LMFDB - Embedded newform 572.2.i.c.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 $ x^10 - x^9 + 9x^8 + 6x^7 + 59x^6 + 2x^5 + 47x^4 - 26x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$0.194431 - 0.336764i$ of defining polynomial
Character	$\chi$	$=$	572.529
Dual form			572.2.i.c.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194431 - 0.336764i) q^{3} +2.23435 q^{5} +(0.258355 + 0.447484i) q^{7} +(1.42439 + 2.46712i) q^{9} +O(q^{10})$	\(q+(0.194431 - 0.336764i) q^{3} +2.23435 q^{5} +(0.258355 + 0.447484i) q^{7} +(1.42439 + 2.46712i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.353971 + 3.58813i) q^{13} +(0.434426 - 0.752448i) q^{15} +(0.907221 + 1.57135i) q^{17} +(-1.34714 - 2.33331i) q^{19} +0.200929 q^{21} +(2.70596 - 4.68686i) q^{23} -0.00768164 q^{25} +2.27437 q^{27} +(0.181561 - 0.314473i) q^{29} +4.11656 q^{31} +(0.194431 + 0.336764i) q^{33} +(0.577256 + 0.999837i) q^{35} +(-0.813255 + 1.40860i) q^{37} +(1.27718 + 0.578439i) q^{39} +(-0.518360 + 0.897825i) q^{41} +(-0.382825 - 0.663073i) q^{43} +(3.18259 + 5.51241i) q^{45} -1.64218 q^{47} +(3.36651 - 5.83096i) q^{49} +0.705567 q^{51} +2.30304 q^{53} +(-1.11717 + 1.93500i) q^{55} -1.04770 q^{57} +(1.37434 + 2.38043i) q^{59} +(0.688394 + 1.19233i) q^{61} +(-0.735999 + 1.27479i) q^{63} +(0.790895 + 8.01715i) q^{65} +(5.08267 - 8.80345i) q^{67} +(-1.05224 - 1.82254i) q^{69} +(-3.80642 - 6.59292i) q^{71} -1.43120 q^{73} +(-0.00149355 + 0.00258690i) q^{75} -0.516710 q^{77} -9.23605 q^{79} +(-3.83097 + 6.63544i) q^{81} -2.93754 q^{83} +(2.02705 + 3.51095i) q^{85} +(-0.0706021 - 0.122286i) q^{87} +(1.59232 - 2.75797i) q^{89} +(-1.51418 + 1.08541i) q^{91} +(0.800385 - 1.38631i) q^{93} +(-3.00998 - 5.21343i) q^{95} +(-6.14142 - 10.6372i) q^{97} -2.84879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.194431	−	0.336764i	0.112255	−	0.194431i	−0.804424	−	0.594055i	$-0.797526\pi$
$3$	0.194431	−	0.336764i	0.112255	−	0.194431i	0.916679	+	0.399624i	$0.130859\pi$
$4$		0			0
$5$	2.23435			0.999232			0.499616	−	0.866247i	$-0.333475\pi$
$5$	2.23435			0.999232			0.499616	+	0.866247i	$0.333475\pi$
$6$		0			0
$7$	0.258355	+	0.447484i	0.0976491	+	0.169133i	0.910711	−	0.413044i	$-0.135534\pi$
$7$	0.258355	+	0.447484i	0.0976491	+	0.169133i	−0.813062	+	0.582177i	$0.802201\pi$
$8$		0			0
$9$	1.42439	+	2.46712i	0.474798	+	0.822374i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	0.353971	+	3.58813i	0.0981738	+	0.995169i
$13$	0.353971	+	3.58813i	0.0981738	+	0.995169i
$14$		0			0
$15$	0.434426	−	0.752448i	0.112168	−	0.194281i
$16$		0			0
$17$	0.907221	+	1.57135i	0.220033	+	0.381109i	0.954818	−	0.297192i	$-0.0960500\pi$
$17$	0.907221	+	1.57135i	0.220033	+	0.381109i	−0.734784	+	0.678301i	$0.762717\pi$
$18$		0			0
$19$	−1.34714	−	2.33331i	−0.309055	−	0.535298i	0.669101	−	0.743171i	$-0.266679\pi$
$19$	−1.34714	−	2.33331i	−0.309055	−	0.535298i	−0.978156	+	0.207873i	$0.933346\pi$
$20$		0			0
$21$	0.200929			0.0438463
$22$		0			0
$23$	2.70596	−	4.68686i	0.564231	−	0.977277i	−0.432890	−	0.901447i	$-0.642506\pi$
$23$	2.70596	−	4.68686i	0.564231	−	0.977277i	0.997121	−	0.0758300i	$-0.0241606\pi$
$24$		0			0
$25$	−0.00768164			−0.00153633
$26$		0			0
$27$	2.27437			0.437702
$28$		0			0
$29$	0.181561	−	0.314473i	0.0337150	−	0.0583962i	−0.848676	−	0.528914i	$-0.822599\pi$
$29$	0.181561	−	0.314473i	0.0337150	−	0.0583962i	0.882391	+	0.470518i	$0.155933\pi$
$30$		0			0
$31$	4.11656			0.739356			0.369678	−	0.929160i	$-0.379468\pi$
$31$	4.11656			0.739356			0.369678	+	0.929160i	$0.379468\pi$
$32$		0			0
$33$	0.194431	+	0.336764i	0.0338460	+	0.0586231i
$34$		0			0
$35$	0.577256	+	0.999837i	0.0975741	+	0.169003i
$36$		0			0
$37$	−0.813255	+	1.40860i	−0.133698	+	0.231572i	−0.925099	−	0.379725i	$-0.876019\pi$
$37$	−0.813255	+	1.40860i	−0.133698	+	0.231572i	0.791401	+	0.611297i	$0.209352\pi$
$38$		0			0
$39$	1.27718	+	0.578439i	0.204512	+	0.0926243i
$40$		0			0
$41$	−0.518360	+	0.897825i	−0.0809542	+	0.140217i	−0.903660	−	0.428251i	$-0.859130\pi$
$41$	−0.518360	+	0.897825i	−0.0809542	+	0.140217i	0.822706	+	0.568467i	$0.192463\pi$
$42$		0			0
$43$	−0.382825	−	0.663073i	−0.0583803	−	0.101118i	0.835358	−	0.549706i	$-0.185260\pi$
$43$	−0.382825	−	0.663073i	−0.0583803	−	0.101118i	−0.893738	+	0.448588i	$0.851927\pi$
$44$		0			0
$45$	3.18259	+	5.51241i	0.474433	+	0.821742i
$46$		0			0
$47$	−1.64218			−0.239537			−0.119769	−	0.992802i	$-0.538215\pi$
$47$	−1.64218			−0.239537			−0.119769	+	0.992802i	$0.538215\pi$
$48$		0			0
$49$	3.36651	−	5.83096i	0.480929	−	0.832994i
$50$		0			0
$51$	0.705567			0.0987991
$52$		0			0
$53$	2.30304			0.316347			0.158173	−	0.987411i	$-0.449440\pi$
$53$	2.30304			0.316347			0.158173	+	0.987411i	$0.449440\pi$
$54$		0			0
$55$	−1.11717	+	1.93500i	−0.150640	+	0.260916i
$56$		0			0
$57$	−1.04770			−0.138771
$58$		0			0
$59$	1.37434	+	2.38043i	0.178924	+	0.309906i	0.941512	−	0.336979i	$-0.109405\pi$
$59$	1.37434	+	2.38043i	0.178924	+	0.309906i	−0.762588	+	0.646884i	$0.776072\pi$
$60$		0			0
$61$	0.688394	+	1.19233i	0.0881399	+	0.152663i	0.906725	−	0.421723i	$-0.138574\pi$
$61$	0.688394	+	1.19233i	0.0881399	+	0.152663i	−0.818585	+	0.574385i	$0.805241\pi$
$62$		0			0
$63$	−0.735999	+	1.27479i	−0.0927272	+	0.160608i
$64$		0			0
$65$	0.790895	+	8.01715i	0.0980984	+	0.994405i
$66$		0			0
$67$	5.08267	−	8.80345i	0.620948	−	1.07551i	−0.368362	−	0.929682i	$-0.620081\pi$
$67$	5.08267	−	8.80345i	0.620948	−	1.07551i	0.989310	−	0.145830i	$-0.0465853\pi$
$68$		0			0
$69$	−1.05224	−	1.82254i	−0.126675	−	0.219408i
$70$		0			0
$71$	−3.80642	−	6.59292i	−0.451739	−	0.782435i	0.546755	−	0.837293i	$-0.315863\pi$
$71$	−3.80642	−	6.59292i	−0.451739	−	0.782435i	−0.998494	+	0.0548575i	$0.982530\pi$
$72$		0			0
$73$	−1.43120			−0.167509			−0.0837546	−	0.996486i	$-0.526691\pi$
$73$	−1.43120			−0.167509			−0.0837546	+	0.996486i	$0.526691\pi$
$74$		0			0
$75$	−0.00149355	+	0.00258690i	−0.000172460	+	0.000298709i
$76$		0			0
$77$	−0.516710			−0.0588846
$78$		0			0
$79$	−9.23605			−1.03914			−0.519569	−	0.854429i	$-0.673907\pi$
$79$	−9.23605			−1.03914			−0.519569	+	0.854429i	$0.673907\pi$
$80$		0			0
$81$	−3.83097	+	6.63544i	−0.425664	+	0.737271i
$82$		0			0
$83$	−2.93754			−0.322437			−0.161219	−	0.986919i	$-0.551542\pi$
