LMFDB - Embedded newform 357.2.f.a.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(169,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("357.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.f (of order $2$, degree $1$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.5
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	357.169
Dual form			357.2.f.a.169.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48119 q^{2} -1.00000i q^{3} +4.15633 q^{4} -0.675131i q^{5} -2.48119i q^{6} +1.00000i q^{7} +5.35026 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.48119 q^{2} -1.00000i q^{3} +4.15633 q^{4} -0.675131i q^{5} -2.48119i q^{6} +1.00000i q^{7} +5.35026 q^{8} -1.00000 q^{9} -1.67513i q^{10} +1.80606i q^{11} -4.15633i q^{12} -2.28726 q^{13} +2.48119i q^{14} -0.675131 q^{15} +4.96239 q^{16} +(-3.67513 - 1.86907i) q^{17} -2.48119 q^{18} +0.518806 q^{19} -2.80606i q^{20} +1.00000 q^{21} +4.48119i q^{22} -0.0376114i q^{23} -5.35026i q^{24} +4.54420 q^{25} -5.67513 q^{26} +1.00000i q^{27} +4.15633i q^{28} +0.806063i q^{29} -1.67513 q^{30} +1.28726i q^{31} +1.61213 q^{32} +1.80606 q^{33} +(-9.11871 - 4.63752i) q^{34} +0.675131 q^{35} -4.15633 q^{36} +7.83146i q^{37} +1.28726 q^{38} +2.28726i q^{39} -3.61213i q^{40} -0.518806i q^{41} +2.48119 q^{42} -3.57452 q^{43} +7.50659i q^{44} +0.675131i q^{45} -0.0933212i q^{46} -3.98778 q^{47} -4.96239i q^{48} -1.00000 q^{49} +11.2750 q^{50} +(-1.86907 + 3.67513i) q^{51} -9.50659 q^{52} -4.09332 q^{53} +2.48119i q^{54} +1.21933 q^{55} +5.35026i q^{56} -0.518806i q^{57} +2.00000i q^{58} +10.2496 q^{59} -2.80606 q^{60} -14.5623i q^{61} +3.19394i q^{62} -1.00000i q^{63} -5.92478 q^{64} +1.54420i q^{65} +4.48119 q^{66} +9.81924 q^{67} +(-15.2750 - 7.76845i) q^{68} -0.0376114 q^{69} +1.67513 q^{70} -13.6932i q^{71} -5.35026 q^{72} +12.0508i q^{73} +19.4314i q^{74} -4.54420i q^{75} +2.15633 q^{76} -1.80606 q^{77} +5.67513i q^{78} -4.99508i q^{79} -3.35026i q^{80} +1.00000 q^{81} -1.28726i q^{82} +2.26187 q^{83} +4.15633 q^{84} +(-1.26187 + 2.48119i) q^{85} -8.86907 q^{86} +0.806063 q^{87} +9.66291i q^{88} -13.2750 q^{89} +1.67513i q^{90} -2.28726i q^{91} -0.156325i q^{92} +1.28726 q^{93} -9.89446 q^{94} -0.350262i q^{95} -1.61213i q^{96} +13.3503i q^{97} -2.48119 q^{98} -1.80606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9	$ 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9} - 2 q^{13} + 6 q^{15} + 8 q^{16} - 12 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{21} + 8 q^{25} - 24 q^{26} + 8 q^{32} + 10 q^{33} - 12 q^{34} - 6 q^{35} - 4 q^{36} - 4 q^{38} + 4 q^{42} + 2 q^{43} + 28 q^{47} - 6 q^{49} + 4 q^{50} - 2 q^{51} - 16 q^{52} - 12 q^{53} - 22 q^{55} + 28 q^{59} - 16 q^{60} + 8 q^{64} + 16 q^{66} - 24 q^{67} - 28 q^{68} - 22 q^{69} - 12 q^{72} - 8 q^{76} - 10 q^{77} + 6 q^{81} + 32 q^{83} + 4 q^{84} - 26 q^{85} - 44 q^{86} + 4 q^{87} - 16 q^{89} - 4 q^{93} - 20 q^{94} - 4 q^{98}+O(q^{100}) $ 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9 - 2 * q^13 + 6 * q^15 + 8 * q^16 - 12 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^21 + 8 * q^25 - 24 * q^26 + 8 * q^32 + 10 * q^33 - 12 * q^34 - 6 * q^35 - 4 * q^36 - 4 * q^38 + 4 * q^42 + 2 * q^43 + 28 * q^47 - 6 * q^49 + 4 * q^50 - 2 * q^51 - 16 * q^52 - 12 * q^53 - 22 * q^55 + 28 * q^59 - 16 * q^60 + 8 * q^64 + 16 * q^66 - 24 * q^67 - 28 * q^68 - 22 * q^69 - 12 * q^72 - 8 * q^76 - 10 * q^77 + 6 * q^81 + 32 * q^83 + 4 * q^84 - 26 * q^85 - 44 * q^86 + 4 * q^87 - 16 * q^89 - 4 * q^93 - 20 * q^94 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	2.48119			1.75447			0.877235	−	0.480062i	$-0.159386\pi$
$2$	2.48119			1.75447			0.877235	+	0.480062i	$0.159386\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	4.15633			2.07816
$5$		−	0.675131i		−	0.301928i	−0.988539	−	0.150964i	$-0.951762\pi$
$5$		−	0.675131i		−	0.301928i	0.988539	−	0.150964i	$-0.0482377\pi$
$6$		−	2.48119i		−	1.01294i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	5.35026			1.89160
$9$	−1.00000			−0.333333
$10$		−	1.67513i		−	0.529723i
$11$			1.80606i			0.544549i	0.962220	+	0.272274i	$0.0877758\pi$
$11$			1.80606i			0.544549i	−0.962220	+	0.272274i	$0.912224\pi$
$12$		−	4.15633i		−	1.19983i
$13$	−2.28726			−0.634371			−0.317186	−	0.948363i	$-0.602738\pi$
$13$	−2.28726			−0.634371			−0.317186	+	0.948363i	$0.602738\pi$
$14$			2.48119i			0.663127i
$15$	−0.675131			−0.174318
$16$	4.96239			1.24060
$17$	−3.67513	−	1.86907i	−0.891350	−	0.453315i
$17$	−3.67513	−	1.86907i	−0.891350	−	0.453315i
$18$	−2.48119			−0.584823
$19$	0.518806			0.119022			0.0595111	−	0.998228i	$-0.481046\pi$
$19$	0.518806			0.119022			0.0595111	+	0.998228i	$0.481046\pi$
$20$		−	2.80606i		−	0.627455i
$21$	1.00000			0.218218
$22$			4.48119i			0.955394i
$23$		−	0.0376114i		−	0.00784252i	−0.999992	−	0.00392126i	$-0.998752\pi$
$23$		−	0.0376114i		−	0.00784252i	0.999992	−	0.00392126i	$-0.00124818\pi$
$24$		−	5.35026i		−	1.09212i
$25$	4.54420			0.908840
$26$	−5.67513			−1.11298
$27$			1.00000i			0.192450i
$28$			4.15633i			0.785472i
$29$			0.806063i			0.149682i	0.997195	+	0.0748411i	$0.0238450\pi$
$29$			0.806063i			0.149682i	−0.997195	+	0.0748411i	$0.976155\pi$
$30$	−1.67513			−0.305836
$31$			1.28726i			0.231198i	0.993296	+	0.115599i	$0.0368788\pi$
$31$			1.28726i			0.231198i	−0.993296	+	0.115599i	$0.963121\pi$
$32$	1.61213			0.284986
$33$	1.80606			0.314395
$34$	−9.11871	−	4.63752i	−1.56385	−	0.795328i
$35$	0.675131			0.114118
$36$	−4.15633			−0.692721
$37$			7.83146i			1.28748i	0.765243	+	0.643742i	$0.222619\pi$
$37$			7.83146i			1.28748i	−0.765243	+	0.643742i	$0.777381\pi$
$38$	1.28726			0.208821
$39$			2.28726i			0.366254i
$40$		−	3.61213i		−	0.571127i
$41$		−	0.518806i		−	0.0810238i	−0.999179	−	0.0405119i	$-0.987101\pi$
$41$		−	0.518806i		−	0.0810238i	0.999179	−	0.0405119i	$-0.0128989\pi$
$42$	2.48119			0.382857
$43$	−3.57452			−0.545108			−0.272554	−	0.962140i	$-0.587868\pi$
$43$	−3.57452			−0.545108			−0.272554	+	0.962140i	$0.587868\pi$
$44$			7.50659i			1.13166i
$45$			0.675131i			0.100643i
$46$		−	0.0933212i		−	0.0137595i
$47$	−3.98778			−0.581678			−0.290839	−	0.956772i	$-0.593934\pi$
$47$	−3.98778			−0.581678			−0.290839	+	0.956772i	$0.593934\pi$
$48$		−	4.96239i		−	0.716259i
$49$	−1.00000			−0.142857
$50$	11.2750			1.59453
$51$	−1.86907	+	3.67513i	−0.261722	+	0.514621i
$52$	−9.50659			−1.31833
$53$	−4.09332			−0.562261			−0.281130	−	0.959670i	$-0.590709\pi$
$53$	−4.09332			−0.562261			−0.281130	+	0.959670i	$0.590709\pi$
$54$			2.48119i			0.337648i
$55$	1.21933			0.164414
$56$			5.35026i			0.714959i
$57$		−	0.518806i		−	0.0687175i
$58$			2.00000i			0.262613i
$59$	10.2496			1.33439			0.667195	−	0.744883i	$-0.267495\pi$
$59$	10.2496			1.33439			0.667195	+	0.744883i	$0.267495\pi$
