LMFDB - Embedded newform 600.2.w.k.293.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

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")

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

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			293.26
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18496 - 0.771921i) q^{2} +(0.713099 - 1.57845i) q^{3} +(0.808275 - 1.82940i) q^{4} +(-0.373439 - 2.42086i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(-0.454373 - 2.79169i) q^{8} +(-1.98298 - 2.25118i) q^{9} +O(q^{10})$	\(q+(1.18496 - 0.771921i) q^{2} +(0.713099 - 1.57845i) q^{3} +(0.808275 - 1.82940i) q^{4} +(-0.373439 - 2.42086i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(-0.454373 - 2.79169i) q^{8} +(-1.98298 - 2.25118i) q^{9} -0.641278 q^{11} +(-2.31122 - 2.58036i) 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} +(-4.08749 - 1.13686i) q^{18} +4.93129 q^{19} +(1.25173 + 3.31474i) q^{21} +(-0.759891 + 0.495016i) q^{22} +(3.73619 - 3.73619i) q^{23} +(-4.73055 - 1.27355i) q^{24} +(0.839729 - 3.97842i) q^{26} +(-4.96742 + 1.52471i) q^{27} +(1.47706 + 3.81541i) q^{28} +9.84421i q^{29} +5.23032 q^{31} +(-5.47437 - 1.42523i) q^{32} +(-0.457295 + 1.01222i) q^{33} +(-8.57043 - 1.80897i) q^{34} +(-5.72109 + 1.80808i) q^{36} +(3.44271 + 3.44271i) q^{37} +(5.84339 - 3.80656i) q^{38} +(-1.75928 - 4.65879i) q^{39} +7.20930i q^{41} +(4.04197 + 2.96160i) 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} +(-6.58860 + 2.14250i) q^{48} +2.81523i q^{49} +(-10.0361 + 3.78989i) q^{51} +(-2.07598 - 5.36248i) q^{52} +(3.83383 + 3.83383i) q^{53} +(-4.70925 + 5.64118i) q^{54} +(4.69546 + 3.38095i) q^{56} +(3.51650 - 7.78377i) q^{57} +(7.59896 + 11.6650i) q^{58} -2.50346i q^{59} +9.64270i q^{61} +(6.19774 - 4.03740i) q^{62} +(6.12474 + 0.387949i) q^{63} +(-7.58709 + 2.53694i) q^{64} +(0.239478 + 1.55244i) q^{66} +(2.59686 + 2.59686i) q^{67} +(-11.5520 + 4.47213i) q^{68} +(-3.23310 - 8.56166i) q^{69} -16.7173i q^{71} +(-5.38358 + 6.55874i) 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} +(-5.68090 - 4.16247i) q^{78} +5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(5.56501 + 8.54275i) q^{82} +(-2.20075 - 2.20075i) q^{83} +(7.07571 + 0.389310i) q^{84} +(1.80557 - 8.55430i) q^{86} +(15.5386 + 7.01990i) q^{87} +(0.291380 + 1.79025i) q^{88} +3.96596 q^{89} +5.88160i q^{91} +(-3.81511 - 9.85485i) q^{92} +(3.72974 - 8.25578i) q^{93} +(7.99313 + 1.68712i) q^{94} +(-6.15341 + 7.62467i) 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}+O(q^{10}) $ 64 * q + 12 * q^6	$ 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.713099	−	1.57845i	0.411708	−	0.911316i
$3$	0.713099	−	1.57845i	0.411708	−	0.911316i
$4$	0.808275	−	1.82940i	0.404138	−	0.914698i
$5$		0			0
$5$		0			0
$6$	−0.373439	−	2.42086i	−0.152456	−	0.988310i
$7$	−1.44651	+	1.44651i	−0.546728	+	0.546728i	−0.925493	−	0.378765i	$-0.876349\pi$
$7$	−1.44651	+	1.44651i	−0.546728	+	0.546728i	0.378765	+	0.925493i	$0.376349\pi$
$8$	−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	$-0.530821\pi$
$11$	−0.641278			−0.193353			−0.0966764	+	0.995316i	$0.530821\pi$
$12$	−2.31122	−	2.58036i	−0.667192	−	0.744886i
$13$	2.03304	−	2.03304i	0.563863	−	0.563863i	−0.366540	−	0.930402i	$-0.619458\pi$
$13$	2.03304	−	2.03304i	0.563863	−	0.563863i	0.930402	+	0.366540i	$0.119458\pi$
$14$	−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	−0.997932	−	0.0642843i	$-0.979524\pi$
$17$	−4.37963	−	4.37963i	−1.06222	−	1.06222i	−0.0642843	−	0.997932i	$-0.520476\pi$
$18$	−4.08749	−	1.13686i	−0.963430	−	0.267960i
$19$	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	$-0.564295\pi$
$23$	3.73619	−	3.73619i	0.779050	−	0.779050i	0.979669	+	0.200619i	$0.0642953\pi$
$24$	−4.73055	−	1.27355i	−0.965619	−	0.259962i
$25$		0			0
$26$	0.839729	−	3.97842i	0.164684	−	0.780232i
$27$	−4.96742	+	1.52471i	−0.955980	+	0.293431i
$28$	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
$33$	−0.457295	+	1.01222i	−0.0796049	+	0.176205i
$34$	−8.57043	−	1.80897i	−1.46982	−	0.310236i
$35$		0			0
$36$	−5.72109	+	1.80808i	−0.953514	+	0.301347i
$37$	3.44271	+	3.44271i	0.565978	+	0.565978i	0.930999	−	0.365022i	$-0.118938\pi$
$37$	3.44271	+	3.44271i	0.565978	+	0.565978i	−0.365022	+	0.930999i	$0.618938\pi$
$38$	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	$0.809666\pi$
$42$	4.04197	+	2.96160i	0.623689	+	0.456985i
$43$	4.37139	−	4.37139i	0.666630	−	0.666630i	−0.290304	−	0.956934i	$-0.593756\pi$
$43$	4.37139	−	4.37139i	0.666630	−	0.666630i	0.956934	+	0.290304i	$0.0937564\pi$
$44$	−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	$-0.111575\pi$
$47$	4.08462	+	4.08462i	0.595803	+	0.595803i	−0.343390	+	0.939193i	$0.611575\pi$
$48$	−6.58860	+	2.14250i	−0.950983	+	0.309243i
$49$			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	$-0.128544\pi$
$53$	3.83383	+	3.83383i	0.526616	+	0.526616i	−0.392945	+	0.919562i	$0.628544\pi$
$54$	−4.70925	+	5.64118i	−0.640848	+	0.767668i
$55$		0			0
$56$	4.69546	+	3.38095i	0.627457	+	0.451798i
$57$	3.51650	−	7.78377i	0.465771	−	1.03098i
$58$	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	$0.211778\pi$
$61$			9.64270i			1.23462i	−0.786720	+	0.617311i	$0.788222\pi$
$62$	6.19774	−	4.03740i	0.787114	−	0.512750i
$63$	6.12474	+	0.387949i	0.771644	+	0.0488770i
$64$	−7.58709	+	2.53694i	−0.948386	+	0.317118i
$65$		0			0
$66$	0.239478	+	1.55244i	0.0294778	+	0.191092i
$67$	2.59686	+	2.59686i	0.317257	+	0.317257i	0.847713	−	0.530456i	$-0.177979\pi$
$67$	2.59686	+	2.59686i	0.317257	+	0.317257i	−0.530456	+	0.847713i	$0.677979\pi$
