LMFDB - Embedded newform 1638.2.bj.f.1135.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1135.2
Root			$1.72124 + 0.193255i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.f.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.05596i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.05596i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.52798 - 2.64654i) q^{10} +(2.98127 + 1.72124i) q^{11} +(3.25253 + 1.55596i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.41449 + 2.44997i) q^{17} +(1.49425 - 0.862708i) q^{19} +(-2.64654 + 1.52798i) q^{20} +(-1.72124 - 2.98127i) q^{22} +(-1.53130 + 2.65229i) q^{23} -4.33891 q^{25} +(-2.03880 - 2.97377i) q^{26} +(0.866025 + 0.500000i) q^{28} +(1.92531 - 3.33473i) q^{29} -0.978370i q^{31} +(0.866025 - 0.500000i) q^{32} -2.82898i q^{34} +(1.52798 + 2.64654i) q^{35} +(4.58394 + 2.64654i) q^{37} -1.72542 q^{38} +3.05596 q^{40} +(-8.62781 - 4.98127i) q^{41} +(-1.51082 - 2.61681i) q^{43} +3.44247i q^{44} +(2.65229 - 1.53130i) q^{46} -8.04447i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.75760 + 2.16945i) q^{50} +(0.278764 + 3.59476i) q^{52} +8.33405 q^{53} +(-5.26003 + 9.11064i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-3.33473 + 1.92531i) q^{58} +(-8.64080 + 4.98877i) q^{59} +(5.77260 + 9.99843i) q^{61} +(-0.489185 + 0.847293i) q^{62} -1.00000 q^{64} +(-4.75496 + 9.93962i) q^{65} +(4.11410 + 2.37527i) q^{67} +(-1.41449 + 2.44997i) q^{68} -3.05596i q^{70} +(3.17784 - 1.83473i) q^{71} +10.1119i q^{73} +(-2.64654 - 4.58394i) q^{74} +(1.49425 + 0.862708i) q^{76} +3.44247 q^{77} -4.49843 q^{79} +(-2.64654 - 1.52798i) q^{80} +(4.98127 + 8.62781i) q^{82} -7.15869i q^{83} +(-7.48701 + 4.32263i) q^{85} +3.02163i q^{86} +(1.72124 - 2.98127i) q^{88} +(6.84426 + 3.95154i) q^{89} +(3.59476 - 0.278764i) q^{91} -3.06260 q^{92} +(-4.02224 + 6.96672i) q^{94} +(2.63640 + 4.56638i) q^{95} +(-7.88016 + 4.54961i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$			3.05596i			1.36667i	0.730106	+	0.683334i	$0.239471\pi$
$5$			3.05596i			1.36667i	−0.730106	+	0.683334i	$0.760529\pi$
$6$		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
$10$	1.52798	−	2.64654i	0.483190	−	0.836910i
$11$	2.98127	+	1.72124i	0.898886	+	0.518972i	0.876839	−	0.480785i	$-0.159648\pi$
$11$	2.98127	+	1.72124i	0.898886	+	0.518972i	0.0220475	+	0.999757i	$0.492982\pi$
$12$		0			0
$13$	3.25253	+	1.55596i	0.902091	+	0.431546i
$13$	3.25253	+	1.55596i	0.902091	+	0.431546i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41449	+	2.44997i	0.343064	+	0.594205i	0.985000	−	0.172554i	$-0.0552018\pi$
$17$	1.41449	+	2.44997i	0.343064	+	0.594205i	−0.641936	+	0.766758i	$0.721868\pi$
$18$		0			0
$19$	1.49425	−	0.862708i	0.342805	−	0.197919i	−0.318707	−	0.947853i	$-0.603248\pi$
$19$	1.49425	−	0.862708i	0.342805	−	0.197919i	0.661512	+	0.749935i	$0.269915\pi$
$20$	−2.64654	+	1.52798i	−0.591785	+	0.341667i
$21$		0			0
$22$	−1.72124	−	2.98127i	−0.366969	−	0.635608i
$23$	−1.53130	+	2.65229i	−0.319298	+	0.553040i	−0.980342	−	0.197307i	$-0.936780\pi$
$23$	−1.53130	+	2.65229i	−0.319298	+	0.553040i	0.661044	+	0.750347i	$0.270114\pi$
$24$		0			0
$25$	−4.33891			−0.867781
$26$	−2.03880	−	2.97377i	−0.399841	−	0.583204i
$27$		0			0
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	1.92531	−	3.33473i	0.357520	−	0.619243i	−0.630026	−	0.776574i	$-0.716956\pi$
$29$	1.92531	−	3.33473i	0.357520	−	0.619243i	0.987546	+	0.157331i	$0.0502890\pi$
$30$		0			0
$31$		−	0.978370i		−	0.175720i	−0.996133	−	0.0878602i	$-0.971997\pi$
$31$		−	0.978370i		−	0.175720i	0.996133	−	0.0878602i	$-0.0280029\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	2.82898i		−	0.485166i
$35$	1.52798	+	2.64654i	0.258276	+	0.447347i
$36$		0			0
$37$	4.58394	+	2.64654i	0.753596	+	0.435089i	0.826992	−	0.562214i	$-0.190050\pi$
$37$	4.58394	+	2.64654i	0.753596	+	0.435089i	−0.0733959	+	0.997303i	$0.523384\pi$
$38$	−1.72542			−0.279899
$39$		0			0
$40$	3.05596			0.483190
$41$	−8.62781	−	4.98127i	−1.34744	−	0.777943i	−0.359551	−	0.933125i	$-0.617070\pi$
$41$	−8.62781	−	4.98127i	−1.34744	−	0.777943i	−0.987886	+	0.155182i	$0.950404\pi$
$42$		0			0
$43$	−1.51082	−	2.61681i	−0.230397	−	0.399060i	0.727528	−	0.686078i	$-0.240669\pi$
$43$	−1.51082	−	2.61681i	−0.230397	−	0.399060i	−0.957925	+	0.287019i	$0.907336\pi$
$44$			3.44247i			0.518972i
$45$		0			0
$46$	2.65229	−	1.53130i	0.391058	−	0.225778i
$47$		−	8.04447i		−	1.17341i	−0.809802	−	0.586703i	$-0.800425\pi$
$47$		−	8.04447i		−	1.17341i	0.809802	−	0.586703i	$-0.199575\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	3.75760	+	2.16945i	0.531405	+	0.306807i
$51$		0			0
$52$	0.278764	+	3.59476i	0.0386576	+	0.498503i
$53$	8.33405			1.14477			0.572385	−	0.819985i	$-0.306018\pi$
$53$	8.33405			1.14477			0.572385	+	0.819985i	$0.306018\pi$
$54$		0			0
$55$	−5.26003	+	9.11064i	−0.709263	+	1.22848i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−3.33473	+	1.92531i	−0.437871	+	0.252805i
$59$	−8.64080	+	4.98877i	−1.12494	+	0.649482i	−0.942656	−	0.333765i	$-0.891681\pi$
$59$	−8.64080	+	4.98877i	−1.12494	+	0.649482i	−0.182279	+	0.983247i	$0.558348\pi$
$60$		0			0
$61$	5.77260	+	9.99843i	0.739106	+	1.28017i	0.952899	+	0.303289i	$0.0980849\pi$
$61$	5.77260	+	9.99843i	0.739106	+	1.28017i	−0.213793	+	0.976879i	$0.568582\pi$
$62$	−0.489185	+	0.847293i	−0.0621266	+	0.107606i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.75496	+	9.93962i	−0.589781	+	1.23286i
$66$		0			0
$67$	4.11410	+	2.37527i	0.502617	+	0.290186i	0.729794	−	0.683668i	$-0.239616\pi$
$67$	4.11410	+	2.37527i	0.502617	+	0.290186i	−0.227177	+	0.973854i	$0.572950\pi$
$68$	−1.41449	+	2.44997i	−0.171532	+	0.297102i
$69$		0			0
$70$		−	3.05596i		−	0.365257i
$71$	3.17784	−	1.83473i	0.377140	−	0.217742i	−0.299433	−	0.954117i	$-0.596798\pi$
$71$	3.17784	−	1.83473i	0.377140	−	0.217742i	0.676573	+	0.736375i	$0.263464\pi$
$72$		0			0
$73$			10.1119i			1.18351i	0.806117	+	0.591756i	$0.201565\pi$
$73$			10.1119i			1.18351i	−0.806117	+	0.591756i	$0.798435\pi$
$74$	−2.64654	−	4.58394i	−0.307654	−	0.532873i
$75$		0			0
$76$	1.49425	+	0.862708i	0.171403	+	0.0989594i
$77$	3.44247			0.392306
$78$		0			0
$79$	−4.49843			−0.506113			−0.253057	−	0.967451i	$-0.581436\pi$
$79$	−4.49843			−0.506113			−0.253057	+	0.967451i	$0.581436\pi$
$80$	−2.64654	−	1.52798i	−0.295892	−	0.170833i
$81$		0			0
$82$	4.98127	+	8.62781i	0.550089	+	0.952782i
$83$		−	7.15869i		−	0.785768i	−0.919588	−	0.392884i	$-0.871477\pi$
$83$		−	7.15869i		−	0.785768i	0.919588	−	0.392884i	$-0.128523\pi$
$84$		0			0
$85$	−7.48701	+	4.32263i	−0.812081	+	0.468855i
$86$			3.02163i			0.325831i
$87$		0			0
$88$	1.72124	−	2.98127i	0.183484	−	0.317804i
$89$	6.84426	+	3.95154i	0.725490	+	0.418862i	0.816770	−	0.576963i	$-0.195762\pi$
$89$	6.84426	+	3.95154i	0.725490	+	0.418862i	−0.0912800	+	0.995825i	$0.529096\pi$
$90$		0			0
