LMFDB - Embedded newform 741.2.d.a.740.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [741,2,Mod(740,741)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("741.740"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(741, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 741 = 3 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	741.d (of order $2$, degree $1$, 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:	$5.91691478978$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			740.10
Character	$\chi$	$=$	741.740
Dual form			741.2.d.a.740.77

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.19415i q^{2} +(-1.62296 + 0.604979i) q^{3} -2.81428 q^{4} +1.77589 q^{5} +(1.32741 + 3.56101i) q^{6} +2.44560i q^{7} +1.78666i q^{8} +(2.26800 - 1.96372i) q^{9} -3.89657i q^{10} -3.41871 q^{11} +(4.56747 - 1.70258i) q^{12} +(-3.55149 - 0.622039i) q^{13} +5.36600 q^{14} +(-2.88220 + 1.07438i) q^{15} -1.70838 q^{16} -0.383868i q^{17} +(-4.30868 - 4.97633i) q^{18} +(-2.15458 + 3.78917i) q^{19} -4.99786 q^{20} +(-1.47954 - 3.96911i) q^{21} +7.50114i q^{22} +1.45851i q^{23} +(-1.08089 - 2.89967i) q^{24} -1.84621 q^{25} +(-1.36485 + 7.79249i) q^{26} +(-2.49287 + 4.55912i) q^{27} -6.88260i q^{28} -4.42214 q^{29} +(2.35734 + 6.32398i) q^{30} -0.673992 q^{31} +7.32175i q^{32} +(5.54842 - 2.06825i) q^{33} -0.842262 q^{34} +4.34312i q^{35} +(-6.38279 + 5.52645i) q^{36} -5.01097 q^{37} +(8.31399 + 4.72747i) q^{38} +(6.14024 - 1.13903i) q^{39} +3.17291i q^{40} +3.03845i q^{41} +(-8.70880 + 3.24632i) q^{42} +2.64413 q^{43} +9.62120 q^{44} +(4.02772 - 3.48735i) q^{45} +3.20018 q^{46} -10.4132 q^{47} +(2.77263 - 1.03353i) q^{48} +1.01906 q^{49} +4.05085i q^{50} +(0.232232 + 0.623002i) q^{51} +(9.99489 + 1.75059i) q^{52} +8.49420 q^{53} +(10.0034 + 5.46972i) q^{54} -6.07125 q^{55} -4.36944 q^{56} +(1.20443 - 7.45314i) q^{57} +9.70283i q^{58} -10.9052i q^{59} +(8.11133 - 3.02360i) q^{60} +4.27333 q^{61} +1.47884i q^{62} +(4.80246 + 5.54661i) q^{63} +12.6482 q^{64} +(-6.30706 - 1.10468i) q^{65} +(-4.53804 - 12.1741i) q^{66} +5.69814 q^{67} +1.08031i q^{68} +(-0.882368 - 2.36710i) q^{69} +9.52944 q^{70} +13.1942i q^{71} +(3.50848 + 4.05213i) q^{72} -1.84337i q^{73} +10.9948i q^{74} +(2.99632 - 1.11692i) q^{75} +(6.06360 - 10.6638i) q^{76} -8.36078i q^{77} +(-2.49920 - 13.4726i) q^{78} +16.2314i q^{79} -3.03390 q^{80} +(1.28765 - 8.90741i) q^{81} +6.66681 q^{82} -12.3912 q^{83} +(4.16383 + 11.1702i) q^{84} -0.681708i q^{85} -5.80161i q^{86} +(7.17696 - 2.67530i) q^{87} -6.10805i q^{88} +5.81937i q^{89} +(-7.65175 - 8.83742i) q^{90} +(1.52126 - 8.68551i) q^{91} -4.10466i q^{92} +(1.09386 - 0.407751i) q^{93} +22.8481i q^{94} +(-3.82630 + 6.72915i) q^{95} +(-4.42951 - 11.8829i) q^{96} -8.97647 q^{97} -2.23596i q^{98} +(-7.75362 + 6.71336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) $ 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/741\mathbb{Z}\right)^\times$.

$n$	$40$	$248$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	2.19415i		−	1.55150i	−0.631043	−	0.775748i	$-0.717373\pi$
$2$		−	2.19415i		−	1.55150i	0.631043	−	0.775748i	$-0.282627\pi$
$3$	−1.62296	+	0.604979i	−0.937017	+	0.349285i
$3$	−1.62296	+	0.604979i	−0.937017	+	0.349285i
$4$	−2.81428			−1.40714
$5$	1.77589			0.794203			0.397102	−	0.917775i	$-0.370016\pi$
$5$	1.77589			0.794203			0.397102	+	0.917775i	$0.370016\pi$
$6$	1.32741	+	3.56101i	0.541914	+	1.45378i
$7$			2.44560i			0.924349i	0.886789	+	0.462174i	$0.152931\pi$
$7$			2.44560i			0.924349i	−0.886789	+	0.462174i	$0.847069\pi$
$8$			1.78666i			0.631678i
$9$	2.26800	−	1.96372i	0.756000	−	0.654572i
$10$		−	3.89657i		−	1.23220i
$11$	−3.41871			−1.03078			−0.515389	−	0.856956i	$-0.672353\pi$
$11$	−3.41871			−1.03078			−0.515389	+	0.856956i	$0.672353\pi$
$12$	4.56747	−	1.70258i	1.31851	−	0.491493i
$13$	−3.55149	−	0.622039i	−0.985006	−	0.172523i
$13$	−3.55149	−	0.622039i	−0.985006	−	0.172523i
$14$	5.36600			1.43412
$15$	−2.88220	+	1.07438i	−0.744182	+	0.277403i
$16$	−1.70838			−0.427095
$17$		−	0.383868i		−	0.0931016i	−0.998916	−	0.0465508i	$-0.985177\pi$
$17$		−	0.383868i		−	0.0931016i	0.998916	−	0.0465508i	$-0.0148229\pi$
$18$	−4.30868	−	4.97633i	−1.01557	−	1.17293i
$19$	−2.15458	+	3.78917i	−0.494295	+	0.869294i
$19$	−2.15458	+	3.78917i	−0.494295	+	0.869294i
$20$	−4.99786			−1.11756
$21$	−1.47954	−	3.96911i	−0.322861	−	0.866130i
$22$			7.50114i			1.59925i
$23$			1.45851i			0.304120i	0.988371	+	0.152060i	$0.0485907\pi$
$23$			1.45851i			0.304120i	−0.988371	+	0.152060i	$0.951409\pi$
$24$	−1.08089	−	2.89967i	−0.220636	−	0.591893i
$25$	−1.84621			−0.369241
$26$	−1.36485	+	7.79249i	−0.267668	+	1.52823i
$27$	−2.49287	+	4.55912i	−0.479752	+	0.877404i
$28$		−	6.88260i		−	1.30069i
$29$	−4.42214			−0.821171			−0.410585	−	0.911822i	$-0.634676\pi$
$29$	−4.42214			−0.821171			−0.410585	+	0.911822i	$0.634676\pi$
$30$	2.35734	+	6.32398i	0.430390	+	1.15460i
$31$	−0.673992			−0.121052			−0.0605262	−	0.998167i	$-0.519278\pi$
$31$	−0.673992			−0.121052			−0.0605262	+	0.998167i	$0.519278\pi$
$32$			7.32175i			1.29431i
$33$	5.54842	−	2.06825i	0.965857	−	0.360036i
$34$	−0.842262			−0.144447
$35$			4.34312i			0.734121i
$36$	−6.38279	+	5.52645i	−1.06380	+	0.921075i
$37$	−5.01097			−0.823799			−0.411900	−	0.911229i	$-0.635135\pi$
$37$	−5.01097			−0.823799			−0.411900	+	0.911229i	$0.635135\pi$
$38$	8.31399	+	4.72747i	1.34871	+	0.766897i
$39$	6.14024	−	1.13903i	0.983226	−	0.182391i
$40$			3.17291i			0.501681i
$41$			3.03845i			0.474526i	0.971445	+	0.237263i	$0.0762504\pi$
$41$			3.03845i			0.474526i	−0.971445	+	0.237263i	$0.923750\pi$
$42$	−8.70880	+	3.24632i	−1.34380	+	0.500918i
$43$	2.64413			0.403226			0.201613	−	0.979465i	$-0.435382\pi$
$43$	2.64413			0.403226			0.201613	+	0.979465i	$0.435382\pi$
$44$	9.62120			1.45045
$45$	4.02772	−	3.48735i	0.600418	−	0.519863i
$46$	3.20018			0.471841
$47$	−10.4132			−1.51892			−0.759459	−	0.650555i	$-0.774536\pi$
$47$	−10.4132			−1.51892			−0.759459	+	0.650555i	$0.774536\pi$
$48$	2.77263	−	1.03353i	0.400195	−	0.149178i
$49$	1.01906			0.145579
$50$			4.05085i			0.572876i
$51$	0.232232	+	0.623002i	0.0325190	+	0.0872377i
$52$	9.99489	+	1.75059i	1.38604	+	0.242764i
$53$	8.49420			1.16677			0.583384	−	0.812196i	$-0.301728\pi$
$53$	8.49420			1.16677			0.583384	+	0.812196i	$0.301728\pi$
$54$	10.0034	+	5.46972i	1.36129	+	0.744334i
$55$	−6.07125			−0.818648
$56$	−4.36944			−0.583891
$57$	1.20443	−	7.45314i	0.159531	−	0.987193i
$58$			9.70283i			1.27404i
$59$		−	10.9052i		−	1.41973i	−0.704337	−	0.709865i	$-0.748756\pi$
$59$		−	10.9052i		−	1.41973i	0.704337	−	0.709865i	$-0.251244\pi$
$60$	8.11133	−	3.02360i	1.04717	−	0.390346i
$61$	4.27333			0.547144			0.273572	−	0.961852i	$-0.411795\pi$
$61$	4.27333			0.547144			0.273572	+	0.961852i	$0.411795\pi$
$62$			1.47884i			0.187812i
$63$	4.80246	+	5.54661i	0.605053	+	0.698808i
$64$	12.6482			1.58103
$65$	−6.30706	−	1.10468i	−0.782295	−	0.137018i
$66$	−4.53804	−	12.1741i	−0.558594	−	1.49852i
$67$	5.69814			0.696138			0.348069	−	0.937469i	$-0.386837\pi$
$67$	5.69814			0.696138			0.348069	+	0.937469i	$0.386837\pi$
$68$			1.08031i			0.131007i
$69$	−0.882368	−	2.36710i	−0.106225	−	0.284966i
$70$	9.52944			1.13899
$71$			13.1942i			1.56587i	0.622105	+	0.782934i	$0.286278\pi$
$71$			13.1942i			1.56587i	−0.622105	+	0.782934i	$0.713722\pi$
$72$	3.50848	+	4.05213i	0.413479	+	0.477549i
$73$		−	1.84337i		−	0.215750i	−0.994164	−	0.107875i	$-0.965595\pi$
