LMFDB - Embedded newform 128.5.h.a.15.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, not 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:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			15.12
Character	$\chi$	$=$	128.15
Dual form			128.5.h.a.111.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.9321 - 4.52821i) q^{3} +(-0.302610 - 0.125345i) q^{5} +(32.5244 - 32.5244i) q^{7} +(41.7299 - 41.7299i) q^{9} +O(q^{10})$	\(q+(10.9321 - 4.52821i) q^{3} +(-0.302610 - 0.125345i) q^{5} +(32.5244 - 32.5244i) q^{7} +(41.7299 - 41.7299i) q^{9} +(-92.7415 - 38.4148i) q^{11} +(301.220 - 124.769i) q^{13} -3.87574 q^{15} +147.668i q^{17} +(-136.379 - 329.248i) q^{19} +(208.281 - 502.836i) q^{21} +(317.468 + 317.468i) q^{23} +(-441.866 - 441.866i) q^{25} +(-99.5530 + 240.342i) q^{27} +(255.045 + 615.733i) q^{29} -1011.30i q^{31} -1187.81 q^{33} +(-13.9190 + 5.76542i) q^{35} +(223.060 + 92.3947i) q^{37} +(2727.97 - 2727.97i) q^{39} +(1696.60 - 1696.60i) q^{41} +(2004.14 + 830.142i) q^{43} +(-17.8585 + 7.39723i) q^{45} -2551.27 q^{47} +285.332i q^{49} +(668.673 + 1614.32i) q^{51} +(287.645 - 694.436i) q^{53} +(23.2494 + 23.2494i) q^{55} +(-2981.81 - 2981.81i) q^{57} +(-1475.01 + 3560.99i) q^{59} +(2159.39 + 5213.22i) q^{61} -2714.47i q^{63} -106.791 q^{65} +(-6707.73 + 2778.43i) q^{67} +(4908.15 + 2033.02i) q^{69} +(-2342.67 + 2342.67i) q^{71} +(-4595.51 + 4595.51i) q^{73} +(-6831.37 - 2829.65i) q^{75} +(-4265.77 + 1766.94i) q^{77} -1462.20 q^{79} +7858.45i q^{81} +(4961.57 + 11978.3i) q^{83} +(18.5095 - 44.6858i) q^{85} +(5576.34 + 5576.34i) q^{87} +(-5366.25 - 5366.25i) q^{89} +(5738.94 - 13855.0i) q^{91} +(-4579.38 - 11055.6i) q^{93} +116.728i q^{95} +2087.46 q^{97} +(-5473.13 + 2267.05i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 1156 q^{23} - 4 q^{25} - 3644 q^{27} - 4 q^{29} - 8 q^{33} + 5188 q^{35} - 4 q^{37} + 2692 q^{39} - 4 q^{41} - 5564 q^{43} - 328 q^{45} + 8 q^{47} - 8384 q^{51} + 956 q^{53} + 11780 q^{55} - 4 q^{57} + 13060 q^{59} + 7548 q^{61} - 8 q^{65} - 18876 q^{67} - 19588 q^{69} - 19964 q^{71} - 4 q^{73} + 200 q^{75} + 9404 q^{77} + 50184 q^{79} - 10556 q^{83} + 2496 q^{85} - 49276 q^{87} - 4 q^{89} - 31868 q^{91} + 320 q^{93} - 8 q^{97} + 46920 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 1156 * q^23 - 4 * q^25 - 3644 * q^27 - 4 * q^29 - 8 * q^33 + 5188 * q^35 - 4 * q^37 + 2692 * q^39 - 4 * q^41 - 5564 * q^43 - 328 * q^45 + 8 * q^47 - 8384 * q^51 + 956 * q^53 + 11780 * q^55 - 4 * q^57 + 13060 * q^59 + 7548 * q^61 - 8 * q^65 - 18876 * q^67 - 19588 * q^69 - 19964 * q^71 - 4 * q^73 + 200 * q^75 + 9404 * q^77 + 50184 * q^79 - 10556 * q^83 + 2496 * q^85 - 49276 * q^87 - 4 * q^89 - 31868 * q^91 + 320 * q^93 - 8 * q^97 + 46920 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	10.9321	−	4.52821i	1.21467	−	0.503135i	0.318962	−	0.947768i	$-0.396666\pi$
$3$	10.9321	−	4.52821i	1.21467	−	0.503135i	0.895713	+	0.444633i	$0.146666\pi$
$4$		0			0
$5$	−0.302610	−	0.125345i	−0.0121044	−	0.00501380i	0.376623	−	0.926367i	$-0.377085\pi$
$5$	−0.302610	−	0.125345i	−0.0121044	−	0.00501380i	−0.388727	+	0.921353i	$0.627085\pi$
$6$		0			0
$7$	32.5244	−	32.5244i	0.663763	−	0.663763i	−0.292502	−	0.956265i	$-0.594488\pi$
$7$	32.5244	−	32.5244i	0.663763	−	0.663763i	0.956265	+	0.292502i	$0.0944879\pi$
$8$		0			0
$9$	41.7299	−	41.7299i	0.515184	−	0.515184i
$10$		0			0
$11$	−92.7415	−	38.4148i	−0.766459	−	0.317478i	−0.0350215	−	0.999387i	$-0.511150\pi$
$11$	−92.7415	−	38.4148i	−0.766459	−	0.317478i	−0.731437	+	0.681909i	$0.761150\pi$
$12$		0			0
$13$	301.220	−	124.769i	1.78237	−	0.738280i	0.790275	−	0.612752i	$-0.209938\pi$
$13$	301.220	−	124.769i	1.78237	−	0.738280i	0.992090	−	0.125527i	$-0.0400623\pi$
$14$		0			0
$15$	−3.87574			−0.0172255
$16$		0			0
$17$			147.668i			0.510962i	0.966814	+	0.255481i	$0.0822339\pi$
$17$			147.668i			0.510962i	−0.966814	+	0.255481i	$0.917766\pi$
$18$		0			0
$19$	−136.379	−	329.248i	−0.377781	−	0.912045i	−0.992381	−	0.123206i	$-0.960683\pi$
$19$	−136.379	−	329.248i	−0.377781	−	0.912045i	0.614600	−	0.788839i	$-0.289317\pi$
$20$		0			0
$21$	208.281	−	502.836i	0.472294	−	1.14022i
$22$		0			0
$23$	317.468	+	317.468i	0.600129	+	0.600129i	0.940347	−	0.340217i	$-0.110501\pi$
$23$	317.468	+	317.468i	0.600129	+	0.600129i	−0.340217	+	0.940347i	$0.610501\pi$
$24$		0			0
$25$	−441.866	−	441.866i	−0.706985	−	0.706985i
$26$		0			0
$27$	−99.5530	+	240.342i	−0.136561	+	0.329688i
$28$		0			0
$29$	255.045	+	615.733i	0.303264	+	0.732144i	0.999892	+	0.0147113i	$0.00468291\pi$
$29$	255.045	+	615.733i	0.303264	+	0.732144i	−0.696628	+	0.717433i	$0.745317\pi$
$30$		0			0
$31$		−	1011.30i		−	1.05234i	−0.850379	−	0.526171i	$-0.823627\pi$
$31$		−	1011.30i		−	1.05234i	0.850379	−	0.526171i	$-0.176373\pi$
$32$		0			0
$33$	−1187.81			−1.09073
$34$		0			0
$35$	−13.9190	+	5.76542i	−0.0113624	+	0.00470646i
$36$		0			0
$37$	223.060	+	92.3947i	0.162937	+	0.0674906i	0.462661	−	0.886535i	$-0.346895\pi$
$37$	223.060	+	92.3947i	0.162937	+	0.0674906i	−0.299724	+	0.954026i	$0.596895\pi$
$38$		0			0
$39$	2727.97	−	2727.97i	1.79354	−	1.79354i
$40$		0			0
$41$	1696.60	−	1696.60i	1.00928	−	1.00928i	0.00932633	−	0.999957i	$-0.497031\pi$
$41$	1696.60	−	1696.60i	1.00928	−	1.00928i	0.999957	−	0.00932633i	$-0.00296871\pi$
$42$		0			0
$43$	2004.14	+	830.142i	1.08390	+	0.448968i	0.851877	−	0.523741i	$-0.175464\pi$
$43$	2004.14	+	830.142i	1.08390	+	0.448968i	0.232027	+	0.972709i	$0.425464\pi$
$44$		0			0
$45$	−17.8585	+	7.39723i	−0.00881901	+	0.00365295i
$46$		0			0
$47$	−2551.27			−1.15494			−0.577472	−	0.816411i	$-0.695961\pi$
$47$	−2551.27			−1.15494			−0.577472	+	0.816411i	$0.695961\pi$
$48$		0			0
$49$			285.332i			0.118839i
$50$		0			0
$51$	668.673	+	1614.32i	0.257083	+	0.620653i
$52$		0			0
$53$	287.645	−	694.436i	0.102401	−	0.247218i	−0.864373	−	0.502852i	$-0.832284\pi$
$53$	287.645	−	694.436i	0.102401	−	0.247218i	0.966774	+	0.255634i	$0.0822841\pi$
$54$		0			0
$55$	23.2494	+	23.2494i	0.00768574	+	0.00768574i
$56$		0			0
$57$	−2981.81	−	2981.81i	−0.917763	−	0.917763i
$58$		0			0
$59$	−1475.01	+	3560.99i	−0.423732	+	1.02298i	0.557505	+	0.830174i	$0.311759\pi$
$59$	−1475.01	+	3560.99i	−0.423732	+	1.02298i	−0.981237	+	0.192806i	$0.938241\pi$
$60$		0			0
$61$	2159.39	+	5213.22i	0.580324	+	1.40103i	0.892520	+	0.451009i	$0.148936\pi$
$61$	2159.39	+	5213.22i	0.580324	+	1.40103i	−0.312195	+	0.950018i	$0.601064\pi$
$62$		0			0
$63$		−	2714.47i		−	0.683919i
$64$		0			0
$65$	−106.791			−0.0252760
$66$		0			0
$67$	−6707.73	+	2778.43i	−1.49426	+	0.618943i	−0.972239	−	0.233990i	$-0.924822\pi$
$67$	−6707.73	+	2778.43i	−1.49426	+	0.618943i	−0.522021	+	0.852933i	$0.674822\pi$
