LMFDB - Embedded newform 600.2.w.k.557.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(293,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.293"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.8
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18496 - 0.771921i) q^{2} +(1.57845 + 0.713099i) q^{3} +(0.808275 + 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 - 1.44651i) q^{7} +(0.454373 - 2.79169i) q^{8} +(1.98298 + 2.25118i) q^{9} +0.641278 q^{11} +(-0.0287228 + 3.46398i) q^{12} +(2.03304 + 2.03304i) q^{13} +(0.597468 + 2.83065i) q^{14} +(-2.69338 + 2.95731i) q^{16} +(4.37963 - 4.37963i) q^{17} +(-0.612026 - 4.19826i) q^{18} +4.93129 q^{19} +(-1.25173 - 3.31474i) q^{21} +(-0.759891 - 0.495016i) q^{22} +(-3.73619 - 3.73619i) q^{23} +(2.70796 - 4.08252i) q^{24} +(-0.839729 - 3.97842i) q^{26} +(1.52471 + 4.96742i) q^{27} +(1.47706 - 3.81541i) q^{28} +9.84421i q^{29} +5.23032 q^{31} +(5.47437 - 1.42523i) q^{32} +(1.01222 + 0.457295i) q^{33} +(-8.57043 + 1.80897i) q^{34} +(-2.51550 + 5.44722i) q^{36} +(3.44271 - 3.44271i) q^{37} +(-5.84339 - 3.80656i) q^{38} +(1.75928 + 4.65879i) q^{39} +7.20930i q^{41} +(-1.07546 + 4.89408i) q^{42} +(4.37139 + 4.37139i) q^{43} +(0.518329 + 1.17315i) q^{44} +(1.54320 + 7.31130i) q^{46} +(-4.08462 + 4.08462i) q^{47} +(-6.36021 + 2.74731i) q^{48} -2.81523i q^{49} +(10.0361 - 3.78989i) q^{51} +(-2.07598 + 5.36248i) q^{52} +(-3.83383 + 3.83383i) q^{53} +(2.02773 - 7.06317i) q^{54} +(-4.69546 + 3.38095i) q^{56} +(7.78377 + 3.51650i) q^{57} +(7.59896 - 11.6650i) q^{58} -2.50346i q^{59} -9.64270i q^{61} +(-6.19774 - 4.03740i) q^{62} +(0.387949 - 6.12474i) q^{63} +(-7.58709 - 2.53694i) q^{64} +(-0.846451 - 1.32323i) q^{66} +(2.59686 - 2.59686i) q^{67} +(11.5520 + 4.47213i) q^{68} +(-3.23310 - 8.56166i) q^{69} -16.7173i q^{71} +(7.18560 - 4.51299i) q^{72} +(-8.40725 + 8.40725i) q^{73} +(-6.73698 + 1.42198i) q^{74} +(3.98584 + 9.02128i) q^{76} +(-0.927614 - 0.927614i) q^{77} +(1.51154 - 6.87852i) q^{78} -5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(5.56501 - 8.54275i) q^{82} +(2.20075 - 2.20075i) q^{83} +(5.05222 - 4.96913i) q^{84} +(-1.80557 - 8.55430i) q^{86} +(-7.01990 + 15.5386i) q^{87} +(0.291380 - 1.79025i) q^{88} -3.96596 q^{89} -5.88160i q^{91} +(3.81511 - 9.85485i) q^{92} +(8.25578 + 3.72974i) q^{93} +(7.99313 - 1.68712i) q^{94} +(9.65732 + 1.65413i) q^{96} +(1.11334 + 1.11334i) q^{97} +(-2.17314 + 3.33595i) q^{98} +(1.27164 + 1.44363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) $ 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.18496	−	0.771921i	−0.837895	−	0.545831i
$2$	−1.18496	−	0.771921i	−0.837895	−	0.545831i
$3$	1.57845	+	0.713099i	0.911316	+	0.411708i
$3$	1.57845	+	0.713099i	0.911316	+	0.411708i
$4$	0.808275	+	1.82940i	0.404138	+	0.914698i
$5$		0			0
$5$		0			0
$6$	−1.31994	−	2.06343i	−0.538864	−	0.842392i
$7$	−1.44651	−	1.44651i	−0.546728	−	0.546728i	0.378765	−	0.925493i	$-0.376349\pi$
$7$	−1.44651	−	1.44651i	−0.546728	−	0.546728i	−0.925493	+	0.378765i	$0.876349\pi$
$8$	0.454373	−	2.79169i	0.160645	−	0.987012i
$9$	1.98298	+	2.25118i	0.660993	+	0.750392i
$10$		0			0
$11$	0.641278			0.193353			0.0966764	−	0.995316i	$-0.469179\pi$
$11$	0.641278			0.193353			0.0966764	+	0.995316i	$0.469179\pi$
$12$	−0.0287228	+	3.46398i	−0.00829157	+	0.999966i
$13$	2.03304	+	2.03304i	0.563863	+	0.563863i	0.930402	−	0.366540i	$-0.119458\pi$
$13$	2.03304	+	2.03304i	0.563863	+	0.563863i	−0.366540	+	0.930402i	$0.619458\pi$
$14$	0.597468	+	2.83065i	0.159680	+	0.756522i
$15$		0			0
$16$	−2.69338	+	2.95731i	−0.673346	+	0.739328i
$17$	4.37963	−	4.37963i	1.06222	−	1.06222i	0.0642843	−	0.997932i	$-0.479524\pi$
$17$	4.37963	−	4.37963i	1.06222	−	1.06222i	0.997932	−	0.0642843i	$-0.0204764\pi$
$18$	−0.612026	−	4.19826i	−0.144256	−	0.989540i
$19$	4.93129			1.13131			0.565657	−	0.824640i	$-0.308622\pi$
$19$	4.93129			1.13131			0.565657	+	0.824640i	$0.308622\pi$
$20$		0			0
$21$	−1.25173	−	3.31474i	−0.273150	−	0.723335i
$22$	−0.759891	−	0.495016i	−0.162009	−	0.105538i
$23$	−3.73619	−	3.73619i	−0.779050	−	0.779050i	0.200619	−	0.979669i	$-0.435705\pi$
$23$	−3.73619	−	3.73619i	−0.779050	−	0.779050i	−0.979669	+	0.200619i	$0.935705\pi$
$24$	2.70796	−	4.08252i	0.552759	−	0.833341i
$25$		0			0
$26$	−0.839729	−	3.97842i	−0.164684	−	0.780232i
$27$	1.52471	+	4.96742i	0.293431	+	0.955980i
$28$	1.47706	−	3.81541i	0.279138	−	0.721045i
$29$			9.84421i			1.82802i	0.405687	+	0.914012i	$0.367032\pi$
$29$			9.84421i			1.82802i	−0.405687	+	0.914012i	$0.632968\pi$
$30$		0			0
$31$	5.23032			0.939394			0.469697	−	0.882828i	$-0.344363\pi$
$31$	5.23032			0.939394			0.469697	+	0.882828i	$0.344363\pi$
$32$	5.47437	−	1.42523i	0.967741	−	0.251947i
$33$	1.01222	+	0.457295i	0.176205	+	0.0796049i
$34$	−8.57043	+	1.80897i	−1.46982	+	0.310236i
$35$		0			0
$36$	−2.51550	+	5.44722i	−0.419250	+	0.907871i
$37$	3.44271	−	3.44271i	0.565978	−	0.565978i	−0.365022	−	0.930999i	$-0.618938\pi$
$37$	3.44271	−	3.44271i	0.565978	−	0.565978i	0.930999	+	0.365022i	$0.118938\pi$
$38$	−5.84339	−	3.80656i	−0.947923	−	0.617506i
$39$	1.75928	+	4.65879i	0.281710	+	0.746004i
$40$		0			0
$41$			7.20930i			1.12590i	0.826490	+	0.562951i	$0.190334\pi$
$41$			7.20930i			1.12590i	−0.826490	+	0.562951i	$0.809666\pi$
$42$	−1.07546	+	4.89408i	−0.165947	+	0.755172i
$43$	4.37139	+	4.37139i	0.666630	+	0.666630i	0.956934	−	0.290304i	$-0.0937564\pi$
$43$	4.37139	+	4.37139i	0.666630	+	0.666630i	−0.290304	+	0.956934i	$0.593756\pi$
$44$	0.518329	+	1.17315i	0.0781411	+	0.176859i
$45$		0			0
$46$	1.54320	+	7.31130i	0.227533	+	1.07799i
$47$	−4.08462	+	4.08462i	−0.595803	+	0.595803i	−0.939193	−	0.343390i	$-0.888425\pi$
$47$	−4.08462	+	4.08462i	−0.595803	+	0.595803i	0.343390	+	0.939193i	$0.388425\pi$
$48$	−6.36021	+	2.74731i	−0.918018	+	0.396539i
$49$		−	2.81523i		−	0.402176i
$50$		0			0
$51$	10.0361	−	3.78989i	1.40534	−	0.530691i
$52$	−2.07598	+	5.36248i	−0.287886	+	0.743642i
$53$	−3.83383	+	3.83383i	−0.526616	+	0.526616i	−0.919562	−	0.392945i	$-0.871456\pi$
$53$	−3.83383	+	3.83383i	−0.526616	+	0.526616i	0.392945	+	0.919562i	$0.371456\pi$
$54$	2.02773	−	7.06317i	0.275939	−	0.961175i
$55$		0			0
$56$	−4.69546	+	3.38095i	−0.627457	+	0.451798i
$57$	7.78377	+	3.51650i	1.03098	+	0.465771i
$58$	7.59896	−	11.6650i	0.997792	−	1.53169i
$59$		−	2.50346i		−	0.325923i	−0.986632	−	0.162961i	$-0.947895\pi$
$59$		−	2.50346i		−	0.325923i	0.986632	−	0.162961i	$-0.0521046\pi$
$60$		0			0
$61$		−	9.64270i		−	1.23462i	−0.786720	−	0.617311i	$-0.788222\pi$
$61$		−	9.64270i		−	1.23462i	0.786720	−	0.617311i	$-0.211778\pi$
$62$	−6.19774	−	4.03740i	−0.787114	−	0.512750i
$63$	0.387949	−	6.12474i	0.0488770	−	0.771644i
$64$	−7.58709	−	2.53694i	−0.948386	−	0.317118i
$65$		0			0
$66$	−0.846451	−	1.32323i	−0.104191	−	0.162879i
$67$	2.59686	−	2.59686i	0.317257	−	0.317257i	−0.530456	−	0.847713i	$-0.677979\pi$
$67$	2.59686	−	2.59686i	0.317257	−	0.317257i	0.847713	+	0.530456i	$0.177979\pi$
$68$	11.5520	+	4.47213i	1.40089	+	0.542326i
$69$	−3.23310	−	8.56166i	−0.389220	−	1.03070i
$70$		0			0
$71$		−	16.7173i		−	1.98398i	−0.126324	−	0.991989i	$-0.540318\pi$
$71$		−	16.7173i		−	1.98398i	0.126324	−	0.991989i	$-0.459682\pi$
$72$	7.18560	−	4.51299i	0.846832	−	0.531861i
$73$	−8.40725	+	8.40725i	−0.983994	+	0.983994i	−0.999874	−	0.0158800i	$-0.994945\pi$
$73$	−8.40725	+	8.40725i	−0.983994	+	0.983994i	0.0158800	+	0.999874i	$0.494945\pi$
$74$	−6.73698	+	1.42198i	−0.783158	+	0.165302i
$75$		0			0
$76$	3.98584	+	9.02128i	0.457207	+	1.03481i
$77$	−0.927614	−	0.927614i	−0.105711	−	0.105711i
$78$	1.51154	−	6.87852i	0.171148	−	0.778839i
$79$		−	5.31759i		−	0.598275i	−0.954210	−	0.299138i	$-0.903301\pi$
$79$		−	5.31759i		−	0.598275i	0.954210	−	0.299138i	$-0.0966989\pi$
$80$		0			0
$81$	−1.13559	+	8.92807i	−0.126176	+	0.992008i
$82$	5.56501	−	8.54275i	0.614552	−	0.943389i
$83$	2.20075	−	2.20075i	0.241564	−	0.241564i	−0.575933	−	0.817497i	$-0.695361\pi$
