LMFDB - Embedded newform 1805.2.b.k.1084.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,2,Mod(1084,1805)] 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("1805.1084"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-18,-3,-12,0,0,-12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.11
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.249751i q^{2} -2.30156i q^{3} +1.93762 q^{4} +(-2.08007 - 0.820550i) q^{5} -0.574816 q^{6} +3.96043i q^{7} -0.983424i q^{8} -2.29718 q^{9} +(-0.204933 + 0.519499i) q^{10} +3.13464 q^{11} -4.45956i q^{12} +2.65927i q^{13} +0.989119 q^{14} +(-1.88855 + 4.78741i) q^{15} +3.62964 q^{16} +2.25718i q^{17} +0.573722i q^{18} +(-4.03040 - 1.58992i) q^{20} +9.11516 q^{21} -0.782879i q^{22} +7.58941i q^{23} -2.26341 q^{24} +(3.65339 + 3.41361i) q^{25} +0.664153 q^{26} -1.61758i q^{27} +7.67382i q^{28} -1.36269 q^{29} +(1.19566 + 0.471666i) q^{30} +0.894474 q^{31} -2.87335i q^{32} -7.21457i q^{33} +0.563731 q^{34} +(3.24973 - 8.23797i) q^{35} -4.45107 q^{36} +6.62537i q^{37} +6.12046 q^{39} +(-0.806949 + 2.04559i) q^{40} +6.23645 q^{41} -2.27652i q^{42} +1.77237i q^{43} +6.07376 q^{44} +(4.77830 + 1.88495i) q^{45} +1.89546 q^{46} +0.176361i q^{47} -8.35383i q^{48} -8.68497 q^{49} +(0.852550 - 0.912438i) q^{50} +5.19503 q^{51} +5.15266i q^{52} -6.77526i q^{53} -0.403992 q^{54} +(-6.52028 - 2.57213i) q^{55} +3.89478 q^{56} +0.340331i q^{58} +7.81595 q^{59} +(-3.65929 + 9.27620i) q^{60} -1.03941 q^{61} -0.223395i q^{62} -9.09781i q^{63} +6.54166 q^{64} +(2.18206 - 5.53146i) q^{65} -1.80184 q^{66} +15.2111i q^{67} +4.37356i q^{68} +17.4675 q^{69} +(-2.05744 - 0.811622i) q^{70} +10.4376 q^{71} +2.25910i q^{72} -4.18114i q^{73} +1.65469 q^{74} +(7.85662 - 8.40851i) q^{75} +12.4145i q^{77} -1.52859i q^{78} -11.2084 q^{79} +(-7.54991 - 2.97830i) q^{80} -10.6145 q^{81} -1.55756i q^{82} -13.2542i q^{83} +17.6618 q^{84} +(1.85213 - 4.69509i) q^{85} +0.442650 q^{86} +3.13630i q^{87} -3.08269i q^{88} -1.48477 q^{89} +(0.470768 - 1.19338i) q^{90} -10.5318 q^{91} +14.7054i q^{92} -2.05869i q^{93} +0.0440463 q^{94} -6.61320 q^{96} -15.3864i q^{97} +2.16908i q^{98} -7.20085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.249751i		−	0.176600i	−0.996094	−	0.0883002i	$-0.971857\pi$
$2$		−	0.249751i		−	0.176600i	0.996094	−	0.0883002i	$-0.0281435\pi$
$3$		−	2.30156i		−	1.32881i	−0.747374	−	0.664403i	$-0.768686\pi$
$3$		−	2.30156i		−	1.32881i	0.747374	−	0.664403i	$-0.231314\pi$
$4$	1.93762			0.968812
$5$	−2.08007	−	0.820550i	−0.930236	−	0.366961i
$5$	−2.08007	−	0.820550i	−0.930236	−	0.366961i
$6$	−0.574816			−0.234668
$7$			3.96043i			1.49690i	0.663191	+	0.748450i	$0.269202\pi$
$7$			3.96043i			1.49690i	−0.663191	+	0.748450i	$0.730798\pi$
$8$		−	0.983424i		−	0.347693i
$9$	−2.29718			−0.765727
$10$	−0.204933	+	0.519499i	−0.0648055	+	0.164280i
$11$	3.13464			0.945131			0.472565	−	0.881296i	$-0.343328\pi$
$11$	3.13464			0.945131			0.472565	+	0.881296i	$0.343328\pi$
$12$		−	4.45956i		−	1.28736i
$13$			2.65927i			0.737548i	0.929519	+	0.368774i	$0.120222\pi$
$13$			2.65927i			0.737548i	−0.929519	+	0.368774i	$0.879778\pi$
$14$	0.989119			0.264353
$15$	−1.88855	+	4.78741i	−0.487621	+	1.23610i
$16$	3.62964			0.907410
$17$			2.25718i			0.547446i	0.961809	+	0.273723i	$0.0882551\pi$
$17$			2.25718i			0.547446i	−0.961809	+	0.273723i	$0.911745\pi$
$18$			0.573722i			0.135228i
$19$		0			0
$19$		0			0
$20$	−4.03040	−	1.58992i	−0.901224	−	0.355517i
$21$	9.11516			1.98909
$22$		−	0.782879i		−	0.166910i
$23$			7.58941i			1.58250i	0.611492	+	0.791251i	$0.290570\pi$
$23$			7.58941i			1.58250i	−0.611492	+	0.791251i	$0.709430\pi$
$24$	−2.26341			−0.462017
$25$	3.65339	+	3.41361i	0.730679	+	0.682721i
$26$	0.664153			0.130251
$27$		−	1.61758i		−	0.311303i
$28$			7.67382i			1.45022i
$29$	−1.36269			−0.253044			−0.126522	−	0.991964i	$-0.540381\pi$
$29$	−1.36269			−0.253044			−0.126522	+	0.991964i	$0.540381\pi$
$30$	1.19566	+	0.471666i	0.218296	+	0.0861140i
$31$	0.894474			0.160652			0.0803261	−	0.996769i	$-0.474404\pi$
$31$	0.894474			0.160652			0.0803261	+	0.996769i	$0.474404\pi$
$32$		−	2.87335i		−	0.507942i
$33$		−	7.21457i		−	1.25590i
$34$	0.563731			0.0966791
$35$	3.24973	−	8.23797i	0.549304	−	1.39247i
$36$	−4.45107			−0.741846
$37$			6.62537i			1.08920i	0.838695	+	0.544602i	$0.183319\pi$
$37$			6.62537i			1.08920i	−0.838695	+	0.544602i	$0.816681\pi$
$38$		0			0
$39$	6.12046			0.980058
$40$	−0.806949	+	2.04559i	−0.127590	+	0.323437i
$41$	6.23645			0.973970			0.486985	−	0.873410i	$-0.338097\pi$
$41$	6.23645			0.973970			0.486985	+	0.873410i	$0.338097\pi$
$42$		−	2.27652i		−	0.351274i
$43$			1.77237i			0.270283i	0.990826	+	0.135142i	$0.0431489\pi$
$43$			1.77237i			0.270283i	−0.990826	+	0.135142i	$0.956851\pi$
$44$	6.07376			0.915654
$45$	4.77830	+	1.88495i	0.712307	+	0.280992i
$46$	1.89546			0.279470
$47$			0.176361i			0.0257249i	0.999917	+	0.0128625i	$0.00409436\pi$
$47$			0.176361i			0.0257249i	−0.999917	+	0.0128625i	$0.995906\pi$
$48$		−	8.35383i		−	1.20577i
$49$	−8.68497			−1.24071
$50$	0.852550	−	0.912438i	0.120569	−	0.129038i
$51$	5.19503			0.727450
$52$			5.15266i			0.714545i
$53$		−	6.77526i		−	0.930653i	−0.885139	−	0.465326i	$-0.845937\pi$
$53$		−	6.77526i		−	0.930653i	0.885139	−	0.465326i	$-0.154063\pi$
$54$	−0.403992			−0.0549763
$55$	−6.52028	−	2.57213i	−0.879195	−	0.346826i
$56$	3.89478			0.520462
$57$		0			0
$58$			0.340331i			0.0446877i
$59$	7.81595			1.01755			0.508775	−	0.860899i	$-0.330098\pi$
$59$	7.81595			1.01755			0.508775	+	0.860899i	$0.330098\pi$
$60$	−3.65929	+	9.27620i	−0.472413	+	1.19755i
$61$	−1.03941			−0.133082			−0.0665412	−	0.997784i	$-0.521196\pi$
$61$	−1.03941			−0.133082			−0.0665412	+	0.997784i	$0.521196\pi$
$62$		−	0.223395i		−	0.0283712i
$63$		−	9.09781i		−	1.14622i
$64$	6.54166			0.817707
$65$	2.18206	−	5.53146i	0.270651	−	0.686094i
$66$	−1.80184			−0.221792
$67$			15.2111i			1.85834i	0.369656	+	0.929169i	$0.379476\pi$
$67$			15.2111i			1.85834i	−0.369656	+	0.929169i	$0.620524\pi$
$68$			4.37356i			0.530372i
$69$	17.4675			2.10284
$70$	−2.05744	−	0.811622i	−0.245911	−	0.0970073i
$71$	10.4376			1.23872			0.619360	−	0.785107i	$-0.287392\pi$
$71$	10.4376			1.23872			0.619360	+	0.785107i	$0.287392\pi$
$72$			2.25910i			0.266238i
$73$		−	4.18114i		−	0.489366i	−0.969603	−	0.244683i	$-0.921316\pi$
$73$		−	4.18114i		−	0.489366i	0.969603	−	0.244683i	$-0.0786839\pi$
$74$	1.65469			0.192354
$75$	7.85662	−	8.40851i	0.907205	−	0.970931i
$76$		0			0
$77$			12.4145i			1.41477i
$78$		−	1.52859i		−	0.173079i
$79$	−11.2084			−1.26105			−0.630524	−	0.776170i	$-0.717160\pi$
$79$	−11.2084			−1.26105			−0.630524	+	0.776170i	$0.717160\pi$
$80$	−7.54991	−	2.97830i	−0.844105	−	0.332984i
$81$	−10.6145			−1.17939
$82$		−	1.55756i		−	0.172004i
