LMFDB - Embedded newform 539.2.i.c.362.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(362,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("539.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.i (of order $6$, degree $2$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 47x^{8} - 122x^{6} + 233x^{4} - 119x^{2} + 49 $ x^12 - 8x^10 + 47x^8 - 122x^6 + 233x^4 - 119*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.1
Root			$-1.87742 + 1.08393i$ of defining polynomial
Character	$\chi$	$=$	539.362
Dual form			539.2.i.c.472.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87742 - 1.08393i) q^{2} +(0.555632 - 0.320794i) q^{3} +(1.34981 + 2.33795i) q^{4} +(2.93818 + 1.69636i) q^{5} -1.39088 q^{6} -1.51670i q^{8} +(-1.29418 + 2.24159i) q^{9} +O(q^{10})$	\(q+(-1.87742 - 1.08393i) q^{2} +(0.555632 - 0.320794i) q^{3} +(1.34981 + 2.33795i) q^{4} +(2.93818 + 1.69636i) q^{5} -1.39088 q^{6} -1.51670i q^{8} +(-1.29418 + 2.24159i) q^{9} +(-3.67747 - 6.36957i) q^{10} +(0.318720 - 3.30128i) q^{11} +(1.50000 + 0.866025i) q^{12} +2.36397 q^{13} +2.17673 q^{15} +(1.05563 - 1.82841i) q^{16} +(1.31350 + 2.27505i) q^{17} +(4.85946 - 2.80561i) q^{18} +(-2.70437 + 4.68411i) q^{19} +9.15907i q^{20} +(-4.17673 + 5.85242i) q^{22} +(-0.705818 + 1.22251i) q^{23} +(-0.486548 - 0.842726i) q^{24} +(3.25526 + 5.63828i) q^{25} +(-4.43818 - 2.56238i) q^{26} +3.58543i q^{27} +4.96005i q^{29} +(-4.08664 - 2.35942i) q^{30} +(2.54944 - 1.47192i) q^{31} +(-6.59074 + 3.80516i) q^{32} +(-0.881939 - 1.93654i) q^{33} -5.69497i q^{34} -6.98762 q^{36} +(-0.699628 + 1.21179i) q^{37} +(10.1545 - 5.86271i) q^{38} +(1.31350 - 0.758349i) q^{39} +(2.57286 - 4.45633i) q^{40} +7.09192 q^{41} -4.74568i q^{43} +(8.14842 - 3.71096i) q^{44} +(-7.60507 + 4.39079i) q^{45} +(2.65024 - 1.53012i) q^{46} +(4.60507 + 2.65874i) q^{47} -1.35456i q^{48} -14.1139i q^{50} +(1.45964 + 0.842726i) q^{51} +(3.19092 + 5.52684i) q^{52} +(3.73236 + 6.46464i) q^{53} +(3.88636 - 6.73137i) q^{54} +(6.53660 - 9.15907i) q^{55} +3.47019i q^{57} +(5.37636 - 9.31212i) q^{58} +(0.610575 - 0.352516i) q^{59} +(2.93818 + 5.08907i) q^{60} +(6.11882 - 10.5981i) q^{61} -6.38185 q^{62} +12.2756 q^{64} +(6.94577 + 4.01014i) q^{65} +(-0.443300 + 4.59166i) q^{66} +(-7.98762 - 13.8350i) q^{67} +(-3.54596 + 6.14178i) q^{68} +0.905690i q^{69} +3.81089 q^{71} +(3.39981 + 1.96288i) q^{72} +(-0.618061 - 1.07051i) q^{73} +(2.62700 - 1.51670i) q^{74} +(3.61745 + 2.08854i) q^{75} -14.6016 q^{76} -3.28799 q^{78} +(-2.08631 - 1.20453i) q^{79} +(6.20327 - 3.58146i) q^{80} +(-2.73236 - 4.73259i) q^{81} +(-13.3145 - 7.68715i) q^{82} -12.3924 q^{83} +8.91266i q^{85} +(-5.14400 + 8.90966i) q^{86} +(1.59116 + 2.75596i) q^{87} +(-5.00704 - 0.483402i) q^{88} +(2.33929 + 1.35059i) q^{89} +19.0373 q^{90} -3.81089 q^{92} +(0.944368 - 1.63569i) q^{93} +(-5.76378 - 9.98317i) q^{94} +(-15.8919 + 9.17517i) q^{95} +(-2.44135 + 4.22854i) q^{96} -1.92477i q^{97} +(6.98762 + 4.98689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 4 * q^4 - 4 * q^9	$ 12 q + 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} + 18 q^{12} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} - 18 q^{26} - 6 q^{31} - 18 q^{33} - 12 q^{36} + 16 q^{37} + 48 q^{38} + 20 q^{44} - 54 q^{45} + 18 q^{47} - 2 q^{53} - 6 q^{58} + 12 q^{59} + 28 q^{64} + 42 q^{66} - 24 q^{67} + 20 q^{71} + 78 q^{75} + 8 q^{78} - 30 q^{80} + 14 q^{81} - 54 q^{82} - 38 q^{86} - 4 q^{88} + 66 q^{89} - 20 q^{92} + 12 q^{93} + 12 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 + 18 * q^12 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 - 18 * q^26 - 6 * q^31 - 18 * q^33 - 12 * q^36 + 16 * q^37 + 48 * q^38 + 20 * q^44 - 54 * q^45 + 18 * q^47 - 2 * q^53 - 6 * q^58 + 12 * q^59 + 28 * q^64 + 42 * q^66 - 24 * q^67 + 20 * q^71 + 78 * q^75 + 8 * q^78 - 30 * q^80 + 14 * q^81 - 54 * q^82 - 38 * q^86 - 4 * q^88 + 66 * q^89 - 20 * q^92 + 12 * q^93 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.87742	−	1.08393i	−1.32754	−	0.766455i	−0.342621	−	0.939474i	$-0.611315\pi$
$2$	−1.87742	−	1.08393i	−1.32754	−	0.766455i	−0.984919	+	0.173019i	$0.944648\pi$
$3$	0.555632	−	0.320794i	0.320794	−	0.185211i	−0.330952	−	0.943648i	$-0.607370\pi$
$3$	0.555632	−	0.320794i	0.320794	−	0.185211i	0.651747	+	0.758437i	$0.274037\pi$
$4$	1.34981	+	2.33795i	0.674907	+	1.16897i
$5$	2.93818	+	1.69636i	1.31399	+	0.758634i	0.982755	−	0.184913i	$-0.0592003\pi$
$5$	2.93818	+	1.69636i	1.31399	+	0.758634i	0.331238	+	0.943547i	$0.392534\pi$
$6$	−1.39088			−0.567823
$7$		0			0
$7$		0			0
$8$		−	1.51670i		−	0.536234i
$9$	−1.29418	+	2.24159i	−0.431394	+	0.747196i
$10$	−3.67747	−	6.36957i	−1.16292	−	2.01423i
$11$	0.318720	−	3.30128i	0.0960977	−	0.995372i
$11$	0.318720	−	3.30128i	0.0960977	−	0.995372i
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	2.36397			0.655648			0.327824	−	0.944739i	$-0.393685\pi$
$13$	2.36397			0.655648			0.327824	+	0.944739i	$0.393685\pi$
$14$		0			0
$15$	2.17673			0.562029
$16$	1.05563	−	1.82841i	0.263908	−	0.457102i
$17$	1.31350	+	2.27505i	0.318570	+	0.551780i	0.980190	−	0.198060i	$-0.0634640\pi$
$17$	1.31350	+	2.27505i	0.318570	+	0.551780i	−0.661620	+	0.749840i	$0.730131\pi$
$18$	4.85946	−	2.80561i	1.14538	−	0.661288i
$19$	−2.70437	+	4.68411i	−0.620426	+	1.07461i	0.368980	+	0.929437i	$0.379707\pi$
$19$	−2.70437	+	4.68411i	−0.620426	+	1.07461i	−0.989406	+	0.145172i	$0.953626\pi$
$20$			9.15907i			2.04803i
$21$		0			0
$22$	−4.17673	+	5.85242i	−0.890481	+	1.24774i
$23$	−0.705818	+	1.22251i	−0.147173	+	0.254912i	−0.930182	−	0.367100i	$-0.880351\pi$
$23$	−0.705818	+	1.22251i	−0.147173	+	0.254912i	0.783008	+	0.622011i	$0.213684\pi$
$24$	−0.486548	−	0.842726i	−0.0993162	−	0.172021i
$25$	3.25526	+	5.63828i	0.651052	+	1.12766i
$26$	−4.43818	−	2.56238i	−0.870398	−	0.502525i
$27$			3.58543i			0.690017i
$28$		0			0
$29$			4.96005i			0.921059i	0.887644	+	0.460529i	$0.152340\pi$
$29$			4.96005i			0.921059i	−0.887644	+	0.460529i	$0.847660\pi$
$30$	−4.08664	−	2.35942i	−0.746115	−	0.430770i
$31$	2.54944	−	1.47192i	0.457893	−	0.264365i	−0.253265	−	0.967397i	$-0.581504\pi$
$31$	2.54944	−	1.47192i	0.457893	−	0.264365i	0.711158	+	0.703032i	$0.248171\pi$
$32$	−6.59074	+	3.80516i	−1.16509	+	0.672664i
$33$	−0.881939	−	1.93654i	−0.153526	−	0.337108i
$34$		−	5.69497i		−	0.976679i
$35$		0			0
$36$	−6.98762			−1.16460
$37$	−0.699628	+	1.21179i	−0.115018	+	0.199217i	−0.917787	−	0.397073i	$-0.870026\pi$
$37$	−0.699628	+	1.21179i	−0.115018	+	0.199217i	0.802769	+	0.596290i	$0.203359\pi$
$38$	10.1545	−	5.86271i	1.64728	−	0.951058i
$39$	1.31350	−	0.758349i	0.210328	−	0.121433i
$40$	2.57286	−	4.45633i	0.406805	−	0.704607i
$41$	7.09192			1.10757			0.553786	−	0.832659i	$-0.313183\pi$
$41$	7.09192			1.10757			0.553786	+	0.832659i	$0.313183\pi$
$42$		0			0
$43$		−	4.74568i		−	0.723710i	−0.932234	−	0.361855i	$-0.882144\pi$
$43$		−	4.74568i		−	0.723710i	0.932234	−	0.361855i	$-0.117856\pi$
$44$	8.14842	−	3.71096i	1.22842	−	0.559448i
$45$	−7.60507	+	4.39079i	−1.13370	+	0.654541i
$46$	2.65024	−	1.53012i	0.390756	−	0.225603i
$47$	4.60507	+	2.65874i	0.671719	+	0.387817i	0.796728	−	0.604338i	$-0.206563\pi$
$47$	4.60507	+	2.65874i	0.671719	+	0.387817i	−0.125009	+	0.992156i	$0.539896\pi$
$48$		−	1.35456i		−	0.195514i
$49$		0			0
$50$		−	14.1139i		−	1.99601i
$51$	1.45964	+	0.842726i	0.204391	+	0.118005i
$52$	3.19092	+	5.52684i	0.442501	+	0.766435i
$53$	3.73236	+	6.46464i	0.512679	+	0.887986i	0.999892	+	0.0147030i	$0.00468026\pi$
$53$	3.73236	+	6.46464i	0.512679	+	0.887986i	−0.487213	+	0.873283i	$0.661986\pi$
$54$	3.88636	−	6.73137i	0.528867	−	0.916024i
$55$	6.53660	−	9.15907i	0.881395	−	1.23501i
$56$		0			0
$57$			3.47019i			0.459638i
$58$	5.37636	−	9.31212i	0.705950	−	1.22274i
$59$	0.610575	−	0.352516i	0.0794902	−	0.0458937i	−0.459728	−	0.888060i	$-0.652053\pi$
$59$	0.610575	−	0.352516i	0.0794902	−	0.0458937i	0.539218	+	0.842166i	$0.318720\pi$
$60$	2.93818	+	5.08907i	0.379317	+	0.656997i
$61$	6.11882	−	10.5981i	0.783435	−	1.35695i	−0.146495	−	0.989211i	$-0.546799\pi$
$61$	6.11882	−	10.5981i	0.783435	−	1.35695i	0.929930	−	0.367737i	$-0.119867\pi$
$62$	−6.38185			−0.810495
$63$		0			0
$64$	12.2756			1.53445
$65$	6.94577	+	4.01014i	0.861517	+	0.497397i
$66$	−0.443300	+	4.59166i	−0.0545665	+	0.565195i
$67$	−7.98762	−	13.8350i	−0.975843	−	1.69021i	−0.677124	−	0.735869i	$-0.736774\pi$
