LMFDB - Embedded newform 1170.2.bj.c.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.6
Root			$1.40719 + 0.536449i$ of defining polynomial
Character	$\chi$	$=$	1170.199
Dual form			1170.2.bj.c.829.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(-0.213026 + 2.22590i) q^{10} +(0.515171 + 0.297434i) q^{11} +(1.10975 + 3.43052i) q^{13} +2.80495 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.98222 - 2.87649i) q^{17} +(-6.59574 + 3.80805i) q^{19} +(-1.82117 - 1.29743i) q^{20} +(-0.515171 + 0.297434i) q^{22} +(4.02317 + 2.32278i) q^{23} +(3.27591 - 3.77735i) q^{25} +(-3.52579 - 0.754186i) q^{26} +(-1.40247 + 2.42916i) q^{28} +(1.26235 - 2.18645i) q^{29} -6.59309i q^{31} +(-0.500000 - 0.866025i) q^{32} +5.75297i q^{34} +(-5.10829 - 3.63924i) q^{35} +(5.18679 - 8.98379i) q^{37} -7.61611i q^{38} +(2.03420 - 0.928463i) q^{40} +(4.98222 + 2.87649i) q^{41} +(3.67593 - 2.12230i) q^{43} -0.594869i q^{44} +(-4.02317 + 2.32278i) q^{46} +2.89798 q^{47} +(-0.433868 + 0.751482i) q^{49} +(1.63333 + 4.72570i) q^{50} +(2.41604 - 2.67633i) q^{52} -13.8960i q^{53} +(1.32412 + 0.126722i) q^{55} +(-1.40247 - 2.42916i) q^{56} +(1.26235 + 2.18645i) q^{58} +(-8.40299 + 4.85147i) q^{59} +(-3.41309 - 5.91165i) q^{61} +(5.70978 + 3.29654i) q^{62} +1.00000 q^{64} +(5.44256 + 5.94798i) q^{65} +(3.93121 - 6.80906i) q^{67} +(-4.98222 - 2.87649i) q^{68} +(5.70582 - 2.60429i) q^{70} +(1.11257 - 0.642342i) q^{71} -14.5400 q^{73} +(5.18679 + 8.98379i) q^{74} +(6.59574 + 3.80805i) q^{76} -1.66858i q^{77} -1.83150 q^{79} +(-0.213026 + 2.22590i) q^{80} +(-4.98222 + 2.87649i) q^{82} +4.19184 q^{83} +(7.46410 - 10.4771i) q^{85} +4.24460i q^{86} +(0.515171 + 0.297434i) q^{88} +(5.24333 + 3.02724i) q^{89} +(6.77687 - 7.50697i) q^{91} -4.64555i q^{92} +(-1.44899 + 2.50973i) q^{94} +(-9.88140 + 13.8702i) q^{95} +(8.45318 + 14.6413i) q^{97} +(-0.433868 - 0.751482i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.03420	−	0.928463i	0.909720	−	0.415221i
$5$	2.03420	−	0.928463i	0.909720	−	0.415221i
$6$		0			0
$7$	−1.40247	−	2.42916i	−0.530085	−	0.918135i	−0.999384	−	0.0350954i	$-0.988827\pi$
$7$	−1.40247	−	2.42916i	−0.530085	−	0.918135i	0.469299	−	0.883040i	$-0.344507\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.213026	+	2.22590i	−0.0673646	+	0.703891i
$11$	0.515171	+	0.297434i	0.155330	+	0.0896798i	0.575650	−	0.817696i	$-0.304749\pi$
$11$	0.515171	+	0.297434i	0.155330	+	0.0896798i	−0.420320	+	0.907376i	$0.638082\pi$
$12$		0			0
$13$	1.10975	+	3.43052i	0.307790	+	0.951454i
$13$	1.10975	+	3.43052i	0.307790	+	0.951454i
$14$	2.80495			0.749654
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.98222	−	2.87649i	1.20837	−	0.697650i	0.245963	−	0.969279i	$-0.420896\pi$
$17$	4.98222	−	2.87649i	1.20837	−	0.697650i	0.962402	+	0.271629i	$0.0875623\pi$
$18$		0			0
$19$	−6.59574	+	3.80805i	−1.51317	+	0.873628i	−0.513286	+	0.858218i	$0.671572\pi$
$19$	−6.59574	+	3.80805i	−1.51317	+	0.873628i	−0.999881	+	0.0154099i	$0.995095\pi$
$20$	−1.82117	−	1.29743i	−0.407226	−	0.290115i
$21$		0			0
$22$	−0.515171	+	0.297434i	−0.109835	+	0.0634132i
$23$	4.02317	+	2.32278i	0.838888	+	0.484332i	0.856886	−	0.515506i	$-0.172396\pi$
$23$	4.02317	+	2.32278i	0.838888	+	0.484332i	−0.0179978	+	0.999838i	$0.505729\pi$
$24$		0			0
$25$	3.27591	−	3.77735i	0.655182	−	0.755471i
$26$	−3.52579	−	0.754186i	−0.691465	−	0.147908i
$27$		0			0
$28$	−1.40247	+	2.42916i	−0.265043	+	0.459067i
$29$	1.26235	−	2.18645i	0.234412	−	0.406013i	−0.724690	−	0.689075i	$-0.758017\pi$
$29$	1.26235	−	2.18645i	0.234412	−	0.406013i	0.959102	+	0.283062i	$0.0913502\pi$
$30$		0			0
$31$		−	6.59309i		−	1.18415i	−0.805882	−	0.592077i	$-0.798308\pi$
$31$		−	6.59309i		−	1.18415i	0.805882	−	0.592077i	$-0.201692\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$			5.75297i			0.986626i
$35$	−5.10829	−	3.63924i	−0.863459	−	0.615143i
$36$		0			0
$37$	5.18679	−	8.98379i	0.852703	−	1.47693i	−0.0260561	−	0.999660i	$-0.508295\pi$
$37$	5.18679	−	8.98379i	0.852703	−	1.47693i	0.878759	−	0.477265i	$-0.158372\pi$
$38$		−	7.61611i		−	1.23550i
$39$		0			0
$40$	2.03420	−	0.928463i	0.321635	−	0.146803i
$41$	4.98222	+	2.87649i	0.778092	+	0.449232i	0.835754	−	0.549105i	$-0.185031\pi$
$41$	4.98222	+	2.87649i	0.778092	+	0.449232i	−0.0576618	+	0.998336i	$0.518364\pi$
$42$		0			0
$43$	3.67593	−	2.12230i	0.560574	−	0.323648i	−0.192802	−	0.981238i	$-0.561757\pi$
$43$	3.67593	−	2.12230i	0.560574	−	0.323648i	0.753376	+	0.657590i	$0.228424\pi$
$44$		−	0.594869i		−	0.0896798i
$45$		0			0
$46$	−4.02317	+	2.32278i	−0.593184	+	0.342475i
$47$	2.89798			0.422715			0.211357	−	0.977409i	$-0.432212\pi$
$47$	2.89798			0.422715			0.211357	+	0.977409i	$0.432212\pi$
$48$		0			0
$49$	−0.433868	+	0.751482i	−0.0619812	+	0.107355i
$50$	1.63333	+	4.72570i	0.230987	+	0.668315i
$51$		0			0
$52$	2.41604	−	2.67633i	0.335044	−	0.371140i
$53$		−	13.8960i		−	1.90876i	−0.298598	−	0.954379i	$-0.596519\pi$
$53$		−	13.8960i		−	1.90876i	0.298598	−	0.954379i	$-0.403481\pi$
$54$		0			0
$55$	1.32412	+	0.126722i	0.178544	+	0.0170872i
$56$	−1.40247	−	2.42916i	−0.187414	−	0.324610i
$57$		0			0
$58$	1.26235	+	2.18645i	0.165754	+	0.287095i
$59$	−8.40299	+	4.85147i	−1.09398	+	0.631607i	−0.934632	−	0.355616i	$-0.884271\pi$
$59$	−8.40299	+	4.85147i	−1.09398	+	0.631607i	−0.159344	+	0.987223i	$0.550938\pi$
$60$		0			0
$61$	−3.41309	−	5.91165i	−0.437002	−	0.756910i	0.560455	−	0.828185i	$-0.310626\pi$
$61$	−3.41309	−	5.91165i	−0.437002	−	0.756910i	−0.997457	+	0.0712755i	$0.977293\pi$
$62$	5.70978	+	3.29654i	0.725143	+	0.418661i
$63$		0			0
$64$	1.00000			0.125000
$65$	5.44256	+	5.94798i	0.675067	+	0.737757i
$66$		0			0
$67$	3.93121	−	6.80906i	0.480274	−	0.831859i	−0.519470	−	0.854489i	$-0.673871\pi$
$67$	3.93121	−	6.80906i	0.480274	−	0.831859i	0.999744	+	0.0226299i	$0.00720394\pi$
$68$	−4.98222	−	2.87649i	−0.604183	−	0.348825i
$69$		0			0
$70$	5.70582	−	2.60429i	0.681976	−	0.311272i
$71$	1.11257	−	0.642342i	0.132038	−	0.0762320i	−0.432526	−	0.901621i	$-0.642378\pi$
$71$	1.11257	−	0.642342i	0.132038	−	0.0762320i	0.564564	+	0.825389i	$0.309044\pi$
$72$		0			0
$73$	−14.5400			−1.70178			−0.850892	−	0.525341i	$-0.823938\pi$
$73$	−14.5400			−1.70178			−0.850892	+	0.525341i	$0.823938\pi$
$74$	5.18679	+	8.98379i	0.602952	+	1.04434i
$75$		0			0
$76$	6.59574	+	3.80805i	0.756584	+	0.436814i
$77$		−	1.66858i		−	0.190152i
$78$		0			0
$79$	−1.83150			−0.206060			−0.103030	−	0.994678i	$-0.532854\pi$
$79$	−1.83150			−0.206060			−0.103030	+	0.994678i	$0.532854\pi$
$80$	−0.213026	+	2.22590i	−0.0238170	+	0.248863i
$81$		0			0
$82$	−4.98222	+	2.87649i	−0.550194	+	0.317655i
$83$	4.19184			0.460114			0.230057	−	0.973177i	$-0.426109\pi$
$83$	4.19184			0.460114			0.230057	+	0.973177i	$0.426109\pi$
$84$		0			0
$85$	7.46410	−	10.4771i	0.809595	−	1.13641i
$86$			4.24460i			0.457707i
$87$		0			0
$88$	0.515171	+	0.297434i	0.0549175	+	0.0317066i
$89$	5.24333	+	3.02724i	0.555792	+	0.320886i	0.751455	−	0.659785i	$-0.229353\pi$
$89$	5.24333	+	3.02724i	0.555792	+	0.320886i	−0.195663	+	0.980671i	$0.562686\pi$
$90$		0			0
