LMFDB - Embedded newform 1512.2.j.d.323.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.15
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743762 - 1.20284i) q^{2} +(-0.893635 + 1.78925i) q^{4} +3.69622 q^{5} -1.00000i q^{7} +(2.81683 - 0.255879i) q^{8} +O(q^{10})$	\(q+(-0.743762 - 1.20284i) q^{2} +(-0.893635 + 1.78925i) q^{4} +3.69622 q^{5} -1.00000i q^{7} +(2.81683 - 0.255879i) q^{8} +(-2.74911 - 4.44595i) q^{10} +2.05843i q^{11} +4.65027i q^{13} +(-1.20284 + 0.743762i) q^{14} +(-2.40283 - 3.19787i) q^{16} +5.73497i q^{17} +3.27215 q^{19} +(-3.30307 + 6.61346i) q^{20} +(2.47596 - 1.53098i) q^{22} +4.45085 q^{23} +8.66201 q^{25} +(5.59351 - 3.45869i) q^{26} +(1.78925 + 0.893635i) q^{28} -10.2594 q^{29} -1.26066i q^{31} +(-2.05939 + 5.26867i) q^{32} +(6.89824 - 4.26546i) q^{34} -3.69622i q^{35} +3.25539i q^{37} +(-2.43370 - 3.93586i) q^{38} +(10.4116 - 0.945784i) q^{40} +8.72747i q^{41} -2.56921 q^{43} +(-3.68305 - 1.83949i) q^{44} +(-3.31038 - 5.35365i) q^{46} -2.03048 q^{47} -1.00000 q^{49} +(-6.44248 - 10.4190i) q^{50} +(-8.32049 - 4.15564i) q^{52} -10.0794 q^{53} +7.60840i q^{55} +(-0.255879 - 2.81683i) q^{56} +(7.63056 + 12.3404i) q^{58} -0.851213i q^{59} -2.31448i q^{61} +(-1.51637 + 0.937634i) q^{62} +(7.86905 - 1.44153i) q^{64} +17.1884i q^{65} +15.4289 q^{67} +(-10.2613 - 5.12497i) q^{68} +(-4.44595 + 2.74911i) q^{70} +4.44544 q^{71} -6.97349 q^{73} +(3.91571 - 2.42124i) q^{74} +(-2.92411 + 5.85469i) q^{76} +2.05843 q^{77} -11.6750i q^{79} +(-8.88139 - 11.8200i) q^{80} +(10.4977 - 6.49116i) q^{82} +12.8349i q^{83} +21.1977i q^{85} +(1.91088 + 3.09035i) q^{86} +(0.526709 + 5.79825i) q^{88} +2.35419i q^{89} +4.65027 q^{91} +(-3.97744 + 7.96369i) q^{92} +(1.51020 + 2.44234i) q^{94} +12.0946 q^{95} +4.02539 q^{97} +(0.743762 + 1.20284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.743762	−	1.20284i	−0.525919	−	0.850534i
$2$	−0.743762	−	1.20284i	−0.525919	−	0.850534i
$3$		0			0
$3$		0			0
$4$	−0.893635	+	1.78925i	−0.446818	+	0.894625i
$5$	3.69622			1.65300			0.826499	−	0.562938i	$-0.190329\pi$
$5$	3.69622			1.65300			0.826499	+	0.562938i	$0.190329\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.81683	−	0.255879i	0.995899	−	0.0904669i
$9$		0			0
$10$	−2.74911	−	4.44595i	−0.869344	−	1.40593i
$11$			2.05843i			0.620640i	0.950632	+	0.310320i	$0.100436\pi$
$11$			2.05843i			0.620640i	−0.950632	+	0.310320i	$0.899564\pi$
$12$		0			0
$13$			4.65027i			1.28975i	0.764287	+	0.644876i	$0.223091\pi$
$13$			4.65027i			1.28975i	−0.764287	+	0.644876i	$0.776909\pi$
$14$	−1.20284	+	0.743762i	−0.321472	+	0.198779i
$15$		0			0
$16$	−2.40283	−	3.19787i	−0.600708	−	0.799468i
$17$			5.73497i			1.39094i	0.718557	+	0.695468i	$0.244803\pi$
$17$			5.73497i			1.39094i	−0.718557	+	0.695468i	$0.755197\pi$
$18$		0			0
$19$	3.27215			0.750682			0.375341	−	0.926887i	$-0.377526\pi$
$19$	3.27215			0.750682			0.375341	+	0.926887i	$0.377526\pi$
$20$	−3.30307	+	6.61346i	−0.738589	+	1.47881i
$21$		0			0
$22$	2.47596	−	1.53098i	0.527876	−	0.326407i
$23$	4.45085			0.928067			0.464033	−	0.885818i	$-0.346402\pi$
$23$	4.45085			0.928067			0.464033	+	0.885818i	$0.346402\pi$
$24$		0			0
$25$	8.66201			1.73240
$26$	5.59351	−	3.45869i	1.09698	−	0.678306i
$27$		0			0
$28$	1.78925	+	0.893635i	0.338136	+	0.168881i
$29$	−10.2594			−1.90512			−0.952561	−	0.304346i	$-0.901562\pi$
$29$	−10.2594			−1.90512			−0.952561	+	0.304346i	$0.901562\pi$
$30$		0			0
$31$		−	1.26066i		−	0.226422i	−0.993571	−	0.113211i	$-0.963886\pi$
$31$		−	1.26066i		−	0.226422i	0.993571	−	0.113211i	$-0.0361136\pi$
$32$	−2.05939	+	5.26867i	−0.364051	+	0.931379i
$33$		0			0
$34$	6.89824	−	4.26546i	1.18304	−	0.731520i
$35$		−	3.69622i		−	0.624775i
$36$		0			0
$37$			3.25539i			0.535183i	0.963532	+	0.267592i	$0.0862278\pi$
$37$			3.25539i			0.535183i	−0.963532	+	0.267592i	$0.913772\pi$
$38$	−2.43370	−	3.93586i	−0.394798	−	0.638481i
$39$		0			0
$40$	10.4116	−	0.945784i	1.64622	−	0.149542i
$41$			8.72747i			1.36300i	0.731817	+	0.681501i	$0.238673\pi$
$41$			8.72747i			1.36300i	−0.731817	+	0.681501i	$0.761327\pi$
$42$		0			0
$43$	−2.56921			−0.391801			−0.195901	−	0.980624i	$-0.562763\pi$
$43$	−2.56921			−0.391801			−0.195901	+	0.980624i	$0.562763\pi$
$44$	−3.68305	−	1.83949i	−0.555240	−	0.277313i
$45$		0			0
$46$	−3.31038	−	5.35365i	−0.488088	−	0.789353i
$47$	−2.03048			−0.296176			−0.148088	−	0.988974i	$-0.547312\pi$
$47$	−2.03048			−0.296176			−0.148088	+	0.988974i	$0.547312\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−6.44248	−	10.4190i	−0.911104	−	1.47347i
$51$		0			0
$52$	−8.32049	−	4.15564i	−1.15384	−	0.576284i
$53$	−10.0794			−1.38451			−0.692253	−	0.721655i	$-0.743382\pi$
$53$	−10.0794			−1.38451			−0.692253	+	0.721655i	$0.743382\pi$
$54$		0			0
$55$			7.60840i			1.02592i
$56$	−0.255879	−	2.81683i	−0.0341933	−	0.376415i
$57$		0			0
$58$	7.63056	+	12.3404i	1.00194	+	1.62037i
$59$		−	0.851213i		−	0.110818i	−0.998464	−	0.0554092i	$-0.982354\pi$
$59$		−	0.851213i		−	0.110818i	0.998464	−	0.0554092i	$-0.0176463\pi$
$60$		0			0
$61$		−	2.31448i		−	0.296339i	−0.988962	−	0.148170i	$-0.952662\pi$
$61$		−	2.31448i		−	0.296339i	0.988962	−	0.148170i	$-0.0473382\pi$
$62$	−1.51637	+	0.937634i	−0.192580	+	0.119080i
$63$		0			0
$64$	7.86905	−	1.44153i	0.983631	−	0.180192i
$65$			17.1884i			2.13196i
$66$		0			0
$67$	15.4289			1.88494			0.942468	−	0.334296i	$-0.108499\pi$
$67$	15.4289			1.88494			0.942468	+	0.334296i	$0.108499\pi$
$68$	−10.2613	−	5.12497i	−1.24437	−	0.621494i
$69$		0			0
$70$	−4.44595	+	2.74911i	−0.531392	+	0.328581i
$71$	4.44544			0.527576			0.263788	−	0.964581i	$-0.415028\pi$
$71$	4.44544			0.527576			0.263788	+	0.964581i	$0.415028\pi$
$72$		0			0
$73$	−6.97349			−0.816186			−0.408093	−	0.912940i	$-0.633806\pi$
$73$	−6.97349			−0.816186			−0.408093	+	0.912940i	$0.633806\pi$
$74$	3.91571	−	2.42124i	0.455192	−	0.281463i
$75$		0			0
$76$	−2.92411	+	5.85469i	−0.335418	+	0.671579i
$77$	2.05843			0.234580
$78$		0			0
$79$		−	11.6750i		−	1.31354i	−0.754092	−	0.656769i	$-0.771923\pi$
$79$		−	11.6750i		−	1.31354i	0.754092	−	0.656769i	$-0.228077\pi$
$80$	−8.88139	−	11.8200i	−0.992969	−	1.32152i
$81$		0			0
$82$	10.4977	−	6.49116i	1.15928	−	0.716829i
$83$			12.8349i			1.40882i	0.709796	+	0.704408i	$0.248787\pi$
$83$			12.8349i			1.40882i	−0.709796	+	0.704408i	$0.751213\pi$
$84$		0			0
$85$			21.1977i			2.29921i