$68$		0			0
$69$	4908.15	+	2033.02i	1.03091	+	0.427016i
$70$		0			0
$71$	−2342.67	+	2342.67i	−0.464723	+	0.464723i	−0.900200	−	0.435477i	$-0.856580\pi$
$71$	−2342.67	+	2342.67i	−0.464723	+	0.464723i	0.435477	+	0.900200i	$0.356580\pi$
$72$		0			0
$73$	−4595.51	+	4595.51i	−0.862359	+	0.862359i	−0.991612	−	0.129253i	$-0.958742\pi$
$73$	−4595.51	+	4595.51i	−0.862359	+	0.862359i	0.129253	+	0.991612i	$0.458742\pi$
$74$		0			0
$75$	−6831.37	−	2829.65i	−1.21447	−	0.503048i
$76$		0			0
$77$	−4265.77	+	1766.94i	−0.719476	+	0.298017i
$78$		0			0
$79$	−1462.20			−0.234289			−0.117145	−	0.993115i	$-0.537374\pi$
$79$	−1462.20			−0.234289			−0.117145	+	0.993115i	$0.537374\pi$
$80$		0			0
$81$			7858.45i			1.19775i
$82$		0			0
$83$	4961.57	+	11978.3i	0.720216	+	1.73876i	0.672734	+	0.739884i	$0.265120\pi$
$83$	4961.57	+	11978.3i	0.720216	+	1.73876i	0.0474820	+	0.998872i	$0.484880\pi$
$84$		0			0
$85$	18.5095	−	44.6858i	0.00256186	−	0.00618488i
$86$		0			0
$87$	5576.34	+	5576.34i	0.736734	+	0.736734i
$88$		0			0
$89$	−5366.25	−	5366.25i	−0.677471	−	0.677471i	0.281956	−	0.959427i	$-0.409017\pi$
$89$	−5366.25	−	5366.25i	−0.677471	−	0.677471i	−0.959427	+	0.281956i	$0.909017\pi$
$90$		0			0
$91$	5738.94	−	13855.0i	0.693025	−	1.67311i
$92$		0			0
$93$	−4579.38	−	11055.6i	−0.529470	−	1.27825i
$94$		0			0
$95$			116.728i			0.0129339i
$96$		0			0
$97$	2087.46			0.221858			0.110929	−	0.993828i	$-0.464617\pi$
$97$	2087.46			0.221858			0.110929	+	0.993828i	$0.464617\pi$
$98$		0			0
$99$	−5473.13	+	2267.05i	−0.558426	+	0.231308i
$100$		0			0
$101$	15368.4	+	6365.80i	1.50656	+	0.624037i	0.974844	−	0.222887i	$-0.0715482\pi$
$101$	15368.4	+	6365.80i	1.50656	+	0.624037i	0.531714	+	0.846924i	$0.321548\pi$
$102$		0			0
$103$	3295.94	−	3295.94i	0.310674	−	0.310674i	−0.534497	−	0.845171i	$-0.679499\pi$
$103$	3295.94	−	3295.94i	0.310674	−	0.310674i	0.845171	+	0.534497i	$0.179499\pi$
$104$		0			0
$105$	−126.056	+	126.056i	−0.0114336	+	0.0114336i
$106$		0			0
$107$	1482.21	+	613.950i	0.129462	+	0.0536247i	0.446474	−	0.894797i	$-0.352680\pi$
$107$	1482.21	+	613.950i	0.129462	+	0.0536247i	−0.317012	+	0.948421i	$0.602680\pi$
$108$		0			0
$109$	−11814.9	+	4893.88i	−0.994435	+	0.411908i	−0.819753	−	0.572717i	$-0.805890\pi$
$109$	−11814.9	+	4893.88i	−0.994435	+	0.411908i	−0.174681	+	0.984625i	$0.555890\pi$
$110$		0			0
$111$	2856.90			0.231872
$112$		0			0
$113$			602.741i			0.0472035i	0.999721	+	0.0236017i	$0.00751337\pi$
$113$			602.741i			0.0472035i	−0.999721	+	0.0236017i	$0.992487\pi$
$114$		0			0
$115$	−56.2759	−	135.862i	−0.00425527	−	0.0102731i
$116$		0			0
$117$	7363.25	−	17776.5i	0.537896	−	1.29859i
$118$		0			0
$119$	4802.81	+	4802.81i	0.339158	+	0.339158i
$120$		0			0
$121$	−3227.46	−	3227.46i	−0.220440	−	0.220440i
$122$		0			0
$123$	10864.8	−	26230.0i	0.718145	−	1.73376i
$124$		0			0
$125$	156.668	+	378.230i	0.0100267	+	0.0242067i
$126$		0			0
$127$			883.269i			0.0547628i	0.999625	+	0.0273814i	$0.00871686\pi$
$127$			883.269i			0.0547628i	−0.999625	+	0.0273814i	$0.991283\pi$
$128$		0			0
$129$	25668.5			1.54248
$130$		0			0
$131$	2977.25	−	1233.22i	0.173489	−	0.0718616i	−0.294248	−	0.955729i	$-0.595069\pi$
$131$	2977.25	−	1233.22i	0.173489	−	0.0718616i	0.467738	+	0.883867i	$0.345069\pi$
$132$		0			0
$133$	−15144.2	−	6272.94i	−0.856138	−	0.354624i
$134$		0			0
$135$	60.2514	−	60.2514i	0.00330597	−	0.00330597i
$136$		0			0
$137$	4311.36	−	4311.36i	0.229707	−	0.229707i	−0.582863	−	0.812570i	$-0.698068\pi$
$137$	4311.36	−	4311.36i	0.229707	−	0.229707i	0.812570	+	0.582863i	$0.198068\pi$
$138$		0			0
$139$	11088.9	+	4593.17i	0.573929	+	0.237729i	0.650720	−	0.759318i	$-0.274467\pi$
$139$	11088.9	+	4593.17i	0.573929	+	0.237729i	−0.0767906	+	0.997047i	$0.524467\pi$
$140$		0			0
$141$	−27890.7	+	11552.7i	−1.40288	+	0.581092i
$142$		0			0
$143$	−32728.5			−1.60050
$144$		0			0
$145$		−	218.295i		−	0.0103827i
$146$		0			0
$147$	1292.04	+	3119.27i	0.0597919	+	0.144350i
$148$		0			0
$149$	−1352.10	+	3264.25i	−0.0609026	+	0.147032i	−0.951401	−	0.307954i	$-0.900356\pi$
$149$	−1352.10	+	3264.25i	−0.0609026	+	0.147032i	0.890499	+	0.454986i	$0.150356\pi$
$150$		0			0
$151$	−6871.17	−	6871.17i	−0.301354	−	0.301354i	0.540190	−	0.841543i	$-0.318353\pi$
$151$	−6871.17	−	6871.17i	−0.301354	−	0.301354i	−0.841543	+	0.540190i	$0.818353\pi$
$152$		0			0
$153$	6162.17	+	6162.17i	0.263239	+	0.263239i
$154$		0			0
$155$	−126.761	+	306.029i	−0.00527623	+	0.0127380i
$156$		0			0
$157$	−3068.71	−	7408.52i	−0.124496	−	0.300561i	0.849327	−	0.527867i	$-0.177008\pi$
$157$	−3068.71	−	7408.52i	−0.124496	−	0.300561i	−0.973823	+	0.227306i	$0.927008\pi$
$158$		0			0
$159$		−	8894.15i		−	0.351812i
$160$		0			0
$161$	20650.9			0.796687
$162$		0			0
$163$	16136.5	−	6683.97i	0.607344	−	0.251570i	−0.0577482	−	0.998331i	$-0.518392\pi$
$163$	16136.5	−	6683.97i	0.607344	−	0.251570i	0.665093	+	0.746761i	$0.268392\pi$
$164$		0			0
$165$	359.442	+	148.886i	0.0132026	+	0.00546871i
$166$		0			0
$167$	−4158.99	+	4158.99i	−0.149127	+	0.149127i	−0.777728	−	0.628601i	$-0.783628\pi$
$167$	−4158.99	+	4158.99i	−0.149127	+	0.149127i	0.628601	+	0.777728i	$0.283628\pi$
$168$		0			0
$169$	54970.3	−	54970.3i	1.92466	−	1.92466i
$170$		0			0
$171$	−19430.6	−	8048.40i	−0.664497	−	0.275244i
$172$		0			0
$173$	26841.8	−	11118.3i	0.896851	−	0.371488i	0.113842	−	0.993499i	$-0.463684\pi$
$173$	26841.8	−	11118.3i	0.896851	−	0.371488i	0.783008	+	0.622011i	$0.213684\pi$
$174$		0			0
$175$	−28742.8			−0.938541
$176$		0			0
$177$			45608.2i			1.45578i
$178$		0			0
$179$	−5305.52	−	12808.7i	−0.165585	−	0.399758i	0.819206	−	0.573499i	$-0.194414\pi$
$179$	−5305.52	−	12808.7i	−0.165585	−	0.399758i	−0.984791	+	0.173741i	$0.944414\pi$
$180$		0			0
$181$	10061.3	−	24290.2i	0.307113	−	0.741437i	−0.692683	−	0.721243i	$-0.743571\pi$
$181$	10061.3	−	24290.2i	0.307113	−	0.741437i	0.999796	−	0.0201949i	$-0.00642868\pi$
$182$		0			0
$183$	47213.1	+	47213.1i	1.40981	+	1.40981i
$184$		0			0
$185$	−55.9190	−	55.9190i	−0.00163387	−	0.00163387i
$186$		0			0
$187$	5672.64	−	13695.0i	0.162219	−	0.391631i
$188$		0			0
$189$	4579.08	+	11054.9i	0.128190	+	0.309478i
$190$		0			0
$191$			27070.1i			0.742033i	0.928626	+	0.371016i	$0.120991\pi$
$191$			27070.1i			0.742033i	−0.928626	+	0.371016i	$0.879009\pi$
$192$		0			0
$193$	−45387.5			−1.21849			−0.609244	−	0.792983i	$-0.708527\pi$
$193$	−45387.5			−1.21849			−0.609244	+	0.792983i	$0.708527\pi$
$194$		0			0
$195$	−1167.45	+	483.573i	−0.0307021	+	0.0127172i
$196$		0			0
$197$	−47676.6	−	19748.3i	−1.22849	−	0.508858i	−0.328393	−	0.944541i	$-0.606507\pi$
$197$	−47676.6	−	19748.3i	−1.22849	−	0.508858i	−0.900100	+	0.435683i	$0.856507\pi$
