LMFDB - Embedded newform 256.4.g.b.33.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(33,256)]

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([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("256.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.g (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:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			33.11
Character	$\chi$	$=$	256.33
Dual form			256.4.g.b.225.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.28810 - 7.93817i) q^{3} +(-11.2895 + 4.67626i) q^{5} +(-11.8490 + 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +O(q^{10})$	\(q+(3.28810 - 7.93817i) q^{3} +(-11.2895 + 4.67626i) q^{5} +(-11.8490 + 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +(23.5791 + 56.9250i) q^{11} +(13.6580 + 5.65734i) q^{13} +104.994i q^{15} +44.1663i q^{17} +(-66.5184 - 27.5528i) q^{19} +(55.0988 + 133.020i) q^{21} +(60.0240 + 60.0240i) q^{23} +(17.1966 - 17.1966i) q^{25} +(-157.383 + 65.1901i) q^{27} +(14.3335 - 34.6041i) q^{29} -174.518 q^{31} +529.411 q^{33} +(78.3602 - 189.178i) q^{35} +(118.428 - 49.0545i) q^{37} +(89.8179 - 89.8179i) q^{39} +(15.5284 + 15.5284i) q^{41} +(87.3822 + 210.959i) q^{43} +(528.642 + 218.971i) q^{45} +228.677i q^{47} +62.2017i q^{49} +(350.600 + 145.223i) q^{51} +(-258.652 - 624.440i) q^{53} +(-532.392 - 532.392i) q^{55} +(-437.438 + 437.438i) q^{57} +(-456.272 + 188.994i) q^{59} +(-242.128 + 584.548i) q^{61} +784.667 q^{63} -180.647 q^{65} +(-332.601 + 802.971i) q^{67} +(673.845 - 279.116i) q^{69} +(-550.460 + 550.460i) q^{71} +(69.2096 + 69.2096i) q^{73} +(-79.9655 - 193.054i) q^{75} +(-953.895 - 395.116i) q^{77} +518.934i q^{79} +199.379i q^{81} +(595.241 + 246.557i) q^{83} +(-206.533 - 498.615i) q^{85} +(-227.563 - 227.563i) q^{87} +(656.135 - 656.135i) q^{89} +(-228.868 + 94.8003i) q^{91} +(-573.832 + 1385.35i) q^{93} +879.802 q^{95} -388.503 q^{97} +(1104.12 - 2665.58i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	3.28810	−	7.93817i	0.632795	−	1.52770i	−0.203300	−	0.979116i	$-0.565167\pi$
$3$	3.28810	−	7.93817i	0.632795	−	1.52770i	0.836095	−	0.548585i	$-0.184833\pi$
$4$		0			0
$5$	−11.2895	+	4.67626i	−1.00976	+	0.418257i	−0.825368	−	0.564595i	$-0.809032\pi$
$5$	−11.2895	+	4.67626i	−1.00976	+	0.418257i	−0.184394	+	0.982852i	$0.559032\pi$
$6$		0			0
$7$	−11.8490	+	11.8490i	−0.639787	+	0.639787i	−0.950503	−	0.310716i	$-0.899431\pi$
$7$	−11.8490	+	11.8490i	−0.639787	+	0.639787i	0.310716	+	0.950503i	$0.399431\pi$
$8$		0			0
$9$	−33.1111	−	33.1111i	−1.22634	−	1.22634i
$10$		0			0
$11$	23.5791	+	56.9250i	0.646306	+	1.56032i	0.818029	+	0.575176i	$0.195067\pi$
$11$	23.5791	+	56.9250i	0.646306	+	1.56032i	−0.171723	+	0.985145i	$0.554933\pi$
$12$		0			0
$13$	13.6580	+	5.65734i	0.291389	+	0.120697i	0.523590	−	0.851971i	$-0.324593\pi$
$13$	13.6580	+	5.65734i	0.291389	+	0.120697i	−0.232200	+	0.972668i	$0.574593\pi$
$14$		0			0
$15$			104.994i			1.80728i
$16$		0			0
$17$			44.1663i			0.630112i	0.949073	+	0.315056i	$0.102023\pi$
$17$			44.1663i			0.630112i	−0.949073	+	0.315056i	$0.897977\pi$
$18$		0			0
$19$	−66.5184	−	27.5528i	−0.803177	−	0.332687i	−0.0569490	−	0.998377i	$-0.518137\pi$
$19$	−66.5184	−	27.5528i	−0.803177	−	0.332687i	−0.746228	+	0.665690i	$0.768137\pi$
$20$		0			0
$21$	55.0988	+	133.020i	0.572549	+	1.38226i
$22$		0			0
$23$	60.0240	+	60.0240i	0.544168	+	0.544168i	0.924748	−	0.380580i	$-0.124276\pi$
$23$	60.0240	+	60.0240i	0.544168	+	0.544168i	−0.380580	+	0.924748i	$0.624276\pi$
$24$		0			0
$25$	17.1966	−	17.1966i	0.137573	−	0.137573i
$26$		0			0
$27$	−157.383	+	65.1901i	−1.12179	+	0.464661i
$28$		0			0
$29$	14.3335	−	34.6041i	0.0917813	−	0.221580i	−0.871322	−	0.490712i	$-0.836737\pi$
$29$	14.3335	−	34.6041i	0.0917813	−	0.221580i	0.963103	+	0.269132i	$0.0867368\pi$
$30$		0			0
$31$	−174.518			−1.01111			−0.505554	−	0.862795i	$-0.668712\pi$
$31$	−174.518			−1.01111			−0.505554	+	0.862795i	$0.668712\pi$
$32$		0			0
$33$	529.411			2.79268
$34$		0			0
$35$	78.3602	−	189.178i	0.378437	−	0.913627i
$36$		0			0
$37$	118.428	−	49.0545i	0.526201	−	0.217960i	−0.103737	−	0.994605i	$-0.533080\pi$
$37$	118.428	−	49.0545i	0.526201	−	0.217960i	0.629938	+	0.776645i	$0.283080\pi$
$38$		0			0
$39$	89.8179	−	89.8179i	0.368779	−	0.368779i
$40$		0			0
$41$	15.5284	+	15.5284i	0.0591494	+	0.0591494i	0.736063	−	0.676913i	$-0.236683\pi$
$41$	15.5284	+	15.5284i	0.0591494	+	0.0591494i	−0.676913	+	0.736063i	$0.736683\pi$
$42$		0			0
$43$	87.3822	+	210.959i	0.309899	+	0.748163i	0.999708	+	0.0241712i	$0.00769467\pi$
$43$	87.3822	+	210.959i	0.309899	+	0.748163i	−0.689809	+	0.723992i	$0.742305\pi$
$44$		0			0
$45$	528.642	+	218.971i	1.75123	+	0.725383i
$46$		0			0
$47$			228.677i			0.709703i	0.934923	+	0.354851i	$0.115469\pi$
$47$			228.677i			0.709703i	−0.934923	+	0.354851i	$0.884531\pi$
$48$		0			0
$49$			62.2017i			0.181346i
$50$		0			0
$51$	350.600	+	145.223i	0.962623	+	0.398731i
$52$		0			0
$53$	−258.652	−	624.440i	−0.670349	−	1.61837i	−0.781017	−	0.624509i	$-0.785299\pi$
$53$	−258.652	−	624.440i	−0.670349	−	1.61837i	0.110668	−	0.993857i	$-0.464701\pi$
$54$		0			0
$55$	−532.392	−	532.392i	−1.30523	−	1.30523i
$56$		0			0
$57$	−437.438	+	437.438i	−1.01649	+	1.01649i
$58$		0			0
$59$	−456.272	+	188.994i	−1.00681	+	0.417033i	−0.824289	−	0.566169i	$-0.808425\pi$
$59$	−456.272	+	188.994i	−1.00681	+	0.417033i	−0.182518	+	0.983203i	$0.558425\pi$
$60$		0			0
$61$	−242.128	+	584.548i	−0.508218	+	1.22695i	0.436690	+	0.899612i	$0.356151\pi$
$61$	−242.128	+	584.548i	−0.508218	+	1.22695i	−0.944908	+	0.327335i	$0.893849\pi$
$62$		0			0
$63$	784.667			1.56919
$64$		0			0
$65$	−180.647			−0.344716
$66$		0			0
$67$	−332.601	+	802.971i	−0.606473	+	1.46416i	0.260337	+	0.965518i	$0.416166\pi$
$67$	−332.601	+	802.971i	−0.606473	+	1.46416i	−0.866810	+	0.498639i	$0.833834\pi$
$68$		0			0
$69$	673.845	−	279.116i	1.17567	−	0.486980i
$70$		0			0
$71$	−550.460	+	550.460i	−0.920107	+	0.920107i	−0.997037	−	0.0769293i	$-0.975488\pi$
$71$	−550.460	+	550.460i	−0.920107	+	0.920107i	0.0769293	+	0.997037i	$0.475488\pi$
$72$		0			0
$73$	69.2096	+	69.2096i	0.110964	+	0.110964i	0.760409	−	0.649445i	$-0.224999\pi$
$73$	69.2096	+	69.2096i	0.110964	+	0.110964i	−0.649445	+	0.760409i	$0.724999\pi$
$74$		0			0
$75$	−79.9655	−	193.054i	−0.123115	−	0.297226i
$76$		0			0
$77$	−953.895	−	395.116i	−1.41177	−	0.584775i
$78$		0			0
$79$			518.934i			0.739046i	0.929222	+	0.369523i	$0.120479\pi$
