LMFDB - Embedded newform 128.5.h.a.15.10

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			15.10
Character	$\chi$	$=$	128.15
Dual form			128.5.h.a.111.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.25478 - 1.76239i) q^{3} +(-19.2280 - 7.96449i) q^{5} +(-0.0963230 + 0.0963230i) q^{7} +(-42.2785 + 42.2785i) q^{9} +O(q^{10})$	\(q+(4.25478 - 1.76239i) q^{3} +(-19.2280 - 7.96449i) q^{5} +(-0.0963230 + 0.0963230i) q^{7} +(-42.2785 + 42.2785i) q^{9} +(26.9896 + 11.1795i) q^{11} +(-160.492 + 66.4782i) q^{13} -95.8473 q^{15} +483.907i q^{17} +(22.7250 + 54.8630i) q^{19} +(-0.240075 + 0.579591i) q^{21} +(-311.538 - 311.538i) q^{23} +(-135.660 - 135.660i) q^{25} +(-248.128 + 599.034i) q^{27} +(-39.7168 - 95.8847i) q^{29} +1036.08i q^{31} +134.537 q^{33} +(2.61926 - 1.08493i) q^{35} +(-865.295 - 358.417i) q^{37} +(-565.700 + 565.700i) q^{39} +(-1141.23 + 1141.23i) q^{41} +(1041.97 + 431.597i) q^{43} +(1149.66 - 476.203i) q^{45} -4376.40 q^{47} +2400.98i q^{49} +(852.832 + 2058.92i) q^{51} +(1457.72 - 3519.24i) q^{53} +(-429.917 - 429.917i) q^{55} +(193.380 + 193.380i) q^{57} +(2447.74 - 5909.36i) q^{59} +(-137.261 - 331.378i) q^{61} -8.14478i q^{63} +3615.41 q^{65} +(6324.57 - 2619.72i) q^{67} +(-1874.58 - 776.475i) q^{69} +(5377.34 - 5377.34i) q^{71} +(-2783.69 + 2783.69i) q^{73} +(-816.288 - 338.117i) q^{75} +(-3.67656 + 1.52288i) q^{77} -1467.96 q^{79} -1857.00i q^{81} +(2633.82 + 6358.61i) q^{83} +(3854.07 - 9304.56i) q^{85} +(-337.972 - 337.972i) q^{87} +(-2028.99 - 2028.99i) q^{89} +(9.05574 - 21.8625i) q^{91} +(1825.98 + 4408.30i) q^{93} -1235.90i q^{95} +11014.5 q^{97} +(-1613.73 + 668.429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	4.25478	−	1.76239i	0.472753	−	0.195821i	−0.133569	−	0.991039i	$-0.542644\pi$
$3$	4.25478	−	1.76239i	0.472753	−	0.195821i	0.606323	+	0.795219i	$0.292644\pi$
$4$		0			0
$5$	−19.2280	−	7.96449i	−0.769119	−	0.318580i	−0.0366035	−	0.999330i	$-0.511654\pi$
$5$	−19.2280	−	7.96449i	−0.769119	−	0.318580i	−0.732516	+	0.680750i	$0.761654\pi$
$6$		0			0
$7$	−0.0963230	+	0.0963230i	−0.00196577	+	0.00196577i	−0.708089	−	0.706123i	$-0.750442\pi$
$7$	−0.0963230	+	0.0963230i	−0.00196577	+	0.00196577i	0.706123	+	0.708089i	$0.250442\pi$
$8$		0			0
$9$	−42.2785	+	42.2785i	−0.521957	+	0.521957i
$10$		0			0
$11$	26.9896	+	11.1795i	0.223055	+	0.0923923i	0.491412	−	0.870927i	$-0.336481\pi$
$11$	26.9896	+	11.1795i	0.223055	+	0.0923923i	−0.268358	+	0.963319i	$0.586481\pi$
$12$		0			0
$13$	−160.492	+	66.4782i	−0.949660	+	0.393362i	−0.803103	−	0.595840i	$-0.796819\pi$
$13$	−160.492	+	66.4782i	−0.949660	+	0.393362i	−0.146557	+	0.989202i	$0.546819\pi$
$14$		0			0
$15$	−95.8473			−0.425988
$16$		0			0
$17$			483.907i			1.67442i	0.546882	+	0.837210i	$0.315815\pi$
$17$			483.907i			1.67442i	−0.546882	+	0.837210i	$0.684185\pi$
$18$		0			0
$19$	22.7250	+	54.8630i	0.0629501	+	0.151975i	0.952224	−	0.305399i	$-0.0987899\pi$
$19$	22.7250	+	54.8630i	0.0629501	+	0.151975i	−0.889274	+	0.457374i	$0.848790\pi$
$20$		0			0
$21$	−0.240075	+	0.579591i	−0.000544387	+	0.00131427i
$22$		0			0
$23$	−311.538	−	311.538i	−0.588919	−	0.588919i	0.348420	−	0.937339i	$-0.386718\pi$
$23$	−311.538	−	311.538i	−0.588919	−	0.588919i	−0.937339	+	0.348420i	$0.886718\pi$
$24$		0			0
$25$	−135.660	−	135.660i	−0.217056	−	0.217056i
$26$		0			0
$27$	−248.128	+	599.034i	−0.340368	+	0.821720i
$28$		0			0
$29$	−39.7168	−	95.8847i	−0.0472256	−	0.114013i	0.898506	−	0.438961i	$-0.144653\pi$
$29$	−39.7168	−	95.8847i	−0.0472256	−	0.114013i	−0.945732	+	0.324948i	$0.894653\pi$
$30$		0			0
$31$			1036.08i			1.07813i	0.842264	+	0.539065i	$0.181222\pi$
$31$			1036.08i			1.07813i	−0.842264	+	0.539065i	$0.818778\pi$
$32$		0			0
$33$	134.537			0.123542
$34$		0			0
$35$	2.61926	−	1.08493i	0.00213817	−	0.000885659i
$36$		0			0
$37$	−865.295	−	358.417i	−0.632064	−	0.261809i	0.0435660	−	0.999051i	$-0.486128\pi$
$37$	−865.295	−	358.417i	−0.632064	−	0.261809i	−0.675630	+	0.737241i	$0.736128\pi$
$38$		0			0
$39$	−565.700	+	565.700i	−0.371926	+	0.371926i
$40$		0			0
$41$	−1141.23	+	1141.23i	−0.678902	+	0.678902i	−0.959752	−	0.280850i	$-0.909384\pi$
$41$	−1141.23	+	1141.23i	−0.678902	+	0.678902i	0.280850	+	0.959752i	$0.409384\pi$
$42$		0			0
$43$	1041.97	+	431.597i	0.563531	+	0.233422i	0.646217	−	0.763154i	$-0.276350\pi$
$43$	1041.97	+	431.597i	0.563531	+	0.233422i	−0.0826866	+	0.996576i	$0.526350\pi$
$44$		0			0
$45$	1149.66	−	476.203i	0.567732	−	0.235162i
$46$		0			0
$47$	−4376.40			−1.98117			−0.990583	−	0.136910i	$-0.956283\pi$
$47$	−4376.40			−1.98117			−0.990583	+	0.136910i	$0.956283\pi$
$48$		0			0
$49$			2400.98i			0.999992i
$50$		0			0
$51$	852.832	+	2058.92i	0.327886	+	0.791587i
$52$		0			0
$53$	1457.72	−	3519.24i	0.518945	−	1.25284i	−0.419607	−	0.907706i	$-0.637832\pi$
$53$	1457.72	−	3519.24i	0.518945	−	1.25284i	0.938552	−	0.345138i	$-0.112168\pi$
$54$		0			0
$55$	−429.917	−	429.917i	−0.142121	−	0.142121i
$56$		0			0
$57$	193.380	+	193.380i	0.0595198	+	0.0595198i
$58$		0			0
$59$	2447.74	−	5909.36i	0.703171	−	1.69760i	−0.0132266	−	0.999913i	$-0.504210\pi$
$59$	2447.74	−	5909.36i	0.703171	−	1.69760i	0.716398	−	0.697692i	$-0.245790\pi$
$60$		0			0
$61$	−137.261	−	331.378i	−0.0368883	−	0.0890562i	0.904362	−	0.426767i	$-0.140347\pi$
$61$	−137.261	−	331.378i	−0.0368883	−	0.0890562i	−0.941250	+	0.337711i	$0.890347\pi$
$62$		0			0
$63$		−	8.14478i		−	0.00205210i
$64$		0			0
$65$	3615.41			0.855718
$66$		0			0
$67$	6324.57	−	2619.72i	1.40890	−	0.583587i	0.456857	−	0.889540i	$-0.348975\pi$
$67$	6324.57	−	2619.72i	1.40890	−	0.583587i	0.952047	+	0.305953i	$0.0989750\pi$
$68$		0			0
$69$	−1874.58	−	776.475i	−0.393736	−	0.163091i
$70$		0			0
$71$	5377.34	−	5377.34i	1.06672	−	1.06672i	0.0691121	−	0.997609i	$-0.477983\pi$
$71$	5377.34	−	5377.34i	1.06672	−	1.06672i	0.997609	−	0.0691121i	$-0.0220166\pi$
$72$		0			0
$73$	−2783.69	+	2783.69i	−0.522366	+	0.522366i	−0.918285	−	0.395919i	$-0.870426\pi$
$73$	−2783.69	+	2783.69i	−0.522366	+	0.522366i	0.395919	+	0.918285i	$0.370426\pi$
$74$		0			0
$75$	−816.288	−	338.117i	−0.145118	−	0.0601098i
$76$		0			0
$77$	−3.67656	+	1.52288i	−0.000620098	+	0.000256853i
$78$		0			0
$79$	−1467.96			−0.235212			−0.117606	−	0.993060i	$-0.537522\pi$
$79$	−1467.96			−0.235212			−0.117606	+	0.993060i	$0.537522\pi$
$80$		0			0
$81$		−	1857.00i		−	0.283036i
$82$		0			0
$83$	2633.82	+	6358.61i	0.382323	+	0.923009i	0.991516	+	0.129987i	$0.0414935\pi$
