LMFDB - Embedded newform 1176.2.p.a.979.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1176,2,Mod(979,1176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1176, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1176.979"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.5
Character	$\chi$	$=$	1176.979
Dual form			1176.2.p.a.979.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04886 - 0.948630i) q^{2} +1.00000i q^{3} +(0.200203 + 1.98995i) q^{4} +2.88284 q^{5} +(0.948630 - 1.04886i) q^{6} +(1.67775 - 2.27710i) q^{8} -1.00000 q^{9} +(-3.02369 - 2.73475i) q^{10} -5.82680 q^{11} +(-1.98995 + 0.200203i) q^{12} -1.04841 q^{13} +2.88284i q^{15} +(-3.91984 + 0.796791i) q^{16} +6.82499i q^{17} +(1.04886 + 0.948630i) q^{18} -0.681229i q^{19} +(0.577155 + 5.73673i) q^{20} +(6.11148 + 5.52748i) q^{22} +2.14701i q^{23} +(2.27710 + 1.67775i) q^{24} +3.31079 q^{25} +(1.09963 + 0.994552i) q^{26} -1.00000i q^{27} +6.61515i q^{29} +(2.73475 - 3.02369i) q^{30} -3.83116 q^{31} +(4.86721 + 2.88275i) q^{32} -5.82680i q^{33} +(6.47439 - 7.15845i) q^{34} +(-0.200203 - 1.98995i) q^{36} +2.38082i q^{37} +(-0.646234 + 0.714512i) q^{38} -1.04841i q^{39} +(4.83668 - 6.56452i) q^{40} +1.19919i q^{41} +1.34319 q^{43} +(-1.16655 - 11.5951i) q^{44} -2.88284 q^{45} +(2.03672 - 2.25191i) q^{46} -11.0534 q^{47} +(-0.796791 - 3.91984i) q^{48} +(-3.47255 - 3.14072i) q^{50} -6.82499 q^{51} +(-0.209895 - 2.08629i) q^{52} +8.07845i q^{53} +(-0.948630 + 1.04886i) q^{54} -16.7978 q^{55} +0.681229 q^{57} +(6.27533 - 6.93835i) q^{58} -7.87073i q^{59} +(-5.73673 + 0.577155i) q^{60} +3.26942 q^{61} +(4.01834 + 3.63435i) q^{62} +(-2.37034 - 7.64078i) q^{64} -3.02240 q^{65} +(-5.52748 + 6.11148i) q^{66} +13.3126 q^{67} +(-13.5814 + 1.36639i) q^{68} -2.14701 q^{69} +1.08533i q^{71} +(-1.67775 + 2.27710i) q^{72} -5.64507i q^{73} +(2.25851 - 2.49714i) q^{74} +3.31079i q^{75} +(1.35561 - 0.136384i) q^{76} +(-0.994552 + 1.09963i) q^{78} +12.6589i q^{79} +(-11.3003 + 2.29703i) q^{80} +1.00000 q^{81} +(1.13758 - 1.25778i) q^{82} -0.482042i q^{83} +19.6754i q^{85} +(-1.40882 - 1.27419i) q^{86} -6.61515 q^{87} +(-9.77589 + 13.2682i) q^{88} +12.3909i q^{89} +(3.02369 + 2.73475i) q^{90} +(-4.27246 + 0.429839i) q^{92} -3.83116i q^{93} +(11.5934 + 10.4856i) q^{94} -1.96388i q^{95} +(-2.88275 + 4.86721i) q^{96} +3.63532i q^{97} +5.82680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.04886	−	0.948630i	−0.741654	−	0.670782i
$2$	−1.04886	−	0.948630i	−0.741654	−	0.670782i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.200203	+	1.98995i	0.100102	+	0.994977i
$5$	2.88284			1.28925			0.644624	−	0.764500i	$-0.277014\pi$
$5$	2.88284			1.28925			0.644624	+	0.764500i	$0.277014\pi$
$6$	0.948630	−	1.04886i	0.387276	−	0.428194i
$7$		0			0
$7$		0			0
$8$	1.67775	−	2.27710i	0.593172	−	0.805075i
$9$	−1.00000			−0.333333
$10$	−3.02369	−	2.73475i	−0.956176	−	0.864805i
$11$	−5.82680			−1.75685			−0.878423	−	0.477883i	$-0.841404\pi$
$11$	−5.82680			−1.75685			−0.878423	+	0.477883i	$0.841404\pi$
$12$	−1.98995	+	0.200203i	−0.574450	+	0.0577937i
$13$	−1.04841			−0.290776			−0.145388	−	0.989375i	$-0.546443\pi$
$13$	−1.04841			−0.290776			−0.145388	+	0.989375i	$0.546443\pi$
$14$		0			0
$15$			2.88284i			0.744347i
$16$	−3.91984	+	0.796791i	−0.979959	+	0.199198i
$17$			6.82499i			1.65530i	0.561241	+	0.827652i	$0.310324\pi$
$17$			6.82499i			1.65530i	−0.561241	+	0.827652i	$0.689676\pi$
$18$	1.04886	+	0.948630i	0.247218	+	0.223594i
$19$		−	0.681229i		−	0.156285i	−0.996942	−	0.0781423i	$-0.975101\pi$
$19$		−	0.681229i		−	0.156285i	0.996942	−	0.0781423i	$-0.0248989\pi$
$20$	0.577155	+	5.73673i	0.129056	+	1.28277i
$21$		0			0
$22$	6.11148	+	5.52748i	1.30297	+	1.17846i
$23$			2.14701i			0.447683i	0.974626	+	0.223841i	$0.0718598\pi$
$23$			2.14701i			0.447683i	−0.974626	+	0.223841i	$0.928140\pi$
$24$	2.27710	+	1.67775i	0.464811	+	0.342468i
$25$	3.31079			0.662159
$26$	1.09963	+	0.994552i	0.215655	+	0.195048i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			6.61515i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$29$			6.61515i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$30$	2.73475	−	3.02369i	0.499295	−	0.552048i
$31$	−3.83116			−0.688096			−0.344048	−	0.938952i	$-0.611798\pi$
$31$	−3.83116			−0.688096			−0.344048	+	0.938952i	$0.611798\pi$
$32$	4.86721	+	2.88275i	0.860409	+	0.509604i
$33$		−	5.82680i		−	1.01432i
$34$	6.47439	−	7.15845i	1.11035	−	1.22766i
$35$		0			0
$36$	−0.200203	−	1.98995i	−0.0333672	−	0.331659i
$37$			2.38082i			0.391404i	0.980663	+	0.195702i	$0.0626985\pi$
$37$			2.38082i			0.391404i	−0.980663	+	0.195702i	$0.937302\pi$
$38$	−0.646234	+	0.714512i	−0.104833	+	0.115909i
$39$		−	1.04841i		−	0.167880i
$40$	4.83668	−	6.56452i	0.764746	−	1.03794i
$41$			1.19919i			0.187281i	0.995606	+	0.0936407i	$0.0298505\pi$
$41$			1.19919i			0.187281i	−0.995606	+	0.0936407i	$0.970149\pi$
$42$		0			0
$43$	1.34319			0.204835			0.102418	−	0.994741i	$-0.467342\pi$
$43$	1.34319			0.204835			0.102418	+	0.994741i	$0.467342\pi$
$44$	−1.16655	−	11.5951i	−0.175863	−	1.74802i
$45$	−2.88284			−0.429749
$46$	2.03672	−	2.25191i	0.300298	−	0.332026i
$47$	−11.0534			−1.61230			−0.806152	−	0.591708i	$-0.798454\pi$
$47$	−11.0534			−1.61230			−0.806152	+	0.591708i	$0.798454\pi$
$48$	−0.796791	−	3.91984i	−0.115007	−	0.565780i
$49$		0			0
$50$	−3.47255	−	3.14072i	−0.491093	−	0.444165i
$51$	−6.82499			−0.955690
$52$	−0.209895	−	2.08629i	−0.0291072	−	0.289316i
$53$			8.07845i			1.10966i	0.831963	+	0.554830i	$0.187217\pi$
$53$			8.07845i			1.10966i	−0.831963	+	0.554830i	$0.812783\pi$
$54$	−0.948630	+	1.04886i	−0.129092	+	0.142731i
$55$	−16.7978			−2.26501
$56$		0			0
$57$	0.681229			0.0902310
$58$	6.27533	−	6.93835i	0.823991	−	0.911050i
$59$		−	7.87073i		−	1.02468i	−0.858782	−	0.512341i	$-0.828778\pi$
$59$		−	7.87073i		−	1.02468i	0.858782	−	0.512341i	$-0.171222\pi$
$60$	−5.73673	+	0.577155i	−0.740609	+	0.0745104i
$61$	3.26942			0.418607			0.209303	−	0.977851i	$-0.432880\pi$
$61$	3.26942			0.418607			0.209303	+	0.977851i	$0.432880\pi$
$62$	4.01834	+	3.63435i	0.510329	+	0.461563i
$63$		0			0
$64$	−2.37034	−	7.64078i	−0.296293	−	0.955097i
$65$	−3.02240			−0.374883
$66$	−5.52748	+	6.11148i	−0.680385	+	0.752272i
$67$	13.3126			1.62639			0.813195	−	0.581991i	$-0.197726\pi$
$67$	13.3126			1.62639			0.813195	+	0.581991i	$0.197726\pi$
$68$	−13.5814	+	1.36639i	−1.64699	+	0.165699i
$69$	−2.14701			−0.258470
$70$		0			0
$71$			1.08533i			0.128805i	0.997924	+	0.0644027i	$0.0205142\pi$
$71$			1.08533i			0.128805i	−0.997924	+	0.0644027i	$0.979486\pi$
$72$	−1.67775	+	2.27710i	−0.197724	+	0.268358i
$73$		−	5.64507i		−	0.660706i	−0.943858	−	0.330353i	$-0.892832\pi$
$73$		−	5.64507i		−	0.660706i	0.943858	−	0.330353i	$-0.107168\pi$
$74$	2.25851	−	2.49714i	0.262547	−	0.290286i
$75$			3.31079i			0.382298i
$76$	1.35561	−	0.136384i	0.155500	−	0.0156444i
$77$		0			0
$78$	−0.994552	+	1.09963i	−0.112611	+	0.124509i
$79$			12.6589i			1.42424i	0.702057	+	0.712120i	$0.252265\pi$
$79$			12.6589i			1.42424i	−0.702057	+	0.712120i	$0.747735\pi$
$80$	−11.3003	+	2.29703i	−1.26341	+	0.256815i
$81$	1.00000			0.111111
$82$	1.13758	−	1.25778i	0.125625	−	0.138898i
$83$		−	0.482042i		−	0.0529110i	−0.999650	−	0.0264555i	$-0.991578\pi$