$79$			518.934i			0.739046i	−0.929222	+	0.369523i	$0.879521\pi$
$80$		0			0
$81$			199.379i			0.273496i
$82$		0			0
$83$	595.241	+	246.557i	0.787183	+	0.326062i	0.739810	−	0.672815i	$-0.234915\pi$
$83$	595.241	+	246.557i	0.787183	+	0.326062i	0.0473726	+	0.998877i	$0.484915\pi$
$84$		0			0
$85$	−206.533	−	498.615i	−0.263549	−	0.636263i
$86$		0			0
$87$	−227.563	−	227.563i	−0.280429	−	0.280429i
$88$		0			0
$89$	656.135	−	656.135i	0.781462	−	0.781462i	−0.198615	−	0.980078i	$-0.563644\pi$
$89$	656.135	−	656.135i	0.781462	−	0.781462i	0.980078	+	0.198615i	$0.0636445\pi$
$90$		0			0
$91$	−228.868	+	94.8003i	−0.263647	+	0.109206i
$92$		0			0
$93$	−573.832	+	1385.35i	−0.639823	+	1.54467i
$94$		0			0
$95$	879.802			0.950166
$96$		0			0
$97$	−388.503			−0.406665			−0.203333	−	0.979110i	$-0.565177\pi$
$97$	−388.503			−0.406665			−0.203333	+	0.979110i	$0.565177\pi$
$98$		0			0
$99$	1104.12	−	2665.58i	1.12089	−	2.70607i
$100$		0			0
$101$	−658.558	+	272.784i	−0.648802	+	0.268742i	−0.682718	−	0.730682i	$-0.739202\pi$
$101$	−658.558	+	272.784i	−0.648802	+	0.268742i	0.0339161	+	0.999425i	$0.489202\pi$
$102$		0			0
$103$	467.607	−	467.607i	0.447327	−	0.447327i	−0.447138	−	0.894465i	$-0.647557\pi$
$103$	467.607	−	467.607i	0.447327	−	0.447327i	0.894465	+	0.447138i	$0.147557\pi$
$104$		0			0
$105$	−1244.07	−	1244.07i	−1.15628	−	1.15628i
$106$		0			0
$107$	−237.456	−	573.269i	−0.214539	−	0.517944i	0.779571	−	0.626314i	$-0.215437\pi$
$107$	−237.456	−	573.269i	−0.214539	−	0.517944i	−0.994111	+	0.108369i	$0.965437\pi$
$108$		0			0
$109$	117.568	+	48.6982i	0.103311	+	0.0427930i	0.433741	−	0.901038i	$-0.357193\pi$
$109$	117.568	+	48.6982i	0.103311	+	0.0427930i	−0.330429	+	0.943831i	$0.607193\pi$
$110$		0			0
$111$		−	1101.40i		−	0.941802i
$112$		0			0
$113$		−	1440.10i		−	1.19887i	−0.800422	−	0.599437i	$-0.795391\pi$
$113$		−	1440.10i		−	1.19887i	0.800422	−	0.599437i	$-0.204609\pi$
$114$		0			0
$115$	−958.327	−	396.952i	−0.777083	−	0.321878i
$116$		0			0
$117$	−264.911	−	639.553i	−0.209325	−	0.505356i
$118$		0			0
$119$	−523.327	−	523.327i	−0.403137	−	0.403137i
$120$		0			0
$121$	−1743.32	+	1743.32i	−1.30978	+	1.30978i
$122$		0			0
$123$	174.326	−	72.2081i	0.127792	−	0.0529332i
$124$		0			0
$125$	470.807	−	1136.63i	0.336882	−	0.813305i
$126$		0			0
$127$	340.683			0.238037			0.119019	−	0.992892i	$-0.462025\pi$
$127$	340.683			0.238037			0.119019	+	0.992892i	$0.462025\pi$
$128$		0			0
$129$	1961.95			1.33907
$130$		0			0
$131$	460.465	−	1111.66i	0.307107	−	0.741421i	−0.692689	−	0.721236i	$-0.743574\pi$
$131$	460.465	−	1111.66i	0.307107	−	0.741421i	0.999796	−	0.0201855i	$-0.00642567\pi$
$132$		0			0
$133$	1114.65	−	461.704i	0.726711	−	0.301013i
$134$		0			0
$135$	1471.93	−	1471.93i	0.938394	−	0.938394i
$136$		0			0
$137$	−109.800	−	109.800i	−0.0684732	−	0.0684732i	0.672041	−	0.740514i	$-0.265418\pi$
$137$	−109.800	−	109.800i	−0.0684732	−	0.0684732i	−0.740514	+	0.672041i	$0.765418\pi$
$138$		0			0
$139$	−199.529	−	481.706i	−0.121754	−	0.293941i	0.851238	−	0.524781i	$-0.175853\pi$
$139$	−199.529	−	481.706i	−0.121754	−	0.293941i	−0.972992	+	0.230840i	$0.925853\pi$
$140$		0			0
$141$	1815.28	+	751.914i	1.08421	+	0.449096i
$142$		0			0
$143$			910.879i			0.532668i
$144$		0			0
$145$			457.689i			0.262131i
$146$		0			0
$147$	493.767	+	204.525i	0.277042	+	0.114755i
$148$		0			0
$149$	917.500	+	2215.04i	0.504460	+	1.21787i	0.947031	+	0.321141i	$0.104066\pi$
$149$	917.500	+	2215.04i	0.504460	+	1.21787i	−0.442572	+	0.896733i	$0.645934\pi$
$150$		0			0
$151$	191.904	+	191.904i	0.103423	+	0.103423i	0.756925	−	0.653502i	$-0.226701\pi$
$151$	191.904	+	191.904i	0.103423	+	0.103423i	−0.653502	+	0.756925i	$0.726701\pi$
$152$		0			0
$153$	1462.39	−	1462.39i	0.772729	−	0.772729i
$154$		0			0
$155$	1970.22	−	816.090i	1.02098	−	0.422903i
$156$		0			0
$157$	572.497	−	1382.13i	0.291021	−	0.702586i	−0.708976	−	0.705233i	$-0.750842\pi$
$157$	572.497	−	1382.13i	0.291021	−	0.702586i	0.999996	+	0.00264665i	$0.000842456\pi$
$158$		0			0
$159$	−5807.38			−2.89657
$160$		0			0
$161$	−1422.45			−0.696303
$162$		0			0
$163$	−1331.47	+	3214.44i	−0.639807	+	1.54463i	0.187130	+	0.982335i	$0.440081\pi$
$163$	−1331.47	+	3214.44i	−0.639807	+	1.54463i	−0.826937	+	0.562295i	$0.809919\pi$
$164$		0			0
$165$	−5976.77	+	2475.66i	−2.81995	+	1.16806i
$166$		0			0
$167$	214.549	−	214.549i	0.0994149	−	0.0994149i	−0.655650	−	0.755065i	$-0.727605\pi$
$167$	214.549	−	214.549i	0.0994149	−	0.0994149i	0.755065	+	0.655650i	$0.227605\pi$
$168$		0			0
$169$	−1398.98	−	1398.98i	−0.636767	−	0.636767i
$170$		0			0
$171$	1290.19	+	3114.80i	0.576979	+	1.39295i
$172$		0			0
$173$	−3387.83	−	1403.29i	−1.48886	−	0.616705i	−0.517789	−	0.855509i	$-0.673245\pi$
$173$	−3387.83	−	1403.29i	−1.48886	−	0.616705i	−0.971068	+	0.238804i	$0.923245\pi$
$174$		0			0
$175$			407.526i			0.176035i
$176$		0			0
$177$			4243.40i			1.80200i
$178$		0			0
$179$	−1642.06	−	680.162i	−0.685659	−	0.284009i	0.0125313	−	0.999921i	$-0.496011\pi$
$179$	−1642.06	−	680.162i	−0.685659	−	0.284009i	−0.698190	+	0.715912i	$0.746011\pi$
$180$		0			0
$181$	−1072.59	−	2589.47i	−0.440471	−	1.06339i	−0.975784	−	0.218736i	$-0.929807\pi$
$181$	−1072.59	−	2589.47i	−0.440471	−	1.06339i	0.535313	−	0.844653i	$-0.320193\pi$
$182$		0			0
$183$	3844.10	+	3844.10i	1.55281	+	1.55281i
$184$		0			0
$185$	−1107.60	+	1107.60i	−0.440175	+	0.440175i
$186$		0			0
$187$	−2514.17	+	1041.40i	−0.983177	+	0.407245i
$188$		0			0
$189$	1092.39	−	2637.27i	0.420423	−	1.01499i
$190$		0			0
$191$	3774.95			1.43008			0.715042	−	0.699082i	$-0.246408\pi$
$191$	3774.95			1.43008			0.715042	+	0.699082i	$0.246408\pi$
$192$		0			0
$193$	−1118.54			−0.417172			−0.208586	−	0.978004i	$-0.566886\pi$
$193$	−1118.54			−0.417172			−0.208586	+	0.978004i	$0.566886\pi$
$194$		0			0
$195$	−593.986	+	1434.01i	−0.218134	+	0.526623i
$196$		0			0
$197$	4025.41	−	1667.38i	1.45583	−	0.603024i	0.492252	−	0.870453i	$-0.336174\pi$
$197$	4025.41	−	1667.38i	1.45583	−	0.603024i	0.963578	+	0.267429i	$0.0861740\pi$
$198$		0			0
$199$	−776.416	+	776.416i	−0.276576	+	0.276576i	−0.831741	−	0.555165i	$-0.812655\pi$
$199$	−776.416	+	776.416i	−0.276576	+	0.276576i	0.555165	+	0.831741i	$0.312655\pi$
$200$		0			0
$201$	5280.49	+	5280.49i	1.85302	+	1.85302i
$202$		0			0
$203$	240.186	+	579.861i	0.0830433	+	0.200484i
$204$		0			0
$205$	−247.922	−	102.693i	−0.0844665	−	0.0349872i
$206$		0			0
