LMFDB - Embedded newform 416.2.ba.c.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(17,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Root			$-0.741068 - 1.20450i$ of defining polynomial
Character	$\chi$	$=$	416.17
Dual form			416.2.ba.c.49.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.779193 + 0.449867i) q^{3} -0.893415 q^{5} +(-3.65473 + 2.11006i) q^{7} +(-1.09524 - 1.89701i) q^{9} +(-3.01779 + 5.22697i) q^{11} +(0.579883 + 3.55861i) q^{13} +(-0.696143 - 0.401918i) q^{15} +(1.00567 + 1.74186i) q^{17} +(1.59258 + 2.75843i) q^{19} -3.79699 q^{21} +(2.65473 - 4.59813i) q^{23} -4.20181 q^{25} -4.67005i q^{27} +(4.50378 + 2.60026i) q^{29} -2.51626i q^{31} +(-4.70289 + 2.71521i) q^{33} +(3.26519 - 1.88516i) q^{35} +(1.00002 - 1.73208i) q^{37} +(-1.14906 + 3.03372i) q^{39} +(-0.0169974 - 0.00981345i) q^{41} +(-3.45944 + 1.99731i) q^{43} +(0.978503 + 1.69482i) q^{45} +3.22446i q^{47} +(5.40470 - 9.36121i) q^{49} +1.80966i q^{51} +3.34691i q^{53} +(2.69614 - 4.66986i) q^{55} +2.86580i q^{57} +(-3.15097 - 5.45764i) q^{59} +(-6.79553 + 3.92340i) q^{61} +(8.00560 + 4.62204i) q^{63} +(-0.518077 - 3.17932i) q^{65} +(1.53943 - 2.66638i) q^{67} +(4.13709 - 2.38855i) q^{69} +(-2.22056 + 1.28204i) q^{71} +12.1386i q^{73} +(-3.27402 - 1.89026i) q^{75} -25.4709i q^{77} -3.01133 q^{79} +(-1.18481 + 2.05215i) q^{81} +8.90367 q^{83} +(-0.898477 - 1.55621i) q^{85} +(2.33954 + 4.05220i) q^{87} +(7.52934 + 4.34707i) q^{89} +(-9.62820 - 11.7822i) q^{91} +(1.13198 - 1.96065i) q^{93} +(-1.42284 - 2.46443i) q^{95} +(9.79132 - 5.65302i) q^{97} +13.2208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) $ 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.779193	+	0.449867i	0.449867	+	0.259731i	0.707774	−	0.706439i	$-0.249699\pi$
$3$	0.779193	+	0.449867i	0.449867	+	0.259731i	−0.257907	+	0.966170i	$0.583033\pi$
$4$		0			0
$5$	−0.893415			−0.399548			−0.199774	−	0.979842i	$-0.564021\pi$
$5$	−0.893415			−0.399548			−0.199774	+	0.979842i	$0.564021\pi$
$6$		0			0
$7$	−3.65473	+	2.11006i	−1.38136	+	0.797527i	−0.992320	−	0.123695i	$-0.960526\pi$
$7$	−3.65473	+	2.11006i	−1.38136	+	0.797527i	−0.389037	+	0.921222i	$0.627192\pi$
$8$		0			0
$9$	−1.09524	−	1.89701i	−0.365080	−	0.632336i
$10$		0			0
$11$	−3.01779	+	5.22697i	−0.909899	+	1.57599i	−0.0956963	+	0.995411i	$0.530508\pi$
$11$	−3.01779	+	5.22697i	−0.909899	+	1.57599i	−0.814203	+	0.580581i	$0.802826\pi$
$12$		0			0
$13$	0.579883	+	3.55861i	0.160831	+	0.986982i
$13$	0.579883	+	3.55861i	0.160831	+	0.986982i
$14$		0			0
$15$	−0.696143	−	0.401918i	−0.179743	−	0.103775i
$16$		0			0
$17$	1.00567	+	1.74186i	0.243910	+	0.422464i	0.961825	−	0.273667i	$-0.0882366\pi$
$17$	1.00567	+	1.74186i	0.243910	+	0.422464i	−0.717915	+	0.696131i	$0.754903\pi$
$18$		0			0
$19$	1.59258	+	2.75843i	0.365364	+	0.632828i	0.988834	−	0.149018i	$-0.0476113\pi$
$19$	1.59258	+	2.75843i	0.365364	+	0.632828i	−0.623471	+	0.781847i	$0.714278\pi$
$20$		0			0
$21$	−3.79699			−0.828570
$22$		0			0
$23$	2.65473	−	4.59813i	0.553549	−	0.958776i	−0.444466	−	0.895796i	$-0.646606\pi$
$23$	2.65473	−	4.59813i	0.553549	−	0.958776i	0.998015	−	0.0629796i	$-0.0200603\pi$
$24$		0			0
$25$	−4.20181			−0.840362
$26$		0			0
$27$		−	4.67005i		−	0.898752i
$28$		0			0
$29$	4.50378	+	2.60026i	0.836330	+	0.482855i	0.856015	−	0.516951i	$-0.172933\pi$
$29$	4.50378	+	2.60026i	0.836330	+	0.482855i	−0.0196850	+	0.999806i	$0.506266\pi$
$30$		0			0
$31$		−	2.51626i		−	0.451934i	−0.974135	−	0.225967i	$-0.927446\pi$
$31$		−	2.51626i		−	0.451934i	0.974135	−	0.225967i	$-0.0725541\pi$
$32$		0			0
$33$	−4.70289	+	2.71521i	−0.818668	+	0.472658i
$34$		0			0
$35$	3.26519	−	1.88516i	0.551918	−	0.318650i
$36$		0			0
$37$	1.00002	−	1.73208i	0.164402	−	0.284752i	−0.772041	−	0.635573i	$-0.780764\pi$
$37$	1.00002	−	1.73208i	0.164402	−	0.284752i	0.936443	+	0.350821i	$0.114097\pi$
$38$		0			0
$39$	−1.14906	+	3.03372i	−0.183997	+	0.485784i
$40$		0			0
$41$	−0.0169974	−	0.00981345i	−0.00265455	−	0.00153260i	0.498672	−	0.866791i	$-0.333821\pi$
$41$	−0.0169974	−	0.00981345i	−0.00265455	−	0.00153260i	−0.501327	+	0.865258i	$0.667155\pi$
$42$		0			0
$43$	−3.45944	+	1.99731i	−0.527560	+	0.304587i	−0.740022	−	0.672583i	$-0.765185\pi$
$43$	−3.45944	+	1.99731i	−0.527560	+	0.304587i	0.212463	+	0.977169i	$0.431852\pi$
$44$		0			0
$45$	0.978503	+	1.69482i	0.145867	+	0.252648i
$46$		0			0
$47$			3.22446i			0.470335i	0.971955	+	0.235168i	$0.0755639\pi$
$47$			3.22446i			0.470335i	−0.971955	+	0.235168i	$0.924436\pi$
$48$		0			0
$49$	5.40470	−	9.36121i	0.772100	−	1.33732i
$50$		0			0
$51$			1.80966i			0.253404i
$52$		0			0
$53$			3.34691i			0.459733i	0.973222	+	0.229867i	$0.0738290\pi$
$53$			3.34691i			0.459733i	−0.973222	+	0.229867i	$0.926171\pi$
$54$		0			0
$55$	2.69614	−	4.66986i	0.363548	−	0.629683i
$56$		0			0
$57$			2.86580i			0.379585i
$58$		0			0
$59$	−3.15097	−	5.45764i	−0.410221	−	0.710524i	0.584692	−	0.811255i	$-0.301215\pi$
$59$	−3.15097	−	5.45764i	−0.410221	−	0.710524i	−0.994914	+	0.100731i	$0.967882\pi$
$60$		0			0
$61$	−6.79553	+	3.92340i	−0.870078	+	0.502340i	−0.867374	−	0.497657i	$-0.834194\pi$
$61$	−6.79553	+	3.92340i	−0.870078	+	0.502340i	−0.00270378	+	0.999996i	$0.500861\pi$
$62$		0			0
$63$	8.00560	+	4.62204i	1.00861	+	0.582322i
$64$		0			0
$65$	−0.518077	−	3.17932i	−0.0642595	−	0.394346i
$66$		0			0
$67$	1.53943	−	2.66638i	0.188072	−	0.325750i	−0.756536	−	0.653952i	$-0.773110\pi$
$67$	1.53943	−	2.66638i	0.188072	−	0.325750i	0.944607	+	0.328203i	$0.106443\pi$
$68$		0			0
$69$	4.13709	−	2.38855i	0.498048	−	0.287548i
$70$		0			0
$71$	−2.22056	+	1.28204i	−0.263532	+	0.152150i	−0.625945	−	0.779867i	$-0.715286\pi$
$71$	−2.22056	+	1.28204i	−0.263532	+	0.152150i	0.362413	+	0.932018i	$0.381953\pi$
$72$		0			0
$73$			12.1386i			1.42072i	0.703840	+	0.710359i	$0.251467\pi$
$73$			12.1386i			1.42072i	−0.703840	+	0.710359i	$0.748533\pi$
$74$		0			0
$75$	−3.27402	−	1.89026i	−0.378051	−	0.218268i
$76$		0			0
$77$		−	25.4709i		−	2.90268i
$78$		0			0
$79$	−3.01133			−0.338801			−0.169401	−	0.985547i	$-0.554183\pi$
$79$	−3.01133			−0.338801			−0.169401	+	0.985547i	$0.554183\pi$
$80$		0			0
$81$	−1.18481	+	2.05215i	−0.131646	+	0.228017i
$82$		0			0
$83$	8.90367			0.977304			0.488652	−	0.872479i	$-0.337489\pi$
$83$	8.90367			0.977304			0.488652	+	0.872479i	$0.337489\pi$
$84$		0			0
