LMFDB - Embedded newform 392.2.b.c.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(197,392)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.3
Root			$-0.780776 + 1.17915i$ of defining polynomial
Character	$\chi$	$=$	392.197
Dual form			392.2.b.c.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 - 1.17915i) q^{2} -3.02045i q^{3} +(-0.780776 - 1.84130i) q^{4} +1.69614i q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} -6.12311 q^{9} +O(q^{10})$	\(q+(0.780776 - 1.17915i) q^{2} -3.02045i q^{3} +(-0.780776 - 1.84130i) q^{4} +1.69614i q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} -6.12311 q^{9} +(2.00000 + 1.32431i) q^{10} -1.32431i q^{11} +(-5.56155 + 2.35829i) q^{12} -1.69614i q^{13} +5.12311 q^{15} +(-2.78078 + 2.87529i) q^{16} -2.00000 q^{17} +(-4.78078 + 7.22004i) q^{18} -3.02045i q^{19} +(3.12311 - 1.32431i) q^{20} +(-1.56155 - 1.03399i) q^{22} +5.12311 q^{23} +(-1.56155 + 8.39919i) q^{24} +2.12311 q^{25} +(-2.00000 - 1.32431i) q^{26} +9.43318i q^{27} -6.04090i q^{29} +(4.00000 - 6.04090i) q^{30} +10.2462 q^{31} +(1.21922 + 5.52390i) q^{32} -4.00000 q^{33} +(-1.56155 + 2.35829i) q^{34} +(4.78078 + 11.2745i) q^{36} +6.04090i q^{37} +(-3.56155 - 2.35829i) q^{38} -5.12311 q^{39} +(0.876894 - 4.71659i) q^{40} -4.24621 q^{41} -1.32431i q^{43} +(-2.43845 + 1.03399i) q^{44} -10.3857i q^{45} +(4.00000 - 6.04090i) q^{46} +(8.68466 + 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +6.04090i q^{51} +(-3.12311 + 1.32431i) q^{52} -2.64861i q^{53} +(11.1231 + 7.36520i) q^{54} +2.24621 q^{55} -9.12311 q^{57} +(-7.12311 - 4.71659i) q^{58} +0.371834i q^{59} +(-4.00000 - 9.43318i) q^{60} -1.69614i q^{61} +(8.00000 - 12.0818i) q^{62} +(7.46543 + 2.87529i) q^{64} +2.87689 q^{65} +(-3.12311 + 4.71659i) q^{66} -11.5012i q^{67} +(1.56155 + 3.68260i) q^{68} -15.4741i q^{69} -8.00000 q^{71} +(17.0270 + 3.16561i) q^{72} +6.00000 q^{73} +(7.12311 + 4.71659i) q^{74} -6.41273i q^{75} +(-5.56155 + 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-4.87689 - 4.71659i) q^{80} +10.1231 q^{81} +(-3.31534 + 5.00691i) q^{82} +5.66906i q^{83} -3.39228i q^{85} +(-1.56155 - 1.03399i) q^{86} -18.2462 q^{87} +(-0.684658 + 3.68260i) q^{88} +16.2462 q^{89} +(-12.2462 - 8.10887i) q^{90} +(-4.00000 - 9.43318i) q^{92} -30.9481i q^{93} +5.12311 q^{95} +(16.6847 - 3.68260i) q^{96} -12.2462 q^{97} +8.10887i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} - 6 q^{6} - 7 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^4 - 6 * q^6 - 7 * q^8 - 8 * q^9	$ 4 q - q^{2} + q^{4} - 6 q^{6} - 7 q^{8} - 8 q^{9} + 8 q^{10} - 14 q^{12} + 4 q^{15} - 7 q^{16} - 8 q^{17} - 15 q^{18} - 4 q^{20} + 2 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{30} + 8 q^{31} + 9 q^{32} - 16 q^{33} + 2 q^{34} + 15 q^{36} - 6 q^{38} - 4 q^{39} + 20 q^{40} + 16 q^{41} - 18 q^{44} + 16 q^{46} + 10 q^{48} + 19 q^{50} + 4 q^{52} + 28 q^{54} - 24 q^{55} - 20 q^{57} - 12 q^{58} - 16 q^{60} + 32 q^{62} + q^{64} + 28 q^{65} + 4 q^{66} - 2 q^{68} - 32 q^{71} + 31 q^{72} + 24 q^{73} + 12 q^{74} - 14 q^{76} - 16 q^{78} - 36 q^{80} + 24 q^{81} - 38 q^{82} + 2 q^{86} - 40 q^{87} + 22 q^{88} + 32 q^{89} - 16 q^{90} - 16 q^{92} + 4 q^{95} + 42 q^{96} - 16 q^{97}+O(q^{100}) $ 4 * q - q^2 + q^4 - 6 * q^6 - 7 * q^8 - 8 * q^9 + 8 * q^10 - 14 * q^12 + 4 * q^15 - 7 * q^16 - 8 * q^17 - 15 * q^18 - 4 * q^20 + 2 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^30 + 8 * q^31 + 9 * q^32 - 16 * q^33 + 2 * q^34 + 15 * q^36 - 6 * q^38 - 4 * q^39 + 20 * q^40 + 16 * q^41 - 18 * q^44 + 16 * q^46 + 10 * q^48 + 19 * q^50 + 4 * q^52 + 28 * q^54 - 24 * q^55 - 20 * q^57 - 12 * q^58 - 16 * q^60 + 32 * q^62 + q^64 + 28 * q^65 + 4 * q^66 - 2 * q^68 - 32 * q^71 + 31 * q^72 + 24 * q^73 + 12 * q^74 - 14 * q^76 - 16 * q^78 - 36 * q^80 + 24 * q^81 - 38 * q^82 + 2 * q^86 - 40 * q^87 + 22 * q^88 + 32 * q^89 - 16 * q^90 - 16 * q^92 + 4 * q^95 + 42 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$3$		−	3.02045i		−	1.74386i	−0.489634	−	0.871928i	$-0.662870\pi$
$3$		−	3.02045i		−	1.74386i	0.489634	−	0.871928i	$-0.337130\pi$
$4$	−0.780776	−	1.84130i	−0.390388	−	0.920650i
$5$			1.69614i			0.758537i	0.925287	+	0.379269i	$0.123824\pi$
$5$			1.69614i			0.758537i	−0.925287	+	0.379269i	$0.876176\pi$
$6$	−3.56155	−	2.35829i	−1.45400	−	0.962770i
$7$		0			0
$7$		0			0
$8$	−2.78078	−	0.516994i	−0.983153	−	0.182785i
$9$	−6.12311			−2.04104
$10$	2.00000	+	1.32431i	0.632456	+	0.418783i
$11$		−	1.32431i		−	0.399294i	−0.979868	−	0.199647i	$-0.936021\pi$
$11$		−	1.32431i		−	0.399294i	0.979868	−	0.199647i	$-0.0639795\pi$
$12$	−5.56155	+	2.35829i	−1.60548	+	0.680781i
$13$		−	1.69614i		−	0.470425i	−0.971944	−	0.235212i	$-0.924421\pi$
$13$		−	1.69614i		−	0.470425i	0.971944	−	0.235212i	$-0.0755786\pi$
$14$		0			0
$15$	5.12311			1.32278
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	−4.78078	+	7.22004i	−1.12684	+	1.70178i
$19$		−	3.02045i		−	0.692938i	−0.938061	−	0.346469i	$-0.887381\pi$
$19$		−	3.02045i		−	0.692938i	0.938061	−	0.346469i	$-0.112619\pi$
$20$	3.12311	−	1.32431i	0.698348	−	0.296124i
$21$		0			0
$22$	−1.56155	−	1.03399i	−0.332924	−	0.220447i
$23$	5.12311			1.06824			0.534121	−	0.845408i	$-0.320643\pi$
$23$	5.12311			1.06824			0.534121	+	0.845408i	$0.320643\pi$
$24$	−1.56155	+	8.39919i	−0.318751	+	1.71448i
$25$	2.12311			0.424621
$26$	−2.00000	−	1.32431i	−0.392232	−	0.259718i
$27$			9.43318i			1.81542i
$28$		0			0
$29$		−	6.04090i		−	1.12177i	−0.827895	−	0.560883i	$-0.810462\pi$
$29$		−	6.04090i		−	1.12177i	0.827895	−	0.560883i	$-0.189538\pi$
$30$	4.00000	−	6.04090i	0.730297	−	1.10291i
$31$	10.2462			1.84027			0.920137	−	0.391597i	$-0.128077\pi$
$31$	10.2462			1.84027			0.920137	+	0.391597i	$0.128077\pi$
$32$	1.21922	+	5.52390i	0.215530	+	0.976497i
$33$	−4.00000			−0.696311
$34$	−1.56155	+	2.35829i	−0.267804	+	0.404444i
$35$		0			0
$36$	4.78078	+	11.2745i	0.796796	+	1.87908i
$37$			6.04090i			0.993117i	0.868003	+	0.496559i	$0.165403\pi$
$37$			6.04090i			0.993117i	−0.868003	+	0.496559i	$0.834597\pi$
$38$	−3.56155	−	2.35829i	−0.577760	−	0.382566i
$39$	−5.12311			−0.820353
$40$	0.876894	−	4.71659i	0.138649	−	0.745758i
$41$	−4.24621			−0.663147			−0.331573	−	0.943429i	$-0.607579\pi$
$41$	−4.24621			−0.663147			−0.331573	+	0.943429i	$0.607579\pi$
$42$		0			0
$43$		−	1.32431i		−	0.201955i	−0.994889	−	0.100977i	$-0.967803\pi$
$43$		−	1.32431i		−	0.201955i	0.994889	−	0.100977i	$-0.0321970\pi$
$44$	−2.43845	+	1.03399i	−0.367610	+	0.155879i
$45$		−	10.3857i		−	1.54820i
$46$	4.00000	−	6.04090i	0.589768	−	0.890681i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	8.68466	+	8.39919i	1.25352	+	1.21232i
$49$		0			0
$50$	1.65767	−	2.50345i	0.234430	−	0.354042i
$51$			6.04090i			0.845895i
$52$	−3.12311	+	1.32431i	−0.433097	+	0.183648i
$53$		−	2.64861i		−	0.363815i	−0.983316	−	0.181908i	$-0.941773\pi$
$53$		−	2.64861i		−	0.363815i	0.983316	−	0.181908i	$-0.0582272\pi$
$54$	11.1231	+	7.36520i	1.51366	+	1.00228i
$55$	2.24621			0.302879
$56$		0			0
$57$	−9.12311			−1.20838
$58$	−7.12311	−	4.71659i	−0.935310	−	0.619318i
$59$			0.371834i			0.0484087i	0.999707	+	0.0242043i	$0.00770523\pi$
$59$			0.371834i			0.0484087i	−0.999707	+	0.0242043i	$0.992295\pi$
$60$	−4.00000	−	9.43318i	−0.516398	−	1.21782i
$61$		−	1.69614i		−	0.217169i	−0.994087	−	0.108584i	$-0.965368\pi$
$61$		−	1.69614i		−	0.217169i	0.994087	−	0.108584i	$-0.0346317\pi$
