LMFDB - Embedded newform 288.2.i.f.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(97,288)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("288.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.i (of order $3$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.1
Root			$0.335728 - 1.37379i$ of defining polynomial
Character	$\chi$	$=$	288.97
Dual form			288.2.i.f.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35760 + 1.07561i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-1.10489 + 1.91373i) q^{7} +(0.686141 - 2.92048i) q^{9} +O(q^{10})$	\(q+(-1.35760 + 1.07561i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-1.10489 + 1.91373i) q^{7} +(0.686141 - 2.92048i) q^{9} +(2.96790 - 5.14055i) q^{11} +(-2.18614 - 3.78651i) q^{13} +(3.82009 + 1.51330i) q^{15} +3.37228 q^{17} -3.72601 q^{19} +(-0.558422 - 3.78651i) q^{21} +(-1.10489 - 1.91373i) q^{23} +(-0.313859 + 0.543620i) q^{25} +(2.20979 + 4.70285i) q^{27} +(-0.186141 + 0.322405i) q^{29} +(-4.83090 - 8.36737i) q^{31} +(1.50000 + 10.1711i) q^{33} +5.24224 q^{35} +4.00000 q^{37} +(7.04069 + 2.78912i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-2.96790 + 5.14055i) q^{43} +(-6.81386 + 2.05446i) q^{45} +(-1.10489 + 1.91373i) q^{47} +(1.05842 + 1.83324i) q^{49} +(-4.57820 + 3.62725i) q^{51} -4.00000 q^{53} -14.0814 q^{55} +(5.05842 - 4.00772i) q^{57} +(-5.17769 - 8.96801i) q^{59} +(-7.55842 + 13.0916i) q^{61} +(4.83090 + 4.53991i) q^{63} +(-5.18614 + 8.98266i) q^{65} +(5.17769 + 8.96801i) q^{67} +(3.55842 + 1.40965i) q^{69} +4.41957 q^{71} +4.62772 q^{73} +(-0.158627 - 1.07561i) q^{75} +(6.55842 + 11.3595i) q^{77} +(4.83090 - 8.36737i) q^{79} +(-8.05842 - 4.00772i) q^{81} +(7.04069 - 12.1948i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-0.0940770 - 0.637910i) q^{87} +1.25544 q^{89} +9.66181 q^{91} +(15.5584 + 6.16337i) q^{93} +(4.41957 + 7.65492i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-12.9765 - 12.1948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 2 * q^5 - 6 * q^9	$ 8 q + 2 q^{5} - 6 q^{9} - 6 q^{13} + 4 q^{17} + 30 q^{21} - 14 q^{25} + 10 q^{29} + 12 q^{33} + 32 q^{37} - 4 q^{41} - 66 q^{45} - 26 q^{49} - 32 q^{53} + 6 q^{57} - 26 q^{61} - 30 q^{65} - 6 q^{69} + 60 q^{73} + 18 q^{77} - 30 q^{81} - 32 q^{85} + 56 q^{89} + 90 q^{93} - 36 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 6 * q^9 - 6 * q^13 + 4 * q^17 + 30 * q^21 - 14 * q^25 + 10 * q^29 + 12 * q^33 + 32 * q^37 - 4 * q^41 - 66 * q^45 - 26 * q^49 - 32 * q^53 + 6 * q^57 - 26 * q^61 - 30 * q^65 - 6 * q^69 + 60 * q^73 + 18 * q^77 - 30 * q^81 - 32 * q^85 + 56 * q^89 + 90 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.35760	+	1.07561i	−0.783809	+	0.621002i
$3$	−1.35760	+	1.07561i	−0.783809	+	0.621002i
$4$		0			0
$5$	−1.18614	−	2.05446i	−0.530458	−	0.918781i	−0.999368	−	0.0355348i	$-0.988687\pi$
$5$	−1.18614	−	2.05446i	−0.530458	−	0.918781i	0.468910	−	0.883246i	$-0.344647\pi$
$6$		0			0
$7$	−1.10489	+	1.91373i	−0.417610	+	0.723322i	−0.995699	−	0.0926519i	$-0.970466\pi$
$7$	−1.10489	+	1.91373i	−0.417610	+	0.723322i	0.578088	+	0.815974i	$0.303799\pi$
$8$		0			0
$9$	0.686141	−	2.92048i	0.228714	−	0.973494i
$10$		0			0
$11$	2.96790	−	5.14055i	0.894855	−	1.54993i	0.0608712	−	0.998146i	$-0.480612\pi$
$11$	2.96790	−	5.14055i	0.894855	−	1.54993i	0.833984	−	0.551789i	$-0.186055\pi$
$12$		0			0
$13$	−2.18614	−	3.78651i	−0.606326	−	1.05019i	−0.991840	−	0.127486i	$-0.959309\pi$
$13$	−2.18614	−	3.78651i	−0.606326	−	1.05019i	0.385514	−	0.922702i	$-0.374024\pi$
$14$		0			0
$15$	3.82009	+	1.51330i	0.986342	+	0.390733i
$16$		0			0
$17$	3.37228			0.817898			0.408949	−	0.912557i	$-0.365895\pi$
$17$	3.37228			0.817898			0.408949	+	0.912557i	$0.365895\pi$
$18$		0			0
$19$	−3.72601			−0.854805			−0.427403	−	0.904061i	$-0.640571\pi$
$19$	−3.72601			−0.854805			−0.427403	+	0.904061i	$0.640571\pi$
$20$		0			0
$21$	−0.558422	−	3.78651i	−0.121858	−	0.826284i
$22$		0			0
$23$	−1.10489	−	1.91373i	−0.230386	−	0.399041i	0.727536	−	0.686070i	$-0.240666\pi$
$23$	−1.10489	−	1.91373i	−0.230386	−	0.399041i	−0.957922	+	0.287029i	$0.907332\pi$
$24$		0			0
$25$	−0.313859	+	0.543620i	−0.0627719	+	0.108724i
$26$		0			0
$27$	2.20979	+	4.70285i	0.425274	+	0.905065i
$28$		0			0
$29$	−0.186141	+	0.322405i	−0.0345655	+	0.0598691i	−0.882791	−	0.469767i	$-0.844338\pi$
$29$	−0.186141	+	0.322405i	−0.0345655	+	0.0598691i	0.848225	+	0.529636i	$0.177671\pi$
$30$		0			0
$31$	−4.83090	−	8.36737i	−0.867656	−	1.50282i	−0.864386	−	0.502830i	$-0.832292\pi$
$31$	−4.83090	−	8.36737i	−0.867656	−	1.50282i	−0.00327038	−	0.999995i	$-0.501041\pi$
$32$		0			0
$33$	1.50000	+	10.1711i	0.261116	+	1.77056i
$34$		0			0
$35$	5.24224			0.886099
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$	7.04069	+	2.78912i	1.12741	+	0.446617i
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$		0			0
$43$	−2.96790	+	5.14055i	−0.452600	+	0.783927i	−0.998547	−	0.0538934i	$-0.982837\pi$
$43$	−2.96790	+	5.14055i	−0.452600	+	0.783927i	0.545946	+	0.837820i	$0.316170\pi$
$44$		0			0
$45$	−6.81386	+	2.05446i	−1.01575	+	0.306260i
$46$		0			0
$47$	−1.10489	+	1.91373i	−0.161165	+	0.279146i	−0.935287	−	0.353891i	$-0.884859\pi$
$47$	−1.10489	+	1.91373i	−0.161165	+	0.279146i	0.774122	+	0.633037i	$0.218192\pi$
$48$		0			0
$49$	1.05842	+	1.83324i	0.151203	+	0.261892i
$50$		0			0
$51$	−4.57820	+	3.62725i	−0.641076	+	0.507916i
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	−14.0814			−1.89873
$56$		0			0
$57$	5.05842	−	4.00772i	0.670004	−	0.530836i
$58$		0			0
$59$	−5.17769	−	8.96801i	−0.674077	−	1.16754i	−0.976738	−	0.214437i	$-0.931208\pi$
$59$	−5.17769	−	8.96801i	−0.674077	−	1.16754i	0.302661	−	0.953098i	$-0.402125\pi$
$60$		0			0
$61$	−7.55842	+	13.0916i	−0.967757	+	1.67620i	−0.265738	+	0.964045i	$0.585616\pi$
$61$	−7.55842	+	13.0916i	−0.967757	+	1.67620i	−0.702019	+	0.712159i	$0.747718\pi$
$62$		0			0
$63$	4.83090	+	4.53991i	0.608637	+	0.571975i
$64$		0			0
$65$	−5.18614	+	8.98266i	−0.643262	+	1.11416i
$66$		0			0
$67$	5.17769	+	8.96801i	0.632555	+	1.09562i	0.987028	+	0.160551i	$0.0513271\pi$
$67$	5.17769	+	8.96801i	0.632555	+	1.09562i	−0.354473	+	0.935066i	$0.615340\pi$
$68$		0			0
$69$	3.55842	+	1.40965i	0.428384	+	0.169701i
$70$		0			0
$71$	4.41957			0.524507			0.262253	−	0.964999i	$-0.415534\pi$
$71$	4.41957			0.524507			0.262253	+	0.964999i	$0.415534\pi$
$72$		0			0
$73$	4.62772			0.541634			0.270817	−	0.962631i	$-0.412706\pi$
$73$	4.62772			0.541634			0.270817	+	0.962631i	$0.412706\pi$
$74$		0			0
$75$	−0.158627	−	1.07561i	−0.0183167	−	0.124200i
$76$		0			0
$77$	6.55842	+	11.3595i	0.747402	+	1.29454i
