LMFDB - Embedded newform 1152.2.i.h.769.3

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			769.3
Root			$-1.13593 + 1.30754i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.h.385.3

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

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

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	−0.251372	−	0.967891i	$-0.580882\pi$
$5$	1.59327	−	2.75962i	0.712532	−	1.23414i	0.963904	−	0.266251i	$-0.0857850\pi$
$6$		0			0
$7$	0.607060	+	1.05146i	0.229447	+	0.397414i	0.957644	−	0.287954i	$-0.0929749\pi$
$7$	0.607060	+	1.05146i	0.229447	+	0.397414i	−0.728197	+	0.685368i	$0.759642\pi$
$8$		0			0
$9$	−2.36290	−	1.84844i	−0.787632	−	0.616145i
$10$		0			0
$11$	0.312284	+	0.540892i	0.0941572	+	0.163085i	0.909257	−	0.416236i	$-0.136651\pi$
$11$	0.312284	+	0.540892i	0.0941572	+	0.163085i	−0.815099	+	0.579321i	$0.803318\pi$
$12$		0			0
$13$	1.06440	−	1.84360i	0.295212	−	0.511323i	−0.679822	−	0.733377i	$-0.737943\pi$
$13$	1.06440	−	1.84360i	0.295212	−	0.511323i	0.975034	+	0.222054i	$0.0712763\pi$
$14$		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	$-0.781266\pi$
$23$	0.780986	−	1.35271i	0.162847	−	0.282059i	0.935889	+	0.352296i	$0.114599\pi$
$24$		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	−0.820434	−	0.571742i	$-0.806268\pi$
$29$	−4.87551	−	8.44463i	−0.905360	−	1.56813i	−0.0849260	−	0.996387i	$-0.527065\pi$
$30$		0			0
$31$	3.32024	−	5.75083i	0.596333	−	1.03288i	−0.397024	−	0.917808i	$-0.629957\pi$
$31$	3.32024	−	5.75083i	0.596333	−	1.03288i	0.993357	−	0.115071i	$-0.0367095\pi$
$32$		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	$-0.686755\pi$
$37$	−6.73511			−1.10724			−0.553622	+	0.832768i	$0.686755\pi$
$38$		0			0
$39$	−2.41817	−	2.78351i	−0.387217	−	0.445718i
$40$		0			0
$41$	−5.64365	+	9.77508i	−0.881389	+	1.52661i	−0.0315923	+	0.999501i	$0.510058\pi$
$41$	−5.64365	+	9.77508i	−0.881389	+	1.52661i	−0.849797	+	0.527110i	$0.823276\pi$
$42$		0			0
$43$	4.51144	+	7.81404i	0.687988	+	1.19163i	0.972488	+	0.232954i	$0.0748391\pi$
$43$	4.51144	+	7.81404i	0.687988	+	1.19163i	−0.284500	+	0.958676i	$0.591828\pi$
$44$		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	$-0.230254\pi$
$47$	−1.36043	−	2.35634i	−0.198440	−	0.343708i	−0.948023	+	0.318203i	$0.896921\pi$
$48$		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	$-0.325160\pi$
$53$	7.60144			1.04414			0.522069	+	0.852903i	$0.325160\pi$
$54$		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	0.475536	+	0.879696i	$0.342254\pi$
$59$	−4.02547	+	6.97231i	−0.524071	+	0.907718i	−0.999607	+	0.0280214i	$0.991079\pi$
$60$		0			0
$61$	2.79700	+	4.84455i	0.358119	+	0.620281i	0.987647	−	0.156698i	$-0.0500848\pi$
$61$	2.79700	+	4.84455i	0.358119	+	0.620281i	−0.629527	+	0.776978i	$0.716751\pi$
$62$		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	−0.999826	−	0.0186768i	$-0.994055\pi$
$67$	−3.95957	+	6.85817i	−0.483738	+	0.837859i	0.516087	+	0.856536i	$0.327388\pi$
$68$		0			0
$69$	−1.77428	−	2.04235i	−0.213599	−	0.245870i
$70$		0			0
$71$	−8.11222			−0.962743			−0.481371	−	0.876517i	$-0.659861\pi$
$71$	−8.11222			−0.962743			−0.481371	+	0.876517i	$0.659861\pi$
$72$		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	$-0.0488904\pi$