$207$		−	3974.92i		−	1.33467i
$208$		0			0
$209$		−	4436.23i		−	1.46823i
$210$		0			0
$211$	1455.68	+	602.962i	0.474944	+	0.196728i	0.607298	−	0.794474i	$-0.292254\pi$
$211$	1455.68	+	602.962i	0.474944	+	0.196728i	−0.132354	+	0.991203i	$0.542254\pi$
$212$		0			0
$213$	2559.68	+	6179.61i	0.823410	+	1.98789i
$214$		0			0
$215$	−1973.00	−	1973.00i	−0.625849	−	0.625849i
$216$		0			0
$217$	2067.86	−	2067.86i	0.646893	−	0.646893i
$218$		0			0
$219$	776.966	−	321.830i	0.239737	−	0.0993025i
$220$		0			0
$221$	−249.864	+	603.225i	−0.0760528	+	0.183608i
$222$		0			0
$223$	1454.48			0.436768			0.218384	−	0.975863i	$-0.429921\pi$
$223$	1454.48			0.436768			0.218384	+	0.975863i	$0.429921\pi$
$224$		0			0
$225$	−1138.80			−0.337421
$226$		0			0
$227$	−1309.75	+	3162.03i	−0.382958	+	0.924542i	0.608433	+	0.793605i	$0.291798\pi$
$227$	−1309.75	+	3162.03i	−0.382958	+	0.924542i	−0.991391	+	0.130937i	$0.958202\pi$
$228$		0			0
$229$	5746.77	−	2380.39i	1.65833	−	0.686903i	0.660381	−	0.750930i	$-0.270395\pi$
$229$	5746.77	−	2380.39i	1.65833	−	0.686903i	0.997948	+	0.0640278i	$0.0203946\pi$
$230$		0			0
$231$	−6273.00	+	6273.00i	−1.78672	+	1.78672i
$232$		0			0
$233$	1497.10	+	1497.10i	0.420938	+	0.420938i	0.885526	−	0.464589i	$-0.153798\pi$
$233$	1497.10	+	1497.10i	0.420938	+	0.420938i	−0.464589	+	0.885526i	$0.653798\pi$
$234$		0			0
$235$	−1069.35	−	2581.65i	−0.296838	−	0.716631i
$236$		0			0
$237$	4119.39	+	1706.31i	1.12904	+	0.467665i
$238$		0			0
$239$			1039.75i			0.281404i	0.990052	+	0.140702i	$0.0449360\pi$
$239$			1039.75i			0.281404i	−0.990052	+	0.140702i	$0.955064\pi$
$240$		0			0
$241$		−	120.503i		−	0.0322087i	−0.999870	−	0.0161043i	$-0.994874\pi$
$241$		−	120.503i		−	0.0322087i	0.999870	−	0.0161043i	$-0.00512639\pi$
$242$		0			0
$243$	−2666.64	−	1104.56i	−0.703970	−	0.291594i
$244$		0			0
$245$	−290.871	−	702.224i	−0.0758492	−	0.183116i
$246$		0			0
$247$	−752.635	−	752.635i	−0.193883	−	0.193883i
$248$		0			0
$249$	3914.42	−	3914.42i	0.996250	−	0.996250i
$250$		0			0
$251$	5865.74	−	2429.67i	1.47507	−	0.610994i	0.507061	−	0.861910i	$-0.330732\pi$
$251$	5865.74	−	2429.67i	1.47507	−	0.610994i	0.968009	+	0.250916i	$0.0807319\pi$
$252$		0			0
$253$	−2001.55	+	4832.18i	−0.497378	+	1.20078i
$254$		0			0
$255$	−4637.19			−1.13879
$256$		0			0
$257$	−4520.96			−1.09731			−0.548657	−	0.836048i	$-0.684861\pi$
$257$	−4520.96			−1.09731			−0.548657	+	0.836048i	$0.684861\pi$
$258$		0			0
$259$	−822.008	+	1984.50i	−0.197209	+	0.476104i
$260$		0			0
$261$	−1620.37	+	671.180i	−0.384286	+	0.159176i
$262$		0			0
$263$	449.651	−	449.651i	0.105425	−	0.105425i	−0.652427	−	0.757852i	$-0.726249\pi$
$263$	449.651	−	449.651i	0.105425	−	0.105425i	0.757852	+	0.652427i	$0.226249\pi$
$264$		0			0
$265$	5840.08	+	5840.08i	1.35379	+	1.35379i
$266$		0			0
$267$	−3051.07	−	7365.94i	−0.699336	−	1.68835i
$268$		0			0
$269$	2436.90	+	1009.40i	0.552343	+	0.228788i	0.641357	−	0.767243i	$-0.278372\pi$
$269$	2436.90	+	1009.40i	0.552343	+	0.228788i	−0.0890145	+	0.996030i	$0.528372\pi$
$270$		0			0
$271$		−	1662.12i		−	0.372570i	−0.982496	−	0.186285i	$-0.940355\pi$
$271$		−	1662.12i		−	0.372570i	0.982496	−	0.186285i	$-0.0596448\pi$
$272$		0			0
$273$			2128.51i			0.471880i
$274$		0			0
$275$	1384.40	+	573.437i	0.303572	+	0.125744i
$276$		0			0
$277$	2447.54	+	5908.88i	0.530897	+	1.28170i	0.930930	+	0.365198i	$0.118999\pi$
$277$	2447.54	+	5908.88i	0.530897	+	1.28170i	−0.400033	+	0.916501i	$0.631001\pi$
$278$		0			0
$279$	5778.47	+	5778.47i	1.23996	+	1.23996i
$280$		0			0
$281$	3546.76	−	3546.76i	0.752960	−	0.752960i	−0.222070	−	0.975031i	$-0.571281\pi$
$281$	3546.76	−	3546.76i	0.752960	−	0.752960i	0.975031	+	0.222070i	$0.0712814\pi$
$282$		0			0
$283$	2136.81	−	885.094i	0.448834	−	0.185913i	−0.146805	−	0.989165i	$-0.546899\pi$
$283$	2136.81	−	885.094i	0.448834	−	0.185913i	0.595639	+	0.803252i	$0.296899\pi$
$284$		0			0
$285$	2892.87	−	6984.02i	0.601260	−	1.45157i
$286$		0			0
$287$	−367.992			−0.0756860
$288$		0			0
$289$	2962.34			0.602959
$290$		0			0
$291$	−1277.44	+	3084.00i	−0.257336	+	0.621263i
$292$		0			0
$293$	−7533.04	+	3120.29i	−1.50200	+	0.622147i	−0.973888	−	0.227029i	$-0.927099\pi$
$293$	−7533.04	+	3120.29i	−1.50200	+	0.622147i	−0.528109	+	0.849177i	$0.677099\pi$
$294$		0			0
$295$	4267.29	−	4267.29i	0.842208	−	0.842208i
$296$		0			0
$297$	−7421.90	−	7421.90i	−1.45004	−	1.45004i
$298$		0			0
$299$	480.234	+	1159.39i	0.0928851	+	0.224244i
$300$		0			0
$301$	−3535.05	−	1464.27i	−0.676934	−	0.280395i
$302$		0			0
$303$			6124.68i			1.16123i
$304$		0			0
$305$		−	7731.50i		−	1.45149i
$306$		0			0
$307$	3320.22	+	1375.28i	0.617247	+	0.255672i	0.669324	−	0.742971i	$-0.266584\pi$
$307$	3320.22	+	1375.28i	0.617247	+	0.255672i	−0.0520765	+	0.998643i	$0.516584\pi$
$308$		0			0
$309$	−2174.41	−	5249.49i	−0.400316	−	0.966449i
$310$		0			0
$311$	2136.23	+	2136.23i	0.389499	+	0.389499i	0.874509	−	0.485010i	$-0.161184\pi$
$311$	2136.23	+	2136.23i	0.389499	+	0.389499i	−0.485010	+	0.874509i	$0.661184\pi$
$312$		0			0
$313$	−7352.03	+	7352.03i	−1.32767	+	1.32767i	−0.420274	+	0.907397i	$0.638066\pi$
$313$	−7352.03	+	7352.03i	−1.32767	+	1.32767i	−0.907397	+	0.420274i	$0.861934\pi$
$314$		0			0
$315$	−8858.48	+	3669.30i	−1.58450	+	0.656323i
$316$		0			0
$317$	−321.560	+	776.314i	−0.0569735	+	0.137546i	−0.949803	−	0.312849i	$-0.898717\pi$
$317$	−321.560	+	776.314i	−0.0569735	+	0.137546i	0.892829	+	0.450395i	$0.148717\pi$
$318$		0			0
$319$	2307.81			0.405054
$320$		0			0
$321$	−5331.49			−0.927023
$322$		0			0
$323$	1216.91	−	2937.87i	0.209630	−	0.506092i
$324$		0			0
$325$	332.159	−	137.585i	0.0566920	−	0.0234826i
$326$		0			0
$327$	773.148	−	773.148i	0.130750	−	0.130750i
$328$		0			0
$329$	−2709.60	−	2709.60i	−0.454058	−	0.454058i
$330$		0			0
$331$	383.476	+	925.792i	0.0636789	+	0.153735i	0.952516	−	0.304489i	$-0.0984858\pi$
$331$	383.476	+	925.792i	0.0636789	+	0.153735i	−0.888837	+	0.458224i	$0.848486\pi$
$332$		0			0
$333$	−5545.52	−	2297.03i	−0.912590	−	0.378007i
$334$		0			0
$335$		−	10620.4i		−	1.73211i
$336$		0			0
$337$			6360.72i			1.02816i	0.857742	+	0.514081i	$0.171867\pi$
$337$			6360.72i			1.02816i	−0.857742	+	0.514081i	$0.828133\pi$
$338$		0			0
$339$	−11431.7	−	4735.17i	−1.83152	−	0.758641i
$340$		0			0
$341$	−4114.98	−	9934.43i	−0.653485	−	1.57765i
$342$		0			0
$343$	−4801.24	−	4801.24i	−0.755809	−	0.755809i
$344$		0			0
$345$	−6302.15	+	6302.15i	−0.983467	+	0.983467i
