LMFDB - Embedded newform 1152.2.i.g.385.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.3
Root			$-1.13593 - 1.30754i$ of defining polynomial
Character	$\chi$	$=$	1152.385
Dual form			1152.2.i.g.769.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.564403 + 1.63751i) q^{3} +(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(-2.36290 + 1.84844i) q^{9} +O(q^{10})$	\(q+(0.564403 + 1.63751i) q^{3} +(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(-2.36290 + 1.84844i) q^{9} +(0.312284 - 0.540892i) q^{11} +(-1.06440 - 1.84360i) q^{13} +(3.61967 - 4.16654i) q^{15} -1.83869 q^{17} +7.15403 q^{19} +(-2.06440 - 0.400622i) q^{21} +(-0.780986 - 1.35271i) q^{23} +(-2.57702 + 4.46352i) q^{25} +(-4.36047 - 2.82601i) q^{27} +(4.87551 - 8.44463i) q^{29} +(-3.32024 - 5.75083i) q^{31} +(1.06197 + 0.206088i) q^{33} +3.86884 q^{35} +6.73511 q^{37} +(2.41817 - 2.78351i) q^{39} +(-5.64365 - 9.77508i) q^{41} +(4.51144 - 7.81404i) q^{43} +(8.86572 + 3.57565i) q^{45} +(1.36043 - 2.35634i) q^{47} +(2.76296 + 4.78558i) q^{49} +(-1.03776 - 3.01087i) q^{51} -7.60144 q^{53} -1.99021 q^{55} +(4.03776 + 11.7148i) q^{57} +(-4.02547 - 6.97231i) q^{59} +(-2.79700 + 4.84455i) q^{61} +(-0.509134 - 3.60660i) q^{63} +(-3.39176 + 5.87471i) q^{65} +(-3.95957 - 6.85817i) q^{67} +(1.77428 - 2.04235i) q^{69} +8.11222 q^{71} -5.66806 q^{73} +(-8.76356 - 1.70067i) q^{75} +(0.379150 + 0.656707i) q^{77} +(-3.21415 + 5.56707i) q^{79} +(2.16657 - 8.73533i) q^{81} +(-3.27735 + 5.67653i) q^{83} +(2.92953 + 5.07409i) q^{85} +(16.5800 + 3.21753i) q^{87} +5.02926 q^{89} +2.58463 q^{91} +(7.54310 - 8.68272i) q^{93} +(-11.3983 - 19.7424i) q^{95} +(-4.70138 + 8.14302i) q^{97} +(0.261909 + 1.85531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} - 4 q^{7} - q^{9}+O(q^{10}) $ 10 * q + q^3 - 4 * q^7 - q^9	$ 10 q + q^{3} - 4 q^{7} - q^{9} - q^{11} - 6 q^{13} + 12 q^{15} - 6 q^{17} + 18 q^{19} - 16 q^{21} + 4 q^{23} + q^{25} - 2 q^{27} + 4 q^{29} - 8 q^{31} - 13 q^{33} - 24 q^{35} + 20 q^{37} - 18 q^{39} - 5 q^{41} - 13 q^{43} + 12 q^{45} - 6 q^{47} + 3 q^{49} + 3 q^{51} + 12 q^{55} + 27 q^{57} - 13 q^{59} - 10 q^{61} - 20 q^{63} - 17 q^{67} + 10 q^{69} + 8 q^{71} - 34 q^{73} - 29 q^{75} - 8 q^{77} - 6 q^{79} - q^{81} + 12 q^{83} - 18 q^{85} + 10 q^{87} + 44 q^{89} + 36 q^{91} - 26 q^{93} - 6 q^{95} + 27 q^{97} + 34 q^{99}+O(q^{100}) $ 10 * q + q^3 - 4 * q^7 - q^9 - q^11 - 6 * q^13 + 12 * q^15 - 6 * q^17 + 18 * q^19 - 16 * q^21 + 4 * q^23 + q^25 - 2 * q^27 + 4 * q^29 - 8 * q^31 - 13 * q^33 - 24 * q^35 + 20 * q^37 - 18 * q^39 - 5 * q^41 - 13 * q^43 + 12 * q^45 - 6 * q^47 + 3 * q^49 + 3 * q^51 + 12 * q^55 + 27 * q^57 - 13 * q^59 - 10 * q^61 - 20 * q^63 - 17 * q^67 + 10 * q^69 + 8 * q^71 - 34 * q^73 - 29 * q^75 - 8 * q^77 - 6 * q^79 - q^81 + 12 * q^83 - 18 * q^85 + 10 * q^87 + 44 * q^89 + 36 * q^91 - 26 * q^93 - 6 * q^95 + 27 * q^97 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.564403	+	1.63751i	0.325858	+	0.945419i
$3$	0.564403	+	1.63751i	0.325858	+	0.945419i
$4$		0			0
$5$	−1.59327	−	2.75962i	−0.712532	−	1.23414i	−0.963904	−	0.266251i	$-0.914215\pi$
$5$	−1.59327	−	2.75962i	−0.712532	−	1.23414i	0.251372	−	0.967891i	$-0.419118\pi$
$6$		0			0
$7$	−0.607060	+	1.05146i	−0.229447	+	0.397414i	−0.957644	−	0.287954i	$-0.907025\pi$
$7$	−0.607060	+	1.05146i	−0.229447	+	0.397414i	0.728197	+	0.685368i	$0.240358\pi$
$8$		0			0
$9$	−2.36290	+	1.84844i	−0.787632	+	0.616145i
$10$		0			0
$11$	0.312284	−	0.540892i	0.0941572	−	0.163085i	−0.815099	−	0.579321i	$-0.803318\pi$
$11$	0.312284	−	0.540892i	0.0941572	−	0.163085i	0.909257	+	0.416236i	$0.136651\pi$
$12$		0			0
$13$	−1.06440	−	1.84360i	−0.295212	−	0.511323i	0.679822	−	0.733377i	$-0.262057\pi$
$13$	−1.06440	−	1.84360i	−0.295212	−	0.511323i	−0.975034	+	0.222054i	$0.928724\pi$
$14$		0			0
$15$	3.61967	−	4.16654i	0.934596	−	1.07580i
$16$		0			0
$17$	−1.83869			−0.445947			−0.222974	−	0.974824i	$-0.571576\pi$
$17$	−1.83869			−0.445947			−0.222974	+	0.974824i	$0.571576\pi$
$18$		0			0
$19$	7.15403			1.64125			0.820624	−	0.571469i	$-0.193626\pi$
$19$	7.15403			1.64125			0.820624	+	0.571469i	$0.193626\pi$
$20$		0			0
$21$	−2.06440	−	0.400622i	−0.450490	−	0.0874228i
$22$		0			0
$23$	−0.780986	−	1.35271i	−0.162847	−	0.282059i	0.773042	−	0.634355i	$-0.218734\pi$
$23$	−0.780986	−	1.35271i	−0.162847	−	0.282059i	−0.935889	+	0.352296i	$0.885401\pi$
$24$		0			0
$25$	−2.57702	+	4.46352i	−0.515403	+	0.892705i
$26$		0			0
$27$	−4.36047	−	2.82601i	−0.839172	−	0.543866i
$28$		0			0
$29$	4.87551	−	8.44463i	0.905360	−	1.56813i	0.0849260	−	0.996387i	$-0.472935\pi$
$29$	4.87551	−	8.44463i	0.905360	−	1.56813i	0.820434	−	0.571742i	$-0.193732\pi$
$30$		0			0
$31$	−3.32024	−	5.75083i	−0.596333	−	1.03288i	−0.993357	−	0.115071i	$-0.963290\pi$
$31$	−3.32024	−	5.75083i	−0.596333	−	1.03288i	0.397024	−	0.917808i	$-0.370043\pi$
$32$		0			0
$33$	1.06197	+	0.206088i	0.184866	+	0.0358753i
$34$		0			0
$35$	3.86884			0.653953
$36$		0			0
$37$	6.73511			1.10724			0.553622	−	0.832768i	$-0.313245\pi$
$37$	6.73511			1.10724			0.553622	+	0.832768i	$0.313245\pi$
$38$		0			0
$39$	2.41817	−	2.78351i	0.387217	−	0.445718i
$40$		0			0
$41$	−5.64365	−	9.77508i	−0.881389	−	1.52661i	−0.849797	−	0.527110i	$-0.823276\pi$
$41$	−5.64365	−	9.77508i	−0.881389	−	1.52661i	−0.0315923	−	0.999501i	$-0.510058\pi$
$42$		0			0
$43$	4.51144	−	7.81404i	0.687988	−	1.19163i	−0.284500	−	0.958676i	$-0.591828\pi$
$43$	4.51144	−	7.81404i	0.687988	−	1.19163i	0.972488	−	0.232954i	$-0.0748391\pi$
$44$		0			0
$45$	8.86572	+	3.57565i	1.32162	+	0.533027i
$46$		0			0
$47$	1.36043	−	2.35634i	0.198440	−	0.343708i	−0.749583	−	0.661910i	$-0.769746\pi$
$47$	1.36043	−	2.35634i	0.198440	−	0.343708i	0.948023	+	0.318203i	$0.103079\pi$
$48$		0			0
$49$	2.76296	+	4.78558i	0.394708	+	0.683655i
$50$		0			0
$51$	−1.03776	−	3.01087i	−0.145316	−	0.421607i
$52$		0			0
$53$	−7.60144			−1.04414			−0.522069	−	0.852903i	$-0.674840\pi$
$53$	−7.60144			−1.04414			−0.522069	+	0.852903i	$0.674840\pi$
$54$		0			0
$55$	−1.99021			−0.268360
$56$		0			0
$57$	4.03776	+	11.7148i	0.534815	+	1.55167i
$58$		0			0
$59$	−4.02547	−	6.97231i	−0.524071	−	0.907718i	−0.999607	−	0.0280214i	$-0.991079\pi$
$59$	−4.02547	−	6.97231i	−0.524071	−	0.907718i	0.475536	−	0.879696i	$-0.342254\pi$
$60$		0			0
$61$	−2.79700	+	4.84455i	−0.358119	+	0.620281i	−0.987647	−	0.156698i	$-0.949915\pi$
$61$	−2.79700	+	4.84455i	−0.358119	+	0.620281i	0.629527	+	0.776978i	$0.283249\pi$
$62$		0			0
$63$	−0.509134	−	3.60660i	−0.0641448	−	0.454389i
$64$		0			0
$65$	−3.39176	+	5.87471i	−0.420697	+	0.728668i
$66$		0			0
$67$	−3.95957	−	6.85817i	−0.483738	−	0.837859i	0.516087	−	0.856536i	$-0.327388\pi$
$67$	−3.95957	−	6.85817i	−0.483738	−	0.837859i	−0.999826	+	0.0186768i	$0.994055\pi$
