LMFDB - Embedded newform 603.2.bj.a.503.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(44,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 61]))

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

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

chi := DirichletCharacter("603.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.bj (of order $66$, degree $20$, 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:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			503.15
Character	$\chi$	$=$	603.503
Dual form			603.2.bj.a.404.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0482573 + 1.01304i) q^{2} +(0.967014 - 0.0923386i) q^{4} +(2.18885 + 2.52606i) q^{5} +(0.971904 - 1.88523i) q^{7} +(0.428878 + 2.98291i) q^{8} +O(q^{10})$	\(q+(0.0482573 + 1.01304i) q^{2} +(0.967014 - 0.0923386i) q^{4} +(2.18885 + 2.52606i) q^{5} +(0.971904 - 1.88523i) q^{7} +(0.428878 + 2.98291i) q^{8} +(-2.45339 + 2.33930i) q^{10} +(-0.754740 + 2.18068i) q^{11} +(-1.23751 + 1.57363i) q^{13} +(1.95672 + 0.893606i) q^{14} +(-1.09341 + 0.210738i) q^{16} +(0.565225 - 5.91930i) q^{17} +(-0.435883 + 0.224713i) q^{19} +(2.34990 + 2.24062i) q^{20} +(-2.24555 - 0.659352i) q^{22} +(1.13932 + 0.276395i) q^{23} +(-0.878373 + 6.10922i) q^{25} +(-1.65387 - 1.17772i) q^{26} +(0.765765 - 1.91279i) q^{28} +(0.886695 - 0.511934i) q^{29} +(-5.08043 - 6.46029i) q^{31} +(1.15471 + 4.75977i) q^{32} +(6.02379 + 0.286949i) q^{34} +(6.88956 - 1.67139i) q^{35} +(3.35039 - 5.80305i) q^{37} +(-0.248679 - 0.430725i) q^{38} +(-6.59627 + 7.61251i) q^{40} +(1.24087 - 1.74255i) q^{41} +(-2.81062 + 1.28357i) q^{43} +(-0.528483 + 2.17844i) q^{44} +(-0.225020 + 1.16752i) q^{46} +(-5.69090 + 5.96844i) q^{47} +(1.45090 + 2.03750i) q^{49} +(-6.23129 - 0.595017i) q^{50} +(-1.05139 + 1.63599i) q^{52} +(-4.67578 + 10.2385i) q^{53} +(-7.16054 + 2.86665i) q^{55} +(6.04031 + 2.09057i) q^{56} +(0.561401 + 0.873557i) q^{58} +(-2.36828 + 0.340507i) q^{59} +(4.34407 - 1.50350i) q^{61} +(6.29939 - 5.45845i) q^{62} +(-6.90299 + 2.02690i) q^{64} +(-6.68381 + 0.318389i) q^{65} +(4.89300 - 6.56190i) q^{67} -5.77624i q^{68} +(2.02566 + 6.89877i) q^{70} +(-0.902966 - 9.45629i) q^{71} +(1.83379 + 5.29840i) q^{73} +(6.04043 + 3.11406i) q^{74} +(-0.400755 + 0.257550i) q^{76} +(3.37755 + 3.54227i) q^{77} +(1.34195 + 3.35203i) q^{79} +(-2.92564 - 2.30075i) q^{80} +(1.82517 + 1.17296i) q^{82} +(-1.24922 - 6.48155i) q^{83} +(16.1897 - 11.5286i) q^{85} +(-1.43594 - 2.78534i) q^{86} +(-6.82846 - 1.31608i) q^{88} +(-0.513954 + 1.75037i) q^{89} +(1.76391 + 3.86242i) q^{91} +(1.12726 + 0.162075i) q^{92} +(-6.32092 - 5.47711i) q^{94} +(-1.52172 - 0.609205i) q^{95} +(-10.6214 - 6.13229i) q^{97} +(-1.99406 + 1.56815i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 20 q^{4}+O(q^{10}) $ 440 * q + 20 * q^4	$ 440 q + 20 q^{4} + 18 q^{13} + 8 q^{16} + 36 q^{19} - 12 q^{22} - 44 q^{25} - 128 q^{28} + 82 q^{31} + 24 q^{34} - 8 q^{37} - 32 q^{40} - 44 q^{43} + 80 q^{46} - 10 q^{49} + 132 q^{52} - 64 q^{55} - 176 q^{58} - 86 q^{61} - 136 q^{64} - 78 q^{67} - 352 q^{70} + 180 q^{73} - 256 q^{76} + 104 q^{79} + 88 q^{82} - 84 q^{85} - 268 q^{88} - 328 q^{91} + 88 q^{94} - 6 q^{97}+O(q^{100}) $ 440 * q + 20 * q^4 + 18 * q^13 + 8 * q^16 + 36 * q^19 - 12 * q^22 - 44 * q^25 - 128 * q^28 + 82 * q^31 + 24 * q^34 - 8 * q^37 - 32 * q^40 - 44 * q^43 + 80 * q^46 - 10 * q^49 + 132 * q^52 - 64 * q^55 - 176 * q^58 - 86 * q^61 - 136 * q^64 - 78 * q^67 - 352 * q^70 + 180 * q^73 - 256 * q^76 + 104 * q^79 + 88 * q^82 - 84 * q^85 - 268 * q^88 - 328 * q^91 + 88 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{65}{66}\right)$	$-1$

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 $

$2$	0.0482573	+	1.01304i	0.0341230	+	0.716331i	0.949506	+	0.313747i	$0.101585\pi$
$2$	0.0482573	+	1.01304i	0.0341230	+	0.716331i	−0.915383	+	0.402583i	$0.868112\pi$
$3$		0			0
$3$		0			0
$4$	0.967014	−	0.0923386i	0.483507	−	0.0461693i
$5$	2.18885	+	2.52606i	0.978882	+	1.12969i	0.991544	+	0.129770i	$0.0414238\pi$
$5$	2.18885	+	2.52606i	0.978882	+	1.12969i	−0.0126626	+	0.999920i	$0.504031\pi$
$6$		0			0
$7$	0.971904	−	1.88523i	0.367345	−	0.712550i	−0.630635	−	0.776080i	$-0.717205\pi$
$7$	0.971904	−	1.88523i	0.367345	−	0.712550i	0.997980	+	0.0635294i	$0.0202357\pi$
$8$	0.428878	+	2.98291i	0.151631	+	1.05462i
$9$		0			0
$10$	−2.45339	+	2.33930i	−0.775829	+	0.739751i
$11$	−0.754740	+	2.18068i	−0.227563	+	0.657499i	0.772193	+	0.635388i	$0.219160\pi$
$11$	−0.754740	+	2.18068i	−0.227563	+	0.657499i	−0.999756	+	0.0221110i	$0.992961\pi$
$12$		0			0
$13$	−1.23751	+	1.57363i	−0.343225	+	0.436446i	−0.926767	−	0.375637i	$-0.877424\pi$
$13$	−1.23751	+	1.57363i	−0.343225	+	0.436446i	0.583542	+	0.812083i	$0.301666\pi$
$14$	1.95672	+	0.893606i	0.522957	+	0.238826i
$15$		0			0
$16$	−1.09341	+	0.210738i	−0.273353	+	0.0526844i
$17$	0.565225	−	5.91930i	0.137087	−	1.43564i	−0.621165	−	0.783680i	$-0.713340\pi$
$17$	0.565225	−	5.91930i	0.137087	−	1.43564i	0.758252	−	0.651962i	$-0.226054\pi$
$18$		0			0
$19$	−0.435883	+	0.224713i	−0.0999985	+	0.0515528i	−0.507500	−	0.861652i	$-0.669430\pi$
$19$	−0.435883	+	0.224713i	−0.0999985	+	0.0515528i	0.407502	+	0.913204i	$0.366400\pi$
$20$	2.34990	+	2.24062i	0.525453	+	0.501018i
$21$		0			0
$22$	−2.24555	−	0.659352i	−0.478752	−	0.140574i
$23$	1.13932	+	0.276395i	0.237564	+	0.0576323i	0.352773	−	0.935709i	$-0.385239\pi$
$23$	1.13932	+	0.276395i	0.237564	+	0.0576323i	−0.115209	+	0.993341i	$0.536754\pi$
$24$		0			0
$25$	−0.878373	+	6.10922i	−0.175675	+	1.22184i
$26$	−1.65387	−	1.17772i	−0.324351	−	0.230970i
$27$		0			0
$28$	0.765765	−	1.91279i	0.144716	−	0.361483i
$29$	0.886695	−	0.511934i	0.164655	−	0.0950637i	−0.415408	−	0.909635i	$-0.636361\pi$
$29$	0.886695	−	0.511934i	0.164655	−	0.0950637i	0.580063	+	0.814571i	$0.303028\pi$
$30$		0			0
$31$	−5.08043	−	6.46029i	−0.912472	−	1.16030i	−0.986617	−	0.163055i	$-0.947865\pi$
$31$	−5.08043	−	6.46029i	−0.912472	−	1.16030i	0.0741453	−	0.997247i	$-0.476377\pi$
$32$	1.15471	+	4.75977i	0.204125	+	0.841417i
$33$		0			0
$34$	6.02379	+	0.286949i	1.03307	+	0.0492113i
$35$	6.88956	−	1.67139i	1.16455	−	0.282516i
$36$		0			0
$37$	3.35039	−	5.80305i	0.550801	−	0.954015i	−0.447416	−	0.894326i	$-0.647656\pi$
$37$	3.35039	−	5.80305i	0.550801	−	0.954015i	0.998217	−	0.0596893i	$-0.0190110\pi$
$38$	−0.248679	−	0.430725i	−0.0403411	−	0.0698728i
$39$		0			0
$40$	−6.59627	+	7.61251i	−1.04296	+	1.20364i
$41$	1.24087	−	1.74255i	0.193791	−	0.272141i	−0.706235	−	0.707977i	$-0.749608\pi$
$41$	1.24087	−	1.74255i	0.193791	−	0.272141i	0.900026	+	0.435836i	$0.143547\pi$
$42$		0			0
$43$	−2.81062	+	1.28357i	−0.428616	+	0.195742i	−0.618029	−	0.786155i	$-0.712069\pi$
$43$	−2.81062	+	1.28357i	−0.428616	+	0.195742i	0.189413	+	0.981897i	$0.439341\pi$
$44$	−0.528483	+	2.17844i	−0.0796718	+	0.328412i
$45$		0			0
$46$	−0.225020	+	1.16752i	−0.0331774	+	0.172141i
$47$	−5.69090	+	5.96844i	−0.830102	+	0.870586i	−0.993247	−	0.116016i	$-0.962988\pi$
$47$	−5.69090	+	5.96844i	−0.830102	+	0.870586i	0.163145	+	0.986602i	$0.447836\pi$
$48$		0			0
$49$	1.45090	+	2.03750i	0.207271	+	0.291072i
$50$	−6.23129	−	0.595017i	−0.881238	−	0.0841480i
$51$		0			0
$52$	−1.05139	+	1.63599i	−0.145801	+	0.226871i
$53$	−4.67578	+	10.2385i	−0.642268	+	1.40637i	0.255894	+	0.966705i	$0.417630\pi$
$53$	−4.67578	+	10.2385i	−0.642268	+	1.40637i	−0.898162	+	0.439666i	$0.855097\pi$
$54$		0			0
$55$	−7.16054	+	2.86665i	−0.965527	+	0.386539i
$56$	6.04031	+	2.09057i	0.807170	+	0.279364i
$57$		0			0
$58$	0.561401	+	0.873557i	0.0737156	+	0.114704i
$59$	−2.36828	+	0.340507i	−0.308324	+	0.0443303i	−0.294740	−	0.955577i	$-0.595233\pi$
$59$	−2.36828	+	0.340507i	−0.308324	+	0.0443303i	−0.0135837	+	0.999908i	$0.504324\pi$
$60$		0			0
$61$	4.34407	−	1.50350i	0.556201	−	0.192503i	−0.0344842	−	0.999405i	$-0.510979\pi$
$61$	4.34407	−	1.50350i	0.556201	−	0.192503i	0.590685	+	0.806902i	$0.298858\pi$
