LMFDB - Embedded newform 675.2.r.a.46.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.9
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +O(q^{10})$	\(q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +(-0.566103 + 2.60508i) q^{10} +(-1.93450 - 2.14848i) q^{11} +(4.36810 - 4.85127i) q^{13} +(-0.367525 + 0.0781199i) q^{14} +(2.45317 + 0.521438i) q^{16} +(-0.794350 + 0.577129i) q^{17} +(-5.88399 + 4.27497i) q^{19} +(-1.12341 + 0.641816i) q^{20} +(-0.360286 + 3.42790i) q^{22} +(-1.28104 + 0.272294i) q^{23} +(-1.58820 + 4.74106i) q^{25} -7.78284 q^{26} +(-0.147528 - 0.107185i) q^{28} +(3.94048 - 1.75442i) q^{29} +(-7.91741 - 3.52506i) q^{31} +(1.57924 + 2.73533i) q^{32} +(1.14502 + 0.243382i) q^{34} +(-0.701179 + 0.0704794i) q^{35} +(0.00738727 + 0.0227357i) q^{37} +(8.48155 + 1.80281i) q^{38} +(6.52812 + 2.15393i) q^{40} +(-3.06561 + 3.40470i) q^{41} +(-1.34599 + 2.33132i) q^{43} +(-1.35333 + 0.983252i) q^{44} +(1.26320 + 0.917772i) q^{46} +(4.76261 - 2.12045i) q^{47} +(3.45034 + 5.97616i) q^{49} +(5.46752 - 2.37504i) q^{50} +(-2.52745 - 2.80701i) q^{52} +(3.44104 + 2.50006i) q^{53} +(-1.37277 + 6.31717i) q^{55} +(0.101275 + 0.963571i) q^{56} +(-4.69792 - 2.09165i) q^{58} +(-3.46632 + 3.84974i) q^{59} +(-4.95936 - 5.50792i) q^{61} +(3.19295 + 9.82688i) q^{62} +(2.71365 - 8.35176i) q^{64} +(-14.5101 - 1.59172i) q^{65} +(-2.27694 - 1.01376i) q^{67} +(0.284062 + 0.492010i) q^{68} +(0.621810 + 0.565014i) q^{70} +(-9.63629 - 7.00118i) q^{71} +(-0.283594 + 0.872814i) q^{73} +(0.0142504 - 0.0246825i) q^{74} +(2.10413 + 3.64447i) q^{76} +(-0.891228 + 0.189436i) q^{77} +(-10.3980 + 4.62948i) q^{79} +(-2.25770 - 5.13348i) q^{80} +5.46212 q^{82} +(-1.03926 - 9.88793i) q^{83} +(2.08497 + 0.687930i) q^{85} +(3.13929 - 0.667278i) q^{86} +(8.69369 + 1.84790i) q^{88} +(-3.78718 + 11.6557i) q^{89} +(-0.635757 - 1.95666i) q^{91} +(0.0792106 + 0.753639i) q^{92} +(-5.67808 - 2.52804i) q^{94} +(15.4440 + 5.09571i) q^{95} +(-6.75362 + 3.00691i) q^{97} +(2.54232 - 7.82445i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.797750	−	0.885991i	−0.564095	−	0.626491i	0.391853	−	0.920028i	$-0.371834\pi$
$2$	−0.797750	−	0.885991i	−0.564095	−	0.626491i	−0.955948	+	0.293537i	$0.905168\pi$
$3$		0			0
$3$		0			0
$4$	0.0604816	−	0.575444i	0.0302408	−	0.287722i
$5$	−1.30610	−	1.81497i	−0.584106	−	0.811678i
$5$	−1.30610	−	1.81497i	−0.584106	−	0.811678i
$6$		0			0
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	−0.834708	−	0.550692i	$-0.814364\pi$
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	0.894268	+	0.447533i	$0.147697\pi$
$8$	−2.48714	+	1.80701i	−0.879336	+	0.638875i
$9$		0			0
$10$	−0.566103	+	2.60508i	−0.179017	+	0.823800i
$11$	−1.93450	−	2.14848i	−0.583273	−	0.647790i	0.377210	−	0.926128i	$-0.376883\pi$
$11$	−1.93450	−	2.14848i	−0.583273	−	0.647790i	−0.960483	+	0.278337i	$0.910217\pi$
$12$		0			0
$13$	4.36810	−	4.85127i	1.21149	−	1.34550i	0.290039	−	0.957015i	$-0.406332\pi$
$13$	4.36810	−	4.85127i	1.21149	−	1.34550i	0.921455	−	0.388486i	$-0.127002\pi$
$14$	−0.367525	+	0.0781199i	−0.0982253	+	0.0208784i
$15$		0			0
$16$	2.45317	+	0.521438i	0.613293	+	0.130359i
$17$	−0.794350	+	0.577129i	−0.192658	+	0.139974i	−0.679933	−	0.733274i	$-0.737991\pi$
$17$	−0.794350	+	0.577129i	−0.192658	+	0.139974i	0.487275	+	0.873249i	$0.337991\pi$
$18$		0			0
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.350863	+	0.936427i	$0.614112\pi$
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.999017	+	0.0443190i	$0.985888\pi$
$20$	−1.12341	+	0.641816i	−0.251201	+	0.143514i
$21$		0			0
$22$	−0.360286	+	3.42790i	−0.0768133	+	0.730830i
$23$	−1.28104	+	0.272294i	−0.267116	+	0.0567773i	−0.339523	−	0.940598i	$-0.610266\pi$
$23$	−1.28104	+	0.272294i	−0.267116	+	0.0567773i	0.0724063	+	0.997375i	$0.476932\pi$
$24$		0			0
$25$	−1.58820	+	4.74106i	−0.317641	+	0.948211i
$26$	−7.78284			−1.52634
$27$		0			0
$28$	−0.147528	−	0.107185i	−0.0278801	−	0.0202561i
$29$	3.94048	−	1.75442i	0.731729	−	0.325787i	−0.00682892	−	0.999977i	$-0.502174\pi$
$29$	3.94048	−	1.75442i	0.731729	−	0.325787i	0.738558	+	0.674190i	$0.235507\pi$
$30$		0			0
$31$	−7.91741	−	3.52506i	−1.42201	−	0.633120i	−0.455614	−	0.890178i	$-0.650580\pi$
$31$	−7.91741	−	3.52506i	−1.42201	−	0.633120i	−0.966396	+	0.257058i	$0.917247\pi$
$32$	1.57924	+	2.73533i	0.279173	+	0.483542i
$33$		0			0
$34$	1.14502	+	0.243382i	0.196370	+	0.0417397i
$35$	−0.701179	+	0.0704794i	−0.118521	+	0.0119132i
$36$		0			0
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	0.951662	−	0.307148i	$-0.0993745\pi$
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	−0.950447	+	0.310885i	$0.899375\pi$
$38$	8.48155	+	1.80281i	1.37589	+	0.292454i
$39$		0			0
$40$	6.52812	+	2.15393i	1.03219	+	0.340567i
$41$	−3.06561	+	3.40470i	−0.478767	+	0.531725i	−0.933344	−	0.358983i	$-0.883124\pi$
$41$	−3.06561	+	3.40470i	−0.478767	+	0.531725i	0.454577	+	0.890707i	$0.349790\pi$
$42$		0			0
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	−0.950216	−	0.311592i	$-0.899138\pi$
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	0.744955	+	0.667115i	$0.232471\pi$
$44$	−1.35333	+	0.983252i	−0.204022	+	0.148231i
$45$		0			0
$46$	1.26320	+	0.917772i	0.186249	+	0.135318i
$47$	4.76261	−	2.12045i	0.694698	−	0.309300i	−0.0288398	−	0.999584i	$-0.509181\pi$
$47$	4.76261	−	2.12045i	0.694698	−	0.309300i	0.723538	+	0.690284i	$0.242515\pi$
$48$		0			0
$49$	3.45034	+	5.97616i	0.492905	+	0.853737i
$50$	5.46752	−	2.37504i	0.773225	−	0.335882i
$51$		0			0
$52$	−2.52745	−	2.80701i	−0.350494	−	0.389263i
$53$	3.44104	+	2.50006i	0.472663	+	0.343410i	0.798478	−	0.602024i	$-0.205639\pi$
$53$	3.44104	+	2.50006i	0.472663	+	0.343410i	−0.325815	+	0.945433i	$0.605639\pi$
$54$		0			0
$55$	−1.37277	+	6.31717i	−0.185104	+	0.851808i
$56$	0.101275	+	0.963571i	0.0135335	+	0.128763i
$57$		0			0
$58$	−4.69792	−	2.09165i	−0.616867	−	0.274647i
$59$	−3.46632	+	3.84974i	−0.451276	+	0.501193i	−0.925256	−	0.379342i	$-0.876150\pi$
$59$	−3.46632	+	3.84974i	−0.451276	+	0.501193i	0.473980	+	0.880536i	$0.342817\pi$
$60$		0			0
$61$	−4.95936	−	5.50792i	−0.634980	−	0.705217i	0.336674	−	0.941621i	$-0.390698\pi$
$61$	−4.95936	−	5.50792i	−0.634980	−	0.705217i	−0.971655	+	0.236404i	$0.924031\pi$
$62$	3.19295	+	9.82688i	0.405505	+	1.24801i
$63$		0			0
$64$	2.71365	−	8.35176i	0.339207	−	1.04397i
$65$	−14.5101	−	1.59172i	−1.79975	−	0.197428i
$66$		0			0
$67$	−2.27694	−	1.01376i	−0.278173	−	0.123851i	0.262908	−	0.964821i	$-0.415318\pi$
$67$	−2.27694	−	1.01376i	−0.278173	−	0.123851i	−0.541081	+	0.840970i	$0.681985\pi$
$68$	0.284062	+	0.492010i	0.0344476	+	0.0596649i
$69$		0			0
$70$	0.621810	+	0.565014i	0.0743205	+	0.0675321i
$71$	−9.63629	−	7.00118i	−1.14362	−	0.830887i	−0.155999	−	0.987757i	$-0.549860\pi$
$71$	−9.63629	−	7.00118i	−1.14362	−	0.830887i	−0.987619	+	0.156870i	$0.949860\pi$
$72$		0			0
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	−0.966280	−	0.257493i	$-0.917103\pi$
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	0.933088	+	0.359649i	$0.117103\pi$
$74$	0.0142504	−	0.0246825i	0.00165658	−	0.00286928i
$75$		0			0
$76$	2.10413	+	3.64447i	0.241361	+	0.418049i
$77$	−0.891228	+	0.189436i	−0.101565	+	0.0215883i
$78$		0			0
$79$	−10.3980	+	4.62948i	−1.16986	+	0.520857i	−0.897361	−	0.441298i	$-0.854518\pi$
$79$	−10.3980	+	4.62948i	−1.16986	+	0.520857i	−0.272503	+	0.962155i	$0.587851\pi$
$80$	−2.25770	−	5.13348i	−0.252418	−	0.573940i
$81$		0			0
$82$	5.46212			0.603191
$83$	−1.03926	−	9.88793i	−0.114074	−	1.08534i	−0.890453	−	0.455075i	$-0.849612\pi$
$83$	−1.03926	−	9.88793i	−0.114074	−	1.08534i	0.776379	−	0.630266i	$-0.217054\pi$
