LMFDB - Embedded newform 603.2.v.a.8.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(8,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("603.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.v (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			8.13
Character	$\chi$	$=$	603.8
Dual form			603.2.v.a.377.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0114821 - 0.0798595i) q^{2} +(1.91274 + 0.561631i) q^{4} +(2.63879 + 1.69585i) q^{5} +(-2.31288 - 0.332541i) q^{7} +(0.133846 - 0.293081i) q^{8} +O(q^{10})$	\(q+(0.0114821 - 0.0798595i) q^{2} +(1.91274 + 0.561631i) q^{4} +(2.63879 + 1.69585i) q^{5} +(-2.31288 - 0.332541i) q^{7} +(0.133846 - 0.293081i) q^{8} +(0.165728 - 0.191261i) q^{10} +(-0.145936 - 0.0937877i) q^{11} +(4.36545 - 1.99363i) q^{13} +(-0.0531132 + 0.180887i) q^{14} +(3.33219 + 2.14147i) q^{16} +(1.35657 + 4.62006i) q^{17} +(-0.934472 - 6.49940i) q^{19} +(4.09488 + 4.72574i) q^{20} +(-0.00916549 + 0.0105775i) q^{22} +(-3.78200 + 3.27712i) q^{23} +(2.01024 + 4.40181i) q^{25} +(-0.109086 - 0.371514i) q^{26} +(-4.23716 - 1.93505i) q^{28} +4.84004i q^{29} +(-7.61790 - 3.47898i) q^{31} +(0.631267 - 0.728521i) q^{32} +(0.384532 - 0.0552874i) q^{34} +(-5.53925 - 4.79979i) q^{35} +1.81545 q^{37} -0.529769 q^{38} +(0.850213 - 0.546398i) q^{40} +(2.92289 - 0.858239i) q^{41} +(2.19587 + 7.47845i) q^{43} +(-0.226464 - 0.261354i) q^{44} +(0.218284 + 0.339657i) q^{46} +(4.57158 - 3.96130i) q^{47} +(-1.47764 - 0.433875i) q^{49} +(0.374608 - 0.109995i) q^{50} +(9.46965 - 1.36153i) q^{52} +(-9.22372 - 2.70833i) q^{53} +(-0.226046 - 0.494972i) q^{55} +(-0.407030 + 0.633352i) q^{56} +(0.386524 + 0.0555737i) q^{58} +(3.20199 + 1.46230i) q^{59} +(2.52885 + 3.93496i) q^{61} +(-0.365299 + 0.568416i) q^{62} +(5.13686 + 5.92825i) q^{64} +(14.9004 + 2.14235i) q^{65} +(-2.91564 - 7.64847i) q^{67} +9.59888i q^{68} +(-0.446911 + 0.387251i) q^{70} +(4.15000 - 14.1336i) q^{71} +(4.48574 - 2.88281i) q^{73} +(0.0208451 - 0.144981i) q^{74} +(1.86286 - 12.9565i) q^{76} +(0.306345 + 0.265449i) q^{77} +(2.74835 - 1.25513i) q^{79} +(5.16135 + 11.3018i) q^{80} +(-0.0349777 - 0.243275i) q^{82} +(-8.16036 + 12.6978i) q^{83} +(-4.25521 + 14.4919i) q^{85} +(0.622439 - 0.0894932i) q^{86} +(-0.0470204 + 0.0302182i) q^{88} +(-10.9830 - 9.51686i) q^{89} +(-10.7597 + 3.15933i) q^{91} +(-9.07452 + 4.14419i) q^{92} +(-0.263856 - 0.410568i) q^{94} +(8.55611 - 18.7353i) q^{95} -3.03018i q^{97} +(-0.0516154 + 0.113022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 28 q^{4}+O(q^{10}) $ 240 * q - 28 * q^4	$ 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) $ 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

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 $

$2$	0.0114821	−	0.0798595i	0.00811905	−	0.0564692i	−0.985359	−	0.170492i	$-0.945464\pi$
$2$	0.0114821	−	0.0798595i	0.00811905	−	0.0564692i	0.993478	+	0.114022i	$0.0363735\pi$
$3$		0			0
$3$		0			0
$4$	1.91274	+	0.561631i	0.956370	+	0.280816i
$5$	2.63879	+	1.69585i	1.18010	+	0.758406i	0.975405	−	0.220419i	$-0.0707425\pi$
$5$	2.63879	+	1.69585i	1.18010	+	0.758406i	0.204698	+	0.978825i	$0.434379\pi$
$6$		0			0
$7$	−2.31288	−	0.332541i	−0.874185	−	0.125689i	−0.309405	−	0.950930i	$-0.600130\pi$
$7$	−2.31288	−	0.332541i	−0.874185	−	0.125689i	−0.564780	+	0.825242i	$0.691039\pi$
$8$	0.133846	−	0.293081i	0.0473216	−	0.103620i
$9$		0			0
$10$	0.165728	−	0.191261i	0.0524079	−	0.0604820i
$11$	−0.145936	−	0.0937877i	−0.0440015	−	0.0282780i	0.518455	−	0.855105i	$-0.326507\pi$
$11$	−0.145936	−	0.0937877i	−0.0440015	−	0.0282780i	−0.562457	+	0.826827i	$0.690144\pi$
$12$		0			0
$13$	4.36545	−	1.99363i	1.21076	−	0.552934i	0.295321	−	0.955398i	$-0.404573\pi$
$13$	4.36545	−	1.99363i	1.21076	−	0.552934i	0.915436	+	0.402464i	$0.131846\pi$
$14$	−0.0531132	+	0.180887i	−0.0141951	+	0.0483441i
$15$		0			0
$16$	3.33219	+	2.14147i	0.833048	+	0.535368i
$17$	1.35657	+	4.62006i	0.329017	+	1.12053i	0.943437	+	0.331551i	$0.107572\pi$
$17$	1.35657	+	4.62006i	0.329017	+	1.12053i	−0.614420	+	0.788979i	$0.710610\pi$
$18$		0			0
$19$	−0.934472	−	6.49940i	−0.214383	−	1.49106i	−0.758289	−	0.651918i	$-0.773965\pi$
$19$	−0.934472	−	6.49940i	−0.214383	−	1.49106i	0.543907	−	0.839146i	$-0.316945\pi$
$20$	4.09488	+	4.72574i	0.915643	+	1.05671i
$21$		0			0
$22$	−0.00916549	+	0.0105775i	−0.00195409	+	0.00225514i
$23$	−3.78200	+	3.27712i	−0.788602	+	0.683327i	−0.952968	−	0.303072i	$-0.901988\pi$
$23$	−3.78200	+	3.27712i	−0.788602	+	0.683327i	0.164366	+	0.986399i	$0.447442\pi$
$24$		0			0
$25$	2.01024	+	4.40181i	0.402048	+	0.880363i
$26$	−0.109086	−	0.371514i	−0.0213936	−	0.0728598i
$27$		0			0
$28$	−4.23716	−	1.93505i	−0.800749	−	0.365690i
$29$			4.84004i			0.898774i	0.893337	+	0.449387i	$0.148358\pi$
$29$			4.84004i			0.898774i	−0.893337	+	0.449387i	$0.851642\pi$
$30$		0			0
$31$	−7.61790	−	3.47898i	−1.36822	−	0.624843i	−0.410315	−	0.911944i	$-0.634581\pi$
$31$	−7.61790	−	3.47898i	−1.36822	−	0.624843i	−0.957900	+	0.287101i	$0.907308\pi$
$32$	0.631267	−	0.728521i	0.111593	−	0.128785i
$33$		0			0
$34$	0.384532	−	0.0552874i	0.0659468	−	0.00948171i
$35$	−5.53925	−	4.79979i	−0.936305	−	0.811313i
$36$		0			0
$37$	1.81545			0.298458			0.149229	−	0.988803i	$-0.452321\pi$
$37$	1.81545			0.298458			0.149229	+	0.988803i	$0.452321\pi$
$38$	−0.529769			−0.0859398
$39$		0			0
$40$	0.850213	−	0.546398i	0.134430	−	0.0863932i
$41$	2.92289	−	0.858239i	0.456479	−	0.134034i	−0.0454061	−	0.998969i	$-0.514458\pi$
$41$	2.92289	−	0.858239i	0.456479	−	0.134034i	0.501885	+	0.864934i	$0.332640\pi$
$42$		0			0
$43$	2.19587	+	7.47845i	0.334867	+	1.14045i	0.939100	+	0.343645i	$0.111662\pi$
$43$	2.19587	+	7.47845i	0.334867	+	1.14045i	−0.604232	+	0.796808i	$0.706520\pi$
$44$	−0.226464	−	0.261354i	−0.0341408	−	0.0394006i
$45$		0			0
$46$	0.218284	+	0.339657i	0.0321843	+	0.0500797i
$47$	4.57158	−	3.96130i	0.666834	−	0.577815i	−0.254270	−	0.967133i	$-0.581835\pi$
$47$	4.57158	−	3.96130i	0.666834	−	0.577815i	0.921103	+	0.389319i	$0.127290\pi$
$48$		0			0
$49$	−1.47764	−	0.433875i	−0.211092	−	0.0619821i
$50$	0.374608	−	0.109995i	0.0529776	−	0.0155556i
$51$		0			0
$52$	9.46965	−	1.36153i	1.31320	−	0.188810i
$53$	−9.22372	−	2.70833i	−1.26698	−	0.372018i	−0.421889	−	0.906647i	$-0.638633\pi$
$53$	−9.22372	−	2.70833i	−1.26698	−	0.372018i	−0.845087	+	0.534630i	$0.820451\pi$
$54$		0			0
$55$	−0.226046	−	0.494972i	−0.0304801	−	0.0667420i
$56$	−0.407030	+	0.633352i	−0.0543917	+	0.0846352i
$57$		0			0
$58$	0.386524	+	0.0555737i	0.0507531	+	0.00729719i
$59$	3.20199	+	1.46230i	0.416863	+	0.190375i	0.612794	−	0.790243i	$-0.290046\pi$
$59$	3.20199	+	1.46230i	0.416863	+	0.190375i	−0.195931	+	0.980618i	$0.562773\pi$
$60$		0			0
$61$	2.52885	+	3.93496i	0.323786	+	0.503821i	0.964544	−	0.263922i	$-0.0850162\pi$
$61$	2.52885	+	3.93496i	0.323786	+	0.503821i	−0.640758	+	0.767743i	$0.721380\pi$
$62$	−0.365299	+	0.568416i	−0.0463930	+	0.0721889i
$63$		0			0
$64$	5.13686	+	5.92825i	0.642107	+	0.741031i
$65$	14.9004	+	2.14235i	1.84817	+	0.265726i
$66$		0			0
$67$	−2.91564	−	7.64847i	−0.356202	−	0.934409i
$67$	−2.91564	−	7.64847i	−0.356202	−	0.934409i
$68$			9.59888i			1.16403i
$69$		0			0
$70$	−0.446911	+	0.387251i	−0.0534161	+	0.0462853i
$71$	4.15000	−	14.1336i	0.492514	−	1.67735i	−0.219846	−	0.975535i	$-0.570555\pi$
$71$	4.15000	−	14.1336i	0.492514	−	1.67735i	0.712360	−	0.701815i	$-0.247626\pi$
$72$		0			0
$73$	4.48574	−	2.88281i	0.525016	−	0.337407i	−0.251137	−	0.967951i	$-0.580805\pi$
$73$	4.48574	−	2.88281i	0.525016	−	0.337407i	0.776153	+	0.630544i	$0.217168\pi$
$74$	0.0208451	−	0.144981i	0.00242320	−	0.0168537i
$75$		0			0
$76$	1.86286	−	12.9565i	0.213685	−	1.48621i