$83$	−2.93754			−0.322437			−0.161219	+	0.986919i	$0.551542\pi$
$84$		0			0
$85$	2.02705	+	3.51095i	0.219864	+	0.380816i
$86$		0			0
$87$	−0.0706021	−	0.122286i	−0.00756934	−	0.0131105i
$88$		0			0
$89$	1.59232	−	2.75797i	0.168785	−	0.292345i	−0.769208	−	0.638999i	$-0.779349\pi$
$89$	1.59232	−	2.75797i	0.168785	−	0.292345i	0.937993	+	0.346654i	$0.112682\pi$
$90$		0			0
$91$	−1.51418	+	1.08541i	−0.158730	+	0.113782i
$92$		0			0
$93$	0.800385	−	1.38631i	0.0829961	−	0.143753i
$94$		0			0
$95$	−3.00998	−	5.21343i	−0.308817	−	0.534887i
$96$		0			0
$97$	−6.14142	−	10.6372i	−0.623566	−	1.08005i	−0.988816	−	0.149139i	$-0.952350\pi$
$97$	−6.14142	−	10.6372i	−0.623566	−	1.08005i	0.365250	−	0.930909i	$-0.380983\pi$
$98$		0			0
$99$	−2.84879			−0.286314
$100$		0			0
$101$	1.61553	−	2.79817i	0.160751	−	0.278429i	−0.774387	−	0.632712i	$-0.781942\pi$
$101$	1.61553	−	2.79817i	0.160751	−	0.278429i	0.935138	+	0.354283i	$0.115275\pi$
$102$		0			0
$103$	−6.88299			−0.678201			−0.339101	−	0.940750i	$-0.610123\pi$
$103$	−6.88299			−0.678201			−0.339101	+	0.940750i	$0.610123\pi$
$104$		0			0
$105$	0.448945			0.0438126
$106$		0			0
$107$	−3.36815	+	5.83381i	−0.325612	+	0.563976i	−0.981636	−	0.190764i	$-0.938904\pi$
$107$	−3.36815	+	5.83381i	−0.325612	+	0.563976i	0.656024	+	0.754740i	$0.272237\pi$
$108$		0			0
$109$	−11.7754			−1.12788			−0.563940	−	0.825816i	$-0.690715\pi$
$109$	−11.7754			−1.12788			−0.563940	+	0.825816i	$0.690715\pi$
$110$		0			0
$111$	0.316243	+	0.547750i	0.0300165	+	0.0519901i
$112$		0			0
$113$	2.21962	+	3.84450i	0.208805	+	0.361660i	0.951338	−	0.308149i	$-0.0997094\pi$
$113$	2.21962	+	3.84450i	0.208805	+	0.361660i	−0.742534	+	0.669809i	$0.766376\pi$
$114$		0			0
$115$	6.04605	−	10.4721i	0.563797	−	0.976526i
$116$		0			0
$117$	−8.34817	+	5.98420i	−0.771789	+	0.553240i
$118$		0			0
$119$	−0.468771	+	0.811935i	−0.0429721	+	0.0744299i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	0.201570	+	0.349130i	0.0181750	+	0.0314800i
$124$		0			0
$125$	−11.1889			−1.00077
$126$		0			0
$127$	5.46834	−	9.47144i	0.485236	−	0.840454i	−0.514620	−	0.857419i	$-0.672067\pi$
$127$	5.46834	−	9.47144i	0.485236	−	0.840454i	0.999856	+	0.0169644i	$0.00540021\pi$
$128$		0			0
$129$	−0.297732			−0.0262138
$130$		0			0
$131$	−18.6173			−1.62660			−0.813300	−	0.581845i	$-0.802331\pi$
$131$	−18.6173			−1.62660			−0.813300	+	0.581845i	$0.802331\pi$
$132$		0			0
$133$	0.696080	−	1.20565i	0.0603578	−	0.104543i
$134$		0			0
$135$	5.08173			0.437366
$136$		0			0
$137$	2.29343	+	3.97233i	0.195941	+	0.339379i	0.947208	−	0.320618i	$-0.103891\pi$
$137$	2.29343	+	3.97233i	0.195941	+	0.339379i	−0.751268	+	0.659997i	$0.770557\pi$
$138$		0			0
$139$	−0.746677	−	1.29328i	−0.0633323	−	0.109695i	0.832621	−	0.553844i	$-0.186839\pi$
$139$	−0.746677	−	1.29328i	−0.0633323	−	0.109695i	−0.895953	+	0.444149i	$0.853506\pi$
$140$		0			0
$141$	−0.319291	+	0.553028i	−0.0268892	+	0.0465734i
$142$		0			0
$143$	−3.28440	−	1.48752i	−0.274655	−	0.124393i
$144$		0			0
$145$	0.405671	−	0.702643i	0.0336891	−	0.0583513i
$146$		0			0
$147$	−1.30910	−	2.26743i	−0.107973	−	0.187015i
$148$		0			0
$149$	−1.91287	−	3.31318i	−0.156708	−	0.271427i	0.776972	−	0.629536i	$-0.216755\pi$
$149$	−1.91287	−	3.31318i	−0.156708	−	0.271427i	−0.933680	+	0.358109i	$0.883422\pi$
$150$		0			0
$151$	−17.0221			−1.38524			−0.692621	−	0.721302i	$-0.743544\pi$
$151$	−17.0221			−1.38524			−0.692621	+	0.721302i	$0.743544\pi$
$152$		0			0
$153$	−2.58448	+	4.47645i	−0.208943	+	0.361900i
$154$		0			0
$155$	9.19783			0.738787
$156$		0			0
$157$	8.27783			0.660643			0.330321	−	0.943869i	$-0.392843\pi$
$157$	8.27783			0.660643			0.330321	+	0.943869i	$0.392843\pi$
$158$		0			0
$159$	0.447781	−	0.775580i	0.0355114	−	0.0615075i
$160$		0			0
$161$	2.79639			0.220387
$162$		0			0
$163$	−0.881566	−	1.52692i	−0.0690496	−	0.119597i	0.829434	−	0.558605i	$-0.188663\pi$
$163$	−0.881566	−	1.52692i	−0.0690496	−	0.119597i	−0.898483	+	0.439008i	$0.855330\pi$
$164$		0			0
$165$	0.434426	+	0.752448i	0.0338200	+	0.0585780i
$166$		0			0
$167$	2.51983	−	4.36447i	0.194990	−	0.337733i	−0.751907	−	0.659269i	$-0.770866\pi$
$167$	2.51983	−	4.36447i	0.194990	−	0.337733i	0.946897	+	0.321536i	$0.104199\pi$
$168$		0			0
$169$	−12.7494	+	2.54019i	−0.980724	+	0.195399i
$170$		0			0
$171$	3.83771	−	6.64710i	0.293477	−	0.508317i
$172$		0			0
$173$	5.91292	+	10.2415i	0.449551	+	0.778645i	0.998357	−	0.0573046i	$-0.0182506\pi$
$173$	5.91292	+	10.2415i	0.449551	+	0.778645i	−0.548806	+	0.835950i	$0.684917\pi$
$174$		0			0
$175$	−0.00198459	−	0.00343741i	−0.000150021	−	0.000259844i
$176$		0			0
$177$	1.06886			0.0803403
$178$		0			0
$179$	1.81122	−	3.13712i	0.135377	−	0.234479i	−0.790365	−	0.612637i	$-0.790109\pi$
$179$	1.81122	−	3.13712i	0.135377	−	0.234479i	0.925741	+	0.378158i	$0.123442\pi$
$180$		0			0
$181$	11.6433			0.865442			0.432721	−	0.901528i	$-0.357554\pi$
$181$	11.6433			0.865442			0.432721	+	0.901528i	$0.357554\pi$
$182$		0			0
$183$	0.535380			0.0395764
$184$		0			0
$185$	−1.81710	+	3.14730i	−0.133596	+	0.231394i
$186$		0			0
$187$	−1.81444			−0.132685
$188$		0			0
$189$	0.587595	+	1.01774i	0.0427412	+	0.0740300i
$190$		0			0
$191$	11.8990	+	20.6096i	0.860979	+	1.49126i	0.870985	+	0.491310i	$0.163482\pi$
$191$	11.8990	+	20.6096i	0.860979	+	1.49126i	−0.0100051	+	0.999950i	$0.503185\pi$
$192$		0			0
$193$	13.2989	−	23.0344i	0.957275	−	1.65805i	0.228201	−	0.973614i	$-0.426716\pi$
$193$	13.2989	−	23.0344i	0.957275	−	1.65805i	0.729074	−	0.684435i	$-0.239951\pi$
$194$		0			0
$195$	2.85366	+	1.29243i	0.204355	+	0.0925532i
$196$		0			0
$197$	−12.6856	+	21.9721i	−0.903809	+	1.56544i	−0.0813019	+	0.996690i	$0.525908\pi$
$197$	−12.6856	+	21.9721i	−0.903809	+	1.56544i	−0.822508	+	0.568754i	$0.807426\pi$
$198$		0			0
$199$	−10.1939	−	17.6564i	−0.722629	−	1.25163i	−0.959942	−	0.280197i	$-0.909600\pi$
$199$	−10.1939	−	17.6564i	−0.722629	−	1.25163i	0.237313	−	0.971433i	$-0.423733\pi$
$200$		0			0
$201$	−1.97646	−	3.42332i	−0.139408	−	0.241463i
$202$		0			0
$203$	0.187629			0.0131690
$204$		0			0
$205$	−1.15820	+	2.00606i	−0.0808920	+	0.140109i
$206$		0			0
$207$	15.4174			1.07158
$208$		0			0
$209$	2.69427			0.186367
$210$		0			0
$211$	3.03811	−	5.26217i	0.209152	−	0.362263i	−0.742295	−	0.670073i	$-0.766263\pi$
