LMFDB - Embedded newform 273.2.l.c.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$-0.828334 - 1.43472i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.c.256.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.65667 q^{2} +(-0.500000 + 0.866025i) q^{3} +0.744548 q^{4} +(1.05011 - 1.81885i) q^{5} +(0.828334 - 1.43472i) q^{6} +(-1.49221 + 2.18479i) q^{7} +2.07987 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.73968 + 3.01322i) q^{10} +(0.152120 - 0.263480i) q^{11} +(-0.372274 + 0.644798i) q^{12} +(-0.494423 - 3.57149i) q^{13} +(2.47210 - 3.61947i) q^{14} +(1.05011 + 1.81885i) q^{15} -4.93474 q^{16} +5.81185 q^{17} +(0.828334 + 1.43472i) q^{18} +(3.74378 + 6.48442i) q^{19} +(0.781858 - 1.35422i) q^{20} +(-1.14598 - 2.38469i) q^{21} +(-0.252013 + 0.436500i) q^{22} +6.01656 q^{23} +(-1.03993 + 1.80122i) q^{24} +(0.294535 + 0.510150i) q^{25} +(0.819095 + 5.91677i) q^{26} +1.00000 q^{27} +(-1.11102 + 1.62668i) q^{28} +(1.09353 + 1.89405i) q^{29} +(-1.73968 - 3.01322i) q^{30} +(3.51152 + 6.08213i) q^{31} +4.01550 q^{32} +(0.152120 + 0.263480i) q^{33} -9.62831 q^{34} +(2.40681 + 5.00837i) q^{35} +(-0.372274 - 0.644798i) q^{36} -0.104897 q^{37} +(-6.20220 - 10.7425i) q^{38} +(3.34021 + 1.35756i) q^{39} +(2.18409 - 3.78295i) q^{40} +(-1.00378 - 1.73860i) q^{41} +(1.89850 + 3.95064i) q^{42} +(4.03998 - 6.99746i) q^{43} +(0.113261 - 0.196174i) q^{44} -2.10022 q^{45} -9.96744 q^{46} +(4.30078 - 7.44916i) q^{47} +(2.46737 - 4.27361i) q^{48} +(-2.54661 - 6.52034i) q^{49} +(-0.487947 - 0.845149i) q^{50} +(-2.90593 + 5.03321i) q^{51} +(-0.368122 - 2.65915i) q^{52} +(-1.10014 - 1.90550i) q^{53} -1.65667 q^{54} +(-0.319487 - 0.553367i) q^{55} +(-3.10360 + 4.54407i) q^{56} -7.48756 q^{57} +(-1.81161 - 3.13781i) q^{58} -13.6842 q^{59} +(0.781858 + 1.35422i) q^{60} +(5.51315 + 9.54905i) q^{61} +(-5.81742 - 10.0761i) q^{62} +(2.63819 + 0.199899i) q^{63} +3.21714 q^{64} +(-7.01519 - 2.85118i) q^{65} +(-0.252013 - 0.436500i) q^{66} +(-5.04073 + 8.73079i) q^{67} +4.32721 q^{68} +(-3.00828 + 5.21049i) q^{69} +(-3.98728 - 8.29721i) q^{70} +(-0.149636 + 0.259177i) q^{71} +(-1.03993 - 1.80122i) q^{72} +(-2.96778 - 5.14034i) q^{73} +0.173779 q^{74} -0.589070 q^{75} +(2.78743 + 4.82796i) q^{76} +(0.348653 + 0.725520i) q^{77} +(-5.53362 - 2.24903i) q^{78} +(6.54933 - 11.3438i) q^{79} +(-5.18203 + 8.97554i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.66293 + 2.88028i) q^{82} -9.33190 q^{83} +(-0.853235 - 1.77552i) q^{84} +(6.10309 - 10.5709i) q^{85} +(-6.69291 + 11.5925i) q^{86} -2.18706 q^{87} +(0.316390 - 0.548004i) q^{88} +3.09538 q^{89} +3.47937 q^{90} +(8.54074 + 4.24921i) q^{91} +4.47962 q^{92} -7.02304 q^{93} +(-7.12496 + 12.3408i) q^{94} +15.7255 q^{95} +(-2.00775 + 3.47753i) q^{96} +(-3.19711 + 5.53756i) q^{97} +(4.21888 + 10.8020i) q^{98} -0.304241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.65667			−1.17144			−0.585721	−	0.810513i	$-0.699188\pi$
$2$	−1.65667			−1.17144			−0.585721	+	0.810513i	$0.699188\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.744548			0.372274
$5$	1.05011	−	1.81885i	0.469624	−	0.813412i	−0.529773	−	0.848139i	$-0.677723\pi$
$5$	1.05011	−	1.81885i	0.469624	−	0.813412i	0.999397	+	0.0347272i	$0.0110562\pi$
$6$	0.828334	−	1.43472i	0.338166	−	0.585721i
$7$	−1.49221	+	2.18479i	−0.564003	+	0.825773i
$7$	−1.49221	+	2.18479i	−0.564003	+	0.825773i
$8$	2.07987			0.735344
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.73968	+	3.01322i	−0.550137	+	0.952865i
$11$	0.152120	−	0.263480i	0.0458660	−	0.0794423i	−0.842181	−	0.539195i	$-0.818729\pi$
$11$	0.152120	−	0.263480i	0.0458660	−	0.0794423i	0.888047	+	0.459753i	$0.152062\pi$
$12$	−0.372274	+	0.644798i	−0.107466	+	0.186137i
$13$	−0.494423	−	3.57149i	−0.137128	−	0.990553i
$13$	−0.494423	−	3.57149i	−0.137128	−	0.990553i
$14$	2.47210	−	3.61947i	0.660696	−	0.967344i
$15$	1.05011	+	1.81885i	0.271137	+	0.469624i
$16$	−4.93474			−1.23369
$17$	5.81185			1.40958			0.704791	−	0.709415i	$-0.251041\pi$
$17$	5.81185			1.40958			0.704791	+	0.709415i	$0.251041\pi$
$18$	0.828334	+	1.43472i	0.195240	+	0.338166i
$19$	3.74378	+	6.48442i	0.858882	+	1.48763i	0.872996	+	0.487727i	$0.162174\pi$
$19$	3.74378	+	6.48442i	0.858882	+	1.48763i	−0.0141142	+	0.999900i	$0.504493\pi$
$20$	0.781858	−	1.35422i	0.174829	−	0.302812i
$21$	−1.14598	−	2.38469i	−0.250073	−	0.520382i
$22$	−0.252013	+	0.436500i	−0.0537294	+	0.0930620i
$23$	6.01656			1.25454			0.627270	−	0.778802i	$-0.284172\pi$
$23$	6.01656			1.25454			0.627270	+	0.778802i	$0.284172\pi$
$24$	−1.03993	+	1.80122i	−0.212275	+	0.367672i
$25$	0.294535	+	0.510150i	0.0589070	+	0.102030i
$26$	0.819095	+	5.91677i	0.160638	+	1.16037i
$27$	1.00000			0.192450
$28$	−1.11102	+	1.62668i	−0.209964	+	0.307414i
$29$	1.09353	+	1.89405i	0.203063	+	0.351716i	0.949514	−	0.313725i	$-0.101577\pi$
$29$	1.09353	+	1.89405i	0.203063	+	0.351716i	−0.746451	+	0.665441i	$0.768244\pi$
$30$	−1.73968	−	3.01322i	−0.317622	−	0.550137i
$31$	3.51152	+	6.08213i	0.630687	+	1.09238i	0.987411	+	0.158173i	$0.0505603\pi$
$31$	3.51152	+	6.08213i	0.630687	+	1.09238i	−0.356724	+	0.934210i	$0.616106\pi$
$32$	4.01550			0.709847
$33$	0.152120	+	0.263480i	0.0264808	+	0.0458660i
$34$	−9.62831			−1.65124
$35$	2.40681	+	5.00837i	0.406824	+	0.846569i
$36$	−0.372274	−	0.644798i	−0.0620457	−	0.107466i
$37$	−0.104897			−0.0172449			−0.00862246	−	0.999963i	$-0.502745\pi$
$37$	−0.104897			−0.0172449			−0.00862246	+	0.999963i	$0.502745\pi$
$38$	−6.20220	−	10.7425i	−1.00613	−	1.74267i
$39$	3.34021	+	1.35756i	0.534862	+	0.217384i
$40$	2.18409	−	3.78295i	0.345335	−	0.598138i
$41$	−1.00378	−	1.73860i	−0.156764	−	0.271524i	0.776936	−	0.629580i	$-0.216773\pi$
$41$	−1.00378	−	1.73860i	−0.156764	−	0.271524i	−0.933700	+	0.358056i	$0.883440\pi$
$42$	1.89850	+	3.95064i	0.292945	+	0.609596i
$43$	4.03998	−	6.99746i	0.616092	−	1.06710i	−0.374100	−	0.927388i	$-0.622048\pi$
$43$	4.03998	−	6.99746i	0.616092	−	1.06710i	0.990192	−	0.139714i	$-0.0446183\pi$
$44$	0.113261	−	0.196174i	0.0170747	−	0.0295743i
$45$	−2.10022			−0.313083
$46$	−9.96744			−1.46962
$47$	4.30078	−	7.44916i	0.627333	−	1.08657i	−0.360752	−	0.932662i	$-0.617480\pi$
$47$	4.30078	−	7.44916i	0.627333	−	1.08657i	0.988085	−	0.153910i	$-0.0491867\pi$
$48$	2.46737	−	4.27361i	0.356135	−	0.616843i
$49$	−2.54661	−	6.52034i	−0.363801	−	0.931477i
$50$	−0.487947	−	0.845149i	−0.0690061	−	0.119522i
$51$	−2.90593	+	5.03321i	−0.406911	+	0.704791i
$52$	−0.368122	−	2.65915i	−0.0510494	−	0.368757i
$53$	−1.10014	−	1.90550i	−0.151116	−	0.261741i	0.780522	−	0.625128i	$-0.214953\pi$
$53$	−1.10014	−	1.90550i	−0.151116	−	0.261741i	−0.931638	+	0.363388i	$0.881620\pi$
$54$	−1.65667			−0.225444
$55$	−0.319487	−	0.553367i	−0.0430796	−	0.0746160i
$56$	−3.10360	+	4.54407i	−0.414736	+	0.607227i
$57$	−7.48756			−0.991752
$58$	−1.81161	−	3.13781i	−0.237877	−	0.412014i
$59$	−13.6842			−1.78153			−0.890766	−	0.454462i	$-0.849832\pi$
$59$	−13.6842			−1.78153			−0.890766	+	0.454462i	$0.849832\pi$
$60$	0.781858	+	1.35422i	0.100937	+	0.174829i
$61$	5.51315	+	9.54905i	0.705886	+	1.22263i	0.966371	+	0.257153i	$0.0827844\pi$
$61$	5.51315	+	9.54905i	0.705886	+	1.22263i	−0.260484	+	0.965478i	$0.583882\pi$
$62$	−5.81742	−	10.0761i	−0.738813	−	1.27966i
$63$	2.63819	+	0.199899i	0.332381	+	0.0251849i
$64$	3.21714			0.402142
$65$	−7.01519	−	2.85118i	−0.870127	−	0.353645i
$66$	−0.252013	−	0.436500i	−0.0310207	−	0.0537294i
$67$	−5.04073	+	8.73079i	−0.615823	+	1.06664i	0.374417	+	0.927261i	$0.377843\pi$
$67$	−5.04073	+	8.73079i	−0.615823	+	1.06664i	−0.990240	+	0.139376i	$0.955490\pi$
$68$	4.32721			0.524751
$69$	−3.00828	+	5.21049i	−0.362154	+	0.627270i
$70$	−3.98728	−	8.29721i	−0.476571	−	0.991706i
$71$	−0.149636	+	0.259177i	−0.0177585	+	0.0307587i	−0.874768	−	0.484542i	$-0.838986\pi$
$71$	−0.149636	+	0.259177i	−0.0177585	+	0.0307587i	0.857010	+	0.515300i	$0.172320\pi$
$72$	−1.03993	−	1.80122i	−0.122557	−	0.212275i
$73$	−2.96778	−	5.14034i	−0.347352	−	0.601631i	0.638426	−	0.769683i	$-0.279586\pi$
$73$	−2.96778	−	5.14034i	−0.347352	−	0.601631i	−0.985778	+	0.168052i	$0.946252\pi$
$74$	0.173779			0.0202014
$75$	−0.589070			−0.0680200
$76$	2.78743	+	4.82796i	0.319740	+	0.553805i
$77$	0.348653	+	0.725520i	0.0397327	+	0.0826806i
$78$	−5.53362	−	2.24903i	−0.626560	−	0.254652i
$79$	6.54933	−	11.3438i	0.736857	−	1.27627i	−0.217047	−	0.976161i	$-0.569642\pi$
$79$	6.54933	−	11.3438i	0.736857	−	1.27627i	0.953904	−	0.300112i	$-0.0970242\pi$
