LMFDB - Embedded newform 1520.2.bq.r.1471.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(31,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("1520.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.bq (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:	$12.1372611072$
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} + 15x^{10} + 177x^{8} + 718x^{6} + 2289x^{4} + 48x^{2} + 1 $ x^12 + 15x^10 + 177x^8 + 718x^6 + 2289x^4 + 48*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1471.6
Root			$-1.61160 - 2.79137i$ of defining polynomial
Character	$\chi$	$=$	1520.1471
Dual form			1520.2.bq.r.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61160 - 2.79137i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.62482i q^{7} +(-3.69449 - 6.39905i) q^{9} +O(q^{10})$	\(q+(1.61160 - 2.79137i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.62482i q^{7} +(-3.69449 - 6.39905i) q^{9} +5.58274i q^{11} +(-1.50000 + 0.866025i) q^{13} +(-1.61160 - 2.79137i) q^{15} +(3.19449 - 5.53303i) q^{17} +(-3.69496 + 2.31241i) q^{19} +(-12.9096 - 7.45335i) q^{21} +(-3.53984 + 2.04373i) q^{23} +(-0.500000 - 0.866025i) q^{25} -14.1466 q^{27} +(4.82611 - 2.78635i) q^{29} +3.53345 q^{31} +(15.5835 + 8.99713i) q^{33} +(-4.00521 - 2.31241i) q^{35} -2.10860i q^{37} +5.58274i q^{39} +(-1.82611 - 1.05430i) q^{41} +(8.37463 + 4.83510i) q^{43} -7.38899 q^{45} +(5.66437 - 3.27033i) q^{47} -14.3890 q^{49} +(-10.2965 - 17.8340i) q^{51} +(3.58348 - 2.06892i) q^{53} +(4.83479 + 2.79137i) q^{55} +(0.500000 + 14.0407i) q^{57} +(-6.91816 + 11.9826i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-29.5945 + 17.0864i) q^{63} +1.73205i q^{65} +(-3.22320 - 5.58274i) q^{67} +13.1747i q^{69} +(5.46169 - 9.45992i) q^{71} +(-0.694494 + 1.20290i) q^{73} -3.22320 q^{75} +25.8192 q^{77} +(0.310251 - 0.537371i) q^{79} +(-11.7151 + 20.2911i) q^{81} +5.04537i q^{83} +(-3.19449 - 5.53303i) q^{85} -17.9619i q^{87} +(9.00000 - 5.19615i) q^{89} +(4.00521 + 6.93723i) q^{91} +(5.69449 - 9.86315i) q^{93} +(0.155126 + 4.35614i) q^{95} +(0.326105 + 0.188277i) q^{97} +(35.7242 - 20.6254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 12 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 - 12 * q^9	$ 12 q + 6 q^{5} - 12 q^{9} - 18 q^{13} + 6 q^{17} - 24 q^{21} - 6 q^{25} + 24 q^{29} + 90 q^{33} + 12 q^{41} - 24 q^{45} - 108 q^{49} - 54 q^{53} + 6 q^{57} - 6 q^{61} + 24 q^{73} + 48 q^{77} - 42 q^{81} - 6 q^{85} + 108 q^{89} + 36 q^{93} - 30 q^{97}+O(q^{100}) $ 12 * q + 6 * q^5 - 12 * q^9 - 18 * q^13 + 6 * q^17 - 24 * q^21 - 6 * q^25 + 24 * q^29 + 90 * q^33 + 12 * q^41 - 24 * q^45 - 108 * q^49 - 54 * q^53 + 6 * q^57 - 6 * q^61 + 24 * q^73 + 48 * q^77 - 42 * q^81 - 6 * q^85 + 108 * q^89 + 36 * q^93 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.61160	−	2.79137i	0.930456	−	1.61160i	0.147914	−	0.989000i	$-0.452744\pi$
$3$	1.61160	−	2.79137i	0.930456	−	1.61160i	0.782542	−	0.622598i	$-0.213923\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		−	4.62482i		−	1.74802i	−0.485909	−	0.874009i	$-0.661511\pi$
$7$		−	4.62482i		−	1.74802i	0.485909	−	0.874009i	$-0.338489\pi$
$8$		0			0
$9$	−3.69449	−	6.39905i	−1.23150	−	2.13302i
$10$		0			0
$11$			5.58274i			1.68326i	0.540055	+	0.841629i	$0.318403\pi$
$11$			5.58274i			1.68326i	−0.540055	+	0.841629i	$0.681597\pi$
$12$		0			0
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−1.61160	−	2.79137i	−0.416113	−	0.720728i
$16$		0			0
$17$	3.19449	−	5.53303i	0.774779	−	1.34196i	−0.160140	−	0.987094i	$-0.551195\pi$
$17$	3.19449	−	5.53303i	0.774779	−	1.34196i	0.934919	−	0.354862i	$-0.115472\pi$
$18$		0			0
$19$	−3.69496	+	2.31241i	−0.847683	+	0.530504i
$19$	−3.69496	+	2.31241i	−0.847683	+	0.530504i
$20$		0			0
$21$	−12.9096	−	7.45335i	−2.81710	−	1.62646i
$22$		0			0
$23$	−3.53984	+	2.04373i	−0.738107	+	0.426146i	−0.821381	−	0.570380i	$-0.806796\pi$
$23$	−3.53984	+	2.04373i	−0.738107	+	0.426146i	0.0832735	+	0.996527i	$0.473462\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−14.1466			−2.72251
$28$		0			0
$29$	4.82611	−	2.78635i	0.896185	−	0.517413i	0.0202247	−	0.999795i	$-0.493562\pi$
$29$	4.82611	−	2.78635i	0.896185	−	0.517413i	0.875961	+	0.482383i	$0.160229\pi$
$30$		0			0
$31$	3.53345			0.634626			0.317313	−	0.948321i	$-0.397219\pi$
$31$	3.53345			0.634626			0.317313	+	0.948321i	$0.397219\pi$
$32$		0			0
$33$	15.5835	+	8.99713i	2.71274	+	1.56620i
$34$		0			0
$35$	−4.00521	−	2.31241i	−0.677005	−	0.390869i
$36$		0			0
$37$		−	2.10860i		−	0.346652i	−0.984864	−	0.173326i	$-0.944548\pi$
$37$		−	2.10860i		−	0.346652i	0.984864	−	0.173326i	$-0.0554515\pi$
$38$		0			0
$39$			5.58274i			0.893954i
$40$		0			0
$41$	−1.82611	−	1.05430i	−0.285190	−	0.164654i	0.350581	−	0.936532i	$-0.385984\pi$
$41$	−1.82611	−	1.05430i	−0.285190	−	0.164654i	−0.635771	+	0.771878i	$0.719318\pi$
$42$		0			0
$43$	8.37463	+	4.83510i	1.27712	+	0.737345i	0.976318	−	0.216342i	$-0.0694125\pi$
$43$	8.37463	+	4.83510i	1.27712	+	0.737345i	0.300801	+	0.953687i	$0.402746\pi$
$44$		0			0
$45$	−7.38899			−1.10149
$46$		0			0
$47$	5.66437	−	3.27033i	0.826234	−	0.477026i	−0.0263278	−	0.999653i	$-0.508381\pi$
$47$	5.66437	−	3.27033i	0.826234	−	0.477026i	0.852561	+	0.522627i	$0.175048\pi$
$48$		0			0
$49$	−14.3890			−2.05557
$50$		0			0
$51$	−10.2965	−	17.8340i	−1.44180	−	2.49726i
$52$		0			0
$53$	3.58348	−	2.06892i	0.492229	−	0.284189i	−0.233270	−	0.972412i	$-0.574942\pi$
$53$	3.58348	−	2.06892i	0.492229	−	0.284189i	0.725499	+	0.688223i	$0.241609\pi$
$54$		0			0
$55$	4.83479	+	2.79137i	0.651923	+	0.376388i
$56$		0			0
$57$	0.500000	+	14.0407i	0.0662266	+	1.85973i
$58$		0			0
$59$	−6.91816	+	11.9826i	−0.900668	+	1.56000i	−0.0740380	+	0.997255i	$0.523589\pi$
$59$	−6.91816	+	11.9826i	−0.900668	+	1.56000i	−0.826630	+	0.562747i	$0.809745\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−29.5945	+	17.0864i	−3.72855	+	2.15268i
$64$		0			0
$65$			1.73205i			0.214834i
$66$		0			0
$67$	−3.22320	−	5.58274i	−0.393776	−	0.682040i	0.599168	−	0.800623i	$-0.295498\pi$
$67$	−3.22320	−	5.58274i	−0.393776	−	0.682040i	−0.992944	+	0.118583i	$0.962165\pi$
$68$		0			0
$69$			13.1747i			1.58604i
$70$		0			0
$71$	5.46169	−	9.45992i	0.648183	−	1.12269i	−0.335374	−	0.942085i	$-0.608863\pi$
$71$	5.46169	−	9.45992i	0.648183	−	1.12269i	0.983557	−	0.180601i	$-0.0578041\pi$
$72$		0			0
$73$	−0.694494	+	1.20290i	−0.0812844	+	0.140789i	−0.903802	−	0.427951i	$-0.859236\pi$