$78$		0			0
$79$	4.83090	−	8.36737i	0.543519	−	0.941403i	−0.455179	−	0.890400i	$-0.650425\pi$
$79$	4.83090	−	8.36737i	0.543519	−	0.941403i	0.998698	−	0.0510030i	$-0.0162418\pi$
$80$		0			0
$81$	−8.05842	−	4.00772i	−0.895380	−	0.445302i
$82$		0			0
$83$	7.04069	−	12.1948i	0.772816	−	1.33856i	−0.163198	−	0.986593i	$-0.552181\pi$
$83$	7.04069	−	12.1948i	0.772816	−	1.33856i	0.936014	−	0.351963i	$-0.114486\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$		0			0
$87$	−0.0940770	−	0.637910i	−0.0100861	−	0.0683912i
$88$		0			0
$89$	1.25544			0.133076			0.0665380	−	0.997784i	$-0.478805\pi$
$89$	1.25544			0.133076			0.0665380	+	0.997784i	$0.478805\pi$
$90$		0			0
$91$	9.66181			1.01283
$92$		0			0
$93$	15.5584	+	6.16337i	1.61333	+	0.639111i
$94$		0			0
$95$	4.41957	+	7.65492i	0.453439	+	0.785379i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$		0			0
$99$	−12.9765	−	12.1948i	−1.30419	−	1.22563i
$100$		0			0
$101$	7.55842	−	13.0916i	0.752091	−	1.30266i	−0.194716	−	0.980860i	$-0.562379\pi$
$101$	7.55842	−	13.0916i	0.752091	−	1.30266i	0.946808	−	0.321800i	$-0.104288\pi$
$102$		0			0
$103$	1.10489	+	1.91373i	0.108868	+	0.188566i	0.915312	−	0.402745i	$-0.131944\pi$
$103$	1.10489	+	1.91373i	0.108868	+	0.188566i	−0.806444	+	0.591311i	$0.798611\pi$
$104$		0			0
$105$	−7.11684	+	5.63858i	−0.694533	+	0.550269i
$106$		0			0
$107$	−3.72601			−0.360207			−0.180104	−	0.983648i	$-0.557643\pi$
$107$	−3.72601			−0.360207			−0.180104	+	0.983648i	$0.557643\pi$
$108$		0			0
$109$	17.4891			1.67515			0.837577	−	0.546319i	$-0.183971\pi$
$109$	17.4891			1.67515			0.837577	+	0.546319i	$0.183971\pi$
$110$		0			0
$111$	−5.43039	+	4.30243i	−0.515430	+	0.408368i
$112$		0			0
$113$	−5.81386	−	10.0699i	−0.546922	−	0.947296i	−0.998483	−	0.0550564i	$-0.982466\pi$
$113$	−5.81386	−	10.0699i	−0.546922	−	0.947296i	0.451561	−	0.892240i	$-0.350867\pi$
$114$		0			0
$115$	−2.62112	+	4.53991i	−0.244420	+	0.423349i
$116$		0			0
$117$	−12.5584	+	3.78651i	−1.16103	+	0.350063i
$118$		0			0
$119$	−3.72601	+	6.45364i	−0.341563	+	0.591604i
$120$		0			0
$121$	−12.1168	−	20.9870i	−1.10153	−	1.90791i
$122$		0			0
$123$	1.61030	+	0.637910i	0.145196	+	0.0575184i
$124$		0			0
$125$	−10.3723			−0.927725
$126$		0			0
$127$	7.45202			0.661260			0.330630	−	0.943760i	$-0.392739\pi$
$127$	7.45202			0.661260			0.330630	+	0.943760i	$0.392739\pi$
$128$		0			0
$129$	−1.50000	−	10.1711i	−0.132068	−	0.895515i
$130$		0			0
$131$	4.83090	+	8.36737i	0.422078	+	0.731061i	0.996143	−	0.0877494i	$-0.0279675\pi$
$131$	4.83090	+	8.36737i	0.422078	+	0.731061i	−0.574065	+	0.818810i	$0.694634\pi$
$132$		0			0
$133$	4.11684	−	7.13058i	0.356976	−	0.618300i
$134$		0			0
$135$	7.04069	−	10.1182i	0.605966	−	0.870832i
$136$		0			0
$137$	6.24456	−	10.8159i	0.533509	−	0.924065i	−0.465725	−	0.884930i	$-0.654206\pi$
$137$	6.24456	−	10.8159i	0.533509	−	0.924065i	0.999234	−	0.0391351i	$-0.0124603\pi$
$138$		0			0
$139$	−1.45167	−	2.51437i	−0.123129	−	0.213266i	0.797871	−	0.602829i	$-0.205960\pi$
$139$	−1.45167	−	2.51437i	−0.123129	−	0.213266i	−0.921000	+	0.389562i	$0.872626\pi$
$140$		0			0
$141$	−0.558422	−	3.78651i	−0.0470276	−	0.318881i
$142$		0			0
$143$	−25.9530			−2.17030
$144$		0			0
$145$	0.883156			0.0733421
$146$		0			0
$147$	−3.40876	−	1.35036i	−0.281150	−	0.111376i
$148$		0			0
$149$	5.81386	+	10.0699i	0.476290	+	0.824958i	0.999631	−	0.0271650i	$-0.00864795\pi$
$149$	5.81386	+	10.0699i	0.476290	+	0.824958i	−0.523341	+	0.852123i	$0.675315\pi$
$150$		0			0
$151$	1.10489	−	1.91373i	0.0899149	−	0.155737i	−0.817560	−	0.575843i	$-0.804674\pi$
$151$	1.10489	−	1.91373i	0.0899149	−	0.155737i	0.907475	+	0.420106i	$0.138007\pi$
$152$		0			0
$153$	2.31386	−	9.84868i	0.187064	−	0.796219i
$154$		0			0
$155$	−11.4603	+	19.8498i	−0.920510	+	1.59437i
$156$		0			0
$157$	1.55842	+	2.69927i	0.124376	+	0.215425i	0.921489	−	0.388405i	$-0.126974\pi$
$157$	1.55842	+	2.69927i	0.124376	+	0.215425i	−0.797113	+	0.603830i	$0.793641\pi$
$158$		0			0
$159$	5.43039	−	4.30243i	0.430658	−	0.341205i
$160$		0			0
$161$	4.88316			0.384847
$162$		0			0
$163$	8.83915			0.692335			0.346168	−	0.938173i	$-0.387483\pi$
$163$	8.83915			0.692335			0.346168	+	0.938173i	$0.387483\pi$
$164$		0			0
$165$	19.1168	−	15.1460i	1.48824	−	1.17912i
$166$		0			0
$167$	4.83090	+	8.36737i	0.373827	+	0.647487i	0.990151	−	0.140006i	$-0.0447122\pi$
$167$	4.83090	+	8.36737i	0.373827	+	0.647487i	−0.616324	+	0.787493i	$0.711379\pi$
$168$		0			0
$169$	−3.05842	+	5.29734i	−0.235263	+	0.407488i
$170$		0			0
$171$	−2.55657	+	10.8817i	−0.195506	+	0.832148i
$172$		0			0
$173$	0.186141	−	0.322405i	0.0141520	−	0.0245120i	−0.858863	−	0.512206i	$-0.828828\pi$
$173$	0.186141	−	0.322405i	0.0141520	−	0.0245120i	0.873015	+	0.487694i	$0.162162\pi$
$174$		0			0
$175$	−0.693562	−	1.20128i	−0.0524284	−	0.0908086i
$176$		0			0
$177$	16.6753	+	6.60580i	1.25339	+	0.496522i
$178$		0			0
$179$	8.83915			0.660669			0.330334	−	0.943864i	$-0.392838\pi$
$179$	8.83915			0.660669			0.330334	+	0.943864i	$0.392838\pi$
$180$		0			0
$181$	−8.23369			−0.612005			−0.306003	−	0.952031i	$-0.598992\pi$
$181$	−8.23369			−0.612005			−0.306003	+	0.952031i	$0.598992\pi$
$182$		0			0
$183$	−3.82009	−	25.9030i	−0.282389	−	1.91480i
$184$		0			0
$185$	−4.74456	−	8.21782i	−0.348827	−	0.604186i
$186$		0			0
$187$	10.0086	−	17.3354i	0.731901	−	1.26769i
$188$		0			0
$189$	−11.4416	−	0.967215i	−0.832252	−	0.0703546i
$190$		0			0
$191$	−8.55691	+	14.8210i	−0.619157	+	1.07241i	0.370483	+	0.928839i	$0.379192\pi$
$191$	−8.55691	+	14.8210i	−0.619157	+	1.07241i	−0.989640	+	0.143572i	$0.954141\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$		0			0
$195$	−2.62112	−	17.7731i	−0.187702	−	1.27276i
$196$		0			0
$197$	0.744563			0.0530479			0.0265239	−	0.999648i	$-0.491556\pi$
$197$	0.744563			0.0530479			0.0265239	+	0.999648i	$0.491556\pi$
$198$		0			0
$199$	20.7107			1.46815			0.734073	−	0.679071i	$-0.237617\pi$
$199$	20.7107			1.46815			0.734073	+	0.679071i	$0.237617\pi$
$200$		0			0
$201$	−16.6753	−	6.60580i	−1.17618	−	0.465937i
$202$		0			0
$203$	−0.411331	−	0.712446i	−0.0288698	−	0.0500039i
$204$		0			0
$205$	−1.18614	+	2.05446i	−0.0828437	+	0.143489i
$206$		0			0
$207$	−6.34713	+	1.91373i	−0.441156	+	0.133014i
$208$		0			0
$209$	−11.0584	+	19.1537i	−0.764927	+	1.32489i
$210$		0			0
$211$	2.62112	+	4.53991i	0.180445	+	0.312540i	0.942032	−	0.335522i	$-0.108913\pi$
$211$	2.62112	+	4.53991i	0.180445	+	0.312540i	−0.761587	+	0.648063i	$0.775579\pi$
$212$		0			0
$213$	−6.00000	+	4.75372i	−0.411113	+	0.325720i
$214$		0			0
$215$	14.0814			0.960342
$216$		0			0
$217$	21.3505			1.44937
