LMFDB - Embedded newform 600.2.w.k.293.9

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			293.9
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.771921 + 1.18496i) q^{2} +(-0.713099 + 1.57845i) q^{3} +(-0.808275 - 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(2.79169 + 0.454373i) q^{8} +(-1.98298 - 2.25118i) q^{9} +O(q^{10})$	\(q+(-0.771921 + 1.18496i) q^{2} +(-0.713099 + 1.57845i) q^{3} +(-0.808275 - 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(2.79169 + 0.454373i) q^{8} +(-1.98298 - 2.25118i) q^{9} +0.641278 q^{11} +(3.46398 + 0.0287228i) 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} +(4.19826 - 0.612026i) q^{18} -4.93129 q^{19} +(-1.25173 - 3.31474i) q^{21} +(-0.495016 + 0.759891i) q^{22} +(3.73619 - 3.73619i) q^{23} +(-2.70796 + 4.08252i) q^{24} +(-0.839729 - 3.97842i) q^{26} +(4.96742 - 1.52471i) q^{27} +(3.81541 + 1.47706i) q^{28} -9.84421i q^{29} +5.23032 q^{31} +(-1.42523 - 5.47437i) q^{32} +(-0.457295 + 1.01222i) q^{33} +(8.57043 - 1.80897i) q^{34} +(-2.51550 + 5.44722i) q^{36} +(-3.44271 - 3.44271i) q^{37} +(3.80656 - 5.84339i) q^{38} +(-1.75928 - 4.65879i) q^{39} +7.20930i q^{41} +(4.89408 + 1.07546i) 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} +(-2.74731 - 6.36021i) q^{48} +2.81523i q^{49} +(10.0361 - 3.78989i) q^{51} +(5.36248 + 2.07598i) q^{52} +(-3.83383 - 3.83383i) q^{53} +(-2.02773 + 7.06317i) q^{54} +(-4.69546 + 3.38095i) q^{56} +(3.51650 - 7.78377i) q^{57} +(11.6650 + 7.59896i) q^{58} +2.50346i q^{59} -9.64270i q^{61} +(-4.03740 + 6.19774i) q^{62} +(6.12474 + 0.387949i) q^{63} +(7.58709 + 2.53694i) q^{64} +(-0.846451 - 1.32323i) q^{66} +(-2.59686 - 2.59686i) q^{67} +(-4.47213 + 11.5520i) q^{68} +(3.23310 + 8.56166i) q^{69} -16.7173i q^{71} +(-4.51299 - 7.18560i) 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} +(6.87852 + 1.51154i) q^{78} +5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(-8.54275 - 5.56501i) q^{82} +(2.20075 + 2.20075i) q^{83} +(-5.05222 + 4.96913i) q^{84} +(-1.80557 - 8.55430i) q^{86} +(15.5386 + 7.01990i) q^{87} +(1.79025 + 0.291380i) q^{88} +3.96596 q^{89} -5.88160i q^{91} +(-9.85485 - 3.81511i) q^{92} +(-3.72974 + 8.25578i) q^{93} +(-7.99313 + 1.68712i) q^{94} +(9.65732 + 1.65413i) 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
$3$	−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
$6$	−1.31994	−	2.06343i	−0.538864	−	0.842392i
$7$	−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	$-0.469179\pi$
$11$	0.641278			0.193353			0.0966764	+	0.995316i	$0.469179\pi$
$12$	3.46398	+	0.0287228i	0.999966	+	0.00829157i
$13$	−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	$-0.979524\pi$
$17$	−4.37963	−	4.37963i	−1.06222	−	1.06222i	−0.0642843	−	0.997932i	$-0.520476\pi$
$18$	4.19826	−	0.612026i	0.989540	−	0.144256i
$19$	−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	−0.200619	−	0.979669i	$-0.564295\pi$
$23$	3.73619	−	3.73619i	0.779050	−	0.779050i	0.979669	+	0.200619i	$0.0642953\pi$
$24$	−2.70796	+	4.08252i	−0.552759	+	0.833341i
$25$		0			0
$26$	−0.839729	−	3.97842i	−0.164684	−	0.780232i
$27$	4.96742	−	1.52471i	0.955980	−	0.293431i
$28$	3.81541	+	1.47706i	0.721045	+	0.279138i
$29$		−	9.84421i		−	1.82802i	−0.405687	−	0.914012i	$-0.632968\pi$
$29$		−	9.84421i		−	1.82802i	0.405687	−	0.914012i	$-0.367032\pi$
$30$		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
$33$	−0.457295	+	1.01222i	−0.0796049	+	0.176205i
$34$	8.57043	−	1.80897i	1.46982	−	0.310236i
$35$		0			0
$36$	−2.51550	+	5.44722i	−0.419250	+	0.907871i
$37$	−3.44271	−	3.44271i	−0.565978	−	0.565978i	0.365022	−	0.930999i	$-0.381062\pi$
$37$	−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	$0.190334\pi$
$41$			7.20930i			1.12590i	−0.826490	+	0.562951i	$0.809666\pi$
$42$	4.89408	+	1.07546i	0.755172	+	0.165947i
$43$	−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	0.939193	−	0.343390i	$-0.111575\pi$
$47$	4.08462	+	4.08462i	0.595803	+	0.595803i	−0.343390	+	0.939193i	$0.611575\pi$
$48$	−2.74731	−	6.36021i	−0.396539	−	0.918018i
$49$			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	0.392945	−	0.919562i	$-0.371456\pi$
$53$	−3.83383	−	3.83383i	−0.526616	−	0.526616i	−0.919562	+	0.392945i	$0.871456\pi$
$54$	−2.02773	+	7.06317i	−0.275939	+	0.961175i
$55$		0			0
$56$	−4.69546	+	3.38095i	−0.627457	+	0.451798i
$57$	3.51650	−	7.78377i	0.465771	−	1.03098i
$58$	11.6650	+	7.59896i	1.53169	+	0.997792i
$59$			2.50346i			0.325923i	0.986632	+	0.162961i	$0.0521046\pi$
$59$			2.50346i			0.325923i	−0.986632	+	0.162961i	$0.947895\pi$
$60$		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
$63$	6.12474	+	0.387949i	0.771644	+	0.0488770i
$64$	7.58709	+	2.53694i	0.948386	+	0.317118i
$65$		0			0
$66$	−0.846451	−	1.32323i	−0.104191	−	0.162879i
$67$	−2.59686	−	2.59686i	−0.317257	−	0.317257i	0.530456	−	0.847713i	$-0.322021\pi$
