LMFDB - Embedded newform 490.2.c.e.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.2.c.e.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-2.22474 - 0.224745i) q^{5} -2.44949 q^{6} -1.00000i q^{8} -3.00000 q^{9} +(0.224745 - 2.22474i) q^{10} -4.89898 q^{11} -2.44949i q^{12} -4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -3.00000i q^{18} +1.55051 q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} +2.89898i q^{23} +2.44949 q^{24} +(4.89898 + 1.00000i) q^{25} +4.44949 q^{26} -6.89898 q^{29} +(5.44949 + 0.550510i) q^{30} -8.89898 q^{31} +1.00000i q^{32} -12.0000i q^{33} -2.00000 q^{34} +3.00000 q^{36} -2.00000i q^{37} +1.55051i q^{38} +10.8990 q^{39} +(-0.224745 + 2.22474i) q^{40} +1.10102 q^{41} -0.898979i q^{43} +4.89898 q^{44} +(6.67423 + 0.674235i) q^{45} -2.89898 q^{46} +8.89898i q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} -4.89898 q^{51} +4.44949i q^{52} -10.8990i q^{53} +(10.8990 + 1.10102i) q^{55} +3.79796i q^{57} -6.89898i q^{58} -1.55051 q^{59} +(-0.550510 + 5.44949i) q^{60} -3.55051 q^{61} -8.89898i q^{62} -1.00000 q^{64} +(-1.00000 + 9.89898i) q^{65} +12.0000 q^{66} +8.00000i q^{67} -2.00000i q^{68} -7.10102 q^{69} -1.10102 q^{71} +3.00000i q^{72} -2.89898i q^{73} +2.00000 q^{74} +(-2.44949 + 12.0000i) q^{75} -1.55051 q^{76} +10.8990i q^{78} -6.89898 q^{79} +(-2.22474 - 0.224745i) q^{80} -9.00000 q^{81} +1.10102i q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +0.898979 q^{86} -16.8990i q^{87} +4.89898i q^{88} -10.0000 q^{89} +(-0.674235 + 6.67423i) q^{90} -2.89898i q^{92} -21.7980i q^{93} -8.89898 q^{94} +(-3.44949 - 0.348469i) q^{95} -2.44949 q^{96} +15.7980i q^{97} +14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5} - 12 q^{9} - 4 q^{10} + 12 q^{15} + 4 q^{16} + 16 q^{19} + 4 q^{20} + 8 q^{26} - 8 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} + 12 q^{36} + 24 q^{39} + 4 q^{40} + 24 q^{41} + 12 q^{45}+ \cdots - 4 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 - 12 * q^9 - 4 * q^10 + 12 * q^15 + 4 * q^16 + 16 * q^19 + 4 * q^20 + 8 * q^26 - 8 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 + 12 * q^36 + 24 * q^39 + 4 * q^40 + 24 * q^41 + 12 * q^45 + 8 * q^46 - 4 * q^50 + 24 * q^55 - 16 * q^59 - 12 * q^60 - 24 * q^61 - 4 * q^64 - 4 * q^65 + 48 * q^66 - 48 * q^69 - 24 * q^71 + 8 * q^74 - 16 * q^76 - 8 * q^79 - 4 * q^80 - 36 * q^81 - 8 * q^85 - 16 * q^86 - 40 * q^89 + 12 * q^90 - 16 * q^94 - 4 * q^95

Character values

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

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			2.44949i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$3$			2.44949i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$4$	−1.00000			−0.500000
$5$	−2.22474	−	0.224745i	−0.994936	−	0.100509i
$5$	−2.22474	−	0.224745i	−0.994936	−	0.100509i
$6$	−2.44949			−1.00000
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−3.00000			−1.00000
$10$	0.224745	−	2.22474i	0.0710706	−	0.703526i
$11$	−4.89898			−1.47710			−0.738549	−	0.674200i	$-0.764489\pi$
$11$	−4.89898			−1.47710			−0.738549	+	0.674200i	$0.764489\pi$
$12$		−	2.44949i		−	0.707107i
$13$		−	4.44949i		−	1.23407i	−0.786937	−	0.617033i	$-0.788334\pi$
$13$		−	4.44949i		−	1.23407i	0.786937	−	0.617033i	$-0.211666\pi$
$14$		0			0
$15$	0.550510	−	5.44949i	0.142141	−	1.40705i
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	3.00000i		−	0.707107i
$19$	1.55051			0.355711			0.177856	−	0.984057i	$-0.443084\pi$
$19$	1.55051			0.355711			0.177856	+	0.984057i	$0.443084\pi$
$20$	2.22474	+	0.224745i	0.497468	+	0.0502545i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$			2.89898i			0.604479i	0.953232	+	0.302240i	$0.0977342\pi$
$23$			2.89898i			0.604479i	−0.953232	+	0.302240i	$0.902266\pi$
$24$	2.44949			0.500000
$25$	4.89898	+	1.00000i	0.979796	+	0.200000i
$26$	4.44949			0.872617
$27$		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	$0.721295\pi$
$30$	5.44949	+	0.550510i	0.994936	+	0.100509i
$31$	−8.89898			−1.59830			−0.799152	−	0.601129i	$-0.794718\pi$
$31$	−8.89898			−1.59830			−0.799152	+	0.601129i	$0.794718\pi$
$32$			1.00000i			0.176777i
$33$		−	12.0000i		−	2.08893i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	3.00000			0.500000
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$			1.55051i			0.251526i
$39$	10.8990			1.74523
$40$	−0.224745	+	2.22474i	−0.0355353	+	0.351763i
$41$	1.10102			0.171951			0.0859753	−	0.996297i	$-0.472599\pi$
$41$	1.10102			0.171951			0.0859753	+	0.996297i	$0.472599\pi$
$42$		0			0
$43$		−	0.898979i		−	0.137093i	−0.997648	−	0.0685465i	$-0.978164\pi$
$43$		−	0.898979i		−	0.137093i	0.997648	−	0.0685465i	$-0.0218362\pi$
$44$	4.89898			0.738549
$45$	6.67423	+	0.674235i	0.994936	+	0.100509i
$46$	−2.89898			−0.427431
$47$			8.89898i			1.29805i	0.760767	+	0.649025i	$0.224823\pi$
$47$			8.89898i			1.29805i	−0.760767	+	0.649025i	$0.775177\pi$
$48$			2.44949i			0.353553i
$49$		0			0
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	−4.89898			−0.685994
$52$			4.44949i			0.617033i
$53$		−	10.8990i		−	1.49709i	−0.663084	−	0.748545i	$-0.730753\pi$
$53$		−	10.8990i		−	1.49709i	0.663084	−	0.748545i	$-0.269247\pi$
$54$		0			0
$55$	10.8990	+	1.10102i	1.46962	+	0.148462i
$56$		0			0
$57$			3.79796i			0.503052i
$58$		−	6.89898i		−	0.905880i
$59$	−1.55051			−0.201859			−0.100930	−	0.994894i	$-0.532182\pi$
$59$	−1.55051			−0.201859			−0.100930	+	0.994894i	$0.532182\pi$
$60$	−0.550510	+	5.44949i	−0.0710706	+	0.703526i
$61$	−3.55051			−0.454596			−0.227298	−	0.973825i	$-0.572989\pi$
$61$	−3.55051			−0.454596			−0.227298	+	0.973825i	$0.572989\pi$
$62$		−	8.89898i		−	1.13017i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.00000	+	9.89898i	−0.124035	+	1.22782i
$66$	12.0000			1.47710
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		−	2.00000i		−	0.242536i
$69$	−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	$0.520811\pi$
$72$			3.00000i			0.353553i
$73$		−	2.89898i		−	0.339300i	−0.985504	−	0.169650i	$-0.945736\pi$
$73$		−	2.89898i		−	0.339300i	0.985504	−	0.169650i	$-0.0542637\pi$
$74$	2.00000			0.232495
$75$	−2.44949	+	12.0000i	−0.282843	+	1.38564i
$76$	−1.55051			−0.177856
$77$		0			0
$78$			10.8990i			1.23407i
$79$	−6.89898			−0.776196			−0.388098	−	0.921618i	$-0.626868\pi$