$60$	−2.80606			−0.362261
$61$		−	14.5623i		−	1.86451i	−0.361801	−	0.932256i	$-0.617838\pi$
$61$		−	14.5623i		−	1.86451i	0.361801	−	0.932256i	$-0.382162\pi$
$62$			3.19394i			0.405630i
$63$		−	1.00000i		−	0.125988i
$64$	−5.92478			−0.740597
$65$			1.54420i			0.191534i
$66$	4.48119			0.551597
$67$	9.81924			1.19961			0.599805	−	0.800146i	$-0.295245\pi$
$67$	9.81924			1.19961			0.599805	+	0.800146i	$0.295245\pi$
$68$	−15.2750	−	7.76845i	−1.85237	−	0.942063i
$69$	−0.0376114			−0.00452788
$70$	1.67513			0.200216
$71$		−	13.6932i		−	1.62509i	−0.582900	−	0.812544i	$-0.698082\pi$
$71$		−	13.6932i		−	1.62509i	0.582900	−	0.812544i	$-0.301918\pi$
$72$	−5.35026			−0.630534
$73$			12.0508i			1.41044i	0.708990	+	0.705219i	$0.249151\pi$
$73$			12.0508i			1.41044i	−0.708990	+	0.705219i	$0.750849\pi$
$74$			19.4314i			2.25885i
$75$		−	4.54420i		−	0.524719i
$76$	2.15633			0.247347
$77$	−1.80606			−0.205820
$78$			5.67513i			0.642582i
$79$		−	4.99508i		−	0.561990i	−0.959709	−	0.280995i	$-0.909336\pi$
$79$		−	4.99508i		−	0.561990i	0.959709	−	0.280995i	$-0.0906644\pi$
$80$		−	3.35026i		−	0.374571i
$81$	1.00000			0.111111
$82$		−	1.28726i		−	0.142154i
$83$	2.26187			0.248272			0.124136	−	0.992265i	$-0.460384\pi$
$83$	2.26187			0.248272			0.124136	+	0.992265i	$0.460384\pi$
$84$	4.15633			0.453492
$85$	−1.26187	+	2.48119i	−0.136868	+	0.269123i
$86$	−8.86907			−0.956376
$87$	0.806063			0.0864191
$88$			9.66291i			1.03007i
$89$	−13.2750			−1.40715			−0.703576	−	0.710620i	$-0.748414\pi$
$89$	−13.2750			−1.40715			−0.703576	+	0.710620i	$0.748414\pi$
$90$			1.67513i			0.176574i
$91$		−	2.28726i		−	0.239770i
$92$		−	0.156325i		−	0.0162980i
$93$	1.28726			0.133482
$94$	−9.89446			−1.02054
$95$		−	0.350262i		−	0.0359361i
$96$		−	1.61213i		−	0.164537i
$97$			13.3503i			1.35551i	0.735286	+	0.677757i	$0.237048\pi$
$97$			13.3503i			1.35551i	−0.735286	+	0.677757i	$0.762952\pi$
$98$	−2.48119			−0.250638
$99$		−	1.80606i		−	0.181516i
$100$	18.8872			1.88872
$101$	9.47390			0.942688			0.471344	−	0.881949i	$-0.343769\pi$
$101$	9.47390			0.942688			0.471344	+	0.881949i	$0.343769\pi$
$102$	−4.63752	+	9.11871i	−0.459183	+	0.902887i
$103$	6.47390			0.637892			0.318946	−	0.947773i	$-0.396671\pi$
$103$	6.47390			0.637892			0.318946	+	0.947773i	$0.396671\pi$
$104$	−12.2374			−1.19998
$105$		−	0.675131i		−	0.0658860i
$106$	−10.1563			−0.986470
$107$		−	17.3634i		−	1.67859i	−0.543679	−	0.839293i	$-0.682969\pi$
$107$		−	17.3634i		−	1.67859i	0.543679	−	0.839293i	$-0.317031\pi$
$108$			4.15633i			0.399943i
$109$			5.56959i			0.533470i	0.963770	+	0.266735i	$0.0859449\pi$
$109$			5.56959i			0.533470i	−0.963770	+	0.266735i	$0.914055\pi$
$110$	3.02539			0.288460
$111$	7.83146			0.743329
$112$			4.96239i			0.468902i
$113$		−	17.0059i		−	1.59978i	−0.600148	−	0.799889i	$-0.704891\pi$
$113$		−	17.0059i		−	1.59978i	0.600148	−	0.799889i	$-0.295109\pi$
$114$		−	1.28726i		−	0.120563i
$115$	−0.0253926			−0.00236787
$116$			3.35026i			0.311064i
$117$	2.28726			0.211457
$118$	25.4314			2.34115
$119$	1.86907	−	3.67513i	0.171337	−	0.336899i
$120$	−3.61213			−0.329741
$121$	7.73813			0.703467
$122$		−	36.1319i		−	3.27123i
$123$	−0.518806			−0.0467791
$124$			5.35026i			0.480468i
$125$		−	6.44358i		−	0.576332i
$126$		−	2.48119i		−	0.221042i
$127$	4.45580			0.395388			0.197694	−	0.980264i	$-0.436655\pi$
$127$	4.45580			0.395388			0.197694	+	0.980264i	$0.436655\pi$
$128$	−17.9248			−1.58434
$129$			3.57452i			0.314719i
$130$			3.83146i			0.336041i
$131$		−	14.4133i		−	1.25929i	−0.776882	−	0.629646i	$-0.783200\pi$
$131$		−	14.4133i		−	1.25929i	0.776882	−	0.629646i	$-0.216800\pi$
$132$	7.50659			0.653365
$133$			0.518806i			0.0449862i
$134$	24.3634			2.10468
$135$	0.675131			0.0581060
$136$	−19.6629	−	10.0000i	−1.68608	−	0.857493i
$137$	6.79384			0.580437			0.290219	−	0.956960i	$-0.406272\pi$
$137$	6.79384			0.580437			0.290219	+	0.956960i	$0.406272\pi$
$138$	−0.0933212			−0.00794403
$139$			14.4993i			1.22981i	0.788600	+	0.614907i	$0.210806\pi$
$139$			14.4993i			1.22981i	−0.788600	+	0.614907i	$0.789194\pi$
$140$	2.80606			0.237156
$141$			3.98778i			0.335832i
$142$		−	33.9756i		−	2.85117i
$143$		−	4.13093i		−	0.345446i
$144$	−4.96239			−0.413532
$145$	0.544198			0.0451932
$146$			29.9003i			2.47457i
$147$			1.00000i			0.0824786i
$148$			32.5501i			2.67560i
$149$	−21.9003			−1.79415			−0.897073	−	0.441883i	$-0.854311\pi$
$149$	−21.9003			−1.79415			−0.897073	+	0.441883i	$0.854311\pi$
$150$		−	11.2750i		−	0.920603i
$151$	18.8061			1.53042			0.765208	−	0.643783i	$-0.222636\pi$
$151$	18.8061			1.53042			0.765208	+	0.643783i	$0.222636\pi$
$152$	2.77575			0.225143
$153$	3.67513	+	1.86907i	0.297117	+	0.151105i
$154$	−4.48119			−0.361105
$155$	0.869067			0.0698052
$156$			9.50659i			0.761136i
$157$	0.756233			0.0603540			0.0301770	−	0.999545i	$-0.490393\pi$
$157$	0.756233			0.0603540			0.0301770	+	0.999545i	$0.490393\pi$
$158$		−	12.3938i		−	0.985994i
$159$			4.09332i			0.324621i
$160$		−	1.08840i		−	0.0860453i
$161$	0.0376114			0.00296419
$162$	2.48119			0.194941
$163$		−	9.01317i		−	0.705966i	−0.935630	−	0.352983i	$-0.885167\pi$
$163$		−	9.01317i		−	0.705966i	0.935630	−	0.352983i	$-0.114833\pi$
$164$		−	2.15633i		−	0.168381i
$165$		−	1.21933i		−	0.0949246i
$166$	5.61213			0.435586
$167$			17.1441i			1.32665i	0.748331	+	0.663325i	$0.230855\pi$
$167$			17.1441i			1.32665i	−0.748331	+	0.663325i	$0.769145\pi$
$168$	5.35026			0.412782
$169$	−7.76845			−0.597573
$170$	−3.13093	+	6.15633i	−0.240132	+	0.472169i
$171$	−0.518806			−0.0396741
$172$	−14.8568			−1.13282
$173$		−	0.488489i		−	0.0371391i	−0.999828	−	0.0185695i	$-0.994089\pi$
$173$		−	0.488489i		−	0.0371391i	0.999828	−	0.0185695i	$-0.00591121\pi$
$174$	2.00000			0.151620
$175$			4.54420i			0.343509i
$176$			8.96239i			0.675565i
$177$		−	10.2496i		−	0.770411i
$178$	−32.9380			−2.46880
$179$	−3.41090			−0.254942			−0.127471	−	0.991842i	$-0.540686\pi$
$179$	−3.41090			−0.254942			−0.127471	+	0.991842i	$0.540686\pi$
$180$			2.80606i			0.209152i
$181$			5.14903i			0.382724i	0.981519	+	0.191362i	$0.0612905\pi$
$181$			5.14903i			0.382724i	−0.981519	+	0.191362i	$0.938709\pi$
$182$		−	5.67513i		−	0.420669i
$183$	−14.5623			−1.07648
$184$		−	0.201231i		−	0.0148349i
$185$	5.28726			0.388727
$186$	3.19394			0.234191
$187$	3.37565	−	6.63752i	0.246852	−	0.485383i
$188$	−16.5745			−1.20882
$189$	−1.00000			−0.0727393
$190$		−	0.869067i		−	0.0630488i
$191$	−0.775746			−0.0561310			−0.0280655	−	0.999606i	$-0.508935\pi$
$191$	−0.775746			−0.0561310			−0.0280655	+	0.999606i	$0.508935\pi$
$192$			5.92478i			0.427584i
$193$			25.4944i			1.83512i	0.397592	+	0.917562i	$0.369846\pi$
$193$			25.4944i			1.83512i	−0.397592	+	0.917562i	$0.630154\pi$