$67$	−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	$-0.540318\pi$
$71$		−	16.7173i		−	1.98398i	0.126324	−	0.991989i	$-0.459682\pi$
$72$	−4.51299	−	7.18560i	−0.531861	−	0.846832i
$73$	−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
$78$	6.87852	+	1.51154i	0.778839	+	0.171148i
$79$			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	0.817497	−	0.575933i	$-0.195361\pi$
$83$	2.20075	+	2.20075i	0.241564	+	0.241564i	−0.575933	+	0.817497i	$0.695361\pi$
$84$	−5.05222	+	4.96913i	−0.551243	+	0.542176i
$85$		0			0
$86$	−1.80557	−	8.55430i	−0.194699	−	0.922434i
$87$	15.5386	+	7.01990i	1.66591	+	0.752612i
$88$	1.79025	+	0.291380i	0.190841	+	0.0310612i
$89$	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
$92$	−9.85485	−	3.81511i	−1.02744	−	0.397752i
$93$	−3.72974	+	8.25578i	−0.386756	+	0.856085i
$94$	−7.99313	+	1.68712i	−0.824428	+	0.174013i
$95$		0			0
$96$	9.65732	+	1.65413i	0.985646	+	0.168824i
$97$	1.11334	−	1.11334i	0.113043	−	0.113043i	−0.648323	−	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	$-0.431010\pi$
$101$	4.32234			0.430089			0.215045	+	0.976604i	$0.431010\pi$
$102$	−3.25620	+	14.8179i	−0.322412	+	1.46719i
$103$	−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	−1.00000		4.33477e-5i	$-0.999986\pi$
$107$	−10.3436	+	10.3436i	−0.999957	+	0.999957i	4.33477e−5		1.00000i	$0.499986\pi$
$108$	−6.80434	−	7.85499i	−0.654748	−	0.755847i
$109$	−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	−0.961292	−	0.275531i	$-0.911146\pi$
$113$	−7.28974	+	7.28974i	−0.685761	+	0.685761i	0.275531	+	0.961292i	$0.411146\pi$
$114$	6.50902	+	10.1754i	0.609625	+	0.953011i
$115$		0			0
$116$	−18.0090	+	7.95683i	−1.67209	+	0.738773i
$117$	8.60819	+	0.545254i	0.795827	+	0.0504088i
$118$	−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
$123$	−11.3795	−	5.14094i	−1.02605	−	0.463543i
$124$	−4.22754	−	9.56834i	−0.379644	−	0.859262i
$125$		0			0
$126$	−5.18752	+	6.95812i	−0.462141	+	0.619879i
$127$	−11.4720	+	11.4720i	−1.01797	+	1.01797i	−0.0181391	+	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	$-0.739522\pi$
$131$	−15.6449			−1.36690			−0.683452	+	0.729995i	$0.739522\pi$
$132$	2.22138	+	0.0184193i	0.193346	+	0.00160320i
$133$	7.13314	−	7.13314i	0.618522	−	0.618522i
$134$	5.08176	−	1.07261i	0.438997	−	0.0926596i
$135$		0			0
$136$	−10.2366	−	14.2166i	−0.877780	−	1.21906i
$137$	−8.94191	−	8.94191i	−0.763959	−	0.763959i	0.213077	−	0.977035i	$-0.431652\pi$
$137$	−8.94191	−	8.94191i	−0.763959	−	0.763959i	−0.977035	+	0.213077i	$0.931652\pi$
$138$	−12.6409	−	2.77782i	−1.07607	−	0.236464i
$139$	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
$144$	11.9983	+	0.198991i	0.999862	+	0.0165826i
$145$		0			0
$146$	16.4520	−	3.47255i	1.36158	−	0.287390i
$147$	−4.44369	−	2.00754i	−0.366510	−	0.165579i
$148$	−3.51542	+	9.08073i	−0.288966	+	0.746432i
$149$			3.01841i			0.247278i	0.992327	+	0.123639i	$0.0394565\pi$
$149$			3.01841i			0.247278i	−0.992327	+	0.123639i	$0.960544\pi$
$150$		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
$153$	−1.17460	+	18.5440i	−0.0949611	+	1.49920i
$154$	−0.383143	−	1.81523i	−0.0308746	−	0.146276i
$155$		0			0
$156$	−7.10080	+	6.98401i	−0.568519	+	0.559168i
$157$	6.08638	+	6.08638i	0.485746	+	0.485746i	0.906961	−	0.421215i	$-0.138396\pi$
$157$	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
$162$	−9.70285	−	8.23740i	−0.762328	−	0.647191i
$163$	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	0.959800	−	0.280683i	$-0.0905610\pi$
$167$	8.77613	+	8.77613i	0.679117	+	0.679117i	−0.280683	+	0.959800i	$0.590561\pi$
$168$	−1.98832	−	9.82247i	−0.153402	−	0.757820i
$169$			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	$-0.943082\pi$
$173$	−15.2826	−	15.2826i	−1.16192	−	1.16192i	−0.177862	−	0.984056i	$-0.556918\pi$
$174$	−20.3129	+	12.9938i	−1.53991	+	0.985057i
$175$		0			0
$176$	−1.72721	+	1.89646i	−0.130193	+	0.142951i
$177$	−3.95157	−	1.78521i	−0.297018	−	0.134185i
$178$	−3.06141	+	4.69951i	−0.229462	+	0.352243i
$179$		−	2.11966i		−	0.158431i	−0.996858	−	0.0792153i	$-0.974759\pi$
$179$		−	2.11966i		−	0.158431i	0.996858	−	0.0792153i	$-0.0252415\pi$
$180$		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
$183$	15.2205	+	6.87620i	1.12513	+	0.508303i
$184$	12.1279	−	8.73268i	0.894083	−	0.643781i
$185$		0			0
$186$	−6.90373	−	10.7924i	−0.506206	−	0.791338i
$187$	−2.80856	−	2.80856i	−0.205382	−	0.205382i
$188$	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	$0.0307391\pi$
$191$			2.66510i			0.192840i	−0.995341	+	0.0964198i	$0.969261\pi$
$192$	−9.41477	+	10.1667i	−0.679453	+	0.733719i
$193$	−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	−0.370960	−	0.928649i	$-0.620971\pi$
$197$	7.82754	−	7.82754i	0.557689	−	0.557689i	0.928649	+	0.370960i	$0.120971\pi$
$198$	2.69226	−	0.392479i	0.191330	−	0.0278923i
