LMFDB - Embedded newform 2940.2.bb.i.949.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(949,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.949"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-2,0,0,0,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.81284711803392324796416.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 20 x^{13} - 12 x^{12} + 124 x^{11} - 24 x^{10} + 328 x^{9} + 1132 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 2x^14 - 20x^13 - 12x^12 + 124x^11 - 24x^10 + 328x^9 + 1132x^8 - 760x^7 + 96x^6 - 640x^5 + 96x^4 + 224x^3 + 32x^2 + 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.5
Root			$-0.389934 + 0.104482i$ of defining polynomial
Character	$\chi$	$=$	2940.949
Dual form			2940.2.bb.i.1549.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} +(-1.77792 + 1.35609i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} +5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(-0.205328 - 0.118546i) q^{17} +(-2.37016 - 4.10523i) q^{19} +(5.86244 - 3.38468i) q^{23} +(1.32201 - 4.82206i) q^{25} +1.00000i q^{27} -6.03549 q^{29} +(-5.26936 + 9.12679i) q^{31} +(-2.53947 + 1.46616i) q^{33} +(2.66227 - 1.53706i) q^{37} +(-2.88468 + 4.99641i) q^{39} -1.06768 q^{41} +9.79697i q^{43} +(-2.06337 - 0.861678i) q^{45} +(3.21530 - 1.85635i) q^{47} +(-0.118546 - 0.205328i) q^{51} +(-9.53186 - 5.50322i) q^{53} +(-0.837035 - 6.50322i) q^{55} -4.74032i q^{57} +(4.65633 - 8.06499i) q^{59} +(-4.06861 - 7.04704i) q^{61} +(-7.82379 - 10.2575i) q^{65} +(-1.94296 - 1.12177i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(3.28827 + 1.89848i) q^{73} +(3.55593 - 3.51502i) q^{75} +(0.00873900 + 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(-5.22689 - 3.01774i) q^{87} +(-8.97583 - 15.5466i) q^{89} +(-9.12679 + 5.26936i) q^{93} +(9.78104 + 4.08463i) q^{95} +2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} - 8 q^{19} + 12 q^{25} + 24 q^{29} - 4 q^{39} - 48 q^{41} + 2 q^{45} + 4 q^{51} + 40 q^{55} + 28 q^{59} + 32 q^{61} - 26 q^{65} + 24 q^{69} - 56 q^{71} + 8 q^{75}+ \cdots - 16 q^{99}+O(q^{100}) $ 16 * q - 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 - 8 * q^19 + 12 * q^25 + 24 * q^29 - 4 * q^39 - 48 * q^41 + 2 * q^45 + 4 * q^51 + 40 * q^55 + 28 * q^59 + 32 * q^61 - 26 * q^65 + 24 * q^69 - 56 * q^71 + 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 + 16 * q^89 + 22 * q^95 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−1.77792	+	1.35609i	−0.795111	+	0.606464i
$5$	−1.77792	+	1.35609i	−0.795111	+	0.606464i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	−0.997843	−	0.0656529i	$-0.979087\pi$
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	0.555778	+	0.831330i	$0.312420\pi$
$12$		0			0
$13$			5.76936i			1.60013i	0.599912	+	0.800066i	$0.295202\pi$
$13$			5.76936i			1.60013i	−0.599912	+	0.800066i	$0.704798\pi$
$14$		0			0
$15$	−2.21777	+	0.285451i	−0.572627	+	0.0737032i
$16$		0			0
$17$	−0.205328	−	0.118546i	−0.0497993	−	0.0287516i	0.474894	−	0.880043i	$-0.342487\pi$
$17$	−0.205328	−	0.118546i	−0.0497993	−	0.0287516i	−0.524693	+	0.851292i	$0.675820\pi$
$18$		0			0
$19$	−2.37016	−	4.10523i	−0.543752	−	0.941805i	−0.998684	−	0.0512796i	$-0.983670\pi$
$19$	−2.37016	−	4.10523i	−0.543752	−	0.941805i	0.454933	−	0.890526i	$-0.349663\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.86244	−	3.38468i	1.22240	−	0.705754i	0.256973	−	0.966419i	$-0.417275\pi$
$23$	5.86244	−	3.38468i	1.22240	−	0.705754i	0.965429	+	0.260664i	$0.0839416\pi$
$24$		0			0
$25$	1.32201	−	4.82206i	0.264403	−	0.964412i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−6.03549			−1.12076			−0.560381	−	0.828235i	$-0.689345\pi$
$29$	−6.03549			−1.12076			−0.560381	+	0.828235i	$0.689345\pi$
$30$		0			0
$31$	−5.26936	+	9.12679i	−0.946404	+	1.63922i	−0.193490	+	0.981102i	$0.561981\pi$
$31$	−5.26936	+	9.12679i	−0.946404	+	1.63922i	−0.752915	+	0.658118i	$0.771353\pi$
$32$		0			0
$33$	−2.53947	+	1.46616i	−0.442064	+	0.255226i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.66227	−	1.53706i	0.437675	−	0.252692i	−0.264936	−	0.964266i	$-0.585351\pi$
$37$	2.66227	−	1.53706i	0.437675	−	0.252692i	0.702611	+	0.711574i	$0.252018\pi$
$38$		0			0
$39$	−2.88468	+	4.99641i	−0.461918	+	0.800066i
$40$		0			0
$41$	−1.06768			−0.166743			−0.0833717	−	0.996519i	$-0.526569\pi$
$41$	−1.06768			−0.166743			−0.0833717	+	0.996519i	$0.526569\pi$
$42$		0			0
$43$			9.79697i			1.49402i	0.664811	+	0.747012i	$0.268512\pi$
$43$			9.79697i			1.49402i	−0.664811	+	0.747012i	$0.731488\pi$
$44$		0			0
$45$	−2.06337	−	0.861678i	−0.307590	−	0.128451i
$46$		0			0
$47$	3.21530	−	1.85635i	0.469000	−	0.270777i	−0.246821	−	0.969061i	$-0.579386\pi$
$47$	3.21530	−	1.85635i	0.469000	−	0.270777i	0.715821	+	0.698284i	$0.246053\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.118546	−	0.205328i	−0.0165998	−	0.0287516i
$52$		0			0
$53$	−9.53186	−	5.50322i	−1.30930	−	0.755926i	−0.327323	−	0.944913i	$-0.606146\pi$
$53$	−9.53186	−	5.50322i	−1.30930	−	0.755926i	−0.981980	+	0.188987i	$0.939480\pi$
$54$		0			0
$55$	−0.837035	−	6.50322i	−0.112866	−	0.876895i
$56$		0			0
$57$		−	4.74032i		−	0.627870i
$58$		0			0
$59$	4.65633	−	8.06499i	0.606202	−	1.04997i	−0.385658	−	0.922642i	$-0.626026\pi$
$59$	4.65633	−	8.06499i	0.606202	−	1.04997i	0.991860	−	0.127331i	$-0.0406410\pi$
$60$		0			0
$61$	−4.06861	−	7.04704i	−0.520932	−	0.902281i	−0.999704	−	0.0243418i	$-0.992251\pi$
$61$	−4.06861	−	7.04704i	−0.520932	−	0.902281i	0.478771	−	0.877940i	$-0.341082\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.82379	−	10.2575i	−0.970422	−	1.27228i
$66$		0			0
$67$	−1.94296	−	1.12177i	−0.237371	−	0.137046i	0.376597	−	0.926377i	$-0.377094\pi$
$67$	−1.94296	−	1.12177i	−0.237371	−	0.137046i	−0.613968	+	0.789331i	$0.710428\pi$
$68$		0			0
$69$	6.76936			0.814935
$70$		0			0
$71$	−11.8421			−1.40539			−0.702696	−	0.711490i	$-0.748021\pi$
$71$	−11.8421			−1.40539			−0.702696	+	0.711490i	$0.748021\pi$
$72$		0			0
$73$	3.28827	+	1.89848i	0.384863	+	0.222201i	0.679932	−	0.733275i	$-0.262009\pi$
$73$	3.28827	+	1.89848i	0.384863	+	0.222201i	−0.295069	+	0.955476i	$0.595343\pi$
$74$		0			0
$75$	3.55593	−	3.51502i	0.410603	−	0.405880i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.00873900	+	0.0151364i	0.000983215	+	0.00170298i	0.866517	−	0.499148i	$-0.166354\pi$
