LMFDB - Embedded newform 260.2.z.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(49,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("260.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.z (of order $6$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 $ x^16 - 7x^14 + 21x^12 - 22x^10 - 26x^8 - 198x^6 + 1701x^4 - 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$1.72890 - 0.104392i$ of defining polynomial
Character	$\chi$	$=$	260.49
Dual form			260.2.z.a.69.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.180812 + 0.104392i) q^{3} +(1.60081 + 1.56122i) q^{5} +(1.72890 - 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +O(q^{10})$	\(q+(-0.180812 + 0.104392i) q^{3} +(1.60081 + 1.56122i) q^{5} +(1.72890 - 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +(0.625212 - 0.360966i) q^{11} +(3.18457 + 1.69071i) q^{13} +(-0.452424 - 0.115174i) q^{15} +(-3.10921 - 1.79510i) q^{17} +(6.51351 + 3.76057i) q^{19} +0.721933i q^{21} +(2.05486 - 1.18637i) q^{23} +(0.125212 + 4.99843i) q^{25} -1.24360i q^{27} +(-3.68231 - 6.37795i) q^{29} +0.668447i q^{31} +(-0.0753639 + 0.130534i) q^{33} +(7.44278 - 2.09452i) q^{35} +(-3.36538 - 5.82902i) q^{37} +(-0.752305 + 0.0267426i) q^{39} +(-6.32932 + 3.65423i) q^{41} +(-7.06075 - 4.07653i) q^{43} +(-6.36355 + 1.79081i) q^{45} -6.40326 q^{47} +(-2.47820 - 4.29238i) q^{49} +0.749576 q^{51} +11.7433i q^{53} +(1.56439 + 0.398251i) q^{55} -1.57029 q^{57} +(-4.20410 - 2.42724i) q^{59} +(2.68231 - 4.64590i) q^{61} +(5.11134 + 8.85310i) q^{63} +(2.45834 + 7.67832i) q^{65} +(-7.80620 - 13.5207i) q^{67} +(-0.247695 + 0.429021i) q^{69} +(-4.10530 - 2.37019i) q^{71} +6.36914 q^{73} +(-0.544435 - 0.890705i) q^{75} -2.49630i q^{77} +5.20683 q^{79} +(-4.30479 - 7.45612i) q^{81} -13.3902 q^{83} +(-2.17472 - 7.72777i) q^{85} +(1.33161 + 0.768806i) q^{87} +(4.20410 - 2.42724i) q^{89} +(10.5687 - 6.61328i) q^{91} +(-0.0697804 - 0.120863i) q^{93} +(4.55585 + 16.1890i) q^{95} +(-1.83435 + 3.17719i) q^{97} +2.13433i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.180812	+	0.104392i	−0.104392	+	0.0602706i	−0.551287	−	0.834316i	$-0.685863\pi$
$3$	−0.180812	+	0.104392i	−0.104392	+	0.0602706i	0.446895	+	0.894586i	$0.352530\pi$
$4$		0			0
$5$	1.60081	+	1.56122i	0.715906	+	0.698197i
$5$	1.60081	+	1.56122i	0.715906	+	0.698197i
$6$		0			0
$7$	1.72890	−	2.99455i	0.653464	−	1.13183i	−0.328813	−	0.944395i	$-0.606649\pi$
$7$	1.72890	−	2.99455i	0.653464	−	1.13183i	0.982277	−	0.187437i	$-0.0600181\pi$
$8$		0			0
$9$	−1.47820	+	2.56033i	−0.492735	+	0.853442i
$10$		0			0
$11$	0.625212	−	0.360966i	0.188509	−	0.108835i	−0.402776	−	0.915299i	$-0.631955\pi$
$11$	0.625212	−	0.360966i	0.188509	−	0.108835i	0.591284	+	0.806463i	$0.298621\pi$
$12$		0			0
$13$	3.18457	+	1.69071i	0.883241	+	0.468919i
$13$	3.18457	+	1.69071i	0.883241	+	0.468919i
$14$		0			0
$15$	−0.452424	−	0.115174i	−0.116815	−	0.0297379i
$16$		0			0
$17$	−3.10921	−	1.79510i	−0.754094	−	0.435376i	0.0730774	−	0.997326i	$-0.476718\pi$
$17$	−3.10921	−	1.79510i	−0.754094	−	0.435376i	−0.827171	+	0.561950i	$0.810051\pi$
$18$		0			0
$19$	6.51351	+	3.76057i	1.49430	+	0.862735i	0.999979	−	0.00654367i	$-0.00208293\pi$
$19$	6.51351	+	3.76057i	1.49430	+	0.862735i	0.494322	+	0.869279i	$0.335416\pi$
$20$		0			0
$21$			0.721933i			0.157539i
$22$		0			0
$23$	2.05486	−	1.18637i	0.428468	−	0.247376i	−0.270226	−	0.962797i	$-0.587098\pi$
$23$	2.05486	−	1.18637i	0.428468	−	0.247376i	0.698694	+	0.715421i	$0.253765\pi$
$24$		0			0
$25$	0.125212	+	4.99843i	0.0250424	+	0.999686i
$26$		0			0
$27$		−	1.24360i		−	0.239331i
$28$		0			0
$29$	−3.68231	−	6.37795i	−0.683788	−	1.18435i	−0.973816	−	0.227337i	$-0.926998\pi$
$29$	−3.68231	−	6.37795i	−0.683788	−	1.18435i	0.290028	−	0.957018i	$-0.406335\pi$
$30$		0			0
$31$			0.668447i			0.120057i	0.998197	+	0.0600284i	$0.0191191\pi$
$31$			0.668447i			0.120057i	−0.998197	+	0.0600284i	$0.980881\pi$
$32$		0			0
$33$	−0.0753639	+	0.130534i	−0.0131192	+	0.0227231i
$34$		0			0
$35$	7.44278	−	2.09452i	1.25806	−	0.354039i
$36$		0			0
$37$	−3.36538	−	5.82902i	−0.553266	−	0.958284i	−0.998036	−	0.0626397i	$-0.980048\pi$
$37$	−3.36538	−	5.82902i	−0.553266	−	0.958284i	0.444771	−	0.895645i	$-0.353285\pi$
$38$		0			0
$39$	−0.752305	+	0.0267426i	−0.120465	+	0.00428225i
$40$		0			0
$41$	−6.32932	+	3.65423i	−0.988473	+	0.570695i	−0.904818	−	0.425799i	$-0.859993\pi$
$41$	−6.32932	+	3.65423i	−0.988473	+	0.570695i	−0.0836556	+	0.996495i	$0.526660\pi$
$42$		0			0
$43$	−7.06075	−	4.07653i	−1.07675	−	0.621665i	−0.146736	−	0.989176i	$-0.546877\pi$
$43$	−7.06075	−	4.07653i	−1.07675	−	0.621665i	−0.930019	+	0.367511i	$0.880210\pi$
$44$		0			0
$45$	−6.36355	+	1.79081i	−0.948622	+	0.266958i
$46$		0			0
$47$	−6.40326			−0.934011			−0.467005	−	0.884254i	$-0.654667\pi$
$47$	−6.40326			−0.934011			−0.467005	+	0.884254i	$0.654667\pi$
$48$		0			0
$49$	−2.47820	−	4.29238i	−0.354029	−	0.613197i
$50$		0			0
$51$	0.749576			0.104962
$52$		0			0
$53$			11.7433i			1.61306i	0.591193	+	0.806530i	$0.298657\pi$
$53$			11.7433i			1.61306i	−0.591193	+	0.806530i	$0.701343\pi$
$54$		0			0
$55$	1.56439	+	0.398251i	0.210943	+	0.0537001i
$56$		0			0
$57$	−1.57029			−0.207990
$58$		0			0
$59$	−4.20410	−	2.42724i	−0.547328	−	0.316000i	0.200716	−	0.979650i	$-0.435673\pi$
$59$	−4.20410	−	2.42724i	−0.547328	−	0.316000i	−0.748044	+	0.663650i	$0.769007\pi$
$60$		0			0
$61$	2.68231	−	4.64590i	0.343435	−	0.594846i	−0.641634	−	0.767011i	$-0.721743\pi$
$61$	2.68231	−	4.64590i	0.343435	−	0.594846i	0.985068	+	0.172165i	$0.0550763\pi$
$62$		0			0
$63$	5.11134	+	8.85310i	0.643969	+	1.11539i
$64$		0			0
$65$	2.45834	+	7.67832i	0.304920	+	0.952378i
$66$		0			0
$67$	−7.80620	−	13.5207i	−0.953679	−	1.65182i	−0.737362	−	0.675498i	$-0.763929\pi$
$67$	−7.80620	−	13.5207i	−0.953679	−	1.65182i	−0.216318	−	0.976323i	$-0.569405\pi$
$68$		0			0
$69$	−0.247695	+	0.429021i	−0.0298190	+	0.0516480i
$70$		0			0
$71$	−4.10530	−	2.37019i	−0.487209	−	0.281290i	0.236207	−	0.971703i	$-0.424096\pi$
$71$	−4.10530	−	2.37019i	−0.487209	−	0.281290i	−0.723416	+	0.690412i	$0.757429\pi$
$72$		0			0
$73$	6.36914			0.745452			0.372726	−	0.927941i	$-0.378423\pi$
$73$	6.36914			0.745452			0.372726	+	0.927941i	$0.378423\pi$
$74$		0			0
$75$	−0.544435	−	0.890705i	−0.0628660	−	0.102850i
$76$		0			0
$77$		−	2.49630i		−	0.284480i
$78$		0			0
$79$	5.20683			0.585815			0.292907	−	0.956141i	$-0.405377\pi$
$79$	5.20683			0.585815			0.292907	+	0.956141i	$0.405377\pi$
$80$		0			0
$81$	−4.30479	−	7.45612i	−0.478310	−	0.828458i
$82$		0			0
$83$	−13.3902			−1.46977			−0.734883	−	0.678194i	$-0.762763\pi$