$83$	2633.82	+	6358.61i	0.382323	+	0.923009i	−0.609193	+	0.793022i	$0.708506\pi$
$84$		0			0
$85$	3854.07	−	9304.56i	0.533436	−	1.28783i
$86$		0			0
$87$	−337.972	−	337.972i	−0.0446522	−	0.0446522i
$88$		0			0
$89$	−2028.99	−	2028.99i	−0.256154	−	0.256154i	0.567334	−	0.823488i	$-0.307975\pi$
$89$	−2028.99	−	2028.99i	−0.256154	−	0.256154i	−0.823488	+	0.567334i	$0.807975\pi$
$90$		0			0
$91$	9.05574	−	21.8625i	0.00109356	−	0.00264008i
$92$		0			0
$93$	1825.98	+	4408.30i	0.211120	+	0.509689i
$94$		0			0
$95$		−	1235.90i		−	0.136942i
$96$		0			0
$97$	11014.5			1.17063			0.585317	−	0.810805i	$-0.300970\pi$
$97$	11014.5			1.17063			0.585317	+	0.810805i	$0.300970\pi$
$98$		0			0
$99$	−1613.73	+	668.429i	−0.164650	+	0.0682001i
$100$		0			0
$101$	2138.91	+	885.964i	0.209676	+	0.0868507i	0.485050	−	0.874487i	$-0.338802\pi$
$101$	2138.91	+	885.964i	0.209676	+	0.0868507i	−0.275373	+	0.961337i	$0.588802\pi$
$102$		0			0
$103$	166.703	−	166.703i	0.0157134	−	0.0157134i	−0.699206	−	0.714920i	$-0.746463\pi$
$103$	166.703	−	166.703i	0.0157134	−	0.0157134i	0.714920	+	0.699206i	$0.246463\pi$
$104$		0			0
$105$	9.23230	−	9.23230i	0.000837397	−	0.000837397i
$106$		0			0
$107$	−16720.2	−	6925.74i	−1.46041	−	0.604921i	−0.495759	−	0.868460i	$-0.665110\pi$
$107$	−16720.2	−	6925.74i	−1.46041	−	0.604921i	−0.964649	+	0.263540i	$0.915110\pi$
$108$		0			0
$109$	−12723.1	+	5270.06i	−1.07087	+	0.443570i	−0.847299	−	0.531116i	$-0.821773\pi$
$109$	−12723.1	+	5270.06i	−1.07087	+	0.443570i	−0.223575	+	0.974687i	$0.571773\pi$
$110$		0			0
$111$	−4313.31			−0.350078
$112$		0			0
$113$		−	415.468i		−	0.0325372i	−0.999868	−	0.0162686i	$-0.994821\pi$
$113$		−	415.468i		−	0.0325372i	0.999868	−	0.0162686i	$-0.00517868\pi$
$114$		0			0
$115$	3509.01	+	8471.49i	0.265331	+	0.640566i
$116$		0			0
$117$	3974.78	−	9595.98i	0.290363	−	0.700999i
$118$		0			0
$119$	−46.6114	−	46.6114i	−0.00329153	−	0.00329153i
$120$		0			0
$121$	−9749.29	−	9749.29i	−0.665890	−	0.665890i
$122$		0			0
$123$	−2844.40	+	6867.00i	−0.188010	+	0.453896i
$124$		0			0
$125$	6505.81	+	15706.4i	0.416372	+	1.00521i
$126$		0			0
$127$			28223.1i			1.74984i	0.484270	+	0.874919i	$0.339085\pi$
$127$			28223.1i			1.74984i	−0.484270	+	0.874919i	$0.660915\pi$
$128$		0			0
$129$	5193.99			0.312120
$130$		0			0
$131$	3902.82	−	1616.60i	0.227424	−	0.0942020i	−0.266062	−	0.963956i	$-0.585723\pi$
$131$	3902.82	−	1616.60i	0.227424	−	0.0942020i	0.493486	+	0.869754i	$0.335723\pi$
$132$		0			0
$133$	−7.47350	−	3.09563i	−0.000422494	−	0.000175003i
$134$		0			0
$135$	9542.00	−	9542.00i	0.523567	−	0.523567i
$136$		0			0
$137$	−9991.78	+	9991.78i	−0.532355	+	0.532355i	−0.921273	−	0.388917i	$-0.872849\pi$
$137$	−9991.78	+	9991.78i	−0.532355	+	0.532355i	0.388917	+	0.921273i	$0.372849\pi$
$138$		0			0
$139$	−18106.8	−	7500.07i	−0.937155	−	0.388182i	−0.138767	−	0.990325i	$-0.544314\pi$
$139$	−18106.8	−	7500.07i	−0.937155	−	0.388182i	−0.798388	+	0.602143i	$0.794314\pi$
$140$		0			0
$141$	−18620.6	+	7712.91i	−0.936603	+	0.387954i
$142$		0			0
$143$	−5074.82			−0.248170
$144$		0			0
$145$			2159.99i			0.102734i
$146$		0			0
$147$	4231.46	+	10215.6i	0.195819	+	0.472750i
$148$		0			0
$149$	−8977.70	+	21674.1i	−0.404383	+	0.976266i	0.582206	+	0.813041i	$0.302190\pi$
$149$	−8977.70	+	21674.1i	−0.404383	+	0.976266i	−0.986589	+	0.163225i	$0.947810\pi$
$150$		0			0
$151$	18832.3	+	18832.3i	0.825941	+	0.825941i	0.986953	−	0.161011i	$-0.0514756\pi$
$151$	18832.3	+	18832.3i	0.825941	+	0.825941i	−0.161011	+	0.986953i	$0.551476\pi$
$152$		0			0
$153$	−20458.9	−	20458.9i	−0.873974	−	0.873974i
$154$		0			0
$155$	8251.86	−	19921.8i	0.343470	−	0.829210i
$156$		0			0
$157$	13546.2	+	32703.4i	0.549564	+	1.32676i	0.917804	+	0.397033i	$0.129960\pi$
$157$	13546.2	+	32703.4i	0.549564	+	1.32676i	−0.368241	+	0.929730i	$0.620040\pi$
$158$		0			0
$159$		−	17542.6i		−	0.693906i
$160$		0			0
$161$	60.0165			0.00231536
$162$		0			0
$163$	−40162.0	+	16635.7i	−1.51161	+	0.626131i	−0.975890	−	0.218263i	$-0.929961\pi$
$163$	−40162.0	+	16635.7i	−1.51161	+	0.626131i	−0.535723	+	0.844394i	$0.679961\pi$
$164$		0			0
$165$	−2586.88	−	1071.52i	−0.0950187	−	0.0393580i
$166$		0			0
$167$	23691.3	−	23691.3i	0.849487	−	0.849487i	−0.140582	−	0.990069i	$-0.544897\pi$
$167$	23691.3	−	23691.3i	0.849487	−	0.849487i	0.990069	+	0.140582i	$0.0448973\pi$
$168$		0			0
$169$	1142.81	−	1142.81i	0.0400129	−	0.0400129i
$170$		0			0
$171$	−3280.30	−	1358.75i	−0.112182	−	0.0464672i
$172$		0			0
$173$	16259.4	−	6734.87i	0.543266	−	0.225028i	−0.0941363	−	0.995559i	$-0.530009\pi$
$173$	16259.4	−	6734.87i	0.543266	−	0.225028i	0.637402	+	0.770531i	$0.280009\pi$
$174$		0			0
$175$	26.1343			0.000853365
$176$		0			0
$177$		−	29456.9i		−	0.940244i
$178$		0			0
$179$	−8846.29	−	21356.8i	−0.276093	−	0.666547i	0.723628	−	0.690191i	$-0.242473\pi$
$179$	−8846.29	−	21356.8i	−0.276093	−	0.666547i	−0.999720	+	0.0236434i	$0.992473\pi$
$180$		0			0
$181$	−5831.93	+	14079.5i	−0.178014	+	0.429765i	−0.987550	−	0.157306i	$-0.949719\pi$
$181$	−5831.93	+	14079.5i	−0.178014	+	0.429765i	0.809536	+	0.587071i	$0.199719\pi$
$182$		0			0
$183$	−1168.03	−	1168.03i	−0.0348781	−	0.0348781i
$184$		0			0
$185$	13783.3	+	13783.3i	0.402725	+	0.402725i
$186$		0			0
$187$	−5409.82	+	13060.5i	−0.154703	+	0.373487i
$188$		0			0
$189$	−33.8003	−	81.6012i	−0.000946231	−	0.00228440i
$190$		0			0
$191$			23418.5i			0.641938i	0.947090	+	0.320969i	$0.104008\pi$
$191$			23418.5i			0.641938i	−0.947090	+	0.320969i	$0.895992\pi$
$192$		0			0
$193$	11363.1			0.305057			0.152528	−	0.988299i	$-0.451258\pi$
$193$	11363.1			0.305057			0.152528	+	0.988299i	$0.451258\pi$
$194$		0			0
$195$	15382.8	−	6371.75i	0.404544	−	0.167568i
$196$		0			0
$197$	−30324.7	−	12560.9i	−0.781382	−	0.323659i	−0.0439091	−	0.999036i	$-0.513981\pi$
$197$	−30324.7	−	12560.9i	−0.781382	−	0.323659i	−0.737473	+	0.675376i	$0.763981\pi$
$198$		0			0
$199$	−5712.36	+	5712.36i	−0.144248	+	0.144248i	−0.775543	−	0.631295i	$-0.782524\pi$
$199$	−5712.36	+	5712.36i	−0.144248	+	0.144248i	0.631295	+	0.775543i	$0.282524\pi$
$200$		0			0
$201$	22292.7	−	22292.7i	0.551786	−	0.551786i
$202$		0			0
$203$	13.0615	+	5.41026i	0.000316958	+	0.000131288i
$204$		0			0
$205$	31033.0	−	12854.3i	0.738441	−	0.305872i
$206$		0			0
$207$	26342.7			0.614780
$208$		0			0
$209$			1734.78i			0.0397149i
$210$		0			0
$211$	7578.29	+	18295.6i	0.170218	+	0.410943i	0.985850	−	0.167628i	$-0.0536106\pi$