$86$	1.91088	+	3.09035i	0.206056	+	0.333241i
$87$		0			0
$88$	0.526709	+	5.79825i	0.0561474	+	0.618095i
$89$			2.35419i			0.249544i	0.992185	+	0.124772i	$0.0398200\pi$
$89$			2.35419i			0.249544i	−0.992185	+	0.124772i	$0.960180\pi$
$90$		0			0
$91$	4.65027			0.487480
$92$	−3.97744	+	7.96369i	−0.414677	+	0.830272i
$93$		0			0
$94$	1.51020	+	2.44234i	0.155765	+	0.251908i
$95$	12.0946			1.24088
$96$		0			0
$97$	4.02539			0.408717			0.204358	−	0.978896i	$-0.434489\pi$
$97$	4.02539			0.408717			0.204358	+	0.978896i	$0.434489\pi$
$98$	0.743762	+	1.20284i	0.0751313	+	0.121505i
$99$		0			0
$100$	−7.74068	+	15.4985i	−0.774068	+	1.54985i
$101$	14.2008			1.41303			0.706517	−	0.707696i	$-0.250265\pi$
$101$	14.2008			1.41303			0.706517	+	0.707696i	$0.250265\pi$
$102$		0			0
$103$		−	5.30631i		−	0.522846i	−0.965224	−	0.261423i	$-0.915808\pi$
$103$		−	5.30631i		−	0.522846i	0.965224	−	0.261423i	$-0.0841918\pi$
$104$	1.18991	+	13.0990i	0.116680	+	1.28446i
$105$		0			0
$106$	7.49664	+	12.1238i	0.728138	+	1.17757i
$107$		−	13.3669i		−	1.29223i	−0.763240	−	0.646115i	$-0.776392\pi$
$107$		−	13.3669i		−	1.29223i	0.763240	−	0.646115i	$-0.223608\pi$
$108$		0			0
$109$		−	5.91832i		−	0.566872i	−0.958991	−	0.283436i	$-0.908526\pi$
$109$		−	5.91832i		−	0.566872i	0.958991	−	0.283436i	$-0.0914743\pi$
$110$	9.15167	−	5.65884i	0.872577	−	0.539549i
$111$		0			0
$112$	−3.19787	+	2.40283i	−0.302171	+	0.227046i
$113$		−	18.5535i		−	1.74537i	−0.488287	−	0.872683i	$-0.662378\pi$
$113$		−	18.5535i		−	1.74537i	0.488287	−	0.872683i	$-0.337622\pi$
$114$		0			0
$115$	16.4513			1.53409
$116$	9.16816	−	18.3566i	0.851242	−	1.70437i
$117$		0			0
$118$	−1.02387	+	0.633100i	−0.0942549	+	0.0582816i
$119$	5.73497			0.525724
$120$		0			0
$121$	6.76287			0.614806
$122$	−2.78395	+	1.72143i	−0.252047	+	0.155851i
$123$		0			0
$124$	2.25564	+	1.12657i	0.202563	+	0.101169i
$125$	13.5356			1.21066
$126$		0			0
$127$		−	9.76963i		−	0.866915i	−0.901174	−	0.433457i	$-0.857293\pi$
$127$		−	9.76963i		−	0.866915i	0.901174	−	0.433457i	$-0.142707\pi$
$128$	−7.58664	−	8.39303i	−0.670570	−	0.741846i
$129$		0			0
$130$	20.6748	−	12.7841i	1.81330	−	1.12124i
$131$			15.5661i			1.36002i	0.733204	+	0.680009i	$0.238024\pi$
$131$			15.5661i			1.36002i	−0.733204	+	0.680009i	$0.761976\pi$
$132$		0			0
$133$		−	3.27215i		−	0.283731i
$134$	−11.4754	−	18.5584i	−0.991324	−	1.60320i
$135$		0			0
$136$	1.46746	+	16.1544i	0.125834	+	1.38523i
$137$			8.54964i			0.730445i	0.930920	+	0.365223i	$0.119007\pi$
$137$			8.54964i			0.730445i	−0.930920	+	0.365223i	$0.880993\pi$
$138$		0			0
$139$	−15.4607			−1.31136			−0.655679	−	0.755040i	$-0.727617\pi$
$139$	−15.4607			−1.31136			−0.655679	+	0.755040i	$0.727617\pi$
$140$	6.61346	+	3.30307i	0.558939	+	0.279160i
$141$		0			0
$142$	−3.30635	−	5.34714i	−0.277463	−	0.448722i
$143$	−9.57225			−0.800472
$144$		0			0
$145$	−37.9210			−3.14916
$146$	5.18662	+	8.38798i	0.429248	+	0.694194i
$147$		0			0
$148$	−5.82471	−	2.90913i	−0.478788	−	0.239129i
$149$	8.91181			0.730084			0.365042	−	0.930991i	$-0.381055\pi$
$149$	8.91181			0.730084			0.365042	+	0.930991i	$0.381055\pi$
$150$		0			0
$151$		−	14.8040i		−	1.20473i	−0.798219	−	0.602367i	$-0.794224\pi$
$151$		−	14.8040i		−	1.20473i	0.798219	−	0.602367i	$-0.205776\pi$
$152$	9.21708	−	0.837274i	0.747604	−	0.0679119i
$153$		0			0
$154$	−1.53098	−	2.47596i	−0.123370	−	0.199518i
$155$		−	4.65968i		−	0.374275i
$156$		0			0
$157$		−	14.3716i		−	1.14698i	−0.819214	−	0.573488i	$-0.805590\pi$
$157$		−	14.3716i		−	1.14698i	0.819214	−	0.573488i	$-0.194410\pi$
$158$	−14.0431	+	8.68341i	−1.11721	+	0.690815i
$159$		0			0
$160$	−7.61194	+	19.4742i	−0.601776	+	1.53957i
$161$		−	4.45085i		−	0.350776i
$162$		0			0
$163$	21.7846			1.70630			0.853149	−	0.521667i	$-0.174690\pi$
$163$	21.7846			1.70630			0.853149	+	0.521667i	$0.174690\pi$
$164$	−15.6156	−	7.79918i	−1.21938	−	0.609013i
$165$		0			0
$166$	15.4383	−	9.54613i	1.19825	−	0.740923i
$167$	13.4031			1.03717			0.518583	−	0.855027i	$-0.326460\pi$
$167$	13.4031			1.03717			0.518583	+	0.855027i	$0.326460\pi$
$168$		0			0
$169$	−8.62498			−0.663460
$170$	25.4974	−	15.7661i	1.95556	−	1.20920i
$171$		0			0
$172$	2.29594	−	4.59697i	0.175064	−	0.350515i
$173$	13.3221			1.01286			0.506429	−	0.862282i	$-0.330965\pi$
$173$	13.3221			1.01286			0.506429	+	0.862282i	$0.330965\pi$
$174$		0			0
$175$		−	8.66201i		−	0.654787i
$176$	6.58260	−	4.94606i	0.496182	−	0.372823i
$177$		0			0
$178$	2.83171	−	1.75096i	0.212246	−	0.131240i
$179$			12.6787i			0.947648i	0.880619	+	0.473824i	$0.157127\pi$
$179$			12.6787i			0.947648i	−0.880619	+	0.473824i	$0.842873\pi$
$180$		0			0
$181$		−	11.1255i		−	0.826951i	−0.910515	−	0.413476i	$-0.864315\pi$
$181$		−	11.1255i		−	0.826951i	0.910515	−	0.413476i	$-0.135685\pi$
$182$	−3.45869	−	5.59351i	−0.256375	−	0.414619i
$183$		0			0
$184$	12.5373	−	1.13888i	0.924261	−	0.0839593i
$185$			12.0326i			0.884657i
$186$		0			0
$187$	−11.8050			−0.863270
$188$	1.81451	−	3.63304i	0.132337	−	0.264967i
$189$		0			0
$190$	−8.99548	−	14.5478i	−0.652601	−	1.05541i
$191$	−7.76387			−0.561774			−0.280887	−	0.959741i	$-0.590629\pi$
$191$	−7.76387			−0.561774			−0.280887	+	0.959741i	$0.590629\pi$
$192$		0			0
$193$	9.09582			0.654731			0.327366	−	0.944898i	$-0.393839\pi$
$193$	9.09582			0.654731			0.327366	+	0.944898i	$0.393839\pi$
$194$	−2.99393	−	4.84189i	−0.214952	−	0.347628i
$195$		0			0
$196$	0.893635	−	1.78925i	0.0638311	−	0.127804i
$197$	10.3722			0.738988			0.369494	−	0.929233i	$-0.379531\pi$
$197$	10.3722			0.738988			0.369494	+	0.929233i	$0.379531\pi$
$198$		0			0
$199$		−	9.92379i		−	0.703479i	−0.936098	−	0.351739i	$-0.885590\pi$
$199$		−	9.92379i		−	0.703479i	0.936098	−	0.351739i	$-0.114410\pi$
$200$	24.3994	−	2.21643i	1.72530	−	0.156725i
$201$		0			0
$202$	−10.5620	−	17.0813i	−0.743142	−	1.20183i
$203$			10.2594i			0.720069i
$204$		0			0
$205$			32.2586i			2.25304i
$206$	−6.38263	+	3.94663i	−0.444699	+	0.274975i
$207$		0			0
$208$	14.8710	−	11.1738i	1.03112	−	0.774764i
$209$			6.73549i			0.465903i
$210$		0			0
$211$	−10.9624			−0.754680			−0.377340	−	0.926075i	$-0.623161\pi$
$211$	−10.9624			−0.754680			−0.377340	+	0.926075i	$0.623161\pi$
$212$	9.00726	−	18.0345i	0.618621	−	1.23861i
$213$		0			0
$214$	−16.0783	+	9.94183i	−1.09909	+	0.679609i
$215$	−9.49637			−0.647647
$216$		0			0
$217$	−1.26066			−0.0855794
$218$	−7.11877	+	4.40182i	−0.482144	+	0.298129i
