LMFDB - Embedded newform 2940.2.bb.i.1549.4

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			1549.4
Root			$0.104482 - 0.389934i$ of defining polynomial
Character	$\chi$	$=$	2940.1549
Dual form			2940.2.bb.i.949.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(2.06337 + 0.861678i) q^{5} +(0.500000 - 0.866025i) q^{9} +(-1.46616 - 2.53947i) q^{11} +5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(0.205328 - 0.118546i) q^{17} +(-2.37016 + 4.10523i) q^{19} +(-5.86244 - 3.38468i) q^{23} +(3.51502 + 3.55593i) q^{25} +1.00000i q^{27} -6.03549 q^{29} +(-5.26936 - 9.12679i) q^{31} +(2.53947 + 1.46616i) q^{33} +(-2.66227 - 1.53706i) q^{37} +(-2.88468 - 4.99641i) q^{39} -1.06768 q^{41} +9.79697i q^{43} +(1.77792 - 1.35609i) q^{45} +(-3.21530 - 1.85635i) q^{47} +(-0.118546 + 0.205328i) q^{51} +(9.53186 - 5.50322i) q^{53} +(-0.837035 - 6.50322i) q^{55} -4.74032i q^{57} +(4.65633 + 8.06499i) q^{59} +(-4.06861 + 7.04704i) q^{61} +(-4.97133 + 11.9043i) q^{65} +(1.94296 - 1.12177i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(-3.28827 + 1.89848i) q^{73} +(-4.82206 - 1.32201i) q^{75} +(0.00873900 - 0.0151364i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(5.22689 - 3.01774i) q^{87} +(-8.97583 + 15.5466i) q^{89} +(9.12679 + 5.26936i) q^{93} +(-8.42791 + 6.42832i) q^{95} +2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

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

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
$5$	2.06337	+	0.861678i	0.922769	+	0.385354i
$5$	2.06337	+	0.861678i	0.922769	+	0.385354i
$6$		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	0.555778	−	0.831330i	$-0.312420\pi$
$11$	−1.46616	−	2.53947i	−0.442064	−	0.765678i	−0.997843	+	0.0656529i	$0.979087\pi$
$12$		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	$-0.657513\pi$
$17$	0.205328	−	0.118546i	0.0497993	−	0.0287516i	0.524693	+	0.851292i	$0.324180\pi$
$18$		0			0
$19$	−2.37016	+	4.10523i	−0.543752	+	0.941805i	0.454933	+	0.890526i	$0.349663\pi$
$19$	−2.37016	+	4.10523i	−0.543752	+	0.941805i	−0.998684	+	0.0512796i	$0.983670\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.86244	−	3.38468i	−1.22240	−	0.705754i	−0.256973	−	0.966419i	$-0.582725\pi$
$23$	−5.86244	−	3.38468i	−1.22240	−	0.705754i	−0.965429	+	0.260664i	$0.916058\pi$
$24$		0			0
$25$	3.51502	+	3.55593i	0.703004	+	0.711186i
$26$		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	−0.752915	−	0.658118i	$-0.771353\pi$
$31$	−5.26936	−	9.12679i	−0.946404	−	1.63922i	−0.193490	−	0.981102i	$-0.561981\pi$
$32$		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	$-0.414649\pi$
$37$	−2.66227	−	1.53706i	−0.437675	−	0.252692i	−0.702611	+	0.711574i	$0.747982\pi$
$38$		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
$45$	1.77792	−	1.35609i	0.265037	−	0.202155i
$46$		0			0
$47$	−3.21530	−	1.85635i	−0.469000	−	0.270777i	0.246821	−	0.969061i	$-0.420614\pi$
$47$	−3.21530	−	1.85635i	−0.469000	−	0.270777i	−0.715821	+	0.698284i	$0.753947\pi$
$48$		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	$-0.393854\pi$
$53$	9.53186	−	5.50322i	1.30930	−	0.755926i	0.981980	+	0.188987i	$0.0605203\pi$
$54$		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	0.991860	+	0.127331i	$0.0406410\pi$
$59$	4.65633	+	8.06499i	0.606202	+	1.04997i	−0.385658	+	0.922642i	$0.626026\pi$
$60$		0			0
$61$	−4.06861	+	7.04704i	−0.520932	+	0.902281i	0.478771	+	0.877940i	$0.341082\pi$
$61$	−4.06861	+	7.04704i	−0.520932	+	0.902281i	−0.999704	+	0.0243418i	$0.992251\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.97133	+	11.9043i	−0.616618	+	1.47655i
$66$		0			0
$67$	1.94296	−	1.12177i	0.237371	−	0.137046i	−0.376597	−	0.926377i	$-0.622906\pi$
$67$	1.94296	−	1.12177i	0.237371	−	0.137046i	0.613968	+	0.789331i	$0.289572\pi$
