LMFDB - Embedded newform 510.2.p.d.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(361,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("510.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.p (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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			361.3
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	510.361
Dual form			510.2.p.d.421.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.84776 - 1.84776i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.84776 - 1.84776i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 0.707107i) q^{10} +(-1.19891 - 1.19891i) q^{11} +(-0.707107 + 0.707107i) q^{12} -2.72965 q^{13} +(-1.84776 + 1.84776i) q^{14} -1.00000i q^{15} +1.00000 q^{16} +(1.19891 - 3.94495i) q^{17} -1.00000 q^{18} -0.663643i q^{19} +(-0.707107 + 0.707107i) q^{20} -2.61313 q^{21} +(-1.19891 + 1.19891i) q^{22} +(-0.249429 - 0.249429i) q^{23} +(0.707107 + 0.707107i) q^{24} -1.00000i q^{25} +2.72965i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.84776 + 1.84776i) q^{28} +(-5.08239 + 5.08239i) q^{29} -1.00000 q^{30} +(6.72286 - 6.72286i) q^{31} -1.00000i q^{32} -1.69552 q^{33} +(-3.94495 - 1.19891i) q^{34} -2.61313 q^{35} +1.00000i q^{36} +(0.352746 - 0.352746i) q^{37} -0.663643 q^{38} +(-1.93015 + 1.93015i) q^{39} +(0.707107 + 0.707107i) q^{40} +(5.42676 + 5.42676i) q^{41} +2.61313i q^{42} -9.41838i q^{43} +(1.19891 + 1.19891i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(-0.249429 + 0.249429i) q^{46} -3.33636 q^{47} +(0.707107 - 0.707107i) q^{48} -0.171573i q^{49} -1.00000 q^{50} +(-1.94174 - 3.63726i) q^{51} +2.72965 q^{52} +5.06147i q^{53} +(-0.707107 + 0.707107i) q^{54} -1.69552 q^{55} +(1.84776 - 1.84776i) q^{56} +(-0.469266 - 0.469266i) q^{57} +(5.08239 + 5.08239i) q^{58} +10.7161i q^{59} +1.00000i q^{60} +(5.19891 + 5.19891i) q^{61} +(-6.72286 - 6.72286i) q^{62} +(-1.84776 + 1.84776i) q^{63} -1.00000 q^{64} +(-1.93015 + 1.93015i) q^{65} +1.69552i q^{66} +3.14423 q^{67} +(-1.19891 + 3.94495i) q^{68} -0.352746 q^{69} +2.61313i q^{70} +(1.21371 - 1.21371i) q^{71} +1.00000 q^{72} +(10.6530 - 10.6530i) q^{73} +(-0.352746 - 0.352746i) q^{74} +(-0.707107 - 0.707107i) q^{75} +0.663643i q^{76} +4.43060i q^{77} +(1.93015 + 1.93015i) q^{78} +(1.85577 + 1.85577i) q^{79} +(0.707107 - 0.707107i) q^{80} -1.00000 q^{81} +(5.42676 - 5.42676i) q^{82} -11.3910i q^{83} +2.61313 q^{84} +(-1.94174 - 3.63726i) q^{85} -9.41838 q^{86} +7.18759i q^{87} +(1.19891 - 1.19891i) q^{88} -5.25903 q^{89} +(-0.707107 + 0.707107i) q^{90} +(5.04373 + 5.04373i) q^{91} +(0.249429 + 0.249429i) q^{92} -9.50756i q^{93} +3.33636i q^{94} +(-0.469266 - 0.469266i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-8.43355 + 8.43355i) q^{97} -0.171573 q^{98} +(-1.19891 + 1.19891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 8 q^{16} - 8 q^{18} - 8 q^{23} - 32 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{33} - 8 q^{34} + 16 q^{37} + 8 q^{39} - 8 q^{46} - 32 q^{47} - 8 q^{50} - 16 q^{51} + 16 q^{55} - 16 q^{57} + 32 q^{58} + 32 q^{61} + 8 q^{62} - 8 q^{64} + 8 q^{65} + 80 q^{67} - 16 q^{69} + 8 q^{72} - 16 q^{74} - 8 q^{78} - 40 q^{79} - 8 q^{81} - 16 q^{85} + 16 q^{86} - 16 q^{89} + 16 q^{91} + 8 q^{92} - 16 q^{95} - 64 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 8 * q^16 - 8 * q^18 - 8 * q^23 - 32 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^33 - 8 * q^34 + 16 * q^37 + 8 * q^39 - 8 * q^46 - 32 * q^47 - 8 * q^50 - 16 * q^51 + 16 * q^55 - 16 * q^57 + 32 * q^58 + 32 * q^61 + 8 * q^62 - 8 * q^64 + 8 * q^65 + 80 * q^67 - 16 * q^69 + 8 * q^72 - 16 * q^74 - 8 * q^78 - 40 * q^79 - 8 * q^81 - 16 * q^85 + 16 * q^86 - 16 * q^89 + 16 * q^91 + 8 * q^92 - 16 * q^95 - 64 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−1.84776	−	1.84776i	−0.698387	−	0.698387i	0.265675	−	0.964063i	$-0.414405\pi$
$7$	−1.84776	−	1.84776i	−0.698387	−	0.698387i	−0.964063	+	0.265675i	$0.914405\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−0.707107	−	0.707107i	−0.223607	−	0.223607i
$11$	−1.19891	−	1.19891i	−0.361486	−	0.361486i	0.502874	−	0.864360i	$-0.332276\pi$
$11$	−1.19891	−	1.19891i	−0.361486	−	0.361486i	−0.864360	+	0.502874i	$0.832276\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−2.72965			−0.757068			−0.378534	−	0.925587i	$-0.623572\pi$
$13$	−2.72965			−0.757068			−0.378534	+	0.925587i	$0.623572\pi$
$14$	−1.84776	+	1.84776i	−0.493834	+	0.493834i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$	1.19891	−	3.94495i	0.290779	−	0.956790i
$17$	1.19891	−	3.94495i	0.290779	−	0.956790i
$18$	−1.00000			−0.235702
$19$		−	0.663643i		−	0.152250i	−0.997098	−	0.0761250i	$-0.975745\pi$
$19$		−	0.663643i		−	0.152250i	0.997098	−	0.0761250i	$-0.0242548\pi$
$20$	−0.707107	+	0.707107i	−0.158114	+	0.158114i
$21$	−2.61313			−0.570231
$22$	−1.19891	+	1.19891i	−0.255609	+	0.255609i
$23$	−0.249429	−	0.249429i	−0.0520096	−	0.0520096i	0.680624	−	0.732633i	$-0.261709\pi$
$23$	−0.249429	−	0.249429i	−0.0520096	−	0.0520096i	−0.732633	+	0.680624i	$0.761709\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$		−	1.00000i		−	0.200000i
$26$			2.72965i			0.535328i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.84776	+	1.84776i	0.349194	+	0.349194i
$29$	−5.08239	+	5.08239i	−0.943777	+	0.943777i	−0.998501	−	0.0547249i	$-0.982572\pi$
$29$	−5.08239	+	5.08239i	−0.943777	+	0.943777i	0.0547249	+	0.998501i	$0.482572\pi$
$30$	−1.00000			−0.182574
$31$	6.72286	−	6.72286i	1.20746	−	1.20746i	0.235614	−	0.971847i	$-0.424290\pi$
$31$	6.72286	−	6.72286i	1.20746	−	1.20746i	0.971847	−	0.235614i	$-0.0757102\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.69552			−0.295152
$34$	−3.94495	−	1.19891i	−0.676553	−	0.205612i
$35$	−2.61313			−0.441699
$36$			1.00000i			0.166667i
$37$	0.352746	−	0.352746i	0.0579911	−	0.0579911i	−0.677516	−	0.735508i	$-0.736944\pi$
$37$	0.352746	−	0.352746i	0.0579911	−	0.0579911i	0.735508	+	0.677516i	$0.236944\pi$
$38$	−0.663643			−0.107657
$39$	−1.93015	+	1.93015i	−0.309072	+	0.309072i
$40$	0.707107	+	0.707107i	0.111803	+	0.111803i
$41$	5.42676	+	5.42676i	0.847517	+	0.847517i	0.989823	−	0.142306i	$-0.0454516\pi$
$41$	5.42676	+	5.42676i	0.847517	+	0.847517i	−0.142306	+	0.989823i	$0.545452\pi$
$42$			2.61313i			0.403214i
$43$		−	9.41838i		−	1.43629i	−0.695894	−	0.718144i	$-0.744992\pi$
$43$		−	9.41838i		−	1.43629i	0.695894	−	0.718144i	$-0.255008\pi$
$44$	1.19891	+	1.19891i	0.180743	+	0.180743i
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$	−0.249429	+	0.249429i	−0.0367763	+	0.0367763i
$47$	−3.33636			−0.486658			−0.243329	−	0.969944i	$-0.578239\pi$
$47$	−3.33636			−0.486658			−0.243329	+	0.969944i	$0.578239\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	0.171573i		−	0.0245104i
$50$	−1.00000			−0.141421
$51$	−1.94174	−	3.63726i	−0.271898	−	0.509318i
$52$	2.72965			0.378534
$53$			5.06147i			0.695246i	0.937634	+	0.347623i	$0.113011\pi$
$53$			5.06147i			0.695246i	−0.937634	+	0.347623i	$0.886989\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−1.69552			−0.228624
$56$	1.84776	−	1.84776i	0.246917	−	0.246917i
$57$	−0.469266	−	0.469266i	−0.0621558	−	0.0621558i
$58$	5.08239	+	5.08239i	0.667351	+	0.667351i
$59$			10.7161i			1.39511i	0.716530	+	0.697557i	$0.245729\pi$
$59$			10.7161i			1.39511i	−0.716530	+	0.697557i	$0.754271\pi$
$60$			1.00000i			0.129099i
$61$	5.19891	+	5.19891i	0.665653	+	0.665653i	0.956707	−	0.291054i	$-0.0940060\pi$
$61$	5.19891	+	5.19891i	0.665653	+	0.665653i	−0.291054	+	0.956707i	$0.594006\pi$
$62$	−6.72286	−	6.72286i	−0.853804	−	0.853804i
$63$	−1.84776	+	1.84776i	−0.232796	+	0.232796i
$64$	−1.00000			−0.125000
$65$	−1.93015	+	1.93015i	−0.239406	+	0.239406i
$66$			1.69552i			0.208704i
$67$	3.14423			0.384129			0.192065	−	0.981382i	$-0.438482\pi$
$67$	3.14423			0.384129			0.192065	+	0.981382i	$0.438482\pi$
$68$	−1.19891	+	3.94495i	−0.145389	+	0.478395i
$69$	−0.352746			−0.0424656
$70$			2.61313i			0.312328i
$71$	1.21371	−	1.21371i	0.144041	−	0.144041i	−0.631409	−	0.775450i	$-0.717523\pi$
$71$	1.21371	−	1.21371i	0.144041	−	0.144041i	0.775450	+	0.631409i	$0.217523\pi$
