LMFDB - Embedded newform 256.3.h.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, 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("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.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:	$6.97549476762$
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			31.6
Character	$\chi$	$=$	256.31
Dual form			256.3.h.a.223.6

$q$-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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	2.49683	−	1.03422i	0.832276	−	0.344740i	0.0744725	−	0.997223i	$-0.476273\pi$
$3$	2.49683	−	1.03422i	0.832276	−	0.344740i	0.757803	+	0.652483i	$0.226273\pi$
$4$		0			0
$5$	0.452310	+	0.187353i	0.0904620	+	0.0374706i	0.427456	−	0.904036i	$-0.359410\pi$
$5$	0.452310	+	0.187353i	0.0904620	+	0.0374706i	−0.336994	+	0.941507i	$0.609410\pi$
$6$		0			0
$7$	−0.429965	+	0.429965i	−0.0614236	+	0.0614236i	−0.737151	−	0.675728i	$-0.763830\pi$
$7$	−0.429965	+	0.429965i	−0.0614236	+	0.0614236i	0.675728	+	0.737151i	$0.263830\pi$
$8$		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	$-0.0498567\pi$
$11$	17.3350	+	7.18039i	1.57591	+	0.652763i	0.588149	+	0.808752i	$0.299857\pi$
$12$		0			0
$13$	19.9596	−	8.26755i	1.53536	−	0.635965i	0.554761	−	0.832010i	$-0.312810\pi$
$13$	19.9596	−	8.26755i	1.53536	−	0.635965i	0.980595	+	0.196044i	$0.0628096\pi$
$14$		0			0
$15$	1.32310			0.0882069
$16$		0			0
$17$		−	13.5961i		−	0.799770i	−0.916565	−	0.399885i	$-0.869050\pi$
$17$		−	13.5961i		−	0.799770i	0.916565	−	0.399885i	$-0.130950\pi$
$18$		0			0
$19$	−3.45810	−	8.34859i	−0.182005	−	0.439399i	0.806374	−	0.591405i	$-0.201427\pi$
$19$	−3.45810	−	8.34859i	−0.182005	−	0.439399i	−0.988380	+	0.152006i	$0.951427\pi$
$20$		0			0
$21$	−0.628870	+	1.51823i	−0.0299462	+	0.0722965i
$22$		0			0
$23$	16.8850	+	16.8850i	0.734131	+	0.734131i	0.971435	−	0.237304i	$-0.0762639\pi$
$23$	16.8850	+	16.8850i	0.734131	+	0.734131i	−0.237304	+	0.971435i	$0.576264\pi$
$24$		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	−0.960921	−	0.276821i	$-0.910719\pi$
$29$	−13.8385	−	33.4091i	−0.477190	−	1.15204i	0.483732	−	0.875216i	$-0.339281\pi$
$30$		0			0
$31$			24.5614i			0.792305i	0.918185	+	0.396152i	$0.129655\pi$
$31$			24.5614i			0.792305i	−0.918185	+	0.396152i	$0.870345\pi$
$32$		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	$-0.421237\pi$
$37$	−9.89595	−	4.09904i	−0.267458	−	0.110785i	−0.512382	+	0.858757i	$0.671237\pi$
$38$		0			0
$39$	41.2853	−	41.2853i	1.05860	−	1.05860i
$40$		0			0
$41$	14.4867	−	14.4867i	0.353334	−	0.353334i	−0.508015	−	0.861348i	$-0.669620\pi$
$41$	14.4867	−	14.4867i	0.353334	−	0.353334i	0.861348	+	0.508015i	$0.169620\pi$
$42$		0			0
$43$	17.8494	+	7.39348i	0.415103	+	0.171941i	0.580453	−	0.814294i	$-0.302875\pi$
$43$	17.8494	+	7.39348i	0.415103	+	0.171941i	−0.165350	+	0.986235i	$0.552875\pi$
$44$		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	0.402367	+	0.915478i	$0.368188\pi$
$53$	−28.0630	+	67.7501i	−0.529490	+	1.27830i	−0.931857	+	0.362825i	$0.881812\pi$
$54$		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	$-0.863005\pi$
$59$	1.70130	−	4.10730i	0.0288356	−	0.0696153i	0.937641	+	0.347604i	$0.113005\pi$
$60$		0			0
$61$	−3.53360	−	8.53087i	−0.0579279	−	0.139850i	0.892266	−	0.451511i	$-0.149115\pi$
$61$	−3.53360	−	8.53087i	−0.0579279	−	0.139850i	−0.950193	+	0.311661i	$0.899115\pi$
$62$		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	$-0.625772\pi$