$199$			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
$204$	−15.0452	−	15.2968i	−1.05337	−	1.07099i
$205$		0			0
$206$	16.6700	−	3.51856i	1.16145	−	0.245150i
$207$	−15.8196	−	1.00204i	−1.09954	−	0.0696464i
$208$	−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
$213$	26.3873	+	11.9211i	1.80803	+	0.816820i
$214$	−4.27235	−	20.2413i	−0.292052	−	1.38367i
$215$		0			0
$216$	14.5603	−	1.99946i	0.990702	−	0.136046i
$217$	−7.56570	+	7.56570i	−0.513593	+	0.513593i
$218$	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
$222$	−2.55961	+	11.6480i	−0.171790	+	0.781760i
$223$	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	−0.704449	−	0.709755i	$-0.748806\pi$
$227$	0.0799436	−	0.0799436i	0.00530604	−	0.00530604i	0.709755	+	0.704449i	$0.248806\pi$
$228$	−17.0819	−	0.141640i	−1.13128	−	0.00938037i
$229$	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	−0.633892	−	0.773422i	$-0.718544\pi$
$233$	2.12983	−	2.12983i	0.139530	−	0.139530i	0.773422	+	0.633892i	$0.218544\pi$
$234$	−7.29095	+	9.77949i	−0.476624	+	0.639306i
$235$		0			0
$236$	4.57982	−	2.02348i	0.298121	−	0.131718i
$237$	−8.39352	−	3.79197i	−0.545218	−	0.246315i
$238$	−9.78050	+	15.0139i	−0.633975	+	0.973205i
$239$	−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	$0.548237\pi$
$242$	8.17369	−	12.5473i	0.525425	−	0.806571i
$243$	−13.2827	−	8.15906i	−0.852085	−	0.523404i
$244$	−17.6403	+	7.79396i	−1.12931	+	0.498957i
$245$		0			0
$246$	14.8759	−	9.51586i	0.948452	−	0.606709i
$247$	10.0255	−	10.0255i	0.637906	−	0.637906i
$248$	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	$-0.696436\pi$
$251$	−18.3364			−1.15738			−0.578691	+	0.815547i	$0.696436\pi$
$252$	−4.24076	−	11.5181i	−0.267143	−	0.725575i
$253$	2.39594	−	2.39594i	0.150632	−	0.150632i
$254$	−4.73841	−	22.4494i	−0.297314	−	1.40860i
$255$		0			0
$256$	−1.49138	−	15.9303i	−0.0932115	−	0.995646i
$257$	1.28687	+	1.28687i	0.0802726	+	0.0802726i	0.746103	−	0.665830i	$-0.231923\pi$
$257$	1.28687	+	1.28687i	0.0802726	+	0.0802726i	−0.665830	+	0.746103i	$0.731923\pi$
$258$	14.7900	+	3.25008i	0.920788	+	0.202341i
$259$	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	−0.574361	−	0.818602i	$-0.694750\pi$
$263$	3.96091	−	3.96091i	0.244240	−	0.244240i	0.818602	+	0.574361i	$0.194750\pi$
$264$	−1.73655	+	2.61803i	−0.106878	+	0.161129i
$265$		0			0
$266$	2.94629	+	13.9587i	0.180648	+	0.855865i
$267$	−2.82812	+	6.26005i	−0.173078	+	0.383109i
$268$	−2.65171	+	6.84967i	−0.161979	+	0.418410i
$269$			1.81888i			0.110899i	0.998461	+	0.0554497i	$0.0176592\pi$
$269$			1.81888i			0.110899i	−0.998461	+	0.0554497i	$0.982341\pi$
$270$		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
$273$	9.28379	+	4.19417i	0.561880	+	0.253843i
$274$	17.4983	−	3.69338i	1.05711	−	0.223125i
$275$		0			0
$276$	13.0494	−	12.8348i	0.785483	−	0.772564i
$277$	6.09911	+	6.09911i	0.366460	+	0.366460i	0.866184	−	0.499724i	$-0.166565\pi$
$277$	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	$0.0411511\pi$
$281$			4.32219i			0.257840i	−0.991655	+	0.128920i	$0.958849\pi$
$282$	3.03687	−	13.8198i	0.180843	−	0.822957i
$283$	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
$288$	−9.49758	+	14.0640i	−0.559650	+	0.828729i
$289$			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	0.810730	−	0.585421i	$-0.199071\pi$
$293$	3.85667	+	3.85667i	0.225309	+	0.225309i	−0.585421	+	0.810730i	$0.699071\pi$
$294$	5.80904	−	3.71595i	0.338790	−	0.216718i
$295$		0			0
$296$	−8.04670	−	11.1753i	−0.467705	−	0.649548i
$297$	3.18550	−	0.977765i	0.184841	−	0.0567357i
$298$	−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
$303$	−3.08226	+	6.82258i	−0.177071	+	0.391947i
$304$	13.2818	−	14.5834i	0.761766	−	0.836413i
$305$		0			0
$306$	−21.0673	−	15.7064i	−1.20434	−	0.897875i
$307$	3.22023	+	3.22023i	0.183788	+	0.183788i	0.793004	−	0.609216i	$-0.208516\pi$
$307$	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	$-0.886175\pi$
$311$		−	12.3453i		−	0.700036i	0.936743	−	0.350018i	$-0.113825\pi$
$312$	−2.79454	−	13.8053i	−0.158209	−	0.781570i
$313$	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	−0.547304	−	0.836934i	$-0.684346\pi$
$317$	5.15672	−	5.15672i	0.289631	−	0.289631i	0.836934	+	0.547304i	$0.184346\pi$
$318$	−2.85041	+	12.9713i	−0.159843	+	0.727393i
$319$		−	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
$324$	17.2508	−	5.13890i	0.958380	−	0.285494i
$325$		0			0
$326$	5.59604	+	26.5125i	0.309936	+	1.46839i
$327$	8.16221	−	18.0670i	0.451371	−	0.999110i
$328$	−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
$333$	−0.923324	+	14.5770i	−0.0505979	+	0.798812i
$334$	−17.1739	+	3.62491i	−0.939713	+	0.198346i
$335$		0			0
$336$	13.1741	+	5.22610i	0.718706	+	0.285107i
$337$	10.5701	−	10.5701i	0.575791	−	0.575791i	−0.357950	−	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
$342$	−20.7028	+	3.01808i	−1.11948	+	0.163199i
