LMFDB - Embedded newform 256.4.g.a.97.7

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			97.7
Character	$\chi$	$=$	256.97
Dual form			256.4.g.a.161.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.143768 - 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +O(q^{10})$	\(q+(0.143768 - 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +(-36.9342 - 15.2986i) q^{11} +(-4.49594 - 10.8542i) q^{13} -0.312111i q^{15} +53.8999i q^{17} +(-31.9796 - 77.2056i) q^{19} +(1.11366 + 0.461293i) q^{21} +(-50.0867 + 50.0867i) q^{23} +(85.5438 + 85.5438i) q^{25} +(-3.21429 + 7.75999i) q^{27} +(-156.098 + 64.6581i) q^{29} -207.668 q^{31} -6.22100 q^{33} +(14.3538 - 5.94555i) q^{35} +(-73.7055 + 177.941i) q^{37} +(-1.29274 - 1.29274i) q^{39} +(-293.943 + 293.943i) q^{41} +(-342.438 - 141.843i) q^{43} +(20.7050 + 49.9864i) q^{45} -510.799i q^{47} -282.996i q^{49} +(3.20978 + 7.74908i) q^{51} +(590.228 + 244.481i) q^{53} +(-56.6971 + 56.6971i) q^{55} +(-9.19528 - 9.19528i) q^{57} +(-257.808 + 622.403i) q^{59} +(-424.302 + 175.752i) q^{61} -208.961 q^{63} -23.5637 q^{65} +(482.813 - 199.988i) q^{67} +(-4.21817 + 10.1836i) q^{69} +(199.873 + 199.873i) q^{71} +(-127.360 + 127.360i) q^{73} +(17.3927 + 7.20427i) q^{75} +(-118.507 - 286.101i) q^{77} -237.438i q^{79} -727.039i q^{81} +(9.62194 + 23.2294i) q^{83} +(99.8771 + 41.3704i) q^{85} +(-18.5915 + 18.5915i) q^{87} +(329.123 + 329.123i) q^{89} +(34.8265 - 84.0787i) q^{91} +(-29.8560 + 12.3667i) q^{93} -167.608 q^{95} +776.518 q^{97} +(996.329 - 412.693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

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

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
$3$	0.143768	−	0.0595506i	0.0276682	−	0.0114605i	−0.368806	−	0.929506i	$-0.620233\pi$
$3$	0.143768	−	0.0595506i	0.0276682	−	0.0114605i	0.396475	+	0.918046i	$0.370233\pi$
$4$		0			0
$5$	0.767542	−	1.85301i	0.0686510	−	0.165738i	−0.885830	−	0.464010i	$-0.846410\pi$
$5$	0.767542	−	1.85301i	0.0686510	−	0.165738i	0.954481	+	0.298272i	$0.0964102\pi$
$6$		0			0
$7$	5.47741	+	5.47741i	0.295752	+	0.295752i	0.839348	−	0.543595i	$-0.182937\pi$
$7$	5.47741	+	5.47741i	0.295752	+	0.295752i	−0.543595	+	0.839348i	$0.682937\pi$
$8$		0			0
$9$	−19.0748	+	19.0748i	−0.706473	+	0.706473i
$10$		0			0
$11$	−36.9342	−	15.2986i	−1.01237	−	0.419338i	−0.186052	−	0.982540i	$-0.559569\pi$
$11$	−36.9342	−	15.2986i	−1.01237	−	0.419338i	−0.826319	+	0.563202i	$0.809569\pi$
$12$		0			0
$13$	−4.49594	−	10.8542i	−0.0959191	−	0.231569i	0.868636	−	0.495451i	$-0.164997\pi$
$13$	−4.49594	−	10.8542i	−0.0959191	−	0.231569i	−0.964555	+	0.263882i	$0.914997\pi$
$14$		0			0
$15$		−	0.312111i		−	0.00537245i
$16$		0			0
$17$			53.8999i			0.768980i	0.923129	+	0.384490i	$0.125623\pi$
$17$			53.8999i			0.768980i	−0.923129	+	0.384490i	$0.874377\pi$
$18$		0			0
$19$	−31.9796	−	77.2056i	−0.386138	−	0.932220i	−0.990750	−	0.135700i	$-0.956672\pi$
$19$	−31.9796	−	77.2056i	−0.386138	−	0.932220i	0.604612	−	0.796520i	$-0.293328\pi$
$20$		0			0
$21$	1.11366	+	0.461293i	0.0115724	+	0.00479344i
$22$		0			0
$23$	−50.0867	+	50.0867i	−0.454078	+	0.454078i	−0.896706	−	0.442628i	$-0.854046\pi$
$23$	−50.0867	+	50.0867i	−0.454078	+	0.454078i	0.442628	+	0.896706i	$0.354046\pi$
$24$		0			0
$25$	85.5438	+	85.5438i	0.684351	+	0.684351i
$26$		0			0
$27$	−3.21429	+	7.75999i	−0.0229108	+	0.0553115i
$28$		0			0
$29$	−156.098	+	64.6581i	−0.999543	+	0.414024i	−0.821629	−	0.570022i	$-0.806935\pi$
$29$	−156.098	+	64.6581i	−0.999543	+	0.414024i	−0.177913	+	0.984046i	$0.556935\pi$
$30$		0			0
$31$	−207.668			−1.20317			−0.601584	−	0.798810i	$-0.705463\pi$
$31$	−207.668			−1.20317			−0.601584	+	0.798810i	$0.705463\pi$
$32$		0			0
$33$	−6.22100			−0.0328163
$34$		0			0
$35$	14.3538	−	5.94555i	0.0693211	−	0.0287138i
$36$		0			0
$37$	−73.7055	+	177.941i	−0.327489	+	0.790629i	0.671288	+	0.741197i	$0.265741\pi$
$37$	−73.7055	+	177.941i	−0.327489	+	0.790629i	−0.998777	+	0.0494328i	$0.984259\pi$
$38$		0			0
$39$	−1.29274	−	1.29274i	−0.00530781	−	0.00530781i
$40$		0			0
$41$	−293.943	+	293.943i	−1.11966	+	1.11966i	−0.127875	+	0.991790i	$0.540815\pi$
$41$	−293.943	+	293.943i	−1.11966	+	1.11966i	−0.991790	+	0.127875i	$0.959185\pi$
$42$		0			0
$43$	−342.438	−	141.843i	−1.21445	−	0.503041i	−0.318808	−	0.947819i	$-0.603283\pi$
$43$	−342.438	−	141.843i	−1.21445	−	0.503041i	−0.895641	+	0.444778i	$0.853283\pi$
$44$		0			0
$45$	20.7050	+	49.9864i	0.0685894	+	0.165590i
$46$		0			0
$47$		−	510.799i		−	1.58527i	−0.609697	−	0.792635i	$-0.708709\pi$
$47$		−	510.799i		−	1.58527i	0.609697	−	0.792635i	$-0.291291\pi$
$48$		0			0
$49$		−	282.996i		−	0.825061i
$50$		0			0
$51$	3.20978	+	7.74908i	0.00881291	+	0.0212762i
$52$		0			0
$53$	590.228	+	244.481i	1.52970	+	0.633622i	0.979506	−	0.201414i	$-0.0645538\pi$
$53$	590.228	+	244.481i	1.52970	+	0.633622i	0.550194	+	0.835037i	$0.314554\pi$
$54$		0			0
$55$	−56.6971	+	56.6971i	−0.139001	+	0.139001i
$56$		0			0
$57$	−9.19528	−	9.19528i	−0.0213675	−	0.0213675i
$58$		0			0
$59$	−257.808	+	622.403i	−0.568877	+	1.37339i	0.333626	+	0.942706i	$0.391728\pi$
$59$	−257.808	+	622.403i	−0.568877	+	1.37339i	−0.902503	+	0.430685i	$0.858272\pi$
$60$		0			0
$61$	−424.302	+	175.752i	−0.890596	+	0.368897i	−0.780597	−	0.625035i	$-0.785085\pi$
$61$	−424.302	+	175.752i	−0.890596	+	0.368897i	−0.109999	+	0.993932i	$0.535085\pi$
$62$		0			0
$63$	−208.961			−0.417882
$64$		0			0
$65$	−23.5637			−0.0449648
$66$		0			0
$67$	482.813	−	199.988i	0.880373	−	0.364663i	0.103732	−	0.994605i	$-0.466922\pi$
$67$	482.813	−	199.988i	0.880373	−	0.364663i	0.776642	+	0.629943i	$0.216922\pi$
$68$		0			0
$69$	−4.21817	+	10.1836i	−0.00735953	+	0.0177675i
$70$		0			0
$71$	199.873	+	199.873i	0.334092	+	0.334092i	0.854138	−	0.520046i	$-0.174085\pi$
$71$	199.873	+	199.873i	0.334092	+	0.334092i	−0.520046	+	0.854138i	$0.674085\pi$
$72$		0			0
$73$	−127.360	+	127.360i	−0.204197	+	0.204197i	−0.801796	−	0.597598i	$-0.796122\pi$
$73$	−127.360	+	127.360i	−0.204197	+	0.204197i	0.597598	+	0.801796i	$0.296122\pi$
$74$		0			0
$75$	17.3927	+	7.20427i	0.0267777	+	0.0110917i
$76$		0			0
$77$	−118.507	−	286.101i	−0.175391	−	0.423431i
$78$		0			0
$79$		−	237.438i		−	0.338150i	−0.985603	−	0.169075i	$-0.945922\pi$
$79$		−	237.438i		−	0.338150i	0.985603	−	0.169075i	$-0.0540780\pi$
$80$		0			0
$81$		−	727.039i		−	0.997310i
$82$		0			0
$83$	9.62194	+	23.2294i	0.0127246	+	0.0307200i	0.930114	−	0.367271i	$-0.119708\pi$