$218$		0			0
$219$	−6.28258	+	4.97760i	−0.424537	+	0.336355i
$220$		0			0
$221$	−7.37228	−	12.7692i	−0.495913	−	0.858947i
$222$		0			0
$223$	−1.10489	+	1.91373i	−0.0739891	+	0.128153i	−0.900646	−	0.434553i	$-0.856906\pi$
$223$	−1.10489	+	1.91373i	−0.0739891	+	0.128153i	0.826657	+	0.562706i	$0.190240\pi$
$224$		0			0
$225$	1.37228	+	1.28962i	0.0914854	+	0.0859747i
$226$		0			0
$227$	−4.48412	+	7.76673i	−0.297622	+	0.515496i	−0.975591	−	0.219594i	$-0.929527\pi$
$227$	−4.48412	+	7.76673i	−0.297622	+	0.515496i	0.677970	+	0.735090i	$0.262860\pi$
$228$		0			0
$229$	2.18614	+	3.78651i	0.144464	+	0.250219i	0.929173	−	0.369645i	$-0.120521\pi$
$229$	2.18614	+	3.78651i	0.144464	+	0.250219i	−0.784709	+	0.619865i	$0.787187\pi$
$230$		0			0
$231$	−21.1221	−	8.36737i	−1.38973	−	0.550533i
$232$		0			0
$233$	2.86141			0.187457			0.0937285	−	0.995598i	$-0.470121\pi$
$233$	2.86141			0.187457			0.0937285	+	0.995598i	$0.470121\pi$
$234$		0			0
$235$	5.24224			0.341966
$236$		0			0
$237$	2.44158	+	16.5557i	0.158598	+	1.07541i
$238$		0			0
$239$	−8.55691	−	14.8210i	−0.553501	−	0.958692i	−0.998018	−	0.0629214i	$-0.979958\pi$
$239$	−8.55691	−	14.8210i	−0.553501	−	0.958692i	0.444518	−	0.895770i	$-0.353375\pi$
$240$		0			0
$241$	−0.127719	+	0.221215i	−0.00822708	+	0.0142497i	−0.870110	−	0.492858i	$-0.835952\pi$
$241$	−0.127719	+	0.221215i	−0.00822708	+	0.0142497i	0.861883	+	0.507108i	$0.169285\pi$
$242$		0			0
$243$	15.2508	−	3.22682i	0.978341	−	0.207001i
$244$		0			0
$245$	2.51087	−	4.34896i	0.160414	−	0.277845i
$246$		0			0
$247$	8.14558	+	14.1086i	0.518291	+	0.897706i
$248$		0			0
$249$	3.55842	+	24.1287i	0.225506	+	1.52909i
$250$		0			0
$251$	−11.1780			−0.705551			−0.352776	−	0.935708i	$-0.614762\pi$
$251$	−11.1780			−0.705551			−0.352776	+	0.935708i	$0.614762\pi$
$252$		0			0
$253$	−13.1168			−0.824649
$254$		0			0
$255$	12.8824	+	5.10328i	0.806728	+	0.319580i
$256$		0			0
$257$	3.24456	+	5.61975i	0.202390	+	0.350550i	0.949298	−	0.314377i	$-0.101796\pi$
$257$	3.24456	+	5.61975i	0.202390	+	0.350550i	−0.746908	+	0.664928i	$0.768462\pi$
$258$		0			0
$259$	−4.41957	+	7.65492i	−0.274619	+	0.475654i
$260$		0			0
$261$	0.813859	+	0.764836i	0.0503766	+	0.0473421i
$262$		0			0
$263$	8.55691	−	14.8210i	0.527642	−	0.913903i	−0.471839	−	0.881685i	$-0.656410\pi$
$263$	8.55691	−	14.8210i	0.527642	−	0.913903i	0.999481	−	0.0322179i	$-0.0102571\pi$
$264$		0			0
$265$	4.74456	+	8.21782i	0.291456	+	0.504817i
$266$		0			0
$267$	−1.70438	+	1.35036i	−0.104306	+	0.0826405i
$268$		0			0
$269$	9.48913			0.578562			0.289281	−	0.957244i	$-0.406584\pi$
$269$	9.48913			0.578562			0.289281	+	0.957244i	$0.406584\pi$
$270$		0			0
$271$	14.9040			0.905356			0.452678	−	0.891674i	$-0.350469\pi$
$271$	14.9040			0.905356			0.452678	+	0.891674i	$0.350469\pi$
$272$		0			0
$273$	−13.1168	+	10.3923i	−0.793868	+	0.628971i
$274$		0			0
$275$	1.86301	+	3.22682i	0.112343	+	0.194585i
$276$		0			0
$277$	−6.55842	+	11.3595i	−0.394057	+	0.682527i	−0.992980	−	0.118279i	$-0.962262\pi$
$277$	−6.55842	+	11.3595i	−0.394057	+	0.682527i	0.598923	+	0.800807i	$0.295596\pi$
$278$		0			0
$279$	−27.7514	+	8.36737i	−1.66143	+	0.500941i
$280$		0			0
$281$	−12.9307	+	22.3966i	−0.771381	+	1.33607i	0.165425	+	0.986222i	$0.447100\pi$
$281$	−12.9307	+	22.3966i	−0.771381	+	1.33607i	−0.936806	+	0.349849i	$0.886233\pi$
$282$		0			0
$283$	−2.62112	−	4.53991i	−0.155809	−	0.269870i	0.777544	−	0.628828i	$-0.216465\pi$
$283$	−2.62112	−	4.53991i	−0.155809	−	0.269870i	−0.933353	+	0.358959i	$0.883132\pi$
$284$		0			0
$285$	−14.2337	−	5.63858i	−0.843131	−	0.334001i
$286$		0			0
$287$	2.20979			0.130440
$288$		0			0
$289$	−5.62772			−0.331042
$290$		0			0
$291$	−2.27434	−	15.4217i	−0.133324	−	0.904033i
$292$		0			0
$293$	10.1861	+	17.6429i	0.595081	+	1.03071i	0.993535	+	0.113522i	$0.0362132\pi$
$293$	10.1861	+	17.6429i	0.595081	+	1.03071i	−0.398455	+	0.917188i	$0.630453\pi$
$294$		0			0
$295$	−12.2829	+	21.2747i	−0.715140	+	1.23866i
$296$		0			0
$297$	30.7337	+	2.59808i	1.78335	+	0.150756i
$298$		0			0
$299$	−4.83090	+	8.36737i	−0.279378	+	0.483898i
$300$		0			0
$301$	−6.55842	−	11.3595i	−0.378021	−	0.654752i
$302$		0			0
$303$	3.82009	+	25.9030i	0.219458	+	1.48809i
$304$		0			0
$305$	35.8614			2.05342
$306$		0			0
$307$	−28.8563			−1.64692			−0.823459	−	0.567376i	$-0.807959\pi$
$307$	−28.8563			−1.64692			−0.823459	+	0.567376i	$0.807959\pi$
$308$		0			0
$309$	−3.55842	−	1.40965i	−0.202432	−	0.0801919i
$310$		0			0
$311$	6.34713	+	10.9935i	0.359913	+	0.623387i	0.987946	−	0.154800i	$-0.0494732\pi$
$311$	6.34713	+	10.9935i	0.359913	+	0.623387i	−0.628033	+	0.778186i	$0.716140\pi$
$312$		0			0
$313$	−9.61684	+	16.6569i	−0.543576	+	0.941502i	0.455119	+	0.890431i	$0.349597\pi$
$313$	−9.61684	+	16.6569i	−0.543576	+	0.941502i	−0.998695	+	0.0510708i	$0.983737\pi$
$314$		0			0
$315$	3.59691	−	15.3098i	0.202663	−	0.862612i
$316$		0			0
$317$	−4.18614	+	7.25061i	−0.235117	+	0.407235i	−0.959307	−	0.282366i	$-0.908881\pi$
$317$	−4.18614	+	7.25061i	−0.235117	+	0.407235i	0.724190	+	0.689601i	$0.242214\pi$
$318$		0			0
$319$	1.10489	+	1.91373i	0.0618621	+	0.107148i
$320$		0			0
$321$	5.05842	−	4.00772i	0.282334	−	0.223689i
$322$		0			0
$323$	−12.5652			−0.699144
$324$		0			0
$325$	2.74456			0.152241
$326$		0			0
$327$	−23.7432	+	18.8114i	−1.31300	+	1.04027i
$328$		0			0
$329$	−2.44158	−	4.22894i	−0.134609	−	0.233149i
$330$		0			0
$331$	16.7025	−	28.9296i	0.918052	−	1.59011i	0.115682	−	0.993286i	$-0.463095\pi$
$331$	16.7025	−	28.9296i	0.918052	−	1.59011i	0.802370	−	0.596827i	$-0.203572\pi$
$332$		0			0
$333$	2.74456	−	11.6819i	0.150401	−	0.640166i
$334$		0			0
$335$	12.2829	−	21.2747i	0.671088	−	1.16236i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$		0			0
$339$	18.7241	+	7.41744i	1.01696	+	0.402860i
$340$		0			0
$341$	−57.3505			−3.10571
$342$		0			0
$343$	−20.1463			−1.08780
$344$		0			0
$345$	−1.32473	−	8.98266i	−0.0713213	−	0.483610i
$346$		0			0
$347$	5.17769	+	8.96801i	0.277953	+	0.481428i	0.970876	−	0.239583i	$-0.0770108\pi$
$347$	5.17769	+	8.96801i	0.277953	+	0.481428i	−0.692923	+	0.721011i	$0.743677\pi$
$348$		0			0
$349$	11.5584	−	20.0198i	0.618708	−	1.07163i	−0.371014	−	0.928627i	$-0.620990\pi$
$349$	11.5584	−	20.0198i	0.618708	−	1.07163i	0.989722	−	0.143007i	$-0.0456770\pi$
$350$		0			0
$351$	12.9765	−	18.6485i	0.692634	−	0.995382i
$352$		0			0
$353$	9.61684	−	16.6569i	0.511853	−	0.886555i	−0.488053	−	0.872814i	$-0.662293\pi$
$353$	9.61684	−	16.6569i	0.511853	−	0.886555i	0.999906	−	0.0137411i	$-0.00437407\pi$
$354$		0			0
$355$	−5.24224	−	9.07982i	−0.278229	−	0.481907i
$356$		0			0