$211$	7578.29	+	18295.6i	0.170218	+	0.410943i	−0.815632	+	0.578571i	$0.803611\pi$
$212$		0			0
$213$	13402.4	−	32356.4i	0.295410	−	0.713182i
$214$		0			0
$215$	−16597.5	−	16597.5i	−0.359059	−	0.359059i
$216$		0			0
$217$	−99.7985	−	99.7985i	−0.00211936	−	0.00211936i
$218$		0			0
$219$	−6938.05	+	16749.9i	−0.144660	+	0.349241i
$220$		0			0
$221$	−32169.3	−	77663.5i	−0.658653	−	1.59013i
$222$		0			0
$223$		−	30688.1i		−	0.617108i	−0.951207	−	0.308554i	$-0.900155\pi$
$223$		−	30688.1i		−	0.617108i	0.951207	−	0.308554i	$-0.0998450\pi$
$224$		0			0
$225$	11471.0			0.226587
$226$		0			0
$227$	37054.2	−	15348.4i	0.719094	−	0.297859i	0.00703232	−	0.999975i	$-0.497762\pi$
$227$	37054.2	−	15348.4i	0.719094	−	0.297859i	0.712062	+	0.702117i	$0.247762\pi$
$228$		0			0
$229$	54035.1	+	22382.1i	1.03040	+	0.426805i	0.832856	−	0.553489i	$-0.186704\pi$
$229$	54035.1	+	22382.1i	1.03040	+	0.426805i	0.197542	+	0.980294i	$0.436704\pi$
$230$		0			0
$231$	−12.9590	+	12.9590i	−0.000242856	+	0.000242856i
$232$		0			0
$233$	32696.7	−	32696.7i	0.602272	−	0.602272i	−0.338643	−	0.940915i	$-0.609968\pi$
$233$	32696.7	−	32696.7i	0.602272	−	0.602272i	0.940915	+	0.338643i	$0.109968\pi$
$234$		0			0
$235$	84149.3	+	34855.8i	1.52375	+	0.631159i
$236$		0			0
$237$	−6245.85	+	2587.12i	−0.111197	+	0.0460595i
$238$		0			0
$239$	−24842.9			−0.434918			−0.217459	−	0.976069i	$-0.569777\pi$
$239$	−24842.9			−0.434918			−0.217459	+	0.976069i	$0.569777\pi$
$240$		0			0
$241$			57619.9i			0.992061i	0.868305	+	0.496031i	$0.165210\pi$
$241$			57619.9i			0.992061i	−0.868305	+	0.496031i	$0.834790\pi$
$242$		0			0
$243$	−23371.1	−	56422.9i	−0.395792	−	0.955527i
$244$		0			0
$245$	19122.6	−	46166.0i	0.318577	−	0.769113i
$246$		0			0
$247$	−7294.38	−	7294.38i	−0.119562	−	0.119562i
$248$		0			0
$249$	22412.7	+	22412.7i	0.361489	+	0.361489i
$250$		0			0
$251$	26353.9	−	63623.8i	0.418308	−	1.00989i	−0.564529	−	0.825413i	$-0.690942\pi$
$251$	26353.9	−	63623.8i	0.418308	−	1.00989i	0.982838	−	0.184473i	$-0.0590578\pi$
$252$		0			0
$253$	−4925.46	−	11891.1i	−0.0769496	−	0.185773i
$254$		0			0
$255$		−	46381.2i		−	0.713283i
$256$		0			0
$257$	−35214.2			−0.533153			−0.266577	−	0.963814i	$-0.585893\pi$
$257$	−35214.2			−0.533153			−0.266577	+	0.963814i	$0.585893\pi$
$258$		0			0
$259$	117.872	−	48.8240i	0.00175715	−	0.000727836i
$260$		0			0
$261$	5733.03	+	2374.70i	0.0841595	+	0.0348600i
$262$		0			0
$263$	−70731.4	+	70731.4i	−1.02259	+	1.02259i	−0.0228498	+	0.999739i	$0.507274\pi$
$263$	−70731.4	+	70731.4i	−1.02259	+	1.02259i	−0.999739	+	0.0228498i	$0.992726\pi$
$264$		0			0
$265$	−56057.9	+	56057.9i	−0.798261	+	0.798261i
$266$		0			0
$267$	−12208.8	−	5057.05i	−0.171258	−	0.0709373i
$268$		0			0
$269$	3582.79	−	1484.04i	0.0495128	−	0.0205089i	−0.357790	−	0.933802i	$-0.616470\pi$
$269$	3582.79	−	1484.04i	0.0495128	−	0.0205089i	0.407302	+	0.913293i	$0.366470\pi$
$270$		0			0
$271$	57362.1			0.781064			0.390532	−	0.920589i	$-0.372291\pi$
$271$	57362.1			0.781064			0.390532	+	0.920589i	$0.372291\pi$
$272$		0			0
$273$		−	108.980i		−	0.00146225i
$274$		0			0
$275$	−2144.80	−	5178.01i	−0.0283610	−	0.0684695i
$276$		0			0
$277$	−49854.5	+	120359.i	−0.649748	+	1.56863i	0.163392	+	0.986561i	$0.447757\pi$
$277$	−49854.5	+	120359.i	−0.649748	+	1.56863i	−0.813139	+	0.582069i	$0.802243\pi$
$278$		0			0
$279$	−43804.0	−	43804.0i	−0.562737	−	0.562737i
$280$		0			0
$281$	42262.1	+	42262.1i	0.535228	+	0.535228i	0.922123	−	0.386896i	$-0.126453\pi$
$281$	42262.1	+	42262.1i	0.535228	+	0.535228i	−0.386896	+	0.922123i	$0.626453\pi$
$282$		0			0
$283$	−43622.6	+	105314.i	−0.544677	+	1.31497i	0.376714	+	0.926330i	$0.377054\pi$
$283$	−43622.6	+	105314.i	−0.544677	+	1.31497i	−0.921391	+	0.388637i	$0.872946\pi$
$284$		0			0
$285$	−2178.13	−	5258.47i	−0.0268160	−	0.0647396i
$286$		0			0
$287$		−	219.854i		−	0.00266914i
$288$		0			0
$289$	−150645.			−1.80368
$290$		0			0
$291$	46864.3	−	19411.8i	0.553421	−	0.229235i
$292$		0			0
$293$	−26931.5	−	11155.4i	−0.313708	−	0.129942i	0.220274	−	0.975438i	$-0.429305\pi$
$293$	−26931.5	−	11155.4i	−0.313708	−	0.129942i	−0.533982	+	0.845496i	$0.679305\pi$
$294$		0			0
$295$	−94130.1	+	94130.1i	−1.08164	+	1.08164i
$296$		0			0
$297$	−13393.8	+	13393.8i	−0.151841	+	0.151841i
$298$		0			0
$299$	70710.0	+	29289.0i	0.790931	+	0.327614i
$300$		0			0
$301$	−141.938	+	58.7927i	−0.00156663	+	0.000648919i
$302$		0			0
$303$	10662.0			0.116132
$304$		0			0
$305$			7464.95i			0.0802467i
$306$		0			0
$307$	−7683.00	−	18548.4i	−0.0815181	−	0.196802i	0.877865	−	0.478908i	$-0.158967\pi$
$307$	−7683.00	−	18548.4i	−0.0815181	−	0.196802i	−0.959383	+	0.282106i	$0.908967\pi$
$308$		0			0
$309$	415.489	−	1003.08i	0.00435154	−	0.0105055i
$310$		0			0
$311$	17775.4	+	17775.4i	0.183780	+	0.183780i	0.793001	−	0.609221i	$-0.208518\pi$
$311$	17775.4	+	17775.4i	0.183780	+	0.183780i	−0.609221	+	0.793001i	$0.708518\pi$
$312$		0			0
$313$	86212.3	+	86212.3i	0.879996	+	0.879996i	0.993534	−	0.113537i	$-0.0362182\pi$
$313$	86212.3	+	86212.3i	0.879996	+	0.879996i	−0.113537	+	0.993534i	$0.536218\pi$
$314$		0			0
$315$	−64.8690	+	156.608i	−0.000653757	+	0.00157831i
$316$		0			0
$317$	−65298.9	−	157645.i	−0.649811	−	1.56878i	−0.813048	−	0.582197i	$-0.802193\pi$
$317$	−65298.9	−	157645.i	−0.649811	−	1.56878i	0.163237	−	0.986587i	$-0.447807\pi$
$318$		0			0
$319$		−	3031.90i		−	0.0297944i
$320$		0			0
$321$	−83346.6			−0.808869
$322$		0			0
$323$	−26548.6	+	10996.8i	−0.254470	+	0.105405i
$324$		0			0
$325$	30790.8	+	12754.0i	0.291510	+	0.120748i
$326$		0			0
$327$	−44845.9	+	44845.9i	−0.419399	+	0.419399i
$328$		0			0
$329$	421.548	−	421.548i	0.00389453	−	0.00389453i
$330$		0			0
$331$	75692.8	+	31353.0i	0.690873	+	0.286169i	0.700364	−	0.713786i	$-0.253021\pi$
$331$	75692.8	+	31353.0i	0.690873	+	0.286169i	−0.00949058	+	0.999955i	$0.503021\pi$
$332$		0			0
$333$	51736.7	−	21430.0i	0.466563	−	0.193257i
$334$		0			0
$335$	−142473.			−1.26953
$336$		0			0
$337$			22016.6i			0.193861i	0.995291	+	0.0969306i	$0.0309025\pi$
$337$			22016.6i			0.193861i	−0.995291	+	0.0969306i	$0.969098\pi$
$338$		0			0
$339$	−732.215	−	1767.72i	−0.00637146	−	0.0153821i
$340$		0			0
$341$	−11582.8	+	27963.5i	−0.0996108	+	0.240482i
$342$		0			0
$343$	−462.541	−	462.541i	−0.00393153	−	0.00393153i
$344$		0			0
$345$	29860.1	+	29860.1i	0.250873	+	0.250873i
$346$		0			0
$347$	−6426.22	+	15514.3i	−0.0533700	+	0.128847i	−0.948316	−	0.317329i	$-0.897214\pi$