$83$	9.62194	+	23.2294i	0.0127246	+	0.0307200i	−0.917390	+	0.397991i	$0.869708\pi$
$84$		0			0
$85$	99.8771	+	41.3704i	0.127449	+	0.0527912i
$86$		0			0
$87$	−18.5915	+	18.5915i	−0.0229106	+	0.0229106i
$88$		0			0
$89$	329.123	+	329.123i	0.391989	+	0.391989i	0.875396	−	0.483407i	$-0.160601\pi$
$89$	329.123	+	329.123i	0.391989	+	0.391989i	−0.483407	+	0.875396i	$0.660601\pi$
$90$		0			0
$91$	34.8265	−	84.0787i	0.0401188	−	0.0968554i
$92$		0			0
$93$	−29.8560	+	12.3667i	−0.0332894	+	0.0137889i
$94$		0			0
$95$	−167.608			−0.181013
$96$		0			0
$97$	776.518			0.812819			0.406410	−	0.913691i	$-0.366781\pi$
$97$	776.518			0.812819			0.406410	+	0.913691i	$0.366781\pi$
$98$		0			0
$99$	996.329	−	412.693i	1.01146	−	0.418962i
$100$		0			0
$101$	370.061	−	893.405i	0.364578	−	0.880170i	−0.630040	−	0.776563i	$-0.716962\pi$
$101$	370.061	−	893.405i	0.364578	−	0.880170i	0.994618	−	0.103607i	$-0.0330384\pi$
$102$		0			0
$103$	1445.50	+	1445.50i	1.38281	+	1.38281i	0.839595	+	0.543212i	$0.182792\pi$
$103$	1445.50	+	1445.50i	1.38281	+	1.38281i	0.543212	+	0.839595i	$0.317208\pi$
$104$		0			0
$105$	1.70956	−	1.70956i	0.00158891	−	0.00158891i
$106$		0			0
$107$	−8.88527	−	3.68040i	−0.00802777	−	0.00332521i	0.378666	−	0.925533i	$-0.376383\pi$
$107$	−8.88527	−	3.68040i	−0.00802777	−	0.00332521i	−0.386694	+	0.922208i	$0.626383\pi$
$108$		0			0
$109$	−648.092	−	1564.63i	−0.569505	−	1.37491i	−0.901973	−	0.431791i	$-0.857882\pi$
$109$	−648.092	−	1564.63i	−0.569505	−	1.37491i	0.332469	−	0.943114i	$-0.392118\pi$
$110$		0			0
$111$			29.9714i			0.0256285i
$112$		0			0
$113$		−	729.808i		−	0.607562i	−0.952742	−	0.303781i	$-0.901751\pi$
$113$		−	729.808i		−	0.607562i	0.952742	−	0.303781i	$-0.0982492\pi$
$114$		0			0
$115$	54.3675	+	131.255i	0.0440852	+	0.106431i
$116$		0			0
$117$	292.799	+	121.281i	0.231362	+	0.0958331i
$118$		0			0
$119$	−295.232	+	295.232i	−0.227427	+	0.227427i
$120$		0			0
$121$	188.928	+	188.928i	0.141944	+	0.141944i
$122$		0			0
$123$	−24.7551	+	59.7642i	−0.0181471	+	0.0438110i
$124$		0			0
$125$	455.798	−	188.798i	0.326143	−	0.135093i
$126$		0			0
$127$	1559.09			1.08934			0.544671	−	0.838650i	$-0.316654\pi$
$127$	1559.09			1.08934			0.544671	+	0.838650i	$0.316654\pi$
$128$		0			0
$129$	−57.6784			−0.0393667
$130$		0			0
$131$	508.328	−	210.556i	0.339029	−	0.140431i	−0.206672	−	0.978410i	$-0.566263\pi$
$131$	508.328	−	210.556i	0.339029	−	0.140431i	0.545701	+	0.837980i	$0.316263\pi$
$132$		0			0
$133$	247.721	−	598.052i	0.161505	−	0.389907i
$134$		0			0
$135$	11.9122	+	11.9122i	0.00759438	+	0.00759438i
$136$		0			0
$137$	−118.150	+	118.150i	−0.0736806	+	0.0736806i	−0.742987	−	0.669306i	$-0.766591\pi$
$137$	−118.150	+	118.150i	−0.0736806	+	0.0736806i	0.669306	+	0.742987i	$0.266591\pi$
$138$		0			0
$139$	1.49385	+	0.618775i	0.000911562	+	0.000377581i	0.383139	−	0.923691i	$-0.374843\pi$
$139$	1.49385	+	0.618775i	0.000911562	+	0.000377581i	−0.382228	+	0.924068i	$0.624843\pi$
$140$		0			0
$141$	−30.4184	−	73.4365i	−0.0181680	−	0.0438615i
$142$		0			0
$143$			469.671i			0.274657i
$144$		0			0
$145$			338.880i			0.194086i
$146$		0			0
$147$	−16.8526	−	40.6858i	−0.00945563	−	0.0228279i
$148$		0			0
$149$	527.451	+	218.478i	0.290003	+	0.120123i	0.522942	−	0.852368i	$-0.324834\pi$
$149$	527.451	+	218.478i	0.290003	+	0.120123i	−0.232939	+	0.972491i	$0.574834\pi$
$150$		0			0
$151$	893.493	−	893.493i	0.481533	−	0.481533i	−0.424088	−	0.905621i	$-0.639405\pi$
$151$	893.493	−	893.493i	0.481533	−	0.481533i	0.905621	+	0.424088i	$0.139405\pi$
$152$		0			0
$153$	−1028.13	−	1028.13i	−0.543263	−	0.543263i
$154$		0			0
$155$	−159.394	+	384.810i	−0.0825987	+	0.199411i
$156$		0			0
$157$	277.684	−	115.020i	0.141157	−	0.0584690i	−0.310987	−	0.950414i	$-0.600659\pi$
$157$	277.684	−	115.020i	0.141157	−	0.0584690i	0.452143	+	0.891945i	$0.350659\pi$
$158$		0			0
$159$	99.4149			0.0495856
$160$		0			0
$161$	−548.690			−0.268589
$162$		0			0
$163$	−2082.24	+	862.493i	−1.00058	+	0.414452i	−0.822008	−	0.569476i	$-0.807146\pi$
$163$	−2082.24	+	862.493i	−1.00058	+	0.414452i	−0.178567	+	0.983928i	$0.557146\pi$
$164$		0			0
$165$	−4.77488	+	11.5276i	−0.00225287	+	0.00543891i
$166$		0			0
$167$	−1423.70	−	1423.70i	−0.659697	−	0.659697i	0.295611	−	0.955308i	$-0.404477\pi$
$167$	−1423.70	−	1423.70i	−0.659697	−	0.659697i	−0.955308	+	0.295611i	$0.904477\pi$
$168$		0			0
$169$	1455.91	−	1455.91i	0.662683	−	0.662683i
$170$		0			0
$171$	2082.68	+	862.675i	0.931384	+	0.385792i
$172$		0			0
$173$	1398.51	+	3376.31i	0.614606	+	1.48379i	0.857889	+	0.513835i	$0.171776\pi$
$173$	1398.51	+	3376.31i	0.614606	+	1.48379i	−0.243283	+	0.969955i	$0.578224\pi$
$174$		0			0
$175$			937.117i			0.404796i
$176$		0			0
$177$			104.834i			0.0445188i
$178$		0			0
$179$	664.405	+	1604.01i	0.277430	+	0.669775i	0.999763	−	0.0217704i	$-0.00693027\pi$
$179$	664.405	+	1604.01i	0.277430	+	0.669775i	−0.722333	+	0.691545i	$0.756930\pi$
$180$		0			0
$181$	−2978.79	−	1233.86i	−1.22327	−	0.506695i	−0.324822	−	0.945775i	$-0.605304\pi$
$181$	−2978.79	−	1233.86i	−1.22327	−	0.506695i	−0.898448	+	0.439080i	$0.855304\pi$
$182$		0			0
$183$	−50.5350	+	50.5350i	−0.0204134	+	0.0204134i
$184$		0			0
$185$	273.154	+	273.154i	0.108555	+	0.108555i
$186$		0			0
$187$	824.596	−	1990.75i	0.322462	−	0.778493i
$188$		0			0
$189$	−60.1106	+	24.8986i	−0.0231344	+	0.00958259i
$190$		0			0
$191$	−3559.03			−1.34829			−0.674143	−	0.738601i	$-0.735487\pi$
$191$	−3559.03			−1.34829			−0.674143	+	0.738601i	$0.735487\pi$
$192$		0			0
$193$	150.055			0.0559648			0.0279824	−	0.999608i	$-0.491092\pi$
$193$	150.055			0.0559648			0.0279824	+	0.999608i	$0.491092\pi$
$194$		0			0
$195$	−3.38770	+	1.40323i	−0.00124409	+	0.000515320i
$196$		0			0
$197$	−1519.90	+	3669.37i	−0.549689	+	1.32707i	0.368022	+	0.929817i	$0.380035\pi$
$197$	−1519.90	+	3669.37i	−0.549689	+	1.32707i	−0.917711	+	0.397249i	$0.869965\pi$
$198$		0			0
$199$	−3083.86	−	3083.86i	−1.09854	−	1.09854i	−0.994582	−	0.103955i	$-0.966850\pi$
$199$	−3083.86	−	3083.86i	−1.09854	−	1.09854i	−0.103955	−	0.994582i	$-0.533150\pi$
$200$		0			0
$201$	57.5037	−	57.5037i	0.0201791	−	0.0201791i
$202$		0			0
$203$	−1209.17	−	500.856i	−0.418066	−	0.173168i
$204$		0			0
$205$	319.066	+	770.294i	0.108705	+	0.262437i
$206$		0			0
$207$		−	1910.78i		−	0.641587i
$208$		0			0
$209$			3340.77i			1.10567i
$210$		0			0
$211$	−868.746	−	2097.34i	−0.283445	−	0.684297i	0.716466	−	0.697622i	$-0.245758\pi$