$343$	−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	$-0.0284671\pi$
$348$	0.282754	−	34.1002i	0.0151572	−	1.82796i
$349$	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	$-0.485074\pi$
$353$	19.6483	−	19.6483i	1.04578	−	1.04578i	0.998901	−	0.0468748i	$-0.0149262\pi$
$354$	5.16572	−	3.30442i	0.274555	−	0.175628i
$355$		0			0
$356$	−3.20559	−	7.25531i	−0.169896	−	0.384531i
$357$	−9.03520	+	19.9994i	−0.478194	+	1.05848i
$358$	2.51171	+	1.63621i	0.132748	+	0.0864763i
$359$	−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
$362$	−23.0348	−	15.0056i	−1.21068	−	0.788674i
$363$	7.55084	−	16.7138i	0.396316	−	0.877246i
$364$	−10.7598	+	4.75395i	−0.563966	+	0.249175i
$365$		0			0
$366$	−19.8971	+	12.7278i	−1.04004	+	0.665293i
$367$	−2.17316	+	2.17316i	−0.113438	+	0.113438i	−0.761547	−	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
$372$	18.1178	+	0.150230i	0.939362	+	0.00778905i
$373$	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
$378$	−7.28380	−	13.1500i	−0.374638	−	0.676365i
$379$	−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	−0.990778	−	0.135495i	$-0.956738\pi$
$383$	−16.7382	+	16.7382i	−0.855284	+	0.855284i	0.135495	+	0.990778i	$0.456738\pi$
$384$	−4.77972	−	19.0041i	−0.243914	−	0.969797i
$385$		0			0
$386$	15.1413	−	3.19588i	0.770670	−	0.162666i
$387$	18.5091	+	1.17239i	0.940872	+	0.0595961i
$388$	−2.93663	−	1.13686i	−0.149085	−	0.0577152i
$389$		−	20.9924i		−	1.06435i	−0.846633	−	0.532177i	$-0.821374\pi$
$389$		−	20.9924i		−	1.06435i	0.846633	−	0.532177i	$-0.178626\pi$
$390$		0			0
$391$	−32.7263			−1.65504
$392$	−1.27917	+	7.85926i	−0.0646077	+	0.396953i
$393$	11.1564	−	24.6947i	0.562765	−	1.24568i
$394$	3.23310	+	15.3176i	0.162881	+	0.771689i
$395$		0			0
$396$	−1.61314	+	3.49319i	−0.0810631	+	0.175539i
$397$	−22.7486	−	22.7486i	−1.14172	−	1.14172i	−0.988136	−	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	$-0.792959\pi$
$401$		−	24.2516i		−	1.21107i	0.795819	−	0.605535i	$-0.207041\pi$
$402$	−1.93074	+	8.78615i	−0.0962964	+	0.438213i
$403$	−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
$408$	29.7398	−	6.02007i	1.47234	−	0.298038i
$409$		−	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
$414$	13.3989	−	17.9722i	0.658519	−	0.883284i
$415$		0			0
$416$	14.0271	+	8.23206i	0.687737	+	0.403610i
$417$	−0.724763	+	1.60426i	−0.0354918	+	0.0785611i
$418$	2.44107	−	3.74724i	0.119397	−	0.183284i
$419$			39.9565i			1.95200i	0.217767	+	0.976001i	$0.430123\pi$
$419$			39.9565i			1.95200i	−0.217767	+	0.976001i	$0.569877\pi$
$420$		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
$423$	1.09548	−	17.2949i	0.0532642	−	0.840907i
$424$	−8.96087	−	12.4448i	−0.435178	−	0.604375i
$425$		0			0
$426$	−34.4950	+	22.0659i	−1.67129	+	1.06910i
$427$	13.9482	+	13.9482i	0.675002	+	0.675002i
$428$	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	$0.268018\pi$
$431$			30.9739i			1.49196i	−0.665969	+	0.745979i	$0.731982\pi$
$432$	−8.87011	+	18.7968i	−0.426763	+	0.904363i
$433$	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
$438$	−6.25069	+	28.4449i	−0.298670	+	1.35915i
$439$		−	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	0.553998	−	0.832518i	$-0.313102\pi$
$443$	−5.86218	−	5.86218i	−0.278521	−	0.278521i	−0.832518	+	0.553998i	$0.813102\pi$
$444$	−11.8266	−	12.0244i	−0.561265	−	0.570651i
$445$		0			0
$446$	−16.4609	+	3.47442i	−0.779445	+	0.164518i
$447$	−4.76440	−	2.15243i	−0.225348	−	0.101806i
$448$	−14.6445	+	7.30508i	−0.691887	+	0.345132i
$449$	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
$452$	19.2279	+	7.44371i	0.904406	+	0.350122i
$453$	5.32079	−	11.7776i	0.249993	−	0.553358i
$454$	0.0330201	+	0.156440i	0.00154971	+	0.00734211i
$455$		0			0
$456$	13.3537	−	20.1321i	0.625345	−	0.942771i
$457$	−16.7031	+	16.7031i	−0.781338	+	0.781338i	−0.980057	−	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	$-0.190113\pi$
$461$	35.5078			1.65376			0.826882	+	0.562376i	$0.190113\pi$
$462$	3.13847	+	0.689670i	0.146015	+	0.0320864i
$463$	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	−0.868683	−	0.495369i	$-0.835033\pi$
$467$	−8.06737	+	8.06737i	−0.373313	+	0.373313i	0.495369	+	0.868683i	$0.335033\pi$
$468$	−5.96030	−	16.1885i	−0.275515	−	0.748314i
$469$	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
$474$	10.9725	−	7.01891i	0.503982	−	0.322389i
$475$		0			0
$476$	−10.2411	−	23.1791i	−0.469401	−	1.06241i
$477$	−1.02822	+	16.2330i	−0.0470790	+	0.743258i
$478$	12.9044	−	19.8094i	0.590235	−	0.906060i
$479$	−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
$482$	3.61809	−	5.55406i	0.164799	−	0.252981i
$483$	−17.0612	−	7.70779i	−0.776312	−	0.350717i
$484$	8.55863	+	19.3710i	0.389029	+	0.880502i
$485$		0			0
$486$	19.9214	−	9.44134i	0.903652	−	0.428268i