$91$	6.77687	−	7.50697i	0.710409	−	0.786945i
$92$		−	4.64555i		−	0.484332i
$93$		0			0
$94$	−1.44899	+	2.50973i	−0.149452	+	0.258859i
$95$	−9.88140	+	13.8702i	−1.01381	+	1.42306i
$96$		0			0
$97$	8.45318	+	14.6413i	0.858291	+	1.48660i	0.873558	+	0.486719i	$0.161807\pi$
$97$	8.45318	+	14.6413i	0.858291	+	1.48660i	−0.0152677	+	0.999883i	$0.504860\pi$
$98$	−0.433868	−	0.751482i	−0.0438273	−	0.0759111i
$99$		0			0
$100$	−4.90924	−	0.948346i	−0.490924	−	0.0948346i
$101$	−2.72360	+	4.71741i	−0.271008	+	0.469400i	−0.969120	−	0.246589i	$-0.920690\pi$
$101$	−2.72360	+	4.71741i	−0.271008	+	0.469400i	0.698112	+	0.715988i	$0.254024\pi$
$102$		0			0
$103$			13.7529i			1.35511i	0.735471	+	0.677556i	$0.236961\pi$
$103$			13.7529i			1.35511i	−0.735471	+	0.677556i	$0.763039\pi$
$104$	1.10975	+	3.43052i	0.108820	+	0.336390i
$105$		0			0
$106$	12.0343	+	6.94798i	1.16887	+	0.674848i
$107$	3.66407	+	2.11545i	0.354219	+	0.204509i	0.666542	−	0.745468i	$-0.267774\pi$
$107$	3.66407	+	2.11545i	0.354219	+	0.204509i	−0.312323	+	0.949976i	$0.601107\pi$
$108$		0			0
$109$		−	0.447358i		−	0.0428491i	−0.999770	−	0.0214246i	$-0.993180\pi$
$109$		−	0.447358i		−	0.0428491i	0.999770	−	0.0214246i	$-0.00682017\pi$
$110$	−0.771803	+	1.08336i	−0.0735885	+	0.103294i
$111$		0			0
$112$	2.80495			0.265043
$113$	8.11206	−	4.68350i	0.763119	−	0.440587i	−0.0672956	−	0.997733i	$-0.521437\pi$
$113$	8.11206	−	4.68350i	0.763119	−	0.440587i	0.830414	+	0.557146i	$0.188104\pi$
$114$		0			0
$115$	10.3405	+	0.989622i	0.964259	+	0.0922827i
$116$	−2.52469			−0.234412
$117$		0			0
$118$		−	9.70293i		−	0.893227i
$119$	−13.9749	−	8.06839i	−1.28107	−	0.739628i
$120$		0			0
$121$	−5.32307	−	9.21982i	−0.483915	−	0.838165i
$122$	6.82619			0.618014
$123$		0			0
$124$	−5.70978	+	3.29654i	−0.512753	+	0.296038i
$125$	3.15672	−	10.7254i	0.282345	−	0.959313i
$126$		0			0
$127$	5.79190	+	3.34395i	0.513948	+	0.296728i	0.734455	−	0.678658i	$-0.237438\pi$
$127$	5.79190	+	3.34395i	0.513948	+	0.296728i	−0.220507	+	0.975385i	$0.570771\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.87239	+	1.73941i	−0.690454	+	0.152556i
$131$	11.6724			1.01982			0.509911	−	0.860227i	$-0.329678\pi$
$131$	11.6724			1.01982			0.509911	+	0.860227i	$0.329678\pi$
$132$		0			0
$133$	18.5007	+	10.6814i	1.60422	+	0.926194i
$134$	3.93121	+	6.80906i	0.339605	+	0.588213i
$135$		0			0
$136$	4.98222	−	2.87649i	0.427222	−	0.246657i
$137$	3.40142	+	5.89144i	0.290603	+	0.503339i	0.973953	−	0.226752i	$-0.0728107\pi$
$137$	3.40142	+	5.89144i	0.290603	+	0.503339i	−0.683349	+	0.730092i	$0.739477\pi$
$138$		0			0
$139$	−3.54908	−	6.14719i	−0.301029	−	0.521397i	0.675340	−	0.737506i	$-0.263997\pi$
$139$	−3.54908	−	6.14719i	−0.301029	−	0.521397i	−0.976369	+	0.216109i	$0.930663\pi$
$140$	−0.597526	+	6.24353i	−0.0505001	+	0.527674i
$141$		0			0
$142$			1.28468i			0.107808i
$143$	−0.448642	+	2.09738i	−0.0375173	+	0.175392i
$144$		0			0
$145$	0.537824	−	5.61971i	0.0446639	−	0.466691i
$146$	7.27002	−	12.5920i	0.601671	−	1.04213i
$147$		0			0
$148$	−10.3736			−0.852703
$149$	3.02342	−	1.74557i	0.247688	−	0.143003i	−0.371017	−	0.928626i	$-0.620991\pi$
$149$	3.02342	−	1.74557i	0.247688	−	0.143003i	0.618705	+	0.785623i	$0.287658\pi$
$150$		0			0
$151$			4.54988i			0.370264i	0.982714	+	0.185132i	$0.0592713\pi$
$151$			4.54988i			0.370264i	−0.982714	+	0.185132i	$0.940729\pi$
$152$	−6.59574	+	3.80805i	−0.534985	+	0.308874i
$153$		0			0
$154$	1.44503	+	0.834288i	0.116444	+	0.0672288i
$155$	−6.12144	−	13.4116i	−0.491686	−	1.07725i
$156$		0			0
$157$			11.4957i			0.917460i	0.888576	+	0.458730i	$0.151695\pi$
$157$			11.4957i			0.917460i	−0.888576	+	0.458730i	$0.848305\pi$
$158$	0.915751	−	1.58613i	0.0728532	−	0.126186i
$159$		0			0
$160$	−1.82117	−	1.29743i	−0.143976	−	0.102571i
$161$		−	13.0305i		−	1.02695i
$162$		0			0
$163$	−6.91443	−	11.9762i	−0.541580	−	0.938045i	−0.998814	−	0.0486977i	$-0.984493\pi$
$163$	−6.91443	−	11.9762i	−0.541580	−	0.938045i	0.457233	−	0.889347i	$-0.348840\pi$
$164$		−	5.75297i		−	0.449232i
$165$		0			0
$166$	−2.09592	+	3.63024i	−0.162675	+	0.281761i
$167$	−10.7700	+	18.6542i	−0.833409	+	1.44351i	0.0619099	+	0.998082i	$0.480281\pi$
$167$	−10.7700	+	18.6542i	−0.833409	+	1.44351i	−0.895319	+	0.445425i	$0.853052\pi$
$168$		0			0
$169$	−10.5369	+	7.61404i	−0.810531	+	0.585696i
$170$	5.34142	+	11.7027i	0.409668	+	0.897554i
$171$		0			0
$172$	−3.67593	−	2.12230i	−0.280287	−	0.161824i
$173$	−11.8342	+	6.83251i	−0.899741	+	0.519466i	−0.877116	−	0.480278i	$-0.840536\pi$
$173$	−11.8342	+	6.83251i	−0.899741	+	0.519466i	−0.0226249	+	0.999744i	$0.507202\pi$
$174$		0			0
$175$	−13.7702	−	2.66006i	−1.04093	−	0.201082i
$176$	−0.515171	+	0.297434i	−0.0388325	+	0.0224200i
$177$		0			0
$178$	−5.24333	+	3.02724i	−0.393004	+	0.226901i
$179$	−5.37886	+	9.31647i	−0.402035	+	0.696345i	−0.993971	−	0.109639i	$-0.965030\pi$
$179$	−5.37886	+	9.31647i	−0.402035	+	0.696345i	0.591936	+	0.805985i	$0.298364\pi$
$180$		0			0
$181$	5.86469			0.435919			0.217959	−	0.975958i	$-0.430060\pi$
$181$	5.86469			0.435919			0.217959	+	0.975958i	$0.430060\pi$
$182$	3.11280	+	9.62243i	0.230736	+	0.713262i
$183$		0			0
$184$	4.02317	+	2.32278i	0.296592	+	0.171237i
$185$	2.20984	−	23.0905i	0.162471	−	1.69765i
$186$		0			0
$187$	3.42226			0.250261
$188$	−1.44899	−	2.50973i	−0.105679	−	0.183041i
$189$		0			0
$190$	−7.07128	−	15.4927i	−0.513004	−	1.12396i
$191$	−6.91728	−	11.9811i	−0.500517	−	0.866921i	−1.00000		0.000597179i	$-0.999810\pi$
$191$	−6.91728	−	11.9811i	−0.500517	−	0.866921i	0.499483	−	0.866324i	$-0.333523\pi$
$192$		0			0
$193$	−8.50322	+	14.7280i	−0.612075	+	1.06014i	0.378815	+	0.925472i	$0.376332\pi$
$193$	−8.50322	+	14.7280i	−0.612075	+	1.06014i	−0.990890	+	0.134673i	$0.957002\pi$
$194$	−16.9064			−1.21381
$195$		0			0
$196$	0.867736			0.0619812
$197$	3.16487	−	5.48171i	0.225487	−	0.390556i	−0.730978	−	0.682401i	$-0.760936\pi$
$197$	3.16487	−	5.48171i	0.225487	−	0.390556i	0.956466	+	0.291845i	$0.0942692\pi$
$198$		0			0
$199$	8.31782	+	14.4069i	0.589634	+	1.02128i	0.994280	+	0.106803i	$0.0340615\pi$
$199$	8.31782	+	14.4069i	0.589634	+	1.02128i	−0.404646	+	0.914473i	$0.632605\pi$
$200$	3.27591	−	3.77735i	0.231642	−	0.267099i
$201$		0			0
$202$	−2.72360	−	4.71741i	−0.191632	−	0.331916i
$203$	−7.08163			−0.497033
$204$		0			0
$205$	12.8055	+	1.22553i	0.894377	+	0.0855947i
$206$	−11.9104	−	6.87645i	−0.829834	−	0.479105i
$207$		0			0
$208$	−3.52579	−	0.754186i	−0.244470	−	0.0522934i
$209$	−4.53058			−0.313387
$210$		0			0
$211$	−8.27443	+	14.3317i	−0.569635	+	0.986637i	0.426967	+	0.904267i	$0.359582\pi$
$211$	−8.27443	+	14.3317i	−0.569635	+	0.986637i	−0.996602	+	0.0823697i	$0.973751\pi$
$212$	−12.0343	+	6.94798i	−0.826516	+	0.477190i
$213$		0			0
$214$	−3.66407	+	2.11545i	−0.250471	+	0.144609i
$215$	5.50709	−	7.73014i	0.375580	−	0.527191i
$216$		0			0
$217$	−16.0156	+	9.24663i	−1.08721	+	0.627702i
$218$	0.387423	+	0.223679i	0.0262396	+	0.0151495i
$219$		0			0
$220$	−0.552314	−	1.21008i	−0.0372370	−	0.0815836i
$221$	15.3969	+	13.8994i	1.03570	+	0.934975i
$222$		0			0
