LMFDB - Embedded newform 1205.2.b.c.724.18

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

$q$-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	$-0.913322\pi$
$2$		−	0.760721i		−	0.537911i	0.963153	−	0.268956i	$-0.0866785\pi$
$3$		−	1.12938i		−	0.652049i	−0.945361	−	0.326025i	$-0.894291\pi$
$3$		−	1.12938i		−	0.652049i	0.945361	−	0.326025i	$-0.105709\pi$
$4$	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	$0.159268\pi$
$7$			2.53853i			0.959473i	−0.877413	+	0.479737i	$0.840732\pi$
$8$		−	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	$0.231635\pi$
$13$			4.79651i			1.33031i	−0.746705	+	0.665156i	$0.768365\pi$
$14$	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	$-0.923915\pi$
$17$		−	1.95237i		−	0.473518i	0.971568	−	0.236759i	$-0.0760852\pi$
$18$		−	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	$-0.909659\pi$
$23$		−	2.68585i		−	0.560039i	0.959994	−	0.280019i	$-0.0903409\pi$
$24$	−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	$0.268222\pi$
$37$			9.08041i			1.49281i	−0.665492	+	0.746405i	$0.731778\pi$
$38$		−	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	$-0.920632\pi$
$43$		−	3.23632i		−	0.493534i	0.969075	−	0.246767i	$-0.0793682\pi$
$44$	−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	$-0.900239\pi$
$47$		−	4.22721i		−	0.616603i	0.951289	−	0.308301i	$-0.0997605\pi$
$48$		−	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	$0.142947\pi$
$53$			6.32114i			0.868276i	−0.900846	+	0.434138i	$0.857053\pi$
$54$	−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	$-0.972683\pi$
$67$		−	1.40319i		−	0.171427i	0.996320	−	0.0857134i	$-0.0273170\pi$
$68$		−	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	$-0.964535\pi$
$73$		−	1.89995i		−	0.222373i	0.993800	−	0.111186i	$-0.0354651\pi$
$74$	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	$0.116099\pi$
$83$			6.49943i			0.713405i	−0.934218	+	0.356703i	$0.883901\pi$
$84$	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	$-0.758480\pi$
$97$		−	13.5524i		−	1.37604i	0.725691	−	0.688020i	$-0.241520\pi$
$98$		−	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	$-0.765827\pi$
$103$		−	13.6216i		−	1.34218i	0.741377	−	0.671088i	$-0.234173\pi$
$104$	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	$-0.766966\pi$
$107$		−	13.8286i		−	1.33686i	0.743773	−	0.668432i	$-0.233034\pi$
$108$		−	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	$-0.898214\pi$
$113$		−	6.68313i		−	0.628696i	0.949308	−	0.314348i	$-0.101786\pi$
$114$	−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	$0.0658834\pi$
$127$			4.63183i			0.411008i	−0.978656	+	0.205504i	$0.934117\pi$
$128$		−	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	$-0.712717\pi$
$137$		−	18.3739i		−	1.56979i	0.619629	−	0.784895i	$-0.287283\pi$
$138$			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	$-0.909893\pi$
$157$		−	6.99961i		−	0.558630i	0.960200	−	0.279315i	$-0.0901073\pi$
$158$		−	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	$0.0926262\pi$
$163$			7.32590i			0.573809i	−0.957959	+	0.286904i	$0.907374\pi$
$164$	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	$0.137423\pi$
$167$			10.8149i			0.836882i	−0.908244	+	0.418441i	$0.862577\pi$
$168$		−	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	$-0.894141\pi$
$173$		−	8.58809i		−	0.652941i	0.945207	−	0.326470i	$-0.105859\pi$
$174$	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	$0.194960\pi$
$193$			15.9736i			1.14981i	−0.818221	+	0.574903i	$0.805040\pi$
$194$	−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	$0.331152\pi$
$197$			24.2137i			1.72516i	−0.505922	+	0.862579i	$0.668848\pi$
$198$			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	$0.0899944\pi$
$223$			8.33195i			0.557949i	−0.960299	+	0.278974i	$0.910006\pi$
$224$	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	$0.0459917\pi$
$227$			4.33870i			0.287970i	−0.989580	+	0.143985i	$0.954008\pi$
$228$		−	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	$0.140353\pi$
$233$			13.0291i			0.853563i	−0.904355	+	0.426781i	$0.859647\pi$
$234$	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	$-0.834324\pi$
$257$		−	15.9448i		−	0.994607i	0.867577	−	0.497303i	$-0.165676\pi$
$258$			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	$-0.994074\pi$
$263$		−	0.603786i		−	0.0372310i	0.999827	−	0.0186155i	$-0.00592584\pi$