$67$	−7.98762	−	13.8350i	−0.975843	−	1.69021i	−0.298719	−	0.954341i	$-0.596559\pi$
$68$	−3.54596	+	6.14178i	−0.430011	+	0.744800i
$69$			0.905690i			0.109032i
$70$		0			0
$71$	3.81089			0.452270			0.226135	−	0.974096i	$-0.427391\pi$
$71$	3.81089			0.452270			0.226135	+	0.974096i	$0.427391\pi$
$72$	3.39981	+	1.96288i	0.400672	+	0.231328i
$73$	−0.618061	−	1.07051i	−0.0723385	−	0.125294i	0.827587	−	0.561337i	$-0.189713\pi$
$73$	−0.618061	−	1.07051i	−0.0723385	−	0.125294i	−0.899926	+	0.436043i	$0.856380\pi$
$74$	2.62700	−	1.51670i	0.305382	−	0.176313i
$75$	3.61745	+	2.08854i	0.417708	+	0.241164i
$76$	−14.6016			−1.67492
$77$		0			0
$78$	−3.28799			−0.372292
$79$	−2.08631	−	1.20453i	−0.234729	−	0.135521i	0.378023	−	0.925796i	$-0.376604\pi$
$79$	−2.08631	−	1.20453i	−0.234729	−	0.135521i	−0.612752	+	0.790276i	$0.709937\pi$
$80$	6.20327	−	3.58146i	0.693547	−	0.400419i
$81$	−2.73236	−	4.73259i	−0.303596	−	0.525843i
$82$	−13.3145	−	7.68715i	−1.47034	−	0.848904i
$83$	−12.3924			−1.36024			−0.680121	−	0.733100i	$-0.738073\pi$
$83$	−12.3924			−1.36024			−0.680121	+	0.733100i	$0.738073\pi$
$84$		0			0
$85$			8.91266i			0.966713i
$86$	−5.14400	+	8.90966i	−0.554691	+	0.960754i
$87$	1.59116	+	2.75596i	0.170590	+	0.295470i
$88$	−5.00704	−	0.483402i	−0.533752	−	0.0515308i
$89$	2.33929	+	1.35059i	0.247965	+	0.143162i	0.618832	−	0.785523i	$-0.287606\pi$
$89$	2.33929	+	1.35059i	0.247965	+	0.143162i	−0.370867	+	0.928686i	$0.620940\pi$
$90$	19.0373			2.00670
$91$		0			0
$92$	−3.81089			−0.397313
$93$	0.944368	−	1.63569i	0.0979264	−	0.169613i
$94$	−5.76378	−	9.98317i	−0.594489	−	1.02969i
$95$	−15.8919	+	9.17517i	−1.63047	+	0.941353i
$96$	−2.44135	+	4.22854i	−0.249169	+	0.431574i
$97$		−	1.92477i		−	0.195430i	−0.995214	−	0.0977152i	$-0.968847\pi$
$97$		−	1.92477i		−	0.195430i	0.995214	−	0.0977152i	$-0.0311534\pi$
$98$		0			0
$99$	6.98762	+	4.98689i	0.702282	+	0.501201i
$100$	−8.78799	+	15.2212i	−0.878799	+	1.52212i
$101$	8.96934	+	15.5354i	0.892483	+	1.54583i	0.836889	+	0.547372i	$0.184372\pi$
$101$	8.96934	+	15.5354i	0.892483	+	1.54583i	0.0555932	+	0.998453i	$0.482295\pi$
$102$	−1.82691	−	3.16431i	−0.180891	−	0.313313i
$103$	−0.0185696	−	0.0107211i	−0.00182971	−	0.00105639i	0.499085	−	0.866553i	$-0.333670\pi$
$103$	−0.0185696	−	0.0107211i	−0.00182971	−	0.00105639i	−0.500915	+	0.865497i	$0.667003\pi$
$104$		−	3.58543i		−	0.351580i
$105$		0			0
$106$		−	16.1825i		−	1.57178i
$107$	7.06867	+	4.08110i	0.683355	+	0.394535i	0.801118	−	0.598507i	$-0.204239\pi$
$107$	7.06867	+	4.08110i	0.683355	+	0.394535i	−0.117763	+	0.993042i	$0.537572\pi$
$108$	−8.38255	+	4.83967i	−0.806611	+	0.465697i
$109$	10.5312	−	6.08021i	1.00871	−	0.582378i	0.0978956	−	0.995197i	$-0.468789\pi$
$109$	10.5312	−	6.08021i	1.00871	−	0.582378i	0.910813	+	0.412818i	$0.135456\pi$
$110$	−22.1998	+	10.1102i	−2.11667	+	0.963973i
$111$			0.897747i			0.0852104i
$112$		0			0
$113$	−12.3869			−1.16526			−0.582630	−	0.812738i	$-0.697976\pi$
$113$	−12.3869			−1.16526			−0.582630	+	0.812738i	$0.697976\pi$
$114$	3.76145	−	6.51502i	0.352292	−	0.610188i
$115$	−4.14764	+	2.39464i	−0.386769	+	0.223301i
$116$	−11.5963	+	6.69515i	−1.07669	+	0.621629i
$117$	−3.05941	+	5.29905i	−0.282843	+	0.489898i
$118$	−1.52841			−0.140702
$119$		0			0
$120$		−	3.30144i		−	0.301379i
$121$	−10.7968	−	2.10436i	−0.981530	−	0.191306i
$122$	−22.9752	+	13.2648i	−2.08008	+	1.20094i
$123$	3.94050	−	2.27505i	0.355303	−	0.205134i
$124$	6.88255	+	3.97364i	0.618071	+	0.356843i
$125$			5.12477i			0.458373i
$126$		0			0
$127$		−	14.2371i		−	1.26333i	−0.775240	−	0.631667i	$-0.782371\pi$
$127$		−	14.2371i		−	1.26333i	0.775240	−	0.631667i	$-0.217629\pi$
$128$	−9.86506	−	5.69559i	−0.871956	−	0.503424i
$129$	−1.52239	−	2.63685i	−0.134039	−	0.232162i
$130$	−8.69344	−	15.0575i	−0.762465	−	1.32063i
$131$	2.79638	−	4.84348i	0.244321	−	0.423177i	−0.717619	−	0.696436i	$-0.754768\pi$
$131$	2.79638	−	4.84348i	0.244321	−	0.423177i	0.961941	+	0.273259i	$0.0881015\pi$
$132$	3.33707	−	4.67589i	0.290454	−	0.406984i
$133$		0			0
$134$			34.6321i			2.99176i
$135$	−6.08217	+	10.5346i	−0.523470	+	0.906677i
$136$	3.45056	−	1.99218i	0.295883	−	0.170828i
$137$	1.42147	+	2.46205i	0.121444	+	0.210348i	0.920337	−	0.391125i	$-0.127914\pi$
$137$	1.42147	+	2.46205i	0.121444	+	0.210348i	−0.798893	+	0.601473i	$0.794581\pi$
$138$	0.981705	−	1.70036i	0.0835683	−	0.144745i
$139$	6.90790			0.585920			0.292960	−	0.956125i	$-0.405360\pi$
$139$	6.90790			0.585920			0.292960	+	0.956125i	$0.405360\pi$
$140$		0			0
$141$	3.41164			0.287312
$142$	−7.15466	−	4.13075i	−0.600406	−	0.346644i
$143$	0.753445	−	7.80412i	0.0630062	−	0.652613i
$144$	2.73236	+	4.73259i	0.227697	+	0.394382i
$145$	−8.41402	+	14.5735i	−0.698747	+	1.21026i
$146$			2.67974i			0.221777i
$147$		0			0
$148$	−3.77747			−0.310506
$149$	−8.86270	−	5.11688i	−0.726060	−	0.419191i	0.0909187	−	0.995858i	$-0.471020\pi$
$149$	−8.86270	−	5.11688i	−0.726060	−	0.419191i	−0.816979	+	0.576667i	$0.804353\pi$
$150$	−4.52766	−	7.84214i	−0.369682	−	0.640308i
$151$	−1.29026	+	0.744930i	−0.105000	+	0.0606216i	−0.551580	−	0.834122i	$-0.685975\pi$
$151$	−1.29026	+	0.744930i	−0.105000	+	0.0606216i	0.446581	+	0.894743i	$0.352642\pi$
$152$	7.10439	+	4.10172i	0.576242	+	0.332693i
$153$	−6.79963			−0.549717
$154$		0			0
$155$	9.98762			0.802225
$156$	3.54596	+	2.04726i	0.283904	+	0.163912i
$157$	−14.3640	+	8.29305i	−1.14637	+	0.661857i	−0.948000	−	0.318270i	$-0.896898\pi$
$157$	−14.3640	+	8.29305i	−1.14637	+	0.661857i	−0.198370	+	0.980127i	$0.563565\pi$
$158$	2.61126	+	4.52284i	0.207741	+	0.359818i
$159$	4.14764	+	2.39464i	0.328929	+	0.189907i
$160$	−25.8197			−2.04122
$161$		0			0
$162$			11.8468i			0.930770i
$163$	−4.38874	+	7.60151i	−0.343752	+	0.595396i	−0.985126	−	0.171832i	$-0.945031\pi$
$163$	−4.38874	+	7.60151i	−0.343752	+	0.595396i	0.641374	+	0.767228i	$0.278365\pi$
$164$	9.57277	+	16.5805i	0.747508	+	1.29472i
$165$	0.693767	−	7.18598i	0.0540097	−	0.559428i
$166$	23.2658	+	13.4325i	1.80577	+	1.04256i
$167$	−13.8451			−1.07136			−0.535681	−	0.844420i	$-0.679945\pi$
$167$	−13.8451			−1.07136			−0.535681	+	0.844420i	$0.679945\pi$
$168$		0			0
$169$	−7.41164			−0.570126
$170$	9.66071	−	16.7328i	0.740942	−	1.28335i
$171$	−6.99991	−	12.1242i	−0.535296	−	0.927160i
$172$	11.0952	−	6.40579i	0.845998	−	0.488437i
$173$	3.25367	−	5.63552i	0.247372	−	0.428460i	−0.715424	−	0.698691i	$-0.753766\pi$
$173$	3.25367	−	5.63552i	0.247372	−	0.428460i	0.962796	+	0.270230i	$0.0870998\pi$
$174$		−	6.89882i		−	0.522998i
$175$		0			0
$176$	−5.69963	−	4.06768i	−0.429626	−	0.306613i
$177$	0.226170	−	0.391738i	0.0170000	−	0.0294449i
$178$	−2.92790	−	5.07127i	−0.219455	−	0.380108i
$179$	2.23236	+	3.86656i	0.166854	+	0.289000i	0.937312	−	0.348491i	$-0.113306\pi$
$179$	2.23236	+	3.86656i	0.166854	+	0.289000i	−0.770458	+	0.637491i	$0.779972\pi$
$180$	−20.5309	−	11.8535i	−1.53028	−	0.883508i
$181$			2.23087i			0.165819i	0.996557	+	0.0829095i	$0.0264213\pi$
$181$			2.23087i			0.165819i	−0.996557	+	0.0829095i	$0.973579\pi$
$182$		0			0
$183$		−	7.85153i		−	0.580402i
$184$	1.85418	+	1.07051i	0.136692	+	0.0789192i
$185$	−4.11126	+	2.37364i	−0.302266	+	0.174513i
$186$	−3.54596	+	2.04726i	−0.260002	+	0.150112i
$187$	7.92919	−	3.61112i	0.579840	−	0.264071i
$188$			14.3552i			1.04696i
$189$		0			0
$190$	39.7810			2.88602
$191$	6.86584	−	11.8920i	0.496794	−	0.860473i	−0.503199	−	0.864171i	$-0.667844\pi$
$191$	6.86584	−	11.8920i	0.496794	−	0.860473i	0.999993	+	0.00369752i	$0.00117696\pi$
$192$	6.82072	−	3.93795i	0.492243	−	0.284197i
$193$	−10.7634	+	6.21423i	−0.774764	+	0.447310i	−0.834571	−	0.550900i	$-0.814285\pi$
$193$	−10.7634	+	6.21423i	−0.774764	+	0.447310i	0.0598075	+	0.998210i	$0.480951\pi$
$194$	−2.08631	+	3.61360i	−0.149789	+	0.259442i
$195$	5.14572			0.368493
$196$		0			0
$197$		−	24.7576i		−	1.76391i	−0.471335	−	0.881954i	$-0.656228\pi$
$197$		−	24.7576i		−	1.76391i	0.471335	−	0.881954i	$-0.343772\pi$
$198$	−7.71328	−	16.9366i	−0.548159	−	1.20363i
$199$	14.5123	−	8.37868i	1.02875	−	0.593949i	0.112124	−	0.993694i	$-0.464235\pi$
$199$	14.5123	−	8.37868i	1.02875	−	0.593949i	0.916626	+	0.399745i	$0.130901\pi$
$200$	8.55156	−	4.93725i	0.604687	−	0.349116i
$201$	−8.87636	−	5.12477i	−0.626090	−	0.361473i
$202$		−	38.8886i		−	2.73619i
$203$		0			0
$204$			4.55009i			0.318570i
$205$	20.8373	+	12.0304i	1.45534	+	0.840242i