$83$		−	0.482042i		−	0.0529110i	0.999650	−	0.0264555i	$-0.00842203\pi$
$84$		0			0
$85$			19.6754i			2.13410i
$86$	−1.40882	−	1.27419i	−0.151917	−	0.137400i
$87$	−6.61515			−0.709218
$88$	−9.77589	+	13.2682i	−1.04211	+	1.41439i
$89$			12.3909i			1.31343i	0.754140	+	0.656714i	$0.228054\pi$
$89$			12.3909i			1.31343i	−0.754140	+	0.656714i	$0.771946\pi$
$90$	3.02369	+	2.73475i	0.318725	+	0.288268i
$91$		0			0
$92$	−4.27246	+	0.429839i	−0.445434	+	0.0448138i
$93$		−	3.83116i		−	0.397272i
$94$	11.5934	+	10.4856i	1.19577	+	1.08151i
$95$		−	1.96388i		−	0.201490i
$96$	−2.88275	+	4.86721i	−0.294220	+	0.496758i
$97$			3.63532i			0.369111i	0.982822	+	0.184556i	$0.0590846\pi$
$97$			3.63532i			0.369111i	−0.982822	+	0.184556i	$0.940915\pi$
$98$		0			0
$99$	5.82680			0.585616
$100$	0.662832	+	6.58833i	0.0662832	+	0.658833i
$101$	−2.50468			−0.249225			−0.124612	−	0.992206i	$-0.539769\pi$
$101$	−2.50468			−0.249225			−0.124612	+	0.992206i	$0.539769\pi$
$102$	7.15845	+	6.47439i	0.708792	+	0.641060i
$103$	4.62644			0.455857			0.227928	−	0.973678i	$-0.426805\pi$
$103$	4.62644			0.455857			0.227928	+	0.973678i	$0.426805\pi$
$104$	−1.75896	+	2.38733i	−0.172480	+	0.234097i
$105$		0			0
$106$	7.66346	−	8.47315i	0.744341	−	0.822985i
$107$	−6.06946			−0.586757			−0.293378	−	0.955996i	$-0.594780\pi$
$107$	−6.06946			−0.586757			−0.293378	+	0.955996i	$0.594780\pi$
$108$	1.98995	−	0.200203i	0.191483	−	0.0192646i
$109$		−	14.5645i		−	1.39503i	−0.716573	−	0.697513i	$-0.754290\pi$
$109$		−	14.5645i		−	1.39503i	0.716573	−	0.697513i	$-0.245710\pi$
$110$	17.6185	+	15.9349i	1.67985	+	1.51933i
$111$	−2.38082			−0.225977
$112$		0			0
$113$	−3.82875			−0.360179			−0.180089	−	0.983650i	$-0.557639\pi$
$113$	−3.82875			−0.360179			−0.180089	+	0.983650i	$0.557639\pi$
$114$	−0.714512	−	0.646234i	−0.0669202	−	0.0605254i
$115$			6.18950i			0.577174i
$116$	−13.1638	+	1.32438i	−1.22223	+	0.122965i
$117$	1.04841			0.0969254
$118$	−7.46641	+	8.25527i	−0.687339	+	0.759959i
$119$		0			0
$120$	6.56452	+	4.83668i	0.599256	+	0.441526i
$121$	22.9516			2.08651
$122$	−3.42916	−	3.10147i	−0.310461	−	0.280794i
$123$	−1.19919			−0.108127
$124$	−0.767011	−	7.62383i	−0.0688796	−	0.684640i
$125$	−4.86972			−0.435561
$126$		0			0
$127$			0.550415i			0.0488415i	0.999702	+	0.0244207i	$0.00777413\pi$
$127$			0.550415i			0.0488415i	−0.999702	+	0.0244207i	$0.992226\pi$
$128$	−4.76212	+	10.2627i	−0.420916	+	0.907100i
$129$			1.34319i			0.118262i
$130$	3.17007	+	2.86714i	0.278033	+	0.251465i
$131$		−	2.80383i		−	0.244971i	−0.992470	−	0.122486i	$-0.960913\pi$
$131$		−	2.80383i		−	0.244971i	0.992470	−	0.122486i	$-0.0390866\pi$
$132$	11.5951	−	1.16655i	1.00922	−	0.101535i
$133$		0			0
$134$	−13.9630	−	12.6287i	−1.20622	−	1.09095i
$135$		−	2.88284i		−	0.248116i
$136$	15.5412	+	11.4506i	1.33264	+	0.981881i
$137$	12.7630			1.09041			0.545206	−	0.838302i	$-0.316451\pi$
$137$	12.7630			1.09041			0.545206	+	0.838302i	$0.316451\pi$
$138$	2.25191	+	2.03672i	0.191695	+	0.173377i
$139$		−	6.11761i		−	0.518889i	−0.965758	−	0.259444i	$-0.916461\pi$
$139$		−	6.11761i		−	0.518889i	0.965758	−	0.259444i	$-0.0835394\pi$
$140$		0			0
$141$		−	11.0534i		−	0.930864i
$142$	1.02958	−	1.13836i	0.0864004	−	0.0955290i
$143$	6.10887			0.510849
$144$	3.91984	−	0.796791i	0.326653	−	0.0663993i
$145$			19.0704i			1.58371i
$146$	−5.35508	+	5.92087i	−0.443190	+	0.490015i
$147$		0			0
$148$	−4.73771	+	0.476647i	−0.389438	+	0.0391802i
$149$		−	2.02260i		−	0.165698i	−0.996562	−	0.0828491i	$-0.973598\pi$
$149$		−	2.02260i		−	0.165698i	0.996562	−	0.0828491i	$-0.0264019\pi$
$150$	3.14072	−	3.47255i	0.256439	−	0.283533i
$151$			14.0681i			1.14484i	0.819959	+	0.572422i	$0.193996\pi$
$151$			14.0681i			1.14484i	−0.819959	+	0.572422i	$0.806004\pi$
$152$	−1.55122	−	1.14293i	−0.125821	−	0.0927037i
$153$		−	6.82499i		−	0.551768i
$154$		0			0
$155$	−11.0446			−0.887126
$156$	2.08629	−	0.209895i	0.167037	−	0.0168050i
$157$	5.23477			0.417780			0.208890	−	0.977939i	$-0.433015\pi$
$157$	5.23477			0.417780			0.208890	+	0.977939i	$0.433015\pi$
$158$	12.0086	−	13.2774i	0.955356	−	1.05629i
$159$	−8.07845			−0.640663
$160$	14.0314	+	8.31053i	1.10928	+	0.657005i
$161$		0			0
$162$	−1.04886	−	0.948630i	−0.0824060	−	0.0745314i
$163$	0.976425			0.0764795			0.0382397	−	0.999269i	$-0.487825\pi$
$163$	0.976425			0.0764795			0.0382397	+	0.999269i	$0.487825\pi$
$164$	−2.38633	+	0.240081i	−0.186341	+	0.0187472i
$165$		−	16.7978i		−	1.30770i
$166$	−0.457280	+	0.505594i	−0.0354918	+	0.0392417i
$167$	2.08267			0.161162			0.0805808	−	0.996748i	$-0.474322\pi$
$167$	2.08267			0.161162			0.0805808	+	0.996748i	$0.474322\pi$
$168$		0			0
$169$	−11.9008			−0.915449
$170$	18.6647	−	20.6367i	1.43151	−	1.58276i
$171$			0.681229i			0.0520949i
$172$	0.268912	+	2.67290i	0.0205043	+	0.203806i
$173$	−21.3463			−1.62293			−0.811465	−	0.584402i	$-0.801329\pi$
$173$	−21.3463			−1.62293			−0.811465	+	0.584402i	$0.801329\pi$
$174$	6.93835	+	6.27533i	0.525995	+	0.475731i
$175$		0			0
$176$	22.8401	−	4.64274i	1.72164	−	0.349960i
$177$	7.87073			0.591600
$178$	11.7543	−	12.9962i	0.881025	−	0.974110i
$179$	−6.94974			−0.519448			−0.259724	−	0.965683i	$-0.583632\pi$
$179$	−6.94974			−0.519448			−0.259724	+	0.965683i	$0.583632\pi$
$180$	−0.577155	−	5.73673i	−0.0430186	−	0.427591i
$181$	7.67619			0.570566			0.285283	−	0.958443i	$-0.407912\pi$
$181$	7.67619			0.570566			0.285283	+	0.958443i	$0.407912\pi$
$182$		0			0
$183$			3.26942i			0.241683i
$184$	4.88895	+	3.60214i	0.360418	+	0.265553i
$185$			6.86352i			0.504616i
$186$	−3.63435	+	4.01834i	−0.266483	+	0.294639i
$187$		−	39.7679i		−	2.90812i
$188$	−2.21293	−	21.9958i	−0.161394	−	1.60421i
$189$		0			0
$190$	−1.86299	+	2.05983i	−0.135156	+	0.149436i
$191$			17.8099i			1.28868i	0.764739	+	0.644340i	$0.222868\pi$
$191$			17.8099i			1.28868i	−0.764739	+	0.644340i	$0.777132\pi$
$192$	7.64078	−	2.37034i	0.551426	−	0.171065i
$193$	−13.7959			−0.993054			−0.496527	−	0.868021i	$-0.665392\pi$
$193$	−13.7959			−0.993054			−0.496527	+	0.868021i	$0.665392\pi$
$194$	3.44858	−	3.81294i	0.247593	−	0.273753i
$195$		−	3.02240i		−	0.216439i
$196$		0			0
$197$			1.13180i			0.0806374i	0.999187	+	0.0403187i	$0.0128373\pi$
$197$			1.13180i			0.0806374i	−0.999187	+	0.0403187i	$0.987163\pi$
$198$	−6.11148	−	5.52748i	−0.434324	−	0.392821i
$199$	−8.53186			−0.604808			−0.302404	−	0.953180i	$-0.597789\pi$
$199$	−8.53186			−0.604808			−0.302404	+	0.953180i	$0.597789\pi$
$200$	5.55467	−	7.53900i	0.392774	−	0.533088i
$201$			13.3126i			0.938997i
$202$	2.62705	+	2.37601i	0.184838	+	0.167175i
$203$		0			0
$204$	−1.36639	−	13.5814i	−0.0956662	−	0.950890i
$205$			3.45707i			0.241452i
$206$	−4.85247	−	4.38878i	−0.338088	−	0.305781i
$207$		−	2.14701i		−	0.149228i
$208$	4.10959	−	0.835363i	0.284949	−	0.0579220i
$209$			3.96939i			0.274568i
$210$		0			0
$211$	21.2436			1.46247			0.731237	−	0.682124i	$-0.238944\pi$
$211$	21.2436			1.46247			0.731237	+	0.682124i	$0.238944\pi$
$212$	−16.0758	+	1.61733i	−1.10409	+	0.111079i
$213$	−1.08533			−0.0743658
$214$	6.36600	+	5.75767i	0.435171	+	0.393586i
$215$	3.87222			0.264083
$216$	−2.27710	−	1.67775i	−0.154937	−	0.114156i
$217$		0			0
$218$	−13.8163	+	15.2761i	−0.935758	+	1.03463i