$84$		0			0
$85$	2.08497	+	0.687930i	0.226147	+	0.0746165i
$86$	3.13929	−	0.667278i	0.338519	−	0.0719544i
$87$		0			0
$88$	8.69369	+	1.84790i	0.926750	+	0.196987i
$89$	−3.78718	+	11.6557i	−0.401440	+	1.23551i	0.522391	+	0.852706i	$0.325040\pi$
$89$	−3.78718	+	11.6557i	−0.401440	+	1.23551i	−0.923831	+	0.382800i	$0.874960\pi$
$90$		0			0
$91$	−0.635757	−	1.95666i	−0.0666455	−	0.205114i
$92$	0.0792106	+	0.753639i	0.00825828	+	0.0785723i
$93$		0			0
$94$	−5.67808	−	2.52804i	−0.585649	−	0.260748i
$95$	15.4440	+	5.09571i	1.58452	+	0.522809i
$96$		0			0
$97$	−6.75362	+	3.00691i	−0.685726	+	0.305305i	−0.719867	−	0.694112i	$-0.755797\pi$
$97$	−6.75362	+	3.00691i	−0.685726	+	0.305305i	0.0341407	+	0.999417i	$0.489131\pi$
$98$	2.54232	−	7.82445i	0.256813	−	0.790389i
$99$		0			0
$100$	2.63216	+	1.20067i	0.263216	+	0.120067i
$101$	5.77262	−	9.99848i	0.574397	−	0.994885i	−0.421709	−	0.906731i	$-0.638570\pi$
$101$	5.77262	−	9.99848i	0.574397	−	0.994885i	0.996107	−	0.0881544i	$-0.0280969\pi$
$102$		0			0
$103$	1.71092	−	16.2783i	0.168582	−	1.60395i	−0.503851	−	0.863790i	$-0.668084\pi$
$103$	1.71092	−	16.2783i	0.168582	−	1.60395i	0.672433	−	0.740158i	$-0.265249\pi$
$104$	−2.09778	+	19.9590i	−0.205704	+	1.95714i
$105$		0			0
$106$	−0.530057	−	5.04315i	−0.0514837	−	0.489834i
$107$	10.1611			0.982314			0.491157	−	0.871071i	$-0.336574\pi$
$107$	10.1611			0.982314			0.491157	+	0.871071i	$0.336574\pi$
$108$		0			0
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	0.970082	+	0.242777i	$0.0780584\pi$
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	−0.642112	+	0.766611i	$0.721942\pi$
$110$	6.69209	−	3.82327i	0.638065	−	0.364534i
$111$		0			0
$112$	0.528885	−	0.587387i	0.0499750	−	0.0555028i
$113$	9.81486	−	10.9005i	0.923305	−	1.02543i	−0.0762934	−	0.997085i	$-0.524309\pi$
$113$	9.81486	−	10.9005i	0.923305	−	1.02543i	0.999598	−	0.0283484i	$-0.00902478\pi$
$114$		0			0
$115$	2.16738	+	1.96941i	0.202109	+	0.183648i
$116$	−0.771242	−	2.37364i	−0.0716080	−	0.220387i
$117$		0			0
$118$	6.17609			0.568555
$119$	0.0323456	+	0.307748i	0.00296512	+	0.0282112i
$120$		0			0
$121$	0.276140	−	2.62729i	0.0251036	−	0.238845i
$122$	−0.923645	+	8.78789i	−0.0836229	+	0.795618i
$123$		0			0
$124$	−2.50733	+	4.34283i	−0.225165	+	0.389998i
$125$	10.6792	−	3.30976i	0.955178	−	0.296034i
$126$		0			0
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	−0.483710	−	0.875228i	$-0.660711\pi$
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	0.905776	−	0.423757i	$-0.139289\pi$
$128$	−3.79357	+	1.68900i	−0.335307	+	0.149288i
$129$		0			0
$130$	10.1652	+	14.1256i	0.891544	+	1.23890i
$131$	−3.04960	−	1.35777i	−0.266445	−	0.118629i	0.269166	−	0.963094i	$-0.413252\pi$
$131$	−3.04960	−	1.35777i	−0.266445	−	0.118629i	−0.535611	+	0.844465i	$0.679919\pi$
$132$		0			0
$133$	0.239594	+	2.27959i	0.0207754	+	0.197665i
$134$	0.918249	+	2.82608i	0.0793247	+	0.244136i
$135$		0			0
$136$	0.932779	−	2.87080i	0.0799851	−	0.246169i
$137$	−8.26092	−	1.75591i	−0.705778	−	0.150018i	−0.158979	−	0.987282i	$-0.550820\pi$
$137$	−8.26092	−	1.75591i	−0.705778	−	0.150018i	−0.546799	+	0.837264i	$0.684154\pi$
$138$		0			0
$139$	1.39912	−	0.297391i	0.118671	−	0.0252244i	−0.148193	−	0.988958i	$-0.547346\pi$
$139$	1.39912	−	0.297391i	0.118671	−	0.0252244i	0.266864	+	0.963734i	$0.414012\pi$
$140$	−0.00185147	+	0.407752i	−0.000156477	+	0.0344613i
$141$		0			0
$142$	1.48437	+	14.1229i	0.124566	+	1.18516i
$143$	−18.8729			−1.57823
$144$		0			0
$145$	−8.33087	−	4.86040i	−0.691841	−	0.403634i
$146$	0.999543	−	0.445025i	0.0827228	−	0.0368305i
$147$		0			0
$148$	0.0135299	−	0.00287587i	0.00111215	−	0.000236395i
$149$	−10.3534	−	17.9326i	−0.848181	−	1.46909i	−0.882830	−	0.469693i	$-0.844365\pi$
$149$	−10.3534	−	17.9326i	−0.848181	−	1.46909i	0.0346486	−	0.999400i	$-0.488969\pi$
$150$		0			0
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.00232675	−	0.999997i	$-0.499259\pi$
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.864860	−	0.502014i	$-0.167407\pi$
$152$	6.90938	−	21.2649i	0.560425	−	1.72481i
$153$		0			0
$154$	0.878816	+	0.638497i	0.0708170	+	0.0514516i
$155$	3.94307	+	18.9739i	0.316715	+	1.52402i
$156$		0			0
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	−0.997728	−	0.0673760i	$-0.978537\pi$
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	0.440514	−	0.897746i	$-0.354796\pi$
$158$	12.3967	+	5.51935i	0.986226	+	0.439096i
$159$		0			0
$160$	2.90188	−	6.43889i	0.229414	−	0.509039i
$161$	−0.127547	+	0.392548i	−0.0100521	+	0.0309371i
$162$		0			0
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	0.943329	−	0.331858i	$-0.107675\pi$
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	−0.958231	+	0.285997i	$0.907675\pi$
$164$	1.77380	+	1.97001i	0.138511	+	0.153832i
$165$		0			0
$166$	−7.93155	+	8.80888i	−0.615608	+	0.683702i
$167$	4.93325	+	2.19642i	0.381746	+	0.169964i	0.588633	−	0.808401i	$-0.299666\pi$
$167$	4.93325	+	2.19642i	0.381746	+	0.169964i	−0.206887	+	0.978365i	$0.566333\pi$
$168$		0			0
$169$	−3.09563	−	29.4529i	−0.238125	−	2.26561i
$170$	−1.05378	−	2.39606i	−0.0808216	−	0.183769i
$171$		0			0
$172$	1.26014	+	0.915544i	0.0960846	+	0.0698096i
$173$	0.243366	+	0.270286i	0.0185028	+	0.0205494i	0.752325	−	0.658792i	$-0.228932\pi$
$173$	0.243366	+	0.270286i	0.0185028	+	0.0205494i	−0.733822	+	0.679341i	$0.762266\pi$
$174$		0			0
$175$	1.04373	+	1.18056i	0.0788984	+	0.0892422i
$176$	−3.62536	−	6.27931i	−0.273272	−	0.473321i
$177$		0			0
$178$	13.3481	−	5.94296i	1.00048	−	0.445444i
$179$	−12.2855	−	8.92591i	−0.918259	−	0.667154i	0.0248313	−	0.999692i	$-0.492095\pi$
$179$	−12.2855	−	8.92591i	−0.918259	−	0.667154i	−0.943090	+	0.332538i	$0.892095\pi$
$180$		0			0
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	−0.586065	−	0.810264i	$-0.699324\pi$
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	0.589503	+	0.807766i	$0.299324\pi$
$182$	−1.22641	+	2.12420i	−0.0909074	+	0.157456i
$183$		0			0
$184$	2.69410	−	2.99210i	0.198611	−	0.220580i
$185$	0.0316160	−	0.0431027i	0.00232445	−	0.00316898i
$186$		0			0
$187$	2.77662	+	0.590188i	0.203046	+	0.0431588i
$188$	−0.932151	−	2.86887i	−0.0679841	−	0.209234i
$189$		0			0
$190$	−7.80571	−	17.7484i	−0.566286	−	1.28760i
$191$	2.34418	+	0.498271i	0.169619	+	0.0360536i	0.291938	−	0.956437i	$-0.405700\pi$
$191$	2.34418	+	0.498271i	0.169619	+	0.0360536i	−0.122319	+	0.992491i	$0.539033\pi$
$192$		0			0
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	0.952397	−	0.304860i	$-0.0986095\pi$
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	−0.740215	+	0.672370i	$0.765276\pi$
$194$	8.05179	+	3.58489i	0.578085	+	0.257380i
$195$		0			0
$196$	3.64763	−	1.62403i	0.260545	−	0.116002i
$197$	12.8434	+	9.33130i	0.915057	+	0.664828i	0.942289	−	0.334801i	$-0.108669\pi$
$197$	12.8434	+	9.33130i	0.915057	+	0.664828i	−0.0272318	+	0.999629i	$0.508669\pi$
$198$		0			0
$199$	4.61006			0.326798			0.163399	−	0.986560i	$-0.447754\pi$
$199$	4.61006			0.326798			0.163399	+	0.986560i	$0.447754\pi$
$200$	−4.61706	−	14.6616i	−0.326475	−	1.03673i
$201$		0			0
$202$	−13.4637	+	2.86179i	−0.947301	+	0.201355i
$203$	0.142096	−	1.35195i	0.00997316	−	0.0948882i
$204$		0			0
$205$	10.1834	+	1.11709i	0.711240	+	0.0780211i
$206$	−15.7873	+	11.4702i	−1.09995	+	0.799164i
$207$		0			0
$208$	13.2453	−	9.62331i	0.918400	−	0.667256i
$209$	20.5673	+	4.37170i	1.42267	+	0.302397i
$210$		0			0
$211$	−0.144843	+	0.0307873i	−0.00997140	+	0.00211949i	−0.212895	−	0.977075i	$-0.568289\pi$
$211$	−0.144843	+	0.0307873i	−0.00997140	+	0.00211949i	0.202923	+	0.979195i	$0.434956\pi$
$212$	1.64676	−	1.82892i	0.113100	−	0.125611i
$213$		0			0