$346$		0			0
$347$	10094.1	−	4181.11i	1.56161	−	0.646840i	0.576242	−	0.817279i	$-0.304518\pi$
$347$	10094.1	−	4181.11i	1.56161	−	0.646840i	0.985368	+	0.170438i	$0.0545184\pi$
$348$		0			0
$349$	−697.242	+	1683.29i	−0.106941	+	0.258179i	−0.968287	−	0.249840i	$-0.919622\pi$
$349$	−697.242	+	1683.29i	−0.106941	+	0.258179i	0.861346	+	0.508019i	$0.169622\pi$
$350$		0			0
$351$	−2518.34			−0.382961
$352$		0			0
$353$	3236.30			0.487963			0.243982	−	0.969780i	$-0.421546\pi$
$353$	3236.30			0.487963			0.243982	+	0.969780i	$0.421546\pi$
$354$		0			0
$355$	3640.32	−	8788.50i	0.544248	−	1.31393i
$356$		0			0
$357$	−5875.01	+	2433.51i	−0.870976	+	0.360770i
$358$		0			0
$359$	5424.53	−	5424.53i	0.797482	−	0.797482i	−0.185216	−	0.982698i	$-0.559299\pi$
$359$	5424.53	−	5424.53i	0.797482	−	0.797482i	0.982698	+	0.185216i	$0.0592985\pi$
$360$		0			0
$361$	−1184.51	−	1184.51i	−0.172694	−	0.172694i
$362$		0			0
$363$	8106.58	+	19571.0i	1.17214	+	2.82978i
$364$		0			0
$365$	−1104.98	−	457.699i	−0.158459	−	0.0656358i
$366$		0			0
$367$			10914.3i			1.55237i	0.630503	+	0.776187i	$0.282849\pi$
$367$			10914.3i			1.55237i	−0.630503	+	0.776187i	$0.717151\pi$
$368$		0			0
$369$		−	1028.32i		−	0.145074i
$370$		0			0
$371$	10463.8	+	4334.23i	1.46429	+	0.606529i
$372$		0			0
$373$	3921.61	+	9467.61i	0.544379	+	1.31425i	0.921606	+	0.388127i	$0.126878\pi$
$373$	3921.61	+	9467.61i	0.544379	+	1.31425i	−0.377227	+	0.926121i	$0.623122\pi$
$374$		0			0
$375$	−7474.69	−	7474.69i	−1.02931	−	1.02931i
$376$		0			0
$377$	391.534	−	391.534i	0.0534881	−	0.0534881i
$378$		0			0
$379$	−10042.4	+	4159.68i	−1.36106	+	0.563769i	−0.939349	−	0.342962i	$-0.888570\pi$
$379$	−10042.4	+	4159.68i	−1.36106	+	0.563769i	−0.421710	+	0.906731i	$0.638570\pi$
$380$		0			0
$381$	1120.20	−	2704.40i	0.150629	−	0.363650i
$382$		0			0
$383$	1609.29			0.214702			0.107351	−	0.994221i	$-0.465763\pi$
$383$	1609.29			0.214702			0.107351	+	0.994221i	$0.465763\pi$
$384$		0			0
$385$	12616.6			1.67014
$386$		0			0
$387$	4091.77	−	9878.41i	0.537458	−	1.29754i
$388$		0			0
$389$	3941.97	−	1632.82i	0.513793	−	0.212820i	−0.110695	−	0.993854i	$-0.535308\pi$
$389$	3941.97	−	1632.82i	0.513793	−	0.212820i	0.624488	+	0.781034i	$0.285308\pi$
$390$		0			0
$391$	−2651.04	+	2651.04i	−0.342887	+	0.342887i
$392$		0			0
$393$	−7310.49	−	7310.49i	−0.938335	−	0.938335i
$394$		0			0
$395$	−2426.67	−	5858.50i	−0.309111	−	0.746261i
$396$		0			0
$397$	−2995.05	−	1240.59i	−0.378632	−	0.156835i	0.185247	−	0.982692i	$-0.440692\pi$
$397$	−2995.05	−	1240.59i	−0.378632	−	0.156835i	−0.563879	+	0.825857i	$0.690692\pi$
$398$		0			0
$399$		−	10366.4i		−	1.30068i
$400$		0			0
$401$			8084.70i			1.00681i	0.864051	+	0.503405i	$0.167919\pi$
$401$			8084.70i			1.00681i	−0.864051	+	0.503405i	$0.832081\pi$
$402$		0			0
$403$	−2383.57	−	987.308i	−0.294626	−	0.122038i
$404$		0			0
$405$	−932.346	−	2250.88i	−0.114392	−	0.276166i
$406$		0			0
$407$	5584.85	+	5584.85i	0.680174	+	0.680174i
$408$		0			0
$409$	4621.85	−	4621.85i	0.558767	−	0.558767i	−0.370189	−	0.928956i	$-0.620707\pi$
$409$	4621.85	−	4621.85i	0.558767	−	0.558767i	0.928956	+	0.370189i	$0.120707\pi$
$410$		0			0
$411$	−1232.64	+	510.577i	−0.147936	+	0.0612771i
$412$		0			0
$413$	3166.98	−	7645.77i	0.377329	−	0.910954i
$414$		0			0
$415$	−7872.92			−0.931245
$416$		0			0
$417$	−4479.93			−0.526099
$418$		0			0
$419$	2131.19	−	5145.14i	0.248485	−	0.599897i	−0.749590	−	0.661902i	$-0.769750\pi$
$419$	2131.19	−	5145.14i	0.248485	−	0.599897i	0.998076	+	0.0620052i	$0.0197495\pi$
$420$		0			0
$421$	8558.20	−	3544.92i	0.990739	−	0.410378i	0.172346	−	0.985036i	$-0.444865\pi$
$421$	8558.20	−	3544.92i	0.990739	−	0.410378i	0.818393	+	0.574659i	$0.194865\pi$
$422$		0			0
$423$	7571.75	−	7571.75i	0.870334	−	0.870334i
$424$		0			0
$425$	759.512	+	759.512i	0.0866864	+	0.0866864i
$426$		0			0
$427$	−4057.35	−	9795.30i	−0.459833	−	1.11014i
$428$		0			0
$429$	7230.71	+	2995.06i	0.813758	+	0.337069i
$430$		0			0
$431$		−	6610.79i		−	0.738818i	−0.929267	−	0.369409i	$-0.879560\pi$
$431$		−	6610.79i		−	0.738818i	0.929267	−	0.369409i	$-0.120440\pi$
$432$		0			0
$433$			8705.35i			0.966172i	0.875573	+	0.483086i	$0.160484\pi$
$433$			8705.35i			0.966172i	−0.875573	+	0.483086i	$0.839516\pi$
$434$		0			0
$435$	3633.21	+	1504.92i	0.400458	+	0.165875i
$436$		0			0
$437$	−2338.87	−	5646.53i	−0.256026	−	0.618101i
$438$		0			0
$439$	−11344.9	−	11344.9i	−1.23341	−	1.23341i	−0.962648	−	0.270757i	$-0.912726\pi$
$439$	−11344.9	−	11344.9i	−1.23341	−	1.23341i	−0.270757	−	0.962648i	$-0.587274\pi$
$440$		0			0
$441$	2059.56	−	2059.56i	0.222391	−	0.222391i
$442$		0			0
$443$	1931.24	−	799.946i	0.207124	−	0.0857936i	−0.276709	−	0.960954i	$-0.589244\pi$
$443$	1931.24	−	799.946i	0.207124	−	0.0857936i	0.483834	+	0.875160i	$0.339244\pi$
$444$		0			0
$445$	−4339.16	+	10475.7i	−0.462239	+	1.11594i
$446$		0			0
$447$	20600.2			2.17977
$448$		0			0
$449$	1770.44			0.186085			0.0930426	−	0.995662i	$-0.470341\pi$
$449$	1770.44			0.186085			0.0930426	+	0.995662i	$0.470341\pi$
$450$		0			0
$451$	−517.808	+	1250.10i	−0.0540635	+	0.130521i
$452$		0			0
$453$	2154.36	−	892.366i	0.223445	−	0.0925541i
$454$		0			0
$455$	2140.49	−	2140.49i	0.220545	−	0.220545i
$456$		0			0
$457$	−7694.10	−	7694.10i	−0.787560	−	0.787560i	0.193534	−	0.981094i	$-0.438005\pi$
$457$	−7694.10	−	7694.10i	−0.787560	−	0.787560i	−0.981094	+	0.193534i	$0.938005\pi$
$458$		0			0
$459$	−2879.21	−	6951.02i	−0.292788	−	0.706854i
$460$		0			0
$461$	5291.40	+	2191.77i	0.534588	+	0.221433i	0.633611	−	0.773652i	$-0.281572\pi$
$461$	5291.40	+	2191.77i	0.534588	+	0.221433i	−0.0990235	+	0.995085i	$0.531572\pi$
$462$		0			0
$463$			13153.5i			1.32029i	0.751138	+	0.660145i	$0.229505\pi$
$463$			13153.5i			1.32029i	−0.751138	+	0.660145i	$0.770495\pi$
$464$		0			0
$465$		−	18323.3i		−	1.82736i
$466$		0			0
$467$	−7862.87	−	3256.91i	−0.779122	−	0.322723i	−0.0425611	−	0.999094i	$-0.513552\pi$
$467$	−7862.87	−	3256.91i	−0.779122	−	0.322723i	−0.736561	+	0.676371i	$0.763552\pi$
$468$		0			0
$469$	−5573.41	−	13455.4i	−0.548734	−	1.32476i
$470$		0			0
$471$	−9089.16	−	9089.16i	−0.889185	−	0.889185i
$472$		0			0
$473$	−9948.47	+	9948.47i	−0.967085	+	0.967085i
$474$		0			0
$475$	−1617.71	+	670.076i	−0.156264	+	0.0647268i
$476$		0			0
$477$	−12111.6	+	29240.1i	−1.16259	+	2.80673i
$478$		0			0
$479$	15687.9			1.49645			0.748224	−	0.663446i	$-0.230907\pi$