$198$		0			0
$199$	17271.6	−	17271.6i	0.436140	−	0.436140i	−0.454571	−	0.890711i	$-0.650207\pi$
$199$	17271.6	−	17271.6i	0.436140	−	0.436140i	0.890711	+	0.454571i	$0.150207\pi$
$200$		0			0
$201$	−60748.1	+	60748.1i	−1.50363	+	1.50363i
$202$		0			0
$203$	28321.5	+	11731.2i	0.687265	+	0.284674i
$204$		0			0
$205$	−726.070	+	300.748i	−0.0172771	+	0.00715641i
$206$		0			0
$207$	26495.8			0.618354
$208$		0			0
$209$			35773.9i			0.818981i
$210$		0			0
$211$	−24374.9	−	58846.1i	−0.547491	−	1.32176i	−0.919339	−	0.393467i	$-0.871276\pi$
$211$	−24374.9	−	58846.1i	−0.547491	−	1.32176i	0.371848	−	0.928294i	$-0.378724\pi$
$212$		0			0
$213$	−15002.1	+	36218.3i	−0.330669	+	0.798305i
$214$		0			0
$215$	−502.418	−	502.418i	−0.0108690	−	0.0108690i
$216$		0			0
$217$	−32891.9	−	32891.9i	−0.698505	−	0.698505i
$218$		0			0
$219$	−29429.0	+	71047.9i	−0.613603	+	1.48137i
$220$		0			0
$221$	18424.4	+	44480.5i	0.377233	+	0.910721i
$222$		0			0
$223$			19714.6i			0.396441i	0.980157	+	0.198220i	$0.0635162\pi$
$223$			19714.6i			0.396441i	−0.980157	+	0.198220i	$0.936484\pi$
$224$		0			0
$225$	−36878.0			−0.728455
$226$		0			0
$227$	−30870.6	+	12787.0i	−0.599092	+	0.248152i	−0.661557	−	0.749895i	$-0.730104\pi$
$227$	−30870.6	+	12787.0i	−0.599092	+	0.248152i	0.0624645	+	0.998047i	$0.480104\pi$
$228$		0			0
$229$	22231.8	+	9208.73i	0.423940	+	0.175602i	0.584445	−	0.811433i	$-0.301312\pi$
$229$	22231.8	+	9208.73i	0.423940	+	0.175602i	−0.160505	+	0.987035i	$0.551312\pi$
$230$		0			0
$231$	−38632.7	+	38632.7i	−0.723987	+	0.723987i
$232$		0			0
$233$	−18497.7	+	18497.7i	−0.340726	+	0.340726i	−0.856640	−	0.515914i	$-0.827452\pi$
$233$	−18497.7	+	18497.7i	−0.340726	+	0.340726i	0.515914	+	0.856640i	$0.327452\pi$
$234$		0			0
$235$	772.039	+	319.789i	0.0139799	+	0.00579066i
$236$		0			0
$237$	−15984.9	+	6621.16i	−0.284586	+	0.117879i
$238$		0			0
$239$	24120.1			0.422263			0.211131	−	0.977458i	$-0.432285\pi$
$239$	24120.1			0.422263			0.211131	+	0.977458i	$0.432285\pi$
$240$		0			0
$241$		−	76476.6i		−	1.31672i	−0.752702	−	0.658361i	$-0.771250\pi$
$241$		−	76476.6i		−	1.31672i	0.752702	−	0.658361i	$-0.228750\pi$
$242$		0			0
$243$	27520.9	+	66441.4i	0.466069	+	1.12519i
$244$		0			0
$245$	35.7649	−	86.3441i	0.000595833	−	0.00143847i
$246$		0			0
$247$	−82160.1	−	82160.1i	−1.34669	−	1.34669i
$248$		0			0
$249$	108481.	+	108481.i	1.74966	+	1.74966i
$250$		0			0
$251$	−19118.0	+	46155.0i	−0.303456	+	0.732607i	0.696432	+	0.717623i	$0.254770\pi$
$251$	−19118.0	+	46155.0i	−0.303456	+	0.732607i	−0.999888	+	0.0149843i	$0.995230\pi$
$252$		0			0
$253$	−17247.0	−	41638.0i	−0.269447	−	0.650502i
$254$		0			0
$255$		−	572.323i		−	0.00880159i
$256$		0			0
$257$	−23773.2			−0.359932			−0.179966	−	0.983673i	$-0.557599\pi$
$257$	−23773.2			−0.359932			−0.179966	+	0.983673i	$0.557599\pi$
$258$		0			0
$259$	10260.0	−	4249.82i	0.152949	−	0.0633536i
$260$		0			0
$261$	36337.5	+	15051.5i	0.533425	+	0.220952i
$262$		0			0
$263$	36826.9	−	36826.9i	0.532419	−	0.532419i	−0.388872	−	0.921292i	$-0.627135\pi$
$263$	36826.9	−	36826.9i	0.532419	−	0.532419i	0.921292	+	0.388872i	$0.127135\pi$
$264$		0			0
$265$	−174.088	+	174.088i	−0.00247901	+	0.00247901i
$266$		0			0
$267$	−82963.7	−	34364.7i	−1.16377	−	0.482048i
$268$		0			0
$269$	89650.5	−	37134.4i	1.23893	−	0.513183i	0.335553	−	0.942021i	$-0.391077\pi$
$269$	89650.5	−	37134.4i	1.23893	−	0.513183i	0.903381	+	0.428838i	$0.141077\pi$
$270$		0			0
$271$	48628.7			0.662147			0.331073	−	0.943605i	$-0.392589\pi$
$271$	48628.7			0.662147			0.331073	+	0.943605i	$0.392589\pi$
$272$		0			0
$273$		−	177451.i		−	2.38097i
$274$		0			0
$275$	24005.1	+	57953.5i	0.317423	+	0.766327i
$276$		0			0
$277$	−43094.4	+	104039.i	−0.561644	+	1.35593i	0.346806	+	0.937937i	$0.387266\pi$
$277$	−43094.4	+	104039.i	−0.561644	+	1.35593i	−0.908450	+	0.417993i	$0.862734\pi$
$278$		0			0
$279$	−42201.4	−	42201.4i	−0.542149	−	0.542149i
$280$		0			0
$281$	−82723.8	−	82723.8i	−1.04765	−	1.04765i	−0.998806	−	0.0488478i	$-0.984445\pi$
$281$	−82723.8	−	82723.8i	−1.04765	−	1.04765i	−0.0488478	−	0.998806i	$-0.515555\pi$
$282$		0			0
$283$	−2913.87	+	7034.69i	−0.0363828	+	0.0878359i	−0.941027	−	0.338333i	$-0.890137\pi$
$283$	−2913.87	+	7034.69i	−0.0363828	+	0.0878359i	0.904644	+	0.426169i	$0.140137\pi$
$284$		0			0
$285$	528.570	+	1276.08i	0.00650748	+	0.0157104i
$286$		0			0
$287$		−	110362.i		−	1.33985i
$288$		0			0
$289$	61715.1			0.738918
$290$		0			0
$291$	22820.3	−	9452.47i	0.269485	−	0.111624i
$292$		0			0
$293$	109200.	+	45232.2i	1.27200	+	0.526881i	0.913573	−	0.406675i	$-0.133312\pi$
$293$	109200.	+	45232.2i	1.27200	+	0.526881i	0.358431	+	0.933556i	$0.383312\pi$
$294$		0			0
$295$	892.705	−	892.705i	0.0102580	−	0.0102580i
$296$		0			0
$297$	18465.4	−	18465.4i	0.209337	−	0.209337i
$298$		0			0
$299$	135238.	+	56017.4i	1.51271	+	0.626586i
$300$		0			0
$301$	92183.2	−	38183.5i	1.01746	−	0.421447i
$302$		0			0
$303$	196834.			2.14395
$304$		0			0
$305$		−	1848.24i		−	0.0198682i
$306$		0			0
$307$	−38226.8	−	92287.7i	−0.405594	−	0.979190i	−0.986283	−	0.165064i	$-0.947217\pi$
$307$	−38226.8	−	92287.7i	−0.405594	−	0.979190i	0.580689	−	0.814125i	$-0.302783\pi$
$308$		0			0
$309$	21106.7	−	50956.2i	0.221057	−	0.533679i
$310$		0			0
$311$	−101416.	−	101416.i	−1.04854	−	1.04854i	−0.998760	−	0.0497783i	$-0.984149\pi$
$311$	−101416.	−	101416.i	−1.04854	−	1.04854i	−0.0497783	−	0.998760i	$-0.515851\pi$
$312$		0			0
$313$	25981.8	+	25981.8i	0.265204	+	0.265204i	0.827164	−	0.561960i	$-0.189953\pi$
$313$	25981.8	+	25981.8i	0.265204	+	0.265204i	−0.561960	+	0.827164i	$0.689953\pi$
$314$		0			0
$315$	−340.246	+	821.426i	−0.00342903	+	0.00827842i
$316$		0			0
$317$	−4292.28	−	10362.5i	−0.0427140	−	0.103121i	0.901083	−	0.433647i	$-0.142774\pi$
$317$	−4292.28	−	10362.5i	−0.0427140	−	0.103121i	−0.943797	+	0.330527i	$0.892774\pi$
$318$		0			0
$319$		−	66901.5i		−	0.657437i
$320$		0			0
$321$	18983.7			0.184234
$322$		0			0
$323$	48619.4	−	20138.8i	0.466020	−	0.193032i
$324$		0			0
$325$	−188230.	−	77967.4i	−1.78206	−	0.738153i
$326$		0			0
$327$	−107001.	+	107001.i	−1.00067	+	1.00067i
$328$		0			0
$329$	−82978.4	+	82978.4i	−0.766608	+	0.766608i
$330$		0			0
$331$	−82177.2	−	34038.9i	−0.750059	−	0.310685i	−0.0252932	−	0.999680i	$-0.508052\pi$
$331$	−82177.2	−	34038.9i	−0.750059	−	0.310685i	−0.724766	+	0.688996i	$0.758052\pi$
$332$		0			0
$333$	13163.9	−	5452.67i	0.118712	−	0.0491723i
$334$		0			0
$335$	2378.09			0.0211904
$336$		0			0
$337$		−	658.851i		−	0.00580133i	−0.999996	−	0.00290066i	$-0.999077\pi$
$337$		−	658.851i		−	0.00580133i	0.999996	−	0.00290066i	$-0.000923311\pi$
$338$		0			0
$339$	2729.34	+	6589.21i	0.0237497	+	0.0573369i
