LMFDB - Embedded newform 288.2.p.b.239.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(47,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("288.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.7
Root			$0.608741 - 1.27649i$ of defining polynomial
Character	$\chi$	$=$	288.239
Dual form			288.2.p.b.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71646 - 0.231865i) q^{3} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.89248 - 0.795973i) q^{9} +O(q^{10})$	\(q+(1.71646 - 0.231865i) q^{3} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.89248 - 0.795973i) q^{9} +(0.116985 - 0.0675415i) q^{11} +(2.63890 + 1.52357i) q^{13} +(-2.29209 + 5.58677i) q^{15} +4.19800i q^{17} -0.919111 q^{19} +(2.86136 - 2.21096i) q^{21} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(4.78027 - 2.03692i) q^{27} +(-4.24111 - 7.34582i) q^{29} +(-4.39877 - 2.53963i) q^{31} +(0.185140 - 0.143057i) q^{33} +7.27870i q^{35} -1.61676i q^{37} +(4.88284 + 2.00328i) q^{39} +(1.79408 + 1.03581i) q^{41} +(-5.41106 - 9.37224i) q^{43} +(-2.63890 + 10.1209i) q^{45} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +(0.973367 + 7.20570i) q^{51} +0.968137 q^{53} +0.470958i q^{55} +(-1.57762 + 0.213109i) q^{57} +(-3.88770 - 2.24457i) q^{59} +(7.44553 - 4.29868i) q^{61} +(4.39877 - 4.45848i) q^{63} +(-9.20037 + 5.31183i) q^{65} +(-3.15416 + 5.46316i) q^{67} +(0.907092 - 2.21096i) q^{69} -11.9687 q^{71} -4.06264 q^{73} +(-7.57762 - 9.80673i) q^{75} +(0.141008 - 0.244232i) q^{77} +(10.8672 - 6.27416i) q^{79} +(7.73285 - 4.60467i) q^{81} +(-5.23875 + 3.02459i) q^{83} +(-12.6752 - 7.31802i) q^{85} +(-8.98294 - 11.6255i) q^{87} -8.35848i q^{89} +6.36158 q^{91} +(-8.13917 - 3.33926i) q^{93} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +(0.284616 - 0.288479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^3 - 6 * q^9	$ 16 q + 6 q^{3} - 6 q^{9} - 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{27} + 12 q^{33} - 36 q^{41} - 8 q^{43} + 10 q^{49} - 18 q^{51} + 18 q^{57} - 12 q^{59} - 6 q^{65} + 16 q^{67} - 4 q^{73} - 78 q^{75} - 6 q^{81} - 54 q^{83} + 36 q^{91} + 8 q^{97} + 6 q^{99}+O(q^{100}) $ 16 * q + 6 * q^3 - 6 * q^9 - 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^27 + 12 * q^33 - 36 * q^41 - 8 * q^43 + 10 * q^49 - 18 * q^51 + 18 * q^57 - 12 * q^59 - 6 * q^65 + 16 * q^67 - 4 * q^73 - 78 * q^75 - 6 * q^81 - 54 * q^83 + 36 * q^91 + 8 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	1.71646	−	0.231865i	0.990999	−	0.133867i
$3$	1.71646	−	0.231865i	0.990999	−	0.133867i
$4$		0			0
$5$	−1.74322	+	3.01934i	−0.779591	+	1.35029i	0.152587	+	0.988290i	$0.451240\pi$
$5$	−1.74322	+	3.01934i	−0.779591	+	1.35029i	−0.932178	+	0.362001i	$0.882094\pi$
$6$		0			0
$7$	1.80802	−	1.04386i	0.683367	−	0.394542i	−0.117756	−	0.993043i	$-0.537570\pi$
$7$	1.80802	−	1.04386i	0.683367	−	0.394542i	0.801122	+	0.598501i	$0.204237\pi$
$8$		0			0
$9$	2.89248	−	0.795973i	0.964159	−	0.265324i
$10$		0			0
$11$	0.116985	−	0.0675415i	0.0352724	−	0.0203645i	−0.482260	−	0.876028i	$-0.660184\pi$
$11$	0.116985	−	0.0675415i	0.0352724	−	0.0203645i	0.517533	+	0.855664i	$0.326851\pi$
$12$		0			0
$13$	2.63890	+	1.52357i	0.731900	+	0.422563i	0.819117	−	0.573627i	$-0.194464\pi$
$13$	2.63890	+	1.52357i	0.731900	+	0.422563i	−0.0872168	+	0.996189i	$0.527797\pi$
$14$		0			0
$15$	−2.29209	+	5.58677i	−0.591814	+	1.44250i
$16$		0			0
$17$			4.19800i			1.01816i	0.860718	+	0.509082i	$0.170015\pi$
$17$			4.19800i			1.01816i	−0.860718	+	0.509082i	$0.829985\pi$
$18$		0			0
$19$	−0.919111			−0.210858			−0.105429	−	0.994427i	$-0.533622\pi$
$19$	−0.919111			−0.210858			−0.105429	+	0.994427i	$0.533622\pi$
$20$		0			0
$21$	2.86136	−	2.21096i	0.624400	−	0.482471i
$22$		0			0
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	−0.785094	−	0.619377i	$-0.787385\pi$
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	0.928943	+	0.370223i	$0.120719\pi$
$24$		0			0
$25$	−3.57762	−	6.19662i	−0.715524	−	1.23932i
$26$		0			0
$27$	4.78027	−	2.03692i	0.919963	−	0.392005i
$28$		0			0
$29$	−4.24111	−	7.34582i	−0.787555	−	1.36409i	−0.927461	−	0.373921i	$-0.878013\pi$
$29$	−4.24111	−	7.34582i	−0.787555	−	1.36409i	0.139906	−	0.990165i	$-0.455320\pi$
$30$		0			0
$31$	−4.39877	−	2.53963i	−0.790042	−	0.456131i	0.0499352	−	0.998752i	$-0.484099\pi$
$31$	−4.39877	−	2.53963i	−0.790042	−	0.456131i	−0.839977	+	0.542621i	$0.817432\pi$
$32$		0			0
$33$	0.185140	−	0.143057i	0.0322288	−	0.0249030i
$34$		0			0
$35$			7.27870i			1.23033i
$36$		0			0
$37$		−	1.61676i		−	0.265794i	−0.991130	−	0.132897i	$-0.957572\pi$
$37$		−	1.61676i		−	0.265794i	0.991130	−	0.132897i	$-0.0424280\pi$
$38$		0			0
$39$	4.88284	+	2.00328i	0.781880	+	0.320782i
$40$		0			0
$41$	1.79408	+	1.03581i	0.280188	+	0.161767i	0.633509	−	0.773736i	$-0.281614\pi$
$41$	1.79408	+	1.03581i	0.280188	+	0.161767i	−0.353320	+	0.935502i	$0.614947\pi$
$42$		0			0
$43$	−5.41106	−	9.37224i	−0.825180	−	1.42925i	−0.901782	−	0.432191i	$-0.857741\pi$
$43$	−5.41106	−	9.37224i	−0.825180	−	1.42925i	0.0766025	−	0.997062i	$-0.475593\pi$
$44$		0			0
$45$	−2.63890	+	10.1209i	−0.393385	+	1.50874i
$46$		0			0
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$48$		0			0
$49$	−1.32071	+	2.28754i	−0.188673	+	0.326791i
$50$		0			0
$51$	0.973367	+	7.20570i	0.136299	+	1.00900i
$52$		0			0
$53$	0.968137			0.132984			0.0664919	−	0.997787i	$-0.478819\pi$
$53$	0.968137			0.132984			0.0664919	+	0.997787i	$0.478819\pi$
$54$		0			0
$55$			0.470958i			0.0635040i
$56$		0			0
$57$	−1.57762	+	0.213109i	−0.208961	+	0.0282270i
$58$		0			0
$59$	−3.88770	−	2.24457i	−0.506136	−	0.292218i	0.225108	−	0.974334i	$-0.427726\pi$
$59$	−3.88770	−	2.24457i	−0.506136	−	0.292218i	−0.731244	+	0.682116i	$0.761060\pi$
$60$		0			0
$61$	7.44553	−	4.29868i	0.953303	−	0.550390i	0.0591976	−	0.998246i	$-0.481146\pi$
$61$	7.44553	−	4.29868i	0.953303	−	0.550390i	0.894105	+	0.447857i	$0.147812\pi$
$62$		0			0
$63$	4.39877	−	4.45848i	0.554193	−	0.561715i
$64$		0			0
$65$	−9.20037	+	5.31183i	−1.14117	+	0.658852i
$66$		0			0
$67$	−3.15416	+	5.46316i	−0.385342	+	0.667432i	−0.991817	−	0.127671i	$-0.959250\pi$
$67$	−3.15416	+	5.46316i	−0.385342	+	0.667432i	0.606475	+	0.795103i	$0.292583\pi$
$68$		0			0
$69$	0.907092	−	2.21096i	0.109201	−	0.266168i
$70$		0			0
$71$	−11.9687			−1.42042			−0.710210	−	0.703990i	$-0.751400\pi$
$71$	−11.9687			−1.42042			−0.710210	+	0.703990i	$0.751400\pi$
$72$		0			0
$73$	−4.06264			−0.475496			−0.237748	−	0.971327i	$-0.576409\pi$
$73$	−4.06264			−0.475496			−0.237748	+	0.971327i	$0.576409\pi$
$74$		0			0
$75$	−7.57762	−	9.80673i	−0.874988	−	1.13238i
$76$		0			0
$77$	0.141008	−	0.244232i	0.0160693	−	0.0278329i
$78$		0			0
$79$	10.8672	−	6.27416i	1.22265	−	0.705899i	0.257170	−	0.966366i	$-0.417210\pi$
