LMFDB - Embedded newform 128.3.h.a.111.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,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, 3, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.2
Character	$\chi$	$=$	128.111
Dual form			128.3.h.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +O(q^{10})$	\(q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +1.32310 q^{15} +13.5961i q^{17} +(3.45810 - 8.34859i) q^{19} +(0.628870 + 1.51823i) q^{21} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(11.0623 + 26.7067i) q^{27} +(13.8385 - 33.4091i) q^{29} -24.5614i q^{31} +50.7086 q^{33} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(41.2853 + 41.2853i) q^{39} +(14.4867 + 14.4867i) q^{41} +(-17.8494 + 7.39348i) q^{43} +(0.767229 + 0.317796i) q^{45} -43.6087 q^{47} -48.6303i q^{49} +(14.0613 - 33.9471i) q^{51} +(28.0630 + 67.7501i) q^{53} +(6.49552 - 6.49552i) q^{55} +(-17.2685 + 17.2685i) q^{57} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +1.03142i q^{63} +10.5769 q^{65} +(0.300169 + 0.124334i) q^{67} +(-59.6218 + 24.6961i) q^{69} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(61.8222 - 25.6076i) q^{75} +(10.5408 + 4.36612i) q^{77} -67.7588 q^{79} -62.8565i q^{81} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-69.1047 + 69.1047i) q^{87} +(-45.3745 + 45.3745i) q^{89} +(5.02718 + 12.1367i) q^{91} +(-25.4019 + 61.3257i) q^{93} +4.42403i q^{95} -119.312 q^{97} +(29.4044 + 12.1797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 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} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * 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 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

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
$3$	−2.49683	−	1.03422i	−0.832276	−	0.344740i	−0.0744725	−	0.997223i	$-0.523727\pi$
$3$	−2.49683	−	1.03422i	−0.832276	−	0.344740i	−0.757803	+	0.652483i	$0.773727\pi$
$4$		0			0
$5$	−0.452310	+	0.187353i	−0.0904620	+	0.0374706i	−0.427456	−	0.904036i	$-0.640590\pi$
$5$	−0.452310	+	0.187353i	−0.0904620	+	0.0374706i	0.336994	+	0.941507i	$0.390590\pi$
$6$		0			0
$7$	−0.429965	−	0.429965i	−0.0614236	−	0.0614236i	0.675728	−	0.737151i	$-0.263830\pi$
$7$	−0.429965	−	0.429965i	−0.0614236	−	0.0614236i	−0.737151	+	0.675728i	$0.763830\pi$
$8$		0			0
$9$	−1.19943	−	1.19943i	−0.133270	−	0.133270i
$10$		0			0
$11$	−17.3350	+	7.18039i	−1.57591	+	0.652763i	−0.987759	−	0.155990i	$-0.950143\pi$
$11$	−17.3350	+	7.18039i	−1.57591	+	0.652763i	−0.588149	+	0.808752i	$0.700143\pi$
$12$		0			0
$13$	−19.9596	−	8.26755i	−1.53536	−	0.635965i	−0.554761	−	0.832010i	$-0.687190\pi$
$13$	−19.9596	−	8.26755i	−1.53536	−	0.635965i	−0.980595	+	0.196044i	$0.937190\pi$
$14$		0			0
$15$	1.32310			0.0882069
$16$		0			0
$17$			13.5961i			0.799770i	0.916565	+	0.399885i	$0.130950\pi$
$17$			13.5961i			0.799770i	−0.916565	+	0.399885i	$0.869050\pi$
$18$		0			0
$19$	3.45810	−	8.34859i	0.182005	−	0.439399i	−0.806374	−	0.591405i	$-0.798573\pi$
$19$	3.45810	−	8.34859i	0.182005	−	0.439399i	0.988380	+	0.152006i	$0.0485733\pi$
$20$		0			0
$21$	0.628870	+	1.51823i	0.0299462	+	0.0722965i
$22$		0			0
$23$	16.8850	−	16.8850i	0.734131	−	0.734131i	−0.237304	−	0.971435i	$-0.576264\pi$
$23$	16.8850	−	16.8850i	0.734131	−	0.734131i	0.971435	+	0.237304i	$0.0762639\pi$
$24$		0			0
$25$	−17.5082	+	17.5082i	−0.700327	+	0.700327i
$26$		0			0
$27$	11.0623	+	26.7067i	0.409714	+	0.989136i
$28$		0			0
$29$	13.8385	−	33.4091i	0.477190	−	1.15204i	−0.483732	−	0.875216i	$-0.660719\pi$
$29$	13.8385	−	33.4091i	0.477190	−	1.15204i	0.960921	−	0.276821i	$-0.0892810\pi$
$30$		0			0
$31$		−	24.5614i		−	0.792305i	−0.918185	−	0.396152i	$-0.870345\pi$
$31$		−	24.5614i		−	0.792305i	0.918185	−	0.396152i	$-0.129655\pi$
$32$		0			0
$33$	50.7086			1.53662
$34$		0			0
$35$	0.275033	+	0.113922i	0.00785807	+	0.00325492i
$36$		0			0
$37$	9.89595	−	4.09904i	0.267458	−	0.110785i	−0.244924	−	0.969542i	$-0.578763\pi$
$37$	9.89595	−	4.09904i	0.267458	−	0.110785i	0.512382	+	0.858757i	$0.328763\pi$
$38$		0			0
$39$	41.2853	+	41.2853i	1.05860	+	1.05860i
$40$		0			0
$41$	14.4867	+	14.4867i	0.353334	+	0.353334i	0.861348	−	0.508015i	$-0.169620\pi$
$41$	14.4867	+	14.4867i	0.353334	+	0.353334i	−0.508015	+	0.861348i	$0.669620\pi$
$42$		0			0
$43$	−17.8494	+	7.39348i	−0.415103	+	0.171941i	−0.580453	−	0.814294i	$-0.697125\pi$
$43$	−17.8494	+	7.39348i	−0.415103	+	0.171941i	0.165350	+	0.986235i	$0.447125\pi$
$44$		0			0
$45$	0.767229	+	0.317796i	0.0170495	+	0.00706214i
$46$		0			0
$47$	−43.6087			−0.927845			−0.463922	−	0.885876i	$-0.653558\pi$
$47$	−43.6087			−0.927845			−0.463922	+	0.885876i	$0.653558\pi$
$48$		0			0
$49$		−	48.6303i		−	0.992454i
$50$		0			0
$51$	14.0613	−	33.9471i	0.275713	−	0.665629i
$52$		0			0
$53$	28.0630	+	67.7501i	0.529490	+	1.27830i	0.931857	+	0.362825i	$0.118188\pi$
$53$	28.0630	+	67.7501i	0.529490	+	1.27830i	−0.402367	+	0.915478i	$0.631812\pi$
$54$		0			0
$55$	6.49552	−	6.49552i	0.118100	−	0.118100i
$56$		0			0
$57$	−17.2685	+	17.2685i	−0.302957	+	0.302957i
$58$		0			0
$59$	−1.70130	−	4.10730i	−0.0288356	−	0.0696153i	0.908806	−	0.417219i	$-0.136995\pi$
$59$	−1.70130	−	4.10730i	−0.0288356	−	0.0696153i	−0.937641	+	0.347604i	$0.886995\pi$
$60$		0			0
$61$	3.53360	−	8.53087i	0.0579279	−	0.139850i	−0.892266	−	0.451511i	$-0.850885\pi$
$61$	3.53360	−	8.53087i	0.0579279	−	0.139850i	0.950193	+	0.311661i	$0.100885\pi$
$62$		0			0
$63$			1.03142i			0.0163718i
$64$		0			0
$65$	10.5769			0.162721
$66$		0			0
$67$	0.300169	+	0.124334i	0.00448013	+	0.00185573i	0.384922	−	0.922949i	$-0.374228\pi$
$67$	0.300169	+	0.124334i	0.00448013	+	0.00185573i	−0.380442	+	0.924805i	$0.624228\pi$
$68$		0			0
$69$	−59.6218	+	24.6961i	−0.864084	+	0.357915i
$70$		0			0
$71$	29.0914	+	29.0914i	0.409738	+	0.409738i	0.881647	−	0.471909i	$-0.156435\pi$
$71$	29.0914	+	29.0914i	0.409738	+	0.409738i	−0.471909	+	0.881647i	$0.656435\pi$
$72$		0			0
$73$	−68.2273	−	68.2273i	−0.934620	−	0.934620i	0.0633700	−	0.997990i	$-0.479815\pi$
$73$	−68.2273	−	68.2273i	−0.934620	−	0.934620i	−0.997990	+	0.0633700i	$0.979815\pi$
$74$		0			0
$75$	61.8222	−	25.6076i	0.824296	−	0.341435i
$76$		0			0
$77$	10.5408	+	4.36612i	0.136893	+	0.0567029i
$78$		0			0
$79$	−67.7588			−0.857706			−0.428853	−	0.903374i	$-0.641082\pi$
$79$	−67.7588			−0.857706			−0.428853	+	0.903374i	$0.641082\pi$
$80$		0			0
$81$		−	62.8565i		−	0.776007i
$82$		0			0