$347$	−6426.22	+	15514.3i	−0.0533700	+	0.128847i	0.894946	+	0.446175i	$0.147214\pi$
$348$		0			0
$349$	−4857.21	−	11726.3i	−0.0398782	−	0.0962746i	0.902685	−	0.430301i	$-0.141593\pi$
$349$	−4857.21	−	11726.3i	−0.0398782	−	0.0962746i	−0.942564	+	0.334026i	$0.891593\pi$
$350$		0			0
$351$		−	112636.i		−	0.914242i
$352$		0			0
$353$	109650.			0.879956			0.439978	−	0.898009i	$-0.354986\pi$
$353$	109650.			0.879956			0.439978	+	0.898009i	$0.354986\pi$
$354$		0			0
$355$	−146223.	+	60567.6i	−1.16027	+	0.480600i
$356$		0			0
$357$	−280.468	−	116.174i	−0.00220063	−	0.000911532i
$358$		0			0
$359$	−47086.6	+	47086.6i	−0.365349	+	0.365349i	−0.865778	−	0.500429i	$-0.833176\pi$
$359$	−47086.6	+	47086.6i	−0.365349	+	0.365349i	0.500429	+	0.865778i	$0.333176\pi$
$360$		0			0
$361$	89657.3	−	89657.3i	0.687973	−	0.687973i
$362$		0			0
$363$	−58663.1	−	24299.1i	−0.445197	−	0.184407i
$364$		0			0
$365$	75695.4	−	31354.0i	0.568177	−	0.235347i
$366$		0			0
$367$	187280.			1.39046			0.695230	−	0.718787i	$-0.255302\pi$
$367$	187280.			1.39046			0.695230	+	0.718787i	$0.255302\pi$
$368$		0			0
$369$		−	96499.3i		−	0.708715i
$370$		0			0
$371$	198.572	+	479.395i	0.00144268	+	0.00348294i
$372$		0			0
$373$	−33844.6	+	81708.0i	−0.243260	+	0.587283i	−0.997603	−	0.0691985i	$-0.977956\pi$
$373$	−33844.6	+	81708.0i	−0.243260	+	0.587283i	0.754342	+	0.656481i	$0.227956\pi$
$374$		0			0
$375$	55361.6	+	55361.6i	0.393682	+	0.393682i
$376$		0			0
$377$	12748.5	+	12748.5i	0.0896965	+	0.0896965i
$378$		0			0
$379$	5632.15	−	13597.2i	0.0392099	−	0.0946611i	−0.903061	−	0.429511i	$-0.858686\pi$
$379$	5632.15	−	13597.2i	0.0392099	−	0.0946611i	0.942271	+	0.334850i	$0.108686\pi$
$380$		0			0
$381$	49740.1	+	120083.i	0.342655	+	0.827242i
$382$		0			0
$383$			114224.i			0.778680i	0.921094	+	0.389340i	$0.127297\pi$
$383$			114224.i			0.778680i	−0.921094	+	0.389340i	$0.872703\pi$
$384$		0			0
$385$	82.8217			0.000558757
$386$		0			0
$387$	−62300.1	+	25805.6i	−0.415975	+	0.172302i
$388$		0			0
$389$	−144705.	−	59938.7i	−0.956278	−	0.396103i	−0.150691	−	0.988581i	$-0.548150\pi$
$389$	−144705.	−	59938.7i	−0.956278	−	0.396103i	−0.805587	+	0.592478i	$0.798150\pi$
$390$		0			0
$391$	150756.	−	150756.i	0.986097	−	0.986097i
$392$		0			0
$393$	13756.6	−	13756.6i	0.0890687	−	0.0890687i
$394$		0			0
$395$	28225.9	+	11691.6i	0.180906	+	0.0749338i
$396$		0			0
$397$	−68716.8	+	28463.4i	−0.435996	+	0.180595i	−0.589875	−	0.807494i	$-0.700823\pi$
$397$	−68716.8	+	28463.4i	−0.435996	+	0.180595i	0.153880	+	0.988090i	$0.450823\pi$
$398$		0			0
$399$	−37.2538			−0.000234005
$400$		0			0
$401$		−	39692.7i		−	0.246844i	−0.992354	−	0.123422i	$-0.960613\pi$
$401$		−	39692.7i		−	0.246844i	0.992354	−	0.123422i	$-0.0393868\pi$
$402$		0			0
$403$	−68876.8	−	166283.i	−0.424095	−	1.02386i
$404$		0			0
$405$	−14790.1	+	35706.4i	−0.0901695	+	0.217689i
$406$		0			0
$407$	−19347.1	−	19347.1i	−0.116796	−	0.116796i
$408$		0			0
$409$	−190982.	−	190982.i	−1.14169	−	1.14169i	−0.988142	−	0.153544i	$-0.950931\pi$
$409$	−190982.	−	190982.i	−1.14169	−	1.14169i	−0.153544	−	0.988142i	$-0.549069\pi$
$410$		0			0
$411$	−24903.4	+	60122.2i	−0.147426	+	0.355919i
$412$		0			0
$413$	333.434	+	804.981i	0.00195483	+	0.00471938i
$414$		0			0
$415$		−	143240.i		−	0.831704i
$416$		0			0
$417$	−90258.4			−0.519057
$418$		0			0
$419$	181013.	−	74978.1i	1.03106	−	0.427077i	0.197962	−	0.980210i	$-0.436568\pi$
$419$	181013.	−	74978.1i	1.03106	−	0.427077i	0.833093	+	0.553132i	$0.186568\pi$
$420$		0			0
$421$	238796.	+	98912.5i	1.34729	+	0.558068i	0.935538	−	0.353226i	$-0.114915\pi$
$421$	238796.	+	98912.5i	1.34729	+	0.558068i	0.411757	+	0.911294i	$0.364915\pi$
$422$		0			0
$423$	185028.	−	185028.i	1.03408	−	1.03408i
$424$		0			0
$425$	65646.7	−	65646.7i	0.363442	−	0.363442i
$426$		0			0
$427$	45.1407	+	18.6979i	0.000247578	+	0.000102550i
$428$		0			0
$429$	−21592.2	+	8943.80i	−0.117323	+	0.0485968i
$430$		0			0
$431$	345902.			1.86208			0.931041	−	0.364915i	$-0.118902\pi$
$431$	345902.			1.86208			0.931041	+	0.364915i	$0.118902\pi$
$432$		0			0
$433$			37139.4i			0.198088i	0.995083	+	0.0990442i	$0.0315785\pi$
$433$			37139.4i			0.198088i	−0.995083	+	0.0990442i	$0.968421\pi$
$434$		0			0
$435$	3806.75	+	9190.30i	0.0201176	+	0.0485681i
$436$		0			0
$437$	10012.2	−	24171.6i	0.0524285	−	0.126574i
$438$		0			0
$439$	−20991.7	−	20991.7i	−0.108923	−	0.108923i	0.650545	−	0.759468i	$-0.274540\pi$
$439$	−20991.7	−	20991.7i	−0.108923	−	0.108923i	−0.759468	+	0.650545i	$0.774540\pi$
$440$		0			0
$441$	−101510.	−	101510.i	−0.521953	−	0.521953i
$442$		0			0
$443$	37993.2	−	91723.7i	0.193597	−	0.467384i	−0.797037	−	0.603931i	$-0.793600\pi$
$443$	37993.2	−	91723.7i	0.193597	−	0.467384i	0.990634	+	0.136546i	$0.0436003\pi$
$444$		0			0
$445$	22853.5	+	55173.3i	0.115407	+	0.278618i
$446$		0			0
$447$			108041.i			0.540720i
$448$		0			0
$449$	174269.			0.864427			0.432213	−	0.901771i	$-0.357733\pi$
$449$	174269.			0.864427			0.432213	+	0.901771i	$0.357733\pi$
$450$		0			0
$451$	−43559.9	+	18043.1i	−0.214158	+	0.0887070i
$452$		0			0
$453$	113317.	+	46937.5i	0.552203	+	0.228730i
$454$		0			0
$455$	−348.247	+	348.247i	−0.00168215	+	0.00168215i
$456$		0			0
$457$	149698.	−	149698.i	0.716777	−	0.716777i	−0.251167	−	0.967944i	$-0.580814\pi$
$457$	149698.	−	149698.i	0.716777	−	0.716777i	0.967944	+	0.251167i	$0.0808142\pi$
$458$		0			0
$459$	−289877.	−	120071.i	−1.37590	−	0.569918i
$460$		0			0
$461$	−58965.5	+	24424.3i	−0.277457	+	0.114927i	−0.517073	−	0.855941i	$-0.672979\pi$
$461$	−58965.5	+	24424.3i	−0.277457	+	0.114927i	0.239616	+	0.970868i	$0.422979\pi$
$462$		0			0
$463$	−217616.			−1.01515			−0.507573	−	0.861609i	$-0.669457\pi$
$463$	−217616.			−1.01515			−0.507573	+	0.861609i	$0.669457\pi$
$464$		0			0
$465$		−	99305.7i		−	0.459270i
$466$		0			0
$467$	−75272.5	−	181724.i	−0.345146	−	0.833256i	−0.997179	−	0.0750649i	$-0.976084\pi$
$467$	−75272.5	−	181724.i	−0.345146	−	0.833256i	0.652033	−	0.758191i	$-0.273916\pi$
$468$		0			0
$469$	−356.862	+	861.541i	−0.00162239	+	0.00391679i
$470$		0			0
$471$	115272.	+	115272.i	0.519616	+	0.519616i
$472$		0			0
$473$	23297.3	+	23297.3i	0.104132	+	0.104132i
$474$		0			0
$475$	4359.83	−	10525.6i	0.0193234	−	0.0466507i
$476$		0			0
$477$	87158.0	+	210418.i	0.383063	+	0.924797i
$478$		0			0
$479$			220847.i			0.962545i	0.876571	+	0.481272i	$0.159825\pi$
$479$			220847.i			0.962545i	−0.876571	+	0.481272i	$0.840175\pi$
