LMFDB - Embedded newform 900.2.bj.e.487.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			487.25
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.e.523.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29240 + 0.574201i) q^{2} +(1.34059 + 1.48419i) q^{4} +(0.0819943 + 2.23456i) q^{5} +(1.03330 - 1.03330i) q^{7} +(0.880349 + 2.68793i) q^{8} +(-1.17712 + 2.93503i) q^{10} +(3.35595 - 4.61907i) q^{11} +(-0.392815 + 2.48014i) q^{13} +(1.92876 - 0.742115i) q^{14} +(-0.405651 + 3.97938i) q^{16} +(4.26203 - 2.17162i) q^{17} +(-1.72727 + 5.31601i) q^{19} +(-3.20660 + 3.11732i) q^{20} +(6.98950 - 4.04269i) q^{22} +(0.0446569 + 0.281952i) q^{23} +(-4.98655 + 0.366443i) q^{25} +(-1.93177 + 2.97977i) q^{26} +(2.91885 + 0.148387i) q^{28} +(-4.78796 + 1.55570i) q^{29} +(3.26564 + 1.06107i) q^{31} +(-2.80922 + 4.91002i) q^{32} +(6.75519 - 0.359329i) q^{34} +(2.39370 + 2.22425i) q^{35} +(-3.62025 - 0.573391i) q^{37} +(-5.28478 + 5.87859i) q^{38} +(-5.93418 + 2.18759i) q^{40} +(0.181512 - 0.131876i) q^{41} +(-0.707410 - 0.707410i) q^{43} +(11.3545 - 1.21139i) q^{44} +(-0.104183 + 0.390037i) q^{46} +(-5.53664 - 2.82106i) q^{47} +4.86458i q^{49} +(-6.65503 - 2.38969i) q^{50} +(-4.20760 + 2.74183i) q^{52} +(-10.4732 - 5.33638i) q^{53} +(10.5968 + 7.12035i) q^{55} +(3.68711 + 1.86778i) q^{56} +(-7.08124 - 0.738663i) q^{58} +(10.3120 - 7.49212i) q^{59} +(-8.77641 - 6.37643i) q^{61} +(3.61124 + 3.24646i) q^{62} +(-6.44997 + 4.73264i) q^{64} +(-5.57423 - 0.674413i) q^{65} +(-0.542962 - 1.06562i) q^{67} +(8.93672 + 3.41444i) q^{68} +(1.81645 + 4.24909i) q^{70} +(11.1713 - 3.62978i) q^{71} +(14.6329 - 2.31762i) q^{73} +(-4.34956 - 2.81980i) q^{74} +(-10.2055 + 4.56296i) q^{76} +(-1.30518 - 8.24060i) q^{77} +(-0.564003 - 1.73582i) q^{79} +(-8.92544 - 0.580168i) q^{80} +(0.310310 - 0.0662124i) q^{82} +(2.71578 - 1.38376i) q^{83} +(5.20208 + 9.34573i) q^{85} +(-0.508061 - 1.32045i) q^{86} +(15.3702 + 4.95418i) q^{88} +(7.48483 - 10.3020i) q^{89} +(2.15683 + 2.96862i) q^{91} +(-0.358605 + 0.444261i) q^{92} +(-5.53570 - 6.82508i) q^{94} +(-12.0206 - 3.42382i) q^{95} +(2.49688 - 4.90040i) q^{97} +(-2.79324 + 6.28697i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 4 q^{10} + 16 q^{13} - 16 q^{16} + 28 q^{22} - 32 q^{25} + 28 q^{28} - 100 q^{34} - 104 q^{37} + 60 q^{40} + 156 q^{52} + 144 q^{58} - 48 q^{61} + 60 q^{64} + 28 q^{70} + 40 q^{73} + 64 q^{82} + 136 q^{85}+ \cdots - 160 q^{97}+O(q^{100}) $ 224 * q - 4 * q^10 + 16 * q^13 - 16 * q^16 + 28 * q^22 - 32 * q^25 + 28 * q^28 - 100 * q^34 - 104 * q^37 + 60 * q^40 + 156 * q^52 + 144 * q^58 - 48 * q^61 + 60 * q^64 + 28 * q^70 + 40 * q^73 + 64 * q^82 + 136 * q^85 + 148 * q^88 + 40 * q^94 - 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	1.29240	+	0.574201i	0.913864	+	0.406021i
$2$	1.29240	+	0.574201i	0.913864	+	0.406021i
$3$		0			0
$3$		0			0
$4$	1.34059	+	1.48419i	0.670294	+	0.742096i
$5$	0.0819943	+	2.23456i	0.0366690	+	0.999327i
$5$	0.0819943	+	2.23456i	0.0366690	+	0.999327i
$6$		0			0
$7$	1.03330	−	1.03330i	0.390551	−	0.390551i	−0.484333	−	0.874884i	$-0.660938\pi$
$7$	1.03330	−	1.03330i	0.390551	−	0.390551i	0.874884	+	0.484333i	$0.160938\pi$
$8$	0.880349	+	2.68793i	0.311250	+	0.950328i
$9$		0			0
$10$	−1.17712	+	2.93503i	−0.372238	+	0.928137i
$11$	3.35595	−	4.61907i	1.01186	−	1.39270i	0.0940992	−	0.995563i	$-0.470003\pi$
$11$	3.35595	−	4.61907i	1.01186	−	1.39270i	0.917758	−	0.397140i	$-0.129997\pi$
$12$		0			0
$13$	−0.392815	+	2.48014i	−0.108947	+	0.687866i	0.871398	+	0.490577i	$0.163214\pi$
$13$	−0.392815	+	2.48014i	−0.108947	+	0.687866i	−0.980345	+	0.197289i	$0.936786\pi$
$14$	1.92876	−	0.742115i	0.515482	−	0.198338i
$15$		0			0
$16$	−0.405651	+	3.97938i	−0.101413	+	0.994844i
$17$	4.26203	−	2.17162i	1.03370	−	0.526694i	0.147043	−	0.989130i	$-0.453025\pi$
$17$	4.26203	−	2.17162i	1.03370	−	0.526694i	0.886653	+	0.462436i	$0.153025\pi$
$18$		0			0
$19$	−1.72727	+	5.31601i	−0.396264	+	1.21958i	0.531709	+	0.846927i	$0.321550\pi$
$19$	−1.72727	+	5.31601i	−0.396264	+	1.21958i	−0.927973	+	0.372648i	$0.878450\pi$
$20$	−3.20660	+	3.11732i	−0.717018	+	0.697055i
$21$		0			0
$22$	6.98950	−	4.04269i	1.49017	−	0.861905i
$23$	0.0446569	+	0.281952i	0.00931160	+	0.0587911i	0.991907	−	0.126970i	$-0.0405251\pi$
$23$	0.0446569	+	0.281952i	0.00931160	+	0.0587911i	−0.982595	+	0.185761i	$0.940525\pi$
$24$		0			0
$25$	−4.98655	+	0.366443i	−0.997311	+	0.0732886i
$26$	−1.93177	+	2.97977i	−0.378851	+	0.584381i
$27$		0			0
$28$	2.91885	+	0.148387i	0.551610	+	0.0280425i
$29$	−4.78796	+	1.55570i	−0.889102	+	0.288887i	−0.717732	−	0.696320i	$-0.754820\pi$
$29$	−4.78796	+	1.55570i	−0.889102	+	0.288887i	−0.171371	+	0.985207i	$0.554820\pi$
$30$		0			0
$31$	3.26564	+	1.06107i	0.586527	+	0.190574i	0.587222	−	0.809426i	$-0.300221\pi$
$31$	3.26564	+	1.06107i	0.586527	+	0.190574i	−0.000695631		1.00000i	$0.500221\pi$
$32$	−2.80922	+	4.91002i	−0.496605	+	0.867976i
$33$		0			0
$34$	6.75519	−	0.359329i	1.15851	−	0.0616244i
$35$	2.39370	+	2.22425i	0.404610	+	0.375967i
$36$		0			0
$37$	−3.62025	−	0.573391i	−0.595166	−	0.0942650i	−0.148418	−	0.988925i	$-0.547418\pi$
$37$	−3.62025	−	0.573391i	−0.595166	−	0.0942650i	−0.446748	+	0.894660i	$0.647418\pi$
$38$	−5.28478	+	5.87859i	−0.857305	+	0.953634i
$39$		0			0
$40$	−5.93418	+	2.18759i	−0.938276	+	0.345889i
$41$	0.181512	−	0.131876i	0.0283475	−	0.0205956i	−0.573521	−	0.819191i	$-0.694423\pi$
$41$	0.181512	−	0.131876i	0.0283475	−	0.0205956i	0.601869	+	0.798595i	$0.294423\pi$
$42$		0			0
$43$	−0.707410	−	0.707410i	−0.107879	−	0.107879i	0.651107	−	0.758986i	$-0.274305\pi$
$43$	−0.707410	−	0.707410i	−0.107879	−	0.107879i	−0.758986	+	0.651107i	$0.774305\pi$
$44$	11.3545	−	1.21139i	1.71176	−	0.182624i
$45$		0			0
$46$	−0.104183	+	0.390037i	−0.0153609	+	0.0575078i
$47$	−5.53664	−	2.82106i	−0.807603	−	0.411494i	0.000890557	−	1.00000i	$-0.499717\pi$
$47$	−5.53664	−	2.82106i	−0.807603	−	0.411494i	−0.808493	+	0.588505i	$0.799717\pi$
$48$		0			0
$49$			4.86458i			0.694940i
$50$	−6.65503	−	2.38969i	−0.941163	−	0.337953i
$51$		0			0
$52$	−4.20760	+	2.74183i	−0.583489	+	0.380223i
$53$	−10.4732	−	5.33638i	−1.43861	−	0.733009i	−0.451384	−	0.892330i	$-0.649069\pi$
$53$	−10.4732	−	5.33638i	−1.43861	−	0.733009i	−0.987227	+	0.159321i	$0.949069\pi$
$54$		0			0
$55$	10.5968	+	7.12035i	1.42887	+	0.960108i
$56$	3.68711	+	1.86778i	0.492711	+	0.249592i
$57$		0			0
$58$	−7.08124	−	0.738663i	−0.929813	−	0.0969912i
$59$	10.3120	−	7.49212i	1.34251	−	0.975390i	0.343162	−	0.939276i	$-0.388502\pi$
$59$	10.3120	−	7.49212i	1.34251	−	0.975390i	0.999348	−	0.0361143i	$-0.0114980\pi$
$60$		0			0
$61$	−8.77641	−	6.37643i	−1.12370	−	0.816419i	−0.138937	−	0.990301i	$-0.544369\pi$
$61$	−8.77641	−	6.37643i	−1.12370	−	0.816419i	−0.984766	+	0.173883i	$0.944369\pi$
$62$	3.61124	+	3.24646i	0.458628	+	0.412301i
$63$		0			0
$64$	−6.44997	+	4.73264i	−0.806246	+	0.591580i
$65$	−5.57423	−	0.674413i	−0.691398	−	0.0836507i
$66$		0			0
$67$	−0.542962	−	1.06562i	−0.0663334	−	0.130187i	0.855459	−	0.517871i	$-0.173275\pi$
$67$	−0.542962	−	1.06562i	−0.0663334	−	0.130187i	−0.921792	+	0.387684i	$0.873275\pi$
$68$	8.93672	+	3.41444i	1.08374	+	0.414061i
$69$		0			0
$70$	1.81645	+	4.24909i	0.217107	+	0.507863i
$71$	11.1713	−	3.62978i	1.32579	−	0.430776i	0.441312	−	0.897354i	$-0.354513\pi$
$71$	11.1713	−	3.62978i	1.32579	−	0.430776i	0.884480	+	0.466578i	$0.154513\pi$
$72$		0			0
$73$	14.6329	−	2.31762i	1.71265	−	0.271257i	0.778371	−	0.627805i	$-0.216046\pi$
$73$	14.6329	−	2.31762i	1.71265	−	0.271257i	0.934277	+	0.356548i	$0.116046\pi$
$74$	−4.34956	−	2.81980i	−0.505627	−	0.327795i
$75$		0			0
$76$	−10.2055	+	4.56296i	−1.17066	+	0.523408i
$77$	−1.30518	−	8.24060i	−0.148739	−	0.939103i
$78$		0			0
