LMFDB - Embedded newform 1205.2.b.c.724.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.29
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.760721i q^{2} +1.12938i q^{3} +1.42130 q^{4} +(1.88699 - 1.19969i) q^{5} -0.859145 q^{6} -2.53853i q^{7} +2.60266i q^{8} +1.72450 q^{9} +O(q^{10})$	\(q+0.760721i q^{2} +1.12938i q^{3} +1.42130 q^{4} +(1.88699 - 1.19969i) q^{5} -0.859145 q^{6} -2.53853i q^{7} +2.60266i q^{8} +1.72450 q^{9} +(0.912633 + 1.43547i) q^{10} -2.06253 q^{11} +1.60519i q^{12} -4.79651i q^{13} +1.93111 q^{14} +(1.35491 + 2.13113i) q^{15} +0.862709 q^{16} +1.95237i q^{17} +1.31186i q^{18} +1.03825 q^{19} +(2.68199 - 1.70513i) q^{20} +2.86697 q^{21} -1.56901i q^{22} +2.68585i q^{23} -2.93940 q^{24} +(2.12147 - 4.52762i) q^{25} +3.64880 q^{26} +5.33576i q^{27} -3.60802i q^{28} -5.84308 q^{29} +(-1.62120 + 1.03071i) q^{30} +7.76074 q^{31} +5.86160i q^{32} -2.32939i q^{33} -1.48521 q^{34} +(-3.04546 - 4.79018i) q^{35} +2.45103 q^{36} -9.08041i q^{37} +0.789817i q^{38} +5.41709 q^{39} +(3.12239 + 4.91119i) q^{40} +9.18849 q^{41} +2.18096i q^{42} +3.23632i q^{43} -2.93148 q^{44} +(3.25411 - 2.06887i) q^{45} -2.04318 q^{46} +4.22721i q^{47} +0.974328i q^{48} +0.555881 q^{49} +(3.44426 + 1.61385i) q^{50} -2.20497 q^{51} -6.81729i q^{52} -6.32114i q^{53} -4.05903 q^{54} +(-3.89198 + 2.47441i) q^{55} +6.60692 q^{56} +1.17258i q^{57} -4.44495i q^{58} -2.97769 q^{59} +(1.92574 + 3.02899i) q^{60} -11.0977 q^{61} +5.90376i q^{62} -4.37768i q^{63} -2.73362 q^{64} +(-5.75434 - 9.05096i) q^{65} +1.77202 q^{66} +1.40319i q^{67} +2.77490i q^{68} -3.03335 q^{69} +(3.64399 - 2.31674i) q^{70} -6.51732 q^{71} +4.48827i q^{72} +1.89995i q^{73} +6.90766 q^{74} +(5.11342 + 2.39595i) q^{75} +1.47566 q^{76} +5.23580i q^{77} +4.12089i q^{78} +13.9020 q^{79} +(1.62792 - 1.03499i) q^{80} -0.852626 q^{81} +6.98988i q^{82} -6.49943i q^{83} +4.07483 q^{84} +(2.34224 + 3.68410i) q^{85} -2.46194 q^{86} -6.59906i q^{87} -5.36807i q^{88} +0.236437 q^{89} +(1.57383 + 2.47547i) q^{90} -12.1761 q^{91} +3.81741i q^{92} +8.76484i q^{93} -3.21573 q^{94} +(1.95916 - 1.24558i) q^{95} -6.61998 q^{96} +13.5524i q^{97} +0.422870i q^{98} -3.55683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.760721i			0.537911i	0.963153	+	0.268956i	$0.0866785\pi$
$2$			0.760721i			0.537911i	−0.963153	+	0.268956i	$0.913322\pi$
$3$			1.12938i			0.652049i	0.945361	+	0.326025i	$0.105709\pi$
$3$			1.12938i			0.652049i	−0.945361	+	0.326025i	$0.894291\pi$
$4$	1.42130			0.710652
$5$	1.88699	−	1.19969i	0.843888	−	0.536519i
$5$	1.88699	−	1.19969i	0.843888	−	0.536519i
$6$	−0.859145			−0.350745
$7$		−	2.53853i		−	0.959473i	−0.877413	−	0.479737i	$-0.840732\pi$
$7$		−	2.53853i		−	0.959473i	0.877413	−	0.479737i	$-0.159268\pi$
$8$			2.60266i			0.920179i
$9$	1.72450			0.574832
$10$	0.912633	+	1.43547i	0.288600	+	0.453937i
$11$	−2.06253			−0.621877			−0.310939	−	0.950430i	$-0.600643\pi$
$11$	−2.06253			−0.621877			−0.310939	+	0.950430i	$0.600643\pi$
$12$			1.60519i			0.463380i
$13$		−	4.79651i		−	1.33031i	−0.746705	−	0.665156i	$-0.768365\pi$
$13$		−	4.79651i		−	1.33031i	0.746705	−	0.665156i	$-0.231635\pi$
$14$	1.93111			0.516111
$15$	1.35491	+	2.13113i	0.349837	+	0.550256i
$16$	0.862709			0.215677
$17$			1.95237i			0.473518i	0.971568	+	0.236759i	$0.0760852\pi$
$17$			1.95237i			0.473518i	−0.971568	+	0.236759i	$0.923915\pi$
$18$			1.31186i			0.309209i
$19$	1.03825			0.238190			0.119095	−	0.992883i	$-0.462001\pi$
$19$	1.03825			0.238190			0.119095	+	0.992883i	$0.462001\pi$
$20$	2.68199	−	1.70513i	0.599710	−	0.381278i
$21$	2.86697			0.625623
$22$		−	1.56901i		−	0.334515i
$23$			2.68585i			0.560039i	0.959994	+	0.280019i	$0.0903409\pi$
$23$			2.68585i			0.560039i	−0.959994	+	0.280019i	$0.909659\pi$
$24$	−2.93940			−0.600002
$25$	2.12147	−	4.52762i	0.424294	−	0.905525i
$26$	3.64880			0.715589
$27$			5.33576i			1.02687i
$28$		−	3.60802i		−	0.681851i
$29$	−5.84308			−1.08503			−0.542516	−	0.840046i	$-0.682528\pi$
$29$	−5.84308			−1.08503			−0.542516	+	0.840046i	$0.682528\pi$
$30$	−1.62120	+	1.03071i	−0.295989	+	0.188181i
$31$	7.76074			1.39387			0.696935	−	0.717134i	$-0.254547\pi$
$31$	7.76074			1.39387			0.696935	+	0.717134i	$0.254547\pi$
$32$			5.86160i			1.03619i
$33$		−	2.32939i		−	0.405494i
$34$	−1.48521			−0.254711
$35$	−3.04546	−	4.79018i	−0.514776	−	0.809688i
$36$	2.45103			0.408505
$37$		−	9.08041i		−	1.49281i	−0.665492	−	0.746405i	$-0.731778\pi$
$37$		−	9.08041i		−	1.49281i	0.665492	−	0.746405i	$-0.268222\pi$
$38$			0.789817i			0.128125i
$39$	5.41709			0.867428
$40$	3.12239	+	4.91119i	0.493694	+	0.776528i
$41$	9.18849			1.43500			0.717501	−	0.696558i	$-0.245286\pi$
$41$	9.18849			1.43500			0.717501	+	0.696558i	$0.245286\pi$
$42$			2.18096i			0.336530i
$43$			3.23632i			0.493534i	0.969075	+	0.246767i	$0.0793682\pi$
$43$			3.23632i			0.493534i	−0.969075	+	0.246767i	$0.920632\pi$
$44$	−2.93148			−0.441938
$45$	3.25411	−	2.06887i	0.485094	−	0.308409i
$46$	−2.04318			−0.301251
$47$			4.22721i			0.616603i	0.951289	+	0.308301i	$0.0997605\pi$
$47$			4.22721i			0.616603i	−0.951289	+	0.308301i	$0.900239\pi$
$48$			0.974328i			0.140632i
$49$	0.555881			0.0794116
$50$	3.44426	+	1.61385i	0.487092	+	0.228232i
$51$	−2.20497			−0.308757
$52$		−	6.81729i		−	0.945388i
$53$		−	6.32114i		−	0.868276i	−0.900846	−	0.434138i	$-0.857053\pi$
$53$		−	6.32114i		−	0.868276i	0.900846	−	0.434138i	$-0.142947\pi$
$54$	−4.05903			−0.552364
$55$	−3.89198	+	2.47441i	−0.524795	+	0.333649i
$56$	6.60692			0.882887
$57$			1.17258i			0.155312i
$58$		−	4.44495i		−	0.583651i
$59$	−2.97769			−0.387662			−0.193831	−	0.981035i	$-0.562091\pi$
$59$	−2.97769			−0.387662			−0.193831	+	0.981035i	$0.562091\pi$
$60$	1.92574	+	3.02899i	0.248612	+	0.391041i
$61$	−11.0977			−1.42091			−0.710456	−	0.703741i	$-0.751511\pi$
$61$	−11.0977			−1.42091			−0.710456	+	0.703741i	$0.751511\pi$
$62$			5.90376i			0.749778i
$63$		−	4.37768i		−	0.551536i
$64$	−2.73362			−0.341703
$65$	−5.75434	−	9.05096i	−0.713738	−	1.12263i
$66$	1.77202			0.218120
$67$			1.40319i			0.171427i	0.996320	+	0.0857134i	$0.0273170\pi$
$67$			1.40319i			0.171427i	−0.996320	+	0.0857134i	$0.972683\pi$
$68$			2.77490i			0.336506i
$69$	−3.03335			−0.365173
$70$	3.64399	−	2.31674i	0.435540	−	0.276904i
$71$	−6.51732			−0.773464			−0.386732	−	0.922192i	$-0.626396\pi$
$71$	−6.51732			−0.773464			−0.386732	+	0.922192i	$0.626396\pi$
$72$			4.48827i			0.528948i
$73$			1.89995i			0.222373i	0.993800	+	0.111186i	$0.0354651\pi$
$73$			1.89995i			0.222373i	−0.993800	+	0.111186i	$0.964535\pi$
$74$	6.90766			0.802999
$75$	5.11342	+	2.39595i	0.590446	+	0.276660i
$76$	1.47566			0.169270
$77$			5.23580i			0.596674i
$78$			4.12089i			0.466599i
$79$	13.9020			1.56410			0.782050	−	0.623215i	$-0.214174\pi$
