LMFDB - Embedded newform 1890.2.t.c.1601.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.4
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.c.1151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.89754 - 1.84373i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.89754 - 1.84373i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} -0.645696i q^{11} +(-0.230647 + 0.133164i) q^{13} +(2.56518 + 0.647947i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.525609 + 0.910381i) q^{17} +(0.938083 + 0.541602i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.322848 + 0.559189i) q^{22} -3.36670i q^{23} +1.00000 q^{25} +(0.133164 - 0.230647i) q^{26} +(-2.54549 + 0.721453i) q^{28} +(-2.95682 - 1.70712i) q^{29} +(2.57432 + 1.48628i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.910381 - 0.525609i) q^{34} +(1.89754 + 1.84373i) q^{35} +(1.37174 - 2.37592i) q^{37} -1.08320 q^{38} -1.00000i q^{40} +(-2.16896 - 3.75676i) q^{41} +(-5.04758 + 8.74267i) q^{43} +(-0.559189 - 0.322848i) q^{44} +(1.68335 + 2.91565i) q^{46} +(0.0268516 + 0.0465083i) q^{47} +(0.201321 + 6.99710i) q^{49} +(-0.866025 + 0.500000i) q^{50} +0.266328i q^{52} +(-10.1657 + 5.86918i) q^{53} +0.645696i q^{55} +(1.84373 - 1.89754i) q^{56} +3.41425 q^{58} +(2.85148 - 4.93891i) q^{59} +(3.06877 - 1.77175i) q^{61} -2.97257 q^{62} -1.00000 q^{64} +(0.230647 - 0.133164i) q^{65} +(-3.61024 + 6.25312i) q^{67} +1.05122 q^{68} +(-2.56518 - 0.647947i) q^{70} +10.7565i q^{71} +(-13.9150 + 8.03384i) q^{73} +2.74347i q^{74} +(0.938083 - 0.541602i) q^{76} +(-1.19049 + 1.22523i) q^{77} +(2.16082 + 3.74266i) q^{79} +(0.500000 + 0.866025i) q^{80} +(3.75676 + 2.16896i) q^{82} +(1.83015 - 3.16992i) q^{83} +(-0.525609 - 0.910381i) q^{85} -10.0952i q^{86} +0.645696 q^{88} +(-6.12312 + 10.6056i) q^{89} +(0.683180 + 0.172566i) q^{91} +(-2.91565 - 1.68335i) q^{92} +(-0.0465083 - 0.0268516i) q^{94} +(-0.938083 - 0.541602i) q^{95} +(-14.8734 - 8.58718i) q^{97} +(-3.67290 - 5.95901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.89754	−	1.84373i	−0.717203	−	0.696864i
$7$	−1.89754	−	1.84373i	−0.717203	−	0.696864i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$		−	0.645696i		−	0.194685i	−0.995251	−	0.0973424i	$-0.968966\pi$
$11$		−	0.645696i		−	0.194685i	0.995251	−	0.0973424i	$-0.0310342\pi$
$12$		0			0
$13$	−0.230647	+	0.133164i	−0.0639699	+	0.0369331i	−0.531644	−	0.846968i	$-0.678425\pi$
$13$	−0.230647	+	0.133164i	−0.0639699	+	0.0369331i	0.467674	+	0.883901i	$0.345092\pi$
$14$	2.56518	+	0.647947i	0.685574	+	0.173171i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.525609	+	0.910381i	0.127479	+	0.220800i	0.922699	−	0.385521i	$-0.125978\pi$
$17$	0.525609	+	0.910381i	0.127479	+	0.220800i	−0.795220	+	0.606321i	$0.792645\pi$
$18$		0			0
$19$	0.938083	+	0.541602i	0.215211	+	0.124252i	0.603731	−	0.797188i	$-0.293680\pi$
$19$	0.938083	+	0.541602i	0.215211	+	0.124252i	−0.388520	+	0.921440i	$0.627014\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	0.322848	+	0.559189i	0.0688314	+	0.119220i
$23$		−	3.36670i		−	0.702005i	−0.936374	−	0.351003i	$-0.885841\pi$
$23$		−	3.36670i		−	0.702005i	0.936374	−	0.351003i	$-0.114159\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	0.133164	−	0.230647i	0.0261156	−	0.0452336i
$27$		0			0
$28$	−2.54549	+	0.721453i	−0.481052	+	0.136342i
$29$	−2.95682	−	1.70712i	−0.549069	−	0.317005i	0.199678	−	0.979862i	$-0.436010\pi$
$29$	−2.95682	−	1.70712i	−0.549069	−	0.317005i	−0.748746	+	0.662857i	$0.769344\pi$
$30$		0			0
$31$	2.57432	+	1.48628i	0.462361	+	0.266944i	0.713037	−	0.701127i	$-0.247319\pi$
$31$	2.57432	+	1.48628i	0.462361	+	0.266944i	−0.250675	+	0.968071i	$0.580653\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−0.910381	−	0.525609i	−0.156129	−	0.0901412i
$35$	1.89754	+	1.84373i	0.320743	+	0.311647i
$36$		0			0
$37$	1.37174	−	2.37592i	0.225512	−	0.390598i	−0.730961	−	0.682419i	$-0.760928\pi$
$37$	1.37174	−	2.37592i	0.225512	−	0.390598i	0.956473	+	0.291821i	$0.0942612\pi$
$38$	−1.08320			−0.175719
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−2.16896	−	3.75676i	−0.338735	−	0.586707i	0.645460	−	0.763794i	$-0.276666\pi$
$41$	−2.16896	−	3.75676i	−0.338735	−	0.586707i	−0.984195	+	0.177087i	$0.943332\pi$
$42$		0			0
$43$	−5.04758	+	8.74267i	−0.769749	+	1.33325i	0.167949	+	0.985796i	$0.446286\pi$
$43$	−5.04758	+	8.74267i	−0.769749	+	1.33325i	−0.937699	+	0.347449i	$0.887048\pi$
$44$	−0.559189	−	0.322848i	−0.0843010	−	0.0486712i
$45$		0			0
$46$	1.68335	+	2.91565i	0.248196	+	0.429889i
$47$	0.0268516	+	0.0465083i	0.00391670	+	0.00678393i	0.867977	−	0.496604i	$-0.165420\pi$
$47$	0.0268516	+	0.0465083i	0.00391670	+	0.00678393i	−0.864060	+	0.503388i	$0.832087\pi$
$48$		0			0
$49$	0.201321	+	6.99710i	0.0287601	+	0.999586i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$			0.266328i			0.0369331i
$53$	−10.1657	+	5.86918i	−1.39637	+	0.806193i	−0.994010	−	0.109289i	$-0.965143\pi$
$53$	−10.1657	+	5.86918i	−1.39637	+	0.806193i	−0.402358	+	0.915482i	$0.631809\pi$
$54$		0			0
$55$			0.645696i			0.0870657i
$56$	1.84373	−	1.89754i	0.246379	−	0.253570i
$57$		0			0
$58$	3.41425			0.448313
$59$	2.85148	−	4.93891i	0.371231	−	0.642991i	−0.618524	−	0.785766i	$-0.712269\pi$
$59$	2.85148	−	4.93891i	0.371231	−	0.642991i	0.989755	+	0.142775i	$0.0456024\pi$
$60$		0			0
$61$	3.06877	−	1.77175i	0.392916	−	0.226850i	−0.290507	−	0.956873i	$-0.593824\pi$
$61$	3.06877	−	1.77175i	0.392916	−	0.226850i	0.683423	+	0.730023i	$0.260491\pi$
$62$	−2.97257			−0.377516
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.230647	−	0.133164i	0.0286082	−	0.0165170i
$66$		0			0
$67$	−3.61024	+	6.25312i	−0.441061	+	0.763941i	−0.997769	−	0.0667682i	$-0.978731\pi$
$67$	−3.61024	+	6.25312i	−0.441061	+	0.763941i	0.556707	+	0.830709i	$0.312065\pi$
$68$	1.05122			0.127479
$69$		0			0
$70$	−2.56518	−	0.647947i	−0.306598	−	0.0774444i
$71$			10.7565i			1.27656i	0.769806	+	0.638278i	$0.220353\pi$
$71$			10.7565i			1.27656i	−0.769806	+	0.638278i	$0.779647\pi$
$72$		0			0
$73$	−13.9150	+	8.03384i	−1.62863	+	0.940290i	−0.644128	+	0.764918i	$0.722780\pi$
$73$	−13.9150	+	8.03384i	−1.62863	+	0.940290i	−0.984502	+	0.175372i	$0.943887\pi$
$74$			2.74347i			0.318922i
$75$		0			0
$76$	0.938083	−	0.541602i	0.107605	−	0.0621260i
$77$	−1.19049	+	1.22523i	−0.135669	+	0.139628i
$78$		0			0
$79$	2.16082	+	3.74266i	0.243112	+	0.421082i	0.961599	−	0.274458i	$-0.0884985\pi$
$79$	2.16082	+	3.74266i	0.243112	+	0.421082i	−0.718487	+	0.695540i	$0.755165\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	3.75676	+	2.16896i	0.414864	+	0.239522i
$83$	1.83015	−	3.16992i	0.200885	−	0.347944i	−0.747929	−	0.663779i	$-0.768951\pi$
$83$	1.83015	−	3.16992i	0.200885	−	0.347944i	0.948814	+	0.315836i	$0.102285\pi$
$84$		0			0
$85$	−0.525609	−	0.910381i	−0.0570103	−	0.0987447i
$86$		−	10.0952i		−	1.08859i
$87$		0			0
$88$	0.645696			0.0688314
$89$	−6.12312	+	10.6056i	−0.649050	+	1.12419i	0.334301	+	0.942466i	$0.391500\pi$
$89$	−6.12312	+	10.6056i	−0.649050	+	1.12419i	−0.983350	+	0.181720i	$0.941833\pi$
