LMFDB - Embedded newform 490.2.i.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(79,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("490.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.i (of order $6$, degree $2$, not 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	490.79
Dual form			490.2.i.c.459.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.30701 + 1.81431i) q^{5} +2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.30701 + 1.81431i) q^{5} +2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(2.03906 - 0.917738i) q^{10} +(2.44949 + 4.24264i) q^{11} +(-2.12132 - 1.22474i) q^{12} +4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(0.775255 - 1.34278i) q^{19} +(-2.22474 - 0.224745i) q^{20} -4.89898i q^{22} +(-2.51059 - 1.44949i) q^{23} +(1.22474 + 2.12132i) q^{24} +(-1.58346 - 4.74264i) q^{25} +(2.22474 - 3.85337i) q^{26} -6.89898 q^{29} +(-3.20150 + 4.44414i) q^{30} +(-4.44949 - 7.70674i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-10.3923 - 6.00000i) q^{33} +2.00000 q^{34} +3.00000 q^{36} +(1.73205 + 1.00000i) q^{37} +(-1.34278 + 0.775255i) q^{38} +(-5.44949 - 9.43879i) q^{39} +(1.81431 + 1.30701i) q^{40} -1.10102 q^{41} -0.898979i q^{43} +(-2.44949 + 4.24264i) q^{44} +(2.75321 + 6.11717i) q^{45} +(1.44949 + 2.51059i) q^{46} +(7.70674 + 4.44949i) q^{47} -2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(2.44949 - 4.24264i) q^{51} +(-3.85337 + 2.22474i) q^{52} +(-9.43879 + 5.44949i) q^{53} +(-10.8990 - 1.10102i) q^{55} +3.79796i q^{57} +(5.97469 + 3.44949i) q^{58} +(-0.775255 - 1.34278i) q^{59} +(4.99465 - 2.24799i) q^{60} +(-1.77526 + 3.07483i) q^{61} +8.89898i q^{62} -1.00000 q^{64} +(-8.07277 - 5.81552i) q^{65} +(6.00000 + 10.3923i) q^{66} +(6.92820 - 4.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +7.10102 q^{69} -1.10102 q^{71} +(-2.59808 - 1.50000i) q^{72} +(2.51059 - 1.44949i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(9.16756 + 8.12132i) q^{75} +1.55051 q^{76} +10.8990i q^{78} +(3.44949 - 5.97469i) q^{79} +(-0.917738 - 2.03906i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.953512 + 0.550510i) q^{82} -2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +(-0.449490 + 0.778539i) q^{86} +(14.6349 - 8.44949i) q^{87} +(4.24264 - 2.44949i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(0.674235 - 6.67423i) q^{90} -2.89898i q^{92} +(18.8776 + 10.8990i) q^{93} +(-4.44949 - 7.70674i) q^{94} +(1.42296 + 3.16158i) q^{95} +(-1.22474 + 2.12132i) q^{96} -15.7980i q^{97} +14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5 + 12 * q^9	$ 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9} - 4 q^{10} + 24 q^{15} - 4 q^{16} + 16 q^{19} - 8 q^{20} + 8 q^{26} - 16 q^{29} - 12 q^{30} - 16 q^{31} + 16 q^{34} + 24 q^{36} - 24 q^{39} + 4 q^{40} - 48 q^{41} + 12 q^{45} - 8 q^{46} - 8 q^{50} - 48 q^{55} - 16 q^{59} + 12 q^{60} - 24 q^{61} - 8 q^{64} + 4 q^{65} + 48 q^{66} + 96 q^{69} - 48 q^{71} - 8 q^{74} + 32 q^{76} + 8 q^{79} - 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} - 40 q^{89} - 24 q^{90} - 16 q^{94} + 4 q^{95}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 + 12 * q^9 - 4 * q^10 + 24 * q^15 - 4 * q^16 + 16 * q^19 - 8 * q^20 + 8 * q^26 - 16 * q^29 - 12 * q^30 - 16 * q^31 + 16 * q^34 + 24 * q^36 - 24 * q^39 + 4 * q^40 - 48 * q^41 + 12 * q^45 - 8 * q^46 - 8 * q^50 - 48 * q^55 - 16 * q^59 + 12 * q^60 - 24 * q^61 - 8 * q^64 + 4 * q^65 + 48 * q^66 + 96 * q^69 - 48 * q^71 - 8 * q^74 + 32 * q^76 + 8 * q^79 - 4 * q^80 + 36 * q^81 - 16 * q^85 + 16 * q^86 - 40 * q^89 - 24 * q^90 - 16 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−2.12132	+	1.22474i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$3$	−2.12132	+	1.22474i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.30701	+	1.81431i	−0.584511	+	0.811386i
$5$	−1.30701	+	1.81431i	−0.584511	+	0.811386i
$6$	2.44949			1.00000
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	2.03906	−	0.917738i	0.644807	−	0.290214i
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	0.953149	+	0.302502i	$0.0978220\pi$
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	−0.214600	+	0.976702i	$0.568845\pi$
$12$	−2.12132	−	1.22474i	−0.612372	−	0.353553i
$13$			4.44949i			1.23407i	0.786937	+	0.617033i	$0.211666\pi$
$13$			4.44949i			1.23407i	−0.786937	+	0.617033i	$0.788334\pi$
$14$		0			0
$15$	0.550510	−	5.44949i	0.142141	−	1.40705i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$	−2.59808	+	1.50000i	−0.612372	+	0.353553i
$19$	0.775255	−	1.34278i	0.177856	−	0.308055i	−0.763290	−	0.646056i	$-0.776417\pi$
$19$	0.775255	−	1.34278i	0.177856	−	0.308055i	0.941146	+	0.338001i	$0.109751\pi$
$20$	−2.22474	−	0.224745i	−0.497468	−	0.0502545i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$	−2.51059	−	1.44949i	−0.523494	−	0.302240i	0.214869	−	0.976643i	$-0.431068\pi$
$23$	−2.51059	−	1.44949i	−0.523494	−	0.302240i	−0.738363	+	0.674403i	$0.764401\pi$
$24$	1.22474	+	2.12132i	0.250000	+	0.433013i
$25$	−1.58346	−	4.74264i	−0.316693	−	0.948528i
$26$	2.22474	−	3.85337i	0.436308	−	0.755708i
$27$		0			0
$28$		0			0
$29$	−6.89898			−1.28111			−0.640554	−	0.767913i	$-0.721295\pi$
$29$	−6.89898			−1.28111			−0.640554	+	0.767913i	$0.721295\pi$
$30$	−3.20150	+	4.44414i	−0.584511	+	0.811386i
$31$	−4.44949	−	7.70674i	−0.799152	−	1.38417i	−0.920169	−	0.391521i	$-0.871949\pi$
$31$	−4.44949	−	7.70674i	−0.799152	−	1.38417i	0.121017	−	0.992650i	$-0.461384\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−10.3923	−	6.00000i	−1.80907	−	1.04447i
$34$	2.00000			0.342997
$35$		0			0
$36$	3.00000			0.500000
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	0.635571	−	0.772043i	$-0.280765\pi$
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−1.34278	+	0.775255i	−0.217828	+	0.125763i
$39$	−5.44949	−	9.43879i	−0.872617	−	1.51142i
$40$	1.81431	+	1.30701i	0.286868	+	0.206656i
$41$	−1.10102			−0.171951			−0.0859753	−	0.996297i	$-0.527401\pi$
$41$	−1.10102			−0.171951			−0.0859753	+	0.996297i	$0.527401\pi$
$42$		0			0
$43$		−	0.898979i		−	0.137093i	−0.997648	−	0.0685465i	$-0.978164\pi$
$43$		−	0.898979i		−	0.137093i	0.997648	−	0.0685465i	$-0.0218362\pi$
$44$	−2.44949	+	4.24264i	−0.369274	+	0.639602i
$45$	2.75321	+	6.11717i	0.410425	+	0.911894i
$46$	1.44949	+	2.51059i	0.213716	+	0.370166i
$47$	7.70674	+	4.44949i	1.12414	+	0.649025i	0.942456	−	0.334331i	$-0.108510\pi$
$47$	7.70674	+	4.44949i	1.12414	+	0.649025i	0.181688	+	0.983356i	$0.441844\pi$
$48$		−	2.44949i		−	0.353553i
$49$		0			0
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	2.44949	−	4.24264i	0.342997	−	0.594089i
$52$	−3.85337	+	2.22474i	−0.534366	+	0.308517i
$53$	−9.43879	+	5.44949i	−1.29652	+	0.748545i	−0.979801	−	0.199975i	$-0.935914\pi$
$53$	−9.43879	+	5.44949i	−1.29652	+	0.748545i	−0.316717	+	0.948520i	$0.602581\pi$
$54$		0			0
$55$	−10.8990	−	1.10102i	−1.46962	−	0.148462i
$56$		0			0
$57$			3.79796i			0.503052i
$58$	5.97469	+	3.44949i	0.784515	+	0.452940i
$59$	−0.775255	−	1.34278i	−0.100930	−	0.174815i	0.811138	−	0.584854i	$-0.198848\pi$
$59$	−0.775255	−	1.34278i	−0.100930	−	0.174815i	−0.912068	+	0.410039i	$0.865515\pi$
$60$	4.99465	−	2.24799i	0.644807	−	0.290214i
$61$	−1.77526	+	3.07483i	−0.227298	+	0.393692i	−0.957006	−	0.290067i	$-0.906323\pi$
$61$	−1.77526	+	3.07483i	−0.227298	+	0.393692i	0.729708	+	0.683759i	$0.239656\pi$
$62$			8.89898i			1.13017i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.07277	−	5.81552i	−1.00130	−	0.721326i
$66$	6.00000	+	10.3923i	0.738549	+	1.27920i
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$	−1.73205	−	1.00000i	−0.210042	−	0.121268i
$69$	7.10102			0.854862
$70$		0			0
$71$	−1.10102			−0.130667			−0.0653335	−	0.997863i	$-0.520811\pi$
$71$	−1.10102			−0.130667			−0.0653335	+	0.997863i	$0.520811\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	2.51059	−	1.44949i	0.293842	−	0.169650i	−0.345831	−	0.938297i	$-0.612403\pi$
$73$	2.51059	−	1.44949i	0.293842	−	0.169650i	0.639673	+	0.768647i	$0.279070\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	9.16756	+	8.12132i	1.05858	+	0.937769i
