LMFDB - Embedded newform 726.2.b.f.725.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(725,726)] 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("726.725"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,4] 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:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3588489216.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 10x^{6} - 8x^{5} + 8x^{4} + 4x^{3} + 16x^{2} + 32x + 22 $ x^8 - 4x^7 + 10x^6 - 8x^5 + 8x^4 + 4x^3 + 16x^2 + 32*x + 22
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			725.1
Root			$-0.697085 + 0.346269i$ of defining polynomial
Character	$\chi$	$=$	726.725
Dual form			726.2.b.f.725.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-0.697085 - 1.58558i) q^{3} +1.00000 q^{4} +2.86823i q^{5} +(-0.697085 - 1.58558i) q^{6} +0.692538i q^{7} +1.00000 q^{8} +(-2.02814 + 2.21057i) q^{9} +2.86823i q^{10} +(-0.697085 - 1.58558i) q^{12} +7.07467i q^{13} +0.692538i q^{14} +(4.54782 - 1.99940i) q^{15} +1.00000 q^{16} -1.35848 q^{17} +(-2.02814 + 2.21057i) q^{18} -4.07841i q^{19} +2.86823i q^{20} +(1.09808 - 0.482758i) q^{21} +7.41381i q^{23} +(-0.697085 - 1.58558i) q^{24} -3.22674 q^{25} +7.07467i q^{26} +(4.91883 + 1.67483i) q^{27} +0.692538i q^{28} -5.54099 q^{29} +(4.54782 - 1.99940i) q^{30} +7.14682 q^{31} +1.00000 q^{32} -1.35848 q^{34} -1.98636 q^{35} +(-2.02814 + 2.21057i) q^{36} +5.41477 q^{37} -4.07841i q^{38} +(11.2175 - 4.93165i) q^{39} +2.86823i q^{40} -2.78138 q^{41} +(1.09808 - 0.482758i) q^{42} -3.51390i q^{43} +(-6.34043 - 5.81719i) q^{45} +7.41381i q^{46} -4.48648i q^{47} +(-0.697085 - 1.58558i) q^{48} +6.52039 q^{49} -3.22674 q^{50} +(0.946979 + 2.15399i) q^{51} +7.07467i q^{52} -10.2167i q^{53} +(4.91883 + 1.67483i) q^{54} +0.692538i q^{56} +(-6.46665 + 2.84300i) q^{57} -5.54099 q^{58} +2.32145i q^{59} +(4.54782 - 1.99940i) q^{60} +4.14374i q^{61} +7.14682 q^{62} +(-1.53091 - 1.40457i) q^{63} +1.00000 q^{64} -20.2918 q^{65} +5.53403 q^{67} -1.35848 q^{68} +(11.7552 - 5.16805i) q^{69} -1.98636 q^{70} +8.48528i q^{71} +(-2.02814 + 2.21057i) q^{72} +7.37761i q^{73} +5.41477 q^{74} +(2.24931 + 5.11627i) q^{75} -4.07841i q^{76} +(11.2175 - 4.93165i) q^{78} -13.3579i q^{79} +2.86823i q^{80} +(-0.773258 - 8.96672i) q^{81} -2.78138 q^{82} -6.12622 q^{83} +(1.09808 - 0.482758i) q^{84} -3.89644i q^{85} -3.51390i q^{86} +(3.86254 + 8.78570i) q^{87} -1.79675i q^{89} +(-6.34043 - 5.81719i) q^{90} -4.89948 q^{91} +7.41381i q^{92} +(-4.98194 - 11.3319i) q^{93} -4.48648i q^{94} +11.6978 q^{95} +(-0.697085 - 1.58558i) q^{96} -7.11258 q^{97} +6.52039 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{12} - 8 q^{15} + 8 q^{16} - 16 q^{17} - 4 q^{18} - 12 q^{21} + 4 q^{24} - 40 q^{25} + 16 q^{27} + 8 q^{29} - 8 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 8 q^{97}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^12 - 8 * q^15 + 8 * q^16 - 16 * q^17 - 4 * q^18 - 12 * q^21 + 4 * q^24 - 40 * q^25 + 16 * q^27 + 8 * q^29 - 8 * q^30 + 24 * q^31 + 8 * q^32 - 16 * q^34 - 4 * q^36 + 24 * q^37 + 28 * q^39 - 12 * q^42 - 16 * q^45 + 4 * q^48 - 40 * q^50 - 28 * q^51 + 16 * q^54 + 16 * q^57 + 8 * q^58 - 8 * q^60 + 24 * q^62 - 12 * q^63 + 8 * q^64 - 32 * q^65 + 8 * q^67 - 16 * q^68 + 40 * q^69 - 4 * q^72 + 24 * q^74 - 12 * q^75 + 28 * q^78 + 8 * q^81 - 16 * q^83 - 12 * q^84 + 32 * q^87 - 16 * q^90 + 8 * q^91 + 64 * q^95 + 4 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.697085	−	1.58558i	−0.402462	−	0.915437i
$3$	−0.697085	−	1.58558i	−0.402462	−	0.915437i
$4$	1.00000			0.500000
$5$			2.86823i			1.28271i	0.767244	+	0.641356i	$0.221628\pi$
$5$			2.86823i			1.28271i	−0.767244	+	0.641356i	$0.778372\pi$
$6$	−0.697085	−	1.58558i	−0.284584	−	0.647311i
$7$			0.692538i			0.261755i	0.991399	+	0.130877i	$0.0417794\pi$
$7$			0.692538i			0.261755i	−0.991399	+	0.130877i	$0.958221\pi$
$8$	1.00000			0.353553
$9$	−2.02814	+	2.21057i	−0.676048	+	0.736857i
$10$			2.86823i			0.907014i
$11$		0			0
$11$		0			0
$12$	−0.697085	−	1.58558i	−0.201231	−	0.457718i
$13$			7.07467i			1.96216i	0.193601	+	0.981080i	$0.437983\pi$
$13$			7.07467i			1.96216i	−0.193601	+	0.981080i	$0.562017\pi$
$14$			0.692538i			0.185089i
$15$	4.54782	−	1.99940i	1.17424	−	0.516243i
$16$	1.00000			0.250000
$17$	−1.35848			−0.329481			−0.164740	−	0.986337i	$-0.552679\pi$
$17$	−1.35848			−0.329481			−0.164740	+	0.986337i	$0.552679\pi$
$18$	−2.02814	+	2.21057i	−0.478038	+	0.521037i
$19$		−	4.07841i		−	0.935650i	−0.883821	−	0.467825i	$-0.845038\pi$
$19$		−	4.07841i		−	0.935650i	0.883821	−	0.467825i	$-0.154962\pi$
$20$			2.86823i			0.641356i
$21$	1.09808	−	0.482758i	0.239620	−	0.105346i
$22$		0			0
$23$			7.41381i			1.54589i	0.634476	+	0.772943i	$0.281216\pi$
$23$			7.41381i			1.54589i	−0.634476	+	0.772943i	$0.718784\pi$
$24$	−0.697085	−	1.58558i	−0.142292	−	0.323656i
$25$	−3.22674			−0.645348
$26$			7.07467i			1.38746i
$27$	4.91883	+	1.67483i	0.946630	+	0.322322i
$28$			0.692538i			0.130877i
$29$	−5.54099			−1.02894			−0.514468	−	0.857509i	$-0.672011\pi$
$29$	−5.54099			−1.02894			−0.514468	+	0.857509i	$0.672011\pi$
$30$	4.54782	−	1.99940i	0.830314	−	0.365039i
$31$	7.14682			1.28361			0.641804	−	0.766869i	$-0.278186\pi$
$31$	7.14682			1.28361			0.641804	+	0.766869i	$0.278186\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.35848			−0.232978
$35$	−1.98636			−0.335756
$36$	−2.02814	+	2.21057i	−0.338024	+	0.368429i
$37$	5.41477			0.890183			0.445092	−	0.895485i	$-0.353171\pi$
$37$	5.41477			0.890183			0.445092	+	0.895485i	$0.353171\pi$
$38$		−	4.07841i		−	0.661605i
$39$	11.2175	−	4.93165i	1.79623	−	0.789696i
$40$			2.86823i			0.453507i
$41$	−2.78138			−0.434378			−0.217189	−	0.976130i	$-0.569689\pi$
$41$	−2.78138			−0.434378			−0.217189	+	0.976130i	$0.569689\pi$
$42$	1.09808	−	0.482758i	0.169437	−	0.0744912i
$43$		−	3.51390i		−	0.535865i	−0.963438	−	0.267933i	$-0.913660\pi$
$43$		−	3.51390i		−	0.535865i	0.963438	−	0.267933i	$-0.0863405\pi$
$44$		0			0
$45$	−6.34043	−	5.81719i	−0.945175	−	0.867175i
$46$			7.41381i			1.09311i
$47$		−	4.48648i		−	0.654420i	−0.944952	−	0.327210i	$-0.893891\pi$
$47$		−	4.48648i		−	0.654420i	0.944952	−	0.327210i	$-0.106109\pi$
$48$	−0.697085	−	1.58558i	−0.100616	−	0.228859i
$49$	6.52039			0.931484
$50$	−3.22674			−0.456330
$51$	0.946979	+	2.15399i	0.132604	+	0.301619i
$52$			7.07467i			0.981080i
$53$		−	10.2167i		−	1.40337i	−0.712487	−	0.701686i	$-0.752431\pi$
$53$		−	10.2167i		−	1.40337i	0.712487	−	0.701686i	$-0.247569\pi$
$54$	4.91883	+	1.67483i	0.669369	+	0.227916i
$55$		0			0
$56$			0.692538i			0.0925443i
$57$	−6.46665	+	2.84300i	−0.856529	+	0.376564i
$58$	−5.54099			−0.727568
$59$			2.32145i			0.302228i	0.988516	+	0.151114i	$0.0482860\pi$
$59$			2.32145i			0.302228i	−0.988516	+	0.151114i	$0.951714\pi$
$60$	4.54782	−	1.99940i	0.587120	−	0.258121i
$61$			4.14374i			0.530552i	0.964173	+	0.265276i	$0.0854631\pi$
$61$			4.14374i			0.530552i	−0.964173	+	0.265276i	$0.914537\pi$
$62$	7.14682			0.907648
$63$	−1.53091	−	1.40457i	−0.192876	−	0.176959i
$64$	1.00000			0.125000
$65$	−20.2918			−2.51689
$66$		0			0
$67$	5.53403			0.676090			0.338045	−	0.941130i	$-0.390234\pi$
$67$	5.53403			0.676090			0.338045	+	0.941130i	$0.390234\pi$