$77$	0.306345	+	0.265449i	0.0349112	+	0.0302507i
$78$		0			0
$79$	2.74835	−	1.25513i	0.309214	−	0.141213i	−0.254764	−	0.967003i	$-0.581998\pi$
$79$	2.74835	−	1.25513i	0.309214	−	0.141213i	0.563978	+	0.825790i	$0.309270\pi$
$80$	5.16135	+	11.3018i	0.577057	+	1.26358i
$81$		0			0
$82$	−0.0349777	−	0.243275i	−0.00386264	−	0.0268653i
$83$	−8.16036	+	12.6978i	−0.895715	+	1.39376i	0.0233805	+	0.999727i	$0.492557\pi$
$83$	−8.16036	+	12.6978i	−0.895715	+	1.39376i	−0.919096	+	0.394034i	$0.871079\pi$
$84$		0			0
$85$	−4.25521	+	14.4919i	−0.461543	+	1.57187i
$86$	0.622439	−	0.0894932i	0.0671193	−	0.00965030i
$87$		0			0
$88$	−0.0470204	+	0.0302182i	−0.00501239	+	0.00322127i
$89$	−10.9830	−	9.51686i	−1.16420	−	1.00879i	−0.999749	−	0.0223997i	$-0.992869\pi$
$89$	−10.9830	−	9.51686i	−1.16420	−	1.00879i	−0.164451	−	0.986385i	$-0.552585\pi$
$90$		0			0
$91$	−10.7597	+	3.15933i	−1.12792	+	0.331188i
$92$	−9.07452	+	4.14419i	−0.946084	+	0.432062i
$93$		0			0
$94$	−0.263856	−	0.410568i	−0.0272147	−	0.0423469i
$95$	8.55611	−	18.7353i	0.877838	−	1.92220i
$96$		0			0
$97$		−	3.03018i		−	0.307668i	−0.988097	−	0.153834i	$-0.950838\pi$
$97$		−	3.03018i		−	0.307668i	0.988097	−	0.153834i	$-0.0491620\pi$
$98$	−0.0516154	+	0.113022i	−0.00521394	+	0.0114169i
$99$		0			0
$100$	1.37287	+	9.54854i	0.137287	+	0.954854i
$101$	−2.05615	−	14.3009i	−0.204595	−	1.42299i	−0.790427	−	0.612556i	$-0.790141\pi$
$101$	−2.05615	−	14.3009i	−0.204595	−	1.42299i	0.585833	−	0.810432i	$-0.300768\pi$
$102$		0			0
$103$	3.28792	−	7.19954i	0.323968	−	0.709391i	−0.675644	−	0.737228i	$-0.736134\pi$
$103$	3.28792	−	7.19954i	0.323968	−	0.709391i	0.999612	+	0.0278364i	$0.00886175\pi$
$104$		−	1.54627i		−	0.151624i
$105$		0			0
$106$	−0.322193	+	0.705505i	−0.0312942	+	0.0685247i
$107$	0.878148	+	1.36643i	0.0848938	+	0.132097i	0.881104	−	0.472923i	$-0.156801\pi$
$107$	0.878148	+	1.36643i	0.0848938	+	0.132097i	−0.796210	+	0.605021i	$0.793165\pi$
$108$		0			0
$109$	−8.56436	+	3.91121i	−0.820317	+	0.374626i	−0.780946	−	0.624599i	$-0.785263\pi$
$109$	−8.56436	+	3.91121i	−0.820317	+	0.374626i	−0.0393707	+	0.999225i	$0.512535\pi$
$110$	−0.0421237	+	0.0123686i	−0.00401634	+	0.00117930i
$111$		0			0
$112$	−6.99482	−	6.06105i	−0.660949	−	0.572715i
$113$	−6.94048	+	4.46037i	−0.652905	+	0.419597i	−0.824727	−	0.565531i	$-0.808671\pi$
$113$	−6.94048	+	4.46037i	−0.652905	+	0.419597i	0.171822	+	0.985128i	$0.445035\pi$
$114$		0			0
$115$	−15.5374	+	2.23394i	−1.44887	+	0.208316i
$116$	−2.71832	+	9.25775i	−0.252390	+	0.859560i
$117$		0			0
$118$	0.153544	−	0.238919i	0.0141349	−	0.0219943i
$119$	−1.60122	−	11.1367i	−0.146784	−	1.02090i
$120$		0			0
$121$	−4.55706	−	9.97858i	−0.414279	−	0.907143i
$122$	0.343281	−	0.156771i	0.0310792	−	0.0141934i
$123$		0			0
$124$	−12.6172	−	10.9328i	−1.13305	−	0.981797i
$125$	0.0718202	−	0.499520i	0.00642379	−	0.0446784i
$126$		0			0
$127$	−0.493468	+	3.43215i	−0.0437882	+	0.304554i	0.956144	+	0.292897i	$0.0946195\pi$
$127$	−0.493468	+	3.43215i	−0.0437882	+	0.304554i	−0.999932	+	0.0116562i	$0.996290\pi$
$128$	2.15430	−	1.38448i	0.190415	−	0.122372i
$129$		0			0
$130$	0.342175	−	1.16534i	0.0300107	−	0.102207i
$131$	−1.67140	+	1.44828i	−0.146031	+	0.126537i	−0.724813	−	0.688946i	$-0.758074\pi$
$131$	−1.67140	+	1.44828i	−0.146031	+	0.126537i	0.578782	+	0.815483i	$0.303528\pi$
$132$		0			0
$133$			15.3430i			1.33041i
$134$	−0.644281	+	0.145021i	−0.0556574	+	0.0125279i
$135$		0			0
$136$	1.53563	+	0.220790i	0.131679	+	0.0189326i
$137$	−9.39562	−	10.8431i	−0.802722	−	0.926390i	0.195806	−	0.980643i	$-0.437268\pi$
$137$	−9.39562	−	10.8431i	−0.802722	−	0.926390i	−0.998527	+	0.0542526i	$0.982722\pi$
$138$		0			0
$139$	−5.60808	+	8.72635i	−0.475672	+	0.740159i	−0.993315	−	0.115437i	$-0.963173\pi$
$139$	−5.60808	+	8.72635i	−0.475672	+	0.740159i	0.517643	+	0.855597i	$0.326809\pi$
$140$	−7.89944	−	12.2918i	−0.667625	−	1.03884i
$141$		0			0
$142$	−1.08105	−	0.493700i	−0.0907199	−	0.0414304i
$143$	−0.824056	−	0.118481i	−0.0689110	−	0.00990791i
$144$		0			0
$145$	−8.20798	+	12.7719i	−0.681635	+	1.06065i
$146$	−0.178714	−	0.391330i	−0.0147905	−	0.0323867i
$147$		0			0
$148$	3.47248	+	1.01961i	0.285436	+	0.0838117i
$149$	−10.0828	+	1.44969i	−0.826018	+	0.118763i	−0.542343	−	0.840157i	$-0.682463\pi$
$149$	−10.0828	+	1.44969i	−0.826018	+	0.118763i	−0.283675	+	0.958921i	$0.591554\pi$
$150$		0			0
$151$	−4.78114	+	1.40387i	−0.389084	+	0.114245i	−0.470423	−	0.882441i	$-0.655899\pi$
$151$	−4.78114	+	1.40387i	−0.389084	+	0.114245i	0.0813390	+	0.996686i	$0.474080\pi$
$152$	−2.02993	−	0.596041i	−0.164649	−	0.0483453i
$153$		0			0
$154$	0.0247161	−	0.0214166i	0.00199168	−	0.00172580i
$155$	−14.2022	−	22.0991i	−1.14075	−	1.77504i
$156$		0			0
$157$	11.8661	+	13.6942i	0.947019	+	1.09292i	0.995563	+	0.0940966i	$0.0299963\pi$
$157$	11.8661	+	13.6942i	0.947019	+	1.09292i	−0.0485446	+	0.998821i	$0.515458\pi$
$158$	−0.0686774	−	0.233894i	−0.00546368	−	0.0186076i
$159$		0			0
$160$	2.90124	−	0.851881i	0.229363	−	0.0673471i
$161$	9.83707	−	6.32190i	0.775270	−	0.498236i
$162$		0			0
$163$	8.70002			0.681438			0.340719	−	0.940165i	$-0.389329\pi$
$163$	8.70002			0.681438			0.340719	+	0.940165i	$0.389329\pi$
$164$	6.07275			0.474202
$165$		0			0
$166$	0.920340	+	0.797479i	0.0714322	+	0.0618964i
$167$	−10.5333	+	1.51446i	−0.815093	+	0.117193i	−0.537238	−	0.843430i	$-0.680532\pi$
$167$	−10.5333	+	1.51446i	−0.815093	+	0.117193i	−0.277855	+	0.960623i	$0.589623\pi$
$168$		0			0
$169$	6.56936	−	7.58145i	0.505335	−	0.583188i
$170$	1.10846	+	0.506217i	0.0850150	+	0.0388250i
$171$		0			0
$172$			15.5376i			1.18473i
$173$	18.0122	+	8.22589i	1.36944	+	0.625402i	0.958193	−	0.286121i	$-0.0923661\pi$
$173$	18.0122	+	8.22589i	1.36944	+	0.625402i	0.411247	+	0.911524i	$0.365093\pi$
$174$		0			0
$175$	−3.18565	−	10.8493i	−0.240813	−	0.820133i
$176$	−0.285445	−	0.625037i	−0.0215162	−	0.0471140i
$177$		0			0
$178$	−0.886120	+	0.767827i	−0.0664175	+	0.0575511i
$179$	9.09745	−	10.4990i	0.679976	−	0.784734i	−0.305927	−	0.952055i	$-0.598966\pi$
$179$	9.09745	−	10.4990i	0.679976	−	0.784734i	0.985902	+	0.167321i	$0.0535117\pi$
$180$		0			0
$181$	−8.98385	−	10.3679i	−0.667764	−	0.770641i	0.316261	−	0.948672i	$-0.397573\pi$
$181$	−8.98385	−	10.3679i	−0.667764	−	0.770641i	−0.984025	+	0.178031i	$0.943027\pi$
$182$	0.128759	+	0.895540i	0.00954427	+	0.0663819i
$183$		0			0
$184$	0.454259	+	1.54706i	0.0334884	+	0.114051i
$185$	4.79059	+	3.07873i	0.352211	+	0.226352i
$186$		0			0
$187$	0.235332	−	0.801466i	0.0172091	−	0.0586090i
$188$	10.9690	−	5.00939i	0.799999	−	0.365347i
$189$		0			0
$190$	−1.39795	−	0.898407i	−0.101418	−	0.0651773i
$191$	−9.77622	+	11.2824i	−0.707382	+	0.816363i	−0.989730	−	0.142949i	$-0.954341\pi$
$191$	−9.77622	+	11.2824i	−0.707382	+	0.816363i	0.282348	+	0.959312i	$0.408887\pi$
$192$		0			0
$193$	8.07720	−	17.6866i	0.581410	−	1.27311i	−0.359086	−	0.933304i	$-0.616912\pi$
$193$	8.07720	−	17.6866i	0.581410	−	1.27311i	0.940496	−	0.339805i	$-0.110361\pi$
$194$	−0.241988	−	0.0347927i	−0.0173738	−	0.00249797i
$195$		0			0
$196$	−2.58267	−	1.65978i	−0.184476	−	0.118556i
$197$	19.6077	+	5.75735i	1.39699	+	0.410194i	0.891650	−	0.452725i	$-0.149548\pi$
$197$	19.6077	+	5.75735i	1.39699	+	0.410194i	0.505342	+	0.862919i	$0.331366\pi$
$198$		0			0
$199$	−0.196771	+	1.36857i	−0.0139487	+	0.0970156i	−0.995606	−	0.0936360i	$-0.970151\pi$
$199$	−0.196771	+	1.36857i	−0.0139487	+	0.0970156i	0.981658	+	0.190652i	$0.0610601\pi$
$200$	1.55915			0.110249
$201$		0			0
$202$	−1.16567			−0.0820161
$203$	1.60951	−	11.1944i	0.112966	−	0.785694i
$204$		0			0
$205$	9.16834	+	2.69207i	0.640345	+	0.188022i