$85$	−0.898477	−	1.55621i	−0.0974535	−	0.168794i
$86$		0			0
$87$	2.33954	+	4.05220i	0.250825	+	0.434442i
$88$		0			0
$89$	7.52934	+	4.34707i	0.798109	+	0.460788i	0.842809	−	0.538212i	$-0.180900\pi$
$89$	7.52934	+	4.34707i	0.798109	+	0.460788i	−0.0447006	+	0.999000i	$0.514233\pi$
$90$		0			0
$91$	−9.62820	−	11.7822i	−1.00931	−	1.23511i
$92$		0			0
$93$	1.13198	−	1.96065i	0.117381	−	0.203310i
$94$		0			0
$95$	−1.42284	−	2.46443i	−0.145980	−	0.252845i
$96$		0			0
$97$	9.79132	−	5.65302i	0.994158	−	0.573977i	0.0876432	−	0.996152i	$-0.472066\pi$
$97$	9.79132	−	5.65302i	0.994158	−	0.573977i	0.906514	+	0.422175i	$0.138733\pi$
$98$		0			0
$99$	13.2208			1.32874
$100$		0			0
$101$	11.0712	+	6.39194i	1.10162	+	0.636021i	0.936646	−	0.350276i	$-0.113912\pi$
$101$	11.0712	+	6.39194i	1.10162	+	0.636021i	0.164975	+	0.986298i	$0.447246\pi$
$102$		0			0
$103$	6.35829			0.626501			0.313251	−	0.949671i	$-0.398582\pi$
$103$	6.35829			0.626501			0.313251	+	0.949671i	$0.398582\pi$
$104$		0			0
$105$	3.39229			0.331053
$106$		0			0
$107$	3.64486	+	2.10436i	0.352362	+	0.203436i	0.665725	−	0.746197i	$-0.268122\pi$
$107$	3.64486	+	2.10436i	0.352362	+	0.203436i	−0.313363	+	0.949633i	$0.601456\pi$
$108$		0			0
$109$	−15.3480			−1.47007			−0.735036	−	0.678028i	$-0.762835\pi$
$109$	−15.3480			−1.47007			−0.735036	+	0.678028i	$0.762835\pi$
$110$		0			0
$111$	1.55841	−	0.899749i	0.147918	−	0.0854004i
$112$		0			0
$113$	5.31512	+	9.20607i	0.500005	+	0.866034i	1.00000		5.57645e-6i	$1.77504e-6\pi$
$113$	5.31512	+	9.20607i	0.500005	+	0.866034i	−0.499995	+	0.866028i	$0.666665\pi$
$114$		0			0
$115$	−2.37178	+	4.10804i	−0.221169	+	0.383076i
$116$		0			0
$117$	6.11561	−	4.99758i	0.565389	−	0.462026i
$118$		0			0
$119$	−7.35087	−	4.24403i	−0.673853	−	0.389049i
$120$		0			0
$121$	−12.7142	−	22.0216i	−1.15583	−	2.00196i
$122$		0			0
$123$	−0.00882951	−	0.0152932i	−0.000796130	−	0.00137894i
$124$		0			0
$125$	8.22104			0.735312
$126$		0			0
$127$	1.26804	−	2.19632i	0.112521	−	0.194892i	−0.804265	−	0.594271i	$-0.797441\pi$
$127$	1.26804	−	2.19632i	0.112521	−	0.194892i	0.916786	+	0.399379i	$0.130774\pi$
$128$		0			0
$129$	−3.59410			−0.316442
$130$		0			0
$131$		−	2.01357i		−	0.175927i	−0.996124	−	0.0879633i	$-0.971964\pi$
$131$		−	2.01357i		−	0.175927i	0.996124	−	0.0879633i	$-0.0280358\pi$
$132$		0			0
$133$	−11.6409	−	6.72089i	−1.00940	−	0.582775i
$134$		0			0
$135$			4.17230i			0.359094i
$136$		0			0
$137$	11.8095	−	6.81819i	1.00895	−	0.582518i	0.0980660	−	0.995180i	$-0.468734\pi$
$137$	11.8095	−	6.81819i	1.00895	−	0.582518i	0.910884	+	0.412662i	$0.135401\pi$
$138$		0			0
$139$	−15.6208	+	9.01865i	−1.32494	+	0.764952i	−0.984512	−	0.175320i	$-0.943904\pi$
$139$	−15.6208	+	9.01865i	−1.32494	+	0.764952i	−0.340424	+	0.940272i	$0.610571\pi$
$140$		0			0
$141$	−1.45058	+	2.51247i	−0.122161	+	0.211589i
$142$		0			0
$143$	−20.3507	−	7.70813i	−1.70181	−	0.644586i
$144$		0			0
$145$	−4.02374	−	2.32311i	−0.334154	−	0.192924i
$146$		0			0
$147$	8.42261	−	4.86279i	0.694685	−	0.401076i
$148$		0			0
$149$	0.706789	+	1.22419i	0.0579024	+	0.100290i	0.893524	−	0.449016i	$-0.148225\pi$
$149$	0.706789	+	1.22419i	0.0579024	+	0.100290i	−0.835621	+	0.549306i	$0.814892\pi$
$150$		0			0
$151$			5.82833i			0.474303i	0.971473	+	0.237152i	$0.0762138\pi$
$151$			5.82833i			0.474303i	−0.971473	+	0.237152i	$0.923786\pi$
$152$		0			0
$153$	2.20289	−	3.81551i	0.178093	−	0.308466i
$154$		0			0
$155$			2.24807i			0.180569i
$156$		0			0
$157$			3.13281i			0.250025i	0.992155	+	0.125013i	$0.0398971\pi$
$157$			3.13281i			0.250025i	−0.992155	+	0.125013i	$0.960103\pi$
$158$		0			0
$159$	−1.50567	+	2.60789i	−0.119407	+	0.206819i
$160$		0			0
$161$			22.4065i			1.76588i
$162$		0			0
$163$	1.93896	+	3.35838i	0.151871	+	0.263048i	0.931915	−	0.362676i	$-0.118137\pi$
$163$	1.93896	+	3.35838i	0.151871	+	0.263048i	−0.780044	+	0.625724i	$0.784803\pi$
$164$		0			0
$165$	4.20163	−	2.42581i	0.327097	−	0.188849i
$166$		0			0
$167$	13.6659	+	7.89003i	1.05750	+	0.610549i	0.924740	−	0.380599i	$-0.124282\pi$
$167$	13.6659	+	7.89003i	1.05750	+	0.610549i	0.132761	+	0.991148i	$0.457616\pi$
$168$		0			0
$169$	−12.3275	+	4.12716i	−0.948267	+	0.317474i
$170$		0			0
$171$	3.48852	−	6.04229i	0.266774	−	0.462065i
$172$		0			0
$173$	0.538065	−	0.310652i	0.0409083	−	0.0236184i	−0.479406	−	0.877593i	$-0.659148\pi$
$173$	0.538065	−	0.310652i	0.0409083	−	0.0236184i	0.520315	+	0.853975i	$0.325815\pi$
$174$		0			0
$175$	15.3565	−	8.86606i	1.16084	−	0.670211i
$176$		0			0
$177$		−	5.67007i		−	0.426189i
$178$		0			0
$179$	9.39825	+	5.42608i	0.702458	+	0.405564i	0.808262	−	0.588823i	$-0.200408\pi$
$179$	9.39825	+	5.42608i	0.702458	+	0.405564i	−0.105804	+	0.994387i	$0.533742\pi$
$180$		0			0
$181$			16.0515i			1.19310i	0.802577	+	0.596548i	$0.203461\pi$
$181$			16.0515i			1.19310i	−0.802577	+	0.596548i	$0.796539\pi$
$182$		0			0
$183$	−7.06004			−0.521893
$184$		0			0
$185$	−0.893430	+	1.54747i	−0.0656863	+	0.113772i
$186$		0			0
$187$	−12.1396			−0.887733
$188$		0			0
$189$	9.85409	+	17.0678i	0.716779	+	1.24150i
$190$		0			0
$191$	10.9755	+	19.0102i	0.794161	+	1.37553i	0.923371	+	0.383909i	$0.125423\pi$
$191$	10.9755	+	19.0102i	0.794161	+	1.37553i	−0.129210	+	0.991617i	$0.541244\pi$
$192$		0			0
$193$	−7.45812	−	4.30595i	−0.536847	−	0.309949i	0.206953	−	0.978351i	$-0.433645\pi$
$193$	−7.45812	−	4.30595i	−0.536847	−	0.309949i	−0.743800	+	0.668402i	$0.766979\pi$
$194$		0			0
$195$	1.02659	−	2.71037i	0.0735157	−	0.194094i
$196$		0			0
$197$	−4.57874	+	7.93061i	−0.326222	+	0.565033i	−0.981759	−	0.190130i	$-0.939109\pi$
$197$	−4.57874	+	7.93061i	−0.326222	+	0.565033i	0.655537	+	0.755163i	$0.272442\pi$
$198$		0			0
$199$	−7.83948	−	13.5784i	−0.555726	−	0.962545i	−0.997847	−	0.0655898i	$-0.979107\pi$
$199$	−7.83948	−	13.5784i	−0.555726	−	0.962545i	0.442121	−	0.896955i	$-0.354226\pi$
$200$		0			0
$201$	2.39903	−	1.38508i	0.169215	−	0.0976961i
$202$		0			0
$203$	−21.9468			−1.54036
$204$		0			0
$205$	0.0151857	+	0.00876749i	0.00106062	+	0.000612348i
$206$		0			0
$207$	−11.6302			−0.808358
$208$		0			0
$209$	−19.2243			−1.32978
$210$		0			0
$211$	14.2765	+	8.24253i	0.982834	+	0.567439i	0.903124	−	0.429379i	$-0.141267\pi$
$211$	14.2765	+	8.24253i	0.982834	+	0.567439i	0.0797093	+	0.996818i	$0.474601\pi$
$212$		0			0
$213$	−2.30699			−0.158073
$214$		0			0
$215$	3.09072	−	1.78443i	0.210785	−	0.121697i