$62$	6.29939	−	5.45845i	0.800024	−	0.693224i
$63$		0			0
$64$	−6.90299	+	2.02690i	−0.862874	+	0.253363i
$65$	−6.68381	+	0.318389i	−0.829025	+	0.0394913i
$66$		0			0
$67$	4.89300	−	6.56190i	0.597776	−	0.801663i
$67$	4.89300	−	6.56190i	0.597776	−	0.801663i
$68$		−	5.77624i		−	0.700472i
$69$		0			0
$70$	2.02566	+	6.89877i	0.242113	+	0.824561i
$71$	−0.902966	−	9.45629i	−0.107162	−	1.12226i	−0.875834	−	0.482612i	$-0.839688\pi$
$71$	−0.902966	−	9.45629i	−0.107162	−	1.12226i	0.768672	−	0.639643i	$-0.220918\pi$
$72$		0			0
$73$	1.83379	+	5.29840i	0.214629	+	0.620130i	0.999999	+	0.00110394i	$0.000351394\pi$
$73$	1.83379	+	5.29840i	0.214629	+	0.620130i	−0.785370	+	0.619026i	$0.787527\pi$
$74$	6.04043	+	3.11406i	0.702185	+	0.362002i
$75$		0			0
$76$	−0.400755	+	0.257550i	−0.0459698	+	0.0295430i
$77$	3.37755	+	3.54227i	0.384907	+	0.403679i
$78$		0			0
$79$	1.34195	+	3.35203i	0.150981	+	0.377132i	0.984506	−	0.175349i	$-0.0561053\pi$
$79$	1.34195	+	3.35203i	0.150981	+	0.377132i	−0.833525	+	0.552481i	$0.813681\pi$
$80$	−2.92564	−	2.30075i	−0.327097	−	0.257232i
$81$		0			0
$82$	1.82517	+	1.17296i	0.201556	+	0.129532i
$83$	−1.24922	−	6.48155i	−0.137119	−	0.711443i	−0.983790	−	0.179325i	$-0.942609\pi$
$83$	−1.24922	−	6.48155i	−0.137119	−	0.711443i	0.846671	−	0.532117i	$-0.178604\pi$
$84$		0			0
$85$	16.1897	−	11.5286i	1.75602	−	1.25046i
$86$	−1.43594	−	2.78534i	−0.154842	−	0.300351i
$87$		0			0
$88$	−6.82846	−	1.31608i	−0.727917	−	0.140294i
$89$	−0.513954	+	1.75037i	−0.0544790	+	0.185538i	−0.982237	−	0.187643i	$-0.939915\pi$
$89$	−0.513954	+	1.75037i	−0.0544790	+	0.185538i	0.927758	+	0.373182i	$0.121733\pi$
$90$		0			0
$91$	1.76391	+	3.86242i	0.184908	+	0.404891i
$92$	1.12726	+	0.162075i	0.117525	+	0.0168975i
$93$		0			0
$94$	−6.32092	−	5.47711i	−0.651953	−	0.564921i
$95$	−1.52172	−	0.609205i	−0.156125	−	0.0625031i
$96$		0			0
$97$	−10.6214	−	6.13229i	−1.07844	−	0.622640i	−0.147968	−	0.988992i	$-0.547273\pi$
$97$	−10.6214	−	6.13229i	−1.07844	−	0.622640i	−0.930476	+	0.366352i	$0.880606\pi$
$98$	−1.99406	+	1.56815i	−0.201431	+	0.158407i
$99$		0			0
$100$	−0.285282	+	5.98880i	−0.0285282	+	0.598880i
$101$	0.420729	−	8.83218i	0.0418641	−	0.878835i	−0.876090	−	0.482148i	$-0.839857\pi$
$101$	0.420729	−	8.83218i	0.0418641	−	0.878835i	0.917954	−	0.396687i	$-0.129840\pi$
$102$		0			0
$103$	6.99117	−	5.49791i	0.688860	−	0.541725i	−0.211226	−	0.977437i	$-0.567746\pi$
$103$	6.99117	−	5.49791i	0.688860	−	0.541725i	0.900086	+	0.435712i	$0.143503\pi$
$104$	−5.22474	−	3.01650i	−0.512328	−	0.295793i
$105$		0			0
$106$	−10.5977	−	4.24269i	−1.02934	−	0.412087i
$107$	−14.4951	−	12.5601i	−1.40130	−	1.21423i	−0.946113	−	0.323836i	$-0.895028\pi$
$107$	−14.4951	−	12.5601i	−1.40130	−	1.21423i	−0.455185	−	0.890397i	$-0.650427\pi$
$108$		0			0
$109$	10.7011	+	1.53859i	1.02498	+	0.147370i	0.634244	−	0.773133i	$-0.281312\pi$
$109$	10.7011	+	1.53859i	1.02498	+	0.147370i	0.390735	+	0.920503i	$0.372221\pi$
$110$	−3.24959	−	7.11561i	−0.309836	−	0.678447i
$111$		0			0
$112$	−0.665402	+	2.26615i	−0.0628745	+	0.214131i
$113$	18.7413	+	3.61209i	1.76303	+	0.339797i	0.964887	−	0.262666i	$-0.0846018\pi$
$113$	18.7413	+	3.61209i	1.76303	+	0.339797i	0.798147	+	0.602463i	$0.205814\pi$
$114$		0			0
$115$	1.79560	+	3.48297i	0.167440	+	0.324789i
$116$	0.810175	−	0.576923i	0.0752229	−	0.0535660i
$117$		0			0
$118$	−0.459236	−	2.38274i	−0.0422761	−	0.219349i
$119$	−10.6099	−	6.81857i	−0.972609	−	0.625058i
$120$		0			0
$121$	4.46086	+	3.50806i	0.405533	+	0.318914i
$122$	1.73274	+	4.32818i	0.156875	+	0.391855i
$123$		0			0
$124$	−5.50938	−	5.77807i	−0.494757	−	0.518886i
$125$	−3.29560	+	2.11795i	−0.294768	+	0.189436i
$126$		0			0
$127$	−13.1422	−	6.77526i	−1.16618	−	0.601207i	−0.237244	−	0.971450i	$-0.576244\pi$
$127$	−13.1422	−	6.77526i	−1.16618	−	0.601207i	−0.928935	+	0.370243i	$0.879274\pi$
$128$	0.817388	+	2.36169i	0.0722476	+	0.208746i
$129$		0			0
$130$	−0.645085	−	6.75564i	−0.0565777	−	0.592508i
$131$	0.445447	+	1.51705i	0.0389189	+	0.132545i	0.976661	−	0.214787i	$-0.0689057\pi$
$131$	0.445447	+	1.51705i	0.0389189	+	0.132545i	−0.937742	+	0.347332i	$0.887088\pi$
$132$		0			0
$133$			1.04014i			0.0901916i
$134$	6.88362	+	4.64017i	0.594654	+	0.400850i
$135$		0			0
$136$	17.8992	−	0.852642i	1.53484	−	0.0731135i
$137$	−19.5004	+	5.72584i	−1.66603	+	0.489191i	−0.972824	−	0.231546i	$-0.925621\pi$
$137$	−19.5004	+	5.72584i	−1.66603	+	0.489191i	−0.693208	+	0.720738i	$0.743803\pi$
$138$		0			0
$139$	12.0237	−	10.4186i	1.01984	−	0.883694i	0.0265828	−	0.999647i	$-0.491537\pi$
$139$	12.0237	−	10.4186i	1.01984	−	0.883694i	0.993255	+	0.115952i	$0.0369920\pi$
$140$	6.50796	−	2.25243i	0.550023	−	0.190365i
$141$		0			0
$142$	9.53607	−	1.37108i	0.800249	−	0.115058i
$143$	−2.49757	−	3.88630i	−0.208858	−	0.324989i
$144$		0			0
$145$	3.23402	+	1.11930i	0.268570	+	0.0929531i
$146$	−5.27902	+	2.11340i	−0.436895	+	0.174906i
$147$		0			0
$148$	2.70403	−	5.92100i	0.222270	−	0.486703i
$149$	−6.05335	+	9.41920i	−0.495910	+	0.771651i	−0.995515	−	0.0946023i	$-0.969842\pi$
$149$	−6.05335	+	9.41920i	−0.495910	+	0.771651i	0.499605	+	0.866253i	$0.333478\pi$
$150$		0			0
$151$	11.5439	+	1.10230i	0.939426	+	0.0897043i	0.553522	−	0.832835i	$-0.313284\pi$
$151$	11.5439	+	1.10230i	0.939426	+	0.0897043i	0.385904	+	0.922539i	$0.373890\pi$
$152$	−0.857241	−	1.20383i	−0.0695314	−	0.0976432i
$153$		0			0
$154$	−3.42549	+	3.59255i	−0.276034	+	0.289496i
$155$	5.19882	−	26.9741i	0.417579	−	2.16661i
$156$		0			0
$157$	4.57711	−	18.8671i	0.365293	−	1.50576i	−0.431838	−	0.901951i	$-0.642135\pi$
$157$	4.57711	−	18.8671i	0.365293	−	1.50576i	0.797131	−	0.603807i	$-0.206350\pi$
$158$	−3.33099	+	1.52121i	−0.264999	+	0.121021i
$159$		0			0
$160$	−9.49600	+	13.3353i	−0.750725	+	1.05425i
$161$	1.62837	−	1.87924i	0.128334	−	0.148105i
$162$		0			0
$163$	−6.50439	−	11.2659i	−0.509463	−	0.882416i	−0.999940	−	0.0109616i	$-0.996511\pi$
$163$	−6.50439	−	11.2659i	−0.509463	−	0.882416i	0.490477	−	0.871454i	$-0.336823\pi$
$164$	1.03903	−	1.79965i	0.0811347	−	0.140529i
$165$		0			0
$166$	6.50582	−	1.57829i	0.504949	−	0.122499i
$167$	−4.71981	−	0.224832i	−0.365230	−	0.0173980i	−0.135835	−	0.990731i	$-0.543372\pi$
$167$	−4.71981	−	0.224832i	−0.365230	−	0.0173980i	−0.229395	+	0.973333i	$0.573675\pi$
$168$		0			0
$169$	2.12000	+	8.73877i	0.163077	+	0.672213i
$170$	12.4603	+	15.8446i	0.955661	+	1.21522i
$171$		0			0
$172$	−2.59939	+	1.50076i	−0.198201	+	0.114432i
$173$	5.69217	−	14.2183i	0.432768	−	1.08100i	−0.538418	−	0.842678i	$-0.680978\pi$
$173$	5.69217	−	14.2183i	0.432768	−	1.08100i	0.971186	−	0.238323i	$-0.0765978\pi$
$174$		0			0
$175$	10.6636	+	7.59351i	0.806092	+	0.574015i
$176$	0.365690	−	2.54343i	0.0275649	−	0.191718i
$177$		0			0
$178$	−1.79800	−	0.436190i	−0.134766	−	0.0326938i
$179$	−10.3584	−	3.04150i	−0.774222	−	0.227332i	−0.129326	−	0.991602i	$-0.541281\pi$
$179$	−10.3584	−	3.04150i	−0.774222	−	0.227332i	−0.644896	+	0.764270i	$0.723099\pi$
$180$		0			0
$181$	9.19524	+	8.76764i	0.683477	+	0.651694i	0.950042	−	0.312123i	$-0.101040\pi$
$181$	9.19524	+	8.76764i	0.683477	+	0.651694i	−0.266565	+	0.963817i	$0.585889\pi$
$182$	−3.82768	+	1.97331i	−0.283726	+	0.146271i
$183$		0			0
$184$	−0.335835	+	3.51702i	−0.0247580	+	0.259278i
$185$	21.9924	−	4.23868i	1.61691	−	0.311634i
$186$		0			0
$187$	12.4815	+	5.70011i	0.912737	+	0.416833i
$188$	−4.95206	+	6.29705i	−0.361166	+	0.459260i
$189$		0			0
$190$	0.543718	−	1.57097i	0.0394454	−	0.113970i
$191$	−15.3067	+	14.5949i	−1.10755	+	1.05605i	−0.109479	+	0.993989i	$0.534918\pi$
$191$	−15.3067	+	14.5949i	−1.10755	+	1.05605i	−0.998072	+	0.0620589i	$0.980233\pi$
$192$		0			0
$193$	−3.54779	−	24.6755i	−0.255376	−	1.77618i	−0.564774	−	0.825246i	$-0.691037\pi$
$193$	−3.54779	−	24.6755i	−0.255376	−	1.77618i	0.309398	−	0.950933i	$-0.399872\pi$
$194$	5.69972	−	11.0559i	0.409216	−	0.793769i
$195$		0			0
$196$	1.59118	+	1.83632i	0.113656	+	0.131166i
