LMFDB - Embedded newform 1216.2.i.p.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.39075800976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 $ x^8 - x^7 + 12x^6 - 13x^5 + 125x^4 - 116x^3 + 232x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$-0.236942 + 0.410396i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.p.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.684999 - 1.18645i) q^{3} +(0.780776 - 1.35234i) q^{5} +(0.561553 + 0.972638i) q^{9} +O(q^{10})$	\(q+(0.684999 - 1.18645i) q^{3} +(0.780776 - 1.35234i) q^{5} +(0.561553 + 0.972638i) q^{9} +3.50932 q^{11} +(-0.219224 - 0.379706i) q^{13} +(-1.06966 - 1.85271i) q^{15} +(0.219224 - 0.379706i) q^{17} +(3.12466 - 3.03916i) q^{19} +(-2.43966 - 4.22562i) q^{23} +(1.28078 + 2.21837i) q^{25} +5.64865 q^{27} +(2.34233 + 4.05703i) q^{29} -2.74000 q^{31} +(2.40388 - 4.16365i) q^{33} +1.12311 q^{37} -0.600672 q^{39} +(-0.500000 + 0.866025i) q^{41} +(3.80966 - 6.59852i) q^{43} +1.75379 q^{45} +(-1.06966 - 1.85271i) q^{47} -7.00000 q^{49} +(-0.300336 - 0.520197i) q^{51} +(0.219224 + 0.379706i) q^{53} +(2.74000 - 4.74581i) q^{55} +(-1.46543 - 5.78908i) q^{57} +(-0.684999 + 1.18645i) q^{59} +(-1.21922 - 2.11176i) q^{61} -0.684658 q^{65} +(-6.93432 - 12.0106i) q^{67} -6.68466 q^{69} +(2.43966 - 4.22562i) q^{71} +(-0.623106 + 1.07925i) q^{73} +3.50932 q^{75} +(-1.06966 + 1.85271i) q^{79} +(2.18466 - 3.78394i) q^{81} -6.24932 q^{83} +(-0.342329 - 0.592932i) q^{85} +6.41797 q^{87} +(5.34233 + 9.25319i) q^{89} +(-1.87689 + 3.25088i) q^{93} +(-1.67033 - 6.59852i) q^{95} +(-5.62311 + 9.73950i) q^{97} +(1.97067 + 3.41330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} - 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^5 - 12 * q^9	$ 8 q - 2 q^{5} - 12 q^{9} - 10 q^{13} + 10 q^{17} + 2 q^{25} - 6 q^{29} - 22 q^{33} - 24 q^{37} - 4 q^{41} + 80 q^{45} - 56 q^{49} + 10 q^{53} + 46 q^{57} - 18 q^{61} + 44 q^{65} - 4 q^{69} + 28 q^{73} - 32 q^{81} + 22 q^{85} + 18 q^{89} - 48 q^{93} - 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 - 12 * q^9 - 10 * q^13 + 10 * q^17 + 2 * q^25 - 6 * q^29 - 22 * q^33 - 24 * q^37 - 4 * q^41 + 80 * q^45 - 56 * q^49 + 10 * q^53 + 46 * q^57 - 18 * q^61 + 44 * q^65 - 4 * q^69 + 28 * q^73 - 32 * q^81 + 22 * q^85 + 18 * q^89 - 48 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	0.684999	−	1.18645i	0.395484	−	0.684999i	−0.597679	−	0.801736i	$-0.703910\pi$
$3$	0.684999	−	1.18645i	0.395484	−	0.684999i	0.993163	+	0.116737i	$0.0372434\pi$
$4$		0			0
$5$	0.780776	−	1.35234i	0.349174	−	0.604787i	−0.636929	−	0.770922i	$-0.719796\pi$
$5$	0.780776	−	1.35234i	0.349174	−	0.604787i	0.986103	+	0.166136i	$0.0531289\pi$
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	0.561553	+	0.972638i	0.187184	+	0.324213i
$10$		0			0
$11$	3.50932			1.05810			0.529050	−	0.848591i	$-0.322548\pi$
$11$	3.50932			1.05810			0.529050	+	0.848591i	$0.322548\pi$
$12$		0			0
$13$	−0.219224	−	0.379706i	−0.0608017	−	0.105312i	0.834022	−	0.551731i	$-0.186032\pi$
$13$	−0.219224	−	0.379706i	−0.0608017	−	0.105312i	−0.894824	+	0.446419i	$0.852699\pi$
$14$		0			0
$15$	−1.06966	−	1.85271i	−0.276186	−	0.478367i
$16$		0			0
$17$	0.219224	−	0.379706i	0.0531695	−	0.0920923i	−0.838216	−	0.545339i	$-0.816401\pi$
$17$	0.219224	−	0.379706i	0.0531695	−	0.0920923i	0.891385	+	0.453247i	$0.149734\pi$
$18$		0			0
$19$	3.12466	−	3.03916i	0.716846	−	0.697232i
$19$	3.12466	−	3.03916i	0.716846	−	0.697232i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.43966	−	4.22562i	−0.508704	−	0.881102i	−0.999949	−	0.0100802i	$-0.996791\pi$
$23$	−2.43966	−	4.22562i	−0.508704	−	0.881102i	0.491245	−	0.871021i	$-0.336542\pi$
$24$		0			0
$25$	1.28078	+	2.21837i	0.256155	+	0.443674i
$26$		0			0
$27$	5.64865			1.08708
$28$		0			0
$29$	2.34233	+	4.05703i	0.434960	+	0.753372i	0.997292	−	0.0735389i	$-0.0234293\pi$
$29$	2.34233	+	4.05703i	0.434960	+	0.753372i	−0.562333	+	0.826911i	$0.690096\pi$
$30$		0			0
$31$	−2.74000			−0.492118			−0.246059	−	0.969255i	$-0.579136\pi$
$31$	−2.74000			−0.492118			−0.246059	+	0.969255i	$0.579136\pi$
$32$		0			0
$33$	2.40388	−	4.16365i	0.418462	−	0.724798i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.12311			0.184637			0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311			0.184637			0.0923187	+	0.995730i	$0.470572\pi$
$38$		0			0
$39$	−0.600672			−0.0961845
$40$		0			0
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	−0.902424	−	0.430848i	$-0.858214\pi$
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	0.824338	+	0.566099i	$0.191548\pi$
$42$		0			0
$43$	3.80966	−	6.59852i	0.580967	−	1.00627i	−0.414398	−	0.910096i	$-0.636008\pi$
$43$	3.80966	−	6.59852i	0.580967	−	1.00627i	0.995365	−	0.0961691i	$-0.0306590\pi$
$44$		0			0
$45$	1.75379			0.261439
$46$		0			0
$47$	−1.06966	−	1.85271i	−0.156026	−	0.270245i	0.777406	−	0.628999i	$-0.216535\pi$
$47$	−1.06966	−	1.85271i	−0.156026	−	0.270245i	−0.933432	+	0.358754i	$0.883202\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	−0.300336	−	0.520197i	−0.0420554	−	0.0728421i
$52$		0			0
$53$	0.219224	+	0.379706i	0.0301127	+	0.0521567i	0.880689	−	0.473695i	$-0.157080\pi$
$53$	0.219224	+	0.379706i	0.0301127	+	0.0521567i	−0.850576	+	0.525852i	$0.823747\pi$
$54$		0			0
$55$	2.74000	−	4.74581i	0.369461	−	0.639925i
$56$		0			0
$57$	−1.46543	−	5.78908i	−0.194102	−	0.766783i
$58$		0			0
$59$	−0.684999	+	1.18645i	−0.0891793	+	0.154463i	−0.907164	−	0.420776i	$-0.861758\pi$
$59$	−0.684999	+	1.18645i	−0.0891793	+	0.154463i	0.817985	+	0.575239i	$0.195091\pi$
$60$		0			0
$61$	−1.21922	−	2.11176i	−0.156106	−	0.270383i	0.777355	−	0.629062i	$-0.216561\pi$
$61$	−1.21922	−	2.11176i	−0.156106	−	0.270383i	−0.933461	+	0.358679i	$0.883227\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.684658			−0.0849214
$66$		0			0
$67$	−6.93432	−	12.0106i	−0.847162	−	1.46733i	−0.883731	−	0.467996i	$-0.844976\pi$
$67$	−6.93432	−	12.0106i	−0.847162	−	1.46733i	0.0365690	−	0.999331i	$-0.488357\pi$
$68$		0			0
$69$	−6.68466			−0.804738
$70$		0			0
$71$	2.43966	−	4.22562i	0.289534	−	0.501488i	−0.684164	−	0.729328i	$-0.739833\pi$
$71$	2.43966	−	4.22562i	0.289534	−	0.501488i	0.973699	+	0.227840i	$0.0731662\pi$
$72$		0			0