$83$	16.4008	−	39.5950i	0.197600	−	0.477048i	−0.793758	−	0.608234i	$-0.791878\pi$
$83$	16.4008	−	39.5950i	0.197600	−	0.477048i	0.991358	+	0.131186i	$0.0418784\pi$
$84$		0			0
$85$	−2.54727	−	6.14965i	−0.0299679	−	0.0723488i
$86$		0			0
$87$	−69.1047	+	69.1047i	−0.794306	+	0.794306i
$88$		0			0
$89$	−45.3745	+	45.3745i	−0.509825	+	0.509825i	−0.914473	−	0.404647i	$-0.867394\pi$
$89$	−45.3745	+	45.3745i	−0.509825	+	0.509825i	0.404647	+	0.914473i	$0.367394\pi$
$90$		0			0
$91$	5.02718	+	12.1367i	0.0552438	+	0.133370i
$92$		0			0
$93$	−25.4019	+	61.3257i	−0.273139	+	0.659416i
$94$		0			0
$95$			4.42403i			0.0465688i
$96$		0			0
$97$	−119.312			−1.23002			−0.615012	−	0.788518i	$-0.710849\pi$
$97$	−119.312			−1.23002			−0.615012	+	0.788518i	$0.710849\pi$
$98$		0			0
$99$	29.4044	+	12.1797i	0.297014	+	0.123027i
$100$		0			0
$101$	98.7914	−	40.9207i	0.978133	−	0.405156i	0.164399	−	0.986394i	$-0.447431\pi$
$101$	98.7914	−	40.9207i	0.978133	−	0.405156i	0.813734	+	0.581238i	$0.197431\pi$
$102$		0			0
$103$	−127.634	−	127.634i	−1.23916	−	1.23916i	−0.960344	−	0.278817i	$-0.910058\pi$
$103$	−127.634	−	127.634i	−1.23916	−	1.23916i	−0.278817	−	0.960344i	$-0.589942\pi$
$104$		0			0
$105$	−0.568888	−	0.568888i	−0.00541798	−	0.00541798i
$106$		0			0
$107$	−94.9289	+	39.3208i	−0.887186	+	0.367484i	−0.779279	−	0.626677i	$-0.784415\pi$
$107$	−94.9289	+	39.3208i	−0.887186	+	0.367484i	−0.107906	+	0.994161i	$0.534415\pi$
$108$		0			0
$109$	−27.8610	−	11.5404i	−0.255605	−	0.105875i	0.251202	−	0.967935i	$-0.419174\pi$
$109$	−27.8610	−	11.5404i	−0.255605	−	0.105875i	−0.506807	+	0.862060i	$0.669174\pi$
$110$		0			0
$111$	−28.9478			−0.260791
$112$		0			0
$113$			140.786i			1.24590i	0.782263	+	0.622948i	$0.214065\pi$
$113$			140.786i			1.24590i	−0.782263	+	0.622948i	$0.785935\pi$
$114$		0			0
$115$	−4.47380	+	10.8007i	−0.0389026	+	0.0939193i
$116$		0			0
$117$	14.0238	+	33.8564i	0.119861	+	0.289371i
$118$		0			0
$119$	5.84584	−	5.84584i	0.0491247	−	0.0491247i
$120$		0			0
$121$	163.384	−	163.384i	1.35028	−	1.35028i
$122$		0			0
$123$	−21.1883	−	51.1532i	−0.172263	−	0.415879i
$124$		0			0
$125$	9.32274	−	22.5071i	0.0745819	−	0.180057i
$126$		0			0
$127$			163.979i			1.29117i	0.763687	+	0.645587i	$0.223387\pi$
$127$			163.979i			1.29117i	−0.763687	+	0.645587i	$0.776613\pi$
$128$		0			0
$129$	52.2134			0.404755
$130$		0			0
$131$	11.2279	+	4.65074i	0.0857090	+	0.0355018i	0.425126	−	0.905134i	$-0.360230\pi$
$131$	11.2279	+	4.65074i	0.0857090	+	0.0355018i	−0.339417	+	0.940636i	$0.610230\pi$
$132$		0			0
$133$	−5.07646	+	2.10274i	−0.0381689	+	0.0158101i
$134$		0			0
$135$	−10.0071	−	10.0071i	−0.0741270	−	0.0741270i
$136$		0			0
$137$	21.2983	+	21.2983i	0.155462	+	0.155462i	0.780552	−	0.625090i	$-0.214938\pi$
$137$	21.2983	+	21.2983i	0.155462	+	0.155462i	−0.625090	+	0.780552i	$0.714938\pi$
$138$		0			0
$139$	154.836	−	64.1351i	1.11393	−	0.461404i	0.251639	−	0.967821i	$-0.419031\pi$
$139$	154.836	−	64.1351i	1.11393	−	0.461404i	0.862288	+	0.506418i	$0.169031\pi$
$140$		0			0
$141$	108.883	+	45.1010i	0.772223	+	0.319865i
$142$		0			0
$143$	405.364			2.83471
$144$		0			0
$145$			17.7039i			0.122096i
$146$		0			0
$147$	−50.2944	+	121.421i	−0.342139	+	0.825996i
$148$		0			0
$149$	−90.9258	−	219.514i	−0.610240	−	1.47325i	−0.862737	−	0.505653i	$-0.831252\pi$
$149$	−90.9258	−	219.514i	−0.610240	−	1.47325i	0.252497	−	0.967598i	$-0.418748\pi$
$150$		0			0
$151$	82.0484	−	82.0484i	0.543367	−	0.543367i	−0.381147	−	0.924514i	$-0.624471\pi$
$151$	82.0484	−	82.0484i	0.543367	−	0.543367i	0.924514	+	0.381147i	$0.124471\pi$
$152$		0			0
$153$	16.3075	−	16.3075i	0.106585	−	0.106585i
$154$		0			0
$155$	4.60166	+	11.1094i	0.0296881	+	0.0716735i
$156$		0			0
$157$	−52.8906	+	127.689i	−0.336883	+	0.813307i	0.661129	+	0.750272i	$0.270078\pi$
$157$	−52.8906	+	127.689i	−0.336883	+	0.813307i	−0.998011	+	0.0630341i	$0.979922\pi$
$158$		0			0
$159$		−	198.183i		−	1.24644i
$160$		0			0
$161$	−14.5199			−0.0901859
$162$		0			0
$163$	−54.8297	−	22.7112i	−0.336379	−	0.139333i	0.208099	−	0.978108i	$-0.433272\pi$
$163$	−54.8297	−	22.7112i	−0.336379	−	0.139333i	−0.544478	+	0.838775i	$0.683272\pi$
$164$		0			0
$165$	−22.9360	+	9.50040i	−0.139006	+	0.0575782i
$166$		0			0
$167$	98.7296	+	98.7296i	0.591195	+	0.591195i	0.937954	−	0.346759i	$-0.112718\pi$
$167$	98.7296	+	98.7296i	0.591195	+	0.591195i	−0.346759	+	0.937954i	$0.612718\pi$
$168$		0			0
$169$	210.533	+	210.533i	1.24576	+	1.24576i
$170$		0			0
$171$	−14.1613	+	5.86578i	−0.0828143	+	0.0343028i
$172$		0			0
$173$	−6.09221	−	2.52348i	−0.0352151	−	0.0145866i	0.365006	−	0.931005i	$-0.381067\pi$
$173$	−6.09221	−	2.52348i	−0.0352151	−	0.0145866i	−0.400221	+	0.916418i	$0.631067\pi$
$174$		0			0
$175$	15.0558			0.0860332
$176$		0			0
$177$			12.0147i			0.0678799i
$178$		0			0
$179$	−80.6673	+	194.748i	−0.450655	+	1.08798i	0.521418	+	0.853301i	$0.325403\pi$
$179$	−80.6673	+	194.748i	−0.450655	+	1.08798i	−0.972073	+	0.234677i	$0.924597\pi$
$180$		0			0
$181$	−59.7464	−	144.241i	−0.330091	−	0.796910i	−0.998584	−	0.0531918i	$-0.983061\pi$
$181$	−59.7464	−	144.241i	−0.330091	−	0.796910i	0.668493	−	0.743718i	$-0.266939\pi$
$182$		0			0
$183$	−17.6456	+	17.6456i	−0.0964240	+	0.0964240i
$184$		0			0
$185$	−3.70807	+	3.70807i	−0.0200436	+	0.0200436i
$186$		0			0
$187$	−97.6252	−	235.688i	−0.522060	−	1.26036i
$188$		0			0
$189$	6.72655	−	16.2393i	0.0355902	−	0.0859223i
$190$		0			0
$191$			107.812i			0.564460i	0.959347	+	0.282230i	$0.0910741\pi$
$191$			107.812i			0.564460i	−0.959347	+	0.282230i	$0.908926\pi$
$192$		0			0
$193$	−174.830			−0.905855			−0.452927	−	0.891547i	$-0.649620\pi$
$193$	−174.830			−0.905855			−0.452927	+	0.891547i	$0.649620\pi$
$194$		0			0
$195$	−26.4087	−	10.9388i	−0.135429	−	0.0560965i
$196$		0			0
$197$	−108.472	+	44.9304i	−0.550618	+	0.228073i	−0.640606	−	0.767870i	$-0.721317\pi$
$197$	−108.472	+	44.9304i	−0.550618	+	0.228073i	0.0899887	+	0.995943i	$0.471317\pi$
$198$		0			0
$199$	−190.347	−	190.347i	−0.956516	−	0.956516i	0.0425770	−	0.999093i	$-0.486443\pi$
$199$	−190.347	−	190.347i	−0.956516	−	0.956516i	−0.999093	+	0.0425770i	$0.986443\pi$
$200$		0			0
$201$	−0.620881	−	0.620881i	−0.00308896	−	0.00308896i
$202$		0			0
$203$	−20.3148	+	8.41467i	−0.100073	+	0.0414516i
$204$		0			0
$205$	−9.26659	−	3.83835i	−0.0452029	−	0.0187237i
$206$		0			0
$207$	−40.5047			−0.195675
$208$		0			0
$209$			169.553i			0.811259i
$210$		0			0
$211$	−86.6725	+	209.246i	−0.410770	+	0.991686i	0.574162	+	0.818742i	$0.305328\pi$