$83$		−	13.2542i		−	1.45484i	−0.686192	−	0.727421i	$-0.740719\pi$
$83$		−	13.2542i		−	1.45484i	0.686192	−	0.727421i	$-0.259281\pi$
$84$	17.6618			1.92706
$85$	1.85213	−	4.69509i	0.200891	−	0.509254i
$86$	0.442650			0.0477321
$87$			3.13630i			0.336247i
$88$		−	3.08269i		−	0.328615i
$89$	−1.48477			−0.157385			−0.0786925	−	0.996899i	$-0.525075\pi$
$89$	−1.48477			−0.157385			−0.0786925	+	0.996899i	$0.525075\pi$
$90$	0.470768	−	1.19338i	0.0496233	−	0.125794i
$91$	−10.5318			−1.10404
$92$			14.7054i			1.53315i
$93$		−	2.05869i		−	0.213476i
$94$	0.0440463			0.00454303
$95$		0			0
$96$	−6.61320			−0.674956
$97$		−	15.3864i		−	1.56225i	−0.624372	−	0.781127i	$-0.714645\pi$
$97$		−	15.3864i		−	1.56225i	0.624372	−	0.781127i	$-0.285355\pi$
$98$			2.16908i			0.219110i
$99$	−7.20085			−0.723712
$100$	7.07891	+	6.61429i	0.707891	+	0.661429i
$101$	5.92336			0.589396			0.294698	−	0.955590i	$-0.404781\pi$
$101$	5.92336			0.589396			0.294698	+	0.955590i	$0.404781\pi$
$102$		−	1.29746i		−	0.128468i
$103$			5.00736i			0.493390i	0.969093	+	0.246695i	$0.0793446\pi$
$103$			5.00736i			0.493390i	−0.969093	+	0.246695i	$0.920655\pi$
$104$	2.61519			0.256440
$105$	−18.9602	−	7.47945i	−1.85032	−	0.729919i
$106$	−1.69212			−0.164354
$107$			2.81845i			0.272470i	0.990677	+	0.136235i	$0.0435002\pi$
$107$			2.81845i			0.272470i	−0.990677	+	0.136235i	$0.956500\pi$
$108$		−	3.13426i		−	0.301595i
$109$	−6.74762			−0.646305			−0.323153	−	0.946347i	$-0.604743\pi$
$109$	−6.74762			−0.646305			−0.323153	+	0.946347i	$0.604743\pi$
$110$	−0.642392	+	1.62845i	−0.0612497	+	0.155266i
$111$	15.2487			1.44734
$112$			14.3749i			1.35830i
$113$		−	7.76636i		−	0.730598i	−0.930890	−	0.365299i	$-0.880967\pi$
$113$		−	7.76636i		−	0.730598i	0.930890	−	0.365299i	$-0.119033\pi$
$114$		0			0
$115$	6.22750	−	15.7865i	0.580717	−	1.47210i
$116$	−2.64037			−0.245152
$117$		−	6.10882i		−	0.564760i
$118$		−	1.95204i		−	0.179700i
$119$	−8.93938			−0.819472
$120$	4.70806	+	1.85724i	0.429785	+	0.169542i
$121$	−1.17400			−0.106728
$122$			0.259593i			0.0235024i
$123$		−	14.3536i		−	1.29422i
$124$	1.73315			0.155642
$125$	−4.79828	−	10.0983i	−0.429172	−	0.903223i
$126$	−2.27218			−0.202422
$127$		−	1.68249i		−	0.149297i	−0.997210	−	0.0746485i	$-0.976217\pi$
$127$		−	1.68249i		−	0.149297i	0.997210	−	0.0746485i	$-0.0237835\pi$
$128$		−	7.38049i		−	0.652349i
$129$	4.07921			0.359154
$130$	−1.38149	−	0.544971i	−0.121164	−	0.0477971i
$131$	−7.67994			−0.670999			−0.335500	−	0.942040i	$-0.608905\pi$
$131$	−7.67994			−0.670999			−0.335500	+	0.942040i	$0.608905\pi$
$132$		−	13.9791i		−	1.21673i
$133$		0			0
$134$	3.79899			0.328183
$135$	−1.32731	+	3.36468i	−0.114236	+	0.289586i
$136$	2.21976			0.190343
$137$		−	9.69477i		−	0.828280i	−0.910213	−	0.414140i	$-0.864082\pi$
$137$		−	9.69477i		−	0.828280i	0.910213	−	0.414140i	$-0.135918\pi$
$138$		−	4.36252i		−	0.371362i
$139$	6.40361			0.543147			0.271573	−	0.962418i	$-0.412456\pi$
$139$	6.40361			0.543147			0.271573	+	0.962418i	$0.412456\pi$
$140$	6.29675	−	15.9621i	0.532173	−	1.34904i
$141$	0.405906			0.0341835
$142$		−	2.60681i		−	0.218758i
$143$			8.33585i			0.697079i
$144$	−8.33794			−0.694828
$145$	2.83448	+	1.11815i	0.235391	+	0.0928574i
$146$	−1.04424			−0.0864222
$147$			19.9890i			1.64866i
$148$			12.8375i			1.05523i
$149$	1.94517			0.159355			0.0796773	−	0.996821i	$-0.474611\pi$
$149$	1.94517			0.159355			0.0796773	+	0.996821i	$0.474611\pi$
$150$	−2.10003	−	1.96220i	−0.171467	−	0.160213i
$151$	−16.7168			−1.36040			−0.680199	−	0.733028i	$-0.738107\pi$
$151$	−16.7168			−1.36040			−0.680199	+	0.733028i	$0.738107\pi$
$152$		0			0
$153$		−	5.18514i		−	0.419194i
$154$	3.10054			0.249848
$155$	−1.86057	−	0.733961i	−0.149445	−	0.0589531i
$156$	11.8592			0.949493
$157$			9.81019i			0.782938i	0.920191	+	0.391469i	$0.128033\pi$
$157$			9.81019i			0.782938i	−0.920191	+	0.391469i	$0.871967\pi$
$158$			2.79932i			0.222702i
$159$	−15.5937			−1.23666
$160$	−2.35773	+	5.97678i	−0.186395	+	0.472506i
$161$	−30.0573			−2.36885
$162$			2.65098i			0.208281i
$163$		−	5.06581i		−	0.396785i	−0.980123	−	0.198393i	$-0.936428\pi$
$163$		−	5.06581i		−	0.396785i	0.980123	−	0.198393i	$-0.0635721\pi$
$164$	12.0839			0.943595
$165$	−5.91992	+	15.0068i	−0.460865	+	1.16828i
$166$	−3.31025			−0.256926
$167$		−	20.1611i		−	1.56011i	−0.625710	−	0.780056i	$-0.715191\pi$
$167$		−	20.1611i		−	1.56011i	0.625710	−	0.780056i	$-0.284809\pi$
$168$		−	8.96407i		−	0.691593i
$169$	5.92830			0.456023
$170$	−1.17260	−	0.462570i	−0.0899344	−	0.0354775i
$171$		0			0
$172$			3.43418i			0.261854i
$173$		−	1.94875i		−	0.148161i	−0.997252	−	0.0740805i	$-0.976398\pi$
$173$		−	1.94875i		−	0.148161i	0.997252	−	0.0740805i	$-0.0236022\pi$
$174$	0.783293			0.0593813
$175$	−13.5193	+	14.4690i	−1.02197	+	1.09375i
$176$	11.3776			0.857621
$177$		−	17.9889i		−	1.35213i
$178$			0.370821i			0.0277942i
$179$	−17.2710			−1.29089			−0.645447	−	0.763805i	$-0.723329\pi$
$179$	−17.2710			−1.29089			−0.645447	+	0.763805i	$0.723329\pi$
$180$	9.25855	+	3.65233i	0.690092	+	0.272229i
$181$	14.4378			1.07315			0.536575	−	0.843852i	$-0.319718\pi$
$181$	14.4378			1.07315			0.536575	+	0.843852i	$0.319718\pi$
$182$			2.63033i			0.194973i
$183$			2.39226i			0.176841i
$184$	7.46361			0.550225
$185$	5.43645	−	13.7812i	0.399696	−	1.01322i
$186$	−0.514158			−0.0376999
$187$			7.07545i			0.517408i
$188$			0.341722i			0.0249226i
$189$	6.40631			0.465990
$190$		0			0
$191$	−8.05176			−0.582605			−0.291302	−	0.956631i	$-0.594089\pi$
$191$	−8.05176			−0.582605			−0.291302	+	0.956631i	$0.594089\pi$
$192$		−	15.0560i		−	1.08657i
$193$			6.13649i			0.441714i	0.975306	+	0.220857i	$0.0708855\pi$
$193$			6.13649i			0.441714i	−0.975306	+	0.220857i	$0.929115\pi$
$194$	−3.84277			−0.275895
$195$	−12.7310	−	5.02215i	−0.911686	−	0.359643i
$196$	−16.8282			−1.20201
$197$			17.4160i			1.24084i	0.784271	+	0.620418i	$0.213037\pi$
$197$			17.4160i			1.24084i	−0.784271	+	0.620418i	$0.786963\pi$
$198$			1.79842i			0.127808i
$199$	−0.0105972			−0.000751213			−0.000375607	−	1.00000i	$-0.500120\pi$
$199$	−0.0105972			−0.000751213			−0.000375607		1.00000i	$0.500120\pi$
$200$	3.35702	−	3.59284i	0.237377	−	0.254052i
$201$	35.0094			2.46937
$202$		−	1.47936i		−	0.104088i
$203$		−	5.39681i		−	0.378782i
$204$	10.0660			0.704762
$205$	−12.9723	−	5.11732i	−0.906023	−	0.357409i
$206$	1.25059			0.0871329
$207$		−	17.4343i		−	1.21176i
$208$			9.65218i			0.669258i
$209$		0			0
$210$	−1.86800	+	4.73532i	−0.128904	+	0.326768i
$211$	27.1262			1.86745			0.933723	−	0.357997i	$-0.116540\pi$
$211$	27.1262			1.86745			0.933723	+	0.357997i	$0.116540\pi$
$212$		−	13.1279i		−	0.901628i
$213$		−	24.0228i		−	1.64602i
$214$	0.703909			0.0481183
$215$	1.45432	−	3.68665i	0.0991835	−	0.251427i
