LMFDB - Embedded newform 600.2.w.k.293.23

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			293.23
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.771921	−	1.18496i	0.545831	−	0.837895i
$2$	0.771921	−	1.18496i	0.545831	−	0.837895i
$3$	−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
$6$	−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	$0.376349\pi$
$8$	−2.79169	−	0.454373i	−0.987012	−	0.160645i
$9$	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	$0.530821\pi$
$12$	2.58036	+	2.31122i	0.744886	+	0.667192i
$13$	−2.03304	+	2.03304i	−0.563863	+	0.563863i	−0.930402	−	0.366540i	$-0.880542\pi$
$13$	−2.03304	+	2.03304i	−0.563863	+	0.563863i	0.366540	+	0.930402i	$0.380542\pi$
$14$	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	$0.0204764\pi$
$17$	4.37963	+	4.37963i	1.06222	+	1.06222i	0.0642843	+	0.997932i	$0.479524\pi$
$18$	−1.13686	−	4.08749i	−0.267960	−	0.963430i
$19$	−4.93129			−1.13131			−0.565657	−	0.824640i	$-0.691378\pi$
$19$	−4.93129			−1.13131			−0.565657	+	0.824640i	$0.691378\pi$
$20$		0			0
$21$	1.25173	−	3.31474i	0.273150	−	0.723335i
$22$	−0.495016	+	0.759891i	−0.105538	+	0.162009i
$23$	−3.73619	+	3.73619i	−0.779050	+	0.779050i	−0.979669	−	0.200619i	$-0.935705\pi$
$23$	−3.73619	+	3.73619i	−0.779050	+	0.779050i	0.200619	+	0.979669i	$0.435705\pi$
$24$	4.73055	−	1.27355i	0.965619	−	0.259962i
$25$		0			0
$26$	0.839729	+	3.97842i	0.164684	+	0.780232i
$27$	−1.52471	+	4.96742i	−0.293431	+	0.955980i
$28$	3.81541	+	1.47706i	0.721045	+	0.279138i
$29$			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	$0.344363\pi$
$32$	1.42523	+	5.47437i	0.251947	+	0.967741i
$33$	1.01222	−	0.457295i	0.176205	−	0.0796049i
$34$	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	0.365022	−	0.930999i	$-0.381062\pi$
$37$	−3.44271	−	3.44271i	−0.565978	−	0.565978i	−0.930999	+	0.365022i	$0.881062\pi$
$38$	−3.80656	+	5.84339i	−0.617506	+	0.947923i
$39$	1.75928	−	4.65879i	0.281710	−	0.746004i
$40$		0			0
$41$		−	7.20930i		−	1.12590i	−0.826490	−	0.562951i	$-0.809666\pi$
$41$		−	7.20930i		−	1.12590i	0.826490	−	0.562951i	$-0.190334\pi$
$42$	−2.96160	−	4.04197i	−0.456985	−	0.623689i
$43$	−4.37139	+	4.37139i	−0.666630	+	0.666630i	−0.956934	−	0.290304i	$-0.906244\pi$
$43$	−4.37139	+	4.37139i	−0.666630	+	0.666630i	0.290304	+	0.956934i	$0.406244\pi$
$44$	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	0.343390	−	0.939193i	$-0.388425\pi$
$47$	−4.08462	−	4.08462i	−0.595803	−	0.595803i	−0.939193	+	0.343390i	$0.888425\pi$
$48$	2.14250	−	6.58860i	0.309243	−	0.950983i
$49$			2.81523i			0.402176i
$50$		0			0
$51$	−10.0361	−	3.78989i	−1.40534	−	0.530691i
$52$	5.36248	+	2.07598i	0.743642	+	0.287886i
$53$	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
$57$	7.78377	−	3.51650i	1.03098	−	0.465771i
$58$	11.6650	+	7.59896i	1.53169	+	0.997792i
$59$		−	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	$-0.211778\pi$
$62$	4.03740	−	6.19774i	0.512750	−	0.787114i
$63$	0.387949	+	6.12474i	0.0488770	+	0.771644i
$64$	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	0.530456	−	0.847713i	$-0.322021\pi$
$67$	−2.59686	−	2.59686i	−0.317257	−	0.317257i	−0.847713	+	0.530456i	$0.822021\pi$
$68$	4.47213	−	11.5520i	0.542326	−	1.40089i
$69$	3.23310	−	8.56166i	0.389220	−	1.03070i
$70$		0			0
$71$			16.7173i			1.98398i	0.126324	+	0.991989i	$0.459682\pi$
$71$			16.7173i			1.98398i	−0.126324	+	0.991989i	$0.540318\pi$
$72$	−6.55874	+	5.38358i	−0.772955	+	0.634461i
$73$	−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
$78$	−4.16247	−	5.68090i	−0.471307	−	0.643236i
$79$			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
$82$	−8.54275	−	5.56501i	−0.943389	−	0.614552i
$83$	−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
$87$	−7.01990	−	15.5386i	−0.752612	−	1.66591i
$88$	1.79025	+	0.291380i	0.190841	+	0.0310612i
$89$	−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
$92$	9.85485	+	3.81511i	1.02744	+	0.397752i
$93$	−8.25578	+	3.72974i	−0.856085	+	0.386756i
$94$	−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	$0.224529\pi$
$98$	3.33595	+	2.17314i	0.336982	+	0.219520i
$99$	−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	$0.568990\pi$
$102$	−12.2380	+	8.96692i	−1.21174	+	0.887858i
$103$	−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	$1.37980e-5\pi$
$108$	10.3198	−	1.22574i	0.993020	−	0.117947i
$109$	−11.4461			−1.09634			−0.548169	−	0.836368i	$-0.684675\pi$
$109$	−11.4461			−1.09634			−0.548169	+	0.836368i	$0.684675\pi$
$110$		0			0
$111$	7.88912	+	2.97913i	0.748802	+	0.282767i
$112$	−0.381776	−	8.17377i	−0.0360744	−	0.772349i
$113$	7.28974	−	7.28974i	0.685761	−	0.685761i	−0.275531	−	0.961292i	$-0.588854\pi$
