LMFDB - Embedded newform 4020.2.q.k.3781.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.5
Root			$1.24942 + 2.16407i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.k.841.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 + 1.86725i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 + 1.86725i) q^{7} +1.00000 q^{9} +(2.31297 + 4.00618i) q^{11} +(2.99885 - 5.19416i) q^{13} -1.00000 q^{15} +(3.06661 - 5.31152i) q^{17} +(2.62213 - 4.54165i) q^{19} +(-1.07806 - 1.86725i) q^{21} +(-0.436687 + 0.756365i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.60303 - 4.50859i) q^{29} +(1.56927 + 2.71805i) q^{31} +(-2.31297 - 4.00618i) q^{33} +(1.07806 + 1.86725i) q^{35} +(1.89501 - 3.28225i) q^{37} +(-2.99885 + 5.19416i) q^{39} +(-4.79372 - 8.30297i) q^{41} -5.46495 q^{43} +1.00000 q^{45} +(-3.90018 - 6.75530i) q^{47} +(1.17558 - 2.03617i) q^{49} +(-3.06661 + 5.31152i) q^{51} -6.77213 q^{53} +(2.31297 + 4.00618i) q^{55} +(-2.62213 + 4.54165i) q^{57} +5.61145 q^{59} +(-1.75300 + 3.03629i) q^{61} +(1.07806 + 1.86725i) q^{63} +(2.99885 - 5.19416i) q^{65} +(3.47231 + 7.41236i) q^{67} +(0.436687 - 0.756365i) q^{69} +(2.58722 + 4.48120i) q^{71} +(-0.841448 + 1.45743i) q^{73} -1.00000 q^{75} +(-4.98703 + 8.63778i) q^{77} +(-2.70536 - 4.68582i) q^{79} +1.00000 q^{81} +(7.83527 - 13.5711i) q^{83} +(3.06661 - 5.31152i) q^{85} +(2.60303 + 4.50859i) q^{87} -7.97892 q^{89} +12.9317 q^{91} +(-1.56927 - 2.71805i) q^{93} +(2.62213 - 4.54165i) q^{95} +(5.01466 - 8.68565i) q^{97} +(2.31297 + 4.00618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.07806	+	1.86725i	0.407468	+	0.705755i	0.994605	−	0.103732i	$-0.0330786\pi$
$7$	1.07806	+	1.86725i	0.407468	+	0.705755i	−0.587138	+	0.809487i	$0.699745\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.31297	+	4.00618i	0.697386	+	1.20791i	0.969370	+	0.245606i	$0.0789869\pi$
$11$	2.31297	+	4.00618i	0.697386	+	1.20791i	−0.271984	+	0.962302i	$0.587680\pi$
$12$		0			0
$13$	2.99885	−	5.19416i	0.831731	−	1.44060i	−0.0649329	−	0.997890i	$-0.520683\pi$
$13$	2.99885	−	5.19416i	0.831731	−	1.44060i	0.896664	−	0.442711i	$-0.145983\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.06661	−	5.31152i	0.743761	−	1.28823i	−0.207010	−	0.978339i	$-0.566373\pi$
$17$	3.06661	−	5.31152i	0.743761	−	1.28823i	0.950771	−	0.309893i	$-0.100293\pi$
$18$		0			0
$19$	2.62213	−	4.54165i	0.601557	−	1.04193i	−0.391029	−	0.920379i	$-0.627881\pi$
$19$	2.62213	−	4.54165i	0.601557	−	1.04193i	0.992585	−	0.121549i	$-0.0387860\pi$
$20$		0			0
$21$	−1.07806	−	1.86725i	−0.235252	−	0.407468i
$22$		0			0
$23$	−0.436687	+	0.756365i	−0.0910556	+	0.157713i	−0.907956	−	0.419066i	$-0.862357\pi$
$23$	−0.436687	+	0.756365i	−0.0910556	+	0.157713i	0.816900	+	0.576779i	$0.195691\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.60303	−	4.50859i	−0.483371	−	0.837223i	0.516447	−	0.856319i	$-0.327254\pi$
$29$	−2.60303	−	4.50859i	−0.483371	−	0.837223i	−0.999818	+	0.0190961i	$0.993921\pi$
$30$		0			0
$31$	1.56927	+	2.71805i	0.281849	+	0.488176i	0.971840	−	0.235641i	$-0.0757190\pi$
$31$	1.56927	+	2.71805i	0.281849	+	0.488176i	−0.689991	+	0.723818i	$0.742386\pi$
$32$		0			0
$33$	−2.31297	−	4.00618i	−0.402636	−	0.697386i
$34$		0			0
$35$	1.07806	+	1.86725i	0.182225	+	0.315623i
$36$		0			0
$37$	1.89501	−	3.28225i	0.311538	−	0.539599i	−0.667158	−	0.744917i	$-0.732489\pi$
$37$	1.89501	−	3.28225i	0.311538	−	0.539599i	0.978695	+	0.205317i	$0.0658226\pi$
$38$		0			0
$39$	−2.99885	+	5.19416i	−0.480200	+	0.831731i
$40$		0			0
$41$	−4.79372	−	8.30297i	−0.748654	−	1.29671i	−0.948468	−	0.316872i	$-0.897367\pi$
$41$	−4.79372	−	8.30297i	−0.748654	−	1.29671i	0.199815	−	0.979834i	$-0.435966\pi$
$42$		0			0
$43$	−5.46495			−0.833396			−0.416698	−	0.909045i	$-0.636813\pi$
$43$	−5.46495			−0.833396			−0.416698	+	0.909045i	$0.636813\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−3.90018	−	6.75530i	−0.568899	−	0.985362i	−0.996675	−	0.0814776i	$-0.974036\pi$
$47$	−3.90018	−	6.75530i	−0.568899	−	0.985362i	0.427776	−	0.903885i	$-0.359297\pi$
$48$		0			0
$49$	1.17558	−	2.03617i	0.167940	−	0.290881i
$50$		0			0
$51$	−3.06661	+	5.31152i	−0.429411	+	0.743761i
$52$		0			0
$53$	−6.77213			−0.930224			−0.465112	−	0.885252i	$-0.653986\pi$
$53$	−6.77213			−0.930224			−0.465112	+	0.885252i	$0.653986\pi$
$54$		0			0
$55$	2.31297	+	4.00618i	0.311880	+	0.540193i
$56$		0			0
$57$	−2.62213	+	4.54165i	−0.347309	+	0.601557i
$58$		0			0
$59$	5.61145			0.730549			0.365274	−	0.930900i	$-0.380975\pi$
$59$	5.61145			0.730549			0.365274	+	0.930900i	$0.380975\pi$
$60$		0			0
$61$	−1.75300	+	3.03629i	−0.224449	+	0.388757i	−0.956154	−	0.292864i	$-0.905392\pi$
$61$	−1.75300	+	3.03629i	−0.224449	+	0.388757i	0.731705	+	0.681622i	$0.238725\pi$
$62$		0			0
$63$	1.07806	+	1.86725i	0.135823	+	0.235252i
$64$		0			0
$65$	2.99885	−	5.19416i	0.371962	−	0.644256i
$66$		0			0
$67$	3.47231	+	7.41236i	0.424210	+	0.905564i
$67$	3.47231	+	7.41236i	0.424210	+	0.905564i
$68$		0			0
$69$	0.436687	−	0.756365i	0.0525710	−	0.0910556i
$70$		0			0
$71$	2.58722	+	4.48120i	0.307047	+	0.531820i	0.977715	−	0.209937i	$-0.0673259\pi$
$71$	2.58722	+	4.48120i	0.307047	+	0.531820i	−0.670668	+	0.741757i	$0.733993\pi$
$72$		0			0
$73$	−0.841448	+	1.45743i	−0.0984840	+	0.170579i	−0.911057	−	0.412280i	$-0.864733\pi$
$73$	−0.841448	+	1.45743i	−0.0984840	+	0.170579i	0.812573	+	0.582859i	$0.198066\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−4.98703	+	8.63778i	−0.568324	+	0.984367i
$78$		0			0
$79$	−2.70536	−	4.68582i	−0.304377	−	0.527196i	0.672745	−	0.739874i	$-0.265115\pi$
$79$	−2.70536	−	4.68582i	−0.304377	−	0.527196i	−0.977122	+	0.212678i	$0.931782\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	7.83527	−	13.5711i	0.860033	−	1.48962i	−0.0118638	−	0.999930i	$-0.503776\pi$
$83$	7.83527	−	13.5711i	0.860033	−	1.48962i	0.871896	−	0.489690i	$-0.162890\pi$
$84$		0			0
$85$	3.06661	−	5.31152i	0.332620	−	0.576115i
$86$		0			0
$87$	2.60303	+	4.50859i	0.279074	+	0.483371i
$88$		0			0
$89$	−7.97892			−0.845764			−0.422882	−	0.906185i	$-0.638982\pi$
$89$	−7.97892			−0.845764			−0.422882	+	0.906185i	$0.638982\pi$