$79$	0.00873900	+	0.0151364i	0.000983215	+	0.00170298i	−0.865533	+	0.500851i	$0.833020\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	7.30162i		−	0.801457i	−0.916197	−	0.400729i	$-0.868757\pi$
$83$		−	7.30162i		−	0.801457i	0.916197	−	0.400729i	$-0.131243\pi$
$84$		0			0
$85$	0.525816	−	0.0676782i	0.0570328	−	0.00734073i
$86$		0			0
$87$	−5.22689	−	3.01774i	−0.560381	−	0.323536i
$88$		0			0
$89$	−8.97583	−	15.5466i	−0.951437	−	1.64794i	−0.742320	−	0.670046i	$-0.766274\pi$
$89$	−8.97583	−	15.5466i	−0.951437	−	1.64794i	−0.209117	−	0.977891i	$-0.567059\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.12679	+	5.26936i	−0.946404	+	0.546407i
$94$		0			0
$95$	9.78104	+	4.08463i	1.00351	+	0.419074i
$96$		0			0
$97$			2.31122i			0.234669i	0.993092	+	0.117334i	$0.0374349\pi$
$97$			2.31122i			0.234669i	−0.993092	+	0.117334i	$0.962565\pi$
$98$		0			0
$99$	−2.93232			−0.294709
$100$		0			0
$101$	−3.92103	+	6.79142i	−0.390157	+	0.675771i	−0.992470	−	0.122489i	$-0.960912\pi$
$101$	−3.92103	+	6.79142i	−0.390157	+	0.675771i	0.602313	+	0.798260i	$0.294246\pi$
$102$		0			0
$103$	3.53388	−	2.04029i	0.348204	−	0.201036i	−0.315690	−	0.948862i	$-0.602236\pi$
$103$	3.53388	−	2.04029i	0.348204	−	0.201036i	0.663894	+	0.747827i	$0.268903\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.8887	+	9.17335i	−1.53602	+	0.886822i	−0.536954	+	0.843611i	$0.680425\pi$
$107$	−15.8887	+	9.17335i	−1.53602	+	0.886822i	−0.999066	+	0.0432102i	$0.986241\pi$
$108$		0			0
$109$	−5.20719	+	9.01912i	−0.498759	+	0.863875i	−0.999999	−	0.00143278i	$-0.999544\pi$
$109$	−5.20719	+	9.01912i	−0.498759	+	0.863875i	0.501240	+	0.865308i	$0.332877\pi$
$110$		0			0
$111$	3.07413			0.291783
$112$		0			0
$113$		−	2.14825i		−	0.202091i	−0.994882	−	0.101045i	$-0.967781\pi$
$113$		−	2.14825i		−	0.202091i	0.994882	−	0.101045i	$-0.0322187\pi$
$114$		0			0
$115$	−5.83301	+	13.9677i	−0.543931	+	1.30250i
$116$		0			0
$117$	−4.99641	+	2.88468i	−0.461918	+	0.266689i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.20074	+	2.07975i	0.109159	+	0.189068i
$122$		0			0
$123$	−0.924636	−	0.533839i	−0.0833717	−	0.0481347i
$124$		0			0
$125$	4.18873	+	10.3660i	0.374652	+	0.927166i
$126$		0			0
$127$			1.82457i			0.161905i	0.996718	+	0.0809524i	$0.0257962\pi$
$127$			1.82457i			0.161905i	−0.996718	+	0.0809524i	$0.974204\pi$
$128$		0			0
$129$	−4.89848	+	8.48442i	−0.431287	+	0.747012i
$130$		0			0
$131$	1.35313	+	2.34369i	0.118223	+	0.204769i	0.919064	−	0.394109i	$-0.128947\pi$
$131$	1.35313	+	2.34369i	0.118223	+	0.204769i	−0.800840	+	0.598878i	$0.795613\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.35609	−	1.77792i	−0.116714	−	0.153019i
$136$		0			0
$137$	8.66460	+	5.00251i	0.740267	+	0.427393i	0.822166	−	0.569247i	$-0.192765\pi$
$137$	8.66460	+	5.00251i	0.740267	+	0.427393i	−0.0818996	+	0.996641i	$0.526099\pi$
$138$		0			0
$139$	−2.07269			−0.175804			−0.0879018	−	0.996129i	$-0.528016\pi$
$139$	−2.07269			−0.175804			−0.0879018	+	0.996129i	$0.528016\pi$
$140$		0			0
$141$	3.71271			0.312666
$142$		0			0
$143$	−14.6511	−	8.45881i	−1.22518	−	0.707361i
$144$		0			0
$145$	10.7306	−	8.18469i	0.891130	−	0.679702i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.551584	−	0.955371i	−0.0451875	−	0.0782671i	0.842547	−	0.538623i	$-0.181055\pi$
$149$	−0.551584	−	0.955371i	−0.0451875	−	0.0782671i	−0.887735	+	0.460356i	$0.847722\pi$
$150$		0			0
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	−0.996489	−	0.0837214i	$-0.973319\pi$
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	0.570749	+	0.821124i	$0.306653\pi$
$152$		0			0
$153$		−	0.237092i		−	0.0191677i
$154$		0			0
$155$	−3.00829	−	23.3725i	−0.241632	−	1.87732i
$156$		0			0
$157$	7.84763	+	4.53083i	0.626309	+	0.361600i	0.779321	−	0.626624i	$-0.215564\pi$
$157$	7.84763	+	4.53083i	0.626309	+	0.361600i	−0.153012	+	0.988224i	$0.548897\pi$
$158$		0			0
$159$	−5.50322	−	9.53186i	−0.436434	−	0.755926i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.22164	−	4.16941i	0.565642	−	0.326574i	−0.189765	−	0.981830i	$-0.560773\pi$
$163$	7.22164	−	4.16941i	0.565642	−	0.326574i	0.755407	+	0.655256i	$0.227439\pi$
$164$		0			0
$165$	2.52672	−	6.05048i	0.196705	−	0.471029i
$166$		0			0
$167$		−	10.2886i		−	0.796158i	−0.917351	−	0.398079i	$-0.869677\pi$
$167$		−	10.2886i		−	0.796158i	0.917351	−	0.398079i	$-0.130323\pi$
$168$		0			0
$169$	−20.2855			−1.56042
$170$		0			0
$171$	2.37016	−	4.10523i	0.181251	−	0.313935i
$172$		0			0
$173$	−14.9768	+	8.64687i	−1.13867	+	0.657409i	−0.946100	−	0.323875i	$-0.895014\pi$
$173$	−14.9768	+	8.64687i	−1.13867	+	0.657409i	−0.192566	+	0.981284i	$0.561681\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.06499	−	4.65633i	0.606202	−	0.349991i
$178$		0			0
$179$	−5.50967	+	9.54303i	−0.411812	+	0.713280i	−0.995088	−	0.0989944i	$-0.968437\pi$
$179$	−5.50967	+	9.54303i	−0.411812	+	0.713280i	0.583276	+	0.812274i	$0.301771\pi$
$180$		0			0
$181$	−4.53685			−0.337221			−0.168611	−	0.985683i	$-0.553928\pi$
$181$	−4.53685			−0.337221			−0.168611	+	0.985683i	$0.553928\pi$
$182$		0			0
$183$		−	8.13722i		−	0.601521i
$184$		0			0
$185$	−2.64891	+	6.34307i	−0.194752	+	0.466352i
$186$		0			0
$187$	0.602087	−	0.347615i	0.0440289	−	0.0254201i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	0.665185	−	0.746679i	$-0.268353\pi$
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	−0.979235	+	0.202728i	$0.935019\pi$
$192$		0			0
$193$	−6.11520	−	3.53061i	−0.440182	−	0.254139i	0.263493	−	0.964661i	$-0.415125\pi$
$193$	−6.11520	−	3.53061i	−0.440182	−	0.254139i	−0.703675	+	0.710522i	$0.748459\pi$
$194$		0			0
$195$	−1.64687	−	12.7951i	−0.117935	−	0.916278i
$196$		0			0
$197$		−	3.58891i		−	0.255700i	−0.991794	−	0.127850i	$-0.959192\pi$
$197$		−	3.58891i		−	0.255700i	0.991794	−	0.127850i	$-0.0408075\pi$
$198$		0			0
$199$	1.49126	−	2.58294i	0.105713	−	0.183100i	−0.808316	−	0.588748i	$-0.799621\pi$
$199$	1.49126	−	2.58294i	0.105713	−	0.183100i	0.914029	+	0.405648i	$0.132954\pi$
$200$		0			0
$201$	−1.12177	−	1.94296i	−0.0791236	−	0.137046i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.89825	−	1.44787i	0.132579	−	0.101124i
$206$		0			0
$207$	5.86244	+	3.38468i	0.407467	+	0.235251i
$208$		0			0
$209$	13.9001			0.961492
$210$		0			0
$211$	−21.4273			−1.47512			−0.737558	−	0.675284i	$-0.764021\pi$
