LMFDB - Embedded newform 128.4.g.a.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([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("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.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:	$7.55224448073$
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			49.6
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +O(q^{10})$	\(q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +(-34.4676 - 14.2769i) q^{11} +(15.3924 + 37.1606i) q^{13} -25.3563i q^{15} -103.310i q^{17} +(-12.4092 - 29.9584i) q^{19} +(-28.0313 - 11.6109i) q^{21} +(72.3950 - 72.3950i) q^{23} +(-120.761 - 120.761i) q^{25} +(-29.2409 + 70.5937i) q^{27} +(23.9061 - 9.90225i) q^{29} +124.769 q^{31} -55.0042 q^{33} +(-326.986 + 135.442i) q^{35} +(18.0425 - 43.5584i) q^{37} +(41.9327 + 41.9327i) q^{39} +(-45.1360 + 45.1360i) q^{41} +(457.470 + 189.490i) q^{43} +(163.395 + 394.469i) q^{45} -582.766i q^{47} +80.5012i q^{49} +(-58.2884 - 140.721i) q^{51} +(395.810 + 163.950i) q^{53} +(-453.698 + 453.698i) q^{55} +(-33.8056 - 33.8056i) q^{57} +(-142.805 + 344.762i) q^{59} +(-34.8958 + 14.4543i) q^{61} +510.904 q^{63} +691.757 q^{65} +(-196.686 + 81.4699i) q^{67} +(57.7649 - 139.457i) q^{69} +(520.831 + 520.831i) q^{71} +(-582.329 + 582.329i) q^{73} +(-232.626 - 96.3570i) q^{75} +(293.807 + 709.314i) q^{77} +157.779i q^{79} -557.655i q^{81} +(-54.5324 - 131.653i) q^{83} +(-1641.51 - 679.936i) q^{85} +(26.9761 - 26.9761i) q^{87} +(-272.884 - 272.884i) q^{89} +(316.763 - 764.733i) q^{91} +(169.951 - 70.3959i) q^{93} -557.686 q^{95} +788.873 q^{97} +(855.703 - 354.444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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
$3$	1.36212	−	0.564209i	0.262140	−	0.108582i	−0.247743	−	0.968826i	$-0.579689\pi$
$3$	1.36212	−	0.564209i	0.262140	−	0.108582i	0.509883	+	0.860244i	$0.329689\pi$
$4$		0			0
$5$	6.58151	−	15.8892i	0.588669	−	1.42117i	−0.296107	−	0.955155i	$-0.595689\pi$
$5$	6.58151	−	15.8892i	0.588669	−	1.42117i	0.884776	−	0.466017i	$-0.154311\pi$
$6$		0			0
$7$	−14.5517	−	14.5517i	−0.785715	−	0.785715i	0.195073	−	0.980789i	$-0.437506\pi$
$7$	−14.5517	−	14.5517i	−0.785715	−	0.785715i	−0.980789	+	0.195073i	$0.937506\pi$
$8$		0			0
$9$	−17.5548	+	17.5548i	−0.650179	+	0.650179i
$10$		0			0
$11$	−34.4676	−	14.2769i	−0.944761	−	0.391333i	−0.143502	−	0.989650i	$-0.545836\pi$
$11$	−34.4676	−	14.2769i	−0.944761	−	0.391333i	−0.801259	+	0.598317i	$0.795836\pi$
$12$		0			0
$13$	15.3924	+	37.1606i	0.328391	+	0.792807i	0.998712	+	0.0507354i	$0.0161565\pi$
$13$	15.3924	+	37.1606i	0.328391	+	0.792807i	−0.670321	+	0.742071i	$0.733843\pi$
$14$		0			0
$15$		−	25.3563i		−	0.436465i
$16$		0			0
$17$		−	103.310i		−	1.47390i	−0.675946	−	0.736951i	$-0.736265\pi$
$17$		−	103.310i		−	1.47390i	0.675946	−	0.736951i	$-0.263735\pi$
$18$		0			0
$19$	−12.4092	−	29.9584i	−0.149835	−	0.361733i	0.831085	−	0.556145i	$-0.187720\pi$
$19$	−12.4092	−	29.9584i	−0.149835	−	0.361733i	−0.980920	+	0.194412i	$0.937720\pi$
$20$		0			0
$21$	−28.0313	−	11.6109i	−0.291282	−	0.120653i
$22$		0			0
$23$	72.3950	−	72.3950i	0.656322	−	0.656322i	−0.298186	−	0.954508i	$-0.596381\pi$
$23$	72.3950	−	72.3950i	0.656322	−	0.656322i	0.954508	+	0.298186i	$0.0963815\pi$
$24$		0			0
$25$	−120.761	−	120.761i	−0.966091	−	0.966091i
$26$		0			0
$27$	−29.2409	+	70.5937i	−0.208422	+	0.503176i
$28$		0			0
$29$	23.9061	−	9.90225i	0.153078	−	0.0634069i	−0.304829	−	0.952407i	$-0.598599\pi$
$29$	23.9061	−	9.90225i	0.153078	−	0.0634069i	0.457907	+	0.889000i	$0.348599\pi$
$30$		0			0
$31$	124.769			0.722877			0.361439	−	0.932396i	$-0.382286\pi$
$31$	124.769			0.722877			0.361439	+	0.932396i	$0.382286\pi$
$32$		0			0
$33$	−55.0042			−0.290152
$34$		0			0
$35$	−326.986	+	135.442i	−1.57916	+	0.654110i
$36$		0			0
$37$	18.0425	−	43.5584i	0.0801667	−	0.193540i	−0.878714	−	0.477348i	$-0.841598\pi$
$37$	18.0425	−	43.5584i	0.0801667	−	0.193540i	0.958881	+	0.283809i	$0.0915980\pi$
$38$		0			0
$39$	41.9327	+	41.9327i	0.172169	+	0.172169i
$40$		0			0
$41$	−45.1360	+	45.1360i	−0.171928	+	0.171928i	−0.787826	−	0.615898i	$-0.788793\pi$
$41$	−45.1360	+	45.1360i	−0.171928	+	0.171928i	0.615898	+	0.787826i	$0.288793\pi$
$42$		0			0
$43$	457.470	+	189.490i	1.62241	+	0.672023i	0.994351	−	0.106144i	$-0.0338506\pi$
$43$	457.470	+	189.490i	1.62241	+	0.672023i	0.628057	+	0.778168i	$0.283851\pi$
$44$		0			0
$45$	163.395	+	394.469i	0.541276	+	1.30676i
$46$		0			0
$47$		−	582.766i		−	1.80862i	−0.426877	−	0.904310i	$-0.640386\pi$
$47$		−	582.766i		−	1.80862i	0.426877	−	0.904310i	$-0.359614\pi$
$48$		0			0
$49$			80.5012i			0.234697i
$50$		0			0
$51$	−58.2884	−	140.721i	−0.160039	−	0.386369i
$52$		0			0
$53$	395.810	+	163.950i	1.02582	+	0.424910i	0.831203	−	0.555969i	$-0.187653\pi$
$53$	395.810	+	163.950i	1.02582	+	0.424910i	0.194620	+	0.980879i	$0.437653\pi$
$54$		0			0
$55$	−453.698	+	453.698i	−1.11230	+	1.11230i
$56$		0			0
$57$	−33.8056	−	33.8056i	−0.0785555	−	0.0785555i
$58$		0			0
$59$	−142.805	+	344.762i	−0.315113	+	0.760750i	0.684387	+	0.729119i	$0.260070\pi$
$59$	−142.805	+	344.762i	−0.315113	+	0.760750i	−0.999500	+	0.0316306i	$0.989930\pi$
$60$		0			0
$61$	−34.8958	+	14.4543i	−0.0732450	+	0.0303391i	−0.419005	−	0.907984i	$-0.637621\pi$
$61$	−34.8958	+	14.4543i	−0.0732450	+	0.0303391i	0.345760	+	0.938323i	$0.387621\pi$
$62$		0			0
$63$	510.904			1.02171
$64$		0			0
$65$	691.757			1.32003
$66$		0			0
$67$	−196.686	+	81.4699i	−0.358642	+	0.148554i	−0.554727	−	0.832033i	$-0.687177\pi$
$67$	−196.686	+	81.4699i	−0.358642	+	0.148554i	0.196085	+	0.980587i	$0.437177\pi$
$68$		0			0
$69$	57.7649	−	139.457i	0.100784	−	0.243313i
$70$		0			0
$71$	520.831	+	520.831i	0.870582	+	0.870582i	0.992536	−	0.121954i	$-0.0389161\pi$
$71$	520.831	+	520.831i	0.870582	+	0.870582i	−0.121954	+	0.992536i	$0.538916\pi$
$72$		0			0
$73$	−582.329	+	582.329i	−0.933649	+	0.933649i	−0.997932	−	0.0642823i	$-0.979524\pi$
$73$	−582.329	+	582.329i	−0.933649	+	0.933649i	0.0642823	+	0.997932i	$0.479524\pi$
$74$		0			0
$75$	−232.626	−	96.3570i	−0.358152	−	0.148351i
$76$		0			0
$77$	293.807	+	709.314i	0.434837	+	1.04979i
$78$		0			0
$79$			157.779i			0.224702i	0.993669	+	0.112351i	$0.0358381\pi$
$79$			157.779i			0.224702i	−0.993669	+	0.112351i	$0.964162\pi$
$80$		0			0
$81$		−	557.655i		−	0.764959i
$82$		0			0
$83$	−54.5324	−	131.653i	−0.0721170	−	0.174106i	0.883711	−	0.468034i	$-0.155037\pi$
