LMFDB - Embedded newform 500.2.i.a.449.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [500,2,Mod(49,500)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("500.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(500, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			449.2
Root			$-0.357358 + 1.86824i$ of defining polynomial
Character	$\chi$	$=$	500.449
Dual form			500.2.i.a.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19625 + 0.713605i) q^{3} +4.21139i q^{7} +(1.88723 + 1.37116i) q^{9} +(0.451659 - 0.328150i) q^{11} +(2.36877 - 3.26033i) q^{13} +(-3.76832 + 1.22440i) q^{17} +(2.14177 + 6.59168i) q^{19} +(-3.00527 + 9.24926i) q^{21} +(0.224115 + 0.308467i) q^{23} +(-0.905698 - 1.24659i) q^{27} +(2.48680 - 7.65359i) q^{29} +(-0.0767462 - 0.236201i) q^{31} +(1.22613 - 0.398393i) q^{33} +(4.21760 - 5.80503i) q^{37} +(7.52900 - 5.47014i) q^{39} +(3.68773 + 2.67929i) q^{41} -0.207272i q^{43} +(-8.80576 - 2.86117i) q^{47} -10.7358 q^{49} -9.14992 q^{51} +(-2.24547 - 0.729597i) q^{53} +16.0054i q^{57} +(2.93557 + 2.13282i) q^{59} +(3.15785 - 2.29431i) q^{61} +(-5.77447 + 7.94787i) q^{63} +(6.56267 - 2.13234i) q^{67} +(0.272088 + 0.837401i) q^{69} +(4.44084 - 13.6675i) q^{71} +(-1.32482 - 1.82346i) q^{73} +(1.38197 + 1.90211i) q^{77} +(-2.35970 + 7.26242i) q^{79} +(-3.26215 - 10.0399i) q^{81} +(7.22667 - 2.34809i) q^{83} +(10.9233 - 15.0346i) q^{87} +(-12.9713 + 9.42417i) q^{89} +(13.7305 + 9.97581i) q^{91} -0.573522i q^{93} +(-3.11093 - 1.01080i) q^{97} +1.30233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{9} + 5 q^{11} + 5 q^{17} - 8 q^{19} - 2 q^{21} + 20 q^{23} - 8 q^{29} - 12 q^{31} - 15 q^{33} + 10 q^{37} + 22 q^{39} + 13 q^{41} - 45 q^{47} + 14 q^{49} - 14 q^{51} - 30 q^{53} + 9 q^{59} + 16 q^{61}+ \cdots + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^9 + 5 * q^11 + 5 * q^17 - 8 * q^19 - 2 * q^21 + 20 * q^23 - 8 * q^29 - 12 * q^31 - 15 * q^33 + 10 * q^37 + 22 * q^39 + 13 * q^41 - 45 * q^47 + 14 * q^49 - 14 * q^51 - 30 * q^53 + 9 * q^59 + 16 * q^61 - 20 * q^63 + 5 * q^67 - 14 * q^69 - q^71 + 60 * q^73 + 20 * q^77 - 24 * q^79 - 3 * q^81 + 10 * q^83 + 55 * q^87 - 37 * q^89 + 32 * q^91 - 25 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$	2.19625	+	0.713605i	1.26801	+	0.412000i	0.864341	−	0.502907i	$-0.167736\pi$
$3$	2.19625	+	0.713605i	1.26801	+	0.412000i	0.403665	+	0.914907i	$0.367736\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.21139i			1.59175i	0.605458	+	0.795877i	$0.292990\pi$
$7$			4.21139i			1.59175i	−0.605458	+	0.795877i	$0.707010\pi$
$8$		0			0
$9$	1.88723	+	1.37116i	0.629078	+	0.457052i
$10$		0			0
$11$	0.451659	−	0.328150i	0.136180	−	0.0989409i	−0.517610	−	0.855617i	$-0.673178\pi$
$11$	0.451659	−	0.328150i	0.136180	−	0.0989409i	0.653790	+	0.756676i	$0.273178\pi$
$12$		0			0
$13$	2.36877	−	3.26033i	0.656978	−	0.904253i	−0.342398	−	0.939555i	$-0.611239\pi$
$13$	2.36877	−	3.26033i	0.656978	−	0.904253i	0.999377	+	0.0353017i	$0.0112392\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.76832	+	1.22440i	−0.913953	+	0.296961i	−0.727984	−	0.685594i	$-0.759542\pi$
$17$	−3.76832	+	1.22440i	−0.913953	+	0.296961i	−0.185969	+	0.982556i	$0.559542\pi$
$18$		0			0
$19$	2.14177	+	6.59168i	0.491355	+	1.51223i	0.822561	+	0.568676i	$0.192544\pi$
$19$	2.14177	+	6.59168i	0.491355	+	1.51223i	−0.331207	+	0.943558i	$0.607456\pi$
$20$		0			0
$21$	−3.00527	+	9.24926i	−0.655803	+	2.01835i
$22$		0			0
$23$	0.224115	+	0.308467i	0.0467311	+	0.0643199i	0.831743	−	0.555161i	$-0.187343\pi$
$23$	0.224115	+	0.308467i	0.0467311	+	0.0643199i	−0.785012	+	0.619481i	$0.787343\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.905698	−	1.24659i	−0.174302	−	0.239906i
$28$		0			0
$29$	2.48680	−	7.65359i	0.461788	−	1.42124i	−0.401190	−	0.915995i	$-0.631403\pi$
$29$	2.48680	−	7.65359i	0.461788	−	1.42124i	0.862978	−	0.505242i	$-0.168597\pi$
$30$		0			0
$31$	−0.0767462	−	0.236201i	−0.0137840	−	0.0424229i	0.943928	−	0.330152i	$-0.107100\pi$
$31$	−0.0767462	−	0.236201i	−0.0137840	−	0.0424229i	−0.957712	+	0.287729i	$0.907100\pi$
$32$		0			0
$33$	1.22613	−	0.398393i	0.213441	−	0.0693513i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.21760	−	5.80503i	0.693370	−	0.954342i	−0.306627	−	0.951830i	$-0.599200\pi$
$37$	4.21760	−	5.80503i	0.693370	−	0.954342i	0.999997	−	0.00251186i	$-0.000799552\pi$
$38$		0			0
$39$	7.52900	−	5.47014i	1.20560	−	0.875923i
$40$		0			0
$41$	3.68773	+	2.67929i	0.575926	+	0.418435i	0.837253	−	0.546815i	$-0.184160\pi$
$41$	3.68773	+	2.67929i	0.575926	+	0.418435i	−0.261327	+	0.965250i	$0.584160\pi$
$42$		0			0
$43$		−	0.207272i		−	0.0316086i	−0.999875	−	0.0158043i	$-0.994969\pi$
$43$		−	0.207272i		−	0.0316086i	0.999875	−	0.0158043i	$-0.00503088\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.80576	−	2.86117i	−1.28445	−	0.417344i	−0.414306	−	0.910138i	$-0.635976\pi$
$47$	−8.80576	−	2.86117i	−1.28445	−	0.417344i	−0.870146	+	0.492794i	$0.835976\pi$
$48$		0			0
$49$	−10.7358			−1.53368
$50$		0			0
$51$	−9.14992			−1.28125
$52$		0			0
$53$	−2.24547	−	0.729597i	−0.308439	−	0.100218i	0.150708	−	0.988578i	$-0.451845\pi$
$53$	−2.24547	−	0.729597i	−0.308439	−	0.100218i	−0.459147	+	0.888361i	$0.651845\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			16.0054i			2.11996i
$58$		0			0
$59$	2.93557	+	2.13282i	0.382179	+	0.277669i	0.762243	−	0.647291i	$-0.224098\pi$
$59$	2.93557	+	2.13282i	0.382179	+	0.277669i	−0.380064	+	0.924960i	$0.624098\pi$
$60$		0			0
$61$	3.15785	−	2.29431i	0.404321	−	0.293757i	−0.366977	−	0.930230i	$-0.619607\pi$
$61$	3.15785	−	2.29431i	0.404321	−	0.293757i	0.771299	+	0.636473i	$0.219607\pi$
$62$		0			0
$63$	−5.77447	+	7.94787i	−0.727514	+	1.00134i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.56267	−	2.13234i	0.801758	−	0.260507i	0.120655	−	0.992695i	$-0.461501\pi$
$67$	6.56267	−	2.13234i	0.801758	−	0.260507i	0.681103	+	0.732187i	$0.261501\pi$
$68$		0			0
$69$	0.272088	+	0.837401i	0.0327556	+	0.100811i
$70$		0			0
$71$	4.44084	−	13.6675i	0.527031	−	1.62203i	−0.233233	−	0.972421i	$-0.574931\pi$
$71$	4.44084	−	13.6675i	0.527031	−	1.62203i	0.760264	−	0.649614i	$-0.225069\pi$
$72$		0			0
$73$	−1.32482	−	1.82346i	−0.155058	−	0.213420i	0.724419	−	0.689360i	$-0.242108\pi$
$73$	−1.32482	−	1.82346i	−0.155058	−	0.213420i	−0.879478	+	0.475940i	$0.842108\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.38197	+	1.90211i	0.157490	+	0.216766i