$90$		0			0
$91$	12.9317			1.35561
$92$		0			0
$93$	−1.56927	−	2.71805i	−0.162725	−	0.281849i
$94$		0			0
$95$	2.62213	−	4.54165i	0.269024	−	0.465964i
$96$		0			0
$97$	5.01466	−	8.68565i	0.509162	−	0.881894i	−0.490782	−	0.871282i	$-0.663289\pi$
$97$	5.01466	−	8.68565i	0.509162	−	0.881894i	0.999944	−	0.0106116i	$-0.00337785\pi$
$98$		0			0
$99$	2.31297	+	4.00618i	0.232462	+	0.402636i
$100$		0			0
$101$	9.06051	+	15.6933i	0.901555	+	1.56154i	0.825476	+	0.564436i	$0.190906\pi$
$101$	9.06051	+	15.6933i	0.901555	+	1.56154i	0.0760781	+	0.997102i	$0.475760\pi$
$102$		0			0
$103$	−4.74446	−	8.21765i	−0.467485	−	0.809709i	0.531824	−	0.846855i	$-0.321507\pi$
$103$	−4.74446	−	8.21765i	−0.467485	−	0.809709i	−0.999310	+	0.0371461i	$0.988173\pi$
$104$		0			0
$105$	−1.07806	−	1.86725i	−0.105208	−	0.182225i
$106$		0			0
$107$	−15.3498			−1.48392			−0.741960	−	0.670445i	$-0.766103\pi$
$107$	−15.3498			−1.48392			−0.741960	+	0.670445i	$0.766103\pi$
$108$		0			0
$109$	−6.26073			−0.599669			−0.299834	−	0.953991i	$-0.596931\pi$
$109$	−6.26073			−0.599669			−0.299834	+	0.953991i	$0.596931\pi$
$110$		0			0
$111$	−1.89501	+	3.28225i	−0.179866	+	0.311538i
$112$		0			0
$113$	6.08157	+	10.5336i	0.572106	+	0.990917i	0.996349	+	0.0853686i	$0.0272068\pi$
$113$	6.08157	+	10.5336i	0.572106	+	0.990917i	−0.424243	+	0.905548i	$0.639460\pi$
$114$		0			0
$115$	−0.436687	+	0.756365i	−0.0407213	+	0.0705314i
$116$		0			0
$117$	2.99885	−	5.19416i	0.277244	−	0.480200i
$118$		0			0
$119$	13.2239			1.21223
$120$		0			0
$121$	−5.19963	+	9.00603i	−0.472694	+	0.818730i
$122$		0			0
$123$	4.79372	+	8.30297i	0.432235	+	0.748654i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.63481	+	11.4918i	0.588744	+	1.01973i	0.994397	+	0.105707i	$0.0337107\pi$
$127$	6.63481	+	11.4918i	0.588744	+	1.01973i	−0.405653	+	0.914027i	$0.632956\pi$
$128$		0			0
$129$	5.46495			0.481162
$130$		0			0
$131$	−0.697341			−0.0609270			−0.0304635	−	0.999536i	$-0.509698\pi$
$131$	−0.697341			−0.0609270			−0.0304635	+	0.999536i	$0.509698\pi$
$132$		0			0
$133$	11.3072			0.980460
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	11.5162			0.983892			0.491946	−	0.870626i	$-0.336286\pi$
$137$	11.5162			0.983892			0.491946	+	0.870626i	$0.336286\pi$
$138$		0			0
$139$	−2.18220			−0.185092			−0.0925460	−	0.995708i	$-0.529501\pi$
$139$	−2.18220			−0.185092			−0.0925460	+	0.995708i	$0.529501\pi$
$140$		0			0
$141$	3.90018	+	6.75530i	0.328454	+	0.568899i
$142$		0			0
$143$	27.7450			2.32015
$144$		0			0
$145$	−2.60303	−	4.50859i	−0.216170	−	0.374418i
$146$		0			0
$147$	−1.17558	+	2.03617i	−0.0969603	+	0.167940i
$148$		0			0
$149$	−8.90881			−0.729838			−0.364919	−	0.931039i	$-0.618903\pi$
$149$	−8.90881			−0.729838			−0.364919	+	0.931039i	$0.618903\pi$
$150$		0			0
$151$	−0.0253744	+	0.0439498i	−0.00206494	+	0.00357659i	−0.867056	−	0.498211i	$-0.833991\pi$
$151$	−0.0253744	+	0.0439498i	−0.00206494	+	0.00357659i	0.864991	+	0.501787i	$0.167324\pi$
$152$		0			0
$153$	3.06661	−	5.31152i	0.247920	−	0.429411i
$154$		0			0
$155$	1.56927	+	2.71805i	0.126047	+	0.218319i
$156$		0			0
$157$	8.62937	−	14.9465i	0.688698	−	1.19286i	−0.283561	−	0.958954i	$-0.591516\pi$
$157$	8.62937	−	14.9465i	0.688698	−	1.19286i	0.972259	−	0.233906i	$-0.0751509\pi$
$158$		0			0
$159$	6.77213			0.537065
$160$		0			0
$161$	−1.88310			−0.148409
$162$		0			0
$163$	−9.40567	−	16.2911i	−0.736709	−	1.27602i	−0.953969	−	0.299904i	$-0.903045\pi$
$163$	−9.40567	−	16.2911i	−0.736709	−	1.27602i	0.217261	−	0.976114i	$-0.430288\pi$
$164$		0			0
$165$	−2.31297	−	4.00618i	−0.180064	−	0.311880i
$166$		0			0
$167$	−1.29815	−	2.24847i	−0.100454	−	0.173991i	0.811418	−	0.584467i	$-0.198696\pi$
$167$	−1.29815	−	2.24847i	−0.100454	−	0.173991i	−0.911872	+	0.410475i	$0.865363\pi$
$168$		0			0
$169$	−11.4862	−	19.8947i	−0.883554	−	1.53036i
$170$		0			0
$171$	2.62213	−	4.54165i	0.200519	−	0.347309i
$172$		0			0
$173$	−9.80640	+	16.9852i	−0.745567	+	1.29136i	0.204362	+	0.978895i	$0.434488\pi$
$173$	−9.80640	+	16.9852i	−0.745567	+	1.29136i	−0.949929	+	0.312465i	$0.898845\pi$
$174$		0			0
$175$	1.07806	+	1.86725i	0.0814935	+	0.141151i
$176$		0			0
$177$	−5.61145			−0.421782
$178$		0			0
$179$	−8.75619			−0.654469			−0.327234	−	0.944943i	$-0.606117\pi$
$179$	−8.75619			−0.654469			−0.327234	+	0.944943i	$0.606117\pi$
$180$		0			0
$181$	2.68166	+	4.64477i	0.199326	+	0.345243i	0.948310	−	0.317345i	$-0.102791\pi$
$181$	2.68166	+	4.64477i	0.199326	+	0.345243i	−0.748984	+	0.662588i	$0.769458\pi$
$182$		0			0
$183$	1.75300	−	3.03629i	0.129586	−	0.224449i
$184$		0			0
$185$	1.89501	−	3.28225i	0.139324	−	0.241316i
$186$		0			0
$187$	28.3718			2.07475
$188$		0			0
$189$	−1.07806	−	1.86725i	−0.0784172	−	0.135823i
$190$		0			0
$191$	−7.83945	+	13.5783i	−0.567242	+	0.982493i	0.429595	+	0.903022i	$0.358656\pi$
$191$	−7.83945	+	13.5783i	−0.567242	+	0.982493i	−0.996837	+	0.0794708i	$0.974677\pi$
$192$		0			0
$193$	3.33316			0.239926			0.119963	−	0.992778i	$-0.461722\pi$
$193$	3.33316			0.239926			0.119963	+	0.992778i	$0.461722\pi$
$194$		0			0
$195$	−2.99885	+	5.19416i	−0.214752	+	0.371962i
$196$		0			0
$197$	−10.9023	−	18.8833i	−0.776756	−	1.34538i	−0.933802	−	0.357789i	$-0.883531\pi$
$197$	−10.9023	−	18.8833i	−0.776756	−	1.34538i	0.157047	−	0.987591i	$-0.449803\pi$
$198$		0			0
$199$	12.6316	−	21.8786i	0.895430	−	1.55093i	0.0621595	−	0.998066i	$-0.480201\pi$
$199$	12.6316	−	21.8786i	0.895430	−	1.55093i	0.833271	−	0.552865i	$-0.186465\pi$
$200$		0			0
$201$	−3.47231	−	7.41236i	−0.244918	−	0.522828i
$202$		0			0
$203$	5.61244	−	9.72104i	0.393916	−	0.682283i
$204$		0			0
$205$	−4.79372	−	8.30297i	−0.334808	−	0.579905i
$206$		0			0
$207$	−0.436687	+	0.756365i	−0.0303519	+	0.0525710i
$208$		0			0
$209$	24.2596			1.67807
$210$		0			0
$211$	2.44395	−	4.23305i	0.168249	−	0.291415i	−0.769556	−	0.638580i	$-0.779522\pi$
$211$	2.44395	−	4.23305i	0.168249	−	0.291415i	0.937804	+	0.347165i	$0.112856\pi$
$212$		0			0
$213$	−2.58722	−	4.48120i	−0.177273	−	0.307047i
$214$		0			0
$215$	−5.46495			−0.372706
$216$		0			0
$217$	−3.38352	+	5.86043i	−0.229689	+	0.397832i