$68$		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	$-0.737991\pi$
$73$	−3.28827	+	1.89848i	−0.384863	+	0.222201i	0.295069	+	0.955476i	$0.404657\pi$
$74$		0			0
$75$	−4.82206	−	1.32201i	−0.556804	−	0.152653i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.00873900	−	0.0151364i	0.000983215	−	0.00170298i	−0.865533	−	0.500851i	$-0.833020\pi$
$79$	0.00873900	−	0.0151364i	0.000983215	−	0.00170298i	0.866517	+	0.499148i	$0.166354\pi$
$80$		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	−0.209117	+	0.977891i	$0.567059\pi$
$89$	−8.97583	+	15.5466i	−0.951437	+	1.64794i	−0.742320	+	0.670046i	$0.766274\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	9.12679	+	5.26936i	0.946404	+	0.546407i
$94$		0			0
$95$	−8.42791	+	6.42832i	−0.864686	+	0.659531i
$96$		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	0.602313	−	0.798260i	$-0.294246\pi$
$101$	−3.92103	−	6.79142i	−0.390157	−	0.675771i	−0.992470	+	0.122489i	$0.960912\pi$
$102$		0			0
$103$	−3.53388	−	2.04029i	−0.348204	−	0.201036i	0.315690	−	0.948862i	$-0.397764\pi$
$103$	−3.53388	−	2.04029i	−0.348204	−	0.201036i	−0.663894	+	0.747827i	$0.731097\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.8887	+	9.17335i	1.53602	+	0.886822i	0.999066	+	0.0432102i	$0.0137585\pi$
$107$	15.8887	+	9.17335i	1.53602	+	0.886822i	0.536954	+	0.843611i	$0.319575\pi$
$108$		0			0
$109$	−5.20719	−	9.01912i	−0.498759	−	0.863875i	0.501240	−	0.865308i	$-0.332877\pi$
$109$	−5.20719	−	9.01912i	−0.498759	−	0.863875i	−0.999999	+	0.00143278i	$0.999544\pi$
$110$		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
$115$	−9.17989	−	12.0354i	−0.856029	−	1.12231i
$116$		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	−0.800840	−	0.598878i	$-0.795613\pi$
$131$	1.35313	−	2.34369i	0.118223	−	0.204769i	0.919064	+	0.394109i	$0.128947\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.861678	+	2.06337i	−0.0741615	+	0.177587i
$136$		0			0
$137$	−8.66460	+	5.00251i	−0.740267	+	0.427393i	−0.822166	−	0.569247i	$-0.807235\pi$
$137$	−8.66460	+	5.00251i	−0.740267	+	0.427393i	0.0818996	+	0.996641i	$0.473901\pi$
$138$		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
$145$	−12.4535	−	5.20065i	−1.03420	−	0.431891i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.551584	+	0.955371i	−0.0451875	+	0.0782671i	−0.887735	−	0.460356i	$-0.847722\pi$
$149$	−0.551584	+	0.955371i	−0.0451875	+	0.0782671i	0.842547	+	0.538623i	$0.181055\pi$
$150$		0			0
$151$	−5.23158	−	9.06136i	−0.425740	−	0.737403i	0.570749	−	0.821124i	$-0.306653\pi$
$151$	−5.23158	−	9.06136i	−0.425740	−	0.737403i	−0.996489	+	0.0837214i	$0.973319\pi$
$152$		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	$-0.784436\pi$
$157$	−7.84763	+	4.53083i	−0.626309	+	0.361600i	0.153012	+	0.988224i	$0.451103\pi$
$158$		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	$-0.439227\pi$
$163$	−7.22164	−	4.16941i	−0.565642	−	0.326574i	−0.755407	+	0.655256i	$0.772561\pi$
$164$		0			0
$165$	3.97651	+	5.21344i	0.309571	+	0.405866i
$166$		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	$-0.104986\pi$
$173$	14.9768	+	8.64687i	1.13867	+	0.657409i	0.192566	+	0.981284i	$0.438319\pi$
$174$		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	0.583276	−	0.812274i	$-0.301771\pi$
$179$	−5.50967	−	9.54303i	−0.411812	−	0.713280i	−0.995088	+	0.0989944i	$0.968437\pi$
$180$		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
$185$	−4.16881	−	5.46556i	−0.306497	−	0.401836i
$186$		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	−0.979235	−	0.202728i	$-0.935019\pi$
$191$	−4.34026	+	7.51755i	−0.314050	+	0.543951i	0.665185	+	0.746679i	$0.268353\pi$
$192$		0			0
$193$	6.11520	−	3.53061i	0.440182	−	0.254139i	−0.263493	−	0.964661i	$-0.584875\pi$
$193$	6.11520	−	3.53061i	0.440182	−	0.254139i	0.703675	+	0.710522i	$0.251541\pi$
