LMFDB - Embedded newform 273.2.e.a.209.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.18
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0920595i q^{2} +(0.749855 + 1.56132i) q^{3} +1.99153 q^{4} -3.32369 q^{5} +(-0.143734 + 0.0690313i) q^{6} +(-0.804490 + 2.52048i) q^{7} +0.367458i q^{8} +(-1.87543 + 2.34153i) q^{9} +O(q^{10})$	\(q+0.0920595i q^{2} +(0.749855 + 1.56132i) q^{3} +1.99153 q^{4} -3.32369 q^{5} +(-0.143734 + 0.0690313i) q^{6} +(-0.804490 + 2.52048i) q^{7} +0.367458i q^{8} +(-1.87543 + 2.34153i) q^{9} -0.305977i q^{10} +2.71131i q^{11} +(1.49336 + 3.10941i) q^{12} -1.00000i q^{13} +(-0.232034 - 0.0740610i) q^{14} +(-2.49229 - 5.18934i) q^{15} +3.94922 q^{16} +5.56306 q^{17} +(-0.215560 - 0.172651i) q^{18} +0.453365i q^{19} -6.61921 q^{20} +(-4.53852 + 0.633926i) q^{21} -0.249602 q^{22} -6.06348i q^{23} +(-0.573719 + 0.275540i) q^{24} +6.04692 q^{25} +0.0920595 q^{26} +(-5.06217 - 1.17234i) q^{27} +(-1.60216 + 5.01959i) q^{28} +2.14111i q^{29} +(0.477728 - 0.229439i) q^{30} -2.57448i q^{31} +1.09848i q^{32} +(-4.23323 + 2.03309i) q^{33} +0.512132i q^{34} +(2.67388 - 8.37728i) q^{35} +(-3.73497 + 4.66321i) q^{36} +5.65146 q^{37} -0.0417366 q^{38} +(1.56132 - 0.749855i) q^{39} -1.22132i q^{40} +11.3354 q^{41} +(-0.0583589 - 0.417814i) q^{42} -4.72802 q^{43} +5.39965i q^{44} +(6.23336 - 7.78251i) q^{45} +0.558201 q^{46} -4.34607 q^{47} +(2.96135 + 6.16600i) q^{48} +(-5.70559 - 4.05540i) q^{49} +0.556676i q^{50} +(4.17149 + 8.68570i) q^{51} -1.99153i q^{52} +10.2361i q^{53} +(0.107925 - 0.466021i) q^{54} -9.01157i q^{55} +(-0.926168 - 0.295616i) q^{56} +(-0.707847 + 0.339958i) q^{57} -0.197110 q^{58} +2.38481 q^{59} +(-4.96345 - 10.3347i) q^{60} -13.7972i q^{61} +0.237005 q^{62} +(-4.39299 - 6.61072i) q^{63} +7.79732 q^{64} +3.32369i q^{65} +(-0.187166 - 0.389709i) q^{66} -7.22179 q^{67} +11.0790 q^{68} +(9.46703 - 4.54673i) q^{69} +(0.771208 + 0.246156i) q^{70} -13.9569i q^{71} +(-0.860412 - 0.689143i) q^{72} +1.59082i q^{73} +0.520270i q^{74} +(4.53432 + 9.44117i) q^{75} +0.902888i q^{76} +(-6.83380 - 2.18123i) q^{77} +(0.0690313 + 0.143734i) q^{78} +10.3323 q^{79} -13.1260 q^{80} +(-1.96550 - 8.78276i) q^{81} +1.04353i q^{82} +0.388942 q^{83} +(-9.03857 + 1.26248i) q^{84} -18.4899 q^{85} -0.435259i q^{86} +(-3.34296 + 1.60553i) q^{87} -0.996293 q^{88} +1.19890 q^{89} +(0.716454 + 0.573840i) q^{90} +(2.52048 + 0.804490i) q^{91} -12.0756i q^{92} +(4.01958 - 1.93049i) q^{93} -0.400097i q^{94} -1.50685i q^{95} +(-1.71508 + 0.823700i) q^{96} +6.25270i q^{97} +(0.373338 - 0.525254i) q^{98} +(-6.34861 - 5.08489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			0.0920595i			0.0650959i	0.999470	+	0.0325479i	$0.0103622\pi$
$2$			0.0920595i			0.0650959i	−0.999470	+	0.0325479i	$0.989638\pi$
$3$	0.749855	+	1.56132i	0.432929	+	0.901428i
$3$	0.749855	+	1.56132i	0.432929	+	0.901428i
$4$	1.99153			0.995763
$5$	−3.32369			−1.48640			−0.743200	−	0.669069i	$-0.766693\pi$
$5$	−3.32369			−1.48640			−0.743200	+	0.669069i	$0.766693\pi$
$6$	−0.143734	+	0.0690313i	−0.0586792	+	0.0281819i
$7$	−0.804490	+	2.52048i	−0.304069	+	0.952650i
$7$	−0.804490	+	2.52048i	−0.304069	+	0.952650i
$8$			0.367458i			0.129916i
$9$	−1.87543	+	2.34153i	−0.625145	+	0.780509i
$10$		−	0.305977i		−	0.0967585i
$11$			2.71131i			0.817492i	0.912648	+	0.408746i	$0.134034\pi$
$11$			2.71131i			0.817492i	−0.912648	+	0.408746i	$0.865966\pi$
$12$	1.49336	+	3.10941i	0.431095	+	0.897608i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.232034	−	0.0740610i	−0.0620136	−	0.0197936i
$15$	−2.49229	−	5.18934i	−0.643506	−	1.33988i
$16$	3.94922			0.987306
$17$	5.56306			1.34924			0.674620	−	0.738166i	$-0.264308\pi$
$17$	5.56306			1.34924			0.674620	+	0.738166i	$0.264308\pi$
$18$	−0.215560	−	0.172651i	−0.0508079	−	0.0406943i
$19$			0.453365i			0.104009i	0.998647	+	0.0520045i	$0.0165610\pi$
$19$			0.453365i			0.104009i	−0.998647	+	0.0520045i	$0.983439\pi$
$20$	−6.61921			−1.48010
$21$	−4.53852	+	0.633926i	−0.990386	+	0.138334i
$22$	−0.249602			−0.0532154
$23$		−	6.06348i		−	1.26432i	−0.774837	−	0.632162i	$-0.782168\pi$
$23$		−	6.06348i		−	1.26432i	0.774837	−	0.632162i	$-0.217832\pi$
$24$	−0.573719	+	0.275540i	−0.117110	+	0.0562444i
$25$	6.04692			1.20938
$26$	0.0920595			0.0180544
$27$	−5.06217	−	1.17234i	−0.974216	−	0.225618i
$28$	−1.60216	+	5.01959i	−0.302780	+	0.948613i
$29$			2.14111i			0.397595i	0.980041	+	0.198798i	$0.0637036\pi$
$29$			2.14111i			0.397595i	−0.980041	+	0.198798i	$0.936296\pi$
$30$	0.477728	−	0.229439i	0.0872208	−	0.0418896i
$31$		−	2.57448i		−	0.462390i	−0.972907	−	0.231195i	$-0.925736\pi$
$31$		−	2.57448i		−	0.462390i	0.972907	−	0.231195i	$-0.0742635\pi$
$32$			1.09848i			0.194185i
$33$	−4.23323	+	2.03309i	−0.736910	+	0.353916i
$34$			0.512132i			0.0878299i
$35$	2.67388	−	8.37728i	0.451968	−	1.41602i
$36$	−3.73497	+	4.66321i	−0.622496	+	0.777202i
$37$	5.65146			0.929094			0.464547	−	0.885549i	$-0.346217\pi$
$37$	5.65146			0.929094			0.464547	+	0.885549i	$0.346217\pi$
$38$	−0.0417366			−0.00677056
$39$	1.56132	−	0.749855i	0.250011	−	0.120073i
$40$		−	1.22132i		−	0.193107i
$41$	11.3354			1.77029			0.885146	−	0.465313i	$-0.154058\pi$
$41$	11.3354			1.77029			0.885146	+	0.465313i	$0.154058\pi$
$42$	−0.0583589	−	0.417814i	−0.00900497	−	0.0644700i
$43$	−4.72802			−0.721017			−0.360508	−	0.932756i	$-0.617397\pi$
$43$	−4.72802			−0.721017			−0.360508	+	0.932756i	$0.617397\pi$
$44$			5.39965i			0.814028i
$45$	6.23336	−	7.78251i	0.929215	−	1.16015i
$46$	0.558201			0.0823022
$47$	−4.34607			−0.633940			−0.316970	−	0.948436i	$-0.602665\pi$
$47$	−4.34607			−0.633940			−0.316970	+	0.948436i	$0.602665\pi$
$48$	2.96135	+	6.16600i	0.427433	+	0.889985i
$49$	−5.70559	−	4.05540i	−0.815084	−	0.579342i
$50$			0.556676i			0.0787259i
$51$	4.17149	+	8.68570i	0.584125	+	1.21624i
$52$		−	1.99153i		−	0.276175i
$53$			10.2361i			1.40604i	0.711171	+	0.703019i	$0.248165\pi$
$53$			10.2361i			1.40604i	−0.711171	+	0.703019i	$0.751835\pi$
$54$	0.107925	−	0.466021i	0.0146868	−	0.0634175i
$55$		−	9.01157i		−	1.21512i
$56$	−0.926168	−	0.295616i	−0.123764	−	0.0395034i
$57$	−0.707847	+	0.339958i	−0.0937567	+	0.0450286i
$58$	−0.197110			−0.0258818
$59$	2.38481			0.310476			0.155238	−	0.987877i	$-0.450386\pi$
$59$	2.38481			0.310476			0.155238	+	0.987877i	$0.450386\pi$
$60$	−4.96345	−	10.3347i	−0.640779	−	1.33420i
$61$		−	13.7972i		−	1.76655i	−0.468854	−	0.883276i	$-0.655333\pi$
$61$		−	13.7972i		−	1.76655i	0.468854	−	0.883276i	$-0.344667\pi$
$62$	0.237005			0.0300997
$63$	−4.39299	−	6.61072i	−0.553465	−	0.832872i
$64$	7.79732			0.974665
$65$			3.32369i			0.412253i
$66$	−0.187166	−	0.389709i	−0.0230385	−	0.0479698i
$67$	−7.22179			−0.882282			−0.441141	−	0.897438i	$-0.645426\pi$
$67$	−7.22179			−0.882282			−0.441141	+	0.897438i	$0.645426\pi$
$68$	11.0790			1.34352
$69$	9.46703	−	4.54673i	1.13970	−	0.547362i
$70$	0.771208	+	0.246156i	0.0921770	+	0.0294212i
$71$		−	13.9569i		−	1.65638i	−0.560445	−	0.828192i	$-0.689370\pi$
$71$		−	13.9569i		−	1.65638i	0.560445	−	0.828192i	$-0.310630\pi$
$72$	−0.860412	−	0.689143i	−0.101401	−	0.0812162i
$73$			1.59082i			0.186192i	0.995657	+	0.0930959i	$0.0296763\pi$
$73$			1.59082i			0.186192i	−0.995657	+	0.0930959i	$0.970324\pi$
$74$			0.520270i			0.0604802i
$75$	4.53432	+	9.44117i	0.523578	+	1.09017i
$76$			0.902888i			0.103568i
$77$	−6.83380	−	2.18123i	−0.778784	−	0.248574i
$78$	0.0690313	+	0.143734i	0.00781626	+	0.0162747i
$79$	10.3323			1.16247			0.581235	−	0.813736i	$-0.302570\pi$