$79$	−6.89898			−0.776196			−0.388098	+	0.921618i	$0.626868\pi$
$80$	−2.22474	−	0.224745i	−0.248734	−	0.0251272i
$81$	−9.00000			−1.00000
$82$			1.10102i			0.121587i
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$		0			0
$85$	0.449490	−	4.44949i	0.0487540	−	0.482615i
$86$	0.898979			0.0969395
$87$		−	16.8990i		−	1.81176i
$88$			4.89898i			0.522233i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$	−0.674235	+	6.67423i	−0.0710706	+	0.703526i
$91$		0			0
$92$		−	2.89898i		−	0.302240i
$93$		−	21.7980i		−	2.26034i
$94$	−8.89898			−0.917860
$95$	−3.44949	−	0.348469i	−0.353910	−	0.0357522i
$96$	−2.44949			−0.250000
$97$			15.7980i			1.60404i	0.597297	+	0.802020i	$0.296241\pi$
$97$			15.7980i			1.60404i	−0.597297	+	0.802020i	$0.703759\pi$
$98$		0			0
$99$	14.6969			1.47710
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$	−3.55051			−0.353289			−0.176644	−	0.984275i	$-0.556524\pi$
$101$	−3.55051			−0.353289			−0.176644	+	0.984275i	$0.556524\pi$
$102$		−	4.89898i		−	0.485071i
$103$		−	12.8990i		−	1.27097i	−0.772111	−	0.635487i	$-0.780799\pi$
$103$		−	12.8990i		−	1.27097i	0.772111	−	0.635487i	$-0.219201\pi$
$104$	−4.44949			−0.436308
$105$		0			0
$106$	10.8990			1.05860
$107$			8.00000i			0.773389i	0.922208	+	0.386695i	$0.126383\pi$
$107$			8.00000i			0.773389i	−0.922208	+	0.386695i	$0.873617\pi$
$108$		0			0
$109$	−6.89898			−0.660802			−0.330401	−	0.943841i	$-0.607184\pi$
$109$	−6.89898			−0.660802			−0.330401	+	0.943841i	$0.607184\pi$
$110$	−1.10102	+	10.8990i	−0.104978	+	1.03918i
$111$	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	$0.618748\pi$
$114$	−3.79796			−0.355711
$115$	0.651531	−	6.44949i	0.0607556	−	0.601418i
$116$	6.89898			0.640554
$117$			13.3485i			1.23407i
$118$		−	1.55051i		−	0.142736i
$119$		0			0
$120$	−5.44949	−	0.550510i	−0.497468	−	0.0502545i
$121$	13.0000			1.18182
$122$		−	3.55051i		−	0.321448i
$123$			2.69694i			0.243175i
$124$	8.89898			0.799152
$125$	−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	$0.770117\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.20204			0.193879
$130$	−9.89898	−	1.00000i	−0.868198	−	0.0877058i
$131$	6.44949			0.563495			0.281747	−	0.959489i	$-0.409086\pi$
$131$	6.44949			0.563495			0.281747	+	0.959489i	$0.409086\pi$
$132$			12.0000i			1.04447i
$133$		0			0
$134$	−8.00000			−0.691095
$135$		0			0
$136$	2.00000			0.171499
$137$			1.79796i			0.153610i	0.997046	+	0.0768050i	$0.0244719\pi$
$137$			1.79796i			0.153610i	−0.997046	+	0.0768050i	$0.975528\pi$
$138$		−	7.10102i		−	0.604479i
$139$	1.55051			0.131513			0.0657563	−	0.997836i	$-0.479054\pi$
$139$	1.55051			0.131513			0.0657563	+	0.997836i	$0.479054\pi$
$140$		0			0
$141$	−21.7980			−1.83572
$142$		−	1.10102i		−	0.0923956i
$143$			21.7980i			1.82284i
$144$	−3.00000			−0.250000
$145$	15.3485	+	1.55051i	1.27462	+	0.128763i
$146$	2.89898			0.239921
$147$		0			0
$148$			2.00000i			0.164399i
$149$	3.79796			0.311141			0.155570	−	0.987825i	$-0.450278\pi$
$149$	3.79796			0.311141			0.155570	+	0.987825i	$0.450278\pi$
$150$	−12.0000	−	2.44949i	−0.979796	−	0.200000i
$151$	19.5959			1.59469			0.797347	−	0.603522i	$-0.206236\pi$
$151$	19.5959			1.59469			0.797347	+	0.603522i	$0.206236\pi$
$152$		−	1.55051i		−	0.125763i
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$	19.7980	+	2.00000i	1.59021	+	0.160644i
$156$	−10.8990			−0.872617
$157$			3.55051i			0.283362i	0.989912	+	0.141681i	$0.0452507\pi$
$157$			3.55051i			0.283362i	−0.989912	+	0.141681i	$0.954749\pi$
$158$		−	6.89898i		−	0.548853i
$159$	26.6969			2.11720
$160$	0.224745	−	2.22474i	0.0177676	−	0.175882i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$		−	7.10102i		−	0.556195i	−0.960553	−	0.278097i	$-0.910296\pi$
$163$		−	7.10102i		−	0.556195i	0.960553	−	0.278097i	$-0.0897038\pi$
$164$	−1.10102			−0.0859753
$165$	−2.69694	+	26.6969i	−0.209956	+	2.07835i
$166$	−2.44949			−0.190117
$167$		−	4.89898i		−	0.379094i	−0.981872	−	0.189547i	$-0.939298\pi$
$167$		−	4.89898i		−	0.379094i	0.981872	−	0.189547i	$-0.0607020\pi$
$168$		0			0
$169$	−6.79796			−0.522920
$170$	4.44949	+	0.449490i	0.341260	+	0.0344743i
$171$	−4.65153			−0.355711
$172$			0.898979i			0.0685465i
$173$			6.24745i			0.474985i	0.971389	+	0.237492i	$0.0763255\pi$
$173$			6.24745i			0.474985i	−0.971389	+	0.237492i	$0.923675\pi$
$174$	16.8990			1.28111
$175$		0			0
$176$	−4.89898			−0.369274
$177$		−	3.79796i		−	0.285472i
$178$		−	10.0000i		−	0.749532i
$179$	−13.7980			−1.03131			−0.515654	−	0.856797i	$-0.672451\pi$
$179$	−13.7980			−1.03131			−0.515654	+	0.856797i	$0.672451\pi$
$180$	−6.67423	−	0.674235i	−0.497468	−	0.0502545i
$181$	10.2474			0.761687			0.380843	−	0.924640i	$-0.375634\pi$
$181$	10.2474			0.761687			0.380843	+	0.924640i	$0.375634\pi$
$182$		0			0
$183$		−	8.69694i		−	0.642896i
$184$	2.89898			0.213716
$185$	−0.449490	+	4.44949i	−0.0330471	+	0.327133i
$186$	21.7980			1.59830
$187$		−	9.79796i		−	0.716498i
$188$		−	8.89898i		−	0.649025i
$189$		0			0
$190$	0.348469	−	3.44949i	0.0252806	−	0.250252i
$191$	12.6969			0.918718			0.459359	−	0.888251i	$-0.348079\pi$
$191$	12.6969			0.918718			0.459359	+	0.888251i	$0.348079\pi$
$192$		−	2.44949i		−	0.176777i
$193$		−	21.5959i		−	1.55451i	−0.629187	−	0.777254i	$-0.716612\pi$
$193$		−	21.5959i		−	1.55451i	0.629187	−	0.777254i	$-0.283388\pi$
$194$	−15.7980			−1.13423
$195$	−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	$-0.235101\pi$
$198$			14.6969i			1.04447i
$199$	16.8990			1.19794			0.598968	−	0.800773i	$-0.295577\pi$
$199$	16.8990			1.19794			0.598968	+	0.800773i	$0.295577\pi$
$200$	1.00000	−	4.89898i	0.0707107	−	0.346410i
$201$	−19.5959			−1.38219
$202$		−	3.55051i		−	0.249813i
$203$		0			0
$204$	4.89898			0.342997
$205$	−2.44949	−	0.247449i	−0.171080	−	0.0172826i
$206$	12.8990			0.898714
$207$		−	8.69694i		−	0.604479i
$208$		−	4.44949i		−	0.308517i
$209$	−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	$0.364461\pi$
$212$			10.8990i			0.748545i
$213$		−	2.69694i		−	0.184791i
$214$	−8.00000			−0.546869
$215$	−0.202041	+	2.00000i	−0.0137791	+	0.136399i
$216$		0			0
$217$		0			0
$218$		−	6.89898i		−	0.467258i
$219$	7.10102			0.479842
$220$	−10.8990	−	1.10102i	−0.734809	−	0.0742308i
$221$	8.89898			0.598610
$222$			4.89898i			0.328798i