$79$	3.21415	+	5.56707i	0.361620	+	0.626344i	−0.626607	+	0.779335i	$0.715557\pi$
$80$		0			0
$81$	2.16657	+	8.73533i	0.240730	+	0.970592i
$82$		0			0
$83$	−3.27735	−	5.67653i	−0.359736	−	0.623080i	0.628181	−	0.778067i	$-0.283800\pi$
$83$	−3.27735	−	5.67653i	−0.359736	−	0.623080i	−0.987917	+	0.154987i	$0.950466\pi$
$84$		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	0.522311	−	0.852755i	$-0.325070\pi$
$97$	−4.70138	−	8.14302i	−0.477353	−	0.826799i	−0.999663	+	0.0259565i	$0.991737\pi$
$98$		0			0
$99$	0.261909	−	1.85531i	0.0263228	−	0.186466i
$100$		0			0
$101$	−6.25154	−	10.8280i	−0.622052	−	1.07743i	−0.989103	−	0.147225i	$-0.952966\pi$
$101$	−6.25154	−	10.8280i	−0.622052	−	1.07743i	0.367051	−	0.930201i	$-0.380367\pi$
$102$		0			0
$103$	−7.87656	+	13.6426i	−0.776100	+	1.34425i	0.158073	+	0.987427i	$0.449472\pi$
$103$	−7.87656	+	13.6426i	−0.776100	+	1.34425i	−0.934174	+	0.356818i	$0.883862\pi$
$104$		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	$-0.218120\pi$
$109$	16.1671			1.54853			0.774265	+	0.632862i	$0.218120\pi$
$110$		0			0
$111$	−3.80132	+	11.0288i	−0.360805	+	1.04681i
$112$		0			0
$113$	2.10460	−	3.64527i	0.197984	−	0.342918i	−0.749891	−	0.661562i	$-0.769894\pi$
$113$	2.10460	−	3.64527i	0.197984	−	0.342918i	0.947875	+	0.318644i	$0.103227\pi$
$114$		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	$-0.492723\pi$
$127$	0.515228			0.0457191			0.0228595	+	0.999739i	$0.492723\pi$
$128$		0			0
$129$	15.3419	−	2.97727i	1.35078	−	0.262134i
$130$		0			0
$131$	11.3026	−	19.5766i	0.987510	−	1.71042i	0.357310	−	0.933986i	$-0.383694\pi$
$131$	11.3026	−	19.5766i	0.987510	−	1.71042i	0.630201	−	0.776432i	$-0.282973\pi$
$132$		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	0.993167	−	0.116702i	$-0.0372321\pi$
$137$	4.62941	+	8.01837i	0.395517	+	0.685055i	−0.597650	+	0.801757i	$0.703899\pi$
$138$		0			0
$139$	−9.22132	+	15.9718i	−0.782142	+	1.35471i	0.148550	+	0.988905i	$0.452540\pi$
$139$	−9.22132	+	15.9718i	−0.782142	+	1.35471i	−0.930692	+	0.365805i	$0.880794\pi$
$140$		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	$-0.759066\pi$
$149$	2.82223	−	4.88824i	0.231206	−	0.400460i	0.958163	+	0.286222i	$0.0923996\pi$
$150$		0			0
$151$	3.11543	+	5.39609i	0.253530	+	0.439128i	0.964495	−	0.264100i	$-0.0850749\pi$
$151$	3.11543	+	5.39609i	0.253530	+	0.439128i	−0.710965	+	0.703228i	$0.751742\pi$
$152$		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	−0.369769	−	0.929124i	$-0.620563\pi$
$157$	7.76557	−	13.4504i	0.619760	−	1.07346i	0.989529	−	0.144332i	$-0.0461034\pi$
$158$		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	$-0.723662\pi$
$167$	4.36488	−	7.56020i	0.337765	−	0.585026i	0.984012	+	0.178102i	$0.0569958\pi$
$168$		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	0.884892	+	0.465795i	$0.154232\pi$
$173$	11.1252	+	19.2695i	0.845837	+	1.46503i	−0.0390556	+	0.999237i	$0.512435\pi$
$174$		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	$-0.579797\pi$
$181$	−6.67493			−0.496143			−0.248072	+	0.968742i	$0.579797\pi$
$182$		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	$-0.170560\pi$
$191$	−0.169031	−	0.292771i	−0.0122307	−	0.0211842i	−0.872076	+	0.489371i	$0.837227\pi$
$192$		0			0
$193$	−6.36013	+	11.0161i	−0.457812	+	0.792954i	−0.998845	−	0.0480477i	$-0.984700\pi$
