LMFDB - Embedded newform 144.3.m.b.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 $ x^16 - 6x^14 + 10x^12 + 88x^10 - 752x^8 + 1408x^6 + 2560x^4 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.8
Root			$-0.136762 + 1.99532i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.b.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99532 + 0.136762i) q^{2} +(3.96259 + 0.545766i) q^{4} +(0.227650 - 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 + 1.63091i) q^{8} +O(q^{10})$	\(q+(1.99532 + 0.136762i) q^{2} +(3.96259 + 0.545766i) q^{4} +(0.227650 - 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 + 1.63091i) q^{8} +(0.485368 - 0.423100i) q^{10} +(-2.21045 - 2.21045i) q^{11} +(5.08526 + 5.08526i) q^{13} +(7.78612 + 0.533670i) q^{14} +(15.4043 + 4.32530i) q^{16} -18.8341 q^{17} +(11.7651 - 11.7651i) q^{19} +(1.02633 - 0.777840i) q^{20} +(-4.10825 - 4.71286i) q^{22} -35.4354 q^{23} +24.8964i q^{25} +(9.45124 + 10.8422i) q^{26} +(15.4628 + 2.12968i) q^{28} +(-21.2499 - 21.2499i) q^{29} -35.9691i q^{31} +(30.1449 + 10.7371i) q^{32} +(-37.5799 - 2.57578i) q^{34} +(0.888334 - 0.888334i) q^{35} +(-34.4199 + 34.4199i) q^{37} +(25.0842 - 21.8661i) q^{38} +(2.15423 - 1.41168i) q^{40} +44.1055i q^{41} +(-28.3018 - 28.3018i) q^{43} +(-7.55273 - 9.96550i) q^{44} +(-70.7049 - 4.84620i) q^{46} -32.8802i q^{47} -33.7729 q^{49} +(-3.40486 + 49.6762i) q^{50} +(17.3754 + 22.9262i) q^{52} +(42.1450 - 42.1450i) q^{53} -1.00642 q^{55} +(30.5620 + 6.36412i) q^{56} +(-39.4941 - 45.3065i) q^{58} +(66.9935 + 66.9935i) q^{59} +(17.3728 + 17.3728i) q^{61} +(4.91919 - 71.7697i) q^{62} +(58.6803 + 25.5465i) q^{64} +2.31532 q^{65} +(39.6756 - 39.6756i) q^{67} +(-74.6317 - 10.2790i) q^{68} +(1.89400 - 1.65102i) q^{70} -63.0272 q^{71} +75.4549i q^{73} +(-73.3859 + 63.9713i) q^{74} +(53.0413 - 40.1993i) q^{76} +(-8.62561 - 8.62561i) q^{77} -59.1583i q^{79} +(4.49144 - 2.52213i) q^{80} +(-6.03194 + 88.0046i) q^{82} +(71.2155 - 71.2155i) q^{83} +(-4.28757 + 4.28757i) q^{85} +(-52.6004 - 60.3416i) q^{86} +(-13.7072 - 20.9173i) q^{88} +150.671i q^{89} +(19.8437 + 19.8437i) q^{91} +(-140.416 - 19.3394i) q^{92} +(4.49675 - 65.6065i) q^{94} -5.35665i q^{95} +51.5586 q^{97} +(-67.3876 - 4.61883i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4}+O(q^{10}) $ 16 * q - 12 * q^4	$ 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.99532	+	0.136762i	0.997659	+	0.0683808i
$2$	1.99532	+	0.136762i	0.997659	+	0.0683808i
$3$		0			0
$3$		0			0
$4$	3.96259	+	0.545766i	0.990648	+	0.136441i
$5$	0.227650	−	0.227650i	0.0455300	−	0.0455300i	−0.683975	−	0.729505i	$-0.739750\pi$
$5$	0.227650	−	0.227650i	0.0455300	−	0.0455300i	0.729505	+	0.683975i	$0.239750\pi$
$6$		0			0
$7$	3.90219			0.557456			0.278728	−	0.960370i	$-0.410087\pi$
$7$	3.90219			0.557456			0.278728	+	0.960370i	$0.410087\pi$
$8$	7.83199	+	1.63091i	0.978999	+	0.203863i
$9$		0			0
$10$	0.485368	−	0.423100i	0.0485368	−	0.0423100i
$11$	−2.21045	−	2.21045i	−0.200950	−	0.200950i	0.599457	−	0.800407i	$-0.295383\pi$
$11$	−2.21045	−	2.21045i	−0.200950	−	0.200950i	−0.800407	+	0.599457i	$0.795383\pi$
$12$		0			0
$13$	5.08526	+	5.08526i	0.391174	+	0.391174i	0.875106	−	0.483932i	$-0.160792\pi$
$13$	5.08526	+	5.08526i	0.391174	+	0.391174i	−0.483932	+	0.875106i	$0.660792\pi$
$14$	7.78612	+	0.533670i	0.556152	+	0.0381193i
$15$		0			0
$16$	15.4043	+	4.32530i	0.962767	+	0.270331i
$17$	−18.8341			−1.10789			−0.553943	−	0.832555i	$-0.686877\pi$
$17$	−18.8341			−1.10789			−0.553943	+	0.832555i	$0.686877\pi$
$18$		0			0
$19$	11.7651	−	11.7651i	0.619216	−	0.619216i	−0.326114	−	0.945330i	$-0.605739\pi$
$19$	11.7651	−	11.7651i	0.619216	−	0.619216i	0.945330	+	0.326114i	$0.105739\pi$
$20$	1.02633	−	0.777840i	0.0513164	−	0.0388920i
$21$		0			0
$22$	−4.10825	−	4.71286i	−0.186739	−	0.214221i
$23$	−35.4354			−1.54067			−0.770335	−	0.637640i	$-0.779911\pi$
$23$	−35.4354			−1.54067			−0.770335	+	0.637640i	$0.779911\pi$
$24$		0			0
$25$			24.8964i			0.995854i
$26$	9.45124	+	10.8422i	0.363509	+	0.417007i
$27$		0			0
$28$	15.4628	+	2.12968i	0.552243	+	0.0760602i
$29$	−21.2499	−	21.2499i	−0.732755	−	0.732755i	0.238410	−	0.971165i	$-0.423374\pi$
$29$	−21.2499	−	21.2499i	−0.732755	−	0.732755i	−0.971165	+	0.238410i	$0.923374\pi$
$30$		0			0
$31$		−	35.9691i		−	1.16029i	−0.814512	−	0.580146i	$-0.802995\pi$
$31$		−	35.9691i		−	1.16029i	0.814512	−	0.580146i	$-0.197005\pi$
$32$	30.1449	+	10.7371i	0.942028	+	0.335533i
$33$		0			0
$34$	−37.5799	−	2.57578i	−1.10529	−	0.0757581i
$35$	0.888334	−	0.888334i	0.0253810	−	0.0253810i
$36$		0			0
$37$	−34.4199	+	34.4199i	−0.930267	+	0.930267i	−0.997722	−	0.0674555i	$-0.978512\pi$
$37$	−34.4199	+	34.4199i	−0.930267	+	0.930267i	0.0674555	+	0.997722i	$0.478512\pi$
$38$	25.0842	−	21.8661i	0.660110	−	0.575425i
$39$		0			0
$40$	2.15423	−	1.41168i	0.0538557	−	0.0352919i
$41$			44.1055i			1.07574i	0.843026	+	0.537872i	$0.180772\pi$
$41$			44.1055i			1.07574i	−0.843026	+	0.537872i	$0.819228\pi$
$42$		0			0
$43$	−28.3018	−	28.3018i	−0.658180	−	0.658180i	0.296769	−	0.954949i	$-0.404091\pi$
$43$	−28.3018	−	28.3018i	−0.658180	−	0.658180i	−0.954949	+	0.296769i	$0.904091\pi$
$44$	−7.55273	−	9.96550i	−0.171653	−	0.226489i
$45$		0			0
$46$	−70.7049	−	4.84620i	−1.53706	−	0.105352i
$47$		−	32.8802i		−	0.699579i	−0.936828	−	0.349790i	$-0.886253\pi$
$47$		−	32.8802i		−	0.699579i	0.936828	−	0.349790i	$-0.113747\pi$
$48$		0			0
$49$	−33.7729			−0.689242
$50$	−3.40486	+	49.6762i	−0.0680973	+	0.993523i
$51$		0			0
$52$	17.3754	+	22.9262i	0.334143	+	0.440888i
$53$	42.1450	−	42.1450i	0.795189	−	0.795189i	−0.187144	−	0.982333i	$-0.559923\pi$
$53$	42.1450	−	42.1450i	0.795189	−	0.795189i	0.982333	+	0.187144i	$0.0599230\pi$
$54$		0			0
$55$	−1.00642			−0.0182985
$56$	30.5620	+	6.36412i	0.545749	+	0.113645i
$57$		0			0
$58$	−39.4941	−	45.3065i	−0.680933	−	0.781146i
$59$	66.9935	+	66.9935i	1.13548	+	1.13548i	0.989250	+	0.146233i	$0.0467149\pi$
$59$	66.9935	+	66.9935i	1.13548	+	1.13548i	0.146233	+	0.989250i	$0.453285\pi$
$60$		0			0
$61$	17.3728	+	17.3728i	0.284800	+	0.284800i	0.835020	−	0.550220i	$-0.185456\pi$
$61$	17.3728	+	17.3728i	0.284800	+	0.284800i	−0.550220	+	0.835020i	$0.685456\pi$
$62$	4.91919	−	71.7697i	0.0793417	−	1.15758i
$63$		0			0
$64$	58.6803	+	25.5465i	0.916879	+	0.399164i
$65$	2.31532			0.0356203
$66$		0			0
$67$	39.6756	−	39.6756i	0.592174	−	0.592174i	−0.346044	−	0.938218i	$-0.612475\pi$
$67$	39.6756	−	39.6756i	0.592174	−	0.592174i	0.938218	+	0.346044i	$0.112475\pi$
$68$	−74.6317	−	10.2790i	−1.09752	−	0.151162i
$69$		0			0
$70$	1.89400	−	1.65102i	0.0270571	−	0.0235860i
$71$	−63.0272			−0.887707			−0.443853	−	0.896099i	$-0.646389\pi$
$71$	−63.0272			−0.887707			−0.443853	+	0.896099i	$0.646389\pi$
$72$		0			0
$73$			75.4549i			1.03363i	0.856097	+	0.516815i	$0.172882\pi$
$73$			75.4549i			1.03363i	−0.856097	+	0.516815i	$0.827118\pi$
$74$	−73.3859	+	63.9713i	−0.991702	+	0.864477i
$75$		0			0
$76$	53.0413	−	40.1993i	0.697912	−	0.528939i
$77$	−8.62561	−	8.62561i	−0.112021	−	0.112021i
$78$		0			0
$79$		−	59.1583i		−	0.748839i	−0.927259	−	0.374419i	$-0.877842\pi$
$79$		−	59.1583i		−	0.748839i	0.927259	−	0.374419i	$-0.122158\pi$