$194$			33.1246i			2.37821i
$195$	1.54420			0.110582
$196$	−4.15633			−0.296880
$197$			7.93207i			0.565137i	0.959247	+	0.282568i	$0.0911864\pi$
$197$			7.93207i			0.565137i	−0.959247	+	0.282568i	$0.908814\pi$
$198$		−	4.48119i		−	0.318465i
$199$			3.21203i			0.227695i	0.993498	+	0.113848i	$0.0363175\pi$
$199$			3.21203i			0.227695i	−0.993498	+	0.113848i	$0.963682\pi$
$200$	24.3127			1.71916
$201$		−	9.81924i		−	0.692596i
$202$	23.5066			1.65392
$203$	−0.806063			−0.0565746
$204$	−7.76845	+	15.2750i	−0.543900	+	1.06947i
$205$	−0.350262			−0.0244633
$206$	16.0630			1.11916
$207$			0.0376114i			0.00261417i
$208$	−11.3503			−0.786999
$209$			0.936996i			0.0648134i
$210$		−	1.67513i		−	0.115595i
$211$		−	22.4060i		−	1.54249i	−0.636538	−	0.771245i	$-0.719634\pi$
$211$		−	22.4060i		−	1.54249i	0.636538	−	0.771245i	$-0.280366\pi$
$212$	−17.0132			−1.16847
$213$	−13.6932			−0.938245
$214$		−	43.0821i		−	2.94503i
$215$			2.41327i			0.164583i
$216$			5.35026i			0.364039i
$217$	−1.28726			−0.0873847
$218$			13.8192i			0.935957i
$219$	12.0508			0.814317
$220$	5.06793			0.341680
$221$	8.40597	+	4.27504i	0.565447	+	0.287570i
$222$	19.4314			1.30415
$223$	−9.37565			−0.627840			−0.313920	−	0.949449i	$-0.601642\pi$
$223$	−9.37565			−0.627840			−0.313920	+	0.949449i	$0.601642\pi$
$224$			1.61213i			0.107715i
$225$	−4.54420			−0.302947
$226$		−	42.1949i		−	2.80676i
$227$		−	6.49437i		−	0.431046i	−0.976499	−	0.215523i	$-0.930854\pi$
$227$		−	6.49437i		−	0.431046i	0.976499	−	0.215523i	$-0.0691457\pi$
$228$		−	2.15633i		−	0.142806i
$229$	7.64244			0.505027			0.252513	−	0.967593i	$-0.418743\pi$
$229$	7.64244			0.505027			0.252513	+	0.967593i	$0.418743\pi$
$230$	−0.0630040			−0.00415436
$231$			1.80606i			0.118830i
$232$			4.31265i			0.283139i
$233$			12.6023i			0.825603i	0.910821	+	0.412801i	$0.135450\pi$
$233$			12.6023i			0.825603i	−0.910821	+	0.412801i	$0.864550\pi$
$234$	5.67513			0.370995
$235$			2.69227i			0.175625i
$236$	42.6009			2.77308
$237$	−4.99508			−0.324465
$238$	4.63752	−	9.11871i	0.300606	−	0.591078i
$239$	15.6810			1.01432			0.507160	−	0.861852i	$-0.330695\pi$
$239$	15.6810			1.01432			0.507160	+	0.861852i	$0.330695\pi$
$240$	−3.35026			−0.216258
$241$		−	2.23743i		−	0.144125i	−0.997400	−	0.0720627i	$-0.977042\pi$
$241$		−	2.23743i		−	0.144125i	0.997400	−	0.0720627i	$-0.0229582\pi$
$242$	19.1998			1.23421
$243$		−	1.00000i		−	0.0641500i
$244$		−	60.5256i		−	3.87476i
$245$			0.675131i			0.0431325i
$246$	−1.28726			−0.0820726
$247$	−1.18664			−0.0755042
$248$			6.88717i			0.437335i
$249$		−	2.26187i		−	0.143340i
$250$		−	15.9878i		−	1.01116i
$251$	21.7767			1.37453			0.687267	−	0.726405i	$-0.258810\pi$
$251$	21.7767			1.37453			0.687267	+	0.726405i	$0.258810\pi$
$252$		−	4.15633i		−	0.261824i
$253$	0.0679286			0.00427063
$254$	11.0557			0.693697
$255$	2.48119	+	1.26187i	0.155378	+	0.0790211i
$256$	−32.6253			−2.03908
$257$	6.51151			0.406177			0.203088	−	0.979160i	$-0.434902\pi$
$257$	6.51151			0.406177			0.203088	+	0.979160i	$0.434902\pi$
$258$			8.86907i			0.552164i
$259$	−7.83146			−0.486623
$260$			6.41819i			0.398039i
$261$		−	0.806063i		−	0.0498941i
$262$		−	35.7621i		−	2.20939i
$263$	−12.1866			−0.751461			−0.375730	−	0.926729i	$-0.622608\pi$
$263$	−12.1866			−0.751461			−0.375730	+	0.926729i	$0.622608\pi$
$264$	9.66291			0.594711
$265$			2.76353i			0.169762i
$266$			1.28726i			0.0789268i
$267$			13.2750i			0.812419i
$268$	40.8119			2.49299
$269$			7.09332i			0.432487i	0.976339	+	0.216244i	$0.0693806\pi$
$269$			7.09332i			0.432487i	−0.976339	+	0.216244i	$0.930619\pi$
$270$	1.67513			0.101945
$271$	−28.1817			−1.71192			−0.855959	−	0.517044i	$-0.827032\pi$
$271$	−28.1817			−1.71192			−0.855959	+	0.517044i	$0.827032\pi$
$272$	−18.2374	−	9.27504i	−1.10581	−	0.562382i
$273$	−2.28726			−0.138431
$274$	16.8568			1.01836
$275$			8.20711i			0.494907i
$276$	−0.156325			−0.00940967
$277$		−	23.3357i		−	1.40210i	−0.713110	−	0.701052i	$-0.752714\pi$
$277$		−	23.3357i		−	1.40210i	0.713110	−	0.701052i	$-0.247286\pi$
$278$			35.9756i			2.15767i
$279$		−	1.28726i		−	0.0770661i
$280$	3.61213			0.215866
$281$	−19.7381			−1.17748			−0.588739	−	0.808323i	$-0.700375\pi$
$281$	−19.7381			−1.17748			−0.588739	+	0.808323i	$0.700375\pi$
$282$			9.89446i			0.589207i
$283$			10.4264i			0.619787i	0.950771	+	0.309894i	$0.100293\pi$
$283$			10.4264i			0.619787i	−0.950771	+	0.309894i	$0.899707\pi$
$284$		−	56.9135i		−	3.37720i
$285$	−0.350262			−0.0207477
$286$		−	10.2496i		−	0.606074i
$287$	0.518806			0.0306241
$288$	−1.61213			−0.0949955
$289$	10.0132	+	13.7381i	0.589010	+	0.808126i
$290$	1.35026			0.0792901
$291$	13.3503			0.782606
$292$			50.0870i			2.93112i
$293$	−12.7250			−0.743400			−0.371700	−	0.928353i	$-0.621225\pi$
$293$	−12.7250			−0.743400			−0.371700	+	0.928353i	$0.621225\pi$
$294$			2.48119i			0.144706i
$295$		−	6.91985i		−	0.402889i
$296$			41.9003i			2.43541i
$297$	−1.80606			−0.104798
$298$	−54.3390			−3.14777
$299$			0.0860269i			0.00497507i
$300$		−	18.8872i		−	1.09045i
$301$		−	3.57452i		−	0.206032i
$302$	46.6615			2.68507
$303$		−	9.47390i		−	0.544261i
$304$	2.57452			0.147659
$305$	−9.83146			−0.562948
$306$	9.11871	+	4.63752i	0.521282	+	0.265109i
$307$	22.6761			1.29419			0.647096	−	0.762408i	$-0.275983\pi$
$307$	22.6761			1.29419			0.647096	+	0.762408i	$0.275983\pi$
$308$	−7.50659			−0.427727
$309$		−	6.47390i		−	0.368287i
$310$	2.15633			0.122471
$311$			26.0508i			1.47720i	0.674141	+	0.738602i	$0.264514\pi$
$311$			26.0508i			1.47720i	−0.674141	+	0.738602i	$0.735486\pi$
$312$			12.2374i			0.692808i
$313$			18.3512i			1.03727i	0.854995	+	0.518636i	$0.173560\pi$
$313$			18.3512i			1.03727i	−0.854995	+	0.518636i	$0.826440\pi$
$314$	1.87636			0.105889
$315$	−0.675131			−0.0380393
$316$		−	20.7612i		−	1.16791i
$317$		−	13.1998i		−	0.741376i	−0.928758	−	0.370688i	$-0.879122\pi$
$317$		−	13.1998i		−	0.741376i	0.928758	−	0.370688i	$-0.120878\pi$
$318$			10.1563i			0.569538i
$319$	−1.45580			−0.0815092
$320$			4.00000i			0.223607i
$321$	−17.3634			−0.969132
$322$	0.0933212			0.00520059
$323$	−1.90668	−	0.969683i	−0.106090	−	0.0539546i
$324$	4.15633			0.230907
$325$	−10.3938			−0.576542
$326$		−	22.3634i		−	1.23860i
$327$	5.56959			0.307999
$328$		−	2.77575i		−	0.153265i
$329$		−	3.98778i		−	0.219853i
$330$		−	3.02539i		−	0.166542i
$331$	3.30677			0.181757			0.0908783	−	0.995862i	$-0.471033\pi$
$331$	3.30677			0.181757			0.0908783	+	0.995862i	$0.471033\pi$
$332$	9.40105			0.515949
$333$		−	7.83146i		−	0.429161i
$334$			42.5379i			2.32757i
$335$		−	6.62927i		−	0.362196i
$336$	4.96239			0.270720
$337$			29.8677i			1.62699i	0.581569	+	0.813497i	$0.302439\pi$
$337$			29.8677i			1.62699i	−0.581569	+	0.813497i	$0.697561\pi$