$73$		−	1.84337i		−	0.215750i	0.994164	−	0.107875i	$-0.0344046\pi$
$74$			10.9948i			1.27812i
$75$	2.99632	−	1.11692i	0.345985	−	0.128970i
$76$	6.06360	−	10.6638i	0.695543	−	1.22322i
$77$		−	8.36078i		−	0.952799i
$78$	−2.49920	−	13.4726i	−0.282979	−	1.52547i
$79$			16.2314i			1.82617i	0.407769	+	0.913085i	$0.366307\pi$
$79$			16.2314i			1.82617i	−0.407769	+	0.913085i	$0.633693\pi$
$80$	−3.03390			−0.339200
$81$	1.28765	−	8.90741i	0.143072	−	0.989712i
$82$	6.66681			0.736226
$83$	−12.3912			−1.36011			−0.680054	−	0.733162i	$-0.738044\pi$
$83$	−12.3912			−1.36011			−0.680054	+	0.733162i	$0.738044\pi$
$84$	4.16383	+	11.1702i	0.454311	+	1.21877i
$85$		−	0.681708i		−	0.0739416i
$86$		−	5.80161i		−	0.625604i
$87$	7.17696	−	2.67530i	0.769451	−	0.286823i
$88$		−	6.10805i		−	0.651120i
$89$			5.81937i			0.616852i	0.951248	+	0.308426i	$0.0998022\pi$
$89$			5.81937i			0.616852i	−0.951248	+	0.308426i	$0.900198\pi$
$90$	−7.65175	−	8.83742i	−0.806566	−	0.931546i
$91$	1.52126	−	8.68551i	0.159471	−	0.910489i
$92$		−	4.10466i		−	0.427940i
$93$	1.09386	−	0.407751i	0.113428	−	0.0422818i
$94$			22.8481i			2.35660i
$95$	−3.82630	+	6.72915i	−0.392571	+	0.690396i
$96$	−4.42951	−	11.8829i	−0.452085	−	1.21279i
$97$	−8.97647			−0.911422			−0.455711	−	0.890128i	$-0.650615\pi$
$97$	−8.97647			−0.911422			−0.455711	+	0.890128i	$0.650615\pi$
$98$		−	2.23596i		−	0.225866i
$99$	−7.75362	+	6.71336i	−0.779268	+	0.674718i
$100$	5.19574			0.519574
$101$		−	19.1114i		−	1.90165i	−0.309725	−	0.950826i	$-0.600237\pi$
$101$		−	19.1114i		−	1.90165i	0.309725	−	0.950826i	$-0.399763\pi$
$102$	1.36696	−	0.509551i	0.135349	−	0.0504531i
$103$			7.85248i			0.773728i	0.922137	+	0.386864i	$0.126442\pi$
$103$			7.85248i			0.773728i	−0.922137	+	0.386864i	$0.873558\pi$
$104$	1.11137	−	6.34529i	0.108979	−	0.622206i
$105$	−2.62750	−	7.04871i	−0.256417	−	0.687883i
$106$		−	18.6375i		−	1.81024i
$107$	−6.92645			−0.669605			−0.334803	−	0.942288i	$-0.608670\pi$
$107$	−6.92645			−0.669605			−0.334803	+	0.942288i	$0.608670\pi$
$108$	7.01563	−	12.8307i	0.675079	−	1.23463i
$109$	−6.11369			−0.585586			−0.292793	−	0.956176i	$-0.594585\pi$
$109$	−6.11369			−0.585586			−0.292793	+	0.956176i	$0.594585\pi$
$110$			13.3212i			1.27013i
$111$	8.13261	−	3.03154i	0.771913	−	0.287741i
$112$		−	4.17801i		−	0.394785i
$113$	−10.2489			−0.964134			−0.482067	−	0.876134i	$-0.660114\pi$
$113$	−10.2489			−0.964134			−0.482067	+	0.876134i	$0.660114\pi$
$114$	−16.3533	−	2.64270i	−1.53163	−	0.247512i
$115$			2.59016i			0.241533i
$116$	12.4451			1.15550
$117$	−9.27628	+	5.56333i	−0.857593	+	0.514330i
$118$	−23.9275			−2.20271
$119$	0.938785			0.0860583
$120$	−1.91954	−	5.14950i	−0.175230	−	0.470083i
$121$	0.687548			0.0625044
$122$		−	9.37631i		−	0.848892i
$123$	−1.83820	−	4.93129i	−0.165745	−	0.444639i
$124$	1.89680			0.170338
$125$	−12.1581			−1.08746
$126$	12.1701	−	10.5373i	1.08420	−	0.938737i
$127$		−	6.06054i		−	0.537786i	−0.963170	−	0.268893i	$-0.913342\pi$
$127$		−	6.06054i		−	0.537786i	0.963170	−	0.268893i	$-0.0866577\pi$
$128$		−	13.1086i		−	1.15865i
$129$	−4.29132	+	1.59964i	−0.377829	+	0.140841i
$130$	−2.42382	+	13.8386i	−0.212583	+	1.21373i
$131$		−	1.81315i		−	0.158416i	−0.996858	−	0.0792080i	$-0.974761\pi$
$131$		−	1.81315i		−	0.158416i	0.996858	−	0.0792080i	$-0.0252391\pi$
$132$	−15.6148	+	5.82063i	−1.35910	+	0.506621i
$133$	−9.26677	−	5.26924i	−0.803531	−	0.456901i
$134$		−	12.5026i		−	1.08006i
$135$	−4.42706	+	8.09652i	−0.381021	+	0.696837i
$136$	0.685839			0.0588102
$137$	−6.67925			−0.570647			−0.285324	−	0.958431i	$-0.592101\pi$
$137$	−6.67925			−0.570647			−0.285324	+	0.958431i	$0.592101\pi$
$138$	−5.19377	+	1.93605i	−0.442123	+	0.164807i
$139$	16.4442			1.39478			0.697390	−	0.716692i	$-0.254345\pi$
$139$	16.4442			1.39478			0.697390	+	0.716692i	$0.254345\pi$
$140$		−	12.2228i		−	1.03301i
$141$	16.9002	−	6.29976i	1.42325	−	0.530536i
$142$	28.9501			2.42944
$143$	12.1415	+	2.12657i	1.01532	+	0.177833i
$144$	−3.87460	+	3.35477i	−0.322884	+	0.279564i
$145$	−7.85325			−0.652177
$146$	−4.04462			−0.334735
$147$	−1.65389	+	0.616508i	−0.136410	+	0.0508487i
$148$	14.1023			1.15920
$149$	9.81281			0.803897			0.401948	−	0.915662i	$-0.368333\pi$
$149$	9.81281			0.803897			0.401948	+	0.915662i	$0.368333\pi$
$150$	−2.45068	−	6.57436i	−0.200097	−	0.536794i
$151$	18.2661			1.48647			0.743237	−	0.669028i	$-0.233290\pi$
$151$	18.2661			1.48647			0.743237	+	0.669028i	$0.233290\pi$
$152$	−6.76993	−	3.84949i	−0.549114	−	0.312235i
$153$	−0.753807	−	0.870612i	−0.0609417	−	0.0703848i
$154$	−18.3448			−1.47826
$155$	−1.19694			−0.0961403
$156$	−17.2804	+	3.20556i	−1.38354	+	0.256650i
$157$	2.52379			0.201420			0.100710	−	0.994916i	$-0.467889\pi$
$157$	2.52379			0.201420			0.100710	+	0.994916i	$0.467889\pi$
$158$	35.6140			2.83330
$159$	−13.7858	+	5.13882i	−1.09328	+	0.407535i
$160$			13.0026i			1.02795i
$161$	−3.56693			−0.281113
$162$	−19.5442	−	2.82529i	−1.53554	−	0.221975i
$163$		−	0.430567i		−	0.0337246i	−0.999858	−	0.0168623i	$-0.994632\pi$
$163$		−	0.430567i		−	0.0337246i	0.999858	−	0.0168623i	$-0.00536769\pi$
$164$		−	8.55106i		−	0.667726i
$165$	9.85340	−	3.67298i	0.767086	−	0.285941i
$166$			27.1881i			2.11020i
$167$		−	12.3352i		−	0.954528i	−0.878760	−	0.477264i	$-0.841629\pi$
$167$		−	12.3352i		−	0.954528i	0.878760	−	0.477264i	$-0.158371\pi$
$168$	7.09143	−	2.64342i	0.547115	−	0.203944i
$169$	12.2261	+	4.41833i	0.940472	+	0.339872i
$170$	−1.49577			−0.114720
$171$	2.55425	+	12.8248i	0.195329	+	0.980738i
$172$	−7.44133			−0.567396
$173$	9.87383			0.750693			0.375347	−	0.926885i	$-0.377524\pi$
$173$	9.87383			0.750693			0.375347	+	0.926885i	$0.377524\pi$
$174$	−5.87001	−	15.7473i	−0.445004	−	1.19380i
$175$		−	4.51507i		−	0.341307i
$176$	5.84045			0.440240
$177$	6.59740	+	17.6986i	0.495891	+	1.33031i
$178$	12.7686			0.957044
$179$	−10.2315			−0.764738			−0.382369	−	0.924010i	$-0.624892\pi$
$179$	−10.2315			−0.764738			−0.382369	+	0.924010i	$0.624892\pi$
$180$	−11.3352	+	9.81438i	−0.844872	+	0.731521i
$181$		−	22.5031i		−	1.67264i	−0.548242	−	0.836320i	$-0.684703\pi$
$181$		−	22.5031i		−	1.67264i	0.548242	−	0.836320i	$-0.315297\pi$
$182$	−19.0573	−	3.33786i	−1.41262	−	0.247419i
$183$	−6.93544	+	2.58528i	−0.512683	+	0.191109i
$184$	−2.60585			−0.192106
$185$	−8.89895			−0.654264
$186$	−0.894666	−	2.40009i	−0.0656001	−	0.175983i
$187$			1.31233i			0.0959671i
$188$	29.3056			2.13733
$189$	−11.1498	−	6.09655i	−0.811027	−	0.443458i
$190$	14.7648	+	8.39548i	1.07115	+	0.609072i
$191$		−	1.21409i		−	0.0878487i	−0.999035	−	0.0439244i	$-0.986014\pi$
$191$		−	1.21409i		−	0.0878487i	0.999035	−	0.0439244i	$-0.0139861\pi$
$192$	−20.5276	+	7.65192i	−1.48145	+	0.552230i
$193$	−5.41054			−0.389459			−0.194729	−	0.980857i	$-0.562383\pi$
$193$	−5.41054			−0.389459			−0.194729	+	0.980857i	$0.562383\pi$
$194$			19.6957i			1.41407i
$195$	10.9044	−	2.02280i	0.780881	−	0.144856i
$196$	−2.86791			−0.204851
$197$	−8.47680			−0.603947			−0.301974	−	0.953316i	$-0.597645\pi$
$197$	−8.47680			−0.603947			−0.301974	+	0.953316i	$0.597645\pi$
$198$	14.7301	+	17.0126i	1.04682	+	1.20903i
$199$	−7.18421			−0.509275			−0.254637	−	0.967037i	$-0.581956\pi$
$199$	−7.18421			−0.509275			−0.254637	+	0.967037i	$0.581956\pi$
$200$		−	3.29853i		−	0.233241i
$201$	−9.24785	+	3.44726i	−0.652293	+	0.243151i
$202$	−41.9332			−2.95041
$203$		−	10.8148i		−	0.759048i
$204$	−0.653566	−	1.75330i	−0.0457588	−	0.122756i
$205$			5.39596i			0.376870i