$68$	−1.35848			−0.164740
$69$	11.7552	−	5.16805i	1.41516	−	0.622161i
$70$	−1.98636			−0.237415
$71$			8.48528i			1.00702i	0.863990	+	0.503509i	$0.167958\pi$
$71$			8.48528i			1.00702i	−0.863990	+	0.503509i	$0.832042\pi$
$72$	−2.02814	+	2.21057i	−0.239019	+	0.260518i
$73$			7.37761i			0.863484i	0.901997	+	0.431742i	$0.142101\pi$
$73$			7.37761i			0.863484i	−0.901997	+	0.431742i	$0.857899\pi$
$74$	5.41477			0.629455
$75$	2.24931	+	5.11627i	0.259728	+	0.590776i
$76$		−	4.07841i		−	0.467825i
$77$		0			0
$78$	11.2175	−	4.93165i	1.27013	−	0.558399i
$79$		−	13.3579i		−	1.50288i	−0.659800	−	0.751441i	$-0.729359\pi$
$79$		−	13.3579i		−	1.50288i	0.659800	−	0.751441i	$-0.270641\pi$
$80$			2.86823i			0.320678i
$81$	−0.773258	−	8.96672i	−0.0859175	−	0.996302i
$82$	−2.78138			−0.307152
$83$	−6.12622			−0.672440			−0.336220	−	0.941783i	$-0.609149\pi$
$83$	−6.12622			−0.672440			−0.336220	+	0.941783i	$0.609149\pi$
$84$	1.09808	−	0.482758i	0.119810	−	0.0526732i
$85$		−	3.89644i		−	0.422629i
$86$		−	3.51390i		−	0.378914i
$87$	3.86254	+	8.78570i	0.414108	+	0.941926i
$88$		0			0
$89$		−	1.79675i		−	0.190456i	−0.995456	−	0.0952278i	$-0.969642\pi$
$89$		−	1.79675i		−	0.190456i	0.995456	−	0.0952278i	$-0.0303580\pi$
$90$	−6.34043	−	5.81719i	−0.668340	−	0.613185i
$91$	−4.89948			−0.513605
$92$			7.41381i			0.772943i
$93$	−4.98194	−	11.3319i	−0.516604	−	1.17506i
$94$		−	4.48648i		−	0.462745i
$95$	11.6978			1.20017
$96$	−0.697085	−	1.58558i	−0.0711459	−	0.161828i
$97$	−7.11258			−0.722173			−0.361086	−	0.932532i	$-0.617594\pi$
$97$	−7.11258			−0.722173			−0.361086	+	0.932532i	$0.617594\pi$
$98$	6.52039			0.658659
$99$		0			0
$100$	−3.22674			−0.322674
$101$	10.3087			1.02576			0.512879	−	0.858461i	$-0.328579\pi$
$101$	10.3087			1.02576			0.512879	+	0.858461i	$0.328579\pi$
$102$	0.946979	+	2.15399i	0.0937649	+	0.213277i
$103$	0.112579			0.0110927			0.00554637	−	0.999985i	$-0.498235\pi$
$103$	0.112579			0.0110927			0.00554637	+	0.999985i	$0.498235\pi$
$104$			7.07467i			0.693729i
$105$	1.38466	+	3.14953i	0.135129	+	0.307363i
$106$		−	10.2167i		−	0.992334i
$107$	−15.4405			−1.49269			−0.746343	−	0.665561i	$-0.768192\pi$
$107$	−15.4405			−1.49269			−0.746343	+	0.665561i	$0.768192\pi$
$108$	4.91883	+	1.67483i	0.473315	+	0.161161i
$109$		−	6.46880i		−	0.619599i	−0.950802	−	0.309799i	$-0.899738\pi$
$109$		−	6.46880i		−	0.619599i	0.950802	−	0.309799i	$-0.100262\pi$
$110$		0			0
$111$	−3.77456	−	8.58557i	−0.358265	−	0.814906i
$112$			0.692538i			0.0654387i
$113$			2.89031i			0.271897i	0.990716	+	0.135949i	$0.0434082\pi$
$113$			2.89031i			0.271897i	−0.990716	+	0.135949i	$0.956592\pi$
$114$	−6.46665	+	2.84300i	−0.605657	+	0.266271i
$115$	−21.2645			−1.98292
$116$	−5.54099			−0.514468
$117$	−15.6391	−	14.3485i	−1.44583	−	1.32652i
$118$			2.32145i			0.213707i
$119$		−	0.940802i		−	0.0862432i
$120$	4.54782	−	1.99940i	0.415157	−	0.182519i
$121$		0			0
$122$			4.14374i			0.375157i
$123$	1.93886	+	4.41011i	0.174821	+	0.397646i
$124$	7.14682			0.641804
$125$			5.08611i			0.454916i
$126$	−1.53091	−	1.40457i	−0.136384	−	0.125129i
$127$			5.40595i			0.479701i	0.970810	+	0.239850i	$0.0770984\pi$
$127$			5.40595i			0.479701i	−0.970810	+	0.239850i	$0.922902\pi$
$128$	1.00000			0.0883883
$129$	−5.57158	+	2.44949i	−0.490551	+	0.215666i
$130$	−20.2918			−1.77971
$131$	6.03122			0.526950			0.263475	−	0.964666i	$-0.415131\pi$
$131$	6.03122			0.526950			0.263475	+	0.964666i	$0.415131\pi$
$132$		0			0
$133$	2.82445			0.244911
$134$	5.53403			0.478068
$135$	−4.80381	+	14.1083i	−0.413446	+	1.21425i
$136$	−1.35848			−0.116489
$137$		−	7.65765i		−	0.654237i	−0.944983	−	0.327118i	$-0.893922\pi$
$137$		−	7.65765i		−	0.654237i	0.944983	−	0.327118i	$-0.106078\pi$
$138$	11.7552	−	5.16805i	1.00067	−	0.439934i
$139$		−	7.07813i		−	0.600359i	−0.953883	−	0.300180i	$-0.902953\pi$
$139$		−	7.07813i		−	0.600359i	0.953883	−	0.300180i	$-0.0970466\pi$
$140$	−1.98636			−0.167878
$141$	−7.11369	+	3.12746i	−0.599080	+	0.263380i
$142$			8.48528i			0.712069i
$143$		0			0
$144$	−2.02814	+	2.21057i	−0.169012	+	0.184214i
$145$		−	15.8928i		−	1.31983i
$146$			7.37761i			0.610575i
$147$	−4.54527	−	10.3386i	−0.374887	−	0.852715i
$148$	5.41477			0.445092
$149$	−13.8207			−1.13224			−0.566119	−	0.824324i	$-0.691556\pi$
$149$	−13.8207			−1.13224			−0.566119	+	0.824324i	$0.691556\pi$
$150$	2.24931	+	5.11627i	0.183656	+	0.417741i
$151$		−	0.270194i		−	0.0219881i	−0.999940	−	0.0109941i	$-0.996500\pi$
$151$		−	0.270194i		−	0.0219881i	0.999940	−	0.0109941i	$-0.00349959\pi$
$152$		−	4.07841i		−	0.330802i
$153$	2.75520	−	3.00303i	0.222745	−	0.242780i
$154$		0			0
$155$			20.4987i			1.64650i
$156$	11.2175	−	4.93165i	0.898117	−	0.394848i
$157$	6.31872			0.504289			0.252144	−	0.967690i	$-0.418864\pi$
$157$	6.31872			0.504289			0.252144	+	0.967690i	$0.418864\pi$
$158$		−	13.3579i		−	1.06270i
$159$	−16.1994	+	7.12191i	−1.28470	+	0.564804i
$160$			2.86823i			0.226753i
$161$	−5.13434			−0.404643
$162$	−0.773258	−	8.96672i	−0.0607529	−	0.704492i
$163$	7.60541			0.595701			0.297851	−	0.954612i	$-0.403730\pi$
$163$	7.60541			0.595701			0.297851	+	0.954612i	$0.403730\pi$
$164$	−2.78138			−0.217189
$165$		0			0
$166$	−6.12622			−0.475487
$167$	3.31425			0.256465			0.128232	−	0.991744i	$-0.459070\pi$
$167$	3.31425			0.256465			0.128232	+	0.991744i	$0.459070\pi$
$168$	1.09808	−	0.482758i	0.0847184	−	0.0372456i
$169$	−37.0510			−2.85007
$170$		−	3.89644i		−	0.298844i
$171$	9.01561	+	8.27160i	0.689441	+	0.632545i
$172$		−	3.51390i		−	0.267933i
$173$	11.2267			0.853553			0.426777	−	0.904357i	$-0.359649\pi$
$173$	11.2267			0.853553			0.426777	+	0.904357i	$0.359649\pi$
$174$	3.86254	+	8.78570i	0.292819	+	0.666043i
$175$		−	2.23464i		−	0.168923i
$176$		0			0
$177$	3.68086	−	1.61825i	0.276670	−	0.121635i
$178$		−	1.79675i		−	0.134672i
$179$		−	12.8632i		−	0.961438i	−0.876875	−	0.480719i	$-0.840376\pi$
$179$		−	12.8632i		−	0.961438i	0.876875	−	0.480719i	$-0.159624\pi$
$180$	−6.34043	−	5.81719i	−0.472588	−	0.433587i
$181$	1.37866			0.102475			0.0512376	−	0.998686i	$-0.483683\pi$
$181$	1.37866			0.102475			0.0512376	+	0.998686i	$0.483683\pi$
$182$	−4.89948			−0.363174
$183$	6.57025	−	2.88854i	0.485687	−	0.213527i
$184$			7.41381i			0.546553i
$185$			15.5308i			1.14185i
$186$	−4.98194	−	11.3319i	−0.365294	−	0.830894i
$187$		0			0
$188$		−	4.48648i		−	0.327210i
$189$	−1.15989	+	3.40648i	−0.0843693	+	0.247785i
$190$	11.6978			0.848648
$191$		−	6.69934i		−	0.484747i	−0.970183	−	0.242374i	$-0.922074\pi$
$191$		−	6.69934i		−	0.484747i	0.970183	−	0.242374i	$-0.0779259\pi$
$192$	−0.697085	−	1.58558i	−0.0503078	−	0.114430i
$193$		−	13.2669i		−	0.954972i	−0.878639	−	0.477486i	$-0.841548\pi$
$193$		−	13.2669i		−	0.954972i	0.878639	−	0.477486i	$-0.158452\pi$
$194$	−7.11258			−0.510653
$195$	14.1451	+	32.1743i	1.01295	+	2.30405i
$196$	6.52039			0.465742
$197$	−0.314252			−0.0223895			−0.0111948	−	0.999937i	$-0.503563\pi$
$197$	−0.314252			−0.0223895			−0.0111948	+	0.999937i	$0.503563\pi$
$198$		0			0
$199$	−9.31425			−0.660270			−0.330135	−	0.943934i	$-0.607094\pi$
$199$	−9.31425			−0.660270			−0.330135	+	0.943934i	$0.607094\pi$
$200$	−3.22674			−0.228165