$479$	15687.9			1.49645			0.748224	+	0.663446i	$0.230907\pi$
$480$		0			0
$481$	1895.01			0.179636
$482$		0			0
$483$	−4677.16	+	11291.7i	−0.440617	+	1.06374i
$484$		0			0
$485$	4386.00	−	1816.74i	0.410635	−	0.170091i
$486$		0			0
$487$	−13515.4	+	13515.4i	−1.25758	+	1.25758i	−0.305330	+	0.952247i	$0.598767\pi$
$487$	−13515.4	+	13515.4i	−1.25758	+	1.25758i	−0.952247	+	0.305330i	$0.901233\pi$
$488$		0			0
$489$	21138.8	+	21138.8i	1.95487	+	1.95487i
$490$		0			0
$491$	1348.48	+	3255.53i	0.123943	+	0.299226i	0.973657	−	0.228019i	$-0.0732249\pi$
$491$	1348.48	+	3255.53i	0.123943	+	0.299226i	−0.849713	+	0.527245i	$0.823225\pi$
$492$		0			0
$493$	1528.33	+	633.056i	0.139620	+	0.0578325i
$494$		0			0
$495$			35256.1i			3.20130i
$496$		0			0
$497$		−	13044.8i		−	1.17734i
$498$		0			0
$499$	13952.2	+	5779.20i	1.25168	+	0.518462i	0.907345	−	0.420386i	$-0.138105\pi$
$499$	13952.2	+	5779.20i	1.25168	+	0.518462i	0.344332	+	0.938848i	$0.388105\pi$
$500$		0			0
$501$	−997.667	−	2408.58i	−0.0889671	−	0.214785i
$502$		0			0
$503$	12832.8	+	12832.8i	1.13755	+	1.13755i	0.988889	+	0.148658i	$0.0474954\pi$
$503$	12832.8	+	12832.8i	1.13755	+	1.13755i	0.148658	+	0.988889i	$0.452505\pi$
$504$		0			0
$505$	6159.17	−	6159.17i	0.542732	−	0.542732i
$506$		0			0
$507$	−15705.3	+	6505.34i	−1.37573	+	0.569847i
$508$		0			0
$509$	294.015	−	709.814i	0.0256031	−	0.0618113i	−0.910561	−	0.413375i	$-0.864350\pi$
$509$	294.015	−	709.814i	0.0256031	−	0.0618113i	0.936164	+	0.351564i	$0.114350\pi$
$510$		0			0
$511$	−1640.13			−0.141987
$512$		0			0
$513$	12265.0			1.05558
$514$		0			0
$515$	−3092.39	+	7465.70i	−0.264596	+	0.638792i
$516$		0			0
$517$	−13017.5	+	5392.01i	−1.10736	+	0.458685i
$518$		0			0
$519$	−22279.0	+	22279.0i	−1.88428	+	1.88428i
$520$		0			0
$521$	−4736.98	−	4736.98i	−0.398332	−	0.398332i	0.479312	−	0.877644i	$-0.340886\pi$
$521$	−4736.98	−	4736.98i	−0.398332	−	0.398332i	−0.877644	+	0.479312i	$0.840886\pi$
$522$		0			0
$523$	−881.013	−	2126.95i	−0.0736597	−	0.177830i	0.882761	−	0.469822i	$-0.155682\pi$
$523$	−881.013	−	2126.95i	−0.0736597	−	0.177830i	−0.956421	+	0.291992i	$0.905682\pi$
$524$		0			0
$525$	3235.01	+	1339.99i	0.268929	+	0.111394i
$526$		0			0
$527$		−	7707.81i		−	0.637111i
$528$		0			0
$529$		−	4961.24i		−	0.407762i
$530$		0			0
$531$	21365.5	+	8849.86i	1.74611	+	0.723260i
$532$		0			0
$533$	124.238	+	299.937i	0.0100963	+	0.0243747i
$534$		0			0
$535$	5361.51	+	5361.51i	0.433268	+	0.433268i
$536$		0			0
$537$	−10798.5	+	10798.5i	−0.867763	+	0.867763i
$538$		0			0
$539$	−3540.83	+	1466.66i	−0.282958	+	0.117205i
$540$		0			0
$541$	−8550.73	+	20643.3i	−0.679528	+	1.64053i	0.0853508	+	0.996351i	$0.472799\pi$
$541$	−8550.73	+	20643.3i	−0.679528	+	1.64053i	−0.764879	+	0.644174i	$0.777201\pi$
$542$		0			0
$543$	−24082.4			−1.90327
$544$		0			0
$545$	−1555.00			−0.122218
$546$		0			0
$547$	2552.53	−	6162.34i	0.199521	−	0.481687i	−0.792174	−	0.610295i	$-0.791051\pi$
$547$	2552.53	−	6162.34i	0.199521	−	0.481687i	0.991696	+	0.128608i	$0.0410509\pi$
$548$		0			0
$549$	27372.1	−	11337.9i	2.12789	−	0.881403i
$550$		0			0
$551$	−1906.88	+	1906.88i	−0.147433	+	0.147433i
$552$		0			0
$553$	−6148.86	−	6148.86i	−0.472832	−	0.472832i
$554$		0			0
$555$	5150.41	+	12434.2i	0.393915	+	0.950995i
$556$		0			0
$557$	2494.05	+	1033.07i	0.189724	+	0.0785863i	0.475523	−	0.879703i	$-0.342259\pi$
$557$	2494.05	+	1033.07i	0.189724	+	0.0785863i	−0.285799	+	0.958290i	$0.592259\pi$
$558$		0			0
$559$			3375.64i			0.255411i
$560$		0			0
$561$			23382.1i			1.75970i
$562$		0			0
$563$	−19457.5	−	8059.54i	−1.45654	−	0.603320i	−0.492798	−	0.870144i	$-0.664026\pi$
$563$	−19457.5	−	8059.54i	−1.45654	−	0.603320i	−0.963745	+	0.266823i	$0.914026\pi$
$564$		0			0
$565$	6734.26	+	16257.9i	0.501438	+	1.21058i
$566$		0			0
$567$	−2362.44	−	2362.44i	−0.174979	−	0.174979i
$568$		0			0
$569$	1740.16	−	1740.16i	0.128209	−	0.128209i	−0.640090	−	0.768300i	$-0.721103\pi$
$569$	1740.16	−	1740.16i	0.128209	−	0.128209i	0.768300	+	0.640090i	$0.221103\pi$
$570$		0			0
$571$	−16395.2	+	6791.10i	−1.20160	+	0.497721i	−0.891517	−	0.452987i	$-0.850358\pi$
$571$	−16395.2	+	6791.10i	−1.20160	+	0.497721i	−0.310088	+	0.950708i	$0.600358\pi$
$572$		0			0
$573$	12412.4	−	29966.2i	0.904949	−	2.18474i
$574$		0			0
$575$	2064.42			0.149726
$576$		0			0
$577$	−13473.2			−0.972091			−0.486046	−	0.873933i	$-0.661561\pi$
$577$	−13473.2			−0.972091			−0.486046	+	0.873933i	$0.661561\pi$
$578$		0			0
$579$	−3677.87	+	8879.15i	−0.263984	+	0.637314i
$580$		0			0
$581$	−9974.48	+	4131.56i	−0.712239	+	0.295019i
$582$		0			0
$583$	29447.5	−	29447.5i	2.09192	−	2.09192i
$584$		0			0
$585$	5981.42	+	5981.42i	0.422737	+	0.422737i
$586$		0			0
$587$	−873.151	−	2107.97i	−0.0613949	−	0.148220i	0.890205	−	0.455560i	$-0.150561\pi$
$587$	−873.151	−	2107.97i	−0.0613949	−	0.148220i	−0.951600	+	0.307340i	$0.900561\pi$
$588$		0			0
$589$	11608.6	+	4808.46i	0.812098	+	0.336382i
$590$		0			0
$591$		−	37436.9i		−	2.60566i
$592$		0			0
$593$			4205.87i			0.291255i	0.989339	+	0.145628i	$0.0465201\pi$
$593$			4205.87i			0.291255i	−0.989339	+	0.145628i	$0.953480\pi$
$594$		0			0
$595$	8355.30	+	3460.88i	0.575688	+	0.238458i
$596$		0			0
$597$	3610.39	+	8716.25i	0.247510	+	0.597541i
$598$		0			0
$599$	−9771.17	−	9771.17i	−0.666510	−	0.666510i	0.290397	−	0.956906i	$-0.406213\pi$
$599$	−9771.17	−	9771.17i	−0.666510	−	0.666510i	−0.956906	+	0.290397i	$0.906213\pi$
$600$		0			0
$601$	15649.6	−	15649.6i	1.06216	−	1.06216i	0.0642295	−	0.997935i	$-0.479541\pi$
$601$	15649.6	−	15649.6i	1.06216	−	1.06216i	0.997935	−	0.0642295i	$-0.0204590\pi$
$602$		0			0
$603$	37600.0	−	15574.4i	2.53929	−	1.05181i
$604$		0			0
$605$	11529.0	−	27833.4i	0.774744	−	1.87040i
$606$		0			0
$607$	−12239.3			−0.818417			−0.409209	−	0.912441i	$-0.634195\pi$
$607$	−12239.3			−0.818417			−0.409209	+	0.912441i	$0.634195\pi$
$608$		0			0
$609$	5392.79			0.358829
$610$		0			0
$611$	−1293.71	+	3123.29i	−0.0856592	+	0.206800i
$612$		0			0
$613$	17070.1	−	7070.67i	1.12472	−	0.465876i	0.258739	−	0.965947i	$-0.416693\pi$
$613$	17070.1	−	7070.67i	1.12472	−	0.465876i	0.865984	+	0.500072i	$0.166693\pi$
$614$		0			0
$615$	−1630.38	+	1630.38i	−0.106900	+	0.106900i
$616$		0			0
$617$	11602.2	+	11602.2i	0.757031	+	0.757031i	0.975781	−	0.218750i	$-0.0701978\pi$
$617$	11602.2	+	11602.2i	0.757031	+	0.757031i	−0.218750	+	0.975781i	$0.570198\pi$
$618$		0			0
$619$	8701.45	+	21007.2i	0.565009	+	1.36405i	0.905717	+	0.423884i	$0.139333\pi$