$211$	−86.6725	+	209.246i	−0.410770	+	0.991686i	−0.984932	+	0.172944i	$0.944672\pi$
$212$		0			0
$213$	−42.5493	−	102.723i	−0.199762	−	0.482269i
$214$		0			0
$215$	6.68829	−	6.68829i	0.0311083	−	0.0311083i
$216$		0			0
$217$	−10.5606	+	10.5606i	−0.0486662	+	0.0486662i
$218$		0			0
$219$	99.7897	+	240.914i	0.455661	+	1.10006i
$220$		0			0
$221$	112.406	−	271.373i	0.508626	−	1.22793i
$222$		0			0
$223$		−	103.845i		−	0.465671i	−0.972516	−	0.232836i	$-0.925200\pi$
$223$		−	103.845i		−	0.465671i	0.972516	−	0.232836i	$-0.0748004\pi$
$224$		0			0
$225$	41.9996			0.186665
$226$		0			0
$227$	−106.086	−	43.9421i	−0.467338	−	0.193578i	0.136572	−	0.990630i	$-0.456391\pi$
$227$	−106.086	−	43.9421i	−0.467338	−	0.193578i	−0.603910	+	0.797052i	$0.706391\pi$
$228$		0			0
$229$	46.1162	−	19.1019i	0.201381	−	0.0834146i	−0.279714	−	0.960083i	$-0.590240\pi$
$229$	46.1162	−	19.1019i	0.201381	−	0.0834146i	0.481094	+	0.876669i	$0.340240\pi$
$230$		0			0
$231$	−21.8029	−	21.8029i	−0.0943849	−	0.0943849i
$232$		0			0
$233$	−62.7031	−	62.7031i	−0.269112	−	0.269112i	0.559630	−	0.828742i	$-0.310943\pi$
$233$	−62.7031	−	62.7031i	−0.269112	−	0.269112i	−0.828742	+	0.559630i	$0.810943\pi$
$234$		0			0
$235$	19.7247	−	8.17022i	0.0839347	−	0.0347669i
$236$		0			0
$237$	169.182	+	70.0775i	0.713848	+	0.295686i
$238$		0			0
$239$	−306.080			−1.28067			−0.640335	−	0.768095i	$-0.721205\pi$
$239$	−306.080			−1.28067			−0.640335	+	0.768095i	$0.721205\pi$
$240$		0			0
$241$		−	245.242i		−	1.01760i	−0.860884	−	0.508801i	$-0.830089\pi$
$241$		−	245.242i		−	1.01760i	0.860884	−	0.508801i	$-0.169911\pi$
$242$		0			0
$243$	34.5529	−	83.4181i	0.142193	−	0.343285i
$244$		0			0
$245$	9.11102	+	21.9960i	0.0371878	+	0.0897794i
$246$		0			0
$247$	−138.045	+	138.045i	−0.558886	+	0.558886i
$248$		0			0
$249$	−81.8998	+	81.8998i	−0.328915	+	0.328915i
$250$		0			0
$251$	−132.845	−	320.715i	−0.529261	−	1.27775i	−0.932008	−	0.362438i	$-0.881944\pi$
$251$	−132.845	−	320.715i	−0.529261	−	1.27775i	0.402747	−	0.915311i	$-0.368056\pi$
$252$		0			0
$253$	−171.461	+	413.942i	−0.677710	+	1.63614i
$254$		0			0
$255$			17.9890i			0.0705453i
$256$		0			0
$257$	−108.814			−0.423399			−0.211700	−	0.977335i	$-0.567900\pi$
$257$	−108.814			−0.423399			−0.211700	+	0.977335i	$0.567900\pi$
$258$		0			0
$259$	−6.01735	−	2.49247i	−0.0232330	−	0.00962343i
$260$		0			0
$261$	−56.6700	+	23.4735i	−0.217126	+	0.0899367i
$262$		0			0
$263$	150.151	+	150.151i	0.570916	+	0.570916i	0.932384	−	0.361468i	$-0.117724\pi$
$263$	150.151	+	150.151i	0.570916	+	0.570916i	−0.361468	+	0.932384i	$0.617724\pi$
$264$		0			0
$265$	−25.3863	−	25.3863i	−0.0957975	−	0.0957975i
$266$		0			0
$267$	160.219	−	66.3650i	0.600072	−	0.248558i
$268$		0			0
$269$	−255.485	−	105.825i	−0.949758	−	0.393403i	−0.146618	−	0.989193i	$-0.546839\pi$
$269$	−255.485	−	105.825i	−0.949758	−	0.393403i	−0.803140	+	0.595791i	$0.796839\pi$
$270$		0			0
$271$	261.648			0.965492			0.482746	−	0.875760i	$-0.339639\pi$
$271$	261.648			0.965492			0.482746	+	0.875760i	$0.339639\pi$
$272$		0			0
$273$		−	35.5024i		−	0.130046i
$274$		0			0
$275$	177.789	−	429.220i	0.646504	−	1.56080i
$276$		0			0
$277$	120.123	+	290.003i	0.433658	+	1.04694i	0.978098	+	0.208143i	$0.0667420\pi$
$277$	120.123	+	290.003i	0.433658	+	1.04694i	−0.544440	+	0.838799i	$0.683258\pi$
$278$		0			0
$279$	−29.4597	+	29.4597i	−0.105590	+	0.105590i
$280$		0			0
$281$	21.7898	−	21.7898i	0.0775437	−	0.0775437i	−0.667271	−	0.744815i	$-0.732538\pi$
$281$	21.7898	−	21.7898i	0.0775437	−	0.0775437i	0.744815	+	0.667271i	$0.232538\pi$
$282$		0			0
$283$	155.937	+	376.466i	0.551016	+	1.33027i	0.916717	+	0.399537i	$0.130829\pi$
$283$	155.937	+	376.466i	0.551016	+	1.33027i	−0.365702	+	0.930732i	$0.619171\pi$
$284$		0			0
$285$	4.57542	−	11.0460i	0.0160541	−	0.0387581i
$286$		0			0
$287$		−	12.4575i		−	0.0434060i
$288$		0			0
$289$	104.146			0.360368
$290$		0			0
$291$	297.902	+	123.395i	1.02372	+	0.424038i
$292$		0			0
$293$	−37.2090	+	15.4125i	−0.126993	+	0.0526023i	−0.445275	−	0.895394i	$-0.646894\pi$
$293$	−37.2090	+	15.4125i	−0.126993	+	0.0526023i	0.318282	+	0.947996i	$0.396894\pi$
$294$		0			0
$295$	1.53903	+	1.53903i	0.00521705	+	0.00521705i
$296$		0			0
$297$	−383.529	−	383.529i	−1.29134	−	1.29134i
$298$		0			0
$299$	−476.616	+	197.421i	−1.59403	+	0.660271i
$300$		0			0
$301$	10.8536	+	4.49569i	0.0360584	+	0.0149359i
$302$		0			0
$303$	−288.986			−0.953750
$304$		0			0
$305$			4.52063i			0.0148217i
$306$		0			0
$307$	101.089	−	244.049i	0.329279	−	0.794949i	−0.669368	−	0.742931i	$-0.733435\pi$
$307$	101.089	−	244.049i	0.329279	−	0.794949i	0.998646	−	0.0520174i	$-0.0165651\pi$
$308$		0			0
$309$	186.678	+	450.680i	0.604136	+	1.45851i
$310$		0			0
$311$	181.395	−	181.395i	0.583264	−	0.583264i	−0.352534	−	0.935799i	$-0.614680\pi$
$311$	181.395	−	181.395i	0.583264	−	0.583264i	0.935799	+	0.352534i	$0.114680\pi$
$312$		0			0
$313$	110.963	−	110.963i	0.354513	−	0.354513i	−0.507273	−	0.861786i	$-0.669346\pi$
$313$	110.963	−	110.963i	0.354513	−	0.354513i	0.861786	+	0.507273i	$0.169346\pi$
$314$		0			0
$315$	−0.193240	−	0.466523i	−0.000613460	−	0.00148102i
$316$		0			0
$317$	134.161	−	323.892i	0.423219	−	1.02174i	−0.558172	−	0.829725i	$-0.688497\pi$
$317$	134.161	−	323.892i	0.423219	−	1.02174i	0.981392	−	0.192017i	$-0.0615028\pi$
$318$		0			0
$319$			678.512i			2.12700i
$320$		0			0
$321$	277.687			0.865070
$322$		0			0
$323$	113.508	+	47.0166i	0.351419	+	0.145562i
$324$		0			0
$325$	494.207	−	204.707i	1.52064	−	0.629868i
$326$		0			0
$327$	57.6287	+	57.6287i	0.176235	+	0.176235i
$328$		0			0
$329$	18.7502	+	18.7502i	0.0569915	+	0.0569915i
$330$		0			0
$331$	580.238	−	240.342i	1.75298	−	0.726110i	0.755506	−	0.655141i	$-0.227391\pi$
$331$	580.238	−	240.342i	1.75298	−	0.726110i	0.997479	−	0.0709686i	$-0.0226090\pi$
$332$		0			0
$333$	−16.7860	−	6.95297i	−0.0504083	−	0.0208798i
$334$		0			0
$335$	−0.159064			−0.000474817
$336$		0			0
$337$		−	130.257i		−	0.386519i	−0.981148	−	0.193259i	$-0.938094\pi$
$337$		−	130.257i		−	0.386519i	0.981148	−	0.193259i	$-0.0619059\pi$
$338$		0			0
$339$	145.604	−	351.519i	0.429510	−	1.03693i
$340$		0			0
$341$	176.361	+	425.772i	0.517187	+	1.24860i
$342$		0			0
$343$	−41.9776	+	41.9776i	−0.122384	+	0.122384i
$344$		0			0
$345$	22.3406	−	22.3406i	0.0647554	−	0.0647554i
$346$		0			0
$347$	54.6775	+	132.003i	0.157572	+	0.380412i	0.982874	−	0.184279i	$-0.0589951\pi$