$218$		0			0
$219$	0.841448	−	1.45743i	0.0568598	−	0.0984840i
$220$		0			0
$221$	−18.3926	−	31.8569i	−1.23722	−	2.14293i
$222$		0			0
$223$	11.1873			0.749156			0.374578	−	0.927195i	$-0.377788\pi$
$223$	11.1873			0.749156			0.374578	+	0.927195i	$0.377788\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.85934	−	11.8807i	−0.455271	−	0.788552i	0.543433	−	0.839452i	$-0.317124\pi$
$227$	−6.85934	−	11.8807i	−0.455271	−	0.788552i	−0.998704	+	0.0509006i	$0.983791\pi$
$228$		0			0
$229$	−2.91018	+	5.04057i	−0.192310	+	0.333090i	−0.946015	−	0.324122i	$-0.894931\pi$
$229$	−2.91018	+	5.04057i	−0.192310	+	0.333090i	0.753705	+	0.657212i	$0.228265\pi$
$230$		0			0
$231$	4.98703	−	8.63778i	0.328122	−	0.568324i
$232$		0			0
$233$	3.33684	+	5.77957i	0.218603	+	0.378632i	0.954381	−	0.298591i	$-0.0965166\pi$
$233$	3.33684	+	5.77957i	0.218603	+	0.378632i	−0.735778	+	0.677223i	$0.763183\pi$
$234$		0			0
$235$	−3.90018	−	6.75530i	−0.254419	−	0.440667i
$236$		0			0
$237$	2.70536	+	4.68582i	0.175732	+	0.304377i
$238$		0			0
$239$	9.78623	+	16.9502i	0.633019	+	1.09642i	0.986931	+	0.161142i	$0.0515177\pi$
$239$	9.78623	+	16.9502i	0.633019	+	1.09642i	−0.353913	+	0.935278i	$0.615149\pi$
$240$		0			0
$241$	−3.36061			−0.216476			−0.108238	−	0.994125i	$-0.534521\pi$
$241$	−3.36061			−0.216476			−0.108238	+	0.994125i	$0.534521\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	1.17558	−	2.03617i	0.0751051	−	0.130086i
$246$		0			0
$247$	−15.7267	−	27.2395i	−1.00067	−	1.73321i
$248$		0			0
$249$	−7.83527	+	13.5711i	−0.496540	+	0.860033i
$250$		0			0
$251$	−4.15611	+	7.19859i	−0.262331	+	0.454371i	−0.966861	−	0.255303i	$-0.917825\pi$
$251$	−4.15611	+	7.19859i	−0.262331	+	0.454371i	0.704530	+	0.709675i	$0.251158\pi$
$252$		0			0
$253$	−4.04017			−0.254003
$254$		0			0
$255$	−3.06661	+	5.31152i	−0.192038	+	0.332620i
$256$		0			0
$257$	4.67272	+	8.09339i	0.291476	+	0.504852i	0.974159	−	0.225863i	$-0.0725203\pi$
$257$	4.67272	+	8.09339i	0.291476	+	0.504852i	−0.682683	+	0.730715i	$0.739187\pi$
$258$		0			0
$259$	8.17173			0.507766
$260$		0			0
$261$	−2.60303	−	4.50859i	−0.161124	−	0.279074i
$262$		0			0
$263$	19.2383			1.18629			0.593144	−	0.805097i	$-0.297887\pi$
$263$	19.2383			1.18629			0.593144	+	0.805097i	$0.297887\pi$
$264$		0			0
$265$	−6.77213			−0.416009
$266$		0			0
$267$	7.97892			0.488302
$268$		0			0
$269$	−7.46217			−0.454977			−0.227488	−	0.973781i	$-0.573051\pi$
$269$	−7.46217			−0.454977			−0.227488	+	0.973781i	$0.573051\pi$
$270$		0			0
$271$	−18.2280			−1.10727			−0.553637	−	0.832758i	$-0.686760\pi$
$271$	−18.2280			−1.10727			−0.553637	+	0.832758i	$0.686760\pi$
$272$		0			0
$273$	−12.9317			−0.782664
$274$		0			0
$275$	2.31297	+	4.00618i	0.139477	+	0.241582i
$276$		0			0
$277$	14.6155			0.878158			0.439079	−	0.898448i	$-0.355305\pi$
$277$	14.6155			0.878158			0.439079	+	0.898448i	$0.355305\pi$
$278$		0			0
$279$	1.56927	+	2.71805i	0.0939496	+	0.162725i
$280$		0			0
$281$	−4.47857	+	7.75710i	−0.267169	+	0.462750i	−0.968130	−	0.250450i	$-0.919421\pi$
$281$	−4.47857	+	7.75710i	−0.267169	+	0.462750i	0.700961	+	0.713200i	$0.252755\pi$
$282$		0			0
$283$	12.3644			0.734988			0.367494	−	0.930026i	$-0.380216\pi$
$283$	12.3644			0.734988			0.367494	+	0.930026i	$0.380216\pi$
$284$		0			0
$285$	−2.62213	+	4.54165i	−0.155321	+	0.269024i
$286$		0			0
$287$	10.3358	−	17.9022i	0.610104	−	1.05673i
$288$		0			0
$289$	−10.3081	−	17.8542i	−0.606362	−	1.05025i
$290$		0			0
$291$	−5.01466	+	8.68565i	−0.293965	+	0.509162i
$292$		0			0
$293$	29.0024			1.69434			0.847170	−	0.531322i	$-0.178304\pi$
$293$	29.0024			1.69434			0.847170	+	0.531322i	$0.178304\pi$
$294$		0			0
$295$	5.61145			0.326711
$296$		0			0
$297$	−2.31297	−	4.00618i	−0.134212	−	0.232462i
$298$		0			0
$299$	2.61912	+	4.53645i	0.151468	+	0.262350i
$300$		0			0
$301$	−5.89153	−	10.2044i	−0.339582	−	0.588173i
$302$		0			0
$303$	−9.06051	−	15.6933i	−0.520513	−	0.901555i
$304$		0			0
$305$	−1.75300	+	3.03629i	−0.100377	+	0.173858i
$306$		0			0
$307$	7.73403	−	13.3957i	0.441404	−	0.764535i	−0.556390	−	0.830922i	$-0.687814\pi$
$307$	7.73403	−	13.3957i	0.441404	−	0.764535i	0.997794	+	0.0663868i	$0.0211471\pi$
$308$		0			0
$309$	4.74446	+	8.21765i	0.269903	+	0.467485i
$310$		0			0
$311$	−18.5549			−1.05215			−0.526076	−	0.850437i	$-0.676337\pi$
$311$	−18.5549			−1.05215			−0.526076	+	0.850437i	$0.676337\pi$
$312$		0			0
$313$	34.3221			1.94000			0.970000	−	0.243106i	$-0.0781661\pi$
$313$	34.3221			1.94000			0.970000	+	0.243106i	$0.0781661\pi$
$314$		0			0
$315$	1.07806	+	1.86725i	0.0607417	+	0.105208i
$316$		0			0
$317$	−7.87420	+	13.6385i	−0.442259	+	0.766015i	−0.997857	−	0.0654359i	$-0.979156\pi$
$317$	−7.87420	+	13.6385i	−0.442259	+	0.766015i	0.555598	+	0.831451i	$0.312490\pi$
$318$		0			0
$319$	12.0415	−	20.8564i	0.674192	−	1.16774i
$320$		0			0
$321$	15.3498			0.856741
$322$		0			0
$323$	−16.0821	−	27.8549i	−0.894829	−	1.54989i
$324$		0			0
$325$	2.99885	−	5.19416i	0.166346	−	0.288120i
$326$		0			0
$327$	6.26073			0.346219
$328$		0			0
$329$	8.40924	−	14.5652i	0.463616	−	0.803007i
$330$		0			0
$331$	14.2382	+	24.6612i	0.782601	+	1.35550i	0.930422	+	0.366490i	$0.119441\pi$
$331$	14.2382	+	24.6612i	0.782601	+	1.35550i	−0.147821	+	0.989014i	$0.547226\pi$
$332$		0			0
$333$	1.89501	−	3.28225i	0.103846	−	0.179866i
$334$		0			0
$335$	3.47231	+	7.41236i	0.189712	+	0.404980i
$336$		0			0
$337$	−15.6567	+	27.1183i	−0.852877	+	1.47723i	0.0257228	+	0.999669i	$0.491811\pi$
$337$	−15.6567	+	27.1183i	−0.852877	+	1.47723i	−0.878600	+	0.477558i	$0.841522\pi$
$338$		0			0
$339$	−6.08157	−	10.5336i	−0.330306	−	0.572106i
$340$		0			0
$341$	−7.25933	+	12.5735i	−0.393115	+	0.680895i
$342$		0			0
$343$	20.1622			1.08866
$344$		0			0
$345$	0.436687	−	0.756365i	0.0235105	−	0.0407213i
$346$		0			0
$347$	5.21446	+	9.03171i	0.279927	+	0.484848i	0.971366	−	0.237587i	$-0.0763564\pi$
$347$	5.21446	+	9.03171i	0.279927	+	0.484848i	−0.691439	+	0.722434i	$0.743023\pi$
$348$		0			0
$349$	17.6385			0.944166			0.472083	−	0.881554i	$-0.343502\pi$
$349$	17.6385			0.944166			0.472083	+	0.881554i	$0.343502\pi$
