LMFDB - Embedded newform 1638.2.x.d.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(307,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,0,0,0,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$0.916813i$ of defining polynomial
Character	$\chi$	$=$	1638.307
Dual form			1638.2.x.d.811.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(1.35539 + 2.27220i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.21338 q^{10} +(-0.355392 + 0.355392i) q^{11} +(2.00000 + 3.00000i) q^{13} +(0.648285 - 2.56510i) q^{14} -1.00000 q^{16} +4.32583 q^{17} +(5.98299 - 5.98299i) q^{19} +(-2.27220 - 2.27220i) q^{20} +0.502600 q^{22} +2.38496i q^{23} -5.32583i q^{25} +(0.707107 - 3.53553i) q^{26} +(-2.27220 + 1.35539i) q^{28} -1.09574 q^{29} +(1.08319 - 1.08319i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.05882 - 3.05882i) q^{34} +(-8.24264 - 2.08319i) q^{35} +(-5.18902 + 5.18902i) q^{37} -8.46122 q^{38} +3.21338i q^{40} +(-3.53186 + 3.53186i) q^{41} +7.44867i q^{43} +(-0.355392 - 0.355392i) q^{44} +(1.68642 - 1.68642i) q^{46} +(4.71078 + 4.71078i) q^{47} +(-3.32583 + 6.15945i) q^{49} +(-3.76593 + 3.76593i) q^{50} +(-3.00000 + 2.00000i) q^{52} +11.2552 q^{53} -1.61504i q^{55} +(2.56510 + 0.648285i) q^{56} +(0.774804 + 0.774804i) q^{58} +(-3.61504 - 3.61504i) q^{59} +4.32583i q^{61} -1.53186 q^{62} -1.00000i q^{64} +(-11.3610 - 2.27220i) q^{65} +(-0.531858 - 0.531858i) q^{67} +4.32583i q^{68} +(4.35539 + 7.30146i) q^{70} +(-6.38496 - 6.38496i) q^{71} +(-5.18902 - 5.18902i) q^{73} +7.33838 q^{74} +(5.98299 + 5.98299i) q^{76} +(-1.28922 - 0.325828i) q^{77} -11.3143 q^{79} +(2.27220 - 2.27220i) q^{80} +4.99480 q^{82} +(-6.71078 + 6.71078i) q^{83} +(-9.82917 + 9.82917i) q^{85} +(5.26701 - 5.26701i) q^{86} +0.502600i q^{88} +(3.75044 + 3.75044i) q^{89} +(-4.10583 + 8.61058i) q^{91} -2.38496 q^{92} -6.66205i q^{94} +27.1891i q^{95} +(-12.9931 + 12.9931i) q^{97} +(6.70711 - 2.00368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.27220	+	2.27220i	−1.01616	+	1.01616i	−0.0162935	+	0.999867i	$0.505187\pi$
$5$	−2.27220	+	2.27220i	−1.01616	+	1.01616i	−0.999867	+	0.0162935i	$0.994813\pi$
$6$		0			0
$7$	1.35539	+	2.27220i	0.512290	+	0.858813i
$7$	1.35539	+	2.27220i	0.512290	+	0.858813i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	3.21338			1.01616
$11$	−0.355392	+	0.355392i	−0.107155	+	0.107155i	−0.758651	−	0.651497i	$-0.774141\pi$
$11$	−0.355392	+	0.355392i	−0.107155	+	0.107155i	0.651497	+	0.758651i	$0.274141\pi$
$12$		0			0
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$	0.648285	−	2.56510i	0.173261	−	0.685551i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.32583			1.04917			0.524584	−	0.851359i	$-0.324221\pi$
$17$	4.32583			1.04917			0.524584	+	0.851359i	$0.324221\pi$
$18$		0			0
$19$	5.98299	−	5.98299i	1.37259	−	1.37259i	0.516007	−	0.856584i	$-0.327418\pi$
$19$	5.98299	−	5.98299i	1.37259	−	1.37259i	0.856584	−	0.516007i	$-0.172582\pi$
$20$	−2.27220	−	2.27220i	−0.508080	−	0.508080i
$21$		0			0
$22$	0.502600			0.107155
$23$			2.38496i			0.497298i	0.968594	+	0.248649i	$0.0799865\pi$
$23$			2.38496i			0.497298i	−0.968594	+	0.248649i	$0.920014\pi$
$24$		0			0
$25$		−	5.32583i		−	1.06517i
$26$	0.707107	−	3.53553i	0.138675	−	0.693375i
$27$		0			0
$28$	−2.27220	+	1.35539i	−0.429406	+	0.256145i
$29$	−1.09574			−0.203474			−0.101737	−	0.994811i	$-0.532440\pi$
$29$	−1.09574			−0.203474			−0.101737	+	0.994811i	$0.532440\pi$
$30$		0			0
$31$	1.08319	−	1.08319i	0.194546	−	0.194546i	−0.603111	−	0.797657i	$-0.706072\pi$
$31$	1.08319	−	1.08319i	0.194546	−	0.194546i	0.797657	+	0.603111i	$0.206072\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−3.05882	−	3.05882i	−0.524584	−	0.524584i
$35$	−8.24264	−	2.08319i	−1.39326	−	0.352123i
$36$		0			0
$37$	−5.18902	+	5.18902i	−0.853069	+	0.853069i	−0.990510	−	0.137441i	$-0.956112\pi$
$37$	−5.18902	+	5.18902i	−0.853069	+	0.853069i	0.137441	+	0.990510i	$0.456112\pi$
$38$	−8.46122			−1.37259
$39$		0			0
$40$			3.21338i			0.508080i
$41$	−3.53186	+	3.53186i	−0.551583	+	0.551583i	−0.926898	−	0.375314i	$-0.877535\pi$
$41$	−3.53186	+	3.53186i	−0.551583	+	0.551583i	0.375314	+	0.926898i	$0.377535\pi$
$42$		0			0
$43$			7.44867i			1.13591i	0.823059	+	0.567956i	$0.192266\pi$
$43$			7.44867i			1.13591i	−0.823059	+	0.567956i	$0.807734\pi$
$44$	−0.355392	−	0.355392i	−0.0535773	−	0.0535773i
$45$		0			0
$46$	1.68642	−	1.68642i	0.248649	−	0.248649i
$47$	4.71078	+	4.71078i	0.687138	+	0.687138i	0.961598	−	0.274460i	$-0.0884991\pi$
$47$	4.71078	+	4.71078i	0.687138	+	0.687138i	−0.274460	+	0.961598i	$0.588499\pi$
$48$		0			0
$49$	−3.32583	+	6.15945i	−0.475118	+	0.879922i
$50$	−3.76593	+	3.76593i	−0.532583	+	0.532583i
$51$		0			0
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	11.2552			1.54602			0.773010	−	0.634394i	$-0.218750\pi$
$53$	11.2552			1.54602			0.773010	+	0.634394i	$0.218750\pi$
$54$		0			0
$55$		−	1.61504i		−	0.217773i
$56$	2.56510	+	0.648285i	0.342776	+	0.0866307i
$57$		0			0
$58$	0.774804	+	0.774804i	0.101737	+	0.101737i
$59$	−3.61504	−	3.61504i	−0.470639	−	0.470639i	0.431483	−	0.902121i	$-0.357991\pi$
$59$	−3.61504	−	3.61504i	−0.470639	−	0.470639i	−0.902121	+	0.431483i	$0.857991\pi$
$60$		0			0
$61$			4.32583i			0.553865i	0.960889	+	0.276933i	$0.0893179\pi$
$61$			4.32583i			0.553865i	−0.960889	+	0.276933i	$0.910682\pi$
$62$	−1.53186			−0.194546
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−11.3610	−	2.27220i	−1.40916	−	0.281832i
$66$		0			0
$67$	−0.531858	−	0.531858i	−0.0649768	−	0.0649768i	0.673872	−	0.738848i	$-0.264630\pi$
$67$	−0.531858	−	0.531858i	−0.0649768	−	0.0649768i	−0.738848	+	0.673872i	$0.764630\pi$
$68$			4.32583i			0.524584i
$69$		0			0
$70$	4.35539	+	7.30146i	0.520569	+	0.872692i
$71$	−6.38496	−	6.38496i	−0.757755	−	0.757755i	0.218159	−	0.975913i	$-0.429995\pi$
$71$	−6.38496	−	6.38496i	−0.757755	−	0.757755i	−0.975913	+	0.218159i	$0.929995\pi$
$72$		0			0
$73$	−5.18902	−	5.18902i	−0.607329	−	0.607329i	0.334919	−	0.942247i	$-0.391291\pi$
$73$	−5.18902	−	5.18902i	−0.607329	−	0.607329i	−0.942247	+	0.334919i	$0.891291\pi$
$74$	7.33838			0.853069
$75$		0			0
$76$	5.98299	+	5.98299i	0.686296	+	0.686296i
$77$	−1.28922	−	0.325828i	−0.146920	−	0.0371315i
$78$		0			0
$79$	−11.3143			−1.27296			−0.636480	−	0.771293i	$-0.719610\pi$
$79$	−11.3143			−1.27296			−0.636480	+	0.771293i	$0.719610\pi$
$80$	2.27220	−	2.27220i	0.254040	−	0.254040i
$81$		0			0
$82$	4.99480			0.551583
$83$	−6.71078	+	6.71078i	−0.736604	+	0.736604i	−0.971919	−	0.235315i	$-0.924388\pi$
$83$	−6.71078	+	6.71078i	−0.736604	+	0.736604i	0.235315	+	0.971919i	$0.424388\pi$
$84$		0			0
$85$	−9.82917	+	9.82917i	−1.06612	+	1.06612i
$86$	5.26701	−	5.26701i	0.567956	−	0.567956i