$79$	13.9020			1.56410			0.782050	+	0.623215i	$0.214174\pi$
$80$	1.62792	−	1.03499i	0.182007	−	0.115715i
$81$	−0.852626			−0.0947362
$82$			6.98988i			0.771904i
$83$		−	6.49943i		−	0.713405i	−0.934218	−	0.356703i	$-0.883901\pi$
$83$		−	6.49943i		−	0.713405i	0.934218	−	0.356703i	$-0.116099\pi$
$84$	4.07483			0.444600
$85$	2.34224	+	3.68410i	0.254052	+	0.399596i
$86$	−2.46194			−0.265477
$87$		−	6.59906i		−	0.707494i
$88$		−	5.36807i		−	0.572238i
$89$	0.236437			0.0250623			0.0125311	−	0.999921i	$-0.496011\pi$
$89$	0.236437			0.0250623			0.0125311	+	0.999921i	$0.496011\pi$
$90$	1.57383	+	2.47547i	0.165896	+	0.260937i
$91$	−12.1761			−1.27640
$92$			3.81741i			0.397992i
$93$			8.76484i			0.908871i
$94$	−3.21573			−0.331677
$95$	1.95916	−	1.24558i	0.201006	−	0.127794i
$96$	−6.61998			−0.675649
$97$			13.5524i			1.37604i	0.725691	+	0.688020i	$0.241520\pi$
$97$			13.5524i			1.37604i	−0.725691	+	0.688020i	$0.758480\pi$
$98$			0.422870i			0.0427164i
$99$	−3.55683			−0.357475
$100$	3.01525	−	6.43512i	0.301525	−	0.643512i
$101$	−12.0004			−1.19409			−0.597044	−	0.802209i	$-0.703658\pi$
$101$	−12.0004			−1.19409			−0.597044	+	0.802209i	$0.703658\pi$
$102$		−	1.67737i		−	0.166084i
$103$			13.6216i			1.34218i	0.741377	+	0.671088i	$0.234173\pi$
$103$			13.6216i			1.34218i	−0.741377	+	0.671088i	$0.765827\pi$
$104$	12.4837			1.22412
$105$	5.40994	−	3.43948i	0.527956	−	0.335659i
$106$	4.80863			0.467055
$107$			13.8286i			1.33686i	0.743773	+	0.668432i	$0.233034\pi$
$107$			13.8286i			1.33686i	−0.743773	+	0.668432i	$0.766966\pi$
$108$			7.58373i			0.729745i
$109$	−13.7652			−1.31846			−0.659232	−	0.751940i	$-0.729118\pi$
$109$	−13.7652			−1.31846			−0.659232	+	0.751940i	$0.729118\pi$
$110$	−1.88234	−	2.96071i	−0.179474	−	0.282293i
$111$	10.2553			0.973386
$112$		−	2.19001i		−	0.206936i
$113$			6.68313i			0.628696i	0.949308	+	0.314348i	$0.101786\pi$
$113$			6.68313i			0.628696i	−0.949308	+	0.314348i	$0.898214\pi$
$114$	−0.892005			−0.0835439
$115$	3.22220	+	5.06818i	0.300472	+	0.472610i
$116$	−8.30478			−0.771080
$117$		−	8.27155i		−	0.764705i
$118$		−	2.26519i		−	0.208528i
$119$	4.95613			0.454328
$120$	−5.54661	+	3.52638i	−0.506334	+	0.321913i
$121$	−6.74596			−0.613269
$122$		−	8.44224i		−	0.764325i
$123$			10.3773i			0.935692i
$124$	11.0304			0.990556
$125$	−1.42857	−	11.0887i	−0.127775	−	0.991803i
$126$	3.33019			0.296677
$127$		−	4.63183i		−	0.411008i	−0.978656	−	0.205504i	$-0.934117\pi$
$127$		−	4.63183i		−	0.411008i	0.978656	−	0.205504i	$-0.0658834\pi$
$128$			9.64367i			0.852388i
$129$	−3.65504			−0.321808
$130$	6.88526	−	4.37745i	0.603877	−	0.383928i
$131$	−10.6049			−0.926558			−0.463279	−	0.886212i	$-0.653327\pi$
$131$	−10.6049			−0.926558			−0.463279	+	0.886212i	$0.653327\pi$
$132$		−	3.31077i		−	0.288165i
$133$		−	2.63562i		−	0.228537i
$134$	−1.06744			−0.0922124
$135$	6.40128	+	10.0685i	0.550935	+	0.866561i
$136$	−5.08134			−0.435721
$137$			18.3739i			1.56979i	0.619629	+	0.784895i	$0.287283\pi$
$137$			18.3739i			1.56979i	−0.619629	+	0.784895i	$0.712717\pi$
$138$		−	2.30754i		−	0.196431i
$139$	5.98608			0.507733			0.253866	−	0.967239i	$-0.418298\pi$
$139$	5.98608			0.507733			0.253866	+	0.967239i	$0.418298\pi$
$140$	−4.32852	−	6.80829i	−0.365826	−	0.575406i
$141$	−4.77414			−0.402055
$142$		−	4.95787i		−	0.416055i
$143$			9.89295i			0.827290i
$144$	1.48774			0.123978
$145$	−11.0258	+	7.00990i	−0.915645	+	0.582141i
$146$	−1.44534			−0.119617
$147$			0.627802i			0.0517802i
$148$		−	12.9060i		−	1.06087i
$149$	6.99343			0.572924			0.286462	−	0.958092i	$-0.407521\pi$
$149$	6.99343			0.572924			0.286462	+	0.958092i	$0.407521\pi$
$150$	−1.82265	+	3.88988i	−0.148819	+	0.317608i
$151$	−23.3270			−1.89833			−0.949164	−	0.314783i	$-0.898068\pi$
$151$	−23.3270			−1.89833			−0.949164	+	0.314783i	$0.898068\pi$
$152$			2.70220i			0.219178i
$153$			3.36685i			0.272193i
$154$	−3.98298			−0.320958
$155$	14.6444	−	9.31051i	1.17627	−	0.747838i
$156$	7.69932			0.616439
$157$			6.99961i			0.558630i	0.960200	+	0.279315i	$0.0901073\pi$
$157$			6.99961i			0.558630i	−0.960200	+	0.279315i	$0.909893\pi$
$158$			10.5756i			0.841347i
$159$	7.13899			0.566158
$160$	7.03212	+	11.0608i	0.555938	+	0.874431i
$161$	6.81811			0.537342
$162$		−	0.648610i		−	0.0509596i
$163$		−	7.32590i		−	0.573809i	−0.957959	−	0.286904i	$-0.907374\pi$
$163$		−	7.32590i		−	0.573809i	0.957959	−	0.286904i	$-0.0926262\pi$
$164$	13.0596			1.01979
$165$	−2.79455	−	4.39553i	−0.217556	−	0.342192i
$166$	4.94426			0.383749
$167$		−	10.8149i		−	0.836882i	−0.908244	−	0.418441i	$-0.862577\pi$
$167$		−	10.8149i		−	0.836882i	0.908244	−	0.418441i	$-0.137423\pi$
$168$			7.46174i			0.575685i
$169$	−10.0065			−0.769728
$170$	−2.80257	+	1.78179i	−0.214947	+	0.136657i
$171$	1.79045			0.136919
$172$			4.59979i			0.350731i
$173$			8.58809i			0.652941i	0.945207	+	0.326470i	$0.105859\pi$
$173$			8.58809i			0.652941i	−0.945207	+	0.326470i	$0.894141\pi$
$174$	5.02005			0.380569
$175$	−11.4935	−	5.38541i	−0.868826	−	0.407098i
$176$	−1.77936			−0.134125
$177$		−	3.36295i		−	0.252775i
$178$			0.179863i			0.0134813i
$179$	−7.06513			−0.528073			−0.264036	−	0.964513i	$-0.585054\pi$
$179$	−7.06513			−0.528073			−0.264036	+	0.964513i	$0.585054\pi$
$180$	4.62507	−	2.94049i	0.344733	−	0.219171i
$181$	−22.5251			−1.67427			−0.837137	−	0.546993i	$-0.815773\pi$
$181$	−22.5251			−1.67427			−0.837137	+	0.546993i	$0.815773\pi$
$182$		−	9.26259i		−	0.686589i
$183$		−	12.5335i		−	0.926505i
$184$	−6.99035			−0.515336
$185$	−10.8937	−	17.1347i	−0.800922	−	1.25976i
$186$	−6.66760			−0.488892
$187$		−	4.02682i		−	0.294470i
$188$			6.00815i			0.438190i
$189$	13.5450			0.985252
$190$	0.947539	+	1.49038i	0.0687417	+	0.108123i
$191$	16.0033			1.15796			0.578981	−	0.815341i	$-0.303451\pi$
$191$	16.0033			1.15796			0.578981	+	0.815341i	$0.303451\pi$
$192$		−	3.08731i		−	0.222807i
$193$		−	15.9736i		−	1.14981i	−0.818221	−	0.574903i	$-0.805040\pi$
$193$		−	15.9736i		−	1.14981i	0.818221	−	0.574903i	$-0.194960\pi$
$194$	−10.3096			−0.740188
$195$	10.2220	−	6.49885i	0.732012	−	0.465392i
$196$	0.790075			0.0564339
$197$		−	24.2137i		−	1.72516i	−0.505922	−	0.862579i	$-0.668848\pi$
$197$		−	24.2137i		−	1.72516i	0.505922	−	0.862579i	$-0.331152\pi$
$198$		−	2.70576i		−	0.192290i
$199$	12.3227			0.873535			0.436768	−	0.899574i	$-0.356123\pi$
$199$	12.3227			0.873535			0.436768	+	0.899574i	$0.356123\pi$
$200$	11.7839	+	5.52146i	0.833244	+	0.390426i
$201$	−1.58474			−0.111779
$202$		−	9.12899i		−	0.642313i
$203$			14.8328i			1.04106i
$204$	−3.13393			−0.219419
$205$	17.3386	−	11.0234i	1.21098	−	0.769906i
$206$	−10.3622			−0.721972
$207$			4.63174i			0.321928i
$208$		−	4.13799i		−	0.286918i
$209$	−2.14142			−0.148125
$210$	2.61649	+	4.11546i	0.180555	+	0.283994i