$90$		0			0
$91$	0.683180	+	0.172566i	0.0716168	+	0.0180899i
$92$	−2.91565	−	1.68335i	−0.303977	−	0.175501i
$93$		0			0
$94$	−0.0465083	−	0.0268516i	−0.00479696	−	0.00276953i
$95$	−0.938083	−	0.541602i	−0.0962452	−	0.0555672i
$96$		0			0
$97$	−14.8734	−	8.58718i	−1.51017	−	0.871896i	−0.999930	−	0.0118630i	$-0.996224\pi$
$97$	−14.8734	−	8.58718i	−1.51017	−	0.871896i	−0.510238	−	0.860033i	$-0.670443\pi$
$98$	−3.67290	−	5.95901i	−0.371019	−	0.601951i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−0.448592			−0.0446366			−0.0223183	−	0.999751i	$-0.507105\pi$
$101$	−0.448592			−0.0446366			−0.0223183	+	0.999751i	$0.507105\pi$
$102$		0			0
$103$			5.66944i			0.558627i	0.960200	+	0.279313i	$0.0901068\pi$
$103$			5.66944i			0.558627i	−0.960200	+	0.279313i	$0.909893\pi$
$104$	−0.133164	−	0.230647i	−0.0130578	−	0.0226168i
$105$		0			0
$106$	5.86918	−	10.1657i	0.570065	−	0.987381i
$107$	−3.32116	−	1.91747i	−0.321069	−	0.185369i	0.330800	−	0.943701i	$-0.392681\pi$
$107$	−3.32116	−	1.91747i	−0.321069	−	0.185369i	−0.651869	+	0.758332i	$0.726015\pi$
$108$		0			0
$109$	7.71722	+	13.3666i	0.739175	+	1.28029i	0.952867	+	0.303388i	$0.0981178\pi$
$109$	7.71722	+	13.3666i	0.739175	+	1.28029i	−0.213692	+	0.976901i	$0.568549\pi$
$110$	−0.322848	−	0.559189i	−0.0307824	−	0.0533166i
$111$		0			0
$112$	−0.647947	+	2.56518i	−0.0612252	+	0.242387i
$113$	−2.73453	+	1.57878i	−0.257243	+	0.148519i	−0.623076	−	0.782161i	$-0.714117\pi$
$113$	−2.73453	+	1.57878i	−0.257243	+	0.148519i	0.365833	+	0.930680i	$0.380784\pi$
$114$		0			0
$115$			3.36670i			0.313946i
$116$	−2.95682	+	1.70712i	−0.274534	+	0.158502i
$117$		0			0
$118$			5.70296i			0.525000i
$119$	0.681133	−	2.69657i	0.0624393	−	0.247194i
$120$		0			0
$121$	10.5831			0.962098
$122$	−1.77175	+	3.06877i	−0.160407	+	0.277833i
$123$		0			0
$124$	2.57432	−	1.48628i	0.231181	−	0.133472i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.18440			0.637512			0.318756	−	0.947837i	$-0.396735\pi$
$127$	7.18440			0.637512			0.318756	+	0.947837i	$0.396735\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.133164	+	0.230647i	−0.0116793	+	0.0202291i
$131$	0.0747982			0.00653515			0.00326757	−	0.999995i	$-0.498960\pi$
$131$	0.0747982			0.00653515			0.00326757	+	0.999995i	$0.498960\pi$
$132$		0			0
$133$	−0.781482	−	2.75728i	−0.0677630	−	0.239087i
$134$		−	7.22048i		−	0.623755i
$135$		0			0
$136$	−0.910381	+	0.525609i	−0.0780645	+	0.0450706i
$137$			7.85974i			0.671503i	0.941951	+	0.335751i	$0.108990\pi$
$137$			7.85974i			0.671503i	−0.941951	+	0.335751i	$0.891010\pi$
$138$		0			0
$139$	−19.3599	+	11.1774i	−1.64209	+	0.948058i	−0.661995	+	0.749509i	$0.730290\pi$
$139$	−19.3599	+	11.1774i	−1.64209	+	0.948058i	−0.980091	+	0.198550i	$0.936377\pi$
$140$	2.54549	−	0.721453i	0.215133	−	0.0609739i
$141$		0			0
$142$	−5.37823	−	9.31536i	−0.451331	−	0.781728i
$143$	0.0859835	+	0.148928i	0.00719030	+	0.0124540i
$144$		0			0
$145$	2.95682	+	1.70712i	0.245551	+	0.141769i
$146$	8.03384	−	13.9150i	0.664885	−	1.15162i
$147$		0			0
$148$	−1.37174	−	2.37592i	−0.112756	−	0.195299i
$149$		−	15.7141i		−	1.28735i	−0.765301	−	0.643673i	$-0.777410\pi$
$149$		−	15.7141i		−	1.28735i	0.765301	−	0.643673i	$-0.222590\pi$
$150$		0			0
$151$	6.46602			0.526197			0.263099	−	0.964769i	$-0.415256\pi$
$151$	6.46602			0.526197			0.263099	+	0.964769i	$0.415256\pi$
$152$	−0.541602	+	0.938083i	−0.0439297	+	0.0760885i
$153$		0			0
$154$	0.418377	−	1.65633i	0.0337138	−	0.133471i
$155$	−2.57432	−	1.48628i	−0.206774	−	0.119381i
$156$		0			0
$157$	−13.1731	−	7.60552i	−1.05133	−	0.606986i	−0.128310	−	0.991734i	$-0.540955\pi$
$157$	−13.1731	−	7.60552i	−1.05133	−	0.606986i	−0.923022	+	0.384748i	$0.874288\pi$
$158$	−3.74266	−	2.16082i	−0.297750	−	0.171906i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−6.20728	+	6.38845i	−0.489202	+	0.503480i
$162$		0			0
$163$	−5.32485	+	9.22290i	−0.417074	+	0.722394i	−0.995644	−	0.0932394i	$-0.970278\pi$
$163$	−5.32485	+	9.22290i	−0.417074	+	0.722394i	0.578570	+	0.815633i	$0.303611\pi$
$164$	−4.33793			−0.338735
$165$		0			0
$166$			3.66030i			0.284095i
$167$	9.89716	+	17.1424i	0.765865	+	1.32652i	0.939788	+	0.341758i	$0.111022\pi$
$167$	9.89716	+	17.1424i	0.765865	+	1.32652i	−0.173923	+	0.984759i	$0.555644\pi$
$168$		0			0
$169$	−6.46453	+	11.1969i	−0.497272	+	0.861300i
$170$	0.910381	+	0.525609i	0.0698230	+	0.0403124i
$171$		0			0
$172$	5.04758	+	8.74267i	0.384875	+	0.666623i
$173$	−7.03552	−	12.1859i	−0.534900	−	0.926475i	−0.999168	−	0.0407797i	$-0.987016\pi$
$173$	−7.03552	−	12.1859i	−0.534900	−	0.926475i	0.464268	−	0.885695i	$-0.346318\pi$
$174$		0			0
$175$	−1.89754	−	1.84373i	−0.143441	−	0.139373i
$176$	−0.559189	+	0.322848i	−0.0421505	+	0.0243356i
$177$		0			0
$178$		−	12.2462i		−	0.917895i
$179$	−12.0062	+	6.93177i	−0.897383	+	0.518105i	−0.876350	−	0.481674i	$-0.840029\pi$
$179$	−12.0062	+	6.93177i	−0.897383	+	0.518105i	−0.0210331	+	0.999779i	$0.506696\pi$
$180$		0			0
$181$		−	9.82773i		−	0.730489i	−0.930912	−	0.365245i	$-0.880985\pi$
$181$		−	9.82773i		−	0.730489i	0.930912	−	0.365245i	$-0.119015\pi$
$182$	−0.677935	+	0.192143i	−0.0502519	+	0.0142426i
$183$		0			0
$184$	3.36670			0.248196
$185$	−1.37174	+	2.37592i	−0.100852	+	0.174681i
$186$		0			0
$187$	0.587830	−	0.339384i	0.0429864	−	0.0248182i
$188$	0.0537031			0.00391670
$189$		0			0
$190$	1.08320			0.0785839
$191$	16.5052	−	9.52928i	1.19427	−	0.689514i	0.235001	−	0.971995i	$-0.424491\pi$
$191$	16.5052	−	9.52928i	1.19427	−	0.689514i	0.959273	+	0.282481i	$0.0911574\pi$
$192$		0			0
$193$	7.28322	−	12.6149i	0.524258	−	0.908041i	−0.475344	−	0.879800i	$-0.657676\pi$
$193$	7.28322	−	12.6149i	0.524258	−	0.908041i	0.999601	−	0.0282405i	$-0.00899044\pi$
$194$	17.1744			1.23305
$195$		0			0
$196$	6.16033	+	3.32420i	0.440024	+	0.237443i
$197$			18.1177i			1.29083i	0.763832	+	0.645415i	$0.223316\pi$
$197$			18.1177i			1.29083i	−0.763832	+	0.645415i	$0.776684\pi$
$198$		0			0
$199$	−13.5035	+	7.79625i	−0.957237	+	0.552661i	−0.895322	−	0.445420i	$-0.853054\pi$
$199$	−13.5035	+	7.79625i	−0.957237	+	0.552661i	−0.0619157	+	0.998081i	$0.519721\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	0.388492	−	0.224296i	0.0273342	−	0.0157814i
$203$	2.46322	+	8.69092i	0.172884	+	0.609983i
$204$		0			0
$205$	2.16896	+	3.75676i	0.151487	+	0.262383i
$206$	−2.83472	−	4.90988i	−0.197504	−	0.342088i
$207$		0			0
$208$	0.230647	+	0.133164i	0.0159925	+	0.00923327i
$209$	0.349710	−	0.605716i	0.0241900	−	0.0418983i
$210$		0			0
$211$	−1.65595	−	2.86818i	−0.114000	−	0.197454i	0.803380	−	0.595467i	$-0.203033\pi$
$211$	−1.65595	−	2.86818i	−0.114000	−	0.197454i	−0.917380	+	0.398013i	$0.869700\pi$
$212$			11.7384i			0.806193i
$213$		0			0
$214$	3.83495			0.262152
$215$	5.04758	−	8.74267i	0.344242	−	0.596245i
$216$		0			0
$217$	−2.14457	−	7.56663i	−0.145583	−	0.513656i
$218$	−13.3666	−	7.71722i	−0.905301	−	0.522676i
$219$		0			0
$220$	0.559189	+	0.322848i	0.0377005	+	0.0217664i
$221$	−0.242460	−	0.139984i	−0.0163096	−	0.00941637i
