LMFDB - Embedded newform 276.2.i.b.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Root			$-0.634872 - 0.408008i$ of defining polynomial
Character	$\chi$	$=$	276.169
Dual form			276.2.i.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(0.0154463 + 0.0178260i) q^{5} +(-3.20986 - 2.06285i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(0.0154463 + 0.0178260i) q^{5} +(-3.20986 - 2.06285i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.735908 - 5.11836i) q^{11} +(4.01404 - 2.57966i) q^{13} +(0.00979847 - 0.0214557i) q^{15} +(-5.10535 + 1.49907i) q^{17} +(-1.10548 - 0.324598i) q^{19} +(-0.543011 + 3.77673i) q^{21} +(0.352170 + 4.78288i) q^{23} +(0.711495 - 4.94856i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-2.41867 + 0.710187i) q^{29} +(4.27711 - 9.36557i) q^{31} +(-4.35011 + 2.79565i) q^{33} +(-0.0128081 - 0.0890824i) q^{35} +(2.16480 - 2.49832i) q^{37} +(-4.01404 - 2.57966i) q^{39} +(7.93135 + 9.15326i) q^{41} +(3.06665 + 6.71503i) q^{43} -0.0235872 q^{45} -3.51134 q^{47} +(3.13992 + 6.87547i) q^{49} +(3.48444 + 4.02126i) q^{51} +(3.14432 + 2.02073i) q^{53} +(0.0798728 - 0.0921781i) q^{55} +(0.163968 + 1.14042i) q^{57} +(2.54134 - 1.63322i) q^{59} +(-1.71848 + 3.76295i) q^{61} +(3.66101 - 1.07497i) q^{63} +(0.107987 + 0.0317079i) q^{65} +(-1.08306 + 7.53282i) q^{67} +(4.20437 - 2.30723i) q^{69} +(1.84801 - 12.8532i) q^{71} +(6.29319 + 1.84785i) q^{73} +(-4.79693 + 1.40851i) q^{75} +(-8.19623 + 17.9472i) q^{77} +(8.76642 - 5.63383i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-5.04709 + 5.82465i) q^{83} +(-0.105581 - 0.0678530i) q^{85} +(1.65076 + 1.90508i) q^{87} +(-3.37306 - 7.38598i) q^{89} -18.2059 q^{91} -10.2960 q^{93} +(-0.0112893 - 0.0247202i) q^{95} +(-4.51475 - 5.21030i) q^{97} +(4.35011 + 2.79565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	0.0154463	+	0.0178260i	0.00690781	+	0.00797203i	0.759193	−	0.650866i	$-0.225594\pi$
$5$	0.0154463	+	0.0178260i	0.00690781	+	0.00797203i	−0.752285	+	0.658838i	$0.771048\pi$
$6$		0			0
$7$	−3.20986	−	2.06285i	−1.21321	−	0.779684i	−0.232018	−	0.972711i	$-0.574533\pi$
$7$	−3.20986	−	2.06285i	−1.21321	−	0.779684i	−0.981193	+	0.193028i	$0.938169\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.735908	−	5.11836i	−0.221885	−	1.54324i	−0.730900	−	0.682485i	$-0.760899\pi$
$11$	−0.735908	−	5.11836i	−0.221885	−	1.54324i	0.509015	−	0.860758i	$-0.330010\pi$
$12$		0			0
$13$	4.01404	−	2.57966i	1.11329	−	0.715470i	0.151285	−	0.988490i	$-0.451659\pi$
$13$	4.01404	−	2.57966i	1.11329	−	0.715470i	0.962008	+	0.273020i	$0.0880225\pi$
$14$		0			0
$15$	0.00979847	−	0.0214557i	0.00252996	−	0.00553983i
$16$		0			0
$17$	−5.10535	+	1.49907i	−1.23823	+	0.363577i	−0.834350	−	0.551235i	$-0.814157\pi$
$17$	−5.10535	+	1.49907i	−1.23823	+	0.363577i	−0.403880	+	0.914812i	$0.632339\pi$
$18$		0			0
$19$	−1.10548	−	0.324598i	−0.253615	−	0.0744680i	0.152454	−	0.988311i	$-0.451282\pi$
$19$	−1.10548	−	0.324598i	−0.253615	−	0.0744680i	−0.406069	+	0.913843i	$0.633101\pi$
$20$		0			0
$21$	−0.543011	+	3.77673i	−0.118495	+	0.824149i
$22$		0			0
$23$	0.352170	+	4.78288i	0.0734325	+	0.997300i
$23$	0.352170	+	4.78288i	0.0734325	+	0.997300i
$24$		0			0
$25$	0.711495	−	4.94856i	0.142299	−	0.989711i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−2.41867	+	0.710187i	−0.449137	+	0.131878i	−0.498476	−	0.866904i	$-0.666107\pi$
$29$	−2.41867	+	0.710187i	−0.449137	+	0.131878i	0.0493391	+	0.998782i	$0.484288\pi$
$30$		0			0
$31$	4.27711	−	9.36557i	0.768192	−	1.68211i	0.0375983	−	0.999293i	$-0.488029\pi$
$31$	4.27711	−	9.36557i	0.768192	−	1.68211i	0.730594	−	0.682813i	$-0.239243\pi$
$32$		0			0
$33$	−4.35011	+	2.79565i	−0.757257	+	0.486660i
$34$		0			0
$35$	−0.0128081	−	0.0890824i	−0.00216497	−	0.0150577i
$36$		0			0
$37$	2.16480	−	2.49832i	0.355892	−	0.410721i	−0.549367	−	0.835581i	$-0.685131\pi$
$37$	2.16480	−	2.49832i	0.355892	−	0.410721i	0.905259	+	0.424860i	$0.139677\pi$
$38$		0			0
$39$	−4.01404	−	2.57966i	−0.642760	−	0.413077i
$40$		0			0
$41$	7.93135	+	9.15326i	1.23867	+	1.42950i	0.864875	+	0.501987i	$0.167397\pi$
$41$	7.93135	+	9.15326i	1.23867	+	1.42950i	0.373793	+	0.927512i	$0.378057\pi$
$42$		0			0
$43$	3.06665	+	6.71503i	0.467660	+	1.02403i	0.985674	+	0.168660i	$0.0539440\pi$
$43$	3.06665	+	6.71503i	0.467660	+	1.02403i	−0.518015	+	0.855372i	$0.673329\pi$
$44$		0			0
$45$	−0.0235872			−0.00351617
$46$		0			0
$47$	−3.51134			−0.512181			−0.256091	−	0.966653i	$-0.582435\pi$
$47$	−3.51134			−0.512181			−0.256091	+	0.966653i	$0.582435\pi$
$48$		0			0
$49$	3.13992	+	6.87547i	0.448560	+	0.982210i
$50$		0			0
$51$	3.48444	+	4.02126i	0.487919	+	0.563089i
$52$		0			0
$53$	3.14432	+	2.02073i	0.431905	+	0.277568i	0.738477	−	0.674279i	$-0.235546\pi$
$53$	3.14432	+	2.02073i	0.431905	+	0.277568i	−0.306572	+	0.951848i	$0.599182\pi$
$54$		0			0
$55$	0.0798728	−	0.0921781i	0.0107700	−	0.0124293i
$56$		0			0
$57$	0.163968	+	1.14042i	0.0217181	+	0.151053i
$58$		0			0
$59$	2.54134	−	1.63322i	0.330854	−	0.212627i	−0.364658	−	0.931142i	$-0.618814\pi$
$59$	2.54134	−	1.63322i	0.330854	−	0.212627i	0.695512	+	0.718515i	$0.255178\pi$
$60$		0			0
$61$	−1.71848	+	3.76295i	−0.220029	+	0.481796i	−0.987168	−	0.159685i	$-0.948952\pi$
$61$	−1.71848	+	3.76295i	−0.220029	+	0.481796i	0.767139	+	0.641481i	$0.221680\pi$
$62$		0			0
$63$	3.66101	−	1.07497i	0.461243	−	0.135433i
$64$		0			0
$65$	0.107987	+	0.0317079i	0.0133942	+	0.00393288i
$66$		0			0
$67$	−1.08306	+	7.53282i	−0.132316	+	0.920280i	0.810208	+	0.586142i	$0.199354\pi$
$67$	−1.08306	+	7.53282i	−0.132316	+	0.920280i	−0.942524	+	0.334138i	$0.891555\pi$
$68$		0			0
$69$	4.20437	−	2.30723i	0.506146	−	0.277757i
$70$		0			0
$71$	1.84801	−	12.8532i	0.219319	−	1.52540i	−0.521244	−	0.853408i	$-0.674532\pi$
$71$	1.84801	−	12.8532i	0.219319	−	1.52540i	0.740563	−	0.671987i	$-0.234559\pi$
$72$		0			0
$73$	6.29319	+	1.84785i	0.736563	+	0.216274i	0.628434	−	0.777863i	$-0.283696\pi$
$73$	6.29319	+	1.84785i	0.736563	+	0.216274i	0.108128	+	0.994137i	$0.465514\pi$
$74$		0			0
$75$	−4.79693	+	1.40851i	−0.553902	+	0.162640i
$76$		0			0
$77$	−8.19623	+	17.9472i	−0.934048	+	2.04528i
$78$		0			0
$79$	8.76642	−	5.63383i	0.986299	−	0.633856i	0.0551435	−	0.998478i	$-0.482438\pi$
$79$	8.76642	−	5.63383i	0.986299	−	0.633856i	0.931155	+	0.364623i	$0.118802\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−5.04709	+	5.82465i	−0.553990	+	0.639339i	−0.961808	−	0.273724i	$-0.911744\pi$
$83$	−5.04709	+	5.82465i	−0.553990	+	0.639339i	0.407818	+	0.913063i	$0.366290\pi$
$84$		0			0
$85$	−0.105581	−	0.0678530i	−0.0114519	−	0.00735969i
$86$		0			0
$87$	1.65076	+	1.90508i	0.176980	+	0.204246i
$88$		0			0