$68$	−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	$-0.459682\pi$
$72$	−5.38358	+	6.55874i	−0.634461	+	0.772955i
$73$	−8.40725	−	8.40725i	−0.983994	−	0.983994i	0.0158800	−	0.999874i	$-0.494945\pi$
$73$	−8.40725	−	8.40725i	−0.983994	−	0.983994i	−0.999874	+	0.0158800i	$0.994945\pi$
$74$	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
$78$	−5.68090	−	4.16247i	−0.643236	−	0.471307i
$79$			5.31759i			0.598275i	0.954210	+	0.299138i	$0.0966989\pi$
$79$			5.31759i			0.598275i	−0.954210	+	0.299138i	$0.903301\pi$
$80$		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	$-0.304639\pi$
$83$	−2.20075	−	2.20075i	−0.241564	−	0.241564i	−0.817497	+	0.575933i	$0.804639\pi$
$84$	7.07571	+	0.389310i	0.772023	+	0.0424772i
$85$		0			0
$86$	1.80557	−	8.55430i	0.194699	−	0.922434i
$87$	15.5386	+	7.01990i	1.66591	+	0.752612i
$88$	0.291380	+	1.79025i	0.0310612	+	0.190841i
$89$	3.96596			0.420391			0.210195	−	0.977659i	$-0.432590\pi$
$89$	3.96596			0.420391			0.210195	+	0.977659i	$0.432590\pi$
$90$		0			0
$91$			5.88160i			0.616560i
$92$	−3.81511	−	9.85485i	−0.397752	−	1.02744i
$93$	3.72974	−	8.25578i	0.386756	−	0.856085i
$94$	7.99313	+	1.68712i	0.824428	+	0.174013i
$95$		0			0
$96$	−6.15341	+	7.62467i	−0.628030	+	0.778189i
$97$	1.11334	−	1.11334i	0.113043	−	0.113043i	−0.648323	−	0.761366i	$-0.724529\pi$
$97$	1.11334	−	1.11334i	0.113043	−	0.113043i	0.761366	+	0.648323i	$0.224529\pi$
$98$	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	$-0.568990\pi$
$101$	−4.32234			−0.430089			−0.215045	+	0.976604i	$0.568990\pi$
$102$	−8.96692	+	12.2380i	−0.887858	+	1.21174i
$103$	−8.51865	−	8.51865i	−0.839368	−	0.839368i	0.149408	−	0.988776i	$-0.452263\pi$
$103$	−8.51865	−	8.51865i	−0.839368	−	0.839368i	−0.988776	+	0.149408i	$0.952263\pi$
$104$	−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	$-0.500014\pi$
$107$	10.3436	−	10.3436i	0.999957	−	0.999957i	1.00000		4.33477e-5i	$1.37980e-5\pi$
$108$	−1.22574	+	10.3198i	−0.117947	+	0.993020i
$109$	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	$-0.911146\pi$
$113$	−7.28974	+	7.28974i	−0.685761	+	0.685761i	0.275531	+	0.961292i	$0.411146\pi$
$114$	−1.84154	−	11.9379i	−0.172476	−	1.11809i
$115$		0			0
$116$	18.0090	+	7.95683i	1.67209	+	0.738773i
$117$	−8.60819	−	0.545254i	−0.795827	−	0.0504088i
$118$	−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
$123$	11.3795	+	5.14094i	1.02605	+	0.463543i
$124$	4.22754	−	9.56834i	0.379644	−	0.859262i
$125$		0			0
$126$	7.55705	−	4.26811i	0.673236	−	0.380233i
$127$	−11.4720	+	11.4720i	−1.01797	+	1.01797i	−0.0181391	+	0.999835i	$0.505774\pi$
$127$	−11.4720	+	11.4720i	−1.01797	+	1.01797i	−0.999835	+	0.0181391i	$0.994226\pi$
$128$	−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	$-0.260478\pi$
$131$	15.6449			1.36690			0.683452	+	0.729995i	$0.260478\pi$
$132$	1.48214	+	1.65473i	0.129003	+	0.144026i
$133$	−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	$-0.431652\pi$
$137$	−8.94191	−	8.94191i	−0.763959	−	0.763959i	−0.977035	+	0.213077i	$0.931652\pi$
$138$	−10.4400	−	7.64955i	−0.888714	−	0.651173i
$139$	−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
$144$	−1.31651	+	11.9276i	−0.109709	+	0.993964i
$145$		0			0
$146$	−16.4520	−	3.47255i	−1.36158	−	0.287390i
$147$	4.44369	+	2.00754i	0.366510	+	0.165579i
$148$	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
$153$	−1.17460	+	18.5440i	−0.0949611	+	1.49920i
$154$	0.383143	−	1.81523i	0.0308746	−	0.146276i
$155$		0			0
$156$	−9.94476	−	0.547167i	−0.796218	−	0.0438084i
$157$	−6.08638	−	6.08638i	−0.485746	−	0.485746i	0.421215	−	0.906961i	$-0.361604\pi$
$157$	−6.08638	−	6.08638i	−0.485746	−	0.485746i	−0.906961	+	0.421215i	$0.861604\pi$
$158$	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
$162$	5.54614	+	11.4560i	0.435746	+	0.900070i
$163$	−13.5483	+	13.5483i	−1.06119	+	1.06119i	−0.0631867	+	0.998002i	$0.520126\pi$
$163$	−13.5483	+	13.5483i	−1.06119	+	1.06119i	−0.998002	+	0.0631867i	$0.979874\pi$
$164$	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	$-0.0905610\pi$
$167$	8.77613	+	8.77613i	0.679117	+	0.679117i	−0.280683	+	0.959800i	$0.590561\pi$
$168$	8.68497	−	5.00057i	0.670060	−	0.385802i
$169$			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	0.984056	+	0.177862i	$0.0569180\pi$
$173$	15.2826	+	15.2826i	1.16192	+	1.16192i	0.177862	+	0.984056i	$0.443082\pi$
$174$	23.8314	−	3.67621i	1.80666	−	0.278693i
$175$		0			0
$176$	1.72721	+	1.89646i	0.130193	+	0.142951i
$177$	−3.95157	−	1.78521i	−0.297018	−	0.134185i
$178$	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	$-0.743014\pi$
$181$		−	19.4392i		−	1.44491i	0.691420	−	0.722453i	$-0.256986\pi$
$182$	4.54013	+	6.96948i	0.336537	+	0.516612i
$183$	15.2205	+	6.87620i	1.12513	+	0.508303i
$184$	−12.1279	−	8.73268i	−0.894083	−	0.643781i
$185$		0			0
$186$	−1.95321	−	12.6619i	−0.143216	−	0.928413i
$187$	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	$0.969261\pi$
$192$	−1.40592	+	13.7849i	−0.101464	+	0.994839i
$193$	−7.73743	−	7.73743i	−0.556952	−	0.556952i	0.371486	−	0.928439i	$-0.378848\pi$
$193$	−7.73743	−	7.73743i	−0.556952	−	0.556952i	−0.928439	+	0.371486i	$0.878848\pi$
$194$	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	$-0.879029\pi$
$197$	−7.82754	+	7.82754i	−0.557689	+	0.557689i	0.370960	+	0.928649i	$0.379029\pi$
$198$	2.62122	+	0.729042i	0.186282	+	0.0518108i
$199$			16.8608i			1.19523i	0.801783	+	0.597615i	$0.203885\pi$
$199$			16.8608i			1.19523i	−0.801783	+	0.597615i	$0.796115\pi$
$200$		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
$204$	−1.17872	+	21.4233i	−0.0825271	+	1.49993i
$205$		0			0