$79$	−0.564003	−	1.73582i	−0.0634553	−	0.195295i	0.914303	−	0.405032i	$-0.132739\pi$
$79$	−0.564003	−	1.73582i	−0.0634553	−	0.195295i	−0.977758	+	0.209736i	$0.932739\pi$
$80$	−8.92544	−	0.580168i	−0.997894	−	0.0648647i
$81$		0			0
$82$	0.310310	−	0.0662124i	0.0342680	−	0.00731194i
$83$	2.71578	−	1.38376i	0.298095	−	0.151887i	−0.298546	−	0.954395i	$-0.596502\pi$
$83$	2.71578	−	1.38376i	0.298095	−	0.151887i	0.596641	+	0.802508i	$0.296502\pi$
$84$		0			0
$85$	5.20208	+	9.34573i	0.564244	+	1.01369i
$86$	−0.508061	−	1.32045i	−0.0547856	−	0.142388i
$87$		0			0
$88$	15.3702	+	4.95418i	1.63846	+	0.528117i
$89$	7.48483	−	10.3020i	0.793390	−	1.09201i	−0.200288	−	0.979737i	$-0.564188\pi$
$89$	7.48483	−	10.3020i	0.793390	−	1.09201i	0.993678	−	0.112270i	$-0.0358123\pi$
$90$		0			0
$91$	2.15683	+	2.96862i	0.226097	+	0.311196i
$92$	−0.358605	+	0.444261i	−0.0373871	+	0.0463174i
$93$		0			0
$94$	−5.53570	−	6.82508i	−0.570963	−	0.703953i
$95$	−12.0206	−	3.42382i	−1.23329	−	0.351277i
$96$		0			0
$97$	2.49688	−	4.90040i	0.253520	−	0.497560i	−0.728811	−	0.684715i	$-0.759927\pi$
$97$	2.49688	−	4.90040i	0.253520	−	0.497560i	0.982330	+	0.187155i	$0.0599267\pi$
$98$	−2.79324	+	6.28697i	−0.282160	+	0.635080i
$99$		0			0
$100$	−7.22878	−	6.90975i	−0.722878	−	0.690975i
$101$	−6.41836			−0.638650			−0.319325	−	0.947645i	$-0.603456\pi$
$101$	−6.41836			−0.638650			−0.319325	+	0.947645i	$0.603456\pi$
$102$		0			0
$103$	−0.573005	+	1.12459i	−0.0564599	+	0.110809i	−0.917512	−	0.397708i	$-0.869806\pi$
$103$	−0.573005	+	1.12459i	−0.0564599	+	0.110809i	0.861052	+	0.508516i	$0.169806\pi$
$104$	−7.01225	+	1.12752i	−0.687608	+	0.110563i
$105$		0			0
$106$	−10.4714	−	12.9105i	−1.01708	−	1.25398i
$107$	6.53996	−	6.53996i	0.632242	−	0.632242i	−0.316388	−	0.948630i	$-0.602470\pi$
$107$	6.53996	−	6.53996i	0.632242	−	0.632242i	0.948630	+	0.316388i	$0.102470\pi$
$108$		0			0
$109$	6.79692	+	9.35516i	0.651027	+	0.896062i	0.999143	−	0.0413893i	$-0.0131784\pi$
$109$	6.79692	+	9.35516i	0.651027	+	0.896062i	−0.348116	+	0.937452i	$0.613178\pi$
$110$	9.60675	+	15.2870i	0.915968	+	1.45756i
$111$		0			0
$112$	3.69274	+	4.53106i	0.348931	+	0.428144i
$113$	−1.59498	+	10.0703i	−0.150043	+	0.947335i	0.791677	+	0.610939i	$0.209208\pi$
$113$	−1.59498	+	10.0703i	−0.150043	+	0.947335i	−0.941721	+	0.336396i	$0.890792\pi$
$114$		0			0
$115$	−0.626379	+	0.122907i	−0.0584101	+	0.0114611i
$116$	−8.72765	−	5.02070i	−0.810342	−	0.466160i
$117$		0			0
$118$	17.6292	−	3.76163i	1.62290	−	0.346287i
$119$	2.16003	−	6.64790i	0.198010	−	0.609412i
$120$		0			0
$121$	−6.67422	−	20.5411i	−0.606747	−	1.86738i
$122$	−7.68126	−	13.2803i	−0.695429	−	1.20234i
$123$		0			0
$124$	2.80305	+	6.26930i	0.251721	+	0.563000i
$125$	−1.22771	−	11.1127i	−0.109810	−	0.993953i
$126$		0			0
$127$	−9.78669	+	1.55006i	−0.868428	+	0.137546i	−0.574721	−	0.818350i	$-0.694889\pi$
$127$	−9.78669	+	1.55006i	−0.868428	+	0.137546i	−0.293708	+	0.955895i	$0.594889\pi$
$128$	−11.0534	+	2.41288i	−0.976993	+	0.213270i
$129$		0			0
$130$	−6.81688	−	4.07234i	−0.597880	−	0.357168i
$131$	−0.0826706	−	0.0268613i	−0.00722296	−	0.00234688i	0.305403	−	0.952223i	$-0.401209\pi$
$131$	−0.0826706	−	0.0268613i	−0.00722296	−	0.00234688i	−0.312626	+	0.949876i	$0.601209\pi$
$132$		0			0
$133$	3.70824	+	7.27783i	0.321545	+	0.631068i
$134$	−0.0898420	−	1.68898i	−0.00776116	−	0.145906i
$135$		0			0
$136$	9.58923	+	9.54429i	0.822270	+	0.818416i
$137$	−7.65388	−	1.21226i	−0.653915	−	0.103570i	−0.179343	−	0.983787i	$-0.557397\pi$
$137$	−7.65388	−	1.21226i	−0.653915	−	0.103570i	−0.474572	+	0.880217i	$0.657397\pi$
$138$		0			0
$139$	12.0808	+	8.77720i	1.02468	+	0.744473i	0.967237	−	0.253876i	$-0.0817056\pi$
$139$	12.0808	+	8.77720i	1.02468	+	0.744473i	0.0574418	+	0.998349i	$0.481706\pi$
$140$	−0.0922509	+	6.53452i	−0.00779663	+	0.552268i
$141$		0			0
$142$	16.5220	+	1.72345i	1.38650	+	0.144629i
$143$	10.1377	+	10.1377i	0.847753	+	0.847753i
$144$		0			0
$145$	−3.86891	−	10.5715i	−0.321295	−	0.877911i
$146$	20.2423	+	5.40692i	1.67526	+	0.447480i
$147$		0			0
$148$	−4.00224	−	6.14183i	−0.328982	−	0.504855i
$149$		−	6.14079i		−	0.503073i	−0.967848	−	0.251537i	$-0.919064\pi$
$149$		−	6.14079i		−	0.503073i	0.967848	−	0.251537i	$-0.0809359\pi$
$150$		0			0
$151$		−	22.7591i		−	1.85211i	−0.377392	−	0.926053i	$-0.623179\pi$
$151$		−	22.7591i		−	1.85211i	0.377392	−	0.926053i	$-0.376821\pi$
$152$	−15.8097	+	0.0371404i	−1.28233	+	0.00301248i
$153$		0			0
$154$	3.04494	−	11.3996i	0.245368	−	0.918604i
$155$	−2.10327	+	7.38429i	−0.168939	+	0.593120i
$156$		0			0
$157$	−9.18517	−	9.18517i	−0.733057	−	0.733057i	0.238167	−	0.971224i	$-0.423453\pi$
$157$	−9.18517	−	9.18517i	−0.733057	−	0.733057i	−0.971224	+	0.238167i	$0.923453\pi$
$158$	0.267794	−	2.56722i	0.0213045	−	0.204237i
$159$		0			0
$160$	−11.2021	−	5.87480i	−0.885603	−	0.464444i
$161$	0.337486	+	0.245198i	0.0265976	+	0.0193243i
$162$		0			0
$163$	−23.4305	−	3.71102i	−1.83521	−	0.290669i	−0.859732	−	0.510745i	$-0.829369\pi$
$163$	−23.4305	−	3.71102i	−1.83521	−	0.290669i	−0.975483	+	0.220076i	$0.929369\pi$
$164$	0.439063	+	0.0926073i	0.0342851	+	0.00723141i
$165$		0			0
$166$	4.30442	−	0.228965i	0.334088	−	0.0177711i
$167$	−4.60373	−	9.03534i	−0.356248	−	0.699175i	0.641438	−	0.767175i	$-0.278338\pi$
$167$	−4.60373	−	9.03534i	−0.356248	−	0.699175i	−0.997685	+	0.0679997i	$0.978338\pi$
$168$		0			0
$169$	6.36696	+	2.06875i	0.489766	+	0.159135i
$170$	1.35683	+	15.0654i	0.104064	+	1.15547i
$171$		0			0
$172$	0.101587	−	1.99828i	0.00774596	−	0.152367i
$173$	8.63186	−	1.36715i	0.656268	−	0.103943i	0.180585	−	0.983559i	$-0.442201\pi$
$173$	8.63186	−	1.36715i	0.656268	−	0.103943i	0.475683	+	0.879617i	$0.342201\pi$
$174$		0			0
$175$	−4.77397	+	5.53126i	−0.360878	+	0.418124i
$176$	17.0197	+	15.2283i	1.28291	+	1.14788i
$177$		0			0
$178$	15.5888	−	9.01647i	1.16843	−	0.675813i
$179$	−5.04948	−	15.5407i	−0.377416	−	1.16157i	−0.941834	−	0.336078i	$-0.890899\pi$
$179$	−5.04948	−	15.5407i	−0.377416	−	1.16157i	0.564418	−	0.825489i	$-0.309101\pi$
$180$		0			0
$181$	−5.68758	+	17.5046i	−0.422755	+	1.30110i	0.482374	+	0.875966i	$0.339775\pi$
$181$	−5.68758	+	17.5046i	−0.422755	+	1.30110i	−0.905128	+	0.425139i	$0.860225\pi$
$182$	1.08290	+	5.07510i	0.0802699	+	0.376191i
$183$		0			0
$184$	−0.718555	+	0.368251i	−0.0529726	+	0.0271478i
$185$	0.984440	−	8.13670i	0.0723775	−	0.598222i
$186$		0			0
$187$	4.27234	−	26.9745i	0.312424	−	1.97257i
$188$	−3.23536	−	11.9993i	−0.235963	−	0.875141i
$189$		0			0
$190$	−13.5694	−	11.3272i	−0.984429	−	0.821759i
$191$	10.3043	+	14.1827i	0.745595	+	1.02622i	0.998277	+	0.0586743i	$0.0186873\pi$
$191$	10.3043	+	14.1827i	0.745595	+	1.02622i	−0.252682	+	0.967549i	$0.581313\pi$
$192$		0			0
$193$	−16.0574	+	16.0574i	−1.15584	+	1.15584i	−0.170475	+	0.985362i	$0.554530\pi$
$193$	−16.0574	+	16.0574i	−1.15584	+	1.15584i	−0.985362	+	0.170475i	$0.945470\pi$
$194$	6.04077	−	4.89956i	0.433702	−	0.351768i
$195$		0			0
$196$	−7.21997	+	6.52139i	−0.515712	+	0.465814i
$197$	−6.26169	+	12.2893i	−0.446127	+	0.875573i	0.552975	+	0.833198i	$0.313493\pi$
$197$	−6.26169	+	12.2893i	−0.446127	+	0.875573i	−0.999102	+	0.0423753i	$0.986507\pi$
$198$		0			0
$199$	−22.2639			−1.57825			−0.789124	−	0.614233i	$-0.789465\pi$
$199$	−22.2639			−1.57825			−0.789124	+	0.614233i	$0.789465\pi$
$200$	−5.37488	−	13.0809i	−0.380062	−	0.924961i
$201$		0			0
$202$	−8.29507	−	3.68542i	−0.583639	−	0.259306i
$203$	−3.33990	+	6.55492i	−0.234415	+	0.460065i
$204$		0			0
$205$	0.309569	+	0.394788i	0.0216213	+	0.0275732i
$206$	−1.38629	+	1.12439i	−0.0965873	+	0.0783401i
$207$		0			0
$208$	−9.71005	−	2.56923i	−0.673271	−	0.178144i
$209$	18.7584	+	25.8187i	1.29754	+	1.78591i
$210$		0			0