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$		0			0
$225$	−14.6969	−	3.00000i	−0.979796	−	0.200000i
$226$	−19.7980			−1.31694
$227$			7.34847i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$227$			7.34847i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$228$		−	3.79796i		−	0.251526i
$229$	−19.1464			−1.26523			−0.632616	−	0.774466i	$-0.718019\pi$
$229$	−19.1464			−1.26523			−0.632616	+	0.774466i	$0.718019\pi$
$230$	6.44949	+	0.651531i	0.425267	+	0.0429607i
$231$		0			0
$232$			6.89898i			0.452940i
$233$			29.7980i			1.95213i	0.217481	+	0.976065i	$0.430216\pi$
$233$			29.7980i			1.95213i	−0.217481	+	0.976065i	$0.569784\pi$
$234$	−13.3485			−0.872617
$235$	2.00000	−	19.7980i	0.130466	−	1.29148i
$236$	1.55051			0.100930
$237$		−	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	$0.435715\pi$
$240$	0.550510	−	5.44949i	0.0355353	−	0.351763i
$241$	8.69694			0.560219			0.280110	−	0.959968i	$-0.409629\pi$
$241$	8.69694			0.560219			0.280110	+	0.959968i	$0.409629\pi$
$242$			13.0000i			0.835672i
$243$		−	22.0454i		−	1.41421i
$244$	3.55051			0.227298
$245$		0			0
$246$	−2.69694			−0.171951
$247$		−	6.89898i		−	0.438972i
$248$			8.89898i			0.565086i
$249$	−6.00000			−0.380235
$250$	3.32577	−	10.6742i	0.210340	−	0.675098i
$251$	6.44949			0.407088			0.203544	−	0.979066i	$-0.434754\pi$
$251$	6.44949			0.407088			0.203544	+	0.979066i	$0.434754\pi$
$252$		0			0
$253$		−	14.2020i		−	0.892875i
$254$	−14.8990			−0.934845
$255$	10.8990	+	1.10102i	0.682521	+	0.0689486i
$256$	1.00000			0.0625000
$257$		−	8.69694i		−	0.542500i	−0.962509	−	0.271250i	$-0.912563\pi$
$257$		−	8.69694i		−	0.542500i	0.962509	−	0.271250i	$-0.0874370\pi$
$258$			2.20204i			0.137093i
$259$		0			0
$260$	1.00000	−	9.89898i	0.0620174	−	0.613909i
$261$	20.6969			1.28111
$262$			6.44949i			0.398451i
$263$			9.79796i			0.604168i	0.953281	+	0.302084i	$0.0976823\pi$
$263$			9.79796i			0.604168i	−0.953281	+	0.302084i	$0.902318\pi$
$264$	−12.0000			−0.738549
$265$	−2.44949	+	24.2474i	−0.150471	+	1.48951i
$266$		0			0
$267$		−	24.4949i		−	1.49906i
$268$		−	8.00000i		−	0.488678i
$269$	19.1464			1.16738			0.583689	−	0.811977i	$-0.301609\pi$
$269$	19.1464			1.16738			0.583689	+	0.811977i	$0.301609\pi$
$270$		0			0
$271$	−12.0000			−0.728948			−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000			−0.728948			−0.364474	+	0.931214i	$0.618751\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−1.79796			−0.108619
$275$	−24.0000	−	4.89898i	−1.44725	−	0.295420i
$276$	7.10102			0.427431
$277$			14.8990i			0.895193i	0.894236	+	0.447596i	$0.147720\pi$
$277$			14.8990i			0.895193i	−0.894236	+	0.447596i	$0.852280\pi$
$278$			1.55051i			0.0929934i
$279$	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	$0.680403\pi$
$282$		−	21.7980i		−	1.29805i
$283$		−	3.75255i		−	0.223066i	−0.993761	−	0.111533i	$-0.964424\pi$
$283$		−	3.75255i		−	0.223066i	0.993761	−	0.111533i	$-0.0355761\pi$
$284$	1.10102			0.0653335
$285$	0.853572	−	8.44949i	0.0505612	−	0.500505i
$286$	−21.7980			−1.28894
$287$		0			0
$288$		−	3.00000i		−	0.176777i
$289$	13.0000			0.764706
$290$	−1.55051	+	15.3485i	−0.0910491	+	0.901293i
$291$	−38.6969			−2.26845
$292$			2.89898i			0.169650i
$293$		−	18.2474i		−	1.06603i	−0.846107	−	0.533014i	$-0.821059\pi$
$293$		−	18.2474i		−	1.06603i	0.846107	−	0.533014i	$-0.178941\pi$
$294$		0			0
$295$	3.44949	+	0.348469i	0.200837	+	0.0202887i
$296$	−2.00000			−0.116248
$297$		0			0
$298$			3.79796i			0.220010i
$299$	12.8990			0.745967
$300$	2.44949	−	12.0000i	0.141421	−	0.692820i
$301$		0			0
$302$			19.5959i			1.12762i
$303$		−	8.69694i		−	0.499626i
$304$	1.55051			0.0889279
$305$	7.89898	+	0.797959i	0.452294	+	0.0456910i
$306$	6.00000			0.342997
$307$		−	20.2474i		−	1.15558i	−0.816184	−	0.577791i	$-0.803915\pi$
$307$		−	20.2474i		−	1.15558i	0.816184	−	0.577791i	$-0.196085\pi$
$308$		0			0
$309$	31.5959			1.79743
$310$	−2.00000	+	19.7980i	−0.113592	+	1.12445i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		−	10.8990i		−	0.617033i
$313$			21.5959i			1.22067i	0.792142	+	0.610337i	$0.208966\pi$
$313$			21.5959i			1.22067i	−0.792142	+	0.610337i	$0.791034\pi$
$314$	−3.55051			−0.200367
$315$		0			0
$316$	6.89898			0.388098
$317$			22.4949i			1.26344i	0.775197	+	0.631720i	$0.217651\pi$
$317$			22.4949i			1.26344i	−0.775197	+	0.631720i	$0.782349\pi$
$318$			26.6969i			1.49709i
$319$	33.7980			1.89232
$320$	2.22474	+	0.224745i	0.124367	+	0.0125636i
$321$	−19.5959			−1.09374
$322$		0			0
$323$			3.10102i			0.172545i
$324$	9.00000			0.500000
$325$	4.44949	−	21.7980i	0.246813	−	1.20913i
$326$	7.10102			0.393289
$327$		−	16.8990i		−	0.934516i
$328$		−	1.10102i		−	0.0607937i
$329$		0			0
$330$	−26.6969	−	2.69694i	−1.46962	−	0.148462i
$331$	−18.6969			−1.02768			−0.513838	−	0.857887i	$-0.671777\pi$
$331$	−18.6969			−1.02768			−0.513838	+	0.857887i	$0.671777\pi$
$332$		−	2.44949i		−	0.134433i
$333$			6.00000i			0.328798i
$334$	4.89898			0.268060
$335$	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	$-0.0841715\pi$
$338$		−	6.79796i		−	0.369760i
$339$	−48.4949			−2.63388
$340$	−0.449490	+	4.44949i	−0.0243770	+	0.241307i
$341$	43.5959			2.36085
$342$		−	4.65153i		−	0.251526i
$343$		0			0
$344$	−0.898979			−0.0484697
$345$	15.7980	+	1.59592i	0.850534	+	0.0859213i
$346$	−6.24745			−0.335865
$347$		−	28.8990i		−	1.55138i	−0.631115	−	0.775689i	$-0.717402\pi$
$347$		−	28.8990i		−	1.55138i	0.631115	−	0.775689i	$-0.282598\pi$
$348$			16.8990i			0.905880i
$349$	−8.44949			−0.452291			−0.226145	−	0.974094i	$-0.572612\pi$
$349$	−8.44949			−0.452291			−0.226145	+	0.974094i	$0.572612\pi$
$350$		0			0
$351$		0			0
$352$		−	4.89898i		−	0.261116i
$353$		−	22.8990i		−	1.21879i	−0.792867	−	0.609395i	$-0.791412\pi$
$353$		−	22.8990i		−	1.21879i	0.792867	−	0.609395i	$-0.208588\pi$
$354$	3.79796			0.201859
$355$	2.44949	+	0.247449i	0.130005	+	0.0131332i
$356$	10.0000			0.529999
$357$		0			0
$358$		−	13.7980i		−	0.729245i
$359$	27.5959			1.45646			0.728228	−	0.685334i	$-0.240344\pi$
$359$	27.5959			1.45646			0.728228	+	0.685334i	$0.240344\pi$
$360$	0.674235	−	6.67423i	0.0355353	−	0.351763i
$361$	−16.5959			−0.873469
$362$			10.2474i			0.538594i
$363$			31.8434i			1.67134i
$364$		0			0
$365$	−0.651531	+	6.44949i	−0.0341027	+	0.337582i
