LMFDB - Embedded newform 128.5.h.a.15.3

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			15.3
Character	$\chi$	$=$	128.15
Dual form			128.5.h.a.111.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.5427 + 4.36694i) q^{3} +(-27.2781 - 11.2990i) q^{5} +(51.6577 - 51.6577i) q^{7} +(34.8033 - 34.8033i) q^{9} +O(q^{10})$	\(q+(-10.5427 + 4.36694i) q^{3} +(-27.2781 - 11.2990i) q^{5} +(51.6577 - 51.6577i) q^{7} +(34.8033 - 34.8033i) q^{9} +(-100.880 - 41.7858i) q^{11} +(-5.43190 + 2.24997i) q^{13} +336.928 q^{15} +283.031i q^{17} +(250.224 + 604.093i) q^{19} +(-319.027 + 770.199i) q^{21} +(75.0559 + 75.0559i) q^{23} +(174.487 + 174.487i) q^{25} +(138.784 - 335.055i) q^{27} +(-241.806 - 583.771i) q^{29} +1204.53i q^{31} +1246.03 q^{33} +(-1992.80 + 825.446i) q^{35} +(2439.75 + 1010.58i) q^{37} +(47.4416 - 47.4416i) q^{39} +(221.065 - 221.065i) q^{41} +(452.993 + 187.636i) q^{43} +(-1342.61 + 556.127i) q^{45} +1495.69 q^{47} -2936.03i q^{49} +(-1235.98 - 2983.92i) q^{51} +(-1076.60 + 2599.15i) q^{53} +(2279.68 + 2279.68i) q^{55} +(-5276.08 - 5276.08i) q^{57} +(1586.03 - 3829.02i) q^{59} +(1386.94 + 3348.37i) q^{61} -3595.72i q^{63} +173.594 q^{65} +(-4454.60 + 1845.16i) q^{67} +(-1119.06 - 463.529i) q^{69} +(-1228.91 + 1228.91i) q^{71} +(4520.59 - 4520.59i) q^{73} +(-2601.54 - 1077.59i) q^{75} +(-7369.78 + 3052.66i) q^{77} +1628.16 q^{79} +8125.22i q^{81} +(548.438 + 1324.05i) q^{83} +(3197.96 - 7720.56i) q^{85} +(5098.59 + 5098.59i) q^{87} +(4397.96 + 4397.96i) q^{89} +(-164.371 + 396.828i) q^{91} +(-5260.12 - 12699.1i) q^{93} -19305.8i q^{95} -11560.0 q^{97} +(-4965.24 + 2056.67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−10.5427	+	4.36694i	−1.17141	+	0.485216i	−0.881660	−	0.471885i	$-0.843574\pi$
$3$	−10.5427	+	4.36694i	−1.17141	+	0.485216i	−0.289754	+	0.957101i	$0.593574\pi$
$4$		0			0
$5$	−27.2781	−	11.2990i	−1.09112	−	0.451959i	−0.236726	−	0.971577i	$-0.576074\pi$
$5$	−27.2781	−	11.2990i	−1.09112	−	0.451959i	−0.854399	+	0.519618i	$0.826074\pi$
$6$		0			0
$7$	51.6577	−	51.6577i	1.05424	−	1.05424i	0.0557963	−	0.998442i	$-0.482230\pi$
$7$	51.6577	−	51.6577i	1.05424	−	1.05424i	0.998442	−	0.0557963i	$-0.0177697\pi$
$8$		0			0
$9$	34.8033	−	34.8033i	0.429670	−	0.429670i
$10$		0			0
$11$	−100.880	−	41.7858i	−0.833719	−	0.345338i	−0.0753449	−	0.997158i	$-0.524006\pi$
$11$	−100.880	−	41.7858i	−0.833719	−	0.345338i	−0.758374	+	0.651820i	$0.774006\pi$
$12$		0			0
$13$	−5.43190	+	2.24997i	−0.0321414	+	0.0133134i	−0.398696	−	0.917083i	$-0.630537\pi$
$13$	−5.43190	+	2.24997i	−0.0321414	+	0.0133134i	0.366555	+	0.930396i	$0.380537\pi$
$14$		0			0
$15$	336.928			1.49746
$16$		0			0
$17$			283.031i			0.979347i	0.871906	+	0.489673i	$0.162884\pi$
$17$			283.031i			0.979347i	−0.871906	+	0.489673i	$0.837116\pi$
$18$		0			0
$19$	250.224	+	604.093i	0.693140	+	1.67339i	0.738356	+	0.674412i	$0.235603\pi$
$19$	250.224	+	604.093i	0.693140	+	1.67339i	−0.0452153	+	0.998977i	$0.514397\pi$
$20$		0			0
$21$	−319.027	+	770.199i	−0.723417	+	1.74648i
$22$		0			0
$23$	75.0559	+	75.0559i	0.141883	+	0.141883i	0.774480	−	0.632598i	$-0.218011\pi$
$23$	75.0559	+	75.0559i	0.141883	+	0.141883i	−0.632598	+	0.774480i	$0.718011\pi$
$24$		0			0
$25$	174.487	+	174.487i	0.279179	+	0.279179i
$26$		0			0
$27$	138.784	−	335.055i	0.190376	−	0.459609i
$28$		0			0
$29$	−241.806	−	583.771i	−0.287522	−	0.694140i	0.712449	−	0.701724i	$-0.247586\pi$
$29$	−241.806	−	583.771i	−0.287522	−	0.694140i	−0.999971	+	0.00758408i	$0.997586\pi$
$30$		0			0
$31$			1204.53i			1.25342i	0.779254	+	0.626708i	$0.215598\pi$
$31$			1204.53i			1.25342i	−0.779254	+	0.626708i	$0.784402\pi$
$32$		0			0
$33$	1246.03			1.14419
$34$		0			0
$35$	−1992.80	+	825.446i	−1.62678	+	0.673833i
$36$		0			0
$37$	2439.75	+	1010.58i	1.78214	+	0.738187i	0.992148	+	0.125070i	$0.0399156\pi$
$37$	2439.75	+	1010.58i	1.78214	+	0.738187i	0.789992	+	0.613117i	$0.210084\pi$
$38$		0			0
$39$	47.4416	−	47.4416i	0.0311911	−	0.0311911i
$40$		0			0
$41$	221.065	−	221.065i	0.131508	−	0.131508i	−0.638289	−	0.769797i	$-0.720357\pi$
$41$	221.065	−	221.065i	0.131508	−	0.131508i	0.769797	+	0.638289i	$0.220357\pi$
$42$		0			0
$43$	452.993	+	187.636i	0.244993	+	0.101480i	0.501801	−	0.864983i	$-0.332671\pi$
$43$	452.993	+	187.636i	0.244993	+	0.101480i	−0.256808	+	0.966462i	$0.582671\pi$
$44$		0			0
$45$	−1342.61	+	556.127i	−0.663017	+	0.274631i
$46$		0			0
$47$	1495.69			0.677089			0.338545	−	0.940950i	$-0.390065\pi$
$47$	1495.69			0.677089			0.338545	+	0.940950i	$0.390065\pi$
$48$		0			0
$49$		−	2936.03i		−	1.22284i
$50$		0			0
$51$	−1235.98	−	2983.92i	−0.475195	−	1.14722i
$52$		0			0
$53$	−1076.60	+	2599.15i	−0.383269	+	0.925294i	0.608060	+	0.793891i	$0.291948\pi$
$53$	−1076.60	+	2599.15i	−0.383269	+	0.925294i	−0.991329	+	0.131403i	$0.958052\pi$
$54$		0			0
$55$	2279.68	+	2279.68i	0.753612	+	0.753612i
$56$		0			0
$57$	−5276.08	−	5276.08i	−1.62391	−	1.62391i
$58$		0			0
$59$	1586.03	−	3829.02i	0.455626	−	1.09998i	−0.514525	−	0.857475i	$-0.672032\pi$
$59$	1586.03	−	3829.02i	0.455626	−	1.09998i	0.970151	−	0.242503i	$-0.0779683\pi$
$60$		0			0
$61$	1386.94	+	3348.37i	0.372734	+	0.899859i	0.993285	+	0.115693i	$0.0369088\pi$
$61$	1386.94	+	3348.37i	0.372734	+	0.899859i	−0.620551	+	0.784166i	$0.713091\pi$
$62$		0			0
$63$		−	3595.72i		−	0.905950i
$64$		0			0
$65$	173.594			0.0410874
$66$		0			0
$67$	−4454.60	+	1845.16i	−0.992338	+	0.411040i	−0.818982	−	0.573819i	$-0.805461\pi$
$67$	−4454.60	+	1845.16i	−0.992338	+	0.411040i	−0.173356	+	0.984859i	$0.555461\pi$
$68$		0			0
$69$	−1119.06	−	463.529i	−0.235047	−	0.0973597i
$70$		0			0
$71$	−1228.91	+	1228.91i	−0.243784	+	0.243784i	−0.818413	−	0.574630i	$-0.805146\pi$
$71$	−1228.91	+	1228.91i	−0.243784	+	0.243784i	0.574630	+	0.818413i	$0.305146\pi$
$72$		0			0
$73$	4520.59	−	4520.59i	0.848300	−	0.848300i	−0.141621	−	0.989921i	$-0.545231\pi$
$73$	4520.59	−	4520.59i	0.848300	−	0.848300i	0.989921	+	0.141621i	$0.0452313\pi$
$74$		0			0
$75$	−2601.54	−	1077.59i	−0.462497	−	0.191572i
$76$		0			0
$77$	−7369.78	+	3052.66i	−1.24301	+	0.514870i
$78$		0			0
$79$	1628.16			0.260881			0.130441	−	0.991456i	$-0.458361\pi$
$79$	1628.16			0.260881			0.130441	+	0.991456i	$0.458361\pi$
$80$		0			0
$81$			8125.22i			1.23841i
$82$		0			0
$83$	548.438	+	1324.05i	0.0796107	+	0.192197i	0.958673	−	0.284509i	$-0.0918306\pi$