$80$	−5.18203	+	8.97554i	−0.579368	+	1.00350i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.66293	+	2.88028i	0.183640	+	0.318074i
$83$	−9.33190			−1.02431			−0.512155	−	0.858893i	$-0.671153\pi$
$83$	−9.33190			−1.02431			−0.512155	+	0.858893i	$0.671153\pi$
$84$	−0.853235	−	1.77552i	−0.0930956	−	0.193725i
$85$	6.10309	−	10.5709i	0.661973	−	1.14657i
$86$	−6.69291	+	11.5925i	−0.721715	+	1.25005i
$87$	−2.18706			−0.234477
$88$	0.316390	−	0.548004i	0.0337273	−	0.0584174i
$89$	3.09538			0.328110			0.164055	−	0.986451i	$-0.447543\pi$
$89$	3.09538			0.328110			0.164055	+	0.986451i	$0.447543\pi$
$90$	3.47937			0.366758
$91$	8.54074	+	4.24921i	0.895313	+	0.445438i
$92$	4.47962			0.467033
$93$	−7.02304			−0.728255
$94$	−7.12496	+	12.3408i	−0.734883	+	1.27286i
$95$	15.7255			1.61341
$96$	−2.00775	+	3.47753i	−0.204915	+	0.354923i
$97$	−3.19711	+	5.53756i	−0.324618	+	0.562254i	−0.981435	−	0.191795i	$-0.938569\pi$
$97$	−3.19711	+	5.53756i	−0.324618	+	0.562254i	0.656817	+	0.754050i	$0.271902\pi$
$98$	4.21888	+	10.8020i	0.426172	+	1.09117i
$99$	−0.304241			−0.0305774
$100$	0.219296	+	0.379831i	0.0219296	+	0.0379831i
$101$	−0.690008	+	1.19513i	−0.0686584	+	0.118920i	−0.898311	−	0.439360i	$-0.855205\pi$
$101$	−0.690008	+	1.19513i	−0.0686584	+	0.118920i	0.829653	+	0.558280i	$0.188539\pi$
$102$	4.81416	−	8.33836i	0.476672	−	0.825621i
$103$	−2.82628	+	4.89525i	−0.278481	+	0.482344i	−0.971008	−	0.239049i	$-0.923164\pi$
$103$	−2.82628	+	4.89525i	−0.278481	+	0.482344i	0.692526	+	0.721393i	$0.256498\pi$
$104$	−1.02833	−	7.42822i	−0.100837	−	0.728397i
$105$	−5.54078	−	0.419832i	−0.540725	−	0.0409714i
$106$	1.82257	+	3.15678i	0.177023	+	0.306614i
$107$	14.1259			1.36560			0.682802	−	0.730604i	$-0.260761\pi$
$107$	14.1259			1.36560			0.682802	+	0.730604i	$0.260761\pi$
$108$	0.744548			0.0716442
$109$	−4.56805	−	7.91209i	−0.437539	−	0.757840i	0.559960	−	0.828520i	$-0.310817\pi$
$109$	−4.56805	−	7.91209i	−0.437539	−	0.757840i	−0.997499	+	0.0706794i	$0.977483\pi$
$110$	0.529283	+	0.916746i	0.0504652	+	0.0874083i
$111$	0.0524484	−	0.0908433i	0.00497818	−	0.00862246i
$112$	7.36368	−	10.7814i	0.695803	−	1.01874i
$113$	5.58957	−	9.68142i	0.525823	−	0.910751i	−0.473725	−	0.880673i	$-0.657091\pi$
$113$	5.58957	−	9.68142i	0.525823	−	0.910751i	0.999548	−	0.0300785i	$-0.00957573\pi$
$114$	12.4044			1.16178
$115$	6.31805	−	10.9432i	0.589161	−	1.02046i
$116$	0.814185	+	1.41021i	0.0755952	+	0.130935i
$117$	−2.84579	+	2.21393i	−0.263093	+	0.204678i
$118$	22.6702			2.08696
$119$	−8.67252	+	12.6977i	−0.795008	+	1.16399i
$120$	2.18409	+	3.78295i	0.199379	+	0.345335i
$121$	5.45372	+	9.44612i	0.495793	+	0.858738i
$122$	−9.13346	−	15.8196i	−0.826904	−	1.43224i
$123$	2.00756			0.181016
$124$	2.61450	+	4.52844i	0.234789	+	0.406666i
$125$	11.7383			1.04990
$126$	−4.37060	−	0.331166i	−0.389364	−	0.0295026i
$127$	−8.41791	−	14.5802i	−0.746969	−	1.29379i	−0.949269	−	0.314464i	$-0.898175\pi$
$127$	−8.41791	−	14.5802i	−0.746969	−	1.29379i	0.202300	−	0.979324i	$-0.435158\pi$
$128$	−13.3607			−1.18093
$129$	4.03998	+	6.99746i	0.355701	+	0.616092i
$130$	11.6218	+	4.72346i	1.01930	+	0.414275i
$131$	−6.97748	+	12.0854i	−0.609625	+	1.05590i	0.381677	+	0.924296i	$0.375347\pi$
$131$	−6.97748	+	12.0854i	−0.609625	+	1.05590i	−0.991302	+	0.131606i	$0.957987\pi$
$132$	0.113261	+	0.196174i	0.00985811	+	0.0170747i
$133$	−19.7536	−	1.49675i	−1.71285	−	0.129785i
$134$	8.35081	−	14.4640i	0.721400	−	1.24950i
$135$	1.05011	−	1.81885i	0.0903791	−	0.156541i
$136$	12.0879			1.03653
$137$	−0.609088			−0.0520379			−0.0260190	−	0.999661i	$-0.508283\pi$
$137$	−0.609088			−0.0520379			−0.0260190	+	0.999661i	$0.508283\pi$
$138$	4.98372	−	8.63206i	0.424242	−	0.734809i
$139$	−4.23753	+	7.33962i	−0.359423	+	0.622539i	−0.987865	−	0.155318i	$-0.950360\pi$
$139$	−4.23753	+	7.33962i	−0.359423	+	0.622539i	0.628442	+	0.777857i	$0.283693\pi$
$140$	1.79198	+	3.72898i	0.151450	+	0.315156i
$141$	4.30078	+	7.44916i	0.362191	+	0.627333i
$142$	0.247897	−	0.429371i	0.0208031	−	0.0360320i
$143$	−1.01623	−	0.413026i	−0.0849814	−	0.0345390i
$144$	2.46737	+	4.27361i	0.205614	+	0.356135i
$145$	4.59330			0.381453
$146$	4.91662	+	8.51583i	0.406902	+	0.704775i
$147$	6.92008	+	1.05474i	0.570759	+	0.0869936i
$148$	−0.0781008			−0.00641984
$149$	−3.31324	−	5.73871i	−0.271431	−	0.470133i	0.697797	−	0.716295i	$-0.254164\pi$
$149$	−3.31324	−	5.73871i	−0.271431	−	0.470133i	−0.969229	+	0.246162i	$0.920830\pi$
$150$	0.975894			0.0796814
$151$	0.762113	+	1.32002i	0.0620199	+	0.107422i	0.895368	−	0.445327i	$-0.146912\pi$
$151$	0.762113	+	1.32002i	0.0620199	+	0.107422i	−0.833348	+	0.552748i	$0.813579\pi$
$152$	7.78656	+	13.4867i	0.631574	+	1.09392i
$153$	−2.90593	−	5.03321i	−0.234930	−	0.406911i
$154$	−0.577602	−	1.20195i	−0.0465445	−	0.0968555i
$155$	14.7499			1.18474
$156$	2.48695	+	1.01077i	0.199115	+	0.0809264i
$157$	8.46505	+	14.6619i	0.675584	+	1.17015i	0.976298	+	0.216432i	$0.0694419\pi$
$157$	8.46505	+	14.6619i	0.675584	+	1.17015i	−0.300713	+	0.953715i	$0.597225\pi$
$158$	−10.8501	+	18.7929i	−0.863184	+	1.49508i
$159$	2.20028			0.174494
$160$	4.21672	−	7.30357i	0.333361	−	0.577398i
$161$	−8.97798	+	13.1449i	−0.707564	+	1.03596i
$162$	0.828334	−	1.43472i	0.0650801	−	0.112722i
$163$	−4.82081	−	8.34989i	−0.377595	−	0.654014i	0.613117	−	0.789992i	$-0.289916\pi$
$163$	−4.82081	−	8.34989i	−0.377595	−	0.654014i	−0.990712	+	0.135978i	$0.956582\pi$
$164$	−0.747364	−	1.29447i	−0.0583593	−	0.101081i
$165$	0.638973			0.0497440
$166$	15.4599			1.19992
$167$	9.10684	+	15.7735i	0.704708	+	1.22059i	0.966797	+	0.255547i	$0.0822555\pi$
$167$	9.10684	+	15.7735i	0.704708	+	1.22059i	−0.262088	+	0.965044i	$0.584411\pi$
$168$	−2.38348	−	4.95983i	−0.183889	−	0.382659i
$169$	−12.5111	+	3.53166i	−0.962392	+	0.271666i
$170$	−10.1108	+	17.5124i	−0.775462	+	1.34314i
$171$	3.74378	−	6.48442i	0.286294	−	0.495876i
$172$	3.00796	−	5.20995i	0.229355	−	0.397255i
$173$	−10.7572	−	18.6320i	−0.817853	−	1.41656i	−0.907261	−	0.420568i	$-0.861831\pi$
$173$	−10.7572	−	18.6320i	−0.817853	−	1.41656i	0.0894078	−	0.995995i	$-0.471503\pi$
$174$	3.62323			0.274676
$175$	−1.55408	−	0.117754i	−0.117477	−	0.00890140i
$176$	−0.750676	+	1.30021i	−0.0565843	+	0.0980069i
$177$	6.84210	−	11.8509i	0.514284	−	0.890766i
$178$	−5.12802			−0.384362
$179$	1.36259	−	2.36007i	0.101845	−	0.176400i	−0.810600	−	0.585600i	$-0.800859\pi$
$179$	1.36259	−	2.36007i	0.101845	−	0.176400i	0.912445	+	0.409200i	$0.134192\pi$
$180$	−1.56372			−0.116553
$181$	−6.47170			−0.481038			−0.240519	−	0.970644i	$-0.577318\pi$
$181$	−6.47170			−0.481038			−0.240519	+	0.970644i	$0.577318\pi$
$182$	−14.1492	−	7.03953i	−1.04881	−	0.521805i
$183$	−11.0263			−0.815087
$184$	12.5136			0.922518
$185$	−0.110153	+	0.190791i	−0.00809863	+	0.0140272i
$186$	11.6348			0.853108
$187$	0.884102	−	1.53131i	0.0646519	−	0.111980i
$188$	3.20214	−	5.54626i	0.233540	−	0.404503i
$189$	−1.49221	+	2.18479i	−0.108542	+	0.158920i
$190$	−26.0520			−1.89001
$191$	−6.37144	−	11.0357i	−0.461021	−	0.798512i	0.537991	−	0.842951i	$-0.319183\pi$
$191$	−6.37144	−	11.0357i	−0.461021	−	0.798512i	−0.999012	+	0.0444385i	$0.985850\pi$
$192$	−1.60857	+	2.78612i	−0.116088	+	0.201071i
$193$	0.326052	−	0.564739i	0.0234698	−	0.0406508i	−0.854052	−	0.520188i	$-0.825862\pi$
$193$	0.326052	−	0.564739i	0.0234698	−	0.0406508i	0.877522	+	0.479537i	$0.159195\pi$
$194$	5.29656	−	9.17390i	0.380271	−	0.658648i
$195$	5.97679	−	4.64974i	0.428007	−	0.332975i
$196$	−1.89607	−	4.85471i	−0.135434	−	0.346765i
$197$	3.03080	+	5.24950i	0.215936	+	0.374011i	0.953562	−	0.301198i	$-0.0973866\pi$
$197$	3.03080	+	5.24950i	0.215936	+	0.374011i	−0.737626	+	0.675209i	$0.764053\pi$
$198$	0.504026			0.0358196
$199$	2.04454			0.144933			0.0724666	−	0.997371i	$-0.476913\pi$
$199$	2.04454			0.144933			0.0724666	+	0.997371i	$0.476913\pi$
$200$	0.612594	+	1.06104i	0.0433169	+	0.0750271i
$201$	−5.04073	−	8.73079i	−0.355545	−	0.615823i
$202$	1.14311	−	1.97993i	0.0804293	−	0.139308i
$203$	−5.76987	−	0.437190i	−0.404966	−	0.0306847i
$204$	−2.16360	+	3.74747i	−0.151483	+	0.262375i
$205$	−4.21632			−0.294481
$206$	4.68220	−	8.10981i	0.326224	−	0.565037i
$207$	−3.00828	−	5.21049i	−0.209090	−	0.362154i
$208$	2.43985	+	17.6244i	0.169173	+	1.22203i
$209$	2.27802			0.157574
$210$	9.17923	+	0.695521i	0.633427	+	0.0479955i
$211$	−2.27669	−	3.94334i	−0.156734	−	0.271471i	0.776955	−	0.629556i	$-0.216763\pi$
$211$	−2.27669	−	3.94334i	−0.156734	−	0.271471i	−0.933689	+	0.358085i	$0.883430\pi$
$212$	−0.819108	−	1.41874i	−0.0562566	−	0.0974392i