$211$	26.5630			1.82867			0.914335	−	0.404959i	$-0.132714\pi$
$211$	26.5630			1.82867			0.914335	+	0.404959i	$0.132714\pi$
$212$		−	8.98426i		−	0.617042i
$213$		−	7.36055i		−	0.504336i
$214$	−10.5197			−0.719114
$215$	3.88259	+	6.10690i	0.264791	+	0.416487i
$216$	−13.8872			−0.944902
$217$		−	19.7008i		−	1.33738i
$218$		−	10.4715i		−	0.709216i
$219$	−2.14577			−0.144998
$220$	−5.53168	+	3.51688i	−0.372946	+	0.237108i
$221$	9.36453			0.629927
$222$			7.80139i			0.523595i
$223$		−	8.33195i		−	0.557949i	−0.960299	−	0.278974i	$-0.910006\pi$
$223$		−	8.33195i		−	0.557949i	0.960299	−	0.278974i	$-0.0899944\pi$
$224$	14.8798			0.994200
$225$	3.65846	−	7.80787i	0.243898	−	0.520525i
$226$	−5.08400			−0.338183
$227$		−	4.33870i		−	0.287970i	−0.989580	−	0.143985i	$-0.954008\pi$
$227$		−	4.33870i		−	0.287970i	0.989580	−	0.143985i	$-0.0459917\pi$
$228$			1.66659i			0.110373i
$229$	−29.3533			−1.93972			−0.969859	−	0.243665i	$-0.921650\pi$
$229$	−29.3533			−1.93972			−0.969859	+	0.243665i	$0.921650\pi$
$230$	−3.85547	+	2.45120i	−0.254222	+	0.161627i
$231$	−5.91321			−0.389061
$232$		−	15.2075i		−	0.998423i
$233$		−	13.0291i		−	0.853563i	−0.904355	−	0.426781i	$-0.859647\pi$
$233$		−	13.0291i		−	0.853563i	0.904355	−	0.426781i	$-0.140353\pi$
$234$	6.29235			0.411344
$235$	5.07136	+	7.97672i	0.330819	+	0.520344i
$236$	−4.23220			−0.275492
$237$			15.7007i			1.01987i
$238$			3.77024i			0.244388i
$239$	−7.27224			−0.470402			−0.235201	−	0.971947i	$-0.575575\pi$
$239$	−7.27224			−0.470402			−0.235201	+	0.971947i	$0.575575\pi$
$240$	1.16889	+	1.83855i	0.0754518	+	0.118678i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	5.13179i		−	0.329884i
$243$			15.0443i			0.965095i
$244$	−15.7732			−1.00977
$245$	1.04894	−	0.666887i	0.0670145	−	0.0426058i
$246$	−7.89425			−0.503319
$247$		−	4.97996i		−	0.316867i
$248$			20.1985i			1.28261i
$249$	7.34034			0.465175
$250$	8.43541	−	1.08674i	0.533502	−	0.0687317i
$251$	−27.8592			−1.75846			−0.879229	−	0.476400i	$-0.841941\pi$
$251$	−27.8592			−1.75846			−0.879229	+	0.476400i	$0.841941\pi$
$252$		−	6.22201i		−	0.391950i
$253$		−	5.53966i		−	0.348275i
$254$	3.52353			0.221086
$255$	−4.16075	+	2.64529i	−0.260556	+	0.165654i
$256$	−12.8034			−0.800212
$257$			15.9448i			0.994607i	0.867577	+	0.497303i	$0.165676\pi$
$257$			15.9448i			0.994607i	−0.867577	+	0.497303i	$0.834324\pi$
$258$		−	2.78047i		−	0.173104i
$259$	−23.0509			−1.43231
$260$	−8.17866	−	12.8642i	−0.507219	−	0.797801i
$261$	−10.0764			−0.623711
$262$		−	8.06741i		−	0.498406i
$263$			0.603786i			0.0372310i	0.999827	+	0.0186155i	$0.00592584\pi$
$263$			0.603786i			0.0372310i	−0.999827	+	0.0186155i	$0.994074\pi$
$264$	6.06260			0.373127
$265$	−7.58344	−	11.9279i	−0.465847	−	0.732728i
$266$	2.00497			0.122933
$267$			0.267028i			0.0163418i
$268$			1.99436i			0.121825i
$269$	23.5550			1.43618			0.718088	−	0.695952i	$-0.245018\pi$
$269$	23.5550			1.43618			0.718088	+	0.695952i	$0.245018\pi$
$270$	−7.65935	+	4.86959i	−0.466133	+	0.296354i
$271$	−9.80993			−0.595911			−0.297955	−	0.954580i	$-0.596305\pi$
$271$	−9.80993			−0.595911			−0.297955	+	0.954580i	$0.596305\pi$
$272$			1.68432i			0.102127i
$273$		−	13.7514i		−	0.832274i
$274$	−13.9774			−0.844407
$275$	−4.37560	+	9.33837i	−0.263859	+	0.563125i
$276$	−4.31131			−0.259511
$277$		−	7.76495i		−	0.466551i	−0.972411	−	0.233275i	$-0.925056\pi$
$277$		−	7.76495i		−	0.466551i	0.972411	−	0.233275i	$-0.0749444\pi$
$278$			4.55374i			0.273115i
$279$	13.3834			0.801241
$280$	12.4672	−	7.92628i	0.745057	−	0.473686i
$281$	−20.7632			−1.23863			−0.619314	−	0.785143i	$-0.712589\pi$
$281$	−20.7632			−1.23863			−0.619314	+	0.785143i	$0.712589\pi$
$282$		−	3.63179i		−	0.216270i
$283$			8.45091i			0.502355i	0.967941	+	0.251177i	$0.0808177\pi$
$283$			8.45091i			0.502355i	−0.967941	+	0.251177i	$0.919182\pi$
$284$	−9.26309			−0.549663
$285$	1.40673	+	2.21264i	0.0833278	+	0.131066i
$286$	−7.52578			−0.445009
$287$		−	23.3252i		−	1.37685i
$288$			10.1083i			0.595637i
$289$	13.1883			0.775781
$290$	−5.33258	−	8.38758i	−0.313140	−	0.492536i
$291$	−15.3059			−0.897246
$292$			2.70041i			0.158030i
$293$		−	13.4756i		−	0.787253i	−0.919271	−	0.393626i	$-0.871220\pi$
$293$		−	13.4756i		−	0.787253i	0.919271	−	0.393626i	$-0.128780\pi$
$294$	−0.477582			−0.0278532
$295$	−5.61887	+	3.57231i	−0.327143	+	0.207988i
$296$	23.6332			1.37365
$297$		−	11.0052i		−	0.638586i
$298$			5.32005i			0.308182i
$299$	12.8827			0.745026
$300$	7.26771	+	3.40537i	0.419602	+	0.196609i
$301$	8.21548			0.473533
$302$		−	17.7454i		−	1.02113i
$303$		−	13.5531i		−	0.778604i
$304$	0.895705			0.0513722
$305$	−20.9412	+	13.3138i	−1.19909	+	0.762347i
$306$	−2.56123			−0.146416
$307$		−	9.67527i		−	0.552197i	−0.961129	−	0.276099i	$-0.910958\pi$
$307$		−	9.67527i		−	0.552197i	0.961129	−	0.276099i	$-0.0890416\pi$
$308$			7.44165i			0.424028i
$309$	−15.3840			−0.875165
$310$	7.08270	+	11.1403i	0.402271	+	0.632729i
$311$	−34.8734			−1.97749			−0.988746	−	0.149607i	$-0.952199\pi$
$311$	−34.8734			−1.97749			−0.988746	+	0.149607i	$0.952199\pi$
$312$			14.0988i			0.798189i
$313$			27.2238i			1.53878i	0.638779	+	0.769391i	$0.279440\pi$
$313$			27.2238i			1.53878i	−0.638779	+	0.769391i	$0.720560\pi$
$314$	−5.32475			−0.300493
$315$	−5.25188	−	8.26064i	−0.295910	−	0.465434i
$316$	19.7590			1.11153
$317$		−	2.90326i		−	0.163063i	−0.996671	−	0.0815316i	$-0.974019\pi$
$317$		−	2.90326i		−	0.163063i	0.996671	−	0.0815316i	$-0.0259811\pi$
$318$			5.43078i			0.304543i
$319$	12.0515			0.674756
$320$	−5.15833	+	3.27951i	−0.288359	+	0.183330i
$321$	−15.6178			−0.871701
$322$			5.18668i			0.289042i
$323$			2.02704i			0.112787i
$324$	−1.21184			−0.0673244
$325$	−21.7168	−	10.1756i	−1.20463	−	0.564443i
$326$	5.57297			0.308658
$327$		−	15.5461i		−	0.859703i
$328$			23.9145i			1.32046i
$329$	10.7309			0.591614
$330$	3.34378	−	2.12588i	0.184069	−	0.117026i
$331$	4.82961			0.265459			0.132730	−	0.991152i	$-0.457626\pi$
$331$	4.82961			0.265459			0.132730	+	0.991152i	$0.457626\pi$
$332$		−	9.23766i		−	0.506983i
$333$		−	15.6591i		−	0.858115i
$334$	8.22712			0.450168
$335$	1.68340	+	2.64781i	0.0919739	+	0.144665i
$336$	2.47336			0.134933
$337$			22.1454i			1.20634i	0.797614	+	0.603168i	$0.206095\pi$
$337$			22.1454i			1.20634i	−0.797614	+	0.603168i	$0.793905\pi$
$338$		−	7.61213i		−	0.414045i
$339$	−7.54781			−0.409941
$340$	3.32903	+	5.23622i	0.180542	+	0.283974i
$341$	−16.0068			−0.866816
$342$			1.36204i			0.0736505i
$343$		−	19.1808i		−	1.03567i
$344$	−8.42303			−0.454139
$345$	−5.72391	+	3.63910i	−0.308165	+	0.195922i
$346$	−6.53315			−0.351224
$347$			20.1874i			1.08372i	0.840470	+	0.541859i	$0.182279\pi$
$347$			20.1874i			1.08372i	−0.840470	+	0.541859i	$0.817721\pi$
