\pi$
$84$		0			0
$85$	−4.24264			−0.460179
$86$	−7.13834	+	4.12132i	−0.769747	+	0.444413i
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	−5.12132	+	3.97141i	−0.536860	+	0.416317i
$92$		−	4.24264i		−	0.442326i
$93$		0			0
$94$	−0.878680	−	0.507306i	−0.0906289	−	0.0523246i
$95$	3.67423	+	2.12132i	0.376969	+	0.217643i
$96$		0			0
$97$		−	3.76127i		−	0.381900i	−0.981600	−	0.190950i	$-0.938843\pi$
$97$		−	3.76127i		−	0.381900i	0.981600	−	0.190950i	$-0.0611568\pi$
$98$	−1.88064	−	6.74264i	−0.189973	−	0.681110i
$99$		0			0
$100$	6.24264	+	10.8126i	0.624264	+	1.08126i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−13.2426	+	7.64564i	−1.30484	+	0.753348i	−0.981229	−	0.192844i	$-0.938229\pi$
$103$	−13.2426	+	7.64564i	−1.30484	+	0.753348i	−0.323607	+	0.946192i	$0.604895\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	1.24264			0.120696
$107$	−4.75039	+	2.74264i	−0.459238	+	0.265141i	−0.711724	−	0.702459i	$-0.752085\pi$
$107$	−4.75039	+	2.74264i	−0.459238	+	0.265141i	0.252486	+	0.967601i	$0.418752\pi$
$108$		0			0
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	−0.900015	−	0.435860i	$-0.856444\pi$
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	0.827473	+	0.561506i	$0.189778\pi$
$110$	6.27231	+	10.8640i	0.598041	+	1.03584i
$111$		0			0
$112$	−1.00000	+	2.44949i	−0.0944911	+	0.231455i
$113$			8.48528i			0.798228i	0.916901	+	0.399114i	$0.130682\pi$
$113$			8.48528i			0.798228i	−0.916901	+	0.399114i	$0.869318\pi$
$114$		0			0
$115$	−15.3640	−	8.87039i	−1.43270	−	0.827168i
$116$	1.07616	+	0.621320i	0.0999188	+	0.0576881i
$117$		0			0
$118$			11.5300i			1.06142i
$119$	−2.65962	+	0.363961i	−0.243807	+	0.0333643i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$	−2.95680	+	5.12132i	−0.267696	+	0.463663i
$123$		0			0
$124$	4.86396	−	2.80821i	0.436797	−	0.252185i
$125$	31.3000			2.79956
$126$		0			0
$127$	−5.24264			−0.465209			−0.232605	−	0.972571i	$-0.574725\pi$
$127$	−5.24264			−0.465209			−0.232605	+	0.972571i	$0.574725\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	5.12132	−	8.87039i	0.449170	−	0.777984i
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	0.956916	−	0.290365i	$-0.0937766\pi$
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	−0.729921	+	0.683531i	$0.760443\pi$
$132$		0			0
$133$	2.48528	+	1.01461i	0.215501	+	0.0879780i
$134$			10.0000i			0.863868i
$135$		0			0
$136$	0.878680	+	0.507306i	0.0753462	+	0.0435011i
$137$	−12.5446	−	7.24264i	−1.07176	−	0.618781i	−0.143098	−	0.989709i	$-0.545706\pi$
$137$	−12.5446	−	7.24264i	−1.07176	−	0.618781i	−0.928662	+	0.370928i	$0.879040\pi$
$138$		0			0
$139$			20.1903i			1.71252i	0.516549	+	0.856258i	$0.327217\pi$
$139$			20.1903i			1.71252i	−0.516549	+	0.856258i	$0.672783\pi$
$140$	6.77962	+	8.74264i	0.572982	+	0.738888i
$141$		0			0
$142$	−5.12132	−	8.87039i	−0.429772	−	0.744386i
$143$	3.67423	−	6.36396i	0.307255	−	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$	−8.36308			−0.692134
$147$		0			0
$148$	−8.24264			−0.677541
$149$	17.7408	−	10.2426i	1.45338	−	0.839110i	0.454709	−	0.890640i	$-0.349743\pi$
$149$	17.7408	−	10.2426i	1.45338	−	0.839110i	0.998671	+	0.0515300i	$0.0164098\pi$
$150$		0			0
$151$	1.62132	−	2.80821i	0.131941	−	0.228529i	−0.792484	−	0.609893i	$-0.791212\pi$
$151$	1.62132	−	2.80821i	0.131941	−	0.228529i	0.924425	+	0.381364i	$0.124546\pi$
$152$	−0.507306	−	0.878680i	−0.0411479	−	0.0712703i
$153$		0			0
$154$	4.86396	+	6.27231i	0.391949	+	0.505437i
$155$		−	23.4853i		−	1.88638i
$156$		0			0
$157$	−12.7279	−	7.34847i	−1.01580	−	0.586472i	−0.102915	−	0.994690i	$-0.532817\pi$
$157$	−12.7279	−	7.34847i	−1.01580	−	0.586472i	−0.912884	+	0.408219i	$0.866150\pi$
$158$	−9.73641	−	5.62132i	−0.774587	−	0.447208i
$159$		0			0
$160$		−	4.18154i		−	0.330580i
$161$	−10.3923	−	4.24264i	−0.819028	−	0.334367i
$162$		0			0
$163$	−3.12132	−	5.40629i	−0.244481	−	0.423453i	0.717505	−	0.696554i	$-0.245284\pi$
$163$	−3.12132	−	5.40629i	−0.244481	−	0.423453i	−0.961985	+	0.273101i	$0.911951\pi$
$164$	−1.01461	+	1.75736i	−0.0792279	+	0.137227i
$165$		0			0
$166$	−2.74264	+	1.58346i	−0.212870	+	0.122901i
$167$	−23.0600			−1.78444			−0.892219	−	0.451603i	$-0.850852\pi$
$167$	−23.0600			−1.78444			−0.892219	+	0.451603i	$0.850852\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	3.67423	−	2.12132i	0.281801	−	0.162698i
$171$		0			0
$172$	4.12132	−	7.13834i	0.314248	−	0.544293i
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	0.925897	+	0.377776i	$0.123311\pi$
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	−0.135785	+	0.990738i	$0.543356\pi$
$174$		0			0
$175$	32.7279	−	4.47871i	2.47400	−	0.338559i
$176$		−	3.00000i		−	0.226134i
$177$		0			0
$178$	9.00000	+	5.19615i	0.674579	+	0.389468i
$179$	−8.23999	−	4.75736i	−0.615886	−	0.355582i	0.159380	−	0.987217i	$-0.449051\pi$
$179$	−8.23999	−	4.75736i	−0.615886	−	0.355582i	−0.775265	+	0.631636i	$0.782384\pi$
$180$		0			0
$181$		−	2.02922i		−	0.150831i	−0.997152	−	0.0754155i	$-0.975972\pi$
$181$		−	2.02922i		−	0.150831i	0.997152	−	0.0754155i	$-0.0240283\pi$
$182$	2.44949	−	6.00000i	0.181568	−	0.444750i
$183$		0			0
$184$	2.12132	+	3.67423i	0.156386	+	0.270868i
$185$	−17.2335	+	29.8492i	−1.26703	+	2.19456i
$186$		0			0
$187$	2.63604	−	1.52192i	0.192766	−	0.111294i
$188$	1.01461			0.0739982
$189$		0			0
$190$	−4.24264			−0.307794
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	−0.209999	−	0.977702i	$-0.567346\pi$
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	0.741715	+	0.670715i	$0.234013\pi$
$192$		0			0
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	−0.699306	−	0.714822i	$-0.746508\pi$
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	0.968707	+	0.248206i	$0.0798409\pi$
$194$	1.88064	+	3.25736i	0.135022	+	0.233865i
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$			9.51472i			0.677896i	0.940805	+	0.338948i	$0.110071\pi$
$197$			9.51472i			0.677896i	−0.940805	+	0.338948i	$0.889929\pi$
$198$		0			0
$199$	−13.9706	−	8.06591i	−0.990347	−	0.571777i	−0.0849690	−	0.996384i	$-0.527079\pi$
$199$	−13.9706	−	8.06591i	−0.990347	−	0.571777i	−0.905378	+	0.424607i	$0.860412\pi$
$200$	−10.8126	−	6.24264i	−0.764564	−	0.441421i
$201$		0			0
$202$		0			0
$203$	2.59808	−	2.01472i	0.182349	−	0.141406i
