LMFDB - Embedded newform 400.2.y.a.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	400.289
Dual form			400.2.y.a.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06909 - 0.672288i) q^{3} +(-2.17229 + 0.530249i) q^{5} +2.72654i q^{7} +(1.40211 + 1.01869i) q^{9} +O(q^{10})$	\(q+(-2.06909 - 0.672288i) q^{3} +(-2.17229 + 0.530249i) q^{5} +2.72654i q^{7} +(1.40211 + 1.01869i) q^{9} +(4.52874 - 3.29032i) q^{11} +(0.282051 - 0.388209i) q^{13} +(4.85114 + 0.363271i) q^{15} +(3.71113 - 1.20582i) q^{17} +(-1.27877 - 3.93564i) q^{19} +(1.83302 - 5.64146i) q^{21} +(0.0930960 + 0.128136i) q^{23} +(4.43767 - 2.30371i) q^{25} +(1.62006 + 2.22982i) q^{27} +(2.17229 - 6.68562i) q^{29} +(-0.133446 - 0.410706i) q^{31} +(-11.5824 + 3.76336i) q^{33} +(-1.44575 - 5.92284i) q^{35} +(-1.56082 + 2.14828i) q^{37} +(-0.844577 + 0.613621i) q^{39} +(6.86650 + 4.98880i) q^{41} -3.49890i q^{43} +(-3.58596 - 1.46943i) q^{45} +(6.43001 + 2.08924i) q^{47} -0.434034 q^{49} -8.48932 q^{51} +(5.31375 + 1.72654i) q^{53} +(-8.09304 + 9.54889i) q^{55} +9.00290i q^{57} +(6.15537 + 4.47214i) q^{59} +(-5.97449 + 4.34072i) q^{61} +(-2.77751 + 3.82292i) q^{63} +(-0.406848 + 0.992859i) q^{65} +(1.96589 - 0.638757i) q^{67} +(-0.106480 - 0.327712i) q^{69} +(2.18146 - 6.71384i) q^{71} +(-7.99885 - 11.0095i) q^{73} +(-10.7307 + 1.78318i) q^{75} +(8.97120 + 12.3478i) q^{77} +(1.95855 - 6.02781i) q^{79} +(-3.45965 - 10.6477i) q^{81} +(-11.0330 + 3.58482i) q^{83} +(-7.42226 + 4.58721i) q^{85} +(-8.98932 + 12.3727i) q^{87} +(1.38197 - 1.00406i) q^{89} +(1.05847 + 0.769023i) q^{91} +0.939503i q^{93} +(4.86472 + 7.87129i) q^{95} +(-11.2840 - 3.66640i) q^{97} +9.70164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{5} - 4 q^{9}+O(q^{10}) $ 8 * q - 10 * q^5 - 4 * q^9	$ 8 q - 10 q^{5} - 4 q^{9} + 4 q^{11} + 20 q^{15} + 10 q^{17} - 10 q^{19} + 16 q^{21} - 10 q^{23} + 10 q^{25} + 10 q^{29} - 6 q^{31} - 30 q^{33} - 10 q^{35} - 10 q^{37} + 8 q^{39} - 14 q^{41} + 10 q^{45} + 30 q^{47} - 16 q^{49} - 16 q^{51} + 10 q^{55} - 14 q^{61} - 20 q^{63} + 50 q^{65} - 10 q^{67} - 8 q^{69} + 34 q^{71} - 10 q^{75} + 40 q^{77} - 12 q^{81} - 50 q^{83} - 20 q^{85} - 20 q^{87} + 20 q^{89} + 4 q^{91} - 20 q^{97} + 28 q^{99}+O(q^{100}) $ 8 * q - 10 * q^5 - 4 * q^9 + 4 * q^11 + 20 * q^15 + 10 * q^17 - 10 * q^19 + 16 * q^21 - 10 * q^23 + 10 * q^25 + 10 * q^29 - 6 * q^31 - 30 * q^33 - 10 * q^35 - 10 * q^37 + 8 * q^39 - 14 * q^41 + 10 * q^45 + 30 * q^47 - 16 * q^49 - 16 * q^51 + 10 * q^55 - 14 * q^61 - 20 * q^63 + 50 * q^65 - 10 * q^67 - 8 * q^69 + 34 * q^71 - 10 * q^75 + 40 * q^77 - 12 * q^81 - 50 * q^83 - 20 * q^85 - 20 * q^87 + 20 * q^89 + 4 * q^91 - 20 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.06909	−	0.672288i	−1.19459	−	0.388146i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	−2.06909	−	0.672288i	−1.19459	−	0.388146i	−0.837768	+	0.546027i	$0.816140\pi$
$4$		0			0
$5$	−2.17229	+	0.530249i	−0.971477	+	0.237134i
$5$	−2.17229	+	0.530249i	−0.971477	+	0.237134i
$6$		0			0
$7$			2.72654i			1.03054i	0.857029	+	0.515268i	$0.172308\pi$
$7$			2.72654i			1.03054i	−0.857029	+	0.515268i	$0.827692\pi$
$8$		0			0
$9$	1.40211	+	1.01869i	0.467371	+	0.339565i
$10$		0			0
$11$	4.52874	−	3.29032i	1.36547	−	0.992069i	0.367391	−	0.930067i	$-0.380251\pi$
$11$	4.52874	−	3.29032i	1.36547	−	0.992069i	0.998076	−	0.0620027i	$-0.0197487\pi$
$12$		0			0
$13$	0.282051	−	0.388209i	0.0782267	−	0.107670i	−0.768110	−	0.640317i	$-0.778803\pi$
$13$	0.282051	−	0.388209i	0.0782267	−	0.107670i	0.846337	+	0.532648i	$0.178803\pi$
$14$		0			0
$15$	4.85114	+	0.363271i	1.25256	+	0.0937962i
$16$		0			0
$17$	3.71113	−	1.20582i	0.900081	−	0.292454i	0.177811	−	0.984065i	$-0.443099\pi$
$17$	3.71113	−	1.20582i	0.900081	−	0.292454i	0.722271	+	0.691611i	$0.243099\pi$
$18$		0			0
$19$	−1.27877	−	3.93564i	−0.293370	−	0.902899i	−0.983764	−	0.179466i	$-0.942563\pi$
$19$	−1.27877	−	3.93564i	−0.293370	−	0.902899i	0.690395	−	0.723433i	$-0.257437\pi$
$20$		0			0
$21$	1.83302	−	5.64146i	0.399998	−	1.23107i
$22$		0			0
$23$	0.0930960	+	0.128136i	0.0194119	+	0.0267181i	0.818613	−	0.574346i	$-0.194744\pi$
$23$	0.0930960	+	0.128136i	0.0194119	+	0.0267181i	−0.799201	+	0.601064i	$0.794744\pi$
$24$		0			0
$25$	4.43767	−	2.30371i	0.887535	−	0.460741i
$26$		0			0
$27$	1.62006	+	2.22982i	0.311781	+	0.429130i
$28$		0			0
$29$	2.17229	−	6.68562i	0.403384	−	1.24149i	−0.518853	−	0.854863i	$-0.673641\pi$
$29$	2.17229	−	6.68562i	0.403384	−	1.24149i	0.922237	−	0.386624i	$-0.126359\pi$
$30$		0			0
$31$	−0.133446	−	0.410706i	−0.0239677	−	0.0737650i	0.938357	−	0.345667i	$-0.112347\pi$
$31$	−0.133446	−	0.410706i	−0.0239677	−	0.0737650i	−0.962325	+	0.271902i	$0.912347\pi$
$32$		0			0
$33$	−11.5824	+	3.76336i	−2.01624	+	0.655116i
$34$		0			0
$35$	−1.44575	−	5.92284i	−0.244376	−	1.00114i
$36$		0			0
$37$	−1.56082	+	2.14828i	−0.256597	+	0.353176i	−0.917808	−	0.397024i	$-0.870043\pi$
$37$	−1.56082	+	2.14828i	−0.256597	+	0.353176i	0.661211	+	0.750200i	$0.270043\pi$
$38$		0			0
$39$	−0.844577	+	0.613621i	−0.135240	+	0.0982580i
$40$		0			0
$41$	6.86650	+	4.98880i	1.07237	+	0.779120i	0.976336	−	0.216258i	$-0.0693854\pi$
$41$	6.86650	+	4.98880i	1.07237	+	0.779120i	0.0960305	+	0.995378i	$0.469385\pi$
$42$		0			0
$43$		−	3.49890i		−	0.533578i	−0.963755	−	0.266789i	$-0.914037\pi$
$43$		−	3.49890i		−	0.533578i	0.963755	−	0.266789i	$-0.0859627\pi$
$44$		0			0
$45$	−3.58596	−	1.46943i	−0.534563	−	0.219050i
$46$		0			0
$47$	6.43001	+	2.08924i	0.937914	+	0.304747i	0.737795	−	0.675025i	$-0.235867\pi$
$47$	6.43001	+	2.08924i	0.937914	+	0.304747i	0.200119	+	0.979772i	$0.435867\pi$
$48$		0			0
$49$	−0.434034			−0.0620049
$50$		0			0
$51$	−8.48932			−1.18874
$52$		0			0
$53$	5.31375	+	1.72654i	0.729900	+	0.237159i	0.650310	−	0.759669i	$-0.274639\pi$
$53$	5.31375	+	1.72654i	0.729900	+	0.237159i	0.0795898	+	0.996828i	$0.474639\pi$
$54$		0			0
$55$	−8.09304	+	9.54889i	−1.09127	+	1.28757i
$56$		0			0
$57$			9.00290i			1.19246i
$58$		0			0
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	0.911313	−	0.411714i	$-0.135070\pi$
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	−0.109952	+	0.993937i	$0.535070\pi$
$60$		0			0
$61$	−5.97449	+	4.34072i	−0.764955	+	0.555772i	−0.900426	−	0.435009i	$-0.856745\pi$
$61$	−5.97449	+	4.34072i	−0.764955	+	0.555772i	0.135471	+	0.990781i	$0.456745\pi$
$62$		0			0
$63$	−2.77751	+	3.82292i	−0.349934	+	0.481643i
$64$		0			0
$65$	−0.406848	+	0.992859i	−0.0504632	+	0.123149i
$66$		0			0
$67$	1.96589	−	0.638757i	0.240172	−	0.0780366i	−0.186458	−	0.982463i	$-0.559701\pi$
$67$	1.96589	−	0.638757i	0.240172	−	0.0780366i	0.426630	+	0.904426i	$0.359701\pi$
$68$		0			0
$69$	−0.106480	−	0.327712i	−0.0128187	−	0.0394519i
$70$		0			0
$71$	2.18146	−	6.71384i	0.258891	−	0.796786i	−0.734147	−	0.678991i	$-0.762418\pi$
$71$	2.18146	−	6.71384i	0.258891	−	0.796786i	0.993038	−	0.117795i	$-0.0375825\pi$