$72$	1.00000			0.117851
$73$	10.6530	−	10.6530i	1.24684	−	1.24684i	0.289733	−	0.957108i	$-0.406434\pi$
$73$	10.6530	−	10.6530i	1.24684	−	1.24684i	0.957108	−	0.289733i	$-0.0935664\pi$
$74$	−0.352746	−	0.352746i	−0.0410059	−	0.0410059i
$75$	−0.707107	−	0.707107i	−0.0816497	−	0.0816497i
$76$			0.663643i			0.0761250i
$77$			4.43060i			0.504914i
$78$	1.93015	+	1.93015i	0.218547	+	0.218547i
$79$	1.85577	+	1.85577i	0.208790	+	0.208790i	0.803753	−	0.594963i	$-0.202833\pi$
$79$	1.85577	+	1.85577i	0.208790	+	0.208790i	−0.594963	+	0.803753i	$0.702833\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	−1.00000			−0.111111
$82$	5.42676	−	5.42676i	0.599285	−	0.599285i
$83$		−	11.3910i		−	1.25033i	−0.780493	−	0.625164i	$-0.785032\pi$
$83$		−	11.3910i		−	1.25033i	0.780493	−	0.625164i	$-0.214968\pi$
$84$	2.61313			0.285115
$85$	−1.94174	−	3.63726i	−0.210611	−	0.394516i
$86$	−9.41838			−1.01561
$87$			7.18759i			0.770590i
$88$	1.19891	−	1.19891i	0.127804	−	0.127804i
$89$	−5.25903			−0.557456			−0.278728	−	0.960370i	$-0.589913\pi$
$89$	−5.25903			−0.557456			−0.278728	+	0.960370i	$0.589913\pi$
$90$	−0.707107	+	0.707107i	−0.0745356	+	0.0745356i
$91$	5.04373	+	5.04373i	0.528726	+	0.528726i
$92$	0.249429	+	0.249429i	0.0260048	+	0.0260048i
$93$		−	9.50756i		−	0.985888i
$94$			3.33636i			0.344119i
$95$	−0.469266	−	0.469266i	−0.0481457	−	0.0481457i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−8.43355	+	8.43355i	−0.856297	+	0.856297i	−0.990900	−	0.134603i	$-0.957024\pi$
$97$	−8.43355	+	8.43355i	−0.856297	+	0.856297i	0.134603	+	0.990900i	$0.457024\pi$
$98$	−0.171573			−0.0173315
$99$	−1.19891	+	1.19891i	−0.120495	+	0.120495i
$100$			1.00000i			0.100000i
$101$	10.1921			1.01415			0.507077	−	0.861901i	$-0.330726\pi$
$101$	10.1921			1.01415			0.507077	+	0.861901i	$0.330726\pi$
$102$	−3.63726	+	1.94174i	−0.360142	+	0.192261i
$103$	13.4238			1.32269			0.661344	−	0.750083i	$-0.269986\pi$
$103$	13.4238			1.32269			0.661344	+	0.750083i	$0.269986\pi$
$104$		−	2.72965i		−	0.267664i
$105$	−1.84776	+	1.84776i	−0.180323	+	0.180323i
$106$	5.06147			0.491613
$107$	12.1052	−	12.1052i	1.17025	−	1.17025i	0.188104	−	0.982149i	$-0.439766\pi$
$107$	12.1052	−	12.1052i	1.17025	−	1.17025i	0.982149	−	0.188104i	$-0.0602343\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	1.28809	+	1.28809i	0.123377	+	0.123377i	0.766099	−	0.642722i	$-0.222195\pi$
$109$	1.28809	+	1.28809i	0.123377	+	0.123377i	−0.642722	+	0.766099i	$0.722195\pi$
$110$			1.69552i			0.161661i
$111$		−	0.498858i		−	0.0473495i
$112$	−1.84776	−	1.84776i	−0.174597	−	0.174597i
$113$	10.8394	+	10.8394i	1.01968	+	1.01968i	0.999802	+	0.0198805i	$0.00632858\pi$
$113$	10.8394	+	10.8394i	1.01968	+	1.01968i	0.0198805	+	0.999802i	$0.493671\pi$
$114$	−0.469266	+	0.469266i	−0.0439508	+	0.0439508i
$115$	−0.352746			−0.0328937
$116$	5.08239	−	5.08239i	0.471888	−	0.471888i
$117$			2.72965i			0.252356i
$118$	10.7161			0.986494
$119$	−9.50461	+	5.07401i	−0.871286	+	0.465134i
$120$	1.00000			0.0912871
$121$		−	8.12522i		−	0.738656i
$122$	5.19891	−	5.19891i	0.470687	−	0.470687i
$123$	7.67459			0.691995
$124$	−6.72286	+	6.72286i	−0.603730	+	0.603730i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.84776	+	1.84776i	0.164611	+	0.164611i
$127$		−	3.26492i		−	0.289714i	−0.989453	−	0.144857i	$-0.953728\pi$
$127$		−	3.26492i		−	0.289714i	0.989453	−	0.144857i	$-0.0462723\pi$
$128$			1.00000i			0.0883883i
$129$	−6.65980	−	6.65980i	−0.586362	−	0.586362i
$130$	1.93015	+	1.93015i	0.169285	+	0.169285i
$131$	−3.47605	+	3.47605i	−0.303704	+	0.303704i	−0.842461	−	0.538757i	$-0.818894\pi$
$131$	−3.47605	+	3.47605i	−0.303704	+	0.303704i	0.538757	+	0.842461i	$0.318894\pi$
$132$	1.69552			0.147576
$133$	−1.22625	+	1.22625i	−0.106330	+	0.106330i
$134$		−	3.14423i		−	0.271620i
$135$	−1.00000			−0.0860663
$136$	3.94495	+	1.19891i	0.338276	+	0.102806i
$137$	8.99321			0.768342			0.384171	−	0.923262i	$-0.374487\pi$
$137$	8.99321			0.768342			0.384171	+	0.923262i	$0.374487\pi$
$138$			0.352746i			0.0300277i
$139$	9.33145	−	9.33145i	0.791483	−	0.791483i	−0.190252	−	0.981735i	$-0.560931\pi$
$139$	9.33145	−	9.33145i	0.791483	−	0.791483i	0.981735	+	0.190252i	$0.0609306\pi$
$140$	2.61313			0.220849
$141$	−2.35916	+	2.35916i	−0.198677	+	0.198677i
$142$	−1.21371	−	1.21371i	−0.101852	−	0.101852i
$143$	3.27261	+	3.27261i	0.273669	+	0.273669i
$144$		−	1.00000i		−	0.0833333i
$145$			7.18759i			0.596897i
$146$	−10.6530	−	10.6530i	−0.881649	−	0.881649i
$147$	−0.121320	−	0.121320i	−0.0100063	−	0.0100063i
$148$	−0.352746	+	0.352746i	−0.0289956	+	0.0289956i
$149$	−5.57484			−0.456708			−0.228354	−	0.973578i	$-0.573334\pi$
$149$	−5.57484			−0.456708			−0.228354	+	0.973578i	$0.573334\pi$
$150$	−0.707107	+	0.707107i	−0.0577350	+	0.0577350i
$151$		−	1.67043i		−	0.135938i	−0.997687	−	0.0679689i	$-0.978348\pi$
$151$		−	1.67043i		−	0.135938i	0.997687	−	0.0679689i	$-0.0216519\pi$
$152$	0.663643			0.0538285
$153$	−3.94495	−	1.19891i	−0.318930	−	0.0969263i
$154$	4.43060			0.357028
$155$		−	9.50756i		−	0.763665i
$156$	1.93015	−	1.93015i	0.154536	−	0.154536i
$157$	4.56036			0.363956			0.181978	−	0.983303i	$-0.441750\pi$
$157$	4.56036			0.363956			0.181978	+	0.983303i	$0.441750\pi$
$158$	1.85577	−	1.85577i	0.147637	−	0.147637i
$159$	3.57900	+	3.57900i	0.283833	+	0.283833i
$160$	−0.707107	−	0.707107i	−0.0559017	−	0.0559017i
$161$			0.921770i			0.0726457i
$162$			1.00000i			0.0785674i
$163$	−7.25359	−	7.25359i	−0.568145	−	0.568145i	0.363463	−	0.931608i	$-0.381594\pi$
$163$	−7.25359	−	7.25359i	−0.568145	−	0.568145i	−0.931608	+	0.363463i	$0.881594\pi$
$164$	−5.42676	−	5.42676i	−0.423759	−	0.423759i
$165$	−1.19891	+	1.19891i	−0.0933352	+	0.0933352i
$166$	−11.3910			−0.884116
$167$	7.17120	−	7.17120i	0.554924	−	0.554924i	−0.372934	−	0.927858i	$-0.621648\pi$
$167$	7.17120	−	7.17120i	0.554924	−	0.554924i	0.927858	+	0.372934i	$0.121648\pi$
$168$		−	2.61313i		−	0.201607i
$169$	−5.54903			−0.426849
$170$	−3.63726	+	1.94174i	−0.278965	+	0.148925i
$171$	−0.663643			−0.0507500
$172$			9.41838i			0.718144i
$173$	−8.65232	+	8.65232i	−0.657824	+	0.657824i	−0.954865	−	0.297041i	$-0.904000\pi$
$173$	−8.65232	+	8.65232i	−0.657824	+	0.657824i	0.297041	+	0.954865i	$0.404000\pi$
$174$	7.18759			0.544890
$175$	−1.84776	+	1.84776i	−0.139677	+	0.139677i
$176$	−1.19891	−	1.19891i	−0.0903714	−	0.0903714i
$177$	7.57741	+	7.57741i	0.569553	+	0.569553i
$178$			5.25903i			0.394181i
$179$			16.2764i			1.21655i	0.793724	+	0.608277i	$0.208139\pi$
$179$			16.2764i			1.21655i	−0.793724	+	0.608277i	$0.791861\pi$
$180$	0.707107	+	0.707107i	0.0527046	+	0.0527046i
$181$	9.50756	+	9.50756i	0.706691	+	0.706691i	0.965838	−	0.259147i	$-0.0834414\pi$
$181$	9.50756	+	9.50756i	0.706691	+	0.706691i	−0.259147	+	0.965838i	$0.583441\pi$
$182$	5.04373	−	5.04373i	0.373866	−	0.373866i
$183$	7.35237			0.543503
$184$	0.249429	−	0.249429i	0.0183882	−	0.0183882i
$185$		−	0.498858i		−	0.0366768i
$186$	−9.50756			−0.697128
$187$	−6.16704	+	3.29226i	−0.450978	+	0.240754i
$188$	3.33636			0.243329
$189$			2.61313i			0.190077i
$190$	−0.469266	+	0.469266i	−0.0340442	+	0.0340442i
$191$	−15.8049			−1.14360			−0.571800	−	0.820393i	$-0.693755\pi$
$191$	−15.8049			−1.14360			−0.571800	+	0.820393i	$0.693755\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−5.19372	−	5.19372i	−0.373852	−	0.373852i	0.495026	−	0.868878i	$-0.335158\pi$
$193$	−5.19372	−	5.19372i	−0.373852	−	0.373852i	−0.868878	+	0.495026i	$0.835158\pi$
$194$	8.43355	+	8.43355i	0.605493	+	0.605493i
$195$			2.72965i			0.195474i
$196$			0.171573i			0.0122552i
$197$	10.3182	+	10.3182i	0.735144	+	0.735144i	0.971634	−	0.236490i	$-0.0759969\pi$
$197$	10.3182	+	10.3182i	0.735144	+	0.735144i	−0.236490	+	0.971634i	$0.575997\pi$
$198$	1.19891	+	1.19891i	0.0852030	+	0.0852030i
$199$	−17.1535	+	17.1535i	−1.21598	+	1.21598i	−0.246948	+	0.969029i	$0.579428\pi$
$199$	−17.1535	+	17.1535i	−1.21598	+	1.21598i	−0.969029	+	0.246948i	$0.920572\pi$
$200$	1.00000			0.0707107
$201$	2.22331	−	2.22331i	0.156820	−	0.156820i
$202$		−	10.1921i		−	0.717115i
$203$	18.7821			1.31824
$204$	1.94174	+	3.63726i	0.135949	+	0.254659i
$205$	7.67459			0.536017