$219$		0			0
$220$	−13.6133	−	6.79914i	−0.917811	−	0.458398i
$221$	−26.6692			−1.79396
$222$		0			0
$223$		−	1.18980i		−	0.0796749i	−0.999206	−	0.0398375i	$-0.987316\pi$
$223$		−	1.18980i		−	0.0796749i	0.999206	−	0.0398375i	$-0.0126840\pi$
$224$	5.26867	+	2.05939i	0.352028	+	0.137599i
$225$		0			0
$226$	−22.3168	+	13.7994i	−1.48449	+	0.917922i
$227$		−	9.62724i		−	0.638983i	−0.947589	−	0.319491i	$-0.896488\pi$
$227$		−	9.62724i		−	0.638983i	0.947589	−	0.319491i	$-0.103512\pi$
$228$		0			0
$229$			21.5143i			1.42170i	0.703343	+	0.710851i	$0.251690\pi$
$229$			21.5143i			1.42170i	−0.703343	+	0.710851i	$0.748310\pi$
$230$	−12.2359	−	19.7882i	−0.806809	−	1.30480i
$231$		0			0
$232$	−28.8990	+	2.62517i	−1.89731	+	0.172351i
$233$		−	6.82082i		−	0.446847i	−0.974722	−	0.223423i	$-0.928277\pi$
$233$		−	6.82082i		−	0.446847i	0.974722	−	0.223423i	$-0.0717232\pi$
$234$		0			0
$235$	−7.50510			−0.489579
$236$	1.52303	+	0.760674i	0.0991410	+	0.0495156i
$237$		0			0
$238$	−4.26546	−	6.89824i	−0.276489	−	0.447147i
$239$	6.24506			0.403959			0.201980	−	0.979390i	$-0.435263\pi$
$239$	6.24506			0.403959			0.201980	+	0.979390i	$0.435263\pi$
$240$		0			0
$241$	25.5573			1.64629			0.823145	−	0.567831i	$-0.192217\pi$
$241$	25.5573			1.64629			0.823145	+	0.567831i	$0.192217\pi$
$242$	−5.02997	−	8.13463i	−0.323338	−	0.522914i
$243$		0			0
$244$	4.14119	+	2.06831i	0.265113	+	0.132410i
$245$	−3.69622			−0.236143
$246$		0			0
$247$			15.2164i			0.968194i
$248$	−0.322577	−	3.55107i	−0.0204837	−	0.225493i
$249$		0			0
$250$	−10.0673	−	16.2811i	−0.636710	−	1.02971i
$251$			0.373698i			0.0235876i	0.999930	+	0.0117938i	$0.00375417\pi$
$251$			0.373698i			0.0235876i	−0.999930	+	0.0117938i	$0.996246\pi$
$252$		0			0
$253$			9.16177i			0.575995i
$254$	−11.7513	+	7.26629i	−0.737341	+	0.455927i
$255$		0			0
$256$	−4.45280	+	15.3679i	−0.278300	+	0.960494i
$257$		−	11.0514i		−	0.689369i	−0.938719	−	0.344684i	$-0.887986\pi$
$257$		−	11.0514i		−	0.689369i	0.938719	−	0.344684i	$-0.112014\pi$
$258$		0			0
$259$	3.25539			0.202280
$260$	−30.7543	−	15.3602i	−1.90730	−	0.952596i
$261$		0			0
$262$	18.7235	−	11.5775i	1.15674	−	0.715260i
$263$	−27.6685			−1.70612			−0.853058	−	0.521817i	$-0.825255\pi$
$263$	−27.6685			−1.70612			−0.853058	+	0.521817i	$0.825255\pi$
$264$		0			0
$265$	−37.2555			−2.28859
$266$	−3.93586	+	2.43370i	−0.241323	+	0.149220i
$267$		0			0
$268$	−13.7878	+	27.6061i	−0.842223	+	1.68631i
$269$	29.3247			1.78796			0.893981	−	0.448105i	$-0.147901\pi$
$269$	29.3247			1.78796			0.893981	+	0.448105i	$0.147901\pi$
$270$		0			0
$271$		−	5.13414i		−	0.311877i	−0.987767	−	0.155938i	$-0.950160\pi$
$271$		−	5.13414i		−	0.311877i	0.987767	−	0.155938i	$-0.0498401\pi$
$272$	18.3397	−	13.7802i	1.11201	−	0.835546i
$273$		0			0
$274$	10.2838	−	6.35890i	0.621269	−	0.384155i
$275$			17.8301i			1.07520i
$276$		0			0
$277$		−	5.93089i		−	0.356353i	−0.983999	−	0.178176i	$-0.942980\pi$
$277$		−	5.93089i		−	0.356353i	0.983999	−	0.178176i	$-0.0570197\pi$
$278$	11.4991	+	18.5967i	0.689668	+	1.11535i
$279$		0			0
$280$	−0.945784	−	10.4116i	−0.0565214	−	0.622213i
$281$		−	10.7827i		−	0.643242i	−0.946868	−	0.321621i	$-0.895772\pi$
$281$		−	10.7827i		−	0.643242i	0.946868	−	0.321621i	$-0.104228\pi$
$282$		0			0
$283$	−18.1556			−1.07924			−0.539619	−	0.841910i	$-0.681432\pi$
$283$	−18.1556			−1.07924			−0.539619	+	0.841910i	$0.681432\pi$
$284$	−3.97260	+	7.95400i	−0.235730	+	0.471983i
$285$		0			0
$286$	7.11948	+	11.5139i	0.420984	+	0.680829i
$287$	8.72747			0.515166
$288$		0			0
$289$	−15.8899			−0.934701
$290$	28.2042	+	45.6127i	1.65621	+	2.67847i
$291$		0			0
$292$	6.23176	−	12.4773i	0.364686	−	0.730180i
$293$	−21.8863			−1.27861			−0.639306	−	0.768953i	$-0.720778\pi$
$293$	−21.8863			−1.27861			−0.639306	+	0.768953i	$0.720778\pi$
$294$		0			0
$295$		−	3.14627i		−	0.183183i
$296$	0.832986	+	9.16988i	0.0484164	+	0.532989i
$297$		0			0
$298$	−6.62827	−	10.7195i	−0.383965	−	0.620961i
$299$			20.6976i			1.19698i
$300$		0			0
$301$			2.56921i			0.148087i
$302$	−17.8068	+	11.0107i	−1.02467	+	0.633593i
$303$		0			0
$304$	−7.86242	−	10.4639i	−0.450941	−	0.600147i
$305$		−	8.55484i		−	0.489848i
$306$		0			0
$307$	16.8301			0.960546			0.480273	−	0.877119i	$-0.340538\pi$
$307$	16.8301			0.960546			0.480273	+	0.877119i	$0.340538\pi$
$308$	−1.83949	+	3.68305i	−0.104814	+	0.209861i
$309$		0			0
$310$	−5.60484	+	3.46570i	−0.318334	+	0.196838i
$311$	−33.1293			−1.87859			−0.939294	−	0.343113i	$-0.888519\pi$
$311$	−33.1293			−1.87859			−0.939294	+	0.343113i	$0.888519\pi$
$312$		0			0
$313$	13.4187			0.758469			0.379235	−	0.925301i	$-0.376187\pi$
$313$	13.4187			0.758469			0.379235	+	0.925301i	$0.376187\pi$
$314$	−17.2867	+	10.6890i	−0.975543	+	0.603217i
$315$		0			0
$316$	20.8895	+	10.4332i	1.17512	+	0.586912i
$317$	0.764835			0.0429574			0.0214787	−	0.999769i	$-0.493163\pi$
$317$	0.764835			0.0429574			0.0214787	+	0.999769i	$0.493163\pi$
$318$		0			0
$319$		−	21.1183i		−	1.18240i
$320$	29.0857	−	5.32822i	1.62594	−	0.297857i
$321$		0			0
$322$	−5.35365	+	3.31038i	−0.298347	+	0.184480i
$323$			18.7657i			1.04415i
$324$		0			0
$325$			40.2807i			2.23437i
$326$	−16.2025	−	26.2033i	−0.897375	−	1.45127i
$327$		0			0
$328$	2.23318	+	24.5838i	0.123307	+	1.35741i
$329$			2.03048i			0.111944i
$330$		0			0
$331$	29.7299			1.63410			0.817051	−	0.576566i	$-0.195608\pi$
$331$	29.7299			1.63410			0.817051	+	0.576566i	$0.195608\pi$
$332$	−22.9649	−	11.4697i	−1.26036	−	0.629484i
$333$		0			0
$334$	−9.96875	−	16.1218i	−0.545466	−	0.882145i
$335$	57.0284			3.11580
$336$		0			0
$337$	−19.0487			−1.03765			−0.518824	−	0.854881i	$-0.673630\pi$
$337$	−19.0487			−1.03765			−0.518824	+	0.854881i	$0.673630\pi$
$338$	6.41494	+	10.3745i	0.348927	+	0.564296i
$339$		0			0
$340$	−37.9280	−	18.9430i	−2.05693	−	1.02733i
$341$	2.59499			0.140526
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−7.23704	+	0.657408i	−0.390195	+	0.0354451i
$345$		0			0
$346$	−9.90844	−	16.0243i	−0.532681	−	0.861470i
$347$			30.0749i			1.61451i	0.590205	+	0.807253i	$0.299047\pi$
$347$			30.0749i			1.61451i	−0.590205	+	0.807253i	$0.700953\pi$
$348$		0			0
$349$			28.7995i			1.54160i	0.637078	+	0.770800i	$0.280143\pi$
$349$			28.7995i			1.54160i	−0.637078	+	0.770800i	$0.719857\pi$
$350$	−10.4190	+	6.44248i	−0.556919	+	0.344365i
$351$		0			0
$352$	−10.8452	−	4.23910i	−0.578051	−	0.225945i