$72$		0			0
$73$	−7.99885	−	11.0095i	−0.936194	−	1.28856i	−0.957394	−	0.288786i	$-0.906749\pi$
$73$	−7.99885	−	11.0095i	−0.936194	−	1.28856i	0.0211995	−	0.999775i	$-0.493251\pi$
$74$		0			0
$75$	−10.7307	+	1.78318i	−1.23907	+	0.205904i
$76$		0			0
$77$	8.97120	+	12.3478i	1.02236	+	1.40716i
$78$		0			0
$79$	1.95855	−	6.02781i	0.220354	−	0.678181i	−0.778376	−	0.627799i	$-0.783956\pi$
$79$	1.95855	−	6.02781i	0.220354	−	0.678181i	0.998730	−	0.0503824i	$-0.0160440\pi$
$80$		0			0
$81$	−3.45965	−	10.6477i	−0.384406	−	1.18308i
$82$		0			0
$83$	−11.0330	+	3.58482i	−1.21102	+	0.393486i	−0.843806	−	0.536649i	$-0.819690\pi$
$83$	−11.0330	+	3.58482i	−1.21102	+	0.393486i	−0.367219	+	0.930135i	$0.619690\pi$
$84$		0			0
$85$	−7.42226	+	4.58721i	−0.805057	+	0.497553i
$86$		0			0
$87$	−8.98932	+	12.3727i	−0.963756	+	1.32650i
$88$		0			0
$89$	1.38197	−	1.00406i	0.146488	−	0.106430i	−0.512127	−	0.858910i	$-0.671142\pi$
$89$	1.38197	−	1.00406i	0.146488	−	0.106430i	0.658615	+	0.752480i	$0.271142\pi$
$90$		0			0
$91$	1.05847	+	0.769023i	0.110958	+	0.0806155i
$92$		0			0
$93$			0.939503i			0.0974219i
$94$		0			0
$95$	4.86472	+	7.87129i	0.499110	+	0.807577i
$96$		0			0
$97$	−11.2840	−	3.66640i	−1.14572	−	0.372267i	−0.326190	−	0.945304i	$-0.605765\pi$
$97$	−11.2840	−	3.66640i	−1.14572	−	0.372267i	−0.819529	+	0.573038i	$0.805765\pi$
$98$		0			0
$99$	9.70164			0.975051
$100$		0			0
$101$	−7.92116			−0.788185			−0.394093	−	0.919071i	$-0.628941\pi$
$101$	−7.92116			−0.788185			−0.394093	+	0.919071i	$0.628941\pi$
$102$		0			0
$103$	5.96740	+	1.93893i	0.587986	+	0.191048i	0.587875	−	0.808952i	$-0.299965\pi$
$103$	5.96740	+	1.93893i	0.587986	+	0.191048i	0.000110715		1.00000i	$0.499965\pi$
$104$		0			0
$105$	−0.990475	+	13.2268i	−0.0966604	+	1.29081i
$106$		0			0
$107$		−	10.9662i		−	1.06014i	−0.847954	−	0.530069i	$-0.822166\pi$
$107$		−	10.9662i		−	1.06014i	0.847954	−	0.530069i	$-0.177834\pi$
$108$		0			0
$109$	6.32234	+	4.59345i	0.605571	+	0.439973i	0.847852	−	0.530233i	$-0.177896\pi$
$109$	6.32234	+	4.59345i	0.605571	+	0.439973i	−0.242281	+	0.970206i	$0.577896\pi$
$110$		0			0
$111$	4.67374	−	3.39567i	0.443612	−	0.322303i
$112$		0			0
$113$	0.811922	−	1.11751i	0.0763792	−	0.105127i	−0.769118	−	0.639107i	$-0.779304\pi$
$113$	0.811922	−	1.11751i	0.0763792	−	0.105127i	0.845497	+	0.533980i	$0.179304\pi$
$114$		0			0
$115$	−0.270175	−	0.228984i	−0.0251940	−	0.0213528i
$116$		0			0
$117$	0.790933	−	0.256990i	0.0731218	−	0.0237587i
$118$		0			0
$119$	3.28772	+	10.1186i	0.301385	+	0.927566i
$120$		0			0
$121$	6.28408	−	19.3404i	0.571280	−	1.75822i
$122$		0			0
$123$	−10.8535	−	14.9385i	−0.978626	−	1.34696i
$124$		0			0
$125$	−8.41837	+	7.35738i	−0.752962	+	0.658064i
$126$		0			0
$127$	0.122790	+	0.169006i	0.0108959	+	0.0149969i	0.814430	−	0.580262i	$-0.197050\pi$
$127$	0.122790	+	0.169006i	0.0108959	+	0.0149969i	−0.803534	+	0.595258i	$0.797050\pi$
$128$		0			0
$129$	−2.35227	+	7.23955i	−0.207106	+	0.637407i
$130$		0			0
$131$	1.83177	+	5.63760i	0.160042	+	0.492560i	0.998637	−	0.0521964i	$-0.0166222\pi$
$131$	1.83177	+	5.63760i	0.160042	+	0.492560i	−0.838594	+	0.544756i	$0.816622\pi$
$132$		0			0
$133$	10.7307	−	3.48662i	0.930470	−	0.302328i
$134$		0			0
$135$	−4.70160	−	3.98479i	−0.404650	−	0.342956i
$136$		0			0
$137$	8.52603	−	11.7351i	0.728428	−	1.00260i	−0.270773	−	0.962643i	$-0.587279\pi$
$137$	8.52603	−	11.7351i	0.728428	−	1.00260i	0.999202	−	0.0399523i	$-0.0127206\pi$
$138$		0			0
$139$	4.89680	−	3.55774i	0.415341	−	0.301763i	−0.360419	−	0.932790i	$-0.617366\pi$
$139$	4.89680	−	3.55774i	0.415341	−	0.301763i	0.775761	+	0.631027i	$0.217366\pi$
$140$		0			0
$141$	−11.8997	−	8.64564i	−1.00214	−	0.728094i
$142$		0			0
$143$		−	2.68614i		−	0.224626i
$144$		0			0
$145$	−1.17380	+	15.6749i	−0.0974785	+	1.30173i
$146$		0			0
$147$	0.898056	+	0.291796i	0.0740704	+	0.0240669i
$148$		0			0
$149$	13.7401			1.12563			0.562815	−	0.826583i	$-0.309718\pi$
$149$	13.7401			1.12563			0.562815	+	0.826583i	$0.309718\pi$
$150$		0			0
$151$	−8.45089			−0.687724			−0.343862	−	0.939020i	$-0.611735\pi$
$151$	−8.45089			−0.687724			−0.343862	+	0.939020i	$0.611735\pi$
$152$		0			0
$153$	6.43179	+	2.08981i	0.519979	+	0.168951i
$154$		0			0
$155$	0.507661	+	0.821412i	0.0407763	+	0.0659774i
$156$		0			0
$157$		−	3.17338i		−	0.253263i	−0.991950	−	0.126632i	$-0.959583\pi$
$157$		−	3.17338i		−	0.253263i	0.991950	−	0.126632i	$-0.0404166\pi$
$158$		0			0
$159$	−9.83390	−	7.14475i	−0.779879	−	0.566615i
$160$		0			0
$161$	−0.349367	+	0.253830i	−0.0275340	+	0.0200046i
$162$		0			0
$163$	−6.50219	+	8.94949i	−0.509291	+	0.700978i	−0.983799	−	0.179272i	$-0.942626\pi$
$163$	−6.50219	+	8.94949i	−0.509291	+	0.700978i	0.474509	+	0.880251i	$0.342626\pi$
$164$		0			0
$165$	23.1648	−	14.3167i	1.80338	−	1.11455i
$166$		0			0
$167$	−1.55458	+	0.505112i	−0.120297	+	0.0390868i	−0.368547	−	0.929609i	$-0.620145\pi$
$167$	−1.55458	+	0.505112i	−0.120297	+	0.0390868i	0.248250	+	0.968696i	$0.420145\pi$
$168$		0			0
$169$	3.94607	+	12.1447i	0.303544	+	0.934211i
$170$		0			0
$171$	2.21624	−	6.82089i	0.169480	−	0.521607i
$172$		0			0
$173$	−9.99228	−	13.7532i	−0.759699	−	1.04564i	−0.997239	−	0.0742585i	$-0.976341\pi$
$173$	−9.99228	−	13.7532i	−0.759699	−	1.04564i	0.237540	−	0.971378i	$-0.423659\pi$
$174$		0			0
$175$	6.28115	+	12.0995i	0.474811	+	0.914636i
$176$		0			0
$177$	−9.72945	−	13.3914i	−0.731310	−	1.00656i
$178$		0			0
$179$	4.08212	−	12.5635i	0.305112	−	0.939038i	−0.674524	−	0.738253i	$-0.735651\pi$
$179$	4.08212	−	12.5635i	0.305112	−	0.939038i	0.979635	−	0.200784i	$-0.0643491\pi$
$180$		0			0
$181$	8.23420	+	25.3423i	0.612043	+	1.88368i	0.438118	+	0.898917i	$0.355645\pi$
$181$	8.23420	+	25.3423i	0.612043	+	1.88368i	0.173925	+	0.984759i	$0.444355\pi$
$182$		0			0
$183$	15.2800	−	4.96476i	1.12953	−	0.367006i
$184$		0			0
$185$	2.25142	−	5.49431i	0.165528	−	0.403950i
$186$		0			0
$187$	12.8392	−	17.6717i	0.938896	−	1.29228i
$188$		0			0
$189$	−6.07971	+	4.41717i	−0.442234	+	0.321302i
$190$		0			0
$191$	7.41747	+	5.38911i	0.536709	+	0.389942i	0.822861	−	0.568242i	$-0.192376\pi$
$191$	7.41747	+	5.38911i	0.536709	+	0.389942i	−0.286152	+	0.958184i	$0.592376\pi$
$192$		0			0
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$		0			0
$195$	1.50929	−	1.78080i	0.108083	−	0.127526i
$196$		0			0
$197$	12.4969	+	4.06050i	0.890369	+	0.289298i	0.718256	−	0.695779i	$-0.244941\pi$
$197$	12.4969	+	4.06050i	0.890369	+	0.289298i	0.172113	+	0.985077i	$0.444941\pi$
$198$		0			0
$199$	7.35469			0.521360			0.260680	−	0.965425i	$-0.416053\pi$
$199$	7.35469			0.521360			0.260680	+	0.965425i	$0.416053\pi$
$200$		0			0
$201$	−4.49704			−0.317197
$202$		0			0
$203$	18.2286	+	5.92284i	1.27940	+	0.415702i
$204$		0			0
$205$	−17.5613	−	7.19616i	−1.22654	−	0.502602i
$206$		0			0
$207$			0.274497i			0.0190789i
$208$		0			0
$209$	−18.7407	−	13.6159i	−1.29632	−	0.941835i
$210$		0			0
