LMFDB - Embedded newform 273.2.g.a.272.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(272,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("273.272");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			272.10
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10741 q^{2} +(-0.669305 + 1.59751i) q^{3} -0.773652 q^{4} -1.62666i q^{5} +(0.741192 - 1.76909i) q^{6} +(2.53337 - 0.762910i) q^{7} +3.07156 q^{8} +(-2.10406 - 2.13844i) q^{9} +O(q^{10})$	\(q-1.10741 q^{2} +(-0.669305 + 1.59751i) q^{3} -0.773652 q^{4} -1.62666i q^{5} +(0.741192 - 1.76909i) q^{6} +(2.53337 - 0.762910i) q^{7} +3.07156 q^{8} +(-2.10406 - 2.13844i) q^{9} +1.80138i q^{10} -2.37294 q^{11} +(0.517809 - 1.23591i) q^{12} +(2.05581 + 2.96204i) q^{13} +(-2.80547 + 0.844851i) q^{14} +(2.59861 + 1.08873i) q^{15} -1.85416 q^{16} +5.91393 q^{17} +(2.33005 + 2.36812i) q^{18} +2.16390 q^{19} +1.25847i q^{20} +(-0.476842 + 4.55770i) q^{21} +2.62781 q^{22} +7.30912i q^{23} +(-2.05581 + 4.90684i) q^{24} +2.35397 q^{25} +(-2.27661 - 3.28018i) q^{26} +(4.82443 - 1.92999i) q^{27} +(-1.95995 + 0.590226i) q^{28} +1.65441i q^{29} +(-2.87771 - 1.20567i) q^{30} +3.64629 q^{31} -4.08981 q^{32} +(1.58822 - 3.79079i) q^{33} -6.54913 q^{34} +(-1.24100 - 4.12094i) q^{35} +(1.62781 + 1.65441i) q^{36} -11.3046i q^{37} -2.39632 q^{38} +(-6.10784 + 1.30167i) q^{39} -4.99639i q^{40} +2.27971i q^{41} +(0.528058 - 5.04722i) q^{42} +2.85416 q^{43} +1.83583 q^{44} +(-3.47852 + 3.42260i) q^{45} -8.09416i q^{46} +9.20825i q^{47} +(1.24100 - 2.96204i) q^{48} +(5.83594 - 3.86547i) q^{49} -2.60680 q^{50} +(-3.95822 + 9.44755i) q^{51} +(-1.59048 - 2.29158i) q^{52} -12.3076i q^{53} +(-5.34261 + 2.13728i) q^{54} +3.85998i q^{55} +(7.78140 - 2.34332i) q^{56} +(-1.44831 + 3.45685i) q^{57} -1.83210i q^{58} -9.86130i q^{59} +(-2.01042 - 0.842300i) q^{60} +2.47183i q^{61} -4.03792 q^{62} +(-6.96181 - 3.81225i) q^{63} +8.23740 q^{64} +(4.81823 - 3.34411i) q^{65} +(-1.75881 + 4.19795i) q^{66} +5.91669i q^{67} -4.57532 q^{68} +(-11.6764 - 4.89202i) q^{69} +(1.37429 + 4.56356i) q^{70} +8.43028 q^{71} +(-6.46275 - 6.56834i) q^{72} -7.77786 q^{73} +12.5188i q^{74} +(-1.57552 + 3.76048i) q^{75} -1.67411 q^{76} +(-6.01154 + 1.81034i) q^{77} +(6.76386 - 1.44147i) q^{78} -12.3650 q^{79} +3.01609i q^{80} +(-0.145840 + 8.99882i) q^{81} -2.52456i q^{82} -5.44970i q^{83} +(0.368910 - 3.52607i) q^{84} -9.61998i q^{85} -3.16071 q^{86} +(-2.64293 - 1.10730i) q^{87} -7.28863 q^{88} +10.4191i q^{89} +(3.85213 - 3.79021i) q^{90} +(7.46789 + 5.93554i) q^{91} -5.65471i q^{92} +(-2.44048 + 5.82497i) q^{93} -10.1973i q^{94} -3.51994i q^{95} +(2.73733 - 6.53350i) q^{96} -4.17355 q^{97} +(-6.46275 + 4.28064i) q^{98} +(4.99282 + 5.07439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.10741			−0.783054			−0.391527	−	0.920167i	$-0.628053\pi$
$2$	−1.10741			−0.783054			−0.391527	+	0.920167i	$0.628053\pi$
$3$	−0.669305	+	1.59751i	−0.386423	+	0.922322i
$3$	−0.669305	+	1.59751i	−0.386423	+	0.922322i
$4$	−0.773652			−0.386826
$5$		−	1.62666i		−	0.727466i	−0.931503	−	0.363733i	$-0.881502\pi$
$5$		−	1.62666i		−	0.727466i	0.931503	−	0.363733i	$-0.118498\pi$
$6$	0.741192	−	1.76909i	0.302590	−	0.722228i
$7$	2.53337	−	0.762910i	0.957524	−	0.288353i
$7$	2.53337	−	0.762910i	0.957524	−	0.288353i
$8$	3.07156			1.08596
$9$	−2.10406	−	2.13844i	−0.701354	−	0.712813i
$10$			1.80138i			0.569646i
$11$	−2.37294			−0.715469			−0.357735	−	0.933823i	$-0.616451\pi$
$11$	−2.37294			−0.715469			−0.357735	+	0.933823i	$0.616451\pi$
$12$	0.517809	−	1.23591i	0.149478	−	0.356778i
$13$	2.05581	+	2.96204i	0.570179	+	0.821521i
$13$	2.05581	+	2.96204i	0.570179	+	0.821521i
$14$	−2.80547	+	0.844851i	−0.749794	+	0.225796i
$15$	2.59861	+	1.08873i	0.670958	+	0.281110i
$16$	−1.85416			−0.463540
$17$	5.91393			1.43434			0.717170	−	0.696899i	$-0.245437\pi$
$17$	5.91393			1.43434			0.717170	+	0.696899i	$0.245437\pi$
$18$	2.33005	+	2.36812i	0.549199	+	0.558171i
$19$	2.16390			0.496434			0.248217	−	0.968705i	$-0.420155\pi$
$19$	2.16390			0.496434			0.248217	+	0.968705i	$0.420155\pi$
$20$			1.25847i			0.281403i
$21$	−0.476842	+	4.55770i	−0.104056	+	0.994571i
$22$	2.62781			0.560251
$23$			7.30912i			1.52406i	0.647544	+	0.762028i	$0.275796\pi$
$23$			7.30912i			1.52406i	−0.647544	+	0.762028i	$0.724204\pi$
$24$	−2.05581	+	4.90684i	−0.419640	+	1.00160i
$25$	2.35397			0.470793
$26$	−2.27661	−	3.28018i	−0.446481	−	0.643295i
$27$	4.82443	−	1.92999i	0.928462	−	0.371427i
$28$	−1.95995	+	0.590226i	−0.370395	+	0.111542i
$29$			1.65441i			0.307216i	0.988132	+	0.153608i	$0.0490892\pi$
$29$			1.65441i			0.307216i	−0.988132	+	0.153608i	$0.950911\pi$
$30$	−2.87771	−	1.20567i	−0.525396	−	0.220124i
$31$	3.64629			0.654893			0.327446	−	0.944870i	$-0.393812\pi$
$31$	3.64629			0.654893			0.327446	+	0.944870i	$0.393812\pi$
$32$	−4.08981			−0.722983
$33$	1.58822	−	3.79079i	0.276474	−	0.659893i
$34$	−6.54913			−1.12317
$35$	−1.24100	−	4.12094i	−0.209767	−	0.696566i
$36$	1.62781	+	1.65441i	0.271302	+	0.275734i
$37$		−	11.3046i		−	1.85846i	−0.369500	−	0.929231i	$-0.620471\pi$
$37$		−	11.3046i		−	1.85846i	0.369500	−	0.929231i	$-0.379529\pi$
$38$	−2.39632			−0.388735
$39$	−6.10784	+	1.30167i	−0.978037	+	0.208433i
$40$		−	4.99639i		−	0.789999i
$41$			2.27971i			0.356031i	0.984028	+	0.178015i	$0.0569677\pi$
$41$			2.27971i			0.356031i	−0.984028	+	0.178015i	$0.943032\pi$
$42$	0.528058	−	5.04722i	0.0814811	−	0.778804i
$43$	2.85416			0.435255			0.217628	−	0.976032i	$-0.430168\pi$
$43$	2.85416			0.435255			0.217628	+	0.976032i	$0.430168\pi$
$44$	1.83583			0.276762
$45$	−3.47852	+	3.42260i	−0.518547	+	0.510211i
$46$		−	8.09416i		−	1.19342i
$47$			9.20825i			1.34316i	0.740931	+	0.671581i	$0.234384\pi$
$47$			9.20825i			1.34316i	−0.740931	+	0.671581i	$0.765616\pi$
$48$	1.24100	−	2.96204i	0.179123	−	0.427533i
$49$	5.83594	−	3.86547i	0.833705	−	0.552210i
$50$	−2.60680			−0.368657
$51$	−3.95822	+	9.44755i	−0.554262	+	1.32292i
$52$	−1.59048	−	2.29158i	−0.220560	−	0.317785i
$53$		−	12.3076i		−	1.69058i	−0.534305	−	0.845292i	$-0.679427\pi$
$53$		−	12.3076i		−	1.69058i	0.534305	−	0.845292i	$-0.320573\pi$
$54$	−5.34261	+	2.13728i	−0.727036	+	0.290847i
$55$			3.85998i			0.520480i
$56$	7.78140	−	2.34332i	1.03983	−	0.313140i
$57$	−1.44831	+	3.45685i	−0.191833	+	0.457871i
$58$		−	1.83210i		−	0.240567i
$59$		−	9.86130i		−	1.28383i	−0.766775	−	0.641916i	$-0.778140\pi$
$59$		−	9.86130i		−	1.28383i	0.766775	−	0.641916i	$-0.221860\pi$
$60$	−2.01042	−	0.842300i	−0.259544	−	0.108741i
$61$			2.47183i			0.316485i	0.987400	+	0.158243i	$0.0505828\pi$
$61$			2.47183i			0.316485i	−0.987400	+	0.158243i	$0.949417\pi$
$62$	−4.03792			−0.512817
$63$	−6.96181	−	3.81225i	−0.877105	−	0.480298i
$64$	8.23740			1.02968
$65$	4.81823	−	3.34411i	0.597628	−	0.414786i
$66$	−1.75881	+	4.19795i	−0.216494	+	0.516732i
$67$			5.91669i			0.722839i	0.932403	+	0.361420i	$0.117708\pi$
$67$			5.91669i			0.722839i	−0.932403	+	0.361420i	$0.882292\pi$
$68$	−4.57532			−0.554840
$69$	−11.6764	−	4.89202i	−1.40567	−	0.588931i
$70$	1.37429	+	4.56356i	0.164259	+	0.545449i
$71$	8.43028			1.00049			0.500245	−	0.865884i	$-0.333243\pi$
$71$	8.43028			1.00049			0.500245	+	0.865884i	$0.333243\pi$
$72$	−6.46275	−	6.56834i	−0.761643	−	0.774086i
$73$	−7.77786			−0.910329			−0.455165	−	0.890407i	$-0.650420\pi$
$73$	−7.77786			−0.910329			−0.455165	+	0.890407i	$0.650420\pi$
$74$			12.5188i			1.45528i
$75$	−1.57552	+	3.76048i	−0.181925	+	0.434223i
$76$	−1.67411			−0.192033
$77$	−6.01154	+	1.81034i	−0.685079	+	0.206308i
$78$	6.76386	−	1.44147i	0.765856	−	0.163215i