$353$		−	26.2377i		−	1.39649i	−0.715857	−	0.698247i	$-0.753964\pi$
$353$		−	26.2377i		−	1.39649i	0.715857	−	0.698247i	$-0.246036\pi$
$354$		0			0
$355$	16.4313			0.872083
$356$	−4.21224	−	2.10379i	−0.223248	−	0.111501i
$357$		0			0
$358$	15.2504	−	9.42992i	0.806008	−	0.498387i
$359$	−18.4178			−0.972053			−0.486027	−	0.873944i	$-0.661554\pi$
$359$	−18.4178			−0.972053			−0.486027	+	0.873944i	$0.661554\pi$
$360$		0			0
$361$	−8.29305			−0.436476
$362$	−13.3822	+	8.27472i	−0.703351	+	0.434910i
$363$		0			0
$364$	−4.15564	+	8.32049i	−0.217815	+	0.436112i
$365$	−25.7755			−1.34915
$366$		0			0
$367$		−	37.2862i		−	1.94632i	−0.230127	−	0.973161i	$-0.573914\pi$
$367$		−	37.2862i		−	1.94632i	0.230127	−	0.973161i	$-0.426086\pi$
$368$	−10.6946	−	14.2333i	−0.557497	−	0.741960i
$369$		0			0
$370$	14.4733	−	8.94942i	0.752431	−	0.465258i
$371$			10.0794i			0.523294i
$372$		0			0
$373$		−	4.59095i		−	0.237711i	−0.992912	−	0.118855i	$-0.962078\pi$
$373$		−	4.59095i		−	0.237711i	0.992912	−	0.118855i	$-0.0379224\pi$
$374$	8.78014	+	14.1995i	0.454010	+	0.734241i
$375$		0			0
$376$	−5.71952	+	0.519557i	−0.294962	+	0.0267941i
$377$		−	47.7090i		−	2.45714i
$378$		0			0
$379$	−21.0149			−1.07947			−0.539733	−	0.841836i	$-0.681475\pi$
$379$	−21.0149			−1.07947			−0.539733	+	0.841836i	$0.681475\pi$
$380$	−10.8081	+	21.6402i	−0.554445	+	1.11012i
$381$		0			0
$382$	5.77447	+	9.33867i	0.295448	+	0.477808i
$383$	9.09047			0.464501			0.232251	−	0.972656i	$-0.425391\pi$
$383$	9.09047			0.464501			0.232251	+	0.972656i	$0.425391\pi$
$384$		0			0
$385$	7.60840			0.387760
$386$	−6.76513	−	10.9408i	−0.344336	−	0.556871i
$387$		0			0
$388$	−3.59723	+	7.20243i	−0.182622	+	0.365648i
$389$	−2.06330			−0.104614			−0.0523068	−	0.998631i	$-0.516657\pi$
$389$	−2.06330			−0.104614			−0.0523068	+	0.998631i	$0.516657\pi$
$390$		0			0
$391$			25.5255i			1.29088i
$392$	−2.81683	+	0.255879i	−0.142271	+	0.0129238i
$393$		0			0
$394$	−7.71445	−	12.4761i	−0.388648	−	0.628535i
$395$		−	43.1533i		−	2.17128i
$396$		0			0
$397$			0.0369436i			0.00185415i	1.00000		0.000927073i	$0.000295096\pi$
$397$			0.0369436i			0.00185415i	−1.00000		0.000927073i	$0.999705\pi$
$398$	−11.9367	+	7.38094i	−0.598333	+	0.369973i
$399$		0			0
$400$	−20.8134	−	27.7000i	−1.04067	−	1.38500i
$401$			18.6814i			0.932906i	0.884546	+	0.466453i	$0.154468\pi$
$401$			18.6814i			0.932906i	−0.884546	+	0.466453i	$0.845532\pi$
$402$		0			0
$403$	5.86242			0.292028
$404$	−12.6904	+	25.4088i	−0.631369	+	1.26414i
$405$		0			0
$406$	12.3404	−	7.63056i	0.612443	−	0.378698i
$407$	−6.70100			−0.332156
$408$		0			0
$409$	−11.5630			−0.571755			−0.285878	−	0.958266i	$-0.592285\pi$
$409$	−11.5630			−0.571755			−0.285878	+	0.958266i	$0.592285\pi$
$410$	38.8019	−	23.9927i	1.91629	−	1.18492i
$411$		0			0
$412$	9.49432	+	4.74191i	0.467751	+	0.233617i
$413$	−0.851213			−0.0418854
$414$		0			0
$415$			47.4406i			2.32877i
$416$	−24.5007	−	9.57670i	−1.20125	−	0.469536i
$417$		0			0
$418$	8.10170	−	5.00960i	0.396267	−	0.245028i
$419$		−	14.5911i		−	0.712822i	−0.934329	−	0.356411i	$-0.884000\pi$
$419$		−	14.5911i		−	0.712822i	0.934329	−	0.356411i	$-0.116000\pi$
$420$		0			0
$421$			17.6204i			0.858767i	0.903122	+	0.429384i	$0.141269\pi$
$421$			17.6204i			0.858767i	−0.903122	+	0.429384i	$0.858731\pi$
$422$	8.15339	+	13.1859i	0.396901	+	0.641882i
$423$		0			0
$424$	−28.3918	+	2.57909i	−1.37883	+	0.125252i
$425$			49.6764i			2.40966i
$426$		0			0
$427$	−2.31448			−0.112006
$428$	23.9168	+	11.9452i	1.15606	+	0.577392i
$429$		0			0
$430$	7.06304	+	11.4226i	0.340610	+	0.550846i
$431$	−17.6500			−0.850170			−0.425085	−	0.905153i	$-0.639756\pi$
$431$	−17.6500			−0.850170			−0.425085	+	0.905153i	$0.639756\pi$
$432$		0			0
$433$	−6.31965			−0.303703			−0.151852	−	0.988403i	$-0.548524\pi$
$433$	−6.31965			−0.303703			−0.151852	+	0.988403i	$0.548524\pi$
$434$	0.937634	+	1.51637i	0.0450079	+	0.0727882i
$435$		0			0
$436$	10.5893	+	5.28882i	0.507138	+	0.253288i
$437$	14.5638			0.696683
$438$		0			0
$439$		−	10.1993i		−	0.486786i	−0.969928	−	0.243393i	$-0.921739\pi$
$439$		−	10.1993i		−	0.486786i	0.969928	−	0.243393i	$-0.0782605\pi$
$440$	1.94683	+	21.4316i	0.0928115	+	1.02171i
$441$		0			0
$442$	19.8355	+	32.0787i	0.943479	+	1.52583i
$443$		−	9.46579i		−	0.449733i	−0.974390	−	0.224867i	$-0.927805\pi$
$443$		−	9.46579i		−	0.449733i	0.974390	−	0.224867i	$-0.0721947\pi$
$444$		0			0
$445$			8.70161i			0.412496i
$446$	−1.43114	+	0.884929i	−0.0677663	+	0.0419026i
$447$		0			0
$448$	−1.44153	−	7.86905i	−0.0681061	−	0.371778i
$449$			28.1482i			1.32840i	0.747556	+	0.664198i	$0.231227\pi$
$449$			28.1482i			1.32840i	−0.747556	+	0.664198i	$0.768773\pi$
$450$		0			0
$451$	−17.9649			−0.845934
$452$	33.1969	+	16.5801i	1.56145	+	0.779861i
$453$		0			0
$454$	−11.5800	+	7.16038i	−0.543477	+	0.336053i
$455$	17.1884			0.805804
$456$		0			0
$457$	−34.9936			−1.63693			−0.818465	−	0.574556i	$-0.805175\pi$
$457$	−34.9936			−1.63693			−0.818465	+	0.574556i	$0.805175\pi$
$458$	25.8781	−	16.0015i	1.20921	−	0.747701i
$459$		0			0
$460$	−14.7015	+	29.4355i	−0.685460	+	1.37244i
$461$	30.2558			1.40915			0.704577	−	0.709628i	$-0.251137\pi$
$461$	30.2558			1.40915			0.704577	+	0.709628i	$0.251137\pi$
$462$		0			0
$463$		−	2.87077i		−	0.133416i	−0.997773	−	0.0667080i	$-0.978750\pi$
$463$		−	2.87077i		−	0.133416i	0.997773	−	0.0667080i	$-0.0212496\pi$
$464$	24.6516	+	32.8083i	1.14442	+	1.52309i
$465$		0			0
$466$	−8.20433	+	5.07307i	−0.380058	+	0.235005i
$467$		−	36.1957i		−	1.67494i	−0.546484	−	0.837469i	$-0.684034\pi$
$467$		−	36.1957i		−	1.67494i	0.546484	−	0.837469i	$-0.315966\pi$
$468$		0			0
$469$		−	15.4289i		−	0.712439i
$470$	5.58201	+	9.02741i	0.257479	+	0.416403i
$471$		0			0
$472$	−0.217808	−	2.39772i	−0.0100254	−	0.110364i
$473$		−	5.28855i		−	0.243168i
$474$		0			0
$475$	28.3434			1.30048
$476$	−5.12497	+	10.2613i	−0.234903	+	0.470326i
$477$		0			0
$478$	−4.64484	−	7.51179i	−0.212450	−	0.343581i
$479$	−17.1156			−0.782030			−0.391015	−	0.920384i	$-0.627876\pi$
$479$	−17.1156			−0.782030			−0.391015	+	0.920384i	$0.627876\pi$
$480$		0			0
$481$	−15.1384			−0.690253
$482$	−19.0086	−	30.7413i	−0.865816	−	1.40023i
$483$		0			0
$484$	−6.04354	+	12.1005i	−0.274706	+	0.550021i
$485$	14.8787			0.675608
$486$		0			0
$487$		−	26.8336i		−	1.21595i	−0.793957	−	0.607974i	$-0.791982\pi$