$213$	−0.149636	−	0.259177i	−0.0102529	−	0.0177585i
$214$	−23.4019			−1.59972
$215$	−8.48486	−	14.6962i	−0.578663	−	1.00227i
$216$	2.07987			0.141517
$217$	−18.5281	−	1.40390i	−1.25777	−	0.0953027i
$218$	7.56773	+	13.1077i	0.512552	+	0.887765i
$219$	5.93555			0.401087
$220$	−0.237873	−	0.412009i	−0.0160374	−	0.0277776i
$221$	−2.87352	−	20.7570i	−0.193294	−	1.39627i
$222$	−0.0868896	+	0.150497i	−0.00583165	+	0.0101007i
$223$	7.85506	+	13.6054i	0.526014	+	0.911082i	0.999541	+	0.0303029i	$0.00964720\pi$
$223$	7.85506	+	13.6054i	0.526014	+	0.911082i	−0.473527	+	0.880779i	$0.657019\pi$
$224$	−5.99198	+	8.77302i	−0.400356	+	0.586172i
$225$	0.294535	−	0.510150i	0.0196357	−	0.0340100i
$226$	−9.26006	+	16.0389i	−0.615970	+	1.06689i
$227$	−12.5434			−0.832533			−0.416267	−	0.909243i	$-0.636662\pi$
$227$	−12.5434			−0.832533			−0.416267	+	0.909243i	$0.636662\pi$
$228$	−5.57485			−0.369204
$229$	−10.3182	+	17.8717i	−0.681849	+	1.18100i	0.292567	+	0.956245i	$0.405490\pi$
$229$	−10.3182	+	17.8717i	−0.681849	+	1.18100i	−0.974416	+	0.224752i	$0.927843\pi$
$230$	−10.4669	+	18.1292i	−0.690168	+	1.19541i
$231$	−0.802645	−	0.0608174i	−0.0528102	−	0.00400149i
$232$	2.27439	+	3.93936i	0.149321	+	0.258632i
$233$	4.00908	−	6.94394i	0.262644	−	0.454912i	−0.704300	−	0.709903i	$-0.748739\pi$
$233$	4.00908	−	6.94394i	0.262644	−	0.454912i	0.966944	+	0.254990i	$0.0820723\pi$
$234$	4.71453	−	3.66774i	0.308198	−	0.239768i
$235$	−9.03258	−	15.6449i	−0.589221	−	1.02056i
$236$	−10.1886			−0.663219
$237$	6.54933	+	11.3438i	0.425425	+	0.736857i
$238$	14.3675	−	21.0358i	0.931305	−	1.36355i
$239$	−1.16836			−0.0755752			−0.0377876	−	0.999286i	$-0.512031\pi$
$239$	−1.16836			−0.0755752			−0.0377876	+	0.999286i	$0.512031\pi$
$240$	−5.18203	−	8.97554i	−0.334498	−	0.579368i
$241$	−1.07215			−0.0690634			−0.0345317	−	0.999404i	$-0.510994\pi$
$241$	−1.07215			−0.0690634			−0.0345317	+	0.999404i	$0.510994\pi$
$242$	−9.03500	−	15.6491i	−0.580792	−	1.00596i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.10481	+	7.10973i	0.262783	+	0.455154i
$245$	−14.5337	−	2.21519i	−0.928524	−	0.141523i
$246$	−3.32586			−0.212049
$247$	21.3080	−	16.5769i	1.35580	−	1.05476i
$248$	7.30349	+	12.6500i	0.463772	+	0.803277i
$249$	4.66595	−	8.08166i	0.295693	−	0.512155i
$250$	−19.4464			−1.22990
$251$	−6.29717	+	10.9070i	−0.397474	+	0.688445i	−0.993414	−	0.114584i	$-0.963446\pi$
$251$	−6.29717	+	10.9070i	−0.397474	+	0.688445i	0.595940	+	0.803029i	$0.296780\pi$
$252$	1.96426	+	0.148834i	0.123737	+	0.00937568i
$253$	0.915242	−	1.58525i	0.0575408	−	0.0996635i
$254$	13.9457	+	24.1546i	0.875030	+	1.51560i
$255$	6.10309	+	10.5709i	0.382190	+	0.661973i
$256$	15.7000			0.981251
$257$	−21.2980			−1.32854			−0.664268	−	0.747495i	$-0.731257\pi$
$257$	−21.2980			−1.32854			−0.664268	+	0.747495i	$0.731257\pi$
$258$	−6.69291	−	11.5925i	−0.416683	−	0.721715i
$259$	0.156528	−	0.229177i	0.00972619	−	0.0142404i
$260$	−5.22315	−	2.12284i	−0.323926	−	0.131653i
$261$	1.09353	−	1.89405i	0.0676877	−	0.117239i
$262$	11.5594	−	20.0214i	0.714140	−	1.23693i
$263$	11.0142	−	19.0772i	0.679167	−	1.17635i	−0.296065	−	0.955168i	$-0.595674\pi$
$263$	11.0142	−	19.0772i	0.679167	−	1.17635i	0.975232	−	0.221184i	$-0.0709922\pi$
$264$	0.316390	+	0.548004i	0.0194725	+	0.0337273i
$265$	−4.62108			−0.283871
$266$	32.7252	+	2.47962i	2.00651	+	0.152035i
$267$	−1.54769	+	2.68068i	−0.0947172	+	0.164055i
$268$	−3.75307	+	6.50050i	−0.229255	+	0.397081i
$269$	17.8586			1.08886			0.544430	−	0.838806i	$-0.316746\pi$
$269$	17.8586			1.08886			0.544430	+	0.838806i	$0.316746\pi$
$270$	−1.73968	+	3.01322i	−0.105874	+	0.183379i
$271$	−7.21063			−0.438015			−0.219007	−	0.975723i	$-0.570282\pi$
$271$	−7.21063			−0.438015			−0.219007	+	0.975723i	$0.570282\pi$
$272$	−28.6800			−1.73898
$273$	−7.95029	+	5.27189i	−0.481174	+	0.319069i
$274$	1.00906			0.0609594
$275$	0.179219			0.0108073
$276$	−2.23981	+	3.87946i	−0.134821	+	0.233516i
$277$	−4.38275			−0.263334			−0.131667	−	0.991294i	$-0.542033\pi$
$277$	−4.38275			−0.263334			−0.131667	+	0.991294i	$0.542033\pi$
$278$	7.02018	−	12.1593i	0.421043	−	0.729267i
$279$	3.51152	−	6.08213i	0.210229	−	0.364127i
$280$	5.00583	+	10.4167i	0.299156	+	0.622520i
$281$	−0.474280			−0.0282932			−0.0141466	−	0.999900i	$-0.504503\pi$
$281$	−0.474280			−0.0282932			−0.0141466	+	0.999900i	$0.504503\pi$
$282$	−7.12496	−	12.3408i	−0.424285	−	0.734883i
$283$	0.563463	−	0.975947i	0.0334944	−	0.0580140i	−0.848792	−	0.528726i	$-0.822670\pi$
$283$	0.563463	−	0.975947i	0.0334944	−	0.0580140i	0.882287	+	0.470712i	$0.156003\pi$
$284$	−0.111411	+	0.192970i	−0.00661104	+	0.0114507i
$285$	−7.86277	+	13.6187i	−0.465750	+	0.806703i
$286$	1.68356	+	0.684247i	0.0995507	+	0.0404604i
$287$	5.29633	+	0.401309i	0.312632	+	0.0236885i
$288$	−2.00775	−	3.47753i	−0.118308	−	0.204915i
$289$	16.7777			0.986921
$290$	−7.60958			−0.446850
$291$	−3.19711	−	5.53756i	−0.187418	−	0.324618i
$292$	−2.20965	−	3.82723i	−0.129310	−	0.223972i
$293$	6.43732	−	11.1498i	0.376072	−	0.651376i	−0.614415	−	0.788983i	$-0.710608\pi$
$293$	6.43732	−	11.1498i	0.376072	−	0.651376i	0.990487	+	0.137607i	$0.0439411\pi$
$294$	−11.4643	−	1.74736i	−0.668610	−	0.101908i
$295$	−14.3699	+	24.8895i	−0.836650	+	1.44912i
$296$	−0.218171			−0.0126810
$297$	0.152120	−	0.263480i	0.00882693	−	0.0152887i
$298$	5.48894	+	9.50713i	0.317966	+	0.550733i
$299$	−2.97473	−	21.4881i	−0.172033	−	1.24269i
$300$	−0.438591			−0.0253221
$301$	9.25946	+	19.2682i	0.533706	+	1.11060i
$302$	−1.26257	−	2.18683i	−0.0726526	−	0.125838i
$303$	−0.690008	−	1.19513i	−0.0396399	−	0.0686584i
$304$	−18.4746	−	31.9989i	−1.05959	−	1.83527i
$305$	23.1577			1.32600
$306$	4.81416	+	8.33836i	0.275207	+	0.476672i
$307$	−8.01524			−0.457454			−0.228727	−	0.973491i	$-0.573456\pi$
$307$	−8.01524			−0.457454			−0.228727	+	0.973491i	$0.573456\pi$
$308$	0.259589	+	0.540185i	0.0147915	+	0.0307799i
$309$	−2.82628	−	4.89525i	−0.160781	−	0.278481i
$310$	−24.4357			−1.38786
$311$	−1.57684	−	2.73117i	−0.0894145	−	0.154871i	0.817849	−	0.575433i	$-0.195166\pi$
$311$	−1.57684	−	2.73117i	−0.0894145	−	0.154871i	−0.907264	+	0.420562i	$0.861833\pi$
$312$	6.94720	+	2.82355i	0.393308	+	0.159852i
$313$	0.264591	−	0.458285i	0.0149556	−	0.0259038i	−0.858451	−	0.512896i	$-0.828573\pi$
$313$	0.264591	−	0.458285i	0.0149556	−	0.0259038i	0.873406	+	0.486992i	$0.161906\pi$
$314$	−14.0238	−	24.2899i	−0.791407	−	1.37076i
$315$	3.13398	−	4.58854i	0.176579	−	0.258535i
$316$	4.87629	−	8.44599i	0.274313	−	0.475124i
$317$	−2.19029	+	3.79369i	−0.123019	+	0.213075i	−0.920957	−	0.389665i	$-0.872591\pi$
$317$	−2.19029	+	3.79369i	−0.123019	+	0.213075i	0.797938	+	0.602739i	$0.205924\pi$
$318$	−3.64514			−0.204409
$319$	0.665392			0.0372548
$320$	3.37835	−	5.85148i	0.188856	−	0.327107i
$321$	−7.06296	+	12.2334i	−0.394216	+	0.682802i
$322$	14.8735	−	21.7768i	0.828870	−	1.21357i
$323$	21.7583	+	37.6865i	1.21066	+	2.09693i
$324$	−0.372274	+	0.644798i	−0.0206819	+	0.0358221i
$325$	1.67637	−	1.30416i	0.0929883	−	0.0723418i
$326$	7.98649	+	13.8330i	0.442331	+	0.766139i
$327$	9.13609			0.505227
$328$	−2.08773	−	3.61605i	−0.115276	−	0.199663i
$329$	9.85718	+	20.5120i	0.543444	+	1.13086i
$330$	−1.05857			−0.0582722
$331$	13.4676	+	23.3266i	0.740246	+	1.28214i	0.952383	+	0.304904i	$0.0986243\pi$
$331$	13.4676	+	23.3266i	0.740246	+	1.28214i	−0.212137	+	0.977240i	$0.568042\pi$
$332$	−6.94805			−0.381324
$333$	0.0524484	+	0.0908433i	0.00287415	+	0.00497818i
$334$	−15.0870	−	26.1315i	−0.825524	−	1.42985i
$335$	10.5866	+	18.3366i	0.578410	+	1.00184i
$336$	5.65510	+	11.7678i	0.308511	+	0.641988i
$337$	20.8356			1.13498			0.567492	−	0.823379i	$-0.307914\pi$
$337$	20.8356			1.13498			0.567492	+	0.823379i	$0.307914\pi$
$338$	20.7267	−	5.85078i	1.12739	−	0.318241i
$339$	5.58957	+	9.68142i	0.303584	+	0.525823i
$340$	4.54405	−	7.87052i	0.246436	−	0.426839i
$341$	2.13670			0.115709
$342$	−6.20220	+	10.7425i	−0.335377	+	0.580889i
$343$	18.0456	+	4.16592i	0.974373	+	0.224939i
$344$	8.40263	−	14.5538i	0.453039	−	0.784687i
$345$	6.31805	+	10.9432i	0.340153	+	0.589161i
$346$	17.8211	+	30.8670i	0.958067	+	1.65942i
$347$	−13.3384			−0.716041			−0.358021	−	0.933714i	$-0.616548\pi$
$347$	−13.3384			−0.716041			−0.358021	+	0.933714i	$0.616548\pi$
$348$	−1.62837			−0.0872898
$349$	−10.2622	−	17.7746i	−0.549322	−	0.951453i	−0.998321	−	0.0579208i	$-0.981553\pi$
$349$	−10.2622	−	17.7746i	−0.549322	−	0.951453i	0.449000	−	0.893532i	$-0.351780\pi$
$350$	2.57459	+	0.195080i	0.137618	+	0.0104275i