$222$		0			0
$223$	−17.3057	−	9.99144i	−1.15887	−	0.669076i	−0.207840	−	0.978163i	$-0.566643\pi$
$223$	−17.3057	−	9.99144i	−1.15887	−	0.669076i	−0.951034	+	0.309087i	$0.899977\pi$
$224$	−0.721453	−	2.54549i	−0.0482041	−	0.170078i
$225$		0			0
$226$	1.57878	−	2.73453i	0.105019	−	0.181898i
$227$	−15.6914			−1.04147			−0.520736	−	0.853718i	$-0.674342\pi$
$227$	−15.6914			−1.04147			−0.520736	+	0.853718i	$0.674342\pi$
$228$		0			0
$229$		−	11.1174i		−	0.734658i	−0.930091	−	0.367329i	$-0.880272\pi$
$229$		−	11.1174i		−	0.734658i	0.930091	−	0.367329i	$-0.119728\pi$
$230$	−1.68335	−	2.91565i	−0.110997	−	0.192252i
$231$		0			0
$232$	1.70712	−	2.95682i	0.112078	−	0.194125i
$233$	−19.8646	−	11.4688i	−1.30137	−	0.751347i	−0.320732	−	0.947170i	$-0.603929\pi$
$233$	−19.8646	−	11.4688i	−1.30137	−	0.751347i	−0.980639	+	0.195823i	$0.937262\pi$
$234$		0			0
$235$	−0.0268516	−	0.0465083i	−0.00175160	−	0.00303387i
$236$	−2.85148	−	4.93891i	−0.185616	−	0.321496i
$237$		0			0
$238$	0.758405	+	2.67586i	0.0491601	+	0.173450i
$239$	−2.23325	+	1.28937i	−0.144457	+	0.0834023i	−0.570486	−	0.821307i	$-0.693245\pi$
$239$	−2.23325	+	1.28937i	−0.144457	+	0.0834023i	0.426029	+	0.904709i	$0.359912\pi$
$240$		0			0
$241$			21.2682i			1.37000i	0.728542	+	0.685002i	$0.240198\pi$
$241$			21.2682i			1.37000i	−0.728542	+	0.685002i	$0.759802\pi$
$242$	−9.16521	+	5.29154i	−0.589162	+	0.340153i
$243$		0			0
$244$		−	3.54351i		−	0.226850i
$245$	−0.201321	−	6.99710i	−0.0128619	−	0.447029i
$246$		0			0
$247$	−0.288488			−0.0183560
$248$	−1.48628	+	2.57432i	−0.0943791	+	0.163469i
$249$		0			0
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	20.0461			1.26530			0.632649	−	0.774439i	$-0.281968\pi$
$251$	20.0461			1.26530			0.632649	+	0.774439i	$0.281968\pi$
$252$		0			0
$253$	−2.17386			−0.136670
$254$	−6.22187	+	3.59220i	−0.390395	+	0.225395i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.69654			0.292962			0.146481	−	0.989213i	$-0.453205\pi$
$257$	4.69654			0.292962			0.146481	+	0.989213i	$0.453205\pi$
$258$		0			0
$259$	−6.98347	+	1.97929i	−0.433932	+	0.122987i
$260$		−	0.266328i		−	0.0165170i
$261$		0			0
$262$	−0.0647771	+	0.0373991i	−0.00400194	+	0.00231052i
$263$			12.1295i			0.747935i	0.927442	+	0.373968i	$0.122003\pi$
$263$			12.1295i			0.747935i	−0.927442	+	0.373968i	$0.877997\pi$
$264$		0			0
$265$	10.1657	−	5.86918i	0.624475	−	0.360541i
$266$	2.05542	+	1.99714i	0.126026	+	0.122452i
$267$		0			0
$268$	3.61024	+	6.25312i	0.220531	+	0.381970i
$269$	−4.72497	−	8.18388i	−0.288086	−	0.498980i	0.685267	−	0.728292i	$-0.259686\pi$
$269$	−4.72497	−	8.18388i	−0.288086	−	0.498980i	−0.973353	+	0.229312i	$0.926352\pi$
$270$		0			0
$271$	−0.709478	−	0.409617i	−0.0430977	−	0.0248825i	0.478296	−	0.878199i	$-0.341254\pi$
$271$	−0.709478	−	0.409617i	−0.0430977	−	0.0248825i	−0.521394	+	0.853316i	$0.674588\pi$
$272$	0.525609	−	0.910381i	0.0318697	−	0.0552000i
$273$		0			0
$274$	−3.92987	−	6.80673i	−0.237412	−	0.411210i
$275$		−	0.645696i		−	0.0389369i
$276$		0			0
$277$	2.42014			0.145412			0.0727060	−	0.997353i	$-0.476837\pi$
$277$	2.42014			0.145412			0.0727060	+	0.997353i	$0.476837\pi$
$278$	11.1774	−	19.3599i	0.670379	−	1.16113i
$279$		0			0
$280$	−1.84373	+	1.89754i	−0.110184	+	0.113400i
$281$	4.46431	+	2.57747i	0.266318	+	0.153759i	0.627213	−	0.778848i	$-0.284195\pi$
$281$	4.46431	+	2.57747i	0.266318	+	0.153759i	−0.360895	+	0.932606i	$0.617529\pi$
$282$		0			0
$283$	−16.1042	−	9.29775i	−0.957294	−	0.552694i	−0.0619545	−	0.998079i	$-0.519733\pi$
$283$	−16.1042	−	9.29775i	−0.957294	−	0.552694i	−0.895339	+	0.445385i	$0.853067\pi$
$284$	9.31536	+	5.37823i	0.552765	+	0.319139i
$285$		0			0
$286$	−0.148928	−	0.0859835i	−0.00880629	−	0.00508431i
$287$	−2.81075	+	11.1276i	−0.165913	+	0.656840i
$288$		0			0
$289$	7.94747	−	13.7654i	0.467498	−	0.809731i
$290$	−3.41425			−0.200491
$291$		0			0
$292$			16.0677i			0.940290i
$293$	13.5315	+	23.4372i	0.790517	+	1.36922i	0.925647	+	0.378388i	$0.123522\pi$
$293$	13.5315	+	23.4372i	0.790517	+	1.36922i	−0.135130	+	0.990828i	$0.543145\pi$
$294$		0			0
$295$	−2.85148	+	4.93891i	−0.166020	+	0.287554i
$296$	2.37592	+	1.37174i	0.138097	+	0.0797305i
$297$		0			0
$298$	7.85703	+	13.6088i	0.455146	+	0.788335i
$299$	0.448323	+	0.776519i	0.0259272	+	0.0449072i
$300$		0			0
$301$	25.6971	−	7.28319i	1.48116	−	0.419796i
$302$	−5.59974	+	3.23301i	−0.322229	+	0.186039i
$303$		0			0
$304$		−	1.08320i		−	0.0621260i
$305$	−3.06877	+	1.77175i	−0.175717	+	0.101450i
$306$		0			0
$307$		−	26.5519i		−	1.51539i	−0.652606	−	0.757697i	$-0.726324\pi$
$307$		−	26.5519i		−	1.51539i	0.652606	−	0.757697i	$-0.273676\pi$
$308$	0.465840	+	1.64361i	0.0265437	+	0.0936535i
$309$		0			0
$310$	2.97257			0.168830
$311$	−7.18458	+	12.4441i	−0.407400	+	0.705638i	−0.994598	−	0.103806i	$-0.966898\pi$
$311$	−7.18458	+	12.4441i	−0.407400	+	0.705638i	0.587197	+	0.809444i	$0.300231\pi$
$312$		0			0
$313$	−9.50068	+	5.48522i	−0.537010	+	0.310043i	−0.743866	−	0.668328i	$-0.767010\pi$
$313$	−9.50068	+	5.48522i	−0.537010	+	0.310043i	0.206856	+	0.978371i	$0.433677\pi$
$314$	15.2110			0.858408
$315$		0			0
$316$	4.32165			0.243112
$317$	−14.4451	+	8.33988i	−0.811317	+	0.468414i	−0.847413	−	0.530934i	$-0.821841\pi$
$317$	−14.4451	+	8.33988i	−0.811317	+	0.468414i	0.0360960	+	0.999348i	$0.488508\pi$
$318$		0			0
$319$	−1.10228	+	1.90921i	−0.0617160	+	0.106895i
$320$	1.00000			0.0559017
$321$		0			0
$322$	2.18144	−	8.63620i	0.121567	−	0.481277i
$323$			1.13868i			0.0633580i
$324$		0			0
$325$	−0.230647	+	0.133164i	−0.0127940	+	0.00738661i
$326$		−	10.6497i		−	0.589832i
$327$		0			0
$328$	3.75676	−	2.16896i	0.207432	−	0.119761i
$329$	0.0347968	−	0.137758i	0.00191841	−	0.00759487i
$330$		0			0
$331$	2.77401	+	4.80472i	0.152473	+	0.264091i	0.932136	−	0.362108i	$-0.117943\pi$
$331$	2.77401	+	4.80472i	0.152473	+	0.264091i	−0.779663	+	0.626199i	$0.784610\pi$
$332$	−1.83015	−	3.16992i	−0.100443	−	0.173972i
$333$		0			0
$334$	−17.1424	−	9.89716i	−0.937989	−	0.541548i
$335$	3.61024	−	6.25312i	0.197249	−	0.341645i
$336$		0			0
$337$	−15.3125	−	26.5220i	−0.834125	−	1.44475i	−0.894741	−	0.446586i	$-0.852640\pi$
$337$	−15.3125	−	26.5220i	−0.834125	−	1.44475i	0.0606161	−	0.998161i	$-0.480693\pi$
$338$		−	12.9291i		−	0.703249i
$339$		0			0
$340$	−1.05122			−0.0570103
$341$	0.959687	−	1.66223i	0.0519700	−	0.0900147i
$342$		0			0
$343$	12.5188	−	13.6485i	0.675949	−	0.736948i
$344$	−8.74267	−	5.04758i	−0.471373	−	0.272148i
$345$		0			0
$346$	12.1859	+	7.03552i	0.655116	+	0.378232i
$347$	31.6290	+	18.2610i	1.69793	+	0.980301i	0.947720	+	0.319104i	$0.103382\pi$
$347$	31.6290	+	18.2610i	1.69793	+	0.980301i	0.750212	+	0.661197i	$0.229951\pi$
$348$		0			0
$349$	0.811147	+	0.468316i	0.0434197	+	0.0250684i	0.521553	−	0.853219i	$-0.325353\pi$
$349$	0.811147	+	0.468316i	0.0434197	+	0.0250684i	−0.478133	+	0.878287i	$0.658686\pi$
$350$	2.56518	+	0.647947i	0.137115	+	0.0346342i
$351$		0			0
$352$	0.322848	−	0.559189i	0.0172079	−	0.0298049i