$73$	−0.694494	+	1.20290i	−0.0812844	+	0.140789i	0.822517	+	0.568740i	$0.192569\pi$
$74$		0			0
$75$	−3.22320			−0.372183
$76$		0			0
$77$	25.8192			2.94237
$78$		0			0
$79$	0.310251	−	0.537371i	0.0349060	−	0.0604589i	−0.848045	−	0.529925i	$-0.822220\pi$
$79$	0.310251	−	0.537371i	0.0349060	−	0.0604589i	0.882951	+	0.469466i	$0.155553\pi$
$80$		0			0
$81$	−11.7151	+	20.2911i	−1.30168	+	2.25457i
$82$		0			0
$83$			5.04537i			0.553801i	0.960899	+	0.276901i	$0.0893072\pi$
$83$			5.04537i			0.553801i	−0.960899	+	0.276901i	$0.910693\pi$
$84$		0			0
$85$	−3.19449	−	5.53303i	−0.346492	−	0.600141i
$86$		0			0
$87$		−	17.9619i		−	1.92572i
$88$		0			0
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.0596775	−	0.998218i	$-0.480993\pi$
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.894321	+	0.447427i	$0.147659\pi$
$90$		0			0
$91$	4.00521	+	6.93723i	0.419861	+	0.727220i
$92$		0			0
$93$	5.69449	−	9.86315i	0.590492	−	1.02276i
$94$		0			0
$95$	0.155126	+	4.35614i	0.0159155	+	0.446930i
$96$		0			0
$97$	0.326105	+	0.188277i	0.0331110	+	0.0191166i	0.516464	−	0.856309i	$-0.327248\pi$
$97$	0.326105	+	0.188277i	0.0331110	+	0.0191166i	−0.483353	+	0.875425i	$0.660581\pi$
$98$		0			0
$99$	35.7242	−	20.6254i	3.59042	−	2.07293i
$100$		0			0
$101$	−0.194494	−	0.336874i	−0.0193529	−	0.0335202i	0.856187	−	0.516666i	$-0.172827\pi$
$101$	−0.194494	−	0.336874i	−0.0193529	−	0.0335202i	−0.875540	+	0.483146i	$0.839494\pi$
$102$		0			0
$103$	−1.87429			−0.184679			−0.0923396	−	0.995728i	$-0.529435\pi$
$103$	−1.87429			−0.184679			−0.0923396	+	0.995728i	$0.529435\pi$
$104$		0			0
$105$	−12.9096	+	7.45335i	−1.25985	+	0.727373i
$106$		0			0
$107$	14.7671			1.42759			0.713793	−	0.700356i	$-0.246976\pi$
$107$	14.7671			1.42759			0.713793	+	0.700356i	$0.246976\pi$
$108$		0			0
$109$	8.40959	+	4.85528i	0.805492	+	0.465051i	0.845388	−	0.534153i	$-0.179369\pi$
$109$	8.40959	+	4.85528i	0.805492	+	0.465051i	−0.0398956	+	0.999204i	$0.512703\pi$
$110$		0			0
$111$	−5.88589	−	3.39822i	−0.558664	−	0.322545i
$112$		0			0
$113$			3.84066i			0.361298i	0.983548	+	0.180649i	$0.0578199\pi$
$113$			3.84066i			0.361298i	−0.983548	+	0.180649i	$0.942180\pi$
$114$		0			0
$115$			4.08745i			0.381157i
$116$		0			0
$117$	11.0835	+	6.39905i	1.02467	+	0.591593i
$118$		0			0
$119$	−25.5893	−	14.7740i	−2.34576	−	1.35433i
$120$		0			0
$121$	−20.1670			−1.83336
$122$		0			0
$123$	−5.88589	+	3.39822i	−0.530713	+	0.306407i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−3.22320	−	5.58274i	−0.286012	−	0.495388i	0.686842	−	0.726807i	$-0.258997\pi$
$127$	−3.22320	−	5.58274i	−0.286012	−	0.495388i	−0.972854	+	0.231419i	$0.925663\pi$
$128$		0			0
$129$	26.9931	−	15.5845i	2.37661	−	1.37213i
$130$		0			0
$131$	−4.00521	−	2.31241i	−0.349937	−	0.202036i	0.314720	−	0.949184i	$-0.398089\pi$
$131$	−4.00521	−	2.31241i	−0.349937	−	0.202036i	−0.664658	+	0.747148i	$0.731423\pi$
$132$		0			0
$133$	10.6945	+	17.0886i	0.927330	+	1.48177i
$134$		0			0
$135$	−7.07328	+	12.2513i	−0.608771	+	1.05442i
$136$		0			0
$137$	−1.36839	−	2.37012i	−0.116909	−	0.202493i	0.801632	−	0.597818i	$-0.203965\pi$
$137$	−1.36839	−	2.37012i	−0.116909	−	0.202493i	−0.918541	+	0.395325i	$0.870632\pi$
$138$		0			0
$139$	−11.4299	+	6.59907i	−0.969473	+	0.559726i	−0.899076	−	0.437794i	$-0.855760\pi$
$139$	−11.4299	+	6.59907i	−0.969473	+	0.559726i	−0.0703975	+	0.997519i	$0.522427\pi$
$140$		0			0
$141$		−	21.0818i		−	1.77541i
$142$		0			0
$143$	−4.83479	−	8.37411i	−0.404306	−	0.700278i
$144$		0			0
$145$		−	5.57271i		−	0.462788i
$146$		0			0
$147$	−23.1893	+	40.1650i	−1.91262	+	3.31275i
$148$		0			0
$149$	8.08348	−	14.0010i	0.662225	−	1.14701i	−0.317805	−	0.948156i	$-0.602946\pi$
$149$	8.08348	−	14.0010i	0.662225	−	1.14701i	0.980030	−	0.198851i	$-0.0637209\pi$
$150$		0			0
$151$	−13.9314			−1.13372			−0.566862	−	0.823813i	$-0.691843\pi$
$151$	−13.9314			−1.13372			−0.566862	+	0.823813i	$0.691843\pi$
$152$		0			0
$153$	−47.2082			−3.81655
$154$		0			0
$155$	1.76672	−	3.06005i	0.141907	−	0.245789i
$156$		0			0
$157$	7.90959	−	13.6998i	0.631254	−	1.09336i	−0.356042	−	0.934470i	$-0.615874\pi$
$157$	7.90959	−	13.6998i	0.631254	−	1.09336i	0.987296	−	0.158894i	$-0.0507927\pi$
$158$		0			0
$159$		−	13.3371i		−	1.05770i
$160$		0			0
$161$	9.45187	+	16.3711i	0.744912	+	1.29023i
$162$		0			0
$163$		−	6.12011i		−	0.479364i	−0.970851	−	0.239682i	$-0.922957\pi$
$163$		−	6.12011i		−	0.479364i	0.970851	−	0.239682i	$-0.0770432\pi$
$164$		0			0
$165$	15.5835	−	8.99713i	1.21317	−	0.700425i
$166$		0			0
$167$	1.09227	+	1.89187i	0.0845224	+	0.146397i	0.905188	−	0.425012i	$-0.139730\pi$
$167$	1.09227	+	1.89187i	0.0845224	+	0.146397i	−0.820665	+	0.571409i	$0.806397\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$	28.4483	+	15.1011i	2.17549	+	1.15481i
$172$		0			0
$173$	−17.3409	−	10.0118i	−1.31840	−	0.761179i	−0.334930	−	0.942243i	$-0.608713\pi$
$173$	−17.3409	−	10.0118i	−1.31840	−	0.761179i	−0.983471	+	0.181064i	$0.942046\pi$
$174$		0			0
$175$	−4.00521	+	2.31241i	−0.302766	+	0.174802i
$176$		0			0
$177$	22.2986	+	38.6223i	1.67606	+	2.90303i
$178$		0			0
$179$	−1.25379			−0.0937124			−0.0468562	−	0.998902i	$-0.514920\pi$
$179$	−1.25379			−0.0937124			−0.0468562	+	0.998902i	$0.514920\pi$
$180$		0			0
$181$	10.5000	−	6.06218i	0.780459	−	0.450598i	−0.0561340	−	0.998423i	$-0.517877\pi$
$181$	10.5000	−	6.06218i	0.780459	−	0.450598i	0.836593	+	0.547825i	$0.184544\pi$
$182$		0			0
$183$	−3.22320			−0.238265
$184$		0			0
$185$	−1.82611	−	1.05430i	−0.134258	−	0.0775139i
$186$		0			0
$187$	30.8894	+	17.8340i	2.25886	+	1.30415i
$188$		0			0
$189$			65.4254i			4.75900i
$190$		0			0
$191$		−	6.25907i		−	0.452891i	−0.974024	−	0.226445i	$-0.927290\pi$
$191$		−	6.25907i		−	0.452891i	0.974024	−	0.226445i	$-0.0727105\pi$
$192$		0			0
$193$	16.2357	+	9.37368i	1.16867	+	0.674732i	0.953367	−	0.301815i	$-0.0975924\pi$
$193$	16.2357	+	9.37368i	1.16867	+	0.674732i	0.215304	+	0.976547i	$0.430926\pi$
$194$		0			0
$195$	4.83479	+	2.79137i	0.346227	+	0.199894i
$196$		0			0
$197$	−22.4302			−1.59808			−0.799042	−	0.601275i	$-0.794660\pi$
$197$	−22.4302			−1.59808			−0.799042	+	0.601275i	$0.794660\pi$
$198$		0			0
$199$	2.02336	−	1.16819i	0.143432	−	0.0828106i	−0.426567	−	0.904456i	$-0.640277\pi$
$199$	2.02336	−	1.16819i	0.143432	−	0.0828106i	0.569999	+	0.821646i	$0.306944\pi$
$200$		0			0
$201$	−20.7780			−1.46557
$202$		0			0