$80$	4.49144	−	2.52213i	0.0561430	−	0.0315266i
$81$		0			0
$82$	−6.03194	+	88.0046i	−0.0735603	+	1.07323i
$83$	71.2155	−	71.2155i	0.858018	−	0.858018i	−0.133086	−	0.991104i	$-0.542489\pi$
$83$	71.2155	−	71.2155i	0.858018	−	0.858018i	0.991104	+	0.133086i	$0.0424887\pi$
$84$		0			0
$85$	−4.28757	+	4.28757i	−0.0504420	+	0.0504420i
$86$	−52.6004	−	60.3416i	−0.611633	−	0.701647i
$87$		0			0
$88$	−13.7072	−	20.9173i	−0.155764	−	0.237696i
$89$			150.671i			1.69293i	0.532443	+	0.846466i	$0.321274\pi$
$89$			150.671i			1.69293i	−0.532443	+	0.846466i	$0.678726\pi$
$90$		0			0
$91$	19.8437	+	19.8437i	0.218062	+	0.218062i
$92$	−140.416	−	19.3394i	−1.52626	−	0.210211i
$93$		0			0
$94$	4.49675	−	65.6065i	0.0478378	−	0.697942i
$95$		−	5.35665i		−	0.0563858i
$96$		0			0
$97$	51.5586			0.531532			0.265766	−	0.964038i	$-0.414375\pi$
$97$	51.5586			0.531532			0.265766	+	0.964038i	$0.414375\pi$
$98$	−67.3876	−	4.61883i	−0.687629	−	0.0471309i
$99$		0			0
$100$	−13.5876	+	98.6541i	−0.135876	+	0.986541i
$101$	139.414	−	139.414i	1.38034	−	1.38034i	0.536327	−	0.844010i	$-0.319811\pi$
$101$	139.414	−	139.414i	1.38034	−	1.38034i	0.844010	−	0.536327i	$-0.180189\pi$
$102$		0			0
$103$	67.9691			0.659894			0.329947	−	0.943999i	$-0.392969\pi$
$103$	67.9691			0.659894			0.329947	+	0.943999i	$0.392969\pi$
$104$	31.5341	+	48.1213i	0.303213	+	0.462705i
$105$		0			0
$106$	89.8565	−	78.3289i	0.847703	−	0.738952i
$107$	129.801	+	129.801i	1.21309	+	1.21309i	0.970004	+	0.243090i	$0.0781609\pi$
$107$	129.801	+	129.801i	1.21309	+	1.21309i	0.243090	+	0.970004i	$0.421839\pi$
$108$		0			0
$109$	30.1323	+	30.1323i	0.276443	+	0.276443i	0.831687	−	0.555244i	$-0.187375\pi$
$109$	30.1323	+	30.1323i	0.276443	+	0.276443i	−0.555244	+	0.831687i	$0.687375\pi$
$110$	−2.00812	−	0.137639i	−0.0182557	−	0.00125127i
$111$		0			0
$112$	60.1105	+	16.8781i	0.536701	+	0.150698i
$113$	5.11034			0.0452243			0.0226121	−	0.999744i	$-0.492802\pi$
$113$	5.11034			0.0452243			0.0226121	+	0.999744i	$0.492802\pi$
$114$		0			0
$115$	−8.06687	+	8.06687i	−0.0701467	+	0.0701467i
$116$	−72.6072	−	95.8021i	−0.625924	−	0.825880i
$117$		0			0
$118$	124.511	+	142.836i	1.05518	+	1.21047i
$119$	−73.4942			−0.617598
$120$		0			0
$121$		−	111.228i		−	0.919238i
$122$	32.2884	+	37.0403i	0.264659	+	0.303609i
$123$		0			0
$124$	19.6307	−	142.531i	0.158312	−	1.14944i
$125$	11.3589	+	11.3589i	0.0908712	+	0.0908712i
$126$		0			0
$127$			123.225i			0.970277i	0.874437	+	0.485138i	$0.161231\pi$
$127$			123.225i			0.970277i	−0.874437	+	0.485138i	$0.838769\pi$
$128$	113.592	+	58.9986i	0.887438	+	0.460927i
$129$		0			0
$130$	4.61980	+	0.316646i	0.0355369	+	0.00243574i
$131$	76.2899	−	76.2899i	0.582365	−	0.582365i	−0.353187	−	0.935553i	$-0.614902\pi$
$131$	76.2899	−	76.2899i	0.582365	−	0.582365i	0.935553	+	0.353187i	$0.114902\pi$
$132$		0			0
$133$	45.9098	−	45.9098i	0.345186	−	0.345186i
$134$	84.5917	−	73.7394i	0.631281	−	0.550294i
$135$		0			0
$136$	−147.508	−	30.7166i	−1.08462	−	0.225857i
$137$			73.0194i			0.532988i	0.963837	+	0.266494i	$0.0858653\pi$
$137$			73.0194i			0.532988i	−0.963837	+	0.266494i	$0.914135\pi$
$138$		0			0
$139$	16.5250	+	16.5250i	0.118885	+	0.118885i	0.764046	−	0.645162i	$-0.223210\pi$
$139$	16.5250	+	16.5250i	0.118885	+	0.118885i	−0.645162	+	0.764046i	$0.723210\pi$
$140$	4.00493	−	3.03528i	0.0286066	−	0.0216806i
$141$		0			0
$142$	−125.759	−	8.61969i	−0.885629	−	0.0607021i
$143$		−	22.4814i		−	0.157213i
$144$		0			0
$145$	−9.67507			−0.0667246
$146$	−10.3193	+	150.557i	−0.0706804	+	1.03121i
$147$		0			0
$148$	−155.177	+	117.607i	−1.04849	+	0.794640i
$149$	22.0334	−	22.0334i	0.147875	−	0.147875i	−0.629293	−	0.777168i	$-0.716656\pi$
$149$	22.0334	−	22.0334i	0.147875	−	0.147875i	0.777168	+	0.629293i	$0.216656\pi$
$150$		0			0
$151$	−161.017			−1.06634			−0.533168	−	0.846010i	$-0.678999\pi$
$151$	−161.017			−1.06634			−0.533168	+	0.846010i	$0.678999\pi$
$152$	111.332	−	72.9565i	0.732448	−	0.479977i
$153$		0			0
$154$	−16.0312	−	18.3905i	−0.104099	−	0.119419i
$155$	−8.18836	−	8.18836i	−0.0528281	−	0.0528281i
$156$		0			0
$157$	−151.888	−	151.888i	−0.967441	−	0.967441i	0.0320455	−	0.999486i	$-0.489798\pi$
$157$	−151.888	−	151.888i	−0.967441	−	0.967441i	−0.999486	+	0.0320455i	$0.989798\pi$
$158$	8.09058	−	118.040i	0.0512062	−	0.747086i
$159$		0			0
$160$	9.30678	−	4.41820i	0.0581674	−	0.0276137i
$161$	−138.276			−0.858856
$162$		0			0
$163$	−186.334	+	186.334i	−1.14315	+	1.14315i	−0.155283	+	0.987870i	$0.549629\pi$
$163$	−186.334	+	186.334i	−1.14315	+	1.14315i	−0.987870	+	0.155283i	$0.950371\pi$
$164$	−24.0713	+	174.772i	−0.146776	+	1.06568i
$165$		0			0
$166$	151.837	−	132.358i	0.914682	−	0.797338i
$167$	−199.590			−1.19515			−0.597576	−	0.801813i	$-0.703869\pi$
$167$	−199.590			−1.19515			−0.597576	+	0.801813i	$0.703869\pi$
$168$		0			0
$169$		−	117.280i		−	0.693966i
$170$	−9.14145	+	7.96870i	−0.0537732	+	0.0468747i
$171$		0			0
$172$	−96.7022	−	127.594i	−0.562222	−	0.741828i
$173$	−138.631	−	138.631i	−0.801333	−	0.801333i	0.181971	−	0.983304i	$-0.441752\pi$
$173$	−138.631	−	138.631i	−0.801333	−	0.801333i	−0.983304	+	0.181971i	$0.941752\pi$
$174$		0			0
$175$			97.1504i			0.555145i
$176$	−24.4895	−	43.6112i	−0.139145	−	0.247791i
$177$		0			0
$178$	−20.6060	+	300.637i	−0.115764	+	1.68897i
$179$	−148.572	+	148.572i	−0.830010	+	0.830010i	−0.987518	−	0.157508i	$-0.949654\pi$
$179$	−148.572	+	148.572i	−0.830010	+	0.830010i	0.157508	+	0.987518i	$0.449654\pi$
$180$		0			0
$181$	99.6006	−	99.6006i	0.550280	−	0.550280i	−0.376242	−	0.926522i	$-0.622784\pi$
$181$	99.6006	−	99.6006i	0.550280	−	0.550280i	0.926522	+	0.376242i	$0.122784\pi$
$182$	36.8806	+	42.3083i	0.202641	+	0.232463i
$183$		0			0
$184$	−277.530	−	57.7918i	−1.50831	−	0.314086i
$185$			15.6714i			0.0847101i
$186$		0			0
$187$	41.6318	+	41.6318i	0.222630	+	0.222630i
$188$	17.9449	−	130.291i	0.0954516	−	0.693037i
$189$		0			0
$190$	0.732584	−	10.6882i	0.00385571	−	0.0562539i
$191$		−	149.517i		−	0.782812i	−0.920218	−	0.391406i	$-0.871989\pi$
$191$		−	149.517i		−	0.782812i	0.920218	−	0.391406i	$-0.128011\pi$
$192$		0			0
$193$	−52.8254			−0.273707			−0.136853	−	0.990591i	$-0.543699\pi$
$193$	−52.8254			−0.273707			−0.136853	+	0.990591i	$0.543699\pi$
$194$	102.876	+	7.05123i	0.530288	+	0.0363466i
$195$		0			0
$196$	−133.828	−	18.4321i	−0.682797	−	0.0940412i
$197$	−108.072	+	108.072i	−0.548590	+	0.548590i	−0.926033	−	0.377443i	$-0.876803\pi$
$197$	−108.072	+	108.072i	−0.548590	+	0.548590i	0.377443	+	0.926033i	$0.376803\pi$
$198$		0			0
$199$	−2.24707			−0.0112918			−0.00564590	−	0.999984i	$-0.501797\pi$
$199$	−2.24707			−0.0112918			−0.00564590	+	0.999984i	$0.501797\pi$
$200$	−40.6036	+	194.988i	−0.203018	+	0.974940i
$201$		0			0
$202$	297.242	−	259.109i	1.47149	−	1.28272i
$203$	−82.9212	−	82.9212i	−0.408479	−	0.408479i
$204$		0			0
$205$	10.0406	+	10.0406i	0.0489787	+	0.0489787i
$206$	135.620	+	9.29556i	0.658349	+	0.0451241i
$207$		0			0
$208$	56.3395	+	100.330i	0.270863	+	0.482356i
$209$	−52.0124			−0.248863
$210$		0			0
$211$	50.4041	−	50.4041i	0.238882	−	0.238882i	−0.577505	−	0.816387i	$-0.695974\pi$
$211$	50.4041	−	50.4041i	0.238882	−	0.238882i	0.816387	+	0.577505i	$0.195974\pi$