$206$	−16.6700	−	3.51856i	−1.16145	−	0.245150i
$207$	−15.8196	−	1.00204i	−1.09954	−	0.0696464i
$208$	−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	$-0.928643\pi$
$211$		−	6.45821i		−	0.444602i	0.974978	−	0.222301i	$-0.0713567\pi$
$212$	10.1124	−	3.91480i	0.694521	−	0.268870i
$213$	−26.3873	−	11.9211i	−1.80803	−	0.816820i
$214$	4.27235	−	20.2413i	0.292052	−	1.38367i
$215$		0			0
$216$	6.51359	+	13.1747i	0.443194	+	0.896426i
$217$	−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
$222$	7.04866	−	9.61994i	0.473075	−	0.645648i
$223$	8.41178	+	8.41178i	0.563294	+	0.563294i	0.930242	−	0.366947i	$-0.119597\pi$
$223$	8.41178	+	8.41178i	0.563294	+	0.563294i	−0.366947	+	0.930242i	$0.619597\pi$
$224$	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	$-0.751194\pi$
$227$	−0.0799436	+	0.0799436i	−0.00530604	+	0.00530604i	0.704449	+	0.709755i	$0.251194\pi$
$228$	−11.3973	−	12.7245i	−0.754804	−	0.842700i
$229$	−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	$-0.718544\pi$
$233$	2.12983	−	2.12983i	0.139530	−	0.139530i	0.773422	+	0.633892i	$0.218544\pi$
$234$	−10.6213	+	5.99874i	−0.694335	+	0.392150i
$235$		0			0
$236$	−4.57982	−	2.02348i	−0.298121	−	0.131718i
$237$	8.39352	+	3.79197i	0.545218	+	0.246315i
$238$	15.0139	−	9.78050i	0.973205	−	0.633975i
$239$	−16.7173			−1.08135			−0.540676	−	0.841231i	$-0.681832\pi$
$239$	−16.7173			−1.08135			−0.540676	+	0.841231i	$0.681832\pi$
$240$		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
$243$	13.2827	+	8.15906i	0.852085	+	0.523404i
$244$	17.6403	+	7.79396i	1.12931	+	0.498957i
$245$		0			0
$246$	17.4527	−	2.69223i	1.11274	−	0.171651i
$247$	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	$-0.303564\pi$
$251$	18.3364			1.15738			0.578691	+	0.815547i	$0.303564\pi$
$252$	5.66019	−	10.8910i	0.356558	−	0.686069i
$253$	−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	$-0.231923\pi$
$257$	1.28687	+	1.28687i	0.0802726	+	0.0802726i	−0.665830	+	0.746103i	$0.731923\pi$
$258$	−12.2149	−	8.95005i	−0.760469	−	0.557206i
$259$	−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	$-0.694750\pi$
$263$	3.96091	−	3.96091i	0.244240	−	0.244240i	0.818602	+	0.574361i	$0.194750\pi$
$264$	3.03360	+	0.816700i	0.186705	+	0.0502644i
$265$		0			0
$266$	−2.94629	+	13.9587i	−0.180648	+	0.855865i
$267$	2.82812	−	6.26005i	0.173078	−	0.383109i
$268$	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
$273$	9.28379	+	4.19417i	0.561880	+	0.253843i
$274$	−17.4983	−	3.69338i	−1.05711	−	0.223125i
$275$		0			0
$276$	−18.2759	−	1.00555i	−1.10008	−	0.0605271i
$277$	−6.09911	−	6.09911i	−0.366460	−	0.366460i	0.499724	−	0.866184i	$-0.333435\pi$
$277$	−6.09911	−	6.09911i	−0.366460	−	0.366460i	−0.866184	+	0.499724i	$0.833435\pi$
$278$	−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	$0.958849\pi$
$282$	8.36292	−	11.4136i	0.498005	−	0.679672i
$283$	−6.55658	+	6.55658i	−0.389748	+	0.389748i	−0.874598	−	0.484849i	$-0.838874\pi$
$283$	−6.55658	+	6.55658i	−0.389748	+	0.389748i	0.484849	+	0.874598i	$0.338874\pi$
$284$	−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
$288$	7.64713	+	15.1500i	0.450611	+	0.892720i
$289$			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	$-0.300929\pi$
$293$	−3.85667	−	3.85667i	−0.225309	−	0.225309i	−0.810730	+	0.585421i	$0.800929\pi$
$294$	6.81527	−	1.05132i	0.397475	−	0.0613141i
$295$		0			0
$296$	8.04670	−	11.1753i	0.467705	−	0.649548i
$297$	3.18550	−	0.977765i	0.184841	−	0.0567357i
$298$	−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
$303$	−3.08226	+	6.82258i	−0.177071	+	0.391947i
$304$	−13.2818	−	14.5834i	−0.761766	−	0.836413i
$305$		0			0
$306$	12.9227	+	22.8807i	0.738740	+	1.30800i
$307$	−3.22023	−	3.22023i	−0.183788	−	0.183788i	0.609216	−	0.793004i	$-0.291484\pi$
$307$	−3.22023	−	3.22023i	−0.183788	−	0.183788i	−0.793004	+	0.609216i	$0.791484\pi$
$308$	−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	$-0.113825\pi$
$312$	−12.2065	+	7.02820i	−0.691060	+	0.397893i
$313$	11.6983	+	11.6983i	0.661226	+	0.661226i	0.955669	−	0.294443i	$-0.0951341\pi$
$313$	11.6983	+	11.6983i	0.661226	+	0.661226i	−0.294443	+	0.955669i	$0.595134\pi$
$314$	−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	$-0.815654\pi$
$317$	−5.15672	+	5.15672i	−0.289631	+	0.289631i	0.547304	+	0.836934i	$0.315654\pi$
$318$	7.84944	−	10.7128i	0.440175	−	0.600746i
$319$		−	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
$324$	15.4151	+	9.29378i	0.856395	+	0.516321i
$325$		0			0
$326$	−5.59604	+	26.5125i	−0.309936	+	1.46839i
$327$	8.16221	−	18.0670i	0.451371	−	0.999110i
$328$	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	$-0.873850\pi$
$331$		−	14.0460i		−	0.772037i	0.922491	−	0.386019i	$-0.126150\pi$
$332$	−5.80486	+	2.24723i	−0.318583	+	0.123333i
$333$	0.923324	−	14.5770i	0.0505979	−	0.798812i
$334$	17.1739	+	3.62491i	0.939713	+	0.198346i
$335$		0			0
$336$	6.43132	−	12.6296i	0.350857	−	0.689001i
$337$	10.5701	−	10.5701i	0.575791	−	0.575791i	−0.357950	−	0.933741i	$-0.616524\pi$
$337$	10.5701	−	10.5701i	0.575791	−	0.575791i	0.933741	+	0.357950i	$0.116524\pi$
$338$	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
$342$	−20.1566	−	5.60617i	−1.08994	−	0.303147i
$343$	−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	−0.0893127	+	0.996004i	$0.528467\pi$
$347$	−20.2172	+	20.2172i	−1.08532	+	1.08532i	−0.996004	+	0.0893127i	$0.971533\pi$
$348$	25.4016	−	22.7522i	1.36167	−	1.21964i
$349$	−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	0.0468748	−	0.998901i	$-0.485074\pi$
$353$	19.6483	−	19.6483i	1.04578	−	1.04578i	0.998901	−	0.0468748i	$-0.0149262\pi$