$204$		0			0
$205$	4.24264	+	7.34847i	0.296319	+	0.513239i
$206$	7.64564	−	13.2426i	0.532697	−	0.922658i
$207$		0			0
$208$	−2.12132	+	1.22474i	−0.147087	+	0.0849208i
$209$	−3.04384			−0.210547
$210$		0			0
$211$	8.24264			0.567447			0.283723	−	0.958906i	$-0.408430\pi$
$211$	8.24264			0.567447			0.283723	+	0.958906i	$0.408430\pi$
$212$	−1.07616	+	0.621320i	−0.0739109	+	0.0426725i
$213$		0			0
$214$	2.74264	−	4.75039i	0.187483	−	0.324730i
$215$	−17.2335	−	29.8492i	−1.17531	−	2.03570i
$216$		0			0
$217$	−2.01472	−	14.7224i	−0.136768	−	0.999424i
$218$		−	1.51472i		−	0.102590i
$219$		0			0
$220$	−10.8640	−	6.27231i	−0.732448	−	0.422879i
$221$	−2.15232	−	1.24264i	−0.144780	−	0.0835891i
$222$		0			0
$223$			12.5446i			0.840050i	0.907513	+	0.420025i	$0.137979\pi$
$223$			12.5446i			0.840050i	−0.907513	+	0.420025i	$0.862021\pi$
$224$	−0.358719	−	2.62132i	−0.0239680	−	0.175144i
$225$		0			0
$226$	−4.24264	−	7.34847i	−0.282216	−	0.488813i
$227$	−7.79423	+	13.5000i	−0.517321	+	0.896026i	0.482476	+	0.875909i	$0.339737\pi$
$227$	−7.79423	+	13.5000i	−0.517321	+	0.896026i	−0.999798	+	0.0201176i	$0.993596\pi$
$228$		0			0
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$	17.7408			1.16979
$231$		0			0
$232$	−1.24264			−0.0815834
$233$	5.82655	−	3.36396i	0.381710	−	0.220380i	−0.296852	−	0.954924i	$-0.595937\pi$
$233$	5.82655	−	3.36396i	0.381710	−	0.220380i	0.678562	+	0.734543i	$0.262603\pi$
$234$		0			0
$235$	2.12132	−	3.67423i	0.138380	−	0.239681i
$236$	−5.76500	−	9.98528i	−0.375270	−	0.649986i
$237$		0			0
$238$	2.12132	−	1.64501i	0.137505	−	0.106630i
$239$			12.7279i			0.823301i	0.911342	+	0.411650i	$0.135048\pi$
$239$			12.7279i			0.823301i	−0.911342	+	0.411650i	$0.864952\pi$
$240$		0			0
$241$	14.7426	+	8.51167i	0.949657	+	0.548285i	0.892974	−	0.450108i	$-0.148614\pi$
$241$	14.7426	+	8.51167i	0.949657	+	0.548285i	0.0566826	+	0.998392i	$0.481948\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$		0			0
$244$		−	5.91359i		−	0.378579i
$245$	28.1946	−	7.86396i	1.80129	−	0.502410i
$246$		0			0
$247$	1.24264	+	2.15232i	0.0790673	+	0.136949i
$248$	−2.80821	+	4.86396i	−0.178321	+	0.308862i
$249$		0			0
$250$	−27.1066	+	15.6500i	−1.71437	+	0.989793i
$251$	17.6177			1.11202			0.556009	−	0.831176i	$-0.312332\pi$
$251$	17.6177			1.11202			0.556009	+	0.831176i	$0.312332\pi$
$252$		0			0
$253$	12.7279			0.800198
$254$	4.54026	−	2.62132i	0.284881	−	0.164476i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	0.930474	+	0.366358i	$0.119395\pi$
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	−0.147962	+	0.988993i	$0.547271\pi$
$258$		0			0
$259$	−8.24264	+	20.1903i	−0.512173	+	1.25456i
$260$			10.2426i			0.635222i
$261$		0			0
$262$	−4.50000	−	2.59808i	−0.278011	−	0.160510i
$263$	23.5673	+	13.6066i	1.45322	+	0.839019i	0.998663	−	0.0516967i	$-0.0164629\pi$
$263$	23.5673	+	13.6066i	1.45322	+	0.839019i	0.454561	+	0.890716i	$0.349796\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$	−2.65962	+	0.363961i	−0.163072	+	0.0223159i
$267$		0			0
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	−5.25770	+	9.10660i	−0.320568	+	0.555239i	−0.980605	−	0.195993i	$-0.937207\pi$
$269$	−5.25770	+	9.10660i	−0.320568	+	0.555239i	0.660038	+	0.751232i	$0.270540\pi$
$270$		0			0
$271$	−9.62132	+	5.55487i	−0.584454	+	0.337434i	−0.762901	−	0.646515i	$-0.776226\pi$
$271$	−9.62132	+	5.55487i	−0.584454	+	0.337434i	0.178448	+	0.983949i	$0.442892\pi$
$272$	−1.01461			−0.0615199
$273$		0			0
$274$	14.4853			0.875088
$275$	−32.4377	+	18.7279i	−1.95607	+	1.12934i
$276$		0			0
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	−0.357552	−	0.933893i	$-0.616388\pi$
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	0.987551	−	0.157298i	$-0.0502783\pi$
$278$	−10.0951	−	17.4853i	−0.605466	−	1.04870i
$279$		0			0
$280$	−10.2426	−	4.18154i	−0.612115	−	0.249895i
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	−5.63604	−	3.25397i	−0.335028	−	0.193428i	0.323043	−	0.946384i	$-0.395294\pi$
$283$	−5.63604	−	3.25397i	−0.335028	−	0.193428i	−0.658071	+	0.752956i	$0.728627\pi$
$284$	8.87039	+	5.12132i	0.526361	+	0.303894i
$285$		0			0
$286$			7.34847i			0.434524i
$287$	3.29002	+	4.24264i	0.194204	+	0.250435i
$288$		0			0
$289$	7.98528	+	13.8309i	0.469722	+	0.813583i
$290$	−2.59808	+	4.50000i	−0.152564	+	0.264249i
$291$		0			0
$292$	7.24264	−	4.18154i	0.423843	−	0.244706i
$293$	−4.18154			−0.244288			−0.122144	−	0.992512i	$-0.538977\pi$
$293$	−4.18154			−0.244288			−0.122144	+	0.992512i	$0.538977\pi$
$294$		0			0
$295$	−48.2132			−2.80708
$296$	7.13834	−	4.12132i	0.414907	−	0.239547i
$297$		0			0
$298$	−10.2426	+	17.7408i	−0.593340	+	1.02770i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	−13.3640	−	17.2335i	−0.770286	−	0.993321i
$302$			3.24264i			0.186593i
$303$		0			0
$304$	0.878680	+	0.507306i	0.0503957	+	0.0290960i
$305$	−21.4150	−	12.3640i	−1.22622	−	0.707958i
$306$		0			0
$307$			24.6690i			1.40793i	0.710233	+	0.703966i	$0.248589\pi$
$307$			24.6690i			1.40793i	−0.710233	+	0.703966i	$0.751411\pi$
$308$	−7.34847	−	3.00000i	−0.418718	−	0.170941i
$309$		0			0
$310$	11.7426	+	20.3389i	0.666937	+	1.15517i
$311$	9.37769	−	16.2426i	0.531760	−	0.921036i	−0.467552	−	0.883965i	$-0.654864\pi$
$311$	9.37769	−	16.2426i	0.531760	−	0.921036i	0.999313	−	0.0370703i	$-0.0118026\pi$
$312$		0			0
$313$	−0.985281	+	0.568852i	−0.0556914	+	0.0321534i	−0.527587	−	0.849501i	$-0.676903\pi$
$313$	−0.985281	+	0.568852i	−0.0556914	+	0.0321534i	0.471896	+	0.881654i	$0.343570\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	−0.313404	−	0.949620i	$-0.601470\pi$
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	0.665693	+	0.746226i	$0.268136\pi$
$318$		0			0
$319$	−1.86396	+	3.22848i	−0.104362	+	0.180760i
$320$	2.09077	+	3.62132i	0.116878	+	0.202438i
$321$		0			0
$322$	11.1213	−	1.52192i	0.619767	−	0.0848132i
$323$			1.02944i			0.0572794i
$324$		0			0
$325$	26.4853	+	15.2913i	1.46914	+	0.848208i
$326$	5.40629	+	3.12132i	0.299426	+	0.172874i
$327$		0			0
$328$		−	2.02922i		−	0.112045i
$329$	1.01461	−	2.48528i	0.0559374	−	0.137018i
$330$		0			0
$331$	−8.72792	−	15.1172i	−0.479730	−	0.830917i	0.520000	−	0.854166i	$-0.325932\pi$
$331$	−8.72792	−	15.1172i	−0.479730	−	0.830917i	−0.999730	+	0.0232497i	$0.992599\pi$