$79$	10.8672	−	6.27416i	1.22265	−	0.705899i	0.965483	+	0.260468i	$0.0838768\pi$
$80$		0			0
$81$	7.73285	−	4.60467i	0.859206	−	0.511630i
$82$		0			0
$83$	−5.23875	+	3.02459i	−0.575027	+	0.331992i	−0.759155	−	0.650910i	$-0.774387\pi$
$83$	−5.23875	+	3.02459i	−0.575027	+	0.331992i	0.184128	+	0.982902i	$0.441054\pi$
$84$		0			0
$85$	−12.6752	−	7.31802i	−1.37482	−	0.793751i
$86$		0			0
$87$	−8.98294	−	11.6255i	−0.963073	−	1.24638i
$88$		0			0
$89$		−	8.35848i		−	0.885997i	−0.896522	−	0.442999i	$-0.853915\pi$
$89$		−	8.35848i		−	0.885997i	0.896522	−	0.442999i	$-0.146085\pi$
$90$		0			0
$91$	6.36158			0.666875
$92$		0			0
$93$	−8.13917	−	3.33926i	−0.843992	−	0.346265i
$94$		0			0
$95$	1.60221	−	2.77511i	0.164383	−	0.284720i
$96$		0			0
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	0.840790	−	0.541362i	$-0.182091\pi$
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	−0.889228	+	0.457464i	$0.848758\pi$
$98$		0			0
$99$	0.284616	−	0.288479i	0.0286050	−	0.0289933i
$100$		0			0
$101$	5.35926	+	9.28250i	0.533266	+	0.923644i	0.999245	+	0.0388479i	$0.0123688\pi$
$101$	5.35926	+	9.28250i	0.533266	+	0.923644i	−0.465979	+	0.884796i	$0.654298\pi$
$102$		0			0
$103$	7.46070	+	4.30743i	0.735124	+	0.424424i	0.820294	−	0.571942i	$-0.193810\pi$
$103$	7.46070	+	4.30743i	0.735124	+	0.424424i	−0.0851696	+	0.996366i	$0.527143\pi$
$104$		0			0
$105$	1.68767	+	12.4936i	0.164700	+	1.21925i
$106$		0			0
$107$		−	4.80774i		−	0.464781i	−0.972623	−	0.232391i	$-0.925345\pi$
$107$		−	4.80774i		−	0.464781i	0.972623	−	0.232391i	$-0.0746548\pi$
$108$		0			0
$109$			7.16698i			0.686472i	0.939249	+	0.343236i	$0.111523\pi$
$109$			7.16698i			0.686472i	−0.939249	+	0.343236i	$0.888477\pi$
$110$		0			0
$111$	−0.374870	−	2.77511i	−0.0355811	−	0.263402i
$112$		0			0
$113$	−0.213928	−	0.123511i	−0.0201246	−	0.0116190i	0.489904	−	0.871776i	$-0.337032\pi$
$113$	−0.213928	−	0.123511i	−0.0201246	−	0.0116190i	−0.510029	+	0.860157i	$0.670365\pi$
$114$		0			0
$115$	2.40521	+	4.16595i	0.224287	+	0.388477i
$116$		0			0
$117$	8.84569	+	2.30640i	0.817784	+	0.213227i
$118$		0			0
$119$	4.38212	+	7.59006i	0.401708	+	0.695779i
$120$		0			0
$121$	−5.49088	+	9.51048i	−0.499171	+	0.864589i
$122$		0			0
$123$	3.31963	+	1.36195i	0.299321	+	0.122803i
$124$		0			0
$125$	7.51409			0.672081
$126$		0			0
$127$			17.6276i			1.56420i	0.623156	+	0.782098i	$0.285850\pi$
$127$			17.6276i			1.56420i	−0.623156	+	0.782098i	$0.714150\pi$
$128$		0			0
$129$	−11.4610	−	14.8324i	−1.00908	−	1.30592i
$130$		0			0
$131$	12.7802	+	7.37864i	1.11661	+	0.644675i	0.940533	−	0.339702i	$-0.110326\pi$
$131$	12.7802	+	7.37864i	1.11661	+	0.644675i	0.176076	+	0.984377i	$0.443659\pi$
$132$		0			0
$133$	−1.66177	+	0.959423i	−0.144094	+	0.0831925i
$134$		0			0
$135$	−2.18289	+	17.9841i	−0.187873	+	1.54782i
$136$		0			0
$137$	14.8589	−	8.57878i	1.26948	−	0.732934i	0.294590	−	0.955624i	$-0.404817\pi$
$137$	14.8589	−	8.57878i	1.26948	−	0.732934i	0.974889	+	0.222689i	$0.0714836\pi$
$138$		0			0
$139$	0.607862	−	1.05285i	0.0515581	−	0.0893013i	−0.839095	−	0.543986i	$-0.816915\pi$
$139$	0.607862	−	1.05285i	0.0515581	−	0.0893013i	0.890653	+	0.454684i	$0.150248\pi$
$140$		0			0
$141$	−0.435915	−	0.564149i	−0.0367107	−	0.0475099i
$142$		0			0
$143$	0.411617			0.0344211
$144$		0			0
$145$	29.5727			2.45588
$146$		0			0
$147$	−1.73655	+	4.23270i	−0.143228	+	0.349107i
$148$		0			0
$149$	4.46357	−	7.73113i	0.365670	−	0.633359i	−0.623214	−	0.782052i	$-0.714173\pi$
$149$	4.46357	−	7.73113i	0.365670	−	0.633359i	0.988883	+	0.148693i	$0.0475066\pi$
$150$		0			0
$151$	−18.9453	+	10.9381i	−1.54175	+	0.890127i	−0.543017	+	0.839722i	$0.682718\pi$
$151$	−18.9453	+	10.9381i	−1.54175	+	0.890127i	−0.998729	+	0.0504058i	$0.983949\pi$
$152$		0			0
$153$	3.34149	+	12.1426i	0.270144	+	0.981672i
$154$		0			0
$155$	15.3360	−	8.85426i	1.23182	−	0.711191i
$156$		0			0
$157$	−4.85478	−	2.80291i	−0.387454	−	0.223697i	0.293602	−	0.955928i	$-0.405146\pi$
$157$	−4.85478	−	2.80291i	−0.387454	−	0.223697i	−0.681056	+	0.732231i	$0.738479\pi$
$158$		0			0
$159$	1.66177	−	0.224477i	0.131787	−	0.0178022i
$160$		0			0
$161$		−	2.88054i		−	0.227018i
$162$		0			0
$163$	17.1763			1.34535			0.672676	−	0.739937i	$-0.265145\pi$
$163$	17.1763			1.34535			0.672676	+	0.739937i	$0.265145\pi$
$164$		0			0
$165$	0.109199	+	0.808381i	0.00850109	+	0.0629324i
$166$		0			0
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	−0.762574	−	0.646901i	$-0.776065\pi$
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	0.941520	+	0.336958i	$0.109398\pi$
$168$		0			0
$169$	−1.85746	−	3.21721i	−0.142881	−	0.247478i
$170$		0			0
$171$	−2.65851	+	0.731587i	−0.203301	+	0.0559459i
$172$		0			0
$173$	1.52076	+	2.63404i	0.115621	+	0.200262i	0.918028	−	0.396516i	$-0.129781\pi$
$173$	1.52076	+	2.63404i	0.115621	+	0.200262i	−0.802407	+	0.596778i	$0.796447\pi$
$174$		0			0
$175$	−12.9368	−	7.46907i	−0.977930	−	0.564608i
$176$		0			0
$177$	−7.19353	−	2.95129i	−0.540699	−	0.221833i
$178$		0			0
$179$		−	17.9997i		−	1.34536i	−0.739935	−	0.672679i	$-0.765144\pi$
$179$		−	17.9997i		−	1.34536i	0.739935	−	0.672679i	$-0.234856\pi$
$180$		0			0
$181$			15.9507i			1.18561i	0.805347	+	0.592804i	$0.201979\pi$
$181$			15.9507i			1.18561i	−0.805347	+	0.592804i	$0.798021\pi$
$182$		0			0
$183$	11.7833	−	9.10488i	0.871044	−	0.673052i
$184$		0			0
$185$	4.88156	+	2.81837i	0.358899	+	0.207211i
$186$		0			0
$187$	0.283539	+	0.491104i	0.0207344	+	0.0359131i
$188$		0			0
$189$	6.51655	−	8.67272i	0.474010	−	0.630848i
$190$		0			0
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	0.935087	−	0.354419i	$-0.115321\pi$
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	−0.774479	+	0.632599i	$0.781988\pi$
$192$		0			0
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	−0.840753	−	0.541419i	$-0.817887\pi$
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	0.889259	+	0.457404i	$0.151221\pi$
$194$		0			0
$195$	−14.5604	+	11.2508i	−1.04270	+	0.805686i
$196$		0			0
$197$	−9.16835			−0.653218			−0.326609	−	0.945160i	$-0.605906\pi$
$197$	−9.16835			−0.653218			−0.326609	+	0.945160i	$0.605906\pi$
$198$		0			0
$199$		−	24.0240i		−	1.70301i	−0.524344	−	0.851507i	$-0.675689\pi$
$199$		−	24.0240i		−	1.70301i	0.524344	−	0.851507i	$-0.324311\pi$
$200$		0			0
$201$	−4.14728	+	10.1086i	−0.292526	+	0.713009i
$202$		0			0
$203$	−15.3360	−	8.85426i	−1.07638	−	0.621447i
$204$		0			0
$205$	−6.25494	+	3.61129i	−0.436864	+	0.252224i
$206$		0			0
$207$	1.04434	−	4.00535i	0.0725869	−	0.278391i
$208$		0			0
$209$	−0.107522	+	0.0620781i	−0.00743748	+	0.00429403i
$210$		0			0
$211$	−10.1275	+	17.5414i	−0.697208	+	1.20760i	0.272223	+	0.962234i	$0.412241\pi$
$211$	−10.1275	+	17.5414i	−0.697208	+	1.20760i	−0.969431	+	0.245365i	$0.921092\pi$