$211$	−1.75573	+	2.41656i	−0.120870	+	0.166363i	−0.865164	−	0.501489i	$-0.832786\pi$
$211$	−1.75573	+	2.41656i	−0.120870	+	0.166363i	0.744294	+	0.667852i	$0.232786\pi$
$212$	−6.12008	−	22.6982i	−0.420329	−	1.55892i
$213$		0			0
$214$	12.2075	−	4.69699i	0.834487	−	0.321079i
$215$	1.52275	−	1.63876i	0.103851	−	0.111762i
$216$		0			0
$217$	4.47080	−	2.27799i	0.303498	−	0.154640i
$218$	3.41259	+	15.9934i	0.231130	+	1.08321i
$219$		0			0
$220$	3.63794	+	25.2731i	0.245270	+	1.70391i
$221$	3.71171	+	11.4235i	0.249677	+	0.768426i
$222$		0			0
$223$	−2.70165	−	17.0575i	−0.180916	−	1.14226i	−0.896275	−	0.443499i	$-0.853737\pi$
$223$	−2.70165	−	17.0575i	−0.180916	−	1.14226i	0.715359	−	0.698757i	$-0.246263\pi$
$224$	2.17075	+	7.97630i	0.145039	+	0.532939i
$225$		0			0
$226$	−7.84373	+	12.0990i	−0.521757	+	0.804815i
$227$	−20.3606	+	3.22480i	−1.35138	+	0.214037i	−0.789789	−	0.613378i	$-0.789810\pi$
$227$	−20.3606	+	3.22480i	−1.35138	+	0.214037i	−0.561590	+	0.827416i	$0.689810\pi$
$228$		0			0
$229$	12.6221	−	4.10118i	0.834095	−	0.271014i	0.139326	−	0.990247i	$-0.455507\pi$
$229$	12.6221	−	4.10118i	0.834095	−	0.271014i	0.694769	+	0.719233i	$0.255507\pi$
$230$	−0.880104	−	0.200822i	−0.0580324	−	0.0132418i
$231$		0			0
$232$	−8.39671	−	11.5002i	−0.551271	−	0.755023i
$233$	0.909143	+	1.78429i	0.0595599	+	0.116893i	0.918867	−	0.394566i	$-0.129105\pi$
$233$	0.909143	+	1.78429i	0.0595599	+	0.116893i	−0.859308	+	0.511459i	$0.829105\pi$
$234$		0			0
$235$	5.84987	−	12.6033i	0.381603	−	0.822149i
$236$	24.9439	+	5.26117i	1.62371	+	0.342473i
$237$		0			0
$238$	6.60885	−	7.35144i	0.428388	−	0.476523i
$239$	−9.83649	−	7.14663i	−0.636270	−	0.462277i	0.222297	−	0.974979i	$-0.428645\pi$
$239$	−9.83649	−	7.14663i	−0.636270	−	0.462277i	−0.858567	+	0.512702i	$0.828645\pi$
$240$		0			0
$241$	12.0473	−	8.75288i	0.776035	−	0.563823i	−0.127751	−	0.991806i	$-0.540776\pi$
$241$	12.0473	−	8.75288i	0.776035	−	0.563823i	0.903786	+	0.427984i	$0.140776\pi$
$242$	3.16898	−	30.3797i	0.203710	−	1.95288i
$243$		0			0
$244$	−2.30169	−	21.5740i	−0.147351	−	1.38114i
$245$	−10.8702	+	0.398868i	−0.694472	+	0.0254827i
$246$		0			0
$247$	−12.5059	−	6.37208i	−0.795732	−	0.405446i
$248$	0.0228155	+	9.71194i	0.00144879	+	0.616709i
$249$		0			0
$250$	4.79425	−	15.0670i	0.303215	−	0.952922i
$251$			2.53046i			0.159721i	0.996806	+	0.0798606i	$0.0254475\pi$
$251$			2.53046i			0.159721i	−0.996806	+	0.0798606i	$0.974552\pi$
$252$		0			0
$253$	1.45222	+	0.739945i	0.0913005	+	0.0465199i
$254$	−13.5383	−	3.61623i	−0.849472	−	0.226902i
$255$		0			0
$256$	−15.6709	−	3.22848i	−0.979431	−	0.201780i
$257$	5.19094	+	5.19094i	0.323802	+	0.323802i	0.850224	−	0.526422i	$-0.176467\pi$
$257$	5.19094	+	5.19094i	0.323802	+	0.323802i	−0.526422	+	0.850224i	$0.676467\pi$
$258$		0			0
$259$	−4.33329	+	3.14832i	−0.269258	+	0.195627i
$260$	−6.47179	−	9.17734i	−0.401363	−	0.569154i
$261$		0			0
$262$	−0.0914195	−	0.0821850i	−0.00564792	−	0.00507740i
$263$	22.7729	+	3.60687i	1.40424	+	0.222409i	0.812142	−	0.583459i	$-0.198301\pi$
$263$	22.7729	+	3.60687i	1.40424	+	0.222409i	0.592094	+	0.805869i	$0.298301\pi$
$264$		0			0
$265$	11.0657	−	23.8407i	0.679763	−	1.46452i
$266$	0.613588	+	11.5351i	0.0376215	+	0.707264i
$267$		0			0
$268$	0.853702	−	2.23442i	0.0521481	−	0.136489i
$269$	3.53603	+	1.14893i	0.215596	+	0.0700513i	0.414823	−	0.909902i	$-0.363843\pi$
$269$	3.53603	+	1.14893i	0.215596	+	0.0700513i	−0.199228	+	0.979953i	$0.563843\pi$
$270$		0			0
$271$	27.3547	−	8.88808i	1.66168	−	0.539912i	0.680456	−	0.732789i	$-0.261782\pi$
$271$	27.3547	−	8.88808i	1.66168	−	0.539912i	0.981223	+	0.192877i	$0.0617817\pi$
$272$	6.91278	+	17.8412i	0.419149	+	1.08178i
$273$		0			0
$274$	−9.19578	−	5.96158i	−0.555538	−	0.360152i
$275$	−15.0420	+	24.2630i	−0.907067	+	1.46311i
$276$		0			0
$277$	3.29668	+	20.8144i	0.198078	+	1.25062i	0.863577	+	0.504217i	$0.168219\pi$
$277$	3.29668	+	20.8144i	0.198078	+	1.25062i	−0.665499	+	0.746399i	$0.731781\pi$
$278$	10.5733	+	18.2804i	0.634145	+	1.09639i
$279$		0			0
$280$	−3.87135	+	8.39223i	−0.231357	+	0.501532i
$281$	−5.22821	+	16.0908i	−0.311889	+	0.959895i	0.665127	+	0.746730i	$0.268377\pi$
$281$	−5.22821	+	16.0908i	−0.311889	+	0.959895i	−0.977016	+	0.213165i	$0.931623\pi$
$282$		0			0
$283$	−27.5538	+	14.0394i	−1.63791	+	0.834554i	−0.640103	+	0.768289i	$0.721108\pi$
$283$	−27.5538	+	14.0394i	−1.63791	+	0.834554i	−0.997802	+	0.0662657i	$0.978892\pi$
$284$	20.3634	+	11.7143i	1.20835	+	0.695118i
$285$		0			0
$286$	7.28084	+	18.9229i	0.430525	+	1.11894i
$287$	0.0512888	−	0.323825i	0.00302748	−	0.0191148i
$288$		0			0
$289$	3.45668	−	4.75771i	0.203334	−	0.279865i
$290$	1.06997	−	15.8841i	0.0628307	−	0.932744i
$291$		0			0
$292$	23.0564	+	18.6110i	1.34928	+	1.08913i
$293$	−5.18767	+	5.18767i	−0.303067	+	0.303067i	−0.842213	−	0.539146i	$-0.818747\pi$
$293$	−5.18767	+	5.18767i	−0.303067	+	0.303067i	0.539146	+	0.842213i	$0.318747\pi$
$294$		0			0
$295$	17.5871	+	22.4285i	1.02396	+	1.30584i
$296$	−1.64585	−	10.2358i	−0.0956629	−	0.594942i
$297$		0			0
$298$	3.52605	−	7.93635i	0.204258	−	0.459741i
$299$	−0.716822			−0.0414549
$300$		0			0
$301$	−1.46194			−0.0842646
$302$	13.0683	−	29.4138i	0.751995	−	1.69257i
$303$		0			0
$304$	−20.4537	−	9.02992i	−1.17310	−	0.517902i
$305$	13.5289	−	20.1343i	0.774665	−	1.15289i
$306$		0			0
$307$	16.7528	−	16.7528i	0.956134	−	0.956134i	−0.0429439	−	0.999077i	$-0.513674\pi$
$307$	16.7528	−	16.7528i	0.956134	−	0.956134i	0.999077	+	0.0429439i	$0.0136737\pi$
$308$	10.4809	−	12.9844i	0.597206	−	0.739854i
$309$		0			0
$310$	−6.95832	+	8.33575i	−0.395206	+	0.473439i
$311$	7.57416	−	10.4249i	0.429491	−	0.591144i	−0.538345	−	0.842724i	$-0.680950\pi$
$311$	7.57416	−	10.4249i	0.429491	−	0.591144i	0.967836	+	0.251581i	$0.0809504\pi$
$312$		0			0
$313$	0.639006	−	4.03453i	0.0361188	−	0.228045i	−0.963025	−	0.269411i	$-0.913171\pi$
$313$	0.639006	−	4.03453i	0.0361188	−	0.228045i	0.999144	+	0.0413661i	$0.0131710\pi$
$314$	−6.59677	−	17.1450i	−0.372277	−	0.967550i
$315$		0			0
$316$	1.82020	−	3.16411i	0.102394	−	0.177995i
$317$	22.1205	−	11.2710i	1.24241	−	0.633041i	0.295749	−	0.955266i	$-0.404431\pi$
$317$	22.1205	−	11.2710i	1.24241	−	0.633041i	0.946663	+	0.322225i	$0.104431\pi$
$318$		0			0
$319$	−8.88227	+	27.3368i	−0.497312	+	1.53057i
$320$	−11.1042	−	14.0248i	−0.620746	−	0.784012i
$321$		0			0
$322$	0.295373	+	0.510677i	0.0164605	+	0.0284589i
$323$	4.18261	+	26.4080i	0.232727	+	1.46938i
$324$		0			0
$325$	1.04996	−	12.5113i	0.0582415	−	0.694001i
$326$	−28.1506	−	18.2499i	−1.55912	−	1.01077i
$327$		0			0
$328$	0.514269	+	0.371796i	0.0283958	+	0.0205290i
$329$	−8.63603	+	2.80602i	−0.476120	+	0.154701i
$330$		0			0
$331$	23.2371	+	7.55019i	1.27723	+	0.414996i	0.867603	−	0.497258i	$-0.165660\pi$
$331$	23.2371	+	7.55019i	1.27723	+	0.414996i	0.409624	+	0.912254i	$0.365660\pi$
$332$	5.69450	+	2.17569i	0.312526	+	0.119406i
$333$		0			0
$334$	−0.761763	−	14.3207i	−0.0416818	−	0.783595i
$335$	2.33668	−	1.30066i	0.127667	−	0.0710626i
$336$		0			0
$337$	−20.2026	−	3.19977i	−1.10050	−	0.174303i	−0.420343	−	0.907365i	$-0.638090\pi$
$337$	−20.2026	−	3.19977i	−1.10050	−	0.174303i	−0.680161	+	0.733063i	$0.738090\pi$
$338$	7.04077	+	6.32957i	0.382968	+	0.344283i
$339$		0			0
$340$	−6.89702	+	20.2496i	−0.374043	+	1.09819i
$341$	15.8605	−	11.5233i	0.858894	−	0.624023i
$342$		0			0
$343$	12.2597	+	12.2597i	0.661961	+	0.661961i
$344$	1.27870	−	2.52424i	0.0689431	−	0.136098i
$345$		0			0
$346$	11.9408	+	3.18951i	0.641942	+	0.171469i
$347$	−11.0443	−	5.62737i	−0.592891	−	0.302093i	0.131681	−	0.991292i	$-0.457963\pi$
$347$	−11.0443	−	5.62737i	−0.592891	−	0.302093i	−0.724572	+	0.689199i	$0.757963\pi$
$348$		0			0
$349$			8.74739i			0.468237i	0.972208	+	0.234119i	$0.0752204\pi$