$89$	−3.37306	−	7.38598i	−0.357544	−	0.782913i	−0.999864	−	0.0164760i	$-0.994755\pi$
$89$	−3.37306	−	7.38598i	−0.357544	−	0.782913i	0.642320	−	0.766436i	$-0.277972\pi$
$90$		0			0
$91$	−18.2059			−1.90850
$92$		0			0
$93$	−10.2960			−1.06765
$94$		0			0
$95$	−0.0112893	−	0.0247202i	−0.00115826	−	0.00253624i
$96$		0			0
$97$	−4.51475	−	5.21030i	−0.458403	−	0.529025i	0.478746	−	0.877953i	$-0.341091\pi$
$97$	−4.51475	−	5.21030i	−0.458403	−	0.529025i	−0.937150	+	0.348928i	$0.886546\pi$
$98$		0			0
$99$	4.35011	+	2.79565i	0.437203	+	0.280973i
$100$		0			0
$101$	2.38554	−	2.75306i	0.237370	−	0.273940i	−0.624549	−	0.780986i	$-0.714717\pi$
$101$	2.38554	−	2.75306i	0.237370	−	0.273940i	0.861919	+	0.507046i	$0.169263\pi$
$102$		0			0
$103$	−0.481809	−	3.35105i	−0.0474740	−	0.330189i	−0.999693	−	0.0247732i	$-0.992114\pi$
$103$	−0.481809	−	3.35105i	−0.0474740	−	0.330189i	0.952219	−	0.305416i	$-0.0987954\pi$
$104$		0			0
$105$	−0.0757115	+	0.0486568i	−0.00738868	+	0.00474842i
$106$		0			0
$107$	1.21817	−	2.66741i	0.117765	−	0.257869i	−0.841566	−	0.540155i	$-0.818366\pi$
$107$	1.21817	−	2.66741i	0.117765	−	0.257869i	0.959330	+	0.282286i	$0.0910929\pi$
$108$		0			0
$109$	15.8221	−	4.64578i	1.51548	−	0.444985i	0.584910	−	0.811098i	$-0.301130\pi$
$109$	15.8221	−	4.64578i	1.51548	−	0.444985i	0.930570	+	0.366113i	$0.119312\pi$
$110$		0			0
$111$	−3.17184	−	0.931337i	−0.301058	−	0.0883986i
$112$		0			0
$113$	0.849504	−	5.90843i	0.0799146	−	0.555818i	−0.910050	−	0.414499i	$-0.863957\pi$
$113$	0.849504	−	5.90843i	0.0799146	−	0.555818i	0.989964	−	0.141319i	$-0.0451342\pi$
$114$		0			0
$115$	−0.0798200	+	0.0801558i	−0.00744325	+	0.00747456i
$116$		0			0
$117$	−0.679054	+	4.72293i	−0.0627786	+	0.436635i
$118$		0			0
$119$	19.4798	+	5.71979i	1.78571	+	0.524332i
$120$		0			0
$121$	−15.1016	+	4.43422i	−1.37287	+	0.403111i
$122$		0			0
$123$	5.03130	−	11.0170i	0.453657	−	0.993370i
$124$		0			0
$125$	0.198417	−	0.127515i	0.0177470	−	0.0114053i
$126$		0			0
$127$	−1.57047	−	10.9228i	−0.139356	−	0.969246i	−0.932747	−	0.360532i	$-0.882595\pi$
$127$	−1.57047	−	10.9228i	−0.139356	−	0.969246i	0.793390	−	0.608713i	$-0.208314\pi$
$128$		0			0
$129$	4.83427	−	5.57905i	0.425634	−	0.491208i
$130$		0			0
$131$	14.5504	+	9.35096i	1.27127	+	0.816997i	0.989785	−	0.142568i	$-0.0455358\pi$
$131$	14.5504	+	9.35096i	1.27127	+	0.816997i	0.281488	+	0.959565i	$0.409172\pi$
$132$		0			0
$133$	2.87884	+	3.32235i	0.249627	+	0.288085i
$134$		0			0
$135$	0.00979847	+	0.0214557i	0.000843318	+	0.00184661i
$136$		0			0
$137$	−16.6370			−1.42139			−0.710697	−	0.703498i	$-0.751620\pi$
$137$	−16.6370			−1.42139			−0.710697	+	0.703498i	$0.751620\pi$
$138$		0			0
$139$	−12.0435			−1.02151			−0.510757	−	0.859725i	$-0.670635\pi$
$139$	−12.0435			−1.02151			−0.510757	+	0.859725i	$0.670635\pi$
$140$		0			0
$141$	1.45866	+	3.19403i	0.122842	+	0.268986i
$142$		0			0
$143$	−16.1576	−	18.6469i	−1.35117	−	1.55933i
$144$		0			0
$145$	−0.0500194	−	0.0321455i	−0.00415389	−	0.00266954i
$146$		0			0
$147$	4.94978	−	5.71235i	0.408251	−	0.471146i
$148$		0			0
$149$	−2.98430	−	20.7563i	−0.244484	−	1.70042i	−0.629083	−	0.777338i	$-0.716569\pi$
$149$	−2.98430	−	20.7563i	−0.244484	−	1.70042i	0.384599	−	0.923084i	$-0.374340\pi$
$150$		0			0
$151$	−11.1544	+	7.16852i	−0.907735	+	0.583366i	−0.909075	−	0.416633i	$-0.863210\pi$
$151$	−11.1544	+	7.16852i	−0.907735	+	0.583366i	0.00133975	+	0.999999i	$0.499574\pi$
$152$		0			0
$153$	2.21038	−	4.84005i	0.178698	−	0.391295i
$154$		0			0
$155$	0.233016	−	0.0684198i	0.0187163	−	0.00549561i
$156$		0			0
$157$	−3.30944	−	0.971738i	−0.264122	−	0.0775532i	0.146990	−	0.989138i	$-0.453041\pi$
$157$	−3.30944	−	0.971738i	−0.264122	−	0.0775532i	−0.411112	+	0.911585i	$0.634860\pi$
$158$		0			0
$159$	0.531924	−	3.69961i	0.0421843	−	0.293398i
$160$		0			0
$161$	8.73595	−	16.0788i	0.688489	−	1.26719i
$162$		0			0
$163$	−2.38978	+	16.6213i	−0.187182	+	1.30188i	0.652078	+	0.758152i	$0.273897\pi$
$163$	−2.38978	+	16.6213i	−0.187182	+	1.30188i	−0.839260	+	0.543730i	$0.817012\pi$
$164$		0			0
$165$	−0.117029	−	0.0343627i	−0.00911066	−	0.00267513i
$166$		0			0
$167$	−7.69223	+	2.25864i	−0.595242	+	0.174779i	−0.565458	−	0.824777i	$-0.691300\pi$
$167$	−7.69223	+	2.25864i	−0.595242	+	0.174779i	−0.0297848	+	0.999556i	$0.509482\pi$
$168$		0			0
$169$	4.05742	−	8.88452i	0.312109	−	0.683424i
$170$		0			0
$171$	0.969251	−	0.622900i	0.0741205	−	0.0476343i
$172$		0			0
$173$	0.341561	+	2.37561i	0.0259684	+	0.180614i	0.998677	−	0.0514142i	$-0.0163729\pi$
$173$	0.341561	+	2.37561i	0.0259684	+	0.180614i	−0.972709	+	0.232028i	$0.925464\pi$
$174$		0			0
$175$	−12.4919	+	14.4164i	−0.944300	+	1.08978i
$176$		0			0
$177$	−2.54134	−	1.63322i	−0.191019	−	0.122760i
$178$		0			0
$179$	−5.84825	−	6.74924i	−0.437119	−	0.504462i	0.493857	−	0.869543i	$-0.335587\pi$
$179$	−5.84825	−	6.74924i	−0.437119	−	0.504462i	−0.930976	+	0.365081i	$0.881041\pi$
$180$		0			0
$181$	0.849136	+	1.85935i	0.0631158	+	0.138204i	0.938561	−	0.345112i	$-0.112159\pi$
$181$	0.849136	+	1.85935i	0.0631158	+	0.138204i	−0.875446	+	0.483317i	$0.839432\pi$
$182$		0			0
$183$	4.13678			0.305800
$184$		0			0
$185$	0.0779733			0.00573271
$186$		0			0
$187$	11.4298	+	25.0278i	0.835832	+	1.83022i
$188$		0			0
$189$	−2.49866	−	2.88361i	−0.181751	−	0.209752i
$190$		0			0
$191$	5.35844	+	3.44366i	0.387723	+	0.249174i	0.719951	−	0.694025i	$-0.244164\pi$
$191$	5.35844	+	3.44366i	0.387723	+	0.249174i	−0.332228	+	0.943199i	$0.607800\pi$
$192$		0			0
$193$	10.3646	−	11.9614i	0.746061	−	0.861000i	−0.248119	−	0.968730i	$-0.579812\pi$
$193$	10.3646	−	11.9614i	0.746061	−	0.861000i	0.994180	+	0.107729i	$0.0343579\pi$
$194$		0			0
$195$	−0.0160170	−	0.111401i	−0.00114700	−	0.00797756i
$196$		0			0
$197$	18.4457	−	11.8544i	1.31420	−	0.844588i	0.319522	−	0.947579i	$-0.396478\pi$
$197$	18.4457	−	11.8544i	1.31420	−	0.844588i	0.994682	+	0.102991i	$0.0328412\pi$
$198$		0			0
$199$	−0.764069	+	1.67308i	−0.0541634	+	0.118601i	−0.934779	−	0.355231i	$-0.884402\pi$
$199$	−0.764069	+	1.67308i	−0.0541634	+	0.118601i	0.880615	+	0.473832i	$0.157130\pi$
$200$		0			0
$201$	7.30201	−	2.14406i	0.515044	−	0.151231i
$202$		0			0
$203$	9.22860	+	2.70976i	0.647721	+	0.190188i
$204$		0			0
$205$	−0.0406560	+	0.282768i	−0.00283954	+	0.0197494i
$206$		0			0
$207$	−3.84528	−	2.86597i	−0.267266	−	0.199199i
$208$		0			0
$209$	−0.847878	+	5.89712i	−0.0586489	+	0.407912i
$210$		0			0
$211$	−6.30872	−	1.85241i	−0.434311	−	0.127525i	0.0572670	−	0.998359i	$-0.481761\pi$
$211$	−6.30872	−	1.85241i	−0.434311	−	0.127525i	−0.491578	+	0.870834i	$0.663580\pi$
$212$		0			0
$213$	−12.4594	+	3.65840i	−0.853703	+	0.250670i
$214$		0			0
$215$	−0.0723337	+	0.158389i	−0.00493312	+	0.0108020i
