LMFDB - Embedded newform 392.2.b.f.197.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(197,392)] 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("392.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1142512.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - x^{4} + 5x^{3} - 2x^{2} - 4x + 8 $ x^6 - x^5 - x^4 + 5x^3 - 2x^2 - 4*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.5
Root			$0.697966 - 1.22998i$ of defining polynomial
Character	$\chi$	$=$	392.197
Dual form			392.2.b.f.197.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32772 - 0.486987i) q^{2} +2.45995i q^{3} +(1.52569 - 1.29317i) q^{4} +1.48598i q^{5} +(1.19797 + 3.26613i) q^{6} +(1.39593 - 2.45995i) q^{8} -3.05137 q^{9} +(0.723653 + 1.97297i) q^{10} +5.04629i q^{11} +(3.18113 + 3.75312i) q^{12} -2.58633i q^{13} -3.65544 q^{15} +(0.655442 - 3.94593i) q^{16} -1.25951 q^{17} +(-4.05137 + 1.48598i) q^{18} -3.09834i q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} -1.39593 q^{23} +(6.05137 + 3.43393i) q^{24} +2.79186 q^{25} +(-1.25951 - 3.43393i) q^{26} -0.126378i q^{27} -0.638384i q^{29} +(-4.85341 + 1.78015i) q^{30} +3.65544 q^{31} +(-1.05137 - 5.55829i) q^{32} -12.4136 q^{33} +(-1.67228 + 0.613365i) q^{34} +(-4.65544 + 3.94593i) q^{36} -6.02026i q^{37} +(-1.50885 - 4.11373i) q^{38} +6.36226 q^{39} +(3.65544 + 2.07433i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(6.52569 + 7.69905i) q^{44} -4.53428i q^{45} +(-1.85341 + 0.679801i) q^{46} +10.9663 q^{47} +(9.70682 + 1.61236i) q^{48} +(3.70682 - 1.35960i) q^{50} -3.09834i q^{51} +(-3.34456 - 3.94593i) q^{52} -5.76750i q^{53} +(-0.0615446 - 0.167795i) q^{54} -7.49868 q^{55} +7.62177 q^{57} +(-0.310885 - 0.847596i) q^{58} -3.48397i q^{59} +(-5.57706 + 4.72709i) q^{60} -12.8881i q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +3.84324 q^{65} +(-16.4818 + 6.04528i) q^{66} -0.512006i q^{67} +(-1.92162 + 1.62876i) q^{68} -3.43393i q^{69} -7.41363 q^{71} +(-4.25951 + 7.50624i) q^{72} -9.89461 q^{73} +(-2.93179 - 7.99323i) q^{74} +6.86786i q^{75} +(-4.00667 - 4.72709i) q^{76} +(8.44731 - 3.09834i) q^{78} +8.70682 q^{79} +(5.86358 + 0.973974i) q^{80} -8.84324 q^{81} +(-8.44731 + 3.09834i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(0.498680 + 1.35960i) q^{86} +1.57040 q^{87} +(12.4136 + 7.04427i) q^{88} +2.58373 q^{89} +(-2.20814 - 6.02026i) q^{90} +(-2.12976 + 1.80517i) q^{92} +8.99222i q^{93} +(14.5602 - 5.34046i) q^{94} +4.60407 q^{95} +(13.6731 - 2.58633i) q^{96} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.32772	−	0.486987i	0.938841	−	0.344352i
$2$	1.32772	−	0.486987i	0.938841	−	0.344352i
$3$			2.45995i			1.42026i	0.704073	+	0.710128i	$0.251363\pi$
$3$			2.45995i			1.42026i	−0.704073	+	0.710128i	$0.748637\pi$
$4$	1.52569	−	1.29317i	0.762844	−	0.646583i
$5$			1.48598i			0.664550i	0.943182	+	0.332275i	$0.107816\pi$
$5$			1.48598i			0.664550i	−0.943182	+	0.332275i	$0.892184\pi$
$6$	1.19797	+	3.26613i	0.489068	+	1.33339i
$7$		0			0
$7$		0			0
$8$	1.39593	−	2.45995i	0.493536	−	0.869725i
$9$	−3.05137			−1.01712
$10$	0.723653	+	1.97297i	0.228839	+	0.623907i
$11$			5.04629i			1.52151i	0.649038	+	0.760756i	$0.275172\pi$
$11$			5.04629i			1.52151i	−0.649038	+	0.760756i	$0.724828\pi$
$12$	3.18113	+	3.75312i	0.918313	+	1.08343i
$13$		−	2.58633i		−	0.717320i	−0.933468	−	0.358660i	$-0.883234\pi$
$13$		−	2.58633i		−	0.717320i	0.933468	−	0.358660i	$-0.116766\pi$
$14$		0			0
$15$	−3.65544			−0.943831
$16$	0.655442	−	3.94593i	0.163861	−	0.986484i
$17$	−1.25951			−0.305476			−0.152738	−	0.988267i	$-0.548809\pi$
$17$	−1.25951			−0.305476			−0.152738	+	0.988267i	$0.548809\pi$
$18$	−4.05137	+	1.48598i	−0.954918	+	0.350249i
$19$		−	3.09834i		−	0.710808i	−0.934713	−	0.355404i	$-0.884343\pi$
$19$		−	3.09834i		−	0.710808i	0.934713	−	0.355404i	$-0.115657\pi$
$20$	1.92162	+	2.26714i	0.429687	+	0.506948i
$21$		0			0
$22$	2.45748	+	6.70006i	0.523936	+	1.42846i
$23$	−1.39593			−0.291072			−0.145536	−	0.989353i	$-0.546491\pi$
$23$	−1.39593			−0.291072			−0.145536	+	0.989353i	$0.546491\pi$
$24$	6.05137	+	3.43393i	1.23523	+	0.700948i
$25$	2.79186			0.558373
$26$	−1.25951	−	3.43393i	−0.247010	−	0.673449i
$27$		−	0.126378i		−	0.0243215i
$28$		0			0
$29$		−	0.638384i		−	0.118545i	−0.998242	−	0.0592725i	$-0.981122\pi$
$29$		−	0.638384i		−	0.118545i	0.998242	−	0.0592725i	$-0.0188781\pi$
$30$	−4.85341	+	1.78015i	−0.886107	+	0.325010i
$31$	3.65544			0.656537			0.328268	−	0.944584i	$-0.393535\pi$
$31$	3.65544			0.656537			0.328268	+	0.944584i	$0.393535\pi$
$32$	−1.05137	−	5.55829i	−0.185858	−	0.982577i
$33$	−12.4136			−2.16094
$34$	−1.67228	+	0.613365i	−0.286793	+	0.105191i
$35$		0			0
$36$	−4.65544	+	3.94593i	−0.775907	+	0.657656i
$37$		−	6.02026i		−	0.989725i	−0.868971	−	0.494862i	$-0.835218\pi$
$37$		−	6.02026i		−	0.989725i	0.868971	−	0.494862i	$-0.164782\pi$
$38$	−1.50885	−	4.11373i	−0.244768	−	0.667335i
$39$	6.36226			1.01878
$40$	3.65544	+	2.07433i	0.577976	+	0.327980i
$41$	−6.36226			−0.993618			−0.496809	−	0.867860i	$-0.665495\pi$
$41$	−6.36226			−0.993618			−0.496809	+	0.867860i	$0.665495\pi$
$42$		0			0
$43$			1.02401i			0.156160i	0.996947	+	0.0780801i	$0.0248790\pi$
$43$			1.02401i			0.156160i	−0.996947	+	0.0780801i	$0.975121\pi$
$44$	6.52569	+	7.69905i	0.983784	+	1.16068i
$45$		−	4.53428i		−	0.675931i
$46$	−1.85341	+	0.679801i	−0.273270	+	0.100231i
$47$	10.9663			1.59960			0.799802	−	0.600264i	$-0.204938\pi$
$47$	10.9663			1.59960			0.799802	+	0.600264i	$0.204938\pi$
$48$	9.70682	+	1.61236i	1.40106	+	0.232724i
$49$		0			0
$50$	3.70682	−	1.35960i	0.524223	−	0.192277i
$51$		−	3.09834i		−	0.433854i
$52$	−3.34456	−	3.94593i	−0.463807	−	0.547203i
$53$		−	5.76750i		−	0.792228i	−0.918201	−	0.396114i	$-0.870359\pi$
$53$		−	5.76750i		−	0.792228i	0.918201	−	0.396114i	$-0.129641\pi$
$54$	−0.0615446	−	0.167795i	−0.00837516	−	0.0228340i
$55$	−7.49868			−1.01112
$56$		0			0
$57$	7.62177			1.00953
$58$	−0.310885	−	0.847596i	−0.0408212	−	0.111295i
$59$		−	3.48397i		−	0.453574i	−0.973944	−	0.226787i	$-0.927178\pi$
$59$		−	3.48397i		−	0.453574i	0.973944	−	0.226787i	$-0.0728221\pi$
$60$	−5.57706	+	4.72709i	−0.719996	+	0.610265i
$61$		−	12.8881i		−	1.65015i	−0.565020	−	0.825077i	$-0.691132\pi$
$61$		−	12.8881i		−	1.65015i	0.565020	−	0.825077i	$-0.308868\pi$
$62$	4.85341	−	1.78015i	0.616383	−	0.226080i
$63$		0			0
$64$	−4.10275	−	6.86786i	−0.512844	−	0.858482i
$65$	3.84324			0.476695
$66$	−16.4818	+	6.04528i	−2.02877	+	0.744122i
$67$		−	0.512006i		−	0.0625515i	−0.999511	−	0.0312757i	$-0.990043\pi$
$67$		−	0.512006i		−	0.0625515i	0.999511	−	0.0312757i	$-0.00995700\pi$
$68$	−1.92162	+	1.62876i	−0.233031	+	0.197516i
$69$		−	3.43393i		−	0.413396i
$70$		0			0
$71$	−7.41363			−0.879836			−0.439918	−	0.898038i	$-0.644993\pi$
$71$	−7.41363			−0.879836			−0.439918	+	0.898038i	$0.644993\pi$
$72$	−4.25951	+	7.50624i	−0.501988	+	0.884619i
$73$	−9.89461			−1.15808			−0.579038	−	0.815300i	$-0.696572\pi$
$73$	−9.89461			−1.15808			−0.579038	+	0.815300i	$0.696572\pi$
$74$	−2.93179	−	7.99323i	−0.340814	−	0.929194i
$75$			6.86786i			0.793032i
$76$	−4.00667	−	4.72709i	−0.459596	−	0.542235i
$77$		0			0
$78$	8.44731	−	3.09834i	0.956469	−	0.350818i
$79$	8.70682			0.979593			0.489797	−	0.871837i	$-0.337071\pi$
$79$	8.70682			0.979593			0.489797	+	0.871837i	$0.337071\pi$