$211$	3.03811	−	5.26217i	0.209152	−	0.362263i	0.951448	+	0.307810i	$0.0995962\pi$
$212$		0			0
$213$	−2.96034			−0.202839
$214$		0			0
$215$	−0.855365	−	1.48154i	−0.0583354	−	0.101040i
$216$		0			0
$217$	1.06353	+	1.84210i	0.0721974	+	0.125050i
$218$		0			0
$219$	−0.278269	+	0.481976i	−0.0188037	+	0.0325689i
$220$		0			0
$221$	−5.31710	+	3.81144i	−0.357667	+	0.256385i
$222$		0			0
$223$	6.63685	−	11.4954i	0.444436	−	0.769786i	−0.553577	−	0.832798i	$-0.686737\pi$
$223$	6.63685	−	11.4954i	0.444436	−	0.769786i	0.998013	+	0.0630122i	$0.0200707\pi$
$224$		0			0
$225$	−0.0109417	−	0.0189515i	−0.000729445	−	0.00126344i
$226$		0			0
$227$	−2.12824	−	3.68622i	−0.141256	−	0.244663i	0.786714	−	0.617318i	$-0.211781\pi$
$227$	−2.12824	−	3.68622i	−0.141256	−	0.244663i	−0.927970	+	0.372655i	$0.878447\pi$
$228$		0			0
$229$	−24.8472			−1.64195			−0.820974	−	0.570965i	$-0.806569\pi$
$229$	−24.8472			−1.64195			−0.820974	+	0.570965i	$0.806569\pi$
$230$		0			0
$231$	−0.100464	+	0.174009i	−0.00661007	+	0.0114490i
$232$		0			0
$233$	24.9835			1.63672			0.818362	−	0.574703i	$-0.194883\pi$
$233$	24.9835			1.63672			0.818362	+	0.574703i	$0.194883\pi$
$234$		0			0
$235$	−3.66921			−0.239353
$236$		0			0
$237$	−1.79577	+	3.11037i	−0.116648	+	0.202040i
$238$		0			0
$239$	−16.2408			−1.05053			−0.525265	−	0.850939i	$-0.676034\pi$
$239$	−16.2408			−1.05053			−0.525265	+	0.850939i	$0.676034\pi$
$240$		0			0
$241$	1.58793	+	2.75038i	0.102288	+	0.177167i	0.912627	−	0.408794i	$-0.134050\pi$
$241$	1.58793	+	2.75038i	0.102288	+	0.177167i	−0.810339	+	0.585961i	$0.800717\pi$
$242$		0			0
$243$	4.90127	+	8.48925i	0.314417	+	0.544585i
$244$		0			0
$245$	7.52195	−	13.0284i	0.480560	−	0.832354i
$246$		0			0
$247$	7.89538	−	5.65963i	0.502371	−	0.360114i
$248$		0			0
$249$	−0.571148	+	0.989258i	−0.0361951	+	0.0626917i
$250$		0			0
$251$	8.05217	+	13.9468i	0.508249	+	0.880312i	0.999954	+	0.00955091i	$0.00304020\pi$
$251$	8.05217	+	13.9468i	0.508249	+	0.880312i	−0.491706	+	0.870761i	$0.663626\pi$
$252$		0			0
$253$	2.70596	+	4.68686i	0.170122	+	0.294660i
$254$		0			0
$255$	1.57648			0.0987232
$256$		0			0
$257$	−6.40142	+	11.0876i	−0.399310	+	0.691624i	−0.993641	−	0.112596i	$-0.964083\pi$
$257$	−6.40142	+	11.0876i	−0.399310	+	0.691624i	0.594331	+	0.804220i	$0.297417\pi$
$258$		0			0
$259$	−0.840435			−0.0522221
$260$		0			0
$261$	1.03446			0.0640313
$262$		0			0
$263$	−9.52370	+	16.4955i	−0.587256	+	1.01716i	0.407334	+	0.913279i	$0.366459\pi$
$263$	−9.52370	+	16.4955i	−0.587256	+	1.01716i	−0.994590	+	0.103878i	$0.966875\pi$
$264$		0			0
$265$	5.14579			0.316104
$266$		0			0
$267$	−0.619191	−	1.07247i	−0.0378939	−	0.0656341i
$268$		0			0
$269$	4.93239	+	8.54314i	0.300733	+	0.520885i	0.976302	−	0.216412i	$-0.0694354\pi$
$269$	4.93239	+	8.54314i	0.300733	+	0.520885i	−0.675569	+	0.737297i	$0.736102\pi$
$270$		0			0
$271$	−3.11184	+	5.38986i	−0.189031	+	0.327410i	−0.944927	−	0.327280i	$-0.893868\pi$
$271$	−3.11184	+	5.38986i	−0.189031	+	0.327410i	0.755897	+	0.654691i	$0.227201\pi$
$272$		0			0
$273$	0.0711229	+	0.720959i	0.00430456	+	0.0436344i
$274$		0			0
$275$	0.00384082	−	0.00665249i	0.000231610	−	0.000401160i
$276$		0			0
$277$	−6.38118	−	11.0525i	−0.383408	−	0.664082i	0.608139	−	0.793830i	$-0.291916\pi$
$277$	−6.38118	−	11.0525i	−0.383408	−	0.664082i	−0.991547	+	0.129749i	$0.958583\pi$
$278$		0			0
$279$	5.86360	+	10.1560i	0.351044	+	0.608027i
$280$		0			0
$281$	22.4506			1.33929			0.669644	−	0.742682i	$-0.266447\pi$
$281$	22.4506			1.33929			0.669644	+	0.742682i	$0.266447\pi$
$282$		0			0
$283$	7.85309	−	13.6019i	0.466818	−	0.808552i	−0.532464	−	0.846453i	$-0.678734\pi$
$283$	7.85309	−	13.6019i	0.466818	−	0.808552i	0.999282	+	0.0379008i	$0.0120671\pi$
$284$		0			0
$285$	−2.34093			−0.138665
$286$		0			0
$287$	−0.535684			−0.0316204
$288$		0			0
$289$	6.85390	−	11.8713i	0.403171	−	0.698312i
$290$		0			0
$291$	−4.77632			−0.279993
$292$		0			0
$293$	2.99766	+	5.19209i	0.175125	+	0.303325i	0.940205	−	0.340610i	$-0.110634\pi$
$293$	2.99766	+	5.19209i	0.175125	+	0.303325i	−0.765080	+	0.643936i	$0.777300\pi$
$294$		0			0
$295$	3.07076	+	5.31872i	0.178787	+	0.309668i
$296$		0			0
$297$	−1.13718	+	1.96966i	−0.0659861	+	0.114291i
$298$		0			0
$299$	17.7749	+	8.05033i	1.02795	+	0.465562i
$300$		0			0
$301$	0.197810	−	0.342617i	0.0114016	−	0.0197481i
$302$		0			0
$303$	−0.628216	−	1.08810i	−0.0360900	−	0.0625098i
$304$		0			0
$305$	1.53811	+	2.66409i	0.0880721	+	0.152545i
$306$		0			0
$307$	−14.1887			−0.809793			−0.404896	−	0.914363i	$-0.632692\pi$
$307$	−14.1887			−0.809793			−0.404896	+	0.914363i	$0.632692\pi$
$308$		0			0
$309$	−1.33826	+	2.31794i	−0.0761312	+	0.131863i
$310$		0			0
$311$	33.0732			1.87541			0.937706	−	0.347430i	$-0.112946\pi$
$311$	33.0732			1.87541			0.937706	+	0.347430i	$0.112946\pi$
$312$		0			0
$313$	19.3433			1.09335			0.546673	−	0.837346i	$-0.315894\pi$
$313$	19.3433			1.09335			0.546673	+	0.837346i	$0.315894\pi$
$314$		0			0
$315$	−1.64448	+	2.84832i	−0.0926559	+	0.160485i
$316$		0			0
$317$	−10.3583			−0.581779			−0.290890	−	0.956757i	$-0.593951\pi$
$317$	−10.3583			−0.581779			−0.290890	+	0.956757i	$0.593951\pi$
$318$		0			0
$319$	0.181561	+	0.314473i	0.0101655	+	0.0176071i
$320$		0			0
$321$	1.30975	+	2.26855i	0.0731029	+	0.126618i
$322$		0			0
$323$	2.44430	−	4.23366i	0.136005	−	0.235567i
$324$		0			0
$325$	−0.00271908	−	0.0275627i	−0.000150827	−	0.00152891i
$326$		0			0
$327$	−2.28950	+	3.96553i	−0.126610	+	0.219294i
$328$		0			0
$329$	−0.424267	−	0.734852i	−0.0233906	−	0.0405137i
$330$		0			0
$331$	8.34652	+	14.4566i	0.458766	+	0.794607i	0.998896	−	0.0469751i	$-0.0149581\pi$
$331$	8.34652	+	14.4566i	0.458766	+	0.794607i	−0.540130	+	0.841582i	$0.681625\pi$
$332$		0			0
$333$	−4.63358			−0.253919
$334$		0			0
$335$	11.3565	−	19.6700i	0.620470	−	1.07469i
$336$		0			0
$337$	32.4301			1.76658			0.883291	−	0.468826i	$-0.155323\pi$
$337$	32.4301			1.76658			0.883291	+	0.468826i	$0.155323\pi$
$338$		0			0
$339$	1.72625			0.0937572
$340$		0			0
$341$	−2.05828	+	3.56504i	−0.111462	+	0.193058i
$342$		0			0
$343$	7.09599			0.383147
$344$		0			0
$345$	−2.35108	−	4.07219i	−0.126578	−	0.219239i
$346$		0			0
$347$	15.4773	+	26.8074i	0.830863	+	1.43910i	0.897355	+	0.441310i	$0.145486\pi$
$347$	15.4773	+	26.8074i	0.830863	+	1.43910i	−0.0664919	+	0.997787i	$0.521181\pi$