$83$	548.438	+	1324.05i	0.0796107	+	0.192197i	−0.879063	+	0.476706i	$0.841831\pi$
$84$		0			0
$85$	3197.96	−	7720.56i	0.442624	−	1.06859i
$86$		0			0
$87$	5098.59	+	5098.59i	0.673615	+	0.673615i
$88$		0			0
$89$	4397.96	+	4397.96i	0.555228	+	0.555228i	0.927945	−	0.372717i	$-0.121574\pi$
$89$	4397.96	+	4397.96i	0.555228	+	0.555228i	−0.372717	+	0.927945i	$0.621574\pi$
$90$		0			0
$91$	−164.371	+	396.828i	−0.0198492	+	0.0479203i
$92$		0			0
$93$	−5260.12	−	12699.1i	−0.608177	−	1.46827i
$94$		0			0
$95$		−	19305.8i		−	2.13915i
$96$		0			0
$97$	−11560.0			−1.22861			−0.614304	−	0.789070i	$-0.710563\pi$
$97$	−11560.0			−1.22861			−0.614304	+	0.789070i	$0.710563\pi$
$98$		0			0
$99$	−4965.24	+	2056.67i	−0.506606	+	0.209843i
$100$		0			0
$101$	1627.22	+	674.016i	0.159516	+	0.0660735i	0.461013	−	0.887394i	$-0.347486\pi$
$101$	1627.22	+	674.016i	0.159516	+	0.0660735i	−0.301497	+	0.953467i	$0.597486\pi$
$102$		0			0
$103$	5447.23	−	5447.23i	0.513454	−	0.513454i	−0.402129	−	0.915583i	$-0.631730\pi$
$103$	5447.23	−	5447.23i	0.513454	−	0.513454i	0.915583	+	0.402129i	$0.131730\pi$
$104$		0			0
$105$	17404.9	−	17404.9i	1.57868	−	1.57868i
$106$		0			0
$107$	1963.21	+	813.188i	0.171474	+	0.0710270i	0.466769	−	0.884379i	$-0.345418\pi$
$107$	1963.21	+	813.188i	0.171474	+	0.0710270i	−0.295295	+	0.955406i	$0.595418\pi$
$108$		0			0
$109$	−717.915	+	297.370i	−0.0604255	+	0.0250291i	−0.412692	−	0.910871i	$-0.635411\pi$
$109$	−717.915	+	297.370i	−0.0604255	+	0.0250291i	0.352266	+	0.935900i	$0.385411\pi$
$110$		0			0
$111$	−30134.8			−2.44580
$112$		0			0
$113$			11632.6i			0.911001i	0.890236	+	0.455500i	$0.150540\pi$
$113$			11632.6i			0.911001i	−0.890236	+	0.455500i	$0.849460\pi$
$114$		0			0
$115$	−1199.33	−	2895.44i	−0.0906866	−	0.218937i
$116$		0			0
$117$	−110.742	+	267.354i	−0.00808984	+	0.0195306i
$118$		0			0
$119$	14620.7	+	14620.7i	1.03247	+	1.03247i
$120$		0			0
$121$	−1922.04	−	1922.04i	−0.131278	−	0.131278i
$122$		0			0
$123$	−1365.25	+	3296.01i	−0.0902406	+	0.217860i
$124$		0			0
$125$	4273.70	+	10317.6i	0.273517	+	0.660328i
$126$		0			0
$127$			21766.6i			1.34953i	0.738033	+	0.674765i	$0.235755\pi$
$127$			21766.6i			1.34953i	−0.738033	+	0.674765i	$0.764245\pi$
$128$		0			0
$129$	−5595.17			−0.336228
$130$		0			0
$131$	6753.66	−	2797.46i	0.393547	−	0.163013i	−0.177129	−	0.984188i	$-0.556681\pi$
$131$	6753.66	−	2797.46i	0.393547	−	0.163013i	0.570676	+	0.821175i	$0.306681\pi$
$132$		0			0
$133$	44132.0	+	18280.1i	2.49489	+	1.03342i
$134$		0			0
$135$	−7571.55	+	7571.55i	−0.415449	+	0.415449i
$136$		0			0
$137$	−17803.6	+	17803.6i	−0.948566	+	0.948566i	−0.998740	−	0.0501747i	$-0.984022\pi$
$137$	−17803.6	+	17803.6i	−0.948566	+	0.948566i	0.0501747	+	0.998740i	$0.484022\pi$
$138$		0			0
$139$	31687.1	+	13125.2i	1.64003	+	0.679324i	0.996301	−	0.0859280i	$-0.0273855\pi$
$139$	31687.1	+	13125.2i	1.64003	+	0.679324i	0.643731	+	0.765252i	$0.277385\pi$
$140$		0			0
$141$	−15768.7	+	6531.59i	−0.793152	+	0.328534i
$142$		0			0
$143$	641.987			0.0313945
$144$		0			0
$145$			18656.3i			0.887341i
$146$		0			0
$147$	12821.5	+	30953.8i	0.593340	+	1.43245i
$148$		0			0
$149$	4140.77	−	9996.70i	0.186513	−	0.450282i	−0.802771	−	0.596287i	$-0.796642\pi$
$149$	4140.77	−	9996.70i	0.186513	−	0.450282i	0.989284	+	0.146006i	$0.0466418\pi$
$150$		0			0
$151$	−4409.75	−	4409.75i	−0.193401	−	0.193401i	0.603763	−	0.797164i	$-0.293667\pi$
$151$	−4409.75	−	4409.75i	−0.193401	−	0.193401i	−0.797164	+	0.603763i	$0.793667\pi$
$152$		0			0
$153$	9850.42	+	9850.42i	0.420796	+	0.420796i
$154$		0			0
$155$	13610.0	−	32857.4i	0.566492	−	1.36763i
$156$		0			0
$157$	−9304.59	−	22463.3i	−0.377483	−	0.911326i	−0.992436	−	0.122762i	$-0.960825\pi$
$157$	−9304.59	−	22463.3i	−0.377483	−	0.911326i	0.614953	−	0.788564i	$-0.289175\pi$
$158$		0			0
$159$		−	32103.6i		−	1.26987i
$160$		0			0
$161$	7754.43			0.299156
$162$		0			0
$163$	−13685.2	+	5668.60i	−0.515082	+	0.213354i	−0.625055	−	0.780581i	$-0.714924\pi$
$163$	−13685.2	+	5668.60i	−0.515082	+	0.213354i	0.109973	+	0.993935i	$0.464924\pi$
$164$		0			0
$165$	−33989.2	−	14078.8i	−1.24846	−	0.517128i
$166$		0			0
$167$	−29132.0	+	29132.0i	−1.04457	+	1.04457i	−0.0456110	+	0.998959i	$0.514523\pi$
$167$	−29132.0	+	29132.0i	−1.04457	+	1.04457i	−0.998959	+	0.0456110i	$0.985477\pi$
$168$		0			0
$169$	−20171.2	+	20171.2i	−0.706251	+	0.706251i
$170$		0			0
$171$	29733.1	+	12315.8i	1.01683	+	0.421184i
$172$		0			0
$173$	32285.0	−	13372.9i	1.07872	−	0.446820i	0.228659	−	0.973507i	$-0.426566\pi$
$173$	32285.0	−	13372.9i	1.07872	−	0.446820i	0.850060	+	0.526687i	$0.176566\pi$
$174$		0			0
$175$	18027.2			0.588643
$176$		0			0
$177$			47294.5i			1.50961i
$178$		0			0
$179$	−6105.32	−	14739.5i	−0.190547	−	0.460021i	0.799516	−	0.600645i	$-0.205089\pi$
$179$	−6105.32	−	14739.5i	−0.190547	−	0.460021i	−0.990063	+	0.140623i	$0.955089\pi$
$180$		0			0
$181$	−803.111	+	1938.88i	−0.0245142	+	0.0591826i	−0.935663	−	0.352896i	$-0.885197\pi$
$181$	−803.111	+	1938.88i	−0.0245142	+	0.0591826i	0.911148	+	0.412078i	$0.135197\pi$
$182$		0			0
$183$	−29244.3	−	29244.3i	−0.873251	−	0.873251i
$184$		0			0
$185$	−55133.3	−	55133.3i	−1.61091	−	1.61091i
$186$		0			0
$187$	11826.7	−	28552.2i	0.338205	−	0.816500i
$188$		0			0
$189$	−10138.9	−	24477.5i	−0.283836	−	0.685240i
$190$		0			0
$191$		−	12606.6i		−	0.345566i	−0.984960	−	0.172783i	$-0.944724\pi$
$191$		−	12606.6i		−	0.345566i	0.984960	−	0.172783i	$-0.0552759\pi$
$192$		0			0
$193$	34591.3			0.928649			0.464325	−	0.885665i	$-0.346297\pi$
$193$	34591.3			0.928649			0.464325	+	0.885665i	$0.346297\pi$
$194$		0			0
$195$	−1830.16	+	758.076i	−0.0481304	+	0.0199363i
$196$		0			0
$197$	4788.59	+	1983.50i	0.123389	+	0.0511093i	0.443524	−	0.896263i	$-0.353728\pi$
$197$	4788.59	+	1983.50i	0.123389	+	0.0511093i	−0.320135	+	0.947372i	$0.603728\pi$
$198$		0			0
$199$	4211.65	−	4211.65i	0.106352	−	0.106352i	−0.651928	−	0.758281i	$-0.726040\pi$
$199$	4211.65	−	4211.65i	0.106352	−	0.106352i	0.758281	+	0.651928i	$0.226040\pi$
$200$		0			0
$201$	38906.0	−	38906.0i	0.962996	−	0.962996i
$202$		0			0
$203$	−42647.4	−	17665.1i	−1.03491	−	0.428672i
$204$		0			0
$205$	−8528.04	+	3532.43i	−0.202928	+	0.0840554i
$206$		0			0
$207$	5224.39			0.121926
$208$		0			0
$209$		−	71396.7i		−	1.63450i
$210$		0			0
$211$	6956.39	+	16794.2i	0.156250	+	0.377220i	0.982547	−	0.186014i	$-0.0595570\pi$