$349$			8.74739i			0.468237i	−0.972208	+	0.234119i	$0.924780\pi$
$350$	−9.34592	+	4.40737i	−0.499560	+	0.235584i
$351$		0			0
$352$	13.2521	+	29.4538i	0.706339	+	1.56989i
$353$	2.59436	+	1.32189i	0.138084	+	0.0703573i	0.521668	−	0.853149i	$-0.325310\pi$
$353$	2.59436	+	1.32189i	0.138084	+	0.0703573i	−0.383583	+	0.923506i	$0.625310\pi$
$354$		0			0
$355$	9.02696	+	24.6654i	0.479101	+	1.30910i
$356$	25.3242	−	2.70178i	1.34218	−	0.143194i
$357$		0			0
$358$	2.39754	−	22.9842i	0.126714	−	1.21475i
$359$	−7.90914	+	5.74633i	−0.417428	+	0.303279i	−0.776602	−	0.629991i	$-0.783058\pi$
$359$	−7.90914	+	5.74633i	−0.417428	+	0.303279i	0.359174	+	0.933271i	$0.383058\pi$
$360$		0			0
$361$	−9.90511	−	7.19648i	−0.521322	−	0.378762i
$362$	−17.4018	+	19.3571i	−0.914616	+	1.01738i
$363$		0			0
$364$	−1.51459	+	7.18085i	−0.0793859	+	0.376379i
$365$	6.37868	+	32.5081i	0.333875	+	1.70155i
$366$		0			0
$367$	−7.02642	−	13.7901i	−0.366776	−	0.719839i	0.631689	−	0.775222i	$-0.282362\pi$
$367$	−7.02642	−	13.7901i	−0.366776	−	0.719839i	−0.998465	+	0.0553831i	$0.982362\pi$
$368$	−1.14011	+	0.0633322i	−0.0594323	+	0.00330142i
$369$		0			0
$370$	5.94438	−	9.95059i	0.309034	−	0.517306i
$371$	−16.3361	+	5.30792i	−0.848128	+	0.275574i
$372$		0			0
$373$	−14.4174	+	2.28349i	−0.746503	+	0.118234i	−0.518086	−	0.855329i	$-0.673355\pi$
$373$	−14.4174	+	2.28349i	−0.746503	+	0.118234i	−0.228418	+	0.973563i	$0.573355\pi$
$374$	21.0103	−	32.4086i	1.08642	−	1.67581i
$375$		0			0
$376$	2.70865	−	17.3657i	0.139688	−	0.895565i
$377$	−1.97757	−	12.4859i	−0.101850	−	0.643057i
$378$		0			0
$379$	5.11250	+	15.7347i	0.262612	+	0.808235i	0.992234	+	0.124385i	$0.0396958\pi$
$379$	5.11250	+	15.7347i	0.262612	+	0.808235i	−0.729622	+	0.683850i	$0.760304\pi$
$380$	−11.0330	−	22.4308i	−0.565982	−	1.15068i
$381$		0			0
$382$	5.17359	+	24.2464i	0.264704	+	1.24056i
$383$	−33.2588	+	16.9462i	−1.69945	+	0.865911i	−0.713134	+	0.701028i	$0.752725\pi$
$383$	−33.2588	+	16.9462i	−1.69945	+	0.865911i	−0.986313	+	0.164883i	$0.947275\pi$
$384$		0			0
$385$	18.3071	−	3.59220i	0.933018	−	0.183075i
$386$	−29.9727	+	11.5324i	−1.52557	+	0.586983i
$387$		0			0
$388$	10.6204	−	2.86357i	0.539170	−	0.145376i
$389$	−15.3486	+	21.1256i	−0.778207	+	1.07111i	0.217270	+	0.976112i	$0.430285\pi$
$389$	−15.3486	+	21.1256i	−0.778207	+	1.07111i	−0.995477	+	0.0949990i	$0.969715\pi$
$390$		0			0
$391$	0.802621	+	1.10471i	0.0405903	+	0.0558677i
$392$	−13.0757	+	4.28253i	−0.660421	+	0.216300i
$393$		0			0
$394$	−15.1491	+	12.2871i	−0.763200	+	0.619018i
$395$	3.83256	−	1.40263i	0.192837	−	0.0705739i
$396$		0			0
$397$	−12.4142	+	24.3642i	−0.623050	+	1.22280i	0.336611	+	0.941644i	$0.390719\pi$
$397$	−12.4142	+	24.3642i	−0.623050	+	1.22280i	−0.959661	+	0.281160i	$0.909281\pi$
$398$	−28.7739	−	12.7840i	−1.44230	−	0.640802i
$399$		0			0
$400$	0.564587	−	19.9920i	0.0282293	−	0.999601i
$401$	17.4002			0.868927			0.434463	−	0.900690i	$-0.356938\pi$
$401$	17.4002			0.868927			0.434463	+	0.900690i	$0.356938\pi$
$402$		0			0
$403$	−3.91440	+	7.68243i	−0.194990	+	0.382689i
$404$	−8.60437	−	9.52607i	−0.428083	−	0.473940i
$405$		0			0
$406$	−8.08032	+	6.55379i	−0.401019	+	0.325259i
$407$	−14.7979	+	14.7979i	−0.733506	+	0.733506i
$408$		0			0
$409$	−0.523349	−	0.720329i	−0.0258780	−	0.0356180i	0.795882	−	0.605452i	$-0.207008\pi$
$409$	−0.523349	−	0.720329i	−0.0258780	−	0.0356180i	−0.821760	+	0.569834i	$0.807008\pi$
$410$	0.173399	+	0.687978i	0.00856359	+	0.0339768i
$411$		0			0
$412$	−2.43726	+	0.657156i	−0.120075	+	0.0323757i
$413$	2.91380	−	18.3970i	0.143379	−	0.905259i
$414$		0			0
$415$	3.31477	+	5.95512i	0.162716	+	0.292325i
$416$	−11.0740	−	8.89599i	−0.542948	−	0.436162i
$417$		0			0
$418$	9.41818	+	44.1391i	0.460658	+	2.15891i
$419$	−1.80356	+	5.55080i	−0.0881098	+	0.271174i	−0.985397	−	0.170273i	$-0.945535\pi$
$419$	−1.80356	+	5.55080i	−0.0881098	+	0.271174i	0.897287	+	0.441448i	$0.145535\pi$
$420$		0			0
$421$	1.31250	+	4.03945i	0.0639672	+	0.196871i	0.977932	−	0.208922i	$-0.0669955\pi$
$421$	1.31250	+	4.03945i	0.0639672	+	0.196871i	−0.913965	+	0.405793i	$0.866995\pi$
$422$	−3.65670	+	2.11502i	−0.178005	+	0.102957i
$423$		0			0
$424$	5.12374	−	32.8493i	0.248831	−	1.59530i
$425$	−20.4571	+	12.3907i	−0.992315	+	0.601036i
$426$		0			0
$427$	−15.6574	+	2.47990i	−0.757717	+	0.120011i
$428$	18.4740	+	0.939169i	0.892972	+	0.0453964i
$429$		0			0
$430$	2.90898	−	1.24356i	0.140283	−	0.0599699i
$431$	−2.24421	−	0.729187i	−0.108100	−	0.0351237i	0.254468	−	0.967081i	$-0.418100\pi$
$431$	−2.24421	−	0.729187i	−0.108100	−	0.0351237i	−0.362567	+	0.931958i	$0.618100\pi$
$432$		0			0
$433$	−0.790129	−	1.55072i	−0.0379712	−	0.0745226i	0.871241	−	0.490855i	$-0.163315\pi$
$433$	−0.790129	−	1.55072i	−0.0379712	−	0.0745226i	−0.909213	+	0.416332i	$0.863315\pi$
$434$	7.08607	−	0.376930i	0.340142	−	0.0180932i
$435$		0			0
$436$	−4.77299	+	22.6294i	−0.228585	+	1.08375i
$437$	−1.57599	−	0.249613i	−0.0753900	−	0.0119406i
$438$		0			0
$439$	1.04510	+	0.759313i	0.0498801	+	0.0362400i	0.612446	−	0.790512i	$-0.290186\pi$
$439$	1.04510	+	0.759313i	0.0498801	+	0.0362400i	−0.562566	+	0.826752i	$0.690186\pi$
$440$	−9.81017	+	34.7518i	−0.467681	+	1.65673i
$441$		0			0
$442$	−1.76235	+	16.8949i	−0.0838267	+	0.803610i
$443$	−25.3395	−	25.3395i	−1.20392	−	1.20392i	−0.972965	−	0.230952i	$-0.925816\pi$
$443$	−25.3395	−	25.3395i	−1.20392	−	1.20392i	−0.230952	−	0.972965i	$-0.574184\pi$
$444$		0			0
$445$	23.6341	+	15.8806i	1.12037	+	0.752814i
$446$	6.30284	−	23.5964i	0.298448	−	1.11732i
$447$		0			0
$448$	−1.77452	+	11.5550i	−0.0838383	+	0.545923i
$449$		−	41.8596i		−	1.97548i	−0.156115	−	0.987739i	$-0.549897\pi$
$449$		−	41.8596i		−	1.97548i	0.156115	−	0.987739i	$-0.450103\pi$
$450$		0			0
$451$		−	1.28099i		−	0.0603194i
$452$	−17.0845	+	11.1329i	−0.803587	+	0.523646i
$453$		0			0
$454$	−28.1657	−	7.52333i	−1.32188	−	0.353088i
$455$	−6.45673	+	5.06299i	−0.302696	+	0.237357i
$456$		0			0
$457$	−1.59546	−	1.59546i	−0.0746326	−	0.0746326i	0.668805	−	0.743438i	$-0.266806\pi$
$457$	−1.59546	−	1.59546i	−0.0746326	−	0.0746326i	−0.743438	+	0.668805i	$0.766806\pi$
$458$	18.6677	+	1.94728i	0.872286	+	0.0909904i
$459$		0			0
$460$	−1.02213	−	0.764899i	−0.0476572	−	0.0356636i
$461$	−8.02498	−	5.83049i	−0.373761	−	0.271553i	0.385008	−	0.922913i	$-0.374199\pi$
$461$	−8.02498	−	5.83049i	−0.373761	−	0.271553i	−0.758769	+	0.651360i	$0.774199\pi$
$462$		0			0
$463$	7.69820	+	1.21927i	0.357766	+	0.0566645i	0.332730	−	0.943022i	$-0.392030\pi$
$463$	7.69820	+	1.21927i	0.357766	+	0.0566645i	0.0250354	+	0.999687i	$0.492030\pi$
$464$	−4.24849	−	19.6842i	−0.197231	−	0.913815i
$465$		0			0
$466$	0.150432	+	2.82805i	0.00696865	+	0.131007i
$467$	−0.287105	−	0.563475i	−0.0132856	−	0.0260745i	0.884268	−	0.466979i	$-0.154658\pi$
$467$	−0.287105	−	0.563475i	−0.0132856	−	0.0260745i	−0.897554	+	0.440905i	$0.854658\pi$
$468$		0			0
$469$	−1.66215	−	0.540067i	−0.0767511	−	0.0249380i
$470$	14.7972	−	12.9295i	0.682543	−	0.596393i
$471$		0			0
$472$	29.2165	+	21.1223i	1.34480	+	0.972234i
$473$	−5.64161	+	0.893544i	−0.259402	+	0.0410852i
$474$		0			0
$475$	6.66514	−	27.1415i	0.305817	−	1.24534i
$476$	12.7625	−	5.70618i	0.584967	−	0.261542i
$477$		0			0
$478$	−8.60907	−	14.8844i	−0.393770	−	0.680797i
$479$	8.38706	+	25.8127i	0.383214	+	1.17941i	0.937767	+	0.347264i	$0.112889\pi$
$479$	8.38706	+	25.8127i	0.383214	+	1.17941i	−0.554553	+	0.832148i	$0.687111\pi$
$480$		0			0
$481$	2.84418	−	8.75348i	0.129683	−	0.399124i
$482$	20.5958	−	4.39464i	0.938114	−	0.200170i
$483$		0			0
$484$	21.5396	−	37.4430i	0.979073	−	1.70195i
$485$	11.1550	+	5.17763i	0.506522	+	0.235104i
$486$		0			0
$487$	−0.993204	+	6.27084i	−0.0450064	+	0.284159i	−0.999919	−	0.0127279i	$-0.995948\pi$