$357$	−1.88316	−	12.7692i	−0.0996672	−	0.675816i
$358$		0			0
$359$	22.3561			1.17991			0.589954	−	0.807437i	$-0.299146\pi$
$359$	22.3561			1.17991			0.589954	+	0.807437i	$0.299146\pi$
$360$		0			0
$361$	−5.11684			−0.269308
$362$		0			0
$363$	39.0235	+	15.4589i	2.04820	+	0.811383i
$364$		0			0
$365$	−5.48913	−	9.50744i	−0.287314	−	0.497642i
$366$		0			0
$367$	13.6700	−	23.6772i	0.713571	−	1.23594i	−0.249937	−	0.968262i	$-0.580410\pi$
$367$	13.6700	−	23.6772i	0.713571	−	1.23594i	0.963508	−	0.267679i	$-0.0862566\pi$
$368$		0			0
$369$	−2.87228	+	0.866025i	−0.149525	+	0.0450835i
$370$		0			0
$371$	4.41957	−	7.65492i	0.229453	−	0.397424i
$372$		0			0
$373$	8.55842	+	14.8236i	0.443138	+	0.767538i	0.997920	−	0.0644576i	$-0.0205317\pi$
$373$	8.55842	+	14.8236i	0.443138	+	0.767538i	−0.554782	+	0.831996i	$0.687198\pi$
$374$		0			0
$375$	14.0814	−	11.1565i	0.727159	−	0.576119i
$376$		0			0
$377$	1.62772			0.0838318
$378$		0			0
$379$	−8.14558			−0.418411			−0.209205	−	0.977872i	$-0.567088\pi$
$379$	−8.14558			−0.418411			−0.209205	+	0.977872i	$0.567088\pi$
$380$		0			0
$381$	−10.1168	+	8.01544i	−0.518302	+	0.410644i
$382$		0			0
$383$	−11.4603	−	19.8498i	−0.585592	−	1.01428i	−0.994801	−	0.101835i	$-0.967529\pi$
$383$	−11.4603	−	19.8498i	−0.585592	−	1.01428i	0.409209	−	0.912441i	$-0.365805\pi$
$384$		0			0
$385$	15.5584	−	26.9480i	0.792931	−	1.37340i
$386$		0			0
$387$	12.9765	+	12.1948i	0.659632	+	0.619898i
$388$		0			0
$389$	9.67527	−	16.7581i	0.490555	−	0.849667i	−0.509385	−	0.860538i	$-0.670127\pi$
$389$	9.67527	−	16.7581i	0.490555	−	0.849667i	0.999941	+	0.0108715i	$0.00346057\pi$
$390$		0			0
$391$	−3.72601	−	6.45364i	−0.188432	−	0.326375i
$392$		0			0
$393$	−15.5584	−	6.16337i	−0.784819	−	0.310901i
$394$		0			0
$395$	−22.9205			−1.15326
$396$		0			0
$397$	−4.00000			−0.200754			−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000			−0.200754			−0.100377	+	0.994949i	$0.532005\pi$
$398$		0			0
$399$	2.08069	+	14.1086i	0.104165	+	0.706312i
$400$		0			0
$401$	−13.9891	−	24.2299i	−0.698584	−	1.20998i	−0.968958	−	0.247227i	$-0.920481\pi$
$401$	−13.9891	−	24.2299i	−0.698584	−	1.20998i	0.270374	−	0.962755i	$-0.412853\pi$
$402$		0			0
$403$	−21.1221	+	36.5845i	−1.05217	+	1.82240i
$404$		0			0
$405$	1.32473	+	21.3094i	0.0658266	+	1.05887i
$406$		0			0
$407$	11.8716	−	20.5622i	0.588453	−	1.01923i
$408$		0			0
$409$	9.12772	+	15.8097i	0.451337	+	0.781738i	0.998469	−	0.0553079i	$-0.0176140\pi$
$409$	9.12772	+	15.8097i	0.451337	+	0.781738i	−0.547133	+	0.837046i	$0.684281\pi$
$410$		0			0
$411$	3.15605	+	21.4003i	0.155677	+	1.05560i
$412$		0			0
$413$	22.8832			1.12601
$414$		0			0
$415$	−33.4050			−1.63979
$416$		0			0
$417$	4.67527	+	1.85208i	0.228949	+	0.0906966i
$418$		0			0
$419$	2.62112	+	4.53991i	0.128050	+	0.221789i	0.922921	−	0.384989i	$-0.125795\pi$
$419$	2.62112	+	4.53991i	0.128050	+	0.221789i	−0.794871	+	0.606778i	$0.792462\pi$
$420$		0			0
$421$	11.1861	−	19.3750i	0.545179	−	0.944278i	−0.453416	−	0.891299i	$-0.649795\pi$
$421$	11.1861	−	19.3750i	0.545179	−	0.944278i	0.998596	−	0.0529792i	$-0.0168717\pi$
$422$		0			0
$423$	4.83090	+	4.53991i	0.234887	+	0.220738i
$424$		0			0
$425$	−1.05842	+	1.83324i	−0.0513410	+	0.0889252i
$426$		0			0
$427$	−16.7025	−	28.9296i	−0.808291	−	1.40000i
$428$		0			0
$429$	35.2337	−	27.9152i	1.70110	−	1.34776i
$430$		0			0
$431$	7.45202			0.358951			0.179476	−	0.983762i	$-0.442560\pi$
$431$	7.45202			0.358951			0.179476	+	0.983762i	$0.442560\pi$
$432$		0			0
$433$	−18.1168			−0.870640			−0.435320	−	0.900276i	$-0.643365\pi$
$433$	−18.1168			−0.870640			−0.435320	+	0.900276i	$0.643365\pi$
$434$		0			0
$435$	−1.19897	+	0.949929i	−0.0574862	+	0.0455456i
$436$		0			0
$437$	4.11684	+	7.13058i	0.196935	+	0.341102i
$438$		0			0
$439$	−11.4603	+	19.8498i	−0.546969	+	0.947377i	0.451512	+	0.892265i	$0.350885\pi$
$439$	−11.4603	+	19.8498i	−0.546969	+	0.947377i	−0.998480	+	0.0551120i	$0.982448\pi$
$440$		0			0
$441$	6.08017	−	1.83324i	0.289532	−	0.0872972i
$442$		0			0
$443$	4.48412	−	7.76673i	0.213047	−	0.369008i	−0.739620	−	0.673025i	$-0.764995\pi$
$443$	4.48412	−	7.76673i	0.213047	−	0.369008i	0.952667	+	0.304017i	$0.0983279\pi$
$444$		0			0
$445$	−1.48913	−	2.57924i	−0.0705913	−	0.122268i
$446$		0			0
$447$	−18.7241	−	7.41744i	−0.885621	−	0.350833i
$448$		0			0
$449$	−18.1168			−0.854987			−0.427493	−	0.904018i	$-0.640603\pi$
$449$	−18.1168			−0.854987			−0.427493	+	0.904018i	$0.640603\pi$
$450$		0			0
$451$	−5.93580			−0.279506
$452$		0			0
$453$	0.558422	+	3.78651i	0.0262370	+	0.177906i
$454$		0			0
$455$	−11.4603	−	19.8498i	−0.537265	−	0.930571i
$456$		0			0
$457$	12.9891	−	22.4978i	0.607606	−	1.05240i	−0.384028	−	0.923321i	$-0.625463\pi$
$457$	12.9891	−	22.4978i	0.607606	−	1.05240i	0.991634	−	0.129083i	$-0.0412032\pi$
$458$		0			0
$459$	7.45202	+	15.8593i	0.347831	+	0.740251i
$460$		0			0
$461$	14.5584	−	25.2159i	0.678053	−	1.17442i	−0.297513	−	0.954718i	$-0.596157\pi$
$461$	14.5584	−	25.2159i	0.678053	−	1.17442i	0.975566	−	0.219705i	$-0.0705095\pi$
$462$		0			0
$463$	18.9123	+	32.7570i	0.878928	+	1.52235i	0.852518	+	0.522697i	$0.175074\pi$
$463$	18.9123	+	32.7570i	0.878928	+	1.52235i	0.0264102	+	0.999651i	$0.491592\pi$
$464$		0			0
$465$	−5.79211	−	39.2747i	−0.268603	−	1.82132i
$466$		0			0
$467$	36.3083			1.68015			0.840075	−	0.542470i	$-0.182511\pi$
$467$	36.3083			1.68015			0.840075	+	0.542470i	$0.182511\pi$
$468$		0			0
$469$	−22.8832			−1.05665
$470$		0			0
$471$	−5.01906	−	1.98827i	−0.231266	−	0.0916145i
$472$		0			0
$473$	17.6168	+	30.5133i	0.810023	+	1.40300i
$474$		0			0
$475$	1.16944	−	2.02554i	0.0536577	−	0.0929379i
$476$		0			0
$477$	−2.74456	+	11.6819i	−0.125665	+	0.534879i
$478$		0			0
$479$	1.10489	−	1.91373i	0.0504839	−	0.0874406i	−0.839679	−	0.543083i	$-0.817257\pi$
$479$	1.10489	−	1.91373i	0.0504839	−	0.0874406i	0.890163	+	0.455642i	$0.150590\pi$
$480$		0			0
$481$	−8.74456	−	15.1460i	−0.398718	−	0.690599i
$482$		0			0
$483$	−6.62936	+	5.25236i	−0.301646	+	0.238990i
$484$		0			0
$485$	21.3505			0.969478
$486$		0			0
$487$	7.45202			0.337683			0.168842	−	0.985643i	$-0.445997\pi$
$487$	7.45202			0.337683			0.168842	+	0.985643i	$0.445997\pi$
$488$		0			0
$489$	−12.0000	+	9.50744i	−0.542659	+	0.429941i
$490$		0			0
$491$	−0.0645501	−	0.111804i	−0.00291310	−	0.00504564i	0.864565	−	0.502521i	$-0.167594\pi$
$491$	−0.0645501	−	0.111804i	−0.00291310	−	0.00504564i	−0.867478	+	0.497475i	$0.834261\pi$
$492$		0			0
$493$	−0.627719	+	1.08724i	−0.0282710	+	0.0489669i
$494$		0			0
$495$	−9.66181	+	41.1244i	−0.434266	+	1.84840i
$496$		0			0
$497$	−4.88316	+	8.45787i	−0.219039	+	0.379388i