$206$	17.2295			1.20044
$207$	2.86410	+	3.30790i	0.199068	+	0.229915i
$208$	6.06729	+	1.06268i	0.420691	+	0.0736836i
$209$	7.36588	−	12.9540i	0.509508	−	0.896050i
$210$	−15.4659	+	5.76511i	−1.06725	+	0.397831i
$211$		−	13.5675i		−	0.934025i	−0.884251	−	0.467012i	$-0.845330\pi$
$211$		−	13.5675i		−	0.934025i	0.884251	−	0.467012i	$-0.154670\pi$
$212$	−23.9051			−1.64181
$213$	−7.98224	−	21.4137i	−0.546934	−	1.46724i
$214$			15.1977i			1.03889i
$215$	4.69569			0.320243
$216$	−8.14558	−	4.45389i	−0.554237	−	0.303049i
$217$		−	1.64831i		−	0.111895i
$218$			13.4143i			0.908534i
$219$	1.11520	+	2.99171i	0.0753581	+	0.202161i
$220$	17.0862			1.15195
$221$	−0.238781	+	1.36330i	−0.0160621	+	0.0917056i
$222$	−6.65164	−	17.8442i	−0.446429	−	1.19762i
$223$	−25.3386			−1.69680			−0.848400	−	0.529356i	$-0.822434\pi$
$223$	−25.3386			−1.69680			−0.848400	+	0.529356i	$0.822434\pi$
$224$	−17.9060			−1.19640
$225$	−4.18719	+	3.62542i	−0.279146	+	0.241695i
$226$			22.4876i			1.49585i
$227$			6.71358i			0.445596i	0.974865	+	0.222798i	$0.0715191\pi$
$227$			6.71358i			0.445596i	−0.974865	+	0.222798i	$0.928481\pi$
$228$	−3.38961	+	20.9752i	−0.224482	+	1.38912i
$229$			2.51631i			0.166283i	0.996538	+	0.0831413i	$0.0264953\pi$
$229$			2.51631i			0.166283i	−0.996538	+	0.0831413i	$0.973505\pi$
$230$	5.68318			0.374738
$231$	5.05810	+	13.5692i	0.332798	+	0.892788i
$232$		−	7.90084i		−	0.518716i
$233$		−	5.09736i		−	0.333939i	−0.985962	−	0.166969i	$-0.946602\pi$
$233$		−	5.09736i		−	0.333939i	0.985962	−	0.166969i	$-0.0533981\pi$
$234$	12.2068	+	20.3535i	0.797981	+	1.33055i
$235$	−18.4927			−1.20633
$236$			30.6902i			1.99776i
$237$	−9.81964	−	26.3428i	−0.637854	−	1.71115i
$238$		−	2.05983i		−	0.133519i
$239$	−0.142934			−0.00924564			−0.00462282	−	0.999989i	$-0.501471\pi$
$239$	−0.142934			−0.00924564			−0.00462282	+	0.999989i	$0.501471\pi$
$240$	4.92390	−	1.83545i	0.317836	−	0.118478i
$241$	17.4195			1.12209			0.561045	−	0.827786i	$-0.310400\pi$
$241$	17.4195			1.12209			0.561045	+	0.827786i	$0.310400\pi$
$242$		−	1.50858i		−	0.0969753i
$243$	3.29900	+	15.2354i	0.211631	+	0.977350i
$244$	−12.0264			−0.769908
$245$	1.80973			0.115620
$246$	−10.8200	+	4.03328i	−0.689856	+	0.257153i
$247$	10.0090	−	12.1169i	0.636856	−	0.770983i
$248$		−	1.20419i		−	0.0764662i
$249$	20.1104	−	7.49640i	1.27444	−	0.475065i
$250$			26.6767i			1.68718i
$251$		−	27.1809i		−	1.71564i	−0.513947	−	0.857822i	$-0.671817\pi$
$251$		−	27.1809i		−	1.71564i	0.513947	−	0.857822i	$-0.328183\pi$
$252$	−13.5155	−	15.6097i	−0.851394	−	0.983321i
$253$		−	4.98621i		−	0.313481i
$254$	−13.2977			−0.834372
$255$	0.412419	+	1.10638i	0.0258267	+	0.0692845i
$256$	−3.46571			−0.216607
$257$	26.5783			1.65791			0.828955	−	0.559315i	$-0.188936\pi$
$257$	26.5783			1.65791			0.828955	+	0.559315i	$0.188936\pi$
$258$	3.50986	+	9.41578i	0.218514	+	0.586201i
$259$		−	12.2548i		−	0.761478i
$260$	17.7499	+	3.10887i	1.10080	+	0.192804i
$261$	−10.0294	+	8.68382i	−0.620805	+	0.537515i
$262$	−3.97832			−0.245782
$263$			20.6763i			1.27495i	0.770470	+	0.637477i	$0.220022\pi$
$263$			20.6763i			1.27495i	−0.770470	+	0.637477i	$0.779978\pi$
$264$	3.69524	+	9.91312i	0.227427	+	0.610110i
$265$	15.0848			0.926652
$266$	−11.5615	+	20.3327i	−0.708880	+	1.24668i
$267$	−3.52060	−	9.44461i	−0.215457	−	0.578001i
$268$	−16.0362			−0.979565
$269$	−19.2226			−1.17202			−0.586011	−	0.810303i	$-0.699302\pi$
$269$	−19.2226			−1.17202			−0.586011	+	0.810303i	$0.699302\pi$
$270$	17.7649	+	9.71363i	1.08114	+	0.591153i
$271$		−	26.4640i		−	1.60757i	−0.594917	−	0.803787i	$-0.702815\pi$
$271$		−	26.4640i		−	1.60757i	0.594917	−	0.803787i	$-0.297185\pi$
$272$			0.655792i			0.0397632i
$273$	2.78561	+	15.0166i	0.168593	+	0.908844i
$274$			14.6553i			0.885357i
$275$	6.31163			0.380606
$276$	2.48323	+	6.66169i	0.149473	+	0.400987i
$277$	−12.2304			−0.734854			−0.367427	−	0.930052i	$-0.619761\pi$
$277$	−12.2304			−0.734854			−0.367427	+	0.930052i	$0.619761\pi$
$278$		−	36.0810i		−	2.16400i
$279$	−1.52861	+	1.32353i	−0.0915156	+	0.0792375i
$280$	−7.75965			−0.463728
$281$			9.72685i			0.580255i	0.956988	+	0.290128i	$0.0936978\pi$
$281$			9.72685i			0.580255i	−0.956988	+	0.290128i	$0.906302\pi$
$282$	−13.8226	−	37.0815i	−0.823124	−	2.20817i
$283$	5.88646			0.349914			0.174957	−	0.984576i	$-0.444021\pi$
$283$	5.88646			0.349914			0.174957	+	0.984576i	$0.444021\pi$
$284$		−	37.1323i		−	2.20340i
$285$	2.13894	−	13.2360i	0.126700	−	0.784032i
$286$	4.66601	−	26.6402i	0.275907	−	1.57527i
$287$	−7.43083			−0.438628
$288$	14.3778	+	16.6057i	0.847222	+	0.978502i
$289$	16.8526			0.991332
$290$			17.2312i			1.01185i
$291$	14.5684	−	5.43058i	0.854018	−	0.318346i
$292$			5.18775i			0.303590i
$293$			23.0301i			1.34543i	0.739900	+	0.672716i	$0.234873\pi$
$293$			23.0301i			1.34543i	−0.739900	+	0.672716i	$0.765127\pi$
$294$	1.35271	+	3.62887i	0.0788916	+	0.211640i
$295$		−	19.3664i		−	1.12755i
$296$		−	8.95288i		−	0.520376i
$297$	8.52238	−	15.5863i	0.494518	−	0.904409i
$298$		−	21.5308i		−	1.24724i
$299$	0.907250	−	5.17988i	0.0524676	−	0.299560i
$300$	−8.43248	+	3.14332i	−0.486850	+	0.181479i
$301$			6.46648i			0.372721i
$302$		−	40.0785i		−	2.30626i
$303$	11.5620	+	31.0170i	0.664219	+	1.78188i
$304$	3.68084	−	6.47333i	0.211111	−	0.371271i
$305$	7.58897			0.434543
$306$	−1.91025	+	1.65396i	−0.109202	+	0.0945508i
$307$	−1.90392			−0.108662			−0.0543311	−	0.998523i	$-0.517303\pi$
$307$	−1.90392			−0.108662			−0.0543311	+	0.998523i	$0.517303\pi$
$308$			23.5296i			1.34072i
$309$	−4.75059	−	12.7443i	−0.270252	−	0.724996i
$310$			2.62626i			0.149161i
$311$			17.7602i			1.00709i	0.863970	+	0.503543i	$0.167971\pi$
$311$			17.7602i			1.00709i	−0.863970	+	0.503543i	$0.832029\pi$
$312$	2.03506	+	10.9705i	0.115212	+	0.621082i
$313$	−28.6638			−1.62018			−0.810088	−	0.586308i	$-0.800581\pi$
$313$	−28.6638			−1.62018			−0.810088	+	0.586308i	$0.800581\pi$
$314$		−	5.53756i		−	0.312503i
$315$	8.52865	+	9.85019i	0.480535	+	0.554995i
$316$		−	45.6796i		−	2.56968i
$317$			2.34835i			0.131896i	0.997823	+	0.0659481i	$0.0210072\pi$
$317$			2.34835i			0.131896i	−0.997823	+	0.0659481i	$0.978993\pi$
$318$	11.2753	+	30.2480i	0.632289	+	1.69622i
$319$	15.1180			0.846445
$320$	22.4619			1.25566
$321$	11.2414	−	4.19036i	0.627431	−	0.233883i
$322$			7.82636i			0.436146i
$323$	1.45454	+	0.827074i	0.0809327	+	0.0460196i
$324$	−3.62380	+	25.0680i	−0.201322	+	1.39266i
$325$	6.55677	+	1.14841i	0.363704	+	0.0637024i
$326$	−0.944728			−0.0523236
$327$	9.92228	−	3.69866i	0.548703	−	0.204536i
$328$	−5.42867			−0.299748
$329$		−	25.4664i		−	1.40401i
$330$	−8.05907	−	21.6198i	−0.443637	−	1.19013i
$331$	19.1482			1.05248			0.526240	−	0.850336i	$-0.323601\pi$
$331$	19.1482			1.05248			0.526240	+	0.850336i	$0.323601\pi$
$332$	34.8723			1.91386
$333$	−11.3649	+	9.84013i	−0.622792	+	0.539236i
$334$	−27.0653			−1.48095
$335$	10.1193			0.552875
$336$	2.52761	+	6.78074i	0.137892	+	0.369920i
$337$			7.90353i			0.430533i	0.976555	+	0.215266i	$0.0690620\pi$
$337$			7.90353i			0.430533i	−0.976555	+	0.215266i	$0.930938\pi$
$338$	9.69447	−	26.8259i	0.527310	−	1.45914i
$339$	16.6335	−	6.20036i	0.903409	−	0.336757i
$340$			1.91852i			0.104046i
$341$	2.30418			0.124778
$342$	28.1395	−	5.60441i	1.52161	−	0.303052i
$343$			19.6114i			1.05891i
$344$			4.72415i			0.254709i
$345$	−1.56699	−	4.20372i	−0.0843640	−	0.226321i
$346$		−	21.6646i		−	1.16470i
$347$			27.8343i			1.49422i	0.664700	+	0.747111i	$0.268559\pi$
