LMFDB - Embedded newform 1710.2.n.f.647.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(647,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1710.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.n (of order $4$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.2
Root			$-0.360409i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.f.1673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.292893 + 2.21680i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.36041 - 1.77462i) q^{10} -5.41421i q^{11} +(-4.43361 + 4.43361i) q^{13} +3.41421 q^{14} -1.00000 q^{16} +(-3.03955 + 3.03955i) q^{17} -1.00000i q^{19} +(2.21680 + 0.292893i) q^{20} +(3.82843 + 3.82843i) q^{22} +(5.33812 + 5.33812i) q^{23} +(-4.82843 - 1.29857i) q^{25} -6.27006i q^{26} +(-2.41421 + 2.41421i) q^{28} +8.86721 q^{29} +1.80904 q^{31} +(0.707107 - 0.707107i) q^{32} -4.29857i q^{34} +(6.05894 - 4.64473i) q^{35} +(1.41421 + 1.41421i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-1.77462 + 1.36041i) q^{40} -9.84782i q^{41} +(6.84782 - 6.84782i) q^{43} -5.41421 q^{44} -7.54925 q^{46} +(7.52909 - 7.52909i) q^{47} +4.65685i q^{49} +(4.33244 - 2.49598i) q^{50} +(4.43361 + 4.43361i) q^{52} +(4.24264 + 4.24264i) q^{53} +(12.0022 + 1.58579i) q^{55} -3.41421i q^{56} +(-6.27006 + 6.27006i) q^{58} -0.980608 q^{59} -3.44164 q^{61} +(-1.27918 + 1.27918i) q^{62} +1.00000i q^{64} +(-8.52985 - 11.1270i) q^{65} +(3.01939 + 3.01939i) q^{67} +(3.03955 + 3.03955i) q^{68} +(-1.00000 + 7.56864i) q^{70} -2.55836i q^{71} +(3.82843 - 3.82843i) q^{73} -2.00000 q^{74} -1.00000 q^{76} +(-13.0711 + 13.0711i) q^{77} +12.1179i q^{79} +(0.292893 - 2.21680i) q^{80} +(6.96346 + 6.96346i) q^{82} +(-5.06697 - 5.06697i) q^{83} +(-5.84782 - 7.62835i) q^{85} +9.68428i q^{86} +(3.82843 - 3.82843i) q^{88} +12.9463 q^{89} +21.4073 q^{91} +(5.33812 - 5.33812i) q^{92} +10.6477i q^{94} +(2.21680 + 0.292893i) q^{95} +(-1.31796 - 1.31796i) q^{97} +(-3.29289 - 3.29289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{7} - 4 q^{10} + 16 q^{14} - 8 q^{16} + 8 q^{22} + 8 q^{23} - 16 q^{25} - 8 q^{28} + 16 q^{31} + 4 q^{40} + 8 q^{43} - 32 q^{44} - 24 q^{46} + 24 q^{47} + 16 q^{50} - 32 q^{59} - 24 q^{62}+ \cdots - 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^7 - 4 * q^10 + 16 * q^14 - 8 * q^16 + 8 * q^22 + 8 * q^23 - 16 * q^25 - 8 * q^28 + 16 * q^31 + 4 * q^40 + 8 * q^43 - 32 * q^44 - 24 * q^46 + 24 * q^47 + 16 * q^50 - 32 * q^59 - 24 * q^62 - 56 * q^65 - 8 * q^70 + 8 * q^73 - 16 * q^74 - 8 * q^76 - 48 * q^77 + 8 * q^80 + 8 * q^82 + 8 * q^88 - 16 * q^89 + 8 * q^92 + 24 * q^97 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.292893	+	2.21680i	−0.130986	+	0.991384i
$5$	−0.292893	+	2.21680i	−0.130986	+	0.991384i
$6$		0			0
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	0.0839804	−	0.996467i	$-0.473237\pi$
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	−0.996467	+	0.0839804i	$0.973237\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.36041	−	1.77462i	−0.430199	−	0.561185i
$11$		−	5.41421i		−	1.63245i	−0.577736	−	0.816223i	$-0.696064\pi$
$11$		−	5.41421i		−	1.63245i	0.577736	−	0.816223i	$-0.303936\pi$
$12$		0			0
$13$	−4.43361	+	4.43361i	−1.22966	+	1.22966i	−0.265569	+	0.964092i	$0.585560\pi$
$13$	−4.43361	+	4.43361i	−1.22966	+	1.22966i	−0.964092	+	0.265569i	$0.914440\pi$
$14$	3.41421			0.912487
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.03955	+	3.03955i	−0.737199	+	0.737199i	−0.972035	−	0.234836i	$-0.924545\pi$
$17$	−3.03955	+	3.03955i	−0.737199	+	0.737199i	0.234836	+	0.972035i	$0.424545\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.21680	+	0.292893i	0.495692	+	0.0654929i
$21$		0			0
$22$	3.82843	+	3.82843i	0.816223	+	0.816223i
$23$	5.33812	+	5.33812i	1.11308	+	1.11308i	0.992732	+	0.120343i	$0.0383995\pi$
$23$	5.33812	+	5.33812i	1.11308	+	1.11308i	0.120343	+	0.992732i	$0.461600\pi$
$24$		0			0
$25$	−4.82843	−	1.29857i	−0.965685	−	0.259715i
$26$		−	6.27006i		−	1.22966i
$27$		0			0
$28$	−2.41421	+	2.41421i	−0.456243	+	0.456243i
$29$	8.86721			1.64660			0.823300	−	0.567607i	$-0.192131\pi$
$29$	8.86721			1.64660			0.823300	+	0.567607i	$0.192131\pi$
$30$		0			0
$31$	1.80904			0.324912			0.162456	−	0.986716i	$-0.448058\pi$
$31$	1.80904			0.324912			0.162456	+	0.986716i	$0.448058\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	4.29857i		−	0.737199i
$35$	6.05894	−	4.64473i	1.02415	−	0.785102i
$36$		0			0
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	0.813733	−	0.581238i	$-0.197432\pi$
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	−0.581238	+	0.813733i	$0.697432\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	−1.77462	+	1.36041i	−0.280593	+	0.215100i
$41$		−	9.84782i		−	1.53797i	−0.639266	−	0.768985i	$-0.720762\pi$
$41$		−	9.84782i		−	1.53797i	0.639266	−	0.768985i	$-0.279238\pi$
$42$		0			0
$43$	6.84782	−	6.84782i	1.04428	−	1.04428i	0.0453096	−	0.998973i	$-0.485573\pi$
$43$	6.84782	−	6.84782i	1.04428	−	1.04428i	0.998973	−	0.0453096i	$-0.0144274\pi$
$44$	−5.41421			−0.816223
$45$		0			0
$46$	−7.54925			−1.11308
$47$	7.52909	−	7.52909i	1.09823	−	1.09823i	0.103613	−	0.994618i	$-0.466960\pi$
$47$	7.52909	−	7.52909i	1.09823	−	1.09823i	0.994618	−	0.103613i	$-0.0330402\pi$
$48$		0			0
$49$			4.65685i			0.665265i
$50$	4.33244	−	2.49598i	0.612700	−	0.352985i
$51$		0			0
$52$	4.43361	+	4.43361i	0.614830	+	0.614830i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$	12.0022	+	1.58579i	1.61838	+	0.213827i
$56$		−	3.41421i		−	0.456243i
$57$		0			0
$58$	−6.27006	+	6.27006i	−0.823300	+	0.823300i
$59$	−0.980608			−0.127664			−0.0638322	−	0.997961i	$-0.520332\pi$
$59$	−0.980608			−0.127664			−0.0638322	+	0.997961i	$0.520332\pi$
$60$		0			0
$61$	−3.44164			−0.440657			−0.220328	−	0.975426i	$-0.570713\pi$
$61$	−3.44164			−0.440657			−0.220328	+	0.975426i	$0.570713\pi$
$62$	−1.27918	+	1.27918i	−0.162456	+	0.162456i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.52985	−	11.1270i	−1.05800	−	1.38013i
$66$		0			0
$67$	3.01939	+	3.01939i	0.368877	+	0.368877i	0.867068	−	0.498190i	$-0.166002\pi$
$67$	3.01939	+	3.01939i	0.368877	+	0.368877i	−0.498190	+	0.867068i	$0.666002\pi$
$68$	3.03955	+	3.03955i	0.368600	+	0.368600i
$69$		0			0
$70$	−1.00000	+	7.56864i	−0.119523	+	0.904625i
$71$		−	2.55836i		−	0.303622i	−0.988410	−	0.151811i	$-0.951490\pi$
$71$		−	2.55836i		−	0.303622i	0.988410	−	0.151811i	$-0.0485105\pi$
$72$		0			0
$73$	3.82843	−	3.82843i	0.448084	−	0.448084i	−0.446634	−	0.894717i	$-0.647377\pi$
$73$	3.82843	−	3.82843i	0.448084	−	0.448084i	0.894717	+	0.446634i	$0.147377\pi$
$74$	−2.00000			−0.232495
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−13.0711	+	13.0711i	−1.48959	+	1.48959i
$78$		0			0
$79$			12.1179i			1.36337i	0.731647	+	0.681684i	$0.238752\pi$