$480$		0			0
$481$	162700.			0.703231
$482$		0			0
$483$	255.357	−	105.772i	0.00109460	−	0.000453397i
$484$		0			0
$485$	−211786.	−	87724.8i	−0.900357	−	0.372940i
$486$		0			0
$487$	−38468.1	+	38468.1i	−0.162197	+	0.162197i	−0.783539	−	0.621342i	$-0.786588\pi$
$487$	−38468.1	+	38468.1i	−0.162197	+	0.162197i	0.621342	+	0.783539i	$0.286588\pi$
$488$		0			0
$489$	−141562.	+	141562.i	−0.592011	+	0.592011i
$490$		0			0
$491$	122634.	+	50796.5i	0.508682	+	0.210703i	0.622237	−	0.782829i	$-0.286224\pi$
$491$	122634.	+	50796.5i	0.508682	+	0.210703i	−0.113555	+	0.993532i	$0.536224\pi$
$492$		0			0
$493$	46399.3	−	19219.2i	0.190905	−	0.0790755i
$494$		0			0
$495$	36352.5			0.148362
$496$		0			0
$497$			1035.92i			0.00419387i
$498$		0			0
$499$	145115.	+	350340.i	0.582791	+	1.40698i	0.890273	+	0.455427i	$0.150514\pi$
$499$	145115.	+	350340.i	0.582791	+	1.40698i	−0.307482	+	0.951554i	$0.599486\pi$
$500$		0			0
$501$	59048.1	−	142555.i	0.235251	−	0.567945i
$502$		0			0
$503$	−148742.	−	148742.i	−0.587893	−	0.587893i	0.349167	−	0.937060i	$-0.386465\pi$
$503$	−148742.	−	148742.i	−0.587893	−	0.587893i	−0.937060	+	0.349167i	$0.886465\pi$
$504$		0			0
$505$	−34070.6	−	34070.6i	−0.133597	−	0.133597i
$506$		0			0
$507$	2848.33	−	6876.48i	0.0110809	−	0.0267516i
$508$		0			0
$509$	60952.5	+	147152.i	0.235264	+	0.567978i	0.996781	−	0.0801666i	$-0.0255452\pi$
$509$	60952.5	+	147152.i	0.235264	+	0.567978i	−0.761517	+	0.648145i	$0.775545\pi$
$510$		0			0
$511$		−	536.266i		−	0.00205371i
$512$		0			0
$513$	−38503.5			−0.146307
$514$		0			0
$515$	−4533.06	+	1877.66i	−0.0170914	+	0.00707949i
$516$		0			0
$517$	−118117.	−	48925.8i	−0.441909	−	0.183045i
$518$		0			0
$519$	57310.8	−	57310.8i	0.212766	−	0.212766i
$520$		0			0
$521$	−293122.	+	293122.i	−1.07987	+	1.07987i	−0.0833527	+	0.996520i	$0.526563\pi$
$521$	−293122.	+	293122.i	−1.07987	+	1.07987i	−0.996520	+	0.0833527i	$0.973437\pi$
$522$		0			0
$523$	−343753.	−	142387.i	−1.25673	−	0.520556i	−0.347828	−	0.937558i	$-0.613081\pi$
$523$	−343753.	−	142387.i	−1.25673	−	0.520556i	−0.908905	+	0.417002i	$0.863081\pi$
$524$		0			0
$525$	111.196	−	46.0588i	0.000403431	−	0.000167107i
$526$		0			0
$527$	−501368.			−1.80524
$528$		0			0
$529$		−	85729.0i		−	0.306349i
$530$		0			0
$531$	146352.	+	353326.i	0.519052	+	1.25310i
$532$		0			0
$533$	107292.	−	259027.i	0.377672	−	0.911780i
$534$		0			0
$535$	266336.	+	266336.i	0.930512	+	0.930512i
$536$		0			0
$537$	−75278.1	−	75278.1i	−0.261048	−	0.261048i
$538$		0			0
$539$	−26841.7	+	64801.6i	−0.0923916	+	0.223053i
$540$		0			0
$541$	−50826.0	−	122705.i	−0.173657	−	0.419245i	0.812956	−	0.582325i	$-0.197857\pi$
$541$	−50826.0	−	122705.i	−0.173657	−	0.419245i	−0.986613	+	0.163081i	$0.947857\pi$
$542$		0			0
$543$			70183.4i			0.238032i
$544$		0			0
$545$	286612.			0.964942
$546$		0			0
$547$	−283133.	+	117277.i	−0.946271	+	0.391958i	−0.801828	−	0.597555i	$-0.796139\pi$
$547$	−283133.	+	117277.i	−0.946271	+	0.391958i	−0.144443	+	0.989513i	$0.546139\pi$
$548$		0			0
$549$	19813.4	+	8206.97i	0.0657376	+	0.0272294i
$550$		0			0
$551$	4357.96	−	4357.96i	0.0143542	−	0.0143542i
$552$		0			0
$553$	141.398	−	141.398i	0.000462374	−	0.000462374i
$554$		0			0
$555$	82936.2	+	34353.3i	0.269252	+	0.111528i
$556$		0			0
$557$	−517671.	+	214426.i	−1.66857	+	0.691143i	−0.998682	−	0.0513222i	$-0.983656\pi$
$557$	−517671.	+	214426.i	−1.66857	+	0.691143i	−0.669885	+	0.742465i	$0.733656\pi$
$558$		0			0
$559$	−195920.			−0.626981
$560$		0			0
$561$			65103.6i			0.206861i
$562$		0			0
$563$	138778.	+	335041.i	0.437830	+	1.05701i	0.976697	+	0.214623i	$0.0688524\pi$
$563$	138778.	+	335041.i	0.437830	+	1.05701i	−0.538867	+	0.842391i	$0.681148\pi$
$564$		0			0
$565$	−3308.99	+	7988.60i	−0.0103657	+	0.0250250i
$566$		0			0
$567$	178.872	+	178.872i	0.000556385	+	0.000556385i
$568$		0			0
$569$	−18905.5	−	18905.5i	−0.0583933	−	0.0583933i	0.677307	−	0.735700i	$-0.263147\pi$
$569$	−18905.5	−	18905.5i	−0.0583933	−	0.0583933i	−0.735700	+	0.677307i	$0.763147\pi$
$570$		0			0
$571$	164837.	−	397953.i	0.505573	−	1.22056i	−0.440836	−	0.897588i	$-0.645318\pi$
$571$	164837.	−	397953.i	0.505573	−	1.22056i	0.946408	−	0.322973i	$-0.104682\pi$
$572$		0			0
$573$	41272.5	+	99640.7i	0.125705	+	0.303478i
$574$		0			0
$575$			84526.4i			0.255656i
$576$		0			0
$577$	−169750.			−0.509868			−0.254934	−	0.966958i	$-0.582054\pi$
$577$	−169750.			−0.509868			−0.254934	+	0.966958i	$0.582054\pi$
$578$		0			0
$579$	48347.3	−	20026.1i	0.144217	−	0.0597365i
$580$		0			0
$581$	−866.177	−	358.782i	−0.00256599	−	0.00106287i
$582$		0			0
$583$	78686.4	−	78686.4i	0.231506	−	0.231506i
$584$		0			0
$585$	−152854.	+	152854.i	−0.446648	+	0.446648i
$586$		0			0
$587$	−514330.	−	213043.i	−1.49268	−	0.618287i	−0.520779	−	0.853691i	$-0.674359\pi$
$587$	−514330.	−	213043.i	−1.49268	−	0.618287i	−0.971898	+	0.235404i	$0.924359\pi$
$588$		0			0
$589$	−56842.6	+	23545.0i	−0.163849	+	0.0678684i
$590$		0			0
$591$	−151162.			−0.432780
$592$		0			0
$593$			623638.i			1.77347i	0.462280	+	0.886734i	$0.347032\pi$
$593$			623638.i			1.77347i	−0.462280	+	0.886734i	$0.652968\pi$
$594$		0			0
$595$	525.007	+	1267.48i	0.00148296	+	0.00358019i
$596$		0			0
$597$	−14237.5	+	34372.3i	−0.0399470	+	0.0964405i
$598$		0			0
$599$	−197935.	−	197935.i	−0.551656	−	0.551656i	0.375262	−	0.926919i	$-0.377553\pi$
$599$	−197935.	−	197935.i	−0.551656	−	0.551656i	−0.926919	+	0.375262i	$0.877553\pi$
$600$		0			0
$601$	208169.	+	208169.i	0.576324	+	0.576324i	0.933888	−	0.357565i	$-0.116393\pi$
$601$	208169.	+	208169.i	0.576324	+	0.576324i	−0.357565	+	0.933888i	$0.616393\pi$
$602$		0			0
$603$	−156635.	+	378151.i	−0.430780	+	1.03999i
$604$		0			0
$605$	109811.	+	265107.i	0.300010	+	0.724287i
$606$		0			0
$607$		−	366929.i		−	0.995876i	−0.867213	−	0.497938i	$-0.834091\pi$
$607$		−	366929.i		−	0.995876i	0.867213	−	0.497938i	$-0.165909\pi$
$608$		0			0
$609$	65.1090			0.000175552
$610$		0			0
$611$	702379.	−	290935.i	1.88143	−	0.779316i
$612$		0			0
$613$	−158274.	−	65559.1i	−0.421199	−	0.174466i	0.162009	−	0.986789i	$-0.448203\pi$
$613$	−158274.	−	65559.1i	−0.421199	−	0.174466i	−0.583208	+	0.812323i	$0.698203\pi$
$614$		0			0
$615$	109384.	−	109384.i	0.289204	−	0.289204i
$616$		0			0
$617$	−368691.	+	368691.i	−0.968482	+	0.968482i	−0.999518	−	0.0310361i	$-0.990119\pi$
$617$	−368691.	+	368691.i	−0.968482	+	0.968482i	0.0310361	+	0.999518i	$0.490119\pi$
$618$		0			0
