LMFDB - Embedded newform 735.2.j.h.197.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(197,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("735.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.8
Character	$\chi$	$=$	735.197
Dual form			735.2.j.h.638.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.347054 - 0.347054i) q^{2} +(-0.176396 + 1.72305i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(0.536770 + 0.659208i) q^{6} +(1.30461 + 1.30461i) q^{8} +(-2.93777 - 0.607876i) q^{9} +(0.256447 + 1.06710i) q^{10} +2.67137i q^{11} +(-3.03102 - 0.310299i) q^{12} +(-2.14945 + 2.14945i) q^{13} +(-3.07954 - 2.34871i) q^{15} -2.61267 q^{16} +(3.26719 - 3.26719i) q^{17} +(-1.23053 + 0.808598i) q^{18} -5.24329i q^{19} +(-3.35432 - 2.05447i) q^{20} +(0.927108 + 0.927108i) q^{22} +(2.54815 + 2.54815i) q^{23} +(-2.47803 + 2.01778i) q^{24} +(-2.27200 - 4.45399i) q^{25} +1.49195i q^{26} +(1.56561 - 4.95468i) q^{27} +2.86924 q^{29} +(-1.88389 + 0.253638i) q^{30} +5.28599 q^{31} +(-3.51596 + 3.51596i) q^{32} +(-4.60289 - 0.471218i) q^{33} -2.26778i q^{34} +(1.06932 - 5.16785i) q^{36} +(-2.14286 - 2.14286i) q^{37} +(-1.81970 - 1.81970i) q^{38} +(-3.32444 - 4.08274i) q^{39} +(-4.01133 + 0.964012i) q^{40} +11.5768i q^{41} +(0.759108 - 0.759108i) q^{43} -4.69922 q^{44} +(4.59015 - 4.89189i) q^{45} +1.76869 q^{46} +(-7.66034 + 7.66034i) q^{47} +(0.460865 - 4.50176i) q^{48} +(-2.33428 - 0.757266i) q^{50} +(5.05320 + 6.20584i) q^{51} +(-3.78111 - 3.78111i) q^{52} +(-4.43577 - 4.43577i) q^{53} +(-1.17619 - 2.26289i) q^{54} +(-5.09384 - 3.11990i) q^{55} +(9.03442 + 0.924894i) q^{57} +(0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +(4.13163 - 5.41724i) q^{60} -4.72534 q^{61} +(1.83452 - 1.83452i) q^{62} -2.78490i q^{64} +(-1.58828 - 6.60897i) q^{65} +(-1.76099 + 1.43391i) q^{66} +(-5.41156 - 5.41156i) q^{67} +(5.74734 + 5.74734i) q^{68} +(-4.84006 + 3.94109i) q^{69} +13.5880i q^{71} +(-3.03961 - 4.62569i) q^{72} +(-4.16486 + 4.16486i) q^{73} -1.48737 q^{74} +(8.07519 - 3.12910i) q^{75} +9.22351 q^{76} +(-2.57069 - 0.263173i) q^{78} +3.89710i q^{79} +(3.05135 - 4.98193i) q^{80} +(8.26097 + 3.57160i) q^{81} +(4.01778 + 4.01778i) q^{82} +(4.03778 + 4.03778i) q^{83} +(2.41421 + 10.0457i) q^{85} -0.526902i q^{86} +(-0.506122 + 4.94383i) q^{87} +(-3.48510 + 3.48510i) q^{88} +3.95125 q^{89} +(-0.104719 - 3.29077i) q^{90} +(-4.48247 + 4.48247i) q^{92} +(-0.932426 + 9.10800i) q^{93} +5.31710i q^{94} +(9.99806 + 6.12366i) q^{95} +(-5.43796 - 6.67836i) q^{96} +(1.86878 + 1.86878i) q^{97} +(1.62386 - 7.84786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45}+ \cdots - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.347054	−	0.347054i	0.245404	−	0.245404i	−0.573677	−	0.819081i	$-0.694484\pi$
$2$	0.347054	−	0.347054i	0.245404	−	0.245404i	0.819081	+	0.573677i	$0.194484\pi$
$3$	−0.176396	+	1.72305i	−0.101842	+	0.994801i
$3$	−0.176396	+	1.72305i	−0.101842	+	0.994801i
$4$			1.75911i			0.879554i
$5$	−1.16790	+	1.90683i	−0.522302	+	0.852760i
$5$	−1.16790	+	1.90683i	−0.522302	+	0.852760i
$6$	0.536770	+	0.659208i	0.219135	+	0.269120i
$7$		0			0
$7$		0			0
$8$	1.30461	+	1.30461i	0.461250	+	0.461250i
$9$	−2.93777	−	0.607876i	−0.979256	−	0.202625i
$10$	0.256447	+	1.06710i	0.0810957	+	0.337446i
$11$			2.67137i			0.805448i	0.915322	+	0.402724i	$0.131936\pi$
$11$			2.67137i			0.805448i	−0.915322	+	0.402724i	$0.868064\pi$
$12$	−3.03102	−	0.310299i	−0.874981	−	0.0895757i
$13$	−2.14945	+	2.14945i	−0.596149	+	0.596149i	−0.939285	−	0.343137i	$-0.888511\pi$
$13$	−2.14945	+	2.14945i	−0.596149	+	0.596149i	0.343137	+	0.939285i	$0.388511\pi$
$14$		0			0
$15$	−3.07954	−	2.34871i	−0.795134	−	0.606434i
$16$	−2.61267			−0.653169
$17$	3.26719	−	3.26719i	0.792410	−	0.792410i	−0.189475	−	0.981886i	$-0.560679\pi$
$17$	3.26719	−	3.26719i	0.792410	−	0.792410i	0.981886	+	0.189475i	$0.0606787\pi$
$18$	−1.23053	+	0.808598i	−0.290038	+	0.190588i
$19$		−	5.24329i		−	1.20289i	−0.798913	−	0.601446i	$-0.794591\pi$
$19$		−	5.24329i		−	1.20289i	0.798913	−	0.601446i	$-0.205409\pi$
$20$	−3.35432	−	2.05447i	−0.750049	−	0.459393i
$21$		0			0
$22$	0.927108	+	0.927108i	0.197660	+	0.197660i
$23$	2.54815	+	2.54815i	0.531326	+	0.531326i	0.920967	−	0.389641i	$-0.127401\pi$
$23$	2.54815	+	2.54815i	0.531326	+	0.531326i	−0.389641	+	0.920967i	$0.627401\pi$
$24$	−2.47803	+	2.01778i	−0.505826	+	0.411877i
$25$	−2.27200	−	4.45399i	−0.454400	−	0.890798i
$26$			1.49195i			0.292595i
$27$	1.56561	−	4.95468i	0.301301	−	0.953529i
$28$		0			0
$29$	2.86924			0.532804			0.266402	−	0.963862i	$-0.414165\pi$
$29$	2.86924			0.532804			0.266402	+	0.963862i	$0.414165\pi$
$30$	−1.88389	+	0.253638i	−0.343950	+	0.0463078i
$31$	5.28599			0.949391			0.474696	−	0.880150i	$-0.342558\pi$
$31$	5.28599			0.949391			0.474696	+	0.880150i	$0.342558\pi$
$32$	−3.51596	+	3.51596i	−0.621540	+	0.621540i
$33$	−4.60289	−	0.471218i	−0.801260	−	0.0820286i
$34$		−	2.26778i		−	0.388921i
$35$		0			0
$36$	1.06932	−	5.16785i	0.178220	−	0.861309i
$37$	−2.14286	−	2.14286i	−0.352284	−	0.352284i	0.508675	−	0.860959i	$-0.330136\pi$
$37$	−2.14286	−	2.14286i	−0.352284	−	0.352284i	−0.860959	+	0.508675i	$0.830136\pi$
$38$	−1.81970	−	1.81970i	−0.295195	−	0.295195i
$39$	−3.32444	−	4.08274i	−0.532336	−	0.653762i
$40$	−4.01133	+	0.964012i	−0.634248	+	0.152424i
$41$			11.5768i			1.80800i	0.427537	+	0.903998i	$0.359381\pi$
$41$			11.5768i			1.80800i	−0.427537	+	0.903998i	$0.640619\pi$
$42$		0			0
$43$	0.759108	−	0.759108i	0.115763	−	0.115763i	−0.646852	−	0.762615i	$-0.723915\pi$
$43$	0.759108	−	0.759108i	0.115763	−	0.115763i	0.762615	+	0.646852i	$0.223915\pi$
$44$	−4.69922			−0.708434
$45$	4.59015	−	4.89189i	0.684259	−	0.729239i
$46$	1.76869			0.260779
$47$	−7.66034	+	7.66034i	−1.11738	+	1.11738i	−0.125250	+	0.992125i	$0.539973\pi$
$47$	−7.66034	+	7.66034i	−1.11738	+	1.11738i	−0.992125	+	0.125250i	$0.960027\pi$
$48$	0.460865	−	4.50176i	0.0665201	−	0.649773i
$49$		0			0
$50$	−2.33428	−	0.757266i	−0.330117	−	0.107094i
$51$	5.05320	+	6.20584i	0.707589	+	0.868991i
$52$	−3.78111	−	3.78111i	−0.524345	−	0.524345i
$53$	−4.43577	−	4.43577i	−0.609300	−	0.609300i	0.333463	−	0.942763i	$-0.391783\pi$
$53$	−4.43577	−	4.43577i	−0.609300	−	0.609300i	−0.942763	+	0.333463i	$0.891783\pi$
$54$	−1.17619	−	2.26289i	−0.160059	−	0.307940i
$55$	−5.09384	−	3.11990i	−0.686854	−	0.420687i
$56$		0			0
$57$	9.03442	+	0.924894i	1.19664	+	0.122505i
$58$	0.995779	−	0.995779i	0.130752	−	0.130752i
$59$	0.159437			0.0207569			0.0103785	−	0.999946i	$-0.496696\pi$
$59$	0.159437			0.0207569			0.0103785	+	0.999946i	$0.496696\pi$
$60$	4.13163	−	5.41724i	0.533391	−	0.699363i
$61$	−4.72534			−0.605018			−0.302509	−	0.953147i	$-0.597824\pi$
$61$	−4.72534			−0.605018			−0.302509	+	0.953147i	$0.597824\pi$
$62$	1.83452	−	1.83452i	0.232984	−	0.232984i
$63$		0			0
$64$		−	2.78490i		−	0.348112i
$65$	−1.58828	−	6.60897i	−0.197002	−	0.819742i
$66$	−1.76099	+	1.43391i	−0.216762	+	0.176502i
$67$	−5.41156	−	5.41156i	−0.661127	−	0.661127i	0.294519	−	0.955646i	$-0.404841\pi$
$67$	−5.41156	−	5.41156i	−0.661127	−	0.661127i	−0.955646	+	0.294519i	$0.904841\pi$
$68$	5.74734	+	5.74734i	0.696967	+	0.696967i
$69$	−4.84006	+	3.94109i	−0.582675	+	0.474452i
$70$		0			0
$71$			13.5880i			1.61260i	0.591508	+	0.806299i	$0.298533\pi$
$71$			13.5880i			1.61260i	−0.591508	+	0.806299i	$0.701467\pi$
$72$	−3.03961	−	4.62569i	−0.358221	−	0.545143i
$73$	−4.16486	+	4.16486i	−0.487460	+	0.487460i	−0.907504	−	0.420044i	$-0.862015\pi$
$73$	−4.16486	+	4.16486i	−0.487460	+	0.487460i	0.420044	+	0.907504i	$0.362015\pi$
$74$	−1.48737			−0.172904
$75$	8.07519	−	3.12910i	0.932443	−	0.361317i
$76$	9.22351			1.05801
$77$		0			0
$78$	−2.57069	−	0.263173i	−0.291073	−	0.0297985i
$79$			3.89710i			0.438458i	0.975673	+	0.219229i	$0.0703542\pi$
$79$			3.89710i			0.438458i	−0.975673	+	0.219229i	$0.929646\pi$
$80$	3.05135	−	4.98193i	0.341152	−	0.556996i
$81$	8.26097	+	3.57160i	0.917886	+	0.396844i
$82$	4.01778	+	4.01778i	0.443689	+	0.443689i
$83$	4.03778	+	4.03778i	0.443204	+	0.443204i	0.893087	−	0.449883i	$-0.148534\pi$