$67$	−0.300169	+	0.124334i	−0.00448013	+	0.00185573i	0.380442	+	0.924805i	$0.375772\pi$
$68$		0			0
$69$	59.6218	+	24.6961i	0.864084	+	0.357915i
$70$		0			0
$71$	29.0914	−	29.0914i	0.409738	−	0.409738i	−0.471909	−	0.881647i	$-0.656435\pi$
$71$	29.0914	−	29.0914i	0.409738	−	0.409738i	0.881647	+	0.471909i	$0.156435\pi$
$72$		0			0
$73$	−68.2273	+	68.2273i	−0.934620	+	0.934620i	−0.997990	−	0.0633700i	$-0.979815\pi$
$73$	−68.2273	+	68.2273i	−0.934620	+	0.934620i	0.0633700	+	0.997990i	$0.479815\pi$
$74$		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	$-0.208122\pi$
$83$	−16.4008	−	39.5950i	−0.197600	−	0.477048i	−0.991358	+	0.131186i	$0.958122\pi$
$84$		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	0.404647	−	0.914473i	$-0.367394\pi$
$89$	−45.3745	−	45.3745i	−0.509825	−	0.509825i	−0.914473	+	0.404647i	$0.867394\pi$
$90$		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	$-0.552569\pi$
$101$	−98.7914	−	40.9207i	−0.978133	−	0.405156i	−0.813734	+	0.581238i	$0.802569\pi$
$102$		0			0
$103$	−127.634	+	127.634i	−1.23916	+	1.23916i	−0.278817	+	0.960344i	$0.589942\pi$
$103$	−127.634	+	127.634i	−1.23916	+	1.23916i	−0.960344	+	0.278817i	$0.910058\pi$
$104$		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	$-0.215585\pi$
$107$	94.9289	+	39.3208i	0.887186	+	0.367484i	0.107906	+	0.994161i	$0.465585\pi$
$108$		0			0
$109$	27.8610	−	11.5404i	0.255605	−	0.105875i	−0.251202	−	0.967935i	$-0.580826\pi$
$109$	27.8610	−	11.5404i	0.255605	−	0.105875i	0.506807	+	0.862060i	$0.330826\pi$
$110$		0			0
$111$	−28.9478			−0.260791
$112$		0			0
$113$		−	140.786i		−	1.24590i	−0.782263	−	0.622948i	$-0.785935\pi$
$113$		−	140.786i		−	1.24590i	0.782263	−	0.622948i	$-0.214065\pi$
$114$		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	$-0.776613\pi$
$127$		−	163.979i		−	1.29117i	0.763687	−	0.645587i	$-0.223387\pi$
$128$		0			0
$129$	52.2134			0.404755
$130$		0			0
$131$	−11.2279	+	4.65074i	−0.0857090	+	0.0355018i	−0.425126	−	0.905134i	$-0.639770\pi$
$131$	−11.2279	+	4.65074i	−0.0857090	+	0.0355018i	0.339417	+	0.940636i	$0.389770\pi$
$132$		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	−0.625090	−	0.780552i	$-0.714938\pi$
$137$	21.2983	−	21.2983i	0.155462	−	0.155462i	0.780552	+	0.625090i	$0.214938\pi$
$138$		0			0
$139$	−154.836	−	64.1351i	−1.11393	−	0.461404i	−0.251639	−	0.967821i	$-0.580969\pi$
$139$	−154.836	−	64.1351i	−1.11393	−	0.461404i	−0.862288	+	0.506418i	$0.830969\pi$
$140$		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	−0.252497	−	0.967598i	$-0.581252\pi$
$149$	90.9258	−	219.514i	0.610240	−	1.47325i	0.862737	−	0.505653i	$-0.168748\pi$
$150$		0			0
$151$	82.0484	+	82.0484i	0.543367	+	0.543367i	0.924514	−	0.381147i	$-0.124471\pi$
$151$	82.0484	+	82.0484i	0.543367	+	0.543367i	−0.381147	+	0.924514i	$0.624471\pi$
$152$		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	0.998011	+	0.0630341i	$0.0200777\pi$
$157$	52.8906	+	127.689i	0.336883	+	0.813307i	−0.661129	+	0.750272i	$0.729922\pi$
$158$		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	$-0.566728\pi$
$163$	54.8297	−	22.7112i	0.336379	−	0.139333i	0.544478	+	0.838775i	$0.316728\pi$
$164$		0			0
$165$	22.9360	+	9.50040i	0.139006	+	0.0575782i
$166$		0			0
$167$	98.7296	−	98.7296i	0.591195	−	0.591195i	−0.346759	−	0.937954i	$-0.612718\pi$
$167$	98.7296	−	98.7296i	0.591195	−	0.591195i	0.937954	+	0.346759i	$0.112718\pi$
$168$		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	$-0.618933\pi$