$206$		−	13.4238i		−	0.935281i
$207$	−0.249429	+	0.249429i	−0.0173365	+	0.0173365i
$208$	−2.72965			−0.189267
$209$	−0.795649	+	0.795649i	−0.0550362	+	0.0550362i
$210$	1.84776	+	1.84776i	0.127507	+	0.127507i
$211$	5.39104	+	5.39104i	0.371134	+	0.371134i	0.867890	−	0.496756i	$-0.165476\pi$
$211$	5.39104	+	5.39104i	0.371134	+	0.371134i	−0.496756	+	0.867890i	$0.665476\pi$
$212$		−	5.06147i		−	0.347623i
$213$		−	1.71644i		−	0.117609i
$214$	−12.1052	−	12.1052i	−0.827494	−	0.827494i
$215$	−6.65980	−	6.65980i	−0.454194	−	0.454194i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−24.8444			−1.68655
$218$	1.28809	−	1.28809i	0.0872407	−	0.0872407i
$219$		−	15.0656i		−	1.01804i
$220$	1.69552			0.114312
$221$	−3.27261	+	10.7683i	−0.220139	+	0.724355i
$222$	−0.498858			−0.0334812
$223$			3.95365i			0.264756i	0.991199	+	0.132378i	$0.0422612\pi$
$223$			3.95365i			0.264756i	−0.991199	+	0.132378i	$0.957739\pi$
$224$	−1.84776	+	1.84776i	−0.123459	+	0.123459i
$225$	−1.00000			−0.0666667
$226$	10.8394	−	10.8394i	0.721025	−	0.721025i
$227$	−10.0042	−	10.0042i	−0.664000	−	0.664000i	0.292321	−	0.956320i	$-0.405573\pi$
$227$	−10.0042	−	10.0042i	−0.664000	−	0.664000i	−0.956320	+	0.292321i	$0.905573\pi$
$228$	0.469266	+	0.469266i	0.0310779	+	0.0310779i
$229$		−	10.9385i		−	0.722839i	−0.932403	−	0.361419i	$-0.882292\pi$
$229$		−	10.9385i		−	0.722839i	0.932403	−	0.361419i	$-0.117708\pi$
$230$			0.352746i			0.0232594i
$231$	3.13291	+	3.13291i	0.206130	+	0.206130i
$232$	−5.08239	−	5.08239i	−0.333675	−	0.333675i
$233$	−7.37690	+	7.37690i	−0.483277	+	0.483277i	−0.906176	−	0.422900i	$-0.861012\pi$
$233$	−7.37690	+	7.37690i	−0.483277	+	0.483277i	0.422900	+	0.906176i	$0.361012\pi$
$234$	2.72965			0.178443
$235$	−2.35916	+	2.35916i	−0.153895	+	0.153895i
$236$		−	10.7161i		−	0.697557i
$237$	2.62445			0.170476
$238$	5.07401	+	9.50461i	0.328899	+	0.616093i
$239$	−4.35916			−0.281971			−0.140985	−	0.990012i	$-0.545027\pi$
$239$	−4.35916			−0.281971			−0.140985	+	0.990012i	$0.545027\pi$
$240$		−	1.00000i		−	0.0645497i
$241$	−11.2877	+	11.2877i	−0.727106	+	0.727106i	−0.970042	−	0.242936i	$-0.921889\pi$
$241$	−11.2877	+	11.2877i	−0.727106	+	0.727106i	0.242936	+	0.970042i	$0.421889\pi$
$242$	−8.12522			−0.522309
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−5.19891	−	5.19891i	−0.332826	−	0.332826i
$245$	−0.121320	−	0.121320i	−0.00775087	−	0.00775087i
$246$		−	7.67459i		−	0.489314i
$247$			1.81151i			0.115264i
$248$	6.72286	+	6.72286i	0.426902	+	0.426902i
$249$	−8.05468	−	8.05468i	−0.510445	−	0.510445i
$250$	−0.707107	+	0.707107i	−0.0447214	+	0.0447214i
$251$	−1.62633			−0.102653			−0.0513265	−	0.998682i	$-0.516345\pi$
$251$	−1.62633			−0.102653			−0.0513265	+	0.998682i	$0.516345\pi$
$252$	1.84776	−	1.84776i	0.116398	−	0.116398i
$253$			0.598087i			0.0376014i
$254$	−3.26492			−0.204859
$255$	−3.94495	−	1.19891i	−0.247042	−	0.0750788i
$256$	1.00000			0.0625000
$257$			13.6987i			0.854502i	0.904133	+	0.427251i	$0.140518\pi$
$257$			13.6987i			0.854502i	−0.904133	+	0.427251i	$0.859482\pi$
$258$	−6.65980	+	6.65980i	−0.414621	+	0.414621i
$259$	−1.30358			−0.0810005
$260$	1.93015	−	1.93015i	0.119703	−	0.119703i
$261$	5.08239	+	5.08239i	0.314592	+	0.314592i
$262$	3.47605	+	3.47605i	0.214751	+	0.214751i
$263$		−	29.4102i		−	1.81351i	−0.421655	−	0.906756i	$-0.638551\pi$
$263$		−	29.4102i		−	1.81351i	0.421655	−	0.906756i	$-0.361449\pi$
$264$		−	1.69552i		−	0.104352i
$265$	3.57900	+	3.57900i	0.219856	+	0.219856i
$266$	1.22625	+	1.22625i	0.0751863	+	0.0751863i
$267$	−3.71870	+	3.71870i	−0.227580	+	0.227580i
$268$	−3.14423			−0.192065
$269$	−12.7634	+	12.7634i	−0.778198	+	0.778198i	−0.979524	−	0.201326i	$-0.935475\pi$
$269$	−12.7634	+	12.7634i	−0.778198	+	0.778198i	0.201326	+	0.979524i	$0.435475\pi$
$270$			1.00000i			0.0608581i
$271$	−3.65685			−0.222138			−0.111069	−	0.993813i	$-0.535427\pi$
$271$	−3.65685			−0.222138			−0.111069	+	0.993813i	$0.535427\pi$
$272$	1.19891	−	3.94495i	0.0726947	−	0.239198i
$273$	7.13291			0.431703
$274$		−	8.99321i		−	0.543300i
$275$	−1.19891	+	1.19891i	−0.0722971	+	0.0722971i
$276$	0.352746			0.0212328
$277$	−19.1918	+	19.1918i	−1.15312	+	1.15312i	−0.167197	+	0.985924i	$0.553472\pi$
$277$	−19.1918	+	19.1918i	−1.15312	+	1.15312i	−0.985924	+	0.167197i	$0.946528\pi$
$278$	−9.33145	−	9.33145i	−0.559663	−	0.559663i
$279$	−6.72286	−	6.72286i	−0.402487	−	0.402487i
$280$		−	2.61313i		−	0.156164i
$281$		−	3.45929i		−	0.206364i	−0.994662	−	0.103182i	$-0.967098\pi$
$281$		−	3.45929i		−	0.206364i	0.994662	−	0.103182i	$-0.0329024\pi$
$282$	2.35916	+	2.35916i	0.140486	+	0.140486i
$283$	−18.5185	−	18.5185i	−1.10081	−	1.10081i	−0.994313	−	0.106498i	$-0.966036\pi$
$283$	−18.5185	−	18.5185i	−1.10081	−	1.10081i	−0.106498	−	0.994313i	$-0.533964\pi$
$284$	−1.21371	+	1.21371i	−0.0720203	+	0.0720203i
$285$	−0.663643			−0.0393108
$286$	3.27261	−	3.27261i	0.193513	−	0.193513i
$287$		−	20.0547i		−	1.18379i
$288$	−1.00000			−0.0589256
$289$	−14.1252	−	9.45929i	−0.830895	−	0.556429i
$290$	7.18759			0.422070
$291$			11.9268i			0.699163i
$292$	−10.6530	+	10.6530i	−0.623420	+	0.623420i
$293$	−22.3616			−1.30638			−0.653189	−	0.757195i	$-0.726569\pi$
$293$	−22.3616			−1.30638			−0.653189	+	0.757195i	$0.726569\pi$
$294$	−0.121320	+	0.121320i	−0.00707555	+	0.00707555i
$295$	7.57741	+	7.57741i	0.441174	+	0.441174i
$296$	0.352746	+	0.352746i	0.0205030	+	0.0205030i
$297$			1.69552i			0.0983839i
$298$			5.57484i			0.322942i
$299$	0.680853	+	0.680853i	0.0393748	+	0.0393748i
$300$	0.707107	+	0.707107i	0.0408248	+	0.0408248i
$301$	−17.4029	+	17.4029i	−1.00309	+	1.00309i
$302$	−1.67043			−0.0961225
$303$	7.20692	−	7.20692i	0.414027	−	0.414027i
$304$		−	0.663643i		−	0.0380625i
$305$	7.35237			0.420996
$306$	−1.19891	+	3.94495i	−0.0685373	+	0.225518i
$307$	7.62951			0.435439			0.217720	−	0.976011i	$-0.430138\pi$
$307$	7.62951			0.435439			0.217720	+	0.976011i	$0.430138\pi$
$308$		−	4.43060i		−	0.252457i
$309$	9.49207	−	9.49207i	0.539985	−	0.539985i
$310$	−9.50756			−0.539993
$311$	7.58194	−	7.58194i	0.429932	−	0.429932i	−0.458673	−	0.888605i	$-0.651675\pi$
$311$	7.58194	−	7.58194i	0.429932	−	0.429932i	0.888605	+	0.458673i	$0.151675\pi$
$312$	−1.93015	−	1.93015i	−0.109273	−	0.109273i
$313$	−14.1451	−	14.1451i	−0.799527	−	0.799527i	0.183494	−	0.983021i	$-0.441259\pi$
$313$	−14.1451	−	14.1451i	−0.799527	−	0.799527i	−0.983021	+	0.183494i	$0.941259\pi$
$314$		−	4.56036i		−	0.257356i
$315$			2.61313i			0.147233i
$316$	−1.85577	−	1.85577i	−0.104395	−	0.104395i
$317$	8.71607	+	8.71607i	0.489543	+	0.489543i	0.908162	−	0.418619i	$-0.137486\pi$
$317$	8.71607	+	8.71607i	0.489543	+	0.489543i	−0.418619	+	0.908162i	$0.637486\pi$
$318$	3.57900	−	3.57900i	0.200700	−	0.200700i
$319$	12.1867			0.682323
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$		−	17.1193i		−	0.955508i
$322$	0.921770			0.0513682
$323$	−2.61804	−	0.795649i	−0.145671	−	0.0442711i
$324$	1.00000			0.0555556
$325$			2.72965i			0.151414i
$326$	−7.25359	+	7.25359i	−0.401739	+	0.401739i
$327$	1.82164			0.100737
$328$	−5.42676	+	5.42676i	−0.299643	+	0.299643i
$329$	6.16478	+	6.16478i	0.339876	+	0.339876i
$330$	1.19891	+	1.19891i	0.0659980	+	0.0659980i
$331$		−	13.5603i		−	0.745343i	−0.927963	−	0.372671i	$-0.878442\pi$
$331$		−	13.5603i		−	0.745343i	0.927963	−	0.372671i	$-0.121558\pi$
$332$			11.3910i			0.625164i
$333$	−0.352746	−	0.352746i	−0.0193304	−	0.0193304i
$334$	−7.17120	−	7.17120i	−0.392391	−	0.392391i
$335$	2.22331	−	2.22331i	0.121472	−	0.121472i
$336$	−2.61313			−0.142558
$337$	−11.2871	+	11.2871i	−0.614845	+	0.614845i	−0.944205	−	0.329359i	$-0.893167\pi$
$337$	−11.2871	+	11.2871i	−0.614845	+	0.614845i	0.329359	+	0.944205i	$0.393167\pi$
$338$			5.54903i			0.301828i
$339$	15.3292			0.832568
$340$	1.94174	+	3.63726i	0.105306	+	0.197258i
$341$	−16.1202			−0.872960
$342$			0.663643i			0.0358857i
$343$	−13.2513	+	13.2513i	−0.715505	+	0.715505i
$344$	9.41838			0.507805
$345$	−0.249429	+	0.249429i	−0.0134288	+	0.0134288i
$346$	8.65232	+	8.65232i	0.465152	+	0.465152i
$347$	11.1403	+	11.1403i	0.598040	+	0.598040i	0.939791	−	0.341750i	$-0.111020\pi$