$73$	−0.623106	+	1.07925i	−0.0729290	+	0.126317i	−0.900184	−	0.435510i	$-0.856568\pi$
$73$	−0.623106	+	1.07925i	−0.0729290	+	0.126317i	0.827255	+	0.561827i	$0.189901\pi$
$74$		0			0
$75$	3.50932			0.405222
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.06966	+	1.85271i	−0.120346	+	0.208446i	−0.919904	−	0.392143i	$-0.871734\pi$
$79$	−1.06966	+	1.85271i	−0.120346	+	0.208446i	0.799558	+	0.600589i	$0.205067\pi$
$80$		0			0
$81$	2.18466	−	3.78394i	0.242740	−	0.420438i
$82$		0			0
$83$	−6.24932			−0.685952			−0.342976	−	0.939344i	$-0.611435\pi$
$83$	−6.24932			−0.685952			−0.342976	+	0.939344i	$0.611435\pi$
$84$		0			0
$85$	−0.342329	−	0.592932i	−0.0371308	−	0.0643125i
$86$		0			0
$87$	6.41797			0.688079
$88$		0			0
$89$	5.34233	+	9.25319i	0.566286	+	0.980836i	0.996929	+	0.0783134i	$0.0249535\pi$
$89$	5.34233	+	9.25319i	0.566286	+	0.980836i	−0.430643	+	0.902522i	$0.641713\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.87689	+	3.25088i	−0.194625	+	0.337100i
$94$		0			0
$95$	−1.67033	−	6.59852i	−0.171373	−	0.676994i
$96$		0			0
$97$	−5.62311	+	9.73950i	−0.570940	+	0.988897i	0.425530	+	0.904944i	$0.360088\pi$
$97$	−5.62311	+	9.73950i	−0.570940	+	0.988897i	−0.996470	+	0.0839525i	$0.973246\pi$
$98$		0			0
$99$	1.97067	+	3.41330i	0.198060	+	0.343050i
$100$		0			0
$101$	−7.90388	−	13.6899i	−0.786466	−	1.36220i	−0.928120	−	0.372282i	$-0.878575\pi$
$101$	−7.90388	−	13.6899i	−0.786466	−	1.36220i	0.141654	−	0.989916i	$-0.454758\pi$
$102$		0			0
$103$	17.9786			1.77149			0.885743	−	0.464175i	$-0.153649\pi$
$103$	17.9786			1.77149			0.885743	+	0.464175i	$0.153649\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.47999			0.529771			0.264885	−	0.964280i	$-0.414666\pi$
$107$	5.47999			0.529771			0.264885	+	0.964280i	$0.414666\pi$
$108$		0			0
$109$	−5.90388	+	10.2258i	−0.565489	+	0.979456i	0.431515	+	0.902106i	$0.357979\pi$
$109$	−5.90388	+	10.2258i	−0.565489	+	0.979456i	−0.997004	+	0.0773503i	$0.975354\pi$
$110$		0			0
$111$	0.769326	−	1.33251i	0.0730212	−	0.126476i
$112$		0			0
$113$	−6.56155			−0.617259			−0.308629	−	0.951182i	$-0.599870\pi$
$113$	−6.56155			−0.617259			−0.308629	+	0.951182i	$0.599870\pi$
$114$		0			0
$115$	−7.61932			−0.710505
$116$		0			0
$117$	0.246211	−	0.426450i	0.0227622	−	0.0394254i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.31534			0.119577
$122$		0			0
$123$	0.684999	+	1.18645i	0.0617643	+	0.106979i
$124$		0			0
$125$	11.8078			1.05612
$126$		0			0
$127$	4.57898	+	7.93103i	0.406319	+	0.703765i	0.994474	−	0.104983i	$-0.0334788\pi$
$127$	4.57898	+	7.93103i	0.406319	+	0.703765i	−0.588155	+	0.808748i	$0.700145\pi$
$128$		0			0
$129$	−5.21922	−	9.03996i	−0.459527	−	0.795924i
$130$		0			0
$131$	−4.79499	+	8.30517i	−0.418940	+	0.725626i	−0.995833	−	0.0911938i	$-0.970932\pi$
$131$	−4.79499	+	8.30517i	−0.418940	+	0.725626i	0.576893	+	0.816820i	$0.304265\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.41033	−	7.63892i	0.379581	−	0.657453i
$136$		0			0
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	0.975913	−	0.218159i	$-0.0700052\pi$
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	−0.676888	+	0.736086i	$0.736672\pi$
$138$		0			0
$139$	−5.56432	−	9.63768i	−0.471959	−	0.817458i	0.527526	−	0.849539i	$-0.323120\pi$
$139$	−5.56432	−	9.63768i	−0.471959	−	0.817458i	−0.999485	+	0.0320813i	$0.989786\pi$
$140$		0			0
$141$	−2.93087			−0.246824
$142$		0			0
$143$	−0.769326	−	1.33251i	−0.0643343	−	0.111430i
$144$		0			0
$145$	7.31534			0.607506
$146$		0			0
$147$	−4.79499	+	8.30517i	−0.395484	+	0.684999i
$148$		0			0
$149$	−4.46543	+	7.73436i	−0.365823	+	0.633623i	−0.988908	−	0.148531i	$-0.952546\pi$
$149$	−4.46543	+	7.73436i	−0.365823	+	0.633623i	0.623085	+	0.782154i	$0.285879\pi$
$150$		0			0
$151$	7.01864			0.571169			0.285585	−	0.958354i	$-0.407812\pi$
$151$	7.01864			0.571169			0.285585	+	0.958354i	$0.407812\pi$
$152$		0			0
$153$	0.492423			0.0398100
$154$		0			0
$155$	−2.13932	+	3.70542i	−0.171835	+	0.297626i
$156$		0			0
$157$	9.90388	−	17.1540i	0.790416	−	1.36904i	−0.135294	−	0.990806i	$-0.543198\pi$
$157$	9.90388	−	17.1540i	0.790416	−	1.36904i	0.925710	−	0.378235i	$-0.123469\pi$
$158$		0			0
$159$	0.600672			0.0476364
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.50932			−0.274871			−0.137436	−	0.990511i	$-0.543886\pi$
$163$	−3.50932			−0.274871			−0.137436	+	0.990511i	$0.543886\pi$
$164$		0			0
$165$	−3.75379	−	6.50175i	−0.292232	−	0.506161i
$166$		0			0
$167$	11.4290	+	19.7956i	0.884401	+	1.53183i	0.846399	+	0.532549i	$0.178766\pi$
$167$	11.4290	+	19.7956i	0.884401	+	1.53183i	0.0380014	+	0.999278i	$0.487901\pi$
$168$		0			0
$169$	6.40388	−	11.0918i	0.492606	−	0.853219i
$170$		0			0
$171$	4.71067	+	1.33251i	0.360234	+	0.101900i
$172$		0			0
$173$	−2.90388	+	5.02967i	−0.220778	+	0.382399i	−0.955044	−	0.296463i	$-0.904193\pi$
$173$	−2.90388	+	5.02967i	−0.220778	+	0.382399i	0.734266	+	0.678861i	$0.237526\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.938447	+	1.62544i	0.0705380	+	0.122175i
$178$		0			0
$179$	−17.5466			−1.31150			−0.655748	−	0.754980i	$-0.727646\pi$
$179$	−17.5466			−1.31150			−0.655748	+	0.754980i	$0.727646\pi$
$180$		0			0
$181$	10.4654	+	18.1267i	0.777890	+	1.34734i	0.933156	+	0.359472i	$0.117043\pi$
$181$	10.4654	+	18.1267i	0.777890	+	1.34734i	−0.155266	+	0.987873i	$0.549624\pi$
$182$		0			0
$183$	−3.34067			−0.246949
$184$		0			0
$185$	0.876894	−	1.51883i	0.0644706	−	0.111666i
$186$		0			0
$187$	0.769326	−	1.33251i	0.0562587	−	0.0974429i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−24.9973			−1.80874			−0.904370	−	0.426750i	$-0.859658\pi$
$191$	−24.9973			−1.80874			−0.904370	+	0.426750i	$0.859658\pi$
$192$		0			0
$193$	4.90388	−	8.49377i	0.352989	−	0.611395i	−0.633783	−	0.773511i	$-0.718499\pi$
$193$	4.90388	−	8.49377i	0.352989	−	0.611395i	0.986772	+	0.162116i	$0.0518319\pi$
$194$		0			0
$195$	−0.468990	+	0.812315i	−0.0335851	+	0.0581711i
$196$		0			0
$197$	19.3693			1.38001			0.690003	−	0.723806i	$-0.257609\pi$
$197$	19.3693			1.38001			0.690003	+	0.723806i	$0.257609\pi$
$198$		0			0
$199$	9.45830	+	16.3823i	0.670481	+	1.16131i	0.977768	+	0.209691i	$0.0672457\pi$
$199$	9.45830	+	16.3823i	0.670481	+	1.16131i	−0.307286	+	0.951617i	$0.599421\pi$