$173$	6.09221	−	2.52348i	0.0352151	−	0.0145866i	0.400221	+	0.916418i	$0.368933\pi$
$174$		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	0.972073	+	0.234677i	$0.0754032\pi$
$179$	80.6673	+	194.748i	0.450655	+	1.08798i	−0.521418	+	0.853301i	$0.674597\pi$
$180$		0			0
$181$	59.7464	−	144.241i	0.330091	−	0.796910i	−0.668493	−	0.743718i	$-0.733061\pi$
$181$	59.7464	−	144.241i	0.330091	−	0.796910i	0.998584	−	0.0531918i	$-0.0169395\pi$
$182$		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	$-0.908926\pi$
$191$		−	107.812i		−	0.564460i	0.959347	−	0.282230i	$-0.0910741\pi$
$192$		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	$-0.278683\pi$
$197$	108.472	+	44.9304i	0.550618	+	0.228073i	−0.0899887	+	0.995943i	$0.528683\pi$
$198$		0			0
$199$	−190.347	+	190.347i	−0.956516	+	0.956516i	−0.999093	−	0.0425770i	$-0.986443\pi$
$199$	−190.347	+	190.347i	−0.956516	+	0.956516i	0.0425770	+	0.999093i	$0.486443\pi$
$200$		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	0.984932	+	0.172944i	$0.0553281\pi$
$211$	86.6725	+	209.246i	0.410770	+	0.991686i	−0.574162	+	0.818742i	$0.694672\pi$
$212$		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	$0.0748004\pi$
$223$			103.845i			0.465671i	−0.972516	+	0.232836i	$0.925200\pi$
$224$		0			0
$225$	41.9996			0.186665
$226$		0			0
$227$	106.086	−	43.9421i	0.467338	−	0.193578i	−0.136572	−	0.990630i	$-0.543609\pi$
$227$	106.086	−	43.9421i	0.467338	−	0.193578i	0.603910	+	0.797052i	$0.293609\pi$
$228$		0			0
$229$	−46.1162	−	19.1019i	−0.201381	−	0.0834146i	0.279714	−	0.960083i	$-0.409760\pi$
$229$	−46.1162	−	19.1019i	−0.201381	−	0.0834146i	−0.481094	+	0.876669i	$0.659760\pi$
$230$		0			0
$231$	−21.8029	+	21.8029i	−0.0943849	+	0.0943849i
$232$		0			0
$233$	−62.7031	+	62.7031i	−0.269112	+	0.269112i	−0.828742	−	0.559630i	$-0.810943\pi$
$233$	−62.7031	+	62.7031i	−0.269112	+	0.269112i	0.559630	+	0.828742i	$0.310943\pi$
$234$		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	$0.169911\pi$
$241$			245.242i			1.01760i	−0.860884	+	0.508801i	$0.830089\pi$
$242$		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	−0.402747	−	0.915311i	$-0.631944\pi$
$251$	132.845	−	320.715i	0.529261	−	1.27775i	0.932008	−	0.362438i	$-0.118056\pi$
$252$		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	−0.361468	−	0.932384i	$-0.617724\pi$
$263$	150.151	−	150.151i	0.570916	−	0.570916i	0.932384	+	0.361468i	$0.117724\pi$
$264$		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	$-0.453161\pi$
$269$	255.485	−	105.825i	0.949758	−	0.393403i	0.803140	+	0.595791i	$0.203161\pi$
$270$		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	0.544440	+	0.838799i	$0.316742\pi$
$277$	−120.123	+	290.003i	−0.433658	+	1.04694i	−0.978098	+	0.208143i	$0.933258\pi$
$278$		0			0
$279$	−29.4597	−	29.4597i	−0.105590	−	0.105590i
$280$		0			0
$281$	21.7898	+	21.7898i	0.0775437	+	0.0775437i	0.744815	−	0.667271i	$-0.232538\pi$
$281$	21.7898	+	21.7898i	0.0775437	+	0.0775437i	−0.667271	+	0.744815i	$0.732538\pi$
$282$		0			0
$283$	−155.937	+	376.466i	−0.551016	+	1.33027i	0.365702	+	0.930732i	$0.380829\pi$
$283$	−155.937	+	376.466i	−0.551016	+	1.33027i	−0.916717	+	0.399537i	$0.869171\pi$
$284$		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	$-0.353106\pi$
$293$	37.2090	+	15.4125i	0.126993	+	0.0526023i	−0.318282	+	0.947996i	$0.603106\pi$
$294$		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	−0.998646	−	0.0520174i	$-0.983435\pi$
$307$	−101.089	−	244.049i	−0.329279	−	0.794949i	0.669368	−	0.742931i	$-0.266565\pi$