$338$	−19.2750			−1.04842
$339$	−17.0059			−0.923633
$340$	−5.24472	+	10.3127i	−0.284435	+	0.559282i
$341$	−2.32487			−0.125899
$342$	−1.28726			−0.0696069
$343$		−	1.00000i		−	0.0539949i
$344$	−19.1246			−1.03113
$345$			0.0253926i			0.00136709i
$346$		−	1.21203i		−	0.0651594i
$347$			29.4821i			1.58268i	0.611373	+	0.791342i	$0.290617\pi$
$347$			29.4821i			1.58268i	−0.611373	+	0.791342i	$0.709383\pi$
$348$	3.35026			0.179593
$349$	−32.2833			−1.72808			−0.864042	−	0.503419i	$-0.832075\pi$
$349$	−32.2833			−1.72808			−0.864042	+	0.503419i	$0.832075\pi$
$350$			11.2750i			0.602676i
$351$		−	2.28726i		−	0.122085i
$352$			2.91160i			0.155189i
$353$	−18.4871			−0.983968			−0.491984	−	0.870604i	$-0.663728\pi$
$353$	−18.4871			−0.983968			−0.491984	+	0.870604i	$0.663728\pi$
$354$		−	25.4314i		−	1.35166i
$355$	−9.24472			−0.490659
$356$	−55.1754			−2.92429
$357$	−3.67513	−	1.86907i	−0.194509	−	0.0989215i
$358$	−8.46310			−0.447289
$359$	3.78067			0.199536			0.0997681	−	0.995011i	$-0.468190\pi$
$359$	3.78067			0.199536			0.0997681	+	0.995011i	$0.468190\pi$
$360$			3.61213i			0.190376i
$361$	−18.7308			−0.985834
$362$			12.7757i			0.671478i
$363$		−	7.73813i		−	0.406147i
$364$		−	9.50659i		−	0.498281i
$365$	8.13586			0.425850
$366$	−36.1319			−1.88864
$367$		−	11.5975i		−	0.605387i	−0.953088	−	0.302693i	$-0.902114\pi$
$367$		−	11.5975i		−	0.605387i	0.953088	−	0.302693i	$-0.0978858\pi$
$368$		−	0.186642i		−	0.00972940i
$369$			0.518806i			0.0270079i
$370$	13.1187			0.682009
$371$		−	4.09332i		−	0.212515i
$372$	5.35026			0.277398
$373$	−17.1187			−0.886373			−0.443187	−	0.896429i	$-0.646152\pi$
$373$	−17.1187			−0.886373			−0.443187	+	0.896429i	$0.646152\pi$
$374$	8.37565	−	16.4690i	0.433095	−	0.851590i
$375$	−6.44358			−0.332745
$376$	−21.3357			−1.10030
$377$		−	1.84367i		−	0.0949541i
$378$	−2.48119			−0.127619
$379$		−	11.5515i		−	0.593360i	−0.954977	−	0.296680i	$-0.904120\pi$
$379$		−	11.5515i		−	0.593360i	0.954977	−	0.296680i	$-0.0958795\pi$
$380$		−	1.45580i		−	0.0746811i
$381$		−	4.45580i		−	0.228278i
$382$	−1.92478			−0.0984802
$383$	−20.4264			−1.04374			−0.521871	−	0.853024i	$-0.674766\pi$
$383$	−20.4264			−1.04374			−0.521871	+	0.853024i	$0.674766\pi$
$384$			17.9248i			0.914720i
$385$			1.21933i			0.0621428i
$386$			63.2565i			3.21967i
$387$	3.57452			0.181703
$388$			55.4880i			2.81698i
$389$	−18.9887			−0.962767			−0.481384	−	0.876510i	$-0.659866\pi$
$389$	−18.9887			−0.962767			−0.481384	+	0.876510i	$0.659866\pi$
$390$	3.83146			0.194013
$391$	−0.0702982	+	0.138227i	−0.00355513	+	0.00699043i
$392$	−5.35026			−0.270229
$393$	−14.4133			−0.727053
$394$			19.6810i			0.991515i
$395$	−3.37233			−0.169680
$396$		−	7.50659i		−	0.377220i
$397$			11.9271i			0.598606i	0.954158	+	0.299303i	$0.0967542\pi$
$397$			11.9271i			0.598606i	−0.954158	+	0.299303i	$0.903246\pi$
$398$			7.96968i			0.399484i
$399$	0.518806			0.0259728
$400$	22.5501			1.12750
$401$			17.3185i			0.864846i	0.901671	+	0.432423i	$0.142341\pi$
$401$			17.3185i			0.864846i	−0.901671	+	0.432423i	$0.857659\pi$
$402$		−	24.3634i		−	1.21514i
$403$		−	2.94429i		−	0.146666i
$404$	39.3766			1.95906
$405$		−	0.675131i		−	0.0335475i
$406$	−2.00000			−0.0992583
$407$	−14.1441			−0.701097
$408$	−10.0000	+	19.6629i	−0.495074	+	0.973459i
$409$	20.4641			1.01188			0.505941	−	0.862568i	$-0.331145\pi$
$409$	20.4641			1.01188			0.505941	+	0.862568i	$0.331145\pi$
$410$	−0.869067			−0.0429202
$411$		−	6.79384i		−	0.335116i
$412$	26.9076			1.32564
$413$			10.2496i			0.504352i
$414$			0.0933212i			0.00458649i
$415$		−	1.52705i		−	0.0749602i
$416$	−3.68735			−0.180787
$417$	14.4993			0.710033
$418$			2.32487i			0.113713i
$419$		−	13.8700i		−	0.677595i	−0.940859	−	0.338797i	$-0.889980\pi$
$419$		−	13.8700i		−	0.677595i	0.940859	−	0.338797i	$-0.110020\pi$
$420$		−	2.80606i		−	0.136922i
$421$	1.43278			0.0698294			0.0349147	−	0.999390i	$-0.488884\pi$
$421$	1.43278			0.0698294			0.0349147	+	0.999390i	$0.488884\pi$
$422$		−	55.5936i		−	2.70625i
$423$	3.98778			0.193893
$424$	−21.9003			−1.06357
$425$	−16.7005	−	8.49341i	−0.810094	−	0.411991i
$426$	−33.9756			−1.64612
$427$	14.5623			0.704719
$428$		−	72.1681i		−	3.48838i
$429$	−4.13093			−0.199443
$430$			5.98778i			0.288756i
$431$			39.3258i			1.89426i	0.320853	+	0.947129i	$0.396031\pi$
$431$			39.3258i			1.89426i	−0.320853	+	0.947129i	$0.603969\pi$
$432$			4.96239i			0.238753i
$433$	24.6810			1.18609			0.593047	−	0.805168i	$-0.297925\pi$
$433$	24.6810			1.18609			0.593047	+	0.805168i	$0.297925\pi$
$434$	−3.19394			−0.153314
$435$		−	0.544198i		−	0.0260923i
$436$			23.1490i			1.10864i
$437$		−	0.0195130i		−	0.000933434i
$438$	29.9003			1.42869
$439$		−	26.7489i		−	1.27666i	−0.769764	−	0.638329i	$-0.779626\pi$
$439$		−	26.7489i		−	1.27666i	0.769764	−	0.638329i	$-0.220374\pi$
$440$	6.52373			0.311007
$441$	1.00000			0.0476190
$442$	20.8568	+	10.6072i	0.992059	+	0.504533i
$443$	20.9199			0.993932			0.496966	−	0.867770i	$-0.334447\pi$
$443$	20.9199			0.993932			0.496966	+	0.867770i	$0.334447\pi$
$444$	32.5501			1.54476
$445$			8.96239i			0.424858i
$446$	−23.2628			−1.10153
$447$			21.9003i			1.03585i
$448$		−	5.92478i		−	0.279919i
$449$		−	19.3561i		−	0.913473i	−0.889602	−	0.456736i	$-0.849018\pi$
$449$		−	19.3561i		−	0.913473i	0.889602	−	0.456736i	$-0.150982\pi$
$450$	−11.2750			−0.531510
$451$	0.936996			0.0441214
$452$		−	70.6820i		−	3.32460i
$453$		−	18.8061i		−	0.883586i
$454$		−	16.1138i		−	0.756258i
$455$	−1.54420			−0.0723931
$456$		−	2.77575i		−	0.129986i
$457$	−31.5296			−1.47489			−0.737446	−	0.675406i	$-0.763969\pi$
$457$	−31.5296			−1.47489			−0.737446	+	0.675406i	$0.763969\pi$
$458$	18.9624			0.886054
$459$	1.86907	−	3.67513i	0.0872406	−	0.171540i
$460$	−0.105540			−0.00492083
$461$	18.7997			0.875590			0.437795	−	0.899075i	$-0.355759\pi$
$461$	18.7997			0.875590			0.437795	+	0.899075i	$0.355759\pi$
$462$			4.48119i			0.208484i
$463$	−5.94525			−0.276299			−0.138149	−	0.990411i	$-0.544115\pi$
$463$	−5.94525			−0.276299			−0.138149	+	0.990411i	$0.544115\pi$
$464$			4.00000i			0.185695i
$465$		−	0.869067i		−	0.0403020i
$466$			31.2687i			1.44849i
$467$	4.52373			0.209333			0.104667	−	0.994507i	$-0.466622\pi$
$467$	4.52373			0.209333			0.104667	+	0.994507i	$0.466622\pi$
$468$	9.50659			0.439442
$469$			9.81924i			0.453410i
$470$			6.68006i			0.308128i
$471$		−	0.756233i		−	0.0348454i
$472$	54.8383			2.52414
$473$		−	6.45580i		−	0.296838i
$474$	−12.3938			−0.569264
$475$	2.35756			0.108172
$476$	7.76845	−	15.2750i	0.356066	−	0.700130i
$477$	4.09332			0.187420
$478$	38.9076			1.77959
$479$			1.94429i			0.0888369i	0.999013	+	0.0444184i	$0.0141435\pi$
$479$			1.94429i			0.0888369i	−0.999013	+	0.0444184i	$0.985857\pi$