$62$	8.00000	−	12.0818i	1.01600	−	1.53439i
$63$		0			0
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$	2.87689			0.356835
$66$	−3.12311	+	4.71659i	−0.384428	+	0.580572i
$67$		−	11.5012i		−	1.40509i	−0.711640	−	0.702545i	$-0.752047\pi$
$67$		−	11.5012i		−	1.40509i	0.711640	−	0.702545i	$-0.247953\pi$
$68$	1.56155	+	3.68260i	0.189366	+	0.446581i
$69$		−	15.4741i		−	1.86286i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	17.0270	+	3.16561i	2.00665	+	0.373070i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	7.12311	+	4.71659i	0.828044	+	0.548292i
$75$		−	6.41273i		−	0.740478i
$76$	−5.56155	+	2.35829i	−0.637954	+	0.270515i
$77$		0			0
$78$	−4.00000	+	6.04090i	−0.452911	+	0.683997i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−4.87689	−	4.71659i	−0.545253	−	0.527331i
$81$	10.1231			1.12479
$82$	−3.31534	+	5.00691i	−0.366118	+	0.552921i
$83$			5.66906i			0.622260i	0.950367	+	0.311130i	$0.100708\pi$
$83$			5.66906i			0.622260i	−0.950367	+	0.311130i	$0.899292\pi$
$84$		0			0
$85$		−	3.39228i		−	0.367945i
$86$	−1.56155	−	1.03399i	−0.168387	−	0.111498i
$87$	−18.2462			−1.95620
$88$	−0.684658	+	3.68260i	−0.0729848	+	0.392567i
$89$	16.2462			1.72209			0.861047	−	0.508525i	$-0.169809\pi$
$89$	16.2462			1.72209			0.861047	+	0.508525i	$0.169809\pi$
$90$	−12.2462	−	8.10887i	−1.29086	−	0.854750i
$91$		0			0
$92$	−4.00000	−	9.43318i	−0.417029	−	0.983477i
$93$		−	30.9481i		−	3.20917i
$94$		0			0
$95$	5.12311			0.525620
$96$	16.6847	−	3.68260i	1.70287	−	0.375854i
$97$	−12.2462			−1.24341			−0.621707	−	0.783250i	$-0.713561\pi$
$97$	−12.2462			−1.24341			−0.621707	+	0.783250i	$0.713561\pi$
$98$		0			0
$99$			8.10887i			0.814972i
$100$	−1.65767	−	3.90928i	−0.165767	−	0.390928i
$101$			10.3857i			1.03341i	0.856163	+	0.516705i	$0.172842\pi$
$101$			10.3857i			1.03341i	−0.856163	+	0.516705i	$0.827158\pi$
$102$	7.12311	+	4.71659i	0.705293	+	0.467012i
$103$	−2.24621			−0.221326			−0.110663	−	0.993858i	$-0.535297\pi$
$103$	−2.24621			−0.221326			−0.110663	+	0.993858i	$0.535297\pi$
$104$	−0.876894	+	4.71659i	−0.0859866	+	0.462500i
$105$		0			0
$106$	−3.12311	−	2.06798i	−0.303343	−	0.200860i
$107$			14.1498i			1.36791i	0.729524	+	0.683955i	$0.239741\pi$
$107$			14.1498i			1.36791i	−0.729524	+	0.683955i	$0.760259\pi$
$108$	17.3693	−	7.36520i	1.67136	−	0.708717i
$109$			18.1227i			1.73584i	0.496705	+	0.867919i	$0.334543\pi$
$109$			18.1227i			1.73584i	−0.496705	+	0.867919i	$0.665457\pi$
$110$	1.75379	−	2.64861i	0.167217	−	0.252535i
$111$	18.2462			1.73185
$112$		0			0
$113$	4.87689			0.458780			0.229390	−	0.973335i	$-0.426327\pi$
$113$	4.87689			0.458780			0.229390	+	0.973335i	$0.426327\pi$
$114$	−7.12311	+	10.7575i	−0.667140	+	1.00753i
$115$			8.68951i			0.810301i
$116$	−11.1231	+	4.71659i	−1.03275	+	0.437924i
$117$			10.3857i			0.960154i
$118$	0.438447	+	0.290319i	0.0403623	+	0.0267261i
$119$		0			0
$120$	−14.2462	−	2.64861i	−1.30050	−	0.241784i
$121$	9.24621			0.840565
$122$	−2.00000	−	1.32431i	−0.181071	−	0.119897i
$123$			12.8255i			1.15643i
$124$	−8.00000	−	18.8664i	−0.718421	−	1.69425i
$125$			12.0818i			1.08063i
$126$		0			0
$127$	13.1231			1.16449			0.582244	−	0.813014i	$-0.302175\pi$
$127$	13.1231			1.16449			0.582244	+	0.813014i	$0.302175\pi$
$128$	9.21922	−	6.55789i	0.814872	−	0.579641i
$129$	−4.00000			−0.352180
$130$	2.24621	−	3.39228i	0.197006	−	0.297523i
$131$			12.4536i			1.08808i	0.839060	+	0.544039i	$0.183106\pi$
$131$			12.4536i			1.08808i	−0.839060	+	0.544039i	$0.816894\pi$
$132$	3.12311	+	7.36520i	0.271831	+	0.641059i
$133$		0			0
$134$	−13.5616	−	8.97983i	−1.17154	−	0.775739i
$135$	−16.0000			−1.37706
$136$	5.56155	+	1.03399i	0.476899	+	0.0886637i
$137$	−16.2462			−1.38801			−0.694004	−	0.719971i	$-0.744155\pi$
$137$	−16.2462			−1.38801			−0.694004	+	0.719971i	$0.744155\pi$
$138$	−18.2462	−	12.0818i	−1.55322	−	1.02847i
$139$		−	8.31768i		−	0.705496i	−0.935718	−	0.352748i	$-0.885247\pi$
$139$		−	8.31768i		−	0.705496i	0.935718	−	0.352748i	$-0.114753\pi$
$140$		0			0
$141$		0			0
$142$	−6.24621	+	9.43318i	−0.524170	+	0.791615i
$143$	−2.24621			−0.187838
$144$	17.0270	−	17.6057i	1.41892	−	1.46714i
$145$	10.2462			0.850902
$146$	4.68466	−	7.07488i	0.387705	−	0.585522i
$147$		0			0
$148$	11.1231	−	4.71659i	0.914314	−	0.387701i
$149$			14.7304i			1.20676i	0.797453	+	0.603381i	$0.206180\pi$
$149$			14.7304i			1.20676i	−0.797453	+	0.603381i	$0.793820\pi$
$150$	−7.56155	−	5.00691i	−0.617398	−	0.408812i
$151$	10.8769			0.885149			0.442575	−	0.896732i	$-0.354065\pi$
$151$	10.8769			0.885149			0.442575	+	0.896732i	$0.354065\pi$
$152$	−1.56155	+	8.39919i	−0.126659	+	0.681264i
$153$	12.2462			0.990048
$154$		0			0
$155$			17.3790i			1.39592i
$156$	4.00000	+	9.43318i	0.320256	+	0.755259i
$157$		−	8.48071i		−	0.676834i	−0.940996	−	0.338417i	$-0.890109\pi$
$157$		−	8.48071i		−	0.676834i	0.940996	−	0.338417i	$-0.109891\pi$
$158$		0			0
$159$	−8.00000			−0.634441
$160$	−9.36932	+	2.06798i	−0.740710	+	0.163488i
$161$		0			0
$162$	7.90388	−	11.9366i	0.620988	−	0.937830i
$163$		−	13.4061i		−	1.05005i	−0.851088	−	0.525023i	$-0.824057\pi$
$163$		−	13.4061i		−	1.05005i	0.851088	−	0.525023i	$-0.175943\pi$
$164$	3.31534	+	7.81855i	0.258885	+	0.610526i
$165$		−	6.78456i		−	0.528178i
$166$	6.68466	+	4.42627i	0.518830	+	0.343545i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	10.1231			0.778700
$170$	−4.00000	−	2.64861i	−0.306786	−	0.203139i
$171$			18.4945i			1.41431i
$172$	−2.43845	+	1.03399i	−0.185930	+	0.0788408i
$173$		−	19.0752i		−	1.45026i	−0.688613	−	0.725129i	$-0.741780\pi$
$173$		−	19.0752i		−	1.45026i	0.688613	−	0.725129i	$-0.258220\pi$
$174$	−14.2462	+	21.5150i	−1.08000	+	1.63105i
$175$		0			0
$176$	3.80776	+	3.68260i	0.287021	+	0.277587i
$177$	1.12311			0.0844178
$178$	12.6847	−	19.1567i	0.950755	−	1.43585i
$179$		−	4.71659i		−	0.352534i	−0.984342	−	0.176267i	$-0.943598\pi$
$179$		−	4.71659i		−	0.352534i	0.984342	−	0.176267i	$-0.0564023\pi$
$180$	−19.1231	+	8.10887i	−1.42535	+	0.604400i
$181$		−	6.99337i		−	0.519813i	−0.965634	−	0.259906i	$-0.916308\pi$
$181$		−	6.99337i		−	0.519813i	0.965634	−	0.259906i	$-0.0836917\pi$
$182$		0			0
$183$	−5.12311			−0.378711
$184$	−14.2462	−	2.64861i	−1.05024	−	0.195258i
$185$	−10.2462			−0.753316
$186$	−36.4924	−	24.1636i	−2.67575	−	1.77176i
$187$			2.64861i			0.193686i
$188$		0			0
$189$		0			0
$190$	4.00000	−	6.04090i	0.290191	−	0.438253i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$	8.68466	−	22.5490i	0.626761	−	1.62733i
$193$	−11.1231			−0.800659			−0.400329	−	0.916371i	$-0.631104\pi$
$193$	−11.1231			−0.800659			−0.400329	+	0.916371i	$0.631104\pi$
$194$	−9.56155	+	14.4401i	−0.686479	+	1.03674i
$195$		−	8.68951i		−	0.622269i
$196$		0			0
$197$			21.5150i			1.53288i	0.642317	+	0.766439i	$0.277973\pi$
$197$			21.5150i			1.53288i	−0.642317	+	0.766439i	$0.722027\pi$
$198$	9.56155	+	6.33122i	0.679510	+	0.449940i
$199$	18.2462			1.29344			0.646720	−	0.762728i	$-0.276140\pi$
$199$	18.2462			1.29344			0.646720	+	0.762728i	$0.276140\pi$
$200$	−5.90388	−	1.09763i	−0.417468	−	0.0776143i
$201$	−34.7386			−2.45027
$202$	12.2462	+	8.10887i	0.861640	+	0.570538i
$203$		0			0
$204$	11.1231	−	4.71659i	0.778773	−	0.330227i
$205$		−	7.20217i		−	0.503022i
$206$	−1.75379	+	2.64861i	−0.122192	+	0.184538i
$207$	−31.3693			−2.18032
$208$	4.87689	+	4.71659i	0.338152	+	0.327037i
$209$	−4.00000			−0.276686
$210$		0			0
$211$		−	4.71659i		−	0.324703i	−0.986733	−	0.162352i	$-0.948092\pi$