$79$			12.1179i			1.36337i	−0.731647	+	0.681684i	$0.761248\pi$
$80$	0.292893	−	2.21680i	0.0327465	−	0.247846i
$81$		0			0
$82$	6.96346	+	6.96346i	0.768985	+	0.768985i
$83$	−5.06697	−	5.06697i	−0.556173	−	0.556173i	0.372043	−	0.928216i	$-0.378657\pi$
$83$	−5.06697	−	5.06697i	−0.556173	−	0.556173i	−0.928216	+	0.372043i	$0.878657\pi$
$84$		0			0
$85$	−5.84782	−	7.62835i	−0.634285	−	0.827410i
$86$			9.68428i			1.04428i
$87$		0			0
$88$	3.82843	−	3.82843i	0.408112	−	0.408112i
$89$	12.9463			1.37231			0.686153	−	0.727457i	$-0.259298\pi$
$89$	12.9463			1.37231			0.686153	+	0.727457i	$0.259298\pi$
$90$		0			0
$91$	21.4073			2.24410
$92$	5.33812	−	5.33812i	0.556538	−	0.556538i
$93$		0			0
$94$			10.6477i			1.09823i
$95$	2.21680	+	0.292893i	0.227439	+	0.0300502i
$96$		0			0
$97$	−1.31796	−	1.31796i	−0.133819	−	0.133819i	0.637025	−	0.770844i	$-0.280165\pi$
$97$	−1.31796	−	1.31796i	−0.133819	−	0.133819i	−0.770844	+	0.637025i	$0.780165\pi$
$98$	−3.29289	−	3.29289i	−0.332632	−	0.332632i
$99$		0			0
$100$	−1.29857	+	4.82843i	−0.129857	+	0.482843i
$101$			10.2426i			1.01918i	0.860417	+	0.509590i	$0.170203\pi$
$101$			10.2426i			1.01918i	−0.860417	+	0.509590i	$0.829797\pi$
$102$		0			0
$103$	7.98285	−	7.98285i	0.786574	−	0.786574i	−0.194357	−	0.980931i	$-0.562262\pi$
$103$	7.98285	−	7.98285i	0.786574	−	0.786574i	0.980931	+	0.194357i	$0.0622621\pi$
$104$	−6.27006			−0.614830
$105$		0			0
$106$	−6.00000			−0.582772
$107$	3.17157	−	3.17157i	0.306608	−	0.306608i	−0.536985	−	0.843592i	$-0.680437\pi$
$107$	3.17157	−	3.17157i	0.306608	−	0.306608i	0.843592	+	0.536985i	$0.180437\pi$
$108$		0			0
$109$		−	3.86388i		−	0.370093i	−0.982730	−	0.185046i	$-0.940756\pi$
$109$		−	3.86388i		−	0.370093i	0.982730	−	0.185046i	$-0.0592436\pi$
$110$	−9.60819	+	7.36555i	−0.916105	+	0.702277i
$111$		0			0
$112$	2.41421	+	2.41421i	0.228122	+	0.228122i
$113$	10.5127	+	10.5127i	0.988952	+	0.988952i	0.999940	−	0.0109875i	$-0.00349751\pi$
$113$	10.5127	+	10.5127i	0.988952	+	0.988952i	−0.0109875	+	0.999940i	$0.503498\pi$
$114$		0			0
$115$	−13.3971	+	10.2701i	−1.24928	+	0.957688i
$116$		−	8.86721i		−	0.823300i
$117$		0			0
$118$	0.693395	−	0.693395i	0.0638322	−	0.0638322i
$119$	14.6762			1.34537
$120$		0			0
$121$	−18.3137			−1.66488
$122$	2.43361	−	2.43361i	0.220328	−	0.220328i
$123$		0			0
$124$		−	1.80904i		−	0.162456i
$125$	4.29289	−	10.3233i	0.383968	−	0.923346i
$126$		0			0
$127$	−4.54121	−	4.54121i	−0.402968	−	0.402968i	0.476310	−	0.879277i	$-0.341974\pi$
$127$	−4.54121	−	4.54121i	−0.402968	−	0.402968i	−0.879277	+	0.476310i	$0.841974\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	13.8995	+	1.83646i	1.21907	+	0.161068i
$131$			9.04682i			0.790424i	0.918590	+	0.395212i	$0.129329\pi$
$131$			9.04682i			0.790424i	−0.918590	+	0.395212i	$0.870671\pi$
$132$		0			0
$133$	−2.41421	+	2.41421i	−0.209339	+	0.209339i
$134$	−4.27006			−0.368877
$135$		0			0
$136$	−4.29857			−0.368600
$137$	9.23051	−	9.23051i	0.788616	−	0.788616i	−0.192651	−	0.981267i	$-0.561709\pi$
$137$	9.23051	−	9.23051i	0.788616	−	0.788616i	0.981267	+	0.192651i	$0.0617086\pi$
$138$		0			0
$139$		−	12.2540i		−	1.03937i	−0.854358	−	0.519685i	$-0.826049\pi$
$139$		−	12.2540i		−	1.03937i	0.854358	−	0.519685i	$-0.173951\pi$
$140$	−4.64473	−	6.05894i	−0.392551	−	0.512074i
$141$		0			0
$142$	1.80904	+	1.80904i	0.151811	+	0.151811i
$143$	24.0045	+	24.0045i	2.00736	+	2.00736i
$144$		0			0
$145$	−2.59715	+	19.6569i	−0.215681	+	1.63241i
$146$			5.41421i			0.448084i
$147$		0			0
$148$	1.41421	−	1.41421i	0.116248	−	0.116248i
$149$	8.89617			0.728802			0.364401	−	0.931242i	$-0.381274\pi$
$149$	8.89617			0.728802			0.364401	+	0.931242i	$0.381274\pi$
$150$		0			0
$151$	−3.36254			−0.273639			−0.136820	−	0.990596i	$-0.543688\pi$
$151$	−3.36254			−0.273639			−0.136820	+	0.990596i	$0.543688\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$		0			0
$154$		−	18.4853i		−	1.48959i
$155$	−0.529854	+	4.01027i	−0.0425589	+	0.322113i
$156$		0			0
$157$	−6.49331	−	6.49331i	−0.518223	−	0.518223i	0.398811	−	0.917033i	$-0.369423\pi$
$157$	−6.49331	−	6.49331i	−0.518223	−	0.518223i	−0.917033	+	0.398811i	$0.869423\pi$
$158$	−8.56864	−	8.56864i	−0.681684	−	0.681684i
$159$		0			0
$160$	1.36041	+	1.77462i	0.107550	+	0.140296i
$161$		−	25.7747i		−	2.03133i
$162$		0			0
$163$	12.5880	−	12.5880i	0.985971	−	0.985971i	−0.0139324	−	0.999903i	$-0.504435\pi$
$163$	12.5880	−	12.5880i	0.985971	−	0.985971i	0.999903	+	0.0139324i	$0.00443497\pi$
$164$	−9.84782			−0.768985
$165$		0			0
$166$	7.16578			0.556173
$167$	1.67292	−	1.67292i	0.129454	−	0.129454i	−0.639411	−	0.768865i	$-0.720822\pi$
$167$	1.67292	−	1.67292i	0.129454	−	0.129454i	0.768865	+	0.639411i	$0.220822\pi$
$168$		0			0
$169$		−	26.3137i		−	2.02413i
$170$	9.52909	+	1.25902i	0.730848	+	0.0965626i
$171$		0			0
$172$	−6.84782	−	6.84782i	−0.522141	−	0.522141i
$173$	8.09046	+	8.09046i	0.615106	+	0.615106i	0.944272	−	0.329166i	$-0.106768\pi$
$173$	8.09046	+	8.09046i	0.615106	+	0.615106i	−0.329166	+	0.944272i	$0.606768\pi$
$174$		0			0
$175$	8.52182	+	14.7919i	0.644189	+	1.11816i
$176$			5.41421i			0.408112i
$177$		0			0
$178$	−9.15442	+	9.15442i	−0.686153	+	0.686153i
$179$	−6.96237			−0.520392			−0.260196	−	0.965556i	$-0.583787\pi$
$179$	−6.96237			−0.520392			−0.260196	+	0.965556i	$0.583787\pi$
$180$		0			0
$181$	1.63260			0.121350			0.0606752	−	0.998158i	$-0.480675\pi$
$181$	1.63260			0.121350			0.0606752	+	0.998158i	$0.480675\pi$
$182$	−15.1373	+	15.1373i	−1.12205	+	1.12205i
$183$		0			0
$184$			7.54925i			0.556538i
$185$	−3.54925	+	2.72082i	−0.260946	+	0.200039i
$186$		0			0
$187$	16.4568	+	16.4568i	1.20344	+	1.20344i
$188$	−7.52909	−	7.52909i	−0.549115	−	0.549115i
$189$		0			0
$190$	−1.77462	+	1.36041i	−0.128745	+	0.0986945i
$191$			1.56486i			0.113229i	0.998396	+	0.0566147i	$0.0180307\pi$
$191$			1.56486i			0.113229i	−0.998396	+	0.0566147i	$0.981969\pi$
$192$		0			0
$193$	−4.33736	+	4.33736i	−0.312210	+	0.312210i	−0.845765	−	0.533555i	$-0.820856\pi$
$193$	−4.33736	+	4.33736i	−0.312210	+	0.312210i	0.533555	+	0.845765i	$0.320856\pi$
$194$	1.86388			0.133819
$195$		0			0
$196$	4.65685			0.332632
$197$	−17.6599	+	17.6599i	−1.25821	+	1.25821i	−0.306268	+	0.951945i	$0.599080\pi$
$197$	−17.6599	+	17.6599i	−1.25821	+	1.25821i	−0.951945	+	0.306268i	$0.900920\pi$
$198$		0			0
$199$		−	11.5450i		−	0.818403i	−0.912444	−	0.409201i	$-0.865807\pi$
$199$		−	11.5450i		−	0.818403i	0.912444	−	0.409201i	$-0.134193\pi$
$200$	−2.49598	−	4.33244i	−0.176493	−	0.306350i
$201$		0			0
$202$	−7.24264	−	7.24264i	−0.509590	−	0.509590i
$203$	−21.4073	−	21.4073i	−1.50250	−	1.50250i
$204$		0			0
$205$	21.8307	+	2.88436i	1.52472	+	0.201452i
$206$			11.2895i			0.786574i
$207$		0			0
$208$	4.43361	−	4.43361i	0.307415	−	0.307415i
$209$	−5.41421			−0.374509
$210$		0			0
$211$	10.7714			0.741534			0.370767	−	0.928726i	$-0.379095\pi$