$194$		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	0.914029	−	0.405648i	$-0.132954\pi$
$199$	1.49126	+	2.58294i	0.105713	+	0.183100i	−0.808316	+	0.588748i	$0.799621\pi$
$200$		0			0
$201$	−1.12177	+	1.94296i	−0.0791236	+	0.137046i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.20302	−	0.919995i	−0.153866	−	0.0642553i
$206$		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
$215$	−8.44183	+	20.2148i	−0.575728	+	1.37864i
$216$		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	$-0.769136\pi$
$227$	−8.25642	+	4.76685i	−0.547998	+	0.316387i	0.200316	+	0.979731i	$0.435803\pi$
$228$		0			0
$229$	−9.05987	+	15.6922i	−0.598693	+	1.03697i	0.394321	+	0.918973i	$0.370980\pi$
$229$	−9.05987	+	15.6922i	−0.598693	+	1.03697i	−0.993014	+	0.117994i	$0.962354\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.4394	−	6.02720i	−0.683909	−	0.394855i	0.117417	−	0.993083i	$-0.462538\pi$
$233$	−10.4394	−	6.02720i	−0.683909	−	0.394855i	−0.801326	+	0.598228i	$0.795872\pi$
$234$		0			0
$235$	−5.03478	−	6.60091i	−0.328433	−	0.430596i
$236$		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	0.998010	+	0.0630593i	$0.0200857\pi$
$241$	8.59443	+	14.8860i	0.553616	+	0.958891i	−0.444394	+	0.895831i	$0.646581\pi$
$242$		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
$255$	−0.421531	+	0.321519i	−0.0263973	+	0.0201343i
$256$		0			0
$257$	−22.6519	−	13.0781i	−1.41299	−	0.815787i	−0.417317	−	0.908761i	$-0.637029\pi$
$257$	−22.6519	−	13.0781i	−1.41299	−	0.815787i	−0.995669	+	0.0929737i	$0.970363\pi$
$258$		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	$-0.590373\pi$
$263$	6.66823	−	3.84991i	0.411181	−	0.237395i	0.691297	+	0.722571i	$0.257040\pi$
$264$		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	−0.941130	−	0.338046i	$-0.890234\pi$
$269$	−12.5194	−	21.6842i	−0.763321	−	1.32211i	0.177809	−	0.984065i	$-0.443099\pi$
$270$		0			0
$271$	9.54423	−	16.5311i	0.579771	−	1.00419i	−0.415735	−	0.909486i	$-0.636476\pi$
$271$	9.54423	−	16.5311i	0.579771	−	1.00419i	0.995505	−	0.0947062i	$-0.0301912\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.87657	−	14.1398i	0.233766	−	0.852664i
$276$		0			0
$277$	−10.5124	+	6.06933i	−0.631628	+	0.364671i	−0.781382	−	0.624053i	$-0.785485\pi$
$277$	−10.5124	+	6.06933i	−0.631628	+	0.364671i	0.149754	+	0.988723i	$0.452152\pi$
$278$		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	$-0.799323\pi$
$283$	−11.7947	+	6.80964i	−0.701119	+	0.404791i	0.106645	+	0.994297i	$0.465989\pi$
$284$		0			0
$285$	4.08463	−	9.78104i	0.241953	−	0.579379i
$286$		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
$305$	−14.4674	+	11.0348i	−0.828398	+	0.631854i
$306$		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	0.898685	−	0.438595i	$-0.144524\pi$
$311$	1.22580	+	2.12314i	0.0695085	+	0.120392i	−0.829177	+	0.558987i	$0.811190\pi$
$312$		0			0
$313$	8.59047	+	4.95971i	0.485562	+	0.280340i	0.722732	−	0.691129i	$-0.242886\pi$
$313$	8.59047	+	4.95971i	0.485562	+	0.280340i	−0.237169	+	0.971468i	$0.576220\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5124	+	12.9975i	1.26442	+	0.730013i	0.973927	−	0.226863i	$-0.0728471\pi$
$317$	22.5124	+	12.9975i	1.26442	+	0.730013i	0.290494	+	0.956877i	$0.406180\pi$
$318$		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
$325$	−20.5154	+	20.2794i	−1.13799	+	1.12490i
$326$		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	−0.950770	−	0.309898i	$-0.899705\pi$
$331$	−3.76613	+	6.52313i	−0.207005	+	0.358544i	0.743764	+	0.668442i	$0.233038\pi$
$332$		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
$345$	13.9677	+	5.83301i	0.751996	+	0.314039i
$346$		0			0
$347$	7.97850	−	4.60639i	0.428309	−	0.247284i	−0.270317	−	0.962771i	$-0.587129\pi$