$347$			27.8343i			1.49422i	−0.664700	+	0.747111i	$0.731441\pi$
$348$	−20.1980	+	7.52906i	−1.08273	+	0.403600i
$349$		−	20.2631i		−	1.08466i	−0.840166	−	0.542330i	$-0.817542\pi$
$349$		−	20.2631i		−	1.08466i	0.840166	−	0.542330i	$-0.182458\pi$
$350$	−9.90674			−0.529537
$351$	11.6893	−	14.6410i	0.623931	−	0.781480i
$352$		−	25.0309i		−	1.33415i
$353$	15.6171			0.831215			0.415607	−	0.909544i	$-0.363569\pi$
$353$	15.6171			0.831215			0.415607	+	0.909544i	$0.363569\pi$
$354$	38.8334	−	14.4757i	2.06397	−	0.769373i
$355$			23.4316i			1.24362i
$356$		−	16.3774i		−	0.867998i
$357$	−1.52361	+	0.567946i	−0.0806381	+	0.0300589i
$358$			22.4494i			1.18649i
$359$	14.4480			0.762537			0.381269	−	0.924464i	$-0.375487\pi$
$359$	14.4480			0.762537			0.381269	+	0.924464i	$0.375487\pi$
$360$	6.23069	+	7.19616i	0.328386	+	0.379271i
$361$	−9.71556	−	16.3281i	−0.511345	−	0.859375i
$362$	−49.3750			−2.59509
$363$	−1.11586	+	0.415952i	−0.0585676	+	0.0218318i
$364$	−4.28125	+	24.4435i	−0.224398	+	1.28119i
$365$		−	3.27362i		−	0.171349i
$366$	5.67248	+	15.2174i	0.296505	+	0.795425i
$367$	−37.3420			−1.94924			−0.974619	−	0.223871i	$-0.928131\pi$
$367$	−37.3420			−1.94924			−0.974619	+	0.223871i	$0.928131\pi$
$368$		−	2.49169i		−	0.129888i
$369$	5.96665	+	6.89121i	0.310612	+	0.358742i
$370$			19.5256i			1.01509i
$371$			20.7734i			1.07850i
$372$	−3.07844	+	1.14753i	−0.159609	+	0.0594965i
$373$		−	23.1218i		−	1.19720i	−0.801048	−	0.598599i	$-0.795724\pi$
$373$		−	23.1218i		−	1.19720i	0.801048	−	0.598599i	$-0.204276\pi$
$374$	2.87945			0.148893
$375$	19.7322	−	7.35542i	1.01896	−	0.379832i
$376$		−	18.6048i		−	0.959468i
$377$	15.7052	+	2.75074i	0.808858	+	0.141671i
$378$	−13.3767	+	24.4643i	−0.688024	+	1.25831i
$379$	12.7725			0.656079			0.328039	−	0.944664i	$-0.393612\pi$
$379$	12.7725			0.656079			0.328039	+	0.944664i	$0.393612\pi$
$380$	10.7683	−	18.9377i	0.552402	−	0.971485i
$381$	3.66650	+	9.83601i	0.187840	+	0.503914i
$382$	−2.66390			−0.136297
$383$		−	16.8247i		−	0.859702i	−0.902900	−	0.429851i	$-0.858566\pi$
$383$		−	16.8247i		−	0.859702i	0.902900	−	0.429851i	$-0.141434\pi$
$384$	7.93043	+	21.2747i	0.404698	+	1.08567i
$385$		−	14.8478i		−	0.756716i
$386$			11.8715i			0.604244i
$387$	5.99689	−	5.19232i	0.304839	−	0.263940i
$388$	25.2623			1.28250
$389$			32.4646i			1.64602i	0.568026	+	0.823011i	$0.307707\pi$
$389$			32.4646i			1.64602i	−0.568026	+	0.823011i	$0.692293\pi$
$390$	−4.43832	−	23.9259i	−0.224743	−	1.21153i
$391$	0.559875			0.0283141
$392$			1.82070i			0.0919594i
$393$	1.09692	+	2.94268i	0.0553323	+	0.148438i
$394$			18.5993i			0.937022i
$395$			28.8251i			1.45035i
$396$	21.8209	−	18.8933i	1.09654	−	0.949424i
$397$			17.6007i			0.883354i	0.897174	+	0.441677i	$0.145616\pi$
$397$			17.6007i			0.883354i	−0.897174	+	0.441677i	$0.854384\pi$
$398$			15.7632i			0.790138i
$399$	18.2274	+	2.94555i	0.912511	+	0.147462i
$400$	3.15402			0.157701
$401$		−	9.21560i		−	0.460205i	−0.973166	−	0.230102i	$-0.926094\pi$
$401$		−	9.21560i		−	0.460205i	0.973166	−	0.230102i	$-0.0739061\pi$
$402$	7.56379	+	20.2911i	0.377247	+	1.01203i
$403$	2.39367	+	0.419249i	0.119237	+	0.0208843i
$404$			53.7848i			2.67589i
$405$	2.28672	−	15.8186i	0.113628	−	0.786033i
$406$	−23.7292			−1.17766
$407$	17.1310			0.849155
$408$	−1.11309	+	0.414919i	−0.0551062	+	0.0205415i
$409$	16.2917			0.805574			0.402787	−	0.915294i	$-0.368042\pi$
$409$	16.2917			0.805574			0.402787	+	0.915294i	$0.368042\pi$
$410$	11.8395			0.584713
$411$	10.8402	−	4.04081i	0.534706	−	0.199319i
$412$		−	22.0991i		−	1.08874i
$413$	26.6696			1.31233
$414$	7.25802	−	6.28425i	0.356712	−	0.308854i
$415$	−22.0054			−1.08020
$416$	4.55442	−	26.0031i	0.223299	−	1.27491i
$417$	−26.6883	+	9.94841i	−1.30693	+	0.487176i
$418$	−28.4231	−	16.1618i	−1.39022	−	0.790501i
$419$			21.2135i			1.03635i	0.855275	+	0.518174i	$0.173388\pi$
$419$			21.2135i			1.03635i	−0.855275	+	0.518174i	$0.826612\pi$
$420$	7.39452	+	19.8371i	0.360816	+	0.967949i
$421$	9.14400			0.445651			0.222826	−	0.974858i	$-0.428472\pi$
$421$	9.14400			0.445651			0.222826	+	0.974858i	$0.428472\pi$
$422$	−29.7691			−1.44914
$423$	−23.6171	+	20.4485i	−1.14830	+	0.994241i
$424$			15.1762i			0.737022i
$425$			0.708698i			0.0343769i
$426$	−46.9849	+	17.5142i	−2.27642	+	0.848567i
$427$			10.4508i			0.505752i
$428$	19.4930			0.942229
$429$	−20.9917	+	3.89402i	−1.01349	+	0.188005i
$430$		−	10.3030i		−	0.496857i
$431$		−	18.1126i		−	0.872453i	−0.899837	−	0.436226i	$-0.856315\pi$
$431$		−	18.1126i		−	0.872453i	0.899837	−	0.436226i	$-0.143685\pi$
$432$	4.25876	−	7.78872i	0.204900	−	0.374735i
$433$			11.4600i			0.550731i	0.961340	+	0.275366i	$0.0887989\pi$
$433$			11.4600i			0.550731i	−0.961340	+	0.275366i	$0.911201\pi$
$434$	−3.61664			−0.173604
$435$	12.7455	−	4.75105i	0.611100	−	0.227796i
$436$	17.2057			0.824002
$437$	−5.52653	−	3.14248i	−0.264370	−	0.150325i
$438$	6.56425	−	2.44691i	0.313652	−	0.116918i
$439$		−	0.442499i		−	0.0211193i	−0.999944	−	0.0105597i	$-0.996639\pi$
$439$		−	0.442499i		−	0.0211193i	0.999944	−	0.0105597i	$-0.00336131\pi$
$440$		−	10.8472i		−	0.517122i
$441$	2.31122	−	2.00114i	0.110058	−	0.0952922i
$442$	2.99128	+	0.523920i	0.142281	+	0.0249203i
$443$			7.68937i			0.365333i	0.983175	+	0.182666i	$0.0584728\pi$
$443$			7.68937i			0.365333i	−0.983175	+	0.182666i	$0.941527\pi$
$444$	−22.8875	+	8.53160i	−1.08619	+	0.404892i
$445$			10.3346i			0.489906i
$446$			55.5967i			2.63258i
$447$	−15.9258	+	5.93655i	−0.753265	+	0.280789i
$448$			30.9325i			1.46142i
$449$			32.9051i			1.55289i	0.630188	+	0.776443i	$0.282978\pi$
$449$			32.9051i			1.55289i	−0.630188	+	0.776443i	$0.717022\pi$
$450$	7.95471	+	9.18732i	0.374988	+	0.433094i
$451$		−	10.3876i		−	0.489132i
$452$	28.8432			1.35667
$453$	−29.6451	+	11.0506i	−1.39285	+	0.519203i
$454$	14.7306			0.691341
$455$	2.70159	−	15.4245i	0.126653	−	0.723113i
$456$	13.3162	+	2.15190i	0.623588	+	0.100772i
$457$			4.84822i			0.226790i	0.993550	+	0.113395i	$0.0361726\pi$
$457$			4.84822i			0.226790i	−0.993550	+	0.113395i	$0.963827\pi$
$458$	5.52116			0.257987
$459$	1.75010	+	0.956931i	0.0816877	+	0.0446657i
$460$		−	7.28943i		−	0.339871i
$461$	−39.4754			−1.83855			−0.919276	−	0.393614i	$-0.871225\pi$
$461$	−39.4754			−1.83855			−0.919276	+	0.393614i	$0.871225\pi$
$462$	29.7728	−	11.0982i	1.38516	−	0.516335i
$463$		−	36.5463i		−	1.69845i	−0.528029	−	0.849226i	$-0.677069\pi$
$463$		−	36.5463i		−	1.69845i	0.528029	−	0.849226i	$-0.322931\pi$
$464$	7.55469			0.350718
$465$	1.94258	−	0.724122i	0.0900850	−	0.0335804i
$466$	−11.1843			−0.518105
$467$		−	29.3316i		−	1.35731i	−0.734459	−	0.678653i	$-0.762564\pi$
$467$		−	29.3316i		−	1.35731i	0.734459	−	0.678653i	$-0.237436\pi$
$468$	26.1061	−	15.6568i	1.20675	−	0.723734i
$469$			13.9353i			0.643474i
$470$			40.5757i			1.87162i
$471$	−4.09601	+	1.52684i	−0.188734	+	0.0703531i
$472$	19.4838			0.896813
$473$	−9.03950			−0.415637
$474$	−57.8001	+	21.5457i	−2.65485	+	0.989628i
$475$	3.97780	−	6.99558i	0.182514	−	0.320979i
$476$	−2.64201			−0.121096
$477$	19.2649	−	16.6802i	0.882077	−	0.763734i
$478$			0.313619i			0.0143446i
$479$	−1.88926			−0.0863225			−0.0431612	−	0.999068i	$-0.513743\pi$
$479$	−1.88926			−0.0863225			−0.0431612	+	0.999068i	$0.513743\pi$
$480$	−7.86633	−	21.1028i	−0.359047	−	0.963205i
$481$	17.7964	+	3.11702i	0.811447	+	0.142124i
$482$		−	38.2210i		−	1.74092i
$483$	5.78898	−	2.15792i	0.263408	−	0.0981886i
$484$	−1.93495			−0.0879525