$83$	−54.5324	−	131.653i	−0.0721170	−	0.174106i	−0.955828	+	0.293928i	$0.905037\pi$
$84$		0			0
$85$	−1641.51	−	679.936i	−2.09467	−	0.867640i
$86$		0			0
$87$	26.9761	−	26.9761i	0.0332430	−	0.0332430i
$88$		0			0
$89$	−272.884	−	272.884i	−0.325007	−	0.325007i	0.525677	−	0.850684i	$-0.323812\pi$
$89$	−272.884	−	272.884i	−0.325007	−	0.325007i	−0.850684	+	0.525677i	$0.823812\pi$
$90$		0			0
$91$	316.763	−	764.733i	0.364898	−	0.880943i
$92$		0			0
$93$	169.951	−	70.3959i	0.189495	−	0.0784915i
$94$		0			0
$95$	−557.686			−0.602288
$96$		0			0
$97$	788.873			0.825752			0.412876	−	0.910787i	$-0.364524\pi$
$97$	788.873			0.825752			0.412876	+	0.910787i	$0.364524\pi$
$98$		0			0
$99$	855.703	−	354.444i	0.868701	−	0.359828i
$100$		0			0
$101$	585.257	−	1412.93i	0.576586	−	1.39200i	−0.319272	−	0.947663i	$-0.603438\pi$
$101$	585.257	−	1412.93i	0.576586	−	1.39200i	0.895858	−	0.444339i	$-0.146562\pi$
$102$		0			0
$103$	−1120.20	−	1120.20i	−1.07161	−	1.07161i	−0.997230	−	0.0743853i	$-0.976301\pi$
$103$	−1120.20	−	1120.20i	−1.07161	−	1.07161i	−0.0743853	−	0.997230i	$-0.523699\pi$
$104$		0			0
$105$	−368.977	+	368.977i	−0.342937	+	0.342937i
$106$		0			0
$107$	1665.63	+	689.926i	1.50488	+	0.623343i	0.974494	−	0.224413i	$-0.0720463\pi$
$107$	1665.63	+	689.926i	1.50488	+	0.623343i	0.530388	+	0.847755i	$0.322046\pi$
$108$		0			0
$109$	−342.786	−	827.559i	−0.301220	−	0.727209i	−0.999930	−	0.0118047i	$-0.996242\pi$
$109$	−342.786	−	827.559i	−0.301220	−	0.727209i	0.698710	−	0.715405i	$-0.253758\pi$
$110$		0			0
$111$		−	69.5116i		−	0.0594392i
$112$		0			0
$113$			924.353i			0.769521i	0.923016	+	0.384760i	$0.125716\pi$
$113$			924.353i			0.769521i	−0.923016	+	0.384760i	$0.874284\pi$
$114$		0			0
$115$	−673.829	−	1626.77i	−0.546390	−	1.31910i
$116$		0			0
$117$	−922.559	−	382.137i	−0.728980	−	0.301953i
$118$		0			0
$119$	−1503.33	+	1503.33i	−1.15807	+	1.15807i
$120$		0			0
$121$	43.0249	+	43.0249i	0.0323253	+	0.0323253i
$122$		0			0
$123$	−36.0145	+	86.9467i	−0.0264010	+	0.0637376i
$124$		0			0
$125$	−727.445	+	301.318i	−0.520517	+	0.215605i
$126$		0			0
$127$	−569.829			−0.398143			−0.199072	−	0.979985i	$-0.563793\pi$
$127$	−569.829			−0.398143			−0.199072	+	0.979985i	$0.563793\pi$
$128$		0			0
$129$	730.042			0.498268
$130$		0			0
$131$	−1171.87	+	485.406i	−0.781581	+	0.323742i	−0.737553	−	0.675289i	$-0.764019\pi$
$131$	−1171.87	+	485.406i	−0.781581	+	0.323742i	−0.0440278	+	0.999030i	$0.514019\pi$
$132$		0			0
$133$	−255.370	+	616.518i	−0.166492	+	0.401947i
$134$		0			0
$135$	929.227	+	929.227i	0.592408	+	0.592408i
$136$		0			0
$137$	946.041	−	946.041i	0.589969	−	0.589969i	−0.347654	−	0.937623i	$-0.613022\pi$
$137$	946.041	−	946.041i	0.589969	−	0.589969i	0.937623	+	0.347654i	$0.113022\pi$
$138$		0			0
$139$	−1313.93	−	544.249i	−0.801772	−	0.332105i	−0.0561063	−	0.998425i	$-0.517869\pi$
$139$	−1313.93	−	544.249i	−0.801772	−	0.332105i	−0.745666	+	0.666320i	$0.767869\pi$
$140$		0			0
$141$	−328.802	−	793.797i	−0.196384	−	0.474112i
$142$		0			0
$143$		−	1500.59i		−	0.877523i
$144$		0			0
$145$		−	445.021i		−	0.254876i
$146$		0			0
$147$	45.4195	+	109.652i	0.0254839	+	0.0615236i
$148$		0			0
$149$	2438.15	+	1009.92i	1.34054	+	0.555272i	0.933644	−	0.358201i	$-0.116610\pi$
$149$	2438.15	+	1009.92i	1.34054	+	0.555272i	0.406900	+	0.913473i	$0.366610\pi$
$150$		0			0
$151$	872.975	−	872.975i	0.470475	−	0.470475i	−0.431594	−	0.902068i	$-0.642049\pi$
$151$	872.975	−	872.975i	0.470475	−	0.470475i	0.902068	+	0.431594i	$0.142049\pi$
$152$		0			0
$153$	1813.59	+	1813.59i	0.958301	+	0.958301i
$154$		0			0
$155$	821.170	−	1982.48i	0.425535	−	1.02733i
$156$		0			0
$157$	−866.489	+	358.912i	−0.440467	+	0.182447i	−0.591885	−	0.806022i	$-0.701616\pi$
$157$	−866.489	+	358.912i	−0.440467	+	0.182447i	0.151418	+	0.988470i	$0.451616\pi$
$158$		0			0
$159$	631.643			0.315047
$160$		0			0
$161$	−2106.94			−1.03136
$162$		0			0
$163$	745.455	−	308.777i	0.358212	−	0.148376i	−0.196318	−	0.980540i	$-0.562898\pi$
$163$	745.455	−	308.777i	0.358212	−	0.148376i	0.554529	+	0.832164i	$0.312898\pi$
$164$		0			0
$165$	−362.011	+	873.972i	−0.170803	+	0.412355i
$166$		0			0
$167$	741.751	+	741.751i	0.343703	+	0.343703i	0.857758	−	0.514055i	$-0.171857\pi$
$167$	741.751	+	741.751i	0.343703	+	0.343703i	−0.514055	+	0.857758i	$0.671857\pi$
$168$		0			0
$169$	409.532	−	409.532i	0.186405	−	0.186405i
$170$		0			0
$171$	743.756	+	308.074i	0.332611	+	0.137772i
$172$		0			0
$173$	−34.3941	−	83.0347i	−0.0151152	−	0.0364914i	0.916142	−	0.400854i	$-0.131287\pi$
$173$	−34.3941	−	83.0347i	−0.0151152	−	0.0364914i	−0.931257	+	0.364363i	$0.881287\pi$
$174$		0			0
$175$			3514.56i			1.51815i
$176$		0			0
$177$			550.180i			0.233639i
$178$		0			0
$179$	1402.83	+	3386.73i	0.585768	+	1.41417i	0.887514	+	0.460781i	$0.152430\pi$
$179$	1402.83	+	3386.73i	0.585768	+	1.41417i	−0.301746	+	0.953388i	$0.597570\pi$
$180$		0			0
$181$	504.860	+	209.120i	0.207326	+	0.0858771i	0.483930	−	0.875107i	$-0.339209\pi$
$181$	504.860	+	209.120i	0.207326	+	0.0858771i	−0.276604	+	0.960984i	$0.589209\pi$
$182$		0			0
$183$	−39.3770	+	39.3770i	−0.0159062	+	0.0159062i
$184$		0			0
$185$	−573.361	−	573.361i	−0.227861	−	0.227861i
$186$		0			0
$187$	−1474.95	+	3560.85i	−0.576786	+	1.39249i
$188$		0			0
$189$	1452.76	−	601.752i	0.559114	−	0.231593i
$190$		0			0
$191$	17.6918			0.00670226			0.00335113	−	0.999994i	$-0.498933\pi$
$191$	17.6918			0.00670226			0.00335113	+	0.999994i	$0.498933\pi$
$192$		0			0
$193$	−3321.63			−1.23884			−0.619420	−	0.785059i	$-0.712632\pi$
$193$	−3321.63			−1.23884			−0.619420	+	0.785059i	$0.712632\pi$
$194$		0			0
$195$	942.256	−	390.295i	0.346033	−	0.143331i
$196$		0			0
$197$	−310.402	+	749.376i	−0.112260	+	0.271020i	−0.970018	−	0.243035i	$-0.921857\pi$
$197$	−310.402	+	749.376i	−0.112260	+	0.271020i	0.857758	+	0.514054i	$0.171857\pi$
$198$		0			0
$199$	−1908.35	−	1908.35i	−0.679795	−	0.679795i	0.280158	−	0.959954i	$-0.409613\pi$
$199$	−1908.35	−	1908.35i	−0.679795	−	0.679795i	−0.959954	+	0.280158i	$0.909613\pi$
$200$		0			0
$201$	−221.944	+	221.944i	−0.0778841	+	0.0778841i
$202$		0			0
$203$	−491.968	−	203.780i	−0.170095	−	0.0704559i
$204$		0			0
$205$	420.110	+	1014.24i	0.143131	+	0.345548i
$206$		0			0
$207$			2541.77i			0.853454i
$208$		0			0
$209$			1209.76i			0.400387i
$210$		0			0
$211$	969.860	+	2341.45i	0.316435	+	0.763943i	0.999438	+	0.0335266i	$0.0106739\pi$