$91$	3.59476	−	0.278764i	0.376833	−	0.0292224i
$92$	−3.06260			−0.319298
$93$		0			0
$94$	−4.02224	+	6.96672i	−0.414862	+	0.718562i
$95$	2.63640	+	4.56638i	0.270489	+	0.468501i
$96$		0			0
$97$	−7.88016	+	4.54961i	−0.800109	+	0.461943i	−0.843509	−	0.537115i	$-0.819514\pi$
$97$	−7.88016	+	4.54961i	−0.800109	+	0.461943i	0.0434004	+	0.999058i	$0.486181\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	−2.16945	−	3.75760i	−0.216945	−	0.375760i
$101$	−9.42664	+	16.3274i	−0.937985	+	1.62464i	−0.168764	+	0.985657i	$0.553977\pi$
$101$	−9.42664	+	16.3274i	−0.937985	+	1.62464i	−0.769222	+	0.638982i	$0.779356\pi$
$102$		0			0
$103$	−13.7079			−1.35068			−0.675338	−	0.737509i	$-0.736002\pi$
$103$	−13.7079			−1.35068			−0.675338	+	0.737509i	$0.736002\pi$
$104$	1.55596	−	3.25253i	0.152575	−	0.318937i
$105$		0			0
$106$	−7.21750	−	4.16702i	−0.701025	−	0.404737i
$107$	−1.65736	+	2.87063i	−0.160223	+	0.277514i	−0.934948	−	0.354784i	$-0.884555\pi$
$107$	−1.65736	+	2.87063i	−0.160223	+	0.277514i	0.774726	+	0.632297i	$0.217888\pi$
$108$		0			0
$109$			8.67525i			0.830938i	0.909607	+	0.415469i	$0.136383\pi$
$109$			8.67525i			0.830938i	−0.909607	+	0.415469i	$0.863617\pi$
$110$	9.11064	−	5.26003i	0.868666	−	0.501524i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	−5.60557	−	9.70914i	−0.527328	−	0.913359i	−0.999493	−	0.0318486i	$-0.989861\pi$
$113$	−5.60557	−	9.70914i	−0.527328	−	0.913359i	0.472165	−	0.881510i	$-0.343473\pi$
$114$		0			0
$115$	−8.10529	−	4.67959i	−0.755822	−	0.436374i
$116$	3.85061			0.357520
$117$		0			0
$118$	9.97753			0.918506
$119$	2.44997	+	1.41449i	0.224588	+	0.129666i
$120$		0			0
$121$	0.425305	+	0.736650i	0.0386641	+	0.0669682i
$122$		−	11.5452i		−	1.04525i
$123$		0			0
$124$	0.847293	−	0.489185i	0.0760892	−	0.0439301i
$125$			2.02028i			0.180699i
$126$		0			0
$127$	2.55753	−	4.42977i	0.226944	−	0.393078i	−0.729957	−	0.683493i	$-0.760460\pi$
$127$	2.55753	−	4.42977i	0.226944	−	0.393078i	0.956901	+	0.290415i	$0.0937932\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	9.08773	−	6.23048i	0.797047	−	0.546450i
$131$	18.7757			1.64044			0.820219	−	0.572049i	$-0.193851\pi$
$131$	18.7757			1.64044			0.820219	+	0.572049i	$0.193851\pi$
$132$		0			0
$133$	0.862708	−	1.49425i	0.0748063	−	0.129568i
$134$	−2.37527	−	4.11410i	−0.205192	−	0.355404i
$135$		0			0
$136$	2.44997	−	1.41449i	0.210083	−	0.121292i
$137$	−2.30457	+	1.33055i	−0.196893	+	0.113676i	−0.595205	−	0.803574i	$-0.702929\pi$
$137$	−2.30457	+	1.33055i	−0.196893	+	0.113676i	0.398312	+	0.917250i	$0.369596\pi$
$138$		0			0
$139$	8.35322	+	14.4682i	0.708511	+	1.22718i	0.965409	+	0.260739i	$0.0839662\pi$
$139$	8.35322	+	14.4682i	0.708511	+	1.22718i	−0.256898	+	0.966439i	$0.582700\pi$
$140$	−1.52798	+	2.64654i	−0.129138	+	0.223674i
$141$		0			0
$142$	−3.66945			−0.307934
$143$	7.01850	+	10.2371i	0.586916	+	0.856071i
$144$		0			0
$145$	10.1908	+	5.88366i	0.846300	+	0.488611i
$146$	5.05596	−	8.75718i	0.418434	−	0.724750i
$147$		0			0
$148$			5.29308i			0.435089i
$149$	−2.16642	+	1.25078i	−0.177480	+	0.102468i	−0.586108	−	0.810233i	$-0.699341\pi$
$149$	−2.16642	+	1.25078i	−0.177480	+	0.102468i	0.408628	+	0.912701i	$0.366007\pi$
$150$		0			0
$151$		−	12.6465i		−	1.02916i	−0.857444	−	0.514578i	$-0.827949\pi$
$151$		−	12.6465i		−	1.02916i	0.857444	−	0.514578i	$-0.172051\pi$
$152$	−0.862708	−	1.49425i	−0.0699749	−	0.121200i
$153$		0			0
$154$	−2.98127	−	1.72124i	−0.240237	−	0.138701i
$155$	2.98986			0.240151
$156$		0			0
$157$	17.8131			1.42164			0.710822	−	0.703372i	$-0.248323\pi$
$157$	17.8131			1.42164			0.710822	+	0.703372i	$0.248323\pi$
$158$	3.89576	+	2.24922i	0.309930	+	0.178938i
$159$		0			0
$160$	1.52798	+	2.64654i	0.120798	+	0.209227i
$161$			3.06260i			0.241366i
$162$		0			0
$163$	−7.68884	+	4.43915i	−0.602236	+	0.347701i	−0.769921	−	0.638139i	$-0.779704\pi$
$163$	−7.68884	+	4.43915i	−0.602236	+	0.347701i	0.167684	+	0.985841i	$0.446371\pi$
$164$		−	9.96254i		−	0.777943i
$165$		0			0
$166$	−3.57934	+	6.19961i	−0.277811	+	0.481183i
$167$	8.46097	+	4.88494i	0.654730	+	0.378008i	0.790266	−	0.612764i	$-0.209942\pi$
$167$	8.46097	+	4.88494i	0.654730	+	0.378008i	−0.135536	+	0.990772i	$0.543276\pi$
$168$		0			0
$169$	8.15796	+	10.1216i	0.627535	+	0.778588i
$170$	8.64526			0.663061
$171$		0			0
$172$	1.51082	−	2.61681i	0.115199	−	0.199530i
$173$	−4.33762	−	7.51299i	−0.329783	−	0.571202i	0.652685	−	0.757629i	$-0.273642\pi$
$173$	−4.33762	−	7.51299i	−0.329783	−	0.571202i	−0.982469	+	0.186427i	$0.940309\pi$
$174$		0			0
$175$	−3.75760	+	2.16945i	−0.284048	+	0.163995i
$176$	−2.98127	+	1.72124i	−0.224722	+	0.129743i
$177$		0			0
$178$	−3.95154	−	6.84426i	−0.296180	−	0.512999i
$179$	11.7139	−	20.2891i	0.875540	−	1.51648i	0.0193531	−	0.999813i	$-0.493839\pi$
$179$	11.7139	−	20.2891i	0.875540	−	1.51648i	0.856187	−	0.516667i	$-0.172827\pi$
$180$		0			0
$181$	7.66632			0.569833			0.284917	−	0.958552i	$-0.408034\pi$
$181$	7.66632			0.569833			0.284917	+	0.958552i	$0.408034\pi$
$182$	−3.25253	−	1.55596i	−0.241094	−	0.115336i
$183$		0			0
$184$	2.65229	+	1.53130i	0.195529	+	0.112889i
$185$	−8.08773	+	14.0084i	−0.594622	+	1.02992i
$186$		0			0
$187$			9.73869i			0.712163i
$188$	6.96672	−	4.02224i	0.508100	−	0.293352i
$189$		0			0
$190$		−	5.27281i		−	0.382530i
$191$	12.7472	+	22.0789i	0.922357	+	1.59757i	0.795757	+	0.605616i	$0.207073\pi$
$191$	12.7472	+	22.0789i	0.922357	+	1.59757i	0.126600	+	0.991954i	$0.459593\pi$
$192$		0			0
$193$	−7.38361	−	4.26293i	−0.531484	−	0.306852i	0.210137	−	0.977672i	$-0.432609\pi$
$193$	−7.38361	−	4.26293i	−0.531484	−	0.306852i	−0.741621	+	0.670820i	$0.765942\pi$
$194$	9.09922			0.653286
$195$		0			0
$196$	1.00000			0.0714286
$197$	−20.5094	−	11.8411i	−1.46124	−	0.843645i	−0.462168	−	0.886792i	$-0.652928\pi$
$197$	−20.5094	−	11.8411i	−1.46124	−	0.843645i	−0.999069	+	0.0431470i	$0.986262\pi$
$198$		0			0
$199$	−12.4233	−	21.5178i	−0.880666	−	1.52536i	−0.850602	−	0.525810i	$-0.823762\pi$
$199$	−12.4233	−	21.5178i	−0.880666	−	1.52536i	−0.0300637	−	0.999548i	$-0.509571\pi$
$200$			4.33891i			0.306807i
$201$		0			0
$202$	16.3274	−	9.42664i	1.14879	−	0.663256i
$203$		−	3.85061i		−	0.270260i
$204$		0			0
$205$	15.2226	−	26.3663i	1.06319	−	1.84150i
$206$	11.8714	+	6.85393i	0.827116	+	0.477536i
$207$		0			0
$208$	−2.97377	+	2.03880i	−0.206194	+	0.141365i
$209$	5.93970			0.410857
$210$		0			0
$211$	−0.386509	+	0.669453i	−0.0266084	+	0.0460871i	−0.879023	−	0.476779i	$-0.841804\pi$
$211$	−0.386509	+	0.669453i	−0.0266084	+	0.0460871i	0.852415	+	0.522867i	$0.175137\pi$
$212$	4.16702	+	7.21750i	0.286192	+	0.495700i
$213$		0			0
$214$	2.87063	−	1.65736i	0.196232	−	0.113295i
$215$	7.99687	−	4.61699i	0.545382	−	0.314876i
$216$		0			0
$217$	−0.489185	−	0.847293i	−0.0332080	−	0.0575180i
$218$	4.33762	−	7.51299i	0.293781	−	0.508844i
$219$		0			0
$220$	−10.5201			−0.709263
$221$	0.788619	+	10.1695i	0.0530482	+	0.684075i