$485$	−15.9412			−0.723855
$486$	33.4287	−	7.23850i	1.51635	−	0.328345i
$487$	−23.1347			−1.04833			−0.524167	−	0.851615i	$-0.675623\pi$
$487$	−23.1347			−1.04833			−0.524167	+	0.851615i	$0.675623\pi$
$488$			7.63497i			0.345619i
$489$	0.260484	+	0.698793i	0.0117795	+	0.0316005i
$490$		−	3.97082i		−	0.179384i
$491$			9.27794i			0.418707i	0.977840	+	0.209354i	$0.0671360\pi$
$491$			9.27794i			0.418707i	−0.977840	+	0.209354i	$0.932864\pi$
$492$	5.17322	+	13.8780i	0.233227	+	0.625670i
$493$			1.69752i			0.0764523i
$494$	−26.5864	−	21.9612i	−1.19618	−	0.988080i
$495$	−13.7696	+	11.9222i	−0.618898	+	0.535864i
$496$	1.15143			0.0517009
$497$	−32.2678			−1.44741
$498$	−16.4482	−	44.1251i	−0.737062	−	1.97729i
$499$			10.8652i			0.486395i	0.969977	+	0.243197i	$0.0781963\pi$
$499$			10.8652i			0.486395i	−0.969977	+	0.243197i	$0.921804\pi$
$500$	34.2164			1.53020
$501$	7.46256	+	20.0196i	0.333402	+	0.894409i
$502$	−59.6389			−2.66181
$503$			30.4683i			1.35851i	0.733901	+	0.679257i	$0.237698\pi$
$503$			30.4683i			1.35851i	−0.733901	+	0.679257i	$0.762302\pi$
$504$	−9.90989	+	8.58033i	−0.441421	+	0.382198i
$505$		−	33.9397i		−	1.51030i
$506$	−10.9405			−0.486364
$507$	−22.5155	+	0.225784i	−0.999950	+	0.0100274i
$508$			17.0561i			0.756740i
$509$			7.44698i			0.330082i	0.986287	+	0.165041i	$0.0527756\pi$
$509$			7.44698i			0.330082i	−0.986287	+	0.165041i	$0.947224\pi$
$510$	2.42757	−	0.904908i	0.107495	−	0.0400700i
$511$	4.50813			0.199428
$512$		−	18.6129i		−	0.822582i
$513$	−11.9042	−	19.2689i	−0.525583	−	0.850742i
$514$		−	58.3168i		−	2.57224i
$515$			13.9452i			0.614497i
$516$	12.0770	−	4.50185i	0.531659	−	0.198183i
$517$	35.5996			1.56567
$518$	−26.8889			−1.18143
$519$	−16.0248	+	5.97346i	−0.703412	+	0.262206i
$520$	1.97367	−	11.2685i	0.0865513	−	0.494158i
$521$	−20.7909			−0.910866			−0.455433	−	0.890270i	$-0.650515\pi$
$521$	−20.7909			−0.910866			−0.455433	+	0.890270i	$0.650515\pi$
$522$	19.0536	+	22.0060i	0.833953	+	0.963177i
$523$		−	27.3557i		−	1.19618i	−0.801429	−	0.598090i	$-0.795927\pi$
$523$		−	27.3557i		−	1.19618i	0.801429	−	0.598090i	$-0.204073\pi$
$524$			5.10272i			0.222914i
$525$	2.73153	+	7.32778i	0.119214	+	0.319811i
$526$	45.3668			1.97809
$527$			0.258724i			0.0112702i
$528$	−9.47881	+	3.53335i	−0.412512	+	0.153769i
$529$	20.8728			0.907511
$530$		−	33.0983i		−	1.43770i
$531$	−21.4146	−	24.7329i	−0.929316	−	1.07332i
$532$	26.0793	+	14.8291i	1.13068	+	0.642924i
$533$	1.89004	−	10.7910i	0.0818666	−	0.467411i
$534$	−20.7229	+	7.72471i	−0.896766	+	0.334281i
$535$	−12.3006			−0.531803
$536$			10.1806i			0.439735i
$537$	16.6053	−	6.18984i	0.716572	−	0.267111i
$538$			42.1772i			1.81839i
$539$	−3.48385			−0.150060
$540$	12.4590	−	22.7859i	0.536150	−	0.980548i
$541$			25.3385i			1.08939i	0.838635	+	0.544694i	$0.183354\pi$
$541$			25.3385i			1.08939i	−0.838635	+	0.544694i	$0.816646\pi$
$542$	−58.0659			−2.49414
$543$	13.6139	+	36.5216i	0.584228	+	1.56729i
$544$	2.81058			0.120503
$545$	−10.8573			−0.465074
$546$	32.9486	−	6.11205i	1.41007	−	0.261571i
$547$			18.3421i			0.784253i	0.919911	+	0.392127i	$0.128260\pi$
$547$			18.3421i			0.784253i	−0.919911	+	0.392127i	$0.871740\pi$
$548$	18.7973			0.802981
$549$	9.69191	−	8.39160i	0.413641	−	0.358145i
$550$		−	13.8486i		−	0.590508i
$551$	9.52786	−	16.7562i	0.405900	−	0.713839i
$552$	4.22920	−	1.57649i	0.180007	−	0.0670998i
$553$	−39.6954			−1.68802
$554$			26.8353i			1.14012i
$555$	14.4426	−	5.38368i	0.613056	−	0.228525i
$556$	−46.2787			−1.96265
$557$	−20.7675			−0.879949			−0.439974	−	0.898010i	$-0.645012\pi$
$557$	−20.7675			−0.879949			−0.439974	+	0.898010i	$0.645012\pi$
$558$	2.90401	+	3.35400i	0.122937	+	0.141986i
$559$	−9.39060	−	1.64475i	−0.397180	−	0.0695656i
$560$		−	7.41969i		−	0.313539i
$561$	−0.793933	−	2.12986i	−0.0335199	−	0.0899228i
$562$	21.3422			0.900264
$563$	−3.44142			−0.145039			−0.0725193	−	0.997367i	$-0.523104\pi$
$563$	−3.44142			−0.145039			−0.0725193	+	0.997367i	$0.523104\pi$
$564$	−47.5619	+	17.7293i	−2.00272	+	0.746538i
$565$	−18.2009			−0.765718
$566$		−	12.9158i		−	0.542890i
$567$	21.7839	+	3.14906i	0.914839	+	0.132248i
$568$	−23.5736			−0.989124
$569$	−5.96717			−0.250157			−0.125078	−	0.992147i	$-0.539918\pi$
$569$	−5.96717			−0.250157			−0.125078	+	0.992147i	$0.539918\pi$
$570$	−29.0417	−	4.69315i	−1.21642	−	0.196575i
$571$	−35.2314			−1.47439			−0.737194	−	0.675681i	$-0.763850\pi$
$571$	−35.2314			−1.47439			−0.737194	+	0.675681i	$0.763850\pi$
$572$	−34.1696	−	5.98477i	−1.42870	−	0.250236i
$573$	0.734502	+	1.97043i	0.0306842	+	0.0823157i
$574$			16.3043i			0.680530i
$575$		−	2.69271i		−	0.112294i
$576$	28.6862	−	24.8375i	1.19526	−	1.03490i
$577$			47.1180i			1.96155i	0.195148	+	0.980774i	$0.437481\pi$
$577$			47.1180i			1.96155i	−0.195148	+	0.980774i	$0.562519\pi$
$578$		−	36.9772i		−	1.53805i
$579$	8.78109	−	3.27326i	0.364929	−	0.136032i
$580$	22.1013			0.917704
$581$		−	30.3038i		−	1.25721i
$582$	−11.9155	−	31.9653i	−0.493913	−	1.32501i
$583$	−29.0392			−1.20268
$584$	3.29346			0.136284
$585$	−16.4737	+	9.87987i	−0.681103	+	0.408482i
$586$	50.5314			2.08743
$587$	−34.3331			−1.41708			−0.708539	−	0.705672i	$-0.750645\pi$
$587$	−34.3331			−1.41708			−0.708539	+	0.705672i	$0.750645\pi$
$588$	4.65451	−	1.73503i	0.191949	−	0.0715513i
$589$	1.45217	−	2.55387i	0.0598356	−	0.105230i
$590$	−42.4927			−1.74940
$591$	13.7575	−	5.12829i	0.565908	−	0.210950i
$592$	8.56065			0.351840
$593$	−8.31173			−0.341322			−0.170661	−	0.985330i	$-0.554590\pi$
$593$	−8.31173			−0.341322			−0.170661	+	0.985330i	$0.554590\pi$
$594$	−34.1986	−	18.6993i	−1.40319	−	0.767244i
$595$	1.66718			0.0683478
$596$	−27.6160			−1.13120
$597$	11.6597	−	4.34630i	0.477199	−	0.177882i
$598$	−11.3654	−	1.99064i	−0.464766	−	0.0814033i
$599$	35.2949			1.44211			0.721056	−	0.692877i	$-0.243657\pi$
$599$	35.2949			1.44211			0.721056	+	0.692877i	$0.243657\pi$
$600$	1.99554	+	5.35339i	0.0814677	+	0.218551i
$601$			28.6869i			1.17016i	0.810974	+	0.585082i	$0.198938\pi$
$601$			28.6869i			1.17016i	−0.810974	+	0.585082i	$0.801062\pi$
$602$	14.1884			0.578276
$603$	12.9234	−	11.1895i	0.526280	−	0.455672i
$604$	−51.4059			−2.09168
$605$	1.22101			0.0496412
$606$	68.0559	−	25.3687i	2.76458	−	1.03053i
$607$			36.6064i			1.48581i	0.669399	+	0.742903i	$0.266552\pi$
$607$			36.6064i			1.48581i	−0.669399	+	0.742903i	$0.733448\pi$
$608$	−27.7433	−	15.7753i	−1.12514	−	0.639773i
$609$	6.54271	+	17.5519i	0.265124	+	0.711241i
$610$		−	16.6513i		−	0.674193i
$611$	36.9823	+	6.47741i	1.49614	+	0.262048i
$612$	2.12142	+	2.45015i	0.0857535	+	0.0990413i
$613$		−	23.9494i		−	0.967306i	−0.875260	−	0.483653i	$-0.839310\pi$
$613$		−	23.9494i		−	0.967306i	0.875260	−	0.483653i	$-0.160690\pi$
$614$			4.17747i			0.168589i
$615$	−3.26445	−	8.75743i	−0.131635	−	0.353134i
$616$	14.9378			0.601862
$617$	34.3448			1.38267			0.691335	−	0.722534i	$-0.257023\pi$
$617$	34.3448			1.38267			0.691335	+	0.722534i	$0.257023\pi$
$618$	−27.9628	+	10.4235i	−1.12483	+	0.419294i
$619$			33.3883i			1.34199i	0.741461	+	0.670995i	$0.234133\pi$
$619$			33.3883i			1.34199i	−0.741461	+	0.670995i	$0.765867\pi$
$620$	3.36852			0.135283
$621$	−6.64953	−	3.63587i	−0.266836	−	0.145902i
$622$	38.9684			1.56249
$623$	−14.2318			−0.570186
$624$	−10.4899	+	1.94590i	−0.419931	+	0.0778983i
$625$	−12.3605			−0.494420
$626$			62.8927i			2.51370i
$627$	−4.11760	+	25.4801i	−0.164441	+	1.01758i
$628$	−7.10265			−0.283427
$629$			1.92355i			0.0766970i