$80$	5.86358	+	0.973974i	0.655568	+	0.108894i
$81$	−8.84324			−0.982582
$82$	−8.44731	+	3.09834i	−0.932849	+	0.342154i
$83$		−	2.97196i		−	0.326215i	−0.986608	−	0.163107i	$-0.947848\pi$
$83$		−	2.97196i		−	0.326215i	0.986608	−	0.163107i	$-0.0521517\pi$
$84$		0			0
$85$		−	1.87161i		−	0.203004i
$86$	0.498680	+	1.35960i	0.0537741	+	0.146610i
$87$	1.57040			0.168364
$88$	12.4136	+	7.04427i	1.32330	+	0.750922i
$89$	2.58373			0.273875			0.136937	−	0.990580i	$-0.456274\pi$
$89$	2.58373			0.273875			0.136937	+	0.990580i	$0.456274\pi$
$90$	−2.20814	−	6.02026i	−0.232758	−	0.634591i
$91$		0			0
$92$	−2.12976	+	1.80517i	−0.222042	+	0.188202i
$93$			8.99222i			0.932450i
$94$	14.5602	−	5.34046i	1.50177	−	0.550826i
$95$	4.60407			0.472367
$96$	13.6731	−	2.58633i	1.39551	−	0.263966i
$97$	1.57040			0.159449			0.0797247	−	0.996817i	$-0.474596\pi$
$97$	1.57040			0.159449			0.0797247	+	0.996817i	$0.474596\pi$
$98$		0			0
$99$		−	15.3981i		−	1.54757i
$100$	4.25951	−	3.61034i	0.425951	−	0.361034i
$101$		−	0.209212i		−	0.0208174i	−0.999946	−	0.0104087i	$-0.996687\pi$
$101$		−	0.209212i		−	0.0208174i	0.999946	−	0.0104087i	$-0.00331325\pi$
$102$	−1.50885	−	4.11373i	−0.149398	−	0.407320i
$103$	−6.87691			−0.677602			−0.338801	−	0.940858i	$-0.610021\pi$
$103$	−6.87691			−0.677602			−0.338801	+	0.940858i	$0.610021\pi$
$104$	−6.36226	−	3.61034i	−0.623871	−	0.354023i
$105$		0			0
$106$	−2.80870	−	7.65764i	−0.272805	−	0.743776i
$107$			12.9382i			1.25078i	0.780313	+	0.625389i	$0.215060\pi$
$107$			12.9382i			1.25078i	−0.780313	+	0.625389i	$0.784940\pi$
$108$	−0.163428	−	0.192814i	−0.0157259	−	0.0185535i
$109$			19.2177i			1.84072i	0.391074	+	0.920359i	$0.372104\pi$
$109$			19.2177i			1.84072i	−0.391074	+	0.920359i	$0.627896\pi$
$110$	−9.95616	+	3.65176i	−0.949282	+	0.348182i
$111$	14.8096			1.40566
$112$		0			0
$113$	−1.05137			−0.0989050			−0.0494525	−	0.998776i	$-0.515748\pi$
$113$	−1.05137			−0.0989050			−0.0494525	+	0.998776i	$0.515748\pi$
$114$	10.1196	−	3.71170i	0.947786	−	0.347633i
$115$		−	2.07433i		−	0.193432i
$116$	−0.825537	−	0.973974i	−0.0766491	−	0.0904312i
$117$			7.89187i			0.729603i
$118$	−1.69665	−	4.62573i	−0.156189	−	0.425833i
$119$		0			0
$120$	−5.10275	+	8.99222i	−0.465815	+	0.820874i
$121$	−14.4650			−1.31500
$122$	−6.27635	−	17.1118i	−0.568234	−	1.54923i
$123$		−	15.6509i		−	1.41119i
$124$	5.57706	−	4.72709i	0.500835	−	0.424506i
$125$			11.5786i			1.03562i
$126$		0			0
$127$	−7.20814			−0.639619			−0.319809	−	0.947482i	$-0.603619\pi$
$127$	−7.20814			−0.639619			−0.319809	+	0.947482i	$0.603619\pi$
$128$	−8.79186	−	7.12061i	−0.777098	−	0.629379i
$129$	−2.51902			−0.221787
$130$	5.10275	−	1.87161i	0.447541	−	0.164151i
$131$			14.7532i			1.28900i	0.764606	+	0.644498i	$0.222934\pi$
$131$			14.7532i			1.28900i	−0.764606	+	0.644498i	$0.777066\pi$
$132$	−18.9393	+	16.0529i	−1.64846	+	1.39722i
$133$		0			0
$134$	−0.249340	−	0.679801i	−0.0215397	−	0.0587258i
$135$	0.187796			0.0161629
$136$	−1.75819	+	3.09834i	−0.150764	+	0.265680i
$137$	−9.36226			−0.799872			−0.399936	−	0.916543i	$-0.630968\pi$
$137$	−9.36226			−0.799872			−0.399936	+	0.916543i	$0.630968\pi$
$138$	−1.67228	−	4.55930i	−0.142354	−	0.388113i
$139$		−	1.69519i		−	0.143784i	−0.997412	−	0.0718921i	$-0.977096\pi$
$139$		−	1.69519i		−	0.143784i	0.997412	−	0.0718921i	$-0.0229037\pi$
$140$		0			0
$141$			26.9767i			2.27184i
$142$	−9.84324	+	3.61034i	−0.826026	+	0.302973i
$143$	13.0514			1.09141
$144$	−2.00000	+	12.0405i	−0.166667	+	1.00338i
$145$	0.948626			0.0787791
$146$	−13.1373	+	4.81855i	−1.08725	+	0.398786i
$147$		0			0
$148$	−7.78520	−	9.18503i	−0.639939	−	0.755005i
$149$			3.68668i			0.302025i	0.988532	+	0.151012i	$0.0482534\pi$
$149$			3.68668i			0.302025i	−0.988532	+	0.151012i	$0.951747\pi$
$150$	3.34456	+	9.11860i	0.273082	+	0.744530i
$151$	−14.2772			−1.16186			−0.580932	−	0.813952i	$-0.697312\pi$
$151$	−14.2772			−1.16186			−0.580932	+	0.813952i	$0.697312\pi$
$152$	−7.62177	−	4.32507i	−0.618207	−	0.350809i
$153$	3.84324			0.310707
$154$		0			0
$155$			5.43191i			0.436302i
$156$	9.70682	−	8.22746i	0.777167	−	0.658724i
$157$			12.8881i			1.02858i	0.857615	+	0.514292i	$0.171945\pi$
$157$			12.8881i			1.02858i	−0.857615	+	0.514292i	$0.828055\pi$
$158$	11.5602	−	4.24011i	0.919682	−	0.337325i
$159$	14.1878			1.12517
$160$	8.25951	−	1.56232i	0.652972	−	0.123512i
$161$		0			0
$162$	−11.7414	+	4.30654i	−0.922488	+	0.338354i
$163$		−	3.23121i		−	0.253088i	−0.991961	−	0.126544i	$-0.959612\pi$
$163$		−	3.23121i		−	0.253088i	0.991961	−	0.126544i	$-0.0403885\pi$
$164$	−9.70682	+	8.22746i	−0.757975	+	0.642457i
$165$		−	18.4464i		−	1.43605i
$166$	−1.44731	−	3.94593i	−0.112333	−	0.306264i
$167$	14.0487			1.08712			0.543562	−	0.839369i	$-0.317075\pi$
$167$	14.0487			1.08712			0.543562	+	0.839369i	$0.317075\pi$
$168$		0			0
$169$	6.31088			0.485453
$170$	−0.911449	−	2.48497i	−0.0699049	−	0.190589i
$171$			9.45419i			0.722980i
$172$	1.32422	+	1.56232i	0.100971	+	0.119126i
$173$		−	6.53876i		−	0.497133i	−0.968615	−	0.248566i	$-0.920041\pi$
$173$		−	6.53876i		−	0.497133i	0.968615	−	0.248566i	$-0.0799594\pi$
$174$	2.08505	−	0.764762i	0.158067	−	0.0579765i
$175$		0			0
$176$	19.9123	+	3.30755i	1.50095	+	0.249316i
$177$	8.57040			0.644190
$178$	3.43047	−	1.25824i	0.257125	−	0.0943092i
$179$		−	0.126378i		−	0.00944596i	−0.999989	−	0.00472298i	$-0.998497\pi$
$179$		−	0.126378i		−	0.00944596i	0.999989	−	0.00472298i	$-0.00150338\pi$
$180$	−5.86358	−	6.91789i	−0.437045	−	0.515629i
$181$		−	2.71920i		−	0.202117i	−0.994880	−	0.101058i	$-0.967777\pi$
$181$		−	2.71920i		−	0.202117i	0.994880	−	0.101058i	$-0.0322229\pi$
$182$		0			0
$183$	31.7042			2.34364
$184$	−1.94863	+	3.43393i	−0.143655	+	0.253153i
$185$	8.94599			0.657722
$186$	4.37910	+	11.9392i	0.321091	+	0.875422i
$187$		−	6.35585i		−	0.464786i
$188$	16.7312	−	14.1813i	1.22025	−	1.03428i
$189$		0			0
$190$	6.11292	−	2.24212i	0.443478	−	0.162661i
$191$	−2.44731			−0.177081			−0.0885404	−	0.996073i	$-0.528220\pi$
$191$	−2.44731			−0.177081			−0.0885404	+	0.996073i	$0.528220\pi$
$192$	16.8946	−	10.0926i	1.21926	−	0.728369i
$193$	3.94863			0.284228			0.142114	−	0.989850i	$-0.454610\pi$
$193$	3.94863			0.284228			0.142114	+	0.989850i	$0.454610\pi$
$194$	2.08505	−	0.764762i	0.149698	−	0.0549067i
$195$			9.45419i			0.677029i
$196$		0			0
$197$		−	19.5468i		−	1.39265i	−0.717727	−	0.696325i	$-0.754817\pi$
$197$		−	19.5468i		−	1.39265i	0.717727	−	0.696325i	$-0.245183\pi$
$198$	−7.49868	−	20.4444i	−0.532908	−	1.45292i
$199$	−20.7962			−1.47421			−0.737103	−	0.675780i	$-0.763807\pi$
$199$	−20.7962			−1.47421			−0.737103	+	0.675780i	$0.763807\pi$
$200$	3.89725	−	6.86786i	0.275577	−	0.485631i
$201$	1.25951			0.0888390
$202$	−0.101884	−	0.277775i	−0.00716850	−	0.0195442i
$203$		0			0
$204$	−4.00667	−	4.72709i	−0.280523	−	0.330963i
$205$		−	9.45419i		−	0.660309i
$206$	−9.13062	+	3.34897i	−0.636160	+	0.233334i
$207$	4.25951			0.296056
$208$	−10.2055	−	1.69519i	−0.707624	−	0.117540i
$209$	15.6351			1.08150
$210$		0			0
$211$			17.2132i			1.18500i	0.805569	+	0.592502i	$0.201860\pi$
$211$			17.2132i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$212$	−7.45834	−	8.79941i	−0.512241	−	0.604346i
$213$		−	18.2372i		−	1.24959i
$214$	6.30071	+	17.1783i	0.430708	+	1.17428i
$215$	−1.52166			−0.103776