$79$	10.3323			1.16247			0.581235	+	0.813736i	$0.302570\pi$
$80$	−13.1260			−1.46753
$81$	−1.96550	−	8.78276i	−0.218389	−	0.975862i
$82$			1.04353i			0.115239i
$83$	0.388942			0.0426920			0.0213460	−	0.999772i	$-0.493205\pi$
$83$	0.388942			0.0426920			0.0213460	+	0.999772i	$0.493205\pi$
$84$	−9.03857	+	1.26248i	−0.986189	+	0.137748i
$85$	−18.4899			−2.00551
$86$		−	0.435259i		−	0.0469352i
$87$	−3.34296	+	1.60553i	−0.358403	+	0.172131i
$88$	−0.996293			−0.106205
$89$	1.19890			0.127083			0.0635417	−	0.997979i	$-0.479760\pi$
$89$	1.19890			0.127083			0.0635417	+	0.997979i	$0.479760\pi$
$90$	0.716454	+	0.573840i	0.0755209	+	0.0604881i
$91$	2.52048	+	0.804490i	0.264218	+	0.0843335i
$92$		−	12.0756i		−	1.25897i
$93$	4.01958	−	1.93049i	0.416811	−	0.200182i
$94$		−	0.400097i		−	0.0412669i
$95$		−	1.50685i		−	0.154599i
$96$	−1.71508	+	0.823700i	−0.175044	+	0.0840686i
$97$			6.25270i			0.634865i	0.948281	+	0.317432i	$0.102821\pi$
$97$			6.25270i			0.634865i	−0.948281	+	0.317432i	$0.897179\pi$
$98$	0.373338	−	0.525254i	0.0377128	−	0.0530586i
$99$	−6.34861	−	5.08489i	−0.638060	−	0.511051i
$100$	12.0426			1.20426
$101$	−9.83704			−0.978822			−0.489411	−	0.872053i	$-0.662788\pi$
$101$	−9.83704			−0.978822			−0.489411	+	0.872053i	$0.662788\pi$
$102$	−0.799601	+	0.384025i	−0.0791723	+	0.0380241i
$103$			1.50987i			0.148772i	0.997230	+	0.0743858i	$0.0236996\pi$
$103$			1.50987i			0.148772i	−0.997230	+	0.0743858i	$0.976300\pi$
$104$	0.367458			0.0360322
$105$	15.0846	−	2.10697i	1.47211	−	0.205620i
$106$	−0.942331			−0.0915273
$107$			10.1758i			0.983728i	0.870672	+	0.491864i	$0.163684\pi$
$107$			10.1758i			0.983728i	−0.870672	+	0.491864i	$0.836316\pi$
$108$	−10.0814	−	2.33475i	−0.970088	−	0.224662i
$109$	12.7280			1.21912			0.609562	−	0.792739i	$-0.291345\pi$
$109$	12.7280			1.21912			0.609562	+	0.792739i	$0.291345\pi$
$110$	0.829600			0.0790993
$111$	4.23778	+	8.82373i	0.402232	+	0.837511i
$112$	−3.17711	+	9.95392i	−0.300209	+	0.940557i
$113$			16.7255i			1.57341i	0.617332	+	0.786703i	$0.288213\pi$
$113$			16.7255i			1.57341i	−0.617332	+	0.786703i	$0.711787\pi$
$114$	−0.0312964	−	0.0651641i	−0.00293117	−	0.00610317i
$115$			20.1531i			1.87929i
$116$			4.26408i			0.395910i
$117$	2.34153	+	1.87543i	0.216474	+	0.173384i
$118$			0.219545i			0.0202107i
$119$	−4.47542	+	14.0215i	−0.410261	+	1.28535i
$120$	1.90686	−	0.915810i	0.174072	−	0.0836017i
$121$	3.64878			0.331707
$122$	1.27016			0.114995
$123$	8.49991	+	17.6982i	0.766411	+	1.59579i
$124$		−	5.12714i		−	0.460430i
$125$	−3.47964			−0.311229
$126$	0.608579	−	0.404417i	0.0542166	−	0.0360283i
$127$	−15.1563			−1.34490			−0.672451	−	0.740141i	$-0.734759\pi$
$127$	−15.1563			−1.34490			−0.672451	+	0.740141i	$0.734759\pi$
$128$			2.91477i			0.257632i
$129$	−3.54533	−	7.38195i	−0.312149	−	0.649945i
$130$	−0.305977			−0.0268360
$131$	5.82816			0.509209			0.254605	−	0.967045i	$-0.418055\pi$
$131$	5.82816			0.509209			0.254605	+	0.967045i	$0.418055\pi$
$132$	−8.43057	+	4.04896i	−0.733787	+	0.352416i
$133$	−1.14270	−	0.364728i	−0.0990842	−	0.0316259i
$134$		−	0.664834i		−	0.0574329i
$135$	16.8251	+	3.89651i	1.44807	+	0.335358i
$136$			2.04419i			0.175288i
$137$		−	16.4383i		−	1.40442i	−0.711970	−	0.702209i	$-0.752197\pi$
$137$		−	16.4383i		−	1.40442i	0.711970	−	0.702209i	$-0.247803\pi$
$138$	0.418570	+	0.871530i	0.0356310	+	0.0741895i
$139$			0.00476993i			0.000404580i	1.00000		0.000202290i	$6.43910e-5\pi$
$139$			0.00476993i			0.000404580i	−1.00000		0.000202290i	$0.999936\pi$
$140$	5.32509	−	16.6836i	0.450053	−	1.41002i
$141$	−3.25893	−	6.78561i	−0.274451	−	0.571451i
$142$	1.28487			0.107824
$143$	2.71131			0.226731
$144$	−7.40650	+	9.24721i	−0.617209	+	0.770601i
$145$		−	7.11640i		−	0.590985i
$146$	−0.146450			−0.0121203
$147$	2.05340	−	11.9492i	0.169361	−	0.985554i
$148$	11.2550			0.925157
$149$		−	8.76010i		−	0.717655i	−0.933404	−	0.358828i	$-0.883177\pi$
$149$		−	8.76010i		−	0.717655i	0.933404	−	0.358828i	$-0.116823\pi$
$150$	−0.869149	+	0.417427i	−0.0709658	+	0.0340828i
$151$	−14.9153			−1.21379			−0.606895	−	0.794782i	$-0.707585\pi$
$151$	−14.9153			−1.21379			−0.606895	+	0.794782i	$0.707585\pi$
$152$	−0.166592			−0.0135124
$153$	−10.4331	+	13.0260i	−0.843469	+	1.05309i
$154$	0.200802	−	0.629116i	0.0161811	−	0.0506956i
$155$			8.55677i			0.687296i
$156$	3.10941	−	1.49336i	0.248952	−	0.119564i
$157$			11.8861i			0.948611i	0.880360	+	0.474306i	$0.157301\pi$
$157$			11.8861i			0.948611i	−0.880360	+	0.474306i	$0.842699\pi$
$158$			0.951182i			0.0756720i
$159$	−15.9818	+	7.67560i	−1.26744	+	0.608715i
$160$		−	3.65100i		−	0.288637i
$161$	15.2829	+	4.87801i	1.20446	+	0.384441i
$162$	0.808536	−	0.180943i	0.0635246	−	0.0142162i
$163$	−3.64049			−0.285145			−0.142573	−	0.989784i	$-0.545537\pi$
$163$	−3.64049			−0.285145			−0.142573	+	0.989784i	$0.545537\pi$
$164$	22.5747			1.76279
$165$	14.0699	−	6.75737i	1.09534	−	0.526061i
$166$			0.0358058i			0.00277907i
$167$	−9.66451			−0.747862			−0.373931	−	0.927456i	$-0.621990\pi$
$167$	−9.66451			−0.747862			−0.373931	+	0.927456i	$0.621990\pi$
$168$	−0.232941	−	1.66771i	−0.0179718	−	0.128667i
$169$	−1.00000			−0.0769231
$170$		−	1.70217i		−	0.130550i
$171$	−1.06157	−	0.850256i	−0.0811800	−	0.0650207i
$172$	−9.41598			−0.717962
$173$	−11.8299			−0.899409			−0.449705	−	0.893177i	$-0.648471\pi$
$173$	−11.8299			−0.899409			−0.449705	+	0.893177i	$0.648471\pi$
$174$	−0.147804	−	0.307751i	−0.0112050	−	0.0233306i
$175$	−4.86469	+	15.2411i	−0.367736	+	1.15212i
$176$			10.7076i			0.807114i
$177$	1.78826	+	3.72345i	0.134414	+	0.279872i
$178$			0.110370i			0.00827260i
$179$		−	5.08254i		−	0.379887i	−0.981795	−	0.189944i	$-0.939169\pi$
$179$		−	5.08254i		−	0.379887i	0.981795	−	0.189944i	$-0.0608305\pi$
$180$	12.4139	−	15.4991i	0.925277	−	1.15523i
$181$		−	15.1549i		−	1.12646i	−0.826301	−	0.563229i	$-0.809559\pi$
$181$		−	15.1549i		−	1.12646i	0.826301	−	0.563229i	$-0.190441\pi$
$182$	−0.0740610	+	0.232034i	−0.00548976	+	0.0171995i
$183$	21.5418	−	10.3459i	1.59242	−	0.764792i
$184$	2.22807			0.164256
$185$	−18.7837			−1.38100
$186$	0.177720	+	0.370041i	0.0130310	+	0.0271327i
$187$			15.0832i			1.10299i
$188$	−8.65532			−0.631254
$189$	7.02733	−	11.8159i	0.511163	−	0.859484i
$190$	0.138719			0.0100638
$191$			1.91278i			0.138404i	0.997603	+	0.0692020i	$0.0220453\pi$
$191$			1.91278i			0.138404i	−0.997603	+	0.0692020i	$0.977955\pi$
$192$	5.84686	+	12.1741i	0.421961	+	0.878590i
$193$	−6.98985			−0.503140			−0.251570	−	0.967839i	$-0.580947\pi$
$193$	−6.98985			−0.503140			−0.251570	+	0.967839i	$0.580947\pi$
$194$	−0.575620			−0.0413271
$195$	−5.18934	+	2.49229i	−0.371616	+	0.178476i
$196$	−11.3628	−	8.07642i	−0.811630	−	0.576887i
$197$		−	23.0413i		−	1.64163i	−0.571197	−	0.820813i	$-0.693521\pi$
$197$		−	23.0413i		−	1.64163i	0.571197	−	0.820813i	$-0.306479\pi$
$198$	0.468112	−	0.584450i	0.0332673	−	0.0415351i
$199$			23.1876i			1.64372i	0.569686	+	0.821862i	$0.307065\pi$
$199$			23.1876i			1.64372i	−0.569686	+	0.821862i	$0.692935\pi$
$200$			2.22199i			0.157118i
$201$	−5.41529	−	11.2755i	−0.381965	−	0.795313i
$202$		−	0.905593i		−	0.0637173i
$203$	−5.39663	−	1.72251i	−0.378769	−	0.120896i
$204$	8.30762	+	17.2978i	0.581650	+	1.21109i
$205$	−37.6754			−2.63136
$206$	−0.138998			−0.00968442
$207$	14.1978	+	11.3717i	0.986816	+	0.790385i
$208$		−	3.94922i		−	0.273829i
$209$	−1.22921			−0.0850266
$210$	0.193967	+	1.38868i	0.0133850	+	0.0958282i
$211$	−12.1514			−0.836536			−0.418268	−	0.908324i	$-0.637363\pi$