$206$	−0.537200	−	0.345237i	−0.0374285	−	0.0240538i
$207$		0			0
$208$	18.8158	+	2.70531i	1.30464	+	0.187579i
$209$	−0.473190	+	1.03614i	−0.0327312	+	0.0716714i
$210$		0			0
$211$	3.38407	−	3.90542i	0.232969	−	0.268860i	−0.627213	−	0.778848i	$-0.715805\pi$
$211$	3.38407	−	3.90542i	0.232969	−	0.268860i	0.860182	+	0.509987i	$0.170350\pi$
$212$	−16.1215	−	10.3607i	−1.10723	−	0.711573i
$213$		0			0
$214$	0.119205	−	0.0544391i	0.00814869	−	0.00372138i
$215$	−6.88787	+	23.4579i	−0.469749	+	1.59982i
$216$		0			0
$217$	16.4624	+	10.5797i	1.11754	+	0.718198i
$218$	0.214011	+	0.728854i	0.0144947	+	0.0493643i
$219$		0			0
$220$	−0.154376	−	1.07371i	−0.0104080	−	0.0723893i
$221$	15.1328	+	17.4641i	1.01794	+	1.17476i
$222$		0			0
$223$	−16.5128	+	19.0568i	−1.10578	+	1.27614i	−0.147888	+	0.989004i	$0.547248\pi$
$223$	−16.5128	+	19.0568i	−1.10578	+	1.27614i	−0.957891	+	0.287133i	$0.907298\pi$
$224$	−1.70230	+	1.47506i	−0.113740	+	0.0985563i
$225$		0			0
$226$	0.276512	+	0.605478i	0.0183933	+	0.0402758i
$227$	−0.00167041	−	0.00568888i	−0.000110869	−	0.000377584i	0.959438	−	0.281921i	$-0.0909717\pi$
$227$	−0.00167041	−	0.00568888i	−0.000110869	−	0.000377584i	−0.959548	+	0.281544i	$0.909154\pi$
$228$		0			0
$229$	−25.3033	−	11.5556i	−1.67209	−	0.763617i	−0.999726	−	0.0233941i	$-0.992553\pi$
$229$	−25.3033	−	11.5556i	−1.67209	−	0.763617i	−0.672362	−	0.740223i	$-0.734720\pi$
$230$			1.26646i			0.0835079i
$231$		0			0
$232$	1.41853	+	0.647820i	0.0931309	+	0.0425315i
$233$	−13.3434	+	15.3991i	−0.874153	+	1.00883i	0.125706	+	0.992068i	$0.459880\pi$
$233$	−13.3434	+	15.3991i	−0.874153	+	1.00883i	−0.999860	+	0.0167593i	$0.994665\pi$
$234$		0			0
$235$	18.7812	−	2.70033i	1.22515	−	0.176150i
$236$	5.30329	+	4.59533i	0.345215	+	0.299131i
$237$		0			0
$238$	−0.907761			−0.0588414
$239$	13.9497			0.902334			0.451167	−	0.892440i	$-0.351008\pi$
$239$	13.9497			0.902334			0.451167	+	0.892440i	$0.351008\pi$
$240$		0			0
$241$	12.8810	−	8.27813i	0.829739	−	0.533241i	−0.0554559	−	0.998461i	$-0.517661\pi$
$241$	12.8810	−	8.27813i	0.829739	−	0.533241i	0.885195	+	0.465220i	$0.154025\pi$
$242$	−0.849209	+	0.249350i	−0.0545892	+	0.0160288i
$243$		0			0
$244$	2.62703	+	8.94684i	0.168178	+	0.572763i
$245$	−3.16340	−	3.65076i	−0.202102	−	0.233238i
$246$		0			0
$247$	−17.0368	−	26.5098i	−1.08403	−	1.68678i
$248$	−2.03925	+	1.76702i	−0.129492	+	0.112206i
$249$		0			0
$250$	−0.0390668	−	0.0114711i	−0.00247080	−	0.000725493i
$251$	−6.23192	+	1.82986i	−0.393355	+	0.115499i	−0.472428	−	0.881369i	$-0.656622\pi$
$251$	−6.23192	+	1.82986i	−0.393355	+	0.115499i	0.0790727	+	0.996869i	$0.474804\pi$
$252$		0			0
$253$	0.859286	−	0.123547i	0.0540228	−	0.00776731i
$254$	0.268424	+	0.0788163i	0.0168424	+	0.00494537i
$255$		0			0
$256$	6.43137	+	14.0827i	0.401960	+	0.880171i
$257$	−14.6405	+	22.7811i	−0.913252	+	1.42105i	−0.00622314	+	0.999981i	$0.501981\pi$
$257$	−14.6405	+	22.7811i	−0.913252	+	1.42105i	−0.907029	+	0.421068i	$0.861655\pi$
$258$		0			0
$259$	−4.19891	−	0.603712i	−0.260908	−	0.0375128i
$260$	27.2974	+	12.4663i	1.69291	+	0.773127i
$261$		0			0
$262$	0.0964678	+	0.150107i	0.00595980	+	0.00927363i
$263$	0.982401	−	1.52865i	0.0605774	−	0.0942603i	−0.809644	−	0.586922i	$-0.800340\pi$
$263$	0.982401	−	1.52865i	0.0605774	−	0.0942603i	0.870221	+	0.492662i	$0.163976\pi$
$264$		0			0
$265$	−19.7466	−	22.7887i	−1.21302	−	1.39990i
$266$	1.22529	+	0.176170i	0.0751273	+	0.0108017i
$267$		0			0
$268$	−1.28124	−	16.2670i	−0.0782639	−	0.993668i
$269$		−	19.2613i		−	1.17438i	−0.809448	−	0.587192i	$-0.800233\pi$
$269$		−	19.2613i		−	1.17438i	0.809448	−	0.587192i	$-0.199767\pi$
$270$		0			0
$271$	7.95077	−	6.88938i	0.482975	−	0.418500i	−0.379042	−	0.925379i	$-0.623747\pi$
$271$	7.95077	−	6.88938i	0.482975	−	0.418500i	0.862017	+	0.506879i	$0.169201\pi$
$272$	−5.37337	+	18.3000i	−0.325808	+	1.10960i
$273$		0			0
$274$	−0.973808	+	0.625828i	−0.0588299	+	0.0378077i
$275$	0.119468	−	0.830921i	0.00720421	−	0.0501064i
$276$		0			0
$277$	0.527789	−	3.67085i	0.0317118	−	0.220560i	−0.967803	−	0.251709i	$-0.919007\pi$
$277$	0.527789	−	3.67085i	0.0317118	−	0.220560i	0.999515	+	0.0311487i	$0.00991655\pi$
$278$	0.632490	+	0.548056i	0.0379342	+	0.0328702i
$279$		0			0
$280$	−2.14814	+	0.981021i	−0.128376	+	0.0586272i
$281$	−6.20941	−	13.5967i	−0.370422	−	0.811112i	−0.999432	−	0.0337139i	$-0.989266\pi$
$281$	−6.20941	−	13.5967i	−0.370422	−	0.811112i	0.629009	−	0.777398i	$-0.283461\pi$
$282$		0			0
$283$	2.12900	+	14.8075i	0.126556	+	0.880216i	0.949873	+	0.312635i	$0.101212\pi$
$283$	2.12900	+	14.8075i	0.126556	+	0.880216i	−0.823317	+	0.567581i	$0.807879\pi$
$284$	15.8757	−	24.7031i	0.942052	−	1.46586i
$285$		0			0
$286$	−0.0189237	+	0.0644483i	−0.00111898	+	0.00381091i
$287$	−7.04569	+	1.01302i	−0.415894	+	0.0597965i
$288$		0			0
$289$	−5.20339	+	3.34401i	−0.306082	+	0.196707i
$290$	0.925711	+	0.802133i	0.0543596	+	0.0471029i
$291$		0			0
$292$	10.1991	−	2.99473i	0.596859	−	0.175254i
$293$	−10.0521	+	4.59065i	−0.587251	+	0.268188i	−0.686803	−	0.726844i	$-0.740986\pi$
$293$	−10.0521	+	4.59065i	−0.587251	+	0.268188i	0.0995519	+	0.995032i	$0.468259\pi$
$294$		0			0
$295$	5.96953	+	9.28878i	0.347560	+	0.540813i
$296$	0.242990	−	0.532075i	0.0141235	−	0.0309262i
$297$		0			0
$298$			0.821856i			0.0476088i
$299$	−9.97674	+	21.8460i	−0.576970	+	1.26339i
$300$		0			0
$301$	−2.59188	−	18.0269i	−0.149394	−	1.03906i
$302$	0.0572150	+	0.397939i	0.00329235	+	0.0228988i
$303$		0			0
$304$	10.8044	−	23.6584i	0.619676	−	1.35690i
$305$			14.6721i			0.840121i
$306$		0			0
$307$	−11.2936	+	24.7294i	−0.644558	+	1.41138i	0.251680	+	0.967810i	$0.419017\pi$
$307$	−11.2936	+	24.7294i	−0.644558	+	1.41138i	−0.896238	+	0.443574i	$0.853710\pi$
$308$	0.436873	+	0.679788i	0.0248932	+	0.0387345i
$309$		0			0
$310$	−1.92789	+	0.880440i	−0.109497	+	0.0500056i
$311$	23.9774	−	7.04040i	1.35963	−	0.399224i	0.481000	−	0.876721i	$-0.340274\pi$
$311$	23.9774	−	7.04040i	1.35963	−	0.399224i	0.878634	+	0.477496i	$0.158456\pi$
$312$		0			0
$313$	4.09314	+	3.54672i	0.231358	+	0.200473i	0.762823	−	0.646608i	$-0.223813\pi$
$313$	4.09314	+	3.54672i	0.231358	+	0.200473i	−0.531465	+	0.847080i	$0.678358\pi$
$314$	1.22986	−	0.790384i	0.0694051	−	0.0446039i
$315$		0			0
$316$	5.96181	−	0.857179i	0.335378	−	0.0482201i
$317$	−2.57330	+	8.76387i	−0.144531	+	0.492228i	−0.999657	−	0.0261928i	$-0.991662\pi$
$317$	−2.57330	+	8.76387i	−0.144531	+	0.492228i	0.855126	+	0.518421i	$0.173480\pi$
$318$		0			0
$319$	0.453937	−	0.706339i	0.0254156	−	0.0395474i
$320$	3.50168	+	24.3547i	0.195750	+	1.36147i
$321$		0			0
$322$	−0.391914	−	0.858173i	−0.0218405	−	0.0478241i
$323$	28.7599	−	13.1342i	1.60025	−	0.730808i
$324$		0			0
$325$	17.5512	+	15.2082i	0.973565	+	0.843599i
$326$	0.0998942	−	0.694780i	0.00553263	−	0.0384803i
$327$		0			0
$328$	0.139683	−	0.971517i	0.00771271	−	0.0536431i
$329$	−11.8908	+	7.64175i	−0.655561	+	0.421303i
$330$		0			0
$331$	−0.225058	+	0.766478i	−0.0123703	+	0.0421294i	−0.965447	−	0.260600i	$-0.916080\pi$
$331$	−0.225058	+	0.766478i	−0.0123703	+	0.0421294i	0.953077	+	0.302729i	$0.0978978\pi$
$332$	−22.7401	+	19.7044i	−1.24803	+	1.08142i
$333$		0			0
$334$			0.858576i			0.0469792i
$335$	5.27688	−	25.1272i	0.288307	−	1.37284i
$336$		0			0
$337$	13.6803	+	1.96693i	0.745212	+	0.107145i	0.504452	−	0.863440i	$-0.331694\pi$
$337$	13.6803	+	1.96693i	0.745212	+	0.107145i	0.240759	+	0.970585i	$0.422604\pi$
$338$	−0.530021	−	0.611677i	−0.0288293	−	0.0332708i
$339$		0			0
$340$	−16.2782	+	25.3294i	−0.882811	+	1.37368i
$341$	0.785444	+	1.22217i	0.0425342	+	0.0661845i
$342$		0			0
$343$	18.1518	+	8.28966i	0.980106	+	0.447599i
$344$	2.48570	+	0.357390i	0.134020	+	0.0192692i