$197$	15.3382	−	1.46462i	1.09280	−	0.104350i	0.466945	−	0.884287i	$-0.345355\pi$
$197$	15.3382	−	1.46462i	1.09280	−	0.104350i	0.625859	+	0.779936i	$0.284749\pi$
$198$		0			0
$199$	0.805661	+	16.9129i	0.0571118	+	1.19892i	0.827544	+	0.561401i	$0.189738\pi$
$199$	0.805661	+	16.9129i	0.0571118	+	1.19892i	−0.770432	+	0.637522i	$0.779959\pi$
$200$	−18.6000			−1.31522
$201$		0			0
$202$	8.96770			0.630965
$203$	−0.103331	−	2.16918i	−0.00725239	−	0.152246i
$204$		0			0
$205$	7.11787	−	0.679674i	0.497134	−	0.0474705i
$206$	5.90701	+	6.81705i	0.411561	+	0.474966i
$207$		0			0
$208$	1.02149	−	1.98141i	0.0708276	−	0.137386i
$209$	−0.161049	−	1.12012i	−0.0111400	−	0.0774804i
$210$		0			0
$211$	13.6346	−	13.0006i	0.938646	−	0.894997i	−0.0559906	−	0.998431i	$-0.517832\pi$
$211$	13.6346	−	13.0006i	0.938646	−	0.894997i	0.994636	+	0.103434i	$0.0329832\pi$
$212$	−3.57613	+	10.3326i	−0.245610	+	0.709643i
$213$		0			0
$214$	12.0245	−	15.2903i	0.821975	−	1.04523i
$215$	−9.39439	−	4.29027i	−0.640692	−	0.292594i
$216$		0			0
$217$	−17.1168	+	3.29900i	−1.16197	+	0.223951i
$218$	−1.04225	+	10.9149i	−0.0705901	+	0.739253i
$219$		0			0
$220$	−6.65964	+	3.43328i	−0.448993	+	0.231472i
$221$	8.61531	+	8.21468i	0.579528	+	0.552579i
$222$		0			0
$223$	−20.3669	−	5.98027i	−1.36387	−	0.400468i	−0.483744	−	0.875210i	$-0.660723\pi$
$223$	−20.3669	−	5.98027i	−1.36387	−	0.400468i	−0.880125	+	0.474741i	$0.842542\pi$
$224$	10.0955	+	2.44915i	0.674536	+	0.163641i
$225$		0			0
$226$	−2.75480	+	19.1601i	−0.183247	+	1.27451i
$227$	11.2349	+	8.00034i	0.745687	+	0.531001i	0.888571	−	0.458738i	$-0.151698\pi$
$227$	11.2349	+	8.00034i	0.745687	+	0.531001i	−0.142885	+	0.989739i	$0.545638\pi$
$228$		0			0
$229$	−7.23776	+	18.0791i	−0.478285	+	1.19470i	0.471520	+	0.881855i	$0.343705\pi$
$229$	−7.23776	+	18.0791i	−0.478285	+	1.19470i	−0.949805	+	0.312842i	$0.898719\pi$
$230$	−3.44175	+	1.98710i	−0.226942	+	0.131025i
$231$		0			0
$232$	1.90734	+	2.42538i	0.125223	+	0.159234i
$233$	3.09064	+	12.7398i	0.202475	+	0.834612i	0.978890	+	0.204390i	$0.0655211\pi$
$233$	3.09064	+	12.7398i	0.202475	+	0.834612i	−0.776415	+	0.630222i	$0.782964\pi$
$234$		0			0
$235$	−27.5331	−	1.31157i	−1.79606	−	0.0855571i
$236$	−2.25872	+	0.547959i	−0.147030	+	0.0356691i
$237$		0			0
$238$	6.39551	−	11.0774i	0.414560	−	0.718038i
$239$	3.30343	+	5.72172i	0.213681	+	0.370107i	0.952864	−	0.303398i	$-0.0981212\pi$
$239$	3.30343	+	5.72172i	0.213681	+	0.370107i	−0.739182	+	0.673505i	$0.764788\pi$
$240$		0			0
$241$	−14.9989	+	17.3097i	−0.966167	+	1.11502i	0.0271544	+	0.999631i	$0.491355\pi$
$241$	−14.9989	+	17.3097i	−0.966167	+	1.11502i	−0.993321	+	0.115384i	$0.963190\pi$
$242$	−3.33855	+	4.68834i	−0.214610	+	0.301378i
$243$		0			0
$244$	4.06194	−	1.85503i	0.260039	−	0.118756i
$245$	−1.97107	+	8.12484i	−0.125927	+	0.519077i
$246$		0			0
$247$	0.185797	−	0.964004i	0.0118220	−	0.0613381i
$248$	17.0916	−	17.9251i	1.08532	−	1.13825i
$249$		0			0
$250$	−2.30462	−	3.23638i	−0.145757	−	0.204687i
$251$	0.190838	+	0.0182228i	0.0120456	+	0.00115021i	0.101077	−	0.994879i	$-0.467771\pi$
$251$	0.190838	+	0.0182228i	0.0120456	+	0.00115021i	−0.0890315	+	0.996029i	$0.528377\pi$
$252$		0			0
$253$	−1.46262	+	2.27587i	−0.0919539	+	0.143083i
$254$	6.22944	−	13.6406i	0.390870	−	0.855885i
$255$		0			0
$256$	−15.7112	+	6.28981i	−0.981949	+	0.393113i
$257$	−15.0840	−	5.22061i	−0.940912	−	0.325653i	−0.186799	−	0.982398i	$-0.559811\pi$
$257$	−15.0840	−	5.22061i	−0.940912	−	0.325653i	−0.754112	+	0.656745i	$0.771933\pi$
$258$		0			0
$259$	−7.68383	−	11.9563i	−0.477450	−	0.742926i
$260$	−6.43394	+	0.925061i	−0.399016	+	0.0573698i
$261$		0			0
$262$	−1.51535	+	0.524466i	−0.0936183	+	0.0324016i
$263$	17.2509	−	14.9480i	1.06374	−	0.921734i	0.0666335	−	0.997778i	$-0.478774\pi$
$263$	17.2509	−	14.9480i	1.06374	−	0.921734i	0.997105	+	0.0760433i	$0.0242287\pi$
$264$		0			0
$265$	−36.0977	+	10.5993i	−2.21747	+	0.651107i
$266$	−1.05371	+	0.0501943i	−0.0646070	+	0.00307761i
$267$		0			0
$268$	4.12568	−	6.79726i	0.252016	−	0.415209i
$269$			3.24807i			0.198039i	0.995086	+	0.0990193i	$0.0315705\pi$
$269$			3.24807i			0.198039i	−0.995086	+	0.0990193i	$0.968429\pi$
$270$		0			0
$271$	5.47616	+	18.6501i	0.332653	+	1.13291i	0.940764	+	0.339061i	$0.110109\pi$
$271$	5.47616	+	18.6501i	0.332653	+	1.13291i	−0.608111	+	0.793852i	$0.708073\pi$
$272$	0.629397	+	6.59134i	0.0381628	+	0.399659i
$273$		0			0
$274$	−6.74156	−	19.4785i	−0.407273	−	1.17674i
$275$	−12.6593	−	6.52632i	−0.763384	−	0.393552i
$276$		0			0
$277$	−16.9500	+	10.8931i	−1.01843	+	0.654505i	−0.939561	−	0.342380i	$-0.888767\pi$
$277$	−16.9500	+	10.8931i	−1.01843	+	0.654505i	−0.0788677	+	0.996885i	$0.525130\pi$
$278$	11.1347	+	11.6778i	0.667817	+	0.700387i
$279$		0			0
$280$	7.94039	+	19.8341i	0.474529	+	1.18532i
$281$	−13.2246	−	10.3999i	−0.788912	−	0.620408i	0.140235	−	0.990118i	$-0.455214\pi$
$281$	−13.2246	−	10.3999i	−0.788912	−	0.620408i	−0.929147	+	0.369711i	$0.879457\pi$
$282$		0			0
$283$	−18.3400	−	11.7864i	−1.09020	−	0.700629i	−0.133309	−	0.991075i	$-0.542560\pi$
$283$	−18.3400	−	11.7864i	−1.09020	−	0.700629i	−0.956892	+	0.290445i	$0.906197\pi$
$284$	−1.74636	−	9.06098i	−0.103627	−	0.537670i
$285$		0			0
$286$	3.81647	−	2.71770i	0.225673	−	0.160701i
$287$	−2.07911	−	4.03292i	−0.122726	−	0.238056i
$288$		0			0
$289$	−18.0259	−	3.47420i	−1.06034	−	0.204365i
$290$	−0.977840	+	3.33022i	−0.0574207	+	0.195557i
$291$		0			0
$292$	2.26255	+	4.95429i	0.132406	+	0.289928i
$293$	−18.1638	−	2.61156i	−1.06114	−	0.152569i	−0.410428	−	0.911893i	$-0.634621\pi$
$293$	−18.1638	−	2.61156i	−1.06114	−	0.152569i	−0.650713	+	0.759324i	$0.725530\pi$
$294$		0			0
$295$	−6.04394	−	5.23711i	−0.351892	−	0.304916i
$296$	18.7469	+	7.50512i	1.08964	+	0.436226i
$297$		0			0
$298$	−9.83419	−	5.67777i	−0.569679	−	0.328904i
$299$	−1.84486	+	1.45082i	−0.106691	+	0.0839029i
$300$		0			0
$301$	−0.311833	+	6.54618i	−0.0179737	+	0.377315i
$302$	−0.559609	+	11.7476i	−0.0322019	+	0.676001i
$303$		0			0
$304$	0.429244	−	0.337561i	0.0246188	−	0.0193605i
$305$	13.3064	+	7.68246i	0.761923	+	0.439897i
$306$		0			0
$307$	27.8367	+	11.1441i	1.58872	+	0.636029i	0.986715	−	0.162459i	$-0.0519426\pi$
$307$	27.8367	+	11.1441i	1.58872	+	0.636029i	0.602010	+	0.798489i	$0.294367\pi$
$308$	3.59322	+	3.11355i	0.204743	+	0.177411i
$309$		0			0
$310$	27.5768	+	3.96494i	1.56626	+	0.225194i
$311$	−3.10278	−	6.79414i	−0.175942	−	0.385260i	0.801030	−	0.598624i	$-0.204285\pi$
$311$	−3.10278	−	6.79414i	−0.175942	−	0.385260i	−0.976973	+	0.213363i	$0.931558\pi$
$312$		0			0
$313$	−5.40945	+	18.4229i	−0.305760	+	1.04132i	0.653059	+	0.757307i	$0.273485\pi$
$313$	−5.40945	+	18.4229i	−0.305760	+	1.04132i	−0.958819	+	0.284016i	$0.908333\pi$
$314$	19.3341	+	3.72634i	1.09109	+	0.210289i
$315$		0			0
$316$	1.60720	+	3.11754i	0.0904123	+	0.175375i
$317$	−2.10331	+	1.49776i	−0.118134	+	0.0841228i	−0.637597	−	0.770370i	$-0.720071\pi$
$317$	−2.10331	+	1.49776i	−0.118134	+	0.0841228i	0.519463	+	0.854493i	$0.326132\pi$
$318$		0			0
$319$	0.447138	+	2.31997i	0.0250349	+	0.129894i
$320$	−20.2297	−	13.0008i	−1.13087	−	0.726768i
$321$		0			0
$322$	1.98234	+	1.55893i	0.110471	+	0.0868757i
$323$	1.08377	+	2.70714i	0.0603028	+	0.150629i
$324$		0			0
$325$	−8.52664	−	8.94248i	−0.472973	−	0.496039i
$326$	11.0990	−	7.13290i	0.614717	−	0.395055i
$327$		0			0
$328$	5.73007	+	2.95406i	0.316390	+	0.163110i
$329$	5.72088	+	16.5294i	0.315402	+	0.911296i
$330$		0			0
$331$	3.26844	+	34.2287i	0.179650	+	1.88138i	0.415505	+	0.909591i	$0.363605\pi$
$331$	3.26844	+	34.2287i	0.179650	+	1.88138i	−0.235855	+	0.971788i	$0.575789\pi$
$332$	−1.80651	−	6.15240i	−0.0991449	−	0.337657i
$333$		0			0
$334$		−	4.79223i		−	0.262219i
$335$	27.2858	−	2.00295i	1.49078	−	0.109433i
$336$		0			0
$337$	−27.9856	+	1.33312i	−1.52447	+	0.0726197i	−0.792989	−	0.609237i	$-0.791476\pi$
$337$	−27.9856	+	1.33312i	−1.52447	+	0.0726197i	−0.731486	+	0.681856i	$0.761173\pi$