$68$		0			0
$69$	1.77428	−	2.04235i	0.213599	−	0.245870i
$70$		0			0
$71$	8.11222			0.962743			0.481371	−	0.876517i	$-0.340139\pi$
$71$	8.11222			0.962743			0.481371	+	0.876517i	$0.340139\pi$
$72$		0			0
$73$	−5.66806			−0.663397			−0.331698	−	0.943386i	$-0.607622\pi$
$73$	−5.66806			−0.663397			−0.331698	+	0.943386i	$0.607622\pi$
$74$		0			0
$75$	−8.76356	−	1.70067i	−1.01193	−	0.196376i
$76$		0			0
$77$	0.379150	+	0.656707i	0.0432082	+	0.0748387i
$78$		0			0
$79$	−3.21415	+	5.56707i	−0.361620	+	0.626344i	−0.988228	−	0.152991i	$-0.951110\pi$
$79$	−3.21415	+	5.56707i	−0.361620	+	0.626344i	0.626607	+	0.779335i	$0.284443\pi$
$80$		0			0
$81$	2.16657	−	8.73533i	0.240730	−	0.970592i
$82$		0			0
$83$	−3.27735	+	5.67653i	−0.359736	+	0.623080i	−0.987917	−	0.154987i	$-0.950466\pi$
$83$	−3.27735	+	5.67653i	−0.359736	+	0.623080i	0.628181	+	0.778067i	$0.283800\pi$
$84$		0			0
$85$	2.92953	+	5.07409i	0.317752	+	0.550362i
$86$		0			0
$87$	16.5800	+	3.21753i	1.77756	+	0.344956i
$88$		0			0
$89$	5.02926			0.533100			0.266550	−	0.963821i	$-0.414116\pi$
$89$	5.02926			0.533100			0.266550	+	0.963821i	$0.414116\pi$
$90$		0			0
$91$	2.58463			0.270942
$92$		0			0
$93$	7.54310	−	8.68272i	0.782183	−	0.900357i
$94$		0			0
$95$	−11.3983	−	19.7424i	−1.16944	−	2.02553i
$96$		0			0
$97$	−4.70138	+	8.14302i	−0.477353	+	0.826799i	−0.999663	−	0.0259565i	$-0.991737\pi$
$97$	−4.70138	+	8.14302i	−0.477353	+	0.826799i	0.522311	+	0.852755i	$0.325070\pi$
$98$		0			0
$99$	0.261909	+	1.85531i	0.0263228	+	0.186466i
$100$		0			0
$101$	6.25154	−	10.8280i	0.622052	−	1.07743i	−0.367051	−	0.930201i	$-0.619633\pi$
$101$	6.25154	−	10.8280i	0.622052	−	1.07743i	0.989103	−	0.147225i	$-0.0470340\pi$
$102$		0			0
$103$	7.87656	+	13.6426i	0.776100	+	1.34425i	0.934174	+	0.356818i	$0.116138\pi$
$103$	7.87656	+	13.6426i	0.776100	+	1.34425i	−0.158073	+	0.987427i	$0.550528\pi$
$104$		0			0
$105$	2.18359	+	6.33528i	0.213096	+	0.618260i
$106$		0			0
$107$	13.8684			1.34071			0.670353	−	0.742043i	$-0.266143\pi$
$107$	13.8684			1.34071			0.670353	+	0.742043i	$0.266143\pi$
$108$		0			0
$109$	−16.1671			−1.54853			−0.774265	−	0.632862i	$-0.781880\pi$
$109$	−16.1671			−1.54853			−0.774265	+	0.632862i	$0.781880\pi$
$110$		0			0
$111$	3.80132	+	11.0288i	0.360805	+	1.04681i
$112$		0			0
$113$	2.10460	+	3.64527i	0.197984	+	0.342918i	0.947875	−	0.318644i	$-0.103227\pi$
$113$	2.10460	+	3.64527i	0.197984	+	0.342918i	−0.749891	+	0.661562i	$0.769894\pi$
$114$		0			0
$115$	−2.48864	+	4.31045i	−0.232067	+	0.401952i
$116$		0			0
$117$	5.92285	+	2.38876i	0.547568	+	0.220841i
$118$		0			0
$119$	1.11619	−	1.93330i	0.102321	−	0.177226i
$120$		0			0
$121$	5.30496	+	9.18846i	0.482269	+	0.835314i
$122$		0			0
$123$	12.8215	−	14.7586i	1.15608	−	1.33074i
$124$		0			0
$125$	0.490836			0.0439017
$126$		0			0
$127$	−0.515228			−0.0457191			−0.0228595	−	0.999739i	$-0.507277\pi$
$127$	−0.515228			−0.0457191			−0.0228595	+	0.999739i	$0.507277\pi$
$128$		0			0
$129$	15.3419	+	2.97727i	1.35078	+	0.262134i
$130$		0			0
$131$	11.3026	+	19.5766i	0.987510	+	1.71042i	0.630201	+	0.776432i	$0.282973\pi$
$131$	11.3026	+	19.5766i	0.987510	+	1.71042i	0.357310	+	0.933986i	$0.383694\pi$
$132$		0			0
$133$	−4.34293	+	7.52217i	−0.376579	+	0.652255i
$134$		0			0
$135$	−0.851332	+	16.5358i	−0.0732710	+	1.42318i
$136$		0			0
$137$	4.62941	−	8.01837i	0.395517	−	0.685055i	−0.597650	−	0.801757i	$-0.703899\pi$
$137$	4.62941	−	8.01837i	0.395517	−	0.685055i	0.993167	+	0.116702i	$0.0372321\pi$
$138$		0			0
$139$	−9.22132	−	15.9718i	−0.782142	−	1.35471i	−0.930692	−	0.365805i	$-0.880794\pi$
$139$	−9.22132	−	15.9718i	−0.782142	−	1.35471i	0.148550	−	0.988905i	$-0.452540\pi$
$140$		0			0
$141$	4.62637	+	0.897802i	0.389611	+	0.0756086i
$142$		0			0
$143$	−1.32958			−0.111185
$144$		0			0
$145$	−31.0720			−2.58039
$146$		0			0
$147$	−6.27703	+	7.22538i	−0.517721	+	0.595939i
$148$		0			0
$149$	−2.82223	−	4.88824i	−0.231206	−	0.400460i	0.726957	−	0.686683i	$-0.240934\pi$
$149$	−2.82223	−	4.88824i	−0.231206	−	0.400460i	−0.958163	+	0.286222i	$0.907600\pi$
$150$		0			0
$151$	−3.11543	+	5.39609i	−0.253530	+	0.439128i	−0.964495	−	0.264100i	$-0.914925\pi$
$151$	−3.11543	+	5.39609i	−0.253530	+	0.439128i	0.710965	+	0.703228i	$0.248258\pi$
$152$		0			0
$153$	4.34463	−	3.39870i	0.351243	−	0.274768i
$154$		0			0
$155$	−10.5801	+	18.3252i	−0.849812	+	1.47192i
$156$		0			0
$157$	−7.76557	−	13.4504i	−0.619760	−	1.07346i	−0.989529	−	0.144332i	$-0.953897\pi$
$157$	−7.76557	−	13.4504i	−0.619760	−	1.07346i	0.369769	−	0.929124i	$-0.379437\pi$
$158$		0			0
$159$	−4.29028	−	12.4475i	−0.340241	−	0.987147i
$160$		0			0
$161$	1.89642			0.149459
$162$		0			0
$163$	15.3264			1.20046			0.600228	−	0.799829i	$-0.295077\pi$
$163$	15.3264			1.20046			0.600228	+	0.799829i	$0.295077\pi$
$164$		0			0
$165$	−1.12328	−	3.25900i	−0.0874474	−	0.253712i
$166$		0			0
$167$	−4.36488	−	7.56020i	−0.337765	−	0.585026i	0.646247	−	0.763128i	$-0.276338\pi$
$167$	−4.36488	−	7.56020i	−0.337765	−	0.585026i	−0.984012	+	0.178102i	$0.943004\pi$
$168$		0			0
$169$	4.23409	−	7.33366i	0.325699	−	0.564128i
$170$		0			0
$171$	−16.9042	+	13.2238i	−1.29270	+	1.01125i
$172$		0			0
$173$	−11.1252	+	19.2695i	−0.845837	+	1.46503i	0.0390556	+	0.999237i	$0.487565\pi$
$173$	−11.1252	+	19.2695i	−0.845837	+	1.46503i	−0.884892	+	0.465795i	$0.845768\pi$
$174$		0			0
$175$	−3.12881	−	5.41925i	−0.236516	−	0.409657i
$176$		0			0
$177$	9.14526	−	10.5269i	0.687400	−	0.791254i
$178$		0			0
$179$	1.29457			0.0967606			0.0483803	−	0.998829i	$-0.484594\pi$
$179$	1.29457			0.0967606			0.0483803	+	0.998829i	$0.484594\pi$
$180$		0			0
$181$	6.67493			0.496143			0.248072	−	0.968742i	$-0.420203\pi$
$181$	6.67493			0.496143			0.248072	+	0.968742i	$0.420203\pi$
$182$		0			0
$183$	−9.51164	−	1.84585i	−0.703121	−	0.136449i
$184$		0			0
$185$	−10.7308	−	18.5864i	−0.788947	−	1.36650i
$186$		0			0
$187$	−0.574193	+	0.994531i	−0.0419891	+	0.0727273i
$188$		0			0
$189$	5.61850	−	2.86929i	0.408686	−	0.208710i
$190$		0			0
$191$	0.169031	−	0.292771i	0.0122307	−	0.0211842i	−0.859845	−	0.510555i	$-0.829440\pi$
$191$	0.169031	−	0.292771i	0.0122307	−	0.0211842i	0.872076	+	0.489371i	$0.162773\pi$
$192$		0			0
$193$	−6.36013	−	11.0161i	−0.457812	−	0.792954i	0.541033	−	0.841001i	$-0.318033\pi$
$193$	−6.36013	−	11.0161i	−0.457812	−	0.792954i	−0.998845	+	0.0480477i	$0.984700\pi$
$194$		0			0
$195$	−11.5342	−	2.23835i	−0.825984	−	0.160292i
$196$		0			0
$197$	−7.25803			−0.517114			−0.258557	−	0.965996i	$-0.583247\pi$
$197$	−7.25803			−0.517114			−0.258557	+	0.965996i	$0.583247\pi$
$198$		0			0
$199$	−0.112216			−0.00795476			−0.00397738	−	0.999992i	$-0.501266\pi$
$199$	−0.112216			−0.00795476			−0.00397738	+	0.999992i	$0.501266\pi$
$200$		0			0