$216$	−1.59077			−0.108238
$217$			3.54250i			0.240480i
$218$			1.68522i			0.114138i
$219$	−9.62316			−0.650273
$220$	−12.6339	−	4.98383i	−0.851775	−	0.336010i
$221$	−6.00243			−0.403767
$222$		−	3.80837i		−	0.255601i
$223$			7.65043i			0.512311i	0.966636	+	0.256155i	$0.0824558\pi$
$223$			7.65043i			0.512311i	−0.966636	+	0.256155i	$0.917544\pi$
$224$	11.3797			0.760338
$225$	−8.39251	−	7.84167i	−0.559501	−	0.522778i
$226$	−1.93965			−0.129024
$227$			25.9617i			1.72314i	0.507638	+	0.861571i	$0.330519\pi$
$227$			25.9617i			1.72314i	−0.507638	+	0.861571i	$0.669481\pi$
$228$		0			0
$229$	6.42130			0.424332			0.212166	−	0.977234i	$-0.431948\pi$
$229$	6.42130			0.424332			0.212166	+	0.977234i	$0.431948\pi$
$230$	−3.94269	−	1.55532i	−0.259974	−	0.102555i
$231$	28.5728			1.87995
$232$			1.34010i			0.0879817i
$233$			19.0954i			1.25098i	0.780231	+	0.625492i	$0.215102\pi$
$233$			19.0954i			1.25098i	−0.780231	+	0.625492i	$0.784898\pi$
$234$	−1.52568			−0.0997369
$235$	0.144713	−	0.366844i	0.00944005	−	0.0239303i
$236$	15.1444			0.985815
$237$			25.7969i			1.67569i
$238$			2.23262i			0.144719i
$239$	8.39178			0.542819			0.271409	−	0.962464i	$-0.412510\pi$
$239$	8.39178			0.542819			0.271409	+	0.962464i	$0.412510\pi$
$240$	−6.85474	+	17.3766i	−0.442472	+	1.12165i
$241$	−8.61689			−0.555063			−0.277531	−	0.960717i	$-0.589516\pi$
$241$	−8.61689			−0.555063			−0.277531	+	0.960717i	$0.589516\pi$
$242$			0.293208i			0.0188481i
$243$			19.5772i			1.25588i
$244$	−2.01398			−0.128932
$245$	18.0654	+	7.12645i	1.15415	+	0.455292i
$246$	−3.58481			−0.228559
$247$		0			0
$248$		−	0.879647i		−	0.0558576i
$249$	−30.5054			−1.93320
$250$	−2.52207	+	1.19837i	−0.159509	+	0.0757919i
$251$	29.2619			1.84700			0.923498	−	0.383604i	$-0.125317\pi$
$251$	29.2619			1.84700			0.923498	+	0.383604i	$0.125317\pi$
$252$		−	17.6281i		−	1.11047i
$253$			23.7901i			1.49567i
$254$	−0.420203			−0.0263659
$255$	−10.8060	−	4.26278i	−0.676700	−	0.266946i
$256$	11.2400			0.702502
$257$		−	5.48068i		−	0.341876i	−0.985282	−	0.170938i	$-0.945320\pi$
$257$		−	5.48068i		−	0.341876i	0.985282	−	0.170938i	$-0.0546797\pi$
$258$		−	1.01878i		−	0.0634268i
$259$	−26.2393			−1.63043
$260$	4.22802	−	10.7179i	0.262210	−	0.664696i
$261$	3.13033			0.193763
$262$			1.91807i			0.118499i
$263$			0.568281i			0.0350417i	0.999846	+	0.0175209i	$0.00557735\pi$
$263$			0.568281i			0.0350417i	−0.999846	+	0.0175209i	$0.994423\pi$
$264$	−7.09499			−0.436666
$265$	−5.55944	+	14.0930i	−0.341514	+	0.865727i
$266$		0			0
$267$			3.41728i			0.209134i
$268$			29.4735i			1.80038i
$269$	4.44312			0.270902			0.135451	−	0.990784i	$-0.456752\pi$
$269$	4.44312			0.270902			0.135451	+	0.990784i	$0.456752\pi$
$270$	0.840332	+	0.331496i	0.0511409	+	0.0201742i
$271$	17.7660			1.07921			0.539605	−	0.841919i	$-0.318574\pi$
$271$	17.7660			1.07921			0.539605	+	0.841919i	$0.318574\pi$
$272$			8.19274i			0.496758i
$273$			24.2396i			1.46705i
$274$	−2.42127			−0.146275
$275$	11.4521	+	10.7004i	0.690587	+	0.645261i
$276$	33.8454			2.03726
$277$			8.10450i			0.486952i	0.969907	+	0.243476i	$0.0782877\pi$
$277$			8.10450i			0.486952i	−0.969907	+	0.243476i	$0.921712\pi$
$278$		−	1.59930i		−	0.0959199i
$279$	−2.05477			−0.123016
$280$	−8.10142	−	3.19586i	−0.484152	−	0.190989i
$281$	7.05224			0.420701			0.210351	−	0.977626i	$-0.432539\pi$
$281$	7.05224			0.420701			0.210351	+	0.977626i	$0.432539\pi$
$282$		−	0.101375i		−	0.00603681i
$283$		−	1.29862i		−	0.0771949i	−0.999255	−	0.0385975i	$-0.987711\pi$
$283$		−	1.29862i		−	0.0771949i	0.999255	−	0.0385975i	$-0.0122890\pi$
$284$	20.2242			1.20009
$285$		0			0
$286$	2.08188			0.123104
$287$			24.6990i			1.45794i
$288$			6.60061i			0.388945i
$289$	11.9052			0.700303
$290$	0.279259	−	0.707914i	0.0163987	−	0.0415701i
$291$	−35.4128			−2.07593
$292$		−	8.10149i		−	0.474104i
$293$		−	14.9498i		−	0.873376i	−0.899613	−	0.436688i	$-0.856151\pi$
$293$		−	14.9498i		−	0.873376i	0.899613	−	0.436688i	$-0.143849\pi$
$294$	4.99226			0.291155
$295$	−16.2577	−	6.41338i	−0.946562	−	0.373401i
$296$	6.51555			0.378708
$297$		−	5.07054i		−	0.294223i
$298$		−	0.485808i		−	0.0281421i
$299$	−20.1823			−1.16717
$300$	15.2232	−	16.2925i	0.878911	−	0.940650i
$301$	−7.01932			−0.404587
$302$			4.17504i			0.240247i
$303$		−	13.6330i		−	0.783194i
$304$		0			0
$305$	2.16204	+	0.852886i	0.123798	+	0.0488361i
$306$	−1.29499			−0.0740298
$307$			5.01371i			0.286147i	0.989712	+	0.143074i	$0.0456986\pi$
$307$			5.01371i			0.286147i	−0.989712	+	0.143074i	$0.954301\pi$
$308$			24.0547i			1.37064i
$309$	11.5248			0.655620
$310$	−0.183307	+	0.464678i	−0.0104111	+	0.0263920i
$311$	−16.7443			−0.949481			−0.474741	−	0.880126i	$-0.657458\pi$
$311$	−16.7443			−0.949481			−0.474741	+	0.880126i	$0.657458\pi$
$312$		−	6.01901i		−	0.340759i
$313$		−	5.73858i		−	0.324363i	−0.986761	−	0.162182i	$-0.948147\pi$
$313$		−	5.73858i		−	0.324363i	0.986761	−	0.162182i	$-0.0518531\pi$
$314$	2.45010			0.138267
$315$	−7.46521	+	18.9241i	−0.420617	+	1.06625i
$316$	−21.7178			−1.22172
$317$			7.94635i			0.446312i	0.974783	+	0.223156i	$0.0716359\pi$
$317$			7.94635i			0.446312i	−0.974783	+	0.223156i	$0.928364\pi$
$318$			3.89453i			0.218394i
$319$	−4.27153			−0.239160
$320$	−13.6071	−	5.36776i	−0.760661	−	0.300067i
$321$	6.48683			0.362060
$322$			7.50683i			0.418339i
$323$		0			0
$324$	−20.5669			−1.14261
$325$	−9.07769	+	9.71535i	−0.503540	+	0.538911i
$326$	−1.26519			−0.0700724
$327$			15.5301i			0.858814i
$328$		−	6.13308i		−	0.338643i
$329$	−0.698465			−0.0385076
$330$	3.74797	+	1.47850i	0.206319	+	0.0813890i
$331$	−20.8177			−1.14424			−0.572121	−	0.820169i	$-0.693879\pi$
$331$	−20.8177			−1.14424			−0.572121	+	0.820169i	$0.693879\pi$
$332$		−	25.6817i		−	1.40947i
$333$		−	15.2197i		−	0.834033i
$334$	−5.03525			−0.275516
$335$	12.4815	−	31.6403i	0.681938	−	1.72869i
$336$	33.0847			1.80492
$337$		−	27.3618i		−	1.49049i	−0.666790	−	0.745245i	$-0.732332\pi$
$337$		−	27.3618i		−	1.49049i	0.666790	−	0.745245i	$-0.267668\pi$
$338$		−	1.48060i		−	0.0805339i
$339$	−17.8748			−0.970824
$340$	3.58873	−	9.09732i	0.194626	−	0.493371i
$341$	2.80386			0.151837
$342$		0			0
$343$		−	6.67319i		−	0.360318i
$344$	1.74299			0.0939756
$345$	−36.3336	−	14.3330i	−1.95614	−	0.771660i
$346$	−0.486703			−0.0261653
$347$		−	20.1999i		−	1.08439i	−0.840254	−	0.542194i	$-0.817594\pi$
$347$		−	20.1999i		−	1.08439i	0.840254	−	0.542194i	$-0.182406\pi$
$348$			6.07698i			0.325760i
$349$	15.6240			0.836332			0.418166	−	0.908371i	$-0.362673\pi$
$349$	15.6240			0.836332			0.418166	+	0.908371i	$0.362673\pi$
$350$	3.61364	+	3.37646i	0.193157	+	0.180479i
$351$	4.30158			0.229601
$352$		−	9.00694i		−	0.480072i
$353$		−	4.59743i		−	0.244696i	−0.992487	−	0.122348i	$-0.960958\pi$