$76$	1.55051			0.177856
$77$		0			0
$78$			10.8990i			1.23407i
$79$	3.44949	−	5.97469i	0.388098	−	0.672205i	−0.604096	−	0.796912i	$-0.706466\pi$
$79$	3.44949	−	5.97469i	0.388098	−	0.672205i	0.992194	+	0.124706i	$0.0397989\pi$
$80$	−0.917738	−	2.03906i	−0.102606	−	0.227974i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	0.953512	+	0.550510i	0.105298	+	0.0607937i
$83$		−	2.44949i		−	0.268866i	−0.990923	−	0.134433i	$-0.957079\pi$
$83$		−	2.44949i		−	0.268866i	0.990923	−	0.134433i	$-0.0429214\pi$
$84$		0			0
$85$	0.449490	−	4.44949i	0.0487540	−	0.482615i
$86$	−0.449490	+	0.778539i	−0.0484697	+	0.0839520i
$87$	14.6349	−	8.44949i	1.56903	−	0.905880i
$88$	4.24264	−	2.44949i	0.452267	−	0.261116i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	0.674235	−	6.67423i	0.0710706	−	0.703526i
$91$		0			0
$92$		−	2.89898i		−	0.302240i
$93$	18.8776	+	10.8990i	1.95751	+	1.13017i
$94$	−4.44949	−	7.70674i	−0.458930	−	0.794890i
$95$	1.42296	+	3.16158i	0.145993	+	0.324371i
$96$	−1.22474	+	2.12132i	−0.125000	+	0.216506i
$97$		−	15.7980i		−	1.60404i	−0.597297	−	0.802020i	$-0.703759\pi$
$97$		−	15.7980i		−	1.60404i	0.597297	−	0.802020i	$-0.296241\pi$
$98$		0			0
$99$	14.6969			1.47710
$100$	3.31552	−	3.74264i	0.331552	−	0.374264i
$101$	−1.77526	−	3.07483i	−0.176644	−	0.305957i	0.764085	−	0.645116i	$-0.223191\pi$
$101$	−1.77526	−	3.07483i	−0.176644	−	0.305957i	−0.940729	+	0.339159i	$0.889858\pi$
$102$	−4.24264	+	2.44949i	−0.420084	+	0.242536i
$103$	−11.1708	−	6.44949i	−1.10070	−	0.635487i	−0.164292	−	0.986412i	$-0.552534\pi$
$103$	−11.1708	−	6.44949i	−1.10070	−	0.635487i	−0.936404	+	0.350925i	$0.885867\pi$
$104$	4.44949			0.436308
$105$		0			0
$106$	10.8990			1.05860
$107$	−6.92820	−	4.00000i	−0.669775	−	0.386695i	0.126217	−	0.992003i	$-0.459717\pi$
$107$	−6.92820	−	4.00000i	−0.669775	−	0.386695i	−0.795991	+	0.605308i	$0.793050\pi$
$108$		0			0
$109$	3.44949	+	5.97469i	0.330401	+	0.572272i	0.982591	−	0.185784i	$-0.0594826\pi$
$109$	3.44949	+	5.97469i	0.330401	+	0.572272i	−0.652189	+	0.758056i	$0.726149\pi$
$110$	8.88828	+	6.40300i	0.847465	+	0.610502i
$111$	−4.89898			−0.464991
$112$		0			0
$113$			19.7980i			1.86244i	0.364464	+	0.931218i	$0.381252\pi$
$113$			19.7980i			1.86244i	−0.364464	+	0.931218i	$0.618748\pi$
$114$	1.89898	−	3.28913i	0.177856	−	0.308055i
$115$	5.91119	−	2.66050i	0.551221	−	0.248093i
$116$	−3.44949	−	5.97469i	−0.320277	−	0.554736i
$117$	11.5601	+	6.67423i	1.06873	+	0.617033i
$118$			1.55051i			0.142736i
$119$		0			0
$120$	−5.44949	−	0.550510i	−0.497468	−	0.0502545i
$121$	−6.50000	+	11.2583i	−0.590909	+	1.02348i
$122$	3.07483	−	1.77526i	0.278382	−	0.160724i
$123$	2.33562	−	1.34847i	0.210596	−	0.121587i
$124$	4.44949	−	7.70674i	0.399576	−	0.692086i
$125$	10.6742	+	3.32577i	0.954733	+	0.297465i
$126$		0			0
$127$			14.8990i			1.32207i	0.750355	+	0.661035i	$0.229883\pi$
$127$			14.8990i			1.32207i	−0.750355	+	0.661035i	$0.770117\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.10102	+	1.90702i	0.0969395	+	0.167904i
$130$	4.08346	+	9.07277i	0.358144	+	0.795734i
$131$	3.22474	−	5.58542i	0.281747	−	0.488001i	−0.690068	−	0.723745i	$-0.742419\pi$
$131$	3.22474	−	5.58542i	0.281747	−	0.488001i	0.971815	+	0.235744i	$0.0757527\pi$
$132$		−	12.0000i		−	1.04447i
$133$		0			0
$134$	−8.00000			−0.691095
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	1.55708	−	0.898979i	0.133030	−	0.0768050i	−0.432008	−	0.901870i	$-0.642195\pi$
$137$	1.55708	−	0.898979i	0.133030	−	0.0768050i	0.565038	+	0.825065i	$0.308861\pi$
$138$	−6.14966	−	3.55051i	−0.523494	−	0.302240i
$139$	−1.55051			−0.131513			−0.0657563	−	0.997836i	$-0.520946\pi$
$139$	−1.55051			−0.131513			−0.0657563	+	0.997836i	$0.520946\pi$
$140$		0			0
$141$	−21.7980			−1.83572
$142$	0.953512	+	0.550510i	0.0800169	+	0.0461978i
$143$	−18.8776	+	10.8990i	−1.57862	+	0.911418i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	9.01702	−	12.5169i	0.748822	−	1.03947i
$146$	−2.89898			−0.239921
$147$		0			0
$148$			2.00000i			0.164399i
$149$	−1.89898	+	3.28913i	−0.155570	+	0.269456i	−0.933267	−	0.359184i	$-0.883055\pi$
$149$	−1.89898	+	3.28913i	−0.155570	+	0.269456i	0.777696	+	0.628640i	$0.216388\pi$
$150$	−3.87868	−	11.6170i	−0.316693	−	0.948528i
$151$	−9.79796	−	16.9706i	−0.797347	−	1.38104i	−0.921338	−	0.388762i	$-0.872903\pi$
$151$	−9.79796	−	16.9706i	−0.797347	−	1.38104i	0.123992	−	0.992283i	$-0.460430\pi$
$152$	−1.34278	−	0.775255i	−0.108914	−	0.0628815i
$153$			6.00000i			0.485071i
$154$		0			0
$155$	19.7980	+	2.00000i	1.59021	+	0.160644i
$156$	5.44949	−	9.43879i	0.436308	−	0.755708i
$157$	−3.07483	+	1.77526i	−0.245398	+	0.141681i	−0.617655	−	0.786449i	$-0.711917\pi$
$157$	−3.07483	+	1.77526i	−0.245398	+	0.141681i	0.372257	+	0.928130i	$0.378584\pi$
$158$	−5.97469	+	3.44949i	−0.475321	+	0.274427i
$159$	13.3485	−	23.1202i	1.05860	−	1.83355i
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$	6.14966	+	3.55051i	0.481679	+	0.278097i	0.721116	−	0.692814i	$-0.243630\pi$
$163$	6.14966	+	3.55051i	0.481679	+	0.278097i	−0.239437	+	0.970912i	$0.576963\pi$
$164$	−0.550510	−	0.953512i	−0.0429876	−	0.0744568i
$165$	24.4687	−	11.0129i	1.90489	−	0.857349i
$166$	−1.22474	+	2.12132i	−0.0950586	+	0.164646i
$167$			4.89898i			0.379094i	0.981872	+	0.189547i	$0.0607020\pi$
$167$			4.89898i			0.379094i	−0.981872	+	0.189547i	$0.939298\pi$
$168$		0			0
$169$	−6.79796			−0.522920
$170$	−2.61401	+	3.62863i	−0.200486	+	0.278303i
$171$	−2.32577	−	4.02834i	−0.177856	−	0.308055i
$172$	0.778539	−	0.449490i	0.0593630	−	0.0342733i
$173$	5.41045	+	3.12372i	0.411349	+	0.237492i	0.691369	−	0.722502i	$-0.257008\pi$
$173$	5.41045	+	3.12372i	0.411349	+	0.237492i	−0.280020	+	0.959994i	$0.590341\pi$
$174$	−16.8990			−1.28111
$175$		0			0
$176$	−4.89898			−0.369274
$177$	3.28913	+	1.89898i	0.247226	+	0.142736i
$178$	8.66025	−	5.00000i	0.649113	−	0.374766i
$179$	6.89898	+	11.9494i	0.515654	+	0.893139i	0.999835	+	0.0181709i	$0.00578431\pi$
$179$	6.89898	+	11.9494i	0.515654	+	0.893139i	−0.484181	+	0.874968i	$0.660882\pi$
$180$	−3.92102	+	5.44294i	−0.292256	+	0.405693i
$181$	−10.2474			−0.761687			−0.380843	−	0.924640i	$-0.624366\pi$
$181$	−10.2474			−0.761687			−0.380843	+	0.924640i	$0.624366\pi$
$182$		0			0
$183$		−	8.69694i		−	0.642896i
$184$	−1.44949	+	2.51059i	−0.106858	+	0.185083i
$185$	−4.07812	+	1.83548i	−0.299829	+	0.134947i
$186$	−10.8990	−	18.8776i	−0.799152	−	1.38417i
$187$	−8.48528	−	4.89898i	−0.620505	−	0.358249i
$188$			8.89898i			0.649025i
$189$		0			0
$190$	0.348469	−	3.44949i	0.0252806	−	0.250252i
$191$	−6.34847	+	10.9959i	−0.459359	+	0.795633i	−0.998927	−	0.0463087i	$-0.985254\pi$
$191$	−6.34847	+	10.9959i	−0.459359	+	0.795633i	0.539568	+	0.841942i	$0.318588\pi$
$192$	2.12132	−	1.22474i	0.153093	−	0.0883883i
$193$	−18.7026	+	10.7980i	−1.34624	+	0.777254i	−0.987715	−	0.156265i	$-0.950055\pi$
$193$	−18.7026	+	10.7980i	−1.34624	+	0.777254i	−0.358528	+	0.933519i	$0.616721\pi$
$194$	−7.89898	+	13.6814i	−0.567114	+	0.982270i
$195$	24.2474	+	2.44949i	1.73640	+	0.175412i
$196$		0			0
$197$		−	18.8990i		−	1.34650i	−0.739417	−	0.673248i	$-0.764899\pi$
$197$		−	18.8990i		−	1.34650i	0.739417	−	0.673248i	$-0.235101\pi$
$198$	−12.7279	−	7.34847i	−0.904534	−	0.522233i
$199$	8.44949	+	14.6349i	0.598968	+	1.03744i	0.992974	+	0.118336i	$0.0377559\pi$
$199$	8.44949	+	14.6349i	0.598968	+	1.03744i	−0.394005	+	0.919108i	$0.628911\pi$
$200$	−4.74264	+	1.58346i	−0.335355	+	0.111968i
$201$	−9.79796	+	16.9706i	−0.691095	+	1.19701i
$202$			3.55051i			0.249813i
$203$		0			0
$204$	4.89898			0.342997
$205$	1.43904	−	1.99760i	0.100507	−	0.139518i
$206$	6.44949	+	11.1708i	0.449357	+	0.778310i
$207$	−7.53177	+	4.34847i	−0.523494	+	0.302240i
$208$	−3.85337	−	2.22474i	−0.267183	−	0.154258i
$209$	7.59592			0.525421
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−9.43879	−	5.44949i	−0.648259	−	0.374272i
$213$	2.33562	−	1.34847i	0.160034	−	0.0923956i
$214$	4.00000	+	6.92820i	0.273434	+	0.473602i
$215$	1.63103	+	1.17497i	0.111235	+	0.0801325i
$216$		0			0
$217$		0			0
$218$		−	6.89898i		−	0.467258i