$201$	8.99555	−	10.3546i	0.634497	−	0.730359i
$202$		0			0
$203$	5.91945	+	10.2528i	0.415464	+	0.719605i
$204$		0			0
$205$	−17.9837	+	31.1487i	−1.25604	+	2.17552i
$206$		0			0
$207$	4.34578	+	1.75271i	0.302053	+	0.121821i
$208$		0			0
$209$	2.23409	−	3.86956i	0.154535	−	0.267663i
$210$		0			0
$211$	0.746256	+	1.29255i	0.0513744	+	0.0889830i	0.890569	−	0.454848i	$-0.150306\pi$
$211$	0.746256	+	1.29255i	0.0513744	+	0.0889830i	−0.839195	+	0.543831i	$0.816973\pi$
$212$		0			0
$213$	4.57856	+	13.2839i	0.313718	+	0.910195i
$214$		0			0
$215$	−28.7517			−1.96085
$216$		0			0
$217$	8.06234			0.547307
$218$		0			0
$219$	−3.19907	−	9.28153i	−0.216173	−	0.627187i
$220$		0			0
$221$	1.95711	+	3.38981i	0.131649	+	0.228023i
$222$		0			0
$223$	−13.7863	+	23.8786i	−0.923200	+	1.59903i	−0.128770	+	0.991674i	$0.541103\pi$
$223$	−13.7863	+	23.8786i	−0.923200	+	1.59903i	−0.794430	+	0.607355i	$0.792230\pi$
$224$		0			0
$225$	−2.16131	−	15.3103i	−0.144087	−	1.02069i
$226$		0			0
$227$	0.586489	−	1.01583i	0.0389267	−	0.0674229i	−0.845906	−	0.533333i	$-0.820939\pi$
$227$	0.586489	−	1.01583i	0.0389267	−	0.0674229i	0.884832	+	0.465910i	$0.154273\pi$
$228$		0			0
$229$	−2.81718	−	4.87950i	−0.186164	−	0.322446i	0.757804	−	0.652482i	$-0.226272\pi$
$229$	−2.81718	−	4.87950i	−0.186164	−	0.322446i	−0.943968	+	0.330036i	$0.892939\pi$
$230$		0			0
$231$	−0.861373	+	0.991511i	−0.0566742	+	0.0652366i
$232$		0			0
$233$	−14.3065			−0.937247			−0.468623	−	0.883398i	$-0.655250\pi$
$233$	−14.3065			−0.937247			−0.468623	+	0.883398i	$0.655250\pi$
$234$		0			0
$235$	−8.67016			−0.565579
$236$		0			0
$237$	−10.9302	−	2.12114i	−0.709995	−	0.137783i
$238$		0			0
$239$	−2.43313	−	4.21431i	−0.157386	−	0.272601i	0.776539	−	0.630069i	$-0.216973\pi$
$239$	−2.43313	−	4.21431i	−0.157386	−	0.272601i	−0.933925	+	0.357468i	$0.883640\pi$
$240$		0			0
$241$	2.68209	−	4.64552i	0.172769	−	0.299244i	−0.766618	−	0.642103i	$-0.778062\pi$
$241$	2.68209	−	4.64552i	0.172769	−	0.299244i	0.939387	+	0.342859i	$0.111395\pi$
$242$		0			0
$243$	15.5270	−	1.38247i	0.996060	−	0.0886852i
$244$		0			0
$245$	8.80427	−	15.2494i	0.562484	−	0.974251i
$246$		0			0
$247$	−7.61478	−	13.1892i	−0.484517	−	0.839208i
$248$		0			0
$249$	−11.1451	−	2.16284i	−0.706294	−	0.137065i
$250$		0			0
$251$	−14.7664			−0.932047			−0.466023	−	0.884772i	$-0.654314\pi$
$251$	−14.7664			−0.932047			−0.466023	+	0.884772i	$0.654314\pi$
$252$		0			0
$253$	−0.975557			−0.0613328
$254$		0			0
$255$	−6.65545	+	7.66097i	−0.416780	+	0.479748i
$256$		0			0
$257$	−4.19564	−	7.26707i	−0.261717	−	0.453307i	0.704981	−	0.709226i	$-0.250955\pi$
$257$	−4.19564	−	7.26707i	−0.261717	−	0.453307i	−0.966698	+	0.255919i	$0.917622\pi$
$258$		0			0
$259$	−4.08861	+	7.08169i	−0.254054	+	0.440035i
$260$		0			0
$261$	4.08903	+	28.9659i	0.253105	+	1.79294i
$262$		0			0
$263$	4.85651	−	8.41172i	0.299465	−	0.518689i	−0.676549	−	0.736398i	$-0.736525\pi$
$263$	4.85651	−	8.41172i	0.299465	−	0.518689i	0.976014	+	0.217709i	$0.0698584\pi$
$264$		0			0
$265$	12.1111	+	20.9771i	0.743981	+	1.28861i
$266$		0			0
$267$	2.83853	+	8.23547i	0.173715	+	0.504003i
$268$		0			0
$269$	−0.519050			−0.0316471			−0.0158235	−	0.999875i	$-0.505037\pi$
$269$	−0.519050			−0.0316471			−0.0158235	+	0.999875i	$0.505037\pi$
$270$		0			0
$271$	16.9533			1.02984			0.514920	−	0.857238i	$-0.327821\pi$
$271$	16.9533			1.02984			0.514920	+	0.857238i	$0.327821\pi$
$272$		0			0
$273$	1.45877	+	4.23236i	0.0882889	+	0.256154i
$274$		0			0
$275$	1.60952	+	2.78777i	0.0970579	+	0.168109i
$276$		0			0
$277$	−11.3626	+	19.6805i	−0.682710	+	1.18249i	0.291441	+	0.956589i	$0.405865\pi$
$277$	−11.3626	+	19.6805i	−0.682710	+	1.18249i	−0.974151	+	0.225899i	$0.927468\pi$
$278$		0			0
$279$	18.4754	+	7.45136i	1.10609	+	0.446101i
$280$		0			0
$281$	5.83592	−	10.1081i	0.348142	−	0.602999i	−0.637778	−	0.770220i	$-0.720146\pi$
$281$	5.83592	−	10.1081i	0.348142	−	0.602999i	0.985919	+	0.167221i	$0.0534795\pi$
$282$		0			0
$283$	13.0284	+	22.5658i	0.774456	+	1.34140i	0.935100	+	0.354385i	$0.115310\pi$
$283$	13.0284	+	22.5658i	0.774456	+	1.34140i	−0.160644	+	0.987012i	$0.551357\pi$
$284$		0			0
$285$	25.8953	−	29.8076i	1.53390	−	1.76565i
$286$		0			0
$287$	13.7041			0.808929
$288$		0			0
$289$	−13.6192			−0.801131
$290$		0			0
$291$	−15.9878	−	3.10262i	−0.937220	−	0.181879i
$292$		0			0
$293$	−14.6664	−	25.4030i	−0.856823	−	1.48406i	−0.874944	−	0.484224i	$-0.839102\pi$
$293$	−14.6664	−	25.4030i	−0.856823	−	1.48406i	0.0181212	−	0.999836i	$-0.494232\pi$
$294$		0			0
$295$	−12.8273	+	22.2175i	−0.746835	+	1.29356i
$296$		0			0
$297$	−2.89027	+	1.47602i	−0.167710	+	0.0856475i
$298$		0			0
$299$	−1.66257	+	2.87965i	−0.0961488	+	0.166535i
$300$		0			0
$301$	5.47742	+	9.48718i	0.315713	+	0.546832i
$302$		0			0
$303$	21.2594	+	4.12563i	1.22132	+	0.237011i
$304$		0			0
$305$	17.8255			1.02069
$306$		0			0
$307$	11.2190			0.640305			0.320152	−	0.947366i	$-0.396266\pi$
$307$	11.2190			0.640305			0.320152	+	0.947366i	$0.396266\pi$
$308$		0			0
$309$	−17.8944	+	20.5979i	−1.01798	+	1.17177i
$310$		0			0
$311$	17.1358	+	29.6801i	0.971682	+	1.68300i	0.690476	+	0.723355i	$0.257401\pi$
$311$	17.1358	+	29.6801i	0.971682	+	1.68300i	0.281206	+	0.959648i	$0.409266\pi$
$312$		0			0
$313$	10.8824	−	18.8489i	0.615109	−	1.06540i	−0.375256	−	0.926921i	$-0.622445\pi$
$313$	10.8824	−	18.8489i	0.615109	−	1.06540i	0.990365	−	0.138479i	$-0.0442214\pi$
$314$		0			0
$315$	−9.14167	+	7.15130i	−0.515075	+	0.402930i
$316$		0			0
$317$	−3.30124	+	5.71791i	−0.185416	+	0.321150i	−0.943717	−	0.330755i	$-0.892697\pi$
$317$	−3.30124	+	5.71791i	−0.185416	+	0.321150i	0.758301	+	0.651905i	$0.226030\pi$
$318$		0			0
$319$	−3.04509	−	5.27425i	−0.170492	−	0.295301i
$320$		0			0
$321$	7.82735	+	22.7096i	0.436880	+	1.26753i
$322$		0			0
$323$	−13.1540			−0.731910
$324$		0			0
$325$	10.9719			0.608614
$326$		0			0
$327$	−9.12478	−	26.4739i	−0.504601	−	1.46401i
$328$		0			0
$329$	1.65173	+	2.86088i	0.0910629	+	0.157725i
$330$		0			0
$331$	5.88444	−	10.1921i	0.323438	−	0.560211i	−0.657757	−	0.753230i	$-0.728495\pi$
$331$	5.88444	−	10.1921i	0.323438	−	0.560211i	0.981195	+	0.193019i	$0.0618280\pi$
$332$		0			0
$333$	−15.9144	+	12.4494i	−0.872102	+	0.682224i
$334$		0			0
$335$	−12.6173	+	21.8538i	−0.689358	+	1.19400i
$336$		0			0
$337$	6.15221	+	10.6559i	0.335132	+	0.580466i	0.983510	−	0.180853i	$-0.0578857\pi$
$337$	6.15221	+	10.6559i	0.335132	+	0.580466i	−0.648378	+	0.761319i	$0.724552\pi$
$338$		0			0
$339$	−4.78133	+	5.50371i	−0.259686	+	0.298920i
$340$		0			0
$341$	−4.14743			−0.224596
$342$		0			0
$343$	−15.2080			−0.821153
$344$		0			0
$345$	−8.46302	−	1.64235i	−0.455634	−	0.0884210i
$346$		0			0
$347$	−3.05467	−	5.29084i	−0.163983	−	0.284027i	0.772310	−	0.635245i	$-0.219101\pi$