$83$	2.20075	−	2.20075i	0.241564	−	0.241564i	0.817497	+	0.575933i	$0.195361\pi$
$84$	5.05222	−	4.96913i	0.551243	−	0.542176i
$85$		0			0
$86$	−1.80557	−	8.55430i	−0.194699	−	0.922434i
$87$	−7.01990	+	15.5386i	−0.752612	+	1.66591i
$88$	0.291380	−	1.79025i	0.0310612	−	0.190841i
$89$	−3.96596			−0.420391			−0.210195	−	0.977659i	$-0.567410\pi$
$89$	−3.96596			−0.420391			−0.210195	+	0.977659i	$0.567410\pi$
$90$		0			0
$91$		−	5.88160i		−	0.616560i
$92$	3.81511	−	9.85485i	0.397752	−	1.02744i
$93$	8.25578	+	3.72974i	0.856085	+	0.386756i
$94$	7.99313	−	1.68712i	0.824428	−	0.174013i
$95$		0			0
$96$	9.65732	+	1.65413i	0.985646	+	0.168824i
$97$	1.11334	+	1.11334i	0.113043	+	0.113043i	0.761366	−	0.648323i	$-0.224529\pi$
$97$	1.11334	+	1.11334i	0.113043	+	0.113043i	−0.648323	+	0.761366i	$0.724529\pi$
$98$	−2.17314	+	3.33595i	−0.219520	+	0.336982i
$99$	1.27164	+	1.44363i	0.127805	+	0.145090i
$100$		0			0
$101$	4.32234			0.430089			0.215045	−	0.976604i	$-0.431010\pi$
$101$	4.32234			0.430089			0.215045	+	0.976604i	$0.431010\pi$
$102$	−14.8179	−	3.25620i	−1.46719	−	0.322412i
$103$	−8.51865	+	8.51865i	−0.839368	+	0.839368i	−0.988776	−	0.149408i	$-0.952263\pi$
$103$	−8.51865	+	8.51865i	−0.839368	+	0.839368i	0.149408	+	0.988776i	$0.452263\pi$
$104$	6.59937	−	4.75185i	0.647121	−	0.465958i
$105$		0			0
$106$	7.50235	−	1.58353i	0.728693	−	0.153806i
$107$	−10.3436	−	10.3436i	−0.999957	−	0.999957i	4.33477e−5	−	1.00000i	$-0.499986\pi$
$107$	−10.3436	−	10.3436i	−0.999957	−	0.999957i	−1.00000		4.33477e-5i	$0.999986\pi$
$108$	−7.85499	+	6.80434i	−0.755847	+	0.654748i
$109$	11.4461			1.09634			0.548169	−	0.836368i	$-0.315325\pi$
$109$	11.4461			1.09634			0.548169	+	0.836368i	$0.315325\pi$
$110$		0			0
$111$	7.88912	−	2.97913i	0.748802	−	0.282767i
$112$	8.17377	−	0.381776i	0.772349	−	0.0360744i
$113$	7.28974	+	7.28974i	0.685761	+	0.685761i	0.961292	−	0.275531i	$-0.0888537\pi$
$113$	7.28974	+	7.28974i	0.685761	+	0.685761i	−0.275531	+	0.961292i	$0.588854\pi$
$114$	−6.50902	−	10.1754i	−0.609625	−	0.953011i
$115$		0			0
$116$	−18.0090	+	7.95683i	−1.67209	+	0.738773i
$117$	−0.545254	+	8.60819i	−0.0504088	+	0.795827i
$118$	−1.93247	+	2.96651i	−0.177899	+	0.273089i
$119$	−12.6703			−1.16149
$120$		0			0
$121$	−10.5888			−0.962615
$122$	−7.44340	+	11.4262i	−0.673894	+	1.03448i
$123$	−5.14094	+	11.3795i	−0.463543	+	1.02605i
$124$	4.22754	+	9.56834i	0.379644	+	0.859262i
$125$		0			0
$126$	−5.18752	+	6.95812i	−0.462141	+	0.619879i
$127$	−11.4720	−	11.4720i	−1.01797	−	1.01797i	−0.999835	−	0.0181391i	$-0.994226\pi$
$127$	−11.4720	−	11.4720i	−1.01797	−	1.01797i	−0.0181391	−	0.999835i	$-0.505774\pi$
$128$	7.03210	+	8.86282i	0.621556	+	0.783370i
$129$	3.78276	+	10.0172i	0.333054	+	0.881968i
$130$		0			0
$131$	−15.6449			−1.36690			−0.683452	−	0.729995i	$-0.739522\pi$
$131$	−15.6449			−1.36690			−0.683452	+	0.729995i	$0.739522\pi$
$132$	−0.0184193	+	2.22138i	−0.00160320	+	0.193346i
$133$	−7.13314	−	7.13314i	−0.618522	−	0.618522i
$134$	−5.08176	+	1.07261i	−0.438997	+	0.0926596i
$135$		0			0
$136$	−10.2366	−	14.2166i	−0.877780	−	1.21906i
$137$	8.94191	−	8.94191i	0.763959	−	0.763959i	−0.213077	−	0.977035i	$-0.568348\pi$
$137$	8.94191	−	8.94191i	0.763959	−	0.763959i	0.977035	+	0.213077i	$0.0683485\pi$
$138$	−2.77782	+	12.6409i	−0.236464	+	1.07607i
$139$	−1.01636			−0.0862063			−0.0431031	−	0.999071i	$-0.513724\pi$
$139$	−1.01636			−0.0862063			−0.0431031	+	0.999071i	$0.513724\pi$
$140$		0			0
$141$	−9.36009	+	3.53461i	−0.788262	+	0.297668i
$142$	−12.9044	+	19.8094i	−1.08292	+	1.66237i
$143$	1.30374	+	1.30374i	0.109024	+	0.109024i
$144$	−11.9983	−	0.198991i	−0.999862	−	0.0165826i
$145$		0			0
$146$	16.4520	−	3.47255i	1.36158	−	0.287390i
$147$	2.00754	−	4.44369i	0.165579	−	0.366510i
$148$	9.08073	+	3.51542i	0.746432	+	0.288966i
$149$		−	3.01841i		−	0.247278i	−0.992327	−	0.123639i	$-0.960544\pi$
$149$		−	3.01841i		−	0.247278i	0.992327	−	0.123639i	$-0.0394565\pi$
$150$		0			0
$151$	−7.46150			−0.607208			−0.303604	−	0.952798i	$-0.598190\pi$
$151$	−7.46150			−0.607208			−0.303604	+	0.952798i	$0.598190\pi$
$152$	2.24065	−	13.7666i	0.181740	−	1.11662i
$153$	18.5440	+	1.17460i	1.49920	+	0.0949611i
$154$	0.383143	+	1.81523i	0.0308746	+	0.146276i
$155$		0			0
$156$	−7.10080	+	6.98401i	−0.568519	+	0.559168i
$157$	−6.08638	+	6.08638i	−0.485746	+	0.485746i	−0.906961	−	0.421215i	$-0.861604\pi$
$157$	−6.08638	+	6.08638i	−0.485746	+	0.485746i	0.421215	+	0.906961i	$0.361604\pi$
$158$	−4.10476	+	6.30114i	−0.326557	+	0.501292i
$159$	−8.78538	+	3.31759i	−0.696726	+	0.263102i
$160$		0			0
$161$			10.8089i			0.851858i
$162$	8.23740	−	9.70285i	0.647191	−	0.762328i
$163$	−13.5483	−	13.5483i	−1.06119	−	1.06119i	−0.998002	−	0.0631867i	$-0.979874\pi$
$163$	−13.5483	−	13.5483i	−1.06119	−	1.06119i	−0.0631867	−	0.998002i	$-0.520126\pi$
$164$	−13.1887	+	5.82710i	−1.02986	+	0.455020i
$165$		0			0
$166$	−4.30662	+	0.909003i	−0.334258	+	0.0705523i
$167$	−8.77613	+	8.77613i	−0.679117	+	0.679117i	−0.959800	−	0.280683i	$-0.909439\pi$
$167$	−8.77613	+	8.77613i	−0.679117	+	0.679117i	0.280683	+	0.959800i	$0.409439\pi$
$168$	−9.82247	+	1.98832i	−0.757820	+	0.153402i
$169$		−	4.73353i		−	0.364118i
$170$		0			0
$171$	9.77864	+	11.1012i	0.747791	+	0.848930i
$172$	−4.46372	+	11.5303i	−0.340355	+	0.879176i
$173$	−15.2826	+	15.2826i	−1.16192	+	1.16192i	−0.177862	+	0.984056i	$0.556918\pi$
$173$	−15.2826	+	15.2826i	−1.16192	+	1.16192i	−0.984056	+	0.177862i	$0.943082\pi$
$174$	20.3129	−	12.9938i	1.53991	−	0.985057i
$175$		0			0
$176$	−1.72721	+	1.89646i	−0.130193	+	0.142951i
$177$	1.78521	−	3.95157i	0.134185	−	0.297018i
$178$	4.69951	+	3.06141i	0.352243	+	0.229462i
$179$			2.11966i			0.158431i	0.996858	+	0.0792153i	$0.0252415\pi$
$179$			2.11966i			0.158431i	−0.996858	+	0.0792153i	$0.974759\pi$
$180$		0			0
$181$			19.4392i			1.44491i	0.691420	+	0.722453i	$0.256986\pi$
$181$			19.4392i			1.44491i	−0.691420	+	0.722453i	$0.743014\pi$
$182$	−4.54013	+	6.96948i	−0.336537	+	0.516612i
$183$	6.87620	−	15.2205i	0.508303	−	1.12513i
$184$	−12.1279	+	8.73268i	−0.894083	+	0.643781i
$185$		0			0
$186$	−6.90373	−	10.7924i	−0.506206	−	0.791338i
$187$	2.80856	−	2.80856i	0.205382	−	0.205382i
$188$	−10.7739	−	4.17089i	−0.785766	−	0.304194i
$189$	4.97990	−	9.39092i	0.362235	−	0.683089i
$190$		0			0
$191$			2.66510i			0.192840i	0.995341	+	0.0964198i	$0.0307391\pi$
$191$			2.66510i			0.192840i	−0.995341	+	0.0964198i	$0.969261\pi$
$192$	−10.1667	−	9.41477i	−0.733719	−	0.679453i
$193$	−7.73743	+	7.73743i	−0.556952	+	0.556952i	−0.928439	−	0.371486i	$-0.878848\pi$
$193$	−7.73743	+	7.73743i	−0.556952	+	0.556952i	0.371486	+	0.928439i	$0.378848\pi$
$194$	−0.459857	−	2.17868i	−0.0330158	−	0.156420i
$195$		0			0
$196$	5.15018	−	2.27548i	0.367870	−	0.162535i
$197$	7.82754	+	7.82754i	0.557689	+	0.557689i	0.928649	−	0.370960i	$-0.120971\pi$
$197$	7.82754	+	7.82754i	0.557689	+	0.557689i	−0.370960	+	0.928649i	$0.620971\pi$
$198$	−0.392479	−	2.69226i	−0.0278923	−	0.191330i
$199$		−	16.8608i		−	1.19523i	−0.801783	−	0.597615i	$-0.796115\pi$
$199$		−	16.8608i		−	1.19523i	0.801783	−	0.597615i	$-0.203885\pi$
$200$		0			0
$201$	5.95082	−	2.24718i	0.419739	−	0.158504i
$202$	−5.12182	−	3.33651i	−0.360370	−	0.234756i
$203$	14.2397	−	14.2397i	0.999433	−	0.999433i
$204$	15.0452	+	15.2968i	1.05337	+	1.07099i
$205$		0			0
$206$	16.6700	−	3.51856i	1.16145	−	0.245150i
$207$	1.00204	−	15.8196i	0.0696464	−	1.09954i
$208$	−11.4881	+	0.536578i	−0.796554	+	0.0372050i
$209$	3.16233			0.218743
$210$		0			0
$211$			6.45821i			0.444602i	0.974978	+	0.222301i	$0.0713567\pi$
$211$			6.45821i			0.444602i	−0.974978	+	0.222301i	$0.928643\pi$
$212$	−10.1124	−	3.91480i	−0.694521	−	0.268870i
$213$	11.9211	−	26.3873i	0.816820	−	1.80803i
$214$	4.27235	+	20.2413i	0.292052	+	1.38367i
$215$		0			0
$216$	14.5603	−	1.99946i	0.990702	−	0.136046i