$222$		0			0
$223$	−18.6502	−	10.7677i	−1.24891	−	0.721060i	−0.278019	−	0.960575i	$-0.589678\pi$
$223$	−18.6502	−	10.7677i	−1.24891	−	0.721060i	−0.970892	+	0.239516i	$0.923011\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$			11.2111i			0.745754i
$227$	−15.1939	+	8.77218i	−1.00845	+	0.582230i	−0.910738	−	0.412985i	$-0.864486\pi$
$227$	−15.1939	+	8.77218i	−1.00845	+	0.582230i	−0.0977139	+	0.995215i	$0.531153\pi$
$228$		0			0
$229$			10.3222i			0.682109i	0.940043	+	0.341055i	$0.110784\pi$
$229$			10.3222i			0.682109i	−0.940043	+	0.341055i	$0.889216\pi$
$230$	4.67959	+	8.10529i	0.308563	+	0.534447i
$231$		0			0
$232$	−3.33473	−	1.92531i	−0.218936	−	0.126402i
$233$	17.8290			1.16802			0.584008	−	0.811748i	$-0.301484\pi$
$233$	17.8290			1.16802			0.584008	+	0.811748i	$0.301484\pi$
$234$		0			0
$235$	24.5836			1.60366
$236$	−8.64080	−	4.98877i	−0.562468	−	0.324741i
$237$		0			0
$238$	−1.41449	−	2.44997i	−0.0916878	−	0.158808i
$239$		−	5.71271i		−	0.369525i	−0.982783	−	0.184762i	$-0.940848\pi$
$239$		−	5.71271i		−	0.369525i	0.982783	−	0.184762i	$-0.0591515\pi$
$240$		0			0
$241$	0.868738	−	0.501566i	0.0559603	−	0.0323087i	−0.471759	−	0.881728i	$-0.656381\pi$
$241$	0.868738	−	0.501566i	0.0559603	−	0.0323087i	0.527719	+	0.849419i	$0.323047\pi$
$242$		−	0.850611i		−	0.0546793i
$243$		0			0
$244$	−5.77260	+	9.99843i	−0.369553	+	0.640084i
$245$	2.64654	+	1.52798i	0.169081	+	0.0976191i
$246$		0			0
$247$	6.20245	−	0.480984i	0.394653	−	0.0306043i
$248$	−0.978370			−0.0621266
$249$		0			0
$250$	1.01014	−	1.74961i	0.0638867	−	0.110655i
$251$	0.336293	+	0.582476i	0.0212266	+	0.0367656i	0.876444	−	0.481505i	$-0.159910\pi$
$251$	0.336293	+	0.582476i	0.0212266	+	0.0367656i	−0.855217	+	0.518270i	$0.826576\pi$
$252$		0			0
$253$	−9.13042	+	5.27145i	−0.574025	+	0.331413i
$254$	−4.42977	+	2.55753i	−0.277948	+	0.160474i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.1717	+	21.0820i	−0.759248	+	1.31506i	0.183986	+	0.982929i	$0.441100\pi$
$257$	−12.1717	+	21.0820i	−0.759248	+	1.31506i	−0.943234	+	0.332128i	$0.892234\pi$
$258$		0			0
$259$	5.29308			0.328896
$260$	−10.9854	+	0.851893i	−0.681289	+	0.0528322i
$261$		0			0
$262$	−16.2602	−	9.38784i	−1.00456	−	0.579983i
$263$	−8.54648	+	14.8029i	−0.526999	+	0.912788i	0.472506	+	0.881327i	$0.343349\pi$
$263$	−8.54648	+	14.8029i	−0.526999	+	0.912788i	−0.999505	+	0.0314610i	$0.989984\pi$
$264$		0			0
$265$			25.4685i			1.56452i
$266$	−1.49425	+	0.862708i	−0.0916186	+	0.0528960i
$267$		0			0
$268$			4.75055i			0.290186i
$269$	−13.3297	−	23.0877i	−0.812727	−	1.40768i	−0.910949	−	0.412519i	$-0.864649\pi$
$269$	−13.3297	−	23.0877i	−0.812727	−	1.40768i	0.0982223	−	0.995165i	$-0.468684\pi$
$270$		0			0
$271$	21.1739	+	12.2247i	1.28622	+	0.742600i	0.977978	−	0.208708i	$-0.0669257\pi$
$271$	21.1739	+	12.2247i	1.28622	+	0.742600i	0.308243	+	0.951308i	$0.400259\pi$
$272$	−2.82898			−0.171532
$273$		0			0
$274$	2.66109			0.160763
$275$	−12.9354	−	7.46828i	−0.780037	−	0.450354i
$276$		0			0
$277$	−14.2406	−	24.6655i	−0.855636	−	1.48201i	−0.876054	−	0.482214i	$-0.839833\pi$
$277$	−14.2406	−	24.6655i	−0.855636	−	1.48201i	0.0204175	−	0.999792i	$-0.493500\pi$
$278$		−	16.7064i		−	1.00199i
$279$		0			0
$280$	2.64654	−	1.52798i	0.158161	−	0.0913143i
$281$		−	9.76032i		−	0.582252i	−0.956685	−	0.291126i	$-0.905970\pi$
$281$		−	9.76032i		−	0.582252i	0.956685	−	0.291126i	$-0.0940298\pi$
$282$		0			0
$283$	5.83562	−	10.1076i	0.346891	−	0.600833i	−0.638804	−	0.769369i	$-0.720571\pi$
$283$	5.83562	−	10.1076i	0.346891	−	0.600833i	0.985696	+	0.168536i	$0.0539039\pi$
$284$	3.17784	+	1.83473i	0.188570	+	0.108871i
$285$		0			0
$286$	−0.959638	−	12.3749i	−0.0567446	−	0.731741i
$287$	−9.96254			−0.588070
$288$		0			0
$289$	4.49843	−	7.79152i	0.264614	−	0.458324i
$290$	−5.88366	−	10.1908i	−0.345500	−	0.598424i
$291$		0			0
$292$	−8.75718	+	5.05596i	−0.512475	+	0.295878i
$293$	−18.8968	+	10.9101i	−1.10396	+	0.637373i	−0.937259	−	0.348634i	$-0.886646\pi$
$293$	−18.8968	+	10.9101i	−1.10396	+	0.637373i	−0.166704	+	0.986007i	$0.553312\pi$
$294$		0			0
$295$	−15.2455	−	26.4059i	−0.887626	−	1.53741i
$296$	2.64654	−	4.58394i	0.153827	−	0.266436i
$297$		0			0
$298$	2.50157			0.144912
$299$	−9.10746	+	6.24401i	−0.526698	+	0.361101i
$300$		0			0
$301$	−2.61681	−	1.51082i	−0.150830	−	0.0870819i
$302$	−6.32323	+	10.9522i	−0.363861	+	0.630226i
$303$		0			0
$304$			1.72542i			0.0989594i
$305$	−30.5548	+	17.6408i	−1.74957	+	1.01011i
$306$		0			0
$307$		−	4.87046i		−	0.277972i	−0.990294	−	0.138986i	$-0.955616\pi$
$307$		−	4.87046i		−	0.277972i	0.990294	−	0.138986i	$-0.0443843\pi$
$308$	1.72124	+	2.98127i	0.0980765	+	0.169874i
$309$		0			0
$310$	−2.58930	−	1.49493i	−0.147062	−	0.0849064i
$311$	3.90344			0.221344			0.110672	−	0.993857i	$-0.464700\pi$
$311$	3.90344			0.221344			0.110672	+	0.993857i	$0.464700\pi$
$312$		0			0
$313$	26.0528			1.47259			0.736297	−	0.676659i	$-0.236573\pi$
$313$	26.0528			1.47259			0.736297	+	0.676659i	$0.236573\pi$
$314$	−15.4266	−	8.90657i	−0.870576	−	0.502627i
$315$		0			0
$316$	−2.24922	−	3.89576i	−0.126528	−	0.219154i
$317$		−	11.1107i		−	0.624040i	−0.950076	−	0.312020i	$-0.898994\pi$
$317$		−	11.1107i		−	0.624040i	0.950076	−	0.312020i	$-0.101006\pi$
$318$		0			0
$319$	11.4797	−	6.62781i	0.642740	−	0.371086i
$320$		−	3.05596i		−	0.170833i
$321$		0			0
$322$	1.53130	−	2.65229i	0.0853359	−	0.147806i
$323$	4.22722	+	2.44058i	0.235209	+	0.135798i
$324$		0			0
$325$	−14.1124	−	6.75118i	−0.782818	−	0.374488i
$326$	8.87831			0.491724
$327$		0			0
$328$	−4.98127	+	8.62781i	−0.275045	+	0.476391i
$329$	−4.02224	−	6.96672i	−0.221753	−	0.384087i
$330$		0			0
$331$	12.6854	−	7.32391i	0.697252	−	0.402559i	−0.109071	−	0.994034i	$-0.534788\pi$
$331$	12.6854	−	7.32391i	0.697252	−	0.402559i	0.806323	+	0.591475i	$0.201454\pi$
$332$	6.19961	−	3.57934i	0.340248	−	0.196442i
$333$		0			0
$334$	−4.88494	−	8.46097i	−0.267292	−	0.462964i
$335$	−7.25875	+	12.5725i	−0.396588	+	0.686910i
$336$		0			0
$337$	−27.5456			−1.50050			−0.750251	−	0.661153i	$-0.770068\pi$
$337$	−27.5456			−1.50050			−0.750251	+	0.661153i	$0.770068\pi$
$338$	−2.00418	−	12.8446i	−0.109013	−	0.698653i
$339$		0			0
$340$	−7.48701	−	4.32263i	−0.406040	−	0.234427i
$341$	1.68401	−	2.91678i	0.0911940	−	0.157953i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.61681	+	1.51082i	−0.141089	+	0.0814577i
$345$		0			0
$346$			8.67525i			0.466384i
$347$	2.62073	+	4.53924i	0.140688	+	0.243679i	0.927756	−	0.373187i	$-0.121735\pi$
$347$	2.62073	+	4.53924i	0.140688	+	0.243679i	−0.787068	+	0.616867i	$0.788402\pi$
$348$		0			0
$349$	−4.52901	−	2.61482i	−0.242432	−	0.139968i	0.373862	−	0.927484i	$-0.378033\pi$
$349$	−4.52901	−	2.61482i	−0.242432	−	0.139968i	−0.616294	+	0.787516i	$0.711367\pi$
$350$	4.33891			0.231924
$351$		0			0
$352$	3.44247			0.183484
$353$	−3.26227	−	1.88348i	−0.173633	−	0.100247i	0.410665	−	0.911786i	$-0.365297\pi$
