LMFDB - Embedded newform 1638.2.j.t.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

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.j (of order $3$, 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 14x^{8} + 63x^{6} + 110x^{4} + 73x^{2} + 12 $ x^10 + 14x^8 + 63x^6 + 110x^4 + 73x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.3
Root			$2.67094i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.t.1171.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.246138 - 0.426324i) q^{5} +(-0.967934 + 2.46234i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.246138 - 0.426324i) q^{5} +(-0.967934 + 2.46234i) q^{7} -1.00000 q^{8} +(0.246138 - 0.426324i) q^{10} +(-2.23159 + 3.86523i) q^{11} -1.00000 q^{13} +(-2.61641 + 0.392913i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.51752 - 2.62842i) q^{17} +(1.21407 + 2.10283i) q^{19} +0.492276 q^{20} -4.46318 q^{22} +(-0.894617 - 1.54952i) q^{23} +(2.37883 - 4.12026i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-1.64848 - 2.06942i) q^{28} -5.72510 q^{29} +(-3.48545 + 6.03698i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.03504 q^{34} +(1.28800 - 0.193422i) q^{35} +(-2.79572 - 4.84233i) q^{37} +(-1.21407 + 2.10283i) q^{38} +(0.246138 + 0.426324i) q^{40} -4.80468 q^{41} -4.59392 q^{43} +(-2.23159 - 3.86523i) q^{44} +(0.894617 - 1.54952i) q^{46} +(-5.79013 - 10.0288i) q^{47} +(-5.12621 - 4.76676i) q^{49} +4.75766 q^{50} +(0.500000 - 0.866025i) q^{52} +(7.06061 - 12.2293i) q^{53} +2.19712 q^{55} +(0.967934 - 2.46234i) q^{56} +(-2.86255 - 4.95808i) q^{58} +(-4.13269 + 7.15804i) q^{59} +(7.11042 + 12.3156i) q^{61} -6.97090 q^{62} +1.00000 q^{64} +(0.246138 + 0.426324i) q^{65} +(-3.82096 + 6.61810i) q^{67} +(1.51752 + 2.62842i) q^{68} +(0.811507 + 1.01873i) q^{70} -10.6294 q^{71} +(-8.35780 + 14.4761i) q^{73} +(2.79572 - 4.84233i) q^{74} -2.42814 q^{76} +(-7.35746 - 9.23621i) q^{77} +(4.78241 + 8.28338i) q^{79} +(-0.246138 + 0.426324i) q^{80} +(-2.40234 - 4.16098i) q^{82} -0.0831764 q^{83} -1.49408 q^{85} +(-2.29696 - 3.97845i) q^{86} +(2.23159 - 3.86523i) q^{88} +(-1.83049 - 3.17049i) q^{89} +(0.967934 - 2.46234i) q^{91} +1.78923 q^{92} +(5.79013 - 10.0288i) q^{94} +(0.597659 - 1.03518i) q^{95} -4.88840 q^{97} +(1.56503 - 6.82281i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.246138	−	0.426324i	−0.110076	−	0.190658i	0.805725	−	0.592290i	$-0.201776\pi$
$5$	−0.246138	−	0.426324i	−0.110076	−	0.190658i	−0.915801	+	0.401633i	$0.868443\pi$
$6$		0			0
$7$	−0.967934	+	2.46234i	−0.365845	+	0.930676i
$7$	−0.967934	+	2.46234i	−0.365845	+	0.930676i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.246138	−	0.426324i	0.0778357	−	0.134815i
$11$	−2.23159	+	3.86523i	−0.672850	+	1.16541i	0.304243	+	0.952595i	$0.401597\pi$
$11$	−2.23159	+	3.86523i	−0.672850	+	1.16541i	−0.977092	+	0.212815i	$0.931737\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.61641	+	0.392913i	−0.699266	+	0.105010i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.51752	−	2.62842i	0.368052	−	0.637485i	−0.621209	−	0.783645i	$-0.713358\pi$
$17$	1.51752	−	2.62842i	0.368052	−	0.637485i	0.989261	+	0.146160i	$0.0466915\pi$
$18$		0			0
$19$	1.21407	+	2.10283i	0.278527	+	0.482423i	0.971019	−	0.239002i	$-0.0768204\pi$
$19$	1.21407	+	2.10283i	0.278527	+	0.482423i	−0.692492	+	0.721426i	$0.743487\pi$
$20$	0.492276			0.110076
$21$		0			0
$22$	−4.46318			−0.951553
$23$	−0.894617	−	1.54952i	−0.186541	−	0.323098i	0.757554	−	0.652773i	$-0.226394\pi$
$23$	−0.894617	−	1.54952i	−0.186541	−	0.323098i	−0.944095	+	0.329675i	$0.893061\pi$
$24$		0			0
$25$	2.37883	−	4.12026i	0.475766	−	0.824052i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	−1.64848	−	2.06942i	−0.311533	−	0.391084i
$29$	−5.72510			−1.06312			−0.531562	−	0.847019i	$-0.678395\pi$
$29$	−5.72510			−1.06312			−0.531562	+	0.847019i	$0.678395\pi$
$30$		0			0
$31$	−3.48545	+	6.03698i	−0.626006	+	1.08427i	0.362340	+	0.932046i	$0.381978\pi$
$31$	−3.48545	+	6.03698i	−0.626006	+	1.08427i	−0.988345	+	0.152227i	$0.951355\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.03504			0.520504
$35$	1.28800	−	0.193422i	0.217711	−	0.0326942i
$36$		0			0
$37$	−2.79572	−	4.84233i	−0.459614	−	0.796074i	0.539327	−	0.842097i	$-0.318679\pi$
$37$	−2.79572	−	4.84233i	−0.459614	−	0.796074i	−0.998940	+	0.0460222i	$0.985346\pi$
$38$	−1.21407	+	2.10283i	−0.196949	+	0.341125i
$39$		0			0
$40$	0.246138	+	0.426324i	0.0389178	+	0.0674077i
$41$	−4.80468			−0.750365			−0.375183	−	0.926951i	$-0.622420\pi$
$41$	−4.80468			−0.750365			−0.375183	+	0.926951i	$0.622420\pi$
$42$		0			0
$43$	−4.59392			−0.700566			−0.350283	−	0.936644i	$-0.613915\pi$
$43$	−4.59392			−0.700566			−0.350283	+	0.936644i	$0.613915\pi$
$44$	−2.23159	−	3.86523i	−0.336425	−	0.582705i
$45$		0			0
$46$	0.894617	−	1.54952i	0.131904	−	0.228465i
$47$	−5.79013	−	10.0288i	−0.844578	−	1.46285i	−0.885987	−	0.463710i	$-0.846518\pi$
$47$	−5.79013	−	10.0288i	−0.844578	−	1.46285i	0.0414093	−	0.999142i	$-0.486815\pi$
$48$		0			0
$49$	−5.12621	−	4.76676i	−0.732315	−	0.680966i
$50$	4.75766			0.672835
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	7.06061	−	12.2293i	0.969850	−	1.67983i	0.273872	−	0.961766i	$-0.411695\pi$
$53$	7.06061	−	12.2293i	0.969850	−	1.67983i	0.695978	−	0.718063i	$-0.254971\pi$
$54$		0			0
$55$	2.19712			0.296259
$56$	0.967934	−	2.46234i	0.129346	−	0.329044i
$57$		0			0
$58$	−2.86255	−	4.95808i	−0.375871	−	0.651028i
$59$	−4.13269	+	7.15804i	−0.538031	+	0.931897i	0.460979	+	0.887411i	$0.347498\pi$
$59$	−4.13269	+	7.15804i	−0.538031	+	0.931897i	−0.999010	+	0.0444859i	$0.985835\pi$
$60$		0			0
$61$	7.11042	+	12.3156i	0.910396	+	1.57685i	0.813505	+	0.581558i	$0.197556\pi$
$61$	7.11042	+	12.3156i	0.910396	+	1.57685i	0.0968910	+	0.995295i	$0.469110\pi$
$62$	−6.97090			−0.885306
$63$		0			0
$64$	1.00000			0.125000
$65$	0.246138	+	0.426324i	0.0305297	+	0.0528789i
$66$		0			0
$67$	−3.82096	+	6.61810i	−0.466805	+	0.808530i	−0.999281	−	0.0379152i	$-0.987928\pi$
$67$	−3.82096	+	6.61810i	−0.466805	+	0.808530i	0.532476	+	0.846445i	$0.321262\pi$
$68$	1.51752	+	2.62842i	0.184026	+	0.318742i
$69$		0			0
$70$	0.811507	+	1.01873i	0.0969936	+	0.121761i
$71$	−10.6294			−1.26148			−0.630739	−	0.775995i	$-0.717248\pi$
$71$	−10.6294			−1.26148			−0.630739	+	0.775995i	$0.717248\pi$
$72$		0			0
$73$	−8.35780	+	14.4761i	−0.978206	+	1.69430i	−0.309285	+	0.950969i	$0.600090\pi$
$73$	−8.35780	+	14.4761i	−0.978206	+	1.69430i	−0.668921	+	0.743333i	$0.733244\pi$
$74$	2.79572	−	4.84233i	0.324996	−	0.562910i
$75$		0			0
$76$	−2.42814			−0.278527
$77$	−7.35746	−	9.23621i	−0.838460	−	1.05256i
$78$		0			0
$79$	4.78241	+	8.28338i	0.538063	+	0.931953i	0.999008	+	0.0445242i	$0.0141772\pi$
$79$	4.78241	+	8.28338i	0.538063	+	0.931953i	−0.460945	+	0.887429i	$0.652489\pi$
$80$	−0.246138	+	0.426324i	−0.0275191	+	0.0476644i
$81$		0			0
$82$	−2.40234	−	4.16098i	−0.265294	−	0.459503i
$83$	−0.0831764			−0.00912979			−0.00456490	−	0.999990i	$-0.501453\pi$