$211$	10.7714			0.741534			0.370767	+	0.928726i	$0.379095\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$			4.48528i			0.306608i
$215$	13.1746	+	17.1859i	0.898499	+	1.17207i
$216$		0			0
$217$	−4.36740	−	4.36740i	−0.296478	−	0.296478i
$218$	2.73218	+	2.73218i	0.185046	+	0.185046i
$219$		0			0
$220$	1.58579	−	12.0022i	0.106914	−	0.809191i
$221$		−	26.9523i		−	1.81301i
$222$		0			0
$223$	−17.2175	+	17.2175i	−1.15297	+	1.15297i	−0.167011	+	0.985955i	$0.553412\pi$
$223$	−17.2175	+	17.2175i	−1.15297	+	1.15297i	−0.985955	+	0.167011i	$0.946588\pi$
$224$	−3.41421			−0.228122
$225$		0			0
$226$	−14.8672			−0.988952
$227$	−4.67625	+	4.67625i	−0.310373	+	0.310373i	−0.845054	−	0.534681i	$-0.820432\pi$
$227$	−4.67625	+	4.67625i	−0.310373	+	0.310373i	0.534681	+	0.845054i	$0.320432\pi$
$228$		0			0
$229$		−	8.57443i		−	0.566614i	−0.959029	−	0.283307i	$-0.908568\pi$
$229$		−	8.57443i		−	0.566614i	0.959029	−	0.283307i	$-0.0914316\pi$
$230$	2.21112	−	16.7352i	0.145797	−	1.10349i
$231$		0			0
$232$	6.27006	+	6.27006i	0.411650	+	0.411650i
$233$	14.1655	+	14.1655i	0.928010	+	0.928010i	0.997577	−	0.0695668i	$-0.0221617\pi$
$233$	14.1655	+	14.1655i	0.928010	+	0.928010i	−0.0695668	+	0.997577i	$0.522162\pi$
$234$		0			0
$235$	14.4853	+	18.8957i	0.944916	+	1.23262i
$236$			0.980608i			0.0638322i
$237$		0			0
$238$	−10.3777	+	10.3777i	−0.672685	+	0.672685i
$239$	−5.49331			−0.355333			−0.177666	−	0.984091i	$-0.556855\pi$
$239$	−5.49331			−0.355333			−0.177666	+	0.984091i	$0.556855\pi$
$240$		0			0
$241$	10.0227			0.645620			0.322810	−	0.946464i	$-0.395373\pi$
$241$	10.0227			0.645620			0.322810	+	0.946464i	$0.395373\pi$
$242$	12.9497	−	12.9497i	0.832441	−	0.832441i
$243$		0			0
$244$			3.44164i			0.220328i
$245$	−10.3233	−	1.36396i	−0.659533	−	0.0871403i
$246$		0			0
$247$	4.43361	+	4.43361i	0.282104	+	0.282104i
$248$	1.27918	+	1.27918i	0.0812281	+	0.0812281i
$249$		0			0
$250$	4.26416	+	10.3352i	0.269689	+	0.653657i
$251$			30.7264i			1.93943i	0.244234	+	0.969716i	$0.421463\pi$
$251$			30.7264i			1.93943i	−0.244234	+	0.969716i	$0.578537\pi$
$252$		0			0
$253$	28.9017	−	28.9017i	1.81704	−	1.81704i
$254$	6.42225			0.402968
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.09046	+	6.09046i	−0.379912	+	0.379912i	−0.871070	−	0.491158i	$-0.836574\pi$
$257$	−6.09046	+	6.09046i	−0.379912	+	0.379912i	0.491158	+	0.871070i	$0.336574\pi$
$258$		0			0
$259$		−	6.82843i		−	0.424298i
$260$	−11.1270	+	8.52985i	−0.690067	+	0.528999i
$261$		0			0
$262$	−6.39706	−	6.39706i	−0.395212	−	0.395212i
$263$	−11.5404	−	11.5404i	−0.711614	−	0.711614i	0.255258	−	0.966873i	$-0.417839\pi$
$263$	−11.5404	−	11.5404i	−0.711614	−	0.711614i	−0.966873	+	0.255258i	$0.917839\pi$
$264$		0			0
$265$	−10.6477	+	8.16246i	−0.654085	+	0.501416i
$266$		−	3.41421i		−	0.209339i
$267$		0			0
$268$	3.01939	−	3.01939i	0.184439	−	0.184439i
$269$	31.9657			1.94898			0.974492	−	0.224424i	$-0.0720500\pi$
$269$	31.9657			1.94898			0.974492	+	0.224424i	$0.0720500\pi$
$270$		0			0
$271$	−7.08243			−0.430227			−0.215113	−	0.976589i	$-0.569012\pi$
$271$	−7.08243			−0.430227			−0.215113	+	0.976589i	$0.569012\pi$
$272$	3.03955	−	3.03955i	0.184300	−	0.184300i
$273$		0			0
$274$			13.0539i			0.788616i
$275$	−7.03075	+	26.1421i	−0.423970	+	1.57643i
$276$		0			0
$277$	0.319049	+	0.319049i	0.0191698	+	0.0191698i	0.716627	−	0.697457i	$-0.245685\pi$
$277$	0.319049	+	0.319049i	0.0191698	+	0.0191698i	−0.697457	+	0.716627i	$0.745685\pi$
$278$	8.66489	+	8.66489i	0.519685	+	0.519685i
$279$		0			0
$280$	7.56864	+	1.00000i	0.452313	+	0.0597614i
$281$		−	4.21368i		−	0.251367i	−0.992070	−	0.125684i	$-0.959888\pi$
$281$		−	4.21368i		−	0.251367i	0.992070	−	0.125684i	$-0.0401124\pi$
$282$		0			0
$283$	−19.3331	+	19.3331i	−1.14923	+	1.14923i	−0.162530	+	0.986704i	$0.551965\pi$
$283$	−19.3331	+	19.3331i	−1.14923	+	1.14923i	−0.986704	+	0.162530i	$0.948035\pi$
$284$	−2.55836			−0.151811
$285$		0			0
$286$	−33.9475			−2.00736
$287$	−23.7747	+	23.7747i	−1.40338	+	1.40338i
$288$		0			0
$289$		−	1.47773i		−	0.0869252i
$290$	−12.0630	−	15.7360i	−0.708366	−	0.924047i
$291$		0			0
$292$	−3.82843	−	3.82843i	−0.224042	−	0.224042i
$293$	−3.79614	−	3.79614i	−0.221773	−	0.221773i	0.587472	−	0.809245i	$-0.300123\pi$
$293$	−3.79614	−	3.79614i	−0.221773	−	0.221773i	−0.809245	+	0.587472i	$0.800123\pi$
$294$		0			0
$295$	0.287214	−	2.17382i	0.0167222	−	0.126564i
$296$			2.00000i			0.116248i
$297$		0			0
$298$	−6.29054	+	6.29054i	−0.364401	+	0.364401i
$299$	−47.3343			−2.73741
$300$		0			0
$301$	−33.0642			−1.90579
$302$	2.37767	−	2.37767i	0.136820	−	0.136820i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	1.00803	−	7.62943i	0.0577198	−	0.436860i
$306$		0			0
$307$	−15.7747	−	15.7747i	−0.900312	−	0.900312i	0.0951510	−	0.995463i	$-0.469667\pi$
$307$	−15.7747	−	15.7747i	−0.900312	−	0.900312i	−0.995463	+	0.0951510i	$0.969667\pi$
$308$	13.0711	+	13.0711i	0.744793	+	0.744793i
$309$		0			0
$310$	−2.46103	−	3.21036i	−0.139777	−	0.182336i
$311$		−	15.9625i		−	0.905152i	−0.891726	−	0.452576i	$-0.850505\pi$
$311$		−	15.9625i		−	0.905152i	0.891726	−	0.452576i	$-0.149495\pi$
$312$		0			0
$313$	−4.57350	+	4.57350i	−0.258509	+	0.258509i	−0.824448	−	0.565938i	$-0.808514\pi$
$313$	−4.57350	+	4.57350i	−0.258509	+	0.258509i	0.565938	+	0.824448i	$0.308514\pi$
$314$	9.18293			0.518223
$315$		0			0
$316$	12.1179			0.681684
$317$	15.1099	−	15.1099i	0.848654	−	0.848654i	−0.141311	−	0.989965i	$-0.545132\pi$
$317$	15.1099	−	15.1099i	0.848654	−	0.848654i	0.989965	+	0.141311i	$0.0451319\pi$
$318$		0			0
$319$		−	48.0090i		−	2.68799i
$320$	−2.21680	−	0.292893i	−0.123923	−	0.0163732i
$321$		0			0
$322$	18.2255	+	18.2255i	1.01567	+	1.01567i
$323$	3.03955	+	3.03955i	0.169125	+	0.169125i
$324$		0			0
$325$	27.1647	−	15.6500i	1.50683	−	0.868105i
$326$			17.8022i			0.985971i
$327$		0			0
$328$	6.96346	−	6.96346i	0.384493	−	0.384493i
$329$	−36.3536			−2.00424
$330$		0			0
$331$	18.6274			1.02386			0.511928	−	0.859029i	$-0.328932\pi$
$331$	18.6274			1.02386			0.511928	+	0.859029i	$0.328932\pi$
$332$	−5.06697	+	5.06697i	−0.278086	+	0.278086i
$333$		0			0
$334$			2.36586i			0.129454i
$335$	−7.57775	+	5.80904i	−0.414017	+	0.317382i
$336$		0			0
$337$	−15.0700	−	15.0700i	−0.820914	−	0.820914i	0.165325	−	0.986239i	$-0.447133\pi$
$337$	−15.0700	−	15.0700i	−0.820914	−	0.820914i	−0.986239	+	0.165325i	$0.947133\pi$
$338$	18.6066	+	18.6066i	1.01207	+	1.01207i
$339$		0			0
$340$	−7.62835	+	5.84782i	−0.413705	+	0.317142i
$341$		−	9.79450i		−	0.530402i
$342$		0			0
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$	9.68428			0.522141
$345$		0			0
$346$	−11.4416			−0.615106
$347$	−7.10576	+	7.10576i	−0.381457	+	0.381457i	−0.871627	−	0.490170i	$-0.836935\pi$
$347$	−7.10576	+	7.10576i	−0.381457	+	0.381457i	0.490170	+	0.871627i	$0.336935\pi$