$211$	−868.746	−	2097.34i	−0.283445	−	0.684297i	−0.999911	+	0.0133249i	$0.995758\pi$
$212$		0			0
$213$	40.6379	+	16.8328i	0.0130726	+	0.00541485i
$214$		0			0
$215$	−525.671	+	525.671i	−0.166746	+	0.166746i
$216$		0			0
$217$	−1137.48	−	1137.48i	−0.355840	−	0.355840i
$218$		0			0
$219$	−10.7260	+	25.8947i	−0.00330956	+	0.00798998i
$220$		0			0
$221$	585.038	−	242.331i	0.178072	−	0.0737599i
$222$		0			0
$223$	3747.63			1.12538			0.562690	−	0.826668i	$-0.309766\pi$
$223$	3747.63			1.12538			0.562690	+	0.826668i	$0.309766\pi$
$224$		0			0
$225$	−3263.46			−0.966950
$226$		0			0
$227$	−5533.41	+	2292.01i	−1.61791	+	0.670159i	−0.993800	−	0.111180i	$-0.964537\pi$
$227$	−5533.41	+	2292.01i	−1.61791	+	0.670159i	−0.624107	+	0.781339i	$0.714537\pi$
$228$		0			0
$229$	−719.189	+	1736.28i	−0.207534	+	0.501032i	−0.993034	−	0.117830i	$-0.962406\pi$
$229$	−719.189	+	1736.28i	−0.207534	+	0.501032i	0.785500	+	0.618862i	$0.212406\pi$
$230$		0			0
$231$	−34.0750	−	34.0750i	−0.00970549	−	0.00970549i
$232$		0			0
$233$	−575.901	+	575.901i	−0.161925	+	0.161925i	−0.783419	−	0.621494i	$-0.786526\pi$
$233$	−575.901	+	575.901i	−0.161925	+	0.161925i	0.621494	+	0.783419i	$0.286526\pi$
$234$		0			0
$235$	−946.515	−	392.059i	−0.262740	−	0.108830i
$236$		0			0
$237$	−14.1396	−	34.1360i	−0.00387538	−	0.00935599i
$238$		0			0
$239$			3712.45i			1.00476i	0.864646	+	0.502381i	$0.167543\pi$
$239$			3712.45i			1.00476i	−0.864646	+	0.502381i	$0.832457\pi$
$240$		0			0
$241$			6285.59i			1.68004i	0.542553	+	0.840021i	$0.317458\pi$
$241$			6285.59i			1.68004i	−0.542553	+	0.840021i	$0.682542\pi$
$242$		0			0
$243$	−130.082	−	314.045i	−0.0343405	−	0.0829052i
$244$		0			0
$245$	−524.394	−	217.211i	−0.136744	−	0.0566413i
$246$		0			0
$247$	−694.223	+	694.223i	−0.178835	+	0.178835i
$248$		0			0
$249$	2.76665	+	2.76665i	0.000704135	+	0.000704135i
$250$		0			0
$251$	639.477	−	1543.83i	0.160810	−	0.388231i	−0.822852	−	0.568256i	$-0.807618\pi$
$251$	639.477	−	1543.83i	0.160810	−	0.388231i	0.983662	+	0.180026i	$0.0576182\pi$
$252$		0			0
$253$	2616.17	−	1083.65i	0.650108	−	0.269283i
$254$		0			0
$255$	16.8228			0.00413130
$256$		0			0
$257$	42.7546			0.0103773			0.00518864	−	0.999987i	$-0.498348\pi$
$257$	42.7546			0.0103773			0.00518864	+	0.999987i	$0.498348\pi$
$258$		0			0
$259$	−1378.37	+	570.939i	−0.330686	+	0.136975i
$260$		0			0
$261$	1744.20	−	4210.88i	0.413653	−	0.998646i
$262$		0			0
$263$	−2360.67	−	2360.67i	−0.553479	−	0.553479i	0.373964	−	0.927443i	$-0.377998\pi$
$263$	−2360.67	−	2360.67i	−0.553479	−	0.553479i	−0.927443	+	0.373964i	$0.877998\pi$
$264$		0			0
$265$	906.050	−	906.050i	0.210031	−	0.210031i
$266$		0			0
$267$	66.9169	+	27.7179i	0.0153380	+	0.00635321i
$268$		0			0
$269$	1665.10	+	4019.90i	0.377408	+	0.911143i	0.992450	+	0.122649i	$0.0391389\pi$
$269$	1665.10	+	4019.90i	0.377408	+	0.911143i	−0.615042	+	0.788494i	$0.710861\pi$
$270$		0			0
$271$			4547.41i			1.01932i	0.860376	+	0.509660i	$0.170229\pi$
$271$			4547.41i			1.01932i	−0.860376	+	0.509660i	$0.829771\pi$
$272$		0			0
$273$		−	14.1618i		−	0.00313959i
$274$		0			0
$275$	−1850.79	−	4468.20i	−0.405843	−	0.979791i
$276$		0			0
$277$	−6747.39	−	2794.86i	−1.46358	−	0.606234i	−0.498194	−	0.867065i	$-0.666003\pi$
$277$	−6747.39	−	2794.86i	−1.46358	−	0.606234i	−0.965384	+	0.260831i	$0.916003\pi$
$278$		0			0
$279$	3961.21	−	3961.21i	0.850005	−	0.850005i
$280$		0			0
$281$	3178.42	+	3178.42i	0.674764	+	0.674764i	0.958811	−	0.284046i	$-0.0916770\pi$
$281$	3178.42	+	3178.42i	0.674764	+	0.674764i	−0.284046	+	0.958811i	$0.591677\pi$
$282$		0			0
$283$	1868.13	−	4510.06i	0.392399	−	0.947334i	−0.597018	−	0.802228i	$-0.703648\pi$
$283$	1868.13	−	4510.06i	0.392399	−	0.947334i	0.989416	−	0.145106i	$-0.0463522\pi$
$284$		0			0
$285$	−24.0967	+	9.98118i	−0.00500830	+	0.00207451i
$286$		0			0
$287$	−3220.10			−0.662287
$288$		0			0
$289$	2007.80			0.408670
$290$		0			0
$291$	111.638	−	46.2421i	0.0224892	−	0.00931533i
$292$		0			0
$293$	−509.398	+	1229.79i	−0.101568	+	0.245206i	−0.966492	−	0.256696i	$-0.917366\pi$
$293$	−509.398	+	1229.79i	−0.101568	+	0.245206i	0.864925	+	0.501902i	$0.167366\pi$
$294$		0			0
$295$	955.441	+	955.441i	0.188569	+	0.188569i
$296$		0			0
$297$	237.435	−	237.435i	0.0463884	−	0.0463884i
$298$		0			0
$299$	768.835	+	318.462i	0.148705	+	0.0615957i
$300$		0			0
$301$	−1098.74	−	2652.60i	−0.210401	−	0.507952i
$302$		0			0
$303$		−	150.480i		−	0.0285309i
$304$		0			0
$305$			921.133i			0.172931i
$306$		0			0
$307$	2519.05	+	6081.52i	0.468305	+	1.13059i	0.964903	+	0.262607i	$0.0845824\pi$
$307$	2519.05	+	6081.52i	0.468305	+	1.13059i	−0.496598	+	0.867981i	$0.665418\pi$
$308$		0			0
$309$	293.897	+	121.736i	0.0541074	+	0.0224120i
$310$		0			0
$311$	−5470.06	+	5470.06i	−0.997358	+	0.997358i	−0.999997	−	0.00263825i	$-0.999160\pi$
$311$	−5470.06	+	5470.06i	−0.997358	+	0.997358i	0.00263825	+	0.999997i	$0.499160\pi$
$312$		0			0
$313$	−4168.95	−	4168.95i	−0.752853	−	0.752853i	0.222158	−	0.975011i	$-0.428690\pi$
$313$	−4168.95	−	4168.95i	−0.752853	−	0.752853i	−0.975011	+	0.222158i	$0.928690\pi$
$314$		0			0
$315$	−160.386	+	387.206i	−0.0286880	+	0.0692590i
$316$		0			0
$317$	−3013.16	+	1248.09i	−0.533868	+	0.221135i	−0.633296	−	0.773909i	$-0.718299\pi$
$317$	−3013.16	+	1248.09i	−0.533868	+	0.221135i	0.0994284	+	0.995045i	$0.468299\pi$
$318$		0			0
$319$	6754.55			1.18552
$320$		0			0
$321$	−1.49659			−0.000260222
$322$		0			0
$323$	4161.38	−	1723.70i	0.716858	−	0.296932i
$324$		0			0
$325$	543.906	−	1313.11i	0.0928322	−	0.224117i
$326$		0			0
$327$	−186.350	−	186.350i	−0.0315143	−	0.0315143i
$328$		0			0
$329$	2797.85	−	2797.85i	0.468847	−	0.468847i
$330$		0			0
$331$	5175.95	+	2143.95i	0.859504	+	0.356018i	0.768513	−	0.639834i	$-0.220997\pi$
$331$	5175.95	+	2143.95i	0.859504	+	0.356018i	0.0909902	+	0.995852i	$0.470997\pi$
$332$		0			0
$333$	−1988.26	−	4800.09i	−0.327196	−	0.789920i
$334$		0			0
$335$		−	1048.16i		−	0.170946i
$336$		0			0
$337$		−	6275.84i		−	1.01444i	−0.861816	−	0.507220i	$-0.830673\pi$
$337$		−	6275.84i		−	1.01444i	0.861816	−	0.507220i	$-0.169327\pi$
$338$		0			0
$339$	−43.4605	−	104.923i	−0.00696298	−	0.0168101i
$340$		0			0
$341$	7670.04	+	3177.03i	1.21805	+	0.504534i
$342$		0			0
$343$	3428.84	−	3428.84i	0.539766	−	0.539766i
$344$		0			0
$345$	15.6326	+	15.6326i	0.00243951	+	0.00243951i
$346$		0			0
$347$	−2873.53	+	6937.32i	−0.444551	+	1.07324i	0.529782	+	0.848134i	$0.322274\pi$
$347$	−2873.53	+	6937.32i	−0.444551	+	1.07324i	−0.974334	+	0.225108i	$0.927726\pi$