$223$	8.32779	−	14.4242i	0.557670	−	0.965913i	−0.440020	−	0.897988i	$-0.645029\pi$
$223$	8.32779	−	14.4242i	0.557670	−	0.965913i	0.997690	−	0.0679254i	$-0.0216380\pi$
$224$	−1.40247	+	2.42916i	−0.0937068	+	0.162305i
$225$		0			0
$226$			9.36701i			0.623084i
$227$	−1.51105	−	2.61722i	−0.100292	−	0.173711i	0.811513	−	0.584334i	$-0.198644\pi$
$227$	−1.51105	−	2.61722i	−0.100292	−	0.173711i	−0.911805	+	0.410624i	$0.865311\pi$
$228$		0			0
$229$			16.4472i			1.08686i	0.839453	+	0.543432i	$0.182875\pi$
$229$			16.4472i			1.08686i	−0.839453	+	0.543432i	$0.817125\pi$
$230$	−6.02730	+	8.46035i	−0.397428	+	0.557859i
$231$		0			0
$232$	1.26235	−	2.18645i	0.0828771	−	0.143547i
$233$			13.8289i			0.905959i	0.891521	+	0.452980i	$0.149639\pi$
$233$			13.8289i			0.905959i	−0.891521	+	0.452980i	$0.850361\pi$
$234$		0			0
$235$	5.89507	−	2.69067i	0.384552	−	0.175520i
$236$	8.40299	+	4.85147i	0.546988	+	0.315804i
$237$		0			0
$238$	13.9749	−	8.06839i	0.905856	−	0.522996i
$239$		−	4.60216i		−	0.297689i	−0.988861	−	0.148845i	$-0.952445\pi$
$239$		−	4.60216i		−	0.297689i	0.988861	−	0.148845i	$-0.0475554\pi$
$240$		0			0
$241$	5.38108	−	3.10677i	0.346626	−	0.200125i	−0.316572	−	0.948568i	$-0.602532\pi$
$241$	5.38108	−	3.10677i	0.346626	−	0.200125i	0.663198	+	0.748444i	$0.269199\pi$
$242$	10.6461			0.684359
$243$		0			0
$244$	−3.41309	+	5.91165i	−0.218501	+	0.378455i
$245$	−0.184850	+	1.93149i	−0.0118096	+	0.123399i
$246$		0			0
$247$	−20.3832	−	18.4008i	−1.29695	−	1.17082i
$248$		−	6.59309i		−	0.418661i
$249$		0			0
$250$	7.71015	+	8.09652i	0.487633	+	0.512069i
$251$	−8.19386	−	14.1922i	−0.517192	−	0.895802i	−0.999801	−	0.0199663i	$-0.993644\pi$
$251$	−8.19386	−	14.1922i	−0.517192	−	0.895802i	0.482609	−	0.875836i	$-0.339689\pi$
$252$		0			0
$253$	1.38175	+	2.39326i	0.0868697	+	0.150463i
$254$	−5.79190	+	3.34395i	−0.363416	+	0.209818i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.28269	+	4.20466i	0.454282	+	0.262280i	0.709637	−	0.704568i	$-0.248859\pi$
$257$	7.28269	+	4.20466i	0.454282	+	0.262280i	−0.255355	+	0.966847i	$0.582192\pi$
$258$		0			0
$259$	−29.0974			−1.80802
$260$	2.42982	−	7.68739i	0.150691	−	0.476752i
$261$		0			0
$262$	−5.83620	+	10.1086i	−0.360562	+	0.624511i
$263$	−5.10152	−	2.94536i	−0.314573	−	0.181619i	0.334398	−	0.942432i	$-0.391467\pi$
$263$	−5.10152	−	2.94536i	−0.314573	−	0.181619i	−0.648971	+	0.760813i	$0.724800\pi$
$264$		0			0
$265$	−12.9019	−	28.2671i	−0.792557	−	1.73644i
$266$	−18.5007	+	10.6814i	−1.13435	+	0.654918i
$267$		0			0
$268$	−7.86242			−0.480274
$269$	−11.4228	−	19.7848i	−0.696459	−	1.20630i	−0.969686	−	0.244352i	$-0.921425\pi$
$269$	−11.4228	−	19.7848i	−0.696459	−	1.20630i	0.273228	−	0.961949i	$-0.411909\pi$
$270$		0			0
$271$	−23.2565	−	13.4271i	−1.41273	−	0.815639i	−0.417084	−	0.908868i	$-0.636948\pi$
$271$	−23.2565	−	13.4271i	−1.41273	−	0.815639i	−0.995645	+	0.0932285i	$0.970281\pi$
$272$			5.75297i			0.348825i
$273$		0			0
$274$	−6.80285			−0.410975
$275$	2.81117	−	0.971616i	0.169520	−	0.0585906i
$276$		0			0
$277$	9.20150	−	5.31249i	0.552865	−	0.319197i	−0.197412	−	0.980321i	$-0.563254\pi$
$277$	9.20150	−	5.31249i	0.552865	−	0.319197i	0.750277	+	0.661124i	$0.229920\pi$
$278$	7.09816			0.425719
$279$		0			0
$280$	−5.10829	−	3.63924i	−0.305279	−	0.217486i
$281$			28.3732i			1.69260i	0.532705	+	0.846301i	$0.321176\pi$
$281$			28.3732i			1.69260i	−0.532705	+	0.846301i	$0.678824\pi$
$282$		0			0
$283$	−4.91005	−	2.83482i	−0.291872	−	0.168512i	0.346914	−	0.937897i	$-0.387230\pi$
$283$	−4.91005	−	2.83482i	−0.291872	−	0.168512i	−0.638786	+	0.769385i	$0.720563\pi$
$284$	−1.11257	−	0.642342i	−0.0660188	−	0.0381160i
$285$		0			0
$286$	−1.59207	−	1.43723i	−0.0941408	−	0.0849850i
$287$		−	16.1368i		−	0.952524i
$288$		0			0
$289$	8.04834	−	13.9401i	0.473431	−	0.820007i
$290$	4.59790	+	3.27562i	0.269998	+	0.192351i
$291$		0			0
$292$	7.27002	+	12.5920i	0.425446	+	0.736894i
$293$	0.829176	+	1.43617i	0.0484410	+	0.0839022i	0.889229	−	0.457462i	$-0.151241\pi$
$293$	0.829176	+	1.43617i	0.0484410	+	0.0839022i	−0.840788	+	0.541364i	$0.817908\pi$
$294$		0			0
$295$	−12.5889	+	17.6707i	−0.732955	+	1.02883i
$296$	5.18679	−	8.98379i	0.301476	−	0.522172i
$297$		0			0
$298$			3.49115i			0.202237i
$299$	−3.50361	+	16.3793i	−0.202619	+	0.947237i
$300$		0			0
$301$	−10.3108	−	5.95294i	−0.594304	−	0.343122i
$302$	−3.94031	−	2.27494i	−0.226740	−	0.130908i
$303$		0			0
$304$		−	7.61611i		−	0.436814i
$305$	−12.4317	−	8.85653i	−0.711835	−	0.507123i
$306$		0			0
$307$	0.384087			0.0219210			0.0109605	−	0.999940i	$-0.496511\pi$
$307$	0.384087			0.0219210			0.0109605	+	0.999940i	$0.496511\pi$
$308$	−1.44503	+	0.834288i	−0.0823382	+	0.0475380i
$309$		0			0
$310$	14.6755	+	1.40450i	0.833514	+	0.0797700i
$311$	11.6920			0.662993			0.331497	−	0.943456i	$-0.392446\pi$
$311$	11.6920			0.662993			0.331497	+	0.943456i	$0.392446\pi$
$312$		0			0
$313$			10.5788i			0.597948i	0.954261	+	0.298974i	$0.0966444\pi$
$313$			10.5788i			0.597948i	−0.954261	+	0.298974i	$0.903356\pi$
$314$	−9.95560	−	5.74787i	−0.561827	−	0.324371i
$315$		0			0
$316$	0.915751	+	1.58613i	0.0515150	+	0.0892266i
$317$	−22.1023			−1.24139			−0.620695	−	0.784052i	$-0.713150\pi$
$317$	−22.1023			−1.24139			−0.620695	+	0.784052i	$0.713150\pi$
$318$		0			0
$319$	1.30065	−	0.750930i	0.0728224	−	0.0420440i
$320$	2.03420	−	0.928463i	0.113715	−	0.0519027i
$321$		0			0
$322$	11.2848	+	6.51527i	0.628876	+	0.363082i
$323$	−21.9076	+	37.9451i	−1.21897	+	2.11132i
$324$		0			0
$325$	16.5937	+	7.04615i	0.920454	+	0.390850i
$326$	13.8289			0.765910
$327$		0			0
$328$	4.98222	+	2.87649i	0.275097	+	0.158827i
$329$	−4.06435	−	7.03966i	−0.224075	−	0.388109i
$330$		0			0
$331$	−5.28809	+	3.05308i	−0.290660	+	0.167812i	−0.638239	−	0.769838i	$-0.720337\pi$
$331$	−5.28809	+	3.05308i	−0.290660	+	0.167812i	0.347580	+	0.937650i	$0.387004\pi$
$332$	−2.09592	−	3.63024i	−0.115029	−	0.199235i
$333$		0			0
$334$	−10.7700	−	18.6542i	−0.589309	−	1.02071i
$335$	1.67490	−	17.5009i	0.0915094	−	0.956179i
$336$		0			0
$337$		−	4.29852i		−	0.234155i	−0.993123	−	0.117078i	$-0.962647\pi$
$337$		−	4.29852i		−	0.234155i	0.993123	−	0.117078i	$-0.0373526\pi$
$338$	−1.32550	−	12.9322i	−0.0720979	−	0.703422i
$339$		0			0
$340$	−12.8055	−	1.22553i	−0.694477	−	0.0664637i
$341$	1.96101	−	3.39657i	0.106195	−	0.183935i
$342$		0			0
$343$	−17.2007			−0.928750
$344$	3.67593	−	2.12230i	0.198193	−	0.114427i
$345$		0			0
$346$		−	13.6650i		−	0.734636i
$347$	29.7444	−	17.1730i	1.59677	−	0.921893i	0.604660	−	0.796484i	$-0.293309\pi$
$347$	29.7444	−	17.1730i	1.59677	−	0.921893i	0.992105	−	0.125409i	$-0.0400244\pi$
$348$		0			0
$349$	13.8581	+	8.00099i	0.741808	+	0.428283i	0.822726	−	0.568438i	$-0.192452\pi$
$349$	13.8581	+	8.00099i	0.741808	+	0.428283i	−0.0809181	+	0.996721i	$0.525785\pi$
$350$	9.18876	−	10.5953i	0.491160	−	0.566342i
$351$		0			0
$352$		−	0.594869i		−	0.0317066i
$353$	−9.69607	+	16.7941i	−0.516070	+	0.893859i	0.483756	+	0.875203i	$0.339272\pi$
$353$	−9.69607	+	16.7941i	−0.516070	+	0.893859i	−0.999826	+	0.0186563i	$0.994061\pi$