$211$	6956.39	+	16794.2i	0.156250	+	0.377220i	−0.826297	+	0.563234i	$0.809557\pi$
$212$		0			0
$213$	7589.51	−	18322.7i	0.167284	−	0.403859i
$214$		0			0
$215$	−10236.7	−	10236.7i	−0.221454	−	0.221454i
$216$		0			0
$217$	62223.4	+	62223.4i	1.32140	+	1.32140i
$218$		0			0
$219$	−27918.2	+	67400.6i	−0.582103	+	1.40532i
$220$		0			0
$221$	−636.811	−	1537.40i	−0.0130385	−	0.0314776i
$222$		0			0
$223$			24483.7i			0.492343i	0.969226	+	0.246171i	$0.0791726\pi$
$223$			24483.7i			0.492343i	−0.969226	+	0.246171i	$0.920827\pi$
$224$		0			0
$225$	12145.5			0.239910
$226$		0			0
$227$	−84273.6	+	34907.3i	−1.63546	+	0.677430i	−0.995828	−	0.0912514i	$-0.970913\pi$
$227$	−84273.6	+	34907.3i	−1.63546	+	0.677430i	−0.639632	+	0.768681i	$0.720913\pi$
$228$		0			0
$229$	−5392.62	−	2233.69i	−0.102832	−	0.0425944i	0.330674	−	0.943745i	$-0.392724\pi$
$229$	−5392.62	−	2233.69i	−0.102832	−	0.0425944i	−0.433506	+	0.901150i	$0.642724\pi$
$230$		0			0
$231$	64366.8	−	64366.8i	1.20625	−	1.20625i
$232$		0			0
$233$	−58076.3	+	58076.3i	−1.06976	+	1.06976i	−0.0723851	+	0.997377i	$0.523061\pi$
$233$	−58076.3	+	58076.3i	−1.06976	+	1.06976i	−0.997377	+	0.0723851i	$0.976939\pi$
$234$		0			0
$235$	−40799.6	−	16899.7i	−0.738789	−	0.306016i
$236$		0			0
$237$	−17165.2	+	7110.07i	−0.305600	+	0.126584i
$238$		0			0
$239$	−7935.87			−0.138931			−0.0694655	−	0.997584i	$-0.522129\pi$
$239$	−7935.87			−0.138931			−0.0694655	+	0.997584i	$0.522129\pi$
$240$		0			0
$241$		−	76441.8i		−	1.31612i	−0.752963	−	0.658062i	$-0.771376\pi$
$241$		−	76441.8i		−	1.31612i	0.752963	−	0.658062i	$-0.228624\pi$
$242$		0			0
$243$	−24240.8	−	58522.6i	−0.410521	−	0.991085i
$244$		0			0
$245$	−33174.1	+	80089.4i	−0.552672	+	1.33427i
$246$		0			0
$247$	−2718.38	−	2718.38i	−0.0445570	−	0.0445570i
$248$		0			0
$249$	−11564.1	−	11564.1i	−0.186514	−	0.186514i
$250$		0			0
$251$	−569.422	+	1374.71i	−0.00903831	+	0.0218204i	−0.928334	−	0.371747i	$-0.878759\pi$
$251$	−569.422	+	1374.71i	−0.00903831	+	0.0218204i	0.919296	+	0.393567i	$0.128759\pi$
$252$		0			0
$253$	−4435.36	−	10707.9i	−0.0692928	−	0.167288i
$254$		0			0
$255$			95361.1i			1.46653i
$256$		0			0
$257$	−81863.6			−1.23944			−0.619719	−	0.784824i	$-0.712753\pi$
$257$	−81863.6			−1.23944			−0.619719	+	0.784824i	$0.712753\pi$
$258$		0			0
$259$	178236.	−	73827.7i	2.65703	−	1.10058i
$260$		0			0
$261$	−28732.8	−	11901.5i	−0.421791	−	0.174712i
$262$		0			0
$263$	34662.4	−	34662.4i	0.501126	−	0.501126i	−0.410662	−	0.911788i	$-0.634702\pi$
$263$	34662.4	−	34662.4i	0.501126	−	0.501126i	0.911788	+	0.410662i	$0.134702\pi$
$264$		0			0
$265$	58735.4	−	58735.4i	0.836389	−	0.836389i
$266$		0			0
$267$	−65572.2	−	27160.9i	−0.919808	−	0.380997i
$268$		0			0
$269$	19212.9	−	7958.23i	0.265514	−	0.109980i	−0.245955	−	0.969281i	$-0.579102\pi$
$269$	19212.9	−	7958.23i	0.265514	−	0.109980i	0.511469	+	0.859302i	$0.329102\pi$
$270$		0			0
$271$	49392.9			0.672552			0.336276	−	0.941764i	$-0.390833\pi$
$271$	49392.9			0.672552			0.336276	+	0.941764i	$0.390833\pi$
$272$		0			0
$273$		−	4901.45i		−	0.0657656i
$274$		0			0
$275$	−10311.2	−	24893.3i	−0.136346	−	0.329168i
$276$		0			0
$277$	13007.4	−	31402.7i	0.169524	−	0.409268i	−0.816170	−	0.577812i	$-0.803907\pi$
$277$	13007.4	−	31402.7i	0.169524	−	0.409268i	0.985694	+	0.168544i	$0.0539066\pi$
$278$		0			0
$279$	41921.7	+	41921.7i	0.538556	+	0.538556i
$280$		0			0
$281$	−10194.9	−	10194.9i	−0.129113	−	0.129113i	0.639597	−	0.768710i	$-0.279101\pi$
$281$	−10194.9	−	10194.9i	−0.129113	−	0.129113i	−0.768710	+	0.639597i	$0.779101\pi$
$282$		0			0
$283$	−9733.11	+	23497.8i	−0.121529	+	0.293396i	−0.972923	−	0.231130i	$-0.925758\pi$
$283$	−9733.11	+	23497.8i	−0.121529	+	0.293396i	0.851394	+	0.524527i	$0.175758\pi$
$284$		0			0
$285$	84307.3	+	203536.i	1.03795	+	2.50583i
$286$		0			0
$287$		−	22839.4i		−	0.277282i
$288$		0			0
$289$	3414.30			0.0408796
$290$		0			0
$291$	121874.	−	50481.7i	1.43921	−	0.596140i
$292$		0			0
$293$	−70102.8	−	29037.5i	−0.816582	−	0.338240i	−0.0650055	−	0.997885i	$-0.520706\pi$
$293$	−70102.8	−	29037.5i	−0.816582	−	0.338240i	−0.751577	+	0.659645i	$0.770706\pi$
$294$		0			0
$295$	−86528.0	+	86528.0i	−0.994289	+	0.994289i
$296$		0			0
$297$	−28001.1	+	28001.1i	−0.317441	+	0.317441i
$298$		0			0
$299$	−576.570	−	238.823i	−0.00644925	−	0.00267137i
$300$		0			0
$301$	33093.4	−	13707.7i	0.365265	−	0.151298i
$302$		0			0
$303$	−20098.7			−0.218919
$304$		0			0
$305$		−	107008.i		−	1.15032i
$306$		0			0
$307$	14592.1	+	35228.3i	0.154824	+	0.373779i	0.982192	−	0.187882i	$-0.0601623\pi$
$307$	14592.1	+	35228.3i	0.154824	+	0.373779i	−0.827367	+	0.561662i	$0.810162\pi$
$308$		0			0
$309$	−33641.0	+	81216.5i	−0.352331	+	0.850603i
$310$		0			0
$311$	23196.5	+	23196.5i	0.239829	+	0.239829i	0.816779	−	0.576950i	$-0.195757\pi$
$311$	23196.5	+	23196.5i	0.239829	+	0.239829i	−0.576950	+	0.816779i	$0.695757\pi$
$312$		0			0
$313$	64149.5	+	64149.5i	0.654794	+	0.654794i	0.954143	−	0.299350i	$-0.0967697\pi$
$313$	64149.5	+	64149.5i	0.654794	+	0.654794i	−0.299350	+	0.954143i	$0.596770\pi$
$314$		0			0
$315$	−40627.9	+	98084.4i	−0.409452	+	0.988504i
$316$		0			0
$317$	59547.3	+	143760.i	0.592575	+	1.43060i	0.881007	+	0.473103i	$0.156866\pi$
$317$	59547.3	+	143760.i	0.592575	+	1.43060i	−0.288432	+	0.957501i	$0.593134\pi$
$318$		0			0
$319$			68994.9i			0.678009i
$320$		0			0
$321$	−24248.7			−0.235331
$322$		0			0
$323$	−170977.	+	70821.1i	−1.63883	+	0.678825i
$324$		0			0
$325$	−1340.39	−	555.206i	−0.0126900	−	0.00525639i
$326$		0			0
$327$	6270.19	−	6270.19i	0.0586388	−	0.0586388i
$328$		0			0
$329$	77263.9	−	77263.9i	0.713813	−	0.713813i
$330$		0			0
$331$	−38400.3	−	15905.9i	−0.350492	−	0.145179i	0.200490	−	0.979696i	$-0.435747\pi$
$331$	−38400.3	−	15905.9i	−0.350492	−	0.145179i	−0.550982	+	0.834517i	$0.685747\pi$
$332$		0			0
$333$	120083.	−	49739.9i	1.08291	−	0.448556i
$334$		0			0
$335$	142362.			1.26854
$336$		0			0
$337$			76295.6i			0.671800i	0.941898	+	0.335900i	$0.109040\pi$
$337$			76295.6i			0.671800i	−0.941898	+	0.335900i	$0.890960\pi$
$338$		0			0
$339$	−50798.7	−	122639.i	−0.442032	−	1.06716i
$340$		0			0
$341$	50332.4	−	121513.i	0.432851	−	1.04500i
$342$		0			0
$343$	−27638.6	−	27638.6i	−0.234924	−	0.234924i
$344$		0			0
$345$	25288.4	+	25288.4i	0.212463	+	0.212463i
$346$		0			0
$347$	−81606.4	+	197015.i	−0.677743	+	1.63622i	0.0903746	+	0.995908i	$0.471194\pi$
