LMFDB - Embedded newform 1638.2.dt.c.1369.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(1297,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dt (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-20,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1369.3
Root			$-1.40613i$ of defining polynomial
Character	$\chi$	$=$	1638.1369
Dual form			1638.2.dt.c.1297.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.552947 + 0.319244i) q^{5} +(2.23753 + 1.41189i) q^{7} +1.00000i q^{8} +(0.319244 + 0.552947i) q^{10} +(-3.93617 + 2.27255i) q^{11} +(2.48206 + 2.61522i) q^{13} +(1.41189 - 2.23753i) q^{14} +1.00000 q^{16} +0.708420 q^{17} +(-6.36190 - 3.67305i) q^{19} +(0.552947 - 0.319244i) q^{20} +(2.27255 + 3.93617i) q^{22} -6.50552 q^{23} +(-2.29617 + 3.97708i) q^{25} +(2.61522 - 2.48206i) q^{26} +(-2.23753 - 1.41189i) q^{28} +(3.63276 - 6.29212i) q^{29} +(-5.75039 - 3.31999i) q^{31} -1.00000i q^{32} -0.708420i q^{34} +(-1.68797 - 0.0663824i) q^{35} +2.10463i q^{37} +(-3.67305 + 6.36190i) q^{38} +(-0.319244 - 0.552947i) q^{40} +(-4.62167 - 2.66832i) q^{41} +(-5.21162 - 9.02680i) q^{43} +(3.93617 - 2.27255i) q^{44} +6.50552i q^{46} +(-1.68367 + 0.972065i) q^{47} +(3.01312 + 6.31832i) q^{49} +(3.97708 + 2.29617i) q^{50} +(-2.48206 - 2.61522i) q^{52} +(-3.20071 + 5.54379i) q^{53} +(1.45099 - 2.51320i) q^{55} +(-1.41189 + 2.23753i) q^{56} +(-6.29212 - 3.63276i) q^{58} -3.31958i q^{59} +(-3.41517 + 5.91525i) q^{61} +(-3.31999 + 5.75039i) q^{62} -1.00000 q^{64} +(-2.20734 - 0.653698i) q^{65} +(-3.39810 + 1.96190i) q^{67} -0.708420 q^{68} +(-0.0663824 + 1.68797i) q^{70} +(9.11772 - 5.26412i) q^{71} +(-5.55335 - 3.20623i) q^{73} +2.10463 q^{74} +(6.36190 + 3.67305i) q^{76} +(-12.0159 - 0.472545i) q^{77} +(5.48418 + 9.49887i) q^{79} +(-0.552947 + 0.319244i) q^{80} +(-2.66832 + 4.62167i) q^{82} +2.41032i q^{83} +(-0.391718 + 0.226159i) q^{85} +(-9.02680 + 5.21162i) q^{86} +(-2.27255 - 3.93617i) q^{88} -5.53328i q^{89} +(1.86127 + 9.35605i) q^{91} +6.50552 q^{92} +(0.972065 + 1.68367i) q^{94} +4.69039 q^{95} +(-7.96131 + 4.59646i) q^{97} +(6.31832 - 3.01312i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 2 q^{7} - 4 q^{10} + 6 q^{11} + 6 q^{13} + 4 q^{14} + 20 q^{16} - 20 q^{17} - 24 q^{19} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 2 q^{28} - 2 q^{29} - 6 q^{31} + 14 q^{38} + 4 q^{40} - 18 q^{41}+ \cdots - 24 q^{98}+O(q^{100}) $ 20 * q - 20 * q^4 + 2 * q^7 - 4 * q^10 + 6 * q^11 + 6 * q^13 + 4 * q^14 + 20 * q^16 - 20 * q^17 - 24 * q^19 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 2 * q^28 - 2 * q^29 - 6 * q^31 + 14 * q^38 + 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 - 18 * q^47 - 6 * q^49 + 12 * q^50 - 6 * q^52 + 4 * q^53 + 2 * q^55 - 4 * q^56 - 24 * q^58 - 4 * q^61 + 24 * q^62 - 20 * q^64 + 6 * q^65 - 60 * q^67 + 20 * q^68 - 48 * q^70 + 18 * q^71 - 72 * q^73 + 24 * q^74 + 24 * q^76 - 42 * q^77 + 42 * q^79 - 16 * q^82 - 12 * q^85 - 42 * q^86 - 2 * q^88 + 14 * q^91 + 16 * q^94 - 24 * q^95 + 78 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.552947	+	0.319244i	−0.247285	+	0.142770i	−0.618521	−	0.785769i	$-0.712268\pi$
$5$	−0.552947	+	0.319244i	−0.247285	+	0.142770i	0.371235	+	0.928539i	$0.378934\pi$
$6$		0			0
$7$	2.23753	+	1.41189i	0.845708	+	0.533645i
$7$	2.23753	+	1.41189i	0.845708	+	0.533645i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.319244	+	0.552947i	0.100954	+	0.174857i
$11$	−3.93617	+	2.27255i	−1.18680	+	0.685199i	−0.957578	−	0.288175i	$-0.906952\pi$
$11$	−3.93617	+	2.27255i	−1.18680	+	0.685199i	−0.229222	+	0.973374i	$0.573618\pi$
$12$		0			0
$13$	2.48206	+	2.61522i	0.688399	+	0.725333i
$13$	2.48206	+	2.61522i	0.688399	+	0.725333i
$14$	1.41189	−	2.23753i	0.377344	−	0.598006i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.708420			0.171817			0.0859085	−	0.996303i	$-0.472621\pi$
$17$	0.708420			0.171817			0.0859085	+	0.996303i	$0.472621\pi$
$18$		0			0
$19$	−6.36190	−	3.67305i	−1.45952	−	0.842654i	−0.460533	−	0.887643i	$-0.652342\pi$
$19$	−6.36190	−	3.67305i	−1.45952	−	0.842654i	−0.998988	+	0.0449884i	$0.985675\pi$
$20$	0.552947	−	0.319244i	0.123643	−	0.0713851i
$21$		0			0
$22$	2.27255	+	3.93617i	0.484509	+	0.839194i
$23$	−6.50552			−1.35650			−0.678248	−	0.734833i	$-0.737260\pi$
$23$	−6.50552			−1.35650			−0.678248	+	0.734833i	$0.737260\pi$
$24$		0			0
$25$	−2.29617	+	3.97708i	−0.459233	+	0.795415i
$26$	2.61522	−	2.48206i	0.512888	−	0.486771i
$27$		0			0
$28$	−2.23753	−	1.41189i	−0.422854	−	0.266823i
$29$	3.63276	−	6.29212i	0.674586	−	1.16842i	−0.302003	−	0.953307i	$-0.597655\pi$
$29$	3.63276	−	6.29212i	0.674586	−	1.16842i	0.976590	−	0.215111i	$-0.0690113\pi$
$30$		0			0
$31$	−5.75039	−	3.31999i	−1.03280	−	0.596288i	−0.115015	−	0.993364i	$-0.536692\pi$
$31$	−5.75039	−	3.31999i	−1.03280	−	0.596288i	−0.917786	+	0.397076i	$0.870025\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	0.708420i		−	0.121493i
$35$	−1.68797	−	0.0663824i	−0.285320	−	0.0112207i
$36$		0			0
$37$			2.10463i			0.345998i	0.984922	+	0.172999i	$0.0553458\pi$
$37$			2.10463i			0.345998i	−0.984922	+	0.172999i	$0.944654\pi$
$38$	−3.67305	+	6.36190i	−0.595847	+	1.03204i
$39$		0			0
$40$	−0.319244	−	0.552947i	−0.0504769	−	0.0874285i
$41$	−4.62167	−	2.66832i	−0.721783	−	0.416722i	0.0936256	−	0.995607i	$-0.470154\pi$
$41$	−4.62167	−	2.66832i	−0.721783	−	0.416722i	−0.815409	+	0.578886i	$0.803488\pi$
$42$		0			0
$43$	−5.21162	−	9.02680i	−0.794765	−	1.37657i	−0.922988	−	0.384828i	$-0.874261\pi$
$43$	−5.21162	−	9.02680i	−0.794765	−	1.37657i	0.128223	−	0.991745i	$-0.459073\pi$
$44$	3.93617	−	2.27255i	0.593400	−	0.342600i
$45$		0			0
$46$			6.50552i			0.959187i
$47$	−1.68367	+	0.972065i	−0.245588	+	0.141790i	−0.617742	−	0.786381i	$-0.711953\pi$
$47$	−1.68367	+	0.972065i	−0.245588	+	0.141790i	0.372154	+	0.928171i	$0.378619\pi$
$48$		0			0
$49$	3.01312	+	6.31832i	0.430445	+	0.902617i
$50$	3.97708	+	2.29617i	0.562444	+	0.324727i
$51$		0			0
$52$	−2.48206	−	2.61522i	−0.344199	−	0.362666i
$53$	−3.20071	+	5.54379i	−0.439652	+	0.761499i	−0.997662	−	0.0683348i	$-0.978231\pi$
$53$	−3.20071	+	5.54379i	−0.439652	+	0.761499i	0.558011	+	0.829834i	$0.311565\pi$
$54$		0			0
$55$	1.45099	−	2.51320i	0.195652	−	0.338879i
$56$	−1.41189	+	2.23753i	−0.188672	+	0.299003i
$57$		0			0
$58$	−6.29212	−	3.63276i	−0.826196	−	0.477005i
$59$		−	3.31958i		−	0.432172i	−0.976374	−	0.216086i	$-0.930671\pi$
$59$		−	3.31958i		−	0.432172i	0.976374	−	0.216086i	$-0.0693292\pi$
$60$		0			0
$61$	−3.41517	+	5.91525i	−0.437268	+	0.757370i	−0.997478	−	0.0709807i	$-0.977387\pi$
$61$	−3.41517	+	5.91525i	−0.437268	+	0.757370i	0.560210	+	0.828351i	$0.310720\pi$
$62$	−3.31999	+	5.75039i	−0.421639	+	0.730300i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.20734	−	0.653698i	−0.273787	−	0.0810812i
$66$		0			0
$67$	−3.39810	+	1.96190i	−0.415144	+	0.239684i	−0.692998	−	0.720940i	$-0.743710\pi$
$67$	−3.39810	+	1.96190i	−0.415144	+	0.239684i	0.277853	+	0.960624i	$0.410377\pi$
$68$	−0.708420			−0.0859085
$69$		0			0
$70$	−0.0663824	+	1.68797i	−0.00793421	+	0.201752i
$71$	9.11772	−	5.26412i	1.08207	−	0.624736i	0.150619	−	0.988592i	$-0.451873\pi$
$71$	9.11772	−	5.26412i	1.08207	−	0.624736i	0.931455	+	0.363856i	$0.118540\pi$
$72$		0			0
$73$	−5.55335	−	3.20623i	−0.649971	−	0.375261i	0.138474	−	0.990366i	$-0.455780\pi$
