LMFDB - Embedded newform 800.2.be.a.369.15

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			369.15
Character	$\chi$	$=$	800.369
Dual form			800.2.be.a.529.15

$q$-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	−0.558876	−	0.829251i	$-0.688767\pi$
$3$	0.0988780	−	0.0718391i	0.0570872	−	0.0414763i	0.615963	+	0.787775i	$0.288767\pi$
$4$		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	−0.264008	−	0.964520i	$-0.585045\pi$
$11$	0.296291	−	0.0962708i	0.0893351	−	0.0290267i	0.353344	+	0.935494i	$0.385045\pi$
$12$		0			0
$13$	1.32691	−	4.08381i	0.368019	−	1.13264i	−0.580050	−	0.814581i	$-0.696967\pi$
$13$	1.32691	−	4.08381i	0.368019	−	1.13264i	0.948069	−	0.318064i	$-0.103033\pi$
$14$		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	−0.320308	−	0.947314i	$-0.603786\pi$
$19$	2.96240	−	4.07740i	0.679622	−	0.935419i	0.999929	+	0.0118946i	$0.00378626\pi$
$20$		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	0.773764	−	0.633473i	$-0.218371\pi$
$29$	−0.365173	−	0.502617i	−0.0678109	−	0.0933337i	−0.841575	+	0.540140i	$0.818371\pi$
$30$		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	$-0.650443\pi$
$37$	2.65457	−	8.16992i	0.436408	−	1.34313i	0.891637	−	0.452751i	$-0.149557\pi$
$38$		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	$-0.445561\pi$
$43$	2.23204			0.340382			0.170191	+	0.985411i	$0.445561\pi$
$44$		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	−0.817988	−	0.575236i	$-0.804910\pi$
$53$	−3.81243	+	2.76989i	−0.523678	+	0.380474i	0.294310	+	0.955710i	$0.404910\pi$
$54$		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	0.472960	−	0.881084i	$-0.343185\pi$
$59$	2.59396	+	0.842829i	0.337705	+	0.109727i	−0.135255	+	0.990811i	$0.543185\pi$
$60$		0			0
$61$	12.9582	−	4.21037i	1.65913	−	0.539082i	0.678437	−	0.734659i	$-0.262658\pi$
$61$	12.9582	−	4.21037i	1.65913	−	0.539082i	0.980688	+	0.195576i	$0.0626577\pi$
$62$		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	0.954847	−	0.297098i	$-0.0960188\pi$
$67$	7.91813	+	5.75286i	0.967354	+	0.702824i	0.0125070	+	0.999922i	$0.496019\pi$
$68$		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	0.855778	−	0.517344i	$-0.173079\pi$
$83$	5.72321	+	4.15816i	0.628204	+	0.456417i	−0.227573	+	0.973761i	$0.573079\pi$
$84$		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	$0.0588267\pi$
$101$			3.69351i			0.367518i	−0.982971	+	0.183759i	$0.941173\pi$
$102$		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	$-0.799168\pi$
$107$	−16.7052			−1.61496			−0.807478	+	0.589897i	$0.799168\pi$
$108$		0			0
$109$	−13.9033	−	4.51745i	−1.33169	−	0.432693i	−0.445198	−	0.895432i	$-0.646867\pi$
$109$	−13.9033	−	4.51745i	−1.33169	−	0.432693i	−0.886494	+	0.462739i	$0.846867\pi$
$110$		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	−0.890273	−	0.455428i	$-0.849486\pi$
$131$	−2.08338	+	2.86752i	−0.182026	+	0.250537i	0.708247	+	0.705965i	$0.249486\pi$
$132$		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	0.129872	−	0.991531i	$-0.458543\pi$
$139$	9.64111	−	3.13259i	0.817749	−	0.265703i	0.687876	+	0.725828i	$0.258543\pi$
$140$		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	$0.200055\pi$
$149$			14.3531i			1.17585i	−0.808916	+	0.587925i	$0.799945\pi$
$150$		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	$-0.779568\pi$
$157$	−19.2873			−1.53930			−0.769648	+	0.638469i	$0.779568\pi$
$158$		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	$0.217100\pi$
$163$	−2.83773	+	8.73364i	−0.222268	+	0.684072i	−0.998557	+	0.0536946i	$0.982900\pi$
$164$		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	$0.0664042\pi$
$173$	4.05868	+	12.4913i	0.308576	+	0.949698i	−0.669743	+	0.742593i	$0.733596\pi$
$174$		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	0.794761	−	0.606922i	$-0.207596\pi$
$179$	−0.375298	−	0.516553i	−0.0280511	−	0.0386090i	−0.822812	+	0.568313i	$0.807596\pi$
$180$		0			0