$347$	−81606.4	+	197015.i	−0.677743	+	1.63622i	−0.768118	+	0.640309i	$0.778806\pi$
$348$		0			0
$349$	2344.51	+	5660.16i	0.0192487	+	0.0464705i	0.933212	−	0.359327i	$-0.116994\pi$
$349$	2344.51	+	5660.16i	0.0192487	+	0.0464705i	−0.913963	+	0.405798i	$0.866994\pi$
$350$		0			0
$351$			2132.25i			0.0173071i
$352$		0			0
$353$	182567.			1.46512			0.732558	−	0.680704i	$-0.238326\pi$
$353$	182567.			1.46512			0.732558	+	0.680704i	$0.238326\pi$
$354$		0			0
$355$	47407.9	−	19637.0i	0.376178	−	0.155818i
$356$		0			0
$357$	−217990.	−	90294.6i	−1.71041	−	0.708476i
$358$		0			0
$359$	57665.8	−	57665.8i	0.447434	−	0.447434i	−0.447066	−	0.894501i	$-0.647531\pi$
$359$	57665.8	−	57665.8i	0.447434	−	0.447434i	0.894501	+	0.447066i	$0.147531\pi$
$360$		0			0
$361$	−210166.	+	210166.i	−1.61268	+	1.61268i
$362$		0			0
$363$	28657.0	+	11870.1i	0.217479	+	0.0900829i
$364$		0			0
$365$	−174391.	+	72235.2i	−1.30900	+	0.542205i
$366$		0			0
$367$	219857.			1.63233			0.816165	−	0.577819i	$-0.196096\pi$
$367$	219857.			1.63233			0.816165	+	0.577819i	$0.196096\pi$
$368$		0			0
$369$		−	15387.6i		−	0.113010i
$370$		0			0
$371$	78651.3	+	189881.i	0.571423	+	1.37954i
$372$		0			0
$373$	−51133.9	+	123448.i	−0.367529	+	0.887293i	0.626625	+	0.779321i	$0.284436\pi$
$373$	−51133.9	+	123448.i	−0.367529	+	0.887293i	−0.994154	+	0.107972i	$0.965564\pi$
$374$		0			0
$375$	−90112.9	−	90112.9i	−0.640803	−	0.640803i
$376$		0			0
$377$	2626.93	+	2626.93i	0.0184827	+	0.0184827i
$378$		0			0
$379$	44920.8	−	108448.i	0.312730	−	0.754997i	−0.686872	−	0.726778i	$-0.741017\pi$
$379$	44920.8	−	108448.i	0.312730	−	0.754997i	0.999602	−	0.0282181i	$-0.00898330\pi$
$380$		0			0
$381$	−95053.3	−	229479.i	−0.654813	−	1.58086i
$382$		0			0
$383$			2200.88i			0.0150037i	0.999972	+	0.00750186i	$0.00238794\pi$
$383$			2200.88i			0.0150037i	−0.999972	+	0.00750186i	$0.997612\pi$
$384$		0			0
$385$	235526.			1.58897
$386$		0			0
$387$	22296.0	−	9235.30i	0.148869	−	0.0616636i
$388$		0			0
$389$	251445.	+	104152.i	1.66167	+	0.688284i	0.998203	−	0.0599256i	$-0.0190863\pi$
$389$	251445.	+	104152.i	1.66167	+	0.688284i	0.663462	+	0.748210i	$0.269086\pi$
$390$		0			0
$391$	−21243.2	+	21243.2i	−0.138952	+	0.138952i
$392$		0			0
$393$	−58985.7	+	58985.7i	−0.381911	+	0.381911i
$394$		0			0
$395$	−44413.1	−	18396.5i	−0.284654	−	0.117907i
$396$		0			0
$397$	194605.	−	80608.0i	1.23473	−	0.511443i	0.332667	−	0.943044i	$-0.392051\pi$
$397$	194605.	−	80608.0i	1.23473	−	0.511443i	0.902064	+	0.431602i	$0.142051\pi$
$398$		0			0
$399$	−545100.			−3.42397
$400$		0			0
$401$		−	211873.i		−	1.31761i	−0.752313	−	0.658806i	$-0.771062\pi$
$401$		−	211873.i		−	1.31761i	0.752313	−	0.658806i	$-0.228938\pi$
$402$		0			0
$403$	−2710.16	−	6542.90i	−0.0166872	−	0.0402866i
$404$		0			0
$405$	91806.6	−	221641.i	0.559711	−	1.35126i
$406$		0			0
$407$	−203894.	−	203894.i	−1.23088	−	1.23088i
$408$		0			0
$409$	−8417.27	−	8417.27i	−0.0503181	−	0.0503181i	0.681500	−	0.731818i	$-0.261328\pi$
$409$	−8417.27	−	8417.27i	−0.0503181	−	0.0503181i	−0.731818	+	0.681500i	$0.761328\pi$
$410$		0			0
$411$	109951.	−	265446.i	0.650905	−	1.57142i
$412$		0			0
$413$	−115868.	−	279729.i	−0.679301	−	1.63998i
$414$		0			0
$415$		−	42314.3i		−	0.245692i
$416$		0			0
$417$	−391385.			−2.25078
$418$		0			0
$419$	106241.	−	44006.4i	0.605150	−	0.250661i	−0.0590031	−	0.998258i	$-0.518792\pi$
$419$	106241.	−	44006.4i	0.605150	−	0.250661i	0.664153	+	0.747596i	$0.268792\pi$
$420$		0			0
$421$	−102502.	−	42457.7i	−0.578320	−	0.239548i	0.0742969	−	0.997236i	$-0.476329\pi$
$421$	−102502.	−	42457.7i	−0.578320	−	0.239548i	−0.652617	+	0.757688i	$0.726329\pi$
$422$		0			0
$423$	52055.0	−	52055.0i	0.290925	−	0.290925i
$424$		0			0
$425$	−49385.3	+	49385.3i	−0.273413	+	0.273413i
$426$		0			0
$427$	244615.	+	101323.i	1.34162	+	0.555715i
$428$		0			0
$429$	−6768.29	+	2803.52i	−0.0367760	+	0.0152331i
$430$		0			0
$431$	167886.			0.903772			0.451886	−	0.892076i	$-0.350751\pi$
$431$	167886.			0.903772			0.451886	+	0.892076i	$0.350751\pi$
$432$		0			0
$433$			148051.i			0.789649i	0.918757	+	0.394825i	$0.129195\pi$
$433$			148051.i			0.789649i	−0.918757	+	0.394825i	$0.870805\pi$
$434$		0			0
$435$	−81471.1	−	196689.i	−0.430552	−	1.03944i
$436$		0			0
$437$	−26560.0	+	64121.6i	−0.139080	+	0.335769i
$438$		0			0
$439$	−108391.	−	108391.i	−0.562425	−	0.562425i	0.367571	−	0.929996i	$-0.380190\pi$
$439$	−108391.	−	108391.i	−0.562425	−	0.562425i	−0.929996	+	0.367571i	$0.880190\pi$
$440$		0			0
$441$	−102184.	−	102184.i	−0.525417	−	0.525417i
$442$		0			0
$443$	76116.3	−	183761.i	0.387856	−	0.936366i	−0.602538	−	0.798090i	$-0.705844\pi$
$443$	76116.3	−	183761.i	0.387856	−	0.936366i	0.990394	−	0.138276i	$-0.0441562\pi$
$444$		0			0
$445$	−70275.7	−	169660.i	−0.354883	−	0.856763i
$446$		0			0
$447$			123475.i			0.617965i
$448$		0			0
$449$	−121056.			−0.600474			−0.300237	−	0.953865i	$-0.597066\pi$
$449$	−121056.			−0.600474			−0.300237	+	0.953865i	$0.597066\pi$
$450$		0			0
$451$	−31538.4	+	13063.6i	−0.155055	+	0.0642260i
$452$		0			0
$453$	65747.9	+	27233.7i	0.320395	+	0.132712i
$454$		0			0
$455$	8967.48	−	8967.48i	0.0433159	−	0.0433159i
$456$		0			0
$457$	105385.	−	105385.i	0.504598	−	0.504598i	−0.408266	−	0.912863i	$-0.633866\pi$
$457$	105385.	−	105385.i	0.504598	−	0.504598i	0.912863	+	0.408266i	$0.133866\pi$
$458$		0			0
$459$	94831.1	+	39280.3i	0.450117	+	0.186445i
$460$		0			0
$461$	−67485.5	+	27953.4i	−0.317547	+	0.131532i	−0.535764	−	0.844368i	$-0.679976\pi$
$461$	−67485.5	+	27953.4i	−0.317547	+	0.131532i	0.218216	+	0.975900i	$0.429976\pi$
$462$		0			0
$463$	−133718.			−0.623776			−0.311888	−	0.950119i	$-0.600961\pi$
$463$	−133718.			−0.623776			−0.311888	+	0.950119i	$0.600961\pi$
$464$		0			0
$465$			405840.i			1.87694i
$466$		0			0
$467$	123908.	+	299140.i	0.568152	+	1.37164i	0.903111	+	0.429407i	$0.141277\pi$
$467$	123908.	+	299140.i	0.568152	+	1.37164i	−0.334959	+	0.942233i	$0.608723\pi$
$468$		0			0
$469$	−134798.	+	325431.i	−0.612827	+	1.47949i
$470$		0			0
$471$	196192.	+	196192.i	0.884379	+	0.884379i
$472$		0			0
$473$	−37857.4	−	37857.4i	−0.169211	−	0.169211i
$474$		0			0
$475$	−61745.7	+	149067.i	−0.273665	+	0.660686i
$476$		0			0
$477$	52989.7	+	127928.i	0.232892	+	0.562251i
$478$		0			0
$479$		−	50405.4i		−	0.219688i	−0.993949	−	0.109844i	$-0.964965\pi$
$479$		−	50405.4i		−	0.219688i	0.993949	−	0.109844i	$-0.0350351\pi$
