LMFDB - Embedded newform 273.2.t.c.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.4
Root			$-1.38488 + 0.286553i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.c.205.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.573107i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.67155 q^{4} +(-2.74304 + 1.58369i) q^{5} +(0.496325 - 0.286553i) q^{6} +(0.0699870 + 2.64483i) q^{7} +2.10419i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+0.573107i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.67155 q^{4} +(-2.74304 + 1.58369i) q^{5} +(0.496325 - 0.286553i) q^{6} +(0.0699870 + 2.64483i) q^{7} +2.10419i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.907626 - 1.57205i) q^{10} +(-0.305703 + 0.176498i) q^{11} +(-0.835774 - 1.44760i) q^{12} +(1.81339 + 3.11635i) q^{13} +(-1.51577 + 0.0401100i) q^{14} +(2.74304 + 1.58369i) q^{15} +2.13717 q^{16} -0.888553 q^{17} +(-0.496325 - 0.286553i) q^{18} +(1.32596 + 0.765541i) q^{19} +(-4.58512 + 2.64722i) q^{20} +(2.25549 - 1.38302i) q^{21} +(-0.101152 - 0.175201i) q^{22} +4.53157 q^{23} +(1.82228 - 1.05209i) q^{24} +(2.51618 - 4.35815i) q^{25} +(-1.78600 + 1.03926i) q^{26} +1.00000 q^{27} +(0.116987 + 4.42095i) q^{28} +(0.213739 - 0.370207i) q^{29} +(-0.907626 + 1.57205i) q^{30} +(-7.47692 - 4.31680i) q^{31} +5.43321i q^{32} +(0.305703 + 0.176498i) q^{33} -0.509236i q^{34} +(-4.38057 - 7.14402i) q^{35} +(-0.835774 + 1.44760i) q^{36} +3.33015i q^{37} +(-0.438737 + 0.759914i) q^{38} +(1.79214 - 3.12861i) q^{39} +(-3.33239 - 5.77187i) q^{40} +(-4.73839 - 2.73571i) q^{41} +(0.792620 + 1.29264i) q^{42} +(-0.380909 - 0.659754i) q^{43} +(-0.510998 + 0.295025i) q^{44} -3.16739i q^{45} +2.59708i q^{46} +(8.53765 - 4.92921i) q^{47} +(-1.06859 - 1.85085i) q^{48} +(-6.99020 + 0.370207i) q^{49} +(2.49768 + 1.44204i) q^{50} +(0.444277 + 0.769510i) q^{51} +(3.03117 + 5.20913i) q^{52} +(2.06487 - 3.57646i) q^{53} +0.573107i q^{54} +(0.559038 - 0.968281i) q^{55} +(-5.56521 + 0.147266i) q^{56} -1.53108i q^{57} +(0.212168 + 0.122495i) q^{58} +11.5102i q^{59} +(4.58512 + 2.64722i) q^{60} +(7.57803 - 13.1255i) q^{61} +(2.47399 - 4.28507i) q^{62} +(-2.32548 - 1.26180i) q^{63} +1.16054 q^{64} +(-9.90954 - 5.67641i) q^{65} +(-0.101152 + 0.175201i) q^{66} +(8.10167 - 4.67750i) q^{67} -1.48526 q^{68} +(-2.26579 - 3.92446i) q^{69} +(4.09429 - 2.51054i) q^{70} +(10.7783 - 6.22283i) q^{71} +(-1.82228 - 1.05209i) q^{72} +(-5.88903 - 3.40003i) q^{73} -1.90853 q^{74} -5.03235 q^{75} +(2.21640 + 1.27964i) q^{76} +(-0.488201 - 0.796179i) q^{77} +(1.79303 + 1.02709i) q^{78} +(-3.48680 - 6.03932i) q^{79} +(-5.86235 + 3.38463i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.56785 - 2.71560i) q^{82} +14.9864i q^{83} +(3.77017 - 2.31179i) q^{84} +(2.43734 - 1.40720i) q^{85} +(0.378110 - 0.218302i) q^{86} -0.427478 q^{87} +(-0.371385 - 0.643258i) q^{88} -6.11094i q^{89} +1.81525 q^{90} +(-8.11528 + 5.01420i) q^{91} +7.57475 q^{92} +8.63360i q^{93} +(2.82497 + 4.89298i) q^{94} -4.84953 q^{95} +(4.70529 - 2.71660i) q^{96} +(11.3769 - 6.56845i) q^{97} +(-0.212168 - 4.00613i) q^{98} -0.352996i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			0.573107i			0.405248i	0.979257	+	0.202624i	$0.0649469\pi$