$206$	0.0232420	+	0.0402563i	0.00161934	+	0.00280479i
$207$	−1.82691	−	3.16431i	−0.126979	−	0.219935i
$208$	2.49548	−	4.32231i	0.173031	−	0.299698i
$209$	14.6016	+	10.4208i	1.01001	+	0.720822i
$210$		0			0
$211$		−	2.06857i		−	0.142406i	−0.997462	−	0.0712032i	$-0.977316\pi$
$211$		−	2.06857i		−	0.142406i	0.997462	−	0.0712032i	$-0.0226839\pi$
$212$	−10.0760	+	17.4521i	−0.692021	+	1.19862i
$213$	2.11745	−	1.22251i	0.145086	−	0.0837652i
$214$	−8.84727	−	15.3239i	−0.604787	−	1.04752i
$215$	8.05038	−	13.9437i	0.549031	−	0.950950i
$216$	5.43801			0.370010
$217$		0			0
$218$	−26.3621			−1.78547
$219$	−0.686829	−	0.396541i	−0.0464116	−	0.0267957i
$220$	30.2366	+	2.91918i	2.03855	+	0.196811i
$221$	3.10507	+	5.37815i	0.208870	+	0.361773i
$222$	0.973096	−	1.68545i	0.0653099	−	0.113120i
$223$		−	2.50291i		−	0.167607i	−0.996482	−	0.0838037i	$-0.973293\pi$
$223$		−	2.50291i		−	0.167607i	0.996482	−	0.0838037i	$-0.0267069\pi$
$224$		0			0
$225$	−16.8516			−1.12344
$226$	23.2554	+	13.4265i	1.54693	+	0.893119i
$227$	7.90423	+	13.6905i	0.524622	+	0.908673i	0.999589	+	0.0286689i	$0.00912684\pi$
$227$	7.90423	+	13.6905i	0.524622	+	0.908673i	−0.474967	+	0.880004i	$0.657540\pi$
$228$	−8.11312	+	4.68411i	−0.537305	+	0.310213i
$229$	15.5989	+	9.00602i	1.03080	+	0.595135i	0.917215	−	0.398393i	$-0.130432\pi$
$229$	15.5989	+	9.00602i	1.03080	+	0.595135i	0.113589	+	0.993528i	$0.463765\pi$
$230$	10.3825			0.684602
$231$		0			0
$232$	7.52290			0.493903
$233$	4.44426	+	2.56590i	0.291153	+	0.168097i	0.638462	−	0.769653i	$-0.279571\pi$
$233$	4.44426	+	2.56590i	0.291153	+	0.168097i	−0.347309	+	0.937751i	$0.612904\pi$
$234$	11.4876	−	6.63238i	0.750969	−	0.433572i
$235$	9.02035	+	15.6237i	0.588423	+	1.01918i
$236$	1.64833	+	0.951662i	0.107297	+	0.0619479i
$237$	−1.54563			−0.100400
$238$		0			0
$239$			2.89148i			0.187034i	0.995618	+	0.0935171i	$0.0298110\pi$
$239$			2.89148i			0.187034i	−0.995618	+	0.0935171i	$0.970189\pi$
$240$	2.29782	−	3.97995i	0.148324	−	0.256905i
$241$	−11.8826	−	20.5813i	−0.765426	−	1.32576i	−0.940021	−	0.341116i	$-0.889195\pi$
$241$	−11.8826	−	20.5813i	−0.765426	−	1.32576i	0.174595	−	0.984640i	$-0.444138\pi$
$242$	17.9893	+	15.6538i	1.15639	+	1.00627i
$243$	−12.3516	−	7.13120i	−0.792355	−	0.457467i
$244$	33.0371			2.11498
$245$		0			0
$246$	−9.86398			−0.628904
$247$	−6.39307	+	11.0731i	−0.406781	+	0.704565i
$248$	−2.23246	−	3.86673i	−0.141761	−	0.245538i
$249$	−6.88561	+	3.97541i	−0.436358	+	0.251931i
$250$	5.55489	−	9.62136i	0.351322	−	0.608508i
$251$			8.92436i			0.563300i	0.959517	+	0.281650i	$0.0908818\pi$
$251$			8.92436i			0.563300i	−0.959517	+	0.281650i	$0.909118\pi$
$252$		0			0
$253$	3.81089	+	2.71974i	0.239589	+	0.170989i
$254$	−15.4320	+	26.7290i	−0.968289	+	1.67713i
$255$	2.85913	+	4.95216i	0.179046	+	0.310116i
$256$	0.0716537	+	0.124108i	0.00447836	+	0.00775674i
$257$	−20.0920	−	11.6001i	−1.25330	−	0.723596i	−0.281541	−	0.959549i	$-0.590845\pi$
$257$	−20.0920	−	11.6001i	−1.25330	−	0.723596i	−0.971764	+	0.235953i	$0.924179\pi$
$258$			6.60066i			0.410939i
$259$		0			0
$260$			21.6518i			1.34279i
$261$	−11.1184	−	6.41921i	−0.688212	−	0.397339i
$262$	−10.5000	+	6.06218i	−0.648692	+	0.374523i
$263$	−2.95879	+	1.70826i	−0.182447	+	0.105336i	−0.588442	−	0.808540i	$-0.700258\pi$
$263$	−2.95879	+	1.70826i	−0.182447	+	0.105336i	0.405995	+	0.913875i	$0.366925\pi$
$264$	−2.93714	+	1.33764i	−0.180769	+	0.0823258i
$265$			25.3257i			1.55574i
$266$		0			0
$267$	1.73305			0.106061
$268$	21.5636	−	37.3493i	1.31721	−	2.28147i
$269$	4.22803	−	2.44105i	0.257788	−	0.148834i	−0.365537	−	0.930797i	$-0.619115\pi$
$269$	4.22803	−	2.44105i	0.257788	−	0.148834i	0.623325	+	0.781963i	$0.285781\pi$
$270$	22.8376	−	13.1853i	1.38985	−	0.802433i
$271$	8.89196	−	15.4013i	0.540148	−	0.935564i	−0.458747	−	0.888567i	$-0.651701\pi$
$271$	8.89196	−	15.4013i	0.540148	−	0.935564i	0.998895	−	0.0469972i	$-0.0149652\pi$
$272$	5.54629			0.336293
$273$		0			0
$274$		−	6.16309i		−	0.372326i
$275$	19.6510	−	8.94948i	1.18500	−	0.539674i
$276$	−2.11745	+	1.22251i	−0.127456	+	0.0735866i
$277$	−17.2914	+	9.98317i	−1.03894	+	0.599830i	−0.919532	−	0.393015i	$-0.871432\pi$
$277$	−17.2914	+	9.98317i	−1.03894	+	0.599830i	−0.119405	+	0.992846i	$0.538099\pi$
$278$	−12.9691	−	7.48768i	−0.777832	−	0.449081i
$279$			7.61974i			0.456182i
$280$		0			0
$281$			5.46631i			0.326093i	0.986618	+	0.163047i	$0.0521321\pi$
$281$			5.46631i			0.326093i	−0.986618	+	0.163047i	$0.947868\pi$
$282$	−6.40509	−	3.69798i	−0.381417	−	0.220211i
$283$	−7.31544	−	12.6707i	−0.434858	−	0.753196i	0.562426	−	0.826847i	$-0.309868\pi$
$283$	−7.31544	−	12.6707i	−0.434858	−	0.753196i	−0.997284	+	0.0736518i	$0.976535\pi$
$284$	5.14400	+	8.90966i	0.305240	+	0.528691i
$285$	−5.88669	+	10.1960i	−0.348697	+	0.603961i
$286$	−9.87367	+	13.8350i	−0.583842	+	0.818079i
$287$		0			0
$288$		−	19.6983i		−	1.16073i
$289$	5.04944	−	8.74589i	0.297026	−	0.514464i
$290$	31.5934	−	18.2404i	1.85523	−	1.07112i
$291$	−0.617454	−	1.06946i	−0.0361958	−	0.0626930i
$292$	1.66853	−	2.88999i	0.0976436	−	0.169124i
$293$	−19.1455			−1.11849			−0.559247	−	0.829001i	$-0.688910\pi$
$293$	−19.1455			−1.11849			−0.559247	+	0.829001i	$0.688910\pi$
$294$		0			0
$295$	2.39197			0.139266
$296$	1.83792	+	1.06112i	0.106827	+	0.0616766i
$297$	11.8365	+	1.14275i	0.686823	+	0.0663090i
$298$	11.0927	+	19.2131i	0.642583	+	1.11299i
$299$	−1.66853	+	2.88999i	−0.0964938	+	0.167132i
$300$			11.2766i			0.651052i
$301$		0			0
$302$	3.22981			0.185855
$303$	9.96731	+	5.75463i	0.572607	+	0.330595i
$304$	5.70965	+	9.88940i	0.327471	+	0.567196i
$305$	35.9564	−	20.7594i	2.05886	−	1.18868i
$306$	12.7658	+	7.37033i	0.729771	+	0.421334i
$307$	−6.93716			−0.395925			−0.197962	−	0.980210i	$-0.563432\pi$
$307$	−6.93716			−0.395925			−0.197962	+	0.980210i	$0.563432\pi$
$308$		0			0
$309$	−0.0137571			−0.000782616
$310$	−18.7510	−	10.8259i	−1.06499	−	0.614869i
$311$	−23.0371	+	13.3005i	−1.30631	+	0.754200i	−0.981479	−	0.191572i	$-0.938642\pi$
$311$	−23.0371	+	13.3005i	−1.30631	+	0.754200i	−0.324833	+	0.945771i	$0.605308\pi$
$312$	−1.15019	−	1.99218i	−0.0651165	−	0.112785i
$313$	−20.3454	−	11.7464i	−1.14999	−	0.663947i	−0.201105	−	0.979570i	$-0.564453\pi$
$313$	−20.3454	−	11.7464i	−1.14999	−	0.663947i	−0.948885	+	0.315622i	$0.897787\pi$
$314$	35.9564			2.02914
$315$		0			0
$316$		−	6.50359i		−	0.365855i
$317$	12.7305	−	22.0499i	0.715016	−	1.23844i	−0.247937	−	0.968776i	$-0.579753\pi$
$317$	12.7305	−	22.0499i	0.715016	−	1.23844i	0.962953	−	0.269668i	$-0.0869140\pi$
$318$	−5.19125	−	8.99151i	−0.291111	−	0.504219i
$319$	16.3745	+	1.58087i	0.916796	+	0.0885116i
$320$	36.0679	+	20.8238i	2.01626	+	1.16409i
$321$	5.23678			0.292288
$322$		0			0
$323$	−14.2088			−0.790597
$324$	7.37636	−	12.7762i	0.409798	−	0.709790i
$325$	7.69534	+	13.3287i	0.426861	+	0.739345i
$326$	16.4790	−	9.51418i	0.912689	−	0.526941i
$327$	3.90099	−	6.75672i	0.215725	−	0.373647i
$328$		−	10.7563i		−	0.593917i
$329$		0			0
$330$	−9.09160	+	12.7391i	−0.500476	+	0.701266i
$331$	−5.97710	+	10.3526i	−0.328531	+	0.569033i	−0.982221	−	0.187730i	$-0.939887\pi$
$331$	−5.97710	+	10.3526i	−0.328531	+	0.569033i	0.653689	+	0.756763i	$0.273220\pi$
$332$	−16.7274	−	28.9728i	−0.918037	−	1.59009i
$333$	−1.81089	−	3.13656i	−0.0992363	−	0.171882i
$334$	25.9930	+	15.0071i	1.42228	+	0.821152i
$335$		−	54.1995i		−	2.96123i
$336$		0			0
$337$			8.06590i			0.439378i	0.975570	+	0.219689i	$0.0705042\pi$
$337$			8.06590i			0.439378i	−0.975570	+	0.219689i	$0.929496\pi$
$338$	13.9148	+	8.03370i	0.756864	+	0.436976i
$339$	−6.88255	+	3.97364i	−0.373809	+	0.215818i
$340$	−20.8373	+	12.0304i	−1.13006	+	0.652442i
$341$	−4.04666	−	8.88554i	−0.219139	−	0.481179i
$342$			30.3497i			1.64112i
$343$		0			0
$344$	−7.19777			−0.388078
$345$	−1.53637	+	2.66108i	−0.0827156	+	0.143268i
$346$	−12.2170	+	7.05350i	−0.656791	+	0.379199i
$347$	−1.66853	+	0.963329i	−0.0895716	+	0.0517142i	−0.544117	−	0.839010i	$-0.683135\pi$
$347$	−1.66853	+	0.963329i	−0.0895716	+	0.0517142i	0.454545	+	0.890724i	$0.349802\pi$
$348$	−4.29553	+	7.44008i	−0.230265	+	0.398830i
$349$	−9.68965			−0.518675			−0.259337	−	0.965787i	$-0.583504\pi$
$349$	−9.68965			−0.518675			−0.259337	+	0.965787i	$0.583504\pi$
$350$		0			0
$351$			8.47586i			0.452408i
$352$	10.4613	+	22.9706i	0.557589	+	1.22434i