$480$	−1.08840			−0.0496783
$481$		−	17.9126i		−	0.816742i
$482$		−	5.55149i		−	0.252864i
$483$		−	0.0376114i		−	0.00171138i
$484$	32.1622			1.46192
$485$	9.01317			0.409267
$486$		−	2.48119i		−	0.112549i
$487$			31.7743i			1.43983i	0.694061	+	0.719916i	$0.255820\pi$
$487$			31.7743i			1.43983i	−0.694061	+	0.719916i	$0.744180\pi$
$488$		−	77.9121i		−	3.52691i
$489$	−9.01317			−0.407590
$490$			1.67513i			0.0756747i
$491$	19.0884			0.861447			0.430724	−	0.902484i	$-0.358258\pi$
$491$	19.0884			0.861447			0.430724	+	0.902484i	$0.358258\pi$
$492$	−2.15633			−0.0972146
$493$	1.50659	−	2.96239i	0.0678533	−	0.133419i
$494$	−2.94429			−0.132470
$495$	−1.21933			−0.0548048
$496$			6.38787i			0.286824i
$497$	13.6932			0.614225
$498$		−	5.61213i		−	0.251485i
$499$			7.94288i			0.355572i	0.984069	+	0.177786i	$0.0568935\pi$
$499$			7.94288i			0.355572i	−0.984069	+	0.177786i	$0.943107\pi$
$500$		−	26.7816i		−	1.19771i
$501$	17.1441			0.765942
$502$	54.0322			2.41158
$503$			36.0616i			1.60791i	0.594692	+	0.803953i	$0.297274\pi$
$503$			36.0616i			1.60791i	−0.594692	+	0.803953i	$0.702726\pi$
$504$		−	5.35026i		−	0.238320i
$505$		−	6.39612i		−	0.284624i
$506$	0.168544			0.00749269
$507$			7.76845i			0.345009i
$508$	18.5198			0.821682
$509$	−22.0362			−0.976737			−0.488369	−	0.872637i	$-0.662408\pi$
$509$	−22.0362			−0.976737			−0.488369	+	0.872637i	$0.662408\pi$
$510$	6.15633	+	3.13093i	0.272607	+	0.138640i
$511$	−12.0508			−0.533095
$512$	−45.1002			−1.99316
$513$			0.518806i			0.0229058i
$514$	16.1563			0.712625
$515$		−	4.37073i		−	0.192597i
$516$			14.8568i			0.654036i
$517$		−	7.20219i		−	0.316752i
$518$	−19.4314			−0.853765
$519$	−0.488489			−0.0214423
$520$			8.26187i			0.362307i
$521$			4.46802i			0.195748i	0.995199	+	0.0978738i	$0.0312041\pi$
$521$			4.46802i			0.195748i	−0.995199	+	0.0978738i	$0.968796\pi$
$522$		−	2.00000i		−	0.0875376i
$523$	−26.0263			−1.13805			−0.569026	−	0.822319i	$-0.692680\pi$
$523$	−26.0263			−1.13805			−0.569026	+	0.822319i	$0.692680\pi$
$524$		−	59.9062i		−	2.61702i
$525$	4.54420			0.198325
$526$	−30.2374			−1.31841
$527$	2.40597	−	4.73084i	0.104806	−	0.206079i
$528$	8.96239			0.390038
$529$	22.9986			0.999938
$530$			6.85685i			0.297842i
$531$	−10.2496			−0.444797
$532$			2.15633i			0.0934886i
$533$			1.18664i			0.0513992i
$534$			32.9380i			1.42536i
$535$	−11.7226			−0.506812
$536$	52.5355			2.26919
$537$			3.41090i			0.147191i
$538$			17.5999i			0.758786i
$539$		−	1.80606i		−	0.0777927i
$540$	2.80606			0.120754
$541$		−	2.57452i		−	0.110687i	−0.998467	−	0.0553435i	$-0.982375\pi$
$541$		−	2.57452i		−	0.110687i	0.998467	−	0.0553435i	$-0.0176254\pi$
$542$	−69.9243			−3.00351
$543$	5.14903			0.220966
$544$	−5.92478	−	3.01317i	−0.254023	−	0.129189i
$545$	3.76020			0.161069
$546$	−5.67513			−0.242873
$547$		−	20.4568i		−	0.874668i	−0.899299	−	0.437334i	$-0.855923\pi$
$547$		−	20.4568i		−	0.874668i	0.899299	−	0.437334i	$-0.144077\pi$
$548$	28.2374			1.20624
$549$			14.5623i			0.621504i
$550$			20.3634i			0.868300i
$551$			0.418190i			0.0178155i
$552$	−0.201231			−0.00856495
$553$	4.99508			0.212412
$554$		−	57.9003i		−	2.45995i
$555$		−	5.28726i		−	0.224432i
$556$			60.2638i			2.55575i
$557$	−18.9199			−0.801660			−0.400830	−	0.916152i	$-0.631278\pi$
$557$	−18.9199			−0.801660			−0.400830	+	0.916152i	$0.631278\pi$
$558$		−	3.19394i		−	0.135210i
$559$	8.17584			0.345801
$560$	3.35026			0.141574
$561$	−6.63752	−	3.37565i	−0.280236	−	0.142520i
$562$	−48.9741			−2.06585
$563$	33.4617			1.41024			0.705121	−	0.709087i	$-0.250893\pi$
$563$	33.4617			1.41024			0.705121	+	0.709087i	$0.250893\pi$
$564$			16.5745i			0.697913i
$565$	−11.4812			−0.483017
$566$			25.8700i			1.08740i
$567$			1.00000i			0.0419961i
$568$		−	73.2624i		−	3.07402i
$569$	7.58769			0.318092			0.159046	−	0.987271i	$-0.449158\pi$
$569$	7.58769			0.318092			0.159046	+	0.987271i	$0.449158\pi$
$570$	−0.869067			−0.0364012
$571$		−	37.4128i		−	1.56568i	−0.622225	−	0.782839i	$-0.713771\pi$
$571$		−	37.4128i		−	1.56568i	0.622225	−	0.782839i	$-0.286229\pi$
$572$		−	17.1695i		−	0.717893i
$573$			0.775746i			0.0324073i
$574$	1.28726			0.0537291
$575$		−	0.170914i		−	0.00712759i
$576$	5.92478			0.246866
$577$	9.70289			0.403937			0.201968	−	0.979392i	$-0.435266\pi$
$577$	9.70289			0.403937			0.201968	+	0.979392i	$0.435266\pi$
$578$	24.8446	+	34.0870i	1.03340	+	1.41783i
$579$	25.4944			1.05951
$580$	2.26187			0.0939188
$581$			2.26187i			0.0938380i
$582$	33.1246			1.37306
$583$		−	7.39280i		−	0.306178i
$584$			64.4749i			2.66799i
$585$		−	1.54420i		−	0.0638447i
$586$	−31.5731			−1.30427
$587$	34.6375			1.42964			0.714822	−	0.699307i	$-0.246508\pi$
$587$	34.6375			1.42964			0.714822	+	0.699307i	$0.246508\pi$
$588$			4.15633i			0.171404i
$589$			0.667837i			0.0275177i
$590$		−	17.1695i		−	0.706857i
$591$	7.93207			0.326282
$592$			38.8627i			1.59725i
$593$	26.3512			1.08211			0.541057	−	0.840986i	$-0.318024\pi$
$593$	26.3512			1.08211			0.541057	+	0.840986i	$0.318024\pi$
$594$	−4.48119			−0.183866
$595$	−2.48119	−	1.26187i	−0.101719	−	0.0517314i
$596$	−91.0249			−3.72853
$597$	3.21203			0.131460
$598$			0.213450i			0.00872860i
$599$	−14.4485			−0.590350			−0.295175	−	0.955443i	$-0.595378\pi$
$599$	−14.4485			−0.590350			−0.295175	+	0.955443i	$0.595378\pi$
$600$		−	24.3127i		−	0.992560i
$601$		−	22.8242i		−	0.931017i	−0.885043	−	0.465508i	$-0.845871\pi$
$601$		−	22.8242i		−	0.931017i	0.885043	−	0.465508i	$-0.154129\pi$
$602$		−	8.86907i		−	0.361476i
$603$	−9.81924			−0.399870
$604$	78.1641			3.18045
$605$		−	5.22425i		−	0.212396i
$606$		−	23.5066i		−	0.954890i
$607$		−	27.1974i		−	1.10391i	−0.833874	−	0.551955i	$-0.813882\pi$
$607$		−	27.1974i		−	1.10391i	0.833874	−	0.551955i	$-0.186118\pi$
$608$	0.836381			0.0339197
$609$			0.806063i			0.0326633i
$610$	−24.3938			−0.987674
$611$	9.12108			0.369000
$612$	15.2750	+	7.76845i	0.617457	+	0.314021i
$613$	11.4387			0.462003			0.231002	−	0.972953i	$-0.425800\pi$
$613$	11.4387			0.462003			0.231002	+	0.972953i	$0.425800\pi$
$614$	56.2638			2.27062
$615$			0.350262i			0.0141239i
$616$	−9.66291			−0.389330
$617$			10.0205i			0.403409i	0.979446	+	0.201704i	$0.0646480\pi$
$617$			10.0205i			0.403409i	−0.979446	+	0.201704i	$0.935352\pi$
$618$		−	16.0630i		−	0.646149i
$619$			1.47390i			0.0592410i	0.999561	+	0.0296205i	$0.00942988\pi$
$619$			1.47390i			0.0592410i	−0.999561	+	0.0296205i	$0.990570\pi$
$620$	3.61213			0.145067
$621$	0.0376114			0.00150929
$622$			64.6371i			2.59171i
$623$		−	13.2750i		−	0.531853i
$624$			11.3503i			0.454374i
$625$	18.3707			0.734829
$626$			45.5329i			1.81986i
$627$	0.936996			0.0374200
$628$	3.14315			0.125425
$629$	14.6375	−	28.7816i	0.583636	−	1.14760i
$630$	−1.67513			−0.0667388
