LMFDB - Embedded newform 600.2.w.k.293.7

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			293.7
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.7

$q$-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	−0.378765	−	0.925493i	$-0.623651\pi$
$7$	1.44651	−	1.44651i	0.546728	−	0.546728i	0.925493	+	0.378765i	$0.123651\pi$
$8$	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	−0.930402	−	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	$0.479524\pi$
$18$	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	−0.979669	−	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
$27$	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	0.365022	−	0.930999i	$-0.381062\pi$
$37$	−3.44271	−	3.44271i	−0.565978	−	0.565978i	−0.930999	+	0.365022i	$0.881062\pi$
$38$	−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	−0.956934	−	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	$0.888425\pi$
$48$	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	0.392945	−	0.919562i	$-0.371456\pi$
$53$	−3.83383	−	3.83383i	−0.526616	−	0.526616i	−0.919562	+	0.392945i	$0.871456\pi$
$54$	−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	0.530456	−	0.847713i	$-0.322021\pi$
$67$	−2.59686	−	2.59686i	−0.317257	−	0.317257i	−0.847713	+	0.530456i	$0.822021\pi$
$68$	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	0.999874	−	0.0158800i	$-0.00505498\pi$
$73$	8.40725	+	8.40725i	0.983994	+	0.983994i	−0.0158800	+	0.999874i	$0.505055\pi$
$74$	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	0.817497	−	0.575933i	$-0.195361\pi$
$83$	2.20075	+	2.20075i	0.241564	+	0.241564i	−0.575933	+	0.817497i	$0.695361\pi$
$84$	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	−0.761366	−	0.648323i	$-0.775471\pi$
$97$	−1.11334	+	1.11334i	−0.113043	+	0.113043i	0.648323	+	0.761366i	$0.275471\pi$
$98$	−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	0.988776	−	0.149408i	$-0.0477368\pi$
$103$	8.51865	+	8.51865i	0.839368	+	0.839368i	−0.149408	+	0.988776i	$0.547737\pi$
$104$	−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	−1.00000		4.33477e-5i	$-0.999986\pi$
$107$	−10.3436	+	10.3436i	−0.999957	+	0.999957i	4.33477e−5		1.00000i	$0.499986\pi$
$108$	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	−0.275531	−	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
$117$	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	$-0.494226\pi$
$127$	11.4720	−	11.4720i	1.01797	−	1.01797i	0.999835	−	0.0181391i	$-0.00577417\pi$
$128$	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	0.977035	−	0.213077i	$-0.0683485\pi$
$137$	8.94191	+	8.94191i	0.763959	+	0.763959i	−0.213077	+	0.977035i	$0.568348\pi$
$138$	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	0.906961	−	0.421215i	$-0.138396\pi$
$157$	6.08638	+	6.08638i	0.485746	+	0.485746i	−0.421215	+	0.906961i	$0.638396\pi$
$158$	−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	$-0.479874\pi$
$163$	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	$0.909439\pi$
$168$	−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	$-0.943082\pi$
$173$	−15.2826	−	15.2826i	−1.16192	−	1.16192i	−0.177862	−	0.984056i	$-0.556918\pi$
$174$	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	0.928439	−	0.371486i	$-0.121152\pi$
$193$	7.73743	+	7.73743i	0.556952	+	0.556952i	−0.371486	+	0.928439i	$0.621152\pi$
$194$	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	−0.370960	−	0.928649i	$-0.620971\pi$
$197$	7.82754	−	7.82754i	0.557689	−	0.557689i	0.928649	+	0.370960i	$0.120971\pi$
$198$	−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	0.366947	−	0.930242i	$-0.380403\pi$
$223$	−8.41178	−	8.41178i	−0.563294	−	0.563294i	−0.930242	+	0.366947i	$0.880403\pi$
$224$	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	−0.704449	−	0.709755i	$-0.748806\pi$
$227$	0.0799436	−	0.0799436i	0.00530604	−	0.00530604i	0.709755	+	0.704449i	$0.248806\pi$
$228$	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	−0.773422	−	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
$237$	−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	0.665830	−	0.746103i	$-0.268077\pi$
$257$	−1.28687	−	1.28687i	−0.0802726	−	0.0802726i	−0.746103	+	0.665830i	$0.768077\pi$
$258$	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	−0.818602	−	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
$267$	−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	0.866184	−	0.499724i	$-0.166565\pi$
$277$	6.09911	+	6.09911i	0.366460	+	0.366460i	−0.499724	+	0.866184i	$0.666565\pi$
$278$	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	−0.484849	−	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
$288$	−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	0.810730	−	0.585421i	$-0.199071\pi$