$216$		0			0
$217$	5.30946	+	9.19625i	0.360430	+	0.624282i
$218$		0			0
$219$	−5.46077	+	9.45832i	−0.369004	+	0.639134i
$220$		0			0
$221$	−5.61545	+	4.58885i	−0.377736	+	0.308680i
$222$		0			0
$223$	−4.14333	−	2.39215i	−0.277458	−	0.160191i	0.354814	−	0.934937i	$-0.384544\pi$
$223$	−4.14333	−	2.39215i	−0.277458	−	0.160191i	−0.632272	+	0.774746i	$0.717878\pi$
$224$		0			0
$225$	4.60198	+	7.97087i	0.306799	+	0.531391i
$226$		0			0
$227$	2.20440	+	3.81814i	0.146311	+	0.253419i	0.929861	−	0.367910i	$-0.119927\pi$
$227$	2.20440	+	3.81814i	0.146311	+	0.253419i	−0.783550	+	0.621329i	$0.786593\pi$
$228$		0			0
$229$	−18.9724			−1.25373			−0.626866	−	0.779127i	$-0.715662\pi$
$229$	−18.9724			−1.25373			−0.626866	+	0.779127i	$0.715662\pi$
$230$		0			0
$231$	11.4585	−	19.8467i	0.753915	−	1.30582i
$232$		0			0
$233$	−16.2038			−1.06155			−0.530774	−	0.847513i	$-0.678099\pi$
$233$	−16.2038			−1.06155			−0.530774	+	0.847513i	$0.678099\pi$
$234$		0			0
$235$		−	2.88078i		−	0.187921i
$236$		0			0
$237$	−2.34641	−	1.35470i	−0.152416	−	0.0879972i
$238$		0			0
$239$		−	3.65538i		−	0.236447i	−0.992987	−	0.118224i	$-0.962280\pi$
$239$		−	3.65538i		−	0.236447i	0.992987	−	0.118224i	$-0.0377200\pi$
$240$		0			0
$241$	−19.7662	+	11.4120i	−1.27325	+	0.735114i	−0.975599	−	0.219559i	$-0.929538\pi$
$241$	−19.7662	+	11.4120i	−1.27325	+	0.735114i	−0.297655	+	0.954673i	$0.596205\pi$
$242$		0			0
$243$	−13.9795	+	8.07110i	−0.896788	+	0.517761i
$244$		0			0
$245$	−4.82864	+	8.36345i	−0.308490	+	0.534321i
$246$		0			0
$247$	−8.89269	+	7.26696i	−0.565828	+	0.462385i
$248$		0			0
$249$	6.93768	+	4.00547i	0.439657	+	0.253836i
$250$		0			0
$251$	−5.22090	+	3.01429i	−0.329540	+	0.190260i	−0.655637	−	0.755076i	$-0.727600\pi$
$251$	−5.22090	+	3.01429i	−0.329540	+	0.190260i	0.326097	+	0.945336i	$0.394267\pi$
$252$		0			0
$253$	16.0228	+	27.7524i	1.00735	+	1.74478i
$254$		0			0
$255$		−	1.61678i		−	0.101247i
$256$		0			0
$257$	11.6246	−	20.1344i	0.725122	−	1.25595i	−0.233802	−	0.972284i	$-0.575117\pi$
$257$	11.6246	−	20.1344i	0.725122	−	1.25595i	0.958924	−	0.283663i	$-0.0915498\pi$
$258$		0			0
$259$			8.44037i			0.524459i
$260$		0			0
$261$		−	11.3916i		−	0.705123i
$262$		0			0
$263$	−1.34527	+	2.33008i	−0.0829529	+	0.143679i	−0.904517	−	0.426437i	$-0.859768\pi$
$263$	−1.34527	+	2.33008i	−0.0829529	+	0.143679i	0.821564	+	0.570116i	$0.193102\pi$
$264$		0			0
$265$		−	2.99018i		−	0.183685i
$266$		0			0
$267$	3.91121	+	6.77441i	0.239362	+	0.414587i
$268$		0			0
$269$	10.8816	−	6.28249i	0.663462	−	0.383050i	−0.130133	−	0.991497i	$-0.541540\pi$
$269$	10.8816	−	6.28249i	0.663462	−	0.383050i	0.793595	+	0.608447i	$0.208207\pi$
$270$		0			0
$271$	−0.248953	−	0.143733i	−0.0151228	−	0.00873116i	0.492420	−	0.870358i	$-0.336113\pi$
$271$	−0.248953	−	0.143733i	−0.0151228	−	0.00873116i	−0.507542	+	0.861627i	$0.669446\pi$
$272$		0			0
$273$	−2.20181	−	13.5120i	−0.133260	−	0.817784i
$274$		0			0
$275$	12.6802	−	21.9627i	0.764644	−	1.32440i
$276$		0			0
$277$	11.9899	−	6.92240i	0.720406	−	0.415926i	−0.0944963	−	0.995525i	$-0.530124\pi$
$277$	11.9899	−	6.92240i	0.720406	−	0.415926i	0.814902	+	0.579599i	$0.196791\pi$
$278$		0			0
$279$	−4.77337	+	2.75591i	−0.285774	+	0.164992i
$280$		0			0
$281$		−	2.18634i		−	0.130426i	−0.997871	−	0.0652132i	$-0.979227\pi$
$281$		−	2.18634i		−	0.130426i	0.997871	−	0.0652132i	$-0.0207727\pi$
$282$		0			0
$283$	12.2639	+	7.08057i	0.729014	+	0.420896i	0.818061	−	0.575131i	$-0.195049\pi$
$283$	12.2639	+	7.08057i	0.729014	+	0.420896i	−0.0890474	+	0.996027i	$0.528382\pi$
$284$		0			0
$285$		−	2.56035i		−	0.151662i
$286$		0			0
$287$	0.0828279			0.00488917
$288$		0			0
$289$	6.47727	−	11.2190i	0.381016	−	0.659939i
$290$		0			0
$291$	10.1724			0.596319
$292$		0			0
$293$	−12.5394	−	21.7189i	−0.732559	−	1.26883i	−0.955786	−	0.294063i	$-0.904992\pi$
$293$	−12.5394	−	21.7189i	−0.732559	−	1.26883i	0.223227	−	0.974767i	$-0.428341\pi$
$294$		0			0
$295$	2.81512	+	4.87594i	0.163903	+	0.283888i
$296$		0			0
$297$	24.4102	+	14.0933i	1.41643	+	0.817774i
$298$		0			0
$299$	17.9024	+	6.78078i	1.03532	+	0.392143i
$300$		0			0
$301$	8.42888	−	14.5992i	0.485832	−	0.841486i
$302$		0			0
$303$	5.75105	+	9.96111i	0.330389	+	0.572251i
$304$		0			0
$305$	6.07123	−	3.50522i	0.347637	−	0.200709i
$306$		0			0
$307$	−15.7714			−0.900120			−0.450060	−	0.892998i	$-0.648597\pi$
$307$	−15.7714			−0.900120			−0.450060	+	0.892998i	$0.648597\pi$
$308$		0			0
$309$	4.95434	+	2.86039i	0.281842	+	0.162722i
$310$		0			0
$311$	−12.8116			−0.726477			−0.363238	−	0.931696i	$-0.618329\pi$
$311$	−12.8116			−0.726477			−0.363238	+	0.931696i	$0.618329\pi$
$312$		0			0
$313$	21.9885			1.24287			0.621433	−	0.783467i	$-0.286551\pi$
$313$	21.9885			1.24287			0.621433	+	0.783467i	$0.286551\pi$
$314$		0			0
$315$	−7.15233	−	4.12940i	−0.402988	−	0.232665i
$316$		0			0
$317$	−17.7840			−0.998846			−0.499423	−	0.866358i	$-0.666455\pi$
$317$	−17.7840			−0.998846			−0.499423	+	0.866358i	$0.666455\pi$
$318$		0			0
$319$	−27.1829	+	15.6941i	−1.52195	+	0.878699i
$320$		0			0
$321$	1.89337	+	3.27941i	0.105677	+	0.183039i
$322$		0			0
$323$	−3.20321	+	5.54813i	−0.178231	+	0.308706i
$324$		0			0
$325$	−2.43656	−	14.9526i	−0.135156	−	0.829422i
$326$		0			0
$327$	−11.9591	−	6.90456i	−0.661337	−	0.381823i
$328$		0			0
$329$	−6.80379	−	11.7845i	−0.375105	−	0.649701i
$330$		0			0
$331$	−14.2386	−	24.6619i	−0.782623	−	1.35554i	−0.930409	−	0.366523i	$-0.880548\pi$
$331$	−14.2386	−	24.6619i	−0.782623	−	1.35554i	0.147786	−	0.989019i	$-0.452785\pi$
$332$		0			0
$333$	−4.38103			−0.240079
$334$		0			0
$335$	−1.37535	+	2.38218i	−0.0751436	+	0.130152i
$336$		0			0
$337$	8.23580			0.448633			0.224316	−	0.974516i	$-0.427985\pi$
$337$	8.23580			0.448633			0.224316	+	0.974516i	$0.427985\pi$
$338$		0			0
$339$			9.56440i			0.519467i
$340$		0			0
$341$	13.1524	+	7.59356i	0.712244	+	0.411214i
$342$		0			0
$343$			16.0761i			0.868027i
$344$		0			0
$345$	−3.69614	+	2.13397i	−0.198994	+	0.114889i
$346$		0			0
$347$	16.9827	−	9.80497i	0.911679	−	0.526358i	0.0307081	−	0.999528i	$-0.490224\pi$
$347$	16.9827	−	9.80497i	0.911679	−	0.526358i	0.880971	+	0.473170i	$0.156890\pi$
$348$		0			0
$349$	−2.31326	+	4.00669i	−0.123826	+	0.214473i	−0.921273	−	0.388915i	$-0.872850\pi$
$349$	−2.31326	+	4.00669i	−0.123826	+	0.214473i	0.797447	+	0.603389i	$0.206183\pi$
