LMFDB - Embedded newform 1638.2.bj.h.1135.3

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.3
Root			$0.830471 + 0.830471i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.h.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.25534i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.25534i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.627670 - 1.08716i) q^{10} +(4.35285 + 2.51312i) q^{11} +(-3.43954 - 1.08148i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.26026 + 3.91489i) q^{17} +(-3.05207 + 1.76211i) q^{19} +(-1.08716 + 0.627670i) q^{20} +(-2.51312 - 4.35285i) q^{22} +(-2.56840 + 4.44859i) q^{23} +3.42412 q^{25} +(2.43799 + 2.65635i) q^{26} +(0.866025 + 0.500000i) q^{28} +(0.765021 - 1.32506i) q^{29} +0.439192i q^{31} +(0.866025 - 0.500000i) q^{32} -4.52053i q^{34} +(0.627670 + 1.08716i) q^{35} +(-8.90090 - 5.13894i) q^{37} +3.52423 q^{38} +1.25534 q^{40} +(8.65130 + 4.99483i) q^{41} +(-1.83219 - 3.17344i) q^{43} +5.02624i q^{44} +(4.44859 - 2.56840i) q^{46} -3.60242i q^{47} +(0.500000 - 0.866025i) q^{49} +(-2.96538 - 1.71206i) q^{50} +(-0.783183 - 3.51946i) q^{52} -8.82264 q^{53} +(-3.15482 + 5.46431i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.32506 + 0.765021i) q^{58} +(0.542230 - 0.313057i) q^{59} +(4.49928 + 7.79299i) q^{61} +(0.219596 - 0.380351i) q^{62} -1.00000 q^{64} +(1.35762 - 4.31779i) q^{65} +(6.40795 + 3.69963i) q^{67} +(-2.26026 + 3.91489i) q^{68} -1.25534i q^{70} +(-5.89350 + 3.40261i) q^{71} +11.5576i q^{73} +(5.13894 + 8.90090i) q^{74} +(-3.05207 - 1.76211i) q^{76} +5.02624 q^{77} -6.74435 q^{79} +(-1.08716 - 0.627670i) q^{80} +(-4.99483 - 8.65130i) q^{82} +9.57207i q^{83} +(-4.91452 + 2.83740i) q^{85} +3.66437i q^{86} +(2.51312 - 4.35285i) q^{88} +(7.28303 + 4.20486i) q^{89} +(-3.51946 + 0.783183i) q^{91} -5.13679 q^{92} +(-1.80121 + 3.11978i) q^{94} +(-2.21205 - 3.83139i) q^{95} +(-2.43543 + 1.40610i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$			1.25534i			0.561405i	0.959795	+	0.280703i	$0.0905674\pi$
$5$			1.25534i			0.561405i	−0.959795	+	0.280703i	$0.909433\pi$
$6$		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
$10$	0.627670	−	1.08716i	0.198487	−	0.343789i
$11$	4.35285	+	2.51312i	1.31243	+	0.757734i	0.982499	−	0.186270i	$-0.0596398\pi$
$11$	4.35285	+	2.51312i	1.31243	+	0.757734i	0.329935	+	0.944004i	$0.392973\pi$
$12$		0			0
$13$	−3.43954	−	1.08148i	−0.953956	−	0.299947i
$13$	−3.43954	−	1.08148i	−0.953956	−	0.299947i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.26026	+	3.91489i	0.548195	+	0.949501i	0.998398	+	0.0565752i	$0.0180181\pi$
$17$	2.26026	+	3.91489i	0.548195	+	0.949501i	−0.450204	+	0.892926i	$0.648649\pi$
$18$		0			0
$19$	−3.05207	+	1.76211i	−0.700193	+	0.404257i	−0.807419	−	0.589978i	$-0.799136\pi$
$19$	−3.05207	+	1.76211i	−0.700193	+	0.404257i	0.107226	+	0.994235i	$0.465803\pi$
$20$	−1.08716	+	0.627670i	−0.243096	+	0.140351i
$21$		0			0
$22$	−2.51312	−	4.35285i	−0.535799	−	0.928031i
$23$	−2.56840	+	4.44859i	−0.535548	+	0.927596i	0.463589	+	0.886050i	$0.346561\pi$
$23$	−2.56840	+	4.44859i	−0.535548	+	0.927596i	−0.999137	+	0.0415454i	$0.986772\pi$
$24$		0			0
$25$	3.42412			0.684824
$26$	2.43799	+	2.65635i	0.478129	+	0.520954i
$27$		0			0
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	0.765021	−	1.32506i	0.142061	−	0.246057i	−0.786212	−	0.617957i	$-0.787960\pi$
$29$	0.765021	−	1.32506i	0.142061	−	0.246057i	0.928273	+	0.371901i	$0.121294\pi$
$30$		0			0
$31$			0.439192i			0.0788812i	0.999222	+	0.0394406i	$0.0125576\pi$
$31$			0.439192i			0.0788812i	−0.999222	+	0.0394406i	$0.987442\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	4.52053i		−	0.775264i
$35$	0.627670	+	1.08716i	0.106096	+	0.183763i
$36$		0			0
$37$	−8.90090	−	5.13894i	−1.46330	−	0.844836i	−0.464137	−	0.885763i	$-0.653636\pi$
$37$	−8.90090	−	5.13894i	−1.46330	−	0.844836i	−0.999162	+	0.0409267i	$0.986969\pi$
$38$	3.52423			0.571705
$39$		0			0
$40$	1.25534			0.198487
$41$	8.65130	+	4.99483i	1.35111	+	0.780061i	0.988404	−	0.151844i	$-0.0485212\pi$
$41$	8.65130	+	4.99483i	1.35111	+	0.780061i	0.362701	+	0.931905i	$0.381855\pi$
$42$		0			0
$43$	−1.83219	−	3.17344i	−0.279406	−	0.483945i	0.691831	−	0.722059i	$-0.256804\pi$
$43$	−1.83219	−	3.17344i	−0.279406	−	0.483945i	−0.971237	+	0.238114i	$0.923471\pi$
$44$			5.02624i			0.757734i
$45$		0			0
$46$	4.44859	−	2.56840i	0.655909	−	0.378689i
$47$		−	3.60242i		−	0.525466i	−0.964869	−	0.262733i	$-0.915376\pi$
$47$		−	3.60242i		−	0.525466i	0.964869	−	0.262733i	$-0.0846239\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−2.96538	−	1.71206i	−0.419368	−	0.242122i
$51$		0			0
$52$	−0.783183	−	3.51946i	−0.108608	−	0.488062i
$53$	−8.82264			−1.21188			−0.605942	−	0.795509i	$-0.707204\pi$
$53$	−8.82264			−1.21188			−0.605942	+	0.795509i	$0.707204\pi$
$54$		0			0
$55$	−3.15482	+	5.46431i	−0.425396	+	0.736807i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−1.32506	+	0.765021i	−0.173988	+	0.100452i
$59$	0.542230	−	0.313057i	0.0705924	−	0.0407565i	−0.464288	−	0.885684i	$-0.653690\pi$
$59$	0.542230	−	0.313057i	0.0705924	−	0.0407565i	0.534881	+	0.844928i	$0.320357\pi$
$60$		0			0
$61$	4.49928	+	7.79299i	0.576074	+	0.997790i	0.995924	+	0.0901963i	$0.0287495\pi$
$61$	4.49928	+	7.79299i	0.576074	+	0.997790i	−0.419850	+	0.907594i	$0.637917\pi$
$62$	0.219596	−	0.380351i	0.0278887	−	0.0483046i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.35762	−	4.31779i	0.168392	−	0.535556i
$66$		0			0
$67$	6.40795	+	3.69963i	0.782856	+	0.451982i	0.837441	−	0.546527i	$-0.184050\pi$
$67$	6.40795	+	3.69963i	0.782856	+	0.451982i	−0.0545856	+	0.998509i	$0.517384\pi$
$68$	−2.26026	+	3.91489i	−0.274097	+	0.474751i
$69$		0			0
$70$		−	1.25534i		−	0.150042i
$71$	−5.89350	+	3.40261i	−0.699430	+	0.403816i	−0.807135	−	0.590367i	$-0.798983\pi$
$71$	−5.89350	+	3.40261i	−0.699430	+	0.403816i	0.107705	+	0.994183i	$0.465650\pi$
$72$		0			0
$73$			11.5576i			1.35272i	0.736572	+	0.676359i	$0.236443\pi$
$73$			11.5576i			1.35272i	−0.736572	+	0.676359i	$0.763557\pi$
$74$	5.13894	+	8.90090i	0.597390	+	1.03471i
$75$		0			0
$76$	−3.05207	−	1.76211i	−0.350097	−	0.202128i
$77$	5.02624			0.572793
$78$		0			0
$79$	−6.74435			−0.758799			−0.379399	−	0.925233i	$-0.623869\pi$
$79$	−6.74435			−0.758799			−0.379399	+	0.925233i	$0.623869\pi$
$80$	−1.08716	−	0.627670i	−0.121548	−	0.0701756i
$81$		0			0
$82$	−4.99483	−	8.65130i	−0.551587	−	0.955376i
$83$			9.57207i			1.05067i	0.850895	+	0.525335i	$0.176060\pi$
$83$			9.57207i			1.05067i	−0.850895	+	0.525335i	$0.823940\pi$
$84$		0			0
$85$	−4.91452	+	2.83740i	−0.533055	+	0.307759i
$86$			3.66437i			0.395140i
$87$		0			0
$88$	2.51312	−	4.35285i	0.267899	−	0.464015i
$89$	7.28303	+	4.20486i	0.772000	+	0.445714i	0.833587	−	0.552388i	$-0.186283\pi$
$89$	7.28303	+	4.20486i	0.772000	+	0.445714i	−0.0615879	+	0.998102i	$0.519616\pi$
$90$		0			0