$203$	−12.8864	−	22.3199i	−0.904447	−	1.56655i
$204$		0			0
$205$	−1.82611	+	1.05430i	−0.127541	+	0.0736357i
$206$		0			0
$207$	26.1558	+	15.1011i	1.81796	+	1.04960i
$208$		0			0
$209$	−12.9096	−	20.6280i	−0.892975	−	1.42687i
$210$		0			0
$211$	−7.06689	+	12.2402i	−0.486505	+	0.842651i	−0.999880	−	0.0155132i	$-0.995062\pi$
$211$	−7.06689	+	12.2402i	−0.486505	+	0.842651i	0.513375	+	0.858165i	$0.328395\pi$
$212$		0			0
$213$	−17.6041	−	30.4912i	−1.20621	−	2.08922i
$214$		0			0
$215$	8.37463	−	4.83510i	0.571145	−	0.329751i
$216$		0			0
$217$		−	16.3416i		−	1.10934i
$218$		0			0
$219$	2.23849	+	3.87718i	0.151263	+	0.261996i
$220$		0			0
$221$			11.0661i			0.744383i
$222$		0			0
$223$	−5.77833	+	10.0084i	−0.386946	+	0.670209i	−0.992037	−	0.125947i	$-0.959803\pi$
$223$	−5.77833	+	10.0084i	−0.386946	+	0.670209i	0.605092	+	0.796156i	$0.293137\pi$
$224$		0			0
$225$	−3.69449	+	6.39905i	−0.246300	+	0.426603i
$226$		0			0
$227$	5.82589			0.386678			0.193339	−	0.981132i	$-0.438068\pi$
$227$	5.82589			0.386678			0.193339	+	0.981132i	$0.438068\pi$
$228$		0			0
$229$	8.12577			0.536966			0.268483	−	0.963284i	$-0.413478\pi$
$229$	8.12577			0.536966			0.268483	+	0.963284i	$0.413478\pi$
$230$		0			0
$231$	41.6101	−	72.0709i	2.73775	−	4.74191i
$232$		0			0
$233$	9.52060	−	16.4902i	0.623715	−	1.08031i	−0.365073	−	0.930979i	$-0.618956\pi$
$233$	9.52060	−	16.4902i	0.623715	−	1.08031i	0.988788	−	0.149327i	$-0.0477108\pi$
$234$		0			0
$235$		−	6.54065i		−	0.426665i
$236$		0			0
$237$	−1.00000	−	1.73205i	−0.0649570	−	0.112509i
$238$		0			0
$239$		−	2.28845i		−	0.148027i	−0.997257	−	0.0740137i	$-0.976419\pi$
$239$		−	2.28845i		−	0.148027i	0.997257	−	0.0740137i	$-0.0235809\pi$
$240$		0			0
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	−0.680640	−	0.732618i	$-0.738298\pi$
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	0.294146	+	0.955761i	$0.404965\pi$
$242$		0			0
$243$	16.5402	+	28.6484i	1.06105	+	1.83780i
$244$		0			0
$245$	−7.19449	+	12.4612i	−0.459639	+	0.796119i
$246$		0			0
$247$	3.53984	−	6.66855i	0.225234	−	0.424310i
$248$		0			0
$249$	14.0835	+	8.13110i	0.892504	+	0.515288i
$250$		0			0
$251$	−4.83479	+	2.79137i	−0.305169	+	0.176190i	−0.644763	−	0.764383i	$-0.723044\pi$
$251$	−4.83479	+	2.79137i	−0.305169	+	0.176190i	0.339593	+	0.940572i	$0.389711\pi$
$252$		0			0
$253$	−11.4096	−	19.7620i	−0.717315	−	1.24243i
$254$		0			0
$255$	−20.5930			−1.28958
$256$		0			0
$257$	5.67389	−	3.27582i	0.353928	−	0.204340i	−0.312486	−	0.949922i	$-0.601162\pi$
$257$	5.67389	−	3.27582i	0.353928	−	0.204340i	0.666414	+	0.745582i	$0.267828\pi$
$258$		0			0
$259$	−9.75192			−0.605955
$260$		0			0
$261$	−35.6600	−	20.5883i	−2.20730	−	1.27439i
$262$		0			0
$263$	20.9983	+	12.1234i	1.29481	+	0.747560i	0.979503	−	0.201429i	$-0.0645584\pi$
$263$	20.9983	+	12.1234i	1.29481	+	0.747560i	0.315309	+	0.948989i	$0.397892\pi$
$264$		0			0
$265$		−	4.13785i		−	0.254186i
$266$		0			0
$267$		−	33.4964i		−	2.04995i
$268$		0			0
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	0.453574	−	0.891219i	$-0.350149\pi$
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	−0.545031	+	0.838416i	$0.683482\pi$
$270$		0			0
$271$	19.5607	+	11.2934i	1.18823	+	0.686024i	0.957903	−	0.287090i	$-0.0926880\pi$
$271$	19.5607	+	11.2934i	1.18823	+	0.686024i	0.230324	+	0.973114i	$0.426021\pi$
$272$		0			0
$273$	25.8192			1.56265
$274$		0			0
$275$	4.83479	−	2.79137i	0.291549	−	0.168326i
$276$		0			0
$277$	8.77798			0.527418			0.263709	−	0.964602i	$-0.415054\pi$
$277$	8.77798			0.527418			0.263709	+	0.964602i	$0.415054\pi$
$278$		0			0
$279$	−13.0543	−	22.6107i	−0.781540	−	1.35367i
$280$		0			0
$281$	−15.2574	+	8.80885i	−0.910179	+	0.525492i	−0.880489	−	0.474067i	$-0.842785\pi$
$281$	−15.2574	+	8.80885i	−0.910179	+	0.525492i	−0.0296902	+	0.999559i	$0.509452\pi$
$282$		0			0
$283$	−3.05529	−	1.76397i	−0.181618	−	0.104857i	0.406435	−	0.913680i	$-0.366772\pi$
$283$	−3.05529	−	1.76397i	−0.181618	−	0.104857i	−0.588053	+	0.808823i	$0.700105\pi$
$284$		0			0
$285$	12.4096	+	6.58733i	0.735081	+	0.390200i
$286$		0			0
$287$	−4.87596	+	8.44541i	−0.287819	+	0.498517i
$288$		0			0
$289$	−11.9096	−	20.6280i	−0.700564	−	1.21341i
$290$		0			0
$291$	1.05110	−	0.606854i	0.0616166	−	0.0355744i
$292$		0			0
$293$		−	23.1904i		−	1.35480i	−0.735616	−	0.677399i	$-0.763107\pi$
$293$		−	23.1904i		−	1.35480i	0.735616	−	0.677399i	$-0.236893\pi$
$294$		0			0
$295$	6.91816	+	11.9826i	0.402791	+	0.697654i
$296$		0			0
$297$		−	78.9766i		−	4.58269i
$298$		0			0
$299$	3.53984	−	6.13118i	0.204714	−	0.354575i
$300$		0			0
$301$	22.3615	−	38.7312i	1.28889	−	2.23243i
$302$		0			0
$303$	−1.25379			−0.0720282
$304$		0			0
$305$	−1.00000			−0.0572598
$306$		0			0
$307$	2.96050	−	5.12774i	0.168965	−	0.292656i	−0.769091	−	0.639139i	$-0.779291\pi$
$307$	2.96050	−	5.12774i	0.168965	−	0.292656i	0.938056	+	0.346483i	$0.112624\pi$
$308$		0			0
$309$	−3.02060	+	5.23183i	−0.171836	+	0.297629i
$310$		0			0
$311$		−	5.46591i		−	0.309943i	−0.987919	−	0.154972i	$-0.950471\pi$
$311$		−	5.46591i		−	0.309943i	0.987919	−	0.154972i	$-0.0495286\pi$
$312$		0			0
$313$	9.34670	+	16.1890i	0.528307	+	0.915055i	0.999455	+	0.0330006i	$0.0105063\pi$
$313$	9.34670	+	16.1890i	0.528307	+	0.915055i	−0.471148	+	0.882054i	$0.656160\pi$
$314$		0			0
$315$			34.1728i			1.92542i
$316$		0			0
$317$	1.24262	−	0.717428i	0.0697926	−	0.0402948i	−0.464698	−	0.885469i	$-0.653837\pi$
$317$	1.24262	−	0.717428i	0.0697926	−	0.0402948i	0.534490	+	0.845175i	$0.320504\pi$
$318$		0			0
$319$	15.5555	+	26.9429i	0.870940	+	1.50851i
$320$		0			0
$321$	23.7986	−	41.2203i	1.32831	−	2.30070i
$322$		0			0
$323$	0.991095	+	27.8313i	0.0551460	+	1.54858i
$324$		0			0
$325$	1.50000	+	0.866025i	0.0832050	+	0.0480384i
$326$		0			0
$327$	27.1057	−	15.6495i	1.49895	−	0.865420i
$328$		0			0
$329$	−15.1247	−	26.1967i	−0.833851	−	1.44427i
$330$		0			0
$331$	34.2141			1.88058			0.940290	−	0.340375i	$-0.110554\pi$
$331$	34.2141			1.88058			0.940290	+	0.340375i	$0.110554\pi$
$332$		0			0
$333$	−13.4931	+	7.79023i	−0.739416	+	0.426902i
$334$		0			0
$335$	−6.44639			−0.352204
$336$		0			0
$337$	−7.16697	−	4.13785i	−0.390410	−	0.225403i	0.291928	−	0.956440i	$-0.405703\pi$
$337$	−7.16697	−	4.13785i	−0.390410	−	0.225403i	−0.682338	+	0.731037i	$0.739037\pi$
$338$		0			0
$339$	10.7207	+	6.18959i	0.582268	+	0.336172i
$340$		0			0
$341$			19.7263i			1.06824i
$342$		0			0