$347$	7.97850	−	4.60639i	0.428309	−	0.247284i	0.698626	+	0.715487i	$0.253795\pi$
$348$		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	$-0.536150\pi$
$353$	12.9725	−	7.48969i	0.690457	−	0.398636i	0.803783	+	0.594922i	$0.202817\pi$
$354$		0			0
$355$	−24.4346	−	10.2040i	−1.29685	−	0.541574i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.4823	−	18.1559i	0.553236	−	0.958233i	−0.444802	−	0.895629i	$-0.646726\pi$
$359$	10.4823	−	18.1559i	0.553236	−	0.958233i	0.998038	−	0.0626045i	$-0.0199407\pi$
$360$		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	$-0.832925\pi$
$367$	−16.5538	+	9.55732i	−0.864099	+	0.498888i	0.00128371	+	0.999999i	$0.499591\pi$
$368$		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	$-0.279393\pi$
$373$	5.64151	+	3.25713i	0.292106	+	0.168648i	−0.346785	+	0.937945i	$0.612727\pi$
$374$		0			0
$375$	−8.81056	−	6.88288i	−0.454975	−	0.355430i
$376$		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	$-0.109719\pi$
$383$	21.9018	+	12.6450i	1.11913	+	0.646131i	0.177952	+	0.984039i	$0.443053\pi$
$384$		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	0.973627	+	0.228148i	$0.0732669\pi$
$389$	13.4984	+	23.3799i	0.684395	+	1.18541i	−0.289232	+	0.957259i	$0.593400\pi$
$390$		0			0
$391$	−1.60496			−0.0811663
$392$		0			0
$393$			2.70626i			0.136513i
$394$		0			0
$395$	0.0310745	−	0.0237018i	0.00156353	−	0.00119257i
$396$		0			0
$397$	−27.3806	−	15.8082i	−1.37419	−	0.793391i	−0.382741	−	0.923856i	$-0.625020\pi$
$397$	−27.3806	−	15.8082i	−1.37419	−	0.793391i	−0.991453	+	0.130464i	$0.958353\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.24497	−	10.8166i	0.311859	−	0.540156i	−0.666906	−	0.745142i	$-0.732382\pi$
$401$	6.24497	−	10.8166i	0.311859	−	0.540156i	0.978765	+	0.204986i	$0.0657150\pi$
$402$		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	0.667935	−	0.744219i	$-0.267178\pi$
$409$	−6.28039	−	10.8779i	−0.310545	−	0.537880i	−0.978480	+	0.206339i	$0.933845\pi$
$410$		0			0
$411$	5.00251	−	8.66460i	0.246756	−	0.427393i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.29165	−	15.0660i	0.308845	−	0.739560i
$416$		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
$425$	1.14327	+	0.313439i	0.0554568	+	0.0152040i
$426$		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	−0.969646	−	0.244512i	$-0.921372\pi$
$431$	−14.4613	−	25.0477i	−0.696577	−	1.20651i	0.273069	−	0.961994i	$-0.411961\pi$
$432$		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	−0.592614	−	0.805487i	$-0.701904\pi$
$439$	8.40744	−	14.5621i	0.401265	−	0.695012i	0.993879	+	0.110475i	$0.0352372\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.81665	+	5.09030i	0.418892	+	0.241847i	0.694603	−	0.719393i	$-0.255580\pi$
$443$	8.81665	+	5.09030i	0.418892	+	0.241847i	−0.275711	+	0.961241i	$0.588913\pi$
$444$		0			0
$445$	−31.9167	+	24.3442i	−1.51300	+	1.15402i
$446$		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	$-0.521091\pi$
$457$	−20.5960	−	11.8911i	−0.963442	−	0.556243i	−0.897231	+	0.441562i	$0.854424\pi$
$458$		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
$465$	14.2915	+	18.7370i	0.662752	+	0.868908i
$466$		0			0
$467$	−7.67142	−	4.42910i	−0.354991	−	0.204954i	0.311890	−	0.950118i	$-0.399038\pi$
$467$	−7.67142	−	4.42910i	−0.354991	−	0.204954i	−0.666881	+	0.745164i	$0.732371\pi$
$468$		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	0.946903	−	0.321518i	$-0.104193\pi$
$479$	4.26797	+	7.39235i	0.195009	+	0.337765i	−0.751895	+	0.659283i	$0.770860\pi$
$480$		0			0
$481$	8.86787	−	15.3596i	0.404340	−	0.700337i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.99153	+	4.76891i	−0.0904306	+	0.216545i
$486$		0			0
$487$	−1.70528	+	0.984545i	−0.0772737	+	0.0446140i	−0.538139	−	0.842856i	$-0.680872\pi$