$350$		0			0
$351$	16.6189	−	2.70809i	0.887052	−	0.144547i
$352$		0			0
$353$	−17.4284	−	10.0623i	−0.927619	−	0.535561i	−0.0415611	−	0.999136i	$-0.513233\pi$
$353$	−17.4284	−	10.0623i	−0.927619	−	0.535561i	−0.886058	+	0.463575i	$0.846566\pi$
$354$		0			0
$355$	1.98388	−	1.14539i	0.105294	−	0.0607912i
$356$		0			0
$357$	−3.81850	−	6.61384i	−0.202096	−	0.350041i
$358$		0			0
$359$			0.0956414i			0.00504776i	0.999997	+	0.00252388i	$0.000803377\pi$
$359$			0.0956414i			0.00504776i	−0.999997	+	0.00252388i	$0.999197\pi$
$360$		0			0
$361$	4.42736	−	7.66841i	0.233019	−	0.403601i
$362$		0			0
$363$		−	22.8787i		−	1.20082i
$364$		0			0
$365$		−	10.8448i		−	0.567644i
$366$		0			0
$367$	15.7850	−	27.3405i	0.823972	−	1.42716i	−0.0787296	−	0.996896i	$-0.525086\pi$
$367$	15.7850	−	27.3405i	0.823972	−	1.42716i	0.902702	−	0.430266i	$-0.141580\pi$
$368$		0			0
$369$			0.0429923i			0.00223809i
$370$		0			0
$371$	−7.06218	−	12.2321i	−0.366650	−	0.635056i
$372$		0			0
$373$	−9.14193	+	5.27810i	−0.473351	+	0.273290i	−0.717642	−	0.696413i	$-0.754778\pi$
$373$	−9.14193	+	5.27810i	−0.473351	+	0.273290i	0.244290	+	0.969702i	$0.421445\pi$
$374$		0			0
$375$	6.40578	+	3.69838i	0.330793	+	0.190983i
$376$		0			0
$377$	−6.64164	+	17.5350i	−0.342062	+	0.903101i
$378$		0			0
$379$	−14.1854	+	24.5699i	−0.728657	+	1.26207i	0.228795	+	0.973475i	$0.426522\pi$
$379$	−14.1854	+	24.5699i	−0.728657	+	1.26207i	−0.957451	+	0.288595i	$0.906812\pi$
$380$		0			0
$381$	1.97610	−	1.14090i	0.101239	−	0.0584503i
$382$		0			0
$383$	21.8939	−	12.6405i	1.11873	−	0.645897i	0.177651	−	0.984094i	$-0.443150\pi$
$383$	21.8939	−	12.6405i	1.11873	−	0.645897i	0.941076	+	0.338196i	$0.109817\pi$
$384$		0			0
$385$			22.7561i			1.15976i
$386$		0			0
$387$	7.57782	+	4.37506i	0.385202	+	0.222397i
$388$		0			0
$389$			15.2123i			0.771294i	0.922646	+	0.385647i	$0.126022\pi$
$389$			15.2123i			0.771294i	−0.922646	+	0.385647i	$0.873978\pi$
$390$		0			0
$391$	10.6791			0.540064
$392$		0			0
$393$	0.905841	−	1.56896i	0.0456936	−	0.0791437i
$394$		0			0
$395$	2.69037			0.135367
$396$		0			0
$397$	−18.8616	−	32.6693i	−0.946638	−	1.63963i	−0.752437	−	0.658664i	$-0.771122\pi$
$397$	−18.8616	−	32.6693i	−0.946638	−	1.63963i	−0.194202	−	0.980962i	$-0.562212\pi$
$398$		0			0
$399$	−6.04702	−	10.4737i	−0.302729	−	0.524343i
$400$		0			0
$401$	28.2674	+	16.3202i	1.41161	+	0.814991i	0.995540	−	0.0943435i	$-0.0300752\pi$
$401$	28.2674	+	16.3202i	1.41161	+	0.814991i	0.416066	+	0.909334i	$0.363409\pi$
$402$		0			0
$403$	8.95440	−	1.45914i	0.446051	−	0.0726848i
$404$		0			0
$405$	1.05853	−	1.83343i	0.0525987	−	0.0911037i
$406$		0			0
$407$	6.03568	+	10.4541i	0.299178	+	0.518191i
$408$		0			0
$409$	3.01700	−	1.74186i	0.149181	−	0.0861296i	−0.423552	−	0.905872i	$-0.639217\pi$
$409$	3.01700	−	1.74186i	0.149181	−	0.0861296i	0.572732	+	0.819742i	$0.305883\pi$
$410$		0			0
$411$	12.2691			0.605192
$412$		0			0
$413$	23.0319	+	13.2975i	1.13332	+	0.654325i
$414$		0			0
$415$	−7.95467			−0.390480
$416$		0			0
$417$	−16.2288			−0.794727
$418$		0			0
$419$	−27.5293	−	15.8940i	−1.34489	−	0.776475i	−0.357373	−	0.933962i	$-0.616328\pi$
$419$	−27.5293	−	15.8940i	−1.34489	−	0.776475i	−0.987521	+	0.157487i	$0.949661\pi$
$420$		0			0
$421$	38.9188			1.89679			0.948394	−	0.317093i	$-0.102707\pi$
$421$	38.9188			1.89679			0.948394	+	0.317093i	$0.102707\pi$
$422$		0			0
$423$	6.11682	−	3.53155i	0.297410	−	0.171710i
$424$		0			0
$425$	−4.22562	−	7.31898i	−0.204972	−	0.355023i
$426$		0			0
$427$	16.5572	−	28.6779i	0.801259	−	1.38782i
$428$		0			0
$429$	−12.3895	−	15.1613i	−0.598172	−	0.731992i
$430$		0			0
$431$	21.0414	+	12.1483i	1.01353	+	0.585161i	0.912223	−	0.409694i	$-0.134364\pi$
$431$	21.0414	+	12.1483i	1.01353	+	0.585161i	0.101306	+	0.994855i	$0.467698\pi$
$432$		0			0
$433$	11.5771	+	20.0521i	0.556360	+	0.963643i	0.997796	+	0.0663510i	$0.0211357\pi$
$433$	11.5771	+	20.0521i	0.556360	+	0.963643i	−0.441437	+	0.897292i	$0.645531\pi$
$434$		0			0
$435$	−2.09018	−	3.62030i	−0.100217	−	0.173580i
$436$		0			0
$437$	16.9115			0.808987
$438$		0			0
$439$	14.7545	−	25.5555i	0.704193	−	1.21970i	−0.262788	−	0.964853i	$-0.584642\pi$
$439$	14.7545	−	25.5555i	0.704193	−	1.21970i	0.966982	−	0.254845i	$-0.0820245\pi$
$440$		0			0
$441$	−23.6777			−1.12751
$442$		0			0
$443$			8.91190i			0.423417i	0.977333	+	0.211709i	$0.0679028\pi$
$443$			8.91190i			0.423417i	−0.977333	+	0.211709i	$0.932097\pi$
$444$		0			0
$445$	−6.72683	−	3.88374i	−0.318882	−	0.184107i
$446$		0			0
$447$			1.27185i			0.0601562i
$448$		0			0
$449$	−8.35715	+	4.82500i	−0.394398	+	0.227706i	−0.684064	−	0.729422i	$-0.739789\pi$
$449$	−8.35715	+	4.82500i	−0.394398	+	0.227706i	0.289666	+	0.957128i	$0.406456\pi$
$450$		0			0
$451$	0.102589	−	0.0592300i	0.00483074	−	0.00278903i
$452$		0			0
$453$	−2.62198	+	4.54140i	−0.123191	+	0.213373i
$454$		0			0
$455$	8.60198	+	10.5264i	0.403267	+	0.493485i
$456$		0			0
$457$	−6.30736	−	3.64156i	−0.295046	−	0.170345i	0.345169	−	0.938540i	$-0.387822\pi$
$457$	−6.30736	−	3.64156i	−0.295046	−	0.170345i	−0.640215	+	0.768196i	$0.721155\pi$
$458$		0			0
$459$	8.13460	−	4.69651i	0.379691	−	0.219214i
$460$		0			0
$461$	−14.1677	−	24.5391i	−0.659855	−	1.14290i	−0.980653	−	0.195754i	$-0.937284\pi$
$461$	−14.1677	−	24.5391i	−0.659855	−	1.14290i	0.320798	−	0.947148i	$-0.396049\pi$
$462$		0			0
$463$			34.4600i			1.60149i	0.599003	+	0.800747i	$0.295564\pi$
$463$			34.4600i			1.60149i	−0.599003	+	0.800747i	$0.704436\pi$
$464$		0			0
$465$	−1.01133	+	1.75168i	−0.0468994	+	0.0812321i
$466$		0			0
$467$		−	33.2473i		−	1.53850i	−0.638946	−	0.769252i	$-0.720629\pi$
$467$		−	33.2473i		−	1.53850i	0.638946	−	0.769252i	$-0.279371\pi$
$468$		0			0
$469$			12.9932i			0.599969i
$470$		0			0
$471$	−1.40935	+	2.44106i	−0.0649393	+	0.112478i
$472$		0			0
$473$		−	24.1099i		−	1.10857i
$474$		0			0
$475$	−6.69173	−	11.5904i	−0.307038	−	0.531805i
$476$		0			0
$477$	6.34912	−	3.66567i	0.290706	−	0.167839i
$478$		0			0
$479$	18.3155	+	10.5745i	0.836858	+	0.483160i	0.856195	−	0.516653i	$-0.172822\pi$
$479$	18.3155	+	10.5745i	0.836858	+	0.483160i	−0.0193371	+	0.999813i	$0.506156\pi$
$480$		0			0
$481$	6.74369	+	2.55427i	0.307486	+	0.116465i
$482$		0			0
$483$	−10.0800	+	17.4590i	−0.458655	+	0.794413i
$484$		0			0
$485$	−8.74771	+	5.05049i	−0.397213	+	0.229331i
$486$		0			0