$351$	−0.494423	−	3.57149i	−0.0263904	−	0.190632i
$352$	0.610840	−	1.05801i	0.0325579	−	0.0563919i
$353$	3.22357	−	5.58339i	0.171573	−	0.297174i	−0.767397	−	0.641173i	$-0.778448\pi$
$353$	3.22357	−	5.58339i	0.171573	−	0.297174i	0.938970	+	0.343999i	$0.111782\pi$
$354$	−11.3351	+	19.6330i	−0.602453	+	1.04348i
$355$	0.314269	+	0.544330i	0.0166797	+	0.0288900i
$356$	2.30466			0.122147
$357$	−6.66025	−	13.8595i	−0.352498	−	0.733520i
$358$	−2.25736	+	3.90986i	−0.119305	+	0.206642i
$359$	−4.38549	+	7.59588i	−0.231457	+	0.400895i	−0.958237	−	0.285975i	$-0.907683\pi$
$359$	−4.38549	+	7.59588i	−0.231457	+	0.400895i	0.726780	+	0.686870i	$0.241016\pi$
$360$	−4.36818			−0.230223
$361$	−18.5318	+	32.0980i	−0.975357	+	1.68937i
$362$	10.7215			0.563507
$363$	−10.9074			−0.572492
$364$	6.35899	+	3.16374i	0.333302	+	0.165825i
$365$	−12.4660			−0.652499
$366$	18.2669			0.954827
$367$	−6.08982	+	10.5479i	−0.317886	+	0.550595i	−0.980047	−	0.198767i	$-0.936306\pi$
$367$	−6.08982	+	10.5479i	−0.317886	+	0.550595i	0.662161	+	0.749362i	$0.269640\pi$
$368$	−29.6902			−1.54771
$369$	−1.00378	+	1.73860i	−0.0522548	+	0.0905079i
$370$	0.182487	−	0.316077i	0.00948707	−	0.0164321i
$371$	5.80476	+	0.439833i	0.301368	+	0.0228350i
$372$	−5.22899			−0.271111
$373$	−15.2988	−	26.4983i	−0.792140	−	1.37203i	−0.924639	−	0.380844i	$-0.875633\pi$
$373$	−15.2988	−	26.4983i	−0.792140	−	1.37203i	0.132499	−	0.991183i	$-0.457700\pi$
$374$	−1.46466	+	2.53687i	−0.0757359	+	0.131179i
$375$	−5.86914	+	10.1657i	−0.303081	+	0.524952i
$376$	8.94504	−	15.4933i	0.461305	−	0.799004i
$377$	6.22391	−	4.84199i	0.320547	−	0.249375i
$378$	2.47210	−	3.61947i	0.127151	−	0.186165i
$379$	−2.54078	−	4.40075i	−0.130511	−	0.226052i	0.793363	−	0.608749i	$-0.208328\pi$
$379$	−2.54078	−	4.40075i	−0.130511	−	0.226052i	−0.923874	+	0.382698i	$0.874995\pi$
$380$	11.7084			0.600629
$381$	16.8358			0.862525
$382$	10.5554	+	18.2824i	0.540059	+	0.935410i
$383$	12.3140	+	21.3285i	0.629217	+	1.08984i	0.987709	+	0.156303i	$0.0499575\pi$
$383$	12.3140	+	21.3285i	0.629217	+	1.08984i	−0.358493	+	0.933533i	$0.616709\pi$
$384$	6.68037	−	11.5707i	0.340906	−	0.590466i
$385$	1.68573	+	0.127730i	0.0859129	+	0.00650972i
$386$	−0.540161	+	0.935585i	−0.0274934	+	0.0476200i
$387$	−8.07997			−0.410728
$388$	−2.38041	+	4.12299i	−0.120847	+	0.209313i
$389$	−9.26991	−	16.0559i	−0.470003	−	0.814069i	0.529409	−	0.848367i	$-0.322414\pi$
$389$	−9.26991	−	16.0559i	−0.470003	−	0.814069i	−0.999412	+	0.0342980i	$0.989080\pi$
$390$	−9.90155	+	7.70308i	−0.501385	+	0.390060i
$391$	34.9674			1.76838
$392$	−5.29660	−	13.5614i	−0.267519	−	0.684956i
$393$	−6.97748	−	12.0854i	−0.351967	−	0.609625i
$394$	−5.02103	−	8.69668i	−0.252956	−	0.438132i
$395$	−13.7550	−	23.8244i	−0.692091	−	1.19874i
$396$	−0.226522			−0.0113832
$397$	−15.6013	−	27.0223i	−0.783007	−	1.35621i	−0.930182	−	0.367098i	$-0.880351\pi$
$397$	−15.6013	−	27.0223i	−0.783007	−	1.35621i	0.147175	−	0.989110i	$-0.452982\pi$
$398$	−3.38712			−0.169781
$399$	11.1730	−	16.3587i	0.559351	−	0.818961i
$400$	−1.45346	−	2.51746i	−0.0726728	−	0.125873i
$401$	−34.2249			−1.70911			−0.854555	−	0.519360i	$-0.826170\pi$
$401$	−34.2249			−1.70911			−0.854555	+	0.519360i	$0.826170\pi$
$402$	8.35081	+	14.4640i	0.416501	+	0.721400i
$403$	19.9861	−	15.5485i	0.995578	−	0.774526i
$404$	−0.513745	+	0.889832i	−0.0255598	+	0.0442708i
$405$	1.05011	+	1.81885i	0.0521804	+	0.0903791i
$406$	9.55876	+	0.724279i	0.474393	+	0.0359453i
$407$	−0.0159570	+	0.0276383i	−0.000790957	+	0.00136998i
$408$	−6.04394	+	10.4684i	−0.299220	+	0.518264i
$409$	−9.95801			−0.492392			−0.246196	−	0.969220i	$-0.579181\pi$
$409$	−9.95801			−0.492392			−0.246196	+	0.969220i	$0.579181\pi$
$410$	6.98505			0.344967
$411$	0.304544	−	0.527486i	0.0150221	−	0.0260190i
$412$	−2.10430	+	3.64475i	−0.103671	+	0.179564i
$413$	20.4197	−	29.8971i	1.00479	−	1.47114i
$414$	4.98372	+	8.63206i	0.244936	+	0.424242i
$415$	−9.79953	+	16.9733i	−0.481040	+	0.833186i
$416$	−1.98536	−	14.3413i	−0.0973402	−	0.703141i
$417$	−4.23753	−	7.33962i	−0.207513	−	0.359423i
$418$	−3.77393			−0.184589
$419$	0.586220	+	1.01536i	0.0286387	+	0.0496037i	0.879990	−	0.474993i	$-0.157549\pi$
$419$	0.586220	+	1.01536i	0.0286387	+	0.0496037i	−0.851351	+	0.524597i	$0.824216\pi$
$420$	−4.12538	−	0.312585i	−0.201298	−	0.0152526i
$421$	−10.2374			−0.498938			−0.249469	−	0.968383i	$-0.580256\pi$
$421$	−10.2374			−0.498938			−0.249469	+	0.968383i	$0.580256\pi$
$422$	3.77172	+	6.53281i	0.183604	+	0.318012i
$423$	−8.60155			−0.418222
$424$	−2.28815	−	3.96318i	−0.111122	−	0.192469i
$425$	1.71180	+	2.96492i	0.0830343	+	0.143820i
$426$	0.247897	+	0.429371i	0.0120107	+	0.0208031i
$427$	−29.0895	−	2.20414i	−1.40774	−	0.106666i
$428$	10.5174			0.508379
$429$	0.865806	−	0.673568i	0.0418015	−	0.0325202i
$430$	14.0566	+	24.3467i	0.677869	+	1.17410i
$431$	−11.8198	+	20.4724i	−0.569338	+	0.986122i	0.427293	+	0.904113i	$0.359467\pi$
$431$	−11.8198	+	20.4724i	−0.569338	+	0.986122i	−0.996632	+	0.0820095i	$0.973866\pi$
$432$	−4.93474			−0.237423
$433$	−0.246165	+	0.426370i	−0.0118299	+	0.0204900i	−0.871880	−	0.489720i	$-0.837099\pi$
$433$	−0.246165	+	0.426370i	−0.0118299	+	0.0204900i	0.860050	+	0.510210i	$0.170432\pi$
$434$	30.6949	+	2.32579i	1.47340	+	0.111641i
$435$	−2.29665	+	3.97792i	−0.110116	+	0.190727i
$436$	−3.40113	−	5.89093i	−0.162885	−	0.282124i
$437$	22.5247	+	39.0139i	1.07750	+	1.86629i
$438$	−9.83324			−0.469850
$439$	−15.0638			−0.718954			−0.359477	−	0.933154i	$-0.617045\pi$
$439$	−15.0638			−0.718954			−0.359477	+	0.933154i	$0.617045\pi$
$440$	−0.664490	−	1.15093i	−0.0316783	−	0.0548684i
$441$	−4.37347	+	5.46560i	−0.208261	+	0.260266i
$442$	4.76046	+	34.3874i	0.226432	+	1.63564i
$443$	−13.3996	+	23.2088i	−0.636635	+	1.10268i	0.349531	+	0.936925i	$0.386341\pi$
$443$	−13.3996	+	23.2088i	−0.636635	+	1.10268i	−0.986166	+	0.165760i	$0.946992\pi$
$444$	0.0390504	−	0.0676372i	0.00185325	−	0.00320992i
$445$	3.25050	−	5.63003i	0.154088	−	0.266889i
$446$	−13.0132	−	22.5396i	−0.616194	−	1.06728i
$447$	6.62649			0.313422
$448$	−4.80065	+	7.02877i	−0.226809	+	0.332078i
$449$	2.26268	−	3.91908i	0.106783	−	0.184953i	−0.807683	−	0.589618i	$-0.799278\pi$
$449$	2.26268	−	3.91908i	0.106783	−	0.184953i	0.914465	+	0.404665i	$0.132612\pi$
$450$	−0.487947	+	0.845149i	−0.0230020	+	0.0398407i
$451$	−0.610783			−0.0287606
$452$	4.16171	−	7.20829i	0.195750	−	0.339049i
$453$	−1.52423			−0.0716144
$454$	20.7802			0.975264
$455$	16.6974	−	11.0721i	0.782785	−	0.519070i
$456$	−15.5731			−0.729278
$457$	34.3540			1.60701			0.803505	−	0.595298i	$-0.202966\pi$
$457$	34.3540			1.60701			0.803505	+	0.595298i	$0.202966\pi$
$458$	17.0939	−	29.6075i	0.798745	−	1.38347i
$459$	5.81185			0.271274
$460$	4.70410	−	8.14773i	0.219330	−	0.379890i
$461$	−0.499436	+	0.865049i	−0.0232611	+	0.0402893i	−0.877422	−	0.479720i	$-0.840738\pi$
$461$	−0.499436	+	0.865049i	−0.0232611	+	0.0402893i	0.854161	+	0.520009i	$0.174072\pi$
$462$	1.32972	+	0.100754i	0.0618640	+	0.00468751i
$463$	32.5538			1.51290			0.756452	−	0.654049i	$-0.226931\pi$
$463$	32.5538			1.51290			0.756452	+	0.654049i	$0.226931\pi$
$464$	−5.39628	−	9.34664i	−0.250516	−	0.433907i
$465$	−7.37497	+	12.7738i	−0.342006	+	0.592372i
$466$	−6.64172	+	11.5038i	−0.307672	+	0.532903i
$467$	12.1056	−	20.9675i	0.560180	−	0.970261i	−0.437300	−	0.899316i	$-0.644065\pi$
$467$	12.1056	−	20.9675i	0.560180	−	0.970261i	0.997480	−	0.0709451i	$-0.0226015\pi$
$468$	−2.11883	+	1.64838i	−0.0979429	+	0.0761963i
$469$	−11.5531	−	24.0411i	−0.533473	−	1.11012i
$470$	14.9640	+	25.9184i	0.690237	+	1.19553i
$471$	−16.9301			−0.780098
$472$	−28.4613			−1.31004
$473$	−1.22913	−	2.12891i	−0.0565154	−	0.0978875i
$474$	−10.8501	−	18.7929i	−0.498360	−	0.863184i
$475$	−2.20535	+	3.81978i	−0.101188	+	0.175263i
$476$	−6.45711	+	9.45404i	−0.295961	+	0.433325i
$477$	−1.10014	+	1.90550i	−0.0503720	+	0.0872468i
$478$	1.93559			0.0885319
$479$	15.1684	−	26.2724i	0.693061	−	1.20042i	−0.277769	−	0.960648i	$-0.589595\pi$
$479$	15.1684	−	26.2724i	0.693061	−	1.20042i	0.970830	−	0.239769i	$-0.0770718\pi$
$480$	4.21672	+	7.30357i	0.192466	+	0.333361i
$481$	0.0518634	+	0.374638i	0.00236477	+	0.0170820i
$482$	1.77620			0.0809037
$483$	−6.89484	−	14.3476i	−0.313726	−	0.652839i
$484$	4.06056	+	7.03309i	0.184571	+	0.319686i
$485$	6.71465	+	11.6301i	0.304896	+	0.528096i
$486$	0.828334	+	1.43472i	0.0375740	+	0.0650801i
$487$	−5.38448			−0.243994			−0.121997	−	0.992530i	$-0.538930\pi$
$487$	−5.38448			−0.243994			−0.121997	+	0.992530i	$0.538930\pi$