$193$	−6.36013	+	11.0161i	−0.457812	+	0.792954i	0.541033	+	0.841001i	$0.318033\pi$
$194$		0			0
$195$	−11.5342	+	2.23835i	−0.825984	+	0.160292i
$196$		0			0
$197$	7.25803			0.517114			0.258557	−	0.965996i	$-0.416753\pi$
$197$	7.25803			0.517114			0.258557	+	0.965996i	$0.416753\pi$
$198$		0			0
$199$	0.112216			0.00795476			0.00397738	−	0.999992i	$-0.498734\pi$
$199$	0.112216			0.00795476			0.00397738	+	0.999992i	$0.498734\pi$
$200$		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	−0.839195	−	0.543831i	$-0.816973\pi$
$211$	0.746256	−	1.29255i	0.0513744	−	0.0889830i	0.890569	+	0.454848i	$0.150306\pi$
$212$		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	0.794430	+	0.607355i	$0.207770\pi$
$223$	13.7863	+	23.8786i	0.923200	+	1.59903i	0.128770	+	0.991674i	$0.458897\pi$
$224$		0			0
$225$	−2.16131	+	15.3103i	−0.144087	+	1.02069i
$226$		0			0
$227$	0.586489	+	1.01583i	0.0389267	+	0.0674229i	0.884832	−	0.465910i	$-0.154273\pi$
$227$	0.586489	+	1.01583i	0.0389267	+	0.0674229i	−0.845906	+	0.533333i	$0.820939\pi$
$228$		0			0
$229$	2.81718	−	4.87950i	0.186164	−	0.322446i	−0.757804	−	0.652482i	$-0.773728\pi$
$229$	2.81718	−	4.87950i	0.186164	−	0.322446i	0.943968	+	0.330036i	$0.107061\pi$
$230$		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	$-0.783027\pi$
$239$	2.43313	−	4.21431i	0.157386	−	0.272601i	0.933925	+	0.357468i	$0.116360\pi$
$240$		0			0
$241$	2.68209	+	4.64552i	0.172769	+	0.299244i	0.939387	−	0.342859i	$-0.111395\pi$
$241$	2.68209	+	4.64552i	0.172769	+	0.299244i	−0.766618	+	0.642103i	$0.778062\pi$
$242$		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	−0.966698	−	0.255919i	$-0.917622\pi$
$257$	−4.19564	+	7.26707i	−0.261717	+	0.453307i	0.704981	+	0.709226i	$0.250955\pi$
$258$		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	$-0.263475\pi$
$263$	−4.85651	−	8.41172i	−0.299465	−	0.518689i	−0.976014	+	0.217709i	$0.930142\pi$
$264$		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	$-0.494963\pi$
$269$	0.519050			0.0316471			0.0158235	+	0.999875i	$0.494963\pi$
$270$		0			0
$271$	−16.9533			−1.02984			−0.514920	−	0.857238i	$-0.672179\pi$
$271$	−16.9533			−1.02984			−0.514920	+	0.857238i	$0.672179\pi$
$272$		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	0.974151	+	0.225899i	$0.0725321\pi$
$277$	11.3626	+	19.6805i	0.682710	+	1.18249i	−0.291441	+	0.956589i	$0.594135\pi$
$278$		0			0
$279$	−18.4754	+	7.45136i	−1.10609	+	0.446101i
$280$		0			0
$281$	5.83592	+	10.1081i	0.348142	+	0.602999i	0.985919	−	0.167221i	$-0.0534795\pi$
$281$	5.83592	+	10.1081i	0.348142	+	0.602999i	−0.637778	+	0.770220i	$0.720146\pi$
$282$		0			0
$283$	13.0284	−	22.5658i	0.774456	−	1.34140i	−0.160644	−	0.987012i	$-0.551357\pi$
$283$	13.0284	−	22.5658i	0.774456	−	1.34140i	0.935100	−	0.354385i	$-0.115310\pi$
$284$		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	−0.0181212	−	0.999836i	$-0.505768\pi$
$293$	14.6664	−	25.4030i	0.856823	−	1.48406i	0.874944	−	0.484224i	$-0.160898\pi$
$294$		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	−0.281206	+	0.959648i	$0.590734\pi$
$311$	−17.1358	+	29.6801i	−0.971682	+	1.68300i	−0.690476	+	0.723355i	$0.742599\pi$
$312$		0			0
$313$	10.8824	+	18.8489i	0.615109	+	1.06540i	0.990365	+	0.138479i	$0.0442214\pi$