$211$	969.860	+	2341.45i	0.316435	+	0.763943i	−0.683002	+	0.730416i	$0.739326\pi$
$212$		0			0
$213$	1003.29	+	415.578i	0.322744	+	0.133685i
$214$		0			0
$215$	6021.69	−	6021.69i	1.91012	−	1.91012i
$216$		0			0
$217$	−1815.60	−	1815.60i	−0.567976	−	0.567976i
$218$		0			0
$219$	−464.647	+	1121.76i	−0.143370	+	0.346125i
$220$		0			0
$221$	3839.06	−	1590.19i	1.16852	−	0.484017i
$222$		0			0
$223$	267.474			0.0803200			0.0401600	−	0.999193i	$-0.487213\pi$
$223$	267.474			0.0803200			0.0401600	+	0.999193i	$0.487213\pi$
$224$		0			0
$225$	4239.89			1.25627
$226$		0			0
$227$	721.748	−	298.958i	0.211031	−	0.0874120i	−0.274664	−	0.961540i	$-0.588567\pi$
$227$	721.748	−	298.958i	0.211031	−	0.0874120i	0.485695	+	0.874128i	$0.338567\pi$
$228$		0			0
$229$	−1403.35	+	3387.98i	−0.404960	+	0.977660i	0.581484	+	0.813558i	$0.302472\pi$
$229$	−1403.35	+	3387.98i	−0.404960	+	0.977660i	−0.986443	+	0.164101i	$0.947528\pi$
$230$		0			0
$231$	800.402	+	800.402i	0.227977	+	0.227977i
$232$		0			0
$233$	95.4522	−	95.4522i	0.0268381	−	0.0268381i	−0.693560	−	0.720399i	$-0.743959\pi$
$233$	95.4522	−	95.4522i	0.0268381	−	0.0268381i	0.720399	+	0.693560i	$0.243959\pi$
$234$		0			0
$235$	−9259.67	−	3835.48i	−2.57036	−	1.06468i
$236$		0			0
$237$	89.0201	+	214.913i	0.0243986	+	0.0589035i
$238$		0			0
$239$		−	2210.32i		−	0.598216i	−0.954219	−	0.299108i	$-0.903311\pi$
$239$		−	2210.32i		−	0.598216i	0.954219	−	0.299108i	$-0.0966890\pi$
$240$		0			0
$241$		−	3029.15i		−	0.809645i	−0.914395	−	0.404823i	$-0.867333\pi$
$241$		−	3029.15i		−	0.809645i	0.914395	−	0.404823i	$-0.132667\pi$
$242$		0			0
$243$	−1104.14	−	2665.62i	−0.291483	−	0.703703i
$244$		0			0
$245$	1279.10	+	529.820i	0.333545	+	0.138159i
$246$		0			0
$247$	922.264	−	922.264i	0.237580	−	0.237580i
$248$		0			0
$249$	−148.560	−	148.560i	−0.0378095	−	0.0378095i
$250$		0			0
$251$	134.300	−	324.230i	0.0337727	−	0.0815346i	−0.906093	−	0.423078i	$-0.860950\pi$
$251$	134.300	−	324.230i	0.0337727	−	0.0815346i	0.939866	+	0.341543i	$0.110950\pi$
$252$		0			0
$253$	−3528.86	+	1461.70i	−0.876908	+	0.363227i
$254$		0			0
$255$	−2619.56			−0.643307
$256$		0			0
$257$	−7459.69			−1.81059			−0.905297	−	0.424779i	$-0.860352\pi$
$257$	−7459.69			−1.81059			−0.905297	+	0.424779i	$0.860352\pi$
$258$		0			0
$259$	−896.396	+	371.299i	−0.215055	+	0.0890788i
$260$		0			0
$261$	−245.836	+	593.501i	−0.0583022	+	0.140754i
$262$		0			0
$263$	−4192.29	−	4192.29i	−0.982919	−	0.982919i	0.0169374	−	0.999857i	$-0.494608\pi$
$263$	−4192.29	−	4192.29i	−0.982919	−	0.982919i	−0.999857	+	0.0169374i	$0.994608\pi$
$264$		0			0
$265$	5210.05	−	5210.05i	1.20774	−	1.20774i
$266$		0			0
$267$	−525.664	−	217.737i	−0.120487	−	0.0499075i
$268$		0			0
$269$	−1275.44	−	3079.18i	−0.289088	−	0.697921i	0.710897	−	0.703296i	$-0.248289\pi$
$269$	−1275.44	−	3079.18i	−0.289088	−	0.697921i	−0.999986	+	0.00537488i	$0.998289\pi$
$270$		0			0
$271$		−	1188.89i		−	0.266494i	−0.991083	−	0.133247i	$-0.957460\pi$
$271$		−	1188.89i		−	0.266494i	0.991083	−	0.133247i	$-0.0425404\pi$
$272$		0			0
$273$		−	1220.38i		−	0.270552i
$274$		0			0
$275$	2438.25	+	5886.46i	0.534662	+	1.29079i
$276$		0			0
$277$	3832.51	+	1587.48i	0.831310	+	0.344340i	0.757421	−	0.652926i	$-0.226459\pi$
$277$	3832.51	+	1587.48i	0.831310	+	0.344340i	0.0738890	+	0.997266i	$0.476459\pi$
$278$		0			0
$279$	−2190.30	+	2190.30i	−0.470000	+	0.470000i
$280$		0			0
$281$	230.048	+	230.048i	0.0488382	+	0.0488382i	0.731104	−	0.682266i	$-0.239005\pi$
$281$	230.048	+	230.048i	0.0488382	+	0.0488382i	−0.682266	+	0.731104i	$0.739005\pi$
$282$		0			0
$283$	405.744	−	979.554i	0.0852261	−	0.205754i	−0.875521	−	0.483181i	$-0.839481\pi$
$283$	405.744	−	979.554i	0.0852261	−	0.205754i	0.960747	+	0.277426i	$0.0894815\pi$
$284$		0			0
$285$	−759.635	+	314.651i	−0.157884	+	0.0653977i
$286$		0			0
$287$	1313.61			0.270173
$288$		0			0
$289$	−5759.94			−1.17239
$290$		0			0
$291$	1074.54	−	445.089i	0.216463	−	0.0896619i
$292$		0			0
$293$	−614.388	+	1483.26i	−0.122501	+	0.295744i	−0.973220	−	0.229878i	$-0.926167\pi$
$293$	−614.388	+	1483.26i	−0.122501	+	0.295744i	0.850718	+	0.525622i	$0.176167\pi$
$294$		0			0
$295$	4538.12	+	4538.12i	0.895659	+	0.895659i
$296$		0			0
$297$	2015.72	−	2015.72i	0.393819	−	0.393819i
$298$		0			0
$299$	3804.58	+	1575.91i	0.735867	+	0.304806i
$300$		0			0
$301$	−3899.55	−	9414.34i	−0.746732	−	1.80277i
$302$		0			0
$303$		−	2254.80i		−	0.427507i
$304$		0			0
$305$			649.596i			0.121953i
$306$		0			0
$307$	−2158.05	−	5210.00i	−0.401194	−	0.968569i	−0.987377	−	0.158390i	$-0.949370\pi$
$307$	−2158.05	−	5210.00i	−0.401194	−	0.968569i	0.586182	−	0.810179i	$-0.300630\pi$
$308$		0			0
$309$	−2157.87	−	893.819i	−0.397272	−	0.164555i
$310$		0			0
$311$	−182.317	+	182.317i	−0.0332420	+	0.0332420i	−0.723532	−	0.690290i	$-0.757483\pi$
$311$	−182.317	+	182.317i	−0.0332420	+	0.0332420i	0.690290	+	0.723532i	$0.257483\pi$
$312$		0			0
$313$	3731.88	+	3731.88i	0.673924	+	0.673924i	0.958618	−	0.284694i	$-0.0918921\pi$
$313$	3731.88	+	3731.88i	0.673924	+	0.673924i	−0.284694	+	0.958618i	$0.591892\pi$
$314$		0			0
$315$	3362.52	−	8117.84i	0.601450	−	1.45203i
$316$		0			0
$317$	2940.58	−	1218.03i	0.521007	−	0.215808i	−0.106652	−	0.994296i	$-0.534013\pi$
$317$	2940.58	−	1218.03i	0.521007	−	0.215808i	0.627659	+	0.778488i	$0.284013\pi$
$318$		0			0
$319$	−965.361			−0.169435
$320$		0			0
$321$	2658.05			0.462174
$322$		0			0
$323$	−3095.00	+	1281.99i	−0.533159	+	0.220842i
$324$		0			0
$325$	2628.75	−	6346.37i	0.448668	−	1.08318i
$326$		0			0
$327$	−933.833	−	933.833i	−0.157924	−	0.157924i
$328$		0			0
$329$	−8480.20	+	8480.20i	−1.42106	+	1.42106i
$330$		0			0
$331$	5918.75	+	2451.63i	0.982852	+	0.407111i	0.815481	−	0.578783i	$-0.196472\pi$
$331$	5918.75	+	2451.63i	0.982852	+	0.407111i	0.167371	+	0.985894i	$0.446472\pi$
$332$		0			0
$333$	447.928	+	1081.39i	0.0737127	+	0.177958i
$334$		0			0
$335$			3661.37i			0.597141i
$336$		0			0
$337$			11283.3i			1.82385i	0.410355	+	0.911926i	$0.365405\pi$
$337$			11283.3i			1.82385i	−0.410355	+	0.911926i	$0.634595\pi$
$338$		0			0
$339$	521.529	+	1259.08i	0.0835562	+	0.201722i
$340$		0			0
$341$	−4300.49	−	1781.32i	−0.682946	−	0.282886i
$342$		0			0
$343$	−3819.79	+	3819.79i	−0.601310	+	0.601310i
$344$		0			0
$345$	−1835.67	−	1835.67i	−0.286462	−	0.286462i
$346$		0			0
$347$	−4803.69	+	11597.1i	−0.743157	+	1.79414i	−0.150630	+	0.988590i	$0.548130\pi$