$83$	−0.0831764			−0.00912979			−0.00456490	+	0.999990i	$0.501453\pi$
$84$		0			0
$85$	−1.49408			−0.162055
$86$	−2.29696	−	3.97845i	−0.247687	−	0.429007i
$87$		0			0
$88$	2.23159	−	3.86523i	0.237888	−	0.412035i
$89$	−1.83049	−	3.17049i	−0.194031	−	0.336072i	0.752551	−	0.658534i	$-0.228823\pi$
$89$	−1.83049	−	3.17049i	−0.194031	−	0.336072i	−0.946582	+	0.322462i	$0.895490\pi$
$90$		0			0
$91$	0.967934	−	2.46234i	0.101467	−	0.258123i
$92$	1.78923			0.186541
$93$		0			0
$94$	5.79013	−	10.0288i	0.597207	−	1.03439i
$95$	0.597659	−	1.03518i	0.0613185	−	0.106207i
$96$		0			0
$97$	−4.88840			−0.496342			−0.248171	−	0.968716i	$-0.579829\pi$
$97$	−4.88840			−0.496342			−0.248171	+	0.968716i	$0.579829\pi$
$98$	1.56503	−	6.82281i	0.158092	−	0.689207i
$99$		0			0
$100$	2.37883	+	4.12026i	0.237883	+	0.412026i
$101$	0.690339	−	1.19570i	0.0686913	−	0.118977i	−0.829634	−	0.558307i	$-0.811451\pi$
$101$	0.690339	−	1.19570i	0.0686913	−	0.118977i	0.898325	+	0.439331i	$0.144784\pi$
$102$		0			0
$103$	−0.230353	−	0.398983i	−0.0226973	−	0.0393129i	0.854454	−	0.519528i	$-0.173892\pi$
$103$	−0.230353	−	0.398983i	−0.0226973	−	0.0393129i	−0.877151	+	0.480215i	$0.840559\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	14.1212			1.37158
$107$	4.28766	+	7.42645i	0.414504	+	0.717942i	0.995376	−	0.0960530i	$-0.0306218\pi$
$107$	4.28766	+	7.42645i	0.414504	+	0.717942i	−0.580872	+	0.813995i	$0.697288\pi$
$108$		0			0
$109$	0.492276	−	0.852647i	0.0471515	−	0.0816688i	−0.841486	−	0.540278i	$-0.818319\pi$
$109$	0.492276	−	0.852647i	0.0471515	−	0.0816688i	0.888638	+	0.458609i	$0.151652\pi$
$110$	1.09856	+	1.90276i	0.104743	+	0.181421i
$111$		0			0
$112$	2.61641	−	0.392913i	0.247228	−	0.0371268i
$113$	−19.1437			−1.80089			−0.900446	−	0.434968i	$-0.856760\pi$
$113$	−19.1437			−1.80089			−0.900446	+	0.434968i	$0.856760\pi$
$114$		0			0
$115$	−0.440399	+	0.762793i	−0.0410674	+	0.0711308i
$116$	2.86255	−	4.95808i	0.265781	−	0.460347i
$117$		0			0
$118$	−8.26539			−0.760891
$119$	5.00319	+	6.28078i	0.458642	+	0.575758i
$120$		0			0
$121$	−4.45999	−	7.72492i	−0.405453	−	0.702266i
$122$	−7.11042	+	12.3156i	−0.643747	+	1.11500i
$123$		0			0
$124$	−3.48545	−	6.03698i	−0.313003	−	0.542137i
$125$	−4.80346			−0.429635
$126$		0			0
$127$	20.2412			1.79612			0.898060	−	0.439873i	$-0.144977\pi$
$127$	20.2412			1.79612			0.898060	+	0.439873i	$0.144977\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.246138	+	0.426324i	−0.0215877	+	0.0373911i
$131$	−2.55854	−	4.43153i	−0.223541	−	0.387185i	0.732340	−	0.680940i	$-0.238428\pi$
$131$	−2.55854	−	4.43153i	−0.223541	−	0.387185i	−0.955881	+	0.293755i	$0.905095\pi$
$132$		0			0
$133$	−6.35303	+	0.954049i	−0.550877	+	0.0827266i
$134$	−7.64193			−0.660162
$135$		0			0
$136$	−1.51752	+	2.62842i	−0.130126	+	0.225385i
$137$	6.56856	−	11.3771i	0.561190	−	0.972010i	−0.436203	−	0.899848i	$-0.643677\pi$
$137$	6.56856	−	11.3771i	0.561190	−	0.972010i	0.997393	−	0.0721615i	$-0.0229897\pi$
$138$		0			0
$139$	−6.44773			−0.546889			−0.273445	−	0.961888i	$-0.588163\pi$
$139$	−6.44773			−0.546889			−0.273445	+	0.961888i	$0.588163\pi$
$140$	−0.476491	+	1.21215i	−0.0402708	+	0.102445i
$141$		0			0
$142$	−5.31470	−	9.20533i	−0.446000	−	0.772494i
$143$	2.23159	−	3.86523i	0.186615	−	0.323227i
$144$		0			0
$145$	1.40917	+	2.44075i	0.117025	+	0.202693i
$146$	−16.7156			−1.38339
$147$		0			0
$148$	5.59144			0.459614
$149$	10.5363	+	18.2494i	0.863165	+	1.49505i	0.868858	+	0.495062i	$0.164855\pi$
$149$	10.5363	+	18.2494i	0.863165	+	1.49505i	−0.00569259	+	0.999984i	$0.501812\pi$
$150$		0			0
$151$	3.36131	−	5.82197i	0.273540	−	0.473785i	−0.696226	−	0.717823i	$-0.745139\pi$
$151$	3.36131	−	5.82197i	0.273540	−	0.473785i	0.969766	+	0.244038i	$0.0784721\pi$
$152$	−1.21407	−	2.10283i	−0.0984743	−	0.170562i
$153$		0			0
$154$	4.32006	−	10.9899i	0.348121	−	0.885588i
$155$	3.43161			0.275633
$156$		0			0
$157$	11.4772	−	19.8791i	0.915979	−	1.58652i	0.110517	−	0.993874i	$-0.464749\pi$
$157$	11.4772	−	19.8791i	0.915979	−	1.58652i	0.805462	−	0.592647i	$-0.201917\pi$
$158$	−4.78241	+	8.28338i	−0.380468	+	0.658990i
$159$		0			0
$160$	−0.492276			−0.0389178
$161$	4.68138	−	0.703014i	0.368944	−	0.0554052i
$162$		0			0
$163$	2.19723	+	3.80571i	0.172100	+	0.298087i	0.939154	−	0.343496i	$-0.111611\pi$
$163$	2.19723	+	3.80571i	0.172100	+	0.298087i	−0.767054	+	0.641583i	$0.778278\pi$
$164$	2.40234	−	4.16098i	0.187591	−	0.324918i
$165$		0			0
$166$	−0.0415882	−	0.0720328i	−0.00322787	−	0.00559083i
$167$	−11.8705			−0.918565			−0.459283	−	0.888290i	$-0.651893\pi$
$167$	−11.8705			−0.918565			−0.459283	+	0.888290i	$0.651893\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−0.747038	−	1.29391i	−0.0572952	−	0.0992382i
$171$		0			0
$172$	2.29696	−	3.97845i	0.175141	−	0.303354i
$173$	10.5654	+	18.2998i	0.803271	+	1.39131i	0.917452	+	0.397846i	$0.130242\pi$
$173$	10.5654	+	18.2998i	0.803271	+	1.39131i	−0.114181	+	0.993460i	$0.536424\pi$
$174$		0			0
$175$	7.84291	+	9.84562i	0.592868	+	0.744259i
$176$	4.46318			0.336425
$177$		0			0
$178$	1.83049	−	3.17049i	0.137201	−	0.237639i
$179$	6.50772	−	11.2717i	0.486410	−	0.842487i	−0.513468	−	0.858109i	$-0.671639\pi$
$179$	6.50772	−	11.2717i	0.486410	−	0.842487i	0.999878	+	0.0156218i	$0.00497277\pi$
$180$		0			0
$181$	12.4823			0.927804			0.463902	−	0.885887i	$-0.346449\pi$
$181$	12.4823			0.927804			0.463902	+	0.885887i	$0.346449\pi$
$182$	2.61641	−	0.392913i	0.193941	−	0.0291247i
$183$		0			0
$184$	0.894617	+	1.54952i	0.0659521	+	0.114232i
$185$	−1.37627	+	2.38376i	−0.101185	+	0.175258i
$186$		0			0
$187$	6.77295	+	11.7311i	0.495287	+	0.857863i
$188$	11.5803			0.844578
$189$		0			0
$190$	1.19532			0.0867174
$191$	−7.85931	−	13.6127i	−0.568679	−	0.984982i	−0.996697	−	0.0812112i	$-0.974121\pi$
$191$	−7.85931	−	13.6127i	−0.568679	−	0.984982i	0.428018	−	0.903770i	$-0.359212\pi$
$192$		0			0
$193$	−7.75953	+	13.4399i	−0.558543	+	0.967425i	0.439075	+	0.898450i	$0.355306\pi$
$193$	−7.75953	+	13.4399i	−0.558543	+	0.967425i	−0.997618	+	0.0689748i	$0.978027\pi$
$194$	−2.44420	−	4.23348i	−0.175483	−	0.303946i
$195$		0			0
$196$	6.69124	−	2.05605i	0.477946	−	0.146860i
$197$	14.9443			1.06474			0.532368	−	0.846513i	$-0.321302\pi$
$197$	14.9443			1.06474			0.532368	+	0.846513i	$0.321302\pi$
$198$		0			0
$199$	−11.3578	+	19.6723i	−0.805133	+	1.39453i	0.111068	+	0.993813i	$0.464573\pi$
$199$	−11.3578	+	19.6723i	−0.805133	+	1.39453i	−0.916201	+	0.400718i	$0.868761\pi$
$200$	−2.37883	+	4.12026i	−0.168209	+	0.291346i
$201$		0			0
$202$	1.38068			0.0971442
$203$	5.54152	−	14.0971i	0.388939	−	0.989425i
$204$		0			0
$205$	1.18262	+	2.04835i	0.0825974	+	0.143063i
$206$	0.230353	−	0.398983i	0.0160494	−	0.0277984i
$207$		0			0
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	−10.8372			−0.749628
$210$		0			0
$211$	5.36221			0.369150			0.184575	−	0.982818i	$-0.440909\pi$
$211$	5.36221			0.369150			0.184575	+	0.982818i	$0.440909\pi$