$73$	−5.55335	−	3.20623i	−0.649971	−	0.375261i	−0.788445	+	0.615105i	$0.789113\pi$
$74$	2.10463			0.244658
$75$		0			0
$76$	6.36190	+	3.67305i	0.729760	+	0.421327i
$77$	−12.0159	−	0.472545i	−1.36934	−	0.0538515i
$78$		0			0
$79$	5.48418	+	9.49887i	0.617018	+	1.06871i	0.990027	+	0.140879i	$0.0449928\pi$
$79$	5.48418	+	9.49887i	0.617018	+	1.06871i	−0.373009	+	0.927828i	$0.621674\pi$
$80$	−0.552947	+	0.319244i	−0.0618213	+	0.0356925i
$81$		0			0
$82$	−2.66832	+	4.62167i	−0.294667	+	0.510378i
$83$			2.41032i			0.264567i	0.991212	+	0.132283i	$0.0422309\pi$
$83$			2.41032i			0.264567i	−0.991212	+	0.132283i	$0.957769\pi$
$84$		0			0
$85$	−0.391718	+	0.226159i	−0.0424878	+	0.0245304i
$86$	−9.02680	+	5.21162i	−0.973384	+	0.561984i
$87$		0			0
$88$	−2.27255	−	3.93617i	−0.242254	−	0.419597i
$89$		−	5.53328i		−	0.586526i	−0.956032	−	0.293263i	$-0.905259\pi$
$89$		−	5.53328i		−	0.586526i	0.956032	−	0.293263i	$-0.0947412\pi$
$90$		0			0
$91$	1.86127	+	9.35605i	0.195114	+	0.980781i
$92$	6.50552			0.678248
$93$		0			0
$94$	0.972065	+	1.68367i	0.100261	+	0.173657i
$95$	4.69039			0.481224
$96$		0			0
$97$	−7.96131	+	4.59646i	−0.808348	+	0.466700i	−0.846382	−	0.532576i	$-0.821224\pi$
$97$	−7.96131	+	4.59646i	−0.808348	+	0.466700i	0.0380337	+	0.999276i	$0.487891\pi$
$98$	6.31832	−	3.01312i	0.638246	−	0.304371i
$99$		0			0
$100$	2.29617	−	3.97708i	0.229617	−	0.397708i
$101$	6.85500	+	11.8732i	0.682098	+	1.18143i	0.974339	+	0.225084i	$0.0722657\pi$
$101$	6.85500	+	11.8732i	0.682098	+	1.18143i	−0.292241	+	0.956345i	$0.594401\pi$
$102$		0			0
$103$	5.40352	+	9.35918i	0.532425	+	0.922187i	0.999283	+	0.0378550i	$0.0120525\pi$
$103$	5.40352	+	9.35918i	0.532425	+	0.922187i	−0.466858	+	0.884332i	$0.654614\pi$
$104$	−2.61522	+	2.48206i	−0.256444	+	0.243386i
$105$		0			0
$106$	5.54379	+	3.20071i	0.538461	+	0.310881i
$107$	−15.3235			−1.48137			−0.740687	−	0.671850i	$-0.765500\pi$
$107$	−15.3235			−1.48137			−0.740687	+	0.671850i	$0.765500\pi$
$108$		0			0
$109$	−1.53605	−	0.886839i	−0.147127	−	0.0849438i	0.424629	−	0.905367i	$-0.360404\pi$
$109$	−1.53605	−	0.886839i	−0.147127	−	0.0849438i	−0.571756	+	0.820423i	$0.693738\pi$
$110$	−2.51320	−	1.45099i	−0.239624	−	0.138347i
$111$		0			0
$112$	2.23753	+	1.41189i	0.211427	+	0.133411i
$113$	−2.62152	−	4.54061i	−0.246612	−	0.427145i	0.715971	−	0.698130i	$-0.245984\pi$
$113$	−2.62152	−	4.54061i	−0.246612	−	0.427145i	−0.962584	+	0.270985i	$0.912651\pi$
$114$		0			0
$115$	3.59721	−	2.07685i	0.335441	−	0.193667i
$116$	−3.63276	+	6.29212i	−0.337293	+	0.584209i
$117$		0			0
$118$	−3.31958			−0.305592
$119$	1.58511	+	1.00021i	0.145307	+	0.0916894i
$120$		0			0
$121$	4.82895	−	8.36399i	0.438996	−	0.760363i
$122$	5.91525	+	3.41517i	0.535541	+	0.309195i
$123$		0			0
$124$	5.75039	+	3.31999i	0.516400	+	0.298144i
$125$		−	6.12459i		−	0.547800i
$126$		0			0
$127$	0.366918	−	0.635520i	0.0325587	−	0.0563933i	−0.849287	−	0.527932i	$-0.822968\pi$
$127$	0.366918	−	0.635520i	0.0325587	−	0.0563933i	0.881846	+	0.471538i	$0.156301\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−0.653698	+	2.20734i	−0.0573331	+	0.193596i
$131$	9.93556	+	17.2089i	0.868074	+	1.50355i	0.863962	+	0.503556i	$0.167975\pi$
$131$	9.93556	+	17.2089i	0.868074	+	1.50355i	0.00411136	+	0.999992i	$0.498691\pi$
$132$		0			0
$133$	−9.04902	−	17.2009i	−0.784650	−	1.49151i
$134$	1.96190	+	3.39810i	0.169482	+	0.293551i
$135$		0			0
$136$			0.708420i			0.0607465i
$137$			10.4636i			0.893968i	0.894542	+	0.446984i	$0.147502\pi$
$137$			10.4636i			0.893968i	−0.894542	+	0.446984i	$0.852498\pi$
$138$		0			0
$139$	0.0315662	+	0.0546743i	0.00267741	+	0.00463741i	0.867361	−	0.497680i	$-0.165814\pi$
$139$	0.0315662	+	0.0546743i	0.00267741	+	0.00463741i	−0.864684	+	0.502317i	$0.832481\pi$
$140$	1.68797	+	0.0663824i	0.142660	+	0.00561033i
$141$		0			0
$142$	−5.26412	−	9.11772i	−0.441755	−	0.765142i
$143$	−15.7130	−	4.65337i	−1.31399	−	0.389134i
$144$		0			0
$145$			4.63894i			0.385243i
$146$	−3.20623	+	5.55335i	−0.265349	+	0.459599i
$147$		0			0
$148$		−	2.10463i		−	0.172999i
$149$	7.69244	+	4.44123i	0.630189	+	0.363840i	0.780825	−	0.624749i	$-0.214799\pi$
$149$	7.69244	+	4.44123i	0.630189	+	0.363840i	−0.150636	+	0.988589i	$0.548132\pi$
$150$		0			0
$151$	−11.4580	−	6.61530i	−0.932441	−	0.538345i	−0.0448584	−	0.998993i	$-0.514284\pi$
$151$	−11.4580	−	6.61530i	−0.932441	−	0.538345i	−0.887583	+	0.460648i	$0.847617\pi$
$152$	3.67305	−	6.36190i	0.297923	−	0.516018i
$153$		0			0
$154$	−0.472545	+	12.0159i	−0.0380788	+	0.968269i
$155$	4.23954			0.340528
$156$		0			0
$157$	−1.49186	+	2.58398i	−0.119063	+	0.206224i	−0.919397	−	0.393331i	$-0.871323\pi$
$157$	−1.49186	+	2.58398i	−0.119063	+	0.206224i	0.800333	+	0.599555i	$0.204656\pi$
$158$	9.49887	−	5.48418i	0.755690	−	0.436298i
$159$		0			0
$160$	0.319244	+	0.552947i	0.0252384	+	0.0437143i
$161$	−14.5563	−	9.18510i	−1.14720	−	0.723887i
$162$		0			0
$163$	−8.59086	−	4.95993i	−0.672888	−	0.388492i	0.124282	−	0.992247i	$-0.460337\pi$
$163$	−8.59086	−	4.95993i	−0.672888	−	0.388492i	−0.797170	+	0.603755i	$0.793671\pi$
$164$	4.62167	+	2.66832i	0.360891	+	0.208361i
$165$		0			0
$166$	2.41032			0.187077
$167$	10.4096	+	6.01000i	0.805521	+	0.465068i	0.845398	−	0.534137i	$-0.179363\pi$
$167$	10.4096	+	6.01000i	0.805521	+	0.465068i	−0.0398771	+	0.999205i	$0.512697\pi$
$168$		0			0
$169$	−0.678789	+	12.9823i	−0.0522146	+	0.998636i
$170$	0.226159	+	0.391718i	0.0173456	+	0.0300434i
$171$		0			0
$172$	5.21162	+	9.02680i	0.397383	+	0.688287i
$173$	−9.75761	+	16.9007i	−0.741857	+	1.28493i	0.209792	+	0.977746i	$0.432721\pi$
$173$	−9.75761	+	16.9007i	−0.741857	+	1.28493i	−0.951649	+	0.307188i	$0.900612\pi$
$174$		0			0
$175$	−10.7530	+	5.65690i	−0.812847	+	0.427622i
$176$	−3.93617	+	2.27255i	−0.296700	+	0.171300i
$177$		0			0
$178$	−5.53328			−0.414737
$179$	−8.07581	−	13.9877i	−0.603615	−	1.04549i	−0.992269	−	0.124108i	$-0.960393\pi$
$179$	−8.07581	−	13.9877i	−0.603615	−	1.04549i	0.388654	−	0.921384i	$-0.372940\pi$
$180$		0			0
$181$	0.281865			0.0209509			0.0104754	−	0.999945i	$-0.496666\pi$
$181$	0.281865			0.0209509			0.0104754	+	0.999945i	$0.496666\pi$
$182$	9.35605	−	1.86127i	0.693517	−	0.137967i
$183$		0			0
$184$		−	6.50552i		−	0.479594i
$185$	−0.671889	−	1.16375i	−0.0493983	−	0.0855603i
$186$		0			0
$187$	−2.78846	+	1.60992i	−0.203912	+	0.117729i
$188$	1.68367	−	0.972065i	0.122794	−	0.0708951i
$189$		0			0
$190$		−	4.69039i		−	0.340277i
$191$	6.21334	−	10.7618i	0.449581	−	0.778698i	−0.548777	−	0.835969i	$-0.684907\pi$
$191$	6.21334	−	10.7618i	0.449581	−	0.778698i	0.998359	+	0.0572709i	$0.0182399\pi$
$192$		0			0
$193$	10.0807	−	5.82010i	0.725626	−	0.418940i	−0.0911941	−	0.995833i	$-0.529068\pi$
$193$	10.0807	−	5.82010i	0.725626	−	0.418940i	0.816820	+	0.576893i	$0.195735\pi$
$194$	4.59646	+	7.96131i	0.330007	+	0.571589i
$195$		0			0
$196$	−3.01312	−	6.31832i	−0.215223	−	0.451308i
$197$	−4.59712	−	2.65415i	−0.327531	−	0.189100i	0.327213	−	0.944950i	$-0.393890\pi$
$197$	−4.59712	−	2.65415i	−0.327531	−	0.189100i	−0.654744	+	0.755850i	$0.727224\pi$
$198$		0			0
$199$	13.7492			0.974658			0.487329	−	0.873219i	$-0.337971\pi$
$199$	13.7492			0.974658			0.487329	+	0.873219i	$0.337971\pi$
$200$	−3.97708	−	2.29617i	−0.281222	−	0.162364i
$201$		0			0
$202$	11.8732	−	6.85500i	0.835396	−	0.482316i
$203$	17.0122	−	8.94977i	1.19402	−	0.628151i
$204$		0			0
$205$	3.40738			0.237982