$347$	−4803.69	+	11597.1i	−0.743157	+	1.79414i	−0.592527	+	0.805550i	$0.701870\pi$
$348$		0			0
$349$	−5191.29	+	2150.30i	−0.796228	+	0.329808i	−0.743445	−	0.668798i	$-0.766809\pi$
$349$	−5191.29	+	2150.30i	−0.796228	+	0.329808i	−0.0527834	+	0.998606i	$0.516809\pi$
$350$		0			0
$351$	−3073.39			−0.467366
$352$		0			0
$353$	9949.61			1.50018			0.750091	−	0.661335i	$-0.230010\pi$
$353$	9949.61			1.50018			0.750091	+	0.661335i	$0.230010\pi$
$354$		0			0
$355$	11703.4	−	4847.72i	1.74973	−	0.724762i
$356$		0			0
$357$	−1199.53	+	2895.91i	−0.177831	+	0.429322i
$358$		0			0
$359$	3301.10	+	3301.10i	0.485308	+	0.485308i	0.906822	−	0.421514i	$-0.138501\pi$
$359$	3301.10	+	3301.10i	0.485308	+	0.485308i	−0.421514	+	0.906822i	$0.638501\pi$
$360$		0			0
$361$	4106.53	−	4106.53i	0.598706	−	0.598706i
$362$		0			0
$363$	82.8802	+	34.3301i	0.0119837	+	0.00496381i
$364$		0			0
$365$	5420.12	+	13085.3i	0.777266	+	1.87649i
$366$		0			0
$367$			10621.1i			1.51067i	0.655340	+	0.755334i	$0.272526\pi$
$367$			10621.1i			1.51067i	−0.655340	+	0.755334i	$0.727474\pi$
$368$		0			0
$369$		−	1584.71i		−	0.223568i
$370$		0			0
$371$	−3373.95	−	8145.43i	−0.472147	−	1.13986i
$372$		0			0
$373$	−527.627	−	218.550i	−0.0732426	−	0.0303381i	0.345761	−	0.938322i	$-0.387621\pi$
$373$	−527.627	−	218.550i	−0.0732426	−	0.0303381i	−0.419004	+	0.907984i	$0.637621\pi$
$374$		0			0
$375$	−820.862	+	820.862i	−0.113038	+	0.113038i
$376$		0			0
$377$	735.947	+	735.947i	0.100539	+	0.100539i
$378$		0			0
$379$	3589.96	−	8666.94i	0.486554	−	1.17465i	−0.469888	−	0.882726i	$-0.655706\pi$
$379$	3589.96	−	8666.94i	0.486554	−	1.17465i	0.956443	−	0.291920i	$-0.0942941\pi$
$380$		0			0
$381$	−776.177	+	321.503i	−0.104369	+	0.0432312i
$382$		0			0
$383$	4350.16			0.580372			0.290186	−	0.956970i	$-0.406283\pi$
$383$	4350.16			0.580372			0.290186	+	0.956970i	$0.406283\pi$
$384$		0			0
$385$	13204.1			1.74791
$386$		0			0
$387$	−11357.3	+	4704.34i	−1.49179	+	0.617920i
$388$		0			0
$389$	763.322	−	1842.82i	0.0994909	−	0.240192i	−0.866295	−	0.499533i	$-0.833505\pi$
$389$	763.322	−	1842.82i	0.0994909	−	0.240192i	0.965786	+	0.259340i	$0.0835051\pi$
$390$		0			0
$391$	−7479.13	−	7479.13i	−0.967355	−	0.967355i
$392$		0			0
$393$	−1322.36	+	1322.36i	−0.169731	+	0.169731i
$394$		0			0
$395$	2506.97	+	1038.42i	0.319340	+	0.132275i
$396$		0			0
$397$	1876.19	+	4529.53i	0.237187	+	0.572621i	0.996990	−	0.0775330i	$-0.0247043\pi$
$397$	1876.19	+	4529.53i	0.237187	+	0.572621i	−0.759802	+	0.650154i	$0.774704\pi$
$398$		0			0
$399$			983.855i			0.123444i
$400$		0			0
$401$		−	14992.8i		−	1.86710i	−0.358450	−	0.933549i	$-0.616695\pi$
$401$		−	14992.8i		−	1.86710i	0.358450	−	0.933549i	$-0.383305\pi$
$402$		0			0
$403$	1920.50	+	4636.49i	0.237387	+	0.573102i
$404$		0			0
$405$	−8860.68	−	3670.21i	−1.08714	−	0.450307i
$406$		0			0
$407$	−1243.76	+	1243.76i	−0.151477	+	0.151477i
$408$		0			0
$409$	8450.62	+	8450.62i	1.02165	+	1.02165i	0.999760	+	0.0218936i	$0.00696949\pi$
$409$	8450.62	+	8450.62i	1.02165	+	1.02165i	0.0218936	+	0.999760i	$0.493031\pi$
$410$		0			0
$411$	754.857	−	1822.39i	0.0905946	−	0.218715i
$412$		0			0
$413$	7094.91	−	2938.81i	0.845322	−	0.350144i
$414$		0			0
$415$	−2450.76			−0.289887
$416$		0			0
$417$	−2096.81			−0.246238
$418$		0			0
$419$	3136.96	−	1299.37i	0.365753	−	0.151500i	−0.192235	−	0.981349i	$-0.561574\pi$
$419$	3136.96	−	1299.37i	0.365753	−	0.151500i	0.557988	+	0.829849i	$0.311574\pi$
$420$		0			0
$421$	3434.08	−	8290.60i	0.397546	−	0.959760i	−0.590701	−	0.806891i	$-0.701149\pi$
$421$	3434.08	−	8290.60i	0.397546	−	0.959760i	0.988246	−	0.152870i	$-0.0488514\pi$
$422$		0			0
$423$	10230.4	+	10230.4i	1.17593	+	1.17593i
$424$		0			0
$425$	−12475.9	+	12475.9i	−1.42392	+	1.42392i
$426$		0			0
$427$	718.125	+	297.457i	0.0813876	+	0.0337118i
$428$		0			0
$429$	−846.648	−	2043.99i	−0.0952833	−	0.230034i
$430$		0			0
$431$		−	15375.3i		−	1.71833i	−0.511699	−	0.859165i	$-0.670984\pi$
$431$		−	15375.3i		−	1.71833i	0.511699	−	0.859165i	$-0.329016\pi$
$432$		0			0
$433$			12522.9i			1.38987i	0.719073	+	0.694934i	$0.244567\pi$
$433$			12522.9i			1.38987i	−0.719073	+	0.694934i	$0.755433\pi$
$434$		0			0
$435$	−251.085	−	606.172i	−0.0276749	−	0.0668132i
$436$		0			0
$437$	−3067.20	−	1270.48i	−0.335753	−	0.139074i
$438$		0			0
$439$	−6689.38	+	6689.38i	−0.727259	+	0.727259i	−0.970073	−	0.242814i	$-0.921929\pi$
$439$	−6689.38	+	6689.38i	−0.727259	+	0.727259i	0.242814	+	0.970073i	$0.421929\pi$
$440$		0			0
$441$	−1413.19	−	1413.19i	−0.152595	−	0.152595i
$442$		0			0
$443$	−1232.30	+	2975.03i	−0.132163	+	0.319070i	−0.976083	−	0.217400i	$-0.930242\pi$
$443$	−1232.30	+	2975.03i	−0.132163	+	0.319070i	0.843920	+	0.536470i	$0.180242\pi$
$444$		0			0
$445$	−6131.88	+	2539.91i	−0.653212	+	0.270569i
$446$		0			0
$447$	3890.86			0.411703
$448$		0			0
$449$	−2465.75			−0.259167			−0.129584	−	0.991569i	$-0.541364\pi$
$449$	−2465.75			−0.259167			−0.129584	+	0.991569i	$0.541364\pi$
$450$		0			0
$451$	2200.13	−	911.324i	0.229712	−	0.0951498i
$452$		0			0
$453$	696.557	−	1681.64i	0.0722453	−	0.174415i
$454$		0			0
$455$	−10066.2	−	10066.2i	−1.03717	−	1.03717i
$456$		0			0
$457$	720.641	−	720.641i	0.0737640	−	0.0737640i	−0.669262	−	0.743026i	$-0.733390\pi$
$457$	720.641	−	720.641i	0.0737640	−	0.0737640i	0.743026	+	0.669262i	$0.233390\pi$
$458$		0			0
$459$	7293.03	+	3020.87i	0.741633	+	0.307194i
$460$		0			0
$461$	94.7149	+	228.662i	0.00956900	+	0.0231016i	0.928592	−	0.371103i	$-0.121020\pi$
$461$	94.7149	+	228.662i	0.00956900	+	0.0231016i	−0.919023	+	0.394204i	$0.871020\pi$
$462$		0			0
$463$		−	6979.44i		−	0.700566i	−0.936644	−	0.350283i	$-0.886085\pi$
$463$		−	6979.44i		−	0.700566i	0.936644	−	0.350283i	$-0.113915\pi$
$464$		0			0
$465$		−	3163.69i		−	0.315511i
$466$		0			0
$467$	−795.725	−	1921.05i	−0.0788475	−	0.190355i	0.879540	−	0.475825i	$-0.157850\pi$
$467$	−795.725	−	1921.05i	−0.0788475	−	0.190355i	−0.958388	+	0.285470i	$0.907850\pi$
$468$		0			0
$469$	4047.63	+	1676.58i	0.398512	+	0.165069i
$470$		0			0
$471$	−977.762	+	977.762i	−0.0956537	+	0.0956537i
$472$		0			0
$473$	−13062.5	−	13062.5i	−1.26980	−	1.26980i
$474$		0			0
$475$	−2119.27	+	5116.37i	−0.204713	+	0.494221i
$476$		0			0
$477$	−9826.49	+	4070.26i	−0.943237	+	0.390702i
$478$		0			0
$479$	−973.751			−0.0928848			−0.0464424	−	0.998921i	$-0.514788\pi$
