LMFDB - Embedded newform 273.2.g.a.272.11

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			272.11
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.12

$q$-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} +(-2.91435 + 3.53646i) 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} +(3.22737 - 3.91630i) 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} +(3.69894 + 7.02267i) 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} +(2.25469 - 2.73599i) 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} +(2.94836 + 9.07233i) 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	$0.118498\pi$
$5$			1.62666i			0.727466i	−0.931503	+	0.363733i	$0.881502\pi$
$6$	−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	$-0.754563\pi$
$17$	−5.91393			−1.43434			−0.717170	+	0.696899i	$0.754563\pi$
$18$	2.33005	+	2.36812i	0.549199	+	0.558171i
$19$	−2.16390			−0.496434			−0.248217	−	0.968705i	$-0.579845\pi$
$19$	−2.16390			−0.496434			−0.248217	+	0.968705i	$0.579845\pi$
$20$		−	1.25847i		−	0.281403i
$21$	−2.91435	+	3.53646i	−0.635964	+	0.771719i
$22$	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	$-0.606188\pi$
$31$	−3.64629			−0.654893			−0.327446	+	0.944870i	$0.606188\pi$
$32$	−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	$-0.943032\pi$
$41$		−	2.27971i		−	0.356031i	0.984028	−	0.178015i	$-0.0569677\pi$
$42$	3.22737	−	3.91630i	0.497994	−	0.604298i
$43$	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	$-0.765616\pi$
$47$		−	9.20825i		−	1.34316i	0.740931	−	0.671581i	$-0.234384\pi$
$48$	−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	$0.221860\pi$
$59$			9.86130i			1.28383i	−0.766775	+	0.641916i	$0.778140\pi$
$60$	−2.01042	−	0.842300i	−0.259544	−	0.108741i
$61$		−	2.47183i		−	0.316485i	−0.987400	−	0.158243i	$-0.949417\pi$
$61$		−	2.47183i		−	0.316485i	0.987400	−	0.158243i	$-0.0505828\pi$
$62$	4.03792			0.512817
$63$	3.69894	+	7.02267i	0.466022	+	0.884773i
$64$	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	$-0.349580\pi$
$73$	7.77786			0.910329			0.455165	+	0.890407i	$0.349580\pi$
$74$			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	$0.0966834\pi$
$83$			5.44970i			0.598182i	−0.954225	+	0.299091i	$0.903317\pi$
$84$	2.25469	−	2.73599i	0.246007	−	0.298521i
$85$		−	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	$-0.813784\pi$
$89$		−	10.4191i		−	1.10442i	0.833704	−	0.552211i	$-0.186216\pi$
$90$	−3.85213	+	3.79021i	−0.406051	+	0.399523i
$91$	2.94836	+	9.07233i	0.309072	+	0.951039i
$92$		−	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	$-0.432041\pi$
$97$	4.17355			0.423759			0.211880	+	0.977296i	$0.432041\pi$
$98$	−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	$-0.648149\pi$
$101$	−9.02078			−0.897602			−0.448801	+	0.893632i	$0.648149\pi$
$102$	4.38336	−	10.4623i	0.434017	−	1.03592i
$103$		−	9.99279i		−	0.984618i	−0.870420	−	0.492309i	$-0.836153\pi$
$103$		−	9.99279i		−	0.984618i	0.870420	−	0.492309i	$-0.163847\pi$
$104$	−6.31454	−	9.09806i	−0.619191	−	0.892139i
$105$	−5.75263	−	4.74067i	−0.561399	−	0.462642i
$106$			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
$126$	−4.09622	−	7.77695i	−0.364921	−	0.692825i
$127$	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	$-0.549730\pi$
$131$	−3.56180			−0.311196			−0.155598	+	0.987820i	$0.549730\pi$
$132$	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	$-0.924837\pi$
$139$		−	5.51633i		−	0.467889i	0.972250	−	0.233945i	$-0.0751634\pi$
$140$	−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
$147$	10.0811	−	6.73578i	0.831478	−	0.555558i
$148$			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	$0.100457\pi$
$157$			7.77818i			0.620767i	−0.950612	+	0.310383i	$0.899543\pi$
$158$	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	$0.125719\pi$