$219$	5.64507			0.381459
$220$	−3.36297	−	33.4268i	−0.226731	−	2.25363i
$221$		−	7.15538i		−	0.481323i
$222$	2.49714	+	2.25851i	0.167597	+	0.151581i
$223$	−3.12207			−0.209069			−0.104535	−	0.994521i	$-0.533335\pi$
$223$	−3.12207			−0.209069			−0.104535	+	0.994521i	$0.533335\pi$
$224$		0			0
$225$	−3.31079			−0.220720
$226$	4.01581	+	3.63207i	0.267128	+	0.241602i
$227$		−	5.22675i		−	0.346911i	−0.984842	−	0.173456i	$-0.944507\pi$
$227$		−	5.22675i		−	0.346911i	0.984842	−	0.173456i	$-0.0554933\pi$
$228$	0.136384	+	1.35561i	0.00903227	+	0.0897778i
$229$	28.4258			1.87843			0.939215	−	0.343329i	$-0.111554\pi$
$229$	28.4258			1.87843			0.939215	+	0.343329i	$0.111554\pi$
$230$	5.87154	−	6.49190i	0.387158	−	0.428063i
$231$		0			0
$232$	15.0633	+	11.0985i	0.988957	+	0.728655i
$233$	6.11941			0.400896			0.200448	−	0.979704i	$-0.435760\pi$
$233$	6.11941			0.400896			0.200448	+	0.979704i	$0.435760\pi$
$234$	−1.09963	−	0.994552i	−0.0718851	−	0.0650159i
$235$	−31.8652			−2.07866
$236$	15.6624	−	1.57575i	1.01954	−	0.102572i
$237$	−12.6589			−0.822286
$238$		0			0
$239$			8.83528i			0.571507i	0.958303	+	0.285753i	$0.0922439\pi$
$239$			8.83528i			0.571507i	−0.958303	+	0.285753i	$0.907756\pi$
$240$	−2.29703	−	11.3003i	−0.148272	−	0.729430i
$241$		−	5.95545i		−	0.383624i	−0.981432	−	0.191812i	$-0.938564\pi$
$241$		−	5.95545i		−	0.383624i	0.981432	−	0.191812i	$-0.0614364\pi$
$242$	−24.0730	−	21.7726i	−1.54747	−	1.39959i
$243$			1.00000i			0.0641500i
$244$	0.654550	+	6.50600i	0.0419032	+	0.416504i
$245$		0			0
$246$	1.25778	+	1.13758i	0.0801928	+	0.0725297i
$247$			0.714206i			0.0454439i
$248$	−6.42770	+	8.72392i	−0.408160	+	0.553969i
$249$	0.482042			0.0305482
$250$	5.10764	+	4.61956i	0.323035	+	0.292167i
$251$			2.13955i			0.135047i	0.997718	+	0.0675235i	$0.0215098\pi$
$251$			2.13955i			0.135047i	−0.997718	+	0.0675235i	$0.978490\pi$
$252$		0			0
$253$		−	12.5102i		−	0.786510i
$254$	0.522140	−	0.577307i	0.0327620	−	0.0362235i
$255$	−19.6754			−1.23212
$256$	14.7302	−	6.24658i	0.920640	−	0.390411i
$257$		−	19.2869i		−	1.20309i	−0.798841	−	0.601543i	$-0.794553\pi$
$257$		−	19.2869i		−	1.20309i	0.798841	−	0.601543i	$-0.205447\pi$
$258$	1.27419	−	1.40882i	0.0793278	−	0.0877092i
$259$		0			0
$260$	−0.605095	−	6.01444i	−0.0375264	−	0.373000i
$261$		−	6.61515i		−	0.409467i
$262$	−2.65979	+	2.94081i	−0.164323	+	0.181684i
$263$			24.3341i			1.50051i	0.661150	+	0.750254i	$0.270069\pi$
$263$			24.3341i			1.50051i	−0.661150	+	0.750254i	$0.729931\pi$
$264$	−13.2682	−	9.77589i	−0.816601	−	0.601664i
$265$			23.2889i			1.43063i
$266$		0			0
$267$	−12.3909			−0.758308
$268$	2.66522	+	26.4914i	0.162804	+	1.61822i
$269$	20.9009			1.27435			0.637176	−	0.770718i	$-0.280102\pi$
$269$	20.9009			1.27435			0.637176	+	0.770718i	$0.280102\pi$
$270$	−2.73475	+	3.02369i	−0.166432	+	0.184016i
$271$	−19.9939			−1.21455			−0.607273	−	0.794493i	$-0.707736\pi$
$271$	−19.9939			−1.21455			−0.607273	+	0.794493i	$0.707736\pi$
$272$	−5.43810	−	26.7529i	−0.329733	−	1.62213i
$273$		0			0
$274$	−13.3865	−	12.1073i	−0.808709	−	0.731430i
$275$	−19.2913			−1.16331
$276$	−0.429839	−	4.27246i	−0.0258733	−	0.257172i
$277$		−	15.2920i		−	0.918807i	−0.888228	−	0.459404i	$-0.848063\pi$
$277$		−	15.2920i		−	0.918807i	0.888228	−	0.459404i	$-0.151937\pi$
$278$	−5.80335	+	6.41650i	−0.348062	+	0.384836i
$279$	3.83116			0.229365
$280$		0			0
$281$	5.59802			0.333950			0.166975	−	0.985961i	$-0.446600\pi$
$281$	5.59802			0.333950			0.166975	+	0.985961i	$0.446600\pi$
$282$	−10.4856	+	11.5934i	−0.624407	+	0.690379i
$283$		−	11.2342i		−	0.667804i	−0.942608	−	0.333902i	$-0.891635\pi$
$283$		−	11.2342i		−	0.667804i	0.942608	−	0.333902i	$-0.108365\pi$
$284$	−2.15976	+	0.217287i	−0.128158	+	0.0128936i
$285$	1.96388			0.116330
$286$	−6.40733	−	5.79505i	−0.378874	−	0.342669i
$287$		0			0
$288$	−4.86721	−	2.88275i	−0.286803	−	0.169868i
$289$	−29.5806			−1.74003
$290$	18.0908	−	20.0022i	1.06233	−	1.17457i
$291$	−3.63532			−0.213106
$292$	11.2334	−	1.13016i	0.657387	−	0.0661378i
$293$	17.7212			1.03528			0.517642	−	0.855598i	$-0.326810\pi$
$293$	17.7212			1.03528			0.517642	+	0.855598i	$0.326810\pi$
$294$		0			0
$295$		−	22.6901i		−	1.32107i
$296$	5.42135	+	3.99440i	0.315109	+	0.232170i
$297$			5.82680i			0.338105i
$298$	−1.91870	+	2.12142i	−0.111147	+	0.122891i
$299$		−	2.25095i		−	0.130176i
$300$	−6.58833	+	0.662832i	−0.380377	+	0.0382686i
$301$		0			0
$302$	13.3454	−	14.7554i	0.767941	−	0.849078i
$303$		−	2.50468i		−	0.143890i
$304$	0.542797	+	2.67031i	0.0311316	+	0.153153i
$305$	9.42524			0.539688
$306$	−6.47439	+	7.15845i	−0.370116	+	0.409221i
$307$		−	20.3724i		−	1.16271i	−0.813649	−	0.581357i	$-0.802522\pi$
$307$		−	20.3724i		−	1.16271i	0.813649	−	0.581357i	$-0.197478\pi$
$308$		0			0
$309$			4.62644i			0.263189i
$310$	11.5842	+	10.4773i	0.657941	+	0.595069i
$311$	28.8727			1.63722			0.818610	−	0.574350i	$-0.194745\pi$
$311$	28.8727			1.63722			0.818610	+	0.574350i	$0.194745\pi$
$312$	−2.38733	−	1.75896i	−0.135156	−	0.0995816i
$313$		−	4.71947i		−	0.266760i	−0.991065	−	0.133380i	$-0.957417\pi$
$313$		−	4.71947i		−	0.266760i	0.991065	−	0.133380i	$-0.0425831\pi$
$314$	−5.49053	−	4.96586i	−0.309848	−	0.280240i
$315$		0			0
$316$	−25.1907	+	2.53436i	−1.41709	+	0.142569i
$317$		−	25.4437i		−	1.42906i	−0.699606	−	0.714529i	$-0.746641\pi$
$317$		−	25.4437i		−	1.42906i	0.699606	−	0.714529i	$-0.253359\pi$
$318$	8.47315	+	7.66346i	0.475150	+	0.429746i
$319$		−	38.5452i		−	2.15811i
$320$	−6.83333	−	22.0272i	−0.381995	−	1.23136i
$321$		−	6.06946i		−	0.338764i
$322$		0			0
$323$	4.64938			0.258699
$324$	0.200203	+	1.98995i	0.0111224	+	0.110553i
$325$	−3.47107			−0.192540
$326$	−1.02413	−	0.926266i	−0.0567213	−	0.0513011i
$327$	14.5645			0.805418
$328$	2.73066	+	2.01193i	0.150776	+	0.111090i
$329$		0			0
$330$	−15.9349	+	17.6185i	−0.877185	+	0.969864i
$331$	−19.7186			−1.08383			−0.541916	−	0.840433i	$-0.682301\pi$
$331$	−19.7186			−1.08383			−0.541916	+	0.840433i	$0.682301\pi$
$332$	0.959242	−	0.0965065i	0.0526453	−	0.00529648i
$333$		−	2.38082i		−	0.130468i
$334$	−2.18442	−	1.97568i	−0.119526	−	0.108104i
$335$	38.3781			2.09682
$336$		0			0
$337$	−24.7720			−1.34942			−0.674709	−	0.738084i	$-0.735731\pi$
$337$	−24.7720			−1.34942			−0.674709	+	0.738084i	$0.735731\pi$
$338$	12.4823	+	11.2895i	0.678947	+	0.614067i
$339$		−	3.82875i		−	0.207949i
$340$	−39.1531	+	3.93908i	−2.12338	+	0.213627i
$341$	22.3234			1.20888
$342$	0.646234	−	0.714512i	0.0349443	−	0.0386364i
$343$		0			0
$344$	2.25354	−	3.05858i	0.121503	−	0.164908i
$345$	−6.18950			−0.333232
$346$	22.3892	+	20.2497i	1.20365	+	1.08863i
$347$	−14.9883			−0.804612			−0.402306	−	0.915505i	$-0.631791\pi$
$347$	−14.9883			−0.804612			−0.402306	+	0.915505i	$0.631791\pi$
$348$	−1.32438	−	13.1638i	−0.0709940	−	0.705656i
$349$	−27.4546			−1.46961			−0.734806	−	0.678278i	$-0.762727\pi$
$349$	−27.4546			−1.46961			−0.734806	+	0.678278i	$0.762727\pi$
$350$		0			0
$351$			1.04841i			0.0559599i
$352$	−28.3603	−	16.7972i	−1.51161	−	0.895296i
$353$		−	24.0043i		−	1.27762i	−0.769364	−	0.638811i	$-0.779427\pi$
$353$		−	24.0043i		−	1.27762i	0.769364	−	0.638811i	$-0.220573\pi$
$354$	−8.25527	−	7.46641i	−0.438763	−	0.396835i
$355$			3.12885i			0.166062i
