LMFDB - Embedded newform 1638.2.bj.i.1135.6

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			1135.6
Root			$0.830471 - 0.830471i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.i.127.7

$q$-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	$-0.909433\pi$
$5$		−	1.25534i		−	0.561405i	0.959795	−	0.280703i	$-0.0905674\pi$
$6$		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	−0.329935	−	0.944004i	$-0.607027\pi$
$11$	−4.35285	−	2.51312i	−1.31243	−	0.757734i	−0.982499	+	0.186270i	$0.940360\pi$
$12$		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	$-0.981982\pi$
$17$	−2.26026	−	3.91489i	−0.548195	−	0.949501i	0.450204	−	0.892926i	$-0.351351\pi$
$18$		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	$-0.653439\pi$
$23$	2.56840	−	4.44859i	0.535548	−	0.927596i	0.999137	−	0.0415454i	$-0.0132281\pi$
$24$		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	−0.928273	−	0.371901i	$-0.878706\pi$
$29$	−0.765021	+	1.32506i	−0.142061	+	0.246057i	0.786212	+	0.617957i	$0.212040\pi$
$30$		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	−0.362701	−	0.931905i	$-0.618145\pi$
$41$	−8.65130	−	4.99483i	−1.35111	−	0.780061i	−0.988404	+	0.151844i	$0.951479\pi$
$42$		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	$0.0846239\pi$
$47$			3.60242i			0.525466i	−0.964869	+	0.262733i	$0.915376\pi$
$48$		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	$-0.292796\pi$
$53$	8.82264			1.21188			0.605942	+	0.795509i	$0.292796\pi$
$54$		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	−0.534881	−	0.844928i	$-0.679643\pi$
$59$	−0.542230	+	0.313057i	−0.0705924	+	0.0407565i	0.464288	+	0.885684i	$0.346310\pi$
$60$		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	−0.107705	−	0.994183i	$-0.534350\pi$
$71$	5.89350	−	3.40261i	0.699430	−	0.403816i	0.807135	+	0.590367i	$0.201017\pi$
$72$		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	$-0.823940\pi$
$83$		−	9.57207i		−	1.05067i	0.850895	−	0.525335i	$-0.176060\pi$
$84$		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	0.0615879	−	0.998102i	$-0.480384\pi$
$89$	−7.28303	−	4.20486i	−0.772000	−	0.445714i	−0.833587	+	0.552388i	$0.813717\pi$
$90$		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	$-0.660417\pi$
$101$	5.19484	−	8.99772i	0.516906	−	0.895307i	0.999807	−	0.0196321i	$-0.00624949\pi$
$102$		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	$-0.597317\pi$
$107$	6.98610	−	12.1003i	0.675371	−	1.16978i	0.976360	−	0.216150i	$-0.0693500\pi$
$108$		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	0.807474	−	0.589904i	$-0.200834\pi$
$113$	−1.13886	−	1.97256i	−0.107135	−	0.185563i	−0.914608	+	0.404341i	$0.867501\pi$
$114$		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	$-0.608218\pi$
$131$	−7.63335			−0.666929			−0.333465	+	0.942763i	$0.608218\pi$
$132$		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	−0.333713	−	0.942675i	$-0.608302\pi$
$137$	3.69647	−	2.13416i	0.315810	−	0.182333i	0.649524	+	0.760341i	$0.274968\pi$
$138$		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	−0.846010	−	0.533166i	$-0.821002\pi$
$149$	−9.85411	+	5.68927i	−0.807280	+	0.466083i	0.0387303	+	0.999250i	$0.487669\pi$
$150$		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	0.693522	−	0.720435i	$-0.256058\pi$
$167$	5.38066	+	3.10652i	0.416368	+	0.240390i	−0.277154	+	0.960825i	$0.589391\pi$
$168$		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	$-0.929483\pi$
$173$	−8.91864	−	15.4475i	−0.678071	−	1.17445i	0.297489	−	0.954725i	$-0.403851\pi$
$174$		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	−0.983604	−	0.180339i	$-0.942280\pi$
$179$	−4.49034	+	7.77750i	−0.335624	+	0.581317i	0.647981	+	0.761657i	$0.275614\pi$