$212$		0			0
$213$	−20.5437	+	2.77511i	−1.40763	+	0.190147i
$214$		0			0
$215$	37.7307			2.57321
$216$		0			0
$217$	−10.6041			−0.719852
$218$		0			0
$219$	−6.97337	+	0.941983i	−0.471216	+	0.0636533i
$220$		0			0
$221$	−6.39595	+	11.0781i	−0.430238	+	0.745194i
$222$		0			0
$223$	0.521119	−	0.300868i	0.0348967	−	0.0201476i	−0.482450	−	0.875923i	$-0.660253\pi$
$223$	0.521119	−	0.300868i	0.0348967	−	0.0201476i	0.517347	+	0.855776i	$0.326920\pi$
$224$		0			0
$225$	−15.2805	−	15.0759i	−1.01870	−	1.00506i
$226$		0			0
$227$	−9.23720	+	5.33310i	−0.613095	+	0.353970i	−0.774176	−	0.632971i	$-0.781835\pi$
$227$	−9.23720	+	5.33310i	−0.613095	+	0.353970i	0.161081	+	0.986941i	$0.448502\pi$
$228$		0			0
$229$	22.1574	+	12.7926i	1.46420	+	0.845356i	0.999201	−	0.0399555i	$-0.0127216\pi$
$229$	22.1574	+	12.7926i	1.46420	+	0.845356i	0.464998	+	0.885312i	$0.346055\pi$
$230$		0			0
$231$	0.185405	−	0.451910i	0.0121988	−	0.0297335i
$232$		0			0
$233$		−	4.71086i		−	0.308619i	−0.988023	−	0.154309i	$-0.950685\pi$
$233$		−	4.71086i		−	0.308619i	0.988023	−	0.154309i	$-0.0493152\pi$
$234$		0			0
$235$	1.43508			0.0936141
$236$		0			0
$237$	17.1983	−	13.2891i	1.11715	−	0.863218i
$238$		0			0
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	−0.999867	−	0.0163162i	$-0.994806\pi$
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	0.514064	+	0.857752i	$0.328139\pi$
$240$		0			0
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	0.898643	+	0.438681i	$0.144554\pi$
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	−0.0694129	+	0.997588i	$0.522113\pi$
$242$		0			0
$243$	12.2055	−	9.69671i	0.782982	−	0.622044i
$244$		0			0
$245$	−4.60458	−	7.97536i	−0.294176	−	0.509527i
$246$		0			0
$247$	−2.42544	−	1.40033i	−0.154327	−	0.0891009i
$248$		0			0
$249$	−8.29081	+	6.40627i	−0.525409	+	0.405981i
$250$		0			0
$251$			5.30436i			0.334808i	0.985888	+	0.167404i	$0.0535385\pi$
$251$			5.30436i			0.334808i	−0.985888	+	0.167404i	$0.946462\pi$
$252$		0			0
$253$		−	0.186381i		−	0.0117177i
$254$		0			0
$255$	−23.4533	−	9.62217i	−1.46870	−	0.602564i
$256$		0			0
$257$	−21.4984	−	12.4121i	−1.34104	−	0.774248i	−0.354077	−	0.935216i	$-0.615205\pi$
$257$	−21.4984	−	12.4121i	−1.34104	−	0.774248i	−0.986959	+	0.160969i	$0.948538\pi$
$258$		0			0
$259$	−1.68767	−	2.92314i	−0.104867	−	0.181635i
$260$		0			0
$261$	−18.1144	−	17.8718i	−1.12125	−	1.10624i
$262$		0			0
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	−0.990546	−	0.137178i	$-0.956197\pi$
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	0.376473	−	0.926427i	$-0.377137\pi$
$264$		0			0
$265$	−1.68767	+	2.92314i	−0.103673	+	0.179567i
$266$		0			0
$267$	−1.93804	−	14.3470i	−0.118606	−	0.878023i
$268$		0			0
$269$	−2.35540			−0.143611			−0.0718057	−	0.997419i	$-0.522876\pi$
$269$	−2.35540			−0.143611			−0.0718057	+	0.997419i	$0.522876\pi$
$270$		0			0
$271$			12.0774i			0.733648i	0.930290	+	0.366824i	$0.119555\pi$
$271$			12.0774i			0.733648i	−0.930290	+	0.366824i	$0.880445\pi$
$272$		0			0
$273$	10.9194	−	1.47503i	0.660873	−	0.0892726i
$274$		0			0
$275$	−0.837057	−	0.483275i	−0.0504764	−	0.0291426i
$276$		0			0
$277$	14.5504	−	8.40069i	0.874250	−	0.504748i	0.00549164	−	0.999985i	$-0.498252\pi$
$277$	14.5504	−	8.40069i	0.874250	−	0.504748i	0.868758	+	0.495237i	$0.164919\pi$
$278$		0			0
$279$	−14.7448	−	3.84452i	−0.882749	−	0.230166i
$280$		0			0
$281$	11.9853	−	6.91973i	0.714984	−	0.412796i	−0.0979194	−	0.995194i	$-0.531219\pi$
$281$	11.9853	−	6.91973i	0.714984	−	0.412796i	0.812904	+	0.582398i	$0.197885\pi$
$282$		0			0
$283$	−2.58123	+	4.47082i	−0.153438	+	0.265763i	−0.932489	−	0.361198i	$-0.882368\pi$
$283$	−2.58123	+	4.47082i	−0.153438	+	0.265763i	0.779051	+	0.626960i	$0.215701\pi$
$284$		0			0
$285$	2.10668	−	5.13486i	0.124789	−	0.304163i
$286$		0			0
$287$	4.32497			0.255295
$288$		0			0
$289$	−0.623177			−0.0366574
$290$		0			0
$291$	−1.01045	−	1.30770i	−0.0592338	−	0.0766586i
$292$		0			0
$293$	5.41881	−	9.38566i	0.316571	−	0.548316i	−0.663200	−	0.748443i	$-0.730802\pi$
$293$	5.41881	−	9.38566i	0.316571	−	0.548316i	0.979770	+	0.200126i	$0.0641353\pi$
$294$		0			0
$295$	13.5542	−	7.82554i	0.789158	−	0.455620i
$296$		0			0
$297$	0.421644	−	0.561156i	0.0244663	−	0.0325616i
$298$		0			0
$299$	3.64104	−	2.10215i	0.210567	−	0.121571i
$300$		0			0
$301$	−19.5666	−	11.2968i	−1.12780	−	0.651136i
$302$		0			0
$303$	11.3512	+	14.6904i	0.652112	+	0.843943i
$304$		0			0
$305$			29.9742i			1.71632i
$306$		0			0
$307$	−16.6551			−0.950557			−0.475279	−	0.879835i	$-0.657653\pi$
$307$	−16.6551			−0.950557			−0.475279	+	0.879835i	$0.657653\pi$
$308$		0			0
$309$	13.8047	+	5.66367i	0.785324	+	0.322195i
$310$		0			0
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	−0.989095	−	0.147277i	$-0.952949\pi$
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	0.622093	+	0.782943i	$0.286283\pi$
$312$		0			0
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	−0.945318	−	0.326149i	$-0.894249\pi$
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	0.190206	−	0.981744i	$-0.439084\pi$
$314$		0			0
$315$	5.79365	+	21.0535i	0.326435	+	1.18623i
$316$		0			0
$317$	12.5342	+	21.7098i	0.703990	+	1.21935i	0.967055	+	0.254568i	$0.0819332\pi$
$317$	12.5342	+	21.7098i	0.703990	+	1.21935i	−0.263065	+	0.964778i	$0.584733\pi$
$318$		0			0
$319$	−0.992296	−	0.572902i	−0.0555579	−	0.0320764i
$320$		0			0
$321$	−1.11474	−	8.25229i	−0.0622189	−	0.460598i
$322$		0			0
$323$		−	3.85842i		−	0.214688i
$324$		0			0
$325$		−	21.8030i		−	1.20941i
$326$		0			0
$327$	1.66177	+	12.3018i	0.0918961	+	0.680294i
$328$		0			0
$329$	−0.744211	−	0.429671i	−0.0410297	−	0.0236885i
$330$		0			0
$331$	8.47956	+	14.6870i	0.466079	+	0.807272i	0.999249	−	0.0387357i	$-0.0123330\pi$
$331$	8.47956	+	14.6870i	0.466079	+	0.807272i	−0.533171	+	0.846008i	$0.679000\pi$
$332$		0			0
$333$	−1.28690	−	4.67645i	−0.0705217	−	0.256268i
$334$		0			0
$335$	−10.9968	−	19.0470i	−0.600818	−	1.04065i
$336$		0			0
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	−0.718125	−	0.695914i	$-0.755000\pi$
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	0.961742	+	0.273958i	$0.0883329\pi$
$338$		0			0
$339$	−0.395836	−	0.162400i	−0.0214989	−	0.00882035i
$340$		0			0
$341$	−0.686122			−0.0371556
$342$		0			0
$343$			20.1286i			1.08684i
$344$		0			0
$345$	5.09439	+	6.59301i	0.274273	+	0.354956i
$346$		0			0
$347$	4.29330	+	2.47874i	0.230476	+	0.133066i	0.610792	−	0.791791i	$-0.290851\pi$
$347$	4.29330	+	2.47874i	0.230476	+	0.133066i	−0.380315	+	0.924857i	$0.624185\pi$
$348$		0			0
$349$	−22.9731	+	13.2635i	−1.22972	+	0.709980i	−0.966972	−	0.254884i	$-0.917963\pi$
$349$	−22.9731	+	13.2635i	−1.22972	+	0.709980i	−0.262749	+	0.964864i	$0.584629\pi$
$350$		0			0