$353$	−3.26227	−	1.88348i	−0.173633	−	0.100247i	−0.584298	+	0.811539i	$0.698630\pi$
$354$		0			0
$355$	5.60686	+	9.71136i	0.297581	+	0.515425i
$356$			7.90307i			0.418862i
$357$		0			0
$358$	−20.2891	+	11.7139i	−1.07231	+	0.619100i
$359$		−	20.6003i		−	1.08724i	−0.839330	−	0.543622i	$-0.817053\pi$
$359$		−	20.6003i		−	1.08724i	0.839330	−	0.543622i	$-0.182947\pi$
$360$		0			0
$361$	−8.01147	+	13.8763i	−0.421656	+	0.730330i
$362$	−6.63923	−	3.83316i	−0.348950	−	0.201466i
$363$		0			0
$364$	2.03880	+	2.97377i	0.106862	+	0.155868i
$365$	−30.9017			−1.61747
$366$		0			0
$367$	13.9579	−	24.1759i	0.728598	−	1.26197i	−0.228877	−	0.973455i	$-0.573505\pi$
$367$	13.9579	−	24.1759i	0.728598	−	1.26197i	0.957476	−	0.288514i	$-0.0931612\pi$
$368$	−1.53130	−	2.65229i	−0.0798245	−	0.138260i
$369$		0			0
$370$	14.0084	−	8.08773i	0.728260	−	0.420461i
$371$	7.21750	−	4.16702i	0.374714	−	0.216341i
$372$		0			0
$373$	−15.7091	−	27.2090i	−0.813388	−	1.40883i	−0.910479	−	0.413554i	$-0.864287\pi$
$373$	−15.7091	−	27.2090i	−0.813388	−	1.40883i	0.0970910	−	0.995276i	$-0.469046\pi$
$374$	4.86934	−	8.43395i	0.251788	−	0.436109i
$375$		0			0
$376$	−8.04447			−0.414862
$377$	11.4508	−	7.85061i	0.589748	−	0.404327i
$378$		0			0
$379$	−27.5747	−	15.9203i	−1.41642	−	0.817770i	−0.420437	−	0.907322i	$-0.638123\pi$
$379$	−27.5747	−	15.9203i	−1.41642	−	0.817770i	−0.995982	+	0.0895514i	$0.971457\pi$
$380$	−2.63640	+	4.56638i	−0.135245	+	0.234251i
$381$		0			0
$382$		−	25.4945i		−	1.30441i
$383$	4.08962	−	2.36114i	0.208970	−	0.120649i	−0.391863	−	0.920024i	$-0.628169\pi$
$383$	4.08962	−	2.36114i	0.208970	−	0.120649i	0.600832	+	0.799375i	$0.294836\pi$
$384$		0			0
$385$			10.5201i			0.536152i
$386$	4.26293	+	7.38361i	0.216977	+	0.375816i
$387$		0			0
$388$	−7.88016	−	4.54961i	−0.400054	−	0.230972i
$389$	30.5902			1.55099			0.775493	−	0.631356i	$-0.217501\pi$
$389$	30.5902			1.55099			0.775493	+	0.631356i	$0.217501\pi$
$390$		0			0
$391$	−8.66403			−0.438159
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	11.8411	+	20.5094i	0.596547	+	1.03325i
$395$		−	13.7470i		−	0.691689i
$396$		0			0
$397$	10.1133	−	5.83891i	0.507571	−	0.293046i	−0.224264	−	0.974529i	$-0.571998\pi$
$397$	10.1133	−	5.83891i	0.507571	−	0.293046i	0.731835	+	0.681482i	$0.238664\pi$
$398$			24.8466i			1.24545i
$399$		0			0
$400$	2.16945	−	3.75760i	0.108473	−	0.187880i
$401$	−8.01677	−	4.62849i	−0.400339	−	0.231136i	0.286292	−	0.958143i	$-0.407577\pi$
$401$	−8.01677	−	4.62849i	−0.400339	−	0.231136i	−0.686630	+	0.727007i	$0.740911\pi$
$402$		0			0
$403$	1.52231	−	3.18218i	0.0758315	−	0.158516i
$404$	−18.8533			−0.937985
$405$		0			0
$406$	−1.92531	+	3.33473i	−0.0955513	+	0.165500i
$407$	9.11064	+	15.7801i	0.451598	+	0.782190i
$408$		0			0
$409$	−22.1693	+	12.7994i	−1.09620	+	0.632891i	−0.935220	−	0.354066i	$-0.884799\pi$
$409$	−22.1693	+	12.7994i	−1.09620	+	0.632891i	−0.160980	+	0.986958i	$0.551465\pi$
$410$	−26.3663	+	15.2226i	−1.30214	+	0.751789i
$411$		0			0
$412$	−6.85393	−	11.8714i	−0.337669	−	0.584860i
$413$	−4.98877	+	8.64080i	−0.245481	+	0.425186i
$414$		0			0
$415$	21.8767			1.07388
$416$	3.59476	−	0.278764i	0.176248	−	0.0136675i
$417$		0			0
$418$	−5.14393	−	2.96985i	−0.251598	−	0.145260i
$419$	14.1018	−	24.4251i	0.688920	−	1.19324i	−0.283268	−	0.959041i	$-0.591419\pi$
$419$	14.1018	−	24.4251i	0.688920	−	1.19324i	0.972188	−	0.234203i	$-0.0752481\pi$
$420$		0			0
$421$			5.07012i			0.247102i	0.992338	+	0.123551i	$0.0394283\pi$
$421$			5.07012i			0.247102i	−0.992338	+	0.123551i	$0.960572\pi$
$422$	0.669453	−	0.386509i	0.0325885	−	0.0188150i
$423$		0			0
$424$		−	8.33405i		−	0.404737i
$425$	−6.13734	−	10.6302i	−0.297705	−	0.515640i
$426$		0			0
$427$	9.99843	+	5.77260i	0.483858	+	0.279356i
$428$	−3.31471			−0.160223
$429$		0			0
$430$	−9.23399			−0.445302
$431$	13.9808	+	8.07185i	0.673434	+	0.388807i	0.797376	−	0.603482i	$-0.206221\pi$
$431$	13.9808	+	8.07185i	0.673434	+	0.388807i	−0.123943	+	0.992289i	$0.539554\pi$
$432$		0			0
$433$	−11.3014	−	19.5747i	−0.543113	−	0.940699i	−0.998723	−	0.0505195i	$-0.983912\pi$
$433$	−11.3014	−	19.5747i	−0.543113	−	0.940699i	0.455610	−	0.890179i	$-0.349421\pi$
$434$			0.978370i			0.0469633i
$435$		0			0
$436$	−7.51299	+	4.33762i	−0.359807	+	0.207735i
$437$			5.28425i			0.252780i
$438$		0			0
$439$	14.1486	−	24.5060i	0.675273	−	1.16961i	−0.301115	−	0.953588i	$-0.597359\pi$
$439$	14.1486	−	24.5060i	0.675273	−	1.16961i	0.976389	−	0.216020i	$-0.0693077\pi$
$440$	9.11064	+	5.26003i	0.434333	+	0.250762i
$441$		0			0
$442$	4.40179	−	9.20136i	0.209372	−	0.437664i
$443$	1.38096			0.0656112			0.0328056	−	0.999462i	$-0.489556\pi$
$443$	1.38096			0.0656112			0.0328056	+	0.999462i	$0.489556\pi$
$444$		0			0
$445$	−12.0757	+	20.9158i	−0.572445	+	0.991504i
$446$	10.7677	+	18.6502i	0.509866	+	0.883114i
$447$		0			0
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	32.0480	−	18.5029i	1.51244	−	0.873208i	0.512547	−	0.858659i	$-0.328702\pi$
$449$	32.0480	−	18.5029i	1.51244	−	0.873208i	0.999894	−	0.0145487i	$-0.00463115\pi$
$450$		0			0
$451$	−17.1479	−	29.7010i	−0.807462	−	1.39856i
$452$	5.60557	−	9.70914i	0.263664	−	0.456679i
$453$		0			0
$454$	17.5444			0.823398
$455$	0.851893	+	10.9854i	0.0399374	+	0.515006i
$456$		0			0
$457$	12.0530	+	6.95878i	0.563813	+	0.325518i	0.754675	−	0.656099i	$-0.227795\pi$
$457$	12.0530	+	6.95878i	0.563813	+	0.325518i	−0.190861	+	0.981617i	$0.561128\pi$
$458$	5.16109	−	8.93928i	0.241162	−	0.417705i
$459$		0			0
$460$		−	9.35918i		−	0.436374i
$461$	−4.19845	+	2.42397i	−0.195541	+	0.112896i	−0.594574	−	0.804041i	$-0.702679\pi$
$461$	−4.19845	+	2.42397i	−0.195541	+	0.112896i	0.399033	+	0.916937i	$0.369346\pi$
$462$		0			0
$463$			24.4377i			1.13571i	0.823127	+	0.567857i	$0.192227\pi$
$463$			24.4377i			1.13571i	−0.823127	+	0.567857i	$0.807773\pi$
$464$	1.92531	+	3.33473i	0.0893801	+	0.154811i
$465$		0			0
$466$	−15.4404	−	8.91449i	−0.715260	−	0.412956i
$467$	36.0027			1.66600			0.833002	−	0.553270i	$-0.186620\pi$
$467$	36.0027			1.66600			0.833002	+	0.553270i	$0.186620\pi$
$468$		0			0
$469$	4.75055			0.219360
$470$	−21.2900	−	12.2918i	−0.982035	−	0.566978i
$471$		0			0
$472$	4.98877	+	8.64080i	0.229627	+	0.397725i
$473$		−	10.4019i		−	0.478279i
$474$		0			0
$475$	−6.48343	+	3.74321i	−0.297480	+	0.171750i
$476$			2.82898i			0.129666i
$477$		0			0
$478$	−2.85636	+	4.94735i	−0.130647	+	0.226287i
$479$	8.22108	+	4.74644i	0.375631	+	0.216870i	0.675915	−	0.736979i	$-0.263748\pi$
$479$	8.22108	+	4.74644i	0.375631	+	0.216870i	−0.300285	+	0.953850i	$0.597082\pi$
$480$		0			0
$481$	10.7915	+	15.7404i	0.492051	+	0.717701i
$482$	−1.00313			−0.0456914
$483$		0			0
$484$	−0.425305	+	0.736650i	−0.0193321	+	0.0334841i
$485$	−13.9034	−	24.0815i	−0.631323	−	1.09348i
$486$		0			0
$487$	−35.4383	+	20.4603i	−1.60586	+	0.927144i	−0.615578	+	0.788076i	$0.711078\pi$