$340$		0			0
$341$	−38848.9	+	93789.5i	−0.334095	+	0.806576i
$342$		0			0
$343$	87371.2	+	87371.2i	0.742643	+	0.742643i
$344$		0			0
$345$	−1230.43	−	1230.43i	−0.0103375	−	0.0103375i
$346$		0			0
$347$	−24616.7	+	59429.9i	−0.204442	+	0.493567i	−0.992531	−	0.121995i	$-0.961071\pi$
$347$	−24616.7	+	59429.9i	−0.204442	+	0.493567i	0.788089	+	0.615562i	$0.211071\pi$
$348$		0			0
$349$	−25777.1	−	62231.5i	−0.211633	−	0.510927i	0.782041	−	0.623226i	$-0.214179\pi$
$349$	−25777.1	−	62231.5i	−0.211633	−	0.510927i	−0.993674	+	0.112299i	$0.964179\pi$
$350$		0			0
$351$			84817.0i			0.688444i
$352$		0			0
$353$	−214331.			−1.72003			−0.860015	−	0.510269i	$-0.829546\pi$
$353$	−214331.			−1.72003			−0.860015	+	0.510269i	$0.829546\pi$
$354$		0			0
$355$	1002.56	−	415.272i	0.00795521	−	0.00329515i
$356$		0			0
$357$	74252.8	+	30756.5i	0.582608	+	0.241324i
$358$		0			0
$359$	132700.	−	132700.i	1.02964	−	1.02964i	0.0300884	−	0.999547i	$-0.490421\pi$
$359$	132700.	−	132700.i	1.02964	−	1.02964i	0.999547	−	0.0300884i	$-0.00957887\pi$
$360$		0			0
$361$	2345.77	−	2345.77i	0.0180000	−	0.0180000i
$362$		0			0
$363$	−49897.5	−	20668.2i	−0.378674	−	0.156852i
$364$		0			0
$365$	1966.67	−	814.621i	0.0147620	−	0.00611463i
$366$		0			0
$367$	63682.8			0.472814			0.236407	−	0.971654i	$-0.424030\pi$
$367$	63682.8			0.472814			0.236407	+	0.971654i	$0.424030\pi$
$368$		0			0
$369$		−	141598.i		−	1.03993i
$370$		0			0
$371$	−13230.6	−	31941.6i	−0.0961242	−	0.232064i
$372$		0			0
$373$	26208.4	−	63272.7i	0.188375	−	0.454777i	−0.801272	−	0.598300i	$-0.795843\pi$
$373$	26208.4	−	63272.7i	0.188375	−	0.454777i	0.989647	+	0.143523i	$0.0458431\pi$
$374$		0			0
$375$	3425.41	+	3425.41i	0.0243585	+	0.0243585i
$376$		0			0
$377$	153649.	+	153649.i	1.08105	+	1.08105i
$378$		0			0
$379$	−20900.5	+	50458.2i	−0.145505	+	0.351280i	−0.979783	−	0.200064i	$-0.935885\pi$
$379$	−20900.5	+	50458.2i	−0.145505	+	0.351280i	0.834278	+	0.551344i	$0.185885\pi$
$380$		0			0
$381$	3999.63	+	9655.96i	0.0275531	+	0.0665190i
$382$		0			0
$383$			270867.i			1.84654i	0.384149	+	0.923271i	$0.374495\pi$
$383$			270867.i			1.84654i	−0.384149	+	0.923271i	$0.625505\pi$
$384$		0			0
$385$	1512.34			0.0102030
$386$		0			0
$387$	118274.	−	48990.8i	0.789711	−	0.327109i
$388$		0			0
$389$	−116250.	−	48152.4i	−0.768235	−	0.318213i	−0.0360777	−	0.999349i	$-0.511486\pi$
$389$	−116250.	−	48152.4i	−0.768235	−	0.318213i	−0.732157	+	0.681136i	$0.761486\pi$
$390$		0			0
$391$	−46880.0	+	46880.0i	−0.306643	+	0.306643i
$392$		0			0
$393$	26963.3	−	26963.3i	0.174577	−	0.174577i
$394$		0			0
$395$	442.476	+	183.280i	0.00283593	+	0.00117468i
$396$		0			0
$397$	162131.	−	67157.0i	1.02869	−	0.426099i	0.196453	−	0.980513i	$-0.437058\pi$
$397$	162131.	−	67157.0i	1.02869	−	0.426099i	0.832241	+	0.554414i	$0.187058\pi$
$398$		0			0
$399$	−193963.			−1.21835
$400$		0			0
$401$			277801.i			1.72760i	0.503831	+	0.863802i	$0.331924\pi$
$401$			277801.i			1.72760i	−0.503831	+	0.863802i	$0.668076\pi$
$402$		0			0
$403$	−126179.	−	304624.i	−0.776923	−	1.87566i
$404$		0			0
$405$	985.017	−	2378.04i	0.00600529	−	0.0144980i
$406$		0			0
$407$	−17137.6	−	17137.6i	−0.103458	−	0.103458i
$408$		0			0
$409$	23476.2	+	23476.2i	0.140340	+	0.140340i	0.773786	−	0.633447i	$-0.218360\pi$
$409$	23476.2	+	23476.2i	0.140340	+	0.140340i	−0.633447	+	0.773786i	$0.718360\pi$
$410$		0			0
$411$	27609.4	−	66654.9i	0.163445	−	0.394592i
$412$		0			0
$413$	67845.2	+	163793.i	0.397758	+	0.960273i
$414$		0			0
$415$		−	4246.65i		−	0.0246576i
$416$		0			0
$417$	142023.			0.816747
$418$		0			0
$419$	−23503.8	+	9735.60i	−0.133878	+	0.0554542i	−0.448617	−	0.893724i	$-0.648083\pi$
$419$	−23503.8	+	9735.60i	−0.133878	+	0.0554542i	0.314738	+	0.949178i	$0.398083\pi$
$420$		0			0
$421$	−143861.	−	59589.2i	−0.811670	−	0.336205i	−0.0620498	−	0.998073i	$-0.519764\pi$
$421$	−143861.	−	59589.2i	−0.811670	−	0.336205i	−0.749620	+	0.661868i	$0.769764\pi$
$422$		0			0
$423$	−106464.	+	106464.i	−0.595008	+	0.595008i
$424$		0			0
$425$	65249.5	−	65249.5i	0.361243	−	0.361243i
$426$		0			0
$427$	239789.	+	99324.0i	1.31515	+	0.544751i
$428$		0			0
$429$	−357791.	+	148202.i	−1.94408	+	0.805265i
$430$		0			0
$431$	−217564.			−1.17120			−0.585602	−	0.810599i	$-0.699142\pi$
$431$	−217564.			−1.17120			−0.585602	+	0.810599i	$0.699142\pi$
$432$		0			0
$433$			168258.i			0.897427i	0.893676	+	0.448714i	$0.148118\pi$
$433$			168258.i			0.897427i	−0.893676	+	0.448714i	$0.851882\pi$
$434$		0			0
$435$	−988.488	−	2386.42i	−0.00522388	−	0.0126116i
$436$		0			0
$437$	61229.8	−	147822.i	0.320627	−	0.774062i
$438$		0			0
$439$	188671.	+	188671.i	0.978983	+	0.978983i	0.999784	−	0.0208006i	$-0.00662151\pi$
$439$	188671.	+	188671.i	0.978983	+	0.978983i	−0.0208006	+	0.999784i	$0.506622\pi$
$440$		0			0
$441$	11906.8	+	11906.8i	0.0612237	+	0.0612237i
$442$		0			0
$443$	−19793.2	+	47785.0i	−0.100857	+	0.243492i	−0.966252	−	0.257600i	$-0.917068\pi$
$443$	−19793.2	+	47785.0i	−0.100857	+	0.243492i	0.865394	+	0.501092i	$0.167068\pi$
$444$		0			0
$445$	951.246	+	2296.51i	0.00480366	+	0.0115971i
$446$		0			0
$447$			41807.7i			0.209238i
$448$		0			0
$449$	90099.3			0.446919			0.223459	−	0.974713i	$-0.428265\pi$
$449$	90099.3			0.446919			0.223459	+	0.974713i	$0.428265\pi$
$450$		0			0
$451$	−222520.	+	92170.9i	−1.09400	+	0.453149i
$452$		0			0
$453$	−106230.	−	44002.0i	−0.517669	−	0.214425i
$454$		0			0
$455$	−3473.32	+	3473.32i	−0.0167773	+	0.0167773i
$456$		0			0
$457$	146399.	−	146399.i	0.700982	−	0.700982i	−0.263639	−	0.964621i	$-0.584923\pi$
$457$	146399.	−	146399.i	0.700982	−	0.700982i	0.964621	+	0.263639i	$0.0849227\pi$
$458$		0			0
$459$	−35490.9	−	14700.8i	−0.168458	−	0.0697775i
$460$		0			0
$461$	−59857.0	+	24793.6i	−0.281652	+	0.116664i	−0.519038	−	0.854751i	$-0.673710\pi$
$461$	−59857.0	+	24793.6i	−0.281652	+	0.116664i	0.237385	+	0.971416i	$0.423710\pi$
$462$		0			0
$463$	−254680.			−1.18804			−0.594022	−	0.804449i	$-0.702461\pi$
$463$	−254680.			−1.18804			−0.594022	+	0.804449i	$0.702461\pi$
$464$		0			0
$465$			3919.54i			0.0181271i
$466$		0			0
$467$	127119.	+	306892.i	0.582875	+	1.40718i	0.890196	+	0.455579i	$0.150568\pi$
$467$	127119.	+	306892.i	0.582875	+	1.40718i	−0.307321	+	0.951606i	$0.599432\pi$
$468$		0			0
$469$	−127798.	+	308532.i	−0.581003	+	1.40266i
$470$		0			0
$471$	−67094.7	−	67094.7i	−0.302445	−	0.302445i
$472$		0			0
$473$	−153977.	−	153977.i	−0.688231	−	0.688231i
$474$		0			0
$475$	−85222.3	+	205745.i	−0.377716	+	0.911888i
$476$		0			0
$477$	−16975.4	−	40982.1i	−0.0746074	−	0.180118i
$478$		0			0
$479$		−	314666.i		−	1.37145i	−0.727862	−	0.685724i	$-0.759486\pi$
$479$		−	314666.i		−	1.37145i	0.727862	−	0.685724i	$-0.240514\pi$