$83$	−13.3902			−1.46977			−0.734883	+	0.678194i	$0.762763\pi$
$84$		0			0
$85$	−2.17472	−	7.72777i	−0.235882	−	0.838194i
$86$		0			0
$87$	1.33161	+	0.768806i	0.142764	+	0.0824246i
$88$		0			0
$89$	4.20410	−	2.42724i	0.445634	−	0.257287i	−0.260350	−	0.965514i	$-0.583838\pi$
$89$	4.20410	−	2.42724i	0.445634	−	0.257287i	0.705985	+	0.708227i	$0.250505\pi$
$90$		0			0
$91$	10.5687	−	6.61328i	1.10790	−	0.693260i
$92$		0			0
$93$	−0.0697804	−	0.120863i	−0.00723589	−	0.0125329i
$94$		0			0
$95$	4.55585	+	16.1890i	0.467420	+	1.66095i
$96$		0			0
$97$	−1.83435	+	3.17719i	−0.186250	+	0.322595i	−0.943997	−	0.329954i	$-0.892967\pi$
$97$	−1.83435	+	3.17719i	−0.186250	+	0.322595i	0.757747	+	0.652548i	$0.226300\pi$
$98$		0			0
$99$			2.13433i			0.214508i
$100$		0			0
$101$	4.85299	+	8.40563i	0.482891	+	0.836391i	0.999807	−	0.0196446i	$-0.00625347\pi$
$101$	4.85299	+	8.40563i	0.482891	+	0.836391i	−0.516916	+	0.856036i	$0.672920\pi$
$102$		0			0
$103$		−	5.36274i		−	0.528407i	−0.964467	−	0.264203i	$-0.914891\pi$
$103$		−	5.36274i		−	0.528407i	0.964467	−	0.264203i	$-0.0851090\pi$
$104$		0			0
$105$	−1.12709	+	1.15568i	−0.109993	+	0.112783i
$106$		0			0
$107$	13.6408	−	7.87552i	1.31871	−	0.761355i	0.335185	−	0.942152i	$-0.391201\pi$
$107$	13.6408	−	7.87552i	1.31871	−	0.761355i	0.983520	+	0.180798i	$0.0578679\pi$
$108$		0			0
$109$			14.4879i			1.38769i	0.720123	+	0.693847i	$0.244085\pi$
$109$			14.4879i			1.38769i	−0.720123	+	0.693847i	$0.755915\pi$
$110$		0			0
$111$	1.21700	+	0.702637i	0.115513	+	0.0666913i
$112$		0			0
$113$	2.74758	+	1.58632i	0.258471	+	0.149228i	0.623637	−	0.781714i	$-0.285654\pi$
$113$	2.74758	+	1.58632i	0.258471	+	0.149228i	−0.365166	+	0.930942i	$0.618988\pi$
$114$		0			0
$115$	5.14163	+	1.30891i	0.479459	+	0.122057i
$116$		0			0
$117$	−9.03622	+	5.65433i	−0.835399	+	0.522743i
$118$		0			0
$119$	−10.7510	+	6.20711i	−0.985546	+	0.569005i
$120$		0			0
$121$	−5.23941	+	9.07492i	−0.476310	+	0.824993i
$122$		0			0
$123$	0.762944	−	1.32146i	0.0687923	−	0.119152i
$124$		0			0
$125$	−7.60319	+	8.19704i	−0.680050	+	0.733166i
$126$		0			0
$127$	1.33161	−	0.768806i	0.118161	−	0.0682205i	−0.439754	−	0.898118i	$-0.644935\pi$
$127$	1.33161	−	0.768806i	0.118161	−	0.0682205i	0.557916	+	0.829898i	$0.311601\pi$
$128$		0			0
$129$	1.70222			0.149872
$130$		0			0
$131$	6.45180			0.563696			0.281848	−	0.959459i	$-0.409053\pi$
$131$	6.45180			0.563696			0.281848	+	0.959459i	$0.409053\pi$
$132$		0			0
$133$	22.5224	−	13.0033i	1.95294	−	1.12753i
$134$		0			0
$135$	1.94153	−	1.99077i	0.167100	−	0.171338i
$136$		0			0
$137$	4.62163	−	8.00490i	0.394853	−	0.683905i	−0.598230	−	0.801325i	$-0.704129\pi$
$137$	4.62163	−	8.00490i	0.394853	−	0.683905i	0.993082	+	0.117420i	$0.0374623\pi$
$138$		0			0
$139$	8.38641	−	14.5257i	0.711326	−	1.23205i	−0.253033	−	0.967458i	$-0.581428\pi$
$139$	8.38641	−	14.5257i	0.711326	−	1.23205i	0.964359	−	0.264596i	$-0.0852385\pi$
$140$		0			0
$141$	1.15778	−	0.668447i	0.0975031	−	0.0562934i
$142$		0			0
$143$	2.60132	−	0.0924708i	0.217534	−	0.00773280i
$144$		0			0
$145$	4.06266	−	15.9588i	0.337385	−	1.32531i
$146$		0			0
$147$	0.896178	+	0.517408i	0.0739155	+	0.0426751i
$148$		0			0
$149$	2.17153	+	1.25373i	0.177899	+	0.102710i	0.586305	−	0.810090i	$-0.300582\pi$
$149$	2.17153	+	1.25373i	0.177899	+	0.102710i	−0.408406	+	0.912800i	$0.633915\pi$
$150$		0			0
$151$			11.0238i			0.897108i	0.893756	+	0.448554i	$0.148061\pi$
$151$			11.0238i			0.897108i	−0.893756	+	0.448554i	$0.851939\pi$
$152$		0			0
$153$	9.19209	−	5.30706i	0.743137	−	0.429050i
$154$		0			0
$155$	−1.04359	+	1.07006i	−0.0838232	+	0.0859493i
$156$		0			0
$157$		−	0.946504i		−	0.0755392i	−0.999286	−	0.0377696i	$-0.987975\pi$
$157$		−	0.946504i		−	0.0755392i	0.999286	−	0.0377696i	$-0.0120253\pi$
$158$		0			0
$159$	−1.22590	−	2.12332i	−0.0972202	−	0.168390i
$160$		0			0
$161$		−	8.20449i		−	0.646604i
$162$		0			0
$163$	−7.20187	+	12.4740i	−0.564094	+	0.977039i	0.433039	+	0.901375i	$0.357441\pi$
$163$	−7.20187	+	12.4740i	−0.564094	+	0.977039i	−0.997133	+	0.0756643i	$0.975892\pi$
$164$		0			0
$165$	−0.324435	+	0.0913015i	−0.0252573	+	0.00710781i
$166$		0			0
$167$	9.35429	+	16.2021i	0.723857	+	1.25376i	0.959443	+	0.281903i	$0.0909658\pi$
$167$	9.35429	+	16.2021i	0.723857	+	1.25376i	−0.235586	+	0.971854i	$0.575701\pi$
$168$		0			0
$169$	7.28300	+	10.7684i	0.560231	+	0.828337i
$170$		0			0
$171$	−19.2566	+	11.1178i	−1.47259	+	0.850199i
$172$		0			0
$173$	−15.3261	−	8.84855i	−1.16523	−	0.672743i	−0.212675	−	0.977123i	$-0.568217\pi$
$173$	−15.3261	−	8.84855i	−1.16523	−	0.672743i	−0.952551	+	0.304380i	$0.901551\pi$
$174$		0			0
$175$	15.1845	+	8.26685i	1.14784	+	0.624915i
$176$		0			0
$177$	1.01354			0.0761820
$178$		0			0
$179$	−4.20410	−	7.28172i	−0.314230	−	0.544262i	0.665044	−	0.746804i	$-0.268413\pi$
$179$	−4.20410	−	7.28172i	−0.314230	−	0.544262i	−0.979273	+	0.202543i	$0.935079\pi$
$180$		0			0
$181$	16.6150			1.23499			0.617493	−	0.786576i	$-0.288148\pi$
$181$	16.6150			1.23499			0.617493	+	0.786576i	$0.288148\pi$
$182$		0			0
$183$			1.12004i			0.0827961i
$184$		0			0
$185$	3.71300	−	14.5853i	0.272985	−	1.07233i
$186$		0			0
$187$	−2.59189			−0.189537
$188$		0			0
$189$	−3.72402	−	2.15006i	−0.270883	−	0.156394i
$190$		0			0
$191$	−8.93461	+	15.4752i	−0.646486	+	1.11975i	0.337470	+	0.941336i	$0.390429\pi$
$191$	−8.93461	+	15.4752i	−0.646486	+	1.11975i	−0.983956	+	0.178410i	$0.942905\pi$
$192$		0			0
$193$	3.62156	+	6.27273i	0.260686	+	0.451521i	0.966424	−	0.256952i	$-0.0827181\pi$
$193$	3.62156	+	6.27273i	0.260686	+	0.451521i	−0.705739	+	0.708472i	$0.749385\pi$
$194$		0			0
$195$	−1.24605	−	1.13170i	−0.0892316	−	0.0810427i
$196$		0			0
$197$	5.36349	+	9.28984i	0.382133	+	0.661873i	0.991367	−	0.131117i	$-0.0418564\pi$
$197$	5.36349	+	9.28984i	0.382133	+	0.661873i	−0.609234	+	0.792990i	$0.708523\pi$
$198$		0			0
$199$	−1.62521	+	2.81495i	−0.115208	+	0.199547i	−0.917863	−	0.396897i	$-0.870087\pi$
$199$	−1.62521	+	2.81495i	−0.115208	+	0.199547i	0.802655	+	0.596444i	$0.203420\pi$
$200$		0			0
$201$	2.82291	+	1.62981i	0.199113	+	0.114958i
$202$		0			0
$203$	−25.4654			−1.78732
$204$		0			0
$205$	−15.8371	−	4.03168i	−1.10611	−	0.281585i
$206$		0			0
$207$			7.01481i			0.487563i
$208$		0			0
$209$	5.42976			0.375585
$210$		0			0
$211$	−11.7639	−	20.3757i	−0.809862	−	1.40272i	−0.912959	−	0.408051i	$-0.866208\pi$
$211$	−11.7639	−	20.3757i	−0.809862	−	1.40272i	0.103097	−	0.994671i	$-0.467125\pi$
$212$		0			0
$213$	0.989715			0.0678142
$214$		0			0
$215$	−4.93861	−	17.5491i	−0.336811	−	1.19684i
$216$		0			0