$487$	−15.5640	+	8.98589i	−0.705273	+	0.407189i	−0.809308	−	0.587384i	$-0.800158\pi$
$487$	−15.5640	+	8.98589i	−0.705273	+	0.407189i	0.104035	+	0.994574i	$0.466824\pi$
$488$		0			0
$489$			3.48910i			0.157783i
$490$		0			0
$491$	4.43288	+	2.55932i	0.200053	+	0.115501i	0.596680	−	0.802479i	$-0.296486\pi$
$491$	4.43288	+	2.55932i	0.200053	+	0.115501i	−0.396627	+	0.917980i	$0.629819\pi$
$492$		0			0
$493$			10.4600i			0.471093i
$494$		0			0
$495$	−11.8117			−0.530896
$496$		0			0
$497$	5.41036	−	9.37102i	0.242688	−	0.420348i
$498$		0			0
$499$	−19.2741			−0.862826			−0.431413	−	0.902155i	$-0.641985\pi$
$499$	−19.2741			−0.862826			−0.431413	+	0.902155i	$0.641985\pi$
$500$		0			0
$501$	7.09893	+	12.2957i	0.317157	+	0.549332i
$502$		0			0
$503$	−12.0244	−	20.8268i	−0.536139	−	0.928621i	−0.999107	−	0.0422456i	$-0.986549\pi$
$503$	−12.0244	−	20.8268i	−0.536139	−	0.928621i	0.462968	−	0.886375i	$-0.346785\pi$
$504$		0			0
$505$	−9.89114	−	5.71065i	−0.440150	−	0.254121i
$506$		0			0
$507$	−11.4622	−	2.32987i	−0.509052	−	0.103473i
$508$		0			0
$509$	−18.5759	+	32.1744i	−0.823362	+	1.42610i	0.0798031	+	0.996811i	$0.474571\pi$
$509$	−18.5759	+	32.1744i	−0.823362	+	1.42610i	−0.903165	+	0.429294i	$0.858762\pi$
$510$		0			0
$511$	−25.6132	−	44.3633i	−1.13306	−	1.96252i
$512$		0			0
$513$	12.8820	−	7.43745i	0.568756	−	0.328371i
$514$		0			0
$515$	−5.68060			−0.250317
$516$		0			0
$517$	−16.8541	−	9.73074i	−0.741244	−	0.427958i
$518$		0			0
$519$	0.559009			0.0245378
$520$		0			0
$521$	−9.09538			−0.398476			−0.199238	−	0.979951i	$-0.563847\pi$
$521$	−9.09538			−0.398476			−0.199238	+	0.979951i	$0.563847\pi$
$522$		0			0
$523$	21.3438	+	12.3228i	0.933298	+	0.538840i	0.887853	−	0.460127i	$-0.152196\pi$
$523$	21.3438	+	12.3228i	0.933298	+	0.538840i	0.0454452	+	0.998967i	$0.485529\pi$
$524$		0			0
$525$	15.9542			0.696299
$526$		0			0
$527$	4.38298	−	2.53052i	0.190926	−	0.110231i
$528$		0			0
$529$	−2.59517	−	4.49497i	−0.112834	−	0.195434i
$530$		0			0
$531$	−6.90213	+	11.9548i	−0.299527	+	0.518796i
$532$		0			0
$533$	0.0250658	−	0.0661779i	0.00108572	−	0.00286648i
$534$		0			0
$535$	−3.25637	−	1.88007i	−0.140785	−	0.0812824i
$536$		0			0
$537$	4.88203	+	8.45593i	0.210675	+	0.364900i
$538$		0			0
$539$	32.6205	+	56.5004i	1.40507	+	2.43364i
$540$		0			0
$541$	−5.07378			−0.218139			−0.109069	−	0.994034i	$-0.534787\pi$
$541$	−5.07378			−0.218139			−0.109069	+	0.994034i	$0.534787\pi$
$542$		0			0
$543$	−7.22103	+	12.5072i	−0.309884	+	0.536735i
$544$		0			0
$545$	13.7121			0.587363
$546$		0			0
$547$			0.158642i			0.00678304i	0.999994	+	0.00339152i	$0.00107956\pi$
$547$			0.158642i			0.00678304i	−0.999994	+	0.00339152i	$0.998920\pi$
$548$		0			0
$549$	14.8854	+	8.59412i	0.635295	+	0.366788i
$550$		0			0
$551$			16.5645i			0.705671i
$552$		0			0
$553$	11.0056	−	6.35409i	0.468006	−	0.270203i
$554$		0			0
$555$	−1.39231	+	0.803850i	−0.0591002	+	0.0341215i
$556$		0			0
$557$	2.30308	−	3.98905i	0.0975847	−	0.169022i	−0.813100	−	0.582124i	$-0.802222\pi$
$557$	2.30308	−	3.98905i	0.0975847	−	0.169022i	0.910684	+	0.413103i	$0.135555\pi$
$558$		0			0
$559$	−9.11372	−	11.1526i	−0.385469	−	0.471705i
$560$		0			0
$561$	−9.45907	−	5.46120i	−0.399362	−	0.230572i
$562$		0			0
$563$	1.29014	−	0.744862i	0.0543729	−	0.0313922i	−0.472567	−	0.881295i	$-0.656673\pi$
$563$	1.29014	−	0.744862i	0.0543729	−	0.0313922i	0.526940	+	0.849902i	$0.323339\pi$
$564$		0			0
$565$	−4.74861	−	8.22484i	−0.199776	−	0.346022i
$566$		0			0
$567$		−	10.0001i		−	0.419964i
$568$		0			0
$569$	−8.32754	+	14.4237i	−0.349108	+	0.604674i	−0.986091	−	0.166204i	$-0.946849\pi$
$569$	−8.32754	+	14.4237i	−0.349108	+	0.604674i	0.636983	+	0.770878i	$0.280182\pi$
$570$		0			0
$571$			21.2857i			0.890779i	0.895337	+	0.445390i	$0.146935\pi$
$571$			21.2857i			0.890779i	−0.895337	+	0.445390i	$0.853065\pi$
$572$		0			0
$573$			19.7501i			0.825073i
$574$		0			0
$575$	−11.1547	+	19.3204i	−0.465182	+	0.805718i
$576$		0			0
$577$		−	7.02758i		−	0.292562i	−0.989243	−	0.146281i	$-0.953270\pi$
$577$		−	7.02758i		−	0.292562i	0.989243	−	0.146281i	$-0.0467304\pi$
$578$		0			0
$579$	−3.87421	−	6.71033i	−0.161007	−	0.278872i
$580$		0			0
$581$	−32.5405	+	18.7873i	−1.35001	+	0.779427i
$582$		0			0
$583$	−17.4942	−	10.1003i	−0.724536	−	0.418311i
$584$		0			0
$585$	−5.46378	+	4.46491i	−0.225900	+	0.184601i
$586$		0			0
$587$	3.96345	−	6.86490i	0.163589	−	0.283345i	−0.772564	−	0.634937i	$-0.781026\pi$
$587$	3.96345	−	6.86490i	0.163589	−	0.283345i	0.936153	+	0.351592i	$0.114360\pi$
$588$		0			0
$589$	6.94094	−	4.00735i	0.285996	−	0.165120i
$590$		0			0
$591$	−7.13545	+	4.11965i	−0.293513	+	0.169460i
$592$		0			0
$593$		−	22.9984i		−	0.944430i	−0.881483	−	0.472215i	$-0.843455\pi$
$593$		−	22.9984i		−	0.944430i	0.881483	−	0.472215i	$-0.156545\pi$
$594$		0			0
$595$	6.56738	+	3.79168i	0.269236	+	0.155444i
$596$		0			0
$597$		−	14.1069i		−	0.577357i
$598$		0			0
$599$	9.32430			0.380980			0.190490	−	0.981689i	$-0.438992\pi$
$599$	9.32430			0.380980			0.190490	+	0.981689i	$0.438992\pi$
$600$		0			0
$601$	−4.24363	+	7.35018i	−0.173101	+	0.299820i	−0.939503	−	0.342542i	$-0.888712\pi$
$601$	−4.24363	+	7.35018i	−0.173101	+	0.299820i	0.766401	+	0.642362i	$0.222045\pi$
$602$		0			0
$603$	−6.74419			−0.274644
$604$		0			0
$605$	11.3590	+	19.6744i	0.461810	+	0.799878i
$606$		0			0
$607$	10.3169	+	17.8694i	0.418749	+	0.725295i	0.995814	−	0.0914036i	$-0.0291353\pi$
$607$	10.3169	+	17.8694i	0.418749	+	0.725295i	−0.577065	+	0.816698i	$0.695802\pi$
$608$		0			0
$609$	−17.1008	−	9.87314i	−0.692958	−	0.400080i
$610$		0			0
$611$	−11.4746	+	1.86981i	−0.464212	+	0.0756443i
$612$		0			0
$613$	18.0557	−	31.2734i	0.729264	−	1.26312i	−0.227931	−	0.973677i	$-0.573196\pi$
$613$	18.0557	−	31.2734i	0.729264	−	1.26312i	0.957195	−	0.289445i	$-0.0934707\pi$
$614$		0			0
$615$	0.00788842	+	0.0136631i	0.000318092	+	0.000550951i
$616$		0			0
$617$	−29.2958	+	16.9139i	−1.17940	+	0.680929i	−0.955877	−	0.293769i	$-0.905090\pi$
$617$	−29.2958	+	16.9139i	−1.17940	+	0.680929i	−0.223527	+	0.974698i	$0.571757\pi$
$618$		0			0
$619$	−3.06121			−0.123040			−0.0615201	−	0.998106i	$-0.519595\pi$
$619$	−3.06121			−0.123040			−0.0615201	+	0.998106i	$0.519595\pi$
$620$		0			0
$621$	−21.4735	−	12.3977i	−0.861702	−	0.497504i
$622$		0			0
$623$	−36.6903			−1.46997
$624$		0			0
$625$	13.6642			0.546570
$626$		0			0