$219$	−3.55051	+	6.14966i	−0.239921	+	0.415556i
$220$	−4.49598	−	9.98930i	−0.303119	−	0.673479i
$221$	−4.44949	−	7.70674i	−0.299305	−	0.518412i
$222$	4.24264	+	2.44949i	0.284747	+	0.164399i
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$		0			0
$225$	−14.6969	−	3.00000i	−0.979796	−	0.200000i
$226$	9.89898	−	17.1455i	0.658470	−	1.14050i
$227$	−6.36396	+	3.67423i	−0.422391	+	0.243868i	−0.696100	−	0.717945i	$-0.745083\pi$
$227$	−6.36396	+	3.67423i	−0.422391	+	0.243868i	0.273709	+	0.961813i	$0.411750\pi$
$228$	−3.28913	+	1.89898i	−0.217828	+	0.125763i
$229$	−9.57321	+	16.5813i	−0.632616	+	1.09572i	0.354399	+	0.935094i	$0.384685\pi$
$229$	−9.57321	+	16.5813i	−0.632616	+	1.09572i	−0.987015	+	0.160628i	$0.948648\pi$
$230$	−6.44949	−	0.651531i	−0.425267	−	0.0429607i
$231$		0			0
$232$			6.89898i			0.452940i
$233$	−25.8058	−	14.8990i	−1.69059	−	0.976065i	−0.954037	−	0.299688i	$-0.903117\pi$
$233$	−25.8058	−	14.8990i	−1.69059	−	0.976065i	−0.736556	−	0.676376i	$-0.763549\pi$
$234$	−6.67423	−	11.5601i	−0.436308	−	0.755708i
$235$	−18.1455	+	8.16693i	−1.18368	+	0.532752i
$236$	0.775255	−	1.34278i	0.0504648	−	0.0874076i
$237$			16.8990i			1.09771i
$238$		0			0
$239$	6.20204			0.401177			0.200588	−	0.979676i	$-0.435715\pi$
$239$	6.20204			0.401177			0.200588	+	0.979676i	$0.435715\pi$
$240$	4.44414	+	3.20150i	0.286868	+	0.206656i
$241$	4.34847	+	7.53177i	0.280110	+	0.485164i	0.971411	−	0.237402i	$-0.0762959\pi$
$241$	4.34847	+	7.53177i	0.280110	+	0.485164i	−0.691302	+	0.722566i	$0.742963\pi$
$242$	11.2583	−	6.50000i	0.723713	−	0.417836i
$243$	−19.0919	−	11.0227i	−1.22474	−	0.707107i
$244$	−3.55051			−0.227298
$245$		0			0
$246$	−2.69694			−0.171951
$247$	5.97469	+	3.44949i	0.380161	+	0.219486i
$248$	−7.70674	+	4.44949i	−0.489379	+	0.282543i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−7.58128	−	8.21731i	−0.479482	−	0.519709i
$251$	−6.44949			−0.407088			−0.203544	−	0.979066i	$-0.565246\pi$
$251$	−6.44949			−0.407088			−0.203544	+	0.979066i	$0.565246\pi$
$252$		0			0
$253$		−	14.2020i		−	0.892875i
$254$	7.44949	−	12.9029i	0.467423	−	0.809600i
$255$	4.49598	+	9.98930i	0.281549	+	0.625554i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.53177	−	4.34847i	−0.469819	−	0.271250i	0.246345	−	0.969182i	$-0.420770\pi$
$257$	−7.53177	−	4.34847i	−0.469819	−	0.271250i	−0.716164	+	0.697932i	$0.754104\pi$
$258$		−	2.20204i		−	0.137093i
$259$		0			0
$260$	1.00000	−	9.89898i	0.0620174	−	0.613909i
$261$	−10.3485	+	17.9241i	−0.640554	+	1.10947i
$262$	−5.58542	+	3.22474i	−0.345069	+	0.199225i
$263$	8.48528	−	4.89898i	0.523225	−	0.302084i	−0.215028	−	0.976608i	$-0.568984\pi$
$263$	8.48528	−	4.89898i	0.523225	−	0.302084i	0.738253	+	0.674524i	$0.235651\pi$
$264$	−6.00000	+	10.3923i	−0.369274	+	0.639602i
$265$	2.44949	−	24.2474i	0.150471	−	1.48951i
$266$		0			0
$267$		−	24.4949i		−	1.49906i
$268$	6.92820	+	4.00000i	0.423207	+	0.244339i
$269$	9.57321	+	16.5813i	0.583689	+	1.01098i	0.995037	+	0.0995010i	$0.0317247\pi$
$269$	9.57321	+	16.5813i	0.583689	+	1.01098i	−0.411348	+	0.911478i	$0.634942\pi$
$270$		0			0
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	−0.988692	−	0.149963i	$-0.952085\pi$
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	0.624218	+	0.781251i	$0.285418\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	−1.79796			−0.108619
$275$	16.2426	−	18.3351i	0.979468	−	1.10565i
$276$	3.55051	+	6.14966i	0.213716	+	0.370166i
$277$	12.9029	−	7.44949i	0.775260	−	0.447596i	−0.0594879	−	0.998229i	$-0.518947\pi$
$277$	12.9029	−	7.44949i	0.775260	−	0.447596i	0.834748	+	0.550633i	$0.185613\pi$
$278$	1.34278	+	0.775255i	0.0805347	+	0.0464967i
$279$	−26.6969			−1.59830
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	18.8776	+	10.8990i	1.12414	+	0.649025i
$283$	3.24980	−	1.87628i	0.193181	−	0.111533i	−0.400290	−	0.916389i	$-0.631091\pi$
$283$	3.24980	−	1.87628i	0.193181	−	0.111533i	0.593471	+	0.804856i	$0.297757\pi$
$284$	−0.550510	−	0.953512i	−0.0326668	−	0.0565805i
$285$	−6.89069	−	4.96396i	−0.408169	−	0.294040i
$286$	21.7980			1.28894
$287$		0			0
$288$		−	3.00000i		−	0.176777i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	−14.0674	+	6.33145i	−0.826067	+	0.371796i
$291$	19.3485	+	33.5125i	1.13423	+	1.96454i
$292$	2.51059	+	1.44949i	0.146921	+	0.0848250i
$293$			18.2474i			1.06603i	0.846107	+	0.533014i	$0.178941\pi$
$293$			18.2474i			1.06603i	−0.846107	+	0.533014i	$0.821059\pi$
$294$		0			0
$295$	3.44949	+	0.348469i	0.200837	+	0.0202887i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	3.28913	−	1.89898i	0.190534	−	0.110005i
$299$	6.44949	−	11.1708i	0.372984	−	0.646027i
$300$	−2.44949	+	12.0000i	−0.141421	+	0.692820i
$301$		0			0
$302$			19.5959i			1.12762i
$303$	7.53177	+	4.34847i	0.432689	+	0.249813i
$304$	0.775255	+	1.34278i	0.0444639	+	0.0770138i
$305$	−3.25844	−	7.23970i	−0.186578	−	0.414544i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$			20.2474i			1.15558i	0.816184	+	0.577791i	$0.196085\pi$
$307$			20.2474i			1.15558i	−0.816184	+	0.577791i	$0.803915\pi$
$308$		0			0
$309$	31.5959			1.79743
$310$	−16.1455	−	11.6310i	−0.917005	−	0.660598i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	−9.43879	+	5.44949i	−0.534366	+	0.308517i
$313$	18.7026	+	10.7980i	1.05713	+	0.610337i	0.924638	−	0.380847i	$-0.124367\pi$
$313$	18.7026	+	10.7980i	1.05713	+	0.610337i	0.132496	+	0.991184i	$0.457701\pi$
$314$	3.55051			0.200367
$315$		0			0
$316$	6.89898			0.388098
$317$	−19.4812	−	11.2474i	−1.09417	−	0.631720i	−0.159487	−	0.987200i	$-0.550984\pi$
$317$	−19.4812	−	11.2474i	−1.09417	−	0.631720i	−0.934684	+	0.355480i	$0.884317\pi$
$318$	−23.1202	+	13.3485i	−1.29652	+	0.748545i
$319$	−16.8990	−	29.2699i	−0.946161	−	1.63880i
$320$	1.30701	−	1.81431i	0.0730639	−	0.101423i
$321$	19.5959			1.09374
$322$		0			0
$323$			3.10102i			0.172545i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	21.1023	−	7.04561i	1.17055	−	0.390820i
$326$	−3.55051	−	6.14966i	−0.196645	−	0.340598i
$327$	−14.6349	−	8.44949i	−0.809314	−	0.467258i
$328$			1.10102i			0.0607937i
$329$		0			0
$330$	−26.6969	−	2.69694i	−1.46962	−	0.148462i
$331$	9.34847	−	16.1920i	0.513838	−	0.889994i	−0.486033	−	0.873941i	$-0.661556\pi$
$331$	9.34847	−	16.1920i	0.513838	−	0.889994i	0.999871	−	0.0160535i	$-0.00511022\pi$
$332$	2.12132	−	1.22474i	0.116423	−	0.0672166i
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$	2.44949	−	4.24264i	0.134030	−	0.232147i
$335$	−1.79796	+	17.7980i	−0.0982330	+	0.972406i
$336$		0			0
$337$		−	9.59592i		−	0.522723i	−0.965241	−	0.261361i	$-0.915829\pi$
$337$		−	9.59592i		−	0.522723i	0.965241	−	0.261361i	$-0.0841715\pi$
$338$	5.88721	+	3.39898i	0.320222	+	0.184880i
$339$	−24.2474	−	41.9978i	−1.31694	−	2.28101i
$340$	4.07812	−	1.83548i	0.221167	−	0.0995426i
$341$	21.7980	−	37.7552i	1.18043	−	2.04456i
$342$			4.65153i			0.251526i
$343$		0			0
$344$	−0.898979			−0.0484697
$345$	−9.28108	+	12.8835i	−0.499677	+	0.693623i
$346$	−3.12372	−	5.41045i	−0.167932	−	0.290868i
$347$	−25.0273	+	14.4495i	−1.34353	+	0.775689i	−0.987324	−	0.158717i	$-0.949264\pi$
$347$	−25.0273	+	14.4495i	−1.34353	+	0.775689i	−0.356209	+	0.934406i	$0.615931\pi$
$348$	14.6349	+	8.44949i	0.784515	+	0.452940i
$349$	8.44949			0.452291			0.226145	−	0.974094i	$-0.427388\pi$
$349$	8.44949			0.452291			0.226145	+	0.974094i	$0.427388\pi$
$350$		0			0
$351$		0			0
$352$	4.24264	+	2.44949i	0.226134	+	0.130558i
$353$	19.8311	−	11.4495i	1.05550	−	0.609395i	0.131318	−	0.991340i	$-0.458079\pi$
$353$	19.8311	−	11.4495i	1.05550	−	0.609395i	0.924185	+	0.381945i	$0.124746\pi$
$354$	−1.89898	−	3.28913i	−0.100930	−	0.174815i
$355$	1.43904	−	1.99760i	0.0763764	−	0.106021i
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	13.7980i		−	0.729245i
$359$	−13.7980	+	23.8988i	−0.728228	+	1.26133i	0.229403	+	0.973332i	$0.426323\pi$
$359$	−13.7980	+	23.8988i	−0.728228	+	1.26133i	−0.957631	+	0.287997i	$0.907011\pi$
$360$	6.11717	−	2.75321i	0.322403	−	0.145107i
$361$	8.29796	+	14.3725i	0.436735	+	0.756447i
$362$	8.87455	+	5.12372i	0.466436	+	0.269297i
$363$		−	31.8434i		−	1.67134i
$364$		0			0