$630$	21.6128	−	18.7131i	0.861073	−	0.745548i
$631$			31.6249i			1.25897i	0.777014	+	0.629483i	$0.216733\pi$
$631$			31.6249i			1.25897i	−0.777014	+	0.629483i	$0.783267\pi$
$632$	−28.9998			−1.15355
$633$	8.20805	+	22.0195i	0.326241	+	0.875196i
$634$	5.15262			0.204636
$635$		−	10.7629i		−	0.427111i
$636$	38.7970	−	14.4621i	1.53840	−	0.573459i
$637$	−3.61917	−	0.633893i	−0.143397	−	0.0251158i
$638$		−	33.1711i		−	1.31326i
$639$	25.9097	+	29.9245i	1.02497	+	1.18380i
$640$		−	23.2795i		−	0.920201i
$641$	−2.12035			−0.0837488			−0.0418744	−	0.999123i	$-0.513333\pi$
$641$	−2.12035			−0.0837488			−0.0418744	+	0.999123i	$0.513333\pi$
$642$	−9.19427	−	24.6652i	−0.362869	−	0.973458i
$643$		−	18.8098i		−	0.741787i	−0.928675	−	0.370893i	$-0.879052\pi$
$643$		−	18.8098i		−	0.741787i	0.928675	−	0.370893i	$-0.120948\pi$
$644$	10.0383			0.395566
$645$	−7.62092	+	2.84080i	−0.300073	+	0.111856i
$646$	1.81472	−	3.19147i	0.0713993	−	0.125567i
$647$			15.3126i			0.601998i	0.953624	+	0.300999i	$0.0973202\pi$
$647$			15.3126i			0.601998i	−0.953624	+	0.300999i	$0.902680\pi$
$648$	15.9145	+	2.30058i	0.625180	+	0.0903753i
$649$			37.2815i			1.46343i
$650$	2.51979	−	14.3865i	0.0988341	−	0.564286i
$651$	0.997195	+	2.67514i	0.0390831	+	0.104847i
$652$			1.21174i			0.0474553i
$653$			18.1328i			0.709591i	0.934944	+	0.354796i	$0.115450\pi$
$653$			18.1328i			0.709591i	−0.934944	+	0.354796i	$0.884550\pi$
$654$	−8.11540	−	21.7709i	−0.317337	−	0.851311i
$655$		−	3.21997i		−	0.125814i
$656$		−	5.19083i		−	0.202668i
$657$	−3.61985	−	4.18075i	−0.141224	−	0.163107i
$658$	−55.8771			−2.17832
$659$	4.10302			0.159831			0.0799154	−	0.996802i	$-0.474535\pi$
$659$	4.10302			0.159831			0.0799154	+	0.996802i	$0.474535\pi$
$660$	−27.7303	+	10.3368i	−1.07940	+	0.402360i
$661$	26.3364			1.02437			0.512184	−	0.858876i	$-0.328837\pi$
$661$	26.3364			1.02437			0.512184	+	0.858876i	$0.328837\pi$
$662$		−	42.0140i		−	1.63292i
$663$	−0.437238	−	2.35704i	−0.0169809	−	0.0915399i
$664$		−	22.1388i		−	0.859150i
$665$	−16.4568	−	9.35760i	−0.638167	−	0.362872i
$666$	21.5907	+	24.9362i	0.836622	+	0.966260i
$667$		−	6.44973i		−	0.249735i
$668$			34.7148i			1.34316i
$669$	41.1236	−	15.3293i	1.58993	−	0.592667i
$670$		−	22.2032i		−	0.857784i
$671$	−14.6093			−0.563984
$672$	29.0608	−	10.8328i	1.12104	−	0.417884i
$673$		−	24.6386i		−	0.949748i	−0.880054	−	0.474874i	$-0.842494\pi$
$673$		−	24.6386i		−	0.949748i	0.880054	−	0.474874i	$-0.157506\pi$
$674$	17.3415			0.667970
$675$	4.60234	−	8.41708i	0.177144	−	0.323974i
$676$	−34.4078	−	12.4344i	−1.32338	−	0.478247i
$677$	23.9665			0.921109			0.460555	−	0.887631i	$-0.347651\pi$
$677$	23.9665			0.921109			0.460555	+	0.887631i	$0.347651\pi$
$678$	−13.6045	−	36.4964i	−0.522478	−	1.40164i
$679$		−	21.9528i		−	0.842472i
$680$	1.21798			0.0467073
$681$	−4.06158	−	10.8959i	−0.155640	−	0.417531i
$682$		−	5.05571i		−	0.193593i
$683$			15.9954i			0.612047i	0.952024	+	0.306023i	$0.0989986\pi$
$683$			15.9954i			0.612047i	−0.952024	+	0.306023i	$0.901001\pi$
$684$	−7.18839	−	36.0926i	−0.274855	−	1.38004i
$685$	−11.8616			−0.453210
$686$	43.0303			1.64290
$687$	−1.52232	−	4.08387i	−0.0580800	−	0.155810i
$688$	−4.51718			−0.172216
$689$	−30.1671	−	5.28373i	−1.14927	−	0.201294i
$690$	−9.22358	+	3.43821i	−0.351136	+	0.130890i
$691$			17.5009i			0.665764i	0.942968	+	0.332882i	$0.108021\pi$
$691$			17.5009i			0.665764i	−0.942968	+	0.332882i	$0.891979\pi$
$692$	−27.7877			−1.05633
$693$	−16.4182	−	18.9622i	−0.623675	−	0.720316i
$694$	61.0725			2.31828
$695$	29.2032			1.10774
$696$	4.77985	+	12.8227i	0.181180	+	0.486045i
$697$	1.16636			0.0441792
$698$	−44.4602			−1.68285
$699$	3.08380	+	8.27281i	0.116640	+	0.312906i
$700$			12.7067i			0.480268i
$701$		−	23.5942i		−	0.891139i	−0.895247	−	0.445570i	$-0.853001\pi$
$701$		−	23.5942i		−	0.891139i	0.895247	−	0.445570i	$-0.146999\pi$
$702$	−32.1245	−	25.6481i	−1.21246	−	0.968026i
$703$	10.7966	−	18.9874i	0.407200	−	0.716124i
$704$	−43.2406			−1.62969
$705$	30.0129	−	11.1877i	1.13035	−	0.421353i
$706$		−	34.2662i		−	1.28963i
$707$	46.7387			1.75779
$708$	−18.5669	−	49.8090i	−0.697788	−	1.87194i
$709$		−	28.8737i		−	1.08438i	−0.840257	−	0.542188i	$-0.817596\pi$
$709$		−	28.8737i		−	1.08438i	0.840257	−	0.542188i	$-0.182404\pi$
$710$	51.4123			1.92947
$711$	31.8738	+	36.8127i	1.19536	+	1.38058i
$712$	−10.3972			−0.389652
$713$		−	0.983023i		−	0.0368145i
$714$	1.24616	+	3.34303i	0.0466363	+	0.125110i
$715$	21.5620	+	3.77656i	0.806373	+	0.141235i
$716$	28.7943			1.07609
$717$	0.231977	−	0.0864722i	0.00866332	−	0.00322937i
$718$		−	31.7011i		−	1.18307i
$719$			45.0706i			1.68085i	0.541928	+	0.840425i	$0.317694\pi$
$719$			45.0706i			1.68085i	−0.541928	+	0.840425i	$0.682306\pi$
$720$	−6.88088	+	5.95771i	−0.256435	+	0.222031i
$721$	−19.2040			−0.715194
$722$	−35.8263	+	21.3174i	−1.33332	+	0.793350i
$723$	−28.2712	+	10.5384i	−1.05142	+	0.391929i
$724$			63.3300i			2.35364i
$725$	8.16418			0.303210
$726$	0.912661	+	2.44837i	0.0338720	+	0.0908674i
$727$	−42.5861			−1.57943			−0.789715	−	0.613474i	$-0.789772\pi$
$727$	−42.5861			−1.57943			−0.789715	+	0.613474i	$0.789772\pi$
$728$	15.5180	+	2.71796i	0.575136	+	0.100734i
$729$	−14.5712	−	22.7306i	−0.539675	−	0.841873i
$730$	−7.18281			−0.265848
$731$		−	1.01500i		−	0.0375410i
$732$	19.5183	−	7.27570i	0.721417	−	0.268918i
$733$			48.9006i			1.80618i	0.429448	+	0.903092i	$0.358708\pi$
$733$			48.9006i			1.80618i	−0.429448	+	0.903092i	$0.641292\pi$
$734$			81.9339i			3.02423i
$735$	−2.93713	+	1.09485i	−0.108338	+	0.0403842i
$736$	−10.6788			−0.393627
$737$	−19.4803			−0.717564
$738$	15.1203	−	13.0917i	0.556587	−	0.481913i
$739$		−	21.2118i		−	0.780287i	−0.920754	−	0.390144i	$-0.872425\pi$
$739$		−	21.2118i		−	0.780287i	0.920754	−	0.390144i	$-0.127575\pi$
$740$	25.0442			0.920642
$741$	−8.91367	+	25.7205i	−0.327452	+	0.944868i
$742$	45.5799			1.67329
$743$		−	5.22071i		−	0.191529i	−0.995404	−	0.0957647i	$-0.969470\pi$
$743$		−	5.22071i		−	0.191529i	0.995404	−	0.0957647i	$-0.0305296\pi$
$744$	0.728511	+	1.95435i	0.0267085	+	0.0716501i
$745$	17.4265			0.638458
$746$	−50.7325			−1.85745
$747$	−28.1032	+	24.3327i	−1.02824	+	0.890288i
$748$		−	3.69327i		−	0.135039i
$749$		−	16.9393i		−	0.618949i
$750$	−16.1389	−	43.2953i	−0.589308	−	1.58092i
$751$		−	14.0346i		−	0.512131i	−0.966659	−	0.256065i	$-0.917574\pi$
$751$		−	14.0346i		−	0.512131i	0.966659	−	0.256065i	$-0.0824262\pi$
$752$	17.7897			0.648722
$753$	16.4439	+	44.1135i	0.599249	+	1.60759i
$754$	6.03554	−	34.4595i	0.219801	−	1.25494i
$755$	32.4386			1.18056
$756$	31.3786	+	17.1574i	1.14123	+	0.624009i
$757$	25.8857			0.940832			0.470416	−	0.882445i	$-0.344104\pi$
$757$	25.8857			0.940832			0.470416	+	0.882445i	$0.344104\pi$
$758$		−	28.0247i		−	1.01790i
$759$	3.01656	+	8.09243i	0.109494	+	0.293736i
$760$	−12.0227	−	6.83629i	−0.436108	−	0.247978i
$761$	33.6515			1.21987			0.609933	−	0.792453i	$-0.291196\pi$
$761$	33.6515			1.21987			0.609933	+	0.792453i	$0.291196\pi$
$762$	21.5817	−	8.04484i	0.781821	−	0.291434i
$763$		−	14.9516i		−	0.541285i
$764$			3.41680i			0.123616i
$765$	−1.33868	−	1.54611i	−0.0484001	−	0.0558998i
$766$	−36.9159			−1.33382
$767$	−6.78344	+	38.7295i	−0.244936	+	1.39844i
$768$	5.62472	−	2.09669i	0.202964	−	0.0756576i
$769$		−	2.31025i		−	0.0833097i	−0.999132	−	0.0416548i	$-0.986737\pi$
$769$		−	2.31025i		−	0.0833097i	0.999132	−	0.0416548i	$-0.0132630\pi$
$770$	−32.5783			−1.17404