$87$		0			0
$88$			0.502600i			0.0535773i
$89$	3.75044	+	3.75044i	0.397546	+	0.397546i	0.877367	−	0.479821i	$-0.159298\pi$
$89$	3.75044	+	3.75044i	0.397546	+	0.397546i	−0.479821	+	0.877367i	$0.659298\pi$
$90$		0			0
$91$	−4.10583	+	8.61058i	−0.430408	+	0.902634i
$92$	−2.38496			−0.248649
$93$		0			0
$94$		−	6.66205i		−	0.687138i
$95$			27.1891i			2.78955i
$96$		0			0
$97$	−12.9931	+	12.9931i	−1.31925	+	1.31925i	−0.404876	+	0.914372i	$0.632685\pi$
$97$	−12.9931	+	12.9931i	−1.31925	+	1.31925i	−0.914372	+	0.404876i	$0.867315\pi$
$98$	6.70711	−	2.00368i	0.677520	−	0.202402i
$99$		0			0
$100$	5.32583			0.532583
$101$	19.7996			1.97013			0.985067	−	0.172171i	$-0.0550783\pi$
$101$	19.7996			1.97013			0.985067	+	0.172171i	$0.0550783\pi$
$102$		0			0
$103$	2.70386			0.266420			0.133210	−	0.991088i	$-0.457472\pi$
$103$	2.70386			0.266420			0.133210	+	0.991088i	$0.457472\pi$
$104$	3.53553	+	0.707107i	0.346688	+	0.0693375i
$105$		0			0
$106$	−7.95862	−	7.95862i	−0.773010	−	0.773010i
$107$	11.6673			1.12792			0.563958	−	0.825804i	$-0.309278\pi$
$107$	11.6673			1.12792			0.563958	+	0.825804i	$0.309278\pi$
$108$		0			0
$109$	−5.29626	−	5.29626i	−0.507290	−	0.507290i	0.406404	−	0.913694i	$-0.366783\pi$
$109$	−5.29626	−	5.29626i	−0.507290	−	0.507290i	−0.913694	+	0.406404i	$0.866783\pi$
$110$	−1.14201	+	1.14201i	−0.108886	+	0.108886i
$111$		0			0
$112$	−1.35539	−	2.27220i	−0.128072	−	0.214703i
$113$	−20.3440			−1.91380			−0.956902	−	0.290412i	$-0.906208\pi$
$113$	−20.3440			−1.91380			−0.956902	+	0.290412i	$0.906208\pi$
$114$		0			0
$115$	−5.41911	−	5.41911i	−0.505334	−	0.505334i
$116$		−	1.09574i		−	0.101737i
$117$		0			0
$118$			5.11245i			0.470639i
$119$	5.86319	+	9.82917i	0.537478	+	0.901038i
$120$		0			0
$121$			10.7474i			0.977036i
$122$	3.05882	−	3.05882i	0.276933	−	0.276933i
$123$		0			0
$124$	1.08319	+	1.08319i	0.0972731	+	0.0972731i
$125$	0.740347	+	0.740347i	0.0662186	+	0.0662186i
$126$		0			0
$127$		−	7.60812i		−	0.675112i	−0.941305	−	0.337556i	$-0.890400\pi$
$127$		−	7.60812i		−	0.675112i	0.941305	−	0.337556i	$-0.109600\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	6.42677	+	9.64015i	0.563665	+	0.845497i
$131$		−	6.87024i		−	0.600255i	−0.953899	−	0.300128i	$-0.902971\pi$
$131$		−	6.87024i		−	0.600255i	0.953899	−	0.300128i	$-0.0970293\pi$
$132$		0			0
$133$	21.7039	+	5.48528i	1.88196	+	0.475634i
$134$			0.752160i			0.0649768i
$135$		0			0
$136$	3.05882	−	3.05882i	0.262292	−	0.262292i
$137$	0.272205	−	0.272205i	0.0232560	−	0.0232560i	−0.695383	−	0.718639i	$-0.744765\pi$
$137$	0.272205	−	0.272205i	0.0232560	−	0.0232560i	0.718639	+	0.695383i	$0.244765\pi$
$138$		0			0
$139$		−	20.3440i		−	1.72556i	−0.505583	−	0.862778i	$-0.668722\pi$
$139$		−	20.3440i		−	1.72556i	0.505583	−	0.862778i	$-0.331278\pi$
$140$	2.08319	−	8.24264i	0.176061	−	0.696630i
$141$		0			0
$142$			9.02969i			0.757755i
$143$	−1.77696	−	0.355392i	−0.148597	−	0.0297193i
$144$		0			0
$145$	2.48974	−	2.48974i	0.206762	−	0.206762i
$146$			7.33838i			0.607329i
$147$		0			0
$148$	−5.18902	−	5.18902i	−0.426535	−	0.426535i
$149$	−10.5685	−	10.5685i	−0.865803	−	0.865803i	0.126202	−	0.992005i	$-0.459721\pi$
$149$	−10.5685	−	10.5685i	−0.865803	−	0.865803i	−0.992005	+	0.126202i	$0.959721\pi$
$150$		0			0
$151$	−0.149362	+	0.149362i	−0.0121549	+	0.0121549i	−0.713158	−	0.701003i	$-0.752736\pi$
$151$	−0.149362	+	0.149362i	−0.0121549	+	0.0121549i	0.701003	+	0.713158i	$0.252736\pi$
$152$		−	8.46122i		−	0.686296i
$153$		0			0
$154$	0.681219	+	1.14201i	0.0548942	+	0.0920257i
$155$			4.92244i			0.395380i
$156$		0			0
$157$			10.7630i			0.858980i	0.903072	+	0.429490i	$0.141307\pi$
$157$			10.7630i			0.858980i	−0.903072	+	0.429490i	$0.858693\pi$
$158$	8.00043	+	8.00043i	0.636480	+	0.636480i
$159$		0			0
$160$	−3.21338			−0.254040
$161$	−5.41911	+	3.23255i	−0.427085	+	0.254761i
$162$		0			0
$163$	−3.40901	+	3.40901i	−0.267015	+	0.267015i	−0.827896	−	0.560881i	$-0.810462\pi$
$163$	−3.40901	+	3.40901i	−0.267015	+	0.267015i	0.560881	+	0.827896i	$0.310462\pi$
$164$	−3.53186	−	3.53186i	−0.275792	−	0.275792i
$165$		0			0
$166$	9.49048			0.736604
$167$	10.0226	+	10.0226i	0.775575	+	0.775575i	0.979075	−	0.203500i	$-0.0652316\pi$
$167$	10.0226	+	10.0226i	0.775575	+	0.775575i	−0.203500	+	0.979075i	$0.565232\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	13.9005			1.06612
$171$		0			0
$172$	−7.44867			−0.567956
$173$	19.7405			1.50084			0.750420	−	0.660961i	$-0.229851\pi$
$173$	19.7405			1.50084			0.750420	+	0.660961i	$0.229851\pi$
$174$		0			0
$175$	12.1014	−	7.21858i	0.914778	−	0.545673i
$176$	0.355392	−	0.355392i	0.0267886	−	0.0267886i
$177$		0			0
$178$		−	5.30392i		−	0.397546i
$179$			9.79960i			0.732457i	0.930525	+	0.366228i	$0.119351\pi$
$179$			9.79960i			0.732457i	−0.930525	+	0.366228i	$0.880649\pi$
$180$		0			0
$181$	10.4372			0.775788			0.387894	−	0.921704i	$-0.373203\pi$
$181$	10.4372			0.775788			0.387894	+	0.921704i	$0.373203\pi$
$182$	8.99186	−	3.18534i	0.666521	−	0.236113i
$183$		0			0
$184$	1.68642	+	1.68642i	0.124324	+	0.124324i
$185$		−	23.5810i		−	1.73371i
$186$		0			0
$187$	−1.53736	+	1.53736i	−0.112423	+	0.112423i
$188$	−4.71078	+	4.71078i	−0.343569	+	0.343569i
$189$		0			0
$190$	19.2256	−	19.2256i	1.39477	−	1.39477i
$191$	−11.1410			−0.806136			−0.403068	−	0.915170i	$-0.632056\pi$
$191$	−11.1410			−0.806136			−0.403068	+	0.915170i	$0.632056\pi$
$192$		0			0
$193$	4.03661	−	4.03661i	0.290562	−	0.290562i	−0.546741	−	0.837302i	$-0.684132\pi$
$193$	4.03661	−	4.03661i	0.290562	−	0.290562i	0.837302	+	0.546741i	$0.184132\pi$
$194$	18.3750			1.31925
$195$		0			0
$196$	−6.15945	−	3.32583i	−0.439961	−	0.237559i
$197$	−0.627596	−	0.627596i	−0.0447144	−	0.0447144i	0.684396	−	0.729110i	$-0.260066\pi$
$197$	−0.627596	−	0.627596i	−0.0447144	−	0.0447144i	−0.729110	+	0.684396i	$0.760066\pi$
$198$		0			0
$199$	16.5375			1.17231			0.586156	−	0.810198i	$-0.300641\pi$
$199$	16.5375			1.17231			0.586156	+	0.810198i	$0.300641\pi$
$200$	−3.76593	−	3.76593i	−0.266291	−	0.266291i
$201$		0			0
$202$	−14.0004	−	14.0004i	−0.985067	−	0.985067i
$203$	−1.48515	−	2.48974i	−0.104237	−	0.174746i
$204$		0			0
$205$		−	16.0502i		−	1.12100i
$206$	−1.91192	−	1.91192i	−0.133210	−	0.133210i
$207$		0			0
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$			4.25261i			0.294159i
$210$		0			0
$211$	−0.551329			−0.0379551			−0.0189775	−	0.999820i	$-0.506041\pi$
$211$	−0.551329			−0.0379551			−0.0189775	+	0.999820i	$0.506041\pi$
$212$			11.2552i			0.773010i
$213$		0			0
$214$	−8.24999	−	8.24999i	−0.563958	−	0.563958i
$215$	−16.9249	−	16.9249i	−1.15427	−	1.15427i
$216$		0			0
$217$	3.92936	+	0.993080i	0.266743	+	0.0674147i
$218$			7.49005i			0.507290i
$219$		0			0