$480$		0			0
$481$	−15526.3			−0.0671083
$482$		0			0
$483$	−81752.9	+	33863.1i	−0.350436	+	0.145155i
$484$		0			0
$485$	315334.	+	130616.i	1.34056	+	0.555280i
$486$		0			0
$487$	−212041.	+	212041.i	−0.894052	+	0.894052i	−0.994902	−	0.100850i	$-0.967844\pi$
$487$	−212041.	+	212041.i	−0.894052	+	0.894052i	0.100850	+	0.994902i	$0.467844\pi$
$488$		0			0
$489$	119525.	−	119525.i	0.499852	−	0.499852i
$490$		0			0
$491$	−223956.	−	92765.6i	−0.928966	−	0.384790i	−0.133680	−	0.991025i	$-0.542679\pi$
$491$	−223956.	−	92765.6i	−0.928966	−	0.384790i	−0.795286	+	0.606234i	$0.792679\pi$
$492$		0			0
$493$	165226.	−	68438.7i	0.679804	−	0.281584i
$494$		0			0
$495$	158681.			0.647610
$496$		0			0
$497$			126966.i			0.514012i
$498$		0			0
$499$	110100.	+	265806.i	0.442169	+	1.06749i	0.975186	+	0.221385i	$0.0710579\pi$
$499$	110100.	+	265806.i	0.442169	+	1.06749i	−0.533018	+	0.846104i	$0.678942\pi$
$500$		0			0
$501$	179913.	−	434349.i	0.716783	−	1.73047i
$502$		0			0
$503$	226266.	+	226266.i	0.894302	+	0.894302i	0.994925	−	0.100623i	$-0.0320834\pi$
$503$	226266.	+	226266.i	0.894302	+	0.894302i	−0.100623	+	0.994925i	$0.532083\pi$
$504$		0			0
$505$	−36771.8	−	36771.8i	−0.144189	−	0.144189i
$506$		0			0
$507$	124573.	−	300746.i	0.484628	−	1.17000i
$508$		0			0
$509$	114809.	+	277174.i	0.443141	+	1.06984i	0.974840	+	0.222904i	$0.0715535\pi$
$509$	114809.	+	277174.i	0.443141	+	1.06984i	−0.531700	+	0.846933i	$0.678446\pi$
$510$		0			0
$511$		−	467047.i		−	1.78862i
$512$		0			0
$513$	237132.			0.901063
$514$		0			0
$515$	−210138.	+	87042.2i	−0.792302	+	0.328182i
$516$		0			0
$517$	−150885.	−	62498.7i	−0.564502	−	0.233824i
$518$		0			0
$519$	−281973.	+	281973.i	−1.04682	+	1.04682i
$520$		0			0
$521$	107417.	−	107417.i	0.395730	−	0.395730i	−0.480994	−	0.876724i	$-0.659724\pi$
$521$	107417.	−	107417.i	0.395730	−	0.395730i	0.876724	+	0.480994i	$0.159724\pi$
$522$		0			0
$523$	−146315.	−	60605.5i	−0.534914	−	0.221569i	0.0988399	−	0.995103i	$-0.468487\pi$
$523$	−146315.	−	60605.5i	−0.534914	−	0.221569i	−0.633754	+	0.773535i	$0.718487\pi$
$524$		0			0
$525$	−190056.	+	78723.7i	−0.689545	+	0.285619i
$526$		0			0
$527$	−340920.			−1.22753
$528$		0			0
$529$		−	268574.i		−	0.959739i
$530$		0			0
$531$	−78063.5	−	188462.i	−0.276859	−	0.668397i
$532$		0			0
$533$	−703.414	+	1698.19i	−0.00247603	+	0.00597768i
$534$		0			0
$535$	−44364.4	−	44364.4i	−0.154999	−	0.154999i
$536$		0			0
$537$	128733.	+	128733.i	0.446419	+	0.446419i
$538$		0			0
$539$	−122685.	+	296187.i	−0.422292	+	1.01950i
$540$		0			0
$541$	−36812.9	−	88874.1i	−0.125778	−	0.303655i	0.848430	−	0.529308i	$-0.177548\pi$
$541$	−36812.9	−	88874.1i	−0.125778	−	0.303655i	−0.974208	+	0.225653i	$0.927548\pi$
$542$		0			0
$543$		−	23948.2i		−	0.0812220i
$544$		0			0
$545$	22943.4			0.0772438
$546$		0			0
$547$	56297.0	−	23319.0i	0.188153	−	0.0779354i	−0.286618	−	0.958045i	$-0.592531\pi$
$547$	56297.0	−	23319.0i	0.188153	−	0.0779354i	0.474771	+	0.880110i	$0.342531\pi$
$548$		0			0
$549$	164805.	+	68264.3i	0.546795	+	0.226490i
$550$		0			0
$551$	292147.	−	292147.i	0.962272	−	0.962272i
$552$		0			0
$553$	84106.9	−	84106.9i	0.275031	−	0.275031i
$554$		0			0
$555$	822019.	+	340492.i	2.66868	+	1.10540i
$556$		0			0
$557$	−230194.	+	95349.7i	−0.741967	+	0.307333i	−0.721459	−	0.692457i	$-0.756528\pi$
$557$	−230194.	+	95349.7i	−0.741967	+	0.307333i	−0.0205076	+	0.999790i	$0.506528\pi$
$558$		0			0
$559$	−2882.79			−0.00922548
$560$		0			0
$561$			352664.i			1.12056i
$562$		0			0
$563$	−108844.	−	262773.i	−0.343391	−	0.829018i	−0.997368	−	0.0725043i	$-0.976901\pi$
$563$	−108844.	−	262773.i	−0.343391	−	0.829018i	0.653977	−	0.756514i	$-0.273099\pi$
$564$		0			0
$565$	131436.	−	317314.i	0.411735	−	0.994015i
$566$		0			0
$567$	419730.	+	419730.i	1.30558	+	1.30558i
$568$		0			0
$569$	−133872.	−	133872.i	−0.413489	−	0.413489i	0.469463	−	0.882952i	$-0.344447\pi$
$569$	−133872.	−	133872.i	−0.413489	−	0.413489i	−0.882952	+	0.469463i	$0.844447\pi$
$570$		0			0
$571$	−102289.	+	246948.i	−0.313731	+	0.757413i	0.685830	+	0.727762i	$0.259439\pi$
$571$	−102289.	+	246948.i	−0.313731	+	0.757413i	−0.999560	+	0.0296506i	$0.990561\pi$
$572$		0			0
$573$	55052.2	+	132908.i	0.167674	+	0.404801i
$574$		0			0
$575$			26192.6i			0.0792214i
$576$		0			0
$577$	−363573.			−1.09204			−0.546021	−	0.837771i	$-0.683858\pi$
$577$	−363573.			−1.09204			−0.546021	+	0.837771i	$0.683858\pi$
$578$		0			0
$579$	−364686.	+	151058.i	−1.08783	+	0.450595i
$580$		0			0
$581$	96728.3	+	40066.2i	0.286550	+	0.118693i
$582$		0			0
$583$	217215.	−	217215.i	0.639078	−	0.639078i
$584$		0			0
$585$	6041.66	−	6041.66i	0.0176540	−	0.0176540i
$586$		0			0
$587$	−122947.	−	50926.2i	−0.356813	−	0.147797i	0.197074	−	0.980389i	$-0.436856\pi$
$587$	−122947.	−	50926.2i	−0.356813	−	0.147797i	−0.553887	+	0.832592i	$0.686856\pi$
$588$		0			0
$589$	−727650.	+	301403.i	−2.09745	+	0.868793i
$590$		0			0
$591$	−59146.7			−0.169338
$592$		0			0
$593$			466197.i			1.32575i	0.748732	+	0.662873i	$0.230663\pi$
$593$			466197.i			1.32575i	−0.748732	+	0.662873i	$0.769337\pi$
$594$		0			0
$595$	−233627.	−	564025.i	−0.659917	−	1.59318i
$596$		0			0
$597$	−26010.3	+	62794.4i	−0.0729787	+	0.176186i
$598$		0			0
$599$	439833.	+	439833.i	1.22584	+	1.22584i	0.965523	+	0.260317i	$0.0838270\pi$
$599$	439833.	+	439833.i	1.22584	+	1.22584i	0.260317	+	0.965523i	$0.416173\pi$
$600$		0			0
$601$	431465.	+	431465.i	1.19453	+	1.19453i	0.975782	+	0.218747i	$0.0701969\pi$
$601$	431465.	+	431465.i	1.19453	+	1.19453i	0.218747	+	0.975782i	$0.429803\pi$
$602$		0			0
$603$	−90817.4	+	219253.i	−0.249767	+	0.602990i
$604$		0			0
$605$	30712.6	+	74146.8i	0.0839085	+	0.202573i
$606$		0			0
$607$		−	346474.i		−	0.940358i	−0.882571	−	0.470179i	$-0.844189\pi$
$607$		−	346474.i		−	0.940358i	0.882571	−	0.470179i	$-0.155811\pi$
$608$		0			0
$609$	526763.			1.42030
$610$		0			0
$611$	−8124.44	+	3365.25i	−0.0217626	+	0.00901437i
$612$		0			0
$613$	−151837.	−	62893.1i	−0.404071	−	0.167372i	0.171386	−	0.985204i	$-0.445176\pi$
$613$	−151837.	−	62893.1i	−0.404071	−	0.167372i	−0.575457	+	0.817832i	$0.695176\pi$
$614$		0			0
$615$	74482.9	−	74482.9i	0.196927	−	0.196927i
$616$		0			0
$617$	435037.	−	435037.i	1.14276	−	1.14276i	0.154819	−	0.987943i	$-0.450520\pi$
$617$	435037.	−	435037.i	1.14276	−	1.14276i	0.987943	−	0.154819i	$-0.0494796\pi$
$618$		0			0
