LMFDB - Embedded newform 783.2.be.a.143.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(8,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.be (of order $84$, degree $24$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			143.7
Character	$\chi$	$=$	783.143
Dual form			783.2.be.a.449.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03117 + 1.39718i) q^{2} +(-0.299298 - 0.970301i) q^{4} +(1.46016 - 3.72043i) q^{5} +(0.524586 + 0.161813i) q^{7} +(-1.61379 - 0.564688i) q^{8} +(3.69245 + 5.87649i) q^{10} +(0.576982 - 3.04942i) q^{11} +(-0.400833 + 0.0300383i) q^{13} +(-0.767018 + 0.566085i) q^{14} +(4.13100 - 2.81647i) q^{16} +(-2.69557 + 2.69557i) q^{17} +(-5.36550 + 3.37137i) q^{19} +(-4.04697 - 0.303278i) q^{20} +(3.66563 + 3.95061i) q^{22} +(1.02148 - 6.77709i) q^{23} +(-8.04430 - 7.46402i) q^{25} +(0.371356 - 0.591010i) q^{26} -0.557437i q^{28} +(-5.11766 - 1.67616i) q^{29} +(1.59052 - 0.693937i) q^{31} +(-0.196775 + 5.25892i) q^{32} +(-0.986616 - 6.54577i) q^{34} +(1.36800 - 1.71542i) q^{35} +(2.74830 - 7.85418i) q^{37} +(0.822313 - 10.9730i) q^{38} +(-4.45727 + 5.17945i) q^{40} +(-0.912701 + 3.40625i) q^{41} +(0.611906 - 1.40250i) q^{43} +(-3.13155 + 0.352841i) q^{44} +(8.41550 + 8.41550i) q^{46} +(-9.57858 - 1.81237i) q^{47} +(-5.53466 - 3.77347i) q^{49} +(18.7236 - 3.54269i) q^{50} +(0.149115 + 0.379938i) q^{52} +(-2.20154 + 1.75567i) q^{53} +(-10.5027 - 6.59928i) q^{55} +(-0.755196 - 0.557360i) q^{56} +(7.61906 - 5.42189i) q^{58} +(1.88972 - 1.09103i) q^{59} +(3.44312 + 6.51471i) q^{61} +(-0.670535 + 2.93781i) q^{62} +(0.673195 + 0.536855i) q^{64} +(-0.473526 + 1.53513i) q^{65} +(4.54628 - 6.66818i) q^{67} +(3.42229 + 1.80873i) q^{68} +(0.986111 + 3.68022i) q^{70} +(12.9810 + 6.25130i) q^{71} +(-0.0593993 - 0.527184i) q^{73} +(8.13976 + 11.9388i) q^{74} +(4.87713 + 4.19711i) q^{76} +(0.796115 - 1.50632i) q^{77} +(9.06925 - 7.80472i) q^{79} +(-4.44655 - 19.4816i) q^{80} +(-3.81799 - 4.78761i) q^{82} +(4.78588 - 5.15796i) q^{83} +(6.09271 + 13.9647i) q^{85} +(1.32857 + 2.30115i) q^{86} +(-2.65310 + 4.59530i) q^{88} +(0.918803 + 0.103524i) q^{89} +(-0.215132 - 0.0491025i) q^{91} +(-6.88155 + 1.03723i) q^{92} +(12.4093 - 11.5141i) q^{94} +(4.70845 + 24.8847i) q^{95} +(9.19060 - 0.343888i) q^{97} +(10.9794 - 3.84185i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) $ 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.03117	+	1.39718i	−0.729144	+	0.987955i	0.270537	+	0.962710i	$0.412799\pi$
$2$	−1.03117	+	1.39718i	−0.729144	+	0.987955i	−0.999681	+	0.0252456i	$0.991963\pi$
$3$		0			0
$3$		0			0
$4$	−0.299298	−	0.970301i	−0.149649	−	0.485151i
$5$	1.46016	−	3.72043i	0.653005	−	1.66383i	−0.0911628	−	0.995836i	$-0.529058\pi$
$5$	1.46016	−	3.72043i	0.653005	−	1.66383i	0.744168	−	0.667993i	$-0.232846\pi$
$6$		0			0
$7$	0.524586	+	0.161813i	0.198275	+	0.0611598i	0.392302	−	0.919836i	$-0.371679\pi$
$7$	0.524586	+	0.161813i	0.198275	+	0.0611598i	−0.194027	+	0.980996i	$0.562155\pi$
$8$	−1.61379	−	0.564688i	−0.570559	−	0.199647i
$9$		0			0
$10$	3.69245	+	5.87649i	1.16765	+	1.85831i
$11$	0.576982	−	3.04942i	0.173967	−	0.919436i	−0.781404	−	0.624026i	$-0.785496\pi$
$11$	0.576982	−	3.04942i	0.173967	−	0.919436i	0.955370	−	0.295410i	$-0.0954563\pi$
$12$		0			0
$13$	−0.400833	+	0.0300383i	−0.111171	+	0.00833112i	−0.130199	−	0.991488i	$-0.541562\pi$
$13$	−0.400833	+	0.0300383i	−0.111171	+	0.00833112i	0.0190283	+	0.999819i	$0.493943\pi$
$14$	−0.767018	+	0.566085i	−0.204994	+	0.151293i
$15$		0			0
$16$	4.13100	−	2.81647i	1.03275	−	0.704117i
$17$	−2.69557	+	2.69557i	−0.653771	+	0.653771i	−0.953899	−	0.300128i	$-0.902971\pi$
$17$	−2.69557	+	2.69557i	−0.653771	+	0.653771i	0.300128	+	0.953899i	$0.402971\pi$
$18$		0			0
$19$	−5.36550	+	3.37137i	−1.23093	+	0.773445i	−0.980847	−	0.194780i	$-0.937601\pi$
$19$	−5.36550	+	3.37137i	−1.23093	+	0.773445i	−0.250083	+	0.968224i	$0.580458\pi$
$20$	−4.04697	−	0.303278i	−0.904929	−	0.0678151i
$21$		0			0
$22$	3.66563	+	3.95061i	0.781515	+	0.842273i
$23$	1.02148	−	6.77709i	0.212994	−	1.41312i	−0.585282	−	0.810829i	$-0.699016\pi$
$23$	1.02148	−	6.77709i	0.212994	−	1.41312i	0.798276	−	0.602292i	$-0.205746\pi$
$24$		0			0
$25$	−8.04430	−	7.46402i	−1.60886	−	1.49280i
$26$	0.371356	−	0.591010i	0.0728290	−	0.115907i
$27$		0			0
$28$		−	0.557437i		−	0.105346i
$29$	−5.11766	−	1.67616i	−0.950326	−	0.311256i
$29$	−5.11766	−	1.67616i	−0.950326	−	0.311256i
$30$		0			0
$31$	1.59052	−	0.693937i	0.285666	−	0.124635i	−0.252174	−	0.967682i	$-0.581145\pi$
$31$	1.59052	−	0.693937i	0.285666	−	0.124635i	0.537839	+	0.843047i	$0.319241\pi$
$32$	−0.196775	+	5.25892i	−0.0347852	+	0.929655i
$33$		0			0
$34$	−0.986616	−	6.54577i	−0.169203	−	1.12259i
$35$	1.36800	−	1.71542i	0.231234	−	0.289958i
$36$		0			0
$37$	2.74830	−	7.85418i	0.451817	−	1.29122i	−0.462643	−	0.886545i	$-0.653099\pi$
$37$	2.74830	−	7.85418i	0.451817	−	1.29122i	0.914460	−	0.404675i	$-0.132615\pi$
$38$	0.822313	−	10.9730i	0.133397	−	1.78006i
$39$		0			0
$40$	−4.45727	+	5.17945i	−0.704757	+	0.818942i
$41$	−0.912701	+	3.40625i	−0.142540	+	0.531966i	0.857313	+	0.514796i	$0.172132\pi$
$41$	−0.912701	+	3.40625i	−0.142540	+	0.531966i	−0.999853	+	0.0171701i	$0.994534\pi$
$42$		0			0
$43$	0.611906	−	1.40250i	0.0933147	−	0.213880i	−0.863645	−	0.504101i	$-0.831824\pi$
$43$	0.611906	−	1.40250i	0.0933147	−	0.213880i	0.956960	+	0.290221i	$0.0937288\pi$
$44$	−3.13155	+	0.352841i	−0.472099	+	0.0531928i
$45$		0			0
$46$	8.41550	+	8.41550i	1.24080	+	1.24080i
$47$	−9.57858	−	1.81237i	−1.39718	−	0.264361i	−0.567855	−	0.823128i	$-0.692227\pi$
$47$	−9.57858	−	1.81237i	−1.39718	−	0.264361i	−0.829324	+	0.558768i	$0.811274\pi$
$48$		0			0
$49$	−5.53466	−	3.77347i	−0.790666	−	0.539067i
$50$	18.7236	−	3.54269i	2.64791	−	0.501012i
$51$		0			0
$52$	0.149115	+	0.379938i	0.0206785	+	0.0526880i
$53$	−2.20154	+	1.75567i	−0.302405	+	0.241160i	−0.762921	−	0.646491i	$-0.776236\pi$
$53$	−2.20154	+	1.75567i	−0.302405	+	0.241160i	0.460517	+	0.887651i	$0.347664\pi$
$54$		0			0
$55$	−10.5027	−	6.59928i	−1.41618	−	0.889847i
$56$	−0.755196	−	0.557360i	−0.100917	−	0.0744804i
$57$		0			0
$58$	7.61906	−	5.42189i	1.00043	−	0.711929i
$59$	1.88972	−	1.09103i	0.246021	−	0.142040i	−0.371920	−	0.928265i	$-0.621300\pi$
$59$	1.88972	−	1.09103i	0.246021	−	0.142040i	0.617941	+	0.786224i	$0.287967\pi$
$60$		0			0
$61$	3.44312	+	6.51471i	0.440847	+	0.834123i	0.999987	+	0.00504999i	$0.00160747\pi$
$61$	3.44312	+	6.51471i	0.440847	+	0.834123i	−0.559140	+	0.829073i	$0.688869\pi$
$62$	−0.670535	+	2.93781i	−0.0851580	+	0.373102i
$63$		0			0
$64$	0.673195	+	0.536855i	0.0841494	+	0.0671069i
$65$	−0.473526	+	1.53513i	−0.0587337	+	0.190410i
$66$		0			0
$67$	4.54628	−	6.66818i	0.555417	−	0.814647i	−0.441150	−	0.897433i	$-0.645429\pi$
$67$	4.54628	−	6.66818i	0.555417	−	0.814647i	0.996567	+	0.0827860i	$0.0263818\pi$
$68$	3.42229	+	1.80873i	0.415014	+	0.219341i
$69$		0			0
$70$	0.986111	+	3.68022i	0.117863	+	0.439870i
$71$	12.9810	+	6.25130i	1.54056	+	0.741892i	0.995342	−	0.0964048i	$-0.0307343\pi$
$71$	12.9810	+	6.25130i	1.54056	+	0.741892i	0.545213	+	0.838297i	$0.316449\pi$
$72$		0			0
$73$	−0.0593993	−	0.527184i	−0.00695217	−	0.0617022i	0.989757	−	0.142762i	$-0.0455982\pi$
$73$	−0.0593993	−	0.527184i	−0.00695217	−	0.0617022i	−0.996709	+	0.0810594i	$0.974170\pi$
$74$	8.13976	+	11.9388i	0.946227	+	1.38786i
$75$		0			0
$76$	4.87713	+	4.19711i	0.559445	+	0.481441i
$77$	0.796115	−	1.50632i	0.0907257	−	0.171661i
$78$		0			0
$79$	9.06925	−	7.80472i	1.02037	−	0.878099i	0.0277804	−	0.999614i	$-0.491156\pi$
$79$	9.06925	−	7.80472i	1.02037	−	0.878099i	0.992590	+	0.121515i	$0.0387751\pi$
$80$	−4.44655	−	19.4816i	−0.497139	−	2.17811i
$81$		0			0