$487$	−0.993204	+	6.27084i	−0.0450064	+	0.284159i	0.954913	+	0.296887i	$0.0959485\pi$
$488$	9.41313	−	29.2039i	0.426112	−	1.32200i
$489$		0			0
$490$	−14.2777	−	5.72619i	−0.645000	−	0.258683i
$491$	15.5886	+	21.4558i	0.703502	+	0.968288i	0.999913	+	0.0132269i	$0.00421038\pi$
$491$	15.5886	+	21.4558i	0.703502	+	0.968288i	−0.296410	+	0.955061i	$0.595790\pi$
$492$		0			0
$493$	−17.0281	+	17.0281i	−0.766906	+	0.766906i
$494$	−12.5038	−	15.4162i	−0.562571	−	0.693607i
$495$		0			0
$496$	−5.54712	+	12.5648i	−0.249073	+	0.564176i
$497$	7.79268	−	15.2940i	0.349549	−	0.686029i
$498$		0			0
$499$	2.17786			0.0974943			0.0487471	−	0.998811i	$-0.484477\pi$
$499$	2.17786			0.0974943			0.0487471	+	0.998811i	$0.484477\pi$
$500$	14.8476	−	16.7197i	0.664003	−	0.747729i
$501$		0			0
$502$	−1.45299	+	3.27036i	−0.0648502	+	0.145963i
$503$	−2.44023	+	4.78922i	−0.108804	+	0.213541i	−0.938988	−	0.343949i	$-0.888235\pi$
$503$	−2.44023	+	4.78922i	−0.108804	+	0.213541i	0.830184	+	0.557490i	$0.188235\pi$
$504$		0			0
$505$	−0.526269	−	14.3422i	−0.0234187	−	0.638221i
$506$	1.45197	+	1.79017i	0.0645482	+	0.0795828i
$507$		0			0
$508$	−15.4205	−	12.4473i	−0.684174	−	0.552261i
$509$	5.20682	+	7.16658i	0.230788	+	0.317653i	0.908668	−	0.417520i	$-0.137101\pi$
$509$	5.20682	+	7.16658i	0.230788	+	0.317653i	−0.677879	+	0.735173i	$0.737101\pi$
$510$		0			0
$511$	12.7254	−	17.5150i	0.562937	−	0.774816i
$512$	−18.3992	−	13.1707i	−0.813139	−	0.582069i
$513$		0			0
$514$	3.72812	+	9.68940i	0.164440	+	0.427381i
$515$	−2.55994	−	1.18821i	−0.112804	−	0.0523586i
$516$		0			0
$517$	−31.6114	+	16.1068i	−1.39027	+	0.708377i
$518$	−7.40811	+	1.58071i	−0.325494	+	0.0694523i
$519$		0			0
$520$	−3.09449	−	15.5769i	−0.135702	−	0.683091i
$521$	5.57418	+	17.1556i	0.244209	+	0.751599i	0.995765	+	0.0919301i	$0.0293036\pi$
$521$	5.57418	+	17.1556i	0.244209	+	0.751599i	−0.751556	+	0.659669i	$0.770696\pi$
$522$		0			0
$523$	−5.95692	−	37.6105i	−0.260478	−	1.64459i	−0.677374	−	0.735639i	$-0.736882\pi$
$523$	−5.95692	−	37.6105i	−0.260478	−	1.64459i	0.416896	−	0.908954i	$-0.363118\pi$
$524$	−0.0709598	−	0.158709i	−0.00309989	−	0.00693323i
$525$		0			0
$526$	27.3606	+	17.7377i	1.19298	+	0.773402i
$527$	16.2225	−	2.56939i	0.706664	−	0.111925i
$528$		0			0
$529$	21.7968	−	7.08221i	0.947687	−	0.307922i
$530$	27.9907	−	24.4577i	1.21584	−	1.06238i
$531$		0			0
$532$	−5.83048	+	15.2603i	−0.252783	+	0.661618i
$533$	0.255771	+	0.501978i	0.0110787	+	0.0217431i
$534$		0			0
$535$	15.1502	+	14.0777i	0.655001	+	0.608633i
$536$	2.38633	−	2.39757i	0.103074	−	0.103559i
$537$		0			0
$538$	3.91025	+	3.51526i	0.168583	+	0.151554i
$539$	22.4698	+	16.3253i	0.967844	+	0.703180i
$540$		0			0
$541$	−7.71293	+	5.60377i	−0.331605	+	0.240925i	−0.741111	−	0.671382i	$-0.765701\pi$
$541$	−7.71293	+	5.60377i	−0.331605	+	0.240925i	0.409506	+	0.912307i	$0.365701\pi$
$542$	40.4567	+	4.22014i	1.73776	+	0.181271i
$543$		0			0
$544$	−1.31035	+	27.0272i	−0.0561806	+	1.15878i
$545$	−20.3474	+	15.9552i	−0.871587	+	0.683447i
$546$		0			0
$547$	9.36904	+	4.77376i	0.400591	+	0.204111i	0.642666	−	0.766146i	$-0.277828\pi$
$547$	9.36904	+	4.77376i	0.400591	+	0.204111i	−0.242075	+	0.970257i	$0.577828\pi$
$548$	−8.46147	−	12.9850i	−0.361456	−	0.554690i
$549$		0			0
$550$	−33.3721	+	22.7203i	−1.42299	+	0.968799i
$551$		−	28.1400i		−	1.19880i
$552$		0			0
$553$	−2.37641	−	1.21084i	−0.101055	−	0.0514903i
$554$	−7.69102	+	28.7934i	−0.326760	+	1.22332i
$555$		0			0
$556$	3.16829	+	29.6968i	0.134365	+	1.25943i
$557$	17.1166	+	17.1166i	0.725256	+	0.725256i	0.969671	−	0.244415i	$-0.0785960\pi$
$557$	17.1166	+	17.1166i	0.725256	+	0.725256i	−0.244415	+	0.969671i	$0.578596\pi$
$558$		0			0
$559$	2.03236	−	1.47659i	0.0859595	−	0.0624532i
$560$	−9.82215	+	8.62317i	−0.415062	+	0.364396i
$561$		0			0
$562$	−15.9963	+	17.7937i	−0.674762	+	0.750580i
$563$	7.44499	+	1.17917i	0.313769	+	0.0496961i	0.311333	−	0.950301i	$-0.399225\pi$
$563$	7.44499	+	1.17917i	0.313769	+	0.0496961i	0.00243601	+	0.999997i	$0.499225\pi$
$564$		0			0
$565$	−22.6335	−	2.73838i	−0.952200	−	0.115204i
$566$	−43.6720	+	2.32304i	−1.83567	+	0.0976448i
$567$		0			0
$568$	19.5913	+	26.8323i	0.822031	+	1.12586i
$569$	14.1155	+	4.58639i	0.591751	+	0.192271i	0.589558	−	0.807726i	$-0.299302\pi$
$569$	14.1155	+	4.58639i	0.591751	+	0.192271i	0.00219278	+	0.999998i	$0.499302\pi$
$570$		0			0
$571$	8.54065	−	2.77502i	0.357415	−	0.116131i	−0.124805	−	0.992181i	$-0.539831\pi$
$571$	8.54065	−	2.77502i	0.357415	−	0.116131i	0.482220	+	0.876050i	$0.339831\pi$
$572$	−1.45581	+	28.6366i	−0.0608707	+	1.19736i
$573$		0			0
$574$	0.252226	−	0.389061i	0.0105277	−	0.0162391i
$575$	−0.326003	−	1.38961i	−0.0135953	−	0.0579506i
$576$		0			0
$577$	−0.765580	−	4.83368i	−0.0318715	−	0.201229i	0.966615	−	0.256235i	$-0.0824821\pi$
$577$	−0.765580	−	4.83368i	−0.0318715	−	0.201229i	−0.998486	+	0.0550063i	$0.982482\pi$
$578$	7.19928	−	4.16403i	0.299451	−	0.173201i
$579$		0			0
$580$	10.5035	−	19.9142i	0.436132	−	0.826890i
$581$	1.37638	−	4.23605i	0.0571017	−	0.175741i
$582$		0			0
$583$	−59.7968	+	30.4680i	−2.47653	+	1.26186i
$584$	19.1116	+	37.2919i	0.790845	+	1.54315i
$585$		0			0
$586$	−9.68331	+	3.72578i	−0.400014	+	0.153910i
$587$	−0.200727	+	1.26734i	−0.00828489	+	0.0523087i	−0.991484	−	0.130225i	$-0.958430\pi$
$587$	−0.200727	+	1.26734i	−0.00828489	+	0.0523087i	0.983200	+	0.182534i	$0.0584300\pi$
$588$		0			0
$589$	−11.2813	+	15.5274i	−0.464839	+	0.639796i
$590$	9.85111	+	39.0852i	0.405564	+	1.60911i
$591$		0			0
$592$	3.75030	−	14.1737i	0.154136	−	0.582537i
$593$	−20.9667	+	20.9667i	−0.860997	+	0.860997i	−0.991454	−	0.130457i	$-0.958356\pi$
$593$	−20.9667	+	20.9667i	−0.860997	+	0.860997i	0.130457	+	0.991454i	$0.458356\pi$
$594$		0			0
$595$	15.0323	+	4.28164i	0.616263	+	0.175530i
$596$	9.11412	−	8.23227i	0.373329	−	0.337207i
$597$		0			0
$598$	−0.926419	−	0.411600i	−0.0378841	−	0.0168316i
$599$	−13.6348			−0.557103			−0.278552	−	0.960421i	$-0.589854\pi$
$599$	−13.6348			−0.557103			−0.278552	+	0.960421i	$0.589854\pi$
$600$		0			0
$601$	−0.304225			−0.0124096			−0.00620481	−	0.999981i	$-0.501975\pi$
$601$	−0.304225			−0.0124096			−0.00620481	+	0.999981i	$0.501975\pi$
$602$	−1.88940	−	0.839444i	−0.0770063	−	0.0342132i
$603$		0			0
$604$	33.7788	−	30.5105i	1.37444	−	1.24146i
$605$	45.3532	−	16.5982i	1.84387	−	0.674814i
$606$		0			0
$607$	0.683237	−	0.683237i	0.0277317	−	0.0277317i	−0.693105	−	0.720837i	$-0.743758\pi$
$607$	0.683237	−	0.683237i	0.0277317	−	0.0277317i	0.720837	+	0.693105i	$0.243758\pi$
$608$	−21.2494	−	23.4148i	−0.861776	−	0.949595i
$609$		0			0
$610$	29.0459	−	18.2532i	1.17603	−	0.739050i
$611$	9.17149	−	12.6235i	0.371039	−	0.510691i
$612$		0			0
$613$	−7.43217	+	46.9249i	−0.300183	+	1.89528i	0.128311	+	0.991734i	$0.459044\pi$
$613$	−7.43217	+	46.9249i	−0.300183	+	1.89528i	−0.428494	+	0.903545i	$0.640956\pi$
$614$	31.2708	−	12.0318i	1.26199	−	0.485565i
$615$		0			0
$616$	21.0012	−	10.7628i	0.846161	−	0.433648i
$617$	−19.5932	+	9.98325i	−0.788794	+	0.401910i	−0.801489	−	0.598009i	$-0.795959\pi$
$617$	−19.5932	+	9.98325i	−0.788794	+	0.401910i	0.0126958	+	0.999919i	$0.495959\pi$
$618$		0			0
$619$	−11.5853	+	35.6558i	−0.465651	+	1.43313i	0.392511	+	0.919747i	$0.371606\pi$
$619$	−11.5853	+	35.6558i	−0.465651	+	1.43313i	−0.858162	+	0.513379i	$0.828394\pi$
$620$	−13.7793	+	6.77763i	−0.553391	+	0.272196i
$621$		0			0
$622$	15.7748	−	9.12408i	0.632513	−	0.365842i
$623$	−2.91097	−	18.3791i	−0.116625	−	0.736344i
$624$		0			0
$625$	24.7314	−	3.65458i	0.989258	−	0.146183i
$626$	3.14248	−	4.84730i	0.125599	−	0.193737i
$627$		0			0
$628$	1.31903	−	25.9461i	0.0526352	−	1.03536i
$629$	−16.6748	+	5.41798i	−0.664869	+	0.216029i
$630$		0			0
