LMFDB - Embedded newform 128.5.h.a.15.15

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			15.15
Character	$\chi$	$=$	128.15
Dual form			128.5.h.a.111.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.8038 - 6.13192i) q^{3} +(5.46900 + 2.26533i) q^{5} +(-27.5680 + 27.5680i) q^{7} +(124.275 - 124.275i) q^{9} +O(q^{10})$	\(q+(14.8038 - 6.13192i) q^{3} +(5.46900 + 2.26533i) q^{5} +(-27.5680 + 27.5680i) q^{7} +(124.275 - 124.275i) q^{9} +(184.903 + 76.5894i) q^{11} +(132.460 - 54.8666i) q^{13} +94.8525 q^{15} -248.836i q^{17} +(39.5004 + 95.3625i) q^{19} +(-239.066 + 577.155i) q^{21} +(-411.396 - 411.396i) q^{23} +(-417.164 - 417.164i) q^{25} +(581.009 - 1402.68i) q^{27} +(-143.216 - 345.754i) q^{29} +1850.47i q^{31} +3206.90 q^{33} +(-213.220 + 88.3187i) q^{35} +(-638.380 - 264.426i) q^{37} +(1624.46 - 1624.46i) q^{39} +(-657.761 + 657.761i) q^{41} +(-624.120 - 258.519i) q^{43} +(961.185 - 398.136i) q^{45} +2822.36 q^{47} +881.007i q^{49} +(-1525.84 - 3683.70i) q^{51} +(-576.805 + 1392.53i) q^{53} +(837.735 + 837.735i) q^{55} +(1169.51 + 1169.51i) q^{57} +(-279.381 + 674.486i) q^{59} +(-811.446 - 1959.00i) q^{61} +6852.04i q^{63} +848.713 q^{65} +(-1817.99 + 753.038i) q^{67} +(-8612.86 - 3567.56i) q^{69} +(-5642.97 + 5642.97i) q^{71} +(-1248.98 + 1248.98i) q^{73} +(-8733.60 - 3617.58i) q^{75} +(-7208.84 + 2986.00i) q^{77} -5321.96 q^{79} -10091.8i q^{81} +(3373.32 + 8143.90i) q^{83} +(563.696 - 1360.88i) q^{85} +(-4240.27 - 4240.27i) q^{87} +(-810.460 - 810.460i) q^{89} +(-2139.09 + 5164.22i) q^{91} +(11346.9 + 27393.9i) q^{93} +611.019i q^{95} +1619.29 q^{97} +(32497.0 - 13460.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	14.8038	−	6.13192i	1.64486	−	0.681324i	0.648087	−	0.761567i	$-0.275569\pi$
$3$	14.8038	−	6.13192i	1.64486	−	0.681324i	0.996775	+	0.0802425i	$0.0255695\pi$
$4$		0			0
$5$	5.46900	+	2.26533i	0.218760	+	0.0906133i	0.489372	−	0.872075i	$-0.337226\pi$
$5$	5.46900	+	2.26533i	0.218760	+	0.0906133i	−0.270612	+	0.962688i	$0.587226\pi$
$6$		0			0
$7$	−27.5680	+	27.5680i	−0.562613	+	0.562613i	−0.930049	−	0.367436i	$-0.880236\pi$
$7$	−27.5680	+	27.5680i	−0.562613	+	0.562613i	0.367436	+	0.930049i	$0.380236\pi$
$8$		0			0
$9$	124.275	−	124.275i	1.53426	−	1.53426i
$10$		0			0
$11$	184.903	+	76.5894i	1.52813	+	0.632970i	0.979199	−	0.202900i	$-0.0650367\pi$
$11$	184.903	+	76.5894i	1.52813	+	0.632970i	0.548926	+	0.835871i	$0.315037\pi$
$12$		0			0
$13$	132.460	−	54.8666i	0.783786	−	0.324655i	0.0453434	−	0.998971i	$-0.485562\pi$
$13$	132.460	−	54.8666i	0.783786	−	0.324655i	0.738442	+	0.674317i	$0.235562\pi$
$14$		0			0
$15$	94.8525			0.421567
$16$		0			0
$17$		−	248.836i		−	0.861023i	−0.902585	−	0.430512i	$-0.858333\pi$
$17$		−	248.836i		−	0.861023i	0.902585	−	0.430512i	$-0.141667\pi$
$18$		0			0
$19$	39.5004	+	95.3625i	0.109419	+	0.264162i	0.969099	−	0.246672i	$-0.0793369\pi$
$19$	39.5004	+	95.3625i	0.109419	+	0.264162i	−0.859680	+	0.510833i	$0.829337\pi$
$20$		0			0
$21$	−239.066	+	577.155i	−0.542099	+	1.30874i
$22$		0			0
$23$	−411.396	−	411.396i	−0.777687	−	0.777687i	0.201750	−	0.979437i	$-0.435337\pi$
$23$	−411.396	−	411.396i	−0.777687	−	0.777687i	−0.979437	+	0.201750i	$0.935337\pi$
$24$		0			0
$25$	−417.164	−	417.164i	−0.667462	−	0.667462i
$26$		0			0
$27$	581.009	−	1402.68i	0.796995	−	1.92412i
$28$		0			0
$29$	−143.216	−	345.754i	−0.170293	−	0.411123i	0.815574	−	0.578652i	$-0.196421\pi$
$29$	−143.216	−	345.754i	−0.170293	−	0.411123i	−0.985867	+	0.167529i	$0.946421\pi$
$30$		0			0
$31$			1850.47i			1.92557i	0.270277	+	0.962783i	$0.412885\pi$
$31$			1850.47i			1.92557i	−0.270277	+	0.962783i	$0.587115\pi$
$32$		0			0
$33$	3206.90			2.94481
$34$		0			0
$35$	−213.220	+	88.3187i	−0.174057	+	0.0720969i
$36$		0			0
$37$	−638.380	−	264.426i	−0.466311	−	0.193152i	0.137141	−	0.990552i	$-0.456209\pi$
$37$	−638.380	−	264.426i	−0.466311	−	0.193152i	−0.603452	+	0.797399i	$0.706209\pi$
$38$		0			0
$39$	1624.46	−	1624.46i	1.06802	−	1.06802i
$40$		0			0
$41$	−657.761	+	657.761i	−0.391291	+	0.391291i	−0.875148	−	0.483856i	$-0.839236\pi$
$41$	−657.761	+	657.761i	−0.391291	+	0.391291i	0.483856	+	0.875148i	$0.339236\pi$
$42$		0			0
$43$	−624.120	−	258.519i	−0.337545	−	0.139816i	0.207472	−	0.978241i	$-0.433477\pi$
$43$	−624.120	−	258.519i	−0.337545	−	0.139816i	−0.545016	+	0.838425i	$0.683477\pi$
$44$		0			0
$45$	961.185	−	398.136i	0.474659	−	0.196610i
$46$		0			0
$47$	2822.36			1.27766			0.638831	−	0.769347i	$-0.279418\pi$
$47$	2822.36			1.27766			0.638831	+	0.769347i	$0.279418\pi$
$48$		0			0
$49$			881.007i			0.366934i
$50$		0			0
$51$	−1525.84	−	3683.70i	−0.586636	−	1.41626i
$52$		0			0
$53$	−576.805	+	1392.53i	−0.205342	+	0.495739i	−0.992679	−	0.120784i	$-0.961459\pi$
$53$	−576.805	+	1392.53i	−0.205342	+	0.495739i	0.787337	+	0.616523i	$0.211459\pi$
$54$		0			0
$55$	837.735	+	837.735i	0.276937	+	0.276937i
$56$		0			0
$57$	1169.51	+	1169.51i	0.359960	+	0.359960i
$58$		0			0
$59$	−279.381	+	674.486i	−0.0802589	+	0.193762i	−0.958915	−	0.283693i	$-0.908441\pi$
$59$	−279.381	+	674.486i	−0.0802589	+	0.193762i	0.878656	+	0.477455i	$0.158441\pi$
$60$		0			0
$61$	−811.446	−	1959.00i	−0.218072	−	0.526473i	0.776548	−	0.630057i	$-0.216969\pi$
$61$	−811.446	−	1959.00i	−0.218072	−	0.526473i	−0.994621	+	0.103585i	$0.966969\pi$
$62$		0			0
$63$			6852.04i			1.72639i
$64$		0			0
$65$	848.713			0.200879
$66$		0			0
$67$	−1817.99	+	753.038i	−0.404989	+	0.167752i	−0.575873	−	0.817539i	$-0.695338\pi$
$67$	−1817.99	+	753.038i	−0.404989	+	0.167752i	0.170884	+	0.985291i	$0.445338\pi$
$68$		0			0
$69$	−8612.86	−	3567.56i	−1.80904	−	0.749331i
$70$		0			0
$71$	−5642.97	+	5642.97i	−1.11942	+	1.11942i	−0.127589	+	0.991827i	$0.540724\pi$
$71$	−5642.97	+	5642.97i	−1.11942	+	1.11942i	−0.991827	+	0.127589i	$0.959276\pi$
$72$		0			0
$73$	−1248.98	+	1248.98i	−0.234375	+	0.234375i	−0.814516	−	0.580141i	$-0.802997\pi$
$73$	−1248.98	+	1248.98i	−0.234375	+	0.234375i	0.580141	+	0.814516i	$0.302997\pi$
$74$		0			0
$75$	−8733.60	−	3617.58i	−1.55264	−	0.643125i
$76$		0			0
$77$	−7208.84	+	2986.00i	−1.21586	+	0.503626i
$78$		0			0
$79$	−5321.96			−0.852741			−0.426370	−	0.904549i	$-0.640208\pi$
$79$	−5321.96			−0.852741			−0.426370	+	0.904549i	$0.640208\pi$
$80$		0			0
$81$		−	10091.8i		−	1.53814i
$82$		0			0
$83$	3373.32	+	8143.90i	0.489667	+	1.18216i	0.954888	+	0.296966i	$0.0959748\pi$
