LMFDB - Embedded newform 1638.2.bj.f.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$0.560908 - 1.63871i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.f.1135.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(2.19962 + 3.80986i) q^{10} +(-0.971521 + 0.560908i) q^{11} +(-2.14345 + 2.89924i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.57781 + 2.73284i) q^{17} +(-6.99395 - 4.03796i) q^{19} +(3.80986 + 2.19962i) q^{20} +(-0.560908 + 0.971521i) q^{22} +(2.70436 + 4.68409i) q^{23} -14.3533 q^{25} +(-0.406663 + 3.58254i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-3.37076 - 5.83834i) q^{29} -5.58592i q^{31} +(-0.866025 - 0.500000i) q^{32} +3.15561i q^{34} +(2.19962 - 3.80986i) q^{35} +(6.59886 - 3.80986i) q^{37} -8.07591 q^{38} +4.39924 q^{40} +(1.78138 - 1.02848i) q^{41} +(0.792959 - 1.37344i) q^{43} +1.12182i q^{44} +(4.68409 + 2.70436i) q^{46} +7.58865i q^{47} +(0.500000 + 0.866025i) q^{49} +(-12.4304 + 7.17667i) q^{50} +(1.43909 + 3.30591i) q^{52} -8.44252 q^{53} +(-2.46757 - 4.27396i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-5.83834 - 3.37076i) q^{58} +(6.30380 + 3.63950i) q^{59} +(-5.20831 + 9.02106i) q^{61} +(-2.79296 - 4.83755i) q^{62} -1.00000 q^{64} +(-12.7545 - 9.42957i) q^{65} +(4.56902 - 2.63792i) q^{67} +(1.57781 + 2.73284i) q^{68} -4.39924i q^{70} +(-7.51422 - 4.33834i) q^{71} +12.7985i q^{73} +(3.80986 - 6.59886i) q^{74} +(-6.99395 + 4.03796i) q^{76} +1.12182 q^{77} -3.52106 q^{79} +(3.80986 - 2.19962i) q^{80} +(1.02848 - 1.78138i) q^{82} +11.1392i q^{83} +(-12.0224 - 6.94115i) q^{85} -1.58592i q^{86} +(0.560908 + 0.971521i) q^{88} +(-9.02707 + 5.21178i) q^{89} +(3.30591 - 1.43909i) q^{91} +5.40872 q^{92} +(3.79432 + 6.57196i) q^{94} +(17.7640 - 30.7681i) q^{95} +(1.06297 + 0.613704i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			4.39924i			1.96740i	0.179814	+	0.983701i	$0.442451\pi$
$5$			4.39924i			1.96740i	−0.179814	+	0.983701i	$0.557549\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.19962	+	3.80986i	0.695581	+	1.20478i
$11$	−0.971521	+	0.560908i	−0.292925	+	0.169120i	−0.639260	−	0.768991i	$-0.720759\pi$
$11$	−0.971521	+	0.560908i	−0.292925	+	0.169120i	0.346335	+	0.938111i	$0.387426\pi$
$12$		0			0
$13$	−2.14345	+	2.89924i	−0.594487	+	0.804105i
$13$	−2.14345	+	2.89924i	−0.594487	+	0.804105i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.57781	+	2.73284i	−0.382674	+	0.662811i	−0.991444	−	0.130536i	$-0.958330\pi$
$17$	−1.57781	+	2.73284i	−0.382674	+	0.662811i	0.608769	+	0.793347i	$0.291663\pi$
$18$		0			0
$19$	−6.99395	−	4.03796i	−1.60452	−	0.926371i	−0.990567	−	0.137029i	$-0.956245\pi$
$19$	−6.99395	−	4.03796i	−1.60452	−	0.926371i	−0.613954	−	0.789342i	$-0.710422\pi$
$20$	3.80986	+	2.19962i	0.851910	+	0.491850i
$21$		0			0
$22$	−0.560908	+	0.971521i	−0.119586	+	0.207129i
$23$	2.70436	+	4.68409i	0.563898	+	0.976700i	0.997151	+	0.0754280i	$0.0240323\pi$
$23$	2.70436	+	4.68409i	0.563898	+	0.976700i	−0.433253	+	0.901272i	$0.642634\pi$
$24$		0			0
$25$	−14.3533			−2.87067
$26$	−0.406663	+	3.58254i	−0.0797531	+	0.702595i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−3.37076	−	5.83834i	−0.625935	−	1.08415i	−0.988359	−	0.152138i	$-0.951384\pi$
$29$	−3.37076	−	5.83834i	−0.625935	−	1.08415i	0.362424	−	0.932013i	$-0.381949\pi$
$30$		0			0
$31$		−	5.58592i		−	1.00326i	−0.865082	−	0.501630i	$-0.832734\pi$
$31$		−	5.58592i		−	1.00326i	0.865082	−	0.501630i	$-0.167266\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			3.15561i			0.541183i
$35$	2.19962	−	3.80986i	0.371804	−	0.643983i
$36$		0			0
$37$	6.59886	−	3.80986i	1.08485	−	0.626337i	0.152647	−	0.988281i	$-0.451220\pi$
$37$	6.59886	−	3.80986i	1.08485	−	0.626337i	0.932200	+	0.361944i	$0.117887\pi$
$38$	−8.07591			−1.31009
$39$		0			0
$40$	4.39924			0.695581
$41$	1.78138	−	1.02848i	0.278204	−	0.160621i	−0.354406	−	0.935092i	$-0.615317\pi$
$41$	1.78138	−	1.02848i	0.278204	−	0.160621i	0.632610	+	0.774470i	$0.281984\pi$
$42$		0			0
$43$	0.792959	−	1.37344i	0.120925	−	0.209448i	−0.799208	−	0.601055i	$-0.794747\pi$
$43$	0.792959	−	1.37344i	0.120925	−	0.209448i	0.920133	+	0.391607i	$0.128081\pi$
$44$			1.12182i			0.169120i
$45$		0			0
$46$	4.68409	+	2.70436i	0.690631	+	0.398736i
$47$			7.58865i			1.10692i	0.832876	+	0.553459i	$0.186692\pi$
$47$			7.58865i			1.10692i	−0.832876	+	0.553459i	$0.813308\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−12.4304	+	7.17667i	−1.75792	+	1.01493i
$51$		0			0
$52$	1.43909	+	3.30591i	0.199566	+	0.458447i
$53$	−8.44252			−1.15967			−0.579834	−	0.814734i	$-0.696883\pi$
$53$	−8.44252			−1.15967			−0.579834	+	0.814734i	$0.696883\pi$
$54$		0			0
$55$	−2.46757	−	4.27396i	−0.332727	−	0.576300i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−5.83834	−	3.37076i	−0.766611	−	0.442603i
$59$	6.30380	+	3.63950i	0.820685	+	0.473823i	0.850653	−	0.525728i	$-0.176207\pi$
$59$	6.30380	+	3.63950i	0.820685	+	0.473823i	−0.0299675	+	0.999551i	$0.509540\pi$
$60$		0			0
$61$	−5.20831	+	9.02106i	−0.666856	+	1.15503i	0.311923	+	0.950107i	$0.399027\pi$
$61$	−5.20831	+	9.02106i	−0.666856	+	1.15503i	−0.978779	+	0.204921i	$0.934306\pi$
$62$	−2.79296	−	4.83755i	−0.354706	−	0.614369i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−12.7545	−	9.42957i	−1.58200	−	1.16959i
$66$		0			0
$67$	4.56902	−	2.63792i	0.558195	−	0.322274i	−0.194226	−	0.980957i	$-0.562219\pi$
$67$	4.56902	−	2.63792i	0.558195	−	0.322274i	0.752421	+	0.658683i	$0.228886\pi$
$68$	1.57781	+	2.73284i	0.191337	+	0.331405i
$69$		0			0
$70$		−	4.39924i		−	0.525810i
$71$	−7.51422	−	4.33834i	−0.891773	−	0.514866i	−0.0172513	−	0.999851i	$-0.505492\pi$
$71$	−7.51422	−	4.33834i	−0.891773	−	0.514866i	−0.874522	+	0.484986i	$0.838825\pi$
$72$		0			0
$73$			12.7985i			1.49795i	0.662599	+	0.748975i	$0.269454\pi$
$73$			12.7985i			1.49795i	−0.662599	+	0.748975i	$0.730546\pi$
$74$	3.80986	−	6.59886i	0.442887	−	0.767102i
$75$		0			0
$76$	−6.99395	+	4.03796i	−0.802261	+	0.463185i
$77$	1.12182			0.127843
$78$		0			0
$79$	−3.52106			−0.396150			−0.198075	−	0.980187i	$-0.563469\pi$
$79$	−3.52106			−0.396150			−0.198075	+	0.980187i	$0.563469\pi$
$80$	3.80986	−	2.19962i	0.425955	−	0.245925i
$81$		0			0
$82$	1.02848	−	1.78138i	0.113576	−	0.196720i
$83$			11.1392i			1.22269i	0.791366	+	0.611343i	$0.209370\pi$
$83$			11.1392i			1.22269i	−0.791366	+	0.611343i	$0.790630\pi$
$84$		0			0
$85$	−12.0224	−	6.94115i	−1.30402	−	0.752873i
$86$		−	1.58592i		−	0.171014i
$87$		0			0
$88$	0.560908	+	0.971521i	0.0597930	+	0.103565i
$89$	−9.02707	+	5.21178i	−0.956867	+	0.552448i	−0.895207	−	0.445650i	$-0.852973\pi$
$89$	−9.02707	+	5.21178i	−0.956867	+	0.552448i	−0.0616598	+	0.998097i	$0.519639\pi$
$90$		0			0
$91$	3.30591	−	1.43909i	0.346553	−	0.150858i
$92$	5.40872			0.563898
$93$		0			0
$94$	3.79432	+	6.57196i	0.391355	+	0.677846i
$95$	17.7640	−	30.7681i	1.82254	−	3.15674i