$308$		0			0
$309$	−186.678	+	450.680i	−0.604136	+	1.45851i
$310$		0			0
$311$	181.395	+	181.395i	0.583264	+	0.583264i	0.935799	−	0.352534i	$-0.114680\pi$
$311$	181.395	+	181.395i	0.583264	+	0.583264i	−0.352534	+	0.935799i	$0.614680\pi$
$312$		0			0
$313$	110.963	+	110.963i	0.354513	+	0.354513i	0.861786	−	0.507273i	$-0.169346\pi$
$313$	110.963	+	110.963i	0.354513	+	0.354513i	−0.507273	+	0.861786i	$0.669346\pi$
$314$		0			0
$315$	0.193240	−	0.466523i	0.000613460	−	0.00148102i
$316$		0			0
$317$	−134.161	−	323.892i	−0.423219	−	1.02174i	−0.981392	−	0.192017i	$-0.938497\pi$
$317$	−134.161	−	323.892i	−0.423219	−	1.02174i	0.558172	−	0.829725i	$-0.311503\pi$
$318$		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	−0.997479	−	0.0709686i	$-0.977391\pi$
$331$	−580.238	−	240.342i	−1.75298	−	0.726110i	−0.755506	−	0.655141i	$-0.772609\pi$
$332$		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	$0.0619059\pi$
$337$			130.257i			0.386519i	−0.981148	+	0.193259i	$0.938094\pi$
$338$		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	$-0.941005\pi$
$347$	−54.6775	+	132.003i	−0.157572	+	0.380412i	0.825302	+	0.564692i	$0.191005\pi$
$348$		0			0
$349$	46.7936	+	112.970i	0.134079	+	0.323696i	0.976632	−	0.214918i	$-0.0689483\pi$
$349$	46.7936	+	112.970i	0.134079	+	0.323696i	−0.842553	+	0.538613i	$0.818948\pi$
$350$		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	−0.584765	−	0.811203i	$-0.698813\pi$
$359$	81.2910	−	81.2910i	0.226437	−	0.226437i	0.811203	+	0.584765i	$0.198813\pi$
$360$		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	−0.459294	−	0.888284i	$-0.651898\pi$
$373$	184.108	−	444.476i	0.493588	−	1.19163i	0.952882	−	0.303342i	$-0.0981024\pi$
$374$		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	$-0.997502\pi$
$379$	−108.900	+	262.908i	−0.287336	+	0.693690i	0.712634	+	0.701536i	$0.247502\pi$
$380$		0			0
$381$	−169.590	−	409.427i	−0.445119	−	1.07461i
$382$		0			0
$383$			476.810i			1.24493i	0.782646	+	0.622467i	$0.213869\pi$
$383$			476.810i			1.24493i	−0.782646	+	0.622467i	$0.786131\pi$
$384$		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	$-0.343263\pi$
$389$	71.5472	+	29.6358i	0.183926	+	0.0761846i	−0.288820	+	0.957383i	$0.593263\pi$
$390$		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	$-0.677464\pi$
$397$	−120.360	+	49.8545i	−0.303173	+	0.125578i	0.225911	+	0.974148i	$0.427464\pi$
$398$		0			0
$399$	14.8497			0.0372174
$400$		0			0
$401$			174.015i			0.433953i	0.976177	+	0.216976i	$0.0696195\pi$
$401$			174.015i			0.433953i	−0.976177	+	0.216976i	$0.930381\pi$
$402$		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	0.561571	−	0.827428i	$-0.310197\pi$
$409$	−108.736	−	108.736i	−0.265857	−	0.265857i	−0.827428	+	0.561571i	$0.810197\pi$
$410$		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	$-0.466221\pi$
$419$	370.373	−	153.414i	0.883946	−	0.366142i	0.778026	+	0.628232i	$0.216221\pi$
$420$		0			0
$421$	600.339	+	248.669i	1.42598	+	0.590662i	0.956357	−	0.292202i	$-0.0943880\pi$
$421$	600.339	+	248.669i	1.42598	+	0.590662i	0.469628	+	0.882864i	$0.344388\pi$
$422$		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	$-0.881731\pi$
$433$		−	314.414i		−	0.726129i	0.931764	−	0.363064i	$-0.118269\pi$
$434$		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	0.913818	+	0.406125i	$0.133120\pi$
$439$	579.455	+	579.455i	1.31994	+	1.31994i	0.406125	+	0.913818i	$0.366880\pi$