$338$	−8.75046	+	2.56937i	−0.475962	+	0.139755i
$339$		0			0
$340$	14.5911	−	12.6433i	0.791315	−	0.685679i
$341$	17.9222	−	6.20294i	0.970542	−	0.335908i
$342$		0			0
$343$	19.9473	−	2.86798i	1.07705	−	0.154857i
$344$	−5.03418	−	7.83334i	−0.271425	−	0.422346i
$345$		0			0
$346$	14.6785	+	5.08028i	0.789121	+	0.273118i
$347$	0.671263	−	0.268733i	0.0360353	−	0.0144264i	−0.353575	−	0.935406i	$-0.615034\pi$
$347$	0.671263	−	0.268733i	0.0360353	−	0.0144264i	0.389610	+	0.920980i	$0.372610\pi$
$348$		0			0
$349$	1.24780	−	2.73230i	0.0667933	−	0.146257i	−0.873291	−	0.487199i	$-0.838019\pi$
$349$	1.24780	−	2.73230i	0.0667933	−	0.146257i	0.940084	+	0.340942i	$0.110746\pi$
$350$	−7.17797	+	11.1691i	−0.383678	+	0.597015i
$351$		0			0
$352$	−11.2510	−	1.07434i	−0.599682	−	0.0572627i
$353$	2.16553	+	3.04106i	0.115260	+	0.161859i	0.868176	−	0.496257i	$-0.165293\pi$
$353$	2.16553	+	3.04106i	0.115260	+	0.161859i	−0.752916	+	0.658117i	$0.771353\pi$
$354$		0			0
$355$	21.9107	−	22.9793i	1.16290	−	1.21961i
$356$	−0.335374	+	1.74009i	−0.0177748	+	0.0922243i
$357$		0			0
$358$	2.58130	−	10.6403i	0.136426	−	0.562356i
$359$	−20.1911	+	9.22096i	−1.06564	+	0.486663i	−0.869511	−	0.493914i	$-0.835566\pi$
$359$	−20.1911	+	9.22096i	−1.06564	+	0.486663i	−0.196133	+	0.980577i	$0.562839\pi$
$360$		0			0
$361$	−10.8816	+	15.2810i	−0.572715	+	0.804266i
$362$	−8.43828	+	9.73829i	−0.443506	+	0.511833i
$363$		0			0
$364$	2.06237	+	3.57213i	0.108098	+	0.187231i
$365$	−9.37019	+	16.2296i	−0.490458	+	0.849498i
$366$		0			0
$367$	10.7530	−	2.60864i	0.561301	−	0.136170i	0.0549365	−	0.998490i	$-0.482504\pi$
$367$	10.7530	−	2.60864i	0.561301	−	0.136170i	0.506364	+	0.862320i	$0.330989\pi$
$368$	−1.30399	−	0.0621166i	−0.0679750	−	0.00323805i
$369$		0			0
$370$	5.35526	+	22.0747i	0.278407	+	1.14761i
$371$	14.7576	+	18.7658i	0.766176	+	0.974272i
$372$		0			0
$373$	5.12595	−	2.95947i	0.265412	−	0.153236i	−0.361389	−	0.932415i	$-0.617697\pi$
$373$	5.12595	−	2.95947i	0.265412	−	0.153236i	0.626801	+	0.779180i	$0.284364\pi$
$374$	−5.17214	+	12.9194i	−0.267445	+	0.668045i
$375$		0			0
$376$	−20.2440	−	14.4157i	−1.04401	−	0.743433i
$377$	−0.291705	+	2.02885i	−0.0150236	+	0.104491i
$378$		0			0
$379$	−6.37574	−	1.54674i	−0.327500	−	0.0794506i	0.0686381	−	0.997642i	$-0.478135\pi$
$379$	−6.37574	−	1.54674i	−0.327500	−	0.0794506i	−0.396138	+	0.918191i	$0.629650\pi$
$380$	−1.52778	−	0.448596i	−0.0783734	−	0.0230125i
$381$		0			0
$382$	−15.5239	−	14.8020i	−0.794273	−	0.757337i
$383$	12.9343	−	6.66812i	0.660914	−	0.340725i	−0.0949229	−	0.995485i	$-0.530260\pi$
$383$	12.9343	−	6.66812i	0.660914	−	0.340725i	0.755837	+	0.654760i	$0.227230\pi$
$384$		0			0
$385$	−1.55507	+	16.2854i	−0.0792535	+	0.829980i
$386$	24.8261	−	4.78484i	1.26362	−	0.243542i
$387$		0			0
$388$	−10.8373	−	4.94924i	−0.550182	−	0.251260i
$389$	−11.9578	+	15.2055i	−0.606282	+	0.770951i	−0.988187	−	0.153251i	$-0.951026\pi$
$389$	−11.9578	+	15.2055i	−0.606282	+	0.770951i	0.381905	+	0.924202i	$0.375268\pi$
$390$		0			0
$391$	2.28003	−	6.58773i	0.115306	−	0.333156i
$392$	−5.45543	+	5.20175i	−0.275541	+	0.262728i
$393$		0			0
$394$	2.22391	+	15.4676i	0.112039	+	0.779248i
$395$	−5.53011	+	10.7269i	−0.278250	+	0.539730i
$396$		0			0
$397$	8.28745	+	9.56423i	0.415935	+	0.480015i	0.924594	−	0.380953i	$-0.124404\pi$
$397$	8.28745	+	9.56423i	0.415935	+	0.480015i	−0.508659	+	0.860968i	$0.669859\pi$
$398$	−17.0946	+	1.63234i	−0.856877	+	0.0818218i
$399$		0			0
$400$	−0.327020	−	6.86499i	−0.0163510	−	0.343250i
$401$	34.7260			1.73413			0.867067	−	0.498192i	$-0.166003\pi$
$401$	34.7260			1.73413			0.867067	+	0.498192i	$0.166003\pi$
$402$		0			0
$403$	16.4532			0.819592
$404$	−0.408701	−	8.57969i	−0.0203336	−	0.426856i
$405$		0			0
$406$	2.19249	−	0.209357i	0.108811	−	0.0103902i
$407$	10.1259	+	11.6859i	0.501923	+	0.579250i
$408$		0			0
$409$	3.02786	−	5.87322i	0.149718	−	0.290412i	−0.802035	−	0.597277i	$-0.796249\pi$
$409$	3.02786	−	5.87322i	0.149718	−	0.290412i	0.951753	+	0.306864i	$0.0992798\pi$
$410$	1.03203	+	7.17792i	0.0509683	+	0.354492i
$411$		0			0
$412$	6.25288	−	5.96211i	0.308057	−	0.293732i
$413$	−1.65981	+	4.79570i	−0.0816737	+	0.235981i
$414$		0			0
$415$	13.6385	−	17.3427i	0.669486	−	0.851320i
$416$	−8.91908	−	4.07321i	−0.437294	−	0.199705i
$417$		0			0
$418$	1.12696	−	0.217204i	0.0551215	−	0.0106238i
$419$	1.18849	−	12.4465i	0.0580616	−	0.608049i	−0.918879	−	0.394539i	$-0.870904\pi$
$419$	1.18849	−	12.4465i	0.0580616	−	0.608049i	0.976941	−	0.213510i	$-0.0684896\pi$
$420$		0			0
$421$	23.4740	−	12.1017i	1.14405	−	0.589800i	0.221305	−	0.975205i	$-0.428968\pi$
$421$	23.4740	−	12.1017i	1.14405	−	0.589800i	0.922748	+	0.385404i	$0.125938\pi$
$422$	13.8281	+	13.1851i	0.673143	+	0.641841i
$423$		0			0
$424$	−32.5460	−	9.55636i	−1.58057	−	0.464098i
$425$	35.6658	+	8.65243i	1.73005	+	0.419705i
$426$		0			0
$427$	1.38758	−	9.65082i	0.0671497	−	0.467036i
$428$	−15.1768	−	10.8073i	−0.733598	−	0.522393i
$429$		0			0
$430$	3.89289	−	9.72397i	0.187732	−	0.468932i
$431$	−13.5012	+	7.79493i	−0.650331	+	0.375469i	−0.788583	−	0.614928i	$-0.789185\pi$
$431$	−13.5012	+	7.79493i	−0.650331	+	0.375469i	0.138252	+	0.990397i	$0.455852\pi$
$432$		0			0
$433$	−0.476648	−	0.606108i	−0.0229063	−	0.0291277i	0.774465	−	0.632617i	$-0.218019\pi$
$433$	−0.476648	−	0.606108i	−0.0229063	−	0.0291277i	−0.797371	+	0.603489i	$0.793777\pi$
$434$	−4.16804	−	17.1809i	−0.200072	−	0.824710i
$435$		0			0
$436$	10.4902	+	0.499709i	0.502388	+	0.0239317i
$437$	−0.558718	+	0.135544i	−0.0267271	+	0.00648393i
$438$		0			0
$439$	7.59143	−	13.1487i	0.362319	−	0.627555i	−0.626023	−	0.779805i	$-0.715318\pi$
$439$	7.59143	−	13.1487i	0.362319	−	0.627555i	0.988342	+	0.152249i	$0.0486517\pi$
$440$	−11.6220	−	20.1298i	−0.554055	−	0.959651i
$441$		0			0
$442$	−7.90608	+	9.12411i	−0.376054	+	0.433989i
$443$	−8.86364	+	12.4472i	−0.421124	+	0.591386i	−0.969574	−	0.244797i	$-0.921279\pi$
$443$	−8.86364	+	12.4472i	−0.421124	+	0.591386i	0.548450	+	0.836183i	$0.315218\pi$
$444$		0			0
$445$	−5.54650	+	2.53300i	−0.262929	+	0.120076i
$446$	5.07542	−	20.9212i	0.240328	−	0.990647i
$447$		0			0
$448$	−2.88787	+	14.9837i	−0.136439	+	0.707913i
$449$	−7.06684	+	7.41149i	−0.333505	+	0.349770i	−0.869039	−	0.494744i	$-0.835262\pi$
$449$	−7.06684	+	7.41149i	−0.333505	+	0.349770i	0.535534	+	0.844514i	$0.320110\pi$
$450$		0			0
$451$	2.86342	+	4.02111i	0.134833	+	0.189347i
$452$	18.4566	+	1.76239i	0.868127	+	0.0828961i
$453$		0			0
$454$	−7.56253	+	11.7675i	−0.354927	+	0.552278i
$455$	−5.89579	+	12.9100i	−0.276399	+	0.605229i
$456$		0			0
$457$	−15.1232	+	6.05443i	−0.707435	+	0.283214i	−0.697346	−	0.716735i	$-0.745636\pi$
$457$	−15.1232	+	6.05443i	−0.707435	+	0.283214i	−0.0100890	+	0.999949i	$0.503211\pi$
$458$	−18.6642	−	6.45973i	−0.872119	−	0.301843i
$459$		0			0
$460$	2.05798	+	3.20228i	0.0959537	+	0.149307i
$461$	29.3481	−	4.21962i	1.36688	−	0.196527i	0.580494	−	0.814265i	$-0.302859\pi$
$461$	29.3481	−	4.21962i	1.36688	−	0.196527i	0.786385	+	0.617737i	$0.211950\pi$
$462$		0			0
$463$	−9.35980	+	3.23946i	−0.434987	+	0.150550i	−0.535781	−	0.844357i	$-0.679983\pi$
$463$	−9.35980	+	3.23946i	−0.434987	+	0.150550i	0.100794	+	0.994907i	$0.467862\pi$
$464$	−0.861639	+	0.746614i	−0.0400006	+	0.0346607i
$465$		0			0
$466$	−12.7568	+	3.74575i	−0.590949	+	0.173518i
$467$	−28.2116	+	1.34388i	−1.30548	+	0.0621875i	−0.688755	−	0.724994i	$-0.741843\pi$
$467$	−28.2116	+	1.34388i	−1.30548	+	0.0621875i	−0.616722	+	0.787181i	$0.711540\pi$
$468$		0			0
$469$	−7.61516	−	15.6020i	−0.351636	−	0.720433i
$470$		−	27.9556i		−	1.28950i
$471$		0			0
$472$	−2.03141	−	6.91833i	−0.0935031	−	0.318442i
$473$	−0.677760	−	7.09782i	−0.0311634	−	0.326358i
$474$		0			0
$475$	−0.989955	−	2.86029i	−0.0454222	−	0.131239i
$476$	−10.8895	−	5.61395i	−0.499121	−	0.257315i
$477$		0			0
$478$	−5.63694	+	3.62264i	−0.257828	+	0.165696i