$353$	−8.33225			−0.443481			−0.221741	−	0.975106i	$-0.571174\pi$
$353$	−8.33225			−0.443481			−0.221741	+	0.975106i	$0.571174\pi$
$354$		0			0
$355$		−	10.7565i		−	0.570893i
$356$	6.12312	+	10.6056i	0.324525	+	0.562093i
$357$		0			0
$358$	6.93177	−	12.0062i	0.366355	−	0.634546i
$359$	20.1878	+	11.6555i	1.06547	+	0.615152i	0.926941	−	0.375206i	$-0.122428\pi$
$359$	20.1878	+	11.6555i	1.06547	+	0.615152i	0.138532	+	0.990358i	$0.455761\pi$
$360$		0			0
$361$	−8.91333	−	15.4383i	−0.469123	−	0.812545i
$362$	4.91386	+	8.51106i	0.258267	+	0.447332i
$363$		0			0
$364$	0.491037	−	0.505368i	0.0257373	−	0.0264885i
$365$	13.9150	−	8.03384i	0.728345	−	0.420510i
$366$		0			0
$367$		−	4.49651i		−	0.234716i	−0.993090	−	0.117358i	$-0.962558\pi$
$367$		−	4.49651i		−	0.234716i	0.993090	−	0.117358i	$-0.0374425\pi$
$368$	−2.91565	+	1.68335i	−0.151989	+	0.0877507i
$369$		0			0
$370$		−	2.74347i		−	0.142626i
$371$	30.1110	+	7.60583i	1.56329	+	0.394875i
$372$		0			0
$373$	31.1446			1.61261			0.806303	−	0.591503i	$-0.201465\pi$
$373$	31.1446			1.61261			0.806303	+	0.591503i	$0.201465\pi$
$374$	−0.339384	+	0.587830i	−0.0175491	+	0.0303959i
$375$		0			0
$376$	−0.0465083	+	0.0268516i	−0.00239848	+	0.00138476i
$377$	0.909310			0.0468318
$378$		0			0
$379$	7.02139			0.360664			0.180332	−	0.983606i	$-0.442283\pi$
$379$	7.02139			0.360664			0.180332	+	0.983606i	$0.442283\pi$
$380$	−0.938083	+	0.541602i	−0.0481226	+	0.0277836i
$381$		0			0
$382$	−9.52928	+	16.5052i	−0.487560	+	0.844479i
$383$	15.9236			0.813657			0.406828	−	0.913505i	$-0.366635\pi$
$383$	15.9236			0.813657			0.406828	+	0.913505i	$0.366635\pi$
$384$		0			0
$385$	1.19049	−	1.22523i	0.0606730	−	0.0624437i
$386$			14.5664i			0.741412i
$387$		0			0
$388$	−14.8734	+	8.58718i	−0.755084	+	0.435948i
$389$			8.94395i			0.453476i	0.973956	+	0.226738i	$0.0728062\pi$
$389$			8.94395i			0.453476i	−0.973956	+	0.226738i	$0.927194\pi$
$390$		0			0
$391$	3.06498	−	1.76957i	0.155003	−	0.0894908i
$392$	−6.99710	+	0.201321i	−0.353407	+	0.0101682i
$393$		0			0
$394$	−9.05884	−	15.6904i	−0.456378	−	0.790469i
$395$	−2.16082	−	3.74266i	−0.108723	−	0.188314i
$396$		0			0
$397$	−1.35910	−	0.784676i	−0.0682112	−	0.0393818i	0.465507	−	0.885044i	$-0.345872\pi$
$397$	−1.35910	−	0.784676i	−0.0682112	−	0.0393818i	−0.533718	+	0.845663i	$0.679206\pi$
$398$	7.79625	−	13.5035i	0.390791	−	0.676869i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	33.8403i		−	1.68991i	−0.534840	−	0.844953i	$-0.679628\pi$
$401$		−	33.8403i		−	1.68991i	0.534840	−	0.844953i	$-0.320372\pi$
$402$		0			0
$403$	−0.791678			−0.0394363
$404$	−0.224296	+	0.388492i	−0.0111591	+	0.0193282i
$405$		0			0
$406$	−6.47867	−	6.29495i	−0.321531	−	0.312413i
$407$	−1.53412	−	0.885725i	−0.0760435	−	0.0439037i
$408$		0			0
$409$	7.47355	+	4.31486i	0.369543	+	0.213356i	0.673259	−	0.739407i	$-0.264894\pi$
$409$	7.47355	+	4.31486i	0.369543	+	0.213356i	−0.303716	+	0.952763i	$0.598227\pi$
$410$	−3.75676	−	2.16896i	−0.185533	−	0.107118i
$411$		0			0
$412$	4.90988	+	2.83472i	0.241892	+	0.139657i
$413$	−14.5168	+	4.11442i	−0.714326	+	0.202457i
$414$		0			0
$415$	−1.83015	+	3.16992i	−0.0898386	+	0.155605i
$416$	−0.266328			−0.0130578
$417$		0			0
$418$			0.699421i			0.0342098i
$419$	6.77897	+	11.7415i	0.331174	+	0.573610i	0.982742	−	0.184980i	$-0.0592219\pi$
$419$	6.77897	+	11.7415i	0.331174	+	0.573610i	−0.651568	+	0.758590i	$0.725889\pi$
$420$		0			0
$421$	−1.64981	+	2.85756i	−0.0804069	+	0.139269i	−0.903425	−	0.428747i	$-0.858955\pi$
$421$	−1.64981	+	2.85756i	−0.0804069	+	0.139269i	0.823018	+	0.568015i	$0.192289\pi$
$422$	2.86818	+	1.65595i	0.139621	+	0.0806102i
$423$		0			0
$424$	−5.86918	−	10.1657i	−0.285032	−	0.493691i
$425$	0.525609	+	0.910381i	0.0254958	+	0.0441600i
$426$		0			0
$427$	−9.08975	−	2.29600i	−0.439884	−	0.111111i
$428$	−3.32116	+	1.91747i	−0.160534	+	0.0926846i
$429$		0			0
$430$			10.0952i			0.486832i
$431$	17.0763	−	9.85901i	0.822537	−	0.474892i	−0.0287538	−	0.999587i	$-0.509154\pi$
$431$	17.0763	−	9.85901i	0.822537	−	0.474892i	0.851290	+	0.524695i	$0.175821\pi$
$432$		0			0
$433$		−	4.54514i		−	0.218426i	−0.994018	−	0.109213i	$-0.965167\pi$
$433$		−	4.54514i		−	0.218426i	0.994018	−	0.109213i	$-0.0348330\pi$
$434$	5.64056	+	5.48061i	0.270756	+	0.263078i
$435$		0			0
$436$	15.4344			0.739175
$437$	1.82341	−	3.15824i	0.0872256	−	0.151079i
$438$		0			0
$439$	15.0163	−	8.66968i	0.716691	−	0.413781i	−0.0968429	−	0.995300i	$-0.530874\pi$
$439$	15.0163	−	8.66968i	0.716691	−	0.413781i	0.813533	+	0.581518i	$0.197541\pi$
$440$	−0.645696			−0.0307824
$441$		0			0
$442$	0.279969			0.0133168
$443$	0.850958	−	0.491301i	0.0404302	−	0.0233424i	−0.479649	−	0.877461i	$-0.659236\pi$
$443$	0.850958	−	0.491301i	0.0404302	−	0.0233424i	0.520079	+	0.854118i	$0.325903\pi$
$444$		0			0
$445$	6.12312	−	10.6056i	0.290264	−	0.502752i
$446$	19.9829			0.946217
$447$		0			0
$448$	1.89754	+	1.84373i	0.0896504	+	0.0871080i
$449$			29.6441i			1.39899i	0.714636	+	0.699496i	$0.246592\pi$
$449$			29.6441i			1.39899i	−0.714636	+	0.699496i	$0.753408\pi$
$450$		0			0
$451$	−2.42572	+	1.40049i	−0.114223	+	0.0659466i
$452$			3.15757i			0.148519i
$453$		0			0
$454$	13.5891	−	7.84568i	0.637769	−	0.368216i
$455$	−0.683180	−	0.172566i	−0.0320280	−	0.00809004i
$456$		0			0
$457$	5.85157	+	10.1352i	0.273725	+	0.474106i	0.969813	−	0.243851i	$-0.0784108\pi$
$457$	5.85157	+	10.1352i	0.273725	+	0.474106i	−0.696088	+	0.717957i	$0.745077\pi$
$458$	5.55869	+	9.62794i	0.259741	+	0.449884i
$459$		0			0
$460$	2.91565	+	1.68335i	0.135943	+	0.0784866i
$461$	18.2593	−	31.6260i	0.850418	−	1.47297i	−0.0304133	−	0.999537i	$-0.509682\pi$
$461$	18.2593	−	31.6260i	0.850418	−	1.47297i	0.880831	−	0.473430i	$-0.156984\pi$
$462$		0			0
$463$	−1.08855	−	1.88543i	−0.0505893	−	0.0876233i	0.839622	−	0.543171i	$-0.182777\pi$
$463$	−1.08855	−	1.88543i	−0.0505893	−	0.0876233i	−0.890211	+	0.455548i	$0.849443\pi$
$464$			3.41425i			0.158502i
$465$		0			0
$466$	22.9376			1.06257
$467$	12.2781	−	21.2663i	0.568164	−	0.984088i	−0.428584	−	0.903502i	$-0.640987\pi$
$467$	12.2781	−	21.2663i	0.568164	−	0.984088i	0.996748	−	0.0805862i	$-0.0256792\pi$
$468$		0			0
$469$	18.3797	−	5.20924i	0.848693	−	0.240541i
$470$	0.0465083	+	0.0268516i	0.00214527	+	0.00123857i
$471$		0			0
$472$	4.93891	+	2.85148i	0.227332	+	0.131250i
$473$	5.64511	+	3.25921i	0.259562	+	0.149858i
$474$		0			0
$475$	0.938083	+	0.541602i	0.0430422	+	0.0248504i
$476$	−1.99473	−	1.93816i	−0.0914282	−	0.0888355i
$477$		0			0
$478$	1.28937	−	2.23325i	0.0589743	−	0.102147i
$479$	−30.1072			−1.37563			−0.687816	−	0.725885i	$-0.741430\pi$
$479$	−30.1072			−1.37563			−0.687816	+	0.725885i	$0.741430\pi$
$480$		0			0
$481$			0.730664i			0.0333154i
$482$	−10.6341	−	18.4188i	−0.484369	−	0.838952i
$483$		0			0
$484$	5.29154	−	9.16521i	0.240524	−	0.416601i
$485$	14.8734	+	8.58718i	0.675368	+	0.389924i
$486$		0			0
$487$	11.3594	+	19.6750i	0.514742	+	0.891560i	0.999854	+	0.0171073i	$0.00544569\pi$
$487$	11.3594	+	19.6750i	0.514742	+	0.891560i	−0.485111	+	0.874452i	$0.661221\pi$