$440$		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	$-0.772072\pi$
$443$	107.736	−	260.098i	0.243197	−	0.587130i	0.997597	+	0.0692856i	$0.0220720\pi$
$444$		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	−0.0197861	−	0.999804i	$-0.506299\pi$
$457$	447.868	−	447.868i	0.980018	−	0.980018i	0.999804	+	0.0197861i	$0.00629852\pi$
$458$		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	$-0.721077\pi$
$461$	−253.222	+	104.888i	−0.549288	+	0.227523i	0.0907394	+	0.995875i	$0.471077\pi$
$462$		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	$-0.0898516\pi$
$467$	39.3875	+	95.0899i	0.0843416	+	0.203619i	−0.876082	+	0.482162i	$0.839852\pi$
$468$		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	$0.353050\pi$
$479$			857.713i			1.79063i	−0.445432	+	0.895316i	$0.646950\pi$
$480$		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	−0.719871	−	0.694108i	$-0.755799\pi$
$487$	−12.5467	+	12.5467i	−0.0257633	+	0.0257633i	0.694108	+	0.719871i	$0.255799\pi$
$488$		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	$-0.342771\pi$
$491$	91.7015	+	37.9840i	0.186765	+	0.0773605i	−0.287341	+	0.957828i	$0.592771\pi$
$492$		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	0.990336	+	0.138688i	$0.0442886\pi$
$499$	193.677	+	467.577i	0.388130	+	0.937029i	−0.602206	+	0.798341i	$0.705711\pi$
$500$		0			0
$501$	144.403	−	348.619i	0.288229	−	0.695846i
$502$		0			0
$503$	−659.583	−	659.583i	−1.31130	−	1.31130i	−0.920459	−	0.390840i	$-0.872184\pi$
$503$	−659.583	−	659.583i	−1.31130	−	1.31130i	−0.390840	−	0.920459i	$-0.627816\pi$
$504$		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	$-0.0139438\pi$
$509$	133.178	+	321.521i	0.261647	+	0.631671i	−0.737394	+	0.675463i	$0.763944\pi$
$510$		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	−0.635371	−	0.772207i	$-0.719153\pi$
$521$	71.2918	−	71.2918i	0.136837	−	0.136837i	0.772207	+	0.635371i	$0.219153\pi$
$522$		0			0
$523$	−376.338	−	155.884i	−0.719576	−	0.298058i	−0.00731529	−	0.999973i	$-0.502329\pi$
$523$	−376.338	−	155.884i	−0.719576	−	0.298058i	−0.712261	+	0.701915i	$0.752329\pi$
$524$		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	$-0.0223377\pi$
$541$	131.242	+	316.846i	0.242591	+	0.585667i	−0.754948	+	0.655785i	$0.772338\pi$
$542$		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	$-0.643171\pi$
$547$	−57.6667	+	23.8863i	−0.105424	+	0.0436679i	0.329348	+	0.944209i	$0.393171\pi$
$548$		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	$-0.753386\pi$
$557$	−403.952	+	167.322i	−0.725228	+	0.300399i	−0.0106383	+	0.999943i	$0.503386\pi$
$558$		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	$-0.123073\pi$
$563$	2.60893	+	6.29851i	0.00463398	+	0.0111874i	−0.921546	+	0.388270i	$0.873073\pi$
$564$		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	0.876820	−	0.480818i	$-0.159660\pi$
$569$	225.325	+	225.325i	0.396002	+	0.396002i	−0.480818	+	0.876820i	$0.659660\pi$
$570$		0			0
$571$	203.081	−	490.280i	0.355658	−	0.858634i	−0.640242	−	0.768173i	$-0.721166\pi$
$571$	203.081	−	490.280i	0.355658	−	0.858634i	0.995900	−	0.0904608i	$-0.0288340\pi$
$572$		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	$-0.606542\pi$
$587$	−721.215	−	298.737i	−1.22865	−	0.508922i	−0.900149	+	0.435583i	$0.856542\pi$
$588$		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	$-0.853884\pi$
$593$		−	525.499i		−	0.886170i	0.896479	−	0.443085i	$-0.146116\pi$
$594$		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	0.940213	−	0.340587i	$-0.110626\pi$