$498$		0			0
$499$	−12.6297	−	21.8753i	−0.565383	−	0.979273i	−0.997014	−	0.0772222i	$-0.975395\pi$
$499$	−12.6297	−	21.8753i	−0.565383	−	0.979273i	0.431631	−	0.902050i	$-0.357938\pi$
$500$		0			0
$501$	−15.5584	−	6.16337i	−0.695099	−	0.275359i
$502$		0			0
$503$	10.4845			0.467479			0.233740	−	0.972299i	$-0.424904\pi$
$503$	10.4845			0.467479			0.233740	+	0.972299i	$0.424904\pi$
$504$		0			0
$505$	−35.8614			−1.59581
$506$		0			0
$507$	−1.54575	−	10.4813i	−0.0686492	−	0.465492i
$508$		0			0
$509$	6.67527	+	11.5619i	0.295876	+	0.512472i	0.975188	−	0.221377i	$-0.0710552\pi$
$509$	6.67527	+	11.5619i	0.295876	+	0.512472i	−0.679312	+	0.733849i	$0.737722\pi$
$510$		0			0
$511$	−5.11313	+	8.85621i	−0.226192	+	0.391776i
$512$		0			0
$513$	−8.23369	−	17.5229i	−0.363526	−	0.773654i
$514$		0			0
$515$	2.62112	−	4.53991i	0.115500	−	0.200052i
$516$		0			0
$517$	6.55842	+	11.3595i	0.288439	+	0.499591i
$518$		0			0
$519$	0.0940770	+	0.637910i	0.00412952	+	0.0280012i
$520$		0			0
$521$	−16.3505			−0.716330			−0.358165	−	0.933658i	$-0.616597\pi$
$521$	−16.3505			−0.716330			−0.358165	+	0.933658i	$0.616597\pi$
$522$		0			0
$523$	−19.3236			−0.844963			−0.422481	−	0.906372i	$-0.638841\pi$
$523$	−19.3236			−0.844963			−0.422481	+	0.906372i	$0.638841\pi$
$524$		0			0
$525$	2.23369	+	0.884861i	0.0974861	+	0.0386185i
$526$		0			0
$527$	−16.2912	−	28.2171i	−0.709654	−	1.22916i
$528$		0			0
$529$	9.05842	−	15.6896i	0.393844	−	0.682159i
$530$		0			0
$531$	−29.7435	+	8.96801i	−1.29076	+	0.389179i
$532$		0			0
$533$	−2.18614	+	3.78651i	−0.0946923	+	0.164012i
$534$		0			0
$535$	4.41957	+	7.65492i	0.191075	+	0.330951i
$536$		0			0
$537$	−12.0000	+	9.50744i	−0.517838	+	0.410276i
$538$		0			0
$539$	12.5652			0.541220
$540$		0			0
$541$	8.74456			0.375958			0.187979	−	0.982173i	$-0.439806\pi$
$541$	8.74456			0.375958			0.187979	+	0.982173i	$0.439806\pi$
$542$		0			0
$543$	11.1780	−	8.85621i	0.479695	−	0.380056i
$544$		0			0
$545$	−20.7446	−	35.9306i	−0.888599	−	1.53910i
$546$		0			0
$547$	−0.758112	+	1.31309i	−0.0324145	+	0.0561436i	−0.881778	−	0.471665i	$-0.843653\pi$
$547$	−0.758112	+	1.31309i	−0.0324145	+	0.0561436i	0.849363	+	0.527809i	$0.176986\pi$
$548$		0			0
$549$	33.0475	+	31.0569i	1.41043	+	1.32548i
$550$		0			0
$551$	0.693562	−	1.20128i	0.0295467	−	0.0511765i
$552$		0			0
$553$	10.6753	+	18.4901i	0.453958	+	0.786279i
$554$		0			0
$555$	15.2804	+	6.05321i	0.648615	+	0.256945i
$556$		0			0
$557$	−18.7446			−0.794233			−0.397116	−	0.917768i	$-0.629989\pi$
$557$	−18.7446			−0.794233			−0.397116	+	0.917768i	$0.629989\pi$
$558$		0			0
$559$	25.9530			1.09769
$560$		0			0
$561$	5.05842	+	34.2998i	0.213567	+	1.44814i
$562$		0			0
$563$	−11.1135	−	19.2491i	−0.468377	−	0.811254i	0.530969	−	0.847391i	$-0.321828\pi$
$563$	−11.1135	−	19.2491i	−0.468377	−	0.811254i	−0.999347	+	0.0361375i	$0.988495\pi$
$564$		0			0
$565$	−13.7921	+	23.8886i	−0.580238	+	1.00500i
$566$		0			0
$567$	16.5734	−	10.9935i	0.696017	−	0.461686i
$568$		0			0
$569$	19.8723	−	34.4198i	0.833089	−	1.44295i	−0.0624872	−	0.998046i	$-0.519903\pi$
$569$	19.8723	−	34.4198i	0.833089	−	1.44295i	0.895577	−	0.444907i	$-0.146763\pi$
$570$		0			0
$571$	0.0645501	+	0.111804i	0.00270134	+	0.00467885i	0.867373	−	0.497659i	$-0.165807\pi$
$571$	0.0645501	+	0.111804i	0.00270134	+	0.00467885i	−0.864672	+	0.502338i	$0.832473\pi$
$572$		0			0
$573$	−4.32473	−	29.3248i	−0.180668	−	1.22506i
$574$		0			0
$575$	1.38712			0.0578471
$576$		0			0
$577$	18.1168			0.754214			0.377107	−	0.926170i	$-0.376919\pi$
$577$	18.1168			0.754214			0.377107	+	0.926170i	$0.376919\pi$
$578$		0			0
$579$	1.61030	+	0.637910i	0.0669218	+	0.0265107i
$580$		0			0
$581$	15.5584	+	26.9480i	0.645472	+	1.11799i
$582$		0			0
$583$	−11.8716	+	20.5622i	−0.491671	+	0.851599i
$584$		0			0
$585$	22.6753	+	21.3094i	0.937507	+	0.881035i
$586$		0			0
$587$	5.87125	−	10.1693i	0.242332	−	0.419732i	−0.719046	−	0.694963i	$-0.755421\pi$
$587$	5.87125	−	10.1693i	0.242332	−	0.419732i	0.961378	+	0.275231i	$0.0887542\pi$
$588$		0			0
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$		0			0
$591$	−1.01082	+	0.800857i	−0.0415794	+	0.0329428i
$592$		0			0
$593$	−17.7228			−0.727789			−0.363894	−	0.931440i	$-0.618553\pi$
$593$	−17.7228			−0.727789			−0.363894	+	0.931440i	$0.618553\pi$
$594$		0			0
$595$	17.6783			0.724739
$596$		0			0
$597$	−28.1168	+	22.2766i	−1.15075	+	0.911721i
$598$		0			0
$599$	13.6700	+	23.6772i	0.558543	+	0.967425i	0.997618	+	0.0689747i	$0.0219728\pi$
$599$	13.6700	+	23.6772i	0.558543	+	0.967425i	−0.439075	+	0.898450i	$0.644694\pi$
$600$		0			0
$601$	1.38316	−	2.39570i	0.0564201	−	0.0977225i	−0.836436	−	0.548065i	$-0.815365\pi$
$601$	1.38316	−	2.39570i	0.0564201	−	0.0977225i	0.892856	+	0.450342i	$0.148698\pi$
$602$		0			0
$603$	29.7435	−	8.96801i	1.21125	−	0.365206i
$604$		0			0
$605$	−28.7446	+	49.7870i	−1.16863	+	2.02413i
$606$		0			0
$607$	−18.9123	−	32.7570i	−0.767626	−	1.32957i	−0.938847	−	0.344335i	$-0.888105\pi$
$607$	−18.9123	−	32.7570i	−0.767626	−	1.32957i	0.171221	−	0.985233i	$-0.445229\pi$
$608$		0			0
$609$	1.32473	+	0.524785i	0.0536809	+	0.0212654i
$610$		0			0
$611$	9.66181			0.390875
$612$		0			0
$613$	36.4674			1.47290			0.736452	−	0.676490i	$-0.236500\pi$
$613$	36.4674			1.47290			0.736452	+	0.676490i	$0.236500\pi$
$614$		0			0
$615$	−0.599485	−	4.06494i	−0.0241736	−	0.163914i
$616$		0			0
$617$	18.8723	+	32.6878i	0.759769	+	1.31596i	0.942968	+	0.332883i	$0.108022\pi$
$617$	18.8723	+	32.6878i	0.759769	+	1.31596i	−0.183199	+	0.983076i	$0.558645\pi$
$618$		0			0
$619$	−0.758112	+	1.31309i	−0.0304711	+	0.0527775i	−0.880859	−	0.473379i	$-0.843034\pi$
$619$	−0.758112	+	1.31309i	−0.0304711	+	0.0527775i	0.850388	+	0.526157i	$0.176367\pi$
$620$		0			0
$621$	6.55842	−	9.42509i	0.263180	−	0.378216i
$622$		0			0
$623$	−1.38712	+	2.40257i	−0.0555740	+	0.0962569i
$624$		0			0
$625$	13.8723	+	24.0275i	0.554891	+	0.961100i
$626$		0			0
$627$	−5.58902	−	37.8976i	−0.223204	−	1.51348i
$628$		0			0
$629$	13.4891			0.537847
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	−8.44158	−	3.34408i	−0.335523	−	0.132915i
$634$		0			0
$635$	−8.83915	−	15.3098i	−0.350771	−	0.607553i
$636$		0			0
$637$	4.62772	−	8.01544i	0.183357	−	0.317583i
$638$		0			0
$639$	3.03245	−	12.9073i	0.119962	−	0.510604i
$640$		0			0
$641$	−6.87228	+	11.9031i	−0.271439	+	0.470146i	−0.969230	−	0.246155i	$-0.920833\pi$
$641$	−6.87228	+	11.9031i	−0.271439	+	0.470146i	0.697792	+	0.716301i	$0.254166\pi$
$642$		0			0
$643$	8.90370	+	15.4217i	0.351127	+	0.608171i	0.986447	−	0.164079i	$-0.0524650\pi$
$643$	8.90370	+	15.4217i	0.351127	+	0.608171i	−0.635320	+	0.772249i	$0.719132\pi$