$96$		0			0
$97$	1.06297	+	0.613704i	0.107928	+	0.0623122i	0.552992	−	0.833186i	$-0.313486\pi$
$97$	1.06297	+	0.613704i	0.107928	+	0.0623122i	−0.445064	+	0.895499i	$0.646819\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	−7.17667	+	12.4304i	−0.717667	+	1.24304i
$101$	5.40714	+	9.36545i	0.538031	+	0.931897i	0.999010	+	0.0444859i	$0.0141650\pi$
$101$	5.40714	+	9.36545i	0.538031	+	0.931897i	−0.460979	+	0.887411i	$0.652502\pi$
$102$		0			0
$103$	17.2910			1.70374			0.851868	−	0.523757i	$-0.175470\pi$
$103$	17.2910			1.70374			0.851868	+	0.523757i	$0.175470\pi$
$104$	2.89924	+	2.14345i	0.284294	+	0.210183i
$105$		0			0
$106$	−7.31143	+	4.22126i	−0.710149	+	0.410005i
$107$	7.10282	+	12.3024i	0.686655	+	1.18932i	0.972914	+	0.231169i	$0.0742550\pi$
$107$	7.10282	+	12.3024i	0.686655	+	1.18932i	−0.286259	+	0.958152i	$0.592412\pi$
$108$		0			0
$109$		−	3.43821i		−	0.329321i	−0.986350	−	0.164660i	$-0.947347\pi$
$109$		−	3.43821i		−	0.329321i	0.986350	−	0.164660i	$-0.0526528\pi$
$110$	−4.27396	−	2.46757i	−0.407506	−	0.235274i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	−3.01295	+	5.21858i	−0.283434	+	0.490922i	−0.972228	−	0.234035i	$-0.924807\pi$
$113$	−3.01295	+	5.21858i	−0.283434	+	0.490922i	0.688794	+	0.724957i	$0.258140\pi$
$114$		0			0
$115$	−20.6065	+	11.8971i	−1.92156	+	1.10941i
$116$	−6.74153			−0.625935
$117$		0			0
$118$	7.27900			0.670087
$119$	2.73284	−	1.57781i	0.250519	−	0.144637i
$120$		0			0
$121$	−4.87076	+	8.43641i	−0.442797	+	0.766946i
$122$			10.4166i			0.943077i
$123$		0			0
$124$	−4.83755	−	2.79296i	−0.434425	−	0.250815i
$125$		−	41.1476i		−	3.68036i
$126$		0			0
$127$	4.87818	+	8.44926i	0.432869	+	0.749751i	0.997119	−	0.0758531i	$-0.0241680\pi$
$127$	4.87818	+	8.44926i	0.432869	+	0.749751i	−0.564250	+	0.825604i	$0.690835\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−15.7605	−	1.78901i	−1.38229	−	0.156906i
$131$	−7.62761			−0.666428			−0.333214	−	0.942851i	$-0.608133\pi$
$131$	−7.62761			−0.666428			−0.333214	+	0.942851i	$0.608133\pi$
$132$		0			0
$133$	4.03796	+	6.99395i	0.350135	+	0.606452i
$134$	2.63792	−	4.56902i	0.227882	−	0.394703i
$135$		0			0
$136$	2.73284	+	1.57781i	0.234339	+	0.135296i
$137$	−6.36818	−	3.67667i	−0.544070	−	0.314119i	0.202657	−	0.979250i	$-0.435042\pi$
$137$	−6.36818	−	3.67667i	−0.544070	−	0.314119i	−0.746727	+	0.665131i	$0.768376\pi$
$138$		0			0
$139$	4.29454	−	7.43835i	0.364258	−	0.630913i	−0.624399	−	0.781106i	$-0.714656\pi$
$139$	4.29454	−	7.43835i	0.364258	−	0.630913i	0.988657	+	0.150193i	$0.0479894\pi$
$140$	−2.19962	−	3.80986i	−0.185902	−	0.321992i
$141$		0			0
$142$	−8.67667			−0.728130
$143$	0.456201	−	4.01896i	0.0381494	−	0.336082i
$144$		0			0
$145$	25.6843	−	14.8288i	2.13296	−	1.23147i
$146$	6.39924	+	11.0838i	0.529605	+	0.917303i
$147$		0			0
$148$		−	7.61971i		−	0.626337i
$149$	3.01285	+	1.73947i	0.246822	+	0.142503i	0.618308	−	0.785936i	$-0.287818\pi$
$149$	3.01285	+	1.73947i	0.246822	+	0.142503i	−0.371486	+	0.928439i	$0.621152\pi$
$150$		0			0
$151$			16.2991i			1.32640i	0.748441	+	0.663202i	$0.230803\pi$
$151$			16.2991i			1.32640i	−0.748441	+	0.663202i	$0.769197\pi$
$152$	−4.03796	+	6.99395i	−0.327522	+	0.567284i
$153$		0			0
$154$	0.971521	−	0.560908i	0.0782874	−	0.0451993i
$155$	24.5738			1.97382
$156$		0			0
$157$	−0.684571			−0.0546347			−0.0273174	−	0.999627i	$-0.508696\pi$
$157$	−0.684571			−0.0546347			−0.0273174	+	0.999627i	$0.508696\pi$
$158$	−3.04933	+	1.76053i	−0.242591	+	0.140060i
$159$		0			0
$160$	2.19962	−	3.80986i	0.173895	−	0.301196i
$161$		−	5.40872i		−	0.426267i
$162$		0			0
$163$	12.1690	+	7.02580i	0.953153	+	0.550303i	0.894059	−	0.447949i	$-0.147846\pi$
$163$	12.1690	+	7.02580i	0.953153	+	0.550303i	0.0590938	+	0.998252i	$0.481179\pi$
$164$		−	2.05696i		−	0.160621i
$165$		0			0
$166$	5.56960	+	9.64683i	0.432285	+	0.748739i
$167$	−0.421983	+	0.243632i	−0.0326540	+	0.0188528i	−0.516238	−	0.856445i	$-0.672668\pi$
$167$	−0.421983	+	0.243632i	−0.0326540	+	0.0188528i	0.483584	+	0.875298i	$0.339335\pi$
$168$		0			0
$169$	−3.81122	−	12.4288i	−0.293171	−	0.956060i
$170$	−13.8823			−1.06472
$171$		0			0
$172$	−0.792959	−	1.37344i	−0.0604625	−	0.104724i
$173$	1.71910	−	2.97757i	0.130701	−	0.226381i	−0.793246	−	0.608901i	$-0.791611\pi$
$173$	1.71910	−	2.97757i	0.130701	−	0.226381i	0.923947	+	0.382521i	$0.124944\pi$
$174$		0			0
$175$	12.4304	+	7.17667i	0.939647	+	0.542505i
$176$	0.971521	+	0.560908i	0.0732312	+	0.0422800i
$177$		0			0
$178$	−5.21178	+	9.02707i	−0.390639	+	0.676607i
$179$	1.08802	+	1.88451i	0.0813225	+	0.140855i	0.903818	−	0.427917i	$-0.140752\pi$
$179$	1.08802	+	1.88451i	0.0813225	+	0.140855i	−0.822496	+	0.568771i	$0.807419\pi$
$180$		0			0
$181$	10.7188			0.796721			0.398361	−	0.917229i	$-0.369579\pi$
$181$	10.7188			0.796721			0.398361	+	0.917229i	$0.369579\pi$
$182$	2.14345	−	2.89924i	0.158883	−	0.214906i
$183$		0			0
$184$	4.68409	−	2.70436i	0.345316	−	0.199368i
$185$	16.7605	+	29.0300i	1.23226	+	2.13433i
$186$		0			0
$187$		−	3.54002i		−	0.258872i
$188$	6.57196	+	3.79432i	0.479310	+	0.276730i
$189$		0			0
$190$		−	35.5279i		−	2.57747i
$191$	7.62813	−	13.2123i	0.551952	−	0.956009i	−0.446181	−	0.894943i	$-0.647216\pi$
$191$	7.62813	−	13.2123i	0.551952	−	0.956009i	0.998134	−	0.0610668i	$-0.0194503\pi$
$192$		0			0
$193$	−12.2800	+	7.08987i	−0.883935	+	0.510340i	−0.871954	−	0.489588i	$-0.837147\pi$
$193$	−12.2800	+	7.08987i	−0.883935	+	0.510340i	−0.0119809	+	0.999928i	$0.503814\pi$
$194$	1.22741			0.0881228
$195$		0			0
$196$	1.00000			0.0714286
$197$	−10.3662	+	5.98495i	−0.738564	+	0.426410i	−0.821547	−	0.570141i	$-0.806889\pi$
$197$	−10.3662	+	5.98495i	−0.738564	+	0.426410i	0.0829831	+	0.996551i	$0.473555\pi$
$198$		0			0
$199$	−2.49684	+	4.32465i	−0.176996	+	0.306566i	−0.940850	−	0.338823i	$-0.889971\pi$
$199$	−2.49684	+	4.32465i	−0.176996	+	0.306566i	0.763854	+	0.645389i	$0.223305\pi$
$200$			14.3533i			1.01493i
$201$		0			0
$202$	9.36545	+	5.40714i	0.658951	+	0.380445i
$203$			6.74153i			0.473163i
$204$		0			0
$205$	4.52453	+	7.83671i	0.316007	+	0.547340i
$206$	14.9745	−	8.64551i	1.04332	−	0.602361i
$207$		0			0
$208$	3.58254	+	0.406663i	0.248405	+	0.0281970i
$209$	9.05969			0.626672
$210$		0			0
$211$	3.27743	+	5.67667i	0.225627	+	0.390798i	0.956507	−	0.291708i	$-0.0942235\pi$
$211$	3.27743	+	5.67667i	0.225627	+	0.390798i	−0.730880	+	0.682506i	$0.760890\pi$
$212$	−4.22126	+	7.31143i	−0.289917	+	0.502151i
$213$		0			0
$214$	12.3024	+	7.10282i	0.840977	+	0.485538i
$215$	6.04212	+	3.48842i	0.412069	+	0.237908i
$216$		0			0
$217$	−2.79296	+	4.83755i	−0.189598	+	0.328394i
$218$	−1.71910	−	2.97757i	−0.116432	−	0.201667i
$219$		0			0
$220$	−4.93514			−0.332727
$221$	−4.54121	−	10.4322i	−0.305475	−	0.701743i
$222$		0			0
$223$	6.43757	−	3.71673i	0.431091	−	0.248891i	−0.268720	−	0.963218i	$-0.586601\pi$