$354$		0			0
$355$	1.66679	−	2.33963i	0.0884642	−	0.124175i
$356$		−	6.05447i		−	0.320886i
$357$		0			0
$358$	−5.37886	−	9.31647i	−0.284282	−	0.492391i
$359$			15.8342i			0.835699i	0.908516	+	0.417850i	$0.137216\pi$
$359$			15.8342i			0.835699i	−0.908516	+	0.417850i	$0.862784\pi$
$360$		0			0
$361$	19.5026	−	33.7794i	1.02645	−	1.77786i
$362$	−2.93234	+	5.07897i	−0.154121	+	0.266945i
$363$		0			0
$364$	−9.88966	−	2.11545i	−0.518359	−	0.110880i
$365$	−29.5773	+	13.4999i	−1.54815	+	0.706617i
$366$		0			0
$367$	13.2440	+	7.64645i	0.691333	+	0.399141i	0.804111	−	0.594479i	$-0.202642\pi$
$367$	13.2440	+	7.64645i	0.691333	+	0.399141i	−0.112778	+	0.993620i	$0.535975\pi$
$368$	−4.02317	+	2.32278i	−0.209722	+	0.121083i
$369$		0			0
$370$	18.8921	+	13.4590i	0.982152	+	0.699702i
$371$	−33.7555	+	19.4887i	−1.75250	+	1.01180i
$372$		0			0
$373$	18.7508	−	10.8258i	0.970881	−	0.560538i	0.0713760	−	0.997449i	$-0.477261\pi$
$373$	18.7508	−	10.8258i	0.970881	−	0.560538i	0.899505	+	0.436911i	$0.143928\pi$
$374$	−1.71113	+	2.96377i	−0.0884805	+	0.153253i
$375$		0			0
$376$	2.89798			0.149452
$377$	8.90154	+	1.90409i	0.458453	+	0.0980655i
$378$		0			0
$379$	7.81479	+	4.51187i	0.401419	+	0.231759i	0.687096	−	0.726567i	$-0.258885\pi$
$379$	7.81479	+	4.51187i	0.401419	+	0.231759i	−0.285677	+	0.958326i	$0.592218\pi$
$380$	16.9527	+	1.62243i	0.869654	+	0.0832287i
$381$		0			0
$382$	13.8346			0.707838
$383$	5.03703	+	8.72439i	0.257380	+	0.445795i	0.965539	−	0.260257i	$-0.0838074\pi$
$383$	5.03703	+	8.72439i	0.257380	+	0.445795i	−0.708159	+	0.706053i	$0.750474\pi$
$384$		0			0
$385$	−1.54921	−	3.39421i	−0.0789551	−	0.172985i
$386$	−8.50322	−	14.7280i	−0.432802	−	0.749636i
$387$		0			0
$388$	8.45318	−	14.6413i	0.429145	−	0.743301i
$389$	24.3591			1.23505			0.617527	−	0.786550i	$-0.288135\pi$
$389$	24.3591			1.23505			0.617527	+	0.786550i	$0.288135\pi$
$390$		0			0
$391$	26.7257			1.35158
$392$	−0.433868	+	0.751482i	−0.0219137	+	0.0379556i
$393$		0			0
$394$	3.16487	+	5.48171i	0.159444	+	0.276165i
$395$	−3.72564	+	1.70048i	−0.187457	+	0.0855606i
$396$		0			0
$397$	−15.0190	−	26.0137i	−0.753784	−	1.30559i	−0.945977	−	0.324234i	$-0.894893\pi$
$397$	−15.0190	−	26.0137i	−0.753784	−	1.30559i	0.192193	−	0.981357i	$-0.438440\pi$
$398$	−16.6356			−0.833869
$399$		0			0
$400$	1.63333	+	4.72570i	0.0816664	+	0.236285i
$401$	−2.35786	−	1.36131i	−0.117746	−	0.0679807i	0.439970	−	0.898012i	$-0.354989\pi$
$401$	−2.35786	−	1.36131i	−0.117746	−	0.0679807i	−0.557716	+	0.830032i	$0.688322\pi$
$402$		0			0
$403$	22.6177	−	7.31669i	1.12667	−	0.364470i
$404$	5.44720			0.271008
$405$		0			0
$406$	3.54082	−	6.13287i	0.175728	−	0.304369i
$407$	5.34417	−	3.08546i	0.264901	−	0.152941i
$408$		0			0
$409$	−33.1032	+	19.1121i	−1.63685	+	0.945034i	−0.654938	+	0.755683i	$0.727305\pi$
$409$	−33.1032	+	19.1121i	−1.63685	+	0.945034i	−0.981909	+	0.189352i	$0.939361\pi$
$410$	−7.46410	+	10.4771i	−0.368626	+	0.517429i
$411$		0			0
$412$	11.9104	−	6.87645i	0.586781	−	0.338778i
$413$	23.5699	+	13.6081i	1.15980	+	0.669612i
$414$		0			0
$415$	8.52703	−	3.89197i	0.418575	−	0.191049i
$416$	2.41604	−	2.67633i	0.118456	−	0.131218i
$417$		0			0
$418$	2.26529	−	3.92360i	0.110799	−	0.191910i
$419$	−14.9365	+	25.8708i	−0.729695	+	1.26387i	0.227317	+	0.973821i	$0.427005\pi$
$419$	−14.9365	+	25.8708i	−0.729695	+	1.26387i	−0.957012	+	0.290048i	$0.906329\pi$
$420$		0			0
$421$			14.2033i			0.692226i	0.938193	+	0.346113i	$0.112499\pi$
$421$			14.2033i			0.692226i	−0.938193	+	0.346113i	$0.887501\pi$
$422$	−8.27443	−	14.3317i	−0.402793	−	0.697658i
$423$		0			0
$424$		−	13.8960i		−	0.674848i
$425$	5.45581	−	28.2427i	0.264646	−	1.36997i
$426$		0			0
$427$	−9.57355	+	16.5819i	−0.463297	+	0.802453i
$428$		−	4.23091i		−	0.204509i
$429$		0			0
$430$	3.94095	+	8.63435i	0.190050	+	0.416385i
$431$	8.09901	+	4.67596i	0.390115	+	0.225233i	0.682210	−	0.731156i	$-0.261019\pi$
$431$	8.09901	+	4.67596i	0.390115	+	0.225233i	−0.292095	+	0.956389i	$0.594352\pi$
$432$		0			0
$433$	3.42954	−	1.98005i	0.164813	−	0.0951549i	−0.415325	−	0.909673i	$-0.636332\pi$
$433$	3.42954	−	1.98005i	0.164813	−	0.0951549i	0.580138	+	0.814518i	$0.302999\pi$
$434$		−	18.4933i		−	0.887705i
$435$		0			0
$436$	−0.387423	+	0.223679i	−0.0185542	+	0.0107123i
$437$	−35.3810			−1.69250
$438$		0			0
$439$	−11.2992	+	19.5708i	−0.539281	+	0.934062i	0.459662	+	0.888094i	$0.347971\pi$
$439$	−11.2992	+	19.5708i	−0.539281	+	0.934062i	−0.998943	+	0.0459680i	$0.985363\pi$
$440$	1.32412	+	0.126722i	0.0631248	+	0.00604125i
$441$		0			0
$442$	−19.7357	+	6.38437i	−0.938730	+	0.303673i
$443$			29.0428i			1.37987i	0.723873	+	0.689933i	$0.242360\pi$
$443$			29.0428i			1.37987i	−0.723873	+	0.689933i	$0.757640\pi$
$444$		0			0
$445$	13.4766	+	1.28976i	0.638854	+	0.0611404i
$446$	8.32779	+	14.4242i	0.394332	+	0.683004i
$447$		0			0
$448$	−1.40247	−	2.42916i	−0.0662607	−	0.114767i
$449$	−23.7886	+	13.7343i	−1.12265	+	0.648164i	−0.942077	−	0.335397i	$-0.891130\pi$
$449$	−23.7886	+	13.7343i	−1.12265	+	0.648164i	−0.180576	+	0.983561i	$0.557796\pi$
$450$		0			0
$451$	1.71113	+	2.96377i	0.0805740	+	0.139558i
$452$	−8.11206	−	4.68350i	−0.381559	−	0.220293i
$453$		0			0
$454$	3.02210			0.141834
$455$	6.81553	−	21.5627i	0.319517	−	1.01088i
$456$		0			0
$457$	−2.19087	+	3.79470i	−0.102485	+	0.177508i	−0.912708	−	0.408613i	$-0.866013\pi$
$457$	−2.19087	+	3.79470i	−0.102485	+	0.177508i	0.810223	+	0.586122i	$0.199346\pi$
$458$	−14.2437	−	8.22361i	−0.665565	−	0.384264i
$459$		0			0
$460$	−4.31323	−	9.44997i	−0.201105	−	0.440607i
$461$	21.0593	−	12.1586i	0.980829	−	0.566282i	0.0783090	−	0.996929i	$-0.475048\pi$
$461$	21.0593	−	12.1586i	0.980829	−	0.566282i	0.902520	+	0.430647i	$0.141715\pi$
$462$		0			0
$463$	−19.0660			−0.886071			−0.443035	−	0.896504i	$-0.646098\pi$
$463$	−19.0660			−0.886071			−0.443035	+	0.896504i	$0.646098\pi$
$464$	1.26235	+	2.18645i	0.0586030	+	0.101503i
$465$		0			0
$466$	−11.9762	−	6.91443i	−0.554784	−	0.320305i
$467$		−	10.1176i		−	0.468188i	−0.972214	−	0.234094i	$-0.924788\pi$
$467$		−	10.1176i		−	0.468188i	0.972214	−	0.234094i	$-0.0752123\pi$
$468$		0			0
$469$	−22.0537			−1.01834
$470$	−0.617345	+	6.45062i	−0.0284760	+	0.297545i
$471$		0			0
$472$	−8.40299	+	4.85147i	−0.386779	+	0.223307i
$473$	2.52498			0.116099
$474$		0			0
$475$	−7.22271	+	37.3893i	−0.331401	+	1.71554i
$476$			16.1368i			0.739628i
$477$		0			0
$478$	3.98559	+	2.30108i	0.182297	+	0.105249i
$479$	24.8215	+	14.3307i	1.13412	+	0.654786i	0.944969	−	0.327161i	$-0.106092\pi$
$479$	24.8215	+	14.3307i	1.13412	+	0.654786i	0.189155	+	0.981947i	$0.439425\pi$
$480$		0			0
$481$	36.5751	+	7.82361i	1.66768	+	0.356726i
$482$			6.21354i			0.283019i
$483$		0			0
$484$	−5.32307	+	9.21982i	−0.241958	+	0.419083i
$485$	30.7894	+	21.9349i	1.39807	+	0.996012i
$486$		0			0
$487$	−8.71990	−	15.1033i	−0.395136	−	0.684396i	0.597982	−	0.801509i	$-0.295969\pi$
$487$	−8.71990	−	15.1033i	−0.395136	−	0.684396i	−0.993119	+	0.117113i	$0.962636\pi$
$488$	−3.41309	−	5.91165i	−0.154504	−	0.267608i
$489$		0			0