$200$		0			0
$201$	−19.0000			−1.34016
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.780776	+	1.35234i	0.0545318	+	0.0944518i
$206$		0			0
$207$	2.74000	−	4.74581i	0.190443	−	0.329857i
$208$		0			0
$209$	10.9654	−	10.6654i	0.758495	−	0.737741i
$210$		0			0
$211$	−3.80966	+	6.59852i	−0.262268	+	0.454261i	−0.966844	−	0.255367i	$-0.917804\pi$
$211$	−3.80966	+	6.59852i	−0.262268	+	0.454261i	0.704576	+	0.709628i	$0.251137\pi$
$212$		0			0
$213$	−3.34233	−	5.78908i	−0.229013	−	0.396662i
$214$		0			0
$215$	−5.94898	−	10.3039i	−0.405717	−	0.702723i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.853653	+	1.47857i	0.0576846	+	0.0999126i
$220$		0			0
$221$	−0.192236			−0.0129312
$222$		0			0
$223$	−9.45830	+	16.3823i	−0.633375	+	1.09704i	0.353482	+	0.935441i	$0.384998\pi$
$223$	−9.45830	+	16.3823i	−0.633375	+	1.09704i	−0.986857	+	0.161596i	$0.948336\pi$
$224$		0			0
$225$	−1.43845	+	2.49146i	−0.0958965	+	0.166098i
$226$		0			0
$227$	−10.5280			−0.698766			−0.349383	−	0.936980i	$-0.613609\pi$
$227$	−10.5280			−0.698766			−0.349383	+	0.936980i	$0.613609\pi$
$228$		0			0
$229$	9.75379			0.644549			0.322274	−	0.946646i	$-0.395553\pi$
$229$	9.75379			0.644549			0.322274	+	0.946646i	$0.395553\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.93845	+	3.35749i	−0.126992	+	0.219956i	−0.922510	−	0.385974i	$-0.873866\pi$
$233$	−1.93845	+	3.35749i	−0.126992	+	0.219956i	0.795518	+	0.605930i	$0.207199\pi$
$234$		0			0
$235$	−3.34067			−0.217921
$236$		0			0
$237$	1.46543	+	2.53821i	0.0951902	+	0.164874i
$238$		0			0
$239$	−29.2759			−1.89370			−0.946851	−	0.321673i	$-0.895755\pi$
$239$	−29.2759			−1.89370			−0.946851	+	0.321673i	$0.895755\pi$
$240$		0			0
$241$	9.74621	+	16.8809i	0.627809	+	1.08740i	0.987991	+	0.154514i	$0.0493813\pi$
$241$	9.74621	+	16.8809i	0.627809	+	1.08740i	−0.360182	+	0.932882i	$0.617285\pi$
$242$		0			0
$243$	5.47999	+	9.49162i	0.351542	+	0.608888i
$244$		0			0
$245$	−5.46543	+	9.46641i	−0.349174	+	0.604787i
$246$		0			0
$247$	−1.83899	−	0.520197i	−0.117012	−	0.0330993i
$248$		0			0
$249$	−4.28078	+	7.41452i	−0.271283	+	0.469876i
$250$		0			0
$251$	10.4436	+	18.0889i	0.659197	+	1.14176i	0.980824	+	0.194896i	$0.0624369\pi$
$251$	10.4436	+	18.0889i	0.659197	+	1.14176i	−0.321627	+	0.946866i	$0.604230\pi$
$252$		0			0
$253$	−8.56155	−	14.8290i	−0.538260	−	0.932294i
$254$		0			0
$255$	−0.937981			−0.0587386
$256$		0			0
$257$	5.62311	+	9.73950i	0.350760	+	0.607534i	0.986383	−	0.164466i	$-0.0525901\pi$
$257$	5.62311	+	9.73950i	0.350760	+	0.607534i	−0.635623	+	0.772000i	$0.719257\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−2.63068	+	4.55648i	−0.162835	+	0.282039i
$262$		0			0
$263$	−11.4290	+	19.7956i	−0.704741	+	1.22065i	0.262044	+	0.965056i	$0.415603\pi$
$263$	−11.4290	+	19.7956i	−0.704741	+	1.22065i	−0.966785	+	0.255591i	$0.917730\pi$
$264$		0			0
$265$	0.684658			0.0420582
$266$		0			0
$267$	14.6380			0.895829
$268$		0			0
$269$	−8.78078	+	15.2088i	−0.535373	+	0.927294i	0.463772	+	0.885955i	$0.346496\pi$
$269$	−8.78078	+	15.2088i	−0.535373	+	0.927294i	−0.999145	+	0.0413392i	$0.986838\pi$
$270$		0			0
$271$	1.06966	−	1.85271i	0.0649773	−	0.112544i	−0.831707	−	0.555215i	$-0.812636\pi$
$271$	1.06966	−	1.85271i	0.0649773	−	0.112544i	0.896684	+	0.442671i	$0.145969\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.49466	+	7.78497i	0.271038	+	0.469452i
$276$		0			0
$277$	4.00000			0.240337			0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000			0.240337			0.120168	+	0.992754i	$0.461657\pi$
$278$		0			0
$279$	−1.53865	−	2.66502i	−0.0921167	−	0.159551i
$280$		0			0
$281$	−11.5000	−	19.9186i	−0.686032	−	1.18824i	−0.973111	−	0.230336i	$-0.926017\pi$
$281$	−11.5000	−	19.9186i	−0.686032	−	1.18824i	0.287079	−	0.957907i	$-0.407316\pi$
$282$		0			0
$283$	−4.79499	+	8.30517i	−0.285033	+	0.493691i	−0.972617	−	0.232413i	$-0.925338\pi$
$283$	−4.79499	+	8.30517i	−0.285033	+	0.493691i	0.687584	+	0.726104i	$0.258671\pi$
$284$		0			0
$285$	−8.97301	−	2.53821i	−0.531515	−	0.150350i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.40388	+	14.5560i	0.494346	+	0.856232i
$290$		0			0
$291$	7.70364	+	13.3431i	0.451596	+	0.782186i
$292$		0			0
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$		0			0
$295$	1.06966	+	1.85271i	0.0622781	+	0.107869i
$296$		0			0
$297$	19.8229			1.15024
$298$		0			0
$299$	−1.06966	+	1.85271i	−0.0618602	+	0.107145i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−21.6566			−1.24414
$304$		0			0
$305$	−3.80776			−0.218032
$306$		0			0
$307$	8.30431	−	14.3835i	0.473952	−	0.820909i	−0.525603	−	0.850730i	$-0.676160\pi$
$307$	8.30431	−	14.3835i	0.473952	−	0.820909i	0.999555	+	0.0298205i	$0.00949358\pi$
$308$		0			0
$309$	12.3153	−	21.3308i	0.700595	−	1.21347i
$310$		0			0
$311$	−13.7000			−0.776855			−0.388427	−	0.921479i	$-0.626982\pi$
$311$	−13.7000			−0.776855			−0.388427	+	0.921479i	$0.626982\pi$
$312$		0			0
$313$	−5.62311	−	9.73950i	−0.317837	−	0.550509i	0.662200	−	0.749327i	$-0.269623\pi$
$313$	−5.62311	−	9.73950i	−0.317837	−	0.550509i	−0.980036	+	0.198818i	$0.936290\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.5885	−	27.0001i	−0.875540	−	1.51648i	−0.856187	−	0.516666i	$-0.827173\pi$
$317$	−15.5885	−	27.0001i	−0.875540	−	1.51648i	−0.0193529	−	0.999813i	$-0.506161\pi$
$318$		0			0
$319$	8.21999	+	14.2374i	0.460231	+	0.797143i
$320$		0			0
$321$	3.75379	−	6.50175i	0.209516	−	0.362892i
$322$		0			0
$323$	−0.468990	−	1.85271i	−0.0260953	−	0.103087i
$324$		0			0
$325$	0.561553	−	0.972638i	0.0311493	−	0.0539522i
$326$		0			0
$327$	8.08831	+	14.0094i	0.447284	+	0.774719i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	21.4879			1.18108			0.590542	−	0.807007i	$-0.298914\pi$
$331$	21.4879			1.18108			0.590542	+	0.807007i	$0.298914\pi$
$332$		0			0
$333$	0.630683	+	1.09238i	0.0345612	+	0.0598618i
$334$		0			0
$335$	−21.6566			−1.18323
$336$		0			0
$337$	−3.06155	+	5.30277i	−0.166773	+	0.288860i	−0.937284	−	0.348568i	$-0.886668\pi$
$337$	−3.06155	+	5.30277i	−0.166773	+	0.288860i	0.770510	+	0.637428i	$0.220002\pi$
$338$		0			0
$339$	−4.49466	+	7.78497i	−0.244116	+	0.422822i
$340$		0			0
$341$	−9.61553			−0.520710