$365$	−0.651531	+	6.44949i	−0.0341027	+	0.337582i
$366$	−4.34847	+	7.53177i	−0.227298	+	0.393692i
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.998277	−	0.0586798i	$-0.981311\pi$
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.448320	+	0.893873i	$0.647978\pi$
$368$	2.51059	−	1.44949i	0.130874	−	0.0755599i
$369$	−1.65153	+	2.86054i	−0.0859753	+	0.148914i
$370$	4.44949	+	0.449490i	0.231318	+	0.0233679i
$371$		0			0
$372$			21.7980i			1.13017i
$373$	4.06767	+	2.34847i	0.210616	+	0.121599i	0.601598	−	0.798799i	$-0.294531\pi$
$373$	4.06767	+	2.34847i	0.210616	+	0.121599i	−0.390982	+	0.920398i	$0.627864\pi$
$374$	4.89898	+	8.48528i	0.253320	+	0.438763i
$375$	−26.7167	+	6.01820i	−1.37964	+	0.310779i
$376$	4.44949	−	7.70674i	0.229465	−	0.397445i
$377$		−	30.6969i		−	1.58097i
$378$		0			0
$379$	−30.6969			−1.57680			−0.788398	−	0.615166i	$-0.789089\pi$
$379$	−30.6969			−1.57680			−0.788398	+	0.615166i	$0.789089\pi$
$380$	−2.02653	+	2.81311i	−0.103959	+	0.144310i
$381$	−18.2474	−	31.6055i	−0.934845	−	1.61920i
$382$	10.9959	−	6.34847i	0.562598	−	0.324816i
$383$	6.14966	+	3.55051i	0.314233	+	0.181423i	0.648819	−	0.760943i	$-0.275263\pi$
$383$	6.14966	+	3.55051i	0.314233	+	0.181423i	−0.334586	+	0.942365i	$0.608596\pi$
$384$	−2.44949			−0.125000
$385$		0			0
$386$	21.5959			1.09920
$387$	−2.33562	−	1.34847i	−0.118726	−	0.0685465i
$388$	13.6814	−	7.89898i	0.694570	−	0.401010i
$389$	6.55051	+	11.3458i	0.332124	+	0.575256i	0.982928	−	0.183990i	$-0.0589014\pi$
$389$	6.55051	+	11.3458i	0.332124	+	0.575256i	−0.650804	+	0.759246i	$0.725568\pi$
$390$	−19.7742	−	14.2450i	−1.00130	−	0.721326i
$391$	5.79796			0.293215
$392$		0			0
$393$			15.7980i			0.796902i
$394$	−9.44949	+	16.3670i	−0.476058	+	0.824557i
$395$	6.33145	+	14.0674i	0.318570	+	0.707809i
$396$	7.34847	+	12.7279i	0.369274	+	0.639602i
$397$	−2.29629	−	1.32577i	−0.115248	−	0.0665383i	0.441268	−	0.897375i	$-0.354529\pi$
$397$	−2.29629	−	1.32577i	−0.115248	−	0.0665383i	−0.556516	+	0.830837i	$0.687862\pi$
$398$		−	16.8990i		−	0.847069i
$399$		0			0
$400$	4.89898	+	1.00000i	0.244949	+	0.0500000i
$401$	14.6969	−	25.4558i	0.733930	−	1.27120i	−0.221261	−	0.975215i	$-0.571017\pi$
$401$	14.6969	−	25.4558i	0.733930	−	1.27120i	0.955191	−	0.295990i	$-0.0956494\pi$
$402$	16.9706	−	9.79796i	0.846415	−	0.488678i
$403$	34.2911	−	19.7980i	1.70816	−	0.986207i
$404$	1.77526	−	3.07483i	0.0883222	−	0.152979i
$405$	−20.0227	−	2.02270i	−0.994936	−	0.100509i
$406$		0			0
$407$			9.79796i			0.485667i
$408$	−4.24264	−	2.44949i	−0.210042	−	0.121268i
$409$	17.2474	+	29.8735i	0.852831	+	1.47715i	0.878642	+	0.477481i	$0.158450\pi$
$409$	17.2474	+	29.8735i	0.852831	+	1.47715i	−0.0258109	+	0.999667i	$0.508217\pi$
$410$	−2.24504	+	1.01045i	−0.110875	+	0.0499025i
$411$	−2.20204	+	3.81405i	−0.108619	+	0.188133i
$412$		−	12.8990i		−	0.635487i
$413$		0			0
$414$	8.69694			0.427431
$415$	4.44414	+	3.20150i	0.218154	+	0.157155i
$416$	2.22474	+	3.85337i	0.109077	+	0.188927i
$417$	3.28913	−	1.89898i	0.161069	−	0.0929934i
$418$	−6.57826	−	3.79796i	−0.321753	−	0.185764i
$419$	1.55051			0.0757474			0.0378737	−	0.999283i	$-0.487942\pi$
$419$	1.55051			0.0757474			0.0378737	+	0.999283i	$0.487942\pi$
$420$		0			0
$421$	−4.20204			−0.204795			−0.102397	−	0.994744i	$-0.532651\pi$
$421$	−4.20204			−0.204795			−0.102397	+	0.994744i	$0.532651\pi$
$422$	−10.3923	−	6.00000i	−0.505889	−	0.292075i
$423$	23.1202	−	13.3485i	1.12414	−	0.649025i
$424$	5.44949	+	9.43879i	0.264651	+	0.458388i
$425$	7.48528	+	6.63103i	0.363089	+	0.321652i
$426$	−2.69694			−0.130667
$427$		0			0
$428$		−	8.00000i		−	0.386695i
$429$	26.6969	−	46.2405i	1.28894	−	2.23251i
$430$	−0.825027	−	1.83307i	−0.0397864	−	0.0883985i
$431$	0.898979	+	1.55708i	0.0433023	+	0.0750018i	0.886864	−	0.462030i	$-0.152879\pi$
$431$	0.898979	+	1.55708i	0.0433023	+	0.0750018i	−0.843562	+	0.537032i	$0.819545\pi$
$432$		0			0
$433$		−	0.202041i		−	0.00970947i	−0.999988	−	0.00485474i	$-0.998455\pi$
$433$		−	0.202041i		−	0.00970947i	0.999988	−	0.00485474i	$-0.00154532\pi$
$434$		0			0
$435$	−3.79796	+	37.5959i	−0.182098	+	1.80259i
$436$	−3.44949	+	5.97469i	−0.165201	+	0.286136i
$437$	−3.89270	+	2.24745i	−0.186213	+	0.107510i
$438$	6.14966	−	3.55051i	0.293842	−	0.169650i
$439$	−10.6969	+	18.5276i	−0.510537	+	0.884276i	0.489388	+	0.872066i	$0.337220\pi$
$439$	−10.6969	+	18.5276i	−0.510537	+	0.884276i	−0.999925	+	0.0122101i	$0.996113\pi$
$440$	−1.10102	+	10.8990i	−0.0524891	+	0.519588i
$441$		0			0
$442$			8.89898i			0.423281i
$443$	−8.48528	−	4.89898i	−0.403148	−	0.232758i	0.284693	−	0.958619i	$-0.408108\pi$
$443$	−8.48528	−	4.89898i	−0.403148	−	0.232758i	−0.687841	+	0.725861i	$0.741442\pi$
$444$	−2.44949	−	4.24264i	−0.116248	−	0.201347i
$445$	−9.17738	−	20.3906i	−0.435049	−	0.966606i
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$		−	9.30306i		−	0.440020i
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$	11.2279	+	9.94655i	0.529289	+	0.468885i
$451$	−2.69694	−	4.67123i	−0.126994	−	0.219960i
$452$	−17.1455	+	9.89898i	−0.806458	+	0.465609i
$453$	41.5692	+	24.0000i	1.95309	+	1.12762i
$454$	7.34847			0.344881
$455$		0			0
$456$	3.79796			0.177856
$457$	25.6308	+	14.7980i	1.19896	+	0.692219i	0.960323	−	0.278890i	$-0.0899664\pi$
$457$	25.6308	+	14.7980i	1.19896	+	0.692219i	0.238636	+	0.971109i	$0.423300\pi$
$458$	16.5813	−	9.57321i	0.774793	−	0.447327i
$459$		0			0
$460$	5.25966	+	3.78899i	0.245233	+	0.176662i
$461$	17.3485			0.807999			0.403999	−	0.914759i	$-0.367620\pi$
$461$	17.3485			0.807999			0.403999	+	0.914759i	$0.367620\pi$
$462$		0			0
$463$			3.59592i			0.167116i	0.996503	+	0.0835582i	$0.0266285\pi$
$463$			3.59592i			0.167116i	−0.996503	+	0.0835582i	$0.973372\pi$
$464$	3.44949	−	5.97469i	0.160139	−	0.277368i
$465$	−44.4473	+	20.0048i	−2.06119	+	0.927701i
$466$	14.8990	+	25.8058i	0.690182	+	1.19543i
$467$	9.04952	+	5.22474i	0.418762	+	0.241772i	0.694548	−	0.719447i	$-0.255605\pi$
$467$	9.04952	+	5.22474i	0.418762	+	0.241772i	−0.275785	+	0.961219i	$0.588938\pi$
$468$			13.3485i			0.617033i
$469$		0			0
$470$	19.7980	+	2.00000i	0.913212	+	0.0922531i
$471$	4.34847	−	7.53177i	0.200367	−	0.347046i
$472$	−1.34278	+	0.775255i	−0.0618065	+	0.0356840i
$473$	3.81405	−	2.20204i	0.175370	−	0.101250i
$474$	8.44949	−	14.6349i	0.388098	−	0.672205i
$475$	−7.59592	−	1.55051i	−0.348525	−	0.0711423i
$476$		0			0
$477$			32.6969i			1.49709i
$478$	−5.37113	−	3.10102i	−0.245670	−	0.141837i
$479$	4.65153	+	8.05669i	0.212534	+	0.368119i	0.952507	−	0.304517i	$-0.0984951\pi$
$479$	4.65153	+	8.05669i	0.212534	+	0.368119i	−0.739973	+	0.672637i	$0.765162\pi$
$480$	−2.24799	−	4.99465i	−0.102606	−	0.227974i
$481$	−4.44949	+	7.70674i	−0.202879	+	0.351397i
$482$		−	8.69694i		−	0.396135i
$483$		0			0
$484$	−13.0000			−0.590909
$485$	28.6624	+	20.6480i	1.30149	+	0.937579i
$486$	11.0227	+	19.0919i	0.500000	+	0.866025i
$487$	6.32464	−	3.65153i	0.286597	−	0.165467i	−0.349809	−	0.936821i	$-0.613754\pi$
$487$	6.32464	−	3.65153i	0.286597	−	0.165467i	0.636406	+	0.771354i	$0.280420\pi$
$488$	3.07483	+	1.77526i	0.139191	+	0.0803620i
$489$	−17.3939			−0.786578
$490$		0			0
$491$	19.5959			0.884351			0.442176	−	0.896928i	$-0.354207\pi$
$491$	19.5959			0.884351			0.442176	+	0.896928i	$0.354207\pi$
$492$	2.33562	+	1.34847i	0.105298	+	0.0607937i
$493$	11.9494	−	6.89898i	0.538173	−	0.310714i
$494$	−3.44949	−	5.97469i	−0.155200	−	0.268814i
$495$	−19.2090	+	26.6648i	−0.863381	+	1.19850i
$496$	8.89898			0.399576
$497$		0			0
$498$		−	6.00000i		−	0.268866i
$499$	3.10102	−	5.37113i	0.138821	−	0.240445i	−0.788230	−	0.615381i	$-0.789002\pi$
$499$	3.10102	−	5.37113i	0.138821	−	0.240445i	0.927051	+	0.374936i	$0.122335\pi$
$500$	2.45692	+	10.9070i	0.109877	+	0.487778i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	5.58542	+	3.22474i	0.249290	+	0.143927i
$503$		−	4.00000i		−	0.178351i	−0.996016	−	0.0891756i	$-0.971577\pi$
$503$		−	4.00000i		−	0.178351i	0.996016	−	0.0891756i	$-0.0284232\pi$
$504$		0			0
$505$	7.89898	+	0.797959i	0.351500	+	0.0355087i
$506$	−7.10102	+	12.2993i	−0.315679	+	0.546772i