$79$	−12.3650			−1.39117			−0.695587	−	0.718442i	$-0.744855\pi$
$79$	−12.3650			−1.39117			−0.695587	+	0.718442i	$0.744855\pi$
$80$			3.01609i			0.337210i
$81$	−0.145840	+	8.99882i	−0.0162045	+	0.999869i
$82$		−	2.52456i		−	0.278791i
$83$		−	5.44970i		−	0.598182i	−0.954225	−	0.299091i	$-0.903317\pi$
$83$		−	5.44970i		−	0.598182i	0.954225	−	0.299091i	$-0.0966834\pi$
$84$	0.368910	−	3.52607i	0.0402514	−	0.384726i
$85$		−	9.61998i		−	1.04343i
$86$	−3.16071			−0.340829
$87$	−2.64293	−	1.10730i	−0.283352	−	0.118715i
$88$	−7.28863			−0.776971
$89$			10.4191i			1.10442i	0.833704	+	0.552211i	$0.186216\pi$
$89$			10.4191i			1.10442i	−0.833704	+	0.552211i	$0.813784\pi$
$90$	3.85213	−	3.79021i	0.406051	−	0.399523i
$91$	7.46789	+	5.93554i	0.782848	+	0.622213i
$92$		−	5.65471i		−	0.589544i
$93$	−2.44048	+	5.82497i	−0.253066	+	0.604022i
$94$		−	10.1973i		−	1.05177i
$95$		−	3.51994i		−	0.361139i
$96$	2.73733	−	6.53350i	0.279377	−	0.666823i
$97$	−4.17355			−0.423759			−0.211880	−	0.977296i	$-0.567959\pi$
$97$	−4.17355			−0.423759			−0.211880	+	0.977296i	$0.567959\pi$
$98$	−6.46275	+	4.28064i	−0.652837	+	0.432410i
$99$	4.99282	+	5.07439i	0.501797	+	0.509996i
$100$	−1.82115			−0.182115
$101$	9.02078			0.897602			0.448801	−	0.893632i	$-0.351851\pi$
$101$	9.02078			0.897602			0.448801	+	0.893632i	$0.351851\pi$
$102$	4.38336	−	10.4623i	0.434017	−	1.03592i
$103$			9.99279i			0.984618i	0.870420	+	0.492309i	$0.163847\pi$
$103$			9.99279i			0.984618i	−0.870420	+	0.492309i	$0.836153\pi$
$104$	6.31454	+	9.09806i	0.619191	+	0.892139i
$105$	7.41384	+	0.775662i	0.723517	+	0.0756969i
$106$			13.6295i			1.32382i
$107$			2.27531i			0.219962i	0.993934	+	0.109981i	$0.0350790\pi$
$107$			2.27531i			0.219962i	−0.993934	+	0.109981i	$0.964921\pi$
$108$	−3.73243	+	1.49314i	−0.359153	+	0.143677i
$109$		−	6.91371i		−	0.662213i	−0.943593	−	0.331107i	$-0.892578\pi$
$109$		−	6.91371i		−	0.662213i	0.943593	−	0.331107i	$-0.107422\pi$
$110$		−	4.27457i		−	0.407564i
$111$	18.0592	+	7.56621i	1.71410	+	0.718153i
$112$	−4.69727	+	1.41456i	−0.443851	+	0.133663i
$113$			2.62247i			0.246701i	0.992363	+	0.123351i	$0.0393640\pi$
$113$			2.62247i			0.246701i	−0.992363	+	0.123351i	$0.960636\pi$
$114$	1.60387	−	3.82814i	0.150216	−	0.358538i
$115$	11.8895			1.10870
$116$		−	1.27993i		−	0.118839i
$117$	2.00858	−	10.6285i	0.185693	−	0.982608i
$118$			10.9205i			1.00531i
$119$	14.9822	−	4.51180i	1.37341	−	0.413596i
$120$	7.98178	+	3.34411i	0.728633	+	0.305274i
$121$	−5.36914			−0.488104
$122$		−	2.73732i		−	0.247825i
$123$	−3.64185	−	1.52582i	−0.328375	−	0.137579i
$124$	−2.82096			−0.253329
$125$		−	11.9624i		−	1.06995i
$126$	7.70955	+	4.22171i	0.686821	+	0.376100i
$127$	2.49981			0.221822			0.110911	−	0.993830i	$-0.464623\pi$
$127$	2.49981			0.221822			0.110911	+	0.993830i	$0.464623\pi$
$128$	−0.942528			−0.0833085
$129$	−1.91030	+	4.55954i	−0.168193	+	0.401445i
$130$	−5.33574	+	3.70329i	−0.467976	+	0.324800i
$131$	3.56180			0.311196			0.155598	−	0.987820i	$-0.450270\pi$
$131$	3.56180			0.311196			0.155598	+	0.987820i	$0.450270\pi$
$132$	−1.22873	+	2.93275i	−0.106947	+	0.255264i
$133$	5.48197	−	1.65086i	0.475347	−	0.143148i
$134$		−	6.55218i		−	0.566022i
$135$	−3.13944	−	7.84773i	−0.270200	−	0.675425i
$136$	18.1650			1.55764
$137$	−10.5526			−0.901566			−0.450783	−	0.892634i	$-0.648855\pi$
$137$	−10.5526			−0.901566			−0.450783	+	0.892634i	$0.648855\pi$
$138$	12.9305	+	5.41746i	1.10072	+	0.461165i
$139$			5.51633i			0.467889i	0.972250	+	0.233945i	$0.0751634\pi$
$139$			5.51633i			0.467889i	−0.972250	+	0.233945i	$0.924837\pi$
$140$	0.960100	+	3.18817i	0.0811433	+	0.269450i
$141$	−14.7103	−	6.16313i	−1.23883	−	0.519029i
$142$	−9.33574			−0.783438
$143$	−4.87832	−	7.02874i	−0.407945	−	0.587773i
$144$	3.90127	+	3.96501i	0.325106	+	0.330417i
$145$	2.69116			0.223489
$146$	8.61325			0.712837
$147$	2.26910	+	11.9101i	0.187152	+	0.982331i
$148$			8.74581i			0.718901i
$149$	−13.4992			−1.10590			−0.552948	−	0.833216i	$-0.686497\pi$
$149$	−13.4992			−1.10590			−0.552948	+	0.833216i	$0.686497\pi$
$150$	1.74474	−	4.16438i	0.142457	−	0.340020i
$151$			14.1337i			1.15018i	0.818089	+	0.575092i	$0.195034\pi$
$151$			14.1337i			1.15018i	−0.818089	+	0.575092i	$0.804966\pi$
$152$	6.64656			0.539107
$153$	−12.4433	−	12.6466i	−1.00598	−	1.02242i
$154$	6.65722	−	2.00478i	0.536454	−	0.161550i
$155$		−	5.93128i		−	0.476412i
$156$	4.72534	−	1.00704i	0.378330	−	0.0806274i
$157$		−	7.77818i		−	0.620767i	−0.950612	−	0.310383i	$-0.899543\pi$
$157$		−	7.77818i		−	0.620767i	0.950612	−	0.310383i	$-0.100457\pi$
$158$	13.6931			1.08936
$159$	19.6615	+	8.23755i	1.55926	+	0.653281i
$160$			6.65274i			0.525946i
$161$	5.57620	+	18.5167i	0.439466	+	1.45932i
$162$	0.161504	−	9.96535i	0.0126890	−	0.782952i
$163$		−	12.9779i		−	1.01651i	−0.861207	−	0.508254i	$-0.830291\pi$
$163$		−	12.9779i		−	1.01651i	0.861207	−	0.508254i	$-0.169709\pi$
$164$		−	1.76370i		−	0.137722i
$165$	−6.16635	−	2.58350i	−0.480050	−	0.201125i
$166$			6.03503i			0.468409i
$167$		−	9.94464i		−	0.769539i	−0.923013	−	0.384770i	$-0.874281\pi$
$167$		−	9.94464i		−	0.769539i	0.923013	−	0.384770i	$-0.125719\pi$
$168$	−1.46465	+	13.9992i	−0.113000	+	1.08006i
$169$	−4.54730	+	12.1788i	−0.349793	+	0.936827i
$170$			10.6532i			0.817065i
$171$	−4.55299	−	4.62738i	−0.348176	−	0.353864i
$172$	−2.20813			−0.168368
$173$	−10.2328			−0.777982			−0.388991	−	0.921242i	$-0.627176\pi$
$173$	−10.2328			−0.777982			−0.388991	+	0.921242i	$0.627176\pi$
$174$	2.92679	+	1.22623i	0.221880	+	0.0929605i
$175$	5.96347	−	1.79586i	0.450796	−	0.135755i
$176$	4.39982			0.331649
$177$	15.7535	+	6.60021i	1.18411	+	0.496102i
$178$		−	11.5382i		−	0.864823i
$179$			11.8979i			0.889288i	0.895707	+	0.444644i	$0.146670\pi$
$179$			11.8979i			0.889288i	−0.895707	+	0.444644i	$0.853330\pi$
$180$	2.69116	−	2.64790i	0.200587	−	0.197363i
$181$		−	0.208736i		−	0.0155152i	−0.999970	−	0.00775761i	$-0.997531\pi$
$181$		−	0.208736i		−	0.0155152i	0.999970	−	0.00775761i	$-0.00246935\pi$
$182$	−8.26999	−	6.57305i	−0.613012	−	0.487227i
$183$	−3.94877	−	1.65441i	−0.291901	−	0.122297i
$184$			22.4504i			1.65506i
$185$	−18.3887			−1.35197
$186$	2.70260	−	6.45061i	0.198164	−	0.472982i
$187$	−14.0334			−1.02623
$188$		−	7.12398i		−	0.519570i
$189$	10.7497	−	8.56999i	0.781923	−	0.623375i
$190$			3.89801i			0.282791i
$191$		−	11.1409i		−	0.806129i	−0.915171	−	0.403065i	$-0.867945\pi$
$191$		−	11.1409i		−	0.806129i	0.915171	−	0.403065i	$-0.132055\pi$
$192$	−5.51333	+	13.1593i	−0.397890	+	0.949692i
$193$		−	8.74581i		−	0.629537i	−0.949168	−	0.314768i	$-0.898073\pi$
$193$		−	8.74581i		−	0.629537i	0.949168	−	0.314768i	$-0.101927\pi$
$194$	4.62181			0.331827
$195$	2.11737	+	9.93539i	0.151628	+	0.711488i
$196$	−4.51498	+	2.99053i	−0.322499	+	0.213609i
$197$	−14.0624			−1.00191			−0.500954	−	0.865474i	$-0.667017\pi$
$197$	−14.0624			−1.00191			−0.500954	+	0.865474i	$0.667017\pi$
$198$	−5.52908	−	5.61941i	−0.392935	−	0.399354i
$199$		−	4.53592i		−	0.321543i	−0.986992	−	0.160771i	$-0.948602\pi$
$199$		−	4.53592i		−	0.321543i	0.986992	−	0.160771i	$-0.0513982\pi$
$200$	7.23034			0.511263
$201$	−9.45196	−	3.96007i	−0.666690	−	0.279322i
$202$	−9.98967			−0.702871
$203$	1.26216	+	4.19123i	0.0885865	+	0.294166i
$204$	3.06229	−	7.30912i	0.214403	−	0.511740i
$205$	3.70832			0.259000
$206$		−	11.0661i		−	0.771010i
$207$	15.6301	−	15.3788i	1.08637	−	1.06890i
$208$	−3.81180	−	5.49209i	−0.264301	−	0.380808i
$209$	−5.13482			−0.355183
$210$	−8.21014	−	0.858973i	−0.566553	−	0.0592748i
$211$	−14.1569			−0.974601			−0.487300	−	0.873234i	$-0.662018\pi$
