LMFDB - Embedded newform 800.2.be.a.369.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			369.14
Character	$\chi$	$=$	800.369
Dual form			800.2.be.a.529.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0988780 + 0.0718391i) q^{3} +(-2.13827 - 0.654056i) q^{5} -4.12326i q^{7} +(-0.922435 + 2.83896i) q^{9} +O(q^{10})$	\(q+(-0.0988780 + 0.0718391i) q^{3} +(-2.13827 - 0.654056i) q^{5} -4.12326i q^{7} +(-0.922435 + 2.83896i) q^{9} +(-0.296291 + 0.0962708i) q^{11} +(-1.32691 + 4.08381i) q^{13} +(0.258415 - 0.0889398i) q^{15} +(1.48123 - 2.03874i) q^{17} +(-2.96240 + 4.07740i) q^{19} +(0.296211 + 0.407699i) q^{21} +(-6.06625 + 1.97104i) q^{23} +(4.14442 + 2.79710i) q^{25} +(-0.226044 - 0.695692i) q^{27} +(0.365173 + 0.502617i) q^{29} +(5.55444 + 4.03554i) q^{31} +(0.0223807 - 0.0308043i) q^{33} +(-2.69684 + 8.81665i) q^{35} +(-2.65457 + 8.16992i) q^{37} +(-0.162175 - 0.499123i) q^{39} +(-1.64354 + 5.05830i) q^{41} -2.23204 q^{43} +(3.82926 - 5.46715i) q^{45} +(-3.74794 - 5.15860i) q^{47} -10.0013 q^{49} +0.307997i q^{51} +(3.81243 - 2.76989i) q^{53} +(0.696517 - 0.0120623i) q^{55} -0.615981i q^{57} +(-2.59396 - 0.842829i) q^{59} +(-12.9582 + 4.21037i) q^{61} +(11.7058 + 3.80344i) q^{63} +(5.50834 - 7.86443i) q^{65} +(-7.91813 - 5.75286i) q^{67} +(0.458220 - 0.630686i) q^{69} +(-6.63373 + 4.81969i) q^{71} +(7.18083 - 2.33319i) q^{73} +(-0.610733 + 0.0211597i) q^{75} +(0.396949 + 1.22168i) q^{77} +(-3.65256 + 2.65374i) q^{79} +(-7.17257 - 5.21118i) q^{81} +(-5.72321 - 4.15816i) q^{83} +(-4.50074 + 3.39058i) q^{85} +(-0.0722151 - 0.0234641i) q^{87} +(-2.63206 - 8.10065i) q^{89} +(16.8386 + 5.47119i) q^{91} -0.839121 q^{93} +(9.00127 - 6.78101i) q^{95} +(-0.465272 - 0.640392i) q^{97} -0.929963i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	−0.0988780	+	0.0718391i	−0.0570872	+	0.0414763i	−0.615963	−	0.787775i	$-0.711233\pi$
$3$	−0.0988780	+	0.0718391i	−0.0570872	+	0.0414763i	0.558876	+	0.829251i	$0.311233\pi$
$4$		0			0
$5$	−2.13827	−	0.654056i	−0.956265	−	0.292503i
$5$	−2.13827	−	0.654056i	−0.956265	−	0.292503i
$6$		0			0
$7$		−	4.12326i		−	1.55844i	−0.626748	−	0.779222i	$-0.715614\pi$
$7$		−	4.12326i		−	1.55844i	0.626748	−	0.779222i	$-0.284386\pi$
$8$		0			0
$9$	−0.922435	+	2.83896i	−0.307478	+	0.946321i
$10$		0			0
$11$	−0.296291	+	0.0962708i	−0.0893351	+	0.0290267i	−0.353344	−	0.935494i	$-0.614955\pi$
$11$	−0.296291	+	0.0962708i	−0.0893351	+	0.0290267i	0.264008	+	0.964520i	$0.414955\pi$
$12$		0			0
$13$	−1.32691	+	4.08381i	−0.368019	+	1.13264i	0.580050	+	0.814581i	$0.303033\pi$
$13$	−1.32691	+	4.08381i	−0.368019	+	1.13264i	−0.948069	+	0.318064i	$0.896967\pi$
$14$		0			0
$15$	0.258415	−	0.0889398i	0.0667224	−	0.0229642i
$16$		0			0
$17$	1.48123	−	2.03874i	0.359252	−	0.494468i	−0.590688	−	0.806900i	$-0.701144\pi$
$17$	1.48123	−	2.03874i	0.359252	−	0.494468i	0.949940	+	0.312432i	$0.101144\pi$
$18$		0			0
$19$	−2.96240	+	4.07740i	−0.679622	+	0.935419i	−0.999929	−	0.0118946i	$-0.996214\pi$
$19$	−2.96240	+	4.07740i	−0.679622	+	0.935419i	0.320308	+	0.947314i	$0.396214\pi$
$20$		0			0
$21$	0.296211	+	0.407699i	0.0646385	+	0.0889673i
$22$		0			0
$23$	−6.06625	+	1.97104i	−1.26490	+	0.410991i	−0.863238	−	0.504797i	$-0.831567\pi$
$23$	−6.06625	+	1.97104i	−1.26490	+	0.410991i	−0.401662	+	0.915788i	$0.631567\pi$
$24$		0			0
$25$	4.14442	+	2.79710i	0.828884	+	0.559420i
$26$		0			0
$27$	−0.226044	−	0.695692i	−0.0435022	−	0.133886i
$28$		0			0
$29$	0.365173	+	0.502617i	0.0678109	+	0.0933337i	0.841575	−	0.540140i	$-0.181629\pi$
$29$	0.365173	+	0.502617i	0.0678109	+	0.0933337i	−0.773764	+	0.633473i	$0.781629\pi$
$30$		0			0
$31$	5.55444	+	4.03554i	0.997607	+	0.724804i	0.961574	−	0.274547i	$-0.0885279\pi$
$31$	5.55444	+	4.03554i	0.997607	+	0.724804i	0.0360329	+	0.999351i	$0.488528\pi$
$32$		0			0
$33$	0.0223807	−	0.0308043i	0.00389597	−	0.00536235i
$34$		0			0
$35$	−2.69684	+	8.81665i	−0.455849	+	1.49029i
$36$		0			0
$37$	−2.65457	+	8.16992i	−0.436408	+	1.34313i	0.455229	+	0.890374i	$0.349557\pi$
$37$	−2.65457	+	8.16992i	−0.436408	+	1.34313i	−0.891637	+	0.452751i	$0.850443\pi$
$38$		0			0
$39$	−0.162175	−	0.499123i	−0.0259688	−	0.0799236i
$40$		0			0
$41$	−1.64354	+	5.05830i	−0.256678	+	0.789974i	0.736816	+	0.676093i	$0.236328\pi$
$41$	−1.64354	+	5.05830i	−0.256678	+	0.789974i	−0.993494	+	0.113881i	$0.963672\pi$
$42$		0			0
$43$	−2.23204			−0.340382			−0.170191	−	0.985411i	$-0.554439\pi$
$43$	−2.23204			−0.340382			−0.170191	+	0.985411i	$0.554439\pi$
$44$		0			0
$45$	3.82926	−	5.46715i	0.570832	−	0.814995i
$46$		0			0
$47$	−3.74794	−	5.15860i	−0.546693	−	0.752459i	0.442866	−	0.896588i	$-0.353962\pi$
$47$	−3.74794	−	5.15860i	−0.546693	−	0.752459i	−0.989559	+	0.144129i	$0.953962\pi$
$48$		0			0
$49$	−10.0013			−1.42875
$50$		0			0
$51$			0.307997i			0.0431283i
$52$		0			0
$53$	3.81243	−	2.76989i	0.523678	−	0.380474i	−0.294310	−	0.955710i	$-0.595090\pi$
$53$	3.81243	−	2.76989i	0.523678	−	0.380474i	0.817988	+	0.575236i	$0.195090\pi$
$54$		0			0
$55$	0.696517	−	0.0120623i	0.0939184	−	0.00162648i
$56$		0			0
$57$		−	0.615981i		−	0.0815887i
$58$		0			0
$59$	−2.59396	−	0.842829i	−0.337705	−	0.109727i	0.135255	−	0.990811i	$-0.456815\pi$
$59$	−2.59396	−	0.842829i	−0.337705	−	0.109727i	−0.472960	+	0.881084i	$0.656815\pi$
$60$		0			0
$61$	−12.9582	+	4.21037i	−1.65913	+	0.539082i	−0.980688	−	0.195576i	$-0.937342\pi$
$61$	−12.9582	+	4.21037i	−1.65913	+	0.539082i	−0.678437	+	0.734659i	$0.737342\pi$
$62$		0			0
$63$	11.7058	+	3.80344i	1.47479	+	0.479188i
$64$		0			0
$65$	5.50834	−	7.86443i	0.683225	−	0.975462i
$66$		0			0
$67$	−7.91813	−	5.75286i	−0.967354	−	0.702824i	−0.0125070	−	0.999922i	$-0.503981\pi$
$67$	−7.91813	−	5.75286i	−0.967354	−	0.702824i	−0.954847	+	0.297098i	$0.903981\pi$
$68$		0			0
$69$	0.458220	−	0.630686i	0.0551633	−	0.0759257i
$70$		0			0
$71$	−6.63373	+	4.81969i	−0.787279	+	0.571992i	−0.907155	−	0.420797i	$-0.861750\pi$
$71$	−6.63373	+	4.81969i	−0.787279	+	0.571992i	0.119876	+	0.992789i	$0.461750\pi$
$72$		0			0
$73$	7.18083	−	2.33319i	0.840452	−	0.273079i	0.143011	−	0.989721i	$-0.454322\pi$
$73$	7.18083	−	2.33319i	0.840452	−	0.273079i	0.697441	+	0.716642i	$0.254322\pi$
$74$		0			0
$75$	−0.610733	+	0.0211597i	−0.0705214	+	0.00244332i
$76$		0			0
$77$	0.396949	+	1.22168i	0.0452366	+	0.139224i
$78$		0			0
$79$	−3.65256	+	2.65374i	−0.410945	+	0.298569i	−0.773984	−	0.633205i	$-0.781739\pi$
$79$	−3.65256	+	2.65374i	−0.410945	+	0.298569i	0.363040	+	0.931774i	$0.381739\pi$
$80$		0			0
$81$	−7.17257	−	5.21118i	−0.796952	−	0.579020i
$82$		0			0
$83$	−5.72321	−	4.15816i	−0.628204	−	0.456417i	0.227573	−	0.973761i	$-0.426921\pi$
$83$	−5.72321	−	4.15816i	−0.628204	−	0.456417i	−0.855778	+	0.517344i	$0.826921\pi$
$84$		0			0