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.21922	+	9.03996i	−0.280994	+	0.486695i
$346$		0			0
$347$	4.79499	−	8.30517i	0.257409	−	0.445845i	−0.708138	−	0.706074i	$-0.750465\pi$
$347$	4.79499	−	8.30517i	0.257409	−	0.445845i	0.965547	+	0.260229i	$0.0837980\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		0			0
$351$	−1.23832	−	2.14483i	−0.0660964	−	0.114482i
$352$		0			0
$353$	−24.8078			−1.32038			−0.660192	−	0.751097i	$-0.729525\pi$
$353$	−24.8078			−1.32038			−0.660192	+	0.751097i	$0.729525\pi$
$354$		0			0
$355$	−3.80966	−	6.59852i	−0.202196	−	0.350213i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.43966	+	4.22562i	−0.128760	+	0.223019i	−0.923197	−	0.384328i	$-0.874433\pi$
$359$	−2.43966	+	4.22562i	−0.128760	+	0.223019i	0.794436	+	0.607348i	$0.207766\pi$
$360$		0			0
$361$	0.526988	−	18.9927i	0.0277362	−	0.999615i
$362$		0			0
$363$	0.901008	−	1.56059i	0.0472906	−	0.0819098i
$364$		0			0
$365$	0.973012	+	1.68531i	0.0509298	+	0.0882130i
$366$		0			0
$367$	9.45830	+	16.3823i	0.493719	+	0.855147i	0.999974	−	0.00723702i	$-0.00230364\pi$
$367$	9.45830	+	16.3823i	0.493719	+	0.855147i	−0.506254	+	0.862384i	$0.668970\pi$
$368$		0			0
$369$	−1.12311			−0.0584665
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−27.6155			−1.42988			−0.714939	−	0.699187i	$-0.753546\pi$
$373$	−27.6155			−1.42988			−0.714939	+	0.699187i	$0.753546\pi$
$374$		0			0
$375$	8.08831	−	14.0094i	0.417678	−	0.723440i
$376$		0			0
$377$	1.02699	−	1.77879i	0.0528926	−	0.0916126i
$378$		0			0
$379$	8.55730			0.439559			0.219779	−	0.975550i	$-0.429466\pi$
$379$	8.55730			0.439559			0.219779	+	0.975550i	$0.429466\pi$
$380$		0			0
$381$	12.5464			0.642771
$382$		0			0
$383$	5.94898	−	10.3039i	0.303979	−	0.526507i	−0.673055	−	0.739593i	$-0.735018\pi$
$383$	5.94898	−	10.3039i	0.303979	−	0.526507i	0.977033	+	0.213086i	$0.0683515\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.55730			0.434992
$388$		0			0
$389$	14.1501	+	24.5087i	0.717438	+	1.24264i	0.962012	+	0.273009i	$0.0880188\pi$
$389$	14.1501	+	24.5087i	0.717438	+	1.24264i	−0.244573	+	0.969631i	$0.578648\pi$
$390$		0			0
$391$	−2.13932			−0.108190
$392$		0			0
$393$	6.56913	+	11.3781i	0.331369	+	0.573948i
$394$		0			0
$395$	1.67033	+	2.89310i	0.0840436	+	0.145568i
$396$		0			0
$397$	−13.7808	+	23.8690i	−0.691637	+	1.19795i	0.279664	+	0.960098i	$0.409777\pi$
$397$	−13.7808	+	23.8690i	−0.691637	+	1.19795i	−0.971301	+	0.237853i	$0.923556\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	−0.996371	−	0.0851195i	$-0.972873\pi$
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	0.571901	+	0.820323i	$0.306206\pi$
$402$		0			0
$403$	0.600672	+	1.04039i	0.0299216	+	0.0518257i
$404$		0			0
$405$	−3.41146	−	5.90882i	−0.169517	−	0.293612i
$406$		0			0
$407$	3.94134			0.195365
$408$		0			0
$409$	9.30776	+	16.1215i	0.460239	+	0.797158i	0.998973	−	0.0453185i	$-0.0144303\pi$
$409$	9.30776	+	16.1215i	0.460239	+	0.797158i	−0.538733	+	0.842476i	$0.681097\pi$
$410$		0			0
$411$	9.58999			0.473039
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.87932	+	8.45123i	−0.239516	+	0.414855i
$416$		0			0
$417$	−15.2462			−0.746610
$418$		0			0
$419$	−30.4773			−1.48891			−0.744456	−	0.667672i	$-0.767291\pi$
$419$	−30.4773			−1.48891			−0.744456	+	0.667672i	$0.767291\pi$
$420$		0			0
$421$	−16.0270	+	27.7596i	−0.781108	+	1.35292i	0.150189	+	0.988657i	$0.452012\pi$
$421$	−16.0270	+	27.7596i	−0.781108	+	1.35292i	−0.931297	+	0.364261i	$0.881322\pi$
$422$		0			0
$423$	1.20134	−	2.08079i	0.0584113	−	0.101171i
$424$		0			0
$425$	1.12311			0.0544786
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.10795			−0.101773
$430$		0			0
$431$	−14.9383	−	25.8739i	−0.719552	−	1.24630i	−0.961177	−	0.275932i	$-0.911014\pi$
$431$	−14.9383	−	25.8739i	−0.719552	−	1.24630i	0.241625	−	0.970370i	$-0.422320\pi$
$432$		0			0
$433$	−15.5885	−	27.0001i	−0.749137	−	1.29754i	−0.948237	−	0.317565i	$-0.897135\pi$
$433$	−15.5885	−	27.0001i	−0.749137	−	1.29754i	0.199099	−	0.979979i	$-0.436198\pi$
$434$		0			0
$435$	5.01100	−	8.67931i	0.240259	−	0.416141i
$436$		0			0
$437$	−20.4654	−	5.78908i	−0.978995	−	0.276929i
$438$		0			0
$439$	2.43966	−	4.22562i	0.116439	−	0.201678i	−0.801915	−	0.597438i	$-0.796186\pi$
$439$	2.43966	−	4.22562i	0.116439	−	0.201678i	0.918354	+	0.395760i	$0.129519\pi$
$440$		0			0
$441$	−3.93087	−	6.80847i	−0.187184	−	0.324213i
$442$		0			0
$443$	−2.05500	−	3.55936i	−0.0976359	−	0.169110i	0.813070	−	0.582166i	$-0.197795\pi$
$443$	−2.05500	−	3.55936i	−0.0976359	−	0.169110i	−0.910706	+	0.413056i	$0.864461\pi$
$444$		0			0
$445$	16.6847			0.790929
$446$		0			0
$447$	6.11764	+	10.5961i	0.289354	+	0.501176i
$448$		0			0
$449$	24.8078			1.17075			0.585375	−	0.810762i	$-0.300947\pi$
$449$	24.8078			1.17075			0.585375	+	0.810762i	$0.300947\pi$
$450$		0			0
$451$	−1.75466	+	3.03916i	−0.0826238	+	0.143109i
$452$		0			0
$453$	4.80776	−	8.32729i	0.225888	−	0.391250i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−32.5616			−1.52317			−0.761583	−	0.648068i	$-0.775577\pi$
$457$	−32.5616			−1.52317			−0.761583	+	0.648068i	$0.775577\pi$
$458$		0			0
$459$	1.23832	−	2.14483i	0.0577997	−	0.100112i
$460$		0			0
$461$	13.7808	−	23.8690i	0.641835	−	1.11169i	−0.343188	−	0.939267i	$-0.611507\pi$
$461$	13.7808	−	23.8690i	0.641835	−	1.11169i	0.985023	−	0.172424i	$-0.0551598\pi$
$462$		0			0
$463$	16.7773			0.779707			0.389853	−	0.920877i	$-0.372526\pi$
$463$	16.7773			0.779707			0.389853	+	0.920877i	$0.372526\pi$
$464$		0			0
$465$	2.93087	+	5.07642i	0.135916	+	0.235413i
$466$		0			0
$467$	−14.4693			−0.669560			−0.334780	−	0.942296i	$-0.608662\pi$
$467$	−14.4693			−0.669560			−0.334780	+	0.942296i	$0.608662\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−13.5683	−	23.5010i	−0.625194	−	1.08287i
$472$		0			0
$473$	13.3693	−	23.1563i	0.614722	−	1.06473i
$474$		0			0
$475$	10.7440	+	3.03916i	0.492967	+	0.139446i
$476$		0			0
$477$	−0.246211	+	0.426450i	−0.0112732	+	0.0195258i
$478$		0			0
$479$	4.41033	+	7.63892i	0.201513	+	0.349031i	0.949016	−	0.315227i	$-0.102081\pi$
$479$	4.41033	+	7.63892i	0.201513	+	0.349031i	−0.747503	+	0.664258i	$0.768747\pi$
$480$		0			0