$211$	−12.1514			−0.836536			−0.418268	+	0.908324i	$0.637363\pi$
$212$			20.3855i			1.40008i
$213$	21.7912	−	10.4657i	1.49311	−	0.717097i
$214$	−0.936775			−0.0640367
$215$	15.7145			1.07172
$216$	0.430787	−	1.86014i	0.0293113	−	0.126566i
$217$	6.48891	+	2.07114i	0.440496	+	0.140598i
$218$			1.17174i			0.0793599i
$219$	−2.48378	+	1.19289i	−0.167838	+	0.0806078i
$220$		−	17.9468i		−	1.20997i
$221$		−	5.56306i		−	0.374212i
$222$	−0.812308	+	0.390127i	−0.0545185	+	0.0261836i
$223$		−	11.4542i		−	0.767030i	−0.923535	−	0.383515i	$-0.874713\pi$
$223$		−	11.4542i		−	0.767030i	0.923535	−	0.383515i	$-0.125287\pi$
$224$	−2.76869	−	0.883716i	−0.184991	−	0.0590457i
$225$	−11.3406	+	14.1590i	−0.756040	+	0.943935i
$226$	−1.53974			−0.102422
$227$	−2.24628			−0.149091			−0.0745454	−	0.997218i	$-0.523751\pi$
$227$	−2.24628			−0.149091			−0.0745454	+	0.997218i	$0.523751\pi$
$228$	−1.40970	+	0.677035i	−0.0933594	+	0.0448378i
$229$			24.6466i			1.62869i	0.580380	+	0.814346i	$0.302904\pi$
$229$			24.6466i			1.62869i	−0.580380	+	0.814346i	$0.697096\pi$
$230$	−1.85529			−0.122334
$231$	−1.71877	−	12.3053i	−0.113087	−	0.809632i
$232$	−0.786769			−0.0516539
$233$		−	18.8269i		−	1.23339i	−0.787203	−	0.616695i	$-0.788471\pi$
$233$		−	18.8269i		−	1.23339i	0.787203	−	0.616695i	$-0.211529\pi$
$234$	−0.172651	+	0.215560i	−0.0112866	+	0.0140916i
$235$	14.4450			0.942288
$236$	4.74941			0.309160
$237$	7.74770	+	16.1320i	0.503267	+	1.04788i
$238$	−1.29082	−	0.412005i	−0.0836712	−	0.0267063i
$239$			9.17761i			0.593650i	0.954932	+	0.296825i	$0.0959279\pi$
$239$			9.17761i			0.593650i	−0.954932	+	0.296825i	$0.904072\pi$
$240$	−9.84260	−	20.4939i	−0.635337	−	1.32287i
$241$		−	4.25627i		−	0.274171i	−0.990559	−	0.137085i	$-0.956227\pi$
$241$		−	4.25627i		−	0.274171i	0.990559	−	0.137085i	$-0.0437735\pi$
$242$			0.335905i			0.0215928i
$243$	12.2388	−	9.65457i	0.785122	−	0.619341i
$244$		−	27.4775i		−	1.75907i
$245$	18.9636	+	13.4789i	1.21154	+	0.861134i
$246$	−1.62929	+	0.782498i	−0.103879	+	0.0498902i
$247$	0.453365			0.0288469
$248$	0.946012			0.0600718
$249$	0.291650	+	0.607263i	0.0184826	+	0.0384837i
$250$		−	0.320334i		−	0.0202597i
$251$	−0.347835			−0.0219551			−0.0109776	−	0.999940i	$-0.503494\pi$
$251$	−0.347835			−0.0219551			−0.0109776	+	0.999940i	$0.503494\pi$
$252$	−8.74875	−	13.1654i	−0.551120	−	0.829343i
$253$	16.4400			1.03357
$254$		−	1.39528i		−	0.0875476i
$255$	−13.8647	−	28.8686i	−0.868243	−	1.80782i
$256$	15.3263			0.957894
$257$	−17.1062			−1.06705			−0.533526	−	0.845784i	$-0.679133\pi$
$257$	−17.1062			−1.06705			−0.533526	+	0.845784i	$0.679133\pi$
$258$	0.679579	−	0.326382i	0.0423087	−	0.0203196i
$259$	−4.54654	+	14.2444i	−0.282508	+	0.885101i
$260$			6.61921i			0.410506i
$261$	−5.01348	−	4.01552i	−0.310327	−	0.248554i
$262$			0.536538i			0.0331474i
$263$		−	13.8523i		−	0.854170i	−0.904212	−	0.427085i	$-0.859541\pi$
$263$		−	13.8523i		−	0.854170i	0.904212	−	0.427085i	$-0.140459\pi$
$264$	−0.747076	−	1.55553i	−0.0459793	−	0.0957363i
$265$		−	34.0217i		−	2.08993i
$266$	0.0335767	−	0.105196i	0.00205872	−	0.00644998i
$267$	0.899003	+	1.87187i	0.0550181	+	0.114556i
$268$	−14.3824			−0.878543
$269$	−4.25645			−0.259520			−0.129760	−	0.991545i	$-0.541421\pi$
$269$	−4.25645			−0.259520			−0.129760	+	0.991545i	$0.541421\pi$
$270$	−0.358710	+	1.54891i	−0.0218304	+	0.0942637i
$271$		−	23.3620i		−	1.41914i	−0.704635	−	0.709570i	$-0.748889\pi$
$271$		−	23.3620i		−	1.41914i	0.704635	−	0.709570i	$-0.251111\pi$
$272$	21.9697			1.33211
$273$	0.633926	+	4.53852i	0.0383669	+	0.274684i
$274$	1.51330			0.0914219
$275$			16.3951i			0.988662i
$276$	18.8538	−	9.05494i	1.13487	−	0.545043i
$277$	13.0793			0.785861			0.392931	−	0.919568i	$-0.371461\pi$
$277$	13.0793			0.785861			0.392931	+	0.919568i	$0.371461\pi$
$278$	−0.000439118	0		−2.63365e−5	0
$279$	6.02821	+	4.82826i	0.360899	+	0.289061i
$280$	3.07830	+	0.982537i	0.183963	+	0.0587178i
$281$		−	22.1388i		−	1.32069i	−0.750963	−	0.660344i	$-0.770411\pi$
$281$		−	22.1388i		−	1.32069i	0.750963	−	0.660344i	$-0.229589\pi$
$282$	0.624680	−	0.300015i	0.0371991	−	0.0178656i
$283$			9.99311i			0.594029i	0.954873	+	0.297014i	$0.0959909\pi$
$283$			9.99311i			0.594029i	−0.954873	+	0.297014i	$0.904009\pi$
$284$		−	27.7956i		−	1.64936i
$285$	2.35267	−	1.12992i	0.139360	−	0.0669305i
$286$			0.249602i			0.0147593i
$287$	−9.11922	+	28.5706i	−0.538291	+	1.68647i
$288$	−2.57212	−	2.06012i	−0.151563	−	0.121394i
$289$	13.9476			0.820446
$290$	0.655132			0.0384707
$291$	−9.76245	+	4.68862i	−0.572285	+	0.274852i
$292$			3.16816i			0.185403i
$293$	−1.23037			−0.0718793			−0.0359396	−	0.999354i	$-0.511442\pi$
$293$	−1.23037			−0.0718793			−0.0359396	+	0.999354i	$0.511442\pi$
$294$	1.10004	+	0.189035i	0.0641555	+	0.0110247i
$295$	−7.92638			−0.461492
$296$			2.07667i			0.120704i
$297$	3.17859	−	13.7251i	0.184441	−	0.796414i
$298$	0.806450			0.0467164
$299$	−6.06348			−0.350660
$300$	9.03020	+	18.8023i	0.521359	+	1.08555i
$301$	3.80365	−	11.9169i	0.219239	−	0.686877i
$302$		−	1.37310i		−	0.0790128i
$303$	−7.37636	−	15.3588i	−0.423761	−	0.882337i
$304$			1.79044i			0.102689i
$305$			45.8576i			2.62580i
$306$	−1.19917	−	0.960470i	−0.0685520	−	0.0549064i
$307$			7.65672i			0.436992i	0.975838	+	0.218496i	$0.0701151\pi$
$307$			7.65672i			0.436992i	−0.975838	+	0.218496i	$0.929885\pi$
$308$	−13.6097	−	4.34397i	−0.775484	−	0.247520i
$309$	−2.35738	+	1.13218i	−0.134107	+	0.0644076i
$310$	−0.787732			−0.0447402
$311$	24.9500			1.41479			0.707393	−	0.706821i	$-0.249871\pi$
$311$	24.9500			1.41479			0.707393	+	0.706821i	$0.249871\pi$
$312$	0.275540	+	0.573719i	0.0155994	+	0.0324804i
$313$		−	15.9860i		−	0.903580i	−0.892124	−	0.451790i	$-0.850786\pi$
$313$		−	15.9860i		−	0.903580i	0.892124	−	0.451790i	$-0.149214\pi$
$314$	−1.09423			−0.0617507
$315$	14.6009	+	21.9720i	0.822670	+	1.23798i
$316$	20.5770			1.15754
$317$		−	15.3979i		−	0.864833i	−0.901674	−	0.432416i	$-0.857661\pi$
$317$		−	15.3979i		−	0.864833i	0.901674	−	0.432416i	$-0.142339\pi$
$318$	−0.706612	−	1.47128i	−0.0396248	−	0.0825053i
$319$	−5.80523			−0.325031
$320$	−25.9159			−1.44874
$321$	−15.8876	+	7.63035i	−0.886760	+	0.425885i
$322$	−0.449067	+	1.40693i	−0.0250255	+	0.0784052i
$323$			2.52209i			0.140333i
$324$	−3.91434	−	17.4911i	−0.217463	−	0.971727i
$325$		−	6.04692i		−	0.335423i
$326$		−	0.335142i		−	0.0185618i
$327$	9.54418	+	19.8725i	0.527794	+	1.09895i
$328$			4.16528i			0.229989i
$329$	3.49638	−	10.9542i	0.192761	−	0.603923i
$330$	0.622080	+	1.29527i	0.0342444	+	0.0713023i
$331$	−2.67071			−0.146795			−0.0733976	−	0.997303i	$-0.523384\pi$
$331$	−2.67071			−0.146795			−0.0733976	+	0.997303i	$0.523384\pi$
$332$	0.774588			0.0425111
$333$	−10.5989	+	13.2330i	−0.580818	+	0.725166i
$334$		−	0.889710i		−	0.0486828i
$335$	24.0030			1.31142
$336$	−17.9236	+	2.50351i	−0.977813	+	0.136578i
$337$	8.85152			0.482173			0.241087	−	0.970504i	$-0.422496\pi$
$337$	8.85152			0.482173			0.241087	+	0.970504i	$0.422496\pi$
$338$		−	0.0920595i		−	0.00500738i
$339$	−26.1139	+	12.5417i	−1.41831	+	0.681173i
$340$	−36.8231			−1.99701
$341$	6.98022			0.378000
$342$	0.0782741	−	0.0977273i	0.00423258	−	0.00528449i
$343$	14.8116	−	11.1183i	0.799752	−	0.600330i
$344$		−	1.73735i		−	0.0936716i
$345$	−31.4655	+	15.1119i	−1.69404	+	0.813599i
$346$		−	1.08905i		−	0.0585479i
$347$		−	4.09936i		−	0.220065i	−0.993928	−	0.110033i	$-0.964904\pi$
$347$		−	4.09936i		−	0.220065i	0.993928	−	0.110033i	$-0.0350955\pi$
$348$	−6.65759	+	3.19745i	−0.356885	+	0.171401i