$211$	−16.3872	+	11.9060i	−1.12814	+	0.819641i	−0.985423	−	0.170123i	$-0.945584\pi$
$211$	−16.3872	+	11.9060i	−1.12814	+	0.819641i	−0.142716	+	0.989764i	$0.545584\pi$
$212$		0			0
$213$	−9.02727	+	12.4250i	−0.618538	+	0.851345i
$214$		0			0
$215$	1.85529	+	7.60063i	0.126530	+	0.518359i
$216$		0			0
$217$	1.11981	−	0.363848i	0.0760175	−	0.0246996i
$218$		0			0
$219$	9.14880	+	28.1571i	0.618219	+	1.90268i
$220$		0			0
$221$	0.578616	−	1.78080i	0.0389219	−	0.119789i
$222$		0			0
$223$	−9.63635	−	13.2633i	−0.645298	−	0.888176i	0.353586	−	0.935402i	$-0.384962\pi$
$223$	−9.63635	−	13.2633i	−0.645298	−	0.888176i	−0.998884	+	0.0472256i	$0.984962\pi$
$224$		0			0
$225$	8.56889	+	1.29058i	0.571259	+	0.0860385i
$226$		0			0
$227$	4.54779	+	6.25950i	0.301847	+	0.415457i	0.932817	−	0.360350i	$-0.117343\pi$
$227$	4.54779	+	6.25950i	0.301847	+	0.415457i	−0.630970	+	0.775808i	$0.717343\pi$
$228$		0			0
$229$	8.20978	−	25.2671i	0.542517	−	1.66970i	−0.184303	−	0.982869i	$-0.559003\pi$
$229$	8.20978	−	25.2671i	0.542517	−	1.66970i	0.726820	−	0.686828i	$-0.240997\pi$
$230$		0			0
$231$	−10.2609	−	31.5800i	−0.675121	−	2.07781i
$232$		0			0
$233$	8.66895	−	2.81671i	0.567922	−	0.184529i	−0.0109607	−	0.999940i	$-0.503489\pi$
$233$	8.66895	−	2.81671i	0.567922	−	0.184529i	0.578883	+	0.815411i	$0.303489\pi$
$234$		0			0
$235$	−15.0757	−	1.12892i	−0.983427	−	0.0736426i
$236$		0			0
$237$	−8.10485	+	11.1554i	−0.526466	+	0.724619i
$238$		0			0
$239$	−16.1448	+	11.7299i	−1.04432	+	0.758742i	−0.971124	−	0.238575i	$-0.923320\pi$
$239$	−16.1448	+	11.7299i	−1.04432	+	0.758742i	−0.0731951	+	0.997318i	$0.523320\pi$
$240$		0			0
$241$	9.58361	+	6.96290i	0.617334	+	0.448520i	0.851989	−	0.523559i	$-0.175396\pi$
$241$	9.58361	+	6.96290i	0.617334	+	0.448520i	−0.234655	+	0.972079i	$0.575396\pi$
$242$		0			0
$243$			16.0883i			1.03207i
$244$		0			0
$245$	0.942847	−	0.230146i	0.0602363	−	0.0147035i
$246$		0			0
$247$	−1.88853	−	0.613621i	−0.120164	−	0.0390438i
$248$		0			0
$249$	25.2382			1.59941
$250$		0			0
$251$	−0.782668			−0.0494016			−0.0247008	−	0.999695i	$-0.507863\pi$
$251$	−0.782668			−0.0494016			−0.0247008	+	0.999695i	$0.507863\pi$
$252$		0			0
$253$	0.843216	+	0.273977i	0.0530125	+	0.0172248i
$254$		0			0
$255$	18.4413	−	4.50145i	1.15484	−	0.281892i
$256$		0			0
$257$			9.43069i			0.588270i	0.955764	+	0.294135i	$0.0950316\pi$
$257$			9.43069i			0.588270i	−0.955764	+	0.294135i	$0.904968\pi$
$258$		0			0
$259$	−5.85738	−	4.25564i	−0.363960	−	0.264433i
$260$		0			0
$261$	9.85640	−	7.16109i	0.610096	−	0.443260i
$262$		0			0
$263$	15.9281	−	21.9231i	0.982168	−	1.35184i	0.0465150	−	0.998918i	$-0.485188\pi$
$263$	15.9281	−	21.9231i	0.982168	−	1.35184i	0.935653	−	0.352921i	$-0.114812\pi$
$264$		0			0
$265$	−12.4585	−	0.932938i	−0.765319	−	0.0573099i
$266$		0			0
$267$	−3.53443	+	1.14841i	−0.216304	+	0.0702813i
$268$		0			0
$269$	−1.08743	−	3.34676i	−0.0663017	−	0.204056i	0.912417	−	0.409262i	$-0.134214\pi$
$269$	−1.08743	−	3.34676i	−0.0663017	−	0.204056i	−0.978719	+	0.205206i	$0.934214\pi$
$270$		0			0
$271$	4.05388	−	12.4765i	0.246255	−	0.757896i	−0.749172	−	0.662376i	$-0.769548\pi$
$271$	4.05388	−	12.4765i	0.246255	−	0.757896i	0.995427	−	0.0955208i	$-0.0304517\pi$
$272$		0			0
$273$	−1.67306	−	2.30277i	−0.101258	−	0.139370i
$274$		0			0
$275$	12.5171	−	25.0343i	0.754811	−	1.50962i
$276$		0			0
$277$	−1.89992	−	2.61502i	−0.114155	−	0.157121i	0.748116	−	0.663568i	$-0.230959\pi$
$277$	−1.89992	−	2.61502i	−0.114155	−	0.157121i	−0.862271	+	0.506447i	$0.830959\pi$
$278$		0			0
$279$	0.231277	−	0.711798i	0.0138462	−	0.0426142i
$280$		0			0
$281$	1.70160	+	5.23700i	0.101509	+	0.312413i	0.988895	−	0.148614i	$-0.0474811\pi$
$281$	1.70160	+	5.23700i	0.101509	+	0.312413i	−0.887386	+	0.461027i	$0.847481\pi$
$282$		0			0
$283$	−5.92877	+	1.92637i	−0.352429	+	0.114511i	−0.479881	−	0.877334i	$-0.659320\pi$
$283$	−5.92877	+	1.92637i	−0.352429	+	0.114511i	0.127452	+	0.991845i	$0.459320\pi$
$284$		0			0
$285$	−4.77378	−	19.5569i	−0.282774	−	1.15845i
$286$		0			0
$287$	−13.6022	+	18.7218i	−0.802911	+	1.10511i
$288$		0			0
$289$	−1.43480	+	1.04245i	−0.0844002	+	0.0613203i
$290$		0			0
$291$	20.8828	+	15.1722i	1.22417	+	0.889412i
$292$		0			0
$293$		−	9.64990i		−	0.563753i	−0.959451	−	0.281877i	$-0.909043\pi$
$293$		−	9.64990i		−	0.563753i	0.959451	−	0.281877i	$-0.0909569\pi$
$294$		0			0
$295$	−15.7426	−	6.45089i	−0.916568	−	0.375586i
$296$		0			0
$297$	14.6737	+	4.76777i	0.851454	+	0.276654i
$298$		0			0
$299$	0.0760012			0.00439527
$300$		0			0
$301$	9.53991			0.549871
$302$		0			0
$303$	16.3896	+	5.32531i	0.941558	+	0.305931i
$304$		0			0
$305$	10.6766	−	12.5973i	0.611343	−	0.721317i
$306$		0			0
$307$			7.69507i			0.439181i	0.975592	+	0.219591i	$0.0704721\pi$
$307$			7.69507i			0.439181i	−0.975592	+	0.219591i	$0.929528\pi$
$308$		0			0
$309$	−11.0436	−	8.02363i	−0.628247	−	0.456448i
$310$		0			0
$311$	−0.341616	+	0.248198i	−0.0193712	+	0.0140740i	−0.597429	−	0.801922i	$-0.703811\pi$
$311$	−0.341616	+	0.248198i	−0.0193712	+	0.0140740i	0.578058	+	0.815996i	$0.303811\pi$
$312$		0			0
$313$	−13.5765	+	18.6865i	−0.767391	+	1.05622i	0.229172	+	0.973386i	$0.426398\pi$
$313$	−13.5765	+	18.6865i	−0.767391	+	1.05622i	−0.996563	+	0.0828371i	$0.973602\pi$
$314$		0			0
$315$	4.00646	−	9.77726i	0.225739	−	0.550886i
$316$		0			0
$317$	−14.6211	+	4.75068i	−0.821203	+	0.266825i	−0.689335	−	0.724442i	$-0.742097\pi$
$317$	−14.6211	+	4.75068i	−0.821203	+	0.266825i	−0.131868	+	0.991267i	$0.542097\pi$
$318$		0			0
$319$	−12.1601	−	37.4249i	−0.680835	−	2.09539i
$320$		0			0
$321$	−7.37242	+	22.6900i	−0.411488	+	1.26643i
$322$		0			0
$323$	−9.49135	−	13.0637i	−0.528113	−	0.726885i
$324$		0			0
$325$	0.357328	−	2.37251i	0.0198210	−	0.131603i
$326$		0			0
$327$	−9.99338	−	13.7547i	−0.552635	−	0.760637i
$328$		0			0
$329$	−5.69639	+	17.5317i	−0.314052	+	0.966554i
$330$		0			0
$331$	9.89931	+	30.4669i	0.544115	+	1.67461i	0.723084	+	0.690760i	$0.242724\pi$
$331$	9.89931	+	30.4669i	0.544115	+	1.67461i	−0.178969	+	0.983855i	$0.557276\pi$
$332$		0			0
$333$	−4.37689	+	1.42214i	−0.239852	+	0.0779326i
$334$		0			0
$335$	−3.93179	+	2.42998i	−0.214816	+	0.132764i
$336$		0			0
$337$	6.86942	−	9.45495i	0.374201	−	0.515044i	−0.579835	−	0.814734i	$-0.696883\pi$
$337$	6.86942	−	9.45495i	0.374201	−	0.515044i	0.954037	+	0.299690i	$0.0968831\pi$
$338$		0			0
$339$	−2.43123	+	1.76639i	−0.132046	+	0.0959373i
$340$		0			0
$341$	−1.95570	−	1.42090i	−0.105907	−	0.0769460i
$342$		0			0
$343$			17.9024i			0.966638i
$344$		0			0
$345$	0.405074	+	0.655423i	0.0218085	+	0.0352868i
$346$		0			0
$347$	19.7811	+	6.42727i	1.06191	+	0.345034i	0.787330	−	0.616532i	$-0.211463\pi$
$347$	19.7811	+	6.42727i	1.06191	+	0.345034i	0.274575	+	0.961566i	$0.411463\pi$
$348$		0			0
$349$	−26.1233			−1.39835			−0.699173	−	0.714952i	$-0.746448\pi$
$349$	−26.1233			−1.39835			−0.699173	+	0.714952i	$0.746448\pi$