$264$	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	$0.0749444\pi$
$277$			7.76495i			0.466551i	−0.972411	+	0.233275i	$0.925056\pi$
$278$		−	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	$-0.919182\pi$
$283$		−	8.45091i		−	0.502355i	0.967941	−	0.251177i	$-0.0808177\pi$
$284$	−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	$0.128780\pi$
$293$			13.4756i			0.787253i	−0.919271	+	0.393626i	$0.871220\pi$
$294$	−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	$0.0890416\pi$
$307$			9.67527i			0.552197i	−0.961129	+	0.276099i	$0.910958\pi$
$308$		−	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	$-0.720560\pi$
$313$		−	27.2238i		−	1.53878i	0.638779	−	0.769391i	$-0.279440\pi$
$314$	−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	$0.0259811\pi$
$317$			2.90326i			0.163063i	−0.996671	+	0.0815316i	$0.974019\pi$
$318$		−	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	$-0.793905\pi$
$337$		−	22.1454i		−	1.20634i	0.797614	−	0.603168i	$-0.206095\pi$
$338$			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	$-0.817721\pi$
$347$		−	20.1874i		−	1.08372i	0.840470	−	0.541859i	$-0.182279\pi$
$348$			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	$0.180935\pi$
$353$			20.2277i			1.07661i	−0.842750	+	0.538305i	$0.819065\pi$
$354$	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	$0.133167\pi$
$367$			15.5656i			0.812516i	−0.913758	+	0.406258i	$0.866833\pi$
$368$		−	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	$0.202061\pi$
$373$			22.9059i			1.18602i	−0.805194	+	0.593011i	$0.797939\pi$
$374$	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	$0.00968831\pi$
$383$			1.19113i			0.0608640i	−0.999537	+	0.0304320i	$0.990312\pi$
$384$	−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	$0.0103998\pi$
$397$			1.30174i			0.0653324i	−0.999466	+	0.0326662i	$0.989600\pi$
$398$		−	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	$0.427542\pi$
$433$			40.5437i			1.94841i	−0.225673	+	0.974203i	$0.572458\pi$
$434$	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	$-0.635227\pi$
$443$		−	38.3533i		−	1.82222i	0.412165	−	0.911109i	$-0.364773\pi$
$444$	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	$-0.900033\pi$
$457$		−	13.2079i		−	0.617838i	0.951088	−	0.308919i	$-0.0999672\pi$
$458$			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	$-0.674326\pi$
$463$		−	36.7408i		−	1.70749i	0.520691	−	0.853745i	$-0.325674\pi$
$464$	−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	$-0.913963\pi$
$467$		−	11.5404i		−	0.534028i	0.963693	−	0.267014i	$-0.0860370\pi$
$468$			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	$0.0591202\pi$
$487$			8.15043i			0.369331i	−0.982801	+	0.184666i	$0.940880\pi$
$488$			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	$-0.949106\pi$
$503$		−	7.14129i		−	0.318415i	0.987245	−	0.159207i	$-0.0508938\pi$
$504$	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	$0.00751599\pi$
$523$			1.07988i			0.0472200i	−0.999721	+	0.0236100i	$0.992484\pi$
$524$	−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	$0.130172\pi$
$547$			18.6002i			0.795286i	−0.917540	+	0.397643i	$0.869828\pi$
$548$		−	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	$0.0107459\pi$
$557$			1.59319i			0.0675055i	−0.999430	+	0.0337528i	$0.989254\pi$
$558$		−	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	$-0.781297\pi$
$563$		−	30.0999i		−	1.26856i	0.773103	−	0.634280i	$-0.218703\pi$
$564$	−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	$0.294852\pi$
$577$			38.4047i			1.59881i	−0.600792	+	0.799405i	$0.705148\pi$
$578$		−	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	$0.237661\pi$
$587$			32.9101i			1.35834i	−0.733979	+	0.679172i	$0.762339\pi$
$588$		−	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	$-0.823994\pi$
$593$		−	25.5785i		−	1.05038i	0.850984	−	0.525191i	$-0.176006\pi$
$594$	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	$-0.909936\pi$
$607$		−	13.7567i		−	0.558368i	0.960238	−	0.279184i	$-0.0900639\pi$
$608$		−	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	$-0.774924\pi$
$613$		−	32.1681i		−	1.29926i	0.760251	−	0.649629i	$-0.225076\pi$
$614$	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	$-0.800546\pi$
$617$		−	29.1316i		−	1.17279i	0.810024	−	0.586397i	$-0.199454\pi$
$618$			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	$-0.786381\pi$
$643$		−	31.5371i		−	1.24370i	0.783136	−	0.621851i	$-0.213619\pi$