$479$	13.4722	+	14.1292i	0.615560	+	0.645581i	0.955543	−	0.294850i	$-0.0952698\pi$
$479$	13.4722	+	14.1292i	0.615560	+	0.645581i	−0.339983	+	0.940432i	$0.610421\pi$
$480$		0			0
$481$	4.98568	+	12.4536i	0.227328	+	0.567837i
$482$	−18.2593	−	14.3593i	−0.831688	−	0.654047i
$483$		0			0
$484$	4.63764	+	2.98043i	0.210802	+	0.135474i
$485$	−7.75814	−	40.2531i	−0.352279	−	1.82780i
$486$		0			0
$487$	−18.6519	+	13.2819i	−0.845198	+	0.601863i	−0.918488	−	0.395448i	$-0.870589\pi$
$487$	−18.6519	+	13.2819i	−0.845198	+	0.601863i	0.0732906	+	0.997311i	$0.476650\pi$
$488$	6.34787	+	12.3132i	0.287355	+	0.557390i
$489$		0			0
$490$	−8.32595	−	1.60469i	−0.376128	−	0.0724927i
$491$	4.72773	−	16.1012i	0.213360	−	0.726636i	−0.781367	−	0.624072i	$-0.785477\pi$
$491$	4.72773	−	16.1012i	0.213360	−	0.726636i	0.994726	−	0.102564i	$-0.0327047\pi$
$492$		0			0
$493$	−2.52911	−	5.53798i	−0.113905	−	0.249418i
$494$	0.985545	+	0.141700i	0.0443418	+	0.00637539i
$495$		0			0
$496$	6.91642	+	5.99311i	0.310557	+	0.269099i
$497$	−18.7049	−	7.48831i	−0.839029	−	0.335897i
$498$		0			0
$499$	19.0851	+	11.0188i	0.854365	+	0.493268i	0.862121	−	0.506702i	$-0.169136\pi$
$499$	19.0851	+	11.0188i	0.854365	+	0.493268i	−0.00775617	+	0.999970i	$0.502469\pi$
$500$	−2.99132	+	2.35240i	−0.133776	+	0.105203i
$501$		0			0
$502$	−0.00925120	+	0.194207i	−0.000412901	+	0.00866786i
$503$	1.52549	−	32.0239i	0.0680182	−	1.42788i	−0.664581	−	0.747216i	$-0.731390\pi$
$503$	1.52549	−	32.0239i	0.0680182	−	1.42788i	0.732599	−	0.680660i	$-0.238307\pi$
$504$		0			0
$505$	23.2316	−	18.2695i	1.03379	−	0.812982i
$506$	−2.37614	−	1.37187i	−0.105632	−	0.0609869i
$507$		0			0
$508$	−13.3343	−	5.33824i	−0.591613	−	0.236846i
$509$	17.1160	+	14.8311i	0.758652	+	0.657376i	0.945724	−	0.324970i	$-0.105354\pi$
$509$	17.1160	+	14.8311i	0.758652	+	0.657376i	−0.187072	+	0.982346i	$0.559900\pi$
$510$		0			0
$511$	11.7710	+	1.69241i	0.520717	+	0.0748678i
$512$	−5.05368	−	11.0660i	−0.223343	−	0.489053i
$513$		0			0
$514$	4.56080	−	15.5327i	0.201168	−	0.685116i
$515$	29.1907	+	5.62604i	1.28629	+	0.247913i
$516$		0			0
$517$	−8.72010	−	16.9146i	−0.383510	−	0.743905i
$518$	11.7414	−	8.36104i	0.515889	−	0.367363i
$519$		0			0
$520$	−3.81627	−	19.8007i	−0.167354	−	0.868317i
$521$	−8.81652	−	5.66604i	−0.386259	−	0.248234i	0.333072	−	0.942902i	$-0.391915\pi$
$521$	−8.81652	−	5.66604i	−0.386259	−	0.248234i	−0.719330	+	0.694668i	$0.755551\pi$
$522$		0			0
$523$	22.0177	+	17.3149i	0.962766	+	0.757128i	0.970065	−	0.242846i	$-0.0780809\pi$
$523$	22.0177	+	17.3149i	0.962766	+	0.757128i	−0.00729879	+	0.999973i	$0.502323\pi$
$524$	0.570835	+	1.42588i	0.0249371	+	0.0622898i
$525$		0			0
$526$	15.9755	+	16.7546i	0.696564	+	0.730536i
$527$	−41.1120	+	26.4211i	−1.79087	+	1.15092i
$528$		0			0
$529$	−19.2216	−	9.90941i	−0.835720	−	0.430844i
$530$	−12.4795	−	36.0571i	−0.542074	−	1.56622i
$531$		0			0
$532$	0.0960451	+	1.00583i	0.00416408	+	0.0436083i
$533$	1.20654	+	4.10910i	0.0522611	+	0.177985i
$534$		0			0
$535$		−	64.1078i		−	2.77162i
$536$	21.6721	+	11.7811i	0.936091	+	0.508868i
$537$		0			0
$538$	−3.29044	+	0.156743i	−0.141861	+	0.00675767i
$539$	−5.53819	+	1.62616i	−0.238547	+	0.0700437i
$540$		0			0
$541$	−17.7521	+	15.3823i	−0.763224	+	0.661337i	−0.946856	−	0.321658i	$-0.895760\pi$
$541$	−17.7521	+	15.3823i	−0.763224	+	0.661337i	0.183632	+	0.982995i	$0.441215\pi$
$542$	−18.6291	+	6.44760i	−0.800189	+	0.276948i
$543$		0			0
$544$	28.8272	−	4.14472i	1.23596	−	0.177704i
$545$	19.5365	+	30.3994i	0.836851	+	1.30217i
$546$		0			0
$547$	19.5055	+	6.75092i	0.833995	+	0.288649i	0.710500	−	0.703697i	$-0.248469\pi$
$547$	19.5055	+	6.75092i	0.833995	+	0.288649i	0.123495	+	0.992345i	$0.460590\pi$
$548$	−18.3284	+	7.33760i	−0.782952	+	0.313447i
$549$		0			0
$550$	6.00055	−	13.1394i	0.255864	−	0.560264i
$551$	−0.271457	+	0.422396i	−0.0115645	+	0.0179947i
$552$		0			0
$553$	7.62359	+	0.727964i	0.324188	+	0.0309562i
$554$	−11.8532	−	16.6455i	−0.503594	−	0.707198i
$555$		0			0
$556$	10.6650	−	11.1852i	0.452299	−	0.474357i
$557$	−1.83882	+	9.54071i	−0.0779134	+	0.404253i	0.921943	+	0.387325i	$0.126601\pi$
$557$	−1.83882	+	9.54071i	−0.0779134	+	0.404253i	−0.999857	+	0.0169282i	$0.994611\pi$
$558$		0			0
$559$	1.45833	−	6.01131i	0.0616807	−	0.254251i
$560$	−7.18090	+	3.27941i	−0.303448	+	0.138580i
$561$		0			0
$562$	9.89741	−	13.8990i	0.417497	−	0.586292i
$563$	2.38260	−	2.74966i	0.100415	−	0.115885i	−0.703318	−	0.710876i	$-0.748299\pi$
$563$	2.38260	−	2.74966i	0.100415	−	0.115885i	0.803732	+	0.594991i	$0.202844\pi$
$564$		0			0
$565$	31.8975	+	55.2480i	1.34194	+	2.32430i
$566$	11.0551	−	19.1480i	0.464681	−	0.804852i
$567$		0			0
$568$	27.8200	−	6.74906i	1.16730	−	0.283184i
$569$	39.3695	+	1.87540i	1.65046	+	0.0786210i	0.852038	−	0.523481i	$-0.175367\pi$
$569$	39.3695	+	1.87540i	1.65046	+	0.0786210i	0.798419	+	0.602102i	$0.205670\pi$
$570$		0			0
$571$	7.10418	+	29.2838i	0.297301	+	1.22549i	0.902946	+	0.429755i	$0.141400\pi$
$571$	7.10418	+	29.2838i	0.297301	+	1.22549i	−0.605645	+	0.795735i	$0.707085\pi$
$572$	−2.77404	−	3.52748i	−0.115989	−	0.147492i
$573$		0			0
$574$	3.98519	−	2.30085i	0.166339	−	0.0960357i
$575$	−2.68930	+	6.71755i	−0.112152	+	0.280141i
$576$		0			0
$577$	20.7728	+	14.7923i	0.864784	+	0.615810i	0.923982	−	0.382437i	$-0.124915\pi$
$577$	20.7728	+	14.7923i	0.864784	+	0.615810i	−0.0591981	+	0.998246i	$0.518854\pi$
$578$	2.64964	−	18.4287i	0.110211	−	0.766531i
$579$		0			0
$580$	3.23069	+	0.783758i	0.134147	+	0.0325438i
$581$	−13.4333	−	3.94438i	−0.557309	−	0.163641i
$582$		0			0
$583$	−18.7979	−	17.9238i	−0.778531	−	0.742328i
$584$	−15.0182	+	7.74241i	−0.621456	+	0.320383i
$585$		0			0
$586$	1.76909	−	18.5268i	0.0730806	−	0.765334i
$587$	−24.8212	+	4.78390i	−1.02448	+	0.197453i	−0.673701	−	0.739004i	$-0.735296\pi$
$587$	−24.8212	+	4.78390i	−1.02448	+	0.197453i	−0.350782	+	0.936457i	$0.614084\pi$
$588$		0			0
$589$	3.66619	+	1.67429i	0.151063	+	0.0689880i
$590$	5.01376	−	6.37551i	0.206413	−	0.262476i
$591$		0			0
$592$	−2.44043	+	7.05117i	−0.100301	+	0.289801i
$593$	6.00238	−	5.72326i	0.246488	−	0.235026i	−0.556756	−	0.830676i	$-0.687954\pi$
$593$	6.00238	−	5.72326i	0.246488	−	0.235026i	0.803244	+	0.595650i	$0.203106\pi$
$594$		0			0
$595$	−5.99931	−	41.7261i	−0.245948	−	1.71060i
$596$	−4.98392	+	9.66745i	−0.204149	+	0.395994i
$597$		0			0
$598$	−1.55877	−	1.79892i	−0.0637428	−	0.0735631i
$599$	−6.15816	+	0.588033i	−0.251616	+	0.0240264i	−0.220102	−	0.975477i	$-0.570639\pi$
$599$	−6.15816	+	0.588033i	−0.251616	+	0.0240264i	−0.0315140	+	0.999503i	$0.510033\pi$
$600$		0			0
$601$	−0.933414	−	19.5948i	−0.0380748	−	0.799287i	−0.934472	−	0.356036i	$-0.884128\pi$
$601$	−0.933414	−	19.5948i	−0.0380748	−	0.799287i	0.896397	−	0.443251i	$-0.146175\pi$
$602$	−6.64662			−0.270896
$603$		0			0
$604$	11.2649			0.458360
$605$	0.902557	+	18.9470i	0.0366942	+	0.770305i
$606$		0			0
$607$	30.2350	−	2.88709i	1.22720	−	0.117183i	0.538749	−	0.842466i	$-0.318897\pi$
$607$	30.2350	−	2.88709i	1.22720	−	0.117183i	0.688451	+	0.725283i	$0.258291\pi$
$608$	−1.57290	−	1.81523i	−0.0637896	−	0.0736171i
$609$		0			0
$610$	−7.14055	+	13.8507i	−0.289112	+	0.560799i
$611$	−2.34954	−	16.3414i	−0.0950521	−	0.661102i
$612$		0			0
$613$	−1.10350	+	1.05218i	−0.0445698	+	0.0424972i	−0.712037	−	0.702142i	$-0.752227\pi$
$613$	−1.10350	+	1.05218i	−0.0445698	+	0.0424972i	0.667467	+	0.744639i	$0.267379\pi$
$614$	−9.94618	+	28.7376i	−0.401395	+	1.15976i
$615$		0			0
$616$	−9.11772	+	11.5941i	−0.367364	+	0.467141i
$617$	9.37410	+	4.28101i	0.377387	+	0.172347i	0.595072	−	0.803672i	$-0.297123\pi$
$617$	9.37410	+	4.28101i	0.377387	+	0.172347i	−0.217685	+	0.976019i	$0.569851\pi$
$618$		0			0
$619$	−38.3021	+	7.38213i	−1.53949	+	0.296713i	−0.887247	−	0.461295i	$-0.847385\pi$
$619$	−38.3021	+	7.38213i	−1.53949	+	0.296713i	−0.652245	+	0.758008i	$0.726173\pi$
$620$	2.53659	−	26.5643i	0.101872	−	1.06685i
$621$		0			0