$348$		0			0
$349$		−	5.49648i		−	0.294220i	−0.989120	−	0.147110i	$-0.953003\pi$
$349$		−	5.49648i		−	0.294220i	0.989120	−	0.147110i	$-0.0469971\pi$
$350$	−16.4853	−	4.43361i	−0.881175	−	0.236986i
$351$		0			0
$352$	−3.82843	−	3.82843i	−0.204056	−	0.204056i
$353$	−1.29826	−	1.29826i	−0.0690992	−	0.0690992i	0.671713	−	0.740812i	$-0.265559\pi$
$353$	−1.29826	−	1.29826i	−0.0690992	−	0.0690992i	−0.740812	+	0.671713i	$0.765559\pi$
$354$		0			0
$355$	5.67138	+	0.749327i	0.301006	+	0.0397702i
$356$		−	12.9463i		−	0.686153i
$357$		0			0
$358$	4.92314	−	4.92314i	0.260196	−	0.260196i
$359$	10.9753			0.579252			0.289626	−	0.957140i	$-0.406469\pi$
$359$	10.9753			0.579252			0.289626	+	0.957140i	$0.406469\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−1.15442	+	1.15442i	−0.0606752	+	0.0606752i
$363$		0			0
$364$		−	21.4073i		−	1.12205i
$365$	7.36555	+	9.60819i	0.385530	+	0.502916i
$366$		0			0
$367$	4.79189	+	4.79189i	0.250134	+	0.250134i	0.821026	−	0.570891i	$-0.193402\pi$
$367$	4.79189	+	4.79189i	0.250134	+	0.250134i	−0.570891	+	0.821026i	$0.693402\pi$
$368$	−5.33812	−	5.33812i	−0.278269	−	0.278269i
$369$		0			0
$370$	0.585786	−	4.43361i	0.0304536	−	0.230492i
$371$		−	20.4853i		−	1.06354i
$372$		0			0
$373$	16.0114	−	16.0114i	0.829037	−	0.829037i	−0.158347	−	0.987384i	$-0.550616\pi$
$373$	16.0114	−	16.0114i	0.829037	−	0.829037i	0.987384	+	0.158347i	$0.0506164\pi$
$374$	−23.2734			−1.20344
$375$		0			0
$376$	10.6477			0.549115
$377$	−39.3137	+	39.3137i	−2.02476	+	2.02476i
$378$		0			0
$379$		−	13.5450i		−	0.695759i	−0.937539	−	0.347880i	$-0.886902\pi$
$379$		−	13.5450i		−	0.695759i	0.937539	−	0.347880i	$-0.113098\pi$
$380$	0.292893	−	2.21680i	0.0150251	−	0.113720i
$381$		0			0
$382$	−1.10652	−	1.10652i	−0.0566147	−	0.0566147i
$383$	−7.88814	−	7.88814i	−0.403065	−	0.403065i	0.476247	−	0.879312i	$-0.341997\pi$
$383$	−7.88814	−	7.88814i	−0.403065	−	0.403065i	−0.879312	+	0.476247i	$0.841997\pi$
$384$		0			0
$385$	−25.1475	−	32.8044i	−1.28164	−	1.67187i
$386$		−	6.13395i		−	0.312210i
$387$		0			0
$388$	−1.31796	+	1.31796i	−0.0669095	+	0.0669095i
$389$	15.6500			0.793485			0.396743	−	0.917930i	$-0.370141\pi$
$389$	15.6500			0.793485			0.396743	+	0.917930i	$0.370141\pi$
$390$		0			0
$391$	−32.4510			−1.64112
$392$	−3.29289	+	3.29289i	−0.166316	+	0.166316i
$393$		0			0
$394$		−	24.9748i		−	1.25821i
$395$	−26.8630	−	3.54925i	−1.35162	−	0.178582i
$396$		0			0
$397$	18.6009	+	18.6009i	0.933554	+	0.933554i	0.997926	−	0.0643724i	$-0.0205046\pi$
$397$	18.6009	+	18.6009i	0.933554	+	0.933554i	−0.0643724	+	0.997926i	$0.520505\pi$
$398$	8.16354	+	8.16354i	0.409201	+	0.409201i
$399$		0			0
$400$	4.82843	+	1.29857i	0.241421	+	0.0649286i
$401$		−	30.0287i		−	1.49956i	−0.661685	−	0.749782i	$-0.730158\pi$
$401$		−	30.0287i		−	1.49956i	0.661685	−	0.749782i	$-0.269842\pi$
$402$		0			0
$403$	−8.02055	+	8.02055i	−0.399532	+	0.399532i
$404$	10.2426			0.509590
$405$		0			0
$406$	30.2745			1.50250
$407$	7.65685	−	7.65685i	0.379536	−	0.379536i
$408$		0			0
$409$			27.0481i			1.33744i	0.743513	+	0.668722i	$0.233158\pi$
$409$			27.0481i			1.33744i	−0.743513	+	0.668722i	$0.766842\pi$
$410$	−17.4762	+	13.3971i	−0.863086	+	0.661634i
$411$		0			0
$412$	−7.98285	−	7.98285i	−0.393287	−	0.393287i
$413$	2.36740	+	2.36740i	0.116492	+	0.116492i
$414$		0			0
$415$	12.7166	−	9.74840i	0.624232	−	0.478530i
$416$			6.27006i			0.307415i
$417$		0			0
$418$	3.82843	−	3.82843i	0.187254	−	0.187254i
$419$	3.35271			0.163791			0.0818953	−	0.996641i	$-0.473903\pi$
$419$	3.35271			0.163791			0.0818953	+	0.996641i	$0.473903\pi$
$420$		0			0
$421$	−25.3540			−1.23568			−0.617840	−	0.786304i	$-0.711992\pi$
$421$	−25.3540			−1.23568			−0.617840	+	0.786304i	$0.711992\pi$
$422$	−7.61654	+	7.61654i	−0.370767	+	0.370767i
$423$		0			0
$424$			6.00000i			0.291386i
$425$	18.6233	−	10.7292i	0.903364	−	0.520441i
$426$		0			0
$427$	8.30885	+	8.30885i	0.402093	+	0.402093i
$428$	−3.17157	−	3.17157i	−0.153304	−	0.153304i
$429$		0			0
$430$	−21.4681	−	2.83646i	−1.03529	−	0.136786i
$431$		−	31.3364i		−	1.50942i	−0.656057	−	0.754711i	$-0.727777\pi$
$431$		−	31.3364i		−	1.50942i	0.656057	−	0.754711i	$-0.272223\pi$
$432$		0			0
$433$	3.33556	−	3.33556i	0.160297	−	0.160297i	−0.622401	−	0.782698i	$-0.713843\pi$
$433$	3.33556	−	3.33556i	0.160297	−	0.160297i	0.782698	+	0.622401i	$0.213843\pi$
$434$	6.17643			0.296478
$435$		0			0
$436$	−3.86388			−0.185046
$437$	5.33812	−	5.33812i	0.255357	−	0.255357i
$438$		0			0
$439$		−	15.6241i		−	0.745697i	−0.927892	−	0.372849i	$-0.878381\pi$
$439$		−	15.6241i		−	0.745697i	0.927892	−	0.372849i	$-0.121619\pi$
$440$	7.36555	+	9.60819i	0.351139	+	0.458052i
$441$		0			0
$442$	19.0582	+	19.0582i	0.906505	+	0.906505i
$443$	3.05561	+	3.05561i	0.145177	+	0.145177i	0.775959	−	0.630783i	$-0.217266\pi$
$443$	3.05561	+	3.05561i	0.145177	+	0.145177i	−0.630783	+	0.775959i	$0.717266\pi$
$444$		0			0
$445$	−3.79189	+	28.6994i	−0.179753	+	1.36048i
$446$		−	24.3492i		−	1.15297i
$447$		0			0
$448$	2.41421	−	2.41421i	0.114061	−	0.114061i
$449$	−34.5547			−1.63074			−0.815368	−	0.578944i	$-0.803465\pi$
$449$	−34.5547			−1.63074			−0.815368	+	0.578944i	$0.803465\pi$
$450$		0			0
$451$	−53.3182			−2.51066
$452$	10.5127	−	10.5127i	0.494476	−	0.494476i
$453$		0			0
$454$		−	6.61321i		−	0.310373i
$455$	−6.27006	+	47.4558i	−0.293945	+	2.22476i
$456$		0			0
$457$	4.87207	+	4.87207i	0.227906	+	0.227906i	0.811817	−	0.583911i	$-0.198478\pi$
$457$	4.87207	+	4.87207i	0.227906	+	0.227906i	−0.583911	+	0.811817i	$0.698478\pi$
$458$	6.06304	+	6.06304i	0.283307	+	0.283307i
$459$		0			0
$460$	10.2701	+	13.3971i	0.478844	+	0.624641i
$461$			16.3788i			0.762835i	0.924403	+	0.381417i	$0.124564\pi$
$461$			16.3788i			0.762835i	−0.924403	+	0.381417i	$0.875436\pi$
$462$		0			0
$463$	29.4439	−	29.4439i	1.36837	−	1.36837i	0.505612	−	0.862761i	$-0.331267\pi$
$463$	29.4439	−	29.4439i	1.36837	−	1.36837i	0.862761	−	0.505612i	$-0.168733\pi$
$464$	−8.86721			−0.411650
$465$		0			0
$466$	−20.0330			−0.928010
$467$	4.13202	−	4.13202i	0.191207	−	0.191207i	−0.605010	−	0.796218i	$-0.706831\pi$
$467$	4.13202	−	4.13202i	0.191207	−	0.191207i	0.796218	+	0.605010i	$0.206831\pi$
$468$		0			0
$469$		−	14.5789i		−	0.673192i
$470$	−23.6039	−	3.11865i	−1.08877	−	0.143853i
$471$		0			0
$472$	−0.693395	−	0.693395i	−0.0319161	−	0.0319161i
$473$	−37.0756	−	37.0756i	−1.70474	−	1.70474i
$474$		0			0
$475$	−1.29857	+	4.82843i	−0.0595826	+	0.221543i
$476$		−	14.6762i		−	0.672685i
$477$		0			0
$478$	3.88436	−	3.88436i	0.177666	−	0.177666i
$479$	6.02742			0.275400			0.137700	−	0.990474i	$-0.456029\pi$
$479$	6.02742			0.275400			0.137700	+	0.990474i	$0.456029\pi$
$480$		0			0
$481$	−12.5401			−0.571781
$482$	−7.08713	+	7.08713i	−0.322810	+	0.322810i
$483$		0			0