$216$	−0.310885	−	0.176415i	−0.0211530	−	0.0120036i
$217$		0			0
$218$	9.35875	+	25.5157i	0.633855	+	1.72814i
$219$		−	24.3403i		−	1.64476i
$220$	−11.4406	+	9.69704i	−0.771328	+	0.653774i
$221$			3.25751i			0.219124i
$222$	19.6630	−	7.21207i	1.31969	−	0.484042i
$223$	−17.5164			−1.17298			−0.586492	−	0.809955i	$-0.699491\pi$
$223$	−17.5164			−1.17298			−0.586492	+	0.809955i	$0.699491\pi$
$224$		0			0
$225$	−8.51902			−0.567935
$226$	−1.39593	+	0.512006i	−0.0928560	+	0.0340581i
$227$			13.1909i			0.875512i	0.899094	+	0.437756i	$0.144227\pi$
$227$			13.1909i			0.875512i	−0.899094	+	0.437756i	$0.855773\pi$
$228$	11.6284	−	9.85621i	0.770112	−	0.652744i
$229$			17.1696i			1.13460i	0.823511	+	0.567301i	$0.192012\pi$
$229$			17.1696i			1.13460i	−0.823511	+	0.567301i	$0.807988\pi$
$230$	−1.01017	−	2.75413i	−0.0666087	−	0.181602i
$231$		0			0
$232$	−1.57040	−	0.891141i	−0.103102	−	0.0585062i
$233$	24.8786			1.62985			0.814927	−	0.579564i	$-0.196777\pi$
$233$	24.8786			1.62985			0.814927	+	0.579564i	$0.196777\pi$
$234$	3.84324	+	10.4782i	0.251240	+	0.684981i
$235$			16.2957i			1.06302i
$236$	−4.50535	−	5.31544i	−0.293273	−	0.346006i
$237$			21.4184i			1.39127i
$238$		0			0
$239$	−13.3242			−0.861872			−0.430936	−	0.902383i	$-0.641817\pi$
$239$	−13.3242			−0.861872			−0.430936	+	0.902383i	$0.641817\pi$
$240$	−2.39593	+	14.4241i	−0.154657	+	0.931074i
$241$	22.2435			1.43283			0.716416	−	0.697673i	$-0.245781\pi$
$241$	22.2435			1.43283			0.716416	+	0.697673i	$0.245781\pi$
$242$	−19.2055	+	7.04427i	−1.23458	+	0.452823i
$243$		−	22.1331i		−	1.41984i
$244$	−16.6665	−	19.6632i	−1.06696	−	1.25881i
$245$		0			0
$246$	−7.62177	−	20.7800i	−0.485946	−	1.32488i
$247$	−8.01333			−0.509876
$248$	5.10275	−	8.99222i	0.324025	−	0.571007i
$249$	7.31088			0.463308
$250$	5.63861	+	15.3731i	0.356617	+	0.972280i
$251$			27.4386i			1.73191i	0.500121	+	0.865955i	$0.333289\pi$
$251$			27.4386i			1.73191i	−0.500121	+	0.865955i	$0.666711\pi$
$252$		0			0
$253$		−	7.04427i		−	0.442870i
$254$	−9.57040	+	3.51027i	−0.600500	+	0.220254i
$255$	4.60407			0.288318
$256$	−15.1408	−	5.17266i	−0.946299	−	0.323292i
$257$	24.1895			1.50890			0.754451	−	0.656357i	$-0.227903\pi$
$257$	24.1895			1.50890			0.754451	+	0.656357i	$0.227903\pi$
$258$	−3.34456	+	1.22673i	−0.208223	+	0.0763729i
$259$		0			0
$260$	5.86358	−	4.96995i	0.363644	−	0.308223i
$261$			1.94795i			0.120575i
$262$	7.18463	+	19.5882i	0.443868	+	1.21016i
$263$	−10.8769			−0.670699			−0.335350	−	0.942094i	$-0.608854\pi$
$263$	−10.8769			−0.670699			−0.335350	+	0.942094i	$0.608854\pi$
$264$	−17.3286	+	30.5370i	−1.06650	+	1.87942i
$265$	8.57040			0.526475
$266$		0			0
$267$			6.35585i			0.388972i
$268$	−0.662108	−	0.781160i	−0.0404447	−	0.0477170i
$269$			24.0047i			1.46359i	0.681523	+	0.731796i	$0.261318\pi$
$269$			24.0047i			1.46359i	−0.681523	+	0.731796i	$0.738682\pi$
$270$	0.249340	−	0.0914540i	0.0151744	−	0.00556571i
$271$	−6.22320			−0.378032			−0.189016	−	0.981974i	$-0.560530\pi$
$271$	−6.22320			−0.378032			−0.189016	+	0.981974i	$0.560530\pi$
$272$	−0.825537	+	4.96995i	−0.0500555	+	0.301347i
$273$		0			0
$274$	−12.4305	+	4.55930i	−0.750952	+	0.275437i
$275$			14.0885i			0.849571i
$276$	−4.44064	−	5.23910i	−0.267295	−	0.315357i
$277$		−	28.0007i		−	1.68240i	−0.540726	−	0.841199i	$-0.681850\pi$
$277$		−	28.0007i		−	1.68240i	0.540726	−	0.841199i	$-0.318150\pi$
$278$	−0.825537	−	2.25074i	−0.0495124	−	0.134991i
$279$	−11.1541			−0.667780
$280$		0			0
$281$	−16.7112			−0.996906			−0.498453	−	0.866917i	$-0.666098\pi$
$281$	−16.7112			−0.996906			−0.498453	+	0.866917i	$0.666098\pi$
$282$	13.1373	+	35.8175i	0.782314	+	2.13290i
$283$		−	27.8506i		−	1.65554i	−0.561065	−	0.827772i	$-0.689608\pi$
$283$		−	27.8506i		−	1.65554i	0.561065	−	0.827772i	$-0.310392\pi$
$284$	−11.3109	+	9.58706i	−0.671178	+	0.568887i
$285$			11.3258i			0.670882i
$286$	17.3286	−	6.35585i	1.02466	−	0.375829i
$287$		0			0
$288$	3.20814	+	16.9604i	0.189041	+	0.999403i
$289$	−15.4136			−0.906684
$290$	1.25951	−	0.461969i	0.0739610	−	0.0271277i
$291$			3.86310i			0.226459i
$292$	−15.0961	+	12.7954i	−0.883431	+	0.748793i
$293$		−	20.1851i		−	1.17923i	−0.807685	−	0.589614i	$-0.799280\pi$
$293$		−	20.1851i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$294$		0			0
$295$	5.17710			0.301423
$296$	−14.8096	−	8.40387i	−0.860788	−	0.488465i
$297$	0.637741			0.0370055
$298$	1.79537	+	4.89489i	0.104003	+	0.283553i
$299$			3.61034i			0.208792i
$300$	8.88128	+	10.4782i	0.512761	+	0.604959i
$301$		0			0
$302$	−18.9562	+	6.95282i	−1.09080	+	0.400090i
$303$	0.514652			0.0295660
$304$	−12.2258	−	2.03078i	−0.701200	−	0.116473i
$305$	19.1515			1.09661
$306$	5.10275	−	1.87161i	0.291705	−	0.106993i
$307$		−	17.8844i		−	1.02071i	−0.859962	−	0.510357i	$-0.829513\pi$
$307$		−	17.8844i		−	1.02071i	0.859962	−	0.510357i	$-0.170487\pi$
$308$		0			0
$309$		−	16.9169i		−	0.962368i
$310$	2.64527	+	7.21207i	0.150241	+	0.409618i
$311$	1.43133			0.0811635			0.0405818	−	0.999176i	$-0.487079\pi$
$311$	1.43133			0.0811635			0.0405818	+	0.999176i	$0.487079\pi$
$312$	8.88128	−	15.6509i	0.502803	−	0.886056i
$313$	−4.85657			−0.274510			−0.137255	−	0.990536i	$-0.543828\pi$
$313$	−4.85657			−0.274510			−0.137255	+	0.990536i	$0.543828\pi$
$314$	6.27635	+	17.1118i	0.354195	+	0.965676i
$315$		0			0
$316$	13.2839	−	11.2594i	0.747277	−	0.633389i
$317$		−	11.2930i		−	0.634278i	−0.948379	−	0.317139i	$-0.897278\pi$
$317$		−	11.2930i		−	0.634278i	0.948379	−	0.317139i	$-0.102722\pi$
$318$	18.8374	−	6.90927i	1.05635	−	0.387453i
$319$	3.22147			0.180368
$320$	10.2055	−	6.09660i	0.570505	−	0.340810i
$321$	−31.8273			−1.77642
$322$		0			0
$323$			3.90239i			0.217135i
$324$	−13.4920	+	11.4358i	−0.749556	+	0.635321i
$325$		−	7.22069i		−	0.400532i
$326$	−1.57356	−	4.29014i	−0.0871513	−	0.237609i
$327$	−47.2746			−2.61429
$328$	−8.88128	+	15.6509i	−0.490387	+	0.864174i
$329$		0			0
$330$	−8.98316	−	24.4917i	−0.494507	−	1.34822i
$331$			23.8348i			1.31008i	0.755595	+	0.655039i	$0.227348\pi$
$331$			23.8348i			1.31008i	−0.755595	+	0.655039i	$0.772652\pi$
$332$	−3.84324	−	4.53428i	−0.210925	−	0.248851i
$333$			18.3701i			1.00667i
$334$	18.6528	−	6.84155i	1.02064	−	0.374353i
$335$	0.760830			0.0415686
$336$		0			0
$337$	16.4650			0.896906			0.448453	−	0.893806i	$-0.351975\pi$
$337$	16.4650			0.896906			0.448453	+	0.893806i	$0.351975\pi$
$338$	8.37910	−	3.07332i	0.455763	−	0.167167i
$339$		−	2.58633i		−	0.140470i
$340$	−2.42030	−	2.85549i	−0.131259	−	0.154861i
$341$			18.4464i			0.998929i
$342$	4.60407	+	12.5525i	0.248959	+	0.678763i
$343$		0			0
$344$	2.51902	+	1.42945i	0.135817	+	0.0770708i
$345$	5.10275			0.274723
$346$	−3.18429	−	8.68165i	−0.171189	−	0.466728i
$347$			3.21822i			0.172763i	0.996262	+	0.0863817i	$0.0275304\pi$
$347$			3.21822i			0.172763i	−0.996262	+	0.0863817i	$0.972470\pi$
$348$	2.39593	−	2.03078i	0.128435	−	0.108861i
$349$		−	22.8716i		−	1.22429i	−0.790747	−	0.612143i	$-0.790308\pi$
$349$		−	22.8716i		−	1.22429i	0.790747	−	0.612143i	$-0.209692\pi$
$350$		0			0
$351$	−0.326856			−0.0174463
$352$	28.0487	−	5.30554i	1.49500	−	0.282786i
$353$	−23.3216			−1.24128			−0.620641	−	0.784095i	$-0.713128\pi$
$353$	−23.3216			−1.24128			−0.620641	+	0.784095i	$0.713128\pi$
$354$	11.3791	−	4.17367i	0.604792	−	0.221828i
$355$		−	11.0165i		−	0.584696i
$356$	3.94196	−	3.34119i	0.208923	−	0.177083i