$220$	1.61504			0.108886
$221$	8.65166	+	12.9775i	0.581973	+	0.872960i
$222$		0			0
$223$	−9.89430	+	9.89430i	−0.662571	+	0.662571i	−0.955985	−	0.293414i	$-0.905208\pi$
$223$	−9.89430	+	9.89430i	−0.662571	+	0.662571i	0.293414	+	0.955985i	$0.405208\pi$
$224$	−0.648285	+	2.56510i	−0.0433153	+	0.171388i
$225$		0			0
$226$	14.3854	+	14.3854i	0.956902	+	0.956902i
$227$	1.67417	−	1.67417i	0.111119	−	0.111119i	−0.649361	−	0.760480i	$-0.724964\pi$
$227$	1.67417	−	1.67417i	0.111119	−	0.111119i	0.760480	+	0.649361i	$0.224964\pi$
$228$		0			0
$229$	1.32583	+	1.32583i	0.0876132	+	0.0876132i	0.749555	−	0.661942i	$-0.230267\pi$
$229$	1.32583	+	1.32583i	0.0876132	+	0.0876132i	−0.661942	+	0.749555i	$0.730267\pi$
$230$			7.66377i			0.505334i
$231$		0			0
$232$	−0.774804	+	0.774804i	−0.0508684	+	0.0508684i
$233$		−	10.2117i		−	0.668988i	−0.942398	−	0.334494i	$-0.891435\pi$
$233$		−	10.2117i		−	0.668988i	0.942398	−	0.334494i	$-0.108565\pi$
$234$		0			0
$235$	−21.4077			−1.39649
$236$	3.61504	−	3.61504i	0.235319	−	0.235319i
$237$		0			0
$238$	2.80437	−	11.0962i	0.181780	−	0.719258i
$239$	15.2212	+	15.2212i	0.984575	+	0.984575i	0.999883	−	0.0153074i	$-0.00487267\pi$
$239$	15.2212	+	15.2212i	0.984575	+	0.984575i	−0.0153074	+	0.999883i	$0.504873\pi$
$240$		0			0
$241$	−3.38496	−	3.38496i	−0.218044	−	0.218044i	0.589630	−	0.807674i	$-0.299274\pi$
$241$	−3.38496	−	3.38496i	−0.218044	−	0.218044i	−0.807674	+	0.589630i	$0.799274\pi$
$242$	7.59955	−	7.59955i	0.488518	−	0.488518i
$243$		0			0
$244$	−4.32583			−0.276933
$245$	−6.43858	−	21.5525i	−0.411346	−	1.37694i
$246$		0			0
$247$	29.9149	+	5.98299i	1.90344	+	0.380688i
$248$		−	1.53186i		−	0.0972731i
$249$		0			0
$250$		−	1.04701i		−	0.0662186i
$251$	−17.2281			−1.08743			−0.543714	−	0.839271i	$-0.682982\pi$
$251$	−17.2281			−1.08743			−0.543714	+	0.839271i	$0.682982\pi$
$252$		0			0
$253$	−0.847593	−	0.847593i	−0.0532877	−	0.0532877i
$254$	−5.37976	+	5.37976i	−0.337556	+	0.337556i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.32324			−0.207298			−0.103649	−	0.994614i	$-0.533052\pi$
$257$	−3.32324			−0.207298			−0.103649	+	0.994614i	$0.533052\pi$
$258$		0			0
$259$	−18.8237	−	4.75736i	−1.16965	−	0.295608i
$260$	2.27220	−	11.3610i	0.140916	−	0.704581i
$261$		0			0
$262$	−4.85799	+	4.85799i	−0.300128	+	0.300128i
$263$	0.818029			0.0504418			0.0252209	−	0.999682i	$-0.491971\pi$
$263$	0.818029			0.0504418			0.0252209	+	0.999682i	$0.491971\pi$
$264$		0			0
$265$	−25.5741	+	25.5741i	−1.57100	+	1.57100i
$266$	−11.4683	−	19.2256i	−0.703165	−	1.17880i
$267$		0			0
$268$	0.531858	−	0.531858i	0.0324884	−	0.0324884i
$269$			21.6081i			1.31747i	0.752375	+	0.658735i	$0.228908\pi$
$269$			21.6081i			1.31747i	−0.752375	+	0.658735i	$0.771092\pi$
$270$		0			0
$271$	15.0422	+	15.0422i	0.913751	+	0.913751i	0.996565	−	0.0828139i	$-0.0263907\pi$
$271$	15.0422	+	15.0422i	0.913751	+	0.913751i	−0.0828139	+	0.996565i	$0.526391\pi$
$272$	−4.32583			−0.262292
$273$		0			0
$274$	−0.384955			−0.0232560
$275$	1.89275	+	1.89275i	0.114137	+	0.114137i
$276$		0			0
$277$		−	17.7996i		−	1.06947i	−0.845018	−	0.534737i	$-0.820411\pi$
$277$		−	17.7996i		−	1.06947i	0.845018	−	0.534737i	$-0.179589\pi$
$278$	−14.3854	+	14.3854i	−0.862778	+	0.862778i
$279$		0			0
$280$	−7.30146	+	4.35539i	−0.436346	+	0.260284i
$281$	−6.20862	+	6.20862i	−0.370375	+	0.370375i	−0.867614	−	0.497239i	$-0.834347\pi$
$281$	−6.20862	+	6.20862i	−0.370375	+	0.370375i	0.497239	+	0.867614i	$0.334347\pi$
$282$		0			0
$283$	25.1090			1.49258			0.746288	−	0.665624i	$-0.231834\pi$
$283$	25.1090			1.49258			0.746288	+	0.665624i	$0.231834\pi$
$284$	6.38496	−	6.38496i	0.378877	−	0.378877i
$285$		0			0
$286$	1.00520	+	1.50780i	0.0594387	+	0.0891580i
$287$	−12.8122	−	3.23805i	−0.756277	−	0.191136i
$288$		0			0
$289$	1.71278			0.100752
$290$	−3.52103			−0.206762
$291$		0			0
$292$	5.18902	−	5.18902i	0.303664	−	0.303664i
$293$	−8.51343	−	8.51343i	−0.497360	−	0.497360i	0.413255	−	0.910615i	$-0.364392\pi$
$293$	−8.51343	−	8.51343i	−0.497360	−	0.497360i	−0.910615	+	0.413255i	$0.864392\pi$
$294$		0			0
$295$	16.4282			0.956489
$296$			7.33838i			0.426535i
$297$		0			0
$298$			14.9461i			0.865803i
$299$	−7.15487	+	4.76991i	−0.413777	+	0.275851i
$300$		0			0
$301$	−16.9249	+	10.0959i	−0.975535	+	0.581916i
$302$	0.211229			0.0121549
$303$		0			0
$304$	−5.98299	+	5.98299i	−0.343148	+	0.343148i
$305$	−9.82917	−	9.82917i	−0.562816	−	0.562816i
$306$		0			0
$307$	10.0397	+	10.0397i	0.572993	+	0.572993i	0.932964	−	0.359970i	$-0.117213\pi$
$307$	10.0397	+	10.0397i	0.572993	+	0.572993i	−0.359970	+	0.932964i	$0.617213\pi$
$308$	0.325828	−	1.28922i	0.0185658	−	0.0734600i
$309$		0			0
$310$	3.48069	−	3.48069i	0.197690	−	0.197690i
$311$	−15.7064			−0.890631			−0.445316	−	0.895374i	$-0.646908\pi$
$311$	−15.7064			−0.890631			−0.445316	+	0.895374i	$0.646908\pi$
$312$		0			0
$313$		−	20.7702i		−	1.17400i	−0.809587	−	0.587000i	$-0.800309\pi$
$313$		−	20.7702i		−	1.17400i	0.809587	−	0.587000i	$-0.199691\pi$
$314$	7.61058	−	7.61058i	0.429490	−	0.429490i
$315$		0			0
$316$		−	11.3143i		−	0.636480i
$317$	−19.0126	−	19.0126i	−1.06785	−	1.06785i	−0.997524	−	0.0703273i	$-0.977596\pi$
$317$	−19.0126	−	19.0126i	−1.06785	−	1.06785i	−0.0703273	−	0.997524i	$-0.522404\pi$
$318$		0			0
$319$	0.389416	−	0.389416i	0.0218031	−	0.0218031i
$320$	2.27220	+	2.27220i	0.127020	+	0.127020i
$321$		0			0
$322$	6.11764	+	1.54613i	0.340923	+	0.0861625i
$323$	25.8814	−	25.8814i	1.44008	−	1.44008i
$324$		0			0
$325$	15.9775	−	10.6517i	0.886271	−	0.590848i
$326$	4.82107			0.267015
$327$		0			0
$328$			4.99480i			0.275792i
$329$	−4.31891	+	17.0888i	−0.238109	+	0.942137i
$330$		0			0
$331$	−13.9785	−	13.9785i	−0.768329	−	0.768329i	0.209483	−	0.977812i	$-0.432822\pi$
$331$	−13.9785	−	13.9785i	−0.768329	−	0.768329i	−0.977812	+	0.209483i	$0.932822\pi$
$332$	−6.71078	−	6.71078i	−0.368302	−	0.368302i
$333$		0			0
$334$		−	14.1742i		−	0.775575i
$335$	2.41698			0.132054
$336$		0			0
$337$		−	1.09574i		−	0.0596887i	−0.999555	−	0.0298443i	$-0.990499\pi$
$337$		−	1.09574i		−	0.0596887i	0.999555	−	0.0298443i	$-0.00950116\pi$
$338$	12.0208	−	4.94975i	0.653846	−	0.269231i
$339$		0			0
$340$	−9.82917	−	9.82917i	−0.533061	−	0.533061i
$341$			0.769911i			0.0416930i
$342$		0			0
$343$	−18.5033	+	0.791511i	−0.999086	+	0.0427376i
$344$	5.26701	+	5.26701i	0.283978	+	0.283978i
$345$		0			0
$346$	−13.9586	−	13.9586i	−0.750420	−	0.750420i
$347$	−32.0983			−1.72313			−0.861564	−	0.507649i	$-0.830515\pi$
$347$	−32.0983			−1.72313			−0.861564	+	0.507649i	$0.830515\pi$
$348$		0			0
$349$	18.9660	+	18.9660i	1.01523	+	1.01523i	0.999882	+	0.0153431i	$0.00488405\pi$
$349$	18.9660	+	18.9660i	1.01523	+	1.01523i	0.0153431	+	0.999882i	$0.495116\pi$