$223$	6.43757	−	3.71673i	0.431091	−	0.248891i	0.699811	+	0.714328i	$0.253267\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$			6.02589i			0.400837i
$227$	−10.1529	−	5.86177i	−0.673870	−	0.389059i	0.123671	−	0.992323i	$-0.460533\pi$
$227$	−10.1529	−	5.86177i	−0.673870	−	0.389059i	−0.797542	+	0.603264i	$0.793867\pi$
$228$		0			0
$229$		−	9.70668i		−	0.641436i	−0.947175	−	0.320718i	$-0.896076\pi$
$229$		−	9.70668i		−	0.641436i	0.947175	−	0.320718i	$-0.103924\pi$
$230$	−11.8971	+	20.6065i	−0.784474	+	1.35875i
$231$		0			0
$232$	−5.83834	+	3.37076i	−0.383305	+	0.221302i
$233$	11.8444			0.775952			0.387976	−	0.921670i	$-0.373174\pi$
$233$	11.8444			0.775952			0.387976	+	0.921670i	$0.373174\pi$
$234$		0			0
$235$	−33.3843			−2.17775
$236$	6.30380	−	3.63950i	0.410343	−	0.236911i
$237$		0			0
$238$	1.57781	−	2.73284i	0.102274	−	0.177144i
$239$		−	1.50484i		−	0.0973397i	−0.998815	−	0.0486698i	$-0.984502\pi$
$239$		−	1.50484i		−	0.0973397i	0.998815	−	0.0486698i	$-0.0154982\pi$
$240$		0			0
$241$	−2.56160	−	1.47894i	−0.165007	−	0.0952669i	0.415222	−	0.909720i	$-0.363704\pi$
$241$	−2.56160	−	1.47894i	−0.165007	−	0.0952669i	−0.580229	+	0.814453i	$0.697037\pi$
$242$			9.74153i			0.626209i
$243$		0			0
$244$	5.20831	+	9.02106i	0.333428	+	0.577514i
$245$	−3.80986	+	2.19962i	−0.243403	+	0.140529i
$246$		0			0
$247$	26.6982	−	11.6220i	1.69877	−	0.739489i
$248$	−5.58592			−0.354706
$249$		0			0
$250$	−20.5738	−	35.6349i	−1.30120	−	2.25375i
$251$	3.81728	−	6.61172i	0.240944	−	0.417328i	−0.720039	−	0.693933i	$-0.755876\pi$
$251$	3.81728	−	6.61172i	0.240944	−	0.417328i	0.960984	+	0.276606i	$0.0892095\pi$
$252$		0			0
$253$	−5.25469	−	3.03380i	−0.330359	−	0.190733i
$254$	8.44926	+	4.87818i	0.530154	+	0.306084i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.6616	+	18.4665i	0.665054	+	1.15191i	0.979271	+	0.202555i	$0.0649246\pi$
$257$	10.6616	+	18.4665i	0.665054	+	1.15191i	−0.314217	+	0.949351i	$0.601742\pi$
$258$		0			0
$259$	−7.61971			−0.473466
$260$	−14.5435	+	6.33092i	−0.901949	+	0.392627i
$261$		0			0
$262$	−6.60571	+	3.81381i	−0.408102	+	0.235618i
$263$	−2.65582	−	4.60002i	−0.163765	−	0.283649i	0.772451	−	0.635074i	$-0.219031\pi$
$263$	−2.65582	−	4.60002i	−0.163765	−	0.283649i	−0.936216	+	0.351425i	$0.885697\pi$
$264$		0			0
$265$		−	37.1407i		−	2.28153i
$266$	6.99395	+	4.03796i	0.428826	+	0.247583i
$267$		0			0
$268$		−	5.27585i		−	0.322274i
$269$	−1.01642	+	1.76048i	−0.0619720	+	0.107339i	−0.895347	−	0.445370i	$-0.853072\pi$
$269$	−1.01642	+	1.76048i	−0.0619720	+	0.107339i	0.833375	+	0.552708i	$0.186406\pi$
$270$		0			0
$271$	1.22099	−	0.704938i	0.0741698	−	0.0428219i	−0.462456	−	0.886642i	$-0.653032\pi$
$271$	1.22099	−	0.704938i	0.0741698	−	0.0428219i	0.536626	+	0.843820i	$0.319699\pi$
$272$	3.15561			0.191337
$273$		0			0
$274$	−7.35334			−0.444232
$275$	13.9446	−	8.05090i	0.840889	−	0.485488i
$276$		0			0
$277$	11.7848	−	20.4119i	0.708080	−	1.22643i	−0.257488	−	0.966281i	$-0.582895\pi$
$277$	11.7848	−	20.4119i	0.708080	−	1.22643i	0.965568	−	0.260149i	$-0.0837718\pi$
$278$		−	8.58907i		−	0.515138i
$279$		0			0
$280$	−3.80986	−	2.19962i	−0.227682	−	0.131453i
$281$			8.12593i			0.484753i	0.970182	+	0.242376i	$0.0779268\pi$
$281$			8.12593i			0.484753i	−0.970182	+	0.242376i	$0.922073\pi$
$282$		0			0
$283$	−9.96358	−	17.2574i	−0.592273	−	1.02585i	−0.993926	−	0.110055i	$-0.964897\pi$
$283$	−9.96358	−	17.2574i	−0.592273	−	1.02585i	0.401652	−	0.915792i	$-0.368436\pi$
$284$	−7.51422	+	4.33834i	−0.445887	+	0.257433i
$285$		0			0
$286$	−1.61440	−	3.70862i	−0.0954613	−	0.219295i
$287$	−2.05696			−0.121418
$288$		0			0
$289$	3.52106	+	6.09865i	0.207121	+	0.358744i
$290$	14.8288	−	25.6843i	0.870778	−	1.50823i
$291$		0			0
$292$	11.0838	+	6.39924i	0.648631	+	0.374487i
$293$	−17.5078	−	10.1081i	−1.02282	−	0.590523i	−0.107898	−	0.994162i	$-0.534412\pi$
$293$	−17.5078	−	10.1081i	−1.02282	−	0.590523i	−0.914918	+	0.403639i	$0.867745\pi$
$294$		0			0
$295$	−16.0111	+	27.7320i	−0.932200	+	1.61462i
$296$	−3.80986	−	6.59886i	−0.221443	−	0.383551i
$297$		0			0
$298$	3.47894			0.201530
$299$	−19.3770	−	2.19953i	−1.12060	−	0.127202i
$300$		0			0
$301$	−1.37344	+	0.792959i	−0.0791641	+	0.0457054i
$302$	8.14956	+	14.1154i	0.468954	+	0.812253i
$303$		0			0
$304$			8.07591i			0.463185i
$305$	−39.6858	−	22.9126i	−2.27240	−	1.31197i
$306$		0			0
$307$		−	26.2764i		−	1.49967i	−0.661624	−	0.749836i	$-0.730132\pi$
$307$		−	26.2764i		−	1.49967i	0.661624	−	0.749836i	$-0.269868\pi$
$308$	0.560908	−	0.971521i	0.0319607	−	0.0553576i
$309$		0			0
$310$	21.2815	−	12.2869i	1.20871	−	0.697849i
$311$	−7.30017			−0.413954			−0.206977	−	0.978346i	$-0.566363\pi$
$311$	−7.30017			−0.413954			−0.206977	+	0.978346i	$0.566363\pi$
$312$		0			0
$313$	25.4414			1.43803			0.719015	−	0.694994i	$-0.244593\pi$
$313$	25.4414			1.43803			0.719015	+	0.694994i	$0.244593\pi$
$314$	−0.592856	+	0.342286i	−0.0334568	+	0.0193163i
$315$		0			0
$316$	−1.76053	+	3.04933i	−0.0990375	+	0.171538i
$317$		−	20.2153i		−	1.13540i	−0.823234	−	0.567702i	$-0.807833\pi$
$317$		−	20.2153i		−	1.13540i	0.823234	−	0.567702i	$-0.192167\pi$
$318$		0			0
$319$	6.54954	+	3.78138i	0.366704	+	0.211716i
$320$		−	4.39924i		−	0.245925i
$321$		0			0
$322$	−2.70436	−	4.68409i	−0.150708	−	0.261034i
$323$	22.0702	−	12.7422i	1.22802	−	0.708996i
$324$		0			0
$325$	30.7657	−	41.6138i	1.70657	−	2.30832i
$326$	14.0516			0.778246
$327$		0			0
$328$	−1.02848	−	1.78138i	−0.0567882	−	0.0983601i
$329$	3.79432	−	6.57196i	0.209188	−	0.362324i
$330$		0			0
$331$	−21.0120	−	12.1313i	−1.15492	−	0.666796i	−0.204842	−	0.978795i	$-0.565668\pi$
$331$	−21.0120	−	12.1313i	−1.15492	−	0.666796i	−0.950083	+	0.311999i	$0.899002\pi$
$332$	9.64683	+	5.56960i	0.529438	+	0.305671i
$333$		0			0
$334$	−0.243632	+	0.421983i	−0.0133310	+	0.0230899i
$335$	11.6049	+	20.1002i	0.634042	+	1.09819i
$336$		0			0
$337$	8.14035			0.443433			0.221717	−	0.975111i	$-0.428834\pi$
$337$	8.14035			0.443433			0.221717	+	0.975111i	$0.428834\pi$
$338$	−9.51501	−	8.85803i	−0.517548	−	0.481813i
$339$		0			0
$340$	−12.0224	+	6.94115i	−0.652008	+	0.376437i
$341$	3.13319	+	5.42684i	0.169672	+	0.293880i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−1.37344	−	0.792959i	−0.0740512	−	0.0427535i
$345$		0			0
$346$		−	3.43821i		−	0.184839i
$347$	−6.73894	+	11.6722i	−0.361765	+	0.626596i	−0.988251	−	0.152836i	$-0.951159\pi$
$347$	−6.73894	+	11.6722i	−0.361765	+	0.626596i	0.626486	+	0.779433i	$0.284493\pi$
$348$		0			0
$349$	−5.64467	+	3.25895i	−0.302152	+	0.174448i	−0.643409	−	0.765522i	$-0.722481\pi$
$349$	−5.64467	+	3.25895i	−0.302152	+	0.174448i	0.341257	+	0.939970i	$0.389147\pi$
$350$	14.3533			0.767218
$351$		0			0
$352$	1.12182			0.0597930
$353$	−20.7274	+	11.9669i	−1.10321	+	0.636936i	−0.937061	−	0.349165i	$-0.886465\pi$
$353$	−20.7274	+	11.9669i	−1.10321	+	0.636936i	−0.166145	+	0.986101i	$0.553132\pi$