$488$	1.77175	+	3.06877i	0.0802035	+	0.138917i
$489$		0			0
$490$	3.67290	+	5.95901i	0.165925	+	0.269201i
$491$	15.8571	−	9.15511i	0.715621	−	0.413164i	−0.0975175	−	0.995234i	$-0.531090\pi$
$491$	15.8571	−	9.15511i	0.715621	−	0.413164i	0.813139	+	0.582070i	$0.197757\pi$
$492$		0			0
$493$		−	3.58912i		−	0.161646i
$494$	0.249838	−	0.144244i	0.0112407	−	0.00648984i
$495$		0			0
$496$		−	2.97257i		−	0.133472i
$497$	19.8320	−	20.4108i	0.889586	−	0.915550i
$498$		0			0
$499$	−22.8391			−1.02242			−0.511210	−	0.859456i	$-0.670802\pi$
$499$	−22.8391			−1.02242			−0.511210	+	0.859456i	$0.670802\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−17.3604	+	10.0230i	−0.774833	+	0.447350i
$503$	17.5765			0.783699			0.391849	−	0.920029i	$-0.371835\pi$
$503$	17.5765			0.783699			0.391849	+	0.920029i	$0.371835\pi$
$504$		0			0
$505$	0.448592			0.0199621
$506$	1.88262	−	1.08693i	0.0836928	−	0.0483200i
$507$		0			0
$508$	3.59220	−	6.22187i	0.159378	−	0.276051i
$509$	−38.2842			−1.69692			−0.848458	−	0.529262i	$-0.822469\pi$
$509$	−38.2842			−1.69692			−0.848458	+	0.529262i	$0.822469\pi$
$510$		0			0
$511$	41.2166	+	10.4110i	1.82331	+	0.460556i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.06732	+	2.34827i	−0.179402	+	0.103578i
$515$		−	5.66944i		−	0.249825i
$516$		0			0
$517$	0.0300302	−	0.0173380i	0.00132073	−	0.000762522i
$518$	5.05822	−	5.20585i	0.222245	−	0.228732i
$519$		0			0
$520$	0.133164	+	0.230647i	0.00583963	+	0.0101145i
$521$	−4.81631	−	8.34209i	−0.211006	−	0.365474i	0.741023	−	0.671479i	$-0.234341\pi$
$521$	−4.81631	−	8.34209i	−0.211006	−	0.365474i	−0.952030	+	0.306006i	$0.901007\pi$
$522$		0			0
$523$	15.4244	+	8.90530i	0.674463	+	0.389401i	0.797766	−	0.602968i	$-0.206015\pi$
$523$	15.4244	+	8.90530i	0.674463	+	0.389401i	−0.123303	+	0.992369i	$0.539349\pi$
$524$	0.0373991	−	0.0647771i	0.00163379	−	0.00282980i
$525$		0			0
$526$	−6.06474	−	10.5044i	−0.264435	−	0.458015i
$527$			3.12481i			0.136119i
$528$		0			0
$529$	11.6653			0.507189
$530$	−5.86918	+	10.1657i	−0.254941	+	0.441570i
$531$		0			0
$532$	−2.77862	−	0.701859i	−0.120468	−	0.0304294i
$533$	1.00053	+	0.577656i	0.0433378	+	0.0250211i
$534$		0			0
$535$	3.32116	+	1.91747i	0.143586	+	0.0828996i
$536$	−6.25312	−	3.61024i	−0.270094	−	0.155939i
$537$		0			0
$538$	8.18388	+	4.72497i	0.352832	+	0.203708i
$539$	4.51800	−	0.129992i	0.194604	−	0.00559915i
$540$		0			0
$541$	16.5362	−	28.6415i	0.710945	−	1.23139i	−0.253558	−	0.967320i	$-0.581601\pi$
$541$	16.5362	−	28.6415i	0.710945	−	1.23139i	0.964503	−	0.264073i	$-0.0850658\pi$
$542$	0.819235			0.0351891
$543$		0			0
$544$			1.05122i			0.0450706i
$545$	−7.71722	−	13.3666i	−0.330569	−	0.572563i
$546$		0			0
$547$	−5.28847	+	9.15990i	−0.226119	+	0.391649i	−0.956654	−	0.291225i	$-0.905937\pi$
$547$	−5.28847	+	9.15990i	−0.226119	+	0.391649i	0.730536	+	0.682874i	$0.239270\pi$
$548$	6.80673	+	3.92987i	0.290769	+	0.167876i
$549$		0			0
$550$	0.322848	+	0.559189i	0.0137663	+	0.0238439i
$551$	−1.84916	−	3.20285i	−0.0787770	−	0.136446i
$552$		0			0
$553$	2.80020	−	11.0858i	0.119077	−	0.471417i
$554$	−2.09590	+	1.21007i	−0.0890463	+	0.0514109i
$555$		0			0
$556$			22.3549i			0.948058i
$557$	6.46701	−	3.73373i	0.274016	−	0.158203i	−0.356695	−	0.934221i	$-0.616097\pi$
$557$	6.46701	−	3.73373i	0.274016	−	0.158203i	0.630711	+	0.776018i	$0.282763\pi$
$558$		0			0
$559$		−	2.68863i		−	0.113717i
$560$	0.647947	−	2.56518i	0.0273807	−	0.108399i
$561$		0			0
$562$	−5.15494			−0.217448
$563$	−7.66915	+	13.2834i	−0.323216	+	0.559827i	−0.981150	−	0.193249i	$-0.938097\pi$
$563$	−7.66915	+	13.2834i	−0.323216	+	0.559827i	0.657934	+	0.753076i	$0.271431\pi$
$564$		0			0
$565$	2.73453	−	1.57878i	0.115043	−	0.0664199i
$566$	18.5955			0.781627
$567$		0			0
$568$	−10.7565			−0.451331
$569$	0.784849	−	0.453133i	0.0329026	−	0.0189963i	−0.483458	−	0.875367i	$-0.660620\pi$
$569$	0.784849	−	0.453133i	0.0329026	−	0.0189963i	0.516361	+	0.856371i	$0.327286\pi$
$570$		0			0
$571$	−17.7429	+	30.7315i	−0.742516	+	1.28607i	0.208831	+	0.977952i	$0.433034\pi$
$571$	−17.7429	+	30.7315i	−0.742516	+	1.28607i	−0.951346	+	0.308123i	$0.900299\pi$
$572$	0.171967			0.00719030
$573$		0			0
$574$	−3.12961	−	11.0421i	−0.130628	−	0.460890i
$575$		−	3.36670i		−	0.140401i
$576$		0			0
$577$	−25.7446	+	14.8636i	−1.07176	+	0.618781i	−0.928662	−	0.370928i	$-0.879040\pi$
$577$	−25.7446	+	14.8636i	−1.07176	+	0.618781i	−0.143098	+	0.989709i	$0.545706\pi$
$578$			15.8949i			0.661142i
$579$		0			0
$580$	2.95682	−	1.70712i	0.122775	−	0.0708844i
$581$	−9.31726	+	2.64074i	−0.386545	+	0.109556i
$582$		0			0
$583$	3.78971	+	6.56396i	0.156954	+	0.271852i
$584$	−8.03384	−	13.9150i	−0.332443	−	0.575808i
$585$		0			0
$586$	−23.4372	−	13.5315i	−0.968182	−	0.558980i
$587$	−15.2602	+	26.4315i	−0.629857	+	1.09095i	0.357723	+	0.933828i	$0.383553\pi$
$587$	−15.2602	+	26.4315i	−0.629857	+	1.09095i	−0.987580	+	0.157117i	$0.949780\pi$
$588$		0			0
$589$	1.60995	+	2.78851i	0.0663368	+	0.114899i
$590$		−	5.70296i		−	0.234787i
$591$		0			0
$592$	−2.74347			−0.112756
$593$	15.1799	−	26.2924i	0.623366	−	1.07970i	−0.365489	−	0.930816i	$-0.619098\pi$
$593$	15.1799	−	26.2924i	0.623366	−	1.07970i	0.988854	−	0.148885i	$-0.0475685\pi$
$594$		0			0
$595$	−0.681133	+	2.69657i	−0.0279237	+	0.110548i
$596$	−13.6088	−	7.85703i	−0.557437	−	0.321837i
$597$		0			0
$598$	−0.776519	−	0.448323i	−0.0317542	−	0.0183333i
$599$	6.15334	+	3.55263i	0.251419	+	0.145157i	0.620414	−	0.784275i	$-0.286965\pi$
$599$	6.15334	+	3.55263i	0.251419	+	0.145157i	−0.368995	+	0.929431i	$0.620298\pi$
$600$		0			0
$601$	22.8386	+	13.1859i	0.931607	+	0.537864i	0.887320	−	0.461155i	$-0.152565\pi$
$601$	22.8386	+	13.1859i	0.931607	+	0.537864i	0.0442879	+	0.999019i	$0.485898\pi$
$602$	−18.6128	+	19.1560i	−0.758600	+	0.780740i
$603$		0			0
$604$	3.23301	−	5.59974i	0.131549	−	0.227850i
$605$	−10.5831			−0.430263
$606$		0			0
$607$			3.86727i			0.156968i	0.996915	+	0.0784839i	$0.0250079\pi$
$607$			3.86727i			0.156968i	−0.996915	+	0.0784839i	$0.974992\pi$
$608$	0.541602	+	0.938083i	0.0219649	+	0.0380443i
$609$		0			0
$610$	1.77175	−	3.06877i	0.0717362	−	0.124251i
$611$	−0.0123865	−	0.00715133i	−0.000501103	−	0.000289312i
$612$		0			0
$613$	10.4441	+	18.0897i	0.421833	+	0.730637i	0.996119	−	0.0880184i	$-0.0280534\pi$
$613$	10.4441	+	18.0897i	0.421833	+	0.730637i	−0.574286	+	0.818655i	$0.694720\pi$
$614$	13.2759	+	22.9946i	0.535773	+	0.927986i
$615$		0			0
$616$	−1.22523	−	1.19049i	−0.0493661	−	0.0479662i
$617$	34.0270	−	19.6455i	1.36987	−	0.790898i	0.378963	−	0.925412i	$-0.376281\pi$
$617$	34.0270	−	19.6455i	1.36987	−	0.790898i	0.990912	+	0.134514i	$0.0429474\pi$
$618$		0			0
$619$			8.31333i			0.334141i	0.985945	+	0.167071i	$0.0534308\pi$
$619$			8.31333i			0.334141i	−0.985945	+	0.167071i	$0.946569\pi$
$620$	−2.57432	+	1.48628i	−0.103387	+	0.0596906i
$621$		0			0
$622$		−	14.3692i		−	0.576151i
$623$	31.1727	−	8.83509i	1.24891	−	0.353971i
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.48522	−	9.50068i	0.219234	−	0.379724i