$214$	−8.10605	−	9.00268i	−0.554118	−	0.615410i
$215$	5.98927	−	0.602015i	0.408465	−	0.0410571i
$216$		0			0
$217$	−2.20972	+	1.60546i	−0.150006	+	0.108986i
$218$	6.60528	−	11.4407i	0.447366	−	0.774861i
$219$		0			0
$220$	3.55215	+	1.17202i	0.239486	+	0.0790178i
$221$	−0.669994	+	6.37456i	−0.0450686	+	0.428800i
$222$		0			0
$223$	−1.10187	−	1.22375i	−0.0737867	−	0.0819485i	0.705121	−	0.709087i	$-0.250893\pi$
$223$	−1.10187	−	1.22375i	−0.0737867	−	0.0819485i	−0.778908	+	0.627139i	$0.784226\pi$
$224$	0.995419			0.0665092
$225$		0			0
$226$	−17.4876			−1.16326
$227$	2.45055	+	2.72161i	0.162648	+	0.180639i	0.818960	−	0.573851i	$-0.194551\pi$
$227$	2.45055	+	2.72161i	0.162648	+	0.180639i	−0.656312	+	0.754490i	$0.727884\pi$
$228$		0			0
$229$	0.0884967	−	0.841990i	0.00584803	−	0.0556403i	−0.991209	−	0.132308i	$-0.957761\pi$
$229$	0.0884967	−	0.841990i	0.00584803	−	0.0556403i	0.997057	+	0.0766674i	$0.0244280\pi$
$230$	0.0158532	−	3.49138i	0.00104533	−	0.230214i
$231$		0			0
$232$	−6.63027	+	11.4840i	−0.435299	+	0.753960i
$233$	−9.04329	+	6.57033i	−0.592445	+	0.430437i	−0.843189	−	0.537617i	$-0.819325\pi$
$233$	−9.04329	+	6.57033i	−0.592445	+	0.430437i	0.250744	+	0.968053i	$0.419325\pi$
$234$		0			0
$235$	−10.0690	−	5.87446i	−0.656829	−	0.383207i
$236$	2.00566	+	2.22751i	0.130557	+	0.144999i
$237$		0			0
$238$	0.246858	−	0.274164i	0.0160015	−	0.0177714i
$239$	−15.9775	+	3.39613i	−1.03350	+	0.219677i	−0.693280	−	0.720669i	$-0.743835\pi$
$239$	−15.9775	+	3.39613i	−1.03350	+	0.219677i	−0.340220	+	0.940346i	$0.610502\pi$
$240$		0			0
$241$	−2.04979	−	0.435696i	−0.132038	−	0.0280656i	0.141418	−	0.989950i	$-0.454834\pi$
$241$	−2.04979	−	0.435696i	−0.132038	−	0.0280656i	−0.273457	+	0.961884i	$0.588167\pi$
$242$	−2.54805	+	1.85127i	−0.163795	+	0.119004i
$243$		0			0
$244$	−3.46945	+	2.52070i	−0.222109	+	0.161372i
$245$	6.34004	−	14.0677i	0.405050	−	0.898753i
$246$		0			0
$247$	−4.96285	+	47.2184i	−0.315779	+	3.00443i
$248$	26.0615	−	5.53955i	1.65491	−	0.351762i
$249$		0			0
$250$	−11.4518	−	6.82133i	−0.724273	−	0.431419i
$251$	15.8673			1.00154			0.500769	−	0.865581i	$-0.333051\pi$
$251$	15.8673			1.00154			0.500769	+	0.865581i	$0.333051\pi$
$252$		0			0
$253$	3.06320	+	2.22554i	0.192582	+	0.139919i
$254$	−16.7643	+	7.46396i	−1.05189	+	0.468330i
$255$		0			0
$256$	−11.5220	−	5.12990i	−0.720122	−	0.320619i
$257$	1.09760	+	1.90109i	0.0684661	+	0.118587i	0.898226	−	0.439533i	$-0.144856\pi$
$257$	1.09760	+	1.90109i	0.0684661	+	0.118587i	−0.829760	+	0.558120i	$0.811523\pi$
$258$		0			0
$259$	0.00736942	+	0.00156642i	0.000457913	+	9.73325e-5i
$260$	−1.79354	+	8.25347i	−0.111230	+	0.511858i
$261$		0			0
$262$	1.22985	+	3.78508i	0.0759801	+	0.233843i
$263$	−29.0145	−	6.16721i	−1.78911	−	0.380287i	−0.810454	−	0.585802i	$-0.800780\pi$
$263$	−29.0145	−	6.16721i	−1.78911	−	0.380287i	−0.978654	+	0.205515i	$0.934113\pi$
$264$		0			0
$265$	0.0431849	−	9.51070i	0.00265283	−	0.584237i
$266$	1.82856	−	2.03082i	0.112116	−	0.124517i
$267$		0			0
$268$	−0.721076	+	1.24894i	−0.0440467	+	0.0762912i
$269$	20.4742	−	14.8754i	1.24833	−	0.906968i	0.250210	−	0.968192i	$-0.419500\pi$
$269$	20.4742	−	14.8754i	1.24833	−	0.906968i	0.998124	+	0.0612238i	$0.0195003\pi$
$270$		0			0
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	0.0200987	−	0.999798i	$-0.493602\pi$
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	−0.944654	+	0.328070i	$0.893602\pi$
$272$	−2.24961	+	1.00159i	−0.136403	+	0.0607305i
$273$		0			0
$274$	5.03443	+	8.71989i	0.304141	+	0.526788i
$275$	13.2584	−	5.75934i	0.799513	−	0.347301i
$276$		0			0
$277$	15.1456	+	16.8209i	0.910012	+	1.01067i	0.999892	+	0.0147182i	$0.00468511\pi$
$277$	15.1456	+	16.8209i	0.910012	+	1.01067i	−0.0898796	+	0.995953i	$0.528648\pi$
$278$	−1.37963	−	1.00236i	−0.0827447	−	0.0601176i
$279$		0			0
$280$	1.61657	−	1.44233i	0.0966087	−	0.0861958i
$281$	−0.0980168	−	0.932568i	−0.00584719	−	0.0556323i	0.991209	−	0.132304i	$-0.0422374\pi$
$281$	−0.0980168	−	0.932568i	−0.00584719	−	0.0556323i	−0.997056	+	0.0766714i	$0.975571\pi$
$282$		0			0
$283$	10.5924	+	4.71605i	0.629653	+	0.280340i	0.696648	−	0.717414i	$-0.254674\pi$
$283$	10.5924	+	4.71605i	0.629653	+	0.280340i	−0.0669940	+	0.997753i	$0.521341\pi$
$284$	−4.61161	+	5.12171i	−0.273648	+	0.303917i
$285$		0			0
$286$	15.0559	+	16.7213i	0.890273	+	0.988748i
$287$	0.446185	+	1.37322i	0.0263375	+	0.0810583i
$288$		0			0
$289$	−4.95538	+	15.2511i	−0.291493	+	0.897122i
$290$	2.33968	+	11.2585i	0.137391	+	0.661120i
$291$		0			0
$292$	0.485103	+	0.215982i	0.0283885	+	0.0126394i
$293$	−11.8547	−	20.5330i	−0.692561	−	1.19955i	−0.970996	−	0.239096i	$-0.923149\pi$
$293$	−11.8547	−	20.5330i	−0.692561	−	1.19955i	0.278435	−	0.960455i	$-0.410184\pi$
$294$		0			0
$295$	11.5145	+	1.26311i	0.670400	+	0.0735411i
$296$	−0.0594568	−	0.0431979i	−0.00345586	−	0.00251083i
$297$		0			0
$298$	−7.62869	+	23.4787i	−0.441918	+	1.36008i
$299$	−4.27476	+	7.40411i	−0.247216	+	0.428190i
$300$		0			0
$301$	0.424198	+	0.734732i	0.0244504	+	0.0423493i
$302$	−24.8537	+	5.28282i	−1.43017	+	0.303992i
$303$		0			0
$304$	−16.6636	+	7.41911i	−0.955722	+	0.425515i
$305$	−3.51928	+	16.1950i	−0.201513	+	0.927321i
$306$		0			0
$307$	−12.6269			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$307$	−12.6269			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$308$	0.0551071	+	0.524309i	0.00314002	+	0.0298753i
$309$		0			0
$310$	13.6651	−	18.6300i	0.776128	−	1.05811i
$311$	−13.8540	+	2.94477i	−0.785590	+	0.166982i	−0.583207	−	0.812324i	$-0.698202\pi$
$311$	−13.8540	+	2.94477i	−0.785590	+	0.166982i	−0.202384	+	0.979306i	$0.564869\pi$
$312$		0			0
$313$	−2.73979	−	0.582360i	−0.154862	−	0.0329169i	0.129828	−	0.991537i	$-0.458557\pi$
$313$	−2.73979	−	0.582360i	−0.154862	−	0.0329169i	−0.284690	+	0.958620i	$0.591891\pi$
$314$	−5.14446	+	15.8330i	−0.290319	+	0.893509i
$315$		0			0
$316$	2.03512	+	6.26345i	0.114484	+	0.352347i
$317$	3.11752	+	29.6613i	0.175098	+	1.66594i	0.630902	+	0.775862i	$0.282685\pi$
$317$	3.11752	+	29.6613i	0.175098	+	1.66594i	−0.455805	+	0.890080i	$0.650649\pi$
$318$		0			0
$319$	−11.3922	−	5.07212i	−0.637839	−	0.283984i
$320$	−18.7025	+	5.98305i	−1.04550	+	0.334463i
$321$		0			0
$322$	0.449545	−	0.200150i	0.0250522	−	0.0111539i
$323$	2.20674	−	6.79164i	0.122786	−	0.377897i
$324$		0			0
$325$	16.0627	+	28.4142i	0.890998	+	1.57614i
$326$	−0.366993	+	0.635650i	−0.0203259	+	0.0352054i
$327$		0			0
$328$	1.47225	−	14.0075i	0.0812916	−	0.773437i
$329$	0.171742	−	1.63402i	0.00946844	−	0.0900862i
$330$		0			0
$331$	2.12974	+	20.2631i	0.117061	+	1.11376i	0.882519	+	0.470277i	$0.155846\pi$
$331$	2.12974	+	20.2631i	0.117061	+	1.11376i	−0.765458	+	0.643486i	$0.777487\pi$
$332$	−5.75281			−0.315726
$333$		0			0
$334$	−1.98949	−	6.12301i	−0.108860	−	0.335036i
$335$	1.13398	+	5.45665i	0.0619557	+	0.298129i
$336$		0			0
$337$	17.7807	−	19.7475i	0.968576	−	1.07571i	−0.0285223	−	0.999593i	$-0.509080\pi$
$337$	17.7807	−	19.7475i	0.968576	−	1.07571i	0.997099	−	0.0761198i	$-0.0242532\pi$
$338$	−23.6255	+	26.2388i	−1.28506	+	1.42720i
$339$		0			0
$340$	0.521967	−	1.15818i	0.0283077	−	0.0628109i
$341$	7.74271	+	23.8296i	0.419291	+	1.29045i
$342$		0			0
$343$	4.38089			0.236546
$344$	−0.865065	−	8.23054i	−0.0466412	−	0.443761i
$345$		0			0
$346$	0.0453252	−	0.431241i	0.00243670	−	0.0231837i
$347$	2.14059	−	20.3664i	0.114913	−	1.09332i	−0.773347	−	0.633983i	$-0.781419\pi$
$347$	2.14059	−	20.3664i	0.114913	−	1.09332i	0.888260	−	0.459341i	$-0.151914\pi$
$348$		0			0
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	−0.778317	−	0.627872i	$-0.783926\pi$