$91$	−3.51946	+	0.783183i	−0.368940	+	0.0820999i
$92$	−5.13679			−0.535548
$93$		0			0
$94$	−1.80121	+	3.11978i	−0.185780	+	0.321781i
$95$	−2.21205	−	3.83139i	−0.226952	−	0.393092i
$96$		0			0
$97$	−2.43543	+	1.40610i	−0.247280	+	0.142767i	−0.618518	−	0.785770i	$-0.712267\pi$
$97$	−2.43543	+	1.40610i	−0.247280	+	0.142767i	0.371238	+	0.928538i	$0.378933\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	1.71206	+	2.96538i	0.171206	+	0.296538i
$101$	−5.19484	+	8.99772i	−0.516906	+	0.895307i	0.482902	+	0.875675i	$0.339583\pi$
$101$	−5.19484	+	8.99772i	−0.516906	+	0.895307i	−0.999807	+	0.0196321i	$0.993751\pi$
$102$		0			0
$103$	13.1058			1.29136			0.645678	−	0.763610i	$-0.276575\pi$
$103$	13.1058			1.29136			0.645678	+	0.763610i	$0.276575\pi$
$104$	−1.08148	+	3.43954i	−0.106047	+	0.337274i
$105$		0			0
$106$	7.64063	+	4.41132i	0.742124	+	0.428466i
$107$	−6.98610	+	12.1003i	−0.675371	+	1.16978i	0.300989	+	0.953628i	$0.402683\pi$
$107$	−6.98610	+	12.1003i	−0.675371	+	1.16978i	−0.976360	+	0.216150i	$0.930650\pi$
$108$		0			0
$109$		−	13.4854i		−	1.29167i	−0.763478	−	0.645833i	$-0.776510\pi$
$109$		−	13.4854i		−	1.29167i	0.763478	−	0.645833i	$-0.223490\pi$
$110$	5.46431	−	3.15482i	0.521001	−	0.300800i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	1.13886	+	1.97256i	0.107135	+	0.185563i	0.914608	−	0.404341i	$-0.132499\pi$
$113$	1.13886	+	1.97256i	0.107135	+	0.185563i	−0.807474	+	0.589904i	$0.799166\pi$
$114$		0			0
$115$	−5.58450	−	3.22421i	−0.520757	−	0.300659i
$116$	1.53004			0.142061
$117$		0			0
$118$	−0.626113			−0.0576384
$119$	3.91489	+	2.26026i	0.358878	+	0.207198i
$120$		0			0
$121$	7.13153	+	12.3522i	0.648321	+	1.12293i
$122$		−	8.99857i		−	0.814692i
$123$		0			0
$124$	−0.380351	+	0.219596i	−0.0341565	+	0.0197203i
$125$			10.5751i			0.945869i
$126$		0			0
$127$	2.13765	−	3.70252i	0.189686	−	0.328546i	−0.755460	−	0.655195i	$-0.772586\pi$
$127$	2.13765	−	3.70252i	0.189686	−	0.328546i	0.945146	+	0.326650i	$0.105920\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.33463	+	3.06050i	−0.292466	+	0.268424i
$131$	7.63335			0.666929			0.333465	−	0.942763i	$-0.391782\pi$
$131$	7.63335			0.666929			0.333465	+	0.942763i	$0.391782\pi$
$132$		0			0
$133$	−1.76211	+	3.05207i	−0.152795	+	0.264648i
$134$	−3.69963	−	6.40795i	−0.319600	−	0.553563i
$135$		0			0
$136$	3.91489	−	2.26026i	0.335699	−	0.193816i
$137$	−3.69647	+	2.13416i	−0.315810	+	0.182333i	−0.649524	−	0.760341i	$-0.725032\pi$
$137$	−3.69647	+	2.13416i	−0.315810	+	0.182333i	0.333713	+	0.942675i	$0.391698\pi$
$138$		0			0
$139$	−3.44043	−	5.95899i	−0.291813	−	0.505435i	0.682425	−	0.730955i	$-0.260925\pi$
$139$	−3.44043	−	5.95899i	−0.291813	−	0.505435i	−0.974239	+	0.225520i	$0.927592\pi$
$140$	−0.627670	+	1.08716i	−0.0530478	+	0.0918815i
$141$		0			0
$142$	6.80523			0.571082
$143$	−12.2539	−	13.3515i	−1.02472	−	1.11651i
$144$		0			0
$145$	1.66339	+	0.960361i	0.138137	+	0.0797537i
$146$	5.77881	−	10.0092i	0.478258	−	0.828367i
$147$		0			0
$148$		−	10.2779i		−	0.844836i
$149$	9.85411	−	5.68927i	0.807280	−	0.466083i	−0.0387303	−	0.999250i	$-0.512331\pi$
$149$	9.85411	−	5.68927i	0.807280	−	0.466083i	0.846010	+	0.533166i	$0.178998\pi$
$150$		0			0
$151$			19.3337i			1.57336i	0.617364	+	0.786678i	$0.288201\pi$
$151$			19.3337i			1.57336i	−0.617364	+	0.786678i	$0.711799\pi$
$152$	1.76211	+	3.05207i	0.142926	+	0.247556i
$153$		0			0
$154$	−4.35285	−	2.51312i	−0.350763	−	0.202513i
$155$	−0.551335			−0.0442843
$156$		0			0
$157$	−19.8938			−1.58770			−0.793848	−	0.608117i	$-0.791925\pi$
$157$	−19.8938			−1.58770			−0.793848	+	0.608117i	$0.791925\pi$
$158$	5.84078	+	3.37218i	0.464667	+	0.268276i
$159$		0			0
$160$	0.627670	+	1.08716i	0.0496217	+	0.0859472i
$161$			5.13679i			0.404836i
$162$		0			0
$163$	14.4812	−	8.36072i	1.13425	−	0.654862i	0.189253	−	0.981928i	$-0.439393\pi$
$163$	14.4812	−	8.36072i	1.13425	−	0.654862i	0.945001	+	0.327067i	$0.106060\pi$
$164$			9.98966i			0.780061i
$165$		0			0
$166$	4.78603	−	8.28965i	0.371468	−	0.643402i
$167$	−5.38066	−	3.10652i	−0.416368	−	0.240390i	0.277154	−	0.960825i	$-0.410609\pi$
$167$	−5.38066	−	3.10652i	−0.416368	−	0.240390i	−0.693522	+	0.720435i	$0.743942\pi$
$168$		0			0
$169$	10.6608	+	7.43955i	0.820063	+	0.572273i
$170$	5.67480			0.435237
$171$		0			0
$172$	1.83219	−	3.17344i	0.139703	−	0.241973i
$173$	8.91864	+	15.4475i	0.678071	+	1.17445i	0.975561	+	0.219729i	$0.0705174\pi$
$173$	8.91864	+	15.4475i	0.678071	+	1.17445i	−0.297489	+	0.954725i	$0.596149\pi$
$174$		0			0
$175$	2.96538	−	1.71206i	0.224161	−	0.129420i
$176$	−4.35285	+	2.51312i	−0.328108	+	0.189433i
$177$		0			0
$178$	−4.20486	−	7.28303i	−0.315168	−	0.545886i
$179$	4.49034	−	7.77750i	0.335624	−	0.581317i	−0.647981	−	0.761657i	$-0.724386\pi$
$179$	4.49034	−	7.77750i	0.335624	−	0.581317i	0.983604	+	0.180339i	$0.0577196\pi$
$180$		0			0
$181$	3.50995			0.260892			0.130446	−	0.991455i	$-0.458359\pi$
$181$	3.50995			0.260892			0.130446	+	0.991455i	$0.458359\pi$
$182$	3.43954	+	1.08148i	0.254955	+	0.0801643i
$183$		0			0
$184$	4.44859	+	2.56840i	0.327955	+	0.189345i
$185$	6.45112	−	11.1737i	0.474295	−	0.821504i
$186$		0			0
$187$			22.7213i			1.66154i
$188$	3.11978	−	1.80121i	0.227534	−	0.131367i
$189$		0			0
$190$			4.42410i			0.320958i
$191$	5.23224	+	9.06251i	0.378592	+	0.655740i	0.990858	−	0.134912i	$-0.0430752\pi$
$191$	5.23224	+	9.06251i	0.378592	+	0.655740i	−0.612266	+	0.790652i	$0.709742\pi$
$192$		0			0
$193$	12.1829	+	7.03378i	0.876942	+	0.506302i	0.869649	−	0.493671i	$-0.164345\pi$
$193$	12.1829	+	7.03378i	0.876942	+	0.506302i	0.00729281	+	0.999973i	$0.497679\pi$
$194$	2.81219			0.201904
$195$		0			0
$196$	1.00000			0.0714286
$197$	−15.3517	−	8.86331i	−1.09376	−	0.631485i	−0.159188	−	0.987248i	$-0.550888\pi$
$197$	−15.3517	−	8.86331i	−1.09376	−	0.631485i	−0.934576	+	0.355763i	$0.884221\pi$
$198$		0			0
$199$	7.13739	+	12.3623i	0.505956	+	0.876342i	0.999976	+	0.00689145i	$0.00219363\pi$
$199$	7.13739	+	12.3623i	0.505956	+	0.876342i	−0.494020	+	0.869451i	$0.664473\pi$
$200$		−	3.42412i		−	0.242122i
$201$		0			0
$202$	8.99772	−	5.19484i	0.633077	−	0.365507i
$203$		−	1.53004i		−	0.107388i
$204$		0			0
$205$	−6.27021	+	10.8603i	−0.437930	+	0.758518i
$206$	−11.3500	−	6.55291i	−0.790790	−	0.456563i
$207$		0			0
$208$	2.65635	−	2.43799i	0.184185	−	0.169044i
$209$	−17.7136			−1.22528
$210$		0			0
$211$	6.59260	−	11.4187i	0.453854	−	0.786097i	−0.544768	−	0.838587i	$-0.683382\pi$
$211$	6.59260	−	11.4187i	0.453854	−	0.786097i	0.998621	+	0.0524894i	$0.0167156\pi$
$212$	−4.41132	−	7.64063i	−0.302971	−	0.524761i
$213$		0			0
$214$	12.1003	−	6.98610i	0.827158	−	0.477560i
$215$	3.98375	−	2.30002i	0.271689	−	0.156860i
$216$		0			0
$217$	0.219596	+	0.380351i	0.0149071	+	0.0258199i
$218$	−6.74270	+	11.6787i	−0.456673	+	0.790981i
$219$		0			0
$220$	−6.30964			−0.425396
$221$	−3.54040	−	15.9098i	−0.238153	−	1.07021i
$222$		0			0