$487$	−6.28516	+	6.28516i	−0.284808	+	0.284808i	−0.835023	−	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	$-0.692078\pi$
$491$	−25.1486			−1.13494			−0.567471	+	0.823393i	$0.692078\pi$
$492$	−0.207071	+	24.9729i	−0.00933550	+	1.12586i
$493$	−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
$498$	1.63623	−	7.44597i	0.0733214	−	0.333662i
$499$	−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	−0.944121	−	0.329598i	$-0.893087\pi$
$503$	−13.7823	+	13.7823i	−0.614523	+	0.614523i	0.329598	+	0.944121i	$0.393087\pi$
$504$	16.9221	+	3.86595i	0.753770	+	0.172203i
$505$		0			0
$506$	0.989624	+	4.68858i	0.0439942	+	0.208433i
$507$	−7.47162	−	3.37548i	−0.331826	−	0.149910i
$508$	30.2593	+	11.7143i	1.34254	+	0.519738i
$509$		−	10.5288i		−	0.466680i	−0.972395	−	0.233340i	$-0.925034\pi$
$509$		−	10.5288i		−	0.466680i	0.972395	−	0.233340i	$-0.0749656\pi$
$510$		0			0
$511$	24.3223			1.07595
$512$	20.0281	+	10.5297i	0.885125	+	0.465353i
$513$	−24.4958	+	7.51879i	−1.08151	+	0.331963i
$514$	−2.51825	+	0.531531i	−0.111075	+	0.0234448i
$515$		0			0
$516$	−15.2680	+	15.0169i	−0.672135	+	0.661080i
$517$	2.61938	+	2.61938i	0.115200	+	0.115200i
$518$	−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	$-0.747327\pi$
$521$		−	32.5500i		−	1.42604i	0.701144	−	0.713020i	$-0.252673\pi$
$522$	−6.02492	−	41.3286i	−0.263703	−	1.80890i
$523$	−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
$528$	−1.76179	−	4.07867i	−0.0766720	−	0.177501i
$529$		−	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
$534$	−5.23484	−	8.18348i	−0.226534	−	0.354134i
$535$		0			0
$536$	−6.06969	−	8.42958i	−0.262171	−	0.364102i
$537$	3.34576	+	1.51153i	0.144380	+	0.0652271i
$538$	−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
$543$	−30.6838	−	13.8621i	−1.31677	−	0.594880i
$544$	−17.7337	+	30.2177i	−0.760328	+	1.29557i
$545$		0			0
$546$	−12.1363	+	7.76338i	−0.519385	+	0.332242i
$547$	−5.74698	−	5.74698i	−0.245723	−	0.245723i	0.573490	−	0.819213i	$-0.305589\pi$
$547$	−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
$552$	5.13563	+	25.3705i	0.218587	+	1.07984i
$553$	−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	$-0.00594902\pi$
$558$	21.9583	−	3.20110i	0.929568	−	0.135513i
$559$		−	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	0.331805	−	0.943348i	$-0.392343\pi$
$563$	−14.5105	−	14.5105i	−0.611544	−	0.611544i	−0.943348	+	0.331805i	$0.892343\pi$
$564$	14.0317	+	14.2664i	0.590842	+	0.600723i
$565$		0			0
$566$	2.70814	+	12.8305i	0.113832	+	0.539305i
$567$	−11.2719	−	14.5572i	−0.473375	−	0.611343i
$568$	7.59590	−	46.6695i	0.318717	−	1.95821i
$569$	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	$-0.756809\pi$
$571$		−	33.0629i		−	1.38364i	0.722070	−	0.691820i	$-0.243191\pi$
$572$	3.43884	+	1.33128i	0.143785	+	0.0556636i
$573$	−4.20671	−	1.90048i	−0.175738	−	0.0793936i
$574$	20.4070	−	4.30732i	0.851771	−	0.179784i
$575$		0			0
$576$	−9.33394	−	22.1106i	−0.388914	−	0.921274i
$577$	−17.5957	+	17.5957i	−0.732519	+	0.732519i	−0.971118	−	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
$582$	−3.76685	−	0.827757i	−0.156141	−	0.0343116i
$583$	−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	$0.189370\pi$
$588$	−0.0808615	+	9.75192i	−0.00333467	+	0.402162i
$589$	−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	−0.750294	−	0.661105i	$-0.770088\pi$
$593$	−2.17189	+	2.17189i	−0.0891890	+	0.0891890i	0.661105	+	0.750294i	$0.270088\pi$
$594$	−1.30034	+	4.52946i	−0.0533535	+	0.185846i
$595$		0			0
$596$	5.52187	−	2.43971i	0.226185	−	0.0999343i
$597$	−26.6138	−	12.0234i	−1.08923	−	0.492086i
$598$	−18.0015	−	11.7267i	−0.736137	−	0.479542i
$599$	−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	$0.296621\pi$
$602$	14.9856	+	9.76209i	0.610768	+	0.397873i
$603$	−0.696471	+	10.9955i	−0.0283625	+	0.447772i
$604$	6.03095	+	13.6500i	0.245396	+	0.555412i
$605$		0			0
$606$	−5.70525	−	8.91886i	−0.231760	−	0.362304i
$607$	28.6094	−	28.6094i	1.16122	−	1.16122i	0.177009	−	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
$612$	34.8738	−	12.8399i	1.40969	−	0.519021i
$613$	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	0.818147	−	0.575009i	$-0.195002\pi$
$617$	6.03941	+	6.03941i	0.243138	+	0.243138i	−0.575009	+	0.818147i	$0.695002\pi$
$618$	−6.33352	+	28.8218i	−0.254772	+	1.15938i
$619$	−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
$624$	18.5159	+	7.34517i	0.741230	+	0.294042i
$625$		0			0
$626$	−22.8922	+	4.83188i	−0.914956	+	0.193121i
$627$	2.25505	−	4.99156i	0.0900582	−	0.199344i
$628$	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
$633$	−10.1939	−	4.60535i	−0.405173	−	0.183046i
$634$	2.12994	+	10.0911i	0.0845909	+	0.400769i
$635$		0			0
$636$	−13.1702	−	13.3904i	−0.522232	−	0.530965i
$637$	−5.72347	−	5.72347i	−0.226772	−	0.226772i
$638$	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	$0.166831\pi$