$313$	10.8824	+	18.8489i	0.615109	+	1.06540i	−0.375256	+	0.926921i	$0.622445\pi$
$314$		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	$-0.107303\pi$
$317$	3.30124	+	5.71791i	0.185416	+	0.321150i	−0.758301	+	0.651905i	$0.773970\pi$
$318$		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	0.981195	−	0.193019i	$-0.0618280\pi$
$331$	5.88444	+	10.1921i	0.323438	+	0.560211i	−0.657757	+	0.753230i	$0.728495\pi$
$332$		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	−0.648378	−	0.761319i	$-0.724552\pi$
$337$	6.15221	−	10.6559i	0.335132	−	0.580466i	0.983510	+	0.180853i	$0.0578857\pi$
$338$		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	−0.936294	−	0.351218i	$-0.885768\pi$
$347$	−3.05467	+	5.29084i	−0.163983	+	0.284027i	0.772310	+	0.635245i	$0.219101\pi$
$348$		0			0
$349$	−11.5970	−	20.0866i	−0.620772	−	1.07521i	−0.989342	−	0.145609i	$-0.953486\pi$
$349$	−11.5970	−	20.0866i	−0.620772	−	1.07521i	0.368570	−	0.929600i	$-0.379847\pi$
$350$		0			0
$351$	0.568743	+	11.0470i	0.0303572	+	0.589644i
$352$		0			0
$353$	5.54985	+	9.61263i	0.295389	+	0.511629i	0.975075	−	0.221874i	$-0.0712174\pi$
$353$	5.54985	+	9.61263i	0.295389	+	0.511629i	−0.679686	+	0.733503i	$0.737884\pi$
$354$		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	$-0.519699\pi$
$359$	−2.34365			−0.123693			−0.0618466	+	0.998086i	$0.519699\pi$
$360$		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	0.999176	+	0.0405961i	$0.0129257\pi$
$367$	10.2442	+	17.7435i	0.534745	+	0.926206i	−0.464431	+	0.885610i	$0.653741\pi$
$368$		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	$-0.898293\pi$
$373$	−3.91408	+	6.77939i	−0.202663	+	0.351023i	0.746722	+	0.665136i	$0.231626\pi$
$374$		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	$-0.968876\pi$
$383$	−8.08388	+	14.0017i	−0.413067	+	0.715453i	0.582157	+	0.813077i	$0.302209\pi$
$384$		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	$-0.174204\pi$
$389$	−0.466974	−	0.808822i	−0.0236765	−	0.0410089i	−0.877621	+	0.479355i	$0.840871\pi$
$390$		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	$-0.663521\pi$
$397$	−19.5828			−0.982833			−0.491417	+	0.870925i	$0.663521\pi$
$398$		0			0
$399$	14.7688	−	2.86606i	0.739365	−	0.143482i
$400$		0			0
$401$	8.55347	−	14.8150i	0.427140	−	0.739828i	−0.569478	−	0.822007i	$-0.692855\pi$
$401$	8.55347	−	14.8150i	0.427140	−	0.739828i	0.996618	+	0.0821788i	$0.0261879\pi$
$402$		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	−0.622300	−	0.782779i	$-0.713801\pi$
$409$	7.41720	−	12.8470i	0.366757	−	0.635242i	0.989056	+	0.147538i	$0.0471348\pi$
$410$		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	−0.982648	−	0.185480i	$-0.940616\pi$
$419$	−6.76913	+	11.7245i	−0.330694	+	0.572778i	0.651954	+	0.758258i	$0.273949\pi$
$420$		0			0
$421$	−10.7346	−	18.5928i	−0.523171	−	0.906158i	−0.999636	−	0.0269650i	$-0.991416\pi$
$421$	−10.7346	−	18.5928i	−0.523171	−	0.906158i	0.476466	−	0.879193i	$-0.341918\pi$
$422$		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	$-0.504817\pi$
$431$	−0.628294			−0.0302638			−0.0151319	+	0.999886i	$0.504817\pi$
$432$		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	−0.889241	−	0.457438i	$-0.848767\pi$
$439$	−17.6162	−	30.5121i	−0.840774	−	1.45626i	0.0484677	−	0.998825i	$-0.484566\pi$
$440$		0			0