$350$		0			0
$351$	−2.99885	+	5.19416i	−0.160067	+	0.277244i
$352$		0			0
$353$	3.33685	−	5.77959i	0.177603	−	0.307617i	−0.763456	−	0.645860i	$-0.776499\pi$
$353$	3.33685	−	5.77959i	0.177603	−	0.307617i	0.941059	+	0.338243i	$0.109832\pi$
$354$		0			0
$355$	2.58722	+	4.48120i	0.137315	+	0.237837i
$356$		0			0
$357$	−13.2239			−0.699884
$358$		0			0
$359$	35.0431			1.84950			0.924752	−	0.380570i	$-0.124272\pi$
$359$	35.0431			1.84950			0.924752	+	0.380570i	$0.124272\pi$
$360$		0			0
$361$	−4.25109	−	7.36310i	−0.223741	−	0.387531i
$362$		0			0
$363$	5.19963	−	9.00603i	0.272910	−	0.472694i
$364$		0			0
$365$	−0.841448	+	1.45743i	−0.0440434	+	0.0762854i
$366$		0			0
$367$	8.12012	+	14.0645i	0.423867	+	0.734159i	0.996314	−	0.0857828i	$-0.0273391\pi$
$367$	8.12012	+	14.0645i	0.423867	+	0.734159i	−0.572447	+	0.819942i	$0.694006\pi$
$368$		0			0
$369$	−4.79372	−	8.30297i	−0.249551	−	0.432235i
$370$		0			0
$371$	−7.30075	−	12.6453i	−0.379036	−	0.656510i
$372$		0			0
$373$	10.0833	+	17.4648i	0.522093	+	0.904291i	0.999670	+	0.0257011i	$0.00818181\pi$
$373$	10.0833	+	17.4648i	0.522093	+	0.904291i	−0.477577	+	0.878590i	$0.658485\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−31.2244			−1.60814
$378$		0			0
$379$	4.69017	−	8.12361i	0.240918	−	0.417282i	−0.720058	−	0.693914i	$-0.755885\pi$
$379$	4.69017	−	8.12361i	0.240918	−	0.417282i	0.960976	+	0.276632i	$0.0892182\pi$
$380$		0			0
$381$	−6.63481	−	11.4918i	−0.339911	−	0.588744i
$382$		0			0
$383$	−7.72118	+	13.3735i	−0.394534	+	0.683353i	−0.993042	−	0.117764i	$-0.962427\pi$
$383$	−7.72118	+	13.3735i	−0.394534	+	0.683353i	0.598508	+	0.801117i	$0.295761\pi$
$384$		0			0
$385$	−4.98703	+	8.63778i	−0.254162	+	0.440222i
$386$		0			0
$387$	−5.46495			−0.277799
$388$		0			0
$389$	−5.36740	+	9.29661i	−0.272138	+	0.471357i	−0.969409	−	0.245451i	$-0.921064\pi$
$389$	−5.36740	+	9.29661i	−0.272138	+	0.471357i	0.697271	+	0.716808i	$0.254397\pi$
$390$		0			0
$391$	2.67830	+	4.63894i	0.135447	+	0.234601i
$392$		0			0
$393$	0.697341			0.0351762
$394$		0			0
$395$	−2.70536	−	4.68582i	−0.136122	−	0.235769i
$396$		0			0
$397$	24.0836			1.20872			0.604360	−	0.796712i	$-0.293429\pi$
$397$	24.0836			1.20872			0.604360	+	0.796712i	$0.293429\pi$
$398$		0			0
$399$	−11.3072			−0.566069
$400$		0			0
$401$	−17.5499			−0.876402			−0.438201	−	0.898877i	$-0.644384\pi$
$401$	−17.5499			−0.876402			−0.438201	+	0.898877i	$0.644384\pi$
$402$		0			0
$403$	18.8240			0.937690
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	17.5324			0.869048
$408$		0			0
$409$	−4.55440	−	7.88845i	−0.225200	−	0.390059i	0.731179	−	0.682185i	$-0.238970\pi$
$409$	−4.55440	−	7.88845i	−0.225200	−	0.390059i	−0.956380	+	0.292127i	$0.905637\pi$
$410$		0			0
$411$	−11.5162			−0.568051
$412$		0			0
$413$	6.04947	+	10.4780i	0.297675	+	0.515588i
$414$		0			0
$415$	7.83527	−	13.5711i	0.384618	−	0.666178i
$416$		0			0
$417$	2.18220			0.106863
$418$		0			0
$419$	−11.1051	+	19.2346i	−0.542519	+	0.939670i	0.456240	+	0.889857i	$0.349196\pi$
$419$	−11.1051	+	19.2346i	−0.542519	+	0.939670i	−0.998759	+	0.0498132i	$0.984137\pi$
$420$		0			0
$421$	−3.36595	+	5.82999i	−0.164046	+	0.284136i	−0.936316	−	0.351158i	$-0.885788\pi$
$421$	−3.36595	+	5.82999i	−0.164046	+	0.284136i	0.772270	+	0.635295i	$0.219121\pi$
$422$		0			0
$423$	−3.90018	−	6.75530i	−0.189633	−	0.328454i
$424$		0			0
$425$	3.06661	−	5.31152i	0.148752	−	0.257646i
$426$		0			0
$427$	−7.55936			−0.365823
$428$		0			0
$429$	−27.7450			−1.33954
$430$		0			0
$431$	9.81730	+	17.0041i	0.472883	+	0.819057i	0.999518	−	0.0310343i	$-0.00988011\pi$
$431$	9.81730	+	17.0041i	0.472883	+	0.819057i	−0.526636	+	0.850091i	$0.676547\pi$
$432$		0			0
$433$	12.5754	+	21.7813i	0.604337	+	1.04674i	0.992156	+	0.125007i	$0.0398954\pi$
$433$	12.5754	+	21.7813i	0.604337	+	1.04674i	−0.387818	+	0.921736i	$0.626771\pi$
$434$		0			0
$435$	2.60303	+	4.50859i	0.124806	+	0.216170i
$436$		0			0
$437$	2.29010	+	3.96657i	0.109550	+	0.189747i
$438$		0			0
$439$	−0.513094	+	0.888705i	−0.0244886	+	0.0424156i	−0.878010	−	0.478642i	$-0.841129\pi$
$439$	−0.513094	+	0.888705i	−0.0244886	+	0.0424156i	0.853521	+	0.521058i	$0.174462\pi$
$440$		0			0
$441$	1.17558	−	2.03617i	0.0559801	−	0.0969603i
$442$		0			0
$443$	10.9969	+	19.0473i	0.522481	+	0.904963i	0.999658	+	0.0261562i	$0.00832671\pi$
$443$	10.9969	+	19.0473i	0.522481	+	0.904963i	−0.477177	+	0.878807i	$0.658340\pi$
$444$		0			0
$445$	−7.97892			−0.378237
$446$		0			0
$447$	8.90881			0.421372
$448$		0			0
$449$	−11.2522	−	19.4894i	−0.531024	−	0.919760i	−0.999345	−	0.0362017i	$-0.988474\pi$
$449$	−11.2522	−	19.4894i	−0.531024	−	0.919760i	0.468321	−	0.883559i	$-0.344859\pi$
$450$		0			0
$451$	22.1754	−	38.4090i	1.04420	−	1.80861i
$452$		0			0
$453$	0.0253744	−	0.0439498i	0.00119220	−	0.00206494i
$454$		0			0
$455$	12.9317			0.606249
$456$		0			0
$457$	15.1792	+	26.2912i	0.710055	+	1.22985i	0.964836	+	0.262852i	$0.0846631\pi$
$457$	15.1792	+	26.2912i	0.710055	+	1.22985i	−0.254782	+	0.966999i	$0.582004\pi$
$458$		0			0
$459$	−3.06661	+	5.31152i	−0.143137	+	0.247920i
$460$		0			0
$461$	13.2096			0.615230			0.307615	−	0.951511i	$-0.400469\pi$
$461$	13.2096			0.615230			0.307615	+	0.951511i	$0.400469\pi$
$462$		0			0
$463$	8.62771	−	14.9436i	0.400964	−	0.694490i	−0.592879	−	0.805292i	$-0.702009\pi$
$463$	8.62771	−	14.9436i	0.400964	−	0.694490i	0.993842	+	0.110802i	$0.0353420\pi$
$464$		0			0
$465$	−1.56927	−	2.71805i	−0.0727730	−	0.126047i
$466$		0			0
$467$	12.3804	−	21.4434i	0.572895	−	0.992283i	−0.423372	−	0.905956i	$-0.639154\pi$
$467$	12.3804	−	21.4434i	0.572895	−	0.992283i	0.996267	−	0.0863268i	$-0.0275129\pi$
$468$		0			0
$469$	−10.0974	+	14.4746i	−0.466254	+	0.668376i
$470$		0			0
$471$	−8.62937	+	14.9465i	−0.397620	+	0.688698i
$472$		0			0
$473$	−12.6402	−	21.8935i	−0.581199	−	1.00667i
$474$		0			0
$475$	2.62213	−	4.54165i	0.120311	−	0.208385i
$476$		0			0
$477$	−6.77213			−0.310075
$478$		0			0
$479$	−7.05677	+	12.2227i	−0.322432	+	0.558469i	−0.980989	−	0.194062i	$-0.937834\pi$
$479$	−7.05677	+	12.2227i	−0.322432	+	0.558469i	0.658557	+	0.752531i	$0.271167\pi$
$480$		0			0