$345$		0			0
$346$	0.863733	−	1.34399i	0.0464345	−	0.0722536i
$347$	−0.768267	−	1.68227i	−0.0412428	−	0.0903090i	0.887889	−	0.460057i	$-0.152171\pi$
$347$	−0.768267	−	1.68227i	−0.0412428	−	0.0903090i	−0.929132	+	0.369748i	$0.879444\pi$
$348$		0			0
$349$	30.8517	+	9.05888i	1.65146	+	0.484911i	0.969215	−	0.246217i	$-0.0791876\pi$
$349$	30.8517	+	9.05888i	1.65146	+	0.484911i	0.682240	+	0.731128i	$0.261006\pi$
$350$	−0.903001	+	0.129832i	−0.0482674	+	0.00693981i
$351$		0			0
$352$	−0.160451	+	0.0471127i	−0.00855207	+	0.00251112i
$353$	−3.63176	−	1.06638i	−0.193299	−	0.0567577i	0.183650	−	0.982992i	$-0.441209\pi$
$353$	−3.63176	−	1.06638i	−0.193299	−	0.0567577i	−0.376949	+	0.926234i	$0.623027\pi$
$354$		0			0
$355$	34.9194	−	30.2578i	1.85333	−	1.60592i
$356$	−15.6627	−	24.3717i	−0.830123	−	1.29170i
$357$		0			0
$358$	−0.733989	−	0.847069i	−0.0387925	−	0.0447690i
$359$	6.46422	+	22.0151i	0.341168	+	1.16191i	0.934205	+	0.356737i	$0.116111\pi$
$359$	6.46422	+	22.0151i	0.341168	+	1.16191i	−0.593036	+	0.805176i	$0.702071\pi$
$360$		0			0
$361$	−23.1386	+	6.79409i	−1.21782	+	0.357584i
$362$	−0.931130	+	0.598401i	−0.0489391	+	0.0314513i
$363$		0			0
$364$	−22.3549			−1.17171
$365$	16.7257			0.875464
$366$		0			0
$367$	9.77249	+	8.46791i	0.510120	+	0.442021i	0.871499	−	0.490398i	$-0.163148\pi$
$367$	9.77249	+	8.46791i	0.510120	+	0.442021i	−0.361379	+	0.932419i	$0.617694\pi$
$368$	−19.6202	+	2.82096i	−1.02277	+	0.147053i
$369$		0			0
$370$	0.300872	−	0.347224i	0.0156416	−	0.0180513i
$371$	20.4327	+	9.33130i	1.06081	+	0.484457i
$372$		0			0
$373$		−	26.9749i		−	1.39671i	−0.715752	−	0.698354i	$-0.753916\pi$
$373$		−	26.9749i		−	1.39671i	0.715752	−	0.698354i	$-0.246084\pi$
$374$	−0.0613026	−	0.0279960i	−0.00316988	−	0.00144764i
$375$		0			0
$376$	−0.549096	−	1.87005i	−0.0283175	−	0.0964404i
$377$	9.64927	+	21.1290i	0.496963	+	1.08820i
$378$		0			0
$379$	20.5839	−	17.8361i	1.05733	−	0.916178i	0.0606916	−	0.998157i	$-0.480669\pi$
$379$	20.5839	−	17.8361i	1.05733	−	0.916178i	0.996634	+	0.0819787i	$0.0261239\pi$
$380$	26.8879	−	31.0303i	1.37932	−	1.59182i
$381$		0			0
$382$	0.788753	+	0.910269i	0.0403561	+	0.0465734i
$383$	−0.741776	−	5.15917i	−0.0379030	−	0.263621i	0.962054	−	0.272858i	$-0.0879689\pi$
$383$	−0.741776	−	5.15917i	−0.0379030	−	0.263621i	−0.999957	+	0.00923683i	$0.997060\pi$
$384$		0			0
$385$	0.358218	+	1.21998i	0.0182565	+	0.0621759i
$386$	−1.31970	−	0.848120i	−0.0671710	−	0.0431682i
$387$		0			0
$388$	1.70184	−	5.79594i	0.0863979	−	0.294244i
$389$	−19.2604	+	8.79592i	−0.976540	+	0.445971i	−0.838766	−	0.544493i	$-0.816722\pi$
$389$	−19.2604	+	8.79592i	−0.976540	+	0.445971i	−0.137774	+	0.990464i	$0.543995\pi$
$390$		0			0
$391$	−20.2711	−	13.0274i	−1.02515	−	0.658825i
$392$	−0.324937	+	0.374997i	−0.0164118	+	0.0189402i
$393$		0			0
$394$	0.684916	−	1.49976i	0.0345056	−	0.0755567i
$395$	9.38084	+	1.34876i	0.472001	+	0.0678636i
$396$		0			0
$397$	26.9409	+	17.3138i	1.35212	+	0.868957i	0.997808	−	0.0661689i	$-0.0210776\pi$
$397$	26.9409	+	17.3138i	1.35212	+	0.868957i	0.354315	+	0.935126i	$0.384714\pi$
$398$	0.107034	+	0.0314281i	0.00536515	+	0.00157535i
$399$		0			0
$400$	−2.72784	+	18.9726i	−0.136392	+	0.948628i
$401$	11.5166			0.575109			0.287555	−	0.957764i	$-0.407158\pi$
$401$	11.5166			0.575109			0.287555	+	0.957764i	$0.407158\pi$
$402$		0			0
$403$	−40.1913			−2.00207
$404$	4.09892	−	28.5086i	0.203929	−	1.41836i
$405$		0			0
$406$	−0.875501	−	0.257070i	−0.0434504	−	0.0127582i
$407$	−0.264940	−	0.170267i	−0.0131326	−	0.00843981i
$408$		0			0
$409$	30.5527	+	4.39282i	1.51073	+	0.217211i	0.847337	−	0.531056i	$-0.178205\pi$
$409$	30.5527	+	4.39282i	1.51073	+	0.217211i	0.663398	+	0.748267i	$0.269114\pi$
$410$	0.320259	−	0.701269i	0.0158165	−	0.0346332i
$411$		0			0
$412$	10.3324	−	11.9242i	0.509042	−	0.587465i
$413$	−6.91952	−	4.44690i	−0.340487	−	0.218818i
$414$		0			0
$415$	−43.0669	+	19.6680i	−2.11407	+	0.965465i
$416$	1.30336	−	4.43883i	0.0639024	−	0.217632i
$417$		0			0
$418$	0.0773126	+	0.0496858i	0.00378148	+	0.00243021i
$419$	5.04318	+	17.1755i	0.246375	+	0.839077i	0.986098	+	0.166165i	$0.0531386\pi$
$419$	5.04318	+	17.1755i	0.246375	+	0.839077i	−0.739723	+	0.672912i	$0.765043\pi$
$420$		0			0
$421$	4.55428	+	31.6757i	0.221962	+	1.54378i	0.730603	+	0.682802i	$0.239239\pi$
$421$	4.55428	+	31.6757i	0.221962	+	1.54378i	−0.508641	+	0.860979i	$0.669852\pi$
$422$	−0.273029	−	0.315092i	−0.0132908	−	0.0153384i
$423$		0			0
$424$	−2.02832	+	2.34080i	−0.0985038	+	0.113680i
$425$	−17.6096	+	15.2588i	−0.854192	+	0.740161i
$426$		0			0
$427$	−4.54037	−	9.94203i	−0.219724	−	0.481128i
$428$	0.912242	+	3.10681i	0.0440949	+	0.150173i
$429$		0			0
$430$	1.79425	+	0.819408i	0.0865265	+	0.0395153i
$431$		−	32.9596i		−	1.58761i	−0.608174	−	0.793804i	$-0.708098\pi$
$431$		−	32.9596i		−	1.58761i	0.608174	−	0.793804i	$-0.291902\pi$
$432$		0			0
$433$	−2.61461	−	1.19405i	−0.125650	−	0.0573825i	0.351598	−	0.936151i	$-0.385638\pi$
$433$	−2.61461	−	1.19405i	−0.125650	−	0.0573825i	−0.477248	+	0.878769i	$0.658366\pi$
$434$	1.03391	−	1.19320i	0.0496294	−	0.0572754i
$435$		0			0
$436$	−18.5780	+	2.67112i	−0.889727	+	0.127923i
$437$	24.8335	+	21.5183i	1.18795	+	1.02936i
$438$		0			0
$439$	14.2430			0.679781			0.339890	−	0.940465i	$-0.389610\pi$
$439$	14.2430			0.679781			0.339890	+	0.940465i	$0.389610\pi$
$440$	−0.175322			−0.00835817
$441$		0			0
$442$	1.56843	−	1.00797i	0.0746027	−	0.0479443i
$443$	−0.926972	+	0.272183i	−0.0440418	+	0.0129318i	−0.303679	−	0.952774i	$-0.598215\pi$
$443$	−0.926972	+	0.272183i	−0.0440418	+	0.0129318i	0.259637	+	0.965706i	$0.416397\pi$
$444$		0			0
$445$	−12.8428	−	43.7386i	−0.608807	−	2.07341i
$446$	1.33227	+	1.53752i	0.0630846	+	0.0728035i
$447$		0			0
$448$	−9.90952	−	15.4195i	−0.468181	−	0.728504i
$449$	−23.5753	+	20.4281i	−1.11259	+	0.964063i	−0.999564	−	0.0295290i	$-0.990599\pi$
$449$	−23.5753	+	20.4281i	−1.11259	+	0.964063i	−0.113024	+	0.993592i	$0.536054\pi$
$450$		0			0
$451$	−0.507049	−	0.148883i	−0.0238760	−	0.00701063i
$452$	−15.7804	+	4.63355i	−0.742248	+	0.217944i
$453$		0			0
$454$	−0.000473491	0	6.80778e-5i	−2.22221e−5	0	3.19505e-6i
$455$	−33.7503	−	9.90999i	−1.58224	−	0.464588i
$456$		0			0
$457$	2.83305	+	6.20352i	0.132525	+	0.290189i	0.964248	−	0.265002i	$-0.0853726\pi$
$457$	2.83305	+	6.20352i	0.132525	+	0.290189i	−0.831723	+	0.555191i	$0.812645\pi$
$458$	−1.21336	+	1.88803i	−0.0566966	+	0.0882217i
$459$		0			0
$460$	−30.9737	−	4.45334i	−1.44415	−	0.207638i
$461$	−8.61951	−	3.93640i	−0.401450	−	0.183336i	0.204450	−	0.978877i	$-0.434460\pi$
$461$	−8.61951	−	3.93640i	−0.401450	−	0.183336i	−0.605900	+	0.795541i	$0.707187\pi$
$462$		0			0
$463$	0.247537	+	0.385175i	0.0115040	+	0.0179006i	0.846958	−	0.531660i	$-0.178432\pi$
$463$	0.247537	+	0.385175i	0.0115040	+	0.0179006i	−0.835454	+	0.549561i	$0.814795\pi$
$464$	−10.3648	+	16.1280i	−0.481174	+	0.748722i
$465$		0			0
$466$	1.07655	+	1.24241i	0.0498704	+	0.0575535i
$467$	2.11155	+	0.303595i	0.0977109	+	0.0140487i	0.190997	−	0.981591i	$-0.438828\pi$
$467$	2.11155	+	0.303595i	0.0977109	+	0.0140487i	−0.0932859	+	0.995639i	$0.529737\pi$
$468$		0			0
$469$	4.20007	+	18.6595i	0.193941	+	0.861617i
$470$		−	1.53086i		−	0.0706135i
$471$		0			0
$472$	0.857145	−	0.742720i	0.0394533	−	0.0341865i
$473$	0.380929	−	1.29732i	0.0175151	−	0.0596510i
$474$		0			0
$475$	26.7306	−	17.1787i	1.22648	−	0.788214i
$476$	3.19202	−	22.2010i	0.146306	−	1.01758i
$477$		0			0
$478$	0.160172	−	1.11402i	0.00732609	−	0.0509541i
$479$	31.0214	+	26.8802i	1.41740	+	1.22819i	0.936147	+	0.351609i	$0.114365\pi$
$479$	31.0214	+	26.8802i	1.41740	+	1.22819i	0.481258	+	0.876579i	$0.340180\pi$