$211$	−14.1569			−0.974601			−0.487300	+	0.873234i	$0.662018\pi$
$212$			9.52182i			0.653961i
$213$	−5.64242	+	13.4674i	−0.386613	+	0.922774i
$214$		−	2.51969i		−	0.172242i
$215$		−	4.64276i		−	0.316633i
$216$	14.8185	−	5.92808i	1.00827	−	0.403355i
$217$	9.23740	−	2.78179i	0.627076	−	0.188840i
$218$			7.65628i			0.518549i
$219$	5.20575	−	12.4252i	0.351772	−	0.839616i
$220$		−	2.98628i		−	0.201335i
$221$	12.1579	+	17.5173i	0.817830	+	1.17834i
$222$	−19.9988	−	8.37886i	−1.34223	−	0.562353i
$223$	−1.82837			−0.122437			−0.0612183	−	0.998124i	$-0.519499\pi$
$223$	−1.82837			−0.122437			−0.0612183	+	0.998124i	$0.519499\pi$
$224$	−10.3610	+	3.12016i	−0.692274	+	0.208474i
$225$	−4.95289	−	5.03381i	−0.330193	−	0.335587i
$226$		−	2.90414i		−	0.193181i
$227$			19.1161i			1.26878i	0.773014	+	0.634388i	$0.218748\pi$
$227$			19.1161i			1.26878i	−0.773014	+	0.634388i	$0.781252\pi$
$228$	1.12049	−	2.67440i	0.0742061	−	0.177116i
$229$	−16.7071			−1.10403			−0.552017	−	0.833833i	$-0.686142\pi$
$229$	−16.7071			−1.10403			−0.552017	+	0.833833i	$0.686142\pi$
$230$	−13.1665			−0.868172
$231$	1.13152	−	10.8152i	0.0744485	−	0.711585i
$232$			5.08161i			0.333624i
$233$			3.83181i			0.251030i	0.992092	+	0.125515i	$0.0400584\pi$
$233$			3.83181i			0.251030i	−0.992092	+	0.125515i	$0.959942\pi$
$234$	−2.22431	+	11.7701i	−0.145408	+	0.769435i
$235$	14.9787			0.977105
$236$			7.62921i			0.496619i
$237$	8.27596	−	19.7532i	0.537582	−	1.28311i
$238$	−16.5914	+	4.99639i	−1.07546	+	0.323868i
$239$	−29.9942			−1.94016			−0.970081	−	0.242781i	$-0.921940\pi$
$239$	−29.9942			−1.94016			−0.970081	+	0.242781i	$0.921940\pi$
$240$	−4.81823	−	2.01869i	−0.311016	−	0.130306i
$241$	−12.8246			−0.826108			−0.413054	−	0.910707i	$-0.635538\pi$
$241$	−12.8246			−0.826108			−0.413054	+	0.910707i	$0.635538\pi$
$242$	5.94582			0.382212
$243$	−14.2781	−	6.25593i	−0.915939	−	0.401318i
$244$		−	1.91233i		−	0.122425i
$245$	−6.28782	−	9.49311i	−0.401714	−	0.606492i
$246$	4.03301	+	1.68970i	0.257135	+	0.107731i
$247$	4.44857	+	6.40956i	0.283056	+	0.407830i
$248$	11.1998			0.711187
$249$	8.70593	+	3.64751i	0.551716	+	0.231151i
$250$			13.2473i			0.837831i
$251$	19.5957			1.23687			0.618435	−	0.785836i	$-0.287767\pi$
$251$	19.5957			1.23687			0.618435	+	0.785836i	$0.287767\pi$
$252$	5.38601	+	2.94935i	0.339287	+	0.185792i
$253$		−	17.3441i		−	1.09042i
$254$	−2.76830			−0.173699
$255$	15.3680	+	6.43870i	0.962381	+	0.403207i
$256$	−15.4310			−0.964440
$257$	9.39236			0.585879			0.292940	−	0.956131i	$-0.405367\pi$
$257$	9.39236			0.585879			0.292940	+	0.956131i	$0.405367\pi$
$258$	2.11548	−	5.04927i	0.131704	−	0.314354i
$259$	−8.62438	−	28.6387i	−0.535893	−	1.77952i
$260$	−3.72764	+	2.58718i	−0.231178	+	0.160450i
$261$	3.53785	−	3.48098i	0.218987	−	0.215467i
$262$	−3.94436			−0.243683
$263$		−	14.6535i		−	0.903575i	−0.892126	−	0.451788i	$-0.850786\pi$
$263$		−	14.6535i		−	0.903575i	0.892126	−	0.451788i	$-0.149214\pi$
$264$	4.87832	−	11.6436i	0.300240	−	0.716617i
$265$	−20.0204			−1.22984
$266$	−6.07077	+	1.82818i	−0.372223	+	0.112093i
$267$	−16.6446	−	6.97355i	−1.01863	−	0.426775i
$268$		−	4.57746i		−	0.279613i
$269$	13.2963			0.810692			0.405346	−	0.914163i	$-0.367151\pi$
$269$	13.2963			0.810692			0.405346	+	0.914163i	$0.367151\pi$
$270$	3.47664	+	8.69062i	0.211582	+	0.528894i
$271$	24.1869			1.46925			0.734624	−	0.678475i	$-0.237359\pi$
$271$	24.1869			1.46925			0.734624	+	0.678475i	$0.237359\pi$
$272$	−10.9654			−0.664874
$273$	−14.4804	+	7.95733i	−0.876391	+	0.481600i
$274$	11.6860			0.705975
$275$	−5.58583			−0.336838
$276$	9.03344	+	3.78472i	0.543749	+	0.227814i
$277$	13.2340			0.795152			0.397576	−	0.917569i	$-0.369852\pi$
$277$	13.2340			0.795152			0.397576	+	0.917569i	$0.369852\pi$
$278$		−	6.10882i		−	0.366383i
$279$	−7.67202	−	7.79736i	−0.459312	−	0.466816i
$280$	−3.81180	−	12.6577i	−0.227798	−	0.756443i
$281$	12.3324			0.735691			0.367845	−	0.929887i	$-0.380096\pi$
$281$	12.3324			0.735691			0.367845	+	0.929887i	$0.380096\pi$
$282$	16.2902	+	6.82508i	0.970069	+	0.406428i
$283$			6.75052i			0.401277i	0.979665	+	0.200638i	$0.0643017\pi$
$283$			6.75052i			0.401277i	−0.979665	+	0.200638i	$0.935698\pi$
$284$	−6.52210			−0.387015
$285$	5.62314	+	2.35591i	0.333086	+	0.139552i
$286$	5.40228	+	7.78367i	0.319443	+	0.460258i
$287$	1.73921	+	5.77535i	0.102662	+	0.340908i
$288$	8.60522	+	8.74581i	0.507067	+	0.515352i
$289$	17.9746			1.05733
$290$	−2.98021			−0.175004
$291$	2.79337	−	6.66727i	0.163750	−	0.390843i
$292$	6.01735			0.352139
$293$			29.1312i			1.70187i	0.525275	+	0.850933i	$0.323963\pi$
$293$			29.1312i			1.70187i	−0.525275	+	0.850933i	$0.676037\pi$
$294$	−2.51281	−	13.1894i	−0.146550	−	0.769219i
$295$	−16.0410			−0.933944
$296$		−	34.7227i		−	2.01822i
$297$	−11.4481	+	4.57976i	−0.664286	+	0.265744i
$298$	14.9491			0.865976
$299$	−21.6499	+	15.0261i	−1.25204	+	0.868984i
$300$	1.21890	−	2.90930i	0.0703734	−	0.167969i
$301$	7.23065	−	2.17747i	0.416768	−	0.125507i
$302$		−	15.6517i		−	0.900656i
$303$	−6.03765	+	14.4108i	−0.346854	+	0.827877i
$304$	−4.01222			−0.230117
$305$	4.02083			0.230232
$306$	13.7798	+	14.0049i	0.787737	+	0.800607i
$307$	−26.6618			−1.52167			−0.760836	−	0.648945i	$-0.775211\pi$
$307$	−26.6618			−1.52167			−0.760836	+	0.648945i	$0.775211\pi$
$308$	4.65084	−	1.40057i	0.265006	−	0.0798051i
$309$	−15.9636	−	6.68822i	−0.908135	−	0.380479i
$310$			6.56834i			0.373057i
$311$	8.80847			0.499482			0.249741	−	0.968313i	$-0.419654\pi$
$311$	8.80847			0.499482			0.249741	+	0.968313i	$0.419654\pi$
$312$	−18.7606	+	3.99815i	−1.06211	+	0.226350i
$313$		−	27.4593i		−	1.55209i	−0.630677	−	0.776045i	$-0.717223\pi$
$313$		−	27.4593i		−	1.55209i	0.630677	−	0.776045i	$-0.282777\pi$
$314$			8.61361i			0.486094i
$315$	−6.20125	+	11.3245i	−0.349401	+	0.638064i
$316$	9.56622			0.538142
$317$	16.1064			0.904626			0.452313	−	0.891859i	$-0.350599\pi$
$317$	16.1064			0.904626			0.452313	+	0.891859i	$0.350599\pi$
$318$	−21.7733	−	9.12232i	−1.22099	−	0.511554i
$319$		−	3.92581i		−	0.219803i
$320$		−	13.3995i		−	0.749054i
$321$	−3.63482	−	1.52287i	−0.202876	−	0.0849984i
$322$	−6.17511	−	20.5055i	−0.344126	−	1.14273i
$323$	12.7972			0.712054
$324$	0.112829	−	6.96195i	0.00626830	−	0.386775i
$325$	4.83930	+	6.97253i	0.268436	+	0.386766i
$326$			14.3718i			0.795981i
$327$	11.0447	+	4.62738i	0.610773	+	0.255894i
$328$			7.00226i			0.386635i
$329$	7.02507	+	23.3279i	0.387305	+	1.28611i
$330$	6.82865	+	2.86099i	0.375905	+	0.157492i
$331$			22.4504i			1.23398i	0.786969	+	0.616992i	$0.211649\pi$
$331$			22.4504i			1.23398i	−0.786969	+	0.616992i	$0.788351\pi$
$332$			4.21617i			0.231392i
$333$	−24.1742	+	23.7855i	−1.32474	+	1.30344i
$334$			11.0128i			0.602591i
$335$	9.62447			0.525841
$336$	0.884142	−	8.45070i	0.0482339	−	0.461024i
$337$	−19.5735			−1.06624			−0.533119	−	0.846040i	$-0.678980\pi$
$337$	−19.5735			−1.06624			−0.533119	+	0.846040i	$0.678980\pi$
$338$	5.03571	−	13.4868i	0.273907	−	0.733587i
$339$	−4.18942	−	1.75523i	−0.227538	−	0.0953311i
$340$			7.44251i			0.403627i
$341$	−8.65243			−0.468556
$342$	5.04201	+	5.12438i	0.272641	+	0.277095i
$343$	11.8356	−	14.2450i	0.639062	−	0.769155i
$344$	8.76672			0.472670
$345$	−7.95768	+	18.9935i	−0.428427	+	1.02258i
$346$	11.3318			0.609202
$347$			2.31344i			0.124192i	0.998070	+	0.0620960i	$0.0197785\pi$
$347$			2.31344i			0.124192i	−0.998070	+	0.0620960i	$0.980221\pi$
$348$	2.04471	+	0.856666i	0.109608	+	0.0459221i
$349$	16.2173			0.868091			0.434046	−	0.900891i	$-0.357086\pi$
$349$	16.2173			0.868091			0.434046	+	0.900891i	$0.357086\pi$