$348$		0			0
$349$	2.75013	−	4.76336i	0.147211	−	0.254977i	−0.782985	−	0.622041i	$-0.786304\pi$
$349$	2.75013	−	4.76336i	0.147211	−	0.254977i	0.930196	+	0.367064i	$0.119637\pi$
$350$		0			0
$351$	0.805060	+	8.16074i	0.0429709	+	0.435588i
$352$		0			0
$353$	10.2458	−	17.7462i	0.545329	−	0.944537i	−0.453257	−	0.891380i	$-0.649738\pi$
$353$	10.2458	−	17.7462i	0.545329	−	0.944537i	0.998586	−	0.0531573i	$-0.0169285\pi$
$354$		0			0
$355$	−8.50488	−	14.7309i	−0.451392	−	0.781834i
$356$		0			0
$357$	0.182287	+	0.315730i	0.00964764	+	0.0167102i
$358$		0			0
$359$	−22.0381			−1.16313			−0.581564	−	0.813501i	$-0.697559\pi$
$359$	−22.0381			−1.16313			−0.581564	+	0.813501i	$0.697559\pi$
$360$		0			0
$361$	5.87044	−	10.1679i	0.308971	−	0.535153i
$362$		0			0
$363$	−0.388861			−0.0204099
$364$		0			0
$365$	−3.19780			−0.167380
$366$		0			0
$367$	−7.77866	+	13.4730i	−0.406043	+	0.703286i	−0.994442	−	0.105284i	$-0.966425\pi$
$367$	−7.77866	+	13.4730i	−0.406043	+	0.703286i	0.588400	+	0.808570i	$0.299758\pi$
$368$		0			0
$369$	−2.95339			−0.153747
$370$		0			0
$371$	0.595002	+	1.03057i	0.0308910	+	0.0535047i
$372$		0			0
$373$	11.3568	+	19.6705i	0.588032	+	1.01850i	0.994490	+	0.104831i	$0.0334303\pi$
$373$	11.3568	+	19.6705i	0.588032	+	1.01850i	−0.406458	+	0.913669i	$0.633236\pi$
$374$		0			0
$375$	−2.17547	+	3.76802i	−0.112341	+	0.194580i
$376$		0			0
$377$	1.19264	+	0.540151i	0.0614240	+	0.0278192i
$378$		0			0
$379$	0.478525	−	0.828830i	0.0245802	−	0.0425741i	−0.853474	−	0.521136i	$-0.825508\pi$
$379$	0.478525	−	0.828830i	0.0245802	−	0.0425741i	0.878054	+	0.478562i	$0.158842\pi$
$380$		0			0
$381$	−2.12643	−	3.68308i	−0.108940	−	0.188690i
$382$		0			0
$383$	4.72112	+	8.17722i	0.241238	+	0.417836i	0.961067	−	0.276315i	$-0.0891133\pi$
$383$	4.72112	+	8.17722i	0.241238	+	0.417836i	−0.719829	+	0.694151i	$0.755780\pi$
$384$		0			0
$385$	−1.15451			−0.0588394
$386$		0			0
$387$	1.09059	−	1.88895i	0.0554377	−	0.0960209i
$388$		0			0
$389$	−28.8869			−1.46463			−0.732313	−	0.680969i	$-0.761559\pi$
$389$	−28.8869			−1.46463			−0.732313	+	0.680969i	$0.761559\pi$
$390$		0			0
$391$	9.81961			0.496599
$392$		0			0
$393$	−3.61977	+	6.26963i	−0.182593	+	0.316261i
$394$		0			0
$395$	−20.6366			−1.03834
$396$		0			0
$397$	−2.03473	−	3.52426i	−0.102120	−	0.176878i	0.810438	−	0.585825i	$-0.199229\pi$
$397$	−2.03473	−	3.52426i	−0.102120	−	0.176878i	−0.912558	+	0.408947i	$0.865896\pi$
$398$		0			0
$399$	−0.270679	−	0.468829i	−0.0135509	−	0.0234708i
$400$		0			0
$401$	14.2458	−	24.6745i	0.711402	−	1.23218i	−0.252930	−	0.967485i	$-0.581394\pi$
$401$	14.2458	−	24.6745i	0.711402	−	1.23218i	0.964331	−	0.264699i	$-0.0852726\pi$
$402$		0			0
$403$	1.45714	+	14.7708i	0.0725854	+	0.735784i
$404$		0			0
$405$	−8.55973	+	14.8259i	−0.425337	+	0.736705i
$406$		0			0
$407$	−0.813255	−	1.40860i	−0.0403115	−	0.0698216i
$408$		0			0
$409$	−18.3256	−	31.7408i	−0.906141	−	1.56948i	−0.819379	−	0.573253i	$-0.805681\pi$
$409$	−18.3256	−	31.7408i	−0.906141	−	1.56948i	−0.0867621	−	0.996229i	$-0.527652\pi$
$410$		0			0
$411$	1.78365			0.0879809
$412$		0			0
$413$	−0.710137	+	1.22999i	−0.0349436	+	0.0605240i
$414$		0			0
$415$	−6.56349			−0.322189
$416$		0			0
$417$	−0.580708			−0.0284374
$418$		0			0
$419$	0.453737	−	0.785896i	0.0221665	−	0.0383935i	−0.854729	−	0.519074i	$-0.826277\pi$
$419$	0.453737	−	0.785896i	0.0221665	−	0.0383935i	0.876896	+	0.480680i	$0.159610\pi$
$420$		0			0
$421$	−4.35823			−0.212407			−0.106204	−	0.994344i	$-0.533870\pi$
$421$	−4.35823			−0.212407			−0.106204	+	0.994344i	$0.533870\pi$
$422$		0			0
$423$	−2.33912	−	4.05147i	−0.113732	−	0.196989i
$424$		0			0
$425$	−0.00696894	−	0.0120706i	−0.000338043	−	0.000585508i
$426$		0			0
$427$	−0.355701	+	0.616092i	−0.0172136	+	0.0298148i
$428$		0			0
$429$	−1.13953	+	0.816848i	−0.0550171	+	0.0394378i
$430$		0			0
$431$	−5.65437	+	9.79365i	−0.272361	+	0.471743i	−0.969466	−	0.245226i	$-0.921138\pi$
$431$	−5.65437	+	9.79365i	−0.272361	+	0.471743i	0.697105	+	0.716969i	$0.254471\pi$
$432$		0			0
$433$	−14.2332	−	24.6527i	−0.684006	−	1.18473i	−0.973748	−	0.227628i	$-0.926903\pi$
$433$	−14.2332	−	24.6527i	−0.684006	−	1.18473i	0.289742	−	0.957105i	$-0.406430\pi$
$434$		0			0
$435$	−0.157750	−	0.273231i	−0.00756352	−	0.0131004i
$436$		0			0
$437$	−14.5812			−0.697513
$438$		0			0
$439$	−15.9359	+	27.6018i	−0.760579	+	1.31736i	0.181973	+	0.983303i	$0.441752\pi$
$439$	−15.9359	+	27.6018i	−0.760579	+	1.31736i	−0.942552	+	0.334058i	$0.891582\pi$
$440$		0			0
$441$	19.1809			0.913377
$442$		0			0
$443$	9.12755			0.433663			0.216832	−	0.976209i	$-0.430428\pi$
$443$	9.12755			0.433663			0.216832	+	0.976209i	$0.430428\pi$
$444$		0			0
$445$	3.55779	−	6.16228i	0.168656	−	0.292120i
$446$		0			0
$447$	−1.48768			−0.0703649
$448$		0			0
$449$	−7.93863	−	13.7501i	−0.374647	−	0.648908i	0.615627	−	0.788038i	$-0.288903\pi$
$449$	−7.93863	−	13.7501i	−0.374647	−	0.648908i	−0.990274	+	0.139130i	$0.955569\pi$
$450$		0			0
$451$	−0.518360	−	0.897825i	−0.0244086	−	0.0422769i
$452$		0			0
$453$	−3.30962	+	5.73244i	−0.155500	+	0.269333i
$454$		0			0
$455$	−3.38322	+	2.42518i	−0.158608	+	0.113694i
$456$		0			0
$457$	10.2126	−	17.6888i	0.477727	−	0.827448i	−0.521947	−	0.852978i	$-0.674794\pi$
$457$	10.2126	−	17.6888i	0.477727	−	0.827448i	0.999674	+	0.0255301i	$0.00812736\pi$
$458$		0			0
$459$	2.06335	+	3.57383i	0.0963091	+	0.166812i
$460$		0			0
$461$	−18.7928	−	32.5500i	−0.875267	−	1.51601i	−0.856478	−	0.516183i	$-0.827352\pi$
$461$	−18.7928	−	32.5500i	−0.875267	−	1.51601i	−0.0187889	−	0.999823i	$-0.505981\pi$
$462$		0			0
$463$	−1.12816			−0.0524301			−0.0262150	−	0.999656i	$-0.508345\pi$
$463$	−1.12816			−0.0524301			−0.0262150	+	0.999656i	$0.508345\pi$
$464$		0			0
$465$	1.78834	−	3.09750i	0.0829323	−	0.143643i
$466$		0			0
$467$	−16.8091			−0.777833			−0.388916	−	0.921273i	$-0.627150\pi$
$467$	−16.8091			−0.777833			−0.388916	+	0.921273i	$0.627150\pi$
$468$		0			0
$469$	5.25254			0.242540
$470$		0			0
$471$	1.60946	−	2.78767i	0.0741602	−	0.128449i
$472$		0			0
$473$	0.765650			0.0352046
$474$		0			0
$475$	0.0103482	+	0.0179236i	0.000474809	+	0.000822393i
$476$		0			0
$477$	3.28043	+	5.68188i	0.150201	+	0.260155i
$478$		0			0
$479$	11.5359	−	19.9807i	0.527086	−	0.912941i	−0.472415	−	0.881376i	$-0.656618\pi$