$357$		0			0
$358$	−0.0615446	−	0.167795i	−0.00325273	−	0.00886825i
$359$	−5.10976			−0.269683			−0.134841	−	0.990867i	$-0.543052\pi$
$359$	−5.10976			−0.269683			−0.134841	+	0.990867i	$0.543052\pi$
$360$	−11.1541	−	6.32955i	−0.587874	−	0.333596i
$361$	9.40030			0.494753
$362$	−1.32422	−	3.61034i	−0.0695993	−	0.189755i
$363$		−	35.5833i		−	1.86764i
$364$		0			0
$365$		−	14.7032i		−	0.769600i
$366$	42.0943	−	15.4395i	2.20030	−	0.807037i
$367$	−28.1559			−1.46972			−0.734862	−	0.678217i	$-0.762753\pi$
$367$	−28.1559			−1.46972			−0.734862	+	0.678217i	$0.762753\pi$
$368$	−0.914953	+	5.50826i	−0.0476952	+	0.287138i
$369$	19.4136			1.01063
$370$	11.8778	−	4.35658i	0.617496	−	0.226488i
$371$		0			0
$372$	11.6284	+	13.7193i	0.602906	+	0.711313i
$373$			7.04427i			0.364739i	0.983230	+	0.182369i	$0.0583766\pi$
$373$			7.04427i			0.364739i	−0.983230	+	0.182369i	$0.941623\pi$
$374$	−3.09522	−	8.43880i	−0.160050	−	0.436360i
$375$	−28.4827			−1.47084
$376$	15.3082	−	26.9767i	0.789462	−	1.39122i
$377$	−1.65107			−0.0850346
$378$		0			0
$379$		−	13.1974i		−	0.677905i	−0.940803	−	0.338953i	$-0.889927\pi$
$379$		−	13.1974i		−	0.677905i	0.940803	−	0.338953i	$-0.110073\pi$
$380$	7.02437	−	5.95383i	0.360342	−	0.305425i
$381$		−	17.7317i		−	0.908422i
$382$	−3.24934	+	1.19181i	−0.166251	+	0.0609781i
$383$	4.93092			0.251958			0.125979	−	0.992033i	$-0.459793\pi$
$383$	4.93092			0.251958			0.125979	+	0.992033i	$0.459793\pi$
$384$	17.5164	−	21.6276i	0.893879	−	1.10368i
$385$		0			0
$386$	5.24267	−	1.92293i	0.266845	−	0.0978746i
$387$		−	3.12464i		−	0.158834i
$388$	2.39593	−	2.03078i	0.121635	−	0.103097i
$389$			22.9479i			1.16350i	0.813366	+	0.581752i	$0.197633\pi$
$389$			22.9479i			1.16350i	−0.813366	+	0.581752i	$0.802367\pi$
$390$	4.60407	+	12.5525i	0.233136	+	0.635622i
$391$	1.75819			0.0889155
$392$		0			0
$393$	−36.2923			−1.83070
$394$	−9.51902	−	25.9527i	−0.479561	−	1.30748i
$395$			12.9382i			0.650989i
$396$	−19.9123	−	23.4927i	−1.00063	−	1.18055i
$397$		−	29.9158i		−	1.50143i	−0.660625	−	0.750716i	$-0.729709\pi$
$397$		−	29.9158i		−	1.50143i	0.660625	−	0.750716i	$-0.270291\pi$
$398$	−27.6116	+	10.1275i	−1.38404	+	0.507646i
$399$		0			0
$400$	1.82991	−	11.0165i	0.0914953	−	0.550826i
$401$	−15.6705			−0.782548			−0.391274	−	0.920274i	$-0.627965\pi$
$401$	−15.6705			−0.782548			−0.391274	+	0.920274i	$0.627965\pi$
$402$	1.67228	−	0.613365i	0.0834057	−	0.0305919i
$403$		−	9.45419i		−	0.470947i
$404$	−0.270546	−	0.319192i	−0.0134602	−	0.0158804i
$405$		−	13.1409i		−	0.652975i
$406$		0			0
$407$	30.3800			1.50588
$408$	−7.62177	−	4.32507i	−0.377334	−	0.214123i
$409$	26.0868			1.28991			0.644954	−	0.764221i	$-0.276876\pi$
$409$	26.0868			1.28991			0.644954	+	0.764221i	$0.276876\pi$
$410$	−4.60407	−	12.5525i	−0.227379	−	0.619925i
$411$		−	23.0307i		−	1.13602i
$412$	−10.4920	+	8.89299i	−0.516904	+	0.438126i
$413$		0			0
$414$	5.65544	−	2.07433i	0.277950	−	0.101948i
$415$	4.41627			0.216786
$416$	−14.3756	+	2.71920i	−0.704821	+	0.133320i
$417$	4.17009			0.204210
$418$	20.7591	−	7.61409i	1.01536	−	0.372417i
$419$		−	0.252757i		−	0.0123480i	−0.999981	−	0.00617398i	$-0.998035\pi$
$419$		−	0.252757i		−	0.0123480i	0.999981	−	0.00617398i	$-0.00196525\pi$
$420$		0			0
$421$			18.3701i			0.895302i	0.894208	+	0.447651i	$0.147739\pi$
$421$			18.3701i			0.895302i	−0.894208	+	0.447651i	$0.852261\pi$
$422$	8.38260	+	22.8543i	0.408059	+	1.11253i
$423$	−33.4624			−1.62700
$424$	−14.1878	−	8.05104i	−0.689020	−	0.390993i
$425$	−3.51638			−0.170570
$426$	−8.88128	−	24.2139i	−0.430299	−	1.17317i
$427$		0			0
$428$	16.7312	+	19.7396i	0.808732	+	0.954148i
$429$			32.1058i			1.55008i
$430$	−2.02034	+	0.741029i	−0.0974295	+	0.0357356i
$431$	27.4447			1.32196			0.660982	−	0.750402i	$-0.270140\pi$
$431$	27.4447			1.32196			0.660982	+	0.750402i	$0.270140\pi$
$432$	−0.498680	−	0.0828337i	−0.0239928	−	0.00398534i
$433$	7.26215			0.348997			0.174498	−	0.984657i	$-0.444170\pi$
$433$	7.26215			0.348997			0.174498	+	0.984657i	$0.444170\pi$
$434$		0			0
$435$			2.33358i			0.111886i
$436$	24.8516	+	29.3201i	1.19018	+	1.40418i
$437$			4.32507i			0.206896i
$438$	−11.8534	−	32.3171i	−0.566378	−	1.54417i
$439$	−30.0044			−1.43203			−0.716015	−	0.698085i	$-0.754036\pi$
$439$	−30.0044			−1.43203			−0.716015	+	0.698085i	$0.754036\pi$
$440$	−10.4676	+	18.4464i	−0.499025	+	0.879398i
$441$		0			0
$442$	1.58637	+	4.32507i	0.0754558	+	0.205723i
$443$		−	35.0842i		−	1.66690i	−0.552593	−	0.833451i	$-0.686362\pi$
$443$		−	35.0842i		−	1.66690i	0.552593	−	0.833451i	$-0.313638\pi$
$444$	22.5948	−	19.1512i	1.07230	−	0.908877i
$445$			3.83937i			0.182003i
$446$	−23.2569	+	8.53025i	−1.10124	+	0.403919i
$447$	−9.06908			−0.428953
$448$		0			0
$449$	−21.0107			−0.991556			−0.495778	−	0.868449i	$-0.665117\pi$
$449$	−21.0107			−0.991556			−0.495778	+	0.868449i	$0.665117\pi$
$450$	−11.3109	+	4.14865i	−0.533200	+	0.195569i
$451$		−	32.1058i		−	1.51180i
$452$	−1.60407	+	1.35960i	−0.0754490	+	0.0639503i
$453$		−	35.1213i		−	1.65014i
$454$	6.42380	+	17.5139i	0.301484	+	0.821966i
$455$		0			0
$456$	10.6395	−	18.7492i	0.498239	−	0.878012i
$457$	13.3756			0.625684			0.312842	−	0.949805i	$-0.398719\pi$
$457$	13.3756			0.625684			0.312842	+	0.949805i	$0.398719\pi$
$458$	8.36139	+	22.7965i	0.390702	+	1.06521i
$459$			0.159175i			0.00742964i
$460$	−2.68245	−	3.16477i	−0.125070	−	0.147558i
$461$			2.68641i			0.125118i	0.998041	+	0.0625592i	$0.0199262\pi$
$461$			2.68641i			0.125118i	−0.998041	+	0.0625592i	$0.980074\pi$
$462$		0			0
$463$	−21.0380			−0.977721			−0.488860	−	0.872362i	$-0.662587\pi$
$463$	−21.0380			−0.977721			−0.488860	+	0.872362i	$0.662587\pi$
$464$	−2.51902	−	0.418424i	−0.116943	−	0.0194248i
$465$	−13.3623			−0.619660
$466$	33.0319	−	12.1156i	1.53017	−	0.561243i
$467$			24.6931i			1.14266i	0.820720	+	0.571331i	$0.193573\pi$
$467$			24.6931i			1.14266i	−0.820720	+	0.571331i	$0.806427\pi$
$468$	10.2055	+	12.0405i	0.471749	+	0.556573i
$469$		0			0
$470$	7.93582	+	21.6362i	0.366052	+	0.998004i
$471$	−31.7042			−1.46085
$472$	−8.57040	−	4.86338i	−0.394484	−	0.223855i
$473$	−5.16745			−0.237600
$474$	10.4305	+	28.4376i	0.479087	+	1.30618i
$475$		−	8.65014i		−	0.396896i
$476$		0			0
$477$			17.5988i			0.805794i
$478$	−17.6908	+	6.48872i	−0.809160	+	0.296787i
$479$	40.9123			1.86933			0.934666	−	0.355528i	$-0.115699\pi$
$479$	40.9123			1.86933			0.934666	+	0.355528i	$0.115699\pi$
$480$	3.84324	+	20.3180i	0.175419	+	0.927386i
$481$	−15.5704			−0.709949
$482$	29.5332	−	10.8323i	1.34520	−	0.493399i
$483$		0			0
$484$	−22.0691	+	18.7057i	−1.00314	+	0.850257i
$485$			2.33358i			0.105962i
$486$	−10.7785	−	29.3866i	−0.488924	−	1.33300i
$487$	17.5341			0.794545			0.397273	−	0.917701i	$-0.369957\pi$
$487$	17.5341			0.794545			0.397273	+	0.917701i	$0.369957\pi$
$488$	−31.7042	−	17.9909i	−1.43518	−	0.814411i
$489$	7.94863			0.359449
$490$		0			0
$491$		−	15.7509i		−	0.710830i	−0.934709	−	0.355415i	$-0.884340\pi$
$491$		−	15.7509i		−	0.710830i	0.934709	−	0.355415i	$-0.115660\pi$
$492$	−20.2392	−	23.8783i	−0.912452	−	1.07652i
$493$			0.804051i			0.0362127i
$494$	−10.6395	+	3.90239i	−0.478692	+	0.175577i
$495$	22.8813			1.02844
$496$	2.39593	−	14.4241i	0.107581	−	0.647663i
$497$		0			0
$498$	9.70682	−	3.56031i	0.434973	−	0.159541i