$212$	7.06061	+	12.2293i	0.484925	+	0.839915i
$213$		0			0
$214$	−4.28766	+	7.42645i	−0.293098	+	0.507661i
$215$	1.13074	+	1.95850i	0.0771157	+	0.133568i
$216$		0			0
$217$	−11.4914	−	14.4258i	−0.780086	−	0.979284i
$218$	0.984552			0.0666823
$219$		0			0
$220$	−1.09856	+	1.90276i	−0.0740648	+	0.128284i
$221$	−1.51752	+	2.62842i	−0.102079	+	0.176807i
$222$		0			0
$223$	12.7276			0.852302			0.426151	−	0.904652i	$-0.359869\pi$
$223$	12.7276			0.852302			0.426151	+	0.904652i	$0.359869\pi$
$224$	1.64848	+	2.06942i	0.110144	+	0.138269i
$225$		0			0
$226$	−9.57187	−	16.5790i	−0.636711	−	1.10282i
$227$	1.60119	−	2.77334i	0.106275	−	0.184073i	−0.807984	−	0.589205i	$-0.799441\pi$
$227$	1.60119	−	2.77334i	0.106275	−	0.184073i	0.914258	+	0.405132i	$0.132774\pi$
$228$		0			0
$229$	−7.54937	−	13.0759i	−0.498877	−	0.864080i	0.501123	−	0.865376i	$-0.332921\pi$
$229$	−7.54937	−	13.0759i	−0.498877	−	0.864080i	−0.999999	+	0.00129667i	$0.999587\pi$
$230$	−0.880798			−0.0580781
$231$		0			0
$232$	5.72510			0.375871
$233$	8.83132	+	15.2963i	0.578559	+	1.00209i	0.995645	+	0.0932264i	$0.0297180\pi$
$233$	8.83132	+	15.2963i	0.578559	+	1.00209i	−0.417086	+	0.908867i	$0.636949\pi$
$234$		0			0
$235$	−2.85034	+	4.93694i	−0.185936	+	0.322051i
$236$	−4.13269	−	7.15804i	−0.269015	−	0.465948i
$237$		0			0
$238$	−2.93771	+	7.47328i	−0.190424	+	0.484421i
$239$	8.00954			0.518094			0.259047	−	0.965865i	$-0.416592\pi$
$239$	8.00954			0.518094			0.259047	+	0.965865i	$0.416592\pi$
$240$		0			0
$241$	−1.95814	+	3.39160i	−0.126135	+	0.218472i	−0.922176	−	0.386771i	$-0.873591\pi$
$241$	−1.95814	+	3.39160i	−0.126135	+	0.218472i	0.796041	+	0.605243i	$0.206924\pi$
$242$	4.45999	−	7.72492i	0.286699	−	0.496577i
$243$		0			0
$244$	−14.2208			−0.910396
$245$	−0.770428	+	3.35870i	−0.0492208	+	0.214580i
$246$		0			0
$247$	−1.21407	−	2.10283i	−0.0772496	−	0.133800i
$248$	3.48545	−	6.03698i	0.221326	−	0.383349i
$249$		0			0
$250$	−2.40173	−	4.15992i	−0.151899	−	0.263097i
$251$	−3.22743			−0.203714			−0.101857	−	0.994799i	$-0.532478\pi$
$251$	−3.22743			−0.203714			−0.101857	+	0.994799i	$0.532478\pi$
$252$		0			0
$253$	7.98568			0.502055
$254$	10.1206	+	17.5294i	0.635024	+	1.09989i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.76014	+	11.7089i	0.421686	+	0.730381i	0.996105	−	0.0881803i	$-0.0281052\pi$
$257$	6.76014	+	11.7089i	0.421686	+	0.730381i	−0.574419	+	0.818562i	$0.694772\pi$
$258$		0			0
$259$	14.6295	−	2.19695i	0.909035	−	0.136512i
$260$	−0.492276			−0.0305297
$261$		0			0
$262$	2.55854	−	4.43153i	0.158067	−	0.273781i
$263$	−8.01629	+	13.8846i	−0.494306	+	0.856163i	−0.999978	−	0.00656258i	$-0.997911\pi$
$263$	−8.01629	+	13.8846i	−0.494306	+	0.856163i	0.505673	+	0.862725i	$0.331244\pi$
$264$		0			0
$265$	−6.95154			−0.427030
$266$	−4.00275	−	5.02486i	−0.245424	−	0.308094i
$267$		0			0
$268$	−3.82096	−	6.61810i	−0.233402	−	0.404265i
$269$	−3.59815	+	6.23219i	−0.219383	+	0.379983i	−0.954620	−	0.297828i	$-0.903738\pi$
$269$	−3.59815	+	6.23219i	−0.219383	+	0.379983i	0.735236	+	0.677811i	$0.237071\pi$
$270$		0			0
$271$	8.59414	+	14.8855i	0.522057	+	0.904229i	0.999671	+	0.0256592i	$0.00816848\pi$
$271$	8.59414	+	14.8855i	0.522057	+	0.904229i	−0.477614	+	0.878570i	$0.658498\pi$
$272$	−3.03504			−0.184026
$273$		0			0
$274$	13.1371			0.793643
$275$	10.6172	+	18.3895i	0.640239	+	1.10893i
$276$		0			0
$277$	−6.29277	+	10.8994i	−0.378096	+	0.654881i	−0.990785	−	0.135443i	$-0.956754\pi$
$277$	−6.29277	+	10.8994i	−0.378096	+	0.654881i	0.612690	+	0.790324i	$0.290088\pi$
$278$	−3.22387	−	5.58390i	−0.193355	−	0.334900i
$279$		0			0
$280$	−1.28800	+	0.193422i	−0.0769726	+	0.0115592i
$281$	−18.3374			−1.09392			−0.546958	−	0.837160i	$-0.684214\pi$
$281$	−18.3374			−1.09392			−0.546958	+	0.837160i	$0.684214\pi$
$282$		0			0
$283$	3.15973	−	5.47282i	0.187827	−	0.325325i	−0.756699	−	0.653764i	$-0.773189\pi$
$283$	3.15973	−	5.47282i	0.187827	−	0.325325i	0.944525	+	0.328438i	$0.106522\pi$
$284$	5.31470	−	9.20533i	0.315369	−	0.546236i
$285$		0			0
$286$	4.46318			0.263913
$287$	4.65062	−	11.8307i	0.274517	−	0.698347i
$288$		0			0
$289$	3.89428	+	6.74509i	0.229075	+	0.396770i
$290$	−1.40917	+	2.44075i	−0.0827491	+	0.143326i
$291$		0			0
$292$	−8.35780	−	14.4761i	−0.489103	−	0.847151i
$293$	7.84511			0.458316			0.229158	−	0.973389i	$-0.426403\pi$
$293$	7.84511			0.458316			0.229158	+	0.973389i	$0.426403\pi$
$294$		0			0
$295$	4.06885			0.236898
$296$	2.79572	+	4.84233i	0.162498	+	0.281455i
$297$		0			0
$298$	−10.5363	+	18.2494i	−0.610350	+	1.05716i
$299$	0.894617	+	1.54952i	0.0517371	+	0.0896112i
$300$		0			0
$301$	4.44661	−	11.3118i	0.256298	−	0.652000i
$302$	6.72263			0.386844
$303$		0			0
$304$	1.21407	−	2.10283i	0.0696318	−	0.120606i
$305$	3.50029	−	6.06268i	0.200426	−	0.347148i
$306$		0			0
$307$	−8.71557			−0.497424			−0.248712	−	0.968578i	$-0.580007\pi$
$307$	−8.71557			−0.497424			−0.248712	+	0.968578i	$0.580007\pi$
$308$	11.6775	−	1.75364i	0.665389	−	0.0999230i
$309$		0			0
$310$	1.71580	+	2.97186i	0.0974511	+	0.168790i
$311$	−9.63517	+	16.6886i	−0.546360	+	0.946324i	0.452160	+	0.891937i	$0.350654\pi$
$311$	−9.63517	+	16.6886i	−0.546360	+	0.946324i	−0.998520	+	0.0543867i	$0.982680\pi$
$312$		0			0
$313$	−1.68351	−	2.91593i	−0.0951579	−	0.164818i	0.814517	−	0.580140i	$-0.197002\pi$
$313$	−1.68351	−	2.91593i	−0.0951579	−	0.164818i	−0.909674	+	0.415322i	$0.863669\pi$
$314$	22.9544			1.29539
$315$		0			0
$316$	−9.56482			−0.538063
$317$	3.89109	+	6.73956i	0.218545	+	0.378531i	0.954363	−	0.298648i	$-0.0965356\pi$
$317$	3.89109	+	6.73956i	0.218545	+	0.378531i	−0.735818	+	0.677179i	$0.763202\pi$
$318$		0			0
$319$	12.7761	−	22.1288i	0.715323	−	1.23898i
$320$	−0.246138	−	0.426324i	−0.0137595	−	0.0238322i
$321$		0			0
$322$	2.94952	+	3.70269i	0.164370	+	0.206343i
$323$	7.36950			0.410050
$324$		0			0
$325$	−2.37883	+	4.12026i	−0.131954	+	0.228551i
$326$	−2.19723	+	3.80571i	−0.121693	+	0.210779i
$327$		0			0
$328$	4.80468			0.265294
$329$	30.2988	−	4.55004i	1.67043	−	0.250852i
$330$		0			0
$331$	−4.24855	−	7.35870i	−0.233521	−	0.404471i	0.725321	−	0.688411i	$-0.241691\pi$
$331$	−4.24855	−	7.35870i	−0.233521	−	0.404471i	−0.958842	+	0.283941i	$0.908358\pi$
$332$	0.0415882	−	0.0720328i	0.00228245	−	0.00395332i
$333$		0			0
$334$	−5.93524	−	10.2801i	−0.324762	−	0.562504i
$335$	3.76194			0.205537
$336$		0			0
$337$	−15.6389			−0.851907			−0.425954	−	0.904745i	$-0.640061\pi$
$337$	−15.6389			−0.851907			−0.425954	+	0.904745i	$0.640061\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	0.747038	−	1.29391i	0.0405138	−	0.0701720i
$341$	−15.5562	−	26.9441i	−0.842415	−	1.45911i
$342$		0			0
$343$	16.6992	−	8.00854i	0.901672	−	0.432421i
$344$	4.59392			0.247687
$345$		0			0
$346$	−10.5654	+	18.2998i	−0.567998	+	0.983802i
$347$	5.28800	−	9.15908i	0.283875	−	0.491685i	−0.688461	−	0.725273i	$-0.741713\pi$
$347$	5.28800	−	9.15908i	0.283875	−	0.491685i	0.972336	+	0.233588i	$0.0750467\pi$
$348$		0			0