$348$		−	9.37927i		−	0.502782i
$349$	−4.22280			−0.226041			−0.113021	−	0.993593i	$-0.536053\pi$
$349$	−4.22280			−0.226041			−0.113021	+	0.993593i	$0.536053\pi$
$350$	4.09679	−	8.74335i	0.218983	−	0.467351i
$351$	25.5930			1.36605
$352$		−	12.0897i		−	0.644385i
$353$		−	20.2277i		−	1.07661i	−0.842750	−	0.538305i	$-0.819065\pi$
$353$		−	20.2277i		−	1.07661i	0.842750	−	0.538305i	$-0.180935\pi$
$354$	2.55826			0.135970
$355$	−12.2981	+	7.81879i	−0.652717	+	0.414978i
$356$	0.336048			0.0178105
$357$			5.59737i			0.296244i
$358$		−	5.37460i		−	0.284056i
$359$	23.0788			1.21805			0.609027	−	0.793149i	$-0.291560\pi$
$359$	23.0788			1.21805			0.609027	+	0.793149i	$0.291560\pi$
$360$	5.38455	+	8.46933i	0.283791	+	0.446373i
$361$	−17.9220			−0.943265
$362$		−	17.1353i		−	0.900611i
$363$		−	7.61876i		−	0.399881i
$364$	−17.3059			−0.907074
$365$	2.27936	+	3.58520i	0.119307	+	0.187658i
$366$	9.53452			0.498377
$367$		−	15.5656i		−	0.812516i	−0.913758	−	0.406258i	$-0.866833\pi$
$367$		−	15.5656i		−	0.812516i	0.913758	−	0.406258i	$-0.133167\pi$
$368$			2.31711i			0.120788i
$369$	15.8455			0.824885
$370$	13.0347	−	8.28708i	0.677642	−	0.430825i
$371$	−16.0464			−0.833087
$372$			12.4575i			0.645891i
$373$		−	22.9059i		−	1.18602i	−0.805194	−	0.593011i	$-0.797939\pi$
$373$		−	22.9059i		−	1.18602i	0.805194	−	0.593011i	$-0.202061\pi$
$374$	3.06329			0.158399
$375$	12.5234	−	1.61340i	0.646704	−	0.0833157i
$376$	−11.0020			−0.567385
$377$			28.0263i			1.44343i
$378$			10.3040i			0.529978i
$379$	9.63127			0.494725			0.247363	−	0.968923i	$-0.420436\pi$
$379$	9.63127			0.494725			0.247363	+	0.968923i	$0.420436\pi$
$380$	2.78456	−	1.77035i	0.142845	−	0.0908168i
$381$	5.23110			0.267997
$382$			12.1741i			0.622880i
$383$		−	1.19113i		−	0.0608640i	−0.999537	−	0.0304320i	$-0.990312\pi$
$383$		−	1.19113i		−	0.0608640i	0.999537	−	0.0304320i	$-0.00968831\pi$
$384$	−10.8914			−0.555799
$385$	6.28135	+	9.87990i	0.320127	+	0.503526i
$386$	12.1515			0.618494
$387$			5.58102i			0.283699i
$388$			19.2621i			0.977885i
$389$	12.0151			0.609188			0.304594	−	0.952482i	$-0.401479\pi$
$389$	12.0151			0.609188			0.304594	+	0.952482i	$0.401479\pi$
$390$	4.94381	+	7.77609i	0.250340	+	0.393758i
$391$	−5.24376			−0.265189
$392$			1.44677i			0.0730728i
$393$		−	11.9770i		−	0.604161i
$394$	18.4199			0.927982
$395$	26.2330	−	16.6782i	1.31993	−	0.839170i
$396$	−5.05533			−0.254040
$397$		−	1.30174i		−	0.0653324i	−0.999466	−	0.0326662i	$-0.989600\pi$
$397$		−	1.30174i		−	0.0653324i	0.999466	−	0.0326662i	$-0.0103998\pi$
$398$			9.37416i			0.469884i
$399$	2.97662			0.149017
$400$	1.83021	−	3.90602i	0.0915105	−	0.195301i
$401$	17.7958			0.888680			0.444340	−	0.895858i	$-0.353438\pi$
$401$	17.7958			0.888680			0.444340	+	0.895858i	$0.353438\pi$
$402$		−	1.20554i		−	0.0601270i
$403$		−	37.2244i		−	1.85428i
$404$	−17.0563			−0.848580
$405$	−1.60890	+	1.02289i	−0.0799467	+	0.0508278i
$406$	−11.2836			−0.559997
$407$			18.7286i			0.928345i
$408$		−	5.73877i		−	0.284112i
$409$	−1.21607			−0.0601305			−0.0300653	−	0.999548i	$-0.509572\pi$
$409$	−1.21607			−0.0601305			−0.0300653	+	0.999548i	$0.509572\pi$
$410$	8.38572	+	13.1898i	0.414141	+	0.651400i
$411$	−20.7512			−1.02358
$412$			19.3604i			0.953820i
$413$			7.55894i			0.371951i
$414$	−3.52346			−0.173169
$415$	−7.79733	−	12.2644i	−0.382756	−	0.602034i
$416$	28.1152			1.37846
$417$			6.76057i			0.331067i
$418$		−	1.62902i		−	0.0796781i
$419$	23.5246			1.14925			0.574626	−	0.818416i	$-0.305147\pi$
$419$	23.5246			1.14925			0.574626	+	0.818416i	$0.305147\pi$
$420$	7.68916	−	4.88855i	0.375193	−	0.238537i
$421$	24.1129			1.17519			0.587596	−	0.809154i	$-0.300074\pi$
$421$	24.1129			1.17519			0.587596	+	0.809154i	$0.300074\pi$
$422$			20.2070i			0.983662i
$423$			7.28982i			0.354443i
$424$	16.4518			0.798969
$425$	8.83958	+	4.14188i	0.428782	+	0.200911i
$426$	5.59933			0.271288
$427$			28.1718i			1.36333i
$428$			19.6547i			0.950045i
$429$	−11.1729			−0.539434
$430$	−4.64565	+	2.95357i	−0.224033	+	0.142434i
$431$	9.23057			0.444621			0.222310	−	0.974976i	$-0.428640\pi$
$431$	9.23057			0.444621			0.222310	+	0.974976i	$0.428640\pi$
$432$			4.60321i			0.221472i
$433$		−	40.5437i		−	1.94841i	−0.225673	−	0.974203i	$-0.572458\pi$
$433$		−	40.5437i		−	1.94841i	0.225673	−	0.974203i	$-0.427542\pi$
$434$	14.9869			0.719392
$435$	−7.91686	−	12.4524i	−0.379584	−	0.597046i
$436$	−19.5645			−0.936968
$437$			2.78858i			0.133396i
$438$		−	1.63234i		−	0.0779960i
$439$	−19.5448			−0.932823			−0.466411	−	0.884568i	$-0.654453\pi$
$439$	−19.5448			−0.932823			−0.466411	+	0.884568i	$0.654453\pi$
$440$	−6.44004	−	10.1295i	−0.307017	−	0.482905i
$441$	0.958614			0.0456483
$442$			7.12380i			0.338845i
$443$			38.3533i			1.82222i	0.412165	+	0.911109i	$0.364773\pi$
$443$			38.3533i			1.82222i	−0.412165	+	0.911109i	$0.635227\pi$
$444$	14.5758			0.691738
$445$	0.446154	−	0.283652i	0.0211497	−	0.0134464i
$446$	6.33829			0.300127
$447$			7.89825i			0.373574i
$448$			6.93938i			0.327855i
$449$	7.15454			0.337643			0.168822	−	0.985647i	$-0.446004\pi$
$449$	7.15454			0.337643			0.168822	+	0.985647i	$0.446004\pi$
$450$	5.93961	+	2.78307i	0.279996	+	0.131195i
$451$	−18.9516			−0.892395
$452$			9.49876i			0.446784i
$453$		−	26.3451i		−	1.23780i
$454$	3.30054			0.154902
$455$	−22.9761	+	14.6075i	−1.07714	+	0.684812i
$456$	−3.05182			−0.142915
$457$			13.2079i			0.617838i	0.951088	+	0.308919i	$0.0999672\pi$
$457$			13.2079i			0.617838i	−0.951088	+	0.308919i	$0.900033\pi$
$458$		−	22.3297i		−	1.04340i
$459$	−10.4174			−0.486241
$460$	4.57972	+	7.20342i	0.213531	+	0.335861i
$461$	25.6149			1.19300			0.596502	−	0.802612i	$-0.296557\pi$
$461$	25.6149			1.19300			0.596502	+	0.802612i	$0.296557\pi$
$462$		−	4.49831i		−	0.209280i
$463$			36.7408i			1.70749i	0.520691	+	0.853745i	$0.325674\pi$
$463$			36.7408i			1.70749i	−0.520691	+	0.853745i	$0.674326\pi$
$464$	−5.04087			−0.234017
$465$	10.5151	+	16.5392i	0.487627	+	0.766986i
$466$	9.91149			0.459141
$467$			11.5404i			0.534028i	0.963693	+	0.267014i	$0.0860370\pi$
$467$			11.5404i			0.534028i	−0.963693	+	0.267014i	$0.913963\pi$
$468$		−	11.7564i		−	0.543439i
$469$	3.56203			0.164479
$470$	−6.06806	+	3.85789i	−0.279899	+	0.177951i
$471$	−7.90524			−0.364254
$472$		−	7.74990i		−	0.356718i
$473$		−	6.67502i		−	0.306918i
$474$	−11.9439			−0.548600
$475$	2.20261	−	4.70079i	0.101063	−	0.215687i
$476$	7.04417			0.322869
$477$		−	10.9008i		−	0.499113i
$478$		−	5.53215i		−	0.253035i
$479$	−29.9925			−1.37039			−0.685197	−	0.728358i	$-0.740284\pi$
$479$	−29.9925			−1.37039			−0.685197	+	0.728358i	$0.740284\pi$
$480$	−12.4918	+	7.94195i	−0.570172	+	0.362499i
$481$	−43.5542			−1.98590
$482$			0.760721i			0.0346499i
$483$			7.70025i			0.350373i
$484$	−9.58805			−0.435820