$481$	−11.3657	−	19.6860i	−0.518231	−	0.897603i
$482$		0			0
$483$	1.88310			0.0856839
$484$		0			0
$485$	5.01466	−	8.68565i	0.227704	−	0.394395i
$486$		0			0
$487$	−10.0847	+	17.4672i	−0.456981	+	0.791514i	−0.998800	−	0.0489814i	$-0.984403\pi$
$487$	−10.0847	+	17.4672i	−0.456981	+	0.791514i	0.541819	+	0.840495i	$0.317736\pi$
$488$		0			0
$489$	9.40567	+	16.2911i	0.425339	+	0.736709i
$490$		0			0
$491$	−27.6864			−1.24947			−0.624736	−	0.780836i	$-0.714793\pi$
$491$	−27.6864			−1.24947			−0.624736	+	0.780836i	$0.714793\pi$
$492$		0			0
$493$	−31.9299			−1.43805
$494$		0			0
$495$	2.31297	+	4.00618i	0.103960	+	0.180064i
$496$		0			0
$497$	−5.57835	+	9.66198i	−0.250223	+	0.433399i
$498$		0			0
$499$	6.02828	−	10.4413i	0.269863	−	0.467416i	−0.698963	−	0.715157i	$-0.746355\pi$
$499$	6.02828	−	10.4413i	0.269863	−	0.467416i	0.968826	+	0.247741i	$0.0796883\pi$
$500$		0			0
$501$	1.29815	+	2.24847i	0.0579972	+	0.100454i
$502$		0			0
$503$	−3.75145	−	6.49770i	−0.167269	−	0.289718i	0.770190	−	0.637815i	$-0.220161\pi$
$503$	−3.75145	−	6.49770i	−0.167269	−	0.289718i	−0.937459	+	0.348096i	$0.886828\pi$
$504$		0			0
$505$	9.06051	+	15.6933i	0.403187	+	0.698341i
$506$		0			0
$507$	11.4862	+	19.8947i	0.510120	+	0.883554i
$508$		0			0
$509$	−14.9289			−0.661711			−0.330856	−	0.943681i	$-0.607337\pi$
$509$	−14.9289			−0.661711			−0.330856	+	0.943681i	$0.607337\pi$
$510$		0			0
$511$	−3.62852			−0.160516
$512$		0			0
$513$	−2.62213	+	4.54165i	−0.115770	+	0.200519i
$514$		0			0
$515$	−4.74446	−	8.21765i	−0.209066	−	0.362113i
$516$		0			0
$517$	18.0420	−	31.2496i	0.793484	−	1.37436i
$518$		0			0
$519$	9.80640	−	16.9852i	0.430453	−	0.745567i
$520$		0			0
$521$	−35.4177			−1.55168			−0.775839	−	0.630931i	$-0.782673\pi$
$521$	−35.4177			−1.55168			−0.775839	+	0.630931i	$0.782673\pi$
$522$		0			0
$523$	−1.34658	+	2.33235i	−0.0588819	+	0.101987i	−0.893964	−	0.448139i	$-0.852087\pi$
$523$	−1.34658	+	2.33235i	−0.0588819	+	0.101987i	0.835082	+	0.550126i	$0.185420\pi$
$524$		0			0
$525$	−1.07806	−	1.86725i	−0.0470503	−	0.0814935i
$526$		0			0
$527$	19.2493			0.838513
$528$		0			0
$529$	11.1186	+	19.2580i	0.483418	+	0.837304i
$530$		0			0
$531$	5.61145			0.243516
$532$		0			0
$533$	−57.5026			−2.49071
$534$		0			0
$535$	−15.3498			−0.663629
$536$		0			0
$537$	8.75619			0.377858
$538$		0			0
$539$	10.8763			0.468476
$540$		0			0
$541$	−9.30439			−0.400027			−0.200013	−	0.979793i	$-0.564099\pi$
$541$	−9.30439			−0.400027			−0.200013	+	0.979793i	$0.564099\pi$
$542$		0			0
$543$	−2.68166	−	4.64477i	−0.115081	−	0.199326i
$544$		0			0
$545$	−6.26073			−0.268180
$546$		0			0
$547$	20.6416	+	35.7523i	0.882572	+	1.52866i	0.848472	+	0.529241i	$0.177523\pi$
$547$	20.6416	+	35.7523i	0.882572	+	1.52866i	0.0341001	+	0.999418i	$0.489143\pi$
$548$		0			0
$549$	−1.75300	+	3.03629i	−0.0748164	+	0.129586i
$550$		0			0
$551$	−27.3019			−1.16310
$552$		0			0
$553$	5.83307	−	10.1032i	0.248048	−	0.429631i
$554$		0			0
$555$	−1.89501	+	3.28225i	−0.0804387	+	0.139324i
$556$		0			0
$557$	−14.6561	−	25.3851i	−0.621000	−	1.07560i	−0.989300	−	0.145896i	$-0.953393\pi$
$557$	−14.6561	−	25.3851i	−0.621000	−	1.07560i	0.368300	−	0.929707i	$-0.379940\pi$
$558$		0			0
$559$	−16.3886	+	28.3858i	−0.693162	+	1.20059i
$560$		0			0
$561$	−28.3718			−1.19786
$562$		0			0
$563$	10.2565			0.432260			0.216130	−	0.976365i	$-0.430656\pi$
$563$	10.2565			0.432260			0.216130	+	0.976365i	$0.430656\pi$
$564$		0			0
$565$	6.08157	+	10.5336i	0.255854	+	0.443151i
$566$		0			0
$567$	1.07806	+	1.86725i	0.0452742	+	0.0784172i
$568$		0			0
$569$	−1.04247	−	1.80560i	−0.0437024	−	0.0756948i	0.843347	−	0.537370i	$-0.180582\pi$
$569$	−1.04247	−	1.80560i	−0.0437024	−	0.0756948i	−0.887049	+	0.461675i	$0.847249\pi$
$570$		0			0
$571$	−2.13139	−	3.69167i	−0.0891958	−	0.154492i	0.817976	−	0.575253i	$-0.195096\pi$
$571$	−2.13139	−	3.69167i	−0.0891958	−	0.154492i	−0.907171	+	0.420761i	$0.861763\pi$
$572$		0			0
$573$	7.83945	−	13.5783i	0.327498	−	0.567242i
$574$		0			0
$575$	−0.436687	+	0.756365i	−0.0182111	+	0.0315426i
$576$		0			0
$577$	−18.6289	−	32.2661i	−0.775529	−	1.34326i	−0.934496	−	0.355972i	$-0.884150\pi$
$577$	−18.6289	−	32.2661i	−0.775529	−	1.34326i	0.158967	−	0.987284i	$-0.449184\pi$
$578$		0			0
$579$	−3.33316			−0.138522
$580$		0			0
$581$	33.7875			1.40174
$582$		0			0
$583$	−15.6637	−	27.1304i	−0.648725	−	1.12362i
$584$		0			0
$585$	2.99885	−	5.19416i	0.123987	−	0.214752i
$586$		0			0
$587$	6.18285	−	10.7090i	0.255194	−	0.442008i	−0.709754	−	0.704449i	$-0.751194\pi$
$587$	6.18285	−	10.7090i	0.255194	−	0.442008i	0.964948	+	0.262441i	$0.0845274\pi$
$588$		0			0
$589$	16.4593			0.678192
$590$		0			0
$591$	10.9023	+	18.8833i	0.448460	+	0.776756i
$592$		0			0
$593$	16.0411	−	27.7840i	0.658730	−	1.14095i	−0.322215	−	0.946666i	$-0.604427\pi$
$593$	16.0411	−	27.7840i	0.658730	−	1.14095i	0.980945	−	0.194287i	$-0.0622392\pi$
$594$		0			0
$595$	13.2239			0.542128
$596$		0			0
$597$	−12.6316	+	21.8786i	−0.516977	+	0.895430i
$598$		0			0
$599$	18.1471	+	31.4317i	0.741471	+	1.28426i	0.951826	+	0.306640i	$0.0992047\pi$
$599$	18.1471	+	31.4317i	0.741471	+	1.28426i	−0.210355	+	0.977625i	$0.567462\pi$
$600$		0			0
$601$	−7.43597	+	12.8795i	−0.303320	+	0.525365i	−0.976886	−	0.213762i	$-0.931428\pi$
$601$	−7.43597	+	12.8795i	−0.303320	+	0.525365i	0.673566	+	0.739127i	$0.264762\pi$
$602$		0			0
$603$	3.47231	+	7.41236i	0.141403	+	0.301855i
$604$		0			0
$605$	−5.19963	+	9.00603i	−0.211395	+	0.366147i
$606$		0			0
$607$	−8.36045	−	14.4807i	−0.339340	−	0.587754i	0.644969	−	0.764209i	$-0.276870\pi$
$607$	−8.36045	−	14.4807i	−0.339340	−	0.587754i	−0.984309	+	0.176455i	$0.943537\pi$
$608$		0			0
$609$	−5.61244	+	9.72104i	−0.227428	+	0.393916i
$610$		0			0
$611$	−46.7842			−1.89269
$612$		0			0
$613$	23.6061	−	40.8870i	0.953442	−	1.65141i	0.215549	−	0.976493i	$-0.430846\pi$
$613$	23.6061	−	40.8870i	0.953442	−	1.65141i	0.737893	−	0.674917i	$-0.235821\pi$
$614$		0			0
$615$	4.79372	+	8.30297i	0.193302	+	0.334808i
$616$		0			0
$617$	−17.4036			−0.700641			−0.350321	−	0.936630i	$-0.613927\pi$