$82$	−3.81799	−	4.78761i	−0.421627	−	0.528703i
$83$	4.78588	−	5.15796i	0.525319	−	0.566159i	−0.413529	−	0.910491i	$-0.635704\pi$
$83$	4.78588	−	5.15796i	0.525319	−	0.566159i	0.938848	+	0.344332i	$0.111894\pi$
$84$		0			0
$85$	6.09271	+	13.9647i	0.660848	+	1.51468i
$86$	1.32857	+	2.30115i	0.143264	+	0.248140i
$87$		0			0
$88$	−2.65310	+	4.59530i	−0.282821	+	0.489861i
$89$	0.918803	+	0.103524i	0.0973929	+	0.0109735i	0.160526	−	0.987032i	$-0.448681\pi$
$89$	0.918803	+	0.103524i	0.0973929	+	0.0109735i	−0.0631335	+	0.998005i	$0.520109\pi$
$90$		0			0
$91$	−0.215132	−	0.0491025i	−0.0225520	−	0.00514734i
$92$	−6.88155	+	1.03723i	−0.717451	+	0.108138i
$93$		0			0
$94$	12.4093	−	11.5141i	1.27992	−	1.18759i
$95$	4.70845	+	24.8847i	0.483077	+	2.55312i
$96$		0			0
$97$	9.19060	−	0.343888i	0.933164	−	0.0349165i	0.433517	−	0.901146i	$-0.357273\pi$
$97$	9.19060	−	0.343888i	0.933164	−	0.0349165i	0.499647	+	0.866229i	$0.333463\pi$
$98$	10.9794	−	3.84185i	1.10908	−	0.388085i
$99$		0			0
$100$	−4.83470	+	10.0394i	−0.483470	+	1.00394i
$101$	12.8283	+	5.59693i	1.27646	+	0.556915i	0.925242	−	0.379378i	$-0.123862\pi$
$101$	12.8283	+	5.59693i	1.27646	+	0.556915i	0.351221	+	0.936293i	$0.385767\pi$
$102$		0			0
$103$	−0.380474	−	5.07708i	−0.0374893	−	0.500259i	−0.984069	−	0.177789i	$-0.943106\pi$
$103$	−0.380474	−	5.07708i	−0.0374893	−	0.500259i	0.946579	−	0.322471i	$-0.104513\pi$
$104$	0.663821	+	0.177870i	0.0650930	+	0.0174416i
$105$		0			0
$106$	−0.182834	−	4.88633i	−0.0177584	−	0.474603i
$107$	−1.02857	−	2.13585i	−0.0994356	−	0.206480i	0.845316	−	0.534266i	$-0.179412\pi$
$107$	−1.02857	−	2.13585i	−0.0994356	−	0.206480i	−0.944752	+	0.327786i	$0.893698\pi$
$108$		0			0
$109$	0.343427	−	0.0783850i	0.0328943	−	0.00750792i	−0.206042	−	0.978543i	$-0.566058\pi$
$109$	0.343427	−	0.0783850i	0.0328943	−	0.00750792i	0.238936	+	0.971035i	$0.423201\pi$
$110$	20.0504	−	7.86920i	1.91173	−	0.750299i
$111$		0			0
$112$	2.62281	−	0.809029i	0.247832	−	0.0764461i
$113$	−19.5885	−	0.732949i	−1.84273	−	0.0689500i	−0.906887	−	0.421373i	$-0.861548\pi$
$113$	−19.5885	−	0.732949i	−1.84273	−	0.0689500i	−0.935841	+	0.352423i	$0.885358\pi$
$114$		0			0
$115$	−23.7222	−	13.6960i	−2.21211	−	1.27716i
$116$	−0.0946761	+	5.46735i	−0.00879045	+	0.507630i
$117$		0			0
$118$	−0.424250	+	3.76532i	−0.0390553	+	0.346626i
$119$	−1.85024	+	0.977879i	−0.169611	+	0.0896420i
$120$		0			0
$121$	1.27353	+	0.499824i	0.115776	+	0.0454386i
$122$	−12.6526	−	1.90708i	−1.14552	−	0.172659i
$123$		0			0
$124$	−1.14937	−	1.33559i	−0.103216	−	0.119939i
$125$	−21.5108	+	10.3591i	−1.92399	+	0.926543i
$126$		0			0
$127$	1.48514	+	4.24429i	0.131785	+	0.376620i	0.990801	−	0.135329i	$-0.0432093\pi$
$127$	1.48514	+	4.24429i	0.131785	+	0.376620i	−0.859016	+	0.511949i	$0.828924\pi$
$128$	−11.6108	+	3.11111i	−1.02626	+	0.274986i
$129$		0			0
$130$	−1.65657	−	2.24458i	−0.145291	−	0.196863i
$131$	−10.2878	−	13.9395i	−0.898848	−	1.21790i	−0.975314	−	0.220824i	$-0.929125\pi$
$131$	−10.2878	−	13.9395i	−0.898848	−	1.21790i	0.0764654	−	0.997072i	$-0.475637\pi$
$132$		0			0
$133$	−3.36020	+	0.900363i	−0.291366	+	0.0780714i
$134$	4.62867	+	13.2280i	0.399856	+	1.14272i
$135$		0			0
$136$	5.87222	−	2.82791i	0.503539	−	0.242492i
$137$	1.72920	+	2.00937i	0.147736	+	0.171672i	0.826964	−	0.562255i	$-0.190066\pi$
$137$	1.72920	+	2.00937i	0.147736	+	0.171672i	−0.679228	+	0.733927i	$0.737685\pi$
$138$		0			0
$139$	2.11112	+	0.318200i	0.179063	+	0.0269894i	0.237961	−	0.971275i	$-0.423521\pi$
$139$	2.11112	+	0.318200i	0.179063	+	0.0269894i	−0.0588987	+	0.998264i	$0.518759\pi$
$140$	−2.07391	−	0.813949i	−0.175277	−	0.0687913i
$141$		0			0
$142$	−22.1197	+	11.6906i	−1.85624	+	0.981053i
$143$	−0.139674	+	1.23964i	−0.0116801	+	0.103664i
$144$		0			0
$145$	−13.7087	+	16.5925i	−1.13844	+	1.37793i
$146$	0.797821	+	0.460622i	0.0660281	+	0.0381214i
$147$		0			0
$148$	−8.44348	−	0.315933i	−0.694050	−	0.0259695i
$149$	−2.07495	+	0.640038i	−0.169987	+	0.0524340i	−0.378580	−	0.925568i	$-0.623588\pi$
$149$	−2.07495	+	0.640038i	−0.169987	+	0.0524340i	0.208594	+	0.978002i	$0.433111\pi$
$150$		0			0
$151$	0.908066	−	0.356390i	0.0738974	−	0.0290026i	−0.328104	−	0.944641i	$-0.606410\pi$
$151$	0.908066	−	0.356390i	0.0738974	−	0.0290026i	0.402002	+	0.915639i	$0.368315\pi$
$152$	10.5625	−	2.41083i	0.856735	−	0.195544i
$153$		0			0
$154$	1.28368	+	2.66558i	0.103442	+	0.214799i
$155$	−0.259328	−	6.93069i	−0.0208297	−	0.556686i
$156$		0			0
$157$	3.66546	+	0.982158i	0.292536	+	0.0783848i	0.402102	−	0.915595i	$-0.368280\pi$
$157$	3.66546	+	0.982158i	0.292536	+	0.0783848i	−0.109566	+	0.993979i	$0.534946\pi$
$158$	1.55270	+	20.7193i	0.123526	+	1.64834i
$159$		0			0
$160$	19.2781	+	8.41097i	1.52407	+	0.664945i
$161$	1.63248	−	3.38988i	0.128657	−	0.267160i
$162$		0			0
$163$	−0.141584	+	0.0495424i	−0.0110897	+	0.00388046i	−0.335818	−	0.941927i	$-0.609013\pi$
$163$	−0.141584	+	0.0495424i	−0.0110897	+	0.00388046i	0.324729	+	0.945807i	$0.394727\pi$
$164$	3.57825	−	0.133889i	0.279415	−	0.0104550i
$165$		0			0
$166$	2.27155	+	12.0054i	0.176307	+	0.931803i
$167$	10.5592	−	9.79747i	0.817092	−	0.758151i	−0.156199	−	0.987726i	$-0.549924\pi$
$167$	10.5592	−	9.79747i	0.817092	−	0.758151i	0.973291	+	0.229575i	$0.0737336\pi$
$168$		0			0
$169$	−12.6950	+	1.91347i	−0.976541	+	0.147190i
$170$	−25.7937	−	5.88725i	−1.97829	−	0.451531i
$171$		0			0
$172$	−1.54399	−	0.173966i	−0.117728	−	0.0132648i
$173$	−4.19462	+	7.26529i	−0.318911	+	0.552370i	−0.980261	−	0.197707i	$-0.936650\pi$
$173$	−4.19462	+	7.26529i	−0.318911	+	0.552370i	0.661350	+	0.750077i	$0.269984\pi$
$174$		0			0
$175$	−3.01215	−	5.21720i	−0.227697	−	0.394383i
$176$	−6.20509	−	14.2222i	−0.467726	−	1.07204i
$177$		0			0
$178$	−1.09208	+	1.17698i	−0.0818548	+	0.0882185i
$179$	11.0513	+	13.8580i	0.826017	+	1.03579i	0.998708	+	0.0508160i	$0.0161822\pi$
$179$	11.0513	+	13.8580i	0.826017	+	1.03579i	−0.172692	+	0.984976i	$0.555246\pi$
$180$		0			0
$181$	4.32644	+	18.9554i	0.321582	+	1.40894i	0.834738	+	0.550647i	$0.185619\pi$
$181$	4.32644	+	18.9554i	0.321582	+	1.40894i	−0.513156	+	0.858295i	$0.671524\pi$
$182$	0.290442	−	0.249946i	0.0215290	−	0.0185272i
$183$		0			0
$184$	−5.47539	+	10.3600i	−0.403651	+	0.763746i
$185$	−25.2080	−	21.6933i	−1.85333	−	1.59492i
$186$		0			0
$187$	6.66463	+	9.77522i	0.487366	+	0.714835i
$188$	1.10831	+	9.83655i	0.0808320	+	0.717404i
$189$		0			0
$190$	−39.6236	−	19.0817i	−2.87460	−	1.38434i
$191$	−4.46461	−	16.6622i	−0.323048	−	1.20563i	−0.916260	−	0.400585i	$-0.868807\pi$
$191$	−4.46461	−	16.6622i	−0.323048	−	1.20563i	0.593212	−	0.805046i	$-0.297860\pi$
$192$		0			0
$193$	1.84801	+	0.976701i	0.133023	+	0.0703045i	0.532456	−	0.846458i	$-0.321269\pi$
$193$	1.84801	+	0.976701i	0.133023	+	0.0703045i	−0.399433	+	0.916762i	$0.630793\pi$
$194$	−8.99655	+	13.1955i	−0.645915	+	0.947383i
$195$		0			0
$196$	−2.00489	+	6.49968i	−0.143206	+	0.464263i
$197$	−11.5562	−	9.21574i	−0.823343	−	0.656595i	0.118385	−	0.992968i	$-0.462228\pi$
$197$	−11.5562	−	9.21574i	−0.823343	−	0.656595i	−0.941729	+	0.336373i	$0.890800\pi$
$198$		0			0
$199$	3.86265	−	16.9234i	0.273816	−	1.19967i	−0.631652	−	0.775252i	$-0.717623\pi$
$199$	3.86265	−	16.9234i	0.273816	−	1.19967i	0.905468	−	0.424415i	$-0.139520\pi$
$200$	8.76693	+	16.5878i	0.619916	+	1.17294i
$201$		0			0
$202$	−21.0480	+	12.1521i	−1.48093	+	0.855017i
$203$	−2.41343	−	1.70740i	−0.169390	−	0.119836i
$204$		0			0
$205$	11.3400	+	8.36932i	0.792022	+	0.584539i
$206$	7.48592	+	4.70372i	0.521569	+	0.327723i
$207$		0			0
$208$	−1.57124	+	1.25302i	−0.108946	+	0.0868814i
$209$	7.18493	+	18.3069i	0.496992	+	1.26632i
$210$		0			0
$211$	0.996034	−	0.188460i	0.0685698	−	0.0129741i	−0.151513	−	0.988455i	$-0.548415\pi$