$487$		−	26.8336i		−	1.21595i	0.793957	−	0.607974i	$-0.208018\pi$
$488$	−0.592228	−	6.51951i	−0.0268089	−	0.295124i
$489$		0			0
$490$	2.74911	+	4.44595i	0.124192	+	0.200847i
$491$		−	7.17336i		−	0.323729i	−0.986813	−	0.161865i	$-0.948249\pi$
$491$		−	7.17336i		−	0.323729i	0.986813	−	0.161865i	$-0.0517508\pi$
$492$		0			0
$493$		−	58.8374i		−	2.64990i
$494$	18.3028	−	11.3174i	0.823482	−	0.509192i
$495$		0			0
$496$	−4.03144	+	3.02916i	−0.181017	+	0.136013i
$497$		−	4.44544i		−	0.199405i
$498$		0			0
$499$	−36.8731			−1.65067			−0.825334	−	0.564646i	$-0.809013\pi$
$499$	−36.8731			−1.65067			−0.825334	+	0.564646i	$0.809013\pi$
$500$	−12.0959	+	24.2186i	−0.540944	+	1.08309i
$501$		0			0
$502$	0.449498	−	0.277943i	0.0200621	−	0.0124052i
$503$	−17.4855			−0.779642			−0.389821	−	0.920891i	$-0.627463\pi$
$503$	−17.4855			−0.779642			−0.389821	+	0.920891i	$0.627463\pi$
$504$		0			0
$505$	52.4893			2.33574
$506$	11.0201	−	6.81418i	0.489904	−	0.302927i
$507$		0			0
$508$	17.4803	+	8.73049i	0.775564	+	0.387353i
$509$	−38.6034			−1.71106			−0.855532	−	0.517750i	$-0.826770\pi$
$509$	−38.6034			−1.71106			−0.855532	+	0.517750i	$0.826770\pi$
$510$		0			0
$511$			6.97349i			0.308489i
$512$	21.7969	−	6.07408i	0.963297	−	0.268439i
$513$		0			0
$514$	−13.2931	+	8.21963i	−0.586332	+	0.362552i
$515$		−	19.6133i		−	0.864264i
$516$		0			0
$517$		−	4.17960i		−	0.183819i
$518$	−2.42124	−	3.91571i	−0.106383	−	0.172046i
$519$		0			0
$520$	4.39815	+	48.4168i	0.192872	+	2.12322i
$521$			29.3406i			1.28543i	0.766104	+	0.642716i	$0.222193\pi$
$521$			29.3406i			1.28543i	−0.766104	+	0.642716i	$0.777807\pi$
$522$		0			0
$523$	−7.90612			−0.345711			−0.172855	−	0.984947i	$-0.555299\pi$
$523$	−7.90612			−0.345711			−0.172855	+	0.984947i	$0.555299\pi$
$524$	−27.8517	−	13.9104i	−1.21671	−	0.607680i
$525$		0			0
$526$	20.5788	+	33.2808i	0.897279	+	1.45111i
$527$	7.22987			0.314938
$528$		0			0
$529$	−3.18992			−0.138692
$530$	27.7092	+	44.8123i	1.20361	+	1.94652i
$531$		0			0
$532$	5.85469	+	2.92411i	0.253833	+	0.126776i
$533$	−40.5851			−1.75793
$534$		0			0
$535$		−	49.4071i		−	2.13606i
$536$	43.4605	−	3.94792i	1.87721	−	0.170524i
$537$		0			0
$538$	−21.8106	−	35.2729i	−0.940324	−	1.52072i
$539$		−	2.05843i		−	0.0886629i
$540$		0			0
$541$			6.25573i			0.268955i	0.990917	+	0.134477i	$0.0429356\pi$
$541$			6.25573i			0.268955i	−0.990917	+	0.134477i	$0.957064\pi$
$542$	−6.17554	+	3.81858i	−0.265262	+	0.164022i
$543$		0			0
$544$	−30.2157	−	11.8105i	−1.29549	−	0.506372i
$545$		−	21.8754i		−	0.937038i
$546$		0			0
$547$	18.4597			0.789279			0.394640	−	0.918836i	$-0.370869\pi$
$547$	18.4597			0.789279			0.394640	+	0.918836i	$0.370869\pi$
$548$	−15.2974	−	7.64026i	−0.653474	−	0.326376i
$549$		0			0
$550$	21.4468	−	13.2614i	0.914493	−	0.565468i
$551$	−33.5703			−1.43014
$552$		0			0
$553$	−11.6750			−0.496471
$554$	−7.13389	+	4.41117i	−0.303090	+	0.187413i
$555$		0			0
$556$	13.8162	−	27.6630i	0.585938	−	1.17317i
$557$	−10.6497			−0.451243			−0.225622	−	0.974215i	$-0.572441\pi$
$557$	−10.6497			−0.451243			−0.225622	+	0.974215i	$0.572441\pi$
$558$		0			0
$559$		−	11.9475i		−	0.505327i
$560$	−11.8200	+	8.88139i	−0.499488	+	0.375307i
$561$		0			0
$562$	−12.9698	+	8.01977i	−0.547100	+	0.338294i
$563$		−	10.9117i		−	0.459874i	−0.973206	−	0.229937i	$-0.926148\pi$
$563$		−	10.9117i		−	0.459874i	0.973206	−	0.229937i	$-0.0738520\pi$
$564$		0			0
$565$		−	68.5778i		−	2.88509i
$566$	13.5034	+	21.8382i	0.567592	+	0.917929i
$567$		0			0
$568$	12.5220	−	1.13749i	0.525413	−	0.0477282i
$569$		−	10.7145i		−	0.449175i	−0.974454	−	0.224588i	$-0.927896\pi$
$569$		−	10.7145i		−	0.449175i	0.974454	−	0.224588i	$-0.0721035\pi$
$570$		0			0
$571$	−21.6134			−0.904493			−0.452247	−	0.891893i	$-0.649377\pi$
$571$	−21.6134			−0.904493			−0.452247	+	0.891893i	$0.649377\pi$
$572$	8.55410	−	17.1271i	0.357665	−	0.716122i
$573$		0			0
$574$	−6.49116	−	10.4977i	−0.270936	−	0.438167i
$575$	38.5533			1.60779
$576$		0			0
$577$	17.2449			0.717914			0.358957	−	0.933354i	$-0.383133\pi$
$577$	17.2449			0.717914			0.358957	+	0.933354i	$0.383133\pi$
$578$	11.8183	+	19.1130i	0.491578	+	0.794996i
$579$		0			0
$580$	33.8875	−	67.8501i	1.40710	−	2.81732i
$581$	12.8349			0.532482
$582$		0			0
$583$		−	20.7476i		−	0.859279i
$584$	−19.6431	+	1.78437i	−0.812839	+	0.0738378i
$585$		0			0
$586$	16.2782	+	26.3257i	0.672446	+	1.08750i
$587$		−	6.83868i		−	0.282263i	−0.989991	−	0.141131i	$-0.954926\pi$
$587$		−	6.83868i		−	0.282263i	0.989991	−	0.141131i	$-0.0450740\pi$
$588$		0			0
$589$		−	4.12508i		−	0.169971i
$590$	−3.78445	+	2.34007i	−0.155803	+	0.0963393i
$591$		0			0
$592$	10.4103	−	7.82216i	0.427862	−	0.321489i
$593$			23.2262i			0.953787i	0.878961	+	0.476893i	$0.158237\pi$
$593$			23.2262i			0.953787i	−0.878961	+	0.476893i	$0.841763\pi$
$594$		0			0
$595$	21.1977			0.869021
$596$	−7.96390	+	15.9455i	−0.326214	+	0.653151i
$597$		0			0
$598$	24.8959	−	15.3941i	1.01807	−	0.629513i
$599$	4.71919			0.192821			0.0964105	−	0.995342i	$-0.469264\pi$
$599$	4.71919			0.192821			0.0964105	+	0.995342i	$0.469264\pi$
$600$		0			0
$601$	−0.230392			−0.00939787			−0.00469893	−	0.999989i	$-0.501496\pi$
$601$	−0.230392			−0.00939787			−0.00469893	+	0.999989i	$0.501496\pi$
$602$	3.09035	−	1.91088i	0.125953	−	0.0778818i
$603$		0			0
$604$	26.4881	+	13.2294i	1.07779	+	0.538296i
$605$	24.9970			1.01627
$606$		0			0
$607$			5.43638i			0.220656i	0.993895	+	0.110328i	$0.0351901\pi$
$607$			5.43638i			0.220656i	−0.993895	+	0.110328i	$0.964810\pi$
$608$	−6.73862	+	17.2399i	−0.273287	+	0.699170i
$609$		0			0
$610$	−10.2901	+	6.36276i	−0.416633	+	0.257621i
$611$		−	9.44228i		−	0.381994i
$612$		0			0
$613$			24.7976i			1.00156i	0.865573	+	0.500782i	$0.166954\pi$
$613$			24.7976i			1.00156i	−0.865573	+	0.500782i	$0.833046\pi$
$614$	−12.5176	−	20.2439i	−0.505170	−	0.816978i
$615$		0			0
$616$	5.79825	−	0.526709i	0.233618	−	0.0212217i
$617$		−	13.4024i		−	0.539561i	−0.962922	−	0.269781i	$-0.913049\pi$
$617$		−	13.4024i		−	0.539561i	0.962922	−	0.269781i	$-0.0869512\pi$
$618$		0			0
$619$	−12.8992			−0.518465			−0.259232	−	0.965815i	$-0.583470\pi$
$619$	−12.8992			−0.518465			−0.259232	+	0.965815i	$0.583470\pi$
$620$	8.33734	+	4.16406i	0.334836	+	0.167233i
$621$		0			0
$622$	24.6403	+	39.8491i	0.987986	+	1.59780i
$623$	2.35419			0.0943188
$624$		0			0
$625$	6.72041			0.268817
$626$	−9.98032	−	16.1405i	−0.398894	−	0.645104i