$2$			0.573107i			0.405248i	−0.979257	+	0.202624i	$0.935053\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.67155			0.835774
$5$	−2.74304	+	1.58369i	−1.22672	+	0.708250i	−0.966343	−	0.257256i	$-0.917182\pi$
$5$	−2.74304	+	1.58369i	−1.22672	+	0.708250i	−0.260381	+	0.965506i	$0.583848\pi$
$6$	0.496325	−	0.286553i	0.202624	−	0.116985i
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$8$			2.10419i			0.743943i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.907626	−	1.57205i	−0.287017	−	0.497127i
$11$	−0.305703	+	0.176498i	−0.0921730	+	0.0532161i	−0.545378	−	0.838190i	$-0.683614\pi$
$11$	−0.305703	+	0.176498i	−0.0921730	+	0.0532161i	0.453205	+	0.891406i	$0.350281\pi$
$12$	−0.835774	−	1.44760i	−0.241267	−	0.417887i
$13$	1.81339	+	3.11635i	0.502943	+	0.864319i
$13$	1.81339	+	3.11635i	0.502943	+	0.864319i
$14$	−1.51577	+	0.0401100i	−0.405106	+	0.0107198i
$15$	2.74304	+	1.58369i	0.708250	+	0.408908i
$16$	2.13717			0.534293
$17$	−0.888553			−0.215506			−0.107753	−	0.994178i	$-0.534366\pi$
$17$	−0.888553			−0.215506			−0.107753	+	0.994178i	$0.534366\pi$
$18$	−0.496325	−	0.286553i	−0.116985	−	0.0675413i
$19$	1.32596	+	0.765541i	0.304195	+	0.175627i	0.644326	−	0.764751i	$-0.277138\pi$
$19$	1.32596	+	0.765541i	0.304195	+	0.175627i	−0.340131	+	0.940378i	$0.610471\pi$
$20$	−4.58512	+	2.64722i	−1.02526	+	0.591937i
$21$	2.25549	−	1.38302i	0.492189	−	0.301800i
$22$	−0.101152	−	0.175201i	−0.0215657	−	0.0373529i
$23$	4.53157			0.944899			0.472449	−	0.881358i	$-0.343370\pi$
$23$	4.53157			0.944899			0.472449	+	0.881358i	$0.343370\pi$
$24$	1.82228	−	1.05209i	0.371972	−	0.214758i
$25$	2.51618	−	4.35815i	0.503235	−	0.871629i
$26$	−1.78600	+	1.03926i	−0.350263	+	0.203817i
$27$	1.00000			0.192450
$28$	0.116987	+	4.42095i	0.0221084	+	0.835482i
$29$	0.213739	−	0.370207i	0.0396903	−	0.0687457i	−0.845498	−	0.533979i	$-0.820696\pi$
$29$	0.213739	−	0.370207i	0.0396903	−	0.0687457i	0.885188	+	0.465233i	$0.154030\pi$
$30$	−0.907626	+	1.57205i	−0.165709	+	0.287017i
$31$	−7.47692	−	4.31680i	−1.34289	−	0.775320i	−0.355663	−	0.934614i	$-0.615745\pi$
$31$	−7.47692	−	4.31680i	−1.34289	−	0.775320i	−0.987231	+	0.159294i	$0.949078\pi$
$32$			5.43321i			0.960464i
$33$	0.305703	+	0.176498i	0.0532161	+	0.0307243i
$34$		−	0.509236i		−	0.0873332i
$35$	−4.38057	−	7.14402i	−0.740452	−	1.20756i
$36$	−0.835774	+	1.44760i	−0.139296	+	0.241267i
$37$			3.33015i			0.547473i	0.961805	+	0.273736i	$0.0882596\pi$
$37$			3.33015i			0.547473i	−0.961805	+	0.273736i	$0.911740\pi$