$349$	−35.5192			−1.90130			−0.950649	−	0.310268i	$-0.899581\pi$
$349$	−35.5192			−1.90130			−0.950649	+	0.310268i	$0.899581\pi$
$350$	−4.60511	+	11.7150i	−0.246153	+	0.626192i
$351$		0			0
$352$	2.23159	+	3.86523i	0.118944	+	0.206017i
$353$	−13.9585	+	24.1768i	−0.742935	+	1.28680i	0.208219	+	0.978082i	$0.433233\pi$
$353$	−13.9585	+	24.1768i	−0.742935	+	1.28680i	−0.951154	+	0.308718i	$0.900100\pi$
$354$		0			0
$355$	2.61630	+	4.53156i	0.138859	+	0.240510i
$356$	3.66097			0.194031
$357$		0			0
$358$	13.0154			0.687888
$359$	−6.30263	−	10.9165i	−0.332640	−	0.576149i	0.650389	−	0.759602i	$-0.274606\pi$
$359$	−6.30263	−	10.9165i	−0.332640	−	0.576149i	−0.983029	+	0.183452i	$0.941273\pi$
$360$		0			0
$361$	6.55206	−	11.3485i	0.344845	−	0.597289i
$362$	6.24116	+	10.8100i	0.328028	+	0.568161i
$363$		0			0
$364$	1.64848	+	2.06942i	0.0864038	+	0.108467i
$365$	8.22869			0.430709
$366$		0			0
$367$	−16.0965	+	27.8799i	−0.840230	+	1.45532i	0.0494709	+	0.998776i	$0.484246\pi$
$367$	−16.0965	+	27.8799i	−0.840230	+	1.45532i	−0.889700	+	0.456545i	$0.849087\pi$
$368$	−0.894617	+	1.54952i	−0.0466352	+	0.0807745i
$369$		0			0
$370$	−2.75253			−0.143097
$371$	23.2786	+	29.2228i	1.20856	+	1.51717i
$372$		0			0
$373$	0.0947026	+	0.164030i	0.00490351	+	0.00849314i	0.868467	−	0.495747i	$-0.165106\pi$
$373$	0.0947026	+	0.164030i	0.00490351	+	0.00849314i	−0.863563	+	0.504241i	$0.831772\pi$
$374$	−6.77295	+	11.7311i	−0.350221	+	0.606601i
$375$		0			0
$376$	5.79013	+	10.0288i	0.298603	+	0.517196i
$377$	5.72510			0.294858
$378$		0			0
$379$	4.43476			0.227798			0.113899	−	0.993492i	$-0.463666\pi$
$379$	4.43476			0.227798			0.113899	+	0.993492i	$0.463666\pi$
$380$	0.597659	+	1.03518i	0.0306592	+	0.0531034i
$381$		0			0
$382$	7.85931	−	13.6127i	0.402117	−	0.696487i
$383$	15.6833	+	27.1643i	0.801379	+	1.38803i	0.918708	+	0.394937i	$0.129233\pi$
$383$	15.6833	+	27.1643i	0.801379	+	1.38803i	−0.117329	+	0.993093i	$0.537433\pi$
$384$		0			0
$385$	−2.12666	+	5.41004i	−0.108385	+	0.275721i
$386$	−15.5191			−0.789899
$387$		0			0
$388$	2.44420	−	4.23348i	0.124086	−	0.214922i
$389$	0.310494	−	0.537791i	0.0157427	−	0.0272671i	−0.858047	−	0.513572i	$-0.828322\pi$
$389$	0.310494	−	0.537791i	0.0157427	−	0.0272671i	0.873789	+	0.486304i	$0.161655\pi$
$390$		0			0
$391$	−5.43039			−0.274627
$392$	5.12621	+	4.76676i	0.258913	+	0.240758i
$393$		0			0
$394$	7.47214	+	12.9421i	0.376441	+	0.652015i
$395$	2.35427	−	4.07771i	0.118456	−	0.205172i
$396$		0			0
$397$	5.33848	+	9.24652i	0.267931	+	0.464070i	0.968327	−	0.249684i	$-0.0803268\pi$
$397$	5.33848	+	9.24652i	0.267931	+	0.464070i	−0.700397	+	0.713754i	$0.746994\pi$
$398$	−22.7156			−1.13863
$399$		0			0
$400$	−4.75766			−0.237883
$401$	16.9522	+	29.3620i	0.846551	+	1.46627i	0.884268	+	0.466980i	$0.154658\pi$
$401$	16.9522	+	29.3620i	0.846551	+	1.46627i	−0.0377172	+	0.999288i	$0.512009\pi$
$402$		0			0
$403$	3.48545	−	6.03698i	0.173623	−	0.300723i
$404$	0.690339	+	1.19570i	0.0343457	+	0.0594884i
$405$		0			0
$406$	14.9792	−	2.24947i	0.743407	−	0.111639i
$407$	24.9556			1.23700
$408$		0			0
$409$	−14.7304	+	25.5139i	−0.728373	+	1.26158i	0.229197	+	0.973380i	$0.426390\pi$
$409$	−14.7304	+	25.5139i	−0.728373	+	1.26158i	−0.957570	+	0.288199i	$0.906943\pi$
$410$	−1.18262	+	2.04835i	−0.0584052	+	0.101161i
$411$		0			0
$412$	0.460706			0.0226973
$413$	−13.6253	−	17.1046i	−0.670458	−	0.841662i
$414$		0			0
$415$	0.0204729	+	0.0354600i	0.00100497	+	0.00174067i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	−5.41862	−	9.38533i	−0.265033	−	0.459051i
$419$	−14.3324			−0.700186			−0.350093	−	0.936715i	$-0.613850\pi$
$419$	−14.3324			−0.700186			−0.350093	+	0.936715i	$0.613850\pi$
$420$		0			0
$421$	−29.4442			−1.43502			−0.717510	−	0.696548i	$-0.754718\pi$
$421$	−29.4442			−1.43502			−0.717510	+	0.696548i	$0.754718\pi$
$422$	2.68111	+	4.64381i	0.130514	+	0.226057i
$423$		0			0
$424$	−7.06061	+	12.2293i	−0.342894	+	0.593909i
$425$	−7.21984	−	12.5051i	−0.350214	−	0.606588i
$426$		0			0
$427$	−37.2076	+	5.58755i	−1.80060	+	0.270401i
$428$	−8.57532			−0.414504
$429$		0			0
$430$	−1.13074	+	1.95850i	−0.0545290	+	0.0944470i
$431$	11.7924	−	20.4251i	0.568021	−	0.983842i	−0.428740	−	0.903428i	$-0.641042\pi$
$431$	11.7924	−	20.4251i	0.568021	−	0.983842i	0.996762	−	0.0804139i	$-0.0256242\pi$
$432$		0			0
$433$	2.06332			0.0991570			0.0495785	−	0.998770i	$-0.484212\pi$
$433$	2.06332			0.0991570			0.0495785	+	0.998770i	$0.484212\pi$
$434$	6.74738	−	17.1647i	0.323884	−	0.823933i
$435$		0			0
$436$	0.492276	+	0.852647i	0.0235757	+	0.0408344i
$437$	2.17226	−	3.76246i	0.103913	−	0.179983i
$438$		0			0
$439$	6.45965	+	11.1884i	0.308302	+	0.533995i	0.977991	−	0.208647i	$-0.0669059\pi$
$439$	6.45965	+	11.1884i	0.308302	+	0.533995i	−0.669689	+	0.742642i	$0.733573\pi$
$440$	−2.19712			−0.104743
$441$		0			0
$442$	−3.03504			−0.144362
$443$	17.8394	+	30.8987i	0.847575	+	1.46804i	0.883366	+	0.468683i	$0.155271\pi$
$443$	17.8394	+	30.8987i	0.847575	+	1.46804i	−0.0357919	+	0.999359i	$0.511395\pi$
$444$		0			0
$445$	−0.901104	+	1.56076i	−0.0427164	+	0.0739870i
$446$	6.36379	+	11.0224i	0.301334	+	0.521926i
$447$		0			0
$448$	−0.967934	+	2.46234i	−0.0457306	+	0.116334i
$449$	13.8185			0.652135			0.326067	−	0.945346i	$-0.394276\pi$
$449$	13.8185			0.652135			0.326067	+	0.945346i	$0.394276\pi$
$450$		0			0
$451$	10.7221	−	18.5712i	0.504883	−	0.874483i
$452$	9.57187	−	16.5790i	0.450223	−	0.779809i
$453$		0			0
$454$	3.20238			0.150295
$455$	−1.28800	+	0.193422i	−0.0603823	+	0.00906775i
$456$		0			0
$457$	−8.77732	−	15.2028i	−0.410586	−	0.711155i	0.584368	−	0.811489i	$-0.301342\pi$
$457$	−8.77732	−	15.2028i	−0.410586	−	0.711155i	−0.994954	+	0.100333i	$0.968009\pi$
$458$	7.54937	−	13.0759i	0.352759	−	0.610997i
$459$		0			0
$460$	−0.440399	−	0.762793i	−0.0205337	−	0.0355654i
$461$	−16.8813			−0.786242			−0.393121	−	0.919487i	$-0.628605\pi$
$461$	−16.8813			−0.786242			−0.393121	+	0.919487i	$0.628605\pi$
$462$		0			0
$463$	−11.4229			−0.530868			−0.265434	−	0.964129i	$-0.585515\pi$
$463$	−11.4229			−0.530868			−0.265434	+	0.964129i	$0.585515\pi$
$464$	2.86255	+	4.95808i	0.132891	+	0.230173i
$465$		0			0
$466$	−8.83132	+	15.2963i	−0.409103	+	0.708587i
$467$	−14.1461	−	24.5017i	−0.654603	−	1.13381i	−0.981993	−	0.188916i	$-0.939503\pi$
$467$	−14.1461	−	24.5017i	−0.654603	−	1.13381i	0.327390	−	0.944889i	$-0.393831\pi$
$468$		0			0
$469$	−12.5976	−	15.8144i	−0.581701	−	0.730241i
$470$	−5.70069			−0.262953
$471$		0			0
$472$	4.13269	−	7.15804i	0.190223	−	0.329475i
$473$	10.2517	−	17.7565i	0.471375	−	0.816446i
$474$		0			0
$475$	11.5523			0.530056
$476$	−7.94091	+	1.19250i	−0.363971	+	0.0546584i
$477$		0			0
$478$	4.00477	+	6.93646i	0.183174	+	0.317266i
$479$	13.1039	−	22.6967i	0.598734	−	1.03704i	−0.394274	−	0.918993i	$-0.629004\pi$
$479$	13.1039	−	22.6967i	0.598734	−	1.03704i	0.993008	−	0.118045i	$-0.0376627\pi$
$480$		0			0
$481$	2.79572	+	4.84233i	0.127474	+	0.220791i