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	0.932911	+	0.360106i	$0.117260\pi$
$350$	0.213335	−	1.86653i	0.0114032	−	0.0997701i
$351$		0			0
$352$	2.82175	−	8.68445i	0.150400	−	0.462883i
$353$	−12.6340	+	5.62502i	−0.672440	+	0.299390i	−0.714408	−	0.699729i	$-0.753304\pi$
$353$	−12.6340	+	5.62502i	−0.672440	+	0.299390i	0.0419678	+	0.999119i	$0.486637\pi$
$354$		0			0
$355$	−0.120935	+	26.6338i	−0.00641857	+	1.41357i
$356$	6.47817	+	2.88427i	0.343342	+	0.152866i
$357$		0			0
$358$	1.89245	+	18.0055i	0.100019	+	0.951618i
$359$	−0.158269	−	0.487102i	−0.00835313	−	0.0257083i	0.946793	−	0.321843i	$-0.104302\pi$
$359$	−0.158269	−	0.487102i	−0.00835313	−	0.0257083i	−0.955146	+	0.296135i	$0.904302\pi$
$360$		0			0
$361$	10.4747	−	32.2377i	0.551299	−	1.69672i
$362$	−0.0666870	−	0.0141748i	−0.00350499	−	0.000745008i
$363$		0			0
$364$	−1.16440	+	0.247501i	−0.0610311	+	0.0129726i
$365$	1.95453	−	0.625268i	0.102305	−	0.0327280i
$366$		0			0
$367$	2.04367	+	19.4442i	0.106679	+	1.01498i	0.908633	+	0.417595i	$0.137127\pi$
$367$	2.04367	+	19.4442i	0.106679	+	1.01498i	−0.801955	+	0.597385i	$0.796207\pi$
$368$	−3.28461			−0.171222
$369$		0			0
$370$	−0.0634103	+	0.00637373i	−0.00329655	+	0.000331354i
$371$	1.22458	−	0.545220i	0.0635773	−	0.0283064i
$372$		0			0
$373$	−24.2570	+	5.15599i	−1.25598	+	0.266967i	−0.787394	−	0.616450i	$-0.788570\pi$
$373$	−24.2570	+	5.15599i	−1.25598	+	0.266967i	−0.468587	+	0.883417i	$0.655237\pi$
$374$	−1.69214	−	2.93088i	−0.0874987	−	0.151552i
$375$		0			0
$376$	−8.01359	+	13.8800i	−0.413270	+	0.715804i
$377$	8.70129	−	26.7798i	0.448139	−	1.37923i
$378$		0			0
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	0.904734	−	0.425977i	$-0.140070\pi$
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	−0.125550	+	0.992087i	$0.540070\pi$
$380$	3.86637	−	8.57897i	0.198341	−	0.440092i
$381$		0			0
$382$	−1.42861	−	2.47442i	−0.0730938	−	0.126602i
$383$	−5.00833	−	2.22985i	−0.255914	−	0.113940i	0.274770	−	0.961510i	$-0.411398\pi$
$383$	−5.00833	−	2.22985i	−0.255914	−	0.113940i	−0.530684	+	0.847570i	$0.678065\pi$
$384$		0			0
$385$	1.50785	+	1.37013i	0.0768473	+	0.0698280i
$386$	2.17198	−	6.68468i	0.110551	−	0.340241i
$387$		0			0
$388$	1.32184	+	4.06819i	0.0671061	+	0.206531i
$389$	1.04925	+	1.16531i	0.0531990	+	0.0590835i	0.769157	−	0.639060i	$-0.220676\pi$
$389$	1.04925	+	1.16531i	0.0531990	+	0.0590835i	−0.715958	+	0.698143i	$0.754010\pi$
$390$		0			0
$391$	0.860448	−	0.955625i	0.0435148	−	0.0483280i
$392$	−19.3805	−	8.62874i	−0.978861	−	0.435817i
$393$		0			0
$394$	−1.97840	−	18.8232i	−0.0996704	−	0.948300i
$395$	21.9831	+	12.8254i	1.10609	+	0.645317i
$396$		0			0
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	0.766742	−	0.641955i	$-0.221876\pi$
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	−0.373599	+	0.927590i	$0.621876\pi$
$398$	−3.67768	−	4.08447i	−0.184345	−	0.204736i
$399$		0			0
$400$	−6.36831	+	10.8025i	−0.318415	+	0.540124i
$401$	0.505309	+	0.875221i	0.0252339	+	0.0437064i	0.878367	−	0.477988i	$-0.158634\pi$
$401$	0.505309	+	0.875221i	0.0252339	+	0.0437064i	−0.853133	+	0.521694i	$0.825300\pi$
$402$		0			0
$403$	−51.6851	+	23.0117i	−2.57462	+	1.14629i
$404$	−5.40443	−	3.92655i	−0.268880	−	0.195353i
$405$		0			0
$406$	−1.31117	+	0.952622i	−0.0650724	+	0.0472779i
$407$	0.0345565	−	0.0598535i	0.00171290	−	0.00296683i
$408$		0			0
$409$	5.36444	−	5.95782i	0.265255	−	0.294595i	−0.595773	−	0.803153i	$-0.703154\pi$
$409$	5.36444	−	5.95782i	0.265255	−	0.294595i	0.861028	+	0.508557i	$0.169821\pi$
$410$	−7.13408	−	9.91357i	−0.352327	−	0.489596i
$411$		0			0
$412$	−9.26377	−	1.96908i	−0.456393	−	0.0970094i
$413$	0.504507	+	1.55271i	0.0248251	+	0.0764040i
$414$		0			0
$415$	−16.5889	+	14.8009i	−0.814316	+	0.726546i
$416$	20.1681	+	4.28687i	0.988823	+	0.210181i
$417$		0			0
$418$	−12.5342	−	21.7099i	−0.613070	−	1.06187i
$419$	−22.8670	−	10.1810i	−1.11713	−	0.497377i	−0.236711	−	0.971580i	$-0.576069\pi$
$419$	−22.8670	−	10.1810i	−1.11713	−	0.497377i	−0.880415	+	0.474204i	$0.842736\pi$
$420$		0			0
$421$	30.1379	−	13.4182i	1.46883	−	0.653965i	0.492512	−	0.870305i	$-0.336079\pi$
$421$	30.1379	−	13.4182i	1.46883	−	0.653965i	0.976318	+	0.216340i	$0.0694120\pi$
$422$	0.142826	+	0.103769i	0.00695265	+	0.00505140i
$423$		0			0
$424$	−13.0760			−0.635026
$425$	−1.47461	−	4.68265i	−0.0715291	−	0.227142i
$426$		0			0
$427$	−2.28479	+	0.485646i	−0.110569	+	0.0235021i
$428$	0.614562	−	5.84717i	0.0297060	−	0.282633i
$429$		0			0
$430$	−5.31132	−	4.82618i	−0.256135	−	0.232739i
$431$	−4.71468	+	3.42542i	−0.227098	+	0.164997i	−0.695516	−	0.718511i	$-0.744824\pi$
$431$	−4.71468	+	3.42542i	−0.227098	+	0.164997i	0.468418	+	0.883507i	$0.344824\pi$
$432$		0			0
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	−0.627567	−	0.778563i	$-0.715949\pi$
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	0.546529	+	0.837440i	$0.315949\pi$
$434$	3.18523	+	0.677041i	0.152896	+	0.0324990i
$435$		0			0
$436$	6.27131	−	1.33301i	0.300341	−	0.0638395i
$437$	6.37361	−	7.07861i	0.304891	−	0.338616i
$438$		0			0
$439$	15.2474	+	16.9340i	0.727721	+	0.808216i	0.987528	−	0.157445i	$-0.0503256\pi$
$439$	15.2474	+	16.9340i	0.727721	+	0.808216i	−0.259807	+	0.965661i	$0.583659\pi$
$440$	−8.00095	−	18.1923i	−0.381430	−	0.867284i
$441$		0			0
$442$	6.18230	−	4.49170i	0.294062	−	0.213648i
$443$	−4.50211	+	7.79787i	−0.213901	+	0.370488i	−0.952932	−	0.303184i	$-0.901950\pi$
$443$	−4.50211	+	7.79787i	−0.213901	+	0.370488i	0.739031	+	0.673672i	$0.235284\pi$
$444$		0			0
$445$	26.1012	−	8.34996i	1.23732	−	0.395826i
$446$	−0.205216	+	1.95250i	−0.00971724	+	0.0924534i
$447$		0			0
$448$	−1.85187	−	2.05671i	−0.0874925	−	0.0971702i
$449$	2.14345			0.101156			0.0505779	−	0.998720i	$-0.483894\pi$
$449$	2.14345			0.101156			0.0505779	+	0.998720i	$0.483894\pi$
$450$		0			0
$451$	13.2453			0.623698
$452$	−5.67902	−	6.30719i	−0.267118	−	0.296665i
$453$		0			0
$454$	0.456397	−	4.34233i	0.0214198	−	0.203795i
$455$	−2.72091	+	3.70947i	−0.127558	+	0.173903i
$456$		0			0
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	−0.541208	−	0.840889i	$-0.682033\pi$
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	0.998835	+	0.0482552i	$0.0153661\pi$
$458$	−0.816594	+	0.593290i	−0.0381569	+	0.0277226i
$459$		0			0
$460$	1.26437	−	1.12809i	0.0589516	−	0.0525976i
$461$	2.55207	+	2.83436i	0.118862	+	0.132009i	0.799639	−	0.600482i	$-0.205024\pi$
$461$	2.55207	+	2.83436i	0.118862	+	0.132009i	−0.680777	+	0.732491i	$0.738358\pi$
$462$		0			0
$463$	6.05576	−	6.72560i	0.281435	−	0.312565i	−0.585808	−	0.810450i	$-0.699223\pi$
$463$	6.05576	−	6.72560i	0.281435	−	0.312565i	0.867243	+	0.497884i	$0.165890\pi$
$464$	10.5815	−	2.24917i	0.491234	−	0.104415i
$465$		0			0
$466$	13.0355	+	2.77079i	0.603860	+	0.128354i
$467$	−24.8972	+	18.0889i	−1.15211	+	0.837053i	−0.988759	−	0.149515i	$-0.952229\pi$
$467$	−24.8972	+	18.0889i	−1.15211	+	0.837053i	−0.163346	+	0.986569i	$0.552229\pi$
$468$		0			0
$469$	−0.635487	+	0.461708i	−0.0293441	+	0.0213197i
$470$	2.82782	+	13.6074i	0.130438	+	0.627662i
$471$		0			0
$472$	1.66469	−	15.8385i	0.0766238	−	0.729027i
$473$	7.61260	−	1.61811i	0.350028	−	0.0744007i
$474$		0			0
$475$	−10.9229	−	34.6859i	−0.501177	−	1.59150i
$476$	0.179048			0.00820666
$477$		0			0
$478$	15.7550	+	11.4467i	0.720617	+	0.523559i
$479$	−11.2505	+	5.00905i	−0.514049	+	0.228870i	−0.647331	−	0.762209i	$-0.724115\pi$
$479$	−11.2505	+	5.00905i	−0.514049	+	0.228870i	0.133282	+	0.991078i	$0.457448\pi$
$480$		0			0
$481$	0.142565	+	0.0634742i	0.00650042	+	0.00289417i
$482$	1.24920	+	2.16367i	0.0568993	+	0.0985524i
$483$		0			0
$484$	−1.49516	−	0.317806i	−0.0679618	−	0.0144457i