$347$	54.6775	+	132.003i	0.157572	+	0.380412i	−0.825302	+	0.564692i	$0.808995\pi$
$348$		0			0
$349$	−46.7936	+	112.970i	−0.134079	+	0.323696i	−0.976632	−	0.214918i	$-0.931052\pi$
$349$	−46.7936	+	112.970i	−0.134079	+	0.323696i	0.842553	+	0.538613i	$0.181052\pi$
$350$		0			0
$351$		−	624.513i		−	1.77924i
$352$		0			0
$353$	382.113			1.08247			0.541236	−	0.840871i	$-0.317957\pi$
$353$	382.113			1.08247			0.541236	+	0.840871i	$0.317957\pi$
$354$		0			0
$355$	−18.6087	−	7.70798i	−0.0524189	−	0.0217126i
$356$		0			0
$357$	−20.6419	+	8.55017i	−0.0578206	+	0.0239501i
$358$		0			0
$359$	81.2910	+	81.2910i	0.226437	+	0.226437i	0.811203	−	0.584765i	$-0.198813\pi$
$359$	81.2910	+	81.2910i	0.226437	+	0.226437i	−0.584765	+	0.811203i	$0.698813\pi$
$360$		0			0
$361$	197.525	+	197.525i	0.547161	+	0.547161i
$362$		0			0
$363$	−576.916	+	238.967i	−1.58930	+	0.658310i
$364$		0			0
$365$	43.6425	+	18.0773i	0.119568	+	0.0495268i
$366$		0			0
$367$	−456.145			−1.24290			−0.621452	−	0.783453i	$-0.713457\pi$
$367$	−456.145			−1.24290			−0.621452	+	0.783453i	$0.713457\pi$
$368$		0			0
$369$		−	34.7514i		−	0.0941773i
$370$		0			0
$371$	17.0640	−	41.1963i	0.0459947	−	0.111041i
$372$		0			0
$373$	−184.108	−	444.476i	−0.493588	−	1.19163i	−0.952882	−	0.303342i	$-0.901898\pi$
$373$	−184.108	−	444.476i	−0.493588	−	1.19163i	0.459294	−	0.888284i	$-0.348102\pi$
$374$		0			0
$375$	−46.5545	+	46.5545i	−0.124145	+	0.124145i
$376$		0			0
$377$	−552.423	+	552.423i	−1.46531	+	1.46531i
$378$		0			0
$379$	108.900	+	262.908i	0.287336	+	0.693690i	0.999969	−	0.00784682i	$-0.00249775\pi$
$379$	108.900	+	262.908i	0.287336	+	0.693690i	−0.712634	+	0.701536i	$0.752498\pi$
$380$		0			0
$381$	169.590	−	409.427i	0.445119	−	1.07461i
$382$		0			0
$383$		−	476.810i		−	1.24493i	−0.782646	−	0.622467i	$-0.786131\pi$
$383$		−	476.810i		−	1.24493i	0.782646	−	0.622467i	$-0.213869\pi$
$384$		0			0
$385$	−5.58569			−0.0145083
$386$		0			0
$387$	30.2770	+	12.5411i	0.0782352	+	0.0324061i
$388$		0			0
$389$	−71.5472	+	29.6358i	−0.183926	+	0.0761846i	−0.472746	−	0.881199i	$-0.656737\pi$
$389$	−71.5472	+	29.6358i	−0.183926	+	0.0761846i	0.288820	+	0.957383i	$0.406737\pi$
$390$		0			0
$391$	229.570	+	229.570i	0.587136	+	0.587136i
$392$		0			0
$393$	−23.2242	−	23.2242i	−0.0590946	−	0.0590946i
$394$		0			0
$395$	30.6480	−	12.6948i	0.0775898	−	0.0321388i
$396$		0			0
$397$	120.360	+	49.8545i	0.303173	+	0.125578i	0.529084	−	0.848570i	$-0.322536\pi$
$397$	120.360	+	49.8545i	0.303173	+	0.125578i	−0.225911	+	0.974148i	$0.572536\pi$
$398$		0			0
$399$	14.8497			0.0372174
$400$		0			0
$401$		−	174.015i		−	0.433953i	−0.976177	−	0.216976i	$-0.930381\pi$
$401$		−	174.015i		−	0.433953i	0.976177	−	0.216976i	$-0.0696195\pi$
$402$		0			0
$403$	−203.063	+	490.237i	−0.503878	+	1.21647i
$404$		0			0
$405$	11.7764	+	28.4306i	0.0290774	+	0.0701991i
$406$		0			0
$407$	−142.114	+	142.114i	−0.349173	+	0.349173i
$408$		0			0
$409$	−108.736	+	108.736i	−0.265857	+	0.265857i	−0.827428	−	0.561571i	$-0.810197\pi$
$409$	−108.736	+	108.736i	−0.265857	+	0.265857i	0.561571	+	0.827428i	$0.310197\pi$
$410$		0			0
$411$	−31.1511	−	75.2054i	−0.0757934	−	0.182981i
$412$		0			0
$413$	−1.03450	+	2.49749i	−0.00250483	+	0.00604720i
$414$		0			0
$415$			20.9819i			0.0505589i
$416$		0			0
$417$	−452.928			−1.08616
$418$		0			0
$419$	−370.373	−	153.414i	−0.883946	−	0.366142i	−0.105920	−	0.994375i	$-0.533779\pi$
$419$	−370.373	−	153.414i	−0.883946	−	0.366142i	−0.778026	+	0.628232i	$0.783779\pi$
$420$		0			0
$421$	−600.339	+	248.669i	−1.42598	+	0.590662i	−0.956357	−	0.292202i	$-0.905612\pi$
$421$	−600.339	+	248.669i	−1.42598	+	0.590662i	−0.469628	+	0.882864i	$0.655612\pi$
$422$		0			0
$423$	52.3054	+	52.3054i	0.123654	+	0.123654i
$424$		0			0
$425$	−238.043	−	238.043i	−0.560101	−	0.560101i
$426$		0			0
$427$	−5.18730	+	2.14865i	−0.0121482	+	0.00503197i
$428$		0			0
$429$	−1012.12	−	419.236i	−2.35926	−	0.977239i
$430$		0			0
$431$	−289.906			−0.672636			−0.336318	−	0.941749i	$-0.609182\pi$
$431$	−289.906			−0.672636			−0.336318	+	0.941749i	$0.609182\pi$
$432$		0			0
$433$			314.414i			0.726129i	0.931764	+	0.363064i	$0.118269\pi$
$433$			314.414i			0.726129i	−0.931764	+	0.363064i	$0.881731\pi$
$434$		0			0
$435$	18.3098	−	44.2037i	0.0420914	−	0.101618i
$436$		0			0
$437$	−82.5760	−	199.356i	−0.188961	−	0.456192i
$438$		0			0
$439$	579.455	−	579.455i	1.31994	−	1.31994i	0.406125	−	0.913818i	$-0.366880\pi$
$439$	579.455	−	579.455i	1.31994	−	1.31994i	0.913818	−	0.406125i	$-0.133120\pi$
$440$		0			0
$441$	−58.3284	+	58.3284i	−0.132264	+	0.132264i
$442$		0			0
$443$	−107.736	−	260.098i	−0.243197	−	0.587130i	0.754400	−	0.656415i	$-0.227928\pi$
$443$	−107.736	−	260.098i	−0.243197	−	0.587130i	−0.997597	+	0.0692856i	$0.977928\pi$
$444$		0			0
$445$	12.0223	−	29.0244i	0.0270164	−	0.0652233i
$446$		0			0
$447$			642.127i			1.43652i
$448$		0			0
$449$	470.997			1.04899			0.524496	−	0.851413i	$-0.324254\pi$
$449$	470.997			1.04899			0.524496	+	0.851413i	$0.324254\pi$
$450$		0			0
$451$	−355.147	−	147.107i	−0.787465	−	0.326179i
$452$		0			0
$453$	−289.717	+	120.005i	−0.639551	+	0.264911i
$454$		0			0
$455$	−4.54769	−	4.54769i	−0.00999493	−	0.00999493i
$456$		0			0
$457$	447.868	+	447.868i	0.980018	+	0.980018i	0.999804	−	0.0197861i	$-0.00629852\pi$
$457$	447.868	+	447.868i	0.980018	+	0.980018i	−0.0197861	+	0.999804i	$0.506299\pi$
$458$		0			0
$459$	−363.106	+	150.404i	−0.791082	+	0.327677i
$460$		0			0
$461$	253.222	+	104.888i	0.549288	+	0.227523i	0.640027	−	0.768352i	$-0.278923\pi$
$461$	253.222	+	104.888i	0.549288	+	0.227523i	−0.0907394	+	0.995875i	$0.528923\pi$
$462$		0			0
$463$	653.753			1.41199			0.705996	−	0.708215i	$-0.250499\pi$
$463$	653.753			1.41199			0.705996	+	0.708215i	$0.250499\pi$
$464$		0			0
$465$		−	32.4973i		−	0.0698868i
$466$		0			0
$467$	−39.3875	+	95.0899i	−0.0843416	+	0.203619i	−0.960424	−	0.278544i	$-0.910148\pi$
$467$	−39.3875	+	95.0899i	−0.0843416	+	0.203619i	0.876082	+	0.482162i	$0.160148\pi$
$468$		0			0
$469$	−0.0756028	−	0.182521i	−0.000161200	−	0.000389171i
$470$		0			0
$471$	264.117	−	264.117i	0.560758	−	0.560758i
$472$		0			0
$473$	256.332	−	256.332i	0.541927	−	0.541927i
$474$		0			0
$475$	85.6236	+	206.714i	0.180260	+	0.435187i
$476$		0			0
$477$	47.6017	−	114.921i	0.0997940	−	0.240924i
$478$		0			0
$479$		−	857.713i		−	1.79063i	−0.445432	−	0.895316i	$-0.646950\pi$
$479$		−	857.713i		−	1.79063i	0.445432	−	0.895316i	$-0.353050\pi$