$479$	−973.751			−0.0928848			−0.0464424	+	0.998921i	$0.514788\pi$
$480$		0			0
$481$	1896.37			0.179766
$482$		0			0
$483$	−2869.90	+	1188.75i	−0.270362	+	0.111988i
$484$		0			0
$485$	5191.98	−	12534.6i	0.486094	−	1.17354i
$486$		0			0
$487$	11379.8	+	11379.8i	1.05887	+	1.05887i	0.998155	+	0.0607112i	$0.0193369\pi$
$487$	11379.8	+	11379.8i	1.05887	+	1.05887i	0.0607112	+	0.998155i	$0.480663\pi$
$488$		0			0
$489$	841.184	−	841.184i	0.0777907	−	0.0777907i
$490$		0			0
$491$	1394.56	+	577.645i	0.128178	+	0.0530932i	0.445851	−	0.895107i	$-0.352901\pi$
$491$	1394.56	+	577.645i	0.128178	+	0.0530932i	−0.317672	+	0.948201i	$0.602901\pi$
$492$		0			0
$493$	−1023.00	−	2469.74i	−0.0934557	−	0.225622i
$494$		0			0
$495$		−	15929.2i		−	1.44639i
$496$		0			0
$497$		−	15157.9i		−	1.36806i
$498$		0			0
$499$	−5429.65	−	13108.3i	−0.487103	−	1.17597i	−0.956171	−	0.292809i	$-0.905410\pi$
$499$	−5429.65	−	13108.3i	−0.487103	−	1.17597i	0.469068	−	0.883162i	$-0.344590\pi$
$500$		0			0
$501$	1428.86	+	591.852i	0.127418	+	0.0527784i
$502$		0			0
$503$	−11037.0	+	11037.0i	−0.978362	+	0.978362i	−0.999771	−	0.0214085i	$-0.993185\pi$
$503$	−11037.0	+	11037.0i	−0.978362	+	0.978362i	0.0214085	+	0.999771i	$0.493185\pi$
$504$		0			0
$505$	−18598.5	−	18598.5i	−1.63886	−	1.63886i
$506$		0			0
$507$	326.770	−	788.893i	0.0286240	−	0.0691045i
$508$		0			0
$509$	13984.8	−	5792.71i	1.21781	−	0.504435i	0.321099	−	0.947046i	$-0.395948\pi$
$509$	13984.8	−	5792.71i	1.21781	−	0.504435i	0.896714	+	0.442611i	$0.145948\pi$
$510$		0			0
$511$	16947.7			1.46717
$512$		0			0
$513$	2477.73			0.213244
$514$		0			0
$515$	−25171.6	+	10426.4i	−2.15377	+	0.892123i
$516$		0			0
$517$	−8320.11	+	20086.5i	−0.707772	+	1.70871i
$518$		0			0
$519$	−93.6978	−	93.6978i	−0.00792462	−	0.00792462i
$520$		0			0
$521$	8504.46	−	8504.46i	0.715139	−	0.715139i	−0.252467	−	0.967606i	$-0.581242\pi$
$521$	8504.46	−	8504.46i	0.715139	−	0.715139i	0.967606	+	0.252467i	$0.0812418\pi$
$522$		0			0
$523$	2991.17	+	1238.98i	0.250086	+	0.103589i	0.504205	−	0.863584i	$-0.331786\pi$
$523$	2991.17	+	1238.98i	0.250086	+	0.103589i	−0.254119	+	0.967173i	$0.581786\pi$
$524$		0			0
$525$	1982.94	+	4787.25i	0.164843	+	0.397967i
$526$		0			0
$527$		−	12889.9i		−	1.06545i
$528$		0			0
$529$			1684.91i			0.138482i
$530$		0			0
$531$	−3545.33	−	8559.17i	−0.289744	−	0.699504i
$532$		0			0
$533$	−2372.03	−	982.527i	−0.192765	−	0.0798461i
$534$		0			0
$535$	21924.7	−	21924.7i	1.77175	−	1.77175i
$536$		0			0
$537$	3821.65	+	3821.65i	0.307107	+	0.307107i
$538$		0			0
$539$	1149.31	−	2774.68i	0.0918448	−	0.221733i
$540$		0			0
$541$	4615.58	−	1911.84i	0.366801	−	0.151934i	−0.191667	−	0.981460i	$-0.561389\pi$
$541$	4615.58	−	1911.84i	0.366801	−	0.151934i	0.558468	+	0.829526i	$0.311389\pi$
$542$		0			0
$543$	805.668			0.0636732
$544$		0			0
$545$	−15405.3			−1.21081
$546$		0			0
$547$	−1759.02	+	728.609i	−0.137496	+	0.0569526i	−0.450370	−	0.892842i	$-0.648708\pi$
$547$	−1759.02	+	728.609i	−0.137496	+	0.0569526i	0.312875	+	0.949794i	$0.398708\pi$
$548$		0			0
$549$	358.847	−	866.332i	0.0278965	−	0.0673482i
$550$		0			0
$551$	−593.311	−	593.311i	−0.0458728	−	0.0458728i
$552$		0			0
$553$	2295.94	−	2295.94i	0.176552	−	0.176552i
$554$		0			0
$555$	−1104.48	−	457.492i	−0.0844733	−	0.0349900i
$556$		0			0
$557$	7305.07	+	17636.0i	0.555702	+	1.34158i	0.913140	+	0.407646i	$0.133650\pi$
$557$	7305.07	+	17636.0i	0.555702	+	1.34158i	−0.357438	+	0.933937i	$0.616350\pi$
$558$		0			0
$559$			19916.6i			1.50694i
$560$		0			0
$561$			5682.48i			0.427655i
$562$		0			0
$563$	−498.470	−	1203.41i	−0.0373144	−	0.0900849i	0.904124	−	0.427271i	$-0.140525\pi$
$563$	−498.470	−	1203.41i	−0.0373144	−	0.0900849i	−0.941438	+	0.337186i	$0.890525\pi$
$564$		0			0
$565$	14687.2	+	6083.65i	1.09362	+	0.452993i
$566$		0			0
$567$	−8114.80	+	8114.80i	−0.601040	+	0.601040i
$568$		0			0
$569$	13188.4	+	13188.4i	0.971684	+	0.971684i	0.999610	−	0.0279264i	$-0.00889041\pi$
$569$	13188.4	+	13188.4i	0.971684	+	0.971684i	−0.0279264	+	0.999610i	$0.508890\pi$
$570$		0			0
$571$	−5719.51	+	13808.1i	−0.419184	+	1.01200i	0.563401	+	0.826184i	$0.309493\pi$
$571$	−5719.51	+	13808.1i	−0.419184	+	1.01200i	−0.982585	+	0.185815i	$0.940507\pi$
$572$		0			0
$573$	24.0983	−	9.98186i	0.00175693	−	0.000727746i
$574$		0			0
$575$	−17485.1			−1.26813
$576$		0			0
$577$	7866.08			0.567538			0.283769	−	0.958893i	$-0.408415\pi$
$577$	7866.08			0.567538			0.283769	+	0.958893i	$0.408415\pi$
$578$		0			0
$579$	−4524.46	+	1874.09i	−0.324750	+	0.134516i
$580$		0			0
$581$	−1122.23	+	2709.30i	−0.0801342	+	0.193461i
$582$		0			0
$583$	−11301.9	−	11301.9i	−0.802877	−	0.802877i
$584$		0			0
$585$	−12143.7	+	12143.7i	−0.858255	+	0.858255i
$586$		0			0
$587$	−13370.3	−	5538.16i	−0.940122	−	0.389411i	−0.140613	−	0.990065i	$-0.544907\pi$
$587$	−13370.3	−	5538.16i	−0.940122	−	0.389411i	−0.799510	+	0.600653i	$0.794907\pi$
$588$		0			0
$589$	−1548.28	−	3737.88i	−0.108312	−	0.261489i
$590$		0			0
$591$			1195.87i			0.0832346i
$592$		0			0
$593$			7176.23i			0.496952i	0.968638	+	0.248476i	$0.0799297\pi$
$593$			7176.23i			0.496952i	−0.968638	+	0.248476i	$0.920070\pi$
$594$		0			0
$595$	13992.5	+	33780.9i	0.964095	+	2.32753i
$596$		0			0
$597$	−3676.11	−	1522.69i	−0.252015	−	0.104388i
$598$		0			0
$599$	11813.4	−	11813.4i	0.805815	−	0.805815i	−0.178183	−	0.983997i	$-0.557022\pi$
$599$	11813.4	−	11813.4i	0.805815	−	0.805815i	0.983997	+	0.178183i	$0.0570218\pi$
$600$		0			0
$601$	−1438.92	−	1438.92i	−0.0976618	−	0.0976618i	0.656588	−	0.754250i	$-0.271999\pi$
$601$	−1438.92	−	1438.92i	−0.0976618	−	0.0976618i	−0.754250	+	0.656588i	$0.771999\pi$
$602$		0			0
$603$	2022.60	−	4882.98i	0.136595	−	0.329768i
$604$		0			0
$605$	966.800	−	400.462i	0.0649686	−	0.0269109i
$606$		0			0
$607$	19331.1			1.29263			0.646314	−	0.763071i	$-0.276309\pi$
$607$	19331.1			1.29263			0.646314	+	0.763071i	$0.276309\pi$
$608$		0			0
$609$	−785.094			−0.0522391
$610$		0			0
$611$	21655.9	−	8970.17i	1.43389	−	0.593935i
$612$		0			0
$613$	2013.56	−	4861.15i	0.132670	−	0.320294i	−0.843559	−	0.537037i	$-0.819543\pi$
$613$	2013.56	−	4861.15i	0.132670	−	0.320294i	0.976229	+	0.216743i	$0.0695435\pi$
$614$		0			0
$615$	1144.48	+	1144.48i	0.0750406	+	0.0750406i
$616$		0			0
$617$	−6574.52	+	6574.52i	−0.428979	+	0.428979i	−0.888281	−	0.459301i	$-0.848100\pi$
$617$	−6574.52	+	6574.52i	−0.428979	+	0.428979i	0.459301	+	0.888281i	$0.348100\pi$