$113$	7.28974	−	7.28974i	0.685761	−	0.685761i	0.961292	+	0.275531i	$0.0888537\pi$
$114$	1.84154	−	11.9379i	0.172476	−	1.11809i
$115$		0			0
$116$	18.0090	−	7.95683i	1.67209	−	0.738773i
$117$	0.545254	+	8.60819i	0.0504088	+	0.795827i
$118$	−2.96651	−	1.93247i	−0.273089	−	0.177899i
$119$	−12.6703			−1.16149
$120$		0			0
$121$	−10.5888			−0.962615
$122$	−11.4262	−	7.44340i	−1.03448	−	0.673894i
$123$	5.14094	+	11.3795i	0.463543	+	1.02605i
$124$	−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	$0.994226\pi$
$128$	8.86282	−	7.03210i	0.783370	−	0.621556i
$129$	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	$0.260478\pi$
$132$	−1.65473	−	1.48214i	−0.144026	−	0.129003i
$133$	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	0.977035	−	0.213077i	$-0.0683485\pi$
$137$	8.94191	+	8.94191i	0.763959	+	0.763959i	−0.213077	+	0.977035i	$0.568348\pi$
$138$	−7.64955	−	10.4400i	−0.651173	−	0.888714i
$139$	1.01636			0.0862063			0.0431031	−	0.999071i	$-0.486276\pi$
$139$	1.01636			0.0862063			0.0431031	+	0.999071i	$0.486276\pi$
$140$		0			0
$141$	9.36009	+	3.53461i	0.788262	+	0.297668i
$142$	19.8094	+	12.9044i	1.66237	+	1.08292i
$143$	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
$147$	−2.00754	−	4.44369i	−0.165579	−	0.366510i
$148$	−3.51542	+	9.08073i	−0.288966	+	0.746432i
$149$		−	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	$0.598190\pi$
$152$	13.7666	+	2.24065i	1.11662	+	0.181740i
$153$	18.5440	−	1.17460i	1.49920	−	0.0949611i
$154$	−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	0.906961	−	0.421215i	$-0.138396\pi$
$157$	6.08638	+	6.08638i	0.485746	+	0.485746i	−0.421215	+	0.906961i	$0.638396\pi$
$158$	6.30114	+	4.10476i	0.501292	+	0.326557i
$159$	−8.78538	−	3.31759i	−0.696726	−	0.263102i
$160$		0			0
$161$		−	10.8089i		−	0.851858i
$162$	−11.4560	−	5.54614i	−0.900070	−	0.435746i
$163$	13.5483	−	13.5483i	1.06119	−	1.06119i	0.0631867	−	0.998002i	$-0.479874\pi$
$163$	13.5483	−	13.5483i	1.06119	−	1.06119i	0.998002	−	0.0631867i	$-0.0201264\pi$
$164$	−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	0.280683	−	0.959800i	$-0.409439\pi$
$167$	−8.77613	−	8.77613i	−0.679117	−	0.679117i	−0.959800	+	0.280683i	$0.909439\pi$
$168$	−5.00057	+	8.68497i	−0.385802	+	0.670060i
$169$			4.73353i			0.364118i
$170$		0			0
$171$	−9.77864	+	11.1012i	−0.747791	+	0.848930i
$172$	11.5303	+	4.46372i	0.879176	+	0.340355i
$173$	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
$177$	1.78521	+	3.95157i	0.134185	+	0.297018i
$178$	−3.06141	+	4.69951i	−0.229462	+	0.352243i
$179$			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	$0.743014\pi$
$182$	−6.96948	−	4.54013i	−0.516612	−	0.336537i
$183$	6.87620	+	15.2205i	0.508303	+	1.12513i
$184$	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
$188$	−4.17089	+	10.7739i	−0.304194	+	0.785766i
$189$	−4.97990	−	9.39092i	−0.362235	−	0.683089i
$190$		0			0
$191$		−	2.66510i		−	0.192840i	−0.995341	−	0.0964198i	$-0.969261\pi$
$191$		−	2.66510i		−	0.192840i	0.995341	−	0.0964198i	$-0.0307391\pi$
$192$	−13.7849	+	1.40592i	−0.994839	+	0.101464i
$193$	−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	$0.379029\pi$
$198$	0.729042	+	2.62122i	0.0518108	+	0.186282i
$199$			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
$202$	−3.33651	+	5.12182i	−0.234756	+	0.360370i
$203$	−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
$207$	1.00204	+	15.8196i	0.0696464	+	1.09954i
$208$	−0.536578	−	11.4881i	−0.0372050	−	0.796554i
$209$	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	$0.928643\pi$
$212$	3.91480	−	10.1124i	0.268870	−	0.694521i
$213$	−11.9211	−	26.3873i	−0.816820	−	1.80803i
$214$	−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
$218$	−8.83549	+	13.5632i	−0.598415	+	0.918617i
$219$	19.2656	+	7.27518i	1.30185	+	0.491611i
$220$		0			0
$221$	−17.8079			−1.19789
$222$	9.61994	−	7.04866i	0.645648	−	0.473075i
$223$	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	$0.251194\pi$
$228$	−12.7245	−	11.3973i	−0.842700	−	0.754804i
$229$	12.9730			0.857282			0.428641	−	0.903475i	$-0.358993\pi$
$229$	12.9730			0.857282			0.428641	+	0.903475i	$0.358993\pi$
$230$		0			0
$231$	−0.802707	+	2.12567i	−0.0528142	+	0.139859i
$232$	4.47295	−	27.4820i	0.293663	−	1.80428i
$233$	−2.12983	+	2.12983i	−0.139530	+	0.139530i	−0.773422	−	0.633892i	$-0.781456\pi$
$233$	−2.12983	+	2.12983i	−0.139530	+	0.139530i	0.633892	+	0.773422i	$0.281456\pi$
$234$	10.6213	+	5.99874i	0.694335	+	0.392150i
$235$		0			0
$236$	−4.57982	+	2.02348i	−0.298121	+	0.131718i
$237$	−3.79197	−	8.39352i	−0.246315	−	0.545218i
$238$	−9.78050	+	15.0139i	−0.633975	+	0.973205i
$239$	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	$0.548237\pi$
$242$	−8.17369	+	12.5473i	−0.525425	+	0.806571i