$488$	11.4666	+	19.8608i	0.519069	+	0.899054i
$489$	9.64163			0.436009
$490$	24.0775	+	3.66983i	1.08771	+	0.165786i
$491$	−17.4920	−	30.2970i	−0.789401	−	1.36728i	−0.926334	−	0.376703i	$-0.877058\pi$
$491$	−17.4920	−	30.2970i	−0.789401	−	1.36728i	0.136933	−	0.990580i	$-0.456275\pi$
$492$	1.49473			0.0673875
$493$	6.35543	+	11.0079i	0.286234	+	0.495772i
$494$	−35.3003	+	27.4625i	−1.58824	+	1.23559i
$495$	−0.319487	+	0.553367i	−0.0143599	+	0.0248720i
$496$	−17.3284	−	30.0137i	−0.778070	−	1.34766i
$497$	−0.342959	−	0.713671i	−0.0153838	−	0.0320125i
$498$	−7.72993	+	13.3886i	−0.346386	+	0.599959i
$499$	−0.527303	+	0.913315i	−0.0236053	+	0.0408856i	−0.877587	−	0.479418i	$-0.840848\pi$
$499$	−0.527303	+	0.913315i	−0.0236053	+	0.0408856i	0.853981	+	0.520303i	$0.174181\pi$
$500$	8.73972			0.390852
$501$	−18.2137			−0.813727
$502$	10.4323	−	18.0693i	0.465617	−	0.806472i
$503$	6.93072	−	12.0044i	0.309026	−	0.535248i	−0.669124	−	0.743151i	$-0.733330\pi$
$503$	6.93072	−	12.0044i	0.309026	−	0.535248i	0.978150	+	0.207903i	$0.0666638\pi$
$504$	5.48708	+	0.415763i	0.244414	+	0.0185195i
$505$	1.44917	+	2.51004i	0.0644872	+	0.111695i
$506$	−1.51625	+	2.62623i	−0.0674056	+	0.116750i
$507$	3.19704	−	12.6008i	0.141986	−	0.559619i
$508$	−6.26754	−	10.8557i	−0.278077	−	0.481644i
$509$	29.2286			1.29554			0.647768	−	0.761838i	$-0.275703\pi$
$509$	29.2286			1.29554			0.647768	+	0.761838i	$0.275703\pi$
$510$	−10.1108	−	17.5124i	−0.447713	−	0.775462i
$511$	15.6591	+	1.18651i	0.692718	+	0.0524881i
$512$	0.711748			0.0314551
$513$	3.74378	+	6.48442i	0.165292	+	0.286294i
$514$	35.2838			1.55630
$515$	5.93581	+	10.2811i	0.261563	+	0.453040i
$516$	3.00796	+	5.20995i	0.132418	+	0.229355i
$517$	−1.30847	−	2.26634i	−0.0575465	−	0.0996735i
$518$	−0.259315	+	0.379671i	−0.0113937	+	0.0166818i
$519$	21.5144			0.944376
$520$	−14.5907	−	5.93007i	−0.639842	−	0.260051i
$521$	−4.13001	−	7.15338i	−0.180939	−	0.313395i	0.761262	−	0.648445i	$-0.224580\pi$
$521$	−4.13001	−	7.15338i	−0.180939	−	0.313395i	−0.942201	+	0.335049i	$0.891247\pi$
$522$	−1.81161	+	3.13781i	−0.0792922	+	0.137338i
$523$	−0.456440			−0.0199587			−0.00997937	−	0.999950i	$-0.503177\pi$
$523$	−0.456440			−0.0199587			−0.00997937	+	0.999950i	$0.503177\pi$
$524$	−5.19507	+	8.99813i	−0.226948	+	0.393085i
$525$	0.879018	−	1.28699i	0.0383635	−	0.0561690i
$526$	−18.2469	+	31.6046i	−0.795604	+	1.37803i
$527$	20.4084	+	35.3484i	0.889005	+	1.53980i
$528$	−0.750676	−	1.30021i	−0.0326690	−	0.0565843i
$529$	13.1990			0.573869
$530$	7.65559			0.332538
$531$	6.84210	+	11.8509i	0.296922	+	0.514284i
$532$	−14.7075	−	1.11441i	−0.637651	−	0.0483156i
$533$	−5.71310	+	4.44460i	−0.247462	+	0.192517i
$534$	2.56401	−	4.44100i	0.110956	−	0.192181i
$535$	14.8338	−	25.6928i	0.641320	−	1.11080i
$536$	−10.4840	+	18.1589i	−0.452841	+	0.784344i
$537$	1.36259	+	2.36007i	0.0588000	+	0.101845i
$538$	−29.5858			−1.27554
$539$	−2.10537	−	0.320895i	−0.0906848	−	0.0138219i
$540$	0.781858	−	1.35422i	0.0336458	−	0.0582763i
$541$	−10.6399	+	18.4289i	−0.457447	+	0.792321i	−0.998825	−	0.0484578i	$-0.984569\pi$
$541$	−10.6399	+	18.4289i	−0.457447	+	0.792321i	0.541378	+	0.840779i	$0.317903\pi$
$542$	11.9456			0.513108
$543$	3.23585	−	5.60466i	0.138864	−	0.240519i
$544$	23.3375			1.00059
$545$	−19.1878			−0.821916
$546$	13.1710	−	8.73377i	0.563667	−	0.373771i
$547$	−43.8895			−1.87658			−0.938290	−	0.345849i	$-0.887591\pi$
$547$	−43.8895			−1.87658			−0.938290	+	0.345849i	$0.887591\pi$
$548$	−0.453496			−0.0193724
$549$	5.51315	−	9.54905i	0.235295	−	0.407544i
$550$	−0.296907			−0.0126602
$551$	−8.18786	+	14.1818i	−0.348815	+	0.604165i
$552$	−6.25682	+	10.8371i	−0.266308	+	0.461259i
$553$	15.0108	+	31.2362i	0.638322	+	1.32830i
$554$	7.26077			0.308480
$555$	−0.110153	−	0.190791i	−0.00467575	−	0.00809863i
$556$	−3.15505	+	5.46470i	−0.133804	+	0.231755i
$557$	18.2941	−	31.6863i	0.775145	−	1.34259i	−0.159568	−	0.987187i	$-0.551010\pi$
$557$	18.2941	−	31.6863i	0.775145	−	1.34259i	0.934713	−	0.355404i	$-0.115657\pi$
$558$	−5.81742	+	10.0761i	−0.246271	+	0.426554i
$559$	−26.9888	−	10.9691i	−1.14151	−	0.463942i
$560$	−11.8770	−	24.7150i	−0.501894	−	1.04440i
$561$	0.884102	+	1.53131i	0.0373268	+	0.0646519i
$562$	0.785724			0.0331438
$563$	−43.2809			−1.82407			−0.912036	−	0.410110i	$-0.865490\pi$
$563$	−43.2809			−1.82407			−0.912036	+	0.410110i	$0.865490\pi$
$564$	3.20214	+	5.54626i	0.134834	+	0.233540i
$565$	−11.7393	−	20.3331i	−0.493877	−	0.855421i
$566$	−0.933471	+	1.61682i	−0.0392367	+	0.0679600i
$567$	−1.14598	−	2.38469i	−0.0481265	−	0.100147i
$568$	−0.311223	+	0.539054i	−0.0130586	+	0.0226182i
$569$	−15.5204			−0.650650			−0.325325	−	0.945602i	$-0.605474\pi$
$569$	−15.5204			−0.650650			−0.325325	+	0.945602i	$0.605474\pi$
$570$	13.0260	−	22.5617i	0.545599	−	0.945005i
$571$	5.62473	+	9.74231i	0.235387	+	0.407703i	0.959385	−	0.282099i	$-0.0910308\pi$
$571$	5.62473	+	9.74231i	0.235387	+	0.407703i	−0.723998	+	0.689802i	$0.757697\pi$
$572$	−0.756632	−	0.307518i	−0.0316364	−	0.0128580i
$573$	12.7429			0.532341
$574$	−8.77426	−	0.664836i	−0.366230	−	0.0277497i
$575$	1.77209	+	3.06935i	0.0739012	+	0.128001i
$576$	−1.60857	−	2.78612i	−0.0670237	−	0.116088i
$577$	13.0442	+	22.5933i	0.543038	+	0.940570i	0.998728	+	0.0504308i	$0.0160594\pi$
$577$	13.0442	+	22.5933i	0.543038	+	0.940570i	−0.455689	+	0.890139i	$0.650607\pi$
$578$	−27.7950			−1.15612
$579$	0.326052	+	0.564739i	0.0135503	+	0.0234698i
$580$	3.41994			0.142005
$581$	13.9252	−	20.3882i	0.577714	−	0.845847i
$582$	5.29656	+	9.17390i	0.219549	+	0.380271i
$583$	−0.669416			−0.0277244
$584$	−6.17258	−	10.6912i	−0.255423	−	0.442406i
$585$	1.03840	+	7.50092i	0.0429325	+	0.310125i
$586$	−10.6645	+	18.4715i	−0.440547	+	0.763049i
$587$	−20.9471	−	36.2815i	−0.864581	−	1.49750i	−0.867463	−	0.497502i	$-0.834251\pi$
$587$	−20.9471	−	36.2815i	−0.864581	−	1.49750i	0.00288215	−	0.999996i	$-0.499083\pi$
$588$	5.15234	+	0.785306i	0.212479	+	0.0323855i
$589$	−26.2927	+	45.5403i	−1.08337	+	1.87646i
$590$	23.8062	−	41.2336i	0.980086	−	1.69756i
$591$	−6.06160			−0.249341
$592$	0.517639			0.0212748
$593$	0.0938527	−	0.162558i	0.00385407	−	0.00667544i	−0.864092	−	0.503334i	$-0.832107\pi$
$593$	0.0938527	−	0.162558i	0.00385407	−	0.00667544i	0.867946	+	0.496659i	$0.165440\pi$
$594$	−0.252013	+	0.436500i	−0.0103402	+	0.0179098i
$595$	13.9880	+	29.1079i	0.573452	+	1.19331i
$596$	−2.46687	−	4.27275i	−0.101047	−	0.175018i
$597$	−1.02227	+	1.77062i	−0.0418386	+	0.0724666i
$598$	4.92814	+	35.5986i	0.201526	+	1.45574i
$599$	11.9802	+	20.7503i	0.489498	+	0.847835i	0.999927	−	0.0120845i	$-0.00384672\pi$
$599$	11.9802	+	20.7503i	0.489498	+	0.847835i	−0.510429	+	0.859920i	$0.670513\pi$
$600$	−1.22519			−0.0500181
$601$	−11.4417	−	19.8176i	−0.466717	−	0.808377i	0.532561	−	0.846392i	$-0.321230\pi$
$601$	−11.4417	−	19.8176i	−0.466717	−	0.808377i	−0.999277	+	0.0380151i	$0.987896\pi$
$602$	−15.3398	−	31.9210i	−0.625206	−	1.30100i
$603$	10.0815			0.410549
$604$	0.567430	+	0.982818i	0.0230884	+	0.0399903i
$605$	22.9080			0.931344
$606$	1.14311	+	1.97993i	0.0464359	+	0.0804293i
$607$	−0.987158	−	1.70981i	−0.0400675	−	0.0693990i	0.845296	−	0.534298i	$-0.179424\pi$
$607$	−0.987158	−	1.70981i	−0.0400675	−	0.0693990i	−0.885364	+	0.464899i	$0.846091\pi$
$608$	15.0332	+	26.0382i	0.609675	+	1.05599i
$609$	3.26355	−	4.77826i	0.132246	−	0.193625i
$610$	−38.3646			−1.55334
$611$	−28.7310	−	11.6771i	−1.16233	−	0.472407i
$612$	−2.16360	−	3.74747i	−0.0874585	−	0.151483i
$613$	−1.57631	+	2.73025i	−0.0636667	+	0.110274i	−0.896102	−	0.443849i	$-0.853613\pi$
$613$	−1.57631	+	2.73025i	−0.0636667	+	0.110274i	0.832435	+	0.554123i	$0.186946\pi$
$614$	13.2786			0.535880
$615$	2.10816	−	3.65144i	0.0850093	−	0.147240i
$616$	0.725152	+	1.50898i	0.0292172	+	0.0607987i
$617$	−6.03895	+	10.4598i	−0.243119	+	0.421094i	−0.961601	−	0.274451i	$-0.911504\pi$
$617$	−6.03895	+	10.4598i	−0.243119	+	0.421094i	0.718482	+	0.695545i	$0.244837\pi$
$618$	4.68220	+	8.10981i	0.188346	+	0.326224i
$619$	−20.4442	−	35.4104i	−0.821722	−	1.42327i	−0.904399	−	0.426689i	$-0.859680\pi$
$619$	−20.4442	−	35.4104i	−0.821722	−	1.42327i	0.0826762	−	0.996576i	$-0.473653\pi$
$620$	10.9820			0.441049
$621$	6.01656			0.241436
$622$	2.61230	+	4.52464i	0.104744	+	0.181422i
$623$	−4.61897	+	6.76276i	−0.185055	+	0.270944i
$624$	−16.4831	−	6.69922i	−0.659852	−	0.268184i
$625$	10.8538	−	18.7994i	0.434153	−	0.751975i
$626$	−0.438340	+	0.759227i	−0.0175196	+	0.0303448i
$627$	−1.13901	+	1.97283i	−0.0454877	+	0.0787871i