$83$	4.03778	+	4.03778i	0.443204	+	0.443204i	−0.449883	+	0.893087i	$0.648534\pi$
$84$		0			0
$85$	2.41421	+	10.0457i	0.261858	+	1.08961i
$86$		−	0.526902i		−	0.0568173i
$87$	−0.506122	+	4.94383i	−0.0542619	+	0.530034i
$88$	−3.48510	+	3.48510i	−0.371513	+	0.371513i
$89$	3.95125			0.418832			0.209416	−	0.977827i	$-0.432844\pi$
$89$	3.95125			0.418832			0.209416	+	0.977827i	$0.432844\pi$
$90$	−0.104719	−	3.29077i	−0.0110384	−	0.346878i
$91$		0			0
$92$	−4.48247	+	4.48247i	−0.467330	+	0.467330i
$93$	−0.932426	+	9.10800i	−0.0966881	+	0.944455i
$94$			5.31710i			0.548417i
$95$	9.99806	+	6.12366i	1.02578	+	0.628274i
$96$	−5.43796	−	6.67836i	−0.555009	−	0.681607i
$97$	1.86878	+	1.86878i	0.189746	+	0.189746i	0.795586	−	0.605840i	$-0.207163\pi$
$97$	1.86878	+	1.86878i	0.189746	+	0.189746i	−0.605840	+	0.795586i	$0.707163\pi$
$98$		0			0
$99$	1.62386	−	7.84786i	0.163204	−	0.788740i
$100$	7.83504	−	3.99670i	0.783504	−	0.399670i
$101$			3.76115i			0.374249i	0.982336	+	0.187124i	$0.0599167\pi$
$101$			3.76115i			0.374249i	−0.982336	+	0.187124i	$0.940083\pi$
$102$	3.90749	+	0.400027i	0.386899	+	0.0396086i
$103$	8.85701	−	8.85701i	0.872707	−	0.872707i	−0.120060	−	0.992767i	$-0.538309\pi$
$103$	8.85701	−	8.85701i	0.872707	−	0.872707i	0.992767	+	0.120060i	$0.0383086\pi$
$104$	−5.60838			−0.549947
$105$		0			0
$106$	−3.07890			−0.299049
$107$	0.710397	−	0.710397i	0.0686766	−	0.0686766i	−0.671934	−	0.740611i	$-0.734536\pi$
$107$	0.710397	−	0.710397i	0.0686766	−	0.0686766i	0.740611	+	0.671934i	$0.234536\pi$
$108$	8.71582	+	2.75407i	0.838680	+	0.265011i
$109$			19.0144i			1.82125i	0.413237	+	0.910623i	$0.364398\pi$
$109$			19.0144i			1.82125i	−0.413237	+	0.910623i	$0.635602\pi$
$110$	−2.85061	+	0.685064i	−0.271795	+	0.0653183i
$111$	4.07024	−	3.31425i	0.386330	−	0.314575i
$112$		0			0
$113$	5.69132	+	5.69132i	0.535394	+	0.535394i	0.922173	−	0.386779i	$-0.126412\pi$
$113$	5.69132	+	5.69132i	0.535394	+	0.535394i	−0.386779	+	0.922173i	$0.626412\pi$
$114$	3.45642	−	2.81444i	0.323723	−	0.263597i
$115$	−7.83488	+	1.88289i	−0.730607	+	0.175581i
$116$			5.04730i			0.468630i
$117$	7.62117	−	5.00798i	0.704577	−	0.462988i
$118$	0.0553332	−	0.0553332i	0.00509383	−	0.00509383i
$119$		0			0
$120$	−0.953453	−	7.08176i	−0.0870380	−	0.646473i
$121$	3.86380			0.351254
$122$	−1.63995	+	1.63995i	−0.148474	+	0.148474i
$123$	−19.9474	−	2.04210i	−1.79859	−	0.184130i
$124$			9.29862i			0.835041i
$125$	11.1465	+	0.869508i	0.996971	+	0.0777712i
$126$		0			0
$127$	−12.1366	−	12.1366i	−1.07695	−	1.07695i	−0.996781	−	0.0801668i	$-0.974455\pi$
$127$	−12.1366	−	12.1366i	−1.07695	−	1.07695i	−0.0801668	−	0.996781i	$-0.525545\pi$
$128$	−7.99843	−	7.99843i	−0.706968	−	0.706968i
$129$	1.17407	+	1.44188i	0.103371	+	0.126950i
$130$	−2.84489	−	1.74245i	−0.249513	−	0.152823i
$131$		−	9.94280i		−	0.868706i	−0.900743	−	0.434353i	$-0.856977\pi$
$131$		−	9.94280i		−	0.868706i	0.900743	−	0.434353i	$-0.143023\pi$
$132$	0.828923	−	8.09697i	0.0721485	−	0.704751i
$133$		0			0
$134$	−3.75620			−0.324486
$135$	7.61926	+	8.77194i	0.655761	+	0.754968i
$136$	8.52483			0.730998
$137$	13.6645	−	13.6645i	1.16744	−	1.16744i	0.184630	−	0.982808i	$-0.440891\pi$
$137$	13.6645	−	13.6645i	1.16744	−	1.16744i	0.982808	−	0.184630i	$-0.0591086\pi$
$138$	−0.311989	+	3.04753i	−0.0265583	+	0.259423i
$139$			16.7933i			1.42439i	0.701982	+	0.712195i	$0.252299\pi$
$139$			16.7933i			1.42439i	−0.701982	+	0.712195i	$0.747701\pi$
$140$		0			0
$141$	−11.8479	−	14.5504i	−0.997770	−	1.22536i
$142$	4.71576	+	4.71576i	0.395738	+	0.395738i
$143$	−5.74196	−	5.74196i	−0.480167	−	0.480167i
$144$	7.67544	+	1.58818i	0.639620	+	0.132349i
$145$	−3.35099	+	5.47115i	−0.278285	+	0.454354i
$146$			2.89086i			0.239249i
$147$		0			0
$148$	3.76952	−	3.76952i	0.309853	−	0.309853i
$149$	9.31256			0.762915			0.381458	−	0.924386i	$-0.375422\pi$
$149$	9.31256			0.762915			0.381458	+	0.924386i	$0.375422\pi$
$150$	1.71656	−	3.88849i	0.140157	−	0.317494i
$151$	20.3868			1.65905			0.829527	−	0.558466i	$-0.188610\pi$
$151$	20.3868			1.65905			0.829527	+	0.558466i	$0.188610\pi$
$152$	6.84046	−	6.84046i	0.554834	−	0.554834i
$153$	−11.5843	+	7.61221i	−0.936535	+	0.615410i
$154$		0			0
$155$	−6.17353	+	10.0795i	−0.495869	+	0.809603i
$156$	7.18199	−	5.84804i	0.575019	−	0.468218i
$157$	−6.32887	−	6.32887i	−0.505098	−	0.505098i	0.407919	−	0.913018i	$-0.366254\pi$
$157$	−6.32887	−	6.32887i	−0.505098	−	0.505098i	−0.913018	+	0.407919i	$0.866254\pi$
$158$	1.35250	+	1.35250i	0.107599	+	0.107599i
$159$	8.42549	−	6.86058i	0.668185	−	0.544080i
$160$	−2.59804	−	10.8106i	−0.205393	−	0.854657i
$161$		0			0
$162$	4.10654	−	1.62746i	0.322640	−	0.127866i
$163$	−6.45638	+	6.45638i	−0.505703	+	0.505703i	−0.913205	−	0.407502i	$-0.866400\pi$
$163$	−6.45638	+	6.45638i	−0.505703	+	0.505703i	0.407502	+	0.913205i	$0.366400\pi$
$164$	−20.3649			−1.59023
$165$	6.27426	−	8.22658i	0.488451	−	0.640439i
$166$	2.80266			0.217528
$167$	−1.58004	+	1.58004i	−0.122268	+	0.122268i	−0.765593	−	0.643325i	$-0.777554\pi$
$167$	−1.58004	+	1.58004i	−0.122268	+	0.122268i	0.643325	+	0.765593i	$0.277554\pi$
$168$		0			0
$169$			3.75977i			0.289213i
$170$	4.32427	+	2.64855i	0.331657	+	0.203134i
$171$	−3.18727	+	15.4036i	−0.243737	+	1.17794i
$172$	1.33535	+	1.33535i	0.101820	+	0.101820i
$173$	1.69970	+	1.69970i	0.129226	+	0.129226i	0.768761	−	0.639536i	$-0.220873\pi$
$173$	1.69970	+	1.69970i	0.129226	+	0.129226i	−0.639536	+	0.768761i	$0.720873\pi$
$174$	1.54012	+	1.89142i	0.116756	+	0.143388i
$175$		0			0
$176$		−	6.97941i		−	0.526093i
$177$	−0.0281240	+	0.274717i	−0.00211393	+	0.0206490i
$178$	1.37130	−	1.37130i	0.102783	−	0.102783i
$179$	−8.44380			−0.631119			−0.315560	−	0.948906i	$-0.602192\pi$
$179$	−8.44380			−0.631119			−0.315560	+	0.948906i	$0.602192\pi$
$180$	8.60535	+	8.07456i	0.641405	+	0.601842i
$181$	−5.51483			−0.409914			−0.204957	−	0.978771i	$-0.565705\pi$
$181$	−5.51483			−0.409914			−0.204957	+	0.978771i	$0.565705\pi$
$182$		0			0
$183$	0.833531	−	8.14198i	0.0616164	−	0.601872i
$184$			6.64869i			0.490148i
$185$	6.58872	−	1.58342i	0.484413	−	0.116415i
$186$	2.83736	+	3.48456i	0.208045	+	0.255501i
$187$	8.72787	+	8.72787i	0.638245	+	0.638245i
$188$	−13.4754	−	13.4754i	−0.982792	−	0.982792i
$189$		0			0
$190$	5.59510	−	1.34463i	0.405911	−	0.0975494i
$191$			0.559524i			0.0404858i	0.999795	+	0.0202429i	$0.00644395\pi$
$191$			0.559524i			0.0404858i	−0.999795	+	0.0202429i	$0.993556\pi$
$192$	4.79850	+	0.491244i	0.346302	+	0.0354525i
$193$	7.05199	−	7.05199i	0.507613	−	0.507613i	−0.406180	−	0.913793i	$-0.633139\pi$
$193$	7.05199	−	7.05199i	0.507613	−	0.507613i	0.913793	+	0.406180i	$0.133139\pi$
$194$	1.29713			0.0931287
$195$	11.6677	−	1.57089i	0.835543	−	0.112493i
$196$		0			0
$197$	−10.1505	+	10.1505i	−0.723190	+	0.723190i	−0.969254	−	0.246064i	$-0.920863\pi$
$197$	−10.1505	+	10.1505i	−0.723190	+	0.723190i	0.246064	+	0.969254i	$0.420863\pi$
$198$	−2.16006	−	3.28719i	−0.153509	−	0.233611i
$199$		−	11.6748i		−	0.827604i	−0.910367	−	0.413802i	$-0.864201\pi$
$199$		−	11.6748i		−	0.827604i	0.910367	−	0.413802i	$-0.135799\pi$
$200$	2.84664	−	8.77481i	0.201288	−	0.620472i
$201$	10.2789	−	8.36978i	0.725020	−	0.590359i
$202$	1.30532	+	1.30532i	0.0918421	+	0.0918421i
$203$		0			0
$204$	−10.9167	+	8.88912i	−0.764324	+	0.622363i
$205$	−22.0750	−	13.5206i	−1.54179	−	0.944320i
$206$		−	6.14771i		−	0.428332i
$207$	−5.93692	−	9.03483i	−0.412644	−	0.627964i
$208$	5.61580	−	5.61580i	0.389386	−	0.389386i
$209$	14.0067			0.968867
$210$		0			0
$211$	−0.777102			−0.0534979			−0.0267490	−	0.999642i	$-0.508515\pi$
$211$	−0.777102			−0.0534979			−0.0267490	+	0.999642i	$0.508515\pi$
$212$	7.80300	−	7.80300i	0.535912	−	0.535912i
$213$	−23.4127	−	2.39687i	−1.60421	−	0.164231i
$214$		−	0.493091i		−	0.0337070i
$215$	0.560925	+	2.33405i	0.0382547	+	0.159181i
$216$	8.50645	−	4.42142i	0.578790	−	0.300840i
$217$		0			0
$218$	6.59901	+	6.59901i	0.446941	+	0.446941i
$219$	−6.44157	−	7.91090i	−0.435281	−	0.534569i
$220$	5.48824	−	8.96062i	0.370017	−	0.604125i