$353$	18.0748	−	10.4355i	0.962025	−	0.555426i	0.0652295	−	0.997870i	$-0.479222\pi$
$353$	18.0748	−	10.4355i	0.962025	−	0.555426i	0.896796	+	0.442445i	$0.145889\pi$
$354$	−0.849235	+	0.490306i	−0.0451363	+	0.0260595i
$355$	11.1971	+	6.46464i	0.594279	+	0.343107i
$356$			7.29219i			0.386485i
$357$		0			0
$358$		−	9.67890i		−	0.511546i
$359$	−19.8951	−	11.4864i	−1.05002	−	0.606231i	−0.127368	−	0.991856i	$-0.540653\pi$
$359$	−19.8951	−	11.4864i	−1.05002	−	0.606231i	−0.922656	+	0.385624i	$0.873986\pi$
$360$	6.65950	+	11.5346i	0.350987	+	0.607927i
$361$	−5.12729	−	8.88072i	−0.269857	−	0.467406i
$362$	2.41811	−	4.18828i	0.127093	−	0.220131i
$363$	−6.67414	+	2.29431i	−0.350301	+	0.120420i
$364$		0			0
$365$		−	4.19381i		−	0.219514i
$366$	−8.51052	+	14.7407i	−0.444852	+	0.770506i
$367$	13.9821	−	8.07258i	0.729861	−	0.421385i	−0.0885105	−	0.996075i	$-0.528211\pi$
$367$	13.9821	−	8.07258i	0.729861	−	0.421385i	0.818371	+	0.574690i	$0.194877\pi$
$368$	1.49017	+	2.58105i	0.0776804	+	0.134546i
$369$	−9.17823	+	15.8972i	−0.477800	+	0.827573i
$370$	10.2914			0.535027
$371$		0			0
$372$	5.09888			0.264365
$373$	−20.0482	−	11.5749i	−1.03806	−	0.599323i	−0.118776	−	0.992921i	$-0.537897\pi$
$373$	−20.0482	−	11.5749i	−1.03806	−	0.599323i	−0.919283	+	0.393598i	$0.871230\pi$
$374$	−18.8007	−	1.81510i	−0.972159	−	0.0938566i
$375$	1.64400	+	2.84748i	0.0848956	+	0.147043i
$376$	4.03251	−	6.98451i	0.207961	−	0.360198i
$377$			11.7254i			0.603890i
$378$		0			0
$379$	17.4968			0.898748			0.449374	−	0.893344i	$-0.351647\pi$
$379$	17.4968			0.898748			0.449374	+	0.893344i	$0.351647\pi$
$380$	−42.9021	−	24.7696i	−2.20083	−	1.27065i
$381$	−4.56717	−	7.91056i	−0.233983	−	0.405270i
$382$	−25.7802	+	14.8842i	−1.31903	+	0.761541i
$383$	−8.40723	−	4.85392i	−0.429589	−	0.248024i	0.269582	−	0.962977i	$-0.413114\pi$
$383$	−8.40723	−	4.85392i	−0.429589	−	0.248024i	−0.699172	+	0.714954i	$0.746448\pi$
$384$	−7.30846			−0.372958
$385$		0			0
$386$	26.9432			1.37137
$387$	10.6379	+	6.14178i	0.540754	+	0.312204i
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	−7.82505	−	13.5534i	−0.396746	−	0.687184i	0.596576	−	0.802556i	$-0.296527\pi$
$389$	−7.82505	−	13.5534i	−0.396746	−	0.687184i	−0.993322	+	0.115372i	$0.963194\pi$
$390$	−9.66071	−	5.57761i	−0.489189	−	0.282433i
$391$	−3.70836			−0.187540
$392$		0			0
$393$		−	3.58826i		−	0.181004i
$394$	−26.8356	+	46.4806i	−1.35196	+	2.34166i
$395$	−4.08664	−	7.07827i	−0.205621	−	0.356146i
$396$	−2.22709	+	23.0681i	−0.111916	+	1.15921i
$397$	22.9615	+	13.2568i	1.15240	+	0.665341i	0.949472	−	0.313852i	$-0.101620\pi$
$397$	22.9615	+	13.2568i	1.15240	+	0.665341i	0.202932	+	0.979193i	$0.434953\pi$
$398$	−36.3277			−1.82094
$399$		0			0
$400$	13.7454			0.687271
$401$	−5.08905	+	8.81450i	−0.254135	+	0.440175i	−0.964660	−	0.263497i	$-0.915124\pi$
$401$	−5.08905	+	8.81450i	−0.254135	+	0.440175i	0.710525	+	0.703672i	$0.248457\pi$
$402$	11.1098	+	19.2427i	0.554106	+	0.959740i
$403$	6.02681	−	3.47958i	0.300217	−	0.173330i
$404$	−24.2139	+	41.9397i	−1.20469	+	2.08658i
$405$		−	18.5402i		−	0.921272i
$406$		0			0
$407$	3.77747	+	2.69589i	0.187242	+	0.133630i
$408$	1.27816	−	2.21384i	0.0632784	−	0.109601i
$409$	−0.0146326	−	0.0253445i	−0.000723538	−	0.00125320i	0.865663	−	0.500626i	$-0.166897\pi$
$409$	−0.0146326	−	0.0253445i	−0.000723538	−	0.00125320i	−0.866387	+	0.499373i	$0.833564\pi$
$410$	−26.0803	−	45.1724i	−1.28801	−	2.23091i
$411$	1.57963	+	0.911998i	0.0779172	+	0.0449855i
$412$		−	0.0578862i		−	0.00285185i
$413$		0			0
$414$			7.92100i			0.389296i
$415$	−36.4111	−	21.0219i	−1.78735	−	1.03193i
$416$	−15.5803	+	8.99530i	−0.763888	+	0.441031i
$417$	3.83825	−	2.21601i	0.187960	−	0.108519i
$418$	−16.1180	−	35.3914i	−0.788356	−	1.73105i
$419$		−	28.1188i		−	1.37369i	−0.726802	−	0.686847i	$-0.758994\pi$
$419$		−	28.1188i		−	1.37369i	0.726802	−	0.686847i	$-0.241006\pi$
$420$		0			0
$421$	−13.3200			−0.649179			−0.324589	−	0.945855i	$-0.605226\pi$
$421$	−13.3200			−0.649179			−0.324589	+	0.945855i	$0.605226\pi$
$422$	−2.24219	+	3.88359i	−0.109148	+	0.189050i
$423$	−11.9196	+	6.88179i	−0.579551	+	0.334604i
$424$	9.80490	−	5.66086i	0.476168	−	0.274916i
$425$	−8.55156	+	14.8117i	−0.414812	+	0.718475i
$426$	−5.30048			−0.256809
$427$		0			0
$428$			22.0349i			1.06510i
$429$	−2.08488	−	4.57792i	−0.100659	−	0.221024i
$430$	−30.2280	+	17.4521i	−1.45772	+	0.841616i
$431$	−13.6664	+	7.89029i	−0.658287	+	0.380062i	−0.791624	−	0.611009i	$-0.790764\pi$
$431$	−13.6664	+	7.89029i	−0.658287	+	0.380062i	0.133337	+	0.991071i	$0.457431\pi$
$432$	6.55563	+	3.78490i	0.315408	+	0.182101i
$433$			19.7441i			0.948840i	0.880298	+	0.474420i	$0.157342\pi$
$433$			19.7441i			0.948840i	−0.880298	+	0.474420i	$0.842658\pi$
$434$		0			0
$435$			10.7967i			0.517661i
$436$	28.4304	+	16.4143i	1.36157	+	0.786103i
$437$	−3.81759	−	6.61226i	−0.182620	−	0.316308i
$438$	0.859646	+	1.48895i	0.0410755	+	0.0711448i
$439$	−5.52400	+	9.56785i	−0.263646	+	0.456649i	−0.967208	−	0.253985i	$-0.918258\pi$
$439$	−5.52400	+	9.56785i	−0.263646	+	0.456649i	0.703562	+	0.710634i	$0.251592\pi$
$440$	−13.8915	−	9.91405i	−0.662253	−	0.472634i
$441$		0			0
$442$		−	13.4627i		−	0.640358i
$443$	2.79487	−	4.84086i	0.132788	−	0.229996i	−0.791962	−	0.610570i	$-0.790940\pi$
$443$	2.79487	−	4.84086i	0.132788	−	0.229996i	0.924750	+	0.380574i	$0.124274\pi$
$444$	−2.09888	+	1.21179i	−0.0996086	+	0.0575091i
$445$	4.58217	+	7.93656i	0.217216	+	0.376229i
$446$	−2.71298	+	4.69903i	−0.128464	+	0.222505i
$447$	−6.56587			−0.310555
$448$		0			0
$449$	−2.71339			−0.128053			−0.0640263	−	0.997948i	$-0.520394\pi$
$449$	−2.71339			−0.128053			−0.0640263	+	0.997948i	$0.520394\pi$
$450$	31.6376	+	18.2660i	1.49141	+	0.861066i
$451$	2.26034	−	23.4124i	0.106435	−	1.10245i
$452$	−16.7200	−	28.9599i	−0.786442	−	1.36216i
$453$	−0.477939	+	0.827814i	−0.0224555	+	0.0388941i
$454$		−	34.2706i		−	1.60840i
$455$		0			0
$456$	5.26323			0.246473
$457$	5.06835	+	2.92621i	0.237087	+	0.136882i	0.613837	−	0.789433i	$-0.289625\pi$
$457$	5.06835	+	2.92621i	0.237087	+	0.136882i	−0.376750	+	0.926315i	$0.622958\pi$
$458$	−19.5238	−	33.8162i	−0.912288	−	1.58013i
$459$	−8.15702	+	4.70946i	−0.380737	+	0.219819i
$460$	−11.1971	−	6.46464i	−0.522067	−	0.301415i
$461$	38.7553			1.80502			0.902508	−	0.430673i	$-0.141724\pi$
$461$	38.7553			1.80502			0.902508	+	0.430673i	$0.141724\pi$
$462$		0			0
$463$	−18.2756			−0.849340			−0.424670	−	0.905348i	$-0.639610\pi$
$463$	−18.2756			−0.849340			−0.424670	+	0.905348i	$0.639610\pi$
$464$	9.06900	+	5.23599i	0.421018	+	0.243075i
$465$	5.54944	−	3.20397i	0.257349	−	0.148581i
$466$	−5.56251	−	9.63455i	−0.257678	−	0.446312i
$467$	21.9691	+	12.6838i	1.01661	+	0.586938i	0.913119	−	0.407693i	$-0.133667\pi$
$467$	21.9691	+	12.6838i	1.01661	+	0.586938i	0.103487	+	0.994631i	$0.467000\pi$
$468$	−16.5185			−0.763570
$469$		0			0
$470$		−	39.1098i		−	1.80400i
$471$	−5.32072	+	9.21576i	−0.245166	+	0.424640i
$472$	−0.534660	−	0.926058i	−0.0246097	−	0.0426253i
$473$	−15.6668	−	1.51254i	−0.720361	−	0.0695469i
$474$	2.90180	+	1.67536i	0.133284	+	0.0769517i
$475$	−35.2138			−1.61572
$476$		0			0
$477$	−19.3214			−0.884667
$478$	3.13416	−	5.42853i	0.143353	−	0.248295i
$479$	4.29553	+	7.44008i	0.196268	+	0.339946i	0.947315	−	0.320302i	$-0.103784\pi$
$479$	4.29553	+	7.44008i	0.196268	+	0.339946i	−0.751048	+	0.660248i	$0.770451\pi$
$480$	−14.3462	+	8.28280i	−0.654813	+	0.378057i
$481$	−1.65390	+	2.86464i	−0.0754114	+	0.130616i
$482$			51.5197i			2.34666i
$483$		0			0
$484$	−9.65383	−	28.0829i	−0.438810	−	1.27650i
$485$	3.26509	−	5.65531i	0.148260	−	0.256794i
$486$	15.4595	+	26.7766i	0.701255	+	1.21461i
$487$	1.02221	+	1.77052i	0.0463208	+	0.0802300i	0.888256	−	0.459348i	$-0.151917\pi$
$487$	1.02221	+	1.77052i	0.0463208	+	0.0802300i	−0.841935	+	0.539578i	$0.818584\pi$
$488$	−16.0741	−	9.28040i	−0.727641	−	0.420104i
$489$			5.63153i			0.254666i
$490$		0			0
$491$		−	20.9738i		−	0.946534i	−0.880919	−	0.473267i	$-0.843075\pi$
$491$		−	20.9738i		−	0.946534i	0.880919	−	0.473267i	$-0.156925\pi$
$492$	10.6379	+	6.14178i	0.479592	+	0.276893i
$493$	−11.2844	+	6.51502i	−0.508222	+	0.293422i
$494$	24.0050	−	13.8593i	1.08004	−	0.623559i
$495$	12.0713	+	26.5059i	0.542566	+	1.19135i
$496$		−	6.21523i		−	0.279072i
$497$		0			0
$498$	17.2363			0.772376
$499$	11.3800	−	19.7107i	0.509439	−	0.882374i	−0.490502	−	0.871440i	$-0.663186\pi$