$243$	8.15906	+	13.2827i	0.523404	+	0.852085i
$244$	−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
$248$	−14.6015	−	2.37652i	−0.927193	−	0.150909i
$249$	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	$0.303564\pi$
$252$	10.8910	−	5.66019i	0.686069	−	0.356558i
$253$	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	0.665830	−	0.746103i	$-0.268077\pi$
$257$	−1.28687	−	1.28687i	−0.0802726	−	0.0802726i	−0.746103	+	0.665830i	$0.768077\pi$
$258$	−8.95005	−	12.2149i	−0.557206	−	0.760469i
$259$	9.95980			0.618872
$260$		0			0
$261$	22.1611	+	19.5209i	1.37173	+	1.20831i
$262$	12.0767	−	18.5387i	0.746098	−	1.14532i
$263$	−3.96091	+	3.96091i	−0.244240	+	0.244240i	−0.818602	−	0.574361i	$-0.805250\pi$
$263$	−3.96091	+	3.96091i	−0.244240	+	0.244240i	0.574361	+	0.818602i	$0.305250\pi$
$264$	−3.03360	+	0.816700i	−0.186705	+	0.0502644i
$265$		0			0
$266$	−2.94629	−	13.9587i	−0.180648	−	0.855865i
$267$	6.26005	−	2.82812i	0.383109	−	0.173078i
$268$	−2.65171	+	6.84967i	−0.161979	+	0.418410i
$269$		−	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	$0.426364\pi$
$272$	−24.7479	+	1.15591i	−1.50056	+	0.0700875i
$273$	4.19417	+	9.28379i	0.253843	+	0.561880i
$274$	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	0.866184	−	0.499724i	$-0.166565\pi$
$277$	6.09911	+	6.09911i	0.366460	+	0.366460i	−0.499724	+	0.866184i	$0.666565\pi$
$278$	0.784548	−	1.20435i	0.0470540	−	0.0722318i
$279$	10.3716	−	11.7744i	0.620933	−	0.704914i
$280$		0			0
$281$		−	4.32219i		−	0.257840i	−0.991655	−	0.128920i	$-0.958849\pi$
$281$		−	4.32219i		−	0.257840i	0.991655	−	0.128920i	$-0.0411511\pi$
$282$	11.4136	−	8.36292i	0.679672	−	0.498005i
$283$	6.55658	−	6.55658i	0.389748	−	0.389748i	−0.484849	−	0.874598i	$-0.661126\pi$
$283$	6.55658	−	6.55658i	0.389748	−	0.389748i	0.874598	+	0.484849i	$0.161126\pi$
$284$	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
$288$	15.1500	+	7.64713i	0.892720	+	0.450611i
$289$			21.3623i			1.25661i
$290$		0			0
$291$	−0.963426	+	2.55127i	−0.0564770	+	0.149558i
$292$	−8.58482	+	22.1756i	−0.502388	+	1.29773i
$293$	−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
$297$	0.977765	−	3.18550i	0.0567357	−	0.184841i
$298$	−3.57671	−	2.32998i	−0.207193	−	0.134972i
$299$		−	15.1916i		−	0.878555i
$300$		0			0
$301$		−	12.6465i		−	0.728932i
$302$	−5.75969	+	8.84160i	−0.331433	+	0.508777i
$303$	6.82258	−	3.08226i	0.391947	−	0.177071i
$304$	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	0.793004	−	0.609216i	$-0.208516\pi$
$307$	3.22023	+	3.22023i	0.183788	+	0.183788i	−0.609216	+	0.793004i	$0.708516\pi$
$308$	−2.44674	−	0.947206i	−0.139416	−	0.0539721i
$309$	19.5209	+	7.37158i	1.11050	+	0.419355i
$310$		0			0
$311$			12.3453i			0.700036i	0.936743	+	0.350018i	$0.113825\pi$
$311$			12.3453i			0.700036i	−0.936743	+	0.350018i	$0.886175\pi$
$312$	−7.02820	+	12.2065i	−0.397893	+	0.691060i
$313$	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	$0.315654\pi$
$318$	−10.7128	+	7.84944i	−0.600746	+	0.440175i
$319$		−	6.31288i		−	0.353453i
$320$		0			0
$321$	−8.95082	+	23.7029i	−0.499586	+	1.32297i
$322$	−12.8081	−	8.34359i	−0.713768	−	0.464970i
$323$	−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
$327$	18.0670	−	8.16221i	0.999110	−	0.451371i
$328$	−3.27571	+	20.1261i	−0.180871	+	1.11128i
$329$	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	$0.873850\pi$
$332$	−2.24723	+	5.80486i	−0.123333	+	0.318583i
$333$	−14.5770	+	0.923324i	−0.798812	+	0.0505979i
$334$	−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	$0.116524\pi$
$338$	5.60906	+	3.65391i	0.305092	+	0.198747i
$339$	−6.30815	+	16.7048i	−0.342612	+	0.907278i
$340$		0			0
$341$	−3.35409			−0.181634
$342$	5.60617	+	20.1566i	0.303147	+	1.08994i
$343$	−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	$0.971533\pi$
$348$	−22.7522	+	25.4016i	−1.21964	+	1.36167i
$349$	0.603017			0.0322788			0.0161394	−	0.999870i	$-0.494862\pi$
$349$	0.603017			0.0322788			0.0161394	+	0.999870i	$0.494862\pi$
$350$		0			0
$351$	−6.99915	−	13.1987i	−0.373587	−	0.704496i
$352$	−0.913967	−	3.51060i	−0.0487146	−	0.187115i
$353$	−19.6483	+	19.6483i	−1.04578	+	1.04578i	−0.0468748	+	0.998901i	$0.514926\pi$
$353$	−19.6483	+	19.6483i	−1.04578	+	1.04578i	−0.998901	+	0.0468748i	$0.985074\pi$
$354$	6.06051	+	0.934890i	0.322113	+	0.0496888i
$355$		0			0
$356$	3.20559	+	7.25531i	0.169896	+	0.384531i
$357$	19.9994	−	9.03520i	1.05848	−	0.478194i
$358$	2.51171	+	1.63621i	0.132748	+	0.0864763i
$359$	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
$362$	23.0348	+	15.0056i	1.21068	+	0.788674i
$363$	16.7138	−	7.55084i	0.877246	−	0.396316i
$364$	−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	$0.275560\pi$