$167$			9.94464i			0.769539i	−0.923013	+	0.384770i	$0.874281\pi$
$168$	−8.95160	+	10.8624i	−0.690631	+	0.838056i
$169$	−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	$-0.372824\pi$
$173$	10.2328			0.777982			0.388991	+	0.921242i	$0.372824\pi$
$174$	−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	$0.00246935\pi$
$181$			0.208736i			0.0155152i	−0.999970	+	0.00775761i	$0.997531\pi$
$182$	−3.26503	−	10.0468i	−0.242020	−	0.744715i
$183$	−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
$189$	13.6945	−	1.20877i	0.996127	−	0.0879254i
$190$			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	$0.0513982\pi$
$199$			4.53592i			0.321543i	−0.986992	+	0.160771i	$0.948602\pi$
$200$	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
$210$	6.37050	+	5.24985i	0.439606	+	0.362274i
$211$	−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	$-0.480501\pi$
$223$	1.82837			0.122437			0.0612183	+	0.998124i	$0.480501\pi$
$224$	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	$-0.781252\pi$
$227$		−	19.1161i		−	1.26878i	0.773014	−	0.634388i	$-0.218748\pi$
$228$	1.12049	−	2.67440i	0.0742061	−	0.177116i
$229$	16.7071			1.10403			0.552017	−	0.833833i	$-0.313858\pi$
$229$	16.7071			1.10403			0.552017	+	0.833833i	$0.313858\pi$
$230$	13.1665			0.868172
$231$	6.91559	−	8.39182i	0.455012	−	0.552141i
$232$			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	$-0.364462\pi$
$241$	12.8246			0.826108			0.413054	+	0.910707i	$0.364462\pi$
$242$	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	$-0.712233\pi$
$251$	−19.5957			−1.23687			−0.618435	+	0.785836i	$0.712233\pi$
$252$	−2.86169	−	5.43310i	−0.180269	−	0.342253i
$253$		−	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	$-0.594633\pi$
$257$	−9.39236			−0.585879			−0.292940	+	0.956131i	$0.594633\pi$
$258$	−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	$-0.632849\pi$
$269$	−13.2963			−0.810692			−0.405346	+	0.914163i	$0.632849\pi$
$270$	3.47664	+	8.69062i	0.211582	+	0.528894i
$271$	−24.1869			−1.46925			−0.734624	−	0.678475i	$-0.762641\pi$
$271$	−24.1869			−1.46925			−0.734624	+	0.678475i	$0.762641\pi$
$272$	10.9654			0.664874
$273$	16.4665	+	1.36212i	0.996596	+	0.0824395i
$274$	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	$-0.935698\pi$
$283$		−	6.75052i		−	0.401277i	0.979665	−	0.200638i	$-0.0643017\pi$
$284$	−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	$-0.676037\pi$
$293$		−	29.1312i		−	1.70187i	0.525275	−	0.850933i	$-0.323963\pi$
$294$	−11.1639	+	7.45924i	−0.651092	+	0.435032i
$295$	−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	$-0.224789\pi$
$307$	26.6618			1.52167			0.760836	+	0.648945i	$0.224789\pi$
$308$	−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	$-0.580346\pi$
$311$	−8.80847			−0.499482			−0.249741	+	0.968313i	$0.580346\pi$
$312$	−18.7606	+	3.99815i	−1.06211	+	0.226350i
$313$			27.4593i			1.55209i	0.630677	+	0.776045i	$0.282777\pi$
$313$			27.4593i			1.55209i	−0.630677	+	0.776045i	$0.717223\pi$
$314$		−	8.61361i		−	0.486094i
$315$	−11.4235	+	6.01692i	−0.643642	+	0.339015i
$316$	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
$336$	5.40367	−	6.55716i	0.294795	−	0.357723i
$337$	−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	$-0.642914\pi$
$349$	−16.2173			−0.868091			−0.434046	+	0.900891i	$0.642914\pi$
$350$	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	$0.161365\pi$
$353$			18.2438i			0.971017i	−0.874232	+	0.485508i	$0.838635\pi$
$354$	−17.4455	−	7.30912i	−0.927219	−	0.388475i
$355$			13.7132i			0.727823i
$356$			8.06076i			0.427219i
$357$	17.2353	−	20.9144i	0.912188	−	1.10691i
$358$		−	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
$364$	−2.28100	−	7.01882i	−0.119557	−	0.367886i
$365$			12.6520i			0.662234i
$366$	4.37289	+	1.83210i	0.228575	+	0.0957654i