$350$	−6.60398	+	1.98875i	−0.352998	+	0.106303i
$351$	15.6348	+	10.3224i	0.834524	+	0.550971i
$352$	9.70488			0.517272
$353$		−	18.2438i		−	0.971017i	−0.874232	−	0.485508i	$-0.838635\pi$
$353$		−	18.2438i		−	0.971017i	0.874232	−	0.485508i	$-0.161365\pi$
$354$	−17.4455	−	7.30912i	−0.927219	−	0.388475i
$355$		−	13.7132i		−	0.727823i
$356$		−	8.06076i		−	0.427219i
$357$	−2.82001	+	26.9539i	−0.149251	+	1.42655i
$358$		−	13.1758i		−	0.696361i
$359$	−1.15402			−0.0609069			−0.0304535	−	0.999536i	$-0.509695\pi$
$359$	−1.15402			−0.0609069			−0.0304535	+	0.999536i	$0.509695\pi$
$360$	−10.6845	+	10.5127i	−0.563122	+	0.554069i
$361$	−14.3175			−0.753554
$362$			0.231156i			0.0121493i
$363$	3.59359	−	8.57725i	0.188615	−	0.450189i
$364$	−5.77755	−	4.59204i	−0.302826	−	0.240688i
$365$			12.6520i			0.662234i
$366$	4.37289	+	1.83210i	0.228575	+	0.0957654i
$367$			3.51046i			0.183245i	0.995794	+	0.0916224i	$0.0292053\pi$
$367$			3.51046i			0.183245i	−0.995794	+	0.0916224i	$0.970795\pi$
$368$		−	13.5523i		−	0.706461i
$369$	4.87502	−	4.79665i	0.253783	−	0.249704i
$370$	20.3638			1.05866
$371$	−9.38961	−	31.1798i	−0.487484	−	1.61877i
$372$	1.88808	−	4.50650i	0.0978923	−	0.233651i
$373$	27.3627			1.41678			0.708392	−	0.705819i	$-0.249421\pi$
$373$	27.3627			1.41678			0.708392	+	0.705819i	$0.249421\pi$
$374$	15.5407			0.803591
$375$	19.1101	+	8.00651i	0.986840	+	0.413454i
$376$			28.2837i			1.45862i
$377$	−4.90041	+	3.40114i	−0.252384	+	0.175168i
$378$	−11.9042	+	9.49046i	−0.612288	+	0.488136i
$379$		−	19.9275i		−	1.02361i	−0.859102	−	0.511805i	$-0.828977\pi$
$379$		−	19.9275i		−	1.02361i	0.859102	−	0.511805i	$-0.171023\pi$
$380$			2.72321i			0.139698i
$381$	−1.67313	+	3.99346i	−0.0857171	+	0.204591i
$382$			12.3375i			0.631243i
$383$		−	13.8202i		−	0.706182i	−0.935589	−	0.353091i	$-0.885131\pi$
$383$		−	13.8202i		−	0.706182i	0.935589	−	0.353091i	$-0.114869\pi$
$384$	0.630839	−	1.50570i	0.0321923	−	0.0768372i
$385$	2.94482	+	9.77876i	0.150082	+	0.498372i
$386$			9.68516i			0.492962i
$387$	−6.00533	−	6.10345i	−0.305268	−	0.310256i
$388$	3.22887			0.163921
$389$		−	27.6901i		−	1.40395i	−0.712204	−	0.701973i	$-0.752303\pi$
$389$		−	27.6901i		−	1.40395i	0.712204	−	0.701973i	$-0.247697\pi$
$390$	−2.34479	−	11.0025i	−0.118733	−	0.557134i
$391$			43.2256i			2.18601i
$392$	17.9254	−	11.8730i	0.905371	−	0.599678i
$393$	−2.38393	+	5.69001i	−0.120253	+	0.287023i
$394$	15.5728			0.784548
$395$			20.1137i			1.01203i
$396$	−3.86270	−	3.92581i	−0.194108	−	0.197279i
$397$	−8.32507			−0.417823			−0.208912	−	0.977935i	$-0.566992\pi$
$397$	−8.32507			−0.417823			−0.208912	+	0.977935i	$0.566992\pi$
$398$			5.02311i			0.251786i
$399$	−1.03184	+	9.86242i	−0.0516567	+	0.493739i
$400$	−4.36463			−0.218231
$401$	−2.56088			−0.127884			−0.0639422	−	0.997954i	$-0.520367\pi$
$401$	−2.56088			−0.127884			−0.0639422	+	0.997954i	$0.520367\pi$
$402$	10.4672	+	4.38541i	0.522055	+	0.218724i
$403$	7.49607	+	10.8004i	0.373406	+	0.538008i
$404$	−6.97894			−0.347215
$405$	14.6381	+	0.237233i	0.727371	+	0.0117882i
$406$	−1.39773	−	4.64139i	−0.0693680	−	0.230348i
$407$			26.8251i			1.32967i
$408$	−12.1579	+	29.0187i	−0.601906	+	1.43664i
$409$	11.4661			0.566963			0.283482	−	0.958978i	$-0.408510\pi$
$409$	11.4661			0.566963			0.283482	+	0.958978i	$0.408510\pi$
$410$	−4.10662			−0.202811
$411$	7.06288	−	16.8578i	0.348386	−	0.831534i
$412$		−	7.73094i		−	0.380876i
$413$	−7.52328	−	24.9823i	−0.370197	−	1.22930i
$414$	−17.3089	+	17.0306i	−0.850684	+	0.837009i
$415$	−8.86482			−0.435157
$416$	−8.40787	−	12.1142i	−0.412230	−	0.593946i
$417$	−8.81238	−	3.69211i	−0.431544	−	0.180803i
$418$	5.68633			0.278128
$419$	−35.5711			−1.73776			−0.868880	−	0.495023i	$-0.835160\pi$
$419$	−35.5711			−1.73776			−0.868880	+	0.495023i	$0.835160\pi$
$420$	−5.73573	−	0.600092i	−0.279875	−	0.0292815i
$421$		−	8.92925i		−	0.435185i	−0.976040	−	0.217592i	$-0.930180\pi$
$421$		−	8.92925i		−	0.435185i	0.976040	−	0.217592i	$-0.0698204\pi$
$422$	15.6774			0.763165
$423$	19.6913	−	19.3747i	0.957423	−	0.942032i
$424$		−	37.8036i		−	1.83591i
$425$	13.9212			0.675277
$426$	6.24846	−	14.9139i	0.302739	−	0.722582i
$427$	1.88578	+	6.26206i	0.0912594	+	0.303042i
$428$		−	1.76029i		−	0.0850870i
$429$	14.4935	−	3.08878i	0.699755	−	0.149128i
$430$			5.14142i			0.247941i
$431$	−12.1519			−0.585338			−0.292669	−	0.956214i	$-0.594543\pi$
$431$	−12.1519			−0.585338			−0.292669	+	0.956214i	$0.594543\pi$
$432$	−8.94527	+	3.57851i	−0.430379	+	0.172171i
$433$			23.6368i			1.13591i	0.823059	+	0.567956i	$0.192266\pi$
$433$			23.6368i			1.13591i	−0.823059	+	0.567956i	$0.807734\pi$
$434$	−10.2296	+	3.08057i	−0.491034	+	0.147872i
$435$	−1.80121	+	4.29915i	−0.0863613	+	0.206129i
$436$			5.34880i			0.256161i
$437$			15.8162i			0.756593i
$438$	−5.76488	+	13.7597i	−0.275457	+	0.657465i
$439$			36.7433i			1.75366i	0.480799	+	0.876831i	$0.340347\pi$
$439$			36.7433i			1.75366i	−0.480799	+	0.876831i	$0.659653\pi$
$440$			11.8562i			0.565220i
$441$	−20.5452	−	4.34661i	−0.978345	−	0.206981i
$442$	−13.4637	−	19.3987i	−0.640405	−	0.922704i
$443$		−	8.51111i		−	0.404375i	−0.979347	−	0.202188i	$-0.935195\pi$
$443$		−	8.51111i		−	0.404375i	0.979347	−	0.202188i	$-0.0648051\pi$
$444$	−13.9715	−	5.85361i	−0.663058	−	0.277800i
$445$	16.9484			0.803430
$446$	2.02475			0.0958745
$447$	9.03506	−	21.5650i	0.427344	−	1.01999i
$448$	20.8684	−	6.28439i	0.985939	−	0.296910i
$449$	17.5491			0.828191			0.414096	−	0.910233i	$-0.364098\pi$
$449$	17.5491			0.828191			0.414096	+	0.910233i	$0.364098\pi$
$450$	5.48486	+	5.57447i	0.258559	+	0.262783i
$451$		−	5.40962i		−	0.254729i
$452$		−	2.02888i		−	0.0954304i
$453$	−22.5787	−	9.45975i	−1.06084	−	0.444458i
$454$		−	21.1692i		−	0.993521i
$455$	9.65512	−	12.1477i	0.452639	−	0.569495i
$456$	−4.44857	+	10.6179i	−0.208323	+	0.497230i
$457$		−	17.0625i		−	0.798150i	−0.916918	−	0.399075i	$-0.869331\pi$
$457$		−	17.0625i		−	0.798150i	0.916918	−	0.399075i	$-0.130669\pi$
$458$	18.5015			0.864519
$459$	28.5314	−	11.4138i	1.33173	−	0.532752i
$460$	−9.19831			−0.428873
$461$		−	17.6433i		−	0.821729i	−0.911696	−	0.410865i	$-0.865227\pi$
$461$		−	17.6433i		−	0.821729i	0.911696	−	0.410865i	$-0.134773\pi$
$462$	−1.25305	+	11.9768i	−0.0582972	+	0.557210i
$463$		−	17.5666i		−	0.816391i	−0.912895	−	0.408196i	$-0.866158\pi$
$463$		−	17.5666i		−	0.816391i	0.912895	−	0.408196i	$-0.133842\pi$
$464$		−	3.06753i		−	0.142407i
$465$	9.47527	+	3.96984i	0.439405	+	0.184097i
$466$		−	4.24337i		−	0.196571i
$467$	7.92389			0.366674			0.183337	−	0.983050i	$-0.441310\pi$
$467$	7.92389			0.366674			0.183337	+	0.983050i	$0.441310\pi$
$468$	−1.55394	+	8.22278i	−0.0718310	+	0.380098i
$469$	4.51390	+	14.9892i	0.208433	+	0.692136i
$470$	−16.5875			−0.765126
$471$	12.4257	+	5.20597i	0.572546	+	0.239879i
$472$		−	30.2896i		−	1.39419i
$473$	−6.77276			−0.311412
$474$	−9.16485	+	21.8748i	−0.420956	+	1.00474i
$475$	5.09376			0.233718
$476$	−11.5910	+	3.49056i	−0.531272	+	0.159990i
$477$	−26.3191	+	25.8960i	−1.20507	+	1.18570i
$478$	33.2157			1.51925
$479$		−	6.82723i		−	0.311944i	−0.987761	−	0.155972i	$-0.950149\pi$
$479$		−	6.82723i		−	0.311944i	0.987761	−	0.155972i	$-0.0498510\pi$
$480$	−10.6278	−	4.45271i	−0.485091	−	0.203238i
$481$	33.4846	−	23.2401i	1.52676	−	1.05966i
$482$	14.2021			0.646888
$483$	−33.3128	−	3.48530i	−1.51578	−	0.158586i
$484$	4.15385			0.188811
$485$			6.78896i			0.308271i
$486$	15.8116	+	6.92786i	0.717230	+	0.314254i
$487$			29.2022i			1.32328i	0.749823	+	0.661638i	$0.230138\pi$
$487$			29.2022i			1.32328i	−0.749823	+	0.661638i	$0.769862\pi$