$211$		−	4.71659i		−	0.324703i	0.986733	−	0.162352i	$-0.0519079\pi$
$212$	−4.87689	+	2.06798i	−0.334946	+	0.142029i
$213$			24.1636i			1.65566i
$214$	16.6847	+	11.0478i	1.14054	+	0.755212i
$215$	2.24621			0.153190
$216$	4.87689	−	26.2316i	0.331831	−	1.78483i
$217$		0			0
$218$	21.3693	+	14.1498i	1.44731	+	0.958343i
$219$		−	18.1227i		−	1.22462i
$220$	−1.75379	−	4.13595i	−0.118240	−	0.278846i
$221$			3.39228i			0.228190i
$222$	14.2462	−	21.5150i	0.956143	−	1.44399i
$223$	5.75379			0.385302			0.192651	−	0.981267i	$-0.438291\pi$
$223$	5.75379			0.385302			0.192651	+	0.981267i	$0.438291\pi$
$224$		0			0
$225$	−13.0000			−0.866667
$226$	3.80776	−	5.75058i	0.253289	−	0.382523i
$227$		−	9.80501i		−	0.650782i	−0.945580	−	0.325391i	$-0.894504\pi$
$227$		−	9.80501i		−	0.650782i	0.945580	−	0.325391i	$-0.105496\pi$
$228$	7.12311	+	16.7984i	0.471739	+	1.11250i
$229$			25.8597i			1.70886i	0.519568	+	0.854429i	$0.326093\pi$
$229$			25.8597i			1.70886i	−0.519568	+	0.854429i	$0.673907\pi$
$230$	10.2462	+	6.78456i	0.675615	+	0.447361i
$231$		0			0
$232$	−3.12311	+	16.7984i	−0.205042	+	1.10287i
$233$	−16.2462			−1.06432			−0.532162	−	0.846642i	$-0.678620\pi$
$233$	−16.2462			−1.06432			−0.532162	+	0.846642i	$0.678620\pi$
$234$	12.2462	+	8.10887i	0.800560	+	0.530093i
$235$		0			0
$236$	0.684658	−	0.290319i	0.0445675	−	0.0188982i
$237$		0			0
$238$		0			0
$239$	−17.6155			−1.13945			−0.569727	−	0.821834i	$-0.692951\pi$
$239$	−17.6155			−1.13945			−0.569727	+	0.821834i	$0.692951\pi$
$240$	−14.2462	+	14.7304i	−0.919589	+	0.950844i
$241$	3.75379			0.241803			0.120901	−	0.992665i	$-0.461422\pi$
$241$	3.75379			0.241803			0.120901	+	0.992665i	$0.461422\pi$
$242$	7.21922	−	10.9026i	0.464069	−	0.700849i
$243$		−	2.27678i		−	0.146055i
$244$	−3.12311	+	1.32431i	−0.199936	+	0.0847801i
$245$		0			0
$246$	15.1231	+	10.0138i	0.964214	+	0.638458i
$247$	−5.12311			−0.325975
$248$	−28.4924	−	5.29723i	−1.80927	−	0.336374i
$249$	17.1231			1.08513
$250$	14.2462	+	9.43318i	0.901010	+	0.596607i
$251$			10.9663i			0.692186i	0.938200	+	0.346093i	$0.112492\pi$
$251$			10.9663i			0.692186i	−0.938200	+	0.346093i	$0.887508\pi$
$252$		0			0
$253$		−	6.78456i		−	0.426542i
$254$	10.2462	−	15.4741i	0.642904	−	0.970930i
$255$	−10.2462			−0.641643
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$	−22.4924			−1.40304			−0.701519	−	0.712650i	$-0.747495\pi$
$257$	−22.4924			−1.40304			−0.701519	+	0.712650i	$0.747495\pi$
$258$	−3.12311	+	4.71659i	−0.194436	+	0.293642i
$259$		0			0
$260$	−2.24621	−	5.29723i	−0.139304	−	0.328520i
$261$			36.9890i			2.28956i
$262$	14.6847	+	9.72350i	0.907221	+	0.600720i
$263$	12.4924			0.770316			0.385158	−	0.922851i	$-0.374147\pi$
$263$	12.4924			0.770316			0.385158	+	0.922851i	$0.374147\pi$
$264$	11.1231	+	2.06798i	0.684580	+	0.127275i
$265$	4.49242			0.275967
$266$		0			0
$267$		−	49.0708i		−	3.00309i
$268$	−21.1771	+	8.97983i	−1.29360	+	0.548530i
$269$			11.8730i			0.723909i	0.932196	+	0.361954i	$0.117890\pi$
$269$			11.8730i			0.723909i	−0.932196	+	0.361954i	$0.882110\pi$
$270$	−12.4924	+	18.8664i	−0.760265	+	1.14817i
$271$	−10.2462			−0.622413			−0.311207	−	0.950342i	$-0.600733\pi$
$271$	−10.2462			−0.622413			−0.311207	+	0.950342i	$0.600733\pi$
$272$	5.56155	−	5.75058i	0.337219	−	0.348680i
$273$		0			0
$274$	−12.6847	+	19.1567i	−0.766308	+	1.15730i
$275$		−	2.81164i		−	0.169548i
$276$	−28.4924	+	12.0818i	−1.71504	+	0.727238i
$277$		−	2.64861i		−	0.159140i	−0.996829	−	0.0795699i	$-0.974645\pi$
$277$		−	2.64861i		−	0.159140i	0.996829	−	0.0795699i	$-0.0253547\pi$
$278$	−9.80776	−	6.49424i	−0.588231	−	0.389499i
$279$	−62.7386			−3.75606
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$		−	21.8868i		−	1.30104i	−0.759491	−	0.650518i	$-0.774552\pi$
$283$		−	21.8868i		−	1.30104i	0.759491	−	0.650518i	$-0.225448\pi$
$284$	6.24621	+	14.7304i	0.370644	+	0.874089i
$285$		−	15.4741i		−	0.916605i
$286$	−1.75379	+	2.64861i	−0.103704	+	0.156616i
$287$		0			0
$288$	−7.46543	−	33.8234i	−0.439905	−	1.99307i
$289$	−13.0000			−0.764706
$290$	8.00000	−	12.0818i	0.469776	−	0.709467i
$291$			36.9890i			2.16834i
$292$	−4.68466	−	11.0478i	−0.274149	−	0.646524i
$293$			10.3857i			0.606736i	0.952873	+	0.303368i	$0.0981112\pi$
$293$			10.3857i			0.606736i	−0.952873	+	0.303368i	$0.901889\pi$
$294$		0			0
$295$	−0.630683			−0.0367198
$296$	3.12311	−	16.7984i	0.181527	−	0.976386i
$297$	12.4924			0.724884
$298$	17.3693	+	11.5012i	1.00618	+	0.666244i
$299$		−	8.68951i		−	0.502527i
$300$	−11.8078	+	5.00691i	−0.681722	+	0.289074i
$301$		0			0
$302$	8.49242	−	12.8255i	0.488684	−	0.738022i
$303$	31.3693			1.80212
$304$	8.68466	+	8.39919i	0.498099	+	0.481727i
$305$	2.87689			0.164730
$306$	9.56155	−	14.4401i	0.546598	−	0.825485i
$307$		−	25.2791i		−	1.44275i	−0.692543	−	0.721377i	$-0.743510\pi$
$307$		−	25.2791i		−	1.44275i	0.692543	−	0.721377i	$-0.256490\pi$
$308$		0			0
$309$			6.78456i			0.385960i
$310$	20.4924	+	13.5691i	1.16389	+	0.770675i
$311$	12.4924			0.708380			0.354190	−	0.935173i	$-0.384757\pi$
$311$	12.4924			0.708380			0.354190	+	0.935173i	$0.384757\pi$
$312$	14.2462	+	2.64861i	0.806533	+	0.149948i
$313$	20.7386			1.17222			0.586108	−	0.810233i	$-0.300659\pi$
$313$	20.7386			1.17222			0.586108	+	0.810233i	$0.300659\pi$
$314$	−10.0000	−	6.62153i	−0.564333	−	0.373675i
$315$		0			0
$316$		0			0
$317$		−	4.13595i		−	0.232298i	−0.993232	−	0.116149i	$-0.962945\pi$
$317$		−	4.13595i		−	0.232298i	0.993232	−	0.116149i	$-0.0370550\pi$
$318$	−6.24621	+	9.43318i	−0.350270	+	0.528986i
$319$	−8.00000			−0.447914
$320$	−4.87689	+	12.6624i	−0.272627	+	0.707851i
$321$	42.7386			2.38544
$322$		0			0
$323$			6.04090i			0.336124i
$324$	−7.90388	−	18.6397i	−0.439105	−	1.03554i
$325$		−	3.60109i		−	0.199752i
$326$	−15.8078	−	10.4672i	−0.875511	−	0.579723i
$327$	54.7386			3.02705
$328$	11.8078	+	2.19526i	0.651975	+	0.121213i
$329$		0			0
$330$	−8.00000	−	5.29723i	−0.440386	−	0.291603i
$331$		−	14.8934i		−	0.818617i	−0.912396	−	0.409309i	$-0.865770\pi$
$331$		−	14.8934i		−	0.818617i	0.912396	−	0.409309i	$-0.134230\pi$
$332$	10.4384	−	4.42627i	0.572884	−	0.242923i
$333$		−	36.9890i		−	2.02699i
$334$	−6.24621	+	9.43318i	−0.341777	+	0.516161i
$335$	19.5076			1.06581
$336$		0			0
$337$	−0.876894			−0.0477675			−0.0238837	−	0.999715i	$-0.507603\pi$
$337$	−0.876894			−0.0477675			−0.0238837	+	0.999715i	$0.507603\pi$
$338$	7.90388	−	11.9366i	0.429915	−	0.649267i
$339$		−	14.7304i		−	0.800046i
$340$	−6.24621	+	2.64861i	−0.338748	+	0.143641i
$341$		−	13.5691i		−	0.734809i
$342$	21.8078	+	14.4401i	1.17923	+	0.780830i
$343$		0			0
$344$	−0.684658	+	3.68260i	−0.0369143	+	0.198553i
$345$	26.2462			1.41305
$346$	−22.4924	−	14.8934i	−1.20920	−	0.800676i
$347$		−	8.10887i		−	0.435307i	−0.976026	−	0.217654i	$-0.930160\pi$
$347$		−	8.10887i		−	0.435307i	0.976026	−	0.217654i	$-0.0698403\pi$
$348$	14.2462	+	33.5968i	0.763677	+	1.80098i
$349$			27.3471i			1.46385i	0.681383	+	0.731927i	$0.261379\pi$
$349$			27.3471i			1.46385i	−0.681383	+	0.731927i	$0.738621\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$	7.31534	−	1.61463i	0.389909	−	0.0860599i
$353$	−7.75379			−0.412693			−0.206346	−	0.978479i	$-0.566157\pi$
$353$	−7.75379			−0.412693			−0.206346	+	0.978479i	$0.566157\pi$
$354$	0.876894	−	1.32431i	0.0466064	−	0.0703861i
$355$		−	13.5691i		−	0.720175i
$356$	−12.6847	−	29.9142i	−0.672286	−	1.58545i