$354$	−6.06051	+	0.934890i	−0.322113	+	0.0496888i
$355$		0			0
$356$	3.20559	−	7.25531i	0.169896	−	0.384531i
$357$	9.03520	−	19.9994i	0.478194	−	1.05848i
$358$	1.63621	+	2.51171i	0.0864763	+	0.132748i
$359$	−12.6703			−0.668714			−0.334357	−	0.942446i	$-0.608519\pi$
$359$	−12.6703			−0.668714			−0.334357	+	0.942446i	$0.608519\pi$
$360$		0			0
$361$	5.31759			0.279873
$362$	−15.0056	−	23.0348i	−0.788674	−	1.21068i
$363$	−7.55084	+	16.7138i	−0.396316	+	0.877246i
$364$	10.7598	+	4.75395i	0.563966	+	0.249175i
$365$		0			0
$366$	23.3436	−	3.60096i	1.22019	−	0.188225i
$367$	−2.17316	+	2.17316i	−0.113438	+	0.113438i	−0.761547	−	0.648109i	$-0.775560\pi$
$367$	−2.17316	+	2.17316i	−0.113438	+	0.113438i	0.648109	+	0.761547i	$0.275560\pi$
$368$	−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
$372$	−12.0884	−	13.4961i	−0.626756	−	0.699741i
$373$	−19.7420	+	19.7420i	−1.02220	+	1.02220i	−0.0224556	+	0.999748i	$0.507148\pi$
$373$	−19.7420	+	19.7420i	−1.02220	+	1.02220i	−0.999748	+	0.0224556i	$0.992852\pi$
$374$	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
$378$	−1.34805	−	14.9720i	−0.0693361	−	0.770076i
$379$	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	$-0.956738\pi$
$383$	−16.7382	+	16.7382i	−0.855284	+	0.855284i	0.135495	+	0.990778i	$0.456738\pi$
$384$	8.97489	+	17.4199i	0.457998	+	0.888953i
$385$		0			0
$386$	−15.1413	−	3.19588i	−0.770670	−	0.162666i
$387$	−18.5091	−	1.17239i	−0.940872	−	0.0595961i
$388$	−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
$393$	11.1564	−	24.6947i	0.562765	−	1.24568i
$394$	−3.23310	+	15.3176i	−0.162881	+	0.771689i
$395$		0			0
$396$	3.66881	−	1.15949i	0.184365	−	0.0582663i
$397$	22.7486	+	22.7486i	1.14172	+	1.14172i	0.988136	+	0.153584i	$0.0490815\pi$
$397$	22.7486	+	22.7486i	1.14172	+	1.14172i	0.153584	+	0.988136i	$0.450918\pi$
$398$	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	$-0.207041\pi$
$402$	5.31686	−	7.25639i	0.265181	−	0.361916i
$403$	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
$408$	15.1404	+	26.2957i	0.749560	+	1.30183i
$409$		−	24.0958i		−	1.19146i	−0.803184	−	0.595731i	$-0.796863\pi$
$409$		−	24.0958i		−	1.19146i	0.803184	−	0.595731i	$-0.203137\pi$
$410$		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
$414$	−19.5192	+	11.0241i	−0.959315	+	0.541806i
$415$		0			0
$416$	−14.0271	+	8.23206i	−0.687737	+	0.403610i
$417$	−0.724763	+	1.60426i	−0.0354918	+	0.0785611i
$418$	−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	$-0.770235\pi$
$421$		−	27.1153i		−	1.32152i	0.750599	−	0.660758i	$-0.229765\pi$
$422$	−4.98523	−	7.65274i	−0.242677	−	0.372530i
$423$	1.09548	−	17.2949i	0.0532642	−	0.840907i
$424$	8.96087	−	12.4448i	0.435178	−	0.604375i
$425$		0			0
$426$	−40.4702	+	6.24289i	−1.96079	+	0.302469i
$427$	−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	$0.731982\pi$
$432$	17.8882	+	10.5836i	0.860647	+	0.509202i
$433$	8.18096	+	8.18096i	0.393152	+	0.393152i	0.875809	−	0.482658i	$-0.160328\pi$
$433$	8.18096	+	8.18096i	0.393152	+	0.393152i	−0.482658	+	0.875809i	$0.660328\pi$
$434$	−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
$438$	−17.2131	+	23.4923i	−0.822476	+	1.12251i
$439$		−	9.63432i		−	0.459821i	−0.973212	−	0.229910i	$-0.926157\pi$
$439$		−	9.63432i		−	0.459821i	0.973212	−	0.229910i	$-0.0738433\pi$
$440$		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	$-0.186898\pi$
$443$	5.86218	+	5.86218i	0.278521	+	0.278521i	−0.553998	+	0.832518i	$0.686898\pi$
$444$	0.926562	−	16.8403i	0.0439727	−	0.799204i
$445$		0			0
$446$	16.4609	+	3.47442i	0.779445	+	0.164518i
$447$	−4.76440	−	2.15243i	−0.225348	−	0.101806i
$448$	7.30508	−	14.6445i	0.345132	−	0.691887i
$449$	6.40566			0.302302			0.151151	−	0.988511i	$-0.451702\pi$
$449$	6.40566			0.302302			0.151151	+	0.988511i	$0.451702\pi$
$450$		0			0
$451$		−	4.62317i		−	0.217696i
$452$	7.44371	+	19.2279i	0.350122	+	0.904406i
$453$	−5.32079	+	11.7776i	−0.249993	+	0.553358i
$454$	−0.0330201	+	0.156440i	−0.00154971	+	0.00734211i
$455$		0			0
$456$	−23.3277	−	6.28024i	−1.09242	−	0.294099i
$457$	−16.7031	+	16.7031i	−0.781338	+	0.781338i	−0.980057	−	0.198719i	$-0.936322\pi$
$457$	−16.7031	+	16.7031i	−0.781338	+	0.781338i	0.198719	+	0.980057i	$0.436322\pi$
$458$	−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	$-0.809887\pi$
$461$	−35.5078			−1.65376			−0.826882	+	0.562376i	$0.809887\pi$
$462$	−2.59203	−	1.89921i	−0.120592	−	0.0883594i
$463$	9.79796	+	9.79796i	0.455350	+	0.455350i	0.897126	−	0.441776i	$-0.145651\pi$
$463$	9.79796	+	9.79796i	0.455350	+	0.455350i	−0.441776	+	0.897126i	$0.645651\pi$
$464$	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	$-0.664967\pi$
$467$	8.06737	−	8.06737i	0.373313	−	0.373313i	0.868683	+	0.495369i	$0.164967\pi$
$468$	−7.95527	+	15.3071i	−0.367733	+	0.707570i
$469$	−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
$474$	12.8731	−	1.98579i	0.591281	−	0.0912106i
$475$		0			0
$476$	10.2411	−	23.1791i	0.469401	−	1.06241i
$477$	1.02822	−	16.2330i	0.0470790	−	0.743258i
$478$	−19.8094	+	12.9044i	−0.906060	+	0.590235i
$479$	−4.04697			−0.184911			−0.0924553	−	0.995717i	$-0.529472\pi$
$479$	−4.04697			−0.184911			−0.0924553	+	0.995717i	$0.529472\pi$
$480$		0			0
$481$	13.9983			0.638267
$482$	−5.55406	+	3.61809i	−0.252981	+	0.164799i
$483$	17.0612	+	7.70779i	0.776312	+	0.350717i
$484$	−8.55863	+	19.3710i	−0.389029	+	0.880502i
$485$		0			0
$486$	22.0376	−	0.584995i	0.999648	−	0.0265359i
$487$	−6.28516	+	6.28516i	−0.284808	+	0.284808i	−0.835023	−	0.550215i	$-0.814546\pi$
$487$	−6.28516	+	6.28516i	−0.284808	+	0.284808i	0.550215	+	0.835023i	$0.314546\pi$