$356$	−24.6572	+	2.48069i	−1.30683	+	0.131476i
$357$		0			0
$358$	7.28928	+	6.59273i	0.385251	+	0.348437i
$359$			13.6543i			0.720645i	0.932828	+	0.360322i	$0.117333\pi$
$359$			13.6543i			0.720645i	−0.932828	+	0.360322i	$0.882667\pi$
$360$	−4.83668	+	6.56452i	−0.254915	+	0.345980i
$361$	18.5359			0.975575
$362$	−8.05122	−	7.28186i	−0.423163	−	0.382726i
$363$			22.9516i			1.20465i
$364$		0			0
$365$		−	16.2739i		−	0.851813i
$366$	3.10147	−	3.42916i	0.162117	−	0.179245i
$367$	34.6847			1.81053			0.905264	−	0.424849i	$-0.139673\pi$
$367$	34.6847			1.81053			0.905264	+	0.424849i	$0.139673\pi$
$368$	−1.71072	−	8.41594i	−0.0891774	−	0.438711i
$369$		−	1.19919i		−	0.0624272i
$370$	6.51094	−	7.19885i	0.338488	−	0.374251i
$371$		0			0
$372$	7.62383	−	0.767011i	0.395277	−	0.0397676i
$373$		−	6.08232i		−	0.314931i	−0.987525	−	0.157465i	$-0.949668\pi$
$373$		−	6.08232i		−	0.314931i	0.987525	−	0.157465i	$-0.0503322\pi$
$374$	−37.7250	+	41.7108i	−1.95071	+	2.15682i
$375$		−	4.86972i		−	0.251471i
$376$	−18.5448	+	25.1697i	−0.956374	+	1.29803i
$377$		−	6.93538i		−	0.357190i
$378$		0			0
$379$	19.0628			0.979189			0.489594	−	0.871950i	$-0.337145\pi$
$379$	19.0628			0.979189			0.489594	+	0.871950i	$0.337145\pi$
$380$	3.90803	−	0.393175i	0.200477	−	0.0201694i
$381$	−0.550415			−0.0281986
$382$	16.8950	−	18.6800i	0.864424	−	0.955754i
$383$	−8.25003			−0.421557			−0.210778	−	0.977534i	$-0.567600\pi$
$383$	−8.25003			−0.421557			−0.210778	+	0.977534i	$0.567600\pi$
$384$	−10.2627	−	4.76212i	−0.523714	−	0.243016i
$385$		0			0
$386$	14.4700	+	13.0872i	0.736502	+	0.666123i
$387$	−1.34319			−0.0682784
$388$	−7.23413	+	0.727804i	−0.367257	+	0.0369487i
$389$			19.6214i			0.994844i	0.867509	+	0.497422i	$0.165720\pi$
$389$			19.6214i			0.994844i	−0.867509	+	0.497422i	$0.834280\pi$
$390$	−2.86714	+	3.17007i	−0.145183	+	0.160523i
$391$	−14.6533			−0.741051
$392$		0			0
$393$	2.80383			0.141434
$394$	1.07366	−	1.18710i	0.0540901	−	0.0598050i
$395$			36.4937i			1.83620i
$396$	1.16655	+	11.5951i	0.0586211	+	0.582674i
$397$	31.3631			1.57407			0.787035	−	0.616908i	$-0.211615\pi$
$397$	31.3631			1.57407			0.787035	+	0.616908i	$0.211615\pi$
$398$	8.94870	+	8.09358i	0.448558	+	0.405694i
$399$		0			0
$400$	−12.9778	+	2.63801i	−0.648889	+	0.131901i
$401$	34.9124			1.74344			0.871722	−	0.490002i	$-0.163004\pi$
$401$	34.9124			1.74344			0.871722	+	0.490002i	$0.163004\pi$
$402$	12.6287	−	13.9630i	0.629863	−	0.696411i
$403$	4.01662			0.200082
$404$	−0.501444	−	4.98419i	−0.0249478	−	0.247973i
$405$	2.88284			0.143250
$406$		0			0
$407$		−	13.8725i		−	0.687636i
$408$	−11.4506	+	15.5412i	−0.566889	+	0.769403i
$409$		−	13.6465i		−	0.674776i	−0.941366	−	0.337388i	$-0.890457\pi$
$409$		−	13.6465i		−	0.674776i	0.941366	−	0.337388i	$-0.109543\pi$
$410$	3.27948	−	3.62597i	0.161962	−	0.179074i
$411$			12.7630i			0.629550i
$412$	0.926229	+	9.20640i	0.0456320	+	0.453567i
$413$		0			0
$414$	−2.03672	+	2.25191i	−0.100099	+	0.110675i
$415$		−	1.38965i		−	0.0682154i
$416$	−5.10282	−	3.02230i	−0.250187	−	0.148181i
$417$	6.11761			0.299581
$418$	3.76548	−	4.16332i	0.184175	−	0.203635i
$419$			4.22322i			0.206318i	0.994665	+	0.103159i	$0.0328950\pi$
$419$			4.22322i			0.206318i	−0.994665	+	0.103159i	$0.967105\pi$
$420$		0			0
$421$			11.6892i			0.569697i	0.958573	+	0.284849i	$0.0919433\pi$
$421$			11.6892i			0.569697i	−0.958573	+	0.284849i	$0.908057\pi$
$422$	−22.2816	−	20.1524i	−1.08465	−	0.981001i
$423$	11.0534			0.537435
$424$	18.3954	+	13.5536i	0.893361	+	0.658220i
$425$			22.5962i			1.09607i
$426$	1.13836	+	1.02958i	0.0551537	+	0.0498833i
$427$		0			0
$428$	−1.21513	−	12.0779i	−0.0587354	−	0.583810i
$429$			6.10887i			0.294939i
$430$	−4.06141	−	3.67330i	−0.195858	−	0.177142i
$431$			34.3020i			1.65227i	0.563471	+	0.826136i	$0.309465\pi$
$431$			34.3020i			1.65227i	−0.563471	+	0.826136i	$0.690535\pi$
$432$	0.796791	+	3.91984i	0.0383356	+	0.188593i
$433$		−	14.1884i		−	0.681853i	−0.940090	−	0.340926i	$-0.889259\pi$
$433$		−	14.1884i		−	0.681853i	0.940090	−	0.340926i	$-0.110741\pi$
$434$		0			0
$435$	−19.0704			−0.914358
$436$	28.9827	−	2.91586i	1.38802	−	0.139644i
$437$	1.46261			0.0699659
$438$	−5.92087	−	5.35508i	−0.282910	−	0.255876i
$439$	−28.0504			−1.33877			−0.669386	−	0.742915i	$-0.733443\pi$
$439$	−28.0504			−1.33877			−0.669386	+	0.742915i	$0.733443\pi$
$440$	−28.1824	+	38.2501i	−1.34354	+	1.82350i
$441$		0			0
$442$	−6.78781	+	7.50498i	−0.322863	+	0.356975i
$443$	11.0208			0.523614			0.261807	−	0.965120i	$-0.415682\pi$
$443$	11.0208			0.523614			0.261807	+	0.965120i	$0.415682\pi$
$444$	−0.476647	−	4.73771i	−0.0226207	−	0.224842i
$445$			35.7209i			1.69333i
$446$	3.27461	+	2.96169i	0.155057	+	0.140240i
$447$	2.02260			0.0956659
$448$		0			0
$449$	30.2270			1.42650			0.713250	−	0.700910i	$-0.247222\pi$
$449$	30.2270			1.42650			0.713250	+	0.700910i	$0.247222\pi$
$450$	3.47255	+	3.14072i	0.163698	+	0.148055i
$451$		−	6.98742i		−	0.329025i
$452$	−0.766529	−	7.61904i	−0.0360545	−	0.358370i
$453$	−14.0681			−0.660976
$454$	−4.95825	+	5.48211i	−0.232702	+	0.257288i
$455$		0			0
$456$	1.14293	−	1.55122i	0.0535225	−	0.0726427i
$457$	25.4772			1.19177			0.595887	−	0.803068i	$-0.296801\pi$
$457$	25.4772			1.19177			0.595887	+	0.803068i	$0.296801\pi$
$458$	−29.8146	−	26.9656i	−1.39315	−	1.26002i
$459$	6.82499			0.318563
$460$	−12.3168	+	1.23916i	−0.574275	+	0.0577761i
$461$	27.9292			1.30079			0.650395	−	0.759596i	$-0.274603\pi$
$461$	27.9292			1.30079			0.650395	+	0.759596i	$0.274603\pi$
$462$		0			0
$463$		−	19.4232i		−	0.902674i	−0.892354	−	0.451337i	$-0.850947\pi$
$463$		−	19.4232i		−	0.902674i	0.892354	−	0.451337i	$-0.149053\pi$
$464$	−5.27089	−	25.9303i	−0.244695	−	1.20378i
$465$		−	11.0446i		−	0.512182i
$466$	−6.41839	−	5.80506i	−0.297326	−	0.268914i
$467$		−	1.50989i		−	0.0698691i	−0.999390	−	0.0349346i	$-0.988878\pi$
$467$		−	1.50989i		−	0.0698691i	0.999390	−	0.0349346i	$-0.0111223\pi$
$468$	0.209895	+	2.08629i	0.00970240	+	0.0964386i
$469$		0			0
$470$	33.4221	+	30.2283i	1.54165	+	1.39433i
$471$			5.23477i			0.241206i
$472$	−17.9224	−	13.2051i	−0.824946	−	0.607813i
$473$	−7.82653			−0.359864
$474$	13.2774	+	12.0086i	0.609852	+	0.551575i
$475$		−	2.25541i		−	0.103485i
$476$		0			0
$477$		−	8.07845i		−	0.369887i
$478$	8.38141	−	9.26695i	0.383357	−	0.423861i
$479$	−14.2406			−0.650669			−0.325335	−	0.945599i	$-0.605477\pi$
$479$	−14.2406			−0.650669			−0.325335	+	0.945599i	$0.605477\pi$
$480$	−8.31053	+	14.0314i	−0.379322	+	0.640443i
$481$		−	2.49607i		−	0.113811i
$482$	−5.64951	+	6.24641i	−0.257328	+	0.284516i
$483$		0			0
$484$	4.59499	+	45.6727i	0.208863	+	2.07603i
$485$			10.4801i			0.475876i
$486$	0.948630	−	1.04886i	0.0430307	−	0.0475771i
$487$			7.39097i			0.334917i	0.985879	+	0.167458i	$0.0535560\pi$
$487$			7.39097i			0.334917i	−0.985879	+	0.167458i	$0.946444\pi$
$488$	5.48526	−	7.44479i	0.248306	−	0.337010i
$489$			0.976425i			0.0441555i
$490$		0			0
$491$	14.0578			0.634420			0.317210	−	0.948355i	$-0.397254\pi$
$491$	14.0578			0.634420			0.317210	+	0.948355i	$0.397254\pi$
$492$	−0.240081	−	2.38633i	−0.0108237	−	0.107584i
$493$	−45.1484			−2.03338
$494$	0.677517	−	0.749100i	0.0304829	−	0.0337036i
$495$	16.7978			0.755003
$496$	15.0175	−	3.05263i	0.674306	−	0.137067i