$368$	−0.986092	−	21.1121i	−0.0514036	−	1.10054i
$369$	−16.2294	−	14.2959i	−0.844868	−	0.744214i
$370$		0			0
$371$	−11.0913			−0.575832
$372$	13.4961	+	12.0884i	0.699741	+	0.626756i
$373$	19.7420	−	19.7420i	1.02220	−	1.02220i	0.0224556	−	0.999748i	$-0.492852\pi$
$373$	19.7420	−	19.7420i	1.02220	−	1.02220i	0.999748	−	0.0224556i	$-0.00714843\pi$
$374$	−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
$378$	−14.9720	−	1.34805i	−0.770076	−	0.0693361i
$379$	−8.76740			−0.450351			−0.225176	−	0.974318i	$-0.572296\pi$
$379$	−8.76740			−0.450351			−0.225176	+	0.974318i	$0.572296\pi$
$380$		0			0
$381$	9.92724	−	26.2886i	0.508588	−	1.34680i
$382$	−3.15804	−	2.05724i	−0.161579	−	0.105258i
$383$	16.7382	−	16.7382i	0.855284	−	0.855284i	−0.135495	−	0.990778i	$-0.543262\pi$
$383$	16.7382	−	16.7382i	0.855284	−	0.855284i	0.990778	+	0.135495i	$0.0432623\pi$
$384$	−8.97489	+	17.4199i	−0.457998	+	0.888953i
$385$		0			0
$386$	−15.1413	+	3.19588i	−0.770670	+	0.162666i
$387$	1.17239	+	18.5091i	0.0595961	+	0.940872i
$388$	−2.93663	−	1.13686i	−0.149085	−	0.0577152i
$389$			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
$392$	1.27917	−	7.85926i	0.0646077	−	0.396953i
$393$	−24.6947	+	11.1564i	−1.24568	+	0.562765i
$394$	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	$-0.950918\pi$
$397$	−22.7486	−	22.7486i	−1.14172	−	1.14172i	−0.153584	−	0.988136i	$-0.549082\pi$
$398$	19.9794	+	13.0152i	1.00148	+	0.652393i
$399$	−6.17264	+	16.3459i	−0.309018	+	0.818319i
$400$		0			0
$401$			24.2516i			1.21107i	0.795819	+	0.605535i	$0.207041\pi$
$401$			24.2516i			1.21107i	−0.795819	+	0.605535i	$0.792959\pi$
$402$	7.25639	−	5.31686i	0.361916	−	0.265181i
$403$	−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
$408$	26.2957	+	15.1404i	1.30183	+	0.749560i
$409$		−	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
$412$	−8.69857	+	22.4694i	−0.428548	+	1.10699i
$413$	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
$417$	−1.60426	+	0.724763i	−0.0785611	+	0.0354918i
$418$	2.44107	−	3.74724i	0.119397	−	0.183284i
$419$		−	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	$0.770235\pi$
$422$	7.65274	+	4.98523i	0.372530	+	0.242677i
$423$	−17.2949	+	1.09548i	−0.840907	+	0.0532642i
$424$	−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
$428$	−27.2831	−	10.5621i	−1.31878	−	0.510538i
$429$	−1.12819	+	2.98758i	−0.0544694	+	0.144242i
$430$		0			0
$431$		−	30.9739i		−	1.49196i	−0.665969	−	0.745979i	$-0.731982\pi$
$431$		−	30.9739i		−	1.49196i	0.665969	−	0.745979i	$-0.268018\pi$
$432$	−10.5836	−	17.8882i	−0.509202	−	0.860647i
$433$	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
$438$	23.4923	−	17.2131i	1.12251	−	0.822476i
$439$		−	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
$442$	−13.7463	+	21.1017i	−0.653844	+	1.00370i
$443$	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
$447$	2.15243	+	4.76440i	0.101806	+	0.225348i
$448$	−14.6445	+	7.30508i	−0.691887	+	0.345132i
$449$	−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
$452$	−19.2279	−	7.44371i	−0.904406	−	0.350122i
$453$	11.7776	−	5.32079i	0.553358	−	0.249993i
$454$	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	$0.436322\pi$
$458$	10.0142	−	15.3726i	0.467931	−	0.718313i
$459$	−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	$0.809887\pi$
$462$	1.89921	+	2.59203i	0.0883594	+	0.120592i
$463$	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	$0.164967\pi$
$468$	15.3071	−	7.95527i	0.707570	−	0.367733i
$469$	7.51276			0.346907
$470$		0			0
$471$	−13.9472	−	5.26682i	−0.642653	−	0.242682i
$472$	−1.13751	+	6.98889i	−0.0523579	+	0.321690i
$473$	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
$477$	16.2330	−	1.02822i	0.743258	−	0.0470790i
$478$	12.9044	−	19.8094i	0.590235	−	0.906060i
$479$	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
$482$	−3.61809	+	5.55406i	−0.164799	+	0.252981i
$483$	7.70779	+	17.0612i	0.350717	+	0.776312i
$484$	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	$0.314546\pi$
$488$	−4.38139	+	26.9194i	−0.198336	+	1.21859i
$489$	−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	$0.307922\pi$
$492$	16.6623	−	18.6026i	0.751194	−	0.838669i
$493$	−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
$498$	6.14955	−	4.50586i	0.275568	−	0.201912i
$499$	−4.01216			−0.179609			−0.0898044	−	0.995959i	$-0.528624\pi$
$499$	−4.01216			−0.179609			−0.0898044	+	0.995959i	$0.528624\pi$
$500$		0			0
$501$	20.1109	+	7.59439i	0.898488	+	0.339292i
$502$	14.1542	−	21.7279i	0.631734	−	0.969765i
$503$	13.7823	−	13.7823i	0.614523	−	0.614523i	−0.329598	−	0.944121i	$-0.606913\pi$
$503$	13.7823	−	13.7823i	0.614523	−	0.614523i	0.944121	+	0.329598i	$0.106913\pi$