$78$		0			0
$79$	−2.35970	+	7.26242i	−0.265487	+	0.817086i	0.726093	+	0.687596i	$0.241334\pi$
$79$	−2.35970	+	7.26242i	−0.265487	+	0.817086i	−0.991581	+	0.129490i	$0.958666\pi$
$80$		0			0
$81$	−3.26215	−	10.0399i	−0.362461	−	1.11554i
$82$		0			0
$83$	7.22667	−	2.34809i	0.793230	−	0.257736i	0.115751	−	0.993278i	$-0.463073\pi$
$83$	7.22667	−	2.34809i	0.793230	−	0.257736i	0.677479	+	0.735542i	$0.263073\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.9233	−	15.0346i	1.17110	−	1.61188i
$88$		0			0
$89$	−12.9713	+	9.42417i	−1.37495	+	0.998960i	−0.377619	+	0.925961i	$0.623257\pi$
$89$	−12.9713	+	9.42417i	−1.37495	+	0.998960i	−0.997332	+	0.0729990i	$0.976743\pi$
$90$		0			0
$91$	13.7305	+	9.97581i	1.43935	+	1.04575i
$92$		0			0
$93$		−	0.573522i		−	0.0594715i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.11093	−	1.01080i	−0.315867	−	0.102631i	0.146793	−	0.989167i	$-0.453105\pi$
$97$	−3.11093	−	1.01080i	−0.315867	−	0.102631i	−0.462660	+	0.886536i	$0.653105\pi$
$98$		0			0
$99$	1.30233			0.130889
$100$		0			0
$101$	−9.34504			−0.929866			−0.464933	−	0.885346i	$-0.653922\pi$
$101$	−9.34504			−0.929866			−0.464933	+	0.885346i	$0.653922\pi$
$102$		0			0
$103$	−5.69721	−	1.85114i	−0.561363	−	0.182398i	0.0145714	−	0.999894i	$-0.495362\pi$
$103$	−5.69721	−	1.85114i	−0.561363	−	0.182398i	−0.575934	+	0.817496i	$0.695362\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	5.60078i		−	0.541448i	−0.962657	−	0.270724i	$-0.912737\pi$
$107$		−	5.60078i		−	0.541448i	0.962657	−	0.270724i	$-0.0872630\pi$
$108$		0			0
$109$	−11.1078	−	8.07030i	−1.06394	−	0.772994i	−0.0891229	−	0.996021i	$-0.528406\pi$
$109$	−11.1078	−	8.07030i	−1.06394	−	0.772994i	−0.974812	+	0.223026i	$0.928406\pi$
$110$		0			0
$111$	13.4054	−	9.73960i	1.27239	−	0.924442i
$112$		0			0
$113$	2.38489	−	3.28252i	0.224351	−	0.308793i	−0.681972	−	0.731378i	$-0.738877\pi$
$113$	2.38489	−	3.28252i	0.224351	−	0.308793i	0.906323	+	0.422585i	$0.138877\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.94084	−	2.90506i	0.826581	−	0.268572i
$118$		0			0
$119$	−5.15643	−	15.8699i	−0.472689	−	1.45479i
$120$		0			0
$121$	−3.30287	+	10.1652i	−0.300261	+	0.924109i
$122$		0			0
$123$	6.18722	+	8.51598i	0.557883	+	0.767860i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.42708	+	3.34059i	0.215369	+	0.296430i	0.903009	−	0.429622i	$-0.141353\pi$
$127$	2.42708	+	3.34059i	0.215369	+	0.296430i	−0.687640	+	0.726052i	$0.741353\pi$
$128$		0			0
$129$	0.147910	−	0.455220i	0.0130228	−	0.0400799i
$130$		0			0
$131$	−4.07116	−	12.5298i	−0.355699	−	1.09473i	−0.955603	−	0.294657i	$-0.904794\pi$
$131$	−4.07116	−	12.5298i	−0.355699	−	1.09473i	0.599904	−	0.800072i	$-0.295206\pi$
$132$		0			0
$133$	−27.7601	+	9.01981i	−2.40711	+	0.782116i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.975024	−	1.34201i	0.0833020	−	0.114655i	−0.765332	−	0.643635i	$-0.777425\pi$
$137$	0.975024	−	1.34201i	0.0833020	−	0.114655i	0.848634	+	0.528980i	$0.177425\pi$
$138$		0			0
$139$	−0.567399	+	0.412240i	−0.0481262	+	0.0349657i	−0.611588	−	0.791176i	$-0.709469\pi$
$139$	−0.567399	+	0.412240i	−0.0481262	+	0.0349657i	0.563462	+	0.826142i	$0.309469\pi$
$140$		0			0
$141$	−17.2979	−	12.5677i	−1.45675	−	1.05839i
$142$		0			0
$143$		−	2.24987i		−	0.188144i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−23.5785	−	7.66111i	−1.94472	−	0.631878i
$148$		0			0
$149$	18.3234			1.50111			0.750556	−	0.660807i	$-0.229786\pi$
$149$	18.3234			1.50111			0.750556	+	0.660807i	$0.229786\pi$
$150$		0			0
$151$	0.0521578			0.00424454			0.00212227	−	0.999998i	$-0.499324\pi$
$151$	0.0521578			0.00424454			0.00212227	+	0.999998i	$0.499324\pi$
$152$		0			0
$153$	−8.79055	−	2.85622i	−0.710674	−	0.230912i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			3.18979i			0.254573i	0.991866	+	0.127287i	$0.0406268\pi$
$157$			3.18979i			0.254573i	−0.991866	+	0.127287i	$0.959373\pi$
$158$		0			0
$159$	−4.41097	−	3.20475i	−0.349812	−	0.254154i
$160$		0			0
$161$	−1.29908	+	0.943834i	−0.102382	+	0.0743845i
$162$		0			0
$163$	−6.88310	+	9.47378i	−0.539126	+	0.742043i	−0.988487	−	0.151307i	$-0.951652\pi$
$163$	−6.88310	+	9.47378i	−0.539126	+	0.742043i	0.449361	+	0.893350i	$0.351652\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.2226	−	5.59596i	1.33272	−	0.433028i	0.445878	−	0.895094i	$-0.352891\pi$
$167$	17.2226	−	5.59596i	1.33272	−	0.433028i	0.886846	+	0.462065i	$0.152891\pi$
$168$		0			0
$169$	−1.00147	−	3.08221i	−0.0770362	−	0.237093i
$170$		0			0
$171$	−4.99620	+	15.3767i	−0.382069	+	1.17589i
$172$		0			0
$173$	−10.1561	−	13.9787i	−0.772154	−	1.06278i	−0.996105	−	0.0881782i	$-0.971896\pi$
$173$	−10.1561	−	13.9787i	−0.772154	−	1.06278i	0.223951	−	0.974600i	$-0.428104\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.92527	+	6.77905i	0.370206	+	0.509544i
$178$		0			0
$179$	−1.23318	+	3.79534i	−0.0921722	+	0.283677i	−0.986506	−	0.163723i	$-0.947650\pi$
$179$	−1.23318	+	3.79534i	−0.0921722	+	0.283677i	0.894334	+	0.447399i	$0.147650\pi$
$180$		0			0
$181$	0.544543	+	1.67593i	0.0404756	+	0.124571i	0.969253	−	0.246068i	$-0.0791387\pi$
$181$	0.544543	+	1.67593i	0.0404756	+	0.124571i	−0.928777	+	0.370639i	$0.879139\pi$
$182$		0			0
$183$	8.57267	−	2.78543i	0.633710	−	0.205905i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.30021	+	1.78959i	−0.0950809	+	0.130868i
$188$		0			0
$189$	5.24986	−	3.81425i	0.381871	−	0.277446i
$190$		0			0
$191$	6.03752	+	4.38652i	0.436860	+	0.317397i	0.784386	−	0.620273i	$-0.212978\pi$
$191$	6.03752	+	4.38652i	0.436860	+	0.317397i	−0.347526	+	0.937670i	$0.612978\pi$
$192$		0			0
$193$			15.6167i			1.12411i	0.827099	+	0.562057i	$0.189990\pi$
$193$			15.6167i			1.12411i	−0.827099	+	0.562057i	$0.810010\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−23.6236	−	7.67578i	−1.68311	−	0.546876i	−0.697601	−	0.716486i	$-0.745749\pi$
$197$	−23.6236	−	7.67578i	−1.68311	−	0.546876i	−0.985511	+	0.169610i	$0.945749\pi$
$198$		0			0
$199$	4.27124			0.302780			0.151390	−	0.988474i	$-0.451625\pi$
$199$	4.27124			0.302780			0.151390	+	0.988474i	$0.451625\pi$
$200$		0			0
$201$	15.9349			1.12396
$202$		0			0
$203$	32.2322	+	10.4729i	2.26226	+	0.735053i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			0.889446i			0.0618208i
$208$		0			0
$209$	3.13041	+	2.27437i	0.216535	+	0.157322i
$210$		0			0