$38$	−0.438737	+	0.759914i	−0.0711725	+	0.123274i
$39$	1.79214	−	3.12861i	0.286973	−	0.500979i
$40$	−3.33239	−	5.77187i	−0.526898	−	0.912613i
$41$	−4.73839	−	2.73571i	−0.740012	−	0.427246i	0.0820619	−	0.996627i	$-0.473849\pi$
$41$	−4.73839	−	2.73571i	−0.740012	−	0.427246i	−0.822074	+	0.569381i	$0.807183\pi$
$42$	0.792620	+	1.29264i	0.122304	+	0.199458i
$43$	−0.380909	−	0.659754i	−0.0580881	−	0.100612i	0.835519	−	0.549462i	$-0.185167\pi$
$43$	−0.380909	−	0.659754i	−0.0580881	−	0.100612i	−0.893607	+	0.448850i	$0.851834\pi$
$44$	−0.510998	+	0.295025i	−0.0770359	+	0.0444767i
$45$		−	3.16739i		−	0.472166i
$46$			2.59708i			0.382918i
$47$	8.53765	−	4.92921i	1.24534	−	0.719000i	0.275167	−	0.961397i	$-0.411267\pi$
$47$	8.53765	−	4.92921i	1.24534	−	0.719000i	0.970177	+	0.242397i	$0.0779336\pi$
$48$	−1.06859	−	1.85085i	−0.154237	−	0.267147i
$49$	−6.99020	+	0.370207i	−0.998601	+	0.0528867i
$50$	2.49768	+	1.44204i	0.353226	+	0.203935i
$51$	0.444277	+	0.769510i	0.0622112	+	0.107753i
$52$	3.03117	+	5.20913i	0.420347	+	0.722376i
$53$	2.06487	−	3.57646i	0.283632	−	0.491265i	−0.688645	−	0.725099i	$-0.741794\pi$
$53$	2.06487	−	3.57646i	0.283632	−	0.491265i	0.972276	+	0.233834i	$0.0751273\pi$
$54$			0.573107i			0.0779899i
$55$	0.559038	−	0.968281i	0.0753806	−	0.130563i
$56$	−5.56521	+	0.147266i	−0.743683	+	0.0196792i
$57$		−	1.53108i		−	0.202797i
$58$	0.212168	+	0.122495i	0.0278590	+	0.0160844i
$59$			11.5102i			1.49850i	0.662287	+	0.749250i	$0.269586\pi$
$59$			11.5102i			1.49850i	−0.662287	+	0.749250i	$0.730414\pi$
$60$	4.58512	+	2.64722i	0.591937	+	0.341755i
$61$	7.57803	−	13.1255i	0.970267	−	1.68055i	0.275523	−	0.961294i	$-0.411149\pi$
$61$	7.57803	−	13.1255i	0.970267	−	1.68055i	0.694744	−	0.719257i	$-0.255518\pi$
$62$	2.47399	−	4.28507i	0.314197	−	0.544204i
$63$	−2.32548	−	1.26180i	−0.292983	−	0.158972i
$64$	1.16054			0.145067
$65$	−9.90954	−	5.67641i	−1.22913	−	0.704073i
$66$	−0.101152	+	0.175201i	−0.0124510	+	0.0215657i
$67$	8.10167	−	4.67750i	0.989777	−	0.571448i	0.0845695	−	0.996418i	$-0.473049\pi$
$67$	8.10167	−	4.67750i	0.989777	−	0.571448i	0.905208	+	0.424970i	$0.139715\pi$
$68$	−1.48526			−0.180114
$69$	−2.26579	−	3.92446i	−0.272769	−	0.472449i
$70$	4.09429	−	2.51054i	0.489361	−	0.300066i
$71$	10.7783	−	6.22283i	1.27914	−	0.738514i	0.302453	−	0.953164i	$-0.402195\pi$
$71$	10.7783	−	6.22283i	1.27914	−	0.738514i	0.976691	+	0.214651i	$0.0688613\pi$
$72$	−1.82228	−	1.05209i	−0.214758	−	0.123991i
$73$	−5.88903	−	3.40003i	−0.689259	−	0.397944i	0.114075	−	0.993472i	$-0.463609\pi$
$73$	−5.88903	−	3.40003i	−0.689259	−	0.397944i	−0.803334	+	0.595528i	$0.796943\pi$
$74$	−1.90853			−0.221862
$75$	−5.03235			−0.581086
$76$	2.21640	+	1.27964i	0.254239	+	0.146785i
$77$	−0.488201	−	0.796179i	−0.0556357	−	0.0907331i
$78$	1.79303	+	1.02709i	0.203021	+	0.116295i
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	0.600456	−	0.799658i	$-0.294986\pi$