$480$		0			0
$481$	78718.2			0.340240
$482$		0			0
$483$	225757.	−	93511.8i	0.967715	−	0.400841i
$484$		0			0
$485$	−631.686	−	261.653i	−0.00268545	−	0.00111235i
$486$		0			0
$487$	−103947.	+	103947.i	−0.438281	+	0.438281i	−0.891433	−	0.453152i	$-0.850299\pi$
$487$	−103947.	+	103947.i	−0.438281	+	0.438281i	0.453152	+	0.891433i	$0.350299\pi$
$488$		0			0
$489$	146139.	−	146139.i	0.611152	−	0.611152i
$490$		0			0
$491$	−102440.	−	42432.1i	−0.424920	−	0.176008i	0.159967	−	0.987122i	$-0.448861\pi$
$491$	−102440.	−	42432.1i	−0.424920	−	0.176008i	−0.584887	+	0.811115i	$0.698861\pi$
$492$		0			0
$493$	−90924.1	+	37662.0i	−0.374098	+	0.154956i
$494$		0			0
$495$	1940.39			0.00791913
$496$		0			0
$497$			152387.i			0.616931i
$498$		0			0
$499$	35396.4	+	85454.6i	0.142154	+	0.343190i	0.978881	−	0.204430i	$-0.0655341\pi$
$499$	35396.4	+	85454.6i	0.142154	+	0.343190i	−0.836727	+	0.547620i	$0.815534\pi$
$500$		0			0
$501$	−26633.6	+	64299.2i	−0.106110	+	0.256171i
$502$		0			0
$503$	85693.9	+	85693.9i	0.338699	+	0.338699i	0.855878	−	0.517179i	$-0.173018\pi$
$503$	85693.9	+	85693.9i	0.338699	+	0.338699i	−0.517179	+	0.855878i	$0.673018\pi$
$504$		0			0
$505$	−3852.70	−	3852.70i	−0.0151072	−	0.0151072i
$506$		0			0
$507$	352022.	−	849856.i	1.36947	−	3.30620i
$508$		0			0
$509$	−60348.3	−	145694.i	−0.232932	−	0.562348i	0.763588	−	0.645704i	$-0.223436\pi$
$509$	−60348.3	−	145694.i	−0.232932	−	0.562348i	−0.996520	+	0.0833562i	$0.973436\pi$
$510$		0			0
$511$			298932.i			1.14480i
$512$		0			0
$513$	92709.2			0.352280
$514$		0			0
$515$	−1410.51	+	584.254i	−0.00531818	+	0.00220286i
$516$		0			0
$517$	236609.	+	98006.5i	0.885216	+	0.366669i
$518$		0			0
$519$	243091.	−	243091.i	0.902473	−	0.902473i
$520$		0			0
$521$	−321244.	+	321244.i	−1.18347	+	1.18347i	−0.204637	+	0.978838i	$0.565601\pi$
$521$	−321244.	+	321244.i	−1.18347	+	1.18347i	−0.978838	+	0.204637i	$0.934399\pi$
$522$		0			0
$523$	−144400.	−	59812.3i	−0.527914	−	0.218669i	0.102775	−	0.994705i	$-0.467228\pi$
$523$	−144400.	−	59812.3i	−0.527914	−	0.218669i	−0.630689	+	0.776035i	$0.717228\pi$
$524$		0			0
$525$	−314219.	+	130154.i	−1.14002	+	0.472213i
$526$		0			0
$527$	149337.			0.537707
$528$		0			0
$529$		−	78268.6i		−	0.279689i
$530$		0			0
$531$	87047.7	+	210152.i	0.308723	+	0.745322i
$532$		0			0
$533$	299367.	−	722735.i	1.05378	−	2.54404i
$534$		0			0
$535$	−371.574	−	371.574i	−0.00129819	−	0.00129819i
$536$		0			0
$537$	−116001.	−	116001.i	−0.402265	−	0.402265i
$538$		0			0
$539$	10960.9	−	26462.1i	0.0377286	−	0.0910849i
$540$		0			0
$541$	−130883.	−	315979.i	−0.447186	−	1.07960i	−0.973371	−	0.229234i	$-0.926378\pi$
$541$	−130883.	−	315979.i	−0.447186	−	1.07960i	0.526185	−	0.850370i	$-0.323622\pi$
$542$		0			0
$543$		−	311103.i		−	1.05512i
$544$		0			0
$545$	4188.72			0.0141023
$546$		0			0
$547$	74801.7	−	30983.9i	0.249998	−	0.103553i	−0.254166	−	0.967161i	$-0.581801\pi$
$547$	74801.7	−	30983.9i	0.249998	−	0.103553i	0.504164	+	0.863608i	$0.331801\pi$
$548$		0			0
$549$	307658.	+	127436.i	1.02076	+	0.422812i
$550$		0			0
$551$	167946.	−	167946.i	0.553181	−	0.553181i
$552$		0			0
$553$	−47557.1	+	47557.1i	−0.155513	+	0.155513i
$554$		0			0
$555$	−864.524	−	358.098i	−0.00280667	−	0.00116256i
$556$		0			0
$557$	536513.	−	222231.i	1.72930	−	0.716298i	0.729831	−	0.683628i	$-0.239599\pi$
$557$	536513.	−	222231.i	1.72930	−	0.716298i	0.999466	−	0.0326701i	$-0.0104011\pi$
$558$		0			0
$559$	707263.			2.26338
$560$		0			0
$561$		−	175401.i		−	0.557323i
$562$		0			0
$563$	−30635.4	−	73960.5i	−0.0966512	−	0.233337i	0.868158	−	0.496288i	$-0.165304\pi$
$563$	−30635.4	−	73960.5i	−0.0966512	−	0.233337i	−0.964809	+	0.262952i	$0.915304\pi$
$564$		0			0
$565$	75.5506	−	182.395i	0.000236669	−	0.000571369i
$566$		0			0
$567$	255591.	+	255591.i	0.795022	+	0.795022i
$568$		0			0
$569$	−337882.	−	337882.i	−1.04362	−	1.04362i	−0.999004	−	0.0446125i	$-0.985795\pi$
$569$	−337882.	−	337882.i	−1.04362	−	1.04362i	−0.0446125	−	0.999004i	$-0.514205\pi$
$570$		0			0
$571$	162780.	−	392985.i	0.499261	−	1.20532i	−0.450621	−	0.892715i	$-0.648798\pi$
$571$	162780.	−	392985.i	0.499261	−	1.20532i	0.949882	−	0.312608i	$-0.101202\pi$
$572$		0			0
$573$	122579.	+	295932.i	0.373343	+	0.901329i
$574$		0			0
$575$		−	280557.i		−	0.848565i
$576$		0			0
$577$	11602.6			0.0348502			0.0174251	−	0.999848i	$-0.494453\pi$
$577$	11602.6			0.0348502			0.0174251	+	0.999848i	$0.494453\pi$
$578$		0			0
$579$	−496179.	+	205524.i	−1.48007	+	0.613064i
$580$		0			0
$581$	550958.	+	228214.i	1.63217	+	0.676069i
$582$		0			0
$583$	−53353.2	+	53353.2i	−0.156973	+	0.156973i
$584$		0			0
$585$	−4456.38	+	4456.38i	−0.0130218	+	0.0130218i
$586$		0			0
$587$	−43746.8	−	18120.5i	−0.126961	−	0.0525889i	0.318299	−	0.947991i	$-0.396889\pi$
$587$	−43746.8	−	18120.5i	−0.126961	−	0.0525889i	−0.445259	+	0.895402i	$0.646889\pi$
$588$		0			0
$589$	−332969.	+	137920.i	−0.959783	+	0.397555i
$590$		0			0
$591$	−610628.			−1.74824
$592$		0			0
$593$		−	193530.i		−	0.550350i	−0.961394	−	0.275175i	$-0.911264\pi$
$593$		−	193530.i		−	0.550350i	0.961394	−	0.275175i	$-0.0887358\pi$
$594$		0			0
$595$	−851.368	−	2055.39i	−0.00240483	−	0.00580576i
$596$		0			0
$597$	110605.	−	267023.i	0.310331	−	0.749205i
$598$		0			0
$599$	−191130.	−	191130.i	−0.532690	−	0.532690i	0.388682	−	0.921372i	$-0.372930\pi$
$599$	−191130.	−	191130.i	−0.532690	−	0.532690i	−0.921372	+	0.388682i	$0.872930\pi$
$600$		0			0
$601$	240200.	+	240200.i	0.665003	+	0.665003i	0.956555	−	0.291552i	$-0.0941718\pi$
$601$	240200.	+	240200.i	0.665003	+	0.665003i	−0.291552	+	0.956555i	$0.594172\pi$
$602$		0			0
$603$	−163969.	+	395857.i	−0.450949	+	1.08869i
$604$		0			0
$605$	572.115	+	1381.21i	0.00156305	+	0.00377353i
$606$		0			0
$607$			59948.5i			0.162705i	0.996685	+	0.0813525i	$0.0259239\pi$
$607$			59948.5i			0.162705i	−0.996685	+	0.0813525i	$0.974076\pi$
$608$		0			0
$609$	362734.			0.978033
$610$		0			0
$611$	−768493.	+	318320.i	−2.05853	+	0.852671i
$612$		0			0
$613$	178619.	+	73986.6i	0.475344	+	0.196894i	0.607476	−	0.794338i	$-0.292182\pi$
$613$	178619.	+	73986.6i	0.475344	+	0.196894i	−0.132132	+	0.991232i	$0.542182\pi$
$614$		0			0
$615$	−6575.60	+	6575.60i	−0.0173854	+	0.0173854i
$616$		0			0
$617$	−61906.8	+	61906.8i	−0.162618	+	0.162618i	−0.783725	−	0.621108i	$-0.786683\pi$
$617$	−61906.8	+	61906.8i	−0.162618	+	0.162618i	0.621108	+	0.783725i	$0.286683\pi$
$618$		0			0
$619$	201488.	+	83458.9i	0.525857	+	0.217817i	0.629787	−	0.776768i	$-0.283142\pi$
$619$	201488.	+	83458.9i	0.525857	+	0.217817i	−0.103931	+	0.994585i	$0.533142\pi$
$620$		0			0
$621$	−107906.	+	44696.1i	−0.279809	+	0.115901i