$221$			14.0453i			0.944789i
$222$	0.262367	−	2.56281i	0.0176089	−	0.172005i
$223$	3.33811	−	3.33811i	0.223536	−	0.223536i	−0.586450	−	0.809986i	$-0.699475\pi$
$223$	3.33811	−	3.33811i	0.223536	−	0.223536i	0.809986	+	0.586450i	$0.199475\pi$
$224$		0			0
$225$	3.96714	+	14.4659i	0.264476	+	0.964392i
$226$	3.95038			0.262776
$227$	−0.242326	+	0.242326i	−0.0160838	+	0.0160838i	−0.715103	−	0.699019i	$-0.753620\pi$
$227$	−0.242326	+	0.242326i	−0.0160838	+	0.0160838i	0.699019	+	0.715103i	$0.253620\pi$
$228$	−1.62699	+	15.8925i	−0.107750	+	1.05251i
$229$			13.4793i			0.890735i	0.895348	+	0.445368i	$0.146927\pi$
$229$			13.4793i			0.890735i	−0.895348	+	0.445368i	$0.853073\pi$
$230$	−2.06566	+	3.37259i	−0.136205	+	0.222382i
$231$		0			0
$232$	3.74324	+	3.74324i	0.245756	+	0.245756i
$233$	1.19260	+	1.19260i	0.0781301	+	0.0781301i	0.745092	−	0.666962i	$-0.232406\pi$
$233$	1.19260	+	1.19260i	0.0781301	+	0.0781301i	−0.666962	+	0.745092i	$0.732406\pi$
$234$	0.906918	−	4.38299i	0.0592871	−	0.286525i
$235$	−5.66043	−	23.5535i	−0.369246	−	1.53646i
$236$			0.280467i			0.0182568i
$237$	−6.71488	−	0.687432i	−0.436178	−	0.0446535i
$238$		0			0
$239$	5.15325			0.333336			0.166668	−	0.986013i	$-0.446699\pi$
$239$	5.15325			0.333336			0.166668	+	0.986013i	$0.446699\pi$
$240$	8.04584	+	6.13641i	0.519357	+	0.396104i
$241$	14.9174			0.960914			0.480457	−	0.877018i	$-0.340471\pi$
$241$	14.9174			0.960914			0.480457	+	0.877018i	$0.340471\pi$
$242$	1.34094	−	1.34094i	0.0861992	−	0.0861992i
$243$	−7.61123	+	13.6040i	−0.488261	+	0.872698i
$244$		−	8.31238i		−	0.532146i
$245$		0			0
$246$	−7.63153	+	6.21409i	−0.486569	+	0.396196i
$247$	11.2702	+	11.2702i	0.717103	+	0.717103i
$248$	6.89616	+	6.89616i	0.437907	+	0.437907i
$249$	−7.66953	+	6.24504i	−0.486037	+	0.395763i
$250$	4.17019	−	3.56666i	0.263746	−	0.225575i
$251$		−	4.30303i		−	0.271605i	−0.990736	−	0.135802i	$-0.956639\pi$
$251$		−	4.30303i		−	0.271605i	0.990736	−	0.135802i	$-0.0433613\pi$
$252$		0			0
$253$	−6.80704	+	6.80704i	−0.427955	+	0.427955i
$254$	−8.42409			−0.528575
$255$	−17.7351	+	2.38777i	−1.11062	+	0.149528i
$256$	0.0180230			0.00112644
$257$	5.82885	−	5.82885i	0.363594	−	0.363594i	−0.501540	−	0.865134i	$-0.667233\pi$
$257$	5.82885	−	5.82885i	0.363594	−	0.363594i	0.865134	+	0.501540i	$0.167233\pi$
$258$	0.907876	+	0.0929433i	0.0565219	+	0.00578640i
$259$		0			0
$260$	11.6259	−	2.79396i	0.721007	−	0.173274i
$261$	−8.42916	−	1.74414i	−0.521752	−	0.107960i
$262$	−3.45068	−	3.45068i	−0.213184	−	0.213184i
$263$	−0.0624909	−	0.0624909i	−0.00385335	−	0.00385335i	0.705177	−	0.709031i	$-0.250867\pi$
$263$	−0.0624909	−	0.0624909i	−0.00385335	−	0.00385335i	−0.709031	+	0.705177i	$0.750867\pi$
$264$	−5.39022	−	6.61974i	−0.331745	−	0.407417i
$265$	13.6388	−	3.27771i	0.837826	−	0.201348i
$266$		0			0
$267$	−0.696985	+	6.80819i	−0.0426548	+	0.416654i
$268$	9.51951	−	9.51951i	0.581497	−	0.581497i
$269$	29.6699			1.80901			0.904504	−	0.426465i	$-0.140241\pi$
$269$	29.6699			1.80901			0.904504	+	0.426465i	$0.140241\pi$
$270$	5.68862	+	0.400043i	0.346199	+	0.0243459i
$271$	−22.6377			−1.37514			−0.687571	−	0.726117i	$-0.741323\pi$
$271$	−22.6377			−1.37514			−0.687571	+	0.726117i	$0.741323\pi$
$272$	−8.53611	+	8.53611i	−0.517578	+	0.517578i
$273$		0			0
$274$		−	9.48463i		−	0.572988i
$275$	11.8982	−	6.06935i	0.717491	−	0.365996i
$276$	−6.93281	−	8.51419i	−0.417306	−	0.512494i
$277$	4.21136	+	4.21136i	0.253036	+	0.253036i	0.822214	−	0.569178i	$-0.192738\pi$
$277$	4.21136	+	4.21136i	0.253036	+	0.253036i	−0.569178	+	0.822214i	$0.692738\pi$
$278$	5.82817	+	5.82817i	0.349551	+	0.349551i
$279$	−15.5290	−	3.21323i	−0.929698	−	0.192371i
$280$		0			0
$281$		−	22.0093i		−	1.31297i	−0.754341	−	0.656483i	$-0.772043\pi$
$281$		−	22.0093i		−	1.31297i	0.754341	−	0.656483i	$-0.227957\pi$
$282$	−9.16160	−	0.937914i	−0.545565	−	0.0558520i
$283$	−9.59899	+	9.59899i	−0.570601	+	0.570601i	−0.932296	−	0.361695i	$-0.882198\pi$
$283$	−9.59899	+	9.59899i	−0.570601	+	0.570601i	0.361695	+	0.932296i	$0.382198\pi$
$284$	−23.9027			−1.41837
$285$	−12.3150	+	16.1469i	−0.729475	+	0.956461i
$286$	−3.98553			−0.235670
$287$		0			0
$288$	12.4664	−	8.19181i	0.734587	−	0.482707i
$289$		−	4.34908i		−	0.255828i
$290$	0.735807	+	3.06176i	0.0432081	+	0.179792i
$291$	−3.54963	+	2.89034i	−0.208083	+	0.169435i
$292$	−7.32643	−	7.32643i	−0.428747	−	0.428747i
$293$	−3.56359	−	3.56359i	−0.208187	−	0.208187i	0.595309	−	0.803497i	$-0.297030\pi$
$293$	−3.56359	−	3.56359i	−0.208187	−	0.208187i	−0.803497	+	0.595309i	$0.797030\pi$
$294$		0			0
$295$	−0.186207	+	0.304019i	−0.0108414	+	0.0177007i
$296$		−	5.59120i		−	0.324982i
$297$	13.2358	+	4.18231i	0.768018	+	0.242683i
$298$	3.23196	−	3.23196i	0.187222	−	0.187222i
$299$	−10.9542			−0.633499
$300$	5.50442	+	14.2051i	0.317798	+	0.820134i
$301$		0			0
$302$	7.07531	−	7.07531i	0.407139	−	0.407139i
$303$	−6.48063	−	0.663452i	−0.372303	−	0.0381143i
$304$			13.6990i			0.785692i
$305$	5.51874	−	9.01042i	0.316002	−	0.515935i
$306$	−1.37853	+	6.66222i	−0.0788053	+	0.380854i
$307$	−10.4746	−	10.4746i	−0.597814	−	0.597814i	0.341916	−	0.939730i	$-0.388924\pi$
$307$	−10.4746	−	10.4746i	−0.597814	−	0.597814i	−0.939730	+	0.341916i	$0.888924\pi$
$308$		0			0
$309$	13.6987	+	16.8234i	0.779291	+	0.957048i
$310$	1.35558	+	5.64066i	0.0769915	+	0.320368i
$311$			20.4344i			1.15873i	0.815068	+	0.579365i	$0.196699\pi$
$311$			20.4344i			1.15873i	−0.815068	+	0.579365i	$0.803301\pi$
$312$	0.989296	−	9.66350i	0.0560078	−	0.547088i
$313$	16.4829	−	16.4829i	0.931670	−	0.931670i	−0.0661408	−	0.997810i	$-0.521069\pi$
$313$	16.4829	−	16.4829i	0.931670	−	0.931670i	0.997810	+	0.0661408i	$0.0210686\pi$
$314$	−4.39291			−0.247906
$315$		0			0
$316$	−6.85542			−0.385647
$317$	−22.9540	+	22.9540i	−1.28922	+	1.28922i	−0.353965	+	0.935259i	$0.615167\pi$
$317$	−22.9540	+	22.9540i	−1.28922	+	1.28922i	−0.935259	+	0.353965i	$0.884833\pi$
$318$	0.543105	−	5.30509i	0.0304558	−	0.297494i
$319$			7.66479i			0.429146i
$320$	5.31032	+	3.25249i	0.296856	+	0.181820i
$321$	1.09873	+	1.34936i	0.0613254	+	0.0753137i
$322$		0			0
$323$	−17.1308	−	17.1308i	−0.953185	−	0.953185i
$324$	−6.28283	+	14.5319i	−0.349046	+	0.807330i
$325$	14.4571	+	4.69006i	0.801938	+	0.260158i
$326$			4.48142i			0.248203i
$327$	−32.7626	−	3.35406i	−1.81178	−	0.185480i
$328$	−15.1033	+	15.1033i	−0.833938	+	0.833938i
$329$		0			0
$330$	−0.677561	−	5.03257i	−0.0372985	−	0.277034i
$331$	−2.21461			−0.121726			−0.0608631	−	0.998146i	$-0.519385\pi$
$331$	−2.21461			−0.121726			−0.0608631	+	0.998146i	$0.519385\pi$
$332$	−7.10290	+	7.10290i	−0.389822	+	0.389822i
$333$	4.99263	+	7.59782i	0.273595	+	0.416358i
$334$			1.09672i			0.0600099i
$335$	16.6391	−	3.99874i	0.909091	−	0.218475i
$336$		0			0
$337$	10.8541	+	10.8541i	0.591263	+	0.591263i	0.937972	−	0.346710i	$-0.112701\pi$
$337$	10.8541	+	10.8541i	0.591263	+	0.591263i	−0.346710	+	0.937972i	$0.612701\pi$
$338$	1.30484	+	1.30484i	0.0709741	+	0.0709741i
$339$	−10.8103	+	8.80247i	−0.587136	+	0.478085i
$340$	−17.6715	+	4.24686i	−0.958374	+	0.230318i
$341$			14.1208i			0.764685i
$342$	4.23971	+	6.45202i	0.229257	+	0.348885i
$343$		0			0
$344$	1.98068			0.106791
$345$	−1.86227	−	13.8320i	−0.100261	−	0.744689i
$346$	1.17977			0.0634251
$347$	−5.06341	+	5.06341i	−0.271818	+	0.271818i	−0.829832	−	0.558014i	$-0.811564\pi$
$347$	−5.06341	+	5.06341i	−0.271818	+	0.271818i	0.558014	+	0.829832i	$0.311564\pi$
$348$	−8.69672	−	0.890323i	−0.466193	−	0.0477263i
$349$			7.42733i			0.397576i	0.980043	+	0.198788i	$0.0637005\pi$
$349$			7.42733i			0.397576i	−0.980043	+	0.198788i	$0.936300\pi$
$350$		0			0
$351$	7.28463	+	14.0150i	0.388825	+	0.748066i
$352$	−9.39243	−	9.39243i	−0.500618	−	0.500618i
$353$	−9.09032	−	9.09032i	−0.483829	−	0.483829i	0.422523	−	0.906352i	$-0.361144\pi$
$353$	−9.09032	−	9.09032i	−0.483829	−	0.483829i	−0.906352	+	0.422523i	$0.861144\pi$
$354$	0.0855810	+	0.105102i	0.00454858	+	0.00558611i
$355$	−25.9100	−	15.8695i	−1.37516	−	0.842264i
$356$			6.95068i			0.368385i
$357$		0			0