$350$	−13.6613	−	3.45265i	−0.730226	−	0.184552i
$351$		0			0
$352$	−0.502600			−0.0267886
$353$	−15.5500	+	15.5500i	−0.827645	+	0.827645i	−0.987191	−	0.159545i	$-0.948997\pi$
$353$	−15.5500	+	15.5500i	−0.827645	+	0.827645i	0.159545	+	0.987191i	$0.448997\pi$
$354$		0			0
$355$	29.0159			1.54000
$356$	−3.75044	+	3.75044i	−0.198773	+	0.198773i
$357$		0			0
$358$	6.92936	−	6.92936i	0.366228	−	0.366228i
$359$	14.1846	−	14.1846i	0.748632	−	0.748632i	−0.225590	−	0.974222i	$-0.572431\pi$
$359$	14.1846	−	14.1846i	0.748632	−	0.748632i	0.974222	+	0.225590i	$0.0724310\pi$
$360$		0			0
$361$		−	52.5923i		−	2.76801i
$362$	−7.38019	−	7.38019i	−0.387894	−	0.387894i
$363$		0			0
$364$	−8.61058	−	4.10583i	−0.451317	−	0.215204i
$365$	23.5810			1.23429
$366$		0			0
$367$		−	11.2552i		−	0.587516i	−0.955880	−	0.293758i	$-0.905094\pi$
$367$		−	11.2552i		−	0.587516i	0.955880	−	0.293758i	$-0.0949060\pi$
$368$		−	2.38496i		−	0.124324i
$369$		0			0
$370$	−16.6743	+	16.6743i	−0.866856	+	0.866856i
$371$	15.2552	+	25.5741i	0.792010	+	1.32774i
$372$		0			0
$373$	17.1479			0.887887			0.443944	−	0.896055i	$-0.353579\pi$
$373$	17.1479			0.887887			0.443944	+	0.896055i	$0.353579\pi$
$374$	2.17416			0.112423
$375$		0			0
$376$	6.66205			0.343569
$377$	−2.19148	−	3.28722i	−0.112867	−	0.169300i
$378$		0			0
$379$	11.5685	+	11.5685i	0.594232	+	0.594232i	0.938772	−	0.344540i	$-0.111965\pi$
$379$	11.5685	+	11.5685i	0.594232	+	0.594232i	−0.344540	+	0.938772i	$0.611965\pi$
$380$	−27.1891			−1.39477
$381$		0			0
$382$	7.87790	+	7.87790i	0.403068	+	0.403068i
$383$	−1.26657	+	1.26657i	−0.0647189	+	0.0647189i	−0.738725	−	0.674007i	$-0.764572\pi$
$383$	−1.26657	+	1.26657i	−0.0647189	+	0.0647189i	0.674007	+	0.738725i	$0.264572\pi$
$384$		0			0
$385$	3.66971	−	2.18902i	0.187026	−	0.111563i
$386$	−5.70863			−0.290562
$387$		0			0
$388$	−12.9931	−	12.9931i	−0.659624	−	0.659624i
$389$		−	7.90685i		−	0.400893i	−0.979705	−	0.200447i	$-0.935761\pi$
$389$		−	7.90685i		−	0.400893i	0.979705	−	0.200447i	$-0.0642393\pi$
$390$		0			0
$391$			10.3169i			0.521748i
$392$	2.00368	+	6.70711i	0.101201	+	0.338760i
$393$		0			0
$394$			0.887555i			0.0447144i
$395$	25.7085	−	25.7085i	1.29353	−	1.29353i
$396$		0			0
$397$	−16.4467	−	16.4467i	−0.825435	−	0.825435i	0.161447	−	0.986881i	$-0.448384\pi$
$397$	−16.4467	−	16.4467i	−0.825435	−	0.825435i	−0.986881	+	0.161447i	$0.948384\pi$
$398$	−11.6938	−	11.6938i	−0.586156	−	0.586156i
$399$		0			0
$400$			5.32583i			0.266291i
$401$	−15.0126	+	15.0126i	−0.749691	+	0.749691i	−0.974421	−	0.224730i	$-0.927850\pi$
$401$	−15.0126	+	15.0126i	−0.749691	+	0.749691i	0.224730	+	0.974421i	$0.427850\pi$
$402$		0			0
$403$	5.41593	+	1.08319i	0.269787	+	0.0539574i
$404$			19.7996i			0.985067i
$405$		0			0
$406$	−0.710351	+	2.81068i	−0.0352541	+	0.139492i
$407$		−	3.68827i		−	0.182821i
$408$		0			0
$409$	19.0477	−	19.0477i	0.941850	−	0.941850i	−0.0565493	−	0.998400i	$-0.518010\pi$
$409$	19.0477	−	19.0477i	0.941850	−	0.941850i	0.998400	+	0.0565493i	$0.0180098\pi$
$410$	−11.3492	+	11.3492i	−0.560498	+	0.560498i
$411$		0			0
$412$			2.70386i			0.133210i
$413$	3.31432	−	13.1139i	0.163087	−	0.645294i
$414$		0			0
$415$		−	30.4965i		−	1.49702i
$416$	−0.707107	+	3.53553i	−0.0346688	+	0.173344i
$417$		0			0
$418$	3.00705	−	3.00705i	0.147079	−	0.147079i
$419$			38.8022i			1.89561i	0.318849	+	0.947805i	$0.396704\pi$
$419$			38.8022i			1.89561i	−0.318849	+	0.947805i	$0.603296\pi$
$420$		0			0
$421$	−19.5375	−	19.5375i	−0.952199	−	0.952199i	0.0467096	−	0.998909i	$-0.485126\pi$
$421$	−19.5375	−	19.5375i	−0.952199	−	0.952199i	−0.998909	+	0.0467096i	$0.985126\pi$
$422$	0.389849	+	0.389849i	0.0189775	+	0.0189775i
$423$		0			0
$424$	7.95862	−	7.95862i	0.386505	−	0.386505i
$425$		−	23.0386i		−	1.11754i
$426$		0			0
$427$	−9.82917	+	5.86319i	−0.475667	+	0.283740i
$428$			11.6673i			0.563958i
$429$		0			0
$430$			23.9354i			1.15427i
$431$	−1.45559	−	1.45559i	−0.0701133	−	0.0701133i	0.671181	−	0.741294i	$-0.265788\pi$
$431$	−1.45559	−	1.45559i	−0.0701133	−	0.0701133i	−0.741294	+	0.671181i	$0.765788\pi$
$432$		0			0
$433$	−35.8137			−1.72110			−0.860548	−	0.509369i	$-0.829879\pi$
$433$	−35.8137			−1.72110			−0.860548	+	0.509369i	$0.829879\pi$
$434$	−2.07627	−	3.48069i	−0.0996640	−	0.167079i
$435$		0			0
$436$	5.29626	−	5.29626i	0.253645	−	0.253645i
$437$	14.2692	+	14.2692i	0.682586	+	0.682586i
$438$		0			0
$439$	14.2667			0.680912			0.340456	−	0.940260i	$-0.389418\pi$
$439$	14.2667			0.680912			0.340456	+	0.940260i	$0.389418\pi$
$440$	−1.14201	−	1.14201i	−0.0544431	−	0.0544431i
$441$		0			0
$442$	3.05882	−	15.2941i	0.145493	−	0.727467i
$443$	20.7019			0.983575			0.491788	−	0.870715i	$-0.336344\pi$
$443$	20.7019			0.983575			0.491788	+	0.870715i	$0.336344\pi$
$444$		0			0
$445$	−17.0435			−0.807941
$446$	13.9926			0.662571
$447$		0			0
$448$	2.27220	−	1.35539i	0.107352	−	0.0640362i
$449$	20.2382	−	20.2382i	0.955099	−	0.955099i	−0.0439356	−	0.999034i	$-0.513990\pi$
$449$	20.2382	−	20.2382i	0.955099	−	0.955099i	0.999034	+	0.0439356i	$0.0139896\pi$
$450$		0			0
$451$		−	2.51038i		−	0.118209i
$452$		−	20.3440i		−	0.956902i
$453$		0			0
$454$	−2.36764			−0.111119
$455$	−10.2357	−	28.8943i	−0.479858	−	1.35459i
$456$		0			0
$457$	−18.1891	−	18.1891i	−0.850852	−	0.850852i	0.139386	−	0.990238i	$-0.455487\pi$
$457$	−18.1891	−	18.1891i	−0.850852	−	0.850852i	−0.990238	+	0.139386i	$0.955487\pi$
$458$		−	1.87500i		−	0.0876132i
$459$		0			0
$460$	5.41911	−	5.41911i	0.252667	−	0.252667i
$461$	1.18339	−	1.18339i	0.0551158	−	0.0551158i	−0.679012	−	0.734127i	$-0.737591\pi$
$461$	1.18339	−	1.18339i	0.0551158	−	0.0551158i	0.734127	+	0.679012i	$0.237591\pi$
$462$		0			0
$463$	4.93946	−	4.93946i	0.229556	−	0.229556i	−0.582951	−	0.812507i	$-0.698102\pi$
$463$	4.93946	−	4.93946i	0.229556	−	0.229556i	0.812507	+	0.582951i	$0.198102\pi$
$464$	1.09574			0.0508684
$465$		0			0
$466$	−7.22074	+	7.22074i	−0.334494	+	0.334494i
$467$	26.6900			1.23507			0.617533	−	0.786545i	$-0.288132\pi$
$467$	26.6900			1.23507			0.617533	+	0.786545i	$0.288132\pi$
$468$		0			0
$469$	0.487614	−	1.92936i	0.0225159	−	0.0890898i
$470$	15.1375	+	15.1375i	0.698243	+	0.698243i
$471$		0			0
$472$	−5.11245			−0.235319
$473$	−2.64719	−	2.64719i	−0.121718	−	0.121718i
$474$		0			0
$475$	−31.8644	−	31.8644i	−1.46204	−	1.46204i
$476$	−9.82917	+	5.86319i	−0.450519	+	0.268739i
$477$		0			0
$478$		−	21.5260i		−	0.984575i
$479$	7.35998	+	7.35998i	0.336286	+	0.336286i	0.854968	−	0.518682i	$-0.173577\pi$
$479$	7.35998	+	7.35998i	0.336286	+	0.336286i	−0.518682	+	0.854968i	$0.673577\pi$
$480$		0			0
$481$	−25.9451	−	5.18902i	−1.18299	−	0.236599i
$482$			4.78705i			0.218044i
$483$		0			0
$484$	−10.7474			−0.488518