$223$	6.35028	+	3.66633i	0.425246	+	0.245516i	0.697319	−	0.716761i	$-0.254376\pi$
$223$	6.35028	+	3.66633i	0.425246	+	0.245516i	−0.272073	+	0.962277i	$0.587709\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$		−	2.27772i		−	0.151512i
$227$	19.7162	−	11.3832i	1.30861	−	0.755526i	0.326746	−	0.945112i	$-0.394048\pi$
$227$	19.7162	−	11.3832i	1.30861	−	0.755526i	0.981864	+	0.189586i	$0.0607145\pi$
$228$		0			0
$229$		−	4.47930i		−	0.296001i	−0.988987	−	0.148000i	$-0.952716\pi$
$229$		−	4.47930i		−	0.296001i	0.988987	−	0.148000i	$-0.0472837\pi$
$230$	3.22421	+	5.58450i	0.212598	+	0.368231i
$231$		0			0
$232$	−1.32506	−	0.765021i	−0.0869941	−	0.0502261i
$233$	−9.17557			−0.601112			−0.300556	−	0.953764i	$-0.597172\pi$
$233$	−9.17557			−0.601112			−0.300556	+	0.953764i	$0.597172\pi$
$234$		0			0
$235$	4.52226			0.295000
$236$	0.542230	+	0.313057i	0.0352962	+	0.0203783i
$237$		0			0
$238$	−2.26026	−	3.91489i	−0.146511	−	0.253765i
$239$		−	19.1232i		−	1.23697i	−0.785795	−	0.618487i	$-0.787746\pi$
$239$		−	19.1232i		−	1.23697i	0.785795	−	0.618487i	$-0.212254\pi$
$240$		0			0
$241$	−18.1292	+	10.4669i	−1.16780	+	0.674231i	−0.953162	−	0.302462i	$-0.902192\pi$
$241$	−18.1292	+	10.4669i	−1.16780	+	0.674231i	−0.214641	+	0.976693i	$0.568858\pi$
$242$		−	14.2631i		−	0.916865i
$243$		0			0
$244$	−4.49928	+	7.79299i	−0.288037	+	0.498895i
$245$	1.08716	+	0.627670i	0.0694559	+	0.0401004i
$246$		0			0
$247$	12.4034	−	2.76012i	0.789209	−	0.175622i
$248$	0.439192			0.0278887
$249$		0			0
$250$	5.28757	−	9.15834i	0.334415	−	0.579224i
$251$	0.619720	+	1.07339i	0.0391164	+	0.0677516i	0.884921	−	0.465742i	$-0.154212\pi$
$251$	0.619720	+	1.07339i	0.0391164	+	0.0677516i	−0.845804	+	0.533493i	$0.820879\pi$
$252$		0			0
$253$	−22.3597	+	12.9094i	−1.40574	+	0.811605i
$254$	−3.70252	+	2.13765i	−0.232317	+	0.134128i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.0028	+	17.3253i	−0.623956	+	1.08072i	0.364786	+	0.931091i	$0.381142\pi$
$257$	−10.0028	+	17.3253i	−0.623956	+	1.08072i	−0.988742	+	0.149631i	$0.952191\pi$
$258$		0			0
$259$	−10.2779			−0.638636
$260$	4.41812	−	0.983161i	0.274000	−	0.0609730i
$261$		0			0
$262$	−6.61068	−	3.81668i	−0.408409	−	0.235795i
$263$	−2.21669	+	3.83942i	−0.136687	+	0.236749i	−0.926241	−	0.376933i	$-0.876979\pi$
$263$	−2.21669	+	3.83942i	−0.136687	+	0.236749i	0.789554	+	0.613682i	$0.210312\pi$
$264$		0			0
$265$		−	11.0754i		−	0.680358i
$266$	3.05207	−	1.76211i	0.187135	−	0.108042i
$267$		0			0
$268$			7.39927i			0.451982i
$269$	4.57552	+	7.92503i	0.278974	+	0.483197i	0.971130	−	0.238551i	$-0.0766723\pi$
$269$	4.57552	+	7.92503i	0.278974	+	0.483197i	−0.692156	+	0.721748i	$0.743339\pi$
$270$		0			0
$271$	4.70984	+	2.71922i	0.286102	+	0.165181i	0.636183	−	0.771538i	$-0.280512\pi$
$271$	4.70984	+	2.71922i	0.286102	+	0.165181i	−0.350081	+	0.936720i	$0.613846\pi$
$272$	−4.52053			−0.274097
$273$		0			0
$274$	4.26831			0.257858
$275$	14.9047	+	8.60523i	0.898787	+	0.518915i
$276$		0			0
$277$	11.2112	+	19.4184i	0.673616	+	1.16674i	0.976871	+	0.213828i	$0.0685932\pi$
$277$	11.2112	+	19.4184i	0.673616	+	1.16674i	−0.303255	+	0.952909i	$0.598073\pi$
$278$			6.88085i			0.412686i
$279$		0			0
$280$	1.08716	−	0.627670i	0.0649700	−	0.0375105i
$281$		−	33.1780i		−	1.97923i	−0.143734	−	0.989616i	$-0.545911\pi$
$281$		−	33.1780i		−	1.97923i	0.143734	−	0.989616i	$-0.454089\pi$
$282$		0			0
$283$	8.04991	−	13.9429i	0.478517	−	0.828817i	−0.521179	−	0.853447i	$-0.674508\pi$
$283$	8.04991	−	13.9429i	0.478517	−	0.828817i	0.999697	+	0.0246308i	$0.00784101\pi$
$284$	−5.89350	−	3.40261i	−0.349715	−	0.201908i
$285$		0			0
$286$	3.93646	+	17.6897i	0.232768	+	1.04601i
$287$	9.98966			0.589671
$288$		0			0
$289$	−1.71759	+	2.97496i	−0.101035	+	0.174998i
$290$	−0.960361	−	1.66339i	−0.0563944	−	0.0976779i
$291$		0			0
$292$	−10.0092	+	5.77881i	−0.585744	+	0.338179i
$293$	16.9781	−	9.80231i	0.991871	−	0.572657i	0.0860380	−	0.996292i	$-0.472579\pi$
$293$	16.9781	−	9.80231i	0.991871	−	0.572657i	0.905833	+	0.423635i	$0.139246\pi$
$294$		0			0
$295$	0.392993	+	0.680683i	0.0228809	+	0.0396309i
$296$	−5.13894	+	8.90090i	−0.298695	+	0.517355i
$297$		0			0
$298$	−11.3785			−0.659141
$299$	13.6451	−	12.5234i	0.789119	−	0.724249i
$300$		0			0
$301$	−3.17344	−	1.83219i	−0.182914	−	0.105606i
$302$	9.66686	−	16.7435i	0.556265	−	0.963479i
$303$		0			0
$304$		−	3.52423i		−	0.202128i
$305$	−9.78285	+	5.64813i	−0.560164	+	0.323411i
$306$		0			0
$307$		−	7.35122i		−	0.419556i	−0.977749	−	0.209778i	$-0.932726\pi$
$307$		−	7.35122i		−	0.419556i	0.977749	−	0.209778i	$-0.0672742\pi$
$308$	2.51312	+	4.35285i	0.143198	+	0.248027i
$309$		0			0
$310$	0.477470	+	0.275667i	0.0271185	+	0.0156569i
$311$	−26.1345			−1.48195			−0.740977	−	0.671530i	$-0.765637\pi$
$311$	−26.1345			−1.48195			−0.740977	+	0.671530i	$0.765637\pi$
$312$		0			0
$313$	−33.3033			−1.88241			−0.941206	−	0.337834i	$-0.890306\pi$
$313$	−33.3033			−1.88241			−0.941206	+	0.337834i	$0.890306\pi$
$314$	17.2285	+	9.94688i	0.972261	+	0.561335i
$315$		0			0
$316$	−3.37218	−	5.84078i	−0.189700	−	0.328570i
$317$		−	21.9861i		−	1.23486i	−0.786624	−	0.617432i	$-0.788173\pi$
$317$		−	21.9861i		−	1.23486i	0.786624	−	0.617432i	$-0.211827\pi$
$318$		0			0
$319$	6.66004	−	3.84518i	0.372891	−	0.215289i
$320$		−	1.25534i		−	0.0701756i
$321$		0			0
$322$	2.56840	−	4.44859i	0.143131	−	0.247910i
$323$	−13.7970	−	7.96569i	−0.767684	−	0.443223i
$324$		0			0
$325$	−11.7774	−	3.70310i	−0.653292	−	0.205411i
$326$	−16.7214			−0.926115
$327$		0			0
$328$	4.99483	−	8.65130i	0.275793	−	0.477688i
$329$	−1.80121	−	3.11978i	−0.0993038	−	0.171999i
$330$		0			0
$331$	26.3251	−	15.1988i	1.44696	−	0.835402i	0.448659	−	0.893703i	$-0.351902\pi$
$331$	26.3251	−	15.1988i	1.44696	−	0.835402i	0.998299	+	0.0583015i	$0.0185685\pi$
$332$	−8.28965	+	4.78603i	−0.454954	+	0.262668i
$333$		0			0
$334$	3.10652	+	5.38066i	0.169981	+	0.294416i
$335$	−4.64430	+	8.04416i	−0.253745	+	0.439499i
$336$		0			0
$337$	−34.0675			−1.85577			−0.927887	−	0.372862i	$-0.878376\pi$
$337$	−34.0675			−1.85577			−0.927887	+	0.372862i	$0.878376\pi$
$338$	−5.51277	−	11.7732i	−0.299855	−	0.640380i
$339$		0			0
$340$	−4.91452	−	2.83740i	−0.266527	−	0.153880i
$341$	−1.10374	+	1.91174i	−0.0597709	+	0.103526i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−3.17344	+	1.83219i	−0.171101	+	0.0987849i
$345$		0			0
$346$		−	17.8373i		−	0.958938i
$347$	−9.55414	−	16.5483i	−0.512893	−	0.888357i	−0.999888	−	0.0149524i	$-0.995240\pi$
$347$	−9.55414	−	16.5483i	−0.512893	−	0.888357i	0.486995	−	0.873405i	$-0.338093\pi$
$348$		0			0
$349$	−19.4584	−	11.2343i	−1.04159	−	0.601360i	−0.121304	−	0.992615i	$-0.538708\pi$
$349$	−19.4584	−	11.2343i	−1.04159	−	0.601360i	−0.920282	+	0.391255i	$0.872041\pi$
$350$	−3.42412			−0.183027
$351$		0			0
$352$	5.02624			0.267899
$353$	−10.6461	−	6.14652i	−0.566634	−	0.327146i	0.189170	−	0.981944i	$-0.439420\pi$