$180$		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	0.612266	−	0.790652i	$-0.290258\pi$
$191$	−5.23224	−	9.06251i	−0.378592	−	0.655740i	−0.990858	+	0.134912i	$0.956925\pi$
$192$		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	0.934576	−	0.355763i	$-0.115779\pi$
$197$	15.3517	+	8.86331i	1.09376	+	0.631485i	0.159188	+	0.987248i	$0.449112\pi$
$198$		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	−0.981864	−	0.189586i	$-0.939286\pi$
$227$	−19.7162	+	11.3832i	−1.30861	+	0.755526i	−0.326746	+	0.945112i	$0.605952\pi$
$228$		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	$-0.402828\pi$
$233$	9.17557			0.601112			0.300556	+	0.953764i	$0.402828\pi$
$234$		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	$0.212254\pi$
$239$			19.1232i			1.23697i	−0.785795	+	0.618487i	$0.787746\pi$
$240$		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	0.845804	−	0.533493i	$-0.179121\pi$
$251$	−0.619720	−	1.07339i	−0.0391164	−	0.0677516i	−0.884921	+	0.465742i	$0.845788\pi$
$252$		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	$-0.618858\pi$
$257$	10.0028	−	17.3253i	0.623956	−	1.08072i	0.988742	−	0.149631i	$-0.0478087\pi$
$258$		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	−0.789554	−	0.613682i	$-0.789688\pi$
$263$	2.21669	−	3.83942i	0.136687	−	0.236749i	0.926241	+	0.376933i	$0.123021\pi$
$264$		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	0.692156	−	0.721748i	$-0.256661\pi$
$269$	−4.57552	−	7.92503i	−0.278974	−	0.483197i	−0.971130	+	0.238551i	$0.923328\pi$
$270$		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	$0.454089\pi$
$281$			33.1780i			1.97923i	−0.143734	+	0.989616i	$0.545911\pi$
$282$		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	−0.905833	−	0.423635i	$-0.860754\pi$
$293$	−16.9781	+	9.80231i	−0.991871	+	0.572657i	−0.0860380	+	0.996292i	$0.527421\pi$
$294$		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	$-0.234363\pi$
$311$	26.1345			1.48195			0.740977	+	0.671530i	$0.234363\pi$
$312$		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	$0.211827\pi$
$317$			21.9861i			1.23486i	−0.786624	+	0.617432i	$0.788173\pi$
$318$		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	$0.00475967\pi$
$347$	9.55414	+	16.5483i	0.512893	+	0.888357i	−0.486995	+	0.873405i	$0.661907\pi$
$348$		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	0.755804	−	0.654798i	$-0.227246\pi$
$353$	10.6461	+	6.14652i	0.566634	+	0.327146i	−0.189170	+	0.981944i	$0.560580\pi$
$354$		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	$0.0173537\pi$
$359$			2.06492i			0.108982i	−0.998514	+	0.0544912i	$0.982646\pi$
$360$		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	−0.687959	−	0.725749i	$-0.741493\pi$
$383$	−7.89512	+	4.55825i	−0.403422	+	0.232916i	0.284538	+	0.958665i	$0.408160\pi$
$384$		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	$-0.445687\pi$
$389$	6.69801			0.339602			0.169801	+	0.985478i	$0.445687\pi$
$390$		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	−0.186241	−	0.982504i	$-0.559631\pi$
$401$	−22.6329	−	13.0671i	−1.13024	−	0.652542i	−0.943994	+	0.329962i	$0.892964\pi$
$402$		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	−0.972070	−	0.234690i	$-0.924593\pi$
$419$	−5.78853	+	10.0260i	−0.282788	+	0.489803i	0.689282	+	0.724493i	$0.257926\pi$
$420$		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	−0.338455	−	0.940982i	$-0.609904\pi$
$431$	−27.4578	−	15.8528i	−1.32260	−	0.763602i	−0.984142	+	0.177380i	$0.943238\pi$
$432$		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	$-0.612716\pi$
$443$	−14.5967			−0.693509			−0.346754	+	0.937956i	$0.612716\pi$