$211$	0.996034	−	0.188460i	0.0685698	−	0.0129741i	0.220083	+	0.975481i	$0.429367\pi$
$212$	2.36245	+	1.61069i	0.162253	+	0.110622i
$213$		0			0
$214$	4.04479	+	0.765316i	0.276496	+	0.0523159i
$215$	−4.32444	−	4.32444i	−0.294924	−	0.294924i
$216$		0			0
$217$	0.946654	−	0.106662i	0.0642630	−	0.00724071i
$218$	−0.244612	+	0.560657i	−0.0165672	+	0.0379725i
$219$		0			0
$220$	−3.25985	+	12.1659i	−0.219779	+	0.820227i
$221$	0.999503	−	1.16144i	0.0672338	−	0.0781271i
$222$		0			0
$223$	1.17013	−	15.6143i	0.0783575	−	1.04561i	−0.809992	−	0.586441i	$-0.800529\pi$
$223$	1.17013	−	15.6143i	0.0783575	−	1.04561i	0.888350	−	0.459168i	$-0.151852\pi$
$224$	−0.954190	+	2.72692i	−0.0637545	+	0.182200i
$225$		0			0
$226$	21.2230	−	26.6128i	1.41173	−	1.77026i
$227$	1.88279	+	12.4915i	0.124965	+	0.829088i	0.960224	+	0.279231i	$0.0900797\pi$
$227$	1.88279	+	12.4915i	0.124965	+	0.829088i	−0.835259	+	0.549857i	$0.814682\pi$
$228$		0			0
$229$	0.286783	−	7.66445i	0.0189512	−	0.506481i	−0.957205	−	0.289411i	$-0.906541\pi$
$229$	0.286783	−	7.66445i	0.0189512	−	0.506481i	0.976156	−	0.217070i	$-0.0696500\pi$
$230$	43.5973	−	19.0213i	2.87472	−	1.25423i
$231$		0			0
$232$	7.31230	+	5.59485i	0.480076	+	0.367320i
$233$		−	25.2517i		−	1.65429i	−0.561985	−	0.827147i	$-0.689962\pi$
$233$		−	25.2517i		−	1.65429i	0.561985	−	0.827147i	$-0.310038\pi$
$234$		0			0
$235$	−20.7291	+	32.9901i	−1.35222	+	2.15204i
$236$	−1.62422	−	1.50706i	−0.105728	−	0.0981011i
$237$		0			0
$238$	0.541628	−	3.59347i	0.0351085	−	0.232930i
$239$	14.3600	+	15.4764i	0.928869	+	1.00108i	0.999993	+	0.00361518i	$0.00115075\pi$
$239$	14.3600	+	15.4764i	0.928869	+	1.00108i	−0.0711245	+	0.997467i	$0.522659\pi$
$240$		0			0
$241$	−23.6484	−	1.77220i	−1.52333	−	0.114158i	−0.713430	−	0.700727i	$-0.752859\pi$
$241$	−23.6484	−	1.77220i	−1.52333	−	0.114158i	−0.809899	+	0.586569i	$0.800478\pi$
$242$	−2.01157	+	1.26395i	−0.129308	+	0.0812498i
$243$		0			0
$244$	5.29071	−	5.29071i	0.338703	−	0.338703i
$245$	−22.1205	+	15.0815i	−1.41322	+	0.963520i
$246$		0			0
$247$	2.04940	−	1.51253i	0.130400	−	0.0962398i
$248$	−2.95862	+	0.221718i	−0.187872	+	0.0140791i
$249$		0			0
$250$	7.70774	−	40.7364i	0.487480	−	2.57639i
$251$	10.9893	+	17.4894i	0.693642	+	1.10392i	0.988911	+	0.148510i	$0.0474478\pi$
$251$	10.9893	+	17.4894i	0.693642	+	1.10392i	−0.295269	+	0.955414i	$0.595409\pi$
$252$		0			0
$253$	−20.0768	−	7.02519i	−1.26222	−	0.441670i
$254$	−7.46146	−	2.30156i	−0.468174	−	0.144412i
$255$		0			0
$256$	6.99675	−	17.8274i	0.437297	−	1.11421i
$257$	−0.608529	−	1.97280i	−0.0379590	−	0.123060i	0.934610	−	0.355674i	$-0.115748\pi$
$257$	−0.608529	−	1.97280i	−0.0379590	−	0.123060i	−0.972569	+	0.232613i	$0.925272\pi$
$258$		0			0
$259$	2.71263	−	3.67549i	0.168555	−	0.228384i
$260$	1.63127			0.101167
$261$		0			0
$262$	30.0843			1.85862
$263$	5.55074	−	7.52099i	0.342273	−	0.463764i	−0.599323	−	0.800507i	$-0.704564\pi$
$263$	5.55074	−	7.52099i	0.342273	−	0.463764i	0.941596	+	0.336743i	$0.109325\pi$
$264$		0			0
$265$	3.31725	+	10.7543i	0.203777	+	0.660628i
$266$	2.20695	−	5.62323i	0.135317	−	0.344782i
$267$		0			0
$268$	−7.83083	−	2.41549i	−0.478344	−	0.147550i
$269$	16.5693	+	5.79784i	1.01025	+	0.353501i	0.784128	−	0.620599i	$-0.213111\pi$
$269$	16.5693	+	5.79784i	1.01025	+	0.353501i	0.226119	+	0.974100i	$0.427396\pi$
$270$		0			0
$271$	4.13972	+	6.58833i	0.251470	+	0.400213i	0.948474	−	0.316855i	$-0.102627\pi$
$271$	4.13972	+	6.58833i	0.251470	+	0.400213i	−0.697004	+	0.717067i	$0.745484\pi$
$272$	−3.54341	+	18.7274i	−0.214851	+	1.13551i
$273$		0			0
$274$	−4.59054	+	0.344013i	−0.277325	+	0.0207826i
$275$	−27.4024	+	20.2239i	−1.65243	+	1.21955i
$276$		0			0
$277$	−6.49120	+	4.42562i	−0.390018	+	0.265910i	−0.742414	−	0.669941i	$-0.766319\pi$
$277$	−6.49120	+	4.42562i	−0.390018	+	0.265910i	0.352396	+	0.935851i	$0.385367\pi$
$278$	−2.62150	+	2.62150i	−0.157227	+	0.157227i
$279$		0			0
$280$	−3.17633	+	1.99582i	−0.189822	+	0.119273i
$281$	26.2974	+	1.97072i	1.56877	+	0.117563i	0.830531	−	0.556972i	$-0.188037\pi$
$281$	26.2974	+	1.97072i	1.56877	+	0.117563i	0.738243	+	0.674535i	$0.235656\pi$
$282$		0			0
$283$	−2.95583	−	3.18562i	−0.175706	−	0.189366i	0.639059	−	0.769158i	$-0.279324\pi$
$283$	−2.95583	−	3.18562i	−0.175706	−	0.189366i	−0.814764	+	0.579792i	$0.803134\pi$
$284$	2.18046	−	14.4664i	0.129387	−	0.858425i
$285$		0			0
$286$	−1.58798	−	1.47343i	−0.0938989	−	0.0871255i
$287$	−1.02997	+	1.63918i	−0.0607970	+	0.0967579i
$288$		0			0
$289$			2.46783i			0.145167i
$290$	−9.04673	−	36.2631i	−0.531242	−	2.12944i
$291$		0			0
$292$	−0.493749	+	0.215420i	−0.0288945	+	0.0126065i
$293$	−0.792751	+	21.1867i	−0.0463130	+	1.23774i	0.761446	+	0.648228i	$0.224490\pi$
$293$	−0.792751	+	21.1867i	−0.0463130	+	1.23774i	−0.807759	+	0.589512i	$0.799320\pi$
$294$		0			0
$295$	−1.29981	−	8.62368i	−0.0756779	−	0.502090i
$296$	−8.87033	+	11.1230i	−0.515577	+	0.646513i
$297$		0			0
$298$	1.24537	−	3.55907i	0.0721424	−	0.206171i
$299$	−0.205872	+	2.74717i	−0.0119059	+	0.158873i
$300$		0			0
$301$	0.547941	−	0.636719i	0.0315828	−	0.0366999i
$302$	−0.438426	+	1.63623i	−0.0252286	+	0.0941544i
$303$		0			0
$304$	−12.6695	+	29.0389i	−0.726647	+	1.66549i
$305$	29.2651	−	3.29738i	1.67571	−	0.188808i
$306$		0			0
$307$	1.42348	+	1.42348i	0.0812425	+	0.0812425i	0.746560	−	0.665318i	$-0.231704\pi$
$307$	1.42348	+	1.42348i	0.0812425	+	0.0812425i	−0.665318	+	0.746560i	$0.731704\pi$
$308$	−1.69986	−	0.321631i	−0.0968587	−	0.0183267i
$309$		0			0
$310$	9.95082	+	6.78436i	0.565169	+	0.385326i
$311$	−5.56844	+	1.05361i	−0.315757	+	0.0597445i	−0.341375	−	0.939927i	$-0.610892\pi$
$311$	−5.56844	+	1.05361i	−0.315757	+	0.0597445i	0.0256174	+	0.999672i	$0.491845\pi$
$312$		0			0
$313$	11.1255	+	28.3474i	0.628851	+	1.60229i	0.788446	+	0.615105i	$0.210886\pi$
$313$	11.1255	+	28.3474i	0.628851	+	1.60229i	−0.159594	+	0.987183i	$0.551019\pi$
$314$	−5.15195	+	4.10854i	−0.290741	+	0.231859i
$315$		0			0
$316$	−10.2873	−	6.46396i	−0.578708	−	0.363626i
$317$	27.8967	+	20.5887i	1.56683	+	1.15638i	0.918772	+	0.394789i	$0.129182\pi$
$317$	27.8967	+	20.5887i	1.56683	+	1.15638i	0.648062	+	0.761588i	$0.275580\pi$
$318$		0			0
$319$	−8.06414	+	14.6388i	−0.451505	+	0.819616i
$320$	2.98031	−	1.72068i	0.166604	−	0.0961890i
$321$		0			0
$322$	3.05291	+	5.77640i	0.170132	+	0.321906i
$323$	5.37532	−	23.5508i	0.299091	−	1.31040i
$324$		0			0
$325$	3.44863	+	2.75019i	0.191295	+	0.152553i
$326$	0.0767769	−	0.248905i	0.00425228	−	0.0137856i
$327$		0			0
$328$	3.39637	−	4.98156i	0.187533	−	0.275061i
$329$	−4.73153	−	2.50069i	−0.260858	−	0.137867i
$330$		0			0
$331$	0.362543	+	1.35303i	0.0199272	+	0.0743692i	0.975173	−	0.221443i	$-0.0710765\pi$
$331$	0.362543	+	1.35303i	0.0199272	+	0.0743692i	−0.955246	+	0.295812i	$0.904410\pi$
$332$	−6.43718	−	3.09998i	−0.353286	−	0.170134i
$333$		0			0
$334$	2.80058	+	24.8559i	0.153241	+	1.36005i
$335$	−18.1702	−	26.6508i	−0.992744	−	1.45609i
$336$		0			0
$337$	−10.4407	−	8.98496i	−0.568742	−	0.489442i	0.320270	−	0.947326i	$-0.396226\pi$
$337$	−10.4407	−	8.98496i	−0.568742	−	0.489442i	−0.889012	+	0.457884i	$0.848607\pi$
$338$	10.4172	−	19.7103i	0.566622	−	1.07210i
$339$		0			0
$340$	11.7264	−	10.0914i	0.635952	−	0.547281i
$341$	−1.19841	−	5.25056i	−0.0648973	−	0.284334i
$342$		0			0
$343$	−4.68878	−	5.87954i	−0.253170	−	0.317465i
$344$	−1.77946	+	1.91780i	−0.0959421	+	0.103401i
$345$		0			0
$346$	−5.82557	−	13.3524i	−0.313185	−	0.717827i
$347$	−3.36991	−	5.83686i	−0.180907	−	0.313339i	0.761283	−	0.648420i	$-0.224570\pi$
$347$	−3.36991	−	5.83686i	−0.180907	−	0.313339i	−0.942189	+	0.335081i	$0.891236\pi$
$348$		0			0