$631$	31.2736			1.24498			0.622492	−	0.782626i	$-0.286120\pi$
$631$	31.2736			1.24498			0.622492	+	0.782626i	$0.286120\pi$
$632$		−	26.7250i		−	1.06306i
$633$	−22.4060			−0.890557
$634$		−	32.7513i		−	1.30072i
$635$		−	3.00825i		−	0.119379i
$636$			17.0132i			0.674616i
$637$	2.28726			0.0906245
$638$	−3.61213			−0.143005
$639$			13.6932i			0.541696i
$640$			12.1016i			0.478357i
$641$			21.4847i			0.848595i	0.905523	+	0.424297i	$0.139479\pi$
$641$			21.4847i			0.848595i	−0.905523	+	0.424297i	$0.860521\pi$
$642$	−43.0821			−1.70031
$643$			17.5633i			0.692627i	0.938119	+	0.346314i	$0.112567\pi$
$643$			17.5633i			0.692627i	−0.938119	+	0.346314i	$0.887433\pi$
$644$	0.156325			0.00616007
$645$	2.41327			0.0950222
$646$	−4.73084	−	2.40597i	−0.186132	−	0.0946617i
$647$	3.88858			0.152876			0.0764379	−	0.997074i	$-0.475645\pi$
$647$	3.88858			0.152876			0.0764379	+	0.997074i	$0.475645\pi$
$648$	5.35026			0.210178
$649$			18.5115i			0.726640i
$650$	−25.7889			−1.01152
$651$			1.28726i			0.0504516i
$652$		−	37.4617i		−	1.46711i
$653$			17.0244i			0.666218i	0.942888	+	0.333109i	$0.108098\pi$
$653$			17.0244i			0.666218i	−0.942888	+	0.333109i	$0.891902\pi$
$654$	13.8192			0.540375
$655$	−9.73084			−0.380215
$656$		−	2.57452i		−	0.100518i
$657$		−	12.0508i		−	0.470146i
$658$		−	9.89446i		−	0.385726i
$659$	−16.0835			−0.626523			−0.313262	−	0.949667i	$-0.601422\pi$
$659$	−16.0835			−0.626523			−0.313262	+	0.949667i	$0.601422\pi$
$660$		−	5.06793i		−	0.197269i
$661$	21.0082			0.817126			0.408563	−	0.912730i	$-0.366030\pi$
$661$	21.0082			0.817126			0.408563	+	0.912730i	$0.366030\pi$
$662$	8.20474			0.318886
$663$	4.27504	−	8.40597i	0.166029	−	0.326461i
$664$	12.1016			0.469632
$665$	0.350262			0.0135826
$666$		−	19.4314i		−	0.752950i
$667$	0.0303172			0.00117389
$668$			71.2565i			2.75700i
$669$			9.37565i			0.362484i
$670$		−	16.4485i		−	0.635461i
$671$	26.3004			1.01532
$672$	1.61213			0.0621891
$673$		−	50.8481i		−	1.96005i	−0.198870	−	0.980026i	$-0.563727\pi$
$673$		−	50.8481i		−	1.96005i	0.198870	−	0.980026i	$-0.436273\pi$
$674$			74.1075i			2.85451i
$675$			4.54420i			0.174906i
$676$	−32.2882			−1.24185
$677$		−	41.1051i		−	1.57980i	−0.613238	−	0.789898i	$-0.710133\pi$
$677$		−	41.1051i		−	1.57980i	0.613238	−	0.789898i	$-0.289867\pi$
$678$	−42.1949			−1.62049
$679$	−13.3503			−0.512336
$680$	−6.75131	+	13.2750i	−0.258901	+	0.509075i
$681$	−6.49437			−0.248865
$682$	−5.76845			−0.220885
$683$			18.0336i			0.690038i	0.938596	+	0.345019i	$0.112128\pi$
$683$			18.0336i			0.690038i	−0.938596	+	0.345019i	$0.887872\pi$
$684$	−2.15633			−0.0824492
$685$		−	4.58673i		−	0.175250i
$686$		−	2.48119i		−	0.0947324i
$687$		−	7.64244i		−	0.291577i
$688$	−17.7381			−0.676260
$689$	9.36248			0.356682
$690$			0.0630040i			0.00239852i
$691$		−	10.3150i		−	0.392402i	−0.980564	−	0.196201i	$-0.937140\pi$
$691$		−	10.3150i		−	0.392402i	0.980564	−	0.196201i	$-0.0628605\pi$
$692$		−	2.03032i		−	0.0771811i
$693$	1.80606			0.0686067
$694$			73.1509i			2.77677i
$695$	9.78892			0.371315
$696$	4.31265			0.163471
$697$	−0.969683	+	1.90668i	−0.0367294	+	0.0722206i
$698$	−80.1011			−3.03187
$699$	12.6023			0.476662
$700$			18.8872i			0.713868i
$701$	−21.2750			−0.803547			−0.401774	−	0.915739i	$-0.631606\pi$
$701$	−21.2750			−0.803547			−0.401774	+	0.915739i	$0.631606\pi$
$702$		−	5.67513i		−	0.214194i
$703$			4.06300i			0.153239i
$704$		−	10.7005i		−	0.403291i
$705$	2.69227			0.101397
$706$	−45.8700			−1.72634
$707$			9.47390i			0.356303i
$708$		−	42.6009i		−	1.60104i
$709$		−	11.8496i		−	0.445019i	−0.974930	−	0.222510i	$-0.928575\pi$
$709$		−	11.8496i		−	0.445019i	0.974930	−	0.222510i	$-0.0714249\pi$
$710$	−22.9380			−0.860846
$711$			4.99508i			0.187330i
$712$	−71.0249			−2.66177
$713$	0.0484156			0.00181318
$714$	−9.11871	−	4.63752i	−0.341259	−	0.173555i
$715$	−2.78892			−0.104300
$716$	−14.1768			−0.529812
$717$		−	15.6810i		−	0.585618i
$718$	9.38058			0.350080
$719$		−	19.5379i		−	0.728639i	−0.931274	−	0.364320i	$-0.881302\pi$
$719$		−	19.5379i		−	0.728639i	0.931274	−	0.364320i	$-0.118698\pi$
$720$			3.35026i			0.124857i
$721$			6.47390i			0.241101i
$722$	−46.4749			−1.72962
$723$	−2.23743			−0.0832108
$724$			21.4010i			0.795364i
$725$			3.66291i			0.136037i
$726$		−	19.1998i		−	0.712572i
$727$	−46.6761			−1.73112			−0.865560	−	0.500805i	$-0.833037\pi$
$727$	−46.6761			−1.73112			−0.865560	+	0.500805i	$0.833037\pi$
$728$		−	12.2374i		−	0.453549i
$729$	−1.00000			−0.0370370
$730$	20.1866			0.747141
$731$	13.1368	+	6.68101i	0.485883	+	0.247106i
$732$	−60.5256			−2.23709
$733$	−9.13918			−0.337563			−0.168782	−	0.985653i	$-0.553983\pi$
$733$	−9.13918			−0.337563			−0.168782	+	0.985653i	$0.553983\pi$
$734$		−	28.7757i		−	1.06213i
$735$	0.675131			0.0249026
$736$		−	0.0606343i		−	0.00223501i
$737$			17.7342i			0.653246i
$738$			1.28726i			0.0473846i
$739$	41.8481			1.53941			0.769704	−	0.638401i	$-0.220404\pi$
$739$	41.8481			1.53941			0.769704	+	0.638401i	$0.220404\pi$
$740$	21.9756			0.807838
$741$			1.18664i			0.0435924i
$742$		−	10.1563i		−	0.372850i
$743$		−	6.33121i		−	0.232270i	−0.993233	−	0.116135i	$-0.962950\pi$
$743$		−	6.33121i		−	0.232270i	0.993233	−	0.116135i	$-0.0370504\pi$
$744$	6.88717			0.252496
$745$			14.7856i			0.541702i
$746$	−42.4749			−1.55511
$747$	−2.26187			−0.0827573
$748$	14.0303	−	27.5877i	0.512999	−	1.00871i
$749$	17.3634			0.634446
$750$	−15.9878			−0.583791
$751$		−	1.04395i		−	0.0380943i	−0.999819	−	0.0190471i	$-0.993937\pi$
$751$		−	1.04395i		−	0.0380943i	0.999819	−	0.0190471i	$-0.00606326\pi$
$752$	−19.7889			−0.721628
$753$		−	21.7767i		−	0.793587i
$754$		−	4.57452i		−	0.166594i
$755$		−	12.6966i		−	0.462075i
$756$	−4.15633			−0.151164
$757$	45.3839			1.64951			0.824753	−	0.565493i	$-0.191314\pi$
$757$	45.3839			1.64951			0.824753	+	0.565493i	$0.191314\pi$
$758$		−	28.6615i		−	1.04103i
$759$		−	0.0679286i		−	0.00246565i
$760$		−	1.87399i		−	0.0679768i
$761$	41.6893			1.51123			0.755617	−	0.655013i	$-0.227337\pi$
$761$	41.6893			1.51123			0.755617	+	0.655013i	$0.227337\pi$
$762$		−	11.0557i		−	0.400506i
$763$	−5.56959			−0.201633
$764$	−3.22425			−0.116649
$765$	1.26187	−	2.48119i	0.0456228	−	0.0897078i
$766$	−50.6820			−1.83121
$767$	−23.4436			−0.846499
$768$			32.6253i			1.17726i
$769$	−47.3122			−1.70612			−0.853061	−	0.521812i	$-0.825256\pi$
$769$	−47.3122			−1.70612			−0.853061	+	0.521812i	$0.825256\pi$
$770$			3.02539i			0.109028i
$771$		−	6.51151i		−	0.234506i
$772$			105.963i			3.81369i
$773$	28.2252			1.01519			0.507595	−	0.861596i	$-0.330535\pi$
$773$	28.2252			1.01519			0.507595	+	0.861596i	$0.330535\pi$
$774$	8.86907			0.318792
$775$			5.84955i			0.210122i
$776$			71.4274i			2.56409i
$777$			7.83146i			0.280952i