$85$	−4.50074	+	3.39058i	−0.488173	+	0.367760i
$86$		0			0
$87$	−0.0722151	−	0.0234641i	−0.00774227	−	0.00251562i
$88$		0			0
$89$	−2.63206	−	8.10065i	−0.278998	−	0.858667i	−0.988134	−	0.153595i	$-0.950915\pi$
$89$	−2.63206	−	8.10065i	−0.278998	−	0.858667i	0.709136	−	0.705072i	$-0.249085\pi$
$90$		0			0
$91$	16.8386	+	5.47119i	1.76516	+	0.573537i
$92$		0			0
$93$	−0.839121			−0.0870128
$94$		0			0
$95$	9.00127	−	6.78101i	0.923511	−	0.695717i
$96$		0			0
$97$	−0.465272	−	0.640392i	−0.0472412	−	0.0650220i	0.784743	−	0.619821i	$-0.212795\pi$
$97$	−0.465272	−	0.640392i	−0.0472412	−	0.0650220i	−0.831984	+	0.554799i	$0.812795\pi$
$98$		0			0
$99$		−	0.929963i		−	0.0934648i
$100$		0			0
$101$		−	3.69351i		−	0.367518i	−0.982971	−	0.183759i	$-0.941173\pi$
$101$		−	3.69351i		−	0.367518i	0.982971	−	0.183759i	$-0.0588267\pi$
$102$		0			0
$103$	8.55853	+	11.7798i	0.843297	+	1.16070i	0.985300	+	0.170833i	$0.0546458\pi$
$103$	8.55853	+	11.7798i	0.843297	+	1.16070i	−0.142003	+	0.989866i	$0.545354\pi$
$104$		0			0
$105$	−0.366722	−	1.06551i	−0.0357884	−	0.103983i
$106$		0			0
$107$	16.7052			1.61496			0.807478	−	0.589897i	$-0.200832\pi$
$107$	16.7052			1.61496			0.807478	+	0.589897i	$0.200832\pi$
$108$		0			0
$109$	13.9033	+	4.51745i	1.33169	+	0.432693i	0.886494	−	0.462739i	$-0.153133\pi$
$109$	13.9033	+	4.51745i	1.33169	+	0.432693i	0.445198	+	0.895432i	$0.353133\pi$
$110$		0			0
$111$	−0.324441	−	0.998526i	−0.0307946	−	0.0947759i
$112$		0			0
$113$	10.2530	+	3.33141i	0.964523	+	0.313393i	0.748603	−	0.663018i	$-0.230725\pi$
$113$	10.2530	+	3.33141i	0.964523	+	0.313393i	0.215920	+	0.976411i	$0.430725\pi$
$114$		0			0
$115$	14.2605	−	0.246963i	1.32980	−	0.0230294i
$116$		0			0
$117$	−10.3698	−	7.53410i	−0.958688	−	0.696528i
$118$		0			0
$119$	−8.40627	−	6.10751i	−0.770601	−	0.559875i
$120$		0			0
$121$	−8.82067	+	6.40859i	−0.801879	+	0.582599i
$122$		0			0
$123$	−0.200874	−	0.618225i	−0.0181122	−	0.0557435i
$124$		0			0
$125$	−7.03244	−	8.69165i	−0.629001	−	0.777405i
$126$		0			0
$127$	2.12921	−	0.691823i	0.188937	−	0.0613894i	−0.213020	−	0.977048i	$-0.568330\pi$
$127$	2.12921	−	0.691823i	0.188937	−	0.0613894i	0.401957	+	0.915658i	$0.368330\pi$
$128$		0			0
$129$	0.220699	−	0.160347i	0.0194315	−	0.0141178i
$130$		0			0
$131$	2.08338	−	2.86752i	0.182026	−	0.250537i	−0.708247	−	0.705965i	$-0.750514\pi$
$131$	2.08338	−	2.86752i	0.182026	−	0.250537i	0.890273	+	0.455428i	$0.150514\pi$
$132$		0			0
$133$	16.8122	+	12.2147i	1.45780	+	1.05915i
$134$		0			0
$135$	0.0283223	+	1.63542i	0.00243760	+	0.140755i
$136$		0			0
$137$	−12.8317	−	4.16928i	−1.09629	−	0.356205i	−0.295614	−	0.955307i	$-0.595524\pi$
$137$	−12.8317	−	4.16928i	−1.09629	−	0.356205i	−0.800673	+	0.599102i	$0.795524\pi$
$138$		0			0
$139$	−9.64111	+	3.13259i	−0.817749	+	0.265703i	−0.687876	−	0.725828i	$-0.741457\pi$
$139$	−9.64111	+	3.13259i	−0.817749	+	0.265703i	−0.129872	+	0.991531i	$0.541457\pi$
$140$		0			0
$141$	0.741178	+	0.240823i	0.0624184	+	0.0202810i
$142$		0			0
$143$		−	1.33774i		−	0.111867i
$144$		0			0
$145$	−0.452099	−	1.31358i	−0.0375448	−	0.109087i
$146$		0			0
$147$	0.988904	−	0.718481i	0.0815634	−	0.0592593i
$148$		0			0
$149$		−	14.3531i		−	1.17585i	−0.808916	−	0.587925i	$-0.799945\pi$
$149$		−	14.3531i		−	1.17585i	0.808916	−	0.587925i	$-0.200055\pi$
$150$		0			0
$151$	−14.4342			−1.17464			−0.587321	−	0.809354i	$-0.699817\pi$
$151$	−14.4342			−1.17464			−0.587321	+	0.809354i	$0.699817\pi$
$152$		0			0
$153$	4.42158	+	6.08578i	0.357463	+	0.492006i
$154$		0			0
$155$	−9.23744	−	12.2620i	−0.741969	−	0.984907i
$156$		0			0
$157$	19.2873			1.53930			0.769648	−	0.638469i	$-0.220432\pi$
$157$	19.2873			1.53930			0.769648	+	0.638469i	$0.220432\pi$
$158$		0			0
$159$	−0.177979	+	0.547763i	−0.0141147	+	0.0434404i
$160$		0			0
$161$	8.12712	+	25.0127i	0.640507	+	1.97128i
$162$		0			0
$163$	2.83773	−	8.73364i	0.222268	−	0.684072i	−0.776289	−	0.630377i	$-0.782900\pi$
$163$	2.83773	−	8.73364i	0.222268	−	0.684072i	0.998557	−	0.0536946i	$-0.0170997\pi$
$164$		0			0
$165$	−0.0680037	+	0.0512299i	−0.00529408	+	0.00398824i
$166$		0			0
$167$	−5.19807	+	7.15453i	−0.402239	+	0.553634i	−0.961304	−	0.275489i	$-0.911160\pi$
$167$	−5.19807	+	7.15453i	−0.402239	+	0.553634i	0.559065	+	0.829124i	$0.311160\pi$
$168$		0			0
$169$	−4.39959	−	3.19649i	−0.338430	−	0.245884i
$170$		0			0
$171$	−8.84296	−	12.1713i	−0.676238	−	0.930761i
$172$		0			0
$173$	−4.05868	−	12.4913i	−0.308576	−	0.949698i	−0.978319	−	0.207105i	$-0.933596\pi$
$173$	−4.05868	−	12.4913i	−0.308576	−	0.949698i	0.669743	−	0.742593i	$-0.266404\pi$
$174$		0			0
$175$	11.5332	−	17.0885i	0.871825	−	1.29177i
$176$		0			0
$177$	0.317034	−	0.103011i	0.0238297	−	0.00774274i
$178$		0			0
$179$	0.375298	+	0.516553i	0.0280511	+	0.0386090i	0.822812	−	0.568313i	$-0.192404\pi$
$179$	0.375298	+	0.516553i	0.0280511	+	0.0386090i	−0.794761	+	0.606922i	$0.792404\pi$
$180$		0			0
$181$	11.7000	−	16.1037i	0.869656	−	1.19698i	−0.109523	−	0.993984i	$-0.534932\pi$
$181$	11.7000	−	16.1037i	0.869656	−	1.19698i	0.979180	−	0.202995i	$-0.0650676\pi$
$182$		0			0
$183$	0.978810	−	1.34722i	0.0723557	−	0.0995891i
$184$		0			0
$185$	11.0198	−	15.7333i	0.810190	−	1.15673i
$186$		0			0
$187$	−0.242605	+	0.746661i	−0.0177410	+	0.0546013i
$188$		0			0
$189$	−2.86852	+	0.932038i	−0.208654	+	0.0677958i
$190$		0			0
$191$	−5.61154	+	17.2706i	−0.406037	+	1.24965i	0.513989	+	0.857797i	$0.328167\pi$
$191$	−5.61154	+	17.2706i	−0.406037	+	1.24965i	−0.920026	+	0.391857i	$0.871833\pi$
$192$		0			0
$193$			16.2523i			1.16986i	0.811083	+	0.584932i	$0.198879\pi$
$193$			16.2523i			1.16986i	−0.811083	+	0.584932i	$0.801121\pi$
$194$		0			0
$195$	0.0203198	+	1.17333i	0.00145513	+	0.0840241i
$196$		0			0
$197$	−9.32654	+	6.77613i	−0.664488	+	0.482779i	−0.868176	−	0.496257i	$-0.834707\pi$
$197$	−9.32654	+	6.77613i	−0.664488	+	0.482779i	0.203687	+	0.979036i	$0.434707\pi$
$198$		0			0
$199$	−14.9527			−1.05997			−0.529983	−	0.848008i	$-0.677802\pi$
$199$	−14.9527			−1.05997			−0.529983	+	0.848008i	$0.677802\pi$
$200$		0			0
$201$	1.19621			0.0843741
$202$		0			0
$203$	2.07242	−	1.50570i	0.145455	−	0.105680i
$204$		0			0
$205$	6.82275	−	9.74106i	0.476522	−	0.680345i
$206$		0			0
$207$		−	19.0400i		−	1.32337i
$208$		0			0
$209$	0.485199	−	1.49329i	0.0335619	−	0.103293i
$210$		0			0
$211$	2.07919	−	0.675570i	0.143137	−	0.0465082i	−0.236572	−	0.971614i	$-0.576024\pi$
$211$	2.07919	−	0.675570i	0.143137	−	0.0465082i	0.379710	+	0.925106i	$0.376024\pi$
$212$		0			0
$213$	0.309688	−	0.953122i	0.0212195	−	0.0653068i
$214$		0			0
$215$	4.77270	+	1.45988i	0.325496	+	0.0995627i
$216$		0			0
$217$	16.6396	−	22.9024i	1.12957	−	1.55471i
$218$		0			0
$219$	−0.542411	+	0.746565i	−0.0366528	+	0.0504482i
$220$		0			0