$353$	−10.6461	−	6.14652i	−0.566634	−	0.327146i	−0.755804	+	0.654798i	$0.772754\pi$
$354$		0			0
$355$	−4.27144	−	7.39835i	−0.226704	−	0.392664i
$356$			8.40972i			0.445714i
$357$		0			0
$358$	−7.77750	+	4.49034i	−0.411053	+	0.237322i
$359$		−	2.06492i		−	0.108982i	−0.998514	−	0.0544912i	$-0.982646\pi$
$359$		−	2.06492i		−	0.108982i	0.998514	−	0.0544912i	$-0.0173537\pi$
$360$		0			0
$361$	−3.28991	+	5.69829i	−0.173153	+	0.299910i
$362$	−3.03970	−	1.75497i	−0.159763	−	0.0922394i
$363$		0			0
$364$	−2.43799	−	2.65635i	−0.127785	−	0.139231i
$365$	−14.5087			−0.759423
$366$		0			0
$367$	−0.0352579	+	0.0610685i	−0.00184045	+	0.00318775i	−0.866944	−	0.498405i	$-0.833919\pi$
$367$	−0.0352579	+	0.0610685i	−0.00184045	+	0.00318775i	0.865104	+	0.501593i	$0.167252\pi$
$368$	−2.56840	−	4.44859i	−0.133887	−	0.231899i
$369$		0			0
$370$	−11.1737	+	6.45112i	−0.580891	+	0.335378i
$371$	−7.64063	+	4.41132i	−0.396682	+	0.229024i
$372$		0			0
$373$	−12.4118	−	21.4978i	−0.642656	−	1.11311i	−0.984838	−	0.173479i	$-0.944499\pi$
$373$	−12.4118	−	21.4978i	−0.642656	−	1.11311i	0.342181	−	0.939634i	$-0.388834\pi$
$374$	11.3606	−	19.6772i	0.587444	−	1.01748i
$375$		0			0
$376$	−3.60242			−0.185780
$377$	−4.06433	+	3.73022i	−0.209324	+	0.192116i
$378$		0			0
$379$	16.2193	+	9.36424i	0.833132	+	0.481009i	0.854924	−	0.518754i	$-0.173604\pi$
$379$	16.2193	+	9.36424i	0.833132	+	0.481009i	−0.0217920	+	0.999763i	$0.506937\pi$
$380$	2.21205	−	3.83139i	0.113476	−	0.196546i
$381$		0			0
$382$		−	10.4645i		−	0.535409i
$383$	7.89512	−	4.55825i	0.403422	−	0.232916i	−0.284538	−	0.958665i	$-0.591840\pi$
$383$	7.89512	−	4.55825i	0.403422	−	0.232916i	0.687959	+	0.725749i	$0.258507\pi$
$384$		0			0
$385$			6.30964i			0.321569i
$386$	−7.03378	−	12.1829i	−0.358010	−	0.620091i
$387$		0			0
$388$	−2.43543	−	1.40610i	−0.123640	−	0.0713837i
$389$	−6.69801			−0.339602			−0.169801	−	0.985478i	$-0.554313\pi$
$389$	−6.69801			−0.339602			−0.169801	+	0.985478i	$0.554313\pi$
$390$		0			0
$391$	−23.2210			−1.17434
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	8.86331	+	15.3517i	0.446527	+	0.773408i
$395$		−	8.46645i		−	0.425994i
$396$		0			0
$397$	9.61349	−	5.55035i	0.482487	−	0.278564i	−0.238965	−	0.971028i	$-0.576808\pi$
$397$	9.61349	−	5.55035i	0.482487	−	0.278564i	0.721452	+	0.692464i	$0.243475\pi$
$398$		−	14.2748i		−	0.715530i
$399$		0			0
$400$	−1.71206	+	2.96538i	−0.0856030	+	0.148269i
$401$	22.6329	+	13.0671i	1.13024	+	0.652542i	0.943994	−	0.329962i	$-0.107036\pi$
$401$	22.6329	+	13.0671i	1.13024	+	0.652542i	0.186241	+	0.982504i	$0.440369\pi$
$402$		0			0
$403$	0.474975	−	1.51062i	0.0236602	−	0.0752491i
$404$	−10.3897			−0.516906
$405$		0			0
$406$	−0.765021	+	1.32506i	−0.0379674	+	0.0657614i
$407$	−25.8295	−	44.7381i	−1.28032	−	2.21758i
$408$		0			0
$409$	29.9918	−	17.3158i	1.48300	−	0.856210i	0.483185	−	0.875518i	$-0.339480\pi$
$409$	29.9918	−	17.3158i	1.48300	−	0.856210i	0.999814	+	0.0193089i	$0.00614658\pi$
$410$	10.8603	−	6.27021i	0.536353	−	0.309664i
$411$		0			0
$412$	6.55291	+	11.3500i	0.322839	+	0.559173i
$413$	0.313057	−	0.542230i	0.0154045	−	0.0266814i
$414$		0			0
$415$	−12.0162			−0.589852
$416$	−3.51946	+	0.783183i	−0.172556	+	0.0383987i
$417$		0			0
$418$	15.3404	+	8.85681i	0.750325	+	0.433201i
$419$	5.78853	−	10.0260i	0.282788	−	0.489803i	−0.689282	−	0.724493i	$-0.742074\pi$
$419$	5.78853	−	10.0260i	0.282788	−	0.489803i	0.972070	+	0.234690i	$0.0754073\pi$
$420$		0			0
$421$		−	3.05347i		−	0.148817i	−0.997228	−	0.0744085i	$-0.976293\pi$
$421$		−	3.05347i		−	0.148817i	0.997228	−	0.0744085i	$-0.0237069\pi$
$422$	−11.4187	+	6.59260i	−0.555855	+	0.320923i
$423$		0			0
$424$			8.82264i			0.428466i
$425$	7.73942	+	13.4051i	0.375417	+	0.650241i
$426$		0			0
$427$	7.79299	+	4.49928i	0.377129	+	0.217736i
$428$	−13.9722			−0.675371
$429$		0			0
$430$	−4.60004			−0.221833
$431$	27.4578	+	15.8528i	1.32260	+	0.763602i	0.984142	−	0.177380i	$-0.0567622\pi$
$431$	27.4578	+	15.8528i	1.32260	+	0.763602i	0.338455	+	0.940982i	$0.390096\pi$
$432$		0			0
$433$	−5.46904	−	9.47265i	−0.262825	−	0.455227i	0.704166	−	0.710035i	$-0.251321\pi$
$433$	−5.46904	−	9.47265i	−0.262825	−	0.455227i	−0.966992	+	0.254808i	$0.917988\pi$
$434$		−	0.439192i		−	0.0210819i
$435$		0			0
$436$	11.6787	−	6.74270i	0.559308	−	0.322917i
$437$		−	18.1032i		−	0.865995i
$438$		0			0
$439$	16.8716	−	29.2225i	0.805240	−	1.39472i	−0.110889	−	0.993833i	$-0.535370\pi$
$439$	16.8716	−	29.2225i	0.805240	−	1.39472i	0.916129	−	0.400883i	$-0.131297\pi$
$440$	5.46431	+	3.15482i	0.260501	+	0.150400i
$441$		0			0
$442$	−4.88884	+	15.5485i	−0.232539	+	0.739568i
$443$	14.5967			0.693509			0.346754	−	0.937956i	$-0.387284\pi$
$443$	14.5967			0.693509			0.346754	+	0.937956i	$0.387284\pi$
$444$		0			0
$445$	−5.27853	+	9.14268i	−0.250226	+	0.433404i
$446$	−3.66633	−	6.35028i	−0.173606	−	0.300694i
$447$		0			0
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−24.6222	+	14.2156i	−1.16199	+	0.670876i	−0.951781	−	0.306780i	$-0.900748\pi$
$449$	−24.6222	+	14.2156i	−1.16199	+	0.670876i	−0.210211	+	0.977656i	$0.567415\pi$
$450$		0			0
$451$	25.1052	+	43.4835i	1.18216	+	2.04756i
$452$	−1.13886	+	1.97256i	−0.0535674	+	0.0927815i
$453$		0			0
$454$	−22.7663			−1.06848
$455$	−0.983161	−	4.41812i	−0.0460913	−	0.207125i
$456$		0			0
$457$	−17.1842	−	9.92129i	−0.803842	−	0.464099i	0.0409707	−	0.999160i	$-0.486955\pi$
$457$	−17.1842	−	9.92129i	−0.803842	−	0.464099i	−0.844813	+	0.535062i	$0.820288\pi$
$458$	−2.23965	+	3.87919i	−0.104652	+	0.181263i
$459$		0			0
$460$		−	6.44842i		−	0.300659i
$461$	18.1145	−	10.4584i	0.843677	−	0.487097i	−0.0148353	−	0.999890i	$-0.504722\pi$
$461$	18.1145	−	10.4584i	0.843677	−	0.487097i	0.858512	+	0.512793i	$0.171389\pi$
$462$		0			0
$463$		−	22.5283i		−	1.04698i	−0.852032	−	0.523489i	$-0.824630\pi$
$463$		−	22.5283i		−	1.04698i	0.852032	−	0.523489i	$-0.175370\pi$
$464$	0.765021	+	1.32506i	0.0355152	+	0.0615141i
$465$		0			0
$466$	7.94628	+	4.58779i	0.368104	+	0.212525i
$467$	−11.7282			−0.542718			−0.271359	−	0.962478i	$-0.587473\pi$
$467$	−11.7282			−0.542718			−0.271359	+	0.962478i	$0.587473\pi$
$468$		0			0
$469$	7.39927			0.341666
$470$	−3.91639	−	2.26113i	−0.180650	−	0.104298i
$471$		0			0
$472$	−0.313057	−	0.542230i	−0.0144096	−	0.0249582i
$473$		−	18.4180i		−	0.846861i
$474$		0			0
$475$	−10.4507	+	6.03369i	−0.479509	+	0.276845i
$476$			4.52053i			0.207198i
$477$		0			0
$478$	−9.56158	+	16.5611i	−0.437337	+	0.757489i
$479$	−16.7817	−	9.68891i	−0.766775	−	0.442698i	0.0649482	−	0.997889i	$-0.479312\pi$
$479$	−16.7817	−	9.68891i	−0.766775	−	0.442698i	−0.831723	+	0.555191i	$0.812645\pi$
$480$		0			0
$481$	25.0573	+	27.3017i	1.14252	+	1.24485i
$482$	20.9338			0.953507
$483$		0			0
$484$	−7.13153	+	12.3522i	−0.324161	+	0.561463i
$485$	−1.76513	−	3.05729i	−0.0801504	−	0.138825i
$486$		0			0