$482$	−3.91628			−0.178382
$483$		0			0
$484$	8.91997			0.405453
$485$	1.20322	+	2.08404i	0.0546355	+	0.0946314i
$486$		0			0
$487$	5.75469	−	9.96742i	0.260770	−	0.451667i	−0.705677	−	0.708534i	$-0.749357\pi$
$487$	5.75469	−	9.96742i	0.260770	−	0.451667i	0.966447	+	0.256867i	$0.0826902\pi$
$488$	−7.11042	−	12.3156i	−0.321874	−	0.557502i
$489$		0			0
$490$	−3.29394	+	1.01214i	−0.148805	+	0.0457239i
$491$	−6.28700			−0.283728			−0.141864	−	0.989886i	$-0.545310\pi$
$491$	−6.28700			−0.283728			−0.141864	+	0.989886i	$0.545310\pi$
$492$		0			0
$493$	−8.68795	+	15.0480i	−0.391285	+	0.677726i
$494$	1.21407	−	2.10283i	0.0546237	−	0.0946110i
$495$		0			0
$496$	6.97090			0.313003
$497$	10.2886	−	26.1732i	0.461505	−	1.17403i
$498$		0			0
$499$	0.542488	+	0.939616i	0.0242851	+	0.0420630i	0.877913	−	0.478821i	$-0.158936\pi$
$499$	0.542488	+	0.939616i	0.0242851	+	0.0420630i	−0.853627	+	0.520884i	$0.825602\pi$
$500$	2.40173	−	4.15992i	0.107409	−	0.186037i
$501$		0			0
$502$	−1.61372	−	2.79504i	−0.0720236	−	0.124749i
$503$	−29.0072			−1.29337			−0.646684	−	0.762758i	$-0.723845\pi$
$503$	−29.0072			−1.29337			−0.646684	+	0.762758i	$0.723845\pi$
$504$		0			0
$505$	−0.679675			−0.0302451
$506$	3.99284	+	6.91580i	0.177503	+	0.307445i
$507$		0			0
$508$	−10.1206	+	17.5294i	−0.449030	+	0.777743i
$509$	10.2481	+	17.7502i	0.454237	+	0.786762i	0.998644	−	0.0520591i	$-0.0165784\pi$
$509$	10.2481	+	17.7502i	0.454237	+	0.786762i	−0.544407	+	0.838822i	$0.683245\pi$
$510$		0			0
$511$	−27.5553	−	34.5917i	−1.21898	−	1.53024i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−6.76014	+	11.7089i	−0.298177	+	0.516458i
$515$	−0.113397	+	0.196410i	−0.00499688	+	0.00865484i
$516$		0			0
$517$	51.6848			2.27310
$518$	9.21738	+	11.5711i	0.404988	+	0.508404i
$519$		0			0
$520$	−0.246138	−	0.426324i	−0.0107939	−	0.0186955i
$521$	−4.85629	+	8.41134i	−0.212758	+	0.368507i	−0.952577	−	0.304299i	$-0.901578\pi$
$521$	−4.85629	+	8.41134i	−0.212758	+	0.368507i	0.739819	+	0.672806i	$0.234911\pi$
$522$		0			0
$523$	5.46565	+	9.46679i	0.238996	+	0.413954i	0.960427	−	0.278533i	$-0.0898483\pi$
$523$	5.46565	+	9.46679i	0.238996	+	0.413954i	−0.721430	+	0.692487i	$0.756515\pi$
$524$	5.11709			0.223541
$525$		0			0
$526$	−16.0326			−0.699054
$527$	10.5785	+	18.3224i	0.460805	+	0.798138i
$528$		0			0
$529$	9.89932	−	17.1461i	0.430405	−	0.745484i
$530$	−3.47577	−	6.02021i	−0.150978	−	0.261501i
$531$		0			0
$532$	2.35028	−	5.97891i	0.101898	−	0.259219i
$533$	4.80468			0.208114
$534$		0			0
$535$	2.11071	−	3.65586i	0.0912541	−	0.158057i
$536$	3.82096	−	6.61810i	0.165040	−	0.285858i
$537$		0			0
$538$	−7.19631			−0.310255
$539$	29.8642	−	9.17650i	1.28634	−	0.395260i
$540$		0			0
$541$	−17.0220	−	29.4829i	−0.731831	−	1.26757i	−0.956100	−	0.293042i	$-0.905333\pi$
$541$	−17.0220	−	29.4829i	−0.731831	−	1.26757i	0.224268	−	0.974527i	$-0.428001\pi$
$542$	−8.59414	+	14.8855i	−0.369150	+	0.639387i
$543$		0			0
$544$	−1.51752	−	2.62842i	−0.0650630	−	0.112692i
$545$	−0.484671			−0.0207610
$546$		0			0
$547$	39.8767			1.70500			0.852502	−	0.522724i	$-0.175084\pi$
$547$	39.8767			1.70500			0.852502	+	0.522724i	$0.175084\pi$
$548$	6.56856	+	11.3771i	0.280595	+	0.486005i
$549$		0			0
$550$	−10.6172	+	18.3895i	−0.452717	+	0.784129i
$551$	−6.95069	−	12.0389i	−0.296109	−	0.512876i
$552$		0			0
$553$	−25.0255	+	3.75814i	−1.06419	+	0.159812i
$554$	−12.5855			−0.534708
$555$		0			0
$556$	3.22387	−	5.58390i	0.136722	−	0.236810i
$557$	1.51702	−	2.62756i	0.0642783	−	0.111333i	−0.832095	−	0.554633i	$-0.812859\pi$
$557$	1.51702	−	2.62756i	0.0642783	−	0.111333i	0.896374	+	0.443299i	$0.146192\pi$
$558$		0			0
$559$	4.59392			0.194302
$560$	−0.811507	−	1.01873i	−0.0342924	−	0.0430491i
$561$		0			0
$562$	−9.16870	−	15.8806i	−0.386758	−	0.669885i
$563$	−17.1981	+	29.7880i	−0.724815	+	1.25542i	0.234236	+	0.972180i	$0.424741\pi$
$563$	−17.1981	+	29.7880i	−0.724815	+	1.25542i	−0.959050	+	0.283236i	$0.908592\pi$
$564$		0			0
$565$	4.71200	+	8.16143i	0.198235	+	0.343354i
$566$	6.31947			0.265627
$567$		0			0
$568$	10.6294			0.446000
$569$	10.1924	+	17.6538i	0.427288	+	0.740085i	0.996631	−	0.0820155i	$-0.0261357\pi$
$569$	10.1924	+	17.6538i	0.427288	+	0.740085i	−0.569343	+	0.822100i	$0.692802\pi$
$570$		0			0
$571$	11.4015	−	19.7480i	0.477139	−	0.826429i	−0.522518	−	0.852628i	$-0.675007\pi$
$571$	11.4015	−	19.7480i	0.477139	−	0.826429i	0.999657	+	0.0261996i	$0.00834055\pi$
$572$	2.23159	+	3.86523i	0.0933075	+	0.161613i
$573$		0			0
$574$	12.5710	−	1.88782i	0.524705	−	0.0787962i
$575$	−8.51258			−0.354999
$576$		0			0
$577$	−2.83402	+	4.90866i	−0.117982	+	0.204350i	−0.918968	−	0.394333i	$-0.870976\pi$
$577$	−2.83402	+	4.90866i	−0.117982	+	0.204350i	0.800986	+	0.598683i	$0.204309\pi$
$578$	−3.89428	+	6.74509i	−0.161981	+	0.280559i
$579$		0			0
$580$	−2.81833			−0.117025
$581$	0.0805092	−	0.204808i	0.00334009	−	0.00849688i
$582$		0			0
$583$	31.5128	+	54.5818i	1.30513	+	2.26055i
$584$	8.35780	−	14.4761i	0.345848	−	0.599026i
$585$		0			0
$586$	3.92256	+	6.79407i	0.162039	+	0.280660i
$587$	−18.0367			−0.744454			−0.372227	−	0.928142i	$-0.621406\pi$
$587$	−18.0367			−0.744454			−0.372227	+	0.928142i	$0.621406\pi$
$588$		0			0
$589$	−16.9264			−0.697438
$590$	2.03443	+	3.52373i	0.0837560	+	0.145070i
$591$		0			0
$592$	−2.79572	+	4.84233i	−0.114903	+	0.199019i
$593$	−9.42688	−	16.3278i	−0.387115	−	0.670504i	0.604945	−	0.796267i	$-0.293195\pi$
$593$	−9.42688	−	16.3278i	−0.387115	−	0.670504i	−0.992060	+	0.125764i	$0.959862\pi$
$594$		0			0
$595$	1.44617	−	3.67892i	0.0592870	−	0.150821i
$596$	−21.0725			−0.863165
$597$		0			0
$598$	−0.894617	+	1.54952i	−0.0365836	+	0.0633647i
$599$	−7.19504	+	12.4622i	−0.293981	+	0.509191i	−0.974747	−	0.223310i	$-0.928314\pi$
$599$	−7.19504	+	12.4622i	−0.293981	+	0.509191i	0.680766	+	0.732501i	$0.261647\pi$
$600$		0			0
$601$	−4.12469			−0.168250			−0.0841249	−	0.996455i	$-0.526809\pi$
$601$	−4.12469			−0.168250			−0.0841249	+	0.996455i	$0.526809\pi$
$602$	12.0196	−	1.80501i	0.489882	−	0.0735667i
$603$		0			0
$604$	3.36131	+	5.82197i	0.136770	+	0.236892i
$605$	−2.19554	+	3.80279i	−0.0892616	+	0.154606i
$606$		0			0
$607$	3.83619	+	6.64447i	0.155706	+	0.269691i	0.933316	−	0.359056i	$-0.116901\pi$
$607$	3.83619	+	6.64447i	0.155706	+	0.269691i	−0.777610	+	0.628747i	$0.783568\pi$
$608$	2.42814			0.0984743
$609$		0			0
$610$	7.00058			0.283445
$611$	5.79013	+	10.0288i	0.234244	+	0.405722i
$612$		0			0
$613$	11.5161	−	19.9465i	0.465132	−	0.805633i	−0.534075	−	0.845437i	$-0.679340\pi$
$613$	11.5161	−	19.9465i	0.465132	−	0.805633i	0.999208	+	0.0398041i	$0.0126734\pi$
$614$	−4.35778	−	7.54790i	−0.175866	−	0.304609i
$615$		0			0
$616$	7.35746	+	9.23621i	0.296440	+	0.372138i
$617$	23.6494			0.952090			0.476045	−	0.879421i	$-0.342070\pi$
$617$	23.6494			0.952090			0.476045	+	0.879421i	$0.342070\pi$
$618$		0			0
$619$	7.91610	−	13.7111i	0.318175	−	0.551095i	−0.661932	−	0.749564i	$-0.730263\pi$