$619$	8701.45	+	21007.2i	0.565009	+	1.36405i	−0.340707	+	0.940169i	$0.610667\pi$
$620$		0			0
$621$	−13359.7	−	5533.78i	−0.863297	−	0.357589i
$622$		0			0
$623$			15549.1i			0.999938i
$624$		0			0
$625$			18073.5i			1.15670i
$626$		0			0
$627$	−35215.6	−	14586.8i	−2.24302	−	0.929089i
$628$		0			0
$629$	2166.56	+	5230.53i	0.137339	+	0.331566i
$630$		0			0
$631$	6552.95	+	6552.95i	0.413421	+	0.413421i	0.882928	−	0.469508i	$-0.155569\pi$
$631$	6552.95	+	6552.95i	0.413421	+	0.413421i	−0.469508	+	0.882928i	$0.655569\pi$
$632$		0			0
$633$	9572.83	−	9572.83i	0.601084	−	0.601084i
$634$		0			0
$635$	−3846.14	+	1593.12i	−0.240361	+	0.0995608i
$636$		0			0
$637$	−351.896	+	849.553i	−0.0218880	+	0.0528422i
$638$		0			0
$639$	36452.6			2.25672
$640$		0			0
$641$	7331.07			0.451731			0.225866	−	0.974158i	$-0.427479\pi$
$641$	7331.07			0.451731			0.225866	+	0.974158i	$0.427479\pi$
$642$		0			0
$643$	6386.47	−	15418.3i	0.391692	−	0.945628i	−0.597879	−	0.801586i	$-0.703990\pi$
$643$	6386.47	−	15418.3i	0.391692	−	0.945628i	0.989572	−	0.144042i	$-0.0460101\pi$
$644$		0			0
$645$	−22149.4	+	9174.59i	−1.35214	+	0.560076i
$646$		0			0
$647$	−2351.92	+	2351.92i	−0.142911	+	0.142911i	−0.774943	−	0.632031i	$-0.782221\pi$
$647$	−2351.92	+	2351.92i	−0.142911	+	0.142911i	0.632031	+	0.774943i	$0.282221\pi$
$648$		0			0
$649$	−21517.0	−	21517.0i	−1.30141	−	1.30141i
$650$		0			0
$651$	−9615.72	−	23214.4i	−0.578909	−	1.39761i
$652$		0			0
$653$	−18790.1	−	7783.11i	−1.12605	−	0.466427i	−0.259616	−	0.965712i	$-0.583596\pi$
$653$	−18790.1	−	7783.11i	−1.12605	−	0.466427i	−0.866438	+	0.499285i	$0.833596\pi$
$654$		0			0
$655$			14703.3i			0.877109i
$656$		0			0
$657$		−	4583.21i		−	0.272158i
$658$		0			0
$659$	−438.021	−	181.434i	−0.0258921	−	0.0107248i	0.369700	−	0.929151i	$-0.379461\pi$
$659$	−438.021	−	181.434i	−0.0258921	−	0.0107248i	−0.395592	+	0.918426i	$0.629461\pi$
$660$		0			0
$661$	−10971.1	−	26486.6i	−0.645577	−	1.55856i	−0.819050	−	0.573722i	$-0.805499\pi$
$661$	−10971.1	−	26486.6i	−0.645577	−	1.55856i	0.173473	−	0.984839i	$-0.444501\pi$
$662$		0			0
$663$	3966.93	+	3966.93i	0.232372	+	0.232372i
$664$		0			0
$665$	−10424.8	+	10424.8i	−0.607904	+	0.607904i
$666$		0			0
$667$	2937.43	−	1216.72i	0.170521	−	0.0706322i
$668$		0			0
$669$	4782.48	−	11545.9i	0.276385	−	0.667251i
$670$		0			0
$671$	−38984.6			−2.24290
$672$		0			0
$673$	27506.8			1.57550			0.787749	−	0.615996i	$-0.211246\pi$
$673$	27506.8			1.57550			0.787749	+	0.615996i	$0.211246\pi$
$674$		0			0
$675$	−1585.40	+	3827.51i	−0.0904034	+	0.218253i
$676$		0			0
$677$	−21591.8	+	8943.62i	−1.22576	+	0.507727i	−0.899237	−	0.437462i	$-0.855878\pi$
$677$	−21591.8	+	8943.62i	−1.22576	+	0.507727i	−0.326524	+	0.945189i	$0.605878\pi$
$678$		0			0
$679$	4603.38	−	4603.38i	0.260179	−	0.260179i
$680$		0			0
$681$	20794.1	+	20794.1i	1.17009	+	1.17009i
$682$		0			0
$683$	11875.5	+	28670.1i	0.665308	+	1.60619i	0.789368	+	0.613920i	$0.210408\pi$
$683$	11875.5	+	28670.1i	0.665308	+	1.60619i	−0.124060	+	0.992275i	$0.539592\pi$
$684$		0			0
$685$	1753.03	+	726.130i	0.0977810	+	0.0405022i
$686$		0			0
$687$		−	53445.8i		−	2.96810i
$688$		0			0
$689$		−	9991.91i		−	0.552484i
$690$		0			0
$691$	2996.03	+	1241.00i	0.164941	+	0.0683209i	0.463626	−	0.886031i	$-0.346548\pi$
$691$	2996.03	+	1241.00i	0.164941	+	0.0683209i	−0.298685	+	0.954352i	$0.596548\pi$
$692$		0			0
$693$	18501.7	+	44667.2i	1.01417	+	2.44843i
$694$		0			0
$695$	4505.16	+	4505.16i	0.245886	+	0.245886i
$696$		0			0
$697$	−685.832	+	685.832i	−0.0372708	+	0.0372708i
$698$		0			0
$699$	16806.9	−	6961.63i	0.909434	−	0.376700i
$700$		0			0
$701$	−1477.30	+	3566.51i	−0.0795959	+	0.192162i	−0.958668	−	0.284528i	$-0.908163\pi$
$701$	−1477.30	+	3566.51i	−0.0795959	+	0.192162i	0.879072	+	0.476689i	$0.158163\pi$
$702$		0			0
$703$	−9229.23			−0.495145
$704$		0			0
$705$	−24009.7			−1.28264
$706$		0			0
$707$	4571.05	−	11035.5i	0.243157	−	0.587032i
$708$		0			0
$709$	−15754.7	+	6525.83i	−0.834530	+	0.345674i	−0.758694	−	0.651447i	$-0.774162\pi$
$709$	−15754.7	+	6525.83i	−0.834530	+	0.345674i	−0.0758356	+	0.997120i	$0.524162\pi$
$710$		0			0
$711$	17182.5	−	17182.5i	0.906319	−	0.906319i
$712$		0			0
$713$	−10475.3	−	10475.3i	−0.550213	−	0.550213i
$714$		0			0
$715$	−4259.50	−	10283.4i	−0.222792	−	0.537868i
$716$		0			0
$717$	8253.69	+	3418.79i	0.429902	+	0.178071i
$718$		0			0
$719$			1013.44i			0.0525657i	0.999655	+	0.0262829i	$0.00836706\pi$
$719$			1013.44i			0.0525657i	−0.999655	+	0.0262829i	$0.991633\pi$
$720$		0			0
$721$			11081.4i			0.572388i
$722$		0			0
$723$	−956.575	−	396.226i	−0.0492053	−	0.0203815i
$724$		0			0
$725$	−348.586	−	841.560i	−0.0178568	−	0.0431100i
$726$		0			0
$727$	3353.13	+	3353.13i	0.171060	+	0.171060i	0.787445	−	0.616385i	$-0.211403\pi$
$727$	3353.13	+	3353.13i	0.171060	+	0.171060i	−0.616385	+	0.787445i	$0.711403\pi$
$728$		0			0
$729$	−21342.8	+	21342.8i	−1.08433	+	1.08433i
$730$		0			0
$731$	−9317.30	+	3859.35i	−0.471426	+	0.195271i
$732$		0			0
$733$	12032.3	−	29048.5i	0.606307	−	1.46375i	−0.260681	−	0.965425i	$-0.583947\pi$
$733$	12032.3	−	29048.5i	0.606307	−	1.46375i	0.866988	−	0.498329i	$-0.166053\pi$
$734$		0			0
$735$	−6530.79			−0.327744
$736$		0			0
$737$	−53551.6			−2.67652
$738$		0			0
$739$	−827.863	+	1998.64i	−0.0412090	+	0.0994873i	−0.943144	−	0.332385i	$-0.892147\pi$
$739$	−827.863	+	1998.64i	−0.0412090	+	0.0994873i	0.901935	+	0.431872i	$0.142147\pi$
$740$		0			0
$741$	−8449.28	+	3499.81i	−0.418883	+	0.173507i
$742$		0			0
$743$	−15379.7	+	15379.7i	−0.759391	+	0.759391i	−0.976211	−	0.216821i	$-0.930431\pi$
$743$	−15379.7	+	15379.7i	−0.759391	+	0.759391i	0.216821	+	0.976211i	$0.430431\pi$
$744$		0			0
$745$	−20716.2	−	20716.2i	−1.01877	−	1.01877i
$746$		0			0
$747$	−11545.3	−	27872.8i	−0.565489	−	1.36521i
$748$		0			0
$749$	9606.29	+	3979.06i	0.468633	+	0.194114i
$750$		0			0
$751$			23971.2i			1.16474i	0.812923	+	0.582371i	$0.197875\pi$
$751$			23971.2i			1.16474i	−0.812923	+	0.582371i	$0.802125\pi$
$752$		0			0
$753$		−	54552.3i		−	2.64010i
$754$		0			0
$755$	−3063.88	−	1269.10i	−0.147690	−	0.0611753i
$756$		0			0
$757$	−9946.89	−	24013.9i	−0.477577	−	1.15297i	−0.960742	−	0.277443i	$-0.910513\pi$
$757$	−9946.89	−	24013.9i	−0.477577	−	1.15297i	0.483165	−	0.875529i	$-0.339487\pi$
$758$		0			0
$759$	31777.4	+	31777.4i	1.51969	+	1.51969i
$760$		0			0