$480$		0			0
$481$	7.92525	−	3.61934i	0.361360	−	0.165028i
$482$	−0.513187	−	1.12372i	−0.0233750	−	0.0511841i
$483$		0			0
$484$	−3.11220	−	21.6458i	−0.141464	−	0.983901i
$485$	5.13872	−	7.99600i	0.233337	−	0.363080i
$486$		0			0
$487$	−8.22099	+	27.9981i	−0.372529	+	1.26872i	0.533608	+	0.845732i	$0.320836\pi$
$487$	−8.22099	+	27.9981i	−0.372529	+	1.26872i	−0.906137	+	0.422984i	$0.860983\pi$
$488$	1.49174	−	0.214480i	0.0675279	−	0.00970905i
$489$		0			0
$490$	−0.327870	+	0.210709i	−0.0148117	+	0.00951888i
$491$	−10.2420	−	8.87474i	−0.462215	−	0.400511i	0.392383	−	0.919802i	$-0.371651\pi$
$491$	−10.2420	−	8.87474i	−0.462215	−	0.400511i	−0.854598	+	0.519291i	$0.826196\pi$
$492$		0			0
$493$	−22.3613	+	6.56587i	−1.00710	+	0.295712i
$494$	−2.31268	+	1.05616i	−0.104052	+	0.0475191i
$495$		0			0
$496$	−17.9342	−	27.9061i	−0.805269	−	1.25302i
$497$	−14.2984	+	31.3092i	−0.641372	+	1.40441i
$498$		0			0
$499$			34.6018i			1.54899i	0.632580	+	0.774495i	$0.281996\pi$
$499$			34.6018i			1.54899i	−0.632580	+	0.774495i	$0.718004\pi$
$500$	0.417919	−	0.915116i	0.0186899	−	0.0409252i
$501$		0			0
$502$	0.0745762	+	0.518689i	0.00332850	+	0.0231502i
$503$	−4.57575	−	31.8250i	−0.204023	−	1.41901i	−0.792193	−	0.610271i	$-0.791061\pi$
$503$	−4.57575	−	31.8250i	−0.204023	−	1.41901i	0.588170	−	0.808737i	$-0.299848\pi$
$504$		0			0
$505$	18.8263	−	41.2239i	0.837760	−	1.83444i
$506$		−	0.0700407i		−	0.00311369i
$507$		0			0
$508$	−2.87148	+	6.28766i	−0.127401	+	0.278970i
$509$	15.5214	+	24.1518i	0.687976	+	1.07051i	0.992994	+	0.118165i	$0.0377012\pi$
$509$	15.5214	+	24.1518i	0.687976	+	1.07051i	−0.305018	+	0.952347i	$0.598662\pi$
$510$		0			0
$511$	−11.3336	+	5.17588i	−0.501369	+	0.228968i
$512$	6.11266	−	1.79484i	0.270144	−	0.0793214i
$513$		0			0
$514$	1.65119	+	1.43076i	0.0728308	+	0.0631082i
$515$	20.8854	−	13.4223i	0.920322	−	0.591455i
$516$		0			0
$517$	−1.03868	+	0.149340i	−0.0456811	+	0.00656796i
$518$	−0.0964243	+	0.328391i	−0.00423664	+	0.0144287i
$519$		0			0
$520$	2.62224	−	4.08028i	0.114993	−	0.178932i
$521$	1.68006	+	11.6851i	0.0736049	+	0.511933i	0.992955	+	0.118493i	$0.0378062\pi$
$521$	1.68006	+	11.6851i	0.0736049	+	0.511933i	−0.919350	+	0.393440i	$0.871285\pi$
$522$		0			0
$523$	0.879510	+	1.92586i	0.0384583	+	0.0842119i	0.927886	−	0.372864i	$-0.121624\pi$
$523$	0.879510	+	1.92586i	0.0384583	+	0.0842119i	−0.889428	+	0.457076i	$0.848897\pi$
$524$	−4.01036	+	1.83147i	−0.175193	+	0.0800081i
$525$		0			0
$526$	−0.110797	−	0.0960061i	−0.00483098	−	0.00418606i
$527$	5.73886	−	39.9147i	0.249989	−	1.73871i
$528$		0			0
$529$	0.290757	−	2.02226i	0.0126416	−	0.0879244i
$530$	−2.04663	+	1.31529i	−0.0888999	+	0.0571325i
$531$		0			0
$532$	−8.61713	+	29.3473i	−0.373600	+	1.27237i
$533$	11.0487	−	9.57377i	0.478573	−	0.414686i
$534$		0			0
$535$			5.09492i			0.220272i
$536$	−2.63187	−	0.169197i	−0.113679	−	0.00730818i
$537$		0			0
$538$	−1.53820	−	0.221160i	−0.0663165	−	0.00953488i
$539$	0.174950	+	0.201903i	0.00753561	+	0.00869656i
$540$		0			0
$541$	9.21952	−	14.3459i	0.396378	−	0.616777i	−0.584501	−	0.811393i	$-0.698710\pi$
$541$	9.21952	−	14.3459i	0.396378	−	0.616777i	0.980879	+	0.194616i	$0.0623461\pi$
$542$	−0.458891	−	0.714049i	−0.0197111	−	0.0306710i
$543$		0			0
$544$	4.22217	+	1.92820i	0.181024	+	0.0826709i
$545$	−29.2324	−	4.20298i	−1.25218	−	0.180036i
$546$		0			0
$547$	−4.00531	+	6.23239i	−0.171255	+	0.266478i	−0.916263	−	0.400578i	$-0.868809\pi$
$547$	−4.00531	+	6.23239i	−0.171255	+	0.266478i	0.745008	+	0.667056i	$0.232446\pi$
$548$	−11.8815	−	26.0169i	−0.507554	−	1.11139i
$549$		0			0
$550$	−0.0649852	−	0.0190814i	−0.00277098	−	0.000813633i
$551$	31.4574	−	4.52289i	1.34013	−	0.192681i
$552$		0			0
$553$	−6.77399	+	1.98902i	−0.288059	+	0.0845818i
$554$	−0.287093	−	0.0842980i	−0.0121974	−	0.00358148i
$555$		0			0
$556$	−15.6278	+	13.5416i	−0.662766	+	0.574290i
$557$	−15.2938	−	23.7977i	−0.648020	−	1.00834i	−0.997449	−	0.0713763i	$-0.977261\pi$
$557$	−15.2938	−	23.7977i	−0.648020	−	1.00834i	0.349429	−	0.936963i	$-0.386375\pi$
$558$		0			0
$559$	24.4952	+	28.2690i	1.03604	+	1.19565i
$560$	−8.17926	−	27.8560i	−0.345637	−	1.17713i
$561$		0			0
$562$	−1.15712	+	0.339762i	−0.0488103	+	0.0143320i
$563$	2.47457	−	1.59031i	0.104291	−	0.0670237i	−0.487456	−	0.873148i	$-0.662075\pi$
$563$	2.47457	−	1.59031i	0.104291	−	0.0670237i	0.591747	+	0.806124i	$0.298439\pi$
$564$		0			0
$565$	−25.8786			−1.08872
$566$	1.20697			0.0507326
$567$		0			0
$568$	−3.58684	−	3.10801i	−0.150500	−	0.130409i
$569$	−24.6462	+	3.54358i	−1.03322	+	0.148555i	−0.638004	−	0.770033i	$-0.720240\pi$
$569$	−24.6462	+	3.54358i	−1.03322	+	0.148555i	−0.395217	+	0.918588i	$0.629331\pi$
$570$		0			0
$571$	−7.86833	+	9.08054i	−0.329280	+	0.380009i	−0.896115	−	0.443822i	$-0.853622\pi$
$571$	−7.86833	+	9.08054i	−0.329280	+	0.380009i	0.566835	+	0.823831i	$0.308168\pi$
$572$	−1.50966	−	0.689440i	−0.0631221	−	0.0288269i
$573$		0			0
$574$			0.574297i			0.0239707i
$575$	−22.0280	−	10.0599i	−0.918631	−	0.419525i
$576$		0			0
$577$	−8.11244	−	27.6284i	−0.337725	−	1.15019i	−0.936908	−	0.349575i	$-0.886326\pi$
$577$	−8.11244	−	27.6284i	−0.337725	−	1.15019i	0.599183	−	0.800612i	$-0.295492\pi$
$578$	0.207306	+	0.453936i	0.00862278	+	0.0188813i
$579$		0			0
$580$	−22.8728	+	19.8194i	−0.949742	+	0.822956i
$581$	23.0964	−	26.6547i	0.958201	−	1.10582i
$582$		0			0
$583$	1.09207	+	1.26032i	0.0452289	+	0.0521970i
$584$	−0.244501	−	1.70054i	−0.0101175	−	0.0703688i
$585$		0			0
$586$	0.251188	+	0.855467i	0.0103765	+	0.0353390i
$587$	−2.64263	−	1.69831i	−0.109073	−	0.0700969i	0.484967	−	0.874532i	$-0.338832\pi$
$587$	−2.64263	−	1.69831i	−0.109073	−	0.0700969i	−0.594040	+	0.804436i	$0.702468\pi$
$588$		0			0
$589$	−15.4925	+	52.7628i	−0.638359	+	2.17405i
$590$	0.810340	−	0.370070i	0.0333612	−	0.0152355i
$591$		0			0
$592$	6.04943	+	3.88773i	0.248630	+	0.159785i
$593$	−27.3643	+	31.5800i	−1.12372	+	1.29684i	−0.173642	+	0.984809i	$0.555554\pi$
$593$	−27.3643	+	31.5800i	−1.12372	+	1.29684i	−0.950073	+	0.312028i	$0.898992\pi$
$594$		0			0
$595$	14.6609	−	32.1030i	0.601040	−	1.31609i
$596$	−20.1000	−	2.88995i	−0.823329	−	0.118377i
$597$		0			0
$598$	1.63006	+	1.04758i	0.0666581	+	0.0428386i
$599$	−41.2565	−	12.1140i	−1.68570	−	0.494965i	−0.708216	−	0.705996i	$-0.750500\pi$
$599$	−41.2565	−	12.1140i	−1.68570	−	0.494965i	−0.977479	+	0.211031i	$0.932318\pi$
$600$		0			0
$601$	−3.05526	+	21.2498i	−0.124627	+	0.866798i	0.827581	+	0.561347i	$0.189717\pi$
$601$	−3.05526	+	21.2498i	−0.124627	+	0.866798i	−0.952208	+	0.305452i	$0.901193\pi$
$602$	−1.46938			−0.0598876
$603$		0			0
$604$	−9.93354			−0.404190
$605$	4.89701	−	34.0595i	0.199092	−	1.38471i
$606$		0			0
$607$	18.1349	+	5.32489i	0.736073	+	0.216131i	0.628219	−	0.778036i	$-0.283784\pi$
$607$	18.1349	+	5.32489i	0.736073	+	0.216131i	0.107854	+	0.994167i	$0.465602\pi$
$608$	−5.32485	−	3.42207i	−0.215951	−	0.138783i
$609$		0			0
$610$	1.17171	+	0.168466i	0.0474410	+	0.00682098i
$611$	12.0596	−	26.4069i	0.487880	−	1.06831i
$612$		0			0
$613$	−0.222989	+	0.257343i	−0.00900644	+	0.0103940i	−0.760235	−	0.649648i	$-0.774916\pi$
$613$	−0.222989	+	0.257343i	−0.00900644	+	0.0103940i	0.751228	+	0.660042i	$0.229462\pi$
$614$	1.84521	+	1.18584i	0.0744666	+	0.0478568i
$615$		0			0
$616$	0.118801	−	0.0542547i	0.00478664	−	0.00218598i
$617$	1.22064	−	4.15711i	0.0491410	−	0.167359i	−0.931267	−	0.364339i	$-0.881295\pi$
$617$	1.22064	−	4.15711i	0.0491410	−	0.167359i	0.980408	+	0.196980i	$0.0631133\pi$
$618$		0			0
$619$	6.64783	+	4.27230i	0.267199	+	0.171718i	0.667379	−	0.744718i	$-0.267416\pi$
$619$	6.64783	+	4.27230i	0.267199	+	0.171718i	−0.400180	+	0.916436i	$0.631052\pi$