$217$	2.00170	+	1.15568i	0.135884	+	0.0784527i
$218$		0			0
$219$	−1.15162	+	0.664886i	−0.0778191	+	0.0449289i
$220$		0			0
$221$	−6.86650	−	10.9734i	−0.461891	−	0.738151i
$222$		0			0
$223$	−6.29378	−	10.9011i	−0.421463	−	0.729995i	0.574620	−	0.818420i	$-0.305150\pi$
$223$	−6.29378	−	10.9011i	−0.421463	−	0.729995i	−0.996083	+	0.0884255i	$0.971816\pi$
$224$		0			0
$225$	−12.9827	−	7.06812i	−0.865514	−	0.471208i
$226$		0			0
$227$	−4.22075	+	7.31055i	−0.280141	+	0.485218i	−0.971419	−	0.237370i	$-0.923715\pi$
$227$	−4.22075	+	7.31055i	−0.280141	+	0.485218i	0.691278	+	0.722589i	$0.257048\pi$
$228$		0			0
$229$		−	8.26510i		−	0.546173i	−0.961989	−	0.273087i	$-0.911955\pi$
$229$		−	8.26510i		−	0.546173i	0.961989	−	0.273087i	$-0.0880445\pi$
$230$		0			0
$231$	0.260593	+	0.451361i	0.0171458	+	0.0296974i
$232$		0			0
$233$			5.31046i			0.347900i	0.984755	+	0.173950i	$0.0556531\pi$
$233$			5.31046i			0.347900i	−0.984755	+	0.173950i	$0.944347\pi$
$234$		0			0
$235$	−10.2504	−	9.99686i	−0.668664	−	0.652123i
$236$		0			0
$237$	−0.941457	+	0.543551i	−0.0611542	+	0.0353074i
$238$		0			0
$239$			4.14744i			0.268276i	0.990963	+	0.134138i	$0.0428265\pi$
$239$			4.14744i			0.268276i	−0.990963	+	0.134138i	$0.957173\pi$
$240$		0			0
$241$	−1.46804	−	0.847571i	−0.0945645	−	0.0545968i	0.451972	−	0.892032i	$-0.350721\pi$
$241$	−1.46804	−	0.847571i	−0.0945645	−	0.0545968i	−0.546536	+	0.837435i	$0.684054\pi$
$242$		0			0
$243$	4.78768	+	2.76417i	0.307130	+	0.177322i
$244$		0			0
$245$	2.73418	−	10.7403i	0.174680	−	0.686173i
$246$		0			0
$247$	14.3847	+	22.9883i	0.915276	+	1.46271i
$248$		0			0
$249$	2.42111	−	1.39783i	0.153431	−	0.0885837i
$250$		0			0
$251$	9.86650	−	17.0893i	0.622768	−	1.07867i	−0.366200	−	0.930536i	$-0.619341\pi$
$251$	9.86650	−	17.0893i	0.622768	−	1.07867i	0.988968	−	0.148130i	$-0.0473252\pi$
$252$		0			0
$253$	0.856482	−	1.48347i	0.0538465	−	0.0932649i
$254$		0			0
$255$	1.19993	+	1.17025i	0.0751426	+	0.0732839i
$256$		0			0
$257$	−10.2231	+	5.90232i	−0.637701	+	0.368177i	−0.783728	−	0.621104i	$-0.786685\pi$
$257$	−10.2231	+	5.90232i	−0.637701	+	0.368177i	0.146027	+	0.989281i	$0.453351\pi$
$258$		0			0
$259$	−23.2737			−1.44616
$260$		0			0
$261$	21.7728			1.34770
$262$		0			0
$263$	−12.3013	+	7.10216i	−0.758531	+	0.437938i	−0.828768	−	0.559592i	$-0.810958\pi$
$263$	−12.3013	+	7.10216i	−0.758531	+	0.437938i	0.0702373	+	0.997530i	$0.477624\pi$
$264$		0			0
$265$	−18.3338	+	18.7988i	−1.12623	+	1.15480i
$266$		0			0
$267$	−0.506768	+	0.877748i	−0.0310137	+	0.0537173i
$268$		0			0
$269$	4.33120	−	7.50185i	0.264078	−	0.457396i	−0.703244	−	0.710949i	$-0.748266\pi$
$269$	4.33120	−	7.50185i	0.264078	−	0.457396i	0.967322	+	0.253553i	$0.0815991\pi$
$270$		0			0
$271$	3.51351	−	2.02852i	0.213430	−	0.123224i	−0.389474	−	0.921037i	$-0.627343\pi$
$271$	3.51351	−	2.02852i	0.213430	−	0.123224i	0.602905	+	0.797813i	$0.294010\pi$
$272$		0			0
$273$	−1.22058	+	2.29905i	−0.0738728	+	0.139145i
$274$		0			0
$275$	1.88255	+	3.07988i	0.113522	+	0.185724i
$276$		0			0
$277$	1.17344	+	0.677485i	0.0705051	+	0.0407061i	0.534838	−	0.844955i	$-0.320373\pi$
$277$	1.17344	+	0.677485i	0.0705051	+	0.0407061i	−0.464333	+	0.885661i	$0.653706\pi$
$278$		0			0
$279$	−1.71144	−	0.988102i	−0.102461	−	0.0591561i
$280$		0			0
$281$		−	20.3840i		−	1.21601i	−0.793934	−	0.608004i	$-0.791970\pi$
$281$		−	20.3840i		−	1.21601i	0.793934	−	0.608004i	$-0.208030\pi$
$282$		0			0
$283$	−2.22779	+	1.28621i	−0.132428	+	0.0764575i	−0.564751	−	0.825262i	$-0.691028\pi$
$283$	−2.22779	+	1.28621i	−0.132428	+	0.0764575i	0.432322	+	0.901719i	$0.357694\pi$
$284$		0			0
$285$	−2.51375	−	2.45157i	−0.148902	−	0.145218i
$286$		0			0
$287$			25.2712i			1.49171i
$288$		0			0
$289$	−2.05522	−	3.55974i	−0.120895	−	0.209396i
$290$		0			0
$291$		−	0.765964i		−	0.0449016i
$292$		0			0
$293$	9.38481	−	16.2550i	0.548267	−	0.949626i	−0.450127	−	0.892965i	$-0.648621\pi$
$293$	9.38481	−	16.2550i	0.548267	−	0.949626i	0.998393	−	0.0566611i	$-0.0180455\pi$
$294$		0			0
$295$	−2.94054	−	10.4491i	−0.171205	−	0.608369i
$296$		0			0
$297$	−0.448898	−	0.777514i	−0.0260477	−	0.0451159i
$298$		0			0
$299$	8.54966	−	0.303920i	0.494439	−	0.0175761i
$300$		0			0
$301$	−24.4147	+	14.0958i	−1.40724	+	0.812470i
$302$		0			0
$303$	−1.75496	−	1.01323i	−0.100820	−	0.0582083i
$304$		0			0
$305$	11.5471	−	3.24955i	0.661186	−	0.186069i
$306$		0			0
$307$	2.93740			0.167646			0.0838230	−	0.996481i	$-0.473287\pi$
$307$	2.93740			0.167646			0.0838230	+	0.996481i	$0.473287\pi$
$308$		0			0
$309$	0.559826	+	0.969647i	0.0318474	+	0.0551613i
$310$		0			0
$311$	4.13623			0.234544			0.117272	−	0.993100i	$-0.462585\pi$
$311$	4.13623			0.234544			0.117272	+	0.993100i	$0.462585\pi$
$312$		0			0
$313$		−	12.2199i		−	0.690710i	−0.938472	−	0.345355i	$-0.887758\pi$
$313$		−	12.2199i		−	0.690710i	0.938472	−	0.345355i	$-0.112242\pi$
$314$		0			0
$315$	−5.63930	+	22.1521i	−0.317738	+	1.24813i
$316$		0			0
$317$	11.6351			0.653490			0.326745	−	0.945112i	$-0.394048\pi$
$317$	11.6351			0.653490			0.326745	+	0.945112i	$0.394048\pi$
$318$		0			0
$319$	−4.60445	−	2.65838i	−0.257800	−	0.148841i
$320$		0			0
$321$	−1.64428	+	2.84797i	−0.0917747	+	0.158958i
$322$		0			0
$323$	−13.5012	−	23.3848i	−0.751229	−	1.30117i
$324$		0			0
$325$	−8.05215	+	16.1296i	−0.446653	+	0.894707i
$326$		0			0
$327$	−1.51242	−	2.61959i	−0.0836372	−	0.144864i
$328$		0			0
$329$	−11.0706	+	19.1748i	−0.610342	+	1.05714i
$330$		0			0
$331$	−11.9346	−	6.89045i	−0.655986	−	0.378734i	0.134760	−	0.990878i	$-0.456974\pi$
$331$	−11.9346	−	6.89045i	−0.655986	−	0.378734i	−0.790746	+	0.612145i	$0.790307\pi$
$332$		0			0
$333$	19.8989			1.09045
$334$		0			0
$335$	8.61251	−	33.8314i	0.470552	−	1.84840i
$336$		0			0
$337$			17.6710i			0.962599i	0.876556	+	0.481299i	$0.159835\pi$
$337$			17.6710i			0.962599i	−0.876556	+	0.481299i	$0.840165\pi$
$338$		0			0
$339$	−0.662395			−0.0359763
$340$		0			0
$341$	0.241287	+	0.417921i	0.0130664	+	0.0226317i
$342$		0			0
$343$	7.06634			0.381546
$344$		0			0
$345$	−1.06631	+	0.300077i	−0.0574081	+	0.0161556i
$346$		0			0
$347$	27.3190	+	15.7726i	1.46656	+	0.846719i	0.999300	−	0.0374015i	$-0.0119080\pi$
$347$	27.3190	+	15.7726i	1.46656	+	0.846719i	0.467260	+	0.884120i	$0.345241\pi$
$348$		0			0
$349$	1.19794	−	0.691629i	0.0641241	−	0.0370221i	−0.467595	−	0.883943i	$-0.654879\pi$
$349$	1.19794	−	0.691629i	0.0641241	−	0.0370221i	0.531719	+	0.846921i	$0.321546\pi$
$350$		0			0
$351$	2.10257	−	3.96034i	0.112227	−	0.211387i
$352$		0			0
$353$	−4.84369	−	8.38952i	−0.257804	−	0.446529i	0.707849	−	0.706363i	$-0.249665\pi$