$622$	6.73303	−	3.47112i	0.269970	−	0.139179i
$623$	2.80033	+	2.67011i	0.112193	+	0.106976i
$624$		0			0
$625$	17.0465	+	5.00530i	0.681859	+	0.200212i
$626$	−18.9242	−	4.59097i	−0.756365	−	0.183492i
$627$		0			0
$628$	2.68396	−	18.6674i	0.107102	−	0.744909i
$629$	−32.4563	−	23.1120i	−1.29412	−	0.921536i
$630$		0			0
$631$	−8.21999	+	20.5325i	−0.327233	+	0.817388i	0.669952	+	0.742404i	$0.266315\pi$
$631$	−8.21999	+	20.5325i	−0.327233	+	0.817388i	−0.997185	+	0.0749833i	$0.976110\pi$
$632$	−9.42326	+	5.44052i	−0.374837	+	0.216412i
$633$		0			0
$634$	−1.61880	−	2.05847i	−0.0642908	−	0.0817524i
$635$	−11.6515	−	48.0280i	−0.462374	−	1.90593i
$636$		0			0
$637$	−5.00178	−	0.238264i	−0.198178	−	0.00944037i
$638$	−2.32866	+	0.564927i	−0.0921925	+	0.0223657i
$639$		0			0
$640$	−4.17663	+	7.23414i	−0.165096	+	0.285955i
$641$	−16.1549	−	27.9811i	−0.638079	−	1.10519i	−0.985854	−	0.167607i	$-0.946396\pi$
$641$	−16.1549	−	27.9811i	−0.638079	−	1.10519i	0.347775	−	0.937578i	$-0.386937\pi$
$642$		0			0
$643$	−16.4949	+	19.0361i	−0.650493	+	0.750709i	−0.981194	−	0.193026i	$-0.938170\pi$
$643$	−16.4949	+	19.0361i	−0.650493	+	0.750709i	0.330700	+	0.943736i	$0.392715\pi$
$644$	1.40113	−	1.96762i	0.0552124	−	0.0775349i
$645$		0			0
$646$	−2.69015	+	1.22855i	−0.105843	+	0.0483367i
$647$	7.36792	−	30.3710i	0.289663	−	1.19401i	−0.621983	−	0.783030i	$-0.713673\pi$
$647$	7.36792	−	30.3710i	0.289663	−	1.19401i	0.911646	−	0.410976i	$-0.134812\pi$
$648$		0			0
$649$	1.04490	−	5.42145i	0.0410159	−	0.212811i
$650$	8.64766	−	9.06940i	0.339189	−	0.355731i
$651$		0			0
$652$	−7.33011	−	10.2937i	−0.287069	−	0.403132i
$653$	7.52908	+	0.718940i	0.294636	+	0.0281343i	0.241327	−	0.970444i	$-0.422417\pi$
$653$	7.52908	+	0.718940i	0.294636	+	0.0281343i	0.0533085	+	0.998578i	$0.483023\pi$
$654$		0			0
$655$	−2.85715	+	4.44582i	−0.111638	+	0.173713i
$656$	−0.989556	+	2.16683i	−0.0386357	+	0.0846004i
$657$		0			0
$658$	−16.4689	+	6.59317i	−0.642026	+	0.257029i
$659$	−6.00467	−	2.07824i	−0.233909	−	0.0809566i	0.207599	−	0.978214i	$-0.433435\pi$
$659$	−6.00467	−	2.07824i	−0.233909	−	0.0809566i	−0.441508	+	0.897257i	$0.645556\pi$
$660$		0			0
$661$	3.38393	+	5.26550i	0.131620	+	0.204804i	0.900808	−	0.434218i	$-0.142975\pi$
$661$	3.38393	+	5.26550i	0.131620	+	0.204804i	−0.769188	+	0.639023i	$0.779339\pi$
$662$	−34.5175	+	4.96286i	−1.34156	+	0.192887i
$663$		0			0
$664$	18.7981	−	6.50610i	0.729509	−	0.252486i
$665$	−2.62746	+	2.27671i	−0.101889	+	0.0882869i
$666$		0			0
$667$	1.15172	−	0.338176i	0.0445949	−	0.0130942i
$668$	−4.58488	+	0.218405i	−0.177394	+	0.00845033i
$669$		0			0
$670$	3.34581	+	27.5451i	0.129260	+	1.06416i
$671$			10.6078i			0.409508i
$672$		0			0
$673$	9.79163	+	33.3472i	0.377440	+	1.28544i	0.901136	+	0.433536i	$0.142734\pi$
$673$	9.79163	+	33.3472i	0.377440	+	1.28544i	−0.523696	+	0.851905i	$0.675447\pi$
$674$	−2.70102	−	28.2864i	−0.104039	−	1.08955i
$675$		0			0
$676$	2.85700	+	8.25475i	0.109885	+	0.317491i
$677$	−4.11554	−	2.12171i	−0.158173	−	0.0815439i	0.377323	−	0.926082i	$-0.376845\pi$
$677$	−4.11554	−	2.12171i	−0.158173	−	0.0815439i	−0.535496	+	0.844538i	$0.679875\pi$
$678$		0			0
$679$	−21.8838	+	14.0639i	−0.839824	+	0.539722i
$680$	41.3323	+	43.3481i	1.58502	+	1.66232i
$681$		0			0
$682$	7.14873	+	17.8567i	0.273739	+	0.683767i
$683$	4.70210	+	3.69777i	0.179921	+	0.141491i	0.704058	−	0.710143i	$-0.251370\pi$
$683$	4.70210	+	3.69777i	0.179921	+	0.141491i	−0.524137	+	0.851634i	$0.675612\pi$
$684$		0			0
$685$	−57.1472	−	36.7263i	−2.18348	−	1.40324i
$686$	3.86800	+	20.0691i	0.147681	+	0.766241i
$687$		0			0
$688$	2.80267	−	1.99577i	0.106851	−	0.0760881i
$689$	−10.3253	−	20.0283i	−0.393362	−	0.763017i
$690$		0			0
$691$	−30.8201	−	5.94009i	−1.17245	−	0.225972i	−0.434403	−	0.900718i	$-0.643041\pi$
$691$	−30.8201	−	5.94009i	−1.17245	−	0.225972i	−0.738049	+	0.674747i	$0.764253\pi$
$692$	4.19150	−	14.2749i	0.159337	−	0.542652i
$693$		0			0
$694$	0.304632	+	0.667051i	0.0115637	+	0.0253209i
$695$	52.6361	+	7.56793i	1.99660	+	0.287068i
$696$		0			0
$697$	−9.61334	−	8.33001i	−0.364131	−	0.315521i
$698$	2.82816	+	1.13222i	0.107047	+	0.0428553i
$699$		0			0
$700$	11.0130	+	6.35836i	0.416253	+	0.240324i
$701$	2.69329	−	2.11803i	0.101724	−	0.0799969i	−0.566001	−	0.824404i	$-0.691510\pi$
$701$	2.69329	−	2.11803i	0.101724	−	0.0799969i	0.667726	+	0.744407i	$0.267268\pi$
$702$		0			0
$703$	−0.156357	+	3.28233i	−0.00589710	+	0.123795i
$704$	0.789945	−	16.5830i	0.0297722	−	0.624995i
$705$		0			0
$706$	−2.97623	+	2.34053i	−0.112012	+	0.0880871i
$707$	−16.2418	−	9.37721i	−0.610836	−	0.352666i
$708$		0			0
$709$	−3.23648	−	1.29569i	−0.121549	−	0.0486608i	0.310091	−	0.950707i	$-0.399641\pi$
$709$	−3.23648	−	1.29569i	−0.121549	−	0.0486608i	−0.431640	+	0.902046i	$0.642065\pi$
$710$	24.3364	+	21.0876i	0.913329	+	0.791404i
$711$		0			0
$712$	−5.44161	−	0.782386i	−0.203933	−	0.0293211i
$713$	−4.00262	−	8.76451i	−0.149899	−	0.328234i
$714$		0			0
$715$	4.35024	−	14.8155i	0.162690	−	0.554070i
$716$	−10.2975	−	1.98469i	−0.384837	−	0.0741713i
$717$		0			0
$718$	−10.3156	−	20.0095i	−0.384975	−	0.746747i
$719$	−21.5022	+	15.3116i	−0.801895	+	0.571027i	−0.905871	−	0.423553i	$-0.860783\pi$
$719$	−21.5022	+	15.3116i	−0.801895	+	0.571027i	0.103976	+	0.994580i	$0.466843\pi$
$720$		0			0
$721$	−3.57009	−	18.5234i	−0.132957	−	0.689848i
$722$	−16.0055	−	10.2861i	−0.595663	−	0.382809i
$723$		0			0
$724$	9.70151	+	7.62935i	0.360554	+	0.283543i
$725$	2.34867	+	5.86668i	0.0872272	+	0.217883i
$726$		0			0
$727$	−24.4902	−	25.6846i	−0.908290	−	0.952587i	0.0907726	−	0.995872i	$-0.471066\pi$
$727$	−24.4902	−	25.6846i	−0.908290	−	0.952587i	−0.999063	+	0.0432843i	$0.986218\pi$
$728$	−10.7648	+	6.91809i	−0.398968	+	0.256401i
$729$		0			0
$730$	−16.8935	−	8.70922i	−0.625258	−	0.322343i
$731$	6.00919	+	17.3624i	0.222258	+	0.642172i
$732$		0			0
$733$	1.03637	+	10.8533i	0.0382791	+	0.400877i	0.994224	+	0.107329i	$0.0342299\pi$
$733$	1.03637	+	10.8533i	0.0382791	+	0.400877i	−0.955944	+	0.293548i	$0.905164\pi$
$734$	3.16158	+	10.7674i	0.116696	+	0.397430i
$735$		0			0
$736$			5.74204i			0.211654i
$737$	10.6164	+	15.6226i	0.391062	+	0.575466i
$738$		0			0
$739$	12.8769	−	0.613400i	0.473683	−	0.0225643i	0.190616	−	0.981665i	$-0.438951\pi$
$739$	12.8769	−	0.613400i	0.473683	−	0.0225643i	0.283066	+	0.959100i	$0.408648\pi$
$740$	20.8755	−	6.12960i	0.767399	−	0.225329i
$741$		0			0
$742$	−18.2984	+	15.8557i	−0.671756	+	0.582080i
$743$	−13.7974	+	4.77532i	−0.506177	+	0.175189i	−0.568208	−	0.822885i	$-0.692363\pi$
$743$	−13.7974	+	4.77532i	−0.506177	+	0.175189i	0.0620316	+	0.998074i	$0.480242\pi$
$744$		0			0
$745$	−37.0433	+	5.32603i	−1.35716	+	0.195131i
$746$	3.24544	+	5.05000i	0.118824	+	0.184894i
$747$		0			0
$748$	12.5961	+	4.35956i	0.460560	+	0.159401i
$749$	−37.7666	+	15.1195i	−1.37996	+	0.552454i
$750$		0			0
$751$	−11.3176	+	24.7822i	−0.412987	+	0.904315i	0.582800	+	0.812616i	$0.301957\pi$
$751$	−11.3176	+	24.7822i	−0.412987	+	0.904315i	−0.995787	+	0.0916990i	$0.970770\pi$
$752$	4.96471	−	7.72524i	0.181044	−	0.281711i
$753$		0			0
$754$	−2.06940	−	0.197603i	−0.0753630	−	0.00719629i
$755$	22.4832	+	31.5733i	0.818249	+	1.14907i
$756$		0			0
$757$	8.47597	−	8.88934i	0.308064	−	0.323088i	−0.551442	−	0.834213i	$-0.685922\pi$
$757$	8.47597	−	8.88934i	0.308064	−	0.323088i	0.859507	+	0.511124i	$0.170771\pi$
$758$	1.25924	−	6.53355i	0.0457376	−	0.237309i
$759$		0			0
$760$	1.16457	−	4.80044i	0.0422435	−	0.174130i
$761$	35.3545	−	16.1458i	1.28160	−	0.585286i	0.345961	−	0.938249i	$-0.387553\pi$
$761$	35.3545	−	16.1458i	1.28160	−	0.585286i	0.935637	+	0.352963i	$0.114826\pi$
$762$		0			0
$763$	13.3010	−	18.6787i	0.481530	−	0.676214i
$764$	−13.4541	+	15.5268i	−0.486752	+	0.561741i
$765$		0			0
$766$	7.37928	+	12.7813i	0.266624	+	0.461807i
$767$	2.39495	−	4.14818i	0.0864766	−	0.149782i
$768$		0			0
$769$	−31.4420	+	7.62775i	−1.13383	+	0.275064i	−0.758401	−	0.651789i	$-0.774019\pi$