$481$	−0.246211	−	0.426450i	−0.0112263	−	0.0194445i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.78078	+	15.2088i	0.398715	+	0.690594i
$486$		0			0
$487$	32.0159			1.45078			0.725390	−	0.688338i	$-0.241660\pi$
$487$	32.0159			1.45078			0.725390	+	0.688338i	$0.241660\pi$
$488$		0			0
$489$	−2.40388	+	4.16365i	−0.108707	+	0.188287i
$490$		0			0
$491$	−16.3083	+	28.2468i	−0.735983	+	1.27476i	0.218308	+	0.975880i	$0.429946\pi$
$491$	−16.3083	+	28.2468i	−0.735983	+	1.27476i	−0.954291	+	0.298880i	$0.903387\pi$
$492$		0			0
$493$	2.05398			0.0925064
$494$		0			0
$495$	6.15461			0.276629
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.33365	−	10.9702i	0.283533	−	0.491093i	−0.688719	−	0.725028i	$-0.741827\pi$
$499$	6.33365	−	10.9702i	0.283533	−	0.491093i	0.972252	+	0.233935i	$0.0751602\pi$
$500$		0			0
$501$	31.3153			1.39907
$502$		0			0
$503$	−14.9383	−	25.8739i	−0.666066	−	1.15366i	−0.978995	−	0.203883i	$-0.934644\pi$
$503$	−14.9383	−	25.8739i	−0.666066	−	1.15366i	0.312930	−	0.949776i	$-0.398690\pi$
$504$		0			0
$505$	−24.6847			−1.09845
$506$		0			0
$507$	−8.77331	−	15.1958i	−0.389636	−	0.674870i
$508$		0			0
$509$	−0.534565	−	0.925894i	−0.0236942	−	0.0410395i	0.853935	−	0.520379i	$-0.174209\pi$
$509$	−0.534565	−	0.925894i	−0.0236942	−	0.0410395i	−0.877629	+	0.479340i	$0.840876\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	17.6501	−	17.1672i	0.779271	−	0.757948i
$514$		0			0
$515$	14.0373	−	24.3133i	0.618557	−	1.07137i
$516$		0			0
$517$	−3.75379	−	6.50175i	−0.165091	−	0.285947i
$518$		0			0
$519$	3.97831	+	6.89064i	0.174629	+	0.302465i
$520$		0			0
$521$	28.4233			1.24525			0.622624	−	0.782522i	$-0.286067\pi$
$521$	28.4233			1.24525			0.622624	+	0.782522i	$0.286067\pi$
$522$		0			0
$523$	−5.94898	−	10.3039i	−0.260131	−	0.450560i	0.706146	−	0.708067i	$-0.250432\pi$
$523$	−5.94898	−	10.3039i	−0.260131	−	0.450560i	−0.966276	+	0.257507i	$0.917099\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.600672	+	1.04039i	−0.0261657	+	0.0453203i
$528$		0			0
$529$	−0.403882	+	0.699544i	−0.0175601	+	0.0304150i
$530$		0			0
$531$	−1.53865			−0.0667718
$532$		0			0
$533$	0.438447			0.0189913
$534$		0			0
$535$	4.27865	−	7.41084i	0.184982	−	0.320398i
$536$		0			0
$537$	−12.0194	+	20.8182i	−0.518676	+	0.898373i
$538$		0			0
$539$	−24.5653			−1.05810
$540$		0			0
$541$	−14.1501	−	24.5087i	−0.608360	−	1.05371i	−0.991511	−	0.130025i	$-0.958494\pi$
$541$	−14.1501	−	24.5087i	−0.608360	−	1.05371i	0.383151	−	0.923686i	$-0.374839\pi$
$542$		0			0
$543$	28.6752			1.23057
$544$		0			0
$545$	9.21922	+	15.9682i	0.394908	+	0.684001i
$546$		0			0
$547$	5.94898	+	10.3039i	0.254360	+	0.440565i	0.964722	−	0.263272i	$-0.0848018\pi$
$547$	5.94898	+	10.3039i	0.254360	+	0.440565i	−0.710361	+	0.703837i	$0.751468\pi$
$548$		0			0
$549$	1.36932	−	2.37173i	0.0584410	−	0.101223i
$550$		0			0
$551$	19.6490	+	5.55813i	0.837074	+	0.236784i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.20134	−	2.08079i	−0.0509942	−	0.0883245i
$556$		0			0
$557$	−5.21922	−	9.03996i	−0.221146	−	0.383035i	0.734011	−	0.679138i	$-0.237646\pi$
$557$	−5.21922	−	9.03996i	−0.221146	−	0.383035i	−0.955156	+	0.296103i	$0.904313\pi$
$558$		0			0
$559$	−3.34067			−0.141295
$560$		0			0
$561$	−1.05398	−	1.82554i	−0.0444989	−	0.0770743i
$562$		0			0
$563$	−32.4479			−1.36752			−0.683759	−	0.729708i	$-0.739656\pi$
$563$	−32.4479			−1.36752			−0.683759	+	0.729708i	$0.739656\pi$
$564$		0			0
$565$	−5.12311	+	8.87348i	−0.215531	+	0.373310i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.630683			0.0264396			0.0132198	−	0.999913i	$-0.495792\pi$
$569$	0.630683			0.0264396			0.0132198	+	0.999913i	$0.495792\pi$
$570$		0			0
$571$	−14.4693			−0.605522			−0.302761	−	0.953067i	$-0.597908\pi$
$571$	−14.4693			−0.605522			−0.302761	+	0.953067i	$0.597908\pi$
$572$		0			0
$573$	−17.1231	+	29.6581i	−0.715328	+	1.23898i
$574$		0			0
$575$	6.24932	−	10.8241i	0.260615	−	0.451398i
$576$		0			0
$577$	24.1771			1.00651			0.503253	−	0.864139i	$-0.332137\pi$
$577$	24.1771			1.00651			0.503253	+	0.864139i	$0.332137\pi$
$578$		0			0
$579$	−6.71831	−	11.6365i	−0.279203	−	0.483594i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.769326	+	1.33251i	0.0318622	+	0.0551870i
$584$		0			0
$585$	−0.384472	−	0.665925i	−0.0158960	−	0.0275326i
$586$		0			0
$587$	10.2276	−	17.7148i	0.422139	−	0.731167i	−0.574009	−	0.818849i	$-0.694613\pi$
$587$	10.2276	−	17.7148i	0.422139	−	0.731167i	0.996149	+	0.0876819i	$0.0279459\pi$
$588$		0			0
$589$	−8.56155	+	8.32729i	−0.352773	+	0.343120i
$590$		0			0
$591$	13.2680	−	22.9808i	0.545771	−	0.945303i
$592$		0			0
$593$	11.1847	+	19.3724i	0.459299	+	0.795529i	0.998924	−	0.0463764i	$-0.0147674\pi$
$593$	11.1847	+	19.3724i	0.459299	+	0.795529i	−0.539625	+	0.841905i	$0.681434\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	25.9157			1.06066
$598$		0			0
$599$	−7.91965	−	13.7172i	−0.323588	−	0.560471i	0.657637	−	0.753335i	$-0.271556\pi$
$599$	−7.91965	−	13.7172i	−0.323588	−	0.560471i	−0.981226	+	0.192863i	$0.938223\pi$
$600$		0			0
$601$	42.4233			1.73048			0.865241	−	0.501356i	$-0.167165\pi$
$601$	42.4233			1.73048			0.865241	+	0.501356i	$0.167165\pi$
$602$		0			0
$603$	7.78797	−	13.4892i	0.317151	−	0.549321i
$604$		0			0
$605$	1.02699	−	1.77879i	0.0417530	−	0.0723183i
$606$		0			0
$607$	39.0346			1.58436			0.792182	−	0.610285i	$-0.208945\pi$
$607$	39.0346			1.58436			0.792182	+	0.610285i	$0.208945\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.468990	+	0.812315i	−0.0189733	+	0.0328628i
$612$		0			0
$613$	22.9039	−	39.6707i	0.925079	−	1.60228i	0.133645	−	0.991029i	$-0.457332\pi$
$613$	22.9039	−	39.6707i	0.925079	−	1.60228i	0.791434	−	0.611255i	$-0.209335\pi$
$614$		0			0
$615$	2.13932			0.0862659
$616$		0			0
$617$	−16.1847	−	28.0327i	−0.651570	−	1.12855i	−0.982742	−	0.184982i	$-0.940777\pi$
$617$	−16.1847	−	28.0327i	−0.651570	−	1.12855i	0.331172	−	0.943570i	$-0.392556\pi$
$618$		0			0
$619$	−19.5173			−0.784466			−0.392233	−	0.919866i	$-0.628297\pi$
$619$	−19.5173			−0.784466			−0.392233	+	0.919866i	$0.628297\pi$
$620$		0			0
$621$	−13.7808	−	23.8690i	−0.553004	−	0.957830i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2.81534	−	4.87631i	0.112614	−	0.195053i