$619$	42979.8	+	17802.8i	0.112172	+	0.0464630i	0.438063	−	0.898944i	$-0.355665\pi$
$619$	42979.8	+	17802.8i	0.112172	+	0.0464630i	−0.325892	+	0.945407i	$0.605665\pi$
$620$		0			0
$621$	35564.5	−	14731.3i	0.0922217	−	0.0381995i
$622$		0			0
$623$	454377.			1.17069
$624$		0			0
$625$		−	483960.i		−	1.23894i
$626$		0			0
$627$	311785.	+	752716.i	0.793086	+	1.91468i
$628$		0			0
$629$	−286025.	+	690526.i	−0.722941	+	1.74533i
$630$		0			0
$631$	103693.	+	103693.i	0.260430	+	0.260430i	0.825229	−	0.564799i	$-0.191046\pi$
$631$	103693.	+	103693.i	0.260430	+	0.260430i	−0.564799	+	0.825229i	$0.691046\pi$
$632$		0			0
$633$	−146679.	−	146679.i	−0.366066	−	0.366066i
$634$		0			0
$635$	245940.	−	593751.i	0.609932	−	1.47251i
$636$		0			0
$637$	6605.98	+	15948.2i	0.0162801	+	0.0393038i
$638$		0			0
$639$			85540.5i			0.209493i
$640$		0			0
$641$	−613243.			−1.49251			−0.746253	−	0.665662i	$-0.768149\pi$
$641$	−613243.			−1.49251			−0.746253	+	0.665662i	$0.768149\pi$
$642$		0			0
$643$	−285323.	+	118185.i	−0.690105	+	0.285851i	−0.700044	−	0.714100i	$-0.746836\pi$
$643$	−285323.	+	118185.i	−0.690105	+	0.285851i	0.00993918	+	0.999951i	$0.496836\pi$
$644$		0			0
$645$	152626.	+	63219.7i	0.366867	+	0.151961i
$646$		0			0
$647$	116787.	−	116787.i	0.278988	−	0.278988i	−0.553717	−	0.832705i	$-0.686791\pi$
$647$	116787.	−	116787.i	0.278988	−	0.278988i	0.832705	+	0.553717i	$0.186791\pi$
$648$		0			0
$649$	−319998.	+	319998.i	−0.759727	+	0.759727i
$650$		0			0
$651$	−927730.	−	384278.i	−2.18907	−	0.906742i
$652$		0			0
$653$	−38032.3	+	15753.5i	−0.0891920	+	0.0369445i	−0.426833	−	0.904330i	$-0.640371\pi$
$653$	−38032.3	+	15753.5i	−0.0891920	+	0.0369445i	0.337641	+	0.941275i	$0.390371\pi$
$654$		0			0
$655$	−215836.			−0.503084
$656$		0			0
$657$		−	314663.i		−	0.728979i
$658$		0			0
$659$	−22762.5	−	54953.5i	−0.0524141	−	0.126539i	0.895503	−	0.445054i	$-0.146816\pi$
$659$	−22762.5	−	54953.5i	−0.0524141	−	0.126539i	−0.947918	+	0.318516i	$0.896816\pi$
$660$		0			0
$661$	−2686.94	+	6486.84i	−0.00614971	+	0.0148467i	−0.926925	−	0.375248i	$-0.877558\pi$
$661$	−2686.94	+	6486.84i	−0.00614971	+	0.0148467i	0.920775	+	0.390094i	$0.127558\pi$
$662$		0			0
$663$	13427.5	+	13427.5i	0.0305469	+	0.0305469i
$664$		0			0
$665$	−997293.	−	997293.i	−2.25517	−	2.25517i
$666$		0			0
$667$	25666.5	−	61964.5i	0.0576920	−	0.139281i
$668$		0			0
$669$	−106919.	−	258125.i	−0.238892	−	0.576737i
$670$		0			0
$671$		−	395738.i		−	0.878948i
$672$		0			0
$673$	−403297.			−0.890421			−0.445210	−	0.895426i	$-0.646871\pi$
$673$	−403297.			−0.890421			−0.445210	+	0.895426i	$0.646871\pi$
$674$		0			0
$675$	82678.9	−	34246.7i	0.181463	−	0.0751642i
$676$		0			0
$677$	827528.	+	342773.i	1.80553	+	0.747876i	0.984111	+	0.177555i	$0.0568188\pi$
$677$	827528.	+	342773.i	1.80553	+	0.747876i	0.821422	+	0.570321i	$0.193181\pi$
$678$		0			0
$679$	−597161.	+	597161.i	−1.29525	+	1.29525i
$680$		0			0
$681$	736036.	−	736036.i	1.58710	−	1.58710i
$682$		0			0
$683$	−118571.	−	49113.5i	−0.254176	−	0.105283i	0.251957	−	0.967738i	$-0.418926\pi$
$683$	−118571.	−	49113.5i	−0.254176	−	0.105283i	−0.506134	+	0.862455i	$0.668926\pi$
$684$		0			0
$685$	686812.	−	284487.i	1.46372	−	0.606291i
$686$		0			0
$687$	66607.3			0.141126
$688$		0			0
$689$		−	16540.7i		−	0.0348429i
$690$		0			0
$691$	−310268.	−	749054.i	−0.649802	−	1.56876i	−0.813062	−	0.582178i	$-0.802201\pi$
$691$	−310268.	−	749054.i	−0.649802	−	1.56876i	0.163259	−	0.986583i	$-0.447799\pi$
$692$		0			0
$693$	−150250.	+	362736.i	−0.312859	+	0.755308i
$694$		0			0
$695$	−716062.	−	716062.i	−1.48245	−	1.48245i
$696$		0			0
$697$	62568.3	+	62568.3i	0.128792	+	0.128792i
$698$		0			0
$699$	358667.	−	865898.i	0.734069	−	1.77220i
$700$		0			0
$701$	44722.7	+	107970.i	0.0910107	+	0.219719i	0.962830	−	0.270109i	$-0.0870596\pi$
$701$	44722.7	+	107970.i	0.0910107	+	0.219719i	−0.871819	+	0.489828i	$0.837060\pi$
$702$		0			0
$703$			1.72671e6i			3.49388i
$704$		0			0
$705$	503939.			1.01391
$706$		0			0
$707$	118876.	−	49240.2i	0.237825	−	0.0985102i
$708$		0			0
$709$	−642955.	−	266321.i	−1.27905	−	0.529801i	−0.363348	−	0.931653i	$-0.618366\pi$
$709$	−642955.	−	266321.i	−1.27905	−	0.529801i	−0.915704	+	0.401853i	$0.868366\pi$
$710$		0			0
$711$	56665.3	−	56665.3i	0.112093	−	0.112093i
$712$		0			0
$713$	−90407.3	+	90407.3i	−0.177838	+	0.177838i
$714$		0			0
$715$	−17512.2	−	7253.79i	−0.0342553	−	0.0141890i
$716$		0			0
$717$	83665.8	−	34655.5i	0.162746	−	0.0674115i
$718$		0			0
$719$	27620.9			0.0534294			0.0267147	−	0.999643i	$-0.491495\pi$
$719$	27620.9			0.0534294			0.0267147	+	0.999643i	$0.491495\pi$
$720$		0			0
$721$		−	562783.i		−	1.08261i
$722$		0			0
$723$	333817.	+	805906.i	0.638604	+	1.54173i
$724$		0			0
$725$	59668.5	−	144053.i	0.113519	−	0.274060i
$726$		0			0
$727$	−713662.	−	713662.i	−1.35028	−	1.35028i	−0.885346	−	0.464933i	$-0.846078\pi$
$727$	−713662.	−	713662.i	−1.35028	−	1.35028i	−0.464933	−	0.885346i	$-0.653922\pi$
$728$		0			0
$729$	45751.7	+	45751.7i	0.0860899	+	0.0860899i
$730$		0			0
$731$	−53106.8	+	128211.i	−0.0993837	+	0.239934i
$732$		0			0
$733$	−248495.	−	599919.i	−0.462497	−	1.11657i	−0.967369	−	0.253373i	$-0.918460\pi$
$733$	−248495.	−	599919.i	−0.462497	−	1.11657i	0.504871	−	0.863195i	$-0.331540\pi$
$734$		0			0
$735$		−	989231.i		−	1.83115i
$736$		0			0
$737$	526482.			0.969278
$738$		0			0
$739$	−354062.	+	146657.i	−0.648322	+	0.268544i	−0.682515	−	0.730872i	$-0.739114\pi$
$739$	−354062.	+	146657.i	−0.648322	+	0.268544i	0.0341933	+	0.999415i	$0.489114\pi$
$740$		0			0
$741$	40530.2	+	16788.1i	0.0738145	+	0.0305750i
$742$		0			0
$743$	500318.	−	500318.i	0.906293	−	0.906293i	−0.0896779	−	0.995971i	$-0.528584\pi$
$743$	500318.	−	500318.i	0.906293	−	0.906293i	0.995971	+	0.0896779i	$0.0285838\pi$
$744$		0			0
$745$	−225905.	+	225905.i	−0.407017	+	0.407017i
$746$		0			0
$747$	65168.7	+	26993.8i	0.116788	+	0.0483751i
$748$		0			0
$749$	143422.	−	59407.4i	0.255654	−	0.105895i
$750$		0			0
$751$	305332.			0.541367			0.270684	−	0.962668i	$-0.412750\pi$
$751$	305332.			0.541367			0.270684	+	0.962668i	$0.412750\pi$
$752$		0			0
$753$		−	16979.8i		−	0.0299463i
$754$		0			0
$755$	70464.0	+	170115.i	0.123616	+	0.298434i
$756$		0			0
$757$	252676.	−	610014.i	0.440933	−	1.06451i	−0.534689	−	0.845049i	$-0.679571\pi$
$757$	252676.	−	610014.i	0.440933	−	1.06451i	0.975622	−	0.219457i	$-0.0704286\pi$