$644$		0			0
$645$	−19.1168	+	15.1460i	−0.752725	+	0.596374i
$646$		0			0
$647$	−40.0344			−1.57391			−0.786956	−	0.617009i	$-0.788344\pi$
$647$	−40.0344			−1.57391			−0.786956	+	0.617009i	$0.788344\pi$
$648$		0			0
$649$	−61.4674			−2.41281
$650$		0			0
$651$	−28.9854	+	22.9648i	−1.13603	+	0.900060i
$652$		0			0
$653$	−20.5584	−	35.6082i	−0.804513	−	1.39346i	−0.916619	−	0.399762i	$-0.869093\pi$
$653$	−20.5584	−	35.6082i	−0.804513	−	1.39346i	0.112106	−	0.993696i	$-0.464240\pi$
$654$		0			0
$655$	11.4603	−	19.8498i	0.447790	−	0.775594i
$656$		0			0
$657$	3.17527	−	13.5152i	0.123879	−	0.527277i
$658$		0			0
$659$	−15.8798	+	27.5047i	−0.618591	+	1.07143i	0.371153	+	0.928572i	$0.378963\pi$
$659$	−15.8798	+	27.5047i	−0.618591	+	1.07143i	−0.989743	+	0.142858i	$0.954371\pi$
$660$		0			0
$661$	1.55842	+	2.69927i	0.0606156	+	0.104989i	0.894741	−	0.446586i	$-0.147360\pi$
$661$	1.55842	+	2.69927i	0.0606156	+	0.104989i	−0.834125	+	0.551575i	$0.814027\pi$
$662$		0			0
$663$	23.7432	+	9.40571i	0.922109	+	0.365287i
$664$		0			0
$665$	−19.5326			−0.757443
$666$		0			0
$667$	0.822662			0.0318536
$668$		0			0
$669$	−0.558422	−	3.78651i	−0.0215898	−	0.146395i
$670$		0			0
$671$	44.8653	+	77.7089i	1.73200	+	2.99992i
$672$		0			0
$673$	−11.6753	+	20.2222i	−0.450048	+	0.779507i	−0.998388	−	0.0567487i	$-0.981927\pi$
$673$	−11.6753	+	20.2222i	−0.450048	+	0.779507i	0.548340	+	0.836255i	$0.315260\pi$
$674$		0			0
$675$	−3.25013	−	0.274750i	−0.125098	−	0.0105751i
$676$		0			0
$677$	−0.675266	+	1.16959i	−0.0259526	+	0.0449512i	−0.878710	−	0.477356i	$-0.841595\pi$
$677$	−0.675266	+	1.16959i	−0.0259526	+	0.0449512i	0.852757	+	0.522307i	$0.174929\pi$
$678$		0			0
$679$	−9.94404	−	17.2236i	−0.381617	−	0.660980i
$680$		0			0
$681$	−2.26631	−	15.3672i	−0.0868453	−	0.588874i
$682$		0			0
$683$	−36.3083			−1.38930			−0.694650	−	0.719348i	$-0.744441\pi$
$683$	−36.3083			−1.38930			−0.694650	+	0.719348i	$0.744441\pi$
$684$		0			0
$685$	−29.6277			−1.13202
$686$		0			0
$687$	−7.04069	−	2.78912i	−0.268619	−	0.106412i
$688$		0			0
$689$	8.74456	+	15.1460i	0.333141	+	0.577018i
$690$		0			0
$691$	23.3319	−	40.4120i	0.887586	−	1.53734i	0.0448646	−	0.998993i	$-0.485714\pi$
$691$	23.3319	−	40.4120i	0.887586	−	1.53734i	0.842721	−	0.538350i	$-0.180952\pi$
$692$		0			0
$693$	37.6753	−	11.3595i	1.43117	−	0.431512i
$694$		0			0
$695$	−3.44378	+	5.96480i	−0.130630	+	0.226258i
$696$		0			0
$697$	−1.68614	−	2.92048i	−0.0638671	−	0.110621i
$698$		0			0
$699$	−3.88464	+	3.07775i	−0.146930	+	0.116411i
$700$		0			0
$701$	34.7446			1.31228			0.656142	−	0.754637i	$-0.272187\pi$
$701$	34.7446			1.31228			0.656142	+	0.754637i	$0.272187\pi$
$702$		0			0
$703$	−14.9040			−0.562117
$704$		0			0
$705$	−7.11684	+	5.63858i	−0.268036	+	0.212361i
$706$		0			0
$707$	16.7025	+	28.9296i	0.628162	+	1.08801i
$708$		0			0
$709$	6.30298	−	10.9171i	0.236714	−	0.410000i	−0.723056	−	0.690790i	$-0.757263\pi$
$709$	6.30298	−	10.9171i	0.236714	−	0.410000i	0.959769	+	0.280790i	$0.0905964\pi$
$710$		0			0
$711$	−21.1221	−	19.8498i	−0.792140	−	0.744424i
$712$		0			0
$713$	−10.6753	+	18.4901i	−0.399792	+	0.692460i
$714$		0			0
$715$	30.7839	+	53.3192i	1.15125	+	1.99403i
$716$		0			0
$717$	27.5584	+	10.9171i	1.02919	+	0.407706i
$718$		0			0
$719$	−32.5823			−1.21512			−0.607558	−	0.794275i	$-0.707851\pi$
$719$	−32.5823			−1.21512			−0.607558	+	0.794275i	$0.707851\pi$
$720$		0			0
$721$	−4.88316			−0.181858
$722$		0			0
$723$	−0.0645501	−	0.437696i	−0.00240064	−	0.0162781i
$724$		0			0
$725$	−0.116844	−	0.202380i	−0.00433948	−	0.00751619i
$726$		0			0
$727$	17.3961	−	30.1309i	0.645184	−	1.11749i	−0.339075	−	0.940759i	$-0.610114\pi$
$727$	17.3961	−	30.1309i	0.645184	−	1.11749i	0.984259	−	0.176732i	$-0.0565527\pi$
$728$		0			0
$729$	−17.2337	+	20.7846i	−0.638285	+	0.769800i
$730$		0			0
$731$	−10.0086	+	17.3354i	−0.370181	+	0.641172i
$732$		0			0
$733$	−11.4416	−	19.8174i	−0.422604	−	0.731972i	0.573589	−	0.819143i	$-0.305551\pi$
$733$	−11.4416	−	19.8174i	−0.422604	−	0.731972i	−0.996193	+	0.0871711i	$0.972217\pi$
$734$		0			0
$735$	1.26902	+	8.60485i	0.0468084	+	0.317395i
$736$		0			0
$737$	61.4674			2.26418
$738$		0			0
$739$	15.5976			0.573767			0.286884	−	0.957965i	$-0.407381\pi$
$739$	15.5976			0.573767			0.286884	+	0.957965i	$0.407381\pi$
$740$		0			0
$741$	−26.2337	−	10.3923i	−0.963719	−	0.381771i
$742$		0			0
$743$	−13.7991	−	23.9008i	−0.506242	−	0.876836i	−0.999974	−	0.00722236i	$-0.997701\pi$
$743$	−13.7991	−	23.9008i	−0.506242	−	0.876836i	0.493732	−	0.869614i	$-0.335632\pi$
$744$		0			0
$745$	13.7921	−	23.8886i	0.505304	−	0.875212i
$746$		0			0
$747$	−30.7839	−	28.9296i	−1.12632	−	1.05848i
$748$		0			0
$749$	4.11684	−	7.13058i	0.150426	−	0.260546i
$750$		0			0
$751$	−11.4603	−	19.8498i	−0.418191	−	0.724328i	0.577567	−	0.816344i	$-0.304002\pi$
$751$	−11.4603	−	19.8498i	−0.418191	−	0.724328i	−0.995758	+	0.0920156i	$0.970669\pi$
$752$		0			0
$753$	15.1753	−	12.0232i	0.553017	−	0.438149i
$754$		0			0
$755$	−5.24224			−0.190784
$756$		0			0
$757$	−34.4674			−1.25274			−0.626369	−	0.779527i	$-0.715460\pi$
$757$	−34.4674			−1.25274			−0.626369	+	0.779527i	$0.715460\pi$
$758$		0			0
$759$	17.8074	−	14.1086i	0.646367	−	0.512108i
$760$		0			0
$761$	−10.1861	−	17.6429i	−0.369247	−	0.639555i	0.620201	−	0.784443i	$-0.287051\pi$
$761$	−10.1861	−	17.6429i	−0.369247	−	0.639555i	−0.989448	+	0.144888i	$0.953718\pi$
$762$		0			0
$763$	−19.3236	+	33.4695i	−0.699562	+	1.21168i
$764$		0			0
$765$	−22.9783	+	6.92820i	−0.830780	+	0.250490i
$766$		0			0
$767$	−22.6383	+	39.2107i	−0.817421	+	1.41582i
$768$		0			0
$769$	7.44158	+	12.8892i	0.268350	+	0.464796i	0.968436	−	0.249263i	$-0.0801882\pi$
$769$	7.44158	+	12.8892i	0.268350	+	0.464796i	−0.700086	+	0.714059i	$0.746855\pi$
$770$		0			0
$771$	−10.4494	−	4.13948i	−0.376328	−	0.149080i
$772$		0			0
$773$	−18.7446			−0.674195			−0.337098	−	0.941470i	$-0.609445\pi$
$773$	−18.7446			−0.674195			−0.337098	+	0.941470i	$0.609445\pi$
$774$		0			0
$775$	6.06490			0.217858
$776$		0			0
$777$	−2.23369	−	15.1460i	−0.0801331	−	0.543361i
$778$		0			0
$779$	1.86301	+	3.22682i	0.0667491	+	0.115613i
$780$		0			0
$781$	13.1168	−	22.7190i	0.469358	−	0.812951i
$782$		0			0
$783$	−1.92756	−	0.162946i	−0.0688852	−	0.00582322i
$784$		0			0
$785$	3.69702	−	6.40342i	0.131952	−	0.228548i
$786$		0			0
$787$	21.1221	+	36.5845i	0.752921	+	1.30410i	0.946402	+	0.322993i	$0.104689\pi$
$787$	21.1221	+	36.5845i	0.752921	+	1.30410i	−0.193481	+	0.981104i	$0.561978\pi$
$788$		0			0
$789$	4.32473	+	29.3248i	0.153965	+	1.04399i
$790$		0			0
$791$	25.6948			0.913601