$485$	16.2588	+	25.5733i	0.738273	+	1.16122i
$486$	−11.4446			−0.519135
$487$		−	8.15043i		−	0.369331i	−0.982801	−	0.184666i	$-0.940880\pi$
$487$		−	8.15043i		−	0.369331i	0.982801	−	0.184666i	$-0.0591202\pi$
$488$		−	28.8835i		−	1.30749i
$489$	8.27374			0.374152
$490$	0.507315	+	0.797953i	0.0229182	+	0.0360478i
$491$	−7.89709			−0.356391			−0.178195	−	0.983995i	$-0.557026\pi$
$491$	−7.89709			−0.356391			−0.178195	+	0.983995i	$0.557026\pi$
$492$			14.7493i			0.664951i
$493$		−	11.4078i		−	0.513782i
$494$	3.78836			0.170446
$495$	−6.71171	+	4.26711i	−0.301669	+	0.191792i
$496$	6.69526			0.300626
$497$			16.5444i			0.742118i
$498$			5.58396i			0.250223i
$499$	22.4351			1.00433			0.502166	−	0.864771i	$-0.332537\pi$
$499$	22.4351			1.00433			0.502166	+	0.864771i	$0.332537\pi$
$500$	−2.03043	−	15.7604i	−0.0908036	−	0.704826i
$501$	12.2142			0.545688
$502$		−	21.1931i		−	0.945894i
$503$			7.14129i			0.318415i	0.987245	+	0.159207i	$0.0508938\pi$
$503$			7.14129i			0.318415i	−0.987245	+	0.159207i	$0.949106\pi$
$504$	11.3936			0.507511
$505$	−22.6447	+	14.3969i	−1.00768	+	0.640651i
$506$	4.21414			0.187341
$507$		−	11.3011i		−	0.501900i
$508$		−	6.58323i		−	0.292084i
$509$	12.5554			0.556506			0.278253	−	0.960508i	$-0.410245\pi$
$509$	12.5554			0.556506			0.278253	+	0.960508i	$0.410245\pi$
$510$	−2.01232	−	3.16517i	−0.0891072	−	0.140156i
$511$	4.82308			0.213361
$512$			9.54752i			0.421945i
$513$			5.53984i			0.244590i
$514$	−12.1295			−0.535010
$515$	16.3418	+	25.7038i	0.720104	+	1.13265i
$516$	−5.19492			−0.228694
$517$		−	8.71877i		−	0.383451i
$518$		−	17.5353i		−	0.770456i
$519$	−9.69924			−0.425749
$520$	23.5566	−	14.9766i	1.03302	−	0.656766i
$521$	4.94447			0.216621			0.108310	−	0.994117i	$-0.465456\pi$
$521$	4.94447			0.216621			0.108310	+	0.994117i	$0.465456\pi$
$522$		−	7.66530i		−	0.335501i
$523$		−	1.07988i		−	0.0472200i	−0.999721	−	0.0236100i	$-0.992484\pi$
$523$		−	1.07988i		−	0.0472200i	0.999721	−	0.0236100i	$-0.00751599\pi$
$524$	−15.0728			−0.658460
$525$	6.08218	−	12.9805i	0.265448	−	0.566517i
$526$	−0.459313			−0.0200270
$527$			15.1518i			0.660023i
$528$		−	2.00958i		−	0.0874559i
$529$	15.7862			0.686357
$530$	9.07384	−	5.76888i	0.394142	−	0.250584i
$531$	−5.13501			−0.222840
$532$		−	3.74601i		−	0.162410i
$533$		−	44.0727i		−	1.90900i
$534$	−0.203134			−0.00879045
$535$	16.5901	+	26.0945i	0.717254	+	1.12816i
$536$	−3.65202			−0.157743
$537$		−	7.97923i		−	0.344329i
$538$			17.9188i			0.772535i
$539$	−1.14652			−0.0493842
$540$	9.09816	+	14.3104i	0.391522	+	0.615823i
$541$	−15.7184			−0.675785			−0.337892	−	0.941185i	$-0.609714\pi$
$541$	−15.7184			−0.675785			−0.337892	+	0.941185i	$0.609714\pi$
$542$		−	7.46262i		−	0.320547i
$543$		−	25.4394i		−	1.09171i
$544$	−11.4440			−0.490657
$545$	−25.9747	+	16.5140i	−1.11264	+	0.707381i
$546$	10.4610			0.447689
$547$		−	18.6002i		−	0.795286i	−0.917540	−	0.397643i	$-0.869828\pi$
$547$		−	18.6002i		−	0.795286i	0.917540	−	0.397643i	$-0.130172\pi$
$548$			26.1149i			1.11557i
$549$	−19.1379			−0.816786
$550$	−7.10390	−	3.32861i	−0.302911	−	0.141932i
$551$	−6.06656			−0.258444
$552$		−	7.89478i		−	0.336024i
$553$		−	35.2907i		−	1.50071i
$554$	5.90697			0.250963
$555$	19.3516	−	12.3032i	0.821428	−	0.522240i
$556$	8.50803			0.360821
$557$		−	1.59319i		−	0.0675055i	−0.999430	−	0.0337528i	$-0.989254\pi$
$557$		−	1.59319i		−	0.0675055i	0.999430	−	0.0337528i	$-0.0107459\pi$
$558$			10.1810i			0.430996i
$559$	15.5230			0.656554
$560$	−2.62734	−	4.13253i	−0.111025	−	0.174631i
$561$	4.54782			0.192009
$562$		−	15.7950i		−	0.666272i
$563$			30.0999i			1.26856i	0.773103	+	0.634280i	$0.218703\pi$
$563$			30.0999i			1.26856i	−0.773103	+	0.634280i	$0.781297\pi$
$564$	−6.78550			−0.285721
$565$	8.01771	+	12.6110i	0.337308	+	0.530549i
$566$	−6.42879			−0.270222
$567$			2.16441i			0.0908968i
$568$		−	16.9624i		−	0.711725i
$569$	1.17755			0.0493656			0.0246828	−	0.999695i	$-0.492142\pi$
$569$	1.17755			0.0493656			0.0246828	+	0.999695i	$0.492142\pi$
$570$	−1.68321	+	1.07013i	−0.0705017	+	0.0448229i
$571$	−9.39221			−0.393052			−0.196526	−	0.980499i	$-0.562966\pi$
$571$	−9.39221			−0.393052			−0.196526	+	0.980499i	$0.562966\pi$
$572$			14.0609i			0.587915i
$573$			18.0739i			0.755048i
$574$	17.7440			0.740621
$575$	12.1605	+	5.69795i	0.507129	+	0.237621i
$576$	−4.71413			−0.196422
$577$		−	38.4047i		−	1.59881i	−0.600792	−	0.799405i	$-0.705148\pi$
$577$		−	38.4047i		−	1.59881i	0.600792	−	0.799405i	$-0.294852\pi$
$578$			10.0326i			0.417301i
$579$	18.0403			0.749730
$580$	−15.6710	+	9.96320i	−0.650705	+	0.413699i
$581$	−16.4990			−0.684493
$582$		−	11.6435i		−	0.482639i
$583$			13.0376i			0.539961i
$584$	−4.94493			−0.204623
$585$	−9.92333	−	15.6083i	−0.410279	−	0.645326i
$586$	10.2512			0.423472
$587$		−	32.9101i		−	1.35834i	−0.733979	−	0.679172i	$-0.762339\pi$
$587$		−	32.9101i		−	1.35834i	0.733979	−	0.679172i	$-0.237661\pi$
$588$			0.892297i			0.0367977i
$589$	8.05757			0.332006
$590$	−2.71753	−	4.27439i	−0.111879	−	0.175974i
$591$	27.3466			1.12489
$592$		−	7.83375i		−	0.321965i
$593$			25.5785i			1.05038i	0.850984	+	0.525191i	$0.176006\pi$
$593$			25.5785i			1.05038i	−0.850984	+	0.525191i	$0.823994\pi$
$594$	8.37188			0.343502
$595$	9.35218	−	5.94584i	0.383402	−	0.243756i
$596$	9.93978			0.407149
$597$			13.9171i			0.569588i
$598$			9.80015i			0.400758i
$599$	0.739459			0.0302135			0.0151067	−	0.999886i	$-0.495191\pi$
$599$	0.739459			0.0302135			0.0151067	+	0.999886i	$0.495191\pi$
$600$	−6.23584	+	13.3085i	−0.254577	+	0.543316i
$601$	−12.2755			−0.500730			−0.250365	−	0.968152i	$-0.580551\pi$
$601$	−12.2755			−0.500730			−0.250365	+	0.968152i	$0.580551\pi$
$602$			6.24969i			0.254718i
$603$			2.41979i			0.0985417i
$604$	−33.1548			−1.34905
$605$	−12.7296	+	8.09308i	−0.517530	+	0.329031i
$606$	10.3101			0.418820
$607$			13.7567i			0.558368i	0.960238	+	0.279184i	$0.0900639\pi$
$607$			13.7567i			0.558368i	−0.960238	+	0.279184i	$0.909936\pi$
$608$			6.08579i			0.246811i
$609$	−16.7519			−0.678821
$610$	−10.1281	−	15.9304i	−0.410075	−	0.645005i
$611$	20.2759			0.820273
$612$			4.78531i			0.193435i
$613$			32.1681i			1.29926i	0.760251	+	0.649629i	$0.225076\pi$
$613$			32.1681i			1.29926i	−0.760251	+	0.649629i	$0.774924\pi$
$614$	7.36019			0.297033
$615$	12.4496	+	19.5819i	0.502017	+	0.789619i
$616$	−13.6270			−0.549047
$617$			29.1316i			1.17279i	0.810024	+	0.586397i	$0.199454\pi$
$617$			29.1316i			1.17279i	−0.810024	+	0.586397i	$0.800546\pi$
$618$		−	11.7029i		−	0.470761i
$619$	−4.25398			−0.170982			−0.0854909	−	0.996339i	$-0.527246\pi$
$619$	−4.25398			−0.170982			−0.0854909	+	0.996339i	$0.527246\pi$
$620$	20.8142	−	13.2331i	0.835918	−	0.531452i
$621$	−14.3311			−0.575086
$622$		−	26.5290i		−	1.06371i