$771$	−43.1356	+	16.0793i	−1.55349	+	0.579083i
$772$	15.2268			0.548024
$773$		−	31.9021i		−	1.14744i	−0.819052	−	0.573720i	$-0.805500\pi$
$773$		−	31.9021i		−	1.14744i	0.819052	−	0.573720i	$-0.194500\pi$
$774$	−11.3927	−	13.1581i	−0.409503	−	0.472956i
$775$	1.24433			0.0446975
$776$		−	16.0379i		−	0.575725i
$777$	7.41392	+	19.8891i	0.265973	+	0.713517i
$778$	71.2322			2.55380
$779$	−11.5132	−	6.54659i	−0.412503	−	0.234556i
$780$	−30.6881	+	5.69273i	−1.09881	+	0.203832i
$781$		−	45.1072i		−	1.61406i
$782$		−	1.22845i		−	0.0439292i
$783$	11.0238	−	20.1611i	0.393959	−	0.720498i
$784$	−1.74093			−0.0621762
$785$	4.48198			0.159969
$786$	6.45666	−	2.40680i	0.230302	−	0.0858479i
$787$	−21.3222			−0.760056			−0.380028	−	0.924975i	$-0.624086\pi$
$787$	−21.3222			−0.760056			−0.380028	+	0.924975i	$0.624086\pi$
$788$	23.8561			0.849839
$789$	−12.5087	−	33.5568i	−0.445322	−	1.19465i
$790$	63.2466			2.25021
$791$		−	25.0646i		−	0.891196i
$792$	−11.9945	−	13.8531i	−0.426205	−	0.492247i
$793$	−15.1767	−	2.65818i	−0.538940	−	0.0943947i
$794$	38.6185			1.37052
$795$	−24.4820	+	9.12599i	−0.868288	+	0.323666i
$796$	20.2184			0.716622
$797$	−41.3353			−1.46417			−0.732085	−	0.681213i	$-0.761453\pi$
$797$	−41.3353			−1.46417			−0.732085	+	0.681213i	$0.761453\pi$
$798$	6.46298	−	39.9936i	0.228787	−	1.41576i
$799$			3.99728i			0.141414i
$800$		−	13.5174i		−	0.477914i
$801$	11.4276	+	13.1983i	0.403774	+	0.466340i
$802$	−20.2204			−0.714006
$803$			6.30193i			0.222390i
$804$	26.0261	−	9.70155i	0.917868	−	0.342147i
$805$	−6.33448			−0.223261
$806$	0.919895	−	5.25207i	0.0324019	−	0.184996i
$807$	31.1975	−	11.6293i	1.09820	−	0.409370i
$808$	34.1454			1.20123
$809$			15.9126i			0.559458i	0.960079	+	0.279729i	$0.0902446\pi$
$809$			15.9126i			0.559458i	−0.960079	+	0.279729i	$0.909755\pi$
$810$	−34.7084	−	5.01740i	−1.21953	−	0.176294i
$811$	−46.4285			−1.63033			−0.815163	−	0.579232i	$-0.803353\pi$
$811$	−46.4285			−1.63033			−0.815163	+	0.579232i	$0.803353\pi$
$812$			30.4358i			1.06809i
$813$	16.0102	+	42.9500i	0.561501	+	1.50632i
$814$		−	37.5880i		−	1.31746i
$815$		−	0.764641i		−	0.0267842i
$816$	−0.396740	−	1.06432i	−0.0138887	−	0.0372588i
$817$	−5.69699	+	10.0190i	−0.199313	+	0.350522i
$818$		−	35.7464i		−	1.24984i
$819$	−13.6057	−	22.6860i	−0.475420	−	0.792715i
$820$		−	15.1858i		−	0.530310i
$821$	12.8136			0.447197			0.223598	−	0.974681i	$-0.428220\pi$
$821$	12.8136			0.447197			0.223598	+	0.974681i	$0.428220\pi$
$822$	−8.86613	−	23.7849i	−0.309242	−	0.829594i
$823$	−34.9116			−1.21694			−0.608472	−	0.793576i	$-0.708217\pi$
$823$	−34.9116			−1.21694			−0.608472	+	0.793576i	$0.708217\pi$
$824$	−14.0297			−0.488747
$825$	−10.2435	+	3.81841i	−0.356634	+	0.132940i
$826$		−	58.5171i		−	2.03607i
$827$		−	10.5979i		−	0.368526i	−0.982877	−	0.184263i	$-0.941010\pi$
$827$		−	10.5979i		−	0.368526i	0.982877	−	0.184263i	$-0.0589899\pi$
$828$	−8.06038	−	9.30936i	−0.280117	−	0.323523i
$829$			35.9849i			1.24981i	0.780702	+	0.624904i	$0.214862\pi$
$829$			35.9849i			1.24981i	−0.780702	+	0.624904i	$0.785138\pi$
$830$			48.2831i			1.67593i
$831$	19.8495	−	7.39914i	0.688570	−	0.256673i
$832$	−44.9200	−	7.86770i	−1.55732	−	0.272763i
$833$		−	0.391183i		−	0.0135537i
$834$	21.8283	+	58.5581i	0.755852	+	2.02770i
$835$		−	21.9060i		−	0.758089i
$836$	−20.7297	+	36.4563i	−0.716950	+	1.26087i
$837$	1.68017	−	3.07281i	0.0580752	−	0.106212i
$838$	46.5455			1.60789
$839$		−	26.0904i		−	0.900741i	−0.892842	−	0.450371i	$-0.851292\pi$
$839$		−	26.0904i		−	0.900741i	0.892842	−	0.450371i	$-0.148708\pi$
$840$	12.5936	−	4.69443i	0.434521	−	0.161973i
$841$	−9.44468			−0.325679
$842$		−	20.0633i		−	0.691427i
$843$	−5.88455	−	15.7863i	−0.202675	−	0.543709i
$844$			38.1827i			1.31430i
$845$	21.7123	+	7.84648i	0.746926	+	0.269927i
$846$	44.8671	+	51.8194i	1.54256	+	1.78159i
$847$			1.68147i			0.0577758i
$848$	−14.5113			−0.498321
$849$	−9.55349	+	3.56119i	−0.327875	+	0.122220i
$850$	1.55499			0.0533357
$851$		−	7.30855i		−	0.250534i
$852$	22.4643	+	60.2643i	0.769614	+	2.06462i
$853$			8.28443i			0.283653i	0.989891	+	0.141827i	$0.0452976\pi$
$853$			8.28443i			0.283653i	−0.989891	+	0.141827i	$0.954702\pi$
$854$	22.9307			0.784672
$855$	4.53608	+	22.7755i	0.155131	+	0.778905i
$856$		−	12.3752i		−	0.422975i
$857$	−16.7955			−0.573725			−0.286862	−	0.957972i	$-0.592612\pi$
$857$	−16.7955			−0.573725			−0.286862	+	0.957972i	$0.592612\pi$
$858$	8.54404	+	46.0589i	0.291689	+	1.57242i
$859$	−31.3596			−1.06998			−0.534988	−	0.844859i	$-0.679684\pi$
$859$	−31.3596			−1.06998			−0.534988	+	0.844859i	$0.679684\pi$
$860$	−13.2150			−0.450628
$861$	12.0599	−	4.49550i	0.411002	−	0.153206i
$862$	−39.7417			−1.35361
$863$			33.0619i			1.12544i	0.826648	+	0.562720i	$0.190245\pi$
$863$			33.0619i			1.12544i	−0.826648	+	0.562720i	$0.809755\pi$
$864$	−33.3808	−	18.2521i	−1.13564	−	0.620950i
$865$	17.5349			0.596203
$866$	25.1449			0.854457
$867$	−27.3512	+	10.1955i	−0.928895	+	0.346257i
$868$			4.63881i			0.157452i
$869$		−	55.4902i		−	1.88238i
$870$	−10.4245	−	27.9655i	−0.353424	−	0.948120i
$871$	−20.2369	−	3.54447i	−0.685700	−	0.120100i
$872$		−	10.9231i		−	0.369902i
$873$	−20.3586	+	17.6272i	−0.689035	+	0.596591i
$874$	−6.89506	+	12.1260i	−0.233229	+	0.410169i
$875$		−	29.7339i		−	1.00519i
$876$	−3.13848	−	8.41952i	−0.106040	−	0.284469i
$877$	39.3895			1.33009			0.665045	−	0.746803i	$-0.268412\pi$
$877$	39.3895			1.33009			0.665045	+	0.746803i	$0.268412\pi$
$878$	−0.970908			−0.0327666
$879$	−13.9327	−	37.3769i	−0.469940	−	1.26069i
$880$	10.3720			0.349640
$881$			8.71472i			0.293606i	0.989166	+	0.146803i	$0.0468984\pi$
$881$			8.71472i			0.293606i	−0.989166	+	0.146803i	$0.953102\pi$
$882$	−4.39079	−	5.07116i	−0.147845	−	0.170755i
$883$	7.76314			0.261250			0.130625	−	0.991432i	$-0.458302\pi$
$883$	7.76314			0.261250			0.130625	+	0.991432i	$0.458302\pi$
$884$	0.671997	−	3.83671i	0.0226017	−	0.129043i
$885$	11.7163	+	31.4309i	0.393838	+	1.05654i
$886$	16.8716			0.566813
$887$	7.76176			0.260614			0.130307	−	0.991474i	$-0.458404\pi$
$887$	7.76176			0.260614			0.130307	+	0.991474i	$0.458404\pi$
$888$	5.41631	+	14.5302i	0.181760	+	0.487601i
$889$	14.8216			0.497101
$890$	22.6756			0.760087
$891$	−4.40208	+	30.4518i	−0.147475	+	1.02017i
$892$	71.3101			2.38764
$893$	22.4360	−	39.4573i	0.750794	−	1.32039i
$894$	13.0257	+	34.9436i	0.435643	+	1.16869i
$895$	−18.1700			−0.607357
$896$	32.0583			1.07099
$897$	1.66129	+	8.95560i	0.0554688	+	0.299019i
$898$	72.1986			2.40930
$899$	2.98048			0.0994047
$900$	11.7839	−	10.2030i	0.392798	−	0.340099i
$901$		−	3.26065i		−	0.108628i
$902$	−22.7919			−0.758886
$903$	−3.91209	−	10.4948i	−0.130186	−	0.349246i
$904$		−	18.3112i		−	0.609022i
$905$		−	39.9630i		−	1.32842i
$906$	24.2467	+	65.0458i	0.805542	+	2.16100i
$907$		−	36.4997i		−	1.21195i	−0.795483	−	0.605976i	$-0.792783\pi$
$907$		−	36.4997i		−	1.21195i	0.795483	−	0.605976i	$-0.207217\pi$
$908$		−	18.8939i		−	0.627017i
$909$	−37.5293	−	43.3446i	−1.24477	−	1.43765i
$910$	−33.8437	−	5.92769i	−1.12191	−	0.196501i
$911$	−2.12265			−0.0703267			−0.0351633	−	0.999382i	$-0.511195\pi$
$911$	−2.12265			−0.0703267			−0.0351633	+	0.999382i	$0.511195\pi$
$912$	−2.05763	+	12.7328i	−0.0681348	+	0.421625i
$913$	42.3618			1.40197
$914$	10.6377			0.351864
$915$	−12.3166	+	4.59117i	−0.407174	+	0.151780i
$916$		−	7.08161i		−	0.233983i
$917$	4.43424			0.146432
$918$	2.09965	−	3.83998i	0.0692987	−	0.126738i
$919$	17.5086			0.577554			0.288777	−	0.957396i	$-0.406751\pi$