$619$	7.91610	−	13.7111i	0.318175	−	0.551095i	0.980107	+	0.198468i	$0.0635967\pi$
$620$	−1.71580	+	2.97186i	−0.0689084	+	0.119353i
$621$		0			0
$622$	−19.2703			−0.772670
$623$	9.57861	−	1.43844i	0.383759	−	0.0576300i
$624$		0			0
$625$	−10.7118	−	18.5535i	−0.428474	−	0.742138i
$626$	1.68351	−	2.91593i	0.0672868	−	0.116544i
$627$		0			0
$628$	11.4772	+	19.8791i	0.457989	+	0.793261i
$629$	−16.9702			−0.676647
$630$		0			0
$631$	6.11902			0.243594			0.121797	−	0.992555i	$-0.461134\pi$
$631$	6.11902			0.243594			0.121797	+	0.992555i	$0.461134\pi$
$632$	−4.78241	−	8.28338i	−0.190234	−	0.329495i
$633$		0			0
$634$	−3.89109	+	6.73956i	−0.154535	+	0.267662i
$635$	−4.98214	−	8.62932i	−0.197710	−	0.342444i
$636$		0			0
$637$	5.12621	+	4.76676i	0.203108	+	0.188866i
$638$	25.5522			1.01162
$639$		0			0
$640$	0.246138	−	0.426324i	0.00972946	−	0.0168519i
$641$	−13.5301	+	23.4347i	−0.534405	+	0.925617i	0.464787	+	0.885423i	$0.346131\pi$
$641$	−13.5301	+	23.4347i	−0.534405	+	0.925617i	−0.999192	+	0.0401942i	$0.987202\pi$
$642$		0			0
$643$	1.97023			0.0776982			0.0388491	−	0.999245i	$-0.487631\pi$
$643$	1.97023			0.0776982			0.0388491	+	0.999245i	$0.487631\pi$
$644$	−1.73186	+	4.40570i	−0.0682449	+	0.173609i
$645$		0			0
$646$	3.68475	+	6.38218i	0.144975	+	0.251103i
$647$	−13.2149	+	22.8889i	−0.519532	+	0.899855i	0.480211	+	0.877153i	$0.340560\pi$
$647$	−13.2149	+	22.8889i	−0.519532	+	0.899855i	−0.999742	+	0.0227019i	$0.992773\pi$
$648$		0			0
$649$	−18.4450	−	31.9476i	−0.724028	−	1.25405i
$650$	−4.75766			−0.186611
$651$		0			0
$652$	−4.39446			−0.172100
$653$	−20.7756	−	35.9845i	−0.813014	−	1.40818i	−0.910745	−	0.412969i	$-0.864492\pi$
$653$	−20.7756	−	35.9845i	−0.813014	−	1.40818i	0.0977314	−	0.995213i	$-0.468841\pi$
$654$		0			0
$655$	−1.25951	+	2.18154i	−0.0492131	+	0.0852397i
$656$	2.40234	+	4.16098i	0.0937957	+	0.162459i
$657$		0			0
$658$	19.0898	+	23.9645i	0.744199	+	0.934233i
$659$	−13.6604			−0.532135			−0.266067	−	0.963954i	$-0.585724\pi$
$659$	−13.6604			−0.532135			−0.266067	+	0.963954i	$0.585724\pi$
$660$		0			0
$661$	19.5952	−	33.9398i	0.762164	−	1.32011i	−0.179569	−	0.983745i	$-0.557470\pi$
$661$	19.5952	−	33.9398i	0.762164	−	1.32011i	0.941733	−	0.336361i	$-0.109196\pi$
$662$	4.24855	−	7.35870i	0.165124	−	0.286004i
$663$		0			0
$664$	0.0831764			0.00322787
$665$	1.97046	+	2.47362i	0.0764110	+	0.0959228i
$666$		0			0
$667$	5.12178	+	8.87118i	0.198316	+	0.343493i
$668$	5.93524	−	10.2801i	0.229641	−	0.397750i
$669$		0			0
$670$	1.88097	+	3.25793i	0.0726682	+	0.125865i
$671$	−63.4702			−2.45024
$672$		0			0
$673$	−39.2161			−1.51167			−0.755836	−	0.654761i	$-0.772769\pi$
$673$	−39.2161			−1.51167			−0.755836	+	0.654761i	$0.772769\pi$
$674$	−7.81947	−	13.5437i	−0.301195	−	0.521684i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−6.49899	−	11.2566i	−0.249776	−	0.432625i	0.713687	−	0.700464i	$-0.247024\pi$
$677$	−6.49899	−	11.2566i	−0.249776	−	0.432625i	−0.963464	+	0.267839i	$0.913690\pi$
$678$		0			0
$679$	4.73165	−	12.0369i	0.181584	−	0.461934i
$680$	1.49408			0.0572952
$681$		0			0
$682$	15.5562	−	26.9441i	0.595678	−	1.03174i
$683$	6.78353	−	11.7494i	0.259565	−	0.449579i	−0.706561	−	0.707652i	$-0.749754\pi$
$683$	6.78353	−	11.7494i	0.259565	−	0.449579i	0.966125	+	0.258073i	$0.0830876\pi$
$684$		0			0
$685$	−6.46709			−0.247095
$686$	15.2852	+	10.4577i	0.583592	+	0.399275i
$687$		0			0
$688$	2.29696	+	3.97845i	0.0875707	+	0.151677i
$689$	−7.06061	+	12.2293i	−0.268988	+	0.465901i
$690$		0			0
$691$	−10.2029	−	17.6719i	−0.388137	−	0.672272i	0.604062	−	0.796937i	$-0.293548\pi$
$691$	−10.2029	−	17.6719i	−0.388137	−	0.672272i	−0.992199	+	0.124665i	$0.960214\pi$
$692$	−21.1308			−0.803271
$693$		0			0
$694$	10.5760			0.401459
$695$	1.58703	+	2.74882i	0.0601996	+	0.104269i
$696$		0			0
$697$	−7.29119	+	12.6287i	−0.276174	+	0.478347i
$698$	−17.7596	−	30.7605i	−0.672210	−	1.16430i
$699$		0			0
$700$	−12.4480	+	1.86935i	−0.470491	+	0.0706547i
$701$	−28.3006			−1.06890			−0.534449	−	0.845201i	$-0.679481\pi$
$701$	−28.3006			−1.06890			−0.534449	+	0.845201i	$0.679481\pi$
$702$		0			0
$703$	6.78842	−	11.7579i	0.256030	−	0.443457i
$704$	−2.23159	+	3.86523i	−0.0841062	+	0.145676i
$705$		0			0
$706$	−27.9169			−1.05067
$707$	2.27602	+	2.85721i	0.0855985	+	0.107456i
$708$		0			0
$709$	−13.3084	−	23.0508i	−0.499807	−	0.865692i	0.500193	−	0.865914i	$-0.333262\pi$
$709$	−13.3084	−	23.0508i	−0.499807	−	0.865692i	−1.00000		0.000222584i	$0.999929\pi$
$710$	−2.61630	+	4.53156i	−0.0981880	+	0.170067i
$711$		0			0
$712$	1.83049	+	3.17049i	0.0686003	+	0.118819i
$713$	12.4726			0.467102
$714$		0			0
$715$	−2.19712			−0.0821675
$716$	6.50772	+	11.2717i	0.243205	+	0.421244i
$717$		0			0
$718$	6.30263	−	10.9165i	0.235212	−	0.407399i
$719$	21.5974	+	37.4078i	0.805446	+	1.39507i	0.915989	+	0.401203i	$0.131408\pi$
$719$	21.5974	+	37.4078i	0.805446	+	1.39507i	−0.110543	+	0.993871i	$0.535259\pi$
$720$		0			0
$721$	1.20540	−	0.181017i	0.0448913	−	0.00674143i
$722$	13.1041			0.487685
$723$		0			0
$724$	−6.24116	+	10.8100i	−0.231951	+	0.401751i
$725$	−13.6191	+	23.5889i	−0.505799	+	0.876070i
$726$		0			0
$727$	45.6799			1.69417			0.847087	−	0.531454i	$-0.178354\pi$
$727$	45.6799			1.69417			0.847087	+	0.531454i	$0.178354\pi$
$728$	−0.967934	+	2.46234i	−0.0358740	+	0.0912603i
$729$		0			0
$730$	4.11434	+	7.12625i	0.152279	+	0.263754i
$731$	−6.97135	+	12.0747i	−0.257845	+	0.446600i
$732$		0			0
$733$	11.0219	+	19.0906i	0.407104	+	0.705126i	0.994564	−	0.104128i	$-0.0332052\pi$
$733$	11.0219	+	19.0906i	0.407104	+	0.705126i	−0.587459	+	0.809254i	$0.699872\pi$
$734$	−32.1930			−1.18826
$735$		0			0
$736$	−1.78923			−0.0659521
$737$	−17.0536	−	29.5378i	−0.628179	−	1.08804i
$738$		0			0
$739$	1.75078	−	3.03244i	0.0644034	−	0.111550i	−0.832026	−	0.554737i	$-0.812819\pi$
$739$	1.75078	−	3.03244i	0.0644034	−	0.111550i	0.896429	+	0.443187i	$0.146152\pi$
$740$	−1.37627	−	2.38376i	−0.0505926	−	0.0876289i
$741$		0			0
$742$	−13.6684	+	34.7712i	−0.501783	+	1.27649i
$743$	37.4603			1.37428			0.687142	−	0.726523i	$-0.258865\pi$
$743$	37.4603			1.37428			0.687142	+	0.726523i	$0.258865\pi$
$744$		0			0
$745$	5.18675	−	8.98372i	0.190028	−	0.329138i
$746$	−0.0947026	+	0.164030i	−0.00346731	+	0.00600555i
$747$		0			0
$748$	−13.5459			−0.495287
$749$	−22.4366	+	3.36936i	−0.819815	+	0.123114i
$750$		0			0
$751$	6.16061	+	10.6705i	0.224804	+	0.389372i	0.956261	−	0.292516i	$-0.0944925\pi$
$751$	6.16061	+	10.6705i	0.224804	+	0.389372i	−0.731457	+	0.681888i	$0.761159\pi$
$752$	−5.79013	+	10.0288i	−0.211144	+	0.365713i
$753$		0			0
$754$	2.86255	+	4.95808i	0.104248	+	0.180563i
$755$	−3.30939			−0.120441
$756$		0			0
$757$	34.3350			1.24793			0.623964	−	0.781453i	$-0.285521\pi$
$757$	34.3350			1.24793			0.623964	+	0.781453i	$0.285521\pi$
$758$	2.21738	+	3.84061i	0.0805388	+	0.139497i
$759$		0			0
$760$	−0.597659	+	1.03518i	−0.0216794	+	0.0375497i
$761$	3.85809	+	6.68240i	0.139856	+	0.242237i	0.927442	−	0.373967i	$-0.122003\pi$