$347$	−3.05467	−	5.29084i	−0.163983	−	0.284027i	−0.936294	+	0.351218i	$0.885768\pi$
$348$		0			0
$349$	11.5970	−	20.0866i	0.620772	−	1.07521i	−0.368570	−	0.929600i	$-0.620153\pi$
$349$	11.5970	−	20.0866i	0.620772	−	1.07521i	0.989342	−	0.145609i	$-0.0465141\pi$
$350$		0			0
$351$	−0.568743	+	11.0470i	−0.0303572	+	0.589644i
$352$		0			0
$353$	5.54985	−	9.61263i	0.295389	−	0.511629i	−0.679686	−	0.733503i	$-0.737884\pi$
$353$	5.54985	−	9.61263i	0.295389	−	0.511629i	0.975075	+	0.221874i	$0.0712174\pi$
$354$		0			0
$355$	−12.9249	−	22.3867i	−0.685985	−	1.18816i
$356$		0			0
$357$	3.79579	+	0.736618i	0.200895	+	0.0389859i
$358$		0			0
$359$	2.34365			0.123693			0.0618466	−	0.998086i	$-0.480301\pi$
$359$	2.34365			0.123693			0.0618466	+	0.998086i	$0.480301\pi$
$360$		0			0
$361$	32.1802			1.69369
$362$		0			0
$363$	−12.0521	+	13.8729i	−0.632570	+	0.728140i
$364$		0			0
$365$	9.03075	+	15.6417i	0.472691	+	0.818725i
$366$		0			0
$367$	−10.2442	+	17.7435i	−0.534745	+	0.926206i	0.464431	+	0.885610i	$0.346259\pi$
$367$	−10.2442	+	17.7435i	−0.534745	+	0.926206i	−0.999176	+	0.0405961i	$0.987074\pi$
$368$		0			0
$369$	31.4040	+	12.6656i	1.63483	+	0.659345i
$370$		0			0
$371$	4.61453	−	7.99259i	0.239574	−	0.414955i
$372$		0			0
$373$	3.91408	+	6.77939i	0.202663	+	0.351023i	0.949386	−	0.314113i	$-0.101707\pi$
$373$	3.91408	+	6.77939i	0.202663	+	0.351023i	−0.746722	+	0.665136i	$0.768374\pi$
$374$		0			0
$375$	0.277029	+	0.803750i	0.0143057	+	0.0415055i
$376$		0			0
$377$	−20.7580			−1.06909
$378$		0			0
$379$	23.6174			1.21314			0.606571	−	0.795029i	$-0.292545\pi$
$379$	23.6174			1.21314			0.606571	+	0.795029i	$0.292545\pi$
$380$		0			0
$381$	−0.290796	−	0.843692i	−0.0148979	−	0.0432237i
$382$		0			0
$383$	8.08388	+	14.0017i	0.413067	+	0.715453i	0.995223	−	0.0976240i	$-0.0311243\pi$
$383$	8.08388	+	14.0017i	0.413067	+	0.715453i	−0.582157	+	0.813077i	$0.697791\pi$
$384$		0			0
$385$	1.20818	−	2.09262i	0.0615744	−	0.106650i
$386$		0			0
$387$	3.78369	+	26.8029i	0.192336	+	1.36247i
$388$		0			0
$389$	0.466974	−	0.808822i	0.0236765	−	0.0410089i	−0.853944	−	0.520364i	$-0.825796\pi$
$389$	0.466974	−	0.808822i	0.0236765	−	0.0410089i	0.877621	+	0.479355i	$0.159129\pi$
$390$		0			0
$391$	1.43599	+	2.48721i	0.0726211	+	0.125783i
$392$		0			0
$393$	−25.6778	+	29.5572i	−1.29527	+	1.49097i
$394$		0			0
$395$	20.4840			1.03066
$396$		0			0
$397$	19.5828			0.982833			0.491417	−	0.870925i	$-0.336479\pi$
$397$	19.5828			0.982833			0.491417	+	0.870925i	$0.336479\pi$
$398$		0			0
$399$	−14.7688	−	2.86606i	−0.739365	−	0.143482i
$400$		0			0
$401$	8.55347	+	14.8150i	0.427140	+	0.739828i	0.996618	−	0.0821788i	$-0.0261879\pi$
$401$	8.55347	+	14.8150i	0.427140	+	0.739828i	−0.569478	+	0.822007i	$0.692855\pi$
$402$		0			0
$403$	−7.06815	+	12.2424i	−0.352090	+	0.609837i
$404$		0			0
$405$	−27.5582	+	7.93882i	−1.36938	+	0.394483i
$406$		0			0
$407$	2.10327	−	3.64296i	0.104255	−	0.180575i
$408$		0			0
$409$	7.41720	+	12.8470i	0.366757	+	0.635242i	0.989056	−	0.147538i	$-0.0471348\pi$
$409$	7.41720	+	12.8470i	0.366757	+	0.635242i	−0.622300	+	0.782779i	$0.713801\pi$
$410$		0			0
$411$	15.7430	+	3.05512i	0.776547	+	0.150698i
$412$		0			0
$413$	9.77479			0.480986
$414$		0			0
$415$	20.8868			1.02529
$416$		0			0
$417$	20.9495	−	24.1146i	1.02590	−	1.18090i
$418$		0			0
$419$	−6.76913	−	11.7245i	−0.330694	−	0.572778i	0.651954	−	0.758258i	$-0.273949\pi$
$419$	−6.76913	−	11.7245i	−0.330694	−	0.572778i	−0.982648	+	0.185480i	$0.940616\pi$
$420$		0			0
$421$	10.7346	−	18.5928i	0.523171	−	0.906158i	−0.476466	−	0.879193i	$-0.658082\pi$
$421$	10.7346	−	18.5928i	0.523171	−	0.906158i	0.999636	−	0.0269650i	$-0.00858426\pi$
$422$		0			0
$423$	1.14098	+	8.08247i	0.0554763	+	0.392983i
$424$		0			0
$425$	4.73833	−	8.20703i	0.229843	−	0.398099i
$426$		0			0
$427$	−3.39589	−	5.88186i	−0.164339	−	0.284643i
$428$		0			0
$429$	−0.750422	−	2.17721i	−0.0362307	−	0.105117i
$430$		0			0
$431$	0.628294			0.0302638			0.0151319	−	0.999886i	$-0.495183\pi$
$431$	0.628294			0.0302638			0.0151319	+	0.999886i	$0.495183\pi$
$432$		0			0
$433$	−13.9996			−0.672777			−0.336389	−	0.941723i	$-0.609206\pi$
$433$	−13.9996			−0.672777			−0.336389	+	0.941723i	$0.609206\pi$
$434$		0			0
$435$	−17.5372	−	50.8808i	−0.840842	−	2.43955i
$436$		0			0
$437$	−5.58720	−	9.67731i	−0.267272	−	0.462929i
$438$		0			0
$439$	17.6162	−	30.5121i	0.840774	−	1.45626i	−0.0484677	−	0.998825i	$-0.515434\pi$
$439$	17.6162	−	30.5121i	0.840774	−	1.45626i	0.889241	−	0.457438i	$-0.151233\pi$
$440$		0			0
$441$	−15.3744	−	6.20069i	−0.732115	−	0.295271i
$442$		0			0
$443$	11.5936	−	20.0806i	0.550827	−	0.954060i	−0.447388	−	0.894340i	$-0.647646\pi$
$443$	11.5936	−	20.0806i	0.550827	−	0.954060i	0.998215	−	0.0597201i	$-0.0190208\pi$
$444$		0			0
$445$	−8.01296	−	13.8789i	−0.379851	−	0.657921i
$446$		0			0
$447$	6.41168	−	7.38037i	0.303262	−	0.349080i
$448$		0			0
$449$	−2.37349			−0.112012			−0.0560061	−	0.998430i	$-0.517837\pi$
$449$	−2.37349			−0.112012			−0.0560061	+	0.998430i	$0.517837\pi$
$450$		0			0
$451$	−7.04968			−0.331956
$452$		0			0
$453$	−10.5945	−	2.05599i	−0.497774	−	0.0965989i
$454$		0			0
$455$	−4.11801	−	7.13260i	−0.193055	−	0.334381i
$456$		0			0
$457$	−2.87416	+	4.97818i	−0.134447	+	0.232870i	−0.925386	−	0.379026i	$-0.876259\pi$
$457$	−2.87416	+	4.97818i	−0.134447	+	0.232870i	0.790939	+	0.611895i	$0.209593\pi$
$458$		0			0
$459$	8.01753	+	5.19615i	0.374226	+	0.242536i
$460$		0			0
$461$	−10.0780	+	17.4555i	−0.469378	+	0.812986i	−0.999387	−	0.0350058i	$-0.988855\pi$
$461$	−10.0780	+	17.4555i	−0.469378	+	0.812986i	0.530009	+	0.847992i	$0.322188\pi$
$462$		0			0
$463$	−13.8516	−	23.9918i	−0.643741	−	1.11499i	−0.984591	−	0.174874i	$-0.944048\pi$
$463$	−13.8516	−	23.9918i	−0.643741	−	1.11499i	0.340850	−	0.940118i	$-0.389285\pi$
$464$		0			0
$465$	−35.9792	−	6.98219i	−1.66850	−	0.323791i
$466$		0			0
$467$	−36.7764			−1.70181			−0.850904	−	0.525322i	$-0.823945\pi$
$467$	−36.7764			−1.70181			−0.850904	+	0.525322i	$0.823945\pi$
$468$		0			0
$469$	9.61478			0.443969
$470$		0			0
$471$	17.6422	−	20.3077i	0.812911	−	0.935727i
$472$		0			0
$473$	−2.81770	−	4.88040i	−0.129558	−	0.224401i
$474$		0			0
$475$	−18.4361	+	31.9322i	−0.845905	+	1.46515i
$476$		0			0
$477$	17.9614	−	14.0508i	0.822397	−	0.643341i
$478$		0			0
$479$	2.76037	−	4.78109i	0.126124	−	0.218454i	−0.796048	−	0.605234i	$-0.793080\pi$
$479$	2.76037	−	4.78109i	0.126124	−	0.218454i	0.922172	+	0.386780i	$0.126413\pi$
$480$		0			0
$481$	−7.16887	−	12.4169i	−0.326872	−	0.566160i
$482$		0			0
$483$	1.07035	+	3.10541i	0.0487024	+	0.141301i
$484$		0			0
$485$	29.9623			1.36052
$486$		0			0
$487$	22.2903			1.01007			0.505035	−	0.863099i	$-0.331480\pi$
$487$	22.2903			1.01007			0.505035	+	0.863099i	$0.331480\pi$