$497$		0			0
$498$	−0.505594	−	0.457280i	−0.0226562	−	0.0204912i
$499$	26.9919			1.20832			0.604162	−	0.796861i	$-0.293508\pi$
$499$	26.9919			1.20832			0.604162	+	0.796861i	$0.293508\pi$
$500$	−0.974934	−	9.69052i	−0.0436004	−	0.433373i
$501$			2.08267i			0.0930467i
$502$	2.02964	−	2.24408i	0.0905871	−	0.100158i
$503$	3.15505			0.140677			0.0703384	−	0.997523i	$-0.477592\pi$
$503$	3.15505			0.140677			0.0703384	+	0.997523i	$0.477592\pi$
$504$		0			0
$505$	−7.22059			−0.321312
$506$	−11.8676	+	13.1214i	−0.527577	+	0.583319i
$507$		−	11.9008i		−	0.528535i
$508$	−1.09530	+	0.110195i	−0.0485961	+	0.00488911i
$509$	−21.7630			−0.964630			−0.482315	−	0.875998i	$-0.660204\pi$
$509$	−21.7630			−0.964630			−0.482315	+	0.875998i	$0.660204\pi$
$510$	20.6367	+	18.6647i	0.913808	+	0.826485i
$511$		0			0
$512$	−21.3756	−	7.42178i	−0.944678	−	0.327999i
$513$	−0.681229			−0.0300770
$514$	−18.2962	+	20.2292i	−0.807009	+	0.892273i
$515$	13.3373			0.587712
$516$	−2.67290	+	0.268912i	−0.117668	+	0.0118382i
$517$	64.4060			2.83257
$518$		0			0
$519$		−	21.3463i		−	0.936999i
$520$	−5.07082	+	6.88230i	−0.222370	+	0.301809i
$521$			40.3946i			1.76972i	0.465856	+	0.884860i	$0.345746\pi$
$521$			40.3946i			1.76972i	−0.465856	+	0.884860i	$0.654254\pi$
$522$	−6.27533	+	6.93835i	−0.274664	+	0.303683i
$523$			29.3834i			1.28485i	0.766349	+	0.642424i	$0.222071\pi$
$523$			29.3834i			1.28485i	−0.766349	+	0.642424i	$0.777929\pi$
$524$	5.57949	−	0.561335i	0.243741	−	0.0245221i
$525$		0			0
$526$	23.0841	−	25.5230i	1.00651	−	1.11286i
$527$		−	26.1476i		−	1.13901i
$528$	4.64274	+	22.8401i	0.202050	+	0.993988i
$529$	18.3903			0.799580
$530$	22.0926	−	24.4268i	0.959640	−	1.06103i
$531$			7.87073i			0.341561i
$532$		0			0
$533$		−	1.25724i		−	0.0544570i
$534$	12.9962	+	11.7543i	0.562402	+	0.508660i
$535$	−17.4973			−0.756475
$536$	22.3351	−	30.3140i	0.964730	−	1.30937i
$537$		−	6.94974i		−	0.299903i
$538$	−21.9221	−	19.8272i	−0.945129	−	0.854813i
$539$		0			0
$540$	5.73673	−	0.577155i	0.246870	−	0.0248368i
$541$		−	30.6975i		−	1.31979i	−0.751359	−	0.659893i	$-0.770601\pi$
$541$		−	30.6975i		−	1.31979i	0.751359	−	0.659893i	$-0.229399\pi$
$542$	20.9708	+	18.9668i	0.900773	+	0.814696i
$543$			7.67619i			0.329417i
$544$	−19.6748	+	33.2187i	−0.843549	+	1.42424i
$545$		−	41.9872i		−	1.79853i
$546$		0			0
$547$	−15.7691			−0.674240			−0.337120	−	0.941462i	$-0.609453\pi$
$547$	−15.7691			−0.674240			−0.337120	+	0.941462i	$0.609453\pi$
$548$	2.55519	+	25.3977i	0.109152	+	1.08494i
$549$	−3.26942			−0.139536
$550$	20.2339	+	18.3003i	0.862775	+	0.780329i
$551$	4.50643			0.191980
$552$	−3.60214	+	4.88895i	−0.153317	+	0.208088i
$553$		0			0
$554$	−14.5064	+	16.0391i	−0.616320	+	0.681437i
$555$	−6.86352			−0.291340
$556$	12.1738	−	1.22477i	0.516283	−	0.0519416i
$557$		−	22.2196i		−	0.941474i	−0.882274	−	0.470737i	$-0.843988\pi$
$557$		−	22.2196i		−	0.941474i	0.882274	−	0.470737i	$-0.156012\pi$
$558$	−4.01834	−	3.63435i	−0.170110	−	0.153854i
$559$	−1.40822			−0.0595612
$560$		0			0
$561$	39.7679			1.67900
$562$	−5.87153	−	5.31045i	−0.247675	−	0.224008i
$563$		−	23.9957i		−	1.01130i	−0.862740	−	0.505648i	$-0.831253\pi$
$563$		−	23.9957i		−	1.01130i	0.862740	−	0.505648i	$-0.168747\pi$
$564$	21.9958	−	2.21293i	0.926189	−	0.0931811i
$565$	−11.0377			−0.464359
$566$	−10.6571	+	11.7831i	−0.447951	+	0.495280i
$567$		0			0
$568$	2.47141	+	1.82091i	0.103698	+	0.0764038i
$569$	1.26379			0.0529810			0.0264905	−	0.999649i	$-0.491567\pi$
$569$	1.26379			0.0529810			0.0264905	+	0.999649i	$0.491567\pi$
$570$	−2.05983	−	1.86299i	−0.0862767	−	0.0780322i
$571$	20.7111			0.866731			0.433365	−	0.901218i	$-0.357326\pi$
$571$	20.7111			0.866731			0.433365	+	0.901218i	$0.357326\pi$
$572$	1.22302	+	12.1564i	0.0511369	+	0.508283i
$573$	−17.8099			−0.744019
$574$		0			0
$575$			7.10831i			0.296437i
$576$	2.37034	+	7.64078i	0.0987643	+	0.318366i
$577$			31.4542i			1.30946i	0.755864	+	0.654728i	$0.227217\pi$
$577$			31.4542i			1.30946i	−0.755864	+	0.654728i	$0.772783\pi$
$578$	31.0258	+	28.0610i	1.29050	+	1.16718i
$579$		−	13.7959i		−	0.573340i
$580$	−37.9493	+	3.81797i	−1.57576	+	0.158533i
$581$		0			0
$582$	3.81294	+	3.44858i	0.158051	+	0.142948i
$583$		−	47.0715i		−	1.94950i
$584$	−12.8544	−	9.47099i	−0.531918	−	0.391912i
$585$	3.02240			0.124961
$586$	−18.5870	−	16.8108i	−0.767822	−	0.694450i
$587$			5.93391i			0.244919i	0.992474	+	0.122459i	$0.0390781\pi$
$587$			5.93391i			0.244919i	−0.992474	+	0.122459i	$0.960922\pi$
$588$		0			0
$589$			2.60989i			0.107539i
$590$	−21.5245	+	23.7987i	−0.886150	+	0.979776i
$591$	−1.13180			−0.0465560
$592$	−1.89701	−	9.33241i	−0.0779667	−	0.383560i
$593$		−	15.7040i		−	0.644885i	−0.946589	−	0.322443i	$-0.895496\pi$
$593$		−	15.7040i		−	0.644885i	0.946589	−	0.322443i	$-0.104504\pi$
$594$	5.52748	−	6.11148i	0.226795	−	0.250757i
$595$		0			0
$596$	4.02489	−	0.404932i	0.164866	−	0.0165867i
$597$		−	8.53186i		−	0.349186i
$598$	−2.13531	+	2.36092i	−0.0873195	+	0.0965452i
$599$			17.3726i			0.709827i	0.934899	+	0.354914i	$0.115490\pi$
$599$			17.3726i			0.709827i	−0.934899	+	0.354914i	$0.884510\pi$
$600$	7.53900	+	5.55467i	0.307778	+	0.226768i
$601$			43.6846i			1.78193i	0.454069	+	0.890966i	$0.349972\pi$
$601$			43.6846i			1.78193i	−0.454069	+	0.890966i	$0.650028\pi$
$602$		0			0
$603$	−13.3126			−0.542130
$604$	−27.9948	+	2.81648i	−1.13909	+	0.114601i
$605$	66.1659			2.69003
$606$	−2.37601	+	2.62705i	−0.0965188	+	0.106716i
$607$	19.2009			0.779341			0.389671	−	0.920954i	$-0.372589\pi$
$607$	19.2009			0.779341			0.389671	+	0.920954i	$0.372589\pi$
$608$	1.96382	−	3.31568i	0.0796432	−	0.134469i
$609$		0			0
$610$	−9.88573	−	8.94106i	−0.400262	−	0.362013i
$611$	11.5885			0.468820
$612$	13.5814	−	1.36639i	0.548997	−	0.0552329i
$613$			17.1672i			0.693375i	0.937981	+	0.346688i	$0.112694\pi$
$613$			17.1672i			0.693375i	−0.937981	+	0.346688i	$0.887306\pi$
$614$	−19.3259	+	21.3677i	−0.779928	+	0.862331i
$615$	−3.45707			−0.139402
$616$		0			0
$617$	−16.8150			−0.676946			−0.338473	−	0.940976i	$-0.609910\pi$
$617$	−16.8150			−0.676946			−0.338473	+	0.940976i	$0.609910\pi$
$618$	4.38878	−	4.85247i	0.176543	−	0.195195i
$619$			34.8225i			1.39964i	0.714322	+	0.699818i	$0.246735\pi$
$619$			34.8225i			1.39964i	−0.714322	+	0.699818i	$0.753265\pi$
$620$	−2.21117	−	21.9783i	−0.0888028	−	0.882670i
$621$	2.14701			0.0861566
$622$	−30.2833	−	27.3895i	−1.21425	−	1.09822i
$623$		0			0
$624$	0.835363	+	4.10959i	0.0334413	+	0.164515i
$625$	−30.5926			−1.22370
$626$	−4.47703	+	4.95005i	−0.178938	+	0.197844i
$627$	−3.96939			−0.158522
$628$	1.04802	+	10.4170i	0.0418205	+	0.415682i
$629$	−16.2491			−0.647892
$630$		0			0
$631$			11.8869i			0.473210i	0.971606	+	0.236605i	$0.0760346\pi$
$631$			11.8869i			0.473210i	−0.971606	+	0.236605i	$0.923965\pi$
$632$	28.8256	+	21.2385i	1.14662	+	0.844820i
$633$			21.2436i			0.844359i
$634$	−24.1366	+	26.6868i	−0.958587	+	1.05987i
$635$			1.58676i			0.0629687i
$636$	−1.61733	−	16.0758i	−0.0641315	−	0.637445i
$637$		0			0
$638$	−36.5651	+	40.4284i	−1.44763	+	1.60057i
$639$		−	1.08533i		−	0.0429351i
$640$	−13.7284	+	29.5857i	−0.542664	+	1.16948i
$641$	−36.8895			−1.45705			−0.728523	−	0.685021i	$-0.759793\pi$