$490$	−1.58030	−	1.12583i	−0.0713905	−	0.0508599i
$491$	11.2233	−	19.4394i	0.506503	−	0.877288i	−0.493469	−	0.869763i	$-0.664271\pi$
$491$	11.2233	−	19.4394i	0.506503	−	0.877288i	0.999972	−	0.00752493i	$-0.00239528\pi$
$492$		0			0
$493$		−	14.5245i		−	0.654150i
$494$	26.1272	−	8.45199i	1.17552	−	0.380273i
$495$		0			0
$496$	5.70978	+	3.29654i	0.256377	+	0.148019i
$497$	−3.12070	−	1.80174i	−0.139983	−	0.0808189i
$498$		0			0
$499$		−	10.4136i		−	0.466177i	−0.972456	−	0.233088i	$-0.925117\pi$
$499$		−	10.4136i		−	0.466177i	0.972456	−	0.233088i	$-0.0748832\pi$
$500$	−10.8669	+	2.62893i	−0.485981	+	0.117569i
$501$		0			0
$502$	16.3877			0.731420
$503$	5.00387	−	2.88899i	0.223112	−	0.128814i	−0.384279	−	0.923217i	$-0.625550\pi$
$503$	5.00387	−	2.88899i	0.223112	−	0.128814i	0.607390	+	0.794404i	$0.292216\pi$
$504$		0			0
$505$	−1.16039	+	12.1249i	−0.0516368	+	0.539551i
$506$	−2.76349			−0.122852
$507$		0			0
$508$		−	6.68791i		−	0.296728i
$509$	6.18024	+	3.56816i	0.273934	+	0.158156i	0.630674	−	0.776048i	$-0.282778\pi$
$509$	6.18024	+	3.56816i	0.273934	+	0.158156i	−0.356740	+	0.934204i	$0.616112\pi$
$510$		0			0
$511$	20.3920	+	35.3200i	0.902090	+	1.56247i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.28269	+	4.20466i	−0.321226	+	0.185460i
$515$	12.7691	+	27.9761i	0.562672	+	1.23277i
$516$		0			0
$517$	1.49296	+	0.861960i	0.0656603	+	0.0379090i
$518$	14.5487	−	25.1991i	0.639232	−	1.10718i
$519$		0			0
$520$	5.44256	+	5.94798i	0.238672	+	0.260836i
$521$	−1.09782			−0.0480965			−0.0240483	−	0.999711i	$-0.507656\pi$
$521$	−1.09782			−0.0480965			−0.0240483	+	0.999711i	$0.507656\pi$
$522$		0			0
$523$	−12.9411	−	7.47153i	−0.565873	−	0.326707i	0.189626	−	0.981856i	$-0.439272\pi$
$523$	−12.9411	−	7.47153i	−0.565873	−	0.326707i	−0.755499	+	0.655149i	$0.772606\pi$
$524$	−5.83620	−	10.1086i	−0.254956	−	0.441596i
$525$		0			0
$526$	5.10152	−	2.94536i	0.222437	−	0.128424i
$527$	−18.9649	−	32.8482i	−0.826125	−	1.43089i
$528$		0			0
$529$	−0.709414	−	1.22874i	−0.0308441	−	0.0534235i
$530$	30.9310	+	2.96020i	1.34356	+	0.128583i
$531$		0			0
$532$		−	21.3628i		−	0.926194i
$533$	−4.33881	+	20.2838i	−0.187935	+	0.878588i
$534$		0			0
$535$	9.41756	+	0.901291i	0.407157	+	0.0389662i
$536$	3.93121	−	6.80906i	0.169802	−	0.294106i
$537$		0			0
$538$	22.8455			0.984941
$539$	−0.447033	+	0.258095i	−0.0192551	+	0.0111169i
$540$		0			0
$541$			19.3888i			0.833589i	0.909001	+	0.416794i	$0.136846\pi$
$541$			19.3888i			0.833589i	−0.909001	+	0.416794i	$0.863154\pi$
$542$	23.2565	−	13.4271i	0.998950	−	0.576744i
$543$		0			0
$544$	−4.98222	−	2.87649i	−0.213611	−	0.123328i
$545$	−0.415355	−	0.910014i	−0.0177919	−	0.0389807i
$546$		0			0
$547$			26.1335i			1.11739i	0.829374	+	0.558693i	$0.188697\pi$
$547$			26.1335i			1.11739i	−0.829374	+	0.558693i	$0.811303\pi$
$548$	3.40142	−	5.89144i	0.145302	−	0.251670i
$549$		0			0
$550$	−0.564141	+	2.92035i	−0.0240551	+	0.124524i
$551$			19.2283i			0.819155i
$552$		0			0
$553$	2.56863	+	4.44901i	0.109229	+	0.189191i
$554$			10.6250i			0.451412i
$555$		0			0
$556$	−3.54908	+	6.14719i	−0.150514	+	0.260699i
$557$	−17.6927	+	30.6446i	−0.749663	+	1.29846i	0.198321	+	0.980137i	$0.436451\pi$
$557$	−17.6927	+	30.6446i	−0.749663	+	1.29846i	−0.947984	+	0.318318i	$0.896882\pi$
$558$		0			0
$559$	11.3600	+	10.2551i	0.480475	+	0.433745i
$560$	5.70582	−	2.60429i	0.241115	−	0.110051i
$561$		0			0
$562$	−24.5719	−	14.1866i	−1.03650	−	0.598425i
$563$	25.8011	−	14.8963i	1.08739	−	0.627804i	0.154509	−	0.987991i	$-0.450621\pi$
$563$	25.8011	−	14.8963i	1.08739	−	0.627804i	0.932880	+	0.360187i	$0.117287\pi$
$564$		0			0
$565$	12.1531	−	17.0589i	0.511284	−	0.717674i
$566$	4.91005	−	2.83482i	0.206385	−	0.119156i
$567$		0			0
$568$	1.11257	−	0.642342i	0.0466824	−	0.0269521i
$569$	7.14388	−	12.3736i	0.299487	−	0.518727i	−0.676532	−	0.736414i	$-0.736518\pi$
$569$	7.14388	−	12.3736i	0.299487	−	0.518727i	0.976019	+	0.217687i	$0.0698511\pi$
$570$		0			0
$571$	−37.4439			−1.56698			−0.783490	−	0.621404i	$-0.786562\pi$
$571$	−37.4439			−1.56698			−0.783490	+	0.621404i	$0.786562\pi$
$572$	2.04071	−	0.660156i	0.0853263	−	0.0276025i
$573$		0			0
$574$	13.9749	+	8.06839i	0.583300	+	0.336768i
$575$	21.9535	−	7.58771i	0.915524	−	0.316430i
$576$		0			0
$577$	−47.6052			−1.98183			−0.990916	−	0.134485i	$-0.957062\pi$
$577$	−47.6052			−1.98183			−0.990916	+	0.134485i	$0.957062\pi$
$578$	8.04834	+	13.9401i	0.334767	+	0.579833i
$579$		0			0
$580$	−5.13572	+	2.34408i	−0.213249	+	0.0973328i
$581$	−5.87895	−	10.1826i	−0.243900	−	0.422447i
$582$		0			0
$583$	4.13314	−	7.15881i	0.171177	−	0.296487i
$584$	−14.5400			−0.601671
$585$		0			0
$586$	−1.65835			−0.0685059
$587$	18.8016	−	32.5654i	0.776027	−	1.34412i	−0.158189	−	0.987409i	$-0.550565\pi$
$587$	18.8016	−	32.5654i	0.776027	−	1.34412i	0.934216	−	0.356709i	$-0.116101\pi$
$588$		0			0
$589$	25.1068	+	43.4863i	1.03451	+	1.79182i
$590$	−9.00882	−	19.7377i	−0.370887	−	0.812587i
$591$		0			0
$592$	5.18679	+	8.98379i	0.213176	+	0.369231i
$593$	24.0046			0.985752			0.492876	−	0.870100i	$-0.335946\pi$
$593$	24.0046			0.985752			0.492876	+	0.870100i	$0.335946\pi$
$594$		0			0
$595$	−35.9188	−	3.43755i	−1.47253	−	0.140926i
$596$	−3.02342	−	1.74557i	−0.123844	−	0.0715014i
$597$		0			0
$598$	−12.4330	−	11.2238i	−0.508425	−	0.458977i
$599$	23.7092			0.968731			0.484365	−	0.874866i	$-0.339051\pi$
$599$	23.7092			0.968731			0.484365	+	0.874866i	$0.339051\pi$
$600$		0			0
$601$	0.918249	−	1.59045i	0.0374562	−	0.0648760i	−0.846690	−	0.532087i	$-0.821408\pi$
$601$	0.918249	−	1.59045i	0.0374562	−	0.0648760i	0.884146	+	0.467211i	$0.154741\pi$
$602$	10.3108	−	5.95294i	0.420237	−	0.242624i
$603$		0			0
$604$	3.94031	−	2.27494i	0.160329	−	0.0925661i
$605$	−19.3884	−	13.8127i	−0.788252	−	0.561564i
$606$		0			0
$607$	30.2214	−	17.4483i	1.22665	−	0.708206i	0.260321	−	0.965522i	$-0.416172\pi$
$607$	30.2214	−	17.4483i	1.22665	−	0.708206i	0.966327	+	0.257316i	$0.0828382\pi$
$608$	6.59574	+	3.80805i	0.267493	+	0.154437i
$609$		0			0
$610$	13.8858	−	6.33786i	0.562220	−	0.256613i
$611$	3.21604	+	9.94159i	0.130107	+	0.402194i
$612$		0			0
$613$	4.70575	−	8.15061i	0.190064	−	0.329200i	−0.755207	−	0.655486i	$-0.772464\pi$
$613$	4.70575	−	8.15061i	0.190064	−	0.329200i	0.945271	+	0.326286i	$0.105797\pi$
$614$	−0.192044	+	0.332629i	−0.00775025	+	0.0134238i
$615$		0			0
$616$		−	1.66858i		−	0.0672288i
$617$	5.47577	+	9.48432i	0.220446	+	0.381824i	0.954944	−	0.296787i	$-0.0959153\pi$
$617$	5.47577	+	9.48432i	0.220446	+	0.381824i	−0.734497	+	0.678612i	$0.762582\pi$
$618$		0			0
$619$		−	1.00216i		−	0.0402803i	−0.999797	−	0.0201402i	$-0.993589\pi$
$619$		−	1.00216i		−	0.0402803i	0.999797	−	0.0201402i	$-0.00641125\pi$
$620$	−8.55410	+	12.0071i	−0.343541	+	0.482218i
$621$		0			0
$622$	−5.84601	+	10.1256i	−0.234404	+	0.405999i
$623$		−	16.9825i		−	0.680389i
$624$		0			0
$625$	−3.53680	−	24.7486i	−0.141472	−	0.989942i
$626$	−9.16150	−	5.28939i	−0.366167	−	0.211407i
$627$		0			0
$628$	9.95560	−	5.74787i	0.397272	−	0.229365i
$629$		−	59.6789i		−	2.37955i
$630$		0			0