$349$			33.5265i			1.79463i	0.441391	+	0.897315i	$0.354485\pi$
$349$			33.5265i			1.79463i	−0.441391	+	0.897315i	$0.645515\pi$
$350$	−1.40309	−	0.447841i	−0.0749983	−	0.0239381i
$351$	−1.17234	+	5.06217i	−0.0625751	+	0.270199i
$352$	−2.97832			−0.158745
$353$	25.8743			1.37715			0.688575	−	0.725165i	$-0.258237\pi$
$353$	25.8743			1.37715			0.688575	+	0.725165i	$0.258237\pi$
$354$	−0.342779	+	0.164627i	−0.0182185	+	0.00874981i
$355$			46.3885i			2.46205i
$356$	2.38764			0.126545
$357$	−25.2480	+	3.52657i	−1.33627	+	0.186646i
$358$	0.467896			0.0247291
$359$		−	1.10405i		−	0.0582696i	−0.999575	−	0.0291348i	$-0.990725\pi$
$359$		−	1.10405i		−	0.0582696i	0.999575	−	0.0291348i	$-0.00927521\pi$
$360$	2.85974	+	2.29050i	0.150722	+	0.120720i
$361$	18.7945			0.989182
$362$	1.39516			0.0733278
$363$	2.73606	+	5.69691i	0.143606	+	0.299010i
$364$	5.01959	+	1.60216i	0.263098	+	0.0839761i
$365$		−	5.28740i		−	0.276755i
$366$	0.952439	+	1.98313i	0.0497848	+	0.103660i
$367$		−	2.36782i		−	0.123599i	−0.998089	−	0.0617996i	$-0.980316\pi$
$367$		−	2.36782i		−	0.123599i	0.998089	−	0.0617996i	$-0.0196840\pi$
$368$		−	23.9460i		−	1.24827i
$369$	−21.2588	+	26.5421i	−1.10669	+	1.38173i
$370$		−	1.72922i		−	0.0898977i
$371$	−25.7999	−	8.23485i	−1.33946	−	0.427532i
$372$	8.00510	−	3.84461i	0.415045	−	0.199334i
$373$	−30.2268			−1.56509			−0.782543	−	0.622597i	$-0.786078\pi$
$373$	−30.2268			−1.56509			−0.782543	+	0.622597i	$0.786078\pi$
$374$	−1.38855			−0.0718002
$375$	−2.60923	−	5.43283i	−0.134740	−	0.280550i
$376$		−	1.59700i		−	0.0823589i
$377$	2.14111			0.110273
$378$	1.08777	+	0.646933i	0.0559488	+	0.0332746i
$379$	29.9052			1.53612			0.768062	−	0.640375i	$-0.221221\pi$
$379$	29.9052			1.53612			0.768062	+	0.640375i	$0.221221\pi$
$380$		−	3.00092i		−	0.153944i
$381$	−11.3650	−	23.6638i	−0.582248	−	1.21233i
$382$	−0.176090			−0.00900954
$383$	15.2465			0.779062			0.389531	−	0.921013i	$-0.372637\pi$
$383$	15.2465			0.779062			0.389531	+	0.921013i	$0.372637\pi$
$384$	−4.55089	+	2.18566i	−0.232237	+	0.111536i
$385$	22.7134	+	7.24972i	1.15758	+	0.369480i
$386$		−	0.643482i		−	0.0327524i
$387$	8.86709	−	11.0708i	0.450740	−	0.562760i
$388$			12.4524i			0.632175i
$389$			18.7745i			0.951905i	0.879471	+	0.475953i	$0.157897\pi$
$389$			18.7745i			0.951905i	−0.879471	+	0.475953i	$0.842103\pi$
$390$	−0.229439	−	0.477728i	−0.0116181	−	0.0241907i
$391$		−	33.7315i		−	1.70587i
$392$	1.49019	−	2.09656i	0.0752658	−	0.105892i
$393$	4.37028	+	9.09962i	0.220451	+	0.459015i
$394$	2.12117			0.106863
$395$	−34.3412			−1.72790
$396$	−12.6434	−	10.1267i	−0.635356	−	0.508885i
$397$		−	11.3297i		−	0.568619i	−0.958733	−	0.284310i	$-0.908236\pi$
$397$		−	11.3297i		−	0.568619i	0.958733	−	0.284310i	$-0.0917644\pi$
$398$	−2.13464			−0.107000
$399$	−0.287400	−	2.05760i	−0.0143880	−	0.103009i
$400$	23.8806			1.19403
$401$		−	4.73706i		−	0.236557i	−0.992980	−	0.118279i	$-0.962262\pi$
$401$		−	4.73706i		−	0.236557i	0.992980	−	0.118279i	$-0.0377376\pi$
$402$	1.03802	−	0.498529i	0.0517716	−	0.0248644i
$403$	−2.57448			−0.128244
$404$	−19.5907			−0.974674
$405$	6.53270	+	29.1912i	0.324613	+	1.45052i
$406$	0.158573	−	0.496811i	0.00786985	−	0.0246563i
$407$			15.3229i			0.759526i
$408$	−3.19163	+	1.53285i	−0.158009	+	0.0758872i
$409$		−	15.3678i		−	0.759886i	−0.925010	−	0.379943i	$-0.875944\pi$
$409$		−	15.3678i		−	0.759886i	0.925010	−	0.379943i	$-0.124056\pi$
$410$		−	3.46838i		−	0.171291i
$411$	25.6654	−	12.3263i	1.26598	−	0.608014i
$412$			3.00694i			0.148141i
$413$	−1.91856	+	6.01086i	−0.0944061	+	0.295775i
$414$	−1.04687	+	1.30704i	−0.0514508	+	0.0642376i
$415$	−1.29272			−0.0634573
$416$	1.09848			0.0538574
$417$	−0.00744739	+	0.00357676i	−0.000364700	+	0.000175155i
$418$		−	0.113161i		−	0.00553488i
$419$	−9.23812			−0.451312			−0.225656	−	0.974207i	$-0.572452\pi$
$419$	−9.23812			−0.451312			−0.225656	+	0.974207i	$0.572452\pi$
$420$	30.0414	−	4.19609i	1.46587	−	0.204748i
$421$	−19.6764			−0.958968			−0.479484	−	0.877551i	$-0.659176\pi$
$421$	−19.6764			−0.958968			−0.479484	+	0.877551i	$0.659176\pi$
$422$		−	1.11865i		−	0.0544550i
$423$	8.15078	−	10.1765i	0.396304	−	0.494796i
$424$	−3.76134			−0.182667
$425$	33.6394			1.63175
$426$	0.963466	+	2.00609i	0.0466801	+	0.0971953i
$427$	34.7755	+	11.0997i	1.68291	+	0.537153i
$428$			20.2653i			0.979560i
$429$	2.03309	+	4.23323i	0.0981587	+	0.204382i
$430$			1.44667i			0.0697645i
$431$		−	32.3745i		−	1.55942i	−0.626139	−	0.779712i	$-0.715366\pi$
$431$		−	32.3745i		−	1.55942i	0.626139	−	0.779712i	$-0.284634\pi$
$432$	−19.9917	−	4.62984i	−0.961849	−	0.222754i
$433$		−	6.45476i		−	0.310196i	−0.987899	−	0.155098i	$-0.950431\pi$
$433$		−	6.45476i		−	0.310196i	0.987899	−	0.155098i	$-0.0495693\pi$
$434$	−0.190668	+	0.597365i	−0.00915237	+	0.0286745i
$435$	11.1110	−	5.33627i	0.532731	−	0.255855i
$436$	25.3482			1.21396
$437$	2.74897			0.131501
$438$	−0.109817	−	0.228656i	−0.00524724	−	0.0109256i
$439$		−	0.479707i		−	0.0228952i	−0.999934	−	0.0114476i	$-0.996356\pi$
$439$		−	0.479707i		−	0.0228952i	0.999934	−	0.0114476i	$-0.00364396\pi$
$440$	3.31137			0.157863
$441$	20.1963	−	5.75417i	0.961727	−	0.274008i
$442$	0.512132			0.0243596
$443$		−	1.23459i		−	0.0586573i	−0.999570	−	0.0293287i	$-0.990663\pi$
$443$		−	1.23459i		−	0.0586573i	0.999570	−	0.0293287i	$-0.00933694\pi$
$444$	8.43964	+	17.5727i	0.400527	+	0.833962i
$445$	−3.98478			−0.188897
$446$	1.05447			0.0499305
$447$	13.6773	−	6.56881i	0.646915	−	0.310694i
$448$	−6.27287	+	19.6529i	−0.296365	+	0.928515i
$449$			17.2815i			0.815564i	0.913079	+	0.407782i	$0.133698\pi$
$449$			17.2815i			0.815564i	−0.913079	+	0.407782i	$0.866302\pi$
$450$	−1.30347	−	1.04401i	−0.0614463	−	0.0492151i
$451$			30.7338i			1.44720i
$452$			33.3093i			1.56674i
$453$	−11.1843	−	23.2875i	−0.525485	−	1.09414i
$454$		−	0.206791i		−	0.00970519i
$455$	−8.37728	−	2.67388i	−0.392733	−	0.125353i
$456$	−0.124920	−	0.260104i	−0.00584993	−	0.0121805i
$457$	−7.24488			−0.338901			−0.169450	−	0.985539i	$-0.554199\pi$
$457$	−7.24488			−0.338901			−0.169450	+	0.985539i	$0.554199\pi$
$458$	−2.26895			−0.106021
$459$	−28.1612	−	6.52181i	−1.31445	−	0.304412i
$460$			40.1355i			1.87133i
$461$	−8.11839			−0.378111			−0.189056	−	0.981966i	$-0.560543\pi$
$461$	−8.11839			−0.378111			−0.189056	+	0.981966i	$0.560543\pi$
$462$	1.13282	−	0.158229i	0.0527037	−	0.00736149i
$463$	−12.9105			−0.600002			−0.300001	−	0.953939i	$-0.596987\pi$
$463$	−12.9105			−0.600002			−0.300001	+	0.953939i	$0.596987\pi$
$464$			8.45574i			0.392548i
$465$	−13.3598	+	6.41634i	−0.619548	+	0.297551i
$466$	1.73319			0.0802886
$467$	−14.0747			−0.651301			−0.325651	−	0.945490i	$-0.605583\pi$
$467$	−14.0747			−0.651301			−0.325651	+	0.945490i	$0.605583\pi$
$468$	4.66321	+	3.73497i	0.215557	+	0.172649i
$469$	5.80986	−	18.2023i	0.268274	−	0.840506i
$470$			1.32980i			0.0613391i
$471$	−18.5579	+	8.91283i	−0.855105	+	0.410682i
$472$			0.876318i			0.0403358i
$473$		−	12.8192i		−	0.589425i
$474$	−1.48510	+	0.713249i	−0.0682129	+	0.0327606i
$475$			2.74146i			0.125787i
$476$	−8.91292	+	27.9243i	−0.408523	+	1.27991i
$477$	−23.9681	−	19.1971i	−1.09743	−	0.878977i
$478$	−0.844886			−0.0386442
$479$	−32.7719			−1.49739			−0.748694	−	0.662916i	$-0.769319\pi$
$479$	−32.7719			−1.49739			−0.748694	+	0.662916i	$0.769319\pi$
$480$	5.70038	−	2.73773i	0.260186	−	0.124959i
$481$		−	5.65146i		−	0.257684i
$482$	0.391830			0.0178474
$483$	3.84380	+	27.5192i	0.174899	+	1.25217i
$484$	7.26664			0.330302
$485$		−	20.7820i		−	0.943663i