$212$	190.005	−	144.002i	0.896249	−	0.679256i
$213$		0			0
$214$	241.243	+	276.746i	1.12730	+	1.29321i
$215$	−12.8858			−0.0599339
$216$		0			0
$217$		−	140.358i		−	0.646812i
$218$	56.0026	+	64.2445i	0.256893	+	0.294699i
$219$		0			0
$220$	−3.98802	−	0.549268i	−0.0181274	−	0.00249667i
$221$	−95.7760	−	95.7760i	−0.433376	−	0.433376i
$222$		0			0
$223$			230.340i			1.03291i	0.856313	+	0.516457i	$0.172749\pi$
$223$			230.340i			1.03291i	−0.856313	+	0.516457i	$0.827251\pi$
$224$	117.631	+	41.8981i	0.525140	+	0.187045i
$225$		0			0
$226$	10.1968	+	0.698898i	0.0451184	+	0.00309247i
$227$	12.1395	−	12.1395i	0.0534779	−	0.0534779i	−0.679862	−	0.733340i	$-0.737960\pi$
$227$	12.1395	−	12.1395i	0.0534779	−	0.0534779i	0.733340	+	0.679862i	$0.237960\pi$
$228$		0			0
$229$	39.1259	−	39.1259i	0.170855	−	0.170855i	−0.616500	−	0.787355i	$-0.711450\pi$
$229$	39.1259	−	39.1259i	0.170855	−	0.170855i	0.787355	+	0.616500i	$0.211450\pi$
$230$	−17.1992	+	14.9927i	−0.0747792	+	0.0651858i
$231$		0			0
$232$	−131.772	−	201.086i	−0.567985	−	0.866748i
$233$		−	36.6784i		−	0.157418i	−0.996898	−	0.0787090i	$-0.974920\pi$
$233$		−	36.6784i		−	0.157418i	0.996898	−	0.0787090i	$-0.0250798\pi$
$234$		0			0
$235$	−7.48518	−	7.48518i	−0.0318518	−	0.0318518i
$236$	228.905	+	302.031i	0.969937	+	1.27979i
$237$		0			0
$238$	−146.644	−	10.0512i	−0.616152	−	0.0422318i
$239$			147.098i			0.615474i	0.951471	+	0.307737i	$0.0995717\pi$
$239$			147.098i			0.615474i	−0.951471	+	0.307737i	$0.900428\pi$
$240$		0			0
$241$	205.488			0.852649			0.426324	−	0.904570i	$-0.359808\pi$
$241$	205.488			0.852649			0.426324	+	0.904570i	$0.359808\pi$
$242$	15.2117	−	221.935i	0.0628582	−	0.917086i
$243$		0			0
$244$	59.3600	+	78.3229i	0.243278	+	0.320996i
$245$	−7.68839	+	7.68839i	−0.0313812	+	0.0313812i
$246$		0			0
$247$	119.657			0.484442
$248$	58.6622	−	281.710i	0.236541	−	1.13593i
$249$		0			0
$250$	21.1112	+	24.2181i	0.0844447	+	0.0968724i
$251$	−55.4867	−	55.4867i	−0.221063	−	0.221063i	0.587883	−	0.808946i	$-0.299961\pi$
$251$	−55.4867	−	55.4867i	−0.221063	−	0.221063i	−0.808946	+	0.587883i	$0.799961\pi$
$252$		0			0
$253$	78.3282	+	78.3282i	0.309598	+	0.309598i
$254$	−16.8525	+	245.873i	−0.0663483	+	0.968005i
$255$		0			0
$256$	218.584	+	133.256i	0.853842	+	0.520532i
$257$	142.878			0.555944			0.277972	−	0.960589i	$-0.410338\pi$
$257$	142.878			0.555944			0.277972	+	0.960589i	$0.410338\pi$
$258$		0			0
$259$	−134.313	+	134.313i	−0.518583	+	0.518583i
$260$	9.17466	+	1.26362i	0.0352872	+	0.00486008i
$261$		0			0
$262$	162.656	−	141.789i	0.620825	−	0.541180i
$263$	242.691			0.922780			0.461390	−	0.887197i	$-0.347351\pi$
$263$	242.691			0.922780			0.461390	+	0.887197i	$0.347351\pi$
$264$		0			0
$265$		−	19.1886i		−	0.0724099i
$266$	97.8833	−	85.3259i	0.367982	−	0.320774i
$267$		0			0
$268$	178.872	−	135.565i	0.667433	−	0.505839i
$269$	292.665	+	292.665i	1.08797	+	1.08797i	0.995737	+	0.0922353i	$0.0294012\pi$
$269$	292.665	+	292.665i	1.08797	+	1.08797i	0.0922353	+	0.995737i	$0.470599\pi$
$270$		0			0
$271$		−	258.180i		−	0.952694i	−0.879257	−	0.476347i	$-0.841961\pi$
$271$		−	258.180i		−	0.952694i	0.879257	−	0.476347i	$-0.158039\pi$
$272$	−290.125	−	81.4629i	−1.06664	−	0.299496i
$273$		0			0
$274$	−9.98625	+	145.697i	−0.0364462	+	0.531741i
$275$	55.0322	−	55.0322i	0.200117	−	0.200117i
$276$		0			0
$277$	63.2023	−	63.2023i	0.228167	−	0.228167i	−0.583759	−	0.811927i	$-0.698419\pi$
$277$	63.2023	−	63.2023i	0.228167	−	0.228167i	0.811927	+	0.583759i	$0.198419\pi$
$278$	30.7126	+	35.2325i	0.110477	+	0.126736i
$279$		0			0
$280$	8.40622	−	5.50864i	0.0300222	−	0.0196737i
$281$		−	421.406i		−	1.49966i	−0.661628	−	0.749832i	$-0.730134\pi$
$281$		−	421.406i		−	1.49966i	0.661628	−	0.749832i	$-0.269866\pi$
$282$		0			0
$283$	275.707	+	275.707i	0.974229	+	0.974229i	0.999676	−	0.0254475i	$-0.00810107\pi$
$283$	275.707	+	275.707i	0.974229	+	0.974229i	−0.0254475	+	0.999676i	$0.508101\pi$
$284$	−249.751	−	34.3981i	−0.879405	−	0.121120i
$285$		0			0
$286$	3.07459	−	44.8576i	0.0107503	−	0.156845i
$287$			172.108i			0.599681i
$288$		0			0
$289$	65.7217			0.227411
$290$	−19.3049	−	1.32318i	−0.0665685	−	0.00456268i
$291$		0			0
$292$	−41.1807	+	298.997i	−0.141030	+	1.02396i
$293$	−181.330	+	181.330i	−0.618873	+	0.618873i	−0.945242	−	0.326369i	$-0.894175\pi$
$293$	−181.330	+	181.330i	−0.618873	+	0.618873i	0.326369	+	0.945242i	$0.394175\pi$
$294$		0			0
$295$	30.5021			0.103397
$296$	−325.712	+	213.441i	−1.10038	+	0.721083i
$297$		0			0
$298$	46.9769	−	40.9503i	0.157641	−	0.137417i
$299$	−180.198	−	180.198i	−0.602669	−	0.602669i
$300$		0			0
$301$	−110.439	−	110.439i	−0.366907	−	0.366907i
$302$	−321.280	−	22.0209i	−1.06384	−	0.0729169i
$303$		0			0
$304$	232.121	−	130.345i	0.763555	−	0.428768i
$305$	7.90985			0.0259339
$306$		0			0
$307$	279.027	−	279.027i	0.908883	−	0.908883i	−0.0872996	−	0.996182i	$-0.527824\pi$
$307$	279.027	−	279.027i	0.908883	−	0.908883i	0.996182	+	0.0872996i	$0.0278237\pi$
$308$	−29.4722	−	38.8873i	−0.0956890	−	0.126258i
$309$		0			0
$310$	−15.2185	−	17.4582i	−0.0490920	−	0.0563169i
$311$	414.511			1.33283			0.666417	−	0.745579i	$-0.267827\pi$
$311$	414.511			1.33283			0.666417	+	0.745579i	$0.267827\pi$
$312$		0			0
$313$			331.008i			1.05753i	0.848767	+	0.528767i	$0.177346\pi$
$313$			331.008i			1.05753i	−0.848767	+	0.528767i	$0.822654\pi$
$314$	−282.293	−	323.838i	−0.899022	−	1.03133i
$315$		0			0
$316$	32.2866	−	234.420i	0.102173	−	0.741836i
$317$	194.563	+	194.563i	0.613764	+	0.613764i	0.943925	−	0.330161i	$-0.107103\pi$
$317$	194.563	+	194.563i	0.613764	+	0.613764i	−0.330161	+	0.943925i	$0.607103\pi$
$318$		0			0
$319$			93.9437i			0.294494i
$320$	19.1742	−	7.54290i	0.0599195	−	0.0235716i
$321$		0			0
$322$	−275.904	−	18.9108i	−0.856846	−	0.0587293i
$323$	−221.585	+	221.585i	−0.686021	+	0.686021i
$324$		0			0
$325$	−126.604	+	126.604i	−0.389552	+	0.389552i
$326$	−397.279	+	346.312i	−1.21865	+	1.06231i
$327$		0			0
$328$	−71.9320	+	345.434i	−0.219305	+	1.05315i
$329$		−	128.305i		−	0.389985i
$330$		0			0
$331$	−462.054	−	462.054i	−1.39593	−	1.39593i	−0.811292	−	0.584641i	$-0.801235\pi$
$331$	−462.054	−	462.054i	−1.39593	−	1.39593i	−0.584641	−	0.811292i	$-0.698765\pi$
$332$	321.065	−	243.331i	0.967063	−	0.732925i
$333$		0			0
$334$	−398.246	−	27.2963i	−1.19235	−	0.0817254i
$335$		−	18.0643i		−	0.0539233i
$336$		0			0
$337$	−472.439			−1.40190			−0.700948	−	0.713212i	$-0.747240\pi$
$337$	−472.439			−1.40190			−0.700948	+	0.713212i	$0.747240\pi$
$338$	16.0394	−	234.012i	0.0474540	−	0.692342i
$339$		0			0
$340$	−19.3299	+	14.6499i	−0.0568527	+	0.0430879i
$341$	−79.5078	+	79.5078i	−0.233161	+	0.233161i
$342$		0			0
$343$	−322.996			−0.941679
$344$	−175.502	−	267.817i	−0.510179	−	0.778537i
$345$		0			0
$346$	−257.653	−	295.572i	−0.744662	−	0.854253i
$347$	−92.8976	−	92.8976i	−0.267716	−	0.267716i	0.560463	−	0.828179i	$-0.310623\pi$
$347$	−92.8976	−	92.8976i	−0.267716	−	0.267716i	−0.828179	+	0.560463i	$0.810623\pi$
$348$		0			0
$349$	264.708	+	264.708i	0.758475	+	0.758475i	0.976045	−	0.217570i	$-0.0698129\pi$
$349$	264.708	+	264.708i	0.758475	+	0.758475i	−0.217570	+	0.976045i	$0.569813\pi$