$479$	11.5359	−	19.9807i	0.527086	−	0.912941i	0.999502	−	0.0315645i	$-0.0100490\pi$
$480$		0			0
$481$	−5.34211	−	2.41946i	−0.243579	−	0.110318i
$482$		0			0
$483$	0.543705	−	0.941724i	0.0247394	−	0.0428499i
$484$		0			0
$485$	−13.7221	−	23.7673i	−0.623087	−	1.07922i
$486$		0			0
$487$	5.03355	+	8.71837i	0.228092	+	0.395067i	0.957243	−	0.289286i	$-0.0934180\pi$
$487$	5.03355	+	8.71837i	0.228092	+	0.395067i	−0.729151	+	0.684353i	$0.760085\pi$
$488$		0			0
$489$	−0.685614			−0.0310046
$490$		0			0
$491$	4.96903	−	8.60662i	0.224249	−	0.388411i	−0.731845	−	0.681472i	$-0.761340\pi$
$491$	4.96903	−	8.60662i	0.224249	−	0.388411i	0.956094	+	0.293060i	$0.0946736\pi$
$492$		0			0
$493$	0.658864			0.0296738
$494$		0			0
$495$	−6.36519			−0.286094
$496$		0			0
$497$	1.96682	−	3.40663i	0.0882238	−	0.152808i
$498$		0			0
$499$	−29.7183			−1.33037			−0.665187	−	0.746677i	$-0.731648\pi$
$499$	−29.7183			−1.33037			−0.665187	+	0.746677i	$0.731648\pi$
$500$		0			0
$501$	−0.979865	−	1.69718i	−0.0437771	−	0.0758242i
$502$		0			0
$503$	10.0862	+	17.4698i	0.449721	+	0.778939i	0.998368	−	0.0571150i	$-0.0181902\pi$
$503$	10.0862	+	17.4698i	0.449721	+	0.778939i	−0.548647	+	0.836054i	$0.684857\pi$
$504$		0			0
$505$	3.60965	−	6.25210i	0.160627	−	0.278215i
$506$		0			0
$507$	−1.62343	+	4.78743i	−0.0720992	+	0.212617i
$508$		0			0
$509$	−11.2621	+	19.5065i	−0.499184	+	0.864612i	−1.00000		0.000942237i	$-0.999700\pi$
$509$	−11.2621	+	19.5065i	−0.499184	+	0.864612i	0.500816	+	0.865554i	$0.333033\pi$
$510$		0			0
$511$	−0.369758	−	0.640439i	−0.0163571	−	0.0283314i
$512$		0			0
$513$	−3.06389	−	5.30681i	−0.135274	−	0.234301i
$514$		0			0
$515$	−15.3790			−0.677680
$516$		0			0
$517$	0.821092	−	1.42217i	0.0361116	−	0.0625471i
$518$		0			0
$519$	4.59861			0.201857
$520$		0			0
$521$	4.26684			0.186934			0.0934668	−	0.995622i	$-0.470205\pi$
$521$	4.26684			0.186934			0.0934668	+	0.995622i	$0.470205\pi$
$522$		0			0
$523$	−11.7236	+	20.3059i	−0.512638	+	0.887916i	0.487254	+	0.873260i	$0.337998\pi$
$523$	−11.7236	+	20.3059i	−0.512638	+	0.887916i	−0.999893	+	0.0146554i	$0.995335\pi$
$524$		0			0
$525$	−0.00154346			−6.73622e−5
$526$		0			0
$527$	3.73463	+	6.46857i	0.162683	+	0.281775i
$528$		0			0
$529$	−3.14441	−	5.44627i	−0.136713	−	0.236795i
$530$		0			0
$531$	−3.91521	+	6.78134i	−0.169906	+	0.294285i
$532$		0			0
$533$	−3.40500	−	1.54214i	−0.147487	−	0.0667975i
$534$		0			0
$535$	−7.52563	+	13.0348i	−0.325362	+	0.563543i
$536$		0			0
$537$	−0.704312	−	1.21990i	−0.0303933	−	0.0526427i
$538$		0			0
$539$	3.36651	+	5.83096i	0.145006	+	0.251157i
$540$		0			0
$541$	−28.4042			−1.22119			−0.610597	−	0.791941i	$-0.709070\pi$
$541$	−28.4042			−1.22119			−0.610597	+	0.791941i	$0.709070\pi$
$542$		0			0
$543$	2.26382	−	3.92105i	0.0971499	−	0.168269i
$544$		0			0
$545$	−26.3104			−1.12701
$546$		0			0
$547$	−10.2484			−0.438192			−0.219096	−	0.975703i	$-0.570311\pi$
$547$	−10.2484			−0.438192			−0.219096	+	0.975703i	$0.570311\pi$
$548$		0			0
$549$	−1.96109	+	3.39671i	−0.0836972	+	0.144968i
$550$		0			0
$551$	−0.978351			−0.0416792
$552$		0			0
$553$	−2.38618	−	4.13299i	−0.101471	−	0.175753i
$554$		0			0
$555$	0.706598	+	1.22386i	0.0299934	+	0.0519502i
$556$		0			0
$557$	−9.47914	+	16.4184i	−0.401644	+	0.695668i	−0.993925	−	0.110064i	$-0.964894\pi$
$557$	−9.47914	+	16.4184i	−0.401644	+	0.695668i	0.592280	+	0.805732i	$0.298228\pi$
$558$		0			0
$559$	2.24368	−	1.60834i	0.0948977	−	0.0680254i
$560$		0			0
$561$	−0.352783	+	0.611039i	−0.0148945	+	0.0257981i
$562$		0			0
$563$	9.63085	+	16.6811i	0.405892	+	0.703025i	0.994425	−	0.105448i	$-0.0336276\pi$
$563$	9.63085	+	16.6811i	0.405892	+	0.703025i	−0.588533	+	0.808473i	$0.700294\pi$
$564$		0			0
$565$	4.95942	+	8.58996i	0.208644	+	0.361382i
$566$		0			0
$567$	−3.95901			−0.166263
$568$		0			0
$569$	5.09062	−	8.81720i	0.213410	−	0.369636i	−0.739370	−	0.673300i	$-0.764876\pi$
$569$	5.09062	−	8.81720i	0.213410	−	0.369636i	0.952779	+	0.303663i	$0.0982098\pi$
$570$		0			0
$571$	14.0131			0.586430			0.293215	−	0.956047i	$-0.405275\pi$
$571$	14.0131			0.586430			0.293215	+	0.956047i	$0.405275\pi$
$572$		0			0
$573$	9.25410			0.386596
$574$		0			0
$575$	−0.0207862	+	0.0360027i	−0.000866844	+	0.00150142i
$576$		0			0
$577$	23.0742			0.960592			0.480296	−	0.877106i	$-0.340529\pi$
$577$	23.0742			0.960592			0.480296	+	0.877106i	$0.340529\pi$
$578$		0			0
$579$	−5.17143	−	8.95717i	−0.214917	−	0.372247i
$580$		0			0
$581$	−0.758929	−	1.31450i	−0.0314857	−	0.0545348i
$582$		0			0
$583$	−1.15152	+	1.99449i	−0.0476911	+	0.0826033i
$584$		0			0
$585$	−18.6527	+	13.3708i	−0.771195	+	0.552815i
$586$		0			0
$587$	17.2669	−	29.9071i	0.712680	−	1.23440i	−0.251167	−	0.967944i	$-0.580814\pi$
$587$	17.2669	−	29.9071i	0.712680	−	1.23440i	0.963847	−	0.266455i	$-0.0858523\pi$
$588$		0			0
$589$	−5.54557	−	9.60521i	−0.228501	−	0.395776i
$590$		0			0
$591$	4.93293	+	8.54408i	0.202914	+	0.351457i
$592$		0			0
$593$	16.7576			0.688152			0.344076	−	0.938942i	$-0.388192\pi$
$593$	16.7576			0.688152			0.344076	+	0.938942i	$0.388192\pi$
$594$		0			0
$595$	−1.04740	+	1.81415i	−0.0429391	+	0.0743727i
$596$		0			0
$597$	−7.92806			−0.324474
$598$		0			0
$599$	−15.8452			−0.647417			−0.323709	−	0.946157i	$-0.604930\pi$
$599$	−15.8452			−0.647417			−0.323709	+	0.946157i	$0.604930\pi$
$600$		0			0
$601$	16.2788	−	28.1957i	0.664027	−	1.15013i	−0.315522	−	0.948918i	$-0.602179\pi$
$601$	16.2788	−	28.1957i	0.664027	−	1.15013i	0.979548	−	0.201210i	$-0.0644872\pi$
$602$		0			0
$603$	28.9589			1.17930
$604$		0			0
$605$	−1.11717	−	1.93500i	−0.0454196	−	0.0786691i
$606$		0			0
$607$	−11.2599	−	19.5026i	−0.457024	−	0.791588i	0.541779	−	0.840521i	$-0.317751\pi$
$607$	−11.2599	−	19.5026i	−0.457024	−	0.791588i	−0.998802	+	0.0489333i	$0.984418\pi$
$608$		0			0
$609$	0.0364808	−	0.0631867i	0.00147828	−	0.00256045i
$610$		0			0
$611$	−0.581285	−	5.89238i	−0.0235163	−	0.238380i
$612$		0			0
$613$	−13.2788	+	22.9995i	−0.536324	+	0.928940i	0.462774	+	0.886476i	$0.346854\pi$
$613$	−13.2788	+	22.9995i	−0.536324	+	0.928940i	−0.999098	+	0.0424639i	$0.986479\pi$
$614$		0			0
$615$	0.450378	+	0.780078i	0.0181610	+	0.0314558i
$616$		0			0
$617$	−13.6034	−	23.5618i	−0.547653	−	0.948562i	−0.998435	−	0.0559282i	$-0.982188\pi$