$631$	−33.5167	+	19.3509i	−1.33428	+	0.770346i	−0.985952	−	0.167027i	$-0.946583\pi$
$631$	−33.5167	+	19.3509i	−1.33428	+	0.770346i	−0.348327	+	0.937373i	$0.613250\pi$
$632$	−1.83150			−0.0728532
$633$		0			0
$634$	11.0512	−	19.1412i	0.438898	−	0.760193i
$635$	14.8866	+	1.42469i	0.590756	+	0.0565373i
$636$		0			0
$637$	−3.05946	−	0.654435i	−0.121220	−	0.0259296i
$638$			1.50186i			0.0594592i
$639$		0			0
$640$	−0.213026	+	2.22590i	−0.00842057	+	0.0879863i
$641$	−4.99961	−	8.65957i	−0.197473	−	0.342033i	0.750236	−	0.661170i	$-0.229940\pi$
$641$	−4.99961	−	8.65957i	−0.197473	−	0.342033i	−0.947708	+	0.319138i	$0.896607\pi$
$642$		0			0
$643$	3.38728	+	5.86694i	0.133581	+	0.231369i	0.925055	−	0.379834i	$-0.124019\pi$
$643$	3.38728	+	5.86694i	0.133581	+	0.231369i	−0.791473	+	0.611204i	$0.790686\pi$
$644$	−11.2848	+	6.51527i	−0.444683	+	0.256738i
$645$		0			0
$646$	−21.9076	−	37.9451i	−0.861944	−	1.49293i
$647$	−14.8850	−	8.59384i	−0.585188	−	0.337859i	0.178004	−	0.984030i	$-0.443036\pi$
$647$	−14.8850	−	8.59384i	−0.585188	−	0.337859i	−0.763193	+	0.646171i	$0.776369\pi$
$648$		0			0
$649$	−5.77197			−0.226570
$650$	−14.3990	+	10.8475i	−0.564776	+	0.425474i
$651$		0			0
$652$	−6.91443	+	11.9762i	−0.270790	+	0.469022i
$653$	21.5401	+	12.4362i	0.842930	+	0.486666i	0.858259	−	0.513217i	$-0.171546\pi$
$653$	21.5401	+	12.4362i	0.842930	+	0.486666i	−0.0153292	+	0.999883i	$0.504880\pi$
$654$		0			0
$655$	23.7440	−	10.8374i	0.927753	−	0.423452i
$656$	−4.98222	+	2.87649i	−0.194523	+	0.112308i
$657$		0			0
$658$	8.12870			0.316890
$659$	4.12151	+	7.13867i	0.160551	+	0.278083i	0.935067	−	0.354472i	$-0.115339\pi$
$659$	4.12151	+	7.13867i	0.160551	+	0.278083i	−0.774515	+	0.632555i	$0.782006\pi$
$660$		0			0
$661$	22.3962	+	12.9305i	0.871112	+	0.502937i	0.867718	−	0.497057i	$-0.165586\pi$
$661$	22.3962	+	12.9305i	0.871112	+	0.502937i	0.00339467	+	0.999994i	$0.498919\pi$
$662$		−	6.10616i		−	0.237323i
$663$		0			0
$664$	4.19184			0.162675
$665$	47.5514	+	4.55082i	1.84396	+	0.176473i
$666$		0			0
$667$	10.1573	−	5.86430i	0.393291	−	0.227067i
$668$	21.5400			0.833409
$669$		0			0
$670$	14.3188	+	10.2010i	0.553184	+	0.394098i
$671$		−	4.06069i		−	0.156761i
$672$		0			0
$673$	5.99820	+	3.46306i	0.231213	+	0.133491i	0.611132	−	0.791529i	$-0.290715\pi$
$673$	5.99820	+	3.46306i	0.231213	+	0.133491i	−0.379918	+	0.925020i	$0.624048\pi$
$674$	3.72263	+	2.14926i	0.143390	+	0.0827864i
$675$		0			0
$676$	11.8624	+	5.31820i	0.456246	+	0.204546i
$677$			4.72639i			0.181650i	0.995867	+	0.0908250i	$0.0289504\pi$
$677$			4.72639i			0.181650i	−0.995867	+	0.0908250i	$0.971050\pi$
$678$		0			0
$679$	23.7107	−	41.0682i	0.909935	−	1.57605i
$680$	7.46410	−	10.4771i	0.286235	−	0.401780i
$681$		0			0
$682$	1.96101	+	3.39657i	0.0750910	+	0.130061i
$683$	−9.78995	−	16.9567i	−0.374602	−	0.648830i	0.615665	−	0.788008i	$-0.288887\pi$
$683$	−9.78995	−	16.9567i	−0.374602	−	0.648830i	−0.990267	+	0.139178i	$0.955554\pi$
$684$		0			0
$685$	12.3891	+	8.82625i	0.473365	+	0.337234i
$686$	8.60034	−	14.8962i	0.328363	−	0.568741i
$687$		0			0
$688$			4.24460i			0.161824i
$689$	47.6704	−	15.4211i	1.81610	−	0.587496i
$690$		0			0
$691$	−10.7079	−	6.18224i	−0.407350	−	0.235183i	0.282301	−	0.959326i	$-0.408902\pi$
$691$	−10.7079	−	6.18224i	−0.407350	−	0.235183i	−0.689650	+	0.724143i	$0.742236\pi$
$692$	11.8342	+	6.83251i	0.449871	+	0.259733i
$693$		0			0
$694$			34.3459i			1.30375i
$695$	−12.9270	−	9.20939i	−0.490348	−	0.349332i
$696$		0			0
$697$	33.0967			1.25363
$698$	−13.8581	+	8.00099i	−0.524538	+	0.302842i
$699$		0			0
$700$	4.58140	+	13.2553i	0.173161	+	0.501005i
$701$	−43.7550			−1.65260			−0.826302	−	0.563227i	$-0.809559\pi$
$701$	−43.7550			−1.65260			−0.826302	+	0.563227i	$0.809559\pi$
$702$		0			0
$703$			79.0063i			2.97978i
$704$	0.515171	+	0.297434i	0.0194163	+	0.0112100i
$705$		0			0
$706$	−9.69607	−	16.7941i	−0.364916	−	0.632054i
$707$	15.2791			0.574630
$708$		0			0
$709$	16.4104	−	9.47457i	0.616307	−	0.355825i	−0.159123	−	0.987259i	$-0.550867\pi$
$709$	16.4104	−	9.47457i	0.616307	−	0.355825i	0.775430	+	0.631434i	$0.217533\pi$
$710$	1.19278	+	2.61330i	0.0447643	+	0.0980754i
$711$		0			0
$712$	5.24333	+	3.02724i	0.196502	+	0.113451i
$713$	15.3143	−	26.5251i	0.573524	−	0.993372i
$714$		0			0
$715$	1.03472	+	4.68304i	0.0386962	+	0.175136i
$716$	10.7577			0.402035
$717$		0			0
$718$	−13.7129	−	7.91712i	−0.511759	−	0.295464i
$719$	23.5155	+	40.7301i	0.876981	+	1.51898i	0.854637	+	0.519225i	$0.173779\pi$
$719$	23.5155	+	40.7301i	0.876981	+	1.51898i	0.0223436	+	0.999750i	$0.492887\pi$
$720$		0			0
$721$	33.4079	−	19.2881i	1.24418	−	0.718326i
$722$	19.5026	+	33.7794i	0.725810	+	1.25714i
$723$		0			0
$724$	−2.93234	−	5.07897i	−0.108980	−	0.188758i
$725$	−4.12365	−	11.9309i	−0.153149	−	0.443104i
$726$		0			0
$727$		−	4.10440i		−	0.152224i	−0.997099	−	0.0761119i	$-0.975749\pi$
$727$		−	4.10440i		−	0.152224i	0.997099	−	0.0761119i	$-0.0242506\pi$
$728$	6.77687	−	7.50697i	0.251167	−	0.278227i
$729$		0			0
$730$	3.09740	−	32.3646i	0.114640	−	1.19787i
$731$	12.2095	−	21.1475i	0.451586	−	0.782169i
$732$		0			0
$733$	24.2968			0.897421			0.448711	−	0.893677i	$-0.351883\pi$
$733$	24.2968			0.897421			0.448711	+	0.893677i	$0.351883\pi$
$734$	−13.2440	+	7.64645i	−0.488847	+	0.282236i
$735$		0			0
$736$		−	4.64555i		−	0.171237i
$737$	4.05050	−	2.33855i	0.149202	−	0.0861418i
$738$		0			0
$739$	−35.0414	−	20.2311i	−1.28902	−	0.744215i	−0.310539	−	0.950561i	$-0.600509\pi$
$739$	−35.0414	−	20.2311i	−1.28902	−	0.744215i	−0.978479	+	0.206346i	$0.933843\pi$
$740$	−21.1019	+	9.63149i	−0.775722	+	0.354061i
$741$		0			0
$742$		−	38.9775i		−	1.43091i
$743$	−15.7497	+	27.2794i	−0.577802	+	1.00078i	0.417929	+	0.908480i	$0.362756\pi$
$743$	−15.7497	+	27.2794i	−0.577802	+	1.00078i	−0.995731	+	0.0923027i	$0.970577\pi$
$744$		0			0
$745$	4.52953	−	6.35797i	0.165949	−	0.232938i
$746$			21.6516i			0.792721i
$747$		0			0
$748$	−1.71113	−	2.96377i	−0.0625651	−	0.108366i
$749$		−	11.8675i		−	0.433628i
$750$		0			0
$751$	−8.37551	+	14.5068i	−0.305627	+	0.529361i	−0.977401	−	0.211395i	$-0.932199\pi$
$751$	−8.37551	+	14.5068i	−0.305627	+	0.529361i	0.671774	+	0.740756i	$0.265533\pi$
$752$	−1.44899	+	2.50973i	−0.0528393	+	0.0915204i
$753$		0			0
$754$	−6.09976	+	6.75692i	−0.222140	+	0.246072i
$755$	4.22440	+	9.25536i	0.153742	+	0.336837i
$756$		0			0
$757$	23.1908	+	13.3892i	0.842885	+	0.486640i	0.858244	−	0.513242i	$-0.171556\pi$
$757$	23.1908	+	13.3892i	0.842885	+	0.486640i	−0.0153589	+	0.999882i	$0.504889\pi$
$758$	−7.81479	+	4.51187i	−0.283846	+	0.163879i
$759$		0			0
$760$	−9.88140	+	13.8702i	−0.358436	+	0.503126i
$761$	0.217029	−	0.125302i	0.00786729	−	0.00454218i	−0.496061	−	0.868288i	$-0.665221\pi$
$761$	0.217029	−	0.125302i	0.00786729	−	0.00454218i	0.503928	+	0.863745i	$0.331888\pi$
$762$		0			0
$763$	−1.08670	+	0.627408i	−0.0393413	+	0.0227137i
$764$	−6.91728	+	11.9811i	−0.250259	+	0.433461i
$765$		0			0
$766$	−10.0741			−0.363990
$767$	−25.9683	−	23.4427i	−0.937660	−	0.846466i
$768$		0			0