$349$	8.53408	−	14.7815i	0.456819	−	0.791233i	−0.541972	−	0.840397i	$-0.682322\pi$
$349$	8.53408	−	14.7815i	0.456819	−	0.791233i	0.998791	+	0.0491632i	$0.0156554\pi$
$350$	10.3954	+	1.17128i	0.555657	+	0.0626075i
$351$		0			0
$352$	15.9231	+	3.63435i	0.848706	+	0.193712i
$353$	−15.9672	+	2.40667i	−0.849848	+	0.128094i	−0.559503	−	0.828828i	$-0.689008\pi$
$353$	−15.9672	+	2.40667i	−0.849848	+	0.128094i	−0.290345	+	0.956922i	$0.593770\pi$
$354$		0			0
$355$	42.2119	−	39.1669i	2.24037	−	2.07876i
$356$	−0.174546	−	0.922500i	−0.00925094	−	0.0488924i
$357$		0			0
$358$	−30.7578	+	1.15088i	−1.62560	+	0.0608257i
$359$	26.6079	−	9.31051i	1.40431	−	0.491390i	0.481434	−	0.876482i	$-0.340116\pi$
$359$	26.6079	−	9.31051i	1.40431	−	0.491390i	0.922878	+	0.385092i	$0.125830\pi$
$360$		0			0
$361$	9.17869	−	19.0597i	0.483089	−	1.00314i
$362$	−30.9453	−	13.5013i	−1.62645	−	0.709613i
$363$		0			0
$364$	0.0167445	+	0.223439i	0.000877648	+	0.0117114i
$365$	−2.04809	−	0.548783i	−0.107202	−	0.0287246i
$366$		0			0
$367$	−0.281578	−	7.52533i	−0.0146983	−	0.392819i	−0.987158	−	0.159748i	$-0.948932\pi$
$367$	−0.281578	−	7.52533i	−0.0146983	−	0.392819i	0.972460	−	0.233071i	$-0.0748776\pi$
$368$	−14.8677	−	30.8731i	−0.775033	−	1.60937i
$369$		0			0
$370$	56.3030	−	12.8508i	2.92705	−	0.668081i
$371$	−1.43899	+	0.564762i	−0.0747086	+	0.0293210i
$372$		0			0
$373$	32.2472	−	9.94695i	1.66970	−	0.515034i	0.691441	−	0.722433i	$-0.256976\pi$
$373$	32.2472	−	9.94695i	1.66970	−	0.515034i	0.978256	+	0.207399i	$0.0664999\pi$
$374$	−20.5301	−	0.768182i	−1.06159	−	0.0397217i
$375$		0			0
$376$	14.4344	+	8.33368i	0.744395	+	0.429777i
$377$	2.10168	+	0.518136i	0.108242	+	0.0266854i
$378$		0			0
$379$	−0.332817	+	2.95383i	−0.0170957	+	0.151728i	−0.999360	−	0.0357736i	$-0.988610\pi$
$379$	−0.332817	+	2.95383i	−0.0170957	+	0.151728i	0.982264	+	0.187502i	$0.0600391\pi$
$380$	22.7365	−	12.0166i	1.16636	−	0.616437i
$381$		0			0
$382$	27.8838	+	10.9436i	1.42666	+	0.559922i
$383$	−14.0475	−	2.11733i	−0.717796	−	0.108190i	−0.220019	−	0.975496i	$-0.570612\pi$
$383$	−14.0475	−	2.11733i	−0.717796	−	0.108190i	−0.497777	+	0.867305i	$0.665850\pi$
$384$		0			0
$385$	−4.44172	−	5.16137i	−0.226371	−	0.263048i
$386$	−3.27023	+	1.57486i	−0.166450	+	0.0801583i
$387$		0			0
$388$	−3.08440	−	8.81472i	−0.156587	−	0.447500i
$389$	−12.0039	+	3.21643i	−0.608621	+	0.163080i	−0.549950	−	0.835198i	$-0.685353\pi$
$389$	−12.0039	+	3.21643i	−0.608621	+	0.163080i	−0.0586716	+	0.998277i	$0.518686\pi$
$390$		0			0
$391$	15.5146	+	21.0216i	0.784609	+	1.06311i
$392$	6.80093	+	9.21493i	0.343499	+	0.465424i
$393$		0			0
$394$	24.7924	−	6.64310i	1.24902	−	0.334674i
$395$	−15.7944	−	45.1377i	−0.794701	−	2.27112i
$396$		0			0
$397$	−8.19230	+	3.94521i	−0.411160	+	0.198004i	−0.628018	−	0.778199i	$-0.716133\pi$
$397$	−8.19230	+	3.94521i	−0.411160	+	0.198004i	0.216858	+	0.976203i	$0.430419\pi$
$398$	19.6620	+	22.8476i	0.985566	+	1.14525i
$399$		0			0
$400$	−54.2531	−	8.17734i	−2.71266	−	0.408867i
$401$	19.5913	+	7.68902i	0.978343	+	0.383971i	0.800002	−	0.599998i	$-0.204832\pi$
$401$	19.5913	+	7.68902i	0.978343	+	0.383971i	0.178341	+	0.983969i	$0.442927\pi$
$402$		0			0
$403$	−0.616689	+	0.325929i	−0.0307194	+	0.0162357i
$404$	1.59122	−	14.1225i	0.0791661	−	0.702618i
$405$		0			0
$406$	4.87419	−	1.61138i	0.241902	−	0.0799717i
$407$	−22.3650	−	12.9124i	−1.10859	−	0.640046i
$408$		0			0
$409$	−23.5962	−	0.882909i	−1.16676	−	0.0436570i	−0.553021	−	0.833167i	$-0.686525\pi$
$409$	−23.5962	−	0.882909i	−1.16676	−	0.0436570i	−0.613738	+	0.789510i	$0.710335\pi$
$410$	−23.3869	+	7.21390i	−1.15500	+	0.356269i
$411$		0			0
$412$	−4.81242	+	1.88874i	−0.237091	+	0.0930513i
$413$	1.16787	−	0.266558i	0.0574670	−	0.0131165i
$414$		0			0
$415$	−12.2017	−	25.3370i	−0.598956	−	1.24375i
$416$	−0.0790951	−	2.11386i	−0.00387796	−	0.103641i
$417$		0			0
$418$	−32.9869	−	8.83881i	−1.61344	−	0.432320i
$419$	−1.54522	−	20.6195i	−0.0754889	−	1.00733i	−0.898405	−	0.439167i	$-0.855274\pi$
$419$	−1.54522	−	20.6195i	−0.0754889	−	1.00733i	0.822916	−	0.568163i	$-0.192346\pi$
$420$		0			0
$421$	10.6450	+	4.64437i	0.518806	+	0.226353i	0.642946	−	0.765912i	$-0.277712\pi$
$421$	10.6450	+	4.64437i	0.518806	+	0.226353i	−0.124139	+	0.992265i	$0.539617\pi$
$422$	−0.763764	+	1.58597i	−0.0371794	+	0.0772039i
$423$		0			0
$424$	4.54422	−	1.59009i	0.220687	−	0.0772216i
$425$	41.8037	−	1.56418i	2.02778	−	0.0758741i
$426$		0			0
$427$	0.752049	+	3.97467i	0.0363942	+	0.192348i
$428$	−1.76457	+	1.63728i	−0.0852935	+	0.0791408i
$429$		0			0
$430$	10.5012	−	1.58281i	0.506414	−	0.0763296i
$431$	−25.2984	−	5.77421i	−1.21858	−	0.278134i	−0.435579	−	0.900150i	$-0.643456\pi$
$431$	−25.2984	−	5.77421i	−1.21858	−	0.278134i	−0.783004	+	0.622017i	$0.786314\pi$
$432$		0			0
$433$	16.3402	+	1.84110i	0.785261	+	0.0884777i	0.495485	−	0.868617i	$-0.334990\pi$
$433$	16.3402	+	1.84110i	0.785261	+	0.0884777i	0.289777	+	0.957094i	$0.406419\pi$
$434$	−0.827130	+	1.43263i	−0.0397035	+	0.0687685i
$435$		0			0
$436$	−0.178844	−	0.309767i	−0.00856508	−	0.0148352i
$437$	17.3673	+	39.8063i	0.830791	+	1.90419i
$438$		0			0
$439$	11.1166	−	11.9809i	0.530568	−	0.571817i	−0.409713	−	0.912214i	$-0.634371\pi$
$439$	11.1166	−	11.9809i	0.530568	−	0.571817i	0.940282	+	0.340398i	$0.110562\pi$
$440$	13.2226	+	16.5806i	0.630361	+	0.790448i
$441$		0			0
$442$	0.592092	+	2.59412i	0.0281629	+	0.123390i
$443$	7.28700	−	6.27097i	0.346216	−	0.297943i	−0.461940	−	0.886911i	$-0.652847\pi$
$443$	7.28700	−	6.27097i	0.346216	−	0.297943i	0.808156	+	0.588968i	$0.200466\pi$
$444$		0			0
$445$	1.72676	−	3.26718i	0.0818561	−	0.154879i
$446$	20.6093	+	17.7358i	0.975880	+	0.839813i
$447$		0			0
$448$	0.266279	+	0.390559i	0.0125805	+	0.0184522i
$449$	0.173703	+	1.54165i	0.00819753	+	0.0727551i	0.997145	−	0.0755119i	$-0.0240591\pi$
$449$	0.173703	+	1.54165i	0.00819753	+	0.0727551i	−0.988947	+	0.148267i	$0.952631\pi$
$450$		0			0
$451$	9.86048	+	4.74856i	0.464312	+	0.223601i
$452$	5.15161	+	19.2261i	0.242312	+	0.904319i
$453$		0			0
$454$	−19.3943	−	10.2502i	−0.910220	−	0.481065i
$455$	−0.496811	+	0.728688i	−0.0232909	+	0.0341614i
$456$		0			0
$457$	4.23695	−	13.7359i	0.198196	−	0.642536i	−0.800850	−	0.598865i	$-0.795618\pi$
$457$	4.23695	−	13.7359i	0.198196	−	0.642536i	0.999046	−	0.0436710i	$-0.0139053\pi$
$458$	10.4129	+	8.30400i	0.486563	+	0.388021i
$459$		0			0
$460$	−6.18925	+	27.1169i	−0.288575	+	1.26433i
$461$	16.1712	+	30.5973i	0.753166	+	1.42506i	0.899996	+	0.435898i	$0.143569\pi$
$461$	16.1712	+	30.5973i	0.753166	+	1.42506i	−0.146830	+	0.989162i	$0.546907\pi$
$462$		0			0
$463$	−13.6253	+	7.86655i	−0.633220	+	0.365589i	−0.781998	−	0.623281i	$-0.785799\pi$
$463$	−13.6253	+	7.86655i	−0.633220	+	0.365589i	0.148778	+	0.988871i	$0.452466\pi$
$464$	−25.8619	+	7.48950i	−1.20061	+	0.347691i
$465$		0			0
$466$	35.2812	+	26.0387i	1.63437	+	1.20622i
$467$	0.946636	+	0.594811i	0.0438051	+	0.0275246i	0.553757	−	0.832679i	$-0.313194\pi$
$467$	0.946636	+	0.594811i	0.0438051	+	0.0275246i	−0.509952	+	0.860203i	$0.670337\pi$
$468$		0			0
$469$	3.46392	−	2.76238i	0.159949	−	0.127555i
$470$	−24.7180	−	62.9805i	−1.14016	−	2.90508i
$471$		0			0
$472$	−3.66570	+	0.693588i	−0.168728	+	0.0319250i
$473$	−3.92377	−	2.67518i	−0.180415	−	0.123005i
$474$		0			0
$475$	68.3256	+	12.9279i	3.13500	+	0.593173i
$476$	1.50261	+	1.50261i	0.0688720	+	0.0688720i
$477$		0			0
$478$	−36.4308	+	4.10476i	−1.66630	+	0.187747i
$479$	−15.6382	+	35.8432i	−0.714528	+	1.63772i	0.0545108	+	0.998513i	$0.482640\pi$
$479$	−15.6382	+	35.8432i	−0.714528	+	1.63772i	−0.769039	+	0.639202i	$0.779265\pi$
$480$		0			0
$481$	−0.865683	+	3.23077i	−0.0394717	+	0.147310i
$482$	26.8615	−	31.2137i	1.22351	−	1.42174i
$483$		0			0