$358$	−2.93045	+	2.93045i	−0.154879	+	0.154879i
$359$	25.2640			1.33338			0.666692	−	0.745333i	$-0.267710\pi$
$359$	25.2640			1.33338			0.666692	+	0.745333i	$0.267710\pi$
$360$	12.3704	−	0.393650i	0.651976	−	0.0207472i
$361$	−8.49208			−0.446951
$362$	−1.91394	+	1.91394i	−0.100594	+	0.100594i
$363$	−0.681558	+	6.65750i	−0.0357725	+	0.349428i
$364$		0			0
$365$	−3.07752	−	12.8058i	−0.161085	−	0.670288i
$366$	−2.53642	−	3.11498i	−0.132581	−	0.162823i
$367$	−1.61189	−	1.61189i	−0.0841399	−	0.0841399i	0.663784	−	0.747924i	$-0.268949\pi$
$367$	−1.61189	−	1.61189i	−0.0841399	−	0.0841399i	−0.747924	+	0.663784i	$0.768949\pi$
$368$	−6.65749	−	6.65749i	−0.347045	−	0.347045i
$369$	7.03727	−	34.0100i	0.366346	−	1.77049i
$370$	1.73711	−	2.83617i	0.0903081	−	0.147445i
$371$		0			0
$372$	−16.0219	−	1.64024i	−0.830699	−	0.0850424i
$373$	13.0455	−	13.0455i	0.675469	−	0.675469i	−0.283502	−	0.958972i	$-0.591496\pi$
$373$	13.0455	−	13.0455i	0.675469	−	0.675469i	0.958972	+	0.283502i	$0.0914964\pi$
$374$	6.05808			0.313256
$375$	−3.46439	+	19.0525i	−0.178901	+	0.983867i
$376$	−19.9875			−1.03078
$377$	−6.16727	+	6.16727i	−0.317630	+	0.317630i
$378$		0			0
$379$		−	19.0635i		−	0.979228i	−0.871939	−	0.489614i	$-0.837138\pi$
$379$		−	19.0635i		−	0.979228i	0.871939	−	0.489614i	$-0.162862\pi$
$380$	−10.7722	+	17.5877i	−0.552601	+	0.902228i
$381$	23.0527	−	18.7710i	1.18103	−	0.961670i
$382$	0.194185	+	0.194185i	0.00993537	+	0.00993537i
$383$	−17.7244	−	17.7244i	−0.905673	−	0.905673i	0.0902463	−	0.995919i	$-0.471235\pi$
$383$	−17.7244	−	17.7244i	−0.905673	−	0.905673i	−0.995919	+	0.0902463i	$0.971235\pi$
$384$	15.1925	−	12.3708i	0.775291	−	0.631293i
$385$		0			0
$386$		−	4.89484i		−	0.249141i
$387$	−2.69153	+	1.76864i	−0.136818	+	0.0899050i
$388$	−3.28738	+	3.28738i	−0.166892	+	0.166892i
$389$	18.3513			0.930446			0.465223	−	0.885193i	$-0.345974\pi$
$389$	18.3513			0.930446			0.465223	+	0.885193i	$0.345974\pi$
$390$	3.50414	−	4.59451i	0.177439	−	0.232652i
$391$	16.6506			0.842056
$392$		0			0
$393$	17.1319	+	1.75387i	0.864189	+	0.0884710i
$394$			7.04550i			0.354947i
$395$	−7.43110	−	4.55144i	−0.373899	−	0.229008i
$396$	13.8052	+	2.85655i	0.693739	+	0.143547i
$397$	10.9124	+	10.9124i	0.547679	+	0.547679i	0.925769	−	0.378090i	$-0.123419\pi$
$397$	10.9124	+	10.9124i	0.547679	+	0.547679i	−0.378090	+	0.925769i	$0.623419\pi$
$398$	−4.05178	−	4.05178i	−0.203097	−	0.203097i
$399$		0			0
$400$	5.93600	+	11.6368i	0.296800	+	0.581841i
$401$			34.4243i			1.71907i	0.511079	+	0.859534i	$0.329246\pi$
$401$			34.4243i			1.71907i	−0.511079	+	0.859534i	$0.670754\pi$
$402$	0.662578	−	6.47210i	0.0330464	−	0.322799i
$403$	−11.3619	+	11.3619i	−0.565979	+	0.565979i
$404$	−6.61627			−0.329172
$405$	−16.4585	+	11.5810i	−0.817827	+	0.575464i
$406$		0			0
$407$	5.72437	−	5.72437i	0.283746	−	0.283746i
$408$	−1.50375	+	14.6887i	−0.0744465	+	0.727198i
$409$			7.59254i			0.375427i	0.982224	+	0.187714i	$0.0601077\pi$
$409$			7.59254i			0.375427i	−0.982224	+	0.187714i	$0.939892\pi$
$410$	−12.3536	+	2.96884i	−0.610101	+	0.146621i
$411$	21.1342	+	25.9549i	1.04247	+	1.28026i
$412$	15.5804	+	15.5804i	0.767593	+	0.767593i
$413$		0			0
$414$	−5.19600	−	1.07514i	−0.255369	−	0.0528404i
$415$	−12.4151	+	2.98363i	−0.609434	+	0.146460i
$416$		−	15.1147i		−	0.741061i
$417$	−28.9356	−	2.96227i	−1.41698	−	0.145063i
$418$	4.86109	−	4.86109i	0.237764	−	0.237764i
$419$	−6.20644			−0.303204			−0.151602	−	0.988442i	$-0.548443\pi$
$419$	−6.20644			−0.303204			−0.151602	+	0.988442i	$0.548443\pi$
$420$		0			0
$421$	25.1339			1.22495			0.612474	−	0.790490i	$-0.290174\pi$
$421$	25.1339			1.22495			0.612474	+	0.790490i	$0.290174\pi$
$422$	−0.269696	+	0.269696i	−0.0131286	+	0.0131286i
$423$	27.1608	−	17.8478i	1.32061	−	0.867788i
$424$		−	11.5739i		−	0.562079i
$425$	−21.9751	−	7.12897i	−1.06595	−	0.345806i
$426$	−8.95731	+	7.29363i	−0.433983	+	0.353377i
$427$		0			0
$428$	1.24966	+	1.24966i	0.0604048	+	0.0604048i
$429$	10.9065	−	8.88079i	0.526571	−	0.428769i
$430$	1.00471	+	0.615371i	0.0484515	+	0.0296758i
$431$		−	8.43225i		−	0.406167i	−0.979161	−	0.203084i	$-0.934904\pi$
$431$		−	8.43225i		−	0.406167i	0.979161	−	0.203084i	$-0.0650963\pi$
$432$	−4.09043	+	12.9450i	−0.196801	+	0.622815i
$433$	18.8277	−	18.8277i	0.904802	−	0.904802i	−0.0910444	−	0.995847i	$-0.529021\pi$
$433$	18.8277	−	18.8277i	0.904802	−	0.904802i	0.995847	+	0.0910444i	$0.0290205\pi$
$434$		0			0
$435$	−8.83593	−	6.73900i	−0.423651	−	0.323110i
$436$	−33.4483			−1.60188
$437$	13.3607	−	13.3607i	0.639128	−	0.639128i
$438$	−4.98108	−	0.509935i	−0.238005	−	0.0243657i
$439$			4.88270i			0.233039i	0.993188	+	0.116519i	$0.0371737\pi$
$439$			4.88270i			0.233039i	−0.993188	+	0.116519i	$0.962826\pi$
$440$	−2.57523	−	10.7157i	−0.122769	−	0.510853i
$441$		0			0
$442$	4.87447	+	4.87447i	0.231855	+	0.231855i
$443$	−23.8960	−	23.8960i	−1.13534	−	1.13534i	−0.989276	−	0.146059i	$-0.953341\pi$
$443$	−23.8960	−	23.8960i	−1.13534	−	1.13534i	−0.146059	−	0.989276i	$-0.546659\pi$
$444$	5.83013	+	7.15998i	0.276686	+	0.339798i
$445$	−4.61468	+	7.53437i	−0.218757	+	0.357163i
$446$		−	2.31700i		−	0.109713i
$447$	−1.64270	+	16.0460i	−0.0776970	+	0.758948i
$448$		0			0
$449$	23.6736			1.11723			0.558613	−	0.829428i	$-0.311334\pi$
$449$	23.6736			1.11723			0.558613	+	0.829428i	$0.311334\pi$
$450$	6.39725	+	3.64363i	0.301569	+	0.171762i
$451$	−30.9259			−1.45625
$452$	−10.0116	+	10.0116i	−0.470908	+	0.470908i
$453$	−3.59615	+	35.1274i	−0.168962	+	1.65043i
$454$			0.168200i			0.00789404i
$455$		0			0
$456$	10.5798	+	12.9930i	0.495444	+	0.608455i
$457$	10.2580	+	10.2580i	0.479849	+	0.479849i	0.905083	−	0.425234i	$-0.139808\pi$
$457$	10.2580	+	10.2580i	0.479849	+	0.479849i	−0.425234	+	0.905083i	$0.639808\pi$
$458$	4.67803	+	4.67803i	0.218590	+	0.218590i
$459$	−11.0728	−	21.3030i	−0.516832	−	0.994341i
$460$	−3.31221	−	13.7824i	−0.154433	−	0.642608i
$461$		−	23.3153i		−	1.08590i	−0.839764	−	0.542951i	$-0.817307\pi$
$461$		−	23.3153i		−	1.08590i	0.839764	−	0.542951i	$-0.182693\pi$
$462$		0			0
$463$	−17.0563	+	17.0563i	−0.792672	+	0.792672i	−0.981928	−	0.189256i	$-0.939392\pi$
$463$	−17.0563	+	17.0563i	−0.792672	+	0.792672i	0.189256	+	0.981928i	$0.439392\pi$
$464$	−7.49639			−0.348011
$465$	−16.2784	−	12.4152i	−0.754893	−	0.575743i
$466$	0.827796			0.0383469
$467$	−8.00621	+	8.00621i	−0.370483	+	0.370483i	−0.867653	−	0.497170i	$-0.834373\pi$
$467$	−8.00621	+	8.00621i	−0.370483	+	0.370483i	0.497170	+	0.867653i	$0.334373\pi$
$468$	8.80957	+	13.4065i	0.407223	+	0.619714i
$469$		0			0
$470$	−10.1388	−	6.20986i	−0.467668	−	0.286439i
$471$	12.0213	−	9.78854i	0.553913	−	0.451032i
$472$	0.208003	+	0.208003i	0.00957413	+	0.00957413i
$473$	2.02786	+	2.02786i	0.0932409	+	0.0932409i
$474$	−2.56900	+	2.09185i	−0.117998	+	0.0960817i
$475$	−23.3535	+	11.9128i	−1.07153	+	0.546595i
$476$		0			0
$477$	10.3349	+	15.7277i	0.473201	+	0.720121i
$478$	1.78845	−	1.78845i	0.0818019	−	0.0818019i
$479$	−20.1199			−0.919304			−0.459652	−	0.888099i	$-0.652026\pi$
$479$	−20.1199			−0.919304			−0.459652	+	0.888099i	$0.652026\pi$
$480$	19.0855	−	2.56958i	0.871131	−	0.117285i
$481$	9.21192			0.420027
$482$	5.17713	−	5.17713i	0.235812	−	0.235812i
$483$		0			0
$484$			6.79683i			0.308947i
$485$	−5.74600	+	1.38089i	−0.260912	+	0.0627030i
$486$	2.07982	+	7.36283i	0.0943425	+	0.333985i
$487$	7.77959	+	7.77959i	0.352527	+	0.352527i	0.861049	−	0.508522i	$-0.169808\pi$
$487$	7.77959	+	7.77959i	0.352527	+	0.352527i	−0.508522	+	0.861049i	$0.669808\pi$
$488$	−6.16474	−	6.16474i	−0.279064	−	0.279064i
$489$	−9.98576	−	12.2635i	−0.451572	−	0.554576i
$490$		0			0
$491$		−	2.29546i		−	0.103593i	−0.998658	−	0.0517963i	$-0.983505\pi$
$491$		−	2.29546i		−	0.103593i	0.998658	−	0.0517963i	$-0.0164947\pi$
$492$	3.59228	−	35.0896i	0.161952	−	1.58196i
$493$	9.37435	−	9.37435i	0.422199	−	0.422199i
$494$	7.82270			0.351960
$495$	13.0680	+	12.2620i	0.587364	+	0.551135i
$496$	−13.8106			−0.620113
$497$		0			0
$498$	−0.494377	+	4.82910i	−0.0221536	+	0.216397i
$499$		−	12.3264i		−	0.551806i	−0.961185	−	0.275903i	$-0.911023\pi$