$486$	0.888794	+	1.12670i	0.0403165	+	0.0511082i
$487$	24.3036			1.10130			0.550651	−	0.834736i	$-0.314380\pi$
$487$	24.3036			1.10130			0.550651	+	0.834736i	$0.314380\pi$
$488$	5.06989			0.229503
$489$	−2.72984	−	5.68397i	−0.123448	−	0.257038i
$490$	−1.24086	+	1.74578i	−0.0560563	+	0.0788663i
$491$			26.6020i			1.20053i	0.799800	+	0.600267i	$0.204939\pi$
$491$			26.6020i			1.20053i	−0.799800	+	0.600267i	$0.795061\pi$
$492$	16.9278	+	35.2464i	0.763164	+	1.58903i
$493$			11.9111i			0.536451i
$494$			0.0417366i			0.00187782i
$495$	21.1008	+	16.9006i	0.948412	+	0.759625i
$496$		−	10.1672i		−	0.456520i
$497$	35.1781	+	11.2282i	1.57795	+	0.503655i
$498$	−0.0559043	+	0.0268492i	−0.00250513	+	0.00120314i
$499$	−20.8709			−0.934309			−0.467155	−	0.884176i	$-0.654721\pi$
$499$	−20.8709			−0.934309			−0.467155	+	0.884176i	$0.654721\pi$
$500$	−6.92979			−0.309910
$501$	−7.24699	−	15.0894i	−0.323771	−	0.674144i
$502$		−	0.0320215i		−	0.00142919i
$503$	−5.65406			−0.252102			−0.126051	−	0.992024i	$-0.540230\pi$
$503$	−5.65406			−0.252102			−0.126051	+	0.992024i	$0.540230\pi$
$504$	2.42916	−	1.61424i	0.108203	−	0.0719039i
$505$	32.6953			1.45492
$506$			1.51346i			0.0672814i
$507$	−0.749855	−	1.56132i	−0.0333022	−	0.0693406i
$508$	−30.1841			−1.33920
$509$	−18.5465			−0.822058			−0.411029	−	0.911622i	$-0.634831\pi$
$509$	−18.5465			−0.822058			−0.411029	+	0.911622i	$0.634831\pi$
$510$	2.65763	−	1.27638i	0.117682	−	0.0565191i
$511$	−4.00963	−	1.27980i	−0.177376	−	0.0566151i
$512$			7.24048i			0.319987i
$513$	0.531500	−	2.29501i	0.0234663	−	0.101327i
$514$		−	1.57478i		−	0.0694607i
$515$		−	5.01833i		−	0.221134i
$516$	−7.06062	−	14.7013i	−0.310827	−	0.647191i
$517$		−	11.7836i		−	0.518241i
$518$	−1.31133	−	0.418552i	−0.0576164	−	0.0183901i
$519$	−8.87070	−	18.4702i	−0.389381	−	0.810753i
$520$	−1.22132			−0.0535582
$521$	32.9133			1.44196			0.720979	−	0.692957i	$-0.243692\pi$
$521$	32.9133			1.44196			0.720979	+	0.692957i	$0.243692\pi$
$522$	0.369667	−	0.461538i	0.0161799	−	0.0202010i
$523$		−	30.2964i		−	1.32477i	−0.749164	−	0.662385i	$-0.769544\pi$
$523$		−	30.2964i		−	1.32477i	0.749164	−	0.662385i	$-0.230456\pi$
$524$	11.6069			0.507051
$525$	−27.4441	+	3.83330i	−1.19776	+	0.167299i
$526$	1.27524			0.0556029
$527$		−	14.3220i		−	0.623874i
$528$	−16.7179	+	8.02914i	−0.727555	+	0.349423i
$529$	−13.7658			−0.598513
$530$	3.13202			0.136046
$531$	−4.47256	+	5.58410i	−0.194092	+	0.242329i
$532$	−2.27571	−	0.726365i	−0.0986644	−	0.0314919i
$533$		−	11.3354i		−	0.490991i
$534$	−0.172323	+	0.0827618i	−0.00745716	+	0.00358145i
$535$		−	33.8211i		−	1.46221i
$536$		−	2.65370i		−	0.114622i
$537$	7.93547	−	3.81117i	0.342441	−	0.164464i
$538$		−	0.391847i		−	0.0168937i
$539$	10.9954	−	15.4696i	0.473608	−	0.666325i
$540$	33.5076	+	7.75999i	1.44194	+	0.333937i
$541$	36.5171			1.56999			0.784997	−	0.619500i	$-0.212665\pi$
$541$	36.5171			1.56999			0.784997	+	0.619500i	$0.212665\pi$
$542$	2.15069			0.0923801
$543$	23.6617	−	11.3640i	1.01542	−	0.487677i
$544$			6.11090i			0.262003i
$545$	−42.3040			−1.81211
$546$	−0.417814	+	0.0583589i	−0.0178808	+	0.00249753i
$547$	−8.35728			−0.357332			−0.178666	−	0.983910i	$-0.557178\pi$
$547$	−8.35728			−0.357332			−0.178666	+	0.983910i	$0.557178\pi$
$548$		−	32.7373i		−	1.39847i
$549$	32.3065	+	25.8757i	1.37881	+	1.10435i
$550$	−1.50932			−0.0643578
$551$	−0.970707			−0.0413535
$552$	1.67073	+	3.47873i	0.0711111	+	0.148065i
$553$	−8.31220	+	26.0422i	−0.353471	+	1.10743i
$554$			1.20408i			0.0511563i
$555$	−14.0851	−	29.3273i	−0.597877	−	1.24488i
$556$			0.00949944i			0.000402866i
$557$			19.5639i			0.828947i	0.910061	+	0.414474i	$0.136034\pi$
$557$			19.5639i			0.828947i	−0.910061	+	0.414474i	$0.863966\pi$
$558$	−0.444487	+	0.554954i	−0.0188166	+	0.0234931i
$559$			4.72802i			0.199974i
$560$	10.5597	−	33.0837i	0.446230	−	1.39804i
$561$	−23.5497	+	11.3102i	−0.994268	+	0.477517i
$562$	2.03808			0.0859713
$563$	12.7980			0.539369			0.269685	−	0.962949i	$-0.413081\pi$
$563$	12.7980			0.539369			0.269685	+	0.962949i	$0.413081\pi$
$564$	−6.49024	−	13.5137i	−0.273288	−	0.569030i
$565$		−	55.5905i		−	2.33871i
$566$	−0.919961			−0.0386688
$567$	23.7179	+	2.11166i	0.996060	+	0.0886812i
$568$	5.12858			0.215191
$569$		−	13.7153i		−	0.574976i	−0.957784	−	0.287488i	$-0.907180\pi$
$569$		−	13.7153i		−	0.574976i	0.957784	−	0.287488i	$-0.0928201\pi$
$570$	0.104019	+	0.216585i	0.00435690	+	0.00907176i
$571$	−6.84388			−0.286407			−0.143204	−	0.989693i	$-0.545740\pi$
$571$	−6.84388			−0.286407			−0.143204	+	0.989693i	$0.545740\pi$
$572$	5.39965			0.225771
$573$	−2.98646	+	1.43431i	−0.124761	+	0.0599192i
$574$	−2.63019	−	0.839511i	−0.109782	−	0.0350405i
$575$		−	36.6654i		−	1.52905i
$576$	−14.6234	+	18.2576i	−0.609306	+	0.760735i
$577$			17.8469i			0.742977i	0.928438	+	0.371488i	$0.121152\pi$
$577$			17.8469i			0.742977i	−0.928438	+	0.371488i	$0.878848\pi$
$578$			1.28401i			0.0534077i
$579$	−5.24138	−	10.9134i	−0.217824	−	0.453545i
$580$		−	14.1725i		−	0.588481i
$581$	−0.312900	+	0.980319i	−0.0129813	+	0.0406705i
$582$	−0.431632	−	0.898726i	−0.0178917	−	0.0372534i
$583$	−27.7533			−1.14942
$584$	−0.584560			−0.0241893
$585$	−7.78251	−	6.23336i	−0.321767	−	0.257718i
$586$		−	0.113268i		−	0.00467905i
$587$	−45.6892			−1.88580			−0.942898	−	0.333082i	$-0.891912\pi$
$587$	−45.6892			−1.88580			−0.942898	+	0.333082i	$0.891912\pi$
$588$	4.08939	−	23.7971i	0.168644	−	0.981378i
$589$	1.16718			0.0480927
$590$		−	0.729698i		−	0.0300412i
$591$	35.9748	−	17.2777i	1.47981	−	0.710708i
$592$	22.3189			0.917299
$593$	20.0862			0.824841			0.412421	−	0.910994i	$-0.364683\pi$
$593$	20.0862			0.824841			0.412421	+	0.910994i	$0.364683\pi$
$594$	1.26353	+	0.292619i	0.0518432	+	0.0120063i
$595$	14.8749	−	46.6033i	0.609813	−	1.91055i
$596$		−	17.4460i		−	0.714614i
$597$	−36.2032	+	17.3873i	−1.48170	+	0.711616i
$598$		−	0.558201i		−	0.0228265i
$599$		−	1.86113i		−	0.0760438i	−0.999277	−	0.0380219i	$-0.987894\pi$
$599$		−	1.86113i		−	0.0760438i	0.999277	−	0.0380219i	$-0.0121057\pi$
$600$	−3.46923	+	1.66617i	−0.141631	+	0.0680211i
$601$		−	22.6914i		−	0.925600i	−0.886463	−	0.462800i	$-0.846845\pi$
$601$		−	22.6914i		−	0.925600i	0.886463	−	0.462800i	$-0.153155\pi$
$602$	1.09706	+	0.350162i	0.0447128	+	0.0142715i
$603$	13.5440	−	16.9100i	0.551553	−	0.688629i
$604$	−29.7042			−1.20865
$605$	−12.1274			−0.493050
$606$	1.41392	−	0.679064i	0.0574365	−	0.0275851i
$607$		−	36.6144i		−	1.48613i	−0.669217	−	0.743067i	$-0.733370\pi$
$607$		−	36.6144i		−	1.48613i	0.669217	−	0.743067i	$-0.266630\pi$
$608$	−0.498012			−0.0201970
$609$	−1.35731	−	9.71749i	−0.0550009	−	0.393772i
$610$	−4.22163			−0.170929
$611$			4.34607i			0.175823i
$612$	−20.7779	+	25.9417i	−0.839895	+	1.04863i
$613$	−0.903017			−0.0364725			−0.0182362	−	0.999834i	$-0.505805\pi$
$613$	−0.903017			−0.0364725			−0.0182362	+	0.999834i	$0.505805\pi$
$614$	−0.704874			−0.0284464
$615$	−28.2511	−	58.8233i	−1.13919	−	2.37198i
$616$	0.801508	−	2.51113i	0.0322937	−	0.101176i
$617$			27.4668i			1.10577i	0.833257	+	0.552886i	$0.186473\pi$
$617$			27.4668i			1.10577i	−0.833257	+	0.552886i	$0.813527\pi$
$618$	−0.104228	−	0.217019i	−0.00419267	−	0.00872980i
$619$			5.50264i			0.221170i	0.993867	+	0.110585i	$0.0352724\pi$
$619$			5.50264i			0.221170i	−0.993867	+	0.110585i	$0.964728\pi$
$620$			17.0410i			0.684384i
$621$	−7.10848	+	30.6944i	−0.285254	+	1.23172i
$622$			2.29688i			0.0920967i
$623$	−0.964505	+	3.02180i	−0.0386421	+	0.121066i
$624$	6.16600	−	2.96135i	0.246837	−	0.118549i