$83$	3373.32	+	8143.90i	0.489667	+	1.18216i	−0.465221	+	0.885194i	$0.654025\pi$
$84$		0			0
$85$	563.696	−	1360.88i	0.0780201	−	0.188357i
$86$		0			0
$87$	−4240.27	−	4240.27i	−0.560216	−	0.560216i
$88$		0			0
$89$	−810.460	−	810.460i	−0.102318	−	0.102318i	0.654095	−	0.756413i	$-0.273050\pi$
$89$	−810.460	−	810.460i	−0.102318	−	0.102318i	−0.756413	+	0.654095i	$0.773050\pi$
$90$		0			0
$91$	−2139.09	+	5164.22i	−0.258313	+	0.623623i
$92$		0			0
$93$	11346.9	+	27393.9i	1.31193	+	3.16729i
$94$		0			0
$95$			611.019i			0.0677029i
$96$		0			0
$97$	1619.29			0.172100			0.0860498	−	0.996291i	$-0.472576\pi$
$97$	1619.29			0.172100			0.0860498	+	0.996291i	$0.472576\pi$
$98$		0			0
$99$	32497.0	−	13460.7i	3.31569	−	1.37340i
$100$		0			0
$101$	−2310.68	−	957.113i	−0.226515	−	0.0938254i	0.266540	−	0.963824i	$-0.414120\pi$
$101$	−2310.68	−	957.113i	−0.226515	−	0.0938254i	−0.493054	+	0.869999i	$0.664120\pi$
$102$		0			0
$103$	12151.7	−	12151.7i	1.14542	−	1.14542i	0.157973	−	0.987443i	$-0.449504\pi$
$103$	12151.7	−	12151.7i	1.14542	−	1.14542i	0.987443	−	0.157973i	$-0.0504958\pi$
$104$		0			0
$105$	−2614.90	+	2614.90i	−0.237179	+	0.237179i
$106$		0			0
$107$	−9865.09	−	4086.25i	−0.861655	−	0.356909i	−0.0923006	−	0.995731i	$-0.529422\pi$
$107$	−9865.09	−	4086.25i	−0.861655	−	0.356909i	−0.769355	+	0.638822i	$0.779422\pi$
$108$		0			0
$109$	687.323	−	284.698i	0.0578506	−	0.0239625i	−0.353571	−	0.935408i	$-0.615033\pi$
$109$	687.323	−	284.698i	0.0578506	−	0.0239625i	0.411421	+	0.911445i	$0.365033\pi$
$110$		0			0
$111$	−11071.9			−0.898617
$112$		0			0
$113$		−	7380.84i		−	0.578028i	−0.957325	−	0.289014i	$-0.906673\pi$
$113$		−	7380.84i		−	0.578028i	0.957325	−	0.289014i	$-0.0933275\pi$
$114$		0			0
$115$	−1317.98	−	3181.87i	−0.0996579	−	0.240595i
$116$		0			0
$117$	9642.90	−	23280.0i	0.704427	−	1.70064i
$118$		0			0
$119$	6859.91	+	6859.91i	0.484423	+	0.484423i
$120$		0			0
$121$	17970.5	+	17970.5i	1.22741	+	1.22741i
$122$		0			0
$123$	−5704.00	+	13770.7i	−0.377024	+	0.910216i
$124$		0			0
$125$	−2752.28	−	6644.60i	−0.176146	−	0.425255i
$126$		0			0
$127$		−	11122.8i		−	0.689612i	−0.938674	−	0.344806i	$-0.887945\pi$
$127$		−	11122.8i		−	0.689612i	0.938674	−	0.344806i	$-0.112055\pi$
$128$		0			0
$129$	−10824.5			−0.650474
$130$		0			0
$131$	−7771.92	+	3219.23i	−0.452882	+	0.187590i	−0.597452	−	0.801905i	$-0.703820\pi$
$131$	−7771.92	+	3219.23i	−0.452882	+	0.187590i	0.144570	+	0.989495i	$0.453820\pi$
$132$		0			0
$133$	−3717.90	−	1540.01i	−0.210182	−	0.0870601i
$134$		0			0
$135$	6355.08	−	6355.08i	0.348701	−	0.348701i
$136$		0			0
$137$	−20632.9	+	20632.9i	−1.09931	+	1.09931i	−0.104818	+	0.994491i	$0.533426\pi$
$137$	−20632.9	+	20632.9i	−1.09931	+	1.09931i	−0.994491	+	0.104818i	$0.966574\pi$
$138$		0			0
$139$	−827.151	−	342.617i	−0.0428110	−	0.0177329i	0.361175	−	0.932498i	$-0.382376\pi$
$139$	−827.151	−	342.617i	−0.0428110	−	0.0177329i	−0.403986	+	0.914765i	$0.632376\pi$
$140$		0			0
$141$	41781.5	−	17306.5i	2.10158	−	0.870503i
$142$		0			0
$143$	28694.4			1.40322
$144$		0			0
$145$		−	2215.36i		−	0.105368i
$146$		0			0
$147$	5402.26	+	13042.2i	0.250001	+	0.603555i
$148$		0			0
$149$	−2146.56	+	5182.25i	−0.0966875	+	0.233424i	−0.964822	−	0.262905i	$-0.915319\pi$
$149$	−2146.56	+	5182.25i	−0.0966875	+	0.233424i	0.868134	+	0.496330i	$0.165319\pi$
$150$		0			0
$151$	−27577.6	−	27577.6i	−1.20949	−	1.20949i	−0.971191	−	0.238301i	$-0.923409\pi$
$151$	−27577.6	−	27577.6i	−1.20949	−	1.20949i	−0.238301	−	0.971191i	$-0.576591\pi$
$152$		0			0
$153$	−30924.1	−	30924.1i	−1.32103	−	1.32103i
$154$		0			0
$155$	−4191.93	+	10120.2i	−0.174482	+	0.421236i
$156$		0			0
$157$	−9255.16	−	22343.9i	−0.375478	−	0.906484i	−0.992801	−	0.119774i	$-0.961783\pi$
$157$	−9255.16	−	22343.9i	−0.375478	−	0.906484i	0.617323	−	0.786710i	$-0.288217\pi$
$158$		0			0
$159$			24151.6i			0.955326i
$160$		0			0
$161$	22682.8			0.875073
$162$		0			0
$163$	−14473.9	+	5995.29i	−0.544767	+	0.225650i	−0.638057	−	0.769989i	$-0.720262\pi$
$163$	−14473.9	+	5995.29i	−0.544767	+	0.225650i	0.0932901	+	0.995639i	$0.470262\pi$
$164$		0			0
$165$	17538.5	+	7264.70i	0.644207	+	0.266839i
$166$		0			0
$167$	14397.3	−	14397.3i	0.516237	−	0.516237i	−0.400194	−	0.916431i	$-0.631057\pi$
$167$	14397.3	−	14397.3i	0.516237	−	0.516237i	0.916431	+	0.400194i	$0.131057\pi$
$168$		0			0
$169$	−5660.44	+	5660.44i	−0.198188	+	0.198188i
$170$		0			0
$171$	16760.1	+	6942.27i	0.573172	+	0.237415i
$172$		0			0
$173$	9749.02	−	4038.18i	0.325738	−	0.134925i	−0.213821	−	0.976873i	$-0.568591\pi$
$173$	9749.02	−	4038.18i	0.325738	−	0.134925i	0.539559	+	0.841948i	$0.318591\pi$
$174$		0			0
$175$	23000.8			0.751045
$176$		0			0
$177$			11698.1i			0.373394i
$178$		0			0
$179$	13526.8	+	32656.5i	0.422171	+	1.01921i	0.981706	+	0.190404i	$0.0609798\pi$
$179$	13526.8	+	32656.5i	0.422171	+	1.01921i	−0.559535	+	0.828807i	$0.689020\pi$
$180$		0			0
$181$	9580.95	−	23130.5i	0.292450	−	0.706037i	−0.707550	−	0.706663i	$-0.750200\pi$
$181$	9580.95	−	23130.5i	0.292450	−	0.706037i	1.00000		0.000626804i	$0.000199518\pi$
$182$		0			0
$183$	−24024.9	−	24024.9i	−0.717397	−	0.717397i
$184$		0			0
$185$	−2892.29	−	2892.29i	−0.0845080	−	0.0845080i
$186$		0			0
$187$	19058.2	−	46010.5i	0.545002	−	1.31575i
$188$		0			0
$189$	22651.9	+	54686.4i	0.634133	+	1.53093i
$190$		0			0
$191$			30274.1i			0.829861i	0.909853	+	0.414930i	$0.136194\pi$
$191$			30274.1i			0.829861i	−0.909853	+	0.414930i	$0.863806\pi$
$192$		0			0
$193$	47207.4			1.26735			0.633673	−	0.773601i	$-0.281546\pi$
$193$	47207.4			1.26735			0.633673	+	0.773601i	$0.281546\pi$
$194$		0			0
$195$	12564.1	−	5204.24i	0.330418	−	0.136864i
$196$		0			0
$197$	−48910.4	−	20259.4i	−1.26029	−	0.522027i	−0.350288	−	0.936642i	$-0.613916\pi$
$197$	−48910.4	−	20259.4i	−1.26029	−	0.522027i	−0.909997	+	0.414615i	$0.863916\pi$
$198$		0			0
$199$	14785.0	−	14785.0i	0.373350	−	0.373350i	−0.495346	−	0.868696i	$-0.664959\pi$
$199$	14785.0	−	14785.0i	0.373350	−	0.373350i	0.868696	+	0.495346i	$0.164959\pi$
$200$		0			0
$201$	−22295.6	+	22295.6i	−0.551857	+	0.551857i
$202$		0			0
$203$	13479.9	+	5583.58i	0.327112	+	0.135494i
$204$		0			0
$205$	−5087.34	+	2107.24i	−0.121055	+	0.0501426i
$206$		0			0
$207$	−102253.			−2.38635
$208$		0			0
$209$			20658.1i			0.472932i
$210$		0			0
$211$	−9300.05	−	22452.3i	−0.208891	−	0.504308i	0.784358	−	0.620309i	$-0.212993\pi$