$357$		0			0
$358$	−5.56155	−	3.68260i	−0.293937	−	0.194632i
$359$	−31.3693			−1.65561			−0.827805	−	0.561017i	$-0.810410\pi$
$359$	−31.3693			−1.65561			−0.827805	+	0.561017i	$0.810410\pi$
$360$	−5.36932	+	28.8802i	−0.282988	+	1.52212i
$361$	9.87689			0.519837
$362$	−8.24621	−	5.46026i	−0.433411	−	0.286985i
$363$		−	27.9277i		−	1.46582i
$364$		0			0
$365$			10.1768i			0.532680i
$366$	−4.00000	+	6.04090i	−0.209083	+	0.315763i
$367$	−10.2462			−0.534848			−0.267424	−	0.963579i	$-0.586172\pi$
$367$	−10.2462			−0.534848			−0.267424	+	0.963579i	$0.586172\pi$
$368$	−14.2462	+	14.7304i	−0.742635	+	0.767875i
$369$	26.0000			1.35351
$370$	−8.00000	+	12.0818i	−0.415900	+	0.628102i
$371$		0			0
$372$	−56.9848	+	24.1636i	−2.95453	+	1.25282i
$373$			14.7304i			0.762711i	0.924428	+	0.381356i	$0.124543\pi$
$373$			14.7304i			0.762711i	−0.924428	+	0.381356i	$0.875457\pi$
$374$	3.12311	+	2.06798i	0.161492	+	0.106932i
$375$	36.4924			1.88446
$376$		0			0
$377$	−10.2462			−0.527707
$378$		0			0
$379$			36.4084i			1.87017i	0.354418	+	0.935087i	$0.384679\pi$
$379$			36.4084i			1.87017i	−0.354418	+	0.935087i	$0.615321\pi$
$380$	−4.00000	−	9.43318i	−0.205196	−	0.483912i
$381$		−	39.6377i		−	2.03070i
$382$	12.4924	−	18.8664i	0.639168	−	0.965287i
$383$	4.49242			0.229552			0.114776	−	0.993391i	$-0.463385\pi$
$383$	4.49242			0.229552			0.114776	+	0.993391i	$0.463385\pi$
$384$	−19.8078	−	27.8462i	−1.01081	−	1.42102i
$385$		0			0
$386$	−8.68466	+	13.1158i	−0.442037	+	0.667576i
$387$			8.10887i			0.412197i
$388$	9.56155	+	22.5490i	0.485414	+	1.14475i
$389$		−	24.9073i		−	1.26285i	−0.775438	−	0.631424i	$-0.782471\pi$
$389$		−	24.9073i		−	1.26285i	0.775438	−	0.631424i	$-0.217529\pi$
$390$	−10.2462	−	6.78456i	−0.518837	−	0.343550i
$391$	−10.2462			−0.518173
$392$		0			0
$393$	37.6155			1.89745
$394$	25.3693	+	16.7984i	1.27809	+	0.846290i
$395$		0			0
$396$	14.9309	−	6.33122i	0.750304	−	0.318156i
$397$			20.5625i			1.03200i	0.856588	+	0.516001i	$0.172580\pi$
$397$			20.5625i			1.03200i	−0.856588	+	0.516001i	$0.827420\pi$
$398$	14.2462	−	21.5150i	0.714098	−	1.07845i
$399$		0			0
$400$	−5.90388	+	6.10454i	−0.295194	+	0.305227i
$401$	−0.876894			−0.0437900			−0.0218950	−	0.999760i	$-0.506970\pi$
$401$	−0.876894			−0.0437900			−0.0218950	+	0.999760i	$0.506970\pi$
$402$	−27.1231	+	40.9620i	−1.35278	+	2.04300i
$403$		−	17.3790i		−	0.865711i
$404$	19.1231	−	8.10887i	0.951410	−	0.403431i
$405$			17.1702i			0.853195i
$406$		0			0
$407$	8.00000			0.396545
$408$	3.12311	−	16.7984i	0.154617	−	0.831644i
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$	−8.49242	−	5.62329i	−0.419411	−	0.277714i
$411$			49.0708i			2.42049i
$412$	1.75379	+	4.13595i	0.0864030	+	0.203764i
$413$		0			0
$414$	−24.4924	+	36.9890i	−1.20374	+	1.81791i
$415$	−9.61553			−0.472008
$416$	9.36932	−	2.06798i	0.459369	−	0.101391i
$417$	−25.1231			−1.23028
$418$	−3.12311	+	4.71659i	−0.152756	+	0.230696i
$419$			27.9277i			1.36436i	0.731185	+	0.682179i	$0.238967\pi$
$419$			27.9277i			1.36436i	−0.731185	+	0.682179i	$0.761033\pi$
$420$		0			0
$421$		−	26.8122i		−	1.30675i	−0.757036	−	0.653373i	$-0.773353\pi$
$421$		−	26.8122i		−	1.30675i	0.757036	−	0.653373i	$-0.226647\pi$
$422$	−5.56155	−	3.68260i	−0.270732	−	0.179266i
$423$		0			0
$424$	−1.36932	+	7.36520i	−0.0664999	+	0.357686i
$425$	−4.24621			−0.205971
$426$	28.4924	+	18.8664i	1.38046	+	0.914078i
$427$		0			0
$428$	26.0540	−	11.0478i	1.25937	−	0.534016i
$429$			6.78456i			0.327562i
$430$	1.75379	−	2.64861i	0.0845752	−	0.127727i
$431$	17.6155			0.848510			0.424255	−	0.905543i	$-0.360536\pi$
$431$	17.6155			0.848510			0.424255	+	0.905543i	$0.360536\pi$
$432$	−27.1231	−	26.2316i	−1.30496	−	1.26207i
$433$	18.4924			0.888689			0.444345	−	0.895856i	$-0.353437\pi$
$433$	18.4924			0.888689			0.444345	+	0.895856i	$0.353437\pi$
$434$		0			0
$435$		−	30.9481i		−	1.48385i
$436$	33.3693	−	14.1498i	1.59810	−	0.677651i
$437$		−	15.4741i		−	0.740225i
$438$	−21.3693	−	14.1498i	−1.02107	−	0.676102i
$439$	−22.7386			−1.08526			−0.542628	−	0.839973i	$-0.682571\pi$
$439$	−22.7386			−1.08526			−0.542628	+	0.839973i	$0.682571\pi$
$440$	−6.24621	−	1.16128i	−0.297776	−	0.0553617i
$441$		0			0
$442$	4.00000	+	2.64861i	0.190261	+	0.125982i
$443$			7.36520i			0.349931i	0.984575	+	0.174966i	$0.0559814\pi$
$443$			7.36520i			0.349931i	−0.984575	+	0.174966i	$0.944019\pi$
$444$	−14.2462	−	33.5968i	−0.676095	−	1.59443i
$445$			27.5559i			1.30627i
$446$	4.49242	−	6.78456i	0.212722	−	0.321258i
$447$	44.4924			2.10442
$448$		0			0
$449$	16.7386			0.789945			0.394972	−	0.918693i	$-0.370754\pi$
$449$	16.7386			0.789945			0.394972	+	0.918693i	$0.370754\pi$
$450$	−10.1501	+	15.3289i	−0.478480	+	0.722612i
$451$			5.62329i			0.264790i
$452$	−3.80776	−	8.97983i	−0.179102	−	0.422376i
$453$		−	32.8531i		−	1.54357i
$454$	−11.5616	−	7.65552i	−0.542611	−	0.359291i
$455$		0			0
$456$	25.3693	+	4.71659i	1.18803	+	0.220875i
$457$	17.3693			0.812502			0.406251	−	0.913761i	$-0.366836\pi$
$457$	17.3693			0.812502			0.406251	+	0.913761i	$0.366836\pi$
$458$	30.4924	+	20.1907i	1.42482	+	0.943448i
$459$		−	18.8664i		−	0.880606i
$460$	16.0000	−	6.78456i	0.746004	−	0.316332i
$461$			24.3724i			1.13514i	0.823327	+	0.567568i	$0.192115\pi$
$461$			24.3724i			1.13514i	−0.823327	+	0.567568i	$0.807885\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	17.3693	+	16.7984i	0.806350	+	0.779845i
$465$	52.4924			2.43428
$466$	−12.6847	+	19.1567i	−0.587605	+	0.887416i
$467$		−	3.02045i		−	0.139770i	−0.997555	−	0.0698848i	$-0.977737\pi$
$467$		−	3.02045i		−	0.139770i	0.997555	−	0.0698848i	$-0.0222632\pi$
$468$	19.1231	−	8.10887i	0.883966	−	0.374833i
$469$		0			0
$470$		0			0
$471$	−25.6155			−1.18030
$472$	0.192236	−	1.03399i	0.00884838	−	0.0475931i
$473$	−1.75379			−0.0806393
$474$		0			0
$475$		−	6.41273i		−	0.294236i
$476$		0			0
$477$			16.2177i			0.742559i
$478$	−13.7538	+	20.7713i	−0.629084	+	0.950057i
$479$	−10.2462			−0.468161			−0.234081	−	0.972217i	$-0.575208\pi$
$479$	−10.2462			−0.468161			−0.234081	+	0.972217i	$0.575208\pi$
$480$	6.24621	+	28.2995i	0.285099	+	1.29169i
$481$	10.2462			0.467187
$482$	2.93087	−	4.42627i	0.133497	−	0.201611i
$483$		0			0
$484$	−7.21922	−	17.0251i	−0.328147	−	0.773866i
$485$		−	20.7713i		−	0.943176i
$486$	−2.68466	−	1.77766i	−0.121779	−	0.0806361i
$487$	0.630683			0.0285790			0.0142895	−	0.999898i	$-0.495451\pi$
$487$	0.630683			0.0285790			0.0142895	+	0.999898i	$0.495451\pi$
$488$	−0.876894	+	4.71659i	−0.0396951	+	0.213510i
$489$	−40.4924			−1.83113
$490$		0			0
$491$		−	34.1774i		−	1.54240i	−0.636590	−	0.771202i	$-0.719656\pi$
$491$		−	34.1774i		−	1.54240i	0.636590	−	0.771202i	$-0.280344\pi$
$492$	23.6155	−	10.0138i	1.06467	−	0.451458i
$493$			12.0818i			0.544137i
$494$	−4.00000	+	6.04090i	−0.179969	+	0.271793i
$495$	−13.7538			−0.618187
$496$	−28.4924	+	29.4608i	−1.27935	+	1.32283i
$497$		0			0
$498$	13.3693	−	20.1907i	0.599093	−	0.904765i
$499$			8.85254i			0.396294i	0.980172	+	0.198147i	$0.0634924\pi$
$499$			8.85254i			0.396294i	−0.980172	+	0.198147i	$0.936508\pi$
$500$	22.2462	−	9.43318i	0.994881	−	0.421865i
$501$			24.1636i			1.07955i
$502$	12.9309	+	8.56222i	0.577133	+	0.382151i
$503$	−13.7538			−0.613251			−0.306626	−	0.951830i	$-0.599200\pi$
$503$	−13.7538			−0.613251			−0.306626	+	0.951830i	$0.599200\pi$
$504$		0			0
$505$	−17.6155			−0.783881
$506$	−8.00000	−	5.29723i	−0.355643	−	0.235490i