$627$		0			0
$628$	−13.1731	+	7.60552i	−0.525666	+	0.303493i
$629$	2.88399			0.114992
$630$		0			0
$631$	11.0713			0.440743			0.220372	−	0.975416i	$-0.429273\pi$
$631$	11.0713			0.440743			0.220372	+	0.975416i	$0.429273\pi$
$632$	−3.74266	+	2.16082i	−0.148875	+	0.0859530i
$633$		0			0
$634$	8.33988	−	14.4451i	0.331219	−	0.573688i
$635$	−7.18440			−0.285104
$636$		0			0
$637$	−0.978197	−	1.58705i	−0.0387576	−	0.0628813i
$638$		−	2.20457i		−	0.0872796i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$		−	30.8884i		−	1.22002i	−0.792394	−	0.610010i	$-0.791166\pi$
$641$		−	30.8884i		−	1.22002i	0.792394	−	0.610010i	$-0.208834\pi$
$642$		0			0
$643$	−14.7423	+	8.51146i	−0.581379	+	0.335659i	−0.761681	−	0.647952i	$-0.775626\pi$
$643$	−14.7423	+	8.51146i	−0.581379	+	0.335659i	0.180302	+	0.983611i	$0.442292\pi$
$644$	2.42892	+	8.56989i	0.0957127	+	0.337701i
$645$		0			0
$646$	−0.569342	−	0.986129i	−0.0224005	−	0.0387987i
$647$	−22.3824	−	38.7675i	−0.879944	−	1.52411i	−0.851402	−	0.524514i	$-0.824247\pi$
$647$	−22.3824	−	38.7675i	−0.879944	−	1.52411i	−0.0285419	−	0.999593i	$-0.509086\pi$
$648$		0			0
$649$	−3.18903	−	1.84119i	−0.125181	−	0.0722730i
$650$	0.133164	−	0.230647i	0.00522312	−	0.00904672i
$651$		0			0
$652$	5.32485	+	9.22290i	0.208537	+	0.361197i
$653$			13.7987i			0.539985i	0.962862	+	0.269993i	$0.0870213\pi$
$653$			13.7987i			0.539985i	−0.962862	+	0.269993i	$0.912979\pi$
$654$		0			0
$655$	−0.0747982			−0.00292261
$656$	−2.16896	+	3.75676i	−0.0846838	+	0.146677i
$657$		0			0
$658$	0.0387443	+	0.136701i	0.00151041	+	0.00532915i
$659$	−39.8972	−	23.0347i	−1.55417	−	0.897303i	−0.997795	−	0.0663746i	$-0.978857\pi$
$659$	−39.8972	−	23.0347i	−1.55417	−	0.897303i	−0.556379	−	0.830928i	$-0.687810\pi$
$660$		0			0
$661$	−13.0963	−	7.56114i	−0.509386	−	0.294094i	0.223195	−	0.974774i	$-0.428351\pi$
$661$	−13.0963	−	7.56114i	−0.509386	−	0.294094i	−0.732581	+	0.680679i	$0.761685\pi$
$662$	−4.80472	−	2.77401i	−0.186741	−	0.107815i
$663$		0			0
$664$	3.16992	+	1.83015i	0.123017	+	0.0710237i
$665$	0.781482	+	2.75728i	0.0303046	+	0.106923i
$666$		0			0
$667$	−5.74737	+	9.95474i	−0.222539	+	0.385449i
$668$	19.7943			0.765865
$669$		0			0
$670$			7.22048i			0.278952i
$671$	−1.14402	−	1.98149i	−0.0441642	−	0.0764947i
$672$		0			0
$673$	−24.9981	+	43.2980i	−0.963607	+	1.66902i	−0.250296	+	0.968169i	$0.580528\pi$
$673$	−24.9981	+	43.2980i	−0.963607	+	1.66902i	−0.713311	+	0.700848i	$0.752805\pi$
$674$	26.5220	+	15.3125i	1.02159	+	0.589815i
$675$		0			0
$676$	6.46453	+	11.1969i	0.248636	+	0.430650i
$677$	−7.48230	−	12.9597i	−0.287568	−	0.498083i	0.685661	−	0.727921i	$-0.259513\pi$
$677$	−7.48230	−	12.9597i	−0.287568	−	0.498083i	−0.973229	+	0.229839i	$0.926180\pi$
$678$		0			0
$679$	12.3905	+	43.7171i	0.475504	+	1.67771i
$680$	0.910381	−	0.525609i	0.0349115	−	0.0201562i
$681$		0			0
$682$			1.91937i			0.0734967i
$683$	−31.4634	+	18.1654i	−1.20391	+	0.695080i	−0.961423	−	0.275074i	$-0.911298\pi$
$683$	−31.4634	+	18.1654i	−1.20391	+	0.695080i	−0.242490	+	0.970154i	$0.577964\pi$
$684$		0			0
$685$		−	7.85974i		−	0.300305i
$686$	−4.01733	+	18.0793i	−0.153382	+	0.690271i
$687$		0			0
$688$	10.0952			0.384875
$689$	1.56313	−	2.70741i	0.0595504	−	0.103144i
$690$		0			0
$691$	21.5677	−	12.4521i	0.820474	−	0.473701i	−0.0301056	−	0.999547i	$-0.509584\pi$
$691$	21.5677	−	12.4521i	0.820474	−	0.473701i	0.850580	+	0.525846i	$0.176251\pi$
$692$	−14.0710			−0.534900
$693$		0			0
$694$	−36.5220			−1.38636
$695$	19.3599	−	11.1774i	0.734363	−	0.423985i
$696$		0			0
$697$	2.28005	−	3.94917i	0.0863632	−	0.149585i
$698$	−0.936631			−0.0354520
$699$		0			0
$700$	−2.54549	+	0.721453i	−0.0962104	+	0.0272684i
$701$		−	35.4297i		−	1.33816i	−0.743190	−	0.669081i	$-0.766688\pi$
$701$		−	35.4297i		−	1.33816i	0.743190	−	0.669081i	$-0.233312\pi$
$702$		0			0
$703$	2.57360	−	1.48587i	0.0970653	−	0.0560407i
$704$			0.645696i			0.0243356i
$705$		0			0
$706$	7.21594	−	4.16613i	0.271576	−	0.156794i
$707$	0.851222	+	0.827083i	0.0320135	+	0.0311056i
$708$		0			0
$709$	−23.7707	−	41.1721i	−0.892728	−	1.54625i	−0.836591	−	0.547828i	$-0.815455\pi$
$709$	−23.7707	−	41.1721i	−0.892728	−	1.54625i	−0.0561372	−	0.998423i	$-0.517878\pi$
$710$	5.37823	+	9.31536i	0.201841	+	0.349599i
$711$		0			0
$712$	−10.6056	−	6.12312i	−0.397460	−	0.229474i
$713$	5.00387	−	8.66695i	0.187396	−	0.324580i
$714$		0			0
$715$	−0.0859835	−	0.148928i	−0.00321560	−	0.00556958i
$716$			13.8635i			0.518105i
$717$		0			0
$718$	−23.3109			−0.869956
$719$	−6.86251	+	11.8862i	−0.255928	+	0.443281i	−0.965147	−	0.261707i	$-0.915714\pi$
$719$	−6.86251	+	11.8862i	−0.255928	+	0.443281i	0.709219	+	0.704988i	$0.249048\pi$
$720$		0			0
$721$	10.4529	−	10.7580i	0.389287	−	0.400649i
$722$	15.4383	+	8.91333i	0.574556	+	0.331720i
$723$		0			0
$724$	−8.51106	−	4.91386i	−0.316311	−	0.182622i
$725$	−2.95682	−	1.70712i	−0.109814	−	0.0634010i
$726$		0			0
$727$	38.0093	+	21.9447i	1.40969	+	0.813883i	0.995358	−	0.0962448i	$-0.0306832\pi$
$727$	38.0093	+	21.9447i	1.40969	+	0.813883i	0.414328	+	0.910127i	$0.364016\pi$
$728$	−0.172566	+	0.683180i	−0.00639574	+	0.0253203i
$729$		0			0
$730$	−8.03384	+	13.9150i	−0.297346	+	0.515018i
$731$	−10.6122			−0.392507
$732$		0			0
$733$		−	9.46051i		−	0.349432i	−0.984619	−	0.174716i	$-0.944099\pi$
$733$		−	9.46051i		−	0.349432i	0.984619	−	0.174716i	$-0.0559007\pi$
$734$	2.24825	+	3.89409i	0.0829845	+	0.143733i
$735$		0			0
$736$	1.68335	−	2.91565i	0.0620491	−	0.107472i
$737$	4.03762	+	2.33112i	0.148728	+	0.0858679i
$738$		0			0
$739$	1.16306	+	2.01449i	0.0427840	+	0.0741041i	0.886624	−	0.462490i	$-0.153044\pi$
$739$	1.16306	+	2.01449i	0.0427840	+	0.0741041i	−0.843840	+	0.536594i	$0.819711\pi$
$740$	1.37174	+	2.37592i	0.0504260	+	0.0873404i
$741$		0			0
$742$	−29.8798	+	8.46868i	−1.09692	+	0.310895i
$743$	−3.14789	+	1.81743i	−0.115485	+	0.0666752i	−0.556630	−	0.830761i	$-0.687906\pi$
$743$	−3.14789	+	1.81743i	−0.115485	+	0.0666752i	0.441145	+	0.897436i	$0.354572\pi$
$744$		0			0
$745$			15.7141i			0.575719i
$746$	−26.9720	+	15.5723i	−0.987515	+	0.570142i
$747$		0			0
$748$		−	0.678767i		−	0.0248182i
$749$	2.76674	+	9.76181i	0.101094	+	0.356689i
$750$		0			0
$751$	−13.4034			−0.489097			−0.244548	−	0.969637i	$-0.578640\pi$
$751$	−13.4034			−0.489097			−0.244548	+	0.969637i	$0.578640\pi$
$752$	0.0268516	−	0.0465083i	0.000979176	−	0.00169598i
$753$		0			0
$754$	−0.787485	+	0.454655i	−0.0286785	+	0.0165576i
$755$	−6.46602			−0.235323
$756$		0			0
$757$	9.85725			0.358268			0.179134	−	0.983825i	$-0.442670\pi$
$757$	9.85725			0.358268			0.179134	+	0.983825i	$0.442670\pi$
$758$	−6.08070	+	3.51069i	−0.220861	+	0.127514i
$759$		0			0
$760$	0.541602	−	0.938083i	0.0196460	−	0.0340278i
$761$	−39.8245			−1.44364			−0.721818	−	0.692083i	$-0.756693\pi$
$761$	−39.8245			−1.44364			−0.721818	+	0.692083i	$0.756693\pi$
$762$		0			0
$763$	10.0007	−	39.5921i	0.362049	−	1.43333i
$764$		−	19.0586i		−	0.689514i
$765$		0			0
$766$	−13.7902	+	7.96179i	−0.498261	+	0.287671i