$343$			34.1728i			1.84516i
$344$		0			0
$345$	11.4096	+	6.58733i	0.614272	+	0.354650i
$346$		0			0
$347$	−6.71547	−	3.87718i	−0.360505	−	0.208138i	0.308797	−	0.951128i	$-0.400074\pi$
$347$	−6.71547	−	3.87718i	−0.360505	−	0.208138i	−0.669302	+	0.742990i	$0.733407\pi$
$348$		0			0
$349$	27.8192			1.48913			0.744563	−	0.667552i	$-0.232658\pi$
$349$	27.8192			1.48913			0.744563	+	0.667552i	$0.232658\pi$
$350$		0			0
$351$	21.2199	−	12.2513i	1.13263	−	0.653925i
$352$		0			0
$353$	−5.61101			−0.298644			−0.149322	−	0.988789i	$-0.547709\pi$
$353$	−5.61101			−0.298644			−0.149322	+	0.988789i	$0.547709\pi$
$354$		0			0
$355$	−5.46169	−	9.45992i	−0.289876	−	0.502080i
$356$		0			0
$357$	−82.4792	+	47.6194i	−4.36526	+	2.52029i
$358$		0			0
$359$	6.23092	+	3.59743i	0.328856	+	0.189865i	0.655333	−	0.755340i	$-0.272528\pi$
$359$	6.23092	+	3.59743i	0.328856	+	0.189865i	−0.326477	+	0.945205i	$0.605862\pi$
$360$		0			0
$361$	8.30551	−	17.0886i	0.437132	−	0.899397i
$362$		0			0
$363$	−32.5010	+	56.2934i	−1.70586	+	2.95464i
$364$		0			0
$365$	0.694494	+	1.20290i	0.0363515	+	0.0629626i
$366$		0			0
$367$	−26.5200	+	15.3113i	−1.38433	+	0.799246i	−0.992669	−	0.120862i	$-0.961434\pi$
$367$	−26.5200	+	15.3113i	−1.38433	+	0.799246i	−0.391665	+	0.920108i	$0.628101\pi$
$368$		0			0
$369$			15.5805i			0.811086i
$370$		0			0
$371$	−9.56841	−	16.5730i	−0.496767	−	0.860426i
$372$		0			0
$373$			35.3068i			1.82811i	0.405585	+	0.914057i	$0.367068\pi$
$373$			35.3068i			1.82811i	−0.405585	+	0.914057i	$0.632932\pi$
$374$		0			0
$375$	−1.61160	+	2.79137i	−0.0832225	+	0.144146i
$376$		0			0
$377$	−4.82611	+	8.35906i	−0.248557	+	0.430513i
$378$		0			0
$379$	29.6420			1.52261			0.761305	−	0.648394i	$-0.224559\pi$
$379$	29.6420			1.52261			0.761305	+	0.648394i	$0.224559\pi$
$380$		0			0
$381$	−20.7780			−1.06449
$382$		0			0
$383$	−5.46169	+	9.45992i	−0.279079	+	0.483379i	−0.971156	−	0.238444i	$-0.923363\pi$
$383$	−5.46169	+	9.45992i	−0.279079	+	0.483379i	0.692077	+	0.721824i	$0.256696\pi$
$384$		0			0
$385$	12.9096	−	22.3601i	0.657934	−	1.13957i
$386$		0			0
$387$		−	71.4529i		−	3.63216i
$388$		0			0
$389$	−2.28491	−	3.95757i	−0.115849	−	0.200657i	0.802270	−	0.596962i	$-0.203626\pi$
$389$	−2.28491	−	3.95757i	−0.115849	−	0.200657i	−0.918119	+	0.396305i	$0.870292\pi$
$390$		0			0
$391$			26.1147i			1.32068i
$392$		0			0
$393$	−12.9096	+	7.45335i	−0.651203	+	0.375972i
$394$		0			0
$395$	−0.310251	−	0.537371i	−0.0156104	−	0.0270381i
$396$		0			0
$397$	−5.82611	+	10.0911i	−0.292404	+	0.506458i	−0.974378	−	0.224918i	$-0.927788\pi$
$397$	−5.82611	+	10.0911i	−0.292404	+	0.506458i	0.681974	+	0.731377i	$0.261122\pi$
$398$		0			0
$399$	64.9357	−	2.31241i	3.25085	−	0.115765i
$400$		0			0
$401$	21.5766	+	12.4572i	1.07748	+	0.622084i	0.930216	−	0.367013i	$-0.119619\pi$
$401$	21.5766	+	12.4572i	1.07748	+	0.622084i	0.147266	+	0.989097i	$0.452953\pi$
$402$		0			0
$403$	−5.30017	+	3.06005i	−0.264020	+	0.152432i
$404$		0			0
$405$	11.7151	+	20.2911i	0.582128	+	1.00827i
$406$		0			0
$407$	11.7718			0.583506
$408$		0			0
$409$	26.0835	−	15.0593i	1.28975	−	0.744635i	0.311137	−	0.950365i	$-0.399290\pi$
$409$	26.0835	−	15.0593i	1.28975	−	0.744635i	0.978609	+	0.205730i	$0.0659570\pi$
$410$		0			0
$411$	−8.82117			−0.435116
$412$		0			0
$413$	55.4174	+	31.9953i	2.72691	+	1.57438i
$414$		0			0
$415$	4.36942	+	2.52268i	0.214486	+	0.123834i
$416$		0			0
$417$			42.5402i			2.08320i
$418$		0			0
$419$			26.5352i			1.29633i	0.761500	+	0.648165i	$0.224463\pi$
$419$			26.5352i			1.29633i	−0.761500	+	0.648165i	$0.775537\pi$
$420$		0			0
$421$	16.4931	+	9.52228i	0.803823	+	0.464087i	0.844806	−	0.535072i	$-0.179716\pi$
$421$	16.4931	+	9.52228i	0.803823	+	0.464087i	−0.0409831	+	0.999160i	$0.513049\pi$
$422$		0			0
$423$	−41.8540	−	24.1644i	−2.03501	−	1.17491i
$424$		0			0
$425$	−6.38899			−0.309911
$426$		0			0
$427$	−4.00521	+	2.31241i	−0.193826	+	0.111905i
$428$		0			0
$429$	−31.1670			−1.50476
$430$		0			0
$431$	−5.66437	−	9.81098i	−0.272843	−	0.472578i	0.696746	−	0.717318i	$-0.254631\pi$
$431$	−5.66437	−	9.81098i	−0.272843	−	0.472578i	−0.969589	+	0.244740i	$0.921297\pi$
$432$		0			0
$433$	15.8409	−	9.14573i	0.761263	−	0.439516i	−0.0684859	−	0.997652i	$-0.521817\pi$
$433$	15.8409	−	9.14573i	0.761263	−	0.439516i	0.829749	+	0.558137i	$0.188483\pi$
$434$		0			0
$435$	−15.5555	−	8.98096i	−0.745828	−	0.430604i
$436$		0			0
$437$	8.35363	−	15.7371i	0.399608	−	0.752805i
$438$		0			0
$439$	17.3222	−	30.0029i	0.826744	−	1.43196i	−0.0738357	−	0.997270i	$-0.523524\pi$
$439$	17.3222	−	30.0029i	0.826744	−	1.43196i	0.900579	−	0.434692i	$-0.143143\pi$
$440$		0			0
$441$	53.1600	+	92.0759i	2.53143	+	4.38457i
$442$		0			0
$443$	13.6748	−	7.89515i	0.649709	−	0.375110i	−0.138635	−	0.990343i	$-0.544272\pi$
$443$	13.6748	−	7.89515i	0.649709	−	0.375110i	0.788345	+	0.615234i	$0.210938\pi$
$444$		0			0
$445$		−	10.3923i		−	0.492642i
$446$		0			0
$447$	−26.0546	−	45.1280i	−1.23234	−	2.13448i
$448$		0			0
$449$			8.73961i			0.412448i	0.978505	+	0.206224i	$0.0661175\pi$
$449$			8.73961i			0.412448i	−0.978505	+	0.206224i	$0.933882\pi$
$450$		0			0
$451$	5.88589	−	10.1947i	0.277156	−	0.480048i
$452$		0			0
$453$	−22.4519	+	38.8878i	−1.05488	+	1.82711i
$454$		0			0
$455$	8.01043			0.375535
$456$		0			0
$457$	23.9449			1.12010			0.560049	−	0.828460i	$-0.310782\pi$
$457$	23.9449			1.12010			0.560049	+	0.828460i	$0.310782\pi$
$458$		0			0
$459$	−45.1911	+	78.2733i	−2.10934	+	3.65349i
$460$		0			0
$461$	−1.56288	+	2.70699i	−0.0727907	+	0.126077i	−0.900123	−	0.435635i	$-0.856524\pi$
$461$	−1.56288	+	2.70699i	−0.0727907	+	0.126077i	0.827333	+	0.561712i	$0.189857\pi$
$462$		0			0
$463$			10.3465i			0.480844i	0.970668	+	0.240422i	$0.0772858\pi$
$463$			10.3465i			0.480844i	−0.970668	+	0.240422i	$0.922714\pi$
$464$		0			0
$465$	−5.69449	−	9.86315i	−0.264076	−	0.457393i
$466$		0			0
$467$		−	5.30116i		−	0.245308i	−0.992449	−	0.122654i	$-0.960859\pi$
$467$		−	5.30116i		−	0.245308i	0.992449	−	0.122654i	$-0.0391406\pi$
$468$		0			0
$469$	−25.8192	+	14.9067i	−1.19222	+	0.688328i
$470$		0			0
$471$	−25.4941	−	44.1572i	−1.17471	−	2.03465i
$472$		0			0
$473$	−26.9931	+	46.7534i	−1.24114	+	2.14972i
$474$		0			0
$475$	3.85009	+	2.04373i	0.176654	+	0.0937726i
$476$		0			0
$477$	−26.4783	−	15.2873i	−1.21236	−	0.699956i
$478$		0			0
$479$	3.05529	−	1.76397i	0.139600	−	0.0805979i	−0.428574	−	0.903507i	$-0.640984\pi$