$484$	0.103814	−	1.38530i	0.00471883	−	0.0629684i
$485$	12.1404	−	34.6952i	0.551265	−	1.57543i
$486$		0			0
$487$	3.07673	−	3.85810i	0.139420	−	0.174827i	−0.707219	−	0.706994i	$-0.750051\pi$
$487$	3.07673	−	3.85810i	0.139420	−	0.174827i	0.846639	+	0.532167i	$0.178622\pi$
$488$	−1.87769	−	12.4576i	−0.0849989	−	0.563931i
$489$		0			0
$490$	1.73833	−	46.4578i	0.0785296	−	2.09875i
$491$	9.12109	−	3.97949i	0.411629	−	0.179592i	−0.183865	−	0.982951i	$-0.558861\pi$
$491$	9.12109	−	3.97949i	0.411629	−	0.179592i	0.595494	+	0.803360i	$0.296956\pi$
$492$		0			0
$493$	18.3132	−	9.27679i	0.824786	−	0.417806i
$494$			4.42305i			0.199002i
$495$		0			0
$496$	4.61598	−	7.34630i	0.207264	−	0.329859i
$497$	5.79809	+	5.37984i	0.260080	+	0.241319i
$498$		0			0
$499$	−6.19589	+	41.1070i	−0.277366	+	1.84020i	0.223532	+	0.974697i	$0.428241\pi$
$499$	−6.19589	+	41.1070i	−0.277366	+	1.84020i	−0.500898	+	0.865507i	$0.666997\pi$
$500$	16.4896	+	17.7715i	0.737436	+	0.794766i
$501$		0			0
$502$	−35.7677	−	2.68042i	−1.59639	−	0.119633i
$503$	−23.6134	+	14.8373i	−1.05287	+	0.661563i	−0.943139	−	0.332398i	$-0.892142\pi$
$503$	−23.6134	+	14.8373i	−1.05287	+	0.661563i	−0.109732	+	0.993961i	$0.534999\pi$
$504$		0			0
$505$	39.5544	−	39.5544i	1.76015	−	1.76015i
$506$	30.5180	−	20.8068i	1.35669	−	0.924976i
$507$		0			0
$508$	3.67374	−	2.71134i	0.162996	−	0.120296i
$509$	24.2619	−	1.81818i	1.07539	−	0.0805893i	0.474759	−	0.880116i	$-0.342535\pi$
$509$	24.2619	−	1.81818i	1.07539	−	0.0805893i	0.600630	+	0.799527i	$0.294916\pi$
$510$		0			0
$511$	0.0541454	−	0.286165i	0.00239525	−	0.0126592i
$512$	4.90282	+	7.80279i	0.216676	+	0.344838i
$513$		0			0
$514$	3.38386	+	1.18406i	0.149255	+	0.0522267i
$515$	−19.4445	−	5.99783i	−0.856827	−	0.264296i
$516$		0			0
$517$	−11.0533	+	28.1635i	−0.486125	+	1.23863i
$518$	2.33814	+	7.58007i	0.102732	+	0.333049i
$519$		0			0
$520$	1.63104	−	2.20998i	0.0715259	−	0.0969142i
$521$	2.60813			0.114264			0.0571322	−	0.998367i	$-0.481804\pi$
$521$	2.60813			0.114264			0.0571322	+	0.998367i	$0.481804\pi$
$522$		0			0
$523$	21.7770			0.952240			0.476120	−	0.879380i	$-0.342043\pi$
$523$	21.7770			0.952240			0.476120	+	0.879380i	$0.342043\pi$
$524$	−10.4464	+	14.1543i	−0.456351	+	0.618334i
$525$		0			0
$526$	4.78444	+	15.5108i	0.208611	+	0.676301i
$527$	−2.41680	+	6.15791i	−0.105277	+	0.268243i
$528$		0			0
$529$	−22.9074	−	7.06598i	−0.995972	−	0.307217i
$530$	−18.4462	−	6.45462i	−0.801254	−	0.280371i
$531$		0			0
$532$	1.87933	+	2.99093i	0.0814791	+	0.129673i
$533$	0.263523	−	1.39275i	0.0114144	−	0.0603268i
$534$		0			0
$535$	−9.44816	+	0.708042i	−0.408480	+	0.0306113i
$536$	−11.1022	+	8.19377i	−0.479541	+	0.353917i
$537$		0			0
$538$	−25.1863	+	17.1717i	−1.08586	+	0.740325i
$539$	−14.7003	+	14.7003i	−0.633187	+	0.633187i
$540$		0			0
$541$	−13.9221	+	8.74785i	−0.598559	+	0.376099i	−0.796969	−	0.604020i	$-0.793565\pi$
$541$	−13.9221	+	8.74785i	−0.598559	+	0.376099i	0.198411	+	0.980119i	$0.436422\pi$
$542$	−13.4738	−	1.00972i	−0.578750	−	0.0433713i
$543$		0			0
$544$	−13.6454	−	14.7062i	−0.585040	−	0.630523i
$545$	0.209833	−	1.39215i	0.00898827	−	0.0596333i
$546$		0			0
$547$	−14.0672	−	13.0524i	−0.601469	−	0.558082i	0.319565	−	0.947564i	$-0.396463\pi$
$547$	−14.0672	−	13.0524i	−0.601469	−	0.558082i	−0.921034	+	0.389483i	$0.872654\pi$
$548$	1.43214	−	2.27925i	0.0611782	−	0.0973645i
$549$		0			0
$550$		−	59.1402i		−	2.52175i
$551$	33.1098	−	8.26007i	1.41052	−	0.351891i
$552$		0			0
$553$	6.02051	−	2.62672i	0.256018	−	0.111700i
$554$	0.510108	−	13.6329i	0.0216724	−	0.579207i
$555$		0			0
$556$	−0.323104	−	2.14366i	−0.0137027	−	0.0909114i
$557$	−8.87207	+	11.1252i	−0.375922	+	0.471391i	−0.933419	−	0.358788i	$-0.883190\pi$
$557$	−8.87207	+	11.1252i	−0.375922	+	0.471391i	0.557498	+	0.830179i	$0.311762\pi$
$558$		0			0
$559$	−0.203143	+	0.580550i	−0.00859204	+	0.0245547i
$560$	0.819787	−	10.9393i	0.0346423	−	0.462270i
$561$		0			0
$562$	−29.8705	+	34.7101i	−1.26001	+	1.46416i
$563$	−4.18320	+	15.6119i	−0.176301	+	0.657963i	0.820026	+	0.572327i	$0.193959\pi$
$563$	−4.18320	+	15.6119i	−0.176301	+	0.657963i	−0.996326	+	0.0856366i	$0.972708\pi$
$564$		0			0
$565$	−31.3292	+	71.8074i	−1.31803	+	3.02096i
$566$	7.49884	−	0.844916i	0.315200	−	0.0355145i
$567$		0			0
$568$	−17.4184	−	17.4184i	−0.730862	−	0.730862i
$569$	−41.4095	−	7.83511i	−1.73598	−	0.328465i	−0.780863	−	0.624702i	$-0.785221\pi$
$569$	−41.4095	−	7.83511i	−1.73598	−	0.328465i	−0.955114	+	0.296237i	$0.904268\pi$
$570$		0			0
$571$	−6.15035	−	4.19324i	−0.257384	−	0.175482i	0.427753	−	0.903896i	$-0.359305\pi$
$571$	−6.15035	−	4.19324i	−0.257384	−	0.175482i	−0.685137	+	0.728414i	$0.740258\pi$
$572$	1.24463	−	0.235497i	0.0520406	−	0.00984661i
$573$		0			0
$574$	−1.22817	−	3.12932i	−0.0512627	−	0.130615i
$575$	−58.8014	+	46.8926i	−2.45219	+	1.95556i
$576$		0			0
$577$	26.0769	+	16.3852i	1.08560	+	0.682125i	0.951129	−	0.308793i	$-0.0999249\pi$
$577$	26.0769	+	16.3852i	1.08560	+	0.682125i	0.134467	+	0.990918i	$0.457068\pi$
$578$	−3.44801	−	2.54474i	−0.143418	−	0.105847i
$579$		0			0
$580$	20.2027	+	8.33545i	0.838870	+	0.346111i
$581$	3.34524	−	1.93137i	0.138784	−	0.0801269i
$582$		0			0
$583$	4.08353	+	7.72642i	0.169123	+	0.319996i
$584$	−0.201837	+	0.884304i	−0.00835205	+	0.0365927i
$585$		0			0
$586$	−28.7842	−	22.9546i	−1.18906	−	0.948246i
$587$	−5.07641	+	16.4573i	−0.209526	+	0.679266i	0.788416	+	0.615142i	$0.210901\pi$
$587$	−5.07641	+	16.4573i	−0.209526	+	0.679266i	−0.997942	+	0.0641239i	$0.979575\pi$
$588$		0			0
$589$	−6.19442	+	9.08555i	−0.255237	+	0.374363i
$590$	13.3892	+	7.07637i	0.551223	+	0.291330i
$591$		0			0
$592$	−10.7678	−	40.1861i	−0.442555	−	1.65164i
$593$	6.27585	+	3.02229i	0.257718	+	0.124111i	0.558282	−	0.829651i	$-0.311461\pi$
$593$	6.27585	+	3.02229i	0.257718	+	0.124111i	−0.300564	+	0.953762i	$0.597175\pi$
$594$		0			0
$595$	0.936487	+	8.31155i	0.0383922	+	0.340740i
$596$	1.24206	+	1.82177i	0.0508767	+	0.0746225i
$597$		0			0
$598$	−3.62600	−	3.12042i	−0.148278	−	0.127604i
$599$	21.7703	−	41.1914i	0.889510	−	1.68303i	0.173629	−	0.984811i	$-0.444451\pi$
$599$	21.7703	−	41.1914i	0.889510	−	1.68303i	0.715880	−	0.698223i	$-0.246026\pi$
$600$		0			0
$601$	32.4819	−	27.9529i	1.32496	−	1.14022i	0.345541	−	0.938404i	$-0.387695\pi$
$601$	32.4819	−	27.9529i	1.32496	−	1.14022i	0.979423	−	0.201820i	$-0.0646855\pi$
$602$	0.324593	+	1.42214i	0.0132294	+	0.0579619i
$603$		0			0
$604$	−0.617588	−	0.774431i	−0.0251293	−	0.0315111i
$605$	3.71913	−	4.00826i	0.151204	−	0.162959i
$606$		0			0
$607$	−14.3541	−	32.8999i	−0.582613	−	1.33536i	−0.919230	−	0.393722i	$-0.871187\pi$
$607$	−14.3541	−	32.8999i	−0.582613	−	1.33536i	0.336616	−	0.941642i	$-0.390717\pi$
$608$	−16.6740	−	28.8801i	−0.676218	−	1.17124i
$609$		0			0
$610$	−25.5701	+	44.2887i	−1.03530	+	1.79320i
$611$	3.89385	+	0.438732i	0.157528	+	0.0177492i
$612$		0			0
$613$	−36.7355	−	8.38463i	−1.48373	−	0.338652i	−0.597491	−	0.801876i	$-0.703835\pi$
$613$	−36.7355	−	8.38463i	−1.48373	−	0.338652i	−0.886241	+	0.463224i	$0.846693\pi$
$614$	−3.45671	+	0.521015i	−0.139501	+	0.0210265i
$615$		0			0
$616$	−2.13536	+	1.98133i	−0.0860362	+	0.0798299i
$617$	−6.44348	−	34.0546i	−0.259405	−	1.37099i	−0.833645	−	0.552300i	$-0.813750\pi$
$617$	−6.44348	−	34.0546i	−0.259405	−	1.37099i	0.574241	−	0.818686i	$-0.305297\pi$
$618$		0			0
$619$	−14.3066	+	0.535315i	−0.575030	+	0.0215161i	−0.323325	−	0.946288i	$-0.604801\pi$
$619$	−14.3066	+	0.535315i	−0.575030	+	0.0215161i	−0.251705	+	0.967804i	$0.580991\pi$
$620$	−6.64724	+	2.32597i	−0.266959	+	0.0934132i
$621$		0			0
$622$	4.26991	−	8.86655i	0.171208	−	0.355516i
$623$	0.465240	+	0.202982i	0.0186394	+	0.00813231i
$624$		0			0