$221$	6.36038	+	8.75431i	0.427845	+	0.588879i
$222$		0			0
$223$	18.9624	−	6.16124i	1.26981	−	0.412587i	0.404832	−	0.914391i	$-0.367330\pi$
$223$	18.9624	−	6.16124i	1.26981	−	0.412587i	0.864981	+	0.501804i	$0.167330\pi$
$224$		0			0
$225$	−11.7638	+	9.18572i	−0.784255	+	0.612381i
$226$		0			0
$227$	−3.46276	−	10.6573i	−0.229832	−	0.707349i	−0.997765	−	0.0668195i	$-0.978715\pi$
$227$	−3.46276	−	10.6573i	−0.229832	−	0.707349i	0.767933	−	0.640530i	$-0.221285\pi$
$228$		0			0
$229$	−4.28891	−	5.90318i	−0.283419	−	0.390093i	0.643444	−	0.765494i	$-0.277505\pi$
$229$	−4.28891	−	5.90318i	−0.283419	−	0.390093i	−0.926863	+	0.375401i	$0.877505\pi$
$230$		0			0
$231$	−0.127014	−	0.0922812i	−0.00835692	−	0.00607166i
$232$		0			0
$233$	−6.79487	+	9.35234i	−0.445147	+	0.612692i	−0.971346	−	0.237669i	$-0.923617\pi$
$233$	−6.79487	+	9.35234i	−0.445147	+	0.612692i	0.526199	+	0.850361i	$0.323617\pi$
$234$		0			0
$235$	4.64011	+	13.4819i	0.302687	+	0.879459i
$236$		0			0
$237$	0.170515	−	0.524792i	0.0110762	−	0.0340889i
$238$		0			0
$239$	0.177923	+	0.547590i	0.0115089	+	0.0354207i	0.956646	−	0.291253i	$-0.0940722\pi$
$239$	0.177923	+	0.547590i	0.0115089	+	0.0354207i	−0.945137	+	0.326674i	$0.894072\pi$
$240$		0			0
$241$	0.273524	−	0.841820i	0.0176192	−	0.0542264i	−0.941860	−	0.336005i	$-0.890924\pi$
$241$	0.273524	−	0.841820i	0.0176192	−	0.0542264i	0.959480	+	0.281778i	$0.0909242\pi$
$242$		0			0
$243$	3.27806			0.210287
$244$		0			0
$245$	21.3854	+	6.54138i	1.36626	+	0.417913i
$246$		0			0
$247$	−12.7205	−	17.5082i	−0.809384	−	1.11402i
$248$		0			0
$249$	0.864618			0.0547929
$250$		0			0
$251$			10.4673i			0.660692i	0.943860	+	0.330346i	$0.107165\pi$
$251$			10.4673i			0.660692i	−0.943860	+	0.330346i	$0.892835\pi$
$252$		0			0
$253$	1.60762	−	1.16800i	0.101070	−	0.0734318i
$254$		0			0
$255$	0.201448	−	0.658583i	0.0126151	−	0.0412420i
$256$		0			0
$257$		−	17.6103i		−	1.09850i	−0.835658	−	0.549250i	$-0.814914\pi$
$257$		−	17.6103i		−	1.09850i	0.835658	−	0.549250i	$-0.185086\pi$
$258$		0			0
$259$	33.6867	+	10.9455i	2.09319	+	0.680118i
$260$		0			0
$261$	−1.76376	+	0.573081i	−0.109174	+	0.0354728i
$262$		0			0
$263$	−20.7083	−	6.72853i	−1.27693	−	0.414899i	−0.409430	−	0.912341i	$-0.634273\pi$
$263$	−20.7083	−	6.72853i	−1.27693	−	0.414899i	−0.867497	+	0.497442i	$0.834273\pi$
$264$		0			0
$265$	−9.96369	+	3.42925i	−0.612064	+	0.210657i
$266$		0			0
$267$	0.842196	+	0.611891i	0.0515416	+	0.0374471i
$268$		0			0
$269$	−7.13157	+	9.81576i	−0.434819	+	0.598477i	−0.969051	−	0.246861i	$-0.920601\pi$
$269$	−7.13157	+	9.81576i	−0.434819	+	0.598477i	0.534232	+	0.845338i	$0.320601\pi$
$270$		0			0
$271$	12.7055	−	9.23111i	0.771806	−	0.560750i	−0.130702	−	0.991422i	$-0.541723\pi$
$271$	12.7055	−	9.23111i	0.771806	−	0.560750i	0.902509	+	0.430672i	$0.141723\pi$
$272$		0			0
$273$	−2.05801	+	0.668689i	−0.124557	+	0.0404709i
$274$		0			0
$275$	−1.49723	−	0.429769i	−0.0902866	−	0.0259160i
$276$		0			0
$277$	0.720234	+	2.21665i	0.0432747	+	0.133186i	0.970360	−	0.241666i	$-0.0776937\pi$
$277$	0.720234	+	2.21665i	0.0432747	+	0.133186i	−0.927085	+	0.374851i	$0.877694\pi$
$278$		0			0
$279$	−16.5803	+	12.0463i	−0.992639	+	0.721195i
$280$		0			0
$281$	11.0233	+	8.00887i	0.657592	+	0.477769i	0.865849	−	0.500305i	$-0.166779\pi$
$281$	11.0233	+	8.00887i	0.657592	+	0.477769i	−0.208257	+	0.978074i	$0.566779\pi$
$282$		0			0
$283$	3.22475	+	2.34292i	0.191691	+	0.139272i	0.679491	−	0.733683i	$-0.262200\pi$
$283$	3.22475	+	2.34292i	0.191691	+	0.139272i	−0.487800	+	0.872955i	$0.662200\pi$
$284$		0			0
$285$	−0.402886	+	1.31714i	−0.0238649	+	0.0780204i
$286$		0			0
$287$	20.8567	+	6.77675i	1.23113	+	0.400019i
$288$		0			0
$289$	3.29087	+	10.1282i	0.193580	+	0.595779i
$290$		0			0
$291$	0.0920104	+	0.0298960i	0.00539374	+	0.00175253i
$292$		0			0
$293$	−9.63185			−0.562699			−0.281349	−	0.959605i	$-0.590782\pi$
$293$	−9.63185			−0.562699			−0.281349	+	0.959605i	$0.590782\pi$
$294$		0			0
$295$	4.99534	+	3.49879i	0.290840	+	0.203708i
$296$		0			0
$297$	0.133950	+	0.184366i	0.00777255	+	0.0106980i
$298$		0			0
$299$		−	27.3888i		−	1.58393i
$300$		0			0
$301$			9.20326i			0.530467i
$302$		0			0
$303$	0.265339	+	0.365207i	0.0152433	+	0.0209806i
$304$		0			0
$305$	30.4619	−	0.527541i	1.74425	−	0.0302069i
$306$		0			0
$307$	−8.12625			−0.463790			−0.231895	−	0.972741i	$-0.574493\pi$
$307$	−8.12625			−0.463790			−0.231895	+	0.972741i	$0.574493\pi$
$308$		0			0
$309$	−1.69250	−	0.549927i	−0.0962830	−	0.0312842i
$310$		0			0
$311$	1.39243	+	4.28546i	0.0789575	+	0.243006i	0.982742	−	0.184982i	$-0.0592226\pi$
$311$	1.39243	+	4.28546i	0.0789575	+	0.243006i	−0.903784	+	0.427988i	$0.859223\pi$
$312$		0			0
$313$	1.88964	+	0.613980i	0.106809	+	0.0347042i	0.361934	−	0.932204i	$-0.382117\pi$
$313$	1.88964	+	0.613980i	0.106809	+	0.0347042i	−0.255125	+	0.966908i	$0.582117\pi$
$314$		0			0
$315$	−22.5425	−	15.7890i	−1.27012	−	0.889610i
$316$		0			0
$317$	−9.97273	−	7.24561i	−0.560124	−	0.406954i	0.271380	−	0.962472i	$-0.412520\pi$
$317$	−9.97273	−	7.24561i	−0.560124	−	0.406954i	−0.831504	+	0.555518i	$0.812520\pi$
$318$		0			0
$319$	−0.156585	−	0.113766i	−0.00876707	−	0.00636965i
$320$		0			0
$321$	−1.65178	+	1.20009i	−0.0921934	+	0.0669824i
$322$		0			0
$323$	3.92476	+	12.0792i	0.218379	+	0.672103i
$324$		0			0
$325$	−16.9221	+	13.2135i	−0.938669	+	0.732955i
$326$		0			0
$327$	−1.69926	+	0.552122i	−0.0939691	+	0.0305324i
$328$		0			0
$329$	−21.2702	+	15.4537i	−1.17267	+	0.851991i
$330$		0			0
$331$	−15.4091	+	21.2088i	−0.846960	+	1.16574i	0.137565	+	0.990493i	$0.456072\pi$
$331$	−15.4091	+	21.2088i	−0.846960	+	1.16574i	−0.984524	+	0.175247i	$0.943928\pi$
$332$		0			0
$333$	−20.7454	−	15.0724i	−1.13684	−	0.825964i
$334$		0			0
$335$	13.1684	+	17.4801i	0.719469	+	0.955039i
$336$		0			0
$337$	−24.2182	−	7.86898i	−1.31925	−	0.428651i	−0.437013	−	0.899455i	$-0.643964\pi$
$337$	−24.2182	−	7.86898i	−1.31925	−	0.428651i	−0.882238	+	0.470805i	$0.843964\pi$
$338$		0			0
$339$	−1.25312	+	0.407164i	−0.0680603	+	0.0221141i
$340$		0			0
$341$	−2.03423	−	0.660963i	−0.110160	−	0.0357931i
$342$		0			0
$343$			12.3749i			0.668184i
$344$		0			0
$345$	−1.39230	+	1.04888i	−0.0749591	+	0.0564697i
$346$		0			0
$347$	−21.6770	+	15.7492i	−1.16368	+	0.845463i	−0.990239	−	0.139381i	$-0.955489\pi$
$347$	−21.6770	+	15.7492i	−1.16368	+	0.845463i	−0.173442	+	0.984844i	$0.555489\pi$
$348$		0			0
$349$			9.22396i			0.493747i	0.969048	+	0.246874i	$0.0794032\pi$
$349$			9.22396i			0.493747i	−0.969048	+	0.246874i	$0.920597\pi$
$350$		0			0
$351$	3.14101			0.167655
$352$		0			0
$353$	−8.49553	−	11.6931i	−0.452172	−	0.622361i	0.520691	−	0.853745i	$-0.325674\pi$
$353$	−8.49553	−	11.6931i	−0.452172	−	0.622361i	−0.972862	+	0.231384i	$0.925674\pi$