$919$	17.5086			0.577554			0.288777	+	0.957396i	$0.406751\pi$
$920$	−4.62772			−0.152571
$921$	3.08998	−	1.15183i	0.101818	−	0.0379541i
$922$			86.6148i			2.85251i
$923$	8.20734	−	46.8592i	0.270148	−	1.54239i
$924$	−14.2349	−	38.1876i	−0.468294	−	1.25628i
$925$	9.25129			0.304180
$926$	−80.1881			−2.63514
$927$	15.4200	+	17.8094i	0.506460	+	0.584938i
$928$		−	32.3778i		−	1.06285i
$929$	26.7441			0.877446			0.438723	−	0.898622i	$-0.355431\pi$
$929$	26.7441			0.877446			0.438723	+	0.898622i	$0.355431\pi$
$930$	−1.58883	−	4.26231i	−0.0520998	−	0.139767i
$931$	−2.19564	+	3.86137i	−0.0719592	+	0.126551i
$932$			14.3454i			0.469899i
$933$	−10.7445	−	28.8240i	−0.351760	−	0.943657i
$934$	−64.3579			−2.10586
$935$			2.33056i			0.0762174i
$936$	−9.93975	−	16.5735i	−0.324891	−	0.541722i
$937$	46.8435			1.53031			0.765156	−	0.643845i	$-0.222662\pi$
$937$	46.8435			1.53031			0.765156	+	0.643845i	$0.222662\pi$
$938$	30.5762			0.998348
$939$	46.5203	−	17.3410i	1.51813	−	0.565903i
$940$	52.0437			1.69748
$941$		−	17.6976i		−	0.576926i	−0.957491	−	0.288463i	$-0.906856\pi$
$941$		−	17.6976i		−	0.576926i	0.957491	−	0.288463i	$-0.0931442\pi$
$942$	3.35011	+	8.98725i	0.109153	+	0.292820i
$943$	−4.43161			−0.144313
$944$			18.6302i			0.606360i
$945$	−19.8008	−	10.8268i	−0.644121	−	0.352196i
$946$			19.8340i			0.644859i
$947$	47.4582			1.54218			0.771092	−	0.636724i	$-0.219711\pi$
$947$	47.4582			1.54218			0.771092	+	0.636724i	$0.219711\pi$
$948$	27.6352	+	74.1362i	0.897550	+	2.40783i
$949$	−1.14665	+	6.54669i	−0.0372217	+	0.212515i
$950$	−15.3493	−	8.72788i	−0.497998	−	0.283170i
$951$	−1.42070	−	3.81127i	−0.0460694	−	0.123589i
$952$			1.67729i			0.0543612i
$953$	−21.2542			−0.688490			−0.344245	−	0.938880i	$-0.611865\pi$
$953$	−21.2542			−0.688490			−0.344245	+	0.938880i	$0.611865\pi$
$954$	−36.5988	−	42.2699i	−1.18493	−	1.36854i
$955$		−	2.15610i		−	0.0697697i
$956$	0.402257			0.0130099
$957$	−24.5359	+	9.14607i	−0.793133	+	0.295651i
$958$			4.14531i			0.133929i
$959$		−	16.3348i		−	0.527477i
$960$	−36.4548	+	13.5890i	−1.17657	+	0.438583i
$961$	−30.5457			−0.985346
$962$	6.83921	−	39.0480i	0.220505	−	1.25896i
$963$	−15.7092	+	13.6016i	−0.506222	+	0.438305i
$964$	−49.0234			−1.57894
$965$	−9.60853			−0.309310
$966$	−4.73479	−	12.7019i	−0.152339	−	0.408676i
$967$		−	38.2279i		−	1.22933i	−0.788790	−	0.614663i	$-0.789292\pi$
$967$		−	38.2279i		−	1.22933i	0.788790	−	0.614663i	$-0.210708\pi$
$968$			1.22841i			0.0394826i
$969$	−2.86102	−	0.462342i	−0.0919092	−	0.0148526i
$970$			34.9774i			1.12306i
$971$	40.8012			1.30937			0.654687	−	0.755901i	$-0.272801\pi$
$971$	40.8012			1.30937			0.654687	+	0.755901i	$0.272801\pi$
$972$	−9.28432	−	42.8766i	−0.297795	−	1.37527i
$973$			40.2159i			1.28926i
$974$			50.7610i			1.62649i
$975$	−11.3362	+	2.10289i	−0.363047	+	0.0673463i
$976$	−7.30047			−0.233682
$977$			0.740787i			0.0236999i	0.999930	+	0.0118499i	$0.00377204\pi$
$977$			0.740787i			0.0236999i	−0.999930	+	0.0118499i	$0.996228\pi$
$978$	1.53326	−	0.571541i	0.0490281	−	0.0182759i
$979$		−	19.8947i		−	0.635838i
$980$	−5.09310			−0.162693
$981$	−13.8659	+	12.0056i	−0.442703	+	0.383308i
$982$	20.3572			0.649623
$983$		−	24.6087i		−	0.784896i	−0.919774	−	0.392448i	$-0.871628\pi$
$983$		−	24.6087i		−	0.784896i	0.919774	−	0.392448i	$-0.128372\pi$
$984$	8.81051	−	3.28423i	0.280869	−	0.104697i
$985$	−15.0539			−0.479657
$986$	3.72460			0.118615
$987$	15.4067	+	41.3310i	0.490400	+	1.31558i
$988$	−28.1681	+	34.1005i	−0.896146	+	1.08488i
$989$			3.85649i			0.122629i
$990$	26.1591	+	30.2125i	0.831391	+	0.960218i
$991$		−	7.68871i		−	0.244240i	−0.992515	−	0.122120i	$-0.961031\pi$
$991$		−	7.68871i		−	0.244240i	0.992515	−	0.122120i	$-0.0389693\pi$
$992$		−	4.93480i		−	0.156680i
$993$	−31.0768	+	11.5843i	−0.986191	+	0.367615i
$994$			70.8003i			2.24565i
$995$	−12.7584			−0.404468
$996$	−56.5963	+	21.0970i	−1.79332	+	0.668484i
$997$	−3.16934			−0.100374			−0.0501870	−	0.998740i	$-0.515982\pi$
$997$	−3.16934			−0.100374			−0.0501870	+	0.998740i	$0.515982\pi$
$998$	23.8399			0.754640
$999$	12.4917	−	22.8457i	0.395220	−	0.722805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	741.2.d.a.740.10	yes	88
3.2	odd	2	inner	741.2.d.a.740.80	yes	88
13.12	even	2	inner	741.2.d.a.740.78	yes	88
19.18	odd	2	inner	741.2.d.a.740.79	yes	88
39.38	odd	2	inner	741.2.d.a.740.12	yes	88
57.56	even	2	inner	741.2.d.a.740.9	✓	88
247.246	odd	2	inner	741.2.d.a.740.11	yes	88
741.740	even	2	inner	741.2.d.a.740.77	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
741.2.d.a.740.9	✓	88	57.56	even	2	inner
741.2.d.a.740.10	yes	88	1.1	even	1	trivial
741.2.d.a.740.11	yes	88	247.246	odd	2	inner
741.2.d.a.740.12	yes	88	39.38	odd	2	inner
741.2.d.a.740.77	yes	88	741.740	even	2	inner
741.2.d.a.740.78	yes	88	13.12	even	2	inner
741.2.d.a.740.79	yes	88	19.18	odd	2	inner
741.2.d.a.740.80	yes	88	3.2	odd	2	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:	\( N \)	\(=\)	\( 741 = 3 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	741.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.19415i q^{2} +(-1.62296 + 0.604979i) q^{3} -2.81428 q^{4} +1.77589 q^{5} +(1.32741 + 3.56101i) q^{6} +2.44560i q^{7} +1.78666i q^{8} +(2.26800 - 1.96372i) q^{9} -3.89657i q^{10} -3.41871 q^{11} +(4.56747 - 1.70258i) q^{12} +(-3.55149 - 0.622039i) q^{13} +5.36600 q^{14} +(-2.88220 + 1.07438i) q^{15} -1.70838 q^{16} -0.383868i q^{17} +(-4.30868 - 4.97633i) q^{18} +(-2.15458 + 3.78917i) q^{19} -4.99786 q^{20} +(-1.47954 - 3.96911i) q^{21} +7.50114i q^{22} +1.45851i q^{23} +(-1.08089 - 2.89967i) q^{24} -1.84621 q^{25} +(-1.36485 + 7.79249i) q^{26} +(-2.49287 + 4.55912i) q^{27} -6.88260i q^{28} -4.42214 q^{29} +(2.35734 + 6.32398i) q^{30} -0.673992 q^{31} +7.32175i q^{32} +(5.54842 - 2.06825i) q^{33} -0.842262 q^{34} +4.34312i q^{35} +(-6.38279 + 5.52645i) q^{36} -5.01097 q^{37} +(8.31399 + 4.72747i) q^{38} +(6.14024 - 1.13903i) q^{39} +3.17291i q^{40} +3.03845i q^{41} +(-8.70880 + 3.24632i) q^{42} +2.64413 q^{43} +9.62120 q^{44} +(4.02772 - 3.48735i) q^{45} +3.20018 q^{46} -10.4132 q^{47} +(2.77263 - 1.03353i) q^{48} +1.01906 q^{49} +4.05085i q^{50} +(0.232232 + 0.623002i) q^{51} +(9.99489 + 1.75059i) q^{52} +8.49420 q^{53} +(10.0034 + 5.46972i) q^{54} -6.07125 q^{55} -4.36944 q^{56} +(1.20443 - 7.45314i) q^{57} +9.70283i q^{58} -10.9052i q^{59} +(8.11133 - 3.02360i) q^{60} +4.27333 q^{61} +1.47884i q^{62} +(4.80246 + 5.54661i) q^{63} +12.6482 q^{64} +(-6.30706 - 1.10468i) q^{65} +(-4.53804 - 12.1741i) q^{66} +5.69814 q^{67} +1.08031i q^{68} +(-0.882368 - 2.36710i) q^{69} +9.52944 q^{70} +13.1942i q^{71} +(3.50848 + 4.05213i) q^{72} -1.84337i q^{73} +10.9948i q^{74} +(2.99632 - 1.11692i) q^{75} +(6.06360 - 10.6638i) q^{76} -8.36078i q^{77} +(-2.49920 - 13.4726i) q^{78} +16.2314i q^{79} -3.03390 q^{80} +(1.28765 - 8.90741i) q^{81} +6.66681 q^{82} -12.3912 q^{83} +(4.16383 + 11.1702i) q^{84} -0.681708i q^{85} -5.80161i q^{86} +(7.17696 - 2.67530i) q^{87} -6.10805i q^{88} +5.81937i q^{89} +(-7.65175 - 8.83742i) q^{90} +(1.52126 - 8.68551i) q^{91} -4.10466i q^{92} +(1.09386 - 0.407751i) q^{93} +22.8481i q^{94} +(-3.82630 + 6.72915i) q^{95} +(-4.42951 - 11.8829i) q^{96} -8.97647 q^{97} -2.23596i q^{98} +(-7.75362 + 6.71336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) \) 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

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