$625$	3.03059	+	40.4404i	0.121223	+	1.61761i
$626$	−51.0786	−	13.6865i	−2.04151	−	0.547021i
$627$		0			0
$628$	−0.144078	−	3.85056i	−0.00574933	−	0.153654i
$629$	13.7633	+	28.5797i	0.548777	+	1.13955i
$630$		0			0
$631$	−14.4465	+	3.29732i	−0.575106	+	0.131264i	−0.500175	−	0.865924i	$-0.666731\pi$
$631$	−14.4465	+	3.29732i	−0.575106	+	0.131264i	−0.0749315	+	0.997189i	$0.523874\pi$
$632$	−19.0430	+	7.47385i	−0.757492	+	0.297294i
$633$		0			0
$634$	−57.5322	+	17.7463i	−2.28490	+	0.704797i
$635$	17.9592	+	0.671984i	0.712687	+	0.0266669i
$636$		0			0
$637$	2.33183	+	1.34628i	0.0923903	+	0.0533416i
$638$	−12.1376	−	26.3621i	−0.480532	−	1.04368i
$639$		0			0
$640$	−5.37901	+	47.7400i	−0.212624	+	1.88709i
$641$	23.3152	−	12.3225i	0.920896	−	0.486708i	0.0615509	−	0.998104i	$-0.480395\pi$
$641$	23.3152	−	12.3225i	0.920896	−	0.486708i	0.859345	+	0.511396i	$0.170872\pi$
$642$		0			0
$643$	−28.7532	−	11.2848i	−1.13391	−	0.445029i	−0.277196	−	0.960813i	$-0.589405\pi$
$643$	−28.7532	−	11.2848i	−1.13391	−	0.445029i	−0.856718	+	0.515785i	$0.827500\pi$
$644$	−3.77780	−	0.569412i	−0.148866	−	0.0224380i
$645$		0			0
$646$	27.3619	+	31.7951i	1.07654	+	1.25096i
$647$	21.5212	−	10.3641i	0.846087	−	0.407454i	0.0399631	−	0.999201i	$-0.487276\pi$
$647$	21.5212	−	10.3641i	0.846087	−	0.407454i	0.806124	+	0.591747i	$0.201562\pi$
$648$		0			0
$649$	−2.23668	−	6.39208i	−0.0877976	−	0.250911i
$650$	−7.39861	+	1.98245i	−0.290198	+	0.0777582i
$651$		0			0
$652$	0.0904469	+	0.122551i	0.00354217	+	0.00479947i
$653$	2.23017	+	3.02177i	0.0872732	+	0.118251i	0.846059	−	0.533089i	$-0.178969\pi$
$653$	2.23017	+	3.02177i	0.0872732	+	0.118251i	−0.758786	+	0.651340i	$0.774207\pi$
$654$		0			0
$655$	−66.8827	+	17.9212i	−2.61332	+	0.700238i
$656$	5.82321	+	16.6418i	0.227358	+	0.649753i
$657$		0			0
$658$	8.37290	−	4.03217i	0.326409	−	0.157191i
$659$	−24.3595	−	28.3063i	−0.948912	−	1.10266i	−0.994609	−	0.103700i	$-0.966932\pi$
$659$	−24.3595	−	28.3063i	−0.948912	−	1.10266i	0.0456967	−	0.998955i	$-0.485449\pi$
$660$		0			0
$661$	29.3605	+	4.42538i	1.14199	+	0.172127i	0.692678	−	0.721247i	$-0.256431\pi$
$661$	29.3605	+	4.42538i	1.14199	+	0.172127i	0.449312	+	0.893375i	$0.351669\pi$
$662$	−2.26427	−	0.888659i	−0.0880032	−	0.0345387i
$663$		0			0
$664$	−10.6360	+	5.62130i	−0.412758	+	0.218149i
$665$	−1.55670	+	13.8161i	−0.0603662	+	0.535765i
$666$		0			0
$667$	−16.5871	+	32.9707i	−0.642256	+	1.27663i
$668$	−12.6668	−	7.31320i	−0.490094	−	0.282956i
$669$		0			0
$670$	55.9724	+	2.09434i	2.16240	+	0.0809114i
$671$	21.8527	−	6.74068i	0.843615	−	0.260221i
$672$		0			0
$673$	−33.4731	+	13.1372i	−1.29029	+	0.506403i	−0.908515	−	0.417852i	$-0.862783\pi$
$673$	−33.4731	+	13.1372i	−1.29029	+	0.506403i	−0.381777	+	0.924254i	$0.624688\pi$
$674$	23.3197	−	5.32257i	0.898242	−	0.205018i
$675$		0			0
$676$	5.65624	+	11.7453i	0.217548	+	0.451743i
$677$	0.118113	+	3.15663i	0.00453944	+	0.121319i	0.999728	+	0.0233373i	$0.00742916\pi$
$677$	0.118113	+	3.15663i	0.00453944	+	0.121319i	−0.995188	+	0.0979818i	$0.968761\pi$
$678$		0			0
$679$	4.87691	+	1.30676i	0.187159	+	0.0501490i
$680$	−1.94666	−	25.9764i	−0.0746512	−	0.996151i
$681$		0			0
$682$	8.57173	+	3.73981i	0.328229	+	0.143205i
$683$	−10.4087	+	21.6139i	−0.398279	+	0.827035i	0.601328	+	0.799002i	$0.294638\pi$
$683$	−10.4087	+	21.6139i	−0.398279	+	0.827035i	−0.999607	+	0.0280324i	$0.991076\pi$
$684$		0			0
$685$	10.0006	−	3.49937i	0.382105	−	0.133704i
$686$	13.0497	−	0.488285i	0.498239	−	0.0186428i
$687$		0			0
$688$	−1.42232	−	7.51715i	−0.0542255	−	0.286588i
$689$	0.829713	−	0.769861i	0.0316095	−	0.0293294i
$690$		0			0
$691$	47.5965	−	7.17402i	1.81066	−	0.272913i	0.845384	−	0.534159i	$-0.179372\pi$
$691$	47.5965	−	7.17402i	1.81066	−	0.272913i	0.965272	+	0.261246i	$0.0841334\pi$
$692$	8.30496	+	1.89555i	0.315707	+	0.0720581i
$693$		0			0
$694$	11.6301	+	1.31040i	0.441472	+	0.0497420i
$695$	4.26642	−	7.38966i	0.161835	−	0.280306i
$696$		0			0
$697$	−6.72152	−	11.6420i	−0.254596	−	0.440973i
$698$	11.8523	+	27.1658i	0.448616	+	1.02824i
$699$		0			0
$700$	−4.16072	+	4.48419i	−0.157261	+	0.169487i
$701$	−16.4837	−	20.6699i	−0.622580	−	0.780691i	0.366125	−	0.930566i	$-0.380684\pi$
$701$	−16.4837	−	20.6699i	−0.622580	−	0.780691i	−0.988705	+	0.149875i	$0.952113\pi$
$702$		0			0
$703$	11.7333	+	51.4072i	0.442532	+	1.93886i
$704$	2.02552	−	1.74310i	0.0763397	−	0.0656956i
$705$		0			0
$706$	13.1023	−	24.7907i	0.493110	−	0.933010i
$707$	5.82389	+	5.01186i	0.219030	+	0.188490i
$708$		0			0
$709$	−7.30713	−	10.7176i	−0.274425	−	0.402508i	0.664141	−	0.747607i	$-0.268798\pi$
$709$	−7.30713	−	10.7176i	−0.274425	−	0.402508i	−0.938566	+	0.345100i	$0.887845\pi$
$710$	11.1958	+	99.3651i	0.420169	+	3.72910i
$711$		0			0
$712$	−1.42429	−	0.685903i	−0.0533776	−	0.0257053i
$713$	−3.07818	−	11.4879i	−0.115279	−	0.430227i
$714$		0			0
$715$	4.40806	+	2.32973i	0.164852	+	0.0871269i
$716$	10.1387	−	14.8708i	0.378902	−	0.555748i
$717$		0			0
$718$	−14.4287	+	46.7767i	−0.538475	+	1.74569i
$719$	27.3782	+	21.8334i	1.02104	+	0.814248i	0.982735	−	0.185018i	$-0.0592343\pi$
$719$	27.3782	+	21.8334i	1.02104	+	0.814248i	0.0383000	+	0.999266i	$0.487806\pi$
$720$		0			0
$721$	0.621948	−	2.72493i	0.0231626	−	0.101482i
$722$	17.1651	+	32.4780i	0.638820	+	1.20871i
$723$		0			0
$724$	17.0975	−	9.87126i	0.635425	−	0.366863i
$725$	28.6571	+	51.6819i	1.06430	+	1.91942i
$726$		0			0
$727$	−24.5048	−	18.0854i	−0.908833	−	0.670749i	0.0356307	−	0.999365i	$-0.488656\pi$
$727$	−24.5048	−	18.0854i	−0.908833	−	0.670749i	−0.944464	+	0.328616i	$0.893418\pi$
$728$	0.319450	+	0.200724i	0.0118396	+	0.00743931i
$729$		0			0
$730$	2.87866	−	2.29566i	0.106544	−	0.0849661i
$731$	2.13111	+	5.42997i	0.0788218	+	0.200835i
$732$		0			0
$733$	−12.7738	+	2.41693i	−0.471809	+	0.0892712i	−0.416379	−	0.909191i	$-0.636701\pi$
$733$	−12.7738	+	2.41693i	−0.471809	+	0.0892712i	−0.0554309	+	0.998463i	$0.517653\pi$
$734$	10.8046	+	7.36645i	0.398805	+	0.271901i
$735$		0			0
$736$	35.4392	+	6.70545i	1.30631	+	0.247166i
$737$	−17.7110	−	17.7110i	−0.652392	−	0.652392i
$738$		0			0
$739$	4.48512	−	0.505351i	0.164988	−	0.0185896i	−0.0290842	−	0.999577i	$-0.509259\pi$
$739$	4.48512	−	0.505351i	0.164988	−	0.0185896i	0.194072	+	0.980987i	$0.437831\pi$
$740$	−13.5043	+	30.9521i	−0.496427	+	1.13782i
$741$		0			0
$742$	0.694763	−	2.59289i	0.0255055	−	0.0951879i
$743$	−3.18401	+	3.69989i	−0.116810	+	0.135736i	−0.813332	−	0.581800i	$-0.802349\pi$
$743$	−3.18401	+	3.69989i	−0.116810	+	0.135736i	0.696522	+	0.717535i	$0.254730\pi$
$744$		0			0
$745$	−0.648549	+	8.65429i	−0.0237610	+	0.317068i
$746$	−19.3545	+	55.3121i	−0.708620	+	2.02512i
$747$		0			0
$748$	7.49020	−	9.39241i	0.273869	−	0.343420i
$749$	−0.193965	−	1.28687i	−0.00708733	−	0.0470213i
$750$		0			0
$751$	0.361792	−	9.66910i	0.0132020	−	0.352830i	−0.977004	−	0.213219i	$-0.931605\pi$
$751$	0.361792	−	9.66910i	0.0132020	−	0.352830i	0.990206	−	0.139611i	$-0.0445853\pi$
$752$	−44.6736	+	19.4909i	−1.62908	+	0.710759i
$753$		0			0
$754$	−2.89111	+	2.40214i	−0.105288	+	0.0874807i
$755$		−	3.89879i		−	0.141891i
$756$		0			0
$757$	11.6705	−	18.5734i	0.424170	−	0.675063i	−0.564455	−	0.825464i	$-0.690914\pi$
$757$	11.6705	−	18.5734i	0.424170	−	0.675063i	0.988625	+	0.150401i	$0.0480564\pi$
$758$	−3.78385	−	3.51090i	−0.137436	−	0.127522i
$759$		0			0
$760$	6.45369	−	42.8174i	0.234100	−	1.55315i
$761$	11.0195	+	11.8762i	0.399455	+	0.430510i	0.900463	−	0.434932i	$-0.143228\pi$
$761$	11.0195	+	11.8762i	0.399455	+	0.430510i	−0.501008	+	0.865443i	$0.667037\pi$
$762$		0			0
$763$	0.192841	+	0.0144514i	0.00698131	+	0.000523177i
$764$	−14.8311	+	9.31897i	−0.536569	+	0.337149i
$765$		0			0