$507$		−	30.5763i		−	1.35794i
$508$	−10.2462	−	24.1636i	−0.454602	−	1.07209i
$509$		−	30.7393i		−	1.36250i	−0.732052	−	0.681249i	$-0.761437\pi$
$509$		−	30.7393i		−	1.36250i	0.732052	−	0.681249i	$-0.238563\pi$
$510$	−8.00000	+	12.0818i	−0.354246	+	0.534991i
$511$		0			0
$512$	−19.2732	−	11.8551i	−0.851763	−	0.523927i
$513$	28.4924			1.25797
$514$	−17.5616	+	26.5219i	−0.774607	+	1.16983i
$515$		−	3.80989i		−	0.167884i
$516$	3.12311	+	7.36520i	0.137487	+	0.324235i
$517$		0			0
$518$		0			0
$519$	−57.6155			−2.52904
$520$	−8.00000	−	1.48734i	−0.350823	−	0.0652240i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$	43.6155	+	28.8802i	1.90900	+	1.26405i
$523$		−	41.1708i		−	1.80027i	−0.435609	−	0.900136i	$-0.643467\pi$
$523$		−	41.1708i		−	1.80027i	0.435609	−	0.900136i	$-0.356533\pi$
$524$	22.9309	−	9.72350i	1.00174	−	0.424773i
$525$		0			0
$526$	9.75379	−	14.7304i	0.425285	−	0.642276i
$527$	−20.4924			−0.892664
$528$	11.1231	−	11.5012i	0.484071	−	0.500523i
$529$	3.24621			0.141140
$530$	3.50758	−	5.29723i	0.152359	−	0.230097i
$531$		−	2.27678i		−	0.0988038i
$532$		0			0
$533$			7.20217i			0.311961i
$534$	−57.8617	−	38.3134i	−2.50392	−	1.65798i
$535$	−24.0000			−1.03761
$536$	−5.94602	+	31.9821i	−0.256829	+	1.38142i
$537$	−14.2462			−0.614769
$538$	14.0000	+	9.27015i	0.603583	+	0.399664i
$539$		0			0
$540$	12.4924	+	29.4608i	0.537588	+	1.26779i
$541$			13.2431i			0.569364i	0.958622	+	0.284682i	$0.0918880\pi$
$541$			13.2431i			0.569364i	−0.958622	+	0.284682i	$0.908112\pi$
$542$	−8.00000	+	12.0818i	−0.343629	+	0.518957i
$543$	−21.1231			−0.906479
$544$	−2.43845	−	11.0478i	−0.104548	−	0.473671i
$545$	−30.7386			−1.31670
$546$		0			0
$547$		−	9.59621i		−	0.410304i	−0.978730	−	0.205152i	$-0.934231\pi$
$547$		−	9.59621i		−	0.410304i	0.978730	−	0.205152i	$-0.0657689\pi$
$548$	12.6847	+	29.9142i	0.541862	+	1.27787i
$549$			10.3857i			0.443249i
$550$	−3.31534	−	2.19526i	−0.141367	−	0.0936064i
$551$	−18.2462			−0.777315
$552$	−8.00000	+	43.0299i	−0.340503	+	1.83148i
$553$		0			0
$554$	−3.12311	−	2.06798i	−0.132688	−	0.0878598i
$555$			30.9481i			1.31368i
$556$	−15.3153	+	6.49424i	−0.649515	+	0.275417i
$557$			2.64861i			0.112225i	0.998424	+	0.0561127i	$0.0178706\pi$
$557$			2.64861i			0.112225i	−0.998424	+	0.0561127i	$0.982129\pi$
$558$	−48.9848	+	73.9781i	−2.07369	+	3.13174i
$559$	−2.24621			−0.0950046
$560$		0			0
$561$	8.00000			0.337760
$562$	−4.68466	+	7.07488i	−0.197610	+	0.298436i
$563$			29.8326i			1.25730i	0.777690	+	0.628648i	$0.216391\pi$
$563$			29.8326i			1.25730i	−0.777690	+	0.628648i	$0.783609\pi$
$564$		0			0
$565$			8.27190i			0.348001i
$566$	−25.8078	−	17.0887i	−1.08478	−	0.718292i
$567$		0			0
$568$	22.2462	+	4.13595i	0.933430	+	0.173541i
$569$	−13.3693			−0.560471			−0.280235	−	0.959931i	$-0.590413\pi$
$569$	−13.3693			−0.560471			−0.280235	+	0.959931i	$0.590413\pi$
$570$	−18.2462	−	12.0818i	−0.764250	−	0.506051i
$571$			9.27015i			0.387944i	0.981007	+	0.193972i	$0.0621370\pi$
$571$			9.27015i			0.387944i	−0.981007	+	0.193972i	$0.937863\pi$
$572$	1.75379	+	4.13595i	0.0733296	+	0.172933i
$573$		−	48.3272i		−	2.01890i
$574$		0			0
$575$	10.8769			0.453598
$576$	−45.7116	−	17.6057i	−1.90465	−	0.733571i
$577$	−7.75379			−0.322794			−0.161397	−	0.986890i	$-0.551600\pi$
$577$	−7.75379			−0.322794			−0.161397	+	0.986890i	$0.551600\pi$
$578$	−10.1501	+	15.3289i	−0.422188	+	0.637599i
$579$			33.5968i			1.39623i
$580$	−8.00000	−	18.8664i	−0.332182	−	0.783383i
$581$		0			0
$582$	43.6155	+	28.8802i	1.80792	+	1.19712i
$583$	−3.50758			−0.145269
$584$	−16.6847	−	3.10196i	−0.690416	−	0.128360i
$585$	−17.6155			−0.728312
$586$	12.2462	+	8.10887i	0.505886	+	0.334974i
$587$		−	21.8868i		−	0.903365i	−0.892179	−	0.451683i	$-0.850824\pi$
$587$		−	21.8868i		−	0.903365i	0.892179	−	0.451683i	$-0.149176\pi$
$588$		0			0
$589$		−	30.9481i		−	1.27520i
$590$	−0.492423	+	0.743668i	−0.0202727	+	0.0306163i
$591$	64.9848			2.67312
$592$	−17.3693	−	16.7984i	−0.713875	−	0.690409i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$	9.75379	−	14.7304i	0.400203	−	0.604396i
$595$		0			0
$596$	27.1231	−	11.5012i	1.11101	−	0.471106i
$597$		−	55.1117i		−	2.25557i
$598$	−10.2462	−	6.78456i	−0.418999	−	0.277441i
$599$	−12.4924			−0.510427			−0.255213	−	0.966885i	$-0.582146\pi$
$599$	−12.4924			−0.510427			−0.255213	+	0.966885i	$0.582146\pi$
$600$	−3.31534	+	17.8324i	−0.135348	+	0.728003i
$601$	16.2462			0.662697			0.331348	−	0.943508i	$-0.392496\pi$
$601$	16.2462			0.662697			0.331348	+	0.943508i	$0.392496\pi$
$602$		0			0
$603$			70.4228i			2.86784i
$604$	−8.49242	−	20.0276i	−0.345552	−	0.814913i
$605$			15.6829i			0.637600i
$606$	24.4924	−	36.9890i	0.994937	−	1.50258i
$607$	−40.9848			−1.66352			−0.831762	−	0.555133i	$-0.812667\pi$
$607$	−40.9848			−1.66352			−0.831762	+	0.555133i	$0.812667\pi$
$608$	16.6847	−	3.68260i	0.676652	−	0.149349i
$609$		0			0
$610$	2.24621	−	3.39228i	0.0909464	−	0.137349i
$611$		0			0
$612$	−9.56155	−	22.5490i	−0.386503	−	0.911488i
$613$			2.23100i			0.0901094i	0.998985	+	0.0450547i	$0.0143462\pi$
$613$			2.23100i			0.0901094i	−0.998985	+	0.0450547i	$0.985654\pi$
$614$	−29.8078	−	19.7373i	−1.20294	−	0.796533i
$615$	−21.7538			−0.877197
$616$		0			0
$617$	−29.3693			−1.18236			−0.591182	−	0.806538i	$-0.701339\pi$
$617$	−29.3693			−1.18236			−0.591182	+	0.806538i	$0.701339\pi$
$618$	8.00000	+	5.29723i	0.321807	+	0.213086i
$619$			19.6558i			0.790033i	0.918674	+	0.395017i	$0.129261\pi$
$619$			19.6558i			0.790033i	−0.918674	+	0.395017i	$0.870739\pi$
$620$	32.0000	−	13.5691i	1.28515	−	0.544949i
$621$			48.3272i			1.93930i
$622$	9.75379	−	14.7304i	0.391091	−	0.590635i
$623$		0			0
$624$	14.2462	−	14.7304i	0.570305	−	0.589688i
$625$	−9.87689			−0.395076
$626$	16.1922	−	24.4539i	0.647172	−	0.977375i
$627$			12.0818i			0.482500i
$628$	−15.6155	+	6.62153i	−0.623127	+	0.264228i
$629$		−	12.0818i		−	0.481733i
$630$		0			0
$631$	−3.50758			−0.139634			−0.0698172	−	0.997560i	$-0.522242\pi$
$631$	−3.50758			−0.139634			−0.0698172	+	0.997560i	$0.522242\pi$
$632$		0			0
$633$	−14.2462			−0.566236
$634$	−4.87689	−	3.22925i	−0.193686	−	0.128250i
$635$			22.2586i			0.883307i
$636$	6.24621	+	14.7304i	0.247678	+	0.584099i
$637$		0			0
$638$	−6.24621	+	9.43318i	−0.247290	+	0.373463i
$639$	48.9848			1.93781
$640$	11.1231	+	15.6371i	0.439679	+	0.618111i
$641$	−5.36932			−0.212075			−0.106038	−	0.994362i	$-0.533816\pi$
$641$	−5.36932			−0.212075			−0.106038	+	0.994362i	$0.533816\pi$
$642$	33.3693	−	50.3951i	1.31698	−	1.98894i
$643$			5.66906i			0.223566i	0.993733	+	0.111783i	$0.0356562\pi$
$643$			5.66906i			0.223566i	−0.993733	+	0.111783i	$0.964344\pi$
$644$		0			0
$645$		−	6.78456i		−	0.267142i
$646$	7.12311	+	4.71659i	0.280255	+	0.185572i
$647$	−43.2311			−1.69959			−0.849794	−	0.527115i	$-0.823274\pi$
$647$	−43.2311			−1.69959			−0.849794	+	0.527115i	$0.823274\pi$
$648$	−28.1501	−	5.23358i	−1.10584	−	0.205595i
$649$	0.492423			0.0193293
$650$	−4.24621	−	2.81164i	−0.166550	−	0.110282i
$651$		0			0
$652$	−24.6847	+	10.4672i	−0.966726	+	0.409926i
$653$			31.6918i			1.24020i	0.784524	+	0.620098i	$0.212907\pi$
$653$			31.6918i			1.24020i	−0.784524	+	0.620098i	$0.787093\pi$
$654$	42.7386	−	64.5449i	1.67121	−	2.52391i
$655$	−21.1231			−0.825348
$656$	11.8078	−	12.2091i	0.461016	−	0.476685i
$657$	−36.7386			−1.43331
$658$		0			0
$659$		−	6.62153i		−	0.257938i	−0.991649	−	0.128969i	$-0.958833\pi$