$366$	8.69694			0.454596
$367$			32.0000i			1.67039i	0.549957	+	0.835193i	$0.314644\pi$
$367$			32.0000i			1.67039i	−0.549957	+	0.835193i	$0.685356\pi$
$368$			2.89898i			0.151120i
$369$	−3.30306			−0.171951
$370$	−4.44949	−	0.449490i	−0.231318	−	0.0233679i
$371$		0			0
$372$			21.7980i			1.13017i
$373$		−	4.69694i		−	0.243198i	−0.992579	−	0.121599i	$-0.961198\pi$
$373$		−	4.69694i		−	0.243198i	0.992579	−	0.121599i	$-0.0388022\pi$
$374$	9.79796			0.506640
$375$	8.14643	−	26.1464i	0.420680	−	1.35020i
$376$	8.89898			0.458930
$377$			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	$0.789089\pi$
$380$	3.44949	+	0.348469i	0.176955	+	0.0178761i
$381$	−36.4949			−1.86969
$382$			12.6969i			0.649632i
$383$			7.10102i			0.362845i	0.983405	+	0.181423i	$0.0580702\pi$
$383$			7.10102i			0.362845i	−0.983405	+	0.181423i	$0.941930\pi$
$384$	2.44949			0.125000
$385$		0			0
$386$	21.5959			1.09920
$387$			2.69694i			0.137093i
$388$		−	15.7980i		−	0.802020i
$389$	−13.1010			−0.664248			−0.332124	−	0.943236i	$-0.607765\pi$
$389$	−13.1010			−0.664248			−0.332124	+	0.943236i	$0.607765\pi$
$390$	2.44949	−	24.2474i	0.124035	−	1.22782i
$391$	−5.79796			−0.293215
$392$		0			0
$393$			15.7980i			0.796902i
$394$	18.8990			0.952117
$395$	15.3485	+	1.55051i	0.772265	+	0.0780146i
$396$	−14.6969			−0.738549
$397$		−	2.65153i		−	0.133077i	−0.997784	−	0.0665383i	$-0.978805\pi$
$397$		−	2.65153i		−	0.133077i	0.997784	−	0.0665383i	$-0.0211954\pi$
$398$			16.8990i			0.847069i
$399$		0			0
$400$	4.89898	+	1.00000i	0.244949	+	0.0500000i
$401$	−29.3939			−1.46786			−0.733930	−	0.679225i	$-0.762316\pi$
$401$	−29.3939			−1.46786			−0.733930	+	0.679225i	$0.762316\pi$
$402$		−	19.5959i		−	0.977356i
$403$			39.5959i			1.97241i
$404$	3.55051			0.176644
$405$	20.0227	+	2.02270i	0.994936	+	0.100509i
$406$		0			0
$407$			9.79796i			0.485667i
$408$			4.89898i			0.242536i
$409$	34.4949			1.70566			0.852831	−	0.522186i	$-0.174883\pi$
$409$	34.4949			1.70566			0.852831	+	0.522186i	$0.174883\pi$
$410$	0.247449	−	2.44949i	0.0122206	−	0.120972i
$411$	−4.40408			−0.217237
$412$			12.8990i			0.635487i
$413$		0			0
$414$	8.69694			0.427431
$415$	0.550510	−	5.44949i	0.0270235	−	0.267505i
$416$	4.44949			0.218154
$417$			3.79796i			0.185987i
$418$		−	7.59592i		−	0.371528i
$419$	−1.55051			−0.0757474			−0.0378737	−	0.999283i	$-0.512058\pi$
$419$	−1.55051			−0.0757474			−0.0378737	+	0.999283i	$0.512058\pi$
$420$		0			0
$421$	−4.20204			−0.204795			−0.102397	−	0.994744i	$-0.532651\pi$
$421$	−4.20204			−0.204795			−0.102397	+	0.994744i	$0.532651\pi$
$422$			12.0000i			0.584151i
$423$		−	26.6969i		−	1.29805i
$424$	−10.8990			−0.529301
$425$	−2.00000	+	9.79796i	−0.0970143	+	0.475271i
$426$	2.69694			0.130667
$427$		0			0
$428$		−	8.00000i		−	0.386695i
$429$	−53.3939			−2.57788
$430$	−2.00000	−	0.202041i	−0.0964486	−	0.00974328i
$431$	−1.79796			−0.0866046			−0.0433023	−	0.999062i	$-0.513788\pi$
$431$	−1.79796			−0.0866046			−0.0433023	+	0.999062i	$0.513788\pi$
$432$		0			0
$433$			0.202041i			0.00970947i	0.999988	+	0.00485474i	$0.00154532\pi$
$433$			0.202041i			0.00970947i	−0.999988	+	0.00485474i	$0.998455\pi$
$434$		0			0
$435$	−3.79796	+	37.5959i	−0.182098	+	1.80259i
$436$	6.89898			0.330401
$437$			4.49490i			0.215020i
$438$			7.10102i			0.339300i
$439$	−21.3939			−1.02107			−0.510537	−	0.859856i	$-0.670553\pi$
$439$	−21.3939			−1.02107			−0.510537	+	0.859856i	$0.670553\pi$
$440$	1.10102	−	10.8990i	0.0524891	−	0.519588i
$441$		0			0
$442$			8.89898i			0.423281i
$443$			9.79796i			0.465515i	0.972535	+	0.232758i	$0.0747749\pi$
$443$			9.79796i			0.465515i	−0.972535	+	0.232758i	$0.925225\pi$
$444$	−4.89898			−0.232495
$445$	22.2474	+	2.24745i	1.05463	+	0.106539i
$446$	−4.00000			−0.189405
$447$			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	$0.424175\pi$
$450$	3.00000	−	14.6969i	0.141421	−	0.692820i
$451$	−5.39388			−0.253988
$452$		−	19.7980i		−	0.931218i
$453$			48.0000i			2.25524i
$454$	−7.34847			−0.344881
$455$		0			0
$456$	3.79796			0.177856
$457$		−	29.5959i		−	1.38444i	−0.721687	−	0.692219i	$-0.756633\pi$
$457$		−	29.5959i		−	1.38444i	0.721687	−	0.692219i	$-0.243367\pi$
$458$		−	19.1464i		−	0.894654i
$459$		0			0
$460$	−0.651531	+	6.44949i	−0.0303778	+	0.300709i
$461$	−17.3485			−0.807999			−0.403999	−	0.914759i	$-0.632380\pi$
$461$	−17.3485			−0.807999			−0.403999	+	0.914759i	$0.632380\pi$
$462$		0			0
$463$			3.59592i			0.167116i	0.996503	+	0.0835582i	$0.0266285\pi$
$463$			3.59592i			0.167116i	−0.996503	+	0.0835582i	$0.973372\pi$
$464$	−6.89898			−0.320277
$465$	−4.89898	+	48.4949i	−0.227185	+	2.24890i
$466$	−29.7980			−1.38036
$467$			10.4495i			0.483545i	0.970333	+	0.241772i	$0.0777287\pi$
$467$			10.4495i			0.483545i	−0.970333	+	0.241772i	$0.922271\pi$
$468$		−	13.3485i		−	0.617033i
$469$		0			0
$470$	19.7980	+	2.00000i	0.913212	+	0.0922531i
$471$	−8.69694			−0.400734
$472$			1.55051i			0.0713680i
$473$			4.40408i			0.202500i
$474$	16.8990			0.776196
$475$	7.59592	+	1.55051i	0.348525	+	0.0711423i
$476$		0			0
$477$			32.6969i			1.49709i
$478$			6.20204i			0.283675i
$479$	9.30306			0.425068			0.212534	−	0.977154i	$-0.431828\pi$
$479$	9.30306			0.425068			0.212534	+	0.977154i	$0.431828\pi$
$480$	5.44949	+	0.550510i	0.248734	+	0.0251272i
$481$	−8.89898			−0.405759
$482$			8.69694i			0.396135i
$483$		0			0
$484$	−13.0000			−0.590909
$485$	3.55051	−	35.1464i	0.161220	−	1.59592i
$486$	22.0454			1.00000
$487$			7.30306i			0.330933i	0.986215	+	0.165467i	$0.0529130\pi$
$487$			7.30306i			0.330933i	−0.986215	+	0.165467i	$0.947087\pi$
$488$			3.55051i			0.160724i
$489$	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	$0.354207\pi$
$492$		−	2.69694i		−	0.121587i
$493$		−	13.7980i		−	0.621429i
$494$	6.89898			0.310400
$495$	−32.6969	−	3.30306i	−1.46962	−	0.148462i
$496$	−8.89898			−0.399576
$497$		0			0
$498$		−	6.00000i		−	0.268866i
$499$	−6.20204			−0.277641			−0.138821	−	0.990318i	$-0.544331\pi$
$499$	−6.20204			−0.277641			−0.138821	+	0.990318i	$0.544331\pi$
$500$	10.6742	+	3.32577i	0.477366	+	0.148733i
$501$	12.0000			0.536120
$502$			6.44949i			0.287855i
$503$			4.00000i			0.178351i	0.996016	+	0.0891756i	$0.0284232\pi$
$503$			4.00000i			0.178351i	−0.996016	+	0.0891756i	$0.971577\pi$