$211$	−21.4273			−1.47512			−0.737558	+	0.675284i	$0.764021\pi$
$212$		0			0
$213$	−10.2555	−	5.92103i	−0.702696	−	0.405702i
$214$		0			0
$215$	−13.2856	−	17.4182i	−0.906071	−	1.18791i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.89848	+	3.28827i	0.128288	+	0.222201i
$220$		0			0
$221$	0.683934	−	1.18461i	0.0460064	−	0.0796854i
$222$		0			0
$223$			16.3969i			1.09802i	0.835816	+	0.549009i	$0.184995\pi$
$223$			16.3969i			1.09802i	−0.835816	+	0.549009i	$0.815005\pi$
$224$		0			0
$225$	4.83704	−	1.26613i	0.322469	−	0.0844088i
$226$		0			0
$227$	8.25642	+	4.76685i	0.547998	+	0.316387i	0.748314	−	0.663344i	$-0.230864\pi$
$227$	8.25642	+	4.76685i	0.547998	+	0.316387i	−0.200316	+	0.979731i	$0.564197\pi$
$228$		0			0
$229$	−9.05987	−	15.6922i	−0.598693	−	1.03697i	−0.993014	−	0.117994i	$-0.962354\pi$
$229$	−9.05987	−	15.6922i	−0.598693	−	1.03697i	0.394321	−	0.918973i	$-0.370980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.4394	−	6.02720i	0.683909	−	0.394855i	−0.117417	−	0.993083i	$-0.537462\pi$
$233$	10.4394	−	6.02720i	0.683909	−	0.394855i	0.801326	+	0.598228i	$0.204128\pi$
$234$		0			0
$235$	−3.19916	+	7.66070i	−0.208690	+	0.499729i
$236$		0			0
$237$			0.0174780i			0.00113532i
$238$		0			0
$239$	21.3868			1.38340			0.691698	−	0.722187i	$-0.256863\pi$
$239$	21.3868			1.38340			0.691698	+	0.722187i	$0.256863\pi$
$240$		0			0
$241$	8.59443	−	14.8860i	0.553616	−	0.958891i	−0.444394	−	0.895831i	$-0.646581\pi$
$241$	8.59443	−	14.8860i	0.553616	−	0.958891i	0.998010	−	0.0630593i	$-0.0200857\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	23.6846	−	13.6743i	1.50701	−	0.870074i
$248$		0			0
$249$	3.65081	−	6.32339i	0.231361	−	0.400729i
$250$		0			0
$251$	−23.1939			−1.46398			−0.731992	−	0.681313i	$-0.761409\pi$
$251$	−23.1939			−1.46398			−0.731992	+	0.681313i	$0.761409\pi$
$252$		0			0
$253$			19.8499i			1.24795i
$254$		0			0
$255$	0.489209	+	0.204297i	0.0306355	+	0.0127936i
$256$		0			0
$257$	22.6519	−	13.0781i	1.41299	−	0.815787i	0.417317	−	0.908761i	$-0.362971\pi$
$257$	22.6519	−	13.0781i	1.41299	−	0.815787i	0.995669	+	0.0929737i	$0.0296372\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.01774	−	5.22689i	−0.186794	−	0.323536i
$262$		0			0
$263$	−6.66823	−	3.84991i	−0.411181	−	0.237395i	0.280116	−	0.959966i	$-0.409627\pi$
$263$	−6.66823	−	3.84991i	−0.411181	−	0.237395i	−0.691297	+	0.722571i	$0.742960\pi$
$264$		0			0
$265$	24.4098	−	3.14181i	1.49948	−	0.193000i
$266$		0			0
$267$		−	17.9517i		−	1.09862i
$268$		0			0
$269$	−12.5194	+	21.6842i	−0.763321	+	1.32211i	0.177809	+	0.984065i	$0.443099\pi$
$269$	−12.5194	+	21.6842i	−0.763321	+	1.32211i	−0.941130	+	0.338046i	$0.890234\pi$
$270$		0			0
$271$	9.54423	+	16.5311i	0.579771	+	1.00419i	0.995505	+	0.0947062i	$0.0301912\pi$
$271$	9.54423	+	16.5311i	0.579771	+	1.00419i	−0.415735	+	0.909486i	$0.636476\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.3072	+	10.4271i	0.621546	+	0.628779i
$276$		0			0
$277$	10.5124	+	6.06933i	0.631628	+	0.364671i	0.781382	−	0.624053i	$-0.214515\pi$
$277$	10.5124	+	6.06933i	0.631628	+	0.364671i	−0.149754	+	0.988723i	$0.547848\pi$
$278$		0			0
$279$	−10.5387			−0.630936
$280$		0			0
$281$	−6.34537			−0.378533			−0.189267	−	0.981926i	$-0.560611\pi$
$281$	−6.34537			−0.378533			−0.189267	+	0.981926i	$0.560611\pi$
$282$		0			0
$283$	11.7947	+	6.80964i	0.701119	+	0.404791i	0.807764	−	0.589506i	$-0.200677\pi$
$283$	11.7947	+	6.80964i	0.701119	+	0.404791i	−0.106645	+	0.994297i	$0.534011\pi$
$284$		0			0
$285$	6.42832	+	8.42791i	0.380781	+	0.499227i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.47189	−	14.6738i	−0.498347	−	0.863162i
$290$		0			0
$291$	−1.15561	+	2.00157i	−0.0677430	+	0.117334i
$292$		0			0
$293$			15.5221i			0.906813i	0.891304	+	0.453406i	$0.149791\pi$
$293$			15.5221i			0.906813i	−0.891304	+	0.453406i	$0.850209\pi$
$294$		0			0
$295$	2.65831	+	20.6533i	0.154773	+	1.20248i
$296$		0			0
$297$	−2.53947	−	1.46616i	−0.147355	−	0.0850753i
$298$		0			0
$299$	19.5274	+	33.8225i	1.12930	+	1.95600i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.79142	+	3.92103i	−0.390157	+	0.225257i
$304$		0			0
$305$	16.7901	+	7.01167i	0.961400	+	0.401487i
$306$		0			0
$307$			13.4406i			0.767093i	0.923521	+	0.383547i	$0.125297\pi$
$307$			13.4406i			0.767093i	−0.923521	+	0.383547i	$0.874703\pi$
$308$		0			0
$309$	4.08058			0.232136
$310$		0			0
$311$	1.22580	−	2.12314i	0.0695085	−	0.120392i	−0.829177	−	0.558987i	$-0.811190\pi$
$311$	1.22580	−	2.12314i	0.0695085	−	0.120392i	0.898685	+	0.438595i	$0.144524\pi$
$312$		0			0
$313$	−8.59047	+	4.95971i	−0.485562	+	0.280340i	−0.722732	−	0.691129i	$-0.757114\pi$
$313$	−8.59047	+	4.95971i	−0.485562	+	0.280340i	0.237169	+	0.971468i	$0.423780\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.5124	+	12.9975i	−1.26442	+	0.730013i	−0.973927	−	0.226863i	$-0.927153\pi$
$317$	−22.5124	+	12.9975i	−1.26442	+	0.730013i	−0.290494	+	0.956877i	$0.593820\pi$
$318$		0			0
$319$	8.84900	−	15.3269i	0.495449	−	0.858142i
$320$		0			0
$321$	−18.3467			−1.02401
$322$		0			0
$323$			1.12389i			0.0625350i
$324$		0			0
$325$	27.8202	+	7.62717i	1.54319	+	0.423080i
$326$		0			0
$327$	−9.01912	+	5.20719i	−0.498759	+	0.287958i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	0.743764	−	0.668442i	$-0.233038\pi$
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	−0.950770	+	0.309898i	$0.899705\pi$
$332$		0			0
$333$	2.66227	+	1.53706i	0.145892	+	0.0842306i
$334$		0			0
$335$	4.97566	−	0.640422i	0.271850	−	0.0349900i
$336$		0			0
$337$			15.7050i			0.855505i	0.903896	+	0.427752i	$0.140694\pi$
$337$			15.7050i			0.855505i	−0.903896	+	0.427752i	$0.859306\pi$
$338$		0			0
$339$	1.07413	−	1.86044i	0.0583386	−	0.101045i
$340$		0			0
$341$	−15.4515	−	26.7627i	−0.836743	−	1.44928i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−12.0354	+	9.17989i	−0.647964	+	0.494229i
$346$		0			0
$347$	−7.97850	−	4.60639i	−0.428309	−	0.247284i	0.270317	−	0.962771i	$-0.412871\pi$
$347$	−7.97850	−	4.60639i	−0.428309	−	0.247284i	−0.698626	+	0.715487i	$0.746205\pi$
$348$		0			0
$349$	21.1518			1.13223			0.566116	−	0.824326i	$-0.308445\pi$
$349$	21.1518			1.13223			0.566116	+	0.824326i	$0.308445\pi$
$350$		0			0
$351$	−5.76936			−0.307945
$352$		0			0
$353$	−12.9725	−	7.48969i	−0.690457	−	0.398636i	0.113326	−	0.993558i	$-0.463850\pi$