$641$			25.3407i			1.00090i	−0.865767	+	0.500448i	$0.833169\pi$
$642$	34.9964	+	7.69037i	1.38120	+	0.303515i
$643$	−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	0.639164	−	0.769071i	$-0.279281\pi$
$647$	−3.30434	−	3.30434i	−0.129907	−	0.129907i	−0.769071	+	0.639164i	$0.779281\pi$
$648$	−7.22689	+	24.4084i	−0.283899	+	0.958854i
$649$			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	0.666860	−	0.745183i	$-0.267638\pi$
$653$	−2.00144	−	2.00144i	−0.0783225	−	0.0783225i	−0.745183	+	0.666860i	$0.767638\pi$
$654$	15.1082	+	23.6183i	0.590778	+	0.923547i
$655$		0			0
$656$	−21.3201	−	19.4174i	−0.832411	−	0.758122i
$657$	−2.25480	+	35.5976i	−0.0879681	+	1.38879i
$658$	9.12169	−	14.0025i	0.355600	−	0.545876i
$659$		−	14.5552i		−	0.566989i	−0.958974	−	0.283495i	$-0.908506\pi$
$659$		−	14.5552i		−	0.566989i	0.958974	−	0.283495i	$-0.0914938\pi$
$660$		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
$663$	−12.6988	+	28.1088i	−0.493180	+	1.09165i
$664$	5.14386	+	7.14379i	0.199620	+	0.277233i
$665$		0			0
$666$	−16.5604	−	12.3464i	−0.641703	−	0.478412i
$667$	−36.7799	−	36.7799i	−1.42412	−	1.42412i
$668$	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
$672$	−16.3621	+	11.5767i	−0.631181	+	0.446580i
$673$	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	−0.779675	−	0.626184i	$-0.784616\pi$
$677$	−3.99371	+	3.99371i	−0.153491	+	0.153491i	0.626184	+	0.779675i	$0.284616\pi$
$678$	24.6639	+	5.41984i	0.947212	+	0.208148i
$679$			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	0.555865	−	0.831273i	$-0.312387\pi$
$683$	−7.19759	−	7.19759i	−0.275408	−	0.275408i	−0.831273	+	0.555865i	$0.812387\pi$
$684$	12.4047	−	26.8618i	0.474304	−	1.02709i
$685$		0			0
$686$	27.7835	−	5.86429i	1.06078	−	0.223900i
$687$	−9.25106	+	20.4772i	−0.352950	+	0.781255i
$688$	−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
$693$	3.92766	+	0.248783i	0.149200	+	0.00945050i
$694$	8.35055	+	39.5627i	0.316983	+	1.50178i
$695$		0			0
$696$	40.1892	+	26.6577i	1.52337	+	1.01046i
$697$	31.5740	−	31.5740i	1.19595	−	1.19595i
$698$	−0.465482	+	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	$-0.301655\pi$
$701$	30.9018			1.16714			0.583572	+	0.812061i	$0.301655\pi$
$702$	−10.2372	−	18.4821i	−0.386379	−	0.697563i
$703$	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
$708$	−0.0719064	+	8.67194i	−0.00270241	+	0.325911i
$709$	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
$714$	−16.7241	−	26.1444i	−0.625884	−	0.978428i
$715$		0			0
$716$	−3.87769	+	1.71327i	−0.144916	+	0.0640277i
$717$	11.9211	−	26.3873i	0.445201	−	0.985453i
$718$	9.78050	−	15.0139i	0.365005	−	0.560313i
$719$	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
$722$	−4.10476	+	6.30114i	−0.152763	+	0.234504i
$723$	3.34238	−	7.39836i	0.124304	−	0.275148i
$724$	35.5621	−	15.7123i	1.32165	−	0.583941i
$725$		0			0
$726$	13.9766	+	21.8492i	0.518719	+	0.810899i
$727$	2.33356	−	2.33356i	0.0865468	−	0.0865468i	−0.662508	−	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
$732$	0.276966	−	33.4021i	0.0102369	−	1.23458i
$733$	−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
$738$	4.41228	+	30.2665i	0.162418	+	1.11413i
$739$	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	−0.740696	−	0.671840i	$-0.765504\pi$
$743$	−1.87689	+	1.87689i	−0.0688563	+	0.0688563i	0.671840	+	0.740696i	$0.265504\pi$
$744$	−14.1635	+	21.3529i	−0.519259	+	0.782835i
$745$		0			0
$746$	8.15428	+	38.6329i	0.298550	+	1.41445i
$747$	0.590235	−	9.31833i	0.0215956	−	0.340940i
$748$	−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
$753$	13.0757	−	28.9430i	0.476503	−	1.05474i
$754$	−39.1644	+	8.26647i	−1.42628	+	0.301047i
$755$		0			0
$756$	21.2048	+	1.51977i	0.771212	+	0.0552735i
$757$	34.9468	+	34.9468i	1.27016	+	1.27016i	0.946002	+	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	$0.0166644\pi$
$761$			2.88711i			0.104657i	−0.998630	+	0.0523287i	$0.983336\pi$
$762$	38.8140	+	8.52929i	1.40608	+	0.308984i
$763$	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
$768$	26.2087	+	9.00584i	0.945724	+	0.324970i
$769$		−	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	0.960595	−	0.277953i	$-0.0896558\pi$
$773$	18.9794	+	18.9794i	0.682642	+	0.682642i	−0.277953	+	0.960595i	$0.589656\pi$
$774$	−15.6768	+	21.0276i	−0.563492	+	0.755823i
$775$		0			0
$776$	3.61398	−	2.60223i	0.129734	−	0.0934148i
$777$	−7.10233	+	15.7210i	−0.254795	+	0.563988i
$778$	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
$783$	−15.0096	−	48.9003i	−0.536399	−	1.74756i
$784$	−8.32552	−	7.58250i	−0.297340	−	0.270804i
$785$		0			0
$786$	20.6504	+	32.2823i	0.736576	+	1.15147i
$787$	28.3424	+	28.3424i	1.01030	+	1.01030i	0.999946	+	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
$792$	−2.89408	−	4.60797i	−0.102837	−	0.163737i
$793$	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	$0.379643\pi$