$351$	15.7181	+	1.90784i	0.838968	+	0.101833i
$352$		0			0
$353$	−28.7458	+	16.5964i	−1.52998	+	0.883337i	−0.530623	+	0.847608i	$0.678042\pi$
$353$	−28.7458	+	16.5964i	−1.52998	+	0.883337i	−0.999362	+	0.0357291i	$0.988625\pi$
$354$		0			0
$355$	20.8640	−	36.1375i	1.10735	−	1.91798i
$356$		0			0
$357$	9.28161	+	12.0120i	0.491235	+	0.635741i
$358$		0			0
$359$	−20.6138			−1.08795			−0.543977	−	0.839100i	$-0.683082\pi$
$359$	−20.6138			−1.08795			−0.543977	+	0.839100i	$0.683082\pi$
$360$		0			0
$361$	−18.1552			−0.955539
$362$		0			0
$363$	−7.21973	+	17.5975i	−0.378938	+	0.923629i
$364$		0			0
$365$	7.08207	−	12.2665i	0.370693	−	0.642058i
$366$		0			0
$367$	10.1478	−	5.85881i	0.529708	−	0.305827i	−0.211189	−	0.977445i	$-0.567734\pi$
$367$	10.1478	−	5.85881i	0.529708	−	0.305827i	0.740898	+	0.671618i	$0.234400\pi$
$368$		0			0
$369$	6.01381	+	1.56802i	0.313067	+	0.0816281i
$370$		0			0
$371$	1.75041	−	1.01060i	0.0908767	−	0.0524677i
$372$		0			0
$373$	3.02771	+	1.74805i	0.156769	+	0.0905105i	0.576332	−	0.817216i	$-0.304483\pi$
$373$	3.02771	+	1.74805i	0.156769	+	0.0905105i	−0.419563	+	0.907726i	$0.637817\pi$
$374$		0			0
$375$	12.8976	−	1.74225i	0.666031	−	0.0899695i
$376$		0			0
$377$		−	25.8466i		−	1.33117i
$378$		0			0
$379$	−20.1604			−1.03557			−0.517785	−	0.855511i	$-0.673243\pi$
$379$	−20.1604			−1.03557			−0.517785	+	0.855511i	$0.673243\pi$
$380$		0			0
$381$	4.08721	+	30.2571i	0.209394	+	1.55012i
$382$		0			0
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	−0.697067	−	0.717006i	$-0.745512\pi$
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	0.969479	+	0.245175i	$0.0788454\pi$
$384$		0			0
$385$	0.491614	+	0.851501i	0.0250550	+	0.0433965i
$386$		0			0
$387$	−23.1114	−	22.8019i	−1.17482	−	1.15909i
$388$		0			0
$389$	−8.34122	−	14.4474i	−0.422917	−	0.732513i	0.573307	−	0.819341i	$-0.305660\pi$
$389$	−8.34122	−	14.4474i	−0.422917	−	0.732513i	−0.996223	+	0.0868277i	$0.972327\pi$
$390$		0			0
$391$	5.01619	+	2.89610i	0.253680	+	0.146462i
$392$		0			0
$393$	23.6475	+	9.70188i	1.19286	+	0.489395i
$394$		0			0
$395$			43.7489i			2.20125i
$396$		0			0
$397$		−	22.9869i		−	1.15368i	−0.816857	−	0.576840i	$-0.804285\pi$
$397$		−	22.9869i		−	1.15368i	0.816857	−	0.576840i	$-0.195715\pi$
$398$		0			0
$399$	−2.62991	+	2.03212i	−0.131660	+	0.101733i
$400$		0			0
$401$	27.3094	+	15.7671i	1.36377	+	0.787371i	0.990123	−	0.140201i	$-0.0447747\pi$
$401$	27.3094	+	15.7671i	1.36377	+	0.787371i	0.373644	+	0.927572i	$0.378108\pi$
$402$		0			0
$403$	−7.73862	−	13.4037i	−0.385488	−	0.667685i
$404$		0			0
$405$	0.423023	+	31.3751i	0.0210202	+	1.55904i
$406$		0			0
$407$	−0.109199	−	0.189137i	−0.00541277	−	0.00937519i
$408$		0			0
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	−0.763430	−	0.645890i	$-0.776486\pi$
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	0.941073	+	0.338205i	$0.109820\pi$
$410$		0			0
$411$	23.5156	−	18.1704i	1.15994	−	0.896279i
$412$		0			0
$413$	−9.37205			−0.461169
$414$		0			0
$415$		−	21.0901i		−	1.03527i
$416$		0			0
$417$	0.799253	−	1.94811i	0.0391396	−	0.0953995i
$418$		0			0
$419$	12.5999	+	7.27453i	0.615543	+	0.355384i	0.775132	−	0.631800i	$-0.217683\pi$
$419$	12.5999	+	7.27453i	0.615543	+	0.355384i	−0.159589	+	0.987184i	$0.551017\pi$
$420$		0			0
$421$	−9.38587	+	5.41893i	−0.457439	+	0.264103i	−0.710967	−	0.703225i	$-0.751742\pi$
$421$	−9.38587	+	5.41893i	−0.457439	+	0.264103i	0.253528	+	0.967328i	$0.418409\pi$
$422$		0			0
$423$	−0.879038	−	0.867266i	−0.0427403	−	0.0421679i
$424$		0			0
$425$	26.0134	−	15.0188i	1.26183	−	0.728520i
$426$		0			0
$427$	8.97444	−	15.5442i	0.434304	−	0.752236i
$428$		0			0
$429$	0.706525	−	0.0954394i	0.0341113	−	0.00460786i
$430$		0			0
$431$	−10.8604			−0.523129			−0.261565	−	0.965186i	$-0.584238\pi$
$431$	−10.8604			−0.523129			−0.261565	+	0.965186i	$0.584238\pi$
$432$		0			0
$433$	9.41382			0.452399			0.226200	−	0.974081i	$-0.427370\pi$
$433$	9.41382			0.452399			0.226200	+	0.974081i	$0.427370\pi$
$434$		0			0
$435$	50.7605	−	6.85687i	2.43378	−	0.328762i
$436$		0			0
$437$	−0.634073	+	1.09825i	−0.0303318	+	0.0525363i
$438$		0			0
$439$	−9.25745	+	5.34479i	−0.441834	+	0.255093i	−0.704375	−	0.709828i	$-0.748773\pi$
$439$	−9.25745	+	5.34479i	−0.441834	+	0.255093i	0.262541	+	0.964921i	$0.415439\pi$
$440$		0			0
$441$	−1.99931	+	7.66791i	−0.0952052	+	0.365139i
$442$		0			0
$443$	−18.9818	+	10.9592i	−0.901854	+	0.520686i	−0.877801	−	0.479025i	$-0.840990\pi$
$443$	−18.9818	+	10.9592i	−0.901854	+	0.520686i	−0.0240526	+	0.999711i	$0.507657\pi$
$444$		0			0
$445$	25.2371	+	14.5707i	1.19635	+	0.690715i
$446$		0			0
$447$	5.86897	−	14.3051i	0.277593	−	0.676609i
$448$		0			0
$449$			18.7436i			0.884565i	0.896876	+	0.442282i	$0.145831\pi$
$449$			18.7436i			0.884565i	−0.896876	+	0.442282i	$0.854169\pi$
$450$		0			0
$451$	0.279841			0.0131772
$452$		0			0
$453$	−29.9827	+	23.1675i	−1.40871	+	1.08850i
$454$		0			0
$455$	−11.0896	+	19.2078i	−0.519890	+	0.900475i
$456$		0			0
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	0.865812	−	0.500370i	$-0.166803\pi$
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	−0.866239	+	0.499630i	$0.833469\pi$
$458$		0			0
$459$	8.55098	+	20.0675i	0.399126	+	0.936673i
$460$		0			0
$461$	1.25915	+	2.18091i	0.0586444	+	0.101575i	0.893857	−	0.448352i	$-0.147989\pi$
$461$	1.25915	+	2.18091i	0.0586444	+	0.101575i	−0.835213	+	0.549927i	$0.814656\pi$
$462$		0			0
$463$	23.9003	+	13.7988i	1.11074	+	0.641286i	0.939021	−	0.343860i	$-0.111735\pi$
$463$	23.9003	+	13.7988i	1.11074	+	0.641286i	0.171719	+	0.985146i	$0.445068\pi$
$464$		0			0
$465$	24.2707	−	18.7539i	1.12553	−	0.869690i
$466$		0			0
$467$		−	28.4629i		−	1.31711i	−0.752533	−	0.658554i	$-0.771168\pi$
$467$		−	28.4629i		−	1.31711i	0.752533	−	0.658554i	$-0.228832\pi$
$468$		0			0
$469$			13.1700i			0.608134i
$470$		0			0
$471$	−8.98294	−	3.68543i	−0.413912	−	0.169816i
$472$		0			0
$473$	−1.26603	−	0.730942i	−0.0582121	−	0.0336088i
$474$		0			0
$475$	3.28823	+	5.69538i	0.150874	+	0.261322i
$476$		0			0
$477$	2.80031	−	0.770611i	0.128218	−	0.0352839i
$478$		0			0
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.856279	+	0.516514i	$0.172771\pi$
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.0191747	+	0.999816i	$0.493896\pi$
$480$		0			0
$481$	2.46325	−	4.26648i	0.112315	−	0.194535i
$482$		0			0
$483$	−0.667895	−	4.94434i	−0.0303903	−	0.224975i
$484$		0			0
$485$	3.32651			0.151049
$486$		0			0
$487$		−	2.25659i		−	0.102256i	−0.998692	−	0.0511280i	$-0.983718\pi$
$487$		−	2.25659i		−	0.102256i	0.998692	−	0.0511280i	$-0.0162817\pi$
$488$		0			0
$489$	29.4825	−	3.98258i	1.33324	−	0.180098i
$490$		0			0
$491$	17.7659	+	10.2572i	0.801765	+	0.462899i	0.844088	−	0.536205i	$-0.180142\pi$