$499$		−	10.1862i		−	0.455995i	−0.973662	−	0.227997i	$-0.926782\pi$
$499$		−	10.1862i		−	0.455995i	0.973662	−	0.227997i	$-0.0732178\pi$
$500$	14.9730	+	17.6652i	0.669613	+	0.790014i
$501$			34.5592i			1.54399i
$502$	13.3623	+	36.4309i	0.596387	+	1.62599i
$503$	−27.1001			−1.20833			−0.604167	−	0.796858i	$-0.706494\pi$
$503$	−27.1001			−1.20833			−0.604167	+	0.796858i	$0.706494\pi$
$504$		0			0
$505$	0.310885			0.0138342
$506$	−3.43047	−	9.35283i	−0.152503	−	0.415784i
$507$			15.5245i			0.689467i
$508$	−10.9974	+	9.32132i	−0.487929	+	0.413567i
$509$			22.4424i			0.994741i	0.867538	+	0.497371i	$0.165701\pi$
$509$			22.4424i			0.994741i	−0.867538	+	0.497371i	$0.834299\pi$
$510$	6.11292	−	2.24212i	0.270685	−	0.0992828i
$511$		0			0
$512$	−22.6218	+	0.505513i	−0.999750	+	0.0223407i
$513$	−0.391563			−0.0172879
$514$	32.1169	−	11.7800i	1.41662	−	0.519593i
$515$		−	10.2190i		−	0.450301i
$516$	−3.84324	+	3.25751i	−0.169189	+	0.143404i
$517$			55.3392i			2.43382i
$518$		0			0
$519$	16.0850			0.706055
$520$	5.36490	−	9.45419i	0.235266	−	0.414594i
$521$	10.2702			0.449946			0.224973	−	0.974365i	$-0.427771\pi$
$521$	10.2702			0.449946			0.224973	+	0.974365i	$0.427771\pi$
$522$	0.948626	+	2.58633i	0.0415202	+	0.113201i
$523$			17.8581i			0.780879i	0.920629	+	0.390439i	$0.127677\pi$
$523$			17.8581i			0.780879i	−0.920629	+	0.390439i	$0.872323\pi$
$524$	19.0784	+	22.5088i	0.833443	+	0.983302i
$525$		0			0
$526$	−14.4415	+	5.29692i	−0.629680	+	0.230956i
$527$	−4.60407			−0.200556
$528$	−8.13642	+	48.9834i	−0.354092	+	2.13173i
$529$	−21.0514			−0.915277
$530$	11.3791	−	4.17367i	0.494276	−	0.181293i
$531$			10.6309i			0.461341i
$532$		0			0
$533$			16.4549i			0.712742i
$534$	3.09522	+	8.43880i	0.133943	+	0.365183i
$535$	−19.2258			−0.831205
$536$	−1.25951	−	0.714725i	−0.0544026	−	0.0308714i
$537$	0.310885			0.0134157
$538$	11.6900	+	31.8716i	0.503991	+	1.37408i
$539$		0			0
$540$	0.286517	−	0.242851i	0.0123297	−	0.0104506i
$541$		−	23.0135i		−	0.989427i	−0.869056	−	0.494714i	$-0.835273\pi$
$541$		−	23.0135i		−	0.989427i	0.869056	−	0.494714i	$-0.164727\pi$
$542$	−8.26267	+	3.03062i	−0.354912	+	0.130176i
$543$	6.68912			0.287057
$544$	1.32422	+	7.00073i	0.0567753	+	0.300154i
$545$	−28.5571			−1.22325
$546$		0			0
$547$		−	9.10136i		−	0.389146i	−0.980888	−	0.194573i	$-0.937668\pi$
$547$		−	9.10136i		−	0.389146i	0.980888	−	0.194573i	$-0.0623321\pi$
$548$	−14.2839	+	12.1070i	−0.610177	+	0.517184i
$549$			39.3265i			1.67841i
$550$	6.86094	+	18.7057i	0.292551	+	0.797612i
$551$	−1.97793			−0.0842626
$552$	−8.44731	−	4.79353i	−0.359541	−	0.204026i
$553$		0			0
$554$	−13.6360	−	37.1771i	−0.579337	−	1.57950i
$555$			22.0067i			0.934133i
$556$	−2.19216	−	2.58633i	−0.0929685	−	0.109685i
$557$		−	17.3223i		−	0.733970i	−0.930227	−	0.366985i	$-0.880390\pi$
$557$		−	17.3223i		−	0.733970i	0.930227	−	0.366985i	$-0.119610\pi$
$558$	−14.8096	+	5.43191i	−0.626939	+	0.229951i
$559$	2.64843			0.112017
$560$		0			0
$561$	15.6351			0.660115
$562$	−22.1878	+	8.13813i	−0.935936	+	0.343286i
$563$		−	7.98545i		−	0.336547i	−0.985740	−	0.168273i	$-0.946181\pi$
$563$		−	7.98545i		−	0.336547i	0.985740	−	0.168273i	$-0.0538191\pi$
$564$	34.8853	+	41.1579i	1.46894	+	1.73306i
$565$		−	1.56232i		−	0.0657273i
$566$	−13.5629	−	36.9778i	−0.570090	−	1.55429i
$567$		0			0
$568$	−10.3489	+	18.2372i	−0.434231	+	0.765216i
$569$	11.9707			0.501838			0.250919	−	0.968008i	$-0.419267\pi$
$569$	11.9707			0.501838			0.250919	+	0.968008i	$0.419267\pi$
$570$	5.51552	+	15.0375i	0.231020	+	0.629852i
$571$		−	42.6103i		−	1.78318i	−0.452839	−	0.891592i	$-0.649589\pi$
$571$		−	42.6103i		−	1.78318i	0.452839	−	0.891592i	$-0.350411\pi$
$572$	19.9123	−	16.8776i	0.832576	−	0.705688i
$573$		−	6.02026i		−	0.251500i
$574$		0			0
$575$	−3.89725			−0.162527
$576$	12.5190	+	20.9564i	0.521626	+	0.873183i
$577$	29.9300			1.24600			0.623001	−	0.782221i	$-0.285913\pi$
$577$	29.9300			1.24600			0.623001	+	0.782221i	$0.285913\pi$
$578$	−20.4650	+	7.50624i	−0.851232	+	0.312218i
$579$			9.71344i			0.403677i
$580$	1.44731	−	1.22673i	0.0600961	−	0.0509372i
$581$		0			0
$582$	1.88128	+	5.12912i	0.0779816	+	0.212609i
$583$	29.1045			1.20538
$584$	−13.8122	+	24.3403i	−0.571553	+	1.00721i
$585$	−11.7272			−0.484858
$586$	−9.82991	−	26.8002i	−0.406070	−	1.10711i
$587$		−	19.4269i		−	0.801833i	−0.916115	−	0.400916i	$-0.868692\pi$
$587$		−	19.4269i		−	0.801833i	0.916115	−	0.400916i	$-0.131308\pi$
$588$		0			0
$589$		−	11.3258i		−	0.466671i
$590$	6.87375	−	2.52118i	0.282988	−	0.103795i
$591$	48.0841			1.97792
$592$	−23.7556	−	3.94593i	−0.976347	−	0.162177i
$593$	18.1541			0.745500			0.372750	−	0.927932i	$-0.378415\pi$
$593$	18.1541			0.745500			0.372750	+	0.927932i	$0.378415\pi$
$594$	0.846742	−	0.310572i	0.0347423	−	0.0127429i
$595$		0			0
$596$	4.76750	+	5.62473i	0.195284	+	0.230398i
$597$		−	51.1578i		−	2.09375i
$598$	1.75819	+	4.79353i	0.0718978	+	0.196022i
$599$	11.1852			0.457013			0.228507	−	0.973542i	$-0.426616\pi$
$599$	11.1852			0.457013			0.228507	+	0.973542i	$0.426616\pi$
$600$	16.8946	+	9.58706i	0.689720	+	0.391390i
$601$	4.21883			0.172090			0.0860448	−	0.996291i	$-0.472577\pi$
$601$	4.21883			0.172090			0.0860448	+	0.996291i	$0.472577\pi$
$602$		0			0
$603$			1.56232i			0.0636226i
$604$	−21.7826	+	18.4628i	−0.886320	+	0.751241i
$605$		−	21.4947i		−	0.873884i
$606$	0.683314	−	0.250629i	0.0277577	−	0.0101811i
$607$	27.2392			1.10560			0.552802	−	0.833313i	$-0.313559\pi$
$607$	27.2392			1.10560			0.552802	+	0.833313i	$0.313559\pi$
$608$	−17.2215	+	3.25751i	−0.698423	+	0.132110i
$609$		0			0
$610$	25.4278	−	9.32653i	1.02954	−	0.377620i
$611$		−	28.3626i		−	1.14743i
$612$	5.86358	−	4.96995i	0.237021	−	0.200898i
$613$			3.69967i			0.149428i	0.997205	+	0.0747141i	$0.0238044\pi$
$613$			3.69967i			0.149428i	−0.997205	+	0.0747141i	$0.976196\pi$
$614$	−8.70946	−	23.7455i	−0.351485	−	0.958288i
$615$	23.2569			0.937808
$616$		0			0
$617$	26.0487			1.04868			0.524341	−	0.851508i	$-0.324312\pi$
$617$	26.0487			1.04868			0.524341	+	0.851508i	$0.324312\pi$
$618$	−8.23830	−	22.4609i	−0.331393	−	0.903510i
$619$			32.0795i			1.28938i	0.764443	+	0.644692i	$0.223014\pi$
$619$			32.0795i			1.28938i	−0.764443	+	0.644692i	$0.776986\pi$
$620$	7.02437	+	8.28740i	0.282105	+	0.332830i
$621$			0.176415i			0.00707931i
$622$	1.90041	−	0.697042i	0.0761996	−	0.0279488i
$623$		0			0
$624$	4.17009	−	25.1051i	0.166937	−	1.00501i
$625$	−3.24618			−0.129847
$626$	−6.44817	+	2.36509i	−0.257721	+	0.0945279i
$627$			38.4616i			1.53601i
$628$	16.6665	+	19.6632i	0.665065	+	0.784648i
$629$			7.58258i			0.302337i
$630$		0			0
$631$	11.7538			0.467912			0.233956	−	0.972247i	$-0.424833\pi$
$631$	11.7538			0.467912			0.233956	+	0.972247i	$0.424833\pi$
$632$	12.1541	−	21.4184i	0.483465	−	0.851977i
$633$	−42.3436			−1.68301
$634$	−5.49955	−	14.9940i	−0.218415	−	0.595486i
$635$		−	10.7111i		−	0.425059i
$636$	21.6461	−	18.3472i	0.858325	−	0.727513i
$637$		0			0
$638$	4.27721	−	1.56881i	0.169336	−	0.0621099i
$639$	22.6218			0.894903
$640$	10.5811	−	13.0645i	0.418254	−	0.516421i
$641$	41.8273			1.65208			0.826039	−	0.563613i	$-0.190589\pi$
$641$	41.8273			1.65208			0.826039	+	0.563613i	$0.190589\pi$
$642$	−42.2577	+	15.4995i	−1.66778	+	0.611715i
$643$			42.9368i			1.69326i	0.532180	+	0.846631i	$0.321373\pi$
$643$			42.9368i			1.69326i	−0.532180	+	0.846631i	$0.678627\pi$