$217$	−7.56570	−	7.56570i	−0.513593	−	0.513593i
$218$	−13.5632	−	8.83549i	−0.918617	−	0.598415i
$219$	−19.2656	+	7.27518i	−1.30185	+	0.491611i
$220$		0			0
$221$	17.8079			1.19789
$222$	−11.6480	−	2.55961i	−0.781760	−	0.171790i
$223$	8.41178	−	8.41178i	0.563294	−	0.563294i	−0.366947	−	0.930242i	$-0.619597\pi$
$223$	8.41178	−	8.41178i	0.563294	−	0.563294i	0.930242	+	0.366947i	$0.119597\pi$
$224$	−9.98032	−	5.85712i	−0.666838	−	0.391345i
$225$		0			0
$226$	−3.01097	−	14.2652i	−0.200287	−	0.948905i
$227$	0.0799436	+	0.0799436i	0.00530604	+	0.00530604i	0.709755	−	0.704449i	$-0.248806\pi$
$227$	0.0799436	+	0.0799436i	0.00530604	+	0.00530604i	−0.704449	+	0.709755i	$0.748806\pi$
$228$	−0.141640	+	17.0819i	−0.00938037	+	1.13128i
$229$	−12.9730			−0.857282			−0.428641	−	0.903475i	$-0.641007\pi$
$229$	−12.9730			−0.857282			−0.428641	+	0.903475i	$0.641007\pi$
$230$		0			0
$231$	−0.802707	−	2.12567i	−0.0528142	−	0.139859i
$232$	27.4820	+	4.47295i	1.80428	+	0.293663i
$233$	−2.12983	−	2.12983i	−0.139530	−	0.139530i	0.633892	−	0.773422i	$-0.281456\pi$
$233$	−2.12983	−	2.12983i	−0.139530	−	0.139530i	−0.773422	+	0.633892i	$0.781456\pi$
$234$	7.29095	−	9.77949i	0.476624	−	0.639306i
$235$		0			0
$236$	4.57982	−	2.02348i	0.298121	−	0.131718i
$237$	3.79197	−	8.39352i	0.246315	−	0.545218i
$238$	15.0139	+	9.78050i	0.973205	+	0.633975i
$239$	16.7173			1.08135			0.540676	−	0.841231i	$-0.318168\pi$
$239$	16.7173			1.08135			0.540676	+	0.841231i	$0.318168\pi$
$240$		0			0
$241$	−4.68712			−0.301924			−0.150962	−	0.988540i	$-0.548237\pi$
$241$	−4.68712			−0.301924			−0.150962	+	0.988540i	$0.548237\pi$
$242$	12.5473	+	8.17369i	0.806571	+	0.525425i
$243$	−8.15906	+	13.2827i	−0.523404	+	0.852085i
$244$	17.6403	−	7.79396i	1.12931	−	0.498957i
$245$		0			0
$246$	14.8759	−	9.51586i	0.948452	−	0.606709i
$247$	10.0255	+	10.0255i	0.637906	+	0.637906i
$248$	2.37652	−	14.6015i	0.150909	−	0.927193i
$249$	5.04312	−	1.90441i	0.319595	−	0.120687i
$250$		0			0
$251$	−18.3364			−1.15738			−0.578691	−	0.815547i	$-0.696436\pi$
$251$	−18.3364			−1.15738			−0.578691	+	0.815547i	$0.696436\pi$
$252$	11.5181	−	4.24076i	0.725575	−	0.267143i
$253$	−2.39594	−	2.39594i	−0.150632	−	0.150632i
$254$	4.73841	+	22.4494i	0.297314	+	1.40860i
$255$		0			0
$256$	−1.49138	−	15.9303i	−0.0932115	−	0.995646i
$257$	−1.28687	+	1.28687i	−0.0802726	+	0.0802726i	−0.746103	−	0.665830i	$-0.768077\pi$
$257$	−1.28687	+	1.28687i	−0.0802726	+	0.0802726i	0.665830	+	0.746103i	$0.268077\pi$
$258$	3.25008	−	14.7900i	0.202341	−	0.920788i
$259$	−9.95980			−0.618872
$260$		0			0
$261$	−22.1611	+	19.5209i	−1.37173	+	1.20831i
$262$	18.5387	+	12.0767i	1.14532	+	0.746098i
$263$	−3.96091	−	3.96091i	−0.244240	−	0.244240i	0.574361	−	0.818602i	$-0.305250\pi$
$263$	−3.96091	−	3.96091i	−0.244240	−	0.244240i	−0.818602	+	0.574361i	$0.805250\pi$
$264$	1.73655	−	2.61803i	0.106878	−	0.161129i
$265$		0			0
$266$	2.94629	+	13.9587i	0.180648	+	0.855865i
$267$	−6.26005	−	2.82812i	−0.383109	−	0.173078i
$268$	6.84967	+	2.65171i	0.418410	+	0.161979i
$269$		−	1.81888i		−	0.110899i	−0.998461	−	0.0554497i	$-0.982341\pi$
$269$		−	1.81888i		−	0.110899i	0.998461	−	0.0554497i	$-0.0176592\pi$
$270$		0			0
$271$	7.54876			0.458555			0.229277	−	0.973361i	$-0.426364\pi$
$271$	7.54876			0.458555			0.229277	+	0.973361i	$0.426364\pi$
$272$	1.15591	+	24.7479i	0.0700875	+	1.50056i
$273$	4.19417	−	9.28379i	0.253843	−	0.561880i
$274$	−17.4983	+	3.69338i	−1.05711	+	0.223125i
$275$		0			0
$276$	13.0494	−	12.8348i	0.785483	−	0.772564i
$277$	−6.09911	+	6.09911i	−0.366460	+	0.366460i	−0.866184	−	0.499724i	$-0.833435\pi$
$277$	−6.09911	+	6.09911i	−0.366460	+	0.366460i	0.499724	+	0.866184i	$0.333435\pi$
$278$	1.20435	+	0.784548i	0.0722318	+	0.0470540i
$279$	10.3716	+	11.7744i	0.620933	+	0.704914i
$280$		0			0
$281$			4.32219i			0.257840i	0.991655	+	0.128920i	$0.0411511\pi$
$281$			4.32219i			0.257840i	−0.991655	+	0.128920i	$0.958849\pi$
$282$	13.8198	+	3.03687i	0.822957	+	0.180843i
$283$	−6.55658	−	6.55658i	−0.389748	−	0.389748i	0.484849	−	0.874598i	$-0.338874\pi$
$283$	−6.55658	−	6.55658i	−0.389748	−	0.389748i	−0.874598	+	0.484849i	$0.838874\pi$
$284$	30.5826	−	13.5122i	1.81474	−	0.801800i
$285$		0			0
$286$	−0.538500	−	2.55127i	−0.0318422	−	0.150860i
$287$	10.4283	−	10.4283i	0.615563	−	0.615563i
$288$	14.0640	+	9.49758i	0.828729	+	0.559650i
$289$		−	21.3623i		−	1.25661i
$290$		0			0
$291$	0.963426	+	2.55127i	0.0564770	+	0.149558i
$292$	−22.1756	−	8.58482i	−1.29773	−	0.502388i
$293$	3.85667	−	3.85667i	0.225309	−	0.225309i	−0.585421	−	0.810730i	$-0.699071\pi$
$293$	3.85667	−	3.85667i	0.225309	−	0.225309i	0.810730	+	0.585421i	$0.199071\pi$
$294$	−5.80904	+	3.71595i	−0.338790	+	0.216718i
$295$		0			0
$296$	−8.04670	−	11.1753i	−0.467705	−	0.649548i
$297$	0.977765	+	3.18550i	0.0567357	+	0.184841i
$298$	−2.32998	+	3.57671i	−0.134972	+	0.207193i
$299$		−	15.1916i		−	0.878555i
$300$		0			0
$301$		−	12.6465i		−	0.728932i
$302$	8.84160	+	5.75969i	0.508777	+	0.331433i
$303$	6.82258	+	3.08226i	0.391947	+	0.177071i
$304$	−13.2818	+	14.5834i	−0.761766	+	0.836413i
$305$		0			0
$306$	−21.0673	−	15.7064i	−1.20434	−	0.897875i
$307$	−3.22023	+	3.22023i	−0.183788	+	0.183788i	−0.793004	−	0.609216i	$-0.791484\pi$
$307$	−3.22023	+	3.22023i	−0.183788	+	0.183788i	0.609216	+	0.793004i	$0.291484\pi$
$308$	0.947206	−	2.44674i	0.0539721	−	0.139416i
$309$	−19.5209	+	7.37158i	−1.11050	+	0.419355i
$310$		0			0
$311$		−	12.3453i		−	0.700036i	−0.936743	−	0.350018i	$-0.886175\pi$
$311$		−	12.3453i		−	0.700036i	0.936743	−	0.350018i	$-0.113825\pi$
$312$	13.8053	−	2.79454i	0.781570	−	0.158209i
$313$	11.6983	−	11.6983i	0.661226	−	0.661226i	−0.294443	−	0.955669i	$-0.595134\pi$
$313$	11.6983	−	11.6983i	0.661226	−	0.661226i	0.955669	+	0.294443i	$0.0951341\pi$
$314$	11.9103	−	2.51393i	0.672139	−	0.141869i
$315$		0			0
$316$	9.72797	−	4.29807i	0.547241	−	0.241785i
$317$	5.15672	+	5.15672i	0.289631	+	0.289631i	0.836934	−	0.547304i	$-0.184346\pi$
$317$	5.15672	+	5.15672i	0.289631	+	0.289631i	−0.547304	+	0.836934i	$0.684346\pi$
$318$	12.9713	+	2.85041i	0.727393	+	0.159843i
$319$			6.31288i			0.353453i
$320$		0			0
$321$	−8.95082	−	23.7029i	−0.499586	−	1.32297i
$322$	8.34359	−	12.8081i	0.464970	−	0.713768i
$323$	21.5972	−	21.5972i	1.20170	−	1.20170i
$324$	−17.2508	+	5.13890i	−0.958380	+	0.285494i
$325$		0			0
$326$	5.59604	+	26.5125i	0.309936	+	1.46839i
$327$	18.0670	+	8.16221i	0.999110	+	0.451371i
$328$	20.1261	+	3.27571i	1.11128	+	0.180871i
$329$	11.8169			0.651485
$330$		0			0
$331$			14.0460i			0.772037i	0.922491	+	0.386019i	$0.126150\pi$
$331$			14.0460i			0.772037i	−0.922491	+	0.386019i	$0.873850\pi$
$332$	5.80486	+	2.24723i	0.318583	+	0.123333i
$333$	14.5770	+	0.923324i	0.798812	+	0.0505979i
$334$	17.1739	−	3.62491i	0.939713	−	0.198346i
$335$		0			0
$336$	13.1741	+	5.22610i	0.718706	+	0.285107i
$337$	10.5701	+	10.5701i	0.575791	+	0.575791i	0.933741	−	0.357950i	$-0.116524\pi$
$337$	10.5701	+	10.5701i	0.575791	+	0.575791i	−0.357950	+	0.933741i	$0.616524\pi$
$338$	−3.65391	+	5.60906i	−0.198747	+	0.305092i
$339$	6.30815	+	16.7048i	0.342612	+	0.907278i
$340$		0			0
$341$	3.35409			0.181634
$342$	−3.01808	−	20.7028i	−0.163199	−	1.11948i
$343$	−14.1978	+	14.1978i	−0.766609	+	0.766609i
$344$	14.1898	−	10.2173i	0.765063	−	0.550881i
$345$		0			0
$346$	29.9063	−	6.31237i	1.60778	−	0.339355i
$347$	20.2172	+	20.2172i	1.08532	+	1.08532i	0.996004	+	0.0893127i	$0.0284671\pi$
$347$	20.2172	+	20.2172i	1.08532	+	1.08532i	0.0893127	+	0.996004i	$0.471533\pi$
$348$	−34.1002	−	0.282754i	−1.82796	−	0.0151572i
$349$	−0.603017			−0.0322788			−0.0161394	−	0.999870i	$-0.505138\pi$
$349$	−0.603017			−0.0322788			−0.0161394	+	0.999870i	$0.505138\pi$
$350$		0			0
$351$	−6.99915	+	13.1987i	−0.373587	+	0.704496i
$352$	3.51060	−	0.913967i	0.187115	−	0.0487146i
$353$	−19.6483	−	19.6483i	−1.04578	−	1.04578i	−0.998901	−	0.0468748i	$-0.985074\pi$