$206$	9.35918	−	5.40352i	0.652085	−	0.376481i
$207$		0			0
$208$	2.48206	+	2.61522i	0.172100	+	0.181333i
$209$	33.3887			2.30954
$210$		0			0
$211$	3.91287	−	6.77729i	0.269373	−	0.466568i	−0.699327	−	0.714802i	$-0.746517\pi$
$211$	3.91287	−	6.77729i	0.269373	−	0.466568i	0.968700	+	0.248234i	$0.0798502\pi$
$212$	3.20071	−	5.54379i	0.219826	−	0.380749i
$213$		0			0
$214$			15.3235i			1.04749i
$215$	5.76350	+	3.32756i	0.393067	+	0.226938i
$216$		0			0
$217$	−8.17922	−	15.5475i	−0.555242	−	1.05543i
$218$	−0.886839	+	1.53605i	−0.0600643	+	0.104034i
$219$		0			0
$220$	−1.45099	+	2.51320i	−0.0978260	+	0.169440i
$221$	1.75834	+	1.85268i	0.118279	+	0.124624i
$222$		0			0
$223$	16.9201	+	9.76882i	1.13305	+	0.654169i	0.944701	−	0.327933i	$-0.106352\pi$
$223$	16.9201	+	9.76882i	1.13305	+	0.654169i	0.188353	+	0.982101i	$0.439685\pi$
$224$	1.41189	−	2.23753i	0.0943361	−	0.149502i
$225$		0			0
$226$	−4.54061	+	2.62152i	−0.302037	+	0.174381i
$227$		−	4.92479i		−	0.326870i	−0.986554	−	0.163435i	$-0.947743\pi$
$227$		−	4.92479i		−	0.326870i	0.986554	−	0.163435i	$-0.0522574\pi$
$228$		0			0
$229$	13.8323	−	7.98610i	0.914066	−	0.527736i	0.0323288	−	0.999477i	$-0.489708\pi$
$229$	13.8323	−	7.98610i	0.914066	−	0.527736i	0.881737	+	0.471741i	$0.156374\pi$
$230$	−2.07685	−	3.59721i	−0.136943	−	0.237193i
$231$		0			0
$232$	6.29212	+	3.63276i	0.413098	+	0.238502i
$233$	−2.62003	−	4.53803i	−0.171644	−	0.297296i	0.767351	−	0.641228i	$-0.221575\pi$
$233$	−2.62003	−	4.53803i	−0.171644	−	0.297296i	−0.938995	+	0.343932i	$0.888241\pi$
$234$		0			0
$235$	0.620651	−	1.07500i	0.0404868	−	0.0701252i
$236$			3.31958i			0.216086i
$237$		0			0
$238$	1.00021	−	1.58511i	0.0648342	−	0.102748i
$239$			23.4449i			1.51652i	0.651952	+	0.758261i	$0.273951\pi$
$239$			23.4449i			1.51652i	−0.651952	+	0.758261i	$0.726049\pi$
$240$		0			0
$241$			11.0560i			0.712181i	0.934451	+	0.356091i	$0.115891\pi$
$241$			11.0560i			0.712181i	−0.934451	+	0.356091i	$0.884109\pi$
$242$	−8.36399	−	4.82895i	−0.537658	−	0.310417i
$243$		0			0
$244$	3.41517	−	5.91525i	0.218634	−	0.378685i
$245$	−3.68318	−	2.53177i	−0.235310	−	0.161749i
$246$		0			0
$247$	−6.18476	−	25.7545i	−0.393527	−	1.63872i
$248$	3.31999	−	5.75039i	0.210819	−	0.365150i
$249$		0			0
$250$	−6.12459			−0.387353
$251$	−12.9898	−	22.4990i	−0.819907	−	1.42012i	−0.905750	−	0.423813i	$-0.860692\pi$
$251$	−12.9898	−	22.4990i	−0.819907	−	1.42012i	0.0858425	−	0.996309i	$-0.472642\pi$
$252$		0			0
$253$	25.6068	−	14.7841i	1.60989	−	0.929469i
$254$	−0.635520	−	0.366918i	−0.0398761	−	0.0230225i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.77336			−0.110619			−0.0553095	−	0.998469i	$-0.517615\pi$
$257$	−1.77336			−0.110619			−0.0553095	+	0.998469i	$0.517615\pi$
$258$		0			0
$259$	−2.97151	+	4.70917i	−0.184640	+	0.292614i
$260$	2.20734	+	0.653698i	0.136893	+	0.0405406i
$261$		0			0
$262$	17.2089	−	9.93556i	1.06317	−	0.613821i
$263$	2.81508	+	4.87586i	0.173585	+	0.300658i	0.939671	−	0.342080i	$-0.111131\pi$
$263$	2.81508	+	4.87586i	0.173585	+	0.300658i	−0.766086	+	0.642739i	$0.777798\pi$
$264$		0			0
$265$		−	4.08723i		−	0.251077i
$266$	−17.2009	+	9.04902i	−1.05465	+	0.554831i
$267$		0			0
$268$	3.39810	−	1.96190i	0.207572	−	0.119842i
$269$	−0.668394			−0.0407527			−0.0203764	−	0.999792i	$-0.506486\pi$
$269$	−0.668394			−0.0407527			−0.0203764	+	0.999792i	$0.506486\pi$
$270$		0			0
$271$		−	20.8423i		−	1.26608i	−0.774119	−	0.633040i	$-0.781807\pi$
$271$		−	20.8423i		−	1.26608i	0.774119	−	0.633040i	$-0.218193\pi$
$272$	0.708420			0.0429543
$273$		0			0
$274$	10.4636			0.632131
$275$		−	20.8726i		−	1.25867i
$276$		0			0
$277$	−7.64182			−0.459153			−0.229576	−	0.973291i	$-0.573734\pi$
$277$	−7.64182			−0.459153			−0.229576	+	0.973291i	$0.573734\pi$
$278$	0.0546743	−	0.0315662i	0.00327915	−	0.00189322i
$279$		0			0
$280$	0.0663824	−	1.68797i	0.00396710	−	0.100876i
$281$			4.17663i			0.249157i	0.992210	+	0.124578i	$0.0397578\pi$
$281$			4.17663i			0.249157i	−0.992210	+	0.124578i	$0.960242\pi$
$282$		0			0
$283$	−3.44853	−	5.97302i	−0.204994	−	0.355059i	0.745137	−	0.666911i	$-0.232384\pi$
$283$	−3.44853	−	5.97302i	−0.204994	−	0.355059i	−0.950131	+	0.311852i	$0.899051\pi$
$284$	−9.11772	+	5.26412i	−0.541037	+	0.312368i
$285$		0			0
$286$	−4.65337	+	15.7130i	−0.275159	+	0.929130i
$287$	−6.57375	−	12.4958i	−0.388036	−	0.737601i
$288$		0			0
$289$	−16.4981			−0.970479
$290$	4.63894			0.272408
$291$		0			0
$292$	5.55335	+	3.20623i	0.324985	+	0.187630i
$293$	−13.3859	+	7.72837i	−0.782014	+	0.451496i	−0.837144	−	0.546983i	$-0.815776\pi$
$293$	−13.3859	+	7.72837i	−0.782014	+	0.451496i	0.0551294	+	0.998479i	$0.482443\pi$
$294$		0			0
$295$	1.05976	+	1.83555i	0.0617013	+	0.106870i
$296$	−2.10463			−0.122329
$297$		0			0
$298$	4.44123	−	7.69244i	0.257274	−	0.445611i
$299$	−16.1471	−	17.0134i	−0.933810	−	0.983910i
$300$		0			0
$301$	1.08369	−	27.5560i	0.0624626	−	1.58830i
$302$	−6.61530	+	11.4580i	−0.380668	+	0.659336i
$303$		0			0
$304$	−6.36190	−	3.67305i	−0.364880	−	0.210664i
$305$		−	4.36109i		−	0.249715i
$306$		0			0
$307$			25.0571i			1.43008i	0.699082	+	0.715042i	$0.253592\pi$
$307$			25.0571i			1.43008i	−0.699082	+	0.715042i	$0.746408\pi$
$308$	12.0159	+	0.472545i	0.684670	+	0.0269258i
$309$		0			0
$310$		−	4.23954i		−	0.240790i
$311$	1.07278	−	1.85810i	0.0608315	−	0.105363i	−0.834006	−	0.551756i	$-0.813958\pi$
$311$	1.07278	−	1.85810i	0.0608315	−	0.105363i	0.894837	+	0.446392i	$0.147291\pi$
$312$		0			0
$313$	14.8734	+	25.7615i	0.840696	+	1.45613i	0.889307	+	0.457311i	$0.151187\pi$
$313$	14.8734	+	25.7615i	0.840696	+	1.45613i	−0.0486108	+	0.998818i	$0.515479\pi$
$314$	2.58398	+	1.49186i	0.145822	+	0.0841906i
$315$		0			0
$316$	−5.48418	−	9.49887i	−0.308509	−	0.534353i
$317$	5.33089	−	3.07779i	0.299413	−	0.172866i	−0.342766	−	0.939421i	$-0.611364\pi$
$317$	5.33089	−	3.07779i	0.299413	−	0.172866i	0.642179	+	0.766555i	$0.278031\pi$
$318$		0			0
$319$			33.0225i			1.84890i
$320$	0.552947	−	0.319244i	0.0309107	−	0.0178463i
$321$		0			0
$322$	−9.18510	+	14.5563i	−0.511866	+	0.811193i
$323$	−4.50690	−	2.60206i	−0.250770	−	0.144782i
$324$		0			0
$325$	−16.1002	+	3.86634i	−0.893076	+	0.214466i
$326$	−4.95993	+	8.59086i	−0.274705	+	0.475804i
$327$		0			0
$328$	2.66832	−	4.62167i	0.147333	−	0.255189i
$329$	−5.13971	−	0.202127i	−0.283361	−	0.0111436i
$330$		0			0
$331$	−24.8252	−	14.3328i	−1.36452	−	0.787804i	−0.374296	−	0.927309i	$-0.622116\pi$
$331$	−24.8252	−	14.3328i	−1.36452	−	0.787804i	−0.990221	+	0.139505i	$0.955449\pi$
$332$		−	2.41032i		−	0.132283i
$333$		0			0
$334$	6.01000	−	10.4096i	0.328853	−	0.569589i
$335$	1.25265	−	2.16965i	0.0684394	−	0.118540i
$336$		0			0
$337$	21.2688			1.15859			0.579294	−	0.815119i	$-0.303328\pi$
$337$	21.2688			1.15859			0.579294	+	0.815119i	$0.303328\pi$
$338$	12.9823	+	0.678789i	0.706142	+	0.0369213i
$339$		0			0
$340$	0.391718	−	0.226159i	0.0212439	−	0.0122652i
$341$	30.1793			1.63430
$342$		0			0
$343$	−2.17883	+	18.3916i	−0.117646	+	0.993056i
$344$	9.02680	−	5.21162i	0.486692	−	0.280992i
$345$		0			0
$346$	16.9007	+	9.75761i	0.908586	+	0.524572i
$347$	−13.9059			−0.746507			−0.373253	−	0.927729i	$-0.621758\pi$
$347$	−13.9059			−0.746507			−0.373253	+	0.927729i	$0.621758\pi$
$348$		0			0
$349$	5.92236	+	3.41927i	0.317016	+	0.183030i	0.650062	−	0.759881i	$-0.274743\pi$
$349$	5.92236	+	3.41927i	0.317016	+	0.183030i	−0.333045	+	0.942911i	$0.608076\pi$