$792$		0			0
$793$	66.0951			2.34711
$794$		0			0
$795$	−15.2804	−	6.05321i	−0.541938	−	0.214685i
$796$		0			0
$797$	−23.0475	−	39.9195i	−0.816386	−	1.41402i	−0.908328	−	0.418258i	$-0.862641\pi$
$797$	−23.0475	−	39.9195i	−0.816386	−	1.41402i	0.0919424	−	0.995764i	$-0.470692\pi$
$798$		0			0
$799$	−3.72601	+	6.45364i	−0.131817	+	0.228313i
$800$		0			0
$801$	0.861407	−	3.66648i	0.0304363	−	0.129549i
$802$		0			0
$803$	13.7346	−	23.7890i	0.484683	−	0.839496i
$804$		0			0
$805$	−5.79211	−	10.0322i	−0.204145	−	0.353590i
$806$		0			0
$807$	−12.8824	+	10.2066i	−0.453482	+	0.359288i
$808$		0			0
$809$	−12.6277			−0.443967			−0.221983	−	0.975050i	$-0.571253\pi$
$809$	−12.6277			−0.443967			−0.221983	+	0.975050i	$0.571253\pi$
$810$		0			0
$811$	33.5341			1.17754			0.588771	−	0.808300i	$-0.299612\pi$
$811$	33.5341			1.17754			0.588771	+	0.808300i	$0.299612\pi$
$812$		0			0
$813$	−20.2337	+	16.0309i	−0.709626	+	0.562228i
$814$		0			0
$815$	−10.4845	−	18.1596i	−0.367255	−	0.636104i
$816$		0			0
$817$	11.0584	−	19.1537i	0.386885	−	0.670105i
$818$		0			0
$819$	6.62936	−	28.2171i	0.231649	−	0.985986i
$820$		0			0
$821$	−4.18614	+	7.25061i	−0.146097	+	0.253048i	−0.929782	−	0.368111i	$-0.880005\pi$
$821$	−4.18614	+	7.25061i	−0.146097	+	0.253048i	0.783684	+	0.621159i	$0.213338\pi$
$822$		0			0
$823$	11.4603	+	19.8498i	0.399480	+	0.691919i	0.993662	−	0.112411i	$-0.0358575\pi$
$823$	11.4603	+	19.8498i	0.399480	+	0.691919i	−0.594182	+	0.804331i	$0.702524\pi$
$824$		0			0
$825$	−6.00000	−	2.37686i	−0.208893	−	0.0827517i
$826$		0			0
$827$	8.83915			0.307367			0.153684	−	0.988120i	$-0.450886\pi$
$827$	8.83915			0.307367			0.153684	+	0.988120i	$0.450886\pi$
$828$		0			0
$829$	−8.23369			−0.285968			−0.142984	−	0.989725i	$-0.545670\pi$
$829$	−8.23369			−0.285968			−0.142984	+	0.989725i	$0.545670\pi$
$830$		0			0
$831$	−3.31468	−	22.4759i	−0.114985	−	0.779682i
$832$		0			0
$833$	3.56930	+	6.18220i	0.123669	+	0.214201i
$834$		0			0
$835$	11.4603	−	19.8498i	0.396599	−	0.686929i
$836$		0			0
$837$	28.6753	−	41.2091i	0.991162	−	1.42440i
$838$		0			0
$839$	−4.83090	+	8.36737i	−0.166781	+	0.288874i	−0.937286	−	0.348560i	$-0.886671\pi$
$839$	−4.83090	+	8.36737i	−0.166781	+	0.288874i	0.770505	+	0.637434i	$0.220004\pi$
$840$		0			0
$841$	14.4307	+	24.9947i	0.497610	+	0.861887i
$842$		0			0
$843$	−6.53528	−	44.3140i	−0.225087	−	1.52625i
$844$		0			0
$845$	14.5109			0.499189
$846$		0			0
$847$	53.5513			1.84004
$848$		0			0
$849$	8.44158	+	3.34408i	0.289714	+	0.114768i
$850$		0			0
$851$	−4.41957	−	7.65492i	−0.151501	−	0.262407i
$852$		0			0
$853$	10.5584	−	18.2877i	0.361513	−	0.626160i	−0.626697	−	0.779263i	$-0.715593\pi$
$853$	10.5584	−	18.2877i	0.361513	−	0.626160i	0.988210	+	0.153104i	$0.0489268\pi$
$854$		0			0
$855$	25.3885	−	7.65492i	0.868269	−	0.261793i
$856$		0			0
$857$	22.0475	−	38.1875i	0.753130	−	1.30446i	−0.193169	−	0.981166i	$-0.561877\pi$
$857$	22.0475	−	38.1875i	0.753130	−	1.30446i	0.946299	−	0.323294i	$-0.104790\pi$
$858$		0			0
$859$	8.90370	+	15.4217i	0.303790	+	0.526180i	0.976991	−	0.213279i	$-0.0684145\pi$
$859$	8.90370	+	15.4217i	0.303790	+	0.526180i	−0.673201	+	0.739459i	$0.735081\pi$
$860$		0			0
$861$	−3.00000	+	2.37686i	−0.102240	+	0.0810032i
$862$		0			0
$863$	17.6783			0.601776			0.300888	−	0.953659i	$-0.402717\pi$
$863$	17.6783			0.601776			0.300888	+	0.953659i	$0.402717\pi$
$864$		0			0
$865$	−0.883156			−0.0300282
$866$		0			0
$867$	7.64018	−	6.05321i	0.259474	−	0.205578i
$868$		0			0
$869$	−28.6753	−	49.6670i	−0.972742	−	1.68484i
$870$		0			0
$871$	22.6383	−	39.2107i	0.767069	−	1.32860i
$872$		0			0
$873$	19.6753	+	18.4901i	0.665907	+	0.625795i
$874$		0			0
$875$	11.4603	−	19.8498i	0.387428	−	0.671044i
$876$		0			0
$877$	6.67527	+	11.5619i	0.225408	+	0.390418i	0.956442	−	0.291923i	$-0.0942953\pi$
$877$	6.67527	+	11.5619i	0.225408	+	0.390418i	−0.731034	+	0.682341i	$0.760962\pi$
$878$		0			0
$879$	−32.8055	−	12.9957i	−1.10650	−	0.438334i
$880$		0			0
$881$	4.23369			0.142637			0.0713183	−	0.997454i	$-0.477279\pi$
$881$	4.23369			0.142637			0.0713183	+	0.997454i	$0.477279\pi$
$882$		0			0
$883$	21.4043			0.720312			0.360156	−	0.932892i	$-0.382723\pi$
$883$	21.4043			0.720312			0.360156	+	0.932892i	$0.382723\pi$
$884$		0			0
$885$	−6.20789	−	42.0940i	−0.208676	−	1.41497i
$886$		0			0
$887$	11.4603	+	19.8498i	0.384798	+	0.666490i	0.991741	−	0.128256i	$-0.0409378\pi$
$887$	11.4603	+	19.8498i	0.384798	+	0.666490i	−0.606943	+	0.794745i	$0.707604\pi$
$888$		0			0
$889$	−8.23369	+	14.2612i	−0.276149	+	0.478304i
$890$		0			0
$891$	−44.5185	+	29.5302i	−1.49143	+	0.989300i
$892$		0			0
$893$	4.11684	−	7.13058i	0.137765	−	0.238616i
$894$		0			0
$895$	−10.4845	−	18.1596i	−0.350457	−	0.607010i
$896$		0			0
$897$	−2.44158	−	16.5557i	−0.0815219	−	0.552778i
$898$		0			0
$899$	3.59691			0.119964
$900$		0			0
$901$	−13.4891			−0.449388
$902$		0			0
$903$	21.1221	+	8.36737i	0.702899	+	0.278449i
$904$		0			0
$905$	9.76631	+	16.9157i	0.324643	+	0.562299i
$906$		0			0
$907$	−14.1459	+	24.5015i	−0.469708	+	0.813558i	−0.999400	−	0.0346319i	$-0.988974\pi$
$907$	−14.1459	+	24.5015i	−0.469708	+	0.813558i	0.529692	+	0.848190i	$0.322307\pi$
$908$		0			0
$909$	−33.0475	−	31.0569i	−1.09612	−	1.03009i
$910$		0			0
$911$	−26.3643	+	45.6643i	−0.873488	+	1.51293i	−0.0151242	+	0.999886i	$0.504814\pi$
$911$	−26.3643	+	45.6643i	−0.873488	+	1.51293i	−0.858364	+	0.513041i	$0.828519\pi$
$912$		0			0
$913$	−41.7921	−	72.3861i	−1.38312	−	2.39563i
$914$		0			0
$915$	−48.6853	+	38.5728i	−1.60949	+	1.27518i
$916$		0			0
$917$	−21.3505			−0.705057
$918$		0			0
$919$	−25.1303			−0.828973			−0.414486	−	0.910056i	$-0.636039\pi$
$919$	−25.1303			−0.828973			−0.414486	+	0.910056i	$0.636039\pi$
$920$		0			0
$921$	39.1753	−	31.0381i	1.29087	−	1.02274i
$922$		0			0
$923$	−9.66181	−	16.7347i	−0.318022	−	0.550831i
$924$		0			0
$925$	−1.25544	+	2.17448i	−0.0412785	+	0.0714965i
$926$		0			0
$927$	6.34713	−	1.91373i	0.208467	−	0.0628552i
$928$		0			0
$929$	−18.1861	+	31.4993i	−0.596668	+	1.03346i	0.396641	+	0.917974i	$0.370176\pi$
$929$	−18.1861	+	31.4993i	−0.596668	+	1.03346i	−0.993309	+	0.115485i	$0.963158\pi$
$930$		0			0
$931$	−3.94369	−	6.83067i	−0.129249	−	0.223866i
$932$		0			0
$933$	−20.4416	−	8.09780i	−0.669227	−	0.265110i
$934$		0			0
$935$	−47.4864			−1.55297
$936$		0			0
$937$	12.2337			0.399657			0.199829	−	0.979831i	$-0.435961\pi$
$937$	12.2337			0.399657			0.199829	+	0.979831i	$0.435961\pi$
$938$		0			0
$939$	−4.86043	−	32.9573i	−0.158614	−	1.07552i
$940$		0			0
$941$	23.0475	+	39.9195i	0.751329	+	1.30134i	0.947179	+	0.320705i	$0.103920\pi$