$627$		0			0
$628$	25.7143	+	12.8429i	1.02611	+	0.512489i
$629$	−18.6696			−0.744405
$630$		0			0
$631$		−	24.0217i		−	0.956288i	−0.878281	−	0.478144i	$-0.841310\pi$
$631$		−	24.0217i		−	0.956288i	0.878281	−	0.478144i	$-0.158690\pi$
$632$	−2.98738	−	32.8864i	−0.118832	−	1.30815i
$633$		0			0
$634$	−0.568856	−	0.919972i	−0.0225921	−	0.0365368i
$635$		−	36.1107i		−	1.43301i
$636$		0			0
$637$		−	4.65027i		−	0.184250i
$638$	−25.4018	+	15.7070i	−1.00567	+	0.621845i
$639$		0			0
$640$	−28.0418	−	31.0225i	−1.10845	−	1.22627i
$641$		−	10.4176i		−	0.411469i	−0.978608	−	0.205735i	$-0.934042\pi$
$641$		−	10.4176i		−	0.411469i	0.978608	−	0.205735i	$-0.0659583\pi$
$642$		0			0
$643$	42.2723			1.66706			0.833528	−	0.552477i	$-0.186317\pi$
$643$	42.2723			1.66706			0.833528	+	0.552477i	$0.186317\pi$
$644$	7.96369	+	3.97744i	0.313813	+	0.156733i
$645$		0			0
$646$	22.5721	−	13.9572i	0.888086	−	0.549139i
$647$	7.75700			0.304959			0.152480	−	0.988307i	$-0.451274\pi$
$647$	7.75700			0.304959			0.152480	+	0.988307i	$0.451274\pi$
$648$		0			0
$649$	1.75216			0.0687784
$650$	48.4511	−	29.9592i	1.90041	−	1.17510i
$651$		0			0
$652$	−19.4674	+	38.9780i	−0.762404	+	1.52650i
$653$	−19.9159			−0.779370			−0.389685	−	0.920948i	$-0.627416\pi$
$653$	−19.9159			−0.779370			−0.389685	+	0.920948i	$0.627416\pi$
$654$		0			0
$655$			57.5357i			2.24811i
$656$	27.9094	−	20.9707i	1.08968	−	0.818766i
$657$		0			0
$658$	2.44234	−	1.51020i	0.0952123	−	0.0588735i
$659$		−	39.4456i		−	1.53658i	−0.640101	−	0.768291i	$-0.721108\pi$
$659$		−	39.4456i		−	1.53658i	0.640101	−	0.768291i	$-0.278892\pi$
$660$		0			0
$661$			35.8650i			1.39499i	0.716591	+	0.697494i	$0.245702\pi$
$661$			35.8650i			1.39499i	−0.716591	+	0.697494i	$0.754298\pi$
$662$	−22.1120	−	35.7602i	−0.859406	−	1.38986i
$663$		0			0
$664$	3.28419	+	36.1538i	0.127451	+	1.40304i
$665$		−	12.0946i		−	0.469007i
$666$		0			0
$667$	−45.6631			−1.76808
$668$	−11.9775	+	23.9816i	−0.463424	+	0.927875i
$669$		0			0
$670$	−42.4156	−	68.5959i	−1.63866	−	2.65009i
$671$	4.76420			0.183920
$672$		0			0
$673$	30.5668			1.17827			0.589133	−	0.808036i	$-0.299470\pi$
$673$	30.5668			1.17827			0.589133	+	0.808036i	$0.299470\pi$
$674$	14.1677	+	22.9125i	0.545719	+	0.882555i
$675$		0			0
$676$	7.70759	−	15.4323i	0.296446	−	0.593548i
$677$	−7.14804			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$677$	−7.14804			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$678$		0			0
$679$		−	4.02539i		−	0.154480i
$680$	5.42405	+	59.7103i	0.208003	+	2.28979i
$681$		0			0
$682$	−1.93005	−	3.12135i	−0.0739056	−	0.119523i
$683$		−	2.07293i		−	0.0793186i	−0.999213	−	0.0396593i	$-0.987373\pi$
$683$		−	2.07293i		−	0.0793186i	0.999213	−	0.0396593i	$-0.0126273\pi$
$684$		0			0
$685$			31.6013i			1.20742i
$686$	1.20284	−	0.743762i	0.0459245	−	0.0283970i
$687$		0			0
$688$	6.17339	+	8.21602i	0.235358	+	0.313233i
$689$		−	46.8717i		−	1.78567i
$690$		0			0
$691$	34.7325			1.32129			0.660644	−	0.750700i	$-0.270283\pi$
$691$	34.7325			1.32129			0.660644	+	0.750700i	$0.270283\pi$
$692$	−11.9051	+	23.8365i	−0.452562	+	0.906127i
$693$		0			0
$694$	36.1752	−	22.3686i	1.37319	−	0.849100i
$695$	−57.1460			−2.16767
$696$		0			0
$697$	−50.0518			−1.89585
$698$	34.6411	−	21.4199i	1.31118	−	0.810757i
$699$		0			0
$700$	15.4985	+	7.74068i	0.585789	+	0.292570i
$701$	30.1113			1.13729			0.568643	−	0.822584i	$-0.307469\pi$
$701$	30.1113			1.13729			0.568643	+	0.822584i	$0.307469\pi$
$702$		0			0
$703$			10.6521i			0.401752i
$704$	2.96730	+	16.1979i	0.111834	+	0.610481i
$705$		0			0
$706$	−31.5597	+	19.5146i	−1.18777	+	0.734443i
$707$		−	14.2008i		−	0.534077i
$708$		0			0
$709$			30.7194i			1.15369i	0.816853	+	0.576846i	$0.195717\pi$
$709$			30.7194i			1.15369i	−0.816853	+	0.576846i	$0.804283\pi$
$710$	−12.2210	−	19.7642i	−0.458645	−	0.741736i
$711$		0			0
$712$	0.602389	+	6.63136i	0.0225755	+	0.248521i
$713$		−	5.61102i		−	0.210135i
$714$		0			0
$715$	−35.3811			−1.32318
$716$	−22.6853	−	11.3301i	−0.847790	−	0.423426i
$717$		0			0
$718$	13.6985	+	22.1536i	0.511222	+	0.826765i
$719$	−1.93357			−0.0721099			−0.0360549	−	0.999350i	$-0.511479\pi$
$719$	−1.93357			−0.0721099			−0.0360549	+	0.999350i	$0.511479\pi$
$720$		0			0
$721$	−5.30631			−0.197617
$722$	6.16805	+	9.97518i	0.229551	+	0.371238i
$723$		0			0
$724$	19.9063	+	9.94213i	0.739811	+	0.369496i
$725$	−88.8671			−3.30044
$726$		0			0
$727$		−	21.4593i		−	0.795881i	−0.917411	−	0.397940i	$-0.869725\pi$
$727$		−	21.4593i		−	0.795881i	0.917411	−	0.397940i	$-0.130275\pi$
$728$	13.0990	−	1.18991i	0.485481	−	0.0441008i
$729$		0			0
$730$	19.1709	+	31.0038i	0.709546	+	1.14750i
$731$		−	14.7344i		−	0.544970i
$732$		0			0
$733$			7.43101i			0.274471i	0.990538	+	0.137235i	$0.0438217\pi$
$733$			7.43101i			0.274471i	−0.990538	+	0.137235i	$0.956178\pi$
$734$	−44.8492	+	27.7320i	−1.65541	+	1.02361i
$735$		0			0
$736$	−9.16602	+	23.4501i	−0.337864	+	0.864382i
$737$			31.7592i			1.16987i
$738$		0			0
$739$	−6.48141			−0.238423			−0.119211	−	0.992869i	$-0.538037\pi$
$739$	−6.48141			−0.238423			−0.119211	+	0.992869i	$0.538037\pi$
$740$	−21.5294	−	10.7528i	−0.791436	−	0.395280i
$741$		0			0
$742$	12.1238	−	7.49664i	0.445079	−	0.275210i
$743$	50.4752			1.85176			0.925879	−	0.377821i	$-0.123327\pi$
$743$	50.4752			1.85176			0.925879	+	0.377821i	$0.123327\pi$
$744$		0			0
$745$	32.9400			1.20683
$746$	−5.52217	+	3.41458i	−0.202181	+	0.125017i
$747$		0			0
$748$	10.5494	−	21.1222i	0.385724	−	0.772303i
$749$	−13.3669			−0.488417
$750$		0			0
$751$			34.8254i			1.27080i	0.772185	+	0.635398i	$0.219164\pi$
$751$			34.8254i			1.27080i	−0.772185	+	0.635398i	$0.780836\pi$
$752$	4.87890	+	6.49322i	0.177915	+	0.236783i
$753$		0			0
$754$	−57.3861	+	35.4841i	−2.08988	+	1.29226i
$755$		−	54.7189i		−	1.99142i
$756$		0			0
$757$		−	15.6422i		−	0.568524i	−0.958747	−	0.284262i	$-0.908251\pi$
$757$		−	15.6422i		−	0.568524i	0.958747	−	0.284262i	$-0.0917485\pi$
$758$	15.6301	+	25.2776i	0.567712	+	0.918122i
$759$		0			0
$760$	34.0683	−	3.09475i	1.23579	−	0.112258i
$761$		−	8.77808i		−	0.318205i	−0.987262	−	0.159103i	$-0.949140\pi$
$761$		−	8.77808i		−	0.318205i	0.987262	−	0.159103i	$-0.0508600\pi$
$762$		0			0
$763$	−5.91832			−0.214257
$764$	6.93807	−	13.8915i	0.251010	−	0.502577i
$765$		0			0
$766$	−6.76115	−	10.9344i	−0.244290	−	0.395074i
$767$	3.95837			0.142928