$504$		0			0
$505$	7.89898	+	0.797959i	0.351500	+	0.0355087i
$506$	14.2020			0.631358
$507$		−	16.6515i		−	0.739520i
$508$		−	14.8990i		−	0.661035i
$509$	−31.5505			−1.39845			−0.699226	−	0.714901i	$-0.746472\pi$
$509$	−31.5505			−1.39845			−0.699226	+	0.714901i	$0.746472\pi$
$510$	−1.10102	+	10.8990i	−0.0487540	+	0.482615i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	8.69694			0.383606
$515$	−2.89898	+	28.6969i	−0.127744	+	1.26454i
$516$	−2.20204			−0.0969395
$517$		−	43.5959i		−	1.91735i
$518$		0			0
$519$	−15.3031			−0.671730
$520$	9.89898	+	1.00000i	0.434099	+	0.0438529i
$521$	−32.6969			−1.43248			−0.716239	−	0.697855i	$-0.754138\pi$
$521$	−32.6969			−1.43248			−0.716239	+	0.697855i	$0.754138\pi$
$522$			20.6969i			0.905880i
$523$			33.1464i			1.44939i	0.689069	+	0.724696i	$0.258020\pi$
$523$			33.1464i			1.44939i	−0.689069	+	0.724696i	$0.741980\pi$
$524$	−6.44949			−0.281747
$525$		0			0
$526$	−9.79796			−0.427211
$527$		−	17.7980i		−	0.775291i
$528$		−	12.0000i		−	0.522233i
$529$	14.5959			0.634605
$530$	−24.2474	−	2.44949i	−1.05324	−	0.106399i
$531$	4.65153			0.201859
$532$		0			0
$533$		−	4.89898i		−	0.212198i
$534$	24.4949			1.06000
$535$	1.79796	−	17.7980i	0.0777325	−	0.769473i
$536$	8.00000			0.345547
$537$		−	33.7980i		−	1.45849i
$538$			19.1464i			0.825461i
$539$		0			0
$540$		0			0
$541$	9.59592			0.412561			0.206280	−	0.978493i	$-0.433864\pi$
$541$	9.59592			0.412561			0.206280	+	0.978493i	$0.433864\pi$
$542$		−	12.0000i		−	0.515444i
$543$			25.1010i			1.07719i
$544$	−2.00000			−0.0857493
$545$	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	$0.869110\pi$
$548$		−	1.79796i		−	0.0768050i
$549$	10.6515			0.454596
$550$	4.89898	−	24.0000i	0.208893	−	1.02336i
$551$	−10.6969			−0.455705
$552$			7.10102i			0.302240i
$553$		0			0
$554$	−14.8990			−0.632997
$555$	−10.8990	−	1.10102i	−0.462636	−	0.0467357i
$556$	−1.55051			−0.0657563
$557$		−	12.6969i		−	0.537987i	−0.963142	−	0.268993i	$-0.913309\pi$
$557$		−	12.6969i		−	0.537987i	0.963142	−	0.268993i	$-0.0866909\pi$
$558$			26.6969i			1.13017i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	24.0000			1.01328
$562$		−	18.0000i		−	0.759284i
$563$			30.0454i			1.26626i	0.774044	+	0.633131i	$0.218231\pi$
$563$			30.0454i			1.26626i	−0.774044	+	0.633131i	$0.781769\pi$
$564$	21.7980			0.917860
$565$	4.44949	−	44.0454i	0.187191	−	1.85300i
$566$	3.75255			0.157731
$567$		0			0
$568$			1.10102i			0.0461978i
$569$	−33.7980			−1.41688			−0.708442	−	0.705769i	$-0.750602\pi$
$569$	−33.7980			−1.41688			−0.708442	+	0.705769i	$0.750602\pi$
$570$	8.44949	+	0.853572i	0.353910	+	0.0357522i
$571$	−11.1010			−0.464563			−0.232282	−	0.972649i	$-0.574619\pi$
$571$	−11.1010			−0.464563			−0.232282	+	0.972649i	$0.574619\pi$
$572$		−	21.7980i		−	0.911418i
$573$			31.1010i			1.29926i
$574$		0			0
$575$	−2.89898	+	14.2020i	−0.120896	+	0.592266i
$576$	3.00000			0.125000
$577$		−	2.49490i		−	0.103864i	−0.998651	−	0.0519320i	$-0.983462\pi$
$577$		−	2.49490i		−	0.103864i	0.998651	−	0.0519320i	$-0.0165379\pi$
$578$			13.0000i			0.540729i
$579$	52.8990			2.19841
$580$	−15.3485	−	1.55051i	−0.637310	−	0.0643814i
$581$		0			0
$582$		−	38.6969i		−	1.60404i
$583$			53.3939i			2.21135i
$584$	−2.89898			−0.119961
$585$	3.00000	−	29.6969i	0.124035	−	1.22782i
$586$	18.2474			0.753795
$587$			1.14643i			0.0473182i	0.999720	+	0.0236591i	$0.00753162\pi$
$587$			1.14643i			0.0473182i	−0.999720	+	0.0236591i	$0.992468\pi$
$588$		0			0
$589$	−13.7980			−0.568535
$590$	−0.348469	+	3.44949i	−0.0143463	+	0.142013i
$591$	46.2929			1.90423
$592$		−	2.00000i		−	0.0821995i
$593$			10.8990i			0.447567i	0.974639	+	0.223784i	$0.0718409\pi$
$593$			10.8990i			0.447567i	−0.974639	+	0.223784i	$0.928159\pi$
$594$		0			0
$595$		0			0
$596$	−3.79796			−0.155570
$597$			41.3939i			1.69414i
$598$			12.8990i			0.527478i
$599$	13.1010			0.535293			0.267647	−	0.963517i	$-0.413754\pi$
$599$	13.1010			0.535293			0.267647	+	0.963517i	$0.413754\pi$
$600$	12.0000	+	2.44949i	0.489898	+	0.100000i
$601$	39.3939			1.60691			0.803455	−	0.595366i	$-0.202993\pi$
$601$	39.3939			1.60691			0.803455	+	0.595366i	$0.202993\pi$
$602$		0			0
$603$		−	24.0000i		−	0.977356i
$604$	−19.5959			−0.797347
$605$	−28.9217	−	2.92168i	−1.17583	−	0.118783i
$606$	8.69694			0.353289
$607$			33.3939i			1.35542i	0.735331	+	0.677708i	$0.237027\pi$
$607$			33.3939i			1.35542i	−0.735331	+	0.677708i	$0.762973\pi$
$608$			1.55051i			0.0628815i
$609$		0			0
$610$	−0.797959	+	7.89898i	−0.0323084	+	0.319820i
$611$	39.5959			1.60188
$612$			6.00000i			0.242536i
$613$		−	27.7980i		−	1.12275i	−0.827562	−	0.561374i	$-0.810273\pi$
$613$		−	27.7980i		−	1.12275i	0.827562	−	0.561374i	$-0.189727\pi$
$614$	20.2474			0.817121
$615$	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	$-0.203142\pi$
$618$			31.5959i			1.27097i
$619$	−41.5505			−1.67006			−0.835028	−	0.550207i	$-0.814549\pi$
$619$	−41.5505			−1.67006			−0.835028	+	0.550207i	$0.814549\pi$
$620$	−19.7980	−	2.00000i	−0.795105	−	0.0803219i
$621$		0			0
$622$		−	12.0000i		−	0.481156i
$623$		0			0
$624$	10.8990			0.436308
$625$	23.0000	+	9.79796i	0.920000	+	0.391918i
$626$	−21.5959			−0.863146
$627$		−	18.6061i		−	0.743057i
$628$		−	3.55051i		−	0.141681i
$629$	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	$0.820905\pi$
$632$			6.89898i			0.274427i
$633$			29.3939i			1.16830i
$634$	−22.4949			−0.893387
$635$	3.34847	−	33.1464i	0.132880	−	1.31538i
$636$	−26.6969			−1.05860
$637$		0			0
$638$			33.7980i			1.33807i
$639$	3.30306			0.130667
$640$	−0.224745	+	2.22474i	−0.00888382	+	0.0879408i
$641$	25.7980			1.01896			0.509479	−	0.860483i	$-0.329838\pi$
$641$	25.7980			1.01896			0.509479	+	0.860483i	$0.329838\pi$
$642$		−	19.5959i		−	0.773389i
$643$		−	25.1464i		−	0.991678i	−0.868414	−	0.495839i	$-0.834861\pi$
$643$		−	25.1464i		−	0.991678i	0.868414	−	0.495839i	$-0.165139\pi$
$644$		0			0
$645$	−4.89898	−	0.494897i	−0.192897	−	0.0194866i
$646$	−3.10102			−0.122008
$647$		−	46.2929i		−	1.81996i	−0.414652	−	0.909980i	$-0.636097\pi$
$647$		−	46.2929i		−	1.81996i	0.414652	−	0.909980i	$-0.363903\pi$
$648$			9.00000i			0.353553i
$649$	7.59592			0.298166
$650$	21.7980	+	4.44949i	0.854986	+	0.174523i
$651$		0			0
$652$			7.10102i			0.278097i