$353$	−4.84369	−	8.38952i	−0.257804	−	0.446529i	−0.965653	+	0.259834i	$0.916332\pi$
$354$		0			0
$355$	−2.87143	−	10.2035i	−0.152400	−	0.541545i
$356$		0			0
$357$	1.29594	−	2.24464i	0.0685886	−	0.118799i
$358$		0			0
$359$			33.1233i			1.74818i	0.485762	+	0.874091i	$0.338542\pi$
$359$			33.1233i			1.74818i	−0.485762	+	0.874091i	$0.661458\pi$
$360$		0			0
$361$	18.7838	+	32.5346i	0.988623	+	1.71235i
$362$		0			0
$363$		−	2.18780i		−	0.114830i
$364$		0			0
$365$	10.1958	+	9.94361i	0.533673	+	0.520472i
$366$		0			0
$367$	1.20396	−	0.695107i	0.0628462	−	0.0362843i	−0.468248	−	0.883597i	$-0.655114\pi$
$367$	1.20396	−	0.695107i	0.0628462	−	0.0362843i	0.531094	+	0.847313i	$0.321781\pi$
$368$		0			0
$369$		−	21.6068i		−	1.12481i
$370$		0			0
$371$	35.1657	+	20.3029i	1.82571	+	1.05408i
$372$		0			0
$373$	9.67280	+	5.58460i	0.500839	+	0.289159i	0.729060	−	0.684450i	$-0.239958\pi$
$373$	9.67280	+	5.58460i	0.500839	+	0.289159i	−0.228221	+	0.973609i	$0.573291\pi$
$374$		0			0
$375$	0.519043	−	2.27583i	0.0268033	−	0.117524i
$376$		0			0
$377$	−0.943318	−	26.5367i	−0.0485834	−	1.36671i
$378$		0			0
$379$	30.3827	−	17.5415i	1.56066	−	0.901045i	0.563466	−	0.826139i	$-0.309468\pi$
$379$	30.3827	−	17.5415i	1.56066	−	0.901045i	0.997191	−	0.0749058i	$-0.0238656\pi$
$380$		0			0
$381$	−0.160514	+	0.278018i	−0.00822338	+	0.0142433i
$382$		0			0
$383$	−8.27327	+	14.3297i	−0.422745	+	0.732215i	−0.996207	−	0.0870169i	$-0.972267\pi$
$383$	−8.27327	+	14.3297i	−0.422745	+	0.732215i	0.573462	+	0.819232i	$0.305600\pi$
$384$		0			0
$385$	3.89727	−	3.99612i	0.198623	−	0.203661i
$386$		0			0
$387$	20.8745	−	12.0519i	1.06111	−	0.612632i
$388$		0			0
$389$	25.6856			1.30231			0.651157	−	0.758943i	$-0.274284\pi$
$389$	25.6856			1.30231			0.651157	+	0.758943i	$0.274284\pi$
$390$		0			0
$391$	−8.51864			−0.430806
$392$		0			0
$393$	−1.16656	+	0.673515i	−0.0588453	+	0.0339743i
$394$		0			0
$395$	8.33517	+	8.12899i	0.419388	+	0.409014i
$396$		0			0
$397$	−9.90231	+	17.1513i	−0.496983	+	0.860799i	−0.999994	−	0.00348048i	$-0.998892\pi$
$397$	−9.90231	+	17.1513i	−0.496983	+	0.860799i	0.503011	+	0.864280i	$0.332225\pi$
$398$		0			0
$399$	−2.71488	+	4.70231i	−0.135914	+	0.235410i
$400$		0			0
$401$	−25.8364	+	14.9167i	−1.29021	+	0.744903i	−0.978691	−	0.205338i	$-0.934171\pi$
$401$	−25.8364	+	14.9167i	−1.29021	+	0.744903i	−0.311518	+	0.950240i	$0.600837\pi$
$402$		0			0
$403$	−1.13015	+	2.12872i	−0.0562968	+	0.106039i
$404$		0			0
$405$	4.74944	−	18.6566i	0.236001	−	0.927052i
$406$		0			0
$407$	−4.20816	−	2.42958i	−0.208591	−	0.120430i
$408$		0			0
$409$	−1.36923	−	0.790524i	−0.0677040	−	0.0390889i	0.465766	−	0.884908i	$-0.345779\pi$
$409$	−1.36923	−	0.790524i	−0.0677040	−	0.0390889i	−0.533470	+	0.845819i	$0.679112\pi$
$410$		0			0
$411$			1.92984i			0.0951921i
$412$		0			0
$413$	−14.5370	+	8.39292i	−0.715318	+	0.412989i
$414$		0			0
$415$	−21.4352	−	20.9050i	−1.05221	−	1.02619i
$416$		0			0
$417$			3.50189i			0.171488i
$418$		0			0
$419$	10.8627	+	18.8148i	0.530679	+	0.919164i	0.999359	+	0.0357956i	$0.0113965\pi$
$419$	10.8627	+	18.8148i	0.530679	+	0.919164i	−0.468680	+	0.883368i	$0.655270\pi$
$420$		0			0
$421$		−	0.356564i		−	0.0173779i	−0.999962	−	0.00868894i	$-0.997234\pi$
$421$		−	0.356564i		−	0.0173779i	0.999962	−	0.00868894i	$-0.00276581\pi$
$422$		0			0
$423$	9.46532	−	16.3944i	0.460220	−	0.797124i
$424$		0			0
$425$	8.58339	−	15.7659i	0.416355	−	0.764760i
$426$		0			0
$427$	−9.27490	−	16.0646i	−0.448844	−	0.777420i
$428$		0			0
$429$	−0.460697	+	0.288277i	−0.0222427	+	0.0139181i
$430$		0			0
$431$	−19.7959	+	11.4292i	−0.953535	+	0.550524i	−0.894177	−	0.447713i	$-0.852239\pi$
$431$	−19.7959	+	11.4292i	−0.953535	+	0.550524i	−0.0593575	+	0.998237i	$0.518905\pi$
$432$		0			0
$433$	32.0555	+	18.5073i	1.54049	+	0.889402i	0.998808	+	0.0488177i	$0.0155453\pi$
$433$	32.0555	+	18.5073i	1.54049	+	0.889402i	0.541681	+	0.840584i	$0.317788\pi$
$434$		0			0
$435$	0.931390	+	3.30965i	0.0446567	+	0.158685i
$436$		0			0
$437$	17.8458			0.853679
$438$		0			0
$439$	−1.04632	−	1.81228i	−0.0499381	−	0.0864953i	0.839976	−	0.542624i	$-0.182569\pi$
$439$	−1.04632	−	1.81228i	−0.0499381	−	0.0864953i	−0.889914	+	0.456128i	$0.849236\pi$
$440$		0			0
$441$	14.6532			0.697770
$442$		0			0
$443$		−	3.10367i		−	0.147460i	−0.997278	−	0.0737298i	$-0.976510\pi$
$443$		−	3.10367i		−	0.147460i	0.997278	−	0.0737298i	$-0.0234902\pi$
$444$		0			0
$445$	10.5194	+	2.67795i	0.498669	+	0.126947i
$446$		0			0
$447$	−0.523518			−0.0247616
$448$		0			0
$449$	−16.0733	−	9.27994i	−0.758547	−	0.437948i	0.0702265	−	0.997531i	$-0.477628\pi$
$449$	−16.0733	−	9.27994i	−0.758547	−	0.437948i	−0.828774	+	0.559583i	$0.810961\pi$
$450$		0			0
$451$	−2.63811	+	4.56934i	−0.124224	+	0.215162i
$452$		0			0
$453$	−1.15080	−	1.99324i	−0.0540692	−	0.0936507i
$454$		0			0
$455$	27.2433	+	5.91343i	1.27719	+	0.277226i
$456$		0			0
$457$	15.2853	+	26.4750i	0.715018	+	1.23845i	0.962953	+	0.269670i	$0.0869147\pi$
$457$	15.2853	+	26.4750i	0.715018	+	1.23845i	−0.247935	+	0.968777i	$0.579752\pi$
$458$		0			0
$459$	−2.23239	+	3.86661i	−0.104199	+	0.180478i
$460$		0			0
$461$	−24.8953	−	14.3733i	−1.15949	−	0.669432i	−0.208308	−	0.978063i	$-0.566796\pi$
$461$	−24.8953	−	14.3733i	−1.15949	−	0.669432i	−0.951182	+	0.308631i	$0.900129\pi$
$462$		0			0
$463$	8.47784			0.393999			0.196999	−	0.980404i	$-0.436880\pi$
$463$	8.47784			0.393999			0.196999	+	0.980404i	$0.436880\pi$
$464$		0			0
$465$	0.0769881	−	0.302422i	0.00357024	−	0.0140245i
$466$		0			0
$467$		−	37.8996i		−	1.75379i	−0.480686	−	0.876893i	$-0.659612\pi$
$467$		−	37.8996i		−	1.75379i	0.480686	−	0.876893i	$-0.340388\pi$
$468$		0			0
$469$	−53.9846			−2.49278
$470$		0			0
$471$	0.0988073	+	0.171139i	0.00455280	+	0.00788568i
$472$		0			0
$473$	−5.88596			−0.270637
$474$		0			0
$475$	−17.9814	+	33.0282i	−0.825044	+	1.51544i
$476$		0			0
$477$	−30.0666	−	17.3589i	−1.37665	−	0.794811i
$478$		0			0
$479$	16.6522	−	9.61417i	0.760860	−	0.439282i	−0.0687447	−	0.997634i	$-0.521899\pi$
$479$	16.6522	−	9.61417i	0.760860	−	0.439282i	0.829604	+	0.558352i	$0.188566\pi$
$480$		0			0
$481$	−0.862130	−	24.2528i	−0.0393097	−	1.10583i
$482$		0			0
$483$	0.856482	+	1.48347i	0.0389713	+	0.0675002i
$484$		0			0
$485$	−7.89673	+	2.22227i	−0.358572	+	0.100908i
$486$		0			0
$487$	−7.32952	+	12.6951i	−0.332132	+	0.575270i	−0.982930	−	0.183982i	$-0.941101\pi$
$487$	−7.32952	+	12.6951i	−0.332132	+	0.575270i	0.650798	+	0.759251i	$0.274435\pi$
$488$		0			0
$489$		−	3.00726i		−	0.135993i
$490$		0			0
$491$	15.2876	+	26.4789i	0.689920	+	1.19498i	0.971863	+	0.235545i	$0.0756877\pi$