$619$	557350.	+	230862.i	1.45461	+	0.602519i	0.963291	−	0.268461i	$-0.0865149\pi$
$619$	557350.	+	230862.i	1.45461	+	0.602519i	0.491319	+	0.870980i	$0.336515\pi$
$620$		0			0
$621$	263923.	−	109321.i	0.684376	−	0.283478i
$622$		0			0
$623$	390.877			0.00100708
$624$		0			0
$625$		−	233910.i		−	0.598811i
$626$		0			0
$627$	3057.36	+	7381.13i	0.00777700	+	0.0187753i
$628$		0			0
$629$	173441.	−	418722.i	0.438378	−	1.05834i
$630$		0			0
$631$	−121429.	−	121429.i	−0.304974	−	0.304974i	0.537982	−	0.842956i	$-0.319187\pi$
$631$	−121429.	−	121429.i	−0.304974	−	0.304974i	−0.842956	+	0.537982i	$0.819187\pi$
$632$		0			0
$633$	64487.9	+	64487.9i	0.160943	+	0.160943i
$634$		0			0
$635$	224783.	−	542674.i	0.557462	−	1.34583i
$636$		0			0
$637$	−159613.	−	385339.i	−0.393359	−	0.949652i
$638$		0			0
$639$			454692.i			1.11356i
$640$		0			0
$641$	627768.			1.52786			0.763929	−	0.645301i	$-0.223268\pi$
$641$	627768.			1.52786			0.763929	+	0.645301i	$0.223268\pi$
$642$		0			0
$643$	203948.	−	84478.0i	0.493284	−	0.204325i	−0.122152	−	0.992511i	$-0.538980\pi$
$643$	203948.	−	84478.0i	0.493284	−	0.204325i	0.615437	+	0.788186i	$0.288980\pi$
$644$		0			0
$645$	−99869.9	−	41367.5i	−0.240057	−	0.0994350i
$646$		0			0
$647$	−176458.	+	176458.i	−0.421533	+	0.421533i	−0.885731	−	0.464198i	$-0.846343\pi$
$647$	−176458.	+	176458.i	−0.421533	+	0.421533i	0.464198	+	0.885731i	$0.346343\pi$
$648$		0			0
$649$	132127.	−	132127.i	0.313691	−	0.313691i
$650$		0			0
$651$	−600.504	−	248.737i	−0.00141695	−	0.000586919i
$652$		0			0
$653$	151424.	−	62721.9i	0.355115	−	0.147093i	−0.197992	−	0.980204i	$-0.563442\pi$
$653$	151424.	−	62721.9i	0.355115	−	0.147093i	0.553107	+	0.833110i	$0.313442\pi$
$654$		0			0
$655$	−87918.7			−0.204927
$656$		0			0
$657$		−	235380.i		−	0.545305i
$658$		0			0
$659$	−5937.53	−	14334.5i	−0.0136721	−	0.0330074i	0.916896	−	0.399126i	$-0.130686\pi$
$659$	−5937.53	−	14334.5i	−0.0136721	−	0.0330074i	−0.930568	+	0.366119i	$0.880686\pi$
$660$		0			0
$661$	211201.	−	509885.i	0.483385	−	1.16700i	−0.474606	−	0.880198i	$-0.657410\pi$
$661$	211201.	−	509885.i	0.483385	−	1.16700i	0.957991	−	0.286797i	$-0.0925905\pi$
$662$		0			0
$663$	−273746.	−	273746.i	−0.622761	−	0.622761i
$664$		0			0
$665$	119.045	+	119.045i	0.000269196	+	0.000269196i
$666$		0			0
$667$	−17498.5	+	42245.0i	−0.0393322	+	0.0949563i
$668$		0			0
$669$	−54084.4	−	130571.i	−0.120843	−	0.291740i
$670$		0			0
$671$		−	10478.3i		−	0.0232726i
$672$		0			0
$673$	−542502.			−1.19776			−0.598882	−	0.800837i	$-0.704388\pi$
$673$	−542502.			−1.19776			−0.598882	+	0.800837i	$0.704388\pi$
$674$		0			0
$675$	114926.	−	47603.8i	0.252238	−	0.104480i
$676$		0			0
$677$	−140978.	−	58395.0i	−0.307591	−	0.127409i	0.223548	−	0.974693i	$-0.428236\pi$
$677$	−140978.	−	58395.0i	−0.307591	−	0.127409i	−0.531140	+	0.847284i	$0.678236\pi$
$678$		0			0
$679$	−1060.95	+	1060.95i	−0.00230120	+	0.00230120i
$680$		0			0
$681$	130608.	−	130608.i	0.281627	−	0.281627i
$682$		0			0
$683$	377337.	+	156298.i	0.808887	+	0.335052i	0.748510	−	0.663123i	$-0.230770\pi$
$683$	377337.	+	156298.i	0.808887	+	0.335052i	0.0603774	+	0.998176i	$0.480770\pi$
$684$		0			0
$685$	271701.	−	112542.i	0.579042	−	0.239847i
$686$		0			0
$687$	269354.			0.570702
$688$		0			0
$689$			661717.i			1.39391i
$690$		0			0
$691$	−142080.	−	343011.i	−0.297561	−	0.718376i	−0.999978	−	0.00661026i	$-0.997896\pi$
$691$	−142080.	−	343011.i	−0.297561	−	0.718376i	0.702417	−	0.711765i	$-0.252104\pi$
$692$		0			0
$693$	91.0543	−	219.824i	0.000189598	−	0.000457730i
$694$		0			0
$695$	288422.	+	288422.i	0.597117	+	0.597117i
$696$		0			0
$697$	−552251.	−	552251.i	−1.13677	−	1.13677i
$698$		0			0
$699$	81493.1	−	196742.i	0.166789	−	0.402664i
$700$		0			0
$701$	6668.05	+	16098.1i	0.0135695	+	0.0327596i	0.930519	−	0.366243i	$-0.119356\pi$
$701$	6668.05	+	16098.1i	0.0135695	+	0.0327596i	−0.916950	+	0.399003i	$0.869356\pi$
$702$		0			0
$703$		−	55617.7i		−	0.112539i
$704$		0			0
$705$	419466.			0.843954
$706$		0			0
$707$	−291.365	+	120.687i	−0.000582905	+	0.000241447i
$708$		0			0
$709$	751755.	+	311387.i	1.49549	+	0.619453i	0.972504	−	0.232887i	$-0.0748173\pi$
$709$	751755.	+	311387.i	1.49549	+	0.619453i	0.522988	+	0.852340i	$0.324817\pi$
$710$		0			0
$711$	62063.2	−	62063.2i	0.122771	−	0.122771i
$712$		0			0
$713$	322779.	−	322779.i	0.634931	−	0.634931i
$714$		0			0
$715$	97578.5	+	40418.3i	0.190872	+	0.0790618i
$716$		0			0
$717$	−105701.	+	43782.9i	−0.205609	+	0.0851660i
$718$		0			0
$719$	−733621.			−1.41910			−0.709551	−	0.704654i	$-0.751102\pi$
$719$	−733621.			−1.41910			−0.709551	+	0.704654i	$0.751102\pi$
$720$		0			0
$721$			32.1146i			6.17778e-5i
$722$		0			0
$723$	101549.	+	245160.i	0.194266	+	0.469000i
$724$		0			0
$725$	−7619.73	+	18395.7i	−0.0144965	+	0.0349977i
$726$		0			0
$727$	−61334.7	−	61334.7i	−0.116048	−	0.116048i	0.646698	−	0.762746i	$-0.276149\pi$
$727$	−61334.7	−	61334.7i	−0.116048	−	0.116048i	−0.762746	+	0.646698i	$0.776149\pi$
$728$		0			0
$729$	−92517.2	−	92517.2i	−0.174087	−	0.174087i
$730$		0			0
$731$	−208853.	+	504216.i	−0.390846	+	0.943586i
$732$		0			0
$733$	−181101.	−	437217.i	−0.337065	−	0.813747i	−0.997995	−	0.0632991i	$-0.979838\pi$
$733$	−181101.	−	437217.i	−0.337065	−	0.813747i	0.660930	−	0.750448i	$-0.270162\pi$
$734$		0			0
$735$		−	230128.i		−	0.425985i
$736$		0			0
$737$	199985.			0.368182
$738$		0			0
$739$	−553639.	+	229325.i	−1.01377	+	0.419916i	−0.826827	−	0.562456i	$-0.809857\pi$
$739$	−553639.	+	229325.i	−1.01377	+	0.419916i	−0.186939	+	0.982372i	$0.559857\pi$
$740$		0			0
$741$	−43891.5	−	18180.5i	−0.0799363	−	0.0331107i
$742$		0			0
$743$	28237.4	−	28237.4i	0.0511502	−	0.0511502i	−0.681069	−	0.732219i	$-0.738485\pi$
$743$	28237.4	−	28237.4i	0.0511502	−	0.0511502i	0.732219	+	0.681069i	$0.238485\pi$
$744$		0			0
$745$	345246.	−	345246.i	0.622037	−	0.622037i
$746$		0			0
$747$	−380186.	−	157478.i	−0.681327	−	0.282215i
$748$		0			0
$749$	2277.65	−	943.432i	0.00405997	−	0.00168169i
$750$		0			0
$751$	948473.			1.68169			0.840844	−	0.541278i	$-0.182059\pi$
$751$	948473.			1.68169			0.840844	+	0.541278i	$0.182059\pi$
$752$		0			0
$753$		−	317151.i		−	0.559341i
$754$		0			0
$755$	−212117.	−	512096.i	−0.372119	−	0.898375i
$756$		0			0
$757$	−274715.	+	663221.i	−0.479392	+	1.15736i	0.480502	+	0.876993i	$0.340454\pi$
$757$	−274715.	+	663221.i	−0.479392	+	1.15736i	−0.959894	+	0.280362i	$0.909546\pi$
$758$		0			0