$659$		−	6.62153i		−	0.257938i	0.991649	−	0.128969i	$-0.0411668\pi$
$660$	−12.4924	+	5.29723i	−0.486267	+	0.206194i
$661$		−	44.7261i		−	1.73964i	−0.493367	−	0.869821i	$-0.664234\pi$
$661$		−	44.7261i		−	1.73964i	0.493367	−	0.869821i	$-0.335766\pi$
$662$	−17.5616	−	11.6284i	−0.682549	−	0.451952i
$663$	10.2462			0.397930
$664$	2.93087	−	15.7644i	0.113740	−	0.611777i
$665$		0			0
$666$	−43.6155	−	28.8802i	−1.69007	−	1.11908i
$667$		−	30.9481i		−	1.19832i
$668$	6.24621	+	14.7304i	0.241673	+	0.569936i
$669$		−	17.3790i		−	0.671912i
$670$	15.2311	−	23.0023i	0.588427	−	0.888657i
$671$	−2.24621			−0.0867140
$672$		0			0
$673$	−38.9848			−1.50276			−0.751378	−	0.659872i	$-0.770610\pi$
$673$	−38.9848			−1.50276			−0.751378	+	0.659872i	$0.770610\pi$
$674$	−0.684658	+	1.03399i	−0.0263721	+	0.0398277i
$675$			20.0276i			0.770864i
$676$	−7.90388	−	18.6397i	−0.303995	−	0.716911i
$677$			17.1702i			0.659905i	0.943998	+	0.329952i	$0.107033\pi$
$677$			17.1702i			0.659905i	−0.943998	+	0.329952i	$0.892967\pi$
$678$	−17.3693	−	11.5012i	−0.667065	−	0.441699i
$679$		0			0
$680$	−1.75379	+	9.43318i	−0.0672547	+	0.361746i
$681$	−29.6155			−1.13487
$682$	−16.0000	−	10.5945i	−0.612672	−	0.405683i
$683$			0.580639i			0.0222175i	0.999938	+	0.0111088i	$0.00353610\pi$
$683$			0.580639i			0.0222175i	−0.999938	+	0.0111088i	$0.996464\pi$
$684$	34.0540	−	14.4401i	1.30209	−	0.552130i
$685$		−	27.5559i		−	1.05286i
$686$		0			0
$687$	78.1080			2.98000
$688$	3.80776	+	3.68260i	0.145170	+	0.140398i
$689$	−4.49242			−0.171148
$690$	20.4924	−	30.9481i	0.780133	−	1.17818i
$691$		−	38.8482i		−	1.47786i	−0.673785	−	0.738928i	$-0.735332\pi$
$691$		−	38.8482i		−	1.47786i	0.673785	−	0.738928i	$-0.264668\pi$
$692$	−35.1231	+	14.8934i	−1.33518	+	0.566163i
$693$		0			0
$694$	−9.56155	−	6.33122i	−0.362952	−	0.240330i
$695$	14.1080			0.535145
$696$	50.7386	+	9.43318i	1.92324	+	0.357564i
$697$	8.49242			0.321673
$698$	32.2462	+	21.3519i	1.22054	+	0.808183i
$699$			49.0708i			1.85603i
$700$		0			0
$701$		−	2.23100i		−	0.0842639i	−0.999112	−	0.0421319i	$-0.986585\pi$
$701$		−	2.23100i		−	0.0842639i	0.999112	−	0.0421319i	$-0.0134150\pi$
$702$	12.4924	−	18.8664i	0.471496	−	0.712065i
$703$	18.2462			0.688169
$704$	3.80776	−	9.88653i	0.143511	−	0.372612i
$705$		0			0
$706$	−6.05398	+	9.14286i	−0.227844	+	0.344096i
$707$		0			0
$708$	−0.876894	−	2.06798i	−0.0329557	−	0.0777193i
$709$		−	28.7171i		−	1.07849i	−0.842147	−	0.539247i	$-0.818709\pi$
$709$		−	28.7171i		−	1.07849i	0.842147	−	0.539247i	$-0.181291\pi$
$710$	−16.0000	−	10.5945i	−0.600469	−	0.397603i
$711$		0			0
$712$	−45.1771	−	8.39919i	−1.69308	−	0.314773i
$713$	52.4924			1.96586
$714$		0			0
$715$		−	3.80989i		−	0.142482i
$716$	−8.68466	+	3.68260i	−0.324561	+	0.137625i
$717$			53.2068i			1.98704i
$718$	−24.4924	+	36.9890i	−0.914049	+	1.38042i
$719$	52.4924			1.95764			0.978819	−	0.204730i	$-0.0656316\pi$
$719$	52.4924			1.95764			0.978819	+	0.204730i	$0.0656316\pi$
$720$	29.8617	+	28.8802i	1.11288	+	1.07630i
$721$		0			0
$722$	7.71165	−	11.6463i	0.286998	−	0.433431i
$723$		−	11.3381i		−	0.421669i
$724$	−12.8769	+	5.46026i	−0.478566	+	0.202929i
$725$		−	12.8255i		−	0.476326i
$726$	−32.9309	−	21.8053i	−1.22218	−	0.809270i
$727$	16.9848			0.629933			0.314967	−	0.949103i	$-0.398007\pi$
$727$	16.9848			0.629933			0.314967	+	0.949103i	$0.398007\pi$
$728$		0			0
$729$	23.4924			0.870090
$730$	12.0000	+	7.94584i	0.444140	+	0.294089i
$731$			2.64861i			0.0979625i
$732$	4.00000	+	9.43318i	0.147844	+	0.348660i
$733$			29.2520i			1.08045i	0.841521	+	0.540224i	$0.181660\pi$
$733$			29.2520i			1.08045i	−0.841521	+	0.540224i	$0.818340\pi$
$734$	−8.00000	+	12.0818i	−0.295285	+	0.445947i
$735$		0			0
$736$	6.24621	+	28.2995i	0.230238	+	1.04313i
$737$	−15.2311			−0.561043
$738$	20.3002	−	30.6578i	0.747260	−	1.12853i
$739$			21.3519i			0.785444i	0.919657	+	0.392722i	$0.128467\pi$
$739$			21.3519i			0.785444i	−0.919657	+	0.392722i	$0.871533\pi$
$740$	8.00000	+	18.8664i	0.294086	+	0.693541i
$741$			15.4741i			0.568454i
$742$		0			0
$743$	0.630683			0.0231375			0.0115688	−	0.999933i	$-0.496317\pi$
$743$	0.630683			0.0231375			0.0115688	+	0.999933i	$0.496317\pi$
$744$	−16.0000	+	86.0599i	−0.586588	+	3.15511i
$745$	−24.9848			−0.915374
$746$	17.3693	+	11.5012i	0.635936	+	0.421087i
$747$		−	34.7123i		−	1.27006i
$748$	4.87689	−	2.06798i	0.178317	−	0.0756127i
$749$		0			0
$750$	28.4924	−	43.0299i	1.04040	−	1.57123i
$751$	8.63068			0.314938			0.157469	−	0.987524i	$-0.449667\pi$
$751$	8.63068			0.314938			0.157469	+	0.987524i	$0.449667\pi$
$752$		0			0
$753$	33.1231			1.20707
$754$	−8.00000	+	12.0818i	−0.291343	+	0.439993i
$755$			18.4487i			0.671419i
$756$		0			0
$757$			26.3946i			0.959328i	0.877452	+	0.479664i	$0.159241\pi$
$757$			26.3946i			0.959328i	−0.877452	+	0.479664i	$0.840759\pi$
$758$	42.9309	+	28.4268i	1.55932	+	1.03251i
$759$	−20.4924			−0.743828
$760$	−14.2462	−	2.64861i	−0.516764	−	0.0960753i
$761$	−8.73863			−0.316775			−0.158388	−	0.987377i	$-0.550630\pi$
$761$	−8.73863			−0.316775			−0.158388	+	0.987377i	$0.550630\pi$
$762$	−46.7386	−	30.9481i	−1.69316	−	1.12113i
$763$		0			0
$764$	−12.4924	−	29.4608i	−0.451960	−	1.06585i
$765$			20.7713i			0.750988i
$766$	3.50758	−	5.29723i	0.126734	−	0.191397i
$767$	0.630683			0.0227726
$768$	−48.3002	+	1.61463i	−1.74288	+	0.0582628i
$769$	40.2462			1.45132			0.725658	−	0.688056i	$-0.241536\pi$
$769$	40.2462			1.45132			0.725658	+	0.688056i	$0.241536\pi$
$770$		0			0
$771$			67.9372i			2.44670i
$772$	8.68466	+	20.4810i	0.312568	+	0.737127i
$773$			1.69614i			0.0610060i	0.999535	+	0.0305030i	$0.00971091\pi$
$773$			1.69614i			0.0610060i	−0.999535	+	0.0305030i	$0.990289\pi$
$774$	9.56155	+	6.33122i	0.343683	+	0.227571i
$775$	21.7538			0.781419
$776$	34.0540	+	6.33122i	1.22247	+	0.227277i
$777$		0			0
$778$	−29.3693	−	19.4470i	−1.05294	−	0.697209i
$779$			12.8255i			0.459520i
$780$	−16.0000	+	6.78456i	−0.572892	+	0.242926i
$781$			10.5945i			0.379099i
$782$	−8.00000	+	12.0818i	−0.286079	+	0.432044i
$783$	56.9848			2.03647
$784$		0			0
$785$	14.3845			0.513404
$786$	29.3693	−	44.3542i	1.04757	−	1.58206i
$787$			10.5487i			0.376020i	0.982167	+	0.188010i	$0.0602037\pi$
$787$			10.5487i			0.376020i	−0.982167	+	0.188010i	$0.939796\pi$
$788$	39.6155	−	16.7984i	1.41124	−	0.598418i
$789$		−	37.7327i		−	1.34332i
$790$		0			0
$791$		0			0
$792$	4.19224	−	22.5490i	0.148965	−	0.801242i
$793$	−2.87689			−0.102162
$794$	24.2462	+	16.0547i	0.860466	+	0.569760i
$795$		−	13.5691i		−	0.481247i
$796$	−14.2462	−	33.5968i	−0.504944	−	1.19081i
$797$		−	25.8597i		−	0.915998i	−0.888953	−	0.457999i	$-0.848566\pi$
$797$		−	25.8597i		−	0.915998i	0.888953	−	0.457999i	$-0.151434\pi$
$798$		0			0
$799$		0			0
$800$	2.58854	+	11.7278i	0.0915187	+	0.414641i
$801$	−99.4773			−3.51486
$802$	−0.684658	+	1.03399i	−0.0241761	+	0.0365114i
$803$		−	7.94584i		−	0.280403i
$804$	27.1231	+	63.9643i	0.956558	+	2.25585i
$805$		0			0
$806$	−20.4924	−	13.5691i	−0.721815	−	0.477952i
$807$	35.8617			1.26239
$808$	5.36932	−	28.8802i	0.188892	−	1.01600i
$809$	37.8617			1.33115			0.665574	−	0.746332i	$-0.268187\pi$
$809$	37.8617			1.33115			0.665574	+	0.746332i	$0.268187\pi$
$810$	20.2462	+	13.4061i	0.711379	+	0.471042i
$811$			15.8459i			0.556425i	0.960520	+	0.278213i	$0.0897420\pi$
$811$			15.8459i			0.556425i	−0.960520	+	0.278213i	$0.910258\pi$
$812$		0			0
$813$			30.9481i			1.08540i