$485$	14.2783	+	8.33027i	0.648346	+	0.378258i
$486$		0			0
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	0.979784	−	0.200056i	$-0.0641125\pi$
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	−0.910252	+	0.414054i	$0.864113\pi$
$488$	22.2875	+	4.73735i	1.00891	+	0.214450i
$489$		0			0
$490$	−17.5216	+	5.60530i	−0.791547	+	0.253221i
$491$	12.7546	−	14.1654i	0.575605	−	0.639274i	−0.383090	−	0.923711i	$-0.625140\pi$
$491$	12.7546	−	14.1654i	0.575605	−	0.639274i	0.958695	+	0.284437i	$0.0918066\pi$
$492$		0			0
$493$	−2.11760	+	3.66778i	−0.0953718	+	0.165189i
$494$	45.7942	−	33.2714i	2.06038	−	1.49695i
$495$		0			0
$496$	−17.5847	−	12.7760i	−0.789576	−	0.573660i
$497$	−3.42933	+	1.52684i	−0.153827	+	0.0684880i
$498$		0			0
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	0.804380	−	0.594115i	$-0.202497\pi$
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	−0.916709	+	0.399557i	$0.869164\pi$
$500$	−1.25868	−	6.34547i	−0.0562900	−	0.283778i
$501$		0			0
$502$	−12.6582	−	14.0583i	−0.564962	−	0.627453i
$503$	5.48055	+	3.98186i	0.244366	+	0.177542i	0.703226	−	0.710966i	$-0.251742\pi$
$503$	5.48055	+	3.98186i	0.244366	+	0.177542i	−0.458860	+	0.888508i	$0.651742\pi$
$504$		0			0
$505$	−25.6865	+	2.58190i	−1.14304	+	0.114893i
$506$	−0.471854	−	4.48939i	−0.0209765	−	0.199578i
$507$		0			0
$508$	−8.13615	−	3.62245i	−0.360983	−	0.160720i
$509$	6.65406	−	7.39008i	0.294936	−	0.327559i	−0.577405	−	0.816458i	$-0.695935\pi$
$509$	6.65406	−	7.39008i	0.294936	−	0.327559i	0.872341	+	0.488899i	$0.162601\pi$
$510$		0			0
$511$	0.193532	+	0.214939i	0.00856136	+	0.00950835i
$512$	7.21302	+	22.1994i	0.318774	+	0.981084i
$513$		0			0
$514$	0.808743	−	2.48906i	0.0356721	−	0.109788i
$515$	−31.7792	+	18.1558i	−1.40036	+	0.800041i
$516$		0			0
$517$	−13.7690	−	6.13035i	−0.605560	−	0.269613i
$518$	−0.00449112	−	0.00777885i	−0.000197329	−	0.000341783i
$519$		0			0
$520$	38.9648	−	22.2611i	1.70872	−	0.976212i
$521$	−15.4969	−	11.2591i	−0.678930	−	0.493272i	0.194072	−	0.980987i	$-0.437830\pi$
$521$	−15.4969	−	11.2591i	−0.678930	−	0.493272i	−0.873003	+	0.487715i	$0.837830\pi$
$522$		0			0
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	−0.949272	−	0.314455i	$-0.898178\pi$
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	0.952809	+	0.303569i	$0.0981783\pi$
$524$	−0.965764	+	1.67275i	−0.0421896	+	0.0730745i
$525$		0			0
$526$	17.6822	+	30.6265i	0.770980	+	1.33538i
$527$	8.32361	−	1.76924i	0.362582	−	0.0770692i
$528$		0			0
$529$	−19.4446	+	8.65730i	−0.845418	+	0.376404i
$530$	−8.46084	+	7.54890i	−0.367516	+	0.327903i
$531$		0			0
$532$	1.32626			0.0575009
$533$	3.12624	+	29.7442i	0.135412	+	1.28836i
$534$		0			0
$535$	−13.2715	−	18.4421i	−0.573775	−	0.797322i
$536$	7.49495	−	1.59310i	0.323733	−	0.0688115i
$537$		0			0
$538$	−29.5128	−	6.27313i	−1.27239	−	0.270454i
$539$	6.16497	−	18.9738i	0.265544	−	0.817261i
$540$		0			0
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	0.990928	+	0.134394i	$0.0429087\pi$
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	−0.722683	+	0.691180i	$0.757091\pi$
$542$	2.34450	+	22.3064i	0.100705	+	0.958143i
$543$		0			0
$544$	−2.83311	−	1.26138i	−0.121468	−	0.0540813i
$545$	14.6545	−	19.9787i	0.627729	−	0.855795i
$546$		0			0
$547$	−6.86422	+	3.05615i	−0.293493	+	0.130671i	−0.548201	−	0.836346i	$-0.684687\pi$
$547$	−6.86422	+	3.05615i	−0.293493	+	0.130671i	0.254708	+	0.967018i	$0.418021\pi$
$548$	−1.51006	+	4.64750i	−0.0645067	+	0.198531i
$549$		0			0
$550$	−15.6796	−	7.15234i	−0.668582	−	0.304977i
$551$	−15.6857	+	27.1684i	−0.668233	+	1.15741i
$552$		0			0
$553$	−0.374956	+	3.56747i	−0.0159447	+	0.151704i
$554$	2.82076	−	26.8378i	0.119843	−	1.14023i
$555$		0			0
$556$	−0.0865112	−	0.823099i	−0.00366889	−	0.0349072i
$557$	−17.2753			−0.731980			−0.365990	−	0.930619i	$-0.619270\pi$
$557$	−17.2753			−0.731980			−0.365990	+	0.930619i	$0.619270\pi$
$558$		0			0
$559$	5.43045	+	16.7132i	0.229684	+	0.706894i
$560$	−1.75686	−	0.192723i	−0.0742411	−	0.00814404i
$561$		0			0
$562$	−0.748054	+	0.830798i	−0.0315548	+	0.0350451i
$563$	−1.80844	+	2.00848i	−0.0762167	+	0.0846473i	−0.780047	−	0.625721i	$-0.784805\pi$
$563$	−1.80844	+	2.00848i	−0.0762167	+	0.0846473i	0.703830	+	0.710368i	$0.251472\pi$
$564$		0			0
$565$	−32.6033	−	3.57649i	−1.37163	−	0.150464i
$566$	−4.27172	−	13.1470i	−0.179554	−	0.552610i
$567$		0			0
$568$	36.6180			1.53646
$569$	−4.46837	−	42.5137i	−0.187324	−	1.78227i	−0.535201	−	0.844725i	$-0.679764\pi$
$569$	−4.46837	−	42.5137i	−0.187324	−	1.78227i	0.347877	−	0.937540i	$-0.386903\pi$
$570$		0			0
$571$	−3.16839	+	30.1452i	−0.132593	+	1.26154i	0.702601	+	0.711584i	$0.252022\pi$
$571$	−3.16839	+	30.1452i	−0.132593	+	1.26154i	−0.835194	+	0.549955i	$0.814645\pi$
$572$	−1.14147	+	10.8603i	−0.0477271	+	0.454093i
$573$		0			0
$574$	0.860713	−	1.49080i	0.0359255	−	0.0622247i
$575$	0.743598	−	6.50596i	0.0310102	−	0.271317i
$576$		0			0
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	−0.329790	−	0.944054i	$-0.606978\pi$
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	0.821707	−	0.569910i	$-0.193022\pi$
$578$	17.4655	−	7.77613i	0.726468	−	0.323444i
$579$		0			0
$580$	−3.30075	+	4.49999i	−0.137056	+	0.186852i
$581$	−2.86252	−	1.27448i	−0.118757	−	0.0528741i
$582$		0			0
$583$	−1.28536	−	12.2294i	−0.0532340	−	0.506488i
$584$	−0.871846	−	2.68327i	−0.0360773	−	0.111034i
$585$		0			0
$586$	−8.73494	+	26.8834i	−0.360837	+	1.11054i
$587$	18.3047	+	3.89078i	0.755515	+	0.160590i	0.569539	−	0.821964i	$-0.307122\pi$
$587$	18.3047	+	3.89078i	0.755515	+	0.160590i	0.185976	+	0.982554i	$0.440455\pi$
$588$		0			0
$589$	61.6556	−	13.1053i	2.54047	−	0.539994i
$590$	−8.06659	−	11.2094i	−0.332096	−	0.461484i
$591$		0			0
$592$	0.00626701	+	0.0596266i	0.000257572	+	0.00245064i
$593$	42.4830			1.74457			0.872284	−	0.489000i	$-0.162638\pi$
$593$	42.4830			1.74457			0.872284	+	0.489000i	$0.162638\pi$
$594$		0			0
$595$	0.516306	−	0.460656i	0.0211665	−	0.0188851i
$596$	−10.9454	+	4.87320i	−0.448340	+	0.199614i
$597$		0			0
$598$	9.97017	−	2.11922i	0.407710	−	0.0866615i
$599$	22.9566	+	39.7621i	0.937983	+	1.62463i	0.769226	+	0.638977i	$0.220642\pi$
$599$	22.9566	+	39.7621i	0.937983	+	1.62463i	0.168757	+	0.985658i	$0.446025\pi$
$600$		0			0
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	−0.432978	−	0.901404i	$-0.642537\pi$
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	0.997128	−	0.0757320i	$-0.0241293\pi$
$602$	0.312563	−	0.961968i	0.0127391	−	0.0392069i
$603$		0			0
$604$	−9.97648	−	7.24834i	−0.405937	−	0.294931i
$605$	−5.12911	+	2.93032i	−0.208528	+	0.119135i
$606$		0			0
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	0.664086	−	0.747656i	$-0.268821\pi$
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	−0.979532	+	0.201287i	$0.935488\pi$
$608$	−20.9857	−	9.34344i	−0.851083	−	0.378926i
$609$		0			0
$610$	17.1561	−	9.80148i	0.694630	−	0.396850i
$611$	10.5167	−	32.3671i	0.425460	−	1.30943i
$612$		0			0
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	−0.766996	−	0.641652i	$-0.778249\pi$
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	0.243359	−	0.969936i	$-0.421751\pi$
$614$	10.0731	+	11.1873i	0.406516	+	0.451482i
$615$		0			0
$616$	1.87429	−	2.08161i	0.0755174	−	0.0838706i
$617$	8.46425	+	3.76852i	0.340758	+	0.151715i	0.569979	−	0.821659i	$-0.306951\pi$
$617$	8.46425	+	3.76852i	0.340758	+	0.151715i	−0.229221	+	0.973374i	$0.573618\pi$
$618$		0			0
$619$	−1.08260	−	10.3002i	−0.0435132	−	0.414001i	−0.994497	−	0.104761i	$-0.966592\pi$
$619$	−1.08260	−	10.3002i	−0.0435132	−	0.414001i	0.950984	−	0.309240i	$-0.100074\pi$