$599$	359.176	+	359.176i	0.599626	+	0.599626i	−0.340587	+	0.940213i	$0.610626\pi$
$600$		0			0
$601$	163.858	+	163.858i	0.272642	+	0.272642i	0.830163	−	0.557521i	$-0.188247\pi$
$601$	163.858	+	163.858i	0.272642	+	0.272642i	−0.557521	+	0.830163i	$0.688247\pi$
$602$		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	$-0.945141\pi$
$607$		−	208.191i		−	0.342984i	0.985186	−	0.171492i	$-0.0548587\pi$
$608$		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	$-0.567234\pi$
$613$	−643.217	−	266.429i	−1.04929	−	0.434632i	−0.839640	+	0.543144i	$0.817234\pi$
$614$		0			0
$615$	19.1674	−	19.1674i	0.0311665	−	0.0311665i
$616$		0			0
$617$	−526.767	+	526.767i	−0.853755	+	0.853755i	−0.990593	−	0.136838i	$-0.956306\pi$
$617$	−526.767	+	526.767i	−0.853755	+	0.853755i	0.136838	+	0.990593i	$0.456306\pi$
$618$		0			0
$619$	−316.799	−	131.222i	−0.511791	−	0.211991i	0.111816	−	0.993729i	$-0.464333\pi$
$619$	−316.799	−	131.222i	−0.511791	−	0.211991i	−0.623607	+	0.781738i	$0.714333\pi$
$620$		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	0.169199	−	0.985582i	$-0.445882\pi$
$631$	−515.138	−	515.138i	−0.816383	−	0.816383i	−0.985582	+	0.169199i	$0.945882\pi$
$632$		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	$-0.543675\pi$
$643$	300.259	−	124.371i	0.466965	−	0.193423i	0.603744	+	0.797178i	$0.293675\pi$
$644$		0			0
$645$	23.6166	+	9.78234i	0.0366150	+	0.0151664i
$646$		0			0
$647$	182.325	−	182.325i	0.281800	−	0.281800i	−0.552027	−	0.833827i	$-0.686145\pi$
$647$	182.325	−	182.325i	0.281800	−	0.281800i	0.833827	+	0.552027i	$0.186145\pi$
$648$		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	$-0.602967\pi$
$653$	83.4520	−	34.5670i	0.127798	−	0.0529356i	0.445666	+	0.895199i	$0.352967\pi$
$654$		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	$-0.101997\pi$
$659$	36.4182	+	87.9213i	0.0552628	+	0.133416i	−0.893837	+	0.448393i	$0.851997\pi$
$660$		0			0
$661$	420.501	−	1015.18i	0.636159	−	1.53582i	−0.195597	−	0.980684i	$-0.562665\pi$
$661$	420.501	−	1015.18i	0.636159	−	1.53582i	0.831757	−	0.555140i	$-0.187335\pi$
$662$		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	$-0.102789\pi$
$677$	944.061	+	391.043i	1.39448	+	0.577611i	0.446165	+	0.894951i	$0.352789\pi$
$678$		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	$-0.419007\pi$
$683$	−173.921	−	72.0404i	−0.254643	−	0.105476i	−0.506353	+	0.862326i	$0.669007\pi$
$684$		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	$-0.0106688\pi$
$691$	185.902	+	448.807i	0.269033	+	0.649503i	−0.730405	+	0.683014i	$0.760669\pi$
$692$		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	$-0.0342576\pi$
$701$	150.886	+	364.271i	0.215244	+	0.519645i	−0.778970	+	0.627061i	$0.784258\pi$
$702$		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	$-0.261527\pi$
$709$	457.191	+	189.375i	0.644839	+	0.267101i	−0.0362043	+	0.999344i	$0.511527\pi$
$710$		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	0.304753	−	0.952432i	$-0.401426\pi$
$727$	−470.863	−	470.863i	−0.647679	−	0.647679i	−0.952432	+	0.304753i	$0.901426\pi$
$728$		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	−0.950982	−	0.309246i	$-0.899923\pi$
$733$	−364.452	−	879.866i	−0.497206	−	1.20036i	0.453776	−	0.891116i	$-0.350077\pi$
$734$		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	$-0.307711\pi$
$739$	1146.65	−	474.958i	1.55162	−	0.642704i	0.983609	+	0.180314i	$0.0577112\pi$
$740$		0			0