$348$		0			0
$349$	4992.75	−	2068.06i	0.765775	−	0.317194i	0.0346154	−	0.999401i	$-0.488979\pi$
$349$	4992.75	−	2068.06i	0.765775	−	0.317194i	0.731160	+	0.682206i	$0.238979\pi$
$350$		0			0
$351$	98.6794			0.0150060
$352$		0			0
$353$	1773.18			0.267356			0.133678	−	0.991025i	$-0.457321\pi$
$353$	1773.18			0.267356			0.133678	+	0.991025i	$0.457321\pi$
$354$		0			0
$355$	523.777	−	216.956i	0.0783076	−	0.0324361i
$356$		0			0
$357$	−24.8636	+	60.0261i	−0.00368606	+	0.00889894i
$358$		0			0
$359$	7338.52	+	7338.52i	1.07886	+	1.07886i	0.996612	+	0.0822522i	$0.0262113\pi$
$359$	7338.52	+	7338.52i	1.07886	+	1.07886i	0.0822522	+	0.996612i	$0.473789\pi$
$360$		0			0
$361$	−87.9631	+	87.9631i	−0.0128245	+	0.0128245i
$362$		0			0
$363$	38.4125	+	15.9110i	0.00555409	+	0.00230058i
$364$		0			0
$365$	138.246	+	333.754i	0.0198249	+	0.0478617i
$366$		0			0
$367$		−	8883.05i		−	1.26346i	−0.775187	−	0.631732i	$-0.782344\pi$
$367$		−	8883.05i		−	1.26346i	0.775187	−	0.631732i	$-0.217656\pi$
$368$		0			0
$369$		−	11213.8i		−	1.58203i
$370$		0			0
$371$	1893.80	+	4572.04i	0.265017	+	0.639808i
$372$		0			0
$373$	3736.23	+	1547.60i	0.518645	+	0.214830i	0.626622	−	0.779323i	$-0.284437\pi$
$373$	3736.23	+	1547.60i	0.518645	+	0.214830i	−0.107976	+	0.994153i	$0.534437\pi$
$374$		0			0
$375$	54.2861	−	54.2861i	0.00747553	−	0.00747553i
$376$		0			0
$377$	1403.62	+	1403.62i	0.191751	+	0.191751i
$378$		0			0
$379$	−619.566	+	1495.76i	−0.0839708	+	0.202724i	−0.960288	−	0.279012i	$-0.909993\pi$
$379$	−619.566	+	1495.76i	−0.0839708	+	0.202724i	0.876317	+	0.481735i	$0.159993\pi$
$380$		0			0
$381$	224.147	−	92.8445i	0.0301401	−	0.0124844i
$382$		0			0
$383$	−2505.69			−0.334294			−0.167147	−	0.985932i	$-0.553455\pi$
$383$	−2505.69			−0.334294			−0.167147	+	0.985932i	$0.553455\pi$
$384$		0			0
$385$	−621.106			−0.0822195
$386$		0			0
$387$	9237.54	−	3826.31i	1.21336	−	0.502590i
$388$		0			0
$389$	1376.18	−	3322.40i	0.179371	−	0.433039i	−0.808464	−	0.588545i	$-0.799701\pi$
$389$	1376.18	−	3322.40i	0.179371	−	0.433039i	0.987835	+	0.155506i	$0.0497009\pi$
$390$		0			0
$391$	−2699.67	−	2699.67i	−0.349177	−	0.349177i
$392$		0			0
$393$	60.5425	−	60.5425i	0.00777091	−	0.00777091i
$394$		0			0
$395$	−439.975	−	182.244i	−0.0560444	−	0.0232143i
$396$		0			0
$397$	−134.074	−	323.683i	−0.0169495	−	0.0409198i	0.915178	−	0.403049i	$-0.132050\pi$
$397$	−134.074	−	323.683i	−0.0169495	−	0.0409198i	−0.932128	+	0.362130i	$0.882050\pi$
$398$		0			0
$399$		−	100.733i		−	0.0126389i
$400$		0			0
$401$		−	1126.07i		−	0.140233i	−0.997539	−	0.0701166i	$-0.977663\pi$
$401$		−	1126.07i		−	0.140233i	0.997539	−	0.0701166i	$-0.0223371\pi$
$402$		0			0
$403$	933.661	+	2254.06i	0.115407	+	0.278617i
$404$		0			0
$405$	−1347.21	−	558.033i	−0.165292	−	0.0684663i
$406$		0			0
$407$	5444.51	−	5444.51i	0.663082	−	0.663082i
$408$		0			0
$409$	−5373.28	−	5373.28i	−0.649612	−	0.649612i	0.303287	−	0.952899i	$-0.401916\pi$
$409$	−5373.28	−	5373.28i	−0.649612	−	0.649612i	−0.952899	+	0.303287i	$0.901916\pi$
$410$		0			0
$411$	−9.95029	+	24.0221i	−0.00119419	+	0.00288303i
$412$		0			0
$413$	−4821.28	+	1997.04i	−0.574430	+	0.237937i
$414$		0			0
$415$	50.4296			0.00596504
$416$		0			0
$417$	0.251617			2.95485e−5
$418$		0			0
$419$	−6114.35	+	2532.65i	−0.712901	+	0.295293i	−0.709504	−	0.704701i	$-0.751081\pi$
$419$	−6114.35	+	2532.65i	−0.712901	+	0.295293i	−0.00339649	+	0.999994i	$0.501081\pi$
$420$		0			0
$421$	1033.34	−	2494.70i	0.119624	−	0.288799i	−0.852713	−	0.522380i	$-0.825044\pi$
$421$	1033.34	−	2494.70i	0.119624	−	0.288799i	0.972337	+	0.233581i	$0.0750444\pi$
$422$		0			0
$423$	9743.36	+	9743.36i	1.11995	+	1.11995i
$424$		0			0
$425$	−4610.81	+	4610.81i	−0.526252	+	0.526252i
$426$		0			0
$427$	−3286.74	−	1361.41i	−0.372498	−	0.154294i
$428$		0			0
$429$	27.9692	+	67.5237i	0.00314771	+	0.00759924i
$430$		0			0
$431$		−	1487.87i		−	0.166283i	−0.996538	−	0.0831417i	$-0.973505\pi$
$431$		−	1487.87i		−	0.166283i	0.996538	−	0.0831417i	$-0.0264954\pi$
$432$		0			0
$433$		−	3672.70i		−	0.407618i	−0.979011	−	0.203809i	$-0.934668\pi$
$433$		−	3672.70i		−	0.407618i	0.979011	−	0.203809i	$-0.0653321\pi$
$434$		0			0
$435$	20.1805	+	48.7200i	0.00222432	+	0.00536999i
$436$		0			0
$437$	5468.72	+	2265.22i	0.598637	+	0.247964i
$438$		0			0
$439$	−7362.81	+	7362.81i	−0.800473	+	0.800473i	−0.983169	−	0.182696i	$-0.941518\pi$
$439$	−7362.81	+	7362.81i	−0.800473	+	0.800473i	0.182696	+	0.983169i	$0.441518\pi$
$440$		0			0
$441$	5398.08	+	5398.08i	0.582883	+	0.582883i
$442$		0			0
$443$	−4893.54	+	11814.0i	−0.524828	+	1.26705i	0.410044	+	0.912066i	$0.365513\pi$
$443$	−4893.54	+	11814.0i	−0.524828	+	1.26705i	−0.934873	+	0.354983i	$0.884487\pi$
$444$		0			0
$445$	862.485	−	357.253i	0.0918780	−	0.0380571i
$446$		0			0
$447$	88.8411			0.00940054
$448$		0			0
$449$	4998.86			0.525414			0.262707	−	0.964876i	$-0.415385\pi$
$449$	4998.86			0.525414			0.262707	+	0.964876i	$0.415385\pi$
$450$		0			0
$451$	15353.5	−	6359.63i	1.60303	−	0.663999i
$452$		0			0
$453$	75.2476	−	181.664i	0.00780450	−	0.0188417i
$454$		0			0
$455$	−129.068	−	129.068i	−0.0132984	−	0.0132984i
$456$		0			0
$457$	−4394.36	+	4394.36i	−0.449801	+	0.449801i	−0.895288	−	0.445487i	$-0.853031\pi$
$457$	−4394.36	+	4394.36i	−0.449801	+	0.449801i	0.445487	+	0.895288i	$0.353031\pi$
$458$		0			0
$459$	−418.263	−	173.250i	−0.0425334	−	0.0176179i
$460$		0			0
$461$	−3050.81	−	7365.31i	−0.308222	−	0.744115i	−0.999763	−	0.0217769i	$-0.993068\pi$
$461$	−3050.81	−	7365.31i	−0.308222	−	0.744115i	0.691540	−	0.722338i	$-0.256932\pi$
$462$		0			0
$463$		−	616.179i		−	0.0618493i	−0.999522	−	0.0309247i	$-0.990155\pi$
$463$		−	616.179i		−	0.0618493i	0.999522	−	0.0309247i	$-0.00984520\pi$
$464$		0			0
$465$			64.8153i			0.00646396i
$466$		0			0
$467$	−7113.42	−	17173.3i	−0.704860	−	1.70168i	−0.712461	−	0.701712i	$-0.752420\pi$
$467$	−7113.42	−	17173.3i	−0.704860	−	1.70168i	0.00760112	−	0.999971i	$-0.497580\pi$
$468$		0			0
$469$	3739.98	+	1549.15i	0.368222	+	0.152523i
$470$		0			0
$471$	33.0725	−	33.0725i	0.00323546	−	0.00323546i
$472$		0			0
$473$	10477.7	+	10477.7i	1.01853	+	1.01853i
$474$		0			0
$475$	3868.80	−	9340.12i	0.373711	−	0.902219i
$476$		0			0
$477$	−15921.9	+	6595.06i	−1.52833	+	0.633054i
$478$		0			0
$479$	−10609.5			−1.01203			−0.506014	−	0.862525i	$-0.668882\pi$
$479$	−10609.5			−1.01203			−0.506014	+	0.862525i	$0.668882\pi$
$480$		0			0
$481$	2262.77			0.214498