$485$		−	59.0459i		−	2.68113i
$486$		0			0
$487$	25.1766	+	25.1766i	1.14086	+	1.14086i	0.988293	+	0.152567i	$0.0487541\pi$
$487$	25.1766	+	25.1766i	1.14086	+	1.14086i	0.152567	+	0.988293i	$0.451246\pi$
$488$	3.05882	+	3.05882i	0.138466	+	0.138466i
$489$		0			0
$490$	−10.6872	+	19.7927i	−0.482797	+	0.894142i
$491$		−	7.77450i		−	0.350858i	−0.984492	−	0.175429i	$-0.943869\pi$
$491$		−	7.77450i		−	0.350858i	0.984492	−	0.175429i	$-0.0561313\pi$
$492$		0			0
$493$	−4.73998			−0.213478
$494$	−16.9224	−	25.3837i	−0.761377	−	1.14207i
$495$		0			0
$496$	−1.08319	+	1.08319i	−0.0486365	+	0.0486365i
$497$	5.85381	−	23.1620i	0.262579	−	1.03896i
$498$		0			0
$499$	23.4592	+	23.4592i	1.05018	+	1.05018i	0.998673	+	0.0515063i	$0.0164022\pi$
$499$	23.4592	+	23.4592i	1.05018	+	1.05018i	0.0515063	+	0.998673i	$0.483598\pi$
$500$	−0.740347	+	0.740347i	−0.0331093	+	0.0331093i
$501$		0			0
$502$	12.1821	+	12.1821i	0.543714	+	0.543714i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	−44.9887	+	44.9887i	−2.00197	+	2.00197i
$506$			1.19868i			0.0532877i
$507$		0			0
$508$	7.60812			0.337556
$509$	−11.0283	+	11.0283i	−0.488820	+	0.488820i	−0.907934	−	0.419114i	$-0.862341\pi$
$509$	−11.0283	+	11.0283i	−0.488820	+	0.488820i	0.419114	+	0.907934i	$0.362341\pi$
$510$		0			0
$511$	4.75736	−	18.8237i	0.210453	−	0.832710i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	2.34989	+	2.34989i	0.103649	+	0.103649i
$515$	−6.14373	+	6.14373i	−0.270725	+	0.270725i
$516$		0			0
$517$	−3.34834			−0.147260
$518$	9.94638	+	16.6743i	0.437019	+	0.732627i
$519$		0			0
$520$	−9.64015	+	6.42677i	−0.422748	+	0.281832i
$521$		−	18.5654i		−	0.813366i	−0.913569	−	0.406683i	$-0.866685\pi$
$521$		−	18.5654i		−	0.813366i	0.913569	−	0.406683i	$-0.133315\pi$
$522$		0			0
$523$		−	27.5741i		−	1.20573i	−0.797843	−	0.602866i	$-0.794026\pi$
$523$		−	27.5741i		−	1.20573i	0.797843	−	0.602866i	$-0.205974\pi$
$524$	6.87024			0.300128
$525$		0			0
$526$	−0.578434	−	0.578434i	−0.0252209	−	0.0252209i
$527$	4.68568	−	4.68568i	0.204111	−	0.204111i
$528$		0			0
$529$	17.3120			0.752695
$530$	36.1672			1.57100
$531$		0			0
$532$	−5.48528	+	21.7039i	−0.237817	+	0.940982i
$533$	−17.6593	−	3.53186i	−0.764909	−	0.152982i
$534$		0			0
$535$	−26.5104	+	26.5104i	−1.14614	+	1.14614i
$536$	−0.752160			−0.0324884
$537$		0			0
$538$	15.2793	−	15.2793i	0.658735	−	0.658735i
$539$	−1.00705	−	3.37099i	−0.0433766	−	0.145199i
$540$		0			0
$541$	−25.5330	+	25.5330i	−1.09775	+	1.09775i	−0.103077	+	0.994673i	$0.532869\pi$
$541$	−25.5330	+	25.5330i	−1.09775	+	1.09775i	−0.994673	+	0.103077i	$0.967131\pi$
$542$		−	21.2729i		−	0.913751i
$543$		0			0
$544$	3.05882	+	3.05882i	0.131146	+	0.131146i
$545$	24.0684			1.03098
$546$		0			0
$547$	44.1966			1.88971			0.944856	−	0.327486i	$-0.106201\pi$
$547$	44.1966			1.88971			0.944856	+	0.327486i	$0.106201\pi$
$548$	0.272205	+	0.272205i	0.0116280	+	0.0116280i
$549$		0			0
$550$		−	2.67676i		−	0.114137i
$551$	−6.55579	+	6.55579i	−0.279286	+	0.279286i
$552$		0			0
$553$	−15.3353	−	25.7085i	−0.652125	−	1.09323i
$554$	−12.5862	+	12.5862i	−0.534737	+	0.534737i
$555$		0			0
$556$	20.3440			0.862778
$557$	11.7755	−	11.7755i	0.498946	−	0.498946i	−0.412164	−	0.911110i	$-0.635227\pi$
$557$	11.7755	−	11.7755i	0.498946	−	0.498946i	0.911110	+	0.412164i	$0.135227\pi$
$558$		0			0
$559$	−22.3460	+	14.8973i	−0.945136	+	0.630090i
$560$	8.24264	+	2.08319i	0.348315	+	0.0880307i
$561$		0			0
$562$	8.78031			0.370375
$563$	45.7636			1.92870			0.964352	−	0.264621i	$-0.0852470\pi$
$563$	45.7636			1.92870			0.964352	+	0.264621i	$0.0852470\pi$
$564$		0			0
$565$	46.2258	−	46.2258i	1.94473	−	1.94473i
$566$	−17.7547	−	17.7547i	−0.746288	−	0.746288i
$567$		0			0
$568$	−9.02969			−0.378877
$569$			39.5061i			1.65618i	0.560595	+	0.828090i	$0.310572\pi$
$569$			39.5061i			1.65618i	−0.560595	+	0.828090i	$0.689428\pi$
$570$		0			0
$571$		−	19.1620i		−	0.801906i	−0.916099	−	0.400953i	$-0.868679\pi$
$571$		−	19.1620i		−	0.801906i	0.916099	−	0.400953i	$-0.131321\pi$
$572$	0.355392	−	1.77696i	0.0148597	−	0.0742983i
$573$		0			0
$574$	6.76991	+	11.3492i	0.282571	+	0.473707i
$575$	12.7019			0.529704
$576$		0			0
$577$	−3.53749	+	3.53749i	−0.147268	+	0.147268i	−0.776896	−	0.629629i	$-0.783207\pi$
$577$	−3.53749	+	3.53749i	−0.147268	+	0.147268i	0.629629	+	0.776896i	$0.283207\pi$
$578$	−1.21112	−	1.21112i	−0.0503760	−	0.0503760i
$579$		0			0
$580$	2.48974	+	2.48974i	0.103381	+	0.103381i
$581$	−24.3440	−	6.15253i	−1.00996	−	0.255250i
$582$		0			0
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	−7.33838			−0.303664
$585$		0			0
$586$			12.0398i			0.497360i
$587$	4.98849	−	4.98849i	0.205897	−	0.205897i	−0.596624	−	0.802521i	$-0.703492\pi$
$587$	4.98849	−	4.98849i	0.205897	−	0.205897i	0.802521	+	0.596624i	$0.203492\pi$
$588$		0			0
$589$		−	12.9614i		−	0.534065i
$590$	−11.6165	−	11.6165i	−0.478245	−	0.478245i
$591$		0			0
$592$	5.18902	−	5.18902i	0.213267	−	0.213267i
$593$	3.14690	+	3.14690i	0.129228	+	0.129228i	0.768762	−	0.639535i	$-0.220873\pi$
$593$	3.14690	+	3.14690i	0.129228	+	0.129228i	−0.639535	+	0.768762i	$0.720873\pi$
$594$		0			0
$595$	−35.6562	−	9.01151i	−1.46176	−	0.369436i
$596$	10.5685	−	10.5685i	0.432901	−	0.432901i
$597$		0			0
$598$	8.43209	+	1.68642i	0.344814	+	0.0689628i
$599$	−14.9244			−0.609796			−0.304898	−	0.952385i	$-0.598622\pi$
$599$	−14.9244			−0.609796			−0.304898	+	0.952385i	$0.598622\pi$
$600$		0			0
$601$		−	14.3189i		−	0.584080i	−0.956406	−	0.292040i	$-0.905666\pi$
$601$		−	14.3189i		−	0.584080i	0.956406	−	0.292040i	$-0.0943341\pi$
$602$	19.1066	+	4.82886i	0.778726	+	0.196810i
$603$		0			0
$604$	−0.149362	−	0.149362i	−0.00607743	−	0.00607743i
$605$	−24.4203	−	24.4203i	−0.992825	−	0.992825i
$606$		0			0
$607$			17.3212i			0.703047i	0.936179	+	0.351524i	$0.114336\pi$
$607$			17.3212i			0.703047i	−0.936179	+	0.351524i	$0.885664\pi$
$608$	8.46122			0.343148
$609$		0			0
$610$			13.9005i			0.562816i
$611$	−4.71078	+	23.5539i	−0.190578	+	0.952889i
$612$		0			0
$613$	28.6700	+	28.6700i	1.15797	+	1.15797i	0.984912	+	0.173057i	$0.0553646\pi$
$613$	28.6700	+	28.6700i	1.15797	+	1.15797i	0.173057	+	0.984912i	$0.444635\pi$
$614$		−	14.1982i		−	0.572993i
$615$		0			0
$616$	−1.14201	+	0.681219i	−0.0460129	+	0.0274471i
$617$	9.91435	+	9.91435i	0.399137	+	0.399137i	0.877929	−	0.478792i	$-0.158925\pi$
$617$	9.91435	+	9.91435i	0.399137	+	0.399137i	−0.478792	+	0.877929i	$0.658925\pi$
$618$		0			0
$619$	−3.87574	−	3.87574i	−0.155779	−	0.155779i	0.624914	−	0.780693i	$-0.285134\pi$
$619$	−3.87574	−	3.87574i	−0.155779	−	0.155779i	−0.780693	+	0.624914i	$0.785134\pi$
$620$	−4.92244			−0.197690
$621$		0			0
$622$	11.1061	+	11.1061i	0.445316	+	0.445316i