$353$	−12.9725	−	7.48969i	−0.690457	−	0.398636i	−0.803783	+	0.594922i	$0.797183\pi$
$354$		0			0
$355$	21.0542	−	16.0589i	1.11744	−	0.852320i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.4823	+	18.1559i	0.553236	+	0.958233i	0.998038	+	0.0626045i	$0.0199407\pi$
$359$	10.4823	+	18.1559i	0.553236	+	0.958233i	−0.444802	+	0.895629i	$0.646726\pi$
$360$		0			0
$361$	−1.73530	+	3.00563i	−0.0913316	+	0.158191i
$362$		0			0
$363$			2.40149i			0.126045i
$364$		0			0
$365$	−8.42081	+	1.08385i	−0.440765	+	0.0567312i
$366$		0			0
$367$	16.5538	+	9.55732i	0.864099	+	0.498888i	0.865383	−	0.501111i	$-0.167075\pi$
$367$	16.5538	+	9.55732i	0.864099	+	0.498888i	−0.00128371	+	0.999999i	$0.500409\pi$
$368$		0			0
$369$	−0.533839	−	0.924636i	−0.0277906	−	0.0481347i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.64151	+	3.25713i	−0.292106	+	0.168648i	−0.638891	−	0.769297i	$-0.720607\pi$
$373$	−5.64151	+	3.25713i	−0.292106	+	0.168648i	0.346785	+	0.937945i	$0.387273\pi$
$374$		0			0
$375$	−1.55546	+	11.0716i	−0.0803239	+	0.571735i
$376$		0			0
$377$		−	34.8209i		−	1.79337i
$378$		0			0
$379$	−14.4254			−0.740984			−0.370492	−	0.928836i	$-0.620811\pi$
$379$	−14.4254			−0.740984			−0.370492	+	0.928836i	$0.620811\pi$
$380$		0			0
$381$	−0.912287	+	1.58013i	−0.0467379	+	0.0809524i
$382$		0			0
$383$	−21.9018	+	12.6450i	−1.11913	+	0.646131i	−0.941179	−	0.337908i	$-0.890281\pi$
$383$	−21.9018	+	12.6450i	−1.11913	+	0.646131i	−0.177952	+	0.984039i	$0.556947\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.48442	+	4.89848i	−0.431287	+	0.249004i
$388$		0			0
$389$	13.4984	−	23.3799i	0.684395	−	1.18541i	−0.289232	−	0.957259i	$-0.593400\pi$
$389$	13.4984	−	23.3799i	0.684395	−	1.18541i	0.973627	−	0.228148i	$-0.0732669\pi$
$390$		0			0
$391$	−1.60496			−0.0811663
$392$		0			0
$393$			2.70626i			0.136513i
$394$		0			0
$395$	−0.0360637	−	0.0150604i	−0.00181456	−	0.000757772i
$396$		0			0
$397$	27.3806	−	15.8082i	1.37419	−	0.793391i	0.382741	−	0.923856i	$-0.374980\pi$
$397$	27.3806	−	15.8082i	1.37419	−	0.793391i	0.991453	+	0.130464i	$0.0416467\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	0.978765	−	0.204986i	$-0.0657150\pi$
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	−0.666906	+	0.745142i	$0.732382\pi$
$402$		0			0
$403$	−52.6557	−	30.4008i	−2.62297	−	1.51437i
$404$		0			0
$405$	−0.285451	−	2.21777i	−0.0141842	−	0.110202i
$406$		0			0
$407$			9.01433i			0.446824i
$408$		0			0
$409$	−6.28039	+	10.8779i	−0.310545	+	0.537880i	−0.978480	−	0.206339i	$-0.933845\pi$
$409$	−6.28039	+	10.8779i	−0.310545	+	0.537880i	0.667935	+	0.744219i	$0.267178\pi$
$410$		0			0
$411$	5.00251	+	8.66460i	0.246756	+	0.427393i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	9.90169	+	12.9817i	0.486055	+	0.637247i
$416$		0			0
$417$	−1.79501	−	1.03635i	−0.0879018	−	0.0507502i
$418$		0			0
$419$	−17.6520			−0.862357			−0.431179	−	0.902267i	$-0.641902\pi$
$419$	−17.6520			−0.862357			−0.431179	+	0.902267i	$0.641902\pi$
$420$		0			0
$421$	29.2634			1.42621			0.713106	−	0.701056i	$-0.247288\pi$
$421$	29.2634			1.42621			0.713106	+	0.701056i	$0.247288\pi$
$422$		0			0
$423$	3.21530	+	1.85635i	0.156333	+	0.0902590i
$424$		0			0
$425$	−0.843082	+	0.833383i	−0.0408955	+	0.0404250i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8.45881	−	14.6511i	−0.408395	−	0.707361i
$430$		0			0
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	0.273069	+	0.961994i	$0.411961\pi$
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	−0.969646	+	0.244512i	$0.921372\pi$
$432$		0			0
$433$		−	10.0338i		−	0.482192i	−0.970501	−	0.241096i	$-0.922493\pi$
$433$		−	10.0338i		−	0.482192i	0.970501	−	0.241096i	$-0.0775069\pi$
$434$		0			0
$435$	13.3853	−	1.72284i	0.641778	−	0.0826038i
$436$		0			0
$437$	−27.7898	−	16.0444i	−1.32937	−	0.767510i
$438$		0			0
$439$	8.40744	+	14.5621i	0.401265	+	0.695012i	0.993879	−	0.110475i	$-0.0352372\pi$
$439$	8.40744	+	14.5621i	0.401265	+	0.695012i	−0.592614	+	0.805487i	$0.701904\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.81665	+	5.09030i	−0.418892	+	0.241847i	−0.694603	−	0.719393i	$-0.744420\pi$
$443$	−8.81665	+	5.09030i	−0.418892	+	0.241847i	0.275711	+	0.961241i	$0.411087\pi$
$444$		0			0
$445$	37.0410	+	15.4686i	1.75591	+	0.733280i
$446$		0			0
$447$		−	1.10317i		−	0.0521780i
$448$		0			0
$449$	33.9937			1.60426			0.802131	−	0.597148i	$-0.203700\pi$
$449$	33.9937			1.60426			0.802131	+	0.597148i	$0.203700\pi$
$450$		0			0
$451$	1.56539	−	2.71133i	0.0737112	−	0.127672i
$452$		0			0
$453$	−9.06136	+	5.23158i	−0.425740	+	0.245801i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	20.5960	−	11.8911i	0.963442	−	0.556243i	0.0662113	−	0.997806i	$-0.478909\pi$
$457$	20.5960	−	11.8911i	0.963442	−	0.556243i	0.897231	+	0.441562i	$0.145576\pi$
$458$		0			0
$459$	0.118546	−	0.205328i	0.00553325	−	0.00958387i
$460$		0			0
$461$	35.2649			1.64245			0.821224	−	0.570606i	$-0.193292\pi$
$461$	35.2649			1.64245			0.821224	+	0.570606i	$0.193292\pi$
$462$		0			0
$463$			38.6505i			1.79624i	0.439750	+	0.898120i	$0.355067\pi$
$463$			38.6505i			1.79624i	−0.439750	+	0.898120i	$0.644933\pi$
$464$		0			0
$465$	9.08098	−	21.7453i	0.421120	−	1.00841i
$466$		0			0
$467$	7.67142	−	4.42910i	0.354991	−	0.204954i	−0.311890	−	0.950118i	$-0.600962\pi$
$467$	7.67142	−	4.42910i	0.354991	−	0.204954i	0.666881	+	0.745164i	$0.267629\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.53083	+	7.84763i	0.208770	+	0.361600i
$472$		0			0
$473$	−24.8791	−	14.3639i	−1.14394	−	0.660454i
$474$		0			0
$475$	−22.9291	+	6.00187i	−1.05206	+	0.275385i
$476$		0			0
$477$		−	11.0064i		−	0.503951i
$478$		0			0
$479$	4.26797	−	7.39235i	0.195009	−	0.337765i	−0.751895	−	0.659283i	$-0.770860\pi$
$479$	4.26797	−	7.39235i	0.195009	−	0.337765i	0.946903	+	0.321518i	$0.104193\pi$
$480$		0			0
$481$	8.86787	+	15.3596i	0.404340	+	0.700337i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.13423	−	4.10917i	−0.142318	−	0.186588i
$486$		0			0
$487$	1.70528	+	0.984545i	0.0772737	+	0.0446140i	0.538139	−	0.842856i	$-0.319128\pi$
$487$	1.70528	+	0.984545i	0.0772737	+	0.0446140i	−0.460865	+	0.887470i	$0.652461\pi$
$488$		0			0
$489$	8.33883			0.377095
$490$		0			0
$491$	21.4549			0.968246			0.484123	−	0.875000i	$-0.339139\pi$
$491$	21.4549			0.968246			0.484123	+	0.875000i	$0.339139\pi$
$492$		0			0