$499$		−	12.3264i		−	0.551806i	0.961185	−	0.275903i	$-0.0889769\pi$
$500$	−1.52956	+	19.6079i	−0.0684039	+	0.876890i
$501$	−2.44378	−	3.00120i	−0.109180	−	0.134084i
$502$	−1.49338	−	1.49338i	−0.0666529	−	0.0666529i
$503$	4.62523	+	4.62523i	0.206229	+	0.206229i	0.802662	−	0.596434i	$-0.203416\pi$
$503$	4.62523	+	4.62523i	0.206229	+	0.206229i	−0.596434	+	0.802662i	$0.703416\pi$
$504$		0			0
$505$	−7.17188	−	4.39266i	−0.319144	−	0.195471i
$506$			4.72482i			0.210044i
$507$	−6.47826	−	0.663208i	−0.287709	−	0.0294541i
$508$	21.3496	−	21.3496i	0.947234	−	0.947234i
$509$	13.6161			0.603525			0.301762	−	0.953383i	$-0.402425\pi$
$509$	13.6161			0.603525			0.301762	+	0.953383i	$0.402425\pi$
$510$	−5.32635	+	6.98372i	−0.235855	+	0.309244i
$511$		0			0
$512$	16.0031	−	16.0031i	0.707245	−	0.707245i
$513$	−25.9788	−	8.20894i	−1.14699	−	0.362433i
$514$		−	4.04585i		−	0.178455i
$515$	6.54468	+	27.2329i	0.288393	+	1.20003i
$516$	−2.53642	+	2.06532i	−0.111660	+	0.0909207i
$517$	−20.4636	−	20.4636i	−0.899987	−	0.899987i
$518$		0			0
$519$	−3.22848	+	2.62884i	−0.141715	+	0.115393i
$520$	6.55005	−	10.6942i	0.287239	−	0.468973i
$521$			18.3870i			0.805550i	0.915299	+	0.402775i	$0.131954\pi$
$521$			18.3870i			0.805550i	−0.915299	+	0.402775i	$0.868046\pi$
$522$	−3.53068	+	2.32006i	−0.154534	+	0.101546i
$523$	8.91043	−	8.91043i	0.389626	−	0.389626i	−0.484928	−	0.874554i	$-0.661154\pi$
$523$	8.91043	−	8.91043i	0.389626	−	0.389626i	0.874554	+	0.484928i	$0.161154\pi$
$524$	17.4905			0.764074
$525$		0			0
$526$	−0.0433754			−0.00189126
$527$	17.2703	−	17.2703i	0.752308	−	0.752308i
$528$	12.0258	+	1.23114i	0.523358	+	0.0535785i
$529$		−	10.0139i		−	0.435385i
$530$	3.59586	−	5.87094i	0.156194	−	0.255017i
$531$	−0.468389	−	0.0969179i	−0.0203264	−	0.00420588i
$532$		0			0
$533$	−24.8837	−	24.8837i	−1.07783	−	1.07783i
$534$	2.12091	+	2.60470i	0.0917810	+	0.112716i
$535$	0.524931	+	2.18428i	0.0226947	+	0.0944347i
$536$		−	14.1200i		−	0.609889i
$537$	1.48945	−	14.5491i	0.0642746	−	0.627838i
$538$	10.2971	−	10.2971i	0.443938	−	0.443938i
$539$		0			0
$540$	−15.4308	+	13.4031i	−0.664035	+	0.576777i
$541$	27.8258			1.19632			0.598162	−	0.801375i	$-0.295898\pi$
$541$	27.8258			1.19632			0.598162	+	0.801375i	$0.295898\pi$
$542$	−7.85649	+	7.85649i	−0.337465	+	0.337465i
$543$	0.972793	−	9.50229i	0.0417465	−	0.407783i
$544$			22.9746i			0.985030i
$545$	−36.2572	−	22.2070i	−1.55309	−	0.951242i
$546$		0			0
$547$	−13.2773	−	13.2773i	−0.567695	−	0.567695i	0.363787	−	0.931482i	$-0.381483\pi$
$547$	−13.2773	−	13.2773i	−0.567695	−	0.567695i	−0.931482	+	0.363787i	$0.881483\pi$
$548$	24.0373	+	24.0373i	1.02682	+	1.02682i
$549$	13.8820	+	2.87242i	0.592468	+	0.122592i
$550$	2.02294	−	6.23572i	0.0862583	−	0.265892i
$551$		−	15.0442i		−	0.640906i
$552$	−11.4560	−	1.17280i	−0.487600	−	0.0499178i
$553$		0			0
$554$	2.92314			0.124192
$555$	1.56607	+	11.6320i	0.0664761	+	0.493750i
$556$	−29.5412			−1.25283
$557$	10.4002	−	10.4002i	0.440672	−	0.440672i	−0.451566	−	0.892238i	$-0.649134\pi$
$557$	10.4002	−	10.4002i	0.440672	−	0.440672i	0.892238	+	0.451566i	$0.149134\pi$
$558$	−6.50456	+	4.27424i	−0.275360	+	0.180943i
$559$			3.26332i			0.138024i
$560$		0			0
$561$	−16.5781	+	13.4990i	−0.699927	+	0.569926i
$562$	−7.63842	−	7.63842i	−0.322207	−	0.322207i
$563$	10.1623	+	10.1623i	0.428291	+	0.428291i	0.888046	−	0.459755i	$-0.152063\pi$
$563$	10.1623	+	10.1623i	0.428291	+	0.428291i	−0.459755	+	0.888046i	$0.652063\pi$
$564$	25.5957	−	20.8417i	1.07777	−	0.877592i
$565$	−17.4993	+	4.20546i	−0.736200	+	0.176925i
$566$			6.66273i			0.280055i
$567$		0			0
$568$	−17.7271	+	17.7271i	−0.743811	+	0.743811i
$569$	−39.8275			−1.66965			−0.834827	−	0.550512i	$-0.814433\pi$
$569$	−39.8275			−1.66965			−0.834827	+	0.550512i	$0.814433\pi$
$570$	1.32990	+	9.87780i	0.0557033	+	0.413735i
$571$	−43.8314			−1.83429			−0.917143	−	0.398558i	$-0.869511\pi$
$571$	−43.8314			−1.83429			−0.917143	+	0.398558i	$0.869511\pi$
$572$	10.1007	−	10.1007i	0.422332	−	0.422332i
$573$	−0.964086	−	0.0986978i	−0.0402753	−	0.00412316i
$574$		0			0
$575$	5.56003	−	17.1388i	0.231869	−	0.714739i
$576$	−1.69287	+	8.18138i	−0.0705363	+	0.340891i
$577$	27.8182	+	27.8182i	1.15809	+	1.15809i	0.984886	+	0.173202i	$0.0554114\pi$
$577$	27.8182	+	27.8182i	1.15809	+	1.15809i	0.173202	+	0.984886i	$0.444589\pi$
$578$	−1.50936	−	1.50936i	−0.0627812	−	0.0627812i
$579$	10.9070	+	13.3948i	0.453278	+	0.556670i
$580$	−9.62434	−	5.89476i	−0.399629	−	0.244767i
$581$		0			0
$582$	−0.228809	+	2.23502i	−0.00948443	+	0.0926445i
$583$	11.8496	−	11.8496i	0.490759	−	0.490759i
$584$	−10.8670			−0.449681
$585$	0.648568	+	20.3811i	0.0268150	+	0.842655i
$586$	−2.47352			−0.102180
$587$	27.2778	−	27.2778i	1.12588	−	1.12588i	0.135034	−	0.990841i	$-0.456886\pi$
$587$	27.2778	−	27.2778i	1.12588	−	1.12588i	0.990841	−	0.135034i	$-0.0431144\pi$
$588$		0			0
$589$		−	27.7160i		−	1.14202i
$590$	0.0408871	+	0.170135i	0.00168330	+	0.00700434i
$591$	−15.6992	−	19.2802i	−0.645779	−	0.793081i
$592$	5.59860	+	5.59860i	0.230101	+	0.230101i
$593$	−1.21000	−	1.21000i	−0.0496886	−	0.0496886i	0.681826	−	0.731515i	$-0.261186\pi$
$593$	−1.21000	−	1.21000i	−0.0496886	−	0.0496886i	−0.731515	+	0.681826i	$0.761186\pi$
$594$	6.04501	−	3.14204i	0.248030	−	0.128919i
$595$		0			0
$596$			16.3818i			0.671025i
$597$	20.1162	+	2.05939i	0.823301	+	0.0842850i
$598$	−3.80170	+	3.80170i	−0.155463	+	0.155463i
$599$	15.6005			0.637421			0.318710	−	0.947852i	$-0.396750\pi$
$599$	15.6005			0.637421			0.318710	+	0.947852i	$0.396750\pi$
$600$	14.6172	+	6.45274i	0.596747	+	0.263432i
$601$	−14.2954			−0.583122			−0.291561	−	0.956552i	$-0.594175\pi$
$601$	−14.2954			−0.583122			−0.291561	+	0.956552i	$0.594175\pi$
$602$		0			0
$603$	12.6083	+	19.1875i	0.513452	+	0.781374i
$604$			35.8626i			1.45923i
$605$	−4.51254	+	7.36760i	−0.183461	+	0.299536i
$606$	−2.47938	+	2.01887i	−0.100718	+	0.0820111i
$607$	26.8784	+	26.8784i	1.09096	+	1.09096i	0.995426	+	0.0955365i	$0.0304567\pi$
$607$	26.8784	+	26.8784i	1.09096	+	1.09096i	0.0955365	+	0.995426i	$0.469543\pi$
$608$	18.4352	+	18.4352i	0.747646	+	0.747646i
$609$		0			0
$610$	−1.21180	−	5.04240i	−0.0490643	−	0.204161i
$611$		−	32.9310i		−	1.33224i
$612$	−13.3907	−	20.3780i	−0.541287	−	0.823733i
$613$	2.77744	−	2.77744i	0.112180	−	0.112180i	−0.648789	−	0.760969i	$-0.724724\pi$
$613$	2.77744	−	2.77744i	0.112180	−	0.112180i	0.760969	+	0.648789i	$0.224724\pi$
$614$	−7.27046			−0.293412
$615$	27.1906	−	35.6513i	1.09643	−	1.43760i
$616$		0			0
$617$	3.21465	−	3.21465i	0.129417	−	0.129417i	−0.639431	−	0.768848i	$-0.720830\pi$
$617$	3.21465	−	3.21465i	0.129417	−	0.129417i	0.768848	+	0.639431i	$0.220830\pi$
$618$	10.5928	+	1.08443i	0.426104	+	0.0436222i
$619$		−	48.7011i		−	1.95746i	−0.205146	−	0.978731i	$-0.565767\pi$
$619$		−	48.7011i		−	1.95746i	0.205146	−	0.978731i	$-0.434233\pi$
$620$	−17.7309	−	10.8599i	−0.712090	−	0.436144i
$621$	16.6147	−	8.63587i	0.666724	−	0.346545i
$622$	7.09184	+	7.09184i	0.284357	+	0.284357i
$623$		0			0
$624$	8.68567	+	10.6669i	0.347705	+	0.427017i
$625$	−14.6760	+	20.2389i	−0.587041	+	0.809557i
$626$		−	11.4409i		−	0.457271i
$627$	−2.47073	+	24.1343i	−0.0986716	+	0.963830i
$628$	11.1332	−	11.1332i	0.444261	−	0.444261i
$629$	−14.0023			−0.558307
$630$		0			0
$631$	15.0588			0.599480			0.299740	−	0.954021i	$-0.403100\pi$
$631$	15.0588			0.599480			0.299740	+	0.954021i	$0.403100\pi$
$632$	−5.08420	+	5.08420i	−0.202239	+	0.202239i
$633$	0.137078	−	1.33898i	0.00544834	−	0.0532197i
$634$			15.9325i			0.632761i
$635$	37.3168	−	8.96805i	1.48087	−	0.355886i
$636$	12.0685	+	14.8213i	0.478547	+	0.587704i
$637$		0			0
$638$	2.66009	+	2.66009i	0.105314	+	0.105314i
$639$	8.25981	−	39.9184i	0.326753	−	1.57915i
$640$	24.5930	−	5.91025i	0.972126	−	0.233623i
$641$		−	45.9720i		−	1.81578i	−0.419204	−	0.907892i	$-0.637691\pi$
$641$		−	45.9720i		−	1.81578i	0.419204	−	0.907892i	$-0.362309\pi$
$642$	0.849619	+	0.0869793i	0.0335318	+	0.00343280i
$643$	5.91991	−	5.91991i	0.233458	−	0.233458i	−0.580676	−	0.814135i	$-0.697212\pi$