$623$	−3.43845	+	13.6051i	−0.137759	+	0.545076i
$624$		0			0
$625$	23.2647			0.930588
$626$	−14.6867	+	14.6867i	−0.587000	+	0.587000i
$627$		0			0
$628$	−10.7630			−0.429490
$629$	−22.4468	+	22.4468i	−0.895012	+	0.895012i
$630$		0			0
$631$	−21.5709	+	21.5709i	−0.858725	+	0.858725i	−0.991188	−	0.132463i	$-0.957711\pi$
$631$	−21.5709	+	21.5709i	−0.858725	+	0.858725i	0.132463	+	0.991188i	$0.457711\pi$
$632$	−8.00043	+	8.00043i	−0.318240	+	0.318240i
$633$		0			0
$634$			26.8878i			1.06785i
$635$	17.2872	+	17.2872i	0.686022	+	0.686022i
$636$		0			0
$637$	−25.1300	+	2.34142i	−0.995688	+	0.0927706i
$638$	−0.550718			−0.0218031
$639$		0			0
$640$		−	3.21338i		−	0.127020i
$641$		−	25.8728i		−	1.02192i	−0.859606	−	0.510958i	$-0.829291\pi$
$641$		−	25.8728i		−	1.02192i	0.859606	−	0.510958i	$-0.170709\pi$
$642$		0			0
$643$	−3.32032	+	3.32032i	−0.130941	+	0.130941i	−0.769540	−	0.638599i	$-0.779514\pi$
$643$	−3.32032	+	3.32032i	−0.130941	+	0.130941i	0.638599	+	0.769540i	$0.279514\pi$
$644$	−3.23255	−	5.41911i	−0.127380	−	0.213543i
$645$		0			0
$646$	−36.6018			−1.44008
$647$	28.6969			1.12819			0.564097	−	0.825709i	$-0.309225\pi$
$647$	28.6969			1.12819			0.564097	+	0.825709i	$0.309225\pi$
$648$		0			0
$649$	2.56951			0.100862
$650$	−18.8296	−	3.76593i	−0.738559	−	0.147712i
$651$		0			0
$652$	−3.40901	−	3.40901i	−0.133507	−	0.133507i
$653$	27.9250			1.09279			0.546395	−	0.837527i	$-0.316000\pi$
$653$	27.9250			1.09279			0.546395	+	0.837527i	$0.316000\pi$
$654$		0			0
$655$	15.6106	+	15.6106i	0.609956	+	0.609956i
$656$	3.53186	−	3.53186i	0.137896	−	0.137896i
$657$		0			0
$658$	15.1375	−	9.02969i	0.590123	−	0.352014i
$659$	38.2258			1.48906			0.744532	−	0.667587i	$-0.232673\pi$
$659$	38.2258			1.48906			0.744532	+	0.667587i	$0.232673\pi$
$660$		0			0
$661$	−4.52189	−	4.52189i	−0.175881	−	0.175881i	0.613676	−	0.789558i	$-0.289690\pi$
$661$	−4.52189	−	4.52189i	−0.175881	−	0.175881i	−0.789558	+	0.613676i	$0.789690\pi$
$662$			19.7686i			0.768329i
$663$		0			0
$664$			9.49048i			0.368302i
$665$	−61.7793	+	36.8519i	−2.39570	+	1.42906i
$666$		0			0
$667$		−	2.61329i		−	0.101187i
$668$	−10.0226	+	10.0226i	−0.387788	+	0.387788i
$669$		0			0
$670$	−1.70906	−	1.70906i	−0.0660268	−	0.0660268i
$671$	−1.53736	−	1.53736i	−0.0593492	−	0.0593492i
$672$		0			0
$673$		−	16.7180i		−	0.644430i	−0.946667	−	0.322215i	$-0.895573\pi$
$673$		−	16.7180i		−	0.644430i	0.946667	−	0.322215i	$-0.104427\pi$
$674$	−0.774804	+	0.774804i	−0.0298443	+	0.0298443i
$675$		0			0
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	37.8247i		−	1.45372i	−0.686785	−	0.726861i	$-0.740979\pi$
$677$		−	37.8247i		−	1.45372i	0.686785	−	0.726861i	$-0.259021\pi$
$678$		0			0
$679$	−47.1336	−	11.9122i	−1.80882	−	0.457149i
$680$			13.9005i			0.533061i
$681$		0			0
$682$	0.544409	−	0.544409i	0.0208465	−	0.0208465i
$683$	−3.10020	+	3.10020i	−0.118626	+	0.118626i	−0.763928	−	0.645302i	$-0.776732\pi$
$683$	−3.10020	+	3.10020i	−0.118626	+	0.118626i	0.645302	+	0.763928i	$0.276732\pi$
$684$		0			0
$685$			1.23701i			0.0472637i
$686$	13.6435	+	12.5242i	0.520912	+	0.478174i
$687$		0			0
$688$		−	7.44867i		−	0.283978i
$689$	22.5104	+	33.7656i	0.857577	+	1.28637i
$690$		0			0
$691$	−11.1083	+	11.1083i	−0.422579	+	0.422579i	−0.886091	−	0.463512i	$-0.846589\pi$
$691$	−11.1083	+	11.1083i	−0.422579	+	0.422579i	0.463512	+	0.886091i	$0.346589\pi$
$692$			19.7405i			0.750420i
$693$		0			0
$694$	22.6969	+	22.6969i	0.861564	+	0.861564i
$695$	46.2258	+	46.2258i	1.75344	+	1.75344i
$696$		0			0
$697$	−15.2782	+	15.2782i	−0.578703	+	0.578703i
$698$		−	26.8219i		−	1.01523i
$699$		0			0
$700$	7.21858	+	12.1014i	0.272837	+	0.457389i
$701$			2.49912i			0.0943905i	0.998886	+	0.0471953i	$0.0150283\pi$
$701$			2.49912i			0.0943905i	−0.998886	+	0.0471953i	$0.984972\pi$
$702$		0			0
$703$			62.0917i			2.34183i
$704$	0.355392	+	0.355392i	0.0133943	+	0.0133943i
$705$		0			0
$706$	21.9911			0.827645
$707$	26.8362	+	44.9887i	1.00928	+	1.69198i
$708$		0			0
$709$	25.3601	−	25.3601i	0.952419	−	0.952419i	−0.0464996	−	0.998918i	$-0.514807\pi$
$709$	25.3601	−	25.3601i	0.952419	−	0.952419i	0.998918	+	0.0464996i	$0.0148066\pi$
$710$	−20.5173	−	20.5173i	−0.770001	−	0.770001i
$711$		0			0
$712$	5.30392			0.198773
$713$	2.58335	+	2.58335i	0.0967473	+	0.0967473i
$714$		0			0
$715$	4.84513	−	3.23009i	0.181198	−	0.120798i
$716$	−9.79960			−0.366228
$717$		0			0
$718$	−20.0600			−0.748632
$719$	−41.5150			−1.54825			−0.774124	−	0.633034i	$-0.781809\pi$
$719$	−41.5150			−1.54825			−0.774124	+	0.633034i	$0.781809\pi$
$720$		0			0
$721$	3.66479	+	6.14373i	0.136484	+	0.228804i
$722$	−37.1884	+	37.1884i	−1.38401	+	1.38401i
$723$		0			0
$724$			10.4372i			0.387894i
$725$			5.83571i			0.216733i
$726$		0			0
$727$	48.1505			1.78580			0.892902	−	0.450251i	$-0.148665\pi$
$727$	48.1505			1.78580			0.892902	+	0.450251i	$0.148665\pi$
$728$	3.18534	+	8.99186i	0.118057	+	0.333261i
$729$		0			0
$730$	−16.6743	−	16.6743i	−0.617143	−	0.617143i
$731$			32.2217i			1.19176i
$732$		0			0
$733$	7.58561	−	7.58561i	0.280181	−	0.280181i	−0.553000	−	0.833181i	$-0.686517\pi$
$733$	7.58561	−	7.58561i	0.280181	−	0.280181i	0.833181	+	0.553000i	$0.186517\pi$
$734$	−7.95862	+	7.95862i	−0.293758	+	0.293758i
$735$		0			0
$736$	−1.68642	+	1.68642i	−0.0621622	+	0.0621622i
$737$	0.378035			0.0139251
$738$		0			0
$739$	0.923733	−	0.923733i	0.0339801	−	0.0339801i	−0.689913	−	0.723893i	$-0.742351\pi$
$739$	0.923733	−	0.923733i	0.0339801	−	0.0339801i	0.723893	+	0.689913i	$0.242351\pi$
$740$	23.5810			0.866856
$741$		0			0
$742$	7.29657	−	28.8707i	0.267865	−	1.05988i
$743$	7.95906	+	7.95906i	0.291989	+	0.291989i	0.837866	−	0.545876i	$-0.183803\pi$
$743$	7.95906	+	7.95906i	0.291989	+	0.291989i	−0.545876	+	0.837866i	$0.683803\pi$
$744$		0			0
$745$	48.0274			1.75959
$746$	−12.1254	−	12.1254i	−0.443944	−	0.443944i
$747$		0			0
$748$	−1.53736	−	1.53736i	−0.0562115	−	0.0562115i
$749$	15.8137	+	26.5104i	0.577820	+	0.968668i
$750$		0			0
$751$			48.2119i			1.75928i	0.475642	+	0.879639i	$0.342216\pi$
$751$			48.2119i			1.75928i	−0.475642	+	0.879639i	$0.657784\pi$
$752$	−4.71078	−	4.71078i	−0.171785	−	0.171785i
$753$		0			0
$754$	−0.774804	+	3.87402i	−0.0282167	+	0.141084i
$755$		−	0.678760i		−	0.0247026i
$756$		0			0
$757$	47.8137			1.73782			0.868909	−	0.494972i	$-0.164822\pi$
$757$	47.8137			1.73782			0.868909	+	0.494972i	$0.164822\pi$
$758$		−	16.3603i		−	0.594232i
$759$		0			0
$760$	19.2256	+	19.2256i	0.697387	+	0.697387i
$761$	−14.6867	−	14.6867i	−0.532393	−	0.532393i	0.388891	−	0.921284i	$-0.372858\pi$
$761$	−14.6867	−	14.6867i	−0.532393	−	0.532393i	−0.921284	+	0.388891i	$0.872858\pi$
$762$		0			0
$763$	4.85568	−	19.2127i	0.175788	−	0.695547i
$764$		−	11.1410i		−	0.403068i