$766$	17.4436	−	17.4436i	0.630264	−	0.630264i
$767$	−0.724691	+	0.494086i	−0.0261671	+	0.0178404i
$768$		0			0
$769$	13.2235	−	9.75941i	0.476853	−	0.351933i	−0.328723	−	0.944426i	$-0.606618\pi$
$769$	13.2235	−	9.75941i	0.476853	−	0.351933i	0.805576	+	0.592493i	$0.201856\pi$
$770$	11.7915	−	0.883652i	0.424937	−	0.0318446i
$771$		0			0
$772$	0.394588	−	2.08545i	0.0142015	−	0.0750570i
$773$	−2.74554	−	4.36951i	−0.0987504	−	0.157160i	0.793695	−	0.608316i	$-0.208155\pi$
$773$	−2.74554	−	4.36951i	−0.0987504	−	0.157160i	−0.892445	+	0.451156i	$0.851012\pi$
$774$		0			0
$775$	−17.9742	−	6.28944i	−0.645651	−	0.225923i
$776$	−15.0258	−	4.63486i	−0.539396	−	0.166382i
$777$		0			0
$778$	7.88406	−	20.0883i	0.282657	−	0.720199i
$779$	−6.58661	−	21.3533i	−0.235990	−	0.765060i
$780$		0			0
$781$	26.5526	−	35.9775i	0.950128	−	1.28738i
$782$	−45.3691			−1.62239
$783$		0			0
$784$	−33.4915			−1.19613
$785$	9.00623	−	12.2030i	0.321446	−	0.435544i
$786$		0			0
$787$	−3.92570	−	12.7268i	−0.139936	−	0.453661i	0.858292	−	0.513161i	$-0.171526\pi$
$787$	−3.92570	−	12.7268i	−0.139936	−	0.453661i	−0.998228	+	0.0594998i	$0.981049\pi$
$788$	−5.48330	+	13.9712i	−0.195335	+	0.497704i
$789$		0			0
$790$	79.3521	+	24.4769i	2.82322	+	0.870848i
$791$	−10.1572	−	3.55417i	−0.361150	−	0.126372i
$792$		0			0
$793$	−1.57581	−	2.50789i	−0.0559586	−	0.0890576i
$794$	2.93546	−	15.5143i	0.104176	−	0.550581i
$795$		0			0
$796$	−17.5769	+	1.31720i	−0.622995	+	0.0466870i
$797$	14.4981	−	10.7001i	0.513551	−	0.379018i	−0.305994	−	0.952034i	$-0.598989\pi$
$797$	14.4981	−	10.7001i	0.513551	−	0.379018i	0.819544	+	0.573016i	$0.194227\pi$
$798$		0			0
$799$	30.7051	−	20.9344i	1.08627	−	0.740604i
$800$	40.8356	−	40.8356i	1.44376	−	1.44376i
$801$		0			0
$802$	−30.9448	+	19.4439i	−1.09270	+	0.686588i
$803$	−1.64188	−	0.123042i	−0.0579407	−	0.00434205i
$804$		0			0
$805$	−10.2281	−	11.0233i	−0.360495	−	0.388521i
$806$	0.180526	−	1.19771i	0.00635876	−	0.0421876i
$807$		0			0
$808$	−17.5416	−	16.2762i	−0.617111	−	0.572595i
$809$	−9.46657	+	15.0660i	−0.332827	+	0.529691i	−0.970651	−	0.240491i	$-0.922692\pi$
$809$	−9.46657	+	15.0660i	−0.332827	+	0.529691i	0.637825	+	0.770182i	$0.279834\pi$
$810$		0			0
$811$		−	20.1055i		−	0.705999i	−0.935623	−	0.353000i	$-0.885162\pi$
$811$		−	20.1055i		−	0.705999i	0.935623	−	0.353000i	$-0.114838\pi$
$812$	−0.934356	+	2.85278i	−0.0327895	+	0.100113i
$813$		0			0
$814$	41.1030	−	17.9331i	1.44066	−	0.628554i
$815$	−0.0224165	+	0.599094i	−0.000785216	+	0.0209853i
$816$		0			0
$817$	1.44517	+	9.58809i	0.0505602	+	0.335445i
$818$	25.5652	−	32.0578i	0.893866	−	1.12087i
$819$		0			0
$820$	4.72671	−	13.5082i	0.165064	−	0.471725i
$821$	−1.06487	+	14.2097i	−0.0371643	+	0.495923i	0.947301	+	0.320344i	$0.103799\pi$
$821$	−1.06487	+	14.2097i	−0.0371643	+	0.495923i	−0.984465	+	0.175579i	$0.943820\pi$
$822$		0			0
$823$	−14.4511	+	16.7925i	−0.503734	+	0.585349i	−0.951054	−	0.309024i	$-0.899997\pi$
$823$	−14.4511	+	16.7925i	−0.503734	+	0.585349i	0.447320	+	0.894374i	$0.352378\pi$
$824$	−2.25296	+	8.40816i	−0.0784856	+	0.292912i
$825$		0			0
$826$	−0.831835	+	1.90659i	−0.0289432	+	0.0663386i
$827$	44.4380	−	5.00696i	1.54526	−	0.174109i	0.702221	−	0.711959i	$-0.252192\pi$
$827$	44.4380	−	5.00696i	1.54526	−	0.174109i	0.843040	+	0.537850i	$0.180763\pi$
$828$		0			0
$829$	−11.9822	−	11.9822i	−0.416158	−	0.416158i	0.467719	−	0.883877i	$-0.345076\pi$
$829$	−11.9822	−	11.9822i	−0.416158	−	0.416158i	−0.883877	+	0.467719i	$0.845076\pi$
$830$	47.9823	+	9.07874i	1.66549	+	0.315128i
$831$		0			0
$832$	−0.285965	−	0.194968i	−0.00991406	−	0.00675929i
$833$	25.0907	−	4.74742i	0.869341	−	0.164488i
$834$		0			0
$835$	−21.0327	−	53.5906i	−0.727868	−	1.85458i
$836$	15.6128	−	12.4508i	0.539979	−	0.430619i
$837$		0			0
$838$	30.4026	+	19.1032i	1.05024	+	0.659909i
$839$	−7.71941	−	5.69718i	−0.266504	−	0.196689i	0.452368	−	0.891831i	$-0.350579\pi$
$839$	−7.71941	−	5.69718i	−0.266504	−	0.196689i	−0.718872	+	0.695143i	$0.755341\pi$
$840$		0			0
$841$	23.3809	+	17.1561i	0.806240	+	0.591589i
$842$	−17.4658	+	10.0839i	−0.601911	+	0.347514i
$843$		0			0
$844$	−0.480974	−	0.910047i	−0.0165558	−	0.0313251i
$845$	−11.4179	+	50.0250i	−0.392787	+	1.72091i
$846$		0			0
$847$	0.587199	+	0.468275i	0.0201764	+	0.0160901i
$848$	−4.14977	+	13.4532i	−0.142504	+	0.461986i
$849$		0			0
$850$	−40.9211	+	60.0202i	−1.40358	+	2.05868i
$851$	−50.4212	−	26.6484i	−1.72842	−	0.913494i
$852$		0			0
$853$	1.46139	+	5.45398i	0.0500370	+	0.186741i	0.986421	−	0.164237i	$-0.0525161\pi$
$853$	1.46139	+	5.45398i	0.0500370	+	0.186741i	−0.936384	+	0.350977i	$0.885849\pi$
$854$	−6.32882	−	3.04780i	−0.216568	−	0.104293i
$855$		0			0
$856$	0.453804	+	4.02762i	0.0155107	+	0.137661i
$857$	−30.7559	−	45.1106i	−1.05060	−	1.54095i	−0.823695	−	0.567033i	$-0.808091\pi$
$857$	−30.7559	−	45.1106i	−1.05060	−	1.54095i	−0.226907	−	0.973916i	$-0.572861\pi$
$858$		0			0
$859$	35.5018	+	30.5518i	1.21131	+	1.04241i	0.997855	+	0.0654604i	$0.0208516\pi$
$859$	35.5018	+	30.5518i	1.21131	+	1.04241i	0.213452	+	0.976954i	$0.431529\pi$
$860$	−2.90171	+	5.49030i	−0.0989475	+	0.187218i
$861$		0			0
$862$	34.1545	−	29.3923i	1.16331	−	1.00111i
$863$	0.932385	+	4.08505i	0.0317388	+	0.139057i	0.988315	−	0.152426i	$-0.0487086\pi$
$863$	0.932385	+	4.08505i	0.0317388	+	0.139057i	−0.956576	+	0.291483i	$0.905851\pi$
$864$		0			0
$865$	20.9052	+	26.2143i	0.710799	+	0.891313i
$866$	−19.4218	+	20.9318i	−0.659981	+	0.711290i
$867$		0			0
$868$	−0.386826	−	0.886615i	−0.0131297	−	0.0300937i
$869$	−18.5671	−	32.1592i	−0.629846	−	1.09092i
$870$		0			0
$871$	−1.62200	+	2.80939i	−0.0549594	+	0.0951925i
$872$	−0.598481	−	0.0674326i	−0.0202671	−	0.00228356i
$873$		0			0
$874$	−73.5251	−	16.7816i	−2.48702	−	0.567647i
$875$	−12.9605	+	1.95348i	−0.438145	+	0.0660398i
$876$		0			0
$877$	−15.7253	+	14.5910i	−0.531006	+	0.492702i	−0.899495	−	0.436930i	$-0.856066\pi$
$877$	−15.7253	+	14.5910i	−0.531006	+	0.492702i	0.368489	+	0.929632i	$0.379875\pi$
$878$	5.27636	+	27.8862i	0.178068	+	0.941115i
$879$		0			0
$880$	−61.9733	+	2.31888i	−2.08912	+	0.0781693i
$881$	5.61368	−	1.96431i	0.189130	−	0.0661794i	−0.234052	−	0.972224i	$-0.575199\pi$
$881$	5.61368	−	1.96431i	0.189130	−	0.0661794i	0.423182	+	0.906045i	$0.360913\pi$
$882$		0			0
$883$	−3.41041	+	7.08180i	−0.114770	+	0.238321i	−0.950439	−	0.310911i	$-0.899366\pi$
$883$	−3.41041	+	7.08180i	−0.114770	+	0.238321i	0.835669	+	0.549233i	$0.185080\pi$
$884$	−1.42610	−	0.622201i	−0.0479649	−	0.0209269i
$885$		0			0
$886$	1.24757	+	16.6477i	0.0419129	+	0.559289i
$887$	17.1389	+	4.59235i	0.575467	+	0.154196i	0.534803	−	0.844977i	$-0.320386\pi$
$887$	17.1389	+	4.59235i	0.575467	+	0.154196i	0.0406644	+	0.999173i	$0.487053\pi$
$888$		0			0
$889$	0.0923016	+	2.46681i	0.00309570	+	0.0827343i
$890$	2.78427	+	5.78160i	0.0933289	+	0.193800i
$891$		0			0
$892$	−15.5008	+	3.53795i	−0.519004	+	0.118459i
$893$	57.5040	−	22.5687i	1.92430	−	0.755232i
$894$		0			0
$895$	67.6944	−	20.8809i	2.26277	−	0.697973i
$896$	−6.59430	−	0.246741i	−0.220300	−	0.00824305i
$897$		0			0
$898$	−2.33308	−	1.34701i	−0.0778560	−	0.0449502i
$899$	−9.30290	+	0.885362i	−0.310269	+	0.0295285i
$900$		0			0
$901$	1.20187	−	10.6669i	0.0400402	−	0.355367i
$902$	−16.8024	+	8.88031i	−0.559458	+	0.295682i
$903$		0			0
$904$	31.1977	+	12.2442i	1.03762	+	0.407236i
$905$	76.8395	+	11.5817i	2.55423	+	0.384989i
$906$		0			0
$907$	4.87330	+	5.66288i	0.161815	+	0.188033i	0.833026	−	0.553234i	$-0.186606\pi$
$907$	4.87330	+	5.66288i	0.161815	+	0.188033i	−0.671211	+	0.741267i	$0.734225\pi$
$908$	11.5570	−	5.56555i	0.383532	−	0.184699i
$909$		0			0
$910$	−0.505813	−	1.44553i	−0.0167676	−	0.0479189i