$504$	1.69988	−	17.2747i	0.0757188	−	0.769474i
$505$		0			0
$506$	−0.989624	−	4.68858i	−0.0439942	−	0.208433i
$507$	−3.37548	−	7.47162i	−0.149910	−	0.331826i
$508$	30.2593	+	11.7143i	1.34254	+	0.519738i
$509$			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
$512$	−20.0281	−	10.5297i	−0.885125	−	0.465353i
$513$	7.51879	−	24.4958i	0.331963	−	1.08151i
$514$	−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
$518$	7.68818	−	11.8020i	0.337799	−	0.518550i
$519$	−35.0208	−	13.2248i	−1.53724	−	0.580503i
$520$		0			0
$521$			32.5500i			1.42604i	0.701144	+	0.713020i	$0.252673\pi$
$521$			32.5500i			1.42604i	−0.701144	+	0.713020i	$0.747327\pi$
$522$	40.2381	−	11.1915i	1.76117	−	0.489837i
$523$	−9.90568	+	9.90568i	−0.433145	+	0.433145i	−0.889697	−	0.456552i	$-0.849084\pi$
$523$	−9.90568	+	9.90568i	−0.433145	+	0.433145i	0.456552	+	0.889697i	$0.349084\pi$
$524$	−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
$528$	−1.37394	+	4.22513i	−0.0597930	+	0.183875i
$529$		−	4.91829i		−	0.213839i
$530$		0			0
$531$	−5.63573	−	4.96431i	−0.244570	−	0.215433i
$532$	−18.8149	−	7.28380i	−0.815729	−	0.315793i
$533$	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
$537$	−1.51153	−	3.34576i	−0.0652271	−	0.144380i
$538$	−2.15531	−	1.40404i	−0.0929220	−	0.0605322i
$539$		−	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	$-0.395230\pi$
$542$	5.82705	−	8.94500i	0.250293	−	0.384221i
$543$	−13.8621	−	30.6838i	−0.594880	−	1.31677i
$544$	−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	0.573490	−	0.819213i	$-0.305589\pi$
$547$	−5.74698	−	5.74698i	−0.245723	−	0.245723i	−0.819213	+	0.573490i	$0.805589\pi$
$548$	9.13077	−	23.5858i	0.390047	−	1.00754i
$549$	−21.7074	−	19.1213i	−0.926450	−	0.816076i
$550$		0			0
$551$		−	48.5446i		−	2.06807i
$552$	−12.9160	+	22.4325i	−0.549742	+	0.954789i
$553$	−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	$0.994051\pi$
$558$	−5.94613	−	21.3789i	−0.251720	−	0.905040i
$559$		−	17.7744i		−	0.751776i
$560$		0			0
$561$	6.43594	+	2.43038i	0.271726	+	0.102611i
$562$	−5.12164	−	3.33639i	−0.216043	−	0.140737i
$563$	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
$567$	14.5572	+	11.2719i	0.611343	+	0.473375i
$568$	7.59590	−	46.6695i	0.318717	−	1.95821i
$569$	−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	$-0.243191\pi$
$572$	−3.43884	−	1.33128i	−0.143785	−	0.0556636i
$573$	1.90048	+	4.20671i	0.0793936	+	0.175738i
$574$	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	$0.423312\pi$
$578$	25.3135	+	16.4900i	1.05290	+	0.685894i
$579$	17.7307	+	6.69556i	0.736861	+	0.278258i
$580$		0			0
$581$	6.36681			0.264140
$582$	2.27948	+	3.11101i	0.0944873	+	0.128955i
$583$	−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	$0.310630\pi$
$588$	−6.50663	+	7.26431i	−0.268329	+	0.299575i
$589$	−25.7922			−1.06275
$590$		0			0
$591$	6.77353	−	17.9372i	0.278626	−	0.737836i
$592$	19.4537	−	0.908632i	0.799542	−	0.0373445i
$593$	2.17189	−	2.17189i	0.0891890	−	0.0891890i	−0.661105	−	0.750294i	$-0.729912\pi$
$593$	2.17189	−	2.17189i	0.0891890	−	0.0891890i	0.750294	+	0.661105i	$0.229912\pi$
$594$	−3.01994	−	3.61757i	−0.123910	−	0.148431i
$595$		0			0
$596$	−5.52187	+	2.43971i	−0.226185	+	0.0999343i
$597$	−12.0234	−	26.6138i	−0.492086	−	1.08923i
$598$	−18.0015	−	11.7267i	−0.736137	−	0.479542i
$599$	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	$0.296621\pi$
$602$	−14.9856	−	9.76209i	−0.610768	−	0.397873i
$603$	−10.9955	+	0.696471i	−0.447772	+	0.0283625i
$604$	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	$-0.0566421\pi$
$608$	−7.02820	−	26.9957i	−0.285031	−	1.09482i
$609$	32.6310	+	12.3223i	1.32227	+	0.499324i
$610$		0			0
$611$	16.6084			0.671902
$612$	−17.1375	−	32.9750i	−0.692742	−	1.33293i
$613$	9.80228	−	9.80228i	0.395910	−	0.395910i	−0.480878	−	0.876788i	$-0.659682\pi$
$613$	9.80228	−	9.80228i	0.395910	−	0.395910i	0.876788	+	0.480878i	$0.159682\pi$
$614$	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	0.575009	−	0.818147i	$-0.304998\pi$
$617$	−6.03941	−	6.03941i	−0.243138	−	0.243138i	−0.818147	+	0.575009i	$0.804998\pi$
$618$	23.8036	−	17.4412i	0.957522	−	0.701589i
$619$	−16.8314			−0.676509			−0.338255	−	0.941055i	$-0.609837\pi$
$619$	−16.8314			−0.676509			−0.338255	+	0.941055i	$0.609837\pi$
$620$		0			0
$621$	−12.8626	−	24.2559i	−0.516159	−	0.973354i
$622$	14.6287	+	9.52958i	0.586557	+	0.382101i
$623$	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
$627$	−4.99156	+	2.25505i	−0.199344	+	0.0900582i
$628$	6.21493	−	16.0539i	0.248003	−	0.640619i
$629$		−	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	$0.366271\pi$
$632$	2.41617	−	14.8451i	0.0961101	−	0.590505i
$633$	−4.60535	−	10.1939i	−0.183046	−	0.405173i