$628$	6.30264	+	10.9165i	0.251503	+	0.435615i
$629$	−0.609645			−0.0243081
$630$	−5.19196	+	7.60169i	−0.206852	+	0.302859i
$631$	17.6950	−	30.6486i	0.704427	−	1.22010i	−0.262471	−	0.964940i	$-0.584537\pi$
$631$	17.6950	−	30.6486i	0.704427	−	1.22010i	0.966898	−	0.255163i	$-0.0821293\pi$
$632$	13.6217	−	23.5935i	0.541843	−	0.938500i
$633$	4.55338			0.180980
$634$	3.62858	−	6.28488i	0.144109	−	0.249604i
$635$	−35.3590			−1.40318
$636$	1.63822			0.0649595
$637$	−22.0282	+	12.3190i	−0.872790	+	0.488096i
$638$	−1.10233			−0.0436418
$639$	0.299272			0.0118390
$640$	−14.0302	+	24.3011i	−0.554594	+	0.960585i
$641$	27.8876			1.10149			0.550747	−	0.834673i	$-0.314343\pi$
$641$	27.8876			1.10149			0.550747	+	0.834673i	$0.314343\pi$
$642$	11.7010	−	20.2667i	0.461801	−	0.799862i
$643$	−3.37661	+	5.84847i	−0.133161	+	0.230641i	−0.924893	−	0.380227i	$-0.875846\pi$
$643$	−3.37661	+	5.84847i	−0.133161	+	0.230641i	0.791733	+	0.610868i	$0.209179\pi$
$644$	−6.68454	+	9.78703i	−0.263408	+	0.385663i
$645$	16.9697			0.668182
$646$	−36.0463	−	62.4340i	−1.41822	−	2.45643i
$647$	−23.0343	+	39.8967i	−0.905574	+	1.56850i	−0.0854282	+	0.996344i	$0.527226\pi$
$647$	−23.0343	+	39.8967i	−0.905574	+	1.56850i	−0.820145	+	0.572155i	$0.806107\pi$
$648$	−1.03993	+	1.80122i	−0.0408524	+	0.0707585i
$649$	−2.08165	+	3.60552i	−0.0817118	+	0.141529i
$650$	−2.77719	+	2.16056i	−0.108930	+	0.0847441i
$651$	10.4799	−	15.3439i	0.410738	−	0.601373i
$652$	−3.58933	−	6.21690i	−0.140569	−	0.243473i
$653$	35.8803			1.40410			0.702052	−	0.712126i	$-0.252267\pi$
$653$	35.8803			1.40410			0.702052	+	0.712126i	$0.252267\pi$
$654$	−15.1355			−0.591844
$655$	14.6543	+	25.3819i	0.572589	+	0.991753i
$656$	4.95340	+	8.57955i	0.193398	+	0.334975i
$657$	−2.96778	+	5.14034i	−0.115784	+	0.200544i
$658$	−16.3301	−	33.9816i	−0.636613	−	1.32474i
$659$	−17.2510	+	29.8796i	−0.672004	+	1.16395i	0.305331	+	0.952246i	$0.401233\pi$
$659$	−17.2510	+	29.8796i	−0.672004	+	1.16395i	−0.977335	+	0.211699i	$0.932100\pi$
$660$	0.475747			0.0185184
$661$	20.2784	−	35.1233i	0.788740	−	1.36614i	−0.137999	−	0.990432i	$-0.544067\pi$
$661$	20.2784	−	35.1233i	0.788740	−	1.36614i	0.926739	−	0.375706i	$-0.122600\pi$
$662$	−22.3113	−	38.6444i	−0.867155	−	1.50196i
$663$	19.4128	+	7.88995i	0.753932	+	0.306420i
$664$	−19.4091			−0.753219
$665$	−23.4658	+	34.3570i	−0.909966	+	1.33231i
$666$	−0.0868896	−	0.150497i	−0.00336690	−	0.00583165i
$667$	6.57928	+	11.3956i	0.254751	+	0.441241i
$668$	6.78048	+	11.7441i	0.262345	+	0.454395i
$669$	−15.7101			−0.607388
$670$	−17.5385	−	30.3777i	−0.677573	−	1.17359i
$671$	3.35465			0.129505
$672$	−4.60167	−	9.57572i	−0.177513	−	0.369391i
$673$	−11.5572	−	20.0177i	−0.445498	−	0.771625i	0.552589	−	0.833454i	$-0.313640\pi$
$673$	−11.5572	−	20.0177i	−0.445498	−	0.771625i	−0.998087	+	0.0618288i	$0.980307\pi$
$674$	−34.5176			−1.32957
$675$	0.294535	+	0.510150i	0.0113367	+	0.0196357i
$676$	−9.31511	+	2.62949i	−0.358274	+	0.101134i
$677$	8.56573	−	14.8363i	0.329208	−	0.570205i	−0.653147	−	0.757231i	$-0.726552\pi$
$677$	8.56573	−	14.8363i	0.329208	−	0.570205i	0.982355	+	0.187026i	$0.0598850\pi$
$678$	−9.26006	−	16.0389i	−0.355631	−	0.615970i
$679$	−7.32764	−	15.2482i	−0.281209	−	0.585174i
$680$	12.6936	−	21.9860i	0.486778	−	0.843124i
$681$	6.27169	−	10.8629i	0.240332	−	0.416267i
$682$	−3.53979			−0.135546
$683$	−44.1844			−1.69067			−0.845335	−	0.534237i	$-0.820599\pi$
$683$	−44.1844			−1.69067			−0.845335	+	0.534237i	$0.820599\pi$
$684$	2.78743	−	4.82796i	0.106580	−	0.184602i
$685$	−0.639610	+	1.10784i	−0.0244382	+	0.0423283i
$686$	−29.8956	−	6.90155i	−1.14142	−	0.263502i
$687$	−10.3182	−	17.8717i	−0.393665	−	0.681849i
$688$	−19.9363	+	34.5307i	−0.760064	+	1.31647i
$689$	−6.26154	+	4.87127i	−0.238546	+	0.185580i
$690$	−10.4669	−	18.1292i	−0.398469	−	0.690168i
$691$	−10.0517			−0.382384			−0.191192	−	0.981553i	$-0.561235\pi$
$691$	−10.0517			−0.382384			−0.191192	+	0.981553i	$0.561235\pi$
$692$	−8.00924	−	13.8724i	−0.304466	−	0.527350i
$693$	0.453992	−	0.664702i	0.0172457	−	0.0252500i
$694$	22.0972			0.838800
$695$	8.89976	+	15.4148i	0.337587	+	0.584718i
$696$	−4.54879			−0.172421
$697$	−5.83383	−	10.1045i	−0.220972	−	0.382735i
$698$	17.0010	+	29.4466i	0.643498	+	1.11457i
$699$	4.00908	+	6.94394i	0.151637	+	0.262644i
$700$	−1.15709	−	0.0876739i	−0.0437338	−	0.00331376i
$701$	11.0843			0.418647			0.209323	−	0.977846i	$-0.432874\pi$
$701$	11.0843			0.418647			0.209323	+	0.977846i	$0.432874\pi$
$702$	0.819095	+	5.91677i	0.0309148	+	0.223314i
$703$	−0.392711	−	0.680195i	−0.0148114	−	0.0256540i
$704$	0.489393	−	0.847653i	0.0184447	−	0.0319471i
$705$	18.0652			0.680373
$706$	−5.34039	+	9.24982i	−0.200988	+	0.348122i
$707$	−1.58147	−	3.29091i	−0.0594772	−	0.123767i
$708$	5.09428	−	8.82355i	0.191455	−	0.331609i
$709$	0.717572	+	1.24287i	0.0269490	+	0.0466770i	0.879185	−	0.476480i	$-0.158087\pi$
$709$	0.717572	+	1.24287i	0.0269490	+	0.0466770i	−0.852236	+	0.523157i	$0.824754\pi$
$710$	−0.520639	−	0.901773i	−0.0195392	−	0.0338430i
$711$	−13.0987			−0.491238
$712$	6.43799			0.241274
$713$	21.1273	+	36.5935i	0.791222	+	1.37044i
$714$	11.0338	+	22.9605i	0.412931	+	0.859276i
$715$	−1.81838	+	1.41464i	−0.0680037	+	0.0529046i
$716$	1.01451	−	1.75719i	0.0379141	−	0.0656692i
$717$	0.584182	−	1.01183i	0.0218167	−	0.0377876i
$718$	7.26529	−	12.5839i	0.271138	−	0.469625i
$719$	18.1353	+	31.4113i	0.676333	+	1.17144i	0.976077	+	0.217423i	$0.0697651\pi$
$719$	18.1353	+	31.4113i	0.676333	+	1.17144i	−0.299745	+	0.954019i	$0.596902\pi$
$720$	10.3641			0.386246
$721$	−6.47770	−	13.4796i	−0.241242	−	0.502006i
$722$	30.7010	−	53.1757i	1.14257	−	1.97899i
$723$	0.536076	−	0.928511i	0.0199369	−	0.0345317i
$724$	−4.81849			−0.179078
$725$	−0.644165	+	1.11573i	−0.0239237	+	0.0414371i
$726$	18.0700			0.670641
$727$	45.0943			1.67245			0.836227	−	0.548384i	$-0.184757\pi$
$727$	45.0943			1.67245			0.836227	+	0.548384i	$0.184757\pi$
$728$	17.7636	+	8.83779i	0.658363	+	0.327550i
$729$	1.00000			0.0370370
$730$	20.6520			0.764364
$731$	23.4798	−	40.6682i	0.868432	−	1.50417i
$732$	−8.20961			−0.303436
$733$	−9.09554	+	15.7539i	−0.335952	+	0.581885i	−0.983667	−	0.179997i	$-0.942391\pi$
$733$	−9.09554	+	15.7539i	−0.335952	+	0.581885i	0.647716	+	0.761882i	$0.275725\pi$
$734$	10.0888	−	17.4743i	0.372385	−	0.644989i
$735$	9.18526	−	11.4790i	0.338803	−	0.423408i
$736$	24.1595			0.890531
$737$	1.53360	+	2.65627i	0.0564907	+	0.0978448i
$738$	1.66293	−	2.88028i	0.0612134	−	0.106025i
$739$	12.9521	−	22.4337i	0.476451	−	0.825237i	−0.523185	−	0.852219i	$-0.675256\pi$
$739$	12.9521	−	22.4337i	0.476451	−	0.825237i	0.999636	+	0.0269820i	$0.00858969\pi$
$740$	−0.0820144	+	0.142053i	−0.00301491	+	0.00522198i
$741$	3.70203	+	26.7418i	0.135997	+	0.982383i
$742$	−9.61656	−	0.728658i	−0.353035	−	0.0267499i
$743$	−22.0599	−	38.2089i	−0.809301	−	1.40175i	−0.913349	−	0.407177i	$-0.866513\pi$
$743$	−22.0599	−	38.2089i	−0.809301	−	1.40175i	0.104049	−	0.994572i	$-0.466820\pi$
$744$	−14.6070			−0.535518
$745$	−13.9171			−0.509883
$746$	25.3450	+	43.8988i	0.927946	+	1.60725i
$747$	4.66595	+	8.08166i	0.170718	+	0.295693i
$748$	0.658257	−	1.14013i	0.0240683	−	0.0416874i
$749$	−21.0789	+	30.8621i	−0.770204	+	1.12768i
$750$	9.72322	−	16.8411i	0.355042	−	0.614950i
$751$	−4.12069			−0.150366			−0.0751831	−	0.997170i	$-0.523954\pi$
$751$	−4.12069			−0.150366			−0.0751831	+	0.997170i	$0.523954\pi$
$752$	−21.2232	+	36.7597i	−0.773932	+	1.34049i
$753$	−6.29717	−	10.9070i	−0.229482	−	0.397474i
$754$	−10.3109	+	8.02157i	−0.375502	+	0.292128i
$755$	3.20121			0.116504
$756$	−1.11102	+	1.62668i	−0.0404076	+	0.0591618i
$757$	20.4854	+	35.4818i	0.744556	+	1.28961i	0.950402	+	0.311024i	$0.100672\pi$
$757$	20.4854	+	35.4818i	0.744556	+	1.28961i	−0.205846	+	0.978584i	$0.565995\pi$
$758$	4.20922	+	7.29059i	0.152886	+	0.264806i
$759$	0.915242	+	1.58525i	0.0332212	+	0.0575408i
$760$	32.7070			1.18641
$761$	−22.1974	−	38.4470i	−0.804654	−	1.39370i	−0.916524	−	0.399979i	$-0.869017\pi$
$761$	−22.1974	−	38.4470i	−0.804654	−	1.39370i	0.111870	−	0.993723i	$-0.464316\pi$
$762$	−27.8914			−1.01040
$763$	24.1027	+	1.82629i	0.872578	+	0.0661162i
$764$	−4.74385	−	8.21658i	−0.171626	−	0.297266i
$765$	−12.2062			−0.441315
$766$	−20.4002	−	35.3342i	−0.737090	−	1.27668i
$767$	6.76579	+	48.8730i	0.244299	+	1.76470i
$768$	−7.85001	+	13.5966i	−0.283263	+	0.490626i
$769$	6.60276	+	11.4363i	0.238101	+	0.412404i	0.960169	−	0.279418i	$-0.0901416\pi$