$347$	11.1403	+	11.1403i	0.598040	+	0.598040i	−0.341750	+	0.939791i	$0.611020\pi$
$348$		−	7.18759i		−	0.385295i
$349$		−	7.83522i		−	0.419409i	−0.977765	−	0.209705i	$-0.932750\pi$
$349$		−	7.83522i		−	0.419409i	0.977765	−	0.209705i	$-0.0672503\pi$
$350$	1.84776	+	1.84776i	0.0987669	+	0.0987669i
$351$	1.93015	+	1.93015i	0.103024	+	0.103024i
$352$	−1.19891	+	1.19891i	−0.0639022	+	0.0639022i
$353$	5.23638			0.278704			0.139352	−	0.990243i	$-0.455498\pi$
$353$	5.23638			0.278704			0.139352	+	0.990243i	$0.455498\pi$
$354$	7.57741	−	7.57741i	0.402735	−	0.402735i
$355$		−	1.71644i		−	0.0910993i
$356$	5.25903			0.278728
$357$	−3.13291	+	10.3086i	−0.165811	+	0.545591i
$358$	16.2764			0.860234
$359$		−	22.7594i		−	1.20120i	−0.799551	−	0.600598i	$-0.794929\pi$
$359$		−	22.7594i		−	1.20120i	0.799551	−	0.600598i	$-0.205071\pi$
$360$	0.707107	−	0.707107i	0.0372678	−	0.0372678i
$361$	18.5596			0.976820
$362$	9.50756	−	9.50756i	0.499706	−	0.499706i
$363$	−5.74540	−	5.74540i	−0.301555	−	0.301555i
$364$	−5.04373	−	5.04373i	−0.264363	−	0.264363i
$365$		−	15.0656i		−	0.788571i
$366$		−	7.35237i		−	0.384315i
$367$	13.9320	+	13.9320i	0.727246	+	0.727246i	0.970070	−	0.242824i	$-0.0780738\pi$
$367$	13.9320	+	13.9320i	0.727246	+	0.727246i	−0.242824	+	0.970070i	$0.578074\pi$
$368$	−0.249429	−	0.249429i	−0.0130024	−	0.0130024i
$369$	5.42676	−	5.42676i	0.282506	−	0.282506i
$370$	−0.498858			−0.0259344
$371$	9.35237	−	9.35237i	0.485551	−	0.485551i
$372$			9.50756i			0.492944i
$373$	−21.4891			−1.11266			−0.556331	−	0.830961i	$-0.687791\pi$
$373$	−21.4891			−1.11266			−0.556331	+	0.830961i	$0.687791\pi$
$374$	3.29226	+	6.16704i	0.170238	+	0.318890i
$375$	−1.00000			−0.0516398
$376$		−	3.33636i		−	0.172059i
$377$	13.8731	−	13.8731i	0.714503	−	0.714503i
$378$	2.61313			0.134405
$379$	12.9099	−	12.9099i	0.663138	−	0.663138i	−0.292981	−	0.956118i	$-0.594647\pi$
$379$	12.9099	−	12.9099i	0.663138	−	0.663138i	0.956118	+	0.292981i	$0.0946471\pi$
$380$	0.469266	+	0.469266i	0.0240729	+	0.0240729i
$381$	−2.30864	−	2.30864i	−0.118275	−	0.118275i
$382$			15.8049i			0.808648i
$383$			20.6584i			1.05559i	0.849370	+	0.527797i	$0.176982\pi$
$383$			20.6584i			1.05559i	−0.849370	+	0.527797i	$0.823018\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	3.13291	+	3.13291i	0.159668	+	0.159668i
$386$	−5.19372	+	5.19372i	−0.264353	+	0.264353i
$387$	−9.41838			−0.478763
$388$	8.43355	−	8.43355i	0.428148	−	0.428148i
$389$			15.6751i			0.794760i	0.917654	+	0.397380i	$0.130081\pi$
$389$			15.6751i			0.794760i	−0.917654	+	0.397380i	$0.869919\pi$
$390$	2.72965			0.138221
$391$	−1.28303	+	0.684941i	−0.0648855	+	0.0346390i
$392$	0.171573			0.00866574
$393$			4.91588i			0.247974i
$394$	10.3182	−	10.3182i	0.519826	−	0.519826i
$395$	2.62445			0.132050
$396$	1.19891	−	1.19891i	0.0602476	−	0.0602476i
$397$	18.6542	+	18.6542i	0.936229	+	0.936229i	0.998085	−	0.0618562i	$-0.0197020\pi$
$397$	18.6542	+	18.6542i	0.936229	+	0.936229i	−0.0618562	+	0.998085i	$0.519702\pi$
$398$	17.1535	+	17.1535i	0.859825	+	0.859825i
$399$			1.73418i			0.0868177i
$400$		−	1.00000i		−	0.0500000i
$401$	21.0836	+	21.0836i	1.05287	+	1.05287i	0.998522	+	0.0543430i	$0.0173064\pi$
$401$	21.0836	+	21.0836i	1.05287	+	1.05287i	0.0543430	+	0.998522i	$0.482694\pi$
$402$	−2.22331	−	2.22331i	−0.110889	−	0.110889i
$403$	−18.3510	+	18.3510i	−0.914130	+	0.914130i
$404$	−10.1921			−0.507077
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$		−	18.7821i		−	0.932139i
$407$	−0.845823			−0.0419259
$408$	3.63726	−	1.94174i	0.180071	−	0.0961305i
$409$	40.3288			1.99413			0.997066	−	0.0765475i	$-0.0243897\pi$
$409$	40.3288			1.99413			0.997066	+	0.0765475i	$0.0243897\pi$
$410$		−	7.67459i		−	0.379021i
$411$	6.35916	−	6.35916i	0.313674	−	0.313674i
$412$	−13.4238			−0.661344
$413$	19.8007	−	19.8007i	0.974329	−	0.974329i
$414$	0.249429	+	0.249429i	0.0122588	+	0.0122588i
$415$	−8.05468	−	8.05468i	−0.395389	−	0.395389i
$416$			2.72965i			0.133832i
$417$		−	13.1967i		−	0.646243i
$418$	0.795649	+	0.795649i	0.0389165	+	0.0389165i
$419$	10.0852	+	10.0852i	0.492694	+	0.492694i	0.909154	−	0.416460i	$-0.136729\pi$
$419$	10.0852	+	10.0852i	0.492694	+	0.492694i	−0.416460	+	0.909154i	$0.636729\pi$
$420$	1.84776	−	1.84776i	0.0901614	−	0.0901614i
$421$	−19.3228			−0.941735			−0.470867	−	0.882204i	$-0.656059\pi$
$421$	−19.3228			−0.941735			−0.470867	+	0.882204i	$0.656059\pi$
$422$	5.39104	−	5.39104i	0.262432	−	0.262432i
$423$			3.33636i			0.162219i
$424$	−5.06147			−0.245807
$425$	−3.94495	−	1.19891i	−0.191358	−	0.0581558i
$426$	−1.71644			−0.0831619
$427$		−	19.2127i		−	0.929767i
$428$	−12.1052	+	12.1052i	−0.585127	+	0.585127i
$429$	4.62816			0.223450
$430$	−6.65980	+	6.65980i	−0.321164	+	0.321164i
$431$	22.4400	+	22.4400i	1.08089	+	1.08089i	0.996426	+	0.0844687i	$0.0269193\pi$
$431$	22.4400	+	22.4400i	1.08089	+	1.08089i	0.0844687	+	0.996426i	$0.473081\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$		−	31.1785i		−	1.49834i	−0.662376	−	0.749172i	$-0.730452\pi$
$433$		−	31.1785i		−	1.49834i	0.662376	−	0.749172i	$-0.269548\pi$
$434$			24.8444i			1.19257i
$435$	5.08239	+	5.08239i	0.243682	+	0.243682i
$436$	−1.28809	−	1.28809i	−0.0616885	−	0.0616885i
$437$	−0.165532	+	0.165532i	−0.00791846	+	0.00791846i
$438$	−15.0656			−0.719864
$439$	−0.574836	+	0.574836i	−0.0274354	+	0.0274354i	−0.720691	−	0.693256i	$-0.756176\pi$
$439$	−0.574836	+	0.574836i	−0.0274354	+	0.0274354i	0.693256	+	0.720691i	$0.256176\pi$
$440$		−	1.69552i		−	0.0808307i
$441$	−0.171573			−0.00817014
$442$	10.7683	+	3.27261i	0.512196	+	0.155662i
$443$	−2.54903			−0.121108			−0.0605541	−	0.998165i	$-0.519287\pi$
$443$	−2.54903			−0.121108			−0.0605541	+	0.998165i	$0.519287\pi$
$444$			0.498858i			0.0236748i
$445$	−3.71870	+	3.71870i	−0.176283	+	0.176283i
$446$	3.95365			0.187211
$447$	−3.94200	+	3.94200i	−0.186450	+	0.186450i
$448$	1.84776	+	1.84776i	0.0872984	+	0.0872984i
$449$	8.01896	+	8.01896i	0.378438	+	0.378438i	0.870538	−	0.492100i	$-0.163771\pi$
$449$	8.01896	+	8.01896i	0.378438	+	0.378438i	−0.492100	+	0.870538i	$0.663771\pi$
$450$			1.00000i			0.0471405i
$451$		−	13.0124i		−	0.612731i
$452$	−10.8394	−	10.8394i	−0.509841	−	0.509841i
$453$	−1.18117	−	1.18117i	−0.0554964	−	0.0554964i
$454$	−10.0042	+	10.0042i	−0.469519	+	0.469519i
$455$	7.13291			0.334396
$456$	0.469266	−	0.469266i	0.0219754	−	0.0219754i
$457$		−	26.0379i		−	1.21800i	−0.793169	−	0.609001i	$-0.791570\pi$
$457$		−	26.0379i		−	1.21800i	0.793169	−	0.609001i	$-0.208430\pi$
$458$	−10.9385			−0.511124
$459$	−3.63726	+	1.94174i	−0.169773	+	0.0906327i
$460$	0.352746			0.0164469
$461$			3.04245i			0.141701i	0.997487	+	0.0708506i	$0.0225713\pi$
$461$			3.04245i			0.141701i	−0.997487	+	0.0708506i	$0.977429\pi$
$462$	3.13291	−	3.13291i	0.145756	−	0.145756i
$463$	−10.4989			−0.487923			−0.243962	−	0.969785i	$-0.578447\pi$
$463$	−10.4989			−0.487923			−0.243962	+	0.969785i	$0.578447\pi$
$464$	−5.08239	+	5.08239i	−0.235944	+	0.235944i
$465$	−6.72286	−	6.72286i	−0.311765	−	0.311765i
$466$	7.37690	+	7.37690i	0.341728	+	0.341728i
$467$		−	9.44646i		−	0.437130i	−0.975822	−	0.218565i	$-0.929862\pi$
$467$		−	9.44646i		−	0.437130i	0.975822	−	0.218565i	$-0.0701376\pi$
$468$		−	2.72965i		−	0.126178i
$469$	−5.80979	−	5.80979i	−0.268271	−	0.268271i
$470$	2.35916	+	2.35916i	0.108820	+	0.108820i
$471$	3.22466	−	3.22466i	0.148584	−	0.148584i
$472$	−10.7161			−0.493247
$473$	−11.2918	+	11.2918i	−0.519198	+	0.519198i
$474$		−	2.62445i		−	0.120545i
$475$	−0.663643			−0.0304500
$476$	9.50461	−	5.07401i	0.435643	−	0.232567i
$477$	5.06147			0.231749
$478$			4.35916i			0.199383i
$479$	18.5069	−	18.5069i	0.845602	−	0.845602i	−0.143979	−	0.989581i	$-0.545990\pi$
$479$	18.5069	−	18.5069i	0.845602	−	0.845602i	0.989581	+	0.143979i	$0.0459898\pi$
$480$	−1.00000			−0.0456435
$481$	−0.962872	+	0.962872i	−0.0439032	+	0.0439032i
$482$	11.2877	+	11.2877i	0.514142	+	0.514142i
$483$	0.651790	+	0.651790i	0.0296575	+	0.0296575i
$484$			8.12522i			0.369328i
$485$			11.9268i			0.541570i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	3.26839	+	3.26839i	0.148105	+	0.148105i	0.777271	−	0.629166i	$-0.216603\pi$