$493$	1.23925	+	0.715483i	0.0558131	+	0.0322237i
$494$		0			0
$495$	5.21344	−	3.97651i	0.234327	−	0.178731i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−7.47239	−	12.9426i	−0.334510	−	0.579389i	0.648880	−	0.760890i	$-0.275238\pi$
$499$	−7.47239	−	12.9426i	−0.334510	−	0.579389i	−0.983391	+	0.181502i	$0.941904\pi$
$500$		0			0
$501$	5.14431	−	8.91021i	0.229831	−	0.398079i
$502$		0			0
$503$			10.9715i			0.489195i	0.969625	+	0.244597i	$0.0786558\pi$
$503$			10.9715i			0.489195i	−0.969625	+	0.244597i	$0.921344\pi$
$504$		0			0
$505$	−2.23852	−	17.3919i	−0.0996130	−	0.773929i
$506$		0			0
$507$	−17.5677	−	10.1427i	−0.780211	−	0.450455i
$508$		0			0
$509$	18.6050	+	32.2247i	0.824650	+	1.42834i	0.902186	+	0.431347i	$0.141961\pi$
$509$	18.6050	+	32.2247i	0.824650	+	1.42834i	−0.0775359	+	0.996990i	$0.524705\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.10523	−	2.37016i	0.181251	−	0.104645i
$514$		0			0
$515$	−3.51614	+	8.41975i	−0.154940	+	0.371019i
$516$		0			0
$517$			10.8869i			0.478803i
$518$		0			0
$519$	−17.2937			−0.759111
$520$		0			0
$521$	8.24999	−	14.2894i	0.361439	−	0.626030i	−0.626759	−	0.779213i	$-0.715619\pi$
$521$	8.24999	−	14.2894i	0.361439	−	0.626030i	0.988198	+	0.153183i	$0.0489524\pi$
$522$		0			0
$523$	−36.6757	+	21.1747i	−1.60372	+	0.925907i	−0.612982	+	0.790097i	$0.710030\pi$
$523$	−36.6757	+	21.1747i	−1.60372	+	0.925907i	−0.990735	+	0.135810i	$0.956636\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.16389	−	1.24932i	0.0942605	−	0.0544213i
$528$		0			0
$529$	11.4121	−	19.7663i	0.496178	−	0.859406i
$530$		0			0
$531$	9.31265			0.404135
$532$		0			0
$533$		−	6.15982i		−	0.266811i
$534$		0			0
$535$	15.8090	−	37.8561i	0.683481	−	1.63666i
$536$		0			0
$537$	−9.54303	+	5.50967i	−0.411812	+	0.237760i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.814550	+	0.580093i	$0.196984\pi$
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.0951000	+	0.995468i	$0.469683\pi$
$542$		0			0
$543$	−3.92902	−	2.26842i	−0.168611	−	0.0973473i
$544$		0			0
$545$	−2.97280	−	23.0967i	−0.127341	−	0.989356i
$546$		0			0
$547$			1.34528i			0.0575199i	0.999586	+	0.0287599i	$0.00915583\pi$
$547$			1.34528i			0.0575199i	−0.999586	+	0.0287599i	$0.990844\pi$
$548$		0			0
$549$	4.06861	−	7.04704i	0.173644	−	0.300760i
$550$		0			0
$551$	14.3051	+	24.7771i	0.609416	+	1.05554i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5.46556	+	4.16881i	−0.232000	+	0.176956i
$556$		0			0
$557$	2.58930	+	1.49493i	0.109712	+	0.0633424i	0.553852	−	0.832615i	$-0.313157\pi$
$557$	2.58930	+	1.49493i	0.109712	+	0.0633424i	−0.444140	+	0.895958i	$0.646491\pi$
$558$		0			0
$559$	−56.5222			−2.39063
$560$		0			0
$561$	0.695230			0.0293526
$562$		0			0
$563$	−15.7647	−	9.10174i	−0.664402	−	0.383592i	0.129550	−	0.991573i	$-0.458647\pi$
$563$	−15.7647	−	9.10174i	−0.664402	−	0.383592i	−0.793952	+	0.607980i	$0.791980\pi$
$564$		0			0
$565$	2.91324	+	3.81943i	0.122561	+	0.160685i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.88700	−	17.1248i	−0.414484	−	0.717908i	0.580890	−	0.813982i	$-0.302705\pi$
$569$	−9.88700	−	17.1248i	−0.414484	−	0.717908i	−0.995374	+	0.0960741i	$0.969371\pi$
$570$		0			0
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	−0.581995	−	0.813193i	$-0.697728\pi$
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	0.995243	+	0.0974259i	$0.0310609\pi$
$572$		0			0
$573$		−	8.68052i		−	0.362634i
$574$		0			0
$575$	−8.57090	−	32.7436i	−0.357431	−	1.36550i
$576$		0			0
$577$	14.7851	+	8.53616i	0.615510	+	0.355365i	0.775119	−	0.631815i	$-0.217690\pi$
$577$	14.7851	+	8.53616i	0.615510	+	0.355365i	−0.159609	+	0.987180i	$0.551023\pi$
$578$		0			0
$579$	−3.53061	−	6.11520i	−0.146727	−	0.254139i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	27.9505	−	16.1372i	1.15759	−	0.668336i
$584$		0			0
$585$	4.97133	−	11.9043i	0.205539	−	0.492184i
$586$		0			0
$587$			17.5308i			0.723575i	0.932261	+	0.361787i	$0.117833\pi$
$587$			17.5308i			0.723575i	−0.932261	+	0.361787i	$0.882167\pi$
$588$		0			0
$589$	49.9568			2.05844
$590$		0			0
$591$	1.79446	−	3.10809i	0.0738141	−	0.127850i
$592$		0			0
$593$	−22.6519	+	13.0781i	−0.930201	+	0.537052i	−0.886875	−	0.462009i	$-0.847129\pi$
$593$	−22.6519	+	13.0781i	−0.930201	+	0.537052i	−0.0433259	+	0.999061i	$0.513795\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.58294	−	1.49126i	0.105713	−	0.0610332i
$598$		0			0
$599$	14.9595	−	25.9107i	0.611229	−	1.05868i	−0.379804	−	0.925067i	$-0.624009\pi$
$599$	14.9595	−	25.9107i	0.611229	−	1.05868i	0.991034	−	0.133614i	$-0.0426581\pi$
$600$		0			0
$601$	−15.6887			−0.639955			−0.319977	−	0.947425i	$-0.603675\pi$
$601$	−15.6887			−0.639955			−0.319977	+	0.947425i	$0.603675\pi$
$602$		0			0
$603$		−	2.24354i		−	0.0913640i
$604$		0			0
$605$	−4.95517	−	2.06931i	−0.201456	−	0.0841295i
$606$		0			0
$607$	−30.0913	+	17.3732i	−1.22137	+	0.705156i	−0.965209	−	0.261479i	$-0.915790\pi$
$607$	−30.0913	+	17.3732i	−1.22137	+	0.705156i	−0.256157	+	0.966635i	$0.582456\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.7100	+	18.5502i	0.433279	+	0.750461i
$612$		0			0
$613$	5.50712	+	3.17954i	0.222430	+	0.128420i	0.607075	−	0.794644i	$-0.292343\pi$
$613$	5.50712	+	3.17954i	0.222430	+	0.128420i	−0.384645	+	0.923065i	$0.625676\pi$
$614$		0			0
$615$	2.36787	−	0.304770i	0.0954817	−	0.0122895i
$616$		0			0
$617$		−	25.1778i		−	1.01362i	−0.862057	−	0.506811i	$-0.830824\pi$
$617$		−	25.1778i		−	1.01362i	0.862057	−	0.506811i	$-0.169176\pi$
$618$		0			0
$619$	−3.35963	+	5.81904i	−0.135035	+	0.233887i	−0.925611	−	0.378477i	$-0.876448\pi$
$619$	−3.35963	+	5.81904i	−0.135035	+	0.233887i	0.790576	+	0.612364i	$0.209781\pi$
$620$		0			0
$621$	3.38468	+	5.86244i	0.135822	+	0.235251i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−21.5046	−	12.7497i	−0.860182	−	0.509987i
$626$		0			0
$627$	12.0379	+	6.95007i	0.480746	+	0.277559i
$628$		0			0
$629$	−0.728851			−0.0290612
$630$		0			0
$631$	0.439228			0.0174854			0.00874269	−	0.999962i	$-0.497217\pi$
$631$	0.439228			0.0174854			0.00874269	+	0.999962i	$0.497217\pi$
$632$		0			0
$633$	−18.5566	−	10.7136i	−0.737558	−	0.425829i
$634$		0			0
$635$	−2.47429	−	3.24395i	−0.0981894	−	0.128732i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.92103	−	10.2555i	−0.234232	−	0.405702i
$640$		0			0