$353$		−	4.59743i		−	0.244696i	0.992487	−	0.122348i	$-0.0390424\pi$
$354$	−4.49274			−0.238786
$355$	−21.7110	−	8.56460i	−1.15230	−	0.454562i
$356$	−2.87692			−0.152476
$357$			20.5745i			1.08892i
$358$			4.31344i			0.227972i
$359$	10.8302			0.571598			0.285799	−	0.958290i	$-0.407741\pi$
$359$	10.8302			0.571598			0.285799	+	0.958290i	$0.407741\pi$
$360$	1.85371	−	4.69910i	0.0976990	−	0.247664i
$361$		0			0
$362$		−	3.60584i		−	0.189519i
$363$			2.70204i			0.141820i
$364$	−20.4067			−1.06960
$365$	−3.43084	+	8.69708i	−0.179578	+	0.455226i
$366$	0.597468			0.0312302
$367$			6.66237i			0.347773i	0.984766	+	0.173887i	$0.0556326\pi$
$367$			6.66237i			0.347773i	−0.984766	+	0.173887i	$0.944367\pi$
$368$			27.5468i			1.43598i
$369$	−14.3263			−0.745795
$370$	−3.44187	−	1.35776i	−0.178934	−	0.0705864i
$371$	26.8329			1.39309
$372$		−	3.98896i		−	0.206818i
$373$			18.1212i			0.938279i	0.883124	+	0.469139i	$0.155436\pi$
$373$			18.1212i			0.938279i	−0.883124	+	0.469139i	$0.844564\pi$
$374$	1.76710			0.0913744
$375$	−23.2419	+	11.0435i	−1.20021	+	0.570286i
$376$	0.173438			0.00894438
$377$		−	3.62374i		−	0.186632i
$378$		−	1.59998i		−	0.0822940i
$379$	−31.9277			−1.64002			−0.820008	−	0.572352i	$-0.806031\pi$
$379$	−31.9277			−1.64002			−0.820008	+	0.572352i	$0.806031\pi$
$380$		0			0
$381$	−3.87236			−0.198387
$382$			2.01093i			0.102888i
$383$		−	13.7847i		−	0.704367i	−0.935931	−	0.352183i	$-0.885439\pi$
$383$		−	13.7847i		−	0.704367i	0.935931	−	0.352183i	$-0.114561\pi$
$384$	−16.9866			−0.866846
$385$	10.1867	−	25.8231i	0.519164	−	1.31607i
$386$	1.53259			0.0780069
$387$		−	4.07145i		−	0.206963i
$388$		−	29.8131i		−	1.51353i
$389$	24.6819			1.25142			0.625712	−	0.780054i	$-0.284809\pi$
$389$	24.6819			1.25142			0.625712	+	0.780054i	$0.284809\pi$
$390$	−1.25428	+	3.17958i	−0.0635132	+	0.161004i
$391$	−17.1306			−0.866334
$392$			8.54101i			0.431386i
$393$			17.6758i			0.891628i
$394$	4.34965			0.219132
$395$	23.3144	+	9.19709i	1.17307	+	0.462756i
$396$	−13.9525			−0.701141
$397$			17.8679i			0.896762i	0.893842	+	0.448381i	$0.147999\pi$
$397$			17.8679i			0.896762i	−0.893842	+	0.448381i	$0.852001\pi$
$398$			0.00264665i			0.000132665i
$399$		0			0
$400$	13.2605	+	12.3902i	0.663025	+	0.619508i
$401$	−22.9321			−1.14517			−0.572587	−	0.819844i	$-0.694060\pi$
$401$	−22.9321			−1.14517			−0.572587	+	0.819844i	$0.694060\pi$
$402$		−	8.74361i		−	0.436092i
$403$			2.37864i			0.118489i
$404$	11.4772			0.571014
$405$	22.0789	+	8.70973i	1.09711	+	0.432790i
$406$	−1.34786			−0.0668930
$407$			20.7682i			1.02944i
$408$		−	5.10892i		−	0.252929i
$409$	−25.1805			−1.24509			−0.622547	−	0.782583i	$-0.713902\pi$
$409$	−25.1805			−1.24509			−0.622547	+	0.782583i	$0.713902\pi$
$410$	−1.27805	+	3.23983i	−0.0631186	+	0.160004i
$411$	−22.3131			−1.10062
$412$			9.70239i			0.478003i
$413$			30.9545i			1.52317i
$414$	−4.35422			−0.213998
$415$	−10.8758	+	27.5698i	−0.533870	+	1.35335i
$416$	7.64101			0.374631
$417$		−	14.7383i		−	0.721737i
$418$		0			0
$419$	−0.249578			−0.0121927			−0.00609635	−	0.999981i	$-0.501941\pi$
$419$	−0.249578			−0.0121927			−0.00609635	+	0.999981i	$0.501941\pi$
$420$	−36.7377	−	14.4924i	−1.79262	−	0.707155i
$421$	30.1682			1.47031			0.735154	−	0.677900i	$-0.237110\pi$
$421$	30.1682			1.47031			0.735154	+	0.677900i	$0.237110\pi$
$422$		−	6.77479i		−	0.329792i
$423$		−	0.405134i		−	0.0196983i
$424$	−6.66295			−0.323581
$425$	−7.70511	+	8.24636i	−0.373753	+	0.400007i
$426$	−5.99972			−0.290687
$427$		−	4.11649i		−	0.199211i
$428$			5.46110i			0.263972i
$429$	19.1855			0.926283
$430$	−0.920743	−	0.363216i	−0.0444022	−	0.0175158i
$431$	15.4165			0.742588			0.371294	−	0.928515i	$-0.378914\pi$
$431$	15.4165			0.742588			0.371294	+	0.928515i	$0.378914\pi$
$432$		−	5.87123i		−	0.282480i
$433$		−	12.5378i		−	0.602529i	−0.953541	−	0.301264i	$-0.902591\pi$
$433$		−	12.5378i		−	0.602529i	0.953541	−	0.301264i	$-0.0974087\pi$
$434$	0.884741			0.0424689
$435$	2.57349	−	6.52373i	0.123390	−	0.312789i
$436$	−13.0744			−0.626148
$437$		0			0
$438$			2.40339i			0.114838i
$439$	−25.3236			−1.20863			−0.604315	−	0.796746i	$-0.706553\pi$
$439$	−25.3236			−1.20863			−0.604315	+	0.796746i	$0.706553\pi$
$440$	−2.52950	+	6.41221i	−0.120589	+	0.305690i
$441$	19.9509			0.950045
$442$			1.49911i			0.0713055i
$443$		−	7.41736i		−	0.352410i	−0.984354	−	0.176205i	$-0.943618\pi$
$443$		−	7.41736i		−	0.352410i	0.984354	−	0.176205i	$-0.0563821\pi$
$444$	29.5462			1.40220
$445$	3.08842	+	1.21833i	0.146405	+	0.0577542i
$446$	1.91070			0.0904742
$447$		−	4.47693i		−	0.211752i
$448$			25.9077i			1.22403i
$449$	−24.0580			−1.13537			−0.567684	−	0.823247i	$-0.692160\pi$
$449$	−24.0580			−1.13537			−0.567684	+	0.823247i	$0.692160\pi$
$450$	−1.95846	+	2.09603i	−0.0923228	+	0.0988080i
$451$	19.5491			0.920529
$452$		−	15.0483i		−	0.707812i
$453$			38.4748i			1.80771i
$454$	6.48396			0.304307
$455$	21.9069	+	8.64189i	1.02701	+	0.405138i
$456$		0			0
$457$		−	6.39908i		−	0.299337i	−0.988736	−	0.149668i	$-0.952179\pi$
$457$		−	6.39908i		−	0.299337i	0.988736	−	0.149668i	$-0.0478206\pi$
$458$		−	1.60372i		−	0.0749371i
$459$	3.65116			0.170422
$460$	12.0665	−	30.5884i	0.562606	−	1.42619i
$461$	−15.2501			−0.710268			−0.355134	−	0.934815i	$-0.615565\pi$
$461$	−15.2501			−0.710268			−0.355134	+	0.934815i	$0.615565\pi$
$462$		−	7.13607i		−	0.332000i
$463$		−	36.4298i		−	1.69304i	−0.532359	−	0.846518i	$-0.678694\pi$
$463$		−	36.4298i		−	1.69304i	0.532359	−	0.846518i	$-0.321306\pi$
$464$	−4.94605			−0.229615
$465$	−1.68926	+	4.28221i	−0.0783373	+	0.198583i
$466$	4.76910			0.220924
$467$		−	28.1967i		−	1.30479i	−0.757880	−	0.652395i	$-0.773765\pi$
$467$		−	28.1967i		−	1.30479i	0.757880	−	0.652395i	$-0.226235\pi$
$468$		−	11.8366i		−	0.547147i
$469$	−60.2426			−2.78175
$470$	−0.0916195	−	0.0361422i	−0.00422609	−	0.00166712i
$471$	22.5787			1.04037
$472$		−	7.68640i		−	0.353795i
$473$			5.55574i			0.255453i
$474$	6.44279			0.295927
$475$		0			0
$476$	−17.3212			−0.793914
$477$			15.5640i			0.712626i
$478$		−	2.09585i		−	0.0958620i
$479$	−29.4311			−1.34474			−0.672371	−	0.740215i	$-0.734724\pi$
$479$	−29.4311			−1.34474			−0.672371	+	0.740215i	$0.734724\pi$
$480$	13.7559	+	5.42646i	0.627869	+	0.247683i
$481$	−17.6186			−0.803340
$482$			2.15207i			0.0980243i
$483$			69.1787i			3.14774i
$484$	−2.27478			−0.103399
$485$	−12.6253	+	32.0048i	−0.573287	+	1.45326i
$486$	4.88941			0.221788
$487$		−	2.72017i		−	0.123263i	−0.998099	−	0.0616313i	$-0.980370\pi$
$487$		−	2.72017i		−	0.123263i	0.998099	−	0.0616313i	$-0.0196303\pi$
$488$			1.02218i			0.0462718i
$489$	−11.6593			−0.527251
$490$	1.77984	−	4.51183i	0.0804048	−	0.203824i
$491$	18.9629			0.855783			0.427891	−	0.903830i	$-0.359257\pi$
$491$	18.9629			0.855783			0.427891	+	0.903830i	$0.359257\pi$