$626$		0			0
$627$	−5.14268	−	20.3158i	−0.205379	−	0.811333i
$628$		0			0
$629$	0.246211	−	0.426450i	0.00981709	−	0.0170037i
$630$		0			0
$631$	−8.08831	−	14.0094i	−0.321990	−	0.557704i	0.658908	−	0.752223i	$-0.271019\pi$
$631$	−8.08831	−	14.0094i	−0.321990	−	0.557704i	−0.980899	+	0.194520i	$0.937685\pi$
$632$		0			0
$633$	5.21922	+	9.03996i	0.207446	+	0.359306i
$634$		0			0
$635$	14.3007			0.567504
$636$		0			0
$637$	1.53457	+	2.65794i	0.0608017	+	0.105312i
$638$		0			0
$639$	5.47999			0.216785
$640$		0			0
$641$	−7.18466	+	12.4442i	−0.283777	+	0.491516i	−0.972312	−	0.233687i	$-0.924921\pi$
$641$	−7.18466	+	12.4442i	−0.283777	+	0.491516i	0.688535	+	0.725203i	$0.258254\pi$
$642$		0			0
$643$	1.28567	−	2.22685i	0.0507019	−	0.0878183i	−0.839561	−	0.543266i	$-0.817187\pi$
$643$	1.28567	−	2.22685i	0.0507019	−	0.0878183i	0.890263	+	0.455448i	$0.150521\pi$
$644$		0			0
$645$	−16.3002			−0.641819
$646$		0			0
$647$	28.9386			1.13769			0.568847	−	0.822443i	$-0.307390\pi$
$647$	28.9386			1.13769			0.568847	+	0.822443i	$0.307390\pi$
$648$		0			0
$649$	−2.40388	+	4.16365i	−0.0943606	+	0.163437i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	40.4924			1.58459			0.792295	−	0.610138i	$-0.208886\pi$
$653$	40.4924			1.58459			0.792295	+	0.610138i	$0.208886\pi$
$654$		0			0
$655$	7.48763	+	12.9690i	0.292566	+	0.506739i
$656$		0			0
$657$	−1.39963			−0.0546046
$658$		0			0
$659$	−5.94898	−	10.3039i	−0.231739	−	0.401384i	0.726581	−	0.687081i	$-0.241108\pi$
$659$	−5.94898	−	10.3039i	−0.231739	−	0.401384i	−0.958320	+	0.285697i	$0.907775\pi$
$660$		0			0
$661$	−2.15009	−	3.72407i	−0.0836289	−	0.144850i	0.821177	−	0.570673i	$-0.193318\pi$
$661$	−2.15009	−	3.72407i	−0.0836289	−	0.144850i	−0.904806	+	0.425824i	$0.859984\pi$
$662$		0			0
$663$	−0.131681	+	0.228079i	−0.00511408	+	0.00885785i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.4290	−	19.7956i	0.442532	−	0.766487i
$668$		0			0
$669$	12.9579	+	22.4437i	0.500980	+	0.867722i
$670$		0			0
$671$	−4.27865	−	7.41084i	−0.165175	−	0.286092i
$672$		0			0
$673$	−25.6155			−0.987406			−0.493703	−	0.869631i	$-0.664357\pi$
$673$	−25.6155			−0.987406			−0.493703	+	0.869631i	$0.664357\pi$
$674$		0			0
$675$	7.23465	+	12.5308i	0.278462	+	0.482310i
$676$		0			0
$677$	−1.12311			−0.0431645			−0.0215822	−	0.999767i	$-0.506870\pi$
$677$	−1.12311			−0.0431645			−0.0215822	+	0.999767i	$0.506870\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−7.21165	+	12.4909i	−0.276351	+	0.478654i
$682$		0			0
$683$	−23.7959			−0.910526			−0.455263	−	0.890357i	$-0.650455\pi$
$683$	−23.7959			−0.910526			−0.455263	+	0.890357i	$0.650455\pi$
$684$		0			0
$685$	10.9309			0.417647
$686$		0			0
$687$	6.68134	−	11.5724i	0.254909	−	0.441515i
$688$		0			0
$689$	0.0961180	−	0.166481i	0.00366180	−	0.00634243i
$690$		0			0
$691$	41.4372			1.57635			0.788174	−	0.615453i	$-0.211027\pi$
$691$	41.4372			1.57635			0.788174	+	0.615453i	$0.211027\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−17.3780			−0.659183
$696$		0			0
$697$	0.219224	+	0.379706i	0.00830369	+	0.0143824i
$698$		0			0
$699$	2.65567	+	4.59975i	0.100447	+	0.173979i
$700$		0			0
$701$	−12.7808	+	22.1370i	−0.482723	+	0.836101i	−0.999803	−	0.0198359i	$-0.993686\pi$
$701$	−12.7808	+	22.1370i	−0.482723	+	0.836101i	0.517080	+	0.855937i	$0.327019\pi$
$702$		0			0
$703$	3.50932	−	3.41330i	0.132357	−	0.128735i
$704$		0			0
$705$	−2.28835	+	3.96355i	−0.0861844	+	0.149276i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−12.9039	−	22.3502i	−0.484615	−	0.839379i	0.515228	−	0.857053i	$-0.327707\pi$
$709$	−12.9039	−	22.3502i	−0.484615	−	0.839379i	−0.999844	+	0.0176744i	$0.994374\pi$
$710$		0			0
$711$	−2.40269			−0.0901078
$712$		0			0
$713$	6.68466	+	11.5782i	0.250342	+	0.433606i
$714$		0			0
$715$	−2.40269			−0.0898554
$716$		0			0
$717$	−20.0540	+	34.7345i	−0.748929	+	1.29718i
$718$		0			0
$719$	17.0776	−	29.5793i	0.636888	−	1.10312i	−0.349224	−	0.937039i	$-0.613555\pi$
$719$	17.0776	−	29.5793i	0.636888	−	1.10312i	0.986112	−	0.166083i	$-0.0531119\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	26.7046			0.993154
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	13.5683	−	23.5010i	0.503220	−	0.871603i	−0.496773	−	0.867881i	$-0.665482\pi$
$727$	13.5683	−	23.5010i	0.503220	−	0.871603i	0.999993	−	0.00372251i	$-0.00118491\pi$
$728$		0			0
$729$	28.1231			1.04160
$730$		0			0
$731$	−1.67033	−	2.89310i	−0.0617795	−	0.107005i
$732$		0			0
$733$	3.36932			0.124449			0.0622243	−	0.998062i	$-0.480181\pi$
$733$	3.36932			0.124449			0.0622243	+	0.998062i	$0.480181\pi$
$734$		0			0
$735$	7.48763	+	12.9690i	0.276186	+	0.478367i
$736$		0			0
$737$	−24.3348	−	42.1490i	−0.896382	−	1.55258i
$738$		0			0
$739$	4.79499	−	8.30517i	0.176387	−	0.305511i	−0.764254	−	0.644916i	$-0.776892\pi$
$739$	4.79499	−	8.30517i	0.176387	−	0.305511i	0.940640	+	0.339405i	$0.110226\pi$
$740$		0			0
$741$	−1.87689	+	1.82554i	−0.0689494	+	0.0670628i
$742$		0			0
$743$	−14.9383	+	25.8739i	−0.548033	+	0.949221i	0.450376	+	0.892839i	$0.351290\pi$
$743$	−14.9383	+	25.8739i	−0.548033	+	0.949221i	−0.998409	+	0.0563821i	$0.982044\pi$
$744$		0			0
$745$	6.97301	+	12.0776i	0.255471	+	0.442489i
$746$		0			0
$747$	−3.50932	−	6.07832i	−0.128399	−	0.222394i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.9569	−	38.0305i	−0.801220	−	1.38775i	−0.918813	−	0.394692i	$-0.870851\pi$
$751$	−21.9569	−	38.0305i	−0.801220	−	1.38775i	0.117593	−	0.993062i	$-0.462482\pi$
$752$		0			0
$753$	28.6155			1.04281
$754$		0			0
$755$	5.47999	−	9.49162i	0.199437	−	0.345436i
$756$		0			0
$757$	−4.65767	+	8.06732i	−0.169286	+	0.293212i	−0.938169	−	0.346178i	$-0.887479\pi$
$757$	−4.65767	+	8.06732i	−0.169286	+	0.293212i	0.768883	+	0.639389i	$0.220813\pi$
$758$		0			0
$759$	−23.4586			−0.851494
$760$		0			0
$761$	−21.9309			−0.794993			−0.397497	−	0.917604i	$-0.630121\pi$
$761$	−21.9309			−0.794993			−0.397497	+	0.917604i	$0.630121\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.384472	−	0.665925i	0.0139006	−	0.0240766i
$766$		0			0
$767$	0.600672			0.0216890
$768$		0			0
$769$	−5.34233	−	9.25319i	−0.192649	−	0.333678i	0.753478	−	0.657473i	$-0.228375\pi$