$653$		−	20.2020i		−	0.790567i	−0.918559	−	0.395283i	$-0.870646\pi$
$653$		−	20.2020i		−	0.790567i	0.918559	−	0.395283i	$-0.129354\pi$
$654$	16.8990			0.660802
$655$	−14.3485	−	1.44949i	−0.560641	−	0.0566363i
$656$	1.10102			0.0429876
$657$			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	$0.606761\pi$
$660$	2.69694	−	26.6969i	0.104978	−	1.03918i
$661$	40.9444			1.59255			0.796276	−	0.604933i	$-0.206800\pi$
$661$	40.9444			1.59255			0.796276	+	0.604933i	$0.206800\pi$
$662$		−	18.6969i		−	0.726677i
$663$			21.7980i			0.846563i
$664$	2.44949			0.0950586
$665$		0			0
$666$	−6.00000			−0.232495
$667$		−	20.0000i		−	0.774403i
$668$			4.89898i			0.189547i
$669$	−9.79796			−0.378811
$670$	17.7980	+	1.79796i	0.687595	+	0.0694612i
$671$	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	$-0.111453\pi$
$674$	9.59592			0.369621
$675$		0			0
$676$	6.79796			0.261460
$677$		−	36.4495i		−	1.40087i	−0.713717	−	0.700434i	$-0.752990\pi$
$677$		−	36.4495i		−	1.40087i	0.713717	−	0.700434i	$-0.247010\pi$
$678$		−	48.4949i		−	1.86244i
$679$		0			0
$680$	−4.44949	−	0.449490i	−0.170630	−	0.0172371i
$681$	−18.0000			−0.689761
$682$			43.5959i			1.66937i
$683$			3.59592i			0.137594i	0.997631	+	0.0687970i	$0.0219161\pi$
$683$			3.59592i			0.137594i	−0.997631	+	0.0687970i	$0.978084\pi$
$684$	4.65153			0.177856
$685$	0.404082	−	4.00000i	0.0154392	−	0.152832i
$686$		0			0
$687$		−	46.8990i		−	1.78931i
$688$		−	0.898979i		−	0.0342733i
$689$	−48.4949			−1.84751
$690$	−1.59592	+	15.7980i	−0.0607556	+	0.601418i
$691$	−21.1464			−0.804448			−0.402224	−	0.915541i	$-0.631763\pi$
$691$	−21.1464			−0.804448			−0.402224	+	0.915541i	$0.631763\pi$
$692$		−	6.24745i		−	0.237492i
$693$		0			0
$694$	28.8990			1.09699
$695$	−3.44949	−	0.348469i	−0.130847	−	0.0132182i
$696$	−16.8990			−0.640554
$697$			2.20204i			0.0834083i
$698$		−	8.44949i		−	0.319818i
$699$	−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
$703$		−	3.10102i		−	0.116957i
$704$	4.89898			0.184637
$705$	48.4949	+	4.89898i	1.82642	+	0.184506i
$706$	22.8990			0.861814
$707$		0			0
$708$			3.79796i			0.142736i
$709$	28.2929			1.06256			0.531280	−	0.847196i	$-0.321711\pi$
$709$	28.2929			1.06256			0.531280	+	0.847196i	$0.321711\pi$
$710$	−0.247449	+	2.44949i	−0.00928658	+	0.0919277i
$711$	20.6969			0.776196
$712$			10.0000i			0.374766i
$713$		−	25.7980i		−	0.966141i
$714$		0			0
$715$	4.89898	−	48.4949i	0.183211	−	1.81361i
$716$	13.7980			0.515654
$717$			15.1918i			0.567350i
$718$			27.5959i			1.02987i
$719$	−4.49490			−0.167631			−0.0838157	−	0.996481i	$-0.526711\pi$
$719$	−4.49490			−0.167631			−0.0838157	+	0.996481i	$0.526711\pi$
$720$	6.67423	+	0.674235i	0.248734	+	0.0251272i
$721$		0			0
$722$		−	16.5959i		−	0.617636i
$723$			21.3031i			0.792269i
$724$	−10.2474			−0.380843
$725$	−33.7980	−	6.89898i	−1.25522	−	0.256222i
$726$	−31.8434			−1.18182
$727$			22.6969i			0.841783i	0.907111	+	0.420891i	$0.138283\pi$
$727$			22.6969i			0.841783i	−0.907111	+	0.420891i	$0.861717\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−6.44949	−	0.651531i	−0.238706	−	0.0241142i
$731$	1.79796			0.0664999
$732$			8.69694i			0.321448i
$733$		−	39.6413i		−	1.46419i	−0.681205	−	0.732093i	$-0.738544\pi$
$733$		−	39.6413i		−	1.46419i	0.681205	−	0.732093i	$-0.261456\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−2.89898			−0.106858
$737$		−	39.1918i		−	1.44365i
$738$		−	3.30306i		−	0.121587i
$739$	−4.49490			−0.165347			−0.0826737	−	0.996577i	$-0.526346\pi$
$739$	−4.49490			−0.165347			−0.0826737	+	0.996577i	$0.526346\pi$
$740$	0.449490	−	4.44949i	0.0165236	−	0.163566i
$741$	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	$-0.305963\pi$
$744$	−21.7980			−0.799152
$745$	−8.44949	−	0.853572i	−0.309565	−	0.0312725i
$746$	4.69694			0.171967
$747$		−	7.34847i		−	0.268866i
$748$			9.79796i			0.358249i
$749$		0			0
$750$	26.1464	+	8.14643i	0.954733	+	0.297465i
$751$	−41.7980			−1.52523			−0.762615	−	0.646853i	$-0.776085\pi$
$751$	−41.7980			−1.52523			−0.762615	+	0.646853i	$0.776085\pi$
$752$			8.89898i			0.324512i
$753$			15.7980i			0.575710i
$754$	−30.6969			−1.11792
$755$	−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	$0.609592\pi$
$758$		−	30.6969i		−	1.11496i
$759$	34.7878			1.26272
$760$	−0.348469	+	3.44949i	−0.0126403	+	0.125126i
$761$	21.1010			0.764911			0.382456	−	0.923974i	$-0.375078\pi$
$761$	21.1010			0.764911			0.382456	+	0.923974i	$0.375078\pi$
$762$		−	36.4949i		−	1.32207i
$763$		0			0
$764$	−12.6969			−0.459359
$765$	−1.34847	+	13.3485i	−0.0487540	+	0.482615i
$766$	−7.10102			−0.256570
$767$			6.89898i			0.249108i
$768$			2.44949i			0.0883883i
$769$	−40.6969			−1.46757			−0.733785	−	0.679382i	$-0.762248\pi$
$769$	−40.6969			−1.46757			−0.733785	+	0.679382i	$0.762248\pi$
$770$		0			0
$771$	21.3031			0.767211
$772$			21.5959i			0.777254i
$773$		−	1.34847i		−	0.0485011i	−0.999706	−	0.0242505i	$-0.992280\pi$
$773$		−	1.34847i		−	0.0485011i	0.999706	−	0.0242505i	$-0.00771994\pi$
$774$	−2.69694			−0.0969395
$775$	−43.5959	−	8.89898i	−1.56601	−	0.319661i
$776$	15.7980			0.567114
$777$		0			0
$778$		−	13.1010i		−	0.469694i
$779$	1.70714			0.0611648
$780$	24.2474	+	2.44949i	0.868198	+	0.0877058i
$781$	5.39388			0.193008
$782$		−	5.79796i		−	0.207335i
$783$		0			0
$784$		0			0
$785$	0.797959	−	7.89898i	0.0284804	−	0.281927i
$786$	−15.7980			−0.563495
$787$			50.4495i			1.79833i	0.437610	+	0.899165i	$0.355825\pi$
$787$			50.4495i			1.79833i	−0.437610	+	0.899165i	$0.644175\pi$
$788$			18.8990i			0.673248i
$789$	−24.0000			−0.854423
$790$	−1.55051	+	15.3485i	−0.0551647	+	0.546074i
$791$		0			0
$792$		−	14.6969i		−	0.522233i
$793$			15.7980i			0.561002i
$794$	2.65153			0.0940993
$795$	−59.3939	−	6.00000i	−2.10648	−	0.212798i
$796$	−16.8990			−0.598968
$797$		−	0.944387i		−	0.0334519i	−0.999860	−	0.0167260i	$-0.994676\pi$
$797$		−	0.944387i		−	0.0334519i	0.999860	−	0.0167260i	$-0.00532429\pi$
$798$		0			0
$799$	−17.7980			−0.629647
$800$	−1.00000	+	4.89898i	−0.0353553	+	0.173205i
$801$	30.0000			1.06000
$802$		−	29.3939i		−	1.03793i
$803$			14.2020i			0.501179i
$804$	19.5959			0.691095
$805$		0			0
$806$	−39.5959			−1.39471
$807$			46.8990i			1.65092i
$808$			3.55051i			0.124907i
$809$	−47.5959			−1.67338			−0.836692	−	0.547674i	$-0.815513\pi$