$479$	3.05529	−	1.76397i	0.139600	−	0.0805979i	0.568173	+	0.822909i	$0.307650\pi$
$480$		0			0
$481$	1.82611	+	3.16291i	0.0832632	+	0.144216i
$482$		0			0
$483$	60.9305			2.77243
$484$		0			0
$485$	0.326105	−	0.188277i	0.0148077	−	0.00854922i
$486$		0			0
$487$	−4.15395			−0.188233			−0.0941167	−	0.995561i	$-0.530003\pi$
$487$	−4.15395			−0.188233			−0.0941167	+	0.995561i	$0.530003\pi$
$488$		0			0
$489$	−17.0835	−	9.86315i	−0.772542	−	0.446027i
$490$		0			0
$491$	−9.89111	−	5.71063i	−0.446379	−	0.257717i	0.259920	−	0.965630i	$-0.416304\pi$
$491$	−9.89111	−	5.71063i	−0.446379	−	0.257717i	−0.706300	+	0.707913i	$0.749637\pi$
$492$		0			0
$493$		−	35.6040i		−	1.60352i
$494$		0			0
$495$		−	41.2508i		−	1.85409i
$496$		0			0
$497$	−43.7504	−	25.2593i	−1.96248	−	1.13304i
$498$		0			0
$499$	31.4752	+	18.1722i	1.40902	+	0.813499i	0.995294	−	0.0969015i	$-0.0308932\pi$
$499$	31.4752	+	18.1722i	1.40902	+	0.813499i	0.413728	+	0.910401i	$0.364227\pi$
$500$		0			0
$501$	7.04120			0.314578
$502$		0			0
$503$	−2.24488	+	1.29608i	−0.100094	+	0.0577895i	−0.549212	−	0.835683i	$-0.685072\pi$
$503$	−2.24488	+	1.29608i	−0.100094	+	0.0577895i	0.449117	+	0.893473i	$0.351739\pi$
$504$		0			0
$505$	−0.388989			−0.0173098
$506$		0			0
$507$	16.1160	+	27.9137i	0.715736	+	1.23969i
$508$		0			0
$509$	−11.9313	+	6.88852i	−0.528844	+	0.305328i	−0.740546	−	0.672006i	$-0.765433\pi$
$509$	−11.9313	+	6.88852i	−0.528844	+	0.305328i	0.211701	+	0.977334i	$0.432100\pi$
$510$		0			0
$511$	5.56320	+	3.21191i	0.246101	+	0.142087i
$512$		0			0
$513$	52.2710	−	32.7127i	2.30782	−	1.44430i
$514$		0			0
$515$	−0.937144	+	1.62318i	−0.0412955	+	0.0715259i
$516$		0			0
$517$	18.2574	+	31.6227i	0.802959	+	1.39077i
$518$		0			0
$519$	−55.8930	+	32.2698i	−2.45343	+	1.41649i
$520$		0			0
$521$			21.0818i			0.923611i	0.886981	+	0.461805i	$0.152798\pi$
$521$			21.0818i			0.923611i	−0.886981	+	0.461805i	$0.847202\pi$
$522$		0			0
$523$	−13.5608	−	23.4881i	−0.592974	−	1.02706i	−0.993829	−	0.110920i	$-0.964620\pi$
$523$	−13.5608	−	23.4881i	−0.592974	−	1.02706i	0.400855	−	0.916142i	$-0.368713\pi$
$524$		0			0
$525$			14.9067i			0.650582i
$526$		0			0
$527$	11.2876	−	19.5507i	0.491694	−	0.851640i
$528$		0			0
$529$	−3.14637	+	5.44967i	−0.136799	+	0.236942i
$530$		0			0
$531$	102.236			4.43668
$532$		0			0
$533$	3.65221			0.158195
$534$		0			0
$535$	7.38354	−	12.7887i	0.319218	−	0.552902i
$536$		0			0
$537$	−2.02060	+	3.49978i	−0.0871953	+	0.151027i
$538$		0			0
$539$		−	80.3300i		−	3.46006i
$540$		0			0
$541$	18.7986	+	32.5601i	0.808214	+	1.39987i	0.914100	+	0.405489i	$0.132899\pi$
$541$	18.7986	+	32.5601i	0.808214	+	1.39987i	−0.105886	+	0.994378i	$0.533768\pi$
$542$		0			0
$543$		−	39.0792i		−	1.67705i
$544$		0			0
$545$	8.40959	−	4.85528i	0.360227	−	0.207977i
$546$		0			0
$547$	0.107566	+	0.186309i	0.00459917	+	0.00796600i	0.868316	−	0.496012i	$-0.165203\pi$
$547$	0.107566	+	0.186309i	0.00459917	+	0.00796600i	−0.863717	+	0.503978i	$0.831869\pi$
$548$		0			0
$549$	−3.69449	+	6.39905i	−0.157677	+	0.273105i
$550$		0			0
$551$	−11.3891	+	21.4554i	−0.485191	+	0.914031i
$552$		0			0
$553$	−2.48524	−	1.43486i	−0.105683	−	0.0610163i
$554$		0			0
$555$	−5.88589	+	3.39822i	−0.249842	+	0.144247i
$556$		0			0
$557$	8.02060	+	13.8921i	0.339844	+	0.588627i	0.984403	−	0.175928i	$-0.0562925\pi$
$557$	8.02060	+	13.8921i	0.339844	+	0.588627i	−0.644559	+	0.764554i	$0.722959\pi$
$558$		0			0
$559$	−16.7493			−0.708418
$560$		0			0
$561$	99.5627	−	57.4826i	4.20354	−	2.42692i
$562$		0			0
$563$	−31.8394			−1.34187			−0.670935	−	0.741517i	$-0.734107\pi$
$563$	−31.8394			−1.34187			−0.670935	+	0.741517i	$0.734107\pi$
$564$		0			0
$565$	3.32611	+	1.92033i	0.139930	+	0.0807888i
$566$		0			0
$567$	93.8429	+	54.1802i	3.94103	+	2.27536i
$568$		0			0
$569$		−	44.2642i		−	1.85565i	−0.373013	−	0.927826i	$-0.621675\pi$
$569$		−	44.2642i		−	1.85565i	0.373013	−	0.927826i	$-0.378325\pi$
$570$		0			0
$571$		−	11.2823i		−	0.472150i	−0.971735	−	0.236075i	$-0.924139\pi$
$571$		−	11.2823i		−	0.472150i	0.971735	−	0.236075i	$-0.0758611\pi$
$572$		0			0
$573$	−17.4714	−	10.0871i	−0.729878	−	0.421395i
$574$		0			0
$575$	3.53984	+	2.04373i	0.147621	+	0.0852293i
$576$		0			0
$577$	−40.4714			−1.68485			−0.842423	−	0.538817i	$-0.818871\pi$
$577$	−40.4714			−1.68485			−0.842423	+	0.538817i	$0.818871\pi$
$578$		0			0
$579$	52.3308	−	30.2132i	2.17479	−	1.25562i
$580$		0			0
$581$	23.3339			0.968055
$582$		0			0
$583$	11.5503	+	20.0056i	0.478363	+	0.828549i
$584$		0			0
$585$	11.0835	−	6.39905i	0.458246	−	0.264568i
$586$		0			0
$587$	−11.7941	−	6.80934i	−0.486795	−	0.281051i	0.236449	−	0.971644i	$-0.424017\pi$
$587$	−11.7941	−	6.80934i	−0.486795	−	0.281051i	−0.723244	+	0.690593i	$0.757350\pi$
$588$		0			0
$589$	−13.0560	+	8.17078i	−0.537961	+	0.336671i
$590$		0			0
$591$	−36.1484	+	62.6109i	−1.48695	+	2.57547i
$592$		0			0
$593$	−3.77798	−	6.54365i	−0.155143	−	0.268715i	0.777968	−	0.628304i	$-0.216250\pi$
$593$	−3.77798	−	6.54365i	−0.155143	−	0.268715i	−0.933111	+	0.359588i	$0.882917\pi$
$594$		0			0
$595$	−25.5893	+	14.7740i	−1.04906	+	0.605674i
$596$		0			0
$597$		−	7.53059i		−	0.308207i
$598$		0			0
$599$	5.40168	+	9.35599i	0.220707	+	0.382275i	0.955023	−	0.296533i	$-0.0958303\pi$
$599$	5.40168	+	9.35599i	0.220707	+	0.382275i	−0.734316	+	0.678808i	$0.762497\pi$
$600$		0			0
$601$		−	6.17510i		−	0.251887i	−0.992037	−	0.125944i	$-0.959804\pi$
$601$		−	6.17510i		−	0.251887i	0.992037	−	0.125944i	$-0.0401959\pi$
$602$		0			0
$603$	−23.8162	+	41.2508i	−0.969869	+	1.67986i
$604$		0			0
$605$	−10.0835	+	17.4651i	−0.409952	+	0.710057i
$606$		0			0
$607$	−43.6807			−1.77295			−0.886473	−	0.462781i	$-0.846852\pi$
$607$	−43.6807			−1.77295			−0.886473	+	0.462781i	$0.846852\pi$
$608$		0			0
$609$	−83.0707			−3.36620
$610$		0			0
$611$	−5.66437	+	9.81098i	−0.229156	+	0.396910i
$612$		0			0
$613$	−7.34670	+	12.7249i	−0.296731	+	0.513953i	−0.975386	−	0.220504i	$-0.929230\pi$
$613$	−7.34670	+	12.7249i	−0.296731	+	0.513953i	0.678655	+	0.734457i	$0.262563\pi$
$614$		0			0
$615$			6.79645i			0.274059i
$616$		0			0
$617$	−5.34670	−	9.26076i	−0.215250	−	0.372824i	0.738100	−	0.674692i	$-0.235723\pi$
$617$	−5.34670	−	9.26076i	−0.215250	−	0.372824i	−0.953350	+	0.301867i	$0.902390\pi$
$618$		0			0
$619$			36.3222i			1.45991i	0.683493	+	0.729957i	$0.260460\pi$
$619$			36.3222i			1.45991i	−0.683493	+	0.729957i	$0.739540\pi$
$620$		0			0