$211$	−6.77130	+	4.91963i	−0.466155	+	0.338682i	−0.795941	−	0.605374i	$-0.793023\pi$
$211$	−6.77130	+	4.91963i	−0.466155	+	0.338682i	0.329786	+	0.944056i	$0.393023\pi$
$212$		0			0
$213$	19.5064	−	26.8483i	1.33656	−	1.83961i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.994732	−	0.323208i	0.0675268	−	0.0219408i
$218$		0			0
$219$	−1.60841	−	4.95017i	−0.108686	−	0.334501i
$220$		0			0
$221$	−4.93433	+	15.1863i	−0.331919	+	1.02154i
$222$		0			0
$223$	−5.22143	−	7.18669i	−0.349653	−	0.481256i	0.597577	−	0.801812i	$-0.296130\pi$
$223$	−5.22143	−	7.18669i	−0.349653	−	0.481256i	−0.947230	+	0.320556i	$0.896130\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.66960	+	9.17991i	0.442677	+	0.609292i	0.970804	−	0.239873i	$-0.0771057\pi$
$227$	6.66960	+	9.17991i	0.442677	+	0.609292i	−0.528128	+	0.849165i	$0.677106\pi$
$228$		0			0
$229$	−8.24697	+	25.3816i	−0.544975	+	1.67726i	0.176074	+	0.984377i	$0.443660\pi$
$229$	−8.24697	+	25.3816i	−0.544975	+	1.67726i	−0.721049	+	0.692884i	$0.756340\pi$
$230$		0			0
$231$	1.67779	+	5.16369i	0.110390	+	0.339746i
$232$		0			0
$233$	18.4566	−	5.99693i	1.20913	−	0.392872i	0.366021	−	0.930607i	$-0.380720\pi$
$233$	18.4566	−	5.99693i	1.20913	−	0.392872i	0.843114	+	0.537735i	$0.180720\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−10.3650	+	14.2662i	−0.673279	+	0.926690i
$238$		0			0
$239$	−3.88485	+	2.82251i	−0.251290	+	0.182573i	−0.706298	−	0.707914i	$-0.749636\pi$
$239$	−3.88485	+	2.82251i	−0.251290	+	0.182573i	0.455008	+	0.890487i	$0.349636\pi$
$240$		0			0
$241$	16.3125	+	11.8517i	1.05078	+	0.763438i	0.972361	−	0.233482i	$-0.0750120\pi$
$241$	16.3125	+	11.8517i	1.05078	+	0.763438i	0.0784214	+	0.996920i	$0.475012\pi$
$242$		0			0
$243$		−	19.7553i		−	1.26730i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	26.5644	+	8.63130i	1.69025	+	0.549196i
$248$		0			0
$249$	17.5472			1.11201
$250$		0			0
$251$	−13.8723			−0.875614			−0.437807	−	0.899069i	$-0.644245\pi$
$251$	−13.8723			−0.875614			−0.437807	+	0.899069i	$0.644245\pi$
$252$		0			0
$253$	0.202447	+	0.0657790i	0.0127277	+	0.00413549i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			4.27079i			0.266405i	0.991089	+	0.133202i	$0.0425260\pi$
$257$			4.27079i			0.266405i	−0.991089	+	0.133202i	$0.957474\pi$
$258$		0			0
$259$	24.4472	+	17.7620i	1.51908	+	1.10367i
$260$		0			0
$261$	15.1874	−	11.0343i	0.940079	−	0.683008i
$262$		0			0
$263$	−6.88718	+	9.47939i	−0.424682	+	0.584524i	−0.966722	−	0.255828i	$-0.917652\pi$
$263$	−6.88718	+	9.47939i	−0.424682	+	0.584524i	0.542041	+	0.840352i	$0.317652\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−35.2133	+	11.4415i	−2.15502	+	0.700208i
$268$		0			0
$269$	3.26685	+	10.0543i	0.199184	+	0.613024i	0.999902	+	0.0139833i	$0.00445118\pi$
$269$	3.26685	+	10.0543i	0.199184	+	0.613024i	−0.800719	+	0.599041i	$0.795549\pi$
$270$		0			0
$271$	4.02897	−	12.3999i	0.244742	−	0.753239i	−0.750936	−	0.660375i	$-0.770398\pi$
$271$	4.02897	−	12.3999i	0.244742	−	0.753239i	0.995679	−	0.0928649i	$-0.0296025\pi$
$272$		0			0
$273$	23.0369	+	31.7075i	1.39426	+	1.91903i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7.36175	+	10.1326i	0.442325	+	0.608808i	0.970727	−	0.240187i	$-0.0772086\pi$
$277$	7.36175	+	10.1326i	0.442325	+	0.608808i	−0.528402	+	0.848994i	$0.677209\pi$
$278$		0			0
$279$	0.179030	−	0.550997i	0.0107182	−	0.0329873i
$280$		0			0
$281$	0.591748	+	1.82121i	0.0353007	+	0.108645i	0.967154	−	0.254190i	$-0.0818089\pi$
$281$	0.591748	+	1.82121i	0.0353007	+	0.108645i	−0.931853	+	0.362835i	$0.881809\pi$
$282$		0			0
$283$	8.25224	−	2.68131i	0.490545	−	0.159388i	−0.0532916	−	0.998579i	$-0.516971\pi$
$283$	8.25224	−	2.68131i	0.490545	−	0.159388i	0.543836	+	0.839191i	$0.316971\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.2835	+	15.5304i	−0.666046	+	0.916733i
$288$		0			0
$289$	−1.05219	+	0.764461i	−0.0618935	+	0.0449683i
$290$		0			0
$291$	−6.11107	−	4.43995i	−0.358237	−	0.260274i
$292$		0			0
$293$			18.1632i			1.06110i	0.847653	+	0.530551i	$0.178015\pi$
$293$			18.1632i			1.06110i	−0.847653	+	0.530551i	$0.821985\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.818134	−	0.265828i	−0.0474730	−	0.0154249i
$298$		0			0
$299$	1.53658			0.0888628
$300$		0			0
$301$	0.872901			0.0503132
$302$		0			0
$303$	−20.5240	−	6.66867i	−1.17908	−	0.383105i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			23.4255i			1.33696i	0.743729	+	0.668481i	$0.233055\pi$
$307$			23.4255i			1.33696i	−0.743729	+	0.668481i	$0.766945\pi$
$308$		0			0
$309$	−11.1915	−	8.13112i	−0.636664	−	0.462563i
$310$		0			0
$311$	−18.8884	+	13.7232i	−1.07106	+	0.778171i	−0.976103	−	0.217310i	$-0.930272\pi$
$311$	−18.8884	+	13.7232i	−1.07106	+	0.778171i	−0.0949585	+	0.995481i	$0.530272\pi$
$312$		0			0
$313$	3.42702	−	4.71689i	0.193707	−	0.266614i	−0.701105	−	0.713058i	$-0.747310\pi$
$313$	3.42702	−	4.71689i	0.193707	−	0.266614i	0.894812	+	0.446444i	$0.147310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.11662	−	2.31233i	0.399709	−	0.129873i	−0.102263	−	0.994757i	$-0.532608\pi$
$317$	7.11662	−	2.31233i	0.399709	−	0.129873i	0.501972	+	0.864884i	$0.332608\pi$
$318$		0			0
$319$	−1.38834	−	4.27286i	−0.0777319	−	0.239234i
$320$		0			0
$321$	3.99674	−	12.3007i	0.223077	−	0.686559i
$322$		0			0
$323$	−16.1417	−	22.2172i	−0.898150	−	1.23620i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−18.6365	−	25.6510i	−1.03060	−	1.41850i
$328$		0			0
$329$	12.0495	−	37.0845i	0.664309	−	2.04453i
$330$		0			0
$331$	9.33063	+	28.7167i	0.512858	+	1.57841i	0.787146	+	0.616766i	$0.211558\pi$
$331$	9.33063	+	28.7167i	0.512858	+	1.57841i	−0.274288	+	0.961647i	$0.588442\pi$
$332$		0			0
$333$	15.9192	−	5.17246i	0.872367	−	0.283449i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	13.1292	−	18.0708i	0.715193	−	0.984379i	−0.284477	−	0.958683i	$-0.591820\pi$
$337$	13.1292	−	18.0708i	0.715193	−	0.984379i	0.999670	−	0.0256956i	$-0.00818008\pi$
$338$		0			0
$339$	7.58023	−	5.50736i	0.411702	−	0.299119i
$340$		0			0
$341$	−0.112172	−	0.0814980i	−0.00607447	−	0.00441336i
$342$		0			0
$343$		−	15.7328i		−	0.849494i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.6197	+	3.45054i	0.570094	+	0.185235i	0.579858	−	0.814717i	$-0.303108\pi$
$347$	10.6197	+	3.45054i	0.570094	+	0.185235i	−0.00976387	+	0.999952i	$0.503108\pi$
$348$		0			0