$201$	−3.85769	−	8.77467i	−0.272101	−	0.618917i
$202$	10.3087			0.725320
$203$		−	3.83735i		−	0.269329i
$204$	0.946979	+	2.15399i	0.0663018	+	0.150809i
$205$		−	7.97763i		−	0.557182i
$206$	0.112579			0.00784376
$207$	−16.3888	−	15.0363i	−1.13910	−	1.04509i
$208$			7.07467i			0.490540i
$209$		0			0
$210$	1.38466	+	3.14953i	0.0955507	+	0.217339i
$211$			0.943585i			0.0649591i	0.999472	+	0.0324795i	$0.0103404\pi$
$211$			0.943585i			0.0649591i	−0.999472	+	0.0324795i	$0.989660\pi$
$212$		−	10.2167i		−	0.701686i
$213$	13.4541	−	5.91496i	0.921861	−	0.405287i
$214$	−15.4405			−1.05549
$215$	10.0787			0.687360
$216$	4.91883	+	1.67483i	0.334684	+	0.113958i
$217$			4.94945i			0.335990i
$218$		−	6.46880i		−	0.438122i
$219$	11.6978	−	5.14282i	0.790464	−	0.347520i
$220$		0			0
$221$		−	9.61083i		−	0.646494i
$222$	−3.77456	−	8.58557i	−0.253332	−	0.576226i
$223$	25.3819			1.69970			0.849849	−	0.527027i	$-0.176693\pi$
$223$	25.3819			1.69970			0.849849	+	0.527027i	$0.176693\pi$
$224$			0.692538i			0.0462721i
$225$	6.54430	−	7.13295i	0.436287	−	0.475530i
$226$			2.89031i			0.192260i
$227$	25.9590			1.72296			0.861480	−	0.507792i	$-0.169538\pi$
$227$	25.9590			1.72296			0.861480	+	0.507792i	$0.169538\pi$
$228$	−6.46665	+	2.84300i	−0.428264	+	0.188282i
$229$	8.26939			0.546457			0.273228	−	0.961949i	$-0.411909\pi$
$229$	8.26939			0.546457			0.273228	+	0.961949i	$0.411909\pi$
$230$	−21.2645			−1.40214
$231$		0			0
$232$	−5.54099			−0.363784
$233$	26.8578			1.75952			0.879758	−	0.475422i	$-0.157705\pi$
$233$	26.8578			1.75952			0.879758	+	0.475422i	$0.157705\pi$
$234$	−15.6391	−	14.3485i	−1.02236	−	0.937988i
$235$	12.8683			0.839433
$236$			2.32145i			0.151114i
$237$	−21.1801	+	9.31160i	−1.37579	+	0.604853i
$238$		−	0.940802i		−	0.0609831i
$239$	15.0121			0.971049			0.485525	−	0.874223i	$-0.338629\pi$
$239$	15.0121			0.971049			0.485525	+	0.874223i	$0.338629\pi$
$240$	4.54782	−	1.99940i	0.293560	−	0.129061i
$241$			9.11248i			0.586987i	0.955961	+	0.293493i	$0.0948178\pi$
$241$			9.11248i			0.586987i	−0.955961	+	0.293493i	$0.905182\pi$
$242$		0			0
$243$	−13.6784	+	7.47663i	−0.877473	+	0.479626i
$244$			4.14374i			0.265276i
$245$			18.7020i			1.19483i
$246$	1.93886	+	4.41011i	0.123617	+	0.281178i
$247$	28.8534			1.83590
$248$	7.14682			0.453824
$249$	4.27050	+	9.71363i	0.270632	+	0.615576i
$250$			5.08611i			0.321674i
$251$		−	17.8203i		−	1.12481i	−0.826863	−	0.562403i	$-0.809877\pi$
$251$		−	17.8203i		−	1.12481i	0.826863	−	0.562403i	$-0.190123\pi$
$252$	−1.53091	−	1.40457i	−0.0964380	−	0.0884794i
$253$		0			0
$254$			5.40595i			0.339200i
$255$	−6.17813	+	2.71615i	−0.386890	+	0.170092i
$256$	1.00000			0.0625000
$257$			20.7056i			1.29158i	0.763516	+	0.645789i	$0.223471\pi$
$257$			20.7056i			1.29158i	−0.763516	+	0.645789i	$0.776529\pi$
$258$	−5.57158	+	2.44949i	−0.346872	+	0.152499i
$259$			3.74994i			0.233010i
$260$	−20.2918			−1.25844
$261$	11.2379	−	12.2488i	0.695611	−	0.758180i
$262$	6.03122			0.372610
$263$	19.4044			1.19652			0.598262	−	0.801300i	$-0.295858\pi$
$263$	19.4044			1.19652			0.598262	+	0.801300i	$0.295858\pi$
$264$		0			0
$265$	29.3038			1.80012
$266$	2.82445			0.173178
$267$	−2.84890	+	1.25249i	−0.174350	+	0.0766512i
$268$	5.53403			0.338045
$269$		−	7.02346i		−	0.428228i	−0.976809	−	0.214114i	$-0.931314\pi$
$269$		−	7.02346i		−	0.428228i	0.976809	−	0.214114i	$-0.0686864\pi$
$270$	−4.80381	+	14.1083i	−0.292351	+	0.858607i
$271$			11.4005i			0.692532i	0.938136	+	0.346266i	$0.112551\pi$
$271$			11.4005i			0.692532i	−0.938136	+	0.346266i	$0.887449\pi$
$272$	−1.35848			−0.0823702
$273$	3.41535	+	7.76853i	0.206707	+	0.470173i
$274$		−	7.65765i		−	0.462615i
$275$		0			0
$276$	11.7552	−	5.16805i	0.707580	−	0.311080i
$277$		−	17.0460i		−	1.02419i	−0.858928	−	0.512096i	$-0.828869\pi$
$277$		−	17.0460i		−	1.02419i	0.858928	−	0.512096i	$-0.171131\pi$
$278$		−	7.07813i		−	0.424518i
$279$	−14.4948	+	15.7986i	−0.867781	+	0.945836i
$280$	−1.98636			−0.118708
$281$	21.2219			1.26599			0.632995	−	0.774156i	$-0.281825\pi$
$281$	21.2219			1.26599			0.632995	+	0.774156i	$0.281825\pi$
$282$	−7.11369	+	3.12746i	−0.423614	+	0.186237i
$283$		−	21.1117i		−	1.25496i	−0.778633	−	0.627479i	$-0.784087\pi$
$283$		−	21.1117i		−	1.25496i	0.778633	−	0.627479i	$-0.215913\pi$
$284$			8.48528i			0.503509i
$285$	−8.15437	−	18.5478i	−0.483023	−	1.09868i
$286$		0			0
$287$		−	1.92621i		−	0.113701i
$288$	−2.02814	+	2.21057i	−0.119510	+	0.130259i
$289$	−15.1545			−0.891442
$290$		−	15.8928i		−	0.933260i
$291$	4.95807	+	11.2776i	0.290647	+	0.661104i
$292$			7.37761i			0.431742i
$293$	−13.4847			−0.787785			−0.393892	−	0.919157i	$-0.628872\pi$
$293$	−13.4847			−0.787785			−0.393892	+	0.919157i	$0.628872\pi$
$294$	−4.54527	−	10.3386i	−0.265085	−	0.602961i
$295$	−6.65846			−0.387671
$296$	5.41477			0.314727
$297$		0			0
$298$	−13.8207			−0.800613
$299$	−52.4502			−3.03328
$300$	2.24931	+	5.11627i	0.129864	+	0.295388i
$301$	2.43351			0.140265
$302$		−	0.270194i		−	0.0155479i
$303$	−7.18606	−	16.3453i	−0.412829	−	0.939016i
$304$		−	4.07841i		−	0.233913i
$305$	−11.8852			−0.680545
$306$	2.75520	−	3.00303i	0.157504	−	0.171672i
$307$			22.7504i			1.29844i	0.760603	+	0.649218i	$0.224904\pi$
$307$			22.7504i			1.29844i	−0.760603	+	0.649218i	$0.775096\pi$
$308$		0			0
$309$	−0.0784772	−	0.178503i	−0.00446441	−	0.0101547i
$310$			20.4987i			1.16425i
$311$			31.2401i			1.77147i	0.464196	+	0.885733i	$0.346343\pi$
$311$			31.2401i			1.77147i	−0.464196	+	0.885733i	$0.653657\pi$
$312$	11.2175	−	4.93165i	0.635065	−	0.279200i
$313$	18.8140			1.06343			0.531716	−	0.846923i	$-0.321547\pi$
$313$	18.8140			1.06343			0.531716	+	0.846923i	$0.321547\pi$
$314$	6.31872			0.356586
$315$	4.02862	−	4.39099i	0.226987	−	0.247404i
$316$		−	13.3579i		−	0.751441i
$317$			12.9975i			0.730013i	0.931005	+	0.365007i	$0.118933\pi$
$317$			12.9975i			0.730013i	−0.931005	+	0.365007i	$0.881067\pi$
$318$	−16.1994	+	7.12191i	−0.908418	+	0.399377i
$319$		0			0
$320$			2.86823i			0.160339i
$321$	10.7633	+	24.4821i	0.600750	+	1.36646i
$322$	−5.13434			−0.286126
$323$			5.54045i			0.308279i
$324$	−0.773258	−	8.96672i	−0.0429588	−	0.498151i
$325$		−	22.8281i		−	1.26628i
$326$	7.60541			0.421224
$327$	−10.2568	+	4.50930i	−0.567203	+	0.249365i
$328$	−2.78138			−0.153576
$329$	3.10706			0.171298
$330$		0			0
$331$	−6.62457			−0.364119			−0.182060	−	0.983287i	$-0.558276\pi$
$331$	−6.62457			−0.364119			−0.182060	+	0.983287i	$0.558276\pi$
$332$	−6.12622			−0.336220
$333$	−10.9819	+	11.9697i	−0.601807	+	0.655938i
$334$	3.31425			0.181348
$335$			15.8729i			0.867228i
$336$	1.09808	−	0.482758i	0.0599050	−	0.0263366i
$337$		−	0.387565i		−	0.0211120i	−0.999944	−	0.0105560i	$-0.996640\pi$
$337$		−	0.387565i		−	0.0211120i	0.999944	−	0.0105560i	$-0.00336014\pi$
$338$	−37.0510			−2.01531
$339$	4.58282	−	2.01479i	0.248905	−	0.109428i
$340$		−	3.89644i		−	0.211314i
$341$		0			0
$342$	9.01561	+	8.27160i	0.487508	+	0.447277i
$343$			9.36338i			0.505575i
$344$		−	3.51390i		−	0.189457i
$345$	14.8232	+	33.7166i	0.798052	+	1.81524i
$346$	11.2267			0.603553
$347$	−17.5869			−0.944113			−0.472056	−	0.881568i	$-0.656488\pi$
$347$	−17.5869			−0.944113			−0.472056	+	0.881568i	$0.656488\pi$