$620$	11.1569	−	1.12144i	0.448073	−	0.0450383i
$621$		0			0
$622$	13.6611	+	9.92537i	0.547760	+	0.397971i
$623$	2.58447	+	2.87034i	0.103545	+	0.114998i
$624$		0			0
$625$	−19.9552	−	15.0595i	−0.798208	−	0.602381i
$626$	1.66970	+	2.89201i	0.0667347	+	0.115588i
$627$		0			0
$628$	−7.38109	+	3.28627i	−0.294537	+	0.131136i
$629$	−0.0189895	−	0.0137967i	−0.000757161	−	0.000550110i
$630$		0			0
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.187960	−	0.982177i	$-0.439813\pi$
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.992188	+	0.124749i	$0.0398126\pi$
$632$	17.4957	−	30.3034i	0.695941	−	1.20541i
$633$		0			0
$634$	23.7926	−	26.4244i	0.944925	−	1.04945i
$635$	−32.7814	+	10.4870i	−1.30089	+	0.416163i
$636$		0			0
$637$	44.0634	+	9.36597i	1.74586	+	0.371093i
$638$	4.59425	+	14.1397i	0.181888	+	0.559794i
$639$		0			0
$640$	8.02026	+	4.67918i	0.317029	+	0.184961i
$641$	−25.7650	−	5.47651i	−1.01766	−	0.216309i	−0.331261	−	0.943539i	$-0.607474\pi$
$641$	−25.7650	−	5.47651i	−1.01766	−	0.216309i	−0.686394	+	0.727230i	$0.740807\pi$
$642$		0			0
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.722651	+	0.691213i	$0.242923\pi$
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.237282	+	0.971441i	$0.423743\pi$
$644$	0.218175	+	0.0971380i	0.00859732	+	0.00382777i
$645$		0			0
$646$	−7.77776	+	3.46288i	−0.306012	+	0.136245i
$647$	−10.6167	−	7.71348i	−0.417386	−	0.303248i	0.359199	−	0.933261i	$-0.383050\pi$
$647$	−10.6167	−	7.71348i	−0.417386	−	0.303248i	−0.776585	+	0.630012i	$0.783050\pi$
$648$		0			0
$649$	14.9767			0.587885
$650$	12.3607	−	36.8989i	0.484828	−	1.44729i
$651$		0			0
$652$	−0.348437	+	0.0740627i	−0.0136459	+	0.00290052i
$653$	−5.05266	+	48.0729i	−0.197726	+	1.88124i	0.224109	+	0.974564i	$0.428053\pi$
$653$	−5.05266	+	48.0729i	−0.197726	+	1.88124i	−0.421835	+	0.906673i	$0.638614\pi$
$654$		0			0
$655$	1.51878	+	7.30830i	0.0593435	+	0.285559i
$656$	−9.29580	+	6.75379i	−0.362940	+	0.263691i
$657$		0			0
$658$	−1.58473	+	1.15137i	−0.0617792	+	0.0448853i
$659$	29.3437	+	6.23721i	1.14307	+	0.242967i	0.740263	−	0.672318i	$-0.234701\pi$
$659$	29.3437	+	6.23721i	1.14307	+	0.242967i	0.402807	+	0.915285i	$0.368034\pi$
$660$		0			0
$661$	−11.7271	+	2.49266i	−0.456130	+	0.0969533i	−0.430246	−	0.902712i	$-0.641573\pi$
$661$	−11.7271	+	2.49266i	−0.456130	+	0.0969533i	−0.0258835	+	0.999665i	$0.508240\pi$
$662$	16.2540	−	18.0519i	0.631729	−	0.701606i
$663$		0			0
$664$	20.4524	+	22.7147i	0.793707	+	0.881501i
$665$	3.82444	−	3.41222i	0.148305	−	0.132320i
$666$		0			0
$667$	−4.57022	+	3.32046i	−0.176959	+	0.128569i
$668$	1.56229	−	2.70596i	0.0604468	−	0.104697i
$669$		0			0
$670$	3.92992	−	5.35774i	0.151826	−	0.206987i
$671$	−2.23978	+	21.3101i	−0.0864659	+	0.822668i
$672$		0			0
$673$	−17.3708	−	19.2922i	−0.669593	−	0.743659i	0.308637	−	0.951180i	$-0.400127\pi$
$673$	−17.3708	−	19.2922i	−0.669593	−	0.743659i	−0.978231	+	0.207521i	$0.933460\pi$
$674$	−31.6806			−1.22029
$675$		0			0
$676$	−17.1357			−0.659067
$677$	−26.3010	−	29.2103i	−1.01083	−	1.12264i	−0.992430	−	0.122810i	$-0.960809\pi$
$677$	−26.3010	−	29.2103i	−1.01083	−	1.12264i	−0.0184004	−	0.999831i	$-0.505857\pi$
$678$		0			0
$679$	−0.243539	+	2.31712i	−0.00934616	+	0.0889227i
$680$	−6.42871	+	2.05659i	−0.246530	+	0.0788666i
$681$		0			0
$682$	14.9361	−	25.8700i	0.571932	−	0.990615i
$683$	26.3578	−	19.1501i	1.00855	−	0.732757i	0.0446482	−	0.999003i	$-0.485783\pi$
$683$	26.3578	−	19.1501i	1.00855	−	0.732757i	0.963905	+	0.266246i	$0.0857833\pi$
$684$		0			0
$685$	7.60267	+	17.2867i	0.290483	+	0.660491i
$686$	−3.49486	−	3.88143i	−0.133434	−	0.148194i
$687$		0			0
$688$	−4.51758	+	5.01729i	−0.172231	+	0.191282i
$689$	27.1593	−	5.77288i	1.03469	−	0.219929i
$690$		0			0
$691$	−32.6488	−	6.93971i	−1.24202	−	0.263999i	−0.460375	−	0.887725i	$-0.652285\pi$
$691$	−32.6488	−	6.93971i	−1.24202	−	0.263999i	−0.781643	+	0.623726i	$0.785618\pi$
$692$	0.170254	−	0.123696i	0.00647207	−	0.00470223i
$693$		0			0
$694$	−19.7521	+	14.3507i	−0.749779	+	0.544746i
$695$	−2.36714	−	2.15092i	−0.0897907	−	0.0815892i
$696$		0			0
$697$	0.470212	−	4.47377i	0.0178106	−	0.169456i
$698$	−6.73592	+	1.43176i	−0.254958	+	0.0541931i
$699$		0			0
$700$	0.742475	−	0.529205i	0.0280629	−	0.0200021i
$701$	47.0156			1.77575			0.887877	−	0.460081i	$-0.152180\pi$
$701$	47.0156			1.77575			0.887877	+	0.460081i	$0.152180\pi$
$702$		0			0
$703$	−0.140661	−	0.102196i	−0.00530513	−	0.00385441i
$704$	−23.1931	+	10.3262i	−0.874124	+	0.389185i
$705$		0			0
$706$	15.0625	+	6.70626i	0.566885	+	0.252393i
$707$	−1.81928	−	3.15109i	−0.0684211	−	0.118509i
$708$		0			0
$709$	2.86671	+	0.609338i	0.107661	+	0.0228842i	0.261427	−	0.965223i	$-0.415807\pi$
$709$	2.86671	+	0.609338i	0.107661	+	0.0228842i	−0.153766	+	0.988107i	$0.549140\pi$
$710$	23.6938	−	21.1400i	0.889212	−	0.793369i
$711$		0			0
$712$	−11.6428	−	35.8329i	−0.436333	−	1.34289i
$713$	11.1024	+	2.35989i	0.415789	+	0.0883786i
$714$		0			0
$715$	24.6499	+	34.2537i	0.921855	+	1.28102i
$716$	−5.87941	+	6.52975i	−0.219724	+	0.244028i
$717$		0			0
$718$	−0.305309	+	0.528811i	−0.0113940	+	0.0197351i
$719$	−13.9385	+	10.1269i	−0.519820	+	0.377671i	−0.816536	−	0.577295i	$-0.804108\pi$
$719$	−13.9385	+	10.1269i	−0.519820	+	0.377671i	0.296716	+	0.954966i	$0.404108\pi$
$720$		0			0
$721$	−4.17330	−	3.03208i	−0.155422	−	0.112920i
$722$	−36.9185	+	16.4372i	−1.37397	+	0.611729i
$723$		0			0
$724$	−0.0165440	−	0.0286550i	−0.000614851	−	0.00106495i
$725$	2.05949	+	21.4684i	0.0764875	+	0.797317i
$726$		0			0
$727$	−0.116229	−	0.129085i	−0.00431069	−	0.00478751i	0.740986	−	0.671521i	$-0.234359\pi$
$727$	−0.116229	−	0.129085i	−0.00431069	−	0.00478751i	−0.745296	+	0.666733i	$0.767692\pi$
$728$	5.11692	+	3.71766i	0.189646	+	0.137786i
$729$		0			0
$730$	−2.11321	−	1.23289i	−0.0782134	−	0.0456313i
$731$	−0.276287	−	2.62869i	−0.0102188	−	0.0972257i
$732$		0			0
$733$	−48.4219	−	21.5588i	−1.78851	−	0.796294i	−0.977401	−	0.211392i	$-0.932200\pi$
$733$	−48.4219	−	21.5588i	−1.78851	−	0.796294i	−0.811104	−	0.584902i	$-0.801133\pi$
$734$	15.5971	−	17.3223i	0.575698	−	0.639378i
$735$		0			0
$736$	−2.76790	−	3.07406i	−0.102026	−	0.113311i
$737$	2.22670	+	6.85308i	0.0820216	+	0.252436i
$738$		0			0
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	−0.972494	−	0.232926i	$-0.925170\pi$
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	0.923675	+	0.383177i	$0.125170\pi$
$740$	−0.0228910	−	0.0208002i	−0.000841491	−	0.000764629i
$741$		0			0
$742$	−1.45997	−	0.650022i	−0.0535973	−	0.0238631i
$743$	15.1680	+	26.2718i	0.556461	+	0.963820i	0.997788	+	0.0664731i	$0.0211746\pi$
$743$	15.1680	+	26.2718i	0.556461	+	0.963820i	−0.441327	+	0.897346i	$0.645492\pi$
$744$		0			0
$745$	−19.0245	+	42.2127i	−0.697002	+	1.54656i
$746$	23.9192	+	17.3783i	0.875745	+	0.636266i
$747$		0			0
$748$	0.507554	−	1.56209i	0.0185580	−	0.0571157i
$749$	1.60118	−	2.77332i	0.0585057	−	0.101335i
$750$		0			0
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	0.999985	+	0.00539081i	$0.00171596\pi$
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	−0.495324	+	0.868708i	$0.664951\pi$
$752$	12.7892	−	2.71843i	0.466374	−	0.0991308i
$753$		0			0
$754$	−30.6681	+	13.6543i	−1.11687	+	0.497262i
$755$	−47.4169	+	4.76614i	−1.72568	+	0.173457i
$756$		0			0
$757$	31.2908			1.13729			0.568643	−	0.822585i	$-0.307469\pi$
$757$	31.2908			1.13729			0.568643	+	0.822585i	$0.307469\pi$
$758$	−2.33664	−	22.2317i	−0.0848707	−	0.807491i
$759$		0			0
$760$	−47.6194	+	15.2338i	−1.72734	+	0.552587i
$761$	−18.0350	+	3.83346i	−0.653769	+	0.138963i	−0.522843	−	0.852429i	$-0.675128\pi$
$761$	−18.0350	+	3.83346i	−0.653769	+	0.138963i	−0.130926	+	0.991392i	$0.541795\pi$