$349$	−4.15360			−0.222337			−0.111168	−	0.993802i	$-0.535459\pi$
$349$	−4.15360			−0.222337			−0.111168	+	0.993802i	$0.535459\pi$
$350$		0			0
$351$	−6.20967			−0.331448
$352$		0			0
$353$	−4.18122	−	1.35856i	−0.222544	−	0.0723088i	0.195623	−	0.980679i	$-0.437327\pi$
$353$	−4.18122	−	1.35856i	−0.222544	−	0.0723088i	−0.418167	+	0.908370i	$0.637327\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	38.5339i		−	2.03943i
$358$		0			0
$359$	−0.385816	−	0.280311i	−0.0203626	−	0.0147943i	0.577557	−	0.816350i	$-0.304006\pi$
$359$	−0.385816	−	0.280311i	−0.0203626	−	0.0147943i	−0.597920	+	0.801556i	$0.704006\pi$
$360$		0			0
$361$	−23.4917	+	17.0677i	−1.23641	+	0.898302i
$362$		0			0
$363$	−14.5079	+	19.9684i	−0.761466	+	1.04807i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.50343	−	0.813414i	0.130678	−	0.0424599i	−0.242948	−	0.970039i	$-0.578114\pi$
$367$	2.50343	−	0.813414i	0.130678	−	0.0424599i	0.373626	+	0.927579i	$0.378114\pi$
$368$		0			0
$369$	3.28588	+	10.1129i	0.171056	+	0.526456i
$370$		0			0
$371$	3.07261	−	9.45653i	0.159522	−	0.490959i
$372$		0			0
$373$	14.7310	+	20.2755i	0.762743	+	1.04983i	0.996981	+	0.0776460i	$0.0247404\pi$
$373$	14.7310	+	20.2755i	0.762743	+	1.04983i	−0.234238	+	0.972179i	$0.575260\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.0626	−	26.2374i	−0.981773	−	1.35129i
$378$		0			0
$379$	0.674898	−	2.07712i	0.0346672	−	0.106695i	−0.932226	−	0.361878i	$-0.882136\pi$
$379$	0.674898	−	2.07712i	0.0346672	−	0.106695i	0.966893	+	0.255183i	$0.0821358\pi$
$380$		0			0
$381$	2.94662	+	9.06876i	0.150960	+	0.464607i
$382$		0			0
$383$	−22.6990	+	7.37534i	−1.15986	+	0.376862i	−0.824850	−	0.565351i	$-0.808741\pi$
$383$	−22.6990	+	7.37534i	−1.15986	+	0.376862i	−0.335013	+	0.942214i	$0.608741\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.284202	−	0.391170i	0.0144468	−	0.0198843i
$388$		0			0
$389$	16.1638	−	11.7437i	0.819537	−	0.595429i	−0.0970428	−	0.995280i	$-0.530938\pi$
$389$	16.1638	−	11.7437i	0.819537	−	0.595429i	0.916580	+	0.399852i	$0.130938\pi$
$390$		0			0
$391$	−1.22222	−	0.887998i	−0.0618106	−	0.0449080i
$392$		0			0
$393$		−	30.4237i		−	1.53467i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	16.0422	+	5.21244i	0.805137	+	0.261605i	0.682537	−	0.730851i	$-0.260877\pi$
$397$	16.0422	+	5.21244i	0.805137	+	0.261605i	0.122600	+	0.992456i	$0.460877\pi$
$398$		0			0
$399$	−67.4047			−3.37446
$400$		0			0
$401$	5.14817			0.257087			0.128544	−	0.991704i	$-0.458970\pi$
$401$	5.14817			0.257087			0.128544	+	0.991704i	$0.458970\pi$
$402$		0			0
$403$	−0.951886	−	0.309287i	−0.0474168	−	0.0154067i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4.00590i		−	0.198565i
$408$		0			0
$409$	−4.36350	−	3.17027i	−0.215761	−	0.156760i	0.474655	−	0.880172i	$-0.342573\pi$
$409$	−4.36350	−	3.17027i	−0.215761	−	0.156760i	−0.690417	+	0.723412i	$0.742573\pi$
$410$		0			0
$411$	3.09906	−	2.25160i	0.152865	−	0.111063i
$412$		0			0
$413$	−8.98213	+	12.3628i	−0.441982	+	0.608336i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.54033	+	0.500482i	−0.0754301	+	0.0245087i
$418$		0			0
$419$	7.67959	+	23.6354i	0.375173	+	1.15466i	0.943362	+	0.331765i	$0.107644\pi$
$419$	7.67959	+	23.6354i	0.375173	+	1.15466i	−0.568190	+	0.822898i	$0.692356\pi$
$420$		0			0
$421$	10.4110	−	32.0418i	0.507401	−	1.56162i	−0.289295	−	0.957240i	$-0.593421\pi$
$421$	10.4110	−	32.0418i	0.507401	−	1.56162i	0.796696	−	0.604380i	$-0.206579\pi$
$422$		0			0
$423$	−12.6954	−	17.4738i	−0.617273	−	0.849603i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	9.66224	+	13.2989i	0.467589	+	0.643581i
$428$		0			0
$429$	1.60552	−	4.94128i	0.0775152	−	0.238567i
$430$		0			0
$431$	−5.55833	−	17.1068i	−0.267736	−	0.824005i	−0.991051	−	0.133487i	$-0.957383\pi$
$431$	−5.55833	−	17.1068i	−0.267736	−	0.824005i	0.723315	−	0.690518i	$-0.242617\pi$
$432$		0			0
$433$	−34.0721	+	11.0707i	−1.63740	+	0.532024i	−0.975956	−	0.217970i	$-0.930057\pi$
$433$	−34.0721	+	11.0707i	−1.63740	+	0.532024i	−0.661445	+	0.749994i	$0.730057\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.55332	+	2.13796i	−0.0743052	+	0.102272i
$438$		0			0
$439$	−3.34595	+	2.43097i	−0.159693	+	0.116024i	−0.664762	−	0.747055i	$-0.731467\pi$
$439$	−3.34595	+	2.43097i	−0.159693	+	0.116024i	0.505069	+	0.863079i	$0.331467\pi$
$440$		0			0
$441$	−20.2609	−	14.7204i	−0.964806	−	0.700973i
$442$		0			0
$443$			24.8979i			1.18293i	0.806329	+	0.591467i	$0.201451\pi$
$443$			24.8979i			1.18293i	−0.806329	+	0.591467i	$0.798549\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	40.2428	+	13.0757i	1.90342	+	0.618458i
$448$		0			0
$449$	0.385885			0.0182111			0.00910553	−	0.999959i	$-0.497102\pi$
$449$	0.385885			0.0182111			0.00910553	+	0.999959i	$0.497102\pi$
$450$		0			0
$451$	2.54481			0.119830
$452$		0			0
$453$	0.114552	+	0.0372200i	0.00538210	+	0.00174875i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	29.8819i		−	1.39781i	−0.715212	−	0.698907i	$-0.753670\pi$
$457$		−	29.8819i		−	1.39781i	0.715212	−	0.698907i	$-0.246330\pi$
$458$		0			0
$459$	4.93929	+	3.58860i	0.230546	+	0.167502i
$460$		0			0
$461$	16.1468	−	11.7313i	0.752029	−	0.546381i	−0.144426	−	0.989516i	$-0.546134\pi$
$461$	16.1468	−	11.7313i	0.752029	−	0.546381i	0.896455	+	0.443134i	$0.146134\pi$
$462$		0			0
$463$	14.6664	−	20.1865i	0.681603	−	0.938146i	−0.318349	−	0.947974i	$-0.603128\pi$
$463$	14.6664	−	20.1865i	0.681603	−	0.938146i	0.999952	+	0.00982748i	$0.00312823\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−35.9768	+	11.6896i	−1.66481	+	0.540928i	−0.981871	−	0.189551i	$-0.939297\pi$
$467$	−35.9768	+	11.6896i	−1.66481	+	0.540928i	−0.682935	+	0.730479i	$0.739297\pi$
$468$		0			0
$469$	8.98012	+	27.6380i	0.414663	+	1.27620i
$470$		0			0
$471$	−2.27625	+	7.00558i	−0.104884	+	0.322800i
$472$		0			0
$473$	−0.0680161	−	0.0936162i	−0.00312739	−	0.00430448i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.23733	−	4.45580i	−0.148227	−	0.204017i
$478$		0			0
$479$	3.70950	−	11.4167i	0.169491	−	0.521641i	−0.829848	−	0.557990i	$-0.811573\pi$
$479$	3.70950	−	11.4167i	0.169491	−	0.521641i	0.999339	+	0.0363490i	$0.0115728\pi$
$480$		0			0
$481$	−8.93580	−	27.5016i	−0.407437	−	1.25396i
$482$		0			0
$483$	−3.52662	+	1.14587i	−0.160467	+	0.0521388i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.73245	+	10.6428i	−0.350391	+	0.482271i	−0.947440	−	0.319933i	$-0.896340\pi$