$350$		0			0
$351$	1.32258			0.0705940
$352$		0			0
$353$	23.1466	+	7.52079i	1.23197	+	0.400291i	0.851428	−	0.524472i	$-0.175737\pi$
$353$	23.1466	+	7.52079i	1.23197	+	0.400291i	0.380542	+	0.924764i	$0.375737\pi$
$354$		0			0
$355$	−1.17875	+	15.7411i	−0.0625616	+	0.835451i
$356$		0			0
$357$		−	23.1465i		−	1.22504i
$358$		0			0
$359$	−26.3001	−	19.1081i	−1.38806	−	1.00849i	−0.996075	−	0.0885176i	$-0.971787\pi$
$359$	−26.3001	−	19.1081i	−1.38806	−	1.00849i	−0.391989	−	0.919970i	$-0.628213\pi$
$360$		0			0
$361$	1.51728	−	1.10237i	0.0798567	−	0.0580193i
$362$		0			0
$363$	−26.0047	+	35.7923i	−1.36489	+	1.87861i
$364$		0			0
$365$	23.2136	+	19.6744i	1.21505	+	1.02980i
$366$		0			0
$367$	−11.4684	+	3.72632i	−0.598648	+	0.194512i	−0.592637	−	0.805469i	$-0.701913\pi$
$367$	−11.4684	+	3.72632i	−0.598648	+	0.194512i	−0.00601051	+	0.999982i	$0.501913\pi$
$368$		0			0
$369$	4.54554	+	13.9897i	0.236631	+	0.728276i
$370$		0			0
$371$	−4.70749	+	14.4882i	−0.244401	+	0.752188i
$372$		0			0
$373$	17.6687	+	24.3188i	0.914849	+	1.25918i	0.965483	+	0.260465i	$0.0838757\pi$
$373$	17.6687	+	24.3188i	0.914849	+	1.25918i	−0.0506342	+	0.998717i	$0.516124\pi$
$374$		0			0
$375$	22.3646	−	9.56352i	1.15491	−	0.493858i
$376$		0			0
$377$	−1.98272	−	2.72898i	−0.102115	−	0.140550i
$378$		0			0
$379$	−7.91486	+	24.3594i	−0.406559	+	1.25126i	0.513027	+	0.858373i	$0.328524\pi$
$379$	−7.91486	+	24.3594i	−0.406559	+	1.25126i	−0.919586	+	0.392888i	$0.871476\pi$
$380$		0			0
$381$	−0.140443	−	0.432239i	−0.00719511	−	0.0221443i
$382$		0			0
$383$	−2.69678	+	0.876237i	−0.137799	+	0.0447736i	−0.377104	−	0.926171i	$-0.623080\pi$
$383$	−2.69678	+	0.876237i	−0.137799	+	0.0447736i	0.239306	+	0.970944i	$0.423080\pi$
$384$		0			0
$385$	−26.0354	−	22.0660i	−1.32689	−	1.12459i
$386$		0			0
$387$	3.56432	−	4.90586i	0.181184	−	0.249379i
$388$		0			0
$389$	−29.3218	+	21.3035i	−1.48667	+	1.08013i	−0.511346	+	0.859375i	$0.670853\pi$
$389$	−29.3218	+	21.3035i	−1.48667	+	1.08013i	−0.975329	+	0.220757i	$0.929147\pi$
$390$		0			0
$391$	0.500000	+	0.363271i	0.0252861	+	0.0183714i
$392$		0			0
$393$		−	12.8962i		−	0.650527i
$394$		0			0
$395$	−1.05831	+	14.1327i	−0.0532491	+	0.711091i
$396$		0			0
$397$	−32.0364	−	10.4093i	−1.60786	−	0.522425i	−0.638826	−	0.769351i	$-0.720580\pi$
$397$	−32.0364	−	10.4093i	−1.60786	−	0.522425i	−0.969034	+	0.246926i	$0.920580\pi$
$398$		0			0
$399$	−24.5468			−1.22888
$400$		0			0
$401$	−21.2631			−1.06183			−0.530915	−	0.847425i	$-0.678152\pi$
$401$	−21.2631			−1.06183			−0.530915	+	0.847425i	$0.678152\pi$
$402$		0			0
$403$	−0.197079	−	0.0640347i	−0.00981718	−	0.00318980i
$404$		0			0
$405$	13.1613	+	21.2954i	0.653990	+	1.05818i
$406$		0			0
$407$			14.8646i			0.736811i
$408$		0			0
$409$	−21.0670	−	15.3061i	−1.04170	−	0.756838i	−0.0710818	−	0.997470i	$-0.522645\pi$
$409$	−21.0670	−	15.3061i	−1.04170	−	0.756838i	−0.970616	+	0.240633i	$0.922645\pi$
$410$		0			0
$411$	−25.5305	+	18.5490i	−1.25933	+	0.914954i
$412$		0			0
$413$	−12.1935	+	16.7829i	−0.600001	+	0.825831i
$414$		0			0
$415$	22.0659	−	13.6375i	1.08317	−	0.669438i
$416$		0			0
$417$	−12.5238	+	4.06921i	−0.613291	+	0.199270i
$418$		0			0
$419$	0.888984	+	2.73601i	0.0434297	+	0.133663i	0.970420	−	0.241422i	$-0.0776137\pi$
$419$	0.888984	+	2.73601i	0.0434297	+	0.133663i	−0.926991	+	0.375085i	$0.877614\pi$
$420$		0			0
$421$	−4.77175	+	14.6859i	−0.232561	+	0.715749i	0.764875	+	0.644179i	$0.222801\pi$
$421$	−4.77175	+	14.6859i	−0.232561	+	0.715749i	−0.997436	+	0.0715697i	$0.977199\pi$
$422$		0			0
$423$	6.88731	+	9.47957i	0.334872	+	0.460912i
$424$		0			0
$425$	13.6909	−	13.9004i	0.664107	−	0.674268i
$426$		0			0
$427$	−11.8352	−	16.2897i	−0.572743	−	0.788313i
$428$		0			0
$429$	−1.80586	+	5.55786i	−0.0871876	+	0.268336i
$430$		0			0
$431$	4.92451	+	15.1561i	0.237205	+	0.730043i	0.996821	+	0.0796708i	$0.0253869\pi$
$431$	4.92451	+	15.1561i	0.237205	+	0.730043i	−0.759616	+	0.650372i	$0.774613\pi$
$432$		0			0
$433$	0.188847	−	0.0613602i	0.00907542	−	0.00294878i	−0.304476	−	0.952520i	$-0.598481\pi$
$433$	0.188847	−	0.0613602i	0.00907542	−	0.00294878i	0.313551	+	0.949571i	$0.398481\pi$
$434$		0			0
$435$	12.9668	−	31.6437i	0.621709	−	1.51720i
$436$		0			0
$437$	0.385248	−	0.530249i	0.0184289	−	0.0253652i
$438$		0			0
$439$	−8.20347	+	5.96017i	−0.391530	+	0.284463i	−0.766082	−	0.642743i	$-0.777797\pi$
$439$	−8.20347	+	5.96017i	−0.391530	+	0.284463i	0.374552	+	0.927206i	$0.377797\pi$
$440$		0			0
$441$	−0.608565	−	0.442148i	−0.0289793	−	0.0210547i
$442$		0			0
$443$		−	30.5446i		−	1.45122i	−0.688107	−	0.725609i	$-0.741558\pi$
$443$		−	30.5446i		−	1.45122i	0.688107	−	0.725609i	$-0.258442\pi$
$444$		0			0
$445$	−2.46963	+	2.91389i	−0.117072	+	0.138131i
$446$		0			0
$447$	−28.4294	−	9.23729i	−1.34467	−	0.436909i
$448$		0			0
$449$	−20.0117			−0.944412			−0.472206	−	0.881488i	$-0.656542\pi$
$449$	−20.0117			−0.944412			−0.472206	+	0.881488i	$0.656542\pi$
$450$		0			0
$451$	47.5113			2.23722
$452$		0			0
$453$	17.4857	+	5.68144i	0.821548	+	0.266937i
$454$		0			0
$455$	−2.70707	−	1.10929i	−0.126910	−	0.0520042i
$456$		0			0
$457$			7.86472i			0.367896i	0.982936	+	0.183948i	$0.0588878\pi$
$457$			7.86472i			0.367896i	−0.982936	+	0.183948i	$0.941112\pi$
$458$		0			0
$459$	8.70103	+	6.32167i	0.406129	+	0.295070i
$460$		0			0
$461$	18.5967	−	13.5113i	0.866134	−	0.629283i	−0.0634130	−	0.997987i	$-0.520199\pi$
$461$	18.5967	−	13.5113i	0.866134	−	0.629283i	0.929547	+	0.368704i	$0.120199\pi$
$462$		0			0
$463$	−16.7111	+	23.0008i	−0.776629	+	1.06894i	0.219016	+	0.975721i	$0.429715\pi$
$463$	−16.7111	+	23.0008i	−0.776629	+	1.06894i	−0.995646	+	0.0932175i	$0.970285\pi$
$464$		0			0
$465$	−0.498170	−	2.04087i	−0.0231021	−	0.0946431i
$466$		0			0
$467$	−0.993171	+	0.322701i	−0.0459585	+	0.0149328i	−0.331906	−	0.943312i	$-0.607692\pi$
$467$	−0.993171	+	0.322701i	−0.0459585	+	0.0149328i	0.285948	+	0.958245i	$0.407692\pi$
$468$		0			0
$469$	1.74160	+	5.36009i	0.0804196	+	0.247506i
$470$		0			0
$471$	−2.13342	+	6.56601i	−0.0983030	+	0.302546i
$472$		0			0
$473$	−11.5125	−	15.8456i	−0.529346	−	0.728583i
$474$		0			0
$475$	−14.7413	−	14.5192i	−0.676378	−	0.666186i
$476$		0			0
$477$	5.69166	+	7.83390i	0.260603	+	0.358690i
$478$		0			0
$479$	−0.113977	+	0.350785i	−0.00520774	+	0.0160278i	−0.953627	−	0.300992i	$-0.902682\pi$
$479$	−0.113977	+	0.350785i	−0.00520774	+	0.0160278i	0.948419	+	0.317020i	$0.102682\pi$
$480$		0			0
$481$	0.393753	+	1.21185i	0.0179536	+	0.0552555i
$482$		0			0
$483$	0.893520	−	0.290322i	0.0406566	−	0.0132101i
$484$		0			0
$485$	26.4563	+	1.98114i	1.20132	+	0.0899590i
$486$		0			0
$487$	24.0229	−	33.0647i	1.08858	−	1.49830i	0.238874	−	0.971051i	$-0.423222\pi$
$487$	24.0229	−	33.0647i	1.08858	−	1.49830i	0.849708	−	0.527253i	$-0.176778\pi$
$488$		0			0
$489$	19.4702	−	14.1460i	0.880475	−	0.639703i
$490$		0			0