$798$	−24.1341	−	5.30341i	−0.854338	−	0.187739i
$799$		−	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
$804$	−8.92089	−	9.07007i	−0.314616	−	0.319877i
$805$		0			0
$806$	−4.39206	−	20.8084i	−0.154704	−	0.732945i
$807$	−2.87101	−	1.29704i	−0.101064	−	0.0456581i
$808$	12.0666	+	1.96396i	0.424503	+	0.0690918i
$809$	−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	$0.121207\pi$
$811$			21.1676i			0.743295i	−0.928374	+	0.371648i	$0.878793\pi$
$812$	14.5405	−	37.5597i	0.510271	−	1.31809i
$813$	−5.38302	+	11.9153i	−0.188791	+	0.417888i
$814$	4.32028	−	0.911887i	0.151426	−	0.0319616i
$815$		0			0
$816$	−15.8232	+	39.8875i	−0.553922	+	1.39634i
$817$	21.5566	−	21.5566i	0.754169	−	0.754169i
$818$	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	$-0.575615\pi$
$821$	−13.4855			−0.470649			−0.235324	+	0.971917i	$0.575615\pi$
$822$	−6.64821	+	30.2538i	−0.231883	+	1.05522i
$823$	−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	$0.610421\pi$
$827$	−36.8216	+	36.8216i	−1.28041	+	1.28041i	−0.940432	+	0.339982i	$0.889579\pi$
$828$	10.9535	+	29.7503i	0.380660	+	1.03389i
$829$	−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
$834$	−1.34153	−	2.09718i	−0.0464535	−	0.0726195i
$835$		0			0
$836$	2.55603	+	5.78515i	0.0884022	+	0.200084i
$837$	25.9812	−	7.97474i	0.898042	−	0.275647i
$838$	−47.3469	−	30.8432i	−1.63557	−	1.06546i
$839$	−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
$842$	−32.1306	−	20.9308i	−1.10729	−	0.721324i
$843$	−6.82234	−	3.08215i	−0.234974	−	0.106155i
$844$	11.8146	−	5.22001i	0.406676	−	0.179680i
$845$		0			0
$846$	19.6482	+	14.6484i	0.675519	+	0.503623i
$847$	15.3167	−	15.3167i	0.526289	−	0.526289i
$848$	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
$852$	0.480168	−	57.9084i	0.0164503	−	1.98391i
$853$	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	0.542368	−	0.840141i	$-0.317528\pi$
$857$	−8.71719	−	8.71719i	−0.297773	−	0.297773i	−0.840141	+	0.542368i	$0.817528\pi$
$858$	4.41105	+	0.969317i	0.150591	+	0.0330920i
$859$	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	−0.0846599	−	0.996410i	$-0.526980\pi$
$863$	26.7844	−	26.7844i	0.911750	−	0.911750i	0.996410	+	0.0846599i	$0.0269804\pi$
$864$	−15.4265	−	25.0204i	−0.524821	−	0.851212i
$865$		0			0
$866$	−16.0092	+	3.37908i	−0.544014	+	0.114826i
$867$	−33.7192	−	15.2334i	−1.14516	−	0.517354i
$868$	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
$873$	−4.71406	−	0.298595i	−0.159547	−	0.0101059i
$874$	−7.60998	−	36.0541i	−0.257412	−	1.21955i
$875$		0			0
$876$	−28.8811	−	29.3640i	−0.975801	−	0.992119i
$877$	13.3952	+	13.3952i	0.452323	+	0.452323i	0.896125	−	0.443802i	$-0.146371\pi$
$877$	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	$-0.936211\pi$
$881$		−	11.8169i		−	0.398120i	0.979987	−	0.199060i	$-0.0637889\pi$
$882$	1.72300	+	11.8191i	0.0580163	+	0.397970i
$883$	−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	0.714989	−	0.699136i	$-0.246432\pi$
$887$	0.472133	+	0.472133i	0.0158527	+	0.0158527i	−0.699136	+	0.714989i	$0.746432\pi$
$888$	23.3776	−	4.73222i	0.784502	−	0.158803i
$889$		−	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
$894$	6.22828	−	3.98413i	0.208305	−	0.133249i
$895$		0			0
$896$	2.64814	−	22.9921i	0.0884683	−	0.768113i
$897$	−23.9792	−	10.8331i	−0.800641	−	0.361708i
$898$	−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
$903$	19.9618	+	9.01820i	0.664287	+	0.300107i
$904$	−23.6630	+	17.0384i	−0.787019	+	0.566690i
$905$		0			0
$906$	9.84875	+	15.3963i	0.327203	+	0.511508i
$907$	38.0394	+	38.0394i	1.26308	+	1.26308i	0.949594	+	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	$-0.688081\pi$
$911$		−	50.1309i		−	1.66091i	0.557086	−	0.830455i	$-0.311919\pi$
$912$	13.5478	+	31.3640i	0.448611	+	1.03857i
$913$	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
$918$	39.8147	−	22.0533i	1.31408	−	0.727869i
$919$			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
$924$	−3.23988	+	3.18659i	−0.106584	+	0.104831i
$925$		0			0
$926$	−19.1735	+	4.04697i	−0.630079	+	0.132992i
$927$	−2.28468	+	36.0693i	−0.0750387	+	1.18467i
$928$	−53.8909	+	14.0302i	−1.76905	+	0.460565i
$929$	−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
$932$	−5.61778	−	2.17481i	−0.184017	−	0.0712383i
$933$	19.4863	+	8.80340i	0.637954	+	0.288211i
$934$	−3.33216	−	15.7869i	−0.109032	−	0.516563i
$935$		0			0
$936$	23.7837	+	5.43352i	0.777394	+	0.177600i
$937$	−7.63736	+	7.63736i	−0.249502	+	0.249502i	−0.820766	−	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	$-0.823741\pi$
$941$	−52.1835			−1.70113			−0.850567	+	0.525867i	$0.823741\pi$
$942$	4.52515	−	20.5925i	0.147437	−	0.670940i
$943$	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	$0.0236948\pi$
$948$	−0.152736	+	18.4200i	−0.00496064	+	0.598255i