$488$			7.59237i			0.343690i
$489$	20.7323	+	8.68617i	0.937547	+	0.392802i
$490$	6.96317	+	10.5127i	0.314564	+	0.474916i
$491$		−	12.6548i		−	0.571103i	−0.958363	−	0.285551i	$-0.907823\pi$
$491$		−	12.6548i		−	0.571103i	0.958363	−	0.285551i	$-0.0921768\pi$
$492$	2.81753	+	1.18045i	0.127024	+	0.0532189i
$493$			9.78405i			0.440651i
$494$	−4.92638	−	7.09799i	−0.221648	−	0.319353i
$495$	8.25433	−	8.12164i	0.371005	−	0.365041i
$496$	−6.76080			−0.303569
$497$	21.3570	−	6.43154i	0.957993	−	0.288494i
$498$	−9.64100	−	4.03927i	−0.432024	−	0.181004i
$499$		−	6.06419i		−	0.271471i	−0.990745	−	0.135735i	$-0.956660\pi$
$499$		−	6.06419i		−	0.271471i	0.990745	−	0.135735i	$-0.0433397\pi$
$500$			9.25475i			0.413885i
$501$	15.8866	+	6.65599i	0.709763	+	0.297368i
$502$	−21.7004			−0.968537
$503$	32.5278			1.45034			0.725171	−	0.688569i	$-0.241761\pi$
$503$	32.5278			1.45034			0.725171	+	0.688569i	$0.241761\pi$
$504$	−21.3836	−	11.7095i	−0.952501	−	0.521585i
$505$		−	14.6738i		−	0.652975i
$506$			19.2070i			0.853854i
$507$	−16.4121	−	15.4156i	−0.728888	−	0.684633i
$508$	−1.93398			−0.0858064
$509$		−	8.16408i		−	0.361867i	−0.983495	−	0.180933i	$-0.942088\pi$
$509$		−	8.16408i		−	0.361867i	0.983495	−	0.180933i	$-0.0579118\pi$
$510$	−17.0186	−	7.13025i	−0.753597	−	0.315733i
$511$	−19.7042	+	5.93380i	−0.871662	+	0.262496i
$512$	18.9735			0.838517
$513$	10.4396	−	4.17631i	0.460920	−	0.184389i
$514$	−10.4012			−0.458775
$515$	16.2549			0.716277
$516$	1.47791	−	3.52750i	0.0650613	−	0.155289i
$517$		−	21.8507i		−	0.960991i
$518$	9.55069	+	31.7147i	0.419633	+	1.39346i
$519$	6.84883	−	16.3469i	0.300630	−	0.717549i
$520$	14.7995	−	10.2716i	0.649001	−	0.450441i
$521$	−32.5057			−1.42410			−0.712050	−	0.702129i	$-0.752233\pi$
$521$	−32.5057			−1.42410			−0.712050	+	0.702129i	$0.752233\pi$
$522$	−3.91783	+	3.85485i	−0.171479	+	0.168722i
$523$		−	4.26772i		−	0.186614i	−0.995637	−	0.0933072i	$-0.970256\pi$
$523$		−	4.26772i		−	0.186614i	0.995637	−	0.0933072i	$-0.0297439\pi$
$524$	−2.75559			−0.120379
$525$	−1.12247	+	10.7287i	−0.0489886	+	0.468237i
$526$			16.2274i			0.707549i
$527$	21.5639			0.939338
$528$	−2.94482	+	7.02874i	−0.128157	+	0.305887i
$529$	−30.4232			−1.32275
$530$	22.1707			0.963033
$531$	−21.0878	+	20.7488i	−0.915132	+	0.900421i
$532$	−4.24114	+	1.27719i	−0.183877	+	0.0553734i
$533$	−6.75258	+	4.68665i	−0.292487	+	0.203001i
$534$	18.4323	+	7.72256i	0.797645	+	0.334188i
$535$	3.70116			0.160015
$536$			18.1735i			0.784974i
$537$	−19.0069	−	7.96329i	−0.820210	−	0.343642i
$538$	−14.7244			−0.634816
$539$	−13.8483	+	9.17253i	−0.596490	+	0.395089i
$540$	2.42884	+	6.07141i	0.104520	+	0.261272i
$541$			12.2984i			0.528752i	0.964420	+	0.264376i	$0.0851659\pi$
$541$			12.2984i			0.528752i	−0.964420	+	0.264376i	$0.914834\pi$
$542$	−26.7847			−1.15050
$543$	0.333458	+	0.139708i	0.0143100	+	0.00599544i
$544$	−24.1869			−1.03700
$545$	−11.2463			−0.481738
$546$	16.0356	−	8.81200i	0.686262	−	0.377119i
$547$	−14.3839			−0.615012			−0.307506	−	0.951546i	$-0.599494\pi$
$547$	−14.3839			−0.615012			−0.307506	+	0.951546i	$0.599494\pi$
$548$	8.16401			0.348749
$549$	5.28585	−	5.20088i	0.225595	−	0.221968i
$550$	6.18578			0.263762
$551$			3.57998i			0.152512i
$552$	−35.8647	−	15.0261i	−1.52650	−	0.639555i
$553$	−31.3252	+	9.43339i	−1.33208	+	0.401149i
$554$	−14.6554			−0.622647
$555$	12.3077	−	29.3762i	0.522432	−	1.24695i
$556$		−	4.26772i		−	0.180992i
$557$	−21.8146			−0.924313			−0.462156	−	0.886798i	$-0.652924\pi$
$557$	−21.8146			−0.924313			−0.462156	+	0.886798i	$0.652924\pi$
$558$	8.49604	+	8.63485i	0.359666	+	0.365542i
$559$	5.86761	+	8.45412i	0.248173	+	0.357571i
$560$	2.30101	+	7.64089i	0.0972353	+	0.322886i
$561$	9.39264	−	22.4185i	0.396557	−	0.946510i
$562$	−13.6570			−0.576086
$563$	−14.5051			−0.611316			−0.305658	−	0.952141i	$-0.598876\pi$
$563$	−14.5051			−0.611316			−0.305658	+	0.952141i	$0.598876\pi$
$564$	11.3806	+	4.76811i	0.479210	+	0.200774i
$565$	4.26588			0.179467
$566$		−	7.47557i		−	0.314222i
$567$	6.49582	+	22.9086i	0.272799	+	0.962071i
$568$	25.8941			1.08649
$569$			19.9639i			0.836931i	0.908233	+	0.418465i	$0.137432\pi$
$569$			19.9639i			0.836931i	−0.908233	+	0.418465i	$0.862568\pi$
$570$	−6.22710	−	2.60895i	−0.260824	−	0.109277i
$571$	24.9902			1.04581			0.522903	−	0.852392i	$-0.324849\pi$
$571$	24.9902			1.04581			0.522903	+	0.852392i	$0.324849\pi$
$572$	3.77412	+	5.43780i	0.157804	+	0.227366i
$573$	17.7977	+	7.45668i	0.743511	+	0.311507i
$574$	−1.92601	−	6.39566i	−0.0803903	−	0.266950i
$575$			17.2054i			0.717515i
$576$	−17.3320	−	17.6152i	−0.722167	−	0.733966i
$577$	19.5750			0.814918			0.407459	−	0.913224i	$-0.366415\pi$
$577$	19.5750			0.814918			0.407459	+	0.913224i	$0.366415\pi$
$578$	−19.9052			−0.827947
$579$	13.9715	+	5.85361i	0.580636	+	0.243268i
$580$	−2.08202			−0.0864513
$581$	−4.15763	−	13.8061i	−0.172487	−	0.572774i
$582$	−3.09340	+	7.38338i	−0.128226	+	0.306051i
$583$			29.2053i			1.20956i
$584$	−23.8901			−0.988581
$585$	−17.2890	−	3.26728i	−0.714814	−	0.135086i
$586$		−	32.2601i		−	1.33265i
$587$			32.0582i			1.32318i	0.749865	+	0.661591i	$0.230119\pi$
$587$			32.0582i			1.32318i	−0.749865	+	0.661591i	$0.769881\pi$
$588$	−1.75549	−	9.21429i	−0.0723952	−	0.379991i
$589$	7.89022			0.325111
$590$	17.7639			0.731329
$591$	9.41206	−	22.4649i	0.387160	−	0.924081i
$592$			20.9605i			0.861471i
$593$		−	6.93462i		−	0.284771i	−0.989811	−	0.142385i	$-0.954523\pi$
$593$		−	6.93462i		−	0.284771i	0.989811	−	0.142385i	$-0.0454772\pi$
$594$	12.6777	−	5.07165i	0.520172	−	0.208092i
$595$	−7.33918	−	24.3710i	−0.300877	−	0.999113i
$596$	10.4437			0.427789
$597$	7.24617	+	3.03591i	0.296566	+	0.124252i
$598$	23.9752	−	16.6400i	0.980418	−	0.680462i
$599$			1.47857i			0.0604128i	0.999544	+	0.0302064i	$0.00961646\pi$
$599$			1.47857i			0.0604128i	−0.999544	+	0.0302064i	$0.990384\pi$
$600$	−4.83930	+	11.5505i	−0.197564	+	0.471548i
$601$		−	19.3691i		−	0.790082i	−0.918664	−	0.395041i	$-0.870730\pi$
$601$		−	19.3691i		−	0.790082i	0.918664	−	0.395041i	$-0.129270\pi$
$602$	−8.00726	+	2.41134i	−0.326352	+	0.0982789i
$603$	12.6525	−	12.4491i	0.515249	−	0.506966i
$604$		−	10.9346i		−	0.444921i
$605$			8.73379i			0.355079i
$606$	6.68613	−	15.9586i	0.271606	−	0.648273i
$607$		−	9.78405i		−	0.397122i	−0.980088	−	0.198561i	$-0.936373\pi$
$607$		−	9.78405i		−	0.397122i	0.980088	−	0.198561i	$-0.0636268\pi$
$608$	−8.84996			−0.358913
$609$	−7.54029	−	0.788891i	−0.305548	−	0.0319675i
$610$	−4.45270			−0.180284
$611$	−27.2752	+	18.9304i	−1.10344	+	0.765842i
$612$	9.62677	+	9.78405i	0.389139	+	0.395497i
$613$		−	42.5254i		−	1.71759i	−0.512323	−	0.858793i	$-0.671215\pi$
$613$		−	42.5254i		−	1.71759i	0.512323	−	0.858793i	$-0.328785\pi$
$614$	29.5255			1.19155
$615$	−2.48200	+	5.92407i	−0.100084	+	0.238882i
$616$	−18.4648	+	5.56057i	−0.743969	+	0.224042i
$617$	0.609461			0.0245360			0.0122680	−	0.999925i	$-0.496095\pi$
$617$	0.609461			0.0245360			0.0122680	+	0.999925i	$0.496095\pi$
$618$	17.6781	+	7.40657i	0.711119	+	0.297936i
$619$	−33.3498			−1.34044			−0.670221	−	0.742162i	$-0.733800\pi$
$619$	−33.3498			−1.34044			−0.670221	+	0.742162i	$0.733800\pi$
$620$			4.58875i			0.184289i
$621$	14.1065	+	35.2623i	0.566075	+	1.41503i
$622$	−9.75455			−0.391122
$623$	7.94884	+	26.3955i	0.318463	+	1.05751i
$624$	11.3249	−	2.41350i	0.453359	−	0.0966172i
$625$	−7.68902			−0.307561
$626$			30.4086i			1.21537i
$627$	3.43676	−	8.20292i	0.137251	−	0.327593i
$628$			6.01760i			0.240129i
$629$		−	66.8545i		−	2.66566i
$630$	6.86730	−	12.5408i	0.273600	−	0.499639i