$499$	11.3800	−	19.7107i	0.509439	−	0.882374i	0.999940	−	0.0109334i	$-0.00348026\pi$
$500$	−11.9814	+	6.91748i	−0.535826	+	0.309359i
$501$	−7.69276	+	4.44142i	−0.343687	+	0.198428i
$502$	9.67339	−	16.7548i	0.431744	−	0.747803i
$503$	19.2710			0.859253			0.429626	−	0.903007i	$-0.358645\pi$
$503$	19.2710			0.859253			0.429626	+	0.903007i	$0.358645\pi$
$504$		0			0
$505$			60.8608i			2.70827i
$506$	−4.20665	−	9.23685i	−0.187008	−	0.410628i
$507$	−4.11814	+	2.37761i	−0.182893	+	0.105593i
$508$	33.2855	−	19.2174i	1.47680	−	0.852633i
$509$	−30.1916	−	17.4311i	−1.33822	−	0.772621i	−0.351675	−	0.936122i	$-0.614388\pi$
$509$	−30.1916	−	17.4311i	−1.33822	−	0.772621i	−0.986543	+	0.163501i	$0.947721\pi$
$510$		−	12.3964i		−	0.548922i
$511$		0			0
$512$			22.4717i			0.993119i
$513$	−16.7946	−	9.69635i	−0.741498	−	0.428104i
$514$	25.1475	+	43.5567i	1.10921	+	1.92120i
$515$	−0.0363738	−	0.0630013i	−0.00160282	−	0.00277617i
$516$	4.10988	−	7.11853i	0.180928	−	0.313376i
$517$	10.2450	−	14.3552i	0.450573	−	0.631342i
$518$		0			0
$519$		−	4.17503i		−	0.183264i
$520$	6.08217	−	10.5346i	0.266721	−	0.461974i
$521$	−4.87017	+	2.81179i	−0.213366	+	0.123187i	−0.602875	−	0.797836i	$-0.705978\pi$
$521$	−4.87017	+	2.81179i	−0.213366	+	0.123187i	0.389509	+	0.921023i	$0.372645\pi$
$522$	13.9160	+	24.1032i	0.609085	+	1.05497i
$523$	−21.7244	+	37.6278i	−0.949943	+	1.64535i	−0.204404	+	0.978887i	$0.565526\pi$
$523$	−21.7244	+	37.6278i	−0.949943	+	1.64535i	−0.745539	+	0.666462i	$0.767808\pi$
$524$	15.0984			0.659577
$525$		0			0
$526$	7.40654			0.322940
$527$	6.69738	+	3.86673i	0.291742	+	0.168438i
$528$	−4.47179	−	0.431726i	−0.194609	−	0.0187885i
$529$	10.5036	+	18.1928i	0.456680	+	0.790993i
$530$	27.4513	−	47.5470i	1.19241	−	2.06531i
$531$			1.82488i			0.0791930i
$532$		0			0
$533$	16.7651			0.726177
$534$	−3.25367	−	1.87851i	−0.140800	−	0.0812909i
$535$	13.8460	+	23.9820i	0.598615	+	1.03683i
$536$	−20.9835	+	12.1148i	−0.906347	+	0.523280i
$537$	2.48074	+	1.43226i	0.107052	+	0.0618064i
$538$	−10.5837			−0.456297
$539$		0			0
$540$	−32.8392			−1.41317
$541$	−3.33965	−	1.92815i	−0.143583	−	0.0828977i	0.426488	−	0.904493i	$-0.359751\pi$
$541$	−3.33965	−	1.92815i	−0.143583	−	0.0828977i	−0.570071	+	0.821596i	$0.693084\pi$
$542$	−33.3880	+	19.2766i	−1.43414	+	0.827999i
$543$	0.715650	+	1.23954i	0.0307115	+	0.0531938i
$544$	−17.3138	−	9.99615i	−0.742325	−	0.428582i
$545$	41.2568			1.76725
$546$		0			0
$547$		−	11.0537i		−	0.472621i	−0.971678	−	0.236311i	$-0.924062\pi$
$547$		−	11.0537i		−	0.472621i	0.971678	−	0.236311i	$-0.0759383\pi$
$548$	−3.83743	+	6.64663i	−0.163927	+	0.283930i
$549$	15.8377	+	27.4318i	0.675938	+	1.17076i
$550$	−46.5939	−	4.49839i	−1.98677	−	0.191812i
$551$	−23.2335	−	13.4138i	−0.989778	−	0.571449i
$552$	1.37366			0.0584667
$553$		0			0
$554$	43.2843			1.83897
$555$	−1.52290	+	2.63774i	−0.0646435	+	0.111966i
$556$	9.32438	+	16.1503i	0.395442	+	0.684925i
$557$	3.85710	−	2.22690i	0.163430	−	0.0943566i	−0.416054	−	0.909340i	$-0.636587\pi$
$557$	3.85710	−	2.22690i	0.163430	−	0.0943566i	0.579484	+	0.814983i	$0.303254\pi$
$558$	8.25927	−	14.3055i	0.349643	−	0.605599i
$559$		−	11.2187i		−	0.474499i
$560$		0			0
$561$	3.24729	−	4.55009i	0.137101	−	0.192105i
$562$	5.92511	−	10.2626i	0.249936	−	0.432901i
$563$	11.9514	+	20.7004i	0.503690	+	0.872417i	0.999991	+	0.00426647i	$0.00135806\pi$
$563$	11.9514	+	20.7004i	0.503690	+	0.872417i	−0.496301	+	0.868151i	$0.665309\pi$
$564$	4.60507	+	7.97622i	0.193909	+	0.335860i
$565$	−36.3948	−	21.0126i	−1.53114	−	0.884006i
$566$			31.7177i			1.33320i
$567$		0			0
$568$		−	5.77997i		−	0.242522i
$569$	27.5303	+	15.8946i	1.15413	+	0.666337i	0.949890	−	0.312584i	$-0.101194\pi$
$569$	27.5303	+	15.8946i	1.15413	+	0.666337i	0.204240	+	0.978921i	$0.434528\pi$
$570$	22.1036	−	12.7615i	0.925819	−	0.534522i
$571$	29.3889	−	16.9677i	1.22989	−	0.710075i	0.262880	−	0.964829i	$-0.415328\pi$
$571$	29.3889	−	16.9677i	1.22989	−	0.710075i	0.967006	+	0.254753i	$0.0819943\pi$
$572$	19.2626	−	8.77260i	0.805411	−	0.366801i
$573$		−	8.81008i		−	0.368047i
$574$		0			0
$575$	−9.19049			−0.383270
$576$	−15.8869	+	27.5169i	−0.661953	+	1.14654i
$577$	36.7767	−	21.2330i	1.53103	−	0.883943i	0.531720	−	0.846920i	$-0.321546\pi$
$577$	36.7767	−	21.2330i	1.53103	−	0.883943i	0.999314	−	0.0370228i	$-0.0117874\pi$
$578$	−18.9599	+	10.9465i	−0.788627	+	0.455314i
$579$	−3.98698	+	6.90565i	−0.165693	+	0.286989i
$580$	−45.4295			−1.88636
$581$		0			0
$582$			2.67711i			0.110970i
$583$	22.5311	−	10.2611i	0.933144	−	0.424973i
$584$	−1.62364	+	0.937411i	−0.0671869	+	0.0387904i
$585$	−17.9782	+	10.3797i	−0.743306	+	0.429148i
$586$	35.9443	+	20.7524i	1.48484	+	0.857276i
$587$		−	14.7612i		−	0.609260i	−0.952471	−	0.304630i	$-0.901467\pi$
$587$		−	14.7612i		−	0.609260i	0.952471	−	0.304630i	$-0.0985329\pi$
$588$		0			0
$589$			15.9225i			0.656075i
$590$	−4.49075	−	2.59273i	−0.184881	−	0.106741i
$591$	−7.94211	−	13.7561i	−0.326695	−	0.565852i
$592$	1.47710	+	2.55841i	0.0607084	+	0.105150i
$593$	13.7222	−	23.7675i	0.563501	−	0.976013i	−0.433686	−	0.901064i	$-0.642787\pi$
$593$	13.7222	−	23.7675i	0.563501	−	0.976013i	0.997187	−	0.0749489i	$-0.0238794\pi$
$594$	−20.9835	−	14.9754i	−0.860962	−	0.614447i
$595$		0			0
$596$		−	27.6274i		−	1.13166i
$597$	5.37567	−	9.31093i	0.220011	−	0.381071i
$598$	6.26509	−	3.61715i	0.256199	−	0.147916i
$599$	−16.6316	−	28.8068i	−0.679549	−	1.17701i	−0.975117	−	0.221692i	$-0.928842\pi$
$599$	−16.6316	−	28.8068i	−0.679549	−	1.17701i	0.295567	−	0.955322i	$-0.404491\pi$
$600$	3.16768	−	5.48658i	0.129320	−	0.223989i
$601$	−9.35087			−0.381430			−0.190715	−	0.981645i	$-0.561081\pi$
$601$	−9.35087			−0.381430			−0.190715	+	0.981645i	$0.561081\pi$
$602$		0			0
$603$	41.3497			1.68389
$604$	−3.48321	−	2.01103i	−0.141730	−	0.0818278i
$605$	−28.1533	−	24.4983i	−1.14459	−	0.995997i
$606$	−12.4752	−	21.6078i	−0.506772	−	0.877755i
$607$	−1.18199	+	2.04726i	−0.0479753	+	0.0830957i	−0.889016	−	0.457876i	$-0.848610\pi$
$607$	−1.18199	+	2.04726i	−0.0479753	+	0.0830957i	0.841041	+	0.540972i	$0.181944\pi$
$608$		−	41.1623i		−	1.66935i
$609$		0			0
$610$	−90.0071			−3.64428
$611$	10.8863	+	6.28519i	0.440411	+	0.254272i
$612$	−9.17823	−	15.8972i	−0.371008	−	0.642605i
$613$	17.5674	−	10.1425i	0.709540	−	0.409653i	−0.101351	−	0.994851i	$-0.532316\pi$
$613$	17.5674	−	10.1425i	0.709540	−	0.409653i	0.810891	+	0.585198i	$0.198983\pi$
$614$	13.0240	+	7.51941i	0.525606	+	0.303459i
$615$	15.4372			0.622487
$616$		0			0
$617$	14.2894			0.575268			0.287634	−	0.957740i	$-0.407131\pi$
$617$	14.2894			0.575268			0.287634	+	0.957740i	$0.407131\pi$
$618$	0.0258280	+	0.0149118i	0.00103895	+	0.000599840i
$619$	36.2967	−	20.9559i	1.45889	−	0.842288i	0.459929	−	0.887956i	$-0.347875\pi$
$619$	36.2967	−	20.9559i	1.45889	−	0.842288i	0.998957	+	0.0456677i	$0.0145415\pi$
$620$	13.4814	+	23.3505i	0.541427	+	0.937780i
$621$	−4.38323	−	2.53066i	−0.175893	−	0.101552i
$622$	57.6671			2.31224
$623$		0			0
$624$		−	3.20215i		−	0.128189i
$625$	7.58286	−	13.1339i	0.303315	−	0.525356i
$626$	25.4646	+	44.1060i	1.01777	+	1.76283i
$627$	11.4561	+	1.10602i	0.457511	+	0.0441702i
$628$	−38.7774	−	22.3881i	−1.54739	−	0.893384i
$629$	−3.67584			−0.146565
$630$		0			0
$631$	34.1679			1.36020			0.680102	−	0.733118i	$-0.261936\pi$
$631$	34.1679			1.36020			0.680102	+	0.733118i	$0.261936\pi$
$632$	−1.82691	+	3.16431i	−0.0726707	+	0.125869i
$633$	−0.663587	−	1.14937i	−0.0263752	−	0.0456832i
$634$	−47.8011	+	27.5980i	−1.89842	+	1.09606i
$635$	24.1511	−	41.8310i	0.958409	−	1.66001i
$636$			12.9293i			0.512679i
$637$		0			0
$638$	−29.0283	−	20.7168i	−1.14924	−	0.820186i
$639$	−4.93199	+	8.54245i	−0.195106	+	0.337934i
$640$	−19.3235	−	33.4693i	−0.763830	−	1.32299i
$641$	8.28249	+	14.3457i	0.327139	+	0.566621i	0.981943	−	0.189178i	$-0.0605822\pi$
$641$	8.28249	+	14.3457i	0.327139	+	0.566621i	−0.654804	+	0.755799i	$0.727249\pi$
$642$	−9.83165	−	5.67631i	−0.388024	−	0.224026i
$643$			18.2753i			0.720706i	0.932816	+	0.360353i	$0.117344\pi$
$643$			18.2753i			0.720706i	−0.932816	+	0.360353i	$0.882656\pi$
$644$		0			0
$645$		−	10.3301i		−	0.406746i
$646$	26.6759	+	15.4013i	1.04955	+	0.605957i
$647$	28.1113	−	16.2300i	1.10517	−	0.638069i	0.167594	−	0.985856i	$-0.446400\pi$
$647$	28.1113	−	16.2300i	1.10517	−	0.638069i	0.937574	+	0.347787i	$0.113067\pi$