$487$	3.26839	+	3.26839i	0.148105	+	0.148105i	−0.629166	+	0.777271i	$0.716603\pi$
$488$	−5.19891	+	5.19891i	−0.235344	+	0.235344i
$489$	−10.2581			−0.463889
$490$	−0.121320	+	0.121320i	−0.00548069	+	0.00548069i
$491$			30.3175i			1.36821i	0.729384	+	0.684105i	$0.239807\pi$
$491$			30.3175i			1.36821i	−0.729384	+	0.684105i	$0.760193\pi$
$492$	−7.67459			−0.345997
$493$	13.9564	+	26.1431i	0.628566	+	1.17743i
$494$	1.81151			0.0815037
$495$			1.69552i			0.0762079i
$496$	6.72286	−	6.72286i	0.301865	−	0.301865i
$497$	−4.48528			−0.201192
$498$	−8.05468	+	8.05468i	−0.360939	+	0.360939i
$499$	29.5467	+	29.5467i	1.32269	+	1.32269i	0.911587	+	0.411107i	$0.134858\pi$
$499$	29.5467	+	29.5467i	1.32269	+	1.32269i	0.411107	+	0.911587i	$0.365142\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$		−	10.1416i		−	0.453094i
$502$			1.62633i			0.0725866i
$503$	−18.6009	−	18.6009i	−0.829373	−	0.829373i	0.158057	−	0.987430i	$-0.449477\pi$
$503$	−18.6009	−	18.6009i	−0.829373	−	0.829373i	−0.987430	+	0.158057i	$0.949477\pi$
$504$	−1.84776	−	1.84776i	−0.0823057	−	0.0823057i
$505$	7.20692	−	7.20692i	0.320704	−	0.320704i
$506$	0.598087			0.0265882
$507$	−3.92376	+	3.92376i	−0.174260	+	0.174260i
$508$			3.26492i			0.144857i
$509$	40.0002			1.77298			0.886489	−	0.462751i	$-0.153137\pi$
$509$	40.0002			1.77298			0.886489	+	0.462751i	$0.153137\pi$
$510$	−1.19891	+	3.94495i	−0.0530887	+	0.174685i
$511$	−39.3684			−1.74155
$512$		−	1.00000i		−	0.0441942i
$513$	−0.469266	+	0.469266i	−0.0207186	+	0.0207186i
$514$	13.6987			0.604224
$515$	9.49207	−	9.49207i	0.418271	−	0.418271i
$516$	6.65980	+	6.65980i	0.293181	+	0.293181i
$517$	4.00000	+	4.00000i	0.175920	+	0.175920i
$518$			1.30358i			0.0572760i
$519$			12.2362i			0.537111i
$520$	−1.93015	−	1.93015i	−0.0846427	−	0.0846427i
$521$	−17.6462	−	17.6462i	−0.773095	−	0.773095i	0.205551	−	0.978646i	$-0.434101\pi$
$521$	−17.6462	−	17.6462i	−0.773095	−	0.773095i	−0.978646	+	0.205551i	$0.934101\pi$
$522$	5.08239	−	5.08239i	0.222450	−	0.222450i
$523$	13.1627			0.575564			0.287782	−	0.957696i	$-0.407082\pi$
$523$	13.1627			0.575564			0.287782	+	0.957696i	$0.407082\pi$
$524$	3.47605	−	3.47605i	0.151852	−	0.151852i
$525$			2.61313i			0.114046i
$526$	−29.4102			−1.28235
$527$	−18.4612	−	34.5814i	−0.804183	−	1.50639i
$528$	−1.69552			−0.0737880
$529$		−	22.8756i		−	0.994590i
$530$	3.57900	−	3.57900i	0.155462	−	0.155462i
$531$	10.7161			0.465038
$532$	1.22625	−	1.22625i	0.0531648	−	0.0531648i
$533$	−14.8131	−	14.8131i	−0.641628	−	0.641628i
$534$	3.71870	+	3.71870i	0.160924	+	0.160924i
$535$		−	17.1193i		−	0.740133i
$536$			3.14423i			0.135810i
$537$	11.5091	+	11.5091i	0.496656	+	0.496656i
$538$	12.7634	+	12.7634i	0.550269	+	0.550269i
$539$	−0.205701	+	0.205701i	−0.00886016	+	0.00886016i
$540$	1.00000			0.0430331
$541$	12.5899	−	12.5899i	0.541284	−	0.541284i	−0.382621	−	0.923905i	$-0.624979\pi$
$541$	12.5899	−	12.5899i	0.541284	−	0.541284i	0.923905	+	0.382621i	$0.124979\pi$
$542$			3.65685i			0.157075i
$543$	13.4457			0.577011
$544$	−3.94495	−	1.19891i	−0.169138	−	0.0514029i
$545$	1.82164			0.0780304
$546$		−	7.13291i		−	0.305260i
$547$	15.7911	−	15.7911i	0.675179	−	0.675179i	−0.283726	−	0.958905i	$-0.591571\pi$
$547$	15.7911	−	15.7911i	0.675179	−	0.675179i	0.958905	+	0.283726i	$0.0915706\pi$
$548$	−8.99321			−0.384171
$549$	5.19891	−	5.19891i	0.221884	−	0.221884i
$550$	1.19891	+	1.19891i	0.0511218	+	0.0511218i
$551$	3.37289	+	3.37289i	0.143690	+	0.143690i
$552$		−	0.352746i		−	0.0150139i
$553$		−	6.85802i		−	0.291633i
$554$	19.1918	+	19.1918i	0.815379	+	0.815379i
$555$	−0.352746	−	0.352746i	−0.0149732	−	0.0149732i
$556$	−9.33145	+	9.33145i	−0.395742	+	0.395742i
$557$	−8.08746			−0.342677			−0.171338	−	0.985212i	$-0.554809\pi$
$557$	−8.08746			−0.342677			−0.171338	+	0.985212i	$0.554809\pi$
$558$	−6.72286	+	6.72286i	−0.284601	+	0.284601i
$559$			25.7088i			1.08737i
$560$	−2.61313			−0.110425
$561$	−2.03278	+	6.68873i	−0.0858239	+	0.282398i
$562$	−3.45929			−0.145921
$563$			26.8176i			1.13023i	0.825014	+	0.565113i	$0.191167\pi$
$563$			26.8176i			1.13023i	−0.825014	+	0.565113i	$0.808833\pi$
$564$	2.35916	−	2.35916i	0.0993386	−	0.0993386i
$565$	15.3292			0.644904
$566$	−18.5185	+	18.5185i	−0.778391	+	0.778391i
$567$	1.84776	+	1.84776i	0.0775986	+	0.0775986i
$568$	1.21371	+	1.21371i	0.0509261	+	0.0509261i
$569$		−	45.8132i		−	1.92059i	−0.278988	−	0.960295i	$-0.589999\pi$
$569$		−	45.8132i		−	1.92059i	0.278988	−	0.960295i	$-0.410001\pi$
$570$			0.663643i			0.0277969i
$571$	22.3337	+	22.3337i	0.934638	+	0.934638i	0.997991	−	0.0633536i	$-0.0201796\pi$
$571$	22.3337	+	22.3337i	0.934638	+	0.934638i	−0.0633536	+	0.997991i	$0.520180\pi$
$572$	−3.27261	−	3.27261i	−0.136835	−	0.136835i
$573$	−11.1757	+	11.1757i	−0.466873	+	0.466873i
$574$	−20.0547			−0.837066
$575$	−0.249429	+	0.249429i	−0.0104019	+	0.0104019i
$576$			1.00000i			0.0416667i
$577$	16.0696			0.668988			0.334494	−	0.942398i	$-0.391435\pi$
$577$	16.0696			0.668988			0.334494	+	0.942398i	$0.391435\pi$
$578$	−9.45929	+	14.1252i	−0.393455	+	0.587532i
$579$	−7.34502			−0.305249
$580$		−	7.18759i		−	0.298448i
$581$	−21.0479	+	21.0479i	−0.873214	+	0.873214i
$582$	11.9268			0.494383
$583$	6.06826	−	6.06826i	0.251321	−	0.251321i
$584$	10.6530	+	10.6530i	0.440825	+	0.440825i
$585$	1.93015	+	1.93015i	0.0798019	+	0.0798019i
$586$			22.3616i			0.923749i
$587$		−	36.3926i		−	1.50208i	−0.660255	−	0.751041i	$-0.729552\pi$
$587$		−	36.3926i		−	1.50208i	0.660255	−	0.751041i	$-0.270448\pi$
$588$	0.121320	+	0.121320i	0.00500317	+	0.00500317i
$589$	−4.46158	−	4.46158i	−0.183836	−	0.183836i
$590$	7.57741	−	7.57741i	0.311957	−	0.311957i
$591$	14.5922			0.600243
$592$	0.352746	−	0.352746i	0.0144978	−	0.0144978i
$593$		−	3.18440i		−	0.130768i	−0.997860	−	0.0653839i	$-0.979173\pi$
$593$		−	3.18440i		−	0.130768i	0.997860	−	0.0653839i	$-0.0208272\pi$
$594$	1.69552			0.0695680
$595$	−3.13291	+	10.3086i	−0.128437	+	0.422613i
$596$	5.57484			0.228354
$597$			24.2587i			0.992841i
$598$	0.680853	−	0.680853i	0.0278422	−	0.0278422i
$599$	−30.6501			−1.25233			−0.626164	−	0.779691i	$-0.715376\pi$
$599$	−30.6501			−1.25233			−0.626164	+	0.779691i	$0.715376\pi$
$600$	0.707107	−	0.707107i	0.0288675	−	0.0288675i
$601$	−5.28453	−	5.28453i	−0.215561	−	0.215561i	0.591064	−	0.806625i	$-0.298708\pi$
$601$	−5.28453	−	5.28453i	−0.215561	−	0.215561i	−0.806625	+	0.591064i	$0.798708\pi$
$602$	17.4029	+	17.4029i	0.709289	+	0.709289i
$603$		−	3.14423i		−	0.128043i
$604$			1.67043i			0.0679689i
$605$	−5.74540	−	5.74540i	−0.233584	−	0.233584i
$606$	−7.20692	−	7.20692i	−0.292761	−	0.292761i
$607$	−23.7833	+	23.7833i	−0.965333	+	0.965333i	−0.999419	−	0.0340861i	$-0.989148\pi$
$607$	−23.7833	+	23.7833i	−0.965333	+	0.965333i	0.0340861	+	0.999419i	$0.489148\pi$
$608$	−0.663643			−0.0269143
$609$	13.2809	−	13.2809i	0.538170	−	0.538170i
$610$		−	7.35237i		−	0.297689i
$611$	9.10707			0.368433
$612$	3.94495	+	1.19891i	0.159465	+	0.0484632i
$613$	−20.7742			−0.839062			−0.419531	−	0.907741i	$-0.637805\pi$
$613$	−20.7742			−0.839062			−0.419531	+	0.907741i	$0.637805\pi$
$614$		−	7.62951i		−	0.307902i
$615$	5.42676	−	5.42676i	0.218828	−	0.218828i
$616$	−4.43060			−0.178514
$617$	34.1144	−	34.1144i	1.37339	−	1.37339i	0.518036	−	0.855359i	$-0.326663\pi$
$617$	34.1144	−	34.1144i	1.37339	−	1.37339i	0.855359	−	0.518036i	$-0.173337\pi$
$618$	−9.49207	−	9.49207i	−0.381827	−	0.381827i
$619$	19.7206	+	19.7206i	0.792638	+	0.792638i	0.981922	−	0.189284i	$-0.0606168\pi$
$619$	19.7206	+	19.7206i	0.792638	+	0.792638i	−0.189284	+	0.981922i	$0.560617\pi$
$620$			9.50756i			0.381833i
$621$			0.352746i			0.0141552i
$622$	−7.58194	−	7.58194i	−0.304008	−	0.304008i
$623$	9.71742	+	9.71742i	0.389320	+	0.389320i
$624$	−1.93015	+	1.93015i	−0.0772679	+	0.0772679i
$625$	−1.00000			−0.0400000
$626$	−14.1451	+	14.1451i	−0.565351	+	0.565351i
$627$			1.12522i			0.0449369i
$628$	−4.56036			−0.181978
$629$	−0.968653	−	1.81448i	−0.0386227	−	0.0723479i
$630$	2.61313			0.104109
$631$			16.7776i			0.667904i	0.942590	+	0.333952i	$0.108382\pi$
$631$			16.7776i			0.667904i	−0.942590	+	0.333952i	$0.891618\pi$
$632$	−1.85577	+	1.85577i	−0.0738184	+	0.0738184i