$488$		0			0
$489$	8.65027	+	25.0972i	0.391179	+	1.13493i
$490$		0			0
$491$	0.207080	+	0.358672i	0.00934537	+	0.0161867i	0.870660	−	0.491885i	$-0.163692\pi$
$491$	0.207080	+	0.358672i	0.00934537	+	0.0161867i	−0.861315	+	0.508071i	$0.830359\pi$
$492$		0			0
$493$	−8.96454	+	15.5270i	−0.403743	+	0.699303i
$494$		0			0
$495$	4.70266	−	3.67878i	0.211369	−	0.165349i
$496$		0			0
$497$	−4.92460	+	8.52966i	−0.220899	+	0.382607i
$498$		0			0
$499$	−10.7069	−	18.5448i	−0.479305	−	0.830181i	0.520413	−	0.853915i	$-0.325778\pi$
$499$	−10.7069	−	18.5448i	−0.479305	−	0.830181i	−0.999718	+	0.0237336i	$0.992445\pi$
$500$		0			0
$501$	9.91637	−	11.4146i	0.443031	−	0.509965i
$502$		0			0
$503$	−20.8397			−0.929198			−0.464599	−	0.885521i	$-0.653802\pi$
$503$	−20.8397			−0.929198			−0.464599	+	0.885521i	$0.653802\pi$
$504$		0			0
$505$	−39.8416			−1.77293
$506$		0			0
$507$	14.3987	+	2.79424i	0.639469	+	0.124096i
$508$		0			0
$509$	−1.79067	−	3.10154i	−0.0793703	−	0.137473i	0.823608	−	0.567159i	$-0.191958\pi$
$509$	−1.79067	−	3.10154i	−0.0793703	−	0.137473i	−0.902978	+	0.429686i	$0.858624\pi$
$510$		0			0
$511$	3.44085	−	5.95973i	0.152214	−	0.263643i
$512$		0			0
$513$	−31.1949	−	20.2174i	−1.37729	−	0.892619i
$514$		0			0
$515$	25.0990	−	43.4727i	1.10599	−	1.91564i
$516$		0			0
$517$	−0.849684	−	1.47170i	−0.0373691	−	0.0647251i
$518$		0			0
$519$	−37.8332	−	7.34197i	−1.66069	−	0.322277i
$520$		0			0
$521$	−6.33816			−0.277680			−0.138840	−	0.990315i	$-0.544337\pi$
$521$	−6.33816			−0.277680			−0.138840	+	0.990315i	$0.544337\pi$
$522$		0			0
$523$	20.9934			0.917978			0.458989	−	0.888442i	$-0.348212\pi$
$523$	20.9934			0.917978			0.458989	+	0.888442i	$0.348212\pi$
$524$		0			0
$525$	7.10819	−	8.18211i	0.310227	−	0.357096i
$526$		0			0
$527$	6.10489	+	10.5740i	0.265933	+	0.460610i
$528$		0			0
$529$	10.2801	−	17.8057i	0.446962	−	0.774161i
$530$		0			0
$531$	22.3996	+	9.03404i	0.972061	+	0.392044i
$532$		0			0
$533$	−12.0142	+	20.8093i	−0.520394	+	0.901349i
$534$		0			0
$535$	−22.0960	−	38.2715i	−0.955295	−	1.65462i
$536$		0			0
$537$	0.730659	+	2.11987i	0.0315303	+	0.0914792i
$538$		0			0
$539$	3.45131			0.148658
$540$		0			0
$541$	1.88956			0.0812384			0.0406192	−	0.999175i	$-0.487067\pi$
$541$	1.88956			0.0812384			0.0406192	+	0.999175i	$0.487067\pi$
$542$		0			0
$543$	3.76735	+	10.9303i	0.161673	+	0.469063i
$544$		0			0
$545$	25.7586	+	44.6152i	1.10338	+	1.91110i
$546$		0			0
$547$	5.95041	−	10.3064i	0.254421	−	0.440671i	−0.710317	−	0.703882i	$-0.751448\pi$
$547$	5.95041	−	10.3064i	0.254421	−	0.440671i	0.964738	+	0.263211i	$0.0847817\pi$
$548$		0			0
$549$	−2.34581	−	16.6172i	−0.100117	−	0.709207i
$550$		0			0
$551$	34.8796	−	60.4132i	1.48592	−	2.57369i
$552$		0			0
$553$	−3.90236	−	6.75909i	−0.165945	−	0.287426i
$554$		0			0
$555$	24.3789	−	28.0621i	1.03483	−	1.19117i
$556$		0			0
$557$	6.55236			0.277632			0.138816	−	0.990318i	$-0.455670\pi$
$557$	6.55236			0.277632			0.138816	+	0.990318i	$0.455670\pi$
$558$		0			0
$559$	−19.2080			−0.812410
$560$		0			0
$561$	−1.95263	−	0.378931i	−0.0824403	−	0.0159985i
$562$		0			0
$563$	1.42079	+	2.46088i	0.0598791	+	0.103714i	0.894411	−	0.447246i	$-0.147595\pi$
$563$	1.42079	+	2.46088i	0.0598791	+	0.103714i	−0.834532	+	0.550960i	$0.814262\pi$
$564$		0			0
$565$	6.70638	−	11.6158i	0.282140	−	0.488680i
$566$		0			0
$567$	7.86960	+	7.58092i	0.330492	+	0.318369i
$568$		0			0
$569$	−6.59442	+	11.4219i	−0.276453	+	0.478830i	−0.970501	−	0.241099i	$-0.922492\pi$
$569$	−6.59442	+	11.4219i	−0.276453	+	0.478830i	0.694048	+	0.719929i	$0.255826\pi$
$570$		0			0
$571$	−9.97548	−	17.2780i	−0.417461	−	0.723064i	0.578222	−	0.815879i	$-0.303747\pi$
$571$	−9.97548	−	17.2780i	−0.417461	−	0.723064i	−0.995683	+	0.0928157i	$0.970413\pi$
$572$		0			0
$573$	0.574818	+	0.111550i	0.0240134	+	0.00466007i
$574$		0			0
$575$	8.05045			0.335727
$576$		0			0
$577$	1.34556			0.0560164			0.0280082	−	0.999608i	$-0.491084\pi$
$577$	1.34556			0.0560164			0.0280082	+	0.999608i	$0.491084\pi$
$578$		0			0
$579$	14.4493	−	16.6323i	0.600491	−	0.691215i
$580$		0			0
$581$	−3.97909	−	6.89199i	−0.165081	−	0.285928i
$582$		0			0
$583$	−2.37381	+	4.11155i	−0.0983131	+	0.170283i
$584$		0			0
$585$	−2.84463	−	20.1508i	−0.117611	−	0.833133i
$586$		0			0
$587$	−10.2237	+	17.7079i	−0.421976	+	0.730884i	−0.996133	−	0.0878615i	$-0.971997\pi$
$587$	−10.2237	+	17.7079i	−0.421976	+	0.730884i	0.574157	+	0.818745i	$0.305330\pi$
$588$		0			0
$589$	−23.7531	−	41.1416i	−0.978730	−	1.69521i
$590$		0			0
$591$	−4.09646	−	11.8851i	−0.168506	−	0.488889i
$592$		0			0
$593$	−25.0810			−1.02995			−0.514976	−	0.857204i	$-0.672199\pi$
$593$	−25.0810			−1.02995			−0.514976	+	0.857204i	$0.672199\pi$
$594$		0			0
$595$	−7.11359			−0.291629
$596$		0			0
$597$	−0.0633349	−	0.183755i	−0.00259213	−	0.00752058i
$598$		0			0
$599$	−2.37676	−	4.11668i	−0.0971119	−	0.168203i	0.813376	−	0.581738i	$-0.197627\pi$
$599$	−2.37676	−	4.11668i	−0.0971119	−	0.168203i	−0.910488	+	0.413535i	$0.864294\pi$
$600$		0			0
$601$	19.9340	−	34.5267i	0.813124	−	1.40837i	−0.0975429	−	0.995231i	$-0.531098\pi$
$601$	19.9340	−	34.5267i	0.813124	−	1.40837i	0.910667	−	0.413141i	$-0.135568\pi$
$602$		0			0
$603$	22.0329	+	8.88615i	0.897251	+	0.361872i
$604$		0			0
$605$	16.9045	−	29.2794i	0.687264	−	1.19038i
$606$		0			0
$607$	21.0643	+	36.4844i	0.854973	+	1.48086i	0.876670	+	0.481093i	$0.159760\pi$
$607$	21.0643	+	36.4844i	0.854973	+	1.48086i	−0.0216961	+	0.999765i	$0.506907\pi$
$608$		0			0
$609$	−13.4481	+	15.4799i	−0.544945	+	0.627277i
$610$		0			0
$611$	−5.79221			−0.234328
$612$		0			0
$613$	37.0554			1.49665			0.748327	−	0.663330i	$-0.230857\pi$
$613$	37.0554			1.49665			0.748327	+	0.663330i	$0.230857\pi$
$614$		0			0
$615$	−61.1564	−	11.8681i	−2.46607	−	0.478569i
$616$		0			0
$617$	12.0793	+	20.9220i	0.486295	+	0.842288i	0.999876	−	0.0157534i	$-0.00501466\pi$
$617$	12.0793	+	20.9220i	0.486295	+	0.842288i	−0.513581	+	0.858041i	$0.671681\pi$
$618$		0			0
$619$	−24.2530	+	42.0074i	−0.974810	+	1.68842i	−0.294248	+	0.955729i	$0.595069\pi$
$619$	−24.2530	+	42.0074i	−0.974810	+	1.68842i	−0.680562	+	0.732691i	$0.738264\pi$
$620$		0			0
$621$	−0.417304	+	8.10551i	−0.0167458	+	0.325263i
$622$		0			0
$623$	−3.05306	+	5.28805i	−0.122318	+	0.211861i
$624$		0			0
$625$	12.1031	+	20.9631i	0.484122	+	0.838524i
$626$		0			0
$627$	7.59738	+	1.47436i	0.303410	+	0.0588803i
$628$		0			0
$629$	−12.3838			−0.493773
$630$		0			0
$631$	38.3164			1.52535			0.762677	−	0.646780i	$-0.223885\pi$
$631$	38.3164			1.52535			0.762677	+	0.646780i	$0.223885\pi$
$632$		0			0
$633$	−1.69538	+	1.95152i	−0.0673854	+	0.0775662i
$634$		0			0
$635$	0.820897	+	1.42184i	0.0325763	+	0.0564238i
$636$		0			0
$637$	5.88180	−	10.1876i	0.233045	−	0.403647i