$621$	50.0766	−	28.9117i	2.00950	−	1.16019i
$622$		0			0
$623$	−24.0313	−	41.6234i	−0.962793	−	1.66761i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−78.3855	+	2.79137i	−3.13041	+	0.111477i
$628$		0			0
$629$	−11.6670	−	6.73593i	−0.465192	−	0.268579i
$630$		0			0
$631$	−34.6316	+	19.9946i	−1.37866	+	0.795972i	−0.991999	−	0.126249i	$-0.959706\pi$
$631$	−34.6316	+	19.9946i	−1.37866	+	0.795972i	−0.386665	+	0.922220i	$0.626373\pi$
$632$		0			0
$633$	22.7780	+	39.4526i	0.905343	+	1.56810i
$634$		0			0
$635$	−6.44639			−0.255817
$636$		0			0
$637$	21.5835	−	12.4612i	0.855169	−	0.493732i
$638$		0			0
$639$	−80.7127			−3.19294
$640$		0			0
$641$	3.72094	+	2.14828i	0.146968	+	0.0848521i	0.571681	−	0.820476i	$-0.306292\pi$
$641$	3.72094	+	2.14828i	0.146968	+	0.0848521i	−0.424713	+	0.905328i	$0.639625\pi$
$642$		0			0
$643$	12.0156	+	6.93723i	0.473851	+	0.273578i	0.717850	−	0.696198i	$-0.245126\pi$
$643$	12.0156	+	6.93723i	0.473851	+	0.273578i	−0.244000	+	0.969775i	$0.578460\pi$
$644$		0			0
$645$		−	31.1689i		−	1.22727i
$646$		0			0
$647$		−	2.33637i		−	0.0918524i	−0.998945	−	0.0459262i	$-0.985376\pi$
$647$		−	2.33637i		−	0.0918524i	0.998945	−	0.0459262i	$-0.0146239\pi$
$648$		0			0
$649$	−66.8957	−	38.6223i	−2.62589	−	1.51606i
$650$		0			0
$651$	−45.6153	−	26.3360i	−1.78781	−	1.03219i
$652$		0			0
$653$	36.9037			1.44416			0.722078	−	0.691812i	$-0.243187\pi$
$653$	36.9037			1.44416			0.722078	+	0.691812i	$0.243187\pi$
$654$		0			0
$655$	−4.00521	+	2.31241i	−0.156497	+	0.0903534i
$656$		0			0
$657$	10.2632			0.400406
$658$		0			0
$659$	−10.2965	−	17.8340i	−0.401094	−	0.694715i	0.592764	−	0.805376i	$-0.298037\pi$
$659$	−10.2965	−	17.8340i	−0.401094	−	0.694715i	−0.993858	+	0.110661i	$0.964703\pi$
$660$		0			0
$661$	−32.3409	+	18.6720i	−1.25791	+	0.726257i	−0.972669	−	0.232198i	$-0.925408\pi$
$661$	−32.3409	+	18.6720i	−1.25791	+	0.726257i	−0.285245	+	0.958455i	$0.592075\pi$
$662$		0			0
$663$	30.8894	+	17.8340i	1.19965	+	0.692616i
$664$		0			0
$665$	20.1464	−	0.717428i	0.781243	−	0.0278207i
$666$		0			0
$667$	−11.3891	+	19.7265i	−0.440987	+	0.763812i
$668$		0			0
$669$	18.6247	+	32.2589i	0.720072	+	1.24720i
$670$		0			0
$671$	4.83479	−	2.79137i	0.186645	−	0.107760i
$672$		0			0
$673$			19.0446i			0.734114i	0.930198	+	0.367057i	$0.119635\pi$
$673$			19.0446i			0.734114i	−0.930198	+	0.367057i	$0.880365\pi$
$674$		0			0
$675$	7.07328	+	12.2513i	0.272251	+	0.471552i
$676$		0			0
$677$		−	29.7421i		−	1.14308i	−0.820574	−	0.571540i	$-0.806346\pi$
$677$		−	29.7421i		−	1.14308i	0.820574	−	0.571540i	$-0.193654\pi$
$678$		0			0
$679$	0.870748	−	1.50818i	0.0334162	−	0.0578786i
$680$		0			0
$681$	9.38899	−	16.2622i	0.359787	−	0.623169i
$682$		0			0
$683$	−28.1980			−1.07897			−0.539484	−	0.841996i	$-0.681380\pi$
$683$	−28.1980			−1.07897			−0.539484	+	0.841996i	$0.681380\pi$
$684$		0			0
$685$	−2.73678			−0.104567
$686$		0			0
$687$	13.0955	−	22.6820i	0.499623	−	0.865373i
$688$		0			0
$689$	−3.58348	+	6.20677i	−0.136520	+	0.236459i
$690$		0			0
$691$			19.2925i			0.733920i	0.930237	+	0.366960i	$0.119601\pi$
$691$			19.2925i			0.733920i	−0.930237	+	0.366960i	$0.880399\pi$
$692$		0			0
$693$	−95.3888	−	165.218i	−3.62352	−	6.27612i
$694$		0			0
$695$			13.1981i			0.500634i
$696$		0			0
$697$	−11.6670	+	6.73593i	−0.441918	+	0.255141i
$698$		0			0
$699$	−30.6868	−	53.1510i	−1.16068	−	2.01036i
$700$		0			0
$701$	−24.7151	+	42.8078i	−0.933476	+	1.61683i	−0.156147	+	0.987734i	$0.549907\pi$
$701$	−24.7151	+	42.8078i	−0.933476	+	1.61683i	−0.777329	+	0.629094i	$0.783426\pi$
$702$		0			0
$703$	4.87596	+	7.79122i	0.183900	+	0.293851i
$704$		0			0
$705$	−18.2574	−	10.5409i	−0.687613	−	0.396993i
$706$		0			0
$707$	−1.55798	+	0.899502i	−0.0585940	+	0.0338293i
$708$		0			0
$709$	20.8261	+	36.0719i	0.782141	+	1.35471i	0.930692	+	0.365803i	$0.119206\pi$
$709$	20.8261	+	36.0719i	0.782141	+	1.35471i	−0.148552	+	0.988905i	$0.547461\pi$
$710$		0			0
$711$	−4.58488			−0.171947
$712$		0			0
$713$	−12.5078	+	7.22140i	−0.468422	+	0.270443i
$714$		0			0
$715$	−9.66959			−0.361622
$716$		0			0
$717$	−6.38790	−	3.68806i	−0.238561	−	0.137733i
$718$		0			0
$719$	−18.5096	−	10.6865i	−0.690291	−	0.398540i	0.113430	−	0.993546i	$-0.463816\pi$
$719$	−18.5096	−	10.6865i	−0.690291	−	0.398540i	−0.803721	+	0.595006i	$0.797150\pi$
$720$		0			0
$721$			8.66825i			0.322823i
$722$		0			0
$723$			22.3310i			0.830497i
$724$		0			0
$725$	−4.82611	−	2.78635i	−0.179237	−	0.103483i
$726$		0			0
$727$	32.4059	+	18.7096i	1.20187	+	0.693899i	0.960970	−	0.276651i	$-0.0892246\pi$
$727$	32.4059	+	18.7096i	1.20187	+	0.693899i	0.240898	+	0.970550i	$0.422558\pi$
$728$		0			0
$729$	36.3339			1.34570
$730$		0			0
$731$	53.5054	−	30.8914i	1.97897	−	1.14256i
$732$		0			0
$733$	−44.6522			−1.64927			−0.824634	−	0.565667i	$-0.808619\pi$
$733$	−44.6522			−1.64927			−0.824634	+	0.565667i	$0.808619\pi$
$734$		0			0
$735$	23.1893	+	40.1650i	0.855349	+	1.48151i
$736$		0			0
$737$	31.1670	−	17.9943i	1.14805	−	0.662827i
$738$		0			0
$739$	33.3782	+	19.2709i	1.22784	+	0.708891i	0.966577	−	0.256377i	$-0.0825289\pi$
$739$	33.3782	+	19.2709i	1.22784	+	0.708891i	0.261259	+	0.965269i	$0.415862\pi$
$740$		0			0
$741$	−12.9096	−	20.6280i	−0.474246	−	0.757789i
$742$		0			0
$743$	6.39244	−	11.0720i	0.234516	−	0.406193i	−0.724616	−	0.689153i	$-0.757983\pi$
$743$	6.39244	−	11.0720i	0.234516	−	0.406193i	0.959132	+	0.282959i	$0.0913162\pi$
$744$		0			0
$745$	−8.08348	−	14.0010i	−0.296156	−	0.512957i
$746$		0			0
$747$	32.2856	−	18.6401i	1.18127	−	0.682005i
$748$		0			0
$749$		−	68.2951i		−	2.49545i
$750$		0			0
$751$	−15.9545	−	27.6339i	−0.582187	−	1.00838i	−0.995220	−	0.0976607i	$-0.968864\pi$
$751$	−15.9545	−	27.6339i	−0.582187	−	1.00838i	0.413033	−	0.910716i	$-0.364469\pi$
$752$		0			0
$753$			17.9943i			0.655747i
$754$		0			0
$755$	−6.96572	+	12.0650i	−0.253508	+	0.439090i
$756$		0			0
$757$	−2.88899	+	5.00388i	−0.105002	+	0.181869i	−0.913739	−	0.406302i	$-0.866818\pi$
$757$	−2.88899	+	5.00388i	−0.105002	+	0.181869i	0.808737	+	0.588170i	$0.200152\pi$
$758$		0			0
$759$	−73.5507			−2.66972
$760$		0			0
$761$	24.3751			0.883598			0.441799	−	0.897114i	$-0.354340\pi$
$761$	24.3751			0.883598			0.441799	+	0.897114i	$0.354340\pi$
$762$		0			0
$763$	22.4548	−	38.8929i	0.812918	−	1.40802i
$764$		0			0
$765$	−23.6041	+	40.8835i	−0.853407	+	1.47814i
$766$		0			0
$767$		−	23.9652i		−	0.865333i