$769$	6.60276	+	11.4363i	0.238101	+	0.412404i	−0.722068	+	0.691822i	$0.756808\pi$
$770$	−2.79270	−	0.211606i	−0.100642	−	0.00762575i
$771$	10.6490	−	18.4446i	0.383515	−	0.664268i
$772$	0.242762	−	0.420476i	0.00873719	−	0.0151333i
$773$	−17.3697			−0.624744			−0.312372	−	0.949960i	$-0.601123\pi$
$773$	−17.3697			−0.624744			−0.312372	+	0.949960i	$0.601123\pi$
$774$	13.3858			0.481144
$775$	−2.06853	+	3.58280i	−0.0743038	+	0.128698i
$776$	−6.64957	+	11.5174i	−0.238706	+	0.413450i
$777$	0.120209	+	0.250146i	0.00431249	+	0.00897394i
$778$	15.3572	+	26.5994i	0.550581	+	0.953634i
$779$	7.51587	−	13.0179i	0.269284	−	0.466414i
$780$	4.45001	−	3.46196i	0.159336	−	0.123958i
$781$	0.0455254	+	0.0788523i	0.00162903	+	0.00282156i
$782$	−57.9293			−2.07155
$783$	1.09353	+	1.89405i	0.0390795	+	0.0676877i
$784$	12.5669	+	32.1762i	0.448816	+	1.14915i
$785$	35.5569			1.26908
$786$	11.5594	+	20.0214i	0.412309	+	0.714140i
$787$	−4.14961			−0.147917			−0.0739587	−	0.997261i	$-0.523563\pi$
$787$	−4.14961			−0.147917			−0.0739587	+	0.997261i	$0.523563\pi$
$788$	2.25658	+	3.90851i	0.0803872	+	0.139235i
$789$	11.0142	+	19.0772i	0.392117	+	0.679167i
$790$	22.7875	+	39.4692i	0.810744	+	1.40425i
$791$	12.8110	+	26.6588i	0.455508	+	0.947876i
$792$	−0.632780			−0.0224849
$793$	31.3785	−	24.4114i	1.11428	−	0.866875i
$794$	25.8462	+	44.7669i	0.917247	+	1.58872i
$795$	2.31054	−	4.00197i	0.0819464	−	0.141935i
$796$	1.52226			0.0539549
$797$	−10.4435	+	18.0887i	−0.369928	+	0.640735i	−0.989554	−	0.144163i	$-0.953951\pi$
$797$	−10.4435	+	18.0887i	−0.369928	+	0.640735i	0.619626	+	0.784897i	$0.287284\pi$
$798$	−18.5100	+	27.1010i	−0.655247	+	0.959365i
$799$	24.9955	−	43.2934i	0.884277	−	1.53161i
$800$	1.18271	+	2.04851i	0.0418150	+	0.0724257i
$801$	−1.54769	−	2.68068i	−0.0546850	−	0.0947172i
$802$	56.6993			2.00212
$803$	−1.80584			−0.0637266
$804$	−3.75307	−	6.50050i	−0.132360	−	0.229255i
$805$	14.4807	+	30.1332i	0.510377	+	1.06205i
$806$	−33.1103	+	25.7587i	−1.16626	+	0.907312i
$807$	−8.92932	+	15.4660i	−0.314327	+	0.544430i
$808$	−1.43512	+	2.48571i	−0.0504875	+	0.0874469i
$809$	−1.79235	+	3.10445i	−0.0630158	+	0.109147i	−0.895812	−	0.444433i	$-0.853405\pi$
$809$	−1.79235	+	3.10445i	−0.0630158	+	0.109147i	0.832796	+	0.553580i	$0.186739\pi$
$810$	−1.73968	−	3.01322i	−0.0611263	−	0.105874i
$811$	47.0892			1.65353			0.826763	−	0.562551i	$-0.190180\pi$
$811$	47.0892			1.65353			0.826763	+	0.562551i	$0.190180\pi$
$812$	−4.29595	−	0.325509i	−0.150758	−	0.0114231i
$813$	3.60531	−	6.24459i	0.126444	−	0.219007i
$814$	0.0264354	−	0.0457874i	0.000926559	−	0.00160485i
$815$	−20.2496			−0.709311
$816$	14.3400	−	24.8376i	0.502001	−	0.869491i
$817$	60.4993			2.11660
$818$	16.4971			0.576808
$819$	−0.590446	−	9.52110i	−0.0206319	−	0.332694i
$820$	−3.13926			−0.109628
$821$	−11.3648			−0.396634			−0.198317	−	0.980138i	$-0.563548\pi$
$821$	−11.3648			−0.396634			−0.198317	+	0.980138i	$0.563548\pi$
$822$	−0.504529	+	0.873869i	−0.0175975	+	0.0304797i
$823$	10.1317			0.353169			0.176584	−	0.984286i	$-0.443495\pi$
$823$	10.1317			0.353169			0.176584	+	0.984286i	$0.443495\pi$
$824$	−5.87828	+	10.1815i	−0.204779	+	0.354688i
$825$	−0.0896097	+	0.155208i	−0.00311981	+	0.00540367i
$826$	−33.8287	+	49.5296i	−1.17705	+	1.72335i
$827$	−47.6358			−1.65646			−0.828230	−	0.560388i	$-0.810652\pi$
$827$	−47.6358			−1.65646			−0.828230	+	0.560388i	$0.810652\pi$
$828$	−2.23981	−	3.87946i	−0.0778388	−	0.134821i
$829$	−9.88328	+	17.1183i	−0.343260	+	0.594545i	−0.985036	−	0.172348i	$-0.944865\pi$
$829$	−9.88328	+	17.1183i	−0.343260	+	0.594545i	0.641776	+	0.766892i	$0.278198\pi$
$830$	16.2346	−	28.1191i	0.563510	−	0.976028i
$831$	2.19138	−	3.79558i	0.0760180	−	0.131667i
$832$	−1.59063	−	11.4900i	−0.0551451	−	0.398343i
$833$	−14.8005	−	37.8952i	−0.512807	−	1.31299i
$834$	7.02018	+	12.1593i	0.243089	+	0.421043i
$835$	38.2528			1.32379
$836$	1.69610			0.0586608
$837$	3.51152	+	6.08213i	0.121376	+	0.210229i
$838$	−0.971172	−	1.68212i	−0.0335486	−	0.0581079i
$839$	−3.47420	+	6.01748i	−0.119943	+	0.207747i	−0.919745	−	0.392517i	$-0.871604\pi$
$839$	−3.47420	+	6.01748i	−0.119943	+	0.207747i	0.799802	+	0.600264i	$0.204938\pi$
$840$	−11.5241	−	0.873193i	−0.397619	−	0.0301280i
$841$	12.1084	−	20.9723i	0.417531	−	0.723184i
$842$	16.9599			0.584477
$843$	0.237140	−	0.410738i	0.00816753	−	0.0141466i
$844$	−1.69511	−	2.93601i	−0.0583479	−	0.101062i
$845$	−6.71449	+	26.4644i	−0.230986	+	0.910402i
$846$	14.2499			0.489922
$847$	−28.7759	−	2.18038i	−0.988751	−	0.0749188i
$848$	5.42891	+	9.40315i	0.186430	+	0.322906i
$849$	0.563463	+	0.975947i	0.0193380	+	0.0334944i
$850$	−2.83588	−	4.91188i	−0.0972698	−	0.168476i
$851$	−0.631118			−0.0216344
$852$	−0.111411	−	0.192970i	−0.00381689	−	0.00661104i
$853$	40.0909			1.37269			0.686343	−	0.727278i	$-0.259215\pi$
$853$	40.0909			1.37269			0.686343	+	0.727278i	$0.259215\pi$
$854$	48.1916	+	3.65153i	1.64908	+	0.124953i
$855$	−7.86277	−	13.6187i	−0.268901	−	0.465750i
$856$	29.3800			1.00419
$857$	2.09069	+	3.62118i	0.0714166	+	0.123697i	0.899522	−	0.436875i	$-0.143915\pi$
$857$	2.09069	+	3.62118i	0.0714166	+	0.123697i	−0.828106	+	0.560572i	$0.810581\pi$
$858$	−1.43435	+	1.11588i	−0.0489680	+	0.0380954i
$859$	−2.22930	+	3.86127i	−0.0760629	+	0.131745i	−0.901548	−	0.432679i	$-0.857568\pi$
$859$	−2.22930	+	3.86127i	−0.0760629	+	0.131745i	0.825485	+	0.564424i	$0.190902\pi$
$860$	−6.31739	−	10.9420i	−0.215421	−	0.373121i
$861$	−2.99571	+	4.38610i	−0.102093	+	0.149478i
$862$	19.5814	−	33.9160i	0.666946	−	1.15518i
$863$	−6.39008	+	11.0680i	−0.217521	+	0.376757i	−0.954049	−	0.299649i	$-0.903130\pi$
$863$	−6.39008	+	11.0680i	−0.217521	+	0.376757i	0.736528	+	0.676407i	$0.236464\pi$
$864$	4.01550			0.136610
$865$	−45.1849			−1.53633
$866$	0.407813	−	0.706353i	0.0138581	−	0.0240029i
$867$	−8.38883	+	14.5299i	−0.284899	+	0.493460i
$868$	−13.7951	−	1.04527i	−0.468235	−	0.0354787i
$869$	−1.99257	−	3.45124i	−0.0675934	−	0.117075i
$870$	3.80479	−	6.59009i	0.128994	−	0.223425i
$871$	33.6742	+	13.6862i	1.14101	+	0.463739i
$872$	−9.50092	−	16.4561i	−0.321742	−	0.557273i
$873$	6.39423			0.216412
$874$	−37.3159	−	64.6330i	−1.26223	−	2.18625i
$875$	−17.5160	+	25.6457i	−0.592149	+	0.866982i
$876$	4.41931			0.149314
$877$	−23.0715	−	39.9611i	−0.779070	−	1.34939i	−0.932478	−	0.361226i	$-0.882358\pi$
$877$	−23.0715	−	39.9611i	−0.779070	−	1.34939i	0.153408	−	0.988163i	$-0.450975\pi$
$878$	24.9557			0.842213
$879$	6.43732	+	11.1498i	0.217125	+	0.376072i
$880$	1.57659	+	2.73073i	0.0531467	+	0.0920527i
$881$	6.60175	+	11.4346i	0.222419	+	0.385240i	0.955542	−	0.294855i	$-0.0952715\pi$
$881$	6.60175	+	11.4346i	0.222419	+	0.385240i	−0.733123	+	0.680096i	$0.761938\pi$
$882$	7.24539	−	9.05468i	0.243965	−	0.304887i
$883$	−23.5256			−0.791701			−0.395850	−	0.918315i	$-0.629550\pi$
$883$	−23.5256			−0.791701			−0.395850	+	0.918315i	$0.629550\pi$
$884$	−2.13947	−	15.4546i	−0.0719583	−	0.519794i
$885$	−14.3699	−	24.8895i	−0.483040	−	0.836650i
$886$	22.1987	−	38.4493i	0.745781	−	1.29173i
$887$	−37.8712			−1.27159			−0.635796	−	0.771857i	$-0.719328\pi$
$887$	−37.8712			−1.27159			−0.635796	+	0.771857i	$0.719328\pi$
$888$	0.109086	−	0.188942i	0.00366068	−	0.00634048i
$889$	44.4161	+	3.36546i	1.48967	+	0.112874i
$890$	−5.38499	+	9.32708i	−0.180505	+	0.312644i
$891$	0.152120	+	0.263480i	0.00509623	+	0.00882693i
$892$	5.84847	+	10.1298i	0.195821	+	0.339172i
$893$	64.4046			2.15522
$894$	−10.9779			−0.367156
$895$	−2.86174	−	4.95667i	−0.0956573	−	0.165683i
$896$	19.9370	−	29.1904i	0.666050	−	0.975182i
$897$	20.0966	+	8.16785i	0.671006	+	0.272717i
$898$	−3.74851	+	6.49261i	−0.125089	+	0.216661i
$899$	−7.67989	+	13.3020i	−0.256139	+	0.443645i
$900$	0.219296	−	0.379831i	0.00730986	−	0.0126610i
$901$	−6.39386	−	11.0745i	−0.213010	−	0.368945i
$902$	1.01186			0.0336914
$903$	−21.3165	−	1.61518i	−0.709368	−	0.0537497i
$904$	11.6256	−	20.1361i	0.386660	−	0.669715i
$905$	−6.79600	+	11.7710i	−0.225907	+	0.391282i
$906$	2.52514			0.0838920
$907$	22.6965	−	39.3115i	0.753625	−	1.30532i	−0.192430	−	0.981311i	$-0.561637\pi$
$907$	22.6965	−	39.3115i	0.753625	−	1.30532i	0.946055	−	0.324006i	$-0.105030\pi$
$908$	−9.33915			−0.309931
$909$	1.38002			0.0457723
$910$	−27.6620	+	18.3429i	−0.916986	+	0.608060i
$911$	−45.3167			−1.50141			−0.750704	−	0.660638i	$-0.770286\pi$
$911$	−45.3167			−1.50141			−0.750704	+	0.660638i	$0.770286\pi$
$912$	36.9492			1.22351
$913$	−1.41957	+	2.45877i	−0.0469810	+	0.0813735i
$914$	−56.9131			−1.88252
$915$	−11.5788	+	20.0551i	−0.382784	+	0.663002i