$211$	−9300.05	−	22452.3i	−0.208891	−	0.504308i	−0.993249	+	0.116000i	$0.962993\pi$
$212$		0			0
$213$	−48935.0	+	118139.i	−1.07860	+	2.60397i
$214$		0			0
$215$	−2827.68	−	2827.68i	−0.0611721	−	0.0611721i
$216$		0			0
$217$	−51013.8	−	51013.8i	−1.08335	−	1.08335i
$218$		0			0
$219$	−10831.0	+	26148.3i	−0.225829	+	0.545200i
$220$		0			0
$221$	−13652.8	−	32960.7i	−0.279535	−	0.674857i
$222$		0			0
$223$		−	34700.2i		−	0.697786i	−0.937163	−	0.348893i	$-0.886558\pi$
$223$		−	34700.2i		−	0.697786i	0.937163	−	0.348893i	$-0.113442\pi$
$224$		0			0
$225$	−103686.			−2.04812
$226$		0			0
$227$	−76535.1	+	31701.9i	−1.48528	+	0.615224i	−0.970284	−	0.241968i	$-0.922207\pi$
$227$	−76535.1	+	31701.9i	−1.48528	+	0.615224i	−0.514997	+	0.857192i	$0.672207\pi$
$228$		0			0
$229$	84007.2	+	34796.9i	1.60194	+	0.663544i	0.991688	−	0.128665i	$-0.0410690\pi$
$229$	84007.2	+	34796.9i	1.60194	+	0.663544i	0.610250	+	0.792209i	$0.291069\pi$
$230$		0			0
$231$	−88408.0	+	88408.0i	−1.65679	+	1.65679i
$232$		0			0
$233$	55774.1	−	55774.1i	1.02735	−	1.02735i	0.0277397	−	0.999615i	$-0.491169\pi$
$233$	55774.1	−	55774.1i	1.02735	−	1.02735i	0.999615	−	0.0277397i	$-0.00883094\pi$
$234$		0			0
$235$	15435.5	+	6393.58i	0.279501	+	0.115773i
$236$		0			0
$237$	−78784.9	+	32633.8i	−1.40264	+	0.580993i
$238$		0			0
$239$	51395.5			0.899765			0.449882	−	0.893088i	$-0.351466\pi$
$239$	51395.5			0.899765			0.449882	+	0.893088i	$0.351466\pi$
$240$		0			0
$241$		−	45648.6i		−	0.785947i	−0.919550	−	0.392973i	$-0.871446\pi$
$241$		−	45648.6i		−	0.785947i	0.919550	−	0.392973i	$-0.128554\pi$
$242$		0			0
$243$	−14820.1	−	35778.8i	−0.250979	−	0.605917i
$244$		0			0
$245$	−1995.78	+	4818.23i	−0.0332491	+	0.0802703i
$246$		0			0
$247$	10464.4	+	10464.4i	0.171523	+	0.171523i
$248$		0			0
$249$	99875.5	+	99875.5i	1.61087	+	1.61087i
$250$		0			0
$251$	−182.790	+	441.295i	−0.00290139	+	0.00700456i	−0.925324	−	0.379178i	$-0.876207\pi$
$251$	−182.790	+	441.295i	−0.00290139	+	0.00700456i	0.922422	+	0.386183i	$0.126207\pi$
$252$		0			0
$253$	−44559.9	−	107577.i	−0.696150	−	1.68066i
$254$		0			0
$255$		−	23602.7i		−	0.362979i
$256$		0			0
$257$	28276.6			0.428116			0.214058	−	0.976821i	$-0.431332\pi$
$257$	28276.6			0.428116			0.214058	+	0.976821i	$0.431332\pi$
$258$		0			0
$259$	24888.6	−	10309.2i	0.371023	−	0.153683i
$260$		0			0
$261$	−60766.9	−	25170.5i	−0.892043	−	0.369496i
$262$		0			0
$263$	6696.53	−	6696.53i	0.0968140	−	0.0968140i	−0.657041	−	0.753855i	$-0.728192\pi$
$263$	6696.53	−	6696.53i	0.0968140	−	0.0968140i	0.753855	+	0.657041i	$0.228192\pi$
$264$		0			0
$265$	−6309.09	+	6309.09i	−0.0898410	+	0.0898410i
$266$		0			0
$267$	−16967.5	−	7028.18i	−0.238010	−	0.0985872i
$268$		0			0
$269$	−41828.3	+	17325.9i	−0.578051	+	0.239436i	−0.652500	−	0.757788i	$-0.726280\pi$
$269$	−41828.3	+	17325.9i	−0.578051	+	0.239436i	0.0744498	+	0.997225i	$0.476280\pi$
$270$		0			0
$271$	62878.5			0.856176			0.428088	−	0.903737i	$-0.359187\pi$
$271$	62878.5			0.856176			0.428088	+	0.903737i	$0.359187\pi$
$272$		0			0
$273$			89566.6i			1.20177i
$274$		0			0
$275$	−45184.6	−	109085.i	−0.597482	−	1.44245i
$276$		0			0
$277$	34575.3	−	83472.1i	0.450615	−	1.08788i	−0.521473	−	0.853268i	$-0.674617\pi$
$277$	34575.3	−	83472.1i	0.450615	−	1.08788i	0.972089	−	0.234614i	$-0.0753827\pi$
$278$		0			0
$279$	229967.	+	229967.i	2.95432	+	2.95432i
$280$		0			0
$281$	28284.1	+	28284.1i	0.358204	+	0.358204i	0.863150	−	0.504947i	$-0.168488\pi$
$281$	28284.1	+	28284.1i	0.358204	+	0.358204i	−0.504947	+	0.863150i	$0.668488\pi$
$282$		0			0
$283$	25819.8	−	62334.5i	0.322389	−	0.778315i	−0.676725	−	0.736235i	$-0.736602\pi$
$283$	25819.8	−	62334.5i	0.322389	−	0.778315i	0.999114	−	0.0420800i	$-0.0133984\pi$
$284$		0			0
$285$	3746.72	+	9045.37i	0.0461276	+	0.111362i
$286$		0			0
$287$		−	36266.3i		−	0.440291i
$288$		0			0
$289$	21601.8			0.258639
$290$		0			0
$291$	23971.5	−	9929.33i	0.283080	−	0.117256i
$292$		0			0
$293$	86832.9	+	35967.4i	1.01146	+	0.418961i	0.825987	−	0.563688i	$-0.190618\pi$
$293$	86832.9	+	35967.4i	1.01146	+	0.418961i	0.185473	+	0.982649i	$0.440618\pi$
$294$		0			0
$295$	−3055.87	+	3055.87i	−0.0351149	+	0.0351149i
$296$		0			0
$297$	214861.	−	214861.i	2.43582	−	2.43582i
$298$		0			0
$299$	−77065.4	−	31921.5i	−0.862019	−	0.357060i
$300$		0			0
$301$	24332.6	−	10078.9i	0.268569	−	0.111245i
$302$		0			0
$303$	−40075.6			−0.436511
$304$		0			0
$305$		−	12552.0i		−	0.134931i
$306$		0			0
$307$	42016.7	+	101437.i	0.445805	+	1.07627i	0.973879	+	0.227070i	$0.0729145\pi$
$307$	42016.7	+	101437.i	0.445805	+	1.07627i	−0.528074	+	0.849199i	$0.677085\pi$
$308$		0			0
$309$	105378.	−	254404.i	1.10365	−	2.66445i
$310$		0			0
$311$	18207.6	+	18207.6i	0.188249	+	0.188249i	0.794939	−	0.606690i	$-0.207503\pi$
$311$	18207.6	+	18207.6i	0.188249	+	0.188249i	−0.606690	+	0.794939i	$0.707503\pi$
$312$		0			0
$313$	32783.9	+	32783.9i	0.334636	+	0.334636i	0.854344	−	0.519708i	$-0.173959\pi$
$313$	32783.9	+	32783.9i	0.334636	+	0.334636i	−0.519708	+	0.854344i	$0.673959\pi$
$314$		0			0
$315$	−15522.2	+	37473.8i	−0.156434	+	0.377665i
$316$		0			0
$317$	54649.2	+	131935.i	0.543833	+	1.31293i	0.922000	+	0.387191i	$0.126554\pi$
$317$	54649.2	+	131935.i	0.543833	+	1.31293i	−0.378167	+	0.925737i	$0.623446\pi$
$318$		0			0
$319$		−	74899.9i		−	0.736037i
$320$		0			0
$321$	−171097.			−1.66047
$322$		0			0
$323$	23729.6	−	9829.11i	0.227450	−	0.0942127i
$324$		0			0
$325$	−78145.7	−	32369.0i	−0.739841	−	0.306452i
$326$		0			0
$327$	8429.21	−	8429.21i	0.0788300	−	0.0788300i
$328$		0			0
$329$	−77806.8	+	77806.8i	−0.718830	+	0.718830i
$330$		0			0
$331$	−951.567	−	394.152i	−0.00868527	−	0.00359756i	0.378337	−	0.925668i	$-0.376496\pi$
$331$	−951.567	−	394.152i	−0.00868527	−	0.00359756i	−0.387022	+	0.922071i	$0.626496\pi$
$332$		0			0
$333$	−112196.	+	46473.3i	−1.01179	+	0.419097i
$334$		0			0
$335$	−11648.5			−0.103796
$336$		0			0
$337$		−	19269.0i		−	0.169668i	−0.996395	−	0.0848339i	$-0.972964\pi$
$337$		−	19269.0i		−	0.169668i	0.996395	−	0.0848339i	$-0.0270360\pi$
$338$		0			0
$339$	−45258.7	−	109264.i	−0.393825	−	0.950777i
$340$		0			0
$341$	−141726.	+	342158.i	−1.21883	+	2.94251i
$342$		0			0
$343$	−90478.5	−	90478.5i	−0.769054	−	0.769054i
$344$		0			0
$345$	−39022.0	−	39022.0i	−0.327847	−	0.327847i
$346$		0			0
$347$	36453.8	−	88007.2i	0.302749	−	0.730902i	−0.697153	−	0.716923i	$-0.745550\pi$