$488$	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	$-0.307922\pi$
$491$	25.1486			1.13494			0.567471	+	0.823393i	$0.307922\pi$
$492$	18.6026	−	16.6623i	0.838669	−	0.751194i
$493$	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
$498$	−4.50586	+	6.14955i	−0.201912	+	0.275568i
$499$	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	$-0.893087\pi$
$503$	−13.7823	+	13.7823i	−0.614523	+	0.614523i	0.329598	+	0.944121i	$0.393087\pi$
$504$	−1.69988	−	17.2747i	−0.0757188	−	0.769474i
$505$		0			0
$506$	−0.989624	+	4.68858i	−0.0439942	+	0.208433i
$507$	7.47162	+	3.37548i	0.331826	+	0.149910i
$508$	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
$513$	−24.4958	+	7.51879i	−1.08151	+	0.331963i
$514$	2.51825	+	0.531531i	0.111075	+	0.0234448i
$515$		0			0
$516$	−21.3830	−	1.17651i	−0.941334	−	0.0517928i
$517$	−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	$-0.252673\pi$
$522$	11.1915	−	40.2381i	0.489837	−	1.76117i
$523$	9.90568	−	9.90568i	0.433145	−	0.433145i	−0.456552	−	0.889697i	$-0.650916\pi$
$523$	9.90568	−	9.90568i	0.433145	−	0.433145i	0.889697	+	0.456552i	$0.150916\pi$
$524$	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
$528$	4.22513	−	1.37394i	0.183875	−	0.0597930i
$529$		−	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
$534$	−1.48104	−	9.60101i	−0.0640910	−	0.415476i
$535$		0			0
$536$	6.06969	−	8.42958i	0.262171	−	0.364102i
$537$	3.34576	+	1.51153i	0.144380	+	0.0652271i
$538$	−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	$0.395230\pi$
$541$			44.0216i			1.89264i	−0.323234	+	0.946319i	$0.604770\pi$
$542$	8.94500	−	5.82705i	0.384221	−	0.250293i
$543$	−30.6838	−	13.8621i	−1.31677	−	0.594880i
$544$	17.7337	+	30.2177i	0.760328	+	1.29557i
$545$		0			0
$546$	14.2385	−	2.19642i	0.609352	−	0.0939981i
$547$	5.74698	+	5.74698i	0.245723	+	0.245723i	0.819213	−	0.573490i	$-0.194411\pi$
$547$	5.74698	+	5.74698i	0.245723	+	0.245723i	−0.573490	+	0.819213i	$0.694411\pi$
$548$	−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
$552$	−22.4325	+	12.9160i	−0.954789	+	0.549742i
$553$	−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	−0.0186883	+	0.999825i	$0.505949\pi$
$557$	−24.0378	+	24.0378i	−1.01851	+	1.01851i	−0.999825	+	0.0186883i	$0.994051\pi$
$558$	−21.3789	−	5.94613i	−0.905040	−	0.251720i
$559$		−	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	$-0.107657\pi$
$563$	14.5105	+	14.5105i	0.611544	+	0.611544i	−0.331805	+	0.943348i	$0.607657\pi$
$564$	1.09933	−	19.9802i	0.0462899	−	0.841320i
$565$		0			0
$566$	−2.70814	+	12.8305i	−0.113832	+	0.539305i
$567$	−11.2719	−	14.5572i	−0.473375	−	0.611343i
$568$	−46.6695	+	7.59590i	−1.95821	+	0.318717i
$569$	31.0050			1.29980			0.649900	−	0.760020i	$-0.274811\pi$
$569$	31.0050			1.29980			0.649900	+	0.760020i	$0.274811\pi$
$570$		0			0
$571$			33.0629i			1.38364i	0.722070	+	0.691820i	$0.243191\pi$
$571$			33.0629i			1.38364i	−0.722070	+	0.691820i	$0.756809\pi$
$572$	1.33128	+	3.43884i	0.0556636	+	0.143785i
$573$	4.20671	+	1.90048i	0.175738	+	0.0793936i
$574$	−20.4070	−	4.30732i	−0.851771	−	0.179784i
$575$		0			0
$576$	20.7561	+	12.0492i	0.864839	+	0.502049i
$577$	−17.5957	+	17.5957i	−0.732519	+	0.732519i	−0.971118	−	0.238599i	$-0.923312\pi$
$577$	−17.5957	+	17.5957i	−0.732519	+	0.732519i	0.238599	+	0.971118i	$0.423312\pi$
$578$	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
$582$	−3.11101	−	2.27948i	−0.128955	−	0.0944873i
$583$	−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	$-0.810630\pi$
$587$	−6.48696	+	6.48696i	−0.267746	+	0.267746i	0.560446	+	0.828191i	$0.310630\pi$
$588$	7.26431	−	6.50663i	0.299575	−	0.268329i
$589$	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	$-0.770088\pi$
$593$	−2.17189	+	2.17189i	−0.0891890	+	0.0891890i	0.661105	+	0.750294i	$0.270088\pi$
$594$	3.01994	−	3.61757i	0.123910	−	0.148431i
$595$		0			0
$596$	−5.52187	−	2.43971i	−0.226185	−	0.0999343i
$597$	26.6138	+	12.0234i	1.08923	+	0.492086i
$598$	−11.7267	−	18.0015i	−0.479542	−	0.736137i
$599$	−7.56553			−0.309119			−0.154560	−	0.987983i	$-0.549396\pi$
$599$	−7.56553			−0.309119			−0.154560	+	0.987983i	$0.549396\pi$
$600$		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
$603$	0.696471	−	10.9955i	0.0283625	−	0.447772i
$604$	−6.03095	+	13.6500i	−0.245396	+	0.555412i
$605$		0			0
$606$	1.61413	+	10.4638i	0.0655696	+	0.425062i
$607$	28.6094	−	28.6094i	1.16122	−	1.16122i	0.177009	−	0.984209i	$-0.443358\pi$
$607$	28.6094	−	28.6094i	1.16122	−	1.16122i	0.984209	−	0.177009i	$-0.0566421\pi$
$608$	−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
$612$	32.9750	+	17.1375i	1.33293	+	0.692742i
$613$	−9.80228	+	9.80228i	−0.395910	+	0.395910i	−0.876788	−	0.480878i	$-0.840318\pi$
$613$	−9.80228	+	9.80228i	−0.395910	+	0.395910i	0.480878	+	0.876788i	$0.340318\pi$
$614$	−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	$-0.195002\pi$
$617$	6.03941	+	6.03941i	0.243138	+	0.243138i	−0.575009	+	0.818147i	$0.695002\pi$
$618$	−17.4412	+	23.8036i	−0.701589	+	0.957522i
$619$	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
$624$	−9.03909	+	17.7506i	−0.361853	+	0.710595i
$625$		0			0
$626$	22.8922	+	4.83188i	0.914956	+	0.193121i
$627$	−2.25505	+	4.99156i	−0.0900582	+	0.199344i
$628$	−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
$633$	−10.1939	−	4.60535i	−0.405173	−	0.183046i
$634$	−2.12994	+	10.0911i	−0.0845909	+	0.400769i
$635$		0			0
$636$	1.03183	−	18.7535i	0.0409146	−	0.743623i
$637$	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	$0.833169\pi$
$642$	−28.9032	−	21.1777i	−1.14072	−	0.835818i
$643$	16.2516	−	16.2516i	0.640899	−	0.640899i	−0.309878	−	0.950776i	$-0.600288\pi$