$767$			1.51886i			0.0548428i
$768$		0			0
$769$	−36.9471	+	21.3314i	−1.33235	+	0.769231i	−0.985659	−	0.168750i	$-0.946027\pi$
$769$	−36.9471	+	21.3314i	−1.33235	+	0.769231i	−0.346688	+	0.937981i	$0.612694\pi$
$770$	−0.418377	+	1.65633i	−0.0150772	+	0.0596900i
$771$		0			0
$772$	−7.28322	−	12.6149i	−0.262129	−	0.454020i
$773$	5.52090	+	9.56248i	0.198573	+	0.343939i	0.948066	−	0.318074i	$-0.103036\pi$
$773$	5.52090	+	9.56248i	0.198573	+	0.343939i	−0.749493	+	0.662012i	$0.769703\pi$
$774$		0			0
$775$	2.57432	+	1.48628i	0.0924722	+	0.0533889i
$776$	8.58718	−	14.8734i	0.308262	−	0.533925i
$777$		0			0
$778$	−4.47198	−	7.74569i	−0.160328	−	0.277696i
$779$		−	4.69886i		−	0.168354i
$780$		0			0
$781$	6.94540			0.248526
$782$	−1.76957	+	3.06498i	−0.0632796	+	0.109603i
$783$		0			0
$784$	5.95901	−	3.67290i	0.212822	−	0.131175i
$785$	13.1731	+	7.60552i	0.470170	+	0.271453i
$786$		0			0
$787$	−11.6514	−	6.72696i	−0.415329	−	0.239790i	0.277748	−	0.960654i	$-0.410412\pi$
$787$	−11.6514	−	6.72696i	−0.415329	−	0.239790i	−0.693077	+	0.720864i	$0.743745\pi$
$788$	15.6904	+	9.05884i	0.558946	+	0.322708i
$789$		0			0
$790$	3.74266	+	2.16082i	0.133158	+	0.0768787i
$791$	8.09974	+	2.04593i	0.287994	+	0.0727451i
$792$		0			0
$793$	−0.471868	+	0.817299i	−0.0167565	+	0.0290231i
$794$	1.56935			0.0556942
$795$		0			0
$796$			15.5925i			0.552661i
$797$	−18.3399	−	31.7656i	−0.649631	−	1.12519i	−0.983211	−	0.182472i	$-0.941590\pi$
$797$	−18.3399	−	31.7656i	−0.649631	−	1.12519i	0.333580	−	0.942722i	$-0.391743\pi$
$798$		0			0
$799$	−0.0282268	+	0.0488903i	−0.000998594	+	0.00172962i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	16.9202	+	29.3066i	0.597472	+	1.03485i
$803$	5.18742	+	8.98488i	0.183060	+	0.317069i
$804$		0			0
$805$	6.20728	−	6.38845i	0.218778	−	0.225163i
$806$	0.685613	−	0.395839i	0.0241497	−	0.0139428i
$807$		0			0
$808$		−	0.448592i		−	0.0157814i
$809$	−14.9049	+	8.60538i	−0.524030	+	0.302549i	−0.738582	−	0.674164i	$-0.764504\pi$
$809$	−14.9049	+	8.60538i	−0.524030	+	0.302549i	0.214552	+	0.976713i	$0.431171\pi$
$810$		0			0
$811$		−	5.81435i		−	0.204169i	−0.994776	−	0.102085i	$-0.967449\pi$
$811$		−	5.81435i		−	0.204169i	0.994776	−	0.102085i	$-0.0325513\pi$
$812$	8.75817	+	2.21225i	0.307351	+	0.0776347i
$813$		0			0
$814$	1.77145			0.0620893
$815$	5.32485	−	9.22290i	0.186521	−	0.323064i
$816$		0			0
$817$	−9.47010	+	5.46757i	−0.331317	+	0.191286i
$818$	−8.62971			−0.301731
$819$		0			0
$820$	4.33793			0.151487
$821$	−27.6833	+	15.9830i	−0.966154	+	0.557810i	−0.898062	−	0.439869i	$-0.855025\pi$
$821$	−27.6833	+	15.9830i	−0.966154	+	0.557810i	−0.0680927	+	0.997679i	$0.521691\pi$
$822$		0			0
$823$	−12.8380	+	22.2360i	−0.447504	+	0.775100i	−0.998223	−	0.0595911i	$-0.981020\pi$
$823$	−12.8380	+	22.2360i	−0.447504	+	0.775100i	0.550719	+	0.834691i	$0.314354\pi$
$824$	−5.66944			−0.197504
$825$		0			0
$826$	10.5147	−	10.8216i	0.365854	−	0.376532i
$827$		−	38.7042i		−	1.34588i	−0.739698	−	0.672939i	$-0.765032\pi$
$827$		−	38.7042i		−	1.34588i	0.739698	−	0.672939i	$-0.234968\pi$
$828$		0			0
$829$	9.07060	−	5.23691i	0.315035	−	0.181885i	−0.334142	−	0.942523i	$-0.608447\pi$
$829$	9.07060	−	5.23691i	0.315035	−	0.181885i	0.649177	+	0.760637i	$0.275113\pi$
$830$		−	3.66030i		−	0.127051i
$831$		0			0
$832$	0.230647	−	0.133164i	0.00799624	−	0.00461663i
$833$	−6.26422	+	3.86102i	−0.217042	+	0.133776i
$834$		0			0
$835$	−9.89716	−	17.1424i	−0.342505	−	0.593237i
$836$	−0.349710	−	0.605716i	−0.0120950	−	0.0209491i
$837$		0			0
$838$	−11.7415	−	6.77897i	−0.405604	−	0.234176i
$839$	−18.1028	+	31.3549i	−0.624977	+	1.08249i	0.363568	+	0.931568i	$0.381558\pi$
$839$	−18.1028	+	31.3549i	−0.624977	+	1.08249i	−0.988545	+	0.150925i	$0.951775\pi$
$840$		0			0
$841$	−8.67146	−	15.0194i	−0.299016	−	0.517911i
$842$		−	3.29962i		−	0.113713i
$843$		0			0
$844$	−3.31189			−0.114000
$845$	6.46453	−	11.1969i	0.222387	−	0.385185i
$846$		0			0
$847$	−20.0818	−	19.5123i	−0.690019	−	0.670452i
$848$	10.1657	+	5.86918i	0.349092	+	0.201548i
$849$		0			0
$850$	−0.910381	−	0.525609i	−0.0312258	−	0.0180282i
$851$	−7.99899	−	4.61822i	−0.274202	−	0.158311i
$852$		0			0
$853$	−36.2033	−	20.9020i	−1.23958	−	0.715671i	−0.270570	−	0.962700i	$-0.587212\pi$
$853$	−36.2033	−	20.9020i	−1.23958	−	0.715671i	−0.969008	+	0.247030i	$0.920545\pi$
$854$	9.01996	−	2.55648i	0.308657	−	0.0874808i
$855$		0			0
$856$	1.91747	−	3.32116i	0.0655379	−	0.113515i
$857$	−14.3813			−0.491256			−0.245628	−	0.969364i	$-0.578994\pi$
$857$	−14.3813			−0.491256			−0.245628	+	0.969364i	$0.578994\pi$
$858$		0			0
$859$		−	16.2444i		−	0.554252i	−0.960834	−	0.277126i	$-0.910618\pi$
$859$		−	16.2444i		−	0.554252i	0.960834	−	0.277126i	$-0.0893819\pi$
$860$	−5.04758	−	8.74267i	−0.172121	−	0.298123i
$861$		0			0
$862$	−9.85901	+	17.0763i	−0.335799	+	0.581621i
$863$	1.73844	+	1.00369i	0.0591773	+	0.0341660i	0.529297	−	0.848437i	$-0.322456\pi$
$863$	1.73844	+	1.00369i	0.0591773	+	0.0341660i	−0.470119	+	0.882603i	$0.655789\pi$
$864$		0			0
$865$	7.03552	+	12.1859i	0.239215	+	0.414332i
$866$	2.27257	+	3.93621i	0.0772251	+	0.133758i
$867$		0			0
$868$	−7.62518	−	1.92606i	−0.258815	−	0.0653749i
$869$	2.41662	−	1.39524i	0.0819782	−	0.0473301i
$870$		0			0
$871$		−	1.92302i		−	0.0651590i
$872$	−13.3666	+	7.71722i	−0.452651	+	0.261338i
$873$		0			0
$874$			3.64682i			0.123356i
$875$	1.89754	+	1.84373i	0.0641486	+	0.0623294i
$876$		0			0
$877$	−47.1351			−1.59164			−0.795819	−	0.605534i	$-0.792959\pi$
$877$	−47.1351			−1.59164			−0.795819	+	0.605534i	$0.792959\pi$
$878$	−8.66968	+	15.0163i	−0.292588	+	0.506777i
$879$		0			0
$880$	0.559189	−	0.322848i	0.0188503	−	0.0108832i
$881$	−45.7938			−1.54283			−0.771416	−	0.636331i	$-0.780451\pi$
$881$	−45.7938			−1.54283			−0.771416	+	0.636331i	$0.780451\pi$
$882$		0			0
$883$	50.8663			1.71179			0.855894	−	0.517151i	$-0.173007\pi$
$883$	50.8663			1.71179			0.855894	+	0.517151i	$0.173007\pi$
$884$	−0.242460	+	0.139984i	−0.00815481	+	0.00470818i
$885$		0			0
$886$	−0.491301	+	0.850958i	−0.0165056	+	0.0285885i
$887$	−14.3175			−0.480733			−0.240367	−	0.970682i	$-0.577268\pi$
$887$	−14.3175			−0.480733			−0.240367	+	0.970682i	$0.577268\pi$
$888$		0			0
$889$	−13.6327	−	13.2461i	−0.457226	−	0.444260i
$890$			12.2462i			0.410495i
$891$		0			0
$892$	−17.3057	+	9.99144i	−0.579437	+	0.334538i
$893$			0.0581715i			0.00194663i
$894$		0			0
$895$	12.0062	−	6.93177i	0.401322	−	0.231703i
$896$	−2.56518	−	0.647947i	−0.0856968	−	0.0216464i
$897$		0			0
$898$	−14.8221	−	25.6726i	−0.494619	−	0.856704i
$899$	−5.07454	−	8.78936i	−0.169245	−	0.293141i
$900$		0			0
$901$	−10.6864	−	6.16978i	−0.356015	−	0.205545i
$902$	1.40049	−	2.42572i	0.0466313	−	0.0807678i
$903$		0			0
$904$	−1.57878	−	2.73453i	−0.0525096	−	0.0909492i
$905$			9.82773i			0.326685i
$906$		0			0
$907$	24.5154			0.814019			0.407010	−	0.913424i	$-0.366572\pi$
$907$	24.5154			0.814019			0.407010	+	0.913424i	$0.366572\pi$
$908$	−7.84568	+	13.5891i	−0.260368	+	0.450971i
$909$		0			0
$910$	0.677935	−	0.192143i	0.0224733	−	0.00636949i