$492$		−	27.8118i		−	1.25385i
$493$		−	3.07582i		−	0.138528i
$494$		0			0
$495$	14.9783	+	5.90866i	0.673223	+	0.265574i
$496$	3.24662			0.145777
$497$			41.3375i			1.85424i
$498$			7.61875i			0.341404i
$499$	6.02343			0.269646			0.134823	−	0.990870i	$-0.456953\pi$
$499$	6.02343			0.269646			0.134823	+	0.990870i	$0.456953\pi$
$500$	−9.29728	−	19.5668i	−0.415787	−	0.875054i
$501$	−46.4020			−2.07309
$502$		−	7.30818i		−	0.326180i
$503$			18.6186i			0.830164i	0.909784	+	0.415082i	$0.136247\pi$
$503$			18.6186i			0.830164i	−0.909784	+	0.415082i	$0.863753\pi$
$504$	−8.94701			−0.398532
$505$	−12.3210	−	4.86041i	−0.548278	−	0.216286i
$506$	5.94159			0.264136
$507$		−	13.6443i		−	0.605967i
$508$		−	3.26004i		−	0.144641i
$509$	−26.1610			−1.15957			−0.579784	−	0.814770i	$-0.696863\pi$
$509$	−26.1610			−1.15957			−0.579784	+	0.814770i	$0.696863\pi$
$510$	−1.06463	+	2.69881i	−0.0471427	+	0.119505i
$511$	16.5591			0.732532
$512$		−	17.5682i		−	0.776411i
$513$		0			0
$514$	−1.36880			−0.0603754
$515$	4.10879	−	10.4157i	0.181055	−	0.458969i
$516$	7.90397			0.347953
$517$			0.552830i			0.0243134i
$518$			6.55327i			0.287934i
$519$	−4.48518			−0.196877
$520$	−5.43978	−	2.14589i	−0.238550	−	0.0941036i
$521$	−3.06917			−0.134463			−0.0672315	−	0.997737i	$-0.521417\pi$
$521$	−3.06917			−0.134463			−0.0672315	+	0.997737i	$0.521417\pi$
$522$		−	0.781803i		−	0.0342186i
$523$			11.5164i			0.503576i	0.967782	+	0.251788i	$0.0810186\pi$
$523$			11.5164i			0.503576i	−0.967782	+	0.251788i	$0.918981\pi$
$524$	−14.8808			−0.650072
$525$	33.3013	+	31.1156i	1.45339	+	1.35799i
$526$	0.141929			0.00618838
$527$			2.01899i			0.0879484i
$528$		−	26.1863i		−	1.13961i
$529$	−34.5992			−1.50431
$530$	3.51974	+	1.38847i	0.152888	+	0.0603114i
$531$	−17.9547			−0.779166
$532$		0			0
$533$			16.5844i			0.718350i
$534$	0.853468			0.0369332
$535$	2.31268	−	5.86258i	0.0999859	−	0.253461i
$536$	14.9590			0.646131
$537$			39.7502i			1.71535i
$538$		−	1.10967i		−	0.0478413i
$539$	−27.2243			−1.17263
$540$	−2.57182	+	6.51949i	−0.110674	+	0.280554i
$541$	−29.8468			−1.28322			−0.641608	−	0.767033i	$-0.721732\pi$
$541$	−29.8468			−1.28322			−0.641608	+	0.767033i	$0.721732\pi$
$542$		−	4.43708i		−	0.190589i
$543$		−	33.2294i		−	1.42601i
$544$	6.48567			0.278071
$545$	14.0355	+	5.53676i	0.601216	+	0.237169i
$546$	6.05386			0.259081
$547$			1.17678i			0.0503155i	0.999683	+	0.0251578i	$0.00800881\pi$
$547$			1.17678i			0.0503155i	−0.999683	+	0.0251578i	$0.991991\pi$
$548$		−	18.7848i		−	0.802448i
$549$	2.38771			0.101905
$550$	2.67244	−	2.86017i	0.113953	−	0.121958i
$551$		0			0
$552$		−	17.1780i		−	0.731142i
$553$		−	44.3902i		−	1.88766i
$554$	2.02410			0.0859959
$555$	−31.7184	−	12.5123i	−1.34637	−	0.531118i
$556$	12.4078			0.526207
$557$			45.9826i			1.94834i	0.225807	+	0.974172i	$0.427498\pi$
$557$			45.9826i			1.94834i	−0.225807	+	0.974172i	$0.572502\pi$
$558$			0.513180i			0.0217246i
$559$	−4.71319			−0.199347
$560$	11.7953	−	29.9008i	0.498444	−	1.26354i
$561$	16.2846			0.687535
$562$		−	1.76130i		−	0.0742960i
$563$			23.7250i			0.999890i	0.866057	+	0.499945i	$0.166647\pi$
$563$			23.7250i			0.999890i	−0.866057	+	0.499945i	$0.833353\pi$
$564$	0.786493			0.0331173
$565$	−6.37269	+	16.1546i	−0.268101	+	0.679629i
$566$	−0.324331			−0.0136327
$567$		−	42.0379i		−	1.76543i
$568$		−	10.2646i		−	0.430694i
$569$	−7.42753			−0.311378			−0.155689	−	0.987806i	$-0.549760\pi$
$569$	−7.42753			−0.311378			−0.155689	+	0.987806i	$0.549760\pi$
$570$		0			0
$571$	35.2355			1.47456			0.737279	−	0.675588i	$-0.236110\pi$
$571$	35.2355			1.47456			0.737279	+	0.675588i	$0.236110\pi$
$572$			16.1518i			0.675339i
$573$			18.5316i			0.774169i
$574$	6.16859			0.257472
$575$	−25.9073	+	27.7271i	−1.08041	+	1.15630i
$576$	−15.0274			−0.626140
$577$		−	31.5680i		−	1.31419i	−0.753807	−	0.657096i	$-0.771784\pi$
$577$		−	31.5680i		−	1.31419i	0.753807	−	0.657096i	$-0.228216\pi$
$578$		−	2.97332i		−	0.123674i
$579$	14.1235			0.586953
$580$	5.49216	+	2.16656i	0.228050	+	0.0899614i
$581$	52.4924			2.17775
$582$			8.84436i			0.366610i
$583$		−	21.2380i		−	0.879589i
$584$	−4.11184			−0.170149
$585$	−5.01259	+	12.7068i	−0.207245	+	0.525360i
$586$	−3.73372			−0.154238
$587$		−	37.2187i		−	1.53618i	−0.640342	−	0.768090i	$-0.721207\pi$
$587$		−	37.2187i		−	1.53618i	0.640342	−	0.768090i	$-0.278793\pi$
$588$			38.7311i			1.59725i
$589$		0			0
$590$	−1.60175	+	4.06038i	−0.0659428	+	0.167163i
$591$	40.0839			1.64883
$592$			24.0477i			0.988354i
$593$		−	37.5290i		−	1.54113i	−0.637360	−	0.770566i	$-0.719974\pi$
$593$		−	37.5290i		−	1.54113i	0.637360	−	0.770566i	$-0.280026\pi$
$594$	−1.26637			−0.0519598
$595$	18.5945	+	7.33521i	0.762302	+	0.300714i
$596$	3.76901			0.154385
$597$			0.0243900i			0.000998217i
$598$			5.04053i			0.206123i
$599$	−2.13127			−0.0870813			−0.0435406	−	0.999052i	$-0.513864\pi$
$599$	−2.13127			−0.0870813			−0.0435406	+	0.999052i	$0.513864\pi$
$600$	−8.26913	−	7.72639i	−0.337586	−	0.315429i
$601$	−0.0853415			−0.00348115			−0.00174058	−	0.999998i	$-0.500554\pi$
$601$	−0.0853415			−0.00348115			−0.00174058	+	0.999998i	$0.500554\pi$
$602$			1.75308i			0.0714502i
$603$		−	34.9428i		−	1.42298i
$604$	−32.3910			−1.31797
$605$	2.44201	+	0.963329i	0.0992819	+	0.0391649i
$606$	−3.40484			−0.138312
$607$		−	21.0800i		−	0.855610i	−0.903871	−	0.427805i	$-0.859287\pi$
$607$		−	21.0800i		−	0.855610i	0.903871	−	0.427805i	$-0.140713\pi$
$608$		0			0
$609$	−12.4211			−0.503328
$610$	0.213009	−	0.539971i	0.00862447	−	0.0218628i
$611$	−0.468991			−0.0189734
$612$		−	10.0469i		−	0.406120i
$613$		−	17.8897i		−	0.722559i	−0.932458	−	0.361280i	$-0.882340\pi$
$613$		−	17.8897i		−	0.722559i	0.932458	−	0.361280i	$-0.117660\pi$
$614$	1.25218			0.0505337
$615$	−11.7778	+	29.8565i	−0.474928	+	1.20393i
$616$	12.2087			0.491904
$617$			1.52526i			0.0614045i	0.999529	+	0.0307022i	$0.00977436\pi$
$617$			1.52526i			0.0614045i	−0.999529	+	0.0307022i	$0.990226\pi$
$618$		−	2.87831i		−	0.115783i
$619$	−11.8121			−0.474769			−0.237384	−	0.971416i	$-0.576290\pi$
$619$	−11.8121			−0.474769			−0.237384	+	0.971416i	$0.576290\pi$
$620$	−3.60508	−	1.42214i	−0.144784	−	0.0571145i
$621$	12.2765			0.492638
$622$			4.18190i			0.167679i
$623$		−	5.88031i		−	0.235589i
$624$	22.2151			0.889314
$625$	1.69458	+	24.9425i	0.0677832	+	0.997700i
$626$	−1.43321			−0.0572827
$627$		0			0
$628$			19.0085i			0.758520i
$629$	−14.9546			−0.596280
$630$	4.72631	+	1.86444i	0.188301	+	0.0742811i
$631$	8.02047			0.319290			0.159645	−	0.987174i	$-0.448965\pi$
$631$	8.02047			0.319290			0.159645	+	0.987174i	$0.448965\pi$
$632$			11.0227i			0.438458i
$633$		−	62.4326i		−	2.48147i
$634$	1.98461			0.0788188
$635$	−1.38057	+	3.49970i	−0.0547862	+	0.138881i