$491$	−31.7128	−	23.0407i	−1.43118	−	1.03981i	−0.989796	−	0.142493i	$-0.954488\pi$
$491$	−31.7128	−	23.0407i	−1.43118	−	1.03981i	−0.441382	−	0.897319i	$-0.645512\pi$
$492$		0			0
$493$		−	27.4306i		−	1.23541i
$494$		0			0
$495$	−21.0748	+	5.14428i	−0.947240	+	0.231218i
$496$		0			0
$497$	18.3056	+	5.94784i	0.821117	+	0.266797i
$498$		0			0
$499$	42.9767			1.92390			0.961950	−	0.273226i	$-0.0880906\pi$
$499$	42.9767			1.92390			0.961950	+	0.273226i	$0.0880906\pi$
$500$		0			0
$501$	3.55614			0.158877
$502$		0			0
$503$	27.8108	+	9.03628i	1.24002	+	0.402908i	0.854335	−	0.519722i	$-0.173964\pi$
$503$	27.8108	+	9.03628i	1.24002	+	0.402908i	0.385687	+	0.922630i	$0.373964\pi$
$504$		0			0
$505$	17.2071	−	4.20019i	0.765704	−	0.186906i
$506$		0			0
$507$		−	27.7815i		−	1.23382i
$508$		0			0
$509$	34.9762	+	25.4117i	1.55029	+	1.12635i	0.943441	+	0.331541i	$0.107569\pi$
$509$	34.9762	+	25.4117i	1.55029	+	1.12635i	0.606854	+	0.794813i	$0.292431\pi$
$510$		0			0
$511$	30.0178	−	21.8092i	1.32791	−	0.964782i
$512$		0			0
$513$	6.70411	−	9.22742i	0.295994	−	0.407400i
$514$		0			0
$515$	−13.9910	−	1.04770i	−0.616518	−	0.0461672i
$516$		0			0
$517$	35.9941	−	11.6952i	1.58302	−	0.514354i
$518$		0			0
$519$	11.4288	+	35.1743i	0.501670	+	1.54398i
$520$		0			0
$521$	−2.57704	+	7.93132i	−0.112902	+	0.347477i	−0.991504	−	0.130078i	$-0.958477\pi$
$521$	−2.57704	+	7.93132i	−0.112902	+	0.347477i	0.878602	+	0.477556i	$0.158477\pi$
$522$		0			0
$523$	22.3741	+	30.7954i	0.978353	+	1.34659i	0.937712	+	0.347413i	$0.112940\pi$
$523$	22.3741	+	30.7954i	0.978353	+	1.34659i	0.0406405	+	0.999174i	$0.487060\pi$
$524$		0			0
$525$	−4.86192	−	29.2577i	−0.212192	−	1.27691i
$526$		0			0
$527$	−0.990475	−	1.36327i	−0.0431457	−	0.0593850i
$528$		0			0
$529$	7.09964	−	21.8504i	0.308680	−	0.950019i
$530$		0			0
$531$	4.07478	+	12.5409i	0.176830	+	0.544228i
$532$		0			0
$533$	3.87340	−	1.25854i	0.167775	−	0.0545136i
$534$		0			0
$535$	5.81479	+	23.8217i	0.251395	+	1.02990i
$536$		0			0
$537$	−16.8925	+	23.2506i	−0.728967	+	1.00334i
$538$		0			0
$539$	−1.96563	+	1.42811i	−0.0846656	+	0.0615131i
$540$		0			0
$541$	16.3032	+	11.8450i	0.700928	+	0.509254i	0.880234	−	0.474539i	$-0.157385\pi$
$541$	16.3032	+	11.8450i	0.700928	+	0.509254i	−0.179306	+	0.983793i	$0.557385\pi$
$542$		0			0
$543$		−	57.9712i		−	2.48778i
$544$		0			0
$545$	−16.1696	−	6.62589i	−0.692631	−	0.283822i
$546$		0			0
$547$	−38.4843	−	12.5043i	−1.64547	−	0.534646i	−0.667720	−	0.744412i	$-0.732730\pi$
$547$	−38.4843	−	12.5043i	−1.64547	−	0.534646i	−0.977752	+	0.209766i	$0.932730\pi$
$548$		0			0
$549$	−12.7988			−0.546238
$550$		0			0
$551$	−29.0901			−1.23928
$552$		0			0
$553$	16.4351	+	5.34008i	0.698890	+	0.227083i
$554$		0			0
$555$	−8.35216	+	9.85462i	−0.354530	+	0.418305i
$556$		0			0
$557$		−	21.4012i		−	0.906799i	−0.891307	−	0.453400i	$-0.850211\pi$
$557$		−	21.4012i		−	0.906799i	0.891307	−	0.453400i	$-0.149789\pi$
$558$		0			0
$559$	−1.35831	−	0.986868i	−0.0574503	−	0.0417401i
$560$		0			0
$561$	−38.4459	+	27.9326i	−1.62319	+	1.17932i
$562$		0			0
$563$	4.46834	−	6.15015i	0.188318	−	0.259198i	−0.704410	−	0.709793i	$-0.748788\pi$
$563$	4.46834	−	6.15015i	0.188318	−	0.259198i	0.892728	+	0.450596i	$0.148788\pi$
$564$		0			0
$565$	−1.17117	+	2.85808i	−0.0492714	+	0.120240i
$566$		0			0
$567$	29.0314	−	9.43288i	1.21921	−	0.396144i
$568$		0			0
$569$	−4.89551	−	15.0668i	−0.205231	−	0.631635i	−0.999704	−	0.0243357i	$-0.992253\pi$
$569$	−4.89551	−	15.0668i	−0.205231	−	0.631635i	0.794473	−	0.607299i	$-0.207747\pi$
$570$		0			0
$571$	−7.21925	+	22.2186i	−0.302116	+	0.929818i	0.678622	+	0.734488i	$0.262578\pi$
$571$	−7.21925	+	22.2186i	−0.302116	+	0.929818i	−0.980738	+	0.195330i	$0.937422\pi$
$572$		0			0
$573$	−11.7244	−	16.1372i	−0.489793	−	0.674142i
$574$		0			0
$575$	0.708317	+	0.354158i	0.0295389	+	0.0147694i
$576$		0			0
$577$	−4.74092	−	6.52531i	−0.197367	−	0.271652i	0.698850	−	0.715268i	$-0.253695\pi$
$577$	−4.74092	−	6.52531i	−0.197367	−	0.271652i	−0.896217	+	0.443616i	$0.853695\pi$
$578$		0			0
$579$	4.03373	−	12.4145i	0.167636	−	0.515931i
$580$		0			0
$581$	−9.77418	−	30.0818i	−0.405501	−	1.24800i
$582$		0			0
$583$	29.7455	−	9.66489i	1.23193	−	0.400279i
$584$		0			0
$585$	−1.58187	+	0.977647i	−0.0654021	+	0.0404207i
$586$		0			0
$587$	21.4035	−	29.4594i	0.883418	−	1.21592i	−0.0920445	−	0.995755i	$-0.529340\pi$
$587$	21.4035	−	29.4594i	0.883418	−	1.21592i	0.975462	−	0.220166i	$-0.0706598\pi$
$588$		0			0
$589$	−1.44575	+	1.05040i	−0.0595709	+	0.0432808i
$590$		0			0
$591$	−23.1274	−	16.8031i	−0.951336	−	0.691186i
$592$		0			0
$593$			15.2692i			0.627029i	0.949583	+	0.313515i	$0.101506\pi$
$593$			15.2692i			0.627029i	−0.949583	+	0.313515i	$0.898494\pi$
$594$		0			0
$595$	−12.5072	−	20.2371i	−0.512746	−	0.829641i
$596$		0			0
$597$	−15.2175	−	4.94447i	−0.622811	−	0.202364i
$598$		0			0
$599$	−8.19555			−0.334861			−0.167431	−	0.985884i	$-0.553547\pi$
$599$	−8.19555			−0.334861			−0.167431	+	0.985884i	$0.553547\pi$
$600$		0			0
$601$	42.6346			1.73910			0.869551	−	0.493844i	$-0.164408\pi$
$601$	42.6346			1.73910			0.869551	+	0.493844i	$0.164408\pi$
$602$		0			0
$603$	3.40710	+	1.10703i	0.138748	+	0.0450819i
$604$		0			0
$605$	−3.39560	+	45.3451i	−0.138051	+	1.84354i
$606$		0			0
$607$			30.2136i			1.22633i	0.789955	+	0.613165i	$0.210104\pi$
$607$			30.2136i			1.22633i	−0.789955	+	0.613165i	$0.789896\pi$
$608$		0			0
$609$	−33.7348	−	24.5098i	−1.36700	−	0.993186i
$610$		0			0
$611$	2.62465	−	1.90692i	0.106182	−	0.0771457i
$612$		0			0
$613$	4.40176	−	6.05850i	0.177785	−	0.244701i	−0.710819	−	0.703375i	$-0.751676\pi$
$613$	4.40176	−	6.05850i	0.177785	−	0.244701i	0.888604	+	0.458674i	$0.151676\pi$
$614$		0			0
$615$	31.4981	+	26.6958i	1.27012	+	1.07648i
$616$		0			0
$617$	−37.7116	+	12.2533i	−1.51821	+	0.493297i	−0.945268	−	0.326296i	$-0.894199\pi$
$617$	−37.7116	+	12.2533i	−1.51821	+	0.493297i	−0.572946	+	0.819593i	$0.694199\pi$
$618$		0			0
$619$	−2.81228	−	8.65530i	−0.113035	−	0.347886i	0.878497	−	0.477748i	$-0.158547\pi$
$619$	−2.81228	−	8.65530i	−0.113035	−	0.347886i	−0.991532	+	0.129862i	$0.958547\pi$
$620$		0			0
$621$	−0.134899	+	0.415176i	−0.00541330	+	0.0166604i
$622$		0			0
$623$	2.73760	+	3.76799i	0.109680	+	0.150961i
$624$		0			0
$625$	14.3859	−	20.4462i	0.575435	−	0.817848i
$626$		0			0
$627$	29.6225	+	40.7718i	1.18301	+	1.62827i
$628$		0			0
$629$	−3.20196	+	9.85462i	−0.127671	+	0.392930i
$630$		0			0
$631$	−4.40146	−	13.5463i	−0.175219	−	0.539269i	0.824424	−	0.565972i	$-0.191499\pi$
$631$	−4.40146	−	13.5463i	−0.175219	−	0.539269i	−0.999643	+	0.0267031i	$0.991499\pi$
$632$		0			0
$633$	41.9108	−	13.6176i	1.66580	−	0.541252i
$634$		0			0
$635$	−0.356351	−	0.302021i	−0.0141413	−	0.0119853i
$636$		0			0
$637$	−0.122420	+	0.168496i	−0.00485044	+	0.00667606i
$638$		0			0
$639$	9.89800	−	7.19132i	0.391559	−	0.284484i
$640$		0			0