$350$	−13.2864	+	193.846i	−0.0379613	+	0.553846i
$351$		0			0
$352$	−42.9001	−	90.3676i	−0.121875	−	0.256726i
$353$	413.360			1.17099			0.585495	−	0.810676i	$-0.300900\pi$
$353$	413.360			1.17099			0.585495	+	0.810676i	$0.300900\pi$
$354$		0			0
$355$	−14.3481	+	14.3481i	−0.0404173	+	0.0404173i
$356$	−82.2311	+	597.048i	−0.230986	+	1.67710i
$357$		0			0
$358$	−316.767	+	276.129i	−0.884824	+	0.771311i
$359$	625.198			1.74150			0.870749	−	0.491728i	$-0.163635\pi$
$359$	625.198			1.74150			0.870749	+	0.491728i	$0.163635\pi$
$360$		0			0
$361$			84.1643i			0.233142i
$362$	212.357	−	185.113i	0.586620	−	0.511363i
$363$		0			0
$364$	67.8024	+	89.4624i	0.186270	+	0.245776i
$365$	17.1773	+	17.1773i	0.0470611	+	0.0470611i
$366$		0			0
$367$		−	601.904i		−	1.64007i	−0.572316	−	0.820033i	$-0.693955\pi$
$367$		−	601.904i		−	1.64007i	0.572316	−	0.820033i	$-0.306045\pi$
$368$	−545.857	−	153.269i	−1.48331	−	0.416491i
$369$		0			0
$370$	−2.14324	+	31.2694i	−0.00579254	+	0.0845118i
$371$	164.458	−	164.458i	0.443283	−	0.443283i
$372$		0			0
$373$	−493.026	+	493.026i	−1.32179	+	1.32179i	−0.409455	+	0.912330i	$0.634281\pi$
$373$	−493.026	+	493.026i	−1.32179	+	1.32179i	−0.912330	+	0.409455i	$0.865719\pi$
$374$	77.3750	+	88.7622i	0.206885	+	0.237332i
$375$		0			0
$376$	53.6246	−	257.518i	0.142619	−	0.684888i
$377$		−	216.122i		−	0.573269i
$378$		0			0
$379$	−144.970	−	144.970i	−0.382506	−	0.382506i	0.489498	−	0.872004i	$-0.337180\pi$
$379$	−144.970	−	144.970i	−0.382506	−	0.382506i	−0.872004	+	0.489498i	$0.837180\pi$
$380$	2.92348	−	21.2262i	0.00769337	−	0.0558585i
$381$		0			0
$382$	20.4482	−	298.334i	0.0535293	−	0.780979i
$383$			417.764i			1.09077i	0.838187	+	0.545384i	$0.183616\pi$
$383$			417.764i			1.09077i	−0.838187	+	0.545384i	$0.816384\pi$
$384$		0			0
$385$	−3.92724			−0.0102006
$386$	−105.403	−	7.22448i	−0.273066	−	0.0187163i
$387$		0			0
$388$	204.306	+	28.1389i	0.526561	+	0.0725230i
$389$	−144.751	+	144.751i	−0.372109	+	0.372109i	−0.868245	−	0.496136i	$-0.834752\pi$
$389$	−144.751	+	144.751i	−0.372109	+	0.372109i	0.496136	+	0.868245i	$0.334752\pi$
$390$		0			0
$391$	667.392			1.70689
$392$	−264.509	−	55.0804i	−0.674768	−	0.140511i
$393$		0			0
$394$	−230.418	+	200.858i	−0.584819	+	0.509793i
$395$	−13.4674	−	13.4674i	−0.0340946	−	0.0340946i
$396$		0			0
$397$	−105.531	−	105.531i	−0.265822	−	0.265822i	0.561592	−	0.827414i	$-0.310189\pi$
$397$	−105.531	−	105.531i	−0.265822	−	0.265822i	−0.827414	+	0.561592i	$0.810189\pi$
$398$	−4.48362	−	0.307313i	−0.0112654	−	0.000772142i
$399$		0			0
$400$	−107.684	+	383.510i	−0.269210	+	0.958776i
$401$	529.383			1.32016			0.660078	−	0.751197i	$-0.270523\pi$
$401$	529.383			1.32016			0.660078	+	0.751197i	$0.270523\pi$
$402$		0			0
$403$	182.912	−	182.912i	0.453876	−	0.453876i
$404$	628.529	−	476.354i	1.55576	−	1.17909i
$405$		0			0
$406$	−154.114	−	176.795i	−0.379591	−	0.435455i
$407$	152.167			0.373874
$408$		0			0
$409$			371.204i			0.907590i	0.891106	+	0.453795i	$0.149930\pi$
$409$			371.204i			0.907590i	−0.891106	+	0.453795i	$0.850070\pi$
$410$	18.6611	+	21.4074i	0.0455148	+	0.0522132i
$411$		0			0
$412$	269.334	+	37.0952i	0.653723	+	0.0900369i
$413$	261.422	+	261.422i	0.632982	+	0.632982i
$414$		0			0
$415$		−	32.4244i		−	0.0781311i
$416$	98.6940	+	207.895i	0.237245	+	0.499748i
$417$		0			0
$418$	−103.781	−	7.11330i	−0.248281	−	0.0170175i
$419$	−124.486	+	124.486i	−0.297103	+	0.297103i	−0.839878	−	0.542775i	$-0.817374\pi$
$419$	−124.486	+	124.486i	−0.297103	+	0.297103i	0.542775	+	0.839878i	$0.317374\pi$
$420$		0			0
$421$	51.7267	−	51.7267i	0.122866	−	0.122866i	−0.643000	−	0.765866i	$-0.722310\pi$
$421$	51.7267	−	51.7267i	0.122866	−	0.122866i	0.765866	+	0.643000i	$0.222310\pi$
$422$	107.465	−	93.6788i	0.254658	−	0.221988i
$423$		0			0
$424$	398.814	−	261.345i	0.940599	−	0.616379i
$425$		−	468.899i		−	1.10329i
$426$		0			0
$427$	67.7922	+	67.7922i	0.158764	+	0.158764i
$428$	443.508	+	585.189i	1.03623	+	1.36727i
$429$		0			0
$430$	−25.7112	−	1.76228i	−0.0597936	−	0.00409833i
$431$		−	424.978i		−	0.986029i	−0.870021	−	0.493014i	$-0.835895\pi$
$431$		−	424.978i		−	0.986029i	0.870021	−	0.493014i	$-0.164105\pi$
$432$		0			0
$433$	283.151			0.653927			0.326964	−	0.945037i	$-0.393975\pi$
$433$	283.151			0.653927			0.326964	+	0.945037i	$0.393975\pi$
$434$	19.1956	−	280.059i	0.0442295	−	0.645298i
$435$		0			0
$436$	102.957	+	135.847i	0.236140	+	0.311576i
$437$	−416.901	+	416.901i	−0.954008	+	0.954008i
$438$		0			0
$439$	−701.459			−1.59786			−0.798928	−	0.601427i	$-0.794599\pi$
$439$	−701.459			−1.59786			−0.798928	+	0.601427i	$0.794599\pi$
$440$	−7.88226	−	1.64137i	−0.0179142	−	0.00373040i
$441$		0			0
$442$	−178.005	−	204.202i	−0.402727	−	0.461996i
$443$	−272.651	−	272.651i	−0.615464	−	0.615464i	0.328900	−	0.944365i	$-0.393322\pi$
$443$	−272.651	−	272.651i	−0.615464	−	0.615464i	−0.944365	+	0.328900i	$0.893322\pi$
$444$		0			0
$445$	34.3002	+	34.3002i	0.0770792	+	0.0770792i
$446$	−31.5016	+	459.601i	−0.0706314	+	1.03050i
$447$		0			0
$448$	228.982	+	99.6875i	0.511120	+	0.222517i
$449$	−614.711			−1.36907			−0.684534	−	0.728981i	$-0.739994\pi$
$449$	−614.711			−1.36907			−0.684534	+	0.728981i	$0.739994\pi$
$450$		0			0
$451$	97.4931	−	97.4931i	0.216171	−	0.216171i
$452$	20.2502	+	2.78905i	0.0448013	+	0.00617046i
$453$		0			0
$454$	25.8823	−	22.5619i	0.0570096	−	0.0496959i
$455$	9.03482			0.0198567
$456$		0			0
$457$			117.859i			0.257898i	0.991651	+	0.128949i	$0.0411603\pi$
$457$			117.859i			0.257898i	−0.991651	+	0.128949i	$0.958840\pi$
$458$	83.4195	−	72.7177i	0.182139	−	0.158772i
$459$		0			0
$460$	−36.3683	+	27.5631i	−0.0790616	+	0.0599198i
$461$	−262.235	−	262.235i	−0.568839	−	0.568839i	0.362964	−	0.931803i	$-0.381765\pi$
$461$	−262.235	−	262.235i	−0.568839	−	0.568839i	−0.931803	+	0.362964i	$0.881765\pi$
$462$		0			0
$463$		−	192.234i		−	0.415192i	−0.978215	−	0.207596i	$-0.933436\pi$
$463$		−	192.234i		−	0.415192i	0.978215	−	0.207596i	$-0.0665640\pi$
$464$	−235.427	−	419.251i	−0.507386	−	0.903559i
$465$		0			0
$466$	5.01619	−	73.1851i	0.0107644	−	0.157049i
$467$	−529.169	+	529.169i	−1.13312	+	1.13312i	−0.143470	+	0.989655i	$0.545826\pi$
$467$	−529.169	+	529.169i	−1.13312	+	1.13312i	−0.989655	+	0.143470i	$0.954174\pi$
$468$		0			0
$469$	154.822	−	154.822i	0.330111	−	0.330111i
$470$	−13.9116	−	15.9590i	−0.0295992	−	0.0339553i
$471$		0			0
$472$	415.433	+	633.953i	0.880154	+	1.34312i
$473$			125.119i			0.264523i
$474$		0			0
$475$	292.908	+	292.908i	0.616649	+	0.616649i
$476$	−291.227	−	40.1106i	−0.611822	−	0.0842660i
$477$		0			0
$478$	−20.1174	+	293.508i	−0.0420866	+	0.614033i
$479$		−	1.43750i		−	0.00300104i	−0.999999	−	0.00150052i	$-0.999522\pi$
$479$		−	1.43750i		−	0.00300104i	0.999999	−	0.00150052i	$-0.000477630\pi$
$480$		0			0
$481$	−350.068			−0.727792
$482$	410.015	+	28.1029i	0.850653	+	0.0583048i
$483$		0			0
$484$	60.7043	−	440.751i	0.125422	−	0.910642i
$485$	11.7373	−	11.7373i	0.0242006	−	0.0242006i
$486$		0			0
$487$	701.238			1.43991			0.719957	−	0.694019i	$-0.244162\pi$
$487$	701.238			1.43991			0.719957	+	0.694019i	$0.244162\pi$
$488$	107.730	+	164.397i	0.220759	+	0.336880i
$489$		0			0
$490$	−16.3923	+	14.2893i	−0.0334536	+	0.0291619i