$636$	−30.2147			−1.19809
$637$		−	23.0956i		−	0.915083i
$638$			1.06682i			0.0422357i
$639$	−23.9771			−0.948521
$640$	−6.05606	+	15.3519i	−0.239387	+	0.606839i
$641$	−42.0011			−1.65894			−0.829472	−	0.558548i	$-0.811358\pi$
$641$	−42.0011			−1.65894			−0.829472	+	0.558548i	$0.811358\pi$
$642$		−	1.62009i		−	0.0639399i
$643$			12.7588i			0.503158i	0.967837	+	0.251579i	$0.0809498\pi$
$643$			12.7588i			0.503158i	−0.967837	+	0.251579i	$0.919050\pi$
$644$	−58.2398			−2.29497
$645$	−8.48504	−	3.34720i	−0.334098	−	0.131796i
$646$		0			0
$647$		−	44.1646i		−	1.73629i	−0.496311	−	0.868145i	$-0.665312\pi$
$647$		−	44.1646i		−	1.73629i	0.496311	−	0.868145i	$-0.334688\pi$
$648$			10.4386i			0.410065i
$649$	24.5002			0.961718
$650$	2.42641	+	2.26716i	0.0951718	+	0.0889253i
$651$	8.15327			0.319552
$652$		−	9.81565i		−	0.384410i
$653$		−	21.7731i		−	0.852048i	−0.904712	−	0.426024i	$-0.859914\pi$
$653$		−	21.7731i		−	0.852048i	0.904712	−	0.426024i	$-0.140086\pi$
$654$	3.87864			0.151667
$655$	15.9748	+	6.30178i	0.624188	+	0.246231i
$656$	22.6361			0.883790
$657$			9.60485i			0.374721i
$658$			0.174442i			0.00680046i
$659$	41.1821			1.60423			0.802114	−	0.597171i	$-0.203709\pi$
$659$	41.1821			1.60423			0.802114	+	0.597171i	$0.203709\pi$
$660$	−11.4706	+	29.0776i	−0.446492	+	1.13184i
$661$	−13.6157			−0.529588			−0.264794	−	0.964305i	$-0.585304\pi$
$661$	−13.6157			−0.529588			−0.264794	+	0.964305i	$0.585304\pi$
$662$			5.19923i			0.202074i
$663$			13.8150i			0.536529i
$664$	−13.0345			−0.505838
$665$		0			0
$666$	−3.80112			−0.147290
$667$		−	10.3420i		−	0.400443i
$668$		−	39.0646i		−	1.51146i
$669$	17.6079			0.680762
$670$	−7.90218	−	3.11727i	−0.305288	−	0.120430i
$671$	−3.25817			−0.125780
$672$		−	26.1911i		−	1.01034i
$673$			16.0356i			0.618129i	0.951041	+	0.309064i	$0.100016\pi$
$673$			16.0356i			0.618129i	−0.951041	+	0.309064i	$0.899984\pi$
$674$	−6.83362			−0.263221
$675$	5.52178	−	5.90966i	0.212534	−	0.227463i
$676$	11.4868			0.441801
$677$			21.8215i			0.838668i	0.907832	+	0.419334i	$0.137736\pi$
$677$			21.8215i			0.838668i	−0.907832	+	0.419334i	$0.862264\pi$
$678$			4.46423i			0.171448i
$679$	60.9367			2.33854
$680$	−4.61726	−	1.82143i	−0.177064	−	0.0698485i
$681$	59.7525			2.28972
$682$		−	0.700265i		−	0.0268145i
$683$		−	13.5921i		−	0.520088i	−0.965597	−	0.260044i	$-0.916263\pi$
$683$		−	13.5921i		−	0.520088i	0.965597	−	0.260044i	$-0.0837370\pi$
$684$		0			0
$685$	−7.95505	+	20.1658i	−0.303947	+	0.770496i
$686$	−1.66663			−0.0636323
$687$		−	14.7790i		−	0.563855i
$688$			6.43305i			0.245258i
$689$	18.0172			0.686401
$690$	−3.57967	+	9.07435i	−0.136276	+	0.345455i
$691$	18.1458			0.690300			0.345150	−	0.938547i	$-0.387828\pi$
$691$	18.1458			0.690300			0.345150	+	0.938547i	$0.387828\pi$
$692$		−	3.77596i		−	0.143540i
$693$		−	28.5184i		−	1.08332i
$694$	−5.04494			−0.191503
$695$	−13.3200	−	5.25448i	−0.505255	−	0.199314i
$696$	3.08432			0.116911
$697$			14.0768i			0.533196i
$698$		−	3.90210i		−	0.147697i
$699$	43.9493			1.66232
$700$	−26.1954	+	28.0355i	−0.990093	+	1.05964i
$701$	−26.8748			−1.01505			−0.507523	−	0.861638i	$-0.669439\pi$
$701$	−26.8748			−1.01505			−0.507523	+	0.861638i	$0.669439\pi$
$702$		−	1.07432i		−	0.0405477i
$703$		0			0
$704$	20.5058			0.772840
$705$	−0.844313	−	0.333066i	−0.0317987	−	0.0125440i
$706$	−1.14821			−0.0432134
$707$			23.4590i			0.882267i
$708$		−	34.8557i		−	1.30996i
$709$	−20.6855			−0.776861			−0.388431	−	0.921478i	$-0.626983\pi$
$709$	−20.6855			−0.776861			−0.388431	+	0.921478i	$0.626983\pi$
$710$	−2.13901	+	5.42234i	−0.0802758	+	0.203497i
$711$	25.7478			0.965619
$712$			1.46016i			0.0547216i
$713$			6.78853i			0.254232i
$714$	5.13850			0.192304
$715$	6.83999	−	17.3392i	0.255801	−	0.648448i
$716$	−33.4647			−1.25063
$717$		−	19.3142i		−	0.721301i
$718$		−	2.70486i		−	0.100944i
$719$	29.1011			1.08529			0.542644	−	0.839963i	$-0.317423\pi$
$719$	29.1011			1.08529			0.542644	+	0.839963i	$0.317423\pi$
$720$	17.3435	+	6.84170i	0.646354	+	0.254975i
$721$	−19.8313			−0.738556
$722$		0			0
$723$			19.8323i			0.737571i
$724$	27.9750			1.03968
$725$	−4.97843	−	4.65167i	−0.184894	−	0.172759i
$726$	0.674837			0.0250455
$727$		−	10.8609i		−	0.402808i	−0.979508	−	0.201404i	$-0.935450\pi$
$727$		−	10.8609i		−	0.402808i	0.979508	−	0.201404i	$-0.0645504\pi$
$728$			10.3573i			0.383865i
$729$	13.2146			0.489428
$730$	2.17210	+	0.856854i	0.0803931	+	0.0317136i
$731$	−4.00054			−0.147965
$732$			4.63530i			0.171326i
$733$			49.4817i			1.82765i	0.406108	+	0.913825i	$0.366886\pi$
$733$			49.4817i			1.82765i	−0.406108	+	0.913825i	$0.633114\pi$
$734$	1.66393			0.0614169
$735$	16.4020	−	41.5785i	0.604996	−	1.53365i
$736$	21.8071			0.803819
$737$			47.6815i			1.75637i
$738$			3.57799i			0.131708i
$739$	31.5052			1.15894			0.579468	−	0.814995i	$-0.303260\pi$
$739$	31.5052			1.15894			0.579468	+	0.814995i	$0.303260\pi$
$740$	10.5338	−	26.7029i	0.387230	−	0.981617i
$741$		0			0
$742$		−	6.70153i		−	0.246021i
$743$		−	35.6669i		−	1.30849i	−0.756282	−	0.654246i	$-0.772986\pi$
$743$		−	35.6669i		−	1.30849i	0.756282	−	0.654246i	$-0.227014\pi$
$744$	−2.02456			−0.0742240
$745$	−4.04610	−	1.59611i	−0.148237	−	0.0584770i
$746$	4.52577			0.165700
$747$			30.4474i			1.11401i
$748$			13.7096i			0.501271i
$749$	−11.1623			−0.407860
$750$	2.75813	+	5.80469i	0.100713	+	0.211957i
$751$	−2.10024			−0.0766389			−0.0383194	−	0.999266i	$-0.512200\pi$
$751$	−2.10024			−0.0766389			−0.0383194	+	0.999266i	$0.512200\pi$
$752$			0.640127i			0.0233430i
$753$		−	67.3481i		−	2.45430i
$754$	−0.905032			−0.0329593
$755$	34.7722	+	13.7170i	1.26549	+	0.499213i
$756$	12.4130			0.451457
$757$		−	1.15817i		−	0.0420945i	−0.999778	−	0.0210473i	$-0.993300\pi$
$757$		−	1.15817i		−	0.0420945i	0.999778	−	0.0210473i	$-0.00670004\pi$
$758$			7.97396i			0.289627i
$759$	54.7544			1.98746
$760$		0			0
$761$	−44.6406			−1.61822			−0.809111	−	0.587656i	$-0.800051\pi$
$761$	−44.6406			−1.61822			−0.809111	+	0.587656i	$0.800051\pi$
$762$			0.967123i			0.0350352i
$763$		−	26.7235i		−	0.967454i
$764$	−15.6013			−0.564435
$765$	−4.25467	+	10.7855i	−0.153828	+	0.389950i
$766$	−3.44275			−0.124391
$767$			20.7847i			0.750492i
$768$		−	25.8696i		−	0.933489i
$769$	−29.7532			−1.07293			−0.536465	−	0.843923i	$-0.680241\pi$
$769$	−29.7532			−1.07293			−0.536465	+	0.843923i	$0.680241\pi$
$770$	−6.44933	−	2.54415i	−0.232418	−	0.0916846i
$771$	−12.6141			−0.454287
$772$			11.8902i			0.427938i
$773$		−	13.6612i		−	0.491360i	−0.969351	−	0.245680i	$-0.920989\pi$
$773$		−	13.6612i		−	0.491360i	0.969351	−	0.245680i	$-0.0790112\pi$
$774$	−1.01685			−0.0365498
$775$	3.26787	+	3.05338i	0.117385	+	0.109681i
$776$	−15.1314			−0.543185
$777$			60.3913i			2.16652i
$778$		−	6.16433i		−	0.221002i