$644$		0			0
$645$		−	3.74321i		−	0.147389i
$646$	1.90041	+	5.18129i	0.0747708	+	0.203855i
$647$	9.11781			0.358458			0.179229	−	0.983807i	$-0.442640\pi$
$647$	9.11781			0.358458			0.179229	+	0.983807i	$0.442640\pi$
$648$	−12.3446	+	21.7540i	−0.484940	+	0.854576i
$649$	17.5811			0.690118
$650$	−3.51638	−	9.58706i	−0.137924	−	0.376035i
$651$		0			0
$652$	−4.17849	−	4.92981i	−0.163642	−	0.193066i
$653$			21.7910i			0.852748i	0.904547	+	0.426374i	$0.140209\pi$
$653$			21.7910i			0.852748i	−0.904547	+	0.426374i	$0.859791\pi$
$654$	−62.7675	+	23.0221i	−2.45440	+	0.900236i
$655$	−21.9230			−0.856603
$656$	−4.17009	+	25.1051i	−0.162815	+	0.980188i
$657$	30.1922			1.17791
$658$		0			0
$659$		−	0.152682i		−	0.00594765i	−0.999996	−	0.00297383i	$-0.999053\pi$
$659$		−	0.152682i		−	0.00594765i	0.999996	−	0.00297383i	$-0.000946600\pi$
$660$	−23.8543	−	28.1434i	−0.928526	−	1.09548i
$661$			28.4061i			1.10487i	0.833556	+	0.552435i	$0.186301\pi$
$661$			28.4061i			1.10487i	−0.833556	+	0.552435i	$0.813699\pi$
$662$	11.6072	+	31.6459i	0.451128	+	1.22995i
$663$	−8.01333			−0.311212
$664$	−7.31088	−	4.14865i	−0.283717	−	0.160999i
$665$		0			0
$666$	8.94599	+	24.3903i	0.346650	+	0.945106i
$667$			0.891141i			0.0345051i
$668$	21.4340	−	18.1673i	0.829305	−	0.702916i
$669$		−	43.0895i		−	1.66594i
$670$	1.01017	−	0.370514i	0.0390263	−	0.0143142i
$671$	65.0371			2.51073
$672$		0			0
$673$	26.2542			1.01203			0.506013	−	0.862526i	$-0.331119\pi$
$673$	26.2542			1.01203			0.506013	+	0.862526i	$0.331119\pi$
$674$	21.8609	−	8.01825i	0.842052	−	0.308851i
$675$		−	0.352831i		−	0.0135805i
$676$	9.62844	−	8.16102i	0.370324	−	0.313885i
$677$		−	4.62361i		−	0.177700i	−0.996045	−	0.0888498i	$-0.971681\pi$
$677$		−	4.62361i		−	0.177700i	0.996045	−	0.0888498i	$-0.0283191\pi$
$678$	−1.25951	−	3.43393i	−0.0483712	−	0.131879i
$679$		0			0
$680$	−4.60407	−	2.61264i	−0.176558	−	0.100190i
$681$	−32.4490			−1.24345
$682$	8.98316	+	24.4917i	0.343983	+	0.937835i
$683$			19.4532i			0.744355i	0.928162	+	0.372178i	$0.121389\pi$
$683$			19.4532i			0.744355i	−0.928162	+	0.372178i	$0.878611\pi$
$684$	12.2258	+	14.4241i	0.467467	+	0.551521i
$685$		−	13.9121i		−	0.531555i
$686$		0			0
$687$	−42.2365			−1.61142
$688$	4.04068	+	0.671180i	0.154050	+	0.0255885i
$689$	−14.9167			−0.568280
$690$	6.77503	−	2.48497i	0.257921	−	0.0946013i
$691$			17.3724i			0.660876i	0.943828	+	0.330438i	$0.107196\pi$
$691$			17.3724i			0.660876i	−0.943828	+	0.330438i	$0.892804\pi$
$692$	−8.45570	−	9.97610i	−0.321438	−	0.379234i
$693$		0			0
$694$	1.56723	+	4.27290i	0.0594914	+	0.162197i
$695$	2.51902			0.0955519
$696$	2.19216	−	3.86310i	0.0830938	−	0.146430i
$697$	8.01333			0.303527
$698$	−11.1382	−	30.3670i	−0.421585	−	1.14941i
$699$			61.2003i			2.31481i
$700$		0			0
$701$		−	25.1180i		−	0.948695i	−0.880338	−	0.474348i	$-0.842684\pi$
$701$		−	25.1180i		−	0.948695i	0.880338	−	0.474348i	$-0.157316\pi$
$702$	−0.433974	+	0.159175i	−0.0163793	+	0.00600766i
$703$	−18.6528			−0.703504
$704$	34.6572	−	20.7036i	1.30619	−	0.780298i
$705$	−40.0868			−1.50976
$706$	−30.9646	+	11.3573i	−1.16537	+	0.427438i
$707$		0			0
$708$	13.0757	−	11.0829i	0.491416	−	0.416523i
$709$			20.1088i			0.755202i	0.925968	+	0.377601i	$0.123251\pi$
$709$			20.1088i			0.755202i	−0.925968	+	0.377601i	$0.876749\pi$
$710$	−5.36490	−	14.6269i	−0.201341	−	0.548936i
$711$	−26.5678			−0.996369
$712$	3.60671	−	6.35585i	0.135167	−	0.238196i
$713$	−5.10275			−0.191099
$714$		0			0
$715$			19.3941i			0.725297i
$716$	−0.163428	−	0.192814i	−0.00610760	−	0.00720579i
$717$		−	32.7770i		−	1.22408i
$718$	−6.78433	+	2.48839i	−0.253189	+	0.0928657i
$719$	38.3933			1.43183			0.715914	−	0.698188i	$-0.246010\pi$
$719$	38.3933			1.43183			0.715914	+	0.698188i	$0.246010\pi$
$720$	−17.8920	−	2.97196i	−0.666794	−	0.110758i
$721$		0			0
$722$	12.4810	−	4.57783i	0.464494	−	0.170369i
$723$			54.7181i			2.03499i
$724$	−3.51638	−	4.14865i	−0.130685	−	0.154183i
$725$		−	1.78228i		−	0.0661923i
$726$	−17.3286	−	47.2446i	−0.643124	−	1.75341i
$727$	−14.8679			−0.551422			−0.275711	−	0.961241i	$-0.588913\pi$
$727$	−14.8679			−0.551422			−0.275711	+	0.961241i	$0.588913\pi$
$728$		0			0
$729$	27.9167			1.03395
$730$	−7.16027	−	19.5217i	−0.265013	−	0.722532i
$731$		−	1.28975i		−	0.0477032i
$732$	48.3707	−	40.9988i	1.78783	−	1.51536i
$733$			42.0892i			1.55460i	0.629130	+	0.777300i	$0.283411\pi$
$733$			42.0892i			1.55460i	−0.629130	+	0.777300i	$0.716589\pi$
$734$	−37.3831	+	13.7115i	−1.37984	+	0.506102i
$735$		0			0
$736$	1.46765	+	7.75900i	0.0540982	+	0.286000i
$737$	2.58373			0.0951728
$738$	25.7759	−	9.45419i	0.948824	−	0.348014i
$739$		−	12.6854i		−	0.466640i	−0.972400	−	0.233320i	$-0.925041\pi$
$739$		−	12.6854i		−	0.466640i	0.972400	−	0.233320i	$-0.0749589\pi$
$740$	13.6488	−	11.5686i	0.501739	−	0.425272i
$741$		−	19.7124i		−	0.724154i
$742$		0			0
$743$	−25.7219			−0.943644			−0.471822	−	0.881694i	$-0.656404\pi$
$743$	−25.7219			−0.943644			−0.471822	+	0.881694i	$0.656404\pi$
$744$	22.1204	+	12.5525i	0.810975	+	0.460198i
$745$	−5.47834			−0.200711
$746$	3.43047	+	9.35283i	0.125598	+	0.342431i
$747$			9.06856i			0.331801i
$748$	−8.21917	−	9.69704i	−0.300523	−	0.354559i
$749$		0			0
$750$	−37.8171	+	13.8707i	−1.38089	+	0.506487i
$751$	35.8609			1.30858			0.654292	−	0.756242i	$-0.272967\pi$
$751$	35.8609			1.30858			0.654292	+	0.756242i	$0.272967\pi$
$752$	7.18780	−	43.2724i	0.262112	−	1.57798i
$753$	−67.4978			−2.45976
$754$	−2.19216	+	0.804051i	−0.0798339	+	0.0292818i
$755$		−	21.2157i		−	0.772117i
$756$		0			0
$757$			30.7289i			1.11686i	0.829551	+	0.558431i	$0.188597\pi$
$757$			30.7289i			1.11686i	−0.829551	+	0.558431i	$0.811403\pi$
$758$	−6.42697	−	17.5225i	−0.233438	−	0.636445i
$759$	17.3286			0.628988
$760$	6.42697	−	11.3258i	0.233131	−	0.410830i
$761$	−45.1248			−1.63577			−0.817887	−	0.575379i	$-0.804854\pi$
$761$	−45.1248			−1.63577			−0.817887	+	0.575379i	$0.804854\pi$
$762$	−8.63510	−	23.5427i	−0.312817	−	0.852863i
$763$		0			0
$764$	−3.73382	+	3.16477i	−0.135085	+	0.114497i
$765$			5.71097i			0.206481i
$766$	6.54689	−	2.40130i	0.236549	−	0.0867624i
$767$	−9.01069			−0.325357
$768$	12.7245	−	37.2457i	0.459156	−	1.34399i
$769$	28.0168			1.01031			0.505156	−	0.863028i	$-0.331435\pi$
$769$	28.0168			1.01031			0.505156	+	0.863028i	$0.331435\pi$
$770$		0			0
$771$			59.5051i			2.14302i
$772$	6.02437	−	5.10623i	0.216822	−	0.183777i
$773$		−	34.6356i		−	1.24576i	−0.782319	−	0.622878i	$-0.785963\pi$
$773$		−	34.6356i		−	1.24576i	0.782319	−	0.622878i	$-0.214037\pi$
$774$	−1.52166	−	4.14865i	−0.0546950	−	0.149120i
$775$	10.2055			0.366592
$776$	2.19216	−	3.86310i	0.0786941	−	0.138677i
$777$		0			0
$778$	11.1753	+	30.4684i	0.400655	+	1.09235i
$779$			19.7124i			0.706271i
$780$	12.2258	+	14.4241i	0.437755	+	0.516467i
$781$		−	37.4113i		−	1.33868i
$782$	2.33439	−	0.856216i	0.0834775	−	0.0306182i
$783$	−0.0806779			−0.00288319
$784$		0			0
$785$	−19.1515			−0.683546
$786$	−48.1860	+	17.6739i	−1.71874	+	0.630406i
$787$			34.2672i			1.22149i	0.791826	+	0.610747i	$0.209131\pi$
$787$			34.2672i			1.22149i	−0.791826	+	0.610747i	$0.790869\pi$
$788$	−25.2772	−	29.8222i	−0.900463	−	1.06237i
$789$		−	26.7567i		−	0.952564i
$790$	6.30071	+	17.1783i	0.224169	+	0.611175i
$791$		0			0