$350$	5.65690	+	10.7530i	0.302374	+	0.574770i
$351$		0			0
$352$	2.27255	+	3.93617i	0.121127	+	0.209799i
$353$	−12.1206	+	6.99785i	−0.645116	+	0.372458i	−0.786583	−	0.617485i	$-0.788152\pi$
$353$	−12.1206	+	6.99785i	−0.645116	+	0.372458i	0.141467	+	0.989943i	$0.454818\pi$
$354$		0			0
$355$	−3.36107	+	5.82155i	−0.178387	+	0.308976i
$356$			5.53328i			0.293263i
$357$		0			0
$358$	−13.9877	+	8.07581i	−0.739274	+	0.426820i
$359$	1.17370	−	0.677638i	0.0619457	−	0.0357644i	−0.468707	−	0.883354i	$-0.655280\pi$
$359$	1.17370	−	0.677638i	0.0619457	−	0.0357644i	0.530653	+	0.847589i	$0.321947\pi$
$360$		0			0
$361$	17.4825	+	30.2806i	0.920133	+	1.59372i
$362$		−	0.281865i		−	0.0148145i
$363$		0			0
$364$	−1.86127	−	9.35605i	−0.0975571	−	0.490390i
$365$	4.09427			0.214304
$366$		0			0
$367$	5.92951	+	10.2702i	0.309518	+	0.536101i	0.978257	−	0.207396i	$-0.0664990\pi$
$367$	5.92951	+	10.2702i	0.309518	+	0.536101i	−0.668739	+	0.743497i	$0.733166\pi$
$368$	−6.50552			−0.339124
$369$		0			0
$370$	−1.16375	+	0.671889i	−0.0605003	+	0.0349298i
$371$	−14.9889	+	7.88537i	−0.778187	+	0.409388i
$372$		0			0
$373$	19.0720	−	33.0337i	0.987511	−	1.71042i	0.357315	−	0.933984i	$-0.383692\pi$
$373$	19.0720	−	33.0337i	0.987511	−	1.71042i	0.630197	−	0.776436i	$-0.282974\pi$
$374$	1.60992	+	2.78846i	0.0832469	+	0.144188i
$375$		0			0
$376$	−0.972065	−	1.68367i	−0.0501304	−	0.0868284i
$377$	25.4720	−	6.11693i	1.31188	−	0.315038i
$378$		0			0
$379$	−27.4201	−	15.8310i	−1.40848	−	0.813185i	−0.413237	−	0.910624i	$-0.635602\pi$
$379$	−27.4201	−	15.8310i	−1.40848	−	0.813185i	−0.995242	+	0.0974383i	$0.968935\pi$
$380$	−4.69039			−0.240612
$381$		0			0
$382$	−10.7618	−	6.21334i	−0.550622	−	0.317902i
$383$	−12.6943	−	7.32908i	−0.648650	−	0.374498i	0.139289	−	0.990252i	$-0.455518\pi$
$383$	−12.6943	−	7.32908i	−0.648650	−	0.374498i	−0.787939	+	0.615753i	$0.788852\pi$
$384$		0			0
$385$	6.79501	−	3.57471i	0.346306	−	0.182184i
$386$	−5.82010	−	10.0807i	−0.296235	−	0.513095i
$387$		0			0
$388$	7.96131	−	4.59646i	0.404174	−	0.233350i
$389$	8.23276	−	14.2596i	0.417418	−	0.722989i	−0.578261	−	0.815852i	$-0.696269\pi$
$389$	8.23276	−	14.2596i	0.417418	−	0.722989i	0.995679	+	0.0928631i	$0.0296019\pi$
$390$		0			0
$391$	−4.60864			−0.233069
$392$	−6.31832	+	3.01312i	−0.319123	+	0.152185i
$393$		0			0
$394$	−2.65415	+	4.59712i	−0.133714	+	0.231599i
$395$	−6.06491	−	3.50158i	−0.305159	−	0.176184i
$396$		0			0
$397$	−14.1163	−	8.15004i	−0.708476	−	0.409039i	0.102020	−	0.994782i	$-0.467469\pi$
$397$	−14.1163	−	8.15004i	−0.708476	−	0.409039i	−0.810497	+	0.585743i	$0.800803\pi$
$398$		−	13.7492i		−	0.689187i
$399$		0			0
$400$	−2.29617	+	3.97708i	−0.114808	+	0.198854i
$401$			20.8495i			1.04118i	0.853808	+	0.520588i	$0.174287\pi$
$401$			20.8495i			1.04118i	−0.853808	+	0.520588i	$0.825713\pi$
$402$		0			0
$403$	−5.59028	−	23.2790i	−0.278472	−	1.15961i
$404$	−6.85500	−	11.8732i	−0.341049	−	0.590714i
$405$		0			0
$406$	−8.94977	−	17.0122i	−0.444170	−	0.844302i
$407$	−4.78287	−	8.28417i	−0.237078	−	0.410631i
$408$		0			0
$409$		−	1.20081i		−	0.0593763i	−0.999559	−	0.0296882i	$-0.990549\pi$
$409$		−	1.20081i		−	0.0593763i	0.999559	−	0.0296882i	$-0.00945142\pi$
$410$		−	3.40738i		−	0.168278i
$411$		0			0
$412$	−5.40352	−	9.35918i	−0.266212	−	0.461094i
$413$	4.68689	−	7.42767i	0.230627	−	0.365492i
$414$		0			0
$415$	−0.769479	−	1.33278i	−0.0377722	−	0.0654234i
$416$	2.61522	−	2.48206i	0.128222	−	0.121693i
$417$		0			0
$418$		−	33.3887i		−	1.63309i
$419$	−9.29434	+	16.0983i	−0.454058	+	0.786452i	−0.998634	−	0.0522602i	$-0.983357\pi$
$419$	−9.29434	+	16.0983i	−0.454058	+	0.786452i	0.544575	+	0.838712i	$0.316691\pi$
$420$		0			0
$421$		−	21.9581i		−	1.07017i	−0.844797	−	0.535087i	$-0.820279\pi$
$421$		−	21.9581i		−	1.07017i	0.844797	−	0.535087i	$-0.179721\pi$
$422$	−6.77729	−	3.91287i	−0.329913	−	0.190476i
$423$		0			0
$424$	−5.54379	−	3.20071i	−0.269230	−	0.155440i
$425$	−1.62665	+	2.81744i	−0.0789041	+	0.136666i
$426$		0			0
$427$	−15.9933	+	8.41372i	−0.773968	+	0.407168i
$428$	15.3235			0.740687
$429$		0			0
$430$	3.32756	−	5.76350i	0.160469	−	0.277941i
$431$	23.8430	−	13.7658i	1.14848	−	0.663074i	0.199962	−	0.979804i	$-0.435918\pi$
$431$	23.8430	−	13.7658i	1.14848	−	0.663074i	0.948516	+	0.316730i	$0.102585\pi$
$432$		0			0
$433$	16.4667	+	28.5212i	0.791339	+	1.37064i	0.925138	+	0.379631i	$0.123949\pi$
$433$	16.4667	+	28.5212i	0.791339	+	1.37064i	−0.133799	+	0.991008i	$0.542718\pi$
$434$	−15.5475	+	8.17922i	−0.746305	+	0.392615i
$435$		0			0
$436$	1.53605	+	0.886839i	0.0735635	+	0.0424719i
$437$	41.3875	+	23.8951i	1.97983	+	1.14306i
$438$		0			0
$439$	12.7172			0.606957			0.303479	−	0.952838i	$-0.401852\pi$
$439$	12.7172			0.606957			0.303479	+	0.952838i	$0.401852\pi$
$440$	2.51320	+	1.45099i	0.119812	+	0.0691734i
$441$		0			0
$442$	1.85268	−	1.75834i	0.0881228	−	0.0836356i
$443$	−14.4934	−	25.1034i	−0.688604	−	1.19270i	−0.972290	−	0.233779i	$-0.924891\pi$
$443$	−14.4934	−	25.1034i	−0.688604	−	1.19270i	0.283686	−	0.958917i	$-0.408443\pi$
$444$		0			0
$445$	1.76647	+	3.05961i	0.0837385	+	0.145039i
$446$	9.76882	−	16.9201i	0.462567	−	0.801190i
$447$		0			0
$448$	−2.23753	−	1.41189i	−0.105714	−	0.0667057i
$449$	0.0241096	−	0.0139197i	0.00113780	−	0.000656909i	−0.499431	−	0.866354i	$-0.666458\pi$
$449$	0.0241096	−	0.0139197i	0.00113780	−	0.000656909i	0.500569	+	0.865697i	$0.333124\pi$
$450$		0			0
$451$	24.2555			1.14215
$452$	2.62152	+	4.54061i	0.123306	+	0.213572i
$453$		0			0
$454$	−4.92479			−0.231132
$455$	−4.01604	−	4.57920i	−0.188275	−	0.214676i
$456$		0			0
$457$		−	30.7861i		−	1.44011i	−0.693915	−	0.720057i	$-0.744116\pi$
$457$		−	30.7861i		−	1.44011i	0.693915	−	0.720057i	$-0.255884\pi$
$458$	−7.98610	−	13.8323i	−0.373166	−	0.646342i
$459$		0			0
$460$	−3.59721	+	2.07685i	−0.167721	+	0.0968336i
$461$	−32.8804	+	18.9835i	−1.53139	+	0.884149i	−0.532093	+	0.846686i	$0.678594\pi$
$461$	−32.8804	+	18.9835i	−1.53139	+	0.884149i	−0.999298	+	0.0374628i	$0.988072\pi$
$462$		0			0
$463$			13.3969i			0.622608i	0.950310	+	0.311304i	$0.100766\pi$
$463$			13.3969i			0.622608i	−0.950310	+	0.311304i	$0.899234\pi$
$464$	3.63276	−	6.29212i	0.168647	−	0.292104i
$465$		0			0
$466$	−4.53803	+	2.62003i	−0.210220	+	0.121371i
$467$	12.9575	+	22.4431i	0.599603	+	1.03854i	0.992880	+	0.119122i	$0.0380081\pi$
$467$	12.9575	+	22.4431i	0.599603	+	1.03854i	−0.393277	+	0.919420i	$0.628659\pi$
$468$		0			0
$469$	−10.3734	−	0.407949i	−0.478997	−	0.0188373i
$470$	−1.07500	−	0.620651i	−0.0495860	−	0.0286285i
$471$		0			0
$472$	3.31958			0.152796
$473$	41.0277	+	23.6873i	1.88645	+	1.08914i
$474$		0			0
$475$	29.2160	−	16.8678i	1.34052	−	0.773950i
$476$	−1.58511	−	1.00021i	−0.0726536	−	0.0458447i
$477$		0			0
$478$	23.4449			1.07234
$479$	0.219038	−	0.126461i	0.0100081	−	0.00577817i	−0.494988	−	0.868900i	$-0.664827\pi$
$479$	0.219038	−	0.126461i	0.0100081	−	0.00577817i	0.504996	+	0.863122i	$0.331494\pi$
$480$		0			0
$481$	−5.50407	+	5.22380i	−0.250964	+	0.238185i
$482$	11.0560			0.503588
$483$		0			0
$484$	−4.82895	+	8.36399i	−0.219498	+	0.380181i
$485$	2.93479	−	5.08320i	0.133262	−	0.230816i
$486$		0			0
$487$		−	30.3567i		−	1.37559i	−0.725904	−	0.687796i	$-0.758578\pi$
$487$		−	30.3567i		−	1.37559i	0.725904	−	0.687796i	$-0.241422\pi$
$488$	−5.91525	−	3.41517i	−0.267771	−	0.154598i