$769$	−31.4420	+	7.62775i	−1.13383	+	0.275064i	−0.375427	+	0.926852i	$0.622504\pi$
$770$	−16.5729	−	0.789462i	−0.597244	−	0.0284503i
$771$		0			0
$772$	−5.70926	−	23.5339i	−0.205481	−	0.847004i
$773$	7.23913	+	9.20530i	0.260373	+	0.331092i	0.898610	−	0.438749i	$-0.144578\pi$
$773$	7.23913	+	9.20530i	0.260373	+	0.331092i	−0.638236	+	0.769840i	$0.720336\pi$
$774$		0			0
$775$	43.9298	−	25.3629i	1.57801	−	0.911062i
$776$	13.7368	−	34.3128i	0.493122	−	1.23176i
$777$		0			0
$778$	−15.9809	−	11.3800i	−0.572944	−	0.407991i
$779$	−0.149298	+	1.03839i	−0.00534915	+	0.0372042i
$780$		0			0
$781$	21.3026	+	5.16796i	0.762268	+	0.184924i
$782$	6.78369	+	1.99187i	0.242584	+	0.0712292i
$783$		0			0
$784$	−2.01581	−	1.92207i	−0.0719932	−	0.0686453i
$785$	57.6780	−	29.7351i	2.05862	−	1.06129i
$786$		0			0
$787$	−1.98408	+	20.7783i	−0.0707250	+	0.740666i	0.888660	+	0.458566i	$0.151637\pi$
$787$	−1.98408	+	20.7783i	−0.0707250	+	0.740666i	−0.959385	+	0.282099i	$0.908969\pi$
$788$	14.6970	−	2.83262i	0.523560	−	0.100908i
$789$		0			0
$790$	−11.1337	−	5.08459i	−0.396120	−	0.180902i
$791$	25.0244	−	31.8211i	0.889764	−	1.13143i
$792$		0			0
$793$	−3.00990	+	8.69654i	−0.106885	+	0.308823i
$794$	−9.28906	+	8.85710i	−0.329657	+	0.314327i
$795$		0			0
$796$	2.34080	+	16.2806i	0.0829674	+	0.577051i
$797$	−12.2367	+	23.7359i	−0.433447	+	0.840770i	0.566414	+	0.824121i	$0.308330\pi$
$797$	−12.2367	+	23.7359i	−0.433447	+	0.840770i	−0.999861	+	0.0166497i	$0.994700\pi$
$798$		0			0
$799$	32.1124	+	37.0596i	1.13605	+	1.31108i
$800$	−30.0927	+	2.87351i	−1.06394	+	0.101594i
$801$		0			0
$802$	1.67578	+	35.1790i	0.0591739	+	1.24221i
$803$	−12.9381			−0.456577
$804$		0			0
$805$	8.31135			0.292937
$806$	0.793986	+	16.6678i	0.0279670	+	0.587099i
$807$		0			0
$808$	26.5261	−	2.53293i	0.933184	−	0.0891083i
$809$	20.5970	+	23.7702i	0.724151	+	0.835715i	0.991800	−	0.127801i	$-0.0407920\pi$
$809$	20.5970	+	23.7702i	0.724151	+	0.835715i	−0.267648	+	0.963517i	$0.586247\pi$
$810$		0			0
$811$	−10.2521	+	19.8864i	−0.360001	+	0.698305i	−0.997387	−	0.0722398i	$-0.976985\pi$
$811$	−10.2521	+	19.8864i	−0.360001	+	0.698305i	0.637386	+	0.770545i	$0.280016\pi$
$812$	−0.300221	−	2.08808i	−0.0105357	−	0.0732773i
$813$		0			0
$814$	−11.3497	+	10.8219i	−0.397807	+	0.379308i
$815$	14.2213	−	41.0899i	0.498152	−	1.43932i
$816$		0			0
$817$	0.936668	−	1.19107i	0.0327699	−	0.0416703i
$818$	6.09595	+	2.78393i	0.213140	+	0.0973378i
$819$		0			0
$820$	6.82032	−	1.31451i	0.238176	−	0.0459046i
$821$	−3.23686	+	33.8979i	−0.112967	+	1.18305i	0.744182	+	0.667977i	$0.232840\pi$
$821$	−3.23686	+	33.8979i	−0.112967	+	1.18305i	−0.857149	+	0.515069i	$0.827766\pi$
$822$		0			0
$823$	−20.2454	+	10.4372i	−0.705709	+	0.363818i	−0.773426	−	0.633886i	$-0.781459\pi$
$823$	−20.2454	+	10.4372i	−0.705709	+	0.363818i	0.0677174	+	0.997705i	$0.478428\pi$
$824$	19.3981	+	18.4961i	0.675767	+	0.644342i
$825$		0			0
$826$	−4.93835	−	1.45003i	−0.171827	−	0.0504530i
$827$	18.5965	+	4.51147i	0.646665	+	0.156879i	0.545660	−	0.838007i	$-0.316279\pi$
$827$	18.5965	+	4.51147i	0.646665	+	0.156879i	0.101005	+	0.994886i	$0.467794\pi$
$828$		0			0
$829$	4.55145	−	31.6560i	0.158078	−	1.09946i	−0.744091	−	0.668078i	$-0.767117\pi$
$829$	4.55145	−	31.6560i	0.158078	−	1.09946i	0.902170	−	0.431382i	$-0.141974\pi$
$830$	18.2271	+	12.9795i	0.632672	+	0.450523i
$831$		0			0
$832$	5.35297	−	13.3711i	0.185581	−	0.463558i
$833$	12.8807	−	7.43666i	0.446289	−	0.257665i
$834$		0			0
$835$	−9.76299	−	12.4147i	−0.337862	−	0.429627i
$836$	−0.259167	−	1.06830i	−0.00896348	−	0.0369480i
$837$		0			0
$838$	12.6662	+	0.603364i	0.437545	+	0.0208429i
$839$	−49.0893	+	11.9089i	−1.69475	+	0.411142i	−0.962800	−	0.270214i	$-0.912905\pi$
$839$	−49.0893	+	11.9089i	−1.69475	+	0.411142i	−0.731951	+	0.681357i	$0.761390\pi$
$840$		0			0
$841$	−13.9758	+	24.2069i	−0.481926	+	0.834720i
$842$	13.3923	+	23.1962i	0.461531	+	0.799395i
$843$		0			0
$844$	11.9844	−	13.8307i	0.412520	−	0.476074i
$845$	−17.4343	+	24.4831i	−0.599759	+	0.842244i
$846$		0			0
$847$	10.9490	−	5.00025i	0.376213	−	0.171811i
$848$	2.95491	−	12.1803i	0.101472	−	0.418273i
$849$		0			0
$850$	−7.04416	+	36.5486i	−0.241613	+	1.25361i
$851$	5.42109	−	5.68547i	0.185832	−	0.194895i
$852$		0			0
$853$	−6.58965	−	9.25387i	−0.225625	−	0.316847i	0.686209	−	0.727404i	$-0.259273\pi$
$853$	−6.58965	−	9.25387i	−0.225625	−	0.316847i	−0.911835	+	0.410558i	$0.865334\pi$
$854$	9.84367	+	0.939957i	0.336844	+	0.0321647i
$855$		0			0
$856$	31.2491	−	48.6245i	1.06807	−	1.66195i
$857$	−15.1541	+	33.1828i	−0.517654	+	1.13350i	0.452666	+	0.891680i	$0.350473\pi$
$857$	−15.1541	+	33.1828i	−0.517654	+	1.13350i	−0.970320	+	0.241824i	$0.922254\pi$
$858$		0			0
$859$	26.2881	−	10.5242i	0.896939	−	0.359080i	0.123050	−	0.992401i	$-0.460733\pi$
$859$	26.2881	−	10.5242i	0.896939	−	0.359080i	0.773890	+	0.633320i	$0.218308\pi$
$860$	−9.48066	−	3.28129i	−0.323288	−	0.111891i
$861$		0			0
$862$	−8.54815	−	13.3012i	−0.291151	−	0.453040i
$863$	−14.2350	+	2.04668i	−0.484565	+	0.0696699i	−0.380268	−	0.924876i	$-0.624168\pi$
$863$	−14.2350	+	2.04668i	−0.484565	+	0.0696699i	−0.104297	+	0.994546i	$0.533259\pi$
$864$		0			0
$865$	48.3757	−	16.7430i	1.64482	−	0.569279i
$866$	0.591012	−	0.512115i	0.0200834	−	0.0174024i
$867$		0			0
$868$	−16.2476	+	4.77072i	−0.551479	+	0.161929i
$869$	−8.32251	+	0.396450i	−0.282322	+	0.0134486i
$870$		0			0
$871$	4.27082	+	15.8202i	0.144711	+	0.536048i
$872$			32.5803i			1.10331i
$873$		0			0
$874$	−0.164274	−	0.559465i	−0.00555665	−	0.0189242i
$875$	0.789825	+	8.27142i	0.0267010	+	0.279625i
$876$		0			0
$877$	−9.66659	−	27.9298i	−0.326418	−	0.943122i	−0.982145	−	0.188124i	$-0.939759\pi$
$877$	−9.66659	−	27.9298i	−0.326418	−	0.943122i	0.655728	−	0.754997i	$-0.272362\pi$
$878$	13.6866	+	7.05593i	0.461900	+	0.238126i
$879$		0			0
$880$	7.22530	−	4.64342i	0.243565	−	0.156530i
$881$	36.1954	+	37.9607i	1.21945	+	1.27893i	0.948663	+	0.316289i	$0.102437\pi$
$881$	36.1954	+	37.9607i	1.21945	+	1.27893i	0.270791	+	0.962638i	$0.412715\pi$
$882$		0			0
$883$	−3.60403	−	9.00243i	−0.121285	−	0.302956i	0.855284	−	0.518160i	$-0.173383\pi$
$883$	−3.60403	−	9.00243i	−0.121285	−	0.302956i	−0.976569	+	0.215204i	$0.930958\pi$
$884$	9.08965	+	7.14818i	0.305718	+	0.240419i
$885$		0			0
$886$	−13.0373	−	8.37859i	−0.437998	−	0.281484i
$887$	−10.7024	−	55.5295i	−0.359352	−	1.86450i	−0.488054	−	0.872814i	$-0.662293\pi$
$887$	−10.7024	−	55.5295i	−0.359352	−	1.86450i	0.128702	−	0.991683i	$-0.458919\pi$
$888$		0			0
$889$	−25.5459	+	18.1911i	−0.856781	+	0.610111i
$890$	−2.83370	−	5.49661i	−0.0949859	−	0.184247i
$891$		0			0
$892$	−20.2473	−	3.90235i	−0.677929	−	0.130660i
$893$	1.13938	−	3.88036i	0.0381278	−	0.129851i
$894$		0			0
$895$	−14.9899	−	32.8233i	−0.501057	−	1.09716i
$896$	5.24675	+	0.754369i	0.175282	+	0.0252017i
$897$		0			0
$898$	−7.84920	−	6.80137i	−0.261931	−	0.226965i
$899$	−7.81203	−	3.12747i	−0.260546	−	0.104307i
$900$		0			0
$901$	57.9621	+	33.4644i	1.93100	+	1.11486i
$902$	−3.93538	+	3.09482i	−0.131034	+	0.103046i
$903$		0			0
$904$	−2.73681	+	57.4528i	−0.0910251	+	1.91085i
$905$	−2.02066	+	42.4188i	−0.0671688	+	1.41005i
$906$		0			0
$907$	−26.1140	+	20.5363i	−0.867101	+	0.681896i	−0.949181	−	0.314730i	$-0.898086\pi$
$907$	−26.1140	+	20.5363i	−0.867101	+	0.681896i	0.0820801	+	0.996626i	$0.473844\pi$
$908$	11.6030	+	6.69902i	0.385060	+	0.222315i
$909$		0			0
$910$	−13.3629	−	5.34970i	−0.442976	−	0.177341i
$911$	−21.0493	−	18.2394i	−0.697396	−	0.604297i	0.232292	−	0.972646i	$-0.425378\pi$
$911$	−21.0493	−	18.2394i	−0.697396	−	0.604297i	−0.929687	+	0.368349i	$0.879923\pi$
$912$		0			0
$913$	15.0770	+	2.16775i	0.498976	+	0.0717420i
$914$	−6.86321	−	15.0283i	−0.227015	−	0.497093i
$915$		0			0
$916$	−5.32962	+	18.1510i	−0.176096	+	0.599727i
$917$	3.29293	+	0.634659i	0.108742	+	0.0209583i
$918$		0			0
$919$	3.49061	+	6.77084i	0.115145	+	0.223349i	0.939364	−	0.342921i	$-0.111416\pi$