$631$	−16.9430	−	5.50512i	−0.674491	−	0.219155i	−0.0483091	−	0.998832i	$-0.515383\pi$
$631$	−16.9430	−	5.50512i	−0.674491	−	0.219155i	−0.626182	+	0.779677i	$0.715383\pi$
$632$	4.16926	−	3.04413i	0.165844	−	0.121089i
$633$		0			0
$634$	35.0603	−	1.86496i	1.39242	−	0.0740672i
$635$	−4.26616	−	21.7419i	−0.169297	−	0.862801i
$636$		0			0
$637$	−12.0648	−	1.91088i	−0.478025	−	0.0757118i
$638$	−27.1762	+	30.2298i	−1.07592	+	1.19681i
$639$		0			0
$640$	−6.29805	−	24.5017i	−0.248952	−	0.968516i
$641$	−0.146686	+	0.106574i	−0.00579376	+	0.00420941i	−0.590678	−	0.806907i	$-0.701140\pi$
$641$	−0.146686	+	0.106574i	−0.00579376	+	0.00420941i	0.584885	+	0.811117i	$0.301140\pi$
$642$		0			0
$643$	10.2095	+	10.2095i	0.402622	+	0.402622i	0.879156	−	0.476534i	$-0.158107\pi$
$643$	10.2095	+	10.2095i	0.402622	+	0.402622i	−0.476534	+	0.879156i	$0.658107\pi$
$644$	0.0885085	+	0.829602i	0.00348773	+	0.0326909i
$645$		0			0
$646$	−9.75787	+	36.5313i	−0.383918	+	1.43730i
$647$	28.0796	+	14.3073i	1.10392	+	0.562477i	0.908350	−	0.418211i	$-0.137343\pi$
$647$	28.0796	+	14.3073i	1.10392	+	0.562477i	0.195574	+	0.980689i	$0.437343\pi$
$648$		0			0
$649$		−	72.7751i		−	2.85667i
$650$	8.54095	−	15.5667i	0.335004	−	0.610575i
$651$		0			0
$652$	−25.9027	−	39.7502i	−1.01443	−	1.55674i
$653$	8.96664	+	4.56873i	0.350892	+	0.178788i	0.620548	−	0.784168i	$-0.286910\pi$
$653$	8.96664	+	4.56873i	0.350892	+	0.178788i	−0.269657	+	0.962957i	$0.586910\pi$
$654$		0			0
$655$	0.0532448	−	0.186935i	0.00208045	−	0.00730416i
$656$	0.451155	+	0.775802i	0.0176147	+	0.0302900i
$657$		0			0
$658$	−12.7724	−	1.33232i	−0.497920	−	0.0519393i
$659$	4.60974	−	3.34918i	0.179570	−	0.130465i	−0.494369	−	0.869252i	$-0.664601\pi$
$659$	4.60974	−	3.34918i	0.179570	−	0.130465i	0.673939	+	0.738787i	$0.264601\pi$
$660$		0			0
$661$	29.9339	+	21.7482i	1.16429	+	0.845909i	0.990315	−	0.138841i	$-0.0443375\pi$
$661$	29.9339	+	21.7482i	1.16429	+	0.845909i	0.173979	+	0.984749i	$0.444338\pi$
$662$	25.6963	+	23.1006i	0.998714	+	0.897831i
$663$		0			0
$664$	6.11028	+	6.08164i	0.237125	+	0.236013i
$665$	−15.9587	+	8.88304i	−0.618853	+	0.344469i
$666$		0			0
$667$	−0.652450	−	1.28050i	−0.0252629	−	0.0495813i
$668$	7.23847	−	18.9455i	0.280065	−	0.733023i
$669$		0			0
$670$	3.76677	−	0.339244i	0.145523	−	0.0131062i
$671$	−58.9064	+	19.1398i	−2.27406	+	0.738886i
$672$		0			0
$673$	−4.01796	+	0.636382i	−0.154881	+	0.0245307i	−0.233393	−	0.972382i	$-0.574983\pi$
$673$	−4.01796	+	0.636382i	−0.154881	+	0.0245307i	0.0785125	+	0.996913i	$0.474983\pi$
$674$	−24.2725	−	15.7357i	−0.934940	−	0.606117i
$675$		0			0
$676$	5.46505	+	12.2231i	0.210194	+	0.470121i
$677$	2.28166	+	14.4058i	0.0876914	+	0.553662i	0.991945	+	0.126667i	$0.0404278\pi$
$677$	2.28166	+	14.4058i	0.0876914	+	0.553662i	−0.904254	+	0.426995i	$0.859572\pi$
$678$		0			0
$679$	−2.48356	−	7.64361i	−0.0953103	−	0.293335i
$680$	−20.5411	+	22.2103i	−0.787714	+	0.851728i
$681$		0			0
$682$	27.1148	−	5.78562i	1.03828	−	0.221543i
$683$	15.7458	−	8.02287i	0.602495	−	0.306986i	−0.126008	−	0.992029i	$-0.540217\pi$
$683$	15.7458	−	8.02287i	0.602495	−	0.306986i	0.728503	+	0.685043i	$0.240217\pi$
$684$		0			0
$685$	2.08129	−	17.2025i	0.0795219	−	0.657273i
$686$	8.80488	+	22.8839i	0.336172	+	0.873712i
$687$		0			0
$688$	3.10201	−	2.52809i	0.118263	−	0.0963826i
$689$	17.3490	−	23.8789i	0.660945	−	0.909712i
$690$		0			0
$691$	−2.97580	−	4.09584i	−0.113205	−	0.155813i	0.748655	−	0.662960i	$-0.230700\pi$
$691$	−2.97580	−	4.09584i	−0.113205	−	0.155813i	−0.861860	+	0.507147i	$0.830700\pi$
$692$	13.6009	+	10.9785i	0.517028	+	0.417342i
$693$		0			0
$694$	−11.0424	−	13.6145i	−0.419165	−	0.516798i
$695$	−18.6227	+	27.7150i	−0.706398	+	1.05129i
$696$		0			0
$697$	0.487227	−	0.956237i	0.0184550	−	0.0362201i
$698$	−5.02276	+	11.3051i	−0.190114	+	0.427905i
$699$		0			0
$700$	−14.6094	+	0.329653i	−0.552182	+	0.0124597i
$701$	−33.5634			−1.26767			−0.633836	−	0.773467i	$-0.718521\pi$
$701$	−33.5634			−1.26767			−0.633836	+	0.773467i	$0.718521\pi$
$702$		0			0
$703$	9.30132	−	18.2549i	0.350806	−	0.688495i
$704$	0.214604	+	45.6754i	0.00808820	+	1.72146i
$705$		0			0
$706$	2.59392	+	3.19810i	0.0976234	+	0.120362i
$707$	−6.63210	+	6.63210i	−0.249426	+	0.249426i
$708$		0			0
$709$	11.9891	+	16.5016i	0.450260	+	0.619730i	0.972453	−	0.233097i	$-0.0748861\pi$
$709$	11.9891	+	16.5016i	0.450260	+	0.619730i	−0.522193	+	0.852827i	$0.674886\pi$
$710$	−2.49646	+	37.0608i	−0.0936904	+	1.39087i
$711$		0			0
$712$	34.2803	+	11.0494i	1.28471	+	0.414093i
$713$	−0.153338	+	0.968139i	−0.00574256	+	0.0362571i
$714$		0			0
$715$	−21.8220	+	23.4845i	−0.816097	+	0.878270i
$716$	16.2961	−	28.3281i	0.609015	−	1.05867i
$717$		0			0
$718$	−13.5213	+	2.88511i	−0.504610	+	0.107671i
$719$	7.42311	−	22.8460i	0.276835	−	0.852012i	−0.711893	−	0.702288i	$-0.752162\pi$
$719$	7.42311	−	22.8460i	0.276835	−	0.852012i	0.988728	−	0.149723i	$-0.0478383\pi$
$720$		0			0
$721$	0.569949	+	1.75412i	0.0212260	+	0.0653269i
$722$	−8.66912	−	14.9882i	−0.322631	−	0.557805i
$723$		0			0
$724$	−33.6048	+	15.0249i	−1.24891	+	0.558398i
$725$	23.3054	−	9.51212i	0.865539	−	0.353271i
$726$		0			0
$727$	33.0708	−	5.23791i	1.22653	−	0.194263i	0.490639	−	0.871363i	$-0.336763\pi$
$727$	33.0708	−	5.23791i	1.22653	−	0.194263i	0.735891	+	0.677100i	$0.236763\pi$
$728$	−6.08070	+	8.41084i	−0.225366	+	0.311727i
$729$		0			0
$730$	−10.4224	+	45.6760i	−0.385749	+	1.69054i
$731$	−4.55123	−	1.47878i	−0.168333	−	0.0546948i
$732$		0			0
$733$	−8.97039	−	17.6054i	−0.331329	−	0.650270i	0.663902	−	0.747820i	$-0.268899\pi$
$733$	−8.97039	−	17.6054i	−0.331329	−	0.650270i	−0.995231	+	0.0975501i	$0.968899\pi$
$734$	−1.16264	−	21.8569i	−0.0429137	−	0.806753i
$735$		0			0
$736$	−1.50984	−	0.572801i	−0.0556535	−	0.0211137i
$737$	−6.74435	−	1.06820i	−0.248431	−	0.0393476i
$738$		0			0
$739$	8.71975	+	6.33527i	0.320761	+	0.233047i	0.736500	−	0.676437i	$-0.236477\pi$
$739$	8.71975	+	6.33527i	0.320761	+	0.233047i	−0.415739	+	0.909484i	$0.636477\pi$
$740$	13.3961	−	9.44686i	0.492452	−	0.347273i
$741$		0			0
$742$	−24.1606	−	2.52025i	−0.886962	−	0.0925213i
$743$	−24.2468	−	24.2468i	−0.889529	−	0.889529i	0.104949	−	0.994478i	$-0.466532\pi$
$743$	−24.2468	−	24.2468i	−0.889529	−	0.889529i	−0.994478	+	0.104949i	$0.966532\pi$
$744$		0			0
$745$	13.7220	−	0.503510i	0.502735	−	0.0184472i
$746$	−19.9442	−	5.32729i	−0.730208	−	0.195046i
$747$		0			0
$748$	45.7627	−	29.8207i	1.67325	−	1.09035i
$749$		−	13.5155i		−	0.493846i
$750$		0			0
$751$			5.70499i			0.208178i	0.994568	+	0.104089i	$0.0331927\pi$
$751$			5.70499i			0.208178i	−0.994568	+	0.104089i	$0.966807\pi$
$752$	13.4720	−	20.8880i	0.491274	−	0.761708i
$753$		0			0
$754$	4.61360	−	17.2723i	0.168017	−	0.629020i
$755$	50.8566	−	1.86611i	1.85086	−	0.0679149i
$756$		0			0
$757$	21.6259	+	21.6259i	0.786008	+	0.786008i	0.980837	−	0.194830i	$-0.0624154\pi$
$757$	21.6259	+	21.6259i	0.786008	+	0.786008i	−0.194830	+	0.980837i	$0.562415\pi$
$758$	−2.42746	+	23.2711i	−0.0881694	+	0.845243i
$759$		0			0
$760$	−1.37930	−	35.3247i	−0.0500323	−	1.28136i
$761$	−31.8588	−	23.1468i	−1.15488	−	0.839070i	−0.165758	−	0.986166i	$-0.553007\pi$
$761$	−31.8588	−	23.1468i	−1.15488	−	0.839070i	−0.989122	+	0.147097i	$0.953007\pi$
$762$		0			0
$763$	16.6900	+	2.64343i	0.604218	+	0.0956987i
$764$	−7.23598	+	34.3067i	−0.261789	+	1.24117i
$765$		0			0
$766$	−52.7142	+	2.80403i	−1.90464	+	0.101314i
$767$	14.5308	+	28.5182i	0.524675	+	1.02973i
$768$		0			0
$769$	−3.21091	−	1.04329i	−0.115788	−	0.0376220i	0.250550	−	0.968104i	$-0.419389\pi$
$769$	−3.21091	−	1.04329i	−0.115788	−	0.0376220i	−0.366338	+	0.930482i	$0.619389\pi$
$770$	25.7227	+	5.86942i	0.926984	+	0.211519i
$771$		0			0
$772$	−45.3586	−	2.30592i	−1.63249	−	0.0829917i