$941$	23.0475	+	39.9195i	0.751329	+	1.30134i	−0.195850	+	0.980634i	$0.562747\pi$
$942$		0			0
$943$	−1.10489	+	1.91373i	−0.0359803	+	0.0623197i
$944$		0			0
$945$	11.5842	+	24.6535i	0.376835	+	0.801977i
$946$		0			0
$947$	−17.0493	+	29.5302i	−0.554027	+	0.959603i	0.443951	+	0.896051i	$0.353576\pi$
$947$	−17.0493	+	29.5302i	−0.554027	+	0.959603i	−0.997979	+	0.0635523i	$0.979757\pi$
$948$		0			0
$949$	−10.1168	−	17.5229i	−0.328407	−	0.568817i
$950$		0			0
$951$	−2.11571	−	14.3460i	−0.0686066	−	0.465202i
$952$		0			0
$953$	−31.6060			−1.02382			−0.511909	−	0.859040i	$-0.671061\pi$
$953$	−31.6060			−1.02382			−0.511909	+	0.859040i	$0.671061\pi$
$954$		0			0
$955$	40.5988			1.31375
$956$		0			0
$957$	−3.55842	−	1.40965i	−0.115027	−	0.0455674i
$958$		0			0
$959$	13.7991	+	23.9008i	0.445598	+	0.771798i
$960$		0			0
$961$	−31.1753	+	53.9971i	−1.00565	+	1.74184i
$962$		0			0
$963$	−2.55657	+	10.8817i	−0.0823842	+	0.350659i
$964$		0			0
$965$	−1.18614	+	2.05446i	−0.0381832	+	0.0661353i
$966$		0			0
$967$	13.7991	+	23.9008i	0.443751	+	0.768599i	0.997964	−	0.0637757i	$-0.0203142\pi$
$967$	13.7991	+	23.9008i	0.443751	+	0.768599i	−0.554214	+	0.832375i	$0.686981\pi$
$968$		0			0
$969$	17.0584	−	13.5152i	0.547995	−	0.434170i
$970$		0			0
$971$	49.1317			1.57671			0.788356	−	0.615220i	$-0.210933\pi$
$971$	49.1317			1.57671			0.788356	+	0.615220i	$0.210933\pi$
$972$		0			0
$973$	6.41578			0.205680
$974$		0			0
$975$	−3.72601	+	2.95207i	−0.119328	+	0.0945419i
$976$		0			0
$977$	−5.38316	−	9.32390i	−0.172222	−	0.298298i	0.766974	−	0.641678i	$-0.221761\pi$
$977$	−5.38316	−	9.32390i	−0.172222	−	0.298298i	−0.939197	+	0.343380i	$0.888428\pi$
$978$		0			0
$979$	3.72601	−	6.45364i	0.119084	−	0.206259i
$980$		0			0
$981$	12.0000	−	51.0767i	0.383131	−	1.63075i
$982$		0			0
$983$	−20.2994	+	35.1596i	−0.647451	+	1.12142i	0.336279	+	0.941762i	$0.390831\pi$
$983$	−20.2994	+	35.1596i	−0.647451	+	1.12142i	−0.983730	+	0.179655i	$0.942502\pi$
$984$		0			0
$985$	−0.883156	−	1.52967i	−0.0281397	−	0.0487394i
$986$		0			0
$987$	7.86335	+	3.11502i	0.250293	+	0.0991521i
$988$		0			0
$989$	13.1168			0.417091
$990$		0			0
$991$	−47.4864			−1.50845			−0.754227	−	0.656613i	$-0.771988\pi$
$991$	−47.4864			−1.50845			−0.754227	+	0.656613i	$0.771988\pi$
$992$		0			0
$993$	8.44158	+	57.2400i	0.267885	+	1.81646i
$994$		0			0
$995$	−24.5659	−	42.5493i	−0.778790	−	1.34890i
$996$		0			0
$997$	−20.6753	+	35.8106i	−0.654792	+	1.13413i	0.327154	+	0.944971i	$0.393911\pi$
$997$	−20.6753	+	35.8106i	−0.654792	+	1.13413i	−0.981946	+	0.189162i	$0.939423\pi$
$998$		0			0
$999$	8.83915	+	18.8114i	0.279658	+	0.595167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.i.f.97.1	✓	8
3.2	odd	2		864.2.i.f.289.3		8
4.3	odd	2	inner	288.2.i.f.97.4	yes	8
8.3	odd	2		576.2.i.n.385.1		8
8.5	even	2		576.2.i.n.385.4		8
9.2	odd	6		2592.2.a.x.1.2		4
9.4	even	3	inner	288.2.i.f.193.1	yes	8
9.5	odd	6		864.2.i.f.577.3		8
9.7	even	3		2592.2.a.u.1.4		4
12.11	even	2		864.2.i.f.289.4		8
24.5	odd	2		1728.2.i.n.1153.1		8
24.11	even	2		1728.2.i.n.1153.2		8
36.7	odd	6		2592.2.a.u.1.3		4
36.11	even	6		2592.2.a.x.1.1		4
36.23	even	6		864.2.i.f.577.4		8
36.31	odd	6	inner	288.2.i.f.193.4	yes	8
72.5	odd	6		1728.2.i.n.577.1		8
72.11	even	6		5184.2.a.cc.1.3		4
72.13	even	6		576.2.i.n.193.4		8
72.29	odd	6		5184.2.a.cc.1.4		4
72.43	odd	6		5184.2.a.cf.1.1		4
72.59	even	6		1728.2.i.n.577.2		8
72.61	even	6		5184.2.a.cf.1.2		4
72.67	odd	6		576.2.i.n.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.f.97.1	✓	8	1.1	even	1	trivial
288.2.i.f.97.4	yes	8	4.3	odd	2	inner
288.2.i.f.193.1	yes	8	9.4	even	3	inner
288.2.i.f.193.4	yes	8	36.31	odd	6	inner
576.2.i.n.193.1		8	72.67	odd	6
576.2.i.n.193.4		8	72.13	even	6
576.2.i.n.385.1		8	8.3	odd	2
576.2.i.n.385.4		8	8.5	even	2
864.2.i.f.289.3		8	3.2	odd	2
864.2.i.f.289.4		8	12.11	even	2
864.2.i.f.577.3		8	9.5	odd	6
864.2.i.f.577.4		8	36.23	even	6
1728.2.i.n.577.1		8	72.5	odd	6
1728.2.i.n.577.2		8	72.59	even	6
1728.2.i.n.1153.1		8	24.5	odd	2
1728.2.i.n.1153.2		8	24.11	even	2
2592.2.a.u.1.3		4	36.7	odd	6
2592.2.a.u.1.4		4	9.7	even	3
2592.2.a.x.1.1		4	36.11	even	6
2592.2.a.x.1.2		4	9.2	odd	6
5184.2.a.cc.1.3		4	72.11	even	6
5184.2.a.cc.1.4		4	72.29	odd	6
5184.2.a.cf.1.1		4	72.43	odd	6
5184.2.a.cf.1.2		4	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35760 + 1.07561i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-1.10489 + 1.91373i) q^{7} +(0.686141 - 2.92048i) q^{9} +O(q^{10})\)	\(q+(-1.35760 + 1.07561i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-1.10489 + 1.91373i) q^{7} +(0.686141 - 2.92048i) q^{9} +(2.96790 - 5.14055i) q^{11} +(-2.18614 - 3.78651i) q^{13} +(3.82009 + 1.51330i) q^{15} +3.37228 q^{17} -3.72601 q^{19} +(-0.558422 - 3.78651i) q^{21} +(-1.10489 - 1.91373i) q^{23} +(-0.313859 + 0.543620i) q^{25} +(2.20979 + 4.70285i) q^{27} +(-0.186141 + 0.322405i) q^{29} +(-4.83090 - 8.36737i) q^{31} +(1.50000 + 10.1711i) q^{33} +5.24224 q^{35} +4.00000 q^{37} +(7.04069 + 2.78912i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-2.96790 + 5.14055i) q^{43} +(-6.81386 + 2.05446i) q^{45} +(-1.10489 + 1.91373i) q^{47} +(1.05842 + 1.83324i) q^{49} +(-4.57820 + 3.62725i) q^{51} -4.00000 q^{53} -14.0814 q^{55} +(5.05842 - 4.00772i) q^{57} +(-5.17769 - 8.96801i) q^{59} +(-7.55842 + 13.0916i) q^{61} +(4.83090 + 4.53991i) q^{63} +(-5.18614 + 8.98266i) q^{65} +(5.17769 + 8.96801i) q^{67} +(3.55842 + 1.40965i) q^{69} +4.41957 q^{71} +4.62772 q^{73} +(-0.158627 - 1.07561i) q^{75} +(6.55842 + 11.3595i) q^{77} +(4.83090 - 8.36737i) q^{79} +(-8.05842 - 4.00772i) q^{81} +(7.04069 - 12.1948i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-0.0940770 - 0.637910i) q^{87} +1.25544 q^{89} +9.66181 q^{91} +(15.5584 + 6.16337i) q^{93} +(4.41957 + 7.65492i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-12.9765 - 12.1948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 2 * q^5 - 6 * q^9	\( 8 q + 2 q^{5} - 6 q^{9} - 6 q^{13} + 4 q^{17} + 30 q^{21} - 14 q^{25} + 10 q^{29} + 12 q^{33} + 32 q^{37} - 4 q^{41} - 66 q^{45} - 26 q^{49} - 32 q^{53} + 6 q^{57} - 26 q^{61} - 30 q^{65} - 6 q^{69} + 60 q^{73} + 18 q^{77} - 30 q^{81} - 32 q^{85} + 56 q^{89} + 90 q^{93} - 36 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 6 * q^9 - 6 * q^13 + 4 * q^17 + 30 * q^21 - 14 * q^25 + 10 * q^29 + 12 * q^33 + 32 * q^37 - 4 * q^41 - 66 * q^45 - 26 * q^49 - 32 * q^53 + 6 * q^57 - 26 * q^61 - 30 * q^65 - 6 * q^69 + 60 * q^73 + 18 * q^77 - 30 * q^81 - 32 * q^85 + 56 * q^89 + 90 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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