$347$	36453.8	−	88007.2i	0.302749	−	0.730902i	0.999902	−	0.0139794i	$-0.00444991\pi$
$348$		0			0
$349$	−43627.9	−	105327.i	−0.358190	−	0.864747i	−0.995555	−	0.0941849i	$-0.969976\pi$
$349$	−43627.9	−	105327.i	−0.358190	−	0.864747i	0.637365	−	0.770562i	$-0.280024\pi$
$350$		0			0
$351$		−	217677.i		−	1.76684i
$352$		0			0
$353$	125554.			1.00759			0.503793	−	0.863824i	$-0.331937\pi$
$353$	125554.			1.00759			0.503793	+	0.863824i	$0.331937\pi$
$354$		0			0
$355$	−43644.6	+	18078.2i	−0.346317	+	0.143449i
$356$		0			0
$357$	143617.	+	59488.0i	1.12686	+	0.466760i
$358$		0			0
$359$	−109112.	+	109112.i	−0.846612	+	0.846612i	−0.989709	−	0.143097i	$-0.954294\pi$
$359$	−109112.	+	109112.i	−0.846612	+	0.846612i	0.143097	+	0.989709i	$0.454294\pi$
$360$		0			0
$361$	84617.1	−	84617.1i	0.649298	−	0.649298i
$362$		0			0
$363$	376225.	+	155837.i	2.85518	+	1.18266i
$364$		0			0
$365$	−9660.05	+	4001.32i	−0.0725093	+	0.0300343i
$366$		0			0
$367$	1701.63			0.0126338			0.00631688	−	0.999980i	$-0.497989\pi$
$367$	1701.63			0.0126338			0.00631688	+	0.999980i	$0.497989\pi$
$368$		0			0
$369$			163487.i			1.20069i
$370$		0			0
$371$	−22487.9	−	54290.7i	−0.163381	−	0.394437i
$372$		0			0
$373$	−59281.0	+	143117.i	−0.426087	+	1.02866i	0.554430	+	0.832230i	$0.312936\pi$
$373$	−59281.0	+	143117.i	−0.426087	+	1.02866i	−0.980517	+	0.196434i	$0.937064\pi$
$374$		0			0
$375$	−81488.3	−	81488.3i	−0.579472	−	0.579472i
$376$		0			0
$377$	−37940.7	−	37940.7i	−0.266946	−	0.266946i
$378$		0			0
$379$	72876.7	−	175940.i	0.507353	−	1.22486i	−0.438049	−	0.898951i	$-0.644330\pi$
$379$	72876.7	−	175940.i	0.507353	−	1.22486i	0.945402	−	0.325907i	$-0.105670\pi$
$380$		0			0
$381$	−68203.8	−	164659.i	−0.469849	−	1.13432i
$382$		0			0
$383$			212175.i			1.44643i	0.690624	+	0.723214i	$0.257336\pi$
$383$			212175.i			1.44643i	−0.690624	+	0.723214i	$0.742664\pi$
$384$		0			0
$385$	−46189.4			−0.311617
$386$		0			0
$387$	−109690.	+	45435.2i	−0.732396	+	0.303368i
$388$		0			0
$389$	164114.	+	67978.1i	1.08454	+	0.449231i	0.852100	−	0.523379i	$-0.175329\pi$
$389$	164114.	+	67978.1i	1.08454	+	0.449231i	0.232440	+	0.972611i	$0.425329\pi$
$390$		0			0
$391$	−102370.	+	102370.i	−0.669606	+	0.669606i
$392$		0			0
$393$	−95313.5	+	95313.5i	−0.617119	+	0.617119i
$394$		0			0
$395$	−29105.8	−	12056.0i	−0.186546	−	0.0772697i
$396$		0			0
$397$	84530.5	−	35013.7i	0.536330	−	0.222155i	−0.0980428	−	0.995182i	$-0.531258\pi$
$397$	84530.5	−	35013.7i	0.536330	−	0.222155i	0.634373	+	0.773027i	$0.281258\pi$
$398$		0			0
$399$	−64482.1			−0.405036
$400$		0			0
$401$		−	265835.i		−	1.65319i	−0.562797	−	0.826595i	$-0.690275\pi$
$401$		−	265835.i		−	1.65319i	0.562797	−	0.826595i	$-0.309725\pi$
$402$		0			0
$403$	101529.	+	245113.i	0.625144	+	1.50923i
$404$		0			0
$405$	22861.2	−	55191.8i	0.139376	−	0.336484i
$406$		0			0
$407$	−97786.3	−	97786.3i	−0.590323	−	0.590323i
$408$		0			0
$409$	−223837.	−	223837.i	−1.33809	−	1.33809i	−0.897911	−	0.440177i	$-0.854916\pi$
$409$	−223837.	−	223837.i	−1.33809	−	1.33809i	−0.440177	−	0.897911i	$-0.645084\pi$
$410$		0			0
$411$	−178925.	+	431964.i	−1.05923	+	2.55720i
$412$		0			0
$413$	−10892.3	−	26296.2i	−0.0638584	−	0.154168i
$414$		0			0
$415$			52180.7i			0.302980i
$416$		0			0
$417$	−14345.8			−0.0825000
$418$		0			0
$419$	−189472.	+	78481.7i	−1.07923	+	0.447034i	−0.850241	−	0.526394i	$-0.823544\pi$
$419$	−189472.	+	78481.7i	−1.07923	+	0.447034i	−0.228994	+	0.973428i	$0.573544\pi$
$420$		0			0
$421$	87255.4	+	36142.4i	0.492298	+	0.203916i	0.615000	−	0.788527i	$-0.289156\pi$
$421$	87255.4	+	36142.4i	0.492298	+	0.203916i	−0.122702	+	0.992444i	$0.539156\pi$
$422$		0			0
$423$	350749.	−	350749.i	1.96027	−	1.96027i
$424$		0			0
$425$	−103805.	+	103805.i	−0.574700	+	0.574700i
$426$		0			0
$427$	76375.9	+	31635.9i	0.418890	+	0.173510i
$428$		0			0
$429$	424786.	−	175952.i	2.30810	−	0.956047i
$430$		0			0
$431$	167368.			0.900986			0.450493	−	0.892780i	$-0.351248\pi$
$431$	167368.			0.900986			0.450493	+	0.892780i	$0.351248\pi$
$432$		0			0
$433$			304052.i			1.62170i	0.585251	+	0.810852i	$0.300996\pi$
$433$			304052.i			1.62170i	−0.585251	+	0.810852i	$0.699004\pi$
$434$		0			0
$435$	−13584.4	−	32795.7i	−0.0717897	−	0.173316i
$436$		0			0
$437$	22981.4	−	55482.1i	0.120341	−	0.290529i
$438$		0			0
$439$	89077.0	+	89077.0i	0.462207	+	0.462207i	0.899378	−	0.437171i	$-0.144020\pi$
$439$	89077.0	+	89077.0i	0.462207	+	0.462207i	−0.437171	+	0.899378i	$0.644020\pi$
$440$		0			0
$441$	109487.	+	109487.i	0.562972	+	0.562972i
$442$		0			0
$443$	54533.4	−	131655.i	0.277878	−	0.670858i	−0.721898	−	0.691999i	$-0.756730\pi$
$443$	54533.4	−	131655.i	0.277878	−	0.670858i	0.999776	+	0.0211416i	$0.00673009\pi$
$444$		0			0
$445$	−2596.44	−	6268.37i	−0.0131117	−	0.0316544i
$446$		0			0
$447$			89879.3i			0.449826i
$448$		0			0
$449$	35958.1			0.178363			0.0891814	−	0.996015i	$-0.471575\pi$
$449$	35958.1			0.178363			0.0891814	+	0.996015i	$0.471575\pi$
$450$		0			0
$451$	−172000.	+	71244.6i	−0.845618	+	0.350267i
$452$		0			0
$453$	−577357.	−	239149.i	−2.81350	−	1.16539i
$454$		0			0
$455$	−23397.4	+	23397.4i	−0.113017	+	0.113017i
$456$		0			0
$457$	−266738.	+	266738.i	−1.27718	+	1.27718i	−0.334942	+	0.942239i	$0.608717\pi$
$457$	−266738.	+	266738.i	−1.27718	+	1.27718i	−0.942239	+	0.334942i	$0.891283\pi$
$458$		0			0
$459$	−349037.	−	144576.i	−1.65671	−	0.686231i
$460$		0			0
$461$	−190757.	+	79014.0i	−0.897589	+	0.371794i	−0.783293	−	0.621653i	$-0.786461\pi$
$461$	−190757.	+	79014.0i	−0.897589	+	0.371794i	−0.114297	+	0.993447i	$0.536461\pi$
$462$		0			0
$463$	−355935.			−1.66039			−0.830193	−	0.557476i	$-0.811770\pi$
$463$	−355935.			−1.66039			−0.830193	+	0.557476i	$0.811770\pi$
$464$		0			0
$465$			175522.i			0.811754i
$466$		0			0
$467$	118604.	+	286334.i	0.543831	+	1.31292i	0.922001	+	0.387188i	$0.126553\pi$
$467$	118604.	+	286334.i	0.543831	+	1.31292i	−0.378170	+	0.925736i	$0.623447\pi$
$468$		0			0
$469$	29358.8	−	70878.3i	0.133473	−	0.322231i
$470$		0			0
$471$	−274022.	−	274022.i	−1.23522	−	1.23522i
$472$		0			0
$473$	−95602.0	−	95602.0i	−0.427312	−	0.427312i
$474$		0			0
$475$	23303.6	−	56259.9i	0.103285	−	0.249351i
$476$		0			0
$477$	101374.	+	244739.i	0.445545	+	1.07564i
$478$		0			0
$479$			130359.i			0.568160i	0.958801	+	0.284080i	$0.0916881\pi$
$479$			130359.i			0.568160i	−0.958801	+	0.284080i	$0.908312\pi$
$480$		0			0