$741$	−487.442	−	201.905i	−0.657817	−	0.272477i
$742$		0			0
$743$	−512.021	+	512.021i	−0.689126	+	0.689126i	−0.962039	−	0.272913i	$-0.912013\pi$
$743$	−512.021	+	512.021i	−0.689126	+	0.689126i	0.272913	+	0.962039i	$0.412013\pi$
$744$		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	$-0.797427\pi$
$757$	139.805	−	337.518i	0.184682	−	0.445863i	0.988921	+	0.148444i	$0.0474265\pi$
$758$		0			0
$759$	856.215	+	856.215i	1.12808	+	1.12808i
$760$		0			0
$761$	495.581	+	495.581i	0.651223	+	0.651223i	0.953288	−	0.302064i	$-0.0976758\pi$
$761$	495.581	+	495.581i	0.651223	+	0.651223i	−0.302064	+	0.953288i	$0.597676\pi$
$762$		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	$-0.252845\pi$
$773$	534.778	+	221.512i	0.691822	+	0.286562i	−0.00893708	+	0.999960i	$0.502845\pi$
$774$		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	−0.995844	−	0.0910769i	$-0.970969\pi$
$787$	−280.233	−	676.541i	−0.356077	−	0.859646i	0.639767	−	0.768569i	$-0.279031\pi$
$788$		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	$-0.173466\pi$
$797$	−92.5205	−	223.364i	−0.116086	−	0.280256i	−0.971234	+	0.238128i	$0.923466\pi$
$798$		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	0.236358	−	0.971666i	$-0.424046\pi$
$809$	977.291	−	977.291i	1.20802	−	1.20802i	0.971666	−	0.236358i	$-0.0759538\pi$
$810$		0			0
$811$	553.320	+	229.193i	0.682269	+	0.282605i	0.696775	−	0.717290i	$-0.254618\pi$
$811$	553.320	+	229.193i	0.682269	+	0.282605i	−0.0145062	+	0.999895i	$0.504618\pi$
$812$		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	0.486665	+	0.873589i	$0.338213\pi$
$821$	−390.123	+	941.839i	−0.475180	+	1.14719i	−0.961844	+	0.273597i	$0.911787\pi$
$822$		0			0
$823$	692.747	+	692.747i	0.841734	+	0.841734i	0.989084	−	0.147350i	$-0.0470744\pi$
$823$	692.747	+	692.747i	0.841734	+	0.841734i	−0.147350	+	0.989084i	$0.547074\pi$
$824$		0			0
$825$	−887.815	−	887.815i	−1.07614	−	1.07614i
$826$		0			0
$827$	−401.669	+	969.714i	−0.485694	+	1.17257i	0.471173	+	0.882041i	$0.343831\pi$
$827$	−401.669	+	969.714i	−0.485694	+	1.17257i	−0.956867	+	0.290528i	$0.906169\pi$
$828$		0			0
$829$	−562.011	−	1356.81i	−0.677938	−	1.63669i	−0.767766	−	0.640730i	$-0.778632\pi$
$829$	−562.011	−	1356.81i	−0.677938	−	1.63669i	0.0898281	−	0.995957i	$-0.471368\pi$
$830$		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	−0.144862	−	0.989452i	$-0.546274\pi$
$839$	708.611	−	708.611i	0.844590	−	0.844590i	0.989452	+	0.144862i	$0.0462737\pi$
$840$		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	$-0.787005\pi$
$853$	178.189	−	430.187i	0.208897	−	0.504322i	0.993250	+	0.115992i	$0.0370049\pi$
$854$		0			0
$855$	5.30630	+	5.30630i	0.00620620	+	0.00620620i
$856$		0			0
$857$	−195.982	−	195.982i	−0.228683	−	0.228683i	0.583459	−	0.812142i	$-0.301699\pi$
$857$	−195.982	−	195.982i	−0.228683	−	0.228683i	−0.812142	+	0.583459i	$0.801699\pi$
$858$		0			0
$859$	−155.060	+	374.347i	−0.180512	+	0.435794i	−0.988072	−	0.153991i	$-0.950787\pi$
$859$	−155.060	+	374.347i	−0.180512	+	0.435794i	0.807560	+	0.589785i	$0.200787\pi$
$860$		0			0
$861$	12.8838	+	31.1043i	0.0149638	+	0.0361258i
$862$		0			0
$863$			63.9126i			0.0740586i	0.999314	+	0.0370293i	$0.0117895\pi$
$863$			63.9126i			0.0740586i	−0.999314	+	0.0370293i	$0.988211\pi$
$864$		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	$-0.618270\pi$
$877$	34.2590	−	14.1905i	0.0390638	−	0.0161808i	0.402130	+	0.915583i	$0.368270\pi$
$878$		0			0
$879$	108.844			0.123827
$880$		0			0