$641$	−7.51057	−	5.45675i	−0.296649	−	0.215528i	0.429497	−	0.903068i	$-0.358691\pi$
$641$	−7.51057	−	5.45675i	−0.296649	−	0.215528i	−0.726147	+	0.687540i	$0.758691\pi$
$642$		0			0
$643$			1.98146i			0.0781411i	0.999236	+	0.0390706i	$0.0124397\pi$
$643$			1.98146i			0.0781411i	−0.999236	+	0.0390706i	$0.987560\pi$
$644$		0			0
$645$	1.27105	−	16.9737i	0.0500476	−	0.668338i
$646$		0			0
$647$	−2.92153	−	0.949261i	−0.114857	−	0.0373193i	0.251025	−	0.967981i	$-0.419232\pi$
$647$	−2.92153	−	0.949261i	−0.114857	−	0.0373193i	−0.365882	+	0.930661i	$0.619232\pi$
$648$		0			0
$649$	42.5908			1.67184
$650$		0			0
$651$	−2.56159			−0.100397
$652$		0			0
$653$	−1.03712	−	0.336982i	−0.0405858	−	0.0131871i	0.288654	−	0.957434i	$-0.406792\pi$
$653$	−1.03712	−	0.336982i	−0.0405858	−	0.0131871i	−0.329240	+	0.944246i	$0.606792\pi$
$654$		0			0
$655$	−6.96846	−	11.2752i	−0.272280	−	0.440559i
$656$		0			0
$657$		−	23.5849i		−	0.920135i
$658$		0			0
$659$	1.39899	+	1.01642i	0.0544968	+	0.0395943i	0.614700	−	0.788761i	$-0.289277\pi$
$659$	1.39899	+	1.01642i	0.0544968	+	0.0395943i	−0.560203	+	0.828355i	$0.689277\pi$
$660$		0			0
$661$	−19.3524	+	14.0604i	−0.752723	+	0.546885i	−0.896670	−	0.442700i	$-0.854021\pi$
$661$	−19.3524	+	14.0604i	−0.752723	+	0.546885i	0.143947	+	0.989585i	$0.454021\pi$
$662$		0			0
$663$	−2.39442	+	3.29563i	−0.0929915	+	0.127992i
$664$		0			0
$665$	−21.4614	+	13.2639i	−0.832237	+	0.514351i
$666$		0			0
$667$	1.05890	−	0.344057i	0.0410007	−	0.0133219i
$668$		0			0
$669$	11.0217	+	33.9214i	0.426124	+	1.31148i
$670$		0			0
$671$	−12.7745	+	39.3160i	−0.493155	+	1.51778i
$672$		0			0
$673$	16.9348	+	23.3088i	0.652789	+	0.898487i	0.999216	−	0.0395903i	$-0.0126053\pi$
$673$	16.9348	+	23.3088i	0.652789	+	0.898487i	−0.346427	+	0.938077i	$0.612605\pi$
$674$		0			0
$675$	12.3262	+	6.16308i	0.474434	+	0.237217i
$676$		0			0
$677$	−25.4770	−	35.0661i	−0.979161	−	1.34770i	−0.937280	−	0.348577i	$-0.886665\pi$
$677$	−25.4770	−	35.0661i	−0.979161	−	1.34770i	−0.0418814	−	0.999123i	$-0.513335\pi$
$678$		0			0
$679$	9.99660	−	30.7664i	0.383634	−	1.18070i
$680$		0			0
$681$	−5.20160	−	16.0089i	−0.199326	−	0.613462i
$682$		0			0
$683$	24.2160	−	7.86826i	0.926600	−	0.301071i	0.193429	−	0.981114i	$-0.438039\pi$
$683$	24.2160	−	7.86826i	0.926600	−	0.301071i	0.733172	+	0.680044i	$0.238039\pi$
$684$		0			0
$685$	−12.2985	+	30.0129i	−0.469901	+	1.14673i
$686$		0			0
$687$	−33.9736	+	46.7606i	−1.29617	+	1.78403i
$688$		0			0
$689$	2.16901	−	1.57588i	0.0826325	−	0.0600361i
$690$		0			0
$691$	−4.00531	−	2.91003i	−0.152369	−	0.110703i	0.508989	−	0.860773i	$-0.330020\pi$
$691$	−4.00531	−	2.91003i	−0.152369	−	0.110703i	−0.661358	+	0.750071i	$0.730020\pi$
$692$		0			0
$693$			26.4519i			1.00483i
$694$		0			0
$695$	−8.75078	+	10.3249i	−0.331936	+	0.391648i
$696$		0			0
$697$	31.4981	+	10.2343i	1.19307	+	0.387653i
$698$		0			0
$699$	−19.8305			−0.750058
$700$		0			0
$701$	−17.5718			−0.663677			−0.331838	−	0.943336i	$-0.607669\pi$
$701$	−17.5718			−0.663677			−0.331838	+	0.943336i	$0.607669\pi$
$702$		0			0
$703$	10.4508	+	3.39567i	0.394159	+	0.128070i
$704$		0			0
$705$	30.4339	+	12.4710i	1.14621	+	0.469686i
$706$		0			0
$707$		−	21.5974i		−	0.812253i
$708$		0			0
$709$	22.8097	+	16.5722i	0.856636	+	0.622382i	0.926968	−	0.375141i	$-0.122406\pi$
$709$	22.8097	+	16.5722i	0.856636	+	0.622382i	−0.0703318	+	0.997524i	$0.522406\pi$
$710$		0			0
$711$	8.88661	−	6.45650i	0.333274	−	0.242138i
$712$		0			0
$713$	0.0402028	−	0.0553344i	0.00150561	−	0.00207229i
$714$		0			0
$715$	1.42432	+	5.83506i	0.0532665	+	0.218219i
$716$		0			0
$717$	41.2909	−	13.4162i	1.54204	−	0.501038i
$718$		0			0
$719$	5.60333	+	17.2453i	0.208969	+	0.643141i	0.999527	+	0.0307534i	$0.00979067\pi$
$719$	5.60333	+	17.2453i	0.208969	+	0.643141i	−0.790558	+	0.612387i	$0.790209\pi$
$720$		0			0
$721$	−5.28656	+	16.2704i	−0.196882	+	0.605940i
$722$		0			0
$723$	−15.1483	−	20.8498i	−0.563370	−	0.775413i
$724$		0			0
$725$	−5.76179	−	34.6729i	−0.213988	−	1.28772i
$726$		0			0
$727$	−26.8609	−	36.9708i	−0.996214	−	1.37117i	−0.927619	−	0.373527i	$-0.878148\pi$
$727$	−26.8609	−	36.9708i	−0.996214	−	1.37117i	−0.0685952	−	0.997645i	$-0.521852\pi$
$728$		0			0
$729$	0.437030	−	1.34504i	0.0161863	−	0.0498163i
$730$		0			0
$731$	−4.21905	−	12.9849i	−0.156047	−	0.480263i
$732$		0			0
$733$	−12.7450	+	4.14109i	−0.470746	+	0.152954i	−0.534777	−	0.844993i	$-0.679604\pi$
$733$	−12.7450	+	4.14109i	−0.470746	+	0.152954i	0.0640312	+	0.997948i	$0.479604\pi$
$734$		0			0
$735$	−2.10556	−	0.157672i	−0.0776648	−	0.00581582i
$736$		0			0
$737$	6.80130	−	9.36119i	0.250529	−	0.344824i
$738$		0			0
$739$	−36.3758	+	26.4286i	−1.33811	+	0.972191i	−0.338595	+	0.940932i	$0.609952\pi$
$739$	−36.3758	+	26.4286i	−1.33811	+	0.972191i	−0.999511	+	0.0312587i	$0.990048\pi$
$740$		0			0
$741$	3.49501	+	2.53927i	0.128392	+	0.0932826i
$742$		0			0
$743$			19.5304i			0.716502i	0.933625	+	0.358251i	$0.116627\pi$
$743$			19.5304i			0.716502i	−0.933625	+	0.358251i	$0.883373\pi$
$744$		0			0
$745$	−29.8474	+	7.28565i	−1.09352	+	0.266926i
$746$		0			0
$747$	−19.1213	−	6.21288i	−0.699611	−	0.227318i
$748$		0			0
$749$	29.8997			1.09251
$750$		0			0
$751$	19.8988			0.726117			0.363058	−	0.931766i	$-0.381733\pi$
$751$	19.8988			0.726117			0.363058	+	0.931766i	$0.381733\pi$
$752$		0			0
$753$	1.61941	+	0.526178i	0.0590146	+	0.0191750i
$754$		0			0
$755$	18.3578	−	4.48108i	0.668108	−	0.163083i
$756$		0			0
$757$		−	13.8807i		−	0.504502i	−0.967662	−	0.252251i	$-0.918829\pi$
$757$		−	13.8807i		−	0.504502i	0.967662	−	0.252251i	$-0.0811709\pi$
$758$		0			0
$759$	−1.56050	−	1.13377i	−0.0566425	−	0.0411532i
$760$		0			0
$761$	10.4454	−	7.58905i	0.378646	−	0.275103i	−0.382141	−	0.924104i	$-0.624813\pi$
$761$	10.4454	−	7.58905i	0.378646	−	0.275103i	0.760787	+	0.649001i	$0.224813\pi$
$762$		0			0
$763$	−12.5242	+	17.2381i	−0.453408	+	0.624063i
$764$		0			0
$765$	−15.0798	−	1.12923i	−0.545212	−	0.0408275i
$766$		0			0
$767$	3.47225	−	1.12820i	0.125376	−	0.0407370i
$768$		0			0
$769$	−1.40694	−	4.33011i	−0.0507355	−	0.156148i	0.922479	−	0.386048i	$-0.126160\pi$
$769$	−1.40694	−	4.33011i	−0.0507355	−	0.156148i	−0.973214	+	0.229900i	$0.926160\pi$
$770$		0			0
$771$	6.34014	−	19.5129i	0.228335	−	0.702742i
$772$		0			0
$773$	−24.9028	−	34.2757i	−0.895691	−	1.23281i	−0.971822	−	0.235715i	$-0.924257\pi$
$773$	−24.9028	−	34.2757i	−0.895691	−	1.23281i	0.0761318	−	0.997098i	$-0.475743\pi$
$774$		0			0
$775$	−1.53834	−	1.51516i	−0.0552587	−	0.0544261i
$776$		0			0
$777$	9.25844	+	12.7432i	0.332145	+	0.457158i
$778$		0			0
$779$	10.8535	−	33.4036i	0.388867	−	1.19681i
$780$		0			0
$781$	−12.2114	−	37.5829i	−0.436959	−	1.34482i
$782$		0			0
$783$	18.4270	−	5.98729i	0.658527	−	0.213968i
$784$		0			0
$785$	1.68268	+	6.89349i	0.0600574	+	0.246039i
$786$		0			0
$787$	−2.67949	+	3.68800i	−0.0955135	+	0.131463i	−0.854099	−	0.520110i	$-0.825891\pi$