$622$		0			0
$623$	−349067.			−0.899359
$624$		0			0
$625$			390424.i			0.999485i
$626$		0			0
$627$	161992.	+	391083.i	0.412058	+	0.994796i
$628$		0			0
$629$	−13643.7	+	32938.9i	−0.0344852	+	0.0832546i
$630$		0			0
$631$	−258125.	−	258125.i	−0.648292	−	0.648292i	0.304288	−	0.952580i	$-0.401582\pi$
$631$	−258125.	−	258125.i	−0.648292	−	0.648292i	−0.952580	+	0.304288i	$0.901582\pi$
$632$		0			0
$633$	−532935.	−	532935.i	−1.33005	−	1.33005i
$634$		0			0
$635$	110.713	−	267.286i	0.000274570	−	0.000662870i
$636$		0			0
$637$	35600.6	+	85947.5i	0.0877362	+	0.211814i
$638$		0			0
$639$			195518.i			0.478835i
$640$		0			0
$641$	−310395.			−0.755437			−0.377718	−	0.925921i	$-0.623291\pi$
$641$	−310395.			−0.755437			−0.377718	+	0.925921i	$0.623291\pi$
$642$		0			0
$643$	215769.	−	89374.3i	0.521875	−	0.216168i	−0.106165	−	0.994348i	$-0.533857\pi$
$643$	215769.	−	89374.3i	0.521875	−	0.216168i	0.628040	+	0.778181i	$0.283857\pi$
$644$		0			0
$645$	−7767.53	−	3217.41i	−0.0186708	−	0.00773370i
$646$		0			0
$647$	199804.	−	199804.i	0.477306	−	0.477306i	−0.426963	−	0.904269i	$-0.640417\pi$
$647$	199804.	−	199804.i	0.477306	−	0.477306i	0.904269	+	0.426963i	$0.140417\pi$
$648$		0			0
$649$	273590.	−	273590.i	0.649546	−	0.649546i
$650$		0			0
$651$	−508518.	−	210635.i	−1.19990	−	0.497014i
$652$		0			0
$653$	−141161.	+	58470.8i	−0.331046	+	0.137124i	−0.542014	−	0.840369i	$-0.682338\pi$
$653$	−141161.	+	58470.8i	−0.331046	+	0.137124i	0.210969	+	0.977493i	$0.432338\pi$
$654$		0			0
$655$	−1055.52			−0.00246028
$656$		0			0
$657$			383540.i			0.888546i
$658$		0			0
$659$	252332.	+	609184.i	0.581035	+	1.40274i	0.891876	+	0.452280i	$0.149389\pi$
$659$	252332.	+	609184.i	0.581035	+	1.40274i	−0.310842	+	0.950462i	$0.600611\pi$
$660$		0			0
$661$	−271054.	+	654383.i	−0.620374	+	1.49771i	0.230892	+	0.972979i	$0.425836\pi$
$661$	−271054.	+	654383.i	−0.620374	+	1.49771i	−0.851266	+	0.524735i	$0.824164\pi$
$662$		0			0
$663$	402835.	+	402835.i	0.916431	+	0.916431i
$664$		0			0
$665$	3796.51	+	3796.51i	0.00858501	+	0.00858501i
$666$		0			0
$667$	−114507.	+	276445.i	−0.257383	+	0.621379i
$668$		0			0
$669$	89271.9	+	215521.i	0.199463	+	0.481547i
$670$		0			0
$671$		−	566434.i		−	1.25807i
$672$		0			0
$673$	−788730.			−1.74140			−0.870699	−	0.491816i	$-0.836333\pi$
$673$	−788730.			−1.74140			−0.870699	+	0.491816i	$0.836333\pi$
$674$		0			0
$675$	150188.	−	62209.9i	0.329631	−	0.136538i
$676$		0			0
$677$	−238474.	−	98779.0i	−0.520311	−	0.215520i	0.107042	−	0.994254i	$-0.465862\pi$
$677$	−238474.	−	98779.0i	−0.520311	−	0.215520i	−0.627354	+	0.778735i	$0.715862\pi$
$678$		0			0
$679$	67893.3	−	67893.3i	0.147261	−	0.147261i
$680$		0			0
$681$	−279578.	+	279578.i	−0.602848	+	0.602848i
$682$		0			0
$683$	431348.	+	178670.i	0.924670	+	0.383011i	0.793654	−	0.608370i	$-0.208176\pi$
$683$	431348.	+	178670.i	0.924670	+	0.383011i	0.131016	+	0.991380i	$0.458176\pi$
$684$		0			0
$685$	−1845.07	+	764.252i	−0.00393216	+	0.00162875i
$686$		0			0
$687$	284739.			0.603300
$688$		0			0
$689$		−	245067.i		−	0.516234i
$690$		0			0
$691$	−12261.5	−	29601.9i	−0.0256796	−	0.0619961i	0.910520	−	0.413466i	$-0.135682\pi$
$691$	−12261.5	−	29601.9i	−0.0256796	−	0.0619961i	−0.936199	+	0.351470i	$0.885682\pi$
$692$		0			0
$693$	−104276.	+	251744.i	−0.217129	+	0.524196i
$694$		0			0
$695$	−2779.87	−	2779.87i	−0.00575513	−	0.00575513i
$696$		0			0
$697$	250534.	+	250534.i	0.515705	+	0.515705i
$698$		0			0
$699$	−118456.	+	285979.i	−0.242440	+	0.585302i
$700$		0			0
$701$	30510.5	+	73659.0i	0.0620889	+	0.149896i	0.951879	−	0.306474i	$-0.0991493\pi$
$701$	30510.5	+	73659.0i	0.0620889	+	0.149896i	−0.889790	+	0.456370i	$0.849149\pi$
$702$		0			0
$703$		−	86042.9i		−	0.174102i
$704$		0			0
$705$	9888.06			0.0198945
$706$		0			0
$707$	706891.	−	292804.i	1.41421	−	0.585784i
$708$		0			0
$709$	4726.11	+	1957.62i	0.00940182	+	0.00389436i	0.387379	−	0.921920i	$-0.373380\pi$
$709$	4726.11	+	1957.62i	0.00940182	+	0.00389436i	−0.377978	+	0.925815i	$0.623380\pi$
$710$		0			0
$711$	−61017.4	+	61017.4i	−0.120702	+	0.120702i
$712$		0			0
$713$	321056.	−	321056.i	0.631541	−	0.631541i
$714$		0			0
$715$	9903.97	+	4102.36i	0.0193730	+	0.00802457i
$716$		0			0
$717$	263682.	−	109221.i	0.512912	−	0.212455i
$718$		0			0
$719$	−803873.			−1.55500			−0.777499	−	0.628885i	$-0.783512\pi$
$719$	−803873.			−1.55500			−0.777499	+	0.628885i	$0.783512\pi$
$720$		0			0
$721$		−	214397.i		−	0.412428i
$722$		0			0
$723$	−346302.	−	836048.i	−0.662489	−	1.59939i
$724$		0			0
$725$	159376.	−	384767.i	0.303212	−	0.732018i
$726$		0			0
$727$	132759.	+	132759.i	0.251186	+	0.251186i	0.821457	−	0.570271i	$-0.193162\pi$
$727$	132759.	+	132759.i	0.251186	+	0.251186i	−0.570271	+	0.821457i	$0.693162\pi$
$728$		0			0
$729$	151624.	+	151624.i	0.285307	+	0.285307i
$730$		0			0
$731$	−122585.	+	295948.i	−0.229406	+	0.553834i
$732$		0			0
$733$	283449.	+	684307.i	0.527554	+	1.27363i	0.933121	+	0.359563i	$0.117074\pi$
$733$	283449.	+	684307.i	0.527554	+	1.27363i	−0.405566	+	0.914066i	$0.632926\pi$
$734$		0			0
$735$		−	1105.87i		−	0.00204706i
$736$		0			0
$737$	728818.			1.34179
$738$		0			0
$739$	−183779.	+	76123.7i	−0.336517	+	0.139390i	−0.544542	−	0.838734i	$-0.683296\pi$
$739$	−183779.	+	76123.7i	−0.336517	+	0.139390i	0.208025	+	0.978124i	$0.433296\pi$
$740$		0			0
$741$	−1.27022e6	−	526142.i	−2.31335	−	0.958223i
$742$		0			0
$743$	−56148.4	+	56148.4i	−0.101709	+	0.101709i	−0.756130	−	0.654421i	$-0.772912\pi$
$743$	−56148.4	+	56148.4i	−0.101709	+	0.101709i	0.654421	+	0.756130i	$0.272912\pi$
$744$		0			0
$745$	818.316	−	818.316i	0.00147438	−	0.00147438i
$746$		0			0
$747$	706898.	+	292807.i	1.26682	+	0.524735i
$748$		0			0
$749$	68176.1	−	28239.5i	0.121526	−	0.0503377i
$750$		0			0
$751$	773735.			1.37187			0.685934	−	0.727664i	$-0.259394\pi$
$751$	773735.			1.37187			0.685934	+	0.727664i	$0.259394\pi$
$752$		0			0
$753$			591140.i			1.04256i
$754$		0			0
$755$	1218.02	+	2940.55i	0.00213678	+	0.00515863i
$756$		0			0
$757$	−96057.8	+	231904.i	−0.167626	+	0.404684i	−0.985262	−	0.171050i	$-0.945284\pi$
$757$	−96057.8	+	231904.i	−0.167626	+	0.404684i	0.817636	+	0.575735i	$0.195284\pi$
$758$		0			0
$759$	−377091.	−	377091.i	−0.654580	−	0.654580i
$760$		0			0
$761$	−736883.	−	736883.i	−1.27242	−	1.27242i	−0.944816	−	0.327600i	$-0.893760\pi$
$761$	−736883.	−	736883.i	−1.27242	−	1.27242i	−0.327600	−	0.944816i	$-0.606240\pi$
$762$		0			0
$763$	−225101.	+	543442.i	−0.386659	+	0.933478i
$764$		0			0
$765$	−1092.33	−	2637.13i	−0.00186652	−	0.00450618i
$766$		0			0
$767$			1.25668e6i			2.13616i
$768$		0			0
$769$	−363250.			−0.614260			−0.307130	−	0.951667i	$-0.599369\pi$