$809$	−47.5959			−1.67338			−0.836692	+	0.547674i	$0.815513\pi$
$810$	−2.02270	+	20.0227i	−0.0710706	+	0.703526i
$811$	−14.9444			−0.524768			−0.262384	−	0.964963i	$-0.584509\pi$
$811$	−14.9444			−0.524768			−0.262384	+	0.964963i	$0.584509\pi$
$812$		0			0
$813$		−	29.3939i		−	1.03089i
$814$	−9.79796			−0.343418
$815$	−1.59592	+	15.7980i	−0.0559026	+	0.553378i
$816$	−4.89898			−0.171499
$817$		−	1.39388i		−	0.0487656i
$818$			34.4949i			1.20609i
$819$		0			0
$820$	2.44949	+	0.247449i	0.0855399	+	0.00864128i
$821$	8.20204			0.286253			0.143127	−	0.989704i	$-0.454284\pi$
$821$	8.20204			0.286253			0.143127	+	0.989704i	$0.454284\pi$
$822$		−	4.40408i		−	0.153610i
$823$		−	39.1918i		−	1.36614i	−0.730352	−	0.683071i	$-0.760644\pi$
$823$		−	39.1918i		−	1.36614i	0.730352	−	0.683071i	$-0.239356\pi$
$824$	−12.8990			−0.449357
$825$	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	$0.912592\pi$
$828$			8.69694i			0.302240i
$829$	−43.6413			−1.51573			−0.757863	−	0.652414i	$-0.773756\pi$
$829$	−43.6413			−1.51573			−0.757863	+	0.652414i	$0.773756\pi$
$830$	5.44949	+	0.550510i	0.189155	+	0.0191085i
$831$	−36.4949			−1.26599
$832$			4.44949i			0.154258i
$833$		0			0
$834$	−3.79796			−0.131513
$835$	−1.10102	+	10.8990i	−0.0381024	+	0.377175i
$836$	7.59592			0.262710
$837$		0			0
$838$		−	1.55051i		−	0.0535615i
$839$	36.8990			1.27389			0.636947	−	0.770907i	$-0.280197\pi$
$839$	36.8990			1.27389			0.636947	+	0.770907i	$0.280197\pi$
$840$		0			0
$841$	18.5959			0.641239
$842$		−	4.20204i		−	0.144812i
$843$		−	44.0908i		−	1.51857i
$844$	−12.0000			−0.413057
$845$	15.1237	+	1.52781i	0.520272	+	0.0525581i
$846$	26.6969			0.917860
$847$		0			0
$848$		−	10.8990i		−	0.374272i
$849$	9.19184			0.315463
$850$	−9.79796	−	2.00000i	−0.336067	−	0.0685994i
$851$	5.79796			0.198751
$852$			2.69694i			0.0923956i
$853$			33.8434i			1.15877i	0.815052	+	0.579387i	$0.196708\pi$
$853$			33.8434i			1.15877i	−0.815052	+	0.579387i	$0.803292\pi$
$854$		0			0
$855$	10.3485	+	1.04541i	0.353910	+	0.0357522i
$856$	8.00000			0.273434
$857$		−	53.1918i		−	1.81700i	−0.417886	−	0.908499i	$-0.637229\pi$
$857$		−	53.1918i		−	1.81700i	0.417886	−	0.908499i	$-0.362771\pi$
$858$		−	53.3939i		−	1.82284i
$859$	53.6413			1.83022			0.915109	−	0.403206i	$-0.132104\pi$
$859$	53.6413			1.83022			0.915109	+	0.403206i	$0.132104\pi$
$860$	0.202041	−	2.00000i	0.00688954	−	0.0681994i
$861$		0			0
$862$		−	1.79796i		−	0.0612387i
$863$		−	45.3939i		−	1.54523i	−0.634878	−	0.772613i	$-0.718949\pi$
$863$		−	45.3939i		−	1.54523i	0.634878	−	0.772613i	$-0.281051\pi$
$864$		0			0
$865$	1.40408	−	13.8990i	0.0477402	−	0.472579i
$866$	−0.202041			−0.00686563
$867$			31.8434i			1.08146i
$868$		0			0
$869$	33.7980			1.14652
$870$	−37.5959	−	3.79796i	−1.27462	−	0.128763i
$871$	35.5959			1.20612
$872$			6.89898i			0.233629i
$873$		−	47.3939i		−	1.60404i
$874$	−4.49490			−0.152042
$875$		0			0
$876$	−7.10102			−0.239921
$877$			39.3939i			1.33024i	0.746738	+	0.665118i	$0.231619\pi$
$877$			39.3939i			1.33024i	−0.746738	+	0.665118i	$0.768381\pi$
$878$		−	21.3939i		−	0.722008i
$879$	44.6969			1.50759
$880$	10.8990	+	1.10102i	0.367405	+	0.0371154i
$881$	−8.20204			−0.276334			−0.138167	−	0.990409i	$-0.544121\pi$
$881$	−8.20204			−0.276334			−0.138167	+	0.990409i	$0.544121\pi$
$882$		0			0
$883$			22.2020i			0.747158i	0.927598	+	0.373579i	$0.121870\pi$
$883$			22.2020i			0.747158i	−0.927598	+	0.373579i	$0.878130\pi$
$884$	−8.89898			−0.299305
$885$	−0.853572	+	8.44949i	−0.0286925	+	0.284026i
$886$	−9.79796			−0.329169
$887$			2.69694i			0.0905543i	0.998974	+	0.0452772i	$0.0144171\pi$
$887$			2.69694i			0.0905543i	−0.998974	+	0.0452772i	$0.985583\pi$
$888$		−	4.89898i		−	0.164399i
$889$		0			0
$890$	−2.24745	+	22.2474i	−0.0753347	+	0.745736i
$891$	44.0908			1.47710
$892$		−	4.00000i		−	0.133930i
$893$			13.7980i			0.461731i
$894$	−9.30306			−0.311141
$895$	30.6969	+	3.10102i	1.02609	+	0.103656i
$896$		0			0
$897$			31.5959i			1.05496i
$898$			10.0000i			0.333704i
$899$	61.3939			2.04760
$900$	14.6969	+	3.00000i	0.489898	+	0.100000i
$901$	21.7980			0.726195
$902$		−	5.39388i		−	0.179596i
$903$		0			0
$904$	19.7980			0.658470
$905$	−22.7980	−	2.30306i	−0.757830	−	0.0765564i
$906$	−48.0000			−1.59469
$907$			41.7980i			1.38788i	0.720034	+	0.693939i	$0.244126\pi$
$907$			41.7980i			1.38788i	−0.720034	+	0.693939i	$0.755874\pi$
$908$		−	7.34847i		−	0.243868i
$909$	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	$0.700743\pi$
$912$			3.79796i			0.125763i
$913$		−	12.0000i		−	0.397142i
$914$	29.5959			0.978946
$915$	−1.95459	+	19.3485i	−0.0646168	+	0.639641i
$916$	19.1464			0.632616
$917$		0			0
$918$		0			0
$919$	26.8990			0.887315			0.443658	−	0.896196i	$-0.353681\pi$
$919$	26.8990			0.887315			0.443658	+	0.896196i	$0.353681\pi$
$920$	−6.44949	−	0.651531i	−0.212633	−	0.0214803i
$921$	49.5959			1.63424
$922$		−	17.3485i		−	0.571341i
$923$			4.89898i			0.161252i
$924$		0			0
$925$	2.00000	−	9.79796i	0.0657596	−	0.322155i
$926$	−3.59592			−0.118169
$927$			38.6969i			1.27097i
$928$		−	6.89898i		−	0.226470i
$929$	−28.2929			−0.928259			−0.464129	−	0.885767i	$-0.653633\pi$
$929$	−28.2929			−0.928259			−0.464129	+	0.885767i	$0.653633\pi$
$930$	−48.4949	−	4.89898i	−1.59021	−	0.160644i
$931$		0			0
$932$		−	29.7980i		−	0.976065i
$933$		−	29.3939i		−	0.962312i
$934$	−10.4495			−0.341918
$935$	−2.20204	+	21.7980i	−0.0720144	+	0.712869i
$936$	13.3485			0.436308
$937$		−	41.1010i		−	1.34271i	−0.741135	−	0.671356i	$-0.765712\pi$
$937$		−	41.1010i		−	1.34271i	0.741135	−	0.671356i	$-0.234288\pi$
$938$		0			0
$939$	−52.8990			−1.72629
$940$	−2.00000	+	19.7980i	−0.0652328	+	0.645738i
$941$	19.5505			0.637328			0.318664	−	0.947868i	$-0.396766\pi$
$941$	19.5505			0.637328			0.318664	+	0.947868i	$0.396766\pi$
$942$		−	8.69694i		−	0.283362i
$943$			3.19184i			0.103940i
$944$	−1.55051			−0.0504648
$945$		0			0
$946$	−4.40408			−0.143189
$947$		−	44.0908i		−	1.43276i	−0.697711	−	0.716379i	$-0.745798\pi$
$947$		−	44.0908i		−	1.43276i	0.697711	−	0.716379i	$-0.254202\pi$
$948$			16.8990i			0.548853i
$949$	−12.8990			−0.418719
$950$	−1.55051	+	7.59592i	−0.0503052	+	0.246444i
$951$	−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	$0.988645\pi$