$625$	−18.6694			−0.746774
$626$	1.47166			0.0588193
$627$	−0.921733	−	1.91920i	−0.0368105	−	0.0766453i
$628$			23.6714i			0.944592i
$629$	31.4394			1.25357
$630$	−2.02273	+	1.34416i	−0.0805875	+	0.0535525i
$631$	−14.7941			−0.588943			−0.294472	−	0.955660i	$-0.595144\pi$
$631$	−14.7941			−0.588943			−0.294472	+	0.955660i	$0.595144\pi$
$632$			3.79667i			0.151023i
$633$	−9.11178	−	18.9722i	−0.362161	−	0.754077i
$634$	1.41752			0.0562971
$635$	50.3748			1.99906
$636$	−31.8282	+	15.2862i	−1.26207	+	0.606136i
$637$	−4.05540	+	5.70559i	−0.160681	+	0.226064i
$638$		−	0.534427i		−	0.0211582i
$639$	32.6805	+	26.1753i	1.29282	+	1.03548i
$640$		−	9.68781i		−	0.382944i
$641$			40.3643i			1.59429i	0.603786	+	0.797146i	$0.293658\pi$
$641$			40.3643i			1.59429i	−0.603786	+	0.797146i	$0.706342\pi$
$642$	−0.702446	−	1.46261i	−0.0277233	−	0.0577244i
$643$			21.6896i			0.855353i	0.903932	+	0.427676i	$0.140668\pi$
$643$			21.6896i			0.855353i	−0.903932	+	0.427676i	$0.859332\pi$
$644$	30.4362	+	9.71468i	1.19935	+	0.382812i
$645$	11.7836	+	24.5353i	0.463979	+	0.966078i
$646$	−0.232183			−0.00913511
$647$	29.6001			1.16370			0.581850	−	0.813296i	$-0.302329\pi$
$647$	29.6001			1.16370			0.581850	+	0.813296i	$0.302329\pi$
$648$	3.22729	−	0.722237i	0.126780	−	0.0283722i
$649$			6.46597i			0.253812i
$650$	0.556676			0.0218346
$651$	1.63203	+	11.6843i	0.0639642	+	0.457944i
$652$	−7.25013			−0.283937
$653$			10.0347i			0.392689i	0.980535	+	0.196345i	$0.0629071\pi$
$653$			10.0347i			0.392689i	−0.980535	+	0.196345i	$0.937093\pi$
$654$	−1.82945	+	0.878632i	−0.0715373	+	0.0343572i
$655$	−19.3710			−0.756888
$656$	44.7660			1.74782
$657$	−3.72495	−	2.98348i	−0.145324	−	0.116397i
$658$	1.00844	+	0.321875i	0.0393129	+	0.0125480i
$659$		−	17.7132i		−	0.690009i	−0.938601	−	0.345005i	$-0.887877\pi$
$659$		−	17.7132i		−	0.690009i	0.938601	−	0.345005i	$-0.112123\pi$
$660$	28.0206	−	13.4575i	1.09070	−	0.523832i
$661$		−	0.652575i		−	0.0253822i	−0.999919	−	0.0126911i	$-0.995960\pi$
$661$		−	0.652575i		−	0.0253822i	0.999919	−	0.0126911i	$-0.00403981\pi$
$662$		−	0.245864i		−	0.00955577i
$663$	8.68570	−	4.17149i	0.337325	−	0.162007i
$664$			0.142920i			0.00554637i
$665$	3.79797	+	1.21224i	0.147279	+	0.0470087i
$666$	−1.21823	−	0.975732i	−0.0472053	−	0.0378089i
$667$	12.9826			0.502689
$668$	−19.2471			−0.744693
$669$	17.8837	−	8.58899i	0.691422	−	0.332070i
$670$			2.20970i			0.0853682i
$671$	37.4086			1.44414
$672$	−0.696354	−	4.98547i	−0.0268625	−	0.192318i
$673$	20.0561			0.773106			0.386553	−	0.922267i	$-0.373666\pi$
$673$	20.0561			0.773106			0.386553	+	0.922267i	$0.373666\pi$
$674$			0.814867i			0.0313875i
$675$	−30.6106	−	7.08907i	−1.17820	−	0.272858i
$676$	−1.99153			−0.0765971
$677$	−31.4041			−1.20696			−0.603480	−	0.797378i	$-0.706220\pi$
$677$	−31.4041			−1.20696			−0.603480	+	0.797378i	$0.706220\pi$
$678$	−1.15458	−	2.40403i	−0.0443416	−	0.0923262i
$679$	−15.7598	−	5.03023i	−0.604804	−	0.193043i
$680$		−	6.79425i		−	0.260548i
$681$	−1.68438	−	3.50716i	−0.0645457	−	0.134395i
$682$			0.642595i			0.0246062i
$683$			36.4578i			1.39502i	0.716575	+	0.697510i	$0.245709\pi$
$683$			36.4578i			1.39502i	−0.716575	+	0.697510i	$0.754291\pi$
$684$	−2.11414	−	1.69331i	−0.0808360	−	0.0647452i
$685$			54.6358i			2.08753i
$686$	1.02354	+	1.36355i	0.0390790	+	0.0520606i
$687$	−38.4812	+	18.4814i	−1.46815	+	0.705108i
$688$	−18.6720			−0.711864
$689$	10.2361			0.389965
$690$	−1.39120	−	2.89670i	−0.0529620	−	0.110275i
$691$		−	45.1358i		−	1.71705i	−0.512774	−	0.858524i	$-0.671382\pi$
$691$		−	45.1358i		−	1.71705i	0.512774	−	0.858524i	$-0.328618\pi$
$692$	−23.5595			−0.895598
$693$	17.9237	−	11.9108i	0.680866	−	0.452453i
$694$	0.377385			0.0143253
$695$		−	0.0158538i		−	0.000601368i
$696$	−0.589963	−	1.22840i	−0.0223625	−	0.0465623i
$697$	63.0595			2.38855
$698$	−3.08643			−0.116823
$699$	29.3947	−	14.1174i	1.11181	−	0.533970i
$700$	−9.68815	+	30.3531i	−0.366178	+	1.14724i
$701$		−	34.5985i		−	1.30677i	−0.757026	−	0.653384i	$-0.773349\pi$
$701$		−	34.5985i		−	1.30677i	0.757026	−	0.653384i	$-0.226651\pi$
$702$	−0.466021	−	0.107925i	−0.0175888	−	0.00407338i
$703$			2.56217i			0.0966342i
$704$			21.1410i			0.796781i
$705$	10.8317	+	22.5533i	0.407944	+	0.849405i
$706$			2.38197i			0.0896468i
$707$	7.91380	−	24.7940i	0.297629	−	0.932475i
$708$	3.56137	+	7.41535i	0.133845	+	0.278686i
$709$	32.6638			1.22671			0.613357	−	0.789806i	$-0.289819\pi$
$709$	32.6638			1.22671			0.613357	+	0.789806i	$0.289819\pi$
$710$	−4.27051			−0.160269
$711$	−19.3775	+	24.1933i	−0.726712	+	0.907318i
$712$			0.440546i			0.0165102i
$713$	−15.6103			−0.584610
$714$	−0.324654	−	2.32432i	−0.0121499	−	0.0869855i
$715$	−9.01157			−0.337014
$716$		−	10.1220i		−	0.378277i
$717$	−14.3292	+	6.88188i	−0.535133	+	0.257009i
$718$	0.101638			0.00379311
$719$	−46.5877			−1.73743			−0.868715	−	0.495312i	$-0.835054\pi$
$719$	−46.5877			−1.73743			−0.868715	+	0.495312i	$0.835054\pi$
$720$	24.6169	−	30.7349i	0.917419	−	1.14542i
$721$	−3.80558	−	1.21467i	−0.141727	−	0.0452368i
$722$			1.73021i			0.0643917i
$723$	6.64540	−	3.19159i	0.247145	−	0.118697i
$724$		−	30.1814i		−	1.12168i
$725$			12.9472i			0.480845i
$726$	−0.524454	+	0.251880i	−0.0194643	+	0.00934814i
$727$			29.7143i			1.10204i	0.834491	+	0.551022i	$0.185762\pi$
$727$			29.7143i			1.10204i	−0.834491	+	0.551022i	$0.814238\pi$
$728$	−0.295616	+	0.926168i	−0.0109563	+	0.0343261i
$729$	24.2512	+	11.8692i	0.898193	+	0.439601i
$730$	0.486756			0.0180156
$731$	−26.3023			−0.972824
$732$	42.9011	−	20.6041i	1.58567	−	0.761551i
$733$			26.9744i			0.996322i	0.867085	+	0.498161i	$0.165991\pi$
$733$			26.9744i			0.996322i	−0.867085	+	0.498161i	$0.834009\pi$
$734$	0.217980			0.00804580
$735$	−6.82486	+	39.7155i	−0.251739	+	1.46493i
$736$	6.66061			0.245513
$737$		−	19.5805i		−	0.721258i
$738$	−2.44346	−	1.95707i	−0.0899449	−	0.0720409i
$739$	−33.8881			−1.24659			−0.623297	−	0.781985i	$-0.714207\pi$
$739$	−33.8881			−1.24659			−0.623297	+	0.781985i	$0.714207\pi$
$740$	−37.4082			−1.37515
$741$	0.339958	+	0.707847i	0.0124887	+	0.0260034i
$742$	0.758096	−	2.37512i	0.0278306	−	0.0871935i
$743$			38.6150i			1.41665i	0.705889	+	0.708323i	$0.250548\pi$
$743$			38.6150i			1.41665i	−0.705889	+	0.708323i	$0.749452\pi$
$744$	0.709372	+	1.47703i	0.0260068	+	0.0541504i
$745$			29.1159i			1.06672i
$746$		−	2.78266i		−	0.101881i
$747$	−0.729435	+	0.910719i	−0.0266886	+	0.0333215i
$748$			30.0385i			1.09832i
$749$	−25.6478	−	8.18630i	−0.937149	−	0.299121i
$750$	0.500144	−	0.240204i	0.0182627	−	0.00877102i
$751$	5.73172			0.209153			0.104577	−	0.994517i	$-0.466651\pi$
$751$	5.73172			0.209153			0.104577	+	0.994517i	$0.466651\pi$
$752$	−17.1636			−0.625893
$753$	−0.260826	−	0.543081i	−0.00950501	−	0.0197910i
$754$			0.197110i			0.00717832i
$755$	49.5739			1.80418
$756$	13.9951	−	23.5318i	0.508997	−	0.855842i
$757$	−27.9414			−1.01555			−0.507774	−	0.861491i	$-0.669531\pi$
$757$	−27.9414			−1.01555			−0.507774	+	0.861491i	$0.669531\pi$
$758$			2.75305i			0.0999954i
$759$	12.3276	+	25.6681i	0.447464	+	0.931692i
$760$	0.553702			0.0200849
$761$	−19.2920			−0.699336			−0.349668	−	0.936874i	$-0.613706\pi$
$761$	−19.2920			−0.699336			−0.349668	+	0.936874i	$0.613706\pi$
$762$	2.17848	−	1.04626i	0.0789179	−	0.0379019i
$763$	−10.2396	+	32.0807i	−0.370697	+	1.16140i
$764$			3.80935i			0.137818i
$765$	34.6765	−	43.2945i	1.25373	−	1.56532i
$766$			1.40359i			0.0507137i
$767$		−	2.38481i		−	0.0861106i
$768$	11.4925	+	23.9293i	0.414700	+	0.863472i