$768$		0			0
$769$	3.54228	+	6.13542i	0.127738	+	0.221249i	0.922800	−	0.385280i	$-0.125895\pi$
$769$	3.54228	+	6.13542i	0.127738	+	0.221249i	−0.795062	+	0.606528i	$0.792562\pi$
$770$		0			0
$771$		−	21.1172i		−	0.760519i
$772$		0			0
$773$	35.0766	−	20.2515i	1.26162	−	0.728394i	0.288229	−	0.957562i	$-0.406934\pi$
$773$	35.0766	−	20.2515i	1.26162	−	0.728394i	0.973387	+	0.229167i	$0.0736003\pi$
$774$		0			0
$775$	−1.76672	−	3.06005i	−0.0634626	−	0.109920i
$776$		0			0
$777$	−15.7162	+	27.2212i	−0.563815	+	0.976556i
$778$		0			0
$779$	9.18537	−	0.327098i	0.329100	−	0.0117195i
$780$		0			0
$781$	52.8122	+	30.4912i	1.88977	+	1.09106i
$782$		0			0
$783$	−68.2728	+	39.4173i	−2.43987	+	1.40866i
$784$		0			0
$785$	−7.90959	−	13.6998i	−0.282305	−	0.488967i
$786$		0			0
$787$	−4.80002			−0.171102			−0.0855510	−	0.996334i	$-0.527265\pi$
$787$	−4.80002			−0.171102			−0.0855510	+	0.996334i	$0.527265\pi$
$788$		0			0
$789$	67.6817	−	39.0761i	2.40953	−	1.39114i
$790$		0			0
$791$	17.7624			0.631557
$792$		0			0
$793$	1.50000	+	0.866025i	0.0532666	+	0.0307535i
$794$		0			0
$795$	−11.5503	−	6.66855i	−0.409646	−	0.236509i
$796$		0			0
$797$		−	26.5672i		−	0.941057i	−0.882385	−	0.470528i	$-0.844063\pi$
$797$		−	26.5672i		−	0.941057i	0.882385	−	0.470528i	$-0.155937\pi$
$798$		0			0
$799$		−	41.7882i		−	1.47836i
$800$		0			0
$801$	−66.5009	−	38.3943i	−2.34969	−	1.35660i
$802$		0			0
$803$	−6.71547	−	3.87718i	−0.236984	−	0.136823i
$804$		0			0
$805$	18.9037			0.666269
$806$		0			0
$807$	−4.83479	+	2.79137i	−0.170193	+	0.0982608i
$808$		0			0
$809$	37.4185			1.31556			0.657782	−	0.753208i	$-0.271495\pi$
$809$	37.4185			1.31556			0.657782	+	0.753208i	$0.271495\pi$
$810$		0			0
$811$	−16.5402	−	28.6484i	−0.580804	−	1.00598i	−0.995384	−	0.0959698i	$-0.969405\pi$
$811$	−16.5402	−	28.6484i	−0.580804	−	1.00598i	0.414580	−	0.910013i	$-0.363929\pi$
$812$		0			0
$813$	63.0479	−	36.4007i	2.21119	−	1.27663i
$814$		0			0
$815$	−5.30017	−	3.06005i	−0.185657	−	0.107189i
$816$		0			0
$817$	−42.1247	+	1.50009i	−1.47376	+	0.0524816i
$818$		0			0
$819$	29.5945	−	51.2591i	1.03411	−	1.79114i
$820$		0			0
$821$	−6.52060	−	11.2940i	−0.227570	−	0.394164i	0.729517	−	0.683963i	$-0.239745\pi$
$821$	−6.52060	−	11.2940i	−0.227570	−	0.394164i	−0.957088	+	0.289799i	$0.906412\pi$
$822$		0			0
$823$	−10.6003	+	6.12011i	−0.369505	+	0.213334i	−0.673242	−	0.739422i	$-0.735099\pi$
$823$	−10.6003	+	6.12011i	−0.369505	+	0.213334i	0.303737	+	0.952756i	$0.401765\pi$
$824$		0			0
$825$		−	17.9943i		−	0.626480i
$826$		0			0
$827$	20.3303	+	35.2131i	0.706953	+	1.22448i	0.965982	+	0.258609i	$0.0832640\pi$
$827$	20.3303	+	35.2131i	0.706953	+	1.22448i	−0.259030	+	0.965869i	$0.583403\pi$
$828$		0			0
$829$		−	25.0732i		−	0.870827i	−0.900230	−	0.435414i	$-0.856602\pi$
$829$		−	25.0732i		−	0.870827i	0.900230	−	0.435414i	$-0.143398\pi$
$830$		0			0
$831$	14.1466	−	24.5026i	0.490739	−	0.849985i
$832$		0			0
$833$	−45.9655	+	79.6147i	−1.59261	+	2.75848i
$834$		0			0
$835$	2.18454			0.0755991
$836$		0			0
$837$	−49.9861			−1.72777
$838$		0			0
$839$	−6.95933	+	12.0539i	−0.240263	+	0.416147i	−0.960789	−	0.277280i	$-0.910567\pi$
$839$	−6.95933	+	12.0539i	−0.240263	+	0.416147i	0.720526	+	0.693428i	$0.243900\pi$
$840$		0			0
$841$	1.02753	−	1.77973i	0.0354320	−	0.0613700i
$842$		0			0
$843$			56.7853i			1.95579i
$844$		0			0
$845$	5.00000	+	8.66025i	0.172005	+	0.297922i
$846$		0			0
$847$			93.2687i			3.20475i
$848$		0			0
$849$	−9.84779	+	5.68562i	−0.337975	+	0.195130i
$850$		0			0
$851$	4.30941	+	7.46412i	0.147725	+	0.255867i
$852$		0			0
$853$	−18.2092	+	31.5393i	−0.623473	+	1.07989i	0.365361	+	0.930866i	$0.380945\pi$
$853$	−18.2092	+	31.5393i	−0.623473	+	1.07989i	−0.988834	+	0.149021i	$0.952388\pi$
$854$		0			0
$855$	27.3020	−	17.0864i	0.933710	−	0.584342i
$856$		0			0
$857$	5.99307	+	3.46010i	0.204719	+	0.118195i	0.598855	−	0.800858i	$-0.295623\pi$
$857$	5.99307	+	3.46010i	0.204719	+	0.118195i	−0.394136	+	0.919052i	$0.628956\pi$
$858$		0			0
$859$	13.3521	−	7.70884i	0.455568	−	0.263022i	−0.254611	−	0.967044i	$-0.581947\pi$
$859$	13.3521	−	7.70884i	0.455568	−	0.263022i	0.710179	+	0.704021i	$0.248614\pi$
$860$		0			0
$861$	15.7162	+	27.2212i	0.535606	+	0.927697i
$862$		0			0
$863$	48.1449			1.63887			0.819436	−	0.573171i	$-0.194287\pi$
$863$	48.1449			1.63887			0.819436	+	0.573171i	$0.194287\pi$
$864$		0			0
$865$	−17.3409	+	10.0118i	−0.589607	+	0.340410i
$866$		0			0
$867$	−76.7739			−2.60738
$868$		0			0
$869$	3.00000	+	1.73205i	0.101768	+	0.0587558i
$870$		0			0
$871$	9.66959	+	5.58274i	0.327641	+	0.189164i
$872$		0			0
$873$		−	2.78235i		−	0.0941684i
$874$		0			0
$875$			4.62482i			0.156348i
$876$		0			0
$877$	−20.3409	−	11.7438i	−0.686862	−	0.396560i	0.115573	−	0.993299i	$-0.463129\pi$
$877$	−20.3409	−	11.7438i	−0.686862	−	0.396560i	−0.802435	+	0.596739i	$0.796463\pi$
$878$		0			0
$879$	−64.7330	−	37.3736i	−2.18339	−	1.26058i
$880$		0			0
$881$	−32.8604			−1.10709			−0.553547	−	0.832818i	$-0.686726\pi$
$881$	−32.8604			−1.10709			−0.553547	+	0.832818i	$0.686726\pi$
$882$		0			0
$883$	−14.2829	+	8.24621i	−0.480656	+	0.277507i	−0.720690	−	0.693257i	$-0.756175\pi$
$883$	−14.2829	+	8.24621i	−0.480656	+	0.277507i	0.240034	+	0.970765i	$0.422842\pi$
$884$		0			0
$885$	44.5972			1.49912
$886$		0			0
$887$	0.0600056	+	0.103933i	0.00201479	+	0.00348972i	0.867031	−	0.498254i	$-0.166025\pi$
$887$	0.0600056	+	0.103933i	0.00201479	+	0.00348972i	−0.865016	+	0.501744i	$0.832692\pi$
$888$		0			0
$889$	−25.8192	+	14.9067i	−0.865947	+	0.499955i
$890$		0			0
$891$	−113.280	−	65.4023i	−3.79503	−	2.19106i
$892$		0			0
$893$	−13.3673	+	25.1821i	−0.447320	+	0.842687i
$894$		0			0
$895$	−0.626893	+	1.08581i	−0.0209547	+	0.0362947i
$896$		0			0
$897$	−11.4096	−	19.7620i	−0.380955	−	0.659834i
$898$		0			0
$899$	17.0528	−	9.84543i	0.568742	−	0.328363i
$900$		0			0
$901$		−	26.4367i		−	0.880733i
$902$		0			0
$903$	−72.0754	−	124.838i	−2.39852	−	4.15435i
$904$		0			0
$905$		−	12.1244i		−	0.403027i
$906$		0			0
$907$	−7.38993	+	12.7997i	−0.245378	+	0.425008i	−0.962238	−	0.272210i	$-0.912246\pi$
$907$	−7.38993	+	12.7997i	−0.245378	+	0.425008i	0.716859	+	0.697218i	$0.245579\pi$
$908$		0			0
$909$	−1.43712	+	2.48916i	−0.0476661	+	0.0825602i
$910$		0			0
$911$	22.6952			0.751924			0.375962	−	0.926635i	$-0.377312\pi$
$911$	22.6952			0.751924			0.375962	+	0.926635i	$0.377312\pi$
$912$		0			0
$913$	−28.1670			−0.932191