$489$		0			0
$490$	−2.53177	+	3.68318i	−0.114374	+	0.166389i
$491$	6.74228	−	11.6780i	0.304275	−	0.527019i	−0.672825	−	0.739802i	$-0.734919\pi$
$491$	6.74228	−	11.6780i	0.304275	−	0.527019i	0.977100	+	0.212782i	$0.0682526\pi$
$492$		0			0
$493$	2.57352	−	4.45746i	0.115905	−	0.200754i
$494$	−25.7545	+	6.18476i	−1.15875	+	0.278266i
$495$		0			0
$496$	−5.75039	−	3.31999i	−0.258200	−	0.149072i
$497$	27.8336	+	1.09460i	1.24851	+	0.0490996i
$498$		0			0
$499$	−1.75032	+	1.01055i	−0.0783551	+	0.0452383i	−0.538666	−	0.842520i	$-0.681071\pi$
$499$	−1.75032	+	1.01055i	−0.0783551	+	0.0452383i	0.460311	+	0.887758i	$0.347738\pi$
$500$			6.12459i			0.273900i
$501$		0			0
$502$	−22.4990	+	12.9898i	−1.00418	+	0.579762i
$503$	2.81234	+	4.87112i	0.125396	+	0.217192i	0.921888	−	0.387457i	$-0.126646\pi$
$503$	2.81234	+	4.87112i	0.125396	+	0.217192i	−0.796492	+	0.604650i	$0.793313\pi$
$504$		0			0
$505$	−7.58090	−	4.37684i	−0.337346	−	0.194767i
$506$	−14.7841	−	25.6068i	−0.657234	−	1.13836i
$507$		0			0
$508$	−0.366918	+	0.635520i	−0.0162793	+	0.0281966i
$509$		−	16.2390i		−	0.719781i	−0.932995	−	0.359890i	$-0.882814\pi$
$509$		−	16.2390i		−	0.719781i	0.932995	−	0.359890i	$-0.117186\pi$
$510$		0			0
$511$	−7.89896	−	15.0148i	−0.349429	−	0.664215i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			1.77336i			0.0782194i
$515$	−5.97572	−	3.45008i	−0.263322	−	0.152029i
$516$		0			0
$517$	4.41813	−	7.65242i	0.194309	−	0.336553i
$518$	4.70917	+	2.97151i	0.206909	+	0.130561i
$519$		0			0
$520$	0.653698	−	2.20734i	0.0286665	−	0.0967982i
$521$	−8.32351	+	14.4167i	−0.364659	+	0.631609i	−0.988721	−	0.149766i	$-0.952148\pi$
$521$	−8.32351	+	14.4167i	−0.364659	+	0.631609i	0.624062	+	0.781375i	$0.285481\pi$
$522$		0			0
$523$	12.8151			0.560363			0.280182	−	0.959947i	$-0.409605\pi$
$523$	12.8151			0.560363			0.280182	+	0.959947i	$0.409605\pi$
$524$	−9.93556	−	17.2089i	−0.434037	−	0.751774i
$525$		0			0
$526$	4.87586	−	2.81508i	0.212598	−	0.122743i
$527$	−4.07369	−	2.35195i	−0.177453	−	0.102452i
$528$		0			0
$529$	19.3218			0.840080
$530$	−4.08723			−0.177538
$531$		0			0
$532$	9.04902	+	17.2009i	0.392325	+	0.745753i
$533$	−4.49298	−	18.7096i	−0.194613	−	0.810403i
$534$		0			0
$535$	8.47305	−	4.89192i	0.366322	−	0.211496i
$536$	−1.96190	−	3.39810i	−0.0847410	−	0.146776i
$537$		0			0
$538$			0.668394i			0.0288165i
$539$	−26.2188	−	18.0225i	−1.12932	−	0.776285i
$540$		0			0
$541$	−5.98399	+	3.45486i	−0.257272	+	0.148536i	−0.623089	−	0.782151i	$-0.714123\pi$
$541$	−5.98399	+	3.45486i	−0.257272	+	0.148536i	0.365818	+	0.930687i	$0.380789\pi$
$542$	−20.8423			−0.895254
$543$		0			0
$544$		−	0.708420i		−	0.0303733i
$545$	1.13247			0.0485098
$546$		0			0
$547$	24.8868			1.06408			0.532041	−	0.846719i	$-0.321425\pi$
$547$	24.8868			1.06408			0.532041	+	0.846719i	$0.321425\pi$
$548$		−	10.4636i		−	0.446984i
$549$		0			0
$550$	−20.8726			−0.890011
$551$	−46.2225	+	26.6866i	−1.96914	+	1.13689i
$552$		0			0
$553$	−1.14036	+	28.9971i	−0.0484930	+	1.23308i
$554$			7.64182i			0.324670i
$555$		0			0
$556$	−0.0315662	−	0.0546743i	−0.00133871	−	0.00231871i
$557$	−10.1308	+	5.84900i	−0.429254	+	0.247830i	−0.699029	−	0.715094i	$-0.746384\pi$
$557$	−10.1308	+	5.84900i	−0.429254	+	0.247830i	0.269775	+	0.962923i	$0.413051\pi$
$558$		0			0
$559$	10.6715	−	36.0346i	0.451358	−	1.52410i
$560$	−1.68797	−	0.0663824i	−0.0713300	−	0.00280517i
$561$		0			0
$562$	4.17663			0.176181
$563$	25.1230			1.05881			0.529404	−	0.848370i	$-0.322415\pi$
$563$	25.1230			1.05881			0.529404	+	0.848370i	$0.322415\pi$
$564$		0			0
$565$	2.89912	+	1.67381i	0.121967	+	0.0704177i
$566$	−5.97302	+	3.44853i	−0.251065	+	0.144952i
$567$		0			0
$568$	5.26412	+	9.11772i	0.220878	+	0.382571i
$569$	25.0757			1.05123			0.525614	−	0.850723i	$-0.323835\pi$
$569$	25.0757			1.05123			0.525614	+	0.850723i	$0.323835\pi$
$570$		0			0
$571$	−4.56201	+	7.90163i	−0.190914	+	0.330673i	−0.945553	−	0.325467i	$-0.894479\pi$
$571$	−4.56201	+	7.90163i	−0.190914	+	0.330673i	0.754639	+	0.656140i	$0.227812\pi$
$572$	15.7130	+	4.65337i	0.656994	+	0.194567i
$573$		0			0
$574$	−12.4958	+	6.57375i	−0.521563	+	0.274383i
$575$	14.9378	−	25.8730i	0.622948	−	1.07898i
$576$		0			0
$577$	−11.1074	−	6.41283i	−0.462405	−	0.266970i	0.250650	−	0.968078i	$-0.419356\pi$
$577$	−11.1074	−	6.41283i	−0.462405	−	0.266970i	−0.713055	+	0.701108i	$0.752689\pi$
$578$			16.4981i			0.686232i
$579$		0			0
$580$		−	4.63894i		−	0.192622i
$581$	−3.40311	+	5.39317i	−0.141185	+	0.223746i
$582$		0			0
$583$		−	29.0951i		−	1.20500i
$584$	3.20623	−	5.55335i	0.132675	−	0.229799i
$585$		0			0
$586$	7.72837	+	13.3859i	0.319256	+	0.552968i
$587$	6.27507	+	3.62291i	0.259000	+	0.149534i	0.623878	−	0.781522i	$-0.285556\pi$
$587$	6.27507	+	3.62291i	0.259000	+	0.149534i	−0.364878	+	0.931055i	$0.618889\pi$
$588$		0			0
$589$	24.3889	+	42.2429i	1.00493	+	1.74059i
$590$	1.83555	−	1.05976i	0.0755684	−	0.0436294i
$591$		0			0
$592$			2.10463i			0.0864996i
$593$	−13.4056	+	7.73971i	−0.550501	+	0.317832i	−0.749324	−	0.662204i	$-0.769621\pi$
$593$	−13.4056	+	7.73971i	−0.550501	+	0.317832i	0.198823	+	0.980035i	$0.436288\pi$
$594$		0			0
$595$	−1.19579	−	0.0470266i	−0.0490228	−	0.00192790i
$596$	−7.69244	−	4.44123i	−0.315095	−	0.181920i
$597$		0			0
$598$	−17.0134	+	16.1471i	−0.695730	+	0.660303i
$599$	−21.5483	+	37.3227i	−0.880438	+	1.52496i	−0.0295828	+	0.999562i	$0.509418\pi$
$599$	−21.5483	+	37.3227i	−0.880438	+	1.52496i	−0.850855	+	0.525401i	$0.823915\pi$
$600$		0			0
$601$	11.6610	−	20.1975i	0.475664	−	0.823873i	−0.523948	−	0.851750i	$-0.675541\pi$
$601$	11.6610	−	20.1975i	0.475664	−	0.823873i	0.999611	+	0.0278770i	$0.00887466\pi$
$602$	−27.5560	−	1.08369i	−1.12310	−	0.0441677i
$603$		0			0
$604$	11.4580	+	6.61530i	0.466221	+	0.269173i
$605$			6.16646i			0.250702i
$606$		0			0
$607$	−15.7844	+	27.3394i	−0.640670	+	1.10967i	0.344614	+	0.938745i	$0.388010\pi$
$607$	−15.7844	+	27.3394i	−0.640670	+	1.10967i	−0.985283	+	0.170928i	$0.945323\pi$
$608$	−3.67305	+	6.36190i	−0.148962	+	0.258009i
$609$		0			0
$610$	−4.36109			−0.176575
$611$	−6.72112	−	1.99044i	−0.271907	−	0.0805247i
$612$		0			0
$613$	−13.6857	+	7.90145i	−0.552761	+	0.319137i	−0.750235	−	0.661171i	$-0.770060\pi$
$613$	−13.6857	+	7.90145i	−0.552761	+	0.319137i	0.197474	+	0.980308i	$0.436726\pi$
$614$	25.0571			1.01122
$615$		0			0
$616$	0.472545	−	12.0159i	0.0190394	−	0.484135i
$617$	−14.3413	+	8.27996i	−0.577360	+	0.333339i	−0.760083	−	0.649826i	$-0.774842\pi$
$617$	−14.3413	+	8.27996i	−0.577360	+	0.333339i	0.182724	+	0.983164i	$0.441509\pi$
$618$		0			0
$619$	−17.3556	−	10.0203i	−0.697581	−	0.402749i	0.108865	−	0.994057i	$-0.465278\pi$
$619$	−17.3556	−	10.0203i	−0.697581	−	0.402749i	−0.806446	+	0.591308i	$0.798612\pi$
$620$	−4.23954			−0.170264
$621$		0			0
$622$	−1.85810	−	1.07278i	−0.0745031	−	0.0430144i
$623$	7.81240	−	12.3809i	0.312997	−	0.496030i
$624$		0			0
$625$	−9.52560	−	16.4988i	−0.381024	−	0.659953i
$626$	25.7615	−	14.8734i	1.02964	−	0.594462i
$627$		0			0
$628$	1.49186	−	2.58398i	0.0595317	−	0.103112i
$629$			1.49096i			0.0594484i
$630$		0			0
$631$	−17.8127	+	10.2842i	−0.709113	+	0.409407i	−0.810733	−	0.585417i	$-0.800931\pi$
$631$	−17.8127	+	10.2842i	−0.709113	+	0.409407i	0.101620	+	0.994823i	$0.467598\pi$
$632$	−9.49887	+	5.48418i	−0.377845	+	0.218149i
$633$		0			0
$634$	−3.07779	−	5.33089i	−0.122235	−	0.211717i