$769$			8.13901i			0.293500i	0.989174	+	0.146750i	$0.0468813\pi$
$769$			8.13901i			0.293500i	−0.989174	+	0.146750i	$0.953119\pi$
$770$	−0.667405	+	2.09099i	−0.0240516	+	0.0753539i
$771$	−12.8271	−	26.7082i	−0.461958	−	0.961871i
$772$	−13.9205			−0.501008
$773$	−28.0316			−1.00823			−0.504113	−	0.863638i	$-0.668180\pi$
$773$	−28.0316			−1.00823			−0.504113	+	0.863638i	$0.668180\pi$
$774$	1.01917	+	0.816300i	0.0366334	+	0.0293413i
$775$		−	15.5677i		−	0.559207i
$776$	−2.29760			−0.0824791
$777$	−25.6492	+	3.58261i	−0.920161	+	0.128525i
$778$	−1.72837			−0.0619651
$779$			5.13907i			0.184126i
$780$	−10.3347	+	4.96345i	−0.370042	+	0.177720i
$781$	37.8416			1.35408
$782$	3.10530			0.111045
$783$	2.51012	−	10.8387i	0.0897044	−	0.387343i
$784$	−22.5326	−	16.0157i	−0.804737	−	0.571988i
$785$		−	39.5056i		−	1.41002i
$786$	−0.837707	+	0.402326i	−0.0298800	+	0.0143505i
$787$			23.1577i			0.825482i	0.910849	+	0.412741i	$0.135428\pi$
$787$			23.1577i			0.825482i	−0.910849	+	0.412741i	$0.864572\pi$
$788$		−	45.8874i		−	1.63467i
$789$	21.6279	−	10.3872i	0.769972	−	0.369795i
$790$		−	3.16144i		−	0.112479i
$791$	−42.1563	−	13.4555i	−1.49890	−	0.478423i
$792$	1.86848	−	2.33285i	0.0663936	−	0.0828941i
$793$	−13.7972			−0.489953
$794$	1.04300			0.0370148
$795$	53.1187	−	25.5113i	1.88393	−	0.904794i
$796$			46.1787i			1.63676i
$797$	28.8209			1.02089			0.510444	−	0.859911i	$-0.329481\pi$
$797$	28.8209			1.02089			0.510444	+	0.859911i	$0.329481\pi$
$798$	0.189422	−	0.0264579i	0.00670547	−	0.000936599i
$799$	−24.1775			−0.855337
$800$			6.64241i			0.234845i
$801$	−2.24846	+	2.80726i	−0.0794455	+	0.0991897i
$802$	0.436091			0.0153989
$803$	−4.31322			−0.152210
$804$	−10.7847	−	22.4555i	−0.380347	−	0.791943i
$805$	−50.7955	−	16.2130i	−1.79031	−	0.571433i
$806$		−	0.237005i		−	0.00834815i
$807$	−3.19172	−	6.64567i	−0.112354	−	0.233939i
$808$		−	3.61470i		−	0.127165i
$809$		−	22.8520i		−	0.803432i	−0.915764	−	0.401716i	$-0.868414\pi$
$809$		−	22.8520i		−	0.803432i	0.915764	−	0.401716i	$-0.131586\pi$
$810$	−2.68732	+	0.601397i	−0.0944229	+	0.0211310i
$811$			5.71874i			0.200812i	0.994947	+	0.100406i	$0.0320142\pi$
$811$			5.71874i			0.200812i	−0.994947	+	0.100406i	$0.967986\pi$
$812$	−10.7475	−	3.43041i	−0.377164	−	0.120384i
$813$	36.4755	−	17.5181i	1.27925	−	0.614387i
$814$	−1.41062			−0.0494420
$815$	12.0999			0.423840
$816$	16.4741	+	34.3018i	0.576710	+	1.20080i
$817$		−	2.14352i		−	0.0749923i
$818$	1.41475			0.0494655
$819$	−6.61072	+	4.39299i	−0.230997	+	0.153504i
$820$	−75.0314			−2.62021
$821$			42.0398i			1.46720i	0.679583	+	0.733599i	$0.262161\pi$
$821$			42.0398i			1.46720i	−0.679583	+	0.733599i	$0.737839\pi$
$822$	1.13476	+	2.36275i	0.0395792	+	0.0824102i
$823$	−53.6065			−1.86861			−0.934303	−	0.356481i	$-0.883976\pi$
$823$	−53.6065			−1.86861			−0.934303	+	0.356481i	$0.883976\pi$
$824$	−0.554812			−0.0193278
$825$	−25.5980	+	12.2940i	−0.891207	+	0.428021i
$826$	−0.553357	−	0.176621i	−0.0192537	−	0.00614545i
$827$			25.7006i			0.893698i	0.894609	+	0.446849i	$0.147454\pi$
$827$			25.7006i			0.893698i	−0.894609	+	0.446849i	$0.852546\pi$
$828$	28.2753	+	22.6469i	0.982634	+	0.787036i
$829$		−	30.4750i		−	1.05844i	−0.848484	−	0.529220i	$-0.822484\pi$
$829$		−	30.4750i		−	1.05844i	0.848484	−	0.529220i	$-0.177516\pi$
$830$		−	0.119007i		−	0.00413081i
$831$	9.80761	+	20.4210i	0.340222	+	0.708397i
$832$		−	7.79732i		−	0.270323i
$833$	−31.7405	−	22.5604i	−1.09974	−	0.781671i
$834$	−0.000329275	0	0.000685603i	−1.14019e−5	0	2.37405e-5i
$835$	32.1218			1.11162
$836$	−2.44801			−0.0846663
$837$	−3.01817	+	13.0325i	−0.104323	+	0.450468i
$838$		−	0.850457i		−	0.0293785i
$839$	18.3600			0.633858			0.316929	−	0.948449i	$-0.397348\pi$
$839$	18.3600			0.633858			0.316929	+	0.948449i	$0.397348\pi$
$840$	0.774224	+	5.54296i	0.0267133	+	0.191250i
$841$	24.4156			0.841918
$842$		−	1.81140i		−	0.0624249i
$843$	34.5657	−	16.6009i	1.19050	−	0.571764i
$844$	−24.1998			−0.832991
$845$	3.32369			0.114338
$846$	0.936839	+	0.750356i	0.0322092	+	0.0257978i
$847$	−2.93541	+	9.19666i	−0.100862	+	0.316001i
$848$			40.4247i			1.38819i
$849$	−15.6024	+	7.49339i	−0.535474	+	0.257172i
$850$			3.09682i			0.106220i
$851$		−	34.2675i		−	1.17467i
$852$	43.3978	−	20.8427i	1.48678	−	0.714058i
$853$			15.1245i			0.517854i	0.965897	+	0.258927i	$0.0833689\pi$
$853$			15.1245i			0.517854i	−0.965897	+	0.258927i	$0.916631\pi$
$854$	−1.02183	+	3.20142i	−0.0349665	+	0.109550i
$855$	3.52832	+	2.82599i	0.120666	+	0.0966468i
$856$	−3.73916			−0.127802
$857$	27.0737			0.924821			0.462410	−	0.886666i	$-0.346985\pi$
$857$	27.0737			0.924821			0.462410	+	0.886666i	$0.346985\pi$
$858$	−0.389709	+	0.187166i	−0.0133044	+	0.00638973i
$859$			32.1197i			1.09591i	0.836508	+	0.547955i	$0.184593\pi$
$859$			32.1197i			1.09591i	−0.836508	+	0.547955i	$0.815407\pi$
$860$	31.2958			1.06718
$861$	−51.4459	+	7.18581i	−1.75327	+	0.244892i
$862$	2.98038			0.101512
$863$			52.7072i			1.79417i	0.441855	+	0.897087i	$0.354321\pi$
$863$			52.7072i			1.79417i	−0.441855	+	0.897087i	$0.645679\pi$
$864$	1.28779	−	5.56069i	0.0438117	−	0.189179i
$865$	39.3189			1.33688
$866$	0.594222			0.0201925
$867$	10.4587	+	21.7766i	0.355195	+	0.739573i
$868$	12.9228	+	4.12473i	0.438629	+	0.140003i
$869$			28.0140i			0.950310i
$870$	0.491255	+	1.02287i	0.0166551	+	0.0346786i
$871$			7.22179i			0.244701i
$872$			4.67701i			0.158384i
$873$	−14.6409	−	11.7265i	−0.495518	−	0.396882i
$874$			0.253069i			0.00856018i
$875$	2.79934	−	8.77035i	0.0946349	−	0.296492i
$876$	−4.94651	+	2.37566i	−0.167127	+	0.0802663i
$877$	31.1348			1.05135			0.525673	−	0.850687i	$-0.323813\pi$
$877$	31.1348			1.05135			0.525673	+	0.850687i	$0.323813\pi$
$878$	0.0441616			0.00149038
$879$	−0.922603	−	1.92101i	−0.0311186	−	0.0647940i
$880$		−	35.5887i		−	1.19969i
$881$	−49.3492			−1.66262			−0.831309	−	0.555810i	$-0.812408\pi$
$881$	−49.3492			−1.66262			−0.831309	+	0.555810i	$0.812408\pi$
$882$	0.529726	+	1.85926i	0.0178368	+	0.0626045i
$883$	−10.8682			−0.365744			−0.182872	−	0.983137i	$-0.558539\pi$
$883$	−10.8682			−0.365744			−0.182872	+	0.983137i	$0.558539\pi$
$884$		−	11.0790i		−	0.372626i
$885$	−5.94364	−	12.3756i	−0.199793	−	0.416001i
$886$	0.113656			0.00381835
$887$	19.1659			0.643530			0.321765	−	0.946820i	$-0.395724\pi$
$887$	19.1659			0.643530			0.321765	+	0.946820i	$0.395724\pi$
$888$	−3.24235	+	1.55720i	−0.108806	+	0.0522563i
$889$	12.1931	−	38.2010i	0.408943	−	1.28122i
$890$		−	0.366837i		−	0.0122964i
$891$	23.8128	−	5.32908i	0.797759	−	0.178531i
$892$		−	22.8113i		−	0.763779i
$893$		−	1.97036i		−	0.0659355i
$894$	0.604721	+	1.25913i	0.0202249	+	0.0421115i
$895$			16.8928i			0.564664i
$896$	−7.34662	−	2.34491i	−0.245433	−	0.0783379i
$897$	−4.54673	−	9.46703i	−0.151811	−	0.316095i
$898$	−1.59093			−0.0530899
$899$	5.51225			0.183844
$900$	−22.5851	+	28.1981i	−0.752836	+	0.939935i
$901$			56.9441i			1.89708i
$902$	−2.82934			−0.0942067
$903$	21.4582	−	2.99722i	0.714085	−	0.0997411i
$904$	−6.14592			−0.204410
$905$			50.3703i			1.67437i
$906$	2.14384	−	1.02962i	0.0712243	−	0.0342069i
$907$	−7.31958			−0.243043			−0.121521	−	0.992589i	$-0.538777\pi$
$907$	−7.31958			−0.243043			−0.121521	+	0.992589i	$0.538777\pi$
$908$	−4.47352			−0.148459
$909$	18.4487	−	23.0337i	0.611905	−	0.763979i
$910$	0.246156	−	0.771208i	0.00815998	−	0.0255653i
$911$			52.8306i			1.75036i	0.483800	+	0.875179i	$0.339256\pi$
$911$			52.8306i			1.75036i	−0.483800	+	0.875179i	$0.660744\pi$
$912$	−2.79545	+	1.34257i	−0.0925665	+	0.0444570i