$634$	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
$638$	−7.48053	−	4.87305i	−0.296157	−	0.192926i
$639$	37.6336	+	33.1500i	1.48876	+	1.31140i
$640$		0			0
$641$		−	25.3407i		−	1.00090i	−0.865767	−	0.500448i	$-0.833169\pi$
$641$		−	25.3407i		−	1.00090i	0.865767	−	0.500448i	$-0.166831\pi$
$642$	21.1777	+	28.9032i	0.835818	+	1.14072i
$643$	−16.2516	+	16.2516i	−0.640899	+	0.640899i	−0.950776	−	0.309878i	$-0.899712\pi$
$643$	−16.2516	+	16.2516i	−0.640899	+	0.640899i	0.309878	+	0.950776i	$0.399712\pi$
$644$	−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	0.769071	−	0.639164i	$-0.220719\pi$
$647$	3.30434	+	3.30434i	0.129907	+	0.129907i	−0.639164	+	0.769071i	$0.720719\pi$
$648$	−0.886466	+	25.4404i	−0.0348237	+	0.999393i
$649$			1.60541i			0.0630180i
$650$		0			0
$651$	6.54695	−	17.3371i	0.256595	−	0.679496i
$652$	−35.7361	−	13.8345i	−1.39953	−	0.541801i
$653$	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
$657$	−35.5976	+	2.25480i	−1.38879	+	0.0879681i
$658$	9.12169	−	14.0025i	0.355600	−	0.545876i
$659$			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	$0.933146\pi$
$662$	16.6440	+	10.8424i	0.646887	+	0.421402i
$663$	28.1088	−	12.6988i	1.09165	−	0.493180i
$664$	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
$668$	−8.96149	+	23.1486i	−0.346731	+	0.895644i
$669$	−19.2760	−	7.27910i	−0.745252	−	0.281426i
$670$		0			0
$671$			6.18365i			0.238717i
$672$	19.9301	+	2.12818i	0.768820	+	0.0820964i
$673$	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	$0.215384\pi$
$678$	14.9251	+	20.3697i	0.573196	+	0.782293i
$679$			3.22091i			0.123607i
$680$		0			0
$681$	0.0691789	−	0.183194i	0.00265094	−	0.00702002i
$682$	−2.58910	+	3.97448i	−0.0991416	+	0.152191i
$683$	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
$687$	−20.4772	+	9.25106i	−0.781255	+	0.352950i
$688$	−1.15374	−	24.7014i	−0.0439859	−	0.941731i
$689$	−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	$-0.152049\pi$
$692$	15.6054	−	40.3106i	0.593229	−	1.53238i
$693$	−0.248783	−	3.92766i	−0.00945050	−	0.149200i
$694$	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
$698$	0.465482	−	0.714553i	0.0176187	−	0.0270462i
$699$	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	$0.698345\pi$
$702$	−21.0428	−	1.89465i	−0.794210	−	0.0715091i
$703$	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
$708$	5.78605	−	6.45982i	0.217453	−	0.242775i
$709$	20.8029			0.781269			0.390634	−	0.920546i	$-0.372256\pi$
$709$	20.8029			0.781269			0.390634	+	0.920546i	$0.372256\pi$
$710$		0			0
$711$	11.9708	+	10.5447i	0.448941	+	0.395456i
$712$	11.0717	+	1.80203i	0.414931	+	0.0675338i
$713$	−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
$717$	−26.3873	+	11.9211i	−0.985453	+	0.445201i
$718$	9.78050	−	15.0139i	0.365005	−	0.560313i
$719$	−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
$722$	4.10476	−	6.30114i	0.152763	−	0.234504i
$723$	7.39836	−	3.34238i	0.275148	−	0.124304i
$724$	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	$0.230508\pi$
$728$	−2.67244	+	16.4196i	−0.0990474	+	0.608552i
$729$	−22.3505	−	15.1478i	−0.827797	−	0.561028i
$730$		0			0
$731$	−38.2901			−1.41621
$732$	22.2864	−	24.8816i	0.823730	−	0.919651i
$733$	−35.6179	+	35.6179i	−1.31558	+	1.31558i	−0.398342	+	0.917237i	$0.630414\pi$
$733$	−35.6179	+	35.6179i	−1.31558	+	1.31558i	−0.917237	+	0.398342i	$0.869586\pi$
$734$	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
$738$	−29.4679	+	8.19594i	−1.08473	+	0.301697i
$739$	14.3621			0.528318			0.264159	−	0.964479i	$-0.414906\pi$
$739$	14.3621			0.528318			0.264159	+	0.964479i	$0.414906\pi$
$740$		0			0
$741$	−8.67551	+	22.9738i	−0.318703	+	0.843965i
$742$	−8.56162	+	13.1428i	−0.314307	+	0.482487i
$743$	1.87689	−	1.87689i	0.0688563	−	0.0688563i	−0.671840	−	0.740696i	$-0.734496\pi$
$743$	1.87689	−	1.87689i	0.0688563	−	0.0688563i	0.740696	+	0.671840i	$0.234496\pi$
$744$	24.7423	−	6.66108i	0.907096	−	0.244207i
$745$		0			0
$746$	−8.15428	−	38.6329i	−0.298550	−	1.41445i
$747$	−9.31833	+	0.590235i	−0.340940	+	0.0215956i
$748$	−2.86788	+	7.40806i	−0.104860	+	0.270866i
$749$			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	$0.684671\pi$
$752$	23.0809	−	1.07805i	0.841675	−	0.0393125i
$753$	−28.9430	+	13.0757i	−1.05474	+	0.476503i
$754$	−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	$0.105082\pi$
$757$	34.9468	+	34.9468i	1.27016	+	1.27016i	0.324162	+	0.946002i	$0.394918\pi$
$758$	−6.76775	+	10.3891i	−0.245816	+	0.377347i
$759$	−2.07332	+	5.49040i	−0.0752567	+	0.199289i
$760$		0			0
$761$		−	2.88711i		−	0.104657i	−0.998630	−	0.0523287i	$-0.983336\pi$
$761$		−	2.88711i		−	0.104657i	0.998630	−	0.0523287i	$-0.0166644\pi$