$487$	−1.70528	+	0.984545i	−0.0772737	+	0.0446140i	0.460865	+	0.887470i	$0.347539\pi$
$488$		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
$495$	−6.05048	−	2.52672i	−0.271949	−	0.113568i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−7.47239	+	12.9426i	−0.334510	+	0.579389i	−0.983391	−	0.181502i	$-0.941904\pi$
$499$	−7.47239	+	12.9426i	−0.334510	+	0.579389i	0.648880	+	0.760890i	$0.275238\pi$
$500$		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	−0.0775359	−	0.996990i	$-0.524705\pi$
$509$	18.6050	−	32.2247i	0.824650	−	1.42834i	0.902186	−	0.431347i	$-0.141961\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.10523	−	2.37016i	−0.181251	−	0.104645i
$514$		0			0
$515$	−5.53365	−	7.25495i	−0.243842	−	0.319691i
$516$		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	0.988198	−	0.153183i	$-0.0489524\pi$
$521$	8.24999	+	14.2894i	0.361439	+	0.626030i	−0.626759	+	0.779213i	$0.715619\pi$
$522$		0			0
$523$	36.6757	+	21.1747i	1.60372	+	0.925907i	0.990735	+	0.135810i	$0.0433637\pi$
$523$	36.6757	+	21.1747i	1.60372	+	0.925907i	0.612982	+	0.790097i	$0.289970\pi$
$524$		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
$535$	24.8799	+	32.6190i	1.07565	+	1.41024i
$536$		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	0.0951000	−	0.995468i	$-0.469683\pi$
$541$	21.1579	−	36.6466i	0.909650	−	1.57556i	0.814550	−	0.580093i	$-0.196984\pi$
$542$		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
$555$	6.34307	+	2.64891i	0.269248	+	0.112440i
$556$		0			0
$557$	−2.58930	+	1.49493i	−0.109712	+	0.0633424i	−0.553852	−	0.832615i	$-0.686843\pi$
$557$	−2.58930	+	1.49493i	−0.109712	+	0.0633424i	0.444140	+	0.895958i	$0.353509\pi$
$558$		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	$-0.541353\pi$
$563$	15.7647	−	9.10174i	0.664402	−	0.383592i	0.793952	+	0.607980i	$0.208020\pi$
$564$		0			0
$565$	1.85110	−	4.43265i	0.0778765	−	0.186483i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.88700	+	17.1248i	−0.414484	+	0.717908i	−0.995374	−	0.0960741i	$-0.969371\pi$
$569$	−9.88700	+	17.1248i	−0.414484	+	0.717908i	0.580890	+	0.813982i	$0.302705\pi$
$570$		0			0
$571$	9.87481	+	17.1037i	0.413248	+	0.715767i	0.995243	−	0.0974259i	$-0.0310609\pi$
$571$	9.87481	+	17.1037i	0.413248	+	0.715767i	−0.581995	+	0.813193i	$0.697728\pi$
$572$		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	$-0.782310\pi$
$577$	−14.7851	+	8.53616i	−0.615510	+	0.355365i	0.159609	+	0.987180i	$0.448977\pi$
$578$		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
$585$	7.82379	+	10.2575i	0.323474	+	0.424094i
$586$		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	$-0.152871\pi$
$593$	22.6519	+	13.0781i	0.930201	+	0.537052i	0.0433259	+	0.999061i	$0.486205\pi$
$594$		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	0.991034	+	0.133614i	$0.0426581\pi$
$599$	14.9595	+	25.9107i	0.611229	+	1.05868i	−0.379804	+	0.925067i	$0.624009\pi$
$600$		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
$605$	4.26966	−	3.25665i	0.173586	−	0.132401i
$606$		0			0
$607$	30.0913	+	17.3732i	1.22137	+	0.705156i	0.965209	−	0.261479i	$-0.0842102\pi$
$607$	30.0913	+	17.3732i	1.22137	+	0.705156i	0.256157	+	0.966635i	$0.417544\pi$
$608$		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	$-0.707657\pi$
$613$	−5.50712	+	3.17954i	−0.222430	+	0.128420i	0.384645	+	0.923065i	$0.374324\pi$
$614$		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	0.790576	−	0.612364i	$-0.209781\pi$
$619$	−3.35963	−	5.81904i	−0.135035	−	0.233887i	−0.925611	+	0.378477i	$0.876448\pi$
$620$		0			0
$621$	3.38468	−	5.86244i	0.135822	−	0.235251i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.289263	+	24.9983i	−0.0115705	+	0.999933i
$626$		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
$635$	−1.57220	+	3.76478i	−0.0623907	+	0.149401i