$620$	−14.7536	−	50.2462i	−0.592520	−	2.01794i
$621$		0			0
$622$	−0.286933	−	1.99566i	−0.0115050	−	0.0800188i
$623$	22.2377	+	25.6636i	0.890933	+	1.02819i
$624$		0			0
$625$	16.8814	−	19.4821i	0.675254	−	0.779285i
$626$	0.330237	−	0.286152i	0.0131989	−	0.0114369i
$627$		0			0
$628$	15.0057	+	32.8579i	0.598792	+	1.31117i
$629$	2.46279	+	8.38749i	0.0981979	+	0.334431i
$630$		0			0
$631$	−34.2509	−	15.6418i	−1.36351	−	0.622692i	−0.406738	−	0.913545i	$-0.633334\pi$
$631$	−34.2509	−	15.6418i	−1.36351	−	0.622692i	−0.956768	+	0.290853i	$0.906061\pi$
$632$		−	0.973486i		−	0.0387232i
$633$		0			0
$634$	0.670332	+	0.306130i	0.0266223	+	0.0121580i
$635$	−7.12256	+	8.21987i	−0.282650	+	0.326195i
$636$		0			0
$637$	−7.31555	+	1.05182i	−0.289853	+	0.0416745i
$638$	−0.0511958	−	0.0443614i	−0.00202686	−	0.00175628i
$639$		0			0
$640$	8.03261			0.317517
$641$	31.2239			1.23327			0.616634	−	0.787250i	$-0.288496\pi$
$641$	31.2239			1.23327			0.616634	+	0.787250i	$0.288496\pi$
$642$		0			0
$643$	−12.2304	+	7.86003i	−0.482322	+	0.309969i	−0.759111	−	0.650961i	$-0.774366\pi$
$643$	−12.2304	+	7.86003i	−0.482322	+	0.309969i	0.276789	+	0.960931i	$0.410730\pi$
$644$	22.3663	−	6.56735i	0.881358	−	0.258790i
$645$		0			0
$646$	−0.718670	−	2.44756i	−0.0282757	−	0.0962981i
$647$	−17.8998	−	20.6574i	−0.703713	−	0.812128i	0.285536	−	0.958368i	$-0.407828\pi$
$647$	−17.8998	−	20.6574i	−0.703713	−	0.812128i	−0.989249	+	0.146240i	$0.953283\pi$
$648$		0			0
$649$	−0.330141	−	0.513709i	−0.0129592	−	0.0201649i
$650$	1.41604	−	1.22701i	0.0555418	−	0.0481272i
$651$		0			0
$652$	16.6409	+	4.88620i	0.651707	+	0.191358i
$653$	44.6814	−	13.1196i	1.74852	−	0.513411i	0.758174	−	0.652052i	$-0.226092\pi$
$653$	44.6814	−	13.1196i	1.74852	−	0.513411i	0.990343	+	0.138641i	$0.0442735\pi$
$654$		0			0
$655$	−6.86654	+	0.987260i	−0.268298	+	0.0385754i
$656$	11.5775	+	3.39947i	0.452027	+	0.132727i
$657$		0			0
$658$	0.473736	+	1.03734i	0.0184681	+	0.0404396i
$659$	1.27534	−	1.98447i	0.0496803	−	0.0773040i	−0.815525	−	0.578722i	$-0.803552\pi$
$659$	1.27534	−	1.98447i	0.0496803	−	0.0773040i	0.865205	+	0.501418i	$0.167188\pi$
$660$		0			0
$661$	14.7770	+	2.12461i	0.574758	+	0.0826378i	0.423564	−	0.905866i	$-0.360779\pi$
$661$	14.7770	+	2.12461i	0.574758	+	0.0826378i	0.151195	+	0.988504i	$0.451688\pi$
$662$	0.0586264	+	0.0267738i	0.00227858	+	0.00104059i
$663$		0			0
$664$	2.62925	+	4.09119i	0.102035	+	0.158769i
$665$	−26.0195	+	40.4871i	−1.00899	+	1.57002i
$666$		0			0
$667$	−15.8614	−	18.3051i	−0.614157	−	0.708774i
$668$	−20.9981	−	3.01907i	−0.812440	−	0.116811i
$669$		0			0
$670$	−1.94606	−	0.709922i	−0.0751827	−	0.0274267i
$671$		−	0.811430i		−	0.0313249i
$672$		0			0
$673$	4.80004	−	4.15926i	0.185028	−	0.160328i	−0.557422	−	0.830230i	$-0.688209\pi$
$673$	4.80004	−	4.15926i	0.185028	−	0.160328i	0.742450	+	0.669902i	$0.233664\pi$
$674$	0.314156	−	1.06992i	0.0121008	−	0.0412116i
$675$		0			0
$676$	16.8235	−	10.8118i	0.647056	−	0.415838i
$677$	−1.03776	+	7.21775i	−0.0398842	+	0.277401i	−0.999998	−	0.00221027i	$-0.999296\pi$
$677$	−1.03776	+	7.21775i	−0.0398842	+	0.277401i	0.960113	+	0.279611i	$0.0902055\pi$
$678$		0			0
$679$	−1.00766	+	7.00842i	−0.0386704	+	0.268958i
$680$	3.67777	+	3.18681i	0.141036	+	0.122208i
$681$		0			0
$682$	0.106621	−	0.0486921i	0.00408272	−	0.00186452i
$683$	−3.85988	−	8.45196i	−0.147694	−	0.323405i	0.821297	−	0.570501i	$-0.193251\pi$
$683$	−3.85988	−	8.45196i	−0.147694	−	0.323405i	−0.968991	+	0.247096i	$0.920524\pi$
$684$		0			0
$685$	−6.40478	−	44.5462i	−0.244714	−	1.70202i
$686$	0.870429	−	1.35441i	0.0332331	−	0.0517118i
$687$		0			0
$688$	−8.69782	+	29.6220i	−0.331601	+	1.12933i
$689$	−45.6651	+	6.56565i	−1.73970	+	0.250131i
$690$		0			0
$691$	19.6802	−	12.6477i	0.748669	−	0.481141i	−0.109833	−	0.993950i	$-0.535032\pi$
$691$	19.6802	−	12.6477i	0.748669	−	0.481141i	0.858502	+	0.512810i	$0.171395\pi$
$692$	29.8327	+	25.8502i	1.13407	+	0.982676i
$693$		0			0
$694$	−0.143167	+	0.0420375i	−0.00543453	+	0.00159572i
$695$	−29.5971	+	13.5166i	−1.12268	+	0.512712i
$696$		0			0
$697$	7.93023	+	12.3397i	0.300379	+	0.467399i
$698$	1.07768	−	2.35979i	0.0407908	−	0.0893194i
$699$		0			0
$700$		−	22.5411i		−	0.851974i
$701$	5.27753	−	11.5562i	0.199330	−	0.436471i	−0.783400	−	0.621518i	$-0.786516\pi$
$701$	5.27753	−	11.5562i	0.199330	−	0.436471i	0.982730	+	0.185047i	$0.0592437\pi$
$702$		0			0
$703$	−1.69649	−	11.7993i	−0.0639842	−	0.445020i
$704$	−0.193658	−	1.34692i	−0.00729876	−	0.0507640i
$705$		0			0
$706$	−0.126861	+	0.277786i	−0.00477447	+	0.0104546i
$707$			33.7598i			1.26967i
$708$		0			0
$709$	−9.72629	+	21.2976i	−0.365278	+	0.799848i	0.634362	+	0.773036i	$0.281263\pi$
$709$	−9.72629	+	21.2976i	−0.365278	+	0.799848i	−0.999640	+	0.0268121i	$0.991464\pi$
$710$	−2.01543	−	3.13607i	−0.0756377	−	0.117695i
$711$		0			0
$712$	−4.25925	+	1.94513i	−0.159622	+	0.0728970i
$713$	40.2119	−	11.8073i	1.50595	−	0.442186i
$714$		0			0
$715$	−1.97358	−	1.71012i	−0.0738079	−	0.0639549i
$716$	23.2976	−	14.9725i	0.870674	−	0.559548i
$717$		0			0
$718$	1.83234	−	0.263451i	0.0683823	−	0.00983189i
$719$	−6.51726	+	22.1957i	−0.243053	+	0.827761i	0.744112	+	0.668055i	$0.232873\pi$
$719$	−6.51726	+	22.1957i	−0.243053	+	0.827761i	−0.987165	+	0.159706i	$0.948945\pi$
$720$		0			0
$721$	−9.99869	+	15.5583i	−0.372371	+	0.579420i
$722$	0.276895	+	1.92585i	0.0103050	+	0.0716725i
$723$		0			0
$724$	−11.3608	−	24.8767i	−0.422222	−	0.924536i
$725$	−21.3050	+	9.72965i	−0.791247	+	0.361350i
$726$		0			0
$727$	−4.15067	−	3.59658i	−0.153940	−	0.133390i	0.574486	−	0.818515i	$-0.305202\pi$
$727$	−4.15067	−	3.59658i	−0.153940	−	0.133390i	−0.728426	+	0.685125i	$0.759748\pi$
$728$	−0.514199	+	3.57633i	−0.0190575	+	0.132548i
$729$		0			0
$730$	0.192046	−	1.33571i	0.00710794	−	0.0494368i
$731$	−31.5721	+	20.2901i	−1.16773	+	0.750458i
$732$		0			0
$733$	0.180653	−	0.615249i	0.00667258	−	0.0227247i	−0.956089	−	0.293075i	$-0.905321\pi$
$733$	0.180653	−	0.615249i	0.00667258	−	0.0227247i	0.962762	+	0.270350i	$0.0871396\pi$
$734$	0.788452	−	0.683198i	0.0291023	−	0.0252173i
$735$		0			0
$736$			4.82400i			0.177815i
$737$	−0.291834	+	1.38964i	−0.0107499	+	0.0511881i
$738$		0			0
$739$	−41.2112	−	5.92528i	−1.51598	−	0.217965i	−0.666467	−	0.745534i	$-0.732194\pi$
$739$	−41.2112	−	5.92528i	−1.51598	−	0.217965i	−0.849512	+	0.527569i	$0.823103\pi$
$740$	7.43405	+	8.57935i	0.273281	+	0.315383i
$741$		0			0
$742$	0.979803	−	1.52460i	0.0359697	−	0.0559699i
$743$	6.31357	+	9.82411i	0.231623	+	0.360412i	0.937537	−	0.347885i	$-0.113100\pi$
$743$	6.31357	+	9.82411i	0.231623	+	0.360412i	−0.705915	+	0.708297i	$0.749464\pi$
$744$		0			0
$745$	−29.0649	−	13.2735i	−1.06486	−	0.486304i
$746$	−2.15420	−	0.309728i	−0.0788710	−	0.0113399i
$747$		0			0
$748$	0.900256	−	1.40083i	0.0329166	−	0.0512193i
$749$	−1.57665	−	3.45239i	−0.0576097	−	0.126148i
$750$		0			0
$751$	−11.6624	−	3.42439i	−0.425567	−	0.124958i	0.0619341	−	0.998080i	$-0.480273\pi$
$751$	−11.6624	−	3.42439i	−0.425567	−	0.124958i	−0.487501	+	0.873123i	$0.662091\pi$
$752$	23.7164	−	3.40990i	0.864848	−	0.124346i
$753$		0			0
$754$	1.79814	−	0.527982i	0.0654845	−	0.0192280i
$755$	−14.9972	−	4.40357i	−0.545803	−	0.160262i
$756$		0			0
$757$	5.62313	−	4.87247i	0.204376	−	0.177093i	−0.546659	−	0.837356i	$-0.684100\pi$
$757$	5.62313	−	4.87247i	0.204376	−	0.177093i	0.751035	+	0.660263i	$0.229555\pi$
$758$	−1.18804	−	1.84862i	−0.0431514	−	0.0671449i
$759$		0			0
$760$	−4.34576	−	5.01528i	−0.157637	−	0.181923i
$761$	9.18837	+	31.2927i	0.333078	+	1.13436i	0.940447	+	0.339940i	$0.110407\pi$
$761$	9.18837	+	31.2927i	0.333078	+	1.13436i	−0.607369	+	0.794420i	$0.707775\pi$