$348$	3.86254	+	8.78570i	0.207054	+	0.470963i
$349$			0.291450i			0.0156010i	0.999970	+	0.00780049i	$0.00248300\pi$
$349$			0.291450i			0.0156010i	−0.999970	+	0.00780049i	$0.997517\pi$
$350$		−	2.23464i		−	0.119447i
$351$	−11.8489	+	34.7991i	−0.632448	+	1.85744i
$352$		0			0
$353$		−	18.9026i		−	1.00608i	−0.864263	−	0.503041i	$-0.832215\pi$
$353$		−	18.9026i		−	1.00608i	0.864263	−	0.503041i	$-0.167785\pi$
$354$	3.68086	−	1.61825i	0.195635	−	0.0860091i
$355$	−24.3377			−1.29171
$356$		−	1.79675i		−	0.0952278i
$357$	−1.49172	+	0.655819i	−0.0789501	+	0.0347096i
$358$		−	12.8632i		−	0.679839i
$359$	−22.7186			−1.19904			−0.599521	−	0.800359i	$-0.704642\pi$
$359$	−22.7186			−1.19904			−0.599521	+	0.800359i	$0.704642\pi$
$360$	−6.34043	−	5.81719i	−0.334170	−	0.306593i
$361$	2.36661			0.124558
$362$	1.37866			0.0724609
$363$		0			0
$364$	−4.89948			−0.256802
$365$	−21.1607			−1.10760
$366$	6.57025	−	2.88854i	0.343432	−	0.150986i
$367$	25.7202			1.34258			0.671292	−	0.741193i	$-0.265740\pi$
$367$	25.7202			1.34258			0.671292	+	0.741193i	$0.265740\pi$
$368$			7.41381i			0.386471i
$369$	5.64104	−	6.14844i	0.293661	−	0.320075i
$370$			15.5308i			0.807409i
$371$	7.07545			0.367339
$372$	−4.98194	−	11.3319i	−0.258302	−	0.587531i
$373$		−	15.4647i		−	0.800730i	−0.916356	−	0.400365i	$-0.868883\pi$
$373$		−	15.4647i		−	0.800730i	0.916356	−	0.400365i	$-0.131117\pi$
$374$		0			0
$375$	8.06445	−	3.54545i	0.416446	−	0.183086i
$376$		−	4.48648i		−	0.231373i
$377$		−	39.2007i		−	2.01894i
$378$	−1.15989	+	3.40648i	−0.0596581	+	0.175210i
$379$	−17.3617			−0.891811			−0.445906	−	0.895080i	$-0.647118\pi$
$379$	−17.3617			−0.891811			−0.445906	+	0.895080i	$0.647118\pi$
$380$	11.6978			0.600085
$381$	8.57158	−	3.76841i	0.439136	−	0.193061i
$382$		−	6.69934i		−	0.342768i
$383$			13.4690i			0.688236i	0.938926	+	0.344118i	$0.111822\pi$
$383$			13.4690i			0.688236i	−0.938926	+	0.344118i	$0.888178\pi$
$384$	−0.697085	−	1.58558i	−0.0355730	−	0.0809139i
$385$		0			0
$386$		−	13.2669i		−	0.675267i
$387$	7.76774	+	7.12671i	0.394856	+	0.362271i
$388$	−7.11258			−0.361086
$389$		−	12.8348i		−	0.650753i	−0.945585	−	0.325376i	$-0.894509\pi$
$389$		−	12.8348i		−	0.650753i	0.945585	−	0.325376i	$-0.105491\pi$
$390$	14.1451	+	32.1743i	0.716265	+	1.62921i
$391$		−	10.0715i		−	0.509340i
$392$	6.52039			0.329329
$393$	−4.20427	−	9.56300i	−0.212078	−	0.482389i
$394$	−0.314252			−0.0158318
$395$	38.3135			1.92776
$396$		0			0
$397$	13.4148			0.673268			0.336634	−	0.941636i	$-0.390711\pi$
$397$	13.4148			0.673268			0.336634	+	0.941636i	$0.390711\pi$
$398$	−9.31425			−0.466881
$399$	−1.96888	−	4.47840i	−0.0985674	−	0.224200i
$400$	−3.22674			−0.161337
$401$		−	20.3361i		−	1.01553i	−0.861494	−	0.507767i	$-0.830471\pi$
$401$		−	20.3361i		−	1.01553i	0.861494	−	0.507767i	$-0.169529\pi$
$402$	−3.85769	−	8.77467i	−0.192404	−	0.437641i
$403$			50.5614i			2.51864i
$404$	10.3087			0.512879
$405$	25.7186	−	2.21788i	1.27797	−	0.110207i
$406$		−	3.83735i		−	0.190444i
$407$		0			0
$408$	0.946979	+	2.15399i	0.0468824	+	0.106638i
$409$			24.3271i			1.20290i	0.798912	+	0.601448i	$0.205409\pi$
$409$			24.3271i			1.20290i	−0.798912	+	0.601448i	$0.794591\pi$
$410$		−	7.97763i		−	0.393987i
$411$	−12.1418	+	5.33803i	−0.598912	+	0.263306i
$412$	0.112579			0.00554637
$413$	−1.60770			−0.0791095
$414$	−16.3888	−	15.0363i	−0.805463	−	0.738992i
$415$		−	17.5714i		−	0.862547i
$416$			7.07467i			0.346864i
$417$	−11.2230	+	4.93406i	−0.549591	+	0.241622i
$418$		0			0
$419$		−	36.1710i		−	1.76707i	−0.468365	−	0.883535i	$-0.655157\pi$
$419$		−	36.1710i		−	1.76707i	0.468365	−	0.883535i	$-0.344843\pi$
$420$	1.38466	+	3.14953i	0.0675645	+	0.153682i
$421$	−29.2490			−1.42551			−0.712754	−	0.701414i	$-0.752553\pi$
$421$	−29.2490			−1.42551			−0.712754	+	0.701414i	$0.752553\pi$
$422$			0.943585i			0.0459330i
$423$	9.91769	+	9.09923i	0.482215	+	0.442420i
$424$		−	10.2167i		−	0.496167i
$425$	4.38348			0.212630
$426$	13.4541	−	5.91496i	0.651854	−	0.286581i
$427$	−2.86970			−0.138874
$428$	−15.4405			−0.746343
$429$		0			0
$430$	10.0787			0.486037
$431$	24.2837			1.16970			0.584851	−	0.811140i	$-0.301153\pi$
$431$	24.2837			1.16970			0.584851	+	0.811140i	$0.301153\pi$
$432$	4.91883	+	1.67483i	0.236658	+	0.0805805i
$433$	0.546515			0.0262638			0.0131319	−	0.999914i	$-0.495820\pi$
$433$	0.546515			0.0262638			0.0131319	+	0.999914i	$0.495820\pi$
$434$			4.94945i			0.237581i
$435$	−25.1994	+	11.0787i	−1.20822	+	0.531181i
$436$		−	6.46880i		−	0.309799i
$437$	30.2365			1.44641
$438$	11.6978	−	5.14282i	0.558943	−	0.245733i
$439$		−	23.6963i		−	1.13096i	−0.824762	−	0.565480i	$-0.808691\pi$
$439$		−	23.6963i		−	1.13096i	0.824762	−	0.565480i	$-0.191309\pi$
$440$		0			0
$441$	−13.2243	+	14.4138i	−0.629728	+	0.686371i
$442$		−	9.61083i		−	0.457140i
$443$			10.9852i			0.521924i	0.965349	+	0.260962i	$0.0840398\pi$
$443$			10.9852i			0.521924i	−0.965349	+	0.260962i	$0.915960\pi$
$444$	−3.77456	−	8.58557i	−0.179133	−	0.407453i
$445$	5.15350			0.244300
$446$	25.3819			1.20187
$447$	9.63422	+	21.9139i	0.455683	+	1.03649i
$448$			0.692538i			0.0327193i
$449$			8.49609i			0.400955i	0.979698	+	0.200478i	$0.0642494\pi$
$449$			8.49609i			0.400955i	−0.979698	+	0.200478i	$0.935751\pi$
$450$	6.54430	−	7.13295i	0.308501	−	0.336250i
$451$		0			0
$452$			2.89031i			0.135949i
$453$	−0.428415	+	0.188348i	−0.0201287	+	0.00884938i
$454$	25.9590			1.21832
$455$		−	14.0528i		−	0.658807i
$456$	−6.46665	+	2.84300i	−0.302829	+	0.133135i
$457$			22.1681i			1.03698i	0.855084	+	0.518489i	$0.173505\pi$
$457$			22.1681i			1.03698i	−0.855084	+	0.518489i	$0.826495\pi$
$458$	8.26939			0.386403
$459$	−6.68216	−	2.27524i	−0.311896	−	0.106199i
$460$	−21.2645			−0.991462
$461$	−29.1890			−1.35947			−0.679735	−	0.733458i	$-0.737905\pi$
$461$	−29.1890			−1.35947			−0.679735	+	0.733458i	$0.737905\pi$
$462$		0			0
$463$	−13.8641			−0.644318			−0.322159	−	0.946686i	$-0.604409\pi$
$463$	−13.8641			−0.644318			−0.322159	+	0.946686i	$0.604409\pi$
$464$	−5.54099			−0.257234
$465$	32.5024	−	14.2894i	1.50726	−	0.662653i
$466$	26.8578			1.24417
$467$			2.67846i			0.123944i	0.998078	+	0.0619722i	$0.0197390\pi$
$467$			2.67846i			0.123944i	−0.998078	+	0.0619722i	$0.980261\pi$
$468$	−15.6391	−	14.3485i	−0.722916	−	0.663258i
$469$			3.83253i			0.176970i
$470$	12.8683			0.593568
$471$	−4.40468	−	10.0188i	−0.202957	−	0.461644i
$472$			2.32145i			0.106854i
$473$		0			0
$474$	−21.1801	+	9.31160i	−0.972833	+	0.427696i
$475$			13.1600i			0.603821i
$476$		−	0.940802i		−	0.0431216i
$477$	22.5847	+	20.7209i	1.03408	+	0.948747i
$478$	15.0121			0.686636
$479$	14.4574			0.660576			0.330288	−	0.943880i	$-0.392854\pi$
$479$	14.4574			0.660576			0.330288	+	0.943880i	$0.392854\pi$
$480$	4.54782	−	1.99940i	0.207578	−	0.0912597i
$481$			38.3077i			1.74668i
$482$			9.11248i			0.415062i
$483$	3.57907	+	8.14092i	0.162853	+	0.370425i
$484$		0			0
$485$		−	20.4005i		−	0.926340i
$486$	−13.6784	+	7.47663i	−0.620467	+	0.339147i
$487$	2.05773			0.0932447			0.0466223	−	0.998913i	$-0.485154\pi$
$487$	2.05773			0.0932447			0.0466223	+	0.998913i	$0.485154\pi$
$488$			4.14374i			0.187578i
$489$	−5.30161	−	12.0590i	−0.239747	−	0.545327i
$490$			18.7020i			0.844869i