$482$		0			0
$483$	−78.8841	+	32.6749i	−0.00743137	+	0.00307817i
$484$		0			0
$485$	596.010	−	1438.89i	0.0558008	−	0.134715i
$486$		0			0
$487$	−2513.20	−	2513.20i	−0.233848	−	0.233848i	0.580449	−	0.814297i	$-0.302877\pi$
$487$	−2513.20	−	2513.20i	−0.233848	−	0.233848i	−0.814297	+	0.580449i	$0.802877\pi$
$488$		0			0
$489$	−247.998	+	247.998i	−0.0229342	+	0.0229342i
$490$		0			0
$491$	−14882.3	−	6164.44i	−1.36788	−	0.566593i	−0.426665	−	0.904410i	$-0.640312\pi$
$491$	−14882.3	−	6164.44i	−1.36788	−	0.566593i	−0.941212	+	0.337817i	$0.890312\pi$
$492$		0			0
$493$	−3485.07	−	8413.69i	−0.318376	−	0.768628i
$494$		0			0
$495$		−	2162.97i		−	0.196400i
$496$		0			0
$497$			2189.57i			0.197617i
$498$		0			0
$499$	4424.27	+	10681.1i	0.396909	+	0.958222i	0.988395	+	0.151907i	$0.0485414\pi$
$499$	4424.27	+	10681.1i	0.396909	+	0.958222i	−0.591486	+	0.806315i	$0.701459\pi$
$500$		0			0
$501$	−289.465	−	119.900i	−0.0258131	−	0.0106921i
$502$		0			0
$503$	−9855.92	+	9855.92i	−0.873666	+	0.873666i	−0.992870	−	0.119204i	$-0.961966\pi$
$503$	−9855.92	+	9855.92i	−0.873666	+	0.873666i	0.119204	+	0.992870i	$0.461966\pi$
$504$		0			0
$505$	−1371.45	−	1371.45i	−0.120849	−	0.120849i
$506$		0			0
$507$	122.613	−	296.014i	0.0107405	−	0.0259299i
$508$		0			0
$509$	−6891.66	+	2854.62i	−0.600132	+	0.248583i	−0.662003	−	0.749501i	$-0.730293\pi$
$509$	−6891.66	+	2854.62i	−0.600132	+	0.248583i	0.0618706	+	0.998084i	$0.480293\pi$
$510$		0			0
$511$	−1395.21			−0.120784
$512$		0			0
$513$	701.906			0.0604092
$514$		0			0
$515$	3788.00	−	1569.04i	0.324115	−	0.134253i
$516$		0			0
$517$	−7814.53	+	18865.9i	−0.664763	+	1.60488i
$518$		0			0
$519$	402.122	+	402.122i	0.0340100	+	0.0340100i
$520$		0			0
$521$	−14514.6	+	14514.6i	−1.22053	+	1.22053i	−0.253088	+	0.967443i	$0.581446\pi$
$521$	−14514.6	+	14514.6i	−1.22053	+	1.22053i	−0.967443	+	0.253088i	$0.918554\pi$
$522$		0			0
$523$	−5451.43	−	2258.06i	−0.455783	−	0.188791i	0.142967	−	0.989727i	$-0.454336\pi$
$523$	−5451.43	−	2258.06i	−0.455783	−	0.188791i	−0.598750	+	0.800936i	$0.704336\pi$
$524$		0			0
$525$	55.8059	+	134.727i	0.00463918	+	0.0112000i
$526$		0			0
$527$		−	11193.3i		−	0.925212i
$528$		0			0
$529$			7149.65i			0.587626i
$530$		0			0
$531$	−6954.57	−	16789.8i	−0.568367	−	1.37216i
$532$		0			0
$533$	4512.06	+	1868.96i	0.366677	+	0.151883i
$534$		0			0
$535$	−13.6396	+	13.6396i	−0.00110223	+	0.00110223i
$536$		0			0
$537$	191.040	+	191.040i	0.0153519	+	0.0153519i
$538$		0			0
$539$	−4329.46	+	10452.2i	−0.345979	+	0.835268i
$540$		0			0
$541$	10798.7	−	4472.96i	0.858172	−	0.355466i	0.0901796	−	0.995926i	$-0.471256\pi$
$541$	10798.7	−	4472.96i	0.858172	−	0.355466i	0.767992	+	0.640459i	$0.221256\pi$
$542$		0			0
$543$	−501.732			−0.0396526
$544$		0			0
$545$	−3396.72			−0.266971
$546$		0			0
$547$	−19366.3	+	8021.78i	−1.51379	+	0.627032i	−0.976335	−	0.216262i	$-0.930614\pi$
$547$	−19366.3	+	8021.78i	−1.51379	+	0.627032i	−0.537453	+	0.843294i	$0.680614\pi$
$548$		0			0
$549$	4741.04	−	11445.9i	0.368566	−	0.889797i
$550$		0			0
$551$	9983.93	+	9983.93i	0.771923	+	0.771923i
$552$		0			0
$553$	1300.54	−	1300.54i	0.100009	−	0.100009i
$554$		0			0
$555$	55.5373	+	23.0043i	0.00424761	+	0.00175942i
$556$		0			0
$557$	4652.66	+	11232.5i	0.353931	+	0.854466i	0.996127	+	0.0879250i	$0.0280236\pi$
$557$	4652.66	+	11232.5i	0.353931	+	0.854466i	−0.642196	+	0.766541i	$0.721976\pi$
$558$		0			0
$559$			4354.59i			0.329480i
$560$		0			0
$561$		−	335.311i		−	0.0252350i
$562$		0			0
$563$	3815.91	+	9212.42i	0.285651	+	0.689622i	0.999948	−	0.0102205i	$-0.00325334\pi$
$563$	3815.91	+	9212.42i	0.285651	+	0.689622i	−0.714297	+	0.699843i	$0.753253\pi$
$564$		0			0
$565$	−1352.34	−	560.158i	−0.100696	−	0.0417098i
$566$		0			0
$567$	3982.29	−	3982.29i	0.294957	−	0.294957i
$568$		0			0
$569$	7598.85	+	7598.85i	0.559860	+	0.559860i	0.929268	−	0.369407i	$-0.120439\pi$
$569$	7598.85	+	7598.85i	0.559860	+	0.559860i	−0.369407	+	0.929268i	$0.620439\pi$
$570$		0			0
$571$	5406.36	−	13052.1i	0.396233	−	0.956591i	−0.592318	−	0.805704i	$-0.701787\pi$
$571$	5406.36	−	13052.1i	0.396233	−	0.956591i	0.988551	−	0.150887i	$-0.0482129\pi$
$572$		0			0
$573$	−511.675	+	211.943i	−0.0373046	+	0.0154521i
$574$		0			0
$575$	−8569.21			−0.621497
$576$		0			0
$577$	−13340.9			−0.962548			−0.481274	−	0.876570i	$-0.659826\pi$
$577$	−13340.9			−0.962548			−0.481274	+	0.876570i	$0.659826\pi$
$578$		0			0
$579$	21.5731	−	8.93589i	0.00154844	−	0.000641386i
$580$		0			0
$581$	−74.5337	+	179.940i	−0.00532217	+	0.0128489i
$582$		0			0
$583$	−18059.4	−	18059.4i	−1.28292	−	1.28292i
$584$		0			0
$585$	449.471	−	449.471i	0.0317664	−	0.0317664i
$586$		0			0
$587$	−8254.52	−	3419.14i	−0.580410	−	0.240414i	0.0731089	−	0.997324i	$-0.476708\pi$
$587$	−8254.52	−	3419.14i	−0.580410	−	0.240414i	−0.653519	+	0.756910i	$0.726708\pi$
$588$		0			0
$589$	6641.13	+	16033.1i	0.464589	+	1.12162i
$590$		0			0
$591$			618.050i			0.0430172i
$592$		0			0
$593$		−	3054.91i		−	0.211552i	−0.994390	−	0.105776i	$-0.966267\pi$
$593$		−	3054.91i		−	0.211552i	0.994390	−	0.105776i	$-0.0337326\pi$
$594$		0			0
$595$	320.465	+	773.670i	0.0220803	+	0.0533065i
$596$		0			0
$597$	−627.006	−	259.714i	−0.0429843	−	0.0178047i
$598$		0			0
$599$	17187.4	−	17187.4i	1.17239	−	1.17239i	0.190748	−	0.981639i	$-0.438909\pi$
$599$	17187.4	−	17187.4i	1.17239	−	1.17239i	0.981639	−	0.190748i	$-0.0610915\pi$
$600$		0			0
$601$	−16155.9	−	16155.9i	−1.09653	−	1.09653i	−0.994814	−	0.101716i	$-0.967567\pi$
$601$	−16155.9	−	16155.9i	−1.09653	−	1.09653i	−0.101716	−	0.994814i	$-0.532433\pi$
$602$		0			0
$603$	−5394.83	+	13024.3i	−0.364336	+	0.879584i
$604$		0			0
$605$	495.095	−	205.075i	0.0332702	−	0.0137810i
$606$		0			0
$607$	5713.13			0.382025			0.191012	−	0.981588i	$-0.438823\pi$
$607$	5713.13			0.382025			0.191012	+	0.981588i	$0.438823\pi$
$608$		0			0
$609$	−203.667			−0.0135517
$610$		0			0
$611$	−5544.29	+	2296.52i	−0.367100	+	0.152058i
$612$		0			0
$613$	−6320.21	+	15258.3i	−0.416429	+	1.00535i	0.566945	+	0.823755i	$0.308125\pi$
$613$	−6320.21	+	15258.3i	−0.416429	+	1.00535i	−0.983374	+	0.181592i	$0.941875\pi$
$614$		0			0
$615$	91.7430	+	91.7430i	0.00601534	+	0.00601534i
$616$		0			0
$617$	4724.98	−	4724.98i	0.308299	−	0.308299i	−0.535951	−	0.844249i	$-0.680047\pi$
$617$	4724.98	−	4724.98i	0.308299	−	0.308299i	0.844249	+	0.535951i	$0.180047\pi$
$618$		0			0
$619$	24539.1	+	10164.4i	1.59339	+	0.660006i	0.990462	−	0.137786i	$-0.0439987\pi$