$484$			18.3137i			0.832441i
$485$	3.30769	−	2.53564i	0.150194	−	0.115138i
$486$		0			0
$487$	−0.0801847	−	0.0801847i	−0.00363351	−	0.00363351i	0.705288	−	0.708921i	$-0.250818\pi$
$487$	−0.0801847	−	0.0801847i	−0.00363351	−	0.00363351i	−0.708921	+	0.705288i	$0.750818\pi$
$488$	−2.43361	−	2.43361i	−0.110164	−	0.110164i
$489$		0			0
$490$	8.26416	−	6.33523i	0.373337	−	0.286196i
$491$		−	32.6190i		−	1.47208i	−0.676941	−	0.736038i	$-0.736695\pi$
$491$		−	32.6190i		−	1.47208i	0.676941	−	0.736038i	$-0.263305\pi$
$492$		0			0
$493$	−26.9523	+	26.9523i	−1.21387	+	1.21387i
$494$	−6.27006			−0.282104
$495$		0			0
$496$	−1.80904			−0.0812281
$497$	−6.17643	+	6.17643i	−0.277051	+	0.277051i
$498$		0			0
$499$			19.9496i			0.893068i	0.894767	+	0.446534i	$0.147342\pi$
$499$			19.9496i			0.893068i	−0.894767	+	0.446534i	$0.852658\pi$
$500$	−10.3233	−	4.29289i	−0.461673	−	0.191984i
$501$		0			0
$502$	−21.7268	−	21.7268i	−0.969716	−	0.969716i
$503$	−7.58076	−	7.58076i	−0.338010	−	0.338010i	0.517608	−	0.855618i	$-0.326822\pi$
$503$	−7.58076	−	7.58076i	−0.338010	−	0.338010i	−0.855618	+	0.517608i	$0.826822\pi$
$504$		0			0
$505$	−22.7059	−	3.00000i	−1.01040	−	0.133498i
$506$			40.8732i			1.81704i
$507$		0			0
$508$	−4.54121	+	4.54121i	−0.201484	+	0.201484i
$509$	37.8926			1.67956			0.839780	−	0.542926i	$-0.182684\pi$
$509$	37.8926			1.67956			0.839780	+	0.542926i	$0.182684\pi$
$510$		0			0
$511$	−18.4853			−0.817741
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	8.61321i		−	0.379912i
$515$	15.3583	+	20.0345i	0.676767	+	0.882827i
$516$		0			0
$517$	−40.7641	−	40.7641i	−1.79280	−	1.79280i
$518$	4.82843	+	4.82843i	0.212149	+	0.212149i
$519$		0			0
$520$	1.83646	−	13.8995i	0.0805341	−	0.609533i
$521$		−	25.0497i		−	1.09745i	−0.836004	−	0.548723i	$-0.815114\pi$
$521$		−	25.0497i		−	1.09745i	0.836004	−	0.548723i	$-0.184886\pi$
$522$		0			0
$523$	25.1776	−	25.1776i	1.10094	−	1.10094i	0.106642	−	0.994298i	$-0.465990\pi$
$523$	25.1776	−	25.1776i	1.10094	−	1.10094i	0.994298	−	0.106642i	$-0.0340098\pi$
$524$	9.04682			0.395212
$525$		0			0
$526$	16.3207			0.711614
$527$	−5.49865	+	5.49865i	−0.239525	+	0.239525i
$528$		0			0
$529$			33.9911i			1.47787i
$530$	1.75736	−	13.3008i	0.0763348	−	0.577750i
$531$		0			0
$532$	2.41421	+	2.41421i	0.104669	+	0.104669i
$533$	43.6613	+	43.6613i	1.89118	+	1.89118i
$534$		0			0
$535$	6.10182	+	7.95968i	0.263805	+	0.344127i
$536$			4.27006i			0.184439i
$537$		0			0
$538$	−22.6032	+	22.6032i	−0.974492	+	0.974492i
$539$	25.2132			1.08601
$540$		0			0
$541$	15.1533			0.651493			0.325746	−	0.945457i	$-0.394384\pi$
$541$	15.1533			0.651493			0.325746	+	0.945457i	$0.394384\pi$
$542$	5.00803	−	5.00803i	0.215113	−	0.215113i
$543$		0			0
$544$			4.29857i			0.184300i
$545$	8.56547	+	1.13171i	0.366904	+	0.0484769i
$546$		0			0
$547$	−11.9900	−	11.9900i	−0.512653	−	0.512653i	0.402685	−	0.915339i	$-0.368077\pi$
$547$	−11.9900	−	11.9900i	−0.512653	−	0.512653i	−0.915339	+	0.402685i	$0.868077\pi$
$548$	−9.23051	−	9.23051i	−0.394308	−	0.394308i
$549$		0			0
$550$	−13.5138	−	23.4568i	−0.576230	−	1.00020i
$551$		−	8.86721i		−	0.377756i
$552$		0			0
$553$	29.2552	−	29.2552i	1.24406	−	1.24406i
$554$	−0.451203			−0.0191698
$555$		0			0
$556$	−12.2540			−0.519685
$557$	14.7684	−	14.7684i	0.625757	−	0.625757i	−0.321240	−	0.946998i	$-0.604100\pi$
$557$	14.7684	−	14.7684i	0.625757	−	0.625757i	0.946998	+	0.321240i	$0.104100\pi$
$558$		0			0
$559$			60.7210i			2.56823i
$560$	−6.05894	+	4.64473i	−0.256037	+	0.196276i
$561$		0			0
$562$	2.97952	+	2.97952i	0.125684	+	0.125684i
$563$	16.4610	+	16.4610i	0.693750	+	0.693750i	0.963055	−	0.269305i	$-0.0867940\pi$
$563$	16.4610	+	16.4610i	0.693750	+	0.693750i	−0.269305	+	0.963055i	$0.586794\pi$
$564$		0			0
$565$	−26.3837	+	20.2255i	−1.10997	+	0.850893i
$566$		−	27.3411i		−	1.14923i
$567$		0			0
$568$	1.80904	−	1.80904i	0.0759054	−	0.0759054i
$569$	13.3282			0.558749			0.279374	−	0.960182i	$-0.409873\pi$
$569$	13.3282			0.558749			0.279374	+	0.960182i	$0.409873\pi$
$570$		0			0
$571$	32.2424			1.34930			0.674652	−	0.738136i	$-0.264294\pi$
$571$	32.2424			1.34930			0.674652	+	0.738136i	$0.264294\pi$
$572$	24.0045	−	24.0045i	1.00368	−	1.00368i
$573$		0			0
$574$		−	33.6226i		−	1.40338i
$575$	−18.8428	−	32.7067i	−0.785799	−	1.36396i
$576$		0			0
$577$	−27.7839	−	27.7839i	−1.15666	−	1.15666i	−0.985190	−	0.171467i	$-0.945149\pi$
$577$	−27.7839	−	27.7839i	−1.15666	−	1.15666i	−0.171467	−	0.985190i	$-0.554851\pi$
$578$	1.04491	+	1.04491i	0.0434626	+	0.0434626i
$579$		0			0
$580$	19.6569	+	2.59715i	0.816206	+	0.107841i
$581$			24.4655i			1.01500i
$582$		0			0
$583$	22.9706	−	22.9706i	0.951344	−	0.951344i
$584$	5.41421			0.224042
$585$		0			0
$586$	5.36856			0.221773
$587$	4.11532	−	4.11532i	0.169858	−	0.169858i	−0.617059	−	0.786917i	$-0.711676\pi$
$587$	4.11532	−	4.11532i	0.169858	−	0.169858i	0.786917	+	0.617059i	$0.211676\pi$
$588$		0			0
$589$		−	1.80904i		−	0.0745400i
$590$	1.33403	+	1.74021i	0.0549211	+	0.0716433i
$591$		0			0
$592$	−1.41421	−	1.41421i	−0.0581238	−	0.0581238i
$593$	−5.42301	−	5.42301i	−0.222696	−	0.222696i	0.586937	−	0.809633i	$-0.300334\pi$
$593$	−5.42301	−	5.42301i	−0.222696	−	0.222696i	−0.809633	+	0.586937i	$0.800334\pi$
$594$		0			0
$595$	−4.29857	+	32.5343i	−0.176224	+	1.33378i
$596$		−	8.89617i		−	0.364401i
$597$		0			0
$598$	33.4704	−	33.4704i	1.36871	−	1.36871i
$599$	28.3476			1.15825			0.579126	−	0.815238i	$-0.303394\pi$
$599$	28.3476			1.15825			0.579126	+	0.815238i	$0.303394\pi$
$600$		0			0
$601$	34.9933			1.42741			0.713703	−	0.700449i	$-0.247017\pi$
$601$	34.9933			1.42741			0.713703	+	0.700449i	$0.247017\pi$
$602$	23.3799	−	23.3799i	0.952894	−	0.952894i
$603$		0			0
$604$			3.36254i			0.136820i
$605$	5.36396	−	40.5979i	0.218076	−	1.65054i
$606$		0			0
$607$	−9.47332	−	9.47332i	−0.384510	−	0.384510i	0.488214	−	0.872724i	$-0.337649\pi$
$607$	−9.47332	−	9.47332i	−0.384510	−	0.384510i	−0.872724	+	0.488214i	$0.837649\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	4.68204	+	6.10761i	0.189570	+	0.247290i
$611$			66.7620i			2.70090i
$612$		0			0
$613$	31.6694	−	31.6694i	1.27911	−	1.27911i	0.337950	−	0.941164i	$-0.390267\pi$
$613$	31.6694	−	31.6694i	1.27911	−	1.27911i	0.941164	−	0.337950i	$-0.109733\pi$
$614$	22.3088			0.900312
$615$		0			0
$616$	−18.4853			−0.744793
$617$	−20.5991	+	20.5991i	−0.829287	+	0.829287i	−0.987418	−	0.158131i	$-0.949453\pi$
$617$	−20.5991	+	20.5991i	−0.829287	+	0.829287i	0.158131	+	0.987418i	$0.449453\pi$
$618$		0			0
$619$		−	9.67509i		−	0.388875i	−0.980915	−	0.194437i	$-0.937712\pi$
$619$		−	9.67509i		−	0.388875i	0.980915	−	0.194437i	$-0.0622881\pi$
$620$	4.01027	+	0.529854i	0.161057	+	0.0212795i
$621$		0			0
$622$	11.2872	+	11.2872i	0.452576	+	0.452576i
$623$	−31.2552	−	31.2552i	−1.25221	−	1.25221i
$624$		0			0