$762$		0			0
$763$	21.1089	−	6.19814i	0.764195	−	0.224388i
$764$	−25.0359	+	16.0896i	−0.905767	+	0.582101i
$765$		0			0
$766$	−0.420526			−0.0151942
$767$	16.8934			0.609985
$768$		0			0
$769$	11.7925	+	10.2183i	0.425250	+	0.368481i	0.841034	−	0.540982i	$-0.181947\pi$
$769$	11.7925	+	10.2183i	0.425250	+	0.368481i	−0.415784	+	0.909463i	$0.636493\pi$
$770$	0.101540	−	0.0145992i	0.00365925	−	0.000526120i
$771$		0			0
$772$	25.3829	−	29.2935i	0.913552	−	1.05430i
$773$	23.3213	+	10.6505i	0.838809	+	0.383071i	0.788029	−	0.615639i	$-0.211102\pi$
$773$	23.3213	+	10.6505i	0.838809	+	0.383071i	0.0507803	+	0.998710i	$0.483829\pi$
$774$		0			0
$775$		−	40.5262i		−	1.45574i
$776$	−0.888088	−	0.405576i	−0.0318805	−	0.0145593i
$777$		0			0
$778$	0.481289	+	1.63912i	0.0172551	+	0.0587653i
$779$	−8.30940	−	18.1950i	−0.297715	−	0.651905i
$780$		0			0
$781$	−1.93119	+	1.67339i	−0.0691035	+	0.0598785i
$782$	−1.27312	+	1.46926i	−0.0455266	+	0.0525405i
$783$		0			0
$784$	−3.99466	−	4.61008i	−0.142666	−	0.164646i
$785$	8.08886	+	56.2593i	0.288704	+	2.00798i
$786$		0			0
$787$	6.27434	+	21.3685i	0.223656	+	0.761703i	0.992498	+	0.122264i	$0.0390153\pi$
$787$	6.27434	+	21.3685i	0.223656	+	0.761703i	−0.768841	+	0.639439i	$0.779166\pi$
$788$	34.2710	+	22.0246i	1.22085	+	0.784595i
$789$		0			0
$790$	0.215423	−	0.733663i	0.00766441	−	0.0261026i
$791$	17.5357	−	8.00829i	0.623498	−	0.284742i
$792$		0			0
$793$	18.8844	+	12.1363i	0.670605	+	0.430972i
$794$	1.69201	−	1.95269i	0.0600473	−	0.0692983i
$795$		0			0
$796$	−1.14501	+	2.50721i	−0.0405837	+	0.0888658i
$797$	25.6237	+	3.68413i	0.907639	+	0.130499i	0.580295	−	0.814407i	$-0.302937\pi$
$797$	25.6237	+	3.68413i	0.907639	+	0.130499i	0.327344	+	0.944905i	$0.393846\pi$
$798$		0			0
$799$	24.5031	+	15.7472i	0.866858	+	0.557096i
$800$	4.47581	+	1.31422i	0.158244	+	0.0464646i
$801$		0			0
$802$	0.132234	−	0.919706i	0.00466934	−	0.0324760i
$803$	−0.925005			−0.0326427
$804$		0			0
$805$	36.6790			1.29276
$806$	−0.461480	+	3.20966i	−0.0162549	+	0.113056i
$807$		0			0
$808$	−4.46652	−	1.31149i	−0.157132	−	0.0461380i
$809$	28.9893	+	18.6303i	1.01921	+	0.655007i	0.939761	−	0.341832i	$-0.111047\pi$
$809$	28.9893	+	18.6303i	1.01921	+	0.655007i	0.0794496	+	0.996839i	$0.474684\pi$
$810$		0			0
$811$	1.18436	+	0.170285i	0.0415885	+	0.00597952i	0.163078	−	0.986613i	$-0.447858\pi$
$811$	1.18436	+	0.170285i	0.0415885	+	0.00597952i	−0.121489	+	0.992593i	$0.538767\pi$
$812$	9.36572	−	20.5081i	0.328672	−	0.719692i
$813$		0			0
$814$	−0.0166395	+	0.0192030i	−0.000583214	+	0.000673065i
$815$	22.9575	+	14.7539i	0.804167	+	0.516807i
$816$		0			0
$817$	46.5534	−	21.2602i	1.62870	−	0.743802i
$818$	0.701617	−	2.38949i	0.0245315	−	0.0835465i
$819$		0			0
$820$	16.0247	+	10.2985i	0.559607	+	0.359638i
$821$	−4.75400	−	16.1906i	−0.165916	−	0.565057i	−0.999912	−	0.0132864i	$-0.995771\pi$
$821$	−4.75400	−	16.1906i	−0.165916	−	0.565057i	0.833996	−	0.551770i	$-0.186048\pi$
$822$		0			0
$823$	−6.89413	−	47.9498i	−0.240314	−	1.67142i	−0.650565	−	0.759451i	$-0.725468\pi$
$823$	−6.89413	−	47.9498i	−0.240314	−	1.67142i	0.410251	−	0.911973i	$-0.365441\pi$
$824$	−1.66998	−	1.92726i	−0.0581764	−	0.0671391i
$825$		0			0
$826$	−0.434578	+	0.501530i	−0.0151209	+	0.0174505i
$827$	−37.3823	+	32.3919i	−1.29991	+	1.12638i	−0.315798	+	0.948826i	$0.602272\pi$
$827$	−37.3823	+	32.3919i	−1.29991	+	1.12638i	−0.984112	+	0.177551i	$0.943182\pi$
$828$		0			0
$829$	−9.18123	−	20.1041i	−0.318877	−	0.698244i	0.680528	−	0.732722i	$-0.261750\pi$
$829$	−9.18123	−	20.1041i	−0.318877	−	0.698244i	−0.999405	+	0.0344779i	$0.989023\pi$
$830$	1.07618	+	3.66514i	0.0373548	+	0.127219i
$831$		0			0
$832$	34.2434	+	15.6384i	1.18718	+	0.542166i
$833$		−	7.41538i		−	0.256928i
$834$		0			0
$835$	−30.3635	−	13.8666i	−1.05077	−	0.479872i
$836$	−1.48702	+	1.71611i	−0.0514296	+	0.0593529i
$837$		0			0
$838$	1.42953	−	0.205536i	0.0493824	−	0.00710012i
$839$	−24.2871	−	21.0449i	−0.838484	−	0.726551i	0.125619	−	0.992079i	$-0.459908\pi$
$839$	−24.2871	−	21.0449i	−0.838484	−	0.726551i	−0.964103	+	0.265528i	$0.914454\pi$
$840$		0			0
$841$	5.57397			0.192206
$842$	2.58190			0.0889782
$843$		0			0
$844$	8.66624	−	5.56946i	0.298304	−	0.191709i
$845$	30.1921	−	8.86521i	1.03864	−	0.304973i
$846$		0			0
$847$	7.22163	+	24.5946i	0.248138	+	0.845081i
$848$	−24.9354	−	28.7770i	−0.856286	−	0.988207i
$849$		0			0
$850$	1.01637	+	1.58150i	0.0348611	+	0.0542450i
$851$	−6.86603	+	5.94945i	−0.235365	+	0.203945i
$852$		0			0
$853$	23.0625	+	6.77176i	0.789645	+	0.231861i	0.651598	−	0.758565i	$-0.274099\pi$
$853$	23.0625	+	6.77176i	0.789645	+	0.231861i	0.138048	+	0.990426i	$0.455917\pi$
$854$	−0.846099	+	0.248437i	−0.0289529	+	0.00850134i
$855$		0			0
$856$	0.518010	−	0.0744787i	0.0177052	−	0.00254563i
$857$	−35.3742	−	10.3868i	−1.20836	−	0.354807i	−0.385317	−	0.922784i	$-0.625908\pi$
$857$	−35.3742	−	10.3868i	−1.20836	−	0.354807i	−0.823044	+	0.567977i	$0.807726\pi$
$858$		0			0
$859$	11.7199	+	25.6629i	0.399877	+	0.875608i	0.997283	+	0.0736691i	$0.0234709\pi$
$859$	11.7199	+	25.6629i	0.399877	+	0.875608i	−0.597406	+	0.801939i	$0.703802\pi$
$860$	−26.3494	+	41.0005i	−0.898507	+	1.39810i
$861$		0			0
$862$	−2.63214	−	0.378444i	−0.0896510	−	0.0128899i
$863$	26.0408	+	11.8924i	0.886440	+	0.404823i	0.805986	−	0.591935i	$-0.201636\pi$
$863$	26.0408	+	11.8924i	0.886440	+	0.404823i	0.0804539	+	0.996758i	$0.474363\pi$
$864$		0			0
$865$	33.5805	+	52.2523i	1.14177	+	1.77663i
$866$	−0.125378	+	0.195091i	−0.00426050	+	0.00662947i
$867$		0			0
$868$	25.5463	+	29.4820i	0.867098	+	1.00068i
$869$	−0.518801	−	0.0745923i	−0.0175991	−	0.00253037i
$870$		0			0
$871$	−27.9763	−	27.5763i	−0.947940	−	0.934386i
$872$			3.03355i			0.102729i
$873$		0			0
$874$	2.00359	−	1.73612i	0.0677723	−	0.0587250i
$875$	−0.332222	+	1.13144i	−0.0112312	+	0.0382498i
$876$		0			0
$877$	−45.9845	+	29.5525i	−1.55279	+	0.997916i	−0.568227	+	0.822872i	$0.692370\pi$
$877$	−45.9845	+	29.5525i	−1.55279	+	0.997916i	−0.984561	+	0.175044i	$0.943993\pi$
$878$	0.163539	−	1.13744i	0.00551917	−	0.0383867i
$879$		0			0
$880$	0.306739	−	2.13341i	0.0103402	−	0.0719174i
$881$	38.2599	+	33.1524i	1.28901	+	1.11693i	0.986495	+	0.163789i	$0.0523717\pi$
$881$	38.2599	+	33.1524i	1.28901	+	1.11693i	0.302515	+	0.953145i	$0.402174\pi$
$882$		0			0
$883$	−53.3043	+	24.3432i	−1.79383	+	0.819215i	−0.827696	+	0.561176i	$0.810349\pi$
$883$	−53.3043	+	24.3432i	−1.79383	+	0.819215i	−0.966134	+	0.258039i	$0.916924\pi$
$884$	19.1366	+	41.9034i	0.643634	+	1.40936i
$885$		0			0
$886$	0.0110929	+	0.0771528i	0.000372673	+	0.00259200i
$887$	−5.93160	+	9.22975i	−0.199164	+	0.309905i	−0.926442	−	0.376438i	$-0.877149\pi$
$887$	−5.93160	+	9.22975i	−0.199164	+	0.309905i	0.727278	+	0.686343i	$0.240785\pi$
$888$		0			0
$889$	2.28266	−	7.77403i	0.0765580	−	0.260733i
$890$	−3.64040	+	0.523411i	−0.122027	+	0.0175448i
$891$		0			0
$892$	−42.2876	+	27.1766i	−1.41589	+	0.909939i
$893$	−30.0181	−	26.0108i	−1.00452	−	0.870418i
$894$		0			0
$895$	41.8110	−	12.2768i	1.39759	−	0.410369i
$896$	−5.44302	+	2.48574i	−0.181839	+	0.0830429i
$897$		0			0
$898$	1.36069	+	2.11727i	0.0454067	+	0.0706543i
$899$	16.8384	−	36.8710i	0.561592	−	1.22972i
$900$		0			0
$901$		−	46.2882i		−	1.54208i
$902$	−0.0177117	+	0.0387832i	−0.000589735	+	0.00129134i
$903$		0			0
$904$	0.378299	+	2.63113i	0.0125820	+	0.0875100i
$905$	−6.12409	−	42.5940i	−0.203572	−	1.41587i
$906$		0			0
$907$	−5.94838	+	13.0251i	−0.197513	+	0.432493i	−0.982311	−	0.187259i	$-0.940040\pi$
$907$	−5.94838	+	13.0251i	−0.197513	+	0.432493i	0.784798	+	0.619752i	$0.212767\pi$
$908$		−	0.0118195i		−	0.000392244i
$909$		0			0