$814$	6.24621	−	9.43318i	0.218930	−	0.330633i
$815$	22.7386			0.796500
$816$	−17.3693	−	16.7984i	−0.608048	−	0.588061i
$817$	−4.00000			−0.139942
$818$	−20.3002	+	30.6578i	−0.709779	+	1.07193i
$819$		0			0
$820$	−13.2614	+	5.62329i	−0.463107	+	0.196374i
$821$		−	33.5968i		−	1.17254i	−0.810118	−	0.586268i	$-0.800597\pi$
$821$		−	33.5968i		−	1.17254i	0.810118	−	0.586268i	$-0.199403\pi$
$822$	57.8617	+	38.3134i	2.01816	+	1.33633i
$823$	−32.9848			−1.14978			−0.574890	−	0.818231i	$-0.694955\pi$
$823$	−32.9848			−1.14978			−0.574890	+	0.818231i	$0.694955\pi$
$824$	6.24621	+	1.16128i	0.217597	+	0.0404550i
$825$	−8.49242			−0.295668
$826$		0			0
$827$		−	6.20393i		−	0.215732i	−0.994165	−	0.107866i	$-0.965598\pi$
$827$		−	6.20393i		−	0.215732i	0.994165	−	0.107866i	$-0.0344017\pi$
$828$	24.4924	+	57.7603i	0.851171	+	2.00731i
$829$			46.6310i			1.61956i	0.586732	+	0.809781i	$0.300414\pi$
$829$			46.6310i			1.61956i	−0.586732	+	0.809781i	$0.699586\pi$
$830$	−7.50758	+	11.3381i	−0.260592	+	0.393552i
$831$	−8.00000			−0.277517
$832$	4.87689	−	12.6624i	0.169076	−	0.438991i
$833$		0			0
$834$	−19.6155	+	29.6238i	−0.679230	+	1.02579i
$835$		−	13.5691i		−	0.469579i
$836$	3.12311	+	7.36520i	0.108015	+	0.254731i
$837$			96.6543i			3.34086i
$838$	32.9309	+	21.8053i	1.13758	+	0.753251i
$839$	6.73863			0.232643			0.116322	−	0.993212i	$-0.462890\pi$
$839$	6.73863			0.232643			0.116322	+	0.993212i	$0.462890\pi$
$840$		0			0
$841$	−7.49242			−0.258359
$842$	−31.6155	−	20.9343i	−1.08954	−	0.721445i
$843$			18.1227i			0.624179i
$844$	−8.68466	+	3.68260i	−0.298938	+	0.126760i
$845$			17.1702i			0.590673i
$846$		0			0
$847$		0			0
$848$	7.61553	+	7.36520i	0.261518	+	0.252922i
$849$	−66.1080			−2.26882
$850$	−3.31534	+	5.00691i	−0.113715	+	0.171736i
$851$			30.9481i			1.06089i
$852$	44.4924	−	18.8664i	1.52429	−	0.646351i
$853$		−	25.4421i		−	0.871121i	−0.900159	−	0.435561i	$-0.856550\pi$
$853$		−	25.4421i		−	0.871121i	0.900159	−	0.435561i	$-0.143450\pi$
$854$		0			0
$855$	−31.3693			−1.07281
$856$	7.31534	−	39.3473i	0.250033	−	1.34486i
$857$	46.9848			1.60497			0.802486	−	0.596671i	$-0.203510\pi$
$857$	46.9848			1.60497			0.802486	+	0.596671i	$0.203510\pi$
$858$	8.00000	+	5.29723i	0.273115	+	0.180844i
$859$			28.3453i			0.967129i	0.875309	+	0.483565i	$0.160658\pi$
$859$			28.3453i			0.967129i	−0.875309	+	0.483565i	$0.839342\pi$
$860$	−1.75379	−	4.13595i	−0.0598037	−	0.141035i
$861$		0			0
$862$	13.7538	−	20.7713i	0.468456	−	0.707473i
$863$	36.4924			1.24222			0.621108	−	0.783725i	$-0.286683\pi$
$863$	36.4924			1.24222			0.621108	+	0.783725i	$0.286683\pi$
$864$	−52.1080	+	11.5012i	−1.77275	+	0.391277i
$865$	32.3542			1.10007
$866$	14.4384	−	21.8053i	0.490638	−	0.740974i
$867$			39.2658i			1.33354i
$868$		0			0
$869$		0			0
$870$	−36.4924	−	24.1636i	−1.23721	−	0.819222i
$871$	−19.5076			−0.660989
$872$	9.36932	−	50.3951i	0.317285	−	1.70659i
$873$	74.9848			2.53785
$874$	−18.2462	−	12.0818i	−0.617187	−	0.408673i
$875$		0			0
$876$	−33.3693	+	14.1498i	−1.12744	+	0.478076i
$877$			35.5017i			1.19881i	0.800447	+	0.599404i	$0.204596\pi$
$877$			35.5017i			1.19881i	−0.800447	+	0.599404i	$0.795404\pi$
$878$	−17.7538	+	26.8122i	−0.599161	+	0.904868i
$879$	31.3693			1.05806
$880$	−6.24621	+	6.45850i	−0.210560	+	0.217716i
$881$	−44.2462			−1.49069			−0.745346	−	0.666677i	$-0.767716\pi$
$881$	−44.2462			−1.49069			−0.745346	+	0.666677i	$0.767716\pi$
$882$		0			0
$883$		−	4.71659i		−	0.158726i	−0.996846	−	0.0793629i	$-0.974711\pi$
$883$		−	4.71659i		−	0.158726i	0.996846	−	0.0793629i	$-0.0252886\pi$
$884$	6.24621	−	2.64861i	0.210083	−	0.0890825i
$885$			1.90495i			0.0640340i
$886$	8.68466	+	5.75058i	0.291767	+	0.193194i
$887$	28.4924			0.956682			0.478341	−	0.878174i	$-0.341238\pi$
$887$	28.4924			0.956682			0.478341	+	0.878174i	$0.341238\pi$
$888$	−50.7386	−	9.43318i	−1.70268	−	0.316557i
$889$		0			0
$890$	32.4924	+	21.5150i	1.08915	+	0.721183i
$891$		−	13.4061i		−	0.449121i
$892$	−4.49242	−	10.5945i	−0.150417	−	0.354729i
$893$		0			0
$894$	34.7386	−	52.4631i	1.16183	−	1.75463i
$895$	8.00000			0.267411
$896$		0			0
$897$	−26.2462			−0.876335
$898$	13.0691	−	19.7373i	0.436123	−	0.658643i
$899$		−	61.8963i		−	2.06436i
$900$	10.1501	+	23.9369i	0.338336	+	0.797897i
$901$			5.29723i			0.176476i
$902$	6.63068	+	4.39053i	0.220778	+	0.146189i
$903$		0			0
$904$	−13.5616	−	2.52132i	−0.451051	−	0.0838580i
$905$	11.8617			0.394298
$906$	−38.7386	−	25.6509i	−1.28700	−	0.852195i
$907$		−	51.5564i		−	1.71190i	−0.517056	−	0.855951i	$-0.672972\pi$
$907$		−	51.5564i		−	1.71190i	0.517056	−	0.855951i	$-0.327028\pi$
$908$	−18.0540	+	7.65552i	−0.599142	+	0.254057i
$909$		−	63.5924i		−	2.10923i
$910$		0			0
$911$	11.8617			0.392997			0.196498	−	0.980504i	$-0.437043\pi$
$911$	11.8617			0.392997			0.196498	+	0.980504i	$0.437043\pi$
$912$	25.3693	−	26.2316i	0.840062	−	0.868614i
$913$	7.50758			0.248465
$914$	13.5616	−	20.4810i	0.448576	−	0.677451i
$915$		−	8.68951i		−	0.287266i
$916$	47.6155	−	20.1907i	1.57326	−	0.667118i
$917$		0			0
$918$	−22.2462	−	14.7304i	−0.734234	−	0.486176i
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$	4.49242	−	24.1636i	0.148111	−	0.796650i
$921$	−76.3542			−2.51596
$922$	28.7386	+	19.0294i	0.946456	+	0.626699i
$923$			13.5691i			0.446633i
$924$		0			0
$925$			12.8255i			0.421699i
$926$		0			0
$927$	13.7538			0.451734
$928$	33.3693	−	7.36520i	1.09540	−	0.241775i
$929$	2.49242			0.0817737			0.0408869	−	0.999164i	$-0.486982\pi$
$929$	2.49242			0.0817737			0.0408869	+	0.999164i	$0.486982\pi$
$930$	40.9848	−	61.8963i	1.34395	−	2.02966i
$931$		0			0
$932$	12.6847	+	29.9142i	0.415500	+	0.979871i
$933$		−	37.7327i		−	1.23531i
$934$	−3.56155	−	2.35829i	−0.116538	−	0.0771658i
$935$	−4.49242			−0.146918
$936$	5.36932	−	28.8802i	0.175502	−	0.943978i
$937$	−34.9848			−1.14291			−0.571453	−	0.820635i	$-0.693620\pi$
$937$	−34.9848			−1.14291			−0.571453	+	0.820635i	$0.693620\pi$
$938$		0			0
$939$		−	62.6400i		−	2.04418i
$940$		0			0
$941$		−	30.7393i		−	1.00207i	−0.865426	−	0.501037i	$-0.832952\pi$
$941$		−	30.7393i		−	1.00207i	0.865426	−	0.501037i	$-0.167048\pi$
$942$	−20.0000	+	30.2045i	−0.651635	+	0.984115i
$943$	−21.7538			−0.708401
$944$	−1.06913	−	1.03399i	−0.0347972	−	0.0336534i
$945$		0			0
$946$	−1.36932	+	2.06798i	−0.0445203	+	0.0672357i
$947$			41.7056i			1.35525i	0.735407	+	0.677625i	$0.236991\pi$
$947$			41.7056i			1.35525i	−0.735407	+	0.677625i	$0.763009\pi$
$948$		0			0
$949$		−	10.1768i		−	0.330354i
$950$	−7.56155	−	5.00691i	−0.245329	−	0.162446i
$951$	−12.4924			−0.405095
$952$		0			0
$953$	−17.5076			−0.567126			−0.283563	−	0.958954i	$-0.591517\pi$
$953$	−17.5076			−0.567126			−0.283563	+	0.958954i	$0.591517\pi$
$954$	19.1231	+	12.6624i	0.619133	+	0.409961i
$955$			27.1383i			0.878173i
$956$	13.7538	+	32.4355i	0.444829	+	1.04904i
$957$			24.1636i			0.781098i
$958$	−8.00000	+	12.0818i	−0.258468	+	0.390345i
$959$		0			0
$960$	38.2462	+	14.7304i	1.23439	+	0.475422i
$961$	73.9848			2.38661
$962$	8.00000	−	12.0818i	0.257930	−	0.389533i
$963$		−	86.6405i		−	2.79195i
$964$	−2.93087	−	6.91185i	−0.0943970	−	0.222616i
$965$		−	18.8664i		−	0.607329i
$966$		0			0
$967$	−10.8769			−0.349777			−0.174889	−	0.984588i	$-0.555957\pi$
$967$	−10.8769			−0.349777			−0.174889	+	0.984588i	$0.555957\pi$
$968$	−25.7116	−	4.78023i	−0.826404	−	0.153643i
$969$	18.2462			0.586153
$970$	−24.4924	−	16.2177i	−0.786404	−	0.520720i