$618$		0			0
$619$	−2395.09	−	992.077i	−0.155520	−	0.0644183i	0.303566	−	0.952810i	$-0.401823\pi$
$619$	−2395.09	−	992.077i	−0.155520	−	0.0644183i	−0.459085	+	0.888392i	$0.651823\pi$
$620$		0			0
$621$	2993.74	+	7227.53i	0.193454	+	0.467038i
$622$		0			0
$623$			7941.81i			0.510726i
$624$		0			0
$625$		−	7806.17i		−	0.499595i
$626$		0			0
$627$	682.557	+	1647.84i	0.0434748	+	0.104957i
$628$		0			0
$629$	−4500.02	−	1863.97i	−0.285258	−	0.118158i
$630$		0			0
$631$	2820.94	−	2820.94i	0.177971	−	0.177971i	−0.612500	−	0.790471i	$-0.709836\pi$
$631$	2820.94	−	2820.94i	0.177971	−	0.177971i	0.790471	+	0.612500i	$0.209836\pi$
$632$		0			0
$633$	2642.13	+	2642.13i	0.165901	+	0.165901i
$634$		0			0
$635$	−3750.34	+	9054.12i	−0.234374	+	0.565830i
$636$		0			0
$637$	−2991.47	+	1239.11i	−0.186070	+	0.0770726i
$638$		0			0
$639$	−18286.2			−1.13207
$640$		0			0
$641$	8220.77			0.506553			0.253277	−	0.967394i	$-0.418492\pi$
$641$	8220.77			0.506553			0.253277	+	0.967394i	$0.418492\pi$
$642$		0			0
$643$	21031.3	−	8711.45i	1.28988	−	0.534286i	0.370932	−	0.928660i	$-0.379038\pi$
$643$	21031.3	−	8711.45i	1.28988	−	0.534286i	0.918950	+	0.394374i	$0.129038\pi$
$644$		0			0
$645$	4804.78	−	11599.8i	0.293315	−	0.708124i
$646$		0			0
$647$	14749.1	+	14749.1i	0.896208	+	0.896208i	0.995098	−	0.0988901i	$-0.0315292\pi$
$647$	14749.1	+	14749.1i	0.896208	+	0.896208i	−0.0988901	+	0.995098i	$0.531529\pi$
$648$		0			0
$649$	9844.31	−	9844.31i	0.595413	−	0.595413i
$650$		0			0
$651$	−3497.44	−	1448.69i	−0.210561	−	0.0872174i
$652$		0			0
$653$	−4279.06	−	10330.6i	−0.256436	−	0.619091i	0.742262	−	0.670110i	$-0.233753\pi$
$653$	−4279.06	−	10330.6i	−0.256436	−	0.619091i	−0.998698	+	0.0510191i	$0.983753\pi$
$654$		0			0
$655$			21814.8i			1.30134i
$656$		0			0
$657$		−	20445.4i		−	1.21408i
$658$		0			0
$659$	11437.1	+	27611.6i	0.676063	+	1.63216i	0.771121	+	0.636689i	$0.219696\pi$
$659$	11437.1	+	27611.6i	0.676063	+	1.63216i	−0.0950580	+	0.995472i	$0.530304\pi$
$660$		0			0
$661$	19843.3	+	8219.36i	1.16765	+	0.483655i	0.880414	−	0.474205i	$-0.157265\pi$
$661$	19843.3	+	8219.36i	1.16765	+	0.483655i	0.287233	+	0.957861i	$0.407265\pi$
$662$		0			0
$663$	4332.06	−	4332.06i	0.253761	−	0.253761i
$664$		0			0
$665$	8115.25	+	8115.25i	0.473227	+	0.473227i
$666$		0			0
$667$	1013.81	−	2447.56i	0.0588530	−	0.142084i
$668$		0			0
$669$	364.332	−	150.911i	0.0210551	−	0.00872132i
$670$		0			0
$671$	1409.14			0.0810717
$672$		0			0
$673$	−13639.3			−0.781216			−0.390608	−	0.920557i	$-0.627735\pi$
$673$	−13639.3			−0.781216			−0.390608	+	0.920557i	$0.627735\pi$
$674$		0			0
$675$	12056.2	−	4993.82i	0.687469	−	0.284759i
$676$		0			0
$677$	−10163.0	+	24535.6i	−0.576951	+	1.39288i	0.318586	+	0.947894i	$0.396792\pi$
$677$	−10163.0	+	24535.6i	−0.576951	+	1.39288i	−0.895537	+	0.444988i	$0.853208\pi$
$678$		0			0
$679$	−11479.4	−	11479.4i	−0.648806	−	0.648806i
$680$		0			0
$681$	814.433	−	814.433i	0.0458284	−	0.0458284i
$682$		0			0
$683$	12279.3	+	5086.25i	0.687928	+	0.284949i	0.699136	−	0.714988i	$-0.253568\pi$
$683$	12279.3	+	5086.25i	0.687928	+	0.284949i	−0.0112089	+	0.999937i	$0.503568\pi$
$684$		0			0
$685$	−8805.43	−	21258.2i	−0.491151	−	1.18574i
$686$		0			0
$687$			5406.62i			0.300255i
$688$		0			0
$689$			17232.1i			0.952817i
$690$		0			0
$691$	−12427.1	−	30001.7i	−0.684153	−	1.65169i	−0.756241	−	0.654293i	$-0.772966\pi$
$691$	−12427.1	−	30001.7i	−0.684153	−	1.65169i	0.0720884	−	0.997398i	$-0.477034\pi$
$692$		0			0
$693$	−17609.6	−	7294.15i	−0.965273	−	0.399829i
$694$		0			0
$695$	−17295.3	+	17295.3i	−0.943956	+	0.943956i
$696$		0			0
$697$	4662.99	+	4662.99i	0.253405	+	0.253405i
$698$		0			0
$699$	76.1625	−	183.873i	0.00412122	−	0.00994950i
$700$		0			0
$701$	−24563.9	+	10174.7i	−1.32349	+	0.548207i	−0.928791	−	0.370605i	$-0.879150\pi$
$701$	−24563.9	+	10174.7i	−1.32349	+	0.548207i	−0.394697	+	0.918811i	$0.629150\pi$
$702$		0			0
$703$	−1528.83			−0.0820214
$704$		0			0
$705$	−14776.8			−0.789399
$706$		0			0
$707$	−29077.0	+	12044.1i	−1.54675	+	0.640685i
$708$		0			0
$709$	−4032.81	+	9736.05i	−0.213618	+	0.515720i	−0.993974	−	0.109616i	$-0.965038\pi$
$709$	−4032.81	+	9736.05i	−0.213618	+	0.515720i	0.780356	+	0.625336i	$0.215038\pi$
$710$		0			0
$711$	−2769.78	−	2769.78i	−0.146097	−	0.146097i
$712$		0			0
$713$	9032.67	−	9032.67i	0.474440	−	0.474440i
$714$		0			0
$715$	−23843.2	−	9876.17i	−1.24711	−	0.516570i
$716$		0			0
$717$	−1247.08	−	3010.72i	−0.0649555	−	0.156816i
$718$		0			0
$719$			2159.37i			0.112004i	0.998431	+	0.0560021i	$0.0178353\pi$
$719$			2159.37i			0.112004i	−0.998431	+	0.0560021i	$0.982165\pi$
$720$		0			0
$721$			32601.4i			1.68397i
$722$		0			0
$723$	−1709.07	−	4126.06i	−0.0879129	−	0.212241i
$724$		0			0
$725$	−4082.75	−	1691.13i	−0.209144	−	0.0866303i
$726$		0			0
$727$	15999.3	−	15999.3i	0.816204	−	0.816204i	−0.169352	−	0.985556i	$-0.554167\pi$
$727$	15999.3	−	15999.3i	0.816204	−	0.816204i	0.985556	+	0.169352i	$0.0541674\pi$
$728$		0			0
$729$	7638.74	+	7638.74i	0.388088	+	0.388088i
$730$		0			0
$731$	19576.2	−	47261.2i	0.990497	−	2.39127i
$732$		0			0
$733$	−2232.08	+	924.559i	−0.112475	+	0.0465885i	−0.438211	−	0.898872i	$-0.644388\pi$
$733$	−2232.08	+	924.559i	−0.112475	+	0.0465885i	0.325737	+	0.945461i	$0.394388\pi$
$734$		0			0
$735$	2041.22			0.102437
$736$		0			0
$737$	7942.43			0.396965
$738$		0			0
$739$	15900.0	−	6585.99i	0.791462	−	0.327834i	0.0499305	−	0.998753i	$-0.484100\pi$
$739$	15900.0	−	6585.99i	0.791462	−	0.327834i	0.741531	+	0.670919i	$0.234100\pi$
$740$		0			0
$741$	735.886	−	1776.59i	0.0364824	−	0.0880762i
$742$		0			0
$743$	6184.20	+	6184.20i	0.305352	+	0.305352i	0.843103	−	0.537751i	$-0.180726\pi$
$743$	6184.20	+	6184.20i	0.305352	+	0.305352i	−0.537751	+	0.843103i	$0.680726\pi$
$744$		0			0
$745$	32093.4	−	32093.4i	1.57827	−	1.57827i
$746$		0			0
$747$	3268.45	+	1353.84i	0.160089	+	0.0663110i
$748$		0			0
$749$	−14198.1	−	34277.2i	−0.692639	−	1.67218i
$750$		0			0
$751$			11095.5i			0.539122i	0.962983	+	0.269561i	$0.0868786\pi$
$751$			11095.5i			0.539122i	−0.962983	+	0.269561i	$0.913121\pi$
$752$		0			0
$753$		−	517.413i		−	0.0250406i
$754$		0			0
$755$	−8125.36	−	19616.3i	−0.391672	−	0.945579i
$756$		0			0
$757$	25020.9	+	10364.0i	1.20132	+	0.497604i	0.891426	−	0.453167i	$-0.149706\pi$
$757$	25020.9	+	10364.0i	1.20132	+	0.497604i	0.309896	+	0.950771i	$0.399706\pi$