$353$	−19.6483	−	19.6483i	−1.04578	−	1.04578i	−0.0468748	−	0.998901i	$-0.514926\pi$
$354$	−5.16572	+	3.30442i	−0.274555	+	0.175628i
$355$		0			0
$356$	−3.20559	−	7.25531i	−0.169896	−	0.384531i
$357$	−19.9994	−	9.03520i	−1.05848	−	0.478194i
$358$	1.63621	−	2.51171i	0.0864763	−	0.132748i
$359$	12.6703			0.668714			0.334357	−	0.942446i	$-0.391481\pi$
$359$	12.6703			0.668714			0.334357	+	0.942446i	$0.391481\pi$
$360$		0			0
$361$	5.31759			0.279873
$362$	15.0056	−	23.0348i	0.788674	−	1.21068i
$363$	−16.7138	−	7.55084i	−0.877246	−	0.396316i
$364$	10.7598	−	4.75395i	0.563966	−	0.249175i
$365$		0			0
$366$	−19.8971	+	12.7278i	−1.04004	+	0.665293i
$367$	−2.17316	−	2.17316i	−0.113438	−	0.113438i	0.648109	−	0.761547i	$-0.275560\pi$
$367$	−2.17316	−	2.17316i	−0.113438	−	0.113438i	−0.761547	+	0.648109i	$0.775560\pi$
$368$	21.1121	−	0.986092i	1.10054	−	0.0514036i
$369$	−16.2294	+	14.2959i	−0.844868	+	0.744214i
$370$		0			0
$371$	11.0913			0.575832
$372$	−0.150230	+	18.1178i	−0.00778905	+	0.939362i
$373$	−19.7420	−	19.7420i	−1.02220	−	1.02220i	−0.999748	−	0.0224556i	$-0.992852\pi$
$373$	−19.7420	−	19.7420i	−1.02220	−	1.02220i	−0.0224556	−	0.999748i	$-0.507148\pi$
$374$	−5.49603	+	1.16005i	−0.284193	+	0.0599849i
$375$		0			0
$376$	9.54706	+	13.2589i	0.492352	+	0.683778i
$377$	−20.0136	+	20.0136i	−1.03075	+	1.03075i
$378$	−13.1500	+	7.28380i	−0.676365	+	0.374638i
$379$	8.76740			0.450351			0.225176	−	0.974318i	$-0.427704\pi$
$379$	8.76740			0.450351			0.225176	+	0.974318i	$0.427704\pi$
$380$		0			0
$381$	−9.92724	−	26.2886i	−0.508588	−	1.34680i
$382$	2.05724	−	3.15804i	0.105258	−	0.161579i
$383$	16.7382	+	16.7382i	0.855284	+	0.855284i	0.990778	−	0.135495i	$-0.0432623\pi$
$383$	16.7382	+	16.7382i	0.855284	+	0.855284i	−0.135495	+	0.990778i	$0.543262\pi$
$384$	4.77972	+	19.0041i	0.243914	+	0.969797i
$385$		0			0
$386$	15.1413	−	3.19588i	0.770670	−	0.162666i
$387$	−1.17239	+	18.5091i	−0.0595961	+	0.940872i
$388$	−1.13686	+	2.93663i	−0.0577152	+	0.149085i
$389$			20.9924i			1.06435i	0.846633	+	0.532177i	$0.178626\pi$
$389$			20.9924i			1.06435i	−0.846633	+	0.532177i	$0.821374\pi$
$390$		0			0
$391$	−32.7263			−1.65504
$392$	−7.85926	−	1.27917i	−0.396953	−	0.0646077i
$393$	−24.6947	−	11.1564i	−1.24568	−	0.562765i
$394$	−3.23310	−	15.3176i	−0.162881	−	0.771689i
$395$		0			0
$396$	−1.61314	+	3.49319i	−0.0810631	+	0.175539i
$397$	22.7486	−	22.7486i	1.14172	−	1.14172i	0.153584	−	0.988136i	$-0.450918\pi$
$397$	22.7486	−	22.7486i	1.14172	−	1.14172i	0.988136	−	0.153584i	$-0.0490815\pi$
$398$	−13.0152	+	19.9794i	−0.652393	+	1.00148i
$399$	−6.17264	−	16.3459i	−0.309018	−	0.818319i
$400$		0			0
$401$		−	24.2516i		−	1.21107i	−0.795819	−	0.605535i	$-0.792959\pi$
$401$		−	24.2516i		−	1.21107i	0.795819	−	0.605535i	$-0.207041\pi$
$402$	−8.78615	−	1.93074i	−0.438213	−	0.0962964i
$403$	10.6334	+	10.6334i	0.529689	+	0.529689i
$404$	3.49364	+	7.90728i	0.173815	+	0.393402i
$405$		0			0
$406$	−27.8655	+	5.88160i	−1.38294	+	0.291899i
$407$	2.20773	−	2.20773i	0.109433	−	0.109433i
$408$	−6.02007	−	29.7398i	−0.298038	−	1.47234i
$409$			24.0958i			1.19146i	0.803184	+	0.595731i	$0.203137\pi$
$409$			24.0958i			1.19146i	−0.803184	+	0.595731i	$0.796863\pi$
$410$		0			0
$411$	20.4908	−	7.73784i	1.01074	−	0.381680i
$412$	−22.4694	−	8.69857i	−1.10699	−	0.428548i
$413$	−3.62127	+	3.62127i	−0.178191	+	0.178191i
$414$	−13.3989	+	17.9722i	−0.658519	+	0.883284i
$415$		0			0
$416$	14.0271	+	8.23206i	0.687737	+	0.403610i
$417$	−1.60426	−	0.724763i	−0.0785611	−	0.0354918i
$418$	−3.74724	−	2.44107i	−0.183284	−	0.119397i
$419$		−	39.9565i		−	1.95200i	−0.217767	−	0.976001i	$-0.569877\pi$
$419$		−	39.9565i		−	1.95200i	0.217767	−	0.976001i	$-0.430123\pi$
$420$		0			0
$421$			27.1153i			1.32152i	0.750599	+	0.660758i	$0.229765\pi$
$421$			27.1153i			1.32152i	−0.750599	+	0.660758i	$0.770235\pi$
$422$	4.98523	−	7.65274i	0.242677	−	0.372530i
$423$	−17.2949	−	1.09548i	−0.840907	−	0.0532642i
$424$	8.96087	+	12.4448i	0.435178	+	0.604375i
$425$		0			0
$426$	−34.4950	+	22.0659i	−1.67129	+	1.06910i
$427$	−13.9482	+	13.9482i	−0.675002	+	0.675002i
$428$	10.5621	−	27.2831i	0.510538	−	1.31878i
$429$	1.12819	+	2.98758i	0.0544694	+	0.144242i
$430$		0			0
$431$			30.9739i			1.49196i	0.665969	+	0.745979i	$0.268018\pi$
$431$			30.9739i			1.49196i	−0.665969	+	0.745979i	$0.731982\pi$
$432$	−18.7968	−	8.87011i	−0.904363	−	0.426763i
$433$	8.18096	−	8.18096i	0.393152	−	0.393152i	−0.482658	−	0.875809i	$-0.660328\pi$
$433$	8.18096	−	8.18096i	0.393152	−	0.393152i	0.875809	+	0.482658i	$0.160328\pi$
$434$	3.12495	+	14.8052i	0.150002	+	0.710673i
$435$		0			0
$436$	9.25160	+	20.9395i	0.443071	+	1.00282i
$437$	−18.4242	−	18.4242i	−0.881351	−	0.881351i
$438$	28.4449	+	6.25069i	1.35915	+	0.298670i
$439$			9.63432i			0.459821i	0.973212	+	0.229910i	$0.0738433\pi$
$439$			9.63432i			0.459821i	−0.973212	+	0.229910i	$0.926157\pi$
$440$		0			0
$441$	6.33759	−	5.58255i	0.301790	−	0.265836i
$442$	−21.1017	−	13.7463i	−1.00370	−	0.653844i
$443$	−5.86218	+	5.86218i	−0.278521	+	0.278521i	−0.832518	−	0.553998i	$-0.813102\pi$
$443$	−5.86218	+	5.86218i	−0.278521	+	0.278521i	0.553998	+	0.832518i	$0.313102\pi$
$444$	11.8266	+	12.0244i	0.561265	+	0.570651i
$445$		0			0
$446$	−16.4609	+	3.47442i	−0.779445	+	0.164518i
$447$	2.15243	−	4.76440i	0.101806	−	0.225348i
$448$	7.30508	+	14.6445i	0.345132	+	0.691887i
$449$	−6.40566			−0.302302			−0.151151	−	0.988511i	$-0.548298\pi$
$449$	−6.40566			−0.302302			−0.151151	+	0.988511i	$0.548298\pi$
$450$		0			0
$451$			4.62317i			0.217696i
$452$	−7.44371	+	19.2279i	−0.350122	+	0.904406i
$453$	−11.7776	−	5.32079i	−0.553358	−	0.249993i
$454$	−0.0330201	−	0.156440i	−0.00154971	−	0.00734211i
$455$		0			0
$456$	13.3537	−	20.1321i	0.625345	−	0.942771i
$457$	−16.7031	−	16.7031i	−0.781338	−	0.781338i	0.198719	−	0.980057i	$-0.436322\pi$
$457$	−16.7031	−	16.7031i	−0.781338	−	0.781338i	−0.980057	+	0.198719i	$0.936322\pi$
$458$	15.3726	+	10.0142i	0.718313	+	0.467931i
$459$	28.4331	+	15.0778i	1.32714	+	0.703770i
$460$		0			0
$461$	35.5078			1.65376			0.826882	−	0.562376i	$-0.190113\pi$
$461$	35.5078			1.65376			0.826882	+	0.562376i	$0.190113\pi$
$462$	−0.689670	+	3.13847i	−0.0320864	+	0.146015i
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	−0.441776	−	0.897126i	$-0.645651\pi$
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	0.897126	+	0.441776i	$0.145651\pi$
$464$	−29.1124	−	26.5142i	−1.35151	−	1.23089i
$465$		0			0
$466$	0.879707	+	4.16782i	0.0407517	+	0.193071i
$467$	−8.06737	−	8.06737i	−0.373313	−	0.373313i	0.495369	−	0.868683i	$-0.335033\pi$
$467$	−8.06737	−	8.06737i	−0.373313	−	0.373313i	−0.868683	+	0.495369i	$0.835033\pi$
$468$	−16.1885	+	5.96030i	−0.748314	+	0.275515i
$469$	−7.51276			−0.346907
$470$		0			0
$471$	−13.9472	+	5.26682i	−0.642653	+	0.242682i
$472$	−6.98889	−	1.13751i	−0.321690	−	0.0523579i
$473$	2.80328	+	2.80328i	0.128895	+	0.128895i
$474$	−10.9725	+	7.01891i	−0.503982	+	0.322389i
$475$		0			0
$476$	−10.2411	−	23.1791i	−0.469401	−	1.06241i
$477$	−16.2330	−	1.02822i	−0.743258	−	0.0470790i
$478$	−19.8094	−	12.9044i	−0.906060	−	0.590235i
$479$	4.04697			0.184911			0.0924553	−	0.995717i	$-0.470528\pi$
$479$	4.04697			0.184911			0.0924553	+	0.995717i	$0.470528\pi$
$480$		0			0
$481$	13.9983			0.638267
$482$	5.55406	+	3.61809i	0.252981	+	0.164799i
$483$	−7.70779	+	17.0612i	−0.350717	+	0.776312i
$484$	−8.55863	−	19.3710i	−0.389029	−	0.880502i
$485$		0			0
$486$	19.9214	−	9.44134i	0.903652	−	0.428268i
$487$	−6.28516	−	6.28516i	−0.284808	−	0.284808i	0.550215	−	0.835023i	$-0.314546\pi$
$487$	−6.28516	−	6.28516i	−0.284808	−	0.284808i	−0.835023	+	0.550215i	$0.814546\pi$
$488$	−26.9194	−	4.38139i	−1.21859	−	0.198336i
$489$	−11.7240	−	31.0466i	−0.530178	−	1.40398i
$490$		0			0
$491$	−25.1486			−1.13494			−0.567471	−	0.823393i	$-0.692078\pi$
$491$	−25.1486			−1.13494			−0.567471	+	0.823393i	$0.692078\pi$