$758$		0			0
$759$	93521.7	+	93521.7i	0.162341	+	0.162341i
$760$		0			0
$761$	670075.	+	670075.i	1.15705	+	1.15705i	0.985106	+	0.171949i	$0.0550065\pi$
$761$	670075.	+	670075.i	1.15705	+	1.15705i	0.171949	+	0.985106i	$0.444994\pi$
$762$		0			0
$763$	−21724.4	+	52447.3i	−0.0373163	+	0.0900895i
$764$		0			0
$765$	−157401.	−	380001.i	−0.268959	−	0.649324i
$766$		0			0
$767$			24367.4i			0.0414208i
$768$		0			0
$769$	−18480.8			−0.0312513			−0.0156256	−	0.999878i	$-0.504974\pi$
$769$	−18480.8			−0.0312513			−0.0156256	+	0.999878i	$0.504974\pi$
$770$		0			0
$771$	863066.	−	357494.i	1.45190	−	0.601395i
$772$		0			0
$773$	−839661.	−	347799.i	−1.40522	−	0.582062i	−0.454120	−	0.890940i	$-0.650046\pi$
$773$	−839661.	−	347799.i	−1.40522	−	0.582062i	−0.951101	+	0.308879i	$0.900046\pi$
$774$		0			0
$775$	−210175.	+	210175.i	−0.349928	+	0.349928i
$776$		0			0
$777$	−1.55669e6	+	1.55669e6i	−2.57846	+	2.57846i
$778$		0			0
$779$	188860.	+	78228.2i	0.311218	+	0.128911i
$780$		0			0
$781$	175324.	−	72621.5i	0.287435	−	0.119059i
$782$		0			0
$783$	−229155.			−0.373770
$784$		0			0
$785$			717888.i			1.16498i
$786$		0			0
$787$	−100288.	−	242117.i	−0.161920	−	0.390910i	0.822008	−	0.569476i	$-0.192854\pi$
$787$	−100288.	−	242117.i	−0.161920	−	0.390910i	−0.983928	+	0.178567i	$0.942854\pi$
$788$		0			0
$789$	−214067.	+	516805.i	−0.343872	+	0.830180i
$790$		0			0
$791$	600912.	+	600912.i	0.960412	+	0.960412i
$792$		0			0
$793$	−15067.5	−	15067.5i	−0.0239604	−	0.0239604i
$794$		0			0
$795$	−362738.	+	875726.i	−0.573929	+	1.38559i
$796$		0			0
$797$	265742.	+	641557.i	0.418353	+	1.00999i	0.982825	+	0.184541i	$0.0590798\pi$
$797$	265742.	+	641557.i	0.418353	+	1.00999i	−0.564472	+	0.825452i	$0.690920\pi$
$798$		0			0
$799$			423327.i			0.663105i
$800$		0			0
$801$	306127.			0.477130
$802$		0			0
$803$	−644934.	+	267140.i	−1.00019	+	0.414294i
$804$		0			0
$805$	−211526.	−	87617.0i	−0.326417	−	0.135206i
$806$		0			0
$807$	−167803.	+	167803.i	−0.257663	+	0.257663i
$808$		0			0
$809$	−140779.	+	140779.i	−0.215100	+	0.215100i	−0.806430	−	0.591330i	$-0.798603\pi$
$809$	−140779.	+	140779.i	−0.215100	+	0.215100i	0.591330	+	0.806430i	$0.298603\pi$
$810$		0			0
$811$	899163.	+	372445.i	1.36709	+	0.566266i	0.940997	−	0.338414i	$-0.109890\pi$
$811$	899163.	+	372445.i	1.36709	+	0.566266i	0.426091	+	0.904680i	$0.359890\pi$
$812$		0			0
$813$	−520736.	+	215696.i	−0.787837	+	0.326333i
$814$		0			0
$815$	437356.			0.658446
$816$		0			0
$817$			320601.i			0.480309i
$818$		0			0
$819$	8090.25	+	19531.6i	0.0120613	+	0.0291185i
$820$		0			0
$821$	402045.	−	970622.i	0.596469	−	1.44000i	−0.280687	−	0.959799i	$-0.590562\pi$
$821$	402045.	−	970622.i	0.596469	−	1.44000i	0.877156	−	0.480205i	$-0.159438\pi$
$822$		0			0
$823$	−800927.	−	800927.i	−1.18248	−	1.18248i	−0.979100	−	0.203379i	$-0.934808\pi$
$823$	−800927.	−	800927.i	−1.18248	−	1.18248i	−0.203379	−	0.979100i	$-0.565192\pi$
$824$		0			0
$825$	217415.	+	217415.i	0.319435	+	0.319435i
$826$		0			0
$827$	−359346.	+	867539.i	−0.525415	+	1.26846i	0.409084	+	0.912497i	$0.365848\pi$
$827$	−359346.	+	867539.i	−0.525415	+	1.26846i	−0.934499	+	0.355966i	$0.884152\pi$
$828$		0			0
$829$	48933.7	+	118136.i	0.0712031	+	0.171900i	0.955474	−	0.295074i	$-0.0953443\pi$
$829$	48933.7	+	118136.i	0.0712031	+	0.171900i	−0.884271	+	0.466974i	$0.845344\pi$
$830$		0			0
$831$			387873.i			0.561678i
$832$		0			0
$833$	830989.			1.19758
$834$		0			0
$835$	1.12383e6	−	465505.i	1.61186	−	0.667654i
$836$		0			0
$837$	403585.	+	167170.i	0.576082	+	0.238621i
$838$		0			0
$839$	270605.	−	270605.i	0.384425	−	0.384425i	−0.488269	−	0.872693i	$-0.662371\pi$
$839$	270605.	−	270605.i	0.384425	−	0.384425i	0.872693	+	0.488269i	$0.162371\pi$
$840$		0			0
$841$	217804.	−	217804.i	0.307946	−	0.307946i
$842$		0			0
$843$	152003.	+	62961.6i	0.213893	+	0.0885974i
$844$		0			0
$845$	778147.	−	322319.i	1.08980	−	0.451412i
$846$		0			0
$847$	−198577.			−0.276797
$848$		0			0
$849$		−	290235.i		−	0.402656i
$850$		0			0
$851$	107268.	+	258968.i	0.148119	+	0.357591i
$852$		0			0
$853$	−534418.	+	1.29020e6i	−0.734485	+	1.77320i	−0.107452	+	0.994210i	$0.534269\pi$
$853$	−534418.	+	1.29020e6i	−0.734485	+	1.77320i	−0.627033	+	0.778993i	$0.715731\pi$
$854$		0			0
$855$	−671905.	−	671905.i	−0.919128	−	0.919128i
$856$		0			0
$857$	160279.	+	160279.i	0.218230	+	0.218230i	0.807752	−	0.589522i	$-0.200684\pi$
$857$	160279.	+	160279.i	0.218230	+	0.218230i	−0.589522	+	0.807752i	$0.700684\pi$
$858$		0			0
$859$	−325796.	+	786541.i	−0.441529	+	1.06595i	0.533883	+	0.845558i	$0.320732\pi$
$859$	−325796.	+	786541.i	−0.441529	+	1.06595i	−0.975412	+	0.220388i	$0.929268\pi$
$860$		0			0
$861$	99738.4	+	240790.i	0.134541	+	0.324812i
$862$		0			0
$863$		−	440927.i		−	0.592033i	−0.955183	−	0.296016i	$-0.904342\pi$
$863$		−	440927.i		−	0.592033i	0.955183	−	0.296016i	$-0.0956583\pi$
$864$		0			0
$865$	−1.03177e6			−1.37896
$866$		0			0
$867$	−35996.1	+	14910.1i	−0.0478869	+	0.0198354i
$868$		0			0
$869$	−164249.	−	68034.0i	−0.217501	−	0.0900920i
$870$		0			0
$871$	20045.4	−	20045.4i	0.0264228	−	0.0264228i
$872$		0			0
$873$	−402325.	+	402325.i	−0.527897	+	0.527897i
$874$		0			0
$875$	753754.	+	312215.i	0.984495	+	0.407791i
$876$		0			0
$877$	205936.	−	85301.4i	0.267752	−	0.110906i	−0.244768	−	0.969582i	$-0.578712\pi$
$877$	205936.	−	85301.4i	0.267752	−	0.110906i	0.512520	+	0.858675i	$0.328712\pi$
$878$		0			0
$879$	865880.			1.12068
$880$		0			0
$881$		−	1.09695e6i		−	1.41330i	−0.707563	−	0.706650i	$-0.750206\pi$
$881$		−	1.09695e6i		−	1.41330i	0.707563	−	0.706650i	$-0.249794\pi$
$882$		0			0
$883$	−411164.	−	992637.i	−0.527343	−	1.27312i	−0.933257	−	0.359208i	$-0.883047\pi$
$883$	−411164.	−	992637.i	−0.527343	−	1.27312i	0.405914	−	0.913911i	$-0.366953\pi$
$884$		0			0
$885$	534378.	−	1.29010e6i	0.682280	−	1.64717i
$886$		0			0
$887$	1.02023e6	+	1.02023e6i	1.29673	+	1.29673i	0.930542	+	0.366186i	$0.119337\pi$
$887$	1.02023e6	+	1.02023e6i	1.29673	+	1.29673i	0.366186	+	0.930542i	$0.380663\pi$
$888$		0			0
$889$	1.12441e6	+	1.12441e6i	1.42273	+	1.42273i
$890$		0			0
$891$	339519.	−	819672.i	0.427670	−	1.03249i
$892$		0			0
$893$	374257.	+	903536.i	0.469318	+	1.13303i
$894$		0			0
$895$			471050.i			0.588060i
$896$		0			0
$897$	7121.55			0.00885094
$898$		0			0
$899$	703172.	−	291263.i	0.870045	−	0.360385i
$900$		0			0