$641$	−36.8895			−1.45705			−0.728523	+	0.685021i	$0.759793\pi$
$642$	−5.75767	+	6.36600i	−0.227237	+	0.251246i
$643$		−	10.0475i		−	0.396235i	−0.980178	−	0.198117i	$-0.936517\pi$
$643$		−	10.0475i		−	0.396235i	0.980178	−	0.198117i	$-0.0634827\pi$
$644$		0			0
$645$			3.87222i			0.152469i
$646$	−4.87654	−	4.41054i	−0.191865	−	0.173530i
$647$	−39.1647			−1.53972			−0.769862	−	0.638210i	$-0.779675\pi$
$647$	−39.1647			−1.53972			−0.769862	+	0.638210i	$0.779675\pi$
$648$	1.67775	−	2.27710i	0.0659081	−	0.0894528i
$649$			45.8612i			1.80021i
$650$	3.64065	+	3.29276i	0.142798	+	0.129153i
$651$		0			0
$652$	0.195484	+	1.94304i	0.00765573	+	0.0760954i
$653$			41.5024i			1.62412i	0.583577	+	0.812058i	$0.301653\pi$
$653$			41.5024i			1.62412i	−0.583577	+	0.812058i	$0.698347\pi$
$654$	−15.2761	−	13.8163i	−0.597342	−	0.540260i
$655$		−	8.08300i		−	0.315829i
$656$	−0.955501	−	4.70062i	−0.0373061	−	0.183528i
$657$			5.64507i			0.220235i
$658$		0			0
$659$	−35.4347			−1.38034			−0.690170	−	0.723647i	$-0.742464\pi$
$659$	−35.4347			−1.38034			−0.690170	+	0.723647i	$0.742464\pi$
$660$	33.4268	−	3.36297i	1.30114	−	0.130903i
$661$	−23.6331			−0.919219			−0.459610	−	0.888121i	$-0.652011\pi$
$661$	−23.6331			−0.919219			−0.459610	+	0.888121i	$0.652011\pi$
$662$	20.6820	+	18.7056i	0.803828	+	0.727015i
$663$	7.15538			0.277892
$664$	−1.09766	−	0.808744i	−0.0425974	−	0.0313854i
$665$		0			0
$666$	−2.25851	+	2.49714i	−0.0875156	+	0.0967620i
$667$	−14.2028			−0.549935
$668$	0.416957	+	4.14441i	0.0161325	+	0.160352i
$669$		−	3.12207i		−	0.120706i
$670$	−40.2532	−	36.4066i	−1.55511	−	1.40651i
$671$	−19.0503			−0.735428
$672$		0			0
$673$	8.69720			0.335253			0.167626	−	0.985851i	$-0.446390\pi$
$673$	8.69720			0.335253			0.167626	+	0.985851i	$0.446390\pi$
$674$	25.9823	+	23.4995i	1.00080	+	0.905166i
$675$		−	3.31079i		−	0.127433i
$676$	−2.38259	−	23.6821i	−0.0916380	−	0.910851i
$677$	10.9189			0.419649			0.209825	−	0.977739i	$-0.432711\pi$
$677$	10.9189			0.419649			0.209825	+	0.977739i	$0.432711\pi$
$678$	−3.63207	+	4.01581i	−0.139489	+	0.154226i
$679$		0			0
$680$	44.8028	+	33.0103i	1.71811	+	1.26589i
$681$	5.22675			0.200289
$682$	−23.4141	−	21.1766i	−0.896570	−	0.810895i
$683$	36.5517			1.39861			0.699305	−	0.714823i	$-0.253493\pi$
$683$	36.5517			1.39861			0.699305	+	0.714823i	$0.253493\pi$
$684$	−1.35561	+	0.136384i	−0.0518332	+	0.00521478i
$685$	36.7936			1.40581
$686$		0			0
$687$			28.4258i			1.08451i
$688$	−5.26510	+	1.07025i	−0.200730	+	0.0408027i
$689$		−	8.46952i		−	0.322663i
$690$	6.49190	+	5.87154i	0.247143	+	0.223526i
$691$		−	5.30956i		−	0.201985i	−0.994887	−	0.100993i	$-0.967798\pi$
$691$		−	5.30956i		−	0.201985i	0.994887	−	0.100993i	$-0.0322018\pi$
$692$	−4.27360	−	42.4782i	−0.162458	−	1.61478i
$693$		0			0
$694$	15.7206	+	14.2183i	0.596744	+	0.539720i
$695$		−	17.6361i		−	0.668976i
$696$	−11.0985	+	15.0633i	−0.420689	+	0.570974i
$697$	−8.18444			−0.310008
$698$	28.7960	+	26.0443i	1.08994	+	0.985789i
$699$			6.11941i			0.231457i
$700$		0			0
$701$			6.16681i			0.232917i	0.993196	+	0.116459i	$0.0371542\pi$
$701$			6.16681i			0.232917i	−0.993196	+	0.116459i	$0.962846\pi$
$702$	0.994552	−	1.09963i	0.0375369	−	0.0415029i
$703$	1.62188			0.0611704
$704$	13.8115	+	44.5213i	0.520541	+	1.67796i
$705$		−	31.8652i		−	1.20011i
$706$	−22.7712	+	25.1771i	−0.857006	+	0.947553i
$707$		0			0
$708$	1.57575	+	15.6624i	0.0592202	+	0.588629i
$709$		−	1.99834i		−	0.0750494i	−0.999296	−	0.0375247i	$-0.988053\pi$
$709$		−	1.99834i		−	0.0750494i	0.999296	−	0.0375247i	$-0.0119473\pi$
$710$	2.96812	−	3.28171i	0.111391	−	0.123161i
$711$		−	12.6589i		−	0.474747i
$712$	28.2152	+	20.7887i	1.05741	+	0.779090i
$713$		−	8.22554i		−	0.308049i
$714$		0			0
$715$	17.6109			0.658611
$716$	−1.39136	−	13.8297i	−0.0519976	−	0.516839i
$717$	−8.83528			−0.329960
$718$	12.9528	−	14.3214i	0.483396	−	0.534469i
$719$	13.4489			0.501560			0.250780	−	0.968044i	$-0.419313\pi$
$719$	13.4489			0.501560			0.250780	+	0.968044i	$0.419313\pi$
$720$	11.3003	−	2.29703i	0.421137	−	0.0856051i
$721$		0			0
$722$	−19.4415	−	17.5837i	−0.723539	−	0.654399i
$723$	5.95545			0.221485
$724$	1.53680	+	15.2753i	0.0571147	+	0.567701i
$725$			21.9014i			0.813398i
$726$	21.7726	−	24.0730i	0.808056	−	0.893432i
$727$	19.6532			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$727$	19.6532			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−15.4379	+	17.0690i	−0.571381	+	0.631751i
$731$			9.16729i			0.339065i
$732$	−6.50600	+	0.654550i	−0.240469	+	0.0241928i
$733$	−25.2279			−0.931814			−0.465907	−	0.884834i	$-0.654272\pi$
$733$	−25.2279			−0.931814			−0.465907	+	0.884834i	$0.654272\pi$
$734$	−36.3793	−	32.9030i	−1.34279	−	1.21447i
$735$		0			0
$736$	−6.18931	+	10.4500i	−0.228141	+	0.385190i
$737$	−77.5698			−2.85732
$738$	−1.13758	+	1.25778i	−0.0418750	+	0.0462994i
$739$	6.70955			0.246815			0.123407	−	0.992356i	$-0.460618\pi$
$739$	6.70955			0.246815			0.123407	+	0.992356i	$0.460618\pi$
$740$	−13.6581	+	1.37410i	−0.502082	+	0.0505129i
$741$	−0.714206			−0.0262370
$742$		0			0
$743$			26.0661i			0.956273i	0.878286	+	0.478137i	$0.158688\pi$
$743$			26.0661i			0.956273i	−0.878286	+	0.478137i	$0.841312\pi$
$744$	−8.72392	−	6.42770i	−0.319834	−	0.235651i
$745$		−	5.83085i		−	0.213626i
$746$	−5.76987	+	6.37949i	−0.211250	+	0.233570i
$747$			0.482042i			0.0176370i
$748$	79.1363	−	7.96167i	2.89351	−	0.291107i
$749$		0			0
$750$	−4.61956	+	5.10764i	−0.168682	+	0.186505i
$751$		−	5.71302i		−	0.208471i	−0.994553	−	0.104236i	$-0.966760\pi$
$751$		−	5.71302i		−	0.208471i	0.994553	−	0.104236i	$-0.0332396\pi$
$752$	43.3275	−	8.80725i	1.57999	−	0.321167i
$753$	−2.13955			−0.0779694
$754$	−6.57911	+	7.27422i	−0.239597	+	0.264912i
$755$			40.5561i			1.47599i
$756$		0			0
$757$			4.75364i			0.172774i	0.996262	+	0.0863869i	$0.0275321\pi$
$757$			4.75364i			0.172774i	−0.996262	+	0.0863869i	$0.972468\pi$
$758$	−19.9941	−	18.0835i	−0.726219	−	0.656823i
$759$	12.5102			0.454092
$760$	−4.47194	−	3.29489i	−0.162214	−	0.119518i
$761$		−	27.3284i		−	0.990654i	−0.868707	−	0.495327i	$-0.835048\pi$
$761$		−	27.3284i		−	0.990654i	0.868707	−	0.495327i	$-0.164952\pi$
$762$	0.577307	+	0.522140i	0.0209136	+	0.0189151i
$763$		0			0
$764$	−35.4409	+	3.56560i	−1.28221	+	0.128999i
$765$		−	19.6754i		−	0.711366i
$766$	8.65310	+	7.82622i	0.312649	+	0.282773i
$767$			8.25174i			0.297953i
$768$	6.24658	+	14.7302i	0.225404	+	0.531532i
$769$			22.7151i			0.819127i	0.912282	+	0.409564i	$0.134319\pi$
$769$			22.7151i			0.819127i	−0.912282	+	0.409564i	$0.865681\pi$
$770$		0			0
$771$	19.2869			0.694602
$772$	−2.76199	−	27.4533i	−0.0994064	−	0.988066i
$773$	−18.1187			−0.651685			−0.325843	−	0.945424i	$-0.605648\pi$
$773$	−18.1187			−0.651685			−0.325843	+	0.945424i	$0.605648\pi$
$774$	1.40882	+	1.27419i	0.0506390	+	0.0458000i
$775$	−12.6842			−0.455629
$776$	8.27799	+	6.09915i	0.297162	+	0.218947i
$777$		0			0
$778$	18.6134	−	20.5800i	0.667324	−	0.737830i
$779$	0.816920			0.0292692
$780$	6.01444	−	0.605095i	0.215351	−	0.0216659i
$781$		−	6.32402i		−	0.226291i
$782$	15.3693	+	13.9006i	0.549604	+	0.497084i
$783$	6.61515			0.236406
$784$		0			0
$785$	15.0910			0.538622
$786$	−2.94081	−	2.65979i	−0.104895	−	0.0948717i