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	−0.992752	+	0.120182i	$0.961652\pi$
$80$	−5.86235	+	3.38463i	−0.655430	+	0.378413i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.56785	−	2.71560i	0.173140	−	0.299888i
$83$			14.9864i			1.64498i	0.568782	+	0.822488i	$0.307415\pi$
$83$			14.9864i			1.64498i	−0.568782	+	0.822488i	$0.692585\pi$
$84$	3.77017	−	2.31179i	0.411359	−	0.252237i
$85$	2.43734	−	1.40720i	0.264366	−	0.152632i
$86$	0.378110	−	0.218302i	0.0407726	−	0.0235401i
$87$	−0.427478			−0.0458304
$88$	−0.371385	−	0.643258i	−0.0395898	−	0.0685715i
$89$		−	6.11094i		−	0.647759i	−0.946098	−	0.323879i	$-0.895013\pi$
$89$		−	6.11094i		−	0.647759i	0.946098	−	0.323879i	$-0.104987\pi$
$90$	1.81525			0.191344
$91$	−8.11528	+	5.01420i	−0.850713	+	0.525631i
$92$	7.57475			0.789722
$93$			8.63360i			0.895262i
$94$	2.82497	+	4.89298i	0.291373	+	0.504673i
$95$	−4.84953			−0.497552
$96$	4.70529	−	2.71660i	0.480232	−	0.277262i
$97$	11.3769	−	6.56845i	1.15515	−	0.666925i	0.205012	−	0.978759i	$-0.434277\pi$
$97$	11.3769	−	6.56845i	1.15515	−	0.666925i	0.950137	+	0.311834i	$0.100943\pi$
$98$	−0.212168	−	4.00613i	−0.0214322	−	0.404681i
$99$		−	0.352996i		−	0.0354774i
$100$	4.20591	−	7.28485i	0.420591	−	0.728485i
$101$	6.02344	+	10.4329i	0.599355	+	1.03811i	0.992916	+	0.118814i	$0.0379093\pi$
$101$	6.02344	+	10.4329i	0.599355	+	1.03811i	−0.393562	+	0.919298i	$0.628757\pi$
$102$	−0.441011	+	0.254618i	−0.0436666	+	0.0252109i
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	0.976615	+	0.214995i	$0.0689734\pi$
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	−0.302117	+	0.953271i	$0.597693\pi$
$104$	−6.55739	+	3.81571i	−0.643005	+	0.374161i
$105$	−3.99662	+	7.36570i	−0.390030	+	0.718819i
$106$	2.04969	+	1.18339i	0.199084	+	0.114941i
$107$	−5.13159			−0.496090			−0.248045	−	0.968749i	$-0.579788\pi$
$107$	−5.13159			−0.496090			−0.248045	+	0.968749i	$0.579788\pi$
$108$	1.67155			0.160845
$109$	0.865142	+	0.499490i	0.0828656	+	0.0478425i	0.540860	−	0.841112i	$-0.318099\pi$
$109$	0.865142	+	0.499490i	0.0828656	+	0.0478425i	−0.457995	+	0.888955i	$0.651432\pi$
$110$	0.554929	+	0.320388i	0.0529104	+	0.0305478i
$111$	2.88399	−	1.66507i	0.273736	−	0.158042i
$112$	0.149574	+	5.65245i	0.0141334	+	0.534106i
$113$	−1.46152	−	2.53143i	−0.137488	−	0.238137i	0.789057	−	0.614320i	$-0.210570\pi$
$113$	−1.46152	−	2.53143i	−0.137488	−	0.238137i	−0.926545	+	0.376183i	$0.877236\pi$
$114$	0.877474			0.0821829
$115$	−12.4303	+	7.17663i	−1.15913	+	0.669224i
$116$	0.357275	−	0.618818i	0.0331722	−	0.0574559i
$117$	−3.60553	+	0.0122653i	−0.333331	+	0.00113393i
$118$	−6.59657			−0.607264
$119$	−0.0621871	−	2.35007i	−0.00570069	−	0.215430i
$120$	−3.33239	+	5.77187i	−0.304204	+	0.526898i
$121$	−5.43770	+	9.41837i	−0.494336	+	0.856215i
$122$	7.52233	+	4.34302i	0.681040	+	0.393198i