$769$	−363250.			−0.614260			−0.307130	+	0.951667i	$0.599369\pi$
$770$		0			0
$771$	−259890.	+	107650.i	−0.437201	+	0.181095i
$772$		0			0
$773$	−53385.7	−	22113.1i	−0.0893442	−	0.0370076i	0.337564	−	0.941303i	$-0.390397\pi$
$773$	−53385.7	−	22113.1i	−0.0893442	−	0.0370076i	−0.426908	+	0.904295i	$0.640397\pi$
$774$		0			0
$775$	−446859.	+	446859.i	−0.743990	+	0.743990i
$776$		0			0
$777$	92918.7	−	92918.7i	0.153908	−	0.153908i
$778$		0			0
$779$	−789985.	−	327223.i	−1.30180	−	0.539223i
$780$		0			0
$781$	307255.	−	127269.i	0.503730	−	0.208652i
$782$		0			0
$783$	−173377.			−0.282793
$784$		0			0
$785$			2626.54i			0.00426230i
$786$		0			0
$787$	−369045.	−	890954.i	−0.595841	−	1.43849i	−0.877784	−	0.479056i	$-0.840979\pi$
$787$	−369045.	−	890954.i	−0.595841	−	1.43849i	0.281943	−	0.959431i	$-0.409021\pi$
$788$		0			0
$789$	235834.	−	569355.i	0.378838	−	0.914595i
$790$		0			0
$791$	19603.8	+	19603.8i	0.0313319	+	0.0313319i
$792$		0			0
$793$	1.30090e6	+	1.30090e6i	2.06870	+	2.06870i
$794$		0			0
$795$	−1114.84	+	2691.45i	−0.00176391	+	0.00425846i
$796$		0			0
$797$	−223785.	−	540265.i	−0.352301	−	0.850530i	−0.996335	−	0.0855336i	$-0.972740\pi$
$797$	−223785.	−	540265.i	−0.352301	−	0.850530i	0.644034	−	0.764997i	$-0.277260\pi$
$798$		0			0
$799$		−	376741.i		−	0.590133i
$800$		0			0
$801$	−447866.			−0.698044
$802$		0			0
$803$	602730.	−	249659.i	0.934742	−	0.387183i
$804$		0			0
$805$	−6249.17	−	2588.49i	−0.00964340	−	0.00399443i
$806$		0			0
$807$	811913.	−	811913.i	1.24670	−	1.24670i
$808$		0			0
$809$	−289146.	+	289146.i	−0.441794	+	0.441794i	−0.892615	−	0.450821i	$-0.851131\pi$
$809$	−289146.	+	289146.i	−0.441794	+	0.441794i	0.450821	+	0.892615i	$0.351131\pi$
$810$		0			0
$811$	762999.	+	316045.i	1.16007	+	0.480515i	0.877897	−	0.478850i	$-0.158946\pi$
$811$	762999.	+	316045.i	1.16007	+	0.480515i	0.282169	+	0.959365i	$0.408946\pi$
$812$		0			0
$813$	531613.	−	220201.i	0.804293	−	0.333149i
$814$		0			0
$815$	−5720.87			−0.00861285
$816$		0			0
$817$		−	773073.i		−	1.15818i
$818$		0			0
$819$	−338683.	−	817653.i	−0.504924	−	1.21899i
$820$		0			0
$821$	−283460.	+	684334.i	−0.420539	+	1.01527i	0.561650	+	0.827375i	$0.310167\pi$
$821$	−283460.	+	684334.i	−0.420539	+	1.01527i	−0.982189	+	0.187895i	$0.939833\pi$
$822$		0			0
$823$	149625.	+	149625.i	0.220904	+	0.220904i	0.808879	−	0.587975i	$-0.200075\pi$
$823$	149625.	+	149625.i	0.220904	+	0.220904i	−0.587975	+	0.808879i	$0.700075\pi$
$824$		0			0
$825$	524851.	+	524851.i	0.771132	+	0.771132i
$826$		0			0
$827$	451404.	−	1.08979e6i	0.660016	−	1.59342i	−0.137759	−	0.990466i	$-0.543990\pi$
$827$	451404.	−	1.08979e6i	0.660016	−	1.59342i	0.797776	−	0.602955i	$-0.206010\pi$
$828$		0			0
$829$	−277211.	−	669245.i	−0.403367	−	0.973815i	−0.986843	−	0.161684i	$-0.948307\pi$
$829$	−277211.	−	669245.i	−0.403367	−	0.973815i	0.583475	−	0.812131i	$-0.301693\pi$
$830$		0			0
$831$			1.33250e6i			1.92960i
$832$		0			0
$833$	−42134.4			−0.0607221
$834$		0			0
$835$	1779.86	−	737.242i	0.00255278	−	0.00105740i
$836$		0			0
$837$	243058.	+	100678.i	0.346944	+	0.143709i
$838$		0			0
$839$	−376356.	+	376356.i	−0.534657	+	0.534657i	−0.921955	−	0.387298i	$-0.873409\pi$
$839$	−376356.	+	376356.i	−0.534657	+	0.534657i	0.387298	+	0.921955i	$0.373409\pi$
$840$		0			0
$841$	186044.	−	186044.i	0.263041	−	0.263041i
$842$		0			0
$843$	−1.27893e6	−	529752.i	−1.79967	−	0.745448i
$844$		0			0
$845$	−23524.8	+	9744.28i	−0.0329467	+	0.0136470i
$846$		0			0
$847$	−209942.			−0.292640
$848$		0			0
$849$			90098.4i			0.124998i
$850$		0			0
$851$	41482.3	+	100147.i	0.0572800	+	0.138286i
$852$		0			0
$853$	136624.	−	329840.i	0.187772	−	0.453321i	−0.801758	−	0.597648i	$-0.796102\pi$
$853$	136624.	−	329840.i	0.187772	−	0.453321i	0.989530	+	0.144327i	$0.0461019\pi$
$854$		0			0
$855$	4871.05	+	4871.05i	0.00666331	+	0.00666331i
$856$		0			0
$857$	483788.	+	483788.i	0.658709	+	0.658709i	0.955075	−	0.296366i	$-0.0957747\pi$
$857$	483788.	+	483788.i	0.658709	+	0.658709i	−0.296366	+	0.955075i	$0.595775\pi$
$858$		0			0
$859$	11857.9	−	28627.6i	0.0160703	−	0.0387970i	−0.915641	−	0.401998i	$-0.868316\pi$
$859$	11857.9	−	28627.6i	0.0160703	−	0.0387970i	0.931711	+	0.363201i	$0.118316\pi$
$860$		0			0
$861$	−499742.	−	1.20649e6i	−0.674124	−	1.62748i
$862$		0			0
$863$		−	893447.i		−	1.19963i	−0.800139	−	0.599815i	$-0.795241\pi$
$863$		−	893447.i		−	1.19963i	0.800139	−	0.599815i	$-0.204759\pi$
$864$		0			0
$865$	−9516.22			−0.0127184
$866$		0			0
$867$	674674.	−	279459.i	0.897545	−	0.371775i
$868$		0			0
$869$	135607.	+	56170.1i	0.179573	+	0.0743816i
$870$		0			0
$871$	−1.67384e6	+	1.67384e6i	−2.20636	+	2.20636i
$872$		0			0
$873$	87109.5	−	87109.5i	0.114298	−	0.114298i
$874$		0			0
$875$	17397.2	+	7206.16i	0.0227229	+	0.00941212i
$876$		0			0
$877$	−11099.4	+	4597.52i	−0.0144311	+	0.00597756i	−0.389887	−	0.920863i	$-0.627486\pi$
$877$	−11099.4	+	4597.52i	−0.0144311	+	0.00597756i	0.375456	+	0.926840i	$0.377486\pi$
$878$		0			0
$879$	1.39861e6			1.81016
$880$		0			0
$881$		−	872540.i		−	1.12417i	−0.827078	−	0.562087i	$-0.809999\pi$
$881$		−	872540.i		−	1.12417i	0.827078	−	0.562087i	$-0.190001\pi$
$882$		0			0
$883$	−3124.65	−	7543.58i	−0.00400756	−	0.00967511i	0.921863	−	0.387516i	$-0.126667\pi$
$883$	−3124.65	−	7543.58i	−0.00400756	−	0.00967511i	−0.925871	+	0.377841i	$0.876667\pi$
$884$		0			0
$885$	5716.76	−	13801.5i	0.00729900	−	0.0176214i
$886$		0			0
$887$	−964296.	−	964296.i	−1.22564	−	1.22564i	−0.965597	−	0.260044i	$-0.916263\pi$
$887$	−964296.	−	964296.i	−1.22564	−	1.22564i	−0.260044	−	0.965597i	$-0.583737\pi$
$888$		0			0
$889$	28727.8	+	28727.8i	0.0363495	+	0.0363495i
$890$		0			0
$891$	301880.	−	728804.i	0.380259	−	0.918027i
$892$		0			0
$893$	347940.	+	840001.i	0.436316	+	1.05336i
$894$		0			0
$895$			4541.04i			0.00566904i
$896$		0			0
$897$	1.73209e6			2.15271
$898$		0			0
$899$	622691.	−	257927.i	0.770466	−	0.319137i
$900$		0			0
$901$	102546.	+	42476.0i	0.126319	+	0.0523231i
$902$		0			0
$903$	834851.	−	834851.i	1.02384	−	1.02384i
$904$		0			0
$905$	−6089.32	+	6089.32i	−0.00743484	+	0.00743484i
$906$		0			0
$907$	913560.	+	378409.i	1.11051	+	0.459988i	0.861113	−	0.508413i	$-0.169768\pi$
$907$	913560.	+	378409.i	1.11051	+	0.459988i	0.249397	+	0.968401i	$0.419768\pi$
$908$		0			0
$909$	906965.	−	375677.i	1.09765	−	0.454660i
$910$		0			0
$911$	1.50517e6			1.81363			0.906813	−	0.421533i	$-0.138508\pi$
$911$	1.50517e6			1.81363			0.906813	+	0.421533i	$0.138508\pi$
$912$		0			0
$913$		−	1.30148e6i		−	1.56134i
$914$		0			0
$915$	−8369.22	−	20205.1i	−0.00999638	−	0.0241334i
$916$		0			0
$917$	56723.6	−	136943.i	0.0674567	−	0.162855i
$918$		0			0