$625$	21.6274	+	12.5401i	0.865097	+	0.501605i
$626$		−	6.46790i		−	0.258509i
$627$		0			0
$628$	−6.49331	+	6.49331i	−0.259111	+	0.259111i
$629$	−8.59715			−0.342791
$630$		0			0
$631$	22.7050			0.903871			0.451936	−	0.892051i	$-0.350734\pi$
$631$	22.7050			0.903871			0.451936	+	0.892051i	$0.350734\pi$
$632$	−8.56864	+	8.56864i	−0.340842	+	0.340842i
$633$		0			0
$634$			21.3686i			0.848654i
$635$	11.3971	−	8.73688i	0.452279	−	0.346713i
$636$		0			0
$637$	−20.6467	−	20.6467i	−0.818050	−	0.818050i
$638$	33.9475	+	33.9475i	1.34399	+	1.34399i
$639$		0			0
$640$	1.77462	−	1.36041i	0.0701481	−	0.0537749i
$641$			22.9075i			0.904793i	0.891817	+	0.452396i	$0.149431\pi$
$641$			22.9075i			0.904793i	−0.891817	+	0.452396i	$0.850569\pi$
$642$		0			0
$643$	6.79297	−	6.79297i	0.267889	−	0.267889i	−0.560360	−	0.828249i	$-0.689337\pi$
$643$	6.79297	−	6.79297i	0.267889	−	0.267889i	0.828249	+	0.560360i	$0.189337\pi$
$644$	−25.7747			−1.01567
$645$		0			0
$646$	−4.29857			−0.169125
$647$	−33.3212	+	33.3212i	−1.30999	+	1.30999i	−0.388574	+	0.921417i	$0.627032\pi$
$647$	−33.3212	+	33.3212i	−1.30999	+	1.30999i	−0.921417	+	0.388574i	$0.872968\pi$
$648$		0			0
$649$			5.30922i			0.208405i
$650$	−8.14214	+	30.2745i	−0.319361	+	1.18747i
$651$		0			0
$652$	−12.5880	−	12.5880i	−0.492985	−	0.492985i
$653$	−32.1666	−	32.1666i	−1.25877	−	1.25877i	−0.951679	−	0.307096i	$-0.900643\pi$
$653$	−32.1666	−	32.1666i	−1.25877	−	1.25877i	−0.307096	−	0.951679i	$-0.599357\pi$
$654$		0			0
$655$	−20.0550	−	2.64975i	−0.783614	−	0.103534i
$656$			9.84782i			0.384493i
$657$		0			0
$658$	25.7059	−	25.7059i	1.00212	−	1.00212i
$659$	−15.4356			−0.601286			−0.300643	−	0.953737i	$-0.597201\pi$
$659$	−15.4356			−0.601286			−0.300643	+	0.953737i	$0.597201\pi$
$660$		0			0
$661$	−21.6210			−0.840960			−0.420480	−	0.907302i	$-0.638138\pi$
$661$	−21.6210			−0.840960			−0.420480	+	0.907302i	$0.638138\pi$
$662$	−13.1716	+	13.1716i	−0.511928	+	0.511928i
$663$		0			0
$664$		−	7.16578i		−	0.278086i
$665$	−4.64473	−	6.05894i	−0.180115	−	0.234956i
$666$		0			0
$667$	47.3343	+	47.3343i	1.83279	+	1.83279i
$668$	−1.67292	−	1.67292i	−0.0647272	−	0.0647272i
$669$		0			0
$670$	1.25067	−	9.46589i	0.0483177	−	0.365699i
$671$			18.6338i			0.719348i
$672$		0			0
$673$	−11.2770	+	11.2770i	−0.434697	+	0.434697i	−0.890223	−	0.455526i	$-0.849451\pi$
$673$	−11.2770	+	11.2770i	−0.434697	+	0.434697i	0.455526	+	0.890223i	$0.349451\pi$
$674$	21.3122			0.820914
$675$		0			0
$676$	−26.3137			−1.01207
$677$	−14.0334	+	14.0334i	−0.539349	+	0.539349i	−0.923338	−	0.383989i	$-0.874550\pi$
$677$	−14.0334	+	14.0334i	−0.539349	+	0.539349i	0.383989	+	0.923338i	$0.374550\pi$
$678$		0			0
$679$			6.36370i			0.244216i
$680$	1.25902	−	9.52909i	0.0482813	−	0.365424i
$681$		0			0
$682$	6.92576	+	6.92576i	0.265201	+	0.265201i
$683$	3.28344	+	3.28344i	0.125637	+	0.125637i	0.767130	−	0.641492i	$-0.221684\pi$
$683$	3.28344	+	3.28344i	0.125637	+	0.125637i	−0.641492	+	0.767130i	$0.721684\pi$
$684$		0			0
$685$	17.7587	+	23.1658i	0.678524	+	0.885119i
$686$		−	8.00000i		−	0.305441i
$687$		0			0
$688$	−6.84782	+	6.84782i	−0.261071	+	0.261071i
$689$	−37.6204			−1.43322
$690$		0			0
$691$	−32.1970			−1.22483			−0.612415	−	0.790536i	$-0.709802\pi$
$691$	−32.1970			−1.22483			−0.612415	+	0.790536i	$0.709802\pi$
$692$	8.09046	−	8.09046i	0.307553	−	0.307553i
$693$		0			0
$694$		−	10.0491i		−	0.381457i
$695$	27.1647	+	3.58911i	1.03042	+	0.136143i
$696$		0			0
$697$	29.9329	+	29.9329i	1.13379	+	1.13379i
$698$	3.88660	+	3.88660i	0.147110	+	0.147110i
$699$		0			0
$700$	14.7919	−	8.52182i	0.559081	−	0.322095i
$701$		−	33.2262i		−	1.25494i	−0.778642	−	0.627468i	$-0.784091\pi$
$701$		−	33.2262i		−	1.25494i	0.778642	−	0.627468i	$-0.215909\pi$
$702$		0			0
$703$	1.41421	−	1.41421i	0.0533381	−	0.0533381i
$704$	5.41421			0.204056
$705$		0			0
$706$	1.83601			0.0690992
$707$	24.7279	−	24.7279i	0.929989	−	0.929989i
$708$		0			0
$709$			44.9363i			1.68762i	0.536645	+	0.843808i	$0.319692\pi$
$709$			44.9363i			1.68762i	−0.536645	+	0.843808i	$0.680308\pi$
$710$	−4.54013	+	3.48042i	−0.170388	+	0.130618i
$711$		0			0
$712$	9.15442	+	9.15442i	0.343077	+	0.343077i
$713$	9.65685	+	9.65685i	0.361652	+	0.361652i
$714$		0			0
$715$	−60.2440	+	46.1825i	−2.25300	+	1.72713i
$716$			6.96237i			0.260196i
$717$		0			0
$718$	−7.76069	+	7.76069i	−0.289626	+	0.289626i
$719$	−7.25384			−0.270523			−0.135261	−	0.990810i	$-0.543187\pi$
$719$	−7.25384			−0.270523			−0.135261	+	0.990810i	$0.543187\pi$
$720$		0			0
$721$	−38.5446			−1.43548
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$		0			0
$724$		−	1.63260i		−	0.0606752i
$725$	−42.8147	−	11.5147i	−1.59010	−	0.427646i
$726$		0			0
$727$	20.0183	+	20.0183i	0.742438	+	0.742438i	0.973047	−	0.230609i	$-0.0740717\pi$
$727$	20.0183	+	20.0183i	0.742438	+	0.742438i	−0.230609	+	0.973047i	$0.574072\pi$
$728$	15.1373	+	15.1373i	0.561025	+	0.561025i
$729$		0			0
$730$	−12.0022	−	1.58579i	−0.444223	−	0.0586926i
$731$			41.6286i			1.53969i
$732$		0			0
$733$	−33.0680	+	33.0680i	−1.22139	+	1.22139i	−0.254257	+	0.967137i	$0.581831\pi$
$733$	−33.0680	+	33.0680i	−1.22139	+	1.22139i	−0.967137	+	0.254257i	$0.918169\pi$
$734$	−6.77675			−0.250134
$735$		0			0
$736$	7.54925			0.278269
$737$	16.3476	−	16.3476i	0.602173	−	0.602173i
$738$		0			0
$739$			15.7278i			0.578555i	0.957245	+	0.289278i	$0.0934151\pi$
$739$			15.7278i			0.578555i	−0.957245	+	0.289278i	$0.906585\pi$
$740$	2.72082	+	3.54925i	0.100019	+	0.130473i
$741$		0			0
$742$	14.4853	+	14.4853i	0.531771	+	0.531771i
$743$	11.9430	+	11.9430i	0.438146	+	0.438146i	0.891388	−	0.453242i	$-0.149733\pi$
$743$	11.9430	+	11.9430i	0.438146	+	0.438146i	−0.453242	+	0.891388i	$0.649733\pi$
$744$		0			0
$745$	−2.60563	+	19.7210i	−0.0954628	+	0.722523i
$746$			22.6435i			0.829037i
$747$		0			0
$748$	16.4568	−	16.4568i	0.601719	−	0.601719i
$749$	−15.3137			−0.559551
$750$		0			0
$751$	−1.59382			−0.0581593			−0.0290796	−	0.999577i	$-0.509258\pi$
$751$	−1.59382			−0.0581593			−0.0290796	+	0.999577i	$0.509258\pi$
$752$	−7.52909	+	7.52909i	−0.274558	+	0.274558i
$753$		0			0
$754$		−	55.5980i		−	2.02476i
$755$	0.984864	−	7.45408i	0.0358429	−	0.271282i
$756$		0			0
$757$	12.9140	+	12.9140i	0.469368	+	0.469368i	0.901710	−	0.432342i	$-0.142313\pi$
$757$	12.9140	+	12.9140i	0.469368	+	0.469368i	−0.432342	+	0.901710i	$0.642313\pi$
$758$	9.57775	+	9.57775i	0.347880	+	0.347880i
$759$		0			0
$760$	1.36041	+	1.77462i	0.0493472	+	0.0643723i
$761$			40.0304i			1.45110i	0.688169	+	0.725550i	$0.258415\pi$
$761$			40.0304i			1.45110i	−0.688169	+	0.725550i	$0.741585\pi$
$762$		0			0
$763$	−9.32824	+	9.32824i	−0.337705	+	0.337705i
$764$	1.56486			0.0566147
$765$		0			0
$766$	11.1555			0.403065
$767$	4.34763	−	4.34763i	0.156984	−	0.156984i
$768$		0			0