$507$	14.4206	−	8.32577i	0.640443	−	0.369760i
$508$	−12.9029	+	7.44949i	−0.572473	+	0.330518i
$509$	−15.7753	+	27.3235i	−0.699226	+	1.21109i	0.269509	+	0.962998i	$0.413139\pi$
$509$	−15.7753	+	27.3235i	−0.699226	+	1.21109i	−0.968735	+	0.248097i	$0.920195\pi$
$510$	1.10102	−	10.8990i	0.0487540	−	0.482615i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	4.34847	+	7.53177i	0.191803	+	0.332212i
$515$	26.3018	−	11.8379i	1.15899	−	0.521639i
$516$	−1.10102	+	1.90702i	−0.0484697	+	0.0839520i
$517$			43.5959i			1.91735i
$518$		0			0
$519$	−15.3031			−0.671730
$520$	−5.81552	+	8.07277i	−0.255027	+	0.354014i
$521$	−16.3485	−	28.3164i	−0.716239	−	1.24056i	−0.962480	−	0.271354i	$-0.912529\pi$
$521$	−16.3485	−	28.3164i	−0.716239	−	1.24056i	0.246240	−	0.969209i	$-0.420805\pi$
$522$	17.9241	−	10.3485i	0.784515	−	0.452940i
$523$	28.7056	+	16.5732i	1.25521	+	0.724696i	0.972140	−	0.234403i	$-0.0753135\pi$
$523$	28.7056	+	16.5732i	1.25521	+	0.724696i	0.283071	+	0.959099i	$0.408647\pi$
$524$	6.44949			0.281747
$525$		0			0
$526$	−9.79796			−0.427211
$527$	15.4135	+	8.89898i	0.671422	+	0.387646i
$528$	10.3923	−	6.00000i	0.452267	−	0.261116i
$529$	−7.29796	−	12.6404i	−0.317303	−	0.549584i
$530$	−14.2450	+	19.7742i	−0.618765	+	0.858935i
$531$	−4.65153			−0.201859
$532$		0			0
$533$		−	4.89898i		−	0.212198i
$534$	−12.2474	+	21.2132i	−0.529999	+	0.917985i
$535$	16.3125	−	7.34190i	0.705249	−	0.317418i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	−29.2699	−	16.8990i	−1.26309	−	0.729245i
$538$		−	19.1464i		−	0.825461i
$539$		0			0
$540$		0			0
$541$	−4.79796	+	8.31031i	−0.206280	+	0.357288i	−0.950540	−	0.310602i	$-0.899469\pi$
$541$	−4.79796	+	8.31031i	−0.206280	+	0.357288i	0.744260	+	0.667891i	$0.232803\pi$
$542$	10.3923	−	6.00000i	0.446388	−	0.257722i
$543$	21.7381	−	12.5505i	0.932872	−	0.538594i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−15.3485	−	1.55051i	−0.657456	−	0.0664166i
$546$		0			0
$547$			18.6969i			0.799423i	0.916641	+	0.399712i	$0.130890\pi$
$547$			18.6969i			0.799423i	−0.916641	+	0.399712i	$0.869110\pi$
$548$	1.55708	+	0.898979i	0.0665151	+	0.0384025i
$549$	5.32577	+	9.22450i	0.227298	+	0.393692i
$550$	−23.2341	+	7.75736i	−0.990705	+	0.330775i
$551$	−5.34847	+	9.26382i	−0.227852	+	0.394652i
$552$		−	7.10102i		−	0.302240i
$553$		0			0
$554$	−14.8990			−0.632997
$555$	6.40300	−	8.88828i	0.271792	−	0.377287i
$556$	−0.775255	−	1.34278i	−0.0328781	−	0.0569466i
$557$	−10.9959	+	6.34847i	−0.465910	+	0.268993i	−0.714526	−	0.699609i	$-0.753358\pi$
$557$	−10.9959	+	6.34847i	−0.465910	+	0.268993i	0.248616	+	0.968602i	$0.420024\pi$
$558$	23.1202	+	13.3485i	0.978757	+	0.565086i
$559$	4.00000			0.169182
$560$		0			0
$561$	24.0000			1.01328
$562$	15.5885	+	9.00000i	0.657559	+	0.379642i
$563$	−26.0201	+	15.0227i	−1.09662	+	0.633131i	−0.935330	−	0.353776i	$-0.884897\pi$
$563$	−26.0201	+	15.0227i	−1.09662	+	0.633131i	−0.161286	+	0.986908i	$0.551564\pi$
$564$	−10.8990	−	18.8776i	−0.458930	−	0.794890i
$565$	−35.9197	−	25.8761i	−1.51115	−	1.08861i
$566$	−3.75255			−0.157731
$567$		0			0
$568$			1.10102i			0.0461978i
$569$	16.8990	−	29.2699i	0.708442	−	1.22706i	−0.256993	−	0.966413i	$-0.582732\pi$
$569$	16.8990	−	29.2699i	0.708442	−	1.22706i	0.965435	−	0.260644i	$-0.0839350\pi$
$570$	3.48553	+	7.74426i	0.145993	+	0.324371i
$571$	5.55051	+	9.61377i	0.232282	+	0.402324i	0.958479	−	0.285162i	$-0.0920476\pi$
$571$	5.55051	+	9.61377i	0.232282	+	0.402324i	−0.726198	+	0.687486i	$0.758714\pi$
$572$	−18.8776	−	10.8990i	−0.789312	−	0.455709i
$573$		−	31.1010i		−	1.29926i
$574$		0			0
$575$	−2.89898	+	14.2020i	−0.120896	+	0.592266i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	2.16064	−	1.24745i	0.0899488	−	0.0519320i	−0.454351	−	0.890823i	$-0.650129\pi$
$577$	2.16064	−	1.24745i	0.0899488	−	0.0519320i	0.544300	+	0.838891i	$0.316795\pi$
$578$	11.2583	−	6.50000i	0.468285	−	0.270364i
$579$	26.4495	−	45.8119i	1.09920	−	1.90388i
$580$	15.3485	+	1.55051i	0.637310	+	0.0643814i
$581$		0			0
$582$		−	38.6969i		−	1.60404i
$583$	−46.2405	−	26.6969i	−1.91508	−	1.10567i
$584$	−1.44949	−	2.51059i	−0.0599803	−	0.103889i
$585$	−27.2183	+	12.2504i	−1.12534	+	0.506491i
$586$	9.12372	−	15.8028i	0.376898	−	0.652806i
$587$		−	1.14643i		−	0.0473182i	−0.999720	−	0.0236591i	$-0.992468\pi$
$587$		−	1.14643i		−	0.0473182i	0.999720	−	0.0236591i	$-0.00753162\pi$
$588$		0			0
$589$	−13.7980			−0.568535
$590$	−2.81311	−	2.02653i	−0.115814	−	0.0834308i
$591$	23.1464	+	40.0908i	0.952117	+	1.64911i
$592$	−1.73205	+	1.00000i	−0.0711868	+	0.0410997i
$593$	9.43879	+	5.44949i	0.387605	+	0.223784i	0.681122	−	0.732170i	$-0.261492\pi$
$593$	9.43879	+	5.44949i	0.387605	+	0.223784i	−0.293517	+	0.955954i	$0.594826\pi$
$594$		0			0
$595$		0			0
$596$	−3.79796			−0.155570
$597$	−35.8481	−	20.6969i	−1.46717	−	0.847069i
$598$	−11.1708	+	6.44949i	−0.456810	+	0.263739i
$599$	−6.55051	−	11.3458i	−0.267647	−	0.463577i	0.700607	−	0.713547i	$-0.252913\pi$
$599$	−6.55051	−	11.3458i	−0.267647	−	0.463577i	−0.968254	+	0.249970i	$0.919579\pi$
$600$	8.12132	−	9.16756i	0.331552	−	0.374264i
$601$	−39.3939			−1.60691			−0.803455	−	0.595366i	$-0.797007\pi$
$601$	−39.3939			−1.60691			−0.803455	+	0.595366i	$0.797007\pi$
$602$		0			0
$603$		−	24.0000i		−	0.977356i
$604$	9.79796	−	16.9706i	0.398673	−	0.690522i
$605$	−11.9306	−	26.5078i	−0.485047	−	1.07769i
$606$	−4.34847	−	7.53177i	−0.176644	−	0.305957i
$607$	28.9199	+	16.6969i	1.17382	+	0.677708i	0.954578	−	0.297962i	$-0.0963068\pi$
$607$	28.9199	+	16.6969i	1.17382	+	0.677708i	0.219247	+	0.975669i	$0.429640\pi$
$608$		−	1.55051i		−	0.0628815i
$609$		0			0
$610$	−0.797959	+	7.89898i	−0.0323084	+	0.319820i
$611$	−19.7980	+	34.2911i	−0.800940	+	1.38727i
$612$	−5.19615	+	3.00000i	−0.210042	+	0.121268i
$613$	−24.0737	+	13.8990i	−0.972329	+	0.561374i	−0.899946	−	0.436002i	$-0.856394\pi$
$613$	−24.0737	+	13.8990i	−0.972329	+	0.561374i	−0.0723836	+	0.997377i	$0.523061\pi$
$614$	10.1237	−	17.5348i	0.408560	−	0.707647i
$615$	−0.606123	+	6.00000i	−0.0244412	+	0.241943i
$616$		0			0
$617$		−	29.5959i		−	1.19149i	−0.803175	−	0.595743i	$-0.796858\pi$
$617$		−	29.5959i		−	1.19149i	0.803175	−	0.595743i	$-0.203142\pi$
$618$	−27.3629	−	15.7980i	−1.10070	−	0.635487i
$619$	−20.7753	−	35.9838i	−0.835028	−	1.44631i	−0.894008	−	0.448052i	$-0.852118\pi$
$619$	−20.7753	−	35.9838i	−0.835028	−	1.44631i	0.0589796	−	0.998259i	$-0.481215\pi$
$620$	8.16693	+	18.1455i	0.327992	+	0.728742i
$621$		0			0
$622$			12.0000i			0.481156i
$623$		0			0
$624$	10.8990			0.436308
$625$	−19.9853	+	15.0196i	−0.799411	+	0.600784i
$626$	−10.7980	−	18.7026i	−0.431573	−	0.747507i
$627$	−16.1134	+	9.30306i	−0.643506	+	0.371528i
$628$	−3.07483	−	1.77526i	−0.122699	−	0.0708404i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	−42.4949			−1.69170			−0.845848	−	0.533425i	$-0.820905\pi$
$631$	−42.4949			−1.69170			−0.845848	+	0.533425i	$0.820905\pi$
$632$	−5.97469	−	3.44949i	−0.237660	−	0.137213i
$633$	−25.4558	+	14.6969i	−1.01178	+	0.584151i
$634$	11.2474	+	19.4812i	0.446693	+	0.773695i
$635$	−27.0314	−	19.4731i	−1.07271	−	0.772765i
$636$	26.6969			1.05860
$637$		0			0
$638$			33.7980i			1.33807i
$639$	−1.65153	+	2.86054i	−0.0653335	+	0.113161i
$640$	−2.03906	+	0.917738i	−0.0806008	+	0.0362768i
$641$	−12.8990	−	22.3417i	−0.509479	−	0.882444i	−0.999940	−	0.0109803i	$-0.996505\pi$
$641$	−12.8990	−	22.3417i	−0.509479	−	0.882444i	0.490461	−	0.871463i	$-0.336829\pi$
$642$	−16.9706	−	9.79796i	−0.669775	−	0.386695i
$643$			25.1464i			0.991678i	0.868414	+	0.495839i	$0.165139\pi$
$643$			25.1464i			0.991678i	−0.868414	+	0.495839i	$0.834861\pi$
$644$		0			0
$645$	−4.89898	−	0.494897i	−0.192897	−	0.0194866i
$646$	1.55051	−	2.68556i	0.0610040	−	0.105662i
$647$	40.0908	−	23.1464i	1.57613	−	0.909980i	0.580740	−	0.814089i	$-0.302763\pi$
$647$	40.0908	−	23.1464i	1.57613	−	0.909980i	0.995392	−	0.0958907i	$-0.0305699\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$	3.79796	−	6.57826i	0.149083	−	0.258219i
$650$	−21.7980	−	4.44949i	−0.854986	−	0.174523i
$651$		0			0
$652$			7.10102i			0.278097i