$216$		0			0
$217$	−33.0487	+	21.2391i	−2.24349	+	1.44180i
$218$		0			0
$219$	−0.933425	−	6.49211i	−0.0630750	−	0.438696i
$220$		0			0
$221$	−16.6260	+	19.1874i	−1.11838	+	1.29069i
$222$		0			0
$223$	−6.01244	−	3.86396i	−0.402623	−	0.258750i	0.323622	−	0.946187i	$-0.395100\pi$
$223$	−6.01244	−	3.86396i	−0.402623	−	0.258750i	−0.726244	+	0.687437i	$0.758736\pi$
$224$		0			0
$225$	3.27394	+	3.77833i	0.218263	+	0.251888i
$226$		0			0
$227$	5.56928	+	12.1950i	0.369646	+	0.809412i	0.999466	+	0.0326709i	$0.0104013\pi$
$227$	5.56928	+	12.1950i	0.369646	+	0.809412i	−0.629820	+	0.776741i	$0.716871\pi$
$228$		0			0
$229$	11.0186			0.728127			0.364064	−	0.931374i	$-0.381389\pi$
$229$	11.0186			0.728127			0.364064	+	0.931374i	$0.381389\pi$
$230$		0			0
$231$	19.7302			1.29815
$232$		0			0
$233$	2.79170	+	6.11297i	0.182890	+	0.400474i	0.978764	−	0.204988i	$-0.0657156\pi$
$233$	2.79170	+	6.11297i	0.182890	+	0.400474i	−0.795874	+	0.605462i	$0.792988\pi$
$234$		0			0
$235$	−0.0542373	−	0.0625932i	−0.00353805	−	0.00408313i
$236$		0			0
$237$	−8.76642	−	5.63383i	−0.569440	−	0.365957i
$238$		0			0
$239$	7.02748	−	8.11015i	0.454570	−	0.524602i	−0.481485	−	0.876454i	$-0.659903\pi$
$239$	7.02748	−	8.11015i	0.454570	−	0.524602i	0.936056	+	0.351852i	$0.114448\pi$
$240$		0			0
$241$	−1.89370	−	13.1710i	−0.121984	−	0.848417i	−0.955304	−	0.295626i	$-0.904472\pi$
$241$	−1.89370	−	13.1710i	−0.121984	−	0.848417i	0.833320	−	0.552791i	$-0.186437\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−0.0740619	+	0.162173i	−0.00473164	+	0.0103609i
$246$		0			0
$247$	−5.27479	+	1.54882i	−0.335627	+	0.0985490i
$248$		0			0
$249$	7.39493	+	2.17135i	0.468635	+	0.137604i
$250$		0			0
$251$	−3.32122	+	23.0996i	−0.209634	+	1.45803i	0.564720	+	0.825282i	$0.308984\pi$
$251$	−3.32122	+	23.0996i	−0.209634	+	1.45803i	−0.774354	+	0.632752i	$0.781925\pi$
$252$		0			0
$253$	24.2213	−	5.32230i	1.52278	−	0.334610i
$254$		0			0
$255$	−0.0178612	+	0.124227i	−0.00111851	+	0.00777942i
$256$		0			0
$257$	5.41717	+	1.59063i	0.337914	+	0.0992205i	0.446287	−	0.894890i	$-0.352746\pi$
$257$	5.41717	+	1.59063i	0.337914	+	0.0992205i	−0.108373	+	0.994110i	$0.534564\pi$
$258$		0			0
$259$	−12.1024	+	3.55357i	−0.752004	+	0.220808i
$260$		0			0
$261$	1.04717	−	2.29299i	0.0648183	−	0.141932i
$262$		0			0
$263$	18.5191	−	11.9015i	1.14194	−	0.733879i	0.173920	−	0.984760i	$-0.444356\pi$
$263$	18.5191	−	11.9015i	1.14194	−	0.733879i	0.968018	+	0.250880i	$0.0807201\pi$
$264$		0			0
$265$	0.0125466	+	0.0872634i	0.000770731	+	0.00536055i
$266$		0			0
$267$	−5.31730	+	6.13650i	−0.325414	+	0.375547i
$268$		0			0
$269$	9.71650	+	6.24441i	0.592425	+	0.380729i	0.802230	−	0.597015i	$-0.203647\pi$
$269$	9.71650	+	6.24441i	0.592425	+	0.380729i	−0.209805	+	0.977743i	$0.567283\pi$
$270$		0			0
$271$	13.8289	+	15.9594i	0.840046	+	0.969465i	0.999844	−	0.0176846i	$-0.00562949\pi$
$271$	13.8289	+	15.9594i	0.840046	+	0.969465i	−0.159797	+	0.987150i	$0.551084\pi$
$272$		0			0
$273$	7.56302	+	16.5607i	0.457735	+	1.00230i
$274$		0			0
$275$	−25.8521			−1.55894
$276$		0			0
$277$	2.83921			0.170591			0.0852957	−	0.996356i	$-0.472817\pi$
$277$	2.83921			0.170591			0.0852957	+	0.996356i	$0.472817\pi$
$278$		0			0
$279$	4.27711	+	9.36557i	0.256064	+	0.560702i
$280$		0			0
$281$	12.7758	+	14.7440i	0.762139	+	0.879556i	0.995686	−	0.0927900i	$-0.0295785\pi$
$281$	12.7758	+	14.7440i	0.762139	+	0.879556i	−0.233546	+	0.972346i	$0.575033\pi$
$282$		0			0
$283$	24.6885	+	15.8663i	1.46758	+	0.943154i	0.998189	+	0.0601627i	$0.0191620\pi$
$283$	24.6885	+	15.8663i	1.46758	+	0.943154i	0.469388	+	0.882992i	$0.344474\pi$
$284$		0			0
$285$	−0.0177965	+	0.0205383i	−0.00105417	+	0.00121658i
$286$		0			0
$287$	−6.57668	−	45.7418i	−0.388209	−	2.70005i
$288$		0			0
$289$	9.51613	−	6.11565i	0.559773	−	0.359744i
$290$		0			0
$291$	−2.86396	+	6.27119i	−0.167888	+	0.367624i
$292$		0			0
$293$	−11.2134	+	3.29256i	−0.655096	+	0.192354i	−0.592356	−	0.805676i	$-0.701802\pi$
$293$	−11.2134	+	3.29256i	−0.655096	+	0.192354i	−0.0627402	+	0.998030i	$0.519984\pi$
$294$		0			0
$295$	0.0683681	+	0.0200747i	0.00398054	+	0.00116879i
$296$		0			0
$297$	0.735908	−	5.11836i	0.0427017	−	0.296997i
$298$		0			0
$299$	13.7519	+	18.2902i	0.795290	+	1.05775i
$300$		0			0
$301$	4.00858	−	27.8803i	0.231051	−	1.60699i
$302$		0			0
$303$	−3.49526	−	1.02630i	−0.200797	−	0.0589595i
$304$		0			0
$305$	−0.0936226	+	0.0274901i	−0.00536081	+	0.00157408i
$306$		0			0
$307$	−6.40055	+	14.0152i	−0.365298	+	0.799892i	0.634341	+	0.773053i	$0.281271\pi$
$307$	−6.40055	+	14.0152i	−0.365298	+	0.799892i	−0.999640	+	0.0268389i	$0.991456\pi$
$308$		0			0
$309$	−2.84807	+	1.83035i	−0.162021	+	0.104125i
$310$		0			0
$311$	4.37364	+	30.4193i	0.248006	+	1.72492i	0.609707	+	0.792627i	$0.291287\pi$
$311$	4.37364	+	30.4193i	0.248006	+	1.72492i	−0.361701	+	0.932294i	$0.617804\pi$
$312$		0			0
$313$	−13.3841	+	15.4461i	−0.756515	+	0.873064i	−0.995183	−	0.0980367i	$-0.968744\pi$
$313$	−13.3841	+	15.4461i	−0.756515	+	0.873064i	0.238668	+	0.971101i	$0.423289\pi$
$314$		0			0
$315$	0.0757115	+	0.0486568i	0.00426586	+	0.00274150i
$316$		0			0
$317$	−12.9522	−	14.9476i	−0.727468	−	0.839543i	0.264716	−	0.964326i	$-0.414722\pi$
$317$	−12.9522	−	14.9476i	−0.727468	−	0.839543i	−0.992184	+	0.124784i	$0.960176\pi$
$318$		0			0
$319$	5.41491	+	11.8570i	0.303177	+	0.663865i
$320$		0			0
$321$	−2.93241			−0.163671
$322$		0			0
$323$	6.13047			0.341108
$324$		0			0
$325$	−9.90965	−	21.6991i	−0.549688	−	1.20365i
$326$		0			0
$327$	−10.7987	−	12.4623i	−0.597169	−	0.689169i
$328$		0			0
$329$	11.2709	+	7.24336i	0.621384	+	0.399339i
$330$		0			0
$331$	6.81861	−	7.86909i	0.374784	−	0.432524i	−0.536754	−	0.843739i	$-0.680350\pi$
$331$	6.81861	−	7.86909i	0.374784	−	0.432524i	0.911539	+	0.411214i	$0.134895\pi$
$332$		0			0
$333$	0.470457	+	3.27210i	0.0257809	+	0.179310i
$334$		0			0
$335$	−0.151009	+	0.0970478i	−0.00825052	+	0.00530229i
$336$		0			0
$337$	1.36174	−	2.98179i	0.0741787	−	0.162429i	−0.868910	−	0.494970i	$-0.835179\pi$
$337$	1.36174	−	2.98179i	0.0741787	−	0.162429i	0.943089	+	0.332542i	$0.107906\pi$
$338$		0			0
$339$	−5.72739	+	1.68171i	−0.311069	+	0.0913381i
$340$		0			0
$341$	−51.0839	−	14.9996i	−2.76635	−	0.812273i
$342$		0			0
$343$	0.303281	−	2.10936i	0.0163756	−	0.113895i
$344$		0			0
$345$	0.106071	+	0.0393089i	0.00571065	+	0.00211632i
$346$		0			0
$347$	−0.982954	+	6.83660i	−0.0527678	+	0.367008i	0.946279	+	0.323352i	$0.104810\pi$
$347$	−0.982954	+	6.83660i	−0.0527678	+	0.367008i	−0.999047	+	0.0436561i	$0.986099\pi$
$348$		0			0
$349$	10.0402	+	2.94806i	0.537438	+	0.157806i	0.539177	−	0.842192i	$-0.318735\pi$
$349$	10.0402	+	2.94806i	0.537438	+	0.157806i	−0.00173902	+	0.999998i	$0.500554\pi$