$623$		−	0.600201i		−	0.0240466i
$624$	4.67337			0.187084
$625$	−15.9987	−	19.2104i	−0.639950	−	0.768417i
$626$	−20.7097			−0.827728
$627$		−	2.41848i		−	0.0965848i
$628$			9.94857i			0.396991i
$629$	17.7283			0.706873
$630$	6.28405	−	3.99521i	0.250362	−	0.159173i
$631$	8.94679			0.356166			0.178083	−	0.984015i	$-0.443010\pi$
$631$	8.94679			0.356166			0.178083	+	0.984015i	$0.443010\pi$
$632$			36.1822i			1.43925i
$633$			29.9997i			1.19238i
$634$	2.20857			0.0877135
$635$	−5.55677	−	8.74021i	−0.220514	−	0.346845i
$636$	10.1467			0.402341
$637$		−	2.66629i		−	0.105642i
$638$			9.16786i			0.362959i
$639$	−11.2391			−0.444612
$640$	11.5694	+	18.1975i	0.457323	+	0.719320i
$641$	11.6413			0.459803			0.229902	−	0.973214i	$-0.426160\pi$
$641$	11.6413			0.459803			0.229902	+	0.973214i	$0.426160\pi$
$642$		−	11.8808i		−	0.468898i
$643$			31.5371i			1.24370i	0.783136	+	0.621851i	$0.213619\pi$
$643$			31.5371i			1.24370i	−0.783136	+	0.621851i	$0.786381\pi$
$644$	9.69060			0.381863
$645$	−6.89703	+	4.38493i	−0.271570	+	0.172656i
$646$	−1.54201			−0.0606696
$647$			7.63153i			0.300027i	0.988684	+	0.150013i	$0.0479316\pi$
$647$			7.63153i			0.300027i	−0.988684	+	0.150013i	$0.952068\pi$
$648$		−	2.21909i		−	0.0871742i
$649$	6.14158			0.241078
$650$	7.74082	−	16.5204i	0.303620	−	0.647984i
$651$	22.2498			0.872038
$652$		−	10.4123i		−	0.407778i
$653$		−	25.3578i		−	0.992328i	−0.868229	−	0.496164i	$-0.834741\pi$
$653$		−	25.3578i		−	0.992328i	0.868229	−	0.496164i	$-0.165259\pi$
$654$	11.8263			0.462444
$655$	−20.0114	+	12.7227i	−0.781911	+	0.497117i
$656$	7.92699			0.309497
$657$			3.27646i			0.127827i
$658$			8.16322i			0.318236i
$659$	39.0160			1.51985			0.759924	−	0.650011i	$-0.225236\pi$
$659$	39.0160			1.51985			0.759924	+	0.650011i	$0.225236\pi$
$660$	−3.97191	−	6.24739i	−0.154606	−	0.243179i
$661$	48.6676			1.89295			0.946474	−	0.322779i	$-0.104617\pi$
$661$	48.6676			1.89295			0.946474	+	0.322779i	$0.104617\pi$
$662$			3.67399i			0.142794i
$663$			10.5761i			0.410743i
$664$	16.9158			0.656460
$665$	−3.16194	−	4.97339i	−0.122615	−	0.192860i
$666$	11.9122			0.461590
$667$		−	15.6936i		−	0.607660i
$668$		−	15.3713i		−	0.594732i
$669$	9.40995			0.363810
$670$	−2.01424	+	1.28060i	−0.0778170	+	0.0494738i
$671$	22.8893			0.883633
$672$			16.8050i			0.648267i
$673$		−	20.8488i		−	0.803664i	−0.915713	−	0.401832i	$-0.868374\pi$
$673$		−	20.8488i		−	0.803664i	0.915713	−	0.401832i	$-0.131626\pi$
$674$	−16.8465			−0.648902
$675$	24.1583	+	11.3197i	0.929854	+	0.435694i
$676$	−14.2222			−0.547008
$677$		−	30.6907i		−	1.17954i	−0.807572	−	0.589769i	$-0.799219\pi$
$677$		−	30.6907i		−	1.17954i	0.807572	−	0.589769i	$-0.200781\pi$
$678$		−	5.74178i		−	0.220512i
$679$	34.4032			1.32027
$680$	−9.58844	+	6.09605i	−0.367700	+	0.233773i
$681$	4.90005			0.187770
$682$		−	12.1767i		−	0.466270i
$683$			22.3276i			0.854344i	0.904170	+	0.427172i	$0.140490\pi$
$683$			22.3276i			0.854344i	−0.904170	+	0.427172i	$0.859510\pi$
$684$	2.54478			0.0973020
$685$	22.0431	+	34.6714i	0.842222	+	1.32473i
$686$	14.5912			0.557096
$687$		−	33.1511i		−	1.26479i
$688$			2.79200i			0.106444i
$689$	−30.3194			−1.15508
$690$	−2.76834	−	4.35430i	−0.105389	−	0.165765i
$691$	−27.0489			−1.02899			−0.514495	−	0.857493i	$-0.672021\pi$
$691$	−27.0489			−1.02899			−0.514495	+	0.857493i	$0.672021\pi$
$692$			12.2063i			0.464013i
$693$			9.02911i			0.342987i
$694$	−15.3570			−0.582944
$695$	11.2957	−	7.18146i	0.428470	−	0.272408i
$696$	17.1751			0.651021
$697$			17.9393i			0.679499i
$698$		−	3.21238i		−	0.121590i
$699$	14.7148			0.556565
$700$	−16.3357	−	7.65429i	−0.617433	−	0.289305i
$701$	−39.0100			−1.47339			−0.736693	−	0.676227i	$-0.763614\pi$
$701$	−39.0100			−1.47339			−0.736693	+	0.676227i	$0.763614\pi$
$702$			19.4691i			0.734816i
$703$		−	9.42771i		−	0.355573i
$704$	5.63819			0.212497
$705$	−9.00876	+	5.72751i	−0.339290	+	0.215710i
$706$	15.3876			0.579121
$707$			30.4634i			1.14570i
$708$		−	4.77977i		−	0.179635i
$709$	12.6642			0.475612			0.237806	−	0.971313i	$-0.423572\pi$
$709$	12.6642			0.475612			0.237806	+	0.971313i	$0.423572\pi$
$710$	−5.94792	−	9.35545i	−0.223222	−	0.351104i
$711$	23.9740			0.899095
$712$			0.615364i			0.0230618i
$713$			20.8442i			0.780621i
$714$	−4.25804			−0.159353
$715$	11.8685	+	18.6679i	0.443857	+	0.698140i
$716$	−10.0417			−0.375276
$717$		−	8.21314i		−	0.306725i
$718$			17.5566i			0.655205i
$719$	−18.1316			−0.676193			−0.338096	−	0.941111i	$-0.609783\pi$
$719$	−18.1316			−0.676193			−0.338096	+	0.941111i	$0.609783\pi$
$720$	2.80735	−	1.78483i	0.104624	−	0.0665167i
$721$	34.5788			1.28778
$722$		−	13.6337i		−	0.507393i
$723$			1.12938i			0.0420022i
$724$	−32.0149			−1.18983
$725$	−12.3959	+	26.4552i	−0.460372	+	0.982523i
$726$	5.79576			0.215101
$727$		−	21.4455i		−	0.795368i	−0.917522	−	0.397684i	$-0.869814\pi$
$727$		−	21.4455i		−	0.795368i	0.917522	−	0.397684i	$-0.130186\pi$
$728$		−	31.6901i		−	1.17451i
$729$	−19.5487			−0.724026
$730$	−2.72734	+	1.73396i	−0.100943	+	0.0641768i
$731$	−6.31848			−0.233697
$732$		−	17.8139i		−	0.658422i
$733$		−	0.379985i		−	0.0140350i	−0.999975	−	0.00701752i	$-0.997766\pi$
$733$		−	0.379985i		−	0.0140350i	0.999975	−	0.00701752i	$-0.00223377\pi$
$734$	11.8411			0.437061
$735$	0.753170	+	1.18466i	0.0277811	+	0.0436967i
$736$	−15.7434			−0.580309
$737$		−	2.89412i		−	0.106606i
$738$			12.0540i			0.443715i
$739$	−42.6584			−1.56921			−0.784607	−	0.619993i	$-0.787135\pi$
$739$	−42.6584			−1.56921			−0.784607	+	0.619993i	$0.787135\pi$
$740$	−15.4833	−	24.3535i	−0.569176	−	0.895254i
$741$	5.62428			0.206613
$742$		−	12.2068i		−	0.448127i
$743$			17.0856i			0.626810i	0.949620	+	0.313405i	$0.101470\pi$
$743$			17.0856i			0.626810i	−0.949620	+	0.313405i	$0.898530\pi$
$744$	−22.8119			−0.836324
$745$	13.1965	−	8.38997i	0.483483	−	0.307385i
$746$	17.4250			0.637975
$747$		−	11.2082i		−	0.410088i
$748$		−	5.72333i		−	0.209266i
$749$	35.1044			1.28269
$750$	1.22735	+	9.52680i	0.0448164	+	0.347870i
$751$	−33.7135			−1.23022			−0.615111	−	0.788441i	$-0.710889\pi$
$751$	−33.7135			−1.23022			−0.615111	+	0.788441i	$0.710889\pi$
$752$			3.64685i			0.132987i
$753$		−	31.4637i		−	1.14660i
$754$	−21.3202			−0.776437
$755$	−44.0179	+	27.9853i	−1.60198	+	1.01849i
$756$	19.2515			0.700171
$757$		−	16.7814i		−	0.609932i	−0.952363	−	0.304966i	$-0.901355\pi$
$757$		−	16.7814i		−	0.609932i	0.952363	−	0.304966i	$-0.0986450\pi$
$758$			7.32671i			0.266118i
$759$	6.25639			0.227093
$760$	3.24182	+	5.09903i	0.117593	+	0.184961i
$761$	−29.8307			−1.08136			−0.540681	−	0.841227i	$-0.681834\pi$
$761$	−29.8307			−1.08136			−0.540681	+	0.841227i	$0.681834\pi$
$762$			3.97941i			0.144159i
$763$			34.9432i			1.26503i
$764$	22.7456			0.822907