$491$	−12.7847			−0.576965			−0.288482	−	0.957485i	$-0.593151\pi$
$491$	−12.7847			−0.576965			−0.288482	+	0.957485i	$0.593151\pi$
$492$	1.93886	+	4.41011i	0.0874105	+	0.198823i
$493$	7.52735			0.339015
$494$	28.8534			1.29818
$495$		0			0
$496$	7.14682			0.320902
$497$	−5.87638			−0.263592
$498$	4.27050	+	9.71363i	0.191366	+	0.435278i
$499$	−5.57668			−0.249647			−0.124823	−	0.992179i	$-0.539836\pi$
$499$	−5.57668			−0.249647			−0.124823	+	0.992179i	$0.539836\pi$
$500$			5.08611i			0.227458i
$501$	−2.31032	−	5.25502i	−0.103217	−	0.234777i
$502$		−	17.8203i		−	0.795358i
$503$	24.0491			1.07230			0.536148	−	0.844124i	$-0.319879\pi$
$503$	24.0491			1.07230			0.536148	+	0.844124i	$0.319879\pi$
$504$	−1.53091	−	1.40457i	−0.0681919	−	0.0625644i
$505$			29.5678i			1.31575i
$506$		0			0
$507$	25.8277	+	58.7474i	1.14705	+	2.60906i
$508$			5.40595i			0.239850i
$509$			8.35461i			0.370311i	0.982709	+	0.185156i	$0.0592790\pi$
$509$			8.35461i			0.370311i	−0.982709	+	0.185156i	$0.940721\pi$
$510$	−6.17813	+	2.71615i	−0.273572	+	0.120273i
$511$	−5.10927			−0.226021
$512$	1.00000			0.0441942
$513$	6.83065	−	20.0610i	0.301581	−	0.885715i
$514$			20.7056i			0.913283i
$515$			0.322903i			0.0142288i
$516$	−5.57158	+	2.44949i	−0.245275	+	0.107833i
$517$		0			0
$518$			3.74994i			0.164763i
$519$	−7.82599	−	17.8009i	−0.343523	−	0.781374i
$520$	−20.2918			−0.889854
$521$			0.209281i			0.00916877i	0.999989	+	0.00458439i	$0.00145926\pi$
$521$			0.209281i			0.00916877i	−0.999989	+	0.00458439i	$0.998541\pi$
$522$	11.2379	−	12.2488i	0.491871	−	0.536114i
$523$			39.0841i			1.70903i	0.519428	+	0.854514i	$0.326145\pi$
$523$			39.0841i			1.70903i	−0.519428	+	0.854514i	$0.673855\pi$
$524$	6.03122			0.263475
$525$	−3.54321	+	1.55774i	−0.154638	+	0.0679851i
$526$	19.4044			0.846070
$527$	−9.70885			−0.422924
$528$		0			0
$529$	−31.9645			−1.38976
$530$	29.3038			1.27288
$531$	−5.13174	−	4.70825i	−0.222699	−	0.204320i
$532$	2.82445			0.122455
$533$		−	19.6773i		−	0.852320i
$534$	−2.84890	+	1.25249i	−0.123284	+	0.0542006i
$535$		−	44.2868i		−	1.91469i
$536$	5.53403			0.239034
$537$	−20.3956	+	8.96672i	−0.880136	+	0.386943i
$538$		−	7.02346i		−	0.302803i
$539$		0			0
$540$	−4.80381	+	14.1083i	−0.206723	+	0.607127i
$541$		−	0.291525i		−	0.0125336i	−0.999980	−	0.00626681i	$-0.998005\pi$
$541$		−	0.291525i		−	0.0125336i	0.999980	−	0.00626681i	$-0.00199480\pi$
$542$			11.4005i			0.489694i
$543$	−0.961045	−	2.18598i	−0.0412424	−	0.0938096i
$544$	−1.35848			−0.0582445
$545$	18.5540			0.794766
$546$	3.41535	+	7.76853i	0.146164	+	0.332462i
$547$		−	6.75558i		−	0.288848i	−0.989516	−	0.144424i	$-0.953867\pi$
$547$		−	6.75558i		−	0.288848i	0.989516	−	0.144424i	$-0.0461328\pi$
$548$		−	7.65765i		−	0.327118i
$549$	−9.16004	−	8.40411i	−0.390941	−	0.358679i
$550$		0			0
$551$			22.5984i			0.962725i
$552$	11.7552	−	5.16805i	0.500335	−	0.219967i
$553$	9.25086			0.393386
$554$		−	17.0460i		−	0.724214i
$555$	24.6254	−	10.8263i	1.04529	−	0.459551i
$556$		−	7.07813i		−	0.300180i
$557$	−27.5579			−1.16766			−0.583832	−	0.811874i	$-0.698447\pi$
$557$	−27.5579			−1.16766			−0.583832	+	0.811874i	$0.698447\pi$
$558$	−14.4948	+	15.7986i	−0.613614	+	0.668807i
$559$	24.8597			1.05145
$560$	−1.98636			−0.0839389
$561$		0			0
$562$	21.2219			0.895190
$563$	3.70002			0.155937			0.0779686	−	0.996956i	$-0.475157\pi$
$563$	3.70002			0.155937			0.0779686	+	0.996956i	$0.475157\pi$
$564$	−7.11369	+	3.12746i	−0.299540	+	0.131690i
$565$	−8.29006			−0.348766
$566$		−	21.1117i		−	0.887390i
$567$	6.20979	−	0.535510i	0.260787	−	0.0224893i
$568$			8.48528i			0.356034i
$569$	−17.6481			−0.739845			−0.369922	−	0.929063i	$-0.620616\pi$
$569$	−17.6481			−0.739845			−0.369922	+	0.929063i	$0.620616\pi$
$570$	−8.15437	−	18.5478i	−0.341549	−	0.776883i
$571$		−	38.7580i		−	1.62197i	−0.585065	−	0.810986i	$-0.698931\pi$
$571$		−	38.7580i		−	1.62197i	0.585065	−	0.810986i	$-0.301069\pi$
$572$		0			0
$573$	−10.6224	+	4.67001i	−0.443755	+	0.195092i
$574$		−	1.92621i		−	0.0803985i
$575$		−	23.9224i		−	0.997635i
$576$	−2.02814	+	2.21057i	−0.0845060	+	0.0921072i
$577$	−7.89073			−0.328495			−0.164248	−	0.986419i	$-0.552520\pi$
$577$	−7.89073			−0.328495			−0.164248	+	0.986419i	$0.552520\pi$
$578$	−15.1545			−0.630345
$579$	−21.0358	+	9.24815i	−0.874216	+	0.384340i
$580$		−	15.8928i		−	0.659915i
$581$		−	4.24264i		−	0.176014i
$582$	4.95807	+	11.2776i	0.205519	+	0.467471i
$583$		0			0
$584$			7.37761i			0.305288i
$585$	41.1547	−	44.8564i	1.70154	−	1.85459i
$586$	−13.4847			−0.557048
$587$		−	41.9815i		−	1.73276i	−0.499382	−	0.866382i	$-0.666440\pi$
$587$		−	41.9815i		−	1.73276i	0.499382	−	0.866382i	$-0.333560\pi$
$588$	−4.54527	−	10.3386i	−0.187444	−	0.426357i
$589$		−	29.1477i		−	1.20101i
$590$	−6.65846			−0.274125
$591$	0.219060	+	0.498273i	0.00901094	+	0.0204962i
$592$	5.41477			0.222546
$593$	46.0907			1.89272			0.946360	−	0.323114i	$-0.104730\pi$
$593$	46.0907			1.89272			0.946360	+	0.323114i	$0.104730\pi$
$594$		0			0
$595$	2.69844			0.110625
$596$	−13.8207			−0.566119
$597$	6.49283	+	14.7685i	0.265734	+	0.604435i
$598$	−52.4502			−2.14485
$599$			10.6378i			0.434650i	0.976099	+	0.217325i	$0.0697331\pi$
$599$			10.6378i			0.434650i	−0.976099	+	0.217325i	$0.930267\pi$
$600$	2.24931	+	5.11627i	0.0918279	+	0.208871i
$601$		−	3.66673i		−	0.149569i	−0.997200	−	0.0747845i	$-0.976173\pi$
$601$		−	3.66673i		−	0.149569i	0.997200	−	0.0747845i	$-0.0238269\pi$
$602$	2.43351			0.0991825
$603$	−11.2238	+	12.2334i	−0.457069	+	0.498182i
$604$		−	0.270194i		−	0.0109941i
$605$		0			0
$606$	−7.18606	−	16.3453i	−0.291914	−	0.663984i
$607$		−	35.2806i		−	1.43199i	−0.698104	−	0.715997i	$-0.745973\pi$
$607$		−	35.2806i		−	1.43199i	0.698104	−	0.715997i	$-0.254027\pi$
$608$		−	4.07841i		−	0.165401i
$609$	−6.08443	+	2.67496i	−0.246554	+	0.108395i
$610$	−11.8852			−0.481218
$611$	31.7404			1.28408
$612$	2.75520	−	3.00303i	0.111372	−	0.121390i
$613$			34.3580i			1.38771i	0.720117	+	0.693853i	$0.244088\pi$
$613$			34.3580i			1.38771i	−0.720117	+	0.693853i	$0.755912\pi$
$614$			22.7504i			0.918133i
$615$	−12.6492	+	5.56109i	−0.510065	+	0.224245i
$616$		0			0
$617$			23.7843i			0.957519i	0.877946	+	0.478760i	$0.158913\pi$
$617$			23.7843i			0.957519i	−0.877946	+	0.478760i	$0.841087\pi$
$618$	−0.0784772	−	0.178503i	−0.00315682	−	0.00718046i
$619$	35.8306			1.44015			0.720076	−	0.693895i	$-0.244107\pi$
$619$	35.8306			1.44015			0.720076	+	0.693895i	$0.244107\pi$
$620$			20.4987i			0.823249i
$621$	−12.4169	+	36.4673i	−0.498273	+	1.46338i
$622$			31.2401i			1.25262i
$623$	1.24432			0.0498527
$624$	11.2175	−	4.93165i	0.449058	−	0.197424i
$625$	−30.7218			−1.22887
$626$	18.8140			0.751960
$627$		0			0
$628$	6.31872			0.252144
$629$	−7.35588			−0.293298
$630$	4.02862	−	4.39099i	0.160504	−	0.174941i
$631$	−24.8261			−0.988311			−0.494156	−	0.869373i	$-0.664523\pi$
$631$	−24.8261			−0.988311			−0.494156	+	0.869373i	$0.664523\pi$
$632$		−	13.3579i		−	0.531349i
$633$	1.49613	−	0.657759i	0.0594659	−	0.0261436i
$634$			12.9975i			0.516197i
$635$	−15.5055			−0.615318
$636$	−16.1994	+	7.12191i	−0.642349	+	0.282402i
$637$			46.1296i			1.82772i
$638$		0			0
$639$	−18.7573	−	17.2094i	−0.742028	−	0.680793i