$619$	24539.1	+	10164.4i	1.59339	+	0.660006i	0.602933	+	0.797792i	$0.293999\pi$
$620$		0			0
$621$	−227.679	−	549.665i	−0.0147125	−	0.0355190i
$622$		0			0
$623$			3605.49i			0.231863i
$624$		0			0
$625$			14132.6i			0.904489i
$626$		0			0
$627$	198.945	+	480.296i	0.0126716	+	0.0305920i
$628$		0			0
$629$	−9591.00	−	3972.72i	−0.607978	−	0.251833i
$630$		0			0
$631$	−15837.8	+	15837.8i	−0.999194	+	0.999194i	−1.00000		0.000805461i	$-0.999744\pi$
$631$	−15837.8	+	15837.8i	−0.999194	+	0.999194i	0.000805461		1.00000i	$0.499744\pi$
$632$		0			0
$633$	−249.796	−	249.796i	−0.0156848	−	0.0156848i
$634$		0			0
$635$	1196.66	−	2889.00i	0.0747844	−	0.180546i
$636$		0			0
$637$	−3071.68	+	1272.33i	−0.191059	+	0.0791391i
$638$		0			0
$639$	−7625.06			−0.472054
$640$		0			0
$641$	4.03221			0.000248460			0.000124230	−	1.00000i	$-0.499960\pi$
$641$	4.03221			0.000248460			0.000124230		1.00000i	$0.499960\pi$
$642$		0			0
$643$	6758.04	−	2799.27i	0.414481	−	0.171683i	−0.165691	−	0.986178i	$-0.552985\pi$
$643$	6758.04	−	2799.27i	0.414481	−	0.171683i	0.580172	+	0.814494i	$0.302985\pi$
$644$		0			0
$645$	−44.2706	+	106.879i	−0.00270256	+	0.00652456i
$646$		0			0
$647$	−17744.9	−	17744.9i	−1.07824	−	1.07824i	−0.996667	−	0.0815765i	$-0.974005\pi$
$647$	−17744.9	−	17744.9i	−1.07824	−	1.07824i	−0.0815765	−	0.996667i	$-0.525995\pi$
$648$		0			0
$649$	19043.9	−	19043.9i	1.15183	−	1.15183i
$650$		0			0
$651$	−231.271	−	95.7956i	−0.0139235	−	0.00576732i
$652$		0			0
$653$	−1174.68	−	2835.93i	−0.0703963	−	0.169952i	0.884765	−	0.466037i	$-0.154319\pi$
$653$	−1174.68	−	2835.93i	−0.0703963	−	0.169952i	−0.955161	+	0.296085i	$0.904319\pi$
$654$		0			0
$655$		−	1103.55i		−	0.0658308i
$656$		0			0
$657$		−	4858.74i		−	0.288520i
$658$		0			0
$659$	−1291.33	−	3117.55i	−0.0763325	−	0.184283i	0.881107	−	0.472917i	$-0.156799\pi$
$659$	−1291.33	−	3117.55i	−0.0763325	−	0.184283i	−0.957440	+	0.288634i	$0.906799\pi$
$660$		0			0
$661$	−5796.90	−	2401.15i	−0.341109	−	0.141292i	0.205551	−	0.978646i	$-0.434101\pi$
$661$	−5796.90	−	2401.15i	−0.341109	−	0.141292i	−0.546661	+	0.837354i	$0.684101\pi$
$662$		0			0
$663$	69.6788	−	69.6788i	0.00408160	−	0.00408160i
$664$		0			0
$665$	−918.059	−	918.059i	−0.0535351	−	0.0535351i
$666$		0			0
$667$	4579.94	−	11057.0i	0.265871	−	0.641870i
$668$		0			0
$669$	538.789	−	223.174i	0.0311372	−	0.0128974i
$670$		0			0
$671$	18360.0			1.05631
$672$		0			0
$673$	19927.1			1.14135			0.570677	−	0.821174i	$-0.306681\pi$
$673$	19927.1			1.14135			0.570677	+	0.821174i	$0.306681\pi$
$674$		0			0
$675$	−938.782	+	388.856i	−0.0535315	+	0.0221735i
$676$		0			0
$677$	1135.03	−	2740.21i	0.0644356	−	0.155561i	−0.888382	−	0.459105i	$-0.848170\pi$
$677$	1135.03	−	2740.21i	0.0644356	−	0.155561i	0.952817	+	0.303544i	$0.0981700\pi$
$678$		0			0
$679$	4253.31	+	4253.31i	0.240393	+	0.240393i
$680$		0			0
$681$	−659.036	+	659.036i	−0.0370841	+	0.0370841i
$682$		0			0
$683$	14514.9	+	6012.25i	0.813171	+	0.336826i	0.750218	−	0.661190i	$-0.229948\pi$
$683$	14514.9	+	6012.25i	0.813171	+	0.336826i	0.0629526	+	0.998017i	$0.479948\pi$
$684$		0			0
$685$	128.248	+	309.618i	0.00715344	+	0.0172699i
$686$		0			0
$687$			292.449i			0.0162411i
$688$		0			0
$689$		−	7505.60i		−	0.415008i
$690$		0			0
$691$	10219.6	+	24672.3i	0.562621	+	1.35829i	0.907663	+	0.419701i	$0.137865\pi$
$691$	10219.6	+	24672.3i	0.562621	+	1.35829i	−0.345041	+	0.938588i	$0.612135\pi$
$692$		0			0
$693$	7717.79	+	3196.81i	0.423051	+	0.175234i
$694$		0			0
$695$	2.29319	−	2.29319i	0.000125159	−	0.000125159i
$696$		0			0
$697$	−15843.5	−	15843.5i	−0.860999	−	0.860999i
$698$		0			0
$699$	−48.5008	+	117.091i	−0.00262442	+	0.00633591i
$700$		0			0
$701$	18637.8	−	7720.05i	1.00420	−	0.415952i	0.180862	−	0.983508i	$-0.442111\pi$
$701$	18637.8	−	7720.05i	1.00420	−	0.415952i	0.823334	+	0.567557i	$0.192111\pi$
$702$		0			0
$703$	16095.1			0.863497
$704$		0			0
$705$	−159.426			−0.00851677
$706$		0			0
$707$	6920.52	−	2866.57i	0.368137	−	0.152487i
$708$		0			0
$709$	7105.65	−	17154.6i	0.376387	−	0.908678i	−0.616250	−	0.787550i	$-0.711349\pi$
$709$	7105.65	−	17154.6i	0.376387	−	0.908678i	0.992637	−	0.121128i	$-0.0386510\pi$
$710$		0			0
$711$	4529.07	+	4529.07i	0.238894	+	0.238894i
$712$		0			0
$713$	10401.4	−	10401.4i	0.546332	−	0.546332i
$714$		0			0
$715$	870.305	+	360.492i	0.0455211	+	0.0188554i
$716$		0			0
$717$	221.079	+	533.731i	0.0115151	+	0.0277999i
$718$		0			0
$719$			26810.6i			1.39064i	0.718702	+	0.695318i	$0.244736\pi$
$719$			26810.6i			1.39064i	−0.718702	+	0.695318i	$0.755264\pi$
$720$		0			0
$721$			15835.2i			0.817937i
$722$		0			0
$723$	374.311	+	903.666i	0.0192542	+	0.0464837i
$724$		0			0
$725$	−18884.4	−	7822.16i	−0.967376	−	0.400700i
$726$		0			0
$727$	17418.8	−	17418.8i	0.888623	−	0.888623i	−0.105768	−	0.994391i	$-0.533730\pi$
$727$	17418.8	−	17418.8i	0.888623	−	0.888623i	0.994391	+	0.105768i	$0.0337302\pi$
$728$		0			0
$729$	13843.1	+	13843.1i	0.703305	+	0.703305i
$730$		0			0
$731$	7645.30	−	18457.4i	0.386829	−	0.933887i
$732$		0			0
$733$	34809.3	−	14418.5i	1.75404	−	0.726547i	0.756690	−	0.653774i	$-0.226815\pi$
$733$	34809.3	−	14418.5i	1.75404	−	0.726547i	0.997349	−	0.0727727i	$-0.0231848\pi$
$734$		0			0
$735$	−88.3261			−0.00443260
$736$		0			0
$737$	−20891.9			−1.04418
$738$		0			0
$739$	−35885.8	+	14864.4i	−1.78630	+	0.739911i	−0.795278	+	0.606245i	$0.792675\pi$
$739$	−35885.8	+	14864.4i	−1.78630	+	0.739911i	−0.991026	+	0.133666i	$0.957325\pi$
$740$		0			0
$741$	−58.4656	+	141.148i	−0.00289850	+	0.00699759i
$742$		0			0
$743$	19477.4	+	19477.4i	0.961718	+	0.961718i	0.999294	−	0.0375762i	$-0.0119637\pi$
$743$	19477.4	+	19477.4i	0.961718	+	0.961718i	−0.0375762	+	0.999294i	$0.511964\pi$
$744$		0			0
$745$	809.682	−	809.682i	0.0398180	−	0.0398180i
$746$		0			0
$747$	−626.632	−	259.559i	−0.0306925	−	0.0127132i
$748$		0			0
$749$	−28.5092	−	68.8273i	−0.00139079	−	0.00335767i
$750$		0			0
$751$			26371.3i			1.28136i	0.767807	+	0.640681i	$0.221348\pi$
$751$			26371.3i			1.28136i	−0.767807	+	0.640681i	$0.778652\pi$
$752$		0			0
$753$		−	260.035i		−	0.0125846i
$754$		0			0
$755$	−969.857	−	2341.44i	−0.0467506	−	0.112866i
$756$		0			0
$757$	−26271.7	−	10882.1i	−1.26137	−	0.522478i	−0.351043	−	0.936359i	$-0.614173\pi$
$757$	−26271.7	−	10882.1i	−1.26137	−	0.522478i	−0.910331	+	0.413881i	$0.864173\pi$
$758$		0			0
$759$	311.589	−	311.589i	0.0149012	−	0.0149012i
$760$		0			0