$916$	−7.68243	+	13.3064i	−0.253835	+	0.439655i
$917$	−15.9921	−	33.2782i	−0.528105	−	1.09894i
$918$	−9.62831			−0.317782
$919$	18.7944	+	32.5528i	0.619970	+	1.07382i	0.989491	+	0.144596i	$0.0461884\pi$
$919$	18.7944	+	32.5528i	0.619970	+	1.07382i	−0.369521	+	0.929222i	$0.620478\pi$
$920$	13.1407	−	22.7604i	0.433236	−	0.750387i
$921$	4.00762	−	6.94140i	0.132056	−	0.228727i
$922$	0.827400	−	1.43310i	0.0272490	−	0.0471966i
$923$	0.999633	+	0.406280i	0.0329033	+	0.0133729i
$924$	−0.597608	−	0.0452815i	−0.0196599	−	0.00148965i
$925$	−0.0308958	−	0.0535131i	−0.00101585	−	0.00175950i
$926$	−53.9308			−1.77228
$927$	5.65255			0.185654
$928$	4.39106	+	7.60555i	0.144144	+	0.249664i
$929$	7.89908	+	13.6816i	0.259160	+	0.448879i	0.966017	−	0.258478i	$-0.0832208\pi$
$929$	7.89908	+	13.6816i	0.259160	+	0.448879i	−0.706857	+	0.707357i	$0.749887\pi$
$930$	12.2179	−	21.1620i	0.400640	−	0.693928i
$931$	32.7466	−	40.9240i	1.07323	−	1.34123i
$932$	2.98496	−	5.17010i	0.0977755	−	0.169352i
$933$	3.15369			0.103247
$934$	−20.0550	+	34.7362i	−0.656218	+	1.13660i
$935$	−1.85681	−	3.21609i	−0.0607242	−	0.105177i
$936$	−5.91886	+	4.60468i	−0.193464	+	0.150509i
$937$	3.77902			0.123455			0.0617276	−	0.998093i	$-0.480339\pi$
$937$	3.77902			0.123455			0.0617276	+	0.998093i	$0.480339\pi$
$938$	19.1397	+	39.8282i	0.624932	+	1.30044i
$939$	0.264591	+	0.458285i	0.00863461	+	0.0149556i
$940$	−6.72519	−	11.6484i	−0.219352	−	0.379928i
$941$	5.19282	+	8.99424i	0.169281	+	0.293204i	0.938167	−	0.346182i	$-0.112522\pi$
$941$	5.19282	+	8.99424i	0.169281	+	0.293204i	−0.768886	+	0.639386i	$0.779189\pi$
$942$	28.0475			0.913838
$943$	−6.03931	−	10.4604i	−0.196667	−	0.340637i
$944$	67.5281			2.19785
$945$	2.40681	+	5.00837i	0.0782934	+	0.162922i
$946$	2.03626	+	3.52690i	0.0662045	+	0.114669i
$947$	−3.03890			−0.0987511			−0.0493755	−	0.998780i	$-0.515723\pi$
$947$	−3.03890			−0.0987511			−0.0493755	+	0.998780i	$0.515723\pi$
$948$	4.87629	+	8.44599i	0.158375	+	0.274313i
$949$	−16.8913	+	13.1409i	−0.548316	+	0.426571i
$950$	3.65353	−	6.32810i	0.118536	−	0.205311i
$951$	−2.19029	−	3.79369i	−0.0710249	−	0.123019i
$952$	−18.0377	+	26.4095i	−0.584604	+	0.855936i
$953$	1.70817	−	2.95863i	0.0553329	−	0.0958394i	−0.837032	−	0.547154i	$-0.815711\pi$
$953$	1.70817	−	2.95863i	0.0553329	−	0.0958394i	0.892365	+	0.451314i	$0.149045\pi$
$954$	1.82257	−	3.15678i	0.0590078	−	0.102205i
$955$	−26.7629			−0.866026
$956$	−0.869904			−0.0281347
$957$	−0.332696	+	0.576247i	−0.0107545	+	0.0186274i
$958$	−25.1290	+	43.5247i	−0.811880	+	1.40622i
$959$	0.908889	−	1.33073i	0.0293496	−	0.0429715i
$960$	3.37835	+	5.85148i	0.109036	+	0.188856i
$961$	−9.16152	+	15.8682i	−0.295533	+	0.511878i
$962$	−0.0859205	−	0.620651i	−0.00277019	−	0.0200106i
$963$	−7.06296	−	12.2334i	−0.227601	−	0.394216i
$964$	−0.798269			−0.0257105
$965$	−0.684782	−	1.18608i	−0.0220439	−	0.0381812i
$966$	11.4225	+	23.7692i	0.367512	+	0.764763i
$967$	2.27084			0.0730254			0.0365127	−	0.999333i	$-0.488375\pi$
$967$	2.27084			0.0730254			0.0365127	+	0.999333i	$0.488375\pi$
$968$	11.3430	+	19.6467i	0.364578	+	0.631468i
$969$	−43.5166			−1.39795
$970$	−11.1239	−	19.2672i	−0.357168	−	0.618633i
$971$	11.0364	+	19.1155i	0.354174	+	0.613447i	0.986976	−	0.160866i	$-0.0514288\pi$
$971$	11.0364	+	19.1155i	0.354174	+	0.613447i	−0.632802	+	0.774313i	$0.718095\pi$
$972$	−0.372274	−	0.644798i	−0.0119407	−	0.0206819i
$973$	−9.71223	−	20.2104i	−0.311360	−	0.647915i
$974$	8.92030			0.285825
$975$	0.291250	+	2.10386i	0.00932747	+	0.0673774i
$976$	−27.2060	−	47.1221i	−0.870842	−	1.50834i
$977$	2.14878	−	3.72180i	0.0687457	−	0.119071i	−0.829604	−	0.558353i	$-0.811434\pi$
$977$	2.14878	−	3.72180i	0.0687457	−	0.119071i	0.898349	+	0.439282i	$0.144767\pi$
$978$	−15.9730			−0.510759
$979$	0.470871	−	0.815573i	0.0150491	−	0.0260658i
$980$	−10.8210	−	1.64932i	−0.345666	−	0.0526855i
$981$	−4.56805	+	7.91209i	−0.145846	+	0.252613i
$982$	28.9784	+	50.1920i	0.924737	+	1.60169i
$983$	−1.81793	−	3.14875i	−0.0579831	−	0.100430i	0.835577	−	0.549374i	$-0.185134\pi$
$983$	−1.81793	−	3.14875i	−0.0579831	−	0.100430i	−0.893560	+	0.448944i	$0.851800\pi$
$984$	4.17546			0.133109
$985$	12.7307			0.405634
$986$	−10.5288	−	18.2365i	−0.335306	−	0.580768i
$987$	−22.6925	−	1.71944i	−0.722311	−	0.0547303i
$988$	15.8649	−	12.3423i	0.504728	−	0.392662i
$989$	24.3068	−	42.1006i	0.772912	−	1.33872i
$990$	0.529283	−	0.916746i	0.0168217	−	0.0291361i
$991$	−1.07100	+	1.85503i	−0.0340214	+	0.0589269i	−0.882535	−	0.470247i	$-0.844165\pi$
$991$	−1.07100	+	1.85503i	−0.0340214	+	0.0589269i	0.848513	+	0.529174i	$0.177498\pi$
$992$	14.1005	+	24.4228i	0.447691	+	0.775424i
$993$	−26.9352			−0.854762
$994$	0.568169	+	1.18232i	0.0180212	+	0.0375008i
$995$	2.14699	−	3.71869i	0.0680641	−	0.117890i
$996$	3.47403	−	6.01719i	0.110079	−	0.190662i
$997$	−22.1051			−0.700077			−0.350038	−	0.936735i	$-0.613831\pi$
$997$	−22.1051			−0.700077			−0.350038	+	0.936735i	$0.613831\pi$
$998$	0.873566	−	1.51306i	0.0276522	−	0.0478951i
$999$	−0.104897			−0.00331879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.16.3	yes	20
3.2	odd	2		819.2.s.f.289.8		20
7.4	even	3		273.2.j.c.172.8	yes	20
13.9	even	3		273.2.j.c.100.8	✓	20
21.11	odd	6		819.2.n.f.172.3		20
39.35	odd	6		819.2.n.f.100.3		20
91.74	even	3	inner	273.2.l.c.256.3	yes	20
273.74	odd	6		819.2.s.f.802.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.8	✓	20	13.9	even	3
273.2.j.c.172.8	yes	20	7.4	even	3
273.2.l.c.16.3	yes	20	1.1	even	1	trivial
273.2.l.c.256.3	yes	20	91.74	even	3	inner
819.2.n.f.100.3		20	39.35	odd	6
819.2.n.f.172.3		20	21.11	odd	6
819.2.s.f.289.8		20	3.2	odd	2
819.2.s.f.802.8		20	273.74	odd	6

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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.65667 q^{2} +(-0.500000 + 0.866025i) q^{3} +0.744548 q^{4} +(1.05011 - 1.81885i) q^{5} +(0.828334 - 1.43472i) q^{6} +(-1.49221 + 2.18479i) q^{7} +2.07987 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.73968 + 3.01322i) q^{10} +(0.152120 - 0.263480i) q^{11} +(-0.372274 + 0.644798i) q^{12} +(-0.494423 - 3.57149i) q^{13} +(2.47210 - 3.61947i) q^{14} +(1.05011 + 1.81885i) q^{15} -4.93474 q^{16} +5.81185 q^{17} +(0.828334 + 1.43472i) q^{18} +(3.74378 + 6.48442i) q^{19} +(0.781858 - 1.35422i) q^{20} +(-1.14598 - 2.38469i) q^{21} +(-0.252013 + 0.436500i) q^{22} +6.01656 q^{23} +(-1.03993 + 1.80122i) q^{24} +(0.294535 + 0.510150i) q^{25} +(0.819095 + 5.91677i) q^{26} +1.00000 q^{27} +(-1.11102 + 1.62668i) q^{28} +(1.09353 + 1.89405i) q^{29} +(-1.73968 - 3.01322i) q^{30} +(3.51152 + 6.08213i) q^{31} +4.01550 q^{32} +(0.152120 + 0.263480i) q^{33} -9.62831 q^{34} +(2.40681 + 5.00837i) q^{35} +(-0.372274 - 0.644798i) q^{36} -0.104897 q^{37} +(-6.20220 - 10.7425i) q^{38} +(3.34021 + 1.35756i) q^{39} +(2.18409 - 3.78295i) q^{40} +(-1.00378 - 1.73860i) q^{41} +(1.89850 + 3.95064i) q^{42} +(4.03998 - 6.99746i) q^{43} +(0.113261 - 0.196174i) q^{44} -2.10022 q^{45} -9.96744 q^{46} +(4.30078 - 7.44916i) q^{47} +(2.46737 - 4.27361i) q^{48} +(-2.54661 - 6.52034i) q^{49} +(-0.487947 - 0.845149i) q^{50} +(-2.90593 + 5.03321i) q^{51} +(-0.368122 - 2.65915i) q^{52} +(-1.10014 - 1.90550i) q^{53} -1.65667 q^{54} +(-0.319487 - 0.553367i) q^{55} +(-3.10360 + 4.54407i) q^{56} -7.48756 q^{57} +(-1.81161 - 3.13781i) q^{58} -13.6842 q^{59} +(0.781858 + 1.35422i) q^{60} +(5.51315 + 9.54905i) q^{61} +(-5.81742 - 10.0761i) q^{62} +(2.63819 + 0.199899i) q^{63} +3.21714 q^{64} +(-7.01519 - 2.85118i) q^{65} +(-0.252013 - 0.436500i) q^{66} +(-5.04073 + 8.73079i) q^{67} +4.32721 q^{68} +(-3.00828 + 5.21049i) q^{69} +(-3.98728 - 8.29721i) q^{70} +(-0.149636 + 0.259177i) q^{71} +(-1.03993 - 1.80122i) q^{72} +(-2.96778 - 5.14034i) q^{73} +0.173779 q^{74} -0.589070 q^{75} +(2.78743 + 4.82796i) q^{76} +(0.348653 + 0.725520i) q^{77} +(-5.53362 - 2.24903i) q^{78} +(6.54933 - 11.3438i) q^{79} +(-5.18203 + 8.97554i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.66293 + 2.88028i) q^{82} -9.33190 q^{83} +(-0.853235 - 1.77552i) q^{84} +(6.10309 - 10.5709i) q^{85} +(-6.69291 + 11.5925i) q^{86} -2.18706 q^{87} +(0.316390 - 0.548004i) q^{88} +3.09538 q^{89} +3.47937 q^{90} +(8.54074 + 4.24921i) q^{91} +4.47962 q^{92} -7.02304 q^{93} +(-7.12496 + 12.3408i) q^{94} +15.7255 q^{95} +(-2.00775 + 3.47753i) q^{96} +(-3.19711 + 5.53756i) q^{97} +(4.21888 + 10.8020i) q^{98} -0.304241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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