$881$		−	1126.03i		−	1.27812i	−0.769155	−	0.639062i	$-0.779323\pi$
$881$		−	1126.03i		−	1.27812i	0.769155	−	0.639062i	$-0.220677\pi$
$882$		0			0
$883$	−114.384	−	276.148i	−0.129540	−	0.312738i	0.845780	−	0.533531i	$-0.179135\pi$
$883$	−114.384	−	276.148i	−0.129540	−	0.312738i	−0.975321	+	0.220793i	$0.929135\pi$
$884$		0			0
$885$	2.25100	−	5.43439i	0.00254350	−	0.00614055i
$886$		0			0
$887$	−65.1075	−	65.1075i	−0.0734020	−	0.0734020i	0.669453	−	0.742855i	$-0.266529\pi$
$887$	−65.1075	−	65.1075i	−0.0734020	−	0.0734020i	−0.742855	+	0.669453i	$0.766529\pi$
$888$		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	$-0.150656\pi$
$907$	1085.79	+	449.751i	1.19713	+	0.495866i	0.307058	+	0.951691i	$0.400656\pi$
$908$		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	0.920119	+	0.391640i	$0.128092\pi$
$919$	1205.51	+	1205.51i	1.31176	+	1.31176i	0.391640	+	0.920119i	$0.371908\pi$
$920$		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	−0.921883	−	0.387467i	$-0.873350\pi$
$937$	−500.748	+	500.748i	−0.534416	+	0.534416i	0.387467	+	0.921883i	$0.373350\pi$
$938$		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	$-0.352639\pi$
$941$	1312.74	−	543.756i	1.39505	−	0.577849i	0.948462	+	0.316891i	$0.102639\pi$
$942$		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	$-0.240247\pi$
$947$	−256.726	−	619.792i	−0.271094	−	0.654480i	−0.999531	+	0.0306337i	$0.990247\pi$
$948$		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	0.999988	−	0.00480927i	$-0.00153084\pi$
$953$	948.406	+	948.406i	0.995179	+	0.995179i	−0.00480927	+	0.999988i	$0.501531\pi$
$954$		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	−0.704104	−	0.710096i	$-0.748651\pi$
$967$	5.79422	−	5.79422i	0.00599196	−	0.00599196i	0.710096	+	0.704104i	$0.248651\pi$
$968$		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	$-0.00608677\pi$
$971$	1644.17	+	681.037i	1.69327	+	0.701377i	0.693457	+	0.720498i	$0.256087\pi$
$972$		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	$0.0889465\pi$
$977$			538.935i			0.551623i	−0.961212	+	0.275811i	$0.911054\pi$
$978$		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	0.614546	−	0.788881i	$-0.289339\pi$
$983$	−171.371	−	171.371i	−0.174335	−	0.174335i	−0.788881	+	0.614546i	$0.789339\pi$
$984$		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	$-0.680834\pi$
$991$		−	1670.67i		−	1.68584i	0.538038	−	0.842921i	$-0.319166\pi$
$992$		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	$-0.612993\pi$
$997$	−1252.59	−	518.840i	−1.25636	−	0.520402i	−0.908791	+	0.417252i	$0.862993\pi$
$998$		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	256.3.h.a.31.6		28
4.3	odd	2		256.3.h.b.31.2		28
8.3	odd	2		32.3.h.a.27.3	yes	28
8.5	even	2		128.3.h.a.15.2		28
24.11	even	2		288.3.u.a.91.5		28
32.3	odd	8		128.3.h.a.111.2		28
32.13	even	8		256.3.h.b.223.2		28
32.19	odd	8	inner	256.3.h.a.223.6		28
32.29	even	8		32.3.h.a.19.3	✓	28
96.29	odd	8		288.3.u.a.19.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.3	✓	28	32.29	even	8
32.3.h.a.27.3	yes	28	8.3	odd	2
128.3.h.a.15.2		28	8.5	even	2
128.3.h.a.111.2		28	32.3	odd	8
256.3.h.a.31.6		28	1.1	even	1	trivial
256.3.h.a.223.6		28	32.19	odd	8	inner
256.3.h.b.31.2		28	4.3	odd	2
256.3.h.b.223.2		28	32.13	even	8
288.3.u.a.19.5		28	96.29	odd	8
288.3.u.a.91.5		28	24.11	even	2

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.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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