$792$	−37.8786	−	21.4947i	−1.34596	−	0.763781i
$793$	−33.3330			−1.18369
$794$	−14.5686	−	39.7199i	−0.517021	−	1.40961i
$795$			21.0828i			0.747729i
$796$	−31.7285	+	26.8930i	−1.12459	+	0.953197i
$797$		−	20.5838i		−	0.729114i	−0.931181	−	0.364557i	$-0.881220\pi$
$797$		−	20.5838i		−	0.729114i	0.931181	−	0.364557i	$-0.118780\pi$
$798$		0			0
$799$	−13.8122			−0.488641
$800$	−2.93529	−	15.5180i	−0.103778	−	0.548644i
$801$	−7.88392			−0.278565
$802$	−20.8061	+	7.63133i	−0.734688	+	0.269472i
$803$		−	49.9310i		−	1.76203i
$804$	1.92162	−	1.62876i	0.0677703	−	0.0574418i
$805$		0			0
$806$	−4.60407	−	12.5525i	−0.162171	−	0.442144i
$807$	−59.0505			−2.07867
$808$	−0.514652	−	0.292046i	−0.0181054	−	0.0102741i
$809$	−46.9007			−1.64894			−0.824471	−	0.565905i	$-0.808527\pi$
$809$	−46.9007			−1.64894			−0.824471	+	0.565905i	$0.808527\pi$
$810$	−6.39944	−	17.4474i	−0.224853	−	0.613040i
$811$		−	22.2462i		−	0.781168i	−0.920567	−	0.390584i	$-0.872273\pi$
$811$		−	22.2462i		−	0.781168i	0.920567	−	0.390584i	$-0.127727\pi$
$812$		0			0
$813$		−	15.3088i		−	0.536902i
$814$	40.3361	−	14.7946i	1.41378	−	0.518552i
$815$	4.80151			0.168190
$816$	−12.2258	−	2.03078i	−0.427990	−	0.0710916i
$817$	3.17273			0.111000
$818$	34.6360	−	12.7039i	1.21102	−	0.444182i
$819$		0			0
$820$	−12.2258	−	14.4241i	−0.426945	−	0.503713i
$821$			32.8007i			1.14475i	0.819991	+	0.572376i	$0.193978\pi$
$821$			32.8007i			1.14475i	−0.819991	+	0.572376i	$0.806022\pi$
$822$	−11.2157	−	30.5784i	−0.391191	−	1.06654i
$823$	−13.7715			−0.480045			−0.240023	−	0.970767i	$-0.577155\pi$
$823$	−13.7715			−0.480045			−0.240023	+	0.970767i	$0.577155\pi$
$824$	−9.59970	+	16.9169i	−0.334421	+	0.589328i
$825$	−34.6572			−1.20661
$826$		0			0
$827$		−	22.0460i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$827$		−	22.0460i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$828$	6.49868	−	5.50826i	0.225845	−	0.191425i
$829$		−	5.48195i		−	0.190396i	−0.995458	−	0.0951980i	$-0.969652\pi$
$829$		−	5.48195i		−	0.190396i	0.995458	−	0.0951980i	$-0.0303484\pi$
$830$	5.86358	−	2.15067i	0.203528	−	0.0746508i
$831$	68.8804			2.38943
$832$	−17.7626	+	10.6111i	−0.615806	+	0.367873i
$833$		0			0
$834$	5.53672	−	2.03078i	0.191721	−	0.0703202i
$835$			20.8761i			0.722449i
$836$	23.8543	−	20.2188i	0.825017	−	0.699281i
$837$		−	0.461969i		−	0.0159680i
$838$	−0.123089	−	0.335590i	−0.00425205	−	0.0115928i
$839$	−28.7512			−0.992601			−0.496301	−	0.868151i	$-0.665309\pi$
$839$	−28.7512			−0.992601			−0.496301	+	0.868151i	$0.665309\pi$
$840$		0			0
$841$	28.5925			0.985947
$842$	8.94599	+	24.3903i	0.308299	+	0.840546i
$843$		−	41.1088i		−	1.41586i
$844$	22.2595	+	26.2619i	0.766204	+	0.903973i
$845$			9.37785i			0.322608i
$846$	−44.4287	+	16.2957i	−1.52749	+	0.560259i
$847$		0			0
$848$	−22.7582	−	3.78027i	−0.781519	−	0.129815i
$849$	68.5111			2.35129
$850$	−4.66877	+	1.71243i	−0.160138	+	0.0587360i
$851$			8.40387i			0.288081i
$852$	−23.5837	−	27.8243i	−0.807965	−	0.953243i
$853$			21.7605i			0.745064i	0.928019	+	0.372532i	$0.121510\pi$
$853$			21.7605i			0.745064i	−0.928019	+	0.372532i	$0.878490\pi$
$854$		0			0
$855$	−14.0487			−0.480457
$856$	31.8273	+	18.0608i	1.08783	+	0.617305i
$857$	−11.7919			−0.402802			−0.201401	−	0.979509i	$-0.564549\pi$
$857$	−11.7919			−0.402802			−0.201401	+	0.979509i	$0.564549\pi$
$858$	15.6351	+	42.6275i	0.533774	+	1.45528i
$859$			4.79353i			0.163553i	0.996651	+	0.0817766i	$0.0260594\pi$
$859$			4.79353i			0.163553i	−0.996651	+	0.0817766i	$0.973941\pi$
$860$	−2.32158	+	1.96776i	−0.0791651	+	0.0671000i
$861$		0			0
$862$	36.4389	−	13.3652i	1.24111	−	0.455220i
$863$	−0.125728			−0.00427985			−0.00213992	−	0.999998i	$-0.500681\pi$
$863$	−0.125728			−0.00427985			−0.00213992	+	0.999998i	$0.500681\pi$
$864$	−0.702447	+	0.132871i	−0.0238977	+	0.00452036i
$865$	9.71646			0.330370
$866$	9.64211	−	3.53657i	0.327652	−	0.120178i
$867$		−	37.9168i		−	1.28772i
$868$		0			0
$869$			43.9371i			1.49046i
$870$	1.13642	+	3.09834i	0.0385283	+	0.105043i
$871$	−1.32422			−0.0448694
$872$	47.2746	+	26.8266i	1.60092	+	0.908462i
$873$	−4.79186			−0.162180
$874$	2.10625	+	5.74249i	0.0712451	+	0.194242i
$875$		0			0
$876$	−31.4760	−	37.1357i	−1.06348	−	1.25470i
$877$		−	29.9684i		−	1.01196i	−0.862545	−	0.505981i	$-0.831131\pi$
$877$		−	29.9684i		−	1.01196i	0.862545	−	0.505981i	$-0.168869\pi$
$878$	−39.8374	+	14.6117i	−1.34445	+	0.493122i
$879$	49.6545			1.67481
$880$	−4.91495	+	29.5893i	−0.165683	+	0.997455i
$881$	30.2728			1.01992			0.509959	−	0.860199i	$-0.329661\pi$
$881$	30.2728			1.01992			0.509959	+	0.860199i	$0.329661\pi$
$882$		0			0
$883$		−	43.3423i		−	1.45858i	−0.684203	−	0.729291i	$-0.739850\pi$
$883$		−	43.3423i		−	1.45858i	0.684203	−	0.729291i	$-0.260150\pi$
$884$	4.21251	+	4.96995i	0.141682	+	0.167157i
$885$			12.7354i			0.428097i
$886$	−17.0856	−	46.5821i	−0.574001	−	1.56496i
$887$	−15.1364			−0.508231			−0.254116	−	0.967174i	$-0.581784\pi$
$887$	−15.1364			−0.508231			−0.254116	+	0.967174i	$0.581784\pi$
$888$	20.6731	−	36.4309i	0.693745	−	1.22254i
$889$		0			0
$890$	1.86972	+	5.09761i	0.0626732	+	0.170872i
$891$		−	44.6255i		−	1.49501i
$892$	−26.7245	+	22.6516i	−0.894803	+	0.758431i
$893$		−	33.9774i		−	1.13701i
$894$	−12.0412	+	4.41652i	−0.402718	+	0.147711i
$895$	0.187796			0.00627731
$896$		0			0
$897$	−8.88128			−0.296537
$898$	−27.8963	+	10.2319i	−0.930913	+	0.341444i
$899$		−	2.33358i		−	0.0778291i
$900$	−12.9974	+	11.0165i	−0.433245	+	0.367217i
$901$			7.26423i			0.242007i
$902$	−15.6351	−	42.6275i	−0.520592	−	1.41934i
$903$		0			0
$904$	−1.46765	+	2.58633i	−0.0488132	+	0.0860201i
$905$	4.04068			0.134317
$906$	−17.1036	−	46.6313i	−0.568229	−	1.54922i
$907$			31.7266i			1.05347i	0.850031	+	0.526733i	$0.176583\pi$
$907$			31.7266i			1.05347i	−0.850031	+	0.526733i	$0.823417\pi$
$908$	17.0580	+	20.1252i	0.566091	+	0.667878i
$909$			0.638384i			0.0211739i
$910$		0			0
$911$	29.4757			0.976574			0.488287	−	0.872683i	$-0.337622\pi$
$911$	29.4757			0.976574			0.488287	+	0.872683i	$0.337622\pi$
$912$	4.99563	−	30.0750i	0.165422	−	0.995883i
$913$	14.9974			0.496340
$914$	17.7591	−	6.51374i	0.587417	−	0.215455i
$915$			47.1118i			1.55747i
$916$	22.2032	+	26.1955i	0.733614	+	0.865524i
$917$		0			0
$918$	0.0775161	+	0.211340i	0.00255841	+	0.00697525i
$919$	17.7175			0.584447			0.292223	−	0.956350i	$-0.405605\pi$
$919$	17.7175			0.584447			0.292223	+	0.956350i	$0.405605\pi$
$920$	−5.10275	−	2.89562i	−0.168233	−	0.0954657i
$921$	43.9947			1.44968
$922$	1.30825	+	3.56680i	0.0430848	+	0.117466i
$923$			19.1741i			0.631124i
$924$		0			0
$925$		−	16.8077i		−	0.552635i
$926$	−27.9327	+	10.2453i	−0.917924	+	0.336680i
$927$	20.9840			0.689206
$928$	−3.54832	+	0.671180i	−0.116479	+	0.0220326i
$929$	−53.2676			−1.74765			−0.873826	−	0.486239i	$-0.838369\pi$
$929$	−53.2676			−1.74765			−0.873826	+	0.486239i	$0.838369\pi$
$930$	−17.7414	+	6.50725i	−0.581762	+	0.213381i
$931$		0			0
$932$	37.9570	−	32.1722i	1.24332	−	1.05384i
$933$			3.52102i			0.115273i
$934$	12.0252	+	32.7856i	0.393478	+	1.07278i
$935$	9.44467			0.308874
$936$	19.4136	+	11.0165i	0.634554	+	0.360086i
$937$	38.2055			1.24812			0.624060	−	0.781377i	$-0.285482\pi$
$937$	38.2055			1.24812			0.624060	+	0.781377i	$0.285482\pi$
$938$		0			0
$939$		−	11.9469i		−	0.389874i
$940$	21.0731	+	24.8622i	0.687329	+	0.810916i