$617$	−13.6034	−	23.5618i	−0.547653	−	0.948562i	0.450782	−	0.892634i	$-0.351145\pi$
$618$		0			0
$619$	−32.2049			−1.29442			−0.647211	−	0.762311i	$-0.724065\pi$
$619$	−32.2049			−1.29442			−0.647211	+	0.762311i	$0.724065\pi$
$620$		0			0
$621$	6.15434	−	10.6596i	0.246965	−	0.427756i
$622$		0			0
$623$	1.64553			0.0659269
$624$		0			0
$625$	−24.9615			−0.998461
$626$		0			0
$627$	0.523850	−	0.907335i	0.0209205	−	0.0362355i
$628$		0			0
$629$	−2.95121			−0.117672
$630$		0			0
$631$	21.3407	+	36.9631i	0.849558	+	1.47148i	0.881603	+	0.471991i	$0.156465\pi$
$631$	21.3407	+	36.9631i	0.849558	+	1.47148i	−0.0320452	+	0.999486i	$0.510202\pi$
$632$		0			0
$633$	−1.18141	−	2.04625i	−0.0469566	−	0.0813313i
$634$		0			0
$635$	12.2182	−	21.1625i	0.484864	−	0.839808i
$636$		0			0
$637$	22.1139	+	10.0155i	0.876185	+	0.396828i
$638$		0			0
$639$	10.8437	−	18.7818i	0.428969	−	0.742997i
$640$		0			0
$641$	6.25454	+	10.8332i	0.247039	+	0.427885i	0.962703	−	0.270560i	$-0.0872090\pi$
$641$	6.25454	+	10.8332i	0.247039	+	0.427885i	−0.715664	+	0.698445i	$0.753876\pi$
$642$		0			0
$643$	8.97199	+	15.5399i	0.353821	+	0.612836i	0.986915	−	0.161239i	$-0.0515489\pi$
$643$	8.97199	+	15.5399i	0.353821	+	0.612836i	−0.633095	+	0.774074i	$0.718216\pi$
$644$		0			0
$645$	−0.665237			−0.0261937
$646$		0			0
$647$	19.5920	−	33.9343i	0.770241	−	1.33410i	−0.167189	−	0.985925i	$-0.553469\pi$
$647$	19.5920	−	33.9343i	0.770241	−	1.33410i	0.937431	−	0.348172i	$-0.113198\pi$
$648$		0			0
$649$	−2.74869			−0.107895
$650$		0			0
$651$	0.827135			0.0324180
$652$		0			0
$653$	−13.8620	+	24.0097i	−0.542463	+	0.939573i	0.456299	+	0.889826i	$0.349175\pi$
$653$	−13.8620	+	24.0097i	−0.542463	+	0.939573i	−0.998762	+	0.0497463i	$0.984159\pi$
$654$		0			0
$655$	−41.5975			−1.62535
$656$		0			0
$657$	−2.03859	−	3.53094i	−0.0795330	−	0.137755i
$658$		0			0
$659$	−14.7045	−	25.4689i	−0.572805	−	0.992127i	−0.996276	−	0.0862173i	$-0.972522\pi$
$659$	−14.7045	−	25.4689i	−0.572805	−	0.992127i	0.423472	−	0.905909i	$-0.360811\pi$
$660$		0			0
$661$	1.02132	−	1.76898i	0.0397249	−	0.0688055i	−0.845479	−	0.534008i	$-0.820685\pi$
$661$	1.02132	−	1.76898i	0.0397249	−	0.0688055i	0.885204	+	0.465203i	$0.154019\pi$
$662$		0			0
$663$	0.249750	+	2.53167i	0.00969949	+	0.0983218i
$664$		0			0
$665$	1.55529	−	2.69383i	0.0603114	−	0.104462i
$666$		0			0
$667$	−0.982593	−	1.70190i	−0.0380462	−	0.0658979i
$668$		0			0
$669$	−2.58081	−	4.47010i	−0.0997801	−	0.172824i
$670$		0			0
$671$	−1.37679			−0.0531503
$672$		0			0
$673$	−10.7194	+	18.5666i	−0.413204	+	0.715690i	−0.995238	−	0.0974740i	$-0.968924\pi$
$673$	−10.7194	+	18.5666i	−0.413204	+	0.715690i	0.582034	+	0.813164i	$0.302257\pi$
$674$		0			0
$675$	−0.0174709			−0.000672454
$676$		0			0
$677$	11.0759			0.425681			0.212840	−	0.977087i	$-0.431729\pi$
$677$	11.0759			0.425681			0.212840	+	0.977087i	$0.431729\pi$
$678$		0			0
$679$	3.17333	−	5.49637i	0.121781	−	0.210931i
$680$		0			0
$681$	−1.65518			−0.0634267
$682$		0			0
$683$	11.1937	+	19.3880i	0.428315	+	0.741863i	0.996724	−	0.0808835i	$-0.0257742\pi$
$683$	11.1937	+	19.3880i	0.428315	+	0.741863i	−0.568409	+	0.822746i	$0.692441\pi$
$684$		0			0
$685$	5.12431	+	8.87557i	0.195790	+	0.339118i
$686$		0			0
$687$	−4.83106	+	8.36764i	−0.184316	+	0.319245i
$688$		0			0
$689$	0.815208	+	8.26361i	0.0310570	+	0.314818i
$690$		0			0
$691$	−16.1528	+	27.9774i	−0.614480	+	1.06431i	0.375995	+	0.926622i	$0.377301\pi$
$691$	−16.1528	+	27.9774i	−0.614480	+	1.06431i	−0.990475	+	0.137689i	$0.956033\pi$
$692$		0			0
$693$	−0.735999	−	1.27479i	−0.0279583	−	0.0484252i
$694$		0			0
$695$	−1.66834	−	2.88965i	−0.0632837	−	0.109610i
$696$		0			0
$697$	−1.88107			−0.0712505
$698$		0			0
$699$	4.85756	−	8.41354i	0.183730	−	0.318229i
$700$		0			0
$701$	−29.5048			−1.11438			−0.557190	−	0.830385i	$-0.688120\pi$
$701$	−29.5048			−1.11438			−0.557190	+	0.830385i	$0.688120\pi$
$702$		0			0
$703$	4.38226			0.165280
$704$		0			0
$705$	−0.713408	+	1.23566i	−0.0268685	+	0.0465376i
$706$		0			0
$707$	1.66952			0.0627887
$708$		0			0
$709$	9.87231	+	17.0994i	0.370763	+	0.642180i	0.989683	−	0.143274i	$-0.0457630\pi$
$709$	9.87231	+	17.0994i	0.370763	+	0.642180i	−0.618921	+	0.785454i	$0.712430\pi$
$710$		0			0
$711$	−13.1558	−	22.7865i	−0.493380	−	0.854559i
$712$		0			0
$713$	11.1392	−	19.2937i	0.417167	−	0.722555i
$714$		0			0
$715$	−7.33850	−	3.32364i	−0.274444	−	0.124297i
$716$		0			0
$717$	−3.15771	+	5.46931i	−0.117927	+	0.204255i
$718$		0			0
$719$	5.28734	+	9.15793i	0.197184	+	0.341533i	0.947614	−	0.319417i	$-0.103487\pi$
$719$	5.28734	+	9.15793i	0.197184	+	0.341533i	−0.750430	+	0.660950i	$0.770154\pi$
$720$		0			0
$721$	−1.77826	−	3.08003i	−0.0662257	−	0.114706i
$722$		0			0
$723$	1.23497			0.0459290
$724$		0			0
$725$	−0.00139469	+	0.00241567i	−5.17974e−5	+	8.97157e-5i
$726$		0			0
$727$	16.1291			0.598195			0.299097	−	0.954223i	$-0.403314\pi$
$727$	16.1291			0.598195			0.299097	+	0.954223i	$0.403314\pi$
$728$		0			0
$729$	−19.1740			−0.710149
$730$		0			0
$731$	0.694614	−	1.20311i	0.0256912	−	0.0444985i
$732$		0			0
$733$	45.4144			1.67742			0.838709	−	0.544580i	$-0.183311\pi$
$733$	45.4144			1.67742			0.838709	+	0.544580i	$0.183311\pi$
$734$		0			0
$735$	−2.92500	−	5.06624i	−0.107890	−	0.186871i
$736$		0			0
$737$	5.08267	+	8.80345i	0.187223	+	0.324279i
$738$		0			0
$739$	−8.06507	+	13.9691i	−0.296678	+	0.513862i	−0.975374	−	0.220558i	$-0.929212\pi$
$739$	−8.06507	+	13.9691i	−0.296678	+	0.513862i	0.678696	+	0.734420i	$0.262546\pi$
$740$		0			0
$741$	−0.370855	−	3.75929i	−0.0136237	−	0.138101i
$742$		0			0
$743$	22.0939	−	38.2678i	0.810548	−	1.40391i	−0.101933	−	0.994791i	$-0.532503\pi$
$743$	22.0939	−	38.2678i	0.810548	−	1.40391i	0.912481	−	0.409119i	$-0.134164\pi$
$744$		0			0
$745$	−4.27401	−	7.40281i	−0.156588	−	0.271218i
$746$		0			0
$747$	−4.18421	−	7.24727i	−0.153092	−	0.265164i
$748$		0			0
$749$	−3.48072			−0.127183
$750$		0			0
$751$	−4.30780	+	7.46132i	−0.157194	+	0.272268i	−0.933856	−	0.357650i	$-0.883578\pi$
$751$	−4.30780	+	7.46132i	−0.157194	+	0.272268i	0.776662	+	0.629918i	$0.216911\pi$
$752$		0			0
$753$	6.26236			0.228213
$754$		0			0
$755$	−38.0334			−1.38418
$756$		0			0
$757$	23.5725	−	40.8288i	0.856758	−	1.48395i	−0.0182473	−	0.999834i	$-0.505809\pi$