$640$			2.86823i			0.113377i
$641$			5.62208i			0.222059i	0.993817	+	0.111029i	$0.0354147\pi$
$641$			5.62208i			0.222059i	−0.993817	+	0.111029i	$0.964585\pi$
$642$	10.7633	+	24.4821i	0.424794	+	0.966233i
$643$	−41.9678			−1.65505			−0.827523	−	0.561431i	$-0.810251\pi$
$643$	−41.9678			−1.65505			−0.827523	+	0.561431i	$0.810251\pi$
$644$	−5.13434			−0.202321
$645$	−7.02570	−	15.9806i	−0.276637	−	0.629235i
$646$			5.54045i			0.217986i
$647$		−	31.0138i		−	1.21928i	−0.792679	−	0.609639i	$-0.791314\pi$
$647$		−	31.0138i		−	1.21928i	0.792679	−	0.609639i	$-0.208686\pi$
$648$	−0.773258	−	8.96672i	−0.0303764	−	0.352246i
$649$		0			0
$650$		−	22.8281i		−	0.895393i
$651$	7.84776	−	3.45019i	0.307578	−	0.135223i
$652$	7.60541			0.297851
$653$		−	41.7547i		−	1.63399i	−0.576645	−	0.816995i	$-0.695638\pi$
$653$		−	41.7547i		−	1.63399i	0.576645	−	0.816995i	$-0.304362\pi$
$654$	−10.2568	+	4.50930i	−0.401073	+	0.176328i
$655$			17.2989i			0.675925i
$656$	−2.78138			−0.108595
$657$	−16.3087	−	14.9629i	−0.636264	−	0.583757i
$658$	3.10706			0.121126
$659$	−38.5660			−1.50232			−0.751159	−	0.660122i	$-0.770505\pi$
$659$	−38.5660			−1.50232			−0.751159	+	0.660122i	$0.770505\pi$
$660$		0			0
$661$	18.7714			0.730123			0.365061	−	0.930983i	$-0.381048\pi$
$661$	18.7714			0.730123			0.365061	+	0.930983i	$0.381048\pi$
$662$	−6.62457			−0.257471
$663$	−15.2388	+	6.69956i	−0.591824	+	0.260190i
$664$	−6.12622			−0.237743
$665$			8.10117i			0.314150i
$666$	−10.9819	+	11.9697i	−0.425542	+	0.463818i
$667$		−	41.0799i		−	1.59062i
$668$	3.31425			0.128232
$669$	−17.6933	−	40.2451i	−0.684064	−	1.55597i
$670$			15.8729i			0.613223i
$671$		0			0
$672$	1.09808	−	0.482758i	0.0423592	−	0.0186228i
$673$			45.1000i			1.73848i	0.494393	+	0.869238i	$0.335390\pi$
$673$			45.1000i			1.73848i	−0.494393	+	0.869238i	$0.664610\pi$
$674$		−	0.387565i		−	0.0149284i
$675$	−15.8718	−	5.40426i	−0.610906	−	0.208010i
$676$	−37.0510			−1.42504
$677$	−44.9158			−1.72625			−0.863127	−	0.504987i	$-0.831497\pi$
$677$	−44.9158			−1.72625			−0.863127	+	0.504987i	$0.831497\pi$
$678$	4.58282	−	2.01479i	0.176002	−	0.0773775i
$679$		−	4.92573i		−	0.189032i
$680$		−	3.89644i		−	0.149422i
$681$	−18.0956	−	41.1601i	−0.693426	−	1.57726i
$682$		0			0
$683$		−	23.9741i		−	0.917342i	−0.888606	−	0.458671i	$-0.848326\pi$
$683$		−	23.9741i		−	0.917342i	0.888606	−	0.458671i	$-0.151674\pi$
$684$	9.01561	+	8.27160i	0.344720	+	0.316272i
$685$	21.9639			0.839197
$686$			9.36338i			0.357496i
$687$	−5.76447	−	13.1118i	−0.219928	−	0.500246i
$688$		−	3.51390i		−	0.133966i
$689$	72.2798			2.75364
$690$	14.8232	+	33.7166i	0.564308	+	1.28357i
$691$	−3.94592			−0.150110			−0.0750550	−	0.997179i	$-0.523913\pi$
$691$	−3.94592			−0.150110			−0.0750550	+	0.997179i	$0.523913\pi$
$692$	11.2267			0.426777
$693$		0			0
$694$	−17.5869			−0.667589
$695$	20.3017			0.770087
$696$	3.86254	+	8.78570i	0.146409	+	0.333021i
$697$	3.77846			0.143119
$698$			0.291450i			0.0110316i
$699$	−18.7222	−	42.5853i	−0.708139	−	1.61073i
$700$		−	2.23464i		−	0.0844615i
$701$	−48.5055			−1.83203			−0.916014	−	0.401146i	$-0.868612\pi$
$701$	−48.5055			−1.83203			−0.916014	+	0.401146i	$0.868612\pi$
$702$	−11.8489	+	34.7991i	−0.447208	+	1.31341i
$703$		−	22.0836i		−	0.832900i
$704$		0			0
$705$	−8.97027	−	20.4037i	−0.337840	−	0.768447i
$706$		−	18.9026i		−	0.711407i
$707$			7.13919i			0.268497i
$708$	3.68086	−	1.61825i	0.138335	−	0.0608176i
$709$	−0.238519			−0.00895777			−0.00447888	−	0.999990i	$-0.501426\pi$
$709$	−0.238519			−0.00895777			−0.00447888	+	0.999990i	$0.501426\pi$
$710$	−24.3377			−0.913379
$711$	29.5286	+	27.0918i	1.10741	+	1.01602i
$712$		−	1.79675i		−	0.0673362i
$713$			52.9852i			1.98431i
$714$	−1.49172	+	0.655819i	−0.0558262	+	0.0245434i
$715$		0			0
$716$		−	12.8632i		−	0.480719i
$717$	−10.4647	−	23.8029i	−0.390811	−	0.888934i
$718$	−22.7186			−0.847851
$719$			0.880489i			0.0328367i	0.999865	+	0.0164183i	$0.00522636\pi$
$719$			0.880489i			0.0328367i	−0.999865	+	0.0164183i	$0.994774\pi$
$720$	−6.34043	−	5.81719i	−0.236294	−	0.216794i
$721$			0.0779653i			0.00290358i
$722$	2.36661			0.0880759
$723$	14.4486	−	6.35218i	0.537349	−	0.236240i
$724$	1.37866			0.0512376
$725$	17.8794			0.664023
$726$		0			0
$727$	37.0384			1.37368			0.686839	−	0.726810i	$-0.258998\pi$
$727$	37.0384			1.37368			0.686839	+	0.726810i	$0.258998\pi$
$728$	−4.89948			−0.181587
$729$	21.3899	+	16.4765i	0.792217	+	0.610239i
$730$	−21.1607			−0.783192
$731$			4.77358i			0.176557i
$732$	6.57025	−	2.88854i	0.242843	−	0.106764i
$733$		−	28.3043i		−	1.04544i	−0.852503	−	0.522722i	$-0.824917\pi$
$733$		−	28.3043i		−	1.04544i	0.852503	−	0.522722i	$-0.175083\pi$
$734$	25.7202			0.949350
$735$	29.6535	−	13.0369i	1.09379	−	0.480872i
$736$			7.41381i			0.273277i
$737$		0			0
$738$	5.64104	−	6.14844i	0.207650	−	0.226327i
$739$		−	21.0634i		−	0.774829i	−0.921906	−	0.387415i	$-0.873368\pi$
$739$		−	21.0634i		−	0.774829i	0.921906	−	0.387415i	$-0.126632\pi$
$740$			15.5308i			0.570924i
$741$	−20.1133	−	45.7494i	−0.738879	−	1.68065i
$742$	7.07545			0.259748
$743$	25.9704			0.952763			0.476381	−	0.879239i	$-0.341948\pi$
$743$	25.9704			0.952763			0.476381	+	0.879239i	$0.341948\pi$
$744$	−4.98194	−	11.3319i	−0.182647	−	0.415447i
$745$		−	39.6410i		−	1.45233i
$746$		−	15.4647i		−	0.566201i
$747$	12.4249	−	13.5425i	0.454602	−	0.495492i
$748$		0			0
$749$		−	10.6931i		−	0.390718i
$750$	8.06445	−	3.54545i	0.294472	−	0.129462i
$751$	20.8196			0.759717			0.379858	−	0.925045i	$-0.375973\pi$
$751$	20.8196			0.759717			0.379858	+	0.925045i	$0.375973\pi$
$752$		−	4.48648i		−	0.163605i
$753$	−28.2555	+	12.4222i	−1.02969	+	0.452692i
$754$		−	39.2007i		−	1.42761i
$755$	0.774980			0.0282044
$756$	−1.15989	+	3.40648i	−0.0421847	+	0.123892i
$757$	−6.52788			−0.237260			−0.118630	−	0.992939i	$-0.537850\pi$
$757$	−6.52788			−0.237260			−0.118630	+	0.992939i	$0.537850\pi$
$758$	−17.3617			−0.630606
$759$		0			0
$760$	11.6978			0.424324
$761$	−18.3169			−0.663985			−0.331993	−	0.943282i	$-0.607721\pi$
$761$	−18.3169			−0.663985			−0.331993	+	0.943282i	$0.607721\pi$
$762$	8.57158	−	3.76841i	0.310516	−	0.136515i
$763$	4.47989			0.162183
$764$		−	6.69934i		−	0.242374i
$765$	8.61337	+	7.90255i	0.311417	+	0.285717i
$766$			13.4690i			0.486656i
$767$	−16.4235			−0.593019
$768$	−0.697085	−	1.58558i	−0.0251539	−	0.0572148i
$769$		−	25.7532i		−	0.928683i	−0.885656	−	0.464341i	$-0.846291\pi$
$769$		−	25.7532i		−	0.928683i	0.885656	−	0.464341i	$-0.153709\pi$
$770$		0			0
$771$	32.8304	−	14.4335i	1.18236	−	0.519811i
$772$		−	13.2669i		−	0.477486i
$773$		−	26.8939i		−	0.967307i	−0.875260	−	0.483654i	$-0.839309\pi$
$773$		−	26.8939i		−	0.967307i	0.875260	−	0.483654i	$-0.160691\pi$
$774$	7.76774	+	7.12671i	0.279206	+	0.256164i
$775$	−23.0610			−0.828374
$776$	−7.11258			−0.255327
$777$	5.94583	−	2.61402i	0.213306	−	0.0937776i
$778$		−	12.8348i		−	0.460152i
$779$			11.3436i			0.406426i
$780$	14.1451	+	32.1743i	0.506476	+	1.15202i
$781$		0			0
$782$		−	10.0715i		−	0.360157i
$783$	−27.2552	−	9.28025i	−0.974023	−	0.331649i
$784$	6.52039			0.232871
$785$			18.1235i			0.646857i
$786$	−4.20427	−	9.56300i	−0.149961	−	0.341101i
$787$			22.6418i			0.807094i	0.914959	+	0.403547i	$0.132223\pi$