$487$	−7.73245	+	10.6428i	−0.350391	+	0.482271i	0.597050	+	0.802204i	$0.296340\pi$
$488$		0			0
$489$	−21.8776	+	15.8950i	−0.989337	+	0.718795i
$490$		0			0
$491$	−15.2130	−	11.0529i	−0.686554	−	0.498810i	0.188972	−	0.981983i	$-0.439485\pi$
$491$	−15.2130	−	11.0529i	−0.686554	−	0.498810i	−0.875525	+	0.483172i	$0.839485\pi$
$492$		0			0
$493$			31.8861i			1.43608i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	57.5592	+	18.7021i	2.58188	+	0.838904i
$498$		0			0
$499$	−23.3350			−1.04462			−0.522309	−	0.852756i	$-0.674929\pi$
$499$	−23.3350			−1.04462			−0.522309	+	0.852756i	$0.674929\pi$
$500$		0			0
$501$	41.8184			1.86831
$502$		0			0
$503$	19.0869	+	6.20170i	0.851041	+	0.276520i	0.701882	−	0.712293i	$-0.252343\pi$
$503$	19.0869	+	6.20170i	0.851041	+	0.276520i	0.149159	+	0.988813i	$0.452343\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	7.48396i		−	0.332374i
$508$		0			0
$509$	−31.0184	−	22.5362i	−1.37487	−	0.998899i	−0.997339	−	0.0729009i	$-0.976774\pi$
$509$	−31.0184	−	22.5362i	−1.37487	−	0.998899i	−0.377528	−	0.925998i	$-0.623226\pi$
$510$		0			0
$511$	7.67929	−	5.57933i	0.339712	−	0.246815i
$512$		0			0
$513$	6.27730	−	8.63997i	0.277150	−	0.381464i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.91610	+	1.59734i	−0.216210	+	0.0702508i
$518$		0			0
$519$	−12.3301	−	37.9481i	−0.541231	−	1.66574i
$520$		0			0
$521$	7.81320	−	24.0466i	0.342303	−	1.05350i	−0.620709	−	0.784041i	$-0.713155\pi$
$521$	7.81320	−	24.0466i	0.342303	−	1.05350i	0.963012	−	0.269458i	$-0.0868446\pi$
$522$		0			0
$523$	0.963505	+	1.32615i	0.0421311	+	0.0579885i	0.829563	−	0.558413i	$-0.188590\pi$
$523$	0.963505	+	1.32615i	0.0421311	+	0.0579885i	−0.787432	+	0.616402i	$0.788590\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.578409	+	0.796112i	0.0251959	+	0.0346792i
$528$		0			0
$529$	7.06247	−	21.7360i	0.307064	−	0.945045i
$530$		0			0
$531$	2.61569	+	8.05026i	0.113511	+	0.349351i
$532$		0			0
$533$	17.4708	−	5.67659i	0.756742	−	0.245880i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.41674	+	7.45551i	−0.233750	+	0.321729i
$538$		0			0
$539$	−4.84892	+	3.52295i	−0.208858	+	0.151744i
$540$		0			0
$541$	−9.24601	−	6.71762i	−0.397517	−	0.288813i	0.371012	−	0.928628i	$-0.379011\pi$
$541$	−9.24601	−	6.71762i	−0.397517	−	0.288813i	−0.768529	+	0.639815i	$0.779011\pi$
$542$		0			0
$543$			4.06936i			0.174633i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.5379	−	5.69840i	−0.749866	−	0.243646i	−0.0909424	−	0.995856i	$-0.528988\pi$
$547$	−17.5379	−	5.69840i	−0.749866	−	0.243646i	−0.658924	+	0.752210i	$0.728988\pi$
$548$		0			0
$549$	9.10546			0.388612
$550$		0			0
$551$	55.7762			2.37614
$552$		0			0
$553$	−30.5849	−	9.93763i	−1.30060	−	0.422591i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			10.1154i			0.428603i	0.976768	+	0.214301i	$0.0687475\pi$
$557$			10.1154i			0.428603i	−0.976768	+	0.214301i	$0.931253\pi$
$558$		0			0
$559$	−0.675774	−	0.490979i	−0.0285822	−	0.0207662i
$560$		0			0
$561$	−4.13265	+	3.00255i	−0.174481	+	0.126768i
$562$		0			0
$563$	−4.92632	+	6.78049i	−0.207619	+	0.285764i	−0.900109	−	0.435664i	$-0.856514\pi$
$563$	−4.92632	+	6.78049i	−0.207619	+	0.285764i	0.692490	+	0.721427i	$0.256514\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	42.2817	−	13.7382i	1.77567	−	0.576949i
$568$		0			0
$569$	7.45871	+	22.9556i	0.312685	+	0.962347i	0.976697	+	0.214624i	$0.0688527\pi$
$569$	7.45871	+	22.9556i	0.312685	+	0.962347i	−0.664011	+	0.747723i	$0.731147\pi$
$570$		0			0
$571$	−10.4189	+	32.0662i	−0.436019	+	1.34193i	0.456019	+	0.889970i	$0.349275\pi$
$571$	−10.4189	+	32.0662i	−0.436019	+	1.34193i	−0.892038	+	0.451960i	$0.850725\pi$
$572$		0			0
$573$	10.1297	+	13.9423i	0.423173	+	0.582448i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−26.6111	−	36.6270i	−1.10783	−	1.52480i	−0.824569	−	0.565762i	$-0.808582\pi$
$577$	−26.6111	−	36.6270i	−1.10783	−	1.52480i	−0.283266	−	0.959041i	$-0.591418\pi$
$578$		0			0
$579$	−11.1441	+	34.2982i	−0.463135	+	1.42538i
$580$		0			0
$581$	9.88870	+	30.4343i	0.410253	+	1.26263i
$582$		0			0
$583$	−1.25360	+	0.407321i	−0.0519190	+	0.0168695i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.5392	−	22.7642i	0.682645	−	0.939581i	−0.317316	−	0.948320i	$-0.602782\pi$
$587$	16.5392	−	22.7642i	0.682645	−	0.939581i	0.999962	+	0.00873900i	$0.00278174\pi$
$588$		0			0
$589$	1.39259	−	1.01177i	0.0573805	−	0.0416894i
$590$		0			0
$591$	−46.4059	−	33.7159i	−1.90888	−	1.38689i
$592$		0			0
$593$		−	1.52944i		−	0.0628064i	−0.999507	−	0.0314032i	$-0.990002\pi$
$593$		−	1.52944i		−	0.0628064i	0.999507	−	0.0314032i	$-0.00999760\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.38072	+	3.04798i	0.383927	+	0.124746i
$598$		0			0
$599$	17.0156			0.695240			0.347620	−	0.937635i	$-0.386990\pi$
$599$	17.0156			0.695240			0.347620	+	0.937635i	$0.386990\pi$
$600$		0			0
$601$	−30.8970			−1.26031			−0.630157	−	0.776468i	$-0.717009\pi$
$601$	−30.8970			−1.26031			−0.630157	+	0.776468i	$0.717009\pi$
$602$		0			0
$603$	15.3091	+	4.97422i	0.623433	+	0.202566i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	29.5437i		−	1.19914i	−0.800322	−	0.599570i	$-0.795338\pi$
$607$		−	29.5437i		−	1.19914i	0.800322	−	0.599570i	$-0.204662\pi$
$608$		0			0
$609$	63.3166	+	46.0022i	2.56572	+	1.86410i
$610$		0			0
$611$	−30.1872	+	21.9323i	−1.22124	+	0.887284i
$612$		0			0
$613$	3.63004	−	4.99633i	0.146616	−	0.201800i	−0.729392	−	0.684096i	$-0.760197\pi$
$613$	3.63004	−	4.99633i	0.146616	−	0.201800i	0.876008	+	0.482296i	$0.160197\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−41.3041	+	13.4205i	−1.66284	+	0.540289i	−0.981464	−	0.191644i	$-0.938618\pi$
$617$	−41.3041	+	13.4205i	−1.66284	+	0.540289i	−0.681376	+	0.731934i	$0.738618\pi$
$618$		0			0
$619$	−15.2560	−	46.9531i	−0.613191	−	1.88721i	−0.425429	−	0.904992i	$-0.639877\pi$
$619$	−15.2560	−	46.9531i	−0.613191	−	1.88721i	−0.187761	−	0.982215i	$-0.560123\pi$
$620$		0			0
$621$	0.181551	−	0.558757i	0.00728539	−	0.0224221i
$622$		0			0
$623$	−39.6888	−	54.6270i	−1.59010	−	2.18858i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.25215	+	7.22897i	0.209751	+	0.288697i
$628$		0			0
$629$	−8.78560	+	27.0393i	−0.350305	+	1.07813i
$630$		0			0
$631$	4.09306	+	12.5971i	0.162942	+	0.501484i	0.998879	−	0.0473418i	$-0.0150750\pi$
$631$	4.09306	+	12.5971i	0.162942	+	0.501484i	−0.835937	+	0.548826i	$0.815075\pi$