$768$		0			0
$769$	20.4092			0.735975			0.367988	−	0.929831i	$-0.380047\pi$
$769$	20.4092			0.735975			0.367988	+	0.929831i	$0.380047\pi$
$770$	−5.65884	−	9.15167i	−0.203931	−	0.329803i
$771$		0			0
$772$	−8.12834	+	16.2747i	−0.292545	+	0.585739i
$773$	−0.204759			−0.00736468			−0.00368234	−	0.999993i	$-0.501172\pi$
$773$	−0.204759			−0.00736468			−0.00368234	+	0.999993i	$0.501172\pi$
$774$		0			0
$775$		−	10.9199i		−	0.392254i
$776$	11.3388	−	1.03001i	0.407041	−	0.0369753i
$777$		0			0
$778$	1.53461	+	2.48182i	0.0550183	+	0.0889775i
$779$			28.5576i			1.02318i
$780$		0			0
$781$			9.15062i			0.327435i
$782$	30.7030	−	18.9849i	1.09794	−	0.678899i
$783$		0			0
$784$	2.40283	+	3.19787i	0.0858154	+	0.114210i
$785$		−	53.1205i		−	1.89595i
$786$		0			0
$787$	51.9705			1.85255			0.926274	−	0.376850i	$-0.122993\pi$
$787$	51.9705			1.85255			0.926274	+	0.376850i	$0.122993\pi$
$788$	−9.26896	+	18.5585i	−0.330193	+	0.661117i
$789$		0			0
$790$	−51.9064	+	32.0958i	−1.84675	+	1.14192i
$791$	−18.5535			−0.659687
$792$		0			0
$793$	10.7630			0.382204
$794$	0.0444371	−	0.0274772i	0.00157701	−	0.000975131i
$795$		0			0
$796$	17.7561	+	8.86824i	0.629350	+	0.314327i
$797$	16.9252			0.599522			0.299761	−	0.954014i	$-0.403093\pi$
$797$	16.9252			0.599522			0.299761	+	0.954014i	$0.403093\pi$
$798$		0			0
$799$		−	11.6448i		−	0.411962i
$800$	−17.8384	+	45.6373i	−0.630684	+	1.61352i
$801$		0			0
$802$	22.4707	−	13.8945i	0.793469	−	0.490634i
$803$		−	14.3544i		−	0.506557i
$804$		0			0
$805$		−	16.4513i		−	0.579832i
$806$	−4.36025	−	7.05154i	−0.153583	−	0.248380i
$807$		0			0
$808$	40.0013	−	3.63369i	1.40724	−	0.127833i
$809$			10.4440i			0.367191i	0.983002	+	0.183596i	$0.0587737\pi$
$809$			10.4440i			0.367191i	−0.983002	+	0.183596i	$0.941226\pi$
$810$		0			0
$811$	15.2976			0.537170			0.268585	−	0.963256i	$-0.413444\pi$
$811$	15.2976			0.537170			0.268585	+	0.963256i	$0.413444\pi$
$812$	−18.3566	−	9.16816i	−0.644192	−	0.321739i
$813$		0			0
$814$	4.98395	+	8.06021i	0.174687	+	0.282510i
$815$	80.5204			2.82051
$816$		0			0
$817$	−8.40685			−0.294118
$818$	8.60015	+	13.9084i	0.300697	+	0.486297i
$819$		0			0
$820$	−57.7187	−	28.8274i	−2.01563	−	1.00670i
$821$	20.7719			0.724946			0.362473	−	0.931994i	$-0.381933\pi$
$821$	20.7719			0.724946			0.362473	+	0.931994i	$0.381933\pi$
$822$		0			0
$823$		−	6.01697i		−	0.209738i	−0.994486	−	0.104869i	$-0.966558\pi$
$823$		−	6.01697i		−	0.209738i	0.994486	−	0.104869i	$-0.0334424\pi$
$824$	−1.35777	−	14.9470i	−0.0473003	−	0.520702i
$825$		0			0
$826$	0.633100	+	1.02387i	0.0220284	+	0.0356250i
$827$			53.8903i			1.87395i	0.349399	+	0.936974i	$0.386386\pi$
$827$			53.8903i			1.87395i	−0.349399	+	0.936974i	$0.613614\pi$
$828$		0			0
$829$			5.69863i			0.197922i	0.995091	+	0.0989608i	$0.0315519\pi$
$829$			5.69863i			0.197922i	−0.995091	+	0.0989608i	$0.968448\pi$
$830$	57.0634	−	35.2846i	1.98070	−	1.22474i
$831$		0			0
$832$	6.70352	+	36.5932i	0.232403	+	1.26864i
$833$		−	5.73497i		−	0.198705i
$834$		0			0
$835$	49.5409			1.71443
$836$	−12.0515	−	6.01907i	−0.416809	−	0.208174i
$837$		0			0
$838$	−17.5507	+	10.8523i	−0.606280	+	0.374887i
$839$	9.43315			0.325668			0.162834	−	0.986653i	$-0.447936\pi$
$839$	9.43315			0.325668			0.162834	+	0.986653i	$0.447936\pi$
$840$		0			0
$841$	76.2553			2.62949
$842$	21.1945	−	13.1054i	0.730411	−	0.451642i
$843$		0			0
$844$	9.79635	−	19.6144i	0.337204	−	0.675156i
$845$	−31.8798			−1.09670
$846$		0			0
$847$		−	6.76287i		−	0.232375i
$848$	24.2190	+	32.2325i	0.831684	+	1.10687i
$849$		0			0
$850$	59.7527	−	36.9474i	2.04950	−	1.26729i
$851$			14.4893i			0.496686i
$852$		0			0
$853$		−	3.49254i		−	0.119582i	−0.998211	−	0.0597912i	$-0.980957\pi$
$853$		−	3.49254i		−	0.119582i	0.998211	−	0.0597912i	$-0.0190435\pi$
$854$	1.72143	+	2.78395i	0.0589060	+	0.0952648i
$855$		0			0
$856$	−3.42032	−	37.6524i	−0.116904	−	1.28693i
$857$			11.2047i			0.382745i	0.981517	+	0.191372i	$0.0612938\pi$
$857$			11.2047i			0.382745i	−0.981517	+	0.191372i	$0.938706\pi$
$858$		0			0
$859$	43.4564			1.48271			0.741357	−	0.671111i	$-0.234183\pi$
$859$	43.4564			1.48271			0.741357	+	0.671111i	$0.234183\pi$
$860$	8.48629	−	16.9914i	0.289380	−	0.579401i
$861$		0			0
$862$	13.1274	+	21.2301i	0.447121	+	0.723099i
$863$	−19.8312			−0.675063			−0.337532	−	0.941314i	$-0.609592\pi$
$863$	−19.8312			−0.675063			−0.337532	+	0.941314i	$0.609592\pi$
$864$		0			0
$865$	49.2412			1.67425
$866$	4.70032	+	7.60151i	0.159723	+	0.258310i
$867$		0			0
$868$	1.12657	−	2.25564i	0.0382384	−	0.0765615i
$869$	24.0321			0.815235
$870$		0			0
$871$			71.7483i			2.43110i
$872$	−1.51437	−	16.6709i	−0.0512831	−	0.564547i
$873$		0			0
$874$	−10.8320	−	17.5179i	−0.366399	−	0.592553i
$875$		−	13.5356i		−	0.457587i
$876$		0			0
$877$		−	40.6652i		−	1.37317i	−0.727051	−	0.686584i	$-0.759110\pi$
$877$		−	40.6652i		−	1.37317i	0.727051	−	0.686584i	$-0.240890\pi$
$878$	−12.2681	+	7.58586i	−0.414028	+	0.256010i
$879$		0			0
$880$	24.3307	−	18.2817i	0.820188	−	0.616276i
$881$			46.8298i			1.57774i	0.614562	+	0.788868i	$0.289333\pi$
$881$			46.8298i			1.57774i	−0.614562	+	0.788868i	$0.710667\pi$
$882$		0			0
$883$	−18.8388			−0.633975			−0.316988	−	0.948430i	$-0.602671\pi$
$883$	−18.8388			−0.633975			−0.316988	+	0.948430i	$0.602671\pi$
$884$	23.8325	−	47.7178i	0.801574	−	1.60492i
$885$		0			0
$886$	−11.3858	+	7.04030i	−0.382514	+	0.236523i
$887$	−1.52873			−0.0513297			−0.0256648	−	0.999671i	$-0.508170\pi$
$887$	−1.52873			−0.0513297			−0.0256648	+	0.999671i	$0.508170\pi$
$888$		0			0
$889$	−9.76963			−0.327663
$890$	10.4666	−	6.47193i	0.350842	−	0.216940i
$891$		0			0
$892$	2.12885	+	1.06325i	0.0712792	+	0.0356002i
$893$	−6.64403			−0.222334
$894$		0			0
$895$			46.8631i			1.56646i
$896$	−8.39303	+	7.58664i	−0.280391	+	0.253452i
$897$		0			0
$898$	33.8577	−	20.9356i	1.12985	−	0.698630i
$899$			12.9336i			0.431361i
$900$		0			0
$901$		−	57.8048i		−	1.92576i
$902$	13.3616	+	21.6088i	0.444893	+	0.719496i
$903$		0			0
$904$	−4.74745	−	52.2620i	−0.157898	−	1.73821i
$905$		−	41.1222i		−	1.36695i
$906$		0			0
$907$	−24.5682			−0.815773			−0.407886	−	0.913033i	$-0.633734\pi$
$907$	−24.5682			−0.815773			−0.407886	+	0.913033i	$0.633734\pi$
$908$	17.2255	+	8.60324i	0.571650	+	0.285509i
$909$		0			0
$910$	−12.7841	−	20.6748i	−0.423788	−	0.685364i
$911$	14.8864			0.493209			0.246604	−	0.969116i	$-0.420685\pi$