$491$	15.2876	+	26.4789i	0.689920	+	1.19498i	−0.281943	+	0.959431i	$0.590979\pi$
$492$		0			0
$493$			26.4405i			1.19082i
$494$		0			0
$495$	−3.33215	+	3.41666i	−0.149769	+	0.153568i
$496$		0			0
$497$	−14.1953	+	8.19567i	−0.636747	+	0.367626i
$498$		0			0
$499$		−	0.440262i		−	0.0197088i	−0.999951	−	0.00985441i	$-0.996863\pi$
$499$		−	0.440262i		−	0.0197088i	0.999951	−	0.00985441i	$-0.00313681\pi$
$500$		0			0
$501$	−3.38273	−	1.95302i	−0.151129	−	0.0872546i
$502$		0			0
$503$	−35.6208	−	20.5657i	−1.58825	−	0.916978i	−0.993595	−	0.112999i	$-0.963954\pi$
$503$	−35.6208	−	20.5657i	−1.58825	−	0.916978i	−0.594657	−	0.803979i	$-0.702712\pi$
$504$		0			0
$505$	−5.35426	+	21.0324i	−0.238261	+	0.935930i
$506$		0			0
$507$	−2.44098	−	1.18677i	−0.108408	−	0.0527061i
$508$		0			0
$509$	22.3434	−	12.9000i	0.990355	−	0.571782i	0.0849747	−	0.996383i	$-0.472919\pi$
$509$	22.3434	−	12.9000i	0.990355	−	0.571782i	0.905380	+	0.424601i	$0.139586\pi$
$510$		0			0
$511$	11.0116	−	19.0727i	0.487126	−	0.843726i
$512$		0			0
$513$	4.67665	−	8.10020i	0.206479	−	0.357633i
$514$		0			0
$515$	8.37240	−	8.58475i	0.368932	−	0.378289i
$516$		0			0
$517$	−4.00339	+	2.31136i	−0.176069	+	0.101654i
$518$		0			0
$519$	3.69487			0.162187
$520$		0			0
$521$	26.1632			1.14623			0.573116	−	0.819474i	$-0.305734\pi$
$521$	26.1632			1.14623			0.573116	+	0.819474i	$0.305734\pi$
$522$		0			0
$523$	−18.3510	+	10.5949i	−0.802433	+	0.463285i	−0.844321	−	0.535838i	$-0.819996\pi$
$523$	−18.3510	+	10.5949i	−0.802433	+	0.463285i	0.0418883	+	0.999122i	$0.486663\pi$
$524$		0			0
$525$	−3.60853	+	0.0903947i	−0.157489	+	0.00394515i
$526$		0			0
$527$	1.19993	−	2.07834i	0.0522698	−	0.0905340i
$528$		0			0
$529$	−8.68504	+	15.0429i	−0.377610	+	0.654040i
$530$		0			0
$531$	12.4291	−	7.17592i	0.539375	−	0.311408i
$532$		0			0
$533$	−26.3344	+	0.936126i	−1.14067	+	0.0405481i
$534$		0			0
$535$	34.1318	+	8.68898i	1.47564	+	0.375657i
$536$		0			0
$537$	1.52030	+	0.877748i	0.0656060	+	0.0378776i
$538$		0			0
$539$	−3.09881	−	1.78910i	−0.133475	−	0.0770619i
$540$		0			0
$541$		−	25.1921i		−	1.08309i	−0.840670	−	0.541547i	$-0.817839\pi$
$541$		−	25.1921i		−	1.08309i	0.840670	−	0.541547i	$-0.182161\pi$
$542$		0			0
$543$	−3.00420	+	1.73447i	−0.128922	+	0.0744334i
$544$		0			0
$545$	−22.6188	+	23.1925i	−0.968883	+	0.993458i
$546$		0			0
$547$		−	22.4525i		−	0.959999i	−0.877269	−	0.479999i	$-0.840637\pi$
$547$		−	22.4525i		−	0.959999i	0.877269	−	0.479999i	$-0.159363\pi$
$548$		0			0
$549$	7.93000	+	13.7352i	0.338444	+	0.586203i
$550$		0			0
$551$		−	55.3904i		−	2.35971i
$552$		0			0
$553$	9.00211	−	15.5921i	0.382808	−	0.663044i
$554$		0			0
$555$	0.851228	+	3.02479i	0.0361326	+	0.128395i
$556$		0			0
$557$	6.72965	+	11.6561i	0.285144	+	0.493885i	0.972644	−	0.232300i	$-0.0746251\pi$
$557$	6.72965	+	11.6561i	0.285144	+	0.493885i	−0.687500	+	0.726185i	$0.741292\pi$
$558$		0			0
$559$	−15.5932	−	24.9197i	−0.659524	−	1.05399i
$560$		0			0
$561$	0.468644	−	0.270572i	0.0197862	−	0.0114235i
$562$		0			0
$563$	38.8796	+	22.4472i	1.63858	+	0.946035i	0.981323	+	0.192368i	$0.0616168\pi$
$563$	38.8796	+	22.4472i	1.63858	+	0.946035i	0.657257	+	0.753666i	$0.271717\pi$
$564$		0			0
$565$	1.92179	+	6.82897i	0.0808502	+	0.287297i
$566$		0			0
$567$	−29.7703			−1.25023
$568$		0			0
$569$	−9.39931	−	16.2801i	−0.394040	−	0.682497i	0.598938	−	0.800795i	$-0.295589\pi$
$569$	−9.39931	−	16.2801i	−0.394040	−	0.682497i	−0.992978	+	0.118298i	$0.962256\pi$
$570$		0			0
$571$	−8.79062			−0.367876			−0.183938	−	0.982938i	$-0.558885\pi$
$571$	−8.79062			−0.367876			−0.183938	+	0.982938i	$0.558885\pi$
$572$		0			0
$573$		−	3.73080i		−	0.155856i
$574$		0			0
$575$	6.18730	+	10.1225i	0.258028	+	0.422138i
$576$		0			0
$577$	−24.2751			−1.01059			−0.505293	−	0.862948i	$-0.668615\pi$
$577$	−24.2751			−1.01059			−0.505293	+	0.862948i	$0.668615\pi$
$578$		0			0
$579$	−1.30964	−	0.756122i	−0.0544269	−	0.0314234i
$580$		0			0
$581$	−23.1503	+	40.0976i	−0.960438	+	1.66353i
$582$		0			0
$583$	4.23892	+	7.34203i	0.175558	+	0.304076i
$584$		0			0
$585$	−23.2929	−	5.05596i	−0.963044	−	0.209038i
$586$		0			0
$587$	−11.5202	−	19.9535i	−0.475489	−	0.823571i	0.524117	−	0.851646i	$-0.324395\pi$
$587$	−11.5202	−	19.9535i	−0.475489	−	0.823571i	−0.999606	+	0.0280755i	$0.991062\pi$
$588$		0			0
$589$	−2.51375	+	4.35394i	−0.103577	+	0.179401i
$590$		0			0
$591$	−1.93957	−	1.11981i	−0.0797831	−	0.0460628i
$592$		0			0
$593$	−27.4174			−1.12590			−0.562949	−	0.826491i	$-0.690333\pi$
$593$	−27.4174			−1.12590			−0.562949	+	0.826491i	$0.690333\pi$
$594$		0			0
$595$	−26.9010	−	6.84825i	−1.10284	−	0.280751i
$596$		0			0
$597$		−	0.678635i		−	0.0277747i
$598$		0			0
$599$	−8.02325			−0.327821			−0.163911	−	0.986475i	$-0.552411\pi$
$599$	−8.02325			−0.327821			−0.163911	+	0.986475i	$0.552411\pi$
$600$		0			0
$601$	−5.18146	−	8.97455i	−0.211356	−	0.366080i	0.740783	−	0.671744i	$-0.234455\pi$
$601$	−5.18146	−	8.97455i	−0.211356	−	0.366080i	−0.952139	+	0.305665i	$0.901121\pi$
$602$		0			0
$603$	46.1567			1.87964
$604$		0			0
$605$	−22.5552	+	6.34742i	−0.917000	+	0.258059i
$606$		0			0
$607$	−28.1239	−	16.2374i	−1.14151	−	0.659054i	−0.194710	−	0.980861i	$-0.562376\pi$
$607$	−28.1239	−	16.2374i	−1.14151	−	0.659054i	−0.946805	+	0.321807i	$0.895710\pi$
$608$		0			0
$609$	4.60445	−	2.65838i	0.186582	−	0.107723i
$610$		0			0
$611$	−20.3916	−	10.8261i	−0.824957	−	0.437975i
$612$		0			0
$613$	17.8135	+	30.8539i	0.719482	+	1.24618i	0.961205	+	0.275833i	$0.0889538\pi$
$613$	17.8135	+	30.8539i	0.719482	+	1.24618i	−0.241724	+	0.970345i	$0.577713\pi$
$614$		0			0
$615$	3.28441	−	0.924288i	0.132440	−	0.0372709i
$616$		0			0
$617$	21.3902	−	37.0490i	0.861139	−	1.49154i	−0.00969198	−	0.999953i	$-0.503085\pi$
$617$	21.3902	−	37.0490i	0.861139	−	1.49154i	0.870831	−	0.491583i	$-0.163582\pi$
$618$		0			0
$619$			6.85102i			0.275366i	0.990476	+	0.137683i	$0.0439655\pi$
$619$			6.85102i			0.275366i	−0.990476	+	0.137683i	$0.956035\pi$
$620$		0			0
$621$	−1.47537	−	2.55542i	−0.0592047	−	0.102546i
$622$		0			0
$623$		−	16.7858i		−	0.672511i
$624$		0			0
$625$	−24.9686	+	1.25173i	−0.998746	+	0.0500691i
$626$		0			0
$627$	−0.981766	+	0.566823i	−0.0392080	+	0.0226367i
$628$		0			0
$629$			24.1648i			0.963515i
$630$		0			0
$631$	38.3170	+	22.1223i	1.52538	+	0.880677i	0.999547	+	0.0300867i	$0.00957833\pi$
$631$	38.3170	+	22.1223i	1.52538	+	0.880677i	0.525829	+	0.850590i	$0.323755\pi$
$632$		0			0
$633$	4.25412	+	2.45612i	0.169086	+	0.0976218i
$634$		0			0
$635$	3.33193	+	0.848216i	0.132224	+	0.0336604i
$636$		0			0
$637$	−0.634856	−	17.8593i	−0.0251539	−	0.707612i