$632$		0			0
$633$	−18.3821	+	5.97272i	−0.730624	+	0.237394i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.4306	+	35.0022i	−1.00760	+	1.38684i
$638$		0			0
$639$	27.1212	−	19.7047i	1.07290	−	0.779506i
$640$		0			0
$641$	11.9102	+	8.65325i	0.470424	+	0.341783i	0.797606	−	0.603178i	$-0.206099\pi$
$641$	11.9102	+	8.65325i	0.470424	+	0.341783i	−0.327183	+	0.944961i	$0.606099\pi$
$642$		0			0
$643$		−	27.1451i		−	1.07050i	−0.844695	−	0.535249i	$-0.820218\pi$
$643$		−	27.1451i		−	1.07050i	0.844695	−	0.535249i	$-0.179782\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.19289	+	0.712513i	0.0862114	+	0.0280118i	0.351805	−	0.936073i	$-0.385568\pi$
$647$	2.19289	+	0.712513i	0.0862114	+	0.0280118i	−0.265594	+	0.964085i	$0.585568\pi$
$648$		0			0
$649$	2.02576			0.0795182
$650$		0			0
$651$	2.41532			0.0946640
$652$		0			0
$653$	−10.7272	−	3.48548i	−0.419788	−	0.136397i	0.0915034	−	0.995805i	$-0.470833\pi$
$653$	−10.7272	−	3.48548i	−0.419788	−	0.136397i	−0.511292	+	0.859407i	$0.670833\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	5.25783i		−	0.205127i
$658$		0			0
$659$	−37.1885	−	27.0190i	−1.44866	−	1.05251i	−0.986142	−	0.165902i	$-0.946946\pi$
$659$	−37.1885	−	27.0190i	−1.44866	−	1.05251i	−0.462517	−	0.886610i	$-0.653054\pi$
$660$		0			0
$661$	−20.3520	+	14.7866i	−0.791600	+	0.575131i	−0.908438	−	0.418020i	$-0.862724\pi$
$661$	−20.3520	+	14.7866i	−0.791600	+	0.575131i	0.116838	+	0.993151i	$0.462724\pi$
$662$		0			0
$663$	−21.6741	+	29.8318i	−0.841750	+	1.15857i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.91821	−	0.948185i	0.112994	−	0.0367139i
$668$		0			0
$669$	−6.33912	−	19.5098i	−0.245085	−	0.754293i
$670$		0			0
$671$	0.673395	−	2.07250i	0.0259961	−	0.0800078i
$672$		0			0
$673$	0.483895	+	0.666024i	0.0186528	+	0.0256733i	0.818242	−	0.574875i	$-0.194949\pi$
$673$	0.483895	+	0.666024i	0.0186528	+	0.0256733i	−0.799589	+	0.600548i	$0.794949\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.1064	+	19.4158i	0.542153	+	0.746210i	0.988921	−	0.148440i	$-0.0474251\pi$
$677$	14.1064	+	19.4158i	0.542153	+	0.746210i	−0.446768	+	0.894650i	$0.647425\pi$
$678$		0			0
$679$	4.25688	−	13.1013i	0.163364	−	0.502783i
$680$		0			0
$681$	8.09728	+	24.9209i	0.310288	+	0.954969i
$682$		0			0
$683$	30.8259	−	10.0159i	1.17952	−	0.383249i	0.347332	−	0.937742i	$-0.387088\pi$
$683$	30.8259	−	10.0159i	1.17952	−	0.383249i	0.832188	+	0.554493i	$0.187088\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−36.2248	+	49.8592i	−1.38206	+	1.90225i
$688$		0			0
$689$	−7.69772	+	5.59272i	−0.293260	+	0.213066i
$690$		0			0
$691$	17.4077	+	12.6474i	0.662221	+	0.481131i	0.867412	−	0.497590i	$-0.165782\pi$
$691$	17.4077	+	12.6474i	0.662221	+	0.481131i	−0.205192	+	0.978722i	$0.565782\pi$
$692$		0			0
$693$			5.48462i			0.208344i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−17.1771	−	5.58117i	−0.650628	−	0.211402i
$698$		0			0
$699$	44.8149			1.69505
$700$		0			0
$701$	−42.0612			−1.58863			−0.794314	−	0.607507i	$-0.792170\pi$
$701$	−42.0612			−1.58863			−0.794314	+	0.607507i	$0.792170\pi$
$702$		0			0
$703$	47.2980	+	15.3681i	1.78388	+	0.579617i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	39.3556i		−	1.48012i
$708$		0			0
$709$	5.55211	+	4.03384i	0.208514	+	0.151494i	0.687141	−	0.726524i	$-0.258865\pi$
$709$	5.55211	+	4.03384i	0.208514	+	0.151494i	−0.478627	+	0.878018i	$0.658865\pi$
$710$		0			0
$711$	−14.4112	+	10.4704i	−0.540463	+	0.392669i
$712$		0			0
$713$	0.0556602	−	0.0766097i	0.00208449	−	0.00286906i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.5463	+	3.42669i	−0.393858	+	0.127972i
$718$		0			0
$719$	11.8881	+	36.5879i	0.443353	+	1.36450i	0.884280	+	0.466957i	$0.154650\pi$
$719$	11.8881	+	36.5879i	0.443353	+	1.36450i	−0.440927	+	0.897543i	$0.645350\pi$
$720$		0			0
$721$	7.79585	−	23.9932i	0.290333	−	0.893552i
$722$		0			0
$723$	27.3689	+	37.6701i	1.01786	+	1.40097i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−5.75632	−	7.92289i	−0.213490	−	0.293844i	0.688819	−	0.724933i	$-0.258129\pi$
$727$	−5.75632	−	7.92289i	−0.213490	−	0.293844i	−0.902309	+	0.431089i	$0.858129\pi$
$728$		0			0
$729$	4.31106	−	13.2681i	0.159669	−	0.491410i
$730$		0			0
$731$	0.253784	+	0.781066i	0.00938654	+	0.0288888i
$732$		0			0
$733$	28.7459	−	9.34010i	1.06175	−	0.344984i	0.274482	−	0.961592i	$-0.411494\pi$
$733$	28.7459	−	9.34010i	1.06175	−	0.344984i	0.787270	+	0.616608i	$0.211494\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.26437	−	3.11663i	0.0834090	−	0.114803i
$738$		0			0
$739$	21.4657	−	15.5958i	0.789629	−	0.573699i	−0.118224	−	0.992987i	$-0.537720\pi$
$739$	21.4657	−	15.5958i	0.789629	−	0.573699i	0.907853	+	0.419288i	$0.137720\pi$
$740$		0			0
$741$	52.1827	+	37.9130i	1.91698	+	1.39277i
$742$		0			0
$743$			1.43832i			0.0527669i	0.999652	+	0.0263835i	$0.00839909\pi$
$743$			1.43832i			0.0527669i	−0.999652	+	0.0263835i	$0.991601\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	16.8580	+	5.47750i	0.616802	+	0.200411i
$748$		0			0
$749$	23.5871			0.861852
$750$		0			0
$751$	34.4429			1.25684			0.628420	−	0.777874i	$-0.283702\pi$
$751$	34.4429			1.25684			0.628420	+	0.777874i	$0.283702\pi$
$752$		0			0
$753$	−30.4671	−	9.89937i	−1.11028	−	0.360753i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	11.5191i		−	0.418668i	−0.977844	−	0.209334i	$-0.932870\pi$
$757$		−	11.5191i		−	0.418668i	0.977844	−	0.209334i	$-0.0671296\pi$
$758$		0			0
$759$	0.397684	+	0.288934i	0.0144350	+	0.0104877i
$760$		0			0
$761$	6.90432	−	5.01628i	0.250281	−	0.181840i	−0.455570	−	0.890200i	$-0.650565\pi$
$761$	6.90432	−	5.01628i	0.250281	−	0.181840i	0.705851	+	0.708360i	$0.250565\pi$
$762$		0			0
$763$	33.9871	−	46.7793i	1.23042	−	1.69352i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.9074	−	4.51879i	0.502167	−	0.163164i
$768$		0			0
$769$	−10.0753	−	31.0086i	−0.363325	−	1.11820i	−0.951023	−	0.309119i	$-0.899966\pi$
$769$	−10.0753	−	31.0086i	−0.363325	−	1.11820i	0.587698	−	0.809080i	$-0.300034\pi$
$770$		0			0
$771$	−3.04766	+	9.37973i	−0.109759	+	0.337803i
$772$		0			0
$773$	17.5389	+	24.1403i	0.630832	+	0.868265i	0.998085	−	0.0618555i	$-0.0197018\pi$
$773$	17.5389	+	24.1403i	0.630832	+	0.868265i	−0.367253	+	0.930121i	$0.619702\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	41.0173	+	56.4554i	1.47149	+	2.02533i