$787$	−2.67949	+	3.68800i	−0.0955135	+	0.131463i	0.758586	+	0.651573i	$0.225891\pi$
$788$		0			0
$789$	−47.6953	+	34.6527i	−1.69800	+	1.23367i
$790$		0			0
$791$	3.04695	+	2.21374i	0.108337	+	0.0787115i
$792$		0			0
$793$			3.54365i			0.125839i
$794$		0			0
$795$	25.1506	+	10.3060i	0.891998	+	0.365517i
$796$		0			0
$797$	−0.410580	−	0.133406i	−0.0145435	−	0.00472547i	0.301736	−	0.953391i	$-0.402434\pi$
$797$	−0.410580	−	0.133406i	−0.0145435	−	0.00472547i	−0.316280	+	0.948666i	$0.602434\pi$
$798$		0			0
$799$	26.3819			0.933323
$800$		0			0
$801$	2.96050			0.104604
$802$		0			0
$803$	−72.4494	−	23.5402i	−2.55668	−	0.830717i
$804$		0			0
$805$	0.624334	−	0.736644i	0.0220049	−	0.0259633i
$806$		0			0
$807$			7.65582i			0.269498i
$808$		0			0
$809$	11.8013	+	8.57415i	0.414912	+	0.301451i	0.775587	−	0.631240i	$-0.217454\pi$
$809$	11.8013	+	8.57415i	0.414912	+	0.301451i	−0.360676	+	0.932691i	$0.617454\pi$
$810$		0			0
$811$	10.3783	−	7.54028i	0.364432	−	0.264775i	−0.390467	−	0.920617i	$-0.627686\pi$
$811$	10.3783	−	7.54028i	0.364432	−	0.264775i	0.754898	+	0.655842i	$0.227686\pi$
$812$		0			0
$813$	−16.7757	+	23.0897i	−0.588349	+	0.809792i
$814$		0			0
$815$	9.37917	−	22.8887i	0.328538	−	0.801754i
$816$		0			0
$817$	−13.7704	+	4.47429i	−0.481767	+	0.156535i
$818$		0			0
$819$	0.700694	+	2.15651i	0.0244842	+	0.0753547i
$820$		0			0
$821$	−12.0441	+	37.0678i	−0.420340	+	1.29367i	0.487046	+	0.873377i	$0.338075\pi$
$821$	−12.0441	+	37.0678i	−0.420340	+	1.29367i	−0.907386	+	0.420298i	$0.861925\pi$
$822$		0			0
$823$	−15.9469	−	21.9490i	−0.555873	−	0.765093i	0.434922	−	0.900468i	$-0.356776\pi$
$823$	−15.9469	−	21.9490i	−0.555873	−	0.765093i	−0.990794	+	0.135375i	$0.956776\pi$
$824$		0			0
$825$	−42.7293	+	43.3830i	−1.48764	+	1.51040i
$826$		0			0
$827$	20.7380	+	28.5435i	0.721133	+	0.992554i	0.999485	+	0.0320749i	$0.0102115\pi$
$827$	20.7380	+	28.5435i	0.721133	+	0.992554i	−0.278353	+	0.960479i	$0.589788\pi$
$828$		0			0
$829$	16.9216	−	52.0792i	0.587710	−	1.80879i	−0.000393222	−	1.00000i	$-0.500125\pi$
$829$	16.9216	−	52.0792i	0.587710	−	1.80879i	0.588103	−	0.808786i	$-0.299875\pi$
$830$		0			0
$831$	2.17306	+	6.68800i	0.0753827	+	0.232004i
$832$		0			0
$833$	−1.61076	+	0.523367i	−0.0558094	+	0.0181336i
$834$		0			0
$835$	3.10915	−	1.92156i	0.107597	−	0.0664984i
$836$		0			0
$837$	0.699611	−	0.962932i	0.0241821	−	0.0332838i
$838$		0			0
$839$	−29.5611	+	21.4774i	−1.02056	+	0.741481i	−0.966398	−	0.257051i	$-0.917249\pi$
$839$	−29.5611	+	21.4774i	−1.02056	+	0.741481i	−0.0541634	+	0.998532i	$0.517249\pi$
$840$		0			0
$841$	−16.5171	−	12.0004i	−0.569556	−	0.413807i
$842$		0			0
$843$		−	11.9798i		−	0.412606i
$844$		0			0
$845$	−15.0117	−	24.2895i	−0.516419	−	0.835584i
$846$		0			0
$847$	52.7324	+	17.1338i	1.81191	+	0.588725i
$848$		0			0
$849$	13.5622			0.465455
$850$		0			0
$851$	−0.420578			−0.0144172
$852$		0			0
$853$	−23.8224	−	7.74038i	−0.815665	−	0.265026i	−0.128670	−	0.991688i	$-0.541071\pi$
$853$	−23.8224	−	7.74038i	−0.815665	−	0.265026i	−0.686995	+	0.726662i	$0.741071\pi$
$854$		0			0
$855$	−1.19755	+	15.9921i	−0.0409553	+	0.546918i
$856$		0			0
$857$			26.2947i			0.898211i	0.893479	+	0.449105i	$0.148257\pi$
$857$			26.2947i			0.898211i	−0.893479	+	0.449105i	$0.851743\pi$
$858$		0			0
$859$	6.35565	+	4.61765i	0.216852	+	0.157552i	0.690908	−	0.722942i	$-0.257211\pi$
$859$	6.35565	+	4.61765i	0.216852	+	0.157552i	−0.474057	+	0.880494i	$0.657211\pi$
$860$		0			0
$861$	40.7306	−	29.5925i	1.38809	−	1.00851i
$862$		0			0
$863$	−30.9896	+	42.6535i	−1.05490	+	1.45194i	−0.170414	+	0.985373i	$0.554510\pi$
$863$	−30.9896	+	42.6535i	−1.05490	+	1.45194i	−0.884484	+	0.466570i	$0.845490\pi$
$864$		0			0
$865$	28.9987	+	24.5775i	0.985987	+	0.835661i
$866$		0			0
$867$	3.66956	−	1.19231i	0.124625	−	0.0404931i
$868$		0			0
$869$	−10.9637	−	33.7426i	−0.371916	−	1.14464i
$870$		0			0
$871$	0.306510	−	0.943339i	0.0103857	−	0.0319638i
$872$		0			0
$873$	−12.0865	−	16.6357i	−0.409067	−	0.563033i
$874$		0			0
$875$	−20.0602	−	22.9530i	−0.678159	−	0.775954i
$876$		0			0
$877$	9.95090	+	13.6962i	0.336018	+	0.462489i	0.943273	−	0.332018i	$-0.107729\pi$
$877$	9.95090	+	13.6962i	0.336018	+	0.462489i	−0.607255	+	0.794507i	$0.707729\pi$
$878$		0			0
$879$	−6.48751	+	19.9665i	−0.218818	+	0.673454i
$880$		0			0
$881$	8.11141	+	24.9644i	0.273280	+	0.841071i	0.989669	+	0.143369i	$0.0457937\pi$
$881$	8.11141	+	24.9644i	0.273280	+	0.841071i	−0.716389	+	0.697701i	$0.754206\pi$
$882$		0			0
$883$	2.00274	−	0.650730i	0.0673976	−	0.0218988i	−0.275124	−	0.961409i	$-0.588719\pi$
$883$	2.00274	−	0.650730i	0.0673976	−	0.0218988i	0.342522	+	0.939510i	$0.388719\pi$
$884$		0			0
$885$	28.2360	+	23.9310i	0.949141	+	0.804433i
$886$		0			0
$887$	−27.2260	+	37.4733i	−0.914158	+	1.25823i	0.0515686	+	0.998669i	$0.483578\pi$
$887$	−27.2260	+	37.4733i	−0.914158	+	1.25823i	−0.965727	+	0.259561i	$0.916422\pi$
$888$		0			0
$889$	−0.460802	+	0.334792i	−0.0154548	+	0.0112286i
$890$		0			0
$891$	−50.7022	−	36.8373i	−1.69859	−	1.23410i
$892$		0			0
$893$		−	27.9779i		−	0.936244i
$894$		0			0
$895$	−2.20577	+	29.4560i	−0.0737309	+	0.984606i
$896$		0			0
$897$	−0.157253	−	0.0510947i	−0.00525054	−	0.00170600i
$898$		0			0
$899$	−3.03571			−0.101247
$900$		0			0
$901$	21.8019			0.726327
$902$		0			0
$903$	−19.7389	−	6.41357i	−0.656871	−	0.213430i
$904$		0			0
$905$	−31.3248	−	50.6845i	−1.04127	−	1.68481i
$906$		0			0
$907$			19.1755i			0.636711i	0.947971	+	0.318355i	$0.103131\pi$
$907$			19.1755i			0.636711i	−0.947971	+	0.318355i	$0.896869\pi$
$908$		0			0
$909$	−11.1064	−	8.06925i	−0.368375	−	0.267640i
$910$		0			0
$911$	16.6977	−	12.1316i	0.553219	−	0.401937i	−0.275752	−	0.961229i	$-0.588927\pi$
$911$	16.6977	−	12.1316i	0.553219	−	0.401937i	0.828971	+	0.559292i	$0.188927\pi$
$912$		0			0
$913$	−38.1702	+	52.5367i	−1.26325	+	1.73871i
$914$		0			0
$915$	−30.5599	+	18.8871i	−1.01028	+	0.624387i
$916$		0			0
$917$	−15.3712	+	4.99440i	−0.507601	+	0.164929i
$918$		0			0
$919$	1.93426	+	5.95303i	0.0638053	+	0.196372i	0.977877	−	0.209180i	$-0.0670793\pi$
$919$	1.93426	+	5.95303i	0.0638053	+	0.196372i	−0.914072	+	0.405552i	$0.867079\pi$
$920$		0			0
$921$	5.17331	−	15.9218i	0.170466	−	0.524641i
$922$		0			0
$923$	−1.99109	−	2.74050i	−0.0655376	−	0.0902047i
$924$		0			0
$925$	−1.97739	+	13.1290i	−0.0650162	+	0.431680i
$926$		0			0
$927$	6.39180	+	8.79755i	0.209934	+	0.288950i
$928$		0			0
$929$	−8.21228	+	25.2748i	−0.269436	+	0.829240i	0.721202	+	0.692725i	$0.243590\pi$
$929$	−8.21228	+	25.2748i	−0.269436	+	0.829240i	−0.990638	+	0.136515i	$0.956410\pi$
$930$		0			0
$931$	0.555029	+	1.70820i	0.0181903	+	0.0559841i
$932$		0			0
$933$	0.873694	−	0.283880i	0.0286035	−	0.00929383i
$934$		0			0
$935$	−18.5201	+	45.1959i	−0.605672	+	1.47806i
$936$		0			0
$937$	−4.74434	+	6.53002i	−0.154991	+	0.213326i	−0.879450	−	0.475991i	$-0.842089\pi$