$293$	3.85667	+	3.85667i	0.225309	+	0.225309i	−0.585421	+	0.810730i	$0.699071\pi$
$294$	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	0.793004	−	0.609216i	$-0.208516\pi$
$307$	3.22023	+	3.22023i	0.183788	+	0.183788i	−0.609216	+	0.793004i	$0.708516\pi$
$308$	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	0.294443	−	0.955669i	$-0.404866\pi$
$313$	−11.6983	−	11.6983i	−0.661226	−	0.661226i	−0.955669	+	0.294443i	$0.904866\pi$
$314$	−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	−0.547304	−	0.836934i	$-0.684346\pi$
$317$	5.15672	−	5.15672i	0.289631	−	0.289631i	0.836934	+	0.547304i	$0.184346\pi$
$318$	−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	−0.933741	−	0.357950i	$-0.883476\pi$
$337$	−10.5701	+	10.5701i	−0.575791	+	0.575791i	0.357950	+	0.933741i	$0.383476\pi$
$338$	−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	$-0.471533\pi$
$347$	20.2172	−	20.2172i	1.08532	−	1.08532i	0.996004	−	0.0893127i	$-0.0284671\pi$
$348$	−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	$0.514926\pi$
$353$	−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
$357$	−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	−0.648109	−	0.761547i	$-0.724440\pi$
$367$	2.17316	−	2.17316i	0.113438	−	0.113438i	0.761547	+	0.648109i	$0.224440\pi$
$368$	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	$-0.492852\pi$
$373$	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
$378$	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	−0.135495	−	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
$387$	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	$-0.950918\pi$
$397$	−22.7486	−	22.7486i	−1.14172	−	1.14172i	−0.153584	−	0.988136i	$-0.549082\pi$
$398$	−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	0.482658	−	0.875809i	$-0.339672\pi$
$433$	−8.18096	−	8.18096i	−0.393152	−	0.393152i	−0.875809	+	0.482658i	$0.839672\pi$
$434$	−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	0.553998	−	0.832518i	$-0.313102\pi$
$443$	−5.86218	−	5.86218i	−0.278521	−	0.278521i	−0.832518	+	0.553998i	$0.813102\pi$
$444$	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	−0.198719	−	0.980057i	$-0.563678\pi$
$457$	16.7031	−	16.7031i	0.781338	−	0.781338i	0.980057	+	0.198719i	$0.0636781\pi$
$458$	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	0.441776	−	0.897126i	$-0.354349\pi$
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	−0.897126	+	0.441776i	$0.854349\pi$
$464$	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	−0.868683	−	0.495369i	$-0.835033\pi$
$467$	−8.06737	+	8.06737i	−0.373313	+	0.373313i	0.495369	+	0.868683i	$0.335033\pi$
$468$	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	−0.550215	−	0.835023i	$-0.685454\pi$
$487$	6.28516	−	6.28516i	0.284808	−	0.284808i	0.835023	+	0.550215i	$0.185454\pi$
$488$	−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	−0.329598	−	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
$507$	−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	−0.889697	−	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
$528$	−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	0.573490	−	0.819213i	$-0.305589\pi$
$547$	−5.74698	−	5.74698i	−0.245723	−	0.245723i	−0.819213	+	0.573490i	$0.805589\pi$
$548$	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	$-0.494051\pi$
$557$	24.0378	−	24.0378i	1.01851	−	1.01851i	0.999825	−	0.0186883i	$-0.00594902\pi$
$558$	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	0.331805	−	0.943348i	$-0.392343\pi$
$563$	−14.5105	−	14.5105i	−0.611544	−	0.611544i	−0.943348	+	0.331805i	$0.892343\pi$
$564$	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	−0.238599	−	0.971118i	$-0.576688\pi$
$577$	17.5957	−	17.5957i	0.732519	−	0.732519i	0.971118	+	0.238599i	$0.0766881\pi$
$578$	−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	−0.560446	−	0.828191i	$-0.689370\pi$
$587$	6.48696	−	6.48696i	0.267746	−	0.267746i	0.828191	+	0.560446i	$0.189370\pi$
$588$	−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	−0.661105	−	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
$597$	−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	$0.556642\pi$
$607$	−28.6094	+	28.6094i	−1.16122	+	1.16122i	−0.984209	+	0.177009i	$0.943358\pi$
$608$	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	−0.480878	−	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	$0.804998\pi$
$618$	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	−0.950776	−	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	$0.720719\pi$
$648$	−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	0.666860	−	0.745183i	$-0.267638\pi$
$653$	−2.00144	−	2.00144i	−0.0783225	−	0.0783225i	−0.745183	+	0.666860i	$0.767638\pi$