$643$	16.2516	−	16.2516i	0.640899	−	0.640899i	0.950776	+	0.309878i	$0.100288\pi$
$644$	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	$-0.279281\pi$
$647$	−3.30434	−	3.30434i	−0.129907	−	0.129907i	−0.769071	+	0.639164i	$0.779281\pi$
$648$	25.4404	−	0.886466i	0.999393	−	0.0348237i
$649$			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	$-0.232362\pi$
$653$	2.00144	+	2.00144i	0.0783225	+	0.0783225i	−0.666860	+	0.745183i	$0.732362\pi$
$654$	−4.27442	−	27.7094i	−0.167143	−	1.08352i
$655$		0			0
$656$	21.3201	−	19.4174i	0.832411	−	0.758122i
$657$	−2.25480	+	35.5976i	−0.0879681	+	1.38879i
$658$	−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	$-0.933146\pi$
$661$		−	10.7204i		−	0.416977i	0.978025	−	0.208488i	$-0.0668544\pi$
$662$	−10.8424	−	16.6440i	−0.421402	−	0.646887i
$663$	−12.6988	+	28.1088i	−0.493180	+	1.09165i
$664$	−5.14386	+	7.14379i	−0.199620	+	0.277233i
$665$		0			0
$666$	−10.1582	−	17.9859i	−0.393621	−	0.696939i
$667$	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
$672$	−2.12818	−	19.9301i	−0.0820964	−	0.768820i
$673$	12.2384	+	12.2384i	0.471755	+	0.471755i	0.902482	−	0.430727i	$-0.141743\pi$
$673$	12.2384	+	12.2384i	0.471755	+	0.471755i	−0.430727	+	0.902482i	$0.641743\pi$
$674$	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	$-0.715384\pi$
$677$	3.99371	−	3.99371i	0.153491	−	0.153491i	0.779675	+	0.626184i	$0.215384\pi$
$678$	20.3697	+	14.9251i	0.782293	+	0.573196i
$679$			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	$-0.187613\pi$
$683$	7.19759	+	7.19759i	0.275408	+	0.275408i	−0.555865	+	0.831273i	$0.687613\pi$
$684$	−28.2123	+	8.91618i	−1.07872	+	0.340919i
$685$		0			0
$686$	−27.7835	−	5.86429i	−1.06078	−	0.223900i
$687$	−9.25106	+	20.4772i	−0.352950	+	0.781255i
$688$	−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	$0.152049\pi$
$691$			24.1691i			0.919434i	−0.888065	+	0.459717i	$0.847951\pi$
$692$	40.3106	−	15.6054i	1.53238	−	0.593229i
$693$	−3.92766	−	0.248783i	−0.149200	−	0.00945050i
$694$	−8.35055	+	39.5627i	−0.316983	+	1.50178i
$695$		0			0
$696$	12.5371	−	46.5685i	0.475217	−	1.76517i
$697$	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	$-0.698345\pi$
$701$	−30.9018			−1.16714			−0.583572	+	0.812061i	$0.698345\pi$
$702$	1.89465	+	21.0428i	0.0715091	+	0.794210i
$703$	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
$708$	−6.45982	+	5.78605i	−0.242775	+	0.217453i
$709$	−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
$714$	−4.73160	−	30.6730i	−0.177076	−	1.14791i
$715$		0			0
$716$	3.87769	+	1.71327i	0.144916	+	0.0640277i
$717$	−11.9211	+	26.3873i	−0.445201	+	0.985453i
$718$	−15.0139	+	9.78050i	−0.560313	+	0.365005i
$719$	34.2881			1.27873			0.639364	−	0.768904i	$-0.279198\pi$
$719$	34.2881			1.27873			0.639364	+	0.768904i	$0.279198\pi$
$720$		0			0
$721$	24.6446			0.917812
$722$	6.30114	−	4.10476i	0.234504	−	0.152763i
$723$	−3.34238	+	7.39836i	−0.124304	+	0.275148i
$724$	−35.5621	−	15.7123i	−1.32165	−	0.583941i
$725$		0			0
$726$	3.95426	+	25.6339i	0.146756	+	0.951362i
$727$	2.33356	−	2.33356i	0.0865468	−	0.0865468i	−0.662508	−	0.749055i	$-0.730508\pi$
$727$	2.33356	−	2.33356i	0.0865468	−	0.0865468i	0.749055	+	0.662508i	$0.230508\pi$
$728$	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
$732$	24.8816	−	22.2864i	0.919651	−	0.823730i
$733$	35.6179	−	35.6179i	1.31558	−	1.31558i	0.398342	−	0.917237i	$-0.369586\pi$
$733$	35.6179	−	35.6179i	1.31558	−	1.31558i	0.917237	−	0.398342i	$-0.130414\pi$
$734$	−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
$738$	8.19594	−	29.4679i	0.301697	−	1.08473i
$739$	−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	$-0.765504\pi$
$743$	−1.87689	+	1.87689i	−0.0688563	+	0.0688563i	0.671840	+	0.740696i	$0.265504\pi$
$744$	−24.7423	−	6.66108i	−0.907096	−	0.244207i
$745$		0			0
$746$	−8.15428	+	38.6329i	−0.298550	+	1.41445i
$747$	−0.590235	+	9.31833i	−0.0215956	+	0.340940i
$748$	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
$753$	13.0757	−	28.9430i	0.476503	−	1.05474i
$754$	39.1644	+	8.26647i	1.42628	+	0.301047i
$755$		0			0
$756$	−13.1546	−	16.7007i	−0.478427	−	0.607397i
$757$	−34.9468	−	34.9468i	−1.27016	−	1.27016i	−0.946002	−	0.324162i	$-0.894918\pi$
$757$	−34.9468	−	34.9468i	−1.27016	−	1.27016i	−0.324162	−	0.946002i	$-0.605082\pi$
$758$	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	$0.983336\pi$
$762$	32.0561	+	23.4879i	1.16127	+	0.850879i
$763$	−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
$768$	24.0817	+	13.7140i	0.868972	+	0.494861i
$769$		−	19.0345i		−	0.686400i	−0.939262	−	0.343200i	$-0.888489\pi$
$769$		−	19.0345i		−	0.686400i	0.939262	−	0.343200i	$-0.111511\pi$
$770$		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	$-0.410344\pi$
$773$	−18.9794	−	18.9794i	−0.682642	−	0.682642i	−0.960595	+	0.277953i	$0.910344\pi$
$774$	−22.8376	+	12.8984i	−0.820882	+	0.463622i
$775$		0			0
$776$	−3.61398	−	2.60223i	−0.129734	−	0.0934148i
$777$	−7.10233	+	15.7210i	−0.254795	+	0.563988i
$778$	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
$783$	−15.0096	−	48.9003i	−0.536399	−	1.74756i
$784$	8.32552	−	7.58250i	0.297340	−	0.270804i
$785$		0			0
$786$	−5.84243	−	37.8741i	−0.208393	−	1.35093i
$787$	−28.3424	−	28.3424i	−1.01030	−	1.01030i	−0.999946	−	0.0103521i	$-0.996705\pi$
$787$	−28.3424	−	28.3424i	−1.01030	−	1.01030i	−0.0103521	−	0.999946i	$-0.503295\pi$
$788$	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
$792$	3.45237	−	4.20598i	0.122675	−	0.149453i
$793$	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	$-0.620357\pi$