$757$	23.5725	−	40.8288i	0.856758	−	1.48395i	0.875005	−	0.484114i	$-0.160858\pi$
$758$		0			0
$759$	2.10448			0.0763880
$760$		0			0
$761$	8.91697	+	15.4446i	0.323240	+	0.559868i	0.981155	−	0.193225i	$-0.0618946\pi$
$761$	8.91697	+	15.4446i	0.323240	+	0.559868i	−0.657915	+	0.753093i	$0.728561\pi$
$762$		0			0
$763$	−3.04224	−	5.26931i	−0.110136	−	0.190762i
$764$		0			0
$765$	−5.77463	+	10.0020i	−0.208782	+	0.361621i
$766$		0			0
$767$	−8.05483	+	5.77393i	−0.290843	+	0.208484i
$768$		0			0
$769$	12.8605	−	22.2751i	0.463762	−	0.803260i	−0.535383	−	0.844610i	$-0.679833\pi$
$769$	12.8605	−	22.2751i	0.463762	−	0.803260i	0.999145	+	0.0413500i	$0.0131659\pi$
$770$		0			0
$771$	2.48927	+	4.31153i	0.0896487	+	0.155276i
$772$		0			0
$773$	5.59564	+	9.69194i	0.201261	+	0.348595i	0.948935	−	0.315471i	$-0.102163\pi$
$773$	5.59564	+	9.69194i	0.201261	+	0.348595i	−0.747674	+	0.664066i	$0.768829\pi$
$774$		0			0
$775$	−0.0316219			−0.00113589
$776$		0			0
$777$	−0.163406	+	0.283028i	−0.00586217	+	0.0101536i
$778$		0			0
$779$	2.79321			0.100077
$780$		0			0
$781$	7.61284			0.272409
$782$		0			0
$783$	0.412937	−	0.715227i	0.0147572	−	0.0255601i
$784$		0			0
$785$	18.4956			0.660135
$786$		0			0
$787$	20.2652	+	35.1004i	0.722377	+	1.25119i	0.960045	+	0.279847i	$0.0902837\pi$
$787$	20.2652	+	35.1004i	0.722377	+	1.25119i	−0.237668	+	0.971347i	$0.576383\pi$
$788$		0			0
$789$	3.70340	+	6.41448i	0.131844	+	0.228361i
$790$		0			0
$791$	−1.14690	+	1.98649i	−0.0407792	+	0.0706316i
$792$		0			0
$793$	−4.03458	+	2.89210i	−0.143272	+	0.102702i
$794$		0			0
$795$	1.00050	−	1.73292i	0.0354841	−	0.0614602i
$796$		0			0
$797$	10.4497	+	18.0995i	0.370148	+	0.641116i	0.989588	−	0.143929i	$-0.0459735\pi$
$797$	10.4497	+	18.0995i	0.370148	+	0.641116i	−0.619440	+	0.785044i	$0.712640\pi$
$798$		0			0
$799$	−1.48982	−	2.58045i	−0.0527062	−	0.0912898i
$800$		0			0
$801$	9.07234			0.320555
$802$		0			0
$803$	0.715599	−	1.23945i	0.0252530	−	0.0437394i
$804$		0			0
$805$	6.24812			0.220217
$806$		0			0
$807$	3.83603			0.135035
$808$		0			0
$809$	−24.3397	+	42.1576i	−0.855738	+	1.48218i	0.0202203	+	0.999796i	$0.493563\pi$
$809$	−24.3397	+	42.1576i	−0.855738	+	1.48218i	−0.875958	+	0.482387i	$0.839770\pi$
$810$		0			0
$811$	34.6081			1.21526			0.607628	−	0.794222i	$-0.292121\pi$
$811$	34.6081			1.21526			0.607628	+	0.794222i	$0.292121\pi$
$812$		0			0
$813$	1.21007	+	2.09591i	0.0424391	+	0.0735067i
$814$		0			0
$815$	−1.96973	−	3.41167i	−0.0689965	−	0.119506i
$816$		0			0
$817$	−1.03144	+	1.78650i	−0.0360854	+	0.0625017i
$818$		0			0
$819$	−4.83463	−	2.18963i	−0.168936	−	0.0765117i
$820$		0			0
$821$	4.24753	−	7.35694i	0.148240	−	0.256759i	−0.782337	−	0.622855i	$-0.785973\pi$
$821$	4.24753	−	7.35694i	0.148240	−	0.256759i	0.930577	+	0.366096i	$0.119306\pi$
$822$		0			0
$823$	15.9849	+	27.6866i	0.557197	+	0.965094i	0.997729	+	0.0673571i	$0.0214567\pi$
$823$	15.9849	+	27.6866i	0.557197	+	0.965094i	−0.440531	+	0.897737i	$0.645210\pi$
$824$		0			0
$825$	−0.00149355	−	0.00258690i	−5.19986e−5	−	9.00642e-5i
$826$		0			0
$827$	37.0984			1.29004			0.645018	−	0.764167i	$-0.276850\pi$
$827$	37.0984			1.29004			0.645018	+	0.764167i	$0.276850\pi$
$828$		0			0
$829$	3.71616	−	6.43657i	0.129067	−	0.223551i	−0.794248	−	0.607594i	$-0.792135\pi$
$829$	3.71616	−	6.43657i	0.129067	−	0.223551i	0.923316	+	0.384042i	$0.125468\pi$
$830$		0			0
$831$	−4.96279			−0.172157
$832$		0			0
$833$	12.2167			0.423282
$834$		0			0
$835$	5.63018	−	9.75176i	0.194840	−	0.337473i
$836$		0			0
$837$	9.36256			0.323618
$838$		0			0
$839$	4.94859	+	8.57121i	0.170844	+	0.295911i	0.938715	−	0.344694i	$-0.112017\pi$
$839$	4.94859	+	8.57121i	0.170844	+	0.295911i	−0.767871	+	0.640604i	$0.778684\pi$
$840$		0			0
$841$	14.4341	+	25.0005i	0.497727	+	0.862088i
$842$		0			0
$843$	4.36508	−	7.56054i	0.150341	−	0.260399i
$844$		0			0
$845$	−28.4866	+	5.67567i	−0.979970	+	0.195249i
$846$		0			0
$847$	0.258355	−	0.447484i	0.00887719	−	0.0153757i
$848$		0			0
$849$	−3.05376	−	5.28927i	−0.104805	−	0.181527i
$850$		0			0
$851$	4.40127	+	7.62322i	0.150873	+	0.261320i
$852$		0			0
$853$	25.0693			0.858357			0.429179	−	0.903220i	$-0.358803\pi$
$853$	25.0693			0.858357			0.429179	+	0.903220i	$0.358803\pi$
$854$		0			0
$855$	8.57478	−	14.8520i	0.293251	−	0.507926i
$856$		0			0
$857$	24.3183			0.830698			0.415349	−	0.909662i	$-0.363659\pi$
$857$	24.3183			0.830698			0.415349	+	0.909662i	$0.363659\pi$
$858$		0			0
$859$	31.0711			1.06013			0.530066	−	0.847957i	$-0.322167\pi$
$859$	31.0711			1.06013			0.530066	+	0.847957i	$0.322167\pi$
$860$		0			0
$861$	−0.104153	+	0.180399i	−0.00354954	+	0.00614798i
$862$		0			0
$863$	−30.2262			−1.02891			−0.514456	−	0.857517i	$-0.672006\pi$
$863$	−30.2262			−1.02891			−0.514456	+	0.857517i	$0.672006\pi$
$864$		0			0
$865$	13.2115	+	22.8831i	0.449206	+	0.778047i
$866$		0			0
$867$	−2.66522	−	4.61629i	−0.0905155	−	0.156777i
$868$		0			0
$869$	4.61803	−	7.99866i	0.156656	−	0.271336i
$870$		0			0
$871$	33.3871	+	15.1212i	1.13128	+	0.512361i
$872$		0			0
$873$	17.4956	−	30.3032i	0.592136	−	1.02561i
$874$		0			0
$875$	−2.89071	−	5.00686i	−0.0977240	−	0.169263i
$876$		0			0
$877$	2.37115	+	4.10695i	0.0800679	+	0.138682i	0.903279	−	0.429054i	$-0.141153\pi$
$877$	2.37115	+	4.10695i	0.0800679	+	0.138682i	−0.823211	+	0.567736i	$0.807820\pi$
$878$		0			0
$879$	2.33135			0.0786344
$880$		0			0
$881$	−21.4430	+	37.1403i	−0.722432	+	1.25129i	0.237591	+	0.971365i	$0.423642\pi$
$881$	−21.4430	+	37.1403i	−0.722432	+	1.25129i	−0.960022	+	0.279923i	$0.909691\pi$
$882$		0			0
$883$	−3.96202			−0.133333			−0.0666663	−	0.997775i	$-0.521236\pi$
$883$	−3.96202			−0.133333			−0.0666663	+	0.997775i	$0.521236\pi$
$884$		0			0
$885$	2.38820			0.0802785
$886$		0			0
$887$	−2.42375	+	4.19805i	−0.0813815	+	0.140957i	−0.903844	−	0.427863i	$-0.859267\pi$
$887$	−2.42375	+	4.19805i	−0.0813815	+	0.140957i	0.822462	+	0.568820i	$0.192600\pi$
$888$		0			0
$889$	5.65109			0.189532
$890$		0			0
$891$	−3.83097	−	6.63544i	−0.128342	−	0.222296i
$892$		0			0
$893$	2.21225	+	3.83173i	0.0740301	+	0.128224i
$894$		0			0
$895$	4.04689	−	7.00942i	0.135273	−	0.234299i
$896$		0			0
$897$	6.16704	−	4.42071i	0.205912	−	0.147603i
$898$		0			0
$899$	0.747407	−	1.29455i	0.0249274	−	0.0431755i
$900$		0			0