$444$		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	0.210211	−	0.977656i	$-0.432585\pi$
$449$	24.6222	−	14.2156i	1.16199	−	0.670876i	0.951781	+	0.306780i	$0.0992515\pi$
$450$		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	−0.858512	−	0.512793i	$-0.828611\pi$
$461$	−18.1145	+	10.4584i	−0.843677	+	0.487097i	0.0148353	+	0.999890i	$0.495278\pi$
$462$		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	$-0.412527\pi$
$467$	11.7282			0.542718			0.271359	+	0.962478i	$0.412527\pi$
$468$		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	0.831723	−	0.555191i	$-0.187355\pi$
$479$	16.7817	+	9.68891i	0.766775	+	0.442698i	−0.0649482	+	0.997889i	$0.520688\pi$
$480$		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	−0.607699	−	0.794168i	$-0.707907\pi$
$491$	8.50710	−	14.7347i	0.383920	−	0.664969i	0.991619	+	0.129199i	$0.0412405\pi$
$492$		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	$-0.909576\pi$
$503$	−16.2080	−	28.0732i	−0.722681	−	1.25172i	0.237240	−	0.971451i	$-0.423757\pi$
$504$		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	$-0.953311\pi$
$509$	−36.3337	−	20.9773i	−1.61046	−	0.929802i	−0.621202	−	0.783650i	$-0.713355\pi$
$510$		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	$-0.251417\pi$
$521$	32.1360			1.40790			0.703951	+	0.710248i	$0.251417\pi$
$522$		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	0.285850	−	0.958274i	$-0.407724\pi$
$557$	−9.46666	−	5.46558i	−0.401115	−	0.231584i	−0.686965	+	0.726690i	$0.741058\pi$
$558$		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	$0.103794\pi$
$563$	17.8211	+	30.8670i	0.751068	+	1.30089i	−0.196238	+	0.980556i	$0.562872\pi$
$564$		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	−0.751589	−	0.659631i	$-0.770712\pi$
$569$	4.66252	−	8.07571i	0.195463	−	0.338552i	0.947052	+	0.321080i	$0.104046\pi$
$570$		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	−0.349097	−	0.937087i	$-0.613512\pi$
$587$	−32.3490	−	18.6767i	−1.33519	−	0.770870i	−0.986089	+	0.166216i	$0.946845\pi$
$588$		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	$0.177948\pi$
$593$			25.8309i			1.06075i	−0.847764	+	0.530374i	$0.822052\pi$
$594$		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	$-0.379090\pi$
$599$	18.1493			0.741562			0.370781	+	0.928720i	$0.379090\pi$
$600$		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	−0.956713	−	0.291033i	$-0.906001\pi$
$617$	−29.3858	+	16.9659i	−1.18303	+	0.683021i	−0.226315	+	0.974054i	$0.572668\pi$
$618$		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	0.722974	−	0.690875i	$-0.242774\pi$
$641$	−5.99600	−	10.3854i	−0.236828	−	0.410198i	−0.959802	+	0.280677i	$0.909441\pi$
$642$		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	$-0.658077\pi$
$647$	13.3079	−	23.0499i	0.523186	−	0.906184i	0.999636	−	0.0269828i	$-0.00858992\pi$
$648$		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	$0.401341\pi$
$653$	−17.1787	+	29.7544i	−0.672255	+	1.16438i	−0.977263	+	0.212030i	$0.931993\pi$
$654$		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	0.996476	−	0.0838807i	$-0.0267315\pi$
$659$	10.9254	+	18.9234i	0.425595	+	0.737152i	−0.570881	+	0.821033i	$0.693398\pi$
$660$		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	$-0.602215\pi$
$677$	−16.4248			−0.631255			−0.315628	+	0.948883i	$0.602215\pi$
$678$		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	0.184427	−	0.982846i	$-0.440957\pi$
$683$	29.4745	−	17.0171i	1.12781	−	0.651142i	0.943383	+	0.331705i	$0.107624\pi$
$684$		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	$-0.453017\pi$
$701$	7.78759			0.294133			0.147067	+	0.989127i	$0.453017\pi$
$702$		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	$-0.995802\pi$