$487$	−35.4383	+	20.4603i	−1.60586	+	0.927144i	−0.990283	+	0.139069i	$0.955589\pi$
$488$	9.99843	−	5.77260i	0.452608	−	0.261313i
$489$		0			0
$490$	−1.52798	−	2.64654i	−0.0690272	−	0.119559i
$491$	2.55753	−	4.42977i	0.115420	−	0.199913i	−0.802528	−	0.596615i	$-0.796512\pi$
$491$	2.55753	−	4.42977i	0.115420	−	0.199913i	0.917947	+	0.396702i	$0.129845\pi$
$492$		0			0
$493$	10.8933			0.490610
$494$	−5.61197	−	2.68468i	−0.252495	−	0.120790i
$495$		0			0
$496$	0.847293	+	0.489185i	0.0380446	+	0.0219651i
$497$	1.83473	−	3.17784i	0.0822987	−	0.142546i
$498$		0			0
$499$			19.5827i			0.876640i	0.898819	+	0.438320i	$0.144426\pi$
$499$			19.5827i			0.876640i	−0.898819	+	0.438320i	$0.855574\pi$
$500$	−1.74961	+	1.01014i	−0.0782450	+	0.0451747i
$501$		0			0
$502$		−	0.672585i		−	0.0300189i
$503$	−14.5429	−	25.1890i	−0.648436	−	1.12312i	−0.983496	−	0.180928i	$-0.942090\pi$
$503$	−14.5429	−	25.1890i	−0.648436	−	1.12312i	0.335060	−	0.942197i	$-0.391243\pi$
$504$		0			0
$505$	−49.8960	−	28.8075i	−2.22034	−	1.28191i
$506$	10.5429			0.468689
$507$		0			0
$508$	5.11506			0.226944
$509$	4.52051	+	2.60992i	0.200368	+	0.115682i	0.596827	−	0.802370i	$-0.296428\pi$
$509$	4.52051	+	2.60992i	0.200368	+	0.115682i	−0.396459	+	0.918052i	$0.629761\pi$
$510$		0			0
$511$	5.05596	+	8.75718i	0.223663	+	0.387395i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	21.0820	−	12.1717i	0.929885	−	0.536870i
$515$		−	41.8907i		−	1.84592i
$516$		0			0
$517$	13.8464	−	23.9827i	0.608965	−	1.05476i
$518$	−4.58394	−	2.64654i	−0.201407	−	0.116282i
$519$		0			0
$520$	9.93962	+	4.75496i	0.435881	+	0.208519i
$521$	14.5259			0.636389			0.318195	−	0.948025i	$-0.396923\pi$
$521$	14.5259			0.636389			0.318195	+	0.948025i	$0.396923\pi$
$522$		0			0
$523$	−13.9367	+	24.1391i	−0.609410	+	1.05553i	0.381927	+	0.924192i	$0.375260\pi$
$523$	−13.9367	+	24.1391i	−0.609410	+	1.05553i	−0.991338	+	0.131337i	$0.958073\pi$
$524$	9.38784	+	16.2602i	0.410110	+	0.710331i
$525$		0			0
$526$	14.8029	−	8.54648i	0.645439	−	0.372644i
$527$	2.39698	−	1.38389i	0.104414	−	0.0602834i
$528$		0			0
$529$	6.81025	+	11.7957i	0.296098	+	0.512856i
$530$	12.7343	−	22.0564i	0.553141	−	0.958069i
$531$		0			0
$532$	1.72542			0.0748063
$533$	−20.3116	−	29.6263i	−0.879792	−	1.28326i
$534$		0			0
$535$	−8.77252	−	5.06482i	−0.379269	−	0.218971i
$536$	2.37527	−	4.11410i	0.102596	−	0.177702i
$537$		0			0
$538$			26.6594i			1.14937i
$539$	2.98127	−	1.72124i	0.128412	−	0.0741389i
$540$		0			0
$541$		−	1.42341i		−	0.0611970i	−0.999532	−	0.0305985i	$-0.990259\pi$
$541$		−	1.42341i		−	0.0611970i	0.999532	−	0.0305985i	$-0.00974133\pi$
$542$	−12.2247	−	21.1739i	−0.525097	−	0.909496i
$543$		0			0
$544$	2.44997	+	1.41449i	0.105042	+	0.0606458i
$545$	−26.5112			−1.13562
$546$		0			0
$547$	−9.33008			−0.398925			−0.199463	−	0.979905i	$-0.563920\pi$
$547$	−9.33008			−0.398925			−0.199463	+	0.979905i	$0.563920\pi$
$548$	−2.30457	−	1.33055i	−0.0984465	−	0.0568381i
$549$		0			0
$550$	7.46828	+	12.9354i	0.318449	+	0.551569i
$551$		−	6.64390i		−	0.283040i
$552$		0			0
$553$	−3.89576	+	2.24922i	−0.165664	+	0.0956464i
$554$			28.4812i			1.21005i
$555$		0			0
$556$	−8.35322	+	14.4682i	−0.354256	+	0.613589i
$557$	−9.34071	−	5.39286i	−0.395779	−	0.228503i	0.288882	−	0.957365i	$-0.406716\pi$
$557$	−9.34071	−	5.39286i	−0.395779	−	0.228503i	−0.684661	+	0.728862i	$0.740050\pi$
$558$		0			0
$559$	−0.842322	−	10.8620i	−0.0356264	−	0.459415i
$560$	−3.05596			−0.129138
$561$		0			0
$562$	−4.88016	+	8.45268i	−0.205857	+	0.356555i
$563$	−12.7541	−	22.0908i	−0.537522	−	0.931016i	−0.999037	−	0.0438831i	$-0.986027\pi$
$563$	−12.7541	−	22.0908i	−0.537522	−	0.931016i	0.461514	−	0.887133i	$-0.347306\pi$
$564$		0			0
$565$	29.6708	−	17.1304i	1.24826	−	0.720682i
$566$	−10.1076	+	5.83562i	−0.424853	+	0.245289i
$567$		0			0
$568$	−1.83473	−	3.17784i	−0.0769834	−	0.133339i
$569$	4.10835	−	7.11587i	0.172231	−	0.298313i	−0.766969	−	0.641685i	$-0.778236\pi$
$569$	4.10835	−	7.11587i	0.172231	−	0.298313i	0.939200	+	0.343372i	$0.111569\pi$
$570$		0			0
$571$	2.70500			0.113201			0.0566003	−	0.998397i	$-0.481974\pi$
$571$	2.70500			0.113201			0.0566003	+	0.998397i	$0.481974\pi$
$572$	−5.35636	+	11.1968i	−0.223961	+	0.468160i
$573$		0			0
$574$	8.62781	+	4.98127i	0.360118	+	0.207914i
$575$	6.64416	−	11.5080i	0.277081	−	0.479918i
$576$		0			0
$577$			21.4253i			0.891946i	0.895046	+	0.445973i	$0.147142\pi$
$577$			21.4253i			0.891946i	−0.895046	+	0.445973i	$0.852858\pi$
$578$	−7.79152	+	4.49843i	−0.324084	+	0.187110i
$579$		0			0
$580$			11.7673i			0.488611i
$581$	−3.57934	−	6.19961i	−0.148496	−	0.257203i
$582$		0			0
$583$	24.8460	+	14.3449i	1.02902	+	0.594104i
$584$	10.1119			0.418434
$585$		0			0
$586$	21.8202			0.901382
$587$	4.96515	+	2.86663i	0.204934	+	0.118319i	0.598955	−	0.800783i	$-0.295583\pi$
$587$	4.96515	+	2.86663i	0.204934	+	0.118319i	−0.394021	+	0.919101i	$0.628916\pi$
$588$		0			0
$589$	−0.844048	−	1.46193i	−0.0347784	−	0.0602379i
$590$			30.4910i			1.25529i
$591$		0			0
$592$	−4.58394	+	2.64654i	−0.188399	+	0.108772i
$593$			17.3442i			0.712240i	0.934440	+	0.356120i	$0.115901\pi$
$593$			17.3442i			0.712240i	−0.934440	+	0.356120i	$0.884099\pi$
$594$		0			0
$595$	−4.32263	+	7.48701i	−0.177211	+	0.306938i
$596$	−2.16642	−	1.25078i	−0.0887400	−	0.0512341i
$597$		0			0
$598$	11.0093	−	0.853743i	0.450204	−	0.0349121i
$599$	31.5835			1.29047			0.645234	−	0.763985i	$-0.276760\pi$
$599$	31.5835			1.29047			0.645234	+	0.763985i	$0.276760\pi$
$600$		0			0
$601$	−12.4478	+	21.5603i	−0.507757	+	0.879462i	0.492202	+	0.870481i	$0.336192\pi$
$601$	−12.4478	+	21.5603i	−0.507757	+	0.879462i	−0.999960	+	0.00898069i	$0.997141\pi$
$602$	1.51082	+	2.61681i	0.0615762	+	0.106653i
$603$		0			0
$604$	10.9522	−	6.32323i	0.445637	−	0.257289i
$605$	−2.25118	+	1.29972i	−0.0915233	+	0.0528410i
$606$		0			0
$607$	−7.62951	−	13.2147i	−0.309672	−	0.536368i	0.668618	−	0.743606i	$-0.266886\pi$
$607$	−7.62951	−	13.2147i	−0.309672	−	0.536368i	−0.978291	+	0.207238i	$0.933553\pi$
$608$	0.862708	−	1.49425i	0.0349874	−	0.0606000i
$609$		0			0
$610$	35.2817			1.42851
$611$	12.5169	−	26.1649i	0.506379	−	1.05852i
$612$		0			0
$613$	−39.6220	−	22.8757i	−1.60032	−	0.923943i	−0.991423	−	0.130690i	$-0.958281\pi$
$613$	−39.6220	−	22.8757i	−1.60032	−	0.923943i	−0.608892	−	0.793253i	$-0.708386\pi$
$614$	−2.43523	+	4.21794i	−0.0982779	+	0.170222i
$615$		0			0
$616$		−	3.44247i		−	0.138701i
$617$	−36.6167	+	21.1406i	−1.47413	+	0.851090i	−0.999575	−	0.0291358i	$-0.990724\pi$
$617$	−36.6167	+	21.1406i	−1.47413	+	0.851090i	−0.474555	+	0.880226i	$0.657391\pi$
$618$		0			0
$619$			22.0261i			0.885303i	0.896694	+	0.442651i	$0.145962\pi$
$619$			22.0261i			0.885303i	−0.896694	+	0.442651i	$0.854038\pi$
$620$	1.49493	+	2.58930i	0.0600379	+	0.103989i
$621$		0			0
$622$	−3.38048	−	1.95172i	−0.135545	−	0.0782569i