$491$	17.7659	+	10.2572i	0.801765	+	0.462899i	−0.0423228	+	0.999104i	$0.513476\pi$
$492$		0			0
$493$	30.8377	−	17.8042i	1.38886	−	0.801860i
$494$		0			0
$495$	0.374870	+	1.36224i	0.0168492	+	0.0612279i
$496$		0			0
$497$	−21.6396	+	12.4936i	−0.970667	+	0.560415i
$498$		0			0
$499$	−1.87815	+	3.25306i	−0.0840777	+	0.145627i	−0.904998	−	0.425416i	$-0.860128\pi$
$499$	−1.87815	+	3.25306i	−0.0840777	+	0.145627i	0.820920	+	0.571043i	$0.193461\pi$
$500$		0			0
$501$	3.04060	−	7.41121i	0.135844	−	0.331109i
$502$		0			0
$503$	−33.3322			−1.48621			−0.743104	−	0.669175i	$-0.766647\pi$
$503$	−33.3322			−1.48621			−0.743104	+	0.669175i	$0.766647\pi$
$504$		0			0
$505$	−37.3694			−1.66292
$506$		0			0
$507$	−3.93421	−	5.09154i	−0.174725	−	0.226123i
$508$		0			0
$509$	−3.41788	+	5.91994i	−0.151495	+	0.262397i	−0.931777	−	0.363031i	$-0.881742\pi$
$509$	−3.41788	+	5.91994i	−0.151495	+	0.262397i	0.780282	+	0.625427i	$0.215075\pi$
$510$		0			0
$511$	−7.34533	+	4.24083i	−0.324938	+	0.187603i
$512$		0			0
$513$	−4.39359	+	1.87216i	−0.193982	+	0.0826577i
$514$		0			0
$515$	−26.0112	+	15.0176i	−1.14619	+	0.661754i
$516$		0			0
$517$	−0.0481531	−	0.0278012i	−0.00211777	−	0.00122270i
$518$		0			0
$519$	3.22107	+	4.16861i	0.141389	+	0.182982i
$520$		0			0
$521$			19.9468i			0.873887i	0.899489	+	0.436943i	$0.143939\pi$
$521$			19.9468i			0.873887i	−0.899489	+	0.436943i	$0.856061\pi$
$522$		0			0
$523$	5.50358			0.240655			0.120327	−	0.992734i	$-0.461606\pi$
$523$	5.50358			0.240655			0.120327	+	0.992734i	$0.461606\pi$
$524$		0			0
$525$	−23.9373	−	9.82077i	−1.04471	−	0.428614i
$526$		0			0
$527$	10.6614	−	18.4660i	0.464416	−	0.804392i
$528$		0			0
$529$	10.5481	+	18.2699i	0.458615	+	0.794344i
$530$		0			0
$531$	−13.0317	−	3.39785i	−0.565528	−	0.147454i
$532$		0			0
$533$	3.15627	+	5.46682i	0.136713	+	0.236794i
$534$		0			0
$535$	14.5162	+	8.38093i	0.627590	+	0.362339i
$536$		0			0
$537$	−4.17348	−	30.8957i	−0.180099	−	1.33325i
$538$		0			0
$539$			0.356811i			0.0153690i
$540$		0			0
$541$		−	12.1375i		−	0.521831i	−0.965362	−	0.260915i	$-0.915976\pi$
$541$		−	12.1375i		−	0.521831i	0.965362	−	0.260915i	$-0.0840243\pi$
$542$		0			0
$543$	3.69841	+	27.3788i	0.158714	+	1.17494i
$544$		0			0
$545$	−21.6396	−	12.4936i	−0.926937	−	0.535167i
$546$		0			0
$547$	−5.02439	−	8.70250i	−0.214827	−	0.372092i	0.738392	−	0.674372i	$-0.235586\pi$
$547$	−5.02439	−	8.70250i	−0.214827	−	0.372092i	−0.953219	+	0.302280i	$0.902252\pi$
$548$		0			0
$549$	18.1144	−	18.3603i	0.773104	−	0.783598i
$550$		0			0
$551$	3.89805	+	6.75163i	0.166063	+	0.287629i
$552$		0			0
$553$	13.0987	−	22.6876i	0.557013	−	0.964775i
$554$		0			0
$555$	9.03249	+	3.70576i	0.383408	+	0.157301i
$556$		0			0
$557$	−15.4323			−0.653887			−0.326944	−	0.945044i	$-0.606019\pi$
$557$	−15.4323			−0.653887			−0.326944	+	0.945044i	$0.606019\pi$
$558$		0			0
$559$		−	32.9766i		−	1.39476i
$560$		0			0
$561$	0.600553	+	0.777218i	0.0253554	+	0.0328142i
$562$		0			0
$563$	−5.08901	−	2.93814i	−0.214476	−	0.123828i	0.388914	−	0.921274i	$-0.372850\pi$
$563$	−5.08901	−	2.93814i	−0.214476	−	0.123828i	−0.603390	+	0.797446i	$0.706184\pi$
$564$		0			0
$565$	0.745845	−	0.430614i	0.0313779	−	0.0181161i
$566$		0			0
$567$	9.17451	−	16.3973i	0.385293	−	0.688624i
$568$		0			0
$569$	−28.3228	+	16.3522i	−1.18735	+	0.685519i	−0.957704	−	0.287754i	$-0.907091\pi$
$569$	−28.3228	+	16.3522i	−1.18735	+	0.685519i	−0.229650	+	0.973273i	$0.573758\pi$
$570$		0			0
$571$	−16.4253	+	28.4495i	−0.687377	+	1.19057i	0.285306	+	0.958437i	$0.407905\pi$
$571$	−16.4253	+	28.4495i	−0.687377	+	1.19057i	−0.972683	+	0.232136i	$0.925428\pi$
$572$		0			0
$573$	4.70133	+	6.08432i	0.196401	+	0.254176i
$574$		0			0
$575$	−9.87246			−0.411710
$576$		0			0
$577$	−16.7158			−0.695887			−0.347943	−	0.937516i	$-0.613120\pi$
$577$	−16.7158			−0.695887			−0.347943	+	0.937516i	$0.613120\pi$
$578$		0			0
$579$	0.886034	−	2.15964i	0.0368223	−	0.0897514i
$580$		0			0
$581$	−6.31450	+	10.9370i	−0.261970	+	0.453745i
$582$		0			0
$583$	0.113258	−	0.0653894i	0.00469066	−	0.00270815i
$584$		0			0
$585$	−22.3838	+	22.6876i	−0.925455	+	0.938017i
$586$		0			0
$587$	23.7005	−	13.6835i	0.978222	−	0.564777i	0.0764895	−	0.997070i	$-0.475629\pi$
$587$	23.7005	−	13.6835i	0.978222	−	0.564777i	0.901733	+	0.432293i	$0.142296\pi$
$588$		0			0
$589$	4.04296	+	2.33420i	0.166587	+	0.0961791i
$590$		0			0
$591$	−15.7371	+	2.12582i	−0.647338	+	0.0874444i
$592$		0			0
$593$		−	25.6865i		−	1.05482i	−0.849612	−	0.527408i	$-0.823164\pi$
$593$		−	25.6865i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$594$		0			0
$595$	−30.5560			−1.25267
$596$		0			0
$597$	−5.57031	−	41.2362i	−0.227977	−	1.68768i
$598$		0			0
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	−0.0915718	−	0.995798i	$-0.529189\pi$
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	0.908173	−	0.418596i	$-0.137478\pi$
$600$		0			0
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	0.904256	−	0.426991i	$-0.140426\pi$
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	−0.821913	+	0.569613i	$0.807093\pi$
$602$		0			0
$603$	−4.77480	+	18.3127i	−0.194445	+	0.745751i
$604$		0			0
$605$	−19.1436	−	33.1577i	−0.778298	−	1.34805i
$606$		0			0
$607$	−11.2251	−	6.48081i	−0.455612	−	0.263048i	0.254585	−	0.967050i	$-0.418061\pi$
$607$	−11.2251	−	6.48081i	−0.455612	−	0.263048i	−0.710198	+	0.704002i	$0.751394\pi$
$608$		0			0
$609$	−28.3767	−	11.6421i	−1.14988	−	0.471762i
$610$		0			0
$611$		−	1.25426i		−	0.0507418i
$612$		0			0
$613$		−	22.0890i		−	0.892167i	−0.894991	−	0.446084i	$-0.852818\pi$
$613$		−	22.0890i		−	0.892167i	0.894991	−	0.446084i	$-0.147182\pi$
$614$		0			0
$615$	−9.89903	+	7.64894i	−0.399168	+	0.308435i
$616$		0			0
$617$	20.0171	+	11.5569i	0.805859	+	0.465263i	0.845516	−	0.533951i	$-0.179293\pi$
$617$	20.0171	+	11.5569i	0.805859	+	0.465263i	−0.0396569	+	0.999213i	$0.512626\pi$
$618$		0			0
$619$	2.24675	+	3.89149i	0.0903046	+	0.156412i	0.907639	−	0.419751i	$-0.137883\pi$
$619$	2.24675	+	3.89149i	0.0903046	+	0.156412i	−0.817335	+	0.576163i	$0.804549\pi$
$620$		0			0
$621$	0.863876	−	7.11718i	0.0346662	−	0.285602i
$622$		0			0
$623$	−8.72509	−	15.1123i	−0.349563	−	0.605461i
$624$		0			0
$625$	4.78939	−	8.29547i	0.191576	−	0.331819i
$626$		0			0
$627$	−0.170164	+	0.131485i	−0.00679571	+	0.00525102i
$628$		0			0
$629$	6.78716			0.270622
$630$		0			0
$631$		−	30.8693i		−	1.22889i	−0.788961	−	0.614443i	$-0.789381\pi$
$631$		−	30.8693i		−	1.22889i	0.788961	−	0.614443i	$-0.210619\pi$
$632$		0			0
$633$	−13.3163	+	32.4573i	−0.529274	+	1.29006i
$634$		0			0
$635$	−53.2237	−	30.7287i	−2.11212	−	1.21943i
$636$		0			0
$637$	−6.97046	+	4.02440i	−0.276180	+	0.159452i
$638$		0			0
$639$	−34.6191	+	9.52674i	−1.36951	+	0.376872i
$640$		0			0