$633$	7.62408			0.303030
$634$	8.71607	−	8.71607i	0.346159	−	0.346159i
$635$	−2.30864	−	2.30864i	−0.0916157	−	0.0916157i
$636$	−3.57900	−	3.57900i	−0.141917	−	0.141917i
$637$			0.468333i			0.0185560i
$638$		−	12.1867i		−	0.482476i
$639$	−1.21371	−	1.21371i	−0.0480136	−	0.0480136i
$640$	0.707107	+	0.707107i	0.0279508	+	0.0279508i
$641$	14.0517	−	14.0517i	0.555010	−	0.555010i	−0.372872	−	0.927883i	$-0.621627\pi$
$641$	14.0517	−	14.0517i	0.555010	−	0.555010i	0.927883	+	0.372872i	$0.121627\pi$
$642$	−17.1193			−0.675646
$643$	−24.9104	+	24.9104i	−0.982372	+	0.982372i	−0.999847	−	0.0174752i	$-0.994437\pi$
$643$	−24.9104	+	24.9104i	−0.982372	+	0.982372i	0.0174752	+	0.999847i	$0.494437\pi$
$644$		−	0.921770i		−	0.0363228i
$645$	−9.41838			−0.370848
$646$	−0.795649	+	2.61804i	−0.0313044	+	0.103005i
$647$	−32.9106			−1.29385			−0.646925	−	0.762553i	$-0.723945\pi$
$647$	−32.9106			−1.29385			−0.646925	+	0.762553i	$0.723945\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	12.8476	−	12.8476i	0.504314	−	0.504314i
$650$	2.72965			0.107066
$651$	−17.5677	+	17.5677i	−0.688531	+	0.688531i
$652$	7.25359	+	7.25359i	0.284073	+	0.284073i
$653$	16.1736	+	16.1736i	0.632923	+	0.632923i	0.948800	−	0.315877i	$-0.102299\pi$
$653$	16.1736	+	16.1736i	0.632923	+	0.632923i	−0.315877	+	0.948800i	$0.602299\pi$
$654$		−	1.82164i		−	0.0712317i
$655$			4.91588i			0.192079i
$656$	5.42676	+	5.42676i	0.211879	+	0.211879i
$657$	−10.6530	−	10.6530i	−0.415613	−	0.415613i
$658$	6.16478	−	6.16478i	0.240328	−	0.240328i
$659$	−14.1116			−0.549710			−0.274855	−	0.961486i	$-0.588630\pi$
$659$	−14.1116			−0.549710			−0.274855	+	0.961486i	$0.588630\pi$
$660$	1.19891	−	1.19891i	0.0466676	−	0.0466676i
$661$			3.01586i			0.117303i	0.998279	+	0.0586517i	$0.0186801\pi$
$661$			3.01586i			0.117303i	−0.998279	+	0.0586517i	$0.981320\pi$
$662$	−13.5603			−0.527037
$663$	5.30026	+	9.92843i	0.205845	+	0.385588i
$664$	11.3910			0.442058
$665$			1.73418i			0.0672487i
$666$	−0.352746	+	0.352746i	−0.0136686	+	0.0136686i
$667$	2.53539			0.0981708
$668$	−7.17120	+	7.17120i	−0.277462	+	0.277462i
$669$	2.79565	+	2.79565i	0.108086	+	0.108086i
$670$	−2.22331	−	2.22331i	−0.0858939	−	0.0858939i
$671$		−	12.4661i		−	0.481248i
$672$			2.61313i			0.100804i
$673$	24.4360	+	24.4360i	0.941938	+	0.941938i	0.998404	−	0.0564665i	$-0.0179834\pi$
$673$	24.4360	+	24.4360i	0.941938	+	0.941938i	−0.0564665	+	0.998404i	$0.517983\pi$
$674$	11.2871	+	11.2871i	0.434761	+	0.434761i
$675$	−0.707107	+	0.707107i	−0.0272166	+	0.0272166i
$676$	5.54903			0.213424
$677$	−18.2300	+	18.2300i	−0.700637	+	0.700637i	−0.964547	−	0.263910i	$-0.914988\pi$
$677$	−18.2300	+	18.2300i	−0.700637	+	0.700637i	0.263910	+	0.964547i	$0.414988\pi$
$678$		−	15.3292i		−	0.588714i
$679$	31.1663			1.19605
$680$	3.63726	−	1.94174i	0.139482	−	0.0744623i
$681$	−14.1480			−0.542153
$682$			16.1202i			0.617276i
$683$	−19.9857	+	19.9857i	−0.764731	+	0.764731i	−0.977173	−	0.212443i	$-0.931858\pi$
$683$	−19.9857	+	19.9857i	−0.764731	+	0.764731i	0.212443	+	0.977173i	$0.431858\pi$
$684$	0.663643			0.0253750
$685$	6.35916	−	6.35916i	0.242971	−	0.242971i
$686$	13.2513	+	13.2513i	0.505938	+	0.505938i
$687$	−7.73471	−	7.73471i	−0.295098	−	0.295098i
$688$		−	9.41838i		−	0.359072i
$689$		−	13.8160i		−	0.526348i
$690$	0.249429	+	0.249429i	0.00949561	+	0.00949561i
$691$	−21.5659	−	21.5659i	−0.820407	−	0.820407i	0.165759	−	0.986166i	$-0.446993\pi$
$691$	−21.5659	−	21.5659i	−0.820407	−	0.820407i	−0.986166	+	0.165759i	$0.946993\pi$
$692$	8.65232	−	8.65232i	0.328912	−	0.328912i
$693$	4.43060			0.168305
$694$	11.1403	−	11.1403i	0.422878	−	0.422878i
$695$		−	13.1967i		−	0.500578i
$696$	−7.18759			−0.272445
$697$	27.9145	−	14.9021i	1.05734	−	0.564456i
$698$	−7.83522			−0.296567
$699$			10.4325i			0.394594i
$700$	1.84776	−	1.84776i	0.0698387	−	0.0698387i
$701$	−14.3286			−0.541185			−0.270593	−	0.962694i	$-0.587220\pi$
$701$	−14.3286			−0.541185			−0.270593	+	0.962694i	$0.587220\pi$
$702$	1.93015	−	1.93015i	0.0728489	−	0.0728489i
$703$	−0.234097	−	0.234097i	−0.00882915	−	0.00882915i
$704$	1.19891	+	1.19891i	0.0451857	+	0.0451857i
$705$			3.33636i			0.125654i
$706$		−	5.23638i		−	0.197074i
$707$	−18.8326	−	18.8326i	−0.708272	−	0.708272i
$708$	−7.57741	−	7.57741i	−0.284776	−	0.284776i
$709$	19.5832	−	19.5832i	0.735461	−	0.735461i	−0.236235	−	0.971696i	$-0.575913\pi$
$709$	19.5832	−	19.5832i	0.735461	−	0.735461i	0.971696	+	0.236235i	$0.0759135\pi$
$710$	−1.71644			−0.0644170
$711$	1.85577	−	1.85577i	0.0695967	−	0.0695967i
$712$		−	5.25903i		−	0.197090i
$713$	−3.35375			−0.125599
$714$	10.3086	+	3.13291i	0.385791	+	0.117246i
$715$	4.62816			0.173084
$716$		−	16.2764i		−	0.608277i
$717$	−3.08239	+	3.08239i	−0.115114	+	0.115114i
$718$	−22.7594			−0.849374
$719$	−23.2903	+	23.2903i	−0.868581	+	0.868581i	−0.992315	−	0.123734i	$-0.960513\pi$
$719$	−23.2903	+	23.2903i	−0.868581	+	0.868581i	0.123734	+	0.992315i	$0.460513\pi$
$720$	−0.707107	−	0.707107i	−0.0263523	−	0.0263523i
$721$	−24.8040	−	24.8040i	−0.923748	−	0.923748i
$722$		−	18.5596i		−	0.690716i
$723$			15.9632i			0.593679i
$724$	−9.50756	−	9.50756i	−0.353346	−	0.353346i
$725$	5.08239	+	5.08239i	0.188755	+	0.188755i
$726$	−5.74540	+	5.74540i	−0.213232	+	0.213232i
$727$	−5.23320			−0.194088			−0.0970442	−	0.995280i	$-0.530939\pi$
$727$	−5.23320			−0.194088			−0.0970442	+	0.995280i	$0.530939\pi$
$728$	−5.04373	+	5.04373i	−0.186933	+	0.186933i
$729$			1.00000i			0.0370370i
$730$	−15.0656			−0.557604
$731$	−37.1550	−	11.2918i	−1.37423	−	0.417643i
$732$	−7.35237			−0.271752
$733$		−	19.8824i		−	0.734373i	−0.930147	−	0.367186i	$-0.880321\pi$
$733$		−	19.8824i		−	0.734373i	0.930147	−	0.367186i	$-0.119679\pi$
$734$	13.9320	−	13.9320i	0.514241	−	0.514241i
$735$	−0.171573			−0.00632856
$736$	−0.249429	+	0.249429i	−0.00919408	+	0.00919408i
$737$	−3.76966	−	3.76966i	−0.138857	−	0.138857i
$738$	−5.42676	−	5.42676i	−0.199762	−	0.199762i
$739$			24.5901i			0.904563i	0.891875	+	0.452281i	$0.149390\pi$
$739$			24.5901i			0.904563i	−0.891875	+	0.452281i	$0.850610\pi$
$740$			0.498858i			0.0183384i
$741$	1.28093	+	1.28093i	0.0470562	+	0.0470562i
$742$	−9.35237	−	9.35237i	−0.343336	−	0.343336i
$743$	14.8281	−	14.8281i	0.543989	−	0.543989i	−0.380707	−	0.924696i	$-0.624319\pi$
$743$	14.8281	−	14.8281i	0.543989	−	0.543989i	0.924696	+	0.380707i	$0.124319\pi$
$744$	9.50756			0.348564
$745$	−3.94200	+	3.94200i	−0.144424	+	0.144424i
$746$			21.4891i			0.786771i
$747$	−11.3910			−0.416776
$748$	6.16704	−	3.29226i	0.225489	−	0.120377i
$749$	−44.7350			−1.63458
$750$			1.00000i			0.0365148i
$751$	28.0617	−	28.0617i	1.02398	−	1.02398i	0.0242790	−	0.999705i	$-0.492271\pi$
$751$	28.0617	−	28.0617i	1.02398	−	1.02398i	0.999705	−	0.0242790i	$-0.00772902\pi$
$752$	−3.33636			−0.121664
$753$	−1.14999	+	1.14999i	−0.0419079	+	0.0419079i
$754$	−13.8731	−	13.8731i	−0.505230	−	0.505230i
$755$	−1.18117	−	1.18117i	−0.0429873	−	0.0429873i
$756$		−	2.61313i		−	0.0950385i
$757$		−	17.2059i		−	0.625357i	−0.949859	−	0.312679i	$-0.898774\pi$
$757$		−	17.2059i		−	0.625357i	0.949859	−	0.312679i	$-0.101226\pi$
$758$	−12.9099	−	12.9099i	−0.468909	−	0.468909i
$759$	0.422912	+	0.422912i	0.0153507	+	0.0153507i
$760$	0.469266	−	0.469266i	0.0170221	−	0.0170221i
$761$	−41.0176			−1.48689			−0.743443	−	0.668800i	$-0.766808\pi$
$761$	−41.0176			−1.48689			−0.743443	+	0.668800i	$0.766808\pi$
$762$	−2.30864	+	2.30864i	−0.0836334	+	0.0836334i
$763$		−	4.76017i		−	0.172330i
$764$	15.8049			0.571800
$765$	−3.63726	+	1.94174i	−0.131505	+	0.0702038i
$766$	20.6584			0.746418
$767$		−	29.2511i		−	1.05620i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	44.6904			1.61158			0.805789	−	0.592203i	$-0.201742\pi$
$769$	44.6904			1.61158			0.805789	+	0.592203i	$0.201742\pi$
$770$	3.13291	−	3.13291i	0.112902	−	0.112902i
$771$	9.68645	+	9.68645i	0.348849	+	0.348849i
$772$	5.19372	+	5.19372i	0.186926	+	0.186926i
$773$			6.61278i			0.237845i	0.992904	+	0.118923i	$0.0379440\pi$
$773$			6.61278i			0.237845i	−0.992904	+	0.118923i	$0.962056\pi$
$774$			9.41838i			0.338537i
$775$	−6.72286	−	6.72286i	−0.241492	−	0.241492i