$491$	−519.668	−	519.668i	−1.05839	−	1.05839i	−0.998186	−	0.0602007i	$-0.980826\pi$
$491$	−519.668	−	519.668i	−1.05839	−	1.05839i	−0.0602007	−	0.998186i	$-0.519174\pi$
$492$		0			0
$493$	400.222	+	400.222i	0.811809	+	0.811809i
$494$	238.754	+	16.3645i	0.483308	+	0.0331265i
$495$		0			0
$496$	155.577	−	554.077i	0.313663	−	1.11709i
$497$	−245.944			−0.494858
$498$		0			0
$499$	359.284	−	359.284i	0.720009	−	0.720009i	−0.248598	−	0.968607i	$-0.579970\pi$
$499$	359.284	−	359.284i	0.720009	−	0.720009i	0.968607	+	0.248598i	$0.0799698\pi$
$500$	38.8114	+	51.2100i	0.0776228	+	0.102420i
$501$		0			0
$502$	−103.125	−	118.302i	−0.205429	−	0.235662i
$503$	−174.376			−0.346671			−0.173335	−	0.984863i	$-0.555454\pi$
$503$	−174.376			−0.346671			−0.173335	+	0.984863i	$0.555454\pi$
$504$		0			0
$505$		−	63.4752i		−	0.125693i
$506$	145.577	+	167.002i	0.287702	+	0.330043i
$507$		0			0
$508$	−67.2521	+	488.291i	−0.132386	+	0.961203i
$509$	−314.247	−	314.247i	−0.617381	−	0.617381i	0.327478	−	0.944859i	$-0.393801\pi$
$509$	−314.247	−	314.247i	−0.617381	−	0.617381i	−0.944859	+	0.327478i	$0.893801\pi$
$510$		0			0
$511$			294.440i			0.576203i
$512$	417.920	+	295.782i	0.816249	+	0.577700i
$513$		0			0
$514$	285.086	+	19.5402i	0.554643	+	0.0380159i
$515$	15.4732	−	15.4732i	0.0300450	−	0.0300450i
$516$		0			0
$517$	−72.6801	+	72.6801i	−0.140580	+	0.140580i
$518$	−286.366	+	249.628i	−0.552830	+	0.481908i
$519$		0			0
$520$	18.1336	+	3.77607i	0.0348722	+	0.00726167i
$521$		−	468.678i		−	0.899575i	−0.893136	−	0.449787i	$-0.851500\pi$
$521$		−	468.678i		−	0.899575i	0.893136	−	0.449787i	$-0.148500\pi$
$522$		0			0
$523$	−417.239	−	417.239i	−0.797780	−	0.797780i	0.184965	−	0.982745i	$-0.440783\pi$
$523$	−417.239	−	417.239i	−0.797780	−	0.797780i	−0.982745	+	0.184965i	$0.940783\pi$
$524$	343.942	−	260.669i	0.656378	−	0.497460i
$525$		0			0
$526$	484.246	+	33.1908i	0.920620	+	0.0631004i
$527$			677.443i			1.28547i
$528$		0			0
$529$	726.667			1.37366
$530$	2.62427	−	38.2874i	0.00495144	−	0.0722404i
$531$		0			0
$532$	206.978	−	156.866i	0.389056	−	0.294860i
$533$	−224.288	+	224.288i	−0.420803	+	0.420803i
$534$		0			0
$535$	59.0984			0.110464
$536$	375.447	−	246.032i	0.700460	−	0.459015i
$537$		0			0
$538$	543.934	+	623.984i	1.01103	+	1.15982i
$539$	74.6533	+	74.6533i	0.138503	+	0.138503i
$540$		0			0
$541$	−163.152	−	163.152i	−0.301574	−	0.301574i	0.540055	−	0.841629i	$-0.318403\pi$
$541$	−163.152	−	163.152i	−0.301574	−	0.301574i	−0.841629	+	0.540055i	$0.818403\pi$
$542$	35.3091	−	515.152i	0.0651460	−	0.950464i
$543$		0			0
$544$	−567.751	−	202.222i	−1.04366	−	0.371732i
$545$	13.7192			0.0251729
$546$		0			0
$547$	−595.267	+	595.267i	−1.08824	+	1.08824i	−0.0925300	+	0.995710i	$0.529495\pi$
$547$	−595.267	+	595.267i	−1.08824	+	1.08824i	−0.995710	+	0.0925300i	$0.970505\pi$
$548$	−39.8515	+	289.346i	−0.0727217	+	0.528004i
$549$		0			0
$550$	117.333	−	102.280i	0.213333	−	0.185964i
$551$	−500.015			−0.907468
$552$		0			0
$553$		−	230.847i		−	0.417445i
$554$	134.752	−	117.465i	0.243235	−	0.212031i
$555$		0			0
$556$	56.4629	+	74.5004i	0.101552	+	0.133994i
$557$	370.177	+	370.177i	0.664590	+	0.664590i	0.956459	−	0.291868i	$-0.0942769\pi$
$557$	370.177	+	370.177i	0.664590	+	0.664590i	−0.291868	+	0.956459i	$0.594277\pi$
$558$		0			0
$559$		−	287.843i		−	0.514926i
$560$	17.5265	−	9.84184i	0.0312973	−	0.0175747i
$561$		0			0
$562$	57.6321	−	840.839i	0.102548	−	1.49615i
$563$	426.543	−	426.543i	0.757625	−	0.757625i	−0.218264	−	0.975890i	$-0.570040\pi$
$563$	426.543	−	426.543i	0.757625	−	0.757625i	0.975890	+	0.218264i	$0.0700395\pi$
$564$		0			0
$565$	1.16337	−	1.16337i	0.00205906	−	0.00205906i
$566$	512.417	+	587.829i	0.905330	+	1.03857i
$567$		0			0
$568$	−493.628	−	102.791i	−0.869064	−	0.180971i
$569$			291.547i			0.512385i	0.966626	+	0.256192i	$0.0824680\pi$
$569$			291.547i			0.512385i	−0.966626	+	0.256192i	$0.917532\pi$
$570$		0			0
$571$	569.328	+	569.328i	0.997071	+	0.997071i	0.999996	−	0.00292477i	$-0.000930984\pi$
$571$	569.328	+	569.328i	0.997071	+	0.997071i	−0.00292477	+	0.999996i	$0.500931\pi$
$572$	12.2696	−	89.0847i	0.0214503	−	0.155743i
$573$		0			0
$574$	−23.5378	+	343.411i	−0.0410066	+	0.598277i
$575$		−	882.212i		−	1.53428i
$576$		0			0
$577$	−360.847			−0.625385			−0.312692	−	0.949854i	$-0.601231\pi$
$577$	−360.847			−0.625385			−0.312692	+	0.949854i	$0.601231\pi$
$578$	131.136	+	8.98820i	0.226878	+	0.0155505i
$579$		0			0
$580$	−38.3384	−	5.28032i	−0.0661006	−	0.00910401i
$581$	277.897	−	277.897i	0.478308	−	0.478308i
$582$		0			0
$583$	−186.319			−0.319586
$584$	−123.060	+	590.963i	−0.210719	+	1.01192i
$585$		0			0
$586$	−386.610	+	337.012i	−0.659744	+	0.575106i
$587$	373.439	+	373.439i	0.636183	+	0.636183i	0.949612	−	0.313429i	$-0.101478\pi$
$587$	373.439	+	373.439i	0.636183	+	0.636183i	−0.313429	+	0.949612i	$0.601478\pi$
$588$		0			0
$589$	−423.180	−	423.180i	−0.718472	−	0.718472i
$590$	60.8615	+	4.17152i	0.103155	+	0.00707037i
$591$		0			0
$592$	−679.089	+	381.337i	−1.14711	+	0.644151i
$593$	−608.053			−1.02538			−0.512692	−	0.858572i	$-0.671352\pi$
$593$	−608.053			−1.02538			−0.512692	+	0.858572i	$0.671352\pi$
$594$		0			0
$595$	−16.7309	+	16.7309i	−0.0281192	+	0.0281192i
$596$	99.3343	−	75.2842i	0.166668	−	0.126316i
$597$		0			0
$598$	−334.909	−	384.197i	−0.560048	−	0.642470i
$599$	−211.563			−0.353194			−0.176597	−	0.984283i	$-0.556509\pi$
$599$	−211.563			−0.353194			−0.176597	+	0.984283i	$0.556509\pi$
$600$		0			0
$601$		−	343.381i		−	0.571349i	−0.958327	−	0.285674i	$-0.907782\pi$
$601$		−	343.381i		−	0.571349i	0.958327	−	0.285674i	$-0.0922176\pi$
$602$	−205.257	−	235.465i	−0.340959	−	0.391137i
$603$		0			0
$604$	−638.043	−	87.8774i	−1.05636	−	0.145492i
$605$	−25.3210	−	25.3210i	−0.0418529	−	0.0418529i
$606$		0			0
$607$			1006.23i			1.65771i	0.559461	+	0.828856i	$0.311008\pi$
$607$			1006.23i			1.65771i	−0.559461	+	0.828856i	$0.688992\pi$
$608$	480.981	−	228.336i	0.791087	−	0.375552i
$609$		0			0
$610$	15.7827	+	1.08176i	0.0258732	+	0.00177338i
$611$	167.204	−	167.204i	0.273657	−	0.273657i
$612$		0			0
$613$	380.705	−	380.705i	0.621052	−	0.621052i	−0.324748	−	0.945801i	$-0.605280\pi$
$613$	380.705	−	380.705i	0.621052	−	0.621052i	0.945801	+	0.324748i	$0.105280\pi$
$614$	594.908	−	518.587i	0.968905	−	0.844605i
$615$		0			0
$616$	−53.4882	−	81.6233i	−0.0868314	−	0.132505i
$617$			693.808i			1.12449i	0.826972	+	0.562243i	$0.190061\pi$
$617$			693.808i			1.12449i	−0.826972	+	0.562243i	$0.809939\pi$
$618$		0			0
$619$	−619.279	−	619.279i	−1.00045	−	1.00045i	−1.00000		0.000450619i	$-0.999857\pi$
$619$	−619.279	−	619.279i	−1.00045	−	1.00045i	−0.000450619	−	1.00000i	$-0.500143\pi$
$620$	−27.9782	−	36.9160i	−0.0451261	−	0.0595420i
$621$		0			0
$622$	827.082	+	56.6892i	1.32971	+	0.0911403i
$623$			587.947i			0.943736i
$624$		0			0
$625$	−617.237			−0.987579
$626$	−45.2692	+	660.467i	−0.0723151	+	1.05506i
$627$		0			0
$628$	−518.976	−	684.767i	−0.826394	−	1.09039i
$629$	648.266	−	648.266i	1.03063	−	1.03063i
$630$		0			0
$631$	−1007.91			−1.59732			−0.798661	−	0.601781i	$-0.794458\pi$
$631$	−1007.91			−1.59732			−0.798661	+	0.601781i	$0.794458\pi$