$653$	17.4955	+	10.1010i	0.684651	+	0.395283i	0.801605	−	0.597854i	$-0.203980\pi$
$653$	17.4955	+	10.1010i	0.684651	+	0.395283i	−0.116954	+	0.993137i	$0.537313\pi$
$654$	8.44949	+	14.6349i	0.330401	+	0.572272i
$655$	5.91894	+	13.1509i	0.231272	+	0.513848i
$656$	0.550510	−	0.953512i	0.0214938	−	0.0372284i
$657$		−	8.69694i		−	0.339300i
$658$		0			0
$659$	−16.8990			−0.658291			−0.329145	−	0.944279i	$-0.606761\pi$
$659$	−16.8990			−0.658291			−0.329145	+	0.944279i	$0.606761\pi$
$660$	21.7718	+	15.6841i	0.847465	+	0.610502i
$661$	20.4722	+	35.4589i	0.796276	+	1.37919i	0.922026	+	0.387129i	$0.126533\pi$
$661$	20.4722	+	35.4589i	0.796276	+	1.37919i	−0.125750	+	0.992062i	$0.540134\pi$
$662$	−16.1920	+	9.34847i	−0.629321	+	0.363339i
$663$	18.8776	+	10.8990i	0.733145	+	0.423281i
$664$	−2.44949			−0.0950586
$665$		0			0
$666$	−6.00000			−0.232495
$667$	17.3205	+	10.0000i	0.670653	+	0.387202i
$668$	−4.24264	+	2.44949i	−0.164153	+	0.0947736i
$669$	4.89898	+	8.48528i	0.189405	+	0.328060i
$670$	10.4561	−	14.5145i	0.403953	−	0.560744i
$671$	−17.3939			−0.671483
$672$		0			0
$673$		−	17.7980i		−	0.686061i	−0.939324	−	0.343030i	$-0.888547\pi$
$673$		−	17.7980i		−	0.686061i	0.939324	−	0.343030i	$-0.111453\pi$
$674$	−4.79796	+	8.31031i	−0.184810	+	0.320101i
$675$		0			0
$676$	−3.39898	−	5.88721i	−0.130730	−	0.226431i
$677$	−31.5662	−	18.2247i	−1.21319	−	0.700434i	−0.249735	−	0.968314i	$-0.580343\pi$
$677$	−31.5662	−	18.2247i	−1.21319	−	0.700434i	−0.963452	+	0.267880i	$0.913677\pi$
$678$			48.4949i			1.86244i
$679$		0			0
$680$	−4.44949	−	0.449490i	−0.170630	−	0.0172371i
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	−37.7552	+	21.7980i	−1.44572	+	0.834687i
$683$	3.11416	−	1.79796i	0.119160	−	0.0687970i	−0.439235	−	0.898372i	$-0.644751\pi$
$683$	3.11416	−	1.79796i	0.119160	−	0.0687970i	0.558395	+	0.829575i	$0.311417\pi$
$684$	2.32577	−	4.02834i	0.0889279	−	0.154028i
$685$	−0.404082	+	4.00000i	−0.0154392	+	0.152832i
$686$		0			0
$687$		−	46.8990i		−	1.78931i
$688$	0.778539	+	0.449490i	0.0296815	+	0.0171366i
$689$	−24.2474	−	41.9978i	−0.923754	−	1.59999i
$690$	14.4794	−	6.51687i	0.551221	−	0.248093i
$691$	−10.5732	+	18.3133i	−0.402224	+	0.696672i	−0.993994	−	0.109434i	$-0.965096\pi$
$691$	−10.5732	+	18.3133i	−0.402224	+	0.696672i	0.591770	+	0.806107i	$0.298429\pi$
$692$			6.24745i			0.237492i
$693$		0			0
$694$	28.8990			1.09699
$695$	2.02653	−	2.81311i	0.0768706	−	0.106707i
$696$	−8.44949	−	14.6349i	−0.320277	−	0.554736i
$697$	1.90702	−	1.10102i	0.0722337	−	0.0417041i
$698$	−7.31747	−	4.22474i	−0.276970	−	0.159909i
$699$	72.9898			2.76073
$700$		0			0
$701$	11.3031			0.426911			0.213455	−	0.976953i	$-0.431528\pi$
$701$	11.3031			0.426911			0.213455	+	0.976953i	$0.431528\pi$
$702$		0			0
$703$	2.68556	−	1.55051i	0.101288	−	0.0584786i
$704$	−2.44949	−	4.24264i	−0.0923186	−	0.159901i
$705$	28.4901	−	39.5483i	1.07300	−	1.48948i
$706$	−22.8990			−0.861814
$707$		0			0
$708$			3.79796i			0.142736i
$709$	−14.1464	+	24.5023i	−0.531280	+	0.920204i	0.468053	+	0.883700i	$0.344956\pi$
$709$	−14.1464	+	24.5023i	−0.531280	+	0.920204i	−0.999334	+	0.0365041i	$0.988378\pi$
$710$	−2.24504	+	1.01045i	−0.0842550	+	0.0379214i
$711$	−10.3485	−	17.9241i	−0.388098	−	0.672205i
$712$	8.66025	+	5.00000i	0.324557	+	0.187383i
$713$			25.7980i			0.966141i
$714$		0			0
$715$	4.89898	−	48.4949i	0.183211	−	1.81361i
$716$	−6.89898	+	11.9494i	−0.257827	+	0.446569i
$717$	−13.1565	+	7.59592i	−0.491339	+	0.283675i
$718$	23.8988	−	13.7980i	0.891894	−	0.514935i
$719$	−2.24745	+	3.89270i	−0.0838157	+	0.145173i	−0.904886	−	0.425654i	$-0.860044\pi$
$719$	−2.24745	+	3.89270i	−0.0838157	+	0.145173i	0.821070	+	0.570827i	$0.193377\pi$
$720$	−6.67423	−	0.674235i	−0.248734	−	0.0251272i
$721$		0			0
$722$		−	16.5959i		−	0.617636i
$723$	−18.4490	−	10.6515i	−0.686125	−	0.396135i
$724$	−5.12372	−	8.87455i	−0.190422	−	0.329820i
$725$	10.9243	+	32.7194i	0.405718	+	1.21517i
$726$	−15.9217	+	27.5772i	−0.590909	+	1.02348i
$727$		−	22.6969i		−	0.841783i	−0.907111	−	0.420891i	$-0.861717\pi$
$727$		−	22.6969i		−	0.841783i	0.907111	−	0.420891i	$-0.138283\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	3.78899	−	5.25966i	0.140237	−	0.194669i
$731$	0.898979	+	1.55708i	0.0332500	+	0.0575906i
$732$	7.53177	−	4.34847i	0.278382	−	0.160724i
$733$	−34.3304	−	19.8207i	−1.26802	−	0.732093i	−0.293409	−	0.955987i	$-0.594790\pi$
$733$	−34.3304	−	19.8207i	−1.26802	−	0.732093i	−0.974613	+	0.223894i	$0.928123\pi$
$734$	32.0000			1.18114
$735$		0			0
$736$	−2.89898			−0.106858
$737$	33.9411	+	19.5959i	1.25024	+	0.721825i
$738$	2.86054	−	1.65153i	0.105298	−	0.0607937i
$739$	2.24745	+	3.89270i	0.0826737	+	0.143195i	0.904398	−	0.426691i	$-0.140321\pi$
$739$	2.24745	+	3.89270i	0.0826737	+	0.143195i	−0.821724	+	0.569886i	$0.806987\pi$
$740$	−3.62863	−	2.61401i	−0.133391	−	0.0960931i
$741$	−16.8990			−0.620800
$742$		0			0
$743$		−	44.6969i		−	1.63977i	−0.572527	−	0.819886i	$-0.694037\pi$
$743$		−	44.6969i		−	1.63977i	0.572527	−	0.819886i	$-0.305963\pi$
$744$	10.8990	−	18.8776i	0.399576	−	0.692086i
$745$	−3.48553	−	7.74426i	−0.127700	−	0.283728i
$746$	−2.34847	−	4.06767i	−0.0859836	−	0.148928i
$747$	−6.36396	−	3.67423i	−0.232845	−	0.134433i
$748$		−	9.79796i		−	0.358249i
$749$		0			0
$750$	26.1464	+	8.14643i	0.954733	+	0.297465i
$751$	20.8990	−	36.1981i	0.762615	−	1.32089i	−0.178884	−	0.983870i	$-0.557249\pi$
$751$	20.8990	−	36.1981i	0.762615	−	1.32089i	0.941499	−	0.337017i	$-0.109418\pi$
$752$	−7.70674	+	4.44949i	−0.281036	+	0.162256i
$753$	13.6814	−	7.89898i	0.498579	−	0.287855i
$754$	−15.3485	+	26.5843i	−0.558958	+	0.968144i
$755$	43.5959	+	4.40408i	1.58662	+	0.160281i
$756$		0			0
$757$			51.7980i			1.88263i	0.337531	+	0.941314i	$0.390408\pi$
$757$			51.7980i			1.88263i	−0.337531	+	0.941314i	$0.609592\pi$
$758$	26.5843	+	15.3485i	0.965586	+	0.557482i
$759$	17.3939	+	30.1271i	0.631358	+	1.09354i
$760$	3.16158	−	1.42296i	0.114683	−	0.0516162i
$761$	10.5505	−	18.2740i	0.382456	−	0.662433i	−0.608957	−	0.793203i	$-0.708412\pi$
$761$	10.5505	−	18.2740i	0.382456	−	0.662433i	0.991413	+	0.130771i	$0.0417451\pi$
$762$			36.4949i			1.32207i
$763$		0			0
$764$	−12.6969			−0.459359
$765$	−10.8859	−	7.84204i	−0.393580	−	0.283530i
$766$	−3.55051	−	6.14966i	−0.128285	−	0.222196i
$767$	5.97469	−	3.44949i	0.215734	−	0.124554i
$768$	2.12132	+	1.22474i	0.0765466	+	0.0441942i
$769$	40.6969			1.46757			0.733785	−	0.679382i	$-0.237752\pi$
$769$	40.6969			1.46757			0.733785	+	0.679382i	$0.237752\pi$
$770$		0			0
$771$	21.3031			0.767211
$772$	−18.7026	−	10.7980i	−0.673122	−	0.388627i
$773$	1.16781	−	0.674235i	0.0420032	−	0.0242505i	−0.478851	−	0.877896i	$-0.658947\pi$
$773$	1.16781	−	0.674235i	0.0420032	−	0.0242505i	0.520855	+	0.853645i	$0.325613\pi$
$774$	1.34847	+	2.33562i	0.0484697	+	0.0839520i
$775$	−29.5047	+	33.3057i	−1.05984	+	1.19638i
$776$	−15.7980			−0.567114
$777$		0			0
$778$		−	13.1010i		−	0.469694i
$779$	−0.853572	+	1.47843i	−0.0305824	+	0.0529702i
$780$	10.0024	+	22.2237i	0.358144	+	0.795734i
$781$	−2.69694	−	4.67123i	−0.0965040	−	0.167150i
$782$	−5.02118	−	2.89898i	−0.179557	−	0.103667i
$783$		0			0
$784$		0			0
$785$	0.797959	−	7.89898i	0.0284804	−	0.281927i
$786$	7.89898	−	13.6814i	0.281747	−	0.488001i
$787$	−43.6905	+	25.2247i	−1.55740	+	0.899165i	−0.559895	+	0.828564i	$0.689159\pi$
$787$	−43.6905	+	25.2247i	−1.55740	+	0.899165i	−0.997505	+	0.0706014i	$0.977508\pi$
$788$	16.3670	−	9.44949i	0.583050	−	0.336624i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	1.55051	−	15.3485i	0.0551647	−	0.546074i
$791$		0			0
$792$		−	14.6969i		−	0.522233i
$793$	−13.6814	−	7.89898i	−0.485842	−	0.280501i
$794$	1.32577	+	2.29629i	0.0470497	+	0.0814924i
$795$	24.5008	+	54.4366i	0.868953	+	1.93067i
$796$	−8.44949	+	14.6349i	−0.299484	+	0.518722i
$797$			0.944387i			0.0334519i	0.999860	+	0.0167260i	$0.00532429\pi$
$797$			0.944387i			0.0334519i	−0.999860	+	0.0167260i	$0.994676\pi$
$798$		0			0
$799$	−17.7980			−0.629647
$800$	−3.74264	−	3.31552i	−0.132322	−	0.117221i
$801$	15.0000	+	25.9808i	0.529999	+	0.917985i
$802$	−25.4558	+	14.6969i	−0.898877	+	0.518967i