$354$		0			0
$355$	19.0854	−	33.0569i	1.01295	−	1.75448i
$356$			10.4236i			0.552448i
$357$		0			0
$358$	1.88451	+	1.08802i	0.0995993	+	0.0575037i
$359$			7.32429i			0.386561i	0.981144	+	0.193281i	$0.0619128\pi$
$359$			7.32429i			0.386561i	−0.981144	+	0.193281i	$0.938087\pi$
$360$		0			0
$361$	23.1102	+	40.0280i	1.21633	+	2.10674i
$362$	9.28274	−	5.35939i	0.487890	−	0.281684i
$363$		0			0
$364$	0.406663	−	3.58254i	0.0213149	−	0.187776i
$365$	−56.3037			−2.94707
$366$		0			0
$367$	−5.11150	−	8.85339i	−0.266818	−	0.462143i	0.701220	−	0.712945i	$-0.252639\pi$
$367$	−5.11150	−	8.85339i	−0.266818	−	0.462143i	−0.968038	+	0.250802i	$0.919306\pi$
$368$	2.70436	−	4.68409i	0.140975	−	0.244175i
$369$		0			0
$370$	29.0300	+	16.7605i	1.50920	+	0.871336i
$371$	7.31143	+	4.22126i	0.379591	+	0.219157i
$372$		0			0
$373$	−0.781422	+	1.35346i	−0.0404605	+	0.0700797i	−0.885547	−	0.464551i	$-0.846216\pi$
$373$	−0.781422	+	1.35346i	−0.0404605	+	0.0700797i	0.845086	+	0.534630i	$0.179549\pi$
$374$	−1.77001	−	3.06574i	−0.0915249	−	0.158526i
$375$		0			0
$376$	7.58865			0.391355
$377$	24.1518	+	2.74153i	1.24388	+	0.141196i
$378$		0			0
$379$	−7.26194	+	4.19268i	−0.373021	+	0.215364i	−0.674777	−	0.738021i	$-0.735760\pi$
$379$	−7.26194	+	4.19268i	−0.373021	+	0.215364i	0.301757	+	0.953385i	$0.402427\pi$
$380$	−17.7640	−	30.7681i	−0.911272	−	1.57837i
$381$		0			0
$382$		−	15.2563i		−	0.780578i
$383$	−7.89645	−	4.55902i	−0.403490	−	0.232955i	0.284499	−	0.958676i	$-0.408173\pi$
$383$	−7.89645	−	4.55902i	−0.403490	−	0.232955i	−0.687989	+	0.725722i	$0.741506\pi$
$384$		0			0
$385$			4.93514i			0.251518i
$386$	−7.08987	+	12.2800i	−0.360865	+	0.625036i
$387$		0			0
$388$	1.06297	−	0.613704i	0.0539639	−	0.0311561i
$389$	−37.1923			−1.88572			−0.942862	−	0.333184i	$-0.891877\pi$
$389$	−37.1923			−1.88572			−0.942862	+	0.333184i	$0.891877\pi$
$390$		0			0
$391$	−17.0678			−0.863157
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	−5.98495	+	10.3662i	−0.301517	+	0.522243i
$395$		−	15.4900i		−	0.779386i
$396$		0			0
$397$	−27.4588	−	15.8533i	−1.37812	−	0.795656i	−0.386184	−	0.922422i	$-0.626207\pi$
$397$	−27.4588	−	15.8533i	−1.37812	−	0.795656i	−0.991933	+	0.126765i	$0.959541\pi$
$398$			4.99368i			0.250310i
$399$		0			0
$400$	7.17667	+	12.4304i	0.358834	+	0.621518i
$401$	23.3818	−	13.4995i	1.16763	−	0.674132i	0.214509	−	0.976722i	$-0.431185\pi$
$401$	23.3818	−	13.4995i	1.16763	−	0.674132i	0.953121	+	0.302590i	$0.0978514\pi$
$402$		0			0
$403$	16.1949	+	11.9731i	0.806727	+	0.596425i
$404$	10.8143			0.538031
$405$		0			0
$406$	3.37076	+	5.83834i	0.167288	+	0.289752i
$407$	−4.27396	+	7.40271i	−0.211852	+	0.366939i
$408$		0			0
$409$	8.94747	+	5.16583i	0.442424	+	0.255434i	0.704625	−	0.709580i	$-0.251115\pi$
$409$	8.94747	+	5.16583i	0.442424	+	0.255434i	−0.262201	+	0.965013i	$0.584448\pi$
$410$	7.83671	+	4.52453i	0.387028	+	0.223451i
$411$		0			0
$412$	8.64551	−	14.9745i	0.425934	−	0.737739i
$413$	−3.63950	−	6.30380i	−0.179088	−	0.310190i
$414$		0			0
$415$	−49.0040			−2.40551
$416$	3.30591	−	1.43909i	0.162085	−	0.0705573i
$417$		0			0
$418$	7.84592	−	4.52984i	0.383757	−	0.221562i
$419$	12.7635	+	22.1070i	0.623536	+	1.08000i	0.988822	+	0.149101i	$0.0476380\pi$
$419$	12.7635	+	22.1070i	0.623536	+	1.08000i	−0.365285	+	0.930896i	$0.619029\pi$
$420$		0			0
$421$			4.31438i			0.210270i	0.994458	+	0.105135i	$0.0335274\pi$
$421$			4.31438i			0.210270i	−0.994458	+	0.105135i	$0.966473\pi$
$422$	5.67667	+	3.27743i	0.276336	+	0.159543i
$423$		0			0
$424$			8.44252i			0.410005i
$425$	22.6468	−	39.2254i	1.09853	−	1.90271i
$426$		0			0
$427$	9.02106	−	5.20831i	0.436560	−	0.252048i
$428$	14.2056			0.686655
$429$		0			0
$430$	6.97684			0.336453
$431$	6.37502	−	3.68062i	0.307074	−	0.177289i	−0.338542	−	0.940951i	$-0.609934\pi$
$431$	6.37502	−	3.68062i	0.307074	−	0.177289i	0.645616	+	0.763662i	$0.276601\pi$
$432$		0			0
$433$	−13.4103	+	23.2273i	−0.644458	+	1.11623i	0.339969	+	0.940437i	$0.389584\pi$
$433$	−13.4103	+	23.2273i	−0.644458	+	1.11623i	−0.984426	+	0.175797i	$0.943750\pi$
$434$			5.58592i			0.268133i
$435$		0			0
$436$	−2.97757	−	1.71910i	−0.142600	−	0.0823301i
$437$		−	43.6804i		−	2.08952i
$438$		0			0
$439$	17.4346	+	30.1976i	0.832109	+	1.44125i	0.896363	+	0.443321i	$0.146200\pi$
$439$	17.4346	+	30.1976i	0.832109	+	1.44125i	−0.0642541	+	0.997934i	$0.520467\pi$
$440$	−4.27396	+	2.46757i	−0.203753	+	0.117637i
$441$		0			0
$442$	−9.14888	−	6.76390i	−0.435168	−	0.321726i
$443$	8.59832			0.408518			0.204259	−	0.978917i	$-0.434521\pi$
$443$	8.59832			0.408518			0.204259	+	0.978917i	$0.434521\pi$
$444$		0			0
$445$	−22.9279	−	39.7123i	−1.08689	−	1.88254i
$446$	3.71673	−	6.43757i	0.175992	−	0.304828i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	27.1348	+	15.6663i	1.28057	+	0.739337i	0.976952	−	0.213458i	$-0.0684726\pi$
$449$	27.1348	+	15.6663i	1.28057	+	0.739337i	0.303616	+	0.952794i	$0.401806\pi$
$450$		0			0
$451$	−1.15376	+	1.99838i	−0.0543286	+	0.0940999i
$452$	3.01295	+	5.21858i	0.141717	+	0.245461i
$453$		0			0
$454$	−11.7235			−0.550213
$455$	6.33092	+	14.5435i	0.296798	+	0.681809i
$456$		0			0
$457$	8.32180	−	4.80459i	0.389277	−	0.224749i	−0.292570	−	0.956244i	$-0.594510\pi$
$457$	8.32180	−	4.80459i	0.389277	−	0.224749i	0.681847	+	0.731495i	$0.261177\pi$
$458$	−4.85334	−	8.40623i	−0.226782	−	0.392797i
$459$		0			0
$460$			23.7943i			1.10941i
$461$	11.5452	+	6.66562i	0.537713	+	0.310449i	0.744151	−	0.668011i	$-0.232854\pi$
$461$	11.5452	+	6.66562i	0.537713	+	0.310449i	−0.206439	+	0.978460i	$0.566187\pi$
$462$		0			0
$463$			5.55011i			0.257935i	0.991649	+	0.128968i	$0.0411664\pi$
$463$			5.55011i			0.257935i	−0.991649	+	0.128968i	$0.958834\pi$
$464$	−3.37076	+	5.83834i	−0.156484	+	0.271038i
$465$		0			0
$466$	10.2575	−	5.92219i	0.475171	−	0.274340i
$467$	16.9272			0.783299			0.391650	−	0.920114i	$-0.371905\pi$
$467$	16.9272			0.783299			0.391650	+	0.920114i	$0.371905\pi$
$468$		0			0
$469$	−5.27585			−0.243616
$470$	−28.9117	+	16.6922i	−1.33360	+	0.769952i
$471$		0			0
$472$	3.63950	−	6.30380i	0.167522	−	0.290156i
$473$			1.77911i			0.0818035i
$474$		0			0
$475$	100.386	+	57.9582i	4.60605	+	2.65930i
$476$		−	3.15561i		−	0.144637i
$477$		0			0
$478$	−0.752418	−	1.30323i	−0.0344148	−	0.0596081i
$479$	−16.7981	+	9.69840i	−0.767526	+	0.443131i	−0.831991	−	0.554789i	$-0.812799\pi$
$479$	−16.7981	+	9.69840i	−0.767526	+	0.443131i	0.0644654	+	0.997920i	$0.479466\pi$
$480$		0			0
$481$	−3.09865	+	27.2980i	−0.141286	+	1.24468i
$482$	−2.95788			−0.134728
$483$		0			0
$484$	4.87076	+	8.43641i	0.221398	+	0.383473i
$485$	−2.69983	+	4.67625i	−0.122593	+	0.212337i
$486$		0			0
$487$	−13.3417	−	7.70283i	−0.604570	−	0.349049i	0.166267	−	0.986081i	$-0.446829\pi$
$487$	−13.3417	−	7.70283i	−0.604570	−	0.349049i	−0.770837	+	0.637032i	$0.780162\pi$