$641$	23.7137	−	13.6911i	0.936633	−	0.540766i	0.0477300	−	0.998860i	$-0.484801\pi$
$641$	23.7137	−	13.6911i	0.936633	−	0.540766i	0.888903	+	0.458095i	$0.151468\pi$
$642$		0			0
$643$	19.9857	−	34.6162i	0.788158	−	1.36513i	−0.138937	−	0.990301i	$-0.544369\pi$
$643$	19.9857	−	34.6162i	0.788158	−	1.36513i	0.927094	−	0.374828i	$-0.122298\pi$
$644$		0			0
$645$	64.7632	−	8.74840i	2.55005	−	0.344468i
$646$		0			0
$647$	30.9768			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$647$	30.9768			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$648$		0			0
$649$	−0.606405			−0.0238035
$650$		0			0
$651$	−18.2015	+	2.45871i	−0.713372	+	0.0963644i
$652$		0			0
$653$	2.78891	−	4.83053i	0.109138	−	0.189033i	−0.806283	−	0.591530i	$-0.798524\pi$
$653$	2.78891	−	4.83053i	0.109138	−	0.189033i	0.915421	+	0.402497i	$0.131857\pi$
$654$		0			0
$655$	−44.5573	+	25.7252i	−1.74100	+	1.00517i
$656$		0			0
$657$	−11.7511	+	3.23375i	−0.458454	+	0.126161i
$658$		0			0
$659$	5.69959	−	3.29066i	0.222025	−	0.128186i	−0.384863	−	0.922974i	$-0.625751\pi$
$659$	5.69959	−	3.29066i	0.222025	−	0.128186i	0.606887	+	0.794788i	$0.292418\pi$
$660$		0			0
$661$	−26.9562	−	15.5632i	−1.04847	−	0.605337i	−0.126253	−	0.991998i	$-0.540295\pi$
$661$	−26.9562	−	15.5632i	−1.04847	−	0.605337i	−0.922222	+	0.386661i	$0.873628\pi$
$662$		0			0
$663$	−8.40978	+	20.4981i	−0.326609	+	0.796082i
$664$		0			0
$665$		−	6.68993i		−	0.259425i
$666$		0			0
$667$	−11.7034			−0.453157
$668$		0			0
$669$	0.824720	−	0.637258i	0.0318855	−	0.0246378i
$670$		0			0
$671$	0.580679	−	1.00576i	0.0224168	−	0.0388271i
$672$		0			0
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	0.789675	−	0.613525i	$-0.210249\pi$
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	−0.926166	+	0.377116i	$0.876916\pi$
$674$		0			0
$675$	−29.7240	−	22.3342i	−1.14408	−	0.859642i
$676$		0			0
$677$	3.18253	+	5.51231i	0.122315	+	0.211855i	0.920680	−	0.390318i	$-0.127635\pi$
$677$	3.18253	+	5.51231i	0.122315	+	0.211855i	−0.798365	+	0.602173i	$0.794302\pi$
$678$		0			0
$679$	−1.72508	−	0.995978i	−0.0662026	−	0.0382221i
$680$		0			0
$681$	−14.6187	+	11.2958i	−0.560191	+	0.432858i
$682$		0			0
$683$			51.9104i			1.98630i	0.116864	+	0.993148i	$0.462716\pi$
$683$			51.9104i			1.98630i	−0.116864	+	0.993148i	$0.537284\pi$
$684$		0			0
$685$			59.8187i			2.28556i
$686$		0			0
$687$	40.9984	+	16.8204i	1.56419	+	0.641739i
$688$		0			0
$689$	2.55482	+	1.47503i	0.0973309	+	0.0561940i
$690$		0			0
$691$	17.9150	+	31.0297i	0.681519	+	1.18043i	0.974517	+	0.224313i	$0.0720138\pi$
$691$	17.9150	+	31.0297i	0.681519	+	1.18043i	−0.292998	+	0.956113i	$0.594653\pi$
$692$		0			0
$693$	0.213459	−	0.818675i	0.00810864	−	0.0310989i
$694$		0			0
$695$	2.11927	+	3.67068i	0.0803885	+	0.139237i
$696$		0			0
$697$	−4.34834	+	7.53154i	−0.164705	+	0.285277i
$698$		0			0
$699$	−1.09228	−	8.08601i	−0.0413139	−	0.305841i
$700$		0			0
$701$	19.0081			0.717927			0.358964	−	0.933352i	$-0.383130\pi$
$701$	19.0081			0.717927			0.358964	+	0.933352i	$0.383130\pi$
$702$		0			0
$703$			1.48598i			0.0560449i
$704$		0			0
$705$	2.46325	−	0.332743i	0.0927715	−	0.0125318i
$706$		0			0
$707$	19.3793	+	11.1886i	0.728832	+	0.420792i
$708$		0			0
$709$	−38.5758	+	22.2717i	−1.44874	+	0.836433i	−0.998407	−	0.0564260i	$-0.982030\pi$
$709$	−38.5758	+	22.2717i	−1.44874	+	0.836433i	−0.450337	+	0.892859i	$0.648696\pi$
$710$		0			0
$711$	26.4390	−	26.7979i	0.991539	−	1.00500i
$712$		0			0
$713$	−6.06922	+	3.50407i	−0.227294	+	0.131228i
$714$		0			0
$715$	−0.717538	+	1.24281i	−0.0268344	+	0.0464786i
$716$		0			0
$717$	−9.87504	+	24.0696i	−0.368790	+	0.898895i
$718$		0			0
$719$	40.5385			1.51183			0.755915	−	0.654670i	$-0.227192\pi$
$719$	40.5385			1.51183			0.755915	+	0.654670i	$0.227192\pi$
$720$		0			0
$721$	17.9854			0.669813
$722$		0			0
$723$	27.2661	+	35.2869i	1.01404	+	1.31233i
$724$		0			0
$725$	−30.3462	+	52.5611i	−1.12703	+	1.95207i
$726$		0			0
$727$	16.5719	−	9.56779i	0.614618	−	0.354850i	−0.160153	−	0.987092i	$-0.551199\pi$
$727$	16.5719	−	9.56779i	0.614618	−	0.354850i	0.774770	+	0.632243i	$0.217865\pi$
$728$		0			0
$729$	18.7019	−	19.4740i	0.692663	−	0.721261i
$730$		0			0
$731$	39.3446	−	22.7156i	1.45521	−	0.840168i
$732$		0			0
$733$	25.4597	+	14.6992i	0.940377	+	0.542927i	0.890078	−	0.455807i	$-0.150649\pi$
$733$	25.4597	+	14.6992i	0.940377	+	0.542927i	0.0502985	+	0.998734i	$0.483983\pi$
$734$		0			0
$735$	−9.75278	−	12.6218i	−0.359737	−	0.465561i
$736$		0			0
$737$			0.852146i			0.0313892i
$738$		0			0
$739$	0.807511			0.0297048			0.0148524	−	0.999890i	$-0.495272\pi$
$739$	0.807511			0.0297048			0.0148524	+	0.999890i	$0.495272\pi$
$740$		0			0
$741$	−4.48787	−	1.84124i	−0.164866	−	0.0676396i
$742$		0			0
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	−0.515121	−	0.857118i	$-0.672253\pi$
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	0.999846	+	0.0175489i	$0.00558629\pi$
$744$		0			0
$745$	15.5620	+	26.9541i	0.570146	+	0.987521i
$746$		0			0
$747$	−12.7455	+	12.9185i	−0.466332	+	0.472662i
$748$		0			0
$749$	−5.01860	−	8.69248i	−0.183376	−	0.317616i
$750$		0			0
$751$	2.08658	+	1.20469i	0.0761405	+	0.0439597i	0.537587	−	0.843208i	$-0.319336\pi$
$751$	2.08658	+	1.20469i	0.0761405	+	0.0439597i	−0.461446	+	0.887168i	$0.652669\pi$
$752$		0			0
$753$	1.22989	+	9.10473i	0.0448198	+	0.331795i
$754$		0			0
$755$		−	76.2698i		−	2.77574i
$756$		0			0
$757$			3.61528i			0.131400i	0.997839	+	0.0656998i	$0.0209280\pi$
$757$			3.61528i			0.131400i	−0.997839	+	0.0656998i	$0.979072\pi$
$758$		0			0
$759$	−0.0432152	−	0.319916i	−0.00156861	−	0.0116122i
$760$		0			0
$761$	7.79878	+	4.50263i	0.282706	+	0.163220i	0.634648	−	0.772802i	$-0.281145\pi$
$761$	7.79878	+	4.50263i	0.282706	+	0.163220i	−0.351942	+	0.936022i	$0.614479\pi$
$762$		0			0
$763$	7.48133	+	12.9580i	0.270842	+	0.469112i
$764$		0			0
$765$	−42.4876	−	11.0781i	−1.53614	−	0.400530i
$766$		0			0
$767$	−6.83951	−	11.8464i	−0.246961	−	0.427748i
$768$		0			0
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	−0.696242	−	0.717807i	$-0.745146\pi$
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	0.969760	+	0.244060i	$0.0784794\pi$
$770$		0			0
$771$	−39.7792	−	16.3202i	−1.43261	−	0.587758i
$772$		0			0
$773$	31.6926			1.13990			0.569952	−	0.821678i	$-0.306962\pi$
$773$	31.6926			1.13990			0.569952	+	0.821678i	$0.306962\pi$
$774$		0			0
$775$			36.3433i			1.30549i
$776$		0			0
$777$	−3.57460	−	4.62614i	−0.128238	−	0.165962i
$778$		0			0
$779$	−1.64896	−	0.952026i	−0.0590800	−	0.0341099i
$780$		0			0
$781$	−1.40016	+	0.808381i	−0.0501016	+	0.0289262i
$782$		0			0
$783$	−35.2365	−	26.4762i	−1.25925	−	0.946182i
$784$		0			0
$785$	16.9259	−	9.77217i	0.604111	−	0.348784i
$786$		0			0