$487$	35.7478	−	20.6390i	1.61989	−	0.935242i	0.632939	−	0.774202i	$-0.281848\pi$
$487$	35.7478	−	20.6390i	1.61989	−	0.935242i	0.986948	−	0.161041i	$-0.0514850\pi$
$488$	7.79299	−	4.49928i	0.352772	−	0.203673i
$489$		0			0
$490$	−0.627670	−	1.08716i	−0.0283552	−	0.0491127i
$491$	−8.50710	+	14.7347i	−0.383920	+	0.664969i	−0.991619	−	0.129199i	$-0.958759\pi$
$491$	−8.50710	+	14.7347i	−0.383920	+	0.664969i	0.607699	+	0.794168i	$0.292093\pi$
$492$		0			0
$493$	6.91660			0.311508
$494$	−12.1217	−	3.81137i	−0.545382	−	0.171482i
$495$		0			0
$496$	−0.380351	−	0.219596i	−0.0170783	−	0.00986014i
$497$	−3.40261	+	5.89350i	−0.152628	+	0.264360i
$498$		0			0
$499$		−	19.5097i		−	0.873373i	−0.899614	−	0.436687i	$-0.856152\pi$
$499$		−	19.5097i		−	0.873373i	0.899614	−	0.436687i	$-0.143848\pi$
$500$	−9.15834	+	5.28757i	−0.409573	+	0.236467i
$501$		0			0
$502$		−	1.23944i		−	0.0553190i
$503$	16.2080	+	28.0732i	0.722681	+	1.25172i	0.959921	+	0.280269i	$0.0904238\pi$
$503$	16.2080	+	28.0732i	0.722681	+	1.25172i	−0.237240	+	0.971451i	$0.576243\pi$
$504$		0			0
$505$	−11.2952	−	6.52129i	−0.502630	−	0.290193i
$506$	25.8187			1.14778
$507$		0			0
$508$	4.27531			0.189686
$509$	36.3337	+	20.9773i	1.61046	+	0.929802i	0.989262	+	0.146152i	$0.0466887\pi$
$509$	36.3337	+	20.9773i	1.61046	+	0.929802i	0.621202	+	0.783650i	$0.286645\pi$
$510$		0			0
$511$	5.77881	+	10.0092i	0.255640	+	0.442781i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	17.3253	−	10.0028i	0.764186	−	0.441203i
$515$			16.4523i			0.724973i
$516$		0			0
$517$	9.05330	−	15.6808i	0.398164	−	0.689640i
$518$	8.90090	+	5.13894i	0.391083	+	0.225792i
$519$		0			0
$520$	−4.31779	−	1.35762i	−0.189347	−	0.0595356i
$521$	−32.1360			−1.40790			−0.703951	−	0.710248i	$-0.748583\pi$
$521$	−32.1360			−1.40790			−0.703951	+	0.710248i	$0.748583\pi$
$522$		0			0
$523$	8.96382	−	15.5258i	0.391961	−	0.678896i	−0.600747	−	0.799439i	$-0.705130\pi$
$523$	8.96382	−	15.5258i	0.391961	−	0.678896i	0.992708	+	0.120543i	$0.0384636\pi$
$524$	3.81668	+	6.61068i	0.166732	+	0.288789i
$525$		0			0
$526$	3.83942	−	2.21669i	0.167407	−	0.0966523i
$527$	−1.71939	+	0.992689i	−0.0748977	+	0.0432422i
$528$		0			0
$529$	−1.69332	−	2.93292i	−0.0736227	−	0.127518i
$530$	−5.53771	+	9.59159i	−0.240543	+	0.416632i
$531$		0			0
$532$	−3.52423			−0.152795
$533$	−24.3547	−	26.5361i	−1.05492	−	1.14940i
$534$		0			0
$535$	−15.1900	−	8.76992i	−0.656719	−	0.379157i
$536$	3.69963	−	6.40795i	0.159800	−	0.276781i
$537$		0			0
$538$		−	9.15103i		−	0.394529i
$539$	4.35285	−	2.51312i	0.187491	−	0.108248i
$540$		0			0
$541$		−	26.4852i		−	1.13869i	−0.822100	−	0.569343i	$-0.807198\pi$
$541$		−	26.4852i		−	1.13869i	0.822100	−	0.569343i	$-0.192802\pi$
$542$	−2.71922	−	4.70984i	−0.116801	−	0.202305i
$543$		0			0
$544$	3.91489	+	2.26026i	0.167850	+	0.0969080i
$545$	16.9288			0.725148
$546$		0			0
$547$	−30.4660			−1.30263			−0.651317	−	0.758806i	$-0.725783\pi$
$547$	−30.4660			−1.30263			−0.651317	+	0.758806i	$0.725783\pi$
$548$	−3.69647	−	2.13416i	−0.157905	−	0.0911666i
$549$		0			0
$550$	−8.60523	−	14.9047i	−0.366928	−	0.635538i
$551$			5.39222i			0.229716i
$552$		0			0
$553$	−5.84078	+	3.37218i	−0.248375	+	0.143399i
$554$		−	22.4224i		−	0.952637i
$555$		0			0
$556$	3.44043	−	5.95899i	0.145907	−	0.252718i
$557$	9.46666	+	5.46558i	0.401115	+	0.231584i	0.686965	−	0.726690i	$-0.258942\pi$
$557$	9.46666	+	5.46558i	0.401115	+	0.231584i	−0.285850	+	0.958274i	$0.592276\pi$
$558$		0			0
$559$	2.86988	+	12.8966i	0.121383	+	0.545469i
$560$	−1.25534			−0.0530478
$561$		0			0
$562$	−16.5890	+	28.7330i	−0.699764	+	1.21203i
$563$	−17.8211	−	30.8670i	−0.751068	−	1.30089i	−0.947306	−	0.320331i	$-0.896206\pi$
$563$	−17.8211	−	30.8670i	−0.751068	−	1.30089i	0.196238	−	0.980556i	$-0.437128\pi$
$564$		0			0
$565$	−2.47624	+	1.42966i	−0.104176	+	0.0601461i
$566$	−13.9429	+	8.04991i	−0.586062	+	0.338363i
$567$		0			0
$568$	3.40261	+	5.89350i	0.142771	+	0.247286i
$569$	−4.66252	+	8.07571i	−0.195463	+	0.338552i	−0.947052	−	0.321080i	$-0.895954\pi$
$569$	−4.66252	+	8.07571i	−0.195463	+	0.338552i	0.751589	+	0.659631i	$0.229288\pi$
$570$		0			0
$571$	−2.80054			−0.117199			−0.0585996	−	0.998282i	$-0.518664\pi$
$571$	−2.80054			−0.117199			−0.0585996	+	0.998282i	$0.518664\pi$
$572$	5.43575	−	17.2879i	0.227280	−	0.722845i
$573$		0			0
$574$	−8.65130	−	4.99483i	−0.361098	−	0.208480i
$575$	−8.79450	+	15.2325i	−0.366756	+	0.635240i
$576$		0			0
$577$			8.85259i			0.368538i	0.982876	+	0.184269i	$0.0589918\pi$
$577$			8.85259i			0.368538i	−0.982876	+	0.184269i	$0.941008\pi$
$578$	2.97496	−	1.71759i	0.123742	−	0.0714425i
$579$		0			0
$580$			1.92072i			0.0797537i
$581$	4.78603	+	8.28965i	0.198558	+	0.343913i
$582$		0			0
$583$	−38.4036	−	22.1724i	−1.59052	−	0.918285i
$584$	11.5576			0.478258
$585$		0			0
$586$	−19.6046			−0.809859
$587$	32.3490	+	18.6767i	1.33519	+	0.770870i	0.986089	−	0.166216i	$-0.0531550\pi$
$587$	32.3490	+	18.6767i	1.33519	+	0.770870i	0.349097	+	0.937087i	$0.386488\pi$
$588$		0			0
$589$	−0.773906	−	1.34044i	−0.0318882	−	0.0552320i
$590$		−	0.785985i		−	0.0323585i
$591$		0			0
$592$	8.90090	−	5.13894i	0.365825	−	0.211209i
$593$		−	25.8309i		−	1.06075i	−0.847764	−	0.530374i	$-0.822052\pi$
$593$		−	25.8309i		−	1.06075i	0.847764	−	0.530374i	$-0.177948\pi$
$594$		0			0
$595$	−2.83740	+	4.91452i	−0.116322	+	0.201476i
$596$	9.85411	+	5.68927i	0.403640	+	0.233042i
$597$		0			0
$598$	−18.0788	+	4.02305i	−0.739295	+	0.164515i
$599$	−18.1493			−0.741562			−0.370781	−	0.928720i	$-0.620910\pi$
$599$	−18.1493			−0.741562			−0.370781	+	0.928720i	$0.620910\pi$
$600$		0			0
$601$	3.56124	−	6.16825i	0.145266	−	0.251608i	−0.784206	−	0.620500i	$-0.786930\pi$
$601$	3.56124	−	6.16825i	0.145266	−	0.251608i	0.929472	+	0.368892i	$0.120263\pi$
$602$	1.83219	+	3.17344i	0.0746744	+	0.129340i
$603$		0			0
$604$	−16.7435	+	9.66686i	−0.681283	+	0.393339i
$605$	−15.5062	+	8.95250i	−0.630416	+	0.363971i
$606$		0			0
$607$	14.6968	+	25.4556i	0.596523	+	1.03321i	0.993330	+	0.115307i	$0.0367851\pi$
$607$	14.6968	+	25.4556i	0.596523	+	1.03321i	−0.396807	+	0.917902i	$0.629882\pi$
$608$	−1.76211	+	3.05207i	−0.0714632	+	0.123778i
$609$		0			0
$610$	11.2963			0.457372
$611$	−3.89593	+	12.3906i	−0.157612	+	0.501272i
$612$		0			0
$613$	−22.6425	−	13.0727i	−0.914522	−	0.528000i	−0.0326390	−	0.999467i	$-0.510391\pi$
$613$	−22.6425	−	13.0727i	−0.914522	−	0.528000i	−0.881883	+	0.471467i	$0.843724\pi$
$614$	−3.67561	+	6.36634i	−0.148336	+	0.256925i
$615$		0			0
$616$		−	5.02624i		−	0.202513i
$617$	29.3858	−	16.9659i	1.18303	−	0.683021i	0.226315	−	0.974054i	$-0.427332\pi$
$617$	29.3858	−	16.9659i	1.18303	−	0.683021i	0.956713	+	0.291033i	$0.0939989\pi$
$618$		0			0
$619$		−	18.1585i		−	0.729852i	−0.931037	−	0.364926i	$-0.881094\pi$
$619$		−	18.1585i		−	0.729852i	0.931037	−	0.364926i	$-0.118906\pi$
$620$	−0.275667	−	0.477470i	−0.0110711	−	0.0191757i