$488$	9.02106	+	5.20831i	0.408364	+	0.235769i
$489$		0			0
$490$	−2.19962	+	3.80986i	−0.0993688	+	0.172112i
$491$	4.87818	+	8.44926i	0.220149	+	0.381310i	0.954853	−	0.297078i	$-0.0960122\pi$
$491$	4.87818	+	8.44926i	0.220149	+	0.381310i	−0.734704	+	0.678388i	$0.762679\pi$
$492$		0			0
$493$	21.2736			0.958117
$494$	17.3103	−	23.4140i	0.778829	−	1.05345i
$495$		0			0
$496$	−4.83755	+	2.79296i	−0.217212	+	0.125408i
$497$	4.33834	+	7.51422i	0.194601	+	0.337059i
$498$		0			0
$499$			5.52642i			0.247397i	0.992320	+	0.123698i	$0.0394755\pi$
$499$			5.52642i			0.247397i	−0.992320	+	0.123698i	$0.960525\pi$
$500$	−35.6349	−	20.5738i	−1.59364	−	0.920089i
$501$		0			0
$502$		−	7.63455i		−	0.340747i
$503$	2.06759	−	3.58117i	0.0921893	−	0.159677i	−0.816243	−	0.577709i	$-0.803947\pi$
$503$	2.06759	−	3.58117i	0.0921893	−	0.159677i	0.908432	+	0.418032i	$0.137280\pi$
$504$		0			0
$505$	−41.2009	+	23.7873i	−1.83342	+	1.05852i
$506$	−6.06759			−0.269737
$507$		0			0
$508$	9.75637			0.432869
$509$	7.70067	−	4.44599i	0.341326	−	0.197065i	−0.319532	−	0.947575i	$-0.603526\pi$
$509$	7.70067	−	4.44599i	0.341326	−	0.197065i	0.660858	+	0.750511i	$0.270192\pi$
$510$		0			0
$511$	6.39924	−	11.0838i	0.283086	−	0.490319i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	18.4665	+	10.6616i	0.814521	+	0.470264i
$515$			76.0674i			3.35193i
$516$		0			0
$517$	−4.25653	−	7.37253i	−0.187202	−	0.324244i
$518$	−6.59886	+	3.80986i	−0.289937	+	0.167395i
$519$		0			0
$520$	−9.42957	+	12.7545i	−0.413514	+	0.559321i
$521$	−8.17974			−0.358361			−0.179180	−	0.983816i	$-0.557345\pi$
$521$	−8.17974			−0.358361			−0.179180	+	0.983816i	$0.557345\pi$
$522$		0			0
$523$	−3.12787	−	5.41763i	−0.136772	−	0.236896i	0.789501	−	0.613749i	$-0.210339\pi$
$523$	−3.12787	−	5.41763i	−0.136772	−	0.236896i	−0.926273	+	0.376853i	$0.877006\pi$
$524$	−3.81381	+	6.60571i	−0.166607	+	0.288572i
$525$		0			0
$526$	−4.60002	−	2.65582i	−0.200570	−	0.115799i
$527$	15.2654	+	8.81349i	0.664972	+	0.383922i
$528$		0			0
$529$	−3.12713	+	5.41635i	−0.135962	+	0.235494i
$530$	−18.5703	−	32.1648i	−0.806644	−	1.39715i
$531$		0			0
$532$	8.07591			0.350135
$533$	−0.836488	+	7.36914i	−0.0362323	+	0.319193i
$534$		0			0
$535$	−54.1214	+	31.2470i	−2.33987	+	1.35093i
$536$	−2.63792	−	4.56902i	−0.113941	−	0.197352i
$537$		0			0
$538$			2.03283i			0.0876416i
$539$	−0.971521	−	0.560908i	−0.0418464	−	0.0241600i
$540$		0			0
$541$		−	35.8526i		−	1.54142i	−0.637183	−	0.770712i	$-0.719901\pi$
$541$		−	35.8526i		−	1.54142i	0.637183	−	0.770712i	$-0.280099\pi$
$542$	0.704938	−	1.22099i	0.0302797	−	0.0524459i
$543$		0			0
$544$	2.73284	−	1.57781i	0.117170	−	0.0676479i
$545$	15.1255			0.647906
$546$		0			0
$547$	16.7073			0.714353			0.357177	−	0.934037i	$-0.383739\pi$
$547$	16.7073			0.714353			0.357177	+	0.934037i	$0.383739\pi$
$548$	−6.36818	+	3.67667i	−0.272035	+	0.157060i
$549$		0			0
$550$	8.05090	−	13.9446i	0.343292	−	0.594599i
$551$			54.4440i			2.31939i
$552$		0			0
$553$	3.04933	+	1.76053i	0.129671	+	0.0748653i
$554$		−	23.5696i		−	1.00138i
$555$		0			0
$556$	−4.29454	−	7.43835i	−0.182129	−	0.315456i
$557$	12.1384	−	7.00811i	0.514321	−	0.296943i	−0.220287	−	0.975435i	$-0.570699\pi$
$557$	12.1384	−	7.00811i	0.514321	−	0.296943i	0.734608	+	0.678492i	$0.237366\pi$
$558$		0			0
$559$	2.28228	+	5.24289i	0.0965302	+	0.221751i
$560$	−4.39924			−0.185902
$561$		0			0
$562$	4.06297	+	7.03726i	0.171386	+	0.296849i
$563$	−13.4476	+	23.2919i	−0.566747	+	0.981635i	0.430138	+	0.902763i	$0.358465\pi$
$563$	−13.4476	+	23.2919i	−0.566747	+	0.981635i	−0.996885	+	0.0788716i	$0.974868\pi$
$564$		0			0
$565$	−22.9578	−	13.2547i	−0.965842	−	0.557629i
$566$	−17.2574	−	9.96358i	−0.725383	−	0.418800i
$567$		0			0
$568$	−4.33834	+	7.51422i	−0.182033	+	0.315290i
$569$	−3.92493	−	6.79817i	−0.164541	−	0.284994i	0.771951	−	0.635682i	$-0.219281\pi$
$569$	−3.92493	−	6.79817i	−0.164541	−	0.284994i	−0.936492	+	0.350688i	$0.885948\pi$
$570$		0			0
$571$	7.24502			0.303195			0.151597	−	0.988442i	$-0.451558\pi$
$571$	7.24502			0.303195			0.151597	+	0.988442i	$0.451558\pi$
$572$	−3.25242	−	2.40456i	−0.135990	−	0.100540i
$573$		0			0
$574$	−1.78138	+	1.02848i	−0.0743533	+	0.0429279i
$575$	−38.8166	−	67.2323i	−1.61876	−	2.80378i
$576$		0			0
$577$		−	31.9688i		−	1.33088i	−0.746451	−	0.665440i	$-0.768244\pi$
$577$		−	31.9688i		−	1.33088i	0.746451	−	0.665440i	$-0.231756\pi$
$578$	6.09865	+	3.52106i	0.253671	+	0.146457i
$579$		0			0
$580$		−	29.6576i		−	1.23147i
$581$	5.56960	−	9.64683i	0.231066	−	0.400218i
$582$		0			0
$583$	8.20208	−	4.73548i	0.339696	−	0.196123i
$584$	12.7985			0.529605
$585$		0			0
$586$	−20.2163			−0.835126
$587$	3.59302	−	2.07443i	0.148300	−	0.0856210i	−0.424014	−	0.905656i	$-0.639379\pi$
$587$	3.59302	−	2.07443i	0.148300	−	0.0856210i	0.572314	+	0.820035i	$0.306046\pi$
$588$		0			0
$589$	−22.5557	+	39.0676i	−0.929391	+	1.60975i
$590$			32.0221i			1.31833i
$591$		0			0
$592$	−6.59886	−	3.80986i	−0.271212	−	0.156584i
$593$		−	21.0163i		−	0.863037i	−0.902104	−	0.431519i	$-0.857978\pi$
$593$		−	21.0163i		−	0.863037i	0.902104	−	0.431519i	$-0.142022\pi$
$594$		0			0
$595$	6.94115	+	12.0224i	0.284559	+	0.492871i
$596$	3.01285	−	1.73947i	0.123411	−	0.0712515i
$597$		0			0
$598$	−17.8807	+	7.78365i	−0.731197	+	0.318297i
$599$	35.0575			1.43241			0.716205	−	0.697890i	$-0.245878\pi$
$599$	35.0575			1.43241			0.716205	+	0.697890i	$0.245878\pi$
$600$		0			0
$601$	15.7586	+	27.2947i	0.642806	+	1.11337i	0.984803	+	0.173672i	$0.0555634\pi$
$601$	15.7586	+	27.2947i	0.642806	+	1.11337i	−0.341997	+	0.939701i	$0.611103\pi$
$602$	−0.792959	+	1.37344i	−0.0323186	+	0.0559774i
$603$		0			0
$604$	14.1154	+	8.14956i	0.574349	+	0.331601i
$605$	−37.1138	−	21.4277i	−1.50889	−	0.871159i
$606$		0			0
$607$	−16.9445	+	29.3488i	−0.687757	+	1.19123i	0.284805	+	0.958586i	$0.408071\pi$
$607$	−16.9445	+	29.3488i	−0.687757	+	1.19123i	−0.972562	+	0.232645i	$0.925262\pi$
$608$	4.03796	+	6.99395i	0.163761	+	0.283642i
$609$		0			0
$610$	−45.8253			−1.85541
$611$	−22.0013	−	16.2659i	−0.890079	−	0.658048i
$612$		0			0
$613$	−7.08979	+	4.09329i	−0.286354	+	0.165327i	−0.636296	−	0.771445i	$-0.719534\pi$
$613$	−7.08979	+	4.09329i	−0.286354	+	0.165327i	0.349942	+	0.936771i	$0.386201\pi$
$614$	−13.1382	−	22.7560i	−0.530214	−	0.918358i
$615$		0			0
$616$		−	1.12182i		−	0.0451993i
$617$	31.4716	+	18.1701i	1.26700	+	0.731502i	0.974419	−	0.224739i	$-0.0721529\pi$
$617$	31.4716	+	18.1701i	1.26700	+	0.731502i	0.292580	+	0.956241i	$0.405486\pi$
$618$		0			0
$619$		−	38.2625i		−	1.53790i	−0.639309	−	0.768950i	$-0.720780\pi$
$619$		−	38.2625i		−	1.53790i	0.639309	−	0.768950i	$-0.279220\pi$
$620$	12.2869	−	21.2815i	0.493454	−	0.854687i
$621$		0			0
$622$	−6.32213	+	3.65008i	−0.253494	+	0.146355i
$623$	10.4236			0.417611
$624$		0			0
$625$	109.252			4.37007
$626$	22.0329	−	12.7207i	0.880610	−	0.508421i