$636$		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	0.954433	−	0.298426i	$-0.0964617\pi$
$641$	5.53886	+	9.59358i	0.218772	+	0.378924i	−0.735661	+	0.677350i	$0.763128\pi$
$642$		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	$-0.837151\pi$
$647$	−22.4844	+	12.9813i	−0.883951	+	0.510349i	−0.0119921	+	0.999928i	$0.503817\pi$
$648$		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	$-0.287562\pi$
$653$	6.34249	+	3.66184i	0.248201	+	0.143299i	−0.370739	+	0.928737i	$0.620896\pi$
$654$		0			0
$655$	4.81152	−	3.66994i	0.188002	−	0.143397i
$656$		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	0.678199	−	0.734878i	$-0.262761\pi$
$661$	−7.64417	−	13.2401i	−0.297324	−	0.514980i	−0.975523	+	0.219898i	$0.929427\pi$
$662$		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
$675$	−3.55593	+	3.51502i	−0.136868	+	0.135293i
$676$		0			0
$677$	28.1167	+	16.2332i	1.08061	+	0.623892i	0.931061	−	0.364862i	$-0.118884\pi$
$677$	28.1167	+	16.2332i	1.08061	+	0.623892i	0.149551	+	0.988754i	$0.452217\pi$
$678$		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	$-0.730256\pi$
$683$	−8.98285	+	5.18625i	−0.343719	+	0.198446i	0.318196	+	0.948025i	$0.396923\pi$
$684$		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	−0.913402	−	0.407058i	$-0.866555\pi$
$691$	−2.73852	+	4.74326i	−0.104178	+	0.180442i	0.809224	+	0.587500i	$0.199888\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.27674	−	1.78600i	−0.162226	−	0.0677467i
$696$		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
$705$	7.66070	+	3.19916i	0.288519	+	0.120487i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.0525	−	34.7319i	0.753086	−	1.30438i	−0.193234	−	0.981153i	$-0.561898\pi$
$709$	20.0525	−	34.7319i	0.753086	−	1.30438i	0.946320	−	0.323231i	$-0.104769\pi$
$710$		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	−0.598193	−	0.801352i	$-0.704114\pi$
$719$	10.5888	−	18.3403i	0.394895	−	0.683979i	0.993088	+	0.117374i	$0.0374476\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−14.8860	−	8.59443i	−0.553616	−	0.319630i
$724$		0			0
$725$	−21.2149	−	21.4618i	−0.787900	−	0.797070i
$726$		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	$-0.568424\pi$
$733$	−31.5698	−	18.2268i	−1.16606	−	0.673222i	−0.952748	+	0.303763i	$0.901757\pi$
$734$		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	−0.966043	−	0.258380i	$-0.916811\pi$
$739$	−19.2136	−	33.2790i	−0.706785	−	1.22419i	0.259258	−	0.965808i	$-0.416522\pi$
$740$		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
$745$	−1.96135	+	1.49600i	−0.0718582	+	0.0548092i
$746$		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	−0.720622	−	0.693328i	$-0.756144\pi$
$751$	6.58058	−	11.3979i	0.240129	−	0.415915i	0.960751	+	0.277413i	$0.0894770\pi$
$752$		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	−0.982534	−	0.186084i	$-0.940420\pi$
$761$	−9.10658	+	15.7731i	−0.330113	+	0.571773i	0.652420	+	0.757857i	$0.273754\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.204297	−	0.489209i	0.00738637	−	0.0176874i
$766$		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	$-0.842899\pi$
$773$	−25.3202	+	14.6186i	−0.910704	+	0.525795i	−0.0300465	+	0.999549i	$0.509566\pi$
$774$		0			0
$775$	13.9323	−	50.8183i	0.500464	−	1.82545i
$776$		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	$-0.625633\pi$
$787$	6.24645	−	3.60639i	0.222662	−	0.128554i	0.607182	+	0.794563i	$0.292300\pi$
$788$		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
$795$	−19.5686	+	14.9258i	−0.694027	+	0.529363i
$796$		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	0.996563	+	0.0828431i	$0.0264000\pi$
$809$	16.2132	+	28.0821i	0.570026	+	0.987313i	−0.426537	+	0.904470i	$0.640267\pi$
$810$		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