$367$		−	3.51046i		−	0.183245i	−0.995794	−	0.0916224i	$-0.970795\pi$
$367$		−	3.51046i		−	0.183245i	0.995794	−	0.0916224i	$-0.0292053\pi$
$368$		−	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
$378$	−15.1654	+	1.33860i	−0.780022	+	0.0688503i
$379$		−	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	$0.114869\pi$
$383$			13.8202i			0.706182i	−0.935589	+	0.353091i	$0.885131\pi$
$384$	−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	$-0.433008\pi$
$397$	8.32507			0.417823			0.208912	+	0.977935i	$0.433008\pi$
$398$		−	5.02311i		−	0.251786i
$399$	6.30638	−	7.65256i	0.315714	−	0.383107i
$400$	−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	$-0.591490\pi$
$409$	−11.4661			−0.566963			−0.283482	+	0.958978i	$0.591490\pi$
$410$	−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	$-0.164840\pi$
$419$	35.5711			1.73776			0.868880	+	0.495023i	$0.164840\pi$
$420$	4.45053	+	3.66763i	0.217164	+	0.178962i
$421$		−	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	$-0.807734\pi$
$433$		−	23.6368i		−	1.13591i	0.823059	−	0.567956i	$-0.192266\pi$
$434$	−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	$-0.659653\pi$
$439$		−	36.7433i		−	1.75366i	0.480799	−	0.876831i	$-0.340347\pi$
$440$		−	11.8562i		−	0.565220i
$441$	−4.01311	−	20.6130i	−0.191101	−	0.981570i
$442$	−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
$455$	−14.7576	+	4.79599i	−0.691848	+	0.224839i
$456$	−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	$0.134773\pi$
$461$			17.6433i			0.821729i	−0.911696	+	0.410865i	$0.865227\pi$
$462$	−7.65837	+	9.29315i	−0.356299	+	0.432357i
$463$		−	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	$-0.558690\pi$
$467$	−7.92389			−0.366674			−0.183337	+	0.983050i	$0.558690\pi$
$468$	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	$0.0498510\pi$
$479$			6.82723i			0.311944i	−0.987761	+	0.155972i	$0.950149\pi$
$480$	−10.6278	−	4.45271i	−0.485091	−	0.203238i
$481$	−33.4846	+	23.2401i	−1.52676	+	1.05966i
$482$	−14.2021			−0.646888
$483$	−25.8484	−	21.3013i	−1.17614	−	0.969244i
$484$	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	$-0.758239\pi$
$503$	−32.5278			−1.45034			−0.725171	+	0.688569i	$0.758239\pi$
$504$	11.3615	+	21.5705i	0.506081	+	0.960828i
$505$		−	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	$0.0579118\pi$
$509$			8.16408i			0.361867i	−0.983495	+	0.180933i	$0.942088\pi$
$510$	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	$-0.247767\pi$
$521$	32.5057			1.42410			0.712050	+	0.702129i	$0.247767\pi$
$522$	−3.91783	+	3.85485i	−0.171479	+	0.168722i
$523$			4.26772i			0.186614i	0.995637	+	0.0933072i	$0.0297439\pi$
$523$			4.26772i			0.186614i	−0.995637	+	0.0933072i	$0.970256\pi$
$524$	2.75559			0.120379
$525$	−6.86028	+	8.32471i	−0.299407	+	0.363320i
$526$			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
$546$	−18.2351	−	1.50843i	−0.780389	−	0.0645546i
$547$	−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	$-0.401124\pi$
$563$	14.5051			0.611316			0.305658	+	0.952141i	$0.401124\pi$
$564$	11.3806	+	4.76811i	0.479210	+	0.200774i
$565$	−4.26588			−0.179467
$566$			7.47557i			0.314222i
$567$	7.23475	−	22.6861i	0.303831	−	0.952726i
$568$	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	$-0.633585\pi$
$577$	−19.5750			−0.814918			−0.407459	+	0.913224i	$0.633585\pi$
$578$	−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	$-0.769881\pi$
$587$		−	32.0582i		−	1.32318i	0.749865	−	0.661591i	$-0.230119\pi$
$588$	−7.79929	+	5.21115i	−0.321637	+	0.214904i
$589$	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	$0.0454772\pi$
$593$			6.93462i			0.284771i	−0.989811	+	0.142385i	$0.954523\pi$
$594$	−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	$0.129270\pi$