$354$		0			0
$355$	17.3371	−	5.96697i	0.920156	−	0.316694i
$356$		0			0
$357$	1.26995			0.0672130
$358$		0			0
$359$	0.995352	−	3.06338i	0.0525327	−	0.161679i	−0.921348	−	0.388738i	$-0.872911\pi$
$359$	0.995352	−	3.06338i	0.0525327	−	0.161679i	0.973881	+	0.227059i	$0.0729111\pi$
$360$		0			0
$361$	−1.97802	−	6.08771i	−0.104106	−	0.320406i
$362$		0			0
$363$	0.411783	−	1.26734i	0.0216130	−	0.0665179i
$364$		0			0
$365$	−16.8806	+	0.292339i	−0.883571	+	0.0153017i
$366$		0			0
$367$	−5.30006	+	7.29490i	−0.276661	+	0.380791i	−0.924624	−	0.380881i	$-0.875621\pi$
$367$	−5.30006	+	7.29490i	−0.276661	+	0.380791i	0.647964	+	0.761671i	$0.275621\pi$
$368$		0			0
$369$	−12.8443	−	9.33191i	−0.668646	−	0.485800i
$370$		0			0
$371$	−11.4210	−	15.7196i	−0.592948	−	0.816123i
$372$		0			0
$373$	2.96932	+	9.13862i	0.153746	+	0.473180i	0.998032	−	0.0627126i	$-0.0199752\pi$
$373$	2.96932	+	9.13862i	0.153746	+	0.473180i	−0.844286	+	0.535893i	$0.819975\pi$
$374$		0			0
$375$	1.31975	+	0.354208i	0.0681518	+	0.0182912i
$376$		0			0
$377$	−2.53715	+	0.824369i	−0.130670	+	0.0424571i
$378$		0			0
$379$	−0.875430	−	1.20493i	−0.0449678	−	0.0618929i	0.785941	−	0.618302i	$-0.212179\pi$
$379$	−0.875430	−	1.20493i	−0.0449678	−	0.0618929i	−0.830909	+	0.556409i	$0.812179\pi$
$380$		0			0
$381$	−0.160832	+	0.221367i	−0.00823969	+	0.0113410i
$382$		0			0
$383$	−7.26441	+	9.99860i	−0.371194	+	0.510905i	−0.953225	−	0.302262i	$-0.902258\pi$
$383$	−7.26441	+	9.99860i	−0.371194	+	0.510905i	0.582031	+	0.813167i	$0.302258\pi$
$384$		0			0
$385$	−0.0497360	−	2.87192i	−0.00253478	−	0.146367i
$386$		0			0
$387$	2.05891	−	6.33667i	0.104660	−	0.322111i
$388$		0			0
$389$	−11.0661	+	3.59560i	−0.561074	+	0.182304i	−0.575805	−	0.817587i	$-0.695311\pi$
$389$	−11.0661	+	3.59560i	−0.561074	+	0.182304i	0.0147301	+	0.999892i	$0.495311\pi$
$390$		0			0
$391$	−4.96708	+	15.2871i	−0.251196	+	0.773102i
$392$		0			0
$393$			0.433203i			0.0218522i
$394$		0			0
$395$	9.54585	−	3.28544i	0.480304	−	0.165308i
$396$		0			0
$397$	2.73979	−	1.99057i	0.137506	−	0.0999040i	−0.516906	−	0.856042i	$-0.672916\pi$
$397$	2.73979	−	1.99057i	0.137506	−	0.0999040i	0.654412	+	0.756138i	$0.272916\pi$
$398$		0			0
$399$	−2.53985			−0.127151
$400$		0			0
$401$	3.08560			0.154088			0.0770439	−	0.997028i	$-0.475452\pi$
$401$	3.08560			0.154088			0.0770439	+	0.997028i	$0.475452\pi$
$402$		0			0
$403$	−23.8506	+	17.3285i	−1.18808	+	0.863193i
$404$		0			0
$405$	11.9285	+	15.8342i	0.592732	+	0.786807i
$406$		0			0
$407$		−	2.67623i		−	0.132656i
$408$		0			0
$409$	3.02158	−	9.29945i	0.149407	−	0.459828i	−0.848144	−	0.529766i	$-0.822280\pi$
$409$	3.02158	−	9.29945i	0.149407	−	0.459828i	0.997551	+	0.0699372i	$0.0222799\pi$
$410$		0			0
$411$	1.56829	−	0.509568i	0.0773581	−	0.0251352i
$412$		0			0
$413$	−3.47520	+	10.6956i	−0.171003	+	0.526295i
$414$		0			0
$415$	9.51812	+	12.6346i	0.467226	+	0.620207i
$416$		0			0
$417$	0.728252	−	1.00235i	0.0356626	−	0.0490854i
$418$		0			0
$419$	−22.2630	+	30.6425i	−1.08762	+	1.49698i	−0.236776	+	0.971564i	$0.576091\pi$
$419$	−22.2630	+	30.6425i	−1.08762	+	1.49698i	−0.850844	+	0.525418i	$0.823909\pi$
$420$		0			0
$421$	8.76743	+	12.0673i	0.427298	+	0.588126i	0.967331	−	0.253519i	$-0.0815879\pi$
$421$	8.76743	+	12.0673i	0.427298	+	0.588126i	−0.540032	+	0.841644i	$0.681588\pi$
$422$		0			0
$423$	18.1023	−	5.88179i	0.880164	−	0.285983i
$424$		0			0
$425$	11.8414	−	4.30626i	0.574394	−	0.208884i
$426$		0			0
$427$	17.3604	+	53.4299i	0.840130	+	2.58566i
$428$		0			0
$429$	0.0961019	+	0.132273i	0.00463984	+	0.00638620i
$430$		0			0
$431$	7.25169	+	5.26866i	0.349302	+	0.253782i	0.748576	−	0.663049i	$-0.230738\pi$
$431$	7.25169	+	5.26866i	0.349302	+	0.253782i	−0.399274	+	0.916831i	$0.630738\pi$
$432$		0			0
$433$	16.5255	−	22.7455i	0.794167	−	1.09308i	−0.199410	−	0.979916i	$-0.563903\pi$
$433$	16.5255	−	22.7455i	0.794167	−	1.09308i	0.993577	−	0.113161i	$-0.0360974\pi$
$434$		0			0
$435$	0.139069	+	0.0974054i	0.00666784	+	0.00467023i
$436$		0			0
$437$	9.93394	−	30.5735i	0.475205	−	1.46253i
$438$		0			0
$439$	1.43731	+	4.42358i	0.0685991	+	0.211126i	0.979479	−	0.201544i	$-0.0645961\pi$
$439$	1.43731	+	4.42358i	0.0685991	+	0.211126i	−0.910880	+	0.412671i	$0.864596\pi$
$440$		0			0
$441$	9.22550	−	28.3932i	0.439310	−	1.35206i
$442$		0			0
$443$	33.9122			1.61122			0.805609	−	0.592448i	$-0.201838\pi$
$443$	33.9122			1.61122			0.805609	+	0.592448i	$0.201838\pi$
$444$		0			0
$445$	0.329786	+	19.0429i	0.0156334	+	0.902721i
$446$		0			0
$447$	1.03111	+	1.41920i	0.0487699	+	0.0671260i
$448$		0			0
$449$	6.81383			0.321565			0.160782	−	0.986990i	$-0.448598\pi$
$449$	6.81383			0.321565			0.160782	+	0.986990i	$0.448598\pi$
$450$		0			0
$451$		−	1.65695i		−	0.0780229i
$452$		0			0
$453$	1.42723	−	1.03694i	0.0670570	−	0.0487198i
$454$		0			0
$455$	−32.4271	−	22.7123i	−1.52020	−	1.06477i
$456$		0			0
$457$			41.0652i			1.92095i	0.278365	+	0.960475i	$0.410208\pi$
$457$			41.0652i			1.92095i	−0.278365	+	0.960475i	$0.589792\pi$
$458$		0			0
$459$	−1.75316	−	0.569637i	−0.0818306	−	0.0265884i
$460$		0			0
$461$	23.5979	−	7.66744i	1.09907	−	0.357108i	0.297323	−	0.954777i	$-0.403906\pi$
$461$	23.5979	−	7.66744i	1.09907	−	0.357108i	0.801743	+	0.597669i	$0.203906\pi$
$462$		0			0
$463$	18.4536	+	5.99593i	0.857610	+	0.278654i	0.704630	−	0.709575i	$-0.251113\pi$
$463$	18.4536	+	5.99593i	0.857610	+	0.278654i	0.152980	+	0.988229i	$0.451113\pi$
$464$		0			0
$465$	1.79427	+	0.548832i	0.0832072	+	0.0254515i
$466$		0			0
$467$	0.0546334	+	0.0396935i	0.00252813	+	0.00183679i	0.589049	−	0.808098i	$-0.299503\pi$
$467$	0.0546334	+	0.0396935i	0.00252813	+	0.00183679i	−0.586520	+	0.809934i	$0.699503\pi$
$468$		0			0
$469$	−23.7205	+	32.6485i	−1.09531	+	1.50757i
$470$		0			0
$471$	−1.90709	+	1.38558i	−0.0878741	+	0.0638443i
$472$		0			0
$473$	0.661332	−	0.214880i	0.0304081	−	0.00988019i
$474$		0			0
$475$	−23.6823	+	8.61232i	−1.08662	+	0.395160i
$476$		0			0
$477$	4.34691	+	13.3784i	0.199031	+	0.612555i
$478$		0			0
$479$	29.8640	−	21.6974i	1.36452	−	0.991381i	0.366376	−	0.930467i	$-0.380598\pi$
$479$	29.8640	−	21.6974i	1.36452	−	0.991381i	0.998143	−	0.0609142i	$-0.0194016\pi$
$480$		0			0
$481$	−29.8420	−	21.6815i	−1.36068	−	0.988591i
$482$		0			0
$483$	−2.60048	−	1.88936i	−0.118326	−	0.0859689i
$484$		0			0
$485$	0.576027	+	1.67365i	0.0261560	+	0.0759964i
$486$		0			0
$487$	5.62357	+	1.82721i	0.254828	+	0.0827987i	0.433645	−	0.901084i	$-0.357227\pi$
$487$	5.62357	+	1.82721i	0.254828	+	0.0827987i	−0.178817	+	0.983882i	$0.557227\pi$
$488$		0			0
$489$	0.346827	+	1.06743i	0.0156841	+	0.0482706i
$490$		0			0
$491$	−33.7674	−	10.9717i	−1.52390	−	0.495146i	−0.577020	−	0.816730i	$-0.695785\pi$