$911$	24.2755	+	14.0155i	0.804283	+	0.464353i	0.844967	−	0.534819i	$-0.179620\pi$
$911$	24.2755	+	14.0155i	0.804283	+	0.464353i	−0.0406837	+	0.999172i	$0.512954\pi$
$912$		0			0
$913$	−2.04680	−	1.18172i	−0.0677393	−	0.0391093i
$914$	−10.1352	−	5.85157i	−0.335243	−	0.193553i
$915$		0			0
$916$	−9.62794	−	5.55869i	−0.318116	−	0.183664i
$917$	−0.141933	−	0.137908i	−0.00468703	−	0.00455411i
$918$		0			0
$919$	4.86440	−	8.42539i	0.160462	−	0.277928i	−0.774573	−	0.632485i	$-0.782035\pi$
$919$	4.86440	−	8.42539i	0.160462	−	0.277928i	0.935034	+	0.354557i	$0.115368\pi$
$920$	−3.36670			−0.110997
$921$		0			0
$922$			36.5185i			1.20267i
$923$	−1.43237	−	2.48094i	−0.0471471	−	0.0816612i
$924$		0			0
$925$	1.37174	−	2.37592i	0.0451024	−	0.0781196i
$926$	1.88543	+	1.08855i	0.0619590	+	0.0357721i
$927$		0			0
$928$	−1.70712	−	2.95682i	−0.0560391	−	0.0970625i
$929$	−3.74795	−	6.49163i	−0.122966	−	0.212984i	0.797970	−	0.602697i	$-0.205907\pi$
$929$	−3.74795	−	6.49163i	−0.122966	−	0.212984i	−0.920936	+	0.389714i	$0.872574\pi$
$930$		0			0
$931$	−3.60079	+	6.67290i	−0.118011	+	0.218695i
$932$	−19.8646	+	11.4688i	−0.650686	+	0.375674i
$933$		0			0
$934$			24.5562i			0.803505i
$935$	−0.587830	+	0.339384i	−0.0192241	+	0.0110990i
$936$		0			0
$937$		−	46.3019i		−	1.51262i	−0.654216	−	0.756308i	$-0.727001\pi$
$937$		−	46.3019i		−	1.51262i	0.654216	−	0.756308i	$-0.272999\pi$
$938$	−13.3126	+	13.7012i	−0.434673	+	0.447359i
$939$		0			0
$940$	−0.0537031			−0.00175160
$941$	−22.1367	+	38.3419i	−0.721637	+	1.24991i	0.238706	+	0.971092i	$0.423277\pi$
$941$	−22.1367	+	38.3419i	−0.721637	+	1.24991i	−0.960343	+	0.278820i	$0.910057\pi$
$942$		0			0
$943$	−12.6479	+	7.30225i	−0.411871	+	0.237794i
$944$	−5.70296			−0.185616
$945$		0			0
$946$	−6.51841			−0.211932
$947$	−44.0948	+	25.4582i	−1.43289	+	0.827279i	−0.997340	−	0.0728856i	$-0.976779\pi$
$947$	−44.0948	+	25.4582i	−1.43289	+	0.827279i	−0.435549	+	0.900165i	$0.643446\pi$
$948$		0			0
$949$	2.13964	−	3.70596i	0.0694556	−	0.120301i
$950$	−1.08320			−0.0351438
$951$		0			0
$952$	2.69657	+	0.681133i	0.0873962	+	0.0220756i
$953$			21.9222i			0.710131i	0.934841	+	0.355066i	$0.115541\pi$
$953$			21.9222i			0.710131i	−0.934841	+	0.355066i	$0.884459\pi$
$954$		0			0
$955$	−16.5052	+	9.52928i	−0.534095	+	0.308360i
$956$			2.57874i			0.0834023i
$957$		0			0
$958$	26.0736	−	15.0536i	0.842399	−	0.486359i
$959$	14.4912	−	14.9142i	0.467946	−	0.481604i
$960$		0			0
$961$	−11.0819	−	19.1945i	−0.357481	−	0.619176i
$962$	−0.365332	−	0.632773i	−0.0117788	−	0.0204014i
$963$		0			0
$964$	18.4188	+	10.6341i	0.593229	+	0.342501i
$965$	−7.28322	+	12.6149i	−0.234455	+	0.406088i
$966$		0			0
$967$	26.5952	+	46.0643i	0.855245	+	1.48133i	0.876417	+	0.481553i	$0.159927\pi$
$967$	26.5952	+	46.0643i	0.855245	+	1.48133i	−0.0211717	+	0.999776i	$0.506740\pi$
$968$			10.5831i			0.340153i
$969$		0			0
$970$	−17.1744			−0.551435
$971$	11.2333	−	19.4567i	0.360494	−	0.624394i	−0.627548	−	0.778578i	$-0.715941\pi$
$971$	11.2333	−	19.4567i	0.360494	−	0.624394i	0.988042	+	0.154184i	$0.0492747\pi$
$972$		0			0
$973$	57.3444	+	14.4848i	1.83838	+	0.464360i
$974$	−19.6750	−	11.3594i	−0.630428	−	0.363978i
$975$		0			0
$976$	−3.06877	−	1.77175i	−0.0982289	−	0.0567125i
$977$	38.3951	+	22.1674i	1.22837	+	0.709199i	0.966688	−	0.255956i	$-0.0823903\pi$
$977$	38.3951	+	22.1674i	1.22837	+	0.709199i	0.261680	+	0.965155i	$0.415724\pi$
$978$		0			0
$979$	6.84797	+	3.95368i	0.218862	+	0.126360i
$980$	−6.16033	−	3.32420i	−0.196785	−	0.106188i
$981$		0			0
$982$	−9.15511	+	15.8571i	−0.292151	+	0.506021i
$983$	2.36362			0.0753878			0.0376939	−	0.999289i	$-0.487999\pi$
$983$	2.36362			0.0753878			0.0376939	+	0.999289i	$0.487999\pi$
$984$		0			0
$985$		−	18.1177i		−	0.577277i
$986$	1.79456	+	3.10827i	0.0571504	+	0.0989874i
$987$		0			0
$988$	−0.144244	+	0.249838i	−0.00458901	+	0.00794840i
$989$	29.4339	+	16.9937i	0.935945	+	0.540368i
$990$		0			0
$991$	−6.59191	−	11.4175i	−0.209399	−	0.362690i	0.742126	−	0.670260i	$-0.233817\pi$
$991$	−6.59191	−	11.4175i	−0.209399	−	0.362690i	−0.951525	+	0.307570i	$0.900484\pi$
$992$	1.48628	+	2.57432i	0.0471895	+	0.0817347i
$993$		0			0
$994$	−6.96961	+	27.5923i	−0.221063	+	0.875174i
$995$	13.5035	−	7.79625i	0.428090	−	0.247158i
$996$		0			0
$997$		−	35.4910i		−	1.12401i	−0.827134	−	0.562005i	$-0.810030\pi$
$997$		−	35.4910i		−	1.12401i	0.827134	−	0.562005i	$-0.189970\pi$
$998$	19.7793	−	11.4196i	0.626101	−	0.361480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1601.4		32
3.2	odd	2		630.2.t.c.551.15	yes	32
7.3	odd	6		1890.2.bk.c.521.9		32
9.4	even	3		630.2.bk.c.131.8	yes	32
9.5	odd	6		1890.2.bk.c.341.9		32
21.17	even	6		630.2.bk.c.101.16	yes	32
63.31	odd	6		630.2.t.c.311.15	✓	32
63.59	even	6	inner	1890.2.t.c.1151.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.15	✓	32	63.31	odd	6
630.2.t.c.551.15	yes	32	3.2	odd	2
630.2.bk.c.101.16	yes	32	21.17	even	6
630.2.bk.c.131.8	yes	32	9.4	even	3
1890.2.t.c.1151.4		32	63.59	even	6	inner
1890.2.t.c.1601.4		32	1.1	even	1	trivial
1890.2.bk.c.341.9		32	9.5	odd	6
1890.2.bk.c.521.9		32	7.3	odd	6

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.89754 - 1.84373i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.89754 - 1.84373i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} -0.645696i q^{11} +(-0.230647 + 0.133164i) q^{13} +(2.56518 + 0.647947i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.525609 + 0.910381i) q^{17} +(0.938083 + 0.541602i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.322848 + 0.559189i) q^{22} -3.36670i q^{23} +1.00000 q^{25} +(0.133164 - 0.230647i) q^{26} +(-2.54549 + 0.721453i) q^{28} +(-2.95682 - 1.70712i) q^{29} +(2.57432 + 1.48628i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.910381 - 0.525609i) q^{34} +(1.89754 + 1.84373i) q^{35} +(1.37174 - 2.37592i) q^{37} -1.08320 q^{38} -1.00000i q^{40} +(-2.16896 - 3.75676i) q^{41} +(-5.04758 + 8.74267i) q^{43} +(-0.559189 - 0.322848i) q^{44} +(1.68335 + 2.91565i) q^{46} +(0.0268516 + 0.0465083i) q^{47} +(0.201321 + 6.99710i) q^{49} +(-0.866025 + 0.500000i) q^{50} +0.266328i q^{52} +(-10.1657 + 5.86918i) q^{53} +0.645696i q^{55} +(1.84373 - 1.89754i) q^{56} +3.41425 q^{58} +(2.85148 - 4.93891i) q^{59} +(3.06877 - 1.77175i) q^{61} -2.97257 q^{62} -1.00000 q^{64} +(0.230647 - 0.133164i) q^{65} +(-3.61024 + 6.25312i) q^{67} +1.05122 q^{68} +(-2.56518 - 0.647947i) q^{70} +10.7565i q^{71} +(-13.9150 + 8.03384i) q^{73} +2.74347i q^{74} +(0.938083 - 0.541602i) q^{76} +(-1.19049 + 1.22523i) q^{77} +(2.16082 + 3.74266i) q^{79} +(0.500000 + 0.866025i) q^{80} +(3.75676 + 2.16896i) q^{82} +(1.83015 - 3.16992i) q^{83} +(-0.525609 - 0.910381i) q^{85} -10.0952i q^{86} +0.645696 q^{88} +(-6.12312 + 10.6056i) q^{89} +(0.683180 + 0.172566i) q^{91} +(-2.91565 - 1.68335i) q^{92} +(-0.0465083 - 0.0268516i) q^{94} +(-0.938083 - 0.541602i) q^{95} +(-14.8734 - 8.58718i) q^{97} +(-3.67290 - 5.95901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more