$761$	26392.4	−	26392.4i	1.25719	−	1.25719i	0.304763	−	0.952428i	$-0.401423\pi$
$761$	26392.4	−	26392.4i	1.25719	−	1.25719i	0.952428	−	0.304763i	$-0.0985771\pi$
$762$		0			0
$763$	−1970.09	+	816.037i	−0.0934757	+	0.0387189i
$764$		0			0
$765$	−9671.13	+	23348.2i	−0.457073	+	1.10347i
$766$		0			0
$767$	−7300.99			−0.343707
$768$		0			0
$769$	−13563.7			−0.636046			−0.318023	−	0.948083i	$-0.603019\pi$
$769$	−13563.7			−0.636046			−0.318023	+	0.948083i	$0.603019\pi$
$770$		0			0
$771$	−14865.3	+	35888.1i	−0.694374	+	1.67637i
$772$		0			0
$773$	−3266.20	+	1352.90i	−0.151975	+	0.0629502i	−0.457374	−	0.889274i	$-0.651210\pi$
$773$	−3266.20	+	1352.90i	−0.151975	+	0.0629502i	0.305399	+	0.952224i	$0.401210\pi$
$774$		0			0
$775$	−3001.12	+	3001.12i	−0.139101	+	0.139101i
$776$		0			0
$777$	13050.5	+	13050.5i	0.602552	+	0.602552i
$778$		0			0
$779$	−605.073	−	1460.77i	−0.0278292	−	0.0671857i
$780$		0			0
$781$	−44314.3	−	18355.6i	−2.03033	−	0.840992i
$782$		0			0
$783$			6380.49i			0.291213i
$784$		0			0
$785$			18280.7i			0.831166i
$786$		0			0
$787$	10905.7	+	4517.30i	0.493960	+	0.204605i	0.615736	−	0.787953i	$-0.288859\pi$
$787$	10905.7	+	4517.30i	0.493960	+	0.204605i	−0.121775	+	0.992558i	$0.538859\pi$
$788$		0			0
$789$	−2090.91	−	5047.90i	−0.0943451	−	0.227769i
$790$		0			0
$791$	17063.7	+	17063.7i	0.767024	+	0.767024i
$792$		0			0
$793$	−6613.98	+	6613.98i	−0.296178	+	0.296178i
$794$		0			0
$795$	65562.3	−	27156.8i	2.92485	−	1.21151i
$796$		0			0
$797$	−1753.95	+	4234.40i	−0.0779523	+	0.188193i	−0.958051	−	0.286597i	$-0.907476\pi$
$797$	−1753.95	+	4234.40i	−0.0779523	+	0.188193i	0.880099	+	0.474790i	$0.157476\pi$
$798$		0			0
$799$	−10099.8			−0.447192
$800$		0			0
$801$	−43450.6			−1.91667
$802$		0			0
$803$	−2307.86	+	5571.66i	−0.101423	+	0.244856i
$804$		0			0
$805$	16058.7	−	6651.74i	0.703100	−	0.291234i
$806$		0			0
$807$	16025.5	−	16025.5i	0.699039	−	0.699039i
$808$		0			0
$809$	7035.78	+	7035.78i	0.305766	+	0.305766i	0.843265	−	0.537499i	$-0.180631\pi$
$809$	7035.78	+	7035.78i	0.305766	+	0.305766i	−0.537499	+	0.843265i	$0.680631\pi$
$810$		0			0
$811$	−12951.5	−	31267.6i	−0.560773	−	1.35383i	−0.909149	−	0.416472i	$-0.863266\pi$
$811$	−12951.5	−	31267.6i	−0.560773	−	1.35383i	0.348375	−	0.937355i	$-0.386734\pi$
$812$		0			0
$813$	−13194.2	−	5465.20i	−0.569176	−	0.235760i
$814$		0			0
$815$		−	42515.7i		−	1.82731i
$816$		0			0
$817$		−	16440.3i		−	0.704007i
$818$		0			0
$819$	10717.0	+	4439.13i	0.457244	+	0.189397i
$820$		0			0
$821$	14509.7	+	35029.4i	0.616798	+	1.48908i	0.855402	+	0.517964i	$0.173310\pi$
$821$	14509.7	+	35029.4i	0.616798	+	1.48908i	−0.238605	+	0.971117i	$0.576690\pi$
$822$		0			0
$823$	−20334.4	−	20334.4i	−0.861254	−	0.861254i	0.130230	−	0.991484i	$-0.458428\pi$
$823$	−20334.4	−	20334.4i	−0.861254	−	0.861254i	−0.991484	+	0.130230i	$0.958428\pi$
$824$		0			0
$825$	9104.08	−	9104.08i	0.384198	−	0.384198i
$826$		0			0
$827$	−8362.20	+	3463.74i	−0.351611	+	0.145642i	−0.551496	−	0.834177i	$-0.685943\pi$
$827$	−8362.20	+	3463.74i	−0.351611	+	0.145642i	0.199885	+	0.979819i	$0.435943\pi$
$828$		0			0
$829$	−10022.4	+	24196.3i	−0.419895	+	1.01372i	0.562482	+	0.826809i	$0.309847\pi$
$829$	−10022.4	+	24196.3i	−0.419895	+	1.01372i	−0.982377	+	0.186908i	$0.940153\pi$
$830$		0			0
$831$	54953.5			2.29400
$832$		0			0
$833$	−2747.22			−0.114268
$834$		0			0
$835$	−1418.86	+	3425.43i	−0.0588044	+	0.141966i
$836$		0			0
$837$	27466.1	−	11376.8i	1.13425	−	0.469822i
$838$		0			0
$839$	−25343.9	+	25343.9i	−1.04287	+	1.04287i	−0.0438328	+	0.999039i	$0.513957\pi$
$839$	−25343.9	+	25343.9i	−1.04287	+	1.04287i	−0.999039	+	0.0438328i	$0.986043\pi$
$840$		0			0
$841$	16253.6	+	16253.6i	0.666433	+	0.666433i
$842$		0			0
$843$	−16492.7	−	39816.9i	−0.673829	−	1.62677i
$844$		0			0
$845$	22335.7	+	9251.75i	0.909315	+	0.376651i
$846$		0			0
$847$		−	41313.3i		−	1.67597i
$848$		0			0
$849$		−	19872.6i		−	0.803328i
$850$		0			0
$851$	10053.0	+	4164.08i	0.404949	+	0.167735i
$852$		0			0
$853$	−380.743	−	919.196i	−0.0152830	−	0.0368964i	0.916054	−	0.401055i	$-0.131356\pi$
$853$	−380.743	−	919.196i	−0.0152830	−	0.0368964i	−0.931337	+	0.364159i	$0.881356\pi$
$854$		0			0
$855$	−29131.2	−	29131.2i	−1.16522	−	1.16522i
$856$		0			0
$857$	13094.2	−	13094.2i	0.521926	−	0.521926i	−0.396227	−	0.918153i	$-0.629681\pi$
$857$	13094.2	−	13094.2i	0.521926	−	0.521926i	0.918153	+	0.396227i	$0.129681\pi$
$858$		0			0
$859$	−11812.2	+	4892.78i	−0.469182	+	0.194342i	−0.604732	−	0.796429i	$-0.706720\pi$
$859$	−11812.2	+	4892.78i	−0.469182	+	0.194342i	0.135550	+	0.990770i	$0.456720\pi$
$860$		0			0
$861$	−1209.99	+	2921.18i	−0.0478937	+	0.115626i
$862$		0			0
$863$	10032.7			0.395732			0.197866	−	0.980229i	$-0.436599\pi$
$863$	10032.7			0.395732			0.197866	+	0.980229i	$0.436599\pi$
$864$		0			0
$865$	44809.0			1.76133
$866$		0			0
$867$	9740.45	−	23515.5i	0.381549	−	0.921141i
$868$		0			0
$869$	−29540.3	+	12236.0i	−1.15315	+	0.477650i
$870$		0			0
$871$	−9085.36	+	9085.36i	−0.353439	+	0.353439i
$872$		0			0
$873$	12863.8	+	12863.8i	0.498708	+	0.498708i
$874$		0			0
$875$	7889.33	+	19046.5i	0.304809	+	0.735874i
$876$		0			0
$877$	−9750.86	−	4038.94i	−0.375442	−	0.155513i	0.186979	−	0.982364i	$-0.440130\pi$
$877$	−9750.86	−	4038.94i	−0.375442	−	0.155513i	−0.562422	+	0.826850i	$0.690130\pi$
$878$		0			0
$879$			70058.4i			2.68829i
$880$		0			0
$881$			16390.5i			0.626800i	0.949621	+	0.313400i	$0.101468\pi$
$881$			16390.5i			0.626800i	−0.949621	+	0.313400i	$0.898532\pi$
$882$		0			0
$883$	−4222.47	−	1749.01i	−0.160926	−	0.0666577i	0.300766	−	0.953698i	$-0.402758\pi$
$883$	−4222.47	−	1749.01i	−0.160926	−	0.0666577i	−0.461692	+	0.887040i	$0.652758\pi$
$884$		0			0
$885$	−19843.2	−	47905.8i	−0.753698	−	1.81959i
$886$		0			0
$887$	−34678.9	−	34678.9i	−1.31274	−	1.31274i	−0.919386	−	0.393358i	$-0.871313\pi$
$887$	−34678.9	−	34678.9i	−1.31274	−	1.31274i	−0.393358	−	0.919386i	$-0.628687\pi$
$888$		0			0
$889$	−4036.76	+	4036.76i	−0.152293	+	0.152293i
$890$		0			0
$891$	−11349.6	+	4701.18i	−0.426742	+	0.176762i
$892$		0			0
$893$	6300.71	−	15211.3i	0.236109	−	0.570017i
$894$		0			0
$895$	21718.6			0.811141
$896$		0			0
$897$	10782.5			0.401356
$898$		0			0
$899$	−2501.45	+	6039.03i	−0.0928008	+	0.224041i
$900$		0			0
$901$	27579.2	−	11423.7i	1.01975	−	0.422395i
$902$		0			0
$903$	−23247.2	+	23247.2i	−0.856720	+	0.856720i
$904$		0			0
$905$	24218.0	+	24218.0i	0.889541	+	0.889541i
$906$		0			0