$910$	−1.17893	+	2.58150i	−0.0390812	+	0.0855759i
$911$	−0.0595398	−	0.0926457i	−0.00197264	−	0.00306949i	0.840266	−	0.542175i	$-0.182399\pi$
$911$	−0.0595398	−	0.0926457i	−0.00197264	−	0.00306949i	−0.842238	+	0.539105i	$0.818763\pi$
$912$		0			0
$913$	2.38179	−	1.08773i	0.0788257	−	0.0359985i
$914$	0.527940	−	0.155017i	0.0174627	−	0.00512751i
$915$		0			0
$916$	−41.9086	−	36.3140i	−1.38470	−	1.19985i
$917$	4.34736	−	2.79388i	0.143563	−	0.0922620i
$918$		0			0
$919$	48.2553	−	6.93807i	1.59180	−	0.228866i	0.711290	−	0.702899i	$-0.248111\pi$
$919$	48.2553	−	6.93807i	1.59180	−	0.228866i	0.880507	+	0.474033i	$0.157202\pi$
$920$	−1.42489	+	4.85273i	−0.0469772	+	0.159990i
$921$		0			0
$922$	−0.413329	+	0.643152i	−0.0136123	+	0.0211811i
$923$	−10.0606	−	69.9730i	−0.331149	−	2.30319i
$924$		0			0
$925$	3.64949	+	7.99127i	0.119995	+	0.262751i
$926$	0.0336021	−	0.0153456i	0.00110423	−	0.000504287i
$927$		0			0
$928$	3.52607	+	3.05536i	0.115749	+	0.100297i
$929$	−1.84868	+	12.8578i	−0.0606532	+	0.421852i	0.936760	+	0.349972i	$0.113809\pi$
$929$	−1.84868	+	12.8578i	−0.0606532	+	0.421852i	−0.997413	+	0.0718799i	$0.977100\pi$
$930$		0			0
$931$	−1.43911	+	10.0092i	−0.0471649	+	0.328039i
$932$	−34.1710	+	21.9604i	−1.11931	+	0.719336i
$933$		0			0
$934$	0.0484899	−	0.165142i	0.00158664	−	0.00540360i
$935$	1.98015	−	1.71581i	0.0647580	−	0.0561131i
$936$		0			0
$937$		−	16.2866i		−	0.532059i	−0.963965	−	0.266029i	$-0.914288\pi$
$937$		−	16.2866i		−	0.532059i	0.963965	−	0.266029i	$-0.0857118\pi$
$938$	1.53837	−	0.121166i	0.0502295	−	0.00395620i
$939$		0			0
$940$	37.4401	+	5.38308i	1.22116	+	0.175577i
$941$	−30.9785	−	35.7511i	−1.00987	−	1.16545i	−0.986171	−	0.165733i	$-0.947001\pi$
$941$	−30.9785	−	35.7511i	−1.00987	−	1.16545i	−0.0236995	−	0.999719i	$-0.507544\pi$
$942$		0			0
$943$	−8.24183	+	12.8245i	−0.268391	+	0.417624i
$944$	7.53817	+	11.7296i	0.245346	+	0.381767i
$945$		0			0
$946$	−0.0992299	−	0.0453168i	−0.00322624	−	0.00147338i
$947$	20.1735	+	2.90051i	0.655550	+	0.0942538i	0.462060	−	0.886849i	$-0.347110\pi$
$947$	20.1735	+	2.90051i	0.655550	+	0.0942538i	0.193489	+	0.981102i	$0.438019\pi$
$948$		0			0
$949$	13.8350	−	21.5277i	0.449103	−	0.698817i
$950$	−1.06496	−	2.33194i	−0.0345519	−	0.0756582i
$951$		0			0
$952$	−3.47829	−	1.02132i	−0.112732	−	0.0331011i
$953$	46.4000	−	6.67131i	1.50304	−	0.216105i	0.658903	−	0.752228i	$-0.271021\pi$
$953$	46.4000	−	6.67131i	1.50304	−	0.216105i	0.844140	+	0.536123i	$0.180112\pi$
$954$		0			0
$955$	−44.9306	+	13.1928i	−1.45392	+	0.426909i
$956$	26.6822	+	7.83461i	0.862965	+	0.253389i
$957$		0			0
$958$	2.50283	−	2.16872i	0.0808628	−	0.0700680i
$959$	18.1251	+	28.2032i	0.585290	+	0.910729i
$960$		0			0
$961$	25.6284	+	29.5768i	0.826723	+	0.954090i
$962$	−0.198041	−	0.674464i	−0.00638508	−	0.0217456i
$963$		0			0
$964$	29.2873	−	8.59952i	0.943280	−	0.276972i
$965$	51.3078	−	32.9735i	1.65166	−	1.06146i
$966$		0			0
$967$	−16.3316			−0.525190			−0.262595	−	0.964906i	$-0.584578\pi$
$967$	−16.3316			−0.525190			−0.262595	+	0.964906i	$0.584578\pi$
$968$	−3.53448			−0.113602
$969$		0			0
$970$	−0.579554	−	0.502186i	−0.0186083	−	0.0161242i
$971$	50.0547	−	7.19678i	1.60633	−	0.230956i	0.719989	−	0.693985i	$-0.244147\pi$
$971$	50.0547	−	7.19678i	1.60633	−	0.230956i	0.886343	+	0.463029i	$0.153238\pi$
$972$		0			0
$973$	15.8727	−	18.3180i	0.508855	−	0.587249i
$974$	2.14152	+	0.978001i	0.0686188	+	0.0313372i
$975$		0			0
$976$			18.5275i			0.593051i
$977$	−36.1361	−	16.5028i	−1.15610	−	0.527972i	−0.257298	−	0.966332i	$-0.582832\pi$
$977$	−36.1361	−	16.5028i	−1.15610	−	0.527972i	−0.898799	+	0.438360i	$0.855559\pi$
$978$		0			0
$979$	0.710262	+	2.41893i	0.0227001	+	0.0773094i
$980$	−4.00038	−	8.75962i	−0.127788	−	0.279816i
$981$		0			0
$982$	−0.826332	+	0.716021i	−0.0263693	+	0.0228491i
$983$	−22.6209	+	26.1060i	−0.721496	+	0.832651i	−0.991486	−	0.130212i	$-0.958434\pi$
$983$	−22.6209	+	26.1060i	−0.721496	+	0.832651i	0.269990	+	0.962863i	$0.412980\pi$
$984$		0			0
$985$	41.9771	+	48.4441i	1.33750	+	1.54356i
$986$	0.267594	+	1.86115i	0.00852192	+	0.0592712i
$987$		0			0
$988$	−17.6983	−	60.2747i	−0.563056	−	1.91759i
$989$	−32.8126	−	21.0874i	−1.04338	−	0.670539i
$990$		0			0
$991$	13.9574	−	47.5345i	0.443371	−	1.50998i	−0.370442	−	0.928856i	$-0.620794\pi$
$991$	13.9574	−	47.5345i	0.443371	−	1.50998i	0.813813	−	0.581127i	$-0.197388\pi$
$992$	−7.34343	+	3.35363i	−0.233154	+	0.106478i
$993$		0			0
$994$	2.33616	+	1.50136i	0.0740986	+	0.0476203i
$995$	−2.84013	+	3.27769i	−0.0900382	+	0.103910i
$996$		0			0
$997$	−9.90240	+	21.6832i	−0.313612	+	0.686714i	−0.999146	−	0.0413264i	$-0.986842\pi$
$997$	−9.90240	+	21.6832i	−0.313612	+	0.686714i	0.685534	+	0.728041i	$0.259569\pi$
$998$	2.76329	+	0.397301i	0.0874703	+	0.0125763i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.v.a.8.13	yes	240
3.2	odd	2	inner	603.2.v.a.8.12	✓	240
67.42	odd	22	inner	603.2.v.a.377.12	yes	240
201.176	even	22	inner	603.2.v.a.377.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.v.a.8.12	✓	240	3.2	odd	2	inner
603.2.v.a.8.13	yes	240	1.1	even	1	trivial
603.2.v.a.377.12	yes	240	67.42	odd	22	inner
603.2.v.a.377.13	yes	240	201.176	even	22	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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0114821 - 0.0798595i) q^{2} +(1.91274 + 0.561631i) q^{4} +(2.63879 + 1.69585i) q^{5} +(-2.31288 - 0.332541i) q^{7} +(0.133846 - 0.293081i) q^{8} +O(q^{10})\)	\(q+(0.0114821 - 0.0798595i) q^{2} +(1.91274 + 0.561631i) q^{4} +(2.63879 + 1.69585i) q^{5} +(-2.31288 - 0.332541i) q^{7} +(0.133846 - 0.293081i) q^{8} +(0.165728 - 0.191261i) q^{10} +(-0.145936 - 0.0937877i) q^{11} +(4.36545 - 1.99363i) q^{13} +(-0.0531132 + 0.180887i) q^{14} +(3.33219 + 2.14147i) q^{16} +(1.35657 + 4.62006i) q^{17} +(-0.934472 - 6.49940i) q^{19} +(4.09488 + 4.72574i) q^{20} +(-0.00916549 + 0.0105775i) q^{22} +(-3.78200 + 3.27712i) q^{23} +(2.01024 + 4.40181i) q^{25} +(-0.109086 - 0.371514i) q^{26} +(-4.23716 - 1.93505i) q^{28} +4.84004i q^{29} +(-7.61790 - 3.47898i) q^{31} +(0.631267 - 0.728521i) q^{32} +(0.384532 - 0.0552874i) q^{34} +(-5.53925 - 4.79979i) q^{35} +1.81545 q^{37} -0.529769 q^{38} +(0.850213 - 0.546398i) q^{40} +(2.92289 - 0.858239i) q^{41} +(2.19587 + 7.47845i) q^{43} +(-0.226464 - 0.261354i) q^{44} +(0.218284 + 0.339657i) q^{46} +(4.57158 - 3.96130i) q^{47} +(-1.47764 - 0.433875i) q^{49} +(0.374608 - 0.109995i) q^{50} +(9.46965 - 1.36153i) q^{52} +(-9.22372 - 2.70833i) q^{53} +(-0.226046 - 0.494972i) q^{55} +(-0.407030 + 0.633352i) q^{56} +(0.386524 + 0.0555737i) q^{58} +(3.20199 + 1.46230i) q^{59} +(2.52885 + 3.93496i) q^{61} +(-0.365299 + 0.568416i) q^{62} +(5.13686 + 5.92825i) q^{64} +(14.9004 + 2.14235i) q^{65} +(-2.91564 - 7.64847i) q^{67} +9.59888i q^{68} +(-0.446911 + 0.387251i) q^{70} +(4.15000 - 14.1336i) q^{71} +(4.48574 - 2.88281i) q^{73} +(0.0208451 - 0.144981i) q^{74} +(1.86286 - 12.9565i) q^{76} +(0.306345 + 0.265449i) q^{77} +(2.74835 - 1.25513i) q^{79} +(5.16135 + 11.3018i) q^{80} +(-0.0349777 - 0.243275i) q^{82} +(-8.16036 + 12.6978i) q^{83} +(-4.25521 + 14.4919i) q^{85} +(0.622439 - 0.0894932i) q^{86} +(-0.0470204 + 0.0302182i) q^{88} +(-10.9830 - 9.51686i) q^{89} +(-10.7597 + 3.15933i) q^{91} +(-9.07452 + 4.14419i) q^{92} +(-0.263856 - 0.410568i) q^{94} +(8.55611 - 18.7353i) q^{95} -3.03018i q^{97} +(-0.0516154 + 0.113022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 28 q^{4}+O(q^{10}) \) 240 * q - 28 * q^4	\( 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) \) 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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