$778$		0			0
$779$	−9.76277	+	30.0467i	−0.349788	+	1.07654i
$780$		0			0
$781$	−2.47924	−	7.63032i	−0.0887142	−	0.273034i
$782$		0			0
$783$	−11.7932	+	3.83183i	−0.421453	+	0.136938i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−31.1195	+	42.8324i	−1.10929	+	1.52681i	−0.286836	+	0.957980i	$0.592603\pi$
$787$	−31.1195	+	42.8324i	−1.10929	+	1.52681i	−0.822456	+	0.568829i	$0.807397\pi$
$788$		0			0
$789$	−21.8905	+	15.9044i	−0.779323	+	0.566211i
$790$		0			0
$791$	13.8239	+	10.0437i	0.491523	+	0.357112i
$792$		0			0
$793$		−	15.7303i		−	0.558601i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.6638	−	4.11472i	−0.448575	−	0.145751i	0.0760136	−	0.997107i	$-0.475781\pi$
$797$	−12.6638	−	4.11472i	−0.448575	−	0.145751i	−0.524588	+	0.851356i	$0.675781\pi$
$798$		0			0
$799$	36.6862			1.29786
$800$		0			0
$801$	−37.4018			−1.32153
$802$		0			0
$803$	−1.19673	−	0.388843i	−0.0422319	−	0.0137220i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			24.4131i			0.859382i
$808$		0			0
$809$	−18.5016	−	13.4422i	−0.650483	−	0.472604i	0.212953	−	0.977063i	$-0.431692\pi$
$809$	−18.5016	−	13.4422i	−0.650483	−	0.472604i	−0.863436	+	0.504459i	$0.831692\pi$
$810$		0			0
$811$	31.8550	−	23.1440i	1.11858	−	0.812695i	0.134586	−	0.990902i	$-0.457030\pi$
$811$	31.8550	−	23.1440i	1.11858	−	0.812695i	0.983993	+	0.178207i	$0.0570296\pi$
$812$		0			0
$813$	17.6972	−	24.3582i	0.620669	−	0.854278i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.36627	−	0.443927i	0.0477997	−	0.0155311i
$818$		0			0
$819$	12.2343	+	37.6534i	0.427502	+	1.31571i
$820$		0			0
$821$	9.98859	−	30.7417i	0.348604	−	1.07289i	−0.611022	−	0.791614i	$-0.709241\pi$
$821$	9.98859	−	30.7417i	0.348604	−	1.07289i	0.959626	−	0.281279i	$-0.0907588\pi$
$822$		0			0
$823$	26.4500	+	36.4053i	0.921989	+	1.26901i	0.962903	+	0.269847i	$0.0869731\pi$
$823$	26.4500	+	36.4053i	0.921989	+	1.26901i	−0.0409138	+	0.999163i	$0.513027\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.99879	+	2.75110i	0.0695048	+	0.0956652i	0.842354	−	0.538924i	$-0.181169\pi$
$827$	1.99879	+	2.75110i	0.0695048	+	0.0956652i	−0.772849	+	0.634590i	$0.781169\pi$
$828$		0			0
$829$	−5.67397	+	17.4627i	−0.197065	+	0.606504i	0.802881	+	0.596139i	$0.203299\pi$
$829$	−5.67397	+	17.4627i	−0.197065	+	0.606504i	−0.999946	+	0.0103649i	$0.996701\pi$
$830$		0			0
$831$	8.93759	+	27.5071i	0.310041	+	0.954209i
$832$		0			0
$833$	40.4559	−	13.1449i	1.40171	−	0.455445i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.224936	+	0.309597i	−0.00777491	+	0.0107012i
$838$		0			0
$839$	−30.6714	+	22.2840i	−1.05889	+	0.769331i	−0.973883	−	0.227049i	$-0.927092\pi$
$839$	−30.6714	+	22.2840i	−1.05889	+	0.769331i	−0.0850097	+	0.996380i	$0.527092\pi$
$840$		0			0
$841$	−28.9318	−	21.0202i	−0.997648	−	0.724834i
$842$		0			0
$843$			4.42212i			0.152306i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−42.8096	−	13.9097i	−1.47095	−	0.477942i
$848$		0			0
$849$	20.0374			0.687681
$850$		0			0
$851$	2.73589			0.0937851
$852$		0			0
$853$	1.72194	+	0.559493i	0.0589582	+	0.0191567i	0.338348	−	0.941021i	$-0.390132\pi$
$853$	1.72194	+	0.559493i	0.0589582	+	0.0191567i	−0.279389	+	0.960178i	$0.590132\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			42.3384i			1.44625i	0.690717	+	0.723126i	$0.257295\pi$
$857$			42.3384i			1.44625i	−0.690717	+	0.723126i	$0.742705\pi$
$858$		0			0
$859$	30.4965	+	22.1570i	1.04053	+	0.755988i	0.970389	−	0.241549i	$-0.0776554\pi$
$859$	30.4965	+	22.1570i	1.04053	+	0.755988i	0.0701401	+	0.997537i	$0.477655\pi$
$860$		0			0
$861$	−35.8641	+	26.0568i	−1.22224	+	0.888012i
$862$		0			0
$863$	−32.1939	+	44.3111i	−1.09589	+	1.50837i	−0.255175	+	0.966895i	$0.582133\pi$
$863$	−32.1939	+	44.3111i	−1.09589	+	1.50837i	−0.840718	+	0.541473i	$0.817867\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.85640	+	0.928099i	−0.0970083	+	0.0315199i
$868$		0			0
$869$	1.31738	+	4.05448i	0.0446891	+	0.137539i
$870$		0			0
$871$	8.59332	−	26.4475i	0.291173	−	0.896140i
$872$		0			0
$873$	−4.48508	−	6.17319i	−0.151797	−	0.208931i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.83181	+	2.52127i	0.0618558	+	0.0851371i	0.838824	−	0.544402i	$-0.183244\pi$
$877$	1.83181	+	2.52127i	0.0618558	+	0.0851371i	−0.776968	+	0.629540i	$0.783244\pi$
$878$		0			0
$879$	−12.9613	+	39.8908i	−0.437174	+	1.34548i
$880$		0			0
$881$	13.2528	+	40.7880i	0.446499	+	1.37418i	0.880832	+	0.473429i	$0.156984\pi$
$881$	13.2528	+	40.7880i	0.446499	+	1.37418i	−0.434333	+	0.900752i	$0.643016\pi$
$882$		0			0
$883$	−5.88188	+	1.91114i	−0.197941	+	0.0643150i	−0.406310	−	0.913735i	$-0.633185\pi$
$883$	−5.88188	+	1.91114i	−0.197941	+	0.0643150i	0.208369	+	0.978050i	$0.433185\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.61212	−	6.34803i	0.154860	−	0.213146i	−0.724537	−	0.689236i	$-0.757946\pi$
$887$	4.61212	−	6.34803i	0.154860	−	0.213146i	0.879397	+	0.476090i	$0.157946\pi$
$888$		0			0
$889$	−14.0685	+	10.2214i	−0.471844	+	0.342814i
$890$		0			0
$891$	−4.76796	−	3.46412i	−0.159733	−	0.116052i
$892$		0			0
$893$		−	64.1727i		−	2.14746i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	3.37472	+	1.09651i	0.112679	+	0.0366115i
$898$		0			0
$899$	−1.99864			−0.0666583
$900$		0			0
$901$	9.35497			0.311659
$902$		0			0
$903$	1.91711	+	0.622907i	0.0637974	+	0.0207290i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			0.385211i			0.0127907i	0.999980	+	0.00639536i	$0.00203572\pi$
$907$			0.385211i			0.0127907i	−0.999980	+	0.00639536i	$0.997964\pi$
$908$		0			0
$909$	−17.6363	−	12.8135i	−0.584958	−	0.424997i
$910$		0			0
$911$	0.507752	−	0.368903i	0.0168226	−	0.0122223i	−0.579342	−	0.815084i	$-0.696691\pi$
$911$	0.507752	−	0.368903i	0.0168226	−	0.0122223i	0.596165	+	0.802862i	$0.296691\pi$
$912$		0			0
$913$	2.49347	−	3.43197i	0.0825218	−	0.113581i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	52.7677	−	17.1452i	1.74254	−	0.566186i
$918$		0			0
$919$	−8.88039	−	27.3310i	−0.292937	−	0.901567i	−0.983907	−	0.178683i	$-0.942816\pi$
$919$	−8.88039	−	27.3310i	−0.292937	−	0.901567i	0.690970	−	0.722884i	$-0.257184\pi$
$920$		0			0
$921$	−16.7165	+	51.4482i	−0.550828	+	1.69528i
$922$		0			0
$923$	−34.0413	−	46.8538i	−1.12048	−	1.54221i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−8.21377	−	11.3053i	−0.269776	−	0.371314i
$928$		0			0