$481$	−99067.8			−0.428196
$482$		0			0
$483$	335790.	−	139089.i	1.43937	−	0.596208i
$484$		0			0
$485$	8855.87	+	3668.22i	0.0376485	+	0.0155945i
$486$		0			0
$487$	−15992.6	+	15992.6i	−0.0674314	+	0.0674314i	−0.740018	−	0.672587i	$-0.765183\pi$
$487$	−15992.6	+	15992.6i	−0.0674314	+	0.0674314i	0.672587	+	0.740018i	$0.265183\pi$
$488$		0			0
$489$	−177506.	+	177506.i	−0.742326	+	0.742326i
$490$		0			0
$491$	−238830.	−	98926.5i	−0.990662	−	0.410346i	−0.172297	−	0.985045i	$-0.555119\pi$
$491$	−238830.	−	98926.5i	−0.990662	−	0.410346i	−0.818365	+	0.574699i	$0.805119\pi$
$492$		0			0
$493$	−86036.0	+	35637.3i	−0.353986	+	0.146626i
$494$		0			0
$495$	208219.			0.849788
$496$		0			0
$497$		−	311131.i		−	1.25960i
$498$		0			0
$499$	−79143.5	−	191069.i	−0.317844	−	0.767343i	−0.999368	−	0.0355476i	$-0.988682\pi$
$499$	−79143.5	−	191069.i	−0.317844	−	0.767343i	0.681524	−	0.731796i	$-0.261318\pi$
$500$		0			0
$501$	124851.	−	301418.i	0.497414	−	1.20086i
$502$		0			0
$503$	8460.69	+	8460.69i	0.0334403	+	0.0334403i	0.723629	−	0.690189i	$-0.242473\pi$
$503$	8460.69	+	8460.69i	0.0334403	+	0.0334403i	−0.690189	+	0.723629i	$0.742473\pi$
$504$		0			0
$505$	−10468.9	−	10468.9i	−0.0410505	−	0.0410505i
$506$		0			0
$507$	−49086.4	+	118505.i	−0.190961	+	0.461021i
$508$		0			0
$509$	2533.75	+	6117.02i	0.00977977	+	0.0236104i	0.928694	−	0.370847i	$-0.120933\pi$
$509$	2533.75	+	6117.02i	0.00977977	+	0.0236104i	−0.918914	+	0.394457i	$0.870933\pi$
$510$		0			0
$511$		−	68864.0i		−	0.263725i
$512$		0			0
$513$	156713.			0.595485
$514$		0			0
$515$	93985.4	−	38930.0i	0.354361	−	0.146781i
$516$		0			0
$517$	521863.	+	216163.i	1.95243	+	0.808723i
$518$		0			0
$519$	119560.	−	119560.i	0.443867	−	0.443867i
$520$		0			0
$521$	266649.	−	266649.i	0.982348	−	0.982348i	−0.0174991	−	0.999847i	$-0.505570\pi$
$521$	266649.	−	266649.i	0.982348	−	0.982348i	0.999847	+	0.0174991i	$0.00557041\pi$
$522$		0			0
$523$	271100.	+	112293.i	0.991118	+	0.410535i	0.818533	−	0.574460i	$-0.194788\pi$
$523$	271100.	+	112293.i	0.991118	+	0.410535i	0.172586	+	0.984995i	$0.444788\pi$
$524$		0			0
$525$	340498.	−	141039.i	1.23537	−	0.511705i
$526$		0			0
$527$	460462.			1.65796
$528$		0			0
$529$			58652.8i			0.209593i
$530$		0			0
$531$	49101.7	+	118542.i	0.174144	+	0.420420i
$532$		0			0
$533$	−51037.7	+	123216.i	−0.179654	+	0.433723i
$534$		0			0
$535$	−44695.4	−	44695.4i	−0.156155	−	0.156155i
$536$		0			0
$537$	400494.	+	400494.i	1.38883	+	1.38883i
$538$		0			0
$539$	−67475.9	+	162901.i	−0.232258	+	0.560721i
$540$		0			0
$541$	93009.7	+	224545.i	0.317785	+	0.767202i	0.999371	+	0.0354633i	$0.0112907\pi$
$541$	93009.7	+	224545.i	0.317785	+	0.767202i	−0.681586	+	0.731738i	$0.738709\pi$
$542$		0			0
$543$		−	401167.i		−	1.36059i
$544$		0			0
$545$	4403.90			0.0148267
$546$		0			0
$547$	487267.	−	201833.i	1.62852	−	0.674554i	0.633453	−	0.773781i	$-0.281637\pi$
$547$	487267.	−	201833.i	1.62852	−	0.674554i	0.995065	+	0.0992267i	$0.0316369\pi$
$548$		0			0
$549$	−344298.	−	142613.i	−1.14233	−	0.473167i
$550$		0			0
$551$	27314.9	−	27314.9i	0.0899696	−	0.0899696i
$552$		0			0
$553$	146716.	−	146716.i	0.479763	−	0.479763i
$554$		0			0
$555$	−60552.0	−	25081.5i	−0.196581	−	0.0814267i
$556$		0			0
$557$	−145446.	+	60245.7i	−0.468804	+	0.194185i	−0.604564	−	0.796557i	$-0.706652\pi$
$557$	−145446.	+	60245.7i	−0.468804	+	0.194185i	0.135760	+	0.990742i	$0.456652\pi$
$558$		0			0
$559$	−96854.9			−0.309954
$560$		0			0
$561$		−	797992.i		−	2.53555i
$562$		0			0
$563$	−145374.	−	350965.i	−0.458639	−	1.10725i	−0.968949	−	0.247261i	$-0.920469\pi$
$563$	−145374.	−	350965.i	−0.458639	−	1.10725i	0.510310	−	0.859991i	$-0.329531\pi$
$564$		0			0
$565$	16720.1	−	40365.8i	0.0523771	−	0.126449i
$566$		0			0
$567$	278210.	+	278210.i	0.865379	+	0.865379i
$568$		0			0
$569$	81901.7	+	81901.7i	0.252970	+	0.252970i	0.822187	−	0.569217i	$-0.192754\pi$
$569$	81901.7	+	81901.7i	0.252970	+	0.252970i	−0.569217	+	0.822187i	$0.692754\pi$
$570$		0			0
$571$	69592.1	−	168010.i	0.213446	−	0.515304i	−0.780503	−	0.625153i	$-0.785037\pi$
$571$	69592.1	−	168010.i	0.213446	−	0.515304i	0.993948	+	0.109849i	$0.0350367\pi$
$572$		0			0
$573$	185639.	+	448171.i	0.565404	+	1.36501i
$574$		0			0
$575$			343239.i			1.03815i
$576$		0			0
$577$	145837.			0.438042			0.219021	−	0.975720i	$-0.429714\pi$
$577$	145837.			0.438042			0.219021	+	0.975720i	$0.429714\pi$
$578$		0			0
$579$	698847.	−	289472.i	2.08461	−	0.863474i
$580$		0			0
$581$	−317507.	−	131516.i	−0.940592	−	0.389606i
$582$		0			0
$583$	−213306.	+	213306.i	−0.627576	+	0.627576i
$584$		0			0
$585$	105474.	−	105474.i	0.308201	−	0.308201i
$586$		0			0
$587$	−357108.	−	147919.i	−1.03639	−	0.429287i	−0.201375	−	0.979514i	$-0.564541\pi$
$587$	−357108.	−	147919.i	−1.03639	−	0.429287i	−0.835015	+	0.550228i	$0.814541\pi$
$588$		0			0
$589$	−176465.	+	73094.3i	−0.508661	+	0.210694i
$590$		0			0
$591$	−848286.			−2.42866
$592$		0			0
$593$		−	458870.i		−	1.30491i	−0.757828	−	0.652454i	$-0.773740\pi$
$593$		−	458870.i		−	1.30491i	0.757828	−	0.652454i	$-0.226260\pi$
$594$		0			0
$595$	21976.8	+	53056.8i	0.0620771	+	0.149867i
$596$		0			0
$597$	128214.	−	309535.i	0.359737	−	0.868482i
$598$		0			0
$599$	278049.	+	278049.i	0.774938	+	0.774938i	0.978965	−	0.204027i	$-0.0654030\pi$
$599$	278049.	+	278049.i	0.774938	+	0.774938i	−0.204027	+	0.978965i	$0.565403\pi$
$600$		0			0
$601$	49256.0	+	49256.0i	0.136367	+	0.136367i	0.771995	−	0.635628i	$-0.219259\pi$
$601$	49256.0	+	49256.0i	0.136367	+	0.136367i	−0.635628	+	0.771995i	$0.719259\pi$
$602$		0			0
$603$	−132348.	+	319516.i	−0.363983	+	0.878734i
$604$		0			0
$605$	57571.5	+	138990.i	0.157288	+	0.379728i
$606$		0			0
$607$		−	49613.7i		−	0.134656i	−0.997731	−	0.0673278i	$-0.978553\pi$
$607$		−	49613.7i		−	0.134656i	0.997731	−	0.0673278i	$-0.0214473\pi$
$608$		0			0
$609$	233792.			0.630369
$610$		0			0
$611$	373849.	−	154853.i	1.00141	−	0.414799i
$612$		0			0
$613$	−360373.	−	149271.i	−0.959028	−	0.397242i	−0.152411	−	0.988317i	$-0.548704\pi$
$613$	−360373.	−	149271.i	−0.959028	−	0.397242i	−0.806617	+	0.591075i	$0.798704\pi$
$614$		0			0
$615$	−62390.3	+	62390.3i	−0.164955	+	0.164955i
$616$		0			0
$617$	−43089.6	+	43089.6i	−0.113188	+	0.113188i	−0.761433	−	0.648244i	$-0.775504\pi$
$617$	−43089.6	+	43089.6i	−0.113188	+	0.113188i	0.648244	+	0.761433i	$0.275504\pi$
$618$		0			0