$627$		0			0
$628$	−0.342286	+	0.592856i	−0.0136587	+	0.0236575i
$629$			24.0449i			0.958731i
$630$		0			0
$631$	−8.77412	−	5.06574i	−0.349292	−	0.201664i	0.315081	−	0.949065i	$-0.397968\pi$
$631$	−8.77412	−	5.06574i	−0.349292	−	0.201664i	−0.664374	+	0.747401i	$0.731302\pi$
$632$			3.52106i			0.140060i
$633$		0			0
$634$	−10.1077	−	17.5070i	−0.401426	−	0.695290i
$635$	−37.1704	+	21.4603i	−1.47506	+	0.851627i
$636$		0			0
$637$	−3.58254	−	0.406663i	−0.141946	−	0.0161126i
$638$	7.56276			0.299412
$639$		0			0
$640$	−2.19962	−	3.80986i	−0.0869477	−	0.150598i
$641$	−13.4520	+	23.2995i	−0.531322	+	0.920276i	0.468010	+	0.883723i	$0.344971\pi$
$641$	−13.4520	+	23.2995i	−0.531322	+	0.920276i	−0.999332	+	0.0365532i	$0.988362\pi$
$642$		0			0
$643$	−28.9459	−	16.7119i	−1.14151	−	0.659053i	−0.194708	−	0.980861i	$-0.562376\pi$
$643$	−28.9459	−	16.7119i	−1.14151	−	0.659053i	−0.946805	+	0.321808i	$0.895709\pi$
$644$	−4.68409	−	2.70436i	−0.184579	−	0.106567i
$645$		0			0
$646$	12.7422	−	22.0702i	0.501336	−	0.868339i
$647$	10.8789	+	18.8428i	0.427693	+	0.740786i	0.996668	−	0.0815693i	$-0.0259932\pi$
$647$	10.8789	+	18.8428i	0.427693	+	0.740786i	−0.568975	+	0.822355i	$0.692660\pi$
$648$		0			0
$649$	−8.16570			−0.320532
$650$	5.83697	−	51.4215i	0.228945	−	2.01692i
$651$		0			0
$652$	12.1690	−	7.02580i	0.476576	−	0.275151i
$653$	3.21872	+	5.57498i	0.125958	+	0.218166i	0.922107	−	0.386935i	$-0.126466\pi$
$653$	3.21872	+	5.57498i	0.125958	+	0.218166i	−0.796149	+	0.605101i	$0.793133\pi$
$654$		0			0
$655$		−	33.5557i		−	1.31113i
$656$	−1.78138	−	1.02848i	−0.0695511	−	0.0401554i
$657$		0			0
$658$		−	7.58865i		−	0.295836i
$659$	4.51690	−	7.82350i	0.175953	−	0.304760i	−0.764537	−	0.644579i	$-0.777033\pi$
$659$	4.51690	−	7.82350i	0.175953	−	0.304760i	0.940491	+	0.339819i	$0.110366\pi$
$660$		0			0
$661$	−8.45556	+	4.88182i	−0.328883	+	0.189881i	−0.655345	−	0.755330i	$-0.727477\pi$
$661$	−8.45556	+	4.88182i	−0.328883	+	0.189881i	0.326462	+	0.945210i	$0.394143\pi$
$662$	−24.2626			−0.942992
$663$		0			0
$664$	11.1392			0.432285
$665$	−30.7681	+	17.7640i	−1.19313	+	0.688857i
$666$		0			0
$667$	18.2315	−	31.5779i	0.705927	−	1.22270i
$668$			0.487264i			0.0188528i
$669$		0			0
$670$	20.1002	+	11.6049i	0.776540	+	0.448335i
$671$		−	11.6855i		−	0.451115i
$672$		0			0
$673$	−20.3902	−	35.3169i	−0.785985	−	1.36137i	−0.928409	−	0.371559i	$-0.878823\pi$
$673$	−20.3902	−	35.3169i	−0.785985	−	1.36137i	0.142425	−	0.989806i	$-0.454510\pi$
$674$	7.04975	−	4.07017i	0.271546	−	0.156777i
$675$		0			0
$676$	−12.6693	−	2.91377i	−0.487279	−	0.112068i
$677$	−28.6313			−1.10039			−0.550195	−	0.835036i	$-0.685447\pi$
$677$	−28.6313			−1.10039			−0.550195	+	0.835036i	$0.685447\pi$
$678$		0			0
$679$	−0.613704	−	1.06297i	−0.0235518	−	0.0407929i
$680$	−6.94115	+	12.0224i	−0.266181	+	0.461039i
$681$		0			0
$682$	5.42684	+	3.13319i	0.207804	+	0.119976i
$683$	−34.7160	−	20.0433i	−1.32837	−	0.766935i	−0.343322	−	0.939218i	$-0.611552\pi$
$683$	−34.7160	−	20.0433i	−1.32837	−	0.766935i	−0.985047	+	0.172283i	$0.944886\pi$
$684$		0			0
$685$	16.1746	−	28.0152i	0.617998	−	1.07040i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−1.58592			−0.0604625
$689$	18.0961	−	24.4769i	0.689408	−	0.932496i
$690$		0			0
$691$	−24.3518	+	14.0595i	−0.926385	+	0.534848i	−0.885666	−	0.464322i	$-0.846298\pi$
$691$	−24.3518	+	14.0595i	−0.926385	+	0.534848i	−0.0407184	+	0.999171i	$0.512965\pi$
$692$	−1.71910	−	2.97757i	−0.0653505	−	0.113190i
$693$		0			0
$694$			13.4779i			0.511614i
$695$	32.7231	+	18.8927i	1.24126	+	0.716641i
$696$		0			0
$697$			6.49096i			0.245863i
$698$	−3.25895	+	5.64467i	−0.123353	+	0.213654i
$699$		0			0
$700$	12.4304	−	7.17667i	0.469823	−	0.271253i
$701$	3.59224			0.135677			0.0678385	−	0.997696i	$-0.478390\pi$
$701$	3.59224			0.135677			0.0678385	+	0.997696i	$0.478390\pi$
$702$		0			0
$703$	−61.5361			−2.32088
$704$	0.971521	−	0.560908i	0.0366156	−	0.0211400i
$705$		0			0
$706$	−11.9669	+	20.7274i	−0.450382	+	0.780085i
$707$		−	10.8143i		−	0.406713i
$708$		0			0
$709$	7.28564	+	4.20637i	0.273618	+	0.157973i	0.630531	−	0.776164i	$-0.282837\pi$
$709$	7.28564	+	4.20637i	0.273618	+	0.157973i	−0.356913	+	0.934138i	$0.616171\pi$
$710$		−	38.1708i		−	1.43252i
$711$		0			0
$712$	5.21178	+	9.02707i	0.195320	+	0.338304i
$713$	26.1649	−	15.1063i	0.979885	−	0.565737i
$714$		0			0
$715$	17.6804	+	2.00694i	0.661208	+	0.0750552i
$716$	2.17604			0.0813225
$717$		0			0
$718$	3.66215	+	6.34302i	0.136670	+	0.236720i
$719$	24.1674	−	41.8591i	0.901290	−	1.56108i	0.0754696	−	0.997148i	$-0.475954\pi$
$719$	24.1674	−	41.8591i	0.901290	−	1.56108i	0.825821	−	0.563933i	$-0.190712\pi$
$720$		0			0
$721$	−14.9745	−	8.64551i	−0.557678	−	0.321976i
$722$	40.0280	+	23.1102i	1.48969	+	0.860072i
$723$		0			0
$724$	5.35939	−	9.28274i	0.199180	−	0.344990i
$725$	48.3817	+	83.7996i	1.79685	+	3.11224i
$726$		0			0
$727$	46.3297			1.71827			0.859137	−	0.511745i	$-0.171001\pi$
$727$	46.3297			1.71827			0.859137	+	0.511745i	$0.171001\pi$
$728$	−1.43909	−	3.30591i	−0.0533363	−	0.122525i
$729$		0			0
$730$	−48.7604	+	28.1518i	−1.80470	+	1.04195i
$731$	2.50227	+	4.33406i	0.0925498	+	0.160301i
$732$		0			0
$733$		−	17.1464i		−	0.633315i	−0.948540	−	0.316658i	$-0.897439\pi$
$733$		−	17.1464i		−	0.633315i	0.948540	−	0.316658i	$-0.102561\pi$
$734$	−8.85339	−	5.11150i	−0.326784	−	0.188669i
$735$		0			0
$736$		−	5.40872i		−	0.199368i
$737$	−2.95927	+	5.12560i	−0.109006	+	0.188804i
$738$		0			0
$739$	−13.0327	+	7.52443i	−0.479416	+	0.276791i	−0.720173	−	0.693795i	$-0.755938\pi$
$739$	−13.0327	+	7.52443i	−0.479416	+	0.276791i	0.240757	+	0.970585i	$0.422604\pi$
$740$	33.5210			1.23226
$741$		0			0
$742$	8.44252			0.309935
$743$	−20.1776	+	11.6496i	−0.740245	+	0.427381i	−0.822158	−	0.569259i	$-0.807230\pi$
$743$	−20.1776	+	11.6496i	−0.740245	+	0.427381i	0.0819132	+	0.996639i	$0.473897\pi$
$744$		0			0
$745$	−7.65235	+	13.2543i	−0.280361	+	0.485599i
$746$			1.56284i			0.0572198i
$747$		0			0
$748$	−3.06574	−	1.77001i	−0.112095	−	0.0647179i
$749$		−	14.2056i		−	0.519062i
$750$		0			0
$751$	15.4534	+	26.7661i	0.563903	+	0.976709i	0.997151	+	0.0754344i	$0.0240343\pi$
$751$	15.4534	+	26.7661i	0.563903	+	0.976709i	−0.433247	+	0.901275i	$0.642632\pi$
$752$	6.57196	−	3.79432i	0.239655	−	0.138365i
$753$		0			0
$754$	22.2869	−	9.70168i	0.811640	−	0.353314i
$755$	−71.7038			−2.60957
$756$		0			0
$757$	−7.58518	−	13.1379i	−0.275688	−	0.477506i	0.694620	−	0.719376i	$-0.255572\pi$
$757$	−7.58518	−	13.1379i	−0.275688	−	0.477506i	−0.970308	+	0.241871i	$0.922239\pi$
$758$	−4.19268	+	7.26194i	−0.152285	+	0.263766i
$759$		0			0
$760$	−30.7681	−	17.7640i	−1.11608	−	0.644366i
$761$	−9.45208	−	5.45716i	−0.342638	−	0.197822i	0.318800	−	0.947822i	$-0.396720\pi$
$761$	−9.45208	−	5.45716i	−0.342638	−	0.197822i	−0.661438	+	0.750000i	$0.730053\pi$