$769$	−5.34233	−	9.25319i	−0.192649	−	0.333678i	−0.946127	+	0.323795i	$0.895041\pi$
$770$		0			0
$771$	15.4073			0.554880
$772$		0			0
$773$	−14.3423	−	24.8416i	−0.515858	−	0.893492i	−0.999831	−	0.0184088i	$-0.994140\pi$
$773$	−14.3423	−	24.8416i	−0.515858	−	0.893492i	0.483973	−	0.875083i	$-0.339193\pi$
$774$		0			0
$775$	−3.50932	−	6.07832i	−0.126059	−	0.218340i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.06966	+	4.22562i	0.0383246	+	0.151398i
$780$		0			0
$781$	8.56155	−	14.8290i	0.306356	−	0.530625i
$782$		0			0
$783$	13.2310	+	22.9167i	0.472837	+	0.818978i
$784$		0			0
$785$	−15.4654	−	26.7869i	−0.551985	−	0.956066i
$786$		0			0
$787$	21.4879			0.765963			0.382981	−	0.923756i	$-0.374897\pi$
$787$	21.4879			0.765963			0.382981	+	0.923756i	$0.374897\pi$
$788$		0			0
$789$	15.6577	+	27.1199i	0.557428	+	0.965493i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.534565	+	0.925894i	−0.0189830	+	0.0328795i
$794$		0			0
$795$	0.468990	−	0.812315i	0.0166334	−	0.0288098i
$796$		0			0
$797$	12.6307			0.447402			0.223701	−	0.974658i	$-0.428186\pi$
$797$	12.6307			0.447402			0.223701	+	0.974658i	$0.428186\pi$
$798$		0			0
$799$	−0.937981			−0.0331834
$800$		0			0
$801$	−6.00000	+	10.3923i	−0.212000	+	0.367194i
$802$		0			0
$803$	−2.18668	+	3.78744i	−0.0771662	+	0.133656i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.0296	+	20.8360i	0.423464	+	0.733460i
$808$		0			0
$809$	−40.1771			−1.41255			−0.706275	−	0.707937i	$-0.749626\pi$
$809$	−40.1771			−1.41255			−0.706275	+	0.707937i	$0.749626\pi$
$810$		0			0
$811$	26.0669	+	45.1493i	0.915334	+	1.58540i	0.806412	+	0.591354i	$0.201407\pi$
$811$	26.0669	+	45.1493i	0.915334	+	1.58540i	0.108922	+	0.994050i	$0.465260\pi$
$812$		0			0
$813$	−1.46543	−	2.53821i	−0.0513950	−	0.0890188i
$814$		0			0
$815$	−2.74000	+	4.74581i	−0.0959779	+	0.166239i
$816$		0			0
$817$	−8.15009	−	32.1963i	−0.285136	−	1.12641i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.71165	−	15.0890i	−0.304039	−	0.526610i	0.673008	−	0.739635i	$-0.265002\pi$
$821$	−8.71165	−	15.0890i	−0.304039	−	0.526610i	−0.977047	+	0.213025i	$0.931668\pi$
$822$		0			0
$823$	−24.0963	−	41.7360i	−0.839943	−	1.45482i	−0.889942	−	0.456075i	$-0.849255\pi$
$823$	−24.0963	−	41.7360i	−0.839943	−	1.45482i	0.0499986	−	0.998749i	$-0.484078\pi$
$824$		0			0
$825$	12.3153			0.428765
$826$		0			0
$827$	3.42499	+	5.93227i	0.119099	+	0.206285i	0.919411	−	0.393299i	$-0.128666\pi$
$827$	3.42499	+	5.93227i	0.119099	+	0.206285i	−0.800312	+	0.599584i	$0.795333\pi$
$828$		0			0
$829$	31.1231			1.08095			0.540475	−	0.841360i	$-0.318245\pi$
$829$	31.1231			1.08095			0.540475	+	0.841360i	$0.318245\pi$
$830$		0			0
$831$	2.74000	−	4.74581i	0.0950494	−	0.164630i
$832$		0			0
$833$	−1.53457	+	2.65794i	−0.0531695	+	0.0920923i
$834$		0			0
$835$	35.6939			1.23524
$836$		0			0
$837$	−15.4773			−0.534973
$838$		0			0
$839$	−25.4663	+	44.1089i	−0.879193	+	1.52281i	−0.0269650	+	0.999636i	$0.508584\pi$
$839$	−25.4663	+	44.1089i	−0.879193	+	1.52281i	−0.852228	+	0.523171i	$0.824749\pi$
$840$		0			0
$841$	3.52699	−	6.10892i	0.121620	−	0.210652i
$842$		0			0
$843$	−31.5100			−1.08526
$844$		0			0
$845$	−10.0000	−	17.3205i	−0.344010	−	0.595844i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6.56913	+	11.3781i	0.225452	+	0.390494i
$850$		0			0
$851$	−2.74000	−	4.74581i	−0.0939258	−	0.162684i
$852$		0			0
$853$	−1.78078	+	3.08440i	−0.0609726	+	0.105608i	−0.894900	−	0.446266i	$-0.852754\pi$
$853$	−1.78078	+	3.08440i	−0.0609726	+	0.105608i	0.833928	+	0.551874i	$0.186087\pi$
$854$		0			0
$855$	5.47999	−	5.33005i	0.187412	−	0.182284i
$856$		0			0
$857$	0.815342	−	1.41221i	0.0278515	−	0.0482403i	−0.851764	−	0.523926i	$-0.824467\pi$
$857$	0.815342	−	1.41221i	0.0278515	−	0.0482403i	0.879615	+	0.475686i	$0.157800\pi$
$858$		0			0
$859$	−26.4516	−	45.8155i	−0.902517	−	1.56321i	−0.824216	−	0.566275i	$-0.808384\pi$
$859$	−26.4516	−	45.8155i	−0.902517	−	1.56321i	−0.0783006	−	0.996930i	$-0.524949\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−33.2173			−1.13073			−0.565364	−	0.824841i	$-0.691264\pi$
$863$	−33.2173			−1.13073			−0.565364	+	0.824841i	$0.691264\pi$
$864$		0			0
$865$	4.53457	+	7.85410i	0.154180	+	0.267047i
$866$		0			0
$867$	23.0266			0.782024
$868$		0			0
$869$	−3.75379	+	6.50175i	−0.127339	+	0.220557i
$870$		0			0
$871$	−3.04033	+	5.26601i	−0.103018	+	0.178432i
$872$		0			0
$873$	−12.6307			−0.427484
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.6577	+	34.0481i	−0.663792	+	1.14972i	0.315819	+	0.948820i	$0.397721\pi$
$877$	−19.6577	+	34.0481i	−0.663792	+	1.14972i	−0.979611	+	0.200903i	$0.935613\pi$
$878$		0			0
$879$	2.74000	−	4.74581i	0.0924178	−	0.160072i
$880$		0			0
$881$	−11.0540			−0.372418			−0.186209	−	0.982510i	$-0.559620\pi$
$881$	−11.0540			−0.372418			−0.186209	+	0.982510i	$0.559620\pi$
$882$		0			0
$883$	17.4623	+	30.2456i	0.587653	+	1.01784i	0.994539	+	0.104365i	$0.0332812\pi$
$883$	17.4623	+	30.2456i	0.587653	+	1.01784i	−0.406886	+	0.913479i	$0.633386\pi$
$884$		0			0
$885$	2.93087			0.0985201
$886$		0			0
$887$	5.94898	+	10.3039i	0.199747	+	0.345972i	0.948446	−	0.316938i	$-0.102655\pi$
$887$	5.94898	+	10.3039i	0.199747	+	0.345972i	−0.748699	+	0.662910i	$0.769321\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.66667	−	13.2791i	0.256843	−	0.444865i
$892$		0			0
$893$	−8.97301	−	2.53821i	−0.300270	−	0.0849379i
$894$		0			0
$895$	−13.7000	+	23.7291i	−0.457940	+	0.793175i
$896$		0			0
$897$	1.46543	+	2.53821i	0.0489294	+	0.0847483i
$898$		0			0
$899$	−6.41797	−	11.1163i	−0.214051	−	0.370748i
$900$		0			0
$901$	0.192236			0.00640431
$902$		0			0
$903$		0			0
$904$		0			0
$905$	32.6847			1.08647
$906$		0			0
$907$	6.76566	−	11.7185i	0.224650	−	0.389105i	−0.731564	−	0.681772i	$-0.761209\pi$
$907$	6.76566	−	11.7185i	0.224650	−	0.389105i	0.956214	+	0.292667i	$0.0945427\pi$
$908$		0			0
$909$	8.87689	−	15.3752i	0.294428	−	0.509964i
$910$		0			0
$911$	−10.0959			−0.334494			−0.167247	−	0.985915i	$-0.553488\pi$
$911$	−10.0959			−0.334494			−0.167247	+	0.985915i	$0.553488\pi$
$912$		0			0
$913$	−21.9309			−0.725806
$914$		0			0
$915$	−2.60831	+	4.51773i	−0.0862282	+	0.149352i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−57.0132			−1.88069			−0.940346	−	0.340220i	$-0.889498\pi$