$491$	−33.7674	−	10.9717i	−1.52390	−	0.495146i	−0.946881	+	0.321584i	$0.895785\pi$
$492$		0			0
$493$	1.56562			0.0705118
$494$		0			0
$495$	−0.608248	+	1.98851i	−0.0273387	+	0.0893771i
$496$		0			0
$497$	19.8728	+	27.3526i	0.891417	+	1.22693i
$498$		0			0
$499$		−	24.7413i		−	1.10757i	−0.832658	−	0.553787i	$-0.813182\pi$
$499$		−	24.7413i		−	1.10757i	0.832658	−	0.553787i	$-0.186818\pi$
$500$		0			0
$501$		−	1.08085i		−	0.0482888i
$502$		0			0
$503$	−7.29652	−	10.0428i	−0.325336	−	0.447786i	0.614751	−	0.788721i	$-0.289256\pi$
$503$	−7.29652	−	10.0428i	−0.325336	−	0.447786i	−0.940087	+	0.340935i	$0.889256\pi$
$504$		0			0
$505$	−2.41577	+	7.89774i	−0.107500	+	0.351445i
$506$		0			0
$507$	0.664655			0.0295184
$508$		0			0
$509$	20.9803	+	6.81693i	0.929937	+	0.302155i	0.734537	−	0.678569i	$-0.237399\pi$
$509$	20.9803	+	6.81693i	0.929937	+	0.302155i	0.195400	+	0.980724i	$0.437399\pi$
$510$		0			0
$511$	−9.62035	−	29.6084i	−0.425579	−	1.30980i
$512$		0			0
$513$	3.50625	+	1.13925i	0.154805	+	0.0502990i
$514$		0			0
$515$	−10.5958	−	30.7862i	−0.466908	−	1.35660i
$516$		0			0
$517$	1.60710	+	1.16763i	0.0706803	+	0.0513523i
$518$		0			0
$519$	1.29868	+	0.943546i	0.0570057	+	0.0414171i
$520$		0			0
$521$	−30.0779	+	21.8528i	−1.31773	+	0.957390i	−0.317777	+	0.948165i	$0.602936\pi$
$521$	−30.0779	+	21.8528i	−1.31773	+	0.957390i	−0.999957	+	0.00922497i	$0.997064\pi$
$522$		0			0
$523$	1.73482	+	5.33924i	0.0758585	+	0.233469i	0.981795	−	0.189946i	$-0.0608313\pi$
$523$	1.73482	+	5.33924i	0.0758585	+	0.233469i	−0.905936	+	0.423415i	$0.860831\pi$
$524$		0			0
$525$	0.0872471	+	2.51821i	0.00380777	+	0.109904i
$526$		0			0
$527$	16.4549	−	5.34651i	0.716785	−	0.232897i
$528$		0			0
$529$	14.3070	−	10.3946i	0.622041	−	0.451940i
$530$		0			0
$531$	4.78552	−	6.58671i	0.207674	−	0.285839i
$532$		0			0
$533$	−18.4763	−	13.4238i	−0.800298	−	0.581450i
$534$		0			0
$535$	−35.7204	−	10.9262i	−1.54433	−	0.472379i
$536$		0			0
$537$	−0.0742173	−	0.0241147i	−0.00320271	−	0.00104063i
$538$		0			0
$539$	2.96328	−	0.962828i	0.127638	−	0.0414720i
$540$		0			0
$541$	−24.9767	−	8.11542i	−1.07383	−	0.348909i	−0.281853	−	0.959458i	$-0.590949\pi$
$541$	−24.9767	−	8.11542i	−1.07383	−	0.348909i	−0.791979	+	0.610549i	$0.790949\pi$
$542$		0			0
$543$			2.43282i			0.104402i
$544$		0			0
$545$	−26.7743	−	18.7531i	−1.14689	−	0.803293i
$546$		0			0
$547$	−25.9886	+	18.8818i	−1.11119	+	0.807327i	−0.982851	−	0.184403i	$-0.940965\pi$
$547$	−25.9886	+	18.8818i	−1.11119	+	0.807327i	−0.128340	+	0.991730i	$0.540965\pi$
$548$		0			0
$549$		−	40.6716i		−	1.73582i
$550$		0			0
$551$	−3.13116			−0.133392
$552$		0			0
$553$	10.9420	+	15.0604i	0.465303	+	0.640434i
$554$		0			0
$555$	0.0406510	+	2.34732i	0.00172554	+	0.0996384i
$556$		0			0
$557$	−10.0696			−0.426664			−0.213332	−	0.976980i	$-0.568432\pi$
$557$	−10.0696			−0.426664			−0.213332	+	0.976980i	$0.568432\pi$
$558$		0			0
$559$	2.96171	−	9.11521i	0.125267	−	0.385532i
$560$		0			0
$561$	−0.0296512	−	0.0912569i	−0.00125187	−	0.00385287i
$562$		0			0
$563$	−8.80460	+	27.0978i	−0.371069	+	1.14203i	0.575023	+	0.818137i	$0.304993\pi$
$563$	−8.80460	+	27.0978i	−0.371069	+	1.14203i	−0.946092	+	0.323897i	$0.895007\pi$
$564$		0			0
$565$	−19.7448	−	13.8295i	−0.830671	−	0.581812i
$566$		0			0
$567$	−21.4870	+	29.5744i	−0.902370	+	1.24201i
$568$		0			0
$569$	21.6286	+	15.7141i	0.906718	+	0.658769i	0.940183	−	0.340671i	$-0.110654\pi$
$569$	21.6286	+	15.7141i	0.906718	+	0.658769i	−0.0334647	+	0.999440i	$0.510654\pi$
$570$		0			0
$571$	16.2766	+	22.4028i	0.681155	+	0.937529i	0.999947	−	0.0102955i	$-0.00327723\pi$
$571$	16.2766	+	22.4028i	0.681155	+	0.937529i	−0.318792	+	0.947825i	$0.603277\pi$
$572$		0			0
$573$	−0.685842	−	2.11081i	−0.0286515	−	0.0881802i
$574$		0			0
$575$	−30.6543	−	8.79907i	−1.27837	−	0.366946i
$576$		0			0
$577$	−3.37588	+	1.09689i	−0.140540	+	0.0456641i	−0.378442	−	0.925625i	$-0.623540\pi$
$577$	−3.37588	+	1.09689i	−0.140540	+	0.0456641i	0.237902	+	0.971289i	$0.423540\pi$
$578$		0			0
$579$	−1.16755	−	1.60699i	−0.0485216	−	0.0667843i
$580$		0			0
$581$	−17.1452	+	23.5983i	−0.711301	+	0.979022i
$582$		0			0
$583$	−0.862930	+	1.18772i	−0.0357389	+	0.0491904i
$584$		0			0
$585$	17.2457	+	22.8924i	0.713023	+	0.946484i
$586$		0			0
$587$	14.4792	−	44.5624i	0.597620	−	1.83929i	0.0563961	−	0.998408i	$-0.482039\pi$
$587$	14.4792	−	44.5624i	0.597620	−	1.83929i	0.541224	−	0.840878i	$-0.317961\pi$
$588$		0			0
$589$	−32.9090	+	10.6928i	−1.35599	+	0.440588i
$590$		0			0
$591$	0.435399	−	1.34002i	0.0179099	−	0.0551210i
$592$		0			0
$593$		−	9.84501i		−	0.404286i	−0.979356	−	0.202143i	$-0.935209\pi$
$593$		−	9.84501i		−	0.404286i	0.979356	−	0.202143i	$-0.0647906\pi$
$594$		0			0
$595$	13.9802	+	18.5577i	0.573134	+	0.760791i
$596$		0			0
$597$	1.47849	−	1.07418i	0.0605105	−	0.0439635i
$598$		0			0
$599$	30.6535			1.25247			0.626235	−	0.779634i	$-0.284595\pi$
$599$	30.6535			1.25247			0.626235	+	0.779634i	$0.284595\pi$
$600$		0			0
$601$	19.2818			0.786520			0.393260	−	0.919427i	$-0.371347\pi$
$601$	19.2818			0.786520			0.393260	+	0.919427i	$0.371347\pi$
$602$		0			0
$603$	23.6361	−	17.1726i	0.962537	−	0.699324i
$604$		0			0
$605$	23.0526	−	7.93410i	0.937220	−	0.322567i
$606$		0			0
$607$			7.58873i			0.308017i	0.988070	+	0.154009i	$0.0492183\pi$
$607$			7.58873i			0.308017i	−0.988070	+	0.154009i	$0.950782\pi$
$608$		0			0
$609$	−0.0967486	+	0.297762i	−0.00392045	+	0.0120659i
$610$		0			0
$611$	26.0399	−	8.46088i	1.05346	−	0.342291i
$612$		0			0
$613$	9.10557	−	28.0241i	0.367771	−	1.13188i	−0.580457	−	0.814291i	$-0.697126\pi$
$613$	9.10557	−	28.0241i	0.367771	−	1.13188i	0.948228	−	0.317591i	$-0.102874\pi$
$614$		0			0
$615$	0.0251686	+	1.45332i	0.00101490	+	0.0586034i
$616$		0			0
$617$	3.79899	−	5.22886i	0.152942	−	0.210506i	−0.725670	−	0.688043i	$-0.758470\pi$
$617$	3.79899	−	5.22886i	0.152942	−	0.210506i	0.878612	+	0.477537i	$0.158470\pi$
$618$		0			0
$619$	25.9223	−	35.6790i	1.04191	−	1.43406i	0.146286	−	0.989242i	$-0.453268\pi$
$619$	25.9223	−	35.6790i	1.04191	−	1.43406i	0.895621	−	0.444819i	$-0.146732\pi$
$620$		0			0
$621$	2.74248	+	3.77470i	0.110052	+	0.151473i
$622$		0			0
$623$	−33.4011	+	10.8527i	−1.33819	+	0.434803i
$624$		0			0
$625$	9.35246	+	23.1847i	0.374098	+	0.927389i
$626$		0			0
$627$	0.0593010	+	0.182510i	0.00236825	+	0.00728873i
$628$		0			0
$629$	12.7243	+	17.5135i	0.507352	+	0.698311i
$630$		0			0
$631$	25.4366	+	18.4808i	1.01262	+	0.735708i	0.964756	−	0.263146i	$-0.0847601\pi$
$631$	25.4366	+	18.4808i	1.01262	+	0.735708i	0.0478593	+	0.998854i	$0.484760\pi$
$632$		0			0
$633$	−0.157054	+	0.216166i	−0.00624233	+	0.00859183i
$634$		0			0
$635$	−5.00533	+	0.0866825i	−0.198630	+	0.00343989i
$636$		0			0