$797$	15.8150	−	15.8150i	0.560195	−	0.560195i	0.929363	+	0.369168i	$0.120357\pi$
$798$	19.9321	+	14.6045i	0.705589	+	0.516994i
$799$		−	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
$804$	0.698913	−	12.7028i	0.0246488	−	0.447992i
$805$		0			0
$806$	4.39206	−	20.8084i	0.154704	−	0.732945i
$807$	−2.87101	−	1.29704i	−0.101064	−	0.0456581i
$808$	1.96396	+	12.0666i	0.0690918	+	0.424503i
$809$	−49.0232			−1.72356			−0.861782	−	0.507279i	$-0.830651\pi$
$809$	−49.0232			−1.72356			−0.861782	+	0.507279i	$0.830651\pi$
$810$		0			0
$811$		−	21.1676i		−	0.743295i	−0.928374	−	0.371648i	$-0.878793\pi$
$811$		−	21.1676i		−	0.743295i	0.928374	−	0.371648i	$-0.121207\pi$
$812$	−37.5597	+	14.5405i	−1.31809	+	0.510271i
$813$	5.38302	−	11.9153i	0.188791	−	0.417888i
$814$	−4.32028	−	0.911887i	−0.151426	−	0.0319616i
$815$		0			0
$816$	38.2390	+	19.4723i	1.33863	+	0.681666i
$817$	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	$-0.424385\pi$
$821$	13.4855			0.470649			0.235324	+	0.971917i	$0.424385\pi$
$822$	−18.3078	+	24.9863i	−0.638558	+	0.871498i
$823$	−19.8632	−	19.8632i	−0.692387	−	0.692387i	0.270370	−	0.962757i	$-0.412854\pi$
$823$	−19.8632	−	19.8632i	−0.692387	−	0.692387i	−0.962757	+	0.270370i	$0.912854\pi$
$824$	−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	0.339982	−	0.940432i	$-0.389579\pi$
$827$	36.8216	−	36.8216i	1.28041	−	1.28041i	0.940432	−	0.339982i	$-0.110421\pi$
$828$	−14.6197	+	28.1304i	−0.508071	+	0.977601i
$829$	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
$834$	0.379547	+	2.46045i	0.0131427	+	0.0851985i
$835$		0			0
$836$	−2.55603	+	5.78515i	−0.0884022	+	0.200084i
$837$	−25.9812	+	7.97474i	−0.898042	+	0.275647i
$838$	−30.8432	−	47.3469i	−1.06546	−	1.63557i
$839$	−19.6854			−0.679616			−0.339808	−	0.940495i	$-0.610362\pi$
$839$	−19.6854			−0.679616			−0.339808	+	0.940495i	$0.610362\pi$
$840$		0			0
$841$	−67.9085			−2.34167
$842$	−20.9308	−	32.1306i	−0.721324	−	1.10729i
$843$	6.82234	+	3.08215i	0.234974	+	0.106155i
$844$	−11.8146	−	5.22001i	−0.406676	−	0.179680i
$845$		0			0
$846$	−12.0522	−	21.3395i	−0.414363	−	0.733666i
$847$	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
$852$	−43.1366	+	38.6374i	−1.47784	+	1.32369i
$853$	−29.0954	+	29.0954i	−0.996209	+	0.996209i	−0.999993	−	0.00378410i	$-0.998795\pi$
$853$	−29.0954	+	29.0954i	−0.996209	+	0.996209i	0.00378410	+	0.999993i	$0.498795\pi$
$854$	−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	$-0.317528\pi$
$857$	−8.71719	−	8.71719i	−0.297773	−	0.297773i	−0.840141	+	0.542368i	$0.817528\pi$
$858$	3.64304	+	2.66930i	0.124371	+	0.0911285i
$859$	−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	$-0.526980\pi$
$863$	26.7844	−	26.7844i	0.911750	−	0.911750i	0.996410	+	0.0846599i	$0.0269804\pi$
$864$	29.3666	−	1.26714i	0.999070	−	0.0431090i
$865$		0			0
$866$	16.0092	+	3.37908i	0.544014	+	0.114826i
$867$	33.7192	+	15.2334i	1.14516	+	0.517354i
$868$	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
$873$	−4.71406	−	0.298595i	−0.159547	−	0.0101059i
$874$	7.60998	−	36.0541i	0.257412	−	1.21955i
$875$		0			0
$876$	−2.26271	+	41.1247i	−0.0764498	+	1.38948i
$877$	−13.3952	−	13.3952i	−0.452323	−	0.452323i	0.443802	−	0.896125i	$-0.353629\pi$
$877$	−13.3952	−	13.3952i	−0.452323	−	0.452323i	−0.896125	+	0.443802i	$0.853629\pi$
$878$	−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	$-0.0637889\pi$
$882$	3.20052	−	11.5072i	0.107767	−	0.387469i
$883$	19.7888	−	19.7888i	0.665947	−	0.665947i	−0.290828	−	0.956775i	$-0.593931\pi$
$883$	19.7888	−	19.7888i	0.665947	−	0.665947i	0.956775	+	0.290828i	$0.0939308\pi$
$884$	−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	$-0.246432\pi$
$887$	0.472133	+	0.472133i	0.0158527	+	0.0158527i	−0.699136	+	0.714989i	$0.746432\pi$
$888$	−11.9014	−	20.6703i	−0.399386	−	0.693651i
$889$		−	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
$894$	−7.30714	+	1.12719i	−0.244387	+	0.0376990i
$895$		0			0
$896$	−2.64814	−	22.9921i	−0.0884683	−	0.768113i
$897$	−23.9792	−	10.8331i	−0.800641	−	0.361708i
$898$	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
$903$	19.9618	+	9.01820i	0.664287	+	0.300107i
$904$	23.6630	+	17.0384i	0.787019	+	0.566690i
$905$		0			0
$906$	2.78642	+	18.0632i	0.0925725	+	0.600110i
$907$	−38.0394	−	38.0394i	−1.26308	−	1.26308i	−0.949594	−	0.313482i	$-0.898505\pi$
$907$	−38.0394	−	38.0394i	−1.26308	−	1.26308i	−0.313482	−	0.949594i	$-0.601495\pi$
$908$	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	$-0.311919\pi$
$912$	−32.4903	+	10.5653i	−1.07586	+	0.349851i
$913$	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
$918$	45.3311	−	4.08152i	1.49615	−	0.134710i
$919$			21.5999i			0.712514i	0.934388	+	0.356257i	$0.115947\pi$
$919$			21.5999i			0.712514i	−0.934388	+	0.356257i	$0.884053\pi$
$920$		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
$924$	−4.53750	−	0.249656i	−0.149273	−	0.00821308i
$925$		0			0
$926$	19.1735	+	4.04697i	0.630079	+	0.132992i
$927$	−2.28468	+	36.0693i	−0.0750387	+	1.18467i
$928$	14.0302	−	53.8909i	0.460565	−	1.76905i
$929$	−0.457555			−0.0150119			−0.00750595	−	0.999972i	$-0.502389\pi$
$929$	−0.457555			−0.0150119			−0.00750595	+	0.999972i	$0.502389\pi$
$930$		0			0
$931$			13.8827i			0.454988i
$932$	−2.17481	−	5.61778i	−0.0712383	−	0.184017i
$933$	−19.4863	−	8.80340i	−0.637954	−	0.288211i
$934$	3.33216	−	15.7869i	0.109032	−	0.516563i
$935$		0			0
$936$	2.38915	+	24.2792i	0.0780918	+	0.793589i
$937$	−7.63736	+	7.63736i	−0.249502	+	0.249502i	−0.820766	−	0.571264i	$-0.806453\pi$
$937$	−7.63736	+	7.63736i	−0.249502	+	0.249502i	0.571264	+	0.820766i	$0.306453\pi$