$787$		−	4.91161i		−	0.175080i	−0.996161	−	0.0875400i	$-0.972099\pi$
$787$		−	4.91161i		−	0.175080i	0.996161	−	0.0875400i	$-0.0279006\pi$
$788$	−2.25223	+	0.226590i	−0.0802324	+	0.00807194i
$789$	−24.3341			−0.866319
$790$	34.6190	−	38.2767i	1.23169	−	1.36182i
$791$		0			0
$792$	9.77589	−	13.2682i	0.347371	−	0.471465i
$793$	−3.42769			−0.121721
$794$	−32.8954	−	29.7520i	−1.16742	−	1.05586i
$795$	−23.2889			−0.825973
$796$	−1.70811	−	16.9780i	−0.0605423	−	0.601770i
$797$	−23.8384			−0.844398			−0.422199	−	0.906503i	$-0.638742\pi$
$797$	−23.8384			−0.844398			−0.422199	+	0.906503i	$0.638742\pi$
$798$		0			0
$799$		−	75.4394i		−	2.66885i
$800$	16.1143	+	9.54420i	0.569728	+	0.337439i
$801$		−	12.3909i		−	0.437809i
$802$	−36.6181	−	33.1190i	−1.29303	−	1.16947i
$803$			32.8927i			1.16076i
$804$	−26.4914	+	2.66522i	−0.934281	+	0.0939952i
$805$		0			0
$806$	−4.21286	−	3.81028i	−0.148392	−	0.134211i
$807$			20.9009i			0.735748i
$808$	−4.20221	+	5.70339i	−0.147833	+	0.200645i
$809$	−1.19583			−0.0420431			−0.0210216	−	0.999779i	$-0.506692\pi$
$809$	−1.19583			−0.0420431			−0.0210216	+	0.999779i	$0.506692\pi$
$810$	−3.02369	−	2.73475i	−0.106242	−	0.0960894i
$811$			6.44559i			0.226335i	0.993576	+	0.113168i	$0.0360997\pi$
$811$			6.44559i			0.226335i	−0.993576	+	0.113168i	$0.963900\pi$
$812$		0			0
$813$		−	19.9939i		−	0.701218i
$814$	−13.1599	+	14.5503i	−0.461254	+	0.509988i
$815$	2.81488			0.0986010
$816$	26.7529	−	5.43810i	0.936538	−	0.190371i
$817$		−	0.915023i		−	0.0320126i
$818$	−12.9455	+	14.3132i	−0.452628	+	0.500450i
$819$		0			0
$820$	−6.87941	+	0.692117i	−0.240239	+	0.0241698i
$821$			2.16738i			0.0756420i	0.999285	+	0.0378210i	$0.0120417\pi$
$821$			2.16738i			0.0756420i	−0.999285	+	0.0378210i	$0.987958\pi$
$822$	12.1073	−	13.3865i	0.422291	−	0.466909i
$823$			5.99900i			0.209112i	0.994519	+	0.104556i	$0.0333422\pi$
$823$			5.99900i			0.209112i	−0.994519	+	0.104556i	$0.966658\pi$
$824$	7.76199	−	10.5349i	0.270402	−	0.366999i
$825$		−	19.2913i		−	0.671638i
$826$		0			0
$827$	21.0143			0.730738			0.365369	−	0.930863i	$-0.380943\pi$
$827$	21.0143			0.730738			0.365369	+	0.930863i	$0.380943\pi$
$828$	4.27246	−	0.429839i	0.148478	−	0.0149379i
$829$	13.1978			0.458379			0.229190	−	0.973382i	$-0.426392\pi$
$829$	13.1978			0.458379			0.229190	+	0.973382i	$0.426392\pi$
$830$	−1.31827	+	1.45755i	−0.0457577	+	0.0505922i
$831$	15.2920			0.530474
$832$	2.48509	+	8.01066i	0.0861549	+	0.277720i
$833$		0			0
$834$	−6.41650	−	5.80335i	−0.222185	−	0.200953i
$835$	6.00400			0.207777
$836$	−7.89890	+	0.794684i	−0.273189	+	0.0274847i
$837$			3.83116i			0.132424i
$838$	4.00627	−	4.42955i	0.138394	−	0.153016i
$839$	33.8661			1.16919			0.584594	−	0.811326i	$-0.301254\pi$
$839$	33.8661			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$840$		0			0
$841$	−14.7602			−0.508973
$842$	11.0887	−	12.2603i	0.382143	−	0.422518i
$843$			5.59802i			0.192806i
$844$	4.25305	+	42.2739i	0.146396	+	1.45513i
$845$	−34.3083			−1.18024
$846$	−11.5934	−	10.4856i	−0.398591	−	0.360502i
$847$		0			0
$848$	−6.43684	−	31.6662i	−0.221042	−	1.08742i
$849$	11.2342			0.385557
$850$	21.4354	−	23.7001i	0.735228	−	0.812908i
$851$	−5.11164			−0.175225
$852$	−0.217287	−	2.15976i	−0.00744414	−	0.0739923i
$853$	−50.0832			−1.71482			−0.857408	−	0.514638i	$-0.827926\pi$
$853$	−50.0832			−1.71482			−0.857408	+	0.514638i	$0.827926\pi$
$854$		0			0
$855$			1.96388i			0.0671632i
$856$	−10.1830	+	13.8208i	−0.348048	+	0.472384i
$857$		−	49.2628i		−	1.68279i	−0.540424	−	0.841393i	$-0.681736\pi$
$857$		−	49.2628i		−	1.68279i	0.540424	−	0.841393i	$-0.318264\pi$
$858$	5.79505	−	6.40733i	0.197840	−	0.218743i
$859$		−	3.91059i		−	0.133428i	−0.997772	−	0.0667139i	$-0.978749\pi$
$859$		−	3.91059i		−	0.133428i	0.997772	−	0.0667139i	$-0.0212515\pi$
$860$	0.775232	+	7.70554i	0.0264352	+	0.262757i
$861$		0			0
$862$	32.5399	−	35.9779i	1.10831	−	1.22541i
$863$		−	43.2124i		−	1.47097i	−0.677542	−	0.735484i	$-0.736955\pi$
$863$		−	43.2124i		−	1.47097i	0.677542	−	0.735484i	$-0.263045\pi$
$864$	2.88275	−	4.86721i	0.0980733	−	0.165586i
$865$	−61.5381			−2.09236
$866$	−13.4596	+	14.8817i	−0.457375	+	0.505699i
$867$		−	29.5806i		−	1.00461i
$868$		0			0
$869$		−	73.7611i		−	2.50217i
$870$	20.0022	+	18.0908i	0.678137	+	0.613335i
$871$	−13.9570			−0.472916
$872$	−33.1648	−	24.4355i	−1.12310	−	0.827490i
$873$		−	3.63532i		−	0.123037i
$874$	−1.53407	−	1.38747i	−0.0518905	−	0.0469319i
$875$		0			0
$876$	1.13016	+	11.2334i	0.0381846	+	0.379543i
$877$			21.1390i			0.713815i	0.934140	+	0.356907i	$0.116169\pi$
$877$			21.1390i			0.713815i	−0.934140	+	0.356907i	$0.883831\pi$
$878$	29.4208	+	26.6094i	0.992905	+	0.898024i
$879$			17.7212i			0.597721i
$880$	65.8445	−	13.3843i	2.21962	−	0.451185i
$881$			49.1167i			1.65478i	0.561625	+	0.827392i	$0.310177\pi$
$881$			49.1167i			1.65478i	−0.561625	+	0.827392i	$0.689823\pi$
$882$		0			0
$883$	37.8457			1.27361			0.636804	−	0.771025i	$-0.280256\pi$
$883$	37.8457			1.27361			0.636804	+	0.771025i	$0.280256\pi$
$884$	14.2389	−	1.43253i	0.478906	−	0.0481813i
$885$	22.6901			0.762719
$886$	−11.5593	−	10.4547i	−0.388341	−	0.351231i
$887$	17.9408			0.602393			0.301196	−	0.953562i	$-0.402614\pi$
$887$	17.9408			0.602393			0.301196	+	0.953562i	$0.402614\pi$
$888$	−3.99440	+	5.42135i	−0.134043	+	0.181929i
$889$		0			0
$890$	33.8859	−	37.4662i	1.13586	−	1.25587i
$891$	−5.82680			−0.195205
$892$	−0.625049	−	6.21278i	−0.0209282	−	0.208019i
$893$			7.52989i			0.251978i
$894$	−2.12142	−	1.91870i	−0.0709510	−	0.0641710i
$895$	−20.0350			−0.669697
$896$		0			0
$897$	2.25095			0.0751569
$898$	−31.7038	−	28.6742i	−1.05797	−	0.956871i
$899$		−	25.3437i		−	0.845259i
$900$	−0.662832	−	6.58833i	−0.0220944	−	0.219611i
$901$	−55.1354			−1.83683
$902$	−6.62848	+	7.32881i	−0.220704	+	0.244023i
$903$		0			0
$904$	−6.42367	+	8.71844i	−0.213648	+	0.289971i
$905$	22.1293			0.735601
$906$	14.7554	+	13.3454i	0.490216	+	0.443371i
$907$	22.1774			0.736388			0.368194	−	0.929749i	$-0.379976\pi$
$907$	22.1774			0.736388			0.368194	+	0.929749i	$0.379976\pi$
$908$	10.4010	−	1.04641i	0.345169	−	0.0347264i
$909$	2.50468			0.0830748
$910$		0			0
$911$			35.2495i			1.16787i	0.811801	+	0.583934i	$0.198487\pi$
$911$			35.2495i			1.16787i	−0.811801	+	0.583934i	$0.801513\pi$
$912$	−2.67031	+	0.542797i	−0.0884227	+	0.0179738i
$913$			2.80877i			0.0929566i
$914$	−26.7220	−	24.1685i	−0.883884	−	0.799421i
$915$			9.42524i			0.311589i
$916$	5.69094	+	56.5661i	0.188034	+	1.86900i
$917$		0			0
$918$	−7.15845	−	6.47439i	−0.236264	−	0.213687i
$919$			17.5326i			0.578348i	0.957277	+	0.289174i	$0.0933806\pi$
$919$			17.5326i			0.578348i	−0.957277	+	0.289174i	$0.906619\pi$
$920$	14.0941	+	10.3844i	0.464669	+	0.342364i
$921$	20.3724			0.671293
$922$	−29.2937	−	26.4944i	−0.964737	−	0.872547i
$923$		−	1.13787i		−	0.0374535i
$924$		0			0
$925$			7.88239i			0.259171i
$926$	−18.4255	+	20.3722i	−0.605498	+	0.669472i
$927$	−4.62644			−0.151952
$928$	−19.0698	+	32.1973i	−0.625998	+	1.05693i
$929$		−	51.8583i		−	1.70142i	−0.525638	−	0.850708i	$-0.676173\pi$
$929$		−	51.8583i		−	1.70142i	0.525638	−	0.850708i	$-0.323827\pi$
$930$	−10.4773	+	11.5842i	−0.343563	+	0.379862i
$931$		0			0
$932$	1.22513	+	12.1774i	0.0401304	+	0.398882i
$933$			28.8727i			0.945249i