$350$		0			0
$351$	4.57821	−	1.34429i	0.244367	−	0.0717526i
$352$		0			0
$353$	11.0778	−	24.2570i	0.589611	−	1.29107i	−0.346065	−	0.938210i	$-0.612482\pi$
$353$	11.0778	−	24.2570i	0.589611	−	1.29107i	0.935677	−	0.352858i	$-0.114790\pi$
$354$		0			0
$355$	0.257666	−	0.165592i	0.0136755	−	0.00878872i
$356$		0			0
$357$	−2.88930	−	20.0955i	−0.152918	−	1.06357i
$358$		0			0
$359$	3.02048	−	3.48582i	0.159415	−	0.183975i	−0.670423	−	0.741979i	$-0.733887\pi$
$359$	3.02048	−	3.48582i	0.159415	−	0.183975i	0.829838	+	0.558004i	$0.188433\pi$
$360$		0			0
$361$	−14.8671	−	9.55450i	−0.782479	−	0.502868i
$362$		0			0
$363$	10.3069	+	11.8948i	0.540974	+	0.624317i
$364$		0			0
$365$	0.0642670	+	0.140725i	0.00336389	+	0.00736588i
$366$		0			0
$367$	5.20383			0.271638			0.135819	−	0.990734i	$-0.456633\pi$
$367$	5.20383			0.271638			0.135819	+	0.990734i	$0.456633\pi$
$368$		0			0
$369$	−12.1115			−0.630499
$370$		0			0
$371$	−5.92434	−	12.9725i	−0.307576	−	0.673498i
$372$		0			0
$373$	5.24687	+	6.05521i	0.271673	+	0.313527i	0.875149	−	0.483854i	$-0.160763\pi$
$373$	5.24687	+	6.05521i	0.271673	+	0.313527i	−0.603476	+	0.797381i	$0.706218\pi$
$374$		0			0
$375$	−0.198417	−	0.127515i	−0.0102462	−	0.00658484i
$376$		0			0
$377$	−7.87660	+	9.09008i	−0.405666	+	0.468163i
$378$		0			0
$379$	−3.83640	−	26.6827i	−0.197063	−	1.37060i	−0.812751	−	0.582611i	$-0.802031\pi$
$379$	−3.83640	−	26.6827i	−0.197063	−	1.37060i	0.615688	−	0.787990i	$-0.288878\pi$
$380$		0			0
$381$	−9.28337	+	5.96606i	−0.475602	+	0.305651i
$382$		0			0
$383$	−12.4421	+	27.2444i	−0.635762	+	1.39213i	0.267719	+	0.963497i	$0.413730\pi$
$383$	−12.4421	+	27.2444i	−0.635762	+	1.39213i	−0.903481	+	0.428628i	$0.858997\pi$
$384$		0			0
$385$	−0.446530	+	0.131113i	−0.0227573	+	0.00668213i
$386$		0			0
$387$	−7.08311	−	2.07979i	−0.360055	−	0.105722i
$388$		0			0
$389$	−0.125346	+	0.871798i	−0.00635527	+	0.0442019i	−0.992752	−	0.120178i	$-0.961653\pi$
$389$	−0.125346	+	0.871798i	−0.00635527	+	0.0442019i	0.986397	+	0.164380i	$0.0525624\pi$
$390$		0			0
$391$	−8.96782	−	23.8904i	−0.453522	−	1.20819i
$392$		0			0
$393$	2.46149	−	17.1200i	0.124166	−	0.863591i
$394$		0			0
$395$	0.235838	+	0.0692482i	0.0118663	+	0.00348425i
$396$		0			0
$397$	−14.6044	+	4.28825i	−0.732976	+	0.215221i	−0.626859	−	0.779133i	$-0.715660\pi$
$397$	−14.6044	+	4.28825i	−0.732976	+	0.215221i	−0.106117	+	0.994354i	$0.533842\pi$
$398$		0			0
$399$	1.82621	−	3.99884i	0.0914247	−	0.200192i
$400$		0			0
$401$	22.1488	−	14.2341i	1.10606	−	0.710819i	0.145626	−	0.989340i	$-0.453480\pi$
$401$	22.1488	−	14.2341i	1.10606	−	0.710819i	0.960430	+	0.278520i	$0.0898439\pi$
$402$		0			0
$403$	−6.99154	−	48.6272i	−0.348273	−	2.42230i
$404$		0			0
$405$	0.0154463	−	0.0178260i	0.000767534	−	0.000885782i
$406$		0			0
$407$	−14.3804	−	9.24171i	−0.712809	−	0.458094i
$408$		0			0
$409$	24.3014	+	28.0453i	1.20163	+	1.38675i	0.901458	+	0.432867i	$0.142498\pi$
$409$	24.3014	+	28.0453i	1.20163	+	1.38675i	0.300170	+	0.953886i	$0.402956\pi$
$410$		0			0
$411$	6.91126	+	15.1335i	0.340907	+	0.746482i
$412$		0			0
$413$	−11.5264			−0.567177
$414$		0			0
$415$	−0.181789			−0.00892369
$416$		0			0
$417$	5.00304	+	10.9551i	0.245000	+	0.536475i
$418$		0			0
$419$	7.96087	+	9.18733i	0.388914	+	0.448830i	0.916118	−	0.400908i	$-0.131305\pi$
$419$	7.96087	+	9.18733i	0.388914	+	0.448830i	−0.527205	+	0.849738i	$0.676760\pi$
$420$		0			0
$421$	−8.63155	−	5.54716i	−0.420676	−	0.270352i	0.313131	−	0.949710i	$-0.398622\pi$
$421$	−8.63155	−	5.54716i	−0.420676	−	0.270352i	−0.733807	+	0.679358i	$0.762258\pi$
$422$		0			0
$423$	2.29944	−	2.65369i	0.111803	−	0.129027i
$424$		0			0
$425$	3.78579	+	26.3307i	0.183638	+	1.27723i
$426$		0			0
$427$	13.2785	−	8.53355i	0.642590	−	0.412968i
$428$		0			0
$429$	−10.2497	+	22.4437i	−0.494859	+	1.08359i
$430$		0			0
$431$	33.0598	−	9.70723i	1.59243	−	0.467581i	0.639005	−	0.769202i	$-0.279346\pi$
$431$	33.0598	−	9.70723i	1.59243	−	0.467581i	0.953428	+	0.301622i	$0.0975279\pi$
$432$		0			0
$433$	−7.00679	−	2.05738i	−0.336725	−	0.0988714i	0.108999	−	0.994042i	$-0.465236\pi$
$433$	−7.00679	−	2.05738i	−0.336725	−	0.0988714i	−0.445724	+	0.895170i	$0.647054\pi$
$434$		0			0
$435$	−0.00846179	+	0.0588530i	−0.000405712	+	0.00282179i
$436$		0			0
$437$	1.16320	−	5.40170i	0.0556434	−	0.258398i
$438$		0			0
$439$	0.221821	−	1.54280i	0.0105870	−	0.0736339i	−0.983843	−	0.179033i	$-0.942703\pi$
$439$	0.221821	−	1.54280i	0.0105870	−	0.0736339i	0.994430	+	0.105399i	$0.0336121\pi$
$440$		0			0
$441$	−7.25234	−	2.12948i	−0.345350	−	0.101404i
$442$		0			0
$443$	−14.4346	+	4.23837i	−0.685807	+	0.201371i	−0.606030	−	0.795442i	$-0.707239\pi$
$443$	−14.4346	+	4.23837i	−0.685807	+	0.201371i	−0.0797767	+	0.996813i	$0.525421\pi$
$444$		0			0
$445$	0.0795611	−	0.174215i	0.00377156	−	0.00825856i
$446$		0			0
$447$	−17.6409	+	11.3371i	−0.834384	+	0.536226i
$448$		0			0
$449$	−2.66072	−	18.5057i	−0.125567	−	0.873338i	−0.951078	−	0.308951i	$-0.900022\pi$
$449$	−2.66072	−	18.5057i	−0.125567	−	0.873338i	0.825511	−	0.564386i	$-0.190887\pi$
$450$		0			0
$451$	41.0129	−	47.3314i	1.93122	−	2.22875i
$452$		0			0
$453$	11.1544	+	7.16852i	0.524081	+	0.336806i
$454$		0			0
$455$	−0.281215	−	0.324539i	−0.0131836	−	0.0152146i
$456$		0			0
$457$	10.6852	+	23.3973i	0.499833	+	1.09448i	0.976524	+	0.215411i	$0.0691090\pi$
$457$	10.6852	+	23.3973i	0.499833	+	1.09448i	−0.476691	+	0.879071i	$0.658164\pi$
$458$		0			0
$459$	−5.32089			−0.248358
$460$		0			0
$461$	−19.3890			−0.903035			−0.451518	−	0.892262i	$-0.649117\pi$
$461$	−19.3890			−0.903035			−0.451518	+	0.892262i	$0.649117\pi$
$462$		0			0
$463$	−10.5395	−	23.0783i	−0.489813	−	1.07254i	−0.979648	−	0.200725i	$-0.935670\pi$
$463$	−10.5395	−	23.0783i	−0.489813	−	1.07254i	0.489835	−	0.871815i	$-0.337057\pi$
$464$		0			0
$465$	−0.159035	−	0.183537i	−0.00737509	−	0.00851130i
$466$		0			0
$467$	−26.7105	−	17.1658i	−1.23601	−	0.794338i	−0.251198	−	0.967936i	$-0.580824\pi$
$467$	−26.7105	−	17.1658i	−1.23601	−	0.794338i	−0.984817	+	0.173597i	$0.944461\pi$
$468$		0			0
$469$	19.0155	−	21.9451i	0.878055	−	1.01333i
$470$		0			0
$471$	0.490866	+	3.41404i	0.0226179	+	0.157311i
$472$		0			0
$473$	32.1131	−	20.6379i	1.47656	−	0.948929i
$474$		0			0
$475$	−2.39284	+	5.23958i	−0.109791	+	0.240409i
$476$		0			0
$477$	−3.58625	+	1.05302i	−0.164203	+	0.0482144i
$478$		0			0
$479$	−38.2696	−	11.2370i	−1.74858	−	0.513430i	−0.758227	−	0.651990i	$-0.773934\pi$
$479$	−38.2696	−	11.2370i	−1.74858	−	0.513430i	−0.990354	+	0.138560i	$0.955752\pi$
$480$		0			0
$481$	2.24478	−	15.6128i	0.102353	−	0.711883i
$482$		0			0
$483$	−18.2549	−	1.26711i	−0.830625	−	0.0576555i