$815$	−11.3082	−	14.8258i	−0.396110	−	0.519325i
$816$		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	−0.0519891	+	0.998648i	$0.516556\pi$
$821$	−25.5256	+	44.2116i	−0.890849	+	1.54300i	−0.838860	+	0.544348i	$0.816777\pi$
$822$		0			0
$823$	44.5317	−	25.7104i	1.55228	−	0.896207i	0.554320	−	0.832303i	$-0.312978\pi$
$823$	44.5317	−	25.7104i	1.55228	−	0.896207i	0.997956	−	0.0639036i	$-0.0203550\pi$
$824$		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	−0.955676	−	0.294421i	$-0.904873\pi$
$829$	−21.0994	−	36.5453i	−0.732814	−	1.26927i	0.222862	−	0.974850i	$-0.428460\pi$
$830$		0			0
$831$	6.06933	−	10.5124i	0.210543	−	0.364671i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.86549	−	21.2293i	0.306803	−	0.734670i
$836$		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
$845$	−41.8565	−	17.4796i	−1.43991	−	0.601315i
$846$		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	$-0.691058\pi$
$857$	−3.88158	+	2.24103i	−0.132592	+	0.0765522i	0.432237	+	0.901760i	$0.357725\pi$
$858$		0			0
$859$	−13.2214	+	22.9002i	−0.451110	+	0.781345i	−0.998455	−	0.0555615i	$-0.982305\pi$
$859$	−13.2214	+	22.9002i	−0.451110	+	0.781345i	0.547345	+	0.836907i	$0.315638\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.9090	+	19.0000i	1.12024	+	0.646768i	0.941461	−	0.337122i	$-0.109453\pi$
$863$	32.9090	+	19.0000i	1.12024	+	0.646768i	0.178775	+	0.983890i	$0.442787\pi$
$864$		0			0
$865$	23.4519	+	30.7469i	0.797390	+	1.04543i
$866$		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	$-0.402992\pi$
$877$	−11.1355	−	6.42910i	−0.376020	−	0.217095i	−0.676085	+	0.736823i	$0.736325\pi$
$878$		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
$885$	−12.6288	−	16.5572i	−0.424514	−	0.556563i
$886$		0			0
$887$	−34.8639	−	20.1287i	−1.17062	−	0.675856i	−0.216791	−	0.976218i	$-0.569559\pi$
$887$	−34.8639	−	20.1287i	−1.17062	−	0.675856i	−0.953825	+	0.300362i	$0.902892\pi$
$888$		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
$905$	−9.36121	−	3.90930i	−0.311177	−	0.129950i
$906$		0			0
$907$	−41.7005	+	24.0758i	−1.38464	+	0.799423i	−0.992705	−	0.120569i	$-0.961528\pi$
$907$	−41.7005	+	24.0758i	−1.38464	+	0.799423i	−0.391936	+	0.919992i	$0.628195\pi$
$908$		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
$915$	7.01167	−	16.7901i	0.231799	−	0.555065i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12.6387	−	21.8908i	0.416911	−	0.722111i	−0.578716	−	0.815529i	$-0.696446\pi$
$919$	12.6387	−	21.8908i	0.416911	−	0.722111i	0.995627	+	0.0934183i	$0.0297794\pi$
$920$		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	−0.544245	−	0.838927i	$-0.683184\pi$
$929$	13.8502	−	23.9892i	0.454409	−	0.787060i	0.998654	+	0.0518664i	$0.0165170\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.12314	−	1.22580i	−0.0695085	−	0.0401308i
$934$		0			0
$935$	−0.942797	−	1.23606i	−0.0308328	−	0.0404236i
$936$		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	0.538737	−	0.842474i	$-0.318902\pi$
$941$	−14.1180	−	24.4532i	−0.460235	−	0.797151i	−0.998972	+	0.0453231i	$0.985568\pi$
$942$		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	$-0.317834\pi$
$947$	2.59436	+	1.49785i	0.0843052	+	0.0486736i	−0.457255	+	0.889336i	$0.651167\pi$
$948$		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
$955$	−15.4333	+	11.7716i	−0.499409	+	0.380920i
$956$		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	−0.381543	−	0.924351i	$-0.624607\pi$
$971$	19.0000	−	32.9090i	0.609740	−	1.05610i	0.991283	−	0.131749i	$-0.0420594\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7.62717	−	27.8202i	0.244265	−	0.890959i
$976$		0			0
$977$	37.0401	−	21.3851i	1.18502	−	0.684170i	0.227848	−	0.973697i	$-0.426831\pi$
$977$	37.0401	−	21.3851i	1.18502	−	0.684170i	0.957170	+	0.289526i	$0.0934978\pi$