$638$		0			0
$639$	−19.1683	+	14.9949i	−0.758288	+	0.593190i
$640$		0			0
$641$	−13.3651	+	23.1491i	−0.527890	+	0.914333i	0.471581	+	0.881823i	$0.343683\pi$
$641$	−13.3651	+	23.1491i	−0.527890	+	0.914333i	−0.999471	+	0.0325101i	$0.989650\pi$
$642$		0			0
$643$	7.35536	+	12.7399i	0.290067	+	0.502411i	0.973825	−	0.227298i	$-0.0729890\pi$
$643$	7.35536	+	12.7399i	0.290067	+	0.502411i	−0.683758	+	0.729709i	$0.739656\pi$
$644$		0			0
$645$	−16.2276	−	47.0814i	−0.638961	−	1.85383i
$646$		0			0
$647$	−7.36931			−0.289717			−0.144859	−	0.989452i	$-0.546273\pi$
$647$	−7.36931			−0.289717			−0.144859	+	0.989452i	$0.546273\pi$
$648$		0			0
$649$	−5.02835			−0.197380
$650$		0			0
$651$	4.55041	+	13.2022i	0.178345	+	0.517434i
$652$		0			0
$653$	12.2260	+	21.1760i	0.478440	+	0.828683i	0.999694	−	0.0247186i	$-0.00786899\pi$
$653$	12.2260	+	21.1760i	0.478440	+	0.828683i	−0.521254	+	0.853401i	$0.674536\pi$
$654$		0			0
$655$	36.0161	−	62.3817i	1.40727	−	2.43746i
$656$		0			0
$657$	13.3930	−	10.4771i	0.522513	−	0.408749i
$658$		0			0
$659$	3.95593	−	6.85187i	0.154101	−	0.266911i	−0.778630	−	0.627483i	$-0.784085\pi$
$659$	3.95593	−	6.85187i	0.154101	−	0.266911i	0.932731	+	0.360572i	$0.117419\pi$
$660$		0			0
$661$	−14.7468	−	25.5423i	−0.573585	−	0.993479i	−0.996194	−	0.0871663i	$-0.972219\pi$
$661$	−14.7468	−	25.5423i	−0.573585	−	0.993479i	0.422609	−	0.906312i	$-0.361114\pi$
$662$		0			0
$663$	−4.44625	+	5.11800i	−0.172678	+	0.198767i
$664$		0			0
$665$	27.6778			1.07330
$666$		0			0
$667$	−15.2308			−0.589740
$668$		0			0
$669$	−46.8826	−	9.09811i	−1.81259	−	0.351753i
$670$		0			0
$671$	1.74692	+	3.02575i	0.0674390	+	0.116808i
$672$		0			0
$673$	−9.26908	+	16.0545i	−0.357297	+	0.618856i	−0.987508	−	0.157567i	$-0.949635\pi$
$673$	−9.26908	+	16.0545i	−0.357297	+	0.618856i	0.630211	+	0.776424i	$0.282968\pi$
$674$		0			0
$675$	23.8510	−	12.1804i	0.918024	−	0.468822i
$676$		0			0
$677$	−12.4799	+	21.6158i	−0.479642	+	0.830764i	−0.999727	−	0.0233505i	$-0.992567\pi$
$677$	−12.4799	+	21.6158i	−0.479642	+	0.830764i	0.520086	+	0.854114i	$0.325900\pi$
$678$		0			0
$679$	−5.70803	−	9.88661i	−0.219054	−	0.379413i
$680$		0			0
$681$	1.99445	+	0.387046i	0.0764275	+	0.0148316i
$682$		0			0
$683$	23.8166			0.911315			0.455658	−	0.890155i	$-0.349404\pi$
$683$	23.8166			0.911315			0.455658	+	0.890155i	$0.349404\pi$
$684$		0			0
$685$	−29.5036			−1.12727
$686$		0			0
$687$	6.40021	−	7.36717i	0.244183	−	0.281075i
$688$		0			0
$689$	8.09100	+	14.0140i	0.308242	+	0.533891i
$690$		0			0
$691$	−0.926507	+	1.60476i	−0.0352460	+	0.0610479i	−0.883110	−	0.469165i	$-0.844555\pi$
$691$	−0.926507	+	1.60476i	−0.0352460	+	0.0610479i	0.847864	+	0.530213i	$0.177888\pi$
$692$		0			0
$693$	−2.10977	−	0.850897i	−0.0801437	−	0.0323229i
$694$		0			0
$695$	−29.3841	+	50.8947i	−1.11460	+	1.93055i
$696$		0			0
$697$	10.3769	+	17.9733i	0.393053	+	0.680788i
$698$		0			0
$699$	−8.07461	−	23.4270i	−0.305410	−	0.886091i
$700$		0			0
$701$	25.9501			0.980122			0.490061	−	0.871688i	$-0.336974\pi$
$701$	25.9501			0.980122			0.490061	+	0.871688i	$0.336974\pi$
$702$		0			0
$703$	48.1832			1.81726
$704$		0			0
$705$	−4.89347	−	14.1975i	−0.184299	−	0.534709i
$706$		0			0
$707$	7.59012	+	13.1465i	0.285456	+	0.494424i
$708$		0			0
$709$	2.18041	−	3.77658i	0.0818869	−	0.141832i	−0.822174	−	0.569237i	$-0.807239\pi$
$709$	2.18041	−	3.77658i	0.0818869	−	0.141832i	0.904060	+	0.427405i	$0.140572\pi$
$710$		0			0
$711$	−2.69567	−	19.0956i	−0.101095	−	0.716140i
$712$		0			0
$713$	−5.18612	+	8.98263i	−0.194222	+	0.336402i
$714$		0			0
$715$	2.11839	+	3.66915i	0.0792232	+	0.137219i
$716$		0			0
$717$	5.52772	−	6.36286i	0.206437	−	0.237625i
$718$		0			0
$719$	30.3650			1.13242			0.566212	−	0.824260i	$-0.308408\pi$
$719$	30.3650			1.13242			0.566212	+	0.824260i	$0.308408\pi$
$720$		0			0
$721$	−19.1262			−0.712296
$722$		0			0
$723$	9.12088	+	1.77001i	0.339209	+	0.0658275i
$724$		0			0
$725$	25.1286	+	43.5239i	0.933251	+	1.61644i
$726$		0			0
$727$	−6.47800	+	11.2202i	−0.240256	+	0.416135i	−0.960787	−	0.277287i	$-0.910565\pi$
$727$	−6.47800	+	11.2202i	−0.240256	+	0.416135i	0.720531	+	0.693422i	$0.243898\pi$
$728$		0			0
$729$	11.0273	+	24.6455i	0.408419	+	0.912794i
$730$		0			0
$731$	−8.29512	+	14.3676i	−0.306806	+	0.531404i
$732$		0			0
$733$	−10.6357	−	18.4216i	−0.392838	−	0.680416i	0.599985	−	0.800012i	$-0.295173\pi$
$733$	−10.6357	−	18.4216i	−0.392838	−	0.680416i	−0.992823	+	0.119596i	$0.961840\pi$
$734$		0			0
$735$	29.9403	+	5.81027i	1.10437	+	0.214315i
$736$		0			0
$737$	−4.94604			−0.182190
$738$		0			0
$739$	−11.4687			−0.421883			−0.210942	−	0.977499i	$-0.567653\pi$
$739$	−11.4687			−0.421883			−0.210942	+	0.977499i	$0.567653\pi$
$740$		0			0
$741$	17.2997	−	19.9133i	0.635519	−	0.731534i
$742$		0			0
$743$	18.0094	+	31.1932i	0.660701	+	1.14437i	0.980432	+	0.196859i	$0.0630740\pi$
$743$	18.0094	+	31.1932i	0.660701	+	1.14437i	−0.319731	+	0.947508i	$0.603593\pi$
$744$		0			0
$745$	−8.99314	+	15.5766i	−0.329483	+	0.570682i
$746$		0			0
$747$	−2.74867	−	19.4710i	−0.100569	−	0.712408i
$748$		0			0
$749$	−8.41893	+	14.5820i	−0.307621	+	0.532815i
$750$		0			0
$751$	4.34620	+	7.52783i	0.158595	+	0.274695i	0.934362	−	0.356325i	$-0.115970\pi$
$751$	4.34620	+	7.52783i	0.158595	+	0.274695i	−0.775767	+	0.631019i	$0.782637\pi$
$752$		0			0
$753$	−8.33421	−	24.1802i	−0.303715	−	0.881174i
$754$		0			0
$755$	19.8549			0.722594
$756$		0			0
$757$	26.7265			0.971390			0.485695	−	0.874128i	$-0.338567\pi$
$757$	26.7265			0.971390			0.485695	+	0.874128i	$0.338567\pi$
$758$		0			0
$759$	−0.550608	−	1.59749i	−0.0199858	−	0.0579851i
$760$		0			0
$761$	12.0267	+	20.8309i	0.435969	+	0.755121i	0.997374	−	0.0724203i	$-0.0230723\pi$
$761$	12.0267	+	20.8309i	0.435969	+	0.755121i	−0.561405	+	0.827541i	$0.689739\pi$
$762$		0			0
$763$	9.81441	−	16.9991i	0.355305	−	0.615407i
$764$		0			0
$765$	−16.3013	−	6.57451i	−0.589374	−	0.237702i
$766$		0			0
$767$	−8.56944	+	14.8427i	−0.309424	+	0.535939i
$768$		0			0
$769$	−1.00296	−	1.73717i	−0.0361675	−	0.0626439i	0.847375	−	0.530995i	$-0.178182\pi$
$769$	−1.00296	−	1.73717i	−0.0361675	−	0.0626439i	−0.883543	+	0.468351i	$0.844848\pi$
$770$		0			0
$771$	9.53188	−	10.9720i	0.343282	−	0.395146i
$772$		0			0
$773$	30.0297			1.08009			0.540046	−	0.841635i	$-0.318407\pi$
$773$	30.0297			1.08009			0.540046	+	0.841635i	$0.318407\pi$
$774$		0			0
$775$	34.2253			1.22941
$776$		0			0
$777$	−13.9040	−	2.69823i	−0.498803	−	0.0967984i
$778$		0			0
$779$	−40.3748	−	69.9313i	−1.44658	−	2.50555i
$780$		0			0
$781$	2.53332	−	4.38783i	0.0906491	−	0.157009i
$782$		0			0
$783$	−45.1241	+	23.0443i	−1.61260	+	0.823535i
$784$		0			0
$785$	−24.7453	+	42.8601i	−0.883198	+	1.52974i
$786$		0			0