$761$	3.85809	+	6.68240i	0.139856	+	0.242237i	−0.787586	+	0.616204i	$0.788670\pi$
$762$		0			0
$763$	1.62301	+	2.03746i	0.0587570	+	0.0737609i
$764$	15.7186			0.568679
$765$		0			0
$766$	−15.6833	+	27.1643i	−0.566661	+	0.981485i
$767$	4.13269	−	7.15804i	0.149223	−	0.258462i
$768$		0			0
$769$	25.9620			0.936215			0.468108	−	0.883671i	$-0.344936\pi$
$769$	25.9620			0.936215			0.468108	+	0.883671i	$0.344936\pi$
$770$	−5.74857	+	0.863276i	−0.207164	+	0.0311103i
$771$		0			0
$772$	−7.75953	−	13.4399i	−0.279272	−	0.483713i
$773$	21.0571	−	36.4720i	0.757371	−	1.31181i	−0.186816	−	0.982395i	$-0.559817\pi$
$773$	21.0571	−	36.4720i	0.757371	−	1.31181i	0.944187	−	0.329410i	$-0.106850\pi$
$774$		0			0
$775$	16.5826	+	28.7219i	0.595665	+	1.03172i
$776$	4.88840			0.175483
$777$		0			0
$778$	0.620987			0.0222635
$779$	−5.83323	−	10.1035i	−0.208997	−	0.361994i
$780$		0			0
$781$	23.7205	−	41.0850i	0.848785	−	1.47014i
$782$	−2.71520	−	4.70286i	−0.0970952	−	0.168174i
$783$		0			0
$784$	−1.56503	+	6.82281i	−0.0558940	+	0.243672i
$785$	−11.2999			−0.403310
$786$		0			0
$787$	−10.9397	+	18.9481i	−0.389959	+	0.675429i	−0.992444	−	0.122702i	$-0.960844\pi$
$787$	−10.9397	+	18.9481i	−0.389959	+	0.675429i	0.602485	+	0.798130i	$0.294177\pi$
$788$	−7.47214	+	12.9421i	−0.266184	+	0.461044i
$789$		0			0
$790$	4.70853			0.167522
$791$	18.5299	−	47.1383i	0.658847	−	1.67605i
$792$		0			0
$793$	−7.11042	−	12.3156i	−0.252498	−	0.437340i
$794$	−5.33848	+	9.24652i	−0.189456	+	0.328147i
$795$		0			0
$796$	−11.3578	−	19.6723i	−0.402566	−	0.697266i
$797$	31.3543			1.11063			0.555313	−	0.831641i	$-0.312598\pi$
$797$	31.3543			1.11063			0.555313	+	0.831641i	$0.312598\pi$
$798$		0			0
$799$	−35.1465			−1.24339
$800$	−2.37883	−	4.12026i	−0.0841044	−	0.145673i
$801$		0			0
$802$	−16.9522	+	29.3620i	−0.598602	+	1.03681i
$803$	−37.3023	−	64.6096i	−1.31637	−	2.28002i
$804$		0			0
$805$	−1.45198	−	1.82274i	−0.0511754	−	0.0642433i
$806$	6.97090			0.245540
$807$		0			0
$808$	−0.690339	+	1.19570i	−0.0242860	+	0.0420647i
$809$	20.0462	−	34.7210i	0.704786	−	1.22073i	−0.261982	−	0.965073i	$-0.584376\pi$
$809$	20.0462	−	34.7210i	0.704786	−	1.22073i	0.966769	−	0.255653i	$-0.0822904\pi$
$810$		0			0
$811$	10.3771			0.364390			0.182195	−	0.983262i	$-0.441680\pi$
$811$	10.3771			0.364390			0.182195	+	0.983262i	$0.441680\pi$
$812$	9.43771	+	11.8477i	0.331199	+	0.415772i
$813$		0			0
$814$	12.4778	+	21.6122i	0.437347	+	0.757507i
$815$	1.08164	−	1.87346i	0.0378883	−	0.0656245i
$816$		0			0
$817$	−5.57735	−	9.66025i	−0.195127	−	0.337969i
$818$	−29.4609			−1.03008
$819$		0			0
$820$	−2.36523			−0.0825974
$821$	8.30780	+	14.3895i	0.289944	+	0.502198i	0.973796	−	0.227423i	$-0.0730300\pi$
$821$	8.30780	+	14.3895i	0.289944	+	0.502198i	−0.683852	+	0.729621i	$0.739697\pi$
$822$		0			0
$823$	8.96536	−	15.5285i	0.312513	−	0.541288i	−0.666393	−	0.745601i	$-0.732163\pi$
$823$	8.96536	−	15.5285i	0.312513	−	0.541288i	0.978906	+	0.204313i	$0.0654959\pi$
$824$	0.230353	+	0.398983i	0.00802472	+	0.0138992i
$825$		0			0
$826$	8.00035	−	20.3522i	0.278368	−	0.708143i
$827$	−40.9087			−1.42254			−0.711268	−	0.702921i	$-0.751879\pi$
$827$	−40.9087			−1.42254			−0.711268	+	0.702921i	$0.751879\pi$
$828$		0			0
$829$	20.6438	−	35.7561i	0.716989	−	1.24186i	−0.245198	−	0.969473i	$-0.578853\pi$
$829$	20.6438	−	35.7561i	0.716989	−	1.24186i	0.962187	−	0.272388i	$-0.0878136\pi$
$830$	−0.0204729	+	0.0354600i	−0.000710624	+	0.00123084i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	−20.3081	+	6.24017i	−0.703636	+	0.216209i
$834$		0			0
$835$	2.92178	+	5.06067i	0.101112	+	0.175132i
$836$	5.41862	−	9.38533i	0.187407	−	0.324598i
$837$		0			0
$838$	−7.16622	−	12.4123i	−0.247553	−	0.428774i
$839$	33.2010			1.14622			0.573112	−	0.819477i	$-0.305736\pi$
$839$	33.2010			1.14622			0.573112	+	0.819477i	$0.305736\pi$
$840$		0			0
$841$	3.77680			0.130235
$842$	−14.7221	−	25.4994i	−0.507356	−	0.878767i
$843$		0			0
$844$	−2.68111	+	4.64381i	−0.0922875	+	0.159847i
$845$	−0.246138	−	0.426324i	−0.00846741	−	0.0146660i
$846$		0			0
$847$	23.3383	−	3.50477i	0.801915	−	0.120425i
$848$	−14.1212			−0.484925
$849$		0			0
$850$	7.21984	−	12.5051i	0.247638	−	0.428922i
$851$	−5.00220	+	8.66407i	−0.171473	+	0.297000i
$852$		0			0
$853$	5.45599			0.186809			0.0934047	−	0.995628i	$-0.470225\pi$
$853$	5.45599			0.186809			0.0934047	+	0.995628i	$0.470225\pi$
$854$	−23.4428	−	29.4290i	−0.802195	−	1.00704i
$855$		0			0
$856$	−4.28766	−	7.42645i	−0.146549	−	0.253831i
$857$	−1.74832	+	3.02818i	−0.0597214	+	0.103441i	−0.894340	−	0.447387i	$-0.852355\pi$
$857$	−1.74832	+	3.02818i	−0.0597214	+	0.103441i	0.834619	+	0.550828i	$0.185688\pi$
$858$		0			0
$859$	−6.45065	−	11.1729i	−0.220093	−	0.381213i	0.734743	−	0.678346i	$-0.237303\pi$
$859$	−6.45065	−	11.1729i	−0.220093	−	0.381213i	−0.954836	+	0.297133i	$0.903970\pi$
$860$	−2.26148			−0.0771157
$861$		0			0
$862$	23.5849			0.803303
$863$	0.346090	+	0.599446i	0.0117811	+	0.0204054i	0.871856	−	0.489763i	$-0.162917\pi$
$863$	0.346090	+	0.599446i	0.0117811	+	0.0204054i	−0.860075	+	0.510168i	$0.829583\pi$
$864$		0			0
$865$	5.20109	−	9.00854i	0.176842	−	0.306300i
$866$	1.03166	+	1.78689i	0.0350573	+	0.0607210i
$867$		0			0
$868$	18.2388	−	2.73896i	0.619064	−	0.0929663i
$869$	−42.6895			−1.44814
$870$		0			0
$871$	3.82096	−	6.61810i	0.129468	−	0.224246i
$872$	−0.492276	+	0.852647i	−0.0166706	+	0.0288743i
$873$		0			0
$874$	4.34452			0.146956
$875$	4.64944	−	11.8277i	0.157180	−	0.399851i
$876$		0			0
$877$	−6.76707	−	11.7209i	−0.228508	−	0.395787i	0.728858	−	0.684665i	$-0.240051\pi$
$877$	−6.76707	−	11.7209i	−0.228508	−	0.395787i	−0.957366	+	0.288877i	$0.906718\pi$
$878$	−6.45965	+	11.1884i	−0.218003	+	0.377592i
$879$		0			0
$880$	−1.09856	−	1.90276i	−0.0370324	−	0.0641420i
$881$	−35.8304			−1.20716			−0.603578	−	0.797304i	$-0.706259\pi$
$881$	−35.8304			−1.20716			−0.603578	+	0.797304i	$0.706259\pi$
$882$		0			0
$883$	−29.1032			−0.979400			−0.489700	−	0.871891i	$-0.662894\pi$
$883$	−29.1032			−0.979400			−0.489700	+	0.871891i	$0.662894\pi$
$884$	−1.51752	−	2.62842i	−0.0510396	−	0.0884033i
$885$		0			0
$886$	−17.8394	+	30.8987i	−0.599326	+	1.03806i
$887$	−19.1932	−	33.2437i	−0.644446	−	1.11621i	−0.984429	−	0.175781i	$-0.943755\pi$
$887$	−19.1932	−	33.2437i	−0.644446	−	1.11621i	0.339984	−	0.940431i	$-0.389578\pi$
$888$		0			0
$889$	−19.5922	+	49.8408i	−0.657101	+	1.67161i
$890$	−1.80221			−0.0604102
$891$		0			0
$892$	−6.36379	+	11.0224i	−0.213075	+	0.369057i
$893$	14.0593	−	24.3514i	0.470476	−	0.814888i
$894$		0			0
$895$	−6.40719			−0.214169
$896$	−2.61641	+	0.392913i	−0.0874082	+	0.0131263i
$897$		0			0
$898$	6.90925	+	11.9672i	0.230565	+	0.399349i
$899$	19.9546	−	34.5623i	0.665522	−	1.15272i
$900$		0			0
$901$	−21.4292	−	37.1165i	−0.713911	−	1.23653i
$902$	21.4442			0.714012
$903$		0			0
$904$	19.1437			0.636711
$905$	−3.07237	−	5.32151i	−0.102129	−	0.176893i
$906$		0			0