$787$	−10.3290	+	17.8904i	−0.368189	+	0.637723i	−0.989283	−	0.146014i	$-0.953356\pi$
$787$	−10.3290	+	17.8904i	−0.368189	+	0.637723i	0.621093	+	0.783737i	$0.286689\pi$
$788$		0			0
$789$	−21.0929	−	27.2978i	−0.750928	−	0.971828i
$790$		0			0
$791$	−0.515713			−0.0183367
$792$		0			0
$793$	26.1974			0.930297
$794$		0			0
$795$	−2.21905	+	5.40876i	−0.0787017	+	0.191829i
$796$		0			0
$797$	17.8453	−	30.9089i	0.632112	−	1.09485i	−0.355007	−	0.934864i	$-0.615521\pi$
$797$	17.8453	−	30.9089i	0.632112	−	1.09485i	0.987119	−	0.159987i	$-0.0511452\pi$
$798$		0			0
$799$	1.49646	−	0.863984i	0.0529411	−	0.0305655i
$800$		0			0
$801$	−6.65313	−	24.1767i	−0.235077	−	0.854243i
$802$		0			0
$803$	−0.475269	+	0.274397i	−0.0167719	+	0.00968325i
$804$		0			0
$805$	8.69734	+	5.02141i	0.306541	+	0.176981i
$806$		0			0
$807$	−4.04296	+	0.546134i	−0.142319	+	0.0192248i
$808$		0			0
$809$		−	18.7528i		−	0.659314i	−0.944101	−	0.329657i	$-0.893067\pi$
$809$		−	18.7528i		−	0.659314i	0.944101	−	0.329657i	$-0.106933\pi$
$810$		0			0
$811$	33.9206			1.19111			0.595556	−	0.803314i	$-0.296932\pi$
$811$	33.9206			1.19111			0.595556	+	0.803314i	$0.296932\pi$
$812$		0			0
$813$	2.80031	+	20.7303i	0.0982113	+	0.727045i
$814$		0			0
$815$	−29.9421	+	51.8612i	−1.04882	+	1.81662i
$816$		0			0
$817$	4.97337	+	8.61412i	0.173996	+	0.301370i
$818$		0			0
$819$	18.4007	−	5.06365i	0.642974	−	0.176938i
$820$		0			0
$821$	5.34636	+	9.26017i	0.186589	+	0.323182i	0.944111	−	0.329628i	$-0.106923\pi$
$821$	5.34636	+	9.26017i	0.186589	+	0.323182i	−0.757522	+	0.652810i	$0.773590\pi$
$822$		0			0
$823$	−33.4172	−	19.2934i	−1.16485	−	0.672527i	−0.212390	−	0.977185i	$-0.568125\pi$
$823$	−33.4172	−	19.2934i	−1.16485	−	0.672527i	−0.952462	+	0.304658i	$0.901458\pi$
$824$		0			0
$825$	−1.54883	−	0.635439i	−0.0539234	−	0.0221231i
$826$		0			0
$827$		−	0.214418i		−	0.00745604i	−0.999993	−	0.00372802i	$-0.998813\pi$
$827$		−	0.214418i		−	0.00745604i	0.999993	−	0.00372802i	$-0.00118667\pi$
$828$		0			0
$829$		−	35.5733i		−	1.23551i	−0.786369	−	0.617757i	$-0.788042\pi$
$829$		−	35.5733i		−	1.23551i	0.786369	−	0.617757i	$-0.211958\pi$
$830$		0			0
$831$	23.0274	−	17.7932i	0.798812	−	0.617239i
$832$		0			0
$833$	−9.60309	−	5.54434i	−0.332727	−	0.192100i
$834$		0			0
$835$	8.06235	+	13.9644i	0.279009	+	0.483258i
$836$		0			0
$837$	−26.2003	−	3.18017i	−0.905615	−	0.109923i
$838$		0			0
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	0.964583	+	0.263778i	$0.0849687\pi$
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	−0.253853	+	0.967243i	$0.581698\pi$
$840$		0			0
$841$	−21.4741	+	37.1942i	−0.740486	+	1.28256i
$842$		0			0
$843$	18.9679	−	14.6564i	0.653289	−	0.504794i
$844$		0			0
$845$	12.9518			0.445556
$846$		0			0
$847$			22.9268i			0.787775i
$848$		0			0
$849$	−3.39395	+	8.27248i	−0.116480	+	0.283911i
$850$		0			0
$851$	−1.93187	−	1.11537i	−0.0662237	−	0.0382343i
$852$		0			0
$853$	30.9858	−	17.8897i	1.06093	−	0.612530i	0.135243	−	0.990812i	$-0.456819\pi$
$853$	30.9858	−	17.8897i	1.06093	−	0.612530i	0.925690	+	0.378282i	$0.123485\pi$
$854$		0			0
$855$	2.42544	−	9.30226i	0.0829484	−	0.318131i
$856$		0			0
$857$	26.3688	−	15.2241i	0.900742	−	0.520044i	0.0233014	−	0.999728i	$-0.492582\pi$
$857$	26.3688	−	15.2241i	0.900742	−	0.520044i	0.877441	+	0.479685i	$0.159249\pi$
$858$		0			0
$859$	11.7147	−	20.2904i	0.399700	−	0.692301i	−0.593989	−	0.804473i	$-0.702448\pi$
$859$	11.7147	−	20.2904i	0.399700	−	0.692301i	0.993689	+	0.112172i	$0.0357809\pi$
$860$		0			0
$861$	7.42364	−	1.00281i	0.252997	−	0.0341756i
$862$		0			0
$863$	−32.2240			−1.09692			−0.548458	−	0.836178i	$-0.684785\pi$
$863$	−32.2240			−1.09692			−0.548458	+	0.836178i	$0.684785\pi$
$864$		0			0
$865$	−10.6041			−0.360549
$866$		0			0
$867$	−1.06966	+	0.144493i	−0.0363275	+	0.00490723i
$868$		0			0
$869$	0.847532	−	1.46797i	0.0287506	−	0.0497974i
$870$		0			0
$871$	−16.6470	+	9.61117i	−0.564063	+	0.325662i
$872$		0			0
$873$	−2.03761	−	2.01032i	−0.0689627	−	0.0680392i
$874$		0			0
$875$	13.5856	−	7.84366i	0.459278	−	0.265164i
$876$		0			0
$877$	1.74081	+	1.00506i	0.0587829	+	0.0339384i	0.529103	−	0.848557i	$-0.322528\pi$
$877$	1.74081	+	1.00506i	0.0587829	+	0.0339384i	−0.470320	+	0.882496i	$0.655862\pi$
$878$		0			0
$879$	7.12498	−	17.3666i	0.240320	−	0.585759i
$880$		0			0
$881$		−	21.6545i		−	0.729558i	−0.931094	−	0.364779i	$-0.881145\pi$
$881$		−	21.6545i		−	0.729558i	0.931094	−	0.364779i	$-0.118855\pi$
$882$		0			0
$883$	23.3462			0.785664			0.392832	−	0.919610i	$-0.371495\pi$
$883$	23.3462			0.785664			0.392832	+	0.919610i	$0.371495\pi$
$884$		0			0
$885$	21.4508	−	16.5750i	0.721062	−	0.557162i
$886$		0			0
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	0.0816710	+	0.996659i	$0.473974\pi$
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	−0.903968	+	0.427600i	$0.859359\pi$
$888$		0			0
$889$	18.4007	+	31.8710i	0.617141	+	1.06892i
$890$		0			0
$891$	0.593624	−	1.06097i	0.0198871	−	0.0355437i
$892$		0			0
$893$	0.189161	+	0.327636i	0.00633003	+	0.0109639i
$894$		0			0
$895$	54.3471	+	31.3773i	1.81662	+	1.04883i
$896$		0			0
$897$	5.76228	−	4.45249i	0.192397	−	0.148664i
$898$		0			0
$899$			43.0834i			1.43691i
$900$		0			0
$901$			4.06424i			0.135399i
$902$		0			0
$903$	−36.2047	−	14.8537i	−1.20482	−	0.494300i
$904$		0			0
$905$	−48.1607	−	27.8056i	−1.60092	−	0.924289i
$906$		0			0
$907$	9.93443	+	17.2069i	0.329867	+	0.571347i	0.982485	−	0.186340i	$-0.0596627\pi$
$907$	9.93443	+	17.2069i	0.329867	+	0.571347i	−0.652618	+	0.757687i	$0.726329\pi$
$908$		0			0
$909$	22.8902	+	22.5836i	0.759218	+	0.749051i
$910$		0			0
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	0.921315	+	0.388817i	$0.127116\pi$
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	−0.123932	+	0.992291i	$0.539550\pi$
$912$		0			0
$913$	−0.408571	+	0.707665i	−0.0135217	+	0.0234203i
$914$		0			0
$915$	6.94995	+	51.4495i	0.229758	+	1.70087i
$916$		0			0
$917$	30.8091			1.01741
$918$		0			0
$919$			34.3644i			1.13358i	0.823864	+	0.566788i	$0.191814\pi$
$919$			34.3644i			1.13358i	−0.823864	+	0.566788i	$0.808186\pi$
$920$		0			0
$921$	−28.5878	+	3.86173i	−0.942002	+	0.127248i
$922$		0			0
$923$	−31.5841	−	18.2351i	−1.03960	−	0.600216i
$924$		0			0
$925$	−10.0185	+	5.78416i	−0.329405	+	0.190182i
$926$		0			0
$927$	25.0085	+	6.52064i	0.821387	+	0.214166i
$928$		0			0
$929$	15.1165	−	8.72750i	0.495955	−	0.286340i	−0.231086	−	0.972933i	$-0.574228\pi$
$929$	15.1165	−	8.72750i	0.495955	−	0.286340i	0.727042	+	0.686593i	$0.240895\pi$
$930$		0			0
$931$	1.21388	−	2.10250i	0.0397833	−	0.0689067i
$932$		0			0
$933$	−8.50998	+	20.7424i	−0.278604	+	0.679075i
$934$		0			0
$935$	−1.97708			−0.0646574
$936$		0			0
$937$	42.3068			1.38210			0.691051	−	0.722806i	$-0.257148\pi$