$949$	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	−0.977204	−	0.212304i	$-0.931903\pi$
$953$	−23.6130	+	23.6130i	−0.764900	+	0.764900i	0.212304	+	0.977204i	$0.431903\pi$
$954$	−18.4418	−	13.7490i	−0.597076	−	0.445141i
$955$		0			0
$956$	13.5122	+	30.5826i	0.437015	+	0.989111i
$957$	9.96454	+	4.50171i	0.322108	+	0.145520i
$958$	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
$963$	43.7965	+	2.77413i	1.41132	+	0.0893952i
$964$	3.78848	+	8.57460i	0.122019	+	0.276169i
$965$		0			0
$966$	22.3034	−	14.2671i	0.717599	−	0.459036i
$967$	3.10676	−	3.10676i	0.0999067	−	0.0999067i	−0.655387	−	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	$-0.586560\pi$
$971$	−16.7395			−0.537196			−0.268598	+	0.963252i	$0.586560\pi$
$972$	−4.19010	+	30.8941i	−0.134397	+	0.990928i
$973$	−1.47017	+	1.47017i	−0.0471314	+	0.0471314i
$974$	−2.59603	−	12.2993i	−0.0831823	−	0.394096i
$975$		0			0
$976$	28.5165	+	25.9715i	0.912790	+	0.831327i
$977$	−38.9727	−	38.9727i	−1.24685	−	1.24685i	−0.957104	−	0.289745i	$-0.906430\pi$
$977$	−38.9727	−	38.9727i	−1.24685	−	1.24685i	−0.289745	−	0.957104i	$-0.593570\pi$
$978$	−45.8391	−	10.0730i	−1.46577	−	0.322100i
$979$	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	−0.267388	−	0.963589i	$-0.586161\pi$
$983$	21.8279	−	21.8279i	0.696200	−	0.696200i	0.963589	+	0.267388i	$0.0861607\pi$
$984$	−29.4321	−	19.5225i	−0.938261	−	0.622353i
$985$		0			0
$986$	−17.8079	−	84.3691i	−0.567119	−	2.68686i
$987$	8.42660	−	18.6523i	0.268222	−	0.593708i
$988$	−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
$993$	−22.1708	−	10.0162i	−0.703570	−	0.317854i
$994$	−47.3208	+	9.98805i	−1.50092	+	0.316802i
$995$		0			0
$996$	7.56016	+	7.68658i	0.239553	+	0.243559i
$997$	−17.8369	−	17.8369i	−0.564900	−	0.564900i	0.365795	−	0.930695i	$-0.380797\pi$
$997$	−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.293.9	yes	64
3.2	odd	2	inner	600.2.w.k.293.23	yes	64
5.2	odd	4	inner	600.2.w.k.557.8	yes	64
5.3	odd	4	inner	600.2.w.k.557.25	yes	64
5.4	even	2	inner	600.2.w.k.293.24	yes	64
8.5	even	2	inner	600.2.w.k.293.26	yes	64
15.2	even	4	inner	600.2.w.k.557.26	yes	64
15.8	even	4	inner	600.2.w.k.557.7	yes	64
15.14	odd	2	inner	600.2.w.k.293.10	yes	64
24.5	odd	2	inner	600.2.w.k.293.8	yes	64
40.13	odd	4	inner	600.2.w.k.557.10	yes	64
40.29	even	2	inner	600.2.w.k.293.7	✓	64
40.37	odd	4	inner	600.2.w.k.557.23	yes	64
120.29	odd	2	inner	600.2.w.k.293.25	yes	64
120.53	even	4	inner	600.2.w.k.557.24	yes	64
120.77	even	4	inner	600.2.w.k.557.9	yes	64

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

\(f(q)\)	\(=\)	\(q+(-0.771921 + 1.18496i) q^{2} +(-0.713099 + 1.57845i) q^{3} +(-0.808275 - 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(2.79169 + 0.454373i) q^{8} +(-1.98298 - 2.25118i) q^{9} +O(q^{10})\)	\(q+(-0.771921 + 1.18496i) q^{2} +(-0.713099 + 1.57845i) q^{3} +(-0.808275 - 1.82940i) q^{4} +(-1.31994 - 2.06343i) q^{6} +(-1.44651 + 1.44651i) q^{7} +(2.79169 + 0.454373i) q^{8} +(-1.98298 - 2.25118i) q^{9} +0.641278 q^{11} +(3.46398 + 0.0287228i) 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} +(4.19826 - 0.612026i) q^{18} -4.93129 q^{19} +(-1.25173 - 3.31474i) q^{21} +(-0.495016 + 0.759891i) q^{22} +(3.73619 - 3.73619i) q^{23} +(-2.70796 + 4.08252i) q^{24} +(-0.839729 - 3.97842i) q^{26} +(4.96742 - 1.52471i) q^{27} +(3.81541 + 1.47706i) q^{28} -9.84421i q^{29} +5.23032 q^{31} +(-1.42523 - 5.47437i) q^{32} +(-0.457295 + 1.01222i) q^{33} +(8.57043 - 1.80897i) q^{34} +(-2.51550 + 5.44722i) q^{36} +(-3.44271 - 3.44271i) q^{37} +(3.80656 - 5.84339i) q^{38} +(-1.75928 - 4.65879i) q^{39} +7.20930i q^{41} +(4.89408 + 1.07546i) 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} +(-2.74731 - 6.36021i) q^{48} +2.81523i q^{49} +(10.0361 - 3.78989i) q^{51} +(5.36248 + 2.07598i) q^{52} +(-3.83383 - 3.83383i) q^{53} +(-2.02773 + 7.06317i) q^{54} +(-4.69546 + 3.38095i) q^{56} +(3.51650 - 7.78377i) q^{57} +(11.6650 + 7.59896i) q^{58} +2.50346i q^{59} -9.64270i q^{61} +(-4.03740 + 6.19774i) q^{62} +(6.12474 + 0.387949i) q^{63} +(7.58709 + 2.53694i) q^{64} +(-0.846451 - 1.32323i) q^{66} +(-2.59686 - 2.59686i) q^{67} +(-4.47213 + 11.5520i) q^{68} +(3.23310 + 8.56166i) q^{69} -16.7173i q^{71} +(-4.51299 - 7.18560i) 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} +(6.87852 + 1.51154i) q^{78} +5.31759i q^{79} +(-1.13559 + 8.92807i) q^{81} +(-8.54275 - 5.56501i) q^{82} +(2.20075 + 2.20075i) q^{83} +(-5.05222 + 4.96913i) q^{84} +(-1.80557 - 8.55430i) q^{86} +(15.5386 + 7.01990i) q^{87} +(1.79025 + 0.291380i) q^{88} +3.96596 q^{89} -5.88160i q^{91} +(-9.85485 - 3.81511i) q^{92} +(-3.72974 + 8.25578i) q^{93} +(-7.99313 + 1.68712i) q^{94} +(9.65732 + 1.65413i) 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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Database

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