$779$		0			0
$780$	−24.6679	−	9.73104i	−0.883252	−	0.348427i
$781$	32.7183			1.17075
$782$			4.27839i			0.152995i
$783$			2.20425i			0.0787736i
$784$	−31.5233			−1.12583
$785$	8.04976	−	20.4059i	0.287308	−	0.728318i
$786$	4.41455			0.157462
$787$		−	49.9989i		−	1.78227i	−0.453740	−	0.891134i	$-0.649911\pi$
$787$		−	49.9989i		−	1.78227i	0.453740	−	0.891134i	$-0.350089\pi$
$788$			33.7456i			1.20214i
$789$	1.30793			0.0465637
$790$	2.29698	−	5.82278i	0.0817228	−	0.207165i
$791$	30.7581			1.09363
$792$			7.08149i			0.251630i
$793$		−	2.76406i		−	0.0981547i
$794$	4.46251			0.158369
$795$	32.4359	+	12.7954i	1.15038	+	0.453805i
$796$	−0.0205333			−0.000727785
$797$		−	11.0649i		−	0.391939i	−0.980610	−	0.195969i	$-0.937215\pi$
$797$		−	11.0649i		−	0.391939i	0.980610	−	0.195969i	$-0.0627853\pi$
$798$		0			0
$799$	−0.398078			−0.0140830
$800$	9.80850	−	10.4975i	0.346783	−	0.371142i
$801$	3.41078			0.120514
$802$			5.72730i			0.202238i
$803$		−	13.1064i		−	0.462515i
$804$	67.8350			2.39236
$805$	62.5213	+	24.6635i	2.20359	+	0.869275i
$806$	0.594068			0.0209251
$807$		−	10.2261i		−	0.359976i
$808$		−	5.82518i		−	0.204929i
$809$	−6.05426			−0.212857			−0.106428	−	0.994320i	$-0.533941\pi$
$809$	−6.05426			−0.212857			−0.106428	+	0.994320i	$0.533941\pi$
$810$	2.17526	−	5.51422i	0.0764309	−	0.193750i
$811$	6.97028			0.244760			0.122380	−	0.992483i	$-0.460947\pi$
$811$	6.97028			0.244760			0.122380	+	0.992483i	$0.460947\pi$
$812$		−	10.4570i		−	0.366969i
$813$		−	40.8896i		−	1.43406i
$814$	5.18686			0.181799
$815$	−4.15676	+	10.5373i	−0.145605	+	0.369104i
$816$	18.8561			0.660095
$817$		0			0
$818$			6.28883i			0.219884i
$819$	24.1935			0.845390
$820$	−25.1354	−	9.91545i	−0.877766	−	0.346263i
$821$	9.65335			0.336904			0.168452	−	0.985710i	$-0.446123\pi$
$821$	9.65335			0.336904			0.168452	+	0.985710i	$0.446123\pi$
$822$			5.57271i			0.194371i
$823$			14.4949i			0.505261i	0.967563	+	0.252631i	$0.0812957\pi$
$823$			14.4949i			0.505261i	−0.967563	+	0.252631i	$0.918704\pi$
$824$	4.92436			0.171548
$825$	24.6277	−	26.3577i	0.857427	−	0.917657i
$826$	7.73090			0.268993
$827$		−	27.7016i		−	0.963279i	−0.876369	−	0.481639i	$-0.840041\pi$
$827$		−	27.7016i		−	0.963279i	0.876369	−	0.481639i	$-0.159959\pi$
$828$		−	33.7810i		−	1.17397i
$829$	32.2071			1.11860			0.559299	−	0.828966i	$-0.311070\pi$
$829$	32.2071			1.11860			0.559299	+	0.828966i	$0.311070\pi$
$830$	6.88556	+	2.71623i	0.239001	+	0.0942817i
$831$	18.6530			0.647065
$832$			17.3960i			0.603098i
$833$		−	19.6035i		−	0.679221i
$834$	−3.68090			−0.127459
$835$	−16.5432	+	41.9365i	−0.572501	+	1.45127i
$836$		0			0
$837$		−	1.44688i		−	0.0500116i
$838$			0.0623324i			0.00215324i
$839$	−45.1856			−1.55998			−0.779990	−	0.625791i	$-0.784776\pi$
$839$	−45.1856			−1.55998			−0.779990	+	0.625791i	$0.784776\pi$
$840$	−7.35547	+	18.6459i	−0.253788	+	0.643345i
$841$	−27.1431			−0.935969
$842$		−	7.53453i		−	0.259657i
$843$		−	16.2312i		−	0.559031i
$844$	52.5604			1.80920
$845$	−12.3313	−	4.86447i	−0.424209	−	0.167343i
$846$	−0.101182			−0.00347872
$847$		−	4.64956i		−	0.159761i
$848$		−	24.5917i		−	0.844483i
$849$	−2.98885			−0.102577
$850$	2.05953	+	1.92436i	0.0706414	+	0.0660049i
$851$	−50.2826			−1.72367
$852$		−	46.5473i		−	1.59468i
$853$		−	41.8087i		−	1.43150i	−0.698355	−	0.715751i	$-0.746084\pi$
$853$		−	41.8087i		−	1.43150i	0.698355	−	0.715751i	$-0.253916\pi$
$854$	−1.02810			−0.0351808
$855$		0			0
$856$	2.77173			0.0947358
$857$			42.4772i			1.45099i	0.688226	+	0.725497i	$0.258390\pi$
$857$			42.4772i			1.45099i	−0.688226	+	0.725497i	$0.741610\pi$
$858$		−	4.79158i		−	0.163582i
$859$	−2.27865			−0.0777467			−0.0388733	−	0.999244i	$-0.512377\pi$
$859$	−2.27865			−0.0777467			−0.0388733	+	0.999244i	$0.512377\pi$
$860$	2.81792	−	7.14334i	0.0960902	−	0.243586i
$861$	56.8463			1.93732
$862$		−	3.85029i		−	0.131141i
$863$		−	41.6831i		−	1.41891i	−0.704751	−	0.709455i	$-0.748941\pi$
$863$		−	41.6831i		−	1.41891i	0.704751	−	0.709455i	$-0.251059\pi$
$864$	−4.64788			−0.158124
$865$	−1.59905	+	4.05355i	−0.0543694	+	0.137825i
$866$	−3.13133			−0.106407
$867$		−	27.4004i		−	0.930567i
$868$			6.86403i			0.232980i
$869$	−35.1345			−1.19186
$870$	−1.62931	−	0.642732i	−0.0552387	−	0.0217906i
$871$	−40.4505			−1.37061
$872$			6.63578i			0.224716i
$873$			35.3454i			1.19626i
$874$		0			0
$875$	39.9937	−	19.0032i	1.35203	−	0.642427i
$876$	−18.6461			−0.629992
$877$		−	5.34370i		−	0.180444i	−0.995922	−	0.0902220i	$-0.971242\pi$
$877$		−	5.34370i		−	0.180444i	0.995922	−	0.0902220i	$-0.0287577\pi$
$878$			6.32458i			0.213444i
$879$	−34.4078			−1.16055
$880$	−23.6663	−	9.33591i	−0.797790	−	0.314714i
$881$	19.1989			0.646827			0.323414	−	0.946258i	$-0.395169\pi$
$881$	19.1989			0.646827			0.323414	+	0.946258i	$0.395169\pi$
$882$		−	4.98276i		−	0.167778i
$883$			28.7091i			0.966138i	0.875582	+	0.483069i	$0.160478\pi$
$883$			28.7091i			0.966138i	−0.875582	+	0.483069i	$0.839522\pi$
$884$	−11.6305			−0.391175
$885$	−14.7608	+	37.4182i	−0.496178	+	1.25780i
$886$	−1.85249			−0.0622357
$887$			10.1948i			0.342307i	0.985244	+	0.171153i	$0.0547494\pi$
$887$			10.1948i			0.342307i	−0.985244	+	0.171153i	$0.945251\pi$
$888$		−	14.9959i		−	0.503230i
$889$	6.66338			0.223483
$890$	0.304278	−	0.771335i	0.0101994	−	0.0258552i
$891$	−33.2727			−1.11468
$892$			14.8237i			0.496333i
$893$		0			0
$894$	−1.11812			−0.0373954
$895$	35.9249	+	14.1717i	1.20084	+	0.473708i
$896$	29.2299			0.976501
$897$			46.4507i			1.55094i
$898$			6.00850i			0.200506i
$899$	−1.21889			−0.0406521
$900$	−16.2615	−	15.1942i	−0.542051	−	0.506474i
$901$	15.2930			0.509482
$902$		−	4.88239i		−	0.162566i
$903$			16.1554i			0.537618i
$904$	−7.63763			−0.254024
$905$	−30.0316	−	11.8469i	−0.998283	−	0.393805i
$906$	9.60911			0.319241
$907$		−	39.0849i		−	1.29779i	−0.760877	−	0.648896i	$-0.775231\pi$
$907$		−	39.0849i		−	1.29779i	0.760877	−	0.648896i	$-0.224769\pi$
$908$			50.3041i			1.66940i
$909$	−13.6070			−0.451317
$910$	2.15832	−	5.47127i	0.0715475	−	0.181371i
$911$	36.6728			1.21502			0.607512	−	0.794310i	$-0.292168\pi$
$911$	36.6728			1.21502			0.607512	+	0.794310i	$0.292168\pi$
$912$		0			0
$913$		−	41.5473i		−	1.37502i
$914$	−1.59818			−0.0528629
$915$	1.96297	−	4.97607i	0.0648937	−	0.164504i
$916$	12.4421			0.411098
$917$		−	30.4158i		−	1.00442i
$918$		−	0.911881i		−	0.0300965i
$919$	20.4855			0.675753			0.337877	−	0.941190i	$-0.390291\pi$
$919$	20.4855			0.675753			0.337877	+	0.941190i	$0.390291\pi$
$920$	−15.5248	−	6.12427i	−0.511839	−	0.201911i
$921$	11.5394			0.380235
$922$			3.80872i			0.125434i
$923$			27.7564i			0.913615i
$924$	55.3633			1.82132
$925$	−22.6164	+	24.2051i	−0.743623	+	0.795858i
$926$	−9.09837			−0.298991
$927$		−	11.5028i		−	0.377802i