$492$	−24.9729	−	0.207071i	−1.12586	−	0.00933550i
$493$	43.1140	+	43.1140i	1.94176	+	1.94176i
$494$	−4.14094	−	19.6187i	−0.186310	−	0.882688i
$495$		0			0
$496$	−14.0873	+	15.4677i	−0.632537	+	0.694520i
$497$	−24.1817	+	24.1817i	−1.08470	+	1.08470i
$498$	−7.44597	−	1.63623i	−0.333662	−	0.0733214i
$499$	4.01216			0.179609			0.0898044	−	0.995959i	$-0.471376\pi$
$499$	4.01216			0.179609			0.0898044	+	0.995959i	$0.471376\pi$
$500$		0			0
$501$	−20.1109	+	7.59439i	−0.898488	+	0.339292i
$502$	21.7279	+	14.1542i	0.969765	+	0.631734i
$503$	13.7823	+	13.7823i	0.614523	+	0.614523i	0.944121	−	0.329598i	$-0.106913\pi$
$503$	13.7823	+	13.7823i	0.614523	+	0.614523i	−0.329598	+	0.944121i	$0.606913\pi$
$504$	−16.9221	−	3.86595i	−0.753770	−	0.172203i
$505$		0			0
$506$	0.989624	+	4.68858i	0.0439942	+	0.208433i
$507$	3.37548	−	7.47162i	0.149910	−	0.331826i
$508$	11.7143	−	30.2593i	0.519738	−	1.34254i
$509$			10.5288i			0.466680i	0.972395	+	0.233340i	$0.0749656\pi$
$509$			10.5288i			0.466680i	−0.972395	+	0.233340i	$0.925034\pi$
$510$		0			0
$511$	24.3223			1.07595
$512$	−10.5297	+	20.0281i	−0.465353	+	0.885125i
$513$	7.51879	+	24.4958i	0.331963	+	1.08151i
$514$	2.51825	−	0.531531i	0.111075	−	0.0234448i
$515$		0			0
$516$	−15.2680	+	15.0169i	−0.672135	+	0.661080i
$517$	−2.61938	+	2.61938i	−0.115200	+	0.115200i
$518$	11.8020	+	7.68818i	0.518550	+	0.337799i
$519$	−35.0208	+	13.2248i	−1.53724	+	0.580503i
$520$		0			0
$521$		−	32.5500i		−	1.42604i	−0.701144	−	0.713020i	$-0.747327\pi$
$521$		−	32.5500i		−	1.42604i	0.701144	−	0.713020i	$-0.252673\pi$
$522$	41.3286	−	6.02492i	1.80890	−	0.263703i
$523$	9.90568	+	9.90568i	0.433145	+	0.433145i	0.889697	−	0.456552i	$-0.150916\pi$
$523$	9.90568	+	9.90568i	0.433145	+	0.433145i	−0.456552	+	0.889697i	$0.650916\pi$
$524$	−12.6454	−	28.6208i	−0.552417	−	1.25030i
$525$		0			0
$526$	1.63602	+	7.75105i	0.0713340	+	0.337962i
$527$	22.9069	−	22.9069i	0.997839	−	0.997839i
$528$	−4.07867	+	1.76179i	−0.177501	+	0.0766720i
$529$			4.91829i			0.213839i
$530$		0			0
$531$	5.63573	−	4.96431i	0.244570	−	0.215433i
$532$	7.28380	−	18.8149i	0.315793	−	0.815729i
$533$	−14.6568	+	14.6568i	−0.634855	+	0.634855i
$534$	5.23484	+	8.18348i	0.226534	+	0.354134i
$535$		0			0
$536$	−6.06969	−	8.42958i	−0.262171	−	0.364102i
$537$	−1.51153	+	3.34576i	−0.0652271	+	0.144380i
$538$	−1.40404	+	2.15531i	−0.0605322	+	0.0929220i
$539$		−	1.80535i		−	0.0777619i
$540$		0			0
$541$		−	44.0216i		−	1.89264i	−0.323234	−	0.946319i	$-0.604770\pi$
$541$		−	44.0216i		−	1.89264i	0.323234	−	0.946319i	$-0.395230\pi$
$542$	−8.94500	−	5.82705i	−0.384221	−	0.250293i
$543$	−13.8621	+	30.6838i	−0.594880	+	1.31677i
$544$	17.7337	−	30.2177i	0.760328	−	1.29557i
$545$		0			0
$546$	−12.1363	+	7.76338i	−0.519385	+	0.332242i
$547$	5.74698	−	5.74698i	0.245723	−	0.245723i	−0.573490	−	0.819213i	$-0.694411\pi$
$547$	5.74698	−	5.74698i	0.245723	−	0.245723i	0.819213	+	0.573490i	$0.194411\pi$
$548$	23.5858	+	9.13077i	1.00754	+	0.390047i
$549$	21.7074	−	19.1213i	0.926450	−	0.816076i
$550$		0			0
$551$			48.5446i			2.06807i
$552$	−25.3705	+	5.13563i	−1.07984	+	0.218587i
$553$	−7.69193	+	7.69193i	−0.327094	+	0.327094i
$554$	11.9352	−	2.51919i	0.507080	−	0.107030i
$555$		0			0
$556$	−0.821496	−	1.85932i	−0.0348392	−	0.0788527i
$557$	24.0378	+	24.0378i	1.01851	+	1.01851i	0.999825	+	0.0186883i	$0.00594902\pi$
$557$	24.0378	+	24.0378i	1.01851	+	1.01851i	0.0186883	+	0.999825i	$0.494051\pi$
$558$	−3.20110	−	21.9583i	−0.135513	−	0.929568i
$559$			17.7744i			0.751776i
$560$		0			0
$561$	6.43594	−	2.43038i	0.271726	−	0.102611i
$562$	3.33639	−	5.12164i	0.140737	−	0.216043i
$563$	−14.5105	+	14.5105i	−0.611544	+	0.611544i	−0.943348	−	0.331805i	$-0.892343\pi$
$563$	−14.5105	+	14.5105i	−0.611544	+	0.611544i	0.331805	+	0.943348i	$0.392343\pi$
$564$	−14.0317	−	14.2664i	−0.590842	−	0.600723i
$565$		0			0
$566$	2.70814	+	12.8305i	0.113832	+	0.539305i
$567$	14.5572	−	11.2719i	0.611343	−	0.473375i
$568$	−46.6695	−	7.59590i	−1.95821	−	0.318717i
$569$	−31.0050			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$569$	−31.0050			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$570$		0			0
$571$		−	33.0629i		−	1.38364i	−0.722070	−	0.691820i	$-0.756809\pi$
$571$		−	33.0629i		−	1.38364i	0.722070	−	0.691820i	$-0.243191\pi$
$572$	−1.33128	+	3.43884i	−0.0556636	+	0.143785i
$573$	−1.90048	+	4.20671i	−0.0793936	+	0.175738i
$574$	−20.4070	+	4.30732i	−0.851771	+	0.179784i
$575$		0			0
$576$	−9.33394	−	22.1106i	−0.388914	−	0.921274i
$577$	−17.5957	−	17.5957i	−0.732519	−	0.732519i	0.238599	−	0.971118i	$-0.423312\pi$
$577$	−17.5957	−	17.5957i	−0.732519	−	0.732519i	−0.971118	+	0.238599i	$0.923312\pi$
$578$	−16.4900	+	25.3135i	−0.685894	+	1.05290i
$579$	−17.7307	+	6.69556i	−0.736861	+	0.278258i
$580$		0			0
$581$	−6.36681			−0.264140
$582$	0.827757	−	3.76685i	0.0343116	−	0.156141i
$583$	−2.45855	+	2.45855i	−0.101823	+	0.101823i
$584$	19.6504	+	27.2905i	0.813140	+	1.12929i
$585$		0			0
$586$	−7.54706	+	1.59297i	−0.311766	+	0.0658048i
$587$	6.48696	+	6.48696i	0.267746	+	0.267746i	0.828191	−	0.560446i	$-0.189370\pi$
$587$	6.48696	+	6.48696i	0.267746	+	0.267746i	−0.560446	+	0.828191i	$0.689370\pi$
$588$	9.75192	+	0.0808615i	0.402162	+	0.00333467i
$589$	25.7922			1.06275
$590$		0			0
$591$	6.77353	+	17.9372i	0.278626	+	0.737836i
$592$	0.908632	+	19.4537i	0.0373445	+	0.799542i
$593$	2.17189	+	2.17189i	0.0891890	+	0.0891890i	0.750294	−	0.661105i	$-0.229912\pi$
$593$	2.17189	+	2.17189i	0.0891890	+	0.0891890i	−0.661105	+	0.750294i	$0.729912\pi$
$594$	1.30034	−	4.52946i	0.0533535	−	0.185846i
$595$		0			0
$596$	5.52187	−	2.43971i	0.226185	−	0.0999343i
$597$	12.0234	−	26.6138i	0.492086	−	1.08923i
$598$	−11.7267	+	18.0015i	−0.479542	+	0.736137i
$599$	7.56553			0.309119			0.154560	−	0.987983i	$-0.450604\pi$
$599$	7.56553			0.309119			0.154560	+	0.987983i	$0.450604\pi$
$600$		0			0
$601$	29.2389			1.19268			0.596339	−	0.802732i	$-0.296621\pi$
$601$	29.2389			1.19268			0.596339	+	0.802732i	$0.296621\pi$
$602$	−9.76209	+	14.9856i	−0.397873	+	0.610768i
$603$	10.9955	+	0.696471i	0.447772	+	0.0283625i
$604$	−6.03095	−	13.6500i	−0.245396	−	0.555412i
$605$		0			0
$606$	−5.70525	−	8.91886i	−0.231760	−	0.362304i
$607$	28.6094	+	28.6094i	1.16122	+	1.16122i	0.984209	+	0.177009i	$0.0566421\pi$
$607$	28.6094	+	28.6094i	1.16122	+	1.16122i	0.177009	+	0.984209i	$0.443358\pi$
$608$	26.9957	−	7.02820i	1.09482	−	0.285031i
$609$	32.6310	−	12.3223i	1.32227	−	0.499324i
$610$		0			0
$611$	−16.6084			−0.671902
$612$	12.8399	+	34.8738i	0.519021	+	1.40969i
$613$	−9.80228	−	9.80228i	−0.395910	−	0.395910i	0.480878	−	0.876788i	$-0.340318\pi$
$613$	−9.80228	−	9.80228i	−0.395910	−	0.395910i	−0.876788	+	0.480878i	$0.840318\pi$
$614$	6.30161	−	1.33009i	0.254312	−	0.0536780i
$615$		0			0
$616$	−3.01110	+	2.16813i	−0.121321	+	0.0873564i
$617$	−6.03941	+	6.03941i	−0.243138	+	0.243138i	−0.818147	−	0.575009i	$-0.804998\pi$
$617$	−6.03941	+	6.03941i	−0.243138	+	0.243138i	0.575009	+	0.818147i	$0.304998\pi$
$618$	28.8218	+	6.33352i	1.15938	+	0.254772i
$619$	16.8314			0.676509			0.338255	−	0.941055i	$-0.390163\pi$
$619$	16.8314			0.676509			0.338255	+	0.941055i	$0.390163\pi$
$620$		0			0
$621$	12.8626	−	24.2559i	0.516159	−	0.973354i
$622$	−9.52958	+	14.6287i	−0.382101	+	0.586557i
$623$	5.73679	+	5.73679i	0.229840	+	0.229840i
$624$	−18.5159	−	7.34517i	−0.741230	−	0.294042i
$625$		0			0
$626$	−22.8922	+	4.83188i	−0.914956	+	0.193121i
$627$	4.99156	+	2.25505i	0.199344	+	0.0900582i
$628$	−16.0539	−	6.21493i	−0.640619	−	0.248003i
$629$		−	30.1556i		−	1.20238i
$630$		0			0
$631$	20.4913			0.815744			0.407872	−	0.913039i	$-0.366271\pi$
$631$	20.4913			0.815744			0.407872	+	0.913039i	$0.366271\pi$
$632$	−14.8451	−	2.41617i	−0.590505	−	0.0961101i
$633$	−4.60535	+	10.1939i	−0.183046	+	0.405173i
$634$	−2.12994	−	10.0911i	−0.0845909	−	0.400769i
$635$		0			0
$636$	−13.1702	−	13.3904i	−0.522232	−	0.530965i