$934$	−1.43232	+	1.58365i	−0.0468670	+	0.0518187i
$935$		−	114.645i		−	3.74928i
$936$	1.75896	−	2.38733i	0.0574935	−	0.0780323i
$937$		−	36.9665i		−	1.20764i	−0.797120	−	0.603821i	$-0.793644\pi$
$937$		−	36.9665i		−	1.20764i	0.797120	−	0.603821i	$-0.206356\pi$
$938$		0			0
$939$	4.71947			0.154014
$940$	−6.37953	−	63.4104i	−0.208077	−	2.06822i
$941$	−52.5502			−1.71309			−0.856544	−	0.516075i	$-0.827393\pi$
$941$	−52.5502			−1.71309			−0.856544	+	0.516075i	$0.827393\pi$
$942$	4.96586	−	5.49053i	0.161796	−	0.178891i
$943$	−2.57467			−0.0838427
$944$	6.27133	+	30.8520i	0.204114	+	1.00415i
$945$		0			0
$946$	8.20891	+	7.42448i	0.266895	+	0.241391i
$947$	26.9341			0.875242			0.437621	−	0.899160i	$-0.355821\pi$
$947$	26.9341			0.875242			0.437621	+	0.899160i	$0.355821\pi$
$948$	−2.53436	−	25.1907i	−0.0823122	−	0.818156i
$949$			5.91834i			0.192118i
$950$	−2.13955	+	2.36560i	−0.0694161	+	0.0767503i
$951$	25.4437			0.825067
$952$		0			0
$953$	−31.5488			−1.02196			−0.510982	−	0.859591i	$-0.670718\pi$
$953$	−31.5488			−1.02196			−0.510982	+	0.859591i	$0.670718\pi$
$954$	−7.66346	+	8.47315i	−0.248114	+	0.274328i
$955$			51.3432i			1.66143i
$956$	−17.5818	+	1.76885i	−0.568636	+	0.0572088i
$957$	38.5452			1.24599
$958$	14.9364	+	13.5091i	0.482572	+	0.436458i
$959$		0			0
$960$	22.0272	−	6.83333i	0.710924	−	0.220545i
$961$	−16.3222			−0.526524
$962$	−2.36784	+	2.61802i	−0.0763424	+	0.0844083i
$963$	6.06946			0.195586
$964$	11.8511	−	1.19230i	0.381697	−	0.0384014i
$965$	−39.7716			−1.28029
$966$		0			0
$967$			60.7635i			1.95402i	0.213187	+	0.977011i	$0.431616\pi$
$967$			60.7635i			1.95402i	−0.213187	+	0.977011i	$0.568384\pi$
$968$	38.5070	−	52.2631i	1.23766	−	1.67980i
$969$			4.64938i			0.149360i
$970$	9.94171	−	10.9921i	0.319209	−	0.352935i
$971$		−	16.0945i		−	0.516496i	−0.966079	−	0.258248i	$-0.916855\pi$
$971$		−	16.0945i		−	0.516496i	0.966079	−	0.258248i	$-0.0831452\pi$
$972$	−1.98995	+	0.200203i	−0.0638278	+	0.00642153i
$973$		0			0
$974$	7.01129	−	7.75207i	0.224656	−	0.248392i
$975$		−	3.47107i		−	0.111163i
$976$	−12.8156	+	2.60505i	−0.410218	+	0.0833855i
$977$	−32.7166			−1.04670			−0.523349	−	0.852119i	$-0.675318\pi$
$977$	−32.7166			−1.04670			−0.523349	+	0.852119i	$0.675318\pi$
$978$	0.926266	−	1.02413i	0.0296187	−	0.0327481i
$979$		−	72.1991i		−	2.30749i
$980$		0			0
$981$			14.5645i			0.465008i
$982$	−14.7446	−	13.3357i	−0.470520	−	0.425558i
$983$	37.1569			1.18512			0.592561	−	0.805525i	$-0.298117\pi$
$983$	37.1569			1.18512			0.592561	+	0.805525i	$0.298117\pi$
$984$	−2.01193	+	2.73066i	−0.0641380	+	0.0870504i
$985$			3.26280i			0.103962i
$986$	47.3542	+	42.8291i	1.50806	+	1.36396i
$987$		0			0
$988$	−1.42124	+	0.142987i	−0.0452156	+	0.00454901i
$989$			2.88385i			0.0917012i
$990$	−17.6185	−	15.9349i	−0.559951	−	0.506443i
$991$		−	44.2149i		−	1.40453i	−0.711915	−	0.702266i	$-0.752172\pi$
$991$		−	44.2149i		−	1.40453i	0.711915	−	0.702266i	$-0.247828\pi$
$992$	−18.6470	−	11.0443i	−0.592044	−	0.350656i
$993$		−	19.7186i		−	0.625750i
$994$		0			0
$995$	−24.5960			−0.779747
$996$	0.0965065	+	0.959242i	0.00305793	+	0.0303948i
$997$	26.6863			0.845165			0.422582	−	0.906325i	$-0.361124\pi$
$997$	26.6863			0.845165			0.422582	+	0.906325i	$0.361124\pi$
$998$	−28.3107	−	25.6053i	−0.896159	−	0.810523i
$999$	2.38082			0.0753257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.p.a.979.5		32
4.3	odd	2		4704.2.p.a.3919.29		32
7.2	even	3		168.2.t.a.115.9	yes	32
7.3	odd	6		168.2.t.a.19.14	yes	32
7.6	odd	2	inner	1176.2.p.a.979.6		32
8.3	odd	2	inner	1176.2.p.a.979.8		32
8.5	even	2		4704.2.p.a.3919.25		32
21.2	odd	6		504.2.bk.c.451.8		32
21.17	even	6		504.2.bk.c.19.3		32
28.3	even	6		672.2.bb.a.271.15		32
28.23	odd	6		672.2.bb.a.367.10		32
28.27	even	2		4704.2.p.a.3919.26		32
56.3	even	6		168.2.t.a.19.9	✓	32
56.13	odd	2		4704.2.p.a.3919.30		32
56.27	even	2	inner	1176.2.p.a.979.7		32
56.37	even	6		672.2.bb.a.367.15		32
56.45	odd	6		672.2.bb.a.271.10		32
56.51	odd	6		168.2.t.a.115.14	yes	32
84.23	even	6		2016.2.bs.c.1711.14		32
84.59	odd	6		2016.2.bs.c.271.3		32
168.59	odd	6		504.2.bk.c.19.8		32
168.101	even	6		2016.2.bs.c.271.14		32
168.107	even	6		504.2.bk.c.451.3		32
168.149	odd	6		2016.2.bs.c.1711.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.9	✓	32	56.3	even	6
168.2.t.a.19.14	yes	32	7.3	odd	6
168.2.t.a.115.9	yes	32	7.2	even	3
168.2.t.a.115.14	yes	32	56.51	odd	6
504.2.bk.c.19.3		32	21.17	even	6
504.2.bk.c.19.8		32	168.59	odd	6
504.2.bk.c.451.3		32	168.107	even	6
504.2.bk.c.451.8		32	21.2	odd	6
672.2.bb.a.271.10		32	56.45	odd	6
672.2.bb.a.271.15		32	28.3	even	6
672.2.bb.a.367.10		32	28.23	odd	6
672.2.bb.a.367.15		32	56.37	even	6
1176.2.p.a.979.5		32	1.1	even	1	trivial
1176.2.p.a.979.6		32	7.6	odd	2	inner
1176.2.p.a.979.7		32	56.27	even	2	inner
1176.2.p.a.979.8		32	8.3	odd	2	inner
2016.2.bs.c.271.3		32	84.59	odd	6
2016.2.bs.c.271.14		32	168.101	even	6
2016.2.bs.c.1711.3		32	168.149	odd	6
2016.2.bs.c.1711.14		32	84.23	even	6
4704.2.p.a.3919.25		32	8.5	even	2
4704.2.p.a.3919.26		32	28.27	even	2
4704.2.p.a.3919.29		32	4.3	odd	2
4704.2.p.a.3919.30		32	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04886 - 0.948630i) q^{2} +1.00000i q^{3} +(0.200203 + 1.98995i) q^{4} +2.88284 q^{5} +(0.948630 - 1.04886i) q^{6} +(1.67775 - 2.27710i) q^{8} -1.00000 q^{9} +(-3.02369 - 2.73475i) q^{10} -5.82680 q^{11} +(-1.98995 + 0.200203i) q^{12} -1.04841 q^{13} +2.88284i q^{15} +(-3.91984 + 0.796791i) q^{16} +6.82499i q^{17} +(1.04886 + 0.948630i) q^{18} -0.681229i q^{19} +(0.577155 + 5.73673i) q^{20} +(6.11148 + 5.52748i) q^{22} +2.14701i q^{23} +(2.27710 + 1.67775i) q^{24} +3.31079 q^{25} +(1.09963 + 0.994552i) q^{26} -1.00000i q^{27} +6.61515i q^{29} +(2.73475 - 3.02369i) q^{30} -3.83116 q^{31} +(4.86721 + 2.88275i) q^{32} -5.82680i q^{33} +(6.47439 - 7.15845i) q^{34} +(-0.200203 - 1.98995i) q^{36} +2.38082i q^{37} +(-0.646234 + 0.714512i) q^{38} -1.04841i q^{39} +(4.83668 - 6.56452i) q^{40} +1.19919i q^{41} +1.34319 q^{43} +(-1.16655 - 11.5951i) q^{44} -2.88284 q^{45} +(2.03672 - 2.25191i) q^{46} -11.0534 q^{47} +(-0.796791 - 3.91984i) q^{48} +(-3.47255 - 3.14072i) q^{50} -6.82499 q^{51} +(-0.209895 - 2.08629i) q^{52} +8.07845i q^{53} +(-0.948630 + 1.04886i) q^{54} -16.7978 q^{55} +0.681229 q^{57} +(6.27533 - 6.93835i) q^{58} -7.87073i q^{59} +(-5.73673 + 0.577155i) q^{60} +3.26942 q^{61} +(4.01834 + 3.63435i) q^{62} +(-2.37034 - 7.64078i) q^{64} -3.02240 q^{65} +(-5.52748 + 6.11148i) q^{66} +13.3126 q^{67} +(-13.5814 + 1.36639i) q^{68} -2.14701 q^{69} +1.08533i q^{71} +(-1.67775 + 2.27710i) q^{72} -5.64507i q^{73} +(2.25851 - 2.49714i) q^{74} +3.31079i q^{75} +(1.35561 - 0.136384i) q^{76} +(-0.994552 + 1.09963i) q^{78} +12.6589i q^{79} +(-11.3003 + 2.29703i) q^{80} +1.00000 q^{81} +(1.13758 - 1.25778i) q^{82} -0.482042i q^{83} +19.6754i q^{85} +(-1.40882 - 1.27419i) q^{86} -6.61515 q^{87} +(-9.77589 + 13.2682i) q^{88} +12.3909i q^{89} +(3.02369 + 2.73475i) q^{90} +(-4.27246 + 0.429839i) q^{92} -3.83116i q^{93} +(11.5934 + 10.4856i) q^{94} -1.96388i q^{95} +(-2.88275 + 4.86721i) q^{96} +3.63532i q^{97} +5.82680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

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