$621$		0			0
$622$	22.6332	+	13.0673i	0.907508	+	0.523950i
$623$	8.40972			0.336928
$624$		0			0
$625$	3.84522			0.153809
$626$	28.8415	+	16.6516i	1.15274	+	0.665533i
$627$		0			0
$628$	−9.94688	−	17.2285i	−0.396924	−	0.687492i
$629$		−	46.4615i		−	1.85254i
$630$		0			0
$631$	23.6255	−	13.6402i	0.940518	−	0.543008i	0.0503955	−	0.998729i	$-0.483952\pi$
$631$	23.6255	−	13.6402i	0.940518	−	0.543008i	0.890123	+	0.455721i	$0.150618\pi$
$632$			6.74435i			0.268276i
$633$		0			0
$634$	−10.9931	+	19.0406i	−0.436591	+	0.756197i
$635$	4.64792	+	2.68348i	0.184447	+	0.106491i
$636$		0			0
$637$	−2.65635	+	2.43799i	−0.105249	+	0.0965966i
$638$	−7.69036			−0.304464
$639$		0			0
$640$	−0.627670	+	1.08716i	−0.0248108	+	0.0429736i
$641$	5.99600	+	10.3854i	0.236828	+	0.410198i	0.959802	−	0.280677i	$-0.0905589\pi$
$641$	5.99600	+	10.3854i	0.236828	+	0.410198i	−0.722974	+	0.690875i	$0.757226\pi$
$642$		0			0
$643$	−23.1022	+	13.3381i	−0.911062	+	0.526002i	−0.880773	−	0.473539i	$-0.842976\pi$
$643$	−23.1022	+	13.3381i	−0.911062	+	0.526002i	−0.0302892	+	0.999541i	$0.509643\pi$
$644$	−4.44859	+	2.56840i	−0.175299	+	0.101209i
$645$		0			0
$646$	7.96569	+	13.7970i	0.313406	+	0.542835i
$647$	−13.3079	+	23.0499i	−0.523186	+	0.906184i	0.476450	+	0.879201i	$0.341923\pi$
$647$	−13.3079	+	23.0499i	−0.523186	+	0.906184i	−0.999636	+	0.0269828i	$0.991410\pi$
$648$		0			0
$649$	3.14700			0.123530
$650$	8.34797	+	9.09568i	0.327434	+	0.356762i
$651$		0			0
$652$	14.4812	+	8.36072i	0.567127	+	0.327431i
$653$	17.1787	−	29.7544i	0.672255	−	1.16438i	−0.305009	−	0.952350i	$-0.598659\pi$
$653$	17.1787	−	29.7544i	0.672255	−	1.16438i	0.977263	−	0.212030i	$-0.0680073\pi$
$654$		0			0
$655$			9.58245i			0.374417i
$656$	−8.65130	+	4.99483i	−0.337776	+	0.195015i
$657$		0			0
$658$			3.60242i			0.140437i
$659$	−10.9254	−	18.9234i	−0.425595	−	0.737152i	0.570881	−	0.821033i	$-0.306602\pi$
$659$	−10.9254	−	18.9234i	−0.425595	−	0.737152i	−0.996476	+	0.0838807i	$0.973269\pi$
$660$		0			0
$661$	−15.4423	−	8.91564i	−0.600637	−	0.346778i	0.168655	−	0.985675i	$-0.446058\pi$
$661$	−15.4423	−	8.91564i	−0.600637	−	0.346778i	−0.769292	+	0.638897i	$0.779391\pi$
$662$	−30.3976			−1.18144
$663$		0			0
$664$	9.57207			0.371468
$665$	−3.83139	−	2.21205i	−0.148575	−	0.0857797i
$666$		0			0
$667$	3.92975	+	6.80654i	0.152161	+	0.263550i
$668$		−	6.21305i		−	0.240390i
$669$		0			0
$670$	8.04416	−	4.64430i	0.310773	−	0.179425i
$671$			45.2289i			1.74604i
$672$		0			0
$673$	12.4997	−	21.6501i	0.481828	−	0.834550i	−0.517955	−	0.855408i	$-0.673306\pi$
$673$	12.4997	−	21.6501i	0.481828	−	0.834550i	0.999782	+	0.0208580i	$0.00663978\pi$
$674$	29.5033	+	17.0337i	1.13642	+	0.656115i
$675$		0			0
$676$	−1.11243	+	12.9523i	−0.0427857	+	0.498166i
$677$	16.4248			0.631255			0.315628	−	0.948883i	$-0.397785\pi$
$677$	16.4248			0.631255			0.315628	+	0.948883i	$0.397785\pi$
$678$		0			0
$679$	−1.40610	+	2.43543i	−0.0539610	+	0.0934632i
$680$	2.83740	+	4.91452i	0.108809	+	0.188463i
$681$		0			0
$682$	1.91174	−	1.10374i	0.0732041	−	0.0422644i
$683$	−29.4745	+	17.0171i	−1.12781	+	0.651142i	−0.943383	−	0.331705i	$-0.892376\pi$
$683$	−29.4745	+	17.0171i	−1.12781	+	0.651142i	−0.184427	+	0.982846i	$0.559043\pi$
$684$		0			0
$685$	−2.67909	−	4.64032i	−0.102363	−	0.177298i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	3.66437			0.139703
$689$	30.3458	+	9.54148i	1.15608	+	0.363501i
$690$		0			0
$691$	10.0415	+	5.79746i	0.381997	+	0.220546i	0.678687	−	0.734428i	$-0.262549\pi$
$691$	10.0415	+	5.79746i	0.381997	+	0.220546i	−0.296690	+	0.954974i	$0.595883\pi$
$692$	−8.91864	+	15.4475i	−0.339036	+	0.587227i
$693$		0			0
$694$			19.1083i			0.725341i
$695$	7.48056	−	4.31890i	0.283754	−	0.163825i
$696$		0			0
$697$			45.1585i			1.71050i
$698$	11.2343	+	19.4584i	0.425226	+	0.736513i
$699$		0			0
$700$	2.96538	+	1.71206i	0.112081	+	0.0647098i
$701$	−7.78759			−0.294133			−0.147067	−	0.989127i	$-0.546983\pi$
$701$	−7.78759			−0.294133			−0.147067	+	0.989127i	$0.546983\pi$
$702$		0			0
$703$	36.2216			1.36612
$704$	−4.35285	−	2.51312i	−0.164054	−	0.0947167i
$705$		0			0
$706$	6.14652	+	10.6461i	0.231327	+	0.400671i
$707$			10.3897i			0.390744i
$708$		0			0
$709$	−13.2538	+	7.65211i	−0.497758	+	0.287381i	−0.727787	−	0.685803i	$-0.759451\pi$
$709$	−13.2538	+	7.65211i	−0.497758	+	0.287381i	0.230029	+	0.973184i	$0.426118\pi$
$710$			8.54288i			0.320608i
$711$		0			0
$712$	4.20486	−	7.28303i	0.157584	−	0.272943i
$713$	−1.95379	−	1.12802i	−0.0731698	−	0.0422446i
$714$		0			0
$715$	16.7606	−	15.3828i	0.626812	−	0.575285i
$716$	8.98068			0.335624
$717$		0			0
$718$	−1.03246	+	1.78827i	−0.0385311	+	0.0667378i
$719$	13.7122	+	23.7502i	0.511378	+	0.885733i	0.999913	+	0.0131889i	$0.00419829\pi$
$719$	13.7122	+	23.7502i	0.511378	+	0.885733i	−0.488535	+	0.872545i	$0.662468\pi$
$720$		0			0
$721$	11.3500	−	6.55291i	0.422695	−	0.244043i
$722$	5.69829	−	3.28991i	0.212068	−	0.122438i
$723$		0			0
$724$	1.75497	+	3.03970i	0.0652231	+	0.112970i
$725$	2.61953	−	4.53715i	0.0972867	−	0.168506i
$726$		0			0
$727$	41.5231			1.54001			0.770004	−	0.638039i	$-0.220254\pi$
$727$	41.5231			1.54001			0.770004	+	0.638039i	$0.220254\pi$
$728$	0.783183	+	3.51946i	0.0290267	+	0.130440i
$729$		0			0
$730$	12.5649	+	7.25437i	0.465049	+	0.268496i
$731$	8.28246	−	14.3456i	0.306338	−	0.530593i
$732$		0			0
$733$			26.3251i			0.972339i	0.873864	+	0.486170i	$0.161606\pi$
$733$			26.3251i			0.972339i	−0.873864	+	0.486170i	$0.838394\pi$
$734$	0.0610685	−	0.0352579i	0.00225408	−	0.00130139i
$735$		0			0
$736$			5.13679i			0.189345i
$737$	18.5952	+	32.2079i	0.684964	+	1.18639i
$738$		0			0
$739$	14.2462	+	8.22505i	0.524055	+	0.302563i	0.738592	−	0.674153i	$-0.235491\pi$
$739$	14.2462	+	8.22505i	0.524055	+	0.302563i	−0.214537	+	0.976716i	$0.568824\pi$
$740$	12.9022			0.474295
$741$		0			0
$742$	8.82264			0.323889
$743$	24.3915	+	14.0824i	0.894837	+	0.516634i	0.875521	−	0.483179i	$-0.160518\pi$
$743$	24.3915	+	14.0824i	0.894837	+	0.516634i	0.0193152	+	0.999813i	$0.493851\pi$
$744$		0			0
$745$	7.14197	+	12.3703i	0.261662	+	0.453211i
$746$			24.8235i			0.908853i
$747$		0			0
$748$	−19.6772	+	11.3606i	−0.719469	+	0.415386i
$749$			13.9722i			0.510533i
$750$		0			0
$751$	4.34508	−	7.52590i	0.158554	−	0.274624i	−0.775793	−	0.630987i	$-0.782650\pi$
$751$	4.34508	−	7.52590i	0.158554	−	0.274624i	0.934348	+	0.356363i	$0.115983\pi$
$752$	3.11978	+	1.80121i	0.113767	+	0.0656833i
$753$		0			0
$754$	5.38493	−	1.19830i	0.196107	−	0.0436396i
$755$	−24.2704			−0.883290
$756$		0			0
$757$	−11.5106	+	19.9369i	−0.418359	+	0.724618i	−0.995775	−	0.0918318i	$-0.970728\pi$
$757$	−11.5106	+	19.9369i	−0.418359	+	0.724618i	0.577416	+	0.816450i	$0.304061\pi$
$758$	−9.36424	−	16.2193i	−0.340125	−	0.589113i
$759$		0			0
$760$	−3.83139	+	2.21205i	−0.138979	+	0.0802396i
$761$	−30.3454	+	17.5199i	−1.10002	+	0.635097i	−0.936226	−	0.351398i	$-0.885706\pi$