$619$	12909.0	+	5347.10i	0.0336909	+	0.0139552i	0.399465	−	0.916748i	$-0.369196\pi$
$619$	12909.0	+	5347.10i	0.0336909	+	0.0139552i	−0.365774	+	0.930704i	$0.619196\pi$
$620$		0			0
$621$	−816083.	+	338032.i	−2.11617	+	0.876547i
$622$		0			0
$623$	44685.6			0.115131
$624$		0			0
$625$			326150.i			0.834943i
$626$		0			0
$627$	126674.	+	305818.i	0.322220	+	0.777908i
$628$		0			0
$629$	−65798.6	+	158852.i	−0.166309	+	0.401505i
$630$		0			0
$631$	−96242.9	−	96242.9i	−0.241719	−	0.241719i	0.575842	−	0.817561i	$-0.304674\pi$
$631$	−96242.9	−	96242.9i	−0.241719	−	0.241719i	−0.817561	+	0.575842i	$0.804674\pi$
$632$		0			0
$633$	−275351.	−	275351.i	−0.687195	−	0.687195i
$634$		0			0
$635$	25196.7	−	60830.3i	0.0624880	−	0.150859i
$636$		0			0
$637$	48337.9	+	116698.i	0.119127	+	0.287597i
$638$		0			0
$639$			1.40256e6i			3.43495i
$640$		0			0
$641$	123298.			0.300081			0.150041	−	0.988680i	$-0.452060\pi$
$641$	123298.			0.300081			0.150041	+	0.988680i	$0.452060\pi$
$642$		0			0
$643$	−716147.	+	296638.i	−1.73213	+	0.717471i	−0.732816	+	0.680427i	$0.761794\pi$
$643$	−716147.	+	296638.i	−1.73213	+	0.717471i	−0.999314	+	0.0370444i	$0.988206\pi$
$644$		0			0
$645$	−59199.4	−	24521.2i	−0.142298	−	0.0589416i
$646$		0			0
$647$	515640.	−	515640.i	1.23179	−	1.23179i	0.268521	−	0.963274i	$-0.413465\pi$
$647$	515640.	−	515640.i	1.23179	−	1.23179i	0.963274	−	0.268521i	$-0.0865348\pi$
$648$		0			0
$649$	−103317.	+	103317.i	−0.245291	+	0.245291i
$650$		0			0
$651$	−1.06801e6	−	442383.i	−2.52007	−	1.04385i
$652$		0			0
$653$	563546.	−	233429.i	1.32161	−	0.547429i	0.393359	−	0.919385i	$-0.371313\pi$
$653$	563546.	−	233429.i	1.32161	−	0.547429i	0.928250	+	0.371956i	$0.121313\pi$
$654$		0			0
$655$	−49797.2			−0.116071
$656$		0			0
$657$			310435.i			0.719185i
$658$		0			0
$659$	−225871.	−	545301.i	−0.520103	−	1.25564i	−0.937839	−	0.347071i	$-0.887176\pi$
$659$	−225871.	−	545301.i	−0.520103	−	1.25564i	0.417735	−	0.908569i	$-0.362824\pi$
$660$		0			0
$661$	239536.	−	578292.i	0.548238	−	1.32356i	−0.370551	−	0.928812i	$-0.620831\pi$
$661$	239536.	−	578292.i	0.548238	−	1.32356i	0.918788	−	0.394750i	$-0.129169\pi$
$662$		0			0
$663$	−404225.	−	404225.i	−0.919593	−	0.919593i
$664$		0			0
$665$	−16844.6	−	16844.6i	−0.0380905	−	0.0380905i
$666$		0			0
$667$	−83323.4	+	201161.i	−0.187290	+	0.452159i
$668$		0			0
$669$	−212779.	−	513693.i	−0.475418	−	1.14776i
$670$		0			0
$671$		−	424375.i		−	0.942550i
$672$		0			0
$673$	106317.			0.234733			0.117366	−	0.993089i	$-0.462555\pi$
$673$	106317.			0.234733			0.117366	+	0.993089i	$0.462555\pi$
$674$		0			0
$675$	−827523.	+	342771.i	−1.81624	+	0.752310i
$676$		0			0
$677$	−453156.	−	187703.i	−0.988713	−	0.409538i	−0.171067	−	0.985259i	$-0.554721\pi$
$677$	−453156.	−	187703.i	−0.988713	−	0.409538i	−0.817646	+	0.575721i	$0.804721\pi$
$678$		0			0
$679$	−44640.5	+	44640.5i	−0.0968255	+	0.0968255i
$680$		0			0
$681$	−938613.	+	938613.i	−2.02392	+	2.02392i
$682$		0			0
$683$	277150.	+	114799.i	0.594120	+	0.246093i	0.659422	−	0.751773i	$-0.270801\pi$
$683$	277150.	+	114799.i	0.594120	+	0.246093i	−0.0653020	+	0.997866i	$0.520801\pi$
$684$		0			0
$685$	−159582.	+	66101.0i	−0.340097	+	0.140873i
$686$		0			0
$687$	1.45699e6			3.08706
$688$		0			0
$689$			216101.i			0.455218i
$690$		0			0
$691$	245915.	+	593691.i	0.515025	+	1.24338i	0.940926	+	0.338611i	$0.109957\pi$
$691$	245915.	+	593691.i	0.515025	+	1.24338i	−0.425901	+	0.904770i	$0.640043\pi$
$692$		0			0
$693$	−524794.	+	1.26697e6i	−1.09275	+	2.63814i
$694$		0			0
$695$	−3747.55	−	3747.55i	−0.00775849	−	0.00775849i
$696$		0			0
$697$	163674.	+	163674.i	0.336911	+	0.336911i
$698$		0			0
$699$	483664.	−	1.16767e6i	0.989895	−	2.38982i
$700$		0			0
$701$	−144159.	−	348030.i	−0.293363	−	0.708241i	−1.00000		0.000664646i	$-0.999788\pi$
$701$	−144159.	−	348030.i	−0.293363	−	0.708241i	0.706637	−	0.707577i	$-0.250212\pi$
$702$		0			0
$703$		−	71322.4i		−	0.144316i
$704$		0			0
$705$	267708.			0.538620
$706$		0			0
$707$	90086.5	−	37315.0i	0.180227	−	0.0746526i
$708$		0			0
$709$	655850.	+	271662.i	1.30470	+	0.540426i	0.923334	−	0.383997i	$-0.125453\pi$
$709$	655850.	+	271662.i	1.30470	+	0.540426i	0.381369	+	0.924423i	$0.375453\pi$
$710$		0			0
$711$	−661387.	+	661387.i	−1.30833	+	1.30833i
$712$		0			0
$713$	761276.	−	761276.i	1.49749	−	1.49749i
$714$		0			0
$715$	156930.	+	65002.5i	0.306968	+	0.127150i
$716$		0			0
$717$	760846.	−	315153.i	1.47999	−	0.613031i
$718$		0			0
$719$	37541.2			0.0726191			0.0363095	−	0.999341i	$-0.488440\pi$
$719$	37541.2			0.0726191			0.0363095	+	0.999341i	$0.488440\pi$
$720$		0			0
$721$			669998.i			1.28885i
$722$		0			0
$723$	−279913.	−	675771.i	−0.535485	−	1.29277i
$724$		0			0
$725$	−84491.5	+	203981.i	−0.160745	+	0.388072i
$726$		0			0
$727$	659267.	+	659267.i	1.24736	+	1.24736i	0.956880	+	0.290482i	$0.0938158\pi$
$727$	659267.	+	659267.i	1.24736	+	1.24736i	0.290482	+	0.956880i	$0.406184\pi$
$728$		0			0
$729$	139226.	+	139226.i	0.261979	+	0.261979i
$730$		0			0
$731$	−64328.8	+	155303.i	−0.120384	+	0.290634i
$732$		0			0
$733$	−193461.	−	467057.i	−0.360069	−	0.869284i	−0.995289	−	0.0969529i	$-0.969090\pi$
$733$	−193461.	−	467057.i	−0.360069	−	0.869284i	0.635220	−	0.772332i	$-0.280910\pi$
$734$		0			0
$735$			83565.8i			0.154687i
$736$		0			0
$737$	−393828.			−0.725056
$738$		0			0
$739$	−828822.	+	343309.i	−1.51765	+	0.628632i	−0.977120	−	0.212691i	$-0.931777\pi$
$739$	−828822.	+	343309.i	−1.51765	+	0.628632i	−0.540533	+	0.841323i	$0.681777\pi$
$740$		0			0
$741$	219080.	+	90745.9i	0.398994	+	0.165269i
$742$		0			0
$743$	−11241.8	+	11241.8i	−0.0203639	+	0.0203639i	−0.717215	−	0.696852i	$-0.754584\pi$
$743$	−11241.8	+	11241.8i	−0.0203639	+	0.0203639i	0.696852	+	0.717215i	$0.254584\pi$
$744$		0			0
$745$	−23479.0	+	23479.0i	−0.0423027	+	0.0423027i
$746$		0			0
$747$	1.43130e6	+	592866.i	2.56502	+	1.06247i
$748$		0			0
$749$	384611.	−	159311.i	0.685580	−	0.283977i
$750$		0			0
$751$	−629186.			−1.11558			−0.557788	−	0.829983i	$-0.688350\pi$
$751$	−629186.			−1.11558			−0.557788	+	0.829983i	$0.688350\pi$
$752$		0			0
$753$			7653.67i			0.0134983i
$754$		0			0
$755$	−88349.5	−	213295.i	−0.154992	−	0.374185i
$756$		0			0
$757$	−257243.	+	621039.i	−0.448902	+	1.08374i	0.523832	+	0.851821i	$0.324502\pi$
$757$	−257243.	+	621039.i	−0.448902	+	1.08374i	−0.972734	+	0.231923i	$0.925498\pi$
$758$		0			0