$441$	−15.3744	+	6.20069i	−0.732115	+	0.295271i
$442$		0			0
$443$	11.5936	+	20.0806i	0.550827	+	0.954060i	0.998215	+	0.0597201i	$0.0190208\pi$
$443$	11.5936	+	20.0806i	0.550827	+	0.954060i	−0.447388	+	0.894340i	$0.647646\pi$
$444$		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	0.790939	−	0.611895i	$-0.209593\pi$
$457$	−2.87416	−	4.97818i	−0.134447	−	0.232870i	−0.925386	+	0.379026i	$0.876259\pi$
$458$		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	$-0.0111450\pi$
$461$	10.0780	+	17.4555i	0.469378	+	0.812986i	−0.530009	+	0.847992i	$0.677812\pi$
$462$		0			0
$463$	13.8516	−	23.9918i	0.643741	−	1.11499i	−0.340850	−	0.940118i	$-0.610715\pi$
$463$	13.8516	−	23.9918i	0.643741	−	1.11499i	0.984591	−	0.174874i	$-0.0559517\pi$
$464$		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	$-0.206920\pi$
$479$	−2.76037	−	4.78109i	−0.126124	−	0.218454i	−0.922172	+	0.386780i	$0.873587\pi$
$480$		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	$-0.668520\pi$
$487$	−22.2903			−1.01007			−0.505035	+	0.863099i	$0.668520\pi$
$488$		0			0
$489$	8.65027	−	25.0972i	0.391179	−	1.13493i
$490$		0			0
$491$	0.207080	−	0.358672i	0.00934537	−	0.0161867i	−0.861315	−	0.508071i	$-0.830359\pi$
$491$	0.207080	−	0.358672i	0.00934537	−	0.0161867i	0.870660	+	0.491885i	$0.163692\pi$
$492$		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	−0.999718	−	0.0237336i	$-0.992445\pi$
$499$	−10.7069	+	18.5448i	−0.479305	+	0.830181i	0.520413	+	0.853915i	$0.325778\pi$
$500$		0			0
$501$	−9.91637	−	11.4146i	−0.443031	−	0.509965i
$502$		0			0
$503$	20.8397			0.929198			0.464599	−	0.885521i	$-0.346198\pi$
$503$	20.8397			0.929198			0.464599	+	0.885521i	$0.346198\pi$
$504$		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	$-0.808042\pi$
$509$	1.79067	−	3.10154i	0.0793703	−	0.137473i	0.902978	+	0.429686i	$0.141376\pi$
$510$		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	$-0.512933\pi$
$541$	−1.88956			−0.0812384			−0.0406192	+	0.999175i	$0.512933\pi$
$542$		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	0.964738	−	0.263211i	$-0.0847817\pi$
$547$	5.95041	+	10.3064i	0.254421	+	0.440671i	−0.710317	+	0.703882i	$0.751448\pi$
$548$		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	$-0.544330\pi$
$557$	−6.55236			−0.277632			−0.138816	+	0.990318i	$0.544330\pi$
$558$		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	−0.834532	−	0.550960i	$-0.814262\pi$
$563$	1.42079	−	2.46088i	0.0598791	−	0.103714i	0.894411	+	0.447246i	$0.147595\pi$
$564$		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	0.694048	−	0.719929i	$-0.255826\pi$
$569$	−6.59442	−	11.4219i	−0.276453	−	0.478830i	−0.970501	+	0.241099i	$0.922492\pi$
$570$		0			0
$571$	−9.97548	+	17.2780i	−0.417461	+	0.723064i	−0.995683	−	0.0928157i	$-0.970413\pi$
$571$	−9.97548	+	17.2780i	−0.417461	+	0.723064i	0.578222	+	0.815879i	$0.303747\pi$
$572$		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	0.574157	−	0.818745i	$-0.305330\pi$
$587$	−10.2237	−	17.7079i	−0.421976	−	0.730884i	−0.996133	+	0.0878615i	$0.971997\pi$
$588$		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	$-0.802373\pi$
$599$	2.37676	−	4.11668i	0.0971119	−	0.168203i	0.910488	+	0.413535i	$0.135706\pi$
$600$		0			0
$601$	19.9340	+	34.5267i	0.813124	+	1.40837i	0.910667	+	0.413141i	$0.135568\pi$