$911$	14.8864			0.493209			0.246604	+	0.969116i	$0.420685\pi$
$912$		0			0
$913$	−26.4198			−0.874367
$914$	26.0269	+	42.0916i	0.860893	+	1.39227i
$915$		0			0
$916$	−38.4944	−	19.2259i	−1.27189	−	0.635241i
$917$	15.5661			0.514038
$918$		0			0
$919$			55.6464i			1.83560i	0.397038	+	0.917802i	$0.370038\pi$
$919$			55.6464i			1.83560i	−0.397038	+	0.917802i	$0.629962\pi$
$920$	46.3405	−	4.20954i	1.52780	−	0.138785i
$921$		0			0
$922$	−22.5031	−	36.3928i	−0.741101	−	1.19853i
$923$			20.6725i			0.680443i
$924$		0			0
$925$			28.1982i			0.927153i
$926$	−3.45307	+	2.13517i	−0.113475	+	0.0701660i
$927$		0			0
$928$	21.1281	−	54.0534i	0.693563	−	1.77439i
$929$		−	29.3098i		−	0.961623i	−0.876824	−	0.480812i	$-0.840342\pi$
$929$		−	29.3098i		−	0.961623i	0.876824	−	0.480812i	$-0.159658\pi$
$930$		0			0
$931$	−3.27215			−0.107240
$932$	12.2041	+	6.09532i	0.399760	+	0.199659i
$933$		0			0
$934$	−43.5376	+	26.9210i	−1.42459	+	0.880883i
$935$	−43.6340			−1.42698
$936$		0			0
$937$	12.6626			0.413669			0.206834	−	0.978376i	$-0.433684\pi$
$937$	12.6626			0.413669			0.206834	+	0.978376i	$0.433684\pi$
$938$	−18.5584	+	11.4754i	−0.605954	+	0.374685i
$939$		0			0
$940$	6.70682	−	13.4285i	0.218752	−	0.437989i
$941$	26.6135			0.867575			0.433788	−	0.901015i	$-0.357177\pi$
$941$	26.6135			0.867575			0.433788	+	0.901015i	$0.357177\pi$
$942$		0			0
$943$			38.8447i			1.26496i
$944$	−2.72207	+	2.04532i	−0.0885959	+	0.0665695i
$945$		0			0
$946$	−6.36126	+	3.93342i	−0.206822	+	0.127887i
$947$			4.05029i			0.131617i	0.997832	+	0.0658084i	$0.0209626\pi$
$947$			4.05029i			0.131617i	−0.997832	+	0.0658084i	$0.979037\pi$
$948$		0			0
$949$		−	32.4286i		−	1.05268i
$950$	−21.0807	−	34.0925i	−0.683950	−	1.10611i
$951$		0			0
$952$	16.1544	−	1.46746i	0.523568	−	0.0475606i
$953$		−	7.19155i		−	0.232957i	−0.993193	−	0.116479i	$-0.962839\pi$
$953$		−	7.19155i		−	0.232957i	0.993193	−	0.116479i	$-0.0371606\pi$
$954$		0			0
$955$	−28.6969			−0.928611
$956$	−5.58080	+	11.1740i	−0.180496	+	0.361392i
$957$		0			0
$958$	12.7299	+	20.5872i	0.411285	+	0.665143i
$959$	8.54964			0.276082
$960$		0			0
$961$	29.4107			0.948733
$962$	11.2594	+	18.2091i	0.363018	+	0.587084i
$963$		0			0
$964$	−22.8389	+	45.7284i	−0.735591	+	1.47281i
$965$	33.6201			1.08227
$966$		0			0
$967$			46.3071i			1.48914i	0.667547	+	0.744568i	$0.267344\pi$
$967$			46.3071i			1.48914i	−0.667547	+	0.744568i	$0.732656\pi$
$968$	19.0498	−	1.73048i	0.612285	−	0.0556196i
$969$		0			0
$970$	−11.0662	−	17.8967i	−0.355315	−	0.574628i
$971$			22.1689i			0.711432i	0.934594	+	0.355716i	$0.115763\pi$
$971$			22.1689i			0.711432i	−0.934594	+	0.355716i	$0.884237\pi$
$972$		0			0
$973$			15.4607i			0.495647i
$974$	−32.2765	+	19.9578i	−1.03421	+	0.639491i
$975$		0			0
$976$	−7.40143	+	5.56132i	−0.236914	+	0.178013i
$977$		−	13.0854i		−	0.418638i	−0.977847	−	0.209319i	$-0.932875\pi$
$977$		−	13.0854i		−	0.418638i	0.977847	−	0.209319i	$-0.0671248\pi$
$978$		0			0
$979$	−4.84594			−0.154877
$980$	3.30307	−	6.61346i	0.105513	−	0.211259i
$981$		0			0
$982$	−8.62839	+	5.33528i	−0.275343	+	0.170256i
$983$	14.9454			0.476684			0.238342	−	0.971181i	$-0.423396\pi$
$983$	14.9454			0.476684			0.238342	+	0.971181i	$0.423396\pi$
$984$		0			0
$985$	38.3379			1.22155
$986$	−70.7718	+	43.7610i	−2.25383	+	1.39364i
$987$		0			0
$988$	−27.2259	−	13.5979i	−0.866171	−	0.432606i
$989$	−11.4352			−0.363618
$990$		0			0
$991$		−	25.6587i		−	0.815075i	−0.913188	−	0.407537i	$-0.866388\pi$
$991$		−	25.6587i		−	0.815075i	0.913188	−	0.407537i	$-0.133612\pi$
$992$	6.64202	+	2.59619i	0.210884	+	0.0824292i
$993$		0			0
$994$	−5.34714	+	3.30635i	−0.169601	+	0.104871i
$995$		−	36.6805i		−	1.16285i
$996$		0			0
$997$			10.1507i			0.321476i	0.986997	+	0.160738i	$0.0513874\pi$
$997$			10.1507i			0.321476i	−0.986997	+	0.160738i	$0.948613\pi$
$998$	27.4248	+	44.3524i	0.868118	+	1.40395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.15	✓	48
3.2	odd	2	inner	1512.2.j.d.323.34	yes	48
4.3	odd	2		6048.2.j.d.5615.46		48
8.3	odd	2	inner	1512.2.j.d.323.33	yes	48
8.5	even	2		6048.2.j.d.5615.4		48
12.11	even	2		6048.2.j.d.5615.3		48
24.5	odd	2		6048.2.j.d.5615.45		48
24.11	even	2	inner	1512.2.j.d.323.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.15	✓	48	1.1	even	1	trivial
1512.2.j.d.323.16	yes	48	24.11	even	2	inner
1512.2.j.d.323.33	yes	48	8.3	odd	2	inner
1512.2.j.d.323.34	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.3		48	12.11	even	2
6048.2.j.d.5615.4		48	8.5	even	2
6048.2.j.d.5615.45		48	24.5	odd	2
6048.2.j.d.5615.46		48	4.3	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743762 - 1.20284i) q^{2} +(-0.893635 + 1.78925i) q^{4} +3.69622 q^{5} -1.00000i q^{7} +(2.81683 - 0.255879i) q^{8} +O(q^{10})\)	\(q+(-0.743762 - 1.20284i) q^{2} +(-0.893635 + 1.78925i) q^{4} +3.69622 q^{5} -1.00000i q^{7} +(2.81683 - 0.255879i) q^{8} +(-2.74911 - 4.44595i) q^{10} +2.05843i q^{11} +4.65027i q^{13} +(-1.20284 + 0.743762i) q^{14} +(-2.40283 - 3.19787i) q^{16} +5.73497i q^{17} +3.27215 q^{19} +(-3.30307 + 6.61346i) q^{20} +(2.47596 - 1.53098i) q^{22} +4.45085 q^{23} +8.66201 q^{25} +(5.59351 - 3.45869i) q^{26} +(1.78925 + 0.893635i) q^{28} -10.2594 q^{29} -1.26066i q^{31} +(-2.05939 + 5.26867i) q^{32} +(6.89824 - 4.26546i) q^{34} -3.69622i q^{35} +3.25539i q^{37} +(-2.43370 - 3.93586i) q^{38} +(10.4116 - 0.945784i) q^{40} +8.72747i q^{41} -2.56921 q^{43} +(-3.68305 - 1.83949i) q^{44} +(-3.31038 - 5.35365i) q^{46} -2.03048 q^{47} -1.00000 q^{49} +(-6.44248 - 10.4190i) q^{50} +(-8.32049 - 4.15564i) q^{52} -10.0794 q^{53} +7.60840i q^{55} +(-0.255879 - 2.81683i) q^{56} +(7.63056 + 12.3404i) q^{58} -0.851213i q^{59} -2.31448i q^{61} +(-1.51637 + 0.937634i) q^{62} +(7.86905 - 1.44153i) q^{64} +17.1884i q^{65} +15.4289 q^{67} +(-10.2613 - 5.12497i) q^{68} +(-4.44595 + 2.74911i) q^{70} +4.44544 q^{71} -6.97349 q^{73} +(3.91571 - 2.42124i) q^{74} +(-2.92411 + 5.85469i) q^{76} +2.05843 q^{77} -11.6750i q^{79} +(-8.88139 - 11.8200i) q^{80} +(10.4977 - 6.49116i) q^{82} +12.8349i q^{83} +21.1977i q^{85} +(1.91088 + 3.09035i) q^{86} +(0.526709 + 5.79825i) q^{88} +2.35419i q^{89} +4.65027 q^{91} +(-3.97744 + 7.96369i) q^{92} +(1.51020 + 2.44234i) q^{94} +12.0946 q^{95} +4.02539 q^{97} +(0.743762 + 1.20284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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