$773$	33.4809	−	5.30286i	1.20422	−	0.190730i	0.478107	−	0.878301i	$-0.341323\pi$
$773$	33.4809	−	5.30286i	1.20422	−	0.190730i	0.726117	+	0.687571i	$0.241323\pi$
$774$		0			0
$775$	−16.6731	−	4.09442i	−0.598916	−	0.147076i
$776$	15.3701	+	2.39738i	0.551753	+	0.0860609i
$777$		0			0
$778$	−31.9669	+	18.4895i	−1.14607	+	0.662880i
$779$	0.387534	+	1.19271i	0.0138849	+	0.0427332i
$780$		0			0
$781$	20.7242	−	63.7825i	0.741570	−	2.28232i
$782$	0.402979	+	1.88859i	0.0144105	+	0.0675360i
$783$		0			0
$784$	−19.3580	−	1.97332i	−0.691357	−	0.0704758i
$785$	19.7717	−	21.2780i	0.705683	−	0.759444i
$786$		0			0
$787$	7.15446	−	45.1715i	0.255029	−	1.61019i	−0.444631	−	0.895714i	$-0.646665\pi$
$787$	7.15446	−	45.1715i	0.255029	−	1.61019i	0.699660	−	0.714476i	$-0.253335\pi$
$788$	−26.6340	+	7.18127i	−0.948795	+	0.255822i
$789$		0			0
$790$	5.75859	+	0.387905i	0.204881	+	0.0138010i
$791$	8.75757	+	12.0538i	0.311383	+	0.428582i
$792$		0			0
$793$	19.2619	−	19.2619i	0.684011	−	0.684011i
$794$	−30.0340	+	24.3600i	−1.06587	+	0.864505i
$795$		0			0
$796$	−29.8468	−	33.0440i	−1.05789	−	1.17121i
$797$	−22.9762	+	45.0933i	−0.813857	+	1.59729i	−0.0118812	+	0.999929i	$0.503782\pi$
$797$	−22.9762	+	45.0933i	−0.813857	+	1.59729i	−0.801976	+	0.597356i	$0.796218\pi$
$798$		0			0
$799$	−29.7236			−1.05155
$800$	12.2091	−	25.5135i	0.431657	−	0.902038i
$801$		0			0
$802$	22.4880	+	9.99123i	0.794080	+	0.352803i
$803$	38.4020	−	75.3681i	1.35518	−	2.65968i
$804$		0			0
$805$	−0.520238	+	0.774238i	−0.0183360	+	0.0272883i
$806$	−9.47022	+	7.68112i	−0.333574	+	0.270556i
$807$		0			0
$808$	−5.65039	−	17.2521i	−0.198780	−	0.606927i
$809$	6.34057	+	8.72704i	0.222923	+	0.306827i	0.905799	−	0.423707i	$-0.139271\pi$
$809$	6.34057	+	8.72704i	0.222923	+	0.306827i	−0.682877	+	0.730534i	$0.739271\pi$
$810$		0			0
$811$	28.8834	−	39.7547i	1.01424	−	1.39597i	0.0980672	−	0.995180i	$-0.468734\pi$
$811$	28.8834	−	39.7547i	1.01424	−	1.39597i	0.916168	−	0.400795i	$-0.131266\pi$
$812$	−14.2062	+	3.83039i	−0.498539	+	0.134420i
$813$		0			0
$814$	−27.6218	+	10.6278i	−0.968143	+	0.372505i
$815$	6.37135	−	52.6611i	0.223179	−	1.84464i
$816$		0			0
$817$	4.98249	−	2.53870i	0.174315	−	0.0888180i
$818$	−0.262763	−	1.23146i	−0.00918729	−	0.0430570i
$819$		0			0
$820$	−0.170936	+	0.988708i	−0.00596935	+	0.0345272i
$821$	−9.02878	−	27.7877i	−0.315107	−	0.969798i	−0.975711	−	0.219064i	$-0.929700\pi$
$821$	−9.02878	−	27.7877i	−0.315107	−	0.969798i	0.660604	−	0.750734i	$-0.270300\pi$
$822$		0			0
$823$	−4.87618	−	30.7870i	−0.169973	−	1.07317i	−0.914207	−	0.405248i	$-0.867185\pi$
$823$	−4.87618	−	30.7870i	−0.169973	−	1.07317i	0.744234	−	0.667919i	$-0.232815\pi$
$824$	−3.52725	−	0.550171i	−0.122878	−	0.0191661i
$825$		0			0
$826$	14.3294	−	22.1032i	0.498583	−	0.769068i
$827$	28.8702	−	4.57260i	1.00392	−	0.159005i	0.367232	−	0.930129i	$-0.380305\pi$
$827$	28.8702	−	4.57260i	1.00392	−	0.159005i	0.636684	+	0.771125i	$0.280305\pi$
$828$		0			0
$829$	−16.3848	+	5.32375i	−0.569069	+	0.184902i	−0.579398	−	0.815045i	$-0.696712\pi$
$829$	−16.3848	+	5.32375i	−0.569069	+	0.184902i	0.0103290	+	0.999947i	$0.496712\pi$
$830$	0.864575	+	9.59973i	0.0300098	+	0.333211i
$831$		0			0
$832$	−9.20394	−	17.8559i	−0.319089	−	0.619040i
$833$	10.5640	+	20.7330i	0.366021	+	0.718356i
$834$		0			0
$835$	19.8126	−	11.0282i	0.685642	−	0.381646i
$836$	−13.1726	+	62.4532i	−0.455585	+	2.15999i
$837$		0			0
$838$	−5.51819	+	6.13823i	−0.190623	+	0.212042i
$839$	−7.13248	−	5.18205i	−0.246241	−	0.178904i	0.457818	−	0.889046i	$-0.348631\pi$
$839$	−7.13248	−	5.18205i	−0.246241	−	0.178904i	−0.704059	+	0.710141i	$0.748631\pi$
$840$		0			0
$841$	−2.95711	+	2.14847i	−0.101969	+	0.0740851i
$842$	−0.623186	+	5.97421i	−0.0214764	+	0.205885i
$843$		0			0
$844$	−5.94035	+	0.633764i	−0.204475	+	0.0218151i
$845$	−4.10070	+	14.3970i	−0.141068	+	0.495272i
$846$		0			0
$847$	−28.1217	−	14.3287i	−0.966272	−	0.492340i
$848$	25.4840	−	39.5123i	0.875123	−	1.35686i
$849$		0			0
$850$	−33.5534	+	4.26721i	−1.15087	+	0.146364i
$851$		−	1.04634i		−	0.0358682i
$852$		0			0
$853$	40.4602	+	20.6155i	1.38533	+	0.705861i	0.978230	−	0.207523i	$-0.0665401\pi$
$853$	40.4602	+	20.6155i	1.38533	+	0.705861i	0.407100	+	0.913384i	$0.366540\pi$
$854$	−21.6596	−	5.78550i	−0.741177	−	0.197976i
$855$		0			0
$856$	23.3364	+	11.8215i	0.797623	+	0.404052i
$857$	−10.3992	−	10.3992i	−0.355231	−	0.355231i	0.506821	−	0.862052i	$-0.330821\pi$
$857$	−10.3992	−	10.3992i	−0.355231	−	0.355231i	−0.862052	+	0.506821i	$0.830821\pi$
$858$		0			0
$859$	−7.29899	+	5.30303i	−0.249038	+	0.180937i	−0.705301	−	0.708908i	$-0.749188\pi$
$859$	−7.29899	+	5.30303i	−0.249038	+	0.180937i	0.456262	+	0.889845i	$0.349188\pi$
$860$	4.47361	+	0.0631561i	0.152549	+	0.00215360i
$861$		0			0
$862$	−2.48171	−	2.23103i	−0.0845274	−	0.0759891i
$863$	29.5714	+	4.68365i	1.00662	+	0.159433i	0.637910	−	0.770111i	$-0.279799\pi$
$863$	29.5714	+	4.68365i	1.00662	+	0.159433i	0.368711	+	0.929544i	$0.379799\pi$
$864$		0			0
$865$	3.76275	+	19.1763i	0.127937	+	0.652015i
$866$	−0.130740	−	2.45783i	−0.00444272	−	0.0835206i
$867$		0			0
$868$	9.37446	+	3.58168i	0.318190	+	0.121570i
$869$	−9.91065	−	3.22017i	−0.336196	−	0.109237i
$870$		0			0
$871$	2.85618	−	0.928028i	0.0967778	−	0.0314450i
$872$	−19.1624	+	26.5055i	−0.648920	+	0.897589i
$873$		0			0
$874$	−1.89348	−	1.22754i	−0.0640481	−	0.0415220i
$875$	−12.7514	−	10.2142i	−0.431076	−	0.345303i
$876$		0			0
$877$	−2.73496	−	17.2678i	−0.0923529	−	0.583093i	−0.989855	−	0.142083i	$-0.954620\pi$
$877$	−2.73496	−	17.2678i	−0.0923529	−	0.583093i	0.897502	−	0.441011i	$-0.145380\pi$
$878$	0.914693	+	1.58143i	0.0308694	+	0.0533708i
$879$		0			0
$880$	−32.6332	+	39.2802i	−1.10006	+	1.32414i
$881$	4.92739	−	15.1650i	0.166008	−	0.510921i	−0.833101	−	0.553121i	$-0.813437\pi$
$881$	4.92739	−	15.1650i	0.166008	−	0.510921i	0.999109	+	0.0422003i	$0.0134368\pi$
$882$		0			0
$883$	−45.5469	+	23.2073i	−1.53278	+	0.780989i	−0.997952	−	0.0639745i	$-0.979622\pi$
$883$	−45.5469	+	23.2073i	−1.53278	+	0.780989i	−0.534825	+	0.844963i	$0.679622\pi$
$884$	−11.9787	+	20.8230i	−0.402889	+	0.700355i
$885$		0			0
$886$	−18.1988	−	47.2987i	−0.611400	−	1.58903i
$887$	0.180536	−	1.13986i	0.00606180	−	0.0382727i	−0.984472	−	0.175541i	$-0.943832\pi$
$887$	0.180536	−	1.13986i	0.00606180	−	0.0382727i	0.990534	+	0.137269i	$0.0438324\pi$
$888$		0			0
$889$	−8.51092	+	11.7143i	−0.285447	+	0.392884i
$890$	21.4261	+	34.0948i	0.718203	+	1.14286i
$891$		0			0
$892$	21.6949	−	26.8769i	0.726397	−	0.899904i
$893$	24.5601	−	24.5601i	0.821872	−	0.821872i
$894$		0			0
$895$	34.3127	−	12.5576i	1.14695	−	0.419756i
$896$	−8.92828	+	13.9147i	−0.298273	+	0.464859i
$897$		0			0
$898$	24.0358	−	54.0993i	0.802086	−	1.80532i
$899$	−17.2865			−0.576537
$900$		0			0
$901$	−56.2259			−1.87316
$902$	0.735545	−	1.65555i	0.0244910	−	0.0551237i
$903$		0			0
$904$	−28.4725	+	4.57819i	−0.946980	+	0.152268i
$905$	−39.5814	−	11.2740i	−1.31573	−	0.374760i
$906$		0			0
$907$	−36.0287	+	36.0287i	−1.19631	+	1.19631i	−0.221052	+	0.975262i	$0.570949\pi$
$907$	−36.0287	+	36.0287i	−1.19631	+	1.19631i	−0.975262	+	0.221052i	$0.929051\pi$
$908$	−32.0814	−	25.8959i	−1.06466	−	0.859385i
$909$		0			0
$910$	−11.2518	+	2.83594i	−0.372995	+	0.0940104i
$911$	31.1031	−	42.8098i	1.03049	−	1.41835i	0.125915	−	0.992041i	$-0.459813\pi$
$911$	31.1031	−	42.8098i	1.03049	−	1.41835i	0.904577	−	0.426310i	$-0.140187\pi$
$912$		0			0
$913$	2.72234	−	17.1882i	0.0900963	−	0.568846i
$914$	−1.14586	−	2.97809i	−0.0379016	−	0.0985065i
$915$		0			0
$916$	23.0080	+	13.2357i	0.760207	+	0.437319i
$917$	−0.113179	+	0.0576678i	−0.00373751	+	0.00190436i
$918$		0			0
$919$	0.519184	−	1.59788i	0.0171263	−	0.0527093i	−0.942128	−	0.335253i	$-0.891178\pi$