$762$	−23.4879	−	32.0561i	−0.850879	−	1.16127i
$763$	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
$768$	13.7140	+	24.0817i	0.494861	+	0.868972i
$769$		−	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
$772$	−7.90085	+	20.4088i	−0.284358	+	0.734529i
$773$	−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
$777$	−15.7210	+	7.10233i	−0.563988	+	0.254795i
$778$	24.8752	+	16.2044i	0.891818	+	0.580958i
$779$			35.5511i			1.27375i
$780$		0			0
$781$		−	10.7204i		−	0.383608i
$782$	−25.2621	+	38.7794i	−0.903371	+	1.38675i
$783$	−48.9003	−	15.0096i	−1.74756	−	0.536399i
$784$	−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	$0.00329522\pi$
$787$	28.3424	+	28.3424i	1.01030	+	1.01030i	0.0103521	+	0.999946i	$0.496705\pi$
$788$	20.6465	+	7.99286i	0.735500	+	0.284734i
$789$	3.42756	−	9.07661i	0.122024	−	0.323136i
$790$		0			0
$791$			21.0893i			0.749850i
$792$	4.20598	−	3.45237i	0.149453	−	0.122675i
$793$	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	$0.120357\pi$
$798$	14.6045	+	19.9321i	0.516994	+	0.705589i
$799$		−	35.7782i		−	1.26574i
$800$		0			0
$801$	−7.86441	+	8.92807i	−0.277875	+	0.315458i
$802$	28.7373	+	18.7204i	1.01475	+	0.661039i
$803$	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
$807$	1.29704	+	2.87101i	0.0456581	+	0.101064i
$808$	12.0666	+	1.96396i	0.424503	+	0.0690918i
$809$	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	$0.878793\pi$
$812$	−14.5405	+	37.5597i	−0.510271	+	1.31809i
$813$	−11.9153	+	5.38302i	−0.417888	+	0.188791i
$814$	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
$818$	−28.5527	−	18.6001i	−0.998320	−	0.650336i
$819$	−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	$0.424385\pi$
$822$	−24.9863	+	18.3078i	−0.871498	+	0.638558i
$823$	−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	$-0.110421\pi$
$828$	28.1304	−	14.6197i	0.977601	−	0.508071i
$829$	−34.1845			−1.18728			−0.593638	−	0.804732i	$-0.702309\pi$
$829$	−34.1845			−1.18728			−0.593638	+	0.804732i	$0.702309\pi$
$830$		0			0
$831$	−13.9764	−	5.27784i	−0.484835	−	0.183086i
$832$	−20.5825	+	10.2671i	−0.713571	+	0.355949i
$833$	−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
$837$	−7.97474	+	25.9812i	−0.275647	+	0.898042i
$838$	−47.3469	−	30.8432i	−1.63557	−	1.06546i
$839$	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
$842$	32.1306	+	20.9308i	1.10729	+	0.721324i
$843$	3.08215	+	6.82234i	0.106155	+	0.234974i
$844$	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
$848$	−21.6638	+	1.01186i	−0.743937	+	0.0347474i
$849$	−5.67371	+	15.0247i	−0.194721	+	0.515647i
$850$		0			0
$851$	25.7252			0.881850
$852$	−38.6374	+	43.1366i	−1.32369	+	1.47784i
$853$	29.0954	−	29.0954i	0.996209	−	0.996209i	−0.00378410	−	0.999993i	$-0.501205\pi$
$853$	29.0954	−	29.0954i	0.996209	−	0.996209i	0.999993	+	0.00378410i	$0.00120452\pi$
$854$	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	0.840141	−	0.542368i	$-0.182472\pi$
$857$	8.71719	+	8.71719i	0.297773	+	0.297773i	−0.542368	+	0.840141i	$0.682472\pi$
$858$	2.66930	+	3.64304i	0.0911285	+	0.124371i
$859$	49.6253			1.69319			0.846597	−	0.532235i	$-0.178648\pi$
$859$	49.6253			1.69319			0.846597	+	0.532235i	$0.178648\pi$
$860$		0			0
$861$	−23.8969	−	9.02409i	−0.814405	−	0.307540i
$862$	−36.7029	−	23.9094i	−1.25011	−	0.814357i
$863$	−26.7844	+	26.7844i	−0.911750	+	0.911750i	−0.996410	−	0.0846599i	$-0.973020\pi$
$863$	−26.7844	+	26.7844i	−0.911750	+	0.911750i	0.0846599	+	0.996410i	$0.473020\pi$
$864$	−29.3666	−	1.26714i	−0.999070	−	0.0431090i
$865$		0			0
$866$	16.0092	−	3.37908i	0.544014	−	0.114826i
$867$	−15.2334	−	33.7192i	−0.517354	−	1.14516i
$868$	19.9558	+	7.72550i	0.677345	+	0.262220i
$869$		−	3.41005i		−	0.115678i
$870$		0			0
$871$	10.5590			0.357779
$872$	31.9540	+	5.20081i	1.08210	+	0.176122i
$873$	−0.298595	−	4.71406i	−0.0101059	−	0.159547i
$874$	−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	0.896125	−	0.443802i	$-0.146371\pi$
$877$	13.3952	+	13.3952i	0.452323	+	0.452323i	−0.443802	+	0.896125i	$0.646371\pi$
$878$	−11.4163	−	7.43694i	−0.385282	−	0.250984i
$879$	8.83773	+	3.33735i	0.298089	+	0.112566i
$880$		0			0
$881$			11.8169i			0.398120i	0.979987	+	0.199060i	$0.0637889\pi$
$881$			11.8169i			0.398120i	−0.979987	+	0.199060i	$0.936211\pi$
$882$	11.5072	−	3.20052i	0.387469	−	0.107767i
$883$	−19.7888	+	19.7888i	−0.665947	+	0.665947i	−0.956775	−	0.290828i	$-0.906069\pi$
$883$	−19.7888	+	19.7888i	−0.665947	+	0.665947i	0.290828	+	0.956775i	$0.406069\pi$
$884$	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	0.699136	−	0.714989i	$-0.253568\pi$
$887$	−0.472133	−	0.472133i	−0.0158527	−	0.0158527i	−0.714989	+	0.699136i	$0.753568\pi$
$888$	−20.6703	−	11.9014i	−0.693651	−	0.399386i