$787$			22.6418i			0.807094i	−0.914959	+	0.403547i	$0.867777\pi$
$788$	−0.314252			−0.0111948
$789$	−13.5265	−	30.7672i	−0.481556	−	1.09534i
$790$	38.3135			1.36313
$791$	−2.00165			−0.0711704
$792$		0			0
$793$	−29.3156			−1.04103
$794$	13.4148			0.476072
$795$	−20.4273	−	46.4637i	−0.724481	−	1.64790i
$796$	−9.31425			−0.330135
$797$			25.2386i			0.893999i	0.894534	+	0.446999i	$0.147507\pi$
$797$			25.2386i			0.893999i	−0.894534	+	0.446999i	$0.852493\pi$
$798$	−1.96888	−	4.47840i	−0.0696977	−	0.158534i
$799$			6.09481i			0.215619i
$800$	−3.22674			−0.114083
$801$	3.97186	+	3.64408i	0.140339	+	0.128757i
$802$		−	20.3361i		−	0.718091i
$803$		0			0
$804$	−3.85769	−	8.77467i	−0.136050	−	0.309459i
$805$		−	14.7265i		−	0.519040i
$806$			50.5614i			1.78095i
$807$	−11.1363	+	4.89595i	−0.392015	+	0.172346i
$808$	10.3087			0.362660
$809$	29.5257			1.03807			0.519034	−	0.854754i	$-0.326292\pi$
$809$	29.5257			1.03807			0.519034	+	0.854754i	$0.326292\pi$
$810$	25.7186	−	2.21788i	0.903660	−	0.0779284i
$811$			16.7554i			0.588362i	0.955750	+	0.294181i	$0.0950468\pi$
$811$			16.7554i			0.588362i	−0.955750	+	0.294181i	$0.904953\pi$
$812$		−	3.83735i		−	0.134665i
$813$	18.0765	−	7.94713i	0.633969	−	0.278718i
$814$		0			0
$815$			21.8141i			0.764113i
$816$	0.946979	+	2.15399i	0.0331509	+	0.0754047i
$817$	−14.3311			−0.501383
$818$			24.3271i			0.850576i
$819$	9.93685	−	10.8307i	0.347222	−	0.378454i
$820$		−	7.97763i		−	0.278591i
$821$	−49.1558			−1.71555			−0.857774	−	0.514027i	$-0.828153\pi$
$821$	−49.1558			−1.71555			−0.857774	+	0.514027i	$0.828153\pi$
$822$	−12.1418	+	5.33803i	−0.423495	+	0.186185i
$823$	−41.4743			−1.44570			−0.722852	−	0.691003i	$-0.757169\pi$
$823$	−41.4743			−1.44570			−0.722852	+	0.691003i	$0.757169\pi$
$824$	0.112579			0.00392188
$825$		0			0
$826$	−1.60770			−0.0559389
$827$	24.1327			0.839176			0.419588	−	0.907715i	$-0.362175\pi$
$827$	24.1327			0.839176			0.419588	+	0.907715i	$0.362175\pi$
$828$	−16.3888	−	15.0363i	−0.569549	−	0.522547i
$829$	−22.0169			−0.764680			−0.382340	−	0.924022i	$-0.624882\pi$
$829$	−22.0169			−0.764680			−0.382340	+	0.924022i	$0.624882\pi$
$830$		−	17.5714i		−	0.609913i
$831$	−27.0278	+	11.8825i	−0.937583	+	0.412199i
$832$			7.07467i			0.245270i
$833$	−8.85785			−0.306906
$834$	−11.2230	+	4.93406i	−0.388619	+	0.170852i
$835$			9.50604i			0.328970i
$836$		0			0
$837$	35.1540	+	11.9697i	1.21510	+	0.413735i
$838$		−	36.1710i		−	1.24951i
$839$			21.6672i			0.748035i	0.927422	+	0.374018i	$0.122020\pi$
$839$			21.6672i			0.748035i	−0.927422	+	0.374018i	$0.877980\pi$
$840$	1.38466	+	3.14953i	0.0477753	+	0.108669i
$841$	1.70262			0.0587111
$842$	−29.2490			−1.00799
$843$	−14.7934	−	33.6490i	−0.509513	−	1.15893i
$844$			0.943585i			0.0324795i
$845$		−	106.271i		−	3.65582i
$846$	9.91769	+	9.09923i	0.340977	+	0.312838i
$847$		0			0
$848$		−	10.2167i		−	0.350843i
$849$	−33.4743	+	14.7166i	−1.14883	+	0.505073i
$850$	4.38348			0.150352
$851$			40.1441i			1.37612i
$852$	13.4541	−	5.91496i	0.460930	−	0.202643i
$853$			17.7700i			0.608434i	0.952603	+	0.304217i	$0.0983948\pi$
$853$			17.7700i			0.608434i	−0.952603	+	0.304217i	$0.901605\pi$
$854$	−2.86970			−0.0981991
$855$	−23.7248	+	25.8588i	−0.811373	+	0.884354i
$856$	−15.4405			−0.527745
$857$	−36.0329			−1.23086			−0.615431	−	0.788191i	$-0.711018\pi$
$857$	−36.0329			−1.23086			−0.615431	+	0.788191i	$0.711018\pi$
$858$		0			0
$859$	−37.2491			−1.27092			−0.635462	−	0.772132i	$-0.719190\pi$
$859$	−37.2491			−1.27092			−0.635462	+	0.772132i	$0.719190\pi$
$860$	10.0787			0.343680
$861$	−3.05417	+	1.34273i	−0.104086	+	0.0457602i
$862$	24.2837			0.827105
$863$		−	24.6107i		−	0.837758i	−0.908042	−	0.418879i	$-0.862423\pi$
$863$		−	24.6107i		−	0.837758i	0.908042	−	0.418879i	$-0.137577\pi$
$864$	4.91883	+	1.67483i	0.167342	+	0.0569790i
$865$			32.2009i			1.09486i
$866$	0.546515			0.0185713
$867$	10.5640	+	24.0287i	0.358772	+	0.816059i
$868$			4.94945i			0.167995i
$869$		0			0
$870$	−25.1994	+	11.0787i	−0.854340	+	0.375602i
$871$			39.1515i			1.32660i
$872$		−	6.46880i		−	0.219061i
$873$	14.4253	−	15.7229i	0.488224	−	0.532138i
$874$	30.2365			1.02277
$875$	−3.52232			−0.119076
$876$	11.6978	−	5.14282i	0.395232	−	0.173760i
$877$			54.1443i			1.82832i	0.405351	+	0.914161i	$0.367149\pi$
$877$			54.1443i			1.82832i	−0.405351	+	0.914161i	$0.632851\pi$
$878$		−	23.6963i		−	0.799710i
$879$	9.39999	+	21.3811i	0.317054	+	0.721167i
$880$		0			0
$881$			41.9541i			1.41347i	0.707478	+	0.706735i	$0.249833\pi$
$881$			41.9541i			1.41347i	−0.707478	+	0.706735i	$0.750167\pi$
$882$	−13.2243	+	14.4138i	−0.445285	+	0.485338i
$883$	0.273470			0.00920299			0.00460150	−	0.999989i	$-0.498535\pi$
$883$	0.273470			0.00920299			0.00460150	+	0.999989i	$0.498535\pi$
$884$		−	9.61083i		−	0.323247i
$885$	4.64152	+	10.5575i	0.156023	+	0.354888i
$886$			10.9852i			0.369056i
$887$	3.11676			0.104651			0.0523253	−	0.998630i	$-0.483337\pi$
$887$	3.11676			0.104651			0.0523253	+	0.998630i	$0.483337\pi$
$888$	−3.77456	−	8.58557i	−0.126666	−	0.288113i
$889$	−3.74383			−0.125564
$890$	5.15350			0.172746
$891$		0			0
$892$	25.3819			0.849849
$893$	−18.2977			−0.612309
$894$	9.63422	+	21.9139i	0.322216	+	0.732910i
$895$	36.8945			1.23325
$896$			0.692538i			0.0231361i
$897$	36.5623	+	83.1642i	1.22078	+	2.77677i
$898$			8.49609i			0.283518i
$899$	−39.6005			−1.32075
$900$	6.54430	−	7.13295i	0.218143	−	0.237765i
$901$			13.8792i			0.462384i
$902$		0			0
$903$	−1.69636	−	3.85853i	−0.0564515	−	0.128404i
$904$			2.89031i			0.0961301i
$905$			3.95432i			0.131446i
$906$	−0.428415	+	0.188348i	−0.0142332	+	0.00625746i
$907$	47.4171			1.57446			0.787229	−	0.616661i	$-0.211515\pi$
$907$	47.4171			1.57446			0.787229	+	0.616661i	$0.211515\pi$
$908$	25.9590			0.861480
$909$	−20.9076	+	22.7882i	−0.693461	+	0.755837i
$910$		−	14.0528i		−	0.465847i
$911$			52.4704i			1.73842i	0.494442	+	0.869211i	$0.335373\pi$
$911$			52.4704i			1.73842i	−0.494442	+	0.869211i	$0.664627\pi$
$912$	−6.46665	+	2.84300i	−0.214132	+	0.0941410i
$913$		0			0
$914$			22.1681i			0.733254i
$915$	8.28500	+	18.8450i	0.273894	+	0.622996i
$916$	8.26939			0.273228
$917$			4.17685i			0.137932i
$918$	−6.68216	−	2.27524i	−0.220544	−	0.0750940i
$919$		−	38.4251i		−	1.26753i	−0.773527	−	0.633764i	$-0.781509\pi$
$919$		−	38.4251i		−	1.26753i	0.773527	−	0.633764i	$-0.218491\pi$
$920$	−21.2645			−0.701070
$921$	36.0727	−	15.8590i	1.18864	−	0.522571i
$922$	−29.1890			−0.961290
$923$	−60.0306			−1.97593
$924$		0			0
$925$	−17.4721			−0.574478
$926$	−13.8641			−0.455602
$927$	−0.228327	+	0.248864i	−0.00749923	+	0.00817377i
$928$	−5.54099			−0.181892
$929$		−	15.6785i		−	0.514396i	−0.966359	−	0.257198i	$-0.917201\pi$
$929$		−	15.6785i		−	0.514396i	0.966359	−	0.257198i	$-0.0827993\pi$
$930$	32.5024	−	14.2894i	1.06580	−	0.468567i
$931$		−	26.5928i		−	0.871544i
$932$	26.8578			0.879758
$933$	49.5338	−	21.7770i	1.62166	−	0.712948i
$934$			2.67846i			0.0876419i
$935$		0			0
$936$	−15.6391	−	14.3485i	−0.511179	−	0.468994i
$937$		−	21.0384i		−	0.687296i	−0.939099	−	0.343648i	$-0.888337\pi$
$937$		−	21.0384i		−	0.687296i	0.939099	−	0.343648i	$-0.111663\pi$
$938$			3.83253i			0.125136i