$759$	−41913.5	−	41913.5i	−0.0727563	−	0.0727563i
$760$		0			0
$761$	551759.	+	551759.i	0.952752	+	0.952752i	0.998933	−	0.0461807i	$-0.0147050\pi$
$761$	551759.	+	551759.i	0.952752	+	0.952752i	−0.0461807	+	0.998933i	$0.514705\pi$
$762$		0			0
$763$	717.894	−	1733.15i	0.00123314	−	0.00297706i
$764$		0			0
$765$	230438.	+	556327.i	0.393760	+	0.950621i
$766$		0			0
$767$			1.11113e6i			1.88875i
$768$		0			0
$769$	−843281.			−1.42600			−0.713000	−	0.701164i	$-0.752664\pi$
$769$	−843281.			−1.42600			−0.713000	+	0.701164i	$0.752664\pi$
$770$		0			0
$771$	−149829.	+	62061.1i	−0.252050	+	0.104403i
$772$		0			0
$773$	−281605.	−	116645.i	−0.471283	−	0.195212i	0.134385	−	0.990929i	$-0.457094\pi$
$773$	−281605.	−	116645.i	−0.471283	−	0.195212i	−0.605668	+	0.795717i	$0.707094\pi$
$774$		0			0
$775$	140555.	−	140555.i	0.234014	−	0.234014i
$776$		0			0
$777$	415.471	−	415.471i	0.000688174	−	0.000688174i
$778$		0			0
$779$	−88546.1	−	36677.0i	−0.145913	−	0.0604392i
$780$		0			0
$781$	205248.	−	85016.6i	0.336494	−	0.139380i
$782$		0			0
$783$	67293.1			0.109761
$784$		0			0
$785$		−	736709.i		−	1.19552i
$786$		0			0
$787$	−181707.	−	438679.i	−0.293374	−	0.708267i	−1.00000		0.000680029i	$-0.999784\pi$
$787$	−181707.	−	438679.i	−0.293374	−	0.708267i	0.706626	−	0.707587i	$-0.250216\pi$
$788$		0			0
$789$	−176291.	+	425603.i	−0.283188	+	0.683677i
$790$		0			0
$791$	40.0191	+	40.0191i	6.39608e−5	+	6.39608e-5i
$792$		0			0
$793$	44058.8	+	44058.8i	0.0700626	+	0.0700626i
$794$		0			0
$795$	−139718.	+	337310.i	−0.221064	+	0.533697i
$796$		0			0
$797$	60029.1	+	144923.i	0.0945029	+	0.228150i	0.964061	−	0.265680i	$-0.0855964\pi$
$797$	60029.1	+	144923.i	0.0945029	+	0.228150i	−0.869558	+	0.493830i	$0.835596\pi$
$798$		0			0
$799$		−	2.11777e6i		−	3.31730i
$800$		0			0
$801$	171566.			0.267402
$802$		0			0
$803$	−106251.	+	44010.5i	−0.164779	+	0.0682536i
$804$		0			0
$805$	−1154.00	−	478.001i	−0.00178079	−	0.000737627i
$806$		0			0
$807$	12628.5	−	12628.5i	0.0193913	−	0.0193913i
$808$		0			0
$809$	−342423.	+	342423.i	−0.523198	+	0.523198i	−0.918536	−	0.395338i	$-0.870628\pi$
$809$	−342423.	+	342423.i	−0.523198	+	0.523198i	0.395338	+	0.918536i	$0.370628\pi$
$810$		0			0
$811$	573123.	+	237396.i	0.871378	+	0.360936i	0.773147	−	0.634227i	$-0.218682\pi$
$811$	573123.	+	237396.i	0.871378	+	0.360936i	0.0982310	+	0.995164i	$0.468682\pi$
$812$		0			0
$813$	244063.	−	101094.i	0.369251	−	0.152949i
$814$		0			0
$815$	904729.			1.36208
$816$		0			0
$817$			66973.5i			0.100337i
$818$		0			0
$819$	541.450	+	1307.18i	0.000807217	+	0.00194880i
$820$		0			0
$821$	−393958.	+	951098.i	−0.584472	+	1.41104i	0.304250	+	0.952592i	$0.401594\pi$
$821$	−393958.	+	951098.i	−0.584472	+	1.41104i	−0.888722	+	0.458447i	$0.848406\pi$
$822$		0			0
$823$	554013.	+	554013.i	0.817938	+	0.817938i	0.985809	−	0.167871i	$-0.0536891\pi$
$823$	554013.	+	554013.i	0.817938	+	0.817938i	−0.167871	+	0.985809i	$0.553689\pi$
$824$		0			0
$825$	−18251.3	−	18251.3i	−0.0268155	−	0.0268155i
$826$		0			0
$827$	85698.1	−	206893.i	0.125303	−	0.302507i	−0.848763	−	0.528774i	$-0.822652\pi$
$827$	85698.1	−	206893.i	0.125303	−	0.302507i	0.974065	+	0.226266i	$0.0726520\pi$
$828$		0			0
$829$	−195068.	−	470936.i	−0.283842	−	0.685256i	0.716076	−	0.698022i	$-0.245936\pi$
$829$	−195068.	−	470936.i	−0.283842	−	0.685256i	−0.999919	+	0.0127664i	$0.995936\pi$
$830$		0			0
$831$			599966.i			0.868810i
$832$		0			0
$833$	−1.16185e6			−1.67441
$834$		0			0
$835$	−644226.	+	266847.i	−0.923986	+	0.382728i
$836$		0			0
$837$	−620649.	−	257081.i	−0.885921	−	0.366960i
$838$		0			0
$839$	−390367.	+	390367.i	−0.554561	+	0.554561i	−0.927754	−	0.373193i	$-0.878263\pi$
$839$	−390367.	+	390367.i	−0.554561	+	0.554561i	0.373193	+	0.927754i	$0.378263\pi$
$840$		0			0
$841$	492507.	−	492507.i	0.696338	−	0.696338i
$842$		0			0
$843$	254298.	+	105334.i	0.357839	+	0.148222i
$844$		0			0
$845$	−31075.8	+	12872.0i	−0.0435220	+	0.0180274i
$846$		0			0
$847$	1878.16			0.00261798
$848$		0			0
$849$			524970.i			0.728314i
$850$		0			0
$851$	157912.	+	381233.i	0.218050	+	0.526419i
$852$		0			0
$853$	−288331.	+	696092.i	−0.396272	+	0.956684i	0.592271	+	0.805739i	$0.298232\pi$
$853$	−288331.	+	696092.i	−0.396272	+	0.956684i	−0.988542	+	0.150945i	$0.951768\pi$
$854$		0			0
$855$	52251.9	+	52251.9i	0.0714776	+	0.0714776i
$856$		0			0
$857$	668098.	+	668098.i	0.909659	+	0.909659i	0.996244	−	0.0865850i	$-0.0275954\pi$
$857$	668098.	+	668098.i	0.909659	+	0.909659i	−0.0865850	+	0.996244i	$0.527595\pi$
$858$		0			0
$859$	−220837.	+	533149.i	−0.299286	+	0.722540i	0.700673	+	0.713483i	$0.252883\pi$
$859$	−220837.	+	533149.i	−0.299286	+	0.722540i	−0.999959	+	0.00905783i	$0.997117\pi$
$860$		0			0
$861$	−387.468	−	935.431i	−0.000522673	−	0.00126184i
$862$		0			0
$863$		−	464855.i		−	0.624160i	−0.950056	−	0.312080i	$-0.898974\pi$
$863$		−	464855.i		−	0.624160i	0.950056	−	0.312080i	$-0.101026\pi$
$864$		0			0
$865$	−366275.			−0.489526
$866$		0			0
$867$	−640962.	+	265495.i	−0.852696	+	0.353198i
$868$		0			0
$869$	−39619.7	−	16411.0i	−0.0524652	−	0.0217318i
$870$		0			0
$871$	−840892.	+	840892.i	−1.10842	+	1.10842i
$872$		0			0
$873$	−465676.	+	465676.i	−0.611020	+	0.611020i
$874$		0			0
$875$	−2139.55	−	886.229i	−0.00279451	−	0.00115752i
$876$		0			0
$877$	−1.07675e6	+	446004.i	−1.39996	+	0.579882i	−0.949741	−	0.313037i	$-0.898654\pi$
$877$	−1.07675e6	+	446004.i	−1.39996	+	0.579882i	−0.450218	+	0.892919i	$0.648654\pi$
$878$		0			0
$879$	−134248.			−0.173752
$880$		0			0
$881$		−	1.12565e6i		−	1.45028i	−0.688600	−	0.725141i	$-0.741774\pi$
$881$		−	1.12565e6i		−	1.45028i	0.688600	−	0.725141i	$-0.258226\pi$
$882$		0			0
$883$	−515412.	−	1.24431e6i	−0.661048	−	1.59591i	−0.796164	−	0.605081i	$-0.793141\pi$
$883$	−515412.	−	1.24431e6i	−0.661048	−	1.59591i	0.135116	−	0.990830i	$-0.456859\pi$
$884$		0			0
$885$	−234609.	+	566397.i	−0.299543	+	0.723160i
$886$		0			0
$887$	14692.0	+	14692.0i	0.0186738	+	0.0186738i	0.716382	−	0.697708i	$-0.245797\pi$
$887$	14692.0	+	14692.0i	0.0186738	+	0.0186738i	−0.697708	+	0.716382i	$0.745797\pi$
$888$		0			0
$889$	−2718.53	−	2718.53i	−0.00343979	−	0.00343979i
$890$		0			0
$891$	20760.3	−	50119.7i	0.0261504	−	0.0631325i
$892$		0			0
$893$	−99453.6	−	240102.i	−0.124715	−	0.301088i
$894$		0			0
$895$			481105.i			0.600612i
$896$		0			0
$897$	352474.			0.438069
$898$		0			0
$899$	99344.4	−	41149.8i	0.122920	−	0.0509153i
$900$		0			0