$617$	−17.4036			−0.700641			−0.350321	+	0.936630i	$0.613927\pi$
$618$		0			0
$619$	−2.13529	+	3.69843i	−0.0858246	+	0.148653i	−0.905742	−	0.423829i	$-0.860686\pi$
$619$	−2.13529	+	3.69843i	−0.0858246	+	0.148653i	0.819918	+	0.572481i	$0.194019\pi$
$620$		0			0
$621$	0.436687	−	0.756365i	0.0175237	−	0.0303519i
$622$		0			0
$623$	−8.60174	−	14.8987i	−0.344622	−	0.596902i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−24.2596			−0.968833
$628$		0			0
$629$	−11.6225	−	20.1308i	−0.463419	−	0.802666i
$630$		0			0
$631$	−20.6879	+	35.8324i	−0.823571	+	1.42647i	0.0794361	+	0.996840i	$0.474688\pi$
$631$	−20.6879	+	35.8324i	−0.823571	+	1.42647i	−0.903007	+	0.429626i	$0.858645\pi$
$632$		0			0
$633$	−2.44395	+	4.23305i	−0.0971384	+	0.168249i
$634$		0			0
$635$	6.63481	+	11.4918i	0.263294	+	0.456039i
$636$		0			0
$637$	−7.05078	−	12.2123i	−0.279362	−	0.483870i
$638$		0			0
$639$	2.58722	+	4.48120i	0.102349	+	0.177273i
$640$		0			0
$641$	17.9342	+	31.0629i	0.708357	+	1.22691i	0.965466	+	0.260528i	$0.0838967\pi$
$641$	17.9342	+	31.0629i	0.708357	+	1.22691i	−0.257109	+	0.966382i	$0.582770\pi$
$642$		0			0
$643$	35.3879			1.39556			0.697781	−	0.716311i	$-0.254171\pi$
$643$	35.3879			1.39556			0.697781	+	0.716311i	$0.254171\pi$
$644$		0			0
$645$	5.46495			0.215182
$646$		0			0
$647$	−17.6557	+	30.5805i	−0.694116	+	1.20224i	0.276361	+	0.961054i	$0.410871\pi$
$647$	−17.6557	+	30.5805i	−0.694116	+	1.20224i	−0.970478	+	0.241191i	$0.922462\pi$
$648$		0			0
$649$	12.9791	+	22.4805i	0.509474	+	0.882435i
$650$		0			0
$651$	3.38352	−	5.86043i	0.132611	−	0.229689i
$652$		0			0
$653$	−6.25811	+	10.8394i	−0.244899	+	0.424177i	−0.962103	−	0.272686i	$-0.912088\pi$
$653$	−6.25811	+	10.8394i	−0.244899	+	0.424177i	0.717204	+	0.696863i	$0.245421\pi$
$654$		0			0
$655$	−0.697341			−0.0272474
$656$		0			0
$657$	−0.841448	+	1.45743i	−0.0328280	+	0.0568598i
$658$		0			0
$659$	15.9834	+	27.6840i	0.622623	+	1.07841i	0.988995	+	0.147947i	$0.0472664\pi$
$659$	15.9834	+	27.6840i	0.622623	+	1.07841i	−0.366372	+	0.930468i	$0.619400\pi$
$660$		0			0
$661$	24.4287			0.950165			0.475083	−	0.879941i	$-0.342418\pi$
$661$	24.4287			0.950165			0.475083	+	0.879941i	$0.342418\pi$
$662$		0			0
$663$	18.3926	+	31.8569i	0.714309	+	1.23722i
$664$		0			0
$665$	11.3072			0.438475
$666$		0			0
$667$	4.54685			0.176055
$668$		0			0
$669$	−11.1873			−0.432526
$670$		0			0
$671$	−16.2186			−0.626111
$672$		0			0
$673$	−12.4012			−0.478032			−0.239016	−	0.971016i	$-0.576825\pi$
$673$	−12.4012			−0.478032			−0.239016	+	0.971016i	$0.576825\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−5.01938	−	8.69382i	−0.192910	−	0.334131i	0.753303	−	0.657674i	$-0.228459\pi$
$677$	−5.01938	−	8.69382i	−0.192910	−	0.334131i	−0.946214	+	0.323543i	$0.895126\pi$
$678$		0			0
$679$	21.6244			0.829868
$680$		0			0
$681$	6.85934	+	11.8807i	0.262851	+	0.455271i
$682$		0			0
$683$	−18.2393	+	31.5915i	−0.697909	+	1.20881i	0.271281	+	0.962500i	$0.412553\pi$
$683$	−18.2393	+	31.5915i	−0.697909	+	1.20881i	−0.969190	+	0.246314i	$0.920781\pi$
$684$		0			0
$685$	11.5162			0.440010
$686$		0			0
$687$	2.91018	−	5.04057i	0.111030	−	0.192310i
$688$		0			0
$689$	−20.3086	+	35.1755i	−0.773697	+	1.34008i
$690$		0			0
$691$	−7.05955	−	12.2275i	−0.268558	−	0.465156i	0.699932	−	0.714210i	$-0.253214\pi$
$691$	−7.05955	−	12.2275i	−0.268558	−	0.465156i	−0.968490	+	0.249054i	$0.919880\pi$
$692$		0			0
$693$	−4.98703	+	8.63778i	−0.189441	+	0.328122i
$694$		0			0
$695$	−2.18220			−0.0827757
$696$		0			0
$697$	−58.8018			−2.22728
$698$		0			0
$699$	−3.33684	−	5.77957i	−0.126211	−	0.218603i
$700$		0			0
$701$	−8.35311	−	14.4680i	−0.315493	−	0.546449i	0.664049	−	0.747689i	$-0.268836\pi$
$701$	−8.35311	−	14.4680i	−0.315493	−	0.546449i	−0.979542	+	0.201239i	$0.935503\pi$
$702$		0			0
$703$	−9.93791	−	17.2130i	−0.374815	−	0.649199i
$704$		0			0
$705$	3.90018	+	6.75530i	0.146889	+	0.254419i
$706$		0			0
$707$	−19.5355	+	33.8365i	−0.734709	+	1.27255i
$708$		0			0
$709$	−3.35461	+	5.81036i	−0.125985	+	0.218213i	−0.922118	−	0.386910i	$-0.873542\pi$
$709$	−3.35461	+	5.81036i	−0.125985	+	0.218213i	0.796132	+	0.605122i	$0.206876\pi$
$710$		0			0
$711$	−2.70536	−	4.68582i	−0.101459	−	0.175732i
$712$		0			0
$713$	−2.74112			−0.102656
$714$		0			0
$715$	27.7450			1.03760
$716$		0			0
$717$	−9.78623	−	16.9502i	−0.365473	−	0.633019i
$718$		0			0
$719$	17.1607	−	29.7233i	0.639988	−	1.10849i	−0.345447	−	0.938438i	$-0.612273\pi$
$719$	17.1607	−	29.7233i	0.639988	−	1.10849i	0.985435	−	0.170053i	$-0.0543939\pi$
$720$		0			0
$721$	10.2296	−	17.7182i	0.380970	−	0.659860i
$722$		0			0
$723$	3.36061			0.124982
$724$		0			0
$725$	−2.60303	−	4.50859i	−0.0966742	−	0.167445i
$726$		0			0
$727$	−17.8567	+	30.9287i	−0.662269	+	1.14708i	0.317749	+	0.948175i	$0.397073\pi$
$727$	−17.8567	+	30.9287i	−0.662269	+	1.14708i	−0.980018	+	0.198908i	$0.936260\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−16.7588	+	29.0272i	−0.619848	+	1.07361i
$732$		0			0
$733$	−20.7429	−	35.9278i	−0.766157	−	1.32702i	−0.939633	−	0.342185i	$-0.888833\pi$
$733$	−20.7429	−	35.9278i	−0.766157	−	1.32702i	0.173475	−	0.984838i	$-0.444500\pi$
$734$		0			0
$735$	−1.17558	+	2.03617i	−0.0433620	+	0.0751051i
$736$		0			0
$737$	−21.6639	+	31.0552i	−0.798000	+	1.14393i
$738$		0			0
$739$	−18.0162	+	31.2050i	−0.662737	+	1.14789i	0.317157	+	0.948373i	$0.397272\pi$
$739$	−18.0162	+	31.2050i	−0.662737	+	1.14789i	−0.979894	+	0.199521i	$0.936061\pi$
$740$		0			0
$741$	15.7267	+	27.2395i	0.577736	+	1.00067i
$742$		0			0
$743$	−17.6137	+	30.5078i	−0.646183	+	1.11922i	0.337844	+	0.941202i	$0.390302\pi$
$743$	−17.6137	+	30.5078i	−0.646183	+	1.11922i	−0.984027	+	0.178020i	$0.943031\pi$
$744$		0			0
$745$	−8.90881			−0.326394
$746$		0			0
$747$	7.83527	−	13.5711i	0.286678	−	0.496540i
$748$		0			0
$749$	−16.5480	−	28.6619i	−0.604649	−	1.04728i
$750$		0			0
$751$	6.11344			0.223083			0.111541	−	0.993760i	$-0.464421\pi$
$751$	6.11344			0.223083			0.111541	+	0.993760i	$0.464421\pi$
$752$		0			0
$753$	4.15611	−	7.19859i	0.151457	−	0.262331i
$754$		0			0
$755$	−0.0253744	+	0.0439498i	−0.000923471	+	0.00159950i