$762$		0			0
$763$	−1.71910	+	2.97757i	−0.0622357	+	0.107795i
$764$	−7.62813	−	13.2123i	−0.275976	−	0.478005i
$765$		0			0
$766$	−9.11803			−0.329448
$767$	−24.0637	+	10.4752i	−0.868890	+	0.378236i
$768$		0			0
$769$	−15.9112	+	9.18636i	−0.573774	+	0.331269i	−0.758655	−	0.651492i	$-0.774143\pi$
$769$	−15.9112	+	9.18636i	−0.573774	+	0.331269i	0.184881	+	0.982761i	$0.440810\pi$
$770$	2.46757	+	4.27396i	0.0889251	+	0.154023i
$771$		0			0
$772$			14.1797i			0.510340i
$773$	12.8159	+	7.39924i	0.460955	+	0.266132i	0.712446	−	0.701727i	$-0.247588\pi$
$773$	12.8159	+	7.39924i	0.460955	+	0.266132i	−0.251491	+	0.967860i	$0.580921\pi$
$774$		0			0
$775$			80.1766i			2.88003i
$776$	0.613704	−	1.06297i	0.0220307	−	0.0381583i
$777$		0			0
$778$	−32.2095	+	18.5961i	−1.15477	+	0.666704i
$779$	−16.6118			−0.595180
$780$		0			0
$781$	9.73363			0.348297
$782$	−14.7812	+	8.53391i	−0.528573	+	0.305172i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	3.01159i		−	0.107488i
$786$		0			0
$787$	−36.8542	−	21.2778i	−1.31371	−	0.758472i	−0.331003	−	0.943630i	$-0.607387\pi$
$787$	−36.8542	−	21.2778i	−1.31371	−	0.758472i	−0.982709	+	0.185158i	$0.940720\pi$
$788$			11.9699i			0.426410i
$789$		0			0
$790$	−7.74500	−	13.4147i	−0.275555	−	0.477275i
$791$	5.21858	−	3.01295i	0.185551	−	0.107128i
$792$		0			0
$793$	−14.9905	−	34.4364i	−0.532327	−	1.22287i
$794$	−31.7067			−1.12523
$795$		0			0
$796$	2.49684	+	4.32465i	0.0884981	+	0.153283i
$797$	−13.1427	+	22.7638i	−0.465537	+	0.806334i	−0.999226	−	0.0393473i	$-0.987472\pi$
$797$	−13.1427	+	22.7638i	−0.465537	+	0.806334i	0.533689	+	0.845681i	$0.320805\pi$
$798$		0			0
$799$	−20.7386	−	11.9734i	−0.733678	−	0.423589i
$800$	12.4304	+	7.17667i	0.439480	+	0.253734i
$801$		0			0
$802$	13.4995	−	23.3818i	0.476683	−	0.825639i
$803$	−7.17877	−	12.4340i	−0.253333	−	0.438786i
$804$		0			0
$805$	23.7943			0.838638
$806$	20.0118	+	2.27158i	0.704886	+	0.0800132i
$807$		0			0
$808$	9.36545	−	5.40714i	0.329475	−	0.190223i
$809$	−22.5282	−	39.0200i	−0.792050	−	1.37187i	−0.924696	−	0.380708i	$-0.875680\pi$
$809$	−22.5282	−	39.0200i	−0.792050	−	1.37187i	0.132645	−	0.991164i	$-0.457653\pi$
$810$		0			0
$811$			40.4251i			1.41952i	0.704444	+	0.709759i	$0.251196\pi$
$811$			40.4251i			1.41952i	−0.704444	+	0.709759i	$0.748804\pi$
$812$	5.83834	+	3.37076i	0.204885	+	0.118291i
$813$		0			0
$814$			8.54792i			0.299604i
$815$	−30.9082	+	53.5346i	−1.08267	+	1.87523i
$816$		0			0
$817$	−11.0918	+	6.40387i	−0.388054	+	0.224043i
$818$	10.3317			0.361238
$819$		0			0
$820$	9.04906			0.316007
$821$	−4.21451	+	2.43325i	−0.147087	+	0.0849210i	−0.571738	−	0.820437i	$-0.693730\pi$
$821$	−4.21451	+	2.43325i	−0.147087	+	0.0849210i	0.424650	+	0.905358i	$0.360397\pi$
$822$		0			0
$823$	−24.4953	+	42.4270i	−0.853851	+	1.47891i	0.0238552	+	0.999715i	$0.492406\pi$
$823$	−24.4953	+	42.4270i	−0.853851	+	1.47891i	−0.877707	+	0.479198i	$0.840927\pi$
$824$		−	17.2910i		−	0.602361i
$825$		0			0
$826$	−6.30380	−	3.63950i	−0.219337	−	0.126634i
$827$			35.9430i			1.24986i	0.780681	+	0.624929i	$0.214872\pi$
$827$			35.9430i			1.24986i	−0.780681	+	0.624929i	$0.785128\pi$
$828$		0			0
$829$	10.6285	+	18.4091i	0.369143	+	0.639374i	0.989432	−	0.144999i	$-0.0463179\pi$
$829$	10.6285	+	18.4091i	0.369143	+	0.639374i	−0.620289	+	0.784374i	$0.712985\pi$
$830$	−42.4387	+	24.5020i	−1.47307	+	0.850477i
$831$		0			0
$832$	2.14345	−	2.89924i	0.0743108	−	0.100513i
$833$	−3.15561			−0.109335
$834$		0			0
$835$	−1.07180	−	1.85641i	−0.0370911	−	0.0642436i
$836$	4.52984	−	7.84592i	0.156668	−	0.271357i
$837$		0			0
$838$	22.1070	+	12.7635i	0.763673	+	0.440907i
$839$	14.3862	+	8.30586i	0.496666	+	0.286750i	0.727336	−	0.686282i	$-0.240758\pi$
$839$	14.3862	+	8.30586i	0.496666	+	0.286750i	−0.230670	+	0.973032i	$0.574092\pi$
$840$		0			0
$841$	−8.22411	+	14.2446i	−0.283590	+	0.491192i
$842$	2.15719	+	3.73636i	0.0743416	+	0.128763i
$843$		0			0
$844$	6.55485			0.225627
$845$	54.6772	−	16.7665i	1.88095	−	0.576785i
$846$		0			0
$847$	8.43641	−	4.87076i	0.289879	−	0.167361i
$848$	4.22126	+	7.31143i	0.144959	+	0.251076i
$849$		0			0
$850$		−	45.2936i		−	1.55356i
$851$	35.6914	+	20.6065i	1.22349	+	0.706380i
$852$		0			0
$853$			38.6728i			1.32413i	0.749446	+	0.662066i	$0.230320\pi$
$853$			38.6728i			1.32413i	−0.749446	+	0.662066i	$0.769680\pi$
$854$	5.20831	−	9.02106i	0.178225	−	0.308694i
$855$		0			0
$856$	12.3024	−	7.10282i	0.420489	−	0.242769i
$857$	34.9400			1.19353			0.596763	−	0.802417i	$-0.296453\pi$
$857$	34.9400			1.19353			0.596763	+	0.802417i	$0.296453\pi$
$858$		0			0
$859$	42.6482			1.45514			0.727570	−	0.686034i	$-0.240650\pi$
$859$	42.6482			1.45514			0.727570	+	0.686034i	$0.240650\pi$
$860$	6.04212	−	3.48842i	0.206035	−	0.118954i
$861$		0			0
$862$	3.68062	−	6.37502i	0.125362	−	0.217134i
$863$		−	25.1857i		−	0.857332i	−0.903463	−	0.428666i	$-0.858984\pi$
$863$		−	25.1857i		−	0.857332i	0.903463	−	0.428666i	$-0.141016\pi$
$864$		0			0
$865$	13.0991	+	7.56276i	0.445382	+	0.257141i
$866$			26.8206i			0.911401i
$867$		0			0
$868$	2.79296	+	4.83755i	0.0947992	+	0.164197i
$869$	3.42078	−	1.97499i	0.116042	−	0.0669970i
$870$		0			0
$871$	−2.14549	+	18.9010i	−0.0726972	+	0.640435i
$872$	−3.43821			−0.116432
$873$		0			0
$874$	−21.8402	−	37.8283i	−0.738755	−	1.27956i
$875$	−20.5738	+	35.6349i	−0.695522	+	1.20468i
$876$		0			0
$877$	−28.8597	−	16.6621i	−0.974522	−	0.562641i	−0.0739104	−	0.997265i	$-0.523548\pi$
$877$	−28.8597	−	16.6621i	−0.974522	−	0.562641i	−0.900612	+	0.434624i	$0.856881\pi$
$878$	30.1976	+	17.4346i	1.01912	+	0.588390i
$879$		0			0
$880$	−2.46757	+	4.27396i	−0.0831818	+	0.144075i
$881$	−9.64767	−	16.7102i	−0.325038	−	0.562983i	0.656482	−	0.754342i	$-0.272044\pi$
$881$	−9.64767	−	16.7102i	−0.325038	−	0.562983i	−0.981520	+	0.191359i	$0.938710\pi$
$882$		0			0
$883$	25.8750			0.870764			0.435382	−	0.900246i	$-0.356613\pi$
$883$	25.8750			0.870764			0.435382	+	0.900246i	$0.356613\pi$
$884$	−11.3051	−	1.28327i	−0.380232	−	0.0431610i
$885$		0			0
$886$	7.44636	−	4.29916i	0.250165	−	0.144433i
$887$	12.2955	+	21.2964i	0.412842	+	0.715064i	0.995199	−	0.0978692i	$-0.0312027\pi$
$887$	12.2955	+	21.2964i	0.412842	+	0.715064i	−0.582357	+	0.812933i	$0.697869\pi$
$888$		0			0
$889$		−	9.75637i		−	0.327218i
$890$	−39.7123	−	22.9279i	−1.33116	−	0.768545i
$891$		0			0
$892$		−	7.43346i		−	0.248891i
$893$	30.6426	−	53.0746i	1.02542	−	1.77607i
$894$		0			0
$895$	−8.29041	+	4.78647i	−0.277118	+	0.159994i
$896$	1.00000			0.0334077
$897$		0			0
$898$	31.3325			1.04558
$899$	−32.6125	+	18.8288i	−1.08769	+	0.627976i
$900$		0			0
$901$	13.3206	−	23.0720i	0.443775	−	0.768641i
$902$			2.30753i			0.0768323i
$903$		0			0
$904$	5.21858	+	3.01295i	0.173567	+	0.100209i
$905$			47.1546i			1.56747i
$906$		0			0
$907$	18.2768	+	31.6563i	0.606870	+	1.05113i	0.991753	+	0.128164i	$0.0409083\pi$