$776$	−8.43355	−	8.43355i	−0.302747	−	0.302747i
$777$	−0.921770	+	0.921770i	−0.0330683	+	0.0330683i
$778$	15.6751			0.561980
$779$	3.60143	−	3.60143i	0.129035	−	0.129035i
$780$		−	2.72965i		−	0.0977370i
$781$	−2.91026			−0.104137
$782$	0.684941	+	1.28303i	0.0244934	+	0.0458810i
$783$	7.18759			0.256863
$784$		−	0.171573i		−	0.00612760i
$785$	3.22466	−	3.22466i	0.115093	−	0.115093i
$786$	4.91588			0.175344
$787$	−9.25584	+	9.25584i	−0.329935	+	0.329935i	−0.852562	−	0.522627i	$-0.824952\pi$
$787$	−9.25584	+	9.25584i	−0.329935	+	0.329935i	0.522627	+	0.852562i	$0.324952\pi$
$788$	−10.3182	−	10.3182i	−0.367572	−	0.367572i
$789$	−20.7962	−	20.7962i	−0.740364	−	0.740364i
$790$		−	2.62445i		−	0.0933738i
$791$		−	40.0571i		−	1.42427i
$792$	−1.19891	−	1.19891i	−0.0426015	−	0.0426015i
$793$	−14.1912	−	14.1912i	−0.503944	−	0.503944i
$794$	18.6542	−	18.6542i	0.662014	−	0.662014i
$795$	5.06147			0.179512
$796$	17.1535	−	17.1535i	0.607988	−	0.607988i
$797$			44.2278i			1.56663i	0.621626	+	0.783314i	$0.286472\pi$
$797$			44.2278i			1.56663i	−0.621626	+	0.783314i	$0.713528\pi$
$798$	1.73418			0.0613894
$799$	−4.00000	+	13.1618i	−0.141510	+	0.465629i
$800$	−1.00000			−0.0353553
$801$			5.25903i			0.185819i
$802$	21.0836	−	21.0836i	0.744488	−	0.744488i
$803$	−25.5440			−0.901430
$804$	−2.22331	+	2.22331i	−0.0784101	+	0.0784101i
$805$	0.651790	+	0.651790i	0.0229726	+	0.0229726i
$806$	18.3510	+	18.3510i	0.646387	+	0.646387i
$807$			18.0502i			0.635396i
$808$			10.1921i			0.358558i
$809$	−13.9667	−	13.9667i	−0.491044	−	0.491044i	0.417591	−	0.908635i	$-0.362874\pi$
$809$	−13.9667	−	13.9667i	−0.491044	−	0.491044i	−0.908635	+	0.417591i	$0.862874\pi$
$810$	0.707107	+	0.707107i	0.0248452	+	0.0248452i
$811$	−29.0740	+	29.0740i	−1.02092	+	1.02092i	−0.0211483	+	0.999776i	$0.506732\pi$
$811$	−29.0740	+	29.0740i	−1.02092	+	1.02092i	−0.999776	+	0.0211483i	$0.993268\pi$
$812$	−18.7821			−0.659122
$813$	−2.58579	+	2.58579i	−0.0906875	+	0.0906875i
$814$			0.845823i			0.0296461i
$815$	−10.2581			−0.359327
$816$	−1.94174	−	3.63726i	−0.0679745	−	0.127330i
$817$	−6.25044			−0.218675
$818$		−	40.3288i		−	1.41006i
$819$	5.04373	−	5.04373i	0.176242	−	0.176242i
$820$	−7.67459			−0.268008
$821$	22.8235	−	22.8235i	0.796546	−	0.796546i	−0.186003	−	0.982549i	$-0.559553\pi$
$821$	22.8235	−	22.8235i	0.796546	−	0.796546i	0.982549	+	0.186003i	$0.0595534\pi$
$822$	−6.35916	−	6.35916i	−0.221801	−	0.221801i
$823$	22.6163	+	22.6163i	0.788353	+	0.788353i	0.981224	−	0.192871i	$-0.0617799\pi$
$823$	22.6163	+	22.6163i	0.788353	+	0.788353i	−0.192871	+	0.981224i	$0.561780\pi$
$824$			13.4238i			0.467641i
$825$			1.69552i			0.0590304i
$826$	−19.8007	−	19.8007i	−0.688955	−	0.688955i
$827$	−22.9469	−	22.9469i	−0.797940	−	0.797940i	0.184830	−	0.982770i	$-0.440827\pi$
$827$	−22.9469	−	22.9469i	−0.797940	−	0.797940i	−0.982770	+	0.184830i	$0.940827\pi$
$828$	0.249429	−	0.249429i	0.00866826	−	0.00866826i
$829$	−10.6602			−0.370244			−0.185122	−	0.982716i	$-0.559268\pi$
$829$	−10.6602			−0.370244			−0.185122	+	0.982716i	$0.559268\pi$
$830$	−8.05468	+	8.05468i	−0.279582	+	0.279582i
$831$			27.1412i			0.941519i
$832$	2.72965			0.0946335
$833$	−0.676846	−	0.205701i	−0.0234513	−	0.00712711i
$834$	−13.1967			−0.456963
$835$		−	10.1416i		−	0.350965i
$836$	0.795649	−	0.795649i	0.0275181	−	0.0275181i
$837$	−9.50756			−0.328629
$838$	10.0852	−	10.0852i	0.348388	−	0.348388i
$839$	−13.3071	−	13.3071i	−0.459410	−	0.459410i	0.439051	−	0.898462i	$-0.355315\pi$
$839$	−13.3071	−	13.3071i	−0.459410	−	0.459410i	−0.898462	+	0.439051i	$0.855315\pi$
$840$	−1.84776	−	1.84776i	−0.0637537	−	0.0637537i
$841$		−	22.6614i		−	0.781428i
$842$			19.3228i			0.665907i
$843$	−2.44609	−	2.44609i	−0.0842478	−	0.0842478i
$844$	−5.39104	−	5.39104i	−0.185567	−	0.185567i
$845$	−3.92376	+	3.92376i	−0.134981	+	0.134981i
$846$	3.33636			0.114706
$847$	−15.0134	+	15.0134i	−0.515868	+	0.515868i
$848$			5.06147i			0.173812i
$849$	−26.1891			−0.898808
$850$	−1.19891	+	3.94495i	−0.0411224	+	0.135311i
$851$	−0.175970			−0.00603219
$852$			1.71644i			0.0588044i
$853$	14.7838	−	14.7838i	0.506188	−	0.506188i	−0.407166	−	0.913354i	$-0.633483\pi$
$853$	14.7838	−	14.7838i	0.506188	−	0.506188i	0.913354	+	0.407166i	$0.133483\pi$
$854$	−19.2127			−0.657444
$855$	−0.469266	+	0.469266i	−0.0160486	+	0.0160486i
$856$	12.1052	+	12.1052i	0.413747	+	0.413747i
$857$	16.4112	+	16.4112i	0.560596	+	0.560596i	0.929477	−	0.368880i	$-0.120259\pi$
$857$	16.4112	+	16.4112i	0.560596	+	0.560596i	−0.368880	+	0.929477i	$0.620259\pi$
$858$		−	4.62816i		−	0.158003i
$859$		−	43.6052i		−	1.48779i	−0.668295	−	0.743896i	$-0.732976\pi$
$859$		−	43.6052i		−	1.48779i	0.668295	−	0.743896i	$-0.267024\pi$
$860$	6.65980	+	6.65980i	0.227097	+	0.227097i
$861$	−14.1808	−	14.1808i	−0.483280	−	0.483280i
$862$	22.4400	−	22.4400i	0.764308	−	0.764308i
$863$	34.7858			1.18412			0.592062	−	0.805893i	$-0.298314\pi$
$863$	34.7858			1.18412			0.592062	+	0.805893i	$0.298314\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$			12.2362i			0.416044i
$866$	−31.1785			−1.05949
$867$	−16.6768	+	3.29931i	−0.566373	+	0.112050i
$868$	24.8444			0.843275
$869$		−	4.44980i		−	0.150949i
$870$	5.08239	−	5.08239i	0.172309	−	0.172309i
$871$	−8.58264			−0.290812
$872$	−1.28809	+	1.28809i	−0.0436203	+	0.0436203i
$873$	8.43355	+	8.43355i	0.285432	+	0.285432i
$874$	0.165532	+	0.165532i	0.00559920	+	0.00559920i
$875$			2.61313i			0.0883398i
$876$			15.0656i			0.509020i
$877$	−2.50527	−	2.50527i	−0.0845971	−	0.0845971i	0.663542	−	0.748139i	$-0.269052\pi$
$877$	−2.50527	−	2.50527i	−0.0845971	−	0.0845971i	−0.748139	+	0.663542i	$0.769052\pi$
$878$	0.574836	+	0.574836i	0.0193998	+	0.0193998i
$879$	−15.8120	+	15.8120i	−0.533327	+	0.533327i
$880$	−1.69552			−0.0571559
$881$	32.1907	−	32.1907i	1.08453	−	1.08453i	0.0884513	−	0.996081i	$-0.471808\pi$
$881$	32.1907	−	32.1907i	1.08453	−	1.08453i	0.996081	−	0.0884513i	$-0.0281918\pi$
$882$			0.171573i			0.00577716i
$883$	−28.3562			−0.954261			−0.477130	−	0.878833i	$-0.658323\pi$
$883$	−28.3562			−0.954261			−0.477130	+	0.878833i	$0.658323\pi$
$884$	3.27261	−	10.7683i	0.110070	−	0.362177i
$885$	10.7161			0.360217
$886$			2.54903i			0.0856364i
$887$	−31.6616	+	31.6616i	−1.06309	+	1.06309i	−0.0652224	+	0.997871i	$0.520776\pi$
$887$	−31.6616	+	31.6616i	−1.06309	+	1.06309i	−0.997871	+	0.0652224i	$0.979224\pi$
$888$	0.498858			0.0167406
$889$	−6.03278	+	6.03278i	−0.202333	+	0.202333i
$890$	3.71870	+	3.71870i	0.124651	+	0.124651i
$891$	1.19891	+	1.19891i	0.0401651	+	0.0401651i
$892$		−	3.95365i		−	0.132378i
$893$			2.21415i			0.0740937i
$894$	3.94200	+	3.94200i	0.131840	+	0.131840i
$895$	11.5091	+	11.5091i	0.384708	+	0.384708i
$896$	1.84776	−	1.84776i	0.0617293	−	0.0617293i
$897$	0.962872			0.0321494
$898$	8.01896	−	8.01896i	0.267596	−	0.267596i
$899$			68.3364i			2.27915i
$900$	1.00000			0.0333333
$901$	19.9672	+	6.06826i	0.665205	+	0.202163i
$902$	−13.0124			−0.433266
$903$			24.6114i			0.819016i
$904$	−10.8394	+	10.8394i	−0.360512	+	0.360512i
$905$	13.4457			0.446951
$906$	−1.18117	+	1.18117i	−0.0392419	+	0.0392419i
$907$	10.5831	+	10.5831i	0.351407	+	0.351407i	0.860633	−	0.509226i	$-0.170068\pi$
$907$	10.5831	+	10.5831i	0.351407	+	0.351407i	−0.509226	+	0.860633i	$0.670068\pi$
$908$	10.0042	+	10.0042i	0.332000	+	0.332000i
$909$		−	10.1921i		−	0.338051i
$910$		−	7.13291i		−	0.236454i
$911$	−0.342112	−	0.342112i	−0.0113347	−	0.0113347i	0.701417	−	0.712751i	$-0.252551\pi$
$911$	−0.342112	−	0.342112i	−0.0113347	−	0.0113347i	−0.712751	+	0.701417i	$0.752551\pi$
$912$	−0.469266	−	0.469266i	−0.0155390	−	0.0155390i
$913$	−13.6569	+	13.6569i	−0.451976	+	0.451976i
$914$	−26.0379			−0.861258
$915$	5.19891	−	5.19891i	0.171871	−	0.171871i
$916$			10.9385i			0.361419i
$917$	12.8458			0.424206
$918$	1.94174	+	3.63726i	0.0640870	+	0.120047i
$919$	54.6848			1.80388			0.901942	−	0.431856i	$-0.142141\pi$
$919$	54.6848			1.80388			0.901942	+	0.431856i	$0.142141\pi$
$920$		−	0.352746i		−	0.0116297i
$921$	5.39488	−	5.39488i	0.177767	−	0.177767i
$922$	3.04245			0.100198
$923$	−3.31299	+	3.31299i	−0.109049	+	0.109049i
$924$	−3.13291	−	3.13291i	−0.103065	−	0.103065i