$914$		0			0
$915$	−1.61160	+	2.79137i	−0.0532778	+	0.0922798i
$916$		0			0
$917$	−10.6945	+	18.5234i	−0.353163	+	0.611697i
$918$		0			0
$919$			18.8030i			0.620254i	0.950695	+	0.310127i	$0.100372\pi$
$919$			18.8030i			0.620254i	−0.950695	+	0.310127i	$0.899628\pi$
$920$		0			0
$921$	−9.54228	−	16.5277i	−0.314429	−	0.544607i
$922$		0			0
$923$			18.9198i			0.622754i
$924$		0			0
$925$	−1.82611	+	1.05430i	−0.0600420	+	0.0346652i
$926$		0			0
$927$	6.92455	+	11.9937i	0.227432	+	0.393924i
$928$		0			0
$929$	−17.4096	+	30.1543i	−0.571190	+	0.989330i	0.425254	+	0.905074i	$0.360185\pi$
$929$	−17.4096	+	30.1543i	−0.571190	+	0.989330i	−0.996444	+	0.0842562i	$0.973149\pi$
$930$		0			0
$931$	53.1668	−	33.2733i	1.74247	−	1.09049i
$932$		0			0
$933$	−15.2574	−	8.80885i	−0.499504	−	0.288389i
$934$		0			0
$935$	30.8894	−	17.8340i	1.01019	−	0.583235i
$936$		0			0
$937$	1.09041	+	1.88865i	0.0356222	+	0.0616995i	0.883287	−	0.468833i	$-0.155325\pi$
$937$	1.09041	+	1.88865i	0.0356222	+	0.0616995i	−0.847665	+	0.530532i	$0.821992\pi$
$938$		0			0
$939$	60.2525			1.96627
$940$		0			0
$941$	−33.6384	+	19.4211i	−1.09658	+	0.633110i	−0.935320	−	0.353802i	$-0.884889\pi$
$941$	−33.6384	+	19.4211i	−1.09658	+	0.633110i	−0.161259	+	0.986912i	$0.551555\pi$
$942$		0			0
$943$	8.61882			0.280667
$944$		0			0
$945$	56.6600	+	32.7127i	1.84315	+	1.06414i
$946$		0			0
$947$	−0.263028	−	0.151859i	−0.00854725	−	0.00493476i	0.495720	−	0.868482i	$-0.334904\pi$
$947$	−0.263028	−	0.151859i	−0.00854725	−	0.00493476i	−0.504268	+	0.863547i	$0.668237\pi$
$948$		0			0
$949$		−	2.40580i		−	0.0780955i
$950$		0			0
$951$		−	4.62482i		−	0.149970i
$952$		0			0
$953$	22.4931	+	12.9864i	0.728622	+	0.420670i	0.817918	−	0.575335i	$-0.195128\pi$
$953$	22.4931	+	12.9864i	0.728622	+	0.420670i	−0.0892958	+	0.996005i	$0.528462\pi$
$954$		0			0
$955$	−5.42052	−	3.12954i	−0.175404	−	0.101269i
$956$		0			0
$957$	100.277			3.24149
$958$		0			0
$959$	−10.9614	+	6.32856i	−0.353962	+	0.204360i
$960$		0			0
$961$	−18.5148			−0.597250
$962$		0			0
$963$	−54.5569	−	94.4953i	−1.75807	−	3.04507i
$964$		0			0
$965$	16.2357	−	9.37368i	0.522645	−	0.301750i
$966$		0			0
$967$	35.3600	+	20.4151i	1.13710	+	0.656506i	0.945711	−	0.325008i	$-0.105367\pi$
$967$	35.3600	+	20.4151i	1.13710	+	0.656506i	0.191391	+	0.981514i	$0.438700\pi$
$968$		0			0
$969$	79.2847	+	42.0864i	2.54699	+	1.35201i
$970$		0			0
$971$	−24.9020	+	43.1316i	−0.799144	+	1.38416i	0.121030	+	0.992649i	$0.461380\pi$
$971$	−24.9020	+	43.1316i	−0.799144	+	1.38416i	−0.920174	+	0.391510i	$0.871953\pi$
$972$		0			0
$973$	30.5195	+	52.8614i	0.978411	+	1.69466i
$974$		0			0
$975$	4.83479	−	2.79137i	0.154837	−	0.0893954i
$976$		0			0
$977$			43.3646i			1.38736i	0.720285	+	0.693679i	$0.244011\pi$
$977$			43.3646i			1.38736i	−0.720285	+	0.693679i	$0.755989\pi$
$978$		0			0
$979$	29.0088	+	50.2446i	0.927124	+	1.60583i
$980$		0			0
$981$		−	71.7512i		−	2.29084i
$982$		0			0
$983$	30.6267	−	53.0471i	0.976842	−	1.69194i	0.303122	−	0.952952i	$-0.401971\pi$
$983$	30.6267	−	53.0471i	0.976842	−	1.69194i	0.673719	−	0.738988i	$-0.264696\pi$
$984$		0			0
$985$	−11.2151	+	19.4251i	−0.357343	+	0.618936i
$986$		0			0
$987$	−97.4996			−3.10345
$988$		0			0
$989$	−39.5264			−1.25687
$990$		0			0
$991$	−28.3059	+	49.0273i	−0.899167	+	1.55740i	−0.0706062	+	0.997504i	$0.522493\pi$
$991$	−28.3059	+	49.0273i	−0.899167	+	1.55740i	−0.828561	+	0.559899i	$0.810840\pi$
$992$		0			0
$993$	55.1394	−	95.5043i	1.74980	−	3.03074i
$994$		0			0
$995$		−	2.33637i		−	0.0740681i
$996$		0			0
$997$	−0.236778	−	0.410112i	−0.00749884	−	0.0129884i	0.862252	−	0.506480i	$-0.169054\pi$
$997$	−0.236778	−	0.410112i	−0.00749884	−	0.0129884i	−0.869750	+	0.493492i	$0.835720\pi$
$998$		0			0
$999$			29.8295i			0.943764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.bq.r.1471.6	yes	12
4.3	odd	2	inner	1520.2.bq.r.1471.1	yes	12
19.12	odd	6	inner	1520.2.bq.r.31.1	✓	12
76.31	even	6	inner	1520.2.bq.r.31.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1520.2.bq.r.31.1	✓	12	19.12	odd	6	inner
1520.2.bq.r.31.6	yes	12	76.31	even	6	inner
1520.2.bq.r.1471.1	yes	12	4.3	odd	2	inner
1520.2.bq.r.1471.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61160 - 2.79137i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.62482i q^{7} +(-3.69449 - 6.39905i) q^{9} +O(q^{10})\)	\(q+(1.61160 - 2.79137i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.62482i q^{7} +(-3.69449 - 6.39905i) q^{9} +5.58274i q^{11} +(-1.50000 + 0.866025i) q^{13} +(-1.61160 - 2.79137i) q^{15} +(3.19449 - 5.53303i) q^{17} +(-3.69496 + 2.31241i) q^{19} +(-12.9096 - 7.45335i) q^{21} +(-3.53984 + 2.04373i) q^{23} +(-0.500000 - 0.866025i) q^{25} -14.1466 q^{27} +(4.82611 - 2.78635i) q^{29} +3.53345 q^{31} +(15.5835 + 8.99713i) q^{33} +(-4.00521 - 2.31241i) q^{35} -2.10860i q^{37} +5.58274i q^{39} +(-1.82611 - 1.05430i) q^{41} +(8.37463 + 4.83510i) q^{43} -7.38899 q^{45} +(5.66437 - 3.27033i) q^{47} -14.3890 q^{49} +(-10.2965 - 17.8340i) q^{51} +(3.58348 - 2.06892i) q^{53} +(4.83479 + 2.79137i) q^{55} +(0.500000 + 14.0407i) q^{57} +(-6.91816 + 11.9826i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-29.5945 + 17.0864i) q^{63} +1.73205i q^{65} +(-3.22320 - 5.58274i) q^{67} +13.1747i q^{69} +(5.46169 - 9.45992i) q^{71} +(-0.694494 + 1.20290i) q^{73} -3.22320 q^{75} +25.8192 q^{77} +(0.310251 - 0.537371i) q^{79} +(-11.7151 + 20.2911i) q^{81} +5.04537i q^{83} +(-3.19449 - 5.53303i) q^{85} -17.9619i q^{87} +(9.00000 - 5.19615i) q^{89} +(4.00521 + 6.93723i) q^{91} +(5.69449 - 9.86315i) q^{93} +(0.155126 + 4.35614i) q^{95} +(0.326105 + 0.188277i) q^{97} +(35.7242 - 20.6254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 12 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 - 12 * q^9	\( 12 q + 6 q^{5} - 12 q^{9} - 18 q^{13} + 6 q^{17} - 24 q^{21} - 6 q^{25} + 24 q^{29} + 90 q^{33} + 12 q^{41} - 24 q^{45} - 108 q^{49} - 54 q^{53} + 6 q^{57} - 6 q^{61} + 24 q^{73} + 48 q^{77} - 42 q^{81} - 6 q^{85} + 108 q^{89} + 36 q^{93} - 30 q^{97}+O(q^{100}) \) 12 * q + 6 * q^5 - 12 * q^9 - 18 * q^13 + 6 * q^17 - 24 * q^21 - 6 * q^25 + 24 * q^29 + 90 * q^33 + 12 * q^41 - 24 * q^45 - 108 * q^49 - 54 * q^53 + 6 * q^57 - 6 * q^61 + 24 * q^73 + 48 * q^77 - 42 * q^81 - 6 * q^85 + 108 * q^89 + 36 * q^93 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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