$601$			19.3691i			0.790082i	−0.918664	+	0.395041i	$0.870730\pi$
$602$	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	$0.0636268\pi$
$607$			9.78405i			0.397122i	−0.980088	+	0.198561i	$0.936373\pi$
$608$	8.84996			0.358913
$609$	−5.85074	−	4.82152i	−0.237084	−	0.195378i
$610$	−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	$-0.266200\pi$
$619$	33.3498			1.34044			0.670221	+	0.742162i	$0.266200\pi$
$620$			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
$630$	12.6505	−	6.66318i	0.504007	−	0.265467i
$631$			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
$637$	−0.547918	−	25.2329i	−0.0217093	−	0.999764i
$638$			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	$-0.402292\pi$
$643$	15.3241			0.604323			0.302161	+	0.953257i	$0.402292\pi$
$644$	−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	$-0.134433\pi$
$647$	46.4025			1.82427			0.912135	+	0.409890i	$0.134433\pi$
$648$	−0.447956	+	27.6404i	−0.0175974	+	1.08582i
$649$		−	23.4003i		−	0.918542i
$650$	5.35907	+	7.72142i	0.210200	+	0.302859i
$651$	10.6266	−	12.8950i	0.416488	−	0.505393i
$652$			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	$-0.439946\pi$
$661$	9.64369			0.375096			0.187548	+	0.982255i	$0.439946\pi$
$662$		−	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
$672$	11.9191	−	14.4635i	0.459791	−	0.557940i
$673$	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	$-0.150935\pi$
$677$	46.2970			1.77934			0.889670	+	0.456605i	$0.150935\pi$
$678$	−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	$-0.339167\pi$
$691$	25.4481			0.968090			0.484045	+	0.875043i	$0.339167\pi$
$692$	−7.91659			−0.300943
$693$	−8.77736	−	16.6644i	−0.333424	−	0.633028i
$694$		−	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
$714$	−19.0865	+	23.1607i	−0.714293	+	0.866768i
$715$	−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	$-0.576838\pi$
$719$	−12.8202			−0.478113			−0.239057	+	0.971006i	$0.576838\pi$
$720$	−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	$0.180423\pi$
$727$			28.9554i			1.07390i	−0.843615	+	0.536948i	$0.819577\pi$
$728$	9.05606	+	27.8662i	0.335640	+	1.03279i
$729$	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	$-0.771343\pi$
$733$	−40.7676			−1.50579			−0.752894	+	0.658142i	$0.771343\pi$
$734$			3.88751i			0.143491i
$735$	10.9568	+	16.3986i	0.404149	+	0.604872i
$736$		−	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
$756$	−10.5948	+	0.935170i	−0.385328	+	0.0340118i
$757$	−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	$-0.961121\pi$
$761$		−	6.72208i		−	0.243675i	0.992550	−	0.121838i	$-0.0388787\pi$
$762$	−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	$-0.692695\pi$
$769$	−31.5613			−1.13813			−0.569065	+	0.822292i	$0.692695\pi$
$770$	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	$-0.706142\pi$
$773$		−	44.3470i		−	1.59505i	0.603285	−	0.797525i	$-0.293858\pi$
$774$	6.65034	+	6.75899i	0.239042	+	0.242947i
$775$	−8.58324			−0.308319
$776$	12.8193			0.460186
$777$	39.9782	+	32.9455i	1.43421	+	1.18191i
$778$			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	$-0.332163\pi$
$787$	28.2320			1.00636			0.503182	+	0.864181i	$0.332163\pi$
$788$	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	$-0.569558\pi$
$797$	−12.2404			−0.433577			−0.216789	+	0.976219i	$0.569558\pi$
$798$	−6.98372	+	8.47449i	−0.247221	+	0.299994i
$799$			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	$-0.453969\pi$
$811$	8.20780			0.288215			0.144107	+	0.989562i	$0.453969\pi$
$812$	−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
$819$	13.1971	−	25.3936i	0.461144	−	0.887326i
$820$	−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	$-0.833641\pi$
$829$		−	28.7442i		−	0.998326i	0.866508	−	0.499163i	$-0.166359\pi$
$830$	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	$-0.799582\pi$