$901$	2.08937	+	3.61889i	0.0696069	+	0.120563i
$902$		0			0
$903$	−0.0769206	−	0.133230i	−0.00255976	−	0.00443363i
$904$		0			0
$905$	26.0153			0.864777
$906$		0			0
$907$	−7.17441	+	12.4264i	−0.238222	+	0.412613i	−0.960204	−	0.279299i	$-0.909898\pi$
$907$	−7.17441	+	12.4264i	−0.238222	+	0.412613i	0.721982	+	0.691912i	$0.243231\pi$
$908$		0			0
$909$	9.20458			0.305297
$910$		0			0
$911$	13.7273			0.454807			0.227403	−	0.973801i	$-0.426976\pi$
$911$	13.7273			0.454807			0.227403	+	0.973801i	$0.426976\pi$
$912$		0			0
$913$	1.46877	−	2.54399i	0.0486092	−	0.0841936i
$914$		0			0
$915$	1.19623			0.0395460
$916$		0			0
$917$	−4.80987	−	8.33094i	−0.158836	−	0.275112i
$918$		0			0
$919$	−4.66632	−	8.08230i	−0.153928	−	0.266610i	0.778740	−	0.627346i	$-0.215859\pi$
$919$	−4.66632	−	8.08230i	−0.153928	−	0.266610i	−0.932668	+	0.360736i	$0.882526\pi$
$920$		0			0
$921$	−2.75872	+	4.77825i	−0.0909030	+	0.157449i
$922$		0			0
$923$	22.3089	−	15.9916i	0.734306	−	0.526372i
$924$		0			0
$925$	0.00624713	−	0.0108203i	0.000205404	−	0.000355771i
$926$		0			0
$927$	−9.80408	−	16.9812i	−0.322008	−	0.557735i
$928$		0			0
$929$	−3.43829	−	5.95529i	−0.112807	−	0.195387i	0.804094	−	0.594502i	$-0.202651\pi$
$929$	−3.43829	−	5.95529i	−0.112807	−	0.195387i	−0.916901	+	0.399115i	$0.869317\pi$
$930$		0			0
$931$	−18.1406			−0.594534
$932$		0			0
$933$	6.43046	−	11.1379i	0.210524	−	0.364638i
$934$		0			0
$935$	−4.05410			−0.132583
$936$		0			0
$937$	−30.9678			−1.01167			−0.505837	−	0.862629i	$-0.668816\pi$
$937$	−30.9678			−1.01167			−0.505837	+	0.862629i	$0.668816\pi$
$938$		0			0
$939$	3.76093	−	6.51412i	0.122733	−	0.212580i
$940$		0			0
$941$	20.2992			0.661736			0.330868	−	0.943677i	$-0.392658\pi$
$941$	20.2992			0.661736			0.330868	+	0.943677i	$0.392658\pi$
$942$		0			0
$943$	2.80532	+	4.85895i	0.0913537	+	0.158229i
$944$		0			0
$945$	1.31289	+	2.27400i	0.0427084	+	0.0739731i
$946$		0			0
$947$	−9.03019	+	15.6408i	−0.293442	+	0.508256i	−0.974621	−	0.223860i	$-0.928134\pi$
$947$	−9.03019	+	15.6408i	−0.293442	+	0.508256i	0.681179	+	0.732117i	$0.261467\pi$
$948$		0			0
$949$	−0.506603	−	5.13533i	−0.0164450	−	0.166700i
$950$		0			0
$951$	−2.01397	+	3.48830i	−0.0653074	+	0.113116i
$952$		0			0
$953$	14.2333	+	24.6528i	0.461061	+	0.798581i	0.999014	−	0.0443937i	$-0.0141356\pi$
$953$	14.2333	+	24.6528i	0.461061	+	0.798581i	−0.537953	+	0.842975i	$0.680802\pi$
$954$		0			0
$955$	26.5865	+	46.0491i	0.860318	+	1.49011i
$956$		0			0
$957$	0.141204			0.00456448
$958$		0			0
$959$	−1.18504	+	2.05254i	−0.0382668	+	0.0662801i
$960$		0			0
$961$	−14.0540			−0.453353
$962$		0			0
$963$	−19.1903			−0.618399
$964$		0			0
$965$	29.7144	−	51.4668i	0.956539	−	1.65677i
$966$		0			0
$967$	6.01197			0.193332			0.0966659	−	0.995317i	$-0.469182\pi$
$967$	6.01197			0.193332			0.0966659	+	0.995317i	$0.469182\pi$
$968$		0			0
$969$	−0.950495	−	1.64631i	−0.0305343	−	0.0528870i
$970$		0			0
$971$	−9.60598	−	16.6380i	−0.308271	−	0.533940i	0.669714	−	0.742620i	$-0.266417\pi$
$971$	−9.60598	−	16.6380i	−0.308271	−	0.533940i	−0.977984	+	0.208679i	$0.933084\pi$
$972$		0			0
$973$	0.385816	−	0.668253i	0.0123687	−	0.0214232i
$974$		0			0
$975$	−0.00981081	−	0.00444336i	−0.000314197	−	0.000142301i
$976$		0			0
$977$	−26.3874	+	45.7044i	−0.844208	+	1.46221i	0.0420985	+	0.999113i	$0.486596\pi$
$977$	−26.3874	+	45.7044i	−0.844208	+	1.46221i	−0.886307	+	0.463098i	$0.846738\pi$
$978$		0			0
$979$	1.59232	+	2.75797i	0.0508907	+	0.0881452i
$980$		0			0
$981$	−16.7728	−	29.0514i	−0.535515	−	0.927538i
$982$		0			0
$983$	42.8304			1.36608			0.683039	−	0.730382i	$-0.260658\pi$
$983$	42.8304			1.36608			0.683039	+	0.730382i	$0.260658\pi$
$984$		0			0
$985$	−28.3440	+	49.0932i	−0.903115	+	1.56424i
$986$		0			0
$987$	−0.329962			−0.0105028
$988$		0			0
$989$	−4.14363			−0.131760
$990$		0			0
$991$	−15.1177	+	26.1846i	−0.480229	+	0.831781i	−0.999743	−	0.0226813i	$-0.992780\pi$
$991$	−15.1177	+	26.1846i	−0.480229	+	0.831781i	0.519514	+	0.854462i	$0.326113\pi$
$992$		0			0
$993$	6.49128			0.205995
$994$		0			0
$995$	−22.7768	−	39.4506i	−0.722074	−	1.25067i
$996$		0			0
$997$	11.2386	+	19.4658i	0.355929	+	0.616488i	0.987277	−	0.159012i	$-0.0508310\pi$
$997$	11.2386	+	19.4658i	0.355929	+	0.616488i	−0.631347	+	0.775500i	$0.717498\pi$
$998$		0			0
$999$	−1.84964	+	3.20367i	−0.0585200	+	0.101360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.c.529.3	yes	10
13.3	even	3	inner	572.2.i.c.133.3	✓	10
13.4	even	6		7436.2.a.q.1.3		5
13.9	even	3		7436.2.a.r.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.c.133.3	✓	10	13.3	even	3	inner
572.2.i.c.529.3	yes	10	1.1	even	1	trivial
7436.2.a.q.1.3		5	13.4	even	6
7436.2.a.r.1.3		5	13.9	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.194431 - 0.336764i) q^{3} +2.23435 q^{5} +(0.258355 + 0.447484i) q^{7} +(1.42439 + 2.46712i) q^{9} +O(q^{10})\)	\(q+(0.194431 - 0.336764i) q^{3} +2.23435 q^{5} +(0.258355 + 0.447484i) q^{7} +(1.42439 + 2.46712i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.353971 + 3.58813i) q^{13} +(0.434426 - 0.752448i) q^{15} +(0.907221 + 1.57135i) q^{17} +(-1.34714 - 2.33331i) q^{19} +0.200929 q^{21} +(2.70596 - 4.68686i) q^{23} -0.00768164 q^{25} +2.27437 q^{27} +(0.181561 - 0.314473i) q^{29} +4.11656 q^{31} +(0.194431 + 0.336764i) q^{33} +(0.577256 + 0.999837i) q^{35} +(-0.813255 + 1.40860i) q^{37} +(1.27718 + 0.578439i) q^{39} +(-0.518360 + 0.897825i) q^{41} +(-0.382825 - 0.663073i) q^{43} +(3.18259 + 5.51241i) q^{45} -1.64218 q^{47} +(3.36651 - 5.83096i) q^{49} +0.705567 q^{51} +2.30304 q^{53} +(-1.11717 + 1.93500i) q^{55} -1.04770 q^{57} +(1.37434 + 2.38043i) q^{59} +(0.688394 + 1.19233i) q^{61} +(-0.735999 + 1.27479i) q^{63} +(0.790895 + 8.01715i) q^{65} +(5.08267 - 8.80345i) q^{67} +(-1.05224 - 1.82254i) q^{69} +(-3.80642 - 6.59292i) q^{71} -1.43120 q^{73} +(-0.00149355 + 0.00258690i) q^{75} -0.516710 q^{77} -9.23605 q^{79} +(-3.83097 + 6.63544i) q^{81} -2.93754 q^{83} +(2.02705 + 3.51095i) q^{85} +(-0.0706021 - 0.122286i) q^{87} +(1.59232 - 2.75797i) q^{89} +(-1.51418 + 1.08541i) q^{91} +(0.800385 - 1.38631i) q^{93} +(-3.00998 - 5.21343i) q^{95} +(-6.14142 - 10.6372i) q^{97} -2.84879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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