$758$		0			0
$759$	−3982.03	+	3982.03i	−0.190433	+	0.190433i
$760$		0			0
$761$	2393.12	+	2393.12i	0.113995	+	0.113995i	0.761804	−	0.647808i	$-0.224314\pi$
$761$	2393.12	+	2393.12i	0.113995	+	0.113995i	−0.647808	+	0.761804i	$0.724314\pi$
$762$		0			0
$763$	−7054.25	+	17030.5i	−0.334706	+	0.808053i
$764$		0			0
$765$	40752.6	−	16880.3i	1.92603	−	0.797788i
$766$		0			0
$767$	−15009.7			−0.706608
$768$		0			0
$769$	−33544.1			−1.57299			−0.786496	−	0.617595i	$-0.788107\pi$
$769$	−33544.1			−1.57299			−0.786496	+	0.617595i	$0.788107\pi$
$770$		0			0
$771$	−10161.0	+	4208.82i	−0.474630	+	0.196598i
$772$		0			0
$773$	9560.71	−	23081.6i	0.444857	−	1.07398i	−0.529366	−	0.848394i	$-0.677570\pi$
$773$	9560.71	−	23081.6i	0.444857	−	1.07398i	0.974223	−	0.225587i	$-0.0724300\pi$
$774$		0			0
$775$	−15067.3	−	15067.3i	−0.698365	−	0.698365i
$776$		0			0
$777$	−1011.51	+	1011.51i	−0.0467023	+	0.0467023i
$778$		0			0
$779$	1912.30	+	792.101i	0.0879529	+	0.0364313i
$780$		0			0
$781$	−10515.9	−	25387.7i	−0.481804	−	1.16318i
$782$		0			0
$783$			1977.17i			0.0902406i
$784$		0			0
$785$			16130.0i			0.733381i
$786$		0			0
$787$	6144.82	+	14834.9i	0.278321	+	0.671927i	0.999789	−	0.0205203i	$-0.00653228\pi$
$787$	6144.82	+	14834.9i	0.278321	+	0.671927i	−0.721468	+	0.692448i	$0.756532\pi$
$788$		0			0
$789$	−8075.74	−	3345.08i	−0.364390	−	0.150935i
$790$		0			0
$791$	13450.9	−	13450.9i	0.604624	−	0.604624i
$792$		0			0
$793$	−1074.26	−	1074.26i	−0.0481060	−	0.0481060i
$794$		0			0
$795$	4157.17	−	10036.3i	0.185458	−	0.447736i
$796$		0			0
$797$	−15066.3	+	6240.66i	−0.669605	+	0.277359i	−0.691474	−	0.722401i	$-0.743038\pi$
$797$	−15066.3	+	6240.66i	−0.669605	+	0.277359i	0.0218691	+	0.999761i	$0.493038\pi$
$798$		0			0
$799$	−60205.5			−2.66573
$800$		0			0
$801$	9580.85			0.422625
$802$		0			0
$803$	28385.3	−	11757.6i	1.24744	−	0.516708i
$804$		0			0
$805$	−13866.8	+	33477.5i	−0.607132	+	1.46575i
$806$		0			0
$807$	−3474.60	−	3474.60i	−0.151563	−	0.151563i
$808$		0			0
$809$	2211.65	−	2211.65i	0.0961154	−	0.0961154i	−0.657414	−	0.753529i	$-0.728350\pi$
$809$	2211.65	−	2211.65i	0.0961154	−	0.0961154i	0.753529	+	0.657414i	$0.228350\pi$
$810$		0			0
$811$	−19941.1	−	8259.86i	−0.863410	−	0.357636i	−0.0933697	−	0.995632i	$-0.529764\pi$
$811$	−19941.1	−	8259.86i	−0.863410	−	0.357636i	−0.770040	+	0.637995i	$0.779764\pi$
$812$		0			0
$813$	−670.782	−	1619.41i	−0.0289365	−	0.0698588i
$814$		0			0
$815$		−	13876.9i		−	0.596425i
$816$		0			0
$817$		−	16056.5i		−	0.687571i
$818$		0			0
$819$	7864.04	+	18985.5i	0.335521	+	0.810020i
$820$		0			0
$821$	−13446.8	−	5569.86i	−0.571617	−	0.236772i	0.0781027	−	0.996945i	$-0.475114\pi$
$821$	−13446.8	−	5569.86i	−0.571617	−	0.236772i	−0.649720	+	0.760174i	$0.725114\pi$
$822$		0			0
$823$	−23548.4	+	23548.4i	−0.997383	+	0.997383i	−0.999997	−	0.00261392i	$-0.999168\pi$
$823$	−23548.4	+	23548.4i	−0.997383	+	0.997383i	0.00261392	+	0.999997i	$0.499168\pi$
$824$		0			0
$825$	6642.39	+	6642.39i	0.280313	+	0.280313i
$826$		0			0
$827$	6650.02	−	16054.6i	0.279618	−	0.675057i	−0.720207	−	0.693759i	$-0.755953\pi$
$827$	6650.02	−	16054.6i	0.279618	−	0.675057i	0.999825	+	0.0187017i	$0.00595330\pi$
$828$		0			0
$829$	1367.19	−	566.309i	0.0572792	−	0.0237258i	−0.353860	−	0.935298i	$-0.615131\pi$
$829$	1367.19	−	566.309i	0.0572792	−	0.0237258i	0.411139	+	0.911573i	$0.365131\pi$
$830$		0			0
$831$	6116.00			0.255309
$832$		0			0
$833$	8316.57			0.345921
$834$		0			0
$835$	16667.7	−	6903.97i	0.690788	−	0.286134i
$836$		0			0
$837$	−3648.36	+	8807.91i	−0.150664	+	0.363735i
$838$		0			0
$839$	10926.4	+	10926.4i	0.449609	+	0.449609i	0.895224	−	0.445616i	$-0.147015\pi$
$839$	10926.4	+	10926.4i	0.449609	+	0.449609i	−0.445616	+	0.895224i	$0.647015\pi$
$840$		0			0
$841$	−16772.2	+	16772.2i	−0.687694	+	0.687694i
$842$		0			0
$843$	443.149	+	183.558i	0.0181054	+	0.00749951i
$844$		0			0
$845$	−3811.78	−	9202.46i	−0.155183	−	0.374644i
$846$		0			0
$847$		−	1252.17i		−	0.0507969i
$848$		0			0
$849$		−	1563.20i		−	0.0631905i
$850$		0			0
$851$	−1847.23	−	4459.60i	−0.0744091	−	0.179640i
$852$		0			0
$853$	−8874.25	−	3675.84i	−0.356212	−	0.147548i	0.197399	−	0.980323i	$-0.436751\pi$
$853$	−8874.25	−	3675.84i	−0.356212	−	0.147548i	−0.553611	+	0.832775i	$0.686751\pi$
$854$		0			0
$855$	9790.08	−	9790.08i	0.391595	−	0.391595i
$856$		0			0
$857$	−16585.9	−	16585.9i	−0.661100	−	0.661100i	0.294539	−	0.955639i	$-0.404834\pi$
$857$	−16585.9	−	16585.9i	−0.661100	−	0.661100i	−0.955639	+	0.294539i	$0.904834\pi$
$858$		0			0
$859$	−8809.72	+	21268.5i	−0.349923	+	0.844788i	0.646706	+	0.762740i	$0.276146\pi$
$859$	−8809.72	+	21268.5i	−0.349923	+	0.844788i	−0.996628	+	0.0820486i	$0.973854\pi$
$860$		0			0
$861$	1789.29	−	741.148i	0.0708233	−	0.0293360i
$862$		0			0
$863$	19940.2			0.786527			0.393263	−	0.919426i	$-0.371346\pi$
$863$	19940.2			0.786527			0.393263	+	0.919426i	$0.371346\pi$
$864$		0			0
$865$	−1545.72			−0.0607584
$866$		0			0
$867$	−7845.74	+	3249.81i	−0.307330	+	0.127300i
$868$		0			0
$869$	2252.60	−	5438.25i	0.0879333	−	0.212290i
$870$		0			0
$871$	−6054.94	−	6054.94i	−0.235550	−	0.235550i
$872$		0			0
$873$	−13848.5	+	13848.5i	−0.536887	+	0.536887i
$874$		0			0
$875$	14970.2	+	6200.86i	0.578383	+	0.239574i
$876$		0			0
$877$	11501.0	+	27765.8i	0.442828	+	1.06908i	0.974952	+	0.222414i	$0.0713938\pi$
$877$	11501.0	+	27765.8i	0.442828	+	1.06908i	−0.532125	+	0.846666i	$0.678606\pi$
$878$		0			0
$879$			2367.03i			0.0908280i
$880$		0			0
$881$		−	18012.3i		−	0.688821i	−0.938819	−	0.344410i	$-0.888079\pi$
$881$		−	18012.3i		−	0.688821i	0.938819	−	0.344410i	$-0.111921\pi$
$882$		0			0
$883$	6581.16	+	15888.3i	0.250819	+	0.605532i	0.998271	−	0.0587851i	$-0.0187227\pi$
$883$	6581.16	+	15888.3i	0.250819	+	0.605532i	−0.747451	+	0.664317i	$0.768723\pi$
$884$		0			0
$885$	8741.91	+	3621.02i	0.332041	+	0.137536i
$886$		0			0
$887$	2226.45	−	2226.45i	0.0842806	−	0.0842806i	−0.663710	−	0.747990i	$-0.731019\pi$
$887$	2226.45	−	2226.45i	0.0842806	−	0.0842806i	0.747990	+	0.663710i	$0.231019\pi$
$888$		0			0
$889$	8291.96	+	8291.96i	0.312827	+	0.312827i
$890$		0			0
$891$	−7961.61	+	19221.0i	−0.299353	+	0.722703i
$892$		0			0
$893$	−17458.7	+	7231.64i	−0.654237	+	0.270994i
$894$		0			0
$895$	63045.1			2.35460
$896$		0			0
$897$	6071.43			0.225997
$898$		0			0
$899$	2982.75	−	1235.49i	0.110657	−	0.0458354i
$900$		0			0