$889$		−	33.1886i		−	1.11311i
$890$		0			0
$891$	0.728228	+	5.72538i	0.0243966	+	0.191807i
$892$	8.58944	−	22.1875i	0.287596	−	0.742893i
$893$	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
$897$	10.8331	+	23.9792i	0.361708	+	0.800641i
$898$	−4.94467	+	7.59048i	−0.165006	+	0.253297i
$899$			51.4884i			1.71723i
$900$		0			0
$901$			33.5815i			1.11876i
$902$	5.47828	+	3.56872i	0.182407	+	0.118825i
$903$	9.01820	+	19.9618i	0.300107	+	0.664287i
$904$	−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	$0.101495\pi$
$907$	38.0394	+	38.0394i	1.26308	+	1.26308i	0.313482	+	0.949594i	$0.398505\pi$
$908$	0.210865	+	0.0816321i	0.00699780	+	0.00270906i
$909$	−8.57111	+	9.73035i	−0.284286	+	0.322735i
$910$		0			0
$911$			50.1309i			1.66091i	0.557086	+	0.830455i	$0.311919\pi$
$911$			50.1309i			1.66091i	−0.557086	+	0.830455i	$0.688081\pi$
$912$	−10.5653	+	32.4903i	−0.349851	+	1.07586i
$913$	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
$918$	−4.08152	+	45.3311i	−0.134710	+	1.49615i
$919$			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
$922$	−27.4092	+	42.0754i	−0.902675	+	1.38568i
$923$	−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
$927$	−36.0693	+	2.28468i	−1.18467	+	0.0750387i
$928$	−53.8909	+	14.0302i	−1.76905	+	0.460565i
$929$	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
$932$	5.61778	+	2.17481i	0.184017	+	0.0712383i
$933$	−8.80340	−	19.4863i	−0.288211	−	0.637954i
$934$	−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	$0.306453\pi$
$938$	5.79926	−	8.90234i	0.189352	−	0.290672i
$939$	−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	$0.176259\pi$
$942$	−17.0071	+	12.4613i	−0.554122	+	0.406013i
$943$	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	$0.476305\pi$
$948$	−12.2901	+	13.7213i	−0.399164	+	0.445647i
$949$	34.1845			1.10968
$950$		0			0
$951$	4.46235	−	11.8169i	0.144702	−	0.383188i
$952$	35.3717	+	5.75706i	1.14640	+	0.186587i
$953$	23.6130	−	23.6130i	0.764900	−	0.764900i	−0.212304	−	0.977204i	$-0.568097\pi$
$953$	23.6130	−	23.6130i	0.764900	−	0.764900i	0.977204	+	0.212304i	$0.0680967\pi$
$954$	11.3122	−	20.0292i	0.366246	−	0.648470i
$955$		0			0
$956$	−13.5122	−	30.5826i	−0.437015	−	0.989111i
$957$	4.50171	+	9.96454i	0.145520	+	0.322108i
$958$	3.12394	−	4.79551i	0.100930	−	0.154936i
$959$	−25.8691			−0.835356
$960$		0			0
$961$	−3.64371			−0.117539
$962$	10.8056	−	16.5875i	0.348386	−	0.534801i
$963$	−2.77413	−	43.7965i	−0.0893952	−	1.41132i
$964$	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	$0.227494\pi$
$968$	29.5606	+	4.81125i	0.950112	+	0.154640i
$969$	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	$0.413440\pi$
$972$	17.7045	−	25.6622i	0.567873	−	0.823116i
$973$	−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	$0.0935704\pi$
$977$	38.9727	+	38.9727i	1.24685	+	1.24685i	0.289745	+	0.957104i	$0.406430\pi$
$978$	27.7391	+	37.8581i	0.886999	+	1.21057i
$979$	2.54328			0.0812837
$980$		0			0
$981$	−22.6974	+	25.7672i	−0.724672	+	0.822683i
$982$	19.4128	−	29.8002i	0.619486	−	0.950963i
$983$	−21.8279	+	21.8279i	−0.696200	+	0.696200i	−0.963589	−	0.267388i	$-0.913839\pi$
$983$	−21.8279	+	21.8279i	−0.696200	+	0.696200i	0.267388	+	0.963589i	$0.413839\pi$
$984$	−9.18140	−	34.1039i	−0.292692	−	1.08719i
$985$		0			0
$986$	17.8079	+	84.3691i	0.567119	+	2.68686i
$987$	−18.6523	+	8.42660i	−0.593708	+	0.268222i
$988$	−26.4439	−	10.2372i	−0.841294	−	0.325690i
$989$		−	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	$0.506516\pi$
$992$	7.45440	+	28.6327i	0.236677	+	0.909090i
$993$	−10.0162	−	22.1708i	−0.317854	−	0.703570i
$994$	−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	0.365795	−	0.930695i	$-0.380797\pi$
$997$	−17.8369	−	17.8369i	−0.564900	−	0.564900i	−0.930695	+	0.365795i	$0.880797\pi$
$998$	−3.09707	+	4.75426i	−0.0980361	+	0.150493i
$999$	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.293.23	yes	64
3.2	odd	2	inner	600.2.w.k.293.9	yes	64
5.2	odd	4	inner	600.2.w.k.557.26	yes	64
5.3	odd	4	inner	600.2.w.k.557.7	yes	64
5.4	even	2	inner	600.2.w.k.293.10	yes	64
8.5	even	2	inner	600.2.w.k.293.8	yes	64
15.2	even	4	inner	600.2.w.k.557.8	yes	64
15.8	even	4	inner	600.2.w.k.557.25	yes	64
15.14	odd	2	inner	600.2.w.k.293.24	yes	64
24.5	odd	2	inner	600.2.w.k.293.26	yes	64
40.13	odd	4	inner	600.2.w.k.557.24	yes	64
40.29	even	2	inner	600.2.w.k.293.25	yes	64
40.37	odd	4	inner	600.2.w.k.557.9	yes	64
120.29	odd	2	inner	600.2.w.k.293.7	✓	64
120.53	even	4	inner	600.2.w.k.557.10	yes	64
120.77	even	4	inner	600.2.w.k.557.23	yes	64

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

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

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