$769$	17.1777	+	9.91755i	0.619444	+	0.357636i	0.776652	−	0.629929i	$-0.216916\pi$
$769$	17.1777	+	9.91755i	0.619444	+	0.357636i	−0.157209	+	0.987565i	$0.550250\pi$
$770$	3.71408	+	0.355449i	0.133846	+	0.0128095i
$771$		0			0
$772$	17.0064			0.612075
$773$	−18.3185	−	31.7285i	−0.658869	−	1.14120i	−0.980909	−	0.194469i	$-0.937702\pi$
$773$	−18.3185	−	31.7285i	−0.658869	−	1.14120i	0.322039	−	0.946726i	$-0.395632\pi$
$774$		0			0
$775$	−24.9044	−	21.5984i	−0.894593	−	0.775836i
$776$	8.45318	+	14.6413i	0.303452	+	0.525594i
$777$		0			0
$778$	−12.1795	+	21.0956i	−0.436658	+	0.756313i
$779$	−43.8152			−1.56984
$780$		0			0
$781$	0.764218			0.0273459
$782$	−13.3629	+	23.1452i	−0.477855	+	0.827669i
$783$		0			0
$784$	−0.433868	−	0.751482i	−0.0154953	−	0.0268386i
$785$	10.6734	+	23.3846i	0.380949	+	0.834632i
$786$		0			0
$787$	−17.9505	−	31.0911i	−0.639865	−	1.10828i	−0.985462	−	0.169896i	$-0.945657\pi$
$787$	−17.9505	−	31.0911i	−0.639865	−	1.10828i	0.345597	−	0.938383i	$-0.387677\pi$
$788$	−6.32974			−0.225487
$789$		0			0
$790$	0.390157	−	4.07674i	0.0138812	−	0.145044i
$791$	−22.7539	−	13.1370i	−0.809036	−	0.467097i
$792$		0			0
$793$	16.4923	−	18.2691i	0.585660	−	0.648756i
$794$	30.0381			1.06601
$795$		0			0
$796$	8.31782	−	14.4069i	0.294817	−	0.510638i
$797$	4.30187	−	2.48369i	0.152380	−	0.0879767i	−0.421871	−	0.906656i	$-0.638627\pi$
$797$	4.30187	−	2.48369i	0.152380	−	0.0879767i	0.574251	+	0.818679i	$0.305293\pi$
$798$		0			0
$799$	14.4384	−	8.33601i	0.510794	−	0.294907i
$800$	−4.90924	−	0.948346i	−0.173568	−	0.0335291i
$801$		0			0
$802$	2.35786	−	1.36131i	0.0832590	−	0.0480696i
$803$	−7.49061	−	4.32471i	−0.264338	−	0.152616i
$804$		0			0
$805$	−12.0984	−	26.5067i	−0.426412	−	0.934238i
$806$	−4.97241	+	23.2458i	−0.175146	+	0.818800i
$807$		0			0
$808$	−2.72360	+	4.71741i	−0.0958159	+	0.165958i
$809$	−20.1296	+	34.8656i	−0.707720	+	1.22581i	0.257980	+	0.966150i	$0.416943\pi$
$809$	−20.1296	+	34.8656i	−0.707720	+	1.22581i	−0.965701	+	0.259658i	$0.916390\pi$
$810$		0			0
$811$			7.62969i			0.267914i	0.990987	+	0.133957i	$0.0427685\pi$
$811$			7.62969i			0.267914i	−0.990987	+	0.133957i	$0.957232\pi$
$812$	3.54082	+	6.13287i	0.124258	+	0.215222i
$813$		0			0
$814$			6.17092i			0.216291i
$815$	−25.1847	−	17.9420i	−0.882183	−	0.628483i
$816$		0			0
$817$	−16.1637	+	27.9963i	−0.565495	+	0.979466i
$818$		−	38.2243i		−	1.33648i
$819$		0			0
$820$	−5.34142	−	11.7027i	−0.186531	−	0.408675i
$821$	20.8682	+	12.0483i	0.728306	+	0.420487i	0.817802	−	0.575500i	$-0.195192\pi$
$821$	20.8682	+	12.0483i	0.728306	+	0.420487i	−0.0894964	+	0.995987i	$0.528526\pi$
$822$		0			0
$823$	−18.6227	+	10.7518i	−0.649145	+	0.374784i	−0.788129	−	0.615511i	$-0.788950\pi$
$823$	−18.6227	+	10.7518i	−0.649145	+	0.374784i	0.138984	+	0.990295i	$0.455616\pi$
$824$			13.7529i			0.479105i
$825$		0			0
$826$	−23.5699	+	13.6081i	−0.820103	+	0.473487i
$827$	−38.8887			−1.35229			−0.676147	−	0.736767i	$-0.736352\pi$
$827$	−38.8887			−1.35229			−0.676147	+	0.736767i	$0.736352\pi$
$828$		0			0
$829$	12.2944	−	21.2945i	0.427001	−	0.739587i	−0.569604	−	0.821919i	$-0.692903\pi$
$829$	12.2944	−	21.2945i	0.427001	−	0.739587i	0.996605	+	0.0823320i	$0.0262368\pi$
$830$	−0.892969	+	9.33061i	−0.0309954	+	0.323870i
$831$		0			0
$832$	1.10975	+	3.43052i	0.0384737	+	0.118932i
$833$			4.99206i			0.172965i
$834$		0			0
$835$	−4.58858	+	47.9459i	−0.158794	+	1.65924i
$836$	2.26529	+	3.92360i	0.0783468	+	0.135701i
$837$		0			0
$838$	−14.9365	−	25.8708i	−0.515972	−	0.893690i
$839$	−45.1686	+	26.0781i	−1.55939	+	0.900316i	−0.562079	+	0.827084i	$0.689998\pi$
$839$	−45.1686	+	26.0781i	−1.55939	+	0.900316i	−0.997315	+	0.0732324i	$0.976669\pi$
$840$		0			0
$841$	11.3130	+	19.5946i	0.390102	+	0.675677i
$842$	−12.3004	−	7.10165i	−0.423900	−	0.244739i
$843$		0			0
$844$	16.5489			0.569635
$845$	−14.3648	+	25.2716i	−0.494163	+	0.869369i
$846$		0			0
$847$	−14.9309	+	25.8611i	−0.513033	+	0.888599i
$848$	12.0343	+	6.94798i	0.413258	+	0.238595i
$849$		0			0
$850$	21.7310	+	18.8462i	0.745367	+	0.646420i
$851$	41.7347	−	24.0955i	1.43065	−	0.825984i
$852$		0			0
$853$	−2.06762			−0.0707938			−0.0353969	−	0.999373i	$-0.511270\pi$
$853$	−2.06762			−0.0707938			−0.0353969	+	0.999373i	$0.511270\pi$
$854$	−9.57355	−	16.5819i	−0.327600	−	0.567420i
$855$		0			0
$856$	3.66407	+	2.11545i	0.125235	+	0.0723047i
$857$			20.1793i			0.689310i	0.938729	+	0.344655i	$0.112004\pi$
$857$			20.1793i			0.689310i	−0.938729	+	0.344655i	$0.887996\pi$
$858$		0			0
$859$	−34.4160			−1.17426			−0.587129	−	0.809493i	$-0.699742\pi$
$859$	−34.4160			−1.17426			−0.587129	+	0.809493i	$0.699742\pi$
$860$	−9.44804	−	0.904208i	−0.322176	−	0.0308332i
$861$		0			0
$862$	−8.09901	+	4.67596i	−0.275853	+	0.159264i
$863$	1.02382			0.0348514			0.0174257	−	0.999848i	$-0.494453\pi$
$863$	1.02382			0.0348514			0.0174257	+	0.999848i	$0.494453\pi$
$864$		0			0
$865$	−17.7295	+	24.8863i	−0.602820	+	0.846160i
$866$			3.96009i			0.134569i
$867$		0			0
$868$	16.0156	+	9.24663i	0.543606	+	0.313851i
$869$	−0.943538	−	0.544752i	−0.0320073	−	0.0184794i
$870$		0			0
$871$	27.7213	+	5.92973i	0.939299	+	0.200921i
$872$		−	0.447358i		−	0.0151495i
$873$		0			0
$874$	17.6905	−	30.6409i	0.598391	−	1.03644i
$875$	−30.4810	+	7.37400i	−1.03045	+	0.249287i
$876$		0			0
$877$	7.46097	+	12.9228i	0.251939	+	0.436371i	0.964060	−	0.265686i	$-0.0855984\pi$
$877$	7.46097	+	12.9228i	0.251939	+	0.436371i	−0.712121	+	0.702057i	$0.752265\pi$
$878$	−11.2992	−	19.5708i	−0.381329	−	0.660481i
$879$		0			0
$880$	−0.771803	+	1.08336i	−0.0260175	+	0.0365200i
$881$	−21.5282	+	37.2879i	−0.725303	+	1.25626i	0.233546	+	0.972346i	$0.424967\pi$
$881$	−21.5282	+	37.2879i	−0.725303	+	1.25626i	−0.958849	+	0.283916i	$0.908366\pi$
$882$		0			0
$883$		−	30.1817i		−	1.01569i	−0.861447	−	0.507847i	$-0.830441\pi$
$883$		−	30.1817i		−	1.01569i	0.861447	−	0.507847i	$-0.169559\pi$
$884$	4.33881	−	20.2838i	0.145930	−	0.682217i
$885$		0			0
$886$	−25.1518	−	14.5214i	−0.844992	−	0.487856i
$887$	18.7593	+	10.8307i	0.629877	+	0.363660i	0.780705	−	0.624900i	$-0.214860\pi$
$887$	18.7593	+	10.8307i	0.629877	+	0.363660i	−0.150827	+	0.988560i	$0.548194\pi$
$888$		0			0
$889$		−	18.7592i		−	0.629164i
$890$	−7.85528	+	11.0262i	−0.263310	+	0.369600i
$891$		0			0
$892$	−16.6556			−0.557670
$893$	−19.1144	+	11.0357i	−0.639638	+	0.369295i
$894$		0			0
$895$	−2.29167	+	23.9456i	−0.0766021	+	0.800413i
$896$	2.80495			0.0937068
$897$		0			0
$898$		−	27.4687i		−	0.916642i
$899$	−14.4154	−	8.32276i	−0.480782	−	0.277580i
$900$		0			0
$901$	−39.9715	−	69.2328i	−1.33165	−	2.30648i
$902$	−3.42226			−0.113949
$903$		0			0
$904$	8.11206	−	4.68350i	0.269803	−	0.155771i
$905$	11.9299	−	5.44515i	0.396564	−	0.181003i
$906$		0			0
$907$	2.42051	+	1.39748i	0.0803717	+	0.0464026i	0.539647	−	0.841891i	$-0.318558\pi$
$907$	2.42051	+	1.39748i	0.0803717	+	0.0464026i	−0.459276	+	0.888294i	$0.651891\pi$
$908$	−1.51105	+	2.61722i	−0.0501460	+	0.0868554i
$909$		0			0
$910$	15.2661	+	16.6838i	0.506067	+	0.553062i
$911$	−24.2193			−0.802422			−0.401211	−	0.915986i	$-0.631411\pi$