$907$	18.2768	+	31.6563i	0.606870	+	1.05113i	−0.384883	+	0.922965i	$0.625758\pi$
$908$	−10.1529	+	5.86177i	−0.336935	+	0.194530i
$909$		0			0
$910$	12.7545	+	9.42957i	0.422807	+	0.312587i
$911$	−16.0638			−0.532218			−0.266109	−	0.963943i	$-0.585738\pi$
$911$	−16.0638			−0.532218			−0.266109	+	0.963943i	$0.585738\pi$
$912$		0			0
$913$	−6.24806	−	10.8220i	−0.206781	−	0.358155i
$914$	4.80459	−	8.32180i	0.158922	−	0.275261i
$915$		0			0
$916$	−8.40623	−	4.85334i	−0.277750	−	0.160359i
$917$	6.60571	+	3.81381i	0.218140	+	0.125943i
$918$		0			0
$919$	11.8590	−	20.5404i	0.391192	−	0.677564i	−0.601415	−	0.798937i	$-0.705396\pi$
$919$	11.8590	−	20.5404i	0.391192	−	0.677564i	0.992607	+	0.121372i	$0.0387295\pi$
$920$	11.8971	+	20.6065i	0.392237	+	0.679375i
$921$		0			0
$922$	13.3312			0.439041
$923$	28.6843	−	12.4865i	0.944154	−	0.410999i
$924$		0			0
$925$	−94.7158	+	54.6842i	−3.11423	+	1.79800i
$926$	2.77505	+	4.80653i	0.0911939	+	0.157953i
$927$		0			0
$928$			6.74153i			0.221302i
$929$	32.7037	+	18.8815i	1.07297	+	0.619482i	0.928993	−	0.370098i	$-0.120676\pi$
$929$	32.7037	+	18.8815i	1.07297	+	0.619482i	0.143982	+	0.989580i	$0.454009\pi$
$930$		0			0
$931$		−	8.07591i		−	0.264677i
$932$	5.92219	−	10.2575i	0.193988	−	0.335997i
$933$		0			0
$934$	14.6594	−	8.46362i	0.479671	−	0.276938i
$935$	15.5734			0.509304
$936$		0			0
$937$	−52.4028			−1.71193			−0.855963	−	0.517037i	$-0.827035\pi$
$937$	−52.4028			−1.71193			−0.855963	+	0.517037i	$0.827035\pi$
$938$	−4.56902	+	2.63792i	−0.149184	+	0.0861313i
$939$		0			0
$940$	−16.6922	+	28.9117i	−0.544438	+	0.942995i
$941$			52.7616i			1.71998i	0.510311	+	0.859990i	$0.329530\pi$
$941$			52.7616i			1.71998i	−0.510311	+	0.859990i	$0.670470\pi$
$942$		0			0
$943$	9.63497	+	5.56276i	0.313758	+	0.181148i
$944$		−	7.27900i		−	0.236911i
$945$		0			0
$946$	0.889554	+	1.54075i	0.0289219	+	0.0500942i
$947$	13.3891	−	7.73020i	0.435087	−	0.251198i	−0.266424	−	0.963856i	$-0.585842\pi$
$947$	13.3891	−	7.73020i	0.435087	−	0.251198i	0.701512	+	0.712658i	$0.252509\pi$
$948$		0			0
$949$	−37.1059	−	27.4329i	−1.20451	−	0.890511i
$950$	115.916			3.76082
$951$		0			0
$952$	−1.57781	−	2.73284i	−0.0511370	−	0.0885718i
$953$	−2.98031	+	5.16204i	−0.0965416	+	0.167215i	−0.910251	−	0.414057i	$-0.864111\pi$
$953$	−2.98031	+	5.16204i	−0.0965416	+	0.167215i	0.813709	+	0.581272i	$0.197445\pi$
$954$		0			0
$955$	58.1242	+	33.5580i	1.88085	+	1.08591i
$956$	−1.30323	−	0.752418i	−0.0421493	−	0.0243349i
$957$		0			0
$958$	−9.69840	+	16.7981i	−0.313341	+	0.542723i
$959$	3.67667	+	6.36818i	0.118726	+	0.205639i
$960$		0			0
$961$	−0.202476			−0.00653149
$962$	10.9655	+	25.1901i	0.353541	+	0.812160i
$963$		0			0
$964$	−2.56160	+	1.47894i	−0.0825036	+	0.0476335i
$965$	−31.1901	−	54.0228i	−1.00404	−	1.73905i
$966$		0			0
$967$		−	13.7140i		−	0.441014i	−0.975385	−	0.220507i	$-0.929229\pi$
$967$		−	13.7140i		−	0.441014i	0.975385	−	0.220507i	$-0.0707712\pi$
$968$	8.43641	+	4.87076i	0.271157	+	0.156552i
$969$		0			0
$970$			5.39967i			0.173373i
$971$	19.8818	−	34.4363i	0.638038	−	1.10511i	−0.347825	−	0.937560i	$-0.613080\pi$
$971$	19.8818	−	34.4363i	0.638038	−	1.10511i	0.985863	−	0.167555i	$-0.0535871\pi$
$972$		0			0
$973$	−7.43835	+	4.29454i	−0.238463	+	0.137677i
$974$	−15.4057			−0.493629
$975$		0			0
$976$	10.4166			0.333428
$977$	−31.0533	+	17.9286i	−0.993483	+	0.573588i	−0.906314	−	0.422606i	$-0.861115\pi$
$977$	−31.0533	+	17.9286i	−0.993483	+	0.573588i	−0.0871693	+	0.996194i	$0.527782\pi$
$978$		0			0
$979$	5.84666	−	10.1267i	0.186860	−	0.323651i
$980$			4.39924i			0.140529i
$981$		0			0
$982$	8.44926	+	4.87818i	0.269627	+	0.155669i
$983$		−	15.1034i		−	0.481724i	−0.970559	−	0.240862i	$-0.922570\pi$
$983$		−	15.1034i		−	0.481724i	0.970559	−	0.240862i	$-0.0774301\pi$
$984$		0			0
$985$	−26.3292	−	45.6036i	−0.838920	−	1.45305i
$986$	18.4235	−	10.6368i	0.586724	−	0.338745i
$987$		0			0
$988$	3.28417	−	28.9323i	0.104483	−	0.920460i
$989$	8.57779			0.272758
$990$		0			0
$991$	−27.3407	−	47.3554i	−0.868505	−	1.50429i	−0.863525	−	0.504307i	$-0.831748\pi$
$991$	−27.3407	−	47.3554i	−0.868505	−	1.50429i	−0.00498027	−	0.999988i	$-0.501585\pi$
$992$	−2.79296	+	4.83755i	−0.0886765	+	0.153592i
$993$		0			0
$994$	7.51422	+	4.33834i	0.238336	+	0.137604i
$995$	−19.0252	−	10.9842i	−0.603139	−	0.348222i
$996$		0			0
$997$	−2.75369	+	4.76953i	−0.0872102	+	0.151052i	−0.906331	−	0.422569i	$-0.861128\pi$
$997$	−2.75369	+	4.76953i	−0.0872102	+	0.151052i	0.819121	+	0.573621i	$0.194462\pi$
$998$	2.76321	+	4.78602i	0.0874679	+	0.151499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.f.127.4		8
3.2	odd	2		546.2.s.e.127.1	yes	8
13.4	even	6	inner	1638.2.bj.f.1135.3		8
39.2	even	12		7098.2.a.cn.1.1		4
39.11	even	12		7098.2.a.co.1.4		4
39.17	odd	6		546.2.s.e.43.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.e.43.2	✓	8	39.17	odd	6
546.2.s.e.127.1	yes	8	3.2	odd	2
1638.2.bj.f.127.4		8	1.1	even	1	trivial
1638.2.bj.f.1135.3		8	13.4	even	6	inner
7098.2.a.cn.1.1		4	39.2	even	12
7098.2.a.co.1.4		4	39.11	even	12

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.39924i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(2.19962 + 3.80986i) q^{10} +(-0.971521 + 0.560908i) q^{11} +(-2.14345 + 2.89924i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.57781 + 2.73284i) q^{17} +(-6.99395 - 4.03796i) q^{19} +(3.80986 + 2.19962i) q^{20} +(-0.560908 + 0.971521i) q^{22} +(2.70436 + 4.68409i) q^{23} -14.3533 q^{25} +(-0.406663 + 3.58254i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-3.37076 - 5.83834i) q^{29} -5.58592i q^{31} +(-0.866025 - 0.500000i) q^{32} +3.15561i q^{34} +(2.19962 - 3.80986i) q^{35} +(6.59886 - 3.80986i) q^{37} -8.07591 q^{38} +4.39924 q^{40} +(1.78138 - 1.02848i) q^{41} +(0.792959 - 1.37344i) q^{43} +1.12182i q^{44} +(4.68409 + 2.70436i) q^{46} +7.58865i q^{47} +(0.500000 + 0.866025i) q^{49} +(-12.4304 + 7.17667i) q^{50} +(1.43909 + 3.30591i) q^{52} -8.44252 q^{53} +(-2.46757 - 4.27396i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-5.83834 - 3.37076i) q^{58} +(6.30380 + 3.63950i) q^{59} +(-5.20831 + 9.02106i) q^{61} +(-2.79296 - 4.83755i) q^{62} -1.00000 q^{64} +(-12.7545 - 9.42957i) q^{65} +(4.56902 - 2.63792i) q^{67} +(1.57781 + 2.73284i) q^{68} -4.39924i q^{70} +(-7.51422 - 4.33834i) q^{71} +12.7985i q^{73} +(3.80986 - 6.59886i) q^{74} +(-6.99395 + 4.03796i) q^{76} +1.12182 q^{77} -3.52106 q^{79} +(3.80986 - 2.19962i) q^{80} +(1.02848 - 1.78138i) q^{82} +11.1392i q^{83} +(-12.0224 - 6.94115i) q^{85} -1.58592i q^{86} +(0.560908 + 0.971521i) q^{88} +(-9.02707 + 5.21178i) q^{89} +(3.30591 - 1.43909i) q^{91} +5.40872 q^{92} +(3.79432 + 6.57196i) q^{94} +(17.7640 - 30.7681i) q^{95} +(1.06297 + 0.613704i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

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