$484$		0			0
$485$	0.0231425	−	0.160960i	0.00105085	−	0.00730881i
$486$		0			0
$487$	22.4767	+	6.59975i	1.01852	+	0.299063i	0.748033	−	0.663662i	$-0.230999\pi$
$487$	22.4767	+	6.59975i	1.01852	+	0.299063i	0.270483	+	0.962725i	$0.412817\pi$
$488$		0			0
$489$	16.1120	−	4.73092i	0.728611	−	0.213940i
$490$		0			0
$491$	−13.3181	+	29.1625i	−0.601035	+	1.31608i	0.327504	+	0.944850i	$0.393793\pi$
$491$	−13.3181	+	29.1625i	−0.601035	+	1.31608i	−0.928539	+	0.371234i	$0.878935\pi$
$492$		0			0
$493$	11.2836	−	7.25151i	0.508187	−	0.326592i
$494$		0			0
$495$	0.0173580	+	0.120728i	0.000780185	+	0.00542630i
$496$		0			0
$497$	−32.4461	+	37.4448i	−1.45541	+	1.67963i
$498$		0			0
$499$	7.42603	+	4.77242i	0.332435	+	0.213643i	0.696200	−	0.717848i	$-0.254873\pi$
$499$	7.42603	+	4.77242i	0.332435	+	0.213643i	−0.363765	+	0.931491i	$0.618509\pi$
$500$		0			0
$501$	5.25000	+	6.05882i	0.234553	+	0.270688i
$502$		0			0
$503$	−11.7356	−	25.6975i	−0.523267	−	1.14579i	−0.968188	−	0.250225i	$-0.919496\pi$
$503$	−11.7356	−	25.6975i	−0.523267	−	1.14579i	0.444921	−	0.895570i	$-0.353232\pi$
$504$		0			0
$505$	0.0859239			0.00382356
$506$		0			0
$507$	−9.76715			−0.433775
$508$		0			0
$509$	12.2295	+	26.7789i	0.542063	+	1.18695i	0.960391	+	0.278657i	$0.0898892\pi$
$509$	12.2295	+	26.7789i	0.542063	+	1.18695i	−0.418328	+	0.908296i	$0.637384\pi$
$510$		0			0
$511$	−16.3884	−	18.9132i	−0.724980	−	0.836672i
$512$		0			0
$513$	−0.969251	−	0.622900i	−0.0427935	−	0.0275017i
$514$		0			0
$515$	0.0522937	−	0.0603502i	0.00230434	−	0.00265935i
$516$		0			0
$517$	2.58402	+	17.9723i	0.113645	+	0.790420i
$518$		0			0
$519$	2.01904	−	1.29756i	0.0886260	−	0.0569565i
$520$		0			0
$521$	6.06719	−	13.2853i	0.265809	−	0.582039i	−0.728918	−	0.684601i	$-0.759977\pi$
$521$	6.06719	−	13.2853i	0.265809	−	0.582039i	0.994727	+	0.102561i	$0.0327038\pi$
$522$		0			0
$523$	−22.3076	+	6.55009i	−0.975441	+	0.286415i	−0.730341	−	0.683082i	$-0.760639\pi$
$523$	−22.3076	+	6.55009i	−0.975441	+	0.286415i	−0.245100	+	0.969498i	$0.578821\pi$
$524$		0			0
$525$	18.3030	+	5.37424i	0.798808	+	0.234551i
$526$		0			0
$527$	−7.79655	+	54.2262i	−0.339623	+	2.36213i
$528$		0			0
$529$	−22.7520	+	3.36878i	−0.989215	+	0.146469i
$530$		0			0
$531$	−0.429918	+	2.99014i	−0.0186568	+	0.129761i
$532$		0			0
$533$	55.4490	+	16.2813i	2.40176	+	0.705222i
$534$		0			0
$535$	0.0663655	−	0.0194867i	0.00286923	−	0.000842483i
$536$		0			0
$537$	−3.70988	+	8.12350i	−0.160093	+	0.350555i
$538$		0			0
$539$	32.8804	−	21.1309i	1.41626	−	0.910174i
$540$		0			0
$541$	3.52452	+	24.5136i	0.151531	+	1.05392i	0.913655	+	0.406490i	$0.133248\pi$
$541$	3.52452	+	24.5136i	0.151531	+	1.05392i	−0.762124	+	0.647431i	$0.775843\pi$
$542$		0			0
$543$	1.33858	−	1.54480i	0.0574439	−	0.0662938i
$544$		0			0
$545$	0.327209	+	0.210284i	0.0140161	+	0.00900759i
$546$		0			0
$547$	12.8067	+	14.7798i	0.547577	+	0.631937i	0.960317	−	0.278912i	$-0.0899736\pi$
$547$	12.8067	+	14.7798i	0.547577	+	0.631937i	−0.412740	+	0.910849i	$0.635428\pi$
$548$		0			0
$549$	−1.71848	−	3.76295i	−0.0733430	−	0.160599i
$550$		0			0
$551$	2.90432			0.123728
$552$		0			0
$553$	−39.7607			−1.69080
$554$		0			0
$555$	−0.0323913	−	0.0709270i	−0.00137493	−	0.00301068i
$556$		0			0
$557$	13.7706	+	15.8921i	0.583479	+	0.673371i	0.968349	−	0.249600i	$-0.0802991\pi$
$557$	13.7706	+	15.8921i	0.583479	+	0.673371i	−0.384870	+	0.922971i	$0.625754\pi$
$558$		0			0
$559$	29.6322	+	19.0434i	1.25331	+	0.805451i
$560$		0			0
$561$	18.0180	−	20.7939i	0.760721	−	0.877919i
$562$		0			0
$563$	−0.632295	−	4.39771i	−0.0266481	−	0.185341i	0.972150	−	0.234360i	$-0.0752996\pi$
$563$	−0.632295	−	4.39771i	−0.0266481	−	0.185341i	−0.998798	+	0.0490191i	$0.984390\pi$
$564$		0			0
$565$	0.118445	−	0.0761202i	0.00498304	−	0.00320240i
$566$		0			0
$567$	−1.58504	+	3.47076i	−0.0665655	+	0.145758i
$568$		0			0
$569$	−24.0926	+	7.07423i	−1.01001	+	0.296567i	−0.744559	−	0.667556i	$-0.767340\pi$
$569$	−24.0926	+	7.07423i	−1.01001	+	0.296567i	−0.265455	+	0.964123i	$0.585522\pi$
$570$		0			0
$571$	2.70365	+	0.793865i	0.113144	+	0.0332222i	0.337815	−	0.941213i	$-0.390312\pi$
$571$	2.70365	+	0.793865i	0.113144	+	0.0332222i	−0.224670	+	0.974435i	$0.572130\pi$
$572$		0			0
$573$	0.906487	−	6.30475i	0.0378690	−	0.263385i
$574$		0			0
$575$	23.9189	+	1.66026i	0.997489	+	0.0692378i
$576$		0			0
$577$	−4.52921	+	31.5014i	−0.188554	+	1.31142i	0.647202	+	0.762318i	$0.275939\pi$
$577$	−4.52921	+	31.5014i	−0.188554	+	1.31142i	−0.835756	+	0.549101i	$0.814970\pi$
$578$		0			0
$579$	−15.1861	−	4.45904i	−0.631112	−	0.185311i
$580$		0			0
$581$	28.2158	−	8.28491i	1.17059	−	0.343716i
$582$		0			0
$583$	8.02888	−	17.5808i	0.332522	−	0.728122i
$584$		0			0
$585$	−0.0946798	+	0.0608470i	−0.00391453	+	0.00251572i
$586$		0			0
$587$	−3.95381	−	27.4993i	−0.163191	−	1.13502i	−0.892570	−	0.450909i	$-0.851100\pi$
$587$	−3.95381	−	27.4993i	−0.163191	−	1.13502i	0.729379	−	0.684110i	$-0.239809\pi$
$588$		0			0
$589$	−7.76831	+	8.96511i	−0.320088	+	0.369401i
$590$		0			0
$591$	−18.4457	−	11.8544i	−0.758756	−	0.487623i
$592$		0			0
$593$	−7.87330	−	9.08628i	−0.323318	−	0.373129i	0.570701	−	0.821158i	$-0.306672\pi$
$593$	−7.87330	−	9.08628i	−0.323318	−	0.373129i	−0.894019	+	0.448029i	$0.852126\pi$
$594$		0			0
$595$	0.198930	+	0.435597i	0.00815535	+	0.0178577i
$596$		0			0
$597$	1.83929			0.0752772
$598$		0			0
$599$	14.4103			0.588788			0.294394	−	0.955684i	$-0.404882\pi$
$599$	14.4103			0.588788			0.294394	+	0.955684i	$0.404882\pi$
$600$		0			0
$601$	9.98181	+	21.8571i	0.407166	+	0.891570i	0.996493	+	0.0836753i	$0.0266659\pi$
$601$	9.98181	+	21.8571i	0.407166	+	0.891570i	−0.589327	+	0.807895i	$0.700607\pi$
$602$		0			0
$603$	−4.98367	−	5.75146i	−0.202951	−	0.234218i
$604$		0			0
$605$	−0.312308	−	0.200708i	−0.0126971	−	0.00815996i
$606$		0			0
$607$	0.120310	−	0.138845i	0.00488322	−	0.00563553i	−0.753303	−	0.657674i	$-0.771540\pi$
$607$	0.120310	−	0.138845i	0.00488322	−	0.00563553i	0.758186	+	0.652038i	$0.226086\pi$
$608$		0			0
$609$	−1.36881	−	9.52031i	−0.0554671	−	0.385782i
$610$		0			0
$611$	−14.0946	+	9.05808i	−0.570208	+	0.366451i
$612$		0			0
$613$	−15.2350	+	33.3600i	−0.615337	+	1.34740i	0.303526	+	0.952823i	$0.401836\pi$
$613$	−15.2350	+	33.3600i	−0.615337	+	1.34740i	−0.918863	+	0.394576i	$0.870891\pi$
$614$		0			0
$615$	0.274104	−	0.0804843i	0.0110530	−	0.00324544i
$616$		0			0
$617$	−25.9216	−	7.61127i	−1.04356	−	0.306418i	−0.285350	−	0.958423i	$-0.592110\pi$
$617$	−25.9216	−	7.61127i	−1.04356	−	0.306418i	−0.758215	+	0.652005i	$0.773928\pi$
$618$		0			0
$619$	−1.75147	+	12.1817i	−0.0703975	+	0.489626i	0.923870	+	0.382706i	$0.125008\pi$
$619$	−1.75147	+	12.1817i	−0.0703975	+	0.489626i	−0.994268	+	0.106920i	$0.965901\pi$