$637$	5.72347	−	5.72347i	0.226772	−	0.226772i
$638$	4.87305	−	7.48053i	0.192926	−	0.296157i
$639$	37.6336	−	33.1500i	1.48876	−	1.31140i
$640$		0			0
$641$			25.3407i			1.00090i	0.865767	+	0.500448i	$0.166831\pi$
$641$			25.3407i			1.00090i	−0.865767	+	0.500448i	$0.833169\pi$
$642$	−7.69037	+	34.9964i	−0.303515	+	1.38120i
$643$	16.2516	+	16.2516i	0.640899	+	0.640899i	0.950776	−	0.309878i	$-0.100288\pi$
$643$	16.2516	+	16.2516i	0.640899	+	0.640899i	−0.309878	+	0.950776i	$0.600288\pi$
$644$	−19.7737	+	8.73654i	−0.779193	+	0.344268i
$645$		0			0
$646$	−42.2632	+	8.92055i	−1.66282	+	0.350974i
$647$	3.30434	−	3.30434i	0.129907	−	0.129907i	−0.639164	−	0.769071i	$-0.720719\pi$
$647$	3.30434	−	3.30434i	0.129907	−	0.129907i	0.769071	+	0.639164i	$0.220719\pi$
$648$	24.4084	+	7.22689i	0.958854	+	0.283899i
$649$		−	1.60541i		−	0.0630180i
$650$		0			0
$651$	−6.54695	−	17.3371i	−0.256595	−	0.679496i
$652$	13.8345	−	35.7361i	0.541801	−	1.39953i
$653$	−2.00144	+	2.00144i	−0.0783225	+	0.0783225i	−0.745183	−	0.666860i	$-0.767638\pi$
$653$	−2.00144	+	2.00144i	−0.0783225	+	0.0783225i	0.666860	+	0.745183i	$0.267638\pi$
$654$	−15.1082	−	23.6183i	−0.590778	−	0.923547i
$655$		0			0
$656$	−21.3201	−	19.4174i	−0.832411	−	0.758122i
$657$	−35.5976	−	2.25480i	−1.38879	−	0.0879681i
$658$	−14.0025	−	9.12169i	−0.545876	−	0.355600i
$659$			14.5552i			0.566989i	0.958974	+	0.283495i	$0.0914938\pi$
$659$			14.5552i			0.566989i	−0.958974	+	0.283495i	$0.908506\pi$
$660$		0			0
$661$			10.7204i			0.416977i	0.978025	+	0.208488i	$0.0668544\pi$
$661$			10.7204i			0.416977i	−0.978025	+	0.208488i	$0.933146\pi$
$662$	10.8424	−	16.6440i	0.421402	−	0.646887i
$663$	28.1088	+	12.6988i	1.09165	+	0.493180i
$664$	−5.14386	−	7.14379i	−0.199620	−	0.277233i
$665$		0			0
$666$	−16.5604	−	12.3464i	−0.641703	−	0.478412i
$667$	36.7799	−	36.7799i	1.42412	−	1.42412i
$668$	−23.1486	−	8.96149i	−0.895644	−	0.346731i
$669$	19.2760	−	7.27910i	0.745252	−	0.281426i
$670$		0			0
$671$		−	6.18365i		−	0.238717i
$672$	−11.5767	−	16.3621i	−0.446580	−	0.631181i
$673$	12.2384	−	12.2384i	0.471755	−	0.471755i	−0.430727	−	0.902482i	$-0.641743\pi$
$673$	12.2384	−	12.2384i	0.471755	−	0.471755i	0.902482	+	0.430727i	$0.141743\pi$
$674$	−4.36590	−	20.6845i	−0.168168	−	0.796737i
$675$		0			0
$676$	8.65950	−	3.82599i	0.333058	−	0.147154i
$677$	−3.99371	−	3.99371i	−0.153491	−	0.153491i	0.626184	−	0.779675i	$-0.284616\pi$
$677$	−3.99371	−	3.99371i	−0.153491	−	0.153491i	−0.779675	+	0.626184i	$0.784616\pi$
$678$	5.41984	−	24.6639i	0.208148	−	0.947212i
$679$		−	3.22091i		−	0.123607i
$680$		0			0
$681$	0.0691789	+	0.183194i	0.00265094	+	0.00702002i
$682$	−3.97448	−	2.58910i	−0.152191	−	0.0991416i
$683$	−7.19759	+	7.19759i	−0.275408	+	0.275408i	−0.831273	−	0.555865i	$-0.812387\pi$
$683$	−7.19759	+	7.19759i	−0.275408	+	0.275408i	0.555865	+	0.831273i	$0.312387\pi$
$684$	−12.4047	+	26.8618i	−0.474304	+	1.02709i
$685$		0			0
$686$	27.7835	−	5.86429i	1.06078	−	0.223900i
$687$	−20.4772	−	9.25106i	−0.781255	−	0.352950i
$688$	−24.7014	+	1.15374i	−0.941731	+	0.0439859i
$689$	−15.5886			−0.593879
$690$		0			0
$691$		−	24.1691i		−	0.919434i	−0.888065	−	0.459717i	$-0.847951\pi$
$691$		−	24.1691i		−	0.919434i	0.888065	−	0.459717i	$-0.152049\pi$
$692$	−40.3106	−	15.6054i	−1.53238	−	0.593229i
$693$	0.248783	−	3.92766i	0.00945050	−	0.149200i
$694$	−8.35055	−	39.5627i	−0.316983	−	1.50178i
$695$		0			0
$696$	40.1892	+	26.6577i	1.52337	+	1.01046i
$697$	31.5740	+	31.5740i	1.19595	+	1.19595i
$698$	0.714553	+	0.465482i	0.0270462	+	0.0176187i
$699$	−1.84304	−	4.88059i	−0.0697100	−	0.184601i
$700$		0			0
$701$	30.9018			1.16714			0.583572	−	0.812061i	$-0.301655\pi$
$701$	30.9018			1.16714			0.583572	+	0.812061i	$0.301655\pi$
$702$	18.4821	−	10.2372i	0.697563	−	0.386379i
$703$	16.9770	−	16.9770i	0.640299	−	0.640299i
$704$	−4.86544	−	1.62689i	−0.183373	−	0.0613156i
$705$		0			0
$706$	8.11559	+	38.4495i	0.305434	+	1.44707i
$707$	−6.25230	−	6.25230i	−0.235142	−	0.235142i
$708$	8.67194	+	0.0719064i	0.325911	+	0.00270241i
$709$	−20.8029			−0.781269			−0.390634	−	0.920546i	$-0.627744\pi$
$709$	−20.8029			−0.781269			−0.390634	+	0.920546i	$0.627744\pi$
$710$		0			0
$711$	11.9708	−	10.5447i	0.448941	−	0.395456i
$712$	−1.80203	+	11.0717i	−0.0675338	+	0.414931i
$713$	−19.5415	−	19.5415i	−0.731835	−	0.731835i
$714$	16.7241	+	26.1444i	0.625884	+	0.978428i
$715$		0			0
$716$	−3.87769	+	1.71327i	−0.144916	+	0.0640277i
$717$	26.3873	+	11.9211i	0.985453	+	0.445201i
$718$	−15.0139	−	9.78050i	−0.560313	−	0.365005i
$719$	−34.2881			−1.27873			−0.639364	−	0.768904i	$-0.720802\pi$
$719$	−34.2881			−1.27873			−0.639364	+	0.768904i	$0.720802\pi$
$720$		0			0
$721$	24.6446			0.917812
$722$	−6.30114	−	4.10476i	−0.234504	−	0.152763i
$723$	−7.39836	−	3.34238i	−0.275148	−	0.124304i
$724$	−35.5621	+	15.7123i	−1.32165	+	0.583941i
$725$		0			0
$726$	13.9766	+	21.8492i	0.518719	+	0.810899i
$727$	2.33356	+	2.33356i	0.0865468	+	0.0865468i	0.749055	−	0.662508i	$-0.230508\pi$
$727$	2.33356	+	2.33356i	0.0865468	+	0.0865468i	−0.662508	+	0.749055i	$0.730508\pi$
$728$	−16.4196	−	2.67244i	−0.608552	−	0.0990474i
$729$	−22.3505	+	15.1478i	−0.827797	+	0.561028i
$730$		0			0
$731$	38.2901			1.41621
$732$	33.4021	+	0.276966i	1.23458	+	0.0102369i
$733$	35.6179	+	35.6179i	1.31558	+	1.31558i	0.917237	+	0.398342i	$0.130414\pi$
$733$	35.6179	+	35.6179i	1.31558	+	1.31558i	0.398342	+	0.917237i	$0.369586\pi$
$734$	0.897608	+	4.25263i	0.0331313	+	0.156967i
$735$		0			0
$736$	−25.7782	−	15.1284i	−0.950198	−	0.557640i
$737$	1.66531	−	1.66531i	0.0613425	−	0.0613425i
$738$	30.2665	−	4.41228i	1.11413	−	0.162418i
$739$	−14.3621			−0.528318			−0.264159	−	0.964479i	$-0.585094\pi$
$739$	−14.3621			−0.528318			−0.264159	+	0.964479i	$0.585094\pi$
$740$		0			0
$741$	8.67551	+	22.9738i	0.318703	+	0.843965i
$742$	−13.1428	−	8.56162i	−0.482487	−	0.314307i
$743$	1.87689	+	1.87689i	0.0688563	+	0.0688563i	0.740696	−	0.671840i	$-0.234496\pi$
$743$	1.87689	+	1.87689i	0.0688563	+	0.0688563i	−0.671840	+	0.740696i	$0.734496\pi$
$744$	14.1635	−	21.3529i	0.519259	−	0.782835i
$745$		0			0
$746$	8.15428	+	38.6329i	0.298550	+	1.41445i
$747$	9.31833	+	0.590235i	0.340940	+	0.0215956i
$748$	7.40806	+	2.86788i	0.270866	+	0.104860i
$749$			29.9243i			1.09341i
$750$		0			0
$751$	−30.0439			−1.09632			−0.548158	−	0.836375i	$-0.684671\pi$
$751$	−30.0439			−1.09632			−0.548158	+	0.836375i	$0.684671\pi$
$752$	−1.07805	−	23.0809i	−0.0393125	−	0.841675i
$753$	−28.9430	−	13.0757i	−1.05474	−	0.476503i
$754$	39.1644	−	8.26647i	1.42628	−	0.301047i
$755$		0			0
$756$	21.2048	+	1.51977i	0.771212	+	0.0552735i
$757$	−34.9468	+	34.9468i	−1.27016	+	1.27016i	−0.324162	+	0.946002i	$0.605082\pi$
$757$	−34.9468	+	34.9468i	−1.27016	+	1.27016i	−0.946002	+	0.324162i	$0.894918\pi$
$758$	−10.3891	−	6.76775i	−0.377347	−	0.245816i
$759$	−2.07332	−	5.49040i	−0.0752567	−	0.199289i
$760$		0			0
$761$			2.88711i			0.104657i	0.998630	+	0.0523287i	$0.0166644\pi$
$761$			2.88711i			0.104657i	−0.998630	+	0.0523287i	$0.983336\pi$
$762$	−8.52929	+	38.8140i	−0.308984	+	1.40608i
$763$	−16.5569	−	16.5569i	−0.599399	−	0.599399i
$764$	−4.87552	+	2.15413i	−0.176390	+	0.0779337i
$765$		0			0
$766$	−6.91359	−	32.7548i	−0.249798	−	1.18348i
$767$	5.08962	−	5.08962i	0.183776	−	0.183776i
$768$	9.00584	−	26.2087i	0.324970	−	0.945724i
$769$			19.0345i			0.686400i	0.939262	+	0.343200i	$0.111511\pi$
$769$			19.0345i			0.686400i	−0.939262	+	0.343200i	$0.888489\pi$
$770$		0			0
$771$	−2.94892	+	1.11359i	−0.106203	+	0.0401048i
$772$	−20.4088	−	7.90085i	−0.734529	−	0.284358i
$773$	18.9794	−	18.9794i	0.682642	−	0.682642i	−0.277953	−	0.960595i	$-0.589656\pi$
$773$	18.9794	−	18.9794i	0.682642	−	0.682642i	0.960595	+	0.277953i	$0.0896558\pi$
$774$	15.6768	−	21.0276i	0.563492	−	0.755823i
$775$		0			0
$776$	3.61398	−	2.60223i	0.129734	−	0.0934148i
$777$	−15.7210	−	7.10233i	−0.563988	−	0.254795i