$765$		0			0
$766$	1.79120			0.0647189
$767$	3.61504	−	18.0752i	0.130532	−	0.652658i
$768$		0			0
$769$	34.5766	−	34.5766i	1.24686	−	1.24686i	0.289765	−	0.957098i	$-0.406423\pi$
$769$	34.5766	−	34.5766i	1.24686	−	1.24686i	0.957098	−	0.289765i	$-0.0935771\pi$
$770$	−4.14275	−	1.04701i	−0.149294	−	0.0377316i
$771$		0			0
$772$	4.03661	+	4.03661i	0.145281	+	0.145281i
$773$	3.88033	−	3.88033i	0.139566	−	0.139566i	−0.633872	−	0.773438i	$-0.718535\pi$
$773$	3.88033	−	3.88033i	0.139566	−	0.139566i	0.773438	+	0.633872i	$0.218535\pi$
$774$		0			0
$775$	−5.76887	−	5.76887i	−0.207224	−	0.207224i
$776$			18.3750i			0.659624i
$777$		0			0
$778$	−5.59099	+	5.59099i	−0.200447	+	0.200447i
$779$			42.2621i			1.51420i
$780$		0			0
$781$	4.53832			0.162394
$782$	7.29515	−	7.29515i	0.260874	−	0.260874i
$783$		0			0
$784$	3.32583	−	6.15945i	0.118780	−	0.219980i
$785$	−24.4557	−	24.4557i	−0.872862	−	0.872862i
$786$		0			0
$787$	7.06054	+	7.06054i	0.251681	+	0.251681i	0.821660	−	0.569978i	$-0.193048\pi$
$787$	7.06054	+	7.06054i	0.251681	+	0.251681i	−0.569978	+	0.821660i	$0.693048\pi$
$788$	0.627596	−	0.627596i	0.0223572	−	0.0223572i
$789$		0			0
$790$	−36.3572			−1.29353
$791$	−27.5741	−	46.2258i	−0.980422	−	1.64360i
$792$		0			0
$793$	−12.9775	+	8.65166i	−0.460844	+	0.307229i
$794$			23.2591i			0.825435i
$795$		0			0
$796$			16.5375i			0.586156i
$797$	−31.7376			−1.12421			−0.562103	−	0.827068i	$-0.690007\pi$
$797$	−31.7376			−1.12421			−0.562103	+	0.827068i	$0.690007\pi$
$798$		0			0
$799$	20.3780	+	20.3780i	0.720923	+	0.720923i
$800$	3.76593	−	3.76593i	0.133146	−	0.133146i
$801$		0			0
$802$	21.2310			0.749691
$803$	3.68827			0.130156
$804$		0			0
$805$	4.96831	−	19.6583i	0.175110	−	0.692865i
$806$	−3.06372	−	4.59557i	−0.107915	−	0.161872i
$807$		0			0
$808$	14.0004	−	14.0004i	0.492533	−	0.492533i
$809$	−5.38754			−0.189416			−0.0947079	−	0.995505i	$-0.530192\pi$
$809$	−5.38754			−0.189416			−0.0947079	+	0.995505i	$0.530192\pi$
$810$		0			0
$811$	−24.4934	+	24.4934i	−0.860079	+	0.860079i	−0.991347	−	0.131268i	$-0.958095\pi$
$811$	−24.4934	+	24.4934i	−0.860079	+	0.860079i	0.131268	+	0.991347i	$0.458095\pi$
$812$	2.48974	−	1.48515i	0.0873728	−	0.0521187i
$813$		0			0
$814$	−2.60800	+	2.60800i	−0.0914103	+	0.0914103i
$815$		−	15.4920i		−	0.542660i
$816$		0			0
$817$	44.5653	+	44.5653i	1.55914	+	1.55914i
$818$	−26.9376			−0.941850
$819$		0			0
$820$	16.0502			0.560498
$821$	14.8664	+	14.8664i	0.518840	+	0.518840i	0.917220	−	0.398381i	$-0.130428\pi$
$821$	14.8664	+	14.8664i	0.518840	+	0.518840i	−0.398381	+	0.917220i	$0.630428\pi$
$822$		0			0
$823$			46.5078i			1.62116i	0.585628	+	0.810580i	$0.300848\pi$
$823$			46.5078i			1.62116i	−0.585628	+	0.810580i	$0.699152\pi$
$824$	1.91192	−	1.91192i	0.0666049	−	0.0666049i
$825$		0			0
$826$	−11.6165	+	6.92936i	−0.404190	+	0.241103i
$827$	2.43470	−	2.43470i	0.0846630	−	0.0846630i	−0.663507	−	0.748170i	$-0.730933\pi$
$827$	2.43470	−	2.43470i	0.0846630	−	0.0846630i	0.748170	+	0.663507i	$0.230933\pi$
$828$		0			0
$829$	−5.61013			−0.194848			−0.0974239	−	0.995243i	$-0.531060\pi$
$829$	−5.61013			−0.194848			−0.0974239	+	0.995243i	$0.531060\pi$
$830$	−21.5643	+	21.5643i	−0.748508	+	0.748508i
$831$		0			0
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	−14.3870	+	26.6447i	−0.498479	+	0.923185i
$834$		0			0
$835$	−45.5470			−1.57622
$836$	−4.25261			−0.147079
$837$		0			0
$838$	27.4373	−	27.4373i	0.947805	−	0.947805i
$839$	−35.6724	−	35.6724i	−1.23155	−	1.23155i	−0.963369	−	0.268180i	$-0.913578\pi$
$839$	−35.6724	−	35.6724i	−1.23155	−	1.23155i	−0.268180	−	0.963369i	$-0.586422\pi$
$840$		0			0
$841$	−27.7994			−0.958599
$842$			27.6302i			0.952199i
$843$		0			0
$844$		−	0.551329i		−	0.0189775i
$845$	−15.9054	−	38.6275i	−0.547164	−	1.32883i
$846$		0			0
$847$	−24.4203	+	14.5669i	−0.839091	+	0.500526i
$848$	−11.2552			−0.386505
$849$		0			0
$850$	−16.2908	+	16.2908i	−0.558768	+	0.558768i
$851$	−12.3756	−	12.3756i	−0.424229	−	0.424229i
$852$		0			0
$853$	9.68368	+	9.68368i	0.331563	+	0.331563i	0.853180	−	0.521617i	$-0.174671\pi$
$853$	9.68368	+	9.68368i	0.331563	+	0.331563i	−0.521617	+	0.853180i	$0.674671\pi$
$854$	11.0962	+	2.80437i	0.379703	+	0.0959635i
$855$		0			0
$856$	8.24999	−	8.24999i	0.281979	−	0.281979i
$857$	−10.6859			−0.365025			−0.182512	−	0.983204i	$-0.558423\pi$
$857$	−10.6859			−0.365025			−0.182512	+	0.983204i	$0.558423\pi$
$858$		0			0
$859$		−	15.4218i		−	0.526186i	−0.964771	−	0.263093i	$-0.915257\pi$
$859$		−	15.4218i		−	0.526186i	0.964771	−	0.263093i	$-0.0847426\pi$
$860$	16.9249	−	16.9249i	0.577134	−	0.577134i
$861$		0			0
$862$			2.05852i			0.0701133i
$863$	13.8546	+	13.8546i	0.471617	+	0.471617i	0.902438	−	0.430820i	$-0.141776\pi$
$863$	13.8546	+	13.8546i	0.471617	+	0.471617i	−0.430820	+	0.902438i	$0.641776\pi$
$864$		0			0
$865$	−44.8544	+	44.8544i	−1.52510	+	1.52510i
$866$	25.3241	+	25.3241i	0.860548	+	0.860548i
$867$		0			0
$868$	−0.993080	+	3.92936i	−0.0337073	+	0.133371i
$869$	4.02101	−	4.02101i	0.136404	−	0.136404i
$870$		0			0
$871$	0.531858	−	2.65929i	0.0180213	−	0.0901065i
$872$	−7.49005			−0.253645
$873$		0			0
$874$		−	20.1796i		−	0.682586i
$875$	−0.678760	+	2.68568i	−0.0229463	+	0.0907926i
$876$		0			0
$877$	6.59203	+	6.59203i	0.222597	+	0.222597i	0.809591	−	0.586994i	$-0.199689\pi$
$877$	6.59203	+	6.59203i	0.222597	+	0.222597i	−0.586994	+	0.809591i	$0.699689\pi$
$878$	−10.0881	−	10.0881i	−0.340456	−	0.340456i
$879$		0			0
$880$			1.61504i			0.0544431i
$881$	4.21366			0.141962			0.0709810	−	0.997478i	$-0.477387\pi$
$881$	4.21366			0.141962			0.0709810	+	0.997478i	$0.477387\pi$
$882$		0			0
$883$		−	22.3169i		−	0.751024i	−0.926818	−	0.375512i	$-0.877467\pi$
$883$		−	22.3169i		−	0.751024i	0.926818	−	0.375512i	$-0.122533\pi$
$884$	−12.9775	+	8.65166i	−0.436480	+	0.290987i
$885$		0			0
$886$	−14.6384	−	14.6384i	−0.491788	−	0.491788i
$887$		−	22.4573i		−	0.754044i	−0.926204	−	0.377022i	$-0.876948\pi$
$887$		−	22.4573i		−	0.754044i	0.926204	−	0.377022i	$-0.123052\pi$
$888$		0			0
$889$	17.2872	−	10.3120i	0.579795	−	0.345853i
$890$	12.0516	+	12.0516i	0.403970	+	0.403970i
$891$		0			0
$892$	−9.89430	−	9.89430i	−0.331286	−	0.331286i
$893$	56.3691			1.88632
$894$		0			0
$895$	−22.2667	−	22.2667i	−0.744294	−	0.744294i
$896$	−2.56510	−	0.648285i	−0.0856939	−	0.0216577i
$897$		0			0
$898$	−28.6211			−0.955099
$899$	−1.18689	+	1.18689i	−0.0395850	+	0.0395850i
$900$		0			0
$901$	48.6880			1.62203
$902$	−1.77511	+	1.77511i	−0.0591047	+	0.0591047i
$903$		0			0
$904$	−14.3854	+	14.3854i	−0.478451	+	0.478451i
$905$	−23.7154	+	23.7154i	−0.788326	+	0.788326i
$906$		0			0
$907$			27.5490i			0.914749i	0.889274	+	0.457375i	$0.151210\pi$