$759$	−1.31931e6	−	1.31931e6i	−2.29014	−	2.29014i
$760$		0			0
$761$	−398805.	−	398805.i	−0.688638	−	0.688638i	0.273293	−	0.961931i	$-0.411887\pi$
$761$	−398805.	−	398805.i	−0.688638	−	0.688638i	−0.961931	+	0.273293i	$0.911887\pi$
$762$		0			0
$763$	−11099.6	+	26796.7i	−0.0190659	+	0.0460291i
$764$		0			0
$765$	−99070.4	−	239177.i	−0.169286	−	0.408693i
$766$		0			0
$767$			104671.i			0.177924i
$768$		0			0
$769$	−260850.			−0.441101			−0.220551	−	0.975376i	$-0.570785\pi$
$769$	−260850.			−0.441101			−0.220551	+	0.975376i	$0.570785\pi$
$770$		0			0
$771$	418601.	−	173390.i	0.704192	−	0.291686i
$772$		0			0
$773$	−237087.	−	98204.5i	−0.396779	−	0.164351i	0.175367	−	0.984503i	$-0.443889\pi$
$773$	−237087.	−	98204.5i	−0.396779	−	0.164351i	−0.572146	+	0.820152i	$0.693889\pi$
$774$		0			0
$775$	771948.	−	771948.i	1.28524	−	1.28524i
$776$		0			0
$777$	305229.	−	305229.i	0.505574	−	0.505574i
$778$		0			0
$779$	−88707.5	−	36743.9i	−0.146179	−	0.0605494i
$780$		0			0
$781$	−1.47560e6	+	611212.i	−2.41917	+	1.00205i
$782$		0			0
$783$	−568192.			−0.926770
$784$		0			0
$785$		−	143165.i		−	0.232326i
$786$		0			0
$787$	93654.3	+	226101.i	0.151209	+	0.365051i	0.981274	−	0.192615i	$-0.0616969\pi$
$787$	93654.3	+	226101.i	0.151209	+	0.365051i	−0.830065	+	0.557666i	$0.811697\pi$
$788$		0			0
$789$	58071.2	−	140196.i	0.0932840	−	0.225207i
$790$		0			0
$791$	203475.	+	203475.i	0.325206	+	0.325206i
$792$		0			0
$793$	−214968.	−	214968.i	−0.341844	−	0.341844i
$794$		0			0
$795$	−54711.4	+	132085.i	−0.0865652	+	0.208987i
$796$		0			0
$797$	345901.	+	835079.i	0.544547	+	1.31465i	0.921485	+	0.388414i	$0.126977\pi$
$797$	345901.	+	835079.i	0.544547	+	1.31465i	−0.376938	+	0.926238i	$0.623023\pi$
$798$		0			0
$799$		−	702303.i		−	1.10010i
$800$		0			0
$801$	−201440.			−0.313965
$802$		0			0
$803$	−326600.	+	135282.i	−0.506507	+	0.209802i
$804$		0			0
$805$	124052.	+	51384.0i	0.191431	+	0.0792933i
$806$		0			0
$807$	−512976.	+	512976.i	−0.787680	+	0.787680i
$808$		0			0
$809$	−261437.	+	261437.i	−0.399456	+	0.399456i	−0.878041	−	0.478585i	$-0.841150\pi$
$809$	−261437.	+	261437.i	−0.399456	+	0.399456i	0.478585	+	0.878041i	$0.341150\pi$
$810$		0			0
$811$	438614.	+	181680.i	0.666870	+	0.276227i	0.690326	−	0.723498i	$-0.257467\pi$
$811$	438614.	+	181680.i	0.666870	+	0.276227i	−0.0234562	+	0.999725i	$0.507467\pi$
$812$		0			0
$813$	930837.	−	385565.i	1.40829	−	0.583334i
$814$		0			0
$815$	−92739.1			−0.139620
$816$		0			0
$817$		−	69729.3i		−	0.104465i
$818$		0			0
$819$	375949.	+	907620.i	0.560481	+	1.35312i
$820$		0			0
$821$	244028.	−	589135.i	0.362037	−	0.874034i	−0.632965	−	0.774180i	$-0.718162\pi$
$821$	244028.	−	589135.i	0.362037	−	0.874034i	0.995002	−	0.0998541i	$-0.0318376\pi$
$822$		0			0
$823$	623890.	+	623890.i	0.921103	+	0.921103i	0.997107	−	0.0760044i	$-0.0242163\pi$
$823$	623890.	+	623890.i	0.921103	+	0.921103i	−0.0760044	+	0.997107i	$0.524216\pi$
$824$		0			0
$825$	−1.33780e6	−	1.33780e6i	−1.96555	−	1.96555i
$826$		0			0
$827$	−316516.	+	764137.i	−0.462791	+	1.11728i	0.504456	+	0.863437i	$0.331693\pi$
$827$	−316516.	+	764137.i	−0.462791	+	1.11728i	−0.967247	+	0.253838i	$0.918307\pi$
$828$		0			0
$829$	−196310.	−	473934.i	−0.285649	−	0.689618i	0.714299	−	0.699841i	$-0.246746\pi$
$829$	−196310.	−	473934.i	−0.285649	−	0.689618i	−0.999948	+	0.0102231i	$0.996746\pi$
$830$		0			0
$831$		−	1.44771e6i		−	2.09643i
$832$		0			0
$833$	219226.			0.315938
$834$		0			0
$835$	111354.	−	46124.2i	0.159710	−	0.0661540i
$836$		0			0
$837$	2.59562e6	+	1.07514e6i	3.70501	+	1.53467i
$838$		0			0
$839$	−100326.	+	100326.i	−0.142524	+	0.142524i	−0.774769	−	0.632245i	$-0.782134\pi$
$839$	−100326.	+	100326.i	−0.142524	+	0.142524i	0.632245	+	0.774769i	$0.282134\pi$
$840$		0			0
$841$	401088.	−	401088.i	0.567084	−	0.567084i
$842$		0			0
$843$	592147.	+	245275.i	0.833249	+	0.345143i
$844$		0			0
$845$	−43779.7	+	18134.1i	−0.0613139	+	0.0253971i
$846$		0			0
$847$	−990823.			−1.38111
$848$		0			0
$849$		−	1.08111e6i		−	1.49987i
$850$		0			0
$851$	153843.	+	371411.i	0.212432	+	0.512856i
$852$		0			0
$853$	469001.	−	1.13227e6i	0.644579	−	1.55615i	−0.175859	−	0.984415i	$-0.556270\pi$
$853$	469001.	−	1.13227e6i	0.644579	−	1.55615i	0.820438	−	0.571736i	$-0.193730\pi$
$854$		0			0
$855$	75934.5	+	75934.5i	0.103874	+	0.103874i
$856$		0			0
$857$	911647.	+	911647.i	1.24127	+	1.24127i	0.959476	+	0.281790i	$0.0909281\pi$
$857$	911647.	+	911647.i	1.24127	+	1.24127i	0.281790	+	0.959476i	$0.409072\pi$
$858$		0			0
$859$	−57560.3	+	138963.i	−0.0780075	+	0.188327i	−0.958072	−	0.286527i	$-0.907499\pi$
$859$	−57560.3	+	138963.i	−0.0780075	+	0.188327i	0.880065	+	0.474854i	$0.157499\pi$
$860$		0			0
$861$	−222382.	−	536878.i	−0.299981	−	0.724218i
$862$		0			0
$863$			322144.i			0.432543i	0.976333	+	0.216271i	$0.0693896\pi$
$863$			322144.i			0.432543i	−0.976333	+	0.216271i	$0.930610\pi$
$864$		0			0
$865$	62465.2			0.0834845
$866$		0			0
$867$	319788.	−	132461.i	0.425426	−	0.176217i
$868$		0			0
$869$	−984047.	−	407606.i	−1.30310	−	0.539760i
$870$		0			0
$871$	−199494.	+	199494.i	−0.262963	+	0.262963i
$872$		0			0
$873$	201237.	−	201237.i	0.264046	−	0.264046i
$874$		0			0
$875$	259054.	+	107304.i	0.338356	+	0.140152i
$876$		0			0
$877$	607958.	−	251825.i	0.790450	−	0.327415i	0.0493258	−	0.998783i	$-0.484293\pi$
$877$	607958.	−	251825.i	0.790450	−	0.327415i	0.741125	+	0.671367i	$0.234293\pi$
$878$		0			0
$879$	1.50600e6			1.94916
$880$		0			0
$881$			680455.i			0.876693i	0.898806	+	0.438346i	$0.144436\pi$
$881$			680455.i			0.876693i	−0.898806	+	0.438346i	$0.855564\pi$
$882$		0			0
$883$	−145507.	−	351286.i	−0.186622	−	0.450546i	0.802683	−	0.596406i	$-0.203405\pi$
$883$	−145507.	−	351286.i	−0.186622	−	0.450546i	−0.989305	+	0.145860i	$0.953405\pi$
$884$		0			0
$885$	−26500.0	+	63976.7i	−0.0338345	+	0.0816837i
$886$		0			0
$887$	−484269.	−	484269.i	−0.615516	−	0.615516i	0.328862	−	0.944378i	$-0.393335\pi$
$887$	−484269.	−	484269.i	−0.615516	−	0.615516i	−0.944378	+	0.328862i	$0.893335\pi$
$888$		0			0
$889$	306632.	+	306632.i	0.387985	+	0.387985i
$890$		0			0
$891$	772922.	−	1.86600e6i	0.973599	−	2.35048i
$892$		0			0
$893$	111484.	+	269147.i	0.139801	+	0.337510i
$894$		0			0
$895$			209241.i			0.261217i
$896$		0			0
$897$	−1.33660e6			−1.66118
$898$		0			0
$899$	639807.	−	265017.i	0.791644	−	0.327909i
$900$		0			0
$901$	346511.	+	143530.i	0.426842	+	0.176804i