$480$		0			0
$481$	−231.408			−0.481099
$482$		0			0
$483$	36.2537	+	15.0168i	0.0750595	+	0.0310907i
$484$		0			0
$485$	53.9661	−	22.3535i	0.111270	−	0.0460897i
$486$		0			0
$487$	−12.5467	−	12.5467i	−0.0257633	−	0.0257633i	0.694108	−	0.719871i	$-0.255799\pi$
$487$	−12.5467	−	12.5467i	−0.0257633	−	0.0257633i	−0.719871	+	0.694108i	$0.755799\pi$
$488$		0			0
$489$	113.412	+	113.412i	0.231926	+	0.231926i
$490$		0			0
$491$	−91.7015	+	37.9840i	−0.186765	+	0.0773605i	−0.474106	−	0.880468i	$-0.657229\pi$
$491$	−91.7015	+	37.9840i	−0.186765	+	0.0773605i	0.287341	+	0.957828i	$0.407229\pi$
$492$		0			0
$493$	454.233	+	188.149i	0.921365	+	0.381642i
$494$		0			0
$495$	−15.5818			−0.0314784
$496$		0			0
$497$		−	25.0166i		−	0.0503352i
$498$		0			0
$499$	−193.677	+	467.577i	−0.388130	+	0.937029i	0.602206	+	0.798341i	$0.294289\pi$
$499$	−193.677	+	467.577i	−0.388130	+	0.937029i	−0.990336	+	0.138688i	$0.955711\pi$
$500$		0			0
$501$	−144.403	−	348.619i	−0.288229	−	0.695846i
$502$		0			0
$503$	−659.583	+	659.583i	−1.31130	+	1.31130i	−0.390840	+	0.920459i	$0.627816\pi$
$503$	−659.583	+	659.583i	−1.31130	+	1.31130i	−0.920459	+	0.390840i	$0.872184\pi$
$504$		0			0
$505$	−37.0177	+	37.0177i	−0.0733024	+	0.0733024i
$506$		0			0
$507$	−307.928	−	743.403i	−0.607353	−	1.46628i
$508$		0			0
$509$	−133.178	+	321.521i	−0.261647	+	0.631671i	−0.999041	−	0.0437918i	$-0.986056\pi$
$509$	−133.178	+	321.521i	−0.261647	+	0.631671i	0.737394	+	0.675463i	$0.236056\pi$
$510$		0			0
$511$			58.6707i			0.114815i
$512$		0			0
$513$	261.217			0.509196
$514$		0			0
$515$	81.6425	+	33.8174i	0.158529	+	0.0656649i
$516$		0			0
$517$	755.957	−	313.127i	1.46220	−	0.605662i
$518$		0			0
$519$	12.6014	+	12.6014i	0.0242801	+	0.0242801i
$520$		0			0
$521$	71.2918	+	71.2918i	0.136837	+	0.136837i	0.772207	−	0.635371i	$-0.219153\pi$
$521$	71.2918	+	71.2918i	0.136837	+	0.136837i	−0.635371	+	0.772207i	$0.719153\pi$
$522$		0			0
$523$	376.338	−	155.884i	0.719576	−	0.298058i	0.00731529	−	0.999973i	$-0.497671\pi$
$523$	376.338	−	155.884i	0.719576	−	0.298058i	0.712261	+	0.701915i	$0.247671\pi$
$524$		0			0
$525$	−37.5918	−	15.5710i	−0.0716033	−	0.0296591i
$526$		0			0
$527$	333.940			0.633662
$528$		0			0
$529$		−	41.2074i		−	0.0778968i
$530$		0			0
$531$	−2.88582	+	6.96699i	−0.00543469	+	0.0131205i
$532$		0			0
$533$	−169.379	−	408.918i	−0.317785	−	0.767201i
$534$		0			0
$535$	35.5704	−	35.5704i	0.0664867	−	0.0664867i
$536$		0			0
$537$	402.825	−	402.825i	0.750139	−	0.750139i
$538$		0			0
$539$	349.184	+	843.005i	0.647837	+	1.56402i
$540$		0			0
$541$	−131.242	+	316.846i	−0.242591	+	0.585667i	−0.997539	−	0.0701185i	$-0.977662\pi$
$541$	−131.242	+	316.846i	−0.242591	+	0.585667i	0.754948	+	0.655785i	$0.227662\pi$
$542$		0			0
$543$			421.935i			0.777044i
$544$		0			0
$545$	14.7639			0.0270898
$546$		0			0
$547$	57.6667	+	23.8863i	0.105424	+	0.0436679i	0.434772	−	0.900541i	$-0.356829\pi$
$547$	57.6667	+	23.8863i	0.105424	+	0.0436679i	−0.329348	+	0.944209i	$0.606829\pi$
$548$		0			0
$549$	−14.4705	+	5.99386i	−0.0263578	+	0.0109178i
$550$		0			0
$551$	−231.064	−	231.064i	−0.419354	−	0.419354i
$552$		0			0
$553$	29.1339	+	29.1339i	0.0526834	+	0.0526834i
$554$		0			0
$555$	13.0934	−	5.42345i	0.0235917	−	0.00977198i
$556$		0			0
$557$	403.952	+	167.322i	0.725228	+	0.300399i	0.714589	−	0.699544i	$-0.246614\pi$
$557$	403.952	+	167.322i	0.725228	+	0.300399i	0.0106383	+	0.999943i	$0.496614\pi$
$558$		0			0
$559$	417.394			0.746680
$560$		0			0
$561$			689.438i			1.22895i
$562$		0			0
$563$	−2.60893	+	6.29851i	−0.00463398	+	0.0111874i	−0.926180	−	0.377083i	$-0.876927\pi$
$563$	−2.60893	+	6.29851i	−0.00463398	+	0.0111874i	0.921546	+	0.388270i	$0.126927\pi$
$564$		0			0
$565$	−26.3767	−	63.6791i	−0.0466845	−	0.112706i
$566$		0			0
$567$	−27.0261	+	27.0261i	−0.0476651	+	0.0476651i
$568$		0			0
$569$	225.325	−	225.325i	0.396002	−	0.396002i	−0.480818	−	0.876820i	$-0.659660\pi$
$569$	225.325	−	225.325i	0.396002	−	0.396002i	0.876820	+	0.480818i	$0.159660\pi$
$570$		0			0
$571$	−203.081	−	490.280i	−0.355658	−	0.858634i	−0.995900	−	0.0904608i	$-0.971166\pi$
$571$	−203.081	−	490.280i	−0.355658	−	0.858634i	0.640242	−	0.768173i	$-0.278834\pi$
$572$		0			0
$573$	111.501	−	269.187i	0.194592	−	0.469786i
$574$		0			0
$575$			591.252i			1.02826i
$576$		0			0
$577$	−1017.81			−1.76396			−0.881980	−	0.471286i	$-0.843790\pi$
$577$	−1017.81			−1.76396			−0.881980	+	0.471286i	$0.843790\pi$
$578$		0			0
$579$	436.520	+	180.813i	0.753921	+	0.312284i
$580$		0			0
$581$	−24.0762	+	9.97270i	−0.0414393	+	0.0171647i
$582$		0			0
$583$	−972.943	−	972.943i	−1.66886	−	1.66886i
$584$		0			0
$585$	−12.6862	−	12.6862i	−0.0216858	−	0.0216858i
$586$		0			0
$587$	721.215	−	298.737i	1.22865	−	0.508922i	0.328498	−	0.944505i	$-0.393458\pi$
$587$	721.215	−	298.737i	1.22865	−	0.508922i	0.900149	+	0.435583i	$0.143458\pi$
$588$		0			0
$589$	−205.053	−	84.9359i	−0.348138	−	0.144204i
$590$		0			0
$591$	317.303			0.536892
$592$		0			0
$593$			525.499i			0.886170i	0.896479	+	0.443085i	$0.146116\pi$
$593$			525.499i			0.886170i	−0.896479	+	0.443085i	$0.853884\pi$
$594$		0			0
$595$	−1.54890	+	3.73937i	−0.00260319	+	0.00628465i
$596$		0			0
$597$	278.403	+	672.123i	0.466336	+	1.12583i
$598$		0			0
$599$	359.176	−	359.176i	0.599626	−	0.599626i	−0.340587	−	0.940213i	$-0.610626\pi$
$599$	359.176	−	359.176i	0.599626	−	0.599626i	0.940213	+	0.340587i	$0.110626\pi$
$600$		0			0
$601$	163.858	−	163.858i	0.272642	−	0.272642i	−0.557521	−	0.830163i	$-0.688247\pi$
$601$	163.858	−	163.858i	0.272642	−	0.272642i	0.830163	+	0.557521i	$0.188247\pi$
$602$		0			0
$603$	−0.210901	−	0.509160i	−0.000349753	−	0.000844378i
$604$		0			0
$605$	−43.2897	+	104.511i	−0.0715533	+	0.172745i
$606$		0			0
$607$			208.191i			0.342984i	0.985186	+	0.171492i	$0.0548587\pi$
$607$			208.191i			0.342984i	−0.985186	+	0.171492i	$0.945141\pi$
$608$		0			0
$609$	59.4252			0.0975783
$610$		0			0
$611$	870.414	+	360.537i	1.42457	+	0.590077i
$612$		0			0
$613$	643.217	−	266.429i	1.04929	−	0.434632i	0.209654	−	0.977776i	$-0.432766\pi$
$613$	643.217	−	266.429i	1.04929	−	0.434632i	0.839640	+	0.543144i	$0.182766\pi$
$614$		0			0
$615$	19.1674	+	19.1674i	0.0311665	+	0.0311665i
$616$		0			0
$617$	−526.767	−	526.767i	−0.853755	−	0.853755i	0.136838	−	0.990593i	$-0.456306\pi$
$617$	−526.767	−	526.767i	−0.853755	−	0.853755i	−0.990593	+	0.136838i	$0.956306\pi$
$618$		0			0
$619$	316.799	−	131.222i	0.511791	−	0.211991i	−0.111816	−	0.993729i	$-0.535667\pi$