$638$		0			0
$639$	12.1369	−	7.00727i	0.480130	−	0.277203i
$640$		0			0
$641$	15.5706	−	26.9691i	0.615002	−	1.06521i	−0.375382	−	0.926870i	$-0.622489\pi$
$641$	15.5706	−	26.9691i	0.615002	−	1.06521i	0.990384	−	0.138344i	$-0.0441781\pi$
$642$		0			0
$643$	−4.83855	+	8.38061i	−0.190814	+	0.330499i	−0.945520	−	0.325564i	$-0.894446\pi$
$643$	−4.83855	+	8.38061i	−0.190814	+	0.330499i	0.754706	+	0.656063i	$0.227779\pi$
$644$		0			0
$645$	2.72494	+	2.65754i	0.107295	+	0.104640i
$646$		0			0
$647$	−19.6951	+	11.3710i	−0.774296	+	0.447040i	−0.834405	−	0.551152i	$-0.814189\pi$
$647$	−19.6951	+	11.3710i	−0.774296	+	0.447040i	0.0601089	+	0.998192i	$0.480855\pi$
$648$		0			0
$649$	−3.50461			−0.137568
$650$		0			0
$651$	−0.482574			−0.0189136
$652$		0			0
$653$	−15.5155	+	8.95789i	−0.607169	+	0.350549i	−0.771857	−	0.635796i	$-0.780672\pi$
$653$	−15.5155	+	8.95789i	−0.607169	+	0.350549i	0.164688	+	0.986346i	$0.447338\pi$
$654$		0			0
$655$	10.3281	+	10.0727i	0.403554	+	0.393571i
$656$		0			0
$657$	−9.41490	+	16.3071i	−0.367310	+	0.636200i
$658$		0			0
$659$	10.2041	−	17.6740i	0.397495	−	0.688482i	−0.595921	−	0.803043i	$-0.703213\pi$
$659$	10.2041	−	17.6740i	0.397495	−	0.688482i	0.993416	+	0.114561i	$0.0365461\pi$
$660$		0			0
$661$	−35.0818	+	20.2545i	−1.36452	+	0.787808i	−0.990222	−	0.139499i	$-0.955451\pi$
$661$	−35.0818	+	20.2545i	−1.36452	+	0.787808i	−0.374302	+	0.927307i	$0.622118\pi$
$662$		0			0
$663$	2.38708	+	1.26732i	0.0927064	+	0.0492185i
$664$		0			0
$665$	56.3552	+	14.3465i	2.18536	+	0.556332i
$666$		0			0
$667$	−15.1332	−	8.73718i	−0.585962	−	0.338305i
$668$		0			0
$669$	2.27598	+	1.31404i	0.0879945	+	0.0508036i
$670$		0			0
$671$		−	3.87289i		−	0.149511i
$672$		0			0
$673$	−18.6979	+	10.7952i	−0.720749	+	0.416125i	−0.815028	−	0.579421i	$-0.803279\pi$
$673$	−18.6979	+	10.7952i	−0.720749	+	0.416125i	0.0942791	+	0.995546i	$0.469945\pi$
$674$		0			0
$675$	6.21605	−	0.155714i	0.239256	−	0.00599343i
$676$		0			0
$677$		−	36.7466i		−	1.41229i	−0.708068	−	0.706144i	$-0.750433\pi$
$677$		−	36.7466i		−	1.41229i	0.708068	−	0.706144i	$-0.249567\pi$
$678$		0			0
$679$	6.34282	+	10.9861i	0.243415	+	0.421608i
$680$		0			0
$681$		−	1.76245i		−	0.0675371i
$682$		0			0
$683$	−16.9494	+	29.3573i	−0.648552	+	1.12332i	0.334917	+	0.942248i	$0.391292\pi$
$683$	−16.9494	+	29.3573i	−0.648552	+	1.12332i	−0.983469	+	0.181077i	$0.942042\pi$
$684$		0			0
$685$	19.8957	−	5.59899i	0.760177	−	0.213927i
$686$		0			0
$687$	0.862808	+	1.49443i	0.0329182	+	0.0570160i
$688$		0			0
$689$	−19.8544	+	37.3973i	−0.756394	+	1.42472i
$690$		0			0
$691$	−40.6461	+	23.4670i	−1.54625	+	0.892727i	−0.547826	+	0.836593i	$0.684544\pi$
$691$	−40.6461	+	23.4670i	−1.54625	+	0.892727i	−0.998423	+	0.0561347i	$0.982122\pi$
$692$		0			0
$693$	6.39135	+	3.69005i	0.242787	+	0.140173i
$694$		0			0
$695$	36.1028	−	10.1599i	1.36946	−	0.385388i
$696$		0			0
$697$	26.2389			0.993869
$698$		0			0
$699$	−0.554368	−	0.960194i	−0.0209681	−	0.0363179i
$700$		0			0
$701$	28.1412			1.06288			0.531439	−	0.847096i	$-0.321651\pi$
$701$	28.1412			1.06288			0.531439	+	0.847096i	$0.321651\pi$
$702$		0			0
$703$		−	50.6231i		−	1.90929i
$704$		0			0
$705$	2.89699	+	0.737492i	0.109107	+	0.0277755i
$706$		0			0
$707$	33.5614			1.26221
$708$		0			0
$709$	26.5939	+	15.3540i	0.998753	+	0.576630i	0.907879	−	0.419232i	$-0.137701\pi$
$709$	26.5939	+	15.3540i	0.998753	+	0.576630i	0.0908741	+	0.995862i	$0.471034\pi$
$710$		0			0
$711$	−7.69677	+	13.3312i	−0.288651	+	0.499959i
$712$		0			0
$713$	0.793028	+	1.37356i	0.0296991	+	0.0514404i
$714$		0			0
$715$	4.30860	+	3.91320i	0.161133	+	0.146345i
$716$		0			0
$717$	−0.432959	−	0.749907i	−0.0161692	−	0.0280058i
$718$		0			0
$719$	24.4815	−	42.4033i	0.913007	−	1.58138i	0.103215	−	0.994659i	$-0.467087\pi$
$719$	24.4815	−	42.4033i	0.913007	−	1.58138i	0.809793	−	0.586716i	$-0.199580\pi$
$720$		0			0
$721$	−16.0590	−	9.27166i	−0.598068	−	0.345294i
$722$		0			0
$723$	0.353918			0.0131623
$724$		0			0
$725$	31.4187	−	19.2044i	1.16686	−	0.713232i
$726$		0			0
$727$		−	17.7593i		−	0.658655i	−0.944216	−	0.329328i	$-0.893178\pi$
$727$		−	17.7593i		−	0.658655i	0.944216	−	0.329328i	$-0.106822\pi$
$728$		0			0
$729$	24.6745			0.913871
$730$		0			0
$731$	14.6356	+	25.3495i	0.541316	+	0.937587i
$732$		0			0
$733$	−11.4924			−0.424481			−0.212241	−	0.977217i	$-0.568076\pi$
$733$	−11.4924			−0.424481			−0.212241	+	0.977217i	$0.568076\pi$
$734$		0			0
$735$	0.626828	+	2.22740i	0.0231209	+	0.0821589i
$736$		0			0
$737$	−9.76107	−	5.63555i	−0.359553	−	0.207588i
$738$		0			0
$739$	−44.6663	+	25.7881i	−1.64308	+	0.948631i	−0.663347	+	0.748312i	$0.730865\pi$
$739$	−44.6663	+	25.7881i	−1.64308	+	0.948631i	−0.979731	+	0.200320i	$0.935802\pi$
$740$		0			0
$741$	−5.00071	−	2.65491i	−0.183706	−	0.0975306i
$742$		0			0
$743$	6.69913	+	11.6032i	0.245767	+	0.425681i	0.962347	−	0.271824i	$-0.0876268\pi$
$743$	6.69913	+	11.6032i	0.245767	+	0.425681i	−0.716580	+	0.697505i	$0.754293\pi$
$744$		0			0
$745$	1.51887	+	5.39722i	0.0556471	+	0.197739i
$746$		0			0
$747$	19.7935	−	34.2833i	0.724205	−	1.25436i
$748$		0			0
$749$		−	54.4640i		−	1.99007i
$750$		0			0
$751$	23.7548	+	41.1445i	0.866825	+	1.50138i	0.865224	+	0.501386i	$0.167176\pi$
$751$	23.7548	+	41.1445i	0.866825	+	1.50138i	0.00160088	+	0.999999i	$0.499490\pi$
$752$		0			0
$753$			4.11993i			0.150138i
$754$		0			0
$755$	−17.2106	+	17.6471i	−0.626358	+	0.642245i
$756$		0			0
$757$	−9.27646	+	5.35576i	−0.337158	+	0.194659i	−0.659015	−	0.752130i	$-0.729027\pi$
$757$	−9.27646	+	5.35576i	−0.337158	+	0.194659i	0.321856	+	0.946789i	$0.395693\pi$
$758$		0			0
$759$			0.357639i			0.0129815i
$760$		0			0
$761$	27.4754	+	15.8629i	0.995982	+	0.575030i	0.907057	−	0.421008i	$-0.138324\pi$
$761$	27.4754	+	15.8629i	0.995982	+	0.575030i	0.0889247	+	0.996038i	$0.471657\pi$
$762$		0			0
$763$	43.3848	+	25.0482i	1.57064	+	0.906807i
$764$		0			0
$765$	23.0003	+	5.85523i	0.831577	+	0.211696i
$766$		0			0
$767$	−9.28451	−	14.8376i	−0.335244	−	0.535756i
$768$		0			0
$769$	10.0143	−	5.78174i	0.361124	−	0.208495i	−0.308450	−	0.951241i	$-0.599810\pi$
$769$	10.0143	−	5.78174i	0.361124	−	0.208495i	0.669574	+	0.742746i	$0.266477\pi$
$770$		0			0
$771$	1.23231	−	2.13442i	0.0443805	−	0.0768693i
$772$		0			0
$773$	13.5093	−	23.3988i	0.485895	−	0.841595i	−0.513973	−	0.857806i	$-0.671827\pi$
$773$	13.5093	−	23.3988i	0.485895	−	0.841595i	0.999869	+	0.0162108i	$0.00516028\pi$
$774$		0			0
$775$	−3.34119	+	0.0836977i	−0.120019	+	0.00300651i
$776$		0			0
$777$	4.20816	−	2.42958i	0.150967	−	0.0871607i
$778$		0			0