$632$	96.4816	−	463.327i	0.152661	−	0.733113i
$633$		0			0
$634$	361.607	+	414.824i	0.570358	+	0.654297i
$635$	28.0522	+	28.0522i	0.0441767	+	0.0441767i
$636$		0			0
$637$	−171.744	−	171.744i	−0.269613	−	0.269613i
$638$	−12.8479	+	187.448i	−0.0201377	+	0.293805i
$639$		0			0
$640$	39.2903	−	12.4282i	0.0613910	−	0.0194191i
$641$	511.481			0.797943			0.398971	−	0.916963i	$-0.369367\pi$
$641$	511.481			0.797943			0.398971	+	0.916963i	$0.369367\pi$
$642$		0			0
$643$	−497.727	+	497.727i	−0.774071	+	0.774071i	−0.978815	−	0.204745i	$-0.934364\pi$
$643$	−497.727	+	497.727i	−0.774071	+	0.774071i	0.204745	+	0.978815i	$0.434364\pi$
$644$	−547.931	−	75.4662i	−0.850824	−	0.117184i
$645$		0			0
$646$	−472.437	+	411.828i	−0.731326	+	0.637505i
$647$	−59.8694			−0.0925339			−0.0462669	−	0.998929i	$-0.514732\pi$
$647$	−59.8694			−0.0925339			−0.0462669	+	0.998929i	$0.514732\pi$
$648$		0			0
$649$		−	296.172i		−	0.456351i
$650$	−269.931	+	235.301i	−0.415278	+	0.362002i
$651$		0			0
$652$	−840.060	+	636.671i	−1.28844	+	0.976489i
$653$	−489.952	−	489.952i	−0.750310	−	0.750310i	0.224227	−	0.974537i	$-0.428014\pi$
$653$	−489.952	−	489.952i	−0.750310	−	0.750310i	−0.974537	+	0.224227i	$0.928014\pi$
$654$		0			0
$655$		−	34.7348i		−	0.0530302i
$656$	−190.769	+	679.414i	−0.290807	+	1.03569i
$657$		0			0
$658$	17.5472	−	256.009i	0.0266675	−	0.389072i
$659$	−234.984	+	234.984i	−0.356577	+	0.356577i	−0.862549	−	0.505973i	$-0.831134\pi$
$659$	−234.984	+	234.984i	−0.356577	+	0.356577i	0.505973	+	0.862549i	$0.331134\pi$
$660$		0			0
$661$	305.060	−	305.060i	0.461512	−	0.461512i	−0.437639	−	0.899151i	$-0.644185\pi$
$661$	305.060	−	305.060i	0.461512	−	0.461512i	0.899151	+	0.437639i	$0.144185\pi$
$662$	−858.753	−	985.136i	−1.29721	−	1.48812i
$663$		0			0
$664$	673.905	−	441.614i	1.01492	−	0.665081i
$665$		−	20.9027i		−	0.0314326i
$666$		0			0
$667$	752.998	+	752.998i	1.12893	+	1.12893i
$668$	−790.895	−	108.930i	−1.18397	−	0.163068i
$669$		0			0
$670$	2.47050	−	36.0441i	0.00368732	−	0.0537971i
$671$		−	76.8036i		−	0.114461i
$672$		0			0
$673$	458.738			0.681632			0.340816	−	0.940130i	$-0.389297\pi$
$673$	458.738			0.681632			0.340816	+	0.940130i	$0.389297\pi$
$674$	−942.666	−	64.6115i	−1.39861	−	0.0958628i
$675$		0			0
$676$	64.0076	−	464.734i	0.0946858	−	0.687476i
$677$	−171.344	+	171.344i	−0.253094	+	0.253094i	−0.822238	−	0.569144i	$-0.807275\pi$
$677$	−171.344	+	171.344i	−0.253094	+	0.253094i	0.569144	+	0.822238i	$0.307275\pi$
$678$		0			0
$679$	201.192			0.296306
$680$	−40.5729	+	26.5876i	−0.0596660	+	0.0390994i
$681$		0			0
$682$	−169.517	+	147.770i	−0.248559	+	0.216671i
$683$	769.447	+	769.447i	1.12657	+	1.12657i	0.990731	+	0.135838i	$0.0433728\pi$
$683$	769.447	+	769.447i	1.12657	+	1.12657i	0.135838	+	0.990731i	$0.456627\pi$
$684$		0			0
$685$	16.6229	+	16.6229i	0.0242670	+	0.0242670i
$686$	−644.480	−	44.1734i	−0.939475	−	0.0643927i
$687$		0			0
$688$	−313.555	−	558.382i	−0.455748	−	0.811601i
$689$	428.636			0.622114
$690$		0			0
$691$	44.7951	−	44.7951i	0.0648264	−	0.0648264i	−0.673950	−	0.738777i	$-0.735404\pi$
$691$	44.7951	−	44.7951i	0.0648264	−	0.0648264i	0.738777	+	0.673950i	$0.235404\pi$
$692$	−473.677	−	624.996i	−0.684504	−	0.903174i
$693$		0			0
$694$	−172.655	−	198.065i	−0.248783	−	0.285396i
$695$	7.52381			0.0108256
$696$		0			0
$697$		−	830.686i		−	1.19180i
$698$	491.975	+	564.378i	0.704835	+	0.808565i
$699$		0			0
$700$	−53.0214	+	384.967i	−0.0757448	+	0.549954i
$701$	−31.7012	−	31.7012i	−0.0452229	−	0.0452229i	0.684134	−	0.729357i	$-0.260180\pi$
$701$	−31.7012	−	31.7012i	−0.0452229	−	0.0452229i	−0.729357	+	0.684134i	$0.760180\pi$
$702$		0			0
$703$			809.907i			1.15207i
$704$	−73.2406	−	186.179i	−0.104035	−	0.264459i
$705$		0			0
$706$	824.784	+	56.5317i	1.16825	+	0.0800732i
$707$	544.021	−	544.021i	0.769478	−	0.769478i
$708$		0			0
$709$	256.706	−	256.706i	0.362068	−	0.362068i	−0.502506	−	0.864574i	$-0.667589\pi$
$709$	256.706	−	256.706i	0.362068	−	0.362068i	0.864574	+	0.502506i	$0.167589\pi$
$710$	−30.5914	+	26.6668i	−0.0430864	+	0.0375589i
$711$		0			0
$712$	−245.730	+	1180.05i	−0.345127	+	1.65738i
$713$			1274.58i			1.78763i
$714$		0			0
$715$	−5.11789	−	5.11789i	−0.00715789	−	0.00715789i
$716$	−669.815	+	507.644i	−0.935496	+	0.709000i
$717$		0			0
$718$	1247.47	+	85.5030i	1.73742	+	0.119085i
$719$		−	1368.29i		−	1.90305i	−0.307574	−	0.951524i	$-0.599517\pi$
$719$		−	1368.29i		−	1.90305i	0.307574	−	0.951524i	$-0.400483\pi$
$720$		0			0
$721$	265.229			0.367862
$722$	−11.5104	+	167.935i	−0.0159424	+	0.232596i
$723$		0			0
$724$	449.035	−	340.318i	0.620215	−	0.470053i
$725$	529.045	−	529.045i	0.729717	−	0.729717i
$726$		0			0
$727$	37.5336			0.0516281			0.0258141	−	0.999667i	$-0.491782\pi$
$727$	37.5336			0.0516281			0.0258141	+	0.999667i	$0.491782\pi$
$728$	123.052	+	187.779i	0.169028	+	0.257938i
$729$		0			0
$730$	31.9250	+	36.6234i	0.0437329	+	0.0501691i
$731$	533.037	+	533.037i	0.729189	+	0.729189i
$732$		0			0
$733$	−385.216	−	385.216i	−0.525534	−	0.525534i	0.393704	−	0.919237i	$-0.371194\pi$
$733$	−385.216	−	385.216i	−0.525534	−	0.525534i	−0.919237	+	0.393704i	$0.871194\pi$
$734$	82.3174	−	1200.99i	0.112149	−	1.63623i
$735$		0			0
$736$	−1068.20	−	380.472i	−1.45135	−	0.516945i
$737$	−175.402			−0.237995
$738$		0			0
$739$	−889.039	+	889.039i	−1.20303	+	1.20303i	−0.229790	+	0.973240i	$0.573804\pi$
$739$	−889.039	+	889.039i	−1.20303	+	1.20303i	−0.973240	+	0.229790i	$0.926196\pi$
$740$	−8.55289	+	62.0992i	−0.0115580	+	0.0839179i
$741$		0			0
$742$	350.638	−	305.655i	0.472557	−	0.411933i
$743$	−506.252			−0.681362			−0.340681	−	0.940179i	$-0.610658\pi$
$743$	−506.252			−0.681362			−0.340681	+	0.940179i	$0.610658\pi$
$744$		0			0
$745$		−	10.0318i		−	0.0134655i
$746$	−1051.17	+	916.317i	−1.40908	+	1.22831i
$747$		0			0
$748$	142.248	+	187.691i	0.190172	+	0.250924i
$749$	506.509	+	506.509i	0.676247	+	0.676247i
$750$		0			0
$751$		−	456.844i		−	0.608314i	−0.952622	−	0.304157i	$-0.901625\pi$
$751$		−	456.844i		−	0.608314i	0.952622	−	0.304157i	$-0.0983748\pi$
$752$	142.217	−	506.496i	0.189118	−	0.673532i
$753$		0			0
$754$	29.5572	−	431.233i	0.0392006	−	0.571927i
$755$	−36.6554	+	36.6554i	−0.0485502	+	0.0485502i
$756$		0			0
$757$	−221.708	+	221.708i	−0.292877	+	0.292877i	−0.838216	−	0.545339i	$-0.816401\pi$
$757$	−221.708	+	221.708i	−0.292877	+	0.292877i	0.545339	+	0.838216i	$0.316401\pi$
$758$	−269.434	−	309.087i	−0.355454	−	0.407766i
$759$		0			0
$760$	8.73621	−	41.9533i	0.0114950	−	0.0552017i
$761$			205.900i			0.270566i	0.990807	+	0.135283i	$0.0431943\pi$
$761$			205.900i			0.270566i	−0.990807	+	0.135283i	$0.956806\pi$
$762$		0			0
$763$	117.582	+	117.582i	0.154105	+	0.154105i
$764$	81.6013	−	592.475i	0.106808	−	0.775491i
$765$		0			0
$766$	−57.1340	+	833.572i	−0.0745875	+	1.08821i
$767$			681.359i			0.888342i
$768$		0			0
$769$	900.133			1.17052			0.585262	−	0.810844i	$-0.300992\pi$
$769$	900.133			1.17052			0.585262	+	0.810844i	$0.300992\pi$
$770$	−7.83609	−	0.537095i	−0.0101767	−	0.000697526i
$771$		0			0
$772$	−209.325	−	28.8303i	−0.271147	−	0.0373449i
$773$	870.407	−	870.407i	1.12601	−	1.12601i	0.135193	−	0.990819i	$-0.456835\pi$