$332$	1.58346	−	2.74264i	0.0869039	−	0.150522i
$333$		0			0
$334$	19.9706	−	11.5300i	1.09274	−	0.630894i
$335$	−41.8154			−2.28462
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	−6.06218	+	3.50000i	−0.329739	+	0.190375i
$339$		0			0
$340$	−2.12132	+	3.67423i	−0.115045	+	0.199263i
$341$	8.42463	+	14.5919i	0.456219	+	0.790195i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$			8.24264i			0.444413i
$345$		0			0
$346$	−18.0000	−	10.3923i	−0.967686	−	0.558694i
$347$	12.5446	+	7.24264i	0.673431	+	0.388805i	0.797375	−	0.603484i	$-0.206221\pi$
$347$	12.5446	+	7.24264i	0.673431	+	0.388805i	−0.123945	+	0.992289i	$0.539555\pi$
$348$		0			0
$349$		−	36.9164i		−	1.97609i	−0.154163	−	0.988045i	$-0.549268\pi$
$349$		−	36.9164i		−	1.97609i	0.154163	−	0.988045i	$-0.450732\pi$
$350$	−26.1039	+	20.2426i	−1.39531	+	1.08201i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	9.37769	−	16.2426i	0.499124	−	0.864509i	−0.500875	−	0.865519i	$-0.666988\pi$
$353$	9.37769	−	16.2426i	0.499124	−	0.864509i	0.999999	+	0.00101095i	$0.000321796\pi$
$354$		0			0
$355$	37.0919	−	21.4150i	1.96863	−	1.13659i
$356$	−10.3923			−0.550791
$357$		0			0
$358$	9.51472			0.502869
$359$	15.5885	−	9.00000i	0.822727	−	0.475002i	−0.0286287	−	0.999590i	$-0.509114\pi$
$359$	15.5885	−	9.00000i	0.822727	−	0.475002i	0.851356	+	0.524588i	$0.175781\pi$
$360$		0			0
$361$	−8.98528	+	15.5630i	−0.472910	+	0.819103i
$362$	1.01461	+	1.75736i	0.0533268	+	0.0923648i
$363$		0			0
$364$	0.878680	+	6.42090i	0.0460553	+	0.336546i
$365$		−	34.9706i		−	1.83044i
$366$		0			0
$367$	16.3492	+	9.43924i	0.853424	+	0.492724i	0.861804	−	0.507241i	$-0.169334\pi$
$367$	16.3492	+	9.43924i	0.853424	+	0.492724i	−0.00838099	+	0.999965i	$0.502668\pi$
$368$	−3.67423	−	2.12132i	−0.191533	−	0.110581i
$369$		0			0
$370$		−	34.4669i		−	1.79185i
$371$	0.445759	+	3.25736i	0.0231427	+	0.169114i
$372$		0			0
$373$	−10.7279	−	18.5813i	−0.555471	−	0.962104i	−0.997867	−	0.0652837i	$-0.979205\pi$
$373$	−10.7279	−	18.5813i	−0.555471	−	0.962104i	0.442396	−	0.896820i	$-0.354129\pi$
$374$	−1.52192	+	2.63604i	−0.0786965	+	0.136306i
$375$		0			0
$376$	−0.878680	+	0.507306i	−0.0453144	+	0.0261623i
$377$	3.04384			0.156766
$378$		0			0
$379$	−4.48528			−0.230393			−0.115197	−	0.993343i	$-0.536750\pi$
$379$	−4.48528			−0.230393			−0.115197	+	0.993343i	$0.536750\pi$
$380$	3.67423	−	2.12132i	0.188484	−	0.108821i
$381$		0			0
$382$	−4.24264	+	7.34847i	−0.217072	+	0.375980i
$383$	6.21076	+	10.7574i	0.317355	+	0.549675i	0.979935	−	0.199316i	$-0.0638719\pi$
$383$	6.21076	+	10.7574i	0.317355	+	0.549675i	−0.662580	+	0.748991i	$0.730539\pi$
$384$		0			0
$385$	−26.2279	+	20.3389i	−1.33670	+	1.03656i
$386$			7.48528i			0.380991i
$387$		0			0
$388$	−3.25736	−	1.88064i	−0.165367	−	0.0954749i
$389$	−16.8493	−	9.72792i	−0.854291	−	0.493225i	0.00780525	−	0.999970i	$-0.497515\pi$
$389$	−16.8493	−	9.72792i	−0.854291	−	0.493225i	−0.862096	+	0.506744i	$0.830849\pi$
$390$		0			0
$391$		−	4.30463i		−	0.217695i
$392$	−6.77962	−	1.74264i	−0.342422	−	0.0880166i
$393$		0			0
$394$	−4.75736	−	8.23999i	−0.239672	−	0.415125i
$395$	23.5058	−	40.7132i	1.18270	−	2.04850i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	16.1318			0.808615
$399$		0			0
$400$	12.4853			0.624264
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	6.87868	−	11.9142i	0.342651	−	0.593490i
$404$		0			0
$405$		0			0
$406$	−1.24264	+	3.04384i	−0.0616712	+	0.151063i
$407$		−	24.7279i		−	1.22572i
$408$		0			0
$409$	−3.98528	−	2.30090i	−0.197059	−	0.113772i	0.398224	−	0.917288i	$-0.369627\pi$
$409$	−3.98528	−	2.30090i	−0.197059	−	0.113772i	−0.595283	+	0.803516i	$0.702960\pi$
$410$	−7.34847	−	4.24264i	−0.362915	−	0.209529i
$411$		0			0
$412$			15.2913i			0.753348i
$413$	−30.2238	+	4.13604i	−1.48722	+	0.203521i
$414$		0			0
$415$	−6.62132	−	11.4685i	−0.325028	−	0.562965i
$416$	1.22474	−	2.12132i	0.0600481	−	0.104006i
$417$		0			0
$418$	2.63604	−	1.52192i	0.128933	−	0.0744394i
$419$	−4.05845			−0.198268			−0.0991341	−	0.995074i	$-0.531607\pi$
$419$	−4.05845			−0.198268			−0.0991341	+	0.995074i	$0.531607\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$	−7.13834	+	4.12132i	−0.347489	+	0.200623i
$423$		0			0
$424$	0.621320	−	1.07616i	0.0301740	−	0.0522629i
$425$	6.33386	+	10.9706i	0.307237	+	0.532150i
$426$		0			0
$427$	−14.4853	−	5.91359i	−0.700992	−	0.286179i
$428$			5.48528i			0.265141i
$429$		0			0
$430$	29.8492	+	17.2335i	1.43946	+	0.831072i
$431$	17.7408	+	10.2426i	0.854543	+	0.493371i	0.862181	−	0.506600i	$-0.169098\pi$
$431$	17.7408	+	10.2426i	0.854543	+	0.493371i	−0.00763808	+	0.999971i	$0.502431\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$	9.10601	+	11.7426i	0.437103	+	0.563665i
$435$		0			0
$436$	0.757359	+	1.31178i	0.0362709	+	0.0628231i
$437$	−2.15232	+	3.72792i	−0.102959	+	0.178331i
$438$		0			0
$439$	23.5919	−	13.6208i	1.12598	−	0.650084i	0.183059	−	0.983102i	$-0.441400\pi$
$439$	23.5919	−	13.6208i	1.12598	−	0.650084i	0.942921	+	0.333018i	$0.108067\pi$
$440$	12.5446			0.598041
$441$		0			0
$442$	2.48528			0.118213
$443$	−29.8396	+	17.2279i	−1.41772	+	0.818523i	−0.996099	−	0.0882469i	$-0.971874\pi$
$443$	−29.8396	+	17.2279i	−1.41772	+	0.818523i	−0.421625	+	0.906770i	$0.638540\pi$
$444$		0			0
$445$	−21.7279	+	37.6339i	−1.03000	+	1.78402i
$446$	−6.27231	−	10.8640i	−0.297003	−	0.514423i
$447$		0			0
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$			10.2426i			0.483380i	0.970354	+	0.241690i	$0.0777017\pi$
$449$			10.2426i			0.483380i	−0.970354	+	0.241690i	$0.922298\pi$
$450$		0			0
$451$	−5.27208	−	3.04384i	−0.248252	−	0.143329i
$452$	7.34847	+	4.24264i	0.345643	+	0.199557i
$453$		0			0
$454$		−	15.5885i		−	0.731603i
$455$	25.0892	+	10.2426i	1.17620	+	0.480182i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$	6.92820	−	12.0000i	0.323734	−	0.560723i
$459$		0			0
$460$	−15.3640	+	8.87039i	−0.716348	+	0.413584i
$461$	−22.8138			−1.06255			−0.531273	−	0.847201i	$-0.678286\pi$
$461$	−22.8138			−1.06255			−0.531273	+	0.847201i	$0.678286\pi$
$462$		0			0
$463$	21.4558			0.997138			0.498569	−	0.866850i	$-0.333859\pi$
$463$	21.4558			0.997138			0.498569	+	0.866850i	$0.333859\pi$
$464$	1.07616	−	0.621320i	0.0499594	−	0.0288441i