$181$	−11.7000	+	16.1037i	−0.869656	+	1.19698i	0.109523	+	0.993984i	$0.465068\pi$
$181$	−11.7000	+	16.1037i	−0.869656	+	1.19698i	−0.979180	+	0.202995i	$0.934932\pi$
$182$		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	−0.203687	−	0.979036i	$-0.565293\pi$
$197$	9.32654	−	6.77613i	0.664488	−	0.482779i	0.868176	+	0.496257i	$0.165293\pi$
$198$		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	−0.379710	−	0.925106i	$-0.623976\pi$
$211$	−2.07919	+	0.675570i	−0.143137	+	0.0465082i	0.236572	+	0.971614i	$0.423976\pi$
$212$		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	$0.0212852\pi$
$227$	3.46276	+	10.6573i	0.229832	+	0.707349i	−0.767933	+	0.640530i	$0.778715\pi$
$228$		0			0
$229$	4.28891	+	5.90318i	0.283419	+	0.390093i	0.926863	−	0.375401i	$-0.122495\pi$
$229$	4.28891	+	5.90318i	0.283419	+	0.390093i	−0.643444	+	0.765494i	$0.722495\pi$
$230$		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	$-0.892835\pi$
$251$		−	10.4673i		−	0.660692i	0.943860	−	0.330346i	$-0.107165\pi$
$252$		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	−0.534232	−	0.845338i	$-0.679399\pi$
$269$	7.13157	−	9.81576i	0.434819	−	0.598477i	0.969051	+	0.246861i	$0.0793990\pi$
$270$		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	0.927085	−	0.374851i	$-0.122306\pi$
$277$	−0.720234	−	2.21665i	−0.0432747	−	0.133186i	−0.970360	+	0.241666i	$0.922306\pi$
$278$		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	0.487800	−	0.872955i	$-0.337800\pi$
$283$	−3.22475	−	2.34292i	−0.191691	−	0.139272i	−0.679491	+	0.733683i	$0.737800\pi$
$284$		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	$-0.409218\pi$
$293$	9.63185			0.562699			0.281349	+	0.959605i	$0.409218\pi$
$294$		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	$-0.425507\pi$
$307$	8.12625			0.463790			0.231895	+	0.972741i	$0.425507\pi$
$308$		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	0.831504	−	0.555518i	$-0.187480\pi$
$317$	9.97273	+	7.24561i	0.560124	+	0.406954i	−0.271380	+	0.962472i	$0.587480\pi$
$318$		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	$-0.543928\pi$
$331$	15.4091	−	21.2088i	0.846960	−	1.16574i	0.984524	−	0.175247i	$-0.0560725\pi$
$332$		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	0.173442	−	0.984844i	$-0.444511\pi$
$347$	21.6770	−	15.7492i	1.16368	−	0.845463i	0.990239	+	0.139381i	$0.0445112\pi$
$348$		0			0
$349$		−	9.22396i		−	0.493747i	−0.969048	−	0.246874i	$-0.920597\pi$
$349$		−	9.22396i		−	0.493747i	0.969048	−	0.246874i	$-0.0794032\pi$
$350$		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	0.844286	−	0.535893i	$-0.180025\pi$
$373$	−2.96932	−	9.13862i	−0.153746	−	0.473180i	−0.998032	+	0.0627126i	$0.980025\pi$
$374$		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	0.830909	−	0.556409i	$-0.187821\pi$
$379$	0.875430	+	1.20493i	0.0449678	+	0.0618929i	−0.785941	+	0.618302i	$0.787821\pi$
$380$		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	−0.0147301	−	0.999892i	$-0.504689\pi$
$389$	11.0661	−	3.59560i	0.561074	−	0.182304i	0.575805	+	0.817587i	$0.304689\pi$
$390$		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	−0.654412	−	0.756138i	$-0.727084\pi$
$397$	−2.73979	+	1.99057i	−0.137506	+	0.0999040i	0.516906	+	0.856042i	$0.327084\pi$
$398$		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	$-0.423909\pi$
$419$	22.2630	−	30.6425i	1.08762	−	1.49698i	0.850844	−	0.525418i	$-0.176091\pi$
$420$		0			0
$421$	−8.76743	−	12.0673i	−0.427298	−	0.588126i	0.540032	−	0.841644i	$-0.318412\pi$
$421$	−8.76743	−	12.0673i	−0.427298	−	0.588126i	−0.967331	+	0.253519i	$0.918412\pi$
$422$		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	$-0.798162\pi$
$443$	−33.9122			−1.61122			−0.805609	+	0.592448i	$0.798162\pi$
$444$		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	−0.801743	−	0.597669i	$-0.796094\pi$
$461$	−23.5979	+	7.66744i	−1.09907	+	0.357108i	−0.297323	+	0.954777i	$0.596094\pi$
$462$		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	0.586520	−	0.809934i	$-0.300497\pi$