$971$			10.9663i			0.351925i	0.984397	+	0.175962i	$0.0563037\pi$
$971$			10.9663i			0.351925i	−0.984397	+	0.175962i	$0.943696\pi$
$972$	−4.19224	+	1.77766i	−0.134466	+	0.0570183i
$973$		0			0
$974$	0.492423	−	0.743668i	0.0157782	−	0.0238287i
$975$	−10.8769			−0.348339
$976$	4.87689	+	4.71659i	0.156106	+	0.150974i
$977$	23.7538			0.759951			0.379976	−	0.924997i	$-0.375932\pi$
$977$	23.7538			0.759951			0.379976	+	0.924997i	$0.375932\pi$
$978$	−31.6155	+	47.7465i	−1.01095	+	1.52677i
$979$		−	21.5150i		−	0.687621i
$980$		0			0
$981$		−	110.967i		−	3.54291i
$982$	−40.3002	−	26.6849i	−1.28603	−	0.851550i
$983$	34.2462			1.09228			0.546142	−	0.837692i	$-0.316096\pi$
$983$	34.2462			1.09228			0.546142	+	0.837692i	$0.316096\pi$
$984$	6.63068	−	35.6647i	0.211378	−	1.13695i
$985$	−36.4924			−1.16275
$986$	14.2462	+	9.43318i	0.453692	+	0.300414i
$987$		0			0
$988$	4.00000	+	9.43318i	0.127257	+	0.300109i
$989$		−	6.78456i		−	0.215737i
$990$	−10.7386	+	16.2177i	−0.341296	+	0.515434i
$991$	−36.4924			−1.15922			−0.579610	−	0.814894i	$-0.696795\pi$
$991$	−36.4924			−1.15922			−0.579610	+	0.814894i	$0.696795\pi$
$992$	12.4924	+	56.5991i	0.396635	+	1.79702i
$993$	−44.9848			−1.42755
$994$		0			0
$995$			30.9481i			0.981122i
$996$	−13.3693	−	31.5288i	−0.423623	−	0.999028i
$997$		−	33.0619i		−	1.04708i	−0.852001	−	0.523540i	$-0.824611\pi$
$997$		−	33.0619i		−	1.04708i	0.852001	−	0.523540i	$-0.175389\pi$
$998$	10.4384	+	6.91185i	0.330423	+	0.218791i
$999$	−56.9848			−1.80292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.b.c.197.3		4
4.3	odd	2		1568.2.b.d.785.4		4
7.2	even	3		392.2.p.e.165.1		8
7.3	odd	6		392.2.p.f.373.3		8
7.4	even	3		392.2.p.e.373.3		8
7.5	odd	6		392.2.p.f.165.1		8
7.6	odd	2		56.2.b.b.29.3	✓	4
8.3	odd	2		1568.2.b.d.785.1		4
8.5	even	2	inner	392.2.b.c.197.4		4
21.20	even	2		504.2.c.d.253.2		4
28.3	even	6		1568.2.t.d.177.1		8
28.11	odd	6		1568.2.t.e.177.4		8
28.19	even	6		1568.2.t.d.753.4		8
28.23	odd	6		1568.2.t.e.753.1		8
28.27	even	2		224.2.b.b.113.1		4
56.3	even	6		1568.2.t.d.177.4		8
56.5	odd	6		392.2.p.f.165.3		8
56.11	odd	6		1568.2.t.e.177.1		8
56.13	odd	2		56.2.b.b.29.4	yes	4
56.19	even	6		1568.2.t.d.753.1		8
56.27	even	2		224.2.b.b.113.4		4
56.37	even	6		392.2.p.e.165.3		8
56.45	odd	6		392.2.p.f.373.1		8
56.51	odd	6		1568.2.t.e.753.4		8
56.53	even	6		392.2.p.e.373.1		8
84.83	odd	2		2016.2.c.c.1009.3		4
112.13	odd	4		1792.2.a.x.1.1		4
112.27	even	4		1792.2.a.v.1.1		4
112.69	odd	4		1792.2.a.x.1.4		4
112.83	even	4		1792.2.a.v.1.4		4
168.83	odd	2		2016.2.c.c.1009.2		4
168.125	even	2		504.2.c.d.253.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.b.b.29.3	✓	4	7.6	odd	2
56.2.b.b.29.4	yes	4	56.13	odd	2
224.2.b.b.113.1		4	28.27	even	2
224.2.b.b.113.4		4	56.27	even	2
392.2.b.c.197.3		4	1.1	even	1	trivial
392.2.b.c.197.4		4	8.5	even	2	inner
392.2.p.e.165.1		8	7.2	even	3
392.2.p.e.165.3		8	56.37	even	6
392.2.p.e.373.1		8	56.53	even	6
392.2.p.e.373.3		8	7.4	even	3
392.2.p.f.165.1		8	7.5	odd	6
392.2.p.f.165.3		8	56.5	odd	6
392.2.p.f.373.1		8	56.45	odd	6
392.2.p.f.373.3		8	7.3	odd	6
504.2.c.d.253.1		4	168.125	even	2
504.2.c.d.253.2		4	21.20	even	2
1568.2.b.d.785.1		4	8.3	odd	2
1568.2.b.d.785.4		4	4.3	odd	2
1568.2.t.d.177.1		8	28.3	even	6
1568.2.t.d.177.4		8	56.3	even	6
1568.2.t.d.753.1		8	56.19	even	6
1568.2.t.d.753.4		8	28.19	even	6
1568.2.t.e.177.1		8	56.11	odd	6
1568.2.t.e.177.4		8	28.11	odd	6
1568.2.t.e.753.1		8	28.23	odd	6
1568.2.t.e.753.4		8	56.51	odd	6
1792.2.a.v.1.1		4	112.27	even	4
1792.2.a.v.1.4		4	112.83	even	4
1792.2.a.x.1.1		4	112.13	odd	4
1792.2.a.x.1.4		4	112.69	odd	4
2016.2.c.c.1009.2		4	168.83	odd	2
2016.2.c.c.1009.3		4	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.780776 - 1.17915i) q^{2} -3.02045i q^{3} +(-0.780776 - 1.84130i) q^{4} +1.69614i q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} -6.12311 q^{9} +O(q^{10})\)	\(q+(0.780776 - 1.17915i) q^{2} -3.02045i q^{3} +(-0.780776 - 1.84130i) q^{4} +1.69614i q^{5} +(-3.56155 - 2.35829i) q^{6} +(-2.78078 - 0.516994i) q^{8} -6.12311 q^{9} +(2.00000 + 1.32431i) q^{10} -1.32431i q^{11} +(-5.56155 + 2.35829i) q^{12} -1.69614i q^{13} +5.12311 q^{15} +(-2.78078 + 2.87529i) q^{16} -2.00000 q^{17} +(-4.78078 + 7.22004i) q^{18} -3.02045i q^{19} +(3.12311 - 1.32431i) q^{20} +(-1.56155 - 1.03399i) q^{22} +5.12311 q^{23} +(-1.56155 + 8.39919i) q^{24} +2.12311 q^{25} +(-2.00000 - 1.32431i) q^{26} +9.43318i q^{27} -6.04090i q^{29} +(4.00000 - 6.04090i) q^{30} +10.2462 q^{31} +(1.21922 + 5.52390i) q^{32} -4.00000 q^{33} +(-1.56155 + 2.35829i) q^{34} +(4.78078 + 11.2745i) q^{36} +6.04090i q^{37} +(-3.56155 - 2.35829i) q^{38} -5.12311 q^{39} +(0.876894 - 4.71659i) q^{40} -4.24621 q^{41} -1.32431i q^{43} +(-2.43845 + 1.03399i) q^{44} -10.3857i q^{45} +(4.00000 - 6.04090i) q^{46} +(8.68466 + 8.39919i) q^{48} +(1.65767 - 2.50345i) q^{50} +6.04090i q^{51} +(-3.12311 + 1.32431i) q^{52} -2.64861i q^{53} +(11.1231 + 7.36520i) q^{54} +2.24621 q^{55} -9.12311 q^{57} +(-7.12311 - 4.71659i) q^{58} +0.371834i q^{59} +(-4.00000 - 9.43318i) q^{60} -1.69614i q^{61} +(8.00000 - 12.0818i) q^{62} +(7.46543 + 2.87529i) q^{64} +2.87689 q^{65} +(-3.12311 + 4.71659i) q^{66} -11.5012i q^{67} +(1.56155 + 3.68260i) q^{68} -15.4741i q^{69} -8.00000 q^{71} +(17.0270 + 3.16561i) q^{72} +6.00000 q^{73} +(7.12311 + 4.71659i) q^{74} -6.41273i q^{75} +(-5.56155 + 2.35829i) q^{76} +(-4.00000 + 6.04090i) q^{78} +(-4.87689 - 4.71659i) q^{80} +10.1231 q^{81} +(-3.31534 + 5.00691i) q^{82} +5.66906i q^{83} -3.39228i q^{85} +(-1.56155 - 1.03399i) q^{86} -18.2462 q^{87} +(-0.684658 + 3.68260i) q^{88} +16.2462 q^{89} +(-12.2462 - 8.10887i) q^{90} +(-4.00000 - 9.43318i) q^{92} -30.9481i q^{93} +5.12311 q^{95} +(16.6847 - 3.68260i) q^{96} -12.2462 q^{97} +8.10887i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} - 6 q^{6} - 7 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^4 - 6 * q^6 - 7 * q^8 - 8 * q^9	\( 4 q - q^{2} + q^{4} - 6 q^{6} - 7 q^{8} - 8 q^{9} + 8 q^{10} - 14 q^{12} + 4 q^{15} - 7 q^{16} - 8 q^{17} - 15 q^{18} - 4 q^{20} + 2 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{30} + 8 q^{31} + 9 q^{32} - 16 q^{33} + 2 q^{34} + 15 q^{36} - 6 q^{38} - 4 q^{39} + 20 q^{40} + 16 q^{41} - 18 q^{44} + 16 q^{46} + 10 q^{48} + 19 q^{50} + 4 q^{52} + 28 q^{54} - 24 q^{55} - 20 q^{57} - 12 q^{58} - 16 q^{60} + 32 q^{62} + q^{64} + 28 q^{65} + 4 q^{66} - 2 q^{68} - 32 q^{71} + 31 q^{72} + 24 q^{73} + 12 q^{74} - 14 q^{76} - 16 q^{78} - 36 q^{80} + 24 q^{81} - 38 q^{82} + 2 q^{86} - 40 q^{87} + 22 q^{88} + 32 q^{89} - 16 q^{90} - 16 q^{92} + 4 q^{95} + 42 q^{96} - 16 q^{97}+O(q^{100}) \) 4 * q - q^2 + q^4 - 6 * q^6 - 7 * q^8 - 8 * q^9 + 8 * q^10 - 14 * q^12 + 4 * q^15 - 7 * q^16 - 8 * q^17 - 15 * q^18 - 4 * q^20 + 2 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^30 + 8 * q^31 + 9 * q^32 - 16 * q^33 + 2 * q^34 + 15 * q^36 - 6 * q^38 - 4 * q^39 + 20 * q^40 + 16 * q^41 - 18 * q^44 + 16 * q^46 + 10 * q^48 + 19 * q^50 + 4 * q^52 + 28 * q^54 - 24 * q^55 - 20 * q^57 - 12 * q^58 - 16 * q^60 + 32 * q^62 + q^64 + 28 * q^65 + 4 * q^66 - 2 * q^68 - 32 * q^71 + 31 * q^72 + 24 * q^73 + 12 * q^74 - 14 * q^76 - 16 * q^78 - 36 * q^80 + 24 * q^81 - 38 * q^82 + 2 * q^86 - 40 * q^87 + 22 * q^88 + 32 * q^89 - 16 * q^90 - 16 * q^92 + 4 * q^95 + 42 * q^96 - 16 * q^97

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