$601$	19.9340	+	34.5267i	0.813124	+	1.40837i	−0.0975429	+	0.995231i	$0.531098\pi$
$602$		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	0.0216961	+	0.999765i	$0.493093\pi$
$607$	−21.0643	+	36.4844i	−0.854973	+	1.48086i	−0.876670	+	0.481093i	$0.840240\pi$
$608$		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	$-0.769143\pi$
$613$	−37.0554			−1.49665			−0.748327	+	0.663330i	$0.769143\pi$
$614$		0			0
$615$	61.1564	−	11.8681i	2.46607	−	0.478569i
$616$		0			0
$617$	12.0793	−	20.9220i	0.486295	−	0.842288i	−0.513581	−	0.858041i	$-0.671681\pi$
$617$	12.0793	−	20.9220i	0.486295	−	0.842288i	0.999876	+	0.0157534i	$0.00501466\pi$
$618$		0			0
$619$	−24.2530	−	42.0074i	−0.974810	−	1.68842i	−0.680562	−	0.732691i	$-0.738264\pi$
$619$	−24.2530	−	42.0074i	−0.974810	−	1.68842i	−0.294248	−	0.955729i	$-0.595069\pi$
$620$		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	$-0.776115\pi$
$631$	−38.3164			−1.52535			−0.762677	+	0.646780i	$0.776115\pi$
$632$		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	−0.999471	−	0.0325101i	$-0.989650\pi$
$641$	−13.3651	−	23.1491i	−0.527890	−	0.914333i	0.471581	−	0.881823i	$-0.343683\pi$
$642$		0			0
$643$	7.35536	−	12.7399i	0.290067	−	0.502411i	−0.683758	−	0.729709i	$-0.739656\pi$
$643$	7.35536	−	12.7399i	0.290067	−	0.502411i	0.973825	+	0.227298i	$0.0729890\pi$
$644$		0			0
$645$	16.2276	−	47.0814i	0.638961	−	1.85383i
$646$		0			0
$647$	7.36931			0.289717			0.144859	−	0.989452i	$-0.453727\pi$
$647$	7.36931			0.289717			0.144859	+	0.989452i	$0.453727\pi$
$648$		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	$-0.992131\pi$
$653$	−12.2260	+	21.1760i	−0.478440	+	0.828683i	0.521254	+	0.853401i	$0.325464\pi$
$654$		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	0.932731	−	0.360572i	$-0.117419\pi$
$659$	3.95593	+	6.85187i	0.154101	+	0.266911i	−0.778630	+	0.627483i	$0.784085\pi$
$660$		0			0
$661$	14.7468	−	25.5423i	0.573585	−	0.993479i	−0.422609	−	0.906312i	$-0.638886\pi$
$661$	14.7468	−	25.5423i	0.573585	−	0.993479i	0.996194	−	0.0871663i	$-0.0277811\pi$
$662$		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	0.630211	−	0.776424i	$-0.282968\pi$
$673$	−9.26908	−	16.0545i	−0.357297	−	0.618856i	−0.987508	+	0.157567i	$0.949635\pi$
$674$		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	$-0.00743337\pi$
$677$	12.4799	+	21.6158i	0.479642	+	0.830764i	−0.520086	+	0.854114i	$0.674100\pi$
$678$		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	0.847864	−	0.530213i	$-0.177888\pi$
$691$	−0.926507	−	1.60476i	−0.0352460	−	0.0610479i	−0.883110	+	0.469165i	$0.844555\pi$
$692$		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	$-0.663026\pi$
$701$	−25.9501			−0.980122			−0.490061	+	0.871688i	$0.663026\pi$
$702$		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	$-0.192761\pi$
$709$	−2.18041	−	3.77658i	−0.0818869	−	0.141832i	−0.904060	+	0.427405i	$0.859428\pi$
$710$		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	$-0.691592\pi$
$719$	−30.3650			−1.13242			−0.566212	+	0.824260i	$0.691592\pi$
$720$		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	$-0.0894354\pi$
$727$	6.47800	+	11.2202i	0.240256	+	0.416135i	−0.720531	+	0.693422i	$0.756102\pi$
$728$		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	$-0.704827\pi$