$954$	−32.6969			−1.05860
$955$	−28.2474	−	2.85357i	−0.914066	−	0.0923394i
$956$	−6.20204			−0.200588
$957$			82.7878i			2.67615i
$958$			9.30306i			0.300568i
$959$		0			0
$960$	−0.550510	+	5.44949i	−0.0177676	+	0.175882i
$961$	48.1918			1.55458
$962$		−	8.89898i		−	0.286915i
$963$		−	24.0000i		−	0.773389i
$964$	−8.69694			−0.280110
$965$	−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	$0.801663\pi$
$968$		−	13.0000i		−	0.417836i
$969$	−7.59592			−0.244016
$970$	35.1464	+	3.55051i	1.12848	+	0.114000i
$971$	9.55051			0.306490			0.153245	−	0.988188i	$-0.451028\pi$
$971$	9.55051			0.306490			0.153245	+	0.988188i	$0.451028\pi$
$972$			22.0454i			0.707107i
$973$		0			0
$974$	−7.30306			−0.234005
$975$	53.3939	+	10.8990i	1.70997	+	0.349047i
$976$	−3.55051			−0.113649
$977$			29.3939i			0.940393i	0.882562	+	0.470197i	$0.155817\pi$
$977$			29.3939i			0.940393i	−0.882562	+	0.470197i	$0.844183\pi$
$978$			17.3939i			0.556195i
$979$	48.9898			1.56572
$980$		0			0
$981$	20.6969			0.660802
$982$			19.5959i			0.625331i
$983$			13.3031i			0.424302i	0.977237	+	0.212151i	$0.0680468\pi$
$983$			13.3031i			0.424302i	−0.977237	+	0.212151i	$0.931953\pi$
$984$	2.69694			0.0859753
$985$	−4.24745	+	42.0454i	−0.135335	+	1.33968i
$986$	13.7980			0.439417
$987$		0			0
$988$			6.89898i			0.219486i
$989$	2.60612			0.0828699
$990$	3.30306	−	32.6969i	0.104978	−	1.03918i
$991$	31.3031			0.994375			0.497187	−	0.867643i	$-0.334366\pi$
$991$	31.3031			0.994375			0.497187	+	0.867643i	$0.334366\pi$
$992$		−	8.89898i		−	0.282543i
$993$		−	45.7980i		−	1.45335i
$994$		0			0
$995$	−37.5959	−	3.79796i	−1.19187	−	0.120403i
$996$	6.00000			0.190117
$997$			57.3485i			1.81624i	0.418705	+	0.908122i	$0.362484\pi$
$997$			57.3485i			1.81624i	−0.418705	+	0.908122i	$0.637516\pi$
$998$		−	6.20204i		−	0.196322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.c.e.99.4		4
5.2	odd	4		2450.2.a.bl.1.2		2
5.3	odd	4		2450.2.a.bq.1.1		2
5.4	even	2	inner	490.2.c.e.99.1		4
7.2	even	3		490.2.i.f.459.3		8
7.3	odd	6		490.2.i.c.79.1		8
7.4	even	3		490.2.i.f.79.2		8
7.5	odd	6		490.2.i.c.459.4		8
7.6	odd	2		70.2.c.a.29.3	yes	4
21.20	even	2		630.2.g.g.379.1		4
28.27	even	2		560.2.g.e.449.4		4
35.4	even	6		490.2.i.f.79.3		8
35.9	even	6		490.2.i.f.459.2		8
35.13	even	4		350.2.a.h.1.2		2
35.19	odd	6		490.2.i.c.459.1		8
35.24	odd	6		490.2.i.c.79.4		8
35.27	even	4		350.2.a.g.1.1		2
35.34	odd	2		70.2.c.a.29.2	✓	4
56.13	odd	2		2240.2.g.j.449.3		4
56.27	even	2		2240.2.g.i.449.1		4
84.83	odd	2		5040.2.t.t.1009.1		4
105.62	odd	4		3150.2.a.bt.1.2		2
105.83	odd	4		3150.2.a.bs.1.2		2
105.104	even	2		630.2.g.g.379.3		4
140.27	odd	4		2800.2.a.bm.1.2		2
140.83	odd	4		2800.2.a.bl.1.1		2
140.139	even	2		560.2.g.e.449.2		4
280.69	odd	2		2240.2.g.j.449.1		4
280.139	even	2		2240.2.g.i.449.3		4
420.419	odd	2		5040.2.t.t.1009.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.c.a.29.2	✓	4	35.34	odd	2
70.2.c.a.29.3	yes	4	7.6	odd	2
350.2.a.g.1.1		2	35.27	even	4
350.2.a.h.1.2		2	35.13	even	4
490.2.c.e.99.1		4	5.4	even	2	inner
490.2.c.e.99.4		4	1.1	even	1	trivial
490.2.i.c.79.1		8	7.3	odd	6
490.2.i.c.79.4		8	35.24	odd	6
490.2.i.c.459.1		8	35.19	odd	6
490.2.i.c.459.4		8	7.5	odd	6
490.2.i.f.79.2		8	7.4	even	3
490.2.i.f.79.3		8	35.4	even	6
490.2.i.f.459.2		8	35.9	even	6
490.2.i.f.459.3		8	7.2	even	3
560.2.g.e.449.2		4	140.139	even	2
560.2.g.e.449.4		4	28.27	even	2
630.2.g.g.379.1		4	21.20	even	2
630.2.g.g.379.3		4	105.104	even	2
2240.2.g.i.449.1		4	56.27	even	2
2240.2.g.i.449.3		4	280.139	even	2
2240.2.g.j.449.1		4	280.69	odd	2
2240.2.g.j.449.3		4	56.13	odd	2
2450.2.a.bl.1.2		2	5.2	odd	4
2450.2.a.bq.1.1		2	5.3	odd	4
2800.2.a.bl.1.1		2	140.83	odd	4
2800.2.a.bm.1.2		2	140.27	odd	4
3150.2.a.bs.1.2		2	105.83	odd	4
3150.2.a.bt.1.2		2	105.62	odd	4
5040.2.t.t.1009.1		4	84.83	odd	2
5040.2.t.t.1009.2		4	420.419	odd	2

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-2.22474 - 0.224745i) q^{5} -2.44949 q^{6} -1.00000i q^{8} -3.00000 q^{9} +(0.224745 - 2.22474i) q^{10} -4.89898 q^{11} -2.44949i q^{12} -4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -3.00000i q^{18} +1.55051 q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} +2.89898i q^{23} +2.44949 q^{24} +(4.89898 + 1.00000i) q^{25} +4.44949 q^{26} -6.89898 q^{29} +(5.44949 + 0.550510i) q^{30} -8.89898 q^{31} +1.00000i q^{32} -12.0000i q^{33} -2.00000 q^{34} +3.00000 q^{36} -2.00000i q^{37} +1.55051i q^{38} +10.8990 q^{39} +(-0.224745 + 2.22474i) q^{40} +1.10102 q^{41} -0.898979i q^{43} +4.89898 q^{44} +(6.67423 + 0.674235i) q^{45} -2.89898 q^{46} +8.89898i q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} -4.89898 q^{51} +4.44949i q^{52} -10.8990i q^{53} +(10.8990 + 1.10102i) q^{55} +3.79796i q^{57} -6.89898i q^{58} -1.55051 q^{59} +(-0.550510 + 5.44949i) q^{60} -3.55051 q^{61} -8.89898i q^{62} -1.00000 q^{64} +(-1.00000 + 9.89898i) q^{65} +12.0000 q^{66} +8.00000i q^{67} -2.00000i q^{68} -7.10102 q^{69} -1.10102 q^{71} +3.00000i q^{72} -2.89898i q^{73} +2.00000 q^{74} +(-2.44949 + 12.0000i) q^{75} -1.55051 q^{76} +10.8990i q^{78} -6.89898 q^{79} +(-2.22474 - 0.224745i) q^{80} -9.00000 q^{81} +1.10102i q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +0.898979 q^{86} -16.8990i q^{87} +4.89898i q^{88} -10.0000 q^{89} +(-0.674235 + 6.67423i) q^{90} -2.89898i q^{92} -21.7980i q^{93} -8.89898 q^{94} +(-3.44949 - 0.348469i) q^{95} -2.44949 q^{96} +15.7980i q^{97} +14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5} - 12 q^{9} - 4 q^{10} + 12 q^{15} + 4 q^{16} + 16 q^{19} + 4 q^{20} + 8 q^{26} - 8 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} + 12 q^{36} + 24 q^{39} + 4 q^{40} + 24 q^{41} + 12 q^{45}+ \cdots - 4 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 - 12 * q^9 - 4 * q^10 + 12 * q^15 + 4 * q^16 + 16 * q^19 + 4 * q^20 + 8 * q^26 - 8 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 + 12 * q^36 + 24 * q^39 + 4 * q^40 + 24 * q^41 + 12 * q^45 + 8 * q^46 - 4 * q^50 + 24 * q^55 - 16 * q^59 - 12 * q^60 - 24 * q^61 - 4 * q^64 - 4 * q^65 + 48 * q^66 - 48 * q^69 - 24 * q^71 + 8 * q^74 - 16 * q^76 - 8 * q^79 - 4 * q^80 - 36 * q^81 - 8 * q^85 - 16 * q^86 - 40 * q^89 + 12 * q^90 - 16 * q^94 - 4 * q^95

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