$907$			27.5490i			0.914749i	−0.889274	+	0.457375i	$0.848790\pi$
$908$	1.67417	+	1.67417i	0.0555594	+	0.0555594i
$909$		0			0
$910$	−13.1936	+	27.6691i	−0.437364	+	0.917222i
$911$	−50.9409			−1.68775			−0.843873	−	0.536542i	$-0.819730\pi$
$911$	−50.9409			−1.68775			−0.843873	+	0.536542i	$0.819730\pi$
$912$		0			0
$913$		−	4.76991i		−	0.157861i
$914$			25.7233i			0.850852i
$915$		0			0
$916$	−1.32583	+	1.32583i	−0.0438066	+	0.0438066i
$917$	15.6106	−	9.31186i	0.515507	−	0.307505i
$918$		0			0
$919$	−7.00433			−0.231052			−0.115526	−	0.993304i	$-0.536855\pi$
$919$	−7.00433			−0.231052			−0.115526	+	0.993304i	$0.536855\pi$
$920$	−7.66377			−0.252667
$921$		0			0
$922$	−1.67356			−0.0551158
$923$	6.38496	−	31.9248i	0.210163	−	1.05082i
$924$		0			0
$925$	27.6358	+	27.6358i	0.908660	+	0.908660i
$926$	−6.98545			−0.229556
$927$		0			0
$928$	−0.774804	−	0.774804i	−0.0254342	−	0.0254342i
$929$	7.38650	−	7.38650i	0.242343	−	0.242343i	−0.575476	−	0.817819i	$-0.695183\pi$
$929$	7.38650	−	7.38650i	0.242343	−	0.242343i	0.817819	+	0.575476i	$0.195183\pi$
$930$		0			0
$931$	16.9536	+	56.7503i	0.555630	+	1.85992i
$932$	10.2117			0.334494
$933$		0			0
$934$	−18.8727	−	18.8727i	−0.617533	−	0.617533i
$935$		−	6.98640i		−	0.228480i
$936$		0			0
$937$			47.1203i			1.53935i	0.638435	+	0.769676i	$0.279582\pi$
$937$			47.1203i			1.53935i	−0.638435	+	0.769676i	$0.720418\pi$
$938$	−1.70906	+	1.01947i	−0.0558029	+	0.0332869i
$939$		0			0
$940$		−	21.4077i		−	0.698243i
$941$	18.1495	−	18.1495i	0.591656	−	0.591656i	−0.346422	−	0.938079i	$-0.612604\pi$
$941$	18.1495	−	18.1495i	0.591656	−	0.591656i	0.938079	+	0.346422i	$0.112604\pi$
$942$		0			0
$943$	−8.42332	−	8.42332i	−0.274301	−	0.274301i
$944$	3.61504	+	3.61504i	0.117660	+	0.117660i
$945$		0			0
$946$			3.74370i			0.121718i
$947$	2.89980	−	2.89980i	0.0942309	−	0.0942309i	−0.658420	−	0.752651i	$-0.728775\pi$
$947$	2.89980	−	2.89980i	0.0942309	−	0.0942309i	0.752651	+	0.658420i	$0.228775\pi$
$948$		0			0
$949$	5.18902	−	25.9451i	0.168443	−	0.842213i
$950$			45.0630i			1.46204i
$951$		0			0
$952$	11.0962	+	2.80437i	0.359629	+	0.0908901i
$953$		−	39.8477i		−	1.29079i	−0.763847	−	0.645397i	$-0.776692\pi$
$953$		−	39.8477i		−	1.29079i	0.763847	−	0.645397i	$-0.223308\pi$
$954$		0			0
$955$	25.3147	−	25.3147i	0.819164	−	0.819164i
$956$	−15.2212	+	15.2212i	−0.492288	+	0.492288i
$957$		0			0
$958$		−	10.4086i		−	0.336286i
$959$	0.987448	+	0.249561i	0.0318864	+	0.00805874i
$960$		0			0
$961$			28.6534i			0.924304i
$962$	14.6768	+	22.0151i	0.473198	+	0.709797i
$963$		0			0
$964$	3.38496	−	3.38496i	0.109022	−	0.109022i
$965$			18.3440i			0.590515i
$966$		0			0
$967$	−19.7373	−	19.7373i	−0.634709	−	0.634709i	0.314537	−	0.949245i	$-0.398151\pi$
$967$	−19.7373	−	19.7373i	−0.634709	−	0.634709i	−0.949245	+	0.314537i	$0.898151\pi$
$968$	7.59955	+	7.59955i	0.244259	+	0.244259i
$969$		0			0
$970$	−41.7517	+	41.7517i	−1.34057	+	1.34057i
$971$			12.5416i			0.402478i	0.979542	+	0.201239i	$0.0644969\pi$
$971$			12.5416i			0.402478i	−0.979542	+	0.201239i	$0.935503\pi$
$972$		0			0
$973$	46.2258	−	27.5741i	1.48193	−	0.883985i
$974$		−	35.6051i		−	1.14086i
$975$		0			0
$976$		−	4.32583i		−	0.138466i
$977$	−13.8123	−	13.8123i	−0.441894	−	0.441894i	0.450754	−	0.892648i	$-0.351155\pi$
$977$	−13.8123	−	13.8123i	−0.441894	−	0.441894i	−0.892648	+	0.450754i	$0.851155\pi$
$978$		0			0
$979$	−2.66575			−0.0851977
$980$	21.5525	−	6.43858i	0.688469	−	0.205673i
$981$		0			0
$982$	−5.49740	+	5.49740i	−0.175429	+	0.175429i
$983$	26.1069	+	26.1069i	0.832680	+	0.832680i	0.987883	−	0.155203i	$-0.0496031\pi$
$983$	26.1069	+	26.1069i	0.832680	+	0.832680i	−0.155203	+	0.987883i	$0.549603\pi$
$984$		0			0
$985$	2.85205			0.0908740
$986$	3.35167	+	3.35167i	0.106739	+	0.106739i
$987$		0			0
$988$	−5.98299	+	29.9149i	−0.190344	+	0.951721i
$989$	−17.7647			−0.564886
$990$		0			0
$991$	7.35727			0.233711			0.116856	−	0.993149i	$-0.462719\pi$
$991$	7.35727			0.233711			0.116856	+	0.993149i	$0.462719\pi$
$992$	1.53186			0.0486365
$993$		0			0
$994$	−20.5173	+	12.2388i	−0.650769	+	0.388190i
$995$	−37.5766	+	37.5766i	−1.19126	+	1.19126i
$996$		0			0
$997$		−	14.1274i		−	0.447420i	−0.974656	−	0.223710i	$-0.928183\pi$
$997$		−	14.1274i		−	0.447420i	0.974656	−	0.223710i	$-0.0718169\pi$
$998$		−	33.1763i		−	1.05018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.d.307.1		8
3.2	odd	2		546.2.o.a.307.4	yes	8
7.6	odd	2		1638.2.x.b.307.2		8
13.5	odd	4		1638.2.x.b.811.2		8
21.20	even	2		546.2.o.d.307.3	yes	8
39.5	even	4		546.2.o.d.265.3	yes	8
91.83	even	4	inner	1638.2.x.d.811.1		8
273.83	odd	4		546.2.o.a.265.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.4	✓	8	273.83	odd	4
546.2.o.a.307.4	yes	8	3.2	odd	2
546.2.o.d.265.3	yes	8	39.5	even	4
546.2.o.d.307.3	yes	8	21.20	even	2
1638.2.x.b.307.2		8	7.6	odd	2
1638.2.x.b.811.2		8	13.5	odd	4
1638.2.x.d.307.1		8	1.1	even	1	trivial
1638.2.x.d.811.1		8	91.83	even	4	inner

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.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(1.35539 + 2.27220i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.21338 q^{10} +(-0.355392 + 0.355392i) q^{11} +(2.00000 + 3.00000i) q^{13} +(0.648285 - 2.56510i) q^{14} -1.00000 q^{16} +4.32583 q^{17} +(5.98299 - 5.98299i) q^{19} +(-2.27220 - 2.27220i) q^{20} +0.502600 q^{22} +2.38496i q^{23} -5.32583i q^{25} +(0.707107 - 3.53553i) q^{26} +(-2.27220 + 1.35539i) q^{28} -1.09574 q^{29} +(1.08319 - 1.08319i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.05882 - 3.05882i) q^{34} +(-8.24264 - 2.08319i) q^{35} +(-5.18902 + 5.18902i) q^{37} -8.46122 q^{38} +3.21338i q^{40} +(-3.53186 + 3.53186i) q^{41} +7.44867i q^{43} +(-0.355392 - 0.355392i) q^{44} +(1.68642 - 1.68642i) q^{46} +(4.71078 + 4.71078i) q^{47} +(-3.32583 + 6.15945i) q^{49} +(-3.76593 + 3.76593i) q^{50} +(-3.00000 + 2.00000i) q^{52} +11.2552 q^{53} -1.61504i q^{55} +(2.56510 + 0.648285i) q^{56} +(0.774804 + 0.774804i) q^{58} +(-3.61504 - 3.61504i) q^{59} +4.32583i q^{61} -1.53186 q^{62} -1.00000i q^{64} +(-11.3610 - 2.27220i) q^{65} +(-0.531858 - 0.531858i) q^{67} +4.32583i q^{68} +(4.35539 + 7.30146i) q^{70} +(-6.38496 - 6.38496i) q^{71} +(-5.18902 - 5.18902i) q^{73} +7.33838 q^{74} +(5.98299 + 5.98299i) q^{76} +(-1.28922 - 0.325828i) q^{77} -11.3143 q^{79} +(2.27220 - 2.27220i) q^{80} +4.99480 q^{82} +(-6.71078 + 6.71078i) q^{83} +(-9.82917 + 9.82917i) q^{85} +(5.26701 - 5.26701i) q^{86} +0.502600i q^{88} +(3.75044 + 3.75044i) q^{89} +(-4.10583 + 8.61058i) q^{91} -2.38496 q^{92} -6.66205i q^{94} +27.1891i q^{95} +(-12.9931 + 12.9931i) q^{97} +(6.70711 - 2.00368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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