$627$	−14.9795	−	8.64841i	−0.598223	−	0.345384i
$628$		0			0
$629$	4.02273			0.160397
$630$		0			0
$631$	23.9926	−	13.8521i	0.955130	−	0.551444i	0.0604589	−	0.998171i	$-0.480744\pi$
$631$	23.9926	−	13.8521i	0.955130	−	0.551444i	0.894671	+	0.446726i	$0.147410\pi$
$632$		0			0
$633$	7.41609	+	12.8450i	0.294763	+	0.510545i
$634$		0			0
$635$	−1.13289	+	1.96222i	−0.0449574	+	0.0778685i
$636$		0			0
$637$	36.4470	+	13.8048i	1.44408	+	0.546967i
$638$		0			0
$639$	4.86409	+	2.80828i	0.192420	+	0.111094i
$640$		0			0
$641$	−11.8526	−	20.5292i	−0.468148	−	0.810856i	0.531189	−	0.847253i	$-0.321745\pi$
$641$	−11.8526	−	20.5292i	−0.468148	−	0.810856i	−0.999337	+	0.0363969i	$0.988412\pi$
$642$		0			0
$643$	10.3454	+	17.9188i	0.407983	+	0.706648i	0.994664	−	0.103171i	$-0.0328988\pi$
$643$	10.3454	+	17.9188i	0.407983	+	0.706648i	−0.586680	+	0.809819i	$0.699565\pi$
$644$		0			0
$645$	3.21102			0.126434
$646$		0			0
$647$	−0.671662	+	1.16335i	−0.0264058	+	0.0457361i	−0.878926	−	0.476958i	$-0.841740\pi$
$647$	−0.671662	+	1.16335i	−0.0264058	+	0.0457361i	0.852521	+	0.522694i	$0.175073\pi$
$648$		0			0
$649$	38.0359			1.49304
$650$		0			0
$651$			9.55421i			0.374459i
$652$		0			0
$653$	−5.18453	−	2.99329i	−0.202887	−	0.117137i	0.395115	−	0.918632i	$-0.370705\pi$
$653$	−5.18453	−	2.99329i	−0.202887	−	0.117137i	−0.598001	+	0.801495i	$0.704038\pi$
$654$		0			0
$655$			1.79896i			0.0702910i
$656$		0			0
$657$	23.0271	−	13.2947i	0.898371	−	0.518675i
$658$		0			0
$659$	−4.31253	+	2.48984i	−0.167992	+	0.0969905i	−0.581639	−	0.813447i	$-0.697588\pi$
$659$	−4.31253	+	2.48984i	−0.167992	+	0.0969905i	0.413646	+	0.910438i	$0.364255\pi$
$660$		0			0
$661$	−14.1524	+	24.5127i	−0.550466	+	0.953435i	0.447775	+	0.894146i	$0.352217\pi$
$661$	−14.1524	+	24.5127i	−0.550466	+	0.953435i	−0.998241	+	0.0592889i	$0.981117\pi$
$662$		0			0
$663$	−6.43990	+	1.04939i	−0.250105	+	0.0407551i
$664$		0			0
$665$	10.4002	+	6.00454i	0.403301	+	0.232846i
$666$		0			0
$667$	23.9126	−	13.8060i	0.925900	−	0.534569i
$668$		0			0
$669$	−2.15230	−	3.72790i	−0.0832129	−	0.144129i
$670$		0			0
$671$		−	47.3600i		−	1.82831i
$672$		0			0
$673$	−11.3696	+	19.6927i	−0.438264	+	0.759096i	−0.997556	−	0.0698751i	$-0.977740\pi$
$673$	−11.3696	+	19.6927i	−0.438264	+	0.759096i	0.559291	+	0.828971i	$0.311073\pi$
$674$		0			0
$675$			19.6227i			0.755277i
$676$		0			0
$677$		−	35.0768i		−	1.34811i	−0.738681	−	0.674056i	$-0.764551\pi$
$677$		−	35.0768i		−	1.34811i	0.738681	−	0.674056i	$-0.235449\pi$
$678$		0			0
$679$	−23.8564	+	41.3205i	−0.915525	+	1.58574i
$680$		0			0
$681$			3.96676i			0.152006i
$682$		0			0
$683$	24.6307	+	42.6617i	0.942469	+	1.63240i	0.760742	+	0.649055i	$0.224835\pi$
$683$	24.6307	+	42.6617i	0.942469	+	1.63240i	0.181727	+	0.983349i	$0.441831\pi$
$684$		0			0
$685$	−10.5508	+	6.09148i	−0.403124	+	0.232743i
$686$		0			0
$687$	−14.7832	−	8.53506i	−0.564013	−	0.325633i
$688$		0			0
$689$	−11.9104	+	1.94082i	−0.453749	+	0.0739392i
$690$		0			0
$691$	−12.6649	+	21.9363i	−0.481797	+	0.834498i	−0.999782	−	0.0208926i	$-0.993349\pi$
$691$	−12.6649	+	21.9363i	−0.481797	+	0.834498i	0.517984	+	0.855390i	$0.326683\pi$
$692$		0			0
$693$	−48.3185	+	27.8967i	−1.83547	+	1.05971i
$694$		0			0
$695$	13.9558	−	8.05740i	0.529375	−	0.305635i
$696$		0			0
$697$		−	0.0394762i		−	0.00149527i
$698$		0			0
$699$	−12.6259	−	7.28958i	−0.477556	−	0.275717i
$700$		0			0
$701$			37.7963i			1.42755i	0.700377	+	0.713773i	$0.253015\pi$
$701$			37.7963i			1.42755i	−0.700377	+	0.713773i	$0.746985\pi$
$702$		0			0
$703$	6.37043			0.240265
$704$		0			0
$705$	1.29597	−	2.24468i	0.0488090	−	0.0845397i
$706$		0			0
$707$	−53.9494			−2.02898
$708$		0			0
$709$	14.8681	+	25.7524i	0.558385	+	0.967151i	0.997632	+	0.0687845i	$0.0219121\pi$
$709$	14.8681	+	25.7524i	0.558385	+	0.967151i	−0.439247	+	0.898367i	$0.644755\pi$
$710$		0			0
$711$	3.29813	+	5.71252i	0.123689	+	0.214236i
$712$		0			0
$713$	−11.5701	−	6.67999i	−0.433303	−	0.250168i
$714$		0			0
$715$	18.1817	+	6.88656i	0.679956	+	0.257543i
$716$		0			0
$717$	1.64444	−	2.84825i	0.0614127	−	0.106370i
$718$		0			0
$719$	12.2000	+	21.1310i	0.454983	+	0.788054i	0.998687	−	0.0512233i	$-0.0163120\pi$
$719$	12.2000	+	21.1310i	0.454983	+	0.788054i	−0.543704	+	0.839277i	$0.682979\pi$
$720$		0			0
$721$	−23.2378	+	13.4164i	−0.865422	+	0.499652i
$722$		0			0
$723$	−20.5356			−0.763728
$724$		0			0
$725$	−18.9240	−	10.9258i	−0.702820	−	0.405773i
$726$		0			0
$727$	44.0720			1.63454			0.817271	−	0.576254i	$-0.195486\pi$
$727$	44.0720			1.63454			0.817271	+	0.576254i	$0.195486\pi$
$728$		0			0
$729$	−7.41482			−0.274623
$730$		0			0
$731$	−6.95808	−	4.01725i	−0.257354	−	0.148583i
$732$		0			0
$733$	28.9063			1.06768			0.533839	−	0.845586i	$-0.320749\pi$
$733$	28.9063			1.06768			0.533839	+	0.845586i	$0.320749\pi$
$734$		0			0
$735$	−7.52489	+	4.34449i	−0.277560	+	0.160249i
$736$		0			0
$737$	9.29138	+	16.0931i	0.342252	+	0.592799i
$738$		0			0
$739$	12.3818	−	21.4460i	0.455474	−	0.788903i	−0.543242	−	0.839576i	$-0.682803\pi$
$739$	12.3818	−	21.4460i	0.455474	−	0.788903i	0.998715	+	0.0506730i	$0.0161366\pi$
$740$		0			0
$741$	−10.1983	+	1.66183i	−0.374644	+	0.0610489i
$742$		0			0
$743$	−44.5277	−	25.7081i	−1.63356	−	0.943139i	−0.982982	−	0.183703i	$-0.941192\pi$
$743$	−44.5277	−	25.7081i	−1.63356	−	0.943139i	−0.650582	−	0.759436i	$-0.725475\pi$
$744$		0			0
$745$	−0.631456	−	1.09371i	−0.0231348	−	0.0400706i
$746$		0			0
$747$	−9.75164	−	16.8903i	−0.356794	−	0.617985i
$748$		0			0
$749$	−17.7613			−0.648983
$750$		0			0
$751$	−10.4756	+	18.1442i	−0.382259	+	0.662093i	−0.991385	−	0.130981i	$-0.958187\pi$
$751$	−10.4756	+	18.1442i	−0.382259	+	0.662093i	0.609125	+	0.793074i	$0.291521\pi$
$752$		0			0
$753$	−5.42412			−0.197666
$754$		0			0
$755$		−	5.20712i		−	0.189507i
$756$		0			0
$757$	21.8620	+	12.6220i	0.794587	+	0.458755i	0.841575	−	0.540140i	$-0.181629\pi$
$757$	21.8620	+	12.6220i	0.794587	+	0.458755i	−0.0469876	+	0.998895i	$0.514962\pi$
$758$		0			0
$759$			28.8326i			1.04656i
$760$		0			0
$761$	−5.11797	+	2.95486i	−0.185526	+	0.107114i	−0.589886	−	0.807486i	$-0.700828\pi$
$761$	−5.11797	+	2.95486i	−0.185526	+	0.107114i	0.404360	+	0.914600i	$0.367494\pi$
$762$		0			0
$763$	56.0928	−	32.3852i	2.03069	−	1.17242i
$764$		0			0
$765$	−1.96809	+	3.40884i	−0.0711566	+	0.123247i
$766$		0			0