$941$			9.59781i			0.312880i	0.987687	+	0.156440i	$0.0500017\pi$
$941$			9.59781i			0.312880i	−0.987687	+	0.156440i	$0.949998\pi$
$942$	−42.0943	+	15.4395i	−1.37151	+	0.503047i
$943$	8.88128			0.289214
$944$	−13.7475	−	2.28354i	−0.447443	−	0.0743229i
$945$		0			0
$946$	−6.86094	+	2.51648i	−0.223068	+	0.0818179i
$947$			16.5485i			0.537754i	0.963175	+	0.268877i	$0.0866525\pi$
$947$			16.5485i			0.537754i	−0.963175	+	0.268877i	$0.913347\pi$
$948$	27.6975	+	32.6777i	0.899573	+	1.06132i
$949$			25.5908i			0.830711i
$950$	−4.21251	−	11.4850i	−0.136672	−	0.372622i
$951$	27.7803			0.900837
$952$		0			0
$953$	6.08942			0.197256			0.0986278	−	0.995124i	$-0.468555\pi$
$953$	6.08942			0.197256			0.0986278	+	0.995124i	$0.468555\pi$
$954$	8.57040	+	23.3663i	0.277477	+	0.756512i
$955$		−	3.63665i		−	0.117679i
$956$	−20.3286	+	17.2304i	−0.657473	+	0.557272i
$957$			7.92466i			0.256168i
$958$	54.3201	−	19.9238i	1.75500	−	0.643708i
$959$		0			0
$960$	14.9974	+	25.1051i	0.484038	+	0.810262i
$961$	−17.6377			−0.568959
$962$	−20.6731	+	7.58258i	−0.666529	+	0.244472i
$963$		−	39.4792i		−	1.27220i
$964$	33.9367	−	28.7646i	1.09303	−	0.926445i
$965$			5.86758i			0.188884i
$966$		0			0
$967$	21.5430			0.692778			0.346389	−	0.938091i	$-0.387408\pi$
$967$	21.5430			0.692778			0.346389	+	0.938091i	$0.387408\pi$
$968$	−20.1922	+	35.5833i	−0.649001	+	1.14369i
$969$	−9.59970			−0.308387
$970$	1.13642	+	3.09834i	0.0364883	+	0.0994816i
$971$			2.62562i			0.0842602i	0.999112	+	0.0421301i	$0.0134144\pi$
$971$			2.62562i			0.0842602i	−0.999112	+	0.0421301i	$0.986586\pi$
$972$	−28.6218	−	33.7682i	−0.918044	−	1.08311i
$973$		0			0
$974$	23.2804	−	8.53887i	0.745951	−	0.273603i
$975$	17.7626			0.568857
$976$	−50.8557	−	8.44742i	−1.62785	−	0.270395i
$977$	−34.4676			−1.10272			−0.551359	−	0.834268i	$-0.685890\pi$
$977$	−34.4676			−1.10272			−0.551359	+	0.834268i	$0.685890\pi$
$978$	10.5536	−	3.87088i	0.337466	−	0.123777i
$979$			13.0382i			0.416704i
$980$		0			0
$981$		−	58.6403i		−	1.87224i
$982$	−7.67050	−	20.9129i	−0.244776	−	0.667356i
$983$	−52.4420			−1.67264			−0.836320	−	0.548241i	$-0.815298\pi$
$983$	−52.4420			−1.67264			−0.836320	+	0.548241i	$0.815298\pi$
$984$	−38.5004	−	21.8475i	−1.22735	−	0.696474i
$985$	29.0461			0.925486
$986$	0.391563	+	1.06756i	0.0124699	+	0.0339979i
$987$		0			0
$988$	−12.2258	+	10.3626i	−0.388956	+	0.329677i
$989$		−	1.42945i		−	0.0454539i
$990$	30.3800	−	11.1429i	0.965539	−	0.354144i
$991$	−16.1611			−0.513375			−0.256688	−	0.966494i	$-0.582631\pi$
$991$	−16.1611			−0.513375			−0.256688	+	0.966494i	$0.582631\pi$
$992$	−3.84324	−	20.3180i	−0.122023	−	0.645098i
$993$	−58.6325			−1.86064
$994$		0			0
$995$		−	30.9028i		−	0.979684i
$996$	11.1541	−	9.45419i	0.353432	−	0.299567i
$997$		−	39.3700i		−	1.24686i	−0.781879	−	0.623430i	$-0.785738\pi$
$997$		−	39.3700i		−	1.24686i	0.781879	−	0.623430i	$-0.214262\pi$
$998$	−4.96053	−	13.5244i	−0.157023	−	0.428107i
$999$	−0.760830			−0.0240716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.b.f.197.5		6
4.3	odd	2		1568.2.b.e.785.1		6
7.2	even	3		392.2.p.g.165.2		12
7.3	odd	6		56.2.p.a.37.4	yes	12
7.4	even	3		392.2.p.g.373.4		12
7.5	odd	6		56.2.p.a.53.2	yes	12
7.6	odd	2		392.2.b.e.197.5		6
8.3	odd	2		1568.2.b.e.785.6		6
8.5	even	2	inner	392.2.b.f.197.6		6
21.5	even	6		504.2.cj.c.109.5		12
21.17	even	6		504.2.cj.c.37.3		12
28.3	even	6		224.2.t.a.177.6		12
28.11	odd	6		1568.2.t.g.177.1		12
28.19	even	6		224.2.t.a.81.1		12
28.23	odd	6		1568.2.t.g.753.6		12
28.27	even	2		1568.2.b.f.785.6		6
56.3	even	6		224.2.t.a.177.1		12
56.5	odd	6		56.2.p.a.53.4	yes	12
56.11	odd	6		1568.2.t.g.177.6		12
56.13	odd	2		392.2.b.e.197.6		6
56.19	even	6		224.2.t.a.81.6		12
56.27	even	2		1568.2.b.f.785.1		6
56.37	even	6		392.2.p.g.165.4		12
56.45	odd	6		56.2.p.a.37.2	✓	12
56.51	odd	6		1568.2.t.g.753.1		12
56.53	even	6		392.2.p.g.373.2		12
84.47	odd	6		2016.2.cr.c.1873.5		12
84.59	odd	6		2016.2.cr.c.1297.2		12
168.5	even	6		504.2.cj.c.109.3		12
168.59	odd	6		2016.2.cr.c.1297.5		12
168.101	even	6		504.2.cj.c.37.5		12
168.131	odd	6		2016.2.cr.c.1873.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	56.45	odd	6
56.2.p.a.37.4	yes	12	7.3	odd	6
56.2.p.a.53.2	yes	12	7.5	odd	6
56.2.p.a.53.4	yes	12	56.5	odd	6
224.2.t.a.81.1		12	28.19	even	6
224.2.t.a.81.6		12	56.19	even	6
224.2.t.a.177.1		12	56.3	even	6
224.2.t.a.177.6		12	28.3	even	6
392.2.b.e.197.5		6	7.6	odd	2
392.2.b.e.197.6		6	56.13	odd	2
392.2.b.f.197.5		6	1.1	even	1	trivial
392.2.b.f.197.6		6	8.5	even	2	inner
392.2.p.g.165.2		12	7.2	even	3
392.2.p.g.165.4		12	56.37	even	6
392.2.p.g.373.2		12	56.53	even	6
392.2.p.g.373.4		12	7.4	even	3
504.2.cj.c.37.3		12	21.17	even	6
504.2.cj.c.37.5		12	168.101	even	6
504.2.cj.c.109.3		12	168.5	even	6
504.2.cj.c.109.5		12	21.5	even	6
1568.2.b.e.785.1		6	4.3	odd	2
1568.2.b.e.785.6		6	8.3	odd	2
1568.2.b.f.785.1		6	56.27	even	2
1568.2.b.f.785.6		6	28.27	even	2
1568.2.t.g.177.1		12	28.11	odd	6
1568.2.t.g.177.6		12	56.11	odd	6
1568.2.t.g.753.1		12	56.51	odd	6
1568.2.t.g.753.6		12	28.23	odd	6
2016.2.cr.c.1297.2		12	84.59	odd	6
2016.2.cr.c.1297.5		12	168.59	odd	6
2016.2.cr.c.1873.2		12	168.131	odd	6
2016.2.cr.c.1873.5		12	84.47	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32772 - 0.486987i) q^{2} +2.45995i q^{3} +(1.52569 - 1.29317i) q^{4} +1.48598i q^{5} +(1.19797 + 3.26613i) q^{6} +(1.39593 - 2.45995i) q^{8} -3.05137 q^{9} +(0.723653 + 1.97297i) q^{10} +5.04629i q^{11} +(3.18113 + 3.75312i) q^{12} -2.58633i q^{13} -3.65544 q^{15} +(0.655442 - 3.94593i) q^{16} -1.25951 q^{17} +(-4.05137 + 1.48598i) q^{18} -3.09834i q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} -1.39593 q^{23} +(6.05137 + 3.43393i) q^{24} +2.79186 q^{25} +(-1.25951 - 3.43393i) q^{26} -0.126378i q^{27} -0.638384i q^{29} +(-4.85341 + 1.78015i) q^{30} +3.65544 q^{31} +(-1.05137 - 5.55829i) q^{32} -12.4136 q^{33} +(-1.67228 + 0.613365i) q^{34} +(-4.65544 + 3.94593i) q^{36} -6.02026i q^{37} +(-1.50885 - 4.11373i) q^{38} +6.36226 q^{39} +(3.65544 + 2.07433i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(6.52569 + 7.69905i) q^{44} -4.53428i q^{45} +(-1.85341 + 0.679801i) q^{46} +10.9663 q^{47} +(9.70682 + 1.61236i) q^{48} +(3.70682 - 1.35960i) q^{50} -3.09834i q^{51} +(-3.34456 - 3.94593i) q^{52} -5.76750i q^{53} +(-0.0615446 - 0.167795i) q^{54} -7.49868 q^{55} +7.62177 q^{57} +(-0.310885 - 0.847596i) q^{58} -3.48397i q^{59} +(-5.57706 + 4.72709i) q^{60} -12.8881i q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +3.84324 q^{65} +(-16.4818 + 6.04528i) q^{66} -0.512006i q^{67} +(-1.92162 + 1.62876i) q^{68} -3.43393i q^{69} -7.41363 q^{71} +(-4.25951 + 7.50624i) q^{72} -9.89461 q^{73} +(-2.93179 - 7.99323i) q^{74} +6.86786i q^{75} +(-4.00667 - 4.72709i) q^{76} +(8.44731 - 3.09834i) q^{78} +8.70682 q^{79} +(5.86358 + 0.973974i) q^{80} -8.84324 q^{81} +(-8.44731 + 3.09834i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(0.498680 + 1.35960i) q^{86} +1.57040 q^{87} +(12.4136 + 7.04427i) q^{88} +2.58373 q^{89} +(-2.20814 - 6.02026i) q^{90} +(-2.12976 + 1.80517i) q^{92} +8.99222i q^{93} +(14.5602 - 5.34046i) q^{94} +4.60407 q^{95} +(13.6731 - 2.58633i) q^{96} +1.57040 q^{97} -15.3981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

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