$765$	4.03919	+	6.35321i	0.146037	+	0.229701i
$766$	0.906120			0.0327394
$767$			14.2825i			0.515711i
$768$		−	14.4599i		−	0.521778i
$769$	−7.89994			−0.284879			−0.142440	−	0.989803i	$-0.545495\pi$
$769$	−7.89994			−0.284879			−0.142440	+	0.989803i	$0.545495\pi$
$770$	−7.51585	+	4.77836i	−0.270852	+	0.172200i
$771$	−18.0077			−0.648532
$772$		−	22.7034i		−	0.817112i
$773$		−	25.4969i		−	0.917061i	−0.888679	−	0.458530i	$-0.848376\pi$
$773$		−	25.4969i		−	0.917061i	0.888679	−	0.458530i	$-0.151624\pi$
$774$	−4.24560			−0.152605
$775$	16.4642	−	35.1377i	0.591410	−	1.26218i
$776$	−35.2723			−1.26620
$777$		−	26.0332i		−	0.933937i
$778$			9.14012i			0.327689i
$779$	9.53993			0.341803
$780$	14.5286	−	9.23683i	0.520206	−	0.330732i
$781$	13.4422			0.480999
$782$		−	3.98904i		−	0.142648i
$783$		−	31.1773i		−	1.11418i
$784$	0.479563			0.0171273
$785$	8.39739	+	13.2082i	0.299716	+	0.471421i
$786$	9.11119			0.324985
$787$			49.0412i			1.74813i	0.485809	+	0.874065i	$0.338525\pi$
$787$			49.0412i			1.74813i	−0.485809	+	0.874065i	$0.661475\pi$
$788$		−	34.4151i		−	1.22599i
$789$	−0.681905			−0.0242764
$790$	12.6874	+	19.9560i	0.451399	+	0.710003i
$791$	16.9653			0.603217
$792$		−	9.25721i		−	0.328941i
$793$			53.2301i			1.89026i
$794$	0.990260			0.0351430
$795$	13.4712	−	8.56460i	0.477774	−	0.303755i
$796$	17.5143			0.620779
$797$			1.15733i			0.0409948i	0.999790	+	0.0204974i	$0.00652499\pi$
$797$			1.15733i			0.0409948i	−0.999790	+	0.0204974i	$0.993475\pi$
$798$			2.26438i			0.0801581i
$799$	−8.25307			−0.291973
$800$	26.5391	+	12.4352i	0.938299	+	0.439651i
$801$	0.407734			0.0144066
$802$			13.5377i			0.478031i
$803$		−	3.91872i		−	0.138289i
$804$	−2.25239			−0.0794357
$805$	12.8657	−	8.17964i	0.453457	−	0.288294i
$806$	28.3174			0.997438
$807$			26.6026i			0.936457i
$808$		−	31.2330i		−	1.09877i
$809$	31.6665			1.11334			0.556668	−	0.830735i	$-0.312080\pi$
$809$	31.6665			1.11334			0.556668	+	0.830735i	$0.312080\pi$
$810$	−0.778134	−	1.22392i	−0.0273408	−	0.0430042i
$811$	36.0360			1.26540			0.632698	−	0.774398i	$-0.281947\pi$
$811$	36.0360			1.26540			0.632698	+	0.774398i	$0.281947\pi$
$812$			21.0819i			0.739830i
$813$		−	11.0792i		−	0.388563i
$814$	−14.2473			−0.499367
$815$	−8.78884	−	13.8239i	−0.307860	−	0.484230i
$816$	−1.90224			−0.0665918
$817$			3.36010i			0.117555i
$818$		−	0.925087i		−	0.0323449i
$819$	−20.9976			−0.733714
$820$	24.6434	−	15.6676i	0.860585	−	0.547135i
$821$	30.1203			1.05121			0.525603	−	0.850730i	$-0.323840\pi$
$821$	30.1203			1.05121			0.525603	+	0.850730i	$0.323840\pi$
$822$		−	15.7859i		−	0.550595i
$823$			21.5975i			0.752843i	0.926449	+	0.376421i	$0.122845\pi$
$823$			21.5975i			0.752843i	−0.926449	+	0.376421i	$0.877155\pi$
$824$	−35.4524			−1.23504
$825$	−10.5466	−	4.94172i	−0.367185	−	0.172049i
$826$	−5.75025			−0.200077
$827$		−	2.37687i		−	0.0826519i	−0.999146	−	0.0413259i	$-0.986842\pi$
$827$		−	2.37687i		−	0.0826519i	0.999146	−	0.0413259i	$-0.0131582\pi$
$828$			6.58311i			0.228779i
$829$	20.4204			0.709230			0.354615	−	0.935012i	$-0.384612\pi$
$829$	20.4204			0.709230			0.354615	+	0.935012i	$0.384612\pi$
$830$	9.32977	−	5.93160i	0.323841	−	0.205889i
$831$	8.76960			0.304214
$832$			13.1118i			0.454571i
$833$			1.08528i			0.0376028i
$834$	−5.14291			−0.178084
$835$	−12.9746	−	20.4076i	−0.449004	−	0.706235i
$836$	−3.04361			−0.105265
$837$			41.4094i			1.43132i
$838$			17.8957i			0.618196i
$839$	−2.84185			−0.0981115			−0.0490557	−	0.998796i	$-0.515621\pi$
$839$	−2.84185			−0.0981115			−0.0490557	+	0.998796i	$0.515621\pi$
$840$	8.95180	+	14.0802i	0.308866	+	0.485814i
$841$	5.14153			0.177294
$842$			18.3432i			0.632149i
$843$		−	23.4496i		−	0.807646i
$844$	37.7540			1.29955
$845$	−18.8821	+	12.0047i	−0.649564	+	0.412974i
$846$	−5.54552			−0.190659
$847$			17.1248i			0.588415i
$848$		−	5.45330i		−	0.187267i
$849$	−9.54431			−0.327560
$850$	−3.15082	+	6.72445i	−0.108072	+	0.230647i
$851$	24.3886			0.836032
$852$		−	10.4616i		−	0.358407i
$853$			13.8008i			0.472530i	0.971689	+	0.236265i	$0.0759233\pi$
$853$			13.8008i			0.472530i	−0.971689	+	0.236265i	$0.924077\pi$
$854$	−21.4309			−0.733349
$855$	3.37857	−	2.14800i	0.115545	−	0.0734599i
$856$	−35.9912			−1.23015
$857$			2.06240i			0.0704502i	0.999379	+	0.0352251i	$0.0112148\pi$
$857$			2.06240i			0.0704502i	−0.999379	+	0.0352251i	$0.988785\pi$
$858$		−	8.49948i		−	0.290167i
$859$	22.7067			0.774742			0.387371	−	0.921924i	$-0.373383\pi$
$859$	22.7067			0.774742			0.387371	+	0.921924i	$0.373383\pi$
$860$	5.51834	+	8.67976i	0.188174	+	0.295977i
$861$	26.3431			0.897771
$862$			7.02189i			0.239166i
$863$		−	25.2543i		−	0.859667i	−0.902908	−	0.429833i	$-0.858572\pi$
$863$		−	25.2543i		−	0.859667i	0.902908	−	0.429833i	$-0.141428\pi$
$864$	−31.2761			−1.06403
$865$	10.3031	+	16.2057i	0.350315	+	0.551009i
$866$	30.8425			1.04807
$867$			14.8946i			0.505847i
$868$		−	28.0009i		−	0.950411i
$869$	−28.6734			−0.972678
$870$	9.47279	−	6.02252i	0.321158	−	0.204183i
$871$	6.73041			0.228051
$872$		−	35.8260i		−	1.21322i
$873$			23.3711i			0.790992i
$874$	−2.12133			−0.0717551
$875$	−28.1490	+	3.62646i	−0.951608	+	0.122597i
$876$	−3.04980			−0.103043
$877$			23.5255i			0.794401i	0.917732	+	0.397200i	$0.130018\pi$
$877$			23.5255i			0.794401i	−0.917732	+	0.397200i	$0.869982\pi$
$878$		−	14.8681i		−	0.501776i
$879$	15.2191			0.513327
$880$	−3.35765	+	2.13469i	−0.113186	+	0.0719605i
$881$	−23.8946			−0.805029			−0.402515	−	0.915414i	$-0.631864\pi$
$881$	−23.8946			−0.805029			−0.402515	+	0.915414i	$0.631864\pi$
$882$			0.729238i			0.0245547i
$883$		−	12.9066i		−	0.434342i	−0.976134	−	0.217171i	$-0.930317\pi$
$883$		−	12.9066i		−	0.434342i	0.976134	−	0.217171i	$-0.0696829\pi$
$884$	13.3098			0.447658
$885$	−4.03451	−	6.34585i	−0.135618	−	0.213313i
$886$	−29.1761			−0.980192
$887$		−	26.6396i		−	0.894471i	−0.894416	−	0.447235i	$-0.852409\pi$
$887$		−	26.6396i		−	0.894471i	0.894416	−	0.447235i	$-0.147591\pi$
$888$			26.6909i			0.895689i
$889$	−11.7580			−0.394351
$890$	0.215780	+	0.339399i	0.00723296	+	0.0113767i
$891$	1.75857			0.0589143
$892$		−	11.8422i		−	0.396507i
$893$			4.38889i			0.146869i
$894$	−6.00837			−0.200950
$895$	−13.3318	+	8.47599i	−0.445634	+	0.283321i
$896$	24.4807			0.817843
$897$			14.5495i			0.485793i
$898$			5.44261i			0.181622i
$899$	−45.3466			−1.51239
$900$	5.19979	−	11.0973i	0.173326	−	0.369912i
$901$	12.3412			0.411144
$902$		−	14.4169i		−	0.480029i
$903$			9.27842i			0.308766i
$904$	−17.3939			−0.578513
$905$	−42.5046	+	27.0232i	−1.41290	+	0.898281i
$906$	20.0413			0.665828
$907$			21.2193i			0.704574i	0.935892	+	0.352287i	$0.114596\pi$
$907$			21.2193i			0.704574i	−0.935892	+	0.352287i	$0.885404\pi$
$908$		−	6.16661i		−	0.204646i
$909$	−20.6947			−0.686400