$767$	17.5944	−	14.3779i	0.635298	−	0.519155i
$768$		0			0
$769$	15.8579	+	9.15556i	0.571850	+	0.330158i	0.757888	−	0.652385i	$-0.226231\pi$
$769$	15.8579	+	9.15556i	0.571850	+	0.330158i	−0.186038	+	0.982543i	$0.559565\pi$
$770$		0			0
$771$	18.1156	−	10.4590i	0.652417	−	0.376673i
$772$		0			0
$773$	−9.59015	−	16.6106i	−0.344934	−	0.597443i	0.640408	−	0.768035i	$-0.278765\pi$
$773$	−9.59015	−	16.6106i	−0.344934	−	0.597443i	−0.985342	+	0.170592i	$0.945432\pi$
$774$		0			0
$775$			10.5728i			0.379788i
$776$		0			0
$777$	−3.79705	+	6.57668i	−0.136218	+	0.235937i
$778$		0			0
$779$		−	0.0625150i		−	0.00223983i
$780$		0			0
$781$		−	15.4757i		−	0.553765i
$782$		0			0
$783$	12.1433	−	21.0329i	0.433967	−	0.751653i
$784$		0			0
$785$		−	2.79890i		−	0.0998970i
$786$		0			0
$787$	−3.92375	−	6.79613i	−0.139867	−	0.242256i	0.787579	−	0.616213i	$-0.211334\pi$
$787$	−3.92375	−	6.79613i	−0.139867	−	0.242256i	−0.927446	+	0.373957i	$0.878001\pi$
$788$		0			0
$789$	−2.09645	+	1.21039i	−0.0746357	+	0.0430909i
$790$		0			0
$791$	−38.8507	−	22.4305i	−1.38137	−	0.797535i
$792$		0			0
$793$	−17.9025	−	21.9075i	−0.635735	−	0.777960i
$794$		0			0
$795$	1.34518	−	2.32993i	0.0477088	−	0.0826341i
$796$		0			0
$797$	22.6302	−	13.0656i	0.801605	−	0.462807i	−0.0424273	−	0.999100i	$-0.513509\pi$
$797$	22.6302	−	13.0656i	0.801605	−	0.462807i	0.844032	+	0.536293i	$0.180176\pi$
$798$		0			0
$799$	−5.61657	+	3.24273i	−0.198700	+	0.114719i
$800$		0			0
$801$		−	19.0443i		−	0.672898i
$802$		0			0
$803$	−63.4482	−	36.6318i	−2.23904	−	1.29271i
$804$		0			0
$805$		−	20.0183i		−	0.705554i
$806$		0			0
$807$	11.3051			0.397960
$808$		0			0
$809$	6.20747	−	10.7517i	0.218243	−	0.378008i	−0.736028	−	0.676951i	$-0.763301\pi$
$809$	6.20747	−	10.7517i	0.218243	−	0.378008i	0.954271	+	0.298943i	$0.0966341\pi$
$810$		0			0
$811$	15.9619			0.560499			0.280249	−	0.959927i	$-0.409583\pi$
$811$	15.9619			0.560499			0.280249	+	0.959927i	$0.409583\pi$
$812$		0			0
$813$	−0.129322	−	0.223992i	−0.00453551	−	0.00785573i
$814$		0			0
$815$	−1.73230	−	3.00043i	−0.0606797	−	0.105100i
$816$		0			0
$817$	−11.0189	−	6.36176i	−0.385502	−	0.222570i
$818$		0			0
$819$	−11.8057	+	31.1691i	−0.412526	+	1.08914i
$820$		0			0
$821$	22.5254	−	39.0152i	0.786144	−	1.36164i	−0.142170	−	0.989842i	$-0.545408\pi$
$821$	22.5254	−	39.0152i	0.786144	−	1.36164i	0.928314	−	0.371798i	$-0.121259\pi$
$822$		0			0
$823$	16.7658	+	29.0393i	0.584420	+	1.01224i	0.994947	+	0.100397i	$0.0320112\pi$
$823$	16.7658	+	29.0393i	0.584420	+	1.01224i	−0.410528	+	0.911848i	$0.634655\pi$
$824$		0			0
$825$	19.7606	−	11.4088i	0.687977	−	0.397204i
$826$		0			0
$827$	51.5687			1.79322			0.896610	−	0.442820i	$-0.146022\pi$
$827$	51.5687			1.79322			0.896610	+	0.442820i	$0.146022\pi$
$828$		0			0
$829$	18.8521	+	10.8842i	0.654759	+	0.378025i	0.790277	−	0.612750i	$-0.209937\pi$
$829$	18.8521	+	10.8842i	0.654759	+	0.378025i	−0.135518	+	0.990775i	$0.543270\pi$
$830$		0			0
$831$	12.4566			0.432116
$832$		0			0
$833$	21.7413			0.753291
$834$		0			0
$835$	−12.2094	−	7.04907i	−0.422522	−	0.243943i
$836$		0			0
$837$	−11.7511			−0.406176
$838$		0			0
$839$	22.6729	−	13.0902i	0.782755	−	0.451924i	−0.0546509	−	0.998506i	$-0.517405\pi$
$839$	22.6729	−	13.0902i	0.782755	−	0.451924i	0.837406	+	0.546582i	$0.184071\pi$
$840$		0			0
$841$	−0.977337	−	1.69280i	−0.0337013	−	0.0583723i
$842$		0			0
$843$	0.983565	−	1.70358i	0.0338758	−	0.0586746i
$844$		0			0
$845$	11.0136	−	3.68727i	0.378878	−	0.126846i
$846$		0			0
$847$	92.9336	+	53.6552i	3.19324	+	1.84362i
$848$		0			0
$849$	6.37064	+	11.0343i	0.218640	+	0.378695i
$850$		0			0
$851$	−5.30954	−	9.19640i	−0.182009	−	0.315249i
$852$		0			0
$853$	33.0664			1.13217			0.566086	−	0.824346i	$-0.308457\pi$
$853$	33.0664			1.13217			0.566086	+	0.824346i	$0.308457\pi$
$854$		0			0
$855$	−3.11669	+	5.39827i	−0.106589	+	0.184617i
$856$		0			0
$857$	27.7866			0.949172			0.474586	−	0.880209i	$-0.342598\pi$
$857$	27.7866			0.949172			0.474586	+	0.880209i	$0.342598\pi$
$858$		0			0
$859$		−	53.8754i		−	1.83820i	−0.394020	−	0.919102i	$-0.628916\pi$
$859$		−	53.8754i		−	1.83820i	0.394020	−	0.919102i	$-0.371084\pi$
$860$		0			0
$861$	0.0645389	+	0.0372616i	0.00219948	+	0.00126987i
$862$		0			0
$863$		−	48.6608i		−	1.65643i	−0.560408	−	0.828217i	$-0.689355\pi$
$863$		−	48.6608i		−	1.65643i	0.560408	−	0.828217i	$-0.310645\pi$
$864$		0			0
$865$	−0.480716	+	0.277541i	−0.0163448	+	0.00943669i
$866$		0			0
$867$	10.0941	−	5.82783i	0.342813	−	0.197923i
$868$		0			0
$869$	9.08758	−	15.7401i	0.308275	−	0.533948i
$870$		0			0
$871$	10.3813	+	3.93206i	0.351757	+	0.133233i
$872$		0			0
$873$	−21.4477	−	12.3828i	−0.725893	−	0.419095i
$874$		0			0
$875$	−30.0457	+	17.3469i	−1.01573	+	0.586431i
$876$		0			0
$877$	−1.83365	−	3.17598i	−0.0619181	−	0.107245i	0.833405	−	0.552663i	$-0.186388\pi$
$877$	−1.83365	−	3.17598i	−0.0619181	−	0.107245i	−0.895323	+	0.445418i	$0.853055\pi$
$878$		0			0
$879$		−	22.5643i		−	0.761074i
$880$		0			0
$881$	−0.624583	+	1.08181i	−0.0210427	+	0.0364471i	−0.876355	−	0.481666i	$-0.840032\pi$
$881$	−0.624583	+	1.08181i	−0.0210427	+	0.0364471i	0.855312	+	0.518113i	$0.173365\pi$
$882$		0			0
$883$		−	4.46615i		−	0.150298i	−0.997172	−	0.0751489i	$-0.976057\pi$
$883$		−	4.46615i		−	0.150298i	0.997172	−	0.0751489i	$-0.0239432\pi$
$884$		0			0
$885$			5.06573i			0.170283i
$886$		0			0
$887$	6.70566	−	11.6145i	0.225154	−	0.389978i	−0.731212	−	0.682151i	$-0.761045\pi$
$887$	6.70566	−	11.6145i	0.225154	−	0.389978i	0.956366	+	0.292173i	$0.0943782\pi$
$888$		0			0
$889$			10.7026i			0.358953i
$890$		0			0
$891$	−7.15103	−	12.3860i	−0.239569	−	0.414945i
$892$		0			0
$893$	−8.89445	+	5.13521i	−0.297641	+	0.171843i
$894$		0			0
$895$	−8.39654	−	4.84774i	−0.280665	−	0.162042i
$896$		0			0
$897$	10.8990	+	13.3372i	0.363906	+	0.445317i
$898$		0			0
$899$	6.54292	−	11.3327i	0.218219	−	0.377966i
$900$		0			0
$901$	−5.82986	+	3.36587i	−0.194221	+	0.112133i
$902$		0			0
$903$	13.1354	−	7.58375i	0.437120	−	0.252371i
$904$		0			0
$905$		−	14.3406i		−	0.476698i
$906$		0			0
$907$	28.1142	+	16.2318i	0.933518	+	0.538967i	0.887923	−	0.459993i	$-0.152148\pi$
$907$	28.1142	+	16.2318i	0.933518	+	0.538967i	0.0455956	+	0.998960i	$0.485481\pi$
$908$		0			0
$909$		−	28.0028i		−	0.928794i
$910$		0			0
$911$	−24.4263			−0.809279			−0.404639	−	0.914476i	$-0.632603\pi$