$803$	12.2993	+	7.10102i	0.434034	+	0.250590i
$804$	−19.5959			−0.691095
$805$		0			0
$806$	−39.5959			−1.39471
$807$	−40.6157	−	23.4495i	−1.42974	−	0.825461i
$808$	−3.07483	+	1.77526i	−0.108172	+	0.0624533i
$809$	23.7980	+	41.2193i	0.836692	+	1.44919i	0.892646	+	0.450759i	$0.148847\pi$
$809$	23.7980	+	41.2193i	0.836692	+	1.44919i	−0.0559539	+	0.998433i	$0.517820\pi$
$810$	16.3288	+	11.7631i	0.573736	+	0.413312i
$811$	14.9444			0.524768			0.262384	−	0.964963i	$-0.415491\pi$
$811$	14.9444			0.524768			0.262384	+	0.964963i	$0.415491\pi$
$812$		0			0
$813$		−	29.3939i		−	1.03089i
$814$	4.89898	−	8.48528i	0.171709	−	0.297409i
$815$	−14.4794	+	6.51687i	−0.507191	+	0.228276i
$816$	2.44949	+	4.24264i	0.0857493	+	0.148522i
$817$	−1.20713	−	0.696938i	−0.0422322	−	0.0243828i
$818$		−	34.4949i		−	1.20609i
$819$		0			0
$820$	2.44949	+	0.247449i	0.0855399	+	0.00864128i
$821$	−4.10102	+	7.10318i	−0.143127	+	0.247903i	−0.928672	−	0.370901i	$-0.879049\pi$
$821$	−4.10102	+	7.10318i	−0.143127	+	0.247903i	0.785546	+	0.618803i	$0.212382\pi$
$822$	3.81405	−	2.20204i	0.133030	−	0.0768050i
$823$	−33.9411	+	19.5959i	−1.18311	+	0.683071i	−0.956733	−	0.290968i	$-0.906023\pi$
$823$	−33.9411	+	19.5959i	−1.18311	+	0.683071i	−0.226381	+	0.974039i	$0.572689\pi$
$824$	−6.44949	+	11.1708i	−0.224679	+	0.389155i
$825$	−12.0000	+	58.7878i	−0.417786	+	2.04673i
$826$		0			0
$827$			15.5959i			0.542323i	0.962534	+	0.271162i	$0.0874078\pi$
$827$			15.5959i			0.542323i	−0.962534	+	0.271162i	$0.912592\pi$
$828$	−7.53177	−	4.34847i	−0.261747	−	0.151120i
$829$	−21.8207	−	37.7945i	−0.757863	−	1.31266i	−0.943938	−	0.330122i	$-0.892910\pi$
$829$	−21.8207	−	37.7945i	−0.757863	−	1.31266i	0.186075	−	0.982535i	$-0.440423\pi$
$830$	−2.24799	−	4.99465i	−0.0780288	−	0.173367i
$831$	−18.2474	+	31.6055i	−0.632997	+	1.09638i
$832$		−	4.44949i		−	0.154258i
$833$		0			0
$834$	−3.79796			−0.131513
$835$	−8.88828	−	6.40300i	−0.307592	−	0.221585i
$836$	3.79796	+	6.57826i	0.131355	+	0.227514i
$837$		0			0
$838$	−1.34278	−	0.775255i	−0.0463856	−	0.0267807i
$839$	−36.8990			−1.27389			−0.636947	−	0.770907i	$-0.719803\pi$
$839$	−36.8990			−1.27389			−0.636947	+	0.770907i	$0.719803\pi$
$840$		0			0
$841$	18.5959			0.641239
$842$	3.63907	+	2.10102i	0.125411	+	0.0724059i
$843$	38.1838	−	22.0454i	1.31512	−	0.759284i
$844$	6.00000	+	10.3923i	0.206529	+	0.357718i
$845$	8.88498	−	12.3336i	0.305653	−	0.424290i
$846$	−26.6969			−0.917860
$847$		0			0
$848$		−	10.8990i		−	0.374272i
$849$	−4.59592	+	7.96036i	−0.157731	+	0.273199i
$850$	−3.16693	−	9.48528i	−0.108625	−	0.325342i
$851$	−2.89898	−	5.02118i	−0.0993757	−	0.172124i
$852$	2.33562	+	1.34847i	0.0800169	+	0.0461978i
$853$		−	33.8434i		−	1.15877i	−0.815052	−	0.579387i	$-0.803292\pi$
$853$		−	33.8434i		−	1.15877i	0.815052	−	0.579387i	$-0.196708\pi$
$854$		0			0
$855$	10.3485	+	1.04541i	0.353910	+	0.0357522i
$856$	−4.00000	+	6.92820i	−0.136717	+	0.236801i
$857$	46.0655	−	26.5959i	1.57357	−	0.908499i	0.577840	−	0.816150i	$-0.303896\pi$
$857$	46.0655	−	26.5959i	1.57357	−	0.908499i	0.995727	−	0.0923493i	$-0.0294376\pi$
$858$	−46.2405	+	26.6969i	−1.57862	+	0.911418i
$859$	26.8207	−	46.4548i	0.915109	−	1.58502i	0.108368	−	0.994111i	$-0.465438\pi$
$859$	26.8207	−	46.4548i	0.915109	−	1.58502i	0.806741	−	0.590905i	$-0.201229\pi$
$860$	−0.202041	+	2.00000i	−0.00688954	+	0.0681994i
$861$		0			0
$862$		−	1.79796i		−	0.0612387i
$863$	39.3123	+	22.6969i	1.33820	+	0.772613i	0.986541	−	0.163514i	$-0.0522828\pi$
$863$	39.3123	+	22.6969i	1.33820	+	0.772613i	0.351664	+	0.936126i	$0.385616\pi$
$864$		0			0
$865$	−12.7389	+	5.73352i	−0.433136	+	0.194945i
$866$	−0.101021	+	0.174973i	−0.00343282	+	0.00594581i
$867$		−	31.8434i		−	1.08146i
$868$		0			0
$869$	33.7980			1.14652
$870$	22.0871	−	30.6600i	0.748822	−	1.03947i
$871$	17.7980	+	30.8270i	0.603061	+	1.04453i
$872$	5.97469	−	3.44949i	0.202329	−	0.116814i
$873$	−41.0443	−	23.6969i	−1.38914	−	0.802020i
$874$	4.49490			0.152042
$875$		0			0
$876$	−7.10102			−0.239921
$877$	−34.1161	−	19.6969i	−1.15202	−	0.665118i	−0.202640	−	0.979253i	$-0.564952\pi$
$877$	−34.1161	−	19.6969i	−1.15202	−	0.665118i	−0.949378	+	0.314135i	$0.898286\pi$
$878$	18.5276	−	10.6969i	0.625278	−	0.361004i
$879$	−22.3485	−	38.7087i	−0.753795	−	1.30561i
$880$	6.40300	−	8.88828i	0.215845	−	0.299624i
$881$	8.20204			0.276334			0.138167	−	0.990409i	$-0.455879\pi$
$881$	8.20204			0.276334			0.138167	+	0.990409i	$0.455879\pi$
$882$		0			0
$883$			22.2020i			0.747158i	0.927598	+	0.373579i	$0.121870\pi$
$883$			22.2020i			0.747158i	−0.927598	+	0.373579i	$0.878130\pi$
$884$	4.44949	−	7.70674i	0.149653	−	0.259206i
$885$	−7.74426	+	3.48553i	−0.260320	+	0.117165i
$886$	4.89898	+	8.48528i	0.164584	+	0.285069i
$887$	2.33562	+	1.34847i	0.0784224	+	0.0452772i	0.538698	−	0.842499i	$-0.318916\pi$
$887$	2.33562	+	1.34847i	0.0784224	+	0.0452772i	−0.460276	+	0.887776i	$0.652250\pi$
$888$			4.89898i			0.164399i
$889$		0			0
$890$	−2.24745	+	22.2474i	−0.0753347	+	0.745736i
$891$	−22.0454	+	38.1838i	−0.738549	+	1.27920i
$892$	3.46410	−	2.00000i	0.115987	−	0.0669650i
$893$	11.9494	−	6.89898i	0.399871	−	0.230866i
$894$	−4.65153	+	8.05669i	−0.155570	+	0.269456i
$895$	−30.6969	−	3.10102i	−1.02609	−	0.103656i
$896$		0			0
$897$			31.5959i			1.05496i
$898$	−8.66025	−	5.00000i	−0.288996	−	0.166852i
$899$	30.6969	+	53.1687i	1.02380	+	1.77327i
$900$	−4.75039	−	14.2279i	−0.158346	−	0.474264i
$901$	10.8990	−	18.8776i	0.363098	−	0.628904i
$902$			5.39388i			0.179596i
$903$		0			0
$904$	19.7980			0.658470
$905$	13.3935	−	18.5921i	0.445215	−	0.618022i
$906$	−24.0000	−	41.5692i	−0.797347	−	1.38104i
$907$	36.1981	−	20.8990i	1.20194	−	0.693939i	0.240952	−	0.970537i	$-0.422540\pi$
$907$	36.1981	−	20.8990i	1.20194	−	0.693939i	0.960986	+	0.276598i	$0.0892070\pi$
$908$	−6.36396	−	3.67423i	−0.211195	−	0.121934i
$909$	−10.6515			−0.353289
$910$		0			0
$911$	−35.5959			−1.17935			−0.589673	−	0.807642i	$-0.700743\pi$
$911$	−35.5959			−1.17935			−0.589673	+	0.807642i	$0.700743\pi$
$912$	−3.28913	−	1.89898i	−0.108914	−	0.0628815i
$913$	10.3923	−	6.00000i	0.343935	−	0.198571i
$914$	−14.7980	−	25.6308i	−0.489473	−	0.847792i
$915$	15.7790	+	11.3670i	0.521637	+	0.375780i
$916$	−19.1464			−0.632616
$917$		0			0
$918$		0			0
$919$	−13.4495	+	23.2952i	−0.443658	+	0.768438i	−0.997958	−	0.0638793i	$-0.979653\pi$
$919$	−13.4495	+	23.2952i	−0.443658	+	0.768438i	0.554300	+	0.832317i	$0.312986\pi$
$920$	−2.66050	−	5.91119i	−0.0877142	−	0.194886i
$921$	−24.7980	−	42.9513i	−0.817121	−	1.41529i
$922$	−15.0242	−	8.67423i	−0.494796	−	0.285671i
$923$		−	4.89898i		−	0.161252i
$924$		0			0
$925$	2.00000	−	9.79796i	0.0657596	−	0.322155i
$926$	1.79796	−	3.11416i	0.0590846	−	0.102338i
$927$	−33.5125	+	19.3485i	−1.10070	+	0.635487i
$928$	−5.97469	+	3.44949i	−0.196129	+	0.113235i
$929$	−14.1464	+	24.5023i	−0.464129	+	0.803895i	−0.999162	−	0.0409360i	$-0.986966\pi$
$929$	−14.1464	+	24.5023i	−0.464129	+	0.803895i	0.535033	+	0.844831i	$0.320299\pi$
$930$	48.4949	+	4.89898i	1.59021	+	0.160644i
$931$		0			0
$932$		−	29.7980i		−	0.976065i
$933$	25.4558	+	14.6969i	0.833387	+	0.481156i
$934$	−5.22474	−	9.04952i	−0.170959	−	0.296109i
$935$	19.9786	−	8.99196i	0.653370	−	0.294068i
$936$	6.67423	−	11.5601i	0.218154	−	0.377854i
$937$			41.1010i			1.34271i	0.741135	+	0.671356i	$0.234288\pi$
$937$			41.1010i			1.34271i	−0.741135	+	0.671356i	$0.765712\pi$
$938$		0			0
$939$	−52.8990			−1.72629
$940$	−16.1455	−	11.6310i	−0.526609	−	0.379362i
$941$	9.77526	+	16.9312i	0.318664	+	0.551943i	0.980210	−	0.197963i	$-0.0634324\pi$
$941$	9.77526	+	16.9312i	0.318664	+	0.551943i	−0.661545	+	0.749905i	$0.730099\pi$
$942$	−7.53177	+	4.34847i	−0.245398	+	0.141681i
$943$	2.76421	+	1.59592i	0.0900151	+	0.0519702i
$944$	1.55051			0.0504648
$945$		0			0
$946$	−4.40408			−0.143189
$947$	38.1838	+	22.0454i	1.24081	+	0.716379i	0.969258	−	0.246046i	$-0.0791313\pi$
$947$	38.1838	+	22.0454i	1.24081	+	0.716379i	0.271547	+	0.962425i	$0.412465\pi$
$948$	−14.6349	+	8.44949i	−0.475321	+	0.274427i
$949$	6.44949	+	11.1708i	0.209359	+	0.362621i