$919$	−57.0132			−1.88069			−0.940346	+	0.340220i	$0.889498\pi$
$920$		0			0
$921$	−11.3769	−	19.7054i	−0.374881	−	0.649314i
$922$		0			0
$923$	−2.13932			−0.0704167
$924$		0			0
$925$	1.43845	+	2.49146i	0.0472959	+	0.0819188i
$926$		0			0
$927$	10.0959	+	17.4867i	0.331594	+	0.574338i
$928$		0			0
$929$	−6.06155	+	10.4989i	−0.198873	+	0.344458i	−0.948163	−	0.317783i	$-0.897061\pi$
$929$	−6.06155	+	10.4989i	−0.198873	+	0.344458i	0.749290	+	0.662242i	$0.230395\pi$
$930$		0			0
$931$	−21.8726	+	21.2741i	−0.716846	+	0.697232i
$932$		0			0
$933$	−9.38447	+	16.2544i	−0.307234	+	0.532145i
$934$		0			0
$935$	−1.20134	−	2.08079i	−0.0392881	−	0.0680490i
$936$		0			0
$937$	20.9924	+	36.3599i	0.685793	+	1.18783i	0.973187	+	0.230015i	$0.0738776\pi$
$937$	20.9924	+	36.3599i	0.685793	+	1.18783i	−0.287394	+	0.957812i	$0.592789\pi$
$938$		0			0
$939$	−15.4073			−0.502798
$940$		0			0
$941$	−3.78078	−	6.54850i	−0.123250	−	0.213475i	0.797798	−	0.602925i	$-0.205998\pi$
$941$	−3.78078	−	6.54850i	−0.123250	−	0.213475i	−0.921047	+	0.389450i	$0.872665\pi$
$942$		0			0
$943$	4.87932			0.158893
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.3269	−	40.4034i	0.758024	−	1.31294i	−0.185833	−	0.982581i	$-0.559498\pi$
$947$	23.3269	−	40.4034i	0.758024	−	1.31294i	0.943857	−	0.330354i	$-0.107168\pi$
$948$		0			0
$949$	0.546398			0.0177368
$950$		0			0
$951$	−42.7125			−1.38505
$952$		0			0
$953$	−28.3078	+	49.0305i	−0.916978	+	1.58825i	−0.113000	+	0.993595i	$0.536046\pi$
$953$	−28.3078	+	49.0305i	−0.916978	+	1.58825i	−0.803979	+	0.594658i	$0.797287\pi$
$954$		0			0
$955$	−19.5173	+	33.8049i	−0.631564	+	1.09390i
$956$		0			0
$957$	22.5227			0.728057
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−23.4924			−0.757820
$962$		0			0
$963$	3.07730	+	5.33005i	0.0991648	+	0.171758i
$964$		0			0
$965$	−7.65767	−	13.2635i	−0.246509	−	0.426966i
$966$		0			0
$967$	−15.5390	+	26.9143i	−0.499700	+	0.865505i	−1.00000		0.000346935i	$-0.999890\pi$
$967$	−15.5390	+	26.9143i	−0.499700	+	0.865505i	0.500300	+	0.865852i	$0.333223\pi$
$968$		0			0
$969$	−2.51941	−	0.712669i	−0.0809351	−	0.0228942i
$970$		0			0
$971$	−5.73297	+	9.92980i	−0.183980	+	0.318662i	−0.943232	−	0.332134i	$-0.892231\pi$
$971$	−5.73297	+	9.92980i	−0.183980	+	0.318662i	0.759252	+	0.650796i	$0.225565\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.769326	−	1.33251i	−0.0246382	−	0.0426745i
$976$		0			0
$977$	37.3002			1.19334			0.596669	−	0.802487i	$-0.296490\pi$
$977$	37.3002			1.19334			0.596669	+	0.802487i	$0.296490\pi$
$978$		0			0
$979$	18.7480	+	32.4724i	0.599187	+	1.03782i
$980$		0			0
$981$	−13.2614			−0.423403
$982$		0			0
$983$	−19.0483	+	32.9926i	−0.607546	+	1.05230i	0.384097	+	0.923293i	$0.374513\pi$
$983$	−19.0483	+	32.9926i	−0.607546	+	1.05230i	−0.991644	+	0.129008i	$0.958821\pi$
$984$		0			0
$985$	15.1231	−	26.1940i	0.481862	−	0.834610i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−37.1771			−1.18216
$990$		0			0
$991$	16.9090	−	29.2872i	0.537131	−	0.930338i	−0.461926	−	0.886919i	$-0.652841\pi$
$991$	16.9090	−	29.2872i	0.537131	−	0.930338i	0.999057	−	0.0434197i	$-0.0138253\pi$
$992$		0			0
$993$	14.7192	−	25.4944i	0.467100	−	0.809042i
$994$		0			0
$995$	29.5393			0.936458
$996$		0			0
$997$	−11.4654	−	19.8587i	−0.363114	−	0.628932i	0.625358	−	0.780338i	$-0.284953\pi$
$997$	−11.4654	−	19.8587i	−0.363114	−	0.628932i	−0.988472	+	0.151406i	$0.951620\pi$
$998$		0			0
$999$	6.34403			0.200716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.p.961.3		8
4.3	odd	2	inner	1216.2.i.p.961.2		8
8.3	odd	2		608.2.i.d.353.3	yes	8
8.5	even	2		608.2.i.d.353.2	✓	8
19.7	even	3	inner	1216.2.i.p.577.3		8
76.7	odd	6	inner	1216.2.i.p.577.2		8
152.45	even	6		608.2.i.d.577.2	yes	8
152.83	odd	6		608.2.i.d.577.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.d.353.2	✓	8	8.5	even	2
608.2.i.d.353.3	yes	8	8.3	odd	2
608.2.i.d.577.2	yes	8	152.45	even	6
608.2.i.d.577.3	yes	8	152.83	odd	6
1216.2.i.p.577.2		8	76.7	odd	6	inner
1216.2.i.p.577.3		8	19.7	even	3	inner
1216.2.i.p.961.2		8	4.3	odd	2	inner
1216.2.i.p.961.3		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.684999 - 1.18645i) q^{3} +(0.780776 - 1.35234i) q^{5} +(0.561553 + 0.972638i) q^{9} +O(q^{10})\)	\(q+(0.684999 - 1.18645i) q^{3} +(0.780776 - 1.35234i) q^{5} +(0.561553 + 0.972638i) q^{9} +3.50932 q^{11} +(-0.219224 - 0.379706i) q^{13} +(-1.06966 - 1.85271i) q^{15} +(0.219224 - 0.379706i) q^{17} +(3.12466 - 3.03916i) q^{19} +(-2.43966 - 4.22562i) q^{23} +(1.28078 + 2.21837i) q^{25} +5.64865 q^{27} +(2.34233 + 4.05703i) q^{29} -2.74000 q^{31} +(2.40388 - 4.16365i) q^{33} +1.12311 q^{37} -0.600672 q^{39} +(-0.500000 + 0.866025i) q^{41} +(3.80966 - 6.59852i) q^{43} +1.75379 q^{45} +(-1.06966 - 1.85271i) q^{47} -7.00000 q^{49} +(-0.300336 - 0.520197i) q^{51} +(0.219224 + 0.379706i) q^{53} +(2.74000 - 4.74581i) q^{55} +(-1.46543 - 5.78908i) q^{57} +(-0.684999 + 1.18645i) q^{59} +(-1.21922 - 2.11176i) q^{61} -0.684658 q^{65} +(-6.93432 - 12.0106i) q^{67} -6.68466 q^{69} +(2.43966 - 4.22562i) q^{71} +(-0.623106 + 1.07925i) q^{73} +3.50932 q^{75} +(-1.06966 + 1.85271i) q^{79} +(2.18466 - 3.78394i) q^{81} -6.24932 q^{83} +(-0.342329 - 0.592932i) q^{85} +6.41797 q^{87} +(5.34233 + 9.25319i) q^{89} +(-1.87689 + 3.25088i) q^{93} +(-1.67033 - 6.59852i) q^{95} +(-5.62311 + 9.73950i) q^{97} +(1.97067 + 3.41330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} - 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^5 - 12 * q^9	\( 8 q - 2 q^{5} - 12 q^{9} - 10 q^{13} + 10 q^{17} + 2 q^{25} - 6 q^{29} - 22 q^{33} - 24 q^{37} - 4 q^{41} + 80 q^{45} - 56 q^{49} + 10 q^{53} + 46 q^{57} - 18 q^{61} + 44 q^{65} - 4 q^{69} + 28 q^{73} - 32 q^{81} + 22 q^{85} + 18 q^{89} - 48 q^{93} - 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 - 12 * q^9 - 10 * q^13 + 10 * q^17 + 2 * q^25 - 6 * q^29 - 22 * q^33 - 24 * q^37 - 4 * q^41 + 80 * q^45 - 56 * q^49 + 10 * q^53 + 46 * q^57 - 18 * q^61 + 44 * q^65 - 4 * q^69 + 28 * q^73 - 32 * q^81 + 22 * q^85 + 18 * q^89 - 48 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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