$778$	16.2044	−	24.8752i	0.580958	−	0.891818i
$779$			35.5511i			1.27375i
$780$		0			0
$781$		−	10.7204i		−	0.383608i
$782$	38.7794	+	25.2621i	1.38675	+	0.903371i
$783$	−48.9003	+	15.0096i	−1.74756	+	0.536399i
$784$	8.32552	+	7.58250i	0.297340	+	0.270804i
$785$		0			0
$786$	20.6504	+	32.2823i	0.736576	+	1.15147i
$787$	−28.3424	+	28.3424i	−1.01030	+	1.01030i	−0.0103521	+	0.999946i	$0.503295\pi$
$787$	−28.3424	+	28.3424i	−1.01030	+	1.01030i	−0.999946	+	0.0103521i	$0.996705\pi$
$788$	−7.99286	+	20.6465i	−0.284734	+	0.735500i
$789$	−3.42756	−	9.07661i	−0.122024	−	0.323136i
$790$		0			0
$791$		−	21.0893i		−	0.749850i
$792$	4.60797	−	2.89408i	0.163737	−	0.102837i
$793$	19.6040	−	19.6040i	0.696157	−	0.696157i
$794$	−44.5164	+	9.39613i	−1.57983	+	0.333456i
$795$		0			0
$796$	30.8451	−	13.6282i	1.09327	−	0.483037i
$797$	−15.8150	−	15.8150i	−0.560195	−	0.560195i	0.369168	−	0.929363i	$-0.379643\pi$
$797$	−15.8150	−	15.8150i	−0.560195	−	0.560195i	−0.929363	+	0.369168i	$0.879643\pi$
$798$	−5.30341	+	24.1341i	−0.187739	+	0.854338i
$799$			35.7782i			1.26574i
$800$		0			0
$801$	−7.86441	−	8.92807i	−0.277875	−	0.315458i
$802$	−18.7204	+	28.7373i	−0.661039	+	1.01475i
$803$	−5.39139	+	5.39139i	−0.190258	+	0.190258i
$804$	8.92089	+	9.07007i	0.314616	+	0.319877i
$805$		0			0
$806$	−4.39206	−	20.8084i	−0.154704	−	0.732945i
$807$	1.29704	−	2.87101i	0.0456581	−	0.101064i
$808$	1.96396	−	12.0666i	0.0690918	−	0.424503i
$809$	49.0232			1.72356			0.861782	−	0.507279i	$-0.169349\pi$
$809$	49.0232			1.72356			0.861782	+	0.507279i	$0.169349\pi$
$810$		0			0
$811$			21.1676i			0.743295i	0.928374	+	0.371648i	$0.121207\pi$
$811$			21.1676i			0.743295i	−0.928374	+	0.371648i	$0.878793\pi$
$812$	37.5597	+	14.5405i	1.31809	+	0.510271i
$813$	11.9153	+	5.38302i	0.417888	+	0.188791i
$814$	−4.32028	+	0.911887i	−0.151426	+	0.0319616i
$815$		0			0
$816$	−15.8232	+	39.8875i	−0.553922	+	1.39634i
$817$	21.5566	+	21.5566i	0.754169	+	0.754169i
$818$	18.6001	−	28.5527i	0.650336	−	0.998320i
$819$	13.2405	−	11.6631i	0.462661	−	0.407542i
$820$		0			0
$821$	−13.4855			−0.470649			−0.235324	−	0.971917i	$-0.575615\pi$
$821$	−13.4855			−0.470649			−0.235324	+	0.971917i	$0.575615\pi$
$822$	−30.2538	−	6.64821i	−1.05522	−	0.231883i
$823$	−19.8632	+	19.8632i	−0.692387	+	0.692387i	−0.962757	−	0.270370i	$-0.912854\pi$
$823$	−19.8632	+	19.8632i	−0.692387	+	0.692387i	0.270370	+	0.962757i	$0.412854\pi$
$824$	19.9108	+	27.6521i	0.693626	+	0.963306i
$825$		0			0
$826$	7.08641	−	1.49574i	0.246568	−	0.0520433i
$827$	−36.8216	−	36.8216i	−1.28041	−	1.28041i	−0.940432	−	0.339982i	$-0.889579\pi$
$827$	−36.8216	−	36.8216i	−1.28041	−	1.28041i	−0.339982	−	0.940432i	$-0.610421\pi$
$828$	29.7503	−	10.9535i	1.03389	−	0.380660i
$829$	34.1845			1.18728			0.593638	−	0.804732i	$-0.297691\pi$
$829$	34.1845			1.18728			0.593638	+	0.804732i	$0.297691\pi$
$830$		0			0
$831$	−13.9764	+	5.27784i	−0.484835	+	0.183086i
$832$	−10.2671	−	20.5825i	−0.355949	−	0.713571i
$833$	−12.3297	−	12.3297i	−0.427198	−	0.427198i
$834$	1.34153	+	2.09718i	0.0464535	+	0.0726195i
$835$		0			0
$836$	2.55603	+	5.78515i	0.0884022	+	0.200084i
$837$	7.97474	+	25.9812i	0.275647	+	0.898042i
$838$	−30.8432	+	47.3469i	−1.06546	+	1.63557i
$839$	19.6854			0.679616			0.339808	−	0.940495i	$-0.389638\pi$
$839$	19.6854			0.679616			0.339808	+	0.940495i	$0.389638\pi$
$840$		0			0
$841$	−67.9085			−2.34167
$842$	20.9308	−	32.1306i	0.721324	−	1.10729i
$843$	−3.08215	+	6.82234i	−0.106155	+	0.234974i
$844$	−11.8146	+	5.22001i	−0.406676	+	0.179680i
$845$		0			0
$846$	19.6482	+	14.6484i	0.675519	+	0.503623i
$847$	15.3167	+	15.3167i	0.526289	+	0.526289i
$848$	−1.01186	−	21.6638i	−0.0347474	−	0.743937i
$849$	−5.67371	−	15.0247i	−0.194721	−	0.515647i
$850$		0			0
$851$	−25.7252			−0.881850
$852$	57.9084	+	0.480168i	1.98391	+	0.0164503i
$853$	−29.0954	−	29.0954i	−0.996209	−	0.996209i	0.00378410	−	0.999993i	$-0.498795\pi$
$853$	−29.0954	−	29.0954i	−0.996209	−	0.996209i	−0.999993	+	0.00378410i	$0.998795\pi$
$854$	27.2951	−	5.76121i	0.934018	−	0.197144i
$855$		0			0
$856$	−33.5761	+	24.1764i	−1.14761	+	0.826331i
$857$	8.71719	−	8.71719i	0.297773	−	0.297773i	−0.542368	−	0.840141i	$-0.682472\pi$
$857$	8.71719	−	8.71719i	0.297773	−	0.297773i	0.840141	+	0.542368i	$0.182472\pi$
$858$	0.969317	−	4.41105i	0.0330920	−	0.150591i
$859$	−49.6253			−1.69319			−0.846597	−	0.532235i	$-0.821352\pi$
$859$	−49.6253			−1.69319			−0.846597	+	0.532235i	$0.821352\pi$
$860$		0			0
$861$	23.8969	−	9.02409i	0.814405	−	0.307540i
$862$	23.9094	−	36.7029i	0.814357	−	1.25011i
$863$	−26.7844	−	26.7844i	−0.911750	−	0.911750i	0.0846599	−	0.996410i	$-0.473020\pi$
$863$	−26.7844	−	26.7844i	−0.911750	−	0.911750i	−0.996410	+	0.0846599i	$0.973020\pi$
$864$	15.4265	+	25.0204i	0.524821	+	0.851212i
$865$		0			0
$866$	−16.0092	+	3.37908i	−0.544014	+	0.114826i
$867$	15.2334	−	33.7192i	0.517354	−	1.14516i
$868$	7.72550	−	19.9558i	0.262220	−	0.677345i
$869$		−	3.41005i		−	0.115678i
$870$		0			0
$871$	10.5590			0.357779
$872$	5.20081	−	31.9540i	0.176122	−	1.08210i
$873$	−0.298595	+	4.71406i	−0.0101059	+	0.159547i
$874$	7.60998	+	36.0541i	0.257412	+	1.21955i
$875$		0			0
$876$	−28.8811	−	29.3640i	−0.975801	−	0.992119i
$877$	−13.3952	+	13.3952i	−0.452323	+	0.452323i	−0.896125	−	0.443802i	$-0.853629\pi$
$877$	−13.3952	+	13.3952i	−0.452323	+	0.452323i	0.443802	+	0.896125i	$0.353629\pi$
$878$	7.43694	−	11.4163i	0.250984	−	0.385282i
$879$	8.83773	−	3.33735i	0.298089	−	0.112566i
$880$		0			0
$881$		−	11.8169i		−	0.398120i	−0.979987	−	0.199060i	$-0.936211\pi$
$881$		−	11.8169i		−	0.398120i	0.979987	−	0.199060i	$-0.0637889\pi$
$882$	−11.8191	+	1.72300i	−0.397970	+	0.0580163i
$883$	19.7888	+	19.7888i	0.665947	+	0.665947i	0.956775	−	0.290828i	$-0.0939308\pi$
$883$	19.7888	+	19.7888i	0.665947	+	0.665947i	−0.290828	+	0.956775i	$0.593931\pi$
$884$	14.3937	+	32.5777i	0.484112	+	1.09571i
$885$		0			0
$886$	11.4716	−	2.42133i	0.385396	−	0.0813461i
$887$	−0.472133	+	0.472133i	−0.0158527	+	0.0158527i	−0.714989	−	0.699136i	$-0.753568\pi$
$887$	−0.472133	+	0.472133i	−0.0158527	+	0.0158527i	0.699136	+	0.714989i	$0.253568\pi$
$888$	−4.73222	−	23.3776i	−0.158803	−	0.784502i
$889$			33.1886i			1.11311i
$890$		0			0
$891$	−0.728228	+	5.72538i	−0.0243966	+	0.191807i
$892$	22.1875	+	8.58944i	0.742893	+	0.287596i
$893$	−20.1424	+	20.1424i	−0.674041	+	0.674041i
$894$	−6.22828	+	3.98413i	−0.208305	+	0.133249i
$895$		0			0
$896$	2.64814	−	22.9921i	0.0884683	−	0.768113i
$897$	10.8331	−	23.9792i	0.361708	−	0.800641i
$898$	7.59048	+	4.94467i	0.253297	+	0.165006i
$899$			51.4884i			1.71723i
$900$		0			0
$901$			33.5815i			1.11876i
$902$	3.56872	−	5.47828i	0.118825	−	0.182407i
$903$	9.01820	−	19.9618i	0.300107	−	0.664287i
$904$	23.6630	−	17.0384i	0.787019	−	0.566690i
$905$		0			0
$906$	9.84875	+	15.3963i	0.327203	+	0.511508i
$907$	−38.0394	+	38.0394i	−1.26308	+	1.26308i	−0.313482	+	0.949594i	$0.601495\pi$
$907$	−38.0394	+	38.0394i	−1.26308	+	1.26308i	−0.949594	+	0.313482i	$0.898505\pi$
$908$	−0.0816321	+	0.210865i	−0.00270906	+	0.00699780i
$909$	8.57111	+	9.73035i	0.284286	+	0.322735i
$910$		0			0
$911$		−	50.1309i		−	1.66091i	−0.557086	−	0.830455i	$-0.688081\pi$
$911$		−	50.1309i		−	1.66091i	0.557086	−	0.830455i	$-0.311919\pi$
$912$	−31.3640	+	13.5478i	−1.03857	+	0.448611i
$913$	1.41129	−	1.41129i	0.0467070	−	0.0467070i
$914$	6.89908	+	32.6860i	0.228201	+	1.08116i
$915$		0			0
$916$	−10.4858	−	23.7328i	−0.346460	−	0.784154i
$917$	22.6305	+	22.6305i	0.747325	+	0.747325i
$918$	−22.0533	−	39.8147i	−0.727869	−	1.31408i
$919$		−	21.5999i		−	0.712514i	−0.934388	−	0.356257i	$-0.884053\pi$
$919$		−	21.5999i		−	0.712514i	0.934388	−	0.356257i	$-0.115947\pi$
$920$		0			0
$921$	−7.37929	+	2.78661i	−0.243156	+	0.0918219i
$922$	−42.0754	−	27.4092i	−1.38568	−	0.902675i
$923$	33.9869	−	33.9869i	1.11869	−	1.11869i
$924$	3.23988	−	3.18659i	0.106584	−	0.104831i