$778$	−47.1147			−1.68915
$779$		−	0.269159i		−	0.00964363i
$780$	6.41819			0.229808
$781$	24.7308			0.884939
$782$	−0.174424	+	0.342968i	−0.00623737	+	0.0122645i
$783$	−0.806063			−0.0288064
$784$	−4.96239			−0.177228
$785$		−	0.510556i		−	0.0182225i
$786$	−35.7621			−1.27559
$787$		−	26.9257i		−	0.959799i	−0.877324	−	0.479899i	$-0.840673\pi$
$787$		−	26.9257i		−	0.959799i	0.877324	−	0.479899i	$-0.159327\pi$
$788$			32.9683i			1.17445i
$789$			12.1866i			0.433856i
$790$	−8.36741			−0.297699
$791$	17.0059			0.604659
$792$		−	9.66291i		−	0.343357i
$793$			33.3077i			1.18279i
$794$			29.5936i			1.05024i
$795$	2.76353			0.0980122
$796$			13.3503i			0.473187i
$797$	−30.2882			−1.07286			−0.536432	−	0.843944i	$-0.680228\pi$
$797$	−30.2882			−1.07286			−0.536432	+	0.843944i	$0.680228\pi$
$798$	1.28726			0.0455684
$799$	14.6556	+	7.45343i	0.518478	+	0.263683i
$800$	7.32582			0.259007
$801$	13.2750			0.469050
$802$			42.9706i			1.51735i
$803$	−21.7645			−0.768052
$804$		−	40.8119i		−	1.43933i
$805$		−	0.0253926i		−	0.000894972i
$806$		−	7.30536i		−	0.257320i
$807$	7.09332			0.249697
$808$	50.6878			1.78319
$809$		−	2.59166i		−	0.0911179i	−0.998962	−	0.0455589i	$-0.985493\pi$
$809$		−	2.59166i		−	0.0911179i	0.998962	−	0.0455589i	$-0.0145069\pi$
$810$		−	1.67513i		−	0.0588581i
$811$		−	27.4128i		−	0.962594i	−0.876558	−	0.481297i	$-0.840166\pi$
$811$		−	27.4128i		−	0.962594i	0.876558	−	0.481297i	$-0.159834\pi$
$812$	−3.35026			−0.117571
$813$			28.1817i			0.988376i
$814$	−35.0943			−1.23005
$815$	−6.08507			−0.213151
$816$	−9.27504	+	18.2374i	−0.324691	+	0.638438i
$817$	−1.85448			−0.0648800
$818$	50.7753			1.77532
$819$			2.28726i			0.0799233i
$820$	−1.45580			−0.0508388
$821$			39.8119i			1.38945i	0.719277	+	0.694723i	$0.244473\pi$
$821$			39.8119i			1.38945i	−0.719277	+	0.694723i	$0.755527\pi$
$822$		−	16.8568i		−	0.587950i
$823$		−	8.95414i		−	0.312122i	−0.987747	−	0.156061i	$-0.950120\pi$
$823$		−	8.95414i		−	0.312122i	0.987747	−	0.156061i	$-0.0498796\pi$
$824$	34.6371			1.20664
$825$	8.20711			0.285735
$826$			25.4314i			0.884870i
$827$			35.7210i			1.24214i	0.783755	+	0.621070i	$0.213302\pi$
$827$			35.7210i			1.24214i	−0.783755	+	0.621070i	$0.786698\pi$
$828$			0.156325i			0.00543268i
$829$	16.8218			0.584245			0.292122	−	0.956381i	$-0.405639\pi$
$829$	16.8218			0.584245			0.292122	+	0.956381i	$0.405639\pi$
$830$		−	3.78892i		−	0.131515i
$831$	−23.3357			−0.809506
$832$	13.5515			0.469813
$833$	3.67513	+	1.86907i	0.127336	+	0.0647593i
$834$	35.9756			1.24573
$835$	11.5745			0.400553
$836$			3.89446i			0.134693i
$837$	−1.28726			−0.0444941
$838$		−	34.4142i		−	1.18882i
$839$		−	50.2541i		−	1.73496i	−0.497468	−	0.867482i	$-0.665737\pi$
$839$		−	50.2541i		−	1.73496i	0.497468	−	0.867482i	$-0.334263\pi$
$840$		−	3.61213i		−	0.124630i
$841$	28.3503			0.977595
$842$	3.55500			0.122513
$843$			19.7381i			0.679817i
$844$		−	93.1265i		−	3.20555i
$845$			5.24472i			0.180424i
$846$	9.89446			0.340179
$847$			7.73813i			0.265885i
$848$	−20.3127			−0.697539
$849$	10.4264			0.357834
$850$	−41.4372	−	21.0738i	−1.42129	−	0.722826i
$851$	0.294552			0.0100971
$852$	−56.9135			−1.94982
$853$			4.10905i			0.140691i	0.997523	+	0.0703456i	$0.0224102\pi$
$853$			4.10905i			0.140691i	−0.997523	+	0.0703456i	$0.977590\pi$
$854$	36.1319			1.23641
$855$			0.350262i			0.0119787i
$856$		−	92.8989i		−	3.17522i
$857$		−	27.9854i		−	0.955963i	−0.878370	−	0.477982i	$-0.841369\pi$
$857$		−	27.9854i		−	0.955963i	0.878370	−	0.477982i	$-0.158631\pi$
$858$	−10.2496			−0.349917
$859$	30.2981			1.03376			0.516878	−	0.856059i	$-0.327094\pi$
$859$	30.2981			1.03376			0.516878	+	0.856059i	$0.327094\pi$
$860$			10.0303i			0.342031i
$861$		−	0.518806i		−	0.0176809i
$862$			97.5750i			3.32342i
$863$	−55.9937			−1.90605			−0.953023	−	0.302897i	$-0.902046\pi$
$863$	−55.9937			−1.90605			−0.953023	+	0.302897i	$0.902046\pi$
$864$			1.61213i			0.0548457i
$865$	−0.329794			−0.0112133
$866$	61.2384			2.08096
$867$	13.7381	−	10.0132i	0.466572	−	0.340065i
$868$	−5.35026			−0.181600
$869$	9.02142			0.306031
$870$		−	1.35026i		−	0.0457782i
$871$	−22.4591			−0.760998
$872$			29.7988i			1.00911i
$873$		−	13.3503i		−	0.451838i
$874$		−	0.0484156i		−	0.00163768i
$875$	6.44358			0.217833
$876$	50.0870			1.69228
$877$			3.31757i			0.112027i	0.998430	+	0.0560133i	$0.0178389\pi$
$877$			3.31757i			0.112027i	−0.998430	+	0.0560133i	$0.982161\pi$
$878$		−	66.3693i		−	2.23986i
$879$			12.7250i			0.429202i
$880$	6.05079			0.203972
$881$		−	51.0640i		−	1.72039i	−0.509967	−	0.860194i	$-0.670342\pi$
$881$		−	51.0640i		−	1.72039i	0.509967	−	0.860194i	$-0.329658\pi$
$882$	2.48119			0.0835462
$883$	−24.0581			−0.809619			−0.404809	−	0.914401i	$-0.632662\pi$
$883$	−24.0581			−0.809619			−0.404809	+	0.914401i	$0.632662\pi$
$884$	34.9380	+	17.7685i	1.17509	+	0.597618i
$885$	−6.91985			−0.232608
$886$	51.9062			1.74382
$887$			37.8446i			1.27070i	0.772225	+	0.635349i	$0.219144\pi$
$887$			37.8446i			1.27070i	−0.772225	+	0.635349i	$0.780856\pi$
$888$	41.9003			1.40608
$889$			4.45580i			0.149443i
$890$			22.2374i			0.745400i
$891$			1.80606i			0.0605054i
$892$	−38.9683			−1.30475
$893$	−2.06888			−0.0692326
$894$			54.3390i			1.81737i
$895$			2.30280i			0.0769742i
$896$		−	17.9248i		−	0.598825i
$897$	0.0860269			0.00287236
$898$		−	48.0263i		−	1.60266i
$899$	−1.03761			−0.0346063
$900$	−18.8872			−0.629572
$901$	15.0435	+	7.65069i	0.501171	+	0.254882i
$902$	2.32487			0.0774097
$903$	−3.57452			−0.118952
$904$		−	90.9859i		−	3.02615i
$905$	3.47627			0.115555
$906$		−	46.6615i		−	1.55022i
$907$			12.1114i			0.402153i	0.979576	+	0.201077i	$0.0644440\pi$
$907$			12.1114i			0.402153i	−0.979576	+	0.201077i	$0.935556\pi$
$908$		−	26.9927i		−	0.895784i
$909$	−9.47390			−0.314229
$910$	−3.83146			−0.127012
$911$			7.69464i			0.254935i	0.991843	+	0.127467i	$0.0406848\pi$
$911$			7.69464i			0.254935i	−0.991843	+	0.127467i	$0.959315\pi$
$912$		−	2.57452i		−	0.0852507i
$913$			4.08507i			0.135196i
$914$	−78.2311			−2.58765
$915$			9.83146i			0.325018i
$916$	31.7645			1.04953
$917$	14.4133			0.475968
$918$	4.63752	−	9.11871i	0.153061	−	0.300962i
$919$	8.54675			0.281931			0.140966	−	0.990014i	$-0.454979\pi$
$919$	8.54675			0.281931			0.140966	+	0.990014i	$0.454979\pi$
$920$	−0.135857			−0.00447908
$921$		−	22.6761i		−	0.747202i
$922$	46.6458			1.53620
$923$			31.3199i			1.03091i
$924$			7.50659i			0.246949i
$925$			35.5877i			1.17012i
$926$	−14.7513			−0.484758
$927$	−6.47390			−0.212631
$928$			1.29948i			0.0426574i
$929$			10.1671i			0.333573i	0.985993	+	0.166786i	$0.0533390\pi$
$929$			10.1671i			0.333573i	−0.985993	+	0.166786i	$0.946661\pi$
$930$		−	2.15633i		−	0.0707087i
$931$	−0.518806			−0.0170032
$932$			52.3792i			1.71574i