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	−0.735661	−	0.677350i	$-0.763128\pi$
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	0.954433	+	0.298426i	$0.0964617\pi$
$642$		0			0
$643$			16.2243i			0.639826i	0.947447	+	0.319913i	$0.103654\pi$
$643$			16.2243i			0.639826i	−0.947447	+	0.319913i	$0.896346\pi$
$644$		0			0
$645$	−2.79656	−	21.7274i	−0.110114	−	0.855517i
$646$		0			0
$647$	22.4844	+	12.9813i	0.883951	+	0.510349i	0.871959	−	0.489579i	$-0.162849\pi$
$647$	22.4844	+	12.9813i	0.883951	+	0.510349i	0.0119921	+	0.999928i	$0.496183\pi$
$648$		0			0
$649$	13.6538	+	23.6492i	0.535960	+	0.928310i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.34249	+	3.66184i	−0.248201	+	0.143299i	−0.618940	−	0.785438i	$-0.712438\pi$
$653$	−6.34249	+	3.66184i	−0.248201	+	0.143299i	0.370739	+	0.928737i	$0.379104\pi$
$654$		0			0
$655$	−5.58402	−	2.33193i	−0.218186	−	0.0911159i
$656$		0			0
$657$			3.79697i			0.148134i
$658$		0			0
$659$	−2.45499			−0.0956328			−0.0478164	−	0.998856i	$-0.515226\pi$
$659$	−2.45499			−0.0956328			−0.0478164	+	0.998856i	$0.515226\pi$
$660$		0			0
$661$	−7.64417	+	13.2401i	−0.297324	+	0.514980i	−0.975523	−	0.219898i	$-0.929427\pi$
$661$	−7.64417	+	13.2401i	−0.297324	+	0.514980i	0.678199	+	0.734878i	$0.262761\pi$
$662$		0			0
$663$	1.18461	−	0.683934i	0.0460064	−	0.0265618i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−35.3827	+	20.4282i	−1.37002	+	0.790983i
$668$		0			0
$669$	−8.19845	+	14.2001i	−0.316971	+	0.549009i
$670$		0			0
$671$	23.8610			0.921142
$672$		0			0
$673$			39.7823i			1.53349i	0.641950	+	0.766747i	$0.278126\pi$
$673$			39.7823i			1.53349i	−0.641950	+	0.766747i	$0.721874\pi$
$674$		0			0
$675$	4.82206	+	1.32201i	0.185601	+	0.0508844i
$676$		0			0
$677$	−28.1167	+	16.2332i	−1.08061	+	0.623892i	−0.931061	−	0.364862i	$-0.881116\pi$
$677$	−28.1167	+	16.2332i	−1.08061	+	0.623892i	−0.149551	+	0.988754i	$0.547783\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4.76685	+	8.25642i	0.182666	+	0.316387i
$682$		0			0
$683$	8.98285	+	5.18625i	0.343719	+	0.198446i	0.661916	−	0.749578i	$-0.269744\pi$
$683$	8.98285	+	5.18625i	0.343719	+	0.198446i	−0.318196	+	0.948025i	$0.603077\pi$
$684$		0			0
$685$	−22.1889	+	2.85595i	−0.847793	+	0.109120i
$686$		0			0
$687$		−	18.1197i		−	0.691311i
$688$		0			0
$689$	31.7501	−	54.9927i	1.20958	−	2.09506i
$690$		0			0
$691$	−2.73852	−	4.74326i	−0.104178	−	0.180442i	0.809224	−	0.587500i	$-0.199888\pi$
$691$	−2.73852	−	4.74326i	−0.104178	−	0.180442i	−0.913402	+	0.407058i	$0.866555\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.68509	−	2.81077i	0.139783	−	0.106619i
$696$		0			0
$697$	0.219224	+	0.126569i	0.00830370	+	0.00479414i
$698$		0			0
$699$	12.0544			0.455939
$700$		0			0
$701$	29.8292			1.12663			0.563317	−	0.826241i	$-0.309525\pi$
$701$	29.8292			1.12663			0.563317	+	0.826241i	$0.309525\pi$
$702$		0			0
$703$	−12.6200	−	7.28617i	−0.475973	−	0.274803i
$704$		0			0
$705$	−6.60091	+	5.03478i	−0.248604	+	0.189621i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.0525	+	34.7319i	0.753086	+	1.30438i	0.946320	+	0.323231i	$0.104769\pi$
$709$	20.0525	+	34.7319i	0.753086	+	1.30438i	−0.193234	+	0.981153i	$0.561898\pi$
$710$		0			0
$711$	−0.00873900	+	0.0151364i	−0.000327738	+	0.000567659i
$712$		0			0
$713$			71.3403i			2.67172i
$714$		0			0
$715$	37.5194	−	4.82915i	1.40315	−	0.180600i
$716$		0			0
$717$	18.5215	+	10.6934i	0.691698	+	0.399352i
$718$		0			0
$719$	10.5888	+	18.3403i	0.394895	+	0.683979i	0.993088	−	0.117374i	$-0.0374476\pi$
$719$	10.5888	+	18.3403i	0.394895	+	0.683979i	−0.598193	+	0.801352i	$0.704114\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14.8860	−	8.59443i	0.553616	−	0.319630i
$724$		0			0
$725$	−7.97901	+	29.1035i	−0.296333	+	1.08088i
$726$		0			0
$727$		−	12.3642i		−	0.458562i	−0.973360	−	0.229281i	$-0.926362\pi$
$727$		−	12.3642i		−	0.458562i	0.973360	−	0.229281i	$-0.0736375\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.16139	−	2.01159i	0.0429556	−	0.0744013i
$732$		0			0
$733$	31.5698	−	18.2268i	1.16606	−	0.673222i	0.213308	−	0.976985i	$-0.431576\pi$
$733$	31.5698	−	18.2268i	1.16606	−	0.673222i	0.952748	+	0.303763i	$0.0982430\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.69739	−	3.28939i	0.209866	−	0.121166i
$738$		0			0
$739$	−19.2136	+	33.2790i	−0.706785	+	1.22419i	0.259258	+	0.965808i	$0.416522\pi$
$739$	−19.2136	+	33.2790i	−0.706785	+	1.22419i	−0.966043	+	0.258380i	$0.916811\pi$
$740$		0			0
$741$	27.3486			1.00468
$742$		0			0
$743$			38.1561i			1.39981i	0.714235	+	0.699906i	$0.246775\pi$
$743$			38.1561i			1.39981i	−0.714235	+	0.699906i	$0.753225\pi$
$744$		0			0
$745$	2.27625	+	0.950576i	0.0833952	+	0.0348264i
$746$		0			0
$747$	6.32339	−	3.65081i	0.231361	−	0.133576i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	0.960751	−	0.277413i	$-0.0894770\pi$
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	−0.720622	+	0.693328i	$0.756144\pi$
$752$		0			0
$753$	−20.0865	−	11.5969i	−0.731992	−	0.422616i
$754$		0			0
$755$	−2.98672	−	23.2049i	−0.108698	−	0.844513i
$756$		0			0
$757$		−	1.92272i		−	0.0698826i	−0.999389	−	0.0349413i	$-0.988876\pi$
$757$		−	1.92272i		−	0.0698826i	0.999389	−	0.0349413i	$-0.0111244\pi$
$758$		0			0
$759$	−9.92497	+	17.1905i	−0.360253	+	0.623977i
$760$		0			0
$761$	−9.10658	−	15.7731i	−0.330113	−	0.571773i	0.652420	−	0.757857i	$-0.273754\pi$
$761$	−9.10658	−	15.7731i	−0.330113	−	0.571773i	−0.982534	+	0.186084i	$0.940420\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.321519	+	0.421531i	0.0116245	+	0.0152405i
$766$		0			0
$767$	46.5298	+	26.8640i	1.68009	+	0.970003i
$768$		0			0
$769$	32.1465			1.15923			0.579617	−	0.814889i	$-0.303202\pi$
$769$	32.1465			1.15923			0.579617	+	0.814889i	$0.303202\pi$
$770$		0			0
$771$	26.1561			0.941990
$772$		0			0
$773$	25.3202	+	14.6186i	0.910704	+	0.525795i	0.880658	−	0.473753i	$-0.157101\pi$
$773$	25.3202	+	14.6186i	0.910704	+	0.525795i	0.0300465	+	0.999549i	$0.490434\pi$
$774$		0			0
$775$	37.0438	+	37.4749i	1.33065	+	1.34614i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.53057	+	4.38307i	0.0906669	+	0.157040i
$780$		0			0
$781$	17.3624	−	30.0725i	0.621274	−	1.07608i
$782$		0			0
$783$		−	6.03549i		−	0.215691i
$784$		0			0
$785$	−20.0967	+	2.58666i	−0.717283	+	0.0923220i
$786$		0			0