$654$	−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	0.430727	−	0.902482i	$-0.358257\pi$
$673$	−12.2384	−	12.2384i	−0.471755	−	0.471755i	−0.902482	+	0.430727i	$0.858257\pi$
$674$	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	−0.779675	−	0.626184i	$-0.784616\pi$
$677$	−3.99371	+	3.99371i	−0.153491	+	0.153491i	0.626184	+	0.779675i	$0.284616\pi$
$678$	−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	0.555865	−	0.831273i	$-0.312387\pi$
$683$	−7.19759	−	7.19759i	−0.275408	−	0.275408i	−0.831273	+	0.555865i	$0.812387\pi$
$684$	−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	−0.749055	−	0.662508i	$-0.769492\pi$
$727$	−2.33356	+	2.33356i	−0.0865468	+	0.0865468i	0.662508	+	0.749055i	$0.269492\pi$
$728$	−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	$0.630414\pi$
$733$	−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
$738$	−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	−0.671840	−	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
$747$	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	$0.105082\pi$
$757$	34.9468	+	34.9468i	1.27016	+	1.27016i	0.324162	+	0.946002i	$0.394918\pi$
$758$	−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	0.960595	−	0.277953i	$-0.0896558\pi$
$773$	18.9794	+	18.9794i	0.682642	+	0.682642i	−0.277953	+	0.960595i	$0.589656\pi$
$774$	−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	$0.00329522\pi$
$787$	28.3424	+	28.3424i	1.01030	+	1.01030i	0.0103521	+	0.999946i	$0.496705\pi$
$788$	−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	−0.929363	−	0.369168i	$-0.879643\pi$
$797$	−15.8150	+	15.8150i	−0.560195	+	0.560195i	0.369168	+	0.929363i	$0.379643\pi$
$798$	−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	0.962757	−	0.270370i	$-0.0871459\pi$
$823$	19.8632	+	19.8632i	0.692387	+	0.692387i	−0.270370	+	0.962757i	$0.587146\pi$
$824$	−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	$0.610421\pi$
$827$	−36.8216	+	36.8216i	−1.28041	+	1.28041i	−0.940432	+	0.339982i	$0.889579\pi$
$828$	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	−0.00378410	−	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	$0.682472\pi$
$858$	−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	−0.996410	−	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
$867$	−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	0.896125	−	0.443802i	$-0.146371\pi$
$877$	13.3952	+	13.3952i	0.452323	+	0.452323i	−0.443802	+	0.896125i	$0.646371\pi$
$878$	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	−0.956775	−	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	$0.753568\pi$
$888$	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	$0.101495\pi$
$907$	38.0394	+	38.0394i	1.26308	+	1.26308i	0.313482	+	0.949594i	$0.398505\pi$
$908$	−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	−0.571264	−	0.820766i	$-0.693547\pi$
$937$	7.63736	−	7.63736i	0.249502	−	0.249502i	0.820766	+	0.571264i	$0.193547\pi$
$938$	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	−0.0743707	−	0.997231i	$-0.523695\pi$
$947$	28.3995	−	28.3995i	0.922860	−	0.922860i	0.997231	+	0.0743707i	$0.0236948\pi$
$948$	−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	−0.212304	−	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
$957$	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	−0.755293	−	0.655387i	$-0.772506\pi$
$967$	−3.10676	+	3.10676i	−0.0999067	+	0.0999067i	0.655387	+	0.755293i	$0.272506\pi$
$968$	−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	$0.0935704\pi$
$977$	38.9727	+	38.9727i	1.24685	+	1.24685i	0.289745	+	0.957104i	$0.406430\pi$
$978$	−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	−0.963589	−	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
$987$	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	0.365795	−	0.930695i	$-0.380797\pi$
$997$	−17.8369	−	17.8369i	−0.564900	−	0.564900i	−0.930695	+	0.365795i	$0.880797\pi$
$998$	−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.293.7	✓	64
3.2	odd	2	inner	600.2.w.k.293.25	yes	64
5.2	odd	4	inner	600.2.w.k.557.10	yes	64
5.3	odd	4	inner	600.2.w.k.557.23	yes	64
5.4	even	2	inner	600.2.w.k.293.26	yes	64
8.5	even	2	inner	600.2.w.k.293.24	yes	64
15.2	even	4	inner	600.2.w.k.557.24	yes	64
15.8	even	4	inner	600.2.w.k.557.9	yes	64
15.14	odd	2	inner	600.2.w.k.293.8	yes	64
24.5	odd	2	inner	600.2.w.k.293.10	yes	64
40.13	odd	4	inner	600.2.w.k.557.8	yes	64
40.29	even	2	inner	600.2.w.k.293.9	yes	64
40.37	odd	4	inner	600.2.w.k.557.25	yes	64
120.29	odd	2	inner	600.2.w.k.293.23	yes	64
120.53	even	4	inner	600.2.w.k.557.26	yes	64
120.77	even	4	inner	600.2.w.k.557.7	yes	64

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

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Database

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