$929$	8.86551	−	27.2852i	0.290868	−	0.895200i	−0.693710	−	0.720254i	$-0.744025\pi$
$929$	8.86551	−	27.2852i	0.290868	−	0.895200i	0.984578	−	0.174945i	$-0.0559749\pi$
$930$		0			0
$931$	−22.9935	−	70.7668i	−0.753583	−	2.31929i
$932$		0			0
$933$	−51.2765	+	16.6608i	−1.67872	+	0.545449i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	21.3726	−	29.4169i	0.698214	−	0.961009i	−0.301757	−	0.953385i	$-0.597573\pi$
$937$	21.3726	−	29.4169i	0.698214	−	0.961009i	0.999971	−	0.00762389i	$-0.00242678\pi$
$938$		0			0
$939$	10.8926	−	7.91393i	0.355466	−	0.258261i
$940$		0			0
$941$	12.2006	+	8.86422i	0.397727	+	0.288965i	0.768614	−	0.639712i	$-0.220947\pi$
$941$	12.2006	+	8.86422i	0.397727	+	0.288965i	−0.370888	+	0.928678i	$0.620947\pi$
$942$		0			0
$943$			1.73801i			0.0565975i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.89882	−	2.56648i	−0.256677	−	0.0833995i	0.177852	−	0.984057i	$-0.443085\pi$
$947$	−7.89882	−	2.56648i	−0.256677	−	0.0833995i	−0.434529	+	0.900658i	$0.643085\pi$
$948$		0			0
$949$	−9.08327			−0.294855
$950$		0			0
$951$	17.2800			0.560341
$952$		0			0
$953$	29.2212	+	9.49453i	0.946566	+	0.307558i	0.741319	−	0.671152i	$-0.234200\pi$
$953$	29.2212	+	9.49453i	0.946566	+	0.307558i	0.205247	+	0.978710i	$0.434200\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	10.3750i		−	0.335376i
$958$		0			0
$959$	5.65171	+	4.10621i	0.182503	+	0.132596i
$960$		0			0
$961$	25.0296	−	18.1851i	0.807407	−	0.586616i
$962$		0			0
$963$	7.67954	−	10.5700i	0.247470	−	0.340613i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−20.4075	+	6.63081i	−0.656262	+	0.213232i	−0.618173	−	0.786042i	$-0.712127\pi$
$967$	−20.4075	+	6.63081i	−0.656262	+	0.213232i	−0.0380888	+	0.999274i	$0.512127\pi$
$968$		0			0
$969$	−19.5970	−	60.3133i	−0.629546	−	1.93754i
$970$		0			0
$971$	−16.5763	+	51.0166i	−0.531959	+	1.63720i	0.218171	+	0.975911i	$0.429991\pi$
$971$	−16.5763	+	51.0166i	−0.531959	+	1.63720i	−0.750130	+	0.661291i	$0.770009\pi$
$972$		0			0
$973$	−1.73610	−	2.38954i	−0.0556568	−	0.0766050i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.0154	−	44.0654i	−1.02426	−	1.40978i	−0.909171	−	0.416423i	$-0.863283\pi$
$977$	−32.0154	−	44.0654i	−1.02426	−	1.40978i	−0.115093	−	0.993355i	$-0.536717\pi$
$978$		0			0
$979$	−2.76605	+	8.51303i	−0.0884034	+	0.272078i
$980$		0			0
$981$	−9.89740	−	30.4611i	−0.316000	−	0.972547i
$982$		0			0
$983$	−2.34276	+	0.761210i	−0.0747225	+	0.0242788i	−0.346140	−	0.938183i	$-0.612508\pi$
$983$	−2.34276	+	0.761210i	−0.0747225	+	0.0242788i	0.271417	+	0.962462i	$0.412508\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	52.9273	−	72.8482i	1.68470	−	2.31878i
$988$		0			0
$989$	0.0639365	−	0.0464526i	0.00203306	−	0.00147711i
$990$		0			0
$991$	−39.3120	−	28.5618i	−1.24879	−	0.907296i	−0.250635	−	0.968082i	$-0.580639\pi$
$991$	−39.3120	−	28.5618i	−1.24879	−	0.907296i	−0.998151	+	0.0607857i	$0.980639\pi$
$992$		0			0
$993$			69.7275i			2.21274i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.5137	−	3.41611i	−0.332972	−	0.108189i	0.137759	−	0.990466i	$-0.456010\pi$
$997$	−10.5137	−	3.41611i	−0.332972	−	0.108189i	−0.470732	+	0.882276i	$0.656010\pi$
$998$		0			0
$999$	−11.0564			−0.349807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.i.a.449.2		8
5.2	odd	4		500.2.g.b.301.4		16
5.3	odd	4		500.2.g.b.301.1		16
5.4	even	2		100.2.i.a.89.1	yes	8
15.14	odd	2		900.2.w.a.289.1		8
20.19	odd	2		400.2.y.b.289.2		8
25.3	odd	20		2500.2.a.f.1.1		8
25.4	even	10		2500.2.c.b.1249.1		8
25.9	even	10	inner	500.2.i.a.49.2		8
25.12	odd	20		500.2.g.b.201.4		16
25.13	odd	20		500.2.g.b.201.1		16
25.16	even	5		100.2.i.a.9.1	✓	8
25.21	even	5		2500.2.c.b.1249.8		8
25.22	odd	20		2500.2.a.f.1.8		8
75.41	odd	10		900.2.w.a.109.1		8
100.3	even	20		10000.2.a.bi.1.8		8
100.47	even	20		10000.2.a.bi.1.1		8
100.91	odd	10		400.2.y.b.209.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.i.a.9.1	✓	8	25.16	even	5
100.2.i.a.89.1	yes	8	5.4	even	2
400.2.y.b.209.2		8	100.91	odd	10
400.2.y.b.289.2		8	20.19	odd	2
500.2.g.b.201.1		16	25.13	odd	20
500.2.g.b.201.4		16	25.12	odd	20
500.2.g.b.301.1		16	5.3	odd	4
500.2.g.b.301.4		16	5.2	odd	4
500.2.i.a.49.2		8	25.9	even	10	inner
500.2.i.a.449.2		8	1.1	even	1	trivial
900.2.w.a.109.1		8	75.41	odd	10
900.2.w.a.289.1		8	15.14	odd	2
2500.2.a.f.1.1		8	25.3	odd	20
2500.2.a.f.1.8		8	25.22	odd	20
2500.2.c.b.1249.1		8	25.4	even	10
2500.2.c.b.1249.8		8	25.21	even	5
10000.2.a.bi.1.1		8	100.47	even	20
10000.2.a.bi.1.8		8	100.3	even	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.19625 + 0.713605i) q^{3} +4.21139i q^{7} +(1.88723 + 1.37116i) q^{9} +(0.451659 - 0.328150i) q^{11} +(2.36877 - 3.26033i) q^{13} +(-3.76832 + 1.22440i) q^{17} +(2.14177 + 6.59168i) q^{19} +(-3.00527 + 9.24926i) q^{21} +(0.224115 + 0.308467i) q^{23} +(-0.905698 - 1.24659i) q^{27} +(2.48680 - 7.65359i) q^{29} +(-0.0767462 - 0.236201i) q^{31} +(1.22613 - 0.398393i) q^{33} +(4.21760 - 5.80503i) q^{37} +(7.52900 - 5.47014i) q^{39} +(3.68773 + 2.67929i) q^{41} -0.207272i q^{43} +(-8.80576 - 2.86117i) q^{47} -10.7358 q^{49} -9.14992 q^{51} +(-2.24547 - 0.729597i) q^{53} +16.0054i q^{57} +(2.93557 + 2.13282i) q^{59} +(3.15785 - 2.29431i) q^{61} +(-5.77447 + 7.94787i) q^{63} +(6.56267 - 2.13234i) q^{67} +(0.272088 + 0.837401i) q^{69} +(4.44084 - 13.6675i) q^{71} +(-1.32482 - 1.82346i) q^{73} +(1.38197 + 1.90211i) q^{77} +(-2.35970 + 7.26242i) q^{79} +(-3.26215 - 10.0399i) q^{81} +(7.22667 - 2.34809i) q^{83} +(10.9233 - 15.0346i) q^{87} +(-12.9713 + 9.42417i) q^{89} +(13.7305 + 9.97581i) q^{91} -0.573522i q^{93} +(-3.11093 - 1.01080i) q^{97} +1.30233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{9} + 5 q^{11} + 5 q^{17} - 8 q^{19} - 2 q^{21} + 20 q^{23} - 8 q^{29} - 12 q^{31} - 15 q^{33} + 10 q^{37} + 22 q^{39} + 13 q^{41} - 45 q^{47} + 14 q^{49} - 14 q^{51} - 30 q^{53} + 9 q^{59} + 16 q^{61}+ \cdots + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^9 + 5 * q^11 + 5 * q^17 - 8 * q^19 - 2 * q^21 + 20 * q^23 - 8 * q^29 - 12 * q^31 - 15 * q^33 + 10 * q^37 + 22 * q^39 + 13 * q^41 - 45 * q^47 + 14 * q^49 - 14 * q^51 - 30 * q^53 + 9 * q^59 + 16 * q^61 - 20 * q^63 + 5 * q^67 - 14 * q^69 - q^71 + 60 * q^73 + 20 * q^77 - 24 * q^79 - 3 * q^81 + 10 * q^83 + 55 * q^87 - 37 * q^89 + 32 * q^91 - 25 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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