$619$	316.799	−	131.222i	0.511791	−	0.211991i	0.623607	+	0.781738i	$0.285667\pi$
$620$		0			0
$621$	637.729	+	264.156i	1.02694	+	0.425372i
$622$		0			0
$623$	39.0188			0.0626306
$624$		0			0
$625$		−	607.081i		−	0.971330i
$626$		0			0
$627$	175.355	−	423.345i	0.279673	−	0.675191i
$628$		0			0
$629$	55.7309	+	134.546i	0.0886024	+	0.213905i
$630$		0			0
$631$	−515.138	+	515.138i	−0.816383	+	0.816383i	−0.985582	−	0.169199i	$-0.945882\pi$
$631$	−515.138	+	515.138i	−0.816383	+	0.816383i	0.169199	+	0.985582i	$0.445882\pi$
$632$		0			0
$633$	432.812	−	432.812i	0.683748	−	0.683748i
$634$		0			0
$635$	−30.7220	−	74.1694i	−0.0483810	−	0.116802i
$636$		0			0
$637$	−402.053	+	970.642i	−0.631167	+	1.52377i
$638$		0			0
$639$		−	69.7861i		−	0.109211i
$640$		0			0
$641$	−827.282			−1.29061			−0.645306	−	0.763925i	$-0.723270\pi$
$641$	−827.282			−1.29061			−0.645306	+	0.763925i	$0.723270\pi$
$642$		0			0
$643$	−300.259	−	124.371i	−0.466965	−	0.193423i	0.136779	−	0.990602i	$-0.456325\pi$
$643$	−300.259	−	124.371i	−0.466965	−	0.193423i	−0.603744	+	0.797178i	$0.706325\pi$
$644$		0			0
$645$	−23.6166	+	9.78234i	−0.0366150	+	0.0151664i
$646$		0			0
$647$	182.325	+	182.325i	0.281800	+	0.281800i	0.833827	−	0.552027i	$-0.186145\pi$
$647$	182.325	+	182.325i	0.281800	+	0.281800i	−0.552027	+	0.833827i	$0.686145\pi$
$648$		0			0
$649$	58.9840	+	58.9840i	0.0908845	+	0.0908845i
$650$		0			0
$651$	37.2898	−	15.4460i	0.0572808	−	0.0237265i
$652$		0			0
$653$	−83.4520	−	34.5670i	−0.127798	−	0.0529356i	0.317868	−	0.948135i	$-0.397033\pi$
$653$	−83.4520	−	34.5670i	−0.127798	−	0.0529356i	−0.445666	+	0.895199i	$0.647033\pi$
$654$		0			0
$655$	−5.94981			−0.00908368
$656$		0			0
$657$			163.667i			0.249113i
$658$		0			0
$659$	−36.4182	+	87.9213i	−0.0552628	+	0.133416i	−0.949099	−	0.314976i	$-0.898003\pi$
$659$	−36.4182	+	87.9213i	−0.0552628	+	0.133416i	0.893837	+	0.448393i	$0.148003\pi$
$660$		0			0
$661$	−420.501	−	1015.18i	−0.636159	−	1.53582i	−0.831757	−	0.555140i	$-0.812665\pi$
$661$	−420.501	−	1015.18i	−0.636159	−	1.53582i	0.195597	−	0.980684i	$-0.437335\pi$
$662$		0			0
$663$	−561.319	+	561.319i	−0.846634	+	0.846634i
$664$		0			0
$665$	1.90218	−	1.90218i	0.00286042	−	0.00286042i
$666$		0			0
$667$	−330.450	−	797.776i	−0.495427	−	1.19607i
$668$		0			0
$669$	−107.398	+	259.282i	−0.160535	+	0.387567i
$670$		0			0
$671$			173.255i			0.258205i
$672$		0			0
$673$	80.3370			0.119372			0.0596858	−	0.998217i	$-0.480990\pi$
$673$	80.3370			0.119372			0.0596858	+	0.998217i	$0.480990\pi$
$674$		0			0
$675$	−661.266	−	273.905i	−0.979653	−	0.405785i
$676$		0			0
$677$	−944.061	+	391.043i	−1.39448	+	0.577611i	−0.948312	−	0.317339i	$-0.897211\pi$
$677$	−944.061	+	391.043i	−1.39448	+	0.577611i	−0.446165	+	0.894951i	$0.647211\pi$
$678$		0			0
$679$	51.3001	+	51.3001i	0.0755524	+	0.0755524i
$680$		0			0
$681$	219.432	+	219.432i	0.322220	+	0.322220i
$682$		0			0
$683$	173.921	−	72.0404i	0.254643	−	0.105476i	−0.251711	−	0.967803i	$-0.580993\pi$
$683$	173.921	−	72.0404i	0.254643	−	0.105476i	0.506353	+	0.862326i	$0.330993\pi$
$684$		0			0
$685$	−13.6237	−	5.64314i	−0.0198887	−	0.00823816i
$686$		0			0
$687$	−134.900			−0.196361
$688$		0			0
$689$		−	1584.28i		−	2.29939i
$690$		0			0
$691$	−185.902	+	448.807i	−0.269033	+	0.649503i	−0.999438	−	0.0335109i	$-0.989331\pi$
$691$	−185.902	+	448.807i	−0.269033	+	0.649503i	0.730405	+	0.683014i	$0.239331\pi$
$692$		0			0
$693$	−7.40601	−	17.8797i	−0.0106869	−	0.0258004i
$694$		0			0
$695$	−58.0179	+	58.0179i	−0.0834790	+	0.0834790i
$696$		0			0
$697$	−196.962	+	196.962i	−0.282586	+	0.282586i
$698$		0			0
$699$	91.7099	+	221.407i	0.131202	+	0.316749i
$700$		0			0
$701$	−150.886	+	364.271i	−0.215244	+	0.519645i	−0.994214	−	0.107416i	$-0.965742\pi$
$701$	−150.886	+	364.271i	−0.215244	+	0.519645i	0.778970	+	0.627061i	$0.215742\pi$
$702$		0			0
$703$		−	96.7921i		−	0.137684i
$704$		0			0
$705$	−57.6989			−0.0818423
$706$		0			0
$707$	−60.0713	−	24.8824i	−0.0849665	−	0.0351943i
$708$		0			0
$709$	−457.191	+	189.375i	−0.644839	+	0.267101i	−0.681043	−	0.732243i	$-0.738473\pi$
$709$	−457.191	+	189.375i	−0.644839	+	0.267101i	0.0362043	+	0.999344i	$0.488473\pi$
$710$		0			0
$711$	81.2717	+	81.2717i	0.114306	+	0.114306i
$712$		0			0
$713$	−414.720	−	414.720i	−0.581656	−	0.581656i
$714$		0			0
$715$	−183.350	+	75.9462i	−0.256434	+	0.106218i
$716$		0			0
$717$	764.230	+	316.554i	1.06587	+	0.441498i
$718$		0			0
$719$	−1277.00			−1.77608			−0.888039	−	0.459768i	$-0.847932\pi$
$719$	−1277.00			−1.77608			−0.888039	+	0.459768i	$0.847932\pi$
$720$		0			0
$721$			109.756i			0.152227i
$722$		0			0
$723$	−253.634	+	612.327i	−0.350808	+	0.846925i
$724$		0			0
$725$	342.646	+	827.219i	0.472614	+	1.14099i
$726$		0			0
$727$	−470.863	+	470.863i	−0.647679	+	0.647679i	−0.952432	−	0.304753i	$-0.901426\pi$
$727$	−470.863	+	470.863i	−0.647679	+	0.647679i	0.304753	+	0.952432i	$0.401426\pi$
$728$		0			0
$729$	−572.562	+	572.562i	−0.785407	+	0.785407i
$730$		0			0
$731$	−100.522	−	242.683i	−0.137514	−	0.331987i
$732$		0			0
$733$	364.452	−	879.866i	0.497206	−	1.20036i	−0.453776	−	0.891116i	$-0.649923\pi$
$733$	364.452	−	879.866i	0.497206	−	1.20036i	0.950982	−	0.309246i	$-0.100077\pi$
$734$		0			0
$735$		−	64.3429i		−	0.0875413i
$736$		0			0
$737$	−6.09619			−0.00827163
$738$		0			0
$739$	−1146.65	−	474.958i	−1.55162	−	0.642704i	−0.568016	−	0.823018i	$-0.692289\pi$
$739$	−1146.65	−	474.958i	−1.55162	−	0.642704i	−0.983609	+	0.180314i	$0.942289\pi$
$740$		0			0
$741$	487.442	−	201.905i	0.657817	−	0.272477i
$742$		0			0
$743$	−512.021	−	512.021i	−0.689126	−	0.689126i	0.272913	−	0.962039i	$-0.412013\pi$
$743$	−512.021	−	512.021i	−0.689126	−	0.689126i	−0.962039	+	0.272913i	$0.912013\pi$
$744$		0			0
$745$	82.2533	+	82.2533i	0.110407	+	0.110407i
$746$		0			0
$747$	−67.1628	+	27.8197i	−0.0899101	+	0.0372420i
$748$		0			0
$749$	57.7227	+	23.9095i	0.0770663	+	0.0319219i
$750$		0			0
$751$	−335.629			−0.446910			−0.223455	−	0.974714i	$-0.571734\pi$
$751$	−335.629			−0.446910			−0.223455	+	0.974714i	$0.571734\pi$
$752$		0			0
$753$			938.161i			1.24590i
$754$		0			0
$755$	−21.7393	+	52.4833i	−0.0287938	+	0.0695143i
$756$		0			0
$757$	−139.805	−	337.518i	−0.184682	−	0.445863i	0.804238	−	0.594307i	$-0.202573\pi$
$757$	−139.805	−	337.518i	−0.184682	−	0.445863i	−0.988921	+	0.148444i	$0.952573\pi$
$758$		0			0
$759$	856.215	−	856.215i	1.12808	−	1.12808i
$760$		0			0