$787$	−6.24645	−	3.60639i	−0.222662	−	0.128554i	0.384520	−	0.923117i	$-0.374367\pi$
$787$	−6.24645	−	3.60639i	−0.222662	−	0.128554i	−0.607182	+	0.794563i	$0.707700\pi$
$788$		0			0
$789$	−3.84991	−	6.66823i	−0.137060	−	0.237395i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	40.6569	−	23.4733i	1.44377	−	0.833561i
$794$		0			0
$795$	22.7104	+	9.48402i	0.805455	+	0.336364i
$796$		0			0
$797$		−	32.3827i		−	1.14706i	−0.819186	−	0.573528i	$-0.805575\pi$
$797$		−	32.3827i		−	1.14706i	0.819186	−	0.573528i	$-0.194425\pi$
$798$		0			0
$799$	−0.880253			−0.0311411
$800$		0			0
$801$	8.97583	−	15.5466i	0.317146	−	0.549312i
$802$		0			0
$803$	−9.64226	+	5.56696i	−0.340268	+	0.196454i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.6842	+	12.5194i	−0.763321	+	0.440704i
$808$		0			0
$809$	16.2132	−	28.0821i	0.570026	−	0.987313i	−0.426537	−	0.904470i	$-0.640267\pi$
$809$	16.2132	−	28.0821i	0.570026	−	0.987313i	0.996563	−	0.0828431i	$-0.0264000\pi$
$810$		0			0
$811$	−5.01118			−0.175966			−0.0879832	−	0.996122i	$-0.528042\pi$
$811$	−5.01118			−0.175966			−0.0879832	+	0.996122i	$0.528042\pi$
$812$		0			0
$813$			19.0885i			0.669461i
$814$		0			0
$815$	−7.18539	+	17.2061i	−0.251693	+	0.602704i
$816$		0			0
$817$	40.2188	−	23.2204i	1.40708	−	0.812377i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.838860	−	0.544348i	$-0.816777\pi$
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.0519891	−	0.998648i	$-0.516556\pi$
$822$		0			0
$823$	−44.5317	−	25.7104i	−1.55228	−	0.896207i	−0.997956	−	0.0639036i	$-0.979645\pi$
$823$	−44.5317	−	25.7104i	−1.55228	−	0.896207i	−0.554320	−	0.832303i	$-0.687022\pi$
$824$		0			0
$825$	3.71271	+	14.1837i	0.129260	+	0.493815i
$826$		0			0
$827$		−	11.7679i		−	0.409211i	−0.978845	−	0.204605i	$-0.934409\pi$
$827$		−	11.7679i		−	0.409211i	0.978845	−	0.204605i	$-0.0655911\pi$
$828$		0			0
$829$	−21.0994	+	36.5453i	−0.732814	+	1.26927i	0.222862	+	0.974850i	$0.428460\pi$
$829$	−21.0994	+	36.5453i	−0.732814	+	1.26927i	−0.955676	+	0.294421i	$0.904873\pi$
$830$		0			0
$831$	6.06933	+	10.5124i	0.210543	+	0.364671i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	13.9524	+	18.2924i	0.482841	+	0.633034i
$836$		0			0
$837$	−9.12679	−	5.26936i	−0.315468	−	0.182136i
$838$		0			0
$839$	−34.6127			−1.19496			−0.597482	−	0.801882i	$-0.703832\pi$
$839$	−34.6127			−1.19496			−0.597482	+	0.801882i	$0.703832\pi$
$840$		0			0
$841$	7.42713			0.256108
$842$		0			0
$843$	−5.49525	−	3.17269i	−0.189267	−	0.109273i
$844$		0			0
$845$	36.0660	−	27.5090i	1.24071	−	0.946339i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6.80964	+	11.7947i	0.233706	+	0.404791i
$850$		0			0
$851$	10.4049	−	18.0219i	0.356676	−	0.617782i
$852$		0			0
$853$			7.87710i			0.269707i	0.990866	+	0.134853i	$0.0430564\pi$
$853$			7.87710i			0.269707i	−0.990866	+	0.134853i	$0.956944\pi$
$854$		0			0
$855$	1.35313	+	10.5129i	0.0462761	+	0.359535i
$856$		0			0
$857$	3.88158	+	2.24103i	0.132592	+	0.0765522i	0.564829	−	0.825208i	$-0.308942\pi$
$857$	3.88158	+	2.24103i	0.132592	+	0.0765522i	−0.432237	+	0.901760i	$0.642275\pi$
$858$		0			0
$859$	−13.2214	−	22.9002i	−0.451110	−	0.781345i	0.547345	−	0.836907i	$-0.315638\pi$
$859$	−13.2214	−	22.9002i	−0.451110	−	0.781345i	−0.998455	+	0.0555615i	$0.982305\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.9090	+	19.0000i	−1.12024	+	0.646768i	−0.941461	−	0.337122i	$-0.890547\pi$
$863$	−32.9090	+	19.0000i	−1.12024	+	0.646768i	−0.178775	+	0.983890i	$0.557213\pi$
$864$		0			0
$865$	14.9016	−	35.6834i	0.506671	−	1.21327i
$866$		0			0
$867$		−	16.9438i		−	0.575441i
$868$		0			0
$869$	−0.0512511			−0.00173858
$870$		0			0
$871$	6.47189	−	11.2096i	0.219292	−	0.379824i
$872$		0			0
$873$	−2.00157	+	1.15561i	−0.0677430	+	0.0391115i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.1355	−	6.42910i	0.376020	−	0.217095i	−0.300065	−	0.953919i	$-0.597008\pi$
$877$	11.1355	−	6.42910i	0.376020	−	0.217095i	0.676085	+	0.736823i	$0.263675\pi$
$878$		0			0
$879$	−7.76107	+	13.4426i	−0.261774	+	0.453406i
$880$		0			0
$881$	−32.9744			−1.11094			−0.555468	−	0.831538i	$-0.687461\pi$
$881$	−32.9744			−1.11094			−0.555468	+	0.831538i	$0.687461\pi$
$882$		0			0
$883$			20.3321i			0.684229i	0.939658	+	0.342115i	$0.111143\pi$
$883$			20.3321i			0.684229i	−0.939658	+	0.342115i	$0.888857\pi$
$884$		0			0
$885$	−8.02451	+	19.2155i	−0.269741	+	0.645921i
$886$		0			0
$887$	34.8639	−	20.1287i	1.17062	−	0.675856i	0.216791	−	0.976218i	$-0.430441\pi$
$887$	34.8639	−	20.1287i	1.17062	−	0.675856i	0.953825	+	0.300362i	$0.0971076\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.46616	−	2.53947i	−0.0491182	−	0.0850753i
$892$		0			0
$893$	−15.2415	−	8.79970i	−0.510039	−	0.294471i
$894$		0			0
$895$	−3.14549	−	24.4384i	−0.105142	−	0.816886i
$896$		0			0
$897$			39.0548i			1.30400i
$898$		0			0
$899$	31.8031	−	55.0847i	1.06069	−	1.83718i
$900$		0			0
$901$	1.30477	+	2.25993i	0.0434682	+	0.0752891i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.06616	−	6.15239i	0.268128	−	0.204512i
$906$		0			0
$907$	41.7005	+	24.0758i	1.38464	+	0.799423i	0.992705	−	0.120569i	$-0.0384720\pi$
$907$	41.7005	+	24.0758i	1.38464	+	0.799423i	0.391936	+	0.919992i	$0.371805\pi$
$908$		0			0
$909$	−7.84205			−0.260104
$910$		0			0
$911$	−30.2224			−1.00131			−0.500656	−	0.865646i	$-0.666908\pi$
$911$	−30.2224			−1.00131			−0.500656	+	0.865646i	$0.666908\pi$
$912$		0			0
$913$	18.5422	+	10.7054i	0.613658	+	0.354295i
$914$		0			0
$915$	11.0348	+	14.4674i	0.364801	+	0.478276i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12.6387	+	21.8908i	0.416911	+	0.722111i	0.995627	−	0.0934183i	$-0.0297794\pi$
$919$	12.6387	+	21.8908i	0.416911	+	0.722111i	−0.578716	+	0.815529i	$0.696446\pi$
$920$		0			0
$921$	−6.72028	+	11.6399i	−0.221441	+	0.383547i
$922$		0			0
$923$		−	68.3210i		−	2.24881i
$924$		0			0
$925$	−3.89225	−	14.8697i	−0.127976	−	0.488911i
$926$		0			0
$927$	3.53388	+	2.04029i	0.116068	+	0.0670118i
$928$		0			0
$929$	13.8502	+	23.9892i	0.454409	+	0.787060i	0.998654	−	0.0518664i	$-0.0165170\pi$
$929$	13.8502	+	23.9892i	0.454409	+	0.787060i	−0.544245	+	0.838927i	$0.683184\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.12314	−	1.22580i	0.0695085	−	0.0401308i
$934$		0			0
$935$	−0.599065	+	1.43452i	−0.0195915	+	0.0469138i
$936$		0			0
$937$		−	30.8163i		−	1.00673i	−0.864075	−	0.503363i	$-0.832096\pi$