$620$		0			0
$621$	−1.00959	+	4.68836i	−0.0405134	+	0.188137i
$622$		0			0
$623$	−4.40911	+	30.6661i	−0.176647	+	1.22861i
$624$		0			0
$625$	−23.9793	−	7.04096i	−0.959173	−	0.281639i
$626$		0			0
$627$	5.71643	−	1.67849i	0.228292	−	0.0670326i
$628$		0			0
$629$	−7.30695	+	16.0000i	−0.291347	+	0.637961i
$630$		0			0
$631$	−18.4423	+	11.8521i	−0.734174	+	0.471825i	−0.853541	−	0.521025i	$-0.825550\pi$
$631$	−18.4423	+	11.8521i	−0.734174	+	0.471825i	0.119367	+	0.992850i	$0.461913\pi$
$632$		0			0
$633$	0.935729	+	6.50814i	0.0371919	+	0.258675i
$634$		0			0
$635$	0.170453	−	0.196713i	0.00676421	−	0.00780632i
$636$		0			0
$637$	30.3402	+	19.4984i	1.20212	+	0.772556i
$638$		0			0
$639$	8.50362	+	9.81370i	0.336398	+	0.388224i
$640$		0			0
$641$	−2.25901	−	4.94654i	−0.0892256	−	0.195377i	0.859758	−	0.510701i	$-0.170614\pi$
$641$	−2.25901	−	4.94654i	−0.0892256	−	0.195377i	−0.948984	+	0.315324i	$0.897887\pi$
$642$		0			0
$643$	5.24450			0.206823			0.103411	−	0.994639i	$-0.467024\pi$
$643$	5.24450			0.206823			0.103411	+	0.994639i	$0.467024\pi$
$644$		0			0
$645$	0.174124			0.00685612
$646$		0			0
$647$	−9.10401	−	19.9350i	−0.357916	−	0.783726i	−0.999856	−	0.0169715i	$-0.994598\pi$
$647$	−9.10401	−	19.9350i	−0.357916	−	0.783726i	0.641940	−	0.766755i	$-0.278130\pi$
$648$		0			0
$649$	−10.2296	−	11.8056i	−0.401546	−	0.463409i
$650$		0			0
$651$	33.0487	+	21.2391i	1.29528	+	0.832425i
$652$		0			0
$653$	−21.1837	+	24.4473i	−0.828983	+	0.956697i	−0.999590	−	0.0286418i	$-0.990882\pi$
$653$	−21.1837	+	24.4473i	−0.828983	+	0.956697i	0.170607	+	0.985339i	$0.445427\pi$
$654$		0			0
$655$	0.0580596	+	0.403813i	0.00226858	+	0.0157783i
$656$		0			0
$657$	−5.51768	+	3.54599i	−0.215265	+	0.138342i
$658$		0			0
$659$	21.2060	−	46.4346i	0.826067	−	1.80884i	0.315775	−	0.948834i	$-0.397736\pi$
$659$	21.2060	−	46.4346i	0.826067	−	1.80884i	0.510293	−	0.860001i	$-0.329537\pi$
$660$		0			0
$661$	19.5246	−	5.73294i	0.759419	−	0.222985i	0.120977	−	0.992655i	$-0.461397\pi$
$661$	19.5246	−	5.73294i	0.759419	−	0.222985i	0.638442	+	0.769670i	$0.279579\pi$
$662$		0			0
$663$	24.3602	+	7.15279i	0.946071	+	0.277791i
$664$		0			0
$665$	−0.0147569	+	0.102636i	−0.000572247	+	0.00398007i
$666$		0			0
$667$	−4.24853	−	11.3181i	−0.164504	−	0.438240i
$668$		0			0
$669$	−1.01712	+	7.07426i	−0.0393243	+	0.273507i
$670$		0			0
$671$	20.5248	+	6.02661i	0.792349	+	0.232655i
$672$		0			0
$673$	37.4379	−	10.9928i	1.44313	−	0.423740i	0.535863	−	0.844305i	$-0.319986\pi$
$673$	37.4379	−	10.9928i	1.44313	−	0.423740i	0.907262	+	0.420565i	$0.138168\pi$
$674$		0			0
$675$	2.07684	−	4.54765i	0.0799378	−	0.175039i
$676$		0			0
$677$	11.1630	−	7.17400i	0.429027	−	0.275719i	−0.308255	−	0.951304i	$-0.599745\pi$
$677$	11.1630	−	7.17400i	0.429027	−	0.275719i	0.737282	+	0.675585i	$0.236109\pi$
$678$		0			0
$679$	3.74363	+	26.0375i	0.143667	+	0.999229i
$680$		0			0
$681$	8.77942	−	10.1320i	0.336428	−	0.388259i
$682$		0			0
$683$	−5.40313	−	3.47238i	−0.206745	−	0.132867i	0.433171	−	0.901312i	$-0.357395\pi$
$683$	−5.40313	−	3.47238i	−0.206745	−	0.132867i	−0.639916	+	0.768445i	$0.721031\pi$
$684$		0			0
$685$	−0.256980	−	0.296571i	−0.00981872	−	0.0113314i
$686$		0			0
$687$	−4.57728	−	10.0228i	−0.174634	−	0.382395i
$688$		0			0
$689$	17.8342			0.679429
$690$		0			0
$691$	39.7112			1.51069			0.755343	−	0.655329i	$-0.227470\pi$
$691$	39.7112			1.51069			0.755343	+	0.655329i	$0.227470\pi$
$692$		0			0
$693$	−8.19623	−	17.9472i	−0.311349	−	0.681760i
$694$		0			0
$695$	−0.186027	−	0.214687i	−0.00705642	−	0.00814354i
$696$		0			0
$697$	−54.2137	−	34.8410i	−2.05349	−	1.31970i
$698$		0			0
$699$	4.40084	−	5.07884i	0.166455	−	0.192099i
$700$		0			0
$701$	0.00495824	+	0.0344853i	0.000187270	+	0.00130249i	0.989915	−	0.141664i	$-0.0452451\pi$
$701$	0.00495824	+	0.0344853i	0.000187270	+	0.00130249i	−0.989728	+	0.142966i	$0.954336\pi$
$702$		0			0
$703$	−3.20410	+	2.05915i	−0.120845	+	0.0776623i
$704$		0			0
$705$	−0.0344058	+	0.0753381i	−0.00129580	+	0.00283740i
$706$		0			0
$707$	−13.3364	+	3.91592i	−0.501566	+	0.147273i
$708$		0			0
$709$	12.5453	+	3.68363i	0.471149	+	0.138342i	0.508684	−	0.860954i	$-0.330132\pi$
$709$	12.5453	+	3.68363i	0.471149	+	0.138342i	−0.0375348	+	0.999295i	$0.511950\pi$
$710$		0			0
$711$	−1.48301	+	10.3146i	−0.0556174	+	0.386827i
$712$		0			0
$713$	46.3007	+	17.1587i	1.73397	+	0.642597i
$714$		0			0
$715$	0.0828237	−	0.576051i	0.00309743	−	0.0215431i
$716$		0			0
$717$	−10.2966	−	3.02335i	−0.384533	−	0.112909i
$718$		0			0
$719$	−33.9212	+	9.96016i	−1.26505	+	0.371451i	−0.844370	−	0.535760i	$-0.820025\pi$
$719$	−33.9212	+	9.96016i	−1.26505	+	0.371451i	−0.420676	+	0.907211i	$0.638207\pi$
$720$		0			0
$721$	−5.36618	+	11.7503i	−0.199847	+	0.437604i
$722$		0			0
$723$	−11.1941	+	7.19399i	−0.416312	+	0.267547i
$724$		0			0
$725$	1.79353	+	12.4742i	0.0666099	+	0.463282i
$726$		0			0
$727$	−12.5187	+	14.4473i	−0.464292	+	0.535821i	−0.938815	−	0.344422i	$-0.888075\pi$
$727$	−12.5187	+	14.4473i	−0.464292	+	0.535821i	0.474523	+	0.880243i	$0.342620\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−25.7226	−	29.6855i	−0.951385	−	1.09796i
$732$		0			0
$733$	4.92513	+	10.7845i	0.181914	+	0.398335i	0.978517	−	0.206167i	$-0.0660991\pi$
$733$	4.92513	+	10.7845i	0.181914	+	0.398335i	−0.796603	+	0.604503i	$0.793372\pi$
$734$		0			0
$735$	0.178284			0.00657611
$736$		0			0
$737$	39.3527			1.44957
$738$		0			0
$739$	3.95914	+	8.66930i	0.145639	+	0.318905i	0.968367	−	0.249530i	$-0.0802762\pi$
$739$	3.95914	+	8.66930i	0.145639	+	0.318905i	−0.822728	+	0.568435i	$0.807549\pi$
$740$		0			0
$741$	3.60008	+	4.15472i	0.132252	+	0.152627i
$742$		0			0
$743$	12.9341	+	8.31222i	0.474505	+	0.304946i	0.755948	−	0.654632i	$-0.227176\pi$
$743$	12.9341	+	8.31222i	0.474505	+	0.304946i	−0.281442	+	0.959578i	$0.590813\pi$
$744$		0			0
$745$	0.323905	−	0.373807i	0.0118670	−	0.0136952i
$746$		0			0
$747$	−1.09684	−	7.62867i	−0.0401312	−	0.279119i
$748$		0			0
$749$	−9.41261	+	6.04912i	−0.343929	+	0.221030i
$750$		0			0
$751$	3.95693	−	8.66448i	0.144391	−	0.316171i	−0.823594	−	0.567179i	$-0.808035\pi$
$751$	3.95693	−	8.66448i	0.144391	−	0.316171i	0.967985	+	0.251008i	$0.0807620\pi$
$752$		0			0
$753$	22.3918	−	6.57484i	0.816004	−	0.239600i
$754$		0			0
$755$	−0.300081	−	0.0881118i	−0.0109211	−	0.00320672i
$756$		0			0
$757$	5.36248	−	37.2968i	0.194903	−	1.35558i	−0.623901	−	0.781503i	$-0.714453\pi$
$757$	5.36248	−	37.2968i	0.194903	−	1.35558i	0.818804	−	0.574074i	$-0.194638\pi$
$758$		0			0
$759$	−14.9032	−	19.8215i	−0.540953	−	0.719476i
$760$		0			0
$761$	4.44958	−	30.9475i	0.161297	−	1.12185i	−0.734895	−	0.678181i	$-0.762768\pi$