$937$	42.3068			1.38210			0.691051	+	0.722806i	$0.257148\pi$
$938$		0			0
$939$	−28.2958	−	36.6196i	−0.923400	−	1.19504i
$940$		0			0
$941$	−11.6752	+	20.2221i	−0.380602	+	0.659222i	−0.991148	−	0.132758i	$-0.957617\pi$
$941$	−11.6752	+	20.2221i	−0.380602	+	0.659222i	0.610546	+	0.791980i	$0.290950\pi$
$942$		0			0
$943$	2.47539	−	1.42917i	0.0806097	−	0.0465400i
$944$		0			0
$945$	14.8261	+	34.7941i	0.482294	+	1.13185i
$946$		0			0
$947$	−28.1206	+	16.2354i	−0.913796	+	0.527580i	−0.881651	−	0.471903i	$-0.843567\pi$
$947$	−28.1206	+	16.2354i	−0.913796	+	0.527580i	−0.0321454	+	0.999483i	$0.510234\pi$
$948$		0			0
$949$	−10.7209	−	6.18973i	−0.348016	−	0.200927i
$950$		0			0
$951$	26.5482	+	34.3579i	0.860884	+	1.11413i
$952$		0			0
$953$			11.0705i			0.358607i	0.983794	+	0.179304i	$0.0573844\pi$
$953$			11.0705i			0.358607i	−0.983794	+	0.179304i	$0.942616\pi$
$954$		0			0
$955$	−15.4772			−0.500832
$956$		0			0
$957$	−1.83607	−	0.753286i	−0.0593518	−	0.0243503i
$958$		0			0
$959$	17.9101	−	31.0212i	0.578347	−	1.00173i
$960$		0			0
$961$	−2.60055	−	4.50429i	−0.0838888	−	0.145300i
$962$		0			0
$963$	−3.82683	−	13.9063i	−0.123318	−	0.448123i
$964$		0			0
$965$	2.34938	+	4.06924i	0.0756291	+	0.130993i
$966$		0			0
$967$	−40.9201	−	23.6252i	−1.31590	−	0.759736i	−0.332835	−	0.942985i	$-0.608005\pi$
$967$	−40.9201	−	23.6252i	−1.31590	−	0.759736i	−0.983066	+	0.183249i	$0.941338\pi$
$968$		0			0
$969$	−0.894632	−	6.62283i	−0.0287397	−	0.212756i
$970$		0			0
$971$		−	33.9428i		−	1.08928i	−0.838671	−	0.544638i	$-0.816667\pi$
$971$		−	33.9428i		−	1.08928i	0.838671	−	0.544638i	$-0.183333\pi$
$972$		0			0
$973$		−	2.53809i		−	0.0813674i
$974$		0			0
$975$	−5.05535	−	37.4241i	−0.161901	−	1.19853i
$976$		0			0
$977$	26.9476	+	15.5582i	0.862131	+	0.497752i	0.864725	−	0.502245i	$-0.167492\pi$
$977$	26.9476	+	15.5582i	0.862131	+	0.497752i	−0.00259421	+	0.999997i	$0.500826\pi$
$978$		0			0
$979$	−0.564544	−	0.977819i	−0.0180429	−	0.0312512i
$980$		0			0
$981$	5.70473	+	20.7303i	0.182138	+	0.661869i
$982$		0			0
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	−0.995313	−	0.0967103i	$-0.969168\pi$
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	0.413903	−	0.910321i	$-0.364165\pi$
$984$		0			0
$985$	15.9824	−	27.6824i	0.509243	−	0.882034i
$986$		0			0
$987$	−1.37704	−	0.564957i	−0.0438315	−	0.0179828i
$988$		0			0
$989$	−14.9319			−0.474806
$990$		0			0
$991$		−	21.5164i		−	0.683490i	−0.939793	−	0.341745i	$-0.888982\pi$
$991$		−	21.5164i		−	0.683490i	0.939793	−	0.341745i	$-0.111018\pi$
$992$		0			0
$993$	17.9602	+	23.2436i	0.569951	+	0.737613i
$994$		0			0
$995$	72.5365	+	41.8790i	2.29956	+	1.32765i
$996$		0			0
$997$	−49.4923	+	28.5744i	−1.56744	+	0.904961i	−0.570971	+	0.820970i	$0.693433\pi$
$997$	−49.4923	+	28.5744i	−1.56744	+	0.904961i	−0.996467	+	0.0839906i	$0.973233\pi$
$998$		0			0
$999$	−3.29322	−	7.72856i	−0.104193	−	0.244521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.p.b.239.7		16
3.2	odd	2		864.2.p.b.719.8		16
4.3	odd	2		72.2.l.b.59.4	yes	16
8.3	odd	2	inner	288.2.p.b.239.8		16
8.5	even	2		72.2.l.b.59.1	yes	16
9.2	odd	6	inner	288.2.p.b.47.8		16
9.4	even	3		2592.2.f.b.1295.16		16
9.5	odd	6		2592.2.f.b.1295.2		16
9.7	even	3		864.2.p.b.143.1		16
12.11	even	2		216.2.l.b.179.5		16
24.5	odd	2		216.2.l.b.179.8		16
24.11	even	2		864.2.p.b.719.1		16
36.7	odd	6		216.2.l.b.35.8		16
36.11	even	6		72.2.l.b.11.1	✓	16
36.23	even	6		648.2.f.b.323.10		16
36.31	odd	6		648.2.f.b.323.7		16
72.5	odd	6		648.2.f.b.323.8		16
72.11	even	6	inner	288.2.p.b.47.7		16
72.13	even	6		648.2.f.b.323.9		16
72.29	odd	6		72.2.l.b.11.4	yes	16
72.43	odd	6		864.2.p.b.143.8		16
72.59	even	6		2592.2.f.b.1295.15		16
72.61	even	6		216.2.l.b.35.5		16
72.67	odd	6		2592.2.f.b.1295.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.1	✓	16	36.11	even	6
72.2.l.b.11.4	yes	16	72.29	odd	6
72.2.l.b.59.1	yes	16	8.5	even	2
72.2.l.b.59.4	yes	16	4.3	odd	2
216.2.l.b.35.5		16	72.61	even	6
216.2.l.b.35.8		16	36.7	odd	6
216.2.l.b.179.5		16	12.11	even	2
216.2.l.b.179.8		16	24.5	odd	2
288.2.p.b.47.7		16	72.11	even	6	inner
288.2.p.b.47.8		16	9.2	odd	6	inner
288.2.p.b.239.7		16	1.1	even	1	trivial
288.2.p.b.239.8		16	8.3	odd	2	inner
648.2.f.b.323.7		16	36.31	odd	6
648.2.f.b.323.8		16	72.5	odd	6
648.2.f.b.323.9		16	72.13	even	6
648.2.f.b.323.10		16	36.23	even	6
864.2.p.b.143.1		16	9.7	even	3
864.2.p.b.143.8		16	72.43	odd	6
864.2.p.b.719.1		16	24.11	even	2
864.2.p.b.719.8		16	3.2	odd	2
2592.2.f.b.1295.1		16	72.67	odd	6
2592.2.f.b.1295.2		16	9.5	odd	6
2592.2.f.b.1295.15		16	72.59	even	6
2592.2.f.b.1295.16		16	9.4	even	3

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71646 - 0.231865i) q^{3} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.89248 - 0.795973i) q^{9} +O(q^{10})\)	\(q+(1.71646 - 0.231865i) q^{3} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.89248 - 0.795973i) q^{9} +(0.116985 - 0.0675415i) q^{11} +(2.63890 + 1.52357i) q^{13} +(-2.29209 + 5.58677i) q^{15} +4.19800i q^{17} -0.919111 q^{19} +(2.86136 - 2.21096i) q^{21} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(4.78027 - 2.03692i) q^{27} +(-4.24111 - 7.34582i) q^{29} +(-4.39877 - 2.53963i) q^{31} +(0.185140 - 0.143057i) q^{33} +7.27870i q^{35} -1.61676i q^{37} +(4.88284 + 2.00328i) q^{39} +(1.79408 + 1.03581i) q^{41} +(-5.41106 - 9.37224i) q^{43} +(-2.63890 + 10.1209i) q^{45} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +(0.973367 + 7.20570i) q^{51} +0.968137 q^{53} +0.470958i q^{55} +(-1.57762 + 0.213109i) q^{57} +(-3.88770 - 2.24457i) q^{59} +(7.44553 - 4.29868i) q^{61} +(4.39877 - 4.45848i) q^{63} +(-9.20037 + 5.31183i) q^{65} +(-3.15416 + 5.46316i) q^{67} +(0.907092 - 2.21096i) q^{69} -11.9687 q^{71} -4.06264 q^{73} +(-7.57762 - 9.80673i) q^{75} +(0.141008 - 0.244232i) q^{77} +(10.8672 - 6.27416i) q^{79} +(7.73285 - 4.60467i) q^{81} +(-5.23875 + 3.02459i) q^{83} +(-12.6752 - 7.31802i) q^{85} +(-8.98294 - 11.6255i) q^{87} -8.35848i q^{89} +6.36158 q^{91} +(-8.13917 - 3.33926i) q^{93} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +(0.284616 - 0.288479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^3 - 6 * q^9	\( 16 q + 6 q^{3} - 6 q^{9} - 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{27} + 12 q^{33} - 36 q^{41} - 8 q^{43} + 10 q^{49} - 18 q^{51} + 18 q^{57} - 12 q^{59} - 6 q^{65} + 16 q^{67} - 4 q^{73} - 78 q^{75} - 6 q^{81} - 54 q^{83} + 36 q^{91} + 8 q^{97} + 6 q^{99}+O(q^{100}) \) 16 * q + 6 * q^3 - 6 * q^9 - 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^27 + 12 * q^33 - 36 * q^41 - 8 * q^43 + 10 * q^49 - 18 * q^51 + 18 * q^57 - 12 * q^59 - 6 * q^65 + 16 * q^67 - 4 * q^73 - 78 * q^75 - 6 * q^81 - 54 * q^83 + 36 * q^91 + 8 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more