$635$			0.468545i			0.0185936i
$636$		0			0
$637$	−9.04508	+	23.5624i	−0.358379	+	0.933576i
$638$	33.0225			1.30737
$639$		0			0
$640$	−0.319244	−	0.552947i	−0.0126192	−	0.0218571i
$641$	34.3713			1.35758			0.678792	−	0.734330i	$-0.262504\pi$
$641$	34.3713			1.35758			0.678792	+	0.734330i	$0.262504\pi$
$642$		0			0
$643$	−7.68629	+	4.43768i	−0.303118	+	0.175005i	−0.643843	−	0.765158i	$-0.722661\pi$
$643$	−7.68629	+	4.43768i	−0.303118	+	0.175005i	0.340725	+	0.940163i	$0.389328\pi$
$644$	14.5563	+	9.18510i	0.573600	+	0.361944i
$645$		0			0
$646$	−2.60206	+	4.50690i	−0.102377	+	0.177321i
$647$	2.26837	+	3.92893i	0.0891788	+	0.154462i	0.907164	−	0.420777i	$-0.138242\pi$
$647$	2.26837	+	3.92893i	0.0891788	+	0.154462i	−0.817985	+	0.575239i	$0.804909\pi$
$648$		0			0
$649$	7.54391	+	13.0664i	0.296124	+	0.512902i
$650$	3.86634	+	16.1002i	0.151650	+	0.631500i
$651$		0			0
$652$	8.59086	+	4.95993i	0.336444	+	0.194246i
$653$	−27.1450			−1.06227			−0.531133	−	0.847288i	$-0.678234\pi$
$653$	−27.1450			−1.06227			−0.531133	+	0.847288i	$0.678234\pi$
$654$		0			0
$655$	−10.9877	−	6.34373i	−0.429324	−	0.247870i
$656$	−4.62167	−	2.66832i	−0.180446	−	0.104180i
$657$		0			0
$658$	−0.202127	+	5.13971i	−0.00787975	+	0.200367i
$659$	13.2645	+	22.9748i	0.516712	+	0.894972i	0.999812	+	0.0194066i	$0.00617770\pi$
$659$	13.2645	+	22.9748i	0.516712	+	0.894972i	−0.483099	+	0.875566i	$0.660489\pi$
$660$		0			0
$661$	26.9057	−	15.5340i	1.04651	−	0.604204i	0.124841	−	0.992177i	$-0.460158\pi$
$661$	26.9057	−	15.5340i	1.04651	−	0.604204i	0.921671	+	0.387973i	$0.126825\pi$
$662$	−14.3328	+	24.8252i	−0.557062	+	0.964859i
$663$		0			0
$664$	−2.41032			−0.0935384
$665$	10.4949	+	6.62233i	0.406975	+	0.256803i
$666$		0			0
$667$	−23.6330	+	40.9335i	−0.915073	+	1.58495i
$668$	−10.4096	−	6.01000i	−0.402760	−	0.232534i
$669$		0			0
$670$	−2.16965	−	1.25265i	−0.0838208	−	0.0483940i
$671$		−	31.0446i		−	1.19846i
$672$		0			0
$673$	−9.48380	+	16.4264i	−0.365574	+	0.633192i	−0.988868	−	0.148795i	$-0.952461\pi$
$673$	−9.48380	+	16.4264i	−0.365574	+	0.633192i	0.623294	+	0.781987i	$0.285794\pi$
$674$		−	21.2688i		−	0.819245i
$675$		0			0
$676$	0.678789	−	12.9823i	0.0261073	−	0.499318i
$677$	8.38565	+	14.5244i	0.322287	+	0.558217i	0.980959	−	0.194212i	$-0.0622151\pi$
$677$	8.38565	+	14.5244i	0.322287	+	0.558217i	−0.658673	+	0.752430i	$0.728882\pi$
$678$		0			0
$679$	−24.3034	−	0.955771i	−0.932679	−	0.0366791i
$680$	−0.226159	−	0.391718i	−0.00867279	−	0.0150217i
$681$		0			0
$682$		−	30.1793i		−	1.15563i
$683$		−	7.44457i		−	0.284858i	−0.989805	−	0.142429i	$-0.954509\pi$
$683$		−	7.44457i		−	0.284858i	0.989805	−	0.142429i	$-0.0454913\pi$
$684$		0			0
$685$	−3.34045	−	5.78583i	−0.127632	−	0.221065i
$686$	18.3916	+	2.17883i	0.702196	+	0.0831883i
$687$		0			0
$688$	−5.21162	−	9.02680i	−0.198691	−	0.344143i
$689$	−22.4426	+	5.38944i	−0.854995	+	0.205321i
$690$		0			0
$691$		−	40.3287i		−	1.53418i	−0.641542	−	0.767088i	$-0.721705\pi$
$691$		−	40.3287i		−	1.53418i	0.641542	−	0.767088i	$-0.278295\pi$
$692$	9.75761	−	16.9007i	0.370929	−	0.642467i
$693$		0			0
$694$			13.9059i			0.527860i
$695$	−0.0349089	−	0.0201546i	−0.00132417	−	0.000764509i
$696$		0			0
$697$	−3.27408	−	1.89029i	−0.124015	−	0.0715999i
$698$	3.41927	−	5.92236i	0.129421	−	0.224165i
$699$		0			0
$700$	10.7530	−	5.65690i	0.406424	−	0.213811i
$701$	−1.32063			−0.0498794			−0.0249397	−	0.999689i	$-0.507939\pi$
$701$	−1.32063			−0.0498794			−0.0249397	+	0.999689i	$0.507939\pi$
$702$		0			0
$703$	7.73039	−	13.3894i	0.291557	−	0.504992i
$704$	3.93617	−	2.27255i	0.148350	−	0.0856499i
$705$		0			0
$706$	6.99785	+	12.1206i	0.263367	+	0.456166i
$707$	−1.42540	+	36.2452i	−0.0536078	+	1.36314i
$708$		0			0
$709$	25.0311	+	14.4517i	0.940063	+	0.542746i	0.889980	−	0.455999i	$-0.150718\pi$
$709$	25.0311	+	14.4517i	0.940063	+	0.542746i	0.0500830	+	0.998745i	$0.484051\pi$
$710$	5.82155	+	3.36107i	0.218479	+	0.126139i
$711$		0			0
$712$	5.53328			0.207368
$713$	37.4093	+	21.5983i	1.40099	+	0.808861i
$714$		0			0
$715$	10.1740	−	2.44322i	0.380487	−	0.0913712i
$716$	8.07581	+	13.9877i	0.301807	+	0.522746i
$717$		0			0
$718$	−0.677638	−	1.17370i	−0.0252892	−	0.0438022i
$719$	−15.7289	+	27.2433i	−0.586590	+	1.01600i	0.408086	+	0.912944i	$0.366197\pi$
$719$	−15.7289	+	27.2433i	−0.586590	+	1.01600i	−0.994675	+	0.103059i	$0.967137\pi$
$720$		0			0
$721$	−1.12359	+	28.5707i	−0.0418446	+	1.06403i
$722$	30.2806	−	17.4825i	1.12693	−	0.650632i
$723$		0			0
$724$	−0.281865			−0.0104754
$725$	16.6828	+	28.8955i	0.619585	+	1.07315i
$726$		0			0
$727$	15.8625			0.588306			0.294153	−	0.955758i	$-0.404962\pi$
$727$	15.8625			0.588306			0.294153	+	0.955758i	$0.404962\pi$
$728$	−9.35605	+	1.86127i	−0.346758	+	0.0689833i
$729$		0			0
$730$		−	4.09427i		−	0.151536i
$731$	−3.69202	−	6.39476i	−0.136554	−	0.236519i
$732$		0			0
$733$	−30.0928	+	17.3741i	−1.11150	+	0.641727i	−0.939219	−	0.343320i	$-0.888448\pi$
$733$	−30.0928	+	17.3741i	−1.11150	+	0.641727i	−0.172285	+	0.985047i	$0.555115\pi$
$734$	10.2702	−	5.92951i	0.379081	−	0.218862i
$735$		0			0
$736$			6.50552i			0.239797i
$737$	8.91701	−	15.4447i	0.328462	−	0.568913i
$738$		0			0
$739$	−21.7681	+	12.5678i	−0.800753	+	0.462315i	−0.843735	−	0.536761i	$-0.819648\pi$
$739$	−21.7681	+	12.5678i	−0.800753	+	0.462315i	0.0429812	+	0.999076i	$0.486314\pi$
$740$	0.671889	+	1.16375i	0.0246991	+	0.0427802i
$741$		0			0
$742$	7.88537	+	14.9889i	0.289481	+	0.550261i
$743$	23.3693	+	13.4923i	0.857336	+	0.494983i	0.863119	−	0.505000i	$-0.168508\pi$
$743$	23.3693	+	13.4923i	0.857336	+	0.494983i	−0.00578361	+	0.999983i	$0.501841\pi$
$744$		0			0
$745$	−5.67134			−0.207782
$746$	−33.0337	−	19.0720i	−1.20945	−	0.698276i
$747$		0			0
$748$	2.78846	−	1.60992i	0.101956	−	0.0588645i
$749$	−34.2868	−	21.6351i	−1.25281	−	0.790529i
$750$		0			0
$751$	16.5460			0.603771			0.301886	−	0.953344i	$-0.402384\pi$
$751$	16.5460			0.603771			0.301886	+	0.953344i	$0.402384\pi$
$752$	−1.68367	+	0.972065i	−0.0613970	+	0.0354475i
$753$		0			0
$754$	−6.11693	−	25.4720i	−0.222765	−	0.927636i
$755$	8.44757			0.307439
$756$		0			0
$757$	−21.1295	+	36.5974i	−0.767965	+	1.33015i	0.170699	+	0.985323i	$0.445397\pi$
$757$	−21.1295	+	36.5974i	−0.767965	+	1.33015i	−0.938665	+	0.344832i	$0.887936\pi$
$758$	−15.8310	+	27.4201i	−0.575009	+	0.995945i
$759$		0			0
$760$			4.69039i			0.170138i
$761$	19.6009	+	11.3166i	0.710531	+	0.410225i	0.811258	−	0.584689i	$-0.198783\pi$
$761$	19.6009	+	11.3166i	0.710531	+	0.410225i	−0.100726	+	0.994914i	$0.532117\pi$
$762$		0			0
$763$	−2.18484	−	4.15307i	−0.0790967	−	0.150351i
$764$	−6.21334	+	10.7618i	−0.224791	+	0.389349i
$765$		0			0
$766$	−7.32908	+	12.6943i	−0.264810	+	0.458665i
$767$	8.68144	−	8.23938i	0.313469	−	0.297507i
$768$		0			0
$769$	38.9093	+	22.4643i	1.40311	+	0.810084i	0.994710	−	0.102721i	$-0.0327548\pi$
$769$	38.9093	+	22.4643i	1.40311	+	0.810084i	0.408396	+	0.912805i	$0.366088\pi$
$770$	−3.57471	−	6.79501i	−0.128824	−	0.244875i
$771$		0			0
$772$	−10.0807	+	5.82010i	−0.362813	+	0.209470i
$773$		−	51.6217i		−	1.85670i	−0.371704	−	0.928351i	$-0.621226\pi$
$773$		−	51.6217i		−	1.85670i	0.371704	−	0.928351i	$-0.378774\pi$
$774$		0			0
$775$	26.4077	−	15.2465i	0.948593	−	0.547670i
$776$	−4.59646	−	7.96131i	−0.165003	−	0.285794i
$777$		0			0
$778$	−14.2596	−	8.23276i	−0.511230	−	0.295159i