$644$	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	$-0.952068\pi$
$647$		−	7.63153i		−	0.300027i	0.988684	−	0.150013i	$-0.0479316\pi$
$648$			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	$0.165259\pi$
$653$			25.3578i			0.992328i	−0.868229	+	0.496164i	$0.834741\pi$
$654$	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	$0.131626\pi$
$673$			20.8488i			0.803664i	−0.915713	+	0.401832i	$0.868374\pi$
$674$	−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	$0.200781\pi$
$677$			30.6907i			1.17954i	−0.807572	+	0.589769i	$0.799219\pi$
$678$			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	$-0.859510\pi$
$683$		−	22.3276i		−	0.854344i	0.904170	−	0.427172i	$-0.140490\pi$
$684$	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	$0.130186\pi$
$727$			21.4455i			0.795368i	−0.917522	+	0.397684i	$0.869814\pi$
$728$			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	$0.00223377\pi$
$733$			0.379985i			0.0140350i	−0.999975	+	0.00701752i	$0.997766\pi$
$734$	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	$-0.898530\pi$
$743$		−	17.0856i		−	0.626810i	0.949620	−	0.313405i	$-0.101470\pi$
$744$	−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	$0.0986450\pi$
$757$			16.7814i			0.609932i	−0.952363	+	0.304966i	$0.901355\pi$
$758$		−	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	$0.151624\pi$
$773$			25.4969i			0.917061i	−0.888679	+	0.458530i	$0.848376\pi$
$774$	−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	$-0.661475\pi$
$787$		−	49.0412i		−	1.74813i	0.485809	−	0.874065i	$-0.338525\pi$
$788$			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	$-0.993475\pi$
$797$		−	1.15733i		−	0.0409948i	0.999790	−	0.0204974i	$-0.00652499\pi$
$798$		−	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	$-0.877155\pi$
$823$		−	21.5975i		−	0.752843i	0.926449	−	0.376421i	$-0.122845\pi$
$824$	−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	$0.0131582\pi$
$827$			2.37687i			0.0826519i	−0.999146	+	0.0413259i	$0.986842\pi$
$828$		−	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	$-0.924077\pi$
$853$		−	13.8008i		−	0.472530i	0.971689	−	0.236265i	$-0.0759233\pi$
$854$	−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	$-0.988785\pi$
$857$		−	2.06240i		−	0.0704502i	0.999379	−	0.0352251i	$-0.0112148\pi$
$858$			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	$0.141428\pi$
$863$			25.2543i			0.859667i	−0.902908	+	0.429833i	$0.858572\pi$
$864$	−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	$-0.869982\pi$
$877$		−	23.5255i		−	0.794401i	0.917732	−	0.397200i	$-0.130018\pi$
$878$			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	$0.0696829\pi$
$883$			12.9066i			0.434342i	−0.976134	+	0.217171i	$0.930317\pi$
$884$	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	$0.147591\pi$
$887$			26.6396i			0.894471i	−0.894416	+	0.447235i	$0.852409\pi$
$888$		−	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	$-0.885404\pi$
$907$		−	21.2193i		−	0.704574i	0.935892	−	0.352287i	$-0.114596\pi$
$908$			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	$0.0823968\pi$
$937$			15.6711i			0.511952i	−0.966683	+	0.255976i	$0.917603\pi$
$938$		−	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	$0.120634\pi$
$947$			22.7709i			0.739954i	−0.929041	+	0.369977i	$0.879366\pi$
$948$		−	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	$0.121577\pi$
$953$			23.0127i			0.745453i	−0.927941	+	0.372727i	$0.878423\pi$
$954$	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	$-0.957706\pi$
$967$		−	8.23926i		−	0.264957i	0.991186	−	0.132478i	$-0.0422935\pi$
$968$			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	$0.0263604\pi$
$977$			5.17109i			0.165438i	−0.996573	+	0.0827189i	$0.973640\pi$
$978$		−	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	$-0.892034\pi$
$983$		−	20.8634i		−	0.665438i	0.943026	−	0.332719i	$-0.107966\pi$
$984$	−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	$0.142943\pi$
$997$			27.4154i			0.868254i	−0.900852	+	0.434127i	$0.857057\pi$
$998$		−	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.724.18	✓	46
5.2	odd	4		6025.2.a.p.1.29		46
5.3	odd	4		6025.2.a.p.1.18		46
5.4	even	2	inner	1205.2.b.c.724.29	yes	46

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

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

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