$901$	16937.6	−	40891.1i	0.626276	−	1.51196i
$902$		0			0
$903$	−10623.3	−	10623.3i	−0.391497	−	0.391497i
$904$		0			0
$905$	6645.49	−	6645.49i	0.244092	−	0.244092i
$906$		0			0
$907$	−43002.0	−	17812.0i	−1.57427	−	0.652082i	−0.586774	−	0.809751i	$-0.699602\pi$
$907$	−43002.0	−	17812.0i	−1.57427	−	0.652082i	−0.987492	+	0.157668i	$0.949602\pi$
$908$		0			0
$909$	14529.8	+	35077.9i	0.530167	+	1.27994i
$910$		0			0
$911$			13008.4i			0.473094i	0.971620	+	0.236547i	$0.0760156\pi$
$911$			13008.4i			0.473094i	−0.971620	+	0.236547i	$0.923984\pi$
$912$		0			0
$913$			5316.32i			0.192710i
$914$		0			0
$915$	366.508	+	884.828i	0.0132419	+	0.0319689i
$916$		0			0
$917$	24116.2	+	9989.25i	0.868469	+	0.359732i
$918$		0			0
$919$	16677.5	−	16677.5i	0.598628	−	0.598628i	−0.341319	−	0.939947i	$-0.610874\pi$
$919$	16677.5	−	16677.5i	0.598628	−	0.598628i	0.939947	+	0.341319i	$0.110874\pi$
$920$		0			0
$921$	−5879.06	−	5879.06i	−0.210338	−	0.210338i
$922$		0			0
$923$	−11337.5	+	27371.2i	−0.404312	+	0.976095i
$924$		0			0
$925$	−7439.02	+	3081.34i	−0.264425	+	0.109529i
$926$		0			0
$927$	39329.8			1.39348
$928$		0			0
$929$	24373.6			0.860786			0.430393	−	0.902642i	$-0.358375\pi$
$929$	24373.6			0.860786			0.430393	+	0.902642i	$0.358375\pi$
$930$		0			0
$931$	2411.69	−	998.953i	0.0848978	−	0.0351658i
$932$		0			0
$933$	−145.473	+	351.203i	−0.00510458	+	0.0123235i
$934$		0			0
$935$	46871.5	+	46871.5i	1.63942	+	1.63942i
$936$		0			0
$937$	−3495.17	+	3495.17i	−0.121859	+	0.121859i	−0.765406	−	0.643547i	$-0.777462\pi$
$937$	−3495.17	+	3495.17i	−0.121859	+	0.121859i	0.643547	+	0.765406i	$0.277462\pi$
$938$		0			0
$939$	7188.83	+	2977.71i	0.249839	+	0.103487i
$940$		0			0
$941$	15711.1	+	37929.9i	0.544279	+	1.31401i	0.921678	+	0.387955i	$0.126818\pi$
$941$	15711.1	+	37929.9i	0.544279	+	1.31401i	−0.377400	+	0.926050i	$0.623182\pi$
$942$		0			0
$943$			6535.24i			0.225680i
$944$		0			0
$945$		−	27043.6i		−	0.930928i
$946$		0			0
$947$	−3104.11	−	7493.99i	−0.106515	−	0.257151i	0.861631	−	0.507535i	$-0.169443\pi$
$947$	−3104.11	−	7493.99i	−0.106515	−	0.257151i	−0.968147	+	0.250384i	$0.919443\pi$
$948$		0			0
$949$	−30603.1	−	12676.2i	−1.04681	−	0.433601i
$950$		0			0
$951$	3318.20	−	3318.20i	0.113144	−	0.113144i
$952$		0			0
$953$	−16440.0	−	16440.0i	−0.558808	−	0.558808i	0.370160	−	0.928968i	$-0.379303\pi$
$953$	−16440.0	−	16440.0i	−0.558808	−	0.558808i	−0.928968	+	0.370160i	$0.879303\pi$
$954$		0			0
$955$	116.439	−	281.108i	0.00394541	−	0.00952506i
$956$		0			0
$957$	−1314.94	+	544.665i	−0.0444158	+	0.0183976i
$958$		0			0
$959$	−27532.9			−0.927095
$960$		0			0
$961$	−14223.7			−0.477449
$962$		0			0
$963$	−41351.4	+	17128.3i	−1.38373	+	0.573159i
$964$		0			0
$965$	−21861.4	+	52778.0i	−0.729267	+	1.76061i
$966$		0			0
$967$	−25408.6	−	25408.6i	−0.844968	−	0.844968i	0.144532	−	0.989500i	$-0.453832\pi$
$967$	−25408.6	−	25408.6i	−0.844968	−	0.844968i	−0.989500	+	0.144532i	$0.953832\pi$
$968$		0			0
$969$	−3492.45	+	3492.45i	−0.115783	+	0.115783i
$970$		0			0
$971$	33005.6	+	13671.4i	1.09083	+	0.451838i	0.854297	−	0.519785i	$-0.173988\pi$
$971$	33005.6	+	13671.4i	1.09083	+	0.451838i	0.236536	+	0.971623i	$0.423988\pi$
$972$		0			0
$973$	11200.2	+	27039.6i	0.369025	+	0.890905i
$974$		0			0
$975$		−	10127.7i		−	0.332662i
$976$		0			0
$977$		−	23994.9i		−	0.785738i	−0.919594	−	0.392869i	$-0.871483\pi$
$977$		−	23994.9i		−	0.785738i	0.919594	−	0.392869i	$-0.128517\pi$
$978$		0			0
$979$	5509.70	+	13301.6i	0.179868	+	0.434239i
$980$		0			0
$981$	20545.2	+	8510.11i	0.668663	+	0.276969i
$982$		0			0
$983$	−11434.9	+	11434.9i	−0.371023	+	0.371023i	−0.867850	−	0.496827i	$-0.834498\pi$
$983$	−11434.9	+	11434.9i	−0.371023	+	0.371023i	0.496827	+	0.867850i	$0.334498\pi$
$984$		0			0
$985$	9864.06	+	9864.06i	0.319081	+	0.319081i
$986$		0			0
$987$	−6766.46	+	16335.7i	−0.218215	+	0.526819i
$988$		0			0
$989$	46836.7	−	19400.4i	1.50589	−	0.623758i
$990$		0			0
$991$	−49651.4			−1.59155			−0.795777	−	0.605590i	$-0.792937\pi$
$991$	−49651.4			−1.59155			−0.795777	+	0.605590i	$0.792937\pi$
$992$		0			0
$993$	9445.29			0.301850
$994$		0			0
$995$	−42881.9	+	17762.3i	−1.36628	+	0.565932i
$996$		0			0
$997$	13807.6	−	33334.5i	0.438607	−	1.05889i	−0.537823	−	0.843058i	$-0.680753\pi$
$997$	13807.6	−	33334.5i	0.438607	−	1.05889i	0.976430	−	0.215833i	$-0.0692468\pi$
$998$		0			0
$999$	2547.37	+	2547.37i	0.0806760	+	0.0806760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.49.6		44
4.3	odd	2		32.4.g.a.21.8	✓	44
8.3	odd	2		256.4.g.b.97.6		44
8.5	even	2		256.4.g.a.97.6		44
32.3	odd	8		32.4.g.a.29.8	yes	44
32.13	even	8		256.4.g.a.161.6		44
32.19	odd	8		256.4.g.b.161.6		44
32.29	even	8	inner	128.4.g.a.81.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.8	✓	44	4.3	odd	2
32.4.g.a.29.8	yes	44	32.3	odd	8
128.4.g.a.49.6		44	1.1	even	1	trivial
128.4.g.a.81.6		44	32.29	even	8	inner
256.4.g.a.97.6		44	8.5	even	2
256.4.g.a.161.6		44	32.13	even	8
256.4.g.b.97.6		44	8.3	odd	2
256.4.g.b.161.6		44	32.19	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +O(q^{10})\)	\(q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +(-34.4676 - 14.2769i) q^{11} +(15.3924 + 37.1606i) q^{13} -25.3563i q^{15} -103.310i q^{17} +(-12.4092 - 29.9584i) q^{19} +(-28.0313 - 11.6109i) q^{21} +(72.3950 - 72.3950i) q^{23} +(-120.761 - 120.761i) q^{25} +(-29.2409 + 70.5937i) q^{27} +(23.9061 - 9.90225i) q^{29} +124.769 q^{31} -55.0042 q^{33} +(-326.986 + 135.442i) q^{35} +(18.0425 - 43.5584i) q^{37} +(41.9327 + 41.9327i) q^{39} +(-45.1360 + 45.1360i) q^{41} +(457.470 + 189.490i) q^{43} +(163.395 + 394.469i) q^{45} -582.766i q^{47} +80.5012i q^{49} +(-58.2884 - 140.721i) q^{51} +(395.810 + 163.950i) q^{53} +(-453.698 + 453.698i) q^{55} +(-33.8056 - 33.8056i) q^{57} +(-142.805 + 344.762i) q^{59} +(-34.8958 + 14.4543i) q^{61} +510.904 q^{63} +691.757 q^{65} +(-196.686 + 81.4699i) q^{67} +(57.7649 - 139.457i) q^{69} +(520.831 + 520.831i) q^{71} +(-582.329 + 582.329i) q^{73} +(-232.626 - 96.3570i) q^{75} +(293.807 + 709.314i) q^{77} +157.779i q^{79} -557.655i q^{81} +(-54.5324 - 131.653i) q^{83} +(-1641.51 - 679.936i) q^{85} +(26.9761 - 26.9761i) q^{87} +(-272.884 - 272.884i) q^{89} +(316.763 - 764.733i) q^{91} +(169.951 - 70.3959i) q^{93} -557.686 q^{95} +788.873 q^{97} +(855.703 - 354.444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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