$648$	−7.17790	+	4.14416i	−0.281975	+	0.162798i
$649$	−0.969149	−	2.12803i	−0.0380424	−	0.0835325i
$650$		−	33.3649i		−	1.30868i
$651$		0			0
$652$	−23.6959			−0.928003
$653$	−9.78544	+	16.9489i	−0.382934	+	0.663261i	−0.991480	−	0.130257i	$-0.958420\pi$
$653$	−9.78544	+	16.9489i	−0.382934	+	0.663261i	0.608546	+	0.793518i	$0.291753\pi$
$654$	−14.6476	+	8.45682i	−0.572768	+	0.330688i
$655$	16.4326	−	9.48734i	0.642073	−	0.370701i
$656$	7.48645	−	12.9669i	0.292297	−	0.506273i
$657$	3.19953			0.124826
$658$		0			0
$659$			6.07485i			0.236643i	0.992975	+	0.118321i	$0.0377513\pi$
$659$			6.07485i			0.236643i	−0.992975	+	0.118321i	$0.962249\pi$
$660$	17.7369	−	8.07774i	0.690407	−	0.314426i
$661$	−25.8763	+	14.9397i	−1.00647	+	0.581086i	−0.910156	−	0.414265i	$-0.864039\pi$
$661$	−25.8763	+	14.9397i	−1.00647	+	0.581086i	−0.0963143	+	0.995351i	$0.530705\pi$
$662$	22.4431	−	12.9575i	0.872276	−	0.503609i
$663$	3.45056	+	1.99218i	0.134009	+	0.0773699i
$664$			18.7955i			0.729408i
$665$		0			0
$666$			7.85153i			0.304241i
$667$	−6.06373	−	3.50089i	−0.234788	−	0.135555i
$668$	−18.6883	−	32.3690i	−0.723070	−	1.25239i
$669$	−0.802920	−	1.39070i	−0.0310427	−	0.0537675i
$670$	−58.7485	+	101.755i	−2.26965	+	3.93115i
$671$	−33.0371	−	23.5777i	−1.27538	−	0.910208i
$672$		0			0
$673$		−	17.9702i		−	0.692701i	−0.938105	−	0.346350i	$-0.887421\pi$
$673$		−	17.9702i		−	0.692701i	0.938105	−	0.346350i	$-0.112579\pi$
$674$	8.74288	−	15.1431i	0.336763	−	0.583291i
$675$	−20.2156	+	11.6715i	−0.778101	+	0.449237i
$676$	−10.0043	−	17.3280i	−0.384782	−	0.666462i
$677$	−22.7147	+	39.3431i	−0.872998	+	1.51208i	−0.0141183	+	0.999900i	$0.504494\pi$
$677$	−22.7147	+	39.3431i	−0.872998	+	1.51208i	−0.858880	+	0.512177i	$0.828839\pi$
$678$	17.2286			0.661661
$679$		0			0
$680$	13.5178			0.518384
$681$	8.78369	+	5.07127i	0.336592	+	0.194331i
$682$	−2.03402	+	21.0682i	−0.0778867	+	0.806744i
$683$	−18.9425	−	32.8094i	−0.724815	−	1.25542i	−0.959050	−	0.283236i	$-0.908592\pi$
$683$	−18.9425	−	32.8094i	−0.724815	−	1.25542i	0.234235	−	0.972180i	$-0.424741\pi$
$684$	18.8971	−	32.7308i	0.722550	−	1.25149i
$685$			9.64527i			0.368527i
$686$		0			0
$687$	11.5563			0.440901
$688$	−8.67705	−	5.00970i	−0.330809	−	0.190993i
$689$	8.82319	+	15.2822i	0.336137	+	0.582206i
$690$	5.76885	−	3.33065i	0.219616	−	0.126796i
$691$	17.7665	+	10.2575i	0.675868	+	0.390213i	0.798297	−	0.602265i	$-0.205735\pi$
$691$	17.7665	+	10.2575i	0.675868	+	0.390213i	−0.122428	+	0.992477i	$0.539068\pi$
$692$	17.5674			0.667812
$693$		0			0
$694$	4.17673			0.158546
$695$	20.2966	+	11.7183i	0.769895	+	0.444499i
$696$	4.17996	−	2.41330i	0.158441	−	0.0914760i
$697$	9.31522	+	16.1344i	0.352839	+	0.611135i
$698$	18.1916	+	10.5029i	0.688561	+	0.397541i
$699$	3.29250			0.124534
$700$		0			0
$701$			30.1196i			1.13760i	0.822476	+	0.568801i	$0.192592\pi$
$701$			30.1196i			1.13760i	−0.822476	+	0.568801i	$0.807408\pi$
$702$	9.18725	−	15.9128i	0.346750	−	0.600589i
$703$	−3.78411	−	6.55428i	−0.142721	−	0.247199i
$704$	3.91248	−	40.5252i	0.147457	−	1.52735i
$705$	10.0240	+	5.78736i	0.377525	+	0.217964i
$706$	−45.2455			−1.70284
$707$		0			0
$708$	1.22115			0.0458937
$709$	0.418515	−	0.724889i	0.0157176	−	0.0272238i	−0.858060	−	0.513550i	$-0.828330\pi$
$709$	0.418515	−	0.724889i	0.0157176	−	0.0272238i	0.873777	+	0.486326i	$0.161663\pi$
$710$	−14.0144	−	24.2737i	−0.525953	−	0.910977i
$711$	5.40014	−	3.11777i	0.202521	−	0.116926i
$712$	2.04844	−	3.54800i	0.0767685	−	0.132967i
$713$			4.15563i			0.155630i
$714$		0			0
$715$	15.4523	−	21.6518i	0.577885	−	0.809731i
$716$	−6.02654	+	10.4383i	−0.225222	+	0.390097i
$717$	0.927570	+	1.60660i	0.0346407	+	0.0599995i
$718$	24.9010	+	43.1299i	0.929299	+	1.60959i
$719$	15.8022	+	9.12338i	0.589321	+	0.340245i	0.764829	−	0.644233i	$-0.222823\pi$
$719$	15.8022	+	9.12338i	0.589321	+	0.340245i	−0.175508	+	0.984478i	$0.556157\pi$
$720$			18.5402i			0.690954i
$721$		0			0
$722$			22.2305i			0.827334i
$723$	−13.2047	−	7.62374i	−0.491089	−	0.283530i
$724$	−5.21565	+	3.01126i	−0.193838	+	0.111912i
$725$	−27.9661	+	16.1463i	−1.03864	+	0.599657i
$726$	15.0171	+	2.92691i	0.557335	+	0.108628i
$727$			34.6901i			1.28658i	0.765621	+	0.643292i	$0.222432\pi$
$727$			34.6901i			1.28658i	−0.765621	+	0.643292i	$0.777568\pi$
$728$		0			0
$729$	7.24357			0.268280
$730$	−4.54580	+	7.87356i	−0.168248	+	0.291413i
$731$	10.7967	−	6.23345i	0.399329	−	0.230553i
$732$	18.3565	−	10.5981i	0.678474	−	0.391717i
$733$	−0.740964	+	1.28339i	−0.0273681	+	0.0474030i	−0.879385	−	0.476111i	$-0.842046\pi$
$733$	−0.740964	+	1.28339i	−0.0273681	+	0.0474030i	0.852017	+	0.523514i	$0.175379\pi$
$734$	−35.0005			−1.29189
$735$		0			0
$736$		−	10.7430i		−	0.395993i
$737$	−48.2188	+	21.9599i	−1.77616	+	0.808902i
$738$	34.4629	−	19.8971i	1.26860	−	0.732424i
$739$	−34.3067	+	19.8070i	−1.26199	+	0.728611i	−0.973460	−	0.228859i	$-0.926501\pi$
$739$	−34.3067	+	19.8070i	−1.26199	+	0.728611i	−0.288532	+	0.957470i	$0.593167\pi$
$740$	−11.0989	−	6.40794i	−0.408003	−	0.235561i
$741$			8.20344i			0.301361i
$742$		0			0
$743$			38.0060i			1.39431i	0.716923	+	0.697153i	$0.245550\pi$
$743$			38.0060i			1.39431i	−0.716923	+	0.697153i	$0.754450\pi$
$744$	−2.48085	−	1.43232i	−0.0909525	−	0.0525114i
$745$	−17.3601	−	30.0686i	−0.636026	−	1.10163i
$746$	25.0927	+	43.4618i	0.918709	+	1.59125i
$747$	16.0380	−	27.7787i	0.586800	−	1.01637i
$748$	19.1455	+	13.6637i	0.700030	+	0.499594i
$749$		0			0
$750$		−	7.12792i		−	0.260275i
$751$	6.68361	−	11.5763i	0.243888	−	0.422427i	−0.717930	−	0.696115i	$-0.754910\pi$
$751$	6.68361	−	11.5763i	0.243888	−	0.422427i	0.961818	+	0.273688i	$0.0882436\pi$
$752$	9.72253	−	5.61330i	0.354544	−	0.204696i
$753$	2.86288	+	4.95866i	0.104329	+	0.180704i
$754$	12.7096	−	22.0136i	0.462855	−	0.801688i
$755$	−5.05467			−0.183958
$756$		0			0
$757$	−4.89740			−0.177999			−0.0889995	−	0.996032i	$-0.528367\pi$
$757$	−4.89740			−0.177999			−0.0889995	+	0.996032i	$0.528367\pi$
$758$	−32.8488	−	18.9653i	−1.19312	−	0.688850i
$759$	2.98993	+	0.288661i	0.108528	+	0.0104777i
$760$	13.9160	+	24.1032i	0.504785	+	0.874314i
$761$	3.29757	−	5.71155i	0.119537	−	0.207044i	−0.800047	−	0.599937i	$-0.795192\pi$
$761$	3.29757	−	5.71155i	0.119537	−	0.207044i	0.919584	+	0.392893i	$0.128526\pi$
$762$			19.8020i			0.717350i
$763$		0			0
$764$	37.0704			1.34116
$765$	−19.9785	−	11.5346i	−0.722325	−	0.417034i
$766$	10.5226	+	18.2257i	0.380198	+	0.658522i
$767$	1.44338	−	0.833338i	0.0521176	−	0.0300901i
$768$	0.0796262	+	0.0459722i	0.00287326	+	0.00165888i
$769$	8.07706			0.291266			0.145633	−	0.989339i	$-0.453478\pi$
$769$	8.07706			0.291266			0.145633	+	0.989339i	$0.453478\pi$
$770$		0			0
$771$	−14.8850			−0.536071
$772$	−29.0571	−	16.7761i	−1.04579	−	0.603786i
$773$	19.3206	−	11.1548i	0.694915	−	0.401210i	−0.110535	−	0.993872i	$-0.535257\pi$
$773$	19.3206	−	11.1548i	0.694915	−	0.401210i	0.805451	+	0.592663i	$0.201923\pi$
$774$	−13.3145	−	23.0614i	−0.478581	−	0.828927i
$775$	16.5982	+	9.58297i	0.596225	+	0.344231i
$776$	−2.91929			−0.104796
$777$		0			0
$778$			33.9273i			1.21635i
$779$	−19.1792	+	33.2193i	−0.687166	+	1.19021i
$780$	6.94577	+	12.0304i	0.248698	+	0.430758i
$781$	1.21461	−	12.5808i	0.0434621	−	0.450177i
$782$	6.96217	+	4.01961i	0.248967	+	0.143741i
$783$	−17.7839			−0.635546
$784$		0			0
$785$	−56.2719			−2.00843
$786$	−3.88942	+	6.73668i	−0.138731	+	0.240289i
$787$	−9.06298	−	15.6975i	−0.323060	−	0.559557i	0.658058	−	0.752968i	$-0.271378\pi$
$787$	−9.06298	−	15.6975i	−0.323060	−	0.559557i	−0.981118	+	0.193411i	$0.938045\pi$
$788$	57.8820	−	33.4182i	2.06196	−	1.19047i
$789$	−1.09600	+	1.89833i	−0.0390186	+	0.0675822i
$790$			17.7186i			0.630398i
$791$		0			0
$792$	7.56360	−	10.5981i	0.268761	−	0.376587i
$793$	14.4647	−	25.0536i	0.513657	−	0.889680i
$794$	−28.7390	−	49.7773i	−1.01991	−	1.76653i
$795$	8.12433	+	14.0718i	0.288140	+	0.499074i
$796$	39.1778	+	22.6193i	1.38862	+	0.801721i
$797$		−	3.97086i		−	0.140655i	−0.997524	−	0.0703276i	$-0.977596\pi$
$797$		−	3.97086i		−	0.140655i	0.997524	−	0.0703276i	$-0.0224045\pi$
$798$		0			0
$799$			13.9690i			0.494188i
$800$	−42.9091	−	24.7736i	−1.51707	−	0.875879i
$801$	−6.05494	+	3.49582i	−0.213941	+	0.123519i
$802$	19.1086	−	11.0324i	0.674749	−	0.389566i
$803$	−3.73104	+	1.69919i	−0.131666	+	0.0599633i
$804$		−	27.6699i		−	0.975843i
$805$		0			0
$806$	−15.0865			−0.531399