$919$	0.519184	−	1.59788i	0.0171263	−	0.0527093i	0.959254	+	0.282544i	$0.0911782\pi$
$920$	−0.881798	−	1.57546i	−0.0290720	−	0.0519415i
$921$		0			0
$922$	−7.02360	−	12.1433i	−0.231310	−	0.399917i
$923$	4.61409	+	29.1322i	0.151875	+	0.958899i
$924$		0			0
$925$	18.2627	+	1.53263i	0.600474	+	0.0503926i
$926$	9.24903	+	5.99610i	0.303942	+	0.197044i
$927$		0			0
$928$	5.81193	−	27.8793i	0.190786	−	0.915183i
$929$	−47.0109	+	15.2748i	−1.54238	+	0.501149i	−0.952031	−	0.306001i	$-0.901009\pi$
$929$	−47.0109	+	15.2748i	−1.54238	+	0.501149i	−0.590347	+	0.807150i	$0.701009\pi$
$930$		0			0
$931$	−25.8601	−	8.40246i	−0.847531	−	0.275380i
$932$	−1.42945	+	3.74134i	−0.0468231	+	0.122552i
$933$		0			0
$934$	−0.0475062	−	0.893091i	−0.00155445	−	0.0292228i
$935$	60.6265	+	7.33506i	1.98270	+	0.239882i
$936$		0			0
$937$	6.48322	+	1.02684i	0.211798	+	0.0335455i	0.261432	−	0.965222i	$-0.415805\pi$
$937$	6.48322	+	1.02684i	0.211798	+	0.0335455i	−0.0496339	+	0.998767i	$0.515805\pi$
$938$	−1.83806	−	1.65239i	−0.0600147	−	0.0539525i
$939$		0			0
$940$	26.5480	−	8.21349i	0.865899	−	0.267895i
$941$	21.2753	−	15.4574i	0.693556	−	0.503898i	−0.184271	−	0.982875i	$-0.558992\pi$
$941$	21.2753	−	15.4574i	0.693556	−	0.503898i	0.877827	+	0.478978i	$0.158992\pi$
$942$		0			0
$943$	0.0452886	+	0.0452886i	0.00147480	+	0.00147480i
$944$	25.6309	+	44.0746i	0.834214	+	1.43451i
$945$		0			0
$946$	−7.80428	−	2.08460i	−0.253739	−	0.0677763i
$947$	22.1792	+	11.3009i	0.720727	+	0.367229i	0.775566	−	0.631267i	$-0.217465\pi$
$947$	22.1792	+	11.3009i	0.720727	+	0.367229i	−0.0548392	+	0.998495i	$0.517465\pi$
$948$		0			0
$949$			37.2019i			1.20763i
$950$	24.1987	−	31.2505i	0.785109	−	1.01390i
$951$		0			0
$952$	19.7707	−	0.0464457i	0.640772	−	0.00150531i
$953$	−45.0654	−	22.9619i	−1.45981	−	0.743810i	−0.469532	−	0.882915i	$-0.655577\pi$
$953$	−45.0654	−	22.9619i	−1.45981	−	0.743810i	−0.990278	+	0.139105i	$0.955577\pi$
$954$		0			0
$955$	−30.8472	+	24.1886i	−0.998193	+	0.782724i
$956$	−2.57971	−	24.1799i	−0.0834337	−	0.782035i
$957$		0			0
$958$	−3.98225	+	38.1761i	−0.128661	+	1.23342i
$959$	−9.16139	+	6.65614i	−0.295837	+	0.214938i
$960$		0			0
$961$	−15.5410	−	11.2912i	−0.501322	−	0.364232i
$962$	8.70206	−	9.67985i	0.280566	−	0.312091i
$963$		0			0
$964$	29.1414	+	6.14651i	0.938582	+	0.197966i
$965$	−37.1979	−	34.5647i	−1.19744	−	1.11268i
$966$		0			0
$967$	−12.1462	−	23.8383i	−0.390597	−	0.766589i	0.609051	−	0.793131i	$-0.291550\pi$
$967$	−12.1462	−	23.8383i	−0.390597	−	0.766589i	−0.999648	+	0.0265419i	$0.991550\pi$
$968$	49.3376	−	36.0232i	1.58577	−	1.15783i
$969$		0			0
$970$	11.4437	+	13.0968i	0.367435	+	0.420512i
$971$	−45.6706	+	14.8393i	−1.46564	+	0.476215i	−0.929787	−	0.368097i	$-0.880009\pi$
$971$	−45.6706	+	14.8393i	−1.46564	+	0.476215i	−0.535852	+	0.844312i	$0.680009\pi$
$972$		0			0
$973$	21.5526	−	3.41359i	0.690944	−	0.109435i
$974$	−4.88434	+	7.53413i	−0.156504	+	0.241409i
$975$		0			0
$976$	28.9344	−	32.3380i	0.926168	−	1.03512i
$977$	−5.08562	−	32.1094i	−0.162703	−	1.02727i	−0.924979	−	0.380017i	$-0.875918\pi$
$977$	−5.08562	−	32.1094i	−0.162703	−	1.02727i	0.762276	−	0.647252i	$-0.224082\pi$
$978$		0			0
$979$	−22.4669	−	69.1459i	−0.718044	−	2.20991i
$980$	−15.1645	−	15.5988i	−0.484411	−	0.498284i
$981$		0			0
$982$	7.82669	+	36.6804i	0.249760	+	1.17052i
$983$	−35.2093	+	17.9400i	−1.12300	+	0.572198i	−0.913999	−	0.405717i	$-0.867022\pi$
$983$	−35.2093	+	17.9400i	−1.12300	+	0.572198i	−0.209003	+	0.977915i	$0.567022\pi$
$984$		0			0
$985$	−27.9746	−	12.9845i	−0.891343	−	0.413720i
$986$	−31.7846	+	12.2295i	−1.01223	+	0.389467i
$987$		0			0
$988$	−7.30788	−	27.1035i	−0.232495	−	0.862278i
$989$	0.167865	−	0.231047i	0.00533780	−	0.00734686i
$990$		0			0
$991$	14.2278	+	19.5828i	0.451960	+	0.622069i	0.972817	−	0.231575i	$-0.0743877\pi$
$991$	14.2278	+	19.5828i	0.451960	+	0.622069i	−0.520858	+	0.853644i	$0.674388\pi$
$992$	−14.3838	+	13.0536i	−0.456686	+	0.414451i
$993$		0			0
$994$	18.8531	−	15.2914i	0.597983	−	0.485013i
$995$	−1.82552	−	49.7502i	−0.0578728	−	1.57719i
$996$		0			0
$997$	3.86738	−	7.59016i	0.122481	−	0.240383i	−0.821622	−	0.570032i	$-0.806931\pi$
$997$	3.86738	−	7.59016i	0.122481	−	0.240383i	0.944103	+	0.329650i	$0.106931\pi$
$998$	2.81466	+	1.25053i	0.0890965	+	0.0395847i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.e.487.25	yes	224
3.2	odd	2	inner	900.2.bj.e.487.4	✓	224
4.3	odd	2	inner	900.2.bj.e.487.7	yes	224
12.11	even	2	inner	900.2.bj.e.487.22	yes	224
25.23	odd	20	inner	900.2.bj.e.523.7	yes	224
75.23	even	20	inner	900.2.bj.e.523.22	yes	224
100.23	even	20	inner	900.2.bj.e.523.25	yes	224
300.23	odd	20	inner	900.2.bj.e.523.4	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bj.e.487.4	✓	224	3.2	odd	2	inner
900.2.bj.e.487.7	yes	224	4.3	odd	2	inner
900.2.bj.e.487.22	yes	224	12.11	even	2	inner
900.2.bj.e.487.25	yes	224	1.1	even	1	trivial
900.2.bj.e.523.4	yes	224	300.23	odd	20	inner
900.2.bj.e.523.7	yes	224	25.23	odd	20	inner
900.2.bj.e.523.22	yes	224	75.23	even	20	inner
900.2.bj.e.523.25	yes	224	100.23	even	20	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29240 + 0.574201i) q^{2} +(1.34059 + 1.48419i) q^{4} +(0.0819943 + 2.23456i) q^{5} +(1.03330 - 1.03330i) q^{7} +(0.880349 + 2.68793i) q^{8} +(-1.17712 + 2.93503i) q^{10} +(3.35595 - 4.61907i) q^{11} +(-0.392815 + 2.48014i) q^{13} +(1.92876 - 0.742115i) q^{14} +(-0.405651 + 3.97938i) q^{16} +(4.26203 - 2.17162i) q^{17} +(-1.72727 + 5.31601i) q^{19} +(-3.20660 + 3.11732i) q^{20} +(6.98950 - 4.04269i) q^{22} +(0.0446569 + 0.281952i) q^{23} +(-4.98655 + 0.366443i) q^{25} +(-1.93177 + 2.97977i) q^{26} +(2.91885 + 0.148387i) q^{28} +(-4.78796 + 1.55570i) q^{29} +(3.26564 + 1.06107i) q^{31} +(-2.80922 + 4.91002i) q^{32} +(6.75519 - 0.359329i) q^{34} +(2.39370 + 2.22425i) q^{35} +(-3.62025 - 0.573391i) q^{37} +(-5.28478 + 5.87859i) q^{38} +(-5.93418 + 2.18759i) q^{40} +(0.181512 - 0.131876i) q^{41} +(-0.707410 - 0.707410i) q^{43} +(11.3545 - 1.21139i) q^{44} +(-0.104183 + 0.390037i) q^{46} +(-5.53664 - 2.82106i) q^{47} +4.86458i q^{49} +(-6.65503 - 2.38969i) q^{50} +(-4.20760 + 2.74183i) q^{52} +(-10.4732 - 5.33638i) q^{53} +(10.5968 + 7.12035i) q^{55} +(3.68711 + 1.86778i) q^{56} +(-7.08124 - 0.738663i) q^{58} +(10.3120 - 7.49212i) q^{59} +(-8.77641 - 6.37643i) q^{61} +(3.61124 + 3.24646i) q^{62} +(-6.44997 + 4.73264i) q^{64} +(-5.57423 - 0.674413i) q^{65} +(-0.542962 - 1.06562i) q^{67} +(8.93672 + 3.41444i) q^{68} +(1.81645 + 4.24909i) q^{70} +(11.1713 - 3.62978i) q^{71} +(14.6329 - 2.31762i) q^{73} +(-4.34956 - 2.81980i) q^{74} +(-10.2055 + 4.56296i) q^{76} +(-1.30518 - 8.24060i) q^{77} +(-0.564003 - 1.73582i) q^{79} +(-8.92544 - 0.580168i) q^{80} +(0.310310 - 0.0662124i) q^{82} +(2.71578 - 1.38376i) q^{83} +(5.20208 + 9.34573i) q^{85} +(-0.508061 - 1.32045i) q^{86} +(15.3702 + 4.95418i) q^{88} +(7.48483 - 10.3020i) q^{89} +(2.15683 + 2.96862i) q^{91} +(-0.358605 + 0.444261i) q^{92} +(-5.53570 - 6.82508i) q^{94} +(-12.0206 - 3.42382i) q^{95} +(2.49688 - 4.90040i) q^{97} +(-2.79324 + 6.28697i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 4 q^{10} + 16 q^{13} - 16 q^{16} + 28 q^{22} - 32 q^{25} + 28 q^{28} - 100 q^{34} - 104 q^{37} + 60 q^{40} + 156 q^{52} + 144 q^{58} - 48 q^{61} + 60 q^{64} + 28 q^{70} + 40 q^{73} + 64 q^{82} + 136 q^{85}+ \cdots - 160 q^{97}+O(q^{100}) \) 224 * q - 4 * q^10 + 16 * q^13 - 16 * q^16 + 28 * q^22 - 32 * q^25 + 28 * q^28 - 100 * q^34 - 104 * q^37 + 60 * q^40 + 156 * q^52 + 144 * q^58 - 48 * q^61 + 60 * q^64 + 28 * q^70 + 40 * q^73 + 64 * q^82 + 136 * q^85 + 148 * q^88 + 40 * q^94 - 160 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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