$787$	−2.04245	−	3.53763i	−0.0728054	−	0.126103i	0.827324	−	0.561724i	$-0.189862\pi$
$787$	−2.04245	−	3.53763i	−0.0728054	−	0.126103i	−0.900130	+	0.435622i	$0.856529\pi$
$788$		0			0
$789$	16.5153	+	3.20499i	0.587961	+	0.114101i
$790$		0			0
$791$	−5.11047			−0.181707
$792$		0			0
$793$	11.9085			0.422885
$794$		0			0
$795$	−27.5147	+	31.6717i	−0.975847	+	1.12328i
$796$		0			0
$797$	8.31103	+	14.3951i	0.294392	+	0.509901i	0.974843	−	0.222892i	$-0.0715496\pi$
$797$	8.31103	+	14.3951i	0.294392	+	0.509901i	−0.680451	+	0.732793i	$0.738216\pi$
$798$		0			0
$799$	−2.50141	+	4.33258i	−0.0884937	+	0.153276i
$800$		0			0
$801$	−11.8836	+	9.29626i	−0.419887	+	0.328467i
$802$		0			0
$803$	−1.77005	+	3.06581i	−0.0624635	+	0.108190i
$804$		0			0
$805$	−3.02151	−	5.23341i	−0.106494	−	0.184453i
$806$		0			0
$807$	−0.292954	−	0.849952i	−0.0103125	−	0.0299197i
$808$		0			0
$809$	48.2163			1.69519			0.847597	−	0.530641i	$-0.178049\pi$
$809$	48.2163			1.69519			0.847597	+	0.530641i	$0.178049\pi$
$810$		0			0
$811$	6.91987			0.242990			0.121495	−	0.992592i	$-0.461231\pi$
$811$	6.91987			0.242990			0.121495	+	0.992592i	$0.461231\pi$
$812$		0			0
$813$	9.56851	+	27.7613i	0.335582	+	0.973631i
$814$		0			0
$815$	−24.4191	−	42.2951i	−0.855363	−	1.48153i
$816$		0			0
$817$	32.2750	−	55.9019i	1.12916	−	1.95576i
$818$		0			0
$819$	−6.10721	+	4.77752i	−0.213403	+	0.166940i
$820$		0			0
$821$	7.53494	−	13.0509i	0.262971	−	0.455479i	−0.704059	−	0.710142i	$-0.748631\pi$
$821$	7.53494	−	13.0509i	0.262971	−	0.455479i	0.967030	+	0.254662i	$0.0819643\pi$
$822$		0			0
$823$	−22.6790	−	39.2812i	−0.790541	−	1.36926i	−0.925632	−	0.378424i	$-0.876466\pi$
$823$	−22.6790	−	39.2812i	−0.790541	−	1.36926i	0.135091	−	0.990833i	$-0.456867\pi$
$824$		0			0
$825$	−3.65660	+	4.20904i	−0.127306	+	0.146540i
$826$		0			0
$827$	11.3507			0.394702			0.197351	−	0.980333i	$-0.436766\pi$
$827$	11.3507			0.394702			0.197351	+	0.980333i	$0.436766\pi$
$828$		0			0
$829$	29.8614			1.03713			0.518566	−	0.855038i	$-0.326466\pi$
$829$	29.8614			1.03713			0.518566	+	0.855038i	$0.326466\pi$
$830$		0			0
$831$	−38.6402	−	7.49858i	−1.34041	−	0.260123i
$832$		0			0
$833$	−5.08021	−	8.79919i	−0.176019	−	0.304874i
$834$		0			0
$835$	−13.9089	+	24.0909i	−0.481336	+	0.833699i
$836$		0			0
$837$	−1.77410	+	34.4593i	−0.0613220	+	1.19109i
$838$		0			0
$839$	13.0215	−	22.5539i	0.449551	−	0.778646i	−0.548805	−	0.835950i	$-0.684917\pi$
$839$	13.0215	−	22.5539i	0.449551	−	0.778646i	0.998357	+	0.0573042i	$0.0182505\pi$
$840$		0			0
$841$	−33.0412	−	57.2291i	−1.13935	−	1.97342i
$842$		0			0
$843$	19.8460	+	3.85134i	0.683531	+	0.132647i
$844$		0			0
$845$	−26.9842			−0.928284
$846$		0			0
$847$	−12.8817			−0.442621
$848$		0			0
$849$	−29.5985	+	34.0703i	−1.01582	+	1.16929i
$850$		0			0
$851$	−5.26002	−	9.11063i	−0.180311	−	0.312308i
$852$		0			0
$853$	1.04718	−	1.81377i	0.0358547	−	0.0621021i	−0.847541	−	0.530730i	$-0.821918\pi$
$853$	1.04718	−	1.81377i	0.0358547	−	0.0621021i	0.883396	+	0.468627i	$0.155251\pi$
$854$		0			0
$855$	63.4257	+	25.5803i	2.16911	+	0.874829i
$856$		0			0
$857$	5.47263	−	9.47887i	0.186941	−	0.323792i	−0.757288	−	0.653082i	$-0.773476\pi$
$857$	5.47263	−	9.47887i	0.186941	−	0.323792i	0.944229	+	0.329290i	$0.106809\pi$
$858$		0			0
$859$	−13.4294	−	23.2603i	−0.458204	−	0.793633i	0.540662	−	0.841240i	$-0.318174\pi$
$859$	−13.4294	−	23.2603i	−0.458204	−	0.793633i	−0.998866	+	0.0476073i	$0.984840\pi$
$860$		0			0
$861$	7.73465	+	22.4407i	0.263596	+	0.764776i
$862$		0			0
$863$	49.4778			1.68424			0.842121	−	0.539288i	$-0.181307\pi$
$863$	49.4778			1.68424			0.842121	+	0.539288i	$0.181307\pi$
$864$		0			0
$865$	70.9021			2.41074
$866$		0			0
$867$	−7.68674	−	22.3017i	−0.261055	−	0.757404i
$868$		0			0
$869$	2.00746	+	3.47701i	0.0680983	+	0.117950i
$870$		0			0
$871$	−8.42916	+	14.5997i	−0.285611	+	0.494693i
$872$		0			0
$873$	−3.94299	−	27.9313i	−0.133450	−	0.945332i
$874$		0			0
$875$	−0.297967	+	0.516093i	−0.0100731	+	0.0174471i
$876$		0			0
$877$	11.3449	+	19.6499i	0.383090	+	0.663531i	0.991502	−	0.130090i	$-0.0415267\pi$
$877$	11.3449	+	19.6499i	0.383090	+	0.663531i	−0.608412	+	0.793621i	$0.708193\pi$
$878$		0			0
$879$	33.3200	−	38.3540i	1.12386	−	1.29365i
$880$		0			0
$881$	10.8224			0.364616			0.182308	−	0.983241i	$-0.441643\pi$
$881$	10.8224			0.364616			0.182308	+	0.983241i	$0.441643\pi$
$882$		0			0
$883$	−32.7591			−1.10243			−0.551215	−	0.834363i	$-0.685836\pi$
$883$	−32.7591			−1.10243			−0.551215	+	0.834363i	$0.685836\pi$
$884$		0			0
$885$	−43.6213	−	8.46522i	−1.46631	−	0.284555i
$886$		0			0
$887$	16.6048	+	28.7604i	0.557535	+	0.965679i	0.997701	+	0.0677629i	$0.0215861\pi$
$887$	16.6048	+	28.7604i	0.557535	+	0.965679i	−0.440166	+	0.897916i	$0.645081\pi$
$888$		0			0
$889$	0.312774	−	0.541741i	0.0104901	−	0.0181694i
$890$		0			0
$891$	−4.04828	−	3.89978i	−0.135623	−	0.130648i
$892$		0			0
$893$	9.73260	−	16.8574i	0.325689	−	0.564110i
$894$		0			0
$895$	−2.06260	−	3.57252i	−0.0689450	−	0.119416i
$896$		0			0
$897$	−5.65383	−	1.09719i	−0.188776	−	0.0366341i
$898$		0			0
$899$	−64.7515			−2.15958
$900$		0			0
$901$	13.9767			0.465630
$902$		0			0
$903$	−12.4439	+	14.3239i	−0.414107	+	0.476671i
$904$		0			0
$905$	−10.6350	−	18.4203i	−0.353518	−	0.612311i
$906$		0			0
$907$	−10.2085	+	17.6816i	−0.338966	+	0.587107i	−0.984239	−	0.176846i	$-0.943411\pi$
$907$	−10.2085	+	17.6816i	−0.338966	+	0.587107i	0.645272	+	0.763953i	$0.276744\pi$
$908$		0			0
$909$	5.24309	+	37.1410i	0.173902	+	1.23189i
$910$		0			0
$911$	−29.7162	+	51.4700i	−0.984541	+	1.70528i	−0.340585	+	0.940214i	$0.610625\pi$
$911$	−29.7162	+	51.4700i	−0.984541	+	1.70528i	−0.643957	+	0.765062i	$0.722708\pi$
$912$		0			0
$913$	2.04693	+	3.54538i	0.0677434	+	0.117335i
$914$		0			0
$915$	10.0608	+	29.1895i	0.332599	+	0.964975i
$916$		0			0
$917$	−27.4454			−0.906325
$918$		0			0
$919$	−23.2045			−0.765447			−0.382724	−	0.923863i	$-0.625014\pi$
$919$	−23.2045			−0.765447			−0.382724	+	0.923863i	$0.625014\pi$
$920$		0			0
$921$	6.33207	+	18.3713i	0.208649	+	0.605356i
$922$		0			0
$923$	−8.63467	−	14.9557i	−0.284214	−	0.492272i
$924$		0			0
$925$	−17.3565	+	30.0623i	−0.570678	+	0.988443i
$926$		0			0
$927$	−43.8290	−	17.6768i	−1.43953	−	0.580581i
$928$		0			0
$929$	−0.370924	+	0.642460i	−0.0121696	+	0.0210784i	−0.872046	−	0.489424i	$-0.837207\pi$
$929$	−0.370924	+	0.642460i	−0.0121696	+	0.0210784i	0.859876	+	0.510502i	$0.170540\pi$
$930$		0			0
$931$	19.7663	+	34.2362i	0.647814	+	1.12205i
$932$		0			0
$933$	−38.9300	+	44.8116i	−1.27451	+	1.46707i
$934$		0			0
$935$	3.65938			0.119674
$936$		0			0
$937$	2.43708			0.0796161			0.0398080	−	0.999207i	$-0.487325\pi$
$937$	2.43708			0.0796161			0.0398080	+	0.999207i	$0.487325\pi$
$938$		0			0
$939$	37.0073	+	7.18170i	1.20769	+	0.234366i