$733$	10.6357	−	18.4216i	0.392838	−	0.680416i	0.992823	+	0.119596i	$0.0381599\pi$
$734$		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	0.319731	+	0.947508i	$0.396407\pi$
$743$	−18.0094	+	31.1932i	−0.660701	+	1.14437i	−0.980432	+	0.196859i	$0.936926\pi$
$744$		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	$-0.884030\pi$
$751$	−4.34620	+	7.52783i	−0.158595	+	0.274695i	0.775767	+	0.631019i	$0.217363\pi$
$752$		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	$-0.661433\pi$
$757$	−26.7265			−0.971390			−0.485695	+	0.874128i	$0.661433\pi$
$758$		0			0
$759$	0.550608	−	1.59749i	0.0199858	−	0.0579851i
$760$		0			0
$761$	12.0267	−	20.8309i	0.435969	−	0.755121i	−0.561405	−	0.827541i	$-0.689739\pi$
$761$	12.0267	−	20.8309i	0.435969	−	0.755121i	0.997374	+	0.0724203i	$0.0230723\pi$
$762$		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	−0.883543	−	0.468351i	$-0.844848\pi$
$769$	−1.00296	+	1.73717i	−0.0361675	+	0.0626439i	0.847375	+	0.530995i	$0.178182\pi$
$770$		0			0
$771$	9.53188	+	10.9720i	0.343282	+	0.395146i
$772$		0			0
$773$	−30.0297			−1.08009			−0.540046	−	0.841635i	$-0.681593\pi$
$773$	−30.0297			−1.08009			−0.540046	+	0.841635i	$0.681593\pi$
$774$		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	−0.900130	−	0.435622i	$-0.856529\pi$
$787$	−2.04245	+	3.53763i	−0.0728054	+	0.126103i	0.827324	+	0.561724i	$0.189862\pi$
$788$		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	$-0.928450\pi$
$797$	−8.31103	+	14.3951i	−0.294392	+	0.509901i	0.680451	+	0.732793i	$0.261784\pi$
$798$		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	$-0.251369\pi$
$821$	−7.53494	−	13.0509i	−0.262971	−	0.455479i	−0.967030	+	0.254662i	$0.918036\pi$
$822$		0			0
$823$	22.6790	−	39.2812i	0.790541	−	1.36926i	−0.135091	−	0.990833i	$-0.543133\pi$
$823$	22.6790	−	39.2812i	0.790541	−	1.36926i	0.925632	−	0.378424i	$-0.123534\pi$
$824$		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	$-0.673534\pi$
$829$	−29.8614			−1.03713			−0.518566	+	0.855038i	$0.673534\pi$
$830$		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	$-0.315083\pi$
$839$	−13.0215	−	22.5539i	−0.449551	−	0.778646i	−0.998357	+	0.0573042i	$0.981749\pi$
$840$		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	$-0.178082\pi$
$853$	−1.04718	−	1.81377i	−0.0358547	−	0.0621021i	−0.883396	+	0.468627i	$0.844749\pi$
$854$		0			0
$855$	−63.4257	+	25.5803i	−2.16911	+	0.874829i
$856$		0			0
$857$	5.47263	+	9.47887i	0.186941	+	0.323792i	0.944229	−	0.329290i	$-0.106809\pi$
$857$	5.47263	+	9.47887i	0.186941	+	0.323792i	−0.757288	+	0.653082i	$0.773476\pi$
$858$		0			0
$859$	−13.4294	+	23.2603i	−0.458204	+	0.793633i	−0.998866	−	0.0476073i	$-0.984840\pi$
$859$	−13.4294	+	23.2603i	−0.458204	+	0.793633i	0.540662	+	0.841240i	$0.318174\pi$
$860$		0			0
$861$	−7.73465	+	22.4407i	−0.263596	+	0.764776i
$862$		0			0
$863$	−49.4778			−1.68424			−0.842121	−	0.539288i	$-0.818693\pi$
$863$	−49.4778			−1.68424			−0.842121	+	0.539288i	$0.818693\pi$
$864$		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	$-0.958473\pi$
$877$	−11.3449	+	19.6499i	−0.383090	+	0.663531i	0.608412	+	0.793621i	$0.291807\pi$
$878$		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	0.440166	+	0.897916i	$0.354919\pi$