$933$	26.0508			0.852864
$934$	11.2243			0.367269
$935$	−4.48119	−	2.27901i	−0.146551	−	0.0745315i
$936$	12.2374			0.399993
$937$	−43.6834			−1.42707			−0.713537	−	0.700618i	$-0.752908\pi$
$937$	−43.6834			−1.42707			−0.713537	+	0.700618i	$0.752908\pi$
$938$			24.3634i			0.795494i
$939$	18.3512			0.598869
$940$			11.1900i			0.364976i
$941$		−	51.2262i		−	1.66993i	−0.550307	−	0.834963i	$-0.685489\pi$
$941$		−	51.2262i		−	1.66993i	0.550307	−	0.834963i	$-0.314511\pi$
$942$		−	1.87636i		−	0.0611352i
$943$	−0.0195130			−0.000635431
$944$	50.8627			1.65544
$945$			0.675131i			0.0219620i
$946$		−	16.0181i		−	0.520793i
$947$		−	30.0713i		−	0.977184i	−0.872512	−	0.488592i	$-0.837511\pi$
$947$		−	30.0713i		−	0.977184i	0.872512	−	0.488592i	$-0.162489\pi$
$948$	−20.7612			−0.674291
$949$		−	27.5633i		−	0.894741i
$950$	5.84955			0.189785
$951$	−13.1998			−0.428033
$952$	10.0000	−	19.6629i	0.324102	−	0.637279i
$953$	3.30582			0.107086			0.0535429	−	0.998566i	$-0.482949\pi$
$953$	3.30582			0.107086			0.0535429	+	0.998566i	$0.482949\pi$
$954$	10.1563			0.328823
$955$			0.523730i			0.0169475i
$956$	65.1754			2.10792
$957$			1.45580i			0.0470594i
$958$			4.82416i			0.155862i
$959$			6.79384i			0.219385i
$960$	4.00000			0.129099
$961$	29.3430			0.946547
$962$		−	44.4445i		−	1.43295i
$963$			17.3634i			0.559529i
$964$		−	9.29948i		−	0.299516i
$965$	17.2120			0.554075
$966$		−	0.0933212i		−	0.00300256i
$967$	−22.2955			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$967$	−22.2955			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$968$	41.4010			1.33068
$969$	−0.969683	+	1.90668i	−0.0311507	+	0.0612513i
$970$	22.3634			0.718047
$971$	37.1754			1.19301			0.596507	−	0.802608i	$-0.296555\pi$
$971$	37.1754			1.19301			0.596507	+	0.802608i	$0.296555\pi$
$972$		−	4.15633i		−	0.133314i
$973$	−14.4993			−0.464826
$974$			78.8383i			2.52614i
$975$			10.3938i			0.332866i
$976$		−	72.2638i		−	2.31311i
$977$	5.39914			0.172734			0.0863668	−	0.996263i	$-0.472474\pi$
$977$	5.39914			0.172734			0.0863668	+	0.996263i	$0.472474\pi$
$978$	−22.3634			−0.715104
$979$		−	23.9756i		−	0.766262i
$980$			2.80606i			0.0896364i
$981$		−	5.56959i		−	0.177823i
$982$	47.3620			1.51138
$983$			8.25694i			0.263356i	0.991293	+	0.131678i	$0.0420364\pi$
$983$			8.25694i			0.263356i	−0.991293	+	0.131678i	$0.957964\pi$
$984$	−2.77575			−0.0884876
$985$	5.35519			0.170630
$986$	3.73813	−	7.35026i	0.119046	−	0.234080i
$987$	−3.98778			−0.126932
$988$	−4.93207			−0.156910
$989$			0.134443i			0.00427502i
$990$	−3.02539			−0.0961533
$991$		−	60.8627i		−	1.93337i	−0.255972	−	0.966684i	$-0.582396\pi$
$991$		−	60.8627i		−	1.93337i	0.255972	−	0.966684i	$-0.417604\pi$
$992$			2.07522i			0.0658884i
$993$		−	3.30677i		−	0.104937i
$994$	33.9756			1.07764
$995$	2.16854			0.0687475
$996$		−	9.40105i		−	0.297884i
$997$		−	56.1768i		−	1.77914i	−0.456802	−	0.889568i	$-0.651005\pi$
$997$		−	56.1768i		−	1.77914i	0.456802	−	0.889568i	$-0.348995\pi$
$998$			19.7078i			0.623840i
$999$	−7.83146			−0.247776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.f.a.169.5	✓	6
3.2	odd	2		1071.2.f.a.883.2		6
17.4	even	4		6069.2.a.k.1.1		3
17.13	even	4		6069.2.a.m.1.1		3
17.16	even	2	inner	357.2.f.a.169.6	yes	6
51.50	odd	2		1071.2.f.a.883.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.f.a.169.5	✓	6	1.1	even	1	trivial
357.2.f.a.169.6	yes	6	17.16	even	2	inner
1071.2.f.a.883.1		6	51.50	odd	2
1071.2.f.a.883.2		6	3.2	odd	2
6069.2.a.k.1.1		3	17.4	even	4
6069.2.a.m.1.1		3	17.13	even	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.48119 q^{2} -1.00000i q^{3} +4.15633 q^{4} -0.675131i q^{5} -2.48119i q^{6} +1.00000i q^{7} +5.35026 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.48119 q^{2} -1.00000i q^{3} +4.15633 q^{4} -0.675131i q^{5} -2.48119i q^{6} +1.00000i q^{7} +5.35026 q^{8} -1.00000 q^{9} -1.67513i q^{10} +1.80606i q^{11} -4.15633i q^{12} -2.28726 q^{13} +2.48119i q^{14} -0.675131 q^{15} +4.96239 q^{16} +(-3.67513 - 1.86907i) q^{17} -2.48119 q^{18} +0.518806 q^{19} -2.80606i q^{20} +1.00000 q^{21} +4.48119i q^{22} -0.0376114i q^{23} -5.35026i q^{24} +4.54420 q^{25} -5.67513 q^{26} +1.00000i q^{27} +4.15633i q^{28} +0.806063i q^{29} -1.67513 q^{30} +1.28726i q^{31} +1.61213 q^{32} +1.80606 q^{33} +(-9.11871 - 4.63752i) q^{34} +0.675131 q^{35} -4.15633 q^{36} +7.83146i q^{37} +1.28726 q^{38} +2.28726i q^{39} -3.61213i q^{40} -0.518806i q^{41} +2.48119 q^{42} -3.57452 q^{43} +7.50659i q^{44} +0.675131i q^{45} -0.0933212i q^{46} -3.98778 q^{47} -4.96239i q^{48} -1.00000 q^{49} +11.2750 q^{50} +(-1.86907 + 3.67513i) q^{51} -9.50659 q^{52} -4.09332 q^{53} +2.48119i q^{54} +1.21933 q^{55} +5.35026i q^{56} -0.518806i q^{57} +2.00000i q^{58} +10.2496 q^{59} -2.80606 q^{60} -14.5623i q^{61} +3.19394i q^{62} -1.00000i q^{63} -5.92478 q^{64} +1.54420i q^{65} +4.48119 q^{66} +9.81924 q^{67} +(-15.2750 - 7.76845i) q^{68} -0.0376114 q^{69} +1.67513 q^{70} -13.6932i q^{71} -5.35026 q^{72} +12.0508i q^{73} +19.4314i q^{74} -4.54420i q^{75} +2.15633 q^{76} -1.80606 q^{77} +5.67513i q^{78} -4.99508i q^{79} -3.35026i q^{80} +1.00000 q^{81} -1.28726i q^{82} +2.26187 q^{83} +4.15633 q^{84} +(-1.26187 + 2.48119i) q^{85} -8.86907 q^{86} +0.806063 q^{87} +9.66291i q^{88} -13.2750 q^{89} +1.67513i q^{90} -2.28726i q^{91} -0.156325i q^{92} +1.28726 q^{93} -9.89446 q^{94} -0.350262i q^{95} -1.61213i q^{96} +13.3503i q^{97} -2.48119 q^{98} -1.80606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9	\( 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9} - 2 q^{13} + 6 q^{15} + 8 q^{16} - 12 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{21} + 8 q^{25} - 24 q^{26} + 8 q^{32} + 10 q^{33} - 12 q^{34} - 6 q^{35} - 4 q^{36} - 4 q^{38} + 4 q^{42} + 2 q^{43} + 28 q^{47} - 6 q^{49} + 4 q^{50} - 2 q^{51} - 16 q^{52} - 12 q^{53} - 22 q^{55} + 28 q^{59} - 16 q^{60} + 8 q^{64} + 16 q^{66} - 24 q^{67} - 28 q^{68} - 22 q^{69} - 12 q^{72} - 8 q^{76} - 10 q^{77} + 6 q^{81} + 32 q^{83} + 4 q^{84} - 26 q^{85} - 44 q^{86} + 4 q^{87} - 16 q^{89} - 4 q^{93} - 20 q^{94} - 4 q^{98}+O(q^{100}) \) 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9 - 2 * q^13 + 6 * q^15 + 8 * q^16 - 12 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^21 + 8 * q^25 - 24 * q^26 + 8 * q^32 + 10 * q^33 - 12 * q^34 - 6 * q^35 - 4 * q^36 - 4 * q^38 + 4 * q^42 + 2 * q^43 + 28 * q^47 - 6 * q^49 + 4 * q^50 - 2 * q^51 - 16 * q^52 - 12 * q^53 - 22 * q^55 + 28 * q^59 - 16 * q^60 + 8 * q^64 + 16 * q^66 - 24 * q^67 - 28 * q^68 - 22 * q^69 - 12 * q^72 - 8 * q^76 - 10 * q^77 + 6 * q^81 + 32 * q^83 + 4 * q^84 - 26 * q^85 - 44 * q^86 + 4 * q^87 - 16 * q^89 - 4 * q^93 - 20 * q^94 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more