$761$	4.44958	−	30.9475i	0.161297	−	1.12185i	0.896192	−	0.443666i	$-0.146322\pi$
$762$		0			0
$763$	−60.3701	−	17.7263i	−2.18555	−	0.641734i
$764$		0			0
$765$	0.120421	−	0.0353588i	0.00435383	−	0.00127840i
$766$		0			0
$767$	5.98786	−	13.1116i	0.216209	−	0.473432i
$768$		0			0
$769$	−40.6172	+	26.1031i	−1.46470	+	0.941302i	−0.466302	+	0.884625i	$0.654414\pi$
$769$	−40.6172	+	26.1031i	−1.46470	+	0.941302i	−0.998393	+	0.0566770i	$0.981949\pi$
$770$		0			0
$771$	−0.803491	−	5.58840i	−0.0289370	−	0.201261i
$772$		0			0
$773$	0.738813	−	0.852636i	0.0265733	−	0.0306672i	−0.742307	−	0.670060i	$-0.766269\pi$
$773$	0.738813	−	0.852636i	0.0265733	−	0.0306672i	0.768881	+	0.639392i	$0.220814\pi$
$774$		0			0
$775$	−43.3029	−	27.8291i	−1.55549	−	0.999650i
$776$		0			0
$777$	8.25995	+	9.53249i	0.296324	+	0.341976i
$778$		0			0
$779$	−5.79681	−	12.6933i	−0.207692	−	0.454783i
$780$		0			0
$781$	−67.1473			−2.40272
$782$		0			0
$783$	−2.52078			−0.0900855
$784$		0			0
$785$	−0.0337964	−	0.0740039i	−0.00120625	−	0.00264131i
$786$		0			0
$787$	15.0404	+	17.3575i	0.536132	+	0.618729i	0.957595	−	0.288116i	$-0.0930289\pi$
$787$	15.0404	+	17.3575i	0.536132	+	0.618729i	−0.421464	+	0.906845i	$0.638483\pi$
$788$		0			0
$789$	−18.5191	−	11.9015i	−0.659298	−	0.423705i
$790$		0			0
$791$	−14.9150	+	17.2128i	−0.530315	+	0.612017i
$792$		0			0
$793$	2.80910	+	19.5377i	0.0997540	+	0.693805i
$794$		0			0
$795$	0.0741656	−	0.0476633i	0.00263038	−	0.00169044i
$796$		0			0
$797$	15.9217	−	34.8636i	0.563975	−	1.23493i	−0.385968	−	0.922512i	$-0.626133\pi$
$797$	15.9217	−	34.8636i	0.563975	−	1.23493i	0.949944	−	0.312422i	$-0.101140\pi$
$798$		0			0
$799$	17.9266	−	5.26373i	0.634199	−	0.186218i
$800$		0			0
$801$	7.79084	+	2.28760i	0.275276	+	0.0808283i
$802$		0			0
$803$	4.82673	−	33.5706i	0.170332	−	1.18468i
$804$		0			0
$805$	0.421560	−	0.0926318i	0.0148580	−	0.00326484i
$806$		0			0
$807$	1.64374	−	11.4325i	0.0578624	−	0.402442i
$808$		0			0
$809$	−43.2929	−	12.7119i	−1.52210	−	0.446928i	−0.589477	−	0.807785i	$-0.700666\pi$
$809$	−43.2929	−	12.7119i	−1.52210	−	0.446928i	−0.932621	+	0.360857i	$0.882484\pi$
$810$		0			0
$811$	−32.3593	+	9.50156i	−1.13629	+	0.333645i	−0.795177	−	0.606377i	$-0.792622\pi$
$811$	−32.3593	+	9.50156i	−1.13629	+	0.333645i	−0.341113	+	0.940022i	$0.610804\pi$
$812$		0			0
$813$	8.77246	−	19.2090i	0.307663	−	0.673689i
$814$		0			0
$815$	−0.333205	+	0.214138i	−0.0116717	+	0.00750092i
$816$		0			0
$817$	−1.21044	−	8.41876i	−0.0423478	−	0.294535i
$818$		0			0
$819$	11.9224	−	13.7591i	0.416601	−	0.480783i
$820$		0			0
$821$	3.43854	+	2.20982i	0.120006	+	0.0771232i	0.599267	−	0.800549i	$-0.295459\pi$
$821$	3.43854	+	2.20982i	0.120006	+	0.0771232i	−0.479261	+	0.877673i	$0.659095\pi$
$822$		0			0
$823$	−14.7144	−	16.9813i	−0.512911	−	0.591931i	0.438931	−	0.898521i	$-0.355357\pi$
$823$	−14.7144	−	16.9813i	−0.512911	−	0.591931i	−0.951842	+	0.306590i	$0.900812\pi$
$824$		0			0
$825$	10.7393	+	23.5159i	0.373896	+	0.818717i
$826$		0			0
$827$	48.7717			1.69596			0.847980	−	0.530029i	$-0.177819\pi$
$827$	48.7717			1.69596			0.847980	+	0.530029i	$0.177819\pi$
$828$		0			0
$829$	−0.591013			−0.0205267			−0.0102634	−	0.999947i	$-0.503267\pi$
$829$	−0.591013			−0.0205267			−0.0102634	+	0.999947i	$0.503267\pi$
$830$		0			0
$831$	−1.17945	−	2.58263i	−0.0409146	−	0.0895905i
$832$		0			0
$833$	−26.3372	−	30.3948i	−0.912530	−	1.05312i
$834$		0			0
$835$	−0.159079	−	0.102234i	−0.00550516	−	0.00353795i
$836$		0			0
$837$	6.74244	−	7.78119i	0.233053	−	0.268957i
$838$		0			0
$839$	−1.45395	−	10.1125i	−0.0501960	−	0.349121i	−0.999406	−	0.0344761i	$-0.989024\pi$
$839$	−1.45395	−	10.1125i	−0.0501960	−	0.349121i	0.949210	−	0.314645i	$-0.101885\pi$
$840$		0			0
$841$	−19.0507	+	12.2432i	−0.656922	+	0.422178i
$842$		0			0
$843$	8.10440	−	17.7462i	0.279130	−	0.611210i
$844$		0			0
$845$	0.221048	−	0.0649055i	0.00760427	−	0.00223282i
$846$		0			0
$847$	57.6210	+	16.9191i	1.97988	+	0.581346i
$848$		0			0
$849$	4.17655	−	29.0485i	0.143339	−	0.996943i
$850$		0			0
$851$	12.7115	+	9.47417i	0.435746	+	0.324771i
$852$		0			0
$853$	3.06357	−	21.3076i	0.104895	−	0.729559i	−0.867706	−	0.497078i	$-0.834406\pi$
$853$	3.06357	−	21.3076i	0.104895	−	0.729559i	0.972601	−	0.232481i	$-0.0746845\pi$
$854$		0			0
$855$	0.0260752	+	0.00765636i	0.000891752	+	0.000261842i
$856$		0			0
$857$	−0.899789	+	0.264202i	−0.0307362	+	0.00902496i	−0.297065	−	0.954857i	$-0.596008\pi$
$857$	−0.899789	+	0.264202i	−0.0307362	+	0.00902496i	0.266328	+	0.963882i	$0.414189\pi$
$858$		0			0
$859$	9.84812	−	21.5644i	0.336014	−	0.735767i	−0.663914	−	0.747809i	$-0.731106\pi$
$859$	9.84812	−	21.5644i	0.336014	−	0.735767i	0.999927	+	0.0120418i	$0.00383311\pi$
$860$		0			0
$861$	−38.8762	+	24.9842i	−1.32490	+	0.851459i
$862$		0			0
$863$	6.15099	+	42.7811i	0.209382	+	1.45629i	0.775179	+	0.631741i	$0.217659\pi$
$863$	6.15099	+	42.7811i	0.209382	+	1.45629i	−0.565797	+	0.824544i	$0.691431\pi$
$864$		0			0
$865$	−0.0370718	+	0.0427831i	−0.00126048	+	0.00145467i
$866$		0			0
$867$	−9.51613	−	6.11565i	−0.323185	−	0.207698i
$868$		0			0
$869$	−35.2872	−	40.7236i	−1.19704	−	1.38146i
$870$		0			0
$871$	15.0847	+	33.0309i	0.511126	+	1.11921i
$872$		0			0
$873$	6.89421			0.233334
$874$		0			0
$875$	−0.899934			−0.0304233
$876$		0			0
$877$	15.9276	+	34.8766i	0.537837	+	1.17770i	0.962234	+	0.272223i	$0.0877590\pi$
$877$	15.9276	+	34.8766i	0.537837	+	1.17770i	−0.424397	+	0.905476i	$0.639514\pi$
$878$		0			0
$879$	7.65325	+	8.83232i	0.258138	+	0.297907i
$880$		0			0
$881$	9.30685	+	5.98115i	0.313556	+	0.201510i	0.687947	−	0.725761i	$-0.258512\pi$
$881$	9.30685	+	5.98115i	0.313556	+	0.201510i	−0.374392	+	0.927271i	$0.622148\pi$
$882$		0			0
$883$	−7.58576	+	8.75444i	−0.255281	+	0.294610i	−0.868895	−	0.494996i	$-0.835170\pi$
$883$	−7.58576	+	8.75444i	−0.255281	+	0.294610i	0.613614	+	0.789606i	$0.289715\pi$
$884$		0			0
$885$	−0.0101406	−	0.0705291i	−0.000340871	−	0.00237081i
$886$		0			0
$887$	−36.4493	+	23.4246i	−1.22385	+	0.786520i	−0.982922	−	0.184024i	$-0.941088\pi$
$887$	−36.4493	+	23.4246i	−1.22385	+	0.786520i	−0.240927	+	0.970543i	$0.577451\pi$
$888$		0			0
$889$	−17.4912	+	38.3004i	−0.586636	+	1.28455i
$890$		0			0
$891$	−4.96153	+	1.45684i	−0.166217	+	0.0488058i
$892$		0			0
$893$	3.88172	+	1.13978i	0.129897	+	0.0381411i
$894$		0			0
$895$	0.0299781	−	0.208502i	0.00100206	−	0.00696946i
$896$		0			0
$897$	10.9246	−	20.1071i	0.364762	−	0.671358i
$898$		0			0
$899$	−3.69364	+	25.6898i	−0.123190	+	0.856803i
$900$		0			0
$901$	−19.0821	−	5.60300i	−0.635715	−	0.186663i
$902$		0			0
$903$	−27.0260	+	7.93556i	−0.899370	+	0.264079i
$904$		0			0
$905$	−0.0200287	+	0.0438568i	−0.000665778	+	0.00145785i