$465$		0			0
$466$	−3.36396	+	5.82655i	−0.155832	+	0.269910i
$467$	9.50079	+	16.4558i	0.439644	+	0.761486i	0.997662	−	0.0683432i	$-0.0217713\pi$
$467$	9.50079	+	16.4558i	0.439644	+	0.761486i	−0.558018	+	0.829829i	$0.688438\pi$
$468$		0			0
$469$	−26.2132	+	3.58719i	−1.21041	+	0.165641i
$470$			4.24264i			0.195698i
$471$		0			0
$472$	9.98528	+	5.76500i	0.459610	+	0.265356i
$473$	21.4150	+	12.3640i	0.984663	+	0.568496i
$474$		0			0
$475$		−	12.6677i		−	0.581235i
$476$	−1.01461	+	2.48528i	−0.0465047	+	0.113913i
$477$		0			0
$478$	−6.36396	−	11.0227i	−0.291081	−	0.504167i
$479$	−18.2481	+	31.6066i	−0.833776	+	1.44414i	0.0612470	+	0.998123i	$0.480492\pi$
$479$	−18.2481	+	31.6066i	−0.833776	+	1.44414i	−0.895023	+	0.446020i	$0.852841\pi$
$480$		0			0
$481$	−17.4853	+	10.0951i	−0.797260	+	0.460298i
$482$	−17.0233			−0.775392
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−13.6208	+	7.86396i	−0.618488	+	0.357084i
$486$		0			0
$487$	−14.1066	+	24.4334i	−0.639231	+	1.10718i	0.346371	+	0.938098i	$0.387414\pi$
$487$	−14.1066	+	24.4334i	−0.639231	+	1.10718i	−0.985602	+	0.169083i	$0.945919\pi$
$488$	2.95680	+	5.12132i	0.133848	+	0.231831i
$489$		0			0
$490$	−20.4853	+	20.9077i	−0.925431	+	0.944514i
$491$		−	19.9706i		−	0.901259i	−0.892711	−	0.450629i	$-0.851200\pi$
$491$		−	19.9706i		−	0.901259i	0.892711	−	0.450629i	$-0.148800\pi$
$492$		0			0
$493$	1.09188	+	0.630399i	0.0491759	+	0.0283917i
$494$	−2.15232	−	1.24264i	−0.0968373	−	0.0559090i
$495$		0			0
$496$		−	5.61642i		−	0.252185i
$497$	21.4150	−	16.6066i	0.960594	−	0.744908i
$498$		0			0
$499$	17.9706	+	31.1259i	0.804473	+	1.39339i	0.916646	+	0.399699i	$0.130885\pi$
$499$	17.9706	+	31.1259i	0.804473	+	1.39339i	−0.112173	+	0.993689i	$0.535781\pi$
$500$	15.6500	−	27.1066i	0.699889	−	1.21224i
$501$		0			0
$502$	−15.2574	+	8.80884i	−0.680969	+	0.393158i
$503$	−3.29002			−0.146695			−0.0733474	−	0.997306i	$-0.523368\pi$
$503$	−3.29002			−0.146695			−0.0733474	+	0.997306i	$0.523368\pi$
$504$		0			0
$505$		0			0
$506$	−11.0227	+	6.36396i	−0.490019	+	0.282913i
$507$		0			0
$508$	−2.62132	+	4.54026i	−0.116302	+	0.201441i
$509$	−20.8462	−	36.1066i	−0.923990	−	1.60040i	−0.793178	−	0.608990i	$-0.791575\pi$
$509$	−20.8462	−	36.1066i	−0.923990	−	1.60040i	−0.130812	−	0.991407i	$-0.541758\pi$
$510$		0			0
$511$	−3.00000	−	21.9223i	−0.132712	−	0.969786i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−21.7279	−	12.5446i	−0.958378	−	0.553320i
$515$	55.3746	+	31.9706i	2.44010	+	1.40879i
$516$		0			0
$517$			3.04384i			0.133868i
$518$	−2.95680	−	21.6066i	−0.129914	−	0.949340i
$519$		0			0
$520$	−5.12132	−	8.87039i	−0.224585	−	0.388992i
$521$	−10.0081	+	17.3345i	−0.438462	+	0.759439i	−0.997571	−	0.0696551i	$-0.977810\pi$
$521$	−10.0081	+	17.3345i	−0.438462	+	0.759439i	0.559109	+	0.829094i	$0.311143\pi$
$522$		0			0
$523$	−23.8492	+	13.7694i	−1.04285	+	0.602092i	−0.920641	−	0.390411i	$-0.872333\pi$
$523$	−23.8492	+	13.7694i	−1.04285	+	0.602092i	−0.122214	+	0.992504i	$0.538999\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$	−27.2132			−1.18655
$527$	4.93503	−	2.84924i	0.214973	−	0.124115i
$528$		0			0
$529$	−2.50000	+	4.33013i	−0.108696	+	0.188266i
$530$	−2.59808	−	4.50000i	−0.112853	−	0.195468i
$531$		0			0
$532$	2.12132	−	1.64501i	0.0919709	−	0.0713203i
$533$			4.97056i			0.215299i
$534$		0			0
$535$	19.8640	+	11.4685i	0.858794	+	0.495825i
$536$	8.66025	+	5.00000i	0.374066	+	0.215967i
$537$		0			0
$538$		−	10.5154i		−	0.453351i
$539$	−14.6969	+	15.0000i	−0.633042	+	0.646096i
$540$		0			0
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	0.957989	−	0.286804i	$-0.0925930\pi$
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	−0.727374	+	0.686241i	$0.759260\pi$
$542$	5.55487	−	9.62132i	0.238602	−	0.413271i
$543$		0			0
$544$	0.878680	−	0.507306i	0.0376731	−	0.0217506i
$545$	6.33386			0.271313
$546$		0			0
$547$	19.6985			0.842246			0.421123	−	0.907003i	$-0.361636\pi$
$547$	19.6985			0.842246			0.421123	+	0.907003i	$0.361636\pi$
$548$	−12.5446	+	7.24264i	−0.535880	+	0.309390i
$549$		0			0
$550$	18.7279	−	32.4377i	0.798561	−	1.38315i
$551$	−0.630399	−	1.09188i	−0.0268559	−	0.0465158i
$552$		0			0
$553$	11.2426	−	27.5387i	0.478086	−	1.17107i
$554$			20.9706i			0.890954i
$555$		0			0
$556$	17.4853	+	10.0951i	0.741541	+	0.428129i
$557$	13.6208	+	7.86396i	0.577131	+	0.333207i	0.759992	−	0.649932i	$-0.225203\pi$
$557$	13.6208	+	7.86396i	0.577131	+	0.333207i	−0.182861	+	0.983139i	$0.558536\pi$
$558$		0			0
$559$		−	20.1903i		−	0.853957i
$560$	10.9612	−	1.50000i	0.463193	−	0.0633866i
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	12.0989	−	20.9558i	0.509906	−	0.883184i	−0.490028	−	0.871707i	$-0.663013\pi$
$563$	12.0989	−	20.9558i	0.509906	−	0.883184i	0.999934	−	0.0114768i	$-0.00365325\pi$
$564$		0			0
$565$	30.7279	−	17.7408i	1.29273	−	0.746360i
$566$	6.50794			0.273549
$567$		0			0
$568$	−10.2426			−0.429772
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	−0.467760	−	0.883856i	$-0.654939\pi$
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	0.531562	+	0.847020i	$0.321605\pi$
$570$		0			0
$571$	8.36396	−	14.4868i	0.350021	−	0.606254i	−0.636232	−	0.771498i	$-0.719508\pi$
$571$	8.36396	−	14.4868i	0.350021	−	0.606254i	0.986253	+	0.165244i	$0.0528412\pi$
$572$	−3.67423	−	6.36396i	−0.153627	−	0.266091i
$573$		0			0
$574$	−4.97056	−	2.02922i	−0.207467	−	0.0846982i
$575$			52.9706i			2.20903i
$576$		0			0
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	0.821573	−	0.570103i	$-0.193097\pi$
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	−0.0829373	+	0.996555i	$0.526430\pi$
$578$	−13.8309	−	7.98528i	−0.575290	−	0.332144i
$579$		0			0
$580$		−	5.19615i		−	0.215758i
$581$	−5.13461	−	6.62132i	−0.213019	−	0.274699i
$582$		0			0
$583$	−1.86396	−	3.22848i	−0.0771974	−	0.133710i
$584$	−4.18154	+	7.24264i	−0.173033	+	0.299703i
$585$		0			0
$586$	3.62132	−	2.09077i	0.149595	−	0.0863689i
$587$	−5.19615			−0.214468			−0.107234	−	0.994234i	$-0.534199\pi$
$587$	−5.19615			−0.214468			−0.107234	+	0.994234i	$0.534199\pi$
$588$		0			0
$589$	−5.69848			−0.234802
$590$	41.7539	−	24.1066i	1.71898	−	0.992453i
$591$		0			0
$592$	−4.12132	+	7.13834i	−0.169385	+	0.293384i