$773$	870.407	−	870.407i	1.12601	−	1.12601i	0.990819	−	0.135193i	$-0.0431654\pi$
$774$		0			0
$775$	895.498			1.15548
$776$	403.807	+	84.0873i	0.520369	+	0.108360i
$777$		0			0
$778$	−308.620	+	269.027i	−0.396683	+	0.345793i
$779$	518.907	+	518.907i	0.666119	+	0.666119i
$780$		0			0
$781$	139.318	+	139.318i	0.178385	+	0.178385i
$782$	1331.66	+	91.2736i	1.70289	+	0.116718i
$783$		0			0
$784$	−520.247	−	146.078i	−0.663580	−	0.186324i
$785$	−69.1547			−0.0880951
$786$		0			0
$787$	1005.24	−	1005.24i	1.27730	−	1.27730i	0.335133	−	0.942171i	$-0.391219\pi$
$787$	1005.24	−	1005.24i	1.27730	−	1.27730i	0.942171	−	0.335133i	$-0.108781\pi$
$788$	−487.228	+	369.264i	−0.618310	+	0.468609i
$789$		0			0
$790$	−25.0299	−	28.7135i	−0.0316834	−	0.0363462i
$791$	19.9415			0.0252106
$792$		0			0
$793$			176.691i			0.222813i
$794$	−196.136	−	225.002i	−0.247023	−	0.283377i
$795$		0			0
$796$	−8.90421	−	1.22637i	−0.0111862	−	0.00154067i
$797$	−434.779	−	434.779i	−0.545520	−	0.545520i	0.379622	−	0.925142i	$-0.376054\pi$
$797$	−434.779	−	434.779i	−0.545520	−	0.545520i	−0.925142	+	0.379622i	$0.876054\pi$
$798$		0			0
$799$			619.268i			0.775054i
$800$	−267.313	+	750.498i	−0.334142	+	0.938123i
$801$		0			0
$802$	1056.29	+	72.3992i	1.31707	+	0.0902733i
$803$	166.789	−	166.789i	0.207708	−	0.207708i
$804$		0			0
$805$	−31.4785	+	31.4785i	−0.0391037	+	0.0391037i
$806$	389.983	−	339.952i	0.483850	−	0.421777i
$807$		0			0
$808$	1319.26	−	864.519i	1.63275	−	1.06995i
$809$			50.0002i			0.0618049i	0.999522	+	0.0309024i	$0.00983812\pi$
$809$			50.0002i			0.0618049i	−0.999522	+	0.0309024i	$0.990162\pi$
$810$		0			0
$811$	−36.9957	−	36.9957i	−0.0456173	−	0.0456173i	0.683930	−	0.729547i	$-0.260269\pi$
$811$	−36.9957	−	36.9957i	−0.0456173	−	0.0456173i	−0.729547	+	0.683930i	$0.760269\pi$
$812$	−283.327	−	373.839i	−0.348925	−	0.460392i
$813$		0			0
$814$	303.621	+	20.8106i	0.372999	+	0.0255658i
$815$			84.8378i			0.104096i
$816$		0			0
$817$	−665.947			−0.815112
$818$	−50.7665	+	740.671i	−0.0620617	+	0.905465i
$819$		0			0
$820$	34.3071	+	45.2667i	0.0418379	+	0.0552033i
$821$	297.373	−	297.373i	0.362208	−	0.362208i	−0.502417	−	0.864625i	$-0.667556\pi$
$821$	297.373	−	297.373i	0.362208	−	0.362208i	0.864625	+	0.502417i	$0.167556\pi$
$822$		0			0
$823$	−345.052			−0.419262			−0.209631	−	0.977781i	$-0.567226\pi$
$823$	−345.052			−0.419262			−0.209631	+	0.977781i	$0.567226\pi$
$824$	532.333	+	110.851i	0.646036	+	0.134528i
$825$		0			0
$826$	485.867	+	557.372i	0.588217	+	0.674785i
$827$	426.416	+	426.416i	0.515618	+	0.515618i	0.916242	−	0.400624i	$-0.131207\pi$
$827$	426.416	+	426.416i	0.515618	+	0.515618i	−0.400624	+	0.916242i	$0.631207\pi$
$828$		0			0
$829$	897.159	+	897.159i	1.08222	+	1.08222i	0.996302	+	0.0859157i	$0.0273816\pi$
$829$	897.159	+	897.159i	1.08222	+	1.08222i	0.0859157	+	0.996302i	$0.472618\pi$
$830$	4.43441	−	64.6970i	0.00534267	−	0.0779482i
$831$		0			0
$832$	168.494	+	428.315i	0.202517	+	0.514802i
$833$	636.080			0.763602
$834$		0			0
$835$	−45.4367	+	45.4367i	−0.0544152	+	0.0544152i
$836$	−206.104	−	28.3866i	−0.246536	−	0.0339552i
$837$		0			0
$838$	−265.414	+	231.364i	−0.316723	+	0.276091i
$839$	−708.037			−0.843906			−0.421953	−	0.906618i	$-0.638655\pi$
$839$	−708.037			−0.843906			−0.421953	+	0.906618i	$0.638655\pi$
$840$		0			0
$841$			62.1159i			0.0738595i
$842$	110.285	−	96.1370i	0.130980	−	0.114177i
$843$		0			0
$844$	227.240	−	172.222i	0.269241	−	0.204054i
$845$	−26.6989	−	26.6989i	−0.0315963	−	0.0315963i
$846$		0			0
$847$		−	434.033i		−	0.512435i
$848$	831.503	−	466.924i	0.980546	−	0.550618i
$849$		0			0
$850$	64.1274	−	935.603i	0.0754440	−	1.10071i
$851$	1219.68	−	1219.68i	1.43323	−	1.43323i
$852$		0			0
$853$	795.484	−	795.484i	0.932572	−	0.932572i	−0.0652942	−	0.997866i	$-0.520799\pi$
$853$	795.484	−	795.484i	0.932572	−	0.932572i	0.997866	+	0.0652942i	$0.0207986\pi$
$854$	125.996	+	144.538i	0.147536	+	0.169249i
$855$		0			0
$856$	804.907	+	1228.29i	0.940312	+	1.43492i
$857$			1447.28i			1.68877i	0.535735	+	0.844386i	$0.320034\pi$
$857$			1447.28i			1.68877i	−0.535735	+	0.844386i	$0.679966\pi$
$858$		0			0
$859$	−99.6061	−	99.6061i	−0.115956	−	0.115956i	0.646748	−	0.762704i	$-0.276129\pi$
$859$	−99.6061	−	99.6061i	−0.115956	−	0.115956i	−0.762704	+	0.646748i	$0.776129\pi$
$860$	−51.0611	−	7.03262i	−0.0593734	−	0.00817747i
$861$		0			0
$862$	58.1207	−	847.967i	0.0674254	−	0.983721i
$863$		−	549.773i		−	0.637049i	−0.947915	−	0.318525i	$-0.896813\pi$
$863$		−	549.773i		−	0.637049i	0.947915	−	0.318525i	$-0.103187\pi$
$864$		0			0
$865$	−63.1185			−0.0729694
$866$	564.976	+	38.7241i	0.652397	+	0.0447161i
$867$		0			0
$868$	76.6028	−	556.183i	0.0882520	−	0.640763i
$869$	−130.766	+	130.766i	−0.150479	+	0.150479i
$870$		0			0
$871$	403.522			0.463286
$872$	186.853	+	285.139i	0.214281	+	0.326994i
$873$		0			0
$874$	−888.867	+	774.835i	−1.01701	+	0.886539i
$875$	44.3246	+	44.3246i	0.0506567	+	0.0506567i
$876$		0			0
$877$	−165.469	−	165.469i	−0.188677	−	0.188677i	0.606447	−	0.795124i	$-0.292594\pi$
$877$	−165.469	−	165.469i	−0.188677	−	0.188677i	−0.795124	+	0.606447i	$0.792594\pi$
$878$	−1399.63	−	95.9326i	−1.59412	−	0.109263i
$879$		0			0
$880$	−15.5031	−	4.35305i	−0.0176172	−	0.00494665i
$881$	−1046.60			−1.18796			−0.593982	−	0.804479i	$-0.702445\pi$
$881$	−1046.60			−1.18796			−0.593982	+	0.804479i	$0.702445\pi$
$882$		0			0
$883$	338.581	−	338.581i	0.383444	−	0.383444i	−0.488897	−	0.872341i	$-0.662601\pi$
$883$	338.581	−	338.581i	0.383444	−	0.383444i	0.872341	+	0.488897i	$0.162601\pi$
$884$	−327.250	−	431.793i	−0.370192	−	0.488453i
$885$		0			0
$886$	−506.737	−	581.313i	−0.571938	−	0.656109i
$887$	−1486.13			−1.67546			−0.837728	−	0.546088i	$-0.816117\pi$
$887$	−1486.13			−1.67546			−0.837728	+	0.546088i	$0.816117\pi$
$888$		0			0
$889$			480.848i			0.540887i
$890$	63.7489	+	73.1309i	0.0716280	+	0.0821695i
$891$		0			0
$892$	−125.711	+	912.742i	−0.140932	+	1.02325i
$893$	−386.840	−	386.840i	−0.433191	−	0.433191i
$894$		0			0
$895$			67.6447i			0.0755807i
$896$	443.258	+	230.224i	0.494708	+	0.256947i
$897$		0			0
$898$	−1226.54	−	84.0689i	−1.36586	−	0.0936179i
$899$	−764.339	+	764.339i	−0.850210	+	0.850210i
$900$		0			0
$901$	−793.761	+	793.761i	−0.880978	+	0.880978i
$902$	207.863	−	181.197i	0.230447	−	0.200883i
$903$		0			0
$904$	40.0242	+	8.33449i	0.0442745	+	0.00921957i
$905$		−	45.3482i		−	0.0501085i
$906$		0			0
$907$	−66.8336	−	66.8336i	−0.0736864	−	0.0736864i	0.669303	−	0.742989i	$-0.266593\pi$
$907$	−66.8336	−	66.8336i	−0.0736864	−	0.0736864i	−0.742989	+	0.669303i	$0.766593\pi$
$908$	54.7291	−	41.4785i	0.0602744	−	0.0456812i
$909$		0			0
$910$	18.0273	+	1.23562i	0.0198103	+	0.00135782i
$911$			227.208i			0.249406i	0.992194	+	0.124703i	$0.0397977\pi$
$911$			227.208i			0.249406i	−0.992194	+	0.124703i	$0.960202\pi$
$912$		0			0
$913$	−314.837			−0.344838
$914$	−16.1186	+	235.167i	−0.0176352	+	0.257294i
$915$		0			0
$916$	176.393	−	133.686i	0.192569	−	0.145946i
$917$	297.698	−	297.698i	0.324643	−	0.324643i
$918$		0			0
$919$	−1375.00			−1.49619			−0.748097	−	0.663589i	$-0.769032\pi$
$919$	−1375.00			−1.49619			−0.748097	+	0.663589i	$0.769032\pi$
$920$	−76.3360	+	50.0233i	−0.0829739	+	0.0543732i