$761$	−30.3454	+	17.5199i	−1.10002	+	0.635097i	−0.163794	+	0.986495i	$0.552373\pi$
$762$		0			0
$763$	−6.74270	−	11.6787i	−0.244102	−	0.422797i
$764$	−5.23224	+	9.06251i	−0.189296	+	0.327870i
$765$		0			0
$766$	−9.11650			−0.329392
$767$	−2.20358	+	0.490361i	−0.0795668	+	0.0177059i
$768$		0			0
$769$	−0.874422	−	0.504848i	−0.0315325	−	0.0182053i	0.484151	−	0.874985i	$-0.339129\pi$
$769$	−0.874422	−	0.504848i	−0.0315325	−	0.0182053i	−0.515683	+	0.856779i	$0.672462\pi$
$770$	3.15482	−	5.46431i	0.113692	−	0.196920i
$771$		0			0
$772$			14.0676i			0.506302i
$773$	−8.78950	+	5.07462i	−0.316136	+	0.182521i	−0.649669	−	0.760217i	$-0.725093\pi$
$773$	−8.78950	+	5.07462i	−0.316136	+	0.182521i	0.333533	+	0.942739i	$0.391759\pi$
$774$		0			0
$775$			1.50385i			0.0540197i
$776$	1.40610	+	2.43543i	0.0504759	+	0.0874269i
$777$		0			0
$778$	5.80064	+	3.34900i	0.207963	+	0.120068i
$779$	−35.2058			−1.26138
$780$		0			0
$781$	−34.2047			−1.22394
$782$	20.1100	+	11.6105i	0.719132	+	0.415191i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		−	24.9734i		−	0.891340i
$786$		0			0
$787$	37.8806	−	21.8704i	1.35030	−	0.779594i	0.362006	−	0.932176i	$-0.382092\pi$
$787$	37.8806	−	21.8704i	1.35030	−	0.779594i	0.988291	+	0.152582i	$0.0487588\pi$
$788$		−	17.7266i		−	0.631485i
$789$		0			0
$790$	−4.23323	+	7.33216i	−0.150611	+	0.260867i
$791$	1.97256	+	1.13886i	0.0701362	+	0.0404932i
$792$		0			0
$793$	−7.04752	−	31.6701i	−0.250265	−	1.12464i
$794$	−11.1007			−0.393949
$795$		0			0
$796$	−7.13739	+	12.3623i	−0.252978	+	0.438171i
$797$	4.57184	+	7.91867i	0.161943	+	0.280494i	0.935565	−	0.353153i	$-0.114891\pi$
$797$	4.57184	+	7.91867i	0.161943	+	0.280494i	−0.773622	+	0.633647i	$0.781557\pi$
$798$		0			0
$799$	14.1031	−	8.14241i	0.498931	−	0.288058i
$800$	2.96538	−	1.71206i	0.104842	−	0.0605305i
$801$		0			0
$802$	−13.0671	−	22.6329i	−0.461417	−	0.799197i
$803$	−29.0457	+	50.3086i	−1.02500	+	1.77535i
$804$		0			0
$805$	−6.44842			−0.227277
$806$	−1.16665	+	1.07074i	−0.0410934	+	0.0377154i
$807$		0			0
$808$	8.99772	+	5.19484i	0.316539	+	0.182754i
$809$	5.56760	−	9.64337i	0.195746	−	0.339043i	−0.751398	−	0.659849i	$-0.770620\pi$
$809$	5.56760	−	9.64337i	0.195746	−	0.339043i	0.947145	+	0.320806i	$0.103954\pi$
$810$		0			0
$811$		−	41.4594i		−	1.45584i	−0.685664	−	0.727919i	$-0.740488\pi$
$811$		−	41.4594i		−	1.45584i	0.685664	−	0.727919i	$-0.259512\pi$
$812$	1.32506	−	0.765021i	0.0465003	−	0.0268470i
$813$		0			0
$814$			51.6591i			1.81065i
$815$	10.4955	+	18.1788i	0.367643	+	0.636776i
$816$		0			0
$817$	11.1839	+	6.45705i	0.391276	+	0.225903i
$818$	−34.6315			−1.21086
$819$		0			0
$820$	−12.5404			−0.437930
$821$	27.7426	+	16.0172i	0.968222	+	0.559003i	0.898694	−	0.438577i	$-0.144517\pi$
$821$	27.7426	+	16.0172i	0.968222	+	0.559003i	0.0695285	+	0.997580i	$0.477851\pi$
$822$		0			0
$823$	−2.72331	−	4.71690i	−0.0949285	−	0.164421i	0.814650	−	0.579953i	$-0.196929\pi$
$823$	−2.72331	−	4.71690i	−0.0949285	−	0.164421i	−0.909579	+	0.415532i	$0.863596\pi$
$824$		−	13.1058i		−	0.456563i
$825$		0			0
$826$	−0.542230	+	0.313057i	−0.0188666	+	0.0108926i
$827$			27.2187i			0.946488i	0.880931	+	0.473244i	$0.156917\pi$
$827$			27.2187i			0.946488i	−0.880931	+	0.473244i	$0.843083\pi$
$828$		0			0
$829$	−13.5506	+	23.4703i	−0.470630	+	0.815156i	−0.999436	−	0.0335874i	$-0.989307\pi$
$829$	−13.5506	+	23.4703i	−0.470630	+	0.815156i	0.528805	+	0.848743i	$0.322640\pi$
$830$	10.4063	+	6.00810i	0.361209	+	0.208544i
$831$		0			0
$832$	3.43954	+	1.08148i	0.119244	+	0.0374934i
$833$	4.52053			0.156627
$834$		0			0
$835$	3.89974	−	6.75455i	0.134956	−	0.233751i
$836$	−8.85681	−	15.3404i	−0.306319	−	0.530560i
$837$		0			0
$838$	−10.0260	+	5.78853i	−0.346343	+	0.199961i
$839$	14.3090	−	8.26132i	0.494002	−	0.285212i	−0.232231	−	0.972661i	$-0.574603\pi$
$839$	14.3090	−	8.26132i	0.494002	−	0.285212i	0.726233	+	0.687448i	$0.241269\pi$
$840$		0			0
$841$	13.3295	+	23.0873i	0.459637	+	0.796115i
$842$	−1.52674	+	2.64438i	−0.0526148	+	0.0911315i
$843$		0			0
$844$	13.1852			0.453854
$845$	−9.33916	+	13.3830i	−0.321277	+	0.460388i
$846$		0			0
$847$	12.3522	+	7.13153i	0.424426	+	0.245042i
$848$	4.41132	−	7.64063i	0.151485	−	0.262380i
$849$		0			0
$850$		−	15.4788i		−	0.530920i
$851$	45.7221	−	26.3977i	1.56733	−	0.904900i
$852$		0			0
$853$		−	21.6390i		−	0.740905i	−0.928851	−	0.370453i	$-0.879203\pi$
$853$		−	21.6390i		−	0.740905i	0.928851	−	0.370453i	$-0.120797\pi$
$854$	−4.49928	−	7.79299i	−0.153962	−	0.266671i
$855$		0			0
$856$	12.1003	+	6.98610i	0.413579	+	0.238780i
$857$	−14.6034			−0.498844			−0.249422	−	0.968395i	$-0.580241\pi$
$857$	−14.6034			−0.498844			−0.249422	+	0.968395i	$0.580241\pi$
$858$		0			0
$859$	−27.7327			−0.946227			−0.473113	−	0.881002i	$-0.656870\pi$
$859$	−27.7327			−0.946227			−0.473113	+	0.881002i	$0.656870\pi$
$860$	3.98375	+	2.30002i	0.135845	+	0.0784300i
$861$		0			0
$862$	−15.8528	−	27.4578i	−0.539948	−	0.935218i
$863$			48.8452i			1.66271i	0.555743	+	0.831354i	$0.312434\pi$
$863$			48.8452i			1.66271i	−0.555743	+	0.831354i	$0.687566\pi$
$864$		0			0
$865$	−19.3919	+	11.1959i	−0.659345	+	0.380673i
$866$			10.9381i			0.371691i
$867$		0			0
$868$	−0.219596	+	0.380351i	−0.00745357	+	0.0129100i
$869$	−29.3571	−	16.9494i	−0.995873	−	0.574968i
$870$		0			0
$871$	−18.0393	−	19.6551i	−0.611239	−	0.665986i
$872$	−13.4854			−0.456673
$873$		0			0
$874$	−9.05162	+	15.6779i	−0.306176	+	0.530312i
$875$	5.28757	+	9.15834i	0.178752	+	0.309608i
$876$		0			0
$877$	32.9705	−	19.0355i	1.11333	−	0.642783i	0.173643	−	0.984809i	$-0.444446\pi$
$877$	32.9705	−	19.0355i	1.11333	−	0.642783i	0.939691	+	0.342025i	$0.111113\pi$
$878$	−29.2225	+	16.8716i	−0.986213	+	0.569390i
$879$		0			0
$880$	−3.15482	−	5.46431i	−0.106349	−	0.184202i
$881$	−25.6726	+	44.4663i	−0.864932	+	1.49811i	0.00218268	+	0.999998i	$0.499305\pi$
$881$	−25.6726	+	44.4663i	−0.864932	+	1.49811i	−0.867115	+	0.498109i	$0.834028\pi$
$882$		0			0
$883$	52.3499			1.76171			0.880857	−	0.473382i	$-0.156967\pi$
$883$	52.3499			1.76171			0.880857	+	0.473382i	$0.156967\pi$
$884$	12.0081	−	11.0210i	0.403877	−	0.370676i
$885$		0			0
$886$	−12.6411	−	7.29833i	−0.424686	−	0.245192i
$887$	24.0002	−	41.5696i	0.805848	−	1.39577i	−0.109869	−	0.993946i	$-0.535043\pi$
$887$	24.0002	−	41.5696i	0.805848	−	1.39577i	0.915717	−	0.401823i	$-0.131623\pi$
$888$		0			0
$889$		−	4.27531i		−	0.143389i
$890$	9.14268	−	5.27853i	0.306463	−	0.176937i
$891$		0			0
$892$			7.33267i			0.245516i
$893$	6.34787	+	10.9948i	0.212423	+	0.367928i
$894$		0			0
$895$	9.76340	+	5.63690i	0.326355	+	0.188421i
$896$	1.00000			0.0334077
$897$		0			0
$898$	28.4312			0.948762
$899$	0.581953	+	0.335991i	0.0194092	+	0.0112059i
$900$		0			0
$901$	−19.9415	−	34.5397i	−0.664348	−	1.15068i
$902$		−	50.2104i		−	1.67182i
$903$		0			0
$904$	1.97256	−	1.13886i	0.0656064	−	0.0378779i