$779$	−54.9681			−1.96944
$780$		0			0
$781$	−3.42224			−0.122457
$782$		0			0
$783$	−7.93162	+	4.57932i	−0.283453	+	0.163652i
$784$		0			0
$785$	1.47770	−	1.51518i	0.0527413	−	0.0540790i
$786$		0			0
$787$	−4.20573	+	7.28453i	−0.149918	+	0.259666i	−0.931197	−	0.364516i	$-0.881234\pi$
$787$	−4.20573	+	7.28453i	−0.149918	+	0.259666i	0.781279	+	0.624182i	$0.214568\pi$
$788$		0			0
$789$	1.48281	−	2.56831i	0.0527896	−	0.0914342i
$790$		0			0
$791$	9.50061	−	5.48518i	0.337803	−	0.195031i
$792$		0			0
$793$	16.3969	−	10.2602i	0.582270	−	0.364350i
$794$		0			0
$795$	1.35252	−	5.31294i	0.0479691	−	0.188430i
$796$		0			0
$797$	3.59259	+	2.07418i	0.127256	+	0.0734714i	0.562277	−	0.826949i	$-0.309926\pi$
$797$	3.59259	+	2.07418i	0.127256	+	0.0734714i	−0.435021	+	0.900421i	$0.643259\pi$
$798$		0			0
$799$	19.9091	+	11.4945i	0.704332	+	0.406646i
$800$		0			0
$801$			14.3518i			0.507097i
$802$		0			0
$803$	3.98207	−	2.29905i	0.140524	−	0.0811316i
$804$		0			0
$805$	12.8090	−	13.1339i	0.451457	−	0.462908i
$806$		0			0
$807$			1.80857i			0.0636645i
$808$		0			0
$809$	15.9082	+	27.5538i	0.559303	+	0.968741i	0.997555	+	0.0698888i	$0.0222644\pi$
$809$	15.9082	+	27.5538i	0.559303	+	0.968741i	−0.438252	+	0.898852i	$0.644402\pi$
$810$		0			0
$811$		−	3.23592i		−	0.113628i	−0.998385	−	0.0568142i	$-0.981906\pi$
$811$		−	3.23592i		−	0.113628i	0.998385	−	0.0568142i	$-0.0180943\pi$
$812$		0			0
$813$	−0.423523	+	0.733563i	−0.0148536	+	0.0257272i
$814$		0			0
$815$	−31.0035	+	8.72489i	−1.08600	+	0.305620i
$816$		0			0
$817$	−30.6602	−	53.1050i	−1.07266	−	1.85791i
$818$		0			0
$819$	1.30940	+	36.8351i	0.0457542	+	1.28712i
$820$		0			0
$821$	3.48771	−	2.01363i	0.121722	−	0.0702762i	−0.437903	−	0.899022i	$-0.644279\pi$
$821$	3.48771	−	2.01363i	0.121722	−	0.0702762i	0.559625	+	0.828746i	$0.310945\pi$
$822$		0			0
$823$	12.0214	+	6.94054i	0.419039	+	0.241932i	0.694666	−	0.719333i	$-0.255552\pi$
$823$	12.0214	+	6.94054i	0.419039	+	0.241932i	−0.275627	+	0.961265i	$0.588886\pi$
$824$		0			0
$825$	−0.661902	−	0.360357i	−0.0230445	−	0.0125460i
$826$		0			0
$827$	3.60853			0.125481			0.0627405	−	0.998030i	$-0.480016\pi$
$827$	3.60853			0.125481			0.0627405	+	0.998030i	$0.480016\pi$
$828$		0			0
$829$	6.47420	+	11.2136i	0.224858	+	0.389466i	0.956277	−	0.292463i	$-0.0944747\pi$
$829$	6.47420	+	11.2136i	0.224858	+	0.389466i	−0.731419	+	0.681929i	$0.761141\pi$
$830$		0			0
$831$	−0.282896			−0.00981354
$832$		0			0
$833$			17.7945i			0.616544i
$834$		0			0
$835$	−10.3205	+	40.5406i	−0.357156	+	1.40297i
$836$		0			0
$837$	0.831282			0.0287333
$838$		0			0
$839$	−5.01931	−	2.89790i	−0.173286	−	0.100047i	0.410849	−	0.911704i	$-0.365233\pi$
$839$	−5.01931	−	2.89790i	−0.173286	−	0.100047i	−0.584134	+	0.811657i	$0.698566\pi$
$840$		0			0
$841$	−12.6188	+	21.8564i	−0.435131	+	0.753669i
$842$		0			0
$843$	2.12792	+	3.68567i	0.0732896	+	0.126941i
$844$		0			0
$845$	−5.15303	+	28.6085i	−0.177270	+	0.984162i
$846$		0			0
$847$	18.1168	+	31.3793i	0.622502	+	1.07821i
$848$		0			0
$849$	0.268540	−	0.465126i	0.00921628	−	0.0159631i
$850$		0			0
$851$	−13.8308	−	7.98520i	−0.474113	−	0.273729i
$852$		0			0
$853$	29.7950			1.02016			0.510080	−	0.860127i	$-0.329616\pi$
$853$	29.7950			1.02016			0.510080	+	0.860127i	$0.329616\pi$
$854$		0			0
$855$	−48.1835	−	12.2662i	−1.64784	−	0.419494i
$856$		0			0
$857$			16.5362i			0.564865i	0.959287	+	0.282433i	$0.0911413\pi$
$857$			16.5362i			0.564865i	−0.959287	+	0.282433i	$0.908859\pi$
$858$		0			0
$859$	24.1978			0.825618			0.412809	−	0.910818i	$-0.364548\pi$
$859$	24.1978			0.825618			0.412809	+	0.910818i	$0.364548\pi$
$860$		0			0
$861$	−2.63811	−	4.56934i	−0.0899066	−	0.155723i
$862$		0			0
$863$	21.2651			0.723874			0.361937	−	0.932203i	$-0.382116\pi$
$863$	21.2651			0.723874			0.361937	+	0.932203i	$0.382116\pi$
$864$		0			0
$865$	−10.7198	−	38.0923i	−0.364484	−	1.29518i
$866$		0			0
$867$	0.743215	+	0.429096i	0.0252409	+	0.0145728i
$868$		0			0
$869$	3.25538	−	1.87949i	0.110431	−	0.0637574i
$870$		0			0
$871$	−1.99976	−	56.2558i	−0.0677593	−	1.90615i
$872$		0			0
$873$	−5.42309	−	9.39307i	−0.183544	−	0.317907i
$874$		0			0
$875$	11.4013	+	36.9400i	0.385433	+	1.24880i
$876$		0			0
$877$	−1.38433	+	2.39774i	−0.0467457	+	0.0809659i	−0.888452	−	0.458970i	$-0.848218\pi$
$877$	−1.38433	+	2.39774i	−0.0467457	+	0.0809659i	0.841706	+	0.539936i	$0.181552\pi$
$878$		0			0
$879$			3.91879i			0.132178i
$880$		0			0
$881$	14.2986	+	24.7659i	0.481733	+	0.834386i	0.999780	−	0.0209661i	$-0.00667421\pi$
$881$	14.2986	+	24.7659i	0.481733	+	0.834386i	−0.518047	+	0.855352i	$0.673341\pi$
$882$		0			0
$883$		−	22.0580i		−	0.742310i	−0.928571	−	0.371155i	$-0.878962\pi$
$883$		−	22.0580i		−	0.742310i	0.928571	−	0.371155i	$-0.121038\pi$
$884$		0			0
$885$	1.62248	+	1.58235i	0.0545392	+	0.0531901i
$886$		0			0
$887$	−35.3455	+	20.4067i	−1.18679	+	0.685191i	−0.957575	−	0.288185i	$-0.906948\pi$
$887$	−35.3455	+	20.4067i	−1.18679	+	0.685191i	−0.229212	+	0.973377i	$0.573615\pi$
$888$		0			0
$889$		−	5.31676i		−	0.178318i
$890$		0			0
$891$	−5.38282	−	3.10777i	−0.180331	−	0.104114i
$892$		0			0
$893$	−41.7077	−	24.0799i	−1.39569	−	0.805804i
$894$		0			0
$895$	4.63835	−	18.2202i	0.155043	−	0.609034i
$896$		0			0
$897$	−1.51415	+	0.947466i	−0.0505561	+	0.0316350i
$898$		0			0
$899$	4.26332	−	2.46143i	0.142190	−	0.0820933i
$900$		0			0
$901$	21.0803	−	36.5122i	0.702288	−	1.21640i
$902$		0			0
$903$	2.94298	−	5.09739i	0.0979362	−	0.169630i
$904$		0			0
$905$	26.5976	+	25.9397i	0.884134	+	0.862264i
$906$		0			0
$907$	20.6530	−	11.9240i	0.685773	−	0.395931i	−0.116253	−	0.993220i	$-0.537088\pi$
$907$	20.6530	−	11.9240i	0.685773	−	0.395931i	0.802027	+	0.597288i	$0.203755\pi$
$908$		0			0
$909$	−28.6949			−0.951749
$910$		0			0
$911$	−11.2559			−0.372924			−0.186462	−	0.982462i	$-0.559702\pi$
$911$	−11.2559			−0.372924			−0.186462	+	0.982462i	$0.559702\pi$
$912$		0			0
$913$	−8.37172	+	4.83341i	−0.277063	+	0.159963i
$914$		0			0
$915$	−1.74863	+	1.79298i	−0.0578079	+	0.0592742i
$916$		0			0
$917$	11.1545	−	19.3202i	0.368355	−	0.638010i
$918$		0			0
$919$	6.81128	−	11.7975i	0.224683	−	0.389163i	−0.731541	−	0.681798i	$-0.761199\pi$
$919$	6.81128	−	11.7975i	0.224683	−	0.389163i	0.956224	+	0.292634i	$0.0945319\pi$
$920$		0			0
$921$	−0.531116	+	0.306640i	−0.0175009	+	0.0101041i
$922$		0			0
$923$	−9.06630	−	14.4889i	−0.298421	−	0.476909i
$924$		0			0
$925$	28.7146	−	17.5515i	0.944129	−	0.577090i
$926$		0			0
$927$	13.7304	+	7.92723i	0.450964	+	0.260364i
$928$		0			0
$929$	−15.4152	−	8.89998i	−0.505757	−	0.291999i	0.225331	−	0.974282i	$-0.427654\pi$