$910$	−11.1123	−	17.4784i	−0.368368	−	0.579404i
$911$	−6.50032			−0.215365			−0.107683	−	0.994185i	$-0.534343\pi$
$911$	−6.50032			−0.215365			−0.107683	+	0.994185i	$0.534343\pi$
$912$			1.01159i			0.0334972i
$913$			13.4053i			0.443650i
$914$	−10.0475			−0.332342
$915$	−15.0364	−	23.6506i	−0.497088	−	0.781866i
$916$	−41.7199			−1.37846
$917$			26.9209i			0.889008i
$918$		−	7.92471i		−	0.261554i
$919$	−19.1428			−0.631461			−0.315731	−	0.948849i	$-0.602250\pi$
$919$	−19.1428			−0.631461			−0.315731	+	0.948849i	$0.602250\pi$
$920$	−13.1907	+	8.38629i	−0.434886	+	0.276488i
$921$	10.9271			0.360060
$922$			19.4858i			0.641730i
$923$			31.2604i			1.02895i
$924$	−8.40447			−0.276487
$925$	−41.1127	−	19.2638i	−1.35178	−	0.633390i
$926$	−27.9495			−0.918478
$927$			23.4904i			0.771526i
$928$		−	34.2498i		−	1.12430i
$929$	58.3414			1.91412			0.957059	−	0.289892i	$-0.0936193\pi$
$929$	58.3414			1.91412			0.957059	+	0.289892i	$0.0936193\pi$
$930$	−12.5817	+	7.99908i	−0.412570	+	0.262300i
$931$	0.577142			0.0189151
$932$		−	18.5183i		−	0.606586i
$933$		−	39.3854i		−	1.28942i
$934$	−8.77906			−0.287260
$935$	−4.83095	−	7.59857i	−0.157989	−	0.248500i
$936$	21.5280			0.703666
$937$		−	15.6711i		−	0.511952i	−0.966683	−	0.255976i	$-0.917603\pi$
$937$		−	15.6711i		−	0.511952i	0.966683	−	0.255976i	$-0.0823968\pi$
$938$			2.70972i			0.0884753i
$939$	−30.7461			−1.00336
$940$	7.20795	+	11.3373i	0.235097	+	0.369783i
$941$	12.8470			0.418799			0.209399	−	0.977830i	$-0.432849\pi$
$941$	12.8470			0.418799			0.209399	+	0.977830i	$0.432849\pi$
$942$		−	6.01368i		−	0.195936i
$943$			24.6789i			0.803657i
$944$	−2.56888			−0.0836098
$945$	25.5592	−	16.2498i	0.831442	−	0.528607i
$946$	5.07783			0.165094
$947$		−	22.7709i		−	0.739954i	−0.929041	−	0.369977i	$-0.879366\pi$
$947$		−	22.7709i		−	0.739954i	0.929041	−	0.369977i	$-0.120634\pi$
$948$			22.3155i			0.724772i
$949$	9.11314			0.295825
$950$	3.57599	+	1.67557i	0.116021	+	0.0543627i
$951$	3.27889			0.106325
$952$			12.8991i			0.418063i
$953$		−	23.0127i		−	0.745453i	−0.927941	−	0.372727i	$-0.878423\pi$
$953$		−	23.0127i		−	0.745453i	0.927941	−	0.372727i	$-0.121577\pi$
$954$	8.29246			0.268478
$955$	30.1982	−	19.1991i	0.977190	−	0.621269i
$956$	−10.3361			−0.334292
$957$			13.6108i			0.439974i
$958$		−	22.8160i		−	0.737150i
$959$	46.6427			1.50617
$960$	−3.70382	−	5.82572i	−0.119540	−	0.188024i
$961$	29.2291			0.942873
$962$		−	33.1326i		−	1.06824i
$963$			23.8474i			0.768472i
$964$	1.42130			0.0457771
$965$	−19.1635	−	30.1421i	−0.616893	−	0.970308i
$966$	−5.85774			−0.188470
$967$			8.23926i			0.264957i	0.991186	+	0.132478i	$0.0422935\pi$
$967$			8.23926i			0.264957i	−0.991186	+	0.132478i	$0.957706\pi$
$968$		−	17.5574i		−	0.564317i
$969$	−2.28930			−0.0735429
$970$	−19.4542	+	12.3684i	−0.624636	+	0.397125i
$971$	−42.6419			−1.36845			−0.684223	−	0.729273i	$-0.739858\pi$
$971$	−42.6419			−1.36845			−0.684223	+	0.729273i	$0.739858\pi$
$972$			21.3826i			0.685846i
$973$		−	15.1958i		−	0.487156i
$974$	6.20021			0.198667
$975$	11.4922	−	24.5265i	0.368044	−	0.785478i
$976$	−9.57407			−0.306458
$977$		−	5.17109i		−	0.165438i	−0.996573	−	0.0827189i	$-0.973640\pi$
$977$		−	5.17109i		−	0.165438i	0.996573	−	0.0827189i	$-0.0263604\pi$
$978$			6.29401i			0.201260i
$979$	−0.487659			−0.0155856
$980$	1.49086	−	0.947848i	0.0476239	−	0.0302779i
$981$	−23.7380			−0.757895
$982$		−	6.00749i		−	0.191707i
$983$			20.8634i			0.665438i	0.943026	+	0.332719i	$0.107966\pi$
$983$			20.8634i			0.665438i	−0.943026	+	0.332719i	$0.892034\pi$
$984$	−27.0086			−0.861003
$985$	−29.0491	−	45.6911i	−0.925581	−	1.45584i
$986$	8.67817			0.276369
$987$			12.1193i			0.385761i
$988$		−	7.07803i		−	0.225182i
$989$	−8.69227			−0.276398
$990$	−3.24608	−	5.10574i	−0.103167	−	0.162271i
$991$	16.2535			0.516311			0.258155	−	0.966103i	$-0.416885\pi$
$991$	16.2535			0.516311			0.258155	+	0.966103i	$0.416885\pi$
$992$			45.4903i			1.44432i
$993$			5.45448i			0.173093i
$994$	−12.5857			−0.399193
$995$	23.2529	−	14.7835i	0.737166	−	0.468669i
$996$	10.4329			0.330578
$997$		−	27.4154i		−	0.868254i	−0.900852	−	0.434127i	$-0.857057\pi$
$997$		−	27.4154i		−	0.868254i	0.900852	−	0.434127i	$-0.142943\pi$
$998$			17.0668i			0.540241i
$999$	48.4509			1.53292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.29	yes	46
5.2	odd	4		6025.2.a.p.1.18		46
5.3	odd	4		6025.2.a.p.1.29		46
5.4	even	2	inner	1205.2.b.c.724.18	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.18	✓	46	5.4	even	2	inner
1205.2.b.c.724.29	yes	46	1.1	even	1	trivial
6025.2.a.p.1.18		46	5.2	odd	4
6025.2.a.p.1.29		46	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.760721i q^{2} +1.12938i q^{3} +1.42130 q^{4} +(1.88699 - 1.19969i) q^{5} -0.859145 q^{6} -2.53853i q^{7} +2.60266i q^{8} +1.72450 q^{9} +O(q^{10})\)	\(q+0.760721i q^{2} +1.12938i q^{3} +1.42130 q^{4} +(1.88699 - 1.19969i) q^{5} -0.859145 q^{6} -2.53853i q^{7} +2.60266i q^{8} +1.72450 q^{9} +(0.912633 + 1.43547i) q^{10} -2.06253 q^{11} +1.60519i q^{12} -4.79651i q^{13} +1.93111 q^{14} +(1.35491 + 2.13113i) q^{15} +0.862709 q^{16} +1.95237i q^{17} +1.31186i q^{18} +1.03825 q^{19} +(2.68199 - 1.70513i) q^{20} +2.86697 q^{21} -1.56901i q^{22} +2.68585i q^{23} -2.93940 q^{24} +(2.12147 - 4.52762i) q^{25} +3.64880 q^{26} +5.33576i q^{27} -3.60802i q^{28} -5.84308 q^{29} +(-1.62120 + 1.03071i) q^{30} +7.76074 q^{31} +5.86160i q^{32} -2.32939i q^{33} -1.48521 q^{34} +(-3.04546 - 4.79018i) q^{35} +2.45103 q^{36} -9.08041i q^{37} +0.789817i q^{38} +5.41709 q^{39} +(3.12239 + 4.91119i) q^{40} +9.18849 q^{41} +2.18096i q^{42} +3.23632i q^{43} -2.93148 q^{44} +(3.25411 - 2.06887i) q^{45} -2.04318 q^{46} +4.22721i q^{47} +0.974328i q^{48} +0.555881 q^{49} +(3.44426 + 1.61385i) q^{50} -2.20497 q^{51} -6.81729i q^{52} -6.32114i q^{53} -4.05903 q^{54} +(-3.89198 + 2.47441i) q^{55} +6.60692 q^{56} +1.17258i q^{57} -4.44495i q^{58} -2.97769 q^{59} +(1.92574 + 3.02899i) q^{60} -11.0977 q^{61} +5.90376i q^{62} -4.37768i q^{63} -2.73362 q^{64} +(-5.75434 - 9.05096i) q^{65} +1.77202 q^{66} +1.40319i q^{67} +2.77490i q^{68} -3.03335 q^{69} +(3.64399 - 2.31674i) q^{70} -6.51732 q^{71} +4.48827i q^{72} +1.89995i q^{73} +6.90766 q^{74} +(5.11342 + 2.39595i) q^{75} +1.47566 q^{76} +5.23580i q^{77} +4.12089i q^{78} +13.9020 q^{79} +(1.62792 - 1.03499i) q^{80} -0.852626 q^{81} +6.98988i q^{82} -6.49943i q^{83} +4.07483 q^{84} +(2.34224 + 3.68410i) q^{85} -2.46194 q^{86} -6.59906i q^{87} -5.36807i q^{88} +0.236437 q^{89} +(1.57383 + 2.47547i) q^{90} -12.1761 q^{91} +3.81741i q^{92} +8.76484i q^{93} -3.21573 q^{94} +(1.95916 - 1.24558i) q^{95} -6.61998 q^{96} +13.5524i q^{97} +0.422870i q^{98} -3.55683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more