$905$			4.40618i			0.146466i
$906$		0			0
$907$	4.59352	−	7.95621i	0.152525	−	0.264182i	−0.779630	−	0.626241i	$-0.784593\pi$
$907$	4.59352	−	7.95621i	0.152525	−	0.264182i	0.932155	+	0.362059i	$0.117926\pi$
$908$	19.7162	+	11.3832i	0.654305	+	0.377763i
$909$		0			0
$910$	−1.35762	+	4.31779i	−0.0450046	+	0.143133i
$911$	42.1182			1.39544			0.697719	−	0.716372i	$-0.254199\pi$
$911$	42.1182			1.39544			0.697719	+	0.716372i	$0.254199\pi$
$912$		0			0
$913$	−24.0557	+	41.6658i	−0.796129	+	1.37894i
$914$	9.92129	+	17.1842i	0.328167	+	0.568402i
$915$		0			0
$916$	3.87919	−	2.23965i	0.128172	−	0.0740002i
$917$	6.61068	−	3.81668i	0.218304	−	0.126038i
$918$		0			0
$919$	−6.14572	−	10.6447i	−0.202728	−	0.351136i	0.746678	−	0.665186i	$-0.231648\pi$
$919$	−6.14572	−	10.6447i	−0.202728	−	0.351136i	−0.949407	+	0.314049i	$0.898314\pi$
$920$	−3.22421	+	5.58450i	−0.106299	+	0.184115i
$921$		0			0
$922$	−20.9168			−0.688860
$923$	23.9508	−	5.32974i	0.788349	−	0.175430i
$924$		0			0
$925$	−30.4778	−	17.5964i	−1.00210	−	0.578565i
$926$	−11.2641	+	19.5101i	−0.370163	+	0.641141i
$927$		0			0
$928$		−	1.53004i		−	0.0502261i
$929$	−18.6858	+	10.7883i	−0.613062	+	0.353952i	−0.774163	−	0.632986i	$-0.781829\pi$
$929$	−18.6858	+	10.7883i	−0.613062	+	0.353952i	0.161101	+	0.986938i	$0.448496\pi$
$930$		0			0
$931$			3.52423i			0.115502i
$932$	−4.58779	−	7.94628i	−0.150278	−	0.260289i
$933$		0			0
$934$	10.1569	+	5.86411i	0.332345	+	0.191880i
$935$	−28.5229			−0.932799
$936$		0			0
$937$	17.3544			0.566942			0.283471	−	0.958981i	$-0.408514\pi$
$937$	17.3544			0.566942			0.283471	+	0.958981i	$0.408514\pi$
$938$	−6.40795	−	3.69963i	−0.209227	−	0.120797i
$939$		0			0
$940$	2.26113	+	3.91639i	0.0737499	+	0.127739i
$941$			27.1164i			0.883969i	0.897023	+	0.441984i	$0.145725\pi$
$941$			27.1164i			0.883969i	−0.897023	+	0.441984i	$0.854275\pi$
$942$		0			0
$943$	−44.4399	+	25.6574i	−1.44716	+	0.835520i
$944$			0.626113i			0.0203783i
$945$		0			0
$946$	−9.20901	+	15.9505i	−0.299411	+	0.518595i
$947$	11.2878	+	6.51704i	0.366806	+	0.211775i	0.672062	−	0.740495i	$-0.265409\pi$
$947$	11.2878	+	6.51704i	0.366806	+	0.211775i	−0.305256	+	0.952270i	$0.598742\pi$
$948$		0			0
$949$	12.4993	−	39.7529i	0.405744	−	1.29043i
$950$	12.0674			0.391518
$951$		0			0
$952$	2.26026	−	3.91489i	0.0732556	−	0.126882i
$953$	1.93182	+	3.34601i	0.0625778	+	0.108388i	0.895617	−	0.444826i	$-0.146735\pi$
$953$	1.93182	+	3.34601i	0.0625778	+	0.108388i	−0.833039	+	0.553214i	$0.813401\pi$
$954$		0			0
$955$	−11.3765	+	6.56824i	−0.368136	+	0.212543i
$956$	16.5611	−	9.56158i	0.535626	−	0.309244i
$957$		0			0
$958$	9.68891	+	16.7817i	0.313034	+	0.542192i
$959$	−2.13416	+	3.69647i	−0.0689155	+	0.119365i
$960$		0			0
$961$	30.8071			0.993778
$962$	−8.04946	−	36.1726i	−0.259525	−	1.16625i
$963$		0			0
$964$	−18.1292	−	10.4669i	−0.583901	−	0.337116i
$965$	−8.82978	+	15.2936i	−0.284241	+	0.492319i
$966$		0			0
$967$		−	19.4789i		−	0.626398i	−0.949688	−	0.313199i	$-0.898599\pi$
$967$		−	19.4789i		−	0.626398i	0.949688	−	0.313199i	$-0.101401\pi$
$968$	12.3522	−	7.13153i	0.397014	−	0.229216i
$969$		0			0
$970$			3.53026i			0.113350i
$971$	2.13960	+	3.70590i	0.0686631	+	0.118928i	0.898313	−	0.439356i	$-0.144793\pi$
$971$	2.13960	+	3.70590i	0.0686631	+	0.118928i	−0.829650	+	0.558284i	$0.811460\pi$
$972$		0			0
$973$	−5.95899	−	3.44043i	−0.191037	−	0.110295i
$974$	−41.2780			−1.32263
$975$		0			0
$976$	−8.99857			−0.288037
$977$	−23.7322	−	13.7018i	−0.759259	−	0.438358i	0.0697706	−	0.997563i	$-0.477773\pi$
$977$	−23.7322	−	13.7018i	−0.759259	−	0.438358i	−0.829030	+	0.559205i	$0.811107\pi$
$978$		0			0
$979$	21.1346	+	36.6062i	0.675465	+	1.16994i
$980$			1.25534i			0.0401004i
$981$		0			0
$982$	14.7347	−	8.50710i	0.470204	−	0.271472i
$983$		−	31.0406i		−	0.990042i	−0.868881	−	0.495021i	$-0.835160\pi$
$983$		−	31.0406i		−	0.990042i	0.868881	−	0.495021i	$-0.164840\pi$
$984$		0			0
$985$	11.1265	−	19.2716i	0.354519	−	0.614045i
$986$	−5.98995	−	3.45830i	−0.190759	−	0.110135i
$987$		0			0
$988$	8.59203	+	9.36160i	0.273349	+	0.297832i
$989$	18.8231			0.598541
$990$		0			0
$991$	13.0134	−	22.5398i	0.413383	−	0.716000i	−0.581874	−	0.813279i	$-0.697680\pi$
$991$	13.0134	−	22.5398i	0.413383	−	0.716000i	0.995257	+	0.0972785i	$0.0310137\pi$
$992$	0.219596	+	0.380351i	0.00697217	+	0.0120762i
$993$		0			0
$994$	5.89350	−	3.40261i	0.186931	−	0.107924i
$995$	−15.5189	+	8.95985i	−0.491983	+	0.284046i
$996$		0			0
$997$	13.6807	+	23.6957i	0.433272	+	0.750449i	0.997153	−	0.0754072i	$-0.0240257\pi$
$997$	13.6807	+	23.6957i	0.433272	+	0.750449i	−0.563881	+	0.825856i	$0.690692\pi$
$998$	−9.75484	+	16.8959i	−0.308784	+	0.534830i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.h.1135.3	yes	16
3.2	odd	2		1638.2.bj.i.1135.6	yes	16
13.10	even	6	inner	1638.2.bj.h.127.2	✓	16
39.23	odd	6		1638.2.bj.i.127.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.2	✓	16	13.10	even	6	inner
1638.2.bj.h.1135.3	yes	16	1.1	even	1	trivial
1638.2.bj.i.127.7	yes	16	39.23	odd	6
1638.2.bj.i.1135.6	yes	16	3.2	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.25534i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.25534i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.627670 - 1.08716i) q^{10} +(4.35285 + 2.51312i) q^{11} +(-3.43954 - 1.08148i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.26026 + 3.91489i) q^{17} +(-3.05207 + 1.76211i) q^{19} +(-1.08716 + 0.627670i) q^{20} +(-2.51312 - 4.35285i) q^{22} +(-2.56840 + 4.44859i) q^{23} +3.42412 q^{25} +(2.43799 + 2.65635i) q^{26} +(0.866025 + 0.500000i) q^{28} +(0.765021 - 1.32506i) q^{29} +0.439192i q^{31} +(0.866025 - 0.500000i) q^{32} -4.52053i q^{34} +(0.627670 + 1.08716i) q^{35} +(-8.90090 - 5.13894i) q^{37} +3.52423 q^{38} +1.25534 q^{40} +(8.65130 + 4.99483i) q^{41} +(-1.83219 - 3.17344i) q^{43} +5.02624i q^{44} +(4.44859 - 2.56840i) q^{46} -3.60242i q^{47} +(0.500000 - 0.866025i) q^{49} +(-2.96538 - 1.71206i) q^{50} +(-0.783183 - 3.51946i) q^{52} -8.82264 q^{53} +(-3.15482 + 5.46431i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.32506 + 0.765021i) q^{58} +(0.542230 - 0.313057i) q^{59} +(4.49928 + 7.79299i) q^{61} +(0.219596 - 0.380351i) q^{62} -1.00000 q^{64} +(1.35762 - 4.31779i) q^{65} +(6.40795 + 3.69963i) q^{67} +(-2.26026 + 3.91489i) q^{68} -1.25534i q^{70} +(-5.89350 + 3.40261i) q^{71} +11.5576i q^{73} +(5.13894 + 8.90090i) q^{74} +(-3.05207 - 1.76211i) q^{76} +5.02624 q^{77} -6.74435 q^{79} +(-1.08716 - 0.627670i) q^{80} +(-4.99483 - 8.65130i) q^{82} +9.57207i q^{83} +(-4.91452 + 2.83740i) q^{85} +3.66437i q^{86} +(2.51312 - 4.35285i) q^{88} +(7.28303 + 4.20486i) q^{89} +(-3.51946 + 0.783183i) q^{91} -5.13679 q^{92} +(-1.80121 + 3.11978i) q^{94} +(-2.21205 - 3.83139i) q^{95} +(-2.43543 + 1.40610i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

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