$593$	−15.2042	−	26.3345i	−0.624363	−	1.08143i	−0.988664	−	0.150148i	$-0.952025\pi$
$593$	−15.2042	−	26.3345i	−0.624363	−	1.08143i	0.364300	−	0.931282i	$-0.381308\pi$
$594$		0			0
$595$	6.87868	+	8.87039i	0.281998	+	0.363650i
$596$		−	20.4853i		−	0.839110i
$597$		0			0
$598$	9.00000	+	5.19615i	0.368037	+	0.212486i
$599$	−37.6339	−	21.7279i	−1.53768	−	0.887779i	−0.998974	−	0.0452836i	$-0.985581\pi$
$599$	−37.6339	−	21.7279i	−1.53768	−	0.887779i	−0.538704	−	0.842495i	$-0.681086\pi$
$600$		0			0
$601$			6.03668i			0.246241i	0.992392	+	0.123121i	$0.0392902\pi$
$601$			6.03668i			0.246241i	−0.992392	+	0.123121i	$0.960710\pi$
$602$	20.1903	+	8.24264i	0.822894	+	0.335945i
$603$		0			0
$604$	−1.62132	−	2.80821i	−0.0659706	−	0.114264i
$605$	−4.18154	+	7.24264i	−0.170004	+	0.294455i
$606$		0			0
$607$	−21.6213	+	12.4831i	−0.877582	+	0.506672i	−0.869860	−	0.493298i	$-0.835791\pi$
$607$	−21.6213	+	12.4831i	−0.877582	+	0.506672i	−0.00772182	+	0.999970i	$0.502458\pi$
$608$	−1.01461			−0.0411479
$609$		0			0
$610$	24.7279			1.00120
$611$	2.15232	−	1.24264i	0.0870734	−	0.0502719i
$612$		0			0
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	−0.913852	−	0.406046i	$-0.866907\pi$
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	0.808573	+	0.588396i	$0.200240\pi$
$614$	−12.3345	−	21.3640i	−0.497779	−	0.862179i
$615$		0			0
$616$	7.86396	−	1.07616i	0.316848	−	0.0433597i
$617$		−	41.6985i		−	1.67872i	−0.543578	−	0.839359i	$-0.682931\pi$
$617$		−	41.6985i		−	1.67872i	0.543578	−	0.839359i	$-0.317069\pi$
$618$		0			0
$619$	−41.3345	−	23.8645i	−1.66137	−	0.959195i	−0.972060	−	0.234733i	$-0.924578\pi$
$619$	−41.3345	−	23.8645i	−1.66137	−	0.959195i	−0.689315	−	0.724462i	$-0.742088\pi$
$620$	−20.3389	−	11.7426i	−0.816828	−	0.471596i
$621$		0			0
$622$			18.7554i			0.752022i
$623$	−10.3923	+	25.4558i	−0.416359	+	1.01987i
$624$		0			0
$625$	−34.2279	−	59.2845i	−1.36912	−	2.37138i
$626$	0.568852	−	0.985281i	0.0227359	−	0.0393798i
$627$		0			0
$628$	−12.7279	+	7.34847i	−0.507899	+	0.293236i
$629$	−8.36308			−0.333458
$630$		0			0
$631$	33.2426			1.32337			0.661684	−	0.749783i	$-0.269842\pi$
$631$	33.2426			1.32337			0.661684	+	0.749783i	$0.269842\pi$
$632$	−9.73641	+	5.62132i	−0.387294	+	0.223604i
$633$		0			0
$634$	−3.62132	+	6.27231i	−0.143821	+	0.249105i
$635$	10.9612	+	18.9853i	0.434980	+	0.753408i
$636$		0			0
$637$	16.6066	+	4.26858i	0.657978	+	0.169127i
$638$		−	3.72792i		−	0.147590i
$639$		0			0
$640$	−3.62132	−	2.09077i	−0.143145	−	0.0826450i
$641$	−36.1119	−	20.8492i	−1.42634	−	0.823496i	−0.429507	−	0.903064i	$-0.641313\pi$
$641$	−36.1119	−	20.8492i	−1.42634	−	0.823496i	−0.996829	+	0.0795681i	$0.974646\pi$
$642$		0			0
$643$		−	2.62357i		−	0.103463i	−0.998661	−	0.0517317i	$-0.983526\pi$
$643$		−	2.62357i		−	0.103463i	0.998661	−	0.0517317i	$-0.0164741\pi$
$644$	−8.87039	+	6.87868i	−0.349542	+	0.271058i
$645$		0			0
$646$	−0.514719	−	0.891519i	−0.0202513	−	0.0350763i
$647$	−5.82655	+	10.0919i	−0.229065	+	0.396753i	−0.957531	−	0.288329i	$-0.906900\pi$
$647$	−5.82655	+	10.0919i	−0.229065	+	0.396753i	0.728466	+	0.685082i	$0.240234\pi$
$648$		0			0
$649$	29.9558	−	17.2950i	1.17587	−	0.678889i
$650$	−30.5826			−1.19955
$651$		0			0
$652$	−6.24264			−0.244481
$653$	−9.31615	+	5.37868i	−0.364569	+	0.210484i	−0.671083	−	0.741382i	$-0.734171\pi$
$653$	−9.31615	+	5.37868i	−0.364569	+	0.210484i	0.306514	+	0.951866i	$0.400837\pi$
$654$		0			0
$655$	10.8640	−	18.8169i	0.424490	−	0.735238i
$656$	1.01461	+	1.75736i	0.0396139	+	0.0686134i
$657$		0			0
$658$	0.363961	+	2.65962i	0.0141887	+	0.103683i
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	35.1213	+	20.2773i	1.36606	+	0.788696i	0.990422	−	0.138071i	$-0.0440901\pi$
$661$	35.1213	+	20.2773i	1.36606	+	0.788696i	0.375639	+	0.926766i	$0.377423\pi$
$662$	15.1172	+	8.72792i	0.587547	+	0.339220i
$663$		0			0
$664$			3.16693i			0.122901i
$665$	−1.52192	−	11.1213i	−0.0590174	−	0.431266i
$666$		0			0
$667$	2.63604	+	4.56575i	0.102068	+	0.176787i
$668$	−11.5300	+	19.9706i	−0.446109	+	0.772684i
$669$		0			0
$670$	36.2132	−	20.9077i	1.39904	−	0.807735i
$671$	17.7408			0.684875
$672$		0			0
$673$	−15.9706			−0.615620			−0.307810	−	0.951448i	$-0.599596\pi$
$673$	−15.9706			−0.615620			−0.307810	+	0.951448i	$0.599596\pi$
$674$	4.33013	−	2.50000i	0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	6.27231	+	10.8640i	0.241064	+	0.417536i	0.961018	−	0.276487i	$-0.0891701\pi$
$677$	6.27231	+	10.8640i	0.241064	+	0.417536i	−0.719953	+	0.694023i	$0.755837\pi$
$678$		0			0
$679$	−7.86396	+	6.09823i	−0.301791	+	0.234029i
$680$		−	4.24264i		−	0.162698i
$681$		0			0
$682$	−14.5919	−	8.42463i	−0.558752	−	0.322596i
$683$	−22.4912	−	12.9853i	−0.860601	−	0.496868i	0.00361277	−	0.999993i	$-0.498850\pi$
$683$	−22.4912	−	12.9853i	−0.860601	−	0.496868i	−0.864213	+	0.503125i	$0.832183\pi$
$684$		0			0
$685$			60.5708i			2.31429i
$686$	−11.0482	+	14.8640i	−0.421822	+	0.567509i
$687$		0			0
$688$	−4.12132	−	7.13834i	−0.157124	−	0.272147i
$689$	−1.52192	+	2.63604i	−0.0579805	+	0.100425i
$690$		0			0
$691$	−0.727922	+	0.420266i	−0.0276915	+	0.0159877i	−0.513782	−	0.857921i	$-0.671756\pi$
$691$	−0.727922	+	0.420266i	−0.0276915	+	0.0159877i	0.486090	+	0.873909i	$0.338423\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	−14.4853			−0.549854
$695$	73.1154	−	42.2132i	2.77343	−	1.60124i
$696$		0			0
$697$	−1.02944	+	1.78304i	−0.0389927	+	0.0675374i
$698$	18.4582	+	31.9706i	0.698654	+	1.21010i
$699$		0			0
$700$	12.4853	−	30.5826i	0.471899	−	1.15591i
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	7.24264	+	4.18154i	0.273161	+	0.157710i
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$			18.7554i			0.705868i
$707$		0			0
$708$		0			0
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	0.924021	−	0.382342i	$-0.124882\pi$
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	−0.793128	+	0.609055i	$0.791549\pi$
$710$	−21.4150	+	37.0919i	−0.803691	+	1.39203i
$711$		0			0
$712$	9.00000	−	5.19615i	0.337289	−	0.194734i
$713$	23.8284			0.892382
$714$		0			0
$715$	−30.7279			−1.14916
$716$	−8.23999	+	4.75736i	−0.307943	+	0.177791i
$717$		0			0
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	−11.5300	−	19.9706i	−0.429997	−	0.744776i	0.566876	−	0.823803i	$-0.308152\pi$