$637$	13.2708	−	40.8432i	0.525807	−	1.61827i
$638$		0			0
$639$	−7.56373	−	23.2788i	−0.299216	−	0.920893i
$640$		0			0
$641$	−4.73875	+	14.5844i	−0.187169	+	0.576048i	−0.999979	−	0.00648140i	$-0.997937\pi$
$641$	−4.73875	+	14.5844i	−0.187169	+	0.576048i	0.812810	+	0.582529i	$0.197937\pi$
$642$		0			0
$643$	−23.5431			−0.928448			−0.464224	−	0.885718i	$-0.653667\pi$
$643$	−23.5431			−0.928448			−0.464224	+	0.885718i	$0.653667\pi$
$644$		0			0
$645$	−0.576791	+	0.198517i	−0.0227111	+	0.00781659i
$646$		0			0
$647$	−7.32343	−	10.0798i	−0.287914	−	0.396280i	0.640421	−	0.768024i	$-0.278760\pi$
$647$	−7.32343	−	10.0798i	−0.287914	−	0.396280i	−0.928335	+	0.371744i	$0.878760\pi$
$648$		0			0
$649$	0.849707			0.0333539
$650$		0			0
$651$			3.45991i			0.135605i
$652$		0			0
$653$	−6.50662	+	4.72734i	−0.254624	+	0.184995i	−0.707773	−	0.706439i	$-0.750300\pi$
$653$	−6.50662	+	4.72734i	−0.254624	+	0.184995i	0.453150	+	0.891434i	$0.350300\pi$
$654$		0			0
$655$	−6.33035	+	4.76890i	−0.247347	+	0.186336i
$656$		0			0
$657$			22.5383i			0.879303i
$658$		0			0
$659$	43.9188	+	14.2701i	1.71083	+	0.555883i	0.990472	−	0.137716i	$-0.0439762\pi$
$659$	43.9188	+	14.2701i	1.71083	+	0.555883i	0.720361	+	0.693599i	$0.243976\pi$
$660$		0			0
$661$	31.8290	−	10.3419i	1.23800	−	0.402252i	0.384396	−	0.923168i	$-0.374410\pi$
$661$	31.8290	−	10.3419i	1.23800	−	0.402252i	0.853607	+	0.520917i	$0.174410\pi$
$662$		0			0
$663$	−1.25780	−	0.408685i	−0.0488490	−	0.0158720i
$664$		0			0
$665$	−27.9599	−	37.1146i	−1.08424	−	1.43924i
$666$		0			0
$667$	−3.20591	−	2.32923i	−0.124133	−	0.0901881i
$668$		0			0
$669$	−1.43234	+	1.97145i	−0.0553775	+	0.0762206i
$670$		0			0
$671$	3.43406	−	2.49499i	0.132570	−	0.0963180i
$672$		0			0
$673$	−30.1023	+	9.78082i	−1.16036	+	0.377023i	−0.825035	−	0.565081i	$-0.808845\pi$
$673$	−30.1023	+	9.78082i	−1.16036	+	0.377023i	−0.335321	+	0.942104i	$0.608845\pi$
$674$		0			0
$675$	1.00910	−	3.51551i	0.0388402	−	0.135312i
$676$		0			0
$677$	10.7847	+	33.1919i	0.414489	+	1.27567i	0.912707	+	0.408615i	$0.133988\pi$
$677$	10.7847	+	33.1919i	0.414489	+	1.27567i	−0.498217	+	0.867052i	$0.666012\pi$
$678$		0			0
$679$	−2.64050	+	1.91844i	−0.101333	+	0.0736229i
$680$		0			0
$681$	1.10800	+	0.805010i	0.0424587	+	0.0308480i
$682$		0			0
$683$	5.66818	+	4.11817i	0.216887	+	0.157578i	0.690924	−	0.722927i	$-0.257204\pi$
$683$	5.66818	+	4.11817i	0.216887	+	0.157578i	−0.474037	+	0.880505i	$0.657204\pi$
$684$		0			0
$685$	24.7108	+	17.3077i	0.944150	+	0.661293i
$686$		0			0
$687$	0.848157	+	0.275583i	0.0323592	+	0.0105141i
$688$		0			0
$689$	6.25297	+	19.2447i	0.238219	+	0.733163i
$690$		0			0
$691$	−7.77133	−	2.52506i	−0.295635	−	0.0960578i	0.157444	−	0.987528i	$-0.449675\pi$
$691$	−7.77133	−	2.52506i	−0.295635	−	0.0960578i	−0.453079	+	0.891470i	$0.649675\pi$
$692$		0			0
$693$	−3.83448			−0.145660
$694$		0			0
$695$	22.6642	−	0.392500i	0.859703	−	0.0148884i
$696$		0			0
$697$	7.87811	+	10.8433i	0.298405	+	0.410719i
$698$		0			0
$699$		−	1.41288i		−	0.0534400i
$700$		0			0
$701$		−	20.0038i		−	0.755534i	−0.925901	−	0.377767i	$-0.876692\pi$
$701$		−	20.0038i		−	0.755534i	0.925901	−	0.377767i	$-0.123308\pi$
$702$		0			0
$703$	−25.4481	−	35.0263i	−0.959793	−	1.32104i
$704$		0			0
$705$	−1.42733	−	0.999717i	−0.0537563	−	0.0376515i
$706$		0			0
$707$	−15.2293			−0.572757
$708$		0			0
$709$	46.7136	+	15.1782i	1.75437	+	0.570029i	0.996592	−	0.0824870i	$-0.0262863\pi$
$709$	46.7136	+	15.1782i	1.75437	+	0.570029i	0.757775	+	0.652516i	$0.226286\pi$
$710$		0			0
$711$	−4.16462	−	12.8174i	−0.156185	−	0.480689i
$712$		0			0
$713$	−41.6488	−	13.5325i	−1.55976	−	0.506797i
$714$		0			0
$715$	−0.874956	+	2.86045i	−0.0327215	+	0.106975i
$716$		0			0
$717$	−0.0569310	−	0.0413628i	−0.00212613	−	0.00154472i
$718$		0			0
$719$	38.2305	+	27.7761i	1.42576	+	1.03587i	0.990787	+	0.135430i	$0.0432415\pi$
$719$	38.2305	+	27.7761i	1.42576	+	1.03587i	0.434971	+	0.900444i	$0.356758\pi$
$720$		0			0
$721$	48.5712	−	35.2890i	1.80889	−	1.31423i
$722$		0			0
$723$	0.0334301	+	0.102887i	0.00124328	+	0.00382642i
$724$		0			0
$725$	0.107559	+	3.10448i	0.00399466	+	0.115298i
$726$		0			0
$727$	1.36442	−	0.443325i	0.0506034	−	0.0164420i	−0.283606	−	0.958941i	$-0.591531\pi$
$727$	1.36442	−	0.443325i	0.0506034	−	0.0164420i	0.334209	+	0.942499i	$0.391531\pi$
$728$		0			0
$729$	21.1936	−	15.3980i	0.784947	−	0.570298i
$730$		0			0
$731$	−3.30617	+	4.55055i	−0.122283	+	0.168308i
$732$		0			0
$733$	30.8009	+	22.3782i	1.13766	+	0.826556i	0.986791	−	0.161998i	$-0.0517938\pi$
$733$	30.8009	+	22.3782i	1.13766	+	0.826556i	0.150866	+	0.988554i	$0.451794\pi$
$734$		0			0
$735$	−2.58447	+	0.889509i	−0.0953297	+	0.0328100i
$736$		0			0
$737$	2.89990	+	0.942236i	0.106819	+	0.0347077i
$738$		0			0
$739$	−30.0806	+	9.77378i	−1.10653	+	0.359534i	−0.804613	−	0.593799i	$-0.797627\pi$
$739$	−30.0806	+	9.77378i	−1.10653	+	0.359534i	−0.301920	+	0.953333i	$0.597627\pi$
$740$		0			0
$741$	2.51555	+	0.817351i	0.0924110	+	0.0300262i
$742$		0			0
$743$		−	13.6505i		−	0.500790i	−0.968144	−	0.250395i	$-0.919440\pi$
$743$		−	13.6505i		−	0.500790i	0.968144	−	0.250395i	$-0.0805605\pi$
$744$		0			0
$745$	−9.38771	+	30.6908i	−0.343939	+	1.12442i
$746$		0			0
$747$	17.0841	−	12.4124i	0.625076	−	0.454144i
$748$		0			0
$749$		−	68.8800i		−	2.51682i
$750$		0			0
$751$	−13.2979			−0.485247			−0.242623	−	0.970121i	$-0.578008\pi$
$751$	−13.2979			−0.485247			−0.242623	+	0.970121i	$0.578008\pi$
$752$		0			0
$753$	−0.751964	−	1.03499i	−0.0274031	−	0.0377171i
$754$		0			0
$755$	30.8643	+	9.44079i	1.12327	+	0.343586i
$756$		0			0
$757$	15.4070			0.559979			0.279989	−	0.960003i	$-0.409669\pi$
$757$	15.4070			0.559979			0.279989	+	0.960003i	$0.409669\pi$
$758$		0			0
$759$	−0.0750499	+	0.230980i	−0.00272414	+	0.00838404i
$760$		0			0
$761$	−6.51536	−	20.0522i	−0.236182	−	0.726893i	−0.996962	−	0.0778836i	$-0.975184\pi$
$761$	−6.51536	−	20.0522i	−0.236182	−	0.726893i	0.760781	−	0.649009i	$-0.224816\pi$
$762$		0			0
$763$	18.6266	−	57.3268i	0.674328	−	2.07537i
$764$		0			0
$765$	−5.47410	−	15.9050i	−0.197916	−	0.575047i
$766$		0			0
$767$	6.88391	−	9.47489i	0.248563	−	0.342118i
$768$		0			0
$769$	12.8730	+	9.35276i	0.464211	+	0.337269i	0.795181	−	0.606372i	$-0.207376\pi$
$769$	12.8730	+	9.35276i	0.464211	+	0.337269i	−0.330970	+	0.943641i	$0.607376\pi$
$770$		0			0
$771$	1.26511	+	1.74127i	0.0455617	+	0.0627103i
$772$		0			0
$773$	−0.718367	−	2.21091i	−0.0258379	−	0.0795208i	0.937306	−	0.348507i	$-0.113311\pi$
$773$	−0.718367	−	2.21091i	−0.0258379	−	0.0795208i	−0.963144	+	0.268986i	$0.913311\pi$
$774$		0			0
$775$	11.7321	+	32.2613i	0.421431	+	1.15886i
$776$		0			0
$777$	−4.11718	+	1.33775i	−0.147703	+	0.0479916i
$778$		0			0