$919$	3.49061	+	6.77084i	0.115145	+	0.223349i	−0.824220	+	0.566270i	$0.808386\pi$
$920$	−9.61930	+	6.84987i	−0.317139	+	0.225834i
$921$		0			0
$922$	5.69093	+	29.5273i	0.187421	+	0.972431i
$923$	15.9981	+	10.2814i	0.526584	+	0.338415i
$924$		0			0
$925$	32.5092	+	25.5655i	1.06890	+	0.840589i
$926$	−3.73339	−	9.32556i	−0.122687	−	0.306457i
$927$		0			0
$928$	3.46056	+	3.62933i	0.113599	+	0.119139i
$929$	−15.4417	+	9.92380i	−0.506627	+	0.325589i	−0.768862	−	0.639415i	$-0.779177\pi$
$929$	−15.4417	+	9.92380i	−0.506627	+	0.325589i	0.262235	+	0.965004i	$0.415540\pi$
$930$		0			0
$931$	−1.09028	−	0.562077i	−0.0357324	−	0.0184213i
$932$	4.16507	+	12.0342i	0.136431	+	0.394193i
$933$		0			0
$934$	−2.72283	−	28.5148i	−0.0890937	−	0.933031i
$935$	12.9212	+	44.0057i	0.422570	+	1.43914i
$936$		0			0
$937$		−	30.8623i		−	1.00823i	−0.863637	−	0.504114i	$-0.831819\pi$
$937$		−	30.8623i		−	1.00823i	0.863637	−	0.504114i	$-0.168181\pi$
$938$	15.4380	−	8.46741i	0.504069	−	0.276471i
$939$		0			0
$940$	−26.7460	+	1.27407i	−0.872359	+	0.0415556i
$941$	8.79598	−	2.58273i	0.286741	−	0.0841947i	−0.135199	−	0.990818i	$-0.543167\pi$
$941$	8.79598	−	2.58273i	0.286741	−	0.0841947i	0.421940	+	0.906624i	$0.361349\pi$
$942$		0			0
$943$	1.89537	−	1.64235i	0.0617219	−	0.0534823i
$944$	2.51775	−	0.871400i	0.0819457	−	0.0283617i
$945$		0			0
$946$	7.15770	−	1.02912i	0.232717	−	0.0334597i
$947$	31.5028	+	49.0194i	1.02370	+	1.59291i	0.782708	+	0.622389i	$0.213838\pi$
$947$	31.5028	+	49.0194i	1.02370	+	1.59291i	0.240996	+	0.970526i	$0.422526\pi$
$948$		0			0
$949$	−10.6071	−	3.67114i	−0.344319	−	0.119170i
$950$	2.84983	−	1.14090i	0.0924605	−	0.0370156i
$951$		0			0
$952$	15.7888	−	34.5728i	0.511720	−	1.12051i
$953$	−19.4707	+	30.2970i	−0.630718	+	0.981416i	0.367952	+	0.929845i	$0.380059\pi$
$953$	−19.4707	+	30.2970i	−0.630718	+	0.981416i	−0.998669	+	0.0515709i	$0.983577\pi$
$954$		0			0
$955$	−70.3715	−	6.71966i	−2.27717	−	0.217443i
$956$	3.72280	+	5.22794i	0.120404	+	0.169084i
$957$		0			0
$958$	−13.6634	+	14.3298i	−0.441445	+	0.462974i
$959$	−8.15800	+	42.3277i	−0.263436	+	1.36683i
$960$		0			0
$961$	−8.61606	+	35.5159i	−0.277938	+	1.14567i
$962$	−12.3755	+	5.65170i	−0.399002	+	0.182218i
$963$		0			0
$964$	−12.9058	+	18.1237i	−0.415669	+	0.583725i
$965$	54.5662	−	62.9727i	1.75655	−	2.02716i
$966$		0			0
$967$	−8.29423	−	14.3660i	−0.266725	−	0.461980i	0.701289	−	0.712877i	$-0.252608\pi$
$967$	−8.29423	−	14.3660i	−0.266725	−	0.461980i	−0.968014	+	0.250896i	$0.919275\pi$
$968$	−8.55106	+	14.8109i	−0.274842	+	0.476040i
$969$		0			0
$970$	40.4038	−	9.80185i	1.29729	−	0.314718i
$971$	39.4823	+	1.88077i	1.26705	+	0.0603568i	0.670310	−	0.742081i	$-0.266161\pi$
$971$	39.4823	+	1.88077i	1.26705	+	0.0603568i	0.596736	+	0.802438i	$0.296464\pi$
$972$		0			0
$973$	−7.95558	−	32.7934i	−0.255044	−	1.05131i
$974$	−14.3553	−	18.2542i	−0.459973	−	0.584904i
$975$		0			0
$976$	−4.43301	+	2.55940i	−0.141897	+	0.0819243i
$977$	−9.21604	+	23.0205i	−0.294847	+	0.736492i	0.704786	+	0.709420i	$0.251043\pi$
$977$	−9.21604	+	23.0205i	−0.294847	+	0.736492i	−0.999633	+	0.0270728i	$0.991381\pi$
$978$		0			0
$979$	−3.42908	−	2.44184i	−0.109594	−	0.0780415i
$980$	−1.15581	+	8.03884i	−0.0369210	+	0.256791i
$981$		0			0
$982$	16.5394	+	4.01241i	0.527792	+	0.128041i
$983$	−5.27714	−	1.54951i	−0.168315	−	0.0494216i	0.196489	−	0.980506i	$-0.437046\pi$
$983$	−5.27714	−	1.54951i	−0.168315	−	0.0494216i	−0.364804	+	0.931084i	$0.618864\pi$
$984$		0			0
$985$	37.2727	+	35.5395i	1.18761	+	1.13238i
$986$	5.48817	−	2.82935i	0.174779	−	0.0901048i
$987$		0			0
$988$	0.0906530	−	0.949362i	0.00288406	−	0.0302032i
$989$	−3.55696	+	0.685547i	−0.113105	+	0.0217991i
$990$		0			0
$991$	−11.3861	−	5.19987i	−0.361692	−	0.165179i	0.226276	−	0.974063i	$-0.427345\pi$
$991$	−11.3861	−	5.19987i	−0.361692	−	0.165179i	−0.587968	+	0.808884i	$0.700072\pi$
$992$	24.8831	−	31.6414i	0.790039	−	1.00462i
$993$		0			0
$994$	6.68334	−	19.3102i	0.211983	−	0.612484i
$995$	−40.9596	+	39.0549i	−1.29851	+	1.23812i
$996$		0			0
$997$	−3.96475	−	27.5754i	−0.125565	−	0.873323i	−0.951080	−	0.308944i	$-0.900025\pi$
$997$	−3.96475	−	27.5754i	−0.125565	−	0.873323i	0.825515	−	0.564380i	$-0.190885\pi$
$998$	−10.2415	+	19.8658i	−0.324189	+	0.628840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.bj.a.503.15	yes	440
3.2	odd	2	inner	603.2.bj.a.503.8	yes	440
67.2	odd	66	inner	603.2.bj.a.404.8	✓	440
201.2	even	66	inner	603.2.bj.a.404.15	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.bj.a.404.8	✓	440	67.2	odd	66	inner
603.2.bj.a.404.15	yes	440	201.2	even	66	inner
603.2.bj.a.503.8	yes	440	3.2	odd	2	inner
603.2.bj.a.503.15	yes	440	1.1	even	1	trivial

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.bj (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0482573 + 1.01304i) q^{2} +(0.967014 - 0.0923386i) q^{4} +(2.18885 + 2.52606i) q^{5} +(0.971904 - 1.88523i) q^{7} +(0.428878 + 2.98291i) q^{8} +O(q^{10})\)	\(q+(0.0482573 + 1.01304i) q^{2} +(0.967014 - 0.0923386i) q^{4} +(2.18885 + 2.52606i) q^{5} +(0.971904 - 1.88523i) q^{7} +(0.428878 + 2.98291i) q^{8} +(-2.45339 + 2.33930i) q^{10} +(-0.754740 + 2.18068i) q^{11} +(-1.23751 + 1.57363i) q^{13} +(1.95672 + 0.893606i) q^{14} +(-1.09341 + 0.210738i) q^{16} +(0.565225 - 5.91930i) q^{17} +(-0.435883 + 0.224713i) q^{19} +(2.34990 + 2.24062i) q^{20} +(-2.24555 - 0.659352i) q^{22} +(1.13932 + 0.276395i) q^{23} +(-0.878373 + 6.10922i) q^{25} +(-1.65387 - 1.17772i) q^{26} +(0.765765 - 1.91279i) q^{28} +(0.886695 - 0.511934i) q^{29} +(-5.08043 - 6.46029i) q^{31} +(1.15471 + 4.75977i) q^{32} +(6.02379 + 0.286949i) q^{34} +(6.88956 - 1.67139i) q^{35} +(3.35039 - 5.80305i) q^{37} +(-0.248679 - 0.430725i) q^{38} +(-6.59627 + 7.61251i) q^{40} +(1.24087 - 1.74255i) q^{41} +(-2.81062 + 1.28357i) q^{43} +(-0.528483 + 2.17844i) q^{44} +(-0.225020 + 1.16752i) q^{46} +(-5.69090 + 5.96844i) q^{47} +(1.45090 + 2.03750i) q^{49} +(-6.23129 - 0.595017i) q^{50} +(-1.05139 + 1.63599i) q^{52} +(-4.67578 + 10.2385i) q^{53} +(-7.16054 + 2.86665i) q^{55} +(6.04031 + 2.09057i) q^{56} +(0.561401 + 0.873557i) q^{58} +(-2.36828 + 0.340507i) q^{59} +(4.34407 - 1.50350i) q^{61} +(6.29939 - 5.45845i) q^{62} +(-6.90299 + 2.02690i) q^{64} +(-6.68381 + 0.318389i) q^{65} +(4.89300 - 6.56190i) q^{67} -5.77624i q^{68} +(2.02566 + 6.89877i) q^{70} +(-0.902966 - 9.45629i) q^{71} +(1.83379 + 5.29840i) q^{73} +(6.04043 + 3.11406i) q^{74} +(-0.400755 + 0.257550i) q^{76} +(3.37755 + 3.54227i) q^{77} +(1.34195 + 3.35203i) q^{79} +(-2.92564 - 2.30075i) q^{80} +(1.82517 + 1.17296i) q^{82} +(-1.24922 - 6.48155i) q^{83} +(16.1897 - 11.5286i) q^{85} +(-1.43594 - 2.78534i) q^{86} +(-6.82846 - 1.31608i) q^{88} +(-0.513954 + 1.75037i) q^{89} +(1.76391 + 3.86242i) q^{91} +(1.12726 + 0.162075i) q^{92} +(-6.32092 - 5.47711i) q^{94} +(-1.52172 - 0.609205i) q^{95} +(-10.6214 - 6.13229i) q^{97} +(-1.99406 + 1.56815i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 20 q^{4}+O(q^{10}) \) 440 * q + 20 * q^4	\( 440 q + 20 q^{4} + 18 q^{13} + 8 q^{16} + 36 q^{19} - 12 q^{22} - 44 q^{25} - 128 q^{28} + 82 q^{31} + 24 q^{34} - 8 q^{37} - 32 q^{40} - 44 q^{43} + 80 q^{46} - 10 q^{49} + 132 q^{52} - 64 q^{55} - 176 q^{58} - 86 q^{61} - 136 q^{64} - 78 q^{67} - 352 q^{70} + 180 q^{73} - 256 q^{76} + 104 q^{79} + 88 q^{82} - 84 q^{85} - 268 q^{88} - 328 q^{91} + 88 q^{94} - 6 q^{97}+O(q^{100}) \) 440 * q + 20 * q^4 + 18 * q^13 + 8 * q^16 + 36 * q^19 - 12 * q^22 - 44 * q^25 - 128 * q^28 + 82 * q^31 + 24 * q^34 - 8 * q^37 - 32 * q^40 - 44 * q^43 + 80 * q^46 - 10 * q^49 + 132 * q^52 - 64 * q^55 - 176 * q^58 - 86 * q^61 - 136 * q^64 - 78 * q^67 - 352 * q^70 + 180 * q^73 - 256 * q^76 + 104 * q^79 + 88 * q^82 - 84 * q^85 - 268 * q^88 - 328 * q^91 + 88 * q^94 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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