$839$		−	34.1126i		−	1.17770i	0.808244	−	0.588848i	$-0.200418\pi$
$840$	−17.6695	−	14.5612i	−0.609657	−	0.502411i
$841$	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	$-0.476995\pi$
$853$	4.21797			0.144420			0.0722102	+	0.997389i	$0.476995\pi$
$854$	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	$-0.786646\pi$
$857$	−45.8822			−1.56731			−0.783653	+	0.621199i	$0.786646\pi$
$858$	−16.0502	+	3.42053i	−0.547946	+	0.116775i
$859$			46.2701i			1.57872i	0.613933	+	0.789358i	$0.289587\pi$
$859$			46.2701i			1.57872i	−0.613933	+	0.789358i	$0.710413\pi$
$860$		−	3.59188i		−	0.122482i
$861$	8.06210	+	6.64387i	0.274756	+	0.226423i
$862$	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	$-0.358703\pi$
$881$	25.4943			0.858926			0.429463	+	0.903084i	$0.358703\pi$
$882$	4.44415	+	22.8269i	0.149642	+	0.768623i
$883$	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	$-0.572607\pi$
$887$	−13.4695			−0.452260			−0.226130	+	0.974097i	$0.572607\pi$
$888$	−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
$903$	−8.31802	+	10.0936i	−0.276807	+	0.335895i
$904$			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
$910$	16.3427	−	5.31111i	0.541755	−	0.176062i
$911$		−	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
$924$	−5.35026	+	6.49235i	−0.176011	+	0.213582i
$925$		−	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	$0.0979467\pi$
$929$			18.4630i			0.605752i	−0.953030	+	0.302876i	$0.902053\pi$
$930$	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	$-0.753027\pi$
$937$		−	42.8761i		−	1.40070i	0.713799	−	0.700351i	$-0.246973\pi$
$938$	−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	$-0.978485\pi$
$941$		−	4.14361i		−	0.135078i	0.997717	−	0.0675388i	$-0.0215147\pi$
$942$	−13.7603	−	5.76513i	−0.448335	−	0.187838i
$943$	16.6627			0.542611
$944$		−	18.2844i		−	0.595107i
$945$	1.96627	+	22.2763i	0.0639627	+	0.724649i
$946$	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
$966$	28.6247	+	23.5892i	0.920984	+	0.758971i
$967$		−	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	$-0.235264\pi$
$971$	46.0603			1.47815			0.739073	+	0.673626i	$0.235264\pi$
$972$	−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	$0.166246\pi$
$983$			31.2811i			0.997713i	−0.866685	+	0.498856i	$0.833754\pi$
$984$	−11.1862	−	4.68665i	−0.356602	−	0.149405i
$985$		−	22.8749i		−	0.728854i
$986$			10.8349i			0.345054i
$987$	32.5646	+	26.8361i	1.03654	+	0.854202i
$988$	−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	$-0.840874\pi$
$997$		−	30.2709i		−	0.958689i	0.877627	−	0.479344i	$-0.159126\pi$
$998$			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.272.11	yes	32
3.2	odd	2	inner	273.2.g.a.272.21	yes	32
7.6	odd	2	inner	273.2.g.a.272.10	yes	32
13.12	even	2	inner	273.2.g.a.272.23	yes	32
21.20	even	2	inner	273.2.g.a.272.24	yes	32
39.38	odd	2	inner	273.2.g.a.272.9	✓	32
91.90	odd	2	inner	273.2.g.a.272.22	yes	32
273.272	even	2	inner	273.2.g.a.272.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.9	✓	32	39.38	odd	2	inner
273.2.g.a.272.10	yes	32	7.6	odd	2	inner
273.2.g.a.272.11	yes	32	1.1	even	1	trivial
273.2.g.a.272.12	yes	32	273.272	even	2	inner
273.2.g.a.272.21	yes	32	3.2	odd	2	inner
273.2.g.a.272.22	yes	32	91.90	odd	2	inner
273.2.g.a.272.23	yes	32	13.12	even	2	inner
273.2.g.a.272.24	yes	32	21.20	even	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} +(-2.91435 + 3.53646i) 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} +(3.22737 - 3.91630i) 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} +(3.69894 + 7.02267i) 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} +(2.25469 - 2.73599i) 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} +(2.94836 + 9.07233i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more