$756$		0			0
$757$	−25.2580	−	43.7481i	−0.918017	−	1.59005i	−0.802423	−	0.596756i	$-0.796456\pi$
$757$	−25.2580	−	43.7481i	−0.918017	−	1.59005i	−0.115595	−	0.993296i	$-0.536877\pi$
$758$		0			0
$759$	4.04017			0.146649
$760$		0			0
$761$	25.7993			0.935224			0.467612	−	0.883934i	$-0.345114\pi$
$761$	25.7993			0.935224			0.467612	+	0.883934i	$0.345114\pi$
$762$		0			0
$763$	−6.74943	−	11.6904i	−0.244346	−	0.423219i
$764$		0			0
$765$	3.06661	−	5.31152i	0.110873	−	0.192038i
$766$		0			0
$767$	16.8279	−	29.1468i	0.607620	−	1.05243i
$768$		0			0
$769$	4.37865	+	7.58404i	0.157898	+	0.273487i	0.934110	−	0.356984i	$-0.116195\pi$
$769$	4.37865	+	7.58404i	0.157898	+	0.273487i	−0.776212	+	0.630471i	$0.782862\pi$
$770$		0			0
$771$	−4.67272	−	8.09339i	−0.168284	−	0.291476i
$772$		0			0
$773$	4.04053	+	6.99840i	0.145328	+	0.251715i	0.929495	−	0.368834i	$-0.120243\pi$
$773$	4.04053	+	6.99840i	0.145328	+	0.251715i	−0.784168	+	0.620549i	$0.786910\pi$
$774$		0			0
$775$	1.56927	+	2.71805i	0.0563698	+	0.0976353i
$776$		0			0
$777$	−8.17173			−0.293159
$778$		0			0
$779$	−50.2790			−1.80143
$780$		0			0
$781$	−11.9683	+	20.7297i	−0.428260	+	0.741768i
$782$		0			0
$783$	2.60303	+	4.50859i	0.0930248	+	0.161124i
$784$		0			0
$785$	8.62937	−	14.9465i	0.307995	−	0.533464i
$786$		0			0
$787$	−19.9342	+	34.5271i	−0.710578	+	1.23076i	0.254062	+	0.967188i	$0.418233\pi$
$787$	−19.9342	+	34.5271i	−0.710578	+	1.23076i	−0.964640	+	0.263570i	$0.915100\pi$
$788$		0			0
$789$	−19.2383			−0.684903
$790$		0			0
$791$	−13.1126	+	22.7116i	−0.466229	+	0.807533i
$792$		0			0
$793$	10.5140	+	18.2108i	0.373363	+	0.646683i
$794$		0			0
$795$	6.77213			0.240183
$796$		0			0
$797$	7.12788	+	12.3458i	0.252482	+	0.437312i	0.964209	−	0.265145i	$-0.0854197\pi$
$797$	7.12788	+	12.3458i	0.252482	+	0.437312i	−0.711726	+	0.702457i	$0.752086\pi$
$798$		0			0
$799$	−47.8412			−1.69250
$800$		0			0
$801$	−7.97892			−0.281921
$802$		0			0
$803$	−7.78496			−0.274725
$804$		0			0
$805$	−1.88310			−0.0663705
$806$		0			0
$807$	7.46217			0.262681
$808$		0			0
$809$	37.9678			1.33488			0.667439	−	0.744665i	$-0.267391\pi$
$809$	37.9678			1.33488			0.667439	+	0.744665i	$0.267391\pi$
$810$		0			0
$811$	−5.63151	−	9.75406i	−0.197749	−	0.342512i	0.750049	−	0.661382i	$-0.230030\pi$
$811$	−5.63151	−	9.75406i	−0.197749	−	0.342512i	−0.947798	+	0.318871i	$0.896696\pi$
$812$		0			0
$813$	18.2280			0.639285
$814$		0			0
$815$	−9.40567	−	16.2911i	−0.329466	−	0.570652i
$816$		0			0
$817$	−14.3298	+	24.8199i	−0.501335	+	0.868338i
$818$		0			0
$819$	12.9317			0.451872
$820$		0			0
$821$	−7.85027	+	13.5971i	−0.273976	+	0.474541i	−0.969876	−	0.243598i	$-0.921672\pi$
$821$	−7.85027	+	13.5971i	−0.273976	+	0.474541i	0.695900	+	0.718139i	$0.255006\pi$
$822$		0			0
$823$	−1.46547	+	2.53826i	−0.0510829	+	0.0884782i	−0.890436	−	0.455108i	$-0.849601\pi$
$823$	−1.46547	+	2.53826i	−0.0510829	+	0.0884782i	0.839353	+	0.543586i	$0.182934\pi$
$824$		0			0
$825$	−2.31297	−	4.00618i	−0.0805272	−	0.139477i
$826$		0			0
$827$	−18.1804	+	31.4894i	−0.632195	+	1.09499i	0.354907	+	0.934902i	$0.384513\pi$
$827$	−18.1804	+	31.4894i	−0.632195	+	1.09499i	−0.987102	+	0.160092i	$0.948821\pi$
$828$		0			0
$829$	43.1490			1.49863			0.749313	−	0.662216i	$-0.230384\pi$
$829$	43.1490			1.49863			0.749313	+	0.662216i	$0.230384\pi$
$830$		0			0
$831$	−14.6155			−0.507005
$832$		0			0
$833$	−7.21009	−	12.4882i	−0.249815	−	0.432692i
$834$		0			0
$835$	−1.29815	−	2.24847i	−0.0449244	−	0.0778113i
$836$		0			0
$837$	−1.56927	−	2.71805i	−0.0542418	−	0.0939496i
$838$		0			0
$839$	9.23592	+	15.9971i	0.318859	+	0.552281i	0.980250	−	0.197761i	$-0.0633669\pi$
$839$	9.23592	+	15.9971i	0.318859	+	0.552281i	−0.661391	+	0.750041i	$0.730034\pi$
$840$		0			0
$841$	0.948437	−	1.64274i	0.0327047	−	0.0566463i
$842$		0			0
$843$	4.47857	−	7.75710i	0.154250	−	0.267169i
$844$		0			0
$845$	−11.4862	−	19.8947i	−0.395137	−	0.684398i
$846$		0			0
$847$	−22.4220			−0.770430
$848$		0			0
$849$	−12.3644			−0.424346
$850$		0			0
$851$	1.65505	+	2.86664i	0.0567345	+	0.0982671i
$852$		0			0
$853$	22.9636	−	39.7741i	0.786258	−	1.36184i	−0.141987	−	0.989869i	$-0.545349\pi$
$853$	22.9636	−	39.7741i	0.786258	−	1.36184i	0.928245	−	0.371970i	$-0.121318\pi$
$854$		0			0
$855$	2.62213	−	4.54165i	0.0896748	−	0.155321i
$856$		0			0
$857$	18.3559			0.627024			0.313512	−	0.949584i	$-0.398494\pi$
$857$	18.3559			0.627024			0.313512	+	0.949584i	$0.398494\pi$
$858$		0			0
$859$	−1.69453	−	2.93501i	−0.0578165	−	0.100141i	0.835669	−	0.549234i	$-0.185080\pi$
$859$	−1.69453	−	2.93501i	−0.0578165	−	0.100141i	−0.893485	+	0.449093i	$0.851747\pi$
$860$		0			0
$861$	−10.3358	+	17.9022i	−0.352244	+	0.610104i
$862$		0			0
$863$	−20.5908			−0.700918			−0.350459	−	0.936578i	$-0.613974\pi$
$863$	−20.5908			−0.700918			−0.350459	+	0.936578i	$0.613974\pi$
$864$		0			0
$865$	−9.80640	+	16.9852i	−0.333428	+	0.577514i
$866$		0			0
$867$	10.3081	+	17.8542i	0.350083	+	0.606362i
$868$		0			0
$869$	12.5148	−	21.6763i	0.424536	−	0.735318i
$870$		0			0
$871$	48.9139	+	4.19283i	1.65738	+	0.142069i
$872$		0			0
$873$	5.01466	−	8.68565i	0.169721	−	0.293965i
$874$		0			0
$875$	1.07806	+	1.86725i	0.0364450	+	0.0631246i
$876$		0			0
$877$	−1.37459	+	2.38085i	−0.0464165	+	0.0803957i	−0.888300	−	0.459263i	$-0.848113\pi$
$877$	−1.37459	+	2.38085i	−0.0464165	+	0.0803957i	0.841884	+	0.539659i	$0.181447\pi$
$878$		0			0
$879$	−29.0024			−0.978228
$880$		0			0
$881$	−26.8206	+	46.4546i	−0.903608	+	1.56509i	−0.0808324	+	0.996728i	$0.525758\pi$
$881$	−26.8206	+	46.4546i	−0.903608	+	1.56509i	−0.822775	+	0.568367i	$0.807575\pi$
$882$		0			0
$883$	−25.3885	−	43.9742i	−0.854391	−	1.47985i	−0.877209	−	0.480109i	$-0.840597\pi$
$883$	−25.3885	−	43.9742i	−0.854391	−	1.47985i	0.0228181	−	0.999740i	$-0.492736\pi$
$884$		0			0
$885$	−5.61145			−0.188627
$886$		0			0
$887$	−1.90287	+	3.29587i	−0.0638921	+	0.110664i	−0.896202	−	0.443646i	$-0.853685\pi$
$887$	−1.90287	+	3.29587i	−0.0638921	+	0.110664i	0.832310	+	0.554311i	$0.187018\pi$
$888$		0			0
$889$	−14.3054	+	24.7777i	−0.479788	+	0.831018i
$890$		0			0