$779$	−15.7559	−	21.6861i	−0.564513	−	0.776985i
$780$		0			0
$781$	1.50152	−	2.06666i	0.0537286	−	0.0739511i
$782$		0			0
$783$	0.267122	−	0.367662i	0.00954615	−	0.0131392i
$784$		0			0
$785$	−41.2415	−	12.6150i	−1.47197	−	0.450248i
$786$		0			0
$787$	11.5499	−	35.5471i	0.411711	−	1.26712i	−0.503449	−	0.864025i	$-0.667936\pi$
$787$	11.5499	−	35.5471i	0.411711	−	1.26712i	0.915160	−	0.403091i	$-0.132064\pi$
$788$		0			0
$789$	2.53096	−	0.822360i	0.0901047	−	0.0292768i
$790$		0			0
$791$	13.7363	−	42.2758i	0.488405	−	1.50316i
$792$		0			0
$793$		−	58.5055i		−	2.07759i
$794$		0			0
$795$	0.738836	−	1.05486i	0.0262038	−	0.0374120i
$796$		0			0
$797$	−27.6045	+	20.0559i	−0.977802	+	0.710415i	−0.957216	−	0.289373i	$-0.906553\pi$
$797$	−27.6045	+	20.0559i	−0.977802	+	0.710415i	−0.0205856	+	0.999788i	$0.506553\pi$
$798$		0			0
$799$	−16.0686			−0.568468
$800$		0			0
$801$	25.4253			0.898361
$802$		0			0
$803$	−1.90300	+	1.38261i	−0.0671553	+	0.0487912i
$804$		0			0
$805$	−1.01829	−	58.7996i	−0.0358901	−	2.07241i
$806$		0			0
$807$		−	1.48289i		−	0.0522001i
$808$		0			0
$809$	0.931838	−	2.86790i	0.0327617	−	0.100830i	−0.933338	−	0.358998i	$-0.883119\pi$
$809$	0.931838	−	2.86790i	0.0327617	−	0.100830i	0.966100	+	0.258167i	$0.0831186\pi$
$810$		0			0
$811$	−27.5066	+	8.93745i	−0.965889	+	0.313836i	−0.749155	−	0.662394i	$-0.769540\pi$
$811$	−27.5066	+	8.93745i	−0.965889	+	0.313836i	−0.216734	+	0.976231i	$0.569540\pi$
$812$		0			0
$813$	−0.593143	+	1.82551i	−0.0208024	+	0.0640233i
$814$		0			0
$815$	−11.7801	+	16.8189i	−0.412640	+	0.589140i
$816$		0			0
$817$	6.61219	−	9.10090i	0.231331	−	0.318400i
$818$		0			0
$819$	−31.0650	+	42.7573i	−1.08550	+	1.49406i
$820$		0			0
$821$	−12.8958	−	17.7496i	−0.450067	−	0.619464i	0.522345	−	0.852734i	$-0.325057\pi$
$821$	−12.8958	−	17.7496i	−0.450067	−	0.619464i	−0.972412	+	0.233270i	$0.925057\pi$
$822$		0			0
$823$	−19.0241	+	6.18129i	−0.663137	+	0.215466i	−0.621198	−	0.783654i	$-0.713354\pi$
$823$	−19.0241	+	6.18129i	−0.663137	+	0.215466i	−0.0419394	+	0.999120i	$0.513354\pi$
$824$		0			0
$825$	0.178918	−	0.0650652i	0.00622911	−	0.00226528i
$826$		0			0
$827$	5.28600	+	16.2686i	0.183812	+	0.565716i	0.999926	−	0.0121758i	$-0.00387576\pi$
$827$	5.28600	+	16.2686i	0.183812	+	0.565716i	−0.816114	+	0.577891i	$0.803876\pi$
$828$		0			0
$829$	−21.2432	−	29.2388i	−0.737807	−	1.01550i	−0.998742	−	0.0501475i	$-0.984031\pi$
$829$	−21.2432	−	29.2388i	−0.737807	−	1.01550i	0.260935	−	0.965356i	$-0.415969\pi$
$830$		0			0
$831$	−0.230458	−	0.167437i	−0.00799448	−	0.00580833i
$832$		0			0
$833$	−14.8142	+	20.3900i	−0.513282	+	0.706472i
$834$		0			0
$835$	15.7944	−	11.8985i	0.546586	−	0.411765i
$836$		0			0
$837$	1.55194	−	4.77639i	0.0536430	−	0.165096i
$838$		0			0
$839$	9.69350	+	29.8335i	0.334657	+	1.02997i	0.966891	+	0.255190i	$0.0821381\pi$
$839$	9.69350	+	29.8335i	0.334657	+	1.02997i	−0.632234	+	0.774777i	$0.717862\pi$
$840$		0			0
$841$	8.84222	−	27.2136i	0.304904	−	0.938398i
$842$		0			0
$843$	−1.66531			−0.0573562
$844$		0			0
$845$	7.31684	+	9.71254i	0.251707	+	0.334122i
$846$		0			0
$847$	26.4243	+	36.3699i	0.907948	+	1.24968i
$848$		0			0
$849$	−0.487170			−0.0167196
$850$		0			0
$851$		−	54.7930i		−	1.87828i
$852$		0			0
$853$	−20.4120	+	14.8302i	−0.698894	+	0.507776i	−0.879572	−	0.475766i	$-0.842171\pi$
$853$	−20.4120	+	14.8302i	−0.698894	+	0.507776i	0.180678	+	0.983542i	$0.442171\pi$
$854$		0			0
$855$	10.9480	+	31.8093i	0.374412	+	1.08786i
$856$		0			0
$857$		−	40.0337i		−	1.36753i	−0.729704	−	0.683763i	$-0.760342\pi$
$857$		−	40.0337i		−	1.36753i	0.729704	−	0.683763i	$-0.239658\pi$
$858$		0			0
$859$	18.4443	+	5.99291i	0.629311	+	0.204475i	0.606270	−	0.795259i	$-0.292665\pi$
$859$	18.4443	+	5.99291i	0.629311	+	0.204475i	0.0230409	+	0.999735i	$0.492665\pi$
$860$		0			0
$861$	−2.54910	+	0.828253i	−0.0868732	+	0.0282268i
$862$		0			0
$863$	−15.3173	−	4.97690i	−0.521408	−	0.169416i	0.0364763	−	0.999335i	$-0.488387\pi$
$863$	−15.3173	−	4.97690i	−0.521408	−	0.169416i	−0.557884	+	0.829919i	$0.688387\pi$
$864$		0			0
$865$	0.508535	+	29.3645i	0.0172907	+	0.998422i
$866$		0			0
$867$	−1.05300	−	0.765048i	−0.0357617	−	0.0259824i
$868$		0			0
$869$	0.826742	−	1.13791i	0.0280453	−	0.0386010i
$870$		0			0
$871$	34.0002	−	24.7026i	1.15205	−	0.837016i
$872$		0			0
$873$	2.24723	−	0.730170i	0.0760573	−	0.0247125i
$874$		0			0
$875$	−35.8379	+	28.9966i	−1.21154	+	0.980263i
$876$		0			0
$877$	3.77880	+	11.6300i	0.127601	+	0.392716i	0.994366	−	0.106001i	$-0.0338048\pi$
$877$	3.77880	+	11.6300i	0.127601	+	0.392716i	−0.866765	+	0.498717i	$0.833805\pi$
$878$		0			0
$879$	0.952378	−	0.691943i	0.0321229	−	0.0233387i
$880$		0			0
$881$	−14.6870	−	10.6707i	−0.494818	−	0.359506i	0.312216	−	0.950011i	$-0.398929\pi$
$881$	−14.6870	−	10.6707i	−0.494818	−	0.359506i	−0.807034	+	0.590505i	$0.798929\pi$
$882$		0			0
$883$	6.74673	+	4.90179i	0.227046	+	0.164958i	0.695492	−	0.718533i	$-0.255186\pi$
$883$	6.74673	+	4.90179i	0.227046	+	0.164958i	−0.468447	+	0.883492i	$0.655186\pi$
$884$		0			0
$885$	−0.745279	+	0.0129068i	−0.0250523	+	0.000433856i
$886$		0			0
$887$	47.8491	+	15.5471i	1.60662	+	0.522021i	0.968732	−	0.248110i	$-0.0798096\pi$
$887$	47.8491	+	15.5471i	1.60662	+	0.522021i	0.637885	+	0.770132i	$0.279810\pi$
$888$		0			0
$889$	−2.85256	−	8.77929i	−0.0956720	−	0.294448i
$890$		0			0
$891$	2.62685	+	0.853516i	0.0880029	+	0.0285939i
$892$		0			0
$893$	32.1366			1.07541
$894$		0			0
$895$	−0.464634	−	1.35000i	−0.0155310	−	0.0451254i
$896$		0			0
$897$	1.96759	+	2.70815i	0.0656958	+	0.0904225i
$898$		0			0
$899$			4.26543i			0.142260i
$900$		0			0
$901$		−	11.8754i		−	0.395628i
$902$		0			0
$903$	−0.661153	−	0.910000i	−0.0220018	−	0.0302829i
$904$		0			0
$905$	−35.5506	+	26.7817i	−1.18174	+	0.890252i
$906$		0			0
$907$	40.7553			1.35326			0.676629	−	0.736324i	$-0.263440\pi$
$907$	40.7553			1.35326			0.676629	+	0.736324i	$0.263440\pi$
$908$		0			0
$909$	10.4858	+	3.40703i	0.347790	+	0.113004i
$910$		0			0
$911$	−0.0419150	−	0.129001i	−0.00138871	−	0.00427400i	0.950360	−	0.311153i	$-0.100715\pi$
$911$	−0.0419150	−	0.129001i	−0.00138871	−	0.00427400i	−0.951748	+	0.306879i	$0.900715\pi$
$912$		0			0
$913$	2.09605	+	0.681046i	0.0693690	+	0.0225393i
$914$		0			0
$915$	−2.97412	+	2.24052i	−0.0983213	+	0.0740693i
$916$		0			0
$917$	−11.8235	−	8.59030i	−0.390448	−	0.283677i
$918$		0			0
$919$	−8.15739	−	5.92669i	−0.269087	−	0.195503i	0.445056	−	0.895503i	$-0.353184\pi$
$919$	−8.15739	−	5.92669i	−0.269087	−	0.195503i	−0.714144	+	0.699999i	$0.753184\pi$
$920$		0			0
$921$	0.803507	−	0.583782i	0.0264765	−	0.0192363i
$922$		0			0
$923$	−10.8803	−	33.4862i	−0.358130	−	1.10221i
$924$		0			0
$925$	−33.8537	+	26.4345i	−1.11310	+	0.869161i
$926$		0			0