$902$		0			0
$903$	298411.	−	298411.i	0.365965	−	0.365965i
$904$		0			0
$905$	104796.	−	104796.i	0.127953	−	0.127953i
$906$		0			0
$907$	−612858.	−	253854.i	−0.744981	−	0.308581i	−0.0222889	−	0.999752i	$-0.507095\pi$
$907$	−612858.	−	253854.i	−0.744981	−	0.308581i	−0.722692	+	0.691170i	$0.757095\pi$
$908$		0			0
$909$	−406105.	+	168214.i	−0.491485	+	0.203580i
$910$		0			0
$911$	282780.			0.340731			0.170366	−	0.985381i	$-0.445505\pi$
$911$	282780.			0.340731			0.170366	+	0.985381i	$0.445505\pi$
$912$		0			0
$913$			1.76419e6i			2.11643i
$914$		0			0
$915$	−76967.8	−	185817.i	−0.0919320	−	0.221943i
$916$		0			0
$917$	125508.	−	303004.i	0.149257	−	0.360338i
$918$		0			0
$919$	925172.	+	925172.i	1.09545	+	1.09545i	0.994936	+	0.100511i	$0.0320477\pi$
$919$	925172.	+	925172.i	1.09545	+	1.09545i	0.100511	+	0.994936i	$0.467952\pi$
$920$		0			0
$921$	1.24401e6	+	1.24401e6i	1.46658	+	1.46658i
$922$		0			0
$923$	−437856.	+	1.05708e6i	−0.513958	+	1.24081i
$924$		0			0
$925$	156000.	+	376618.i	0.182323	+	0.440167i
$926$		0			0
$927$		−	3.02031e6i		−	3.51474i
$928$		0			0
$929$	−403304.			−0.467306			−0.233653	−	0.972320i	$-0.575068\pi$
$929$	−403304.			−0.467306			−0.233653	+	0.972320i	$0.575068\pi$
$930$		0			0
$931$	−84015.0	+	34800.2i	−0.0969299	+	0.0401497i
$932$		0			0
$933$	381189.	+	157894.i	0.437902	+	0.181385i
$934$		0			0
$935$	208458.	−	208458.i	0.238449	−	0.238449i
$936$		0			0
$937$	620070.	−	620070.i	0.706255	−	0.706255i	−0.259491	−	0.965746i	$-0.583555\pi$
$937$	620070.	−	620070.i	0.706255	−	0.706255i	0.965746	+	0.259491i	$0.0835547\pi$
$938$		0			0
$939$	686354.	+	284297.i	0.778425	+	0.322434i
$940$		0			0
$941$	−753055.	+	311926.i	−0.850448	+	0.352267i	−0.764964	−	0.644073i	$-0.777243\pi$
$941$	−753055.	+	311926.i	−0.850448	+	0.352267i	−0.0854834	+	0.996340i	$0.527243\pi$
$942$		0			0
$943$	541201.			0.608604
$944$		0			0
$945$			350394.i			0.392367i
$946$		0			0
$947$	−303582.	−	732913.i	−0.338514	−	0.817245i	−0.997859	−	0.0654045i	$-0.979166\pi$
$947$	−303582.	−	732913.i	−0.338514	−	0.817245i	0.659345	−	0.751841i	$-0.270834\pi$
$948$		0			0
$949$	−96912.6	+	233968.i	−0.107609	+	0.259791i
$950$		0			0
$951$	1.61803e6	+	1.61803e6i	1.78906	+	1.78906i
$952$		0			0
$953$	454307.	+	454307.i	0.500223	+	0.500223i	0.911507	−	0.411284i	$-0.134920\pi$
$953$	454307.	+	454307.i	0.500223	+	0.500223i	−0.411284	+	0.911507i	$0.634920\pi$
$954$		0			0
$955$	−68581.0	+	165569.i	−0.0751964	+	0.181540i
$956$		0			0
$957$	−459280.	−	1.10880e6i	−0.501480	−	1.21068i
$958$		0			0
$959$		−	1.13762e6i		−	1.23697i
$960$		0			0
$961$	−2.50071e6			−2.70780
$962$		0			0
$963$	−1.73381e6	+	718166.i	−1.86960	+	0.774412i
$964$		0			0
$965$	258177.	+	106940.i	0.277245	+	0.114839i
$966$		0			0
$967$	−709212.	+	709212.i	−0.758444	+	0.758444i	−0.976039	−	0.217595i	$-0.930179\pi$
$967$	−709212.	+	709212.i	−0.758444	+	0.758444i	0.217595	+	0.976039i	$0.430179\pi$
$968$		0			0
$969$	291016.	−	291016.i	0.309934	−	0.309934i
$970$		0			0
$971$	−1.65142e6	−	684041.i	−1.75154	−	0.725511i	−0.997651	−	0.0685072i	$-0.978176\pi$
$971$	−1.65142e6	−	684041.i	−1.75154	−	0.725511i	−0.753887	−	0.657004i	$-0.771824\pi$
$972$		0			0
$973$	32248.2	−	13357.6i	0.0340628	−	0.0141093i
$974$		0			0
$975$	−1.35533e6			−1.42573
$976$		0			0
$977$		−	944042.i		−	0.989013i	−0.869174	−	0.494506i	$-0.835349\pi$
$977$		−	944042.i		−	0.989013i	0.869174	−	0.494506i	$-0.164651\pi$
$978$		0			0
$979$	−87784.0	−	211929.i	−0.0915904	−	0.221119i
$980$		0			0
$981$	50036.2	−	120798.i	0.0519932	−	0.125523i
$982$		0			0
$983$	−602426.	−	602426.i	−0.623443	−	0.623443i	0.322967	−	0.946410i	$-0.395320\pi$
$983$	−602426.	−	602426.i	−0.623443	−	0.623443i	−0.946410	+	0.322967i	$0.895320\pi$
$984$		0			0
$985$	−221597.	−	221597.i	−0.228397	−	0.228397i
$986$		0			0
$987$	−674728.	+	1.62894e6i	−0.692620	+	1.67213i
$988$		0			0
$989$	150407.	+	363115.i	0.153771	+	0.371237i
$990$		0			0
$991$		−	701993.i		−	0.714802i	−0.933951	−	0.357401i	$-0.883663\pi$
$991$		−	701993.i		−	0.714802i	0.933951	−	0.357401i	$-0.116337\pi$
$992$		0			0
$993$	−16503.7			−0.0167372
$994$		0			0
$995$	114352.	−	47366.3i	0.115505	−	0.0478436i
$996$		0			0
$997$	−836041.	−	346299.i	−0.841080	−	0.348387i	−0.0798006	−	0.996811i	$-0.525428\pi$
$997$	−836041.	−	346299.i	−0.841080	−	0.348387i	−0.761279	+	0.648424i	$0.775428\pi$
$998$		0			0
$999$	−741810.	+	741810.i	−0.743295	+	0.743295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.h.a.15.15		60
4.3	odd	2		32.5.h.a.27.2	yes	60
32.13	even	8		32.5.h.a.19.2	✓	60
32.19	odd	8	inner	128.5.h.a.111.15		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.5.h.a.19.2	✓	60	32.13	even	8
32.5.h.a.27.2	yes	60	4.3	odd	2
128.5.h.a.15.15		60	1.1	even	1	trivial
128.5.h.a.111.15		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)

\(f(q)\)	\(=\)	\(q+(14.8038 - 6.13192i) q^{3} +(5.46900 + 2.26533i) q^{5} +(-27.5680 + 27.5680i) q^{7} +(124.275 - 124.275i) q^{9} +O(q^{10})\)	\(q+(14.8038 - 6.13192i) q^{3} +(5.46900 + 2.26533i) q^{5} +(-27.5680 + 27.5680i) q^{7} +(124.275 - 124.275i) q^{9} +(184.903 + 76.5894i) q^{11} +(132.460 - 54.8666i) q^{13} +94.8525 q^{15} -248.836i q^{17} +(39.5004 + 95.3625i) q^{19} +(-239.066 + 577.155i) q^{21} +(-411.396 - 411.396i) q^{23} +(-417.164 - 417.164i) q^{25} +(581.009 - 1402.68i) q^{27} +(-143.216 - 345.754i) q^{29} +1850.47i q^{31} +3206.90 q^{33} +(-213.220 + 88.3187i) q^{35} +(-638.380 - 264.426i) q^{37} +(1624.46 - 1624.46i) q^{39} +(-657.761 + 657.761i) q^{41} +(-624.120 - 258.519i) q^{43} +(961.185 - 398.136i) q^{45} +2822.36 q^{47} +881.007i q^{49} +(-1525.84 - 3683.70i) q^{51} +(-576.805 + 1392.53i) q^{53} +(837.735 + 837.735i) q^{55} +(1169.51 + 1169.51i) q^{57} +(-279.381 + 674.486i) q^{59} +(-811.446 - 1959.00i) q^{61} +6852.04i q^{63} +848.713 q^{65} +(-1817.99 + 753.038i) q^{67} +(-8612.86 - 3567.56i) q^{69} +(-5642.97 + 5642.97i) q^{71} +(-1248.98 + 1248.98i) q^{73} +(-8733.60 - 3617.58i) q^{75} +(-7208.84 + 2986.00i) q^{77} -5321.96 q^{79} -10091.8i q^{81} +(3373.32 + 8143.90i) q^{83} +(563.696 - 1360.88i) q^{85} +(-4240.27 - 4240.27i) q^{87} +(-810.460 - 810.460i) q^{89} +(-2139.09 + 5164.22i) q^{91} +(11346.9 + 27393.9i) q^{93} +611.019i q^{95} +1619.29 q^{97} +(32497.0 - 13460.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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