$779$	19.6017	+	33.9512i	0.702304	+	1.21643i
$780$		0			0
$781$	−23.9259	+	41.4409i	−0.856137	+	1.48287i
$782$			4.60864i			0.164805i
$783$		0			0
$784$	3.01312	+	6.31832i	0.107611	+	0.225654i
$785$		−	1.90507i		−	0.0679949i
$786$		0			0
$787$		−	10.0611i		−	0.358638i	−0.983791	−	0.179319i	$-0.942611\pi$
$787$		−	10.0611i		−	0.358638i	0.983791	−	0.179319i	$-0.0573894\pi$
$788$	4.59712	+	2.65415i	0.163766	+	0.0945501i
$789$		0			0
$790$	−3.50158	+	6.06491i	−0.124581	+	0.215780i
$791$	0.545110	−	13.8611i	0.0193819	−	0.492843i
$792$		0			0
$793$	−23.9463	+	5.75055i	−0.850360	+	0.204208i
$794$	−8.15004	+	14.1163i	−0.289234	+	0.500968i
$795$		0			0
$796$	−13.7492			−0.487329
$797$	17.7635	+	30.7672i	0.629214	+	1.08983i	0.987710	+	0.156300i	$0.0499566\pi$
$797$	17.7635	+	30.7672i	0.629214	+	1.08983i	−0.358495	+	0.933532i	$0.616710\pi$
$798$		0			0
$799$	−1.19274	+	0.688630i	−0.0421962	+	0.0243620i
$800$	3.97708	+	2.29617i	0.140611	+	0.0811818i
$801$		0			0
$802$	20.8495			0.736222
$803$	29.1452			1.02851
$804$		0			0
$805$	10.9812	+	0.431852i	0.387035	+	0.0152208i
$806$	−23.2790	+	5.59028i	−0.819966	+	0.196909i
$807$		0			0
$808$	−11.8732	+	6.85500i	−0.417698	+	0.241158i
$809$	−23.7244	−	41.0918i	−0.834104	−	1.44471i	−0.894758	−	0.446551i	$-0.852652\pi$
$809$	−23.7244	−	41.0918i	−0.834104	−	1.44471i	0.0606541	−	0.998159i	$-0.480681\pi$
$810$		0			0
$811$			24.4360i			0.858063i	0.903289	+	0.429032i	$0.141145\pi$
$811$			24.4360i			0.858063i	−0.903289	+	0.429032i	$0.858855\pi$
$812$	−17.0122	+	8.94977i	−0.597012	+	0.314075i
$813$		0			0
$814$	−8.28417	+	4.78287i	−0.290360	+	0.167639i
$815$	6.33371			0.221860
$816$		0			0
$817$			76.5701i			2.67885i
$818$	−1.20081			−0.0419854
$819$		0			0
$820$	−3.40738			−0.118991
$821$		−	47.7273i		−	1.66570i	−0.553502	−	0.832848i	$-0.686709\pi$
$821$		−	47.7273i		−	1.66570i	0.553502	−	0.832848i	$-0.313291\pi$
$822$		0			0
$823$	−17.0671			−0.594922			−0.297461	−	0.954734i	$-0.596140\pi$
$823$	−17.0671			−0.594922			−0.297461	+	0.954734i	$0.596140\pi$
$824$	−9.35918	+	5.40352i	−0.326042	+	0.188241i
$825$		0			0
$826$	−7.42767	−	4.68689i	−0.258442	−	0.163078i
$827$			4.18226i			0.145431i	0.997353	+	0.0727157i	$0.0231666\pi$
$827$			4.18226i			0.145431i	−0.997353	+	0.0727157i	$0.976833\pi$
$828$		0			0
$829$	3.34360	+	5.79129i	0.116128	+	0.201140i	0.918230	−	0.396047i	$-0.129618\pi$
$829$	3.34360	+	5.79129i	0.116128	+	0.201140i	−0.802102	+	0.597187i	$0.796285\pi$
$830$	−1.33278	+	0.769479i	−0.0462613	+	0.0267090i
$831$		0			0
$832$	−2.48206	−	2.61522i	−0.0860498	−	0.0906666i
$833$	2.13455	+	4.47602i	0.0739578	+	0.155085i
$834$		0			0
$835$	−7.67462			−0.265591
$836$	−33.3887			−1.15477
$837$		0			0
$838$	16.0983	+	9.29434i	0.556105	+	0.321068i
$839$	−37.8216	+	21.8363i	−1.30575	+	0.753874i	−0.981383	−	0.192059i	$-0.938484\pi$
$839$	−37.8216	+	21.8363i	−1.30575	+	0.753874i	−0.324364	+	0.945932i	$0.605150\pi$
$840$		0			0
$841$	−11.8939	−	20.6008i	−0.410133	−	0.710372i
$842$	−21.9581			−0.756727
$843$		0			0
$844$	−3.91287	+	6.77729i	−0.134687	+	0.233284i
$845$	−3.76917	−	7.39520i	−0.129664	−	0.254403i
$846$		0			0
$847$	22.6140	−	11.8968i	0.777027	−	0.408777i
$848$	−3.20071	+	5.54379i	−0.109913	+	0.190375i
$849$		0			0
$850$	2.81744	+	1.62665i	0.0966374	+	0.0557936i
$851$		−	13.6917i		−	0.469345i
$852$		0			0
$853$		−	5.72664i		−	0.196076i	−0.995183	−	0.0980382i	$-0.968743\pi$
$853$		−	5.72664i		−	0.196076i	0.995183	−	0.0980382i	$-0.0312567\pi$
$854$	8.41372	+	15.9933i	0.287911	+	0.547278i
$855$		0			0
$856$		−	15.3235i		−	0.523745i
$857$	−15.1817	+	26.2956i	−0.518599	+	0.898239i	0.481168	+	0.876628i	$0.340213\pi$
$857$	−15.1817	+	26.2956i	−0.518599	+	0.898239i	−0.999766	+	0.0216105i	$0.993121\pi$
$858$		0			0
$859$	13.2338	+	22.9216i	0.451531	+	0.782075i	0.998481	−	0.0550902i	$-0.0175446\pi$
$859$	13.2338	+	22.9216i	0.451531	+	0.782075i	−0.546950	+	0.837165i	$0.684211\pi$
$860$	−5.76350	−	3.32756i	−0.196534	−	0.113469i
$861$		0			0
$862$	−13.7658	−	23.8430i	−0.468864	−	0.812096i
$863$	−15.4761	+	8.93514i	−0.526813	+	0.304156i	−0.739718	−	0.672917i	$-0.765041\pi$
$863$	−15.4761	+	8.93514i	−0.526813	+	0.304156i	0.212905	+	0.977073i	$0.431708\pi$
$864$		0			0
$865$		−	12.4602i		−	0.423660i
$866$	28.5212	−	16.4667i	0.969188	−	0.559561i
$867$		0			0
$868$	8.17922	+	15.5475i	0.277621	+	0.527717i
$869$	−43.1733	−	24.9261i	−1.46455	−	0.845560i
$870$		0			0
$871$	−13.5651	−	4.01726i	−0.459635	−	0.136120i
$872$	0.886839	−	1.53605i	0.0300322	−	0.0520172i
$873$		0			0
$874$	23.8951	−	41.3875i	0.808263	−	1.39995i
$875$	8.64726	−	13.7040i	0.292331	−	0.463279i
$876$		0			0
$877$	22.4495	+	12.9612i	0.758065	+	0.437669i	0.828601	−	0.559840i	$-0.189137\pi$
$877$	22.4495	+	12.9612i	0.758065	+	0.437669i	−0.0705353	+	0.997509i	$0.522471\pi$
$878$		−	12.7172i		−	0.429184i
$879$		0			0
$880$	1.45099	−	2.51320i	0.0489130	−	0.0847198i
$881$	7.54044	−	13.0604i	0.254044	−	0.440017i	−0.710592	−	0.703605i	$-0.751573\pi$
$881$	7.54044	−	13.0604i	0.254044	−	0.440017i	0.964635	+	0.263588i	$0.0849059\pi$
$882$		0			0
$883$	−30.6339			−1.03091			−0.515457	−	0.856916i	$-0.672378\pi$
$883$	−30.6339			−1.03091			−0.515457	+	0.856916i	$0.672378\pi$
$884$	−1.75834	−	1.85268i	−0.0591393	−	0.0623122i
$885$		0			0
$886$	−25.1034	+	14.4934i	−0.843364	+	0.486916i
$887$	−15.4673			−0.519340			−0.259670	−	0.965697i	$-0.583614\pi$
$887$	−15.4673			−0.519340			−0.259670	+	0.965697i	$0.583614\pi$
$888$		0			0
$889$	1.71828	−	0.903949i	0.0576292	−	0.0303175i
$890$	3.05961	−	1.76647i	0.102558	−	0.0592120i
$891$		0			0
$892$	−16.9201	−	9.76882i	−0.566527	−	0.327084i
$893$	14.2817			0.477920
$894$		0			0
$895$	8.93099	+	5.15631i	0.298530	+	0.172356i
$896$	−1.41189	+	2.23753i	−0.0471680	+	0.0747508i
$897$		0			0
$898$	−0.0139197	−	0.0241096i	−0.000464505	−	0.000804547i
$899$	−41.7795	+	24.1214i	−1.39343	+	0.804495i
$900$		0			0
$901$	−2.26745	+	3.92733i	−0.0755396	+	0.130838i
$902$		−	24.2555i		−	0.807621i
$903$		0			0
$904$	4.54061	−	2.62152i	0.151019	−	0.0871906i
$905$	−0.155856	+	0.0899837i	−0.00518084	+	0.00299116i
$906$		0			0
$907$	23.7055	+	41.0591i	0.787127	+	1.36334i	0.927720	+	0.373277i	$0.121766\pi$
$907$	23.7055	+	41.0591i	0.787127	+	1.36334i	−0.140593	+	0.990068i	$0.544901\pi$
$908$			4.92479i			0.163435i
$909$		0			0
$910$	−4.57920	+	4.01604i	−0.151799	+	0.133131i
$911$	−36.5790			−1.21192			−0.605958	−	0.795496i	$-0.707210\pi$
$911$	−36.5790			−1.21192			−0.605958	+	0.795496i	$0.707210\pi$
$912$		0			0
$913$	−5.47756	−	9.48742i	−0.181281	−	0.313988i
$914$	−30.7861			−1.01831
$915$		0			0
$916$	−13.8323	+	7.98610i	−0.457033	+	0.263868i
$917$	−2.06596	+	52.5334i	−0.0682241	+	1.73481i
$918$		0			0
$919$	−3.53379	+	6.12071i	−0.116569	+	0.201904i	−0.918406	−	0.395639i	$-0.870523\pi$
$919$	−3.53379	+	6.12071i	−0.116569	+	0.201904i	0.801837	+	0.597543i	$0.203856\pi$
$920$	2.07685	+	3.59721i	0.0684717	+	0.118596i
$921$		0			0
$922$	18.9835	+	32.8804i	0.625188	+	1.08286i
$923$	36.3975	+	10.7790i	1.19804	+	0.354796i
$924$		0			0
$925$	−8.37026	−	4.83257i	−0.275213	−	0.158894i
$926$	13.3969			0.440250
$927$		0			0
$928$	−6.29212	−	3.63276i	−0.206549	−	0.119251i
$929$	41.4922	+	23.9555i	1.36131	+	0.785955i	0.989799	−	0.142472i	$-0.0455051\pi$
$929$	41.4922	+	23.9555i	1.36131	+	0.785955i	0.371515	+	0.928427i	$0.378838\pi$
$930$		0			0