$467$	−0.0546334	−	0.0396935i	−0.00252813	−	0.00183679i	−0.589049	+	0.808098i	$0.700497\pi$
$468$		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	0.946881	−	0.321584i	$-0.104215\pi$
$491$	33.7674	+	10.9717i	1.52390	+	0.495146i	0.577020	+	0.816730i	$0.304215\pi$
$492$		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	$0.186818\pi$
$499$			24.7413i			1.10757i	−0.832658	+	0.553787i	$0.813182\pi$
$500$		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	−0.195400	−	0.980724i	$-0.562601\pi$
$509$	−20.9803	−	6.81693i	−0.929937	−	0.302155i	−0.734537	+	0.678569i	$0.762601\pi$
$510$		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	0.905936	−	0.423415i	$-0.139169\pi$
$523$	−1.73482	−	5.33924i	−0.0758585	−	0.233469i	−0.981795	+	0.189946i	$0.939169\pi$
$524$		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	0.791979	−	0.610549i	$-0.209051\pi$
$541$	24.9767	+	8.11542i	1.07383	+	0.348909i	0.281853	+	0.959458i	$0.409051\pi$
$542$		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	0.128340	−	0.991730i	$-0.459035\pi$
$547$	25.9886	−	18.8818i	1.11119	−	0.807327i	0.982851	+	0.184403i	$0.0590352\pi$
$548$		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	$-0.431568\pi$
$557$	10.0696			0.426664			0.213332	+	0.976980i	$0.431568\pi$
$558$		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	$-0.695007\pi$
$563$	8.80460	−	27.0978i	0.371069	−	1.14203i	0.946092	−	0.323897i	$-0.104993\pi$
$564$		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	0.318792	−	0.947825i	$-0.396723\pi$
$571$	−16.2766	−	22.4028i	−0.681155	−	0.937529i	−0.999947	+	0.0102955i	$0.996723\pi$
$572$		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	$0.517961\pi$
$587$	−14.4792	+	44.5624i	−0.597620	+	1.83929i	−0.541224	+	0.840878i	$0.682039\pi$
$588$		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	$0.302874\pi$
$613$	−9.10557	+	28.0241i	−0.367771	+	1.13188i	−0.948228	+	0.317591i	$0.897126\pi$
$614$		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	$0.546732\pi$
$619$	−25.9223	+	35.6790i	−1.04191	+	1.43406i	−0.895621	+	0.444819i	$0.853268\pi$
$620$		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	$-0.346333\pi$
$643$	23.5431			0.928448			0.464224	+	0.885718i	$0.346333\pi$
$644$		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	−0.453150	−	0.891434i	$-0.649700\pi$
$653$	6.50662	−	4.72734i	0.254624	−	0.184995i	0.707773	+	0.706439i	$0.249700\pi$
$654$		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	−0.720361	−	0.693599i	$-0.756024\pi$
$659$	−43.9188	−	14.2701i	−1.71083	−	0.555883i	−0.990472	+	0.137716i	$0.956024\pi$
$660$		0			0
$661$	−31.8290	+	10.3419i	−1.23800	+	0.402252i	−0.853607	−	0.520917i	$-0.825590\pi$
$661$	−31.8290	+	10.3419i	−1.23800	+	0.402252i	−0.384396	+	0.923168i	$0.625590\pi$
$662$		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	$-0.866012\pi$
$677$	−10.7847	−	33.1919i	−0.414489	−	1.27567i	0.498217	−	0.867052i	$-0.333988\pi$
$678$		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	0.474037	−	0.880505i	$-0.342796\pi$
$683$	−5.66818	−	4.11817i	−0.216887	−	0.157578i	−0.690924	+	0.722927i	$0.742796\pi$
$684$		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	0.453079	−	0.891470i	$-0.350325\pi$
$691$	7.77133	+	2.52506i	0.295635	+	0.0960578i	−0.157444	+	0.987528i	$0.550325\pi$
$692$		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	$0.123308\pi$
$701$			20.0038i			0.755534i	−0.925901	+	0.377767i	$0.876692\pi$
$702$		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	−0.757775	−	0.652516i	$-0.773714\pi$
$709$	−46.7136	−	15.1782i	−1.75437	−	0.570029i	−0.996592	+	0.0824870i	$0.973714\pi$
$710$		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	−0.150866	−	0.988554i	$-0.548206\pi$
$733$	−30.8009	−	22.3782i	−1.13766	−	0.826556i	−0.986791	+	0.161998i	$0.948206\pi$
$734$		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	0.301920	−	0.953333i	$-0.402373\pi$