$623$	7.90307			0.316630
$624$		0			0
$625$	−27.8684			−1.11474
$626$	−22.5624	−	13.0264i	−0.901775	−	0.520640i
$627$		0			0
$628$	8.90657	+	15.4266i	0.355411	+	0.615590i
$629$			14.9740i			0.597054i
$630$		0			0
$631$	18.0721	−	10.4339i	0.719440	−	0.415369i	−0.0951064	−	0.995467i	$-0.530319\pi$
$631$	18.0721	−	10.4339i	0.719440	−	0.415369i	0.814547	+	0.580098i	$0.196986\pi$
$632$			4.49843i			0.178938i
$633$		0			0
$634$	−5.55536	+	9.62216i	−0.220631	+	0.382145i
$635$	13.5372	+	7.81571i	0.537208	+	0.310157i
$636$		0			0
$637$	2.97377	−	2.03880i	0.117825	−	0.0807800i
$638$	−13.2556			−0.524795
$639$		0			0
$640$	−1.52798	+	2.64654i	−0.0603988	+	0.104614i
$641$	10.4526	+	18.1045i	0.412853	+	0.715083i	0.995200	−	0.0978574i	$-0.0311989\pi$
$641$	10.4526	+	18.1045i	0.412853	+	0.715083i	−0.582347	+	0.812940i	$0.697866\pi$
$642$		0			0
$643$	33.8703	−	19.5550i	1.33571	−	0.771174i	0.349544	−	0.936920i	$-0.386337\pi$
$643$	33.8703	−	19.5550i	1.33571	−	0.771174i	0.986168	+	0.165746i	$0.0530032\pi$
$644$	−2.65229	+	1.53130i	−0.104515	+	0.0603416i
$645$		0			0
$646$	−2.44058	−	4.22722i	−0.0960235	−	0.166318i
$647$	3.96755	−	6.87201i	0.155981	−	0.270166i	−0.777435	−	0.628963i	$-0.783480\pi$
$647$	3.96755	−	6.87201i	0.155981	−	0.270166i	0.933416	+	0.358797i	$0.116813\pi$
$648$		0			0
$649$	−34.3474			−1.34825
$650$	8.84615	+	12.9029i	0.346974	+	0.506094i
$651$		0			0
$652$	−7.68884	−	4.43915i	−0.301118	−	0.173851i
$653$	21.3998	−	37.0655i	0.837439	−	1.45049i	−0.0545901	−	0.998509i	$-0.517385\pi$
$653$	21.3998	−	37.0655i	0.837439	−	1.45049i	0.892029	−	0.451978i	$-0.149281\pi$
$654$		0			0
$655$			57.3778i			2.24194i
$656$	8.62781	−	4.98127i	0.336859	−	0.194486i
$657$		0			0
$658$			8.04447i			0.313606i
$659$	0.364274	+	0.630941i	0.0141901	+	0.0245780i	0.873033	−	0.487661i	$-0.162150\pi$
$659$	0.364274	+	0.630941i	0.0141901	+	0.0245780i	−0.858843	+	0.512239i	$0.828816\pi$
$660$		0			0
$661$	−2.04352	−	1.17983i	−0.0794836	−	0.0458899i	0.459731	−	0.888058i	$-0.347946\pi$
$661$	−2.04352	−	1.17983i	−0.0794836	−	0.0458899i	−0.539215	+	0.842168i	$0.681279\pi$
$662$	−14.6478			−0.569304
$663$		0			0
$664$	−7.15869			−0.277811
$665$	4.56638	+	2.63640i	0.177077	+	0.102235i
$666$		0			0
$667$	5.89644	+	10.2129i	0.228311	+	0.395446i
$668$			9.76989i			0.378008i
$669$		0			0
$670$	12.5725	−	7.25875i	0.485719	−	0.280430i
$671$			39.7440i			1.53430i
$672$		0			0
$673$	15.6279	−	27.0682i	0.602410	−	1.04340i	−0.390045	−	0.920796i	$-0.627541\pi$
$673$	15.6279	−	27.0682i	0.602410	−	1.04340i	0.992455	−	0.122609i	$-0.0391260\pi$
$674$	23.8552	+	13.7728i	0.918867	+	0.530508i
$675$		0			0
$676$	−4.68662	+	12.1258i	−0.180255	+	0.466378i
$677$	41.7294			1.60379			0.801895	−	0.597464i	$-0.203825\pi$
$677$	41.7294			1.60379			0.801895	+	0.597464i	$0.203825\pi$
$678$		0			0
$679$	−4.54961	+	7.88016i	−0.174598	+	0.302413i
$680$	4.32263	+	7.48701i	0.165765	+	0.287114i
$681$		0			0
$682$	−2.91678	+	1.68401i	−0.111689	+	0.0644839i
$683$	7.98473	−	4.60999i	0.305527	−	0.176396i	−0.339396	−	0.940644i	$-0.610223\pi$
$683$	7.98473	−	4.60999i	0.305527	−	0.176396i	0.644923	+	0.764247i	$0.276889\pi$
$684$		0			0
$685$	−4.06610	−	7.04269i	−0.155358	−	0.269087i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	3.02163			0.115199
$689$	27.1068	+	12.9675i	1.03269	+	0.494021i
$690$		0			0
$691$	−7.97487	−	4.60429i	−0.303378	−	0.175156i	0.340581	−	0.940215i	$-0.389376\pi$
$691$	−7.97487	−	4.60429i	−0.303378	−	0.175156i	−0.643960	+	0.765060i	$0.722709\pi$
$692$	4.33762	−	7.51299i	0.164892	−	0.285601i
$693$		0			0
$694$		−	5.24146i		−	0.198963i
$695$	−44.2143	+	25.5271i	−1.67714	+	0.968300i
$696$		0			0
$697$		−	28.1838i		−	1.06754i
$698$	2.61482	+	4.52901i	0.0989725	+	0.171425i
$699$		0			0
$700$	−3.75760	−	2.16945i	−0.142024	−	0.0819976i
$701$	−20.8683			−0.788184			−0.394092	−	0.919071i	$-0.628941\pi$
$701$	−20.8683			−0.788184			−0.394092	+	0.919071i	$0.628941\pi$
$702$		0			0
$703$	9.13277			0.344449
$704$	−2.98127	−	1.72124i	−0.112361	−	0.0648715i
$705$		0			0
$706$	1.88348	+	3.26227i	0.0708855	+	0.122777i
$707$			18.8533i			0.709050i
$708$		0			0
$709$	−12.8731	+	7.43226i	−0.483458	+	0.279124i	−0.721856	−	0.692043i	$-0.756711\pi$
$709$	−12.8731	+	7.43226i	−0.483458	+	0.279124i	0.238399	+	0.971167i	$0.423378\pi$
$710$		−	11.2137i		−	0.420843i
$711$		0			0
$712$	3.95154	−	6.84426i	0.148090	−	0.256499i
$713$	2.59492	+	1.49818i	0.0971804	+	0.0561072i
$714$		0			0
$715$	−31.2843	+	21.4483i	−1.16996	+	0.802120i
$716$	23.4278			0.875540
$717$		0			0
$718$	−10.3002	+	17.8404i	−0.384399	+	0.665798i
$719$	12.8265	+	22.2162i	0.478349	+	0.828524i	0.999692	−	0.0248229i	$-0.00790218\pi$
$719$	12.8265	+	22.2162i	0.478349	+	0.828524i	−0.521343	+	0.853347i	$0.674569\pi$
$720$		0			0
$721$	−11.8714	+	6.85393i	−0.442112	+	0.255254i
$722$	13.8763	−	8.01147i	0.516421	−	0.298156i
$723$		0			0
$724$	3.83316	+	6.63923i	0.142458	+	0.246745i
$725$	−8.35372	+	14.4691i	−0.310249	+	0.537368i
$726$		0			0
$727$	41.6568			1.54497			0.772483	−	0.635036i	$-0.219015\pi$
$727$	41.6568			1.54497			0.772483	+	0.635036i	$0.219015\pi$
$728$	−0.278764	−	3.59476i	−0.0103317	−	0.133231i
$729$		0			0
$730$	26.7616	+	15.4508i	0.990492	+	0.571861i
$731$	4.27407	−	7.40290i	0.158082	−	0.273806i
$732$		0			0
$733$		−	26.4965i		−	0.978671i	−0.872096	−	0.489336i	$-0.837239\pi$
$733$		−	26.4965i		−	0.978671i	0.872096	−	0.489336i	$-0.162761\pi$
$734$	−24.1759	+	13.9579i	−0.892347	+	0.515197i
$735$		0			0
$736$			3.06260i			0.112889i
$737$	8.17682	+	14.1627i	0.301197	+	0.521688i
$738$		0			0
$739$	18.1009	+	10.4506i	0.665853	+	0.384431i	0.794504	−	0.607259i	$-0.207731\pi$
$739$	18.1009	+	10.4506i	0.665853	+	0.384431i	−0.128650	+	0.991690i	$0.541064\pi$
$740$	−16.1755			−0.594622
$741$		0			0
$742$	−8.33405			−0.305953
$743$	−4.88999	−	2.82323i	−0.179396	−	0.103574i	0.407613	−	0.913155i	$-0.366361\pi$
$743$	−4.88999	−	2.82323i	−0.179396	−	0.103574i	−0.587009	+	0.809580i	$0.699695\pi$
$744$		0			0
$745$	−3.82235	−	6.62050i	−0.140040	−	0.242556i
$746$			31.4183i			1.15030i
$747$		0			0
$748$	−8.43395	+	4.86934i	−0.308376	+	0.178041i
$749$			3.31471i			0.121117i
$750$		0			0
$751$	7.70439	−	13.3444i	0.281137	−	0.486944i	−0.690528	−	0.723306i	$-0.742622\pi$
$751$	7.70439	−	13.3444i	0.281137	−	0.486944i	0.971665	+	0.236362i	$0.0759551\pi$
$752$	6.96672	+	4.02224i	0.254050	+	0.146676i
$753$		0			0
$754$	−13.8420	+	1.07341i	−0.504097	+	0.0390914i
$755$	38.6471			1.40651
$756$		0			0
$757$	17.7686	−	30.7761i	0.645811	−	1.11858i	−0.338303	−	0.941037i	$-0.609853\pi$
$757$	17.7686	−	30.7761i	0.645811	−	1.11858i	0.984114	−	0.177540i	$-0.0568139\pi$
$758$	15.9203	+	27.5747i	0.578251	+	1.00156i
$759$		0			0
$760$	4.56638	−	2.63640i	0.165640	−	0.0956324i
$761$	−36.2213	+	20.9124i	−1.31302	+	0.758073i	−0.982595	−	0.185759i	$-0.940526\pi$