$937$		−	30.8163i		−	1.00673i	0.864075	−	0.503363i	$-0.167904\pi$
$938$		0			0
$939$	−9.91942			−0.323708
$940$		0			0
$941$	−14.1180	+	24.4532i	−0.460235	+	0.797151i	−0.998972	−	0.0453231i	$-0.985568\pi$
$941$	−14.1180	+	24.4532i	−0.460235	+	0.797151i	0.538737	+	0.842474i	$0.318902\pi$
$942$		0			0
$943$	−6.25919	+	3.61375i	−0.203827	+	0.117680i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.59436	+	1.49785i	−0.0843052	+	0.0486736i	−0.541560	−	0.840662i	$-0.682166\pi$
$947$	−2.59436	+	1.49785i	−0.0843052	+	0.0486736i	0.457255	+	0.889336i	$0.348833\pi$
$948$		0			0
$949$	−10.9530	+	18.9712i	−0.355550	+	0.615831i
$950$		0			0
$951$	−25.9950			−0.842947
$952$		0			0
$953$			10.0423i			0.325303i	0.986684	+	0.162651i	$0.0520046\pi$
$953$			10.0423i			0.325303i	−0.986684	+	0.162651i	$0.947995\pi$
$954$		0			0
$955$	17.9112	+	7.47982i	0.579591	+	0.242041i
$956$		0			0
$957$	15.3269	−	8.84900i	0.495449	−	0.286047i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−40.0322	−	69.3379i	−1.29136	−	2.23671i
$962$		0			0
$963$	−15.8887	−	9.17335i	−0.512007	−	0.295607i
$964$		0			0
$965$	15.6602	−	2.01564i	0.504120	−	0.0648857i
$966$		0			0
$967$			21.3514i			0.686616i	0.939223	+	0.343308i	$0.111547\pi$
$967$			21.3514i			0.686616i	−0.939223	+	0.343308i	$0.888453\pi$
$968$		0			0
$969$	−0.561945	+	0.973318i	−0.0180523	+	0.0312675i
$970$		0			0
$971$	19.0000	+	32.9090i	0.609740	+	1.05610i	0.991283	+	0.131749i	$0.0420594\pi$
$971$	19.0000	+	32.9090i	0.609740	+	1.05610i	−0.381543	+	0.924351i	$0.624607\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	20.2794	+	20.5154i	0.649461	+	0.657019i
$976$		0			0
$977$	−37.0401	−	21.3851i	−1.18502	−	0.684170i	−0.227848	−	0.973697i	$-0.573169\pi$
$977$	−37.0401	−	21.3851i	−1.18502	−	0.684170i	−0.957170	+	0.289526i	$0.906502\pi$
$978$		0			0
$979$	52.6401			1.68238
$980$		0			0
$981$	−10.4144			−0.332506
$982$		0			0
$983$	11.6735	+	6.73968i	0.372326	+	0.214962i	0.674474	−	0.738299i	$-0.264370\pi$
$983$	11.6735	+	6.73968i	0.372326	+	0.214962i	−0.302148	+	0.953261i	$0.597704\pi$
$984$		0			0
$985$	4.86691	+	6.38081i	0.155073	+	0.203310i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	33.1596	+	57.4341i	1.05441	+	1.82630i
$990$		0			0
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	−0.996180	−	0.0873218i	$-0.972169\pi$
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	0.573713	+	0.819056i	$0.305503\pi$
$992$		0			0
$993$		−	7.53226i		−	0.239029i
$994$		0			0
$995$	0.851365	+	6.61456i	0.0269901	+	0.209696i
$996$		0			0
$997$	12.4598	+	7.19366i	0.394605	+	0.227825i	0.684154	−	0.729338i	$-0.260172\pi$
$997$	12.4598	+	7.19366i	0.394605	+	0.227825i	−0.289548	+	0.957163i	$0.593505\pi$
$998$		0			0
$999$	1.53706	+	2.66227i	0.0486305	+	0.0842306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.bb.i.949.5		16
5.4	even	2	inner	2940.2.bb.i.949.4		16
7.2	even	3	inner	2940.2.bb.i.1549.4		16
7.3	odd	6		2940.2.k.f.589.7		8
7.4	even	3		2940.2.k.g.589.2		8
7.5	odd	6		420.2.bb.a.289.5	yes	16
7.6	odd	2		420.2.bb.a.109.4	✓	16
21.5	even	6		1260.2.bm.c.289.7		16
21.20	even	2		1260.2.bm.c.109.2		16
28.19	even	6		1680.2.di.e.289.1		16
28.27	even	2		1680.2.di.e.529.8		16
35.4	even	6		2940.2.k.g.589.6		8
35.9	even	6	inner	2940.2.bb.i.1549.5		16
35.12	even	12		2100.2.q.l.1801.3		8
35.13	even	4		2100.2.q.m.1201.2		8
35.19	odd	6		420.2.bb.a.289.4	yes	16
35.24	odd	6		2940.2.k.f.589.3		8
35.27	even	4		2100.2.q.l.1201.3		8
35.33	even	12		2100.2.q.m.1801.2		8
35.34	odd	2		420.2.bb.a.109.5	yes	16
105.89	even	6		1260.2.bm.c.289.2		16
105.104	even	2		1260.2.bm.c.109.7		16
140.19	even	6		1680.2.di.e.289.8		16
140.139	even	2		1680.2.di.e.529.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.4	✓	16	7.6	odd	2
420.2.bb.a.109.5	yes	16	35.34	odd	2
420.2.bb.a.289.4	yes	16	35.19	odd	6
420.2.bb.a.289.5	yes	16	7.5	odd	6
1260.2.bm.c.109.2		16	21.20	even	2
1260.2.bm.c.109.7		16	105.104	even	2
1260.2.bm.c.289.2		16	105.89	even	6
1260.2.bm.c.289.7		16	21.5	even	6
1680.2.di.e.289.1		16	28.19	even	6
1680.2.di.e.289.8		16	140.19	even	6
1680.2.di.e.529.1		16	140.139	even	2
1680.2.di.e.529.8		16	28.27	even	2
2100.2.q.l.1201.3		8	35.27	even	4
2100.2.q.l.1801.3		8	35.12	even	12
2100.2.q.m.1201.2		8	35.13	even	4
2100.2.q.m.1801.2		8	35.33	even	12
2940.2.k.f.589.3		8	35.24	odd	6
2940.2.k.f.589.7		8	7.3	odd	6
2940.2.k.g.589.2		8	7.4	even	3
2940.2.k.g.589.6		8	35.4	even	6
2940.2.bb.i.949.4		16	5.4	even	2	inner
2940.2.bb.i.949.5		16	1.1	even	1	trivial
2940.2.bb.i.1549.4		16	7.2	even	3	inner
2940.2.bb.i.1549.5		16	35.9	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.77792 + 1.35609i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} +5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(-0.205328 - 0.118546i) q^{17} +(-2.37016 - 4.10523i) q^{19} +(5.86244 - 3.38468i) q^{23} +(1.32201 - 4.82206i) q^{25} +1.00000i q^{27} -6.03549 q^{29} +(-5.26936 + 9.12679i) q^{31} +(-2.53947 + 1.46616i) q^{33} +(2.66227 - 1.53706i) q^{37} +(-2.88468 + 4.99641i) q^{39} -1.06768 q^{41} +9.79697i q^{43} +(-2.06337 - 0.861678i) q^{45} +(3.21530 - 1.85635i) q^{47} +(-0.118546 - 0.205328i) q^{51} +(-9.53186 - 5.50322i) q^{53} +(-0.837035 - 6.50322i) q^{55} -4.74032i q^{57} +(4.65633 - 8.06499i) q^{59} +(-4.06861 - 7.04704i) q^{61} +(-7.82379 - 10.2575i) q^{65} +(-1.94296 - 1.12177i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(3.28827 + 1.89848i) q^{73} +(3.55593 - 3.51502i) q^{75} +(0.00873900 + 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(-5.22689 - 3.01774i) q^{87} +(-8.97583 - 15.5466i) q^{89} +(-9.12679 + 5.26936i) q^{93} +(9.78104 + 4.08463i) q^{95} +2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} - 8 q^{19} + 12 q^{25} + 24 q^{29} - 4 q^{39} - 48 q^{41} + 2 q^{45} + 4 q^{51} + 40 q^{55} + 28 q^{59} + 32 q^{61} - 26 q^{65} + 24 q^{69} - 56 q^{71} + 8 q^{75}+ \cdots - 16 q^{99}+O(q^{100}) \) 16 * q - 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 - 8 * q^19 + 12 * q^25 + 24 * q^29 - 4 * q^39 - 48 * q^41 + 2 * q^45 + 4 * q^51 + 40 * q^55 + 28 * q^59 + 32 * q^61 - 26 * q^65 + 24 * q^69 - 56 * q^71 + 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 + 16 * q^89 + 22 * q^95 - 16 * q^99

Introduction

L-functions

Modular forms

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