$762$		0			0
$763$	3.41583	+	0.726057i	0.123661	+	0.0262850i
$764$	0.428507	−	1.31881i	0.0155028	−	0.0477128i
$765$		0			0
$766$	2.01977	+	6.21620i	0.0729771	+	0.224601i
$767$	3.53488	+	33.6321i	0.127637	+	1.21438i
$768$		0			0
$769$	−15.0205	−	6.68758i	−0.541655	−	0.241160i	0.117625	−	0.993058i	$-0.462472\pi$
$769$	−15.0205	−	6.68758i	−0.541655	−	0.241160i	−0.659280	+	0.751898i	$0.729139\pi$
$770$	0.0110291	−	2.42896i	0.000397461	−	0.0875337i
$771$		0			0
$772$	3.11629	−	1.38746i	0.112158	−	0.0499358i
$773$	−11.8001	+	36.3171i	−0.424421	+	1.30623i	0.479126	+	0.877746i	$0.340954\pi$
$773$	−11.8001	+	36.3171i	−0.424421	+	1.30623i	−0.903547	+	0.428489i	$0.859046\pi$
$774$		0			0
$775$	29.2870	−	31.9384i	1.05202	−	1.14726i
$776$	11.3637	−	19.6825i	0.407932	−	0.706559i
$777$		0			0
$778$	0.195415	−	1.85925i	0.00700597	−	0.0666573i
$779$	3.48301	−	33.1386i	0.124792	−	1.18731i
$780$		0			0
$781$	3.59952	+	34.2471i	0.128801	+	1.22546i
$782$	−1.53310			−0.0548235
$783$		0			0
$784$	5.34808	+	16.4597i	0.191003	+	0.587846i
$785$	−12.8293	+	28.4664i	−0.457896	+	1.01601i
$786$		0			0
$787$	−8.48025	+	9.41827i	−0.302288	+	0.335725i	−0.875082	−	0.483974i	$-0.839193\pi$
$787$	−8.48025	+	9.41827i	−0.302288	+	0.335725i	0.572794	+	0.819699i	$0.305860\pi$
$788$	6.14644	−	6.82631i	0.218958	−	0.243177i
$789$		0			0
$790$	−6.17385	−	29.7083i	−0.219656	−	1.05698i
$791$	−1.42851	−	4.39650i	−0.0507919	−	0.156321i
$792$		0			0
$793$	−48.3834			−1.71814
$794$	−1.20664	−	11.4805i	−0.0428222	−	0.407426i
$795$		0			0
$796$	0.278824	−	2.65283i	0.00988265	−	0.0940271i
$797$	2.19931	−	20.9250i	0.0779034	−	0.741202i	−0.883940	−	0.467601i	$-0.845119\pi$
$797$	2.19931	−	20.9250i	0.0779034	−	0.741202i	0.961843	−	0.273601i	$-0.0882148\pi$
$798$		0			0
$799$	−2.55941	+	4.43302i	−0.0905452	+	0.156829i
$800$	−15.4765	+	3.14302i	−0.547177	+	0.111122i
$801$		0			0
$802$	0.372328	−	1.14591i	0.0131473	−	0.0404634i
$803$	2.42383	−	1.07916i	0.0855352	−	0.0380827i
$804$		0			0
$805$	0.879051	−	0.281215i	0.0309825	−	0.00991151i
$806$	61.6200	+	27.4350i	2.17047	+	0.966356i
$807$		0			0
$808$	3.71005	+	35.2988i	0.130519	+	1.24181i
$809$	11.6292	+	35.7910i	0.408861	+	1.25834i	0.917628	+	0.397441i	$0.130102\pi$
$809$	11.6292	+	35.7910i	0.408861	+	1.25834i	−0.508767	+	0.860904i	$0.669898\pi$
$810$		0			0
$811$	8.42021	−	25.9147i	0.295673	−	0.909989i	−0.687321	−	0.726354i	$-0.741213\pi$
$811$	8.42021	−	25.9147i	0.295673	−	0.909989i	0.982994	−	0.183636i	$-0.0587866\pi$
$812$	−0.769377	−	0.163536i	−0.0269998	−	0.00573899i
$813$		0			0
$814$	−0.0805971	+	0.0171314i	−0.00282493	+	0.000600457i
$815$	−0.814210	+	1.11003i	−0.0285205	+	0.0388826i
$816$		0			0
$817$	−2.04654	−	19.4715i	−0.0715994	−	0.681223i
$818$	−9.55806			−0.334190
$819$		0			0
$820$	1.25873	−	5.79242i	0.0439568	−	0.202280i
$821$	18.4249	−	8.20330i	0.643034	−	0.286297i	−0.0591972	−	0.998246i	$-0.518854\pi$
$821$	18.4249	−	8.20330i	0.643034	−	0.286297i	0.702231	+	0.711949i	$0.252187\pi$
$822$		0			0
$823$	47.1257	−	10.0169i	1.64270	−	0.349166i	0.708442	−	0.705769i	$-0.249398\pi$
$823$	47.1257	−	10.0169i	1.64270	−	0.349166i	0.934256	+	0.356602i	$0.116065\pi$
$824$	25.1598	+	43.5780i	0.876483	+	1.51811i
$825$		0			0
$826$	0.973219	−	1.68566i	0.0338626	−	0.0586518i
$827$	6.10623	−	18.7930i	0.212334	−	0.653498i	−0.786998	−	0.616956i	$-0.788366\pi$
$827$	6.10623	−	18.7930i	0.212334	−	0.653498i	0.999332	−	0.0365422i	$-0.0116343\pi$
$828$		0			0
$829$	21.1194	+	15.3441i	0.733507	+	0.532924i	0.890671	−	0.454648i	$-0.150235\pi$
$829$	21.1194	+	15.3441i	0.733507	+	0.532924i	−0.157164	+	0.987573i	$0.550235\pi$
$830$	26.3472	+	2.89022i	0.914525	+	0.100321i
$831$		0			0
$832$	−28.6631	−	49.6460i	−0.993716	−	1.72117i
$833$	−6.18979	−	2.75587i	−0.214463	−	0.0954853i
$834$		0			0
$835$	−2.45688	−	11.8224i	−0.0850239	−	0.409132i
$836$	3.75961	−	11.5709i	0.130029	−	0.400188i
$837$		0			0
$838$	9.22184	+	28.3819i	0.318563	+	0.980436i
$839$	1.99630	+	2.21712i	0.0689201	+	0.0765435i	0.776619	−	0.629971i	$-0.216933\pi$
$839$	1.99630	+	2.21712i	0.0689201	+	0.0765435i	−0.707699	+	0.706514i	$0.750267\pi$
$840$		0			0
$841$	−6.95536	+	7.72471i	−0.239840	+	0.266369i
$842$	−35.9310	−	15.9975i	−1.23826	−	0.551310i
$843$		0			0
$844$	0.00895605	+	0.0852111i	0.000308280	+	0.00293309i
$845$	−49.4129	+	44.0869i	−1.69985	+	1.51664i
$846$		0			0
$847$	−0.673564	−	0.489373i	−0.0231439	−	0.0168150i
$848$	7.13783	+	7.92737i	0.245114	+	0.272227i
$849$		0			0
$850$	−2.97242	+	5.04208i	−0.101953	+	0.172942i
$851$	−0.0156542	−	0.0271139i	−0.000536620	−	0.000929453i
$852$		0			0
$853$	24.8916	−	11.0825i	0.852274	−	0.379457i	0.0663620	−	0.997796i	$-0.478861\pi$
$853$	24.8916	−	11.0825i	0.852274	−	0.379457i	0.785911	+	0.618339i	$0.212194\pi$
$854$	2.25297	+	1.63688i	0.0770950	+	0.0560128i
$855$		0			0
$856$	−25.2722	+	18.3613i	−0.863784	+	0.627576i
$857$	25.6908	−	44.4978i	0.877582	−	1.52002i	0.0235962	−	0.999722i	$-0.492488\pi$
$857$	25.6908	−	44.4978i	0.877582	−	1.52002i	0.853986	−	0.520296i	$-0.174178\pi$
$858$		0			0
$859$	32.3856	−	35.9678i	1.10498	−	1.22721i	0.133259	−	0.991081i	$-0.457456\pi$
$859$	32.3856	−	35.9678i	1.10498	−	1.22721i	0.971723	−	0.236125i	$-0.0758774\pi$
$860$	0.0158147	−	3.48290i	0.000539276	−	0.118766i
$861$		0			0
$862$	6.79603	+	1.44454i	0.231474	+	0.0492012i
$863$	−0.728582	−	2.24234i	−0.0248012	−	0.0763303i	0.937890	−	0.346933i	$-0.112777\pi$
$863$	−0.728582	−	2.24234i	−0.0248012	−	0.0763303i	−0.962691	+	0.270603i	$0.912777\pi$
$864$		0			0
$865$	0.172699	−	0.794722i	0.00587193	−	0.0270214i
$866$	2.43072	+	0.516667i	0.0825994	+	0.0175570i
$867$		0			0
$868$	0.790204	+	1.36867i	0.0268213	+	0.0464558i
$869$	30.0612	+	13.3841i	1.01976	+	0.454025i
$870$		0			0
$871$	−14.8640	+	6.61786i	−0.503646	+	0.224238i
$872$	−27.5591	−	20.0229i	−0.933269	−	0.678060i
$873$		0			0
$874$	−11.3561			−0.384127
$875$	0.779469	−	3.43626i	0.0263509	−	0.116167i
$876$		0			0
$877$	−26.8040	+	5.69737i	−0.905107	+	0.192386i	−0.636874	−	0.770968i	$-0.719773\pi$
$877$	−26.8040	+	5.69737i	−0.905107	+	0.192386i	−0.268233	+	0.963354i	$0.586440\pi$
$878$	2.83973	−	27.0182i	0.0958362	−	0.911821i
$879$		0			0
$880$	−6.66165	+	14.7813i	−0.224564	+	0.498278i
$881$	34.8348	−	25.3090i	1.17362	−	0.852682i	0.182179	−	0.983265i	$-0.441685\pi$
$881$	34.8348	−	25.3090i	1.17362	−	0.852682i	0.991437	+	0.130584i	$0.0416851\pi$
$882$		0			0
$883$	11.2465	−	8.17107i	0.378475	−	0.274979i	−0.382241	−	0.924063i	$-0.624848\pi$
$883$	11.2465	−	8.17107i	0.378475	−	0.274979i	0.760717	+	0.649084i	$0.224848\pi$
$884$	3.62768	+	0.771088i	0.122012	+	0.0259345i
$885$		0			0
$886$	10.5004	−	2.23193i	0.352768	−	0.0749832i
$887$	3.84956	−	4.27536i	0.129255	−	0.143553i	−0.675043	−	0.737779i	$-0.735875\pi$
$887$	3.84956	−	4.27536i	0.129255	−	0.143553i	0.804298	+	0.594226i	$0.202541\pi$
$888$		0			0
$889$	−3.24592	−	3.60496i	−0.108865	−	0.120906i
$890$	−28.2202	−	16.4643i	−0.945944	−	0.551883i
$891$		0			0
$892$	−0.770844	+	0.560051i	−0.0258098	+	0.0187519i
$893$	−18.9583	+	32.8368i	−0.634416	+	1.09884i
$894$		0			0
$895$	−0.154182	+	33.9558i	−0.00515374	+	1.13502i
$896$	−0.136798	+	1.30154i	−0.00457009	+	0.0434815i
$897$		0			0
$898$	−1.70994	−	1.89908i	−0.0570614	−	0.0633731i
$899$	−37.3829			−1.24679
$900$		0			0
$901$	−4.17624			−0.139131
$902$	−10.5665	−	11.7352i	−0.351825	−	0.390741i
$903$		0			0
$904$	−4.71357	+	44.8467i	−0.156771	+	1.49158i
$905$	−0.121430	−	0.0400655i	−0.00403647	−	0.00133182i
$906$		0			0
$907$	−9.88602	+	17.1231i	−0.328260	+	0.568563i	−0.982167	−	0.188012i	$-0.939796\pi$