$807$	1.56615	−	2.71266i	0.0551312	−	0.0954900i
$808$	23.5624	−	13.6038i	0.828924	−	0.478579i
$809$	30.4772	−	17.5960i	1.07152	−	0.618644i	0.142925	−	0.989734i	$-0.454349\pi$
$809$	30.4772	−	17.5960i	1.07152	−	0.618644i	0.928597	+	0.371090i	$0.121016\pi$
$810$	−20.0963	+	34.8079i	−0.706114	+	1.22302i
$811$	44.7022			1.56971			0.784853	−	0.619682i	$-0.212738\pi$
$811$	44.7022			1.56971			0.784853	+	0.619682i	$0.212738\pi$
$812$		0			0
$813$		−	11.4100i		−	0.400165i
$814$	−4.16976	−	9.15584i	−0.146150	−	0.320912i
$815$	−25.7898	+	14.8897i	−0.903376	+	0.521565i
$816$	3.08169	−	1.77922i	0.107881	−	0.0622851i
$817$	22.2293	+	12.8341i	0.777706	+	0.449009i
$818$			0.0634431i			0.00221824i
$819$		0			0
$820$			64.9554i			2.26834i
$821$	16.2030	+	9.35481i	0.565489	+	0.326485i	0.755346	−	0.655327i	$-0.227469\pi$
$821$	16.2030	+	9.35481i	0.565489	+	0.326485i	−0.189857	+	0.981812i	$0.560802\pi$
$822$	−1.97709	−	3.42441i	−0.0689588	−	0.119440i
$823$	−2.43818	−	4.22305i	−0.0849895	−	0.147206i	0.820397	−	0.571794i	$-0.193752\pi$
$823$	−2.43818	−	4.22305i	−0.0849895	−	0.147206i	−0.905387	+	0.424588i	$0.860419\pi$
$824$	−0.0162607	+	0.0281644i	−0.000566470	+	0.000981154i
$825$	8.04779	−	11.2766i	0.280188	−	0.392599i
$826$		0			0
$827$		−	37.2794i		−	1.29633i	−0.761499	−	0.648166i	$-0.775536\pi$
$827$		−	37.2794i		−	1.29633i	0.761499	−	0.648166i	$-0.224464\pi$
$828$	4.93199	−	8.54245i	0.171398	−	0.296871i
$829$	−40.6985	+	23.4973i	−1.41352	+	0.816094i	−0.995718	−	0.0924461i	$-0.970531\pi$
$829$	−40.6985	+	23.4973i	−1.41352	+	0.816094i	−0.417798	+	0.908540i	$0.637198\pi$
$830$	45.5727	+	78.9342i	1.58185	+	2.73985i
$831$	−6.40509	+	11.0939i	−0.222190	+	0.384844i
$832$	29.0192			1.00606
$833$		0			0
$834$	−9.60803			−0.332699
$835$	−40.6792	−	23.4862i	−1.40776	−	0.812773i
$836$	−4.65383	+	48.2039i	−0.160956	+	1.66717i
$837$	5.27747	+	9.14085i	0.182416	+	0.315954i
$838$	−30.4788	+	52.7909i	−1.05287	+	1.82363i
$839$			43.8626i			1.51431i	0.653237	+	0.757153i	$0.273410\pi$
$839$			43.8626i			1.51431i	−0.653237	+	0.757153i	$0.726590\pi$
$840$		0			0
$841$	4.39788			0.151651
$842$	25.0074	+	14.4380i	0.861810	+	0.497566i
$843$	1.75356	+	3.03726i	0.0603959	+	0.104609i
$844$	4.83621	−	2.79219i	0.166469	−	0.0961111i
$845$	−21.7767	−	12.5728i	−0.749141	−	0.432517i
$846$	29.8375			1.02584
$847$		0			0
$848$	15.7600			0.541200
$849$	−8.12939	−	4.69350i	−0.279000	−	0.161081i
$850$	32.1098	−	18.5386i	1.10136	−	0.635869i
$851$	−0.987620	−	1.71061i	−0.0338552	−	0.0586389i
$852$	5.71634	+	3.30033i	0.195839	+	0.113067i
$853$	5.52907			0.189312			0.0946558	−	0.995510i	$-0.469825\pi$
$853$	5.52907			0.189312			0.0946558	+	0.995510i	$0.469825\pi$
$854$		0			0
$855$		−	47.4974i		−	1.62438i
$856$	6.18980	−	10.7210i	0.211563	−	0.366438i
$857$	−16.0148	−	27.7384i	−0.547054	−	0.947526i	−0.998475	−	0.0552143i	$-0.982416\pi$
$857$	−16.0148	−	27.7384i	−0.547054	−	0.947526i	0.451420	−	0.892311i	$-0.350918\pi$
$858$	−1.04795	+	10.8546i	−0.0357764	+	0.370569i
$859$	−24.7658	−	14.2985i	−0.844998	−	0.487860i	0.0139623	−	0.999903i	$-0.495556\pi$
$859$	−24.7658	−	14.2985i	−0.844998	−	0.487860i	−0.858960	+	0.512043i	$0.828889\pi$
$860$	43.4661			1.48218
$861$		0			0
$862$	34.2101			1.16520
$863$	20.4770	−	35.4672i	0.697046	−	1.20732i	−0.272440	−	0.962173i	$-0.587831\pi$
$863$	20.4770	−	35.4672i	0.697046	−	1.20732i	0.969486	−	0.245146i	$-0.0788360\pi$
$864$	−13.6431	−	23.6306i	−0.464149	−	0.803930i
$865$	19.1197	−	11.0388i	0.650090	−	0.375329i
$866$	21.4012	−	37.0680i	0.727244	−	1.25962i
$867$		−	6.47933i		−	0.220050i
$868$		0			0
$869$	−4.64145	+	6.50359i	−0.157450	+	0.220619i
$870$	11.7029	−	20.2700i	0.396764	−	0.687216i
$871$	−18.8825	−	32.7055i	−0.639809	−	1.10818i
$872$	−9.22184	−	15.9727i	−0.312291	−	0.540904i
$873$	4.31453	+	2.49100i	0.146025	+	0.0843075i
$874$			16.5520i			0.559881i
$875$		0			0
$876$		−	2.14103i		−	0.0723385i
$877$	19.7464	+	11.4006i	0.666788	+	0.384970i	0.794858	−	0.606795i	$-0.207545\pi$
$877$	19.7464	+	11.4006i	0.666788	+	0.384970i	−0.128071	+	0.991765i	$0.540878\pi$
$878$	20.7418	−	11.9753i	0.700001	−	0.404146i
$879$	−10.6379	+	6.14178i	−0.358807	+	0.207157i
$880$	−9.84628	−	21.6202i	−0.331918	−	0.728816i
$881$		−	12.0744i		−	0.406797i	−0.979096	−	0.203399i	$-0.934801\pi$
$881$		−	12.0744i		−	0.406797i	0.979096	−	0.203399i	$-0.0651987\pi$
$882$		0			0
$883$	−40.9977			−1.37968			−0.689841	−	0.723961i	$-0.742319\pi$
$883$	−40.9977			−1.37968			−0.689841	+	0.723961i	$0.742319\pi$
$884$	−8.38255	+	14.5190i	−0.281936	+	0.488327i
$885$	1.32906	−	0.767331i	0.0446758	−	0.0257936i
$886$	−10.4943	+	6.05890i	−0.352563	+	0.203553i
$887$	−11.5757	+	20.0497i	−0.388673	+	0.673202i	−0.992271	−	0.124087i	$-0.960400\pi$
$887$	−11.5757	+	20.0497i	−0.388673	+	0.673202i	0.603598	+	0.797289i	$0.293733\pi$
$888$	1.36161			0.0456927
$889$		0			0
$890$		−	19.8670i		−	0.665945i
$891$	−16.4944	+	7.51190i	−0.552584	+	0.251658i
$892$	5.85167	−	3.37847i	0.195929	−	0.113119i
$893$	−24.9077	+	14.3805i	−0.833504	+	0.481224i
$894$	12.3269	+	7.11695i	0.412274	+	0.238026i
$895$			15.1475i			0.506326i
$896$		0			0
$897$			2.14103i			0.0714867i
$898$	5.09417	+	2.94112i	0.169995	+	0.0981466i
$899$	7.30081	+	12.6454i	0.243496	+	0.421747i
$900$	−22.7465	−	39.3981i	−0.758217	−	1.31327i
$901$	−9.80490	+	16.9826i	−0.326649	+	0.565772i
$902$	−29.6210	+	41.5049i	−0.986272	+	1.38196i
$903$		0			0
$904$			18.7871i			0.624851i
$905$	−3.78435	+	6.55469i	−0.125796	+	0.217885i
$906$	1.79459	−	1.03611i	0.0596212	−	0.0344223i
$907$	6.88688	+	11.9284i	0.228675	+	0.396077i	0.957416	−	0.288713i	$-0.0932274\pi$
$907$	6.88688	+	11.9284i	0.228675	+	0.396077i	−0.728741	+	0.684790i	$0.759894\pi$
$908$	−21.3385	+	36.9594i	−0.708143	+	1.22654i
$909$	−46.4318			−1.54005
$910$		0			0
$911$	−23.9157			−0.792362			−0.396181	−	0.918172i	$-0.629665\pi$
$911$	−23.9157			−0.792362			−0.396181	+	0.918172i	$0.629665\pi$
$912$	6.34493	+	3.66325i	0.210102	+	0.121302i
$913$	−3.94970	+	40.9107i	−0.130716	+	1.35395i
$914$	−6.34362	−	10.9875i	−0.209828	−	0.363434i
$915$	13.3190	−	23.0692i	0.440313	−	0.762644i
$916$			48.6258i			1.60664i
$917$		0			0
$918$	20.4189			0.673925
$919$	18.5816	+	10.7281i	0.612951	+	0.353887i	0.774119	−	0.633040i	$-0.218193\pi$
$919$	18.5816	+	10.7281i	0.612951	+	0.353887i	−0.161169	+	0.986927i	$0.551526\pi$
$920$	3.63194	+	6.29071i	0.119742	+	0.207399i
$921$	−3.85451	+	2.22540i	−0.127010	+	0.0733295i
$922$	−72.7602	−	42.0081i	−2.39623	−	1.38346i
$923$	9.00884			0.296530
$924$		0			0
$925$	−9.10989			−0.299531
$926$	34.3111	+	19.8095i	1.12753	+	0.650981i
$927$	0.0480648	−	0.0277502i	0.00157866	−	0.000911437i
$928$	−18.8738	−	32.6904i	−0.619563	−	1.07311i
$929$	28.5069	+	16.4585i	0.935280	+	0.539984i	0.888478	−	0.458920i	$-0.151763\pi$
$929$	28.5069	+	16.4585i	0.935280	+	0.539984i	0.0468026	+	0.998904i	$0.485097\pi$
$930$	−13.8915			−0.455522
$931$		0			0
$932$			13.8539i			0.453801i
$933$	−8.53342	+	14.7803i	−0.279372	+	0.483886i
$934$	−27.4968	−	47.6259i	−0.899723	−	1.55837i
$935$	29.4231	+	2.84064i	0.962239	+	0.0928989i
$936$	8.03706	+	4.64020i	0.262700	+	0.151670i
$937$	−22.4998			−0.735037			−0.367519	−	0.930016i	$-0.619793\pi$
$937$	−22.4998			−0.735037			−0.367519	+	0.930016i	$0.619793\pi$
$938$		0			0
$939$	−15.0727			−0.491881
$940$	−24.3516	+	42.1782i	−0.794262	+	1.37570i
$941$	28.3839	+	49.1624i	0.925290	+	1.60265i	0.791095	+	0.611693i	$0.209511\pi$
$941$	28.3839	+	49.1624i	0.925290	+	1.60265i	0.134195	+	0.990955i	$0.457155\pi$
$942$	19.9785	−	11.5346i	0.650935	−	0.375818i
$943$	−5.00560	+	8.66996i	−0.163005	+	0.282333i
$944$		−	1.48851i		−	0.0484468i
$945$		0			0
$946$	27.7738	+	19.8214i	0.903003	+	0.644450i
$947$	−9.83558	+	17.0357i	−0.319613	+	0.553586i	−0.980407	−	0.196981i	$-0.936886\pi$
$947$	−9.83558	+	17.0357i	−0.319613	+	0.553586i	0.660794	+	0.750567i	$0.270220\pi$
$948$	−2.08631	−	3.61360i	−0.0677603	−	0.117364i
$949$	−1.46108	−	2.53066i	−0.0474286	−	0.0821488i
$950$	66.1112	+	38.1693i	2.14493	+	1.23838i
$951$		−	16.3355i		−	0.529715i
$952$		0			0
$953$		−	5.48509i		−	0.177680i	−0.996046	−	0.0888398i	$-0.971684\pi$
$953$		−	5.48509i		−	0.177680i	0.996046	−	0.0888398i	$-0.0283159\pi$
$954$	36.2745	+	20.9431i	1.17443	+	0.678057i
$955$	40.3461	−	23.2938i	1.30557	−	0.753771i
$956$	−6.76012	+	3.90296i	−0.218638	+	0.126231i
$957$	9.60533	−	4.37447i	0.310496	−	0.141406i