$901$	−735641.	−	304713.i	−0.906184	−	0.375354i
$902$		0			0
$903$	−289034.	+	289034.i	−0.354465	+	0.354465i
$904$		0			0
$905$	43814.7	−	43814.7i	0.0534961	−	0.0534961i
$906$		0			0
$907$	−1.27013e6	−	526105.i	−1.54395	−	0.639525i	−0.561741	−	0.827313i	$-0.689868\pi$
$907$	−1.27013e6	−	526105.i	−1.54395	−	0.639525i	−0.982210	+	0.187787i	$0.939868\pi$
$908$		0			0
$909$	80090.6	−	33174.6i	0.0969290	−	0.0401493i
$910$		0			0
$911$	−1.61282e6			−1.94335			−0.971673	−	0.236330i	$-0.924055\pi$
$911$	−1.61282e6			−1.94335			−0.971673	+	0.236330i	$0.924055\pi$
$912$		0			0
$913$		−	156487.i		−	0.187731i
$914$		0			0
$915$	467299.	+	1.12816e6i	0.558152	+	1.34750i
$916$		0			0
$917$	204368.	−	493389.i	0.243038	−	0.586747i
$918$		0			0
$919$	−4576.29	−	4576.29i	−0.00541854	−	0.00541854i	0.704392	−	0.709811i	$-0.251220\pi$
$919$	−4576.29	−	4576.29i	−0.00541854	−	0.00541854i	−0.709811	+	0.704392i	$0.751220\pi$
$920$		0			0
$921$	−307680.	−	307680.i	−0.362727	−	0.362727i
$922$		0			0
$923$	3910.32	−	9440.35i	0.00458996	−	0.0110812i
$924$		0			0
$925$	249372.	+	602037.i	0.291450	+	0.703623i
$926$		0			0
$927$		−	379164.i		−	0.441232i
$928$		0			0
$929$	−1.02799e6			−1.19113			−0.595565	−	0.803307i	$-0.703072\pi$
$929$	−1.02799e6			−1.19113			−0.595565	+	0.803307i	$0.703072\pi$
$930$		0			0
$931$	1.77364e6	−	734665.i	2.04628	−	0.847598i
$932$		0			0
$933$	−345853.	−	143257.i	−0.397308	−	0.164571i
$934$		0			0
$935$	−645220.	+	645220.i	−0.738048	+	0.738048i
$936$		0			0
$937$	−316507.	+	316507.i	−0.360500	+	0.360500i	−0.863997	−	0.503497i	$-0.832046\pi$
$937$	−316507.	+	316507.i	−0.360500	+	0.360500i	0.503497	+	0.863997i	$0.332046\pi$
$938$		0			0
$939$	−956448.	−	396174.i	−1.08475	−	0.449319i
$940$		0			0
$941$	442267.	−	183193.i	0.499465	−	0.206885i	−0.118705	−	0.992930i	$-0.537874\pi$
$941$	442267.	−	183193.i	0.499465	−	0.206885i	0.618170	+	0.786044i	$0.287874\pi$
$942$		0			0
$943$	33184.5			0.0373174
$944$		0			0
$945$			782258.i			0.875964i
$946$		0			0
$947$	238191.	+	575044.i	0.265598	+	0.641211i	0.999266	−	0.0382968i	$-0.0121932\pi$
$947$	238191.	+	575044.i	0.265598	+	0.641211i	−0.733668	+	0.679508i	$0.762193\pi$
$948$		0			0
$949$	−14384.2	+	34726.6i	−0.0159718	+	0.0385594i
$950$		0			0
$951$	−1.25558e6	−	1.25558e6i	−1.38830	−	1.38830i
$952$		0			0
$953$	−474715.	−	474715.i	−0.522693	−	0.522693i	0.395691	−	0.918384i	$-0.370505\pi$
$953$	−474715.	−	474715.i	−0.522693	−	0.522693i	−0.918384	+	0.395691i	$0.870505\pi$
$954$		0			0
$955$	−142441.	+	343884.i	−0.156181	+	0.377055i
$956$		0			0
$957$	−301297.	−	727395.i	−0.328981	−	0.794230i
$958$		0			0
$959$			1.83939e6i			2.00003i
$960$		0			0
$961$	−527378.			−0.571051
$962$		0			0
$963$	96627.8	−	40024.5i	0.104196	−	0.0431592i
$964$		0			0
$965$	−943584.	−	390845.i	−1.01327	−	0.419711i
$966$		0			0
$967$	560797.	−	560797.i	0.599726	−	0.599726i	−0.340514	−	0.940240i	$-0.610601\pi$
$967$	560797.	−	560797.i	0.599726	−	0.599726i	0.940240	+	0.340514i	$0.110601\pi$
$968$		0			0
$969$	1.49330e6	−	1.49330e6i	1.59037	−	1.59037i
$970$		0			0
$971$	−1.51201e6	−	626296.i	−1.60368	−	0.664265i	−0.611748	−	0.791053i	$-0.709533\pi$
$971$	−1.51201e6	−	626296.i	−1.60368	−	0.664265i	−0.991930	+	0.126787i	$0.959533\pi$
$972$		0			0
$973$	2.31490e6	−	958862.i	2.44515	−	1.01282i
$974$		0			0
$975$	16555.9			0.0174158
$976$		0			0
$977$			611241.i			0.640359i	0.947357	+	0.320179i	$0.103743\pi$
$977$			611241.i			0.640359i	−0.947357	+	0.320179i	$0.896257\pi$
$978$		0			0
$979$	−259894.	−	627439.i	−0.271163	−	0.654645i
$980$		0			0
$981$	−14636.4	+	35335.3i	−0.0152088	+	0.0367173i
$982$		0			0
$983$	8243.56	+	8243.56i	0.00853115	+	0.00853115i	0.711359	−	0.702828i	$-0.248080\pi$
$983$	8243.56	+	8243.56i	0.00853115	+	0.00853115i	−0.702828	+	0.711359i	$0.748080\pi$
$984$		0			0
$985$	−108212.	−	108212.i	−0.111533	−	0.111533i
$986$		0			0
$987$	−477165.	+	1.15198e6i	−0.489818	+	1.18252i
$988$		0			0
$989$	19916.6	+	48083.0i	0.0203621	+	0.0491585i
$990$		0			0
$991$		−	1.77738e6i		−	1.80981i	−0.425615	−	0.904904i	$-0.639942\pi$
$991$		−	1.77738e6i		−	1.80981i	0.425615	−	0.904904i	$-0.360058\pi$
$992$		0			0
$993$	474304.			0.481014
$994$		0			0
$995$	−162473.	+	67298.6i	−0.164110	+	0.0679767i
$996$		0			0
$997$	398464.	+	165049.i	0.400866	+	0.166044i	0.574002	−	0.818854i	$-0.305390\pi$
$997$	398464.	+	165049.i	0.400866	+	0.166044i	−0.173136	+	0.984898i	$0.555390\pi$
$998$		0			0
$999$	677199.	−	677199.i	0.678555	−	0.678555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.h.a.15.3		60
4.3	odd	2		32.5.h.a.27.15	yes	60
32.13	even	8		32.5.h.a.19.15	✓	60
32.19	odd	8	inner	128.5.h.a.111.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.5.h.a.19.15	✓	60	32.13	even	8
32.5.h.a.27.15	yes	60	4.3	odd	2
128.5.h.a.15.3		60	1.1	even	1	trivial
128.5.h.a.111.3		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)

\(f(q)\)	\(=\)	\(q+(-10.5427 + 4.36694i) q^{3} +(-27.2781 - 11.2990i) q^{5} +(51.6577 - 51.6577i) q^{7} +(34.8033 - 34.8033i) q^{9} +O(q^{10})\)	\(q+(-10.5427 + 4.36694i) q^{3} +(-27.2781 - 11.2990i) q^{5} +(51.6577 - 51.6577i) q^{7} +(34.8033 - 34.8033i) q^{9} +(-100.880 - 41.7858i) q^{11} +(-5.43190 + 2.24997i) q^{13} +336.928 q^{15} +283.031i q^{17} +(250.224 + 604.093i) q^{19} +(-319.027 + 770.199i) q^{21} +(75.0559 + 75.0559i) q^{23} +(174.487 + 174.487i) q^{25} +(138.784 - 335.055i) q^{27} +(-241.806 - 583.771i) q^{29} +1204.53i q^{31} +1246.03 q^{33} +(-1992.80 + 825.446i) q^{35} +(2439.75 + 1010.58i) q^{37} +(47.4416 - 47.4416i) q^{39} +(221.065 - 221.065i) q^{41} +(452.993 + 187.636i) q^{43} +(-1342.61 + 556.127i) q^{45} +1495.69 q^{47} -2936.03i q^{49} +(-1235.98 - 2983.92i) q^{51} +(-1076.60 + 2599.15i) q^{53} +(2279.68 + 2279.68i) q^{55} +(-5276.08 - 5276.08i) q^{57} +(1586.03 - 3829.02i) q^{59} +(1386.94 + 3348.37i) q^{61} -3595.72i q^{63} +173.594 q^{65} +(-4454.60 + 1845.16i) q^{67} +(-1119.06 - 463.529i) q^{69} +(-1228.91 + 1228.91i) q^{71} +(4520.59 - 4520.59i) q^{73} +(-2601.54 - 1077.59i) q^{75} +(-7369.78 + 3052.66i) q^{77} +1628.16 q^{79} +8125.22i q^{81} +(548.438 + 1324.05i) q^{83} +(3197.96 - 7720.56i) q^{85} +(5098.59 + 5098.59i) q^{87} +(4397.96 + 4397.96i) q^{89} +(-164.371 + 396.828i) q^{91} +(-5260.12 - 12699.1i) q^{93} -19305.8i q^{95} -11560.0 q^{97} +(-4965.24 + 2056.67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more