$761$	−36.2213	+	20.9124i	−1.31302	+	0.758073i	−0.330425	+	0.943832i	$0.607192\pi$
$762$		0			0
$763$	4.33762	+	7.51299i	0.157033	+	0.271988i
$764$	−12.7472	+	22.0789i	−0.461179	+	0.798785i
$765$		0			0
$766$	−4.72228			−0.170623
$767$	−35.8668	+	2.78138i	−1.29508	+	0.100430i
$768$		0			0
$769$	15.4609	+	8.92635i	0.557534	+	0.321893i	0.752155	−	0.658986i	$-0.229014\pi$
$769$	15.4609	+	8.92635i	0.557534	+	0.321893i	−0.194621	+	0.980879i	$0.562348\pi$
$770$	5.26003	−	9.11064i	0.189558	−	0.328325i
$771$		0			0
$772$		−	8.52586i		−	0.306852i
$773$	−10.4892	+	6.05596i	−0.377272	+	0.217818i	−0.676630	−	0.736323i	$-0.736561\pi$
$773$	−10.4892	+	6.05596i	−0.377272	+	0.217818i	0.299359	+	0.954141i	$0.403227\pi$
$774$		0			0
$775$			4.24506i			0.152487i
$776$	4.54961	+	7.88016i	0.163322	+	0.282881i
$777$		0			0
$778$	−26.4919	−	15.2951i	−0.949781	−	0.548357i
$779$	−17.1895			−0.615878
$780$		0			0
$781$	12.6320			0.452008
$782$	7.50327	+	4.33201i	0.268316	+	0.154913i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			54.4363i			1.94292i
$786$		0			0
$787$	27.7604	−	16.0275i	0.989551	−	0.571317i	0.0844108	−	0.996431i	$-0.473099\pi$
$787$	27.7604	−	16.0275i	0.989551	−	0.571317i	0.905140	+	0.425114i	$0.139766\pi$
$788$		−	23.6823i		−	0.843645i
$789$		0			0
$790$	−6.87352	+	11.9053i	−0.244549	+	0.423571i
$791$	−9.70914	−	5.60557i	−0.345217	−	0.199311i
$792$		0			0
$793$	3.21839	+	41.5022i	0.114288	+	1.47379i
$794$	−11.6778			−0.414430
$795$		0			0
$796$	12.4233	−	21.5178i	0.440333	−	0.762679i
$797$	−4.56545	−	7.90758i	−0.161716	−	0.280101i	0.773768	−	0.633469i	$-0.218370\pi$
$797$	−4.56545	−	7.90758i	−0.161716	−	0.280101i	−0.935484	+	0.353368i	$0.885036\pi$
$798$		0			0
$799$	19.7087	−	11.3788i	0.697244	−	0.402554i
$800$	−3.75760	+	2.16945i	−0.132851	+	0.0767018i
$801$		0			0
$802$	4.62849	+	8.01677i	0.163438	+	0.283082i
$803$	−17.4050	+	30.1464i	−0.614209	+	1.06384i
$804$		0			0
$805$	−9.35918			−0.329868
$806$	−2.90945	+	1.99470i	−0.102481	+	0.0702602i
$807$		0			0
$808$	16.3274	+	9.42664i	0.574396	+	0.331628i
$809$	10.7311	−	18.5869i	0.377287	−	0.653480i	−0.613380	−	0.789788i	$-0.710190\pi$
$809$	10.7311	−	18.5869i	0.377287	−	0.653480i	0.990666	+	0.136308i	$0.0435238\pi$
$810$		0			0
$811$			44.2671i			1.55443i	0.629236	+	0.777214i	$0.283368\pi$
$811$			44.2671i			1.55443i	−0.629236	+	0.777214i	$0.716632\pi$
$812$	3.33473	−	1.92531i	0.117026	−	0.0675650i
$813$		0			0
$814$		−	18.2213i		−	0.638656i
$815$	−13.5659	−	23.4968i	−0.475192	−	0.823057i
$816$		0			0
$817$	−4.51508	−	2.60678i	−0.157963	−	0.0911998i
$818$	25.5989			0.895043
$819$		0			0
$820$	30.4451			1.06319
$821$	8.07131	+	4.65997i	0.281691	+	0.162634i	0.634188	−	0.773178i	$-0.281334\pi$
$821$	8.07131	+	4.65997i	0.281691	+	0.162634i	−0.352498	+	0.935813i	$0.614668\pi$
$822$		0			0
$823$	14.8426	+	25.7082i	0.517381	+	0.896131i	0.999796	+	0.0201878i	$0.00642642\pi$
$823$	14.8426	+	25.7082i	0.517381	+	0.896131i	−0.482415	+	0.875943i	$0.660240\pi$
$824$			13.7079i			0.477536i
$825$		0			0
$826$	8.64080	−	4.98877i	0.300652	−	0.173581i
$827$		−	22.6364i		−	0.787146i	−0.919293	−	0.393573i	$-0.871239\pi$
$827$		−	22.6364i		−	0.787146i	0.919293	−	0.393573i	$-0.128761\pi$
$828$		0			0
$829$	−4.82167	+	8.35138i	−0.167463	+	0.290055i	−0.937527	−	0.347912i	$-0.886891\pi$
$829$	−4.82167	+	8.35138i	−0.167463	+	0.290055i	0.770064	+	0.637967i	$0.220224\pi$
$830$	−18.9458	−	10.9383i	−0.657617	−	0.379675i
$831$		0			0
$832$	−3.25253	−	1.55596i	−0.112761	−	0.0539433i
$833$	2.82898			0.0980184
$834$		0			0
$835$	−14.9282	+	25.8564i	−0.516612	+	0.894798i
$836$	2.96985	+	5.14393i	0.102714	+	0.177906i
$837$		0			0
$838$	−24.4251	+	14.1018i	−0.843751	+	0.487140i
$839$	28.9983	−	16.7422i	1.00113	−	0.578005i	0.0925499	−	0.995708i	$-0.470498\pi$
$839$	28.9983	−	16.7422i	1.00113	−	0.578005i	0.908583	+	0.417704i	$0.137165\pi$
$840$		0			0
$841$	7.08640	+	12.2740i	0.244359	+	0.423241i
$842$	2.53506	−	4.39085i	0.0873639	−	0.151319i
$843$		0			0
$844$	−0.773018			−0.0266084
$845$	−30.9314	+	24.9304i	−1.06407	+	0.857633i
$846$		0			0
$847$	0.736650	+	0.425305i	0.0253116	+	0.0146137i
$848$	−4.16702	+	7.21750i	−0.143096	+	0.247850i
$849$		0			0
$850$			12.2747i			0.421018i
$851$	−14.0388	+	8.10529i	−0.481243	+	0.277846i
$852$		0			0
$853$		−	23.7246i		−	0.812316i	−0.913803	−	0.406158i	$-0.866868\pi$
$853$		−	23.7246i		−	0.812316i	0.913803	−	0.406158i	$-0.133132\pi$
$854$	−5.77260	−	9.99843i	−0.197534	−	0.342139i
$855$		0			0
$856$	2.87063	+	1.65736i	0.0981159	+	0.0566473i
$857$	24.4823			0.836299			0.418149	−	0.908378i	$-0.362679\pi$
$857$	24.4823			0.836299			0.418149	+	0.908378i	$0.362679\pi$
$858$		0			0
$859$	−26.7787			−0.913676			−0.456838	−	0.889550i	$-0.651018\pi$
$859$	−26.7787			−0.913676			−0.456838	+	0.889550i	$0.651018\pi$
$860$	7.99687	+	4.61699i	0.272691	+	0.157438i
$861$		0			0
$862$	−8.07185	−	13.9808i	−0.274928	−	0.476190i
$863$		−	54.8533i		−	1.86723i	−0.358282	−	0.933614i	$-0.616637\pi$
$863$		−	54.8533i		−	1.86723i	0.358282	−	0.933614i	$-0.383363\pi$
$864$		0			0
$865$	22.9594	−	13.2556i	0.780643	−	0.450705i
$866$			22.6029i			0.768077i
$867$		0			0
$868$	0.489185	−	0.847293i	0.0166040	−	0.0287590i
$869$	−13.4110	−	7.74287i	−0.454938	−	0.262659i
$870$		0			0
$871$	9.68540	+	14.1270i	0.328177	+	0.478677i
$872$	8.67525			0.293781
$873$		0			0
$874$	2.64213	−	4.57630i	0.0893713	−	0.154796i
$875$	1.01014	+	1.74961i	0.0341489	+	0.0591476i
$876$		0			0
$877$	4.67626	−	2.69984i	0.157906	−	0.0911671i	−0.418965	−	0.908002i	$-0.637607\pi$
$877$	4.67626	−	2.69984i	0.157906	−	0.0911671i	0.576871	+	0.816835i	$0.304274\pi$
$878$	−24.5060	+	14.1486i	−0.827038	+	0.477490i
$879$		0			0
$880$	−5.26003	−	9.11064i	−0.177316	−	0.307120i
$881$	8.18333	−	14.1739i	0.275703	−	0.477532i	−0.694609	−	0.719387i	$-0.744423\pi$
$881$	8.18333	−	14.1739i	0.275703	−	0.477532i	0.970312	+	0.241855i	$0.0777559\pi$
$882$		0			0
$883$	10.8294			0.364440			0.182220	−	0.983258i	$-0.441672\pi$
$883$	10.8294			0.364440			0.182220	+	0.983258i	$0.441672\pi$
$884$	−8.41274	+	5.76772i	−0.282951	+	0.193989i
$885$		0			0
$886$	−1.19594	−	0.690478i	−0.0401785	−	0.0231971i
$887$	−16.5776	+	28.7133i	−0.556623	+	0.964099i	0.441153	+	0.897432i	$0.354570\pi$
$887$	−16.5776	+	28.7133i	−0.556623	+	0.964099i	−0.997775	+	0.0666668i	$0.978764\pi$
$888$		0			0
$889$		−	5.11506i		−	0.171553i
$890$	20.9158	−	12.0757i	0.701099	−	0.404780i
$891$		0			0
$892$		−	21.5354i		−	0.721060i
$893$	−6.94003	−	12.0205i	−0.232239	−	0.402250i
$894$		0			0
$895$	62.0028	+	35.7973i	2.07252	+	1.19657i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−37.0059			−1.23490
$899$	−3.26260	−	1.88366i	−0.108814	−	0.0628236i
$900$		0			0
$901$	11.7884	+	20.4182i	0.392730	+	0.680228i
$902$			34.2957i			1.14192i
$903$		0			0
$904$	−9.70914	+	5.60557i	−0.322921	+	0.186439i
$905$			23.4280i			0.778773i
$906$		0			0