$911$	24.1576	−	6.47302i	0.800378	−	0.214461i	0.164628	−	0.986356i	$-0.447358\pi$
$911$	24.1576	−	6.47302i	0.800378	−	0.214461i	0.635750	+	0.771895i	$0.280691\pi$
$912$		0			0
$913$	−12.9674	−	17.5702i	−0.429159	−	0.581490i
$914$	14.8225	+	20.0837i	0.490283	+	0.664310i
$915$		0			0
$916$	−7.52266	+	2.01569i	−0.248556	+	0.0666003i
$917$	−3.14124	−	8.97715i	−0.103733	−	0.296452i
$918$		0			0
$919$	31.6896	−	15.2609i	1.04534	−	0.503410i	0.169260	−	0.985572i	$-0.445862\pi$
$919$	31.6896	−	15.2609i	1.04534	−	0.503410i	0.876082	+	0.482161i	$0.160148\pi$
$920$	30.5486	+	35.4981i	1.00716	+	1.17034i
$921$		0			0
$922$	−59.4251	−	8.95689i	−1.95706	−	0.294980i
$923$	−5.39097	−	2.11580i	−0.177446	−	0.0696425i
$924$		0			0
$925$	−80.7319	+	42.6681i	−2.65445	+	1.40292i
$926$	3.05892	−	27.1486i	0.100522	−	0.892160i
$927$		0			0
$928$	9.82184	−	26.5836i	0.322418	−	0.872648i
$929$	4.85046	+	2.80041i	0.159138	+	0.0918786i	0.577454	−	0.816423i	$-0.304046\pi$
$929$	4.85046	+	2.80041i	0.159138	+	0.0918786i	−0.418316	+	0.908302i	$0.637379\pi$
$930$		0			0
$931$	42.4180	+	1.58717i	1.39019	+	0.0520174i
$932$	−24.5018	+	7.55779i	−0.802582	+	0.247564i
$933$		0			0
$934$	−1.80720	+	0.709272i	−0.0591333	+	0.0232081i
$935$	46.0995	−	10.5219i	1.50762	−	0.344103i
$936$		0			0
$937$	−10.7173	−	22.2548i	−0.350120	−	0.727033i	0.649319	−	0.760516i	$-0.275054\pi$
$937$	−10.7173	−	22.2548i	−0.350120	−	0.727033i	−0.999439	+	0.0334837i	$0.989340\pi$
$938$	0.287672	+	7.68819i	0.00939282	+	0.251028i
$939$		0			0
$940$	38.2145	+	10.2396i	1.24642	+	0.333977i
$941$	−0.708850	−	9.45895i	−0.0231079	−	0.308353i	−0.996767	−	0.0803450i	$-0.974398\pi$
$941$	−0.708850	−	9.45895i	−0.0231079	−	0.308353i	0.973659	−	0.228008i	$-0.0732212\pi$
$942$		0			0
$943$	22.1521	+	9.66487i	0.721373	+	0.314732i
$944$	4.73359	−	9.82940i	0.154065	−	0.319920i
$945$		0			0
$946$	7.78376	−	2.72365i	0.253072	−	0.0885536i
$947$	59.3770	−	2.22173i	1.92949	−	0.0721966i	0.954999	−	0.296609i	$-0.0958557\pi$
$947$	59.3770	−	2.22173i	1.92949	−	0.0721966i	0.974494	+	0.224412i	$0.0720462\pi$
$948$		0			0
$949$	0.0396449	+	0.209528i	0.00128693	+	0.00680158i
$950$	−88.5177	+	82.1324i	−2.87189	+	2.66473i
$951$		0			0
$952$	3.53808	−	0.533280i	0.114670	−	0.0172837i
$953$	15.1319	+	3.45376i	0.490170	+	0.111878i	0.460460	−	0.887680i	$-0.347684\pi$
$953$	15.1319	+	3.45376i	0.490170	+	0.111878i	0.0297101	+	0.999559i	$0.490542\pi$
$954$		0			0
$955$	−68.5095	−	7.71917i	−2.21692	−	0.249786i
$956$	10.7188	−	18.5655i	0.346671	−	0.600452i
$957$		0			0
$958$	−33.9537	−	58.8096i	−1.09700	−	1.90005i
$959$	0.581972	+	1.33390i	0.0187929	+	0.0430737i
$960$		0			0
$961$	−19.0371	+	20.5172i	−0.614102	+	0.661844i
$962$	−3.62131	−	4.54097i	−0.116756	−	0.146407i
$963$		0			0
$964$	5.35836	+	23.4765i	0.172581	+	0.756128i
$965$	6.33215	−	5.44925i	0.203839	−	0.175418i
$966$		0			0
$967$	20.6198	−	39.0147i	0.663090	−	1.25463i	−0.291462	−	0.956582i	$-0.594142\pi$
$967$	20.6198	−	39.0147i	0.663090	−	1.25463i	0.954552	−	0.298044i	$-0.0963344\pi$
$968$	−1.77296	−	1.52576i	−0.0569851	−	0.0490397i
$969$		0			0
$970$	35.9566	+	52.7387i	1.15450	+	1.69334i
$971$	−5.19866	−	46.1394i	−0.166833	−	1.48068i	−0.746257	−	0.665658i	$-0.768151\pi$
$971$	−5.19866	−	46.1394i	−0.166833	−	1.48068i	0.579424	−	0.815027i	$-0.303278\pi$
$972$		0			0
$973$	1.05598	+	0.508531i	0.0338530	+	0.0163028i
$974$	2.21784	+	8.27708i	0.0710641	+	0.265215i
$975$		0			0
$976$	32.5720	+	17.2148i	1.04260	+	0.551032i
$977$	1.40916	−	2.06686i	0.0450830	−	0.0661247i	−0.803035	−	0.595931i	$-0.796783\pi$
$977$	1.40916	−	2.06686i	0.0450830	−	0.0661247i	0.848119	+	0.529807i	$0.177735\pi$
$978$		0			0
$979$	0.845822	−	2.74209i	0.0270326	−	0.0876375i
$980$	21.2542	+	16.9496i	0.678940	+	0.541437i
$981$		0			0
$982$	−3.84529	+	16.8473i	−0.122708	+	0.537619i
$983$	−28.3854	−	53.7078i	−0.905353	−	1.71301i	−0.671898	−	0.740643i	$-0.734521\pi$
$983$	−28.3854	−	53.7078i	−0.905353	−	1.71301i	−0.233455	−	0.972368i	$-0.575003\pi$
$984$		0			0
$985$	−51.1605	+	29.5375i	−1.63011	+	0.941143i
$986$	−5.92261	+	35.1528i	−0.188614	+	1.11949i
$987$		0			0
$988$	−2.08099	−	1.53584i	−0.0662051	−	0.0488616i
$989$	−8.87984	−	5.57957i	−0.282362	−	0.177420i
$990$		0			0
$991$	0.911519	−	0.726912i	0.0289554	−	0.0230911i	−0.608905	−	0.793243i	$-0.708391\pi$
$991$	0.911519	−	0.726912i	0.0289554	−	0.0230911i	0.637861	+	0.770152i	$0.279820\pi$
$992$	3.33638	+	8.50097i	0.105930	+	0.269906i
$993$		0			0
$994$	−13.4954	+	2.55347i	−0.428048	+	0.0809910i
$995$	−57.3222	−	39.0816i	−1.81724	−	1.23897i
$996$		0			0
$997$	−22.2279	−	4.20575i	−0.703965	−	0.133197i	−0.178409	−	0.983956i	$-0.557095\pi$
$997$	−22.2279	−	4.20575i	−0.703965	−	0.133197i	−0.525556	+	0.850759i	$0.676143\pi$
$998$	−51.0449	−	51.0449i	−1.61580	−	1.61580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.be.a.143.7		672
3.2	odd	2		261.2.x.a.56.22	yes	672
9.4	even	3		261.2.x.a.230.7	yes	672
9.5	odd	6	inner	783.2.be.a.665.22		672
29.14	odd	28	inner	783.2.be.a.710.22		672
87.14	even	28		261.2.x.a.101.7	yes	672
261.14	even	84	inner	783.2.be.a.449.7		672
261.130	odd	84		261.2.x.a.14.22	✓	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.22	✓	672	261.130	odd	84
261.2.x.a.56.22	yes	672	3.2	odd	2
261.2.x.a.101.7	yes	672	87.14	even	28
261.2.x.a.230.7	yes	672	9.4	even	3
783.2.be.a.143.7		672	1.1	even	1	trivial
783.2.be.a.449.7		672	261.14	even	84	inner
783.2.be.a.665.22		672	9.5	odd	6	inner
783.2.be.a.710.22		672	29.14	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.be (of order \(84\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03117 + 1.39718i) q^{2} +(-0.299298 - 0.970301i) q^{4} +(1.46016 - 3.72043i) q^{5} +(0.524586 + 0.161813i) q^{7} +(-1.61379 - 0.564688i) q^{8} +(3.69245 + 5.87649i) q^{10} +(0.576982 - 3.04942i) q^{11} +(-0.400833 + 0.0300383i) q^{13} +(-0.767018 + 0.566085i) q^{14} +(4.13100 - 2.81647i) q^{16} +(-2.69557 + 2.69557i) q^{17} +(-5.36550 + 3.37137i) q^{19} +(-4.04697 - 0.303278i) q^{20} +(3.66563 + 3.95061i) q^{22} +(1.02148 - 6.77709i) q^{23} +(-8.04430 - 7.46402i) q^{25} +(0.371356 - 0.591010i) q^{26} -0.557437i q^{28} +(-5.11766 - 1.67616i) q^{29} +(1.59052 - 0.693937i) q^{31} +(-0.196775 + 5.25892i) q^{32} +(-0.986616 - 6.54577i) q^{34} +(1.36800 - 1.71542i) q^{35} +(2.74830 - 7.85418i) q^{37} +(0.822313 - 10.9730i) q^{38} +(-4.45727 + 5.17945i) q^{40} +(-0.912701 + 3.40625i) q^{41} +(0.611906 - 1.40250i) q^{43} +(-3.13155 + 0.352841i) q^{44} +(8.41550 + 8.41550i) q^{46} +(-9.57858 - 1.81237i) q^{47} +(-5.53466 - 3.77347i) q^{49} +(18.7236 - 3.54269i) q^{50} +(0.149115 + 0.379938i) q^{52} +(-2.20154 + 1.75567i) q^{53} +(-10.5027 - 6.59928i) q^{55} +(-0.755196 - 0.557360i) q^{56} +(7.61906 - 5.42189i) q^{58} +(1.88972 - 1.09103i) q^{59} +(3.44312 + 6.51471i) q^{61} +(-0.670535 + 2.93781i) q^{62} +(0.673195 + 0.536855i) q^{64} +(-0.473526 + 1.53513i) q^{65} +(4.54628 - 6.66818i) q^{67} +(3.42229 + 1.80873i) q^{68} +(0.986111 + 3.68022i) q^{70} +(12.9810 + 6.25130i) q^{71} +(-0.0593993 - 0.527184i) q^{73} +(8.13976 + 11.9388i) q^{74} +(4.87713 + 4.19711i) q^{76} +(0.796115 - 1.50632i) q^{77} +(9.06925 - 7.80472i) q^{79} +(-4.44655 - 19.4816i) q^{80} +(-3.81799 - 4.78761i) q^{82} +(4.78588 - 5.15796i) q^{83} +(6.09271 + 13.9647i) q^{85} +(1.32857 + 2.30115i) q^{86} +(-2.65310 + 4.59530i) q^{88} +(0.918803 + 0.103524i) q^{89} +(-0.215132 - 0.0491025i) q^{91} +(-6.88155 + 1.03723i) q^{92} +(12.4093 - 11.5141i) q^{94} +(4.70845 + 24.8847i) q^{95} +(9.19060 - 0.343888i) q^{97} +(10.9794 - 3.84185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) \) 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Introduction

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