$887$	−16.6048	+	28.7604i	−0.557535	+	0.965679i	−0.997701	+	0.0677629i	$0.978414\pi$
$888$		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	0.645272	−	0.763953i	$-0.276744\pi$
$907$	−10.2085	−	17.6816i	−0.338966	−	0.587107i	−0.984239	+	0.176846i	$0.943411\pi$
$908$		0			0
$909$	−5.24309	+	37.1410i	−0.173902	+	1.23189i
$910$		0			0
$911$	29.7162	+	51.4700i	0.984541	+	1.70528i	0.643957	+	0.765062i	$0.277292\pi$
$911$	29.7162	+	51.4700i	0.984541	+	1.70528i	0.340585	+	0.940214i	$0.389375\pi$
$912$		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	$-0.374986\pi$
$919$	23.2045			0.765447			0.382724	+	0.923863i	$0.374986\pi$
$920$		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	0.859876	−	0.510502i	$-0.170540\pi$
$929$	−0.370924	−	0.642460i	−0.0121696	−	0.0210784i	−0.872046	+	0.489424i	$0.837207\pi$
$930$		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	$-0.778537\pi$
$941$	5.25473	−	9.10146i	0.171299	−	0.296699i	0.938874	+	0.344260i	$0.111870\pi$
$942$		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	0.871902	+	0.489680i	$0.162886\pi$
$947$	26.4659	+	45.8403i	0.860026	+	1.48961i	−0.0118761	+	0.999929i	$0.503780\pi$
$948$		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	−0.0244732	+	0.999700i	$0.507791\pi$
$967$	−27.3029	+	47.2900i	−0.878003	+	1.52075i	−0.853529	+	0.521045i	$0.825542\pi$
$968$		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	−0.285404	+	0.958407i	$0.592128\pi$
$977$	−30.4039	+	52.6611i	−0.972707	+	1.68478i	−0.687303	+	0.726371i	$0.741206\pi$
$978$		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	$-0.00844494\pi$
$983$	14.9506	+	25.8952i	0.476851	+	0.825929i	−0.522797	+	0.852457i	$0.675112\pi$
$984$		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	$-0.147280\pi$
$991$	56.3402			1.78971			0.894853	+	0.446361i	$0.147280\pi$
$992$		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	$-0.113334\pi$
$997$	5.26572	+	9.12049i	0.166767	+	0.288849i	−0.770514	+	0.637423i	$0.780001\pi$
$998$		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.h.769.3	yes	10
3.2	odd	2		3456.2.i.h.2305.1		10
4.3	odd	2		1152.2.i.e.769.3	yes	10
8.3	odd	2		1152.2.i.g.769.3	yes	10
8.5	even	2		1152.2.i.f.769.3	yes	10
9.2	odd	6		3456.2.i.h.1153.1		10
9.7	even	3	inner	1152.2.i.h.385.3	yes	10
12.11	even	2		3456.2.i.e.2305.1		10
24.5	odd	2		3456.2.i.g.2305.5		10
24.11	even	2		3456.2.i.f.2305.5		10
36.7	odd	6		1152.2.i.e.385.3	✓	10
36.11	even	6		3456.2.i.e.1153.1		10
72.11	even	6		3456.2.i.f.1153.5		10
72.29	odd	6		3456.2.i.g.1153.5		10
72.43	odd	6		1152.2.i.g.385.3	yes	10
72.61	even	6		1152.2.i.f.385.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.3	✓	10	36.7	odd	6
1152.2.i.e.769.3	yes	10	4.3	odd	2
1152.2.i.f.385.3	yes	10	72.61	even	6
1152.2.i.f.769.3	yes	10	8.5	even	2
1152.2.i.g.385.3	yes	10	72.43	odd	6
1152.2.i.g.769.3	yes	10	8.3	odd	2
1152.2.i.h.385.3	yes	10	9.7	even	3	inner
1152.2.i.h.769.3	yes	10	1.1	even	1	trivial
3456.2.i.e.1153.1		10	36.11	even	6
3456.2.i.e.2305.1		10	12.11	even	2
3456.2.i.f.1153.5		10	72.11	even	6
3456.2.i.f.2305.5		10	24.11	even	2
3456.2.i.g.1153.5		10	72.29	odd	6
3456.2.i.g.2305.5		10	24.5	odd	2
3456.2.i.h.1153.1		10	9.2	odd	6
3456.2.i.h.2305.1		10	3.2	odd	2

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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