$939$	−13.1150	−	29.8312i	−0.427991	−	0.973505i
$940$	12.8683			0.419716
$941$	−14.3191			−0.466791			−0.233395	−	0.972382i	$-0.574984\pi$
$941$	−14.3191			−0.466791			−0.233395	+	0.972382i	$0.574984\pi$
$942$	−4.40468	−	10.0188i	−0.143512	−	0.326432i
$943$		−	20.6206i		−	0.671499i
$944$			2.32145i			0.0755569i
$945$	−9.77057	−	3.32682i	−0.317837	−	0.108221i
$946$		0			0
$947$		−	0.365709i		−	0.0118839i	−0.999982	−	0.00594197i	$-0.998109\pi$
$947$		−	0.365709i		−	0.0118839i	0.999982	−	0.00594197i	$-0.00189140\pi$
$948$	−21.1801	+	9.31160i	−0.687897	+	0.302427i
$949$	−52.1941			−1.69429
$950$			13.1600i			0.426966i
$951$	20.6086	−	9.06037i	0.668281	−	0.293803i
$952$		−	0.940802i		−	0.0304916i
$953$	15.0810			0.488521			0.244260	−	0.969710i	$-0.421455\pi$
$953$	15.0810			0.488521			0.244260	+	0.969710i	$0.421455\pi$
$954$	22.5847	+	20.7209i	0.731208	+	0.670865i
$955$	19.2152			0.621791
$956$	15.0121			0.485525
$957$		0			0
$958$	14.4574			0.467098
$959$	5.30321			0.171250
$960$	4.54782	−	1.99940i	0.146780	−	0.0645304i
$961$	20.0771			0.647648
$962$			38.3077i			1.23509i
$963$	31.3155	−	34.1323i	1.00913	−	1.09990i
$964$			9.11248i			0.293493i
$965$	38.0525			1.22495
$966$	3.57907	+	8.14092i	0.115155	+	0.261930i
$967$		−	4.11107i		−	0.132203i	−0.997813	−	0.0661016i	$-0.978944\pi$
$967$		−	4.11107i		−	0.132203i	0.997813	−	0.0661016i	$-0.0210561\pi$
$968$		0			0
$969$	8.78484	−	3.86216i	0.282210	−	0.124071i
$970$		−	20.4005i		−	0.655021i
$971$		−	26.5282i		−	0.851331i	−0.904881	−	0.425665i	$-0.860040\pi$
$971$		−	26.5282i		−	0.851331i	0.904881	−	0.425665i	$-0.139960\pi$
$972$	−13.6784	+	7.47663i	−0.438736	+	0.239813i
$973$	4.90187			0.157147
$974$	2.05773			0.0659339
$975$	−36.1959	+	15.9132i	−1.15920	+	0.509629i
$976$			4.14374i			0.132638i
$977$			7.98679i			0.255520i	0.991805	+	0.127760i	$0.0407787\pi$
$977$			7.98679i			0.255520i	−0.991805	+	0.127760i	$0.959221\pi$
$978$	−5.30161	−	12.0590i	−0.169527	−	0.385604i
$979$		0			0
$980$			18.7020i			0.597413i
$981$	14.2997	+	13.1197i	0.456556	+	0.418879i
$982$	−12.7847			−0.407976
$983$			18.1119i			0.577681i	0.957377	+	0.288841i	$0.0932698\pi$
$983$			18.1119i			0.577681i	−0.957377	+	0.288841i	$0.906730\pi$
$984$	1.93886	+	4.41011i	0.0618085	+	0.140589i
$985$		−	0.901347i		−	0.0287193i
$986$	7.52735			0.239720
$987$	−2.16588	−	4.92650i	−0.0689408	−	0.156812i
$988$	28.8534			0.917948
$989$	26.0514			0.828386
$990$		0			0
$991$	−29.0245			−0.921995			−0.460997	−	0.887401i	$-0.652508\pi$
$991$	−29.0245			−0.921995			−0.460997	+	0.887401i	$0.652508\pi$
$992$	7.14682			0.226912
$993$	4.61789	+	10.5038i	0.146544	+	0.333328i
$994$	−5.87638			−0.186387
$995$		−	26.7154i		−	0.846936i
$996$	4.27050	+	9.71363i	0.135316	+	0.307788i
$997$			57.2767i			1.81397i	0.421161	+	0.906986i	$0.361623\pi$
$997$			57.2767i			1.81397i	−0.421161	+	0.906986i	$0.638377\pi$
$998$	−5.57668			−0.176527
$999$	26.6344	+	9.06885i	0.842674	+	0.286926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.b.f.725.1	yes	8
3.2	odd	2		726.2.b.d.725.2	yes	8
11.2	odd	10		726.2.h.l.161.1		32
11.3	even	5		726.2.h.k.233.8		32
11.4	even	5		726.2.h.k.215.5		32
11.5	even	5		726.2.h.k.239.6		32
11.6	odd	10		726.2.h.l.239.6		32
11.7	odd	10		726.2.h.l.215.5		32
11.8	odd	10		726.2.h.l.233.8		32
11.9	even	5		726.2.h.k.161.1		32
11.10	odd	2		726.2.b.d.725.1	✓	8
33.2	even	10		726.2.h.k.161.6		32
33.5	odd	10		726.2.h.l.239.1		32
33.8	even	10		726.2.h.k.233.5		32
33.14	odd	10		726.2.h.l.233.5		32
33.17	even	10		726.2.h.k.239.1		32
33.20	odd	10		726.2.h.l.161.6		32
33.26	odd	10		726.2.h.l.215.8		32
33.29	even	10		726.2.h.k.215.8		32
33.32	even	2	inner	726.2.b.f.725.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.b.d.725.1	✓	8	11.10	odd	2
726.2.b.d.725.2	yes	8	3.2	odd	2
726.2.b.f.725.1	yes	8	1.1	even	1	trivial
726.2.b.f.725.2	yes	8	33.32	even	2	inner
726.2.h.k.161.1		32	11.9	even	5
726.2.h.k.161.6		32	33.2	even	10
726.2.h.k.215.5		32	11.4	even	5
726.2.h.k.215.8		32	33.29	even	10
726.2.h.k.233.5		32	33.8	even	10
726.2.h.k.233.8		32	11.3	even	5
726.2.h.k.239.1		32	33.17	even	10
726.2.h.k.239.6		32	11.5	even	5
726.2.h.l.161.1		32	11.2	odd	10
726.2.h.l.161.6		32	33.20	odd	10
726.2.h.l.215.5		32	11.7	odd	10
726.2.h.l.215.8		32	33.26	odd	10
726.2.h.l.233.5		32	33.14	odd	10
726.2.h.l.233.8		32	11.8	odd	10
726.2.h.l.239.1		32	33.5	odd	10
726.2.h.l.239.6		32	11.6	odd	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.697085 - 1.58558i) q^{3} +1.00000 q^{4} +2.86823i q^{5} +(-0.697085 - 1.58558i) q^{6} +0.692538i q^{7} +1.00000 q^{8} +(-2.02814 + 2.21057i) q^{9} +2.86823i q^{10} +(-0.697085 - 1.58558i) q^{12} +7.07467i q^{13} +0.692538i q^{14} +(4.54782 - 1.99940i) q^{15} +1.00000 q^{16} -1.35848 q^{17} +(-2.02814 + 2.21057i) q^{18} -4.07841i q^{19} +2.86823i q^{20} +(1.09808 - 0.482758i) q^{21} +7.41381i q^{23} +(-0.697085 - 1.58558i) q^{24} -3.22674 q^{25} +7.07467i q^{26} +(4.91883 + 1.67483i) q^{27} +0.692538i q^{28} -5.54099 q^{29} +(4.54782 - 1.99940i) q^{30} +7.14682 q^{31} +1.00000 q^{32} -1.35848 q^{34} -1.98636 q^{35} +(-2.02814 + 2.21057i) q^{36} +5.41477 q^{37} -4.07841i q^{38} +(11.2175 - 4.93165i) q^{39} +2.86823i q^{40} -2.78138 q^{41} +(1.09808 - 0.482758i) q^{42} -3.51390i q^{43} +(-6.34043 - 5.81719i) q^{45} +7.41381i q^{46} -4.48648i q^{47} +(-0.697085 - 1.58558i) q^{48} +6.52039 q^{49} -3.22674 q^{50} +(0.946979 + 2.15399i) q^{51} +7.07467i q^{52} -10.2167i q^{53} +(4.91883 + 1.67483i) q^{54} +0.692538i q^{56} +(-6.46665 + 2.84300i) q^{57} -5.54099 q^{58} +2.32145i q^{59} +(4.54782 - 1.99940i) q^{60} +4.14374i q^{61} +7.14682 q^{62} +(-1.53091 - 1.40457i) q^{63} +1.00000 q^{64} -20.2918 q^{65} +5.53403 q^{67} -1.35848 q^{68} +(11.7552 - 5.16805i) q^{69} -1.98636 q^{70} +8.48528i q^{71} +(-2.02814 + 2.21057i) q^{72} +7.37761i q^{73} +5.41477 q^{74} +(2.24931 + 5.11627i) q^{75} -4.07841i q^{76} +(11.2175 - 4.93165i) q^{78} -13.3579i q^{79} +2.86823i q^{80} +(-0.773258 - 8.96672i) q^{81} -2.78138 q^{82} -6.12622 q^{83} +(1.09808 - 0.482758i) q^{84} -3.89644i q^{85} -3.51390i q^{86} +(3.86254 + 8.78570i) q^{87} -1.79675i q^{89} +(-6.34043 - 5.81719i) q^{90} -4.89948 q^{91} +7.41381i q^{92} +(-4.98194 - 11.3319i) q^{93} -4.48648i q^{94} +11.6978 q^{95} +(-0.697085 - 1.58558i) q^{96} -7.11258 q^{97} +6.52039 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{12} - 8 q^{15} + 8 q^{16} - 16 q^{17} - 4 q^{18} - 12 q^{21} + 4 q^{24} - 40 q^{25} + 16 q^{27} + 8 q^{29} - 8 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 8 q^{97}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^12 - 8 * q^15 + 8 * q^16 - 16 * q^17 - 4 * q^18 - 12 * q^21 + 4 * q^24 - 40 * q^25 + 16 * q^27 + 8 * q^29 - 8 * q^30 + 24 * q^31 + 8 * q^32 - 16 * q^34 - 4 * q^36 + 24 * q^37 + 28 * q^39 - 12 * q^42 - 16 * q^45 + 4 * q^48 - 40 * q^50 - 28 * q^51 + 16 * q^54 + 16 * q^57 + 8 * q^58 - 8 * q^60 + 24 * q^62 - 12 * q^63 + 8 * q^64 - 32 * q^65 + 8 * q^67 - 16 * q^68 + 40 * q^69 - 4 * q^72 + 24 * q^74 - 12 * q^75 + 28 * q^78 + 8 * q^81 - 16 * q^83 - 12 * q^84 + 32 * q^87 - 16 * q^90 + 8 * q^91 + 64 * q^95 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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