$937$	−4.74434	+	6.53002i	−0.154991	+	0.213326i	0.724459	+	0.689317i	$0.242089\pi$
$938$		0			0
$939$	40.6538	−	29.5367i	1.32669	−	0.963894i
$940$		0			0
$941$	9.25050	+	6.72088i	0.301558	+	0.219095i	0.728266	−	0.685295i	$-0.240327\pi$
$941$	9.25050	+	6.72088i	0.301558	+	0.219095i	−0.426708	+	0.904390i	$0.640327\pi$
$942$		0			0
$943$			1.34428i			0.0437758i
$944$		0			0
$945$	10.8647	−	12.8191i	0.353428	−	0.417006i
$946$		0			0
$947$	−3.41457	−	1.10946i	−0.110959	−	0.0360527i	0.253011	−	0.967463i	$-0.418579\pi$
$947$	−3.41457	−	1.10946i	−0.110959	−	0.0360527i	−0.363970	+	0.931411i	$0.618579\pi$
$948$		0			0
$949$	−6.53006			−0.211975
$950$		0			0
$951$	33.4462			1.08457
$952$		0			0
$953$	−37.7205	−	12.2561i	−1.22189	−	0.397015i	−0.374117	−	0.927381i	$-0.622054\pi$
$953$	−37.7205	−	12.2561i	−1.22189	−	0.397015i	−0.847768	+	0.530367i	$0.822054\pi$
$954$		0			0
$955$	−18.9704	−	7.77359i	−0.613869	−	0.251547i
$956$		0			0
$957$			85.6107i			2.76740i
$958$		0			0
$959$	31.9962	+	23.2466i	1.03321	+	0.750672i
$960$		0			0
$961$	24.9287	−	18.1117i	0.804150	−	0.584249i
$962$		0			0
$963$	11.1712	−	15.3758i	0.359986	−	0.495478i
$964$		0			0
$965$	−3.18149	−	13.0337i	−0.102416	−	0.419571i
$966$		0			0
$967$	7.72673	−	2.51057i	0.248475	−	0.0807343i	−0.182132	−	0.983274i	$-0.558300\pi$
$967$	7.72673	−	2.51057i	0.248475	−	0.0807343i	0.430606	+	0.902540i	$0.358300\pi$
$968$		0			0
$969$	10.8559	+	33.4109i	0.348741	+	1.07331i
$970$		0			0
$971$	8.61796	−	26.5234i	0.276564	−	0.851175i	−0.712238	−	0.701938i	$-0.752318\pi$
$971$	8.61796	−	26.5234i	0.276564	−	0.851175i	0.988801	−	0.149237i	$-0.0476818\pi$
$972$		0			0
$973$	9.70032	+	13.3513i	0.310978	+	0.428024i
$974$		0			0
$975$	−2.33435	+	4.66870i	−0.0747591	+	0.149518i
$976$		0			0
$977$	25.1902	+	34.6713i	0.805905	+	1.10923i	0.991942	+	0.126690i	$0.0404353\pi$
$977$	25.1902	+	34.6713i	0.805905	+	1.10923i	−0.186038	+	0.982543i	$0.559565\pi$
$978$		0			0
$979$	2.95489	−	9.09423i	0.0944388	−	0.290653i
$980$		0			0
$981$	4.18532	+	12.8811i	0.133627	+	0.411261i
$982$		0			0
$983$	−31.2682	+	10.1596i	−0.997300	+	0.324042i	−0.761786	−	0.647829i	$-0.775677\pi$
$983$	−31.2682	+	10.1596i	−0.997300	+	0.324042i	−0.235514	+	0.971871i	$0.575677\pi$
$984$		0			0
$985$	−29.3000	−	2.19409i	−0.933576	−	0.0699096i
$986$		0			0
$987$	23.5727	−	32.4451i	0.750328	−	1.03274i
$988$		0			0
$989$	0.448335	−	0.325734i	0.0142562	−	0.0103577i
$990$		0			0
$991$	17.8090	+	12.9390i	0.565720	+	0.411020i	0.833548	−	0.552447i	$-0.186306\pi$
$991$	17.8090	+	12.9390i	0.565720	+	0.411020i	−0.267828	+	0.963467i	$0.586306\pi$
$992$		0			0
$993$		−	69.6941i		−	2.21167i
$994$		0			0
$995$	−15.9765	+	3.89981i	−0.506489	+	0.123632i
$996$		0			0
$997$	−30.0965	−	9.77894i	−0.953165	−	0.309702i	−0.209164	−	0.977881i	$-0.567074\pi$
$997$	−30.0965	−	9.77894i	−0.953165	−	0.309702i	−0.744001	+	0.668179i	$0.767074\pi$
$998$		0			0
$999$	−7.31892			−0.231560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.a.289.1		8
4.3	odd	2		50.2.e.a.39.1	yes	8
12.11	even	2		450.2.l.b.289.2		8
20.3	even	4		250.2.d.b.51.1		8
20.7	even	4		250.2.d.c.51.2		8
20.19	odd	2		250.2.e.a.199.2		8
25.3	odd	20		10000.2.a.bb.1.3		4
25.9	even	10	inner	400.2.y.a.209.1		8
25.22	odd	20		10000.2.a.o.1.2		4
100.3	even	20		1250.2.a.i.1.2		4
100.47	even	20		1250.2.a.h.1.3		4
100.59	odd	10		50.2.e.a.9.1	✓	8
100.63	even	20		250.2.d.b.201.1		8
100.71	odd	10		1250.2.b.c.1249.7		8
100.79	odd	10		1250.2.b.c.1249.2		8
100.87	even	20		250.2.d.c.201.2		8
100.91	odd	10		250.2.e.a.49.2		8
300.59	even	10		450.2.l.b.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.9.1	✓	8	100.59	odd	10
50.2.e.a.39.1	yes	8	4.3	odd	2
250.2.d.b.51.1		8	20.3	even	4
250.2.d.b.201.1		8	100.63	even	20
250.2.d.c.51.2		8	20.7	even	4
250.2.d.c.201.2		8	100.87	even	20
250.2.e.a.49.2		8	100.91	odd	10
250.2.e.a.199.2		8	20.19	odd	2
400.2.y.a.209.1		8	25.9	even	10	inner
400.2.y.a.289.1		8	1.1	even	1	trivial
450.2.l.b.109.2		8	300.59	even	10
450.2.l.b.289.2		8	12.11	even	2
1250.2.a.h.1.3		4	100.47	even	20
1250.2.a.i.1.2		4	100.3	even	20
1250.2.b.c.1249.2		8	100.79	odd	10
1250.2.b.c.1249.7		8	100.71	odd	10
10000.2.a.o.1.2		4	25.22	odd	20
10000.2.a.bb.1.3		4	25.3	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.06909 - 0.672288i) q^{3} +(-2.17229 + 0.530249i) q^{5} +2.72654i q^{7} +(1.40211 + 1.01869i) q^{9} +O(q^{10})\)	\(q+(-2.06909 - 0.672288i) q^{3} +(-2.17229 + 0.530249i) q^{5} +2.72654i q^{7} +(1.40211 + 1.01869i) q^{9} +(4.52874 - 3.29032i) q^{11} +(0.282051 - 0.388209i) q^{13} +(4.85114 + 0.363271i) q^{15} +(3.71113 - 1.20582i) q^{17} +(-1.27877 - 3.93564i) q^{19} +(1.83302 - 5.64146i) q^{21} +(0.0930960 + 0.128136i) q^{23} +(4.43767 - 2.30371i) q^{25} +(1.62006 + 2.22982i) q^{27} +(2.17229 - 6.68562i) q^{29} +(-0.133446 - 0.410706i) q^{31} +(-11.5824 + 3.76336i) q^{33} +(-1.44575 - 5.92284i) q^{35} +(-1.56082 + 2.14828i) q^{37} +(-0.844577 + 0.613621i) q^{39} +(6.86650 + 4.98880i) q^{41} -3.49890i q^{43} +(-3.58596 - 1.46943i) q^{45} +(6.43001 + 2.08924i) q^{47} -0.434034 q^{49} -8.48932 q^{51} +(5.31375 + 1.72654i) q^{53} +(-8.09304 + 9.54889i) q^{55} +9.00290i q^{57} +(6.15537 + 4.47214i) q^{59} +(-5.97449 + 4.34072i) q^{61} +(-2.77751 + 3.82292i) q^{63} +(-0.406848 + 0.992859i) q^{65} +(1.96589 - 0.638757i) q^{67} +(-0.106480 - 0.327712i) q^{69} +(2.18146 - 6.71384i) q^{71} +(-7.99885 - 11.0095i) q^{73} +(-10.7307 + 1.78318i) q^{75} +(8.97120 + 12.3478i) q^{77} +(1.95855 - 6.02781i) q^{79} +(-3.45965 - 10.6477i) q^{81} +(-11.0330 + 3.58482i) q^{83} +(-7.42226 + 4.58721i) q^{85} +(-8.98932 + 12.3727i) q^{87} +(1.38197 - 1.00406i) q^{89} +(1.05847 + 0.769023i) q^{91} +0.939503i q^{93} +(4.86472 + 7.87129i) q^{95} +(-11.2840 - 3.66640i) q^{97} +9.70164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{5} - 4 q^{9}+O(q^{10}) \) 8 * q - 10 * q^5 - 4 * q^9	\( 8 q - 10 q^{5} - 4 q^{9} + 4 q^{11} + 20 q^{15} + 10 q^{17} - 10 q^{19} + 16 q^{21} - 10 q^{23} + 10 q^{25} + 10 q^{29} - 6 q^{31} - 30 q^{33} - 10 q^{35} - 10 q^{37} + 8 q^{39} - 14 q^{41} + 10 q^{45} + 30 q^{47} - 16 q^{49} - 16 q^{51} + 10 q^{55} - 14 q^{61} - 20 q^{63} + 50 q^{65} - 10 q^{67} - 8 q^{69} + 34 q^{71} - 10 q^{75} + 40 q^{77} - 12 q^{81} - 50 q^{83} - 20 q^{85} - 20 q^{87} + 20 q^{89} + 4 q^{91} - 20 q^{97} + 28 q^{99}+O(q^{100}) \) 8 * q - 10 * q^5 - 4 * q^9 + 4 * q^11 + 20 * q^15 + 10 * q^17 - 10 * q^19 + 16 * q^21 - 10 * q^23 + 10 * q^25 + 10 * q^29 - 6 * q^31 - 30 * q^33 - 10 * q^35 - 10 * q^37 + 8 * q^39 - 14 * q^41 + 10 * q^45 + 30 * q^47 - 16 * q^49 - 16 * q^51 + 10 * q^55 - 14 * q^61 - 20 * q^63 + 50 * q^65 - 10 * q^67 - 8 * q^69 + 34 * q^71 - 10 * q^75 + 40 * q^77 - 12 * q^81 - 50 * q^83 - 20 * q^85 - 20 * q^87 + 20 * q^89 + 4 * q^91 - 20 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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