$631$			39.6470i			1.57832i	0.614186	+	0.789161i	$0.289484\pi$
$631$			39.6470i			1.57832i	−0.614186	+	0.789161i	$0.710516\pi$
$632$	−37.9799			−1.51076
$633$	9.47527	−	22.6157i	0.376608	−	0.898895i
$634$	−17.8363			−0.708371
$635$		−	4.06634i		−	0.161368i
$636$	−15.2112	−	6.37300i	−0.603163	−	0.252706i
$637$	23.4472	+	9.33959i	0.929013	+	0.370048i
$638$			4.34747i			0.172118i
$639$	−17.7378	−	18.0276i	−0.701698	−	0.713162i
$640$			1.53318i			0.0606041i
$641$		−	8.41322i		−	0.332302i	−0.986100	−	0.166151i	$-0.946866\pi$
$641$		−	8.41322i		−	0.332302i	0.986100	−	0.166151i	$-0.0531339\pi$
$642$	4.02522	+	1.68644i	0.158863	+	0.0665584i
$643$	−15.3241			−0.604323			−0.302161	−	0.953257i	$-0.597708\pi$
$643$	−15.3241			−0.604323			−0.302161	+	0.953257i	$0.597708\pi$
$644$	−4.31403	−	14.3255i	−0.169997	−	0.564503i
$645$	7.41684	+	3.10742i	0.292038	+	0.122355i
$646$	−14.1717			−0.557577
$647$	−46.4025			−1.82427			−0.912135	−	0.409890i	$-0.865567\pi$
$647$	−46.4025			−1.82427			−0.912135	+	0.409890i	$0.865567\pi$
$648$	−0.447956	+	27.6404i	−0.0175974	+	1.08582i
$649$			23.4003i			0.918542i
$650$	−5.35907	−	7.72142i	−0.210200	−	0.302859i
$651$	−1.73870	+	16.6187i	−0.0681452	+	0.651338i
$652$			10.0404i			0.393211i
$653$		−	38.1021i		−	1.49105i	−0.666478	−	0.745525i	$-0.732199\pi$
$653$		−	38.1021i		−	1.49105i	0.666478	−	0.745525i	$-0.267801\pi$
$654$	−12.2310	−	5.12438i	−0.478269	−	0.200379i
$655$		−	5.79385i		−	0.226385i
$656$		−	4.22695i		−	0.165034i
$657$	16.3651	+	16.6325i	0.638463	+	0.648894i
$658$	−7.77960	−	25.8335i	−0.303281	−	1.00709i
$659$		−	13.3736i		−	0.520961i	−0.965479	−	0.260481i	$-0.916119\pi$
$659$		−	13.3736i		−	0.520961i	0.965479	−	0.260481i	$-0.0838810\pi$
$660$	4.77061	+	1.99873i	0.185696	+	0.0778005i
$661$	−9.64369			−0.375096			−0.187548	−	0.982255i	$-0.560054\pi$
$661$	−9.64369			−0.375096			−0.187548	+	0.982255i	$0.560054\pi$
$662$		−	24.8617i		−	0.966277i
$663$	−36.1213	+	7.69797i	−1.40284	+	0.298964i
$664$		−	16.7391i		−	0.649602i
$665$	−2.68540	−	8.91732i	−0.104135	−	0.345799i
$666$	26.7706	−	26.3403i	1.03734	−	1.02066i
$667$	−12.0922			−0.468214
$668$			7.69369i			0.297678i
$669$	1.22374	−	2.92083i	0.0473124	−	0.112926i
$670$	−10.6582			−0.411762
$671$		−	5.86551i		−	0.226435i
$672$	1.95019	−	18.6401i	0.0752304	−	0.719058i
$673$	20.4486			0.788235			0.394117	−	0.919060i	$-0.371050\pi$
$673$	20.4486			0.788235			0.394117	+	0.919060i	$0.371050\pi$
$674$	21.6758			0.834923
$675$	11.3565	−	4.54313i	0.437114	−	0.174865i
$676$	3.51803	−	9.42211i	0.135309	−	0.362389i
$677$	−46.2970			−1.77934			−0.889670	−	0.456605i	$-0.849065\pi$
$677$	−46.2970			−1.77934			−0.889670	+	0.456605i	$0.849065\pi$
$678$	4.63939	+	1.94375i	0.178175	+	0.0746494i
$679$	−10.5731	+	3.18404i	−0.405760	+	0.122192i
$680$		−	29.5483i		−	1.13313i
$681$	−30.5380	−	12.7945i	−1.17022	−	0.490285i
$682$	9.58176			0.366904
$683$	4.86822			0.186277			0.0931387	−	0.995653i	$-0.470310\pi$
$683$	4.86822			0.186277			0.0931387	+	0.995653i	$0.470310\pi$
$684$	3.52243	+	3.57998i	0.134683	+	0.136884i
$685$			17.1655i			0.655859i
$686$	−13.1068	+	15.7750i	−0.500420	+	0.602291i
$687$	11.1821	−	26.6897i	0.426625	−	1.01828i
$688$	−5.29207			−0.201758
$689$	36.4556	−	25.3021i	1.38885	−	0.963934i
$690$	8.81238	−	21.0335i	0.335482	−	0.800733i
$691$	−25.4481			−0.968090			−0.484045	−	0.875043i	$-0.660833\pi$
$691$	−25.4481			−0.968090			−0.484045	+	0.875043i	$0.660833\pi$
$692$	7.91659			0.300943
$693$	16.5200	+	9.04625i	0.627542	+	0.343639i
$694$		−	2.56192i		−	0.0972492i
$695$	8.97322			0.340373
$696$	−8.11791	−	3.40114i	−0.307708	−	0.128920i
$697$			13.4820i			0.510669i
$698$	−17.9591			−0.679763
$699$	−6.12135	−	2.56465i	−0.231531	−	0.0970040i
$700$	−4.61365	+	1.38937i	−0.174379	+	0.0525134i
$701$			19.6520i			0.742247i	0.928583	+	0.371124i	$0.121027\pi$
$701$			19.6520i			0.742247i	−0.928583	+	0.371124i	$0.878973\pi$
$702$	−17.3141	−	11.4311i	−0.653478	−	0.431441i
$703$		−	24.4620i		−	0.922603i
$704$	−19.5469			−0.736701
$705$	−10.0253	+	23.9286i	−0.377576	+	0.901205i
$706$			20.2032i			0.760359i
$707$	22.8530	−	6.88205i	0.859475	−	0.258826i
$708$	−12.1877	−	5.10627i	−0.458043	−	0.191905i
$709$			20.7267i			0.778407i	0.921152	+	0.389204i	$0.127250\pi$
$709$			20.7267i			0.778407i	−0.921152	+	0.389204i	$0.872750\pi$
$710$			15.1861i			0.569925i
$711$	26.0168	+	26.4418i	0.975705	+	0.991646i
$712$			32.0029i			1.19936i
$713$			26.6511i			0.998093i
$714$	3.12290	−	29.8489i	0.116872	−	1.11707i
$715$	−11.4334	+	7.93538i	−0.427585	+	0.296766i
$716$		−	9.20480i		−	0.344000i
$717$	20.0752	−	47.9159i	0.749724	−	1.78945i
$718$	1.27797			0.0476934
$719$	12.8202			0.478113			0.239057	−	0.971006i	$-0.423162\pi$
$719$	12.8202			0.478113			0.239057	+	0.971006i	$0.423162\pi$
$720$	6.44973	−	6.34605i	0.240367	−	0.236503i
$721$	7.62360	+	25.3154i	0.283918	+	0.942796i
$722$	15.8553			0.590074
$723$	8.58360	−	20.4875i	0.319227	−	0.761937i
$724$			0.161489i			0.00600169i
$725$			3.89442i			0.144635i
$726$	−3.97957	+	9.49850i	−0.147696	+	0.352522i
$727$		−	28.9554i		−	1.07390i	−0.843615	−	0.536948i	$-0.819577\pi$
$727$		−	28.9554i		−	1.07390i	0.843615	−	0.536948i	$-0.180423\pi$
$728$	22.9381	+	18.2314i	0.850141	+	0.675699i
$729$	19.5503	−	18.6222i	0.724084	−	0.689711i
$730$		−	14.0109i		−	0.518565i
$731$	16.8793			0.624304
$732$	3.05497	+	1.27993i	0.112915	+	0.0473077i
$733$	40.7676			1.50579			0.752894	−	0.658142i	$-0.228657\pi$
$733$	40.7676			1.50579			0.752894	+	0.658142i	$0.228657\pi$
$734$		−	3.88751i		−	0.143491i
$735$	19.3738	−	3.69105i	0.714612	−	0.136147i
$736$		−	29.8929i		−	1.10187i
$737$		−	14.0400i		−	0.517169i
$738$	−5.39863	+	5.31184i	−0.198726	+	0.195532i
$739$			44.5945i			1.64043i	0.572052	+	0.820217i	$0.306147\pi$
$739$			44.5945i			1.64043i	−0.572052	+	0.820217i	$0.693853\pi$
$740$	14.2265			0.522976
$741$	−13.2168	+	2.81668i	−0.485530	+	0.103473i
$742$	10.3981	+	34.5287i	0.381727	+	1.26759i
$743$	−13.5946			−0.498737			−0.249368	−	0.968409i	$-0.580223\pi$
$743$	−13.5946			−0.498737			−0.249368	+	0.968409i	$0.580223\pi$
$744$	−7.49607	+	17.8917i	−0.274819	+	0.655943i
$745$			21.9586i			0.804501i
$746$	−30.3016			−1.10942
$747$	−11.6538	+	11.4665i	−0.426392	+	0.419537i
$748$	10.8570			0.396971
$749$	1.73585	+	5.76419i	0.0634267	+	0.210619i
$750$	−21.1626	−	8.86646i	−0.772749	−	0.323757i
$751$	−24.3954			−0.890200			−0.445100	−	0.895481i	$-0.646832\pi$
$751$	−24.3954			−0.890200			−0.445100	+	0.895481i	$0.646832\pi$
$752$		−	17.0736i		−	0.622609i
$753$	−13.1155	+	31.3043i	−0.477956	+	1.14079i
$754$	5.42674	−	3.76645i	0.197630	−	0.137166i
$755$	22.9908			0.836720
$756$	−8.31650	+	6.63018i	−0.302468	+	0.241137i
$757$	−38.7152			−1.40713			−0.703565	−	0.710631i	$-0.748410\pi$
$757$	−38.7152			−1.40713			−0.703565	+	0.710631i	$0.748410\pi$
$758$			22.0679i			0.801542i
$759$	27.7074	+	11.6085i	1.00571	+	0.421362i
$760$		−	10.8117i		−	0.392182i
$761$			6.72208i			0.243675i	0.992550	+	0.121838i	$0.0388787\pi$
$761$			6.72208i			0.243675i	−0.992550	+	0.121838i	$0.961121\pi$
$762$	1.85284	−	4.42238i	0.0671212	−	0.160206i
$763$	−5.27454	−	17.5150i	−0.190951	−	0.634085i
$764$			8.61920i			0.311832i
$765$	−20.5717	+	20.2410i	−0.743773	+	0.731816i
$766$			15.3046i			0.552979i
$767$	29.2095	−	20.2729i	1.05469	−	0.732013i
$768$	10.3281	−	24.6512i	0.372682	−	0.889524i
$769$	31.5613			1.13813			0.569065	−	0.822292i	$-0.307305\pi$
$769$	31.5613			1.13813			0.569065	+	0.822292i	$0.307305\pi$
$770$	−3.26111	−	10.8291i	−0.117522	−	0.390252i
$771$	−6.28635	+	15.0044i	−0.226397	+	0.540369i
$772$			6.76621i			0.243521i