$643$	5.91991	−	5.91991i	0.233458	−	0.233458i	0.814135	+	0.580676i	$0.197212\pi$
$644$		0			0
$645$	−4.12062	+	0.554781i	−0.162249	+	0.0218445i
$646$	−11.8906			−0.467831
$647$	−11.1176	+	11.1176i	−0.437079	+	0.437079i	−0.891028	−	0.453949i	$-0.850015\pi$
$647$	−11.1176	+	11.1176i	−0.437079	+	0.437079i	0.453949	+	0.891028i	$0.350015\pi$
$648$	6.11781	+	15.4369i	0.240330	+	0.606419i
$649$			0.425915i			0.0167186i
$650$	6.64511	−	3.38970i	0.260642	−	0.132955i
$651$		0			0
$652$	−11.3575	−	11.3575i	−0.444793	−	0.444793i
$653$	30.6500	+	30.6500i	1.19943	+	1.19943i	0.974339	+	0.225088i	$0.0722669\pi$
$653$	30.6500	+	30.6500i	1.19943	+	1.19943i	0.225088	+	0.974339i	$0.427733\pi$
$654$	−12.5344	+	10.2063i	−0.490135	+	0.399100i
$655$	18.9592	+	11.6122i	0.740798	+	0.453727i
$656$		−	30.2465i		−	1.18093i
$657$	14.7671	−	9.70367i	0.576120	−	0.378576i
$658$		0			0
$659$	−50.9397			−1.98433			−0.992165	−	0.124933i	$-0.960129\pi$
$659$	−50.9397			−1.98433			−0.992165	+	0.124933i	$0.960129\pi$
$660$	14.4714	+	11.0371i	0.563300	+	0.429619i
$661$	20.5394			0.798889			0.399445	−	0.916757i	$-0.369203\pi$
$661$	20.5394			0.798889			0.399445	+	0.916757i	$0.369203\pi$
$662$	−0.768589	+	0.768589i	−0.0298721	+	0.0298721i
$663$	−24.2007	−	2.47753i	−0.939877	−	0.0962194i
$664$			10.5355i			0.408856i
$665$		0			0
$666$	4.36956	+	0.904139i	0.169317	+	0.0350347i
$667$	7.31125	+	7.31125i	0.283093	+	0.283093i
$668$	−2.77947	−	2.77947i	−0.107541	−	0.107541i
$669$	5.16288	+	6.34054i	0.199609	+	0.245139i
$670$	4.38688	−	7.16244i	0.169480	−	0.276709i
$671$		−	12.6231i		−	0.487310i
$672$		0			0
$673$	25.4635	−	25.4635i	0.981544	−	0.981544i	−0.0182887	−	0.999833i	$-0.505822\pi$
$673$	25.4635	−	25.4635i	0.981544	−	0.981544i	0.999833	+	0.0182887i	$0.00582181\pi$
$674$	7.53394			0.290196
$675$	−25.6252	+	4.28384i	−0.986313	+	0.164885i
$676$	−6.61384			−0.254379
$677$	8.67613	−	8.67613i	0.333451	−	0.333451i	−0.520445	−	0.853895i	$-0.674234\pi$
$677$	8.67613	−	8.67613i	0.333451	−	0.333451i	0.853895	+	0.520445i	$0.174234\pi$
$678$	−0.696831	+	6.80669i	−0.0267616	+	0.261409i
$679$		0			0
$680$	−9.95618	+	16.2554i	−0.381802	+	0.623366i
$681$	−0.374794	−	0.460284i	−0.0143621	−	0.0176381i
$682$	4.90068	+	4.90068i	0.187657	+	0.187657i
$683$	24.0010	+	24.0010i	0.918373	+	0.918373i	0.996911	−	0.0785378i	$-0.0250251\pi$
$683$	24.0010	+	24.0010i	0.918373	+	0.918373i	−0.0785378	+	0.996911i	$0.525025\pi$
$684$	−27.0965	−	5.60675i	−1.03606	−	0.214379i
$685$	10.0971	+	42.0147i	0.385789	+	1.60530i
$686$		0			0
$687$	−23.2254	−	2.37769i	−0.886104	−	0.0907145i
$688$	−1.98330	+	1.98330i	−0.0756127	+	0.0756127i
$689$	19.0689			0.726467
$690$	−5.44675	−	4.15413i	−0.207354	−	0.158145i
$691$	32.5680			1.23894			0.619472	−	0.785019i	$-0.287347\pi$
$691$	32.5680			1.23894			0.619472	+	0.785019i	$0.287347\pi$
$692$	−2.98996	+	2.98996i	−0.113661	+	0.113661i
$693$		0			0
$694$			3.51455i			0.133410i
$695$	−32.0220	−	19.6130i	−1.21466	−	0.743962i
$696$	−7.11007	+	5.78948i	−0.269506	+	0.219450i
$697$	37.8237	+	37.8237i	1.43267	+	1.43267i
$698$	2.57768	+	2.57768i	0.0975667	+	0.0975667i
$699$	−2.26528	+	1.84454i	−0.0856808	+	0.0697670i
$700$		0			0
$701$			2.43359i			0.0919155i	0.998943	+	0.0459577i	$0.0146340\pi$
$701$			2.43359i			0.0919155i	−0.998943	+	0.0459577i	$0.985366\pi$
$702$	7.39211	+	2.33580i	0.278997	+	0.0881592i
$703$	−11.2356	+	11.2356i	−0.423760	+	0.423760i
$704$	7.43948			0.280386
$705$	41.5822	−	5.59843i	1.56608	−	0.210849i
$706$	−6.30965			−0.237467
$707$		0			0
$708$	−0.483257	−	0.0494732i	−0.0181619	−	0.00185932i
$709$			12.3477i			0.463728i	0.972748	+	0.231864i	$0.0744825\pi$
$709$			12.3477i			0.463728i	−0.972748	+	0.231864i	$0.925518\pi$
$710$	−14.4997	+	3.48460i	−0.544164	+	0.130775i
$711$	2.36895	−	11.4488i	0.0888427	−	0.429363i
$712$	5.15485	+	5.15485i	0.193186	+	0.193186i
$713$	13.4695	+	13.4695i	0.504436	+	0.504436i
$714$		0			0
$715$	17.6550	−	4.24288i	0.660259	−	0.158675i
$716$		−	14.8536i		−	0.555103i
$717$	−0.909011	+	8.87927i	−0.0339476	+	0.331603i
$718$	8.76797	−	8.76797i	0.327218	−	0.327218i
$719$	24.2165			0.903125			0.451562	−	0.892240i	$-0.350867\pi$
$719$	24.2165			0.903125			0.451562	+	0.892240i	$0.350867\pi$
$720$	−11.9926	+	12.7809i	−0.446936	+	0.476316i
$721$		0			0
$722$	−2.94721	+	2.94721i	−0.109684	+	0.109684i
$723$	−2.63137	+	25.7033i	−0.0978616	+	0.955917i
$724$		−	9.70117i		−	0.360541i
$725$	−6.51891	−	12.7795i	−0.242106	−	0.474621i
$726$	2.07397	+	2.54704i	0.0769723	+	0.0945297i
$727$	25.8923	+	25.8923i	0.960293	+	0.960293i	0.999241	−	0.0389483i	$-0.0124008\pi$
$727$	25.8923	+	25.8923i	0.960293	+	0.960293i	−0.0389483	+	0.999241i	$0.512401\pi$
$728$		0			0
$729$	−22.0977	−	15.5142i	−0.818435	−	0.574599i
$730$	−5.51237	−	3.37624i	−0.204022	−	0.124960i
$731$		−	4.96030i		−	0.183463i
$732$	14.3226	+	1.46627i	0.529379	+	0.0541949i
$733$	−13.4535	+	13.4535i	−0.496918	+	0.496918i	−0.910477	−	0.413559i	$-0.864285\pi$
$733$	−13.4535	+	13.4535i	−0.496918	+	0.496918i	0.413559	+	0.910477i	$0.364285\pi$
$734$	−1.11882			−0.0412965
$735$		0			0
$736$	−17.9184			−0.660481
$737$	14.4563	−	14.4563i	0.532503	−	0.532503i
$738$	−9.36099	−	14.2456i	−0.344583	−	0.524388i
$739$			1.96813i			0.0723987i	0.999345	+	0.0361994i	$0.0115251\pi$
$739$			1.96813i			0.0723987i	−0.999345	+	0.0361994i	$0.988475\pi$
$740$	2.78540	+	11.5903i	0.102393	+	0.426067i
$741$	−21.4070	+	17.4310i	−0.786406	+	0.640343i
$742$		0			0
$743$	4.54680	+	4.54680i	0.166806	+	0.166806i	0.785574	−	0.618768i	$-0.212368\pi$
$743$	4.54680	+	4.54680i	0.166806	+	0.166806i	−0.618768	+	0.785574i	$0.712368\pi$
$744$	−13.0989	+	10.6659i	−0.480227	+	0.391032i
$745$	−10.8762	+	17.7575i	−0.398472	+	0.650584i
$746$		−	9.05496i		−	0.331526i
$747$	−9.40761	−	14.3166i	−0.344206	−	0.523815i
$748$	−15.3533	+	15.3533i	−0.561371	+	0.561371i
$749$		0			0
$750$	5.40991	+	7.81457i	0.197542	+	0.285348i
$751$	−0.491718			−0.0179430			−0.00897152	−	0.999960i	$-0.502856\pi$
$751$	−0.491718			−0.0179430			−0.00897152	+	0.999960i	$0.502856\pi$
$752$	20.0140	−	20.0140i	0.729835	−	0.729835i
$753$	7.41432	+	0.759037i	0.270193	+	0.0276609i
$754$			4.28075i			0.155896i
$755$	−23.8098	+	38.8742i	−0.866528	+	1.41478i
$756$		0			0
$757$	3.50957	+	3.50957i	0.127558	+	0.127558i	0.768003	−	0.640446i	$-0.221250\pi$
$757$	3.50957	+	3.50957i	0.127558	+	0.127558i	−0.640446	+	0.768003i	$0.721250\pi$
$758$	−6.61607	−	6.61607i	−0.240306	−	0.240306i
$759$	−10.5281	−	12.9296i	−0.382146	−	0.469314i
$760$	5.05459	+	21.0326i	0.183349	+	0.762932i
$761$			26.9220i			0.975922i	0.872865	+	0.487961i	$0.162259\pi$
$761$			26.9220i			0.975922i	−0.872865	+	0.487961i	$0.837741\pi$
$762$	1.48598	−	14.5151i	0.0538312	−	0.525826i
$763$		0			0
$764$	−0.984264			−0.0356094
$765$	−0.985834	−	30.9796i	−0.0356429	−	1.12007i
$766$	−12.3026			−0.444512
$767$	−0.342701	+	0.342701i	−0.0123742	+	0.0123742i
$768$	−0.00317918	+	0.0310544i	−0.000114719	+	0.00112058i
$769$		−	31.3935i		−	1.13208i	−0.824378	−	0.566040i	$-0.808475\pi$
$769$		−	31.3935i		−	1.13208i	0.824378	−	0.566040i	$-0.191525\pi$
$770$		0			0
$771$	9.01519	+	11.0716i	0.324674	+	0.398733i
$772$	12.4052	+	12.4052i	0.446473	+	0.446473i
$773$	13.3925	+	13.3925i	0.481693	+	0.481693i	0.905672	−	0.423979i	$-0.139367\pi$
$773$	13.3925	+	13.3925i	0.481693	+	0.481693i	−0.423979	+	0.905672i	$0.639367\pi$
$774$	−0.320291	+	1.54792i	−0.0115126	+	0.0556387i
$775$	−12.0098	−	23.5437i	−0.431404	−	0.845716i
$776$			4.87606i			0.175040i
$777$		0			0
$778$	6.36887	−	6.36887i	0.228335	−	0.228335i
$779$	60.7006			2.17482
$780$	2.76336	+	20.5248i	0.0989440	+	0.734905i
$781$	−36.2985			−1.29886
$782$	5.77865	−	5.77865i	0.206644	−	0.206644i
$783$	4.49210	−	14.2162i	0.160535	−	0.508044i
$784$		0			0
$785$	19.4596	−	4.67657i	0.694542	−	0.166914i
$786$	6.55437	−	5.33700i	0.233787	−	0.190364i
$787$	−22.4712	−	22.4712i	−0.801011	−	0.801011i	0.182243	−	0.983254i	$-0.441664\pi$
$787$	−22.4712	−	22.4712i	−0.801011	−	0.801011i	−0.983254	+	0.182243i	$0.941664\pi$