$907$	6.87530	−	11.9084i	0.228291	−	0.395411i	−0.729011	−	0.684502i	$-0.760020\pi$
$907$	6.87530	−	11.9084i	0.228291	−	0.395411i	0.957302	+	0.289091i	$0.0933530\pi$
$908$	1.60119	+	2.77334i	0.0531373	+	0.0920366i
$909$		0			0
$910$	−0.811507	−	1.01873i	−0.0269012	−	0.0337705i
$911$	−41.9029			−1.38830			−0.694152	−	0.719828i	$-0.744221\pi$
$911$	−41.9029			−1.38830			−0.694152	+	0.719828i	$0.744221\pi$
$912$		0			0
$913$	0.185616	−	0.321496i	0.00614298	−	0.0106399i
$914$	8.77732	−	15.2028i	0.290328	−	0.502863i
$915$		0			0
$916$	15.0987			0.498877
$917$	13.3884	−	2.01057i	0.442125	−	0.0663949i
$918$		0			0
$919$	28.6170	+	49.5660i	0.943987	+	1.63503i	0.757767	+	0.652525i	$0.226290\pi$
$919$	28.6170	+	49.5660i	0.943987	+	1.63503i	0.186219	+	0.982508i	$0.440376\pi$
$920$	0.440399	−	0.762793i	0.0145195	−	0.0251485i
$921$		0			0
$922$	−8.44067	−	14.6197i	−0.277979	−	0.481473i
$923$	10.6294			0.349871
$924$		0			0
$925$	−26.6022			−0.874675
$926$	−5.71145	−	9.89253i	−0.187690	−	0.325089i
$927$		0			0
$928$	−2.86255	+	4.95808i	−0.0939679	+	0.162757i
$929$	−10.3520	−	17.9302i	−0.339639	−	0.588272i	0.644726	−	0.764414i	$-0.276972\pi$
$929$	−10.3520	−	17.9302i	−0.339639	−	0.588272i	−0.984365	+	0.176142i	$0.943638\pi$
$930$		0			0
$931$	3.80012	−	16.5668i	0.124544	−	0.542954i
$932$	−17.6626			−0.578559
$933$		0			0
$934$	14.1461	−	24.5017i	0.462874	−	0.801721i
$935$	3.33416	−	5.77494i	0.109039	−	0.188861i
$936$		0			0
$937$	−30.4958			−0.996253			−0.498127	−	0.867104i	$-0.665979\pi$
$937$	−30.4958			−0.996253			−0.498127	+	0.867104i	$0.665979\pi$
$938$	7.39688	−	18.8170i	0.241517	−	0.614397i
$939$		0			0
$940$	−2.85034	−	4.93694i	−0.0929680	−	0.161025i
$941$	−12.0598	+	20.8882i	−0.393138	+	0.680934i	−0.992862	−	0.119273i	$-0.961944\pi$
$941$	−12.0598	+	20.8882i	−0.393138	+	0.680934i	0.599724	+	0.800207i	$0.295277\pi$
$942$		0			0
$943$	4.29835	+	7.44497i	0.139974	+	0.242441i
$944$	8.26539			0.269015
$945$		0			0
$946$	20.5035			0.666626
$947$	0.995359	+	1.72401i	0.0323448	+	0.0560229i	0.881745	−	0.471727i	$-0.156369\pi$
$947$	0.995359	+	1.72401i	0.0323448	+	0.0560229i	−0.849400	+	0.527750i	$0.823036\pi$
$948$		0			0
$949$	8.35780	−	14.4761i	0.271306	−	0.469915i
$950$	5.77615	+	10.0046i	0.187403	+	0.324591i
$951$		0			0
$952$	−5.00319	−	6.28078i	−0.162154	−	0.203561i
$953$	−43.3675			−1.40481			−0.702405	−	0.711777i	$-0.747891\pi$
$953$	−43.3675			−1.40481			−0.702405	+	0.711777i	$0.747891\pi$
$954$		0			0
$955$	−3.86895	+	6.70121i	−0.125196	+	0.216846i
$956$	−4.00477	+	6.93646i	−0.129523	+	0.224341i
$957$		0			0
$958$	26.2079			0.846738
$959$	21.6563	+	27.1863i	0.699318	+	0.877891i
$960$		0			0
$961$	−8.79675	−	15.2364i	−0.283766	−	0.491497i
$962$	−2.79572	+	4.84233i	−0.0901377	+	0.156123i
$963$		0			0
$964$	−1.95814	−	3.39160i	−0.0630675	−	0.109236i
$965$	7.63966			0.245929
$966$		0			0
$967$	17.8217			0.573108			0.286554	−	0.958064i	$-0.407490\pi$
$967$	17.8217			0.573108			0.286554	+	0.958064i	$0.407490\pi$
$968$	4.45999	+	7.72492i	0.143349	+	0.248288i
$969$		0			0
$970$	−1.20322	+	2.08404i	−0.0386331	+	0.0669145i
$971$	−21.4049	−	37.0743i	−0.686915	−	1.18977i	−0.972831	−	0.231517i	$-0.925631\pi$
$971$	−21.4049	−	37.0743i	−0.686915	−	1.18977i	0.285916	−	0.958255i	$-0.407702\pi$
$972$		0			0
$973$	6.24098	−	15.8765i	0.200077	−	0.508977i
$974$	11.5094			0.368785
$975$		0			0
$976$	7.11042	−	12.3156i	0.227599	−	0.394213i
$977$	4.51065	−	7.81267i	0.144308	−	0.249949i	−0.784806	−	0.619741i	$-0.787238\pi$
$977$	4.51065	−	7.81267i	0.144308	−	0.249949i	0.929115	+	0.369792i	$0.120571\pi$
$978$		0			0
$979$	16.3396			0.522215
$980$	−2.52351	−	2.34656i	−0.0806105	−	0.0749582i
$981$		0			0
$982$	−3.14350	−	5.44470i	−0.100313	−	0.173747i
$983$	15.9867	−	27.6897i	0.509896	−	0.883165i	−0.490039	−	0.871701i	$-0.663017\pi$
$983$	15.9867	−	27.6897i	0.509896	−	0.883165i	0.999934	−	0.0114644i	$-0.00364930\pi$
$984$		0			0
$985$	−3.67836	−	6.37110i	−0.117202	−	0.203000i
$986$	−17.3759			−0.553361
$987$		0			0
$988$	2.42814			0.0772496
$989$	4.10980	+	7.11838i	0.130684	+	0.226351i
$990$		0			0
$991$	7.41637	−	12.8455i	0.235589	−	0.408052i	−0.723855	−	0.689952i	$-0.757631\pi$
$991$	7.41637	−	12.8455i	0.235589	−	0.408052i	0.959444	+	0.281901i	$0.0909648\pi$
$992$	3.48545	+	6.03698i	0.110663	+	0.191674i
$993$		0			0
$994$	27.8109	−	4.17643i	0.882108	−	0.132468i
$995$	11.1823			0.354504
$996$		0			0
$997$	11.8685	−	20.5568i	0.375879	−	0.651041i	−0.614579	−	0.788855i	$-0.710674\pi$
$997$	11.8685	−	20.5568i	0.375879	−	0.651041i	0.990458	+	0.137814i	$0.0440076\pi$
$998$	−0.542488	+	0.939616i	−0.0171722	+	0.0297430i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.t.235.3	yes	10
3.2	odd	2		1638.2.j.s.235.3	✓	10
7.2	even	3	inner	1638.2.j.t.1171.3	yes	10
21.2	odd	6		1638.2.j.s.1171.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.j.s.235.3	✓	10	3.2	odd	2
1638.2.j.s.1171.3	yes	10	21.2	odd	6
1638.2.j.t.235.3	yes	10	1.1	even	1	trivial
1638.2.j.t.1171.3	yes	10	7.2	even	3	inner

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.246138 - 0.426324i) q^{5} +(-0.967934 + 2.46234i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.246138 - 0.426324i) q^{5} +(-0.967934 + 2.46234i) q^{7} -1.00000 q^{8} +(0.246138 - 0.426324i) q^{10} +(-2.23159 + 3.86523i) q^{11} -1.00000 q^{13} +(-2.61641 + 0.392913i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.51752 - 2.62842i) q^{17} +(1.21407 + 2.10283i) q^{19} +0.492276 q^{20} -4.46318 q^{22} +(-0.894617 - 1.54952i) q^{23} +(2.37883 - 4.12026i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-1.64848 - 2.06942i) q^{28} -5.72510 q^{29} +(-3.48545 + 6.03698i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.03504 q^{34} +(1.28800 - 0.193422i) q^{35} +(-2.79572 - 4.84233i) q^{37} +(-1.21407 + 2.10283i) q^{38} +(0.246138 + 0.426324i) q^{40} -4.80468 q^{41} -4.59392 q^{43} +(-2.23159 - 3.86523i) q^{44} +(0.894617 - 1.54952i) q^{46} +(-5.79013 - 10.0288i) q^{47} +(-5.12621 - 4.76676i) q^{49} +4.75766 q^{50} +(0.500000 - 0.866025i) q^{52} +(7.06061 - 12.2293i) q^{53} +2.19712 q^{55} +(0.967934 - 2.46234i) q^{56} +(-2.86255 - 4.95808i) q^{58} +(-4.13269 + 7.15804i) q^{59} +(7.11042 + 12.3156i) q^{61} -6.97090 q^{62} +1.00000 q^{64} +(0.246138 + 0.426324i) q^{65} +(-3.82096 + 6.61810i) q^{67} +(1.51752 + 2.62842i) q^{68} +(0.811507 + 1.01873i) q^{70} -10.6294 q^{71} +(-8.35780 + 14.4761i) q^{73} +(2.79572 - 4.84233i) q^{74} -2.42814 q^{76} +(-7.35746 - 9.23621i) q^{77} +(4.78241 + 8.28338i) q^{79} +(-0.246138 + 0.426324i) q^{80} +(-2.40234 - 4.16098i) q^{82} -0.0831764 q^{83} -1.49408 q^{85} +(-2.29696 - 3.97845i) q^{86} +(2.23159 - 3.86523i) q^{88} +(-1.83049 - 3.17049i) q^{89} +(0.967934 - 2.46234i) q^{91} +1.78923 q^{92} +(5.79013 - 10.0288i) q^{94} +(0.597659 - 1.03518i) q^{95} -4.88840 q^{97} +(1.56503 - 6.82281i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

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