$925$		0			0
$926$	−19.1735	+	4.04697i	−0.630079	+	0.132992i
$927$	−36.0693	−	2.28468i	−1.18467	−	0.0750387i
$928$	14.0302	+	53.8909i	0.460565	+	1.76905i
$929$	0.457555			0.0150119			0.00750595	−	0.999972i	$-0.497611\pi$
$929$	0.457555			0.0150119			0.00750595	+	0.999972i	$0.497611\pi$
$930$		0			0
$931$		−	13.8827i		−	0.454988i
$932$	2.17481	−	5.61778i	0.0712383	−	0.184017i
$933$	8.80340	−	19.4863i	0.288211	−	0.637954i
$934$	3.33216	+	15.7869i	0.109032	+	0.516563i
$935$		0			0
$936$	23.7837	+	5.43352i	0.777394	+	0.177600i
$937$	−7.63736	−	7.63736i	−0.249502	−	0.249502i	0.571264	−	0.820766i	$-0.306453\pi$
$937$	−7.63736	−	7.63736i	−0.249502	−	0.249502i	−0.820766	+	0.571264i	$0.806453\pi$
$938$	8.90234	+	5.79926i	0.290672	+	0.189352i
$939$	26.8071	−	10.1231i	0.874818	−	0.330354i
$940$		0			0
$941$	−52.1835			−1.70113			−0.850567	−	0.525867i	$-0.823741\pi$
$941$	−52.1835			−1.70113			−0.850567	+	0.525867i	$0.823741\pi$
$942$	20.5925	+	4.52515i	0.670940	+	0.147437i
$943$	26.9353	−	26.9353i	0.877135	−	0.877135i
$944$	7.40351	+	6.74277i	0.240964	+	0.219459i
$945$		0			0
$946$	−1.15787	−	5.48569i	−0.0376456	−	0.178355i
$947$	28.3995	+	28.3995i	0.922860	+	0.922860i	0.997231	−	0.0743707i	$-0.0236948\pi$
$947$	28.3995	+	28.3995i	0.922860	+	0.922860i	−0.0743707	+	0.997231i	$0.523695\pi$
$948$	18.4200	+	0.152736i	0.598255	+	0.00496064i
$949$	−34.1845			−1.10968
$950$		0			0
$951$	4.46235	+	11.8169i	0.144702	+	0.383188i
$952$	−5.75706	+	35.3717i	−0.186587	+	1.14640i
$953$	23.6130	+	23.6130i	0.764900	+	0.764900i	0.977204	−	0.212304i	$-0.0680967\pi$
$953$	23.6130	+	23.6130i	0.764900	+	0.764900i	−0.212304	+	0.977204i	$0.568097\pi$
$954$	18.4418	+	13.7490i	0.597076	+	0.445141i
$955$		0			0
$956$	13.5122	+	30.5826i	0.437015	+	0.989111i
$957$	−4.50171	+	9.96454i	−0.145520	+	0.322108i
$958$	−4.79551	−	3.12394i	−0.154936	−	0.100930i
$959$	−25.8691			−0.835356
$960$		0			0
$961$	−3.64371			−0.117539
$962$	−16.5875	−	10.8056i	−0.534801	−	0.348386i
$963$	2.77413	−	43.7965i	0.0893952	−	1.41132i
$964$	−3.78848	−	8.57460i	−0.122019	−	0.276169i
$965$		0			0
$966$	22.3034	−	14.2671i	0.717599	−	0.459036i
$967$	3.10676	+	3.10676i	0.0999067	+	0.0999067i	0.755293	−	0.655387i	$-0.227494\pi$
$967$	3.10676	+	3.10676i	0.0999067	+	0.0999067i	−0.655387	+	0.755293i	$0.727494\pi$
$968$	−4.81125	+	29.5606i	−0.154640	+	0.950112i
$969$	49.4909	−	18.6891i	1.58988	−	0.600379i
$970$		0			0
$971$	−16.7395			−0.537196			−0.268598	−	0.963252i	$-0.586560\pi$
$971$	−16.7395			−0.537196			−0.268598	+	0.963252i	$0.586560\pi$
$972$	−30.8941	−	4.19010i	−0.990928	−	0.134397i
$973$	1.47017	+	1.47017i	0.0471314	+	0.0471314i
$974$	2.59603	+	12.2993i	0.0831823	+	0.394096i
$975$		0			0
$976$	28.5165	+	25.9715i	0.912790	+	0.831327i
$977$	38.9727	−	38.9727i	1.24685	−	1.24685i	0.289745	−	0.957104i	$-0.406430\pi$
$977$	38.9727	−	38.9727i	1.24685	−	1.24685i	0.957104	−	0.289745i	$-0.0935704\pi$
$978$	−10.0730	+	45.8391i	−0.322100	+	1.46577i
$979$	−2.54328			−0.0812837
$980$		0			0
$981$	22.6974	+	25.7672i	0.724672	+	0.822683i
$982$	29.8002	+	19.4128i	0.950963	+	0.619486i
$983$	−21.8279	−	21.8279i	−0.696200	−	0.696200i	0.267388	−	0.963589i	$-0.413839\pi$
$983$	−21.8279	−	21.8279i	−0.696200	−	0.696200i	−0.963589	+	0.267388i	$0.913839\pi$
$984$	29.4321	+	19.5225i	0.938261	+	0.622353i
$985$		0			0
$986$	−17.8079	−	84.3691i	−0.567119	−	2.68686i
$987$	18.6523	+	8.42660i	0.593708	+	0.268222i
$988$	−10.2372	+	26.4439i	−0.325690	+	0.841294i
$989$		−	32.6647i		−	1.03868i
$990$		0			0
$991$	−1.28868			−0.0409363			−0.0204681	−	0.999791i	$-0.506516\pi$
$991$	−1.28868			−0.0409363			−0.0204681	+	0.999791i	$0.506516\pi$
$992$	28.6327	−	7.45440i	0.909090	−	0.236677i
$993$	−10.0162	+	22.1708i	−0.317854	+	0.703570i
$994$	47.3208	−	9.98805i	1.50092	−	0.316802i
$995$		0			0
$996$	7.56016	+	7.68658i	0.239553	+	0.243559i
$997$	17.8369	−	17.8369i	0.564900	−	0.564900i	−0.365795	−	0.930695i	$-0.619203\pi$
$997$	17.8369	−	17.8369i	0.564900	−	0.564900i	0.930695	+	0.365795i	$0.119203\pi$
$998$	−4.75426	−	3.09707i	−0.150493	−	0.0980361i
$999$	22.3505	+	11.8522i	0.707139	+	0.374988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.k.557.8	yes	64
3.2	odd	2	inner	600.2.w.k.557.26	yes	64
5.2	odd	4	inner	600.2.w.k.293.24	yes	64
5.3	odd	4	inner	600.2.w.k.293.9	yes	64
5.4	even	2	inner	600.2.w.k.557.25	yes	64
8.5	even	2	inner	600.2.w.k.557.23	yes	64
15.2	even	4	inner	600.2.w.k.293.10	yes	64
15.8	even	4	inner	600.2.w.k.293.23	yes	64
15.14	odd	2	inner	600.2.w.k.557.7	yes	64
24.5	odd	2	inner	600.2.w.k.557.9	yes	64
40.13	odd	4	inner	600.2.w.k.293.26	yes	64
40.29	even	2	inner	600.2.w.k.557.10	yes	64
40.37	odd	4	inner	600.2.w.k.293.7	✓	64
120.29	odd	2	inner	600.2.w.k.557.24	yes	64
120.53	even	4	inner	600.2.w.k.293.8	yes	64
120.77	even	4	inner	600.2.w.k.293.25	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.k.293.7	✓	64	40.37	odd	4	inner
600.2.w.k.293.8	yes	64	120.53	even	4	inner
600.2.w.k.293.9	yes	64	5.3	odd	4	inner
600.2.w.k.293.10	yes	64	15.2	even	4	inner
600.2.w.k.293.23	yes	64	15.8	even	4	inner
600.2.w.k.293.24	yes	64	5.2	odd	4	inner
600.2.w.k.293.25	yes	64	120.77	even	4	inner
600.2.w.k.293.26	yes	64	40.13	odd	4	inner
600.2.w.k.557.7	yes	64	15.14	odd	2	inner
600.2.w.k.557.8	yes	64	1.1	even	1	trivial
600.2.w.k.557.9	yes	64	24.5	odd	2	inner
600.2.w.k.557.10	yes	64	40.29	even	2	inner
600.2.w.k.557.23	yes	64	8.5	even	2	inner
600.2.w.k.557.24	yes	64	120.29	odd	2	inner
600.2.w.k.557.25	yes	64	5.4	even	2	inner
600.2.w.k.557.26	yes	64	3.2	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18496 - 0.771921i) q^{2} +(1.57845 + 0.713099i) q^{3} +(0.808275 + 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 - 1.44651i) q^{7} +(0.454373 - 2.79169i) q^{8} +(1.98298 + 2.25118i) q^{9} +0.641278 q^{11} +(-0.0287228 + 3.46398i) q^{12} +(2.03304 + 2.03304i) q^{13} +(0.597468 + 2.83065i) q^{14} +(-2.69338 + 2.95731i) q^{16} +(4.37963 - 4.37963i) q^{17} +(-0.612026 - 4.19826i) q^{18} +4.93129 q^{19} +(-1.25173 - 3.31474i) q^{21} +(-0.759891 - 0.495016i) q^{22} +(-3.73619 - 3.73619i) q^{23} +(2.70796 - 4.08252i) q^{24} +(-0.839729 - 3.97842i) q^{26} +(1.52471 + 4.96742i) q^{27} +(1.47706 - 3.81541i) q^{28} +9.84421i q^{29} +5.23032 q^{31} +(5.47437 - 1.42523i) q^{32} +(1.01222 + 0.457295i) q^{33} +(-8.57043 + 1.80897i) q^{34} +(-2.51550 + 5.44722i) q^{36} +(3.44271 - 3.44271i) q^{37} +(-5.84339 - 3.80656i) q^{38} +(1.75928 + 4.65879i) q^{39} +7.20930i q^{41} +(-1.07546 + 4.89408i) q^{42} +(4.37139 + 4.37139i) q^{43} +(0.518329 + 1.17315i) q^{44} +(1.54320 + 7.31130i) q^{46} +(-4.08462 + 4.08462i) q^{47} +(-6.36021 + 2.74731i) q^{48} -2.81523i q^{49} +(10.0361 - 3.78989i) q^{51} +(-2.07598 + 5.36248i) q^{52} +(-3.83383 + 3.83383i) q^{53} +(2.02773 - 7.06317i) q^{54} +(-4.69546 + 3.38095i) q^{56} +(7.78377 + 3.51650i) q^{57} +(7.59896 - 11.6650i) q^{58} -2.50346i q^{59} -9.64270i q^{61} +(-6.19774 - 4.03740i) q^{62} +(0.387949 - 6.12474i) q^{63} +(-7.58709 - 2.53694i) q^{64} +(-0.846451 - 1.32323i) q^{66} +(2.59686 - 2.59686i) q^{67} +(11.5520 + 4.47213i) q^{68} +(-3.23310 - 8.56166i) q^{69} -16.7173i q^{71} +(7.18560 - 4.51299i) q^{72} +(-8.40725 + 8.40725i) q^{73} +(-6.73698 + 1.42198i) q^{74} +(3.98584 + 9.02128i) q^{76} +(-0.927614 - 0.927614i) q^{77} +(1.51154 - 6.87852i) q^{78} -5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(5.56501 - 8.54275i) q^{82} +(2.20075 - 2.20075i) q^{83} +(5.05222 - 4.96913i) q^{84} +(-1.80557 - 8.55430i) q^{86} +(-7.01990 + 15.5386i) q^{87} +(0.291380 - 1.79025i) q^{88} -3.96596 q^{89} -5.88160i q^{91} +(3.81511 - 9.85485i) q^{92} +(8.25578 + 3.72974i) q^{93} +(7.99313 - 1.68712i) q^{94} +(9.65732 + 1.65413i) q^{96} +(1.11334 + 1.11334i) q^{97} +(-2.17314 + 3.33595i) q^{98} +(1.27164 + 1.44363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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