$901$	1.70298e6	+	705399.i	2.09779	+	0.868931i
$902$		0			0
$903$	−500.300	+	500.300i	−0.000613557	+	0.000613557i
$904$		0			0
$905$	224272.	−	224272.i	0.273828	−	0.273828i
$906$		0			0
$907$	−1.06334e6	−	440448.i	−1.29258	−	0.535402i	−0.372824	−	0.927902i	$-0.621610\pi$
$907$	−1.06334e6	−	440448.i	−1.29258	−	0.535402i	−0.919752	+	0.392500i	$0.871610\pi$
$908$		0			0
$909$	−127887.	+	52972.5i	−0.154774	+	0.0641096i
$910$		0			0
$911$	465871.			0.561344			0.280672	−	0.959804i	$-0.409443\pi$
$911$	465871.			0.561344			0.280672	+	0.959804i	$0.409443\pi$
$912$		0			0
$913$			201061.i			0.241205i
$914$		0			0
$915$	13156.1	+	31761.7i	0.0157140	+	0.0379369i
$916$		0			0
$917$	−220.215	+	531.647i	−0.000261884	+	0.000632244i
$918$		0			0
$919$	−49011.9	−	49011.9i	−0.0580324	−	0.0580324i	0.677495	−	0.735527i	$-0.263066\pi$
$919$	−49011.9	−	49011.9i	−0.0580324	−	0.0580324i	−0.735527	+	0.677495i	$0.763066\pi$
$920$		0			0
$921$	−65379.0	−	65379.0i	−0.0770759	−	0.0770759i
$922$		0			0
$923$	−505547.	+	1.22050e6i	−0.593414	+	1.43263i
$924$		0			0
$925$	68762.9	+	166008.i	0.0803658	+	0.194020i
$926$		0			0
$927$			14095.9i			0.0164034i
$928$		0			0
$929$	−673247.			−0.780087			−0.390044	−	0.920796i	$-0.627540\pi$
$929$	−673247.			−0.780087			−0.390044	+	0.920796i	$0.627540\pi$
$930$		0			0
$931$	−131725.	+	54562.3i	−0.151974	+	0.0629496i
$932$		0			0
$933$	106957.	+	44303.2i	0.122871	+	0.0508947i
$934$		0			0
$935$	208040.	−	208040.i	0.237971	−	0.237971i
$936$		0			0
$937$	1.07069e6	−	1.07069e6i	1.21951	−	1.21951i	0.251709	−	0.967803i	$-0.419008\pi$
$937$	1.07069e6	−	1.07069e6i	1.21951	−	1.21951i	0.967803	−	0.251709i	$-0.0809924\pi$
$938$		0			0
$939$	518754.	+	214875.i	0.588343	+	0.243700i
$940$		0			0
$941$	1.28905e6	−	533944.i	1.45577	−	0.602999i	0.492205	−	0.870479i	$-0.336191\pi$
$941$	1.28905e6	−	533944.i	1.45577	−	0.602999i	0.963563	+	0.267481i	$0.0861911\pi$
$942$		0			0
$943$	711076.			0.799636
$944$		0			0
$945$			1838.23i			0.00205843i
$946$		0			0
$947$	17762.4	+	42882.2i	0.0198062	+	0.0478164i	0.933473	−	0.358647i	$-0.116762\pi$
$947$	17762.4	+	42882.2i	0.0198062	+	0.0478164i	−0.913667	+	0.406463i	$0.866762\pi$
$948$		0			0
$949$	261707.	−	631816.i	0.290591	−	0.701549i
$950$		0			0
$951$	−555665.	−	555665.i	−0.614401	−	0.614401i
$952$		0			0
$953$	−621918.	−	621918.i	−0.684774	−	0.684774i	0.276298	−	0.961072i	$-0.410892\pi$
$953$	−621918.	−	621918.i	−0.684774	−	0.684774i	−0.961072	+	0.276298i	$0.910892\pi$
$954$		0			0
$955$	186517.	−	450291.i	0.204508	−	0.493726i
$956$		0			0
$957$	−5343.39	−	12900.1i	−0.00583436	−	0.0140854i
$958$		0			0
$959$		−	1924.87i		−	0.00209298i
$960$		0			0
$961$	−149945.			−0.162362
$962$		0			0
$963$	999715.	−	414096.i	1.07801	−	0.446527i
$964$		0			0
$965$	−218489.	−	90500.9i	−0.234625	−	0.0971848i
$966$		0			0
$967$	−1.01299e6	+	1.01299e6i	−1.08331	+	1.08331i	−0.0871073	+	0.996199i	$0.527762\pi$
$967$	−1.01299e6	+	1.01299e6i	−1.08331	+	1.08331i	−0.996199	+	0.0871073i	$0.972238\pi$
$968$		0			0
$969$	−93577.8	+	93577.8i	−0.0996611	+	0.0996611i
$970$		0			0
$971$	−1.11072e6	−	460077.i	−1.17806	−	0.487969i	−0.294211	−	0.955740i	$-0.595057\pi$
$971$	−1.11072e6	−	460077.i	−1.17806	−	0.487969i	−0.883849	+	0.467772i	$0.845057\pi$
$972$		0			0
$973$	2466.53	−	1021.67i	0.00260531	−	0.00107916i
$974$		0			0
$975$	153485.			0.161457
$976$		0			0
$977$		−	966138.i		−	1.01216i	−0.862486	−	0.506081i	$-0.831094\pi$
$977$		−	966138.i		−	1.01216i	0.862486	−	0.506081i	$-0.168906\pi$
$978$		0			0
$979$	−32078.7	−	77444.8i	−0.0334697	−	0.0808029i
$980$		0			0
$981$	315101.	−	760722.i	0.327425	−	0.790475i
$982$		0			0
$983$	354085.	+	354085.i	0.366438	+	0.366438i	0.866176	−	0.499739i	$-0.166571\pi$
$983$	354085.	+	354085.i	0.366438	+	0.366438i	−0.499739	+	0.866176i	$0.666571\pi$
$984$		0			0
$985$	483041.	+	483041.i	0.497865	+	0.497865i
$986$		0			0
$987$	1050.66	−	2536.52i	0.00107852	−	0.00260378i
$988$		0			0
$989$	−190154.	−	459072.i	−0.194407	−	0.469340i
$990$		0			0
$991$		−	1.03112e6i		−	1.04993i	−0.851124	−	0.524964i	$-0.824079\pi$
$991$		−	1.03112e6i		−	1.04993i	0.851124	−	0.524964i	$-0.175921\pi$
$992$		0			0
$993$	377312.			0.382651
$994$		0			0
$995$	155333.	−	64341.1i	0.156898	−	0.0649894i
$996$		0			0
$997$	400041.	+	165703.i	0.402453	+	0.166701i	0.574722	−	0.818349i	$-0.305110\pi$
$997$	400041.	+	165703.i	0.402453	+	0.166701i	−0.172270	+	0.985050i	$0.555110\pi$
$998$		0			0
$999$	429408.	−	429408.i	0.430268	−	0.430268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.h.a.15.10		60
4.3	odd	2		32.5.h.a.27.8	yes	60
32.13	even	8		32.5.h.a.19.8	✓	60
32.19	odd	8	inner	128.5.h.a.111.10		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.5.h.a.19.8	✓	60	32.13	even	8
32.5.h.a.27.8	yes	60	4.3	odd	2
128.5.h.a.15.10		60	1.1	even	1	trivial
128.5.h.a.111.10		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)

\(f(q)\)	\(=\)	\(q+(4.25478 - 1.76239i) q^{3} +(-19.2280 - 7.96449i) q^{5} +(-0.0963230 + 0.0963230i) q^{7} +(-42.2785 + 42.2785i) q^{9} +O(q^{10})\)	\(q+(4.25478 - 1.76239i) q^{3} +(-19.2280 - 7.96449i) q^{5} +(-0.0963230 + 0.0963230i) q^{7} +(-42.2785 + 42.2785i) q^{9} +(26.9896 + 11.1795i) q^{11} +(-160.492 + 66.4782i) q^{13} -95.8473 q^{15} +483.907i q^{17} +(22.7250 + 54.8630i) q^{19} +(-0.240075 + 0.579591i) q^{21} +(-311.538 - 311.538i) q^{23} +(-135.660 - 135.660i) q^{25} +(-248.128 + 599.034i) q^{27} +(-39.7168 - 95.8847i) q^{29} +1036.08i q^{31} +134.537 q^{33} +(2.61926 - 1.08493i) q^{35} +(-865.295 - 358.417i) q^{37} +(-565.700 + 565.700i) q^{39} +(-1141.23 + 1141.23i) q^{41} +(1041.97 + 431.597i) q^{43} +(1149.66 - 476.203i) q^{45} -4376.40 q^{47} +2400.98i q^{49} +(852.832 + 2058.92i) q^{51} +(1457.72 - 3519.24i) q^{53} +(-429.917 - 429.917i) q^{55} +(193.380 + 193.380i) q^{57} +(2447.74 - 5909.36i) q^{59} +(-137.261 - 331.378i) q^{61} -8.14478i q^{63} +3615.41 q^{65} +(6324.57 - 2619.72i) q^{67} +(-1874.58 - 776.475i) q^{69} +(5377.34 - 5377.34i) q^{71} +(-2783.69 + 2783.69i) q^{73} +(-816.288 - 338.117i) q^{75} +(-3.67656 + 1.52288i) q^{77} -1467.96 q^{79} -1857.00i q^{81} +(2633.82 + 6358.61i) q^{83} +(3854.07 - 9304.56i) q^{85} +(-337.972 - 337.972i) q^{87} +(-2028.99 - 2028.99i) q^{89} +(9.05574 - 21.8625i) q^{91} +(1825.98 + 4408.30i) q^{93} -1235.90i q^{95} +11014.5 q^{97} +(-1613.73 + 668.429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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