$891$	2.31297	+	4.00618i	0.0774873	+	0.134212i
$892$		0			0
$893$	−40.9070			−1.36890
$894$		0			0
$895$	−8.75619			−0.292687
$896$		0			0
$897$	−2.61912	−	4.53645i	−0.0874498	−	0.151468i
$898$		0			0
$899$	8.16971	−	14.1504i	0.272475	−	0.471941i
$900$		0			0
$901$	−20.7675	+	35.9703i	−0.691865	+	1.19834i
$902$		0			0
$903$	5.89153	+	10.2044i	0.196058	+	0.339582i
$904$		0			0
$905$	2.68166	+	4.64477i	0.0891414	+	0.154398i
$906$		0			0
$907$	−24.2823	−	42.0581i	−0.806279	−	1.39652i	−0.915424	−	0.402491i	$-0.868144\pi$
$907$	−24.2823	−	42.0581i	−0.806279	−	1.39652i	0.109144	−	0.994026i	$-0.465189\pi$
$908$		0			0
$909$	9.06051	+	15.6933i	0.300518	+	0.520513i
$910$		0			0
$911$	51.7856			1.71573			0.857866	−	0.513873i	$-0.171790\pi$
$911$	51.7856			1.71573			0.857866	+	0.513873i	$0.171790\pi$
$912$		0			0
$913$	72.4909			2.39910
$914$		0			0
$915$	1.75300	−	3.03629i	0.0579525	−	0.100377i
$916$		0			0
$917$	−0.751774	−	1.30211i	−0.0248258	−	0.0429995i
$918$		0			0
$919$	−13.5294	+	23.4337i	−0.446295	+	0.773005i	−0.998141	−	0.0609402i	$-0.980590\pi$
$919$	−13.5294	+	23.4337i	−0.446295	+	0.773005i	0.551847	+	0.833946i	$0.313923\pi$
$920$		0			0
$921$	−7.73403	+	13.3957i	−0.254845	+	0.441404i
$922$		0			0
$923$	31.0348			1.02152
$924$		0			0
$925$	1.89501	−	3.28225i	0.0623076	−	0.107920i
$926$		0			0
$927$	−4.74446	−	8.21765i	−0.155828	−	0.269903i
$928$		0			0
$929$	−18.6970			−0.613428			−0.306714	−	0.951802i	$-0.599230\pi$
$929$	−18.6970			−0.613428			−0.306714	+	0.951802i	$0.599230\pi$
$930$		0			0
$931$	−6.16504	−	10.6782i	−0.202051	−	0.349963i
$932$		0			0
$933$	18.5549			0.607460
$934$		0			0
$935$	28.3718			0.927858
$936$		0			0
$937$	−19.8350			−0.647983			−0.323991	−	0.946060i	$-0.605025\pi$
$937$	−19.8350			−0.647983			−0.323991	+	0.946060i	$0.605025\pi$
$938$		0			0
$939$	−34.3221			−1.12006
$940$		0			0
$941$	−18.8978			−0.616051			−0.308026	−	0.951378i	$-0.599668\pi$
$941$	−18.8978			−0.616051			−0.308026	+	0.951378i	$0.599668\pi$
$942$		0			0
$943$	8.37343			0.272676
$944$		0			0
$945$	−1.07806	−	1.86725i	−0.0350692	−	0.0607417i
$946$		0			0
$947$	20.0511			0.651573			0.325787	−	0.945443i	$-0.394371\pi$
$947$	20.0511			0.651573			0.325787	+	0.945443i	$0.394371\pi$
$948$		0			0
$949$	5.04675	+	8.74123i	0.163824	+	0.283752i
$950$		0			0
$951$	7.87420	−	13.6385i	0.255338	−	0.442259i
$952$		0			0
$953$	20.6035			0.667414			0.333707	−	0.942677i	$-0.391700\pi$
$953$	20.6035			0.667414			0.333707	+	0.942677i	$0.391700\pi$
$954$		0			0
$955$	−7.83945	+	13.5783i	−0.253678	+	0.439384i
$956$		0			0
$957$	−12.0415	+	20.8564i	−0.389245	+	0.674192i
$958$		0			0
$959$	12.4151	+	21.5036i	0.400904	+	0.694387i
$960$		0			0
$961$	10.5748	−	18.3161i	0.341123	−	0.590842i
$962$		0			0
$963$	−15.3498			−0.494640
$964$		0			0
$965$	3.33316			0.107298
$966$		0			0
$967$	−15.1202	−	26.1890i	−0.486234	−	0.842182i	0.513641	−	0.858005i	$-0.328296\pi$
$967$	−15.1202	−	26.1890i	−0.486234	−	0.842182i	−0.999875	+	0.0158232i	$0.994963\pi$
$968$		0			0
$969$	16.0821	+	27.8549i	0.516630	+	0.894829i
$970$		0			0
$971$	10.3453	+	17.9186i	0.331996	+	0.575034i	0.982903	−	0.184123i	$-0.0589446\pi$
$971$	10.3453	+	17.9186i	0.331996	+	0.575034i	−0.650907	+	0.759157i	$0.725611\pi$
$972$		0			0
$973$	−2.35254	−	4.07472i	−0.0754190	−	0.130630i
$974$		0			0
$975$	−2.99885	+	5.19416i	−0.0960401	+	0.166346i
$976$		0			0
$977$	−16.0434	+	27.7880i	−0.513274	+	0.889016i	0.486608	+	0.873620i	$0.338234\pi$
$977$	−16.0434	+	27.7880i	−0.513274	+	0.889016i	−0.999881	+	0.0153954i	$0.995099\pi$
$978$		0			0
$979$	−18.4550	−	31.9650i	−0.589824	−	1.02160i
$980$		0			0
$981$	−6.26073			−0.199890
$982$		0			0
$983$	−17.7652			−0.566621			−0.283311	−	0.959028i	$-0.591433\pi$
$983$	−17.7652			−0.566621			−0.283311	+	0.959028i	$0.591433\pi$
$984$		0			0
$985$	−10.9023	−	18.8833i	−0.347376	−	0.601672i
$986$		0			0
$987$	−8.40924	+	14.5652i	−0.267669	+	0.463616i
$988$		0			0
$989$	2.38647	−	4.13349i	0.0758854	−	0.131437i
$990$		0			0
$991$	−46.8372			−1.48783			−0.743916	−	0.668273i	$-0.767034\pi$
$991$	−46.8372			−1.48783			−0.743916	+	0.668273i	$0.767034\pi$
$992$		0			0
$993$	−14.2382	−	24.6612i	−0.451835	−	0.782601i
$994$		0			0
$995$	12.6316	−	21.8786i	0.400449	−	0.693597i
$996$		0			0
$997$	21.7027			0.687331			0.343666	−	0.939092i	$-0.388331\pi$
$997$	21.7027			0.687331			0.343666	+	0.939092i	$0.388331\pi$
$998$		0			0
$999$	−1.89501	+	3.28225i	−0.0599555	+	0.103846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.3781.5	yes	14
67.37	even	3	inner	4020.2.q.k.841.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.5	✓	14	67.37	even	3	inner
4020.2.q.k.3781.5	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 + 1.86725i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 + 1.86725i) q^{7} +1.00000 q^{9} +(2.31297 + 4.00618i) q^{11} +(2.99885 - 5.19416i) q^{13} -1.00000 q^{15} +(3.06661 - 5.31152i) q^{17} +(2.62213 - 4.54165i) q^{19} +(-1.07806 - 1.86725i) q^{21} +(-0.436687 + 0.756365i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.60303 - 4.50859i) q^{29} +(1.56927 + 2.71805i) q^{31} +(-2.31297 - 4.00618i) q^{33} +(1.07806 + 1.86725i) q^{35} +(1.89501 - 3.28225i) q^{37} +(-2.99885 + 5.19416i) q^{39} +(-4.79372 - 8.30297i) q^{41} -5.46495 q^{43} +1.00000 q^{45} +(-3.90018 - 6.75530i) q^{47} +(1.17558 - 2.03617i) q^{49} +(-3.06661 + 5.31152i) q^{51} -6.77213 q^{53} +(2.31297 + 4.00618i) q^{55} +(-2.62213 + 4.54165i) q^{57} +5.61145 q^{59} +(-1.75300 + 3.03629i) q^{61} +(1.07806 + 1.86725i) q^{63} +(2.99885 - 5.19416i) q^{65} +(3.47231 + 7.41236i) q^{67} +(0.436687 - 0.756365i) q^{69} +(2.58722 + 4.48120i) q^{71} +(-0.841448 + 1.45743i) q^{73} -1.00000 q^{75} +(-4.98703 + 8.63778i) q^{77} +(-2.70536 - 4.68582i) q^{79} +1.00000 q^{81} +(7.83527 - 13.5711i) q^{83} +(3.06661 - 5.31152i) q^{85} +(2.60303 + 4.50859i) q^{87} -7.97892 q^{89} +12.9317 q^{91} +(-1.56927 - 2.71805i) q^{93} +(2.62213 - 4.54165i) q^{95} +(5.01466 - 8.68565i) q^{97} +(2.31297 + 4.00618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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