$940$		0			0
$941$	−5.25473	−	9.10146i	−0.171299	−	0.296699i	0.767575	−	0.640959i	$-0.221463\pi$
$941$	−5.25473	−	9.10146i	−0.171299	−	0.296699i	−0.938874	+	0.344260i	$0.888130\pi$
$942$		0			0
$943$	−8.81521	+	15.2684i	−0.287063	+	0.497207i
$944$		0			0
$945$	−16.8699	−	10.9334i	−0.548779	−	0.355663i
$946$		0			0
$947$	26.4659	−	45.8403i	0.860026	−	1.48961i	−0.0118761	−	0.999929i	$-0.503780\pi$
$947$	26.4659	−	45.8403i	0.860026	−	1.48961i	0.871902	−	0.489680i	$-0.162886\pi$
$948$		0			0
$949$	6.03311	+	10.4496i	0.195843	+	0.339210i
$950$		0			0
$951$	−11.2264	−	2.17861i	−0.364041	−	0.0706463i
$952$		0			0
$953$	−14.5979			−0.472873			−0.236437	−	0.971647i	$-0.575980\pi$
$953$	−14.5979			−0.472873			−0.236437	+	0.971647i	$0.575980\pi$
$954$		0			0
$955$	−1.07725			−0.0348590
$956$		0			0
$957$	6.91799	−	7.96318i	0.223627	−	0.257413i
$958$		0			0
$959$	5.62065	+	9.73526i	0.181500	+	0.314368i
$960$		0			0
$961$	−6.54800	+	11.3415i	−0.211226	+	0.365854i
$962$		0			0
$963$	−32.7695	+	25.6348i	−1.05598	+	0.826069i
$964$		0			0
$965$	−20.2668	+	35.1031i	−0.652411	+	1.13001i
$966$		0			0
$967$	27.3029	+	47.2900i	0.878003	+	1.52075i	0.853529	+	0.521045i	$0.174458\pi$
$967$	27.3029	+	47.2900i	0.878003	+	1.52075i	0.0244732	+	0.999700i	$0.492209\pi$
$968$		0			0
$969$	−7.42418	−	21.5399i	−0.238499	−	0.691961i
$970$		0			0
$971$	−41.5365			−1.33297			−0.666485	−	0.745519i	$-0.732202\pi$
$971$	−41.5365			−1.33297			−0.666485	+	0.745519i	$0.732202\pi$
$972$		0			0
$973$	22.3916			0.717841
$974$		0			0
$975$	6.19260	+	17.9667i	0.198322	+	0.575395i
$976$		0			0
$977$	−30.4039	−	52.6611i	−0.972707	−	1.68478i	−0.687303	−	0.726371i	$-0.741206\pi$
$977$	−30.4039	−	52.6611i	−0.972707	−	1.68478i	−0.285404	−	0.958407i	$-0.592128\pi$
$978$		0			0
$979$	1.57056	−	2.72028i	0.0501952	−	0.0869406i
$980$		0			0
$981$	38.2012	−	29.8839i	1.21967	−	0.954119i
$982$		0			0
$983$	−14.9506	+	25.8952i	−0.476851	+	0.825929i	−0.999648	−	0.0265275i	$-0.991555\pi$
$983$	−14.9506	+	25.8952i	−0.476851	+	0.825929i	0.522797	+	0.852457i	$0.324888\pi$
$984$		0			0
$985$	11.5640	+	20.0294i	0.368460	+	0.638191i
$986$		0			0
$987$	−3.75249	+	4.31942i	−0.119443	+	0.137489i
$988$		0			0
$989$	−14.0935			−0.448146
$990$		0			0
$991$	−56.3402			−1.78971			−0.894853	−	0.446361i	$-0.852720\pi$
$991$	−56.3402			−1.78971			−0.894853	+	0.446361i	$0.852720\pi$
$992$		0			0
$993$	20.0110	+	3.88336i	0.635029	+	0.123235i
$994$		0			0
$995$	0.178790	+	0.309673i	0.00566802	+	0.00981730i
$996$		0			0
$997$	−5.26572	+	9.12049i	−0.166767	+	0.288849i	−0.937281	−	0.348574i	$-0.886666\pi$
$997$	−5.26572	+	9.12049i	−0.166767	+	0.288849i	0.770514	+	0.637423i	$0.219999\pi$
$998$		0			0
$999$	−29.3682	−	19.0335i	−0.929169	−	0.602193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.g.385.3	yes	10
3.2	odd	2		3456.2.i.f.1153.5		10
4.3	odd	2		1152.2.i.f.385.3	yes	10
8.3	odd	2		1152.2.i.h.385.3	yes	10
8.5	even	2		1152.2.i.e.385.3	✓	10
9.4	even	3	inner	1152.2.i.g.769.3	yes	10
9.5	odd	6		3456.2.i.f.2305.5		10
12.11	even	2		3456.2.i.g.1153.5		10
24.5	odd	2		3456.2.i.e.1153.1		10
24.11	even	2		3456.2.i.h.1153.1		10
36.23	even	6		3456.2.i.g.2305.5		10
36.31	odd	6		1152.2.i.f.769.3	yes	10
72.5	odd	6		3456.2.i.e.2305.1		10
72.13	even	6		1152.2.i.e.769.3	yes	10
72.59	even	6		3456.2.i.h.2305.1		10
72.67	odd	6		1152.2.i.h.769.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.3	✓	10	8.5	even	2
1152.2.i.e.769.3	yes	10	72.13	even	6
1152.2.i.f.385.3	yes	10	4.3	odd	2
1152.2.i.f.769.3	yes	10	36.31	odd	6
1152.2.i.g.385.3	yes	10	1.1	even	1	trivial
1152.2.i.g.769.3	yes	10	9.4	even	3	inner
1152.2.i.h.385.3	yes	10	8.3	odd	2
1152.2.i.h.769.3	yes	10	72.67	odd	6
3456.2.i.e.1153.1		10	24.5	odd	2
3456.2.i.e.2305.1		10	72.5	odd	6
3456.2.i.f.1153.5		10	3.2	odd	2
3456.2.i.f.2305.5		10	9.5	odd	6
3456.2.i.g.1153.5		10	12.11	even	2
3456.2.i.g.2305.5		10	36.23	even	6
3456.2.i.h.1153.1		10	24.11	even	2
3456.2.i.h.2305.1		10	72.59	even	6

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.564403 + 1.63751i) q^{3} +(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(-2.36290 + 1.84844i) q^{9} +O(q^{10})\)	\(q+(0.564403 + 1.63751i) q^{3} +(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(-2.36290 + 1.84844i) q^{9} +(0.312284 - 0.540892i) q^{11} +(-1.06440 - 1.84360i) q^{13} +(3.61967 - 4.16654i) q^{15} -1.83869 q^{17} +7.15403 q^{19} +(-2.06440 - 0.400622i) q^{21} +(-0.780986 - 1.35271i) q^{23} +(-2.57702 + 4.46352i) q^{25} +(-4.36047 - 2.82601i) q^{27} +(4.87551 - 8.44463i) q^{29} +(-3.32024 - 5.75083i) q^{31} +(1.06197 + 0.206088i) q^{33} +3.86884 q^{35} +6.73511 q^{37} +(2.41817 - 2.78351i) q^{39} +(-5.64365 - 9.77508i) q^{41} +(4.51144 - 7.81404i) q^{43} +(8.86572 + 3.57565i) q^{45} +(1.36043 - 2.35634i) q^{47} +(2.76296 + 4.78558i) q^{49} +(-1.03776 - 3.01087i) q^{51} -7.60144 q^{53} -1.99021 q^{55} +(4.03776 + 11.7148i) q^{57} +(-4.02547 - 6.97231i) q^{59} +(-2.79700 + 4.84455i) q^{61} +(-0.509134 - 3.60660i) q^{63} +(-3.39176 + 5.87471i) q^{65} +(-3.95957 - 6.85817i) q^{67} +(1.77428 - 2.04235i) q^{69} +8.11222 q^{71} -5.66806 q^{73} +(-8.76356 - 1.70067i) q^{75} +(0.379150 + 0.656707i) q^{77} +(-3.21415 + 5.56707i) q^{79} +(2.16657 - 8.73533i) q^{81} +(-3.27735 + 5.67653i) q^{83} +(2.92953 + 5.07409i) q^{85} +(16.5800 + 3.21753i) q^{87} +5.02926 q^{89} +2.58463 q^{91} +(7.54310 - 8.68272i) q^{93} +(-11.3983 - 19.7424i) q^{95} +(-4.70138 + 8.14302i) q^{97} +(0.261909 + 1.85531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} - 4 q^{7} - q^{9}+O(q^{10}) \) 10 * q + q^3 - 4 * q^7 - q^9	\( 10 q + q^{3} - 4 q^{7} - q^{9} - q^{11} - 6 q^{13} + 12 q^{15} - 6 q^{17} + 18 q^{19} - 16 q^{21} + 4 q^{23} + q^{25} - 2 q^{27} + 4 q^{29} - 8 q^{31} - 13 q^{33} - 24 q^{35} + 20 q^{37} - 18 q^{39} - 5 q^{41} - 13 q^{43} + 12 q^{45} - 6 q^{47} + 3 q^{49} + 3 q^{51} + 12 q^{55} + 27 q^{57} - 13 q^{59} - 10 q^{61} - 20 q^{63} - 17 q^{67} + 10 q^{69} + 8 q^{71} - 34 q^{73} - 29 q^{75} - 8 q^{77} - 6 q^{79} - q^{81} + 12 q^{83} - 18 q^{85} + 10 q^{87} + 44 q^{89} + 36 q^{91} - 26 q^{93} - 6 q^{95} + 27 q^{97} + 34 q^{99}+O(q^{100}) \) 10 * q + q^3 - 4 * q^7 - q^9 - q^11 - 6 * q^13 + 12 * q^15 - 6 * q^17 + 18 * q^19 - 16 * q^21 + 4 * q^23 + q^25 - 2 * q^27 + 4 * q^29 - 8 * q^31 - 13 * q^33 - 24 * q^35 + 20 * q^37 - 18 * q^39 - 5 * q^41 - 13 * q^43 + 12 * q^45 - 6 * q^47 + 3 * q^49 + 3 * q^51 + 12 * q^55 + 27 * q^57 - 13 * q^59 - 10 * q^61 - 20 * q^63 - 17 * q^67 + 10 * q^69 + 8 * q^71 - 34 * q^73 - 29 * q^75 - 8 * q^77 - 6 * q^79 - q^81 + 12 * q^83 - 18 * q^85 + 10 * q^87 + 44 * q^89 + 36 * q^91 - 26 * q^93 - 6 * q^95 + 27 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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