$921$		0			0
$922$	−487.378	−	559.106i	−0.528610	−	0.606405i
$923$	−320.509	−	320.509i	−0.347247	−	0.347247i
$924$		0			0
$925$	−856.929	−	856.929i	−0.926410	−	0.926410i
$926$	26.2902	−	383.568i	0.0283912	−	0.414220i
$927$		0			0
$928$	−412.415	−	868.737i	−0.444413	−	0.936139i
$929$	−1788.04			−1.92470			−0.962348	−	0.271822i	$-0.912374\pi$
$929$	−1788.04			−1.92470			−0.962348	+	0.271822i	$0.912374\pi$
$930$		0			0
$931$	−397.342	+	397.342i	−0.426790	+	0.426790i
$932$	20.0178	−	145.341i	0.0214783	−	0.155946i
$933$		0			0
$934$	−1128.23	+	983.491i	−1.20796	+	1.05299i
$935$	18.9549			0.0202727
$936$		0			0
$937$			768.834i			0.820527i	0.911967	+	0.410263i	$0.134563\pi$
$937$			768.834i			0.820527i	−0.911967	+	0.410263i	$0.865437\pi$
$938$	330.093	−	287.746i	0.351912	−	0.306765i
$939$		0			0
$940$	−25.5756	−	33.7459i	−0.0272081	−	0.0358999i
$941$	−1016.85	−	1016.85i	−1.08061	−	1.08061i	−0.996453	−	0.0841571i	$-0.973180\pi$
$941$	−1016.85	−	1016.85i	−1.08061	−	1.08061i	−0.0841571	−	0.996453i	$-0.526820\pi$
$942$		0			0
$943$		−	1562.90i		−	1.65737i
$944$	742.220	+	1321.75i	0.786250	+	1.40016i
$945$		0			0
$946$	−17.1115	+	249.653i	−0.0180883	+	0.263904i
$947$	−476.431	+	476.431i	−0.503095	+	0.503095i	−0.912398	−	0.409304i	$-0.865772\pi$
$947$	−476.431	+	476.431i	−0.503095	+	0.503095i	0.409304	+	0.912398i	$0.365772\pi$
$948$		0			0
$949$	−383.708	+	383.708i	−0.404329	+	0.404329i
$950$	544.387	+	624.504i	0.573039	+	0.657373i
$951$		0			0
$952$	−575.606	−	119.862i	−0.604628	−	0.125906i
$953$		−	577.529i		−	0.606011i	−0.952989	−	0.303006i	$-0.902010\pi$
$953$		−	577.529i		−	0.606011i	0.952989	−	0.303006i	$-0.0979901\pi$
$954$		0			0
$955$	−34.0375	−	34.0375i	−0.0356414	−	0.0356414i
$956$	−80.2812	+	582.890i	−0.0839761	+	0.609718i
$957$		0			0
$958$	0.196594	−	2.86827i	0.000205213	−	0.00299401i
$959$			284.936i			0.297118i
$960$		0			0
$961$	−332.773			−0.346278
$962$	−698.497	−	47.8758i	−0.726088	−	0.0497670i
$963$		0			0
$964$	814.266	+	112.148i	0.844675	+	0.116337i
$965$	−12.0257	+	12.0257i	−0.0124619	+	0.0124619i
$966$		0			0
$967$	864.047			0.893534			0.446767	−	0.894650i	$-0.352575\pi$
$967$	864.047			0.893534			0.446767	+	0.894650i	$0.352575\pi$
$968$	181.402	−	871.136i	0.187399	−	0.899934i
$969$		0			0
$970$	25.0249	−	21.8145i	0.0257989	−	0.0224891i
$971$	−898.515	−	898.515i	−0.925350	−	0.925350i	0.0720505	−	0.997401i	$-0.477046\pi$
$971$	−898.515	−	898.515i	−0.925350	−	0.925350i	−0.997401	+	0.0720505i	$0.977046\pi$
$972$		0			0
$973$	64.4836	+	64.4836i	0.0662730	+	0.0662730i
$974$	1399.19	+	95.9024i	1.43654	+	0.0984624i
$975$		0			0
$976$	192.473	+	342.759i	0.197206	+	0.351187i
$977$	538.131			0.550799			0.275400	−	0.961330i	$-0.411190\pi$
$977$	538.131			0.550799			0.275400	+	0.961330i	$0.411190\pi$
$978$		0			0
$979$	333.051	−	333.051i	0.340195	−	0.340195i
$980$	−34.6620	+	26.2699i	−0.0353694	+	0.0268060i
$981$		0			0
$982$	−965.833	−	1107.97i	−0.983536	−	1.12828i
$983$	−759.452			−0.772586			−0.386293	−	0.922376i	$-0.626245\pi$
$983$	−759.452			−0.772586			−0.386293	+	0.922376i	$0.626245\pi$
$984$		0			0
$985$			49.2052i			0.0499546i
$986$	743.835	+	853.305i	0.754396	+	0.865421i
$987$		0			0
$988$	474.153	+	65.3048i	0.479912	+	0.0660980i
$989$	1002.88	+	1002.88i	1.01404	+	1.01404i
$990$		0			0
$991$			514.565i			0.519238i	0.965711	+	0.259619i	$0.0835969\pi$
$991$			514.565i			0.519238i	−0.965711	+	0.259619i	$0.916403\pi$
$992$	386.202	−	1084.28i	0.389316	−	1.09303i
$993$		0			0
$994$	−490.737	−	33.6357i	−0.493699	−	0.0338388i
$995$	−0.511545	+	0.511545i	−0.000514115	+	0.000514115i
$996$		0			0
$997$	−1249.59	+	1249.59i	−1.25335	+	1.25335i	−0.299145	+	0.954208i	$0.596701\pi$
$997$	−1249.59	+	1249.59i	−1.25335	+	1.25335i	−0.954208	+	0.299145i	$0.903299\pi$
$998$	766.023	−	667.751i	0.767558	−	0.669089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.b.19.8	yes	16
3.2	odd	2	inner	144.3.m.b.19.1	✓	16
4.3	odd	2		576.3.m.b.559.5		16
8.3	odd	2		1152.3.m.d.991.4		16
8.5	even	2		1152.3.m.e.991.4		16
12.11	even	2		576.3.m.b.559.4		16
16.3	odd	4		1152.3.m.e.415.4		16
16.5	even	4		576.3.m.b.271.5		16
16.11	odd	4	inner	144.3.m.b.91.8	yes	16
16.13	even	4		1152.3.m.d.415.4		16
24.5	odd	2		1152.3.m.e.991.5		16
24.11	even	2		1152.3.m.d.991.5		16
48.5	odd	4		576.3.m.b.271.4		16
48.11	even	4	inner	144.3.m.b.91.1	yes	16
48.29	odd	4		1152.3.m.d.415.5		16
48.35	even	4		1152.3.m.e.415.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.m.b.19.1	✓	16	3.2	odd	2	inner
144.3.m.b.19.8	yes	16	1.1	even	1	trivial
144.3.m.b.91.1	yes	16	48.11	even	4	inner
144.3.m.b.91.8	yes	16	16.11	odd	4	inner
576.3.m.b.271.4		16	48.5	odd	4
576.3.m.b.271.5		16	16.5	even	4
576.3.m.b.559.4		16	12.11	even	2
576.3.m.b.559.5		16	4.3	odd	2
1152.3.m.d.415.4		16	16.13	even	4
1152.3.m.d.415.5		16	48.29	odd	4
1152.3.m.d.991.4		16	8.3	odd	2
1152.3.m.d.991.5		16	24.11	even	2
1152.3.m.e.415.4		16	16.3	odd	4
1152.3.m.e.415.5		16	48.35	even	4
1152.3.m.e.991.4		16	8.5	even	2
1152.3.m.e.991.5		16	24.5	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99532 + 0.136762i) q^{2} +(3.96259 + 0.545766i) q^{4} +(0.227650 - 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 + 1.63091i) q^{8} +O(q^{10})\)	\(q+(1.99532 + 0.136762i) q^{2} +(3.96259 + 0.545766i) q^{4} +(0.227650 - 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 + 1.63091i) q^{8} +(0.485368 - 0.423100i) q^{10} +(-2.21045 - 2.21045i) q^{11} +(5.08526 + 5.08526i) q^{13} +(7.78612 + 0.533670i) q^{14} +(15.4043 + 4.32530i) q^{16} -18.8341 q^{17} +(11.7651 - 11.7651i) q^{19} +(1.02633 - 0.777840i) q^{20} +(-4.10825 - 4.71286i) q^{22} -35.4354 q^{23} +24.8964i q^{25} +(9.45124 + 10.8422i) q^{26} +(15.4628 + 2.12968i) q^{28} +(-21.2499 - 21.2499i) q^{29} -35.9691i q^{31} +(30.1449 + 10.7371i) q^{32} +(-37.5799 - 2.57578i) q^{34} +(0.888334 - 0.888334i) q^{35} +(-34.4199 + 34.4199i) q^{37} +(25.0842 - 21.8661i) q^{38} +(2.15423 - 1.41168i) q^{40} +44.1055i q^{41} +(-28.3018 - 28.3018i) q^{43} +(-7.55273 - 9.96550i) q^{44} +(-70.7049 - 4.84620i) q^{46} -32.8802i q^{47} -33.7729 q^{49} +(-3.40486 + 49.6762i) q^{50} +(17.3754 + 22.9262i) q^{52} +(42.1450 - 42.1450i) q^{53} -1.00642 q^{55} +(30.5620 + 6.36412i) q^{56} +(-39.4941 - 45.3065i) q^{58} +(66.9935 + 66.9935i) q^{59} +(17.3728 + 17.3728i) q^{61} +(4.91919 - 71.7697i) q^{62} +(58.6803 + 25.5465i) q^{64} +2.31532 q^{65} +(39.6756 - 39.6756i) q^{67} +(-74.6317 - 10.2790i) q^{68} +(1.89400 - 1.65102i) q^{70} -63.0272 q^{71} +75.4549i q^{73} +(-73.3859 + 63.9713i) q^{74} +(53.0413 - 40.1993i) q^{76} +(-8.62561 - 8.62561i) q^{77} -59.1583i q^{79} +(4.49144 - 2.52213i) q^{80} +(-6.03194 + 88.0046i) q^{82} +(71.2155 - 71.2155i) q^{83} +(-4.28757 + 4.28757i) q^{85} +(-52.6004 - 60.3416i) q^{86} +(-13.7072 - 20.9173i) q^{88} +150.671i q^{89} +(19.8437 + 19.8437i) q^{91} +(-140.416 - 19.3394i) q^{92} +(4.49675 - 65.6065i) q^{94} -5.35665i q^{95} +51.5586 q^{97} +(-67.3876 - 4.61883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4}+O(q^{10}) \) 16 * q - 12 * q^4	\( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

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