$978$		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	$-0.735630\pi$
$983$	−11.6735	+	6.73968i	−0.372326	+	0.214962i	0.302148	+	0.953261i	$0.402296\pi$
$984$		0			0
$985$	3.09249	−	7.40527i	0.0985349	−	0.235952i
$986$		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	0.573713	−	0.819056i	$-0.305503\pi$
$991$	−13.2993	−	23.0351i	−0.422467	−	0.731735i	−0.996180	+	0.0873218i	$0.972169\pi$
$992$		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	$-0.739828\pi$
$997$	−12.4598	+	7.19366i	−0.394605	+	0.227825i	0.289548	+	0.957163i	$0.406495\pi$
$998$		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.1549.4		16
5.4	even	2	inner	2940.2.bb.i.1549.5		16
7.2	even	3		2940.2.k.g.589.2		8
7.3	odd	6		420.2.bb.a.109.4	✓	16
7.4	even	3	inner	2940.2.bb.i.949.5		16
7.5	odd	6		2940.2.k.f.589.7		8
7.6	odd	2		420.2.bb.a.289.5	yes	16
21.17	even	6		1260.2.bm.c.109.2		16
21.20	even	2		1260.2.bm.c.289.7		16
28.3	even	6		1680.2.di.e.529.8		16
28.27	even	2		1680.2.di.e.289.1		16
35.3	even	12		2100.2.q.m.1201.2		8
35.4	even	6	inner	2940.2.bb.i.949.4		16
35.9	even	6		2940.2.k.g.589.6		8
35.13	even	4		2100.2.q.m.1801.2		8
35.17	even	12		2100.2.q.l.1201.3		8
35.19	odd	6		2940.2.k.f.589.3		8
35.24	odd	6		420.2.bb.a.109.5	yes	16
35.27	even	4		2100.2.q.l.1801.3		8
35.34	odd	2		420.2.bb.a.289.4	yes	16
105.59	even	6		1260.2.bm.c.109.7		16
105.104	even	2		1260.2.bm.c.289.2		16
140.59	even	6		1680.2.di.e.529.1		16
140.139	even	2		1680.2.di.e.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.4	✓	16	7.3	odd	6
420.2.bb.a.109.5	yes	16	35.24	odd	6
420.2.bb.a.289.4	yes	16	35.34	odd	2
420.2.bb.a.289.5	yes	16	7.6	odd	2
1260.2.bm.c.109.2		16	21.17	even	6
1260.2.bm.c.109.7		16	105.59	even	6
1260.2.bm.c.289.2		16	105.104	even	2
1260.2.bm.c.289.7		16	21.20	even	2
1680.2.di.e.289.1		16	28.27	even	2
1680.2.di.e.289.8		16	140.139	even	2
1680.2.di.e.529.1		16	140.59	even	6
1680.2.di.e.529.8		16	28.3	even	6
2100.2.q.l.1201.3		8	35.17	even	12
2100.2.q.l.1801.3		8	35.27	even	4
2100.2.q.m.1201.2		8	35.3	even	12
2100.2.q.m.1801.2		8	35.13	even	4
2940.2.k.f.589.3		8	35.19	odd	6
2940.2.k.f.589.7		8	7.5	odd	6
2940.2.k.g.589.2		8	7.2	even	3
2940.2.k.g.589.6		8	35.9	even	6
2940.2.bb.i.949.4		16	35.4	even	6	inner
2940.2.bb.i.949.5		16	7.4	even	3	inner
2940.2.bb.i.1549.4		16	1.1	even	1	trivial
2940.2.bb.i.1549.5		16	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(2.06337 + 0.861678i) q^{5} +(0.500000 - 0.866025i) q^{9} +(-1.46616 - 2.53947i) q^{11} +5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(0.205328 - 0.118546i) q^{17} +(-2.37016 + 4.10523i) q^{19} +(-5.86244 - 3.38468i) q^{23} +(3.51502 + 3.55593i) q^{25} +1.00000i q^{27} -6.03549 q^{29} +(-5.26936 - 9.12679i) q^{31} +(2.53947 + 1.46616i) q^{33} +(-2.66227 - 1.53706i) q^{37} +(-2.88468 - 4.99641i) q^{39} -1.06768 q^{41} +9.79697i q^{43} +(1.77792 - 1.35609i) q^{45} +(-3.21530 - 1.85635i) q^{47} +(-0.118546 + 0.205328i) q^{51} +(9.53186 - 5.50322i) q^{53} +(-0.837035 - 6.50322i) q^{55} -4.74032i q^{57} +(4.65633 + 8.06499i) q^{59} +(-4.06861 + 7.04704i) q^{61} +(-4.97133 + 11.9043i) q^{65} +(1.94296 - 1.12177i) q^{67} +6.76936 q^{69} -11.8421 q^{71} +(-3.28827 + 1.89848i) q^{73} +(-4.82206 - 1.32201i) q^{75} +(0.00873900 - 0.0151364i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(5.22689 - 3.01774i) q^{87} +(-8.97583 + 15.5466i) q^{89} +(9.12679 + 5.26936i) q^{93} +(-8.42791 + 6.42832i) q^{95} +2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} - 8 q^{19} + 12 q^{25} + 24 q^{29} - 4 q^{39} - 48 q^{41} + 2 q^{45} + 4 q^{51} + 40 q^{55} + 28 q^{59} + 32 q^{61} - 26 q^{65} + 24 q^{69} - 56 q^{71} + 8 q^{75}+ \cdots - 16 q^{99}+O(q^{100}) \) 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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