$907$	6567.47	+	15855.3i	0.240429	+	0.580447i	0.997326	−	0.0730878i	$-0.0232853\pi$
$907$	6567.47	+	15855.3i	0.240429	+	0.580447i	−0.756897	+	0.653535i	$0.773285\pi$
$908$		0			0
$909$	30837.7	+	12773.4i	1.12522	+	0.466080i
$910$		0			0
$911$		−	21528.6i		−	0.782958i	−0.920187	−	0.391479i	$-0.871964\pi$
$911$		−	21528.6i		−	0.782958i	0.920187	−	0.391479i	$-0.128036\pi$
$912$		0			0
$913$			39697.7i			1.43899i
$914$		0			0
$915$	−61373.9	−	25421.9i	−2.21744	−	0.918495i
$916$		0			0
$917$	7716.03	+	18628.1i	0.277869	+	0.670834i
$918$		0			0
$919$	27666.0	+	27666.0i	0.993054	+	0.993054i	0.999976	−	0.00692164i	$-0.00220324\pi$
$919$	27666.0	+	27666.0i	0.993054	+	0.993054i	−0.00692164	+	0.999976i	$0.502203\pi$
$920$		0			0
$921$	21834.4	−	21834.4i	0.781181	−	0.781181i
$922$		0			0
$923$	−10632.4	+	4404.06i	−0.379164	+	0.157055i
$924$		0			0
$925$	1192.99	−	2880.13i	0.0424057	−	0.102376i
$926$		0			0
$927$	−30965.9			−1.09715
$928$		0			0
$929$	42072.0			1.48583			0.742915	−	0.669386i	$-0.233443\pi$
$929$	42072.0			1.48583			0.742915	+	0.669386i	$0.233443\pi$
$930$		0			0
$931$	1713.83	−	4137.55i	0.0603314	−	0.145653i
$932$		0			0
$933$	23981.8	−	9933.60i	0.841511	−	0.348565i
$934$		0			0
$935$	23513.8	−	23513.8i	0.822442	−	0.822442i
$936$		0			0
$937$	−17029.9	−	17029.9i	−0.593749	−	0.593749i	0.344893	−	0.938642i	$-0.387915\pi$
$937$	−17029.9	−	17029.9i	−0.593749	−	0.593749i	−0.938642	+	0.344893i	$0.887915\pi$
$938$		0			0
$939$	34187.5	+	82535.8i	1.18814	+	2.86843i
$940$		0			0
$941$	50185.8	+	20787.6i	1.73859	+	0.720146i	0.998885	+	0.0472119i	$0.0150336\pi$
$941$	50185.8	+	20787.6i	1.73859	+	0.720146i	0.739702	+	0.672934i	$0.234966\pi$
$942$		0			0
$943$			1864.15i			0.0643745i
$944$		0			0
$945$			34881.7i			1.20074i
$946$		0			0
$947$	4647.70	+	1925.14i	0.159483	+	0.0660599i	0.460997	−	0.887402i	$-0.347492\pi$
$947$	4647.70	+	1925.14i	0.159483	+	0.0660599i	−0.301514	+	0.953462i	$0.597492\pi$
$948$		0			0
$949$	553.725	+	1336.81i	0.0189407	+	0.0457268i
$950$		0			0
$951$	5105.19	+	5105.19i	0.174077	+	0.174077i
$952$		0			0
$953$	−444.450	+	444.450i	−0.0151072	+	0.0151072i	−0.714620	−	0.699513i	$-0.753400\pi$
$953$	−444.450	+	444.450i	−0.0151072	+	0.0151072i	0.699513	+	0.714620i	$0.253400\pi$
$954$		0			0
$955$	−42617.2	+	17652.6i	−1.44404	+	0.598142i
$956$		0			0
$957$	7588.29	−	18319.8i	0.256316	−	0.618802i
$958$		0			0
$959$	2602.04			0.0876165
$960$		0			0
$961$	665.482			0.0223383
$962$		0			0
$963$	−11119.1	+	26844.0i	−0.372076	+	0.898271i
$964$		0			0
$965$	12627.7	−	5230.58i	0.421244	−	0.174485i
$966$		0			0
$967$	30115.1	−	30115.1i	1.00148	−	1.00148i	0.00148526	−	0.999999i	$-0.499527\pi$
$967$	30115.1	−	30115.1i	1.00148	−	1.00148i	0.999999	−	0.00148526i	$-0.000472774\pi$
$968$		0			0
$969$	−19320.0	−	19320.0i	−0.640504	−	0.640504i
$970$		0			0
$971$	2287.20	+	5521.79i	0.0755919	+	0.182495i	0.957158	−	0.289565i	$-0.0935106\pi$
$971$	2287.20	+	5521.79i	0.0755919	+	0.182495i	−0.881566	+	0.472060i	$0.843511\pi$
$972$		0			0
$973$	8071.96	+	3343.52i	0.265956	+	0.110163i
$974$		0			0
$975$		−	3089.13i		−	0.101468i
$976$		0			0
$977$			10157.2i			0.332608i	0.986074	+	0.166304i	$0.0531834\pi$
$977$			10157.2i			0.332608i	−0.986074	+	0.166304i	$0.946817\pi$
$978$		0			0
$979$	52821.5	+	21879.4i	1.72440	+	0.714268i
$980$		0			0
$981$	−2280.34	−	5505.24i	−0.0742159	−	0.179173i
$982$		0			0
$983$	3880.55	+	3880.55i	0.125911	+	0.125911i	0.767254	−	0.641343i	$-0.221623\pi$
$983$	3880.55	+	3880.55i	0.125911	+	0.125911i	−0.641343	+	0.767254i	$0.721623\pi$
$984$		0			0
$985$	−37647.7	+	37647.7i	−1.21782	+	1.21782i
$986$		0			0
$987$	−30418.7	+	12599.8i	−0.980991	+	0.406340i
$988$		0			0
$989$	−7417.60	+	17907.7i	−0.238489	+	0.575764i
$990$		0			0
$991$	15197.2			0.487139			0.243569	−	0.969884i	$-0.421682\pi$
$991$	15197.2			0.487139			0.243569	+	0.969884i	$0.421682\pi$
$992$		0			0
$993$	8610.00			0.275156
$994$		0			0
$995$	5134.61	−	12396.0i	0.163596	−	0.394956i
$996$		0			0
$997$	1293.68	−	535.861i	0.0410946	−	0.0170219i	−0.362041	−	0.932162i	$-0.617920\pi$
$997$	1293.68	−	535.861i	0.0410946	−	0.0170219i	0.403136	+	0.915140i	$0.367920\pi$
$998$		0			0
$999$	−15440.7	+	15440.7i	−0.489010	+	0.489010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.b.33.11		44
4.3	odd	2		256.4.g.a.33.1		44
8.3	odd	2		128.4.g.a.17.11		44
8.5	even	2		32.4.g.a.13.10	yes	44
32.5	even	8	inner	256.4.g.b.225.11		44
32.11	odd	8		128.4.g.a.113.11		44
32.21	even	8		32.4.g.a.5.10	✓	44
32.27	odd	8		256.4.g.a.225.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.10	✓	44	32.21	even	8
32.4.g.a.13.10	yes	44	8.5	even	2
128.4.g.a.17.11		44	8.3	odd	2
128.4.g.a.113.11		44	32.11	odd	8
256.4.g.a.33.1		44	4.3	odd	2
256.4.g.a.225.1		44	32.27	odd	8
256.4.g.b.33.11		44	1.1	even	1	trivial
256.4.g.b.225.11		44	32.5	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.28810 - 7.93817i) q^{3} +(-11.2895 + 4.67626i) q^{5} +(-11.8490 + 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +O(q^{10})\)	\(q+(3.28810 - 7.93817i) q^{3} +(-11.2895 + 4.67626i) q^{5} +(-11.8490 + 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +(23.5791 + 56.9250i) q^{11} +(13.6580 + 5.65734i) q^{13} +104.994i q^{15} +44.1663i q^{17} +(-66.5184 - 27.5528i) q^{19} +(55.0988 + 133.020i) q^{21} +(60.0240 + 60.0240i) q^{23} +(17.1966 - 17.1966i) q^{25} +(-157.383 + 65.1901i) q^{27} +(14.3335 - 34.6041i) q^{29} -174.518 q^{31} +529.411 q^{33} +(78.3602 - 189.178i) q^{35} +(118.428 - 49.0545i) q^{37} +(89.8179 - 89.8179i) q^{39} +(15.5284 + 15.5284i) q^{41} +(87.3822 + 210.959i) q^{43} +(528.642 + 218.971i) q^{45} +228.677i q^{47} +62.2017i q^{49} +(350.600 + 145.223i) q^{51} +(-258.652 - 624.440i) q^{53} +(-532.392 - 532.392i) q^{55} +(-437.438 + 437.438i) q^{57} +(-456.272 + 188.994i) q^{59} +(-242.128 + 584.548i) q^{61} +784.667 q^{63} -180.647 q^{65} +(-332.601 + 802.971i) q^{67} +(673.845 - 279.116i) q^{69} +(-550.460 + 550.460i) q^{71} +(69.2096 + 69.2096i) q^{73} +(-79.9655 - 193.054i) q^{75} +(-953.895 - 395.116i) q^{77} +518.934i q^{79} +199.379i q^{81} +(595.241 + 246.557i) q^{83} +(-206.533 - 498.615i) q^{85} +(-227.563 - 227.563i) q^{87} +(656.135 - 656.135i) q^{89} +(-228.868 + 94.8003i) q^{91} +(-573.832 + 1385.35i) q^{93} +879.802 q^{95} -388.503 q^{97} +(1104.12 - 2665.58i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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