$913$			1.05454i			0.0349003i
$914$		−	0.666960i		−	0.0220611i
$915$	−71.5984	+	34.3866i	−2.36697	+	1.13679i
$916$			49.0843i			1.62179i
$917$	−4.68870	+	14.6897i	−0.154835	+	0.485098i
$918$	0.600395	−	2.59250i	0.0198160	−	0.0855653i
$919$	6.92158			0.228322			0.114161	−	0.993462i	$-0.463582\pi$
$919$	6.92158			0.228322			0.114161	+	0.993462i	$0.463582\pi$
$920$	−7.40543			−0.244150
$921$	−11.9546	+	5.74143i	−0.393917	+	0.189187i
$922$		−	0.747375i		−	0.0246135i
$923$	−13.9569			−0.459398
$924$	−3.42298	−	24.5064i	−0.112608	−	0.806201i
$925$	34.1739			1.12363
$926$		−	1.18853i		−	0.0390577i
$927$	−3.53539	−	2.83165i	−0.116118	−	0.0930037i
$928$	−2.35197			−0.0772072
$929$	6.67864			0.219119			0.109560	−	0.993980i	$-0.465056\pi$
$929$	6.67864			0.219119			0.109560	+	0.993980i	$0.465056\pi$
$930$	−0.590685	−	1.22990i	−0.0193693	−	0.0403300i
$931$	1.83857	−	2.58672i	0.0602569	−	0.0847762i
$932$		−	37.4942i		−	1.22816i
$933$	18.7089	+	38.9549i	0.612502	+	1.27533i
$934$		−	1.29571i		−	0.0423970i
$935$		−	50.1319i		−	1.63949i
$936$	−0.689143	+	0.860412i	−0.0225253	+	0.0281235i
$937$		−	3.78165i		−	0.123541i	−0.998090	−	0.0617705i	$-0.980325\pi$
$937$		−	3.78165i		−	0.123541i	0.998090	−	0.0617705i	$-0.0196747\pi$
$938$	1.67570	+	0.534852i	0.0547135	+	0.0174636i
$939$	24.9592	−	11.9872i	0.814512	−	0.391186i
$940$	28.7676			0.938296
$941$	−27.5238			−0.897252			−0.448626	−	0.893720i	$-0.648086\pi$
$941$	−27.5238			−0.897252			−0.448626	+	0.893720i	$0.648086\pi$
$942$	−0.820511	−	1.70843i	−0.0267337	−	0.0556638i
$943$		−	68.7320i		−	2.23822i
$944$	9.41815			0.306535
$945$	−23.3567	+	39.2726i	−0.759793	+	1.27754i
$946$	1.18012			0.0383692
$947$		−	23.8761i		−	0.775868i	−0.921687	−	0.387934i	$-0.873189\pi$
$947$		−	23.8761i		−	0.775868i	0.921687	−	0.387934i	$-0.126811\pi$
$948$	15.4297	+	32.1272i	0.501135	+	1.04344i
$949$	1.59082			0.0516403
$950$	−0.252378			−0.00818821
$951$	24.0410	−	11.5462i	0.779584	−	0.374411i
$952$	−5.15232	−	1.64453i	−0.166988	−	0.0532995i
$953$		−	37.3748i		−	1.21069i	−0.795964	−	0.605344i	$-0.793036\pi$
$953$		−	37.3748i		−	1.21069i	0.795964	−	0.605344i	$-0.206964\pi$
$954$	1.76728	−	2.20649i	0.0572178	−	0.0714379i
$955$		−	6.35750i		−	0.205724i
$956$			18.2774i			0.591135i
$957$	−4.35309	−	9.06382i	−0.140715	−	0.292992i
$958$		−	3.01697i		−	0.0974738i
$959$	41.4323	+	13.2245i	1.33792	+	0.427040i
$960$	−19.4332	−	40.4630i	−0.627203	−	1.30594i
$961$	24.3721			0.786196
$962$	0.520270			0.0167742
$963$	−23.8268	−	19.0840i	−0.767809	−	0.614972i
$964$		−	8.47648i		−	0.273009i
$965$	23.2321			0.747868
$966$	−2.53340	+	0.353858i	−0.0815110	+	0.0113852i
$967$	−46.7788			−1.50431			−0.752153	−	0.658988i	$-0.770985\pi$
$967$	−46.7788			−1.50431			−0.752153	+	0.658988i	$0.770985\pi$
$968$			1.34077i			0.0430941i
$969$	−3.93779	+	1.89121i	−0.126500	+	0.0607543i
$970$	1.91318			0.0614286
$971$	−53.0805			−1.70343			−0.851717	−	0.524002i	$-0.824438\pi$
$971$	−53.0805			−1.70343			−0.851717	+	0.524002i	$0.824438\pi$
$972$	24.3740	−	19.2273i	0.781795	−	0.616716i
$973$	−0.0120225	−	0.00383737i	−0.000385424	−	0.000123020i
$974$			2.23738i			0.0716902i
$975$	9.44117	−	4.53432i	0.302359	−	0.145214i
$976$		−	54.4882i		−	1.74413i
$977$		−	0.871693i		−	0.0278879i	−0.999903	−	0.0139440i	$-0.995561\pi$
$977$		−	0.871693i		−	0.0278879i	0.999903	−	0.0139440i	$-0.00443864\pi$
$978$	0.523263	−	0.251308i	0.0167321	−	0.00803594i
$979$			3.25060i			0.103890i
$980$	37.7665	+	26.8435i	1.20641	+	0.857485i
$981$	−23.8706	+	29.8030i	−0.762129	+	0.951537i
$982$	−2.44897			−0.0781498
$983$	29.3777			0.937002			0.468501	−	0.883463i	$-0.344794\pi$
$983$	29.3777			0.937002			0.468501	+	0.883463i	$0.344794\pi$
$984$	−6.50333	+	3.12336i	−0.207319	+	0.0995690i
$985$			76.5822i			2.44011i
$986$	−1.09653			−0.0349207
$987$	19.7247	−	2.75509i	0.627845	−	0.0876955i
$988$	0.902888			0.0287247
$989$			28.6683i			0.911598i
$990$	−1.55586	+	1.94253i	−0.0494485	+	0.0617377i
$991$	−24.3281			−0.772809			−0.386404	−	0.922329i	$-0.626283\pi$
$991$	−24.3281			−0.772809			−0.386404	+	0.922329i	$0.626283\pi$
$992$	2.82801			0.0897894
$993$	−2.00264	−	4.16982i	−0.0635519	−	0.132325i
$994$	−1.03366	+	3.23848i	−0.0327858	+	0.102718i
$995$		−	77.0684i		−	2.44323i
$996$	0.580829	+	1.20938i	0.0184043	+	0.0383206i
$997$		−	49.6367i		−	1.57201i	−0.618221	−	0.786005i	$-0.712146\pi$
$997$		−	49.6367i		−	1.57201i	0.618221	−	0.786005i	$-0.287854\pi$
$998$		−	1.92136i		−	0.0608197i
$999$	−28.6087	−	6.62545i	−0.905138	−	0.209620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.18	yes	32
3.2	odd	2	inner	273.2.e.a.209.15	✓	32
7.6	odd	2	inner	273.2.e.a.209.17	yes	32
21.20	even	2	inner	273.2.e.a.209.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.15	✓	32	3.2	odd	2	inner
273.2.e.a.209.16	yes	32	21.20	even	2	inner
273.2.e.a.209.17	yes	32	7.6	odd	2	inner
273.2.e.a.209.18	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.0920595i q^{2} +(0.749855 + 1.56132i) q^{3} +1.99153 q^{4} -3.32369 q^{5} +(-0.143734 + 0.0690313i) q^{6} +(-0.804490 + 2.52048i) q^{7} +0.367458i q^{8} +(-1.87543 + 2.34153i) q^{9} +O(q^{10})\)	\(q+0.0920595i q^{2} +(0.749855 + 1.56132i) q^{3} +1.99153 q^{4} -3.32369 q^{5} +(-0.143734 + 0.0690313i) q^{6} +(-0.804490 + 2.52048i) q^{7} +0.367458i q^{8} +(-1.87543 + 2.34153i) q^{9} -0.305977i q^{10} +2.71131i q^{11} +(1.49336 + 3.10941i) q^{12} -1.00000i q^{13} +(-0.232034 - 0.0740610i) q^{14} +(-2.49229 - 5.18934i) q^{15} +3.94922 q^{16} +5.56306 q^{17} +(-0.215560 - 0.172651i) q^{18} +0.453365i q^{19} -6.61921 q^{20} +(-4.53852 + 0.633926i) q^{21} -0.249602 q^{22} -6.06348i q^{23} +(-0.573719 + 0.275540i) q^{24} +6.04692 q^{25} +0.0920595 q^{26} +(-5.06217 - 1.17234i) q^{27} +(-1.60216 + 5.01959i) q^{28} +2.14111i q^{29} +(0.477728 - 0.229439i) q^{30} -2.57448i q^{31} +1.09848i q^{32} +(-4.23323 + 2.03309i) q^{33} +0.512132i q^{34} +(2.67388 - 8.37728i) q^{35} +(-3.73497 + 4.66321i) q^{36} +5.65146 q^{37} -0.0417366 q^{38} +(1.56132 - 0.749855i) q^{39} -1.22132i q^{40} +11.3354 q^{41} +(-0.0583589 - 0.417814i) q^{42} -4.72802 q^{43} +5.39965i q^{44} +(6.23336 - 7.78251i) q^{45} +0.558201 q^{46} -4.34607 q^{47} +(2.96135 + 6.16600i) q^{48} +(-5.70559 - 4.05540i) q^{49} +0.556676i q^{50} +(4.17149 + 8.68570i) q^{51} -1.99153i q^{52} +10.2361i q^{53} +(0.107925 - 0.466021i) q^{54} -9.01157i q^{55} +(-0.926168 - 0.295616i) q^{56} +(-0.707847 + 0.339958i) q^{57} -0.197110 q^{58} +2.38481 q^{59} +(-4.96345 - 10.3347i) q^{60} -13.7972i q^{61} +0.237005 q^{62} +(-4.39299 - 6.61072i) q^{63} +7.79732 q^{64} +3.32369i q^{65} +(-0.187166 - 0.389709i) q^{66} -7.22179 q^{67} +11.0790 q^{68} +(9.46703 - 4.54673i) q^{69} +(0.771208 + 0.246156i) q^{70} -13.9569i q^{71} +(-0.860412 - 0.689143i) q^{72} +1.59082i q^{73} +0.520270i q^{74} +(4.53432 + 9.44117i) q^{75} +0.902888i q^{76} +(-6.83380 - 2.18123i) q^{77} +(0.0690313 + 0.143734i) q^{78} +10.3323 q^{79} -13.1260 q^{80} +(-1.96550 - 8.78276i) q^{81} +1.04353i q^{82} +0.388942 q^{83} +(-9.03857 + 1.26248i) q^{84} -18.4899 q^{85} -0.435259i q^{86} +(-3.34296 + 1.60553i) q^{87} -0.996293 q^{88} +1.19890 q^{89} +(0.716454 + 0.573840i) q^{90} +(2.52048 + 0.804490i) q^{91} -12.0756i q^{92} +(4.01958 - 1.93049i) q^{93} -0.400097i q^{94} -1.50685i q^{95} +(-1.71508 + 0.823700i) q^{96} +6.25270i q^{97} +(0.373338 - 0.525254i) q^{98} +(-6.34861 - 5.08489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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