$911$	−24.2193			−0.802422			−0.401211	+	0.915986i	$0.631411\pi$
$912$		0			0
$913$	2.15952	+	1.24680i	0.0714695	+	0.0412630i
$914$	−2.19087	−	3.79470i	−0.0724675	−	0.125517i
$915$		0			0
$916$	14.2437	−	8.22361i	0.470626	−	0.271716i
$917$	−16.3702	−	28.3541i	−0.540593	−	0.936334i
$918$		0			0
$919$	−6.54988	−	11.3447i	−0.216061	−	0.374228i	0.737539	−	0.675304i	$-0.235988\pi$
$919$	−6.54988	−	11.3447i	−0.216061	−	0.374228i	−0.953600	+	0.301076i	$0.902654\pi$
$920$	10.3405	+	0.989622i	0.340917	+	0.0326269i
$921$		0			0
$922$			24.3172i			0.800844i
$923$	3.43824	+	3.10385i	0.113171	+	0.102164i
$924$		0			0
$925$	−16.9435	−	49.0224i	−0.557098	−	1.61185i
$926$	9.53298	−	16.5116i	0.313273	−	0.542605i
$927$		0			0
$928$	−2.52469			−0.0828771
$929$	−24.1564	+	13.9467i	−0.792544	+	0.457576i	−0.840858	−	0.541257i	$-0.817949\pi$
$929$	−24.1564	+	13.9467i	−0.792544	+	0.457576i	0.0483131	+	0.998832i	$0.484615\pi$
$930$		0			0
$931$		−	6.60877i		−	0.216594i
$932$	11.9762	−	6.91443i	0.392292	−	0.226490i
$933$		0			0
$934$	8.76211	+	5.05881i	0.286705	+	0.165529i
$935$	6.96155	−	3.17744i	0.227667	−	0.103914i
$936$		0			0
$937$		−	49.9741i		−	1.63258i	−0.577640	−	0.816292i	$-0.696026\pi$
$937$		−	49.9741i		−	1.63258i	0.577640	−	0.816292i	$-0.303974\pi$
$938$	11.0268	−	19.0991i	0.360039	−	0.623606i
$939$		0			0
$940$	−5.27773	−	3.75995i	−0.172140	−	0.122636i
$941$			9.56099i			0.311680i	0.987782	+	0.155840i	$0.0498083\pi$
$941$			9.56099i			0.311680i	−0.987782	+	0.155840i	$0.950192\pi$
$942$		0			0
$943$	13.3629	+	23.1452i	0.435155	+	0.753710i
$944$		−	9.70293i		−	0.315804i
$945$		0			0
$946$	−1.26249	+	2.18670i	−0.0410471	+	0.0710956i
$947$	22.0817	−	38.2466i	0.717558	−	1.24285i	−0.244406	−	0.969673i	$-0.578593\pi$
$947$	22.0817	−	38.2466i	0.717558	−	1.24285i	0.961964	−	0.273175i	$-0.0880737\pi$
$948$		0			0
$949$	−16.1358	−	49.8799i	−0.523791	−	1.61917i
$950$	−28.7687	−	24.9497i	−0.933381	−	0.809475i
$951$		0			0
$952$	−13.9749	−	8.06839i	−0.452928	−	0.261498i
$953$	12.8310	−	7.40798i	0.415637	−	0.239968i	−0.277572	−	0.960705i	$-0.589530\pi$
$953$	12.8310	−	7.40798i	0.415637	−	0.239968i	0.693209	+	0.720737i	$0.256196\pi$
$954$		0			0
$955$	−25.1951	−	17.9494i	−0.815295	−	0.580830i
$956$	−3.98559	+	2.30108i	−0.128903	+	0.0744223i
$957$		0			0
$958$	−24.8215	+	14.3307i	−0.801946	+	0.463004i
$959$	9.54082	−	16.5252i	0.308089	−	0.533626i
$960$		0			0
$961$	−12.4688			−0.402219
$962$	−25.0630	+	27.7632i	−0.808063	+	0.895120i
$963$		0			0
$964$	−5.38108	−	3.10677i	−0.173313	−	0.100062i
$965$	−3.62280	+	37.8546i	−0.116622	+	1.21858i
$966$		0			0
$967$	1.88667			0.0606711			0.0303356	−	0.999540i	$-0.490342\pi$
$967$	1.88667			0.0606711			0.0303356	+	0.999540i	$0.490342\pi$
$968$	−5.32307	−	9.21982i	−0.171090	−	0.296336i
$969$		0			0
$970$	−34.3909	+	15.6969i	−1.10422	+	0.503998i
$971$	−23.9611	−	41.5018i	−0.768947	−	1.33186i	−0.938134	−	0.346271i	$-0.887448\pi$
$971$	−23.9611	−	41.5018i	−0.768947	−	1.33186i	0.169187	−	0.985584i	$-0.445886\pi$
$972$		0			0
$973$	−9.95499	+	17.2425i	−0.319142	+	0.552770i
$974$	17.4398			0.558807
$975$		0			0
$976$	6.82619			0.218501
$977$	−16.1581	+	27.9867i	−0.516945	+	0.895374i	0.482862	+	0.875697i	$0.339597\pi$
$977$	−16.1581	+	27.9867i	−0.516945	+	0.895374i	−0.999806	+	0.0196777i	$0.993736\pi$
$978$		0			0
$979$	1.80081	+	3.11909i	0.0575541	+	0.0996866i
$980$	1.76515	−	0.805661i	0.0563855	−	0.0257359i
$981$		0			0
$982$	11.2233	+	19.4394i	0.358151	+	0.620336i
$983$	20.4850			0.653370			0.326685	−	0.945133i	$-0.394068\pi$
$983$	20.4850			0.653370			0.326685	+	0.945133i	$0.394068\pi$
$984$		0			0
$985$	1.34840	−	14.0893i	0.0429635	−	0.448924i
$986$	12.5786	+	7.26224i	0.400583	+	0.231277i
$987$		0			0
$988$	−5.74396	+	26.8528i	−0.182740	+	0.854302i
$989$	19.7185			0.627012
$990$		0			0
$991$	0.834181	−	1.44484i	0.0264986	−	0.0458970i	−0.852472	−	0.522773i	$-0.824898\pi$
$991$	0.834181	−	1.44484i	0.0264986	−	0.0458970i	0.878971	+	0.476876i	$0.158231\pi$
$992$	−5.70978	+	3.29654i	−0.181286	+	0.104665i
$993$		0			0
$994$	3.12070	−	1.80174i	0.0989826	−	0.0571476i
$995$	30.2963	+	21.5836i	0.960458	+	0.684247i
$996$		0			0
$997$	2.71512	−	1.56758i	0.0859887	−	0.0496456i	−0.456389	−	0.889780i	$-0.650857\pi$
$997$	2.71512	−	1.56758i	0.0859887	−	0.0496456i	0.542378	+	0.840135i	$0.317524\pi$
$998$	9.01844	+	5.20680i	0.285474	+	0.164818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.c.199.6		12
3.2	odd	2		390.2.x.b.199.1	yes	12
5.4	even	2		1170.2.bj.d.199.1		12
13.10	even	6		1170.2.bj.d.829.1		12
15.2	even	4		1950.2.bc.i.901.6		12
15.8	even	4		1950.2.bc.j.901.1		12
15.14	odd	2		390.2.x.a.199.6	yes	12
39.23	odd	6		390.2.x.a.49.6	✓	12
65.49	even	6	inner	1170.2.bj.c.829.6		12
195.23	even	12		1950.2.bc.j.751.1		12
195.62	even	12		1950.2.bc.i.751.6		12
195.179	odd	6		390.2.x.b.49.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.6	✓	12	39.23	odd	6
390.2.x.a.199.6	yes	12	15.14	odd	2
390.2.x.b.49.1	yes	12	195.179	odd	6
390.2.x.b.199.1	yes	12	3.2	odd	2
1170.2.bj.c.199.6		12	1.1	even	1	trivial
1170.2.bj.c.829.6		12	65.49	even	6	inner
1170.2.bj.d.199.1		12	5.4	even	2
1170.2.bj.d.829.1		12	13.10	even	6
1950.2.bc.i.751.6		12	195.62	even	12
1950.2.bc.i.901.6		12	15.2	even	4
1950.2.bc.j.751.1		12	195.23	even	12
1950.2.bc.j.901.1		12	15.8	even	4

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(-0.213026 + 2.22590i) q^{10} +(0.515171 + 0.297434i) q^{11} +(1.10975 + 3.43052i) q^{13} +2.80495 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.98222 - 2.87649i) q^{17} +(-6.59574 + 3.80805i) q^{19} +(-1.82117 - 1.29743i) q^{20} +(-0.515171 + 0.297434i) q^{22} +(4.02317 + 2.32278i) q^{23} +(3.27591 - 3.77735i) q^{25} +(-3.52579 - 0.754186i) q^{26} +(-1.40247 + 2.42916i) q^{28} +(1.26235 - 2.18645i) q^{29} -6.59309i q^{31} +(-0.500000 - 0.866025i) q^{32} +5.75297i q^{34} +(-5.10829 - 3.63924i) q^{35} +(5.18679 - 8.98379i) q^{37} -7.61611i q^{38} +(2.03420 - 0.928463i) q^{40} +(4.98222 + 2.87649i) q^{41} +(3.67593 - 2.12230i) q^{43} -0.594869i q^{44} +(-4.02317 + 2.32278i) q^{46} +2.89798 q^{47} +(-0.433868 + 0.751482i) q^{49} +(1.63333 + 4.72570i) q^{50} +(2.41604 - 2.67633i) q^{52} -13.8960i q^{53} +(1.32412 + 0.126722i) q^{55} +(-1.40247 - 2.42916i) q^{56} +(1.26235 + 2.18645i) q^{58} +(-8.40299 + 4.85147i) q^{59} +(-3.41309 - 5.91165i) q^{61} +(5.70978 + 3.29654i) q^{62} +1.00000 q^{64} +(5.44256 + 5.94798i) q^{65} +(3.93121 - 6.80906i) q^{67} +(-4.98222 - 2.87649i) q^{68} +(5.70582 - 2.60429i) q^{70} +(1.11257 - 0.642342i) q^{71} -14.5400 q^{73} +(5.18679 + 8.98379i) q^{74} +(6.59574 + 3.80805i) q^{76} -1.66858i q^{77} -1.83150 q^{79} +(-0.213026 + 2.22590i) q^{80} +(-4.98222 + 2.87649i) q^{82} +4.19184 q^{83} +(7.46410 - 10.4771i) q^{85} +4.24460i q^{86} +(0.515171 + 0.297434i) q^{88} +(5.24333 + 3.02724i) q^{89} +(6.77687 - 7.50697i) q^{91} -4.64555i q^{92} +(-1.44899 + 2.50973i) q^{94} +(-9.88140 + 13.8702i) q^{95} +(8.45318 + 14.6413i) q^{97} +(-0.433868 - 0.751482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more