$919$	−301808.	−	301808.i	−0.357355	−	0.357355i	0.505482	−	0.862837i	$-0.331315\pi$
$919$	−301808.	−	301808.i	−0.357355	−	0.357355i	−0.862837	+	0.505482i	$0.831315\pi$
$920$		0			0
$921$	−835796.	−	835796.i	−0.985329	−	0.985329i
$922$		0			0
$923$	−413364.	+	997950.i	−0.485210	+	1.17140i
$924$		0			0
$925$	−57736.8	−	139389.i	−0.0674790	−	0.162909i
$926$		0			0
$927$		−	275078.i		−	0.320108i
$928$		0			0
$929$	360881.			0.418150			0.209075	−	0.977900i	$-0.432955\pi$
$929$	360881.			0.418150			0.209075	+	0.977900i	$0.432955\pi$
$930$		0			0
$931$	93944.9	−	38913.2i	0.108386	−	0.0448950i
$932$		0			0
$933$	−1.56792e6	−	649452.i	−1.80119	−	0.746077i
$934$		0			0
$935$	−3433.19	+	3433.19i	−0.00392712	+	0.00392712i
$936$		0			0
$937$	−943677.	+	943677.i	−1.07484	+	1.07484i	−0.0778784	+	0.996963i	$0.524815\pi$
$937$	−943677.	+	943677.i	−1.07484	+	1.07484i	−0.996963	+	0.0778784i	$0.975185\pi$
$938$		0			0
$939$	401686.	+	166384.i	0.455571	+	0.188704i
$940$		0			0
$941$	−1.47745e6	+	611978.i	−1.66852	+	0.691125i	−0.998679	−	0.0513755i	$-0.983639\pi$
$941$	−1.47745e6	+	611978.i	−1.66852	+	0.691125i	−0.669845	+	0.742501i	$0.733639\pi$
$942$		0			0
$943$	1.07724e6			1.21140
$944$		0			0
$945$		−	3919.28i		−	0.00438876i
$946$		0			0
$947$	332536.	+	802814.i	0.370800	+	0.895189i	0.993615	+	0.112821i	$0.0359886\pi$
$947$	332536.	+	802814.i	0.370800	+	0.895189i	−0.622816	+	0.782369i	$0.714011\pi$
$948$		0			0
$949$	−810880.	+	1.95764e6i	−0.900376	+	2.17370i
$950$		0			0
$951$	−93847.1	−	93847.1i	−0.103767	−	0.103767i
$952$		0			0
$953$	838704.	+	838704.i	0.923470	+	0.923470i	0.997273	−	0.0738027i	$-0.0235135\pi$
$953$	838704.	+	838704.i	0.923470	+	0.923470i	−0.0738027	+	0.997273i	$0.523513\pi$
$954$		0			0
$955$	3393.10	−	8191.67i	0.00372041	−	0.00898185i
$956$		0			0
$957$	−302944.	−	731372.i	−0.330780	−	0.798573i
$958$		0			0
$959$		−	280449.i		−	0.304941i
$960$		0			0
$961$	−99207.7			−0.107423
$962$		0			0
$963$	87472.3	−	36232.2i	0.0943231	−	0.0390699i
$964$		0			0
$965$	13734.7	+	5689.09i	0.0147491	+	0.00610926i
$966$		0			0
$967$	−1.02608e6	+	1.02608e6i	−1.09731	+	1.09731i	−0.102588	+	0.994724i	$0.532712\pi$
$967$	−1.02608e6	+	1.02608e6i	−1.09731	+	1.09731i	−0.994724	+	0.102588i	$0.967288\pi$
$968$		0			0
$969$	440318.	−	440318.i	0.468942	−	0.468942i
$970$		0			0
$971$	−505432.	−	209357.i	−0.536073	−	0.222049i	0.0981878	−	0.995168i	$-0.468695\pi$
$971$	−505432.	−	209357.i	−0.536073	−	0.222049i	−0.634261	+	0.773119i	$0.718695\pi$
$972$		0			0
$973$	510049.	−	211269.i	0.538748	−	0.223157i
$974$		0			0
$975$	−2.41080e6			−2.53601
$976$		0			0
$977$			631654.i			0.661744i	0.943676	+	0.330872i	$0.107343\pi$
$977$			631654.i			0.661744i	−0.943676	+	0.330872i	$0.892657\pi$
$978$		0			0
$979$	291530.	+	703817.i	0.304172	+	0.734335i
$980$		0			0
$981$	−288812.	+	697255.i	−0.300108	+	0.724525i
$982$		0			0
$983$	−341371.	−	341371.i	−0.353280	−	0.353280i	0.508048	−	0.861329i	$-0.330367\pi$
$983$	−341371.	−	341371.i	−0.353280	−	0.353280i	−0.861329	+	0.508048i	$0.830367\pi$
$984$		0			0
$985$	11952.0	+	11952.0i	0.0123188	+	0.0123188i
$986$		0			0
$987$	−531382.	+	1.28287e6i	−0.545472	+	1.31689i
$988$		0			0
$989$	372707.	+	899795.i	0.381044	+	0.919922i
$990$		0			0
$991$			220468.i			0.224491i	0.993681	+	0.112245i	$0.0358043\pi$
$991$			220468.i			0.224491i	−0.993681	+	0.112245i	$0.964196\pi$
$992$		0			0
$993$	−1.05250e6			−1.06739
$994$		0			0
$995$	−7391.45	+	3061.64i	−0.00746592	+	0.00309249i
$996$		0			0
$997$	−165879.	−	68709.3i	−0.166879	−	0.0691234i	0.297680	−	0.954666i	$-0.403787\pi$
$997$	−165879.	−	68709.3i	−0.166879	−	0.0691234i	−0.464559	+	0.885542i	$0.653787\pi$
$998$		0			0
$999$	−44412.7	+	44412.7i	−0.0445016	+	0.0445016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.h.a.15.12		60
4.3	odd	2		32.5.h.a.27.13	yes	60
32.13	even	8		32.5.h.a.19.13	✓	60
32.19	odd	8	inner	128.5.h.a.111.12		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.5.h.a.19.13	✓	60	32.13	even	8
32.5.h.a.27.13	yes	60	4.3	odd	2
128.5.h.a.15.12		60	1.1	even	1	trivial
128.5.h.a.111.12		60	32.19	odd	8	inner

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(10.9321 - 4.52821i) q^{3} +(-0.302610 - 0.125345i) q^{5} +(32.5244 - 32.5244i) q^{7} +(41.7299 - 41.7299i) q^{9} +O(q^{10})\)	\(q+(10.9321 - 4.52821i) q^{3} +(-0.302610 - 0.125345i) q^{5} +(32.5244 - 32.5244i) q^{7} +(41.7299 - 41.7299i) q^{9} +(-92.7415 - 38.4148i) q^{11} +(301.220 - 124.769i) q^{13} -3.87574 q^{15} +147.668i q^{17} +(-136.379 - 329.248i) q^{19} +(208.281 - 502.836i) q^{21} +(317.468 + 317.468i) q^{23} +(-441.866 - 441.866i) q^{25} +(-99.5530 + 240.342i) q^{27} +(255.045 + 615.733i) q^{29} -1011.30i q^{31} -1187.81 q^{33} +(-13.9190 + 5.76542i) q^{35} +(223.060 + 92.3947i) q^{37} +(2727.97 - 2727.97i) q^{39} +(1696.60 - 1696.60i) q^{41} +(2004.14 + 830.142i) q^{43} +(-17.8585 + 7.39723i) q^{45} -2551.27 q^{47} +285.332i q^{49} +(668.673 + 1614.32i) q^{51} +(287.645 - 694.436i) q^{53} +(23.2494 + 23.2494i) q^{55} +(-2981.81 - 2981.81i) q^{57} +(-1475.01 + 3560.99i) q^{59} +(2159.39 + 5213.22i) q^{61} -2714.47i q^{63} -106.791 q^{65} +(-6707.73 + 2778.43i) q^{67} +(4908.15 + 2033.02i) q^{69} +(-2342.67 + 2342.67i) q^{71} +(-4595.51 + 4595.51i) q^{73} +(-6831.37 - 2829.65i) q^{75} +(-4265.77 + 1766.94i) q^{77} -1462.20 q^{79} +7858.45i q^{81} +(4961.57 + 11978.3i) q^{83} +(18.5095 - 44.6858i) q^{85} +(5576.34 + 5576.34i) q^{87} +(-5366.25 - 5366.25i) q^{89} +(5738.94 - 13855.0i) q^{91} +(-4579.38 - 11055.6i) q^{93} +116.728i q^{95} +2087.46 q^{97} +(-5473.13 + 2267.05i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 1156 q^{23} - 4 q^{25} - 3644 q^{27} - 4 q^{29} - 8 q^{33} + 5188 q^{35} - 4 q^{37} + 2692 q^{39} - 4 q^{41} - 5564 q^{43} - 328 q^{45} + 8 q^{47} - 8384 q^{51} + 956 q^{53} + 11780 q^{55} - 4 q^{57} + 13060 q^{59} + 7548 q^{61} - 8 q^{65} - 18876 q^{67} - 19588 q^{69} - 19964 q^{71} - 4 q^{73} + 200 q^{75} + 9404 q^{77} + 50184 q^{79} - 10556 q^{83} + 2496 q^{85} - 49276 q^{87} - 4 q^{89} - 31868 q^{91} + 320 q^{93} - 8 q^{97} + 46920 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 1156 * q^23 - 4 * q^25 - 3644 * q^27 - 4 * q^29 - 8 * q^33 + 5188 * q^35 - 4 * q^37 + 2692 * q^39 - 4 * q^41 - 5564 * q^43 - 328 * q^45 + 8 * q^47 - 8384 * q^51 + 956 * q^53 + 11780 * q^55 - 4 * q^57 + 13060 * q^59 + 7548 * q^61 - 8 * q^65 - 18876 * q^67 - 19588 * q^69 - 19964 * q^71 - 4 * q^73 + 200 * q^75 + 9404 * q^77 + 50184 * q^79 - 10556 * q^83 + 2496 * q^85 - 49276 * q^87 - 4 * q^89 - 31868 * q^91 + 320 * q^93 - 8 * q^97 + 46920 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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