$928$			3.91547i			0.128532i
$929$	−17.3877			−0.570472			−0.285236	−	0.958457i	$-0.592072\pi$
$929$	−17.3877			−0.570472			−0.285236	+	0.958457i	$0.592072\pi$
$930$	1.06949	+	0.421893i	0.0350698	+	0.0138344i
$931$		0			0
$932$			36.9998i			1.21197i
$933$			38.5380i			1.26168i
$934$	−7.04215			−0.230426
$935$	5.80576	−	14.7174i	0.189869	−	0.481312i
$936$	−6.00756			−0.196363
$937$		−	33.2075i		−	1.08484i	−0.840107	−	0.542421i	$-0.817508\pi$
$937$		−	33.2075i		−	1.08484i	0.840107	−	0.542421i	$-0.182492\pi$
$938$			15.0456i			0.491257i
$939$	−13.2077			−0.431016
$940$	0.280400	−	0.710806i	0.00914564	−	0.0231839i
$941$	−36.7788			−1.19895			−0.599477	−	0.800392i	$-0.704625\pi$
$941$	−36.7788			−1.19895			−0.599477	+	0.800392i	$0.704625\pi$
$942$		−	5.63906i		−	0.183730i
$943$			47.3310i			1.54131i
$944$	28.3691			0.923335
$945$	−13.3256	−	5.25670i	−0.433481	−	0.171000i
$946$	1.38755			0.0451131
$947$		−	34.9882i		−	1.13696i	−0.822696	−	0.568482i	$-0.807531\pi$
$947$		−	34.9882i		−	1.13696i	0.822696	−	0.568482i	$-0.192469\pi$
$948$			49.9847i			1.62343i
$949$	11.1188			0.360931
$950$		0			0
$951$	18.2890			0.593062
$952$			8.79120i			0.284925i
$953$			53.8985i			1.74594i	0.487771	+	0.872972i	$0.337810\pi$
$953$			53.8985i			1.74594i	−0.487771	+	0.872972i	$0.662190\pi$
$954$	3.88712			0.125850
$955$	16.7482	+	6.60687i	0.541960	+	0.213793i
$956$	16.2601			0.525890
$957$			9.83119i			0.317797i
$958$			7.35043i			0.237482i
$959$	38.3954			1.23985
$960$	−12.3542	+	31.3176i	−0.398731	+	1.01077i
$961$	−30.1999			−0.974191
$962$			4.40026i			0.141870i
$963$		−	6.47449i		−	0.208637i
$964$	−16.6963			−0.537752
$965$	5.03530	−	12.7643i	0.162092	−	0.410899i
$966$	17.2774			0.555892
$967$		−	49.8831i		−	1.60413i	−0.597236	−	0.802066i	$-0.703734\pi$
$967$		−	49.8831i		−	1.60413i	0.597236	−	0.802066i	$-0.296266\pi$
$968$			1.15454i			0.0371084i
$969$		0			0
$970$	7.99323	+	3.15318i	0.256647	+	0.101243i
$971$	13.8066			0.443074			0.221537	−	0.975152i	$-0.428893\pi$
$971$	13.8066			0.443074			0.221537	+	0.975152i	$0.428893\pi$
$972$			37.9332i			1.21671i
$973$			25.3610i			0.813037i
$974$	−0.679364			−0.0217682
$975$	22.3605	+	20.8929i	0.716108	+	0.669107i
$976$	−3.77267			−0.120760
$977$			31.6433i			1.01236i	0.862428	+	0.506180i	$0.168943\pi$
$977$			31.6433i			1.01236i	−0.862428	+	0.506180i	$0.831057\pi$
$978$			2.91191i			0.0931127i
$979$	−4.65421			−0.148749
$980$	35.0039	+	13.8084i	1.11816	+	0.441093i
$981$	15.5005			0.494893
$982$		−	4.73599i		−	0.151132i
$983$			40.1898i			1.28186i	0.767601	+	0.640928i	$0.221450\pi$
$983$			40.1898i			1.28186i	−0.767601	+	0.640928i	$0.778550\pi$
$984$	−14.1157			−0.449991
$985$	14.2907	−	36.2264i	0.455339	−	1.15427i
$986$	−0.768188			−0.0244641
$987$			1.60756i			0.0511692i
$988$		0			0
$989$	−13.4512			−0.427724
$990$	1.47569	−	3.74083i	0.0469005	−	0.118891i
$991$	−19.4757			−0.618667			−0.309333	−	0.950954i	$-0.600106\pi$
$991$	−19.4757			−0.618667			−0.309333	+	0.950954i	$0.600106\pi$
$992$		−	2.57014i		−	0.0816020i
$993$			47.9131i			1.52048i
$994$	10.3241			0.327459
$995$	0.0220429	+	0.00869551i	0.000698806	+	0.000275666i
$996$	−59.1081			−1.87291
$997$			14.1426i			0.447901i	0.974601	+	0.223950i	$0.0718953\pi$
$997$			14.1426i			0.447901i	−0.974601	+	0.223950i	$0.928105\pi$
$998$		−	1.50436i		−	0.0476195i
$999$	10.7171			0.339073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.11		24
5.2	odd	4		9025.2.a.cu.1.14		24
5.3	odd	4		9025.2.a.cu.1.11		24
5.4	even	2	inner	1805.2.b.k.1084.14		24
19.9	even	9		95.2.p.a.24.5	yes	48
19.17	even	9		95.2.p.a.4.4	✓	48
19.18	odd	2		1805.2.b.l.1084.14		24
57.17	odd	18		855.2.da.b.289.5		48
57.47	odd	18		855.2.da.b.784.4		48
95.9	even	18		95.2.p.a.24.4	yes	48
95.17	odd	36		475.2.l.f.251.4		48
95.18	even	4		9025.2.a.ct.1.14		24
95.28	odd	36		475.2.l.f.176.5		48
95.37	even	4		9025.2.a.ct.1.11		24
95.47	odd	36		475.2.l.f.176.4		48
95.74	even	18		95.2.p.a.4.5	yes	48
95.93	odd	36		475.2.l.f.251.5		48
95.94	odd	2		1805.2.b.l.1084.11		24
285.74	odd	18		855.2.da.b.289.4		48
285.104	odd	18		855.2.da.b.784.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.4	✓	48	19.17	even	9
95.2.p.a.4.5	yes	48	95.74	even	18
95.2.p.a.24.4	yes	48	95.9	even	18
95.2.p.a.24.5	yes	48	19.9	even	9
475.2.l.f.176.4		48	95.47	odd	36
475.2.l.f.176.5		48	95.28	odd	36
475.2.l.f.251.4		48	95.17	odd	36
475.2.l.f.251.5		48	95.93	odd	36
855.2.da.b.289.4		48	285.74	odd	18
855.2.da.b.289.5		48	57.17	odd	18
855.2.da.b.784.4		48	57.47	odd	18
855.2.da.b.784.5		48	285.104	odd	18
1805.2.b.k.1084.11		24	1.1	even	1	trivial
1805.2.b.k.1084.14		24	5.4	even	2	inner
1805.2.b.l.1084.11		24	95.94	odd	2
1805.2.b.l.1084.14		24	19.18	odd	2
9025.2.a.ct.1.11		24	95.37	even	4
9025.2.a.ct.1.14		24	95.18	even	4
9025.2.a.cu.1.11		24	5.3	odd	4
9025.2.a.cu.1.14		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.249751i q^{2} -2.30156i q^{3} +1.93762 q^{4} +(-2.08007 - 0.820550i) q^{5} -0.574816 q^{6} +3.96043i q^{7} -0.983424i q^{8} -2.29718 q^{9} +(-0.204933 + 0.519499i) q^{10} +3.13464 q^{11} -4.45956i q^{12} +2.65927i q^{13} +0.989119 q^{14} +(-1.88855 + 4.78741i) q^{15} +3.62964 q^{16} +2.25718i q^{17} +0.573722i q^{18} +(-4.03040 - 1.58992i) q^{20} +9.11516 q^{21} -0.782879i q^{22} +7.58941i q^{23} -2.26341 q^{24} +(3.65339 + 3.41361i) q^{25} +0.664153 q^{26} -1.61758i q^{27} +7.67382i q^{28} -1.36269 q^{29} +(1.19566 + 0.471666i) q^{30} +0.894474 q^{31} -2.87335i q^{32} -7.21457i q^{33} +0.563731 q^{34} +(3.24973 - 8.23797i) q^{35} -4.45107 q^{36} +6.62537i q^{37} +6.12046 q^{39} +(-0.806949 + 2.04559i) q^{40} +6.23645 q^{41} -2.27652i q^{42} +1.77237i q^{43} +6.07376 q^{44} +(4.77830 + 1.88495i) q^{45} +1.89546 q^{46} +0.176361i q^{47} -8.35383i q^{48} -8.68497 q^{49} +(0.852550 - 0.912438i) q^{50} +5.19503 q^{51} +5.15266i q^{52} -6.77526i q^{53} -0.403992 q^{54} +(-6.52028 - 2.57213i) q^{55} +3.89478 q^{56} +0.340331i q^{58} +7.81595 q^{59} +(-3.65929 + 9.27620i) q^{60} -1.03941 q^{61} -0.223395i q^{62} -9.09781i q^{63} +6.54166 q^{64} +(2.18206 - 5.53146i) q^{65} -1.80184 q^{66} +15.2111i q^{67} +4.37356i q^{68} +17.4675 q^{69} +(-2.05744 - 0.811622i) q^{70} +10.4376 q^{71} +2.25910i q^{72} -4.18114i q^{73} +1.65469 q^{74} +(7.85662 - 8.40851i) q^{75} +12.4145i q^{77} -1.52859i q^{78} -11.2084 q^{79} +(-7.54991 - 2.97830i) q^{80} -10.6145 q^{81} -1.55756i q^{82} -13.2542i q^{83} +17.6618 q^{84} +(1.85213 - 4.69509i) q^{85} +0.442650 q^{86} +3.13630i q^{87} -3.08269i q^{88} -1.48477 q^{89} +(0.470768 - 1.19338i) q^{90} -10.5318 q^{91} +14.7054i q^{92} -2.05869i q^{93} +0.0440463 q^{94} -6.61320 q^{96} -15.3864i q^{97} +2.16908i q^{98} -7.20085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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