$773$			44.3470i			1.59505i	0.603285	+	0.797525i	$0.293858\pi$
$773$			44.3470i			1.59505i	−0.603285	+	0.797525i	$0.706142\pi$
$774$	6.65034	+	6.75899i	0.239042	+	0.242947i
$775$	8.58324			0.308319
$776$	−12.8193			−0.460186
$777$	51.5229	+	5.39050i	1.84837	+	0.193383i
$778$			30.6642i			1.09937i
$779$			4.93307i			0.176746i
$780$	−1.63811	−	7.68653i	−0.0586537	−	0.275222i
$781$	−20.0046			−0.715820
$782$		−	47.8683i		−	1.71177i
$783$	3.19299	+	7.98157i	0.114108	+	0.285238i
$784$	−10.8208	+	7.16719i	−0.386456	+	0.255971i
$785$	−12.6525			−0.451587
$786$	2.63998	−	6.30115i	0.0941649	−	0.224754i
$787$	−28.2320			−1.00636			−0.503182	−	0.864181i	$-0.667837\pi$
$787$	−28.2320			−1.00636			−0.503182	+	0.864181i	$0.667837\pi$
$788$	10.8794			0.387564
$789$	23.4091	+	9.80767i	0.833387	+	0.349162i
$790$		−	22.2741i		−	0.792476i
$791$	2.00071	+	6.64369i	0.0711370	+	0.236222i
$792$	15.3357	+	15.5863i	0.544932	+	0.553835i
$793$	−7.32164	+	5.08161i	−0.259999	+	0.180453i
$794$	9.21923			0.327178
$795$	13.3997	−	31.9827i	0.475239	−	1.13431i
$796$			3.50922i			0.124381i
$797$	12.2404			0.433577			0.216789	−	0.976219i	$-0.430442\pi$
$797$	12.2404			0.433577			0.216789	+	0.976219i	$0.430442\pi$
$798$	1.14267	−	10.9217i	0.0404500	−	0.386624i
$799$			54.4570i			1.92655i
$800$	−9.62727			−0.340375
$801$	22.2806	−	21.9224i	0.787247	−	0.774592i
$802$	2.83594			0.100140
$803$	18.4564			0.651313
$804$	7.31253	+	3.06371i	0.257893	+	0.108049i
$805$	30.1204	−	9.07060i	1.06161	−	0.319697i
$806$	−8.30119	−	11.9605i	−0.292397	−	0.421289i
$807$	−8.89930	+	21.2410i	−0.313270	+	0.747719i
$808$	27.7079			0.974760
$809$			38.8209i			1.36487i	0.730946	+	0.682435i	$0.239079\pi$
$809$			38.8209i			1.36487i	−0.730946	+	0.682435i	$0.760921\pi$
$810$	−16.2103	−	0.262713i	−0.569571	−	0.00923079i
$811$	−8.20780			−0.288215			−0.144107	−	0.989562i	$-0.546031\pi$
$811$	−8.20780			−0.288215			−0.144107	+	0.989562i	$0.546031\pi$
$812$	−0.976475	−	3.24255i	−0.0342675	−	0.113791i
$813$	−16.1884	+	38.6387i	−0.567751	+	1.35512i
$814$		−	29.7063i		−	1.04121i
$815$	−21.1107			−0.739475
$816$	7.33918	−	17.5173i	0.256923	−	0.613227i
$817$	6.17613			0.216075
$818$	−12.6977			−0.443963
$819$	−3.02013	−	28.4584i	−0.105532	−	0.994416i
$820$	−2.86895			−0.100188
$821$	16.4362			0.573626			0.286813	−	0.957987i	$-0.407404\pi$
$821$	16.4362			0.573626			0.286813	+	0.957987i	$0.407404\pi$
$822$	−7.82147	+	18.6684i	−0.272805	+	0.651136i
$823$	−12.4998			−0.435716			−0.217858	−	0.975980i	$-0.569907\pi$
$823$	−12.4998			−0.435716			−0.217858	+	0.975980i	$0.569907\pi$
$824$			30.6934i			1.06926i
$825$	3.73862	−	8.92340i	0.130162	−	0.310673i
$826$	8.33133	+	27.6656i	0.289884	+	0.962609i
$827$	−29.0841			−1.01135			−0.505676	−	0.862723i	$-0.668757\pi$
$827$	−29.0841			−1.01135			−0.505676	+	0.862723i	$0.668757\pi$
$828$	−12.0922	+	11.8979i	−0.420235	+	0.413479i
$829$			28.7442i			0.998326i	0.866508	+	0.499163i	$0.166359\pi$
$829$			28.7442i			0.998326i	−0.866508	+	0.499163i	$0.833641\pi$
$830$	9.81696			0.340752
$831$	−8.85755	+	21.1414i	−0.307265	+	0.733386i
$832$	16.9345	+	24.3995i	0.587099	+	0.845899i
$833$	34.5133	−	22.8601i	1.19582	−	0.792056i
$834$	9.75889	+	4.08866i	0.337923	+	0.141579i
$835$	−16.1766			−0.559814
$836$	3.97256			0.137394
$837$	17.5913	−	7.03730i	0.608043	−	0.243245i
$838$	39.3916			1.36076
$839$			34.1126i			1.17770i	0.808244	+	0.588848i	$0.200418\pi$
$839$			34.1126i			1.17770i	−0.808244	+	0.588848i	$0.799582\pi$
$840$	22.7721	+	2.38249i	0.785711	+	0.0822038i
$841$	26.2629			0.905619
$842$			9.88830i			0.340773i
$843$	−8.25415	+	19.7011i	−0.284288	+	0.678543i
$844$	10.9525			0.377001
$845$	19.8107	+	7.39693i	0.681510	+	0.254462i
$846$	−21.8063	+	21.4557i	−0.749714	+	0.737662i
$847$	−13.6020	+	4.09617i	−0.467371	+	0.140746i
$848$			22.8203i			0.783653i
$849$	−10.7840	−	4.51816i	−0.370106	−	0.155063i
$850$	−15.4164			−0.528779
$851$	82.6265			2.83240
$852$	4.36527	−	10.4191i	0.149552	−	0.356953i
$853$	−4.21797			−0.144420			−0.0722102	−	0.997389i	$-0.523005\pi$
$853$	−4.21797			−0.144420			−0.0722102	+	0.997389i	$0.523005\pi$
$854$	−2.08833	−	6.93464i	−0.0714611	−	0.237299i
$855$	−7.52718	+	7.40618i	−0.257424	+	0.253286i
$856$			6.98873i			0.238870i
$857$	45.8822			1.56731			0.783653	−	0.621199i	$-0.213354\pi$
$857$	45.8822			1.56731			0.783653	+	0.621199i	$0.213354\pi$
$858$	−16.0502	+	3.42053i	−0.547946	+	0.116775i
$859$		−	46.2701i		−	1.57872i	−0.613933	−	0.789358i	$-0.710413\pi$
$859$		−	46.2701i		−	1.57872i	0.613933	−	0.789358i	$-0.289587\pi$
$860$			3.59188i			0.122482i
$861$	−10.3902	−	1.08706i	−0.354098	−	0.0370470i
$862$	13.4571			0.458351
$863$	−22.5254			−0.766774			−0.383387	−	0.923588i	$-0.625242\pi$
$863$	−22.5254			−0.766774			−0.383387	+	0.923588i	$0.625242\pi$
$864$	−19.7310	+	7.89329i	−0.671262	+	0.268535i
$865$			16.6452i			0.565955i
$866$		−	26.1756i		−	0.889482i
$867$	−12.0305	+	28.7146i	−0.408577	+	0.975198i
$868$	−7.14653	+	2.15214i	−0.242569	+	0.0730482i
$869$	29.3415			0.995342
$870$	1.99467	−	4.76091i	0.0676256	−	0.161410i
$871$	−17.5255	+	12.1636i	−0.593827	+	0.412147i
$872$		−	21.2359i		−	0.719137i
$873$	8.78140	+	8.92487i	0.297206	+	0.302061i
$874$		−	17.5150i		−	0.592453i
$875$	−9.12625	−	30.3053i	−0.308524	−	1.02451i
$876$	−4.02744	+	9.61277i	−0.136075	+	0.324785i
$877$		−	10.7280i		−	0.362257i	−0.983459	−	0.181129i	$-0.942025\pi$
$877$		−	10.7280i		−	0.362257i	0.983459	−	0.181129i	$-0.0579751\pi$
$878$		−	40.6898i		−	1.37321i
$879$	−46.5374	−	19.4977i	−1.56967	−	0.657640i
$880$		−	7.15702i		−	0.241263i
$881$	−25.4943			−0.858926			−0.429463	−	0.903084i	$-0.641297\pi$
$881$	−25.4943			−0.858926			−0.429463	+	0.903084i	$0.641297\pi$
$882$	22.7519	+	4.81346i	0.766097	+	0.162078i
$883$	7.55187			0.254141			0.127070	−	0.991894i	$-0.459443\pi$
$883$	7.55187			0.254141			0.127070	+	0.991894i	$0.459443\pi$
$884$	−9.40599	−	13.5523i	−0.316358	−	0.455812i
$885$	10.7363	−	25.6256i	0.360898	−	0.861397i
$886$			9.42526i			0.316648i
$887$	13.4695			0.452260			0.226130	−	0.974097i	$-0.427393\pi$
$887$	13.4695			0.452260			0.226130	+	0.974097i	$0.427393\pi$
$888$	55.4698	+	23.2401i	1.86144	+	0.779885i
$889$	6.33293	−	1.90713i	0.212400	−	0.0639630i
$890$	−18.7687			−0.629130
$891$	0.346070	−	21.3537i	0.0115938	−	0.715375i
$892$	1.41452			0.0473616
$893$			19.9258i			0.666791i
$894$	−10.0055	+	23.8813i	−0.334633	+	0.798709i
$895$	19.3538			0.646927
$896$	−2.38777	+	0.719064i	−0.0797699	+	0.0240222i
$897$	−9.51403	−	44.6429i	−0.317664	−	1.49058i
$898$	−19.4339			−0.648519
$899$			6.03244i			0.201193i
$900$	3.83181	+	3.89442i	0.127727	+	0.129814i
$901$		−	72.7865i		−	2.42487i
$902$			5.99065i			0.199467i
$903$	−1.36098	+	13.0084i	−0.0452907	+	0.432893i
$904$			8.05507i			0.267908i
$905$	−0.339543			−0.0112868
$906$	25.0038	+	10.4758i	0.830695	+	0.348035i
$907$	1.96021			0.0650876			0.0325438	−	0.999470i	$-0.489639\pi$
$907$	1.96021			0.0650876			0.0325438	+	0.999470i	$0.489639\pi$
$908$		−	14.7892i		−	0.490796i
$909$	−18.9803	−	19.2904i	−0.629537	−	0.639822i
$910$	−10.6921	+	13.4525i	−0.354441	+	0.445946i
$911$		−	55.5113i		−	1.83917i	−0.392890	−	0.919585i	$-0.628525\pi$
$911$		−	55.5113i		−	1.83917i	0.392890	−	0.919585i	$-0.371475\pi$
$912$	2.68540	−	6.40956i	0.0889225	−	0.212242i
$913$			12.9318i			0.427981i
$914$			18.8951i			0.624995i
$915$	−2.69116	+	6.42331i	−0.0889671	+	0.212348i
$916$	12.9255			0.427069
$917$	9.02336	−	2.71733i	0.297978	−	0.0897342i
$918$	−31.5958	+	12.6397i	−1.04282	+	0.417174i
$919$	−15.7001			−0.517898			−0.258949	−	0.965891i	$-0.583376\pi$