$788$	−17.8557	−	17.8557i	−0.636085	−	0.636085i
$789$	0.118698	−	0.0966515i	0.00422575	−	0.00344088i
$790$	−4.15858	+	0.999399i	−0.147956	+	0.0355570i
$791$		0			0
$792$	12.3569	−	8.11990i	0.439084	−	0.288528i
$793$	10.1569	−	10.1569i	0.360681	−	0.360681i
$794$	7.57440			0.268805
$795$	3.24181	+	24.0785i	0.114975	+	0.853975i
$796$	20.5372			0.727922
$797$	7.83907	−	7.83907i	0.277674	−	0.277674i	−0.554506	−	0.832180i	$-0.687093\pi$
$797$	7.83907	−	7.83907i	0.277674	−	0.277674i	0.832180	+	0.554506i	$0.187093\pi$
$798$		0			0
$799$			50.0556i			1.77084i
$800$	23.6483	+	7.67178i	0.836094	+	0.271238i
$801$	−11.6079	−	2.40187i	−0.410144	−	0.0848660i
$802$	11.9471	+	11.9471i	0.421866	+	0.421866i
$803$	−11.1259	−	11.1259i	−0.392623	−	0.392623i
$804$	14.7233	+	18.0817i	0.519252	+	0.637694i
$805$		0			0
$806$			7.88640i			0.277787i
$807$	−5.23366	+	51.1227i	−0.184233	+	1.79960i
$808$	−4.90684	+	4.90684i	−0.172622	+	0.172622i
$809$	6.27026			0.220451			0.110225	−	0.993907i	$-0.464843\pi$
$809$	6.27026			0.220451			0.110225	+	0.993907i	$0.464843\pi$
$810$	−1.69274	+	9.73119i	−0.0594769	+	0.341919i
$811$	8.90138			0.312570			0.156285	−	0.987712i	$-0.450048\pi$
$811$	8.90138			0.312570			0.156285	+	0.987712i	$0.450048\pi$
$812$		0			0
$813$	3.99320	−	39.0058i	0.140048	−	1.36799i
$814$		−	3.97332i		−	0.139265i
$815$	−4.77079	−	19.8517i	−0.167114	−	0.695373i
$816$	−13.2024	−	16.2138i	−0.462175	−	0.567598i
$817$	−3.98022	−	3.98022i	−0.139250	−	0.139250i
$818$	2.63502	+	2.63502i	0.0921313	+	0.0921313i
$819$		0			0
$820$	23.7842	−	38.8324i	0.830581	−	1.35608i
$821$			16.8442i			0.587867i	0.955826	+	0.293934i	$0.0949645\pi$
$821$			16.8442i			0.587867i	−0.955826	+	0.293934i	$0.905036\pi$
$822$	16.3425	+	1.67305i	0.570008	+	0.0583543i
$823$	32.4880	−	32.4880i	1.13246	−	1.13246i	0.142695	−	0.989767i	$-0.454423\pi$
$823$	32.4880	−	32.4880i	1.13246	−	1.13246i	0.989767	−	0.142695i	$-0.0455767\pi$
$824$	23.1099			0.805072
$825$	8.35897	+	21.5718i	0.291022	+	0.751034i
$826$		0			0
$827$	4.87454	−	4.87454i	0.169504	−	0.169504i	−0.617257	−	0.786762i	$-0.711756\pi$
$827$	4.87454	−	4.87454i	0.169504	−	0.169504i	0.786762	+	0.617257i	$0.211756\pi$
$828$	15.8932	−	10.4437i	0.552329	−	0.362943i
$829$		−	9.82522i		−	0.341244i	−0.985337	−	0.170622i	$-0.945422\pi$
$829$		−	9.82522i		−	0.341244i	0.985337	−	0.170622i	$-0.0545777\pi$
$830$	−3.27323	+	5.34419i	−0.113616	+	0.185499i
$831$	−7.99924	+	6.51350i	−0.277490	+	0.225951i
$832$	5.98598	+	5.98598i	0.207527	+	0.207527i
$833$		0			0
$834$	−11.0703	+	9.01414i	−0.383332	+	0.312134i
$835$	−1.16754	−	4.85822i	−0.0404043	−	0.168126i
$836$			24.6394i			0.852171i
$837$	8.27579	−	26.1904i	0.286053	−	0.905272i
$838$	−2.15397	+	2.15397i	−0.0744075	+	0.0744075i
$839$	13.0314			0.449893			0.224947	−	0.974371i	$-0.427779\pi$
$839$	13.0314			0.449893			0.224947	+	0.974371i	$0.427779\pi$
$840$		0			0
$841$	−20.7675			−0.716120
$842$	8.72279	−	8.72279i	0.300607	−	0.300607i
$843$	37.9231	+	3.88235i	1.30614	+	0.133715i
$844$		−	1.36701i		−	0.0470543i
$845$	−7.16925	−	4.39105i	−0.246630	−	0.151057i
$846$	3.23214	−	15.6204i	0.111123	−	0.537041i
$847$		0			0
$848$	11.5892	+	11.5892i	0.397976	+	0.397976i
$849$	−14.8463	−	18.2327i	−0.509523	−	0.625745i
$850$	−10.1007	+	5.15240i	−0.346450	+	0.176726i
$851$		−	10.9207i		−	0.374355i
$852$	4.21634	−	41.1855i	0.144450	−	1.41099i
$853$	36.7177	−	36.7177i	1.25719	−	1.25719i	0.304761	−	0.952429i	$-0.401424\pi$
$853$	36.7177	−	36.7177i	1.25719	−	1.25719i	0.952429	−	0.304761i	$-0.0985765\pi$
$854$		0			0
$855$	−25.6496	−	24.0675i	−0.877197	−	0.823090i
$856$	1.85358			0.0633542
$857$	−25.5867	+	25.5867i	−0.874024	+	0.874024i	−0.992908	−	0.118884i	$-0.962068\pi$
$857$	−25.5867	+	25.5867i	−0.874024	+	0.874024i	0.118884	+	0.992908i	$0.462068\pi$
$858$	0.703032	−	6.86725i	0.0240011	−	0.234444i
$859$			15.7133i			0.536132i	0.963401	+	0.268066i	$0.0863845\pi$
$859$			15.7133i			0.536132i	−0.963401	+	0.268066i	$0.913615\pi$
$860$	−4.10585	+	0.986727i	−0.140008	+	0.0336471i
$861$		0			0
$862$	−2.92644	−	2.92644i	−0.0996751	−	0.0996751i
$863$	−11.1088	−	11.1088i	−0.378147	−	0.378147i	0.492286	−	0.870433i	$-0.336161\pi$
$863$	−11.1088	−	11.1088i	−0.378147	−	0.378147i	−0.870433	+	0.492286i	$0.836161\pi$
$864$	11.9159	+	22.9251i	0.405386	+	0.779927i
$865$	−5.22613	+	1.25595i	−0.177694	+	0.0427037i
$866$		−	13.0685i		−	0.444084i
$867$	7.49366	+	0.767159i	0.254498	+	0.0260541i
$868$		0			0
$869$	−10.4106			−0.353155
$870$	−5.40534	+	0.727748i	−0.183258	+	0.0246730i
$871$	23.2637			0.788260
$872$	−24.8064	+	24.8064i	−0.840050	+	0.840050i
$873$	−4.35405	−	6.62602i	−0.147362	−	0.224257i
$874$		−	9.27375i		−	0.313689i
$875$		0			0
$876$	13.9161	−	11.3314i	0.470182	−	0.382853i
$877$	−20.7301	−	20.7301i	−0.700006	−	0.700006i	0.264405	−	0.964412i	$-0.414824\pi$
$877$	−20.7301	−	20.7301i	−0.700006	−	0.700006i	−0.964412	+	0.264405i	$0.914824\pi$
$878$	1.69456	+	1.69456i	0.0571886	+	0.0571886i
$879$	6.76884	−	5.51163i	0.228307	−	0.185903i
$880$	13.3086	+	8.15128i	0.448631	+	0.274780i
$881$		−	26.4774i		−	0.892045i	−0.895022	−	0.446023i	$-0.852840\pi$
$881$		−	26.4774i		−	0.892045i	0.895022	−	0.446023i	$-0.147160\pi$
$882$		0			0
$883$	−26.9720	+	26.9720i	−0.907681	+	0.907681i	−0.996085	−	0.0884037i	$-0.971823\pi$
$883$	−26.9720	+	26.9720i	−0.907681	+	0.907681i	0.0884037	+	0.996085i	$0.471823\pi$
$884$	−24.7072			−0.830993
$885$	−0.490993	−	0.374471i	−0.0165045	−	0.0125877i
$886$	−16.5864			−0.557231
$887$	−1.34997	+	1.34997i	−0.0453275	+	0.0453275i	−0.729407	−	0.684080i	$-0.760204\pi$
$887$	−1.34997	+	1.34997i	−0.0453275	+	0.0453275i	0.684080	+	0.729407i	$0.260204\pi$
$888$	9.63389	+	0.986265i	0.323292	+	0.0330969i
$889$		0			0
$890$	1.01329	+	4.21637i	0.0339655	+	0.141333i
$891$	−9.54105	+	22.0681i	−0.319637	+	0.739309i
$892$	5.87209	+	5.87209i	0.196612	+	0.196612i
$893$	40.1654	+	40.1654i	1.34408	+	1.34408i
$894$	4.99871	+	6.13892i	0.167182	+	0.205316i
$895$	9.86155	−	16.1009i	0.329635	−	0.538194i
$896$		0			0
$897$	1.93228	−	18.8746i	0.0645169	−	0.630205i
$898$	8.21601	−	8.21601i	0.274172	−	0.274172i
$899$	15.1668			0.505840
$900$	−25.4470	+	6.97863i	−0.848235	+	0.232621i
$901$	−28.9850			−0.965631
$902$	−10.7330	+	10.7330i	−0.357368	+	0.357368i
$903$		0			0
$904$			14.8499i			0.493901i
$905$	6.44079	−	10.5158i	0.214099	−	0.349558i
$906$	10.9430	+	13.4391i	0.363558	+	0.446486i
$907$	−28.6846	−	28.6846i	−0.952456	−	0.952456i	0.0464640	−	0.998920i	$-0.485205\pi$
$907$	−28.6846	−	28.6846i	−0.952456	−	0.952456i	−0.998920	+	0.0464640i	$0.985205\pi$
$908$	−0.426278	−	0.426278i	−0.0141465	−	0.0141465i
$909$	2.28631	−	11.0494i	0.0758322	−	0.366485i
$910$		0			0
$911$			34.0874i			1.12937i	0.825307	+	0.564684i	$0.191002\pi$
$911$			34.0874i			1.12937i	−0.825307	+	0.564684i	$0.808998\pi$
$912$	−23.6040	−	2.41645i	−0.781607	−	0.0800166i
$913$	−10.7864	+	10.7864i	−0.356978	+	0.356978i
$914$	7.12016			0.235514
$915$	14.5519	+	11.0984i	0.481070	+	0.366903i
$916$	−23.7115			−0.783450
$917$		0			0
$918$	−11.2361	−	3.55046i	−0.370848	−	0.117183i
$919$			2.19661i			0.0724593i	0.999343	+	0.0362297i	$0.0115348\pi$
$919$			2.19661i			0.0724593i	−0.999343	+	0.0362297i	$0.988465\pi$
$920$	−12.6779	−	7.76503i	−0.417979	−	0.256006i
$921$	19.8958	−	16.2005i	0.655589	−	0.533823i
$922$	−8.09166	−	8.09166i	−0.266485	−	0.266485i
$923$	−29.2066	−	29.2066i	−0.961348	−	0.961348i
$924$		0			0
$925$	−4.67569	+	14.4129i	−0.153736	+	0.473892i
$926$			11.8389i			0.389049i
$927$	−31.4038	+	20.6359i	−1.03144	+	0.677771i
$928$	−10.0881	+	10.0881i	−0.331159	+	0.331159i
$929$	−51.2981			−1.68304			−0.841518	−	0.540230i	$-0.818337\pi$
$929$	−51.2981			−1.68304			−0.841518	+	0.540230i	$0.818337\pi$
$930$	−9.95824	+	1.34073i	−0.326543	+	0.0439642i
$931$		0			0
$932$	−2.09792	+	2.09792i	−0.0687197	+	0.0687197i
$933$	−35.2094	−	3.60455i	−1.15271	−	0.118008i
$934$			5.55717i			0.181836i
$935$	−26.8359	+	6.44925i	−0.877627	+	0.210913i
$936$	16.4761	+	3.40920i	0.538539	+	0.111433i
$937$	−16.4279	−	16.4279i	−0.536675	−	0.536675i	0.385876	−	0.922551i	$-0.373899\pi$