$769$		−	25.5107i		−	0.919939i	−0.887935	−	0.459970i	$-0.847860\pi$
$769$		−	25.5107i		−	0.919939i	0.887935	−	0.459970i	$-0.152140\pi$
$770$	40.9782	+	5.41421i	1.47675	+	0.195115i
$771$		0			0
$772$	4.33736	+	4.33736i	0.156105	+	0.156105i
$773$	−4.39329	−	4.39329i	−0.158016	−	0.158016i	0.623671	−	0.781687i	$-0.285640\pi$
$773$	−4.39329	−	4.39329i	−0.158016	−	0.158016i	−0.781687	+	0.623671i	$0.785640\pi$
$774$		0			0
$775$	−8.73480	−	2.34916i	−0.313763	−	0.0843845i
$776$		−	1.86388i		−	0.0669095i
$777$		0			0
$778$	−11.0662	+	11.0662i	−0.396743	+	0.396743i
$779$	−9.84782			−0.352835
$780$		0			0
$781$	−13.8515			−0.495646
$782$	22.9463	−	22.9463i	0.820558	−	0.820558i
$783$		0			0
$784$		−	4.65685i		−	0.166316i
$785$	16.2962	−	12.4925i	0.581638	−	0.445878i
$786$		0			0
$787$	20.5058	+	20.5058i	0.730954	+	0.730954i	0.970809	−	0.239855i	$-0.0770998\pi$
$787$	20.5058	+	20.5058i	0.730954	+	0.730954i	−0.239855	+	0.970809i	$0.577100\pi$
$788$	17.6599	+	17.6599i	0.629107	+	0.629107i
$789$		0			0
$790$	21.5047	−	16.4853i	0.765102	−	0.586520i
$791$		−	50.7598i		−	1.80481i
$792$		0			0
$793$	15.2589	−	15.2589i	0.541858	−	0.541858i
$794$	−26.3057			−0.933554
$795$		0			0
$796$	−11.5450			−0.409201
$797$	4.50669	−	4.50669i	0.159635	−	0.159635i	−0.622770	−	0.782405i	$-0.713993\pi$
$797$	4.50669	−	4.50669i	0.159635	−	0.159635i	0.782405	+	0.622770i	$0.213993\pi$
$798$		0			0
$799$			45.7701i			1.61923i
$800$	−4.33244	+	2.49598i	−0.153175	+	0.0882464i
$801$		0			0
$802$	21.2335	+	21.2335i	0.749782	+	0.749782i
$803$	−20.7279	−	20.7279i	−0.731472	−	0.731472i
$804$		0			0
$805$	57.1375	+	7.54925i	2.01383	+	0.266076i
$806$		−	11.3428i		−	0.399532i
$807$		0			0
$808$	−7.24264	+	7.24264i	−0.254795	+	0.254795i
$809$	−16.7197			−0.587835			−0.293917	−	0.955831i	$-0.594959\pi$
$809$	−16.7197			−0.587835			−0.293917	+	0.955831i	$0.594959\pi$
$810$		0			0
$811$	46.7920			1.64309			0.821544	−	0.570145i	$-0.193113\pi$
$811$	46.7920			1.64309			0.821544	+	0.570145i	$0.193113\pi$
$812$	−21.4073	+	21.4073i	−0.751250	+	0.751250i
$813$		0			0
$814$			10.8284i			0.379536i
$815$	24.2182	+	31.5921i	0.848327	+	1.10662i
$816$		0			0
$817$	−6.84782	−	6.84782i	−0.239575	−	0.239575i
$818$	−19.1259	−	19.1259i	−0.668722	−	0.668722i
$819$		0			0
$820$	2.88436	−	21.8307i	0.100726	−	0.762360i
$821$			3.42023i			0.119367i	0.998217	+	0.0596835i	$0.0190091\pi$
$821$			3.42023i			0.119367i	−0.998217	+	0.0596835i	$0.980991\pi$
$822$		0			0
$823$	−10.5078	+	10.5078i	−0.366280	+	0.366280i	−0.866119	−	0.499838i	$-0.833393\pi$
$823$	−10.5078	+	10.5078i	−0.366280	+	0.366280i	0.499838	+	0.866119i	$0.333393\pi$
$824$	11.2895			0.393287
$825$		0			0
$826$	−3.34801			−0.116492
$827$	−18.6435	+	18.6435i	−0.648297	+	0.648297i	−0.952581	−	0.304284i	$-0.901583\pi$
$827$	−18.6435	+	18.6435i	−0.648297	+	0.648297i	0.304284	+	0.952581i	$0.401583\pi$
$828$		0			0
$829$		−	14.2555i		−	0.495115i	−0.968873	−	0.247558i	$-0.920372\pi$
$829$		−	14.2555i		−	0.495115i	0.968873	−	0.247558i	$-0.0796279\pi$
$830$	−2.09881	+	15.8851i	−0.0728507	+	0.551381i
$831$		0			0
$832$	−4.43361	−	4.43361i	−0.153708	−	0.153708i
$833$	−14.1547	−	14.1547i	−0.490433	−	0.490433i
$834$		0			0
$835$	3.21854	+	4.19852i	0.111382	+	0.145296i
$836$			5.41421i			0.187254i
$837$		0			0
$838$	−2.37073	+	2.37073i	−0.0818953	+	0.0818953i
$839$	38.8177			1.34014			0.670069	−	0.742299i	$-0.266265\pi$
$839$	38.8177			1.34014			0.670069	+	0.742299i	$0.266265\pi$
$840$		0			0
$841$	49.6274			1.71129
$842$	17.9280	−	17.9280i	0.617840	−	0.617840i
$843$		0			0
$844$		−	10.7714i		−	0.370767i
$845$	58.3323	+	7.70711i	2.00669	+	0.265133i
$846$		0			0
$847$	44.2132	+	44.2132i	1.51918	+	1.51918i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$	−5.58201	+	20.7553i	−0.191461	+	0.711902i
$851$			15.0985i			0.517570i
$852$		0			0
$853$	−7.38301	+	7.38301i	−0.252790	+	0.252790i	−0.822113	−	0.569324i	$-0.807205\pi$
$853$	−7.38301	+	7.38301i	−0.252790	+	0.252790i	0.569324	+	0.822113i	$0.307205\pi$
$854$	−11.7505			−0.402093
$855$		0			0
$856$	4.48528			0.153304
$857$	30.9980	−	30.9980i	1.05887	−	1.05887i	0.0607160	−	0.998155i	$-0.480662\pi$
$857$	30.9980	−	30.9980i	1.05887	−	1.05887i	0.998155	−	0.0607160i	$-0.0193384\pi$
$858$		0			0
$859$			31.3913i			1.07106i	0.844517	+	0.535528i	$0.179887\pi$
$859$			31.3913i			1.07106i	−0.844517	+	0.535528i	$0.820113\pi$
$860$	17.1859	−	13.1746i	0.586036	−	0.449250i
$861$		0			0
$862$	22.1582	+	22.1582i	0.754711	+	0.754711i
$863$	15.2916	+	15.2916i	0.520533	+	0.520533i	0.917732	−	0.397199i	$-0.130018\pi$
$863$	15.2916	+	15.2916i	0.520533	+	0.520533i	−0.397199	+	0.917732i	$0.630018\pi$
$864$		0			0
$865$	−20.3046	+	15.5653i	−0.690377	+	0.529236i
$866$			4.71720i			0.160297i
$867$		0			0
$868$	−4.36740	+	4.36740i	−0.148239	+	0.148239i
$869$	65.6088			2.22563
$870$		0			0
$871$	−26.7736			−0.907188
$872$	2.73218	−	2.73218i	0.0925232	−	0.0925232i
$873$		0			0
$874$			7.54925i			0.255357i
$875$	−35.2867	+	14.5588i	−1.19291	+	0.492176i
$876$		0			0
$877$	−18.1475	−	18.1475i	−0.612797	−	0.612797i	0.330877	−	0.943674i	$-0.392655\pi$
$877$	−18.1475	−	18.1475i	−0.612797	−	0.612797i	−0.943674	+	0.330877i	$0.892655\pi$
$878$	11.0479	+	11.0479i	0.372849	+	0.372849i
$879$		0			0
$880$	−12.0022	−	1.58579i	−0.404596	−	0.0534568i
$881$			16.3151i			0.549669i	0.961492	+	0.274835i	$0.0886231\pi$
$881$			16.3151i			0.549669i	−0.961492	+	0.274835i	$0.911377\pi$
$882$		0			0
$883$	20.4031	−	20.4031i	0.686618	−	0.686618i	−0.274865	−	0.961483i	$-0.588633\pi$
$883$	20.4031	−	20.4031i	0.686618	−	0.686618i	0.961483	+	0.274865i	$0.0886330\pi$
$884$	−26.9523			−0.906505
$885$		0			0
$886$	−4.32129			−0.145177
$887$	−23.9042	+	23.9042i	−0.802624	+	0.802624i	−0.983505	−	0.180881i	$-0.942105\pi$
$887$	−23.9042	+	23.9042i	−0.802624	+	0.802624i	0.180881	+	0.983505i	$0.442105\pi$
$888$		0			0
$889$			21.9269i			0.735405i
$890$	−17.6123	−	22.9748i	−0.590365	−	0.770118i
$891$		0			0
$892$	17.2175	+	17.2175i	0.576483	+	0.576483i
$893$	−7.52909	−	7.52909i	−0.251951	−	0.251951i
$894$		0			0
$895$	2.03923	−	15.4342i	0.0681640	−	0.515909i
$896$			3.41421i			0.114061i
$897$		0			0
$898$	24.4338	−	24.4338i	0.815368	−	0.815368i
$899$	16.0411			0.535001
$900$		0			0
$901$	−25.7914			−0.859237
$902$	37.7017	−	37.7017i	1.25533	−	1.25533i
$903$		0			0
$904$			14.8672i			0.494476i
$905$	−0.478178	+	3.61916i	−0.0158952	+	0.120305i
$906$		0			0
$907$	28.4283	+	28.4283i	0.943945	+	0.943945i	0.998510	−	0.0545652i	$-0.0173773\pi$
$907$	28.4283	+	28.4283i	0.943945	+	0.943945i	−0.0545652	+	0.998510i	$0.517377\pi$
$908$	4.67625	+	4.67625i	0.155187	+	0.155187i
$909$		0			0
$910$	−29.1227	−	37.9900i	−0.965410	−	1.25935i
$911$		−	46.1400i		−	1.52869i	−0.644810	−	0.764343i	$-0.723064\pi$
$911$		−	46.1400i		−	1.52869i	0.644810	−	0.764343i	$-0.276936\pi$