$761$	495.581	−	495.581i	0.651223	−	0.651223i	−0.302064	−	0.953288i	$-0.597676\pi$
$761$	495.581	−	495.581i	0.651223	−	0.651223i	0.953288	+	0.302064i	$0.0976758\pi$
$762$		0			0
$763$	7.01728	+	16.9412i	0.00919696	+	0.0222034i
$764$		0			0
$765$	−4.32079	+	10.4313i	−0.00564809	+	0.0136357i
$766$		0			0
$767$			96.0458i			0.125223i
$768$		0			0
$769$	372.267			0.484092			0.242046	−	0.970265i	$-0.422181\pi$
$769$	372.267			0.484092			0.242046	+	0.970265i	$0.422181\pi$
$770$		0			0
$771$	271.689	+	112.537i	0.352385	+	0.145963i
$772$		0			0
$773$	−534.778	+	221.512i	−0.691822	+	0.286562i	−0.700759	−	0.713398i	$-0.747155\pi$
$773$	−534.778	+	221.512i	−0.691822	+	0.286562i	0.00893708	+	0.999960i	$0.497155\pi$
$774$		0			0
$775$	430.026	+	430.026i	0.554873	+	0.554873i
$776$		0			0
$777$	12.4465	+	12.4465i	0.0160187	+	0.0160187i
$778$		0			0
$779$	171.040	−	70.8470i	0.219563	−	0.0909461i
$780$		0			0
$781$	−713.187	−	295.412i	−0.913172	−	0.378248i
$782$		0			0
$783$	1045.33			1.33503
$784$		0			0
$785$		−	67.6643i		−	0.0861965i
$786$		0			0
$787$	280.233	−	676.541i	0.356077	−	0.859646i	−0.639767	−	0.768569i	$-0.720969\pi$
$787$	280.233	−	676.541i	0.356077	−	0.859646i	0.995844	−	0.0910769i	$-0.0290309\pi$
$788$		0			0
$789$	−219.612	−	530.190i	−0.278342	−	0.671978i
$790$		0			0
$791$	60.5332	−	60.5332i	0.0765274	−	0.0765274i
$792$		0			0
$793$	−141.059	+	141.059i	−0.177880	+	0.177880i
$794$		0			0
$795$	37.1303	+	89.6404i	0.0467047	+	0.112755i
$796$		0			0
$797$	92.5205	−	223.364i	0.116086	−	0.280256i	−0.855148	−	0.518384i	$-0.826534\pi$
$797$	92.5205	−	223.364i	0.116086	−	0.280256i	0.971234	+	0.238128i	$0.0765337\pi$
$798$		0			0
$799$		−	592.908i		−	0.742063i
$800$		0			0
$801$	108.847			0.135888
$802$		0			0
$803$	1672.62	+	692.821i	2.08296	+	0.862790i
$804$		0			0
$805$	6.56751	−	2.72035i	0.00815839	−	0.00337932i
$806$		0			0
$807$	528.455	+	528.455i	0.654839	+	0.654839i
$808$		0			0
$809$	977.291	+	977.291i	1.20802	+	1.20802i	0.971666	+	0.236358i	$0.0759538\pi$
$809$	977.291	+	977.291i	1.20802	+	1.20802i	0.236358	+	0.971666i	$0.424046\pi$
$810$		0			0
$811$	−553.320	+	229.193i	−0.682269	+	0.282605i	−0.696775	−	0.717290i	$-0.745382\pi$
$811$	−553.320	+	229.193i	−0.682269	+	0.282605i	0.0145062	+	0.999895i	$0.495382\pi$
$812$		0			0
$813$	−653.290	−	270.602i	−0.803555	−	0.332843i
$814$		0			0
$815$	29.0550			0.0356503
$816$		0			0
$817$			174.585i			0.213690i
$818$		0			0
$819$	8.52734	−	20.5868i	0.0104119	−	0.0251365i
$820$		0			0
$821$	390.123	+	941.839i	0.475180	+	1.14719i	0.961844	+	0.273597i	$0.0882134\pi$
$821$	390.123	+	941.839i	0.475180	+	1.14719i	−0.486665	+	0.873589i	$0.661787\pi$
$822$		0			0
$823$	692.747	−	692.747i	0.841734	−	0.841734i	−0.147350	−	0.989084i	$-0.547074\pi$
$823$	692.747	−	692.747i	0.841734	−	0.841734i	0.989084	+	0.147350i	$0.0470744\pi$
$824$		0			0
$825$	−887.815	+	887.815i	−1.07614	+	1.07614i
$826$		0			0
$827$	401.669	+	969.714i	0.485694	+	1.17257i	0.956867	+	0.290528i	$0.0938309\pi$
$827$	401.669	+	969.714i	0.485694	+	1.17257i	−0.471173	+	0.882041i	$0.656169\pi$
$828$		0			0
$829$	562.011	−	1356.81i	0.677938	−	1.63669i	−0.0898281	−	0.995957i	$-0.528632\pi$
$829$	562.011	−	1356.81i	0.677938	−	1.63669i	0.767766	−	0.640730i	$-0.221368\pi$
$830$		0			0
$831$		−	848.321i		−	1.02084i
$832$		0			0
$833$	661.182			0.793735
$834$		0			0
$835$	−63.1537	−	26.1591i	−0.0756331	−	0.0313283i
$836$		0			0
$837$	655.955	−	271.705i	0.783697	−	0.324618i
$838$		0			0
$839$	708.611	+	708.611i	0.844590	+	0.844590i	0.989452	−	0.144862i	$-0.0462737\pi$
$839$	708.611	+	708.611i	0.844590	+	0.844590i	−0.144862	+	0.989452i	$0.546274\pi$
$840$		0			0
$841$	−329.986	−	329.986i	−0.392374	−	0.392374i
$842$		0			0
$843$	−76.9407	+	31.8699i	−0.0912701	+	0.0378053i
$844$		0			0
$845$	−134.670	−	55.7823i	−0.159373	−	0.0660146i
$846$		0			0
$847$	−140.499			−0.165878
$848$		0			0
$849$		−	1101.24i		−	1.29711i
$850$		0			0
$851$	97.8810	−	236.306i	0.115019	−	0.277680i
$852$		0			0
$853$	−178.189	−	430.187i	−0.208897	−	0.504322i	0.784353	−	0.620315i	$-0.212995\pi$
$853$	−178.189	−	430.187i	−0.208897	−	0.504322i	−0.993250	+	0.115992i	$0.962995\pi$
$854$		0			0
$855$	5.30630	−	5.30630i	0.00620620	−	0.00620620i
$856$		0			0
$857$	−195.982	+	195.982i	−0.228683	+	0.228683i	−0.812142	−	0.583459i	$-0.801699\pi$
$857$	−195.982	+	195.982i	−0.228683	+	0.228683i	0.583459	+	0.812142i	$0.301699\pi$
$858$		0			0
$859$	155.060	+	374.347i	0.180512	+	0.435794i	0.988072	−	0.153991i	$-0.0492126\pi$
$859$	155.060	+	374.347i	0.180512	+	0.435794i	−0.807560	+	0.589785i	$0.799213\pi$
$860$		0			0
$861$	−12.8838	+	31.1043i	−0.0149638	+	0.0361258i
$862$		0			0
$863$		−	63.9126i		−	0.0740586i	−0.999314	−	0.0370293i	$-0.988211\pi$
$863$		−	63.9126i		−	0.0740586i	0.999314	−	0.0370293i	$-0.0117895\pi$
$864$		0			0
$865$	3.22835			0.00373219
$866$		0			0
$867$	−260.035	−	107.710i	−0.299925	−	0.124233i
$868$		0			0
$869$	1174.60	−	486.534i	1.35167	−	0.559879i
$870$		0			0
$871$	−4.96332	−	4.96332i	−0.00569842	−	0.00569842i
$872$		0			0
$873$	143.106	+	143.106i	0.163925	+	0.163925i
$874$		0			0
$875$	−13.6857	+	5.66881i	−0.0156408	+	0.00647864i
$876$		0			0
$877$	−34.2590	−	14.1905i	−0.0390638	−	0.0161808i	0.363066	−	0.931763i	$-0.381730\pi$
$877$	−34.2590	−	14.1905i	−0.0390638	−	0.0161808i	−0.402130	+	0.915583i	$0.631730\pi$
$878$		0			0
$879$	108.844			0.123827
$880$		0			0
$881$			1126.03i			1.27812i	0.769155	+	0.639062i	$0.220677\pi$
$881$			1126.03i			1.27812i	−0.769155	+	0.639062i	$0.779323\pi$
$882$		0			0
$883$	114.384	−	276.148i	0.129540	−	0.312738i	−0.845780	−	0.533531i	$-0.820865\pi$
$883$	114.384	−	276.148i	0.129540	−	0.312738i	0.975321	+	0.220793i	$0.0708646\pi$
$884$		0			0
$885$	−2.25100	−	5.43439i	−0.00254350	−	0.00614055i
$886$		0			0
$887$	−65.1075	+	65.1075i	−0.0734020	+	0.0734020i	−0.742855	−	0.669453i	$-0.766529\pi$
$887$	−65.1075	+	65.1075i	−0.0734020	+	0.0734020i	0.669453	+	0.742855i	$0.266529\pi$
$888$		0			0
$889$	70.5052	−	70.5052i	0.0793085	−	0.0793085i
$890$		0			0
$891$	451.334	+	1089.62i	0.506548	+	1.22292i
$892$		0			0
$893$	−150.803	+	364.071i	−0.168873	+	0.407694i
$894$		0			0
$895$		−	103.200i		−	0.115307i
$896$		0			0
$897$	1394.21			1.55430
$898$		0			0
$899$	−820.576	−	339.894i	−0.912765	−	0.378080i
$900$		0			0
$901$	−921.136	+	381.547i	−1.02235	+	0.423471i
$902$		0			0
$903$	−22.4499	−	22.4499i	−0.0248615	−	0.0248615i
$904$		0			0