$958$		−	18.6242i		−	0.601722i
$959$		0			0
$960$	26.7207			0.862406
$961$	−11.1669	+	19.3416i	−0.360222	+	0.623924i
$962$	6.21015	−	3.58543i	0.200223	−	0.115599i
$963$	−18.2963	+	10.5634i	−0.589590	+	0.340400i
$964$	32.0786	−	55.5618i	1.03318	−	1.78952i
$965$	−42.1662			−1.35738
$966$		0			0
$967$		−	7.87031i		−	0.253092i	−0.991961	−	0.126546i	$-0.959611\pi$
$967$		−	7.87031i		−	0.253092i	0.991961	−	0.126546i	$-0.0403891\pi$
$968$	−3.19169	+	16.3755i	−0.102585	+	0.526330i
$969$	−7.89485	+	4.55809i	−0.253619	+	0.146427i
$970$	−12.2599	+	7.07827i	−0.393642	+	0.227270i
$971$	−24.0913	−	13.9091i	−0.773127	−	0.446365i	0.0608619	−	0.998146i	$-0.480615\pi$
$971$	−24.0913	−	13.9091i	−0.773127	−	0.446365i	−0.833989	+	0.551781i	$0.813948\pi$
$972$		−	38.5032i		−	1.23499i
$973$		0			0
$974$		−	4.43203i		−	0.142011i
$975$	8.55156	+	4.93725i	0.273869	+	0.158118i
$976$	−12.9184	−	22.3754i	−0.413509	−	0.716219i
$977$	15.9022	+	27.5434i	0.508757	+	0.881193i	0.999949	+	0.0101411i	$0.00322807\pi$
$977$	15.9022	+	27.5434i	0.508757	+	0.881193i	−0.491192	+	0.871051i	$0.663439\pi$
$978$	6.10419	−	10.5728i	0.195190	−	0.338080i
$979$	5.20425	−	7.29219i	0.166329	−	0.233059i
$980$		0			0
$981$			31.4756i			1.00494i
$982$	−22.7341	+	39.3767i	−0.725476	+	1.25656i
$983$	−5.72322	+	3.30430i	−0.182542	+	0.105391i	−0.588487	−	0.808507i	$-0.700276\pi$
$983$	−5.72322	+	3.30430i	−0.182542	+	0.105391i	0.405944	+	0.913898i	$0.366943\pi$
$984$	−3.45056	−	5.97654i	−0.110000	−	0.190525i
$985$	41.9978	−	72.7423i	1.33816	−	2.31776i
$986$	28.2473			0.899579
$987$		0			0
$988$	−34.5178			−1.09816
$989$	5.80166	+	3.34959i	0.184482	+	0.106511i
$990$	6.06756	−	62.8473i	0.192840	−	1.99742i
$991$	−8.74838	−	15.1526i	−0.277902	−	0.481340i	0.692962	−	0.720975i	$-0.256306\pi$
$991$	−8.74838	−	15.1526i	−0.277902	−	0.481340i	−0.970863	+	0.239635i	$0.922972\pi$
$992$	−11.2018	+	19.4021i	−0.355657	+	0.616017i
$993$			7.66968i			0.243390i
$994$		0			0
$995$	56.8530			1.80236
$996$	−18.5886	−	10.7321i	−0.589002	−	0.340061i
$997$	13.7119	+	23.7497i	0.434261	+	0.752162i	0.997235	−	0.0743127i	$-0.0236763\pi$
$997$	13.7119	+	23.7497i	0.434261	+	0.752162i	−0.562974	+	0.826474i	$0.690343\pi$
$998$	−42.7302	+	24.6703i	−1.35260	+	0.780924i
$999$	−4.34479	−	2.50847i	−0.137463	−	0.0793644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.i.c.362.1		12
7.2	even	3		539.2.b.b.538.12		12
7.3	odd	6	inner	539.2.i.c.472.6		12
7.4	even	3		77.2.i.a.10.6	yes	12
7.5	odd	6		539.2.b.b.538.11		12
7.6	odd	2		77.2.i.a.54.1	yes	12
11.10	odd	2	inner	539.2.i.c.362.6		12
21.11	odd	6		693.2.bg.a.10.1		12
21.20	even	2		693.2.bg.a.208.6		12
28.11	odd	6		1232.2.bn.a.241.3		12
28.27	even	2		1232.2.bn.a.593.4		12
77.4	even	15		847.2.r.b.94.6		48
77.6	even	10		847.2.r.b.481.1		48
77.10	even	6	inner	539.2.i.c.472.1		12
77.13	even	10		847.2.r.b.40.1		48
77.18	odd	30		847.2.r.b.94.1		48
77.20	odd	10		847.2.r.b.40.6		48
77.25	even	15		847.2.r.b.717.1		48
77.27	odd	10		847.2.r.b.481.6		48
77.32	odd	6		77.2.i.a.10.1	✓	12
77.39	odd	30		847.2.r.b.360.6		48
77.41	even	10		847.2.r.b.838.6		48
77.46	odd	30		847.2.r.b.766.6		48
77.48	odd	10		847.2.r.b.215.6		48
77.53	even	15		847.2.r.b.766.1		48
77.54	even	6		539.2.b.b.538.1		12
77.60	even	15		847.2.r.b.360.1		48
77.62	even	10		847.2.r.b.215.1		48
77.65	odd	6		539.2.b.b.538.2		12
77.69	odd	10		847.2.r.b.838.1		48
77.74	odd	30		847.2.r.b.717.6		48
77.76	even	2		77.2.i.a.54.6	yes	12
231.32	even	6		693.2.bg.a.10.6		12
231.230	odd	2		693.2.bg.a.208.1		12
308.263	even	6		1232.2.bn.a.241.4		12
308.307	odd	2		1232.2.bn.a.593.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.1	✓	12	77.32	odd	6
77.2.i.a.10.6	yes	12	7.4	even	3
77.2.i.a.54.1	yes	12	7.6	odd	2
77.2.i.a.54.6	yes	12	77.76	even	2
539.2.b.b.538.1		12	77.54	even	6
539.2.b.b.538.2		12	77.65	odd	6
539.2.b.b.538.11		12	7.5	odd	6
539.2.b.b.538.12		12	7.2	even	3
539.2.i.c.362.1		12	1.1	even	1	trivial
539.2.i.c.362.6		12	11.10	odd	2	inner
539.2.i.c.472.1		12	77.10	even	6	inner
539.2.i.c.472.6		12	7.3	odd	6	inner
693.2.bg.a.10.1		12	21.11	odd	6
693.2.bg.a.10.6		12	231.32	even	6
693.2.bg.a.208.1		12	231.230	odd	2
693.2.bg.a.208.6		12	21.20	even	2
847.2.r.b.40.1		48	77.13	even	10
847.2.r.b.40.6		48	77.20	odd	10
847.2.r.b.94.1		48	77.18	odd	30
847.2.r.b.94.6		48	77.4	even	15
847.2.r.b.215.1		48	77.62	even	10
847.2.r.b.215.6		48	77.48	odd	10
847.2.r.b.360.1		48	77.60	even	15
847.2.r.b.360.6		48	77.39	odd	30
847.2.r.b.481.1		48	77.6	even	10
847.2.r.b.481.6		48	77.27	odd	10
847.2.r.b.717.1		48	77.25	even	15
847.2.r.b.717.6		48	77.74	odd	30
847.2.r.b.766.1		48	77.53	even	15
847.2.r.b.766.6		48	77.46	odd	30
847.2.r.b.838.1		48	77.69	odd	10
847.2.r.b.838.6		48	77.41	even	10
1232.2.bn.a.241.3		12	28.11	odd	6
1232.2.bn.a.241.4		12	308.263	even	6
1232.2.bn.a.593.3		12	308.307	odd	2
1232.2.bn.a.593.4		12	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87742 - 1.08393i) q^{2} +(0.555632 - 0.320794i) q^{3} +(1.34981 + 2.33795i) q^{4} +(2.93818 + 1.69636i) q^{5} -1.39088 q^{6} -1.51670i q^{8} +(-1.29418 + 2.24159i) q^{9} +O(q^{10})\)	\(q+(-1.87742 - 1.08393i) q^{2} +(0.555632 - 0.320794i) q^{3} +(1.34981 + 2.33795i) q^{4} +(2.93818 + 1.69636i) q^{5} -1.39088 q^{6} -1.51670i q^{8} +(-1.29418 + 2.24159i) q^{9} +(-3.67747 - 6.36957i) q^{10} +(0.318720 - 3.30128i) q^{11} +(1.50000 + 0.866025i) q^{12} +2.36397 q^{13} +2.17673 q^{15} +(1.05563 - 1.82841i) q^{16} +(1.31350 + 2.27505i) q^{17} +(4.85946 - 2.80561i) q^{18} +(-2.70437 + 4.68411i) q^{19} +9.15907i q^{20} +(-4.17673 + 5.85242i) q^{22} +(-0.705818 + 1.22251i) q^{23} +(-0.486548 - 0.842726i) q^{24} +(3.25526 + 5.63828i) q^{25} +(-4.43818 - 2.56238i) q^{26} +3.58543i q^{27} +4.96005i q^{29} +(-4.08664 - 2.35942i) q^{30} +(2.54944 - 1.47192i) q^{31} +(-6.59074 + 3.80516i) q^{32} +(-0.881939 - 1.93654i) q^{33} -5.69497i q^{34} -6.98762 q^{36} +(-0.699628 + 1.21179i) q^{37} +(10.1545 - 5.86271i) q^{38} +(1.31350 - 0.758349i) q^{39} +(2.57286 - 4.45633i) q^{40} +7.09192 q^{41} -4.74568i q^{43} +(8.14842 - 3.71096i) q^{44} +(-7.60507 + 4.39079i) q^{45} +(2.65024 - 1.53012i) q^{46} +(4.60507 + 2.65874i) q^{47} -1.35456i q^{48} -14.1139i q^{50} +(1.45964 + 0.842726i) q^{51} +(3.19092 + 5.52684i) q^{52} +(3.73236 + 6.46464i) q^{53} +(3.88636 - 6.73137i) q^{54} +(6.53660 - 9.15907i) q^{55} +3.47019i q^{57} +(5.37636 - 9.31212i) q^{58} +(0.610575 - 0.352516i) q^{59} +(2.93818 + 5.08907i) q^{60} +(6.11882 - 10.5981i) q^{61} -6.38185 q^{62} +12.2756 q^{64} +(6.94577 + 4.01014i) q^{65} +(-0.443300 + 4.59166i) q^{66} +(-7.98762 - 13.8350i) q^{67} +(-3.54596 + 6.14178i) q^{68} +0.905690i q^{69} +3.81089 q^{71} +(3.39981 + 1.96288i) q^{72} +(-0.618061 - 1.07051i) q^{73} +(2.62700 - 1.51670i) q^{74} +(3.61745 + 2.08854i) q^{75} -14.6016 q^{76} -3.28799 q^{78} +(-2.08631 - 1.20453i) q^{79} +(6.20327 - 3.58146i) q^{80} +(-2.73236 - 4.73259i) q^{81} +(-13.3145 - 7.68715i) q^{82} -12.3924 q^{83} +8.91266i q^{85} +(-5.14400 + 8.90966i) q^{86} +(1.59116 + 2.75596i) q^{87} +(-5.00704 - 0.483402i) q^{88} +(2.33929 + 1.35059i) q^{89} +19.0373 q^{90} -3.81089 q^{92} +(0.944368 - 1.63569i) q^{93} +(-5.76378 - 9.98317i) q^{94} +(-15.8919 + 9.17517i) q^{95} +(-2.44135 + 4.22854i) q^{96} -1.92477i q^{97} +(6.98762 + 4.98689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 4 * q^4 - 4 * q^9	\( 12 q + 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} + 18 q^{12} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} - 18 q^{26} - 6 q^{31} - 18 q^{33} - 12 q^{36} + 16 q^{37} + 48 q^{38} + 20 q^{44} - 54 q^{45} + 18 q^{47} - 2 q^{53} - 6 q^{58} + 12 q^{59} + 28 q^{64} + 42 q^{66} - 24 q^{67} + 20 q^{71} + 78 q^{75} + 8 q^{78} - 30 q^{80} + 14 q^{81} - 54 q^{82} - 38 q^{86} - 4 q^{88} + 66 q^{89} - 20 q^{92} + 12 q^{93} + 12 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 + 18 * q^12 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 - 18 * q^26 - 6 * q^31 - 18 * q^33 - 12 * q^36 + 16 * q^37 + 48 * q^38 + 20 * q^44 - 54 * q^45 + 18 * q^47 - 2 * q^53 - 6 * q^58 + 12 * q^59 + 28 * q^64 + 42 * q^66 - 24 * q^67 + 20 * q^71 + 78 * q^75 + 8 * q^78 - 30 * q^80 + 14 * q^81 - 54 * q^82 - 38 * q^86 - 4 * q^88 + 66 * q^89 - 20 * q^92 + 12 * q^93 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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