$938$	−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	$-0.176259\pi$
$941$	52.1835			1.70113			0.850567	+	0.525867i	$0.176259\pi$
$942$	−12.4613	+	17.0071i	−0.406013	+	0.554122i
$943$	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	$-0.976305\pi$
$947$	−28.3995	+	28.3995i	−0.922860	+	0.922860i	0.0743707	+	0.997231i	$0.476305\pi$
$948$	13.7213	−	12.2901i	0.445647	−	0.399164i
$949$	−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	$-0.931903\pi$
$953$	−23.6130	+	23.6130i	−0.764900	+	0.764900i	0.212304	+	0.977204i	$0.431903\pi$
$954$	−11.3122	−	20.0292i	−0.366246	−	0.648470i
$955$		0			0
$956$	−13.5122	+	30.5826i	−0.437015	+	0.989111i
$957$	−9.96454	−	4.50171i	−0.322108	−	0.145520i
$958$	−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
$963$	−43.7965	−	2.77413i	−1.41132	−	0.0893952i
$964$	−3.78848	+	8.57460i	−0.122019	+	0.276169i
$965$		0			0
$966$	26.1667	−	4.03645i	0.841900	−	0.129871i
$967$	3.10676	−	3.10676i	0.0999067	−	0.0999067i	−0.655387	−	0.755293i	$-0.727494\pi$
$967$	3.10676	−	3.10676i	0.0999067	−	0.0999067i	0.755293	+	0.655387i	$0.227494\pi$
$968$	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	$-0.413440\pi$
$971$	16.7395			0.537196			0.268598	+	0.963252i	$0.413440\pi$
$972$	25.6622	−	17.7045i	0.823116	−	0.567873i
$973$	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	−0.957104	−	0.289745i	$-0.906430\pi$
$977$	−38.9727	−	38.9727i	−1.24685	−	1.24685i	−0.289745	−	0.957104i	$-0.593570\pi$
$978$	37.8581	+	27.7391i	1.21057	+	0.886999i
$979$	−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	$-0.586161\pi$
$983$	21.8279	−	21.8279i	0.696200	−	0.696200i	0.963589	+	0.267388i	$0.0861607\pi$
$984$	9.18140	−	34.1039i	0.292692	−	1.08719i
$985$		0			0
$986$	17.8079	−	84.3691i	0.567119	−	2.68686i
$987$	−8.42660	+	18.6523i	−0.268222	+	0.593708i
$988$	−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
$993$	−22.1708	−	10.0162i	−0.703570	−	0.317854i
$994$	47.3208	+	9.98805i	1.50092	+	0.316802i
$995$		0			0
$996$	−0.592306	+	10.7652i	−0.0187679	+	0.341107i
$997$	17.8369	+	17.8369i	0.564900	+	0.564900i	0.930695	−	0.365795i	$-0.119203\pi$
$997$	17.8369	+	17.8369i	0.564900	+	0.564900i	−0.365795	+	0.930695i	$0.619203\pi$
$998$	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.293.26	yes	64
3.2	odd	2	inner	600.2.w.k.293.8	yes	64
5.2	odd	4	inner	600.2.w.k.557.23	yes	64
5.3	odd	4	inner	600.2.w.k.557.10	yes	64
5.4	even	2	inner	600.2.w.k.293.7	✓	64
8.5	even	2	inner	600.2.w.k.293.9	yes	64
15.2	even	4	inner	600.2.w.k.557.9	yes	64
15.8	even	4	inner	600.2.w.k.557.24	yes	64
15.14	odd	2	inner	600.2.w.k.293.25	yes	64
24.5	odd	2	inner	600.2.w.k.293.23	yes	64
40.13	odd	4	inner	600.2.w.k.557.25	yes	64
40.29	even	2	inner	600.2.w.k.293.24	yes	64
40.37	odd	4	inner	600.2.w.k.557.8	yes	64
120.29	odd	2	inner	600.2.w.k.293.10	yes	64
120.53	even	4	inner	600.2.w.k.557.7	yes	64
120.77	even	4	inner	600.2.w.k.557.26	yes	64

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

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

\(f(q)\)	\(=\)	\(q+(1.18496 - 0.771921i) q^{2} +(0.713099 - 1.57845i) q^{3} +(0.808275 - 1.82940i) q^{4} +(-0.373439 - 2.42086i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(-0.454373 - 2.79169i) q^{8} +(-1.98298 - 2.25118i) q^{9} +O(q^{10})\)	\(q+(1.18496 - 0.771921i) q^{2} +(0.713099 - 1.57845i) q^{3} +(0.808275 - 1.82940i) q^{4} +(-0.373439 - 2.42086i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(-0.454373 - 2.79169i) q^{8} +(-1.98298 - 2.25118i) q^{9} -0.641278 q^{11} +(-2.31122 - 2.58036i) 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} +(-4.08749 - 1.13686i) q^{18} +4.93129 q^{19} +(1.25173 + 3.31474i) q^{21} +(-0.759891 + 0.495016i) q^{22} +(3.73619 - 3.73619i) q^{23} +(-4.73055 - 1.27355i) q^{24} +(0.839729 - 3.97842i) q^{26} +(-4.96742 + 1.52471i) q^{27} +(1.47706 + 3.81541i) q^{28} +9.84421i q^{29} +5.23032 q^{31} +(-5.47437 - 1.42523i) q^{32} +(-0.457295 + 1.01222i) q^{33} +(-8.57043 - 1.80897i) q^{34} +(-5.72109 + 1.80808i) q^{36} +(3.44271 + 3.44271i) q^{37} +(5.84339 - 3.80656i) q^{38} +(-1.75928 - 4.65879i) q^{39} +7.20930i q^{41} +(4.04197 + 2.96160i) 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} +(-6.58860 + 2.14250i) q^{48} +2.81523i q^{49} +(-10.0361 + 3.78989i) q^{51} +(-2.07598 - 5.36248i) q^{52} +(3.83383 + 3.83383i) q^{53} +(-4.70925 + 5.64118i) q^{54} +(4.69546 + 3.38095i) q^{56} +(3.51650 - 7.78377i) q^{57} +(7.59896 + 11.6650i) q^{58} -2.50346i q^{59} +9.64270i q^{61} +(6.19774 - 4.03740i) q^{62} +(6.12474 + 0.387949i) q^{63} +(-7.58709 + 2.53694i) q^{64} +(0.239478 + 1.55244i) q^{66} +(2.59686 + 2.59686i) q^{67} +(-11.5520 + 4.47213i) q^{68} +(-3.23310 - 8.56166i) q^{69} -16.7173i q^{71} +(-5.38358 + 6.55874i) 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} +(-5.68090 - 4.16247i) q^{78} +5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(5.56501 + 8.54275i) q^{82} +(-2.20075 - 2.20075i) q^{83} +(7.07571 + 0.389310i) q^{84} +(1.80557 - 8.55430i) q^{86} +(15.5386 + 7.01990i) q^{87} +(0.291380 + 1.79025i) q^{88} +3.96596 q^{89} +5.88160i q^{91} +(-3.81511 - 9.85485i) q^{92} +(3.72974 - 8.25578i) q^{93} +(7.99313 + 1.68712i) q^{94} +(-6.15341 + 7.62467i) q^{96} +(1.11334 - 1.11334i) q^{97} +(2.17314 + 3.33595i) q^{98} +(1.27164 + 1.44363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 64 * q + 12 * q^6	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 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

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Database

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