$907$	15.5349	−	26.9073i	0.515829	−	0.893442i	−0.484002	−	0.875067i	$-0.660817\pi$
$907$	15.5349	−	26.9073i	0.515829	−	0.893442i	0.999831	−	0.0183754i	$-0.00584940\pi$
$908$	−15.1939	−	8.77218i	−0.504226	−	0.291115i
$909$		0			0
$910$	4.75496	−	9.93962i	0.157625	−	0.329495i
$911$	7.26309			0.240637			0.120318	−	0.992735i	$-0.461608\pi$
$911$	7.26309			0.240637			0.120318	+	0.992735i	$0.461608\pi$
$912$		0			0
$913$	12.3218	−	21.3420i	0.407792	−	0.706316i
$914$	−6.95878	−	12.0530i	−0.230176	−	0.398676i
$915$		0			0
$916$	−8.93928	+	5.16109i	−0.295362	+	0.170527i
$917$	16.2602	−	9.38784i	0.536960	−	0.310014i
$918$		0			0
$919$	−17.0863	−	29.5943i	−0.563625	−	0.976226i	−0.997176	−	0.0750977i	$-0.976073\pi$
$919$	−17.0863	−	29.5943i	−0.563625	−	0.976226i	0.433552	−	0.901129i	$-0.357260\pi$
$920$	−4.67959	+	8.10529i	−0.154282	+	0.267224i
$921$		0			0
$922$	4.84795			0.159659
$923$	13.1908	−	1.02291i	0.434180	−	0.0336696i
$924$		0			0
$925$	−19.8893	−	11.4831i	−0.653956	−	0.377562i
$926$	12.2188	−	21.1636i	0.401536	−	0.695480i
$927$		0			0
$928$		−	3.85061i		−	0.126402i
$929$	11.8252	−	6.82728i	0.387972	−	0.223996i	−0.293309	−	0.956018i	$-0.594756\pi$
$929$	11.8252	−	6.82728i	0.387972	−	0.223996i	0.681281	+	0.732022i	$0.261423\pi$
$930$		0			0
$931$		−	1.72542i		−	0.0565482i
$932$	8.91449	+	15.4404i	0.292004	+	0.505765i
$933$		0			0
$934$	−31.1792	−	18.0013i	−1.02022	−	0.589022i
$935$	−29.7611			−0.973291
$936$		0			0
$937$	43.5716			1.42342			0.711712	−	0.702472i	$-0.247920\pi$
$937$	43.5716			1.42342			0.711712	+	0.702472i	$0.247920\pi$
$938$	−4.11410	−	2.37527i	−0.134330	−	0.0775555i
$939$		0			0
$940$	12.2918	+	21.2900i	0.400914	+	0.694404i
$941$			55.8282i			1.81995i	0.414666	+	0.909973i	$0.363898\pi$
$941$			55.8282i			1.81995i	−0.414666	+	0.909973i	$0.636102\pi$
$942$		0			0
$943$	26.4235	−	15.2556i	0.860468	−	0.496791i
$944$		−	9.97753i		−	0.324741i
$945$		0			0
$946$	−5.20094	+	9.00829i	−0.169097	+	0.292885i
$947$	−45.4573	−	26.2448i	−1.47716	−	0.852842i	−0.477497	−	0.878633i	$-0.658456\pi$
$947$	−45.4573	−	26.2448i	−1.47716	−	0.852842i	−0.999667	+	0.0257916i	$0.991789\pi$
$948$		0			0
$949$	−15.7338	+	32.8894i	−0.510740	+	1.06763i
$950$	7.48642			0.242891
$951$		0			0
$952$	1.41449	−	2.44997i	0.0458439	−	0.0794040i
$953$	3.50985	+	6.07925i	0.113695	+	0.196926i	0.917257	−	0.398295i	$-0.130398\pi$
$953$	3.50985	+	6.07925i	0.113695	+	0.196926i	−0.803562	+	0.595221i	$0.797065\pi$
$954$		0			0
$955$	−67.4721	+	38.9551i	−2.18335	+	1.26056i
$956$	4.94735	−	2.85636i	0.160009	−	0.0923812i
$957$		0			0
$958$	−4.74644	−	8.22108i	−0.153351	−	0.265611i
$959$	−1.33055	+	2.30457i	−0.0429656	+	0.0744186i
$960$		0			0
$961$	30.0428			0.969122
$962$	−1.47552	−	19.0274i	−0.0475727	−	0.613467i
$963$		0			0
$964$	0.868738	+	0.501566i	0.0279802	+	0.0161543i
$965$	13.0274	−	22.5640i	0.419365	−	0.726362i
$966$		0			0
$967$		−	36.8770i		−	1.18588i	−0.805245	−	0.592942i	$-0.797966\pi$
$967$		−	36.8770i		−	1.18588i	0.805245	−	0.592942i	$-0.202034\pi$
$968$	0.736650	−	0.425305i	0.0236768	−	0.0136698i
$969$		0			0
$970$			27.8069i			0.892825i
$971$	13.8202	+	23.9372i	0.443511	+	0.768183i	0.997947	−	0.0640432i	$-0.0203996\pi$
$971$	13.8202	+	23.9372i	0.443511	+	0.768183i	−0.554437	+	0.832226i	$0.687066\pi$
$972$		0			0
$973$	14.4682	+	8.35322i	0.463830	+	0.267792i
$974$	40.9206			1.31118
$975$		0			0
$976$	−11.5452			−0.369553
$977$	48.1904	+	27.8227i	1.54175	+	0.890128i	0.998729	+	0.0504061i	$0.0160516\pi$
$977$	48.1904	+	27.8227i	1.54175	+	0.890128i	0.543017	+	0.839721i	$0.317282\pi$
$978$		0			0
$979$	13.6030	+	23.5612i	0.434755	+	0.753018i
$980$			3.05596i			0.0976191i
$981$		0			0
$982$	−4.42977	+	2.55753i	−0.141360	+	0.0816140i
$983$			25.0022i			0.797446i	0.917071	+	0.398723i	$0.130547\pi$
$983$			25.0022i			0.797446i	−0.917071	+	0.398723i	$0.869453\pi$
$984$		0			0
$985$	36.1860	−	62.6761i	1.15298	−	1.99703i
$986$	−9.43388	−	5.44665i	−0.300436	−	0.173457i
$987$		0			0
$988$	3.51777	+	5.13099i	0.111915	+	0.163239i
$989$	9.25404			0.294261
$990$		0			0
$991$	13.6076	−	23.5690i	0.432258	−	0.748694i	−0.564809	−	0.825222i	$-0.691050\pi$
$991$	13.6076	−	23.5690i	0.432258	−	0.748694i	0.997067	+	0.0765281i	$0.0243835\pi$
$992$	−0.489185	−	0.847293i	−0.0155316	−	0.0269016i
$993$		0			0
$994$	−3.17784	+	1.83473i	−0.100795	+	0.0581940i
$995$	65.7577	−	37.9652i	2.08466	−	1.20358i
$996$		0			0
$997$	8.42706	+	14.5961i	0.266888	+	0.462263i	0.968056	−	0.250732i	$-0.0806714\pi$
$997$	8.42706	+	14.5961i	0.266888	+	0.462263i	−0.701169	+	0.712995i	$0.747338\pi$
$998$	9.79133	−	16.9591i	0.309939	−	0.536830i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.f.1135.2		8
3.2	odd	2		546.2.s.e.43.3	✓	8
13.10	even	6	inner	1638.2.bj.f.127.1		8
39.20	even	12		7098.2.a.co.1.3		4
39.23	odd	6		546.2.s.e.127.4	yes	8
39.32	even	12		7098.2.a.cn.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.e.43.3	✓	8	3.2	odd	2
546.2.s.e.127.4	yes	8	39.23	odd	6
1638.2.bj.f.127.1		8	13.10	even	6	inner
1638.2.bj.f.1135.2		8	1.1	even	1	trivial
7098.2.a.cn.1.2		4	39.32	even	12
7098.2.a.co.1.3		4	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.05596i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.05596i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.52798 - 2.64654i) q^{10} +(2.98127 + 1.72124i) q^{11} +(3.25253 + 1.55596i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.41449 + 2.44997i) q^{17} +(1.49425 - 0.862708i) q^{19} +(-2.64654 + 1.52798i) q^{20} +(-1.72124 - 2.98127i) q^{22} +(-1.53130 + 2.65229i) q^{23} -4.33891 q^{25} +(-2.03880 - 2.97377i) q^{26} +(0.866025 + 0.500000i) q^{28} +(1.92531 - 3.33473i) q^{29} -0.978370i q^{31} +(0.866025 - 0.500000i) q^{32} -2.82898i q^{34} +(1.52798 + 2.64654i) q^{35} +(4.58394 + 2.64654i) q^{37} -1.72542 q^{38} +3.05596 q^{40} +(-8.62781 - 4.98127i) q^{41} +(-1.51082 - 2.61681i) q^{43} +3.44247i q^{44} +(2.65229 - 1.53130i) q^{46} -8.04447i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.75760 + 2.16945i) q^{50} +(0.278764 + 3.59476i) q^{52} +8.33405 q^{53} +(-5.26003 + 9.11064i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-3.33473 + 1.92531i) q^{58} +(-8.64080 + 4.98877i) q^{59} +(5.77260 + 9.99843i) q^{61} +(-0.489185 + 0.847293i) q^{62} -1.00000 q^{64} +(-4.75496 + 9.93962i) q^{65} +(4.11410 + 2.37527i) q^{67} +(-1.41449 + 2.44997i) q^{68} -3.05596i q^{70} +(3.17784 - 1.83473i) q^{71} +10.1119i q^{73} +(-2.64654 - 4.58394i) q^{74} +(1.49425 + 0.862708i) q^{76} +3.44247 q^{77} -4.49843 q^{79} +(-2.64654 - 1.52798i) q^{80} +(4.98127 + 8.62781i) q^{82} -7.15869i q^{83} +(-7.48701 + 4.32263i) q^{85} +3.02163i q^{86} +(1.72124 - 2.98127i) q^{88} +(6.84426 + 3.95154i) q^{89} +(3.59476 - 0.278764i) q^{91} -3.06260 q^{92} +(-4.02224 + 6.96672i) q^{94} +(2.63640 + 4.56638i) q^{95} +(-7.88016 + 4.54961i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more