$919$	−15.7001			−0.517898			−0.258949	+	0.965891i	$0.583376\pi$
$920$	36.5192			1.20400
$921$	17.8449	−	42.5925i	0.588009	−	1.40347i
$922$			19.5383i			0.643459i
$923$	17.3310	+	24.9708i	0.570458	+	0.821923i
$924$	−0.875402	+	8.36717i	−0.0287986	+	0.275260i
$925$		−	26.6106i		−	0.874951i
$926$			19.4534i			0.639279i
$927$	21.3690	−	21.0254i	0.701849	−	0.690566i
$928$		−	6.76621i		−	0.222112i
$929$		−	18.4630i		−	0.605752i	−0.953030	−	0.302876i	$-0.902053\pi$
$929$		−	18.4630i		−	0.605752i	0.953030	−	0.302876i	$-0.0979467\pi$
$930$	−10.4930	−	4.39622i	−0.344078	−	0.144158i
$931$	12.6284	−	8.36450i	0.413879	−	0.274135i
$932$		−	2.96449i		−	0.0971051i
$933$	−5.89555	+	14.0716i	−0.193012	+	0.460683i
$934$	−8.77496			−0.287125
$935$			22.8277i			0.746544i
$936$	6.16947	−	32.6461i	0.201656	−	1.06707i
$937$			42.8761i			1.40070i	0.713799	+	0.700351i	$0.246973\pi$
$937$			42.8761i			1.40070i	−0.713799	+	0.700351i	$0.753027\pi$
$938$	−4.99872	−	16.5991i	−0.163214	−	0.541980i
$939$	43.8664	+	18.3786i	1.43153	+	0.599764i
$940$	−11.5883			−0.377969
$941$			4.14361i			0.135078i	0.997717	+	0.0675388i	$0.0215147\pi$
$941$			4.14361i			0.135078i	−0.997717	+	0.0675388i	$0.978485\pi$
$942$	−13.7603	−	5.76513i	−0.448335	−	0.187838i
$943$	−16.6627			−0.542611
$944$			18.2844i			0.595107i
$945$	−13.9405	−	17.4861i	−0.453484	−	0.568823i
$946$	7.50019			0.243852
$947$	−21.5170			−0.699209			−0.349605	−	0.936897i	$-0.613684\pi$
$947$	−21.5170			−0.699209			−0.349605	+	0.936897i	$0.613684\pi$
$948$	−6.40271	+	15.2821i	−0.207950	+	0.496340i
$949$	−15.9898	−	23.0383i	−0.519050	−	0.747854i
$950$	−5.64086			−0.183014
$951$	−10.7801	+	25.7301i	−0.349568	+	0.834356i
$952$	46.0187	−	13.8583i	1.49147	−	0.449149i
$953$		−	39.1328i		−	1.26763i	−0.773483	−	0.633817i	$-0.781487\pi$
$953$		−	39.1328i		−	1.26763i	0.773483	−	0.633817i	$-0.218513\pi$
$954$	29.1460	−	28.6774i	0.943635	−	0.928466i
$955$	−18.1225			−0.586432
$956$	23.2050			0.750505
$957$	6.27152	+	2.62756i	0.202729	+	0.0849371i
$958$			7.56051i			0.244269i
$959$	−26.7336	+	8.05065i	−0.863272	+	0.259969i
$960$	21.4058	+	8.96833i	0.690868	+	0.289452i
$961$	−17.7046			−0.571116
$962$	−37.0810	+	25.7362i	−1.19554	+	0.829768i
$963$	4.86560	−	4.78738i	0.156792	−	0.154271i
$964$	9.92181			0.319560
$965$	−14.2265			−0.457967
$966$	36.8907	+	3.85964i	1.18694	+	0.124182i
$967$		−	21.1949i		−	0.681582i	−0.940139	−	0.340791i	$-0.889305\pi$
$967$		−	21.1949i		−	0.681582i	0.940139	−	0.340791i	$-0.110695\pi$
$968$	−16.4916			−0.530061
$969$	−8.56521	+	20.4436i	−0.275154	+	0.656743i
$970$		−	7.51813i		−	0.241393i
$971$	−46.0603			−1.47815			−0.739073	−	0.673626i	$-0.764736\pi$
$971$	−46.0603			−1.47815			−0.739073	+	0.673626i	$0.764736\pi$
$972$	11.0463	+	4.83991i	0.354309	+	0.155240i
$973$	4.20846	+	13.9749i	0.134917	+	0.448015i
$974$		−	32.3387i		−	1.03620i
$975$	−14.3776	+	3.06408i	−0.460453	+	0.0981290i
$976$		−	4.58317i		−	0.146704i
$977$	−50.0820			−1.60226			−0.801132	−	0.598487i	$-0.795769\pi$
$977$	−50.0820			−1.60226			−0.801132	+	0.598487i	$0.795769\pi$
$978$	−22.9591	−	9.61912i	−0.734150	−	0.307585i
$979$		−	24.7239i		−	0.790181i
$980$	4.86458	+	7.34436i	0.155393	+	0.234607i
$981$	−14.7845	+	14.5469i	−0.472034	+	0.464446i
$982$			14.0140i			0.447205i
$983$		−	31.2811i		−	0.997713i	−0.866685	−	0.498856i	$-0.833754\pi$
$983$		−	31.2811i		−	0.997713i	0.866685	−	0.498856i	$-0.166246\pi$
$984$	−11.1862	−	4.68665i	−0.356602	−	0.149405i
$985$			22.8749i			0.728854i
$986$		−	10.8349i		−	0.345054i
$987$	−41.9684	−	4.39088i	−1.33587	−	0.139763i
$988$	−3.44164	−	4.95877i	−0.109493	−	0.157759i
$989$			20.8614i			0.663353i
$990$	−9.14090	+	8.99395i	−0.290517	+	0.285847i
$991$	24.6898			0.784297			0.392149	−	0.919902i	$-0.371732\pi$
$991$	24.6898			0.784297			0.392149	+	0.919902i	$0.371732\pi$
$992$	−14.9126			−0.473476
$993$	−35.8647	−	15.0261i	−1.13813	−	0.476840i
$994$	−23.6509	+	7.12233i	−0.750161	+	0.225907i
$995$	−7.37841			−0.233911
$996$	−6.73536	−	2.82190i	−0.213418	−	0.0894153i
$997$			30.2709i			0.958689i	0.877627	+	0.479344i	$0.159126\pi$
$997$			30.2709i			0.958689i	−0.877627	+	0.479344i	$0.840874\pi$
$998$			6.71552i			0.212576i
$999$	−21.8177	−	54.5382i	−0.690282	−	1.72551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.g.a.272.10	yes	32
3.2	odd	2	inner	273.2.g.a.272.24	yes	32
7.6	odd	2	inner	273.2.g.a.272.11	yes	32
13.12	even	2	inner	273.2.g.a.272.22	yes	32
21.20	even	2	inner	273.2.g.a.272.21	yes	32
39.38	odd	2	inner	273.2.g.a.272.12	yes	32
91.90	odd	2	inner	273.2.g.a.272.23	yes	32
273.272	even	2	inner	273.2.g.a.272.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.9	✓	32	273.272	even	2	inner
273.2.g.a.272.10	yes	32	1.1	even	1	trivial
273.2.g.a.272.11	yes	32	7.6	odd	2	inner
273.2.g.a.272.12	yes	32	39.38	odd	2	inner
273.2.g.a.272.21	yes	32	21.20	even	2	inner
273.2.g.a.272.22	yes	32	13.12	even	2	inner
273.2.g.a.272.23	yes	32	91.90	odd	2	inner
273.2.g.a.272.24	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.10741 q^{2} +(-0.669305 + 1.59751i) q^{3} -0.773652 q^{4} -1.62666i q^{5} +(0.741192 - 1.76909i) q^{6} +(2.53337 - 0.762910i) q^{7} +3.07156 q^{8} +(-2.10406 - 2.13844i) q^{9} +O(q^{10})\)	\(q-1.10741 q^{2} +(-0.669305 + 1.59751i) q^{3} -0.773652 q^{4} -1.62666i q^{5} +(0.741192 - 1.76909i) q^{6} +(2.53337 - 0.762910i) q^{7} +3.07156 q^{8} +(-2.10406 - 2.13844i) q^{9} +1.80138i q^{10} -2.37294 q^{11} +(0.517809 - 1.23591i) q^{12} +(2.05581 + 2.96204i) q^{13} +(-2.80547 + 0.844851i) q^{14} +(2.59861 + 1.08873i) q^{15} -1.85416 q^{16} +5.91393 q^{17} +(2.33005 + 2.36812i) q^{18} +2.16390 q^{19} +1.25847i q^{20} +(-0.476842 + 4.55770i) q^{21} +2.62781 q^{22} +7.30912i q^{23} +(-2.05581 + 4.90684i) q^{24} +2.35397 q^{25} +(-2.27661 - 3.28018i) q^{26} +(4.82443 - 1.92999i) q^{27} +(-1.95995 + 0.590226i) q^{28} +1.65441i q^{29} +(-2.87771 - 1.20567i) q^{30} +3.64629 q^{31} -4.08981 q^{32} +(1.58822 - 3.79079i) q^{33} -6.54913 q^{34} +(-1.24100 - 4.12094i) q^{35} +(1.62781 + 1.65441i) q^{36} -11.3046i q^{37} -2.39632 q^{38} +(-6.10784 + 1.30167i) q^{39} -4.99639i q^{40} +2.27971i q^{41} +(0.528058 - 5.04722i) q^{42} +2.85416 q^{43} +1.83583 q^{44} +(-3.47852 + 3.42260i) q^{45} -8.09416i q^{46} +9.20825i q^{47} +(1.24100 - 2.96204i) q^{48} +(5.83594 - 3.86547i) q^{49} -2.60680 q^{50} +(-3.95822 + 9.44755i) q^{51} +(-1.59048 - 2.29158i) q^{52} -12.3076i q^{53} +(-5.34261 + 2.13728i) q^{54} +3.85998i q^{55} +(7.78140 - 2.34332i) q^{56} +(-1.44831 + 3.45685i) q^{57} -1.83210i q^{58} -9.86130i q^{59} +(-2.01042 - 0.842300i) q^{60} +2.47183i q^{61} -4.03792 q^{62} +(-6.96181 - 3.81225i) q^{63} +8.23740 q^{64} +(4.81823 - 3.34411i) q^{65} +(-1.75881 + 4.19795i) q^{66} +5.91669i q^{67} -4.57532 q^{68} +(-11.6764 - 4.89202i) q^{69} +(1.37429 + 4.56356i) q^{70} +8.43028 q^{71} +(-6.46275 - 6.56834i) q^{72} -7.77786 q^{73} +12.5188i q^{74} +(-1.57552 + 3.76048i) q^{75} -1.67411 q^{76} +(-6.01154 + 1.81034i) q^{77} +(6.76386 - 1.44147i) q^{78} -12.3650 q^{79} +3.01609i q^{80} +(-0.145840 + 8.99882i) q^{81} -2.52456i q^{82} -5.44970i q^{83} +(0.368910 - 3.52607i) q^{84} -9.61998i q^{85} -3.16071 q^{86} +(-2.64293 - 1.10730i) q^{87} -7.28863 q^{88} +10.4191i q^{89} +(3.85213 - 3.79021i) q^{90} +(7.46789 + 5.93554i) q^{91} -5.65471i q^{92} +(-2.44048 + 5.82497i) q^{93} -10.1973i q^{94} -3.51994i q^{95} +(2.73733 - 6.53350i) q^{96} -4.17355 q^{97} +(-6.46275 + 4.28064i) q^{98} +(4.99282 + 5.07439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

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