$739$	30.0806	−	9.77378i	1.10653	−	0.359534i	0.804613	+	0.593799i	$0.202373\pi$
$740$		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	$-0.590331\pi$
$757$	−15.4070			−0.559979			−0.279989	+	0.960003i	$0.590331\pi$
$758$		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	0.963144	−	0.268986i	$-0.0866887\pi$
$773$	0.718367	+	2.21091i	0.0258379	+	0.0795208i	−0.937306	+	0.348507i	$0.886689\pi$
$774$		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	$0.332064\pi$
$787$	−11.5499	+	35.5471i	−0.411711	+	1.26712i	−0.915160	+	0.403091i	$0.867936\pi$
$788$		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	0.0205856	−	0.999788i	$-0.493447\pi$
$797$	27.6045	−	20.0559i	0.977802	−	0.710415i	0.957216	+	0.289373i	$0.0934469\pi$
$798$		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	0.216734	−	0.976231i	$-0.430460\pi$
$811$	27.5066	−	8.93745i	0.965889	−	0.313836i	0.749155	+	0.662394i	$0.230460\pi$
$812$		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	0.972412	−	0.233270i	$-0.0749427\pi$
$821$	12.8958	+	17.7496i	0.450067	+	0.619464i	−0.522345	+	0.852734i	$0.674943\pi$
$822$		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	0.816114	−	0.577891i	$-0.196124\pi$
$827$	−5.28600	−	16.2686i	−0.183812	−	0.565716i	−0.999926	+	0.0121758i	$0.996124\pi$
$828$		0			0
$829$	21.2432	+	29.2388i	0.737807	+	1.01550i	0.998742	+	0.0501475i	$0.0159692\pi$
$829$	21.2432	+	29.2388i	0.737807	+	1.01550i	−0.260935	+	0.965356i	$0.584031\pi$
$830$		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	−0.180678	−	0.983542i	$-0.557829\pi$
$853$	20.4120	−	14.8302i	0.698894	−	0.507776i	0.879572	+	0.475766i	$0.157829\pi$
$854$		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	−0.0230409	−	0.999735i	$-0.507335\pi$
$859$	−18.4443	−	5.99291i	−0.629311	−	0.204475i	−0.606270	+	0.795259i	$0.707335\pi$
$860$		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	0.866765	−	0.498717i	$-0.166195\pi$
$877$	−3.77880	−	11.6300i	−0.127601	−	0.392716i	−0.994366	+	0.106001i	$0.966195\pi$
$878$		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	0.468447	−	0.883492i	$-0.344814\pi$
$883$	−6.74673	−	4.90179i	−0.227046	−	0.164958i	−0.695492	+	0.718533i	$0.744814\pi$
$884$		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	$-0.736560\pi$
$907$	−40.7553			−1.35326			−0.676629	+	0.736324i	$0.736560\pi$
$908$		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	−0.293923	−	0.955829i	$-0.594961\pi$
$941$	−33.5449	−	10.8994i	−1.09353	−	0.355311i	−0.799611	+	0.600519i	$0.794961\pi$
$942$		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	−0.781366	−	0.624073i	$-0.785477\pi$
$947$	−13.2108	+	9.59818i	−0.429292	+	0.311899i	0.352074	+	0.935972i	$0.385477\pi$
$948$		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	$-0.925257\pi$
$971$	−27.8358	−	38.3127i	−0.893294	−	1.22951i	0.0792647	−	0.996854i	$-0.474743\pi$
$972$		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	−0.577002	−	0.816742i	$-0.695778\pi$
$997$	0.677675	−	0.492360i	0.0214622	−	0.0155932i	0.598465	+	0.801149i	$0.295778\pi$
$998$		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.369.15		112
4.3	odd	2		200.2.o.a.69.11	yes	112
8.3	odd	2		200.2.o.a.69.18	yes	112
8.5	even	2	inner	800.2.be.a.369.14		112
20.3	even	4		1000.2.t.b.901.8		224
20.7	even	4		1000.2.t.b.901.49		224
20.19	odd	2		1000.2.o.a.349.18		112
25.4	even	10	inner	800.2.be.a.529.14		112
40.3	even	4		1000.2.t.b.901.52		224
40.19	odd	2		1000.2.o.a.349.11		112
40.27	even	4		1000.2.t.b.901.5		224
100.3	even	20		1000.2.t.b.101.52		224
100.47	even	20		1000.2.t.b.101.5		224
100.71	odd	10		1000.2.o.a.149.11		112
100.79	odd	10		200.2.o.a.29.18	yes	112
200.3	even	20		1000.2.t.b.101.8		224
200.29	even	10	inner	800.2.be.a.529.15		112
200.147	even	20		1000.2.t.b.101.49		224
200.171	odd	10		1000.2.o.a.149.18		112
200.179	odd	10		200.2.o.a.29.11	✓	112

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