$929$	−15.4152	−	8.89998i	−0.505757	−	0.291999i	−0.731088	+	0.682283i	$0.760987\pi$
$930$		0			0
$931$		−	37.2779i		−	1.22173i
$932$		0			0
$933$	−0.747880	+	0.431788i	−0.0244845	+	0.0141361i
$934$		0			0
$935$	−4.14913	−	4.04649i	−0.135691	−	0.132334i
$936$		0			0
$937$		−	1.06467i		−	0.0347814i	−0.999849	−	0.0173907i	$-0.994464\pi$
$937$		−	1.06467i		−	0.0347814i	0.999849	−	0.0173907i	$-0.00553591\pi$
$938$		0			0
$939$	1.27566	+	2.20951i	0.0416295	+	0.0721045i
$940$		0			0
$941$		−	32.2630i		−	1.05174i	−0.850564	−	0.525871i	$-0.823739\pi$
$941$		−	32.2630i		−	1.05174i	0.850564	−	0.525871i	$-0.176261\pi$
$942$		0			0
$943$	−8.67057	+	15.0179i	−0.282352	+	0.489049i
$944$		0			0
$945$	−2.60475	−	9.25585i	−0.0847325	−	0.301093i
$946$		0			0
$947$	16.0866	+	27.8628i	0.522745	+	0.905420i	0.999650	+	0.0264656i	$0.00842525\pi$
$947$	16.0866	+	27.8628i	0.522745	+	0.905420i	−0.476905	+	0.878955i	$0.658241\pi$
$948$		0			0
$949$	20.2830	+	10.7684i	0.658414	+	0.349556i
$950$		0			0
$951$	−2.10376	+	1.21461i	−0.0682190	+	0.0393863i
$952$		0			0
$953$	−50.0839	−	28.9160i	−1.62238	−	0.936681i	−0.986282	−	0.165071i	$-0.947215\pi$
$953$	−50.0839	−	28.9160i	−1.62238	−	0.936681i	−0.636097	−	0.771609i	$-0.719452\pi$
$954$		0			0
$955$	−38.4628	+	10.8241i	−1.24463	+	0.350259i
$956$		0			0
$957$	1.11005			0.0358829
$958$		0			0
$959$	−15.9807	−	27.6794i	−0.516044	−	0.893814i
$960$		0			0
$961$	30.5532			0.985586
$962$		0			0
$963$			46.5665i			1.50058i
$964$		0			0
$965$	−3.99563	+	15.6955i	−0.128624	+	0.505256i
$966$		0			0
$967$	−41.8280			−1.34510			−0.672549	−	0.740053i	$-0.734800\pi$
$967$	−41.8280			−1.34510			−0.672549	+	0.740053i	$0.734800\pi$
$968$		0			0
$969$	4.88237	+	2.81884i	0.156844	+	0.0905540i
$970$		0			0
$971$	−2.83949	+	4.91813i	−0.0911234	+	0.157830i	−0.907984	−	0.419005i	$-0.862379\pi$
$971$	−2.83949	+	4.91813i	−0.0911234	+	0.157830i	0.816861	+	0.576835i	$0.195712\pi$
$972$		0			0
$973$	−28.9986	−	50.2270i	−0.929652	−	1.61020i
$974$		0			0
$975$	−0.227869	−	3.75700i	−0.00729765	−	0.120320i
$976$		0			0
$977$	−7.14109	−	12.3687i	−0.228464	−	0.395711i	0.728889	−	0.684632i	$-0.240037\pi$
$977$	−7.14109	−	12.3687i	−0.228464	−	0.395711i	−0.957353	+	0.288921i	$0.906704\pi$
$978$		0			0
$979$	1.75230	−	3.03508i	0.0560039	−	0.0970016i
$980$		0			0
$981$	−37.0939	−	21.4161i	−1.18432	−	0.683765i
$982$		0			0
$983$	18.7988			0.599588			0.299794	−	0.954004i	$-0.403082\pi$
$983$	18.7988			0.599588			0.299794	+	0.954004i	$0.403082\pi$
$984$		0			0
$985$	−5.91749	+	23.2449i	−0.188547	+	0.740643i
$986$		0			0
$987$		−	4.62272i		−	0.147143i
$988$		0			0
$989$	−19.3451			−0.615139
$990$		0			0
$991$	−1.14513	−	1.98342i	−0.0363762	−	0.0630053i	0.847264	−	0.531172i	$-0.178248\pi$
$991$	−1.14513	−	1.98342i	−0.0363762	−	0.0630053i	−0.883640	+	0.468166i	$0.844915\pi$
$992$		0			0
$993$	2.87723			0.0913060
$994$		0			0
$995$	−6.99641	+	1.96891i	−0.221801	+	0.0624185i
$996$		0			0
$997$	35.3308	+	20.3982i	1.11894	+	0.646018i	0.941129	−	0.338047i	$-0.109766\pi$
$997$	35.3308	+	20.3982i	1.11894	+	0.646018i	0.177807	+	0.984065i	$0.443100\pi$
$998$		0			0
$999$	−7.24897	+	4.18519i	−0.229347	+	0.132414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.z.a.49.4	✓	16
3.2	odd	2		2340.2.cr.a.829.2		16
4.3	odd	2		1040.2.df.d.49.5		16
5.2	odd	4		1300.2.y.e.101.5		16
5.3	odd	4		1300.2.y.e.101.4		16
5.4	even	2	inner	260.2.z.a.49.5	yes	16
13.2	odd	12		3380.2.c.e.2029.8		16
13.3	even	3		3380.2.d.d.1689.8		16
13.4	even	6	inner	260.2.z.a.69.5	yes	16
13.10	even	6		3380.2.d.d.1689.7		16
13.11	odd	12		3380.2.c.e.2029.7		16
15.14	odd	2		2340.2.cr.a.829.7		16
20.19	odd	2		1040.2.df.d.49.4		16
39.17	odd	6		2340.2.cr.a.1369.7		16
52.43	odd	6		1040.2.df.d.849.4		16
65.4	even	6	inner	260.2.z.a.69.4	yes	16
65.17	odd	12		1300.2.y.e.901.5		16
65.24	odd	12		3380.2.c.e.2029.9		16
65.29	even	6		3380.2.d.d.1689.9		16
65.43	odd	12		1300.2.y.e.901.4		16
65.49	even	6		3380.2.d.d.1689.10		16
65.54	odd	12		3380.2.c.e.2029.10		16
195.134	odd	6		2340.2.cr.a.1369.2		16
260.199	odd	6		1040.2.df.d.849.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.4	✓	16	1.1	even	1	trivial
260.2.z.a.49.5	yes	16	5.4	even	2	inner
260.2.z.a.69.4	yes	16	65.4	even	6	inner
260.2.z.a.69.5	yes	16	13.4	even	6	inner
1040.2.df.d.49.4		16	20.19	odd	2
1040.2.df.d.49.5		16	4.3	odd	2
1040.2.df.d.849.4		16	52.43	odd	6
1040.2.df.d.849.5		16	260.199	odd	6
1300.2.y.e.101.4		16	5.3	odd	4
1300.2.y.e.101.5		16	5.2	odd	4
1300.2.y.e.901.4		16	65.43	odd	12
1300.2.y.e.901.5		16	65.17	odd	12
2340.2.cr.a.829.2		16	3.2	odd	2
2340.2.cr.a.829.7		16	15.14	odd	2
2340.2.cr.a.1369.2		16	195.134	odd	6
2340.2.cr.a.1369.7		16	39.17	odd	6
3380.2.c.e.2029.7		16	13.11	odd	12
3380.2.c.e.2029.8		16	13.2	odd	12
3380.2.c.e.2029.9		16	65.24	odd	12
3380.2.c.e.2029.10		16	65.54	odd	12
3380.2.d.d.1689.7		16	13.10	even	6
3380.2.d.d.1689.8		16	13.3	even	3
3380.2.d.d.1689.9		16	65.29	even	6
3380.2.d.d.1689.10		16	65.49	even	6

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.180812 + 0.104392i) q^{3} +(1.60081 + 1.56122i) q^{5} +(1.72890 - 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +O(q^{10})\)	\(q+(-0.180812 + 0.104392i) q^{3} +(1.60081 + 1.56122i) q^{5} +(1.72890 - 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +(0.625212 - 0.360966i) q^{11} +(3.18457 + 1.69071i) q^{13} +(-0.452424 - 0.115174i) q^{15} +(-3.10921 - 1.79510i) q^{17} +(6.51351 + 3.76057i) q^{19} +0.721933i q^{21} +(2.05486 - 1.18637i) q^{23} +(0.125212 + 4.99843i) q^{25} -1.24360i q^{27} +(-3.68231 - 6.37795i) q^{29} +0.668447i q^{31} +(-0.0753639 + 0.130534i) q^{33} +(7.44278 - 2.09452i) q^{35} +(-3.36538 - 5.82902i) q^{37} +(-0.752305 + 0.0267426i) q^{39} +(-6.32932 + 3.65423i) q^{41} +(-7.06075 - 4.07653i) q^{43} +(-6.36355 + 1.79081i) q^{45} -6.40326 q^{47} +(-2.47820 - 4.29238i) q^{49} +0.749576 q^{51} +11.7433i q^{53} +(1.56439 + 0.398251i) q^{55} -1.57029 q^{57} +(-4.20410 - 2.42724i) q^{59} +(2.68231 - 4.64590i) q^{61} +(5.11134 + 8.85310i) q^{63} +(2.45834 + 7.67832i) q^{65} +(-7.80620 - 13.5207i) q^{67} +(-0.247695 + 0.429021i) q^{69} +(-4.10530 - 2.37019i) q^{71} +6.36914 q^{73} +(-0.544435 - 0.890705i) q^{75} -2.49630i q^{77} +5.20683 q^{79} +(-4.30479 - 7.45612i) q^{81} -13.3902 q^{83} +(-2.17472 - 7.72777i) q^{85} +(1.33161 + 0.768806i) q^{87} +(4.20410 - 2.42724i) q^{89} +(10.5687 - 6.61328i) q^{91} +(-0.0697804 - 0.120863i) q^{93} +(4.55585 + 16.1890i) q^{95} +(-1.83435 + 3.17719i) q^{97} +2.13433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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