$950$	5.80300	+	5.14074i	0.188274	+	0.166788i
$951$	55.1010			1.78677
$952$		0			0
$953$			2.20204i			0.0713311i	0.999364	+	0.0356656i	$0.0113551\pi$
$953$			2.20204i			0.0713311i	−0.999364	+	0.0356656i	$0.988645\pi$
$954$	16.3485	−	28.3164i	0.529301	−	0.916777i
$955$	−11.6525	−	25.8898i	−0.377065	−	0.837774i
$956$	3.10102	+	5.37113i	0.100294	+	0.173715i
$957$	71.6963	+	41.3939i	2.31761	+	1.33807i
$958$		−	9.30306i		−	0.300568i
$959$		0			0
$960$	−0.550510	+	5.44949i	−0.0177676	+	0.175882i
$961$	−24.0959	+	41.7354i	−0.777288	+	1.34630i
$962$	7.70674	−	4.44949i	0.248475	−	0.143457i
$963$	−20.7846	+	12.0000i	−0.669775	+	0.386695i
$964$	−4.34847	+	7.53177i	−0.140055	+	0.242582i
$965$	4.85357	−	48.0454i	0.156242	−	1.54664i
$966$		0			0
$967$			36.2929i			1.16710i	0.812077	+	0.583550i	$0.198337\pi$
$967$			36.2929i			1.16710i	−0.812077	+	0.583550i	$0.801663\pi$
$968$	11.2583	+	6.50000i	0.361856	+	0.208918i
$969$	−3.79796	−	6.57826i	−0.122008	−	0.211324i
$970$	−14.4984	−	32.2130i	−0.465515	−	1.03430i
$971$	4.77526	−	8.27098i	0.153245	−	0.265429i	−0.779173	−	0.626808i	$-0.784361\pi$
$971$	4.77526	−	8.27098i	0.153245	−	0.265429i	0.932419	+	0.361380i	$0.117694\pi$
$972$		−	22.0454i		−	0.707107i
$973$		0			0
$974$	−7.30306			−0.234005
$975$	−36.1357	+	40.7910i	−1.15727	+	1.30636i
$976$	−1.77526	−	3.07483i	−0.0568245	−	0.0984230i
$977$	25.4558	−	14.6969i	0.814405	−	0.470197i	−0.0340785	−	0.999419i	$-0.510850\pi$
$977$	25.4558	−	14.6969i	0.814405	−	0.470197i	0.848483	+	0.529222i	$0.177516\pi$
$978$	15.0635	+	8.69694i	0.481679	+	0.278097i
$979$	−48.9898			−1.56572
$980$		0			0
$981$	20.6969			0.660802
$982$	−16.9706	−	9.79796i	−0.541552	−	0.312665i
$983$	−11.5208	+	6.65153i	−0.367456	+	0.212151i	−0.672347	−	0.740237i	$-0.734713\pi$
$983$	−11.5208	+	6.65153i	−0.367456	+	0.212151i	0.304890	+	0.952387i	$0.401380\pi$
$984$	−1.34847	−	2.33562i	−0.0429876	−	0.0744568i
$985$	34.2887	+	24.7011i	1.09253	+	0.787043i
$986$	−13.7980			−0.439417
$987$		0			0
$988$			6.89898i			0.219486i
$989$	−1.30306	+	2.25697i	−0.0414349	+	0.0717674i
$990$	29.9679	−	13.4879i	0.952443	−	0.428675i
$991$	−15.6515	−	27.1092i	−0.497187	−	0.861154i	0.502807	−	0.864398i	$-0.332300\pi$
$991$	−15.6515	−	27.1092i	−0.497187	−	0.861154i	−0.999995	+	0.00324483i	$0.998967\pi$
$992$	−7.70674	−	4.44949i	−0.244689	−	0.141271i
$993$			45.7980i			1.45335i
$994$		0			0
$995$	−37.5959	−	3.79796i	−1.19187	−	0.120403i
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	−49.6652	+	28.6742i	−1.57291	+	0.908122i	−0.577104	+	0.816671i	$0.695817\pi$
$997$	−49.6652	+	28.6742i	−1.57291	+	0.908122i	−0.995810	+	0.0914515i	$0.970849\pi$
$998$	−5.37113	+	3.10102i	−0.170020	+	0.0981611i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.i.c.79.1		8
5.4	even	2	inner	490.2.i.c.79.4		8
7.2	even	3		70.2.c.a.29.3	yes	4
7.3	odd	6		490.2.i.f.459.3		8
7.4	even	3	inner	490.2.i.c.459.4		8
7.5	odd	6		490.2.c.e.99.4		4
7.6	odd	2		490.2.i.f.79.2		8
21.2	odd	6		630.2.g.g.379.1		4
28.23	odd	6		560.2.g.e.449.4		4
35.2	odd	12		350.2.a.g.1.1		2
35.4	even	6	inner	490.2.i.c.459.1		8
35.9	even	6		70.2.c.a.29.2	✓	4
35.12	even	12		2450.2.a.bl.1.2		2
35.19	odd	6		490.2.c.e.99.1		4
35.23	odd	12		350.2.a.h.1.2		2
35.24	odd	6		490.2.i.f.459.2		8
35.33	even	12		2450.2.a.bq.1.1		2
35.34	odd	2		490.2.i.f.79.3		8
56.37	even	6		2240.2.g.j.449.3		4
56.51	odd	6		2240.2.g.i.449.1		4
84.23	even	6		5040.2.t.t.1009.1		4
105.2	even	12		3150.2.a.bt.1.2		2
105.23	even	12		3150.2.a.bs.1.2		2
105.44	odd	6		630.2.g.g.379.3		4
140.23	even	12		2800.2.a.bl.1.1		2
140.79	odd	6		560.2.g.e.449.2		4
140.107	even	12		2800.2.a.bm.1.2		2
280.149	even	6		2240.2.g.j.449.1		4
280.219	odd	6		2240.2.g.i.449.3		4
420.359	even	6		5040.2.t.t.1009.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.c.a.29.2	✓	4	35.9	even	6
70.2.c.a.29.3	yes	4	7.2	even	3
350.2.a.g.1.1		2	35.2	odd	12
350.2.a.h.1.2		2	35.23	odd	12
490.2.c.e.99.1		4	35.19	odd	6
490.2.c.e.99.4		4	7.5	odd	6
490.2.i.c.79.1		8	1.1	even	1	trivial
490.2.i.c.79.4		8	5.4	even	2	inner
490.2.i.c.459.1		8	35.4	even	6	inner
490.2.i.c.459.4		8	7.4	even	3	inner
490.2.i.f.79.2		8	7.6	odd	2
490.2.i.f.79.3		8	35.34	odd	2
490.2.i.f.459.2		8	35.24	odd	6
490.2.i.f.459.3		8	7.3	odd	6
560.2.g.e.449.2		4	140.79	odd	6
560.2.g.e.449.4		4	28.23	odd	6
630.2.g.g.379.1		4	21.2	odd	6
630.2.g.g.379.3		4	105.44	odd	6
2240.2.g.i.449.1		4	56.51	odd	6
2240.2.g.i.449.3		4	280.219	odd	6
2240.2.g.j.449.1		4	280.149	even	6
2240.2.g.j.449.3		4	56.37	even	6
2450.2.a.bl.1.2		2	35.12	even	12
2450.2.a.bq.1.1		2	35.33	even	12
2800.2.a.bl.1.1		2	140.23	even	12
2800.2.a.bm.1.2		2	140.107	even	12
3150.2.a.bs.1.2		2	105.23	even	12
3150.2.a.bt.1.2		2	105.2	even	12
5040.2.t.t.1009.1		4	84.23	even	6
5040.2.t.t.1009.2		4	420.359	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.30701 + 1.81431i) q^{5} +2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.30701 + 1.81431i) q^{5} +2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(2.03906 - 0.917738i) q^{10} +(2.44949 + 4.24264i) q^{11} +(-2.12132 - 1.22474i) q^{12} +4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(0.775255 - 1.34278i) q^{19} +(-2.22474 - 0.224745i) q^{20} -4.89898i q^{22} +(-2.51059 - 1.44949i) q^{23} +(1.22474 + 2.12132i) q^{24} +(-1.58346 - 4.74264i) q^{25} +(2.22474 - 3.85337i) q^{26} -6.89898 q^{29} +(-3.20150 + 4.44414i) q^{30} +(-4.44949 - 7.70674i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-10.3923 - 6.00000i) q^{33} +2.00000 q^{34} +3.00000 q^{36} +(1.73205 + 1.00000i) q^{37} +(-1.34278 + 0.775255i) q^{38} +(-5.44949 - 9.43879i) q^{39} +(1.81431 + 1.30701i) q^{40} -1.10102 q^{41} -0.898979i q^{43} +(-2.44949 + 4.24264i) q^{44} +(2.75321 + 6.11717i) q^{45} +(1.44949 + 2.51059i) q^{46} +(7.70674 + 4.44949i) q^{47} -2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(2.44949 - 4.24264i) q^{51} +(-3.85337 + 2.22474i) q^{52} +(-9.43879 + 5.44949i) q^{53} +(-10.8990 - 1.10102i) q^{55} +3.79796i q^{57} +(5.97469 + 3.44949i) q^{58} +(-0.775255 - 1.34278i) q^{59} +(4.99465 - 2.24799i) q^{60} +(-1.77526 + 3.07483i) q^{61} +8.89898i q^{62} -1.00000 q^{64} +(-8.07277 - 5.81552i) q^{65} +(6.00000 + 10.3923i) q^{66} +(6.92820 - 4.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +7.10102 q^{69} -1.10102 q^{71} +(-2.59808 - 1.50000i) q^{72} +(2.51059 - 1.44949i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(9.16756 + 8.12132i) q^{75} +1.55051 q^{76} +10.8990i q^{78} +(3.44949 - 5.97469i) q^{79} +(-0.917738 - 2.03906i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.953512 + 0.550510i) q^{82} -2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +(-0.449490 + 0.778539i) q^{86} +(14.6349 - 8.44949i) q^{87} +(4.24264 - 2.44949i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(0.674235 - 6.67423i) q^{90} -2.89898i q^{92} +(18.8776 + 10.8990i) q^{93} +(-4.44949 - 7.70674i) q^{94} +(1.42296 + 3.16158i) q^{95} +(-1.22474 + 2.12132i) q^{96} -15.7980i q^{97} +14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5 + 12 * q^9	\( 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9} - 4 q^{10} + 24 q^{15} - 4 q^{16} + 16 q^{19} - 8 q^{20} + 8 q^{26} - 16 q^{29} - 12 q^{30} - 16 q^{31} + 16 q^{34} + 24 q^{36} - 24 q^{39} + 4 q^{40} - 48 q^{41} + 12 q^{45} - 8 q^{46} - 8 q^{50} - 48 q^{55} - 16 q^{59} + 12 q^{60} - 24 q^{61} - 8 q^{64} + 4 q^{65} + 48 q^{66} + 96 q^{69} - 48 q^{71} - 8 q^{74} + 32 q^{76} + 8 q^{79} - 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} - 40 q^{89} - 24 q^{90} - 16 q^{94} + 4 q^{95}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 + 12 * q^9 - 4 * q^10 + 24 * q^15 - 4 * q^16 + 16 * q^19 - 8 * q^20 + 8 * q^26 - 16 * q^29 - 12 * q^30 - 16 * q^31 + 16 * q^34 + 24 * q^36 - 24 * q^39 + 4 * q^40 - 48 * q^41 + 12 * q^45 - 8 * q^46 - 8 * q^50 - 48 * q^55 - 16 * q^59 + 12 * q^60 - 24 * q^61 - 8 * q^64 + 4 * q^65 + 48 * q^66 + 96 * q^69 - 48 * q^71 - 8 * q^74 + 32 * q^76 + 8 * q^79 - 4 * q^80 + 36 * q^81 - 16 * q^85 + 16 * q^86 - 40 * q^89 - 24 * q^90 - 16 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more