$761$	−7394.46	−	7394.46i	−0.352233	−	0.352233i	0.508707	−	0.860940i	$-0.330124\pi$
$761$	−7394.46	−	7394.46i	−0.352233	−	0.352233i	−0.860940	+	0.508707i	$0.830124\pi$
$762$		0			0
$763$	5020.27	−	12120.0i	0.238199	−	0.575064i
$764$		0			0
$765$	−2694.26	+	1116.00i	−0.127335	+	0.0527439i
$766$		0			0
$767$	7914.75			0.372601
$768$		0			0
$769$	4771.82			0.223766			0.111883	−	0.993721i	$-0.464312\pi$
$769$	4771.82			0.223766			0.111883	+	0.993721i	$0.464312\pi$
$770$		0			0
$771$	6.14675	−	2.54607i	0.000287120	−	0.000118929i
$772$		0			0
$773$	8895.17	−	21474.8i	0.413890	−	0.999219i	−0.570193	−	0.821511i	$-0.693132\pi$
$773$	8895.17	−	21474.8i	0.413890	−	0.999219i	0.984083	−	0.177709i	$-0.0568684\pi$
$774$		0			0
$775$	−17764.7	−	17764.7i	−0.823389	−	0.823389i
$776$		0			0
$777$	−164.166	+	164.166i	−0.00757967	+	0.00757967i
$778$		0			0
$779$	32094.3	+	13293.9i	1.47612	+	0.611429i
$780$		0			0
$781$	−4324.36	−	10439.9i	−0.198128	−	0.478323i
$782$		0			0
$783$		−	1419.15i		−	0.0647718i
$784$		0			0
$785$		−	602.834i		−	0.0274090i
$786$		0			0
$787$	−7111.73	−	17169.2i	−0.322117	−	0.777659i	−0.999131	−	0.0416884i	$-0.986726\pi$
$787$	−7111.73	−	17169.2i	−0.322117	−	0.777659i	0.677014	−	0.735970i	$-0.263274\pi$
$788$		0			0
$789$	−479.968	−	198.809i	−0.0216569	−	0.00897059i
$790$		0			0
$791$	3997.46	−	3997.46i	0.179688	−	0.179688i
$792$		0			0
$793$	3815.27	+	3815.27i	0.170850	+	0.170850i
$794$		0			0
$795$	76.3051	−	184.217i	0.00340410	−	0.00821823i
$796$		0			0
$797$	−24661.7	+	10215.2i	−1.09606	+	0.454004i	−0.856117	−	0.516782i	$-0.827130\pi$
$797$	−24661.7	+	10215.2i	−1.09606	+	0.454004i	−0.239946	+	0.970786i	$0.577130\pi$
$798$		0			0
$799$	27532.0			1.21904
$800$		0			0
$801$	−12555.9			−0.553859
$802$		0			0
$803$	6652.40	−	2755.51i	0.292351	−	0.121096i
$804$		0			0
$805$	−421.143	+	1016.73i	−0.0184389	+	0.0445155i
$806$		0			0
$807$	478.775	+	478.775i	0.0208844	+	0.0208844i
$808$		0			0
$809$	22540.9	−	22540.9i	0.979600	−	0.979600i	−0.0201963	−	0.999796i	$-0.506429\pi$
$809$	22540.9	−	22540.9i	0.979600	−	0.979600i	0.999796	+	0.0201963i	$0.00642911\pi$
$810$		0			0
$811$	−12287.9	−	5089.83i	−0.532044	−	0.220380i	0.100454	−	0.994942i	$-0.467970\pi$
$811$	−12287.9	−	5089.83i	−0.532044	−	0.220380i	−0.632498	+	0.774562i	$0.717970\pi$
$812$		0			0
$813$	270.801	+	653.772i	0.0116819	+	0.0282027i
$814$		0			0
$815$			4520.41i			0.194286i
$816$		0			0
$817$			30974.2i			1.32638i
$818$		0			0
$819$	939.473	+	2268.09i	0.0400829	+	0.0967686i
$820$		0			0
$821$	15862.2	+	6570.34i	0.674293	+	0.279301i	0.693439	−	0.720515i	$-0.256095\pi$
$821$	15862.2	+	6570.34i	0.674293	+	0.279301i	−0.0191460	+	0.999817i	$0.506095\pi$
$822$		0			0
$823$	−11289.1	+	11289.1i	−0.478146	+	0.478146i	−0.904538	−	0.426392i	$-0.859784\pi$
$823$	−11289.1	+	11289.1i	−0.478146	+	0.478146i	0.426392	+	0.904538i	$0.359784\pi$
$824$		0			0
$825$	−532.168	−	532.168i	−0.0224578	−	0.0224578i
$826$		0			0
$827$	2548.49	−	6152.59i	0.107158	−	0.258702i	−0.861201	−	0.508265i	$-0.830287\pi$
$827$	2548.49	−	6152.59i	0.107158	−	0.258702i	0.968359	+	0.249563i	$0.0802870\pi$
$828$		0			0
$829$	40448.6	−	16754.4i	1.69462	−	0.701934i	0.694768	−	0.719234i	$-0.255507\pi$
$829$	40448.6	−	16754.4i	1.69462	−	0.701934i	0.999850	+	0.0173006i	$0.00550723\pi$
$830$		0			0
$831$	−1136.49			−0.0474423
$832$		0			0
$833$	15253.5			0.634455
$834$		0			0
$835$	−3730.88	+	1545.38i	−0.154626	+	0.0640481i
$836$		0			0
$837$	667.504	−	1611.50i	0.0275655	−	0.0665490i
$838$		0			0
$839$	−2282.23	−	2282.23i	−0.0939108	−	0.0939108i	0.658591	−	0.752501i	$-0.271153\pi$
$839$	−2282.23	−	2282.23i	−0.0939108	−	0.0939108i	−0.752501	+	0.658591i	$0.771153\pi$
$840$		0			0
$841$	2940.42	−	2940.42i	0.120563	−	0.120563i
$842$		0			0
$843$	646.232	+	267.678i	0.0264026	+	0.0109363i
$844$		0			0
$845$	−1580.35	−	3815.30i	−0.0643380	−	0.155326i
$846$		0			0
$847$			2069.67i			0.0839607i
$848$		0			0
$849$		−	759.651i		−	0.0307081i
$850$		0			0
$851$	−5220.80	−	12604.1i	−0.210302	−	0.507713i
$852$		0			0
$853$	−8660.34	−	3587.23i	−0.347625	−	0.143991i	0.202037	−	0.979378i	$-0.435244\pi$
$853$	−8660.34	−	3587.23i	−0.347625	−	0.143991i	−0.549663	+	0.835387i	$0.685244\pi$
$854$		0			0
$855$	3197.09	−	3197.09i	0.127881	−	0.127881i
$856$		0			0
$857$	−10879.0	−	10879.0i	−0.433630	−	0.433630i	0.456231	−	0.889861i	$-0.349199\pi$
$857$	−10879.0	−	10879.0i	−0.433630	−	0.433630i	−0.889861	+	0.456231i	$0.849199\pi$
$858$		0			0
$859$	−816.021	+	1970.05i	−0.0324124	+	0.0782506i	−0.939257	−	0.343215i	$-0.888484\pi$
$859$	−816.021	+	1970.05i	−0.0324124	+	0.0782506i	0.906844	+	0.421465i	$0.138484\pi$
$860$		0			0
$861$	−462.947	+	191.759i	−0.0183243	+	0.00759016i
$862$		0			0
$863$	−17532.1			−0.691541			−0.345771	−	0.938319i	$-0.612383\pi$
$863$	−17532.1			−0.691541			−0.345771	+	0.938319i	$0.612383\pi$
$864$		0			0
$865$	7329.74			0.288114
$866$		0			0
$867$	288.657	−	119.566i	0.0113072	−	0.00468358i
$868$		0			0
$869$	−3632.48	+	8769.58i	−0.141799	+	0.342333i
$870$		0			0
$871$	−4341.40	−	4341.40i	−0.168889	−	0.168889i
$872$		0			0
$873$	−14811.9	+	14811.9i	−0.574234	+	0.574234i
$874$		0			0
$875$	3530.71	+	1462.47i	0.136411	+	0.0565034i
$876$		0			0
$877$	1857.78	+	4485.09i	0.0715313	+	0.172692i	0.955601	−	0.294663i	$-0.0952072\pi$
$877$	1857.78	+	4485.09i	0.0715313	+	0.172692i	−0.884070	+	0.467354i	$0.845207\pi$
$878$		0			0
$879$			207.140i			0.00794842i
$880$		0			0
$881$		−	24865.4i		−	0.950894i	−0.879744	−	0.475447i	$-0.842286\pi$
$881$		−	24865.4i		−	0.950894i	0.879744	−	0.475447i	$-0.157714\pi$
$882$		0			0
$883$	14018.3	+	33843.3i	0.534264	+	1.28983i	0.928676	+	0.370893i	$0.120948\pi$
$883$	14018.3	+	33843.3i	0.534264	+	1.28983i	−0.394412	+	0.918934i	$0.629052\pi$
$884$		0			0
$885$	194.259	+	80.4647i	0.00737847	+	0.00305626i
$886$		0			0
$887$	−4048.92	+	4048.92i	−0.153269	+	0.153269i	−0.779576	−	0.626307i	$-0.784565\pi$
$887$	−4048.92	+	4048.92i	−0.153269	+	0.153269i	0.626307	+	0.779576i	$0.284565\pi$
$888$		0			0
$889$	8539.75	+	8539.75i	0.322175	+	0.322175i
$890$		0			0
$891$	−11122.7	+	26852.6i	−0.418210	+	1.00965i
$892$		0			0
$893$	−39436.5	+	16335.1i	−1.47782	+	0.612133i
$894$		0			0
$895$	3482.21			0.130053
$896$		0			0
$897$	129.498			0.00482032
$898$		0			0
$899$	32416.6	−	13427.4i	1.20262	−	0.498141i
$900$		0			0
$901$	−13177.5	+	31813.3i	−0.487243	+	1.17631i
$902$		0			0
$903$	−315.928	−	315.928i	−0.0116428	−	0.0116428i
$904$		0			0