$719$	−11.5300	−	19.9706i	−0.429997	−	0.744776i	−0.996872	+	0.0790270i	$0.974819\pi$
$720$		0			0
$721$	37.4558	+	15.2913i	1.39493	+	0.569477i
$722$		−	17.9706i		−	0.668795i
$723$		0			0
$724$	−1.75736	−	1.01461i	−0.0653117	−	0.0377078i
$725$	−13.4361	−	7.75736i	−0.499006	−	0.288101i
$726$		0			0
$727$			26.4010i			0.979160i	0.871958	+	0.489580i	$0.162850\pi$
$727$			26.4010i			0.979160i	−0.871958	+	0.489580i	$0.837150\pi$
$728$	−3.97141	−	5.12132i	−0.147190	−	0.189809i
$729$		0			0
$730$	17.4853	+	30.2854i	0.647159	+	1.12091i
$731$	4.18154	−	7.24264i	0.154660	−	0.267879i
$732$		0			0
$733$	−34.0919	+	19.6830i	−1.25921	+	0.727007i	−0.972921	−	0.231136i	$-0.925756\pi$
$733$	−34.0919	+	19.6830i	−1.25921	+	0.727007i	−0.286291	+	0.958143i	$0.592422\pi$
$734$	−18.8785			−0.696817
$735$		0			0
$736$	4.24264			0.156386
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	17.7279	−	30.7057i	0.652132	−	1.12953i	−0.330472	−	0.943816i	$-0.607208\pi$
$739$	17.7279	−	30.7057i	0.652132	−	1.12953i	0.982605	−	0.185710i	$-0.0594586\pi$
$740$	17.2335	+	29.8492i	0.633515	+	1.09728i
$741$		0			0
$742$	−2.01472	−	2.59808i	−0.0739626	−	0.0953784i
$743$		−	21.5147i		−	0.789298i	−0.918832	−	0.394649i	$-0.870866\pi$
$743$		−	21.5147i		−	0.789298i	0.918832	−	0.394649i	$-0.129134\pi$
$744$		0			0
$745$	−74.1838	−	42.8300i	−2.71788	−	1.56917i
$746$	18.5813	+	10.7279i	0.680310	+	0.392777i
$747$		0			0
$748$		−	3.04384i		−	0.111294i
$749$	13.4361	+	5.48528i	0.490946	+	0.200428i
$750$		0			0
$751$	−13.3787	−	23.1726i	−0.488195	−	0.845578i	0.511713	−	0.859157i	$-0.329011\pi$
$751$	−13.3787	−	23.1726i	−0.488195	−	0.845578i	−0.999908	+	0.0135781i	$0.995678\pi$
$752$	0.507306	−	0.878680i	0.0184995	−	0.0320422i
$753$		0			0
$754$	−2.63604	+	1.52192i	−0.0959989	+	0.0554250i
$755$	−13.5592			−0.493471
$756$		0			0
$757$	−42.2426			−1.53533			−0.767667	−	0.640848i	$-0.778583\pi$
$757$	−42.2426			−1.53533			−0.767667	+	0.640848i	$0.778583\pi$
$758$	3.88437	−	2.24264i	0.141087	−	0.0814564i
$759$		0			0
$760$	−2.12132	+	3.67423i	−0.0769484	+	0.133278i
$761$	2.53653	+	4.39340i	0.0919491	+	0.159261i	0.908331	−	0.418252i	$-0.137357\pi$
$761$	2.53653	+	4.39340i	0.0919491	+	0.159261i	−0.816382	+	0.577512i	$0.804024\pi$
$762$		0			0
$763$	3.97056	−	0.543359i	0.143744	−	0.0196709i
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	−10.7574	−	6.21076i	−0.388679	−	0.224404i
$767$	−24.4588	−	14.1213i	−0.883158	−	0.509891i
$768$		0			0
$769$		−	49.0408i		−	1.76846i	−0.467056	−	0.884228i	$-0.654685\pi$
$769$		−	49.0408i		−	1.76846i	0.467056	−	0.884228i	$-0.345315\pi$
$770$	12.5446	−	30.7279i	0.452077	−	1.10736i
$771$		0			0
$772$	−3.74264	−	6.48244i	−0.134701	−	0.233308i
$773$	11.5300	−	19.9706i	0.414706	−	0.718291i	−0.580692	−	0.814123i	$-0.697218\pi$
$773$	11.5300	−	19.9706i	0.414706	−	0.718291i	0.995398	+	0.0958322i	$0.0305512\pi$
$774$		0			0
$775$	−60.7279	+	35.0613i	−2.18141	+	1.25944i
$776$	3.76127			0.135022
$777$		0			0
$778$	19.4558			0.697526
$779$	1.78304	−	1.02944i	0.0638840	−	0.0368834i
$780$		0			0
$781$	−15.3640	+	26.6112i	−0.549766	+	0.952222i
$782$	2.15232	+	3.72792i	0.0769667	+	0.133310i
$783$		0			0
$784$	6.74264	−	1.88064i	0.240809	−	0.0671656i
$785$			61.4558i			2.19345i
$786$		0			0
$787$	32.1213	+	18.5453i	1.14500	+	0.661067i	0.947664	−	0.319269i	$-0.103437\pi$
$787$	32.1213	+	18.5453i	1.14500	+	0.661067i	0.197337	+	0.980336i	$0.436771\pi$
$788$	8.23999	+	4.75736i	0.293537	+	0.169474i
$789$		0			0
$790$			47.0116i			1.67260i
$791$	17.7408	−	13.7574i	0.630789	−	0.489155i
$792$		0			0
$793$	−7.24264	−	12.5446i	−0.257194	−	0.445473i
$794$	−6.92820	+	12.0000i	−0.245873	+	0.425864i
$795$		0			0
$796$	−13.9706	+	8.06591i	−0.495173	+	0.285889i
$797$	37.6339			1.33306			0.666530	−	0.745478i	$-0.267779\pi$
$797$	37.6339			1.33306			0.666530	+	0.745478i	$0.267779\pi$
$798$		0			0
$799$	1.02944			0.0364189
$800$	−10.8126	+	6.24264i	−0.382282	+	0.220711i
$801$		0			0
$802$		0			0
$803$	12.5446	+	21.7279i	0.442690	+	0.766762i
$804$		0			0
$805$	6.36396	+	46.5043i	0.224300	+	1.63906i
$806$			13.7574i			0.484582i
$807$		0			0
$808$		0			0
$809$	35.4815	+	20.4853i	1.24746	+	0.720224i	0.970603	−	0.240686i	$-0.0773723\pi$
$809$	35.4815	+	20.4853i	1.24746	+	0.720224i	0.276862	+	0.960910i	$0.410706\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	−0.445759	−	3.25736i	−0.0156431	−	0.114311i
$813$		0			0
$814$	12.3640	+	21.4150i	0.433357	+	0.750596i
$815$	−13.0519	+	22.6066i	−0.457189	+	0.791875i
$816$		0			0
$817$	−7.24264	+	4.18154i	−0.253388	+	0.146294i
$818$	4.60181			0.160898
$819$		0			0
$820$	8.48528			0.296319
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.999911	−	0.0133172i	$-0.995761\pi$
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.488423	+	0.872607i	$0.662428\pi$
$822$		0			0
$823$	18.9706	−	32.8580i	0.661272	−	1.14536i	−0.319009	−	0.947752i	$-0.603350\pi$
$823$	18.9706	−	32.8580i	0.661272	−	1.14536i	0.980282	−	0.197606i	$-0.0633165\pi$
$824$	−7.64564	−	13.2426i	−0.266349	−	0.461329i
$825$		0			0
$826$	24.1066	−	18.6938i	0.838776	−	0.650442i
$827$		−	4.02944i		−	0.140117i	−0.997543	−	0.0700586i	$-0.977681\pi$
$827$		−	4.02944i		−	0.140117i	0.997543	−	0.0700586i	$-0.0223186\pi$
$828$		0			0
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.260772	−	0.965401i	$-0.583977\pi$
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.966447	+	0.256865i	$0.917310\pi$
$830$	11.4685	+	6.62132i	0.398076	+	0.229829i
$831$		0			0
$832$			2.44949i			0.0849208i
$833$	5.07306	+	4.97056i	0.175771	+	0.172220i
$834$		0			0
$835$	48.2132	+	83.5077i	1.66849	+	2.88990i
$836$	−1.52192	+	2.63604i	−0.0526366	+	0.0911693i
$837$		0			0
$838$	3.51472	−	2.02922i	0.121414	−	0.0700984i
$839$	24.0746			0.831149			0.415574	−	0.909559i	$-0.363581\pi$
$839$	24.0746			0.831149			0.415574	+	0.909559i	$0.363581\pi$
$840$		0			0
$841$	27.4558			0.946753
$842$	4.98602	−	2.87868i	0.171830	−	0.0992059i
$843$		0			0
$844$	4.12132	−	7.13834i	0.141862	−	0.245712i
$845$	−14.6354	−	25.3492i	−0.503473	−	0.872040i
$846$		0			0
$847$	−2.00000	+	4.89898i	−0.0687208	+	0.168331i
$848$			1.24264i			0.0426725i
$849$		0			0
$850$	−10.9706	−	6.33386i	−0.376287	−	0.217250i