$925$	−0.352746	−	0.352746i	−0.0115982	−	0.0115982i
$926$			10.4989i			0.345014i
$927$		−	13.4238i		−	0.440896i
$928$	5.08239	+	5.08239i	0.166838	+	0.166838i
$929$	14.4792	+	14.4792i	0.475046	+	0.475046i	0.903543	−	0.428497i	$-0.140957\pi$
$929$	14.4792	+	14.4792i	0.475046	+	0.475046i	−0.428497	+	0.903543i	$0.640957\pi$
$930$	−6.72286	+	6.72286i	−0.220451	+	0.220451i
$931$	−0.113863			−0.00373171
$932$	7.37690	−	7.37690i	0.241638	−	0.241638i
$933$		−	10.7225i		−	0.351038i
$934$	−9.44646			−0.309098
$935$	−2.03278	+	6.68873i	−0.0664789	+	0.218745i
$936$	−2.72965			−0.0892213
$937$			22.8503i			0.746488i	0.927733	+	0.373244i	$0.121755\pi$
$937$			22.8503i			0.746488i	−0.927733	+	0.373244i	$0.878245\pi$
$938$	−5.80979	+	5.80979i	−0.189696	+	0.189696i
$939$	−20.0042			−0.652811
$940$	2.35916	−	2.35916i	0.0769473	−	0.0769473i
$941$	28.5577	+	28.5577i	0.930954	+	0.930954i	0.997766	−	0.0668112i	$-0.0212825\pi$
$941$	28.5577	+	28.5577i	0.930954	+	0.930954i	−0.0668112	+	0.997766i	$0.521283\pi$
$942$	−3.22466	−	3.22466i	−0.105065	−	0.105065i
$943$		−	2.70718i		−	0.0881580i
$944$			10.7161i			0.348778i
$945$	1.84776	+	1.84776i	0.0601076	+	0.0601076i
$946$	11.2918	+	11.2918i	0.367128	+	0.367128i
$947$	−17.7621	+	17.7621i	−0.577189	+	0.577189i	−0.934128	−	0.356939i	$-0.883820\pi$
$947$	−17.7621	+	17.7621i	−0.577189	+	0.577189i	0.356939	+	0.934128i	$0.383820\pi$
$948$	−2.62445			−0.0852382
$949$	−29.0789	+	29.0789i	−0.943942	+	0.943942i
$950$			0.663643i			0.0215314i
$951$	12.3264			0.399710
$952$	−5.07401	−	9.50461i	−0.164450	−	0.308046i
$953$	55.5498			1.79944			0.899718	−	0.436473i	$-0.143772\pi$
$953$	55.5498			1.79944			0.899718	+	0.436473i	$0.143772\pi$
$954$		−	5.06147i		−	0.163871i
$955$	−11.1757	+	11.1757i	−0.361638	+	0.361638i
$956$	4.35916			0.140985
$957$	8.61729	−	8.61729i	0.278557	−	0.278557i
$958$	−18.5069	−	18.5069i	−0.597931	−	0.597931i
$959$	−16.6173	−	16.6173i	−0.536600	−	0.536600i
$960$			1.00000i			0.0322749i
$961$		−	59.3936i		−	1.91592i
$962$	0.962872	+	0.962872i	0.0310442	+	0.0310442i
$963$	−12.1052	−	12.1052i	−0.390084	−	0.390084i
$964$	11.2877	−	11.2877i	0.363553	−	0.363553i
$965$	−7.34502			−0.236445
$966$	0.651790	−	0.651790i	0.0209710	−	0.0209710i
$967$		−	41.9356i		−	1.34856i	−0.738477	−	0.674278i	$-0.764455\pi$
$967$		−	41.9356i		−	1.34856i	0.738477	−	0.674278i	$-0.235545\pi$
$968$	8.12522			0.261154
$969$	−2.41384	+	1.28862i	−0.0775437	+	0.0413965i
$970$	11.9268			0.382948
$971$		−	8.66409i		−	0.278044i	−0.990289	−	0.139022i	$-0.955604\pi$
$971$		−	8.66409i		−	0.278044i	0.990289	−	0.139022i	$-0.0443959\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−34.4845			−1.10552
$974$	3.26839	−	3.26839i	0.104726	−	0.104726i
$975$	1.93015	+	1.93015i	0.0618143	+	0.0618143i
$976$	5.19891	+	5.19891i	0.166413	+	0.166413i
$977$			22.6138i			0.723481i	0.932279	+	0.361740i	$0.117817\pi$
$977$			22.6138i			0.723481i	−0.932279	+	0.361740i	$0.882183\pi$
$978$			10.2581i			0.328019i
$979$	6.30512	+	6.30512i	0.201512	+	0.201512i
$980$	0.121320	+	0.121320i	0.00387544	+	0.00387544i
$981$	1.28809	−	1.28809i	0.0411256	−	0.0411256i
$982$	30.3175			0.967470
$983$	−39.6338	+	39.6338i	−1.26412	+	1.26412i	−0.315047	+	0.949076i	$0.602020\pi$
$983$	−39.6338	+	39.6338i	−1.26412	+	1.26412i	−0.949076	+	0.315047i	$0.897980\pi$
$984$			7.67459i			0.244657i
$985$	14.5922			0.464946
$986$	26.1431	−	13.9564i	0.832566	−	0.444463i
$987$	8.71832			0.277507
$988$		−	1.81151i		−	0.0576318i
$989$	−2.34922	+	2.34922i	−0.0747008	+	0.0747008i
$990$	1.69552			0.0538871
$991$	−20.3797	+	20.3797i	−0.647383	+	0.647383i	−0.952360	−	0.304977i	$-0.901351\pi$
$991$	−20.3797	+	20.3797i	−0.647383	+	0.647383i	0.304977	+	0.952360i	$0.401351\pi$
$992$	−6.72286	−	6.72286i	−0.213451	−	0.213451i
$993$	−9.58860	−	9.58860i	−0.304285	−	0.304285i
$994$			4.48528i			0.142264i
$995$			24.2587i			0.769051i
$996$	8.05468	+	8.05468i	0.255222	+	0.255222i
$997$	38.2465	+	38.2465i	1.21128	+	1.21128i	0.970607	+	0.240671i	$0.0773674\pi$
$997$	38.2465	+	38.2465i	1.21128	+	1.21128i	0.240671	+	0.970607i	$0.422633\pi$
$998$	29.5467	−	29.5467i	0.935286	−	0.935286i
$999$	−0.498858			−0.0157832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.p.d.361.3	✓	8
3.2	odd	2		1530.2.q.i.361.1		8
17.8	even	8		8670.2.a.bt.1.1		4
17.9	even	8		8670.2.a.bw.1.4		4
17.13	even	4	inner	510.2.p.d.421.3	yes	8
51.47	odd	4		1530.2.q.i.1441.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.p.d.361.3	✓	8	1.1	even	1	trivial
510.2.p.d.421.3	yes	8	17.13	even	4	inner
1530.2.q.i.361.1		8	3.2	odd	2
1530.2.q.i.1441.1		8	51.47	odd	4
8670.2.a.bt.1.1		4	17.8	even	8
8670.2.a.bw.1.4		4	17.9	even	8

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.84776 - 1.84776i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.84776 - 1.84776i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 0.707107i) q^{10} +(-1.19891 - 1.19891i) q^{11} +(-0.707107 + 0.707107i) q^{12} -2.72965 q^{13} +(-1.84776 + 1.84776i) q^{14} -1.00000i q^{15} +1.00000 q^{16} +(1.19891 - 3.94495i) q^{17} -1.00000 q^{18} -0.663643i q^{19} +(-0.707107 + 0.707107i) q^{20} -2.61313 q^{21} +(-1.19891 + 1.19891i) q^{22} +(-0.249429 - 0.249429i) q^{23} +(0.707107 + 0.707107i) q^{24} -1.00000i q^{25} +2.72965i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.84776 + 1.84776i) q^{28} +(-5.08239 + 5.08239i) q^{29} -1.00000 q^{30} +(6.72286 - 6.72286i) q^{31} -1.00000i q^{32} -1.69552 q^{33} +(-3.94495 - 1.19891i) q^{34} -2.61313 q^{35} +1.00000i q^{36} +(0.352746 - 0.352746i) q^{37} -0.663643 q^{38} +(-1.93015 + 1.93015i) q^{39} +(0.707107 + 0.707107i) q^{40} +(5.42676 + 5.42676i) q^{41} +2.61313i q^{42} -9.41838i q^{43} +(1.19891 + 1.19891i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(-0.249429 + 0.249429i) q^{46} -3.33636 q^{47} +(0.707107 - 0.707107i) q^{48} -0.171573i q^{49} -1.00000 q^{50} +(-1.94174 - 3.63726i) q^{51} +2.72965 q^{52} +5.06147i q^{53} +(-0.707107 + 0.707107i) q^{54} -1.69552 q^{55} +(1.84776 - 1.84776i) q^{56} +(-0.469266 - 0.469266i) q^{57} +(5.08239 + 5.08239i) q^{58} +10.7161i q^{59} +1.00000i q^{60} +(5.19891 + 5.19891i) q^{61} +(-6.72286 - 6.72286i) q^{62} +(-1.84776 + 1.84776i) q^{63} -1.00000 q^{64} +(-1.93015 + 1.93015i) q^{65} +1.69552i q^{66} +3.14423 q^{67} +(-1.19891 + 3.94495i) q^{68} -0.352746 q^{69} +2.61313i q^{70} +(1.21371 - 1.21371i) q^{71} +1.00000 q^{72} +(10.6530 - 10.6530i) q^{73} +(-0.352746 - 0.352746i) q^{74} +(-0.707107 - 0.707107i) q^{75} +0.663643i q^{76} +4.43060i q^{77} +(1.93015 + 1.93015i) q^{78} +(1.85577 + 1.85577i) q^{79} +(0.707107 - 0.707107i) q^{80} -1.00000 q^{81} +(5.42676 - 5.42676i) q^{82} -11.3910i q^{83} +2.61313 q^{84} +(-1.94174 - 3.63726i) q^{85} -9.41838 q^{86} +7.18759i q^{87} +(1.19891 - 1.19891i) q^{88} -5.25903 q^{89} +(-0.707107 + 0.707107i) q^{90} +(5.04373 + 5.04373i) q^{91} +(0.249429 + 0.249429i) q^{92} -9.50756i q^{93} +3.33636i q^{94} +(-0.469266 - 0.469266i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-8.43355 + 8.43355i) q^{97} -0.171573 q^{98} +(-1.19891 + 1.19891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 8 q^{16} - 8 q^{18} - 8 q^{23} - 32 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{33} - 8 q^{34} + 16 q^{37} + 8 q^{39} - 8 q^{46} - 32 q^{47} - 8 q^{50} - 16 q^{51} + 16 q^{55} - 16 q^{57} + 32 q^{58} + 32 q^{61} + 8 q^{62} - 8 q^{64} + 8 q^{65} + 80 q^{67} - 16 q^{69} + 8 q^{72} - 16 q^{74} - 8 q^{78} - 40 q^{79} - 8 q^{81} - 16 q^{85} + 16 q^{86} - 16 q^{89} + 16 q^{91} + 8 q^{92} - 16 q^{95} - 64 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 8 * q^16 - 8 * q^18 - 8 * q^23 - 32 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^33 - 8 * q^34 + 16 * q^37 + 8 * q^39 - 8 * q^46 - 32 * q^47 - 8 * q^50 - 16 * q^51 + 16 * q^55 - 16 * q^57 + 32 * q^58 + 32 * q^61 + 8 * q^62 - 8 * q^64 + 8 * q^65 + 80 * q^67 - 16 * q^69 + 8 * q^72 - 16 * q^74 - 8 * q^78 - 40 * q^79 - 8 * q^81 - 16 * q^85 + 16 * q^86 - 16 * q^89 + 16 * q^91 + 8 * q^92 - 16 * q^95 - 64 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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