$927$	−41.3371	+	13.4312i	−1.35769	+	0.441140i
$928$		0			0
$929$	−6.77547	+	4.92267i	−0.222296	+	0.161508i	−0.693360	−	0.720592i	$-0.743870\pi$
$929$	−6.77547	+	4.92267i	−0.222296	+	0.161508i	0.471064	+	0.882099i	$0.343870\pi$
$930$		0			0
$931$	29.6277	−	40.7791i	0.971010	−	1.33648i
$932$		0			0
$933$	−0.445544	−	0.323707i	−0.0145865	−	0.0105977i
$934$		0			0
$935$	1.00711	−	1.43789i	0.0329361	−	0.0470240i
$936$		0			0
$937$	−15.2292	−	4.94826i	−0.497516	−	0.161653i	0.0495015	−	0.998774i	$-0.484237\pi$
$937$	−15.2292	−	4.94826i	−0.497516	−	0.161653i	−0.547017	+	0.837121i	$0.684237\pi$
$938$		0			0
$939$	−0.230951	+	0.0750406i	−0.00753681	+	0.00244886i
$940$		0			0
$941$	33.5449	+	10.8994i	1.09353	+	0.355311i	0.799611	−	0.600519i	$-0.205039\pi$
$941$	33.5449	+	10.8994i	1.09353	+	0.355311i	0.293923	+	0.955829i	$0.405039\pi$
$942$		0			0
$943$		−	33.9244i		−	1.10473i
$944$		0			0
$945$	6.74328	−	0.116780i	0.219359	−	0.00379886i
$946$		0			0
$947$	13.2108	−	9.59818i	0.429292	−	0.311899i	−0.352074	−	0.935972i	$-0.614523\pi$
$947$	13.2108	−	9.59818i	0.429292	−	0.311899i	0.781366	+	0.624073i	$0.214523\pi$
$948$		0			0
$949$			32.4211i			1.05243i
$950$		0			0
$951$	1.50660			0.0488549
$952$		0			0
$953$	−9.40127	−	12.9397i	−0.304537	−	0.419159i	0.629131	−	0.777299i	$-0.283411\pi$
$953$	−9.40127	−	12.9397i	−0.304537	−	0.419159i	−0.933668	+	0.358140i	$0.883411\pi$
$954$		0			0
$955$	23.2949	−	33.2589i	0.753806	−	1.07623i
$956$		0			0
$957$	0.0236556			0.000764677
$958$		0			0
$959$	−17.1910	+	52.9084i	−0.555126	+	1.70850i
$960$		0			0
$961$	4.98671	+	15.3475i	0.160862	+	0.495081i
$962$		0			0
$963$	−15.4095	+	47.4256i	−0.496564	+	1.52827i
$964$		0			0
$965$	10.6299	−	34.7518i	0.342188	−	1.11870i
$966$		0			0
$967$	−27.9288	+	38.4407i	−0.898129	+	1.23617i	0.0729314	+	0.997337i	$0.476765\pi$
$967$	−27.9288	+	38.4407i	−0.898129	+	1.23617i	−0.971061	+	0.238832i	$0.923235\pi$
$968$		0			0
$969$	−1.25583	−	0.912412i	−0.0403430	−	0.0293109i
$970$		0			0
$971$	27.8358	+	38.3127i	0.893294	+	1.22951i	0.972558	+	0.232660i	$0.0747428\pi$
$971$	27.8358	+	38.3127i	0.893294	+	1.22951i	−0.0792647	+	0.996854i	$0.525257\pi$
$972$		0			0
$973$	12.9165	+	39.7528i	0.414083	+	1.27442i
$974$		0			0
$975$	0.723976	−	2.52219i	0.0231858	−	0.0807749i
$976$		0			0
$977$	21.1525	−	6.87286i	0.676728	−	0.219882i	0.0495655	−	0.998771i	$-0.484216\pi$
$977$	21.1525	−	6.87286i	0.676728	−	0.219882i	0.627162	+	0.778889i	$0.284216\pi$
$978$		0			0
$979$	1.55971	+	2.14676i	0.0498486	+	0.0686107i
$980$		0			0
$981$	−25.6497	+	35.3038i	−0.818933	+	1.12716i
$982$		0			0
$983$	27.0299	−	37.2035i	0.862121	−	1.18661i	−0.118938	−	0.992902i	$-0.537949\pi$
$983$	27.0299	−	37.2035i	0.862121	−	1.18661i	0.981060	−	0.193707i	$-0.0620510\pi$
$984$		0			0
$985$	24.3746	−	8.38913i	0.776641	−	0.267300i
$986$		0			0
$987$	0.992976	−	3.05607i	0.0316068	−	0.0972756i
$988$		0			0
$989$	13.5401	−	4.39944i	0.430550	−	0.139894i
$990$		0			0
$991$	4.44841	−	13.6908i	0.141308	−	0.434902i	−0.855209	−	0.518283i	$-0.826572\pi$
$991$	4.44841	−	13.6908i	0.141308	−	0.434902i	0.996518	+	0.0833801i	$0.0265716\pi$
$992$		0			0
$993$		−	3.20406i		−	0.101678i
$994$		0			0
$995$	31.9729	+	9.77987i	1.01361	+	0.310043i
$996$		0			0
$997$	−0.677675	+	0.492360i	−0.0214622	+	0.0155932i	−0.598465	−	0.801149i	$-0.704222\pi$
$997$	−0.677675	+	0.492360i	−0.0214622	+	0.0155932i	0.577002	+	0.816742i	$0.304222\pi$
$998$		0			0
$999$	6.28379			0.198810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.369.14		112
4.3	odd	2		200.2.o.a.69.18	yes	112
8.3	odd	2		200.2.o.a.69.11	yes	112
8.5	even	2	inner	800.2.be.a.369.15		112
20.3	even	4		1000.2.t.b.901.52		224
20.7	even	4		1000.2.t.b.901.5		224
20.19	odd	2		1000.2.o.a.349.11		112
25.4	even	10	inner	800.2.be.a.529.15		112
40.3	even	4		1000.2.t.b.901.8		224
40.19	odd	2		1000.2.o.a.349.18		112
40.27	even	4		1000.2.t.b.901.49		224
100.3	even	20		1000.2.t.b.101.8		224
100.47	even	20		1000.2.t.b.101.49		224
100.71	odd	10		1000.2.o.a.149.18		112
100.79	odd	10		200.2.o.a.29.11	✓	112
200.3	even	20		1000.2.t.b.101.52		224
200.29	even	10	inner	800.2.be.a.529.14		112
200.147	even	20		1000.2.t.b.101.5		224
200.171	odd	10		1000.2.o.a.149.11		112
200.179	odd	10		200.2.o.a.29.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.11	✓	112	100.79	odd	10
200.2.o.a.29.18	yes	112	200.179	odd	10
200.2.o.a.69.11	yes	112	8.3	odd	2
200.2.o.a.69.18	yes	112	4.3	odd	2
800.2.be.a.369.14		112	1.1	even	1	trivial
800.2.be.a.369.15		112	8.5	even	2	inner
800.2.be.a.529.14		112	200.29	even	10	inner
800.2.be.a.529.15		112	25.4	even	10	inner
1000.2.o.a.149.11		112	200.171	odd	10
1000.2.o.a.149.18		112	100.71	odd	10
1000.2.o.a.349.11		112	20.19	odd	2
1000.2.o.a.349.18		112	40.19	odd	2
1000.2.t.b.101.5		224	200.147	even	20
1000.2.t.b.101.8		224	100.3	even	20
1000.2.t.b.101.49		224	100.47	even	20
1000.2.t.b.101.52		224	200.3	even	20
1000.2.t.b.901.5		224	20.7	even	4
1000.2.t.b.901.8		224	40.3	even	4
1000.2.t.b.901.49		224	40.27	even	4
1000.2.t.b.901.52		224	20.3	even	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0988780 + 0.0718391i) q^{3} +(-2.13827 - 0.654056i) q^{5} -4.12326i q^{7} +(-0.922435 + 2.83896i) q^{9} +O(q^{10})\)	\(q+(-0.0988780 + 0.0718391i) q^{3} +(-2.13827 - 0.654056i) q^{5} -4.12326i q^{7} +(-0.922435 + 2.83896i) q^{9} +(-0.296291 + 0.0962708i) q^{11} +(-1.32691 + 4.08381i) q^{13} +(0.258415 - 0.0889398i) q^{15} +(1.48123 - 2.03874i) q^{17} +(-2.96240 + 4.07740i) q^{19} +(0.296211 + 0.407699i) q^{21} +(-6.06625 + 1.97104i) q^{23} +(4.14442 + 2.79710i) q^{25} +(-0.226044 - 0.695692i) q^{27} +(0.365173 + 0.502617i) q^{29} +(5.55444 + 4.03554i) q^{31} +(0.0223807 - 0.0308043i) q^{33} +(-2.69684 + 8.81665i) q^{35} +(-2.65457 + 8.16992i) q^{37} +(-0.162175 - 0.499123i) q^{39} +(-1.64354 + 5.05830i) q^{41} -2.23204 q^{43} +(3.82926 - 5.46715i) q^{45} +(-3.74794 - 5.15860i) q^{47} -10.0013 q^{49} +0.307997i q^{51} +(3.81243 - 2.76989i) q^{53} +(0.696517 - 0.0120623i) q^{55} -0.615981i q^{57} +(-2.59396 - 0.842829i) q^{59} +(-12.9582 + 4.21037i) q^{61} +(11.7058 + 3.80344i) q^{63} +(5.50834 - 7.86443i) q^{65} +(-7.91813 - 5.75286i) q^{67} +(0.458220 - 0.630686i) q^{69} +(-6.63373 + 4.81969i) q^{71} +(7.18083 - 2.33319i) q^{73} +(-0.610733 + 0.0211597i) q^{75} +(0.396949 + 1.22168i) q^{77} +(-3.65256 + 2.65374i) q^{79} +(-7.17257 - 5.21118i) q^{81} +(-5.72321 - 4.15816i) q^{83} +(-4.50074 + 3.39058i) q^{85} +(-0.0722151 - 0.0234641i) q^{87} +(-2.63206 - 8.10065i) q^{89} +(16.8386 + 5.47119i) q^{91} -0.839121 q^{93} +(9.00127 - 6.78101i) q^{95} +(-0.465272 - 0.640392i) q^{97} -0.929963i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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