$851$	−30.2854	−	17.4853i	−1.03817	−	0.599388i
$852$		0			0
$853$			2.27541i			0.0779085i	0.999241	+	0.0389543i	$0.0124027\pi$
$853$			2.27541i			0.0779085i	−0.999241	+	0.0389543i	$0.987597\pi$
$854$	15.5014	−	2.12132i	0.530448	−	0.0725901i
$855$		0			0
$856$	−2.74264	−	4.75039i	−0.0937415	−	0.162365i
$857$	10.0081	−	17.3345i	0.341870	−	0.592136i	−0.642910	−	0.765942i	$-0.722273\pi$
$857$	10.0081	−	17.3345i	0.341870	−	0.592136i	0.984780	+	0.173806i	$0.0556064\pi$
$858$		0			0
$859$	3.87868	−	2.23936i	0.132339	−	0.0764059i	−0.432369	−	0.901697i	$-0.642322\pi$
$859$	3.87868	−	2.23936i	0.132339	−	0.0764059i	0.564708	+	0.825291i	$0.308989\pi$
$860$	−34.4669			−1.17531
$861$		0			0
$862$	−20.4853			−0.697731
$863$	−43.7215	+	25.2426i	−1.48830	+	0.859269i	−0.999911	−	0.0133573i	$-0.995748\pi$
$863$	−43.7215	+	25.2426i	−1.48830	+	0.859269i	−0.488388	+	0.872627i	$0.662415\pi$
$864$		0			0
$865$	43.4558	−	75.2677i	1.47754	−	2.55918i
$866$	−1.73205	−	3.00000i	−0.0588575	−	0.101944i
$867$		0			0
$868$	−13.7574	−	5.61642i	−0.466955	−	0.190634i
$869$			33.7279i			1.14414i
$870$		0			0
$871$	−21.2132	−	12.2474i	−0.718782	−	0.414989i
$872$	−1.31178	−	0.757359i	−0.0444226	−	0.0256474i
$873$		0			0
$874$		−	4.30463i		−	0.145606i
$875$	−50.7473	−	65.4411i	−1.71557	−	2.21231i
$876$		0			0
$877$	6.24264	+	10.8126i	0.210799	+	0.365115i	0.951965	−	0.306207i	$-0.0990601\pi$
$877$	6.24264	+	10.8126i	0.210799	+	0.365115i	−0.741166	+	0.671322i	$0.765727\pi$
$878$	−13.6208	+	23.5919i	−0.459679	+	0.796187i
$879$		0			0
$880$	−10.8640	+	6.27231i	−0.366224	+	0.211440i
$881$	39.7862			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$881$	39.7862			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$882$		0			0
$883$	−9.45584			−0.318214			−0.159107	−	0.987261i	$-0.550862\pi$
$883$	−9.45584			−0.318214			−0.159107	+	0.987261i	$0.550862\pi$
$884$	−2.15232	+	1.24264i	−0.0723902	+	0.0417945i
$885$		0			0
$886$	17.2279	−	29.8396i	0.578783	−	1.00248i
$887$	−22.4296	−	38.8492i	−0.753113	−	1.30443i	−0.946307	−	0.323269i	$-0.895218\pi$
$887$	−22.4296	−	38.8492i	−0.753113	−	1.30443i	0.193194	−	0.981161i	$-0.438115\pi$
$888$		0			0
$889$	8.50000	+	10.9612i	0.285081	+	0.367625i
$890$		−	43.4558i		−	1.45664i
$891$		0			0
$892$	10.8640	+	6.27231i	0.363752	+	0.210012i
$893$	−0.891519	−	0.514719i	−0.0298335	−	0.0172244i
$894$		0			0
$895$			39.7862i			1.32991i
$896$	−2.44949	−	1.00000i	−0.0818317	−	0.0334077i
$897$		0			0
$898$	−5.12132	−	8.87039i	−0.170901	−	0.296009i
$899$	−3.48960	+	6.04416i	−0.116385	+	0.201584i
$900$		0			0
$901$	−1.09188	+	0.630399i	−0.0363759	+	0.0210016i
$902$	6.08767			0.202697
$903$		0			0
$904$	−8.48528			−0.282216
$905$	−7.34847	+	4.24264i	−0.244271	+	0.141030i
$906$		0			0
$907$	−13.8492	+	23.9876i	−0.459857	+	0.796495i	−0.998953	−	0.0457492i	$-0.985433\pi$
$907$	−13.8492	+	23.9876i	−0.459857	+	0.796495i	0.539096	+	0.842244i	$0.318766\pi$
$908$	7.79423	+	13.5000i	0.258661	+	0.448013i
$909$		0			0
$910$	−26.8492	+	3.67423i	−0.890044	+	0.121800i
$911$		−	18.7279i		−	0.620484i	−0.950658	−	0.310242i	$-0.899590\pi$
$911$		−	18.7279i		−	0.620484i	0.950658	−	0.310242i	$-0.100410\pi$
$912$		0			0
$913$	8.22792	+	4.75039i	0.272304	+	0.157215i
$914$	−19.9186	−	11.5000i	−0.658848	−	0.380386i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	5.19615	−	12.7279i	0.171592	−	0.420313i
$918$		0			0
$919$	−9.75736	−	16.9002i	−0.321866	−	0.557488i	0.659007	−	0.752136i	$-0.270977\pi$
$919$	−9.75736	−	16.9002i	−0.321866	−	0.557488i	−0.980873	+	0.194649i	$0.937643\pi$
$920$	8.87039	−	15.3640i	0.292448	−	0.506535i
$921$		0			0
$922$	19.7574	−	11.4069i	0.650674	−	0.375667i
$923$	25.0892			0.825823
$924$		0			0
$925$	102.912			3.38372
$926$	−18.5813	+	10.7279i	−0.610620	+	0.352541i
$927$		0			0
$928$	−0.621320	+	1.07616i	−0.0203958	+	0.0353266i
$929$	−1.64501	−	2.84924i	−0.0539711	−	0.0934806i	0.837778	−	0.546012i	$-0.183855\pi$
$929$	−1.64501	−	2.84924i	−0.0539711	−	0.0934806i	−0.891749	+	0.452531i	$0.850521\pi$
$930$		0			0
$931$	−1.90812	−	6.84116i	−0.0625360	−	0.224210i
$932$		−	6.72792i		−	0.220380i
$933$		0			0
$934$	−16.4558	−	9.50079i	−0.538452	−	0.310875i
$935$	−11.0227	−	6.36396i	−0.360481	−	0.208124i
$936$		0			0
$937$		−	4.00746i		−	0.130918i	−0.997855	−	0.0654590i	$-0.979149\pi$
$937$		−	4.00746i		−	0.130918i	0.997855	−	0.0654590i	$-0.0208512\pi$
$938$	20.9077	−	16.2132i	0.682661	−	0.529380i
$939$		0			0
$940$	−2.12132	−	3.67423i	−0.0691898	−	0.119840i
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	0.0331867	+	0.999449i	$0.489434\pi$
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	−0.882142	+	0.470984i	$0.843899\pi$
$942$		0			0
$943$	−7.45584	+	4.30463i	−0.242796	+	0.140178i
$944$	−11.5300			−0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	−0.787090	−	0.616838i	$-0.788414\pi$
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	0.140652	+	0.990059i	$0.455080\pi$
$948$		0			0
$949$	10.2426	−	17.7408i	0.332490	−	0.575890i
$950$	6.33386	+	10.9706i	0.205497	+	0.355932i
$951$		0			0
$952$	−0.363961	−	2.65962i	−0.0117960	−	0.0861989i
$953$		−	41.6985i		−	1.35075i	−0.737476	−	0.675373i	$-0.763983\pi$
$953$		−	41.6985i		−	1.35075i	0.737476	−	0.675373i	$-0.236017\pi$
$954$		0			0
$955$	−30.7279	−	17.7408i	−0.994332	−	0.574078i
$956$	11.0227	+	6.36396i	0.356500	+	0.205825i
$957$		0			0
$958$		−	36.4962i		−	1.17914i
$959$	5.19615	+	37.9706i	0.167793	+	1.22613i
$960$		0			0
$961$	0.272078	+	0.471253i	0.00877671	+	0.0152017i
$962$	10.0951	−	17.4853i	0.325480	−	0.563748i
$963$		0			0
$964$	14.7426	−	8.51167i	0.474828	−	0.274142i
$965$	−31.3000			−1.00758
$966$		0			0
$967$	22.2721			0.716222			0.358111	−	0.933679i	$-0.383421\pi$
$967$	22.2721			0.716222			0.358111	+	0.933679i	$0.383421\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$	7.86396	−	13.6208i	0.252497	−	0.437337i
$971$	25.6581	+	44.4411i	0.823407	+	1.42618i	0.903130	+	0.429367i	$0.141263\pi$
$971$	25.6581	+	44.4411i	0.823407	+	1.42618i	−0.0797229	+	0.996817i	$0.525404\pi$
$972$		0			0
$973$	42.2132	−	32.7349i	1.35329	−	1.04943i
$974$		−	28.2132i		−	0.904009i
$975$		0			0
$976$	−5.12132	−	2.95680i	−0.163929	−	0.0946447i
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.870622	−	0.491953i	$-0.163717\pi$