$719$	−13.7122	−	23.7502i	−0.511378	−	0.885733i	0.488535	−	0.872545i	$-0.337532\pi$
$720$		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	−0.0193152	−	0.999813i	$-0.506149\pi$
$743$	−24.3915	−	14.0824i	−0.894837	−	0.516634i	−0.875521	+	0.483179i	$0.839482\pi$
$744$		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	0.163794	−	0.986495i	$-0.447627\pi$
$761$	30.3454	−	17.5199i	1.10002	−	0.635097i	0.936226	+	0.351398i	$0.114294\pi$
$762$		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	−0.333533	−	0.942739i	$-0.608241\pi$
$773$	8.78950	−	5.07462i	0.316136	−	0.182521i	0.649669	+	0.760217i	$0.274907\pi$
$774$		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	0.773622	−	0.633647i	$-0.218443\pi$
$797$	−4.57184	−	7.91867i	−0.161943	−	0.280494i	−0.935565	+	0.353153i	$0.885109\pi$
$798$		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	−0.947145	−	0.320806i	$-0.896046\pi$
$809$	−5.56760	+	9.64337i	−0.195746	+	0.339043i	0.751398	+	0.659849i	$0.229380\pi$
$810$		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	−0.0695285	−	0.997580i	$-0.522149\pi$
$821$	−27.7426	−	16.0172i	−0.968222	−	0.559003i	−0.898694	+	0.438577i	$0.855483\pi$
$822$		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	$-0.843083\pi$
$827$		−	27.2187i		−	0.946488i	0.880931	−	0.473244i	$-0.156917\pi$
$828$		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	−0.726233	−	0.687448i	$-0.758731\pi$
$839$	−14.3090	+	8.26132i	−0.494002	+	0.285212i	0.232231	+	0.972661i	$0.425397\pi$
$840$		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	$-0.419759\pi$
$857$	14.6034			0.498844			0.249422	+	0.968395i	$0.419759\pi$
$858$		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	$-0.687566\pi$
$863$		−	48.8452i		−	1.66271i	0.555743	−	0.831354i	$-0.312434\pi$
$864$		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	$-0.500695\pi$
$881$	25.6726	−	44.4663i	0.864932	−	1.49811i	0.867115	−	0.498109i	$-0.165972\pi$
$882$		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	$0.464957\pi$
$887$	−24.0002	+	41.5696i	−0.805848	+	1.39577i	−0.915717	+	0.401823i	$0.868377\pi$
$888$		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	$-0.745801\pi$
$911$	−42.1182			−1.39544			−0.697719	+	0.716372i	$0.745801\pi$
$912$		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	−0.161101	−	0.986938i	$-0.551504\pi$
$929$	18.6858	−	10.7883i	0.613062	−	0.353952i	0.774163	+	0.632986i	$0.218171\pi$
$930$		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	$-0.854275\pi$
$941$		−	27.1164i		−	0.883969i	0.897023	−	0.441984i	$-0.145725\pi$
$942$		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	0.305256	−	0.952270i	$-0.401258\pi$
$947$	−11.2878	−	6.51704i	−0.366806	−	0.211775i	−0.672062	+	0.740495i	$0.734591\pi$
$948$		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	0.833039	−	0.553214i	$-0.186599\pi$
$953$	−1.93182	−	3.34601i	−0.0625778	−	0.108388i	−0.895617	+	0.444826i	$0.853265\pi$
$954$		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	0.829650	−	0.558284i	$-0.188540\pi$
$971$	−2.13960	−	3.70590i	−0.0686631	−	0.118928i	−0.898313	+	0.439356i	$0.855207\pi$
$972$		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	0.829030	−	0.559205i	$-0.188893\pi$
$977$	23.7322	+	13.7018i	0.759259	+	0.438358i	−0.0697706	+	0.997563i	$0.522227\pi$
$978$		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	$0.164840\pi$
$983$			31.0406i			0.990042i	−0.868881	+	0.495021i	$0.835160\pi$
$984$		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.i.1135.6	yes	16
3.2	odd	2		1638.2.bj.h.1135.3	yes	16
13.10	even	6	inner	1638.2.bj.i.127.7	yes	16
39.23	odd	6		1638.2.bj.h.127.2	✓	16

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more