$905$	54.0478	+	54.0478i	0.0597213	+	0.0597213i
$906$		0			0
$907$	−1085.79	+	449.751i	−1.19713	+	0.495866i	−0.890070	−	0.455825i	$-0.849344\pi$
$907$	−1085.79	+	449.751i	−1.19713	+	0.495866i	−0.307058	+	0.951691i	$0.599344\pi$
$908$		0			0
$909$	−167.574	−	69.4116i	−0.184350	−	0.0763604i
$910$		0			0
$911$	37.8649			0.0415641			0.0207821	−	0.999784i	$-0.493384\pi$
$911$	37.8649			0.0415641			0.0207821	+	0.999784i	$0.493384\pi$
$912$		0			0
$913$			804.143i			0.880770i
$914$		0			0
$915$	4.67532	−	11.2872i	0.00510964	−	0.0123358i
$916$		0			0
$917$	−2.82794	−	6.82725i	−0.00308390	−	0.00744520i
$918$		0			0
$919$	1205.51	−	1205.51i	1.31176	−	1.31176i	0.391640	−	0.920119i	$-0.371908\pi$
$919$	1205.51	−	1205.51i	1.31176	−	1.31176i	0.920119	−	0.391640i	$-0.128092\pi$
$920$		0			0
$921$	−504.801	+	504.801i	−0.548101	+	0.548101i
$922$		0			0
$923$	−340.139	−	821.169i	−0.368515	−	0.889674i
$924$		0			0
$925$	−101.493	+	245.027i	−0.109723	+	0.264894i
$926$		0			0
$927$			306.174i			0.330285i
$928$		0			0
$929$	1384.29			1.49009			0.745045	−	0.667014i	$-0.232428\pi$
$929$	1384.29			1.49009			0.745045	+	0.667014i	$0.232428\pi$
$930$		0			0
$931$	−405.994	−	168.168i	−0.436084	−	0.180632i
$932$		0			0
$933$	−640.515	+	265.310i	−0.686511	+	0.284362i
$934$		0			0
$935$	88.3137	+	88.3137i	0.0944532	+	0.0944532i
$936$		0			0
$937$	−500.748	−	500.748i	−0.534416	−	0.534416i	0.387467	−	0.921883i	$-0.373350\pi$
$937$	−500.748	−	500.748i	−0.534416	−	0.534416i	−0.921883	+	0.387467i	$0.873350\pi$
$938$		0			0
$939$	−391.814	+	162.295i	−0.417267	+	0.172838i
$940$		0			0
$941$	−1312.74	−	543.756i	−1.39505	−	0.577849i	−0.446588	−	0.894740i	$-0.647361\pi$
$941$	−1312.74	−	543.756i	−1.39505	−	0.577849i	−0.948462	+	0.316891i	$0.897361\pi$
$942$		0			0
$943$	489.216			0.518787
$944$		0			0
$945$			8.60544i			0.00910629i
$946$		0			0
$947$	256.726	−	619.792i	0.271094	−	0.654480i	−0.728436	−	0.685114i	$-0.759753\pi$
$947$	256.726	−	619.792i	0.271094	−	0.654480i	0.999531	+	0.0306337i	$0.00975255\pi$
$948$		0			0
$949$	797.719	+	1925.86i	0.840589	+	2.02936i
$950$		0			0
$951$	−669.951	+	669.951i	−0.704470	+	0.704470i
$952$		0			0
$953$	948.406	−	948.406i	0.995179	−	0.995179i	−0.00480927	−	0.999988i	$-0.501531\pi$
$953$	948.406	−	948.406i	0.995179	−	0.995179i	0.999988	+	0.00480927i	$0.00153084\pi$
$954$		0			0
$955$	−20.1989	−	48.7643i	−0.0211506	−	0.0510621i
$956$		0			0
$957$	701.730	−	1694.13i	0.733260	−	1.77025i
$958$		0			0
$959$		−	18.3151i		−	0.0190981i
$960$		0			0
$961$	357.735			0.372253
$962$		0			0
$963$	161.023	+	66.6978i	0.167209	+	0.0692604i
$964$		0			0
$965$	79.0773	−	32.7549i	0.0819454	−	0.0339429i
$966$		0			0
$967$	5.79422	+	5.79422i	0.00599196	+	0.00599196i	0.710096	−	0.704104i	$-0.248651\pi$
$967$	5.79422	+	5.79422i	0.00599196	+	0.00599196i	−0.704104	+	0.710096i	$0.748651\pi$
$968$		0			0
$969$	−234.785	−	234.785i	−0.242296	−	0.242296i
$970$		0			0
$971$	−1644.17	+	681.037i	−1.69327	+	0.701377i	−0.999817	−	0.0191210i	$-0.993913\pi$
$971$	−1644.17	+	681.037i	−1.69327	+	0.701377i	−0.693457	+	0.720498i	$0.743913\pi$
$972$		0			0
$973$	−94.1498	−	38.9981i	−0.0967624	−	0.0400803i
$974$		0			0
$975$	−1445.66			−1.48273
$976$		0			0
$977$		−	538.935i		−	0.551623i	−0.961212	−	0.275811i	$-0.911054\pi$
$977$		−	538.935i		−	0.551623i	0.961212	−	0.275811i	$-0.0889465\pi$
$978$		0			0
$979$	460.760	−	1112.37i	0.470643	−	1.13623i
$980$		0			0
$981$	19.5753	+	47.2590i	0.0199545	+	0.0481744i
$982$		0			0
$983$	−171.371	+	171.371i	−0.174335	+	0.174335i	−0.788881	−	0.614546i	$-0.789339\pi$
$983$	−171.371	+	171.371i	−0.174335	+	0.174335i	0.614546	+	0.788881i	$0.289339\pi$
$984$		0			0
$985$	40.6450	−	40.6450i	0.0412639	−	0.0412639i
$986$		0			0
$987$	−27.4242	−	66.2079i	−0.0277854	−	0.0670799i
$988$		0			0
$989$	−176.549	+	426.227i	−0.178513	+	0.430967i
$990$		0			0
$991$			1670.67i			1.68584i	0.538038	+	0.842921i	$0.319166\pi$
$991$			1670.67i			1.68584i	−0.538038	+	0.842921i	$0.680834\pi$
$992$		0			0
$993$	−1697.32			−1.70929
$994$		0			0
$995$	121.758	+	50.4337i	0.122370	+	0.0506871i
$996$		0			0
$997$	1252.59	−	518.840i	1.25636	−	0.520402i	0.347570	−	0.937654i	$-0.387007\pi$
$997$	1252.59	−	518.840i	1.25636	−	0.520402i	0.908791	+	0.417252i	$0.137007\pi$
$998$		0			0
$999$	218.943	+	218.943i	0.219162	+	0.219162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.111.2		28
4.3	odd	2		32.3.h.a.19.3	✓	28
8.3	odd	2		256.3.h.b.223.2		28
8.5	even	2		256.3.h.a.223.6		28
12.11	even	2		288.3.u.a.19.5		28
32.5	even	8		32.3.h.a.27.3	yes	28
32.11	odd	8		256.3.h.a.31.6		28
32.21	even	8		256.3.h.b.31.2		28
32.27	odd	8	inner	128.3.h.a.15.2		28
96.5	odd	8		288.3.u.a.91.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.3	✓	28	4.3	odd	2
32.3.h.a.27.3	yes	28	32.5	even	8
128.3.h.a.15.2		28	32.27	odd	8	inner
128.3.h.a.111.2		28	1.1	even	1	trivial
256.3.h.a.31.6		28	32.11	odd	8
256.3.h.a.223.6		28	8.5	even	2
256.3.h.b.31.2		28	32.21	even	8
256.3.h.b.223.2		28	8.3	odd	2
288.3.u.a.19.5		28	12.11	even	2
288.3.u.a.91.5		28	96.5	odd	8

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +O(q^{10})\)	\(q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +1.32310 q^{15} +13.5961i q^{17} +(3.45810 - 8.34859i) q^{19} +(0.628870 + 1.51823i) q^{21} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(11.0623 + 26.7067i) q^{27} +(13.8385 - 33.4091i) q^{29} -24.5614i q^{31} +50.7086 q^{33} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(41.2853 + 41.2853i) q^{39} +(14.4867 + 14.4867i) q^{41} +(-17.8494 + 7.39348i) q^{43} +(0.767229 + 0.317796i) q^{45} -43.6087 q^{47} -48.6303i q^{49} +(14.0613 - 33.9471i) q^{51} +(28.0630 + 67.7501i) q^{53} +(6.49552 - 6.49552i) q^{55} +(-17.2685 + 17.2685i) q^{57} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +1.03142i q^{63} +10.5769 q^{65} +(0.300169 + 0.124334i) q^{67} +(-59.6218 + 24.6961i) q^{69} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(61.8222 - 25.6076i) q^{75} +(10.5408 + 4.36612i) q^{77} -67.7588 q^{79} -62.8565i q^{81} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-69.1047 + 69.1047i) q^{87} +(-45.3745 + 45.3745i) q^{89} +(5.02718 + 12.1367i) q^{91} +(-25.4019 + 61.3257i) q^{93} +4.42403i q^{95} -119.312 q^{97} +(29.4044 + 12.1797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * 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 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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