$911$	−24.4263			−0.809279			−0.404639	+	0.914476i	$0.632603\pi$
$912$		0			0
$913$	−26.8694	+	46.5392i	−0.889248	+	1.54022i
$914$		0			0
$915$	6.30754			0.208521
$916$		0			0
$917$	4.24876	+	7.35906i	0.140306	+	0.243018i
$918$		0			0
$919$	−22.1908	−	38.4356i	−0.732008	−	1.26787i	−0.956024	−	0.293289i	$-0.905250\pi$
$919$	−22.1908	−	38.4356i	−0.732008	−	1.26787i	0.224016	−	0.974585i	$-0.428083\pi$
$920$		0			0
$921$	−12.2890	−	7.09503i	−0.404935	−	0.233789i
$922$		0			0
$923$	−5.84995	−	7.15868i	−0.192554	−	0.235631i
$924$		0			0
$925$	−4.20188	+	7.27786i	−0.138157	+	0.239295i
$926$		0			0
$927$	−6.96385	−	12.0617i	−0.228723	−	0.396159i
$928$		0			0
$929$	−21.9114	+	12.6505i	−0.718889	+	0.415051i	−0.814344	−	0.580383i	$-0.802903\pi$
$929$	−21.9114	+	12.6505i	−0.718889	+	0.415051i	0.0954546	+	0.995434i	$0.469570\pi$
$930$		0			0
$931$	34.4297			1.12839
$932$		0			0
$933$	−9.98267	−	5.76350i	−0.326818	−	0.188689i
$934$		0			0
$935$	10.8457			0.354692
$936$		0			0
$937$	−41.0474			−1.34096			−0.670479	−	0.741928i	$-0.733912\pi$
$937$	−41.0474			−1.34096			−0.670479	+	0.741928i	$0.733912\pi$
$938$		0			0
$939$	17.1333	+	9.89193i	0.559125	+	0.322811i
$940$		0			0
$941$	−36.6752			−1.19558			−0.597789	−	0.801653i	$-0.703954\pi$
$941$	−36.6752			−1.19558			−0.597789	+	0.801653i	$0.703954\pi$
$942$		0			0
$943$	−0.0902470	+	0.0521041i	−0.00293885	+	0.00169674i
$944$		0			0
$945$	−8.80379	−	15.2486i	−0.286387	−	0.496038i
$946$		0			0
$947$	10.9465	−	18.9599i	0.355714	−	0.616114i	−0.631526	−	0.775355i	$-0.717571\pi$
$947$	10.9465	−	18.9599i	0.355714	−	0.616114i	0.987240	+	0.159240i	$0.0509045\pi$
$948$		0			0
$949$	−43.1966	+	7.03898i	−1.40222	+	0.228495i
$950$		0			0
$951$	−13.8571	−	8.00042i	−0.449348	−	0.259431i
$952$		0			0
$953$	24.7900	+	42.9375i	0.803026	+	1.39088i	0.917616	+	0.397469i	$0.130111\pi$
$953$	24.7900	+	42.9375i	0.803026	+	1.39088i	−0.114590	+	0.993413i	$0.536555\pi$
$954$		0			0
$955$	−9.80570	−	16.9840i	−0.317305	−	0.549588i
$956$		0			0
$957$	−28.2410			−0.912902
$958$		0			0
$959$	−28.7736	+	49.8373i	−0.929147	+	1.60933i
$960$		0			0
$961$	24.6684			0.795756
$962$		0			0
$963$		−	9.21910i		−	0.297081i
$964$		0			0
$965$	6.66320	+	3.84700i	0.214496	+	0.123839i
$966$		0			0
$967$		−	31.4252i		−	1.01057i	−0.862953	−	0.505284i	$-0.831388\pi$
$967$		−	31.4252i		−	1.01057i	0.862953	−	0.505284i	$-0.168612\pi$
$968$		0			0
$969$	−4.99184	+	2.88204i	−0.160361	+	0.0925845i
$970$		0			0
$971$	−42.8554	+	24.7426i	−1.37530	+	0.794028i	−0.991589	−	0.129427i	$-0.958686\pi$
$971$	−42.8554	+	24.7426i	−1.37530	+	0.794028i	−0.383707	+	0.923455i	$0.625353\pi$
$972$		0			0
$973$	38.0598	−	65.9215i	1.22014	−	2.11334i
$974$		0			0
$975$	4.82814	−	12.7471i	0.154624	−	0.408234i
$976$		0			0
$977$	34.7979	+	20.0906i	1.11328	+	0.642754i	0.939678	−	0.342061i	$-0.111125\pi$
$977$	34.7979	+	20.0906i	1.11328	+	0.642754i	0.173605	+	0.984815i	$0.444458\pi$
$978$		0			0
$979$	−45.4440	+	26.2371i	−1.45240	+	0.838542i
$980$		0			0
$981$	16.8097	+	29.1153i	0.536693	+	0.929580i
$982$		0			0
$983$			53.9410i			1.72045i	0.509913	+	0.860226i	$0.329677\pi$
$983$			53.9410i			1.72045i	−0.509913	+	0.860226i	$0.670323\pi$
$984$		0			0
$985$	4.09072	−	7.08533i	0.130341	−	0.225757i
$986$		0			0
$987$		−	12.2432i		−	0.389706i
$988$		0			0
$989$			21.2092i			0.674415i
$990$		0			0
$991$	−21.4117	+	37.0862i	−0.680166	+	1.17808i	0.294764	+	0.955570i	$0.404759\pi$
$991$	−21.4117	+	37.0862i	−0.680166	+	1.17808i	−0.974930	+	0.222512i	$0.928575\pi$
$992$		0			0
$993$		−	25.6219i		−	0.813086i
$994$		0			0
$995$	7.00391	+	12.1311i	0.222039	+	0.384583i
$996$		0			0
$997$	38.5110	−	22.2343i	1.21966	−	0.704168i	0.254811	−	0.966991i	$-0.417987\pi$
$997$	38.5110	−	22.2343i	1.21966	−	0.704168i	0.964844	+	0.262822i	$0.0846533\pi$
$998$		0			0
$999$	−8.08890	−	4.67013i	−0.255921	−	0.147756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.ba.c.17.6		16
4.3	odd	2		104.2.s.c.69.1	✓	16
8.3	odd	2		104.2.s.c.69.2	yes	16
8.5	even	2	inner	416.2.ba.c.17.3		16
12.11	even	2		936.2.dg.d.901.8		16
13.10	even	6	inner	416.2.ba.c.49.3		16
24.11	even	2		936.2.dg.d.901.7		16
52.23	odd	6		104.2.s.c.101.2	yes	16
104.75	odd	6		104.2.s.c.101.1	yes	16
104.101	even	6	inner	416.2.ba.c.49.6		16
156.23	even	6		936.2.dg.d.829.7		16
312.179	even	6		936.2.dg.d.829.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.1	✓	16	4.3	odd	2
104.2.s.c.69.2	yes	16	8.3	odd	2
104.2.s.c.101.1	yes	16	104.75	odd	6
104.2.s.c.101.2	yes	16	52.23	odd	6
416.2.ba.c.17.3		16	8.5	even	2	inner
416.2.ba.c.17.6		16	1.1	even	1	trivial
416.2.ba.c.49.3		16	13.10	even	6	inner
416.2.ba.c.49.6		16	104.101	even	6	inner
936.2.dg.d.829.7		16	156.23	even	6
936.2.dg.d.829.8		16	312.179	even	6
936.2.dg.d.901.7		16	24.11	even	2
936.2.dg.d.901.8		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.779193 + 0.449867i) q^{3} -0.893415 q^{5} +(-3.65473 + 2.11006i) q^{7} +(-1.09524 - 1.89701i) q^{9} +(-3.01779 + 5.22697i) q^{11} +(0.579883 + 3.55861i) q^{13} +(-0.696143 - 0.401918i) q^{15} +(1.00567 + 1.74186i) q^{17} +(1.59258 + 2.75843i) q^{19} -3.79699 q^{21} +(2.65473 - 4.59813i) q^{23} -4.20181 q^{25} -4.67005i q^{27} +(4.50378 + 2.60026i) q^{29} -2.51626i q^{31} +(-4.70289 + 2.71521i) q^{33} +(3.26519 - 1.88516i) q^{35} +(1.00002 - 1.73208i) q^{37} +(-1.14906 + 3.03372i) q^{39} +(-0.0169974 - 0.00981345i) q^{41} +(-3.45944 + 1.99731i) q^{43} +(0.978503 + 1.69482i) q^{45} +3.22446i q^{47} +(5.40470 - 9.36121i) q^{49} +1.80966i q^{51} +3.34691i q^{53} +(2.69614 - 4.66986i) q^{55} +2.86580i q^{57} +(-3.15097 - 5.45764i) q^{59} +(-6.79553 + 3.92340i) q^{61} +(8.00560 + 4.62204i) q^{63} +(-0.518077 - 3.17932i) q^{65} +(1.53943 - 2.66638i) q^{67} +(4.13709 - 2.38855i) q^{69} +(-2.22056 + 1.28204i) q^{71} +12.1386i q^{73} +(-3.27402 - 1.89026i) q^{75} -25.4709i q^{77} -3.01133 q^{79} +(-1.18481 + 2.05215i) q^{81} +8.90367 q^{83} +(-0.898477 - 1.55621i) q^{85} +(2.33954 + 4.05220i) q^{87} +(7.52934 + 4.34707i) q^{89} +(-9.62820 - 11.7822i) q^{91} +(1.13198 - 1.96065i) q^{93} +(-1.42284 - 2.46443i) q^{95} +(9.79132 - 5.65302i) q^{97} +13.2208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) \) 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

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Database

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