$905$	−4572.69	+	4572.69i	−0.167957	+	0.167957i
$906$		0			0
$907$	−30120.4	−	12476.3i	−1.10268	−	0.456745i	−0.244268	−	0.969708i	$-0.578548\pi$
$907$	−30120.4	−	12476.3i	−1.10268	−	0.456745i	−0.858411	+	0.512963i	$0.828548\pi$
$908$		0			0
$909$	9982.67	+	24100.3i	0.364251	+	0.879380i
$910$		0			0
$911$		−	26490.1i		−	0.963400i	−0.876336	−	0.481700i	$-0.840020\pi$
$911$		−	26490.1i		−	0.963400i	0.876336	−	0.481700i	$-0.159980\pi$
$912$		0			0
$913$		−	1005.16i		−	0.0364360i
$914$		0			0
$915$	54.8541	+	132.429i	0.00198188	+	0.00478468i
$916$		0			0
$917$	3937.62	+	1631.02i	0.141801	+	0.0587360i
$918$		0			0
$919$	−2467.15	+	2467.15i	−0.0885570	+	0.0885570i	−0.749998	−	0.661441i	$-0.769945\pi$
$919$	−2467.15	+	2467.15i	−0.0885570	+	0.0885570i	0.661441	+	0.749998i	$0.269945\pi$
$920$		0			0
$921$	724.316	+	724.316i	0.0259143	+	0.0259143i
$922$		0			0
$923$	1270.84	−	3068.07i	0.0453197	−	0.109411i
$924$		0			0
$925$	−21526.8	+	8916.69i	−0.765185	+	0.316950i
$926$		0			0
$927$	−55145.1			−1.95383
$928$		0			0
$929$	−13097.0			−0.462537			−0.231269	−	0.972890i	$-0.574288\pi$
$929$	−13097.0			−0.462537			−0.231269	+	0.972890i	$0.574288\pi$
$930$		0			0
$931$	−21848.9	+	9050.10i	−0.769138	+	0.318588i
$932$		0			0
$933$	−460.673	+	1112.16i	−0.0161648	+	0.0390253i
$934$		0			0
$935$	−3055.97	−	3055.97i	−0.106889	−	0.106889i
$936$		0			0
$937$	−24748.7	+	24748.7i	−0.862864	+	0.862864i	−0.991670	−	0.128806i	$-0.958886\pi$
$937$	−24748.7	+	24748.7i	−0.862864	+	0.862864i	0.128806	+	0.991670i	$0.458886\pi$
$938$		0			0
$939$	−847.625	−	351.098i	−0.0294581	−	0.0122020i
$940$		0			0
$941$	3168.01	+	7648.26i	0.109749	+	0.264959i	0.969207	−	0.246249i	$-0.0791982\pi$
$941$	3168.01	+	7648.26i	0.109749	+	0.264959i	−0.859457	+	0.511208i	$0.829198\pi$
$942$		0			0
$943$		−	29445.3i		−	1.01683i
$944$		0			0
$945$			130.496i			0.00449211i
$946$		0			0
$947$	−4403.80	−	10631.7i	−0.151113	−	0.364820i	0.830137	−	0.557560i	$-0.188262\pi$
$947$	−4403.80	−	10631.7i	−0.151113	−	0.364820i	−0.981250	+	0.192741i	$0.938262\pi$
$948$		0			0
$949$	1954.99	+	809.785i	0.0668723	+	0.0276994i
$950$		0			0
$951$	−358.872	+	358.872i	−0.0122368	+	0.0122368i
$952$		0			0
$953$	−4833.37	−	4833.37i	−0.164290	−	0.164290i	0.620174	−	0.784464i	$-0.287062\pi$
$953$	−4833.37	−	4833.37i	−0.164290	−	0.164290i	−0.784464	+	0.620174i	$0.787062\pi$
$954$		0			0
$955$	−2731.71	+	6594.92i	−0.0925612	+	0.223462i
$956$		0			0
$957$	971.088	−	402.238i	0.0328013	−	0.0135867i
$958$		0			0
$959$	−1294.31			−0.0435824
$960$		0			0
$961$	13334.8			0.447613
$962$		0			0
$963$	239.687	−	99.2817i	0.00802057	−	0.00332223i
$964$		0			0
$965$	115.174	−	278.054i	0.00384204	−	0.00927551i
$966$		0			0
$967$	−11429.8	−	11429.8i	−0.380101	−	0.380101i	0.491037	−	0.871138i	$-0.336618\pi$
$967$	−11429.8	−	11429.8i	−0.380101	−	0.380101i	−0.871138	+	0.491037i	$0.836618\pi$
$968$		0			0
$969$	495.625	−	495.625i	0.0164311	−	0.0164311i
$970$		0			0
$971$	6489.63	+	2688.09i	0.214482	+	0.0888414i	0.487338	−	0.873214i	$-0.337968\pi$
$971$	6489.63	+	2688.09i	0.214482	+	0.0888414i	−0.272856	+	0.962055i	$0.587968\pi$
$972$		0			0
$973$	4.79317	+	11.5717i	0.000157926	+	0.000381267i
$974$		0			0
$975$		−	221.172i		−	0.00726481i
$976$		0			0
$977$		−	19891.1i		−	0.651354i	−0.945481	−	0.325677i	$-0.894408\pi$
$977$		−	19891.1i		−	0.651354i	0.945481	−	0.325677i	$-0.105592\pi$
$978$		0			0
$979$	−7120.77	−	17191.1i	−0.232462	−	0.561214i
$980$		0			0
$981$	42207.2	+	17482.8i	1.37367	+	0.568994i
$982$		0			0
$983$	−606.701	+	606.701i	−0.0196854	+	0.0196854i	−0.716881	−	0.697196i	$-0.754431\pi$
$983$	−606.701	+	606.701i	−0.0196854	+	0.0196854i	0.697196	+	0.716881i	$0.254431\pi$
$984$		0			0
$985$	5632.79	+	5632.79i	0.182209	+	0.182209i
$986$		0			0
$987$	235.628	−	568.856i	0.00759890	−	0.0183454i
$988$		0			0
$989$	24256.0	−	10047.2i	0.779875	−	0.323035i
$990$		0			0
$991$	−2306.07			−0.0739201			−0.0369600	−	0.999317i	$-0.511767\pi$
$991$	−2306.07			−0.0739201			−0.0369600	+	0.999317i	$0.511767\pi$
$992$		0			0
$993$	871.808			0.0278610
$994$		0			0
$995$	−8081.41	+	3347.43i	−0.257485	+	0.106654i
$996$		0			0
$997$	−11827.8	+	28554.9i	−0.375718	+	0.907064i	0.617040	+	0.786932i	$0.288332\pi$
$997$	−11827.8	+	28554.9i	−0.375718	+	0.907064i	−0.992758	+	0.120132i	$0.961668\pi$
$998$		0			0
$999$	−1143.91	−	1143.91i	−0.0362279	−	0.0362279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.a.97.7		44
4.3	odd	2		256.4.g.b.97.5		44
8.3	odd	2		32.4.g.a.21.11	✓	44
8.5	even	2		128.4.g.a.49.5		44
32.3	odd	8		256.4.g.b.161.5		44
32.13	even	8		128.4.g.a.81.5		44
32.19	odd	8		32.4.g.a.29.11	yes	44
32.29	even	8	inner	256.4.g.a.161.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.11	✓	44	8.3	odd	2
32.4.g.a.29.11	yes	44	32.19	odd	8
128.4.g.a.49.5		44	8.5	even	2
128.4.g.a.81.5		44	32.13	even	8
256.4.g.a.97.7		44	1.1	even	1	trivial
256.4.g.a.161.7		44	32.29	even	8	inner
256.4.g.b.97.5		44	4.3	odd	2
256.4.g.b.161.5		44	32.3	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.143768 - 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +O(q^{10})\)	\(q+(0.143768 - 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +(-36.9342 - 15.2986i) q^{11} +(-4.49594 - 10.8542i) q^{13} -0.312111i q^{15} +53.8999i q^{17} +(-31.9796 - 77.2056i) q^{19} +(1.11366 + 0.461293i) q^{21} +(-50.0867 + 50.0867i) q^{23} +(85.5438 + 85.5438i) q^{25} +(-3.21429 + 7.75999i) q^{27} +(-156.098 + 64.6581i) q^{29} -207.668 q^{31} -6.22100 q^{33} +(14.3538 - 5.94555i) q^{35} +(-73.7055 + 177.941i) q^{37} +(-1.29274 - 1.29274i) q^{39} +(-293.943 + 293.943i) q^{41} +(-342.438 - 141.843i) q^{43} +(20.7050 + 49.9864i) q^{45} -510.799i q^{47} -282.996i q^{49} +(3.20978 + 7.74908i) q^{51} +(590.228 + 244.481i) q^{53} +(-56.6971 + 56.6971i) q^{55} +(-9.19528 - 9.19528i) q^{57} +(-257.808 + 622.403i) q^{59} +(-424.302 + 175.752i) q^{61} -208.961 q^{63} -23.5637 q^{65} +(482.813 - 199.988i) q^{67} +(-4.21817 + 10.1836i) q^{69} +(199.873 + 199.873i) q^{71} +(-127.360 + 127.360i) q^{73} +(17.3927 + 7.20427i) q^{75} +(-118.507 - 286.101i) q^{77} -237.438i q^{79} -727.039i q^{81} +(9.62194 + 23.2294i) q^{83} +(99.8771 + 41.3704i) q^{85} +(-18.5915 + 18.5915i) q^{87} +(329.123 + 329.123i) q^{89} +(34.8265 - 84.0787i) q^{91} +(-29.8560 + 12.3667i) q^{93} -167.608 q^{95} +776.518 q^{97} +(996.329 - 412.693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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