$906$		0			0
$907$	27.5628	−	17.7136i	0.915209	−	0.588169i	0.00394503	−	0.999992i	$-0.498744\pi$
$907$	27.5628	−	17.7136i	0.915209	−	0.588169i	0.911264	+	0.411823i	$0.135108\pi$
$908$		0			0
$909$	0.518427	+	3.60574i	0.0171952	+	0.119595i
$910$		0			0
$911$	0.573996	−	0.662426i	0.0190173	−	0.0219472i	−0.746161	−	0.665765i	$-0.768105\pi$
$911$	0.573996	−	0.662426i	0.0190173	−	0.0219472i	0.765179	+	0.643818i	$0.222651\pi$
$912$		0			0
$913$	33.5268	+	21.5464i	1.10958	+	0.713082i
$914$		0			0
$915$	0.0638981	+	0.0737423i	0.00211240	+	0.00243785i
$916$		0			0
$917$	−27.4150	−	60.0305i	−0.905323	−	1.98238i
$918$		0			0
$919$	29.7271			0.980606			0.490303	−	0.871552i	$-0.336886\pi$
$919$	29.7271			0.980606			0.490303	+	0.871552i	$0.336886\pi$
$920$		0			0
$921$	15.4076			0.507697
$922$		0			0
$923$	−25.7390	−	56.3605i	−0.847209	−	1.85513i
$924$		0			0
$925$	−10.8228	−	12.4902i	−0.355852	−	0.410675i
$926$		0			0
$927$	2.84807	+	1.83035i	0.0935430	+	0.0601164i
$928$		0			0
$929$	−3.69991	+	4.26992i	−0.121390	+	0.140092i	−0.813192	−	0.581996i	$-0.802272\pi$
$929$	−3.69991	+	4.26992i	−0.121390	+	0.140092i	0.691802	+	0.722088i	$0.256817\pi$
$930$		0			0
$931$	−1.23936	−	8.61991i	−0.0406183	−	0.282506i
$932$		0			0
$933$	25.8535	−	16.6150i	0.846406	−	0.543952i
$934$		0			0
$935$	−0.269598	+	0.590337i	−0.00881679	+	0.0193061i
$936$		0			0
$937$	−20.4617	+	6.00810i	−0.668455	+	0.196276i	−0.598315	−	0.801261i	$-0.704163\pi$
$937$	−20.4617	+	6.00810i	−0.668455	+	0.196276i	−0.0701399	+	0.997537i	$0.522345\pi$
$938$		0			0
$939$	19.6102	+	5.75808i	0.639955	+	0.187908i
$940$		0			0
$941$	6.16422	−	42.8731i	0.200948	−	1.39762i	−0.600532	−	0.799601i	$-0.705045\pi$
$941$	6.16422	−	42.8731i	0.200948	−	1.39762i	0.801480	−	0.598022i	$-0.204046\pi$
$942$		0			0
$943$	−40.9858	+	41.1582i	−1.33468	+	1.34030i
$944$		0			0
$945$	0.0128081	−	0.0890824i	0.000416648	−	0.00289785i
$946$		0			0
$947$	41.6613	+	12.2329i	1.35381	+	0.397515i	0.876577	−	0.481262i	$-0.159821\pi$
$947$	41.6613	+	12.2329i	1.35381	+	0.397515i	0.477233	+	0.878777i	$0.341640\pi$
$948$		0			0
$949$	30.0279	−	8.81700i	0.974748	−	0.286212i
$950$		0			0
$951$	−8.21631	+	17.9912i	−0.266432	+	0.583405i
$952$		0			0
$953$	31.4075	−	20.1844i	1.01739	−	0.653836i	0.0780937	−	0.996946i	$-0.475117\pi$
$953$	31.4075	−	20.1844i	1.01739	−	0.653836i	0.939295	+	0.343110i	$0.111480\pi$
$954$		0			0
$955$	0.0213815	+	0.148711i	0.000691888	+	0.00481219i
$956$		0			0
$957$	8.53607	−	9.85115i	0.275932	−	0.318443i
$958$		0			0
$959$	53.4023	+	34.3196i	1.72445	+	1.10824i
$960$		0			0
$961$	−49.1195	−	56.6869i	−1.58450	−	1.82861i
$962$		0			0
$963$	1.21817	+	2.66741i	0.0392549	+	0.0859562i
$964$		0			0
$965$	0.373319			0.0120176
$966$		0			0
$967$	25.1166			0.807694			0.403847	−	0.914827i	$-0.367673\pi$
$967$	25.1166			0.807694			0.403847	+	0.914827i	$0.367673\pi$
$968$		0			0
$969$	−2.54669	−	5.57647i	−0.0818114	−	0.179142i
$970$		0			0
$971$	24.9732	+	28.8206i	0.801427	+	0.924896i	0.998459	−	0.0555011i	$-0.0176756\pi$
$971$	24.9732	+	28.8206i	0.801427	+	0.924896i	−0.197032	+	0.980397i	$0.563130\pi$
$972$		0			0
$973$	38.6578	+	24.8439i	1.23931	+	0.796457i
$974$		0			0
$975$	−15.6216	+	18.0283i	−0.500291	+	0.577367i
$976$		0			0
$977$	−0.248944	−	1.73144i	−0.00796441	−	0.0553937i	0.985452	−	0.169956i	$-0.0543625\pi$
$977$	−0.248944	−	1.73144i	−0.00796441	−	0.0553937i	−0.993416	+	0.114562i	$0.963453\pi$
$978$		0			0
$979$	−35.3218	+	22.7000i	−1.12889	+	0.725494i
$980$		0			0
$981$	−6.85021	+	14.9999i	−0.218710	+	0.478909i
$982$		0			0
$983$	−16.6244	+	4.88137i	−0.530237	+	0.155692i	−0.535883	−	0.844292i	$-0.680021\pi$
$983$	−16.6244	+	4.88137i	−0.530237	+	0.155692i	0.00564570	+	0.999984i	$0.498203\pi$
$984$		0			0
$985$	0.496235	+	0.145708i	0.0158114	+	0.00464263i
$986$		0			0
$987$	1.90670	−	13.2614i	0.0606908	−	0.422114i
$988$		0			0
$989$	−31.0372	+	17.0323i	−0.986926	+	0.541594i
$990$		0			0
$991$	2.29002	−	15.9274i	0.0727449	−	0.505952i	−0.920576	−	0.390564i	$-0.872280\pi$
$991$	2.29002	−	15.9274i	0.0727449	−	0.505952i	0.993321	−	0.115387i	$-0.0368110\pi$
$992$		0			0
$993$	−9.99053	−	2.93348i	−0.317040	−	0.0930913i
$994$		0			0
$995$	−0.0416264	+	0.0122226i	−0.00131965	+	0.000387483i
$996$		0			0
$997$	12.4529	−	27.2681i	0.394389	−	0.863590i	−0.603420	−	0.797424i	$-0.706196\pi$
$997$	12.4529	−	27.2681i	0.394389	−	0.863590i	0.997809	−	0.0661669i	$-0.0210770\pi$
$998$		0			0
$999$	2.78097	−	1.78722i	0.0879861	−	0.0565452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.169.1	yes	20
3.2	odd	2		828.2.q.b.721.2		20
23.3	even	11	inner	276.2.i.b.49.1	✓	20
23.7	odd	22		6348.2.a.q.1.5		10
23.16	even	11		6348.2.a.r.1.6		10
69.26	odd	22		828.2.q.b.325.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.49.1	✓	20	23.3	even	11	inner
276.2.i.b.169.1	yes	20	1.1	even	1	trivial
828.2.q.b.325.2		20	69.26	odd	22
828.2.q.b.721.2		20	3.2	odd	2
6348.2.a.q.1.5		10	23.7	odd	22
6348.2.a.r.1.6		10	23.16	even	11

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.0154463 + 0.0178260i) q^{5} +(-3.20986 - 2.06285i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.0154463 + 0.0178260i) q^{5} +(-3.20986 - 2.06285i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.735908 - 5.11836i) q^{11} +(4.01404 - 2.57966i) q^{13} +(0.00979847 - 0.0214557i) q^{15} +(-5.10535 + 1.49907i) q^{17} +(-1.10548 - 0.324598i) q^{19} +(-0.543011 + 3.77673i) q^{21} +(0.352170 + 4.78288i) q^{23} +(0.711495 - 4.94856i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-2.41867 + 0.710187i) q^{29} +(4.27711 - 9.36557i) q^{31} +(-4.35011 + 2.79565i) q^{33} +(-0.0128081 - 0.0890824i) q^{35} +(2.16480 - 2.49832i) q^{37} +(-4.01404 - 2.57966i) q^{39} +(7.93135 + 9.15326i) q^{41} +(3.06665 + 6.71503i) q^{43} -0.0235872 q^{45} -3.51134 q^{47} +(3.13992 + 6.87547i) q^{49} +(3.48444 + 4.02126i) q^{51} +(3.14432 + 2.02073i) q^{53} +(0.0798728 - 0.0921781i) q^{55} +(0.163968 + 1.14042i) q^{57} +(2.54134 - 1.63322i) q^{59} +(-1.71848 + 3.76295i) q^{61} +(3.66101 - 1.07497i) q^{63} +(0.107987 + 0.0317079i) q^{65} +(-1.08306 + 7.53282i) q^{67} +(4.20437 - 2.30723i) q^{69} +(1.84801 - 12.8532i) q^{71} +(6.29319 + 1.84785i) q^{73} +(-4.79693 + 1.40851i) q^{75} +(-8.19623 + 17.9472i) q^{77} +(8.76642 - 5.63383i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-5.04709 + 5.82465i) q^{83} +(-0.105581 - 0.0678530i) q^{85} +(1.65076 + 1.90508i) q^{87} +(-3.37306 - 7.38598i) q^{89} -18.2059 q^{91} -10.2960 q^{93} +(-0.0112893 - 0.0247202i) q^{95} +(-4.51475 - 5.21030i) q^{97} +(4.35011 + 2.79565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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