$937$	−16.4279	−	16.4279i	−0.536675	−	0.536675i	−0.922551	+	0.385876i	$0.873899\pi$
$938$		0			0
$939$	25.4933	+	31.3083i	0.831942	+	1.02171i
$940$	41.4332	−	9.95730i	1.35140	−	0.324771i
$941$		−	57.2870i		−	1.86750i	−0.357922	−	0.933752i	$-0.616515\pi$
$941$		−	57.2870i		−	1.86750i	0.357922	−	0.933752i	$-0.383485\pi$
$942$	0.774891	−	7.56918i	0.0252473	−	0.246617i
$943$	−29.4995	+	29.4995i	−0.960635	+	0.960635i
$944$	−0.416557			−0.0135578
$945$		0			0
$946$	1.40755			0.0457634
$947$	−35.8300	+	35.8300i	−1.16432	+	1.16432i	−0.180799	+	0.983520i	$0.557868\pi$
$947$	−35.8300	+	35.8300i	−1.16432	+	1.16432i	−0.983520	+	0.180799i	$0.942132\pi$
$948$	1.20927	−	11.8122i	0.0392752	−	0.383642i
$949$		−	17.9043i		−	0.581197i
$950$	−3.97056	+	12.2393i	−0.128822	+	0.397095i
$951$	−35.5017	−	43.5997i	−1.15122	−	1.41382i
$952$		0			0
$953$	35.4764	+	35.4764i	1.14919	+	1.14919i	0.986712	+	0.162481i	$0.0519496\pi$
$953$	35.4764	+	35.4764i	1.14919	+	1.14919i	0.162481	+	0.986712i	$0.448050\pi$
$954$	9.04510	+	1.87159i	0.292846	+	0.0605950i
$955$	−1.06692	−	0.653471i	−0.0345247	−	0.0211458i
$956$			9.06511i			0.293187i
$957$	−13.2068	−	1.35204i	−0.426914	−	0.0437051i
$958$	−6.98270	+	6.98270i	−0.225601	+	0.225601i
$959$		0			0
$960$	−6.54091	+	8.57620i	−0.211107	+	0.276796i
$961$	−3.05833			−0.0986558
$962$	3.19703	−	3.19703i	0.103076	−	0.103076i
$963$	−2.51881	+	1.65515i	−0.0811677	+	0.0533364i
$964$			26.2413i			0.845175i
$965$	5.21090	+	21.6830i	0.167745	+	0.698000i
$966$		0			0
$967$	−21.0372	−	21.0372i	−0.676511	−	0.676511i	0.282698	−	0.959209i	$-0.408771\pi$
$967$	−21.0372	−	21.0372i	−0.676511	−	0.676511i	−0.959209	+	0.282698i	$0.908771\pi$
$968$	5.04075	+	5.04075i	0.162016	+	0.162016i
$969$	32.5390	−	26.4954i	1.04530	−	0.851154i
$970$	−1.51493	+	2.47341i	−0.0486413	+	0.0794164i
$971$			23.4561i			0.752742i	0.926469	+	0.376371i	$0.122828\pi$
$971$			23.4561i			0.752742i	−0.926469	+	0.376371i	$0.877172\pi$
$972$	−23.9309	−	13.3890i	−0.767585	−	0.429451i
$973$		0			0
$974$	5.39987			0.173023
$975$	−10.6314	+	24.0830i	−0.340476	+	0.771273i
$976$	12.3458			0.395179
$977$	−9.03422	+	9.03422i	−0.289030	+	0.289030i	−0.836697	−	0.547666i	$-0.815516\pi$
$977$	−9.03422	+	9.03422i	−0.289030	+	0.289030i	0.547666	+	0.836697i	$0.315516\pi$
$978$	−7.72169	−	0.790504i	−0.246913	−	0.0252775i
$979$			10.5552i			0.337347i
$980$		0			0
$981$	11.5584	−	55.8598i	0.369031	−	1.78347i
$982$	−0.796647	−	0.796647i	−0.0254220	−	0.0254220i
$983$	−3.13374	−	3.13374i	−0.0999509	−	0.0999509i	0.655363	−	0.755314i	$-0.272516\pi$
$983$	−3.13374	−	3.13374i	−0.0999509	−	0.0999509i	−0.755314	+	0.655363i	$0.772516\pi$
$984$	−23.3594	−	28.6877i	−0.744672	−	0.914532i
$985$	−7.50044	−	31.2099i	−0.238984	−	0.994432i
$986$		−	6.50680i		−	0.207219i
$987$		0			0
$988$	−19.8254	+	19.8254i	−0.630731	+	0.630731i
$989$	3.86864			0.123016
$990$	8.79086	−	0.279743i	0.279392	−	0.00889082i
$991$	−29.2283			−0.928467			−0.464233	−	0.885713i	$-0.653670\pi$
$991$	−29.2283			−0.928467			−0.464233	+	0.885713i	$0.653670\pi$
$992$	−18.5853	+	18.5853i	−0.590085	+	0.590085i
$993$	0.390649	−	3.81588i	0.0123969	−	0.121093i
$994$		0			0
$995$	22.2618	+	13.6350i	0.705748	+	0.432260i
$996$	−10.9857	−	13.4915i	−0.348095	−	0.427496i
$997$	4.57510	+	4.57510i	0.144895	+	0.144895i	0.775833	−	0.630938i	$-0.217330\pi$
$997$	4.57510	+	4.57510i	0.144895	+	0.144895i	−0.630938	+	0.775833i	$0.717330\pi$
$998$	−4.27793	−	4.27793i	−0.135415	−	0.135415i
$999$	−13.9721	+	7.26231i	−0.442057	+	0.229769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.h.197.8		24
3.2	odd	2	inner	735.2.j.h.197.5		24
5.3	odd	4	inner	735.2.j.h.638.5		24
7.2	even	3		735.2.y.g.557.5		48
7.3	odd	6		735.2.y.j.422.8		48
7.4	even	3		735.2.y.g.422.8		48
7.5	odd	6		735.2.y.j.557.5		48
7.6	odd	2		105.2.j.a.92.8	yes	24
15.8	even	4	inner	735.2.j.h.638.8		24
21.2	odd	6		735.2.y.g.557.8		48
21.5	even	6		735.2.y.j.557.8		48
21.11	odd	6		735.2.y.g.422.5		48
21.17	even	6		735.2.y.j.422.5		48
21.20	even	2		105.2.j.a.92.5	yes	24
35.3	even	12		735.2.y.j.128.8		48
35.13	even	4		105.2.j.a.8.5	✓	24
35.18	odd	12		735.2.y.g.128.8		48
35.23	odd	12		735.2.y.g.263.5		48
35.27	even	4		525.2.j.b.218.8		24
35.33	even	12		735.2.y.j.263.5		48
35.34	odd	2		525.2.j.b.407.5		24
105.23	even	12		735.2.y.g.263.8		48
105.38	odd	12		735.2.y.j.128.5		48
105.53	even	12		735.2.y.g.128.5		48
105.62	odd	4		525.2.j.b.218.5		24
105.68	odd	12		735.2.y.j.263.8		48
105.83	odd	4		105.2.j.a.8.8	yes	24
105.104	even	2		525.2.j.b.407.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.5	✓	24	35.13	even	4
105.2.j.a.8.8	yes	24	105.83	odd	4
105.2.j.a.92.5	yes	24	21.20	even	2
105.2.j.a.92.8	yes	24	7.6	odd	2
525.2.j.b.218.5		24	105.62	odd	4
525.2.j.b.218.8		24	35.27	even	4
525.2.j.b.407.5		24	35.34	odd	2
525.2.j.b.407.8		24	105.104	even	2
735.2.j.h.197.5		24	3.2	odd	2	inner
735.2.j.h.197.8		24	1.1	even	1	trivial
735.2.j.h.638.5		24	5.3	odd	4	inner
735.2.j.h.638.8		24	15.8	even	4	inner
735.2.y.g.128.5		48	105.53	even	12
735.2.y.g.128.8		48	35.18	odd	12
735.2.y.g.263.5		48	35.23	odd	12
735.2.y.g.263.8		48	105.23	even	12
735.2.y.g.422.5		48	21.11	odd	6
735.2.y.g.422.8		48	7.4	even	3
735.2.y.g.557.5		48	7.2	even	3
735.2.y.g.557.8		48	21.2	odd	6
735.2.y.j.128.5		48	105.38	odd	12
735.2.y.j.128.8		48	35.3	even	12
735.2.y.j.263.5		48	35.33	even	12
735.2.y.j.263.8		48	105.68	odd	12
735.2.y.j.422.5		48	21.17	even	6
735.2.y.j.422.8		48	7.3	odd	6
735.2.y.j.557.5		48	7.5	odd	6
735.2.y.j.557.8		48	21.5	even	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347054 - 0.347054i) q^{2} +(-0.176396 + 1.72305i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(0.536770 + 0.659208i) q^{6} +(1.30461 + 1.30461i) q^{8} +(-2.93777 - 0.607876i) q^{9} +(0.256447 + 1.06710i) q^{10} +2.67137i q^{11} +(-3.03102 - 0.310299i) q^{12} +(-2.14945 + 2.14945i) q^{13} +(-3.07954 - 2.34871i) q^{15} -2.61267 q^{16} +(3.26719 - 3.26719i) q^{17} +(-1.23053 + 0.808598i) q^{18} -5.24329i q^{19} +(-3.35432 - 2.05447i) q^{20} +(0.927108 + 0.927108i) q^{22} +(2.54815 + 2.54815i) q^{23} +(-2.47803 + 2.01778i) q^{24} +(-2.27200 - 4.45399i) q^{25} +1.49195i q^{26} +(1.56561 - 4.95468i) q^{27} +2.86924 q^{29} +(-1.88389 + 0.253638i) q^{30} +5.28599 q^{31} +(-3.51596 + 3.51596i) q^{32} +(-4.60289 - 0.471218i) q^{33} -2.26778i q^{34} +(1.06932 - 5.16785i) q^{36} +(-2.14286 - 2.14286i) q^{37} +(-1.81970 - 1.81970i) q^{38} +(-3.32444 - 4.08274i) q^{39} +(-4.01133 + 0.964012i) q^{40} +11.5768i q^{41} +(0.759108 - 0.759108i) q^{43} -4.69922 q^{44} +(4.59015 - 4.89189i) q^{45} +1.76869 q^{46} +(-7.66034 + 7.66034i) q^{47} +(0.460865 - 4.50176i) q^{48} +(-2.33428 - 0.757266i) q^{50} +(5.05320 + 6.20584i) q^{51} +(-3.78111 - 3.78111i) q^{52} +(-4.43577 - 4.43577i) q^{53} +(-1.17619 - 2.26289i) q^{54} +(-5.09384 - 3.11990i) q^{55} +(9.03442 + 0.924894i) q^{57} +(0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +(4.13163 - 5.41724i) q^{60} -4.72534 q^{61} +(1.83452 - 1.83452i) q^{62} -2.78490i q^{64} +(-1.58828 - 6.60897i) q^{65} +(-1.76099 + 1.43391i) q^{66} +(-5.41156 - 5.41156i) q^{67} +(5.74734 + 5.74734i) q^{68} +(-4.84006 + 3.94109i) q^{69} +13.5880i q^{71} +(-3.03961 - 4.62569i) q^{72} +(-4.16486 + 4.16486i) q^{73} -1.48737 q^{74} +(8.07519 - 3.12910i) q^{75} +9.22351 q^{76} +(-2.57069 - 0.263173i) q^{78} +3.89710i q^{79} +(3.05135 - 4.98193i) q^{80} +(8.26097 + 3.57160i) q^{81} +(4.01778 + 4.01778i) q^{82} +(4.03778 + 4.03778i) q^{83} +(2.41421 + 10.0457i) q^{85} -0.526902i q^{86} +(-0.506122 + 4.94383i) q^{87} +(-3.48510 + 3.48510i) q^{88} +3.95125 q^{89} +(-0.104719 - 3.29077i) q^{90} +(-4.48247 + 4.48247i) q^{92} +(-0.932426 + 9.10800i) q^{93} +5.31710i q^{94} +(9.99806 + 6.12366i) q^{95} +(-5.43796 - 6.67836i) q^{96} +(1.86878 + 1.86878i) q^{97} +(1.62386 - 7.84786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45}+ \cdots - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Introduction

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