$907$	−9.88602	+	17.1231i	−0.328260	+	0.568563i	0.653907	+	0.756575i	$0.273129\pi$
$908$	1.71435	−	1.24555i	0.0568926	−	0.0413349i
$909$		0			0
$910$	5.45716	−	0.548530i	0.180903	−	0.0181836i
$911$	14.1994	+	15.7700i	0.470448	+	0.522485i	0.930937	−	0.365180i	$-0.118993\pi$
$911$	14.1994	+	15.7700i	0.470448	+	0.522485i	−0.460489	+	0.887665i	$0.652326\pi$
$912$		0			0
$913$	−19.2335	+	21.3610i	−0.636537	+	0.706947i
$914$	−22.8171	+	4.84992i	−0.754723	+	0.160421i
$915$		0			0
$916$	−0.479166	−	0.101850i	−0.0158321	−	0.00336521i
$917$	−0.851132	+	0.618383i	−0.0281068	+	0.0204208i
$918$		0			0
$919$	−0.706640	+	0.513404i	−0.0233099	+	0.0169356i	−0.599379	−	0.800465i	$-0.704586\pi$
$919$	−0.706640	+	0.513404i	−0.0233099	+	0.0169356i	0.576069	+	0.817401i	$0.304586\pi$
$920$	−8.94932	−	0.981715i	−0.295050	−	0.0323662i
$921$		0			0
$922$	0.475304	−	4.52222i	0.0156533	−	0.148931i
$923$	−76.0569	+	16.1664i	−2.50344	+	0.532124i
$924$		0			0
$925$	−0.119524	−	0.00108546i	−0.00392991	−	3.56896e-5i
$926$	−10.7898			−0.354575
$927$		0			0
$928$	11.0219	+	8.00787i	0.361811	+	0.262871i
$929$	−11.8209	+	5.26300i	−0.387831	+	0.172673i	−0.591383	−	0.806391i	$-0.701418\pi$
$929$	−11.8209	+	5.26300i	−0.387831	+	0.172673i	0.203552	+	0.979064i	$0.434751\pi$
$930$		0			0
$931$	−45.8497	−	20.4136i	−1.50266	−	0.669029i
$932$	3.23391	+	5.60129i	0.105930	+	0.183476i
$933$		0			0
$934$	35.8883	+	7.62830i	1.17430	+	0.249606i
$935$	−2.55537	−	5.81031i	−0.0835694	−	0.190017i
$936$		0			0
$937$	−0.517445	−	1.59253i	−0.0169042	−	0.0520257i	0.942249	−	0.334914i	$-0.108707\pi$
$937$	−0.517445	−	1.59253i	−0.0169042	−	0.0520257i	−0.959153	+	0.282889i	$0.908707\pi$
$938$	0.916030	+	0.194708i	0.0299094	+	0.00635745i
$939$		0			0
$940$	−3.98941	+	5.43885i	−0.130120	+	0.177396i
$941$	6.72992	−	7.47433i	0.219389	−	0.243656i	−0.623396	−	0.781906i	$-0.714248\pi$
$941$	6.72992	−	7.47433i	0.219389	−	0.243656i	0.842785	+	0.538250i	$0.180914\pi$
$942$		0			0
$943$	3.00010	−	5.19632i	0.0976966	−	0.169216i
$944$	−10.5109	+	7.63660i	−0.342100	+	0.248550i
$945$		0			0
$946$	−7.50659	−	5.45386i	−0.244060	−	0.177320i
$947$	37.3142	−	16.6134i	1.21255	−	0.539862i	0.302019	−	0.953302i	$-0.402340\pi$
$947$	37.3142	−	16.6134i	1.21255	−	0.539862i	0.910531	+	0.413440i	$0.135673\pi$
$948$		0			0
$949$	2.99549	+	5.18833i	0.0972376	+	0.168420i
$950$	−22.0176	+	37.3482i	−0.714347	+	1.21174i
$951$		0			0
$952$	−0.636552	−	0.706963i	−0.0206308	−	0.0229128i
$953$	28.0837	+	20.4040i	0.909720	+	0.660951i	0.940944	−	0.338562i	$-0.109940\pi$
$953$	28.0837	+	20.4040i	0.909720	+	0.660951i	−0.0312237	+	0.999512i	$0.509940\pi$
$954$		0			0
$955$	−2.15739	−	4.90540i	−0.0698114	−	0.158735i
$956$	0.987935	+	9.39958i	0.0319521	+	0.304004i
$957$		0			0
$958$	13.4131	+	5.97189i	0.433357	+	0.192943i
$959$	−1.78099	+	1.97799i	−0.0575112	+	0.0638727i
$960$		0			0
$961$	29.5164	+	32.7812i	0.952141	+	1.05746i
$962$	−0.0574940	−	0.176948i	−0.00185368	−	0.00570504i
$963$		0			0
$964$	−0.374693	+	1.15319i	−0.0120680	+	0.0371416i
$965$	5.41650	−	12.0185i	0.174363	−	0.386889i
$966$		0			0
$967$	−19.2260	−	8.55999i	−0.618268	−	0.275271i	0.0736078	−	0.997287i	$-0.476549\pi$
$967$	−19.2260	−	8.55999i	−0.618268	−	0.275271i	−0.691876	+	0.722017i	$0.743215\pi$
$968$	4.06075	+	7.03343i	0.130517	+	0.226063i
$969$		0			0
$970$	−4.01000	−	19.2960i	−0.128753	−	0.619556i
$971$	−27.0192	−	19.6306i	−0.867089	−	0.629977i	0.0627155	−	0.998031i	$-0.480024\pi$
$971$	−27.0192	−	19.6306i	−0.867089	−	0.629977i	−0.929804	+	0.368055i	$0.880024\pi$
$972$		0			0
$973$	0.139302	−	0.428728i	0.00446583	−	0.0137444i
$974$	2.96001	−	5.12688i	0.0948448	−	0.164276i
$975$		0			0
$976$	−9.29412	−	16.0979i	−0.297497	−	0.515281i
$977$	7.57062	−	1.60918i	0.242206	−	0.0514824i	−0.0852093	−	0.996363i	$-0.527156\pi$
$977$	7.57062	−	1.60918i	0.242206	−	0.0514824i	0.327415	+	0.944881i	$0.393823\pi$
$978$		0			0
$979$	32.3684	−	14.4113i	1.03450	−	0.460588i
$980$	−7.71173	−	4.49918i	−0.246342	−	0.143721i
$981$		0			0
$982$	−22.7253			−0.725195
$983$	−5.02975	−	47.8549i	−0.160424	−	1.52633i	−0.717903	−	0.696143i	$-0.754898\pi$
$983$	−5.02975	−	47.8549i	−0.160424	−	1.52633i	0.557479	−	0.830191i	$-0.311769\pi$
$984$		0			0
$985$	0.161185	−	35.4980i	0.00513577	−	1.13106i
$986$	4.93894	−	1.04980i	0.157288	−	0.0334326i
$987$		0			0
$988$	26.8714	+	5.71169i	0.854892	+	0.181713i
$989$	1.08947	−	3.35303i	0.0346430	−	0.106620i
$990$		0			0
$991$	−15.7450	−	48.4581i	−0.500157	−	1.53932i	−0.808763	−	0.588134i	$-0.799863\pi$
$991$	−15.7450	−	48.4581i	−0.500157	−	1.53932i	0.308607	−	0.951190i	$-0.400137\pi$
$992$	−2.86132	−	27.2237i	−0.0908471	−	0.864352i
$993$		0			0
$994$	4.08851	+	1.82032i	0.129680	+	0.0577372i
$995$	−6.02120	−	8.36710i	−0.190885	−	0.265255i
$996$		0			0
$997$	13.8124	−	6.14967i	0.437443	−	0.194762i	−0.176186	−	0.984357i	$-0.556376\pi$
$997$	13.8124	−	6.14967i	0.437443	−	0.194762i	0.613629	+	0.789595i	$0.289709\pi$
$998$	−1.84887	+	5.69025i	−0.0585251	+	0.180122i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.9		224
3.2	odd	2		225.2.q.a.196.20	yes	224
9.4	even	3	inner	675.2.r.a.496.20		224
9.5	odd	6		225.2.q.a.121.9	yes	224
25.6	even	5	inner	675.2.r.a.181.20		224
75.56	odd	10		225.2.q.a.106.9	yes	224
225.31	even	15	inner	675.2.r.a.631.9		224
225.131	odd	30		225.2.q.a.31.20	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.20	✓	224	225.131	odd	30
225.2.q.a.106.9	yes	224	75.56	odd	10
225.2.q.a.121.9	yes	224	9.5	odd	6
225.2.q.a.196.20	yes	224	3.2	odd	2
675.2.r.a.46.9		224	1.1	even	1	trivial
675.2.r.a.181.20		224	25.6	even	5	inner
675.2.r.a.496.20		224	9.4	even	3	inner
675.2.r.a.631.9		224	225.31	even	15	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +O(q^{10})\)	\(q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +(-0.566103 + 2.60508i) q^{10} +(-1.93450 - 2.14848i) q^{11} +(4.36810 - 4.85127i) q^{13} +(-0.367525 + 0.0781199i) q^{14} +(2.45317 + 0.521438i) q^{16} +(-0.794350 + 0.577129i) q^{17} +(-5.88399 + 4.27497i) q^{19} +(-1.12341 + 0.641816i) q^{20} +(-0.360286 + 3.42790i) q^{22} +(-1.28104 + 0.272294i) q^{23} +(-1.58820 + 4.74106i) q^{25} -7.78284 q^{26} +(-0.147528 - 0.107185i) q^{28} +(3.94048 - 1.75442i) q^{29} +(-7.91741 - 3.52506i) q^{31} +(1.57924 + 2.73533i) q^{32} +(1.14502 + 0.243382i) q^{34} +(-0.701179 + 0.0704794i) q^{35} +(0.00738727 + 0.0227357i) q^{37} +(8.48155 + 1.80281i) q^{38} +(6.52812 + 2.15393i) q^{40} +(-3.06561 + 3.40470i) q^{41} +(-1.34599 + 2.33132i) q^{43} +(-1.35333 + 0.983252i) q^{44} +(1.26320 + 0.917772i) q^{46} +(4.76261 - 2.12045i) q^{47} +(3.45034 + 5.97616i) q^{49} +(5.46752 - 2.37504i) q^{50} +(-2.52745 - 2.80701i) q^{52} +(3.44104 + 2.50006i) q^{53} +(-1.37277 + 6.31717i) q^{55} +(0.101275 + 0.963571i) q^{56} +(-4.69792 - 2.09165i) q^{58} +(-3.46632 + 3.84974i) q^{59} +(-4.95936 - 5.50792i) q^{61} +(3.19295 + 9.82688i) q^{62} +(2.71365 - 8.35176i) q^{64} +(-14.5101 - 1.59172i) q^{65} +(-2.27694 - 1.01376i) q^{67} +(0.284062 + 0.492010i) q^{68} +(0.621810 + 0.565014i) q^{70} +(-9.63629 - 7.00118i) q^{71} +(-0.283594 + 0.872814i) q^{73} +(0.0142504 - 0.0246825i) q^{74} +(2.10413 + 3.64447i) q^{76} +(-0.891228 + 0.189436i) q^{77} +(-10.3980 + 4.62948i) q^{79} +(-2.25770 - 5.13348i) q^{80} +5.46212 q^{82} +(-1.03926 - 9.88793i) q^{83} +(2.08497 + 0.687930i) q^{85} +(3.13929 - 0.667278i) q^{86} +(8.69369 + 1.84790i) q^{88} +(-3.78718 + 11.6557i) q^{89} +(-0.635757 - 1.95666i) q^{91} +(0.0792106 + 0.753639i) q^{92} +(-5.67808 - 2.52804i) q^{94} +(15.4440 + 5.09571i) q^{95} +(-6.75362 + 3.00691i) q^{97} +(2.54232 - 7.82445i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more