$912$		0			0
$913$	−27.4337	+	27.4337i	−0.907922	+	0.907922i
$914$	−6.89015			−0.227906
$915$		0			0
$916$	−8.57443			−0.283307
$917$	21.8409	−	21.8409i	0.721252	−	0.721252i
$918$		0			0
$919$		−	7.31371i		−	0.241257i	−0.992698	−	0.120628i	$-0.961509\pi$
$919$		−	7.31371i		−	0.241257i	0.992698	−	0.120628i	$-0.0384910\pi$
$920$	−16.7352	−	2.21112i	−0.551743	−	0.0728986i
$921$		0			0
$922$	−11.5815	−	11.5815i	−0.381417	−	0.381417i
$923$	11.3428	+	11.3428i	0.373352	+	0.373352i
$924$		0			0
$925$	−4.99197	−	8.66489i	−0.164135	−	0.284900i
$926$			41.6399i			1.36837i
$927$		0			0
$928$	6.27006	−	6.27006i	0.205825	−	0.205825i
$929$	2.92106			0.0958367			0.0479184	−	0.998851i	$-0.484741\pi$
$929$	2.92106			0.0958367			0.0479184	+	0.998851i	$0.484741\pi$
$930$		0			0
$931$	4.65685			0.152622
$932$	14.1655	−	14.1655i	0.464005	−	0.464005i
$933$		0			0
$934$			5.84356i			0.191207i
$935$	−41.3015	+	31.6613i	−1.35070	+	1.03544i
$936$		0			0
$937$	−1.26558	−	1.26558i	−0.0413447	−	0.0413447i	0.686132	−	0.727477i	$-0.259307\pi$
$937$	−1.26558	−	1.26558i	−0.0413447	−	0.0413447i	−0.727477	+	0.686132i	$0.759307\pi$
$938$	10.3088	+	10.3088i	0.336596	+	0.336596i
$939$		0			0
$940$	18.8957	−	14.4853i	0.616310	−	0.472458i
$941$		−	6.09670i		−	0.198747i	−0.995050	−	0.0993733i	$-0.968316\pi$
$941$		−	6.09670i		−	0.198747i	0.995050	−	0.0993733i	$-0.0316838\pi$
$942$		0			0
$943$	52.5689	−	52.5689i	1.71188	−	1.71188i
$944$	0.980608			0.0319161
$945$		0			0
$946$	52.4327			1.70474
$947$	−2.81297	+	2.81297i	−0.0914094	+	0.0914094i	−0.751333	−	0.659923i	$-0.770589\pi$
$947$	−2.81297	+	2.81297i	−0.0914094	+	0.0914094i	0.659923	+	0.751333i	$0.270589\pi$
$948$		0			0
$949$			33.9475i			1.10198i
$950$	−2.49598	−	4.33244i	−0.0809804	−	0.140563i
$951$		0			0
$952$	10.3777	+	10.3777i	0.336342	+	0.336342i
$953$	−31.8264	−	31.8264i	−1.03096	−	1.03096i	−0.999505	−	0.0314534i	$-0.989986\pi$
$953$	−31.8264	−	31.8264i	−1.03096	−	1.03096i	−0.0314534	−	0.999505i	$-0.510014\pi$
$954$		0			0
$955$	−3.46899	−	0.458337i	−0.112254	−	0.0148314i
$956$			5.49331i			0.177666i
$957$		0			0
$958$	−4.26203	+	4.26203i	−0.137700	+	0.137700i
$959$	−44.5689			−1.43920
$960$		0			0
$961$	−27.7274			−0.894432
$962$	8.86721	−	8.86721i	0.285890	−	0.285890i
$963$		0			0
$964$		−	10.0227i		−	0.322810i
$965$	−8.34468	−	10.8854i	−0.268625	−	0.350415i
$966$		0			0
$967$	7.06621	+	7.06621i	0.227234	+	0.227234i	0.811536	−	0.584302i	$-0.198632\pi$
$967$	7.06621	+	7.06621i	0.227234	+	0.227234i	−0.584302	+	0.811536i	$0.698632\pi$
$968$	−12.9497	−	12.9497i	−0.416221	−	0.416221i
$969$		0			0
$970$	−0.545919	+	4.13186i	−0.0175284	+	0.132666i
$971$		−	17.7132i		−	0.568445i	−0.958758	−	0.284222i	$-0.908265\pi$
$971$		−	17.7132i		−	0.568445i	0.958758	−	0.284222i	$-0.0917354\pi$
$972$		0			0
$973$	−29.5838	+	29.5838i	−0.948412	+	0.948412i
$974$	0.113398			0.00363351
$975$		0			0
$976$	3.44164			0.110164
$977$	32.7339	−	32.7339i	1.04725	−	1.04725i	0.0484247	−	0.998827i	$-0.484580\pi$
$977$	32.7339	−	32.7339i	1.04725	−	1.04725i	0.998827	−	0.0484247i	$-0.0154201\pi$
$978$		0			0
$979$		−	70.0941i		−	2.24022i
$980$	−1.36396	+	10.3233i	−0.0435701	+	0.329767i
$981$		0			0
$982$	23.0651	+	23.0651i	0.736038	+	0.736038i
$983$	−8.66018	−	8.66018i	−0.276217	−	0.276217i	0.555380	−	0.831597i	$-0.312573\pi$
$983$	−8.66018	−	8.66018i	−0.276217	−	0.276217i	−0.831597	+	0.555380i	$0.812573\pi$
$984$		0			0
$985$	−33.9760	−	44.3209i	−1.08256	−	1.41218i
$986$		−	38.1163i		−	1.21387i
$987$		0			0
$988$	4.43361	−	4.43361i	0.141052	−	0.141052i
$989$	73.1090			2.32473
$990$		0			0
$991$	50.8001			1.61372			0.806860	−	0.590743i	$-0.201165\pi$
$991$	50.8001			1.61372			0.806860	+	0.590743i	$0.201165\pi$
$992$	1.27918	−	1.27918i	0.0406140	−	0.0406140i
$993$		0			0
$994$		−	8.73480i		−	0.277051i
$995$	25.5930	+	3.38145i	0.811351	+	0.107199i
$996$		0			0
$997$	−13.9007	−	13.9007i	−0.440238	−	0.440238i	0.451854	−	0.892092i	$-0.350763\pi$
$997$	−13.9007	−	13.9007i	−0.440238	−	0.440238i	−0.892092	+	0.451854i	$0.850763\pi$
$998$	−14.1065	−	14.1065i	−0.446534	−	0.446534i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.f.647.2	✓	8
3.2	odd	2		1710.2.n.g.647.3	yes	8
5.3	odd	4		1710.2.n.g.1673.4	yes	8
15.8	even	4	inner	1710.2.n.f.1673.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.f.647.2	✓	8	1.1	even	1	trivial
1710.2.n.f.1673.1	yes	8	15.8	even	4	inner
1710.2.n.g.647.3	yes	8	3.2	odd	2
1710.2.n.g.1673.4	yes	8	5.3	odd	4

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.292893 + 2.21680i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.36041 - 1.77462i) q^{10} -5.41421i q^{11} +(-4.43361 + 4.43361i) q^{13} +3.41421 q^{14} -1.00000 q^{16} +(-3.03955 + 3.03955i) q^{17} -1.00000i q^{19} +(2.21680 + 0.292893i) q^{20} +(3.82843 + 3.82843i) q^{22} +(5.33812 + 5.33812i) q^{23} +(-4.82843 - 1.29857i) q^{25} -6.27006i q^{26} +(-2.41421 + 2.41421i) q^{28} +8.86721 q^{29} +1.80904 q^{31} +(0.707107 - 0.707107i) q^{32} -4.29857i q^{34} +(6.05894 - 4.64473i) q^{35} +(1.41421 + 1.41421i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-1.77462 + 1.36041i) q^{40} -9.84782i q^{41} +(6.84782 - 6.84782i) q^{43} -5.41421 q^{44} -7.54925 q^{46} +(7.52909 - 7.52909i) q^{47} +4.65685i q^{49} +(4.33244 - 2.49598i) q^{50} +(4.43361 + 4.43361i) q^{52} +(4.24264 + 4.24264i) q^{53} +(12.0022 + 1.58579i) q^{55} -3.41421i q^{56} +(-6.27006 + 6.27006i) q^{58} -0.980608 q^{59} -3.44164 q^{61} +(-1.27918 + 1.27918i) q^{62} +1.00000i q^{64} +(-8.52985 - 11.1270i) q^{65} +(3.01939 + 3.01939i) q^{67} +(3.03955 + 3.03955i) q^{68} +(-1.00000 + 7.56864i) q^{70} -2.55836i q^{71} +(3.82843 - 3.82843i) q^{73} -2.00000 q^{74} -1.00000 q^{76} +(-13.0711 + 13.0711i) q^{77} +12.1179i q^{79} +(0.292893 - 2.21680i) q^{80} +(6.96346 + 6.96346i) q^{82} +(-5.06697 - 5.06697i) q^{83} +(-5.84782 - 7.62835i) q^{85} +9.68428i q^{86} +(3.82843 - 3.82843i) q^{88} +12.9463 q^{89} +21.4073 q^{91} +(5.33812 - 5.33812i) q^{92} +10.6477i q^{94} +(2.21680 + 0.292893i) q^{95} +(-1.31796 - 1.31796i) q^{97} +(-3.29289 - 3.29289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{7} - 4 q^{10} + 16 q^{14} - 8 q^{16} + 8 q^{22} + 8 q^{23} - 16 q^{25} - 8 q^{28} + 16 q^{31} + 4 q^{40} + 8 q^{43} - 32 q^{44} - 24 q^{46} + 24 q^{47} + 16 q^{50} - 32 q^{59} - 24 q^{62}+ \cdots - 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^7 - 4 * q^10 + 16 * q^14 - 8 * q^16 + 8 * q^22 + 8 * q^23 - 16 * q^25 - 8 * q^28 + 16 * q^31 + 4 * q^40 + 8 * q^43 - 32 * q^44 - 24 * q^46 + 24 * q^47 + 16 * q^50 - 32 * q^59 - 24 * q^62 - 56 * q^65 - 8 * q^70 + 8 * q^73 - 16 * q^74 - 8 * q^76 - 48 * q^77 + 8 * q^80 + 8 * q^82 + 8 * q^88 - 16 * q^89 + 8 * q^92 + 24 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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