$931$	4.03831	−	51.2638i	0.132350	−	1.68010i
$932$	2.62003	+	4.53803i	0.0858220	+	0.148648i
$933$		0			0
$934$	22.4431	−	12.9575i	0.734360	−	0.423983i
$935$	1.02791	−	1.78040i	0.0336164	−	0.0582252i
$936$		0			0
$937$	−7.37114			−0.240805			−0.120402	−	0.992725i	$-0.538418\pi$
$937$	−7.37114			−0.240805			−0.120402	+	0.992725i	$0.538418\pi$
$938$	−0.407949	+	10.3734i	−0.0133200	+	0.338702i
$939$		0			0
$940$	−0.620651	+	1.07500i	−0.0202434	+	0.0350626i
$941$	0.664718	+	0.383775i	0.0216692	+	0.0125107i	0.510795	−	0.859702i	$-0.329351\pi$
$941$	0.664718	+	0.383775i	0.0216692	+	0.0125107i	−0.489126	+	0.872213i	$0.662684\pi$
$942$		0			0
$943$	30.0664	+	17.3588i	0.979095	+	0.565281i
$944$		−	3.31958i		−	0.108043i
$945$		0			0
$946$	23.6873	−	41.0277i	0.770142	−	1.33392i
$947$			32.1360i			1.04428i	0.852860	+	0.522139i	$0.174866\pi$
$947$			32.1360i			1.04428i	−0.852860	+	0.522139i	$0.825134\pi$
$948$		0			0
$949$	−5.39873	−	22.4813i	−0.175250	−	0.729774i
$950$	−16.8678	−	29.2160i	−0.547265	−	0.947891i
$951$		0			0
$952$	−1.00021	+	1.58511i	−0.0324171	+	0.0513738i
$953$	9.10361	+	15.7679i	0.294895	+	0.510773i	0.974960	−	0.222378i	$-0.0713820\pi$
$953$	9.10361	+	15.7679i	0.294895	+	0.510773i	−0.680065	+	0.733151i	$0.738049\pi$
$954$		0			0
$955$			7.93428i			0.256747i
$956$		−	23.4449i		−	0.758261i
$957$		0			0
$958$	−0.126461	−	0.219038i	−0.00408578	−	0.00707678i
$959$	−14.7735	+	23.4127i	−0.477062	+	0.756036i
$960$		0			0
$961$	6.54465	+	11.3357i	0.211118	+	0.365666i
$962$	5.22380	+	5.50407i	0.168422	+	0.177458i
$963$		0			0
$964$		−	11.0560i		−	0.356091i
$965$	−3.71606	+	6.43641i	−0.119624	+	0.207195i
$966$		0			0
$967$			20.3286i			0.653724i	0.945072	+	0.326862i	$0.105991\pi$
$967$			20.3286i			0.653724i	−0.945072	+	0.326862i	$0.894009\pi$
$968$	8.36399	+	4.82895i	0.268829	+	0.155208i
$969$		0			0
$970$	−5.08320	−	2.93479i	−0.163212	−	0.0942303i
$971$	22.3535	−	38.7173i	0.717356	−	1.24250i	−0.244687	−	0.969602i	$-0.578685\pi$
$971$	22.3535	−	38.7173i	0.717356	−	1.24250i	0.962044	−	0.272896i	$-0.0879814\pi$
$972$		0			0
$973$	−0.00656376	+	0.166904i	−0.000210424	+	0.00535069i
$974$	−30.3567			−0.972691
$975$		0			0
$976$	−3.41517	+	5.91525i	−0.109317	+	0.189342i
$977$	17.8956	−	10.3320i	0.572531	−	0.330551i	−0.185629	−	0.982620i	$-0.559432\pi$
$977$	17.8956	−	10.3320i	0.572531	−	0.330551i	0.758160	+	0.652069i	$0.226099\pi$
$978$		0			0
$979$	12.5746	+	21.7799i	0.401887	+	0.696089i
$980$	3.68318	+	2.53177i	0.117655	+	0.0808745i
$981$		0			0
$982$	−11.6780	−	6.74228i	−0.372659	−	0.215155i
$983$	−48.5138	−	28.0095i	−1.54735	−	0.893363i	−0.998343	−	0.0575463i	$-0.981672\pi$
$983$	−48.5138	−	28.0095i	−1.54735	−	0.893363i	−0.549008	−	0.835817i	$-0.684994\pi$
$984$		0			0
$985$	3.38928			0.107991
$986$	−4.45746	−	2.57352i	−0.141955	−	0.0819575i
$987$		0			0
$988$	6.18476	+	25.7545i	0.196764	+	0.819360i
$989$	33.9043	+	58.7240i	1.07810	+	1.86732i
$990$		0			0
$991$	−2.57214	−	4.45508i	−0.0817068	−	0.141520i	0.822276	−	0.569088i	$-0.192704\pi$
$991$	−2.57214	−	4.45508i	−0.0817068	−	0.141520i	−0.903983	+	0.427568i	$0.859370\pi$
$992$	−3.31999	+	5.75039i	−0.105410	+	0.182575i
$993$		0			0
$994$	1.09460	−	27.8336i	0.0347186	−	0.882828i
$995$	−7.60259	+	4.38936i	−0.241018	+	0.139152i
$996$		0			0
$997$	22.5960			0.715624			0.357812	−	0.933794i	$-0.383523\pi$
$997$	22.5960			0.715624			0.357812	+	0.933794i	$0.383523\pi$
$998$	1.01055	+	1.75032i	0.0319883	+	0.0554054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dt.c.1369.3		20
3.2	odd	2		182.2.o.a.95.7	yes	20
7.2	even	3		1638.2.cr.c.667.3		20
13.10	even	6		1638.2.cr.c.361.3		20
21.2	odd	6		182.2.v.a.121.9	yes	20
21.5	even	6		1274.2.v.h.667.7		20
21.11	odd	6		1274.2.m.g.589.2		20
21.17	even	6		1274.2.m.f.589.4		20
21.20	even	2		1274.2.o.h.459.9		20
39.23	odd	6		182.2.v.a.179.9	yes	20
91.23	even	6	inner	1638.2.dt.c.1297.8		20
273.23	odd	6		182.2.o.a.23.2	✓	20
273.62	even	6		1274.2.v.h.361.7		20
273.101	even	6		1274.2.m.f.491.4		20
273.179	odd	6		1274.2.m.g.491.2		20
273.257	even	6		1274.2.o.h.569.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.2	✓	20	273.23	odd	6
182.2.o.a.95.7	yes	20	3.2	odd	2
182.2.v.a.121.9	yes	20	21.2	odd	6
182.2.v.a.179.9	yes	20	39.23	odd	6
1274.2.m.f.491.4		20	273.101	even	6
1274.2.m.f.589.4		20	21.17	even	6
1274.2.m.g.491.2		20	273.179	odd	6
1274.2.m.g.589.2		20	21.11	odd	6
1274.2.o.h.459.9		20	21.20	even	2
1274.2.o.h.569.4		20	273.257	even	6
1274.2.v.h.361.7		20	273.62	even	6
1274.2.v.h.667.7		20	21.5	even	6
1638.2.cr.c.361.3		20	13.10	even	6
1638.2.cr.c.667.3		20	7.2	even	3
1638.2.dt.c.1297.8		20	91.23	even	6	inner
1638.2.dt.c.1369.3		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.552947 + 0.319244i) q^{5} +(2.23753 + 1.41189i) q^{7} +1.00000i q^{8} +(0.319244 + 0.552947i) q^{10} +(-3.93617 + 2.27255i) q^{11} +(2.48206 + 2.61522i) q^{13} +(1.41189 - 2.23753i) q^{14} +1.00000 q^{16} +0.708420 q^{17} +(-6.36190 - 3.67305i) q^{19} +(0.552947 - 0.319244i) q^{20} +(2.27255 + 3.93617i) q^{22} -6.50552 q^{23} +(-2.29617 + 3.97708i) q^{25} +(2.61522 - 2.48206i) q^{26} +(-2.23753 - 1.41189i) q^{28} +(3.63276 - 6.29212i) q^{29} +(-5.75039 - 3.31999i) q^{31} -1.00000i q^{32} -0.708420i q^{34} +(-1.68797 - 0.0663824i) q^{35} +2.10463i q^{37} +(-3.67305 + 6.36190i) q^{38} +(-0.319244 - 0.552947i) q^{40} +(-4.62167 - 2.66832i) q^{41} +(-5.21162 - 9.02680i) q^{43} +(3.93617 - 2.27255i) q^{44} +6.50552i q^{46} +(-1.68367 + 0.972065i) q^{47} +(3.01312 + 6.31832i) q^{49} +(3.97708 + 2.29617i) q^{50} +(-2.48206 - 2.61522i) q^{52} +(-3.20071 + 5.54379i) q^{53} +(1.45099 - 2.51320i) q^{55} +(-1.41189 + 2.23753i) q^{56} +(-6.29212 - 3.63276i) q^{58} -3.31958i q^{59} +(-3.41517 + 5.91525i) q^{61} +(-3.31999 + 5.75039i) q^{62} -1.00000 q^{64} +(-2.20734 - 0.653698i) q^{65} +(-3.39810 + 1.96190i) q^{67} -0.708420 q^{68} +(-0.0663824 + 1.68797i) q^{70} +(9.11772 - 5.26412i) q^{71} +(-5.55335 - 3.20623i) q^{73} +2.10463 q^{74} +(6.36190 + 3.67305i) q^{76} +(-12.0159 - 0.472545i) q^{77} +(5.48418 + 9.49887i) q^{79} +(-0.552947 + 0.319244i) q^{80} +(-2.66832 + 4.62167i) q^{82} +2.41032i q^{83} +(-0.391718 + 0.226159i) q^{85} +(-9.02680 + 5.21162i) q^{86} +(-2.27255 - 3.93617i) q^{88} -5.53328i q^{89} +(1.86127 + 9.35605i) q^{91} +6.50552 q^{92} +(0.972065 + 1.68367i) q^{94} +4.69039 q^{95} +(-7.96131 + 4.59646i) q^{97} +(6.31832 - 3.01312i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 2 q^{7} - 4 q^{10} + 6 q^{11} + 6 q^{13} + 4 q^{14} + 20 q^{16} - 20 q^{17} - 24 q^{19} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 2 q^{28} - 2 q^{29} - 6 q^{31} + 14 q^{38} + 4 q^{40} - 18 q^{41}+ \cdots - 24 q^{98}+O(q^{100}) \) 20 * q - 20 * q^4 + 2 * q^7 - 4 * q^10 + 6 * q^11 + 6 * q^13 + 4 * q^14 + 20 * q^16 - 20 * q^17 - 24 * q^19 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 2 * q^28 - 2 * q^29 - 6 * q^31 + 14 * q^38 + 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 - 18 * q^47 - 6 * q^49 + 12 * q^50 - 6 * q^52 + 4 * q^53 + 2 * q^55 - 4 * q^56 - 24 * q^58 - 4 * q^61 + 24 * q^62 - 20 * q^64 + 6 * q^65 - 60 * q^67 + 20 * q^68 - 48 * q^70 + 18 * q^71 - 72 * q^73 + 24 * q^74 + 24 * q^76 - 42 * q^77 + 42 * q^79 - 16 * q^82 - 12 * q^85 - 42 * q^86 - 2 * q^88 + 14 * q^91 + 16 * q^94 - 24 * q^95 + 78 * q^97 - 24 * q^98

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