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.00926698	+	0.999957i	$0.497050\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$	7.28692	−	28.3492i	0.232772	−	0.905583i
$981$		0			0
$982$	9.98528	+	17.2950i	0.318643	+	0.551906i
$983$	4.05845	−	7.02944i	0.129444	−	0.224204i	−0.794017	−	0.607895i	$-0.792014\pi$
$983$	4.05845	−	7.02944i	0.129444	−	0.224204i	0.923461	+	0.383691i	$0.125347\pi$
$984$		0			0
$985$	34.4558	−	19.8931i	1.09785	−	0.633847i
$986$	−1.26080			−0.0401520
$987$		0			0
$988$	2.48528			0.0790673
$989$	30.2854	−	17.4853i	0.963020	−	0.556000i
$990$		0			0
$991$	−4.89340	+	8.47561i	−0.155444	+	0.269237i	−0.933221	−	0.359304i	$-0.883014\pi$
$991$	−4.89340	+	8.47561i	−0.155444	+	0.269237i	0.777777	+	0.628541i	$0.216347\pi$
$992$	2.80821	+	4.86396i	0.0891607	+	0.154431i
$993$		0			0
$994$	−10.2426	+	25.0892i	−0.324877	+	0.795782i
$995$			67.4558i			2.13849i
$996$		0			0
$997$	−8.27208	−	4.77589i	−0.261979	−	0.151254i	0.363258	−	0.931689i	$-0.381664\pi$
$997$	−8.27208	−	4.77589i	−0.261979	−	0.151254i	−0.625237	+	0.780435i	$0.714998\pi$
$998$	−31.1259	−	17.9706i	−0.985274	−	0.568848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.k.a.17.1	✓	8
3.2	odd	2	inner	126.2.k.a.17.4	yes	8
4.3	odd	2		1008.2.bt.c.17.1		8
5.2	odd	4		3150.2.bp.b.899.4		8
5.3	odd	4		3150.2.bp.e.899.1		8
5.4	even	2		3150.2.bf.a.1151.4		8
7.2	even	3		882.2.k.a.215.3		8
7.3	odd	6		882.2.d.a.881.1		8
7.4	even	3		882.2.d.a.881.4		8
7.5	odd	6	inner	126.2.k.a.89.4	yes	8
7.6	odd	2		882.2.k.a.521.2		8
9.2	odd	6		1134.2.t.e.1025.1		8
9.4	even	3		1134.2.l.f.269.1		8
9.5	odd	6		1134.2.l.f.269.4		8
9.7	even	3		1134.2.t.e.1025.4		8
12.11	even	2		1008.2.bt.c.17.4		8
15.2	even	4		3150.2.bp.e.899.4		8
15.8	even	4		3150.2.bp.b.899.1		8
15.14	odd	2		3150.2.bf.a.1151.2		8
21.2	odd	6		882.2.k.a.215.2		8
21.5	even	6	inner	126.2.k.a.89.1	yes	8
21.11	odd	6		882.2.d.a.881.5		8
21.17	even	6		882.2.d.a.881.8		8
21.20	even	2		882.2.k.a.521.3		8
28.3	even	6		7056.2.k.f.881.2		8
28.11	odd	6		7056.2.k.f.881.8		8
28.19	even	6		1008.2.bt.c.593.4		8
35.12	even	12		3150.2.bp.b.1349.1		8
35.19	odd	6		3150.2.bf.a.1601.2		8
35.33	even	12		3150.2.bp.e.1349.4		8
63.5	even	6		1134.2.t.e.593.4		8
63.40	odd	6		1134.2.t.e.593.1		8
63.47	even	6		1134.2.l.f.215.3		8
63.61	odd	6		1134.2.l.f.215.2		8
84.11	even	6		7056.2.k.f.881.1		8
84.47	odd	6		1008.2.bt.c.593.1		8
84.59	odd	6		7056.2.k.f.881.7		8
105.47	odd	12		3150.2.bp.e.1349.1		8
105.68	odd	12		3150.2.bp.b.1349.4		8
105.89	even	6		3150.2.bf.a.1601.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	1.1	even	1	trivial
126.2.k.a.17.4	yes	8	3.2	odd	2	inner
126.2.k.a.89.1	yes	8	21.5	even	6	inner
126.2.k.a.89.4	yes	8	7.5	odd	6	inner
882.2.d.a.881.1		8	7.3	odd	6
882.2.d.a.881.4		8	7.4	even	3
882.2.d.a.881.5		8	21.11	odd	6
882.2.d.a.881.8		8	21.17	even	6
882.2.k.a.215.2		8	21.2	odd	6
882.2.k.a.215.3		8	7.2	even	3
882.2.k.a.521.2		8	7.6	odd	2
882.2.k.a.521.3		8	21.20	even	2
1008.2.bt.c.17.1		8	4.3	odd	2
1008.2.bt.c.17.4		8	12.11	even	2
1008.2.bt.c.593.1		8	84.47	odd	6
1008.2.bt.c.593.4		8	28.19	even	6
1134.2.l.f.215.2		8	63.61	odd	6
1134.2.l.f.215.3		8	63.47	even	6
1134.2.l.f.269.1		8	9.4	even	3
1134.2.l.f.269.4		8	9.5	odd	6
1134.2.t.e.593.1		8	63.40	odd	6
1134.2.t.e.593.4		8	63.5	even	6
1134.2.t.e.1025.1		8	9.2	odd	6
1134.2.t.e.1025.4		8	9.7	even	3
3150.2.bf.a.1151.2		8	15.14	odd	2
3150.2.bf.a.1151.4		8	5.4	even	2
3150.2.bf.a.1601.2		8	35.19	odd	6
3150.2.bf.a.1601.4		8	105.89	even	6
3150.2.bp.b.899.1		8	15.8	even	4
3150.2.bp.b.899.4		8	5.2	odd	4
3150.2.bp.b.1349.1		8	35.12	even	12
3150.2.bp.b.1349.4		8	105.68	odd	12
3150.2.bp.e.899.1		8	5.3	odd	4
3150.2.bp.e.899.4		8	15.2	even	4
3150.2.bp.e.1349.1		8	105.47	odd	12
3150.2.bp.e.1349.4		8	35.33	even	12
7056.2.k.f.881.1		8	84.11	even	6
7056.2.k.f.881.2		8	28.3	even	6
7056.2.k.f.881.7		8	84.59	odd	6
7056.2.k.f.881.8		8	28.11	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 3.62132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 3.62132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +(3.62132 + 2.09077i) q^{10} +(2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.507306 - 0.878680i) q^{17} +(-0.878680 + 0.507306i) q^{19} -4.18154 q^{20} -3.00000 q^{22} +(3.67423 - 2.12132i) q^{23} +(-6.24264 + 10.8126i) q^{25} +(1.22474 + 2.12132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +1.24264i q^{29} +(4.86396 + 2.80821i) q^{31} +(0.866025 + 0.500000i) q^{32} +1.01461i q^{34} +(-4.18154 + 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} +(0.507306 - 0.878680i) q^{38} +(3.62132 - 2.09077i) q^{40} -2.02922 q^{41} +8.24264 q^{43} +(2.59808 - 1.50000i) q^{44} +(-2.12132 + 3.67423i) q^{46} +(0.507306 + 0.878680i) q^{47} +(-1.74264 + 6.77962i) q^{49} -12.4853i q^{50} +(-2.12132 - 1.22474i) q^{52} +(-1.07616 - 0.621320i) q^{53} -12.5446i q^{55} +(2.09077 - 1.62132i) q^{56} +(-0.621320 - 1.07616i) q^{58} +(5.76500 - 9.98528i) q^{59} +(5.12132 - 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-8.87039 + 5.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} +(-0.507306 - 0.878680i) q^{68} +(-1.50000 - 10.9612i) q^{70} +10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(7.13834 + 4.12132i) q^{74} +1.01461i q^{76} +(-1.07616 - 7.86396i) q^{77} +(5.62132 + 9.73641i) q^{79} +(-2.09077 + 3.62132i) q^{80} +(1.75736 - 1.01461i) q^{82} +3.16693 q^{83} -4.24264 q^{85} +(-7.13834 + 4.12132i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-5.12132 + 3.97141i) q^{91} -4.24264i q^{92} +(-0.878680 - 0.507306i) q^{94} +(3.67423 + 2.12132i) q^{95} -3.76127i q^{97} +(-1.88064 - 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^7	\( 8 q + 4 q^{4} + 4 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} - 24 q^{22} - 16 q^{25} - 4 q^{28} - 12 q^{31} - 16 q^{37} + 12 q^{40} + 32 q^{43} + 20 q^{49} + 12 q^{58} + 24 q^{61} - 8 q^{64} + 40 q^{67} - 12 q^{70} + 24 q^{73} + 28 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 - 24 * q^22 - 16 * q^25 - 4 * q^28 - 12 * q^31 - 16 * q^37 + 12 * q^40 + 32 * q^43 + 20 * q^49 + 12 * q^58 + 24 * q^61 - 8 * q^64 + 40 * q^67 - 12 * q^70 + 24 * q^73 + 28 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more