$123$			5.47142i			0.493341i
$124$	−12.4980	−	7.21574i	−1.12236	−	0.647993i
$125$			0.102477i			0.00916579i
$126$	0.723147	−	1.33275i	0.0644231	−	0.118731i
$127$	−7.80251	+	13.5143i	−0.692361	+	1.19920i	0.278701	+	0.960378i	$0.410096\pi$
$127$	−7.80251	+	13.5143i	−0.692361	+	1.19920i	−0.971062	+	0.238826i	$0.923237\pi$
$128$			11.5315i			1.01925i
$129$	−0.380909	+	0.659754i	−0.0335372	+	0.0580881i
$130$	3.25319	−	5.67922i	0.285324	−	0.498101i
$131$	−2.73134	−	4.73083i	−0.238639	−	0.413334i	0.721685	−	0.692221i	$-0.243368\pi$
$131$	−2.73134	−	4.73083i	−0.238639	−	0.413334i	−0.960324	+	0.278887i	$0.910034\pi$
$132$	0.510998	+	0.295025i	0.0444767	+	0.0256786i
$133$	−1.93192	+	3.56050i	−0.167519	+	0.308735i
$134$	2.68071	+	4.64312i	0.231578	+	0.401105i
$135$	−2.74304	+	1.58369i	−0.236083	+	0.136303i
$136$		−	1.86968i		−	0.160324i
$137$		−	15.7768i		−	1.34790i	−0.738777	−	0.673950i	$-0.764596\pi$
$137$		−	15.7768i		−	1.34790i	0.738777	−	0.673950i	$-0.235404\pi$
$138$	2.24913	−	1.29854i	0.191459	−	0.110539i
$139$	4.66230	+	8.07533i	0.395451	+	0.684941i	0.993159	−	0.116773i	$-0.0372550\pi$
$139$	4.66230	+	8.07533i	0.395451	+	0.684941i	−0.597708	+	0.801714i	$0.703922\pi$
$140$	−7.32234	−	11.9416i	−0.618851	−	1.00925i
$141$	−8.53765	−	4.92921i	−0.719000	−	0.415115i
$142$	3.56634	+	6.17709i	0.299281	+	0.518370i
$143$	−1.10439	−	0.632619i	−0.0923535	−	0.0529023i
$144$	−1.06859	+	1.85085i	−0.0890488	+	0.154237i
$145$			1.35399i			0.112443i
$146$	1.94858	−	3.37504i	0.161266	−	0.279321i
$147$	3.81571	+	5.86859i	0.314714	+	0.484033i
$148$			5.56650i			0.457564i
$149$	−2.42918	−	1.40249i	−0.199006	−	0.114896i	0.397186	−	0.917738i	$-0.369987\pi$
$149$	−2.42918	−	1.40249i	−0.199006	−	0.114896i	−0.596192	+	0.802842i	$0.703320\pi$
$150$		−	2.88408i		−	0.235484i
$151$	−17.5134	−	10.1114i	−1.42522	−	0.822853i	−0.428484	−	0.903549i	$-0.640952\pi$
$151$	−17.5134	−	10.1114i	−1.42522	−	0.822853i	−0.996739	+	0.0806967i	$0.974285\pi$
$152$	−1.61084	+	2.79006i	−0.130657	+	0.226304i
$153$	0.444277	−	0.769510i	0.0359176	−	0.0622112i
$154$	0.456296	−	0.279792i	0.0367694	−	0.0225462i
$155$	27.3460			2.19648
$156$	2.99565	−	5.22963i	0.239844	−	0.418705i
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	−0.758398	−	0.651791i	$-0.774018\pi$
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	0.943667	+	0.330897i	$0.107351\pi$
$158$	3.46117	−	1.99831i	0.275356	−	0.158977i
$159$	−4.12974			−0.327510
$160$	−8.60454	−	14.9035i	−0.680249	−	1.17823i
$161$	0.317151	+	11.9852i	0.0249950	+	0.944568i
$162$	0.496325	−	0.286553i	0.0389950	−	0.0225138i
$163$	2.82608	+	1.63164i	0.221355	+	0.127800i	0.606578	−	0.795024i	$-0.292542\pi$
$163$	2.82608	+	1.63164i	0.221355	+	0.127800i	−0.385222	+	0.922824i	$0.625875\pi$
$164$	−7.92044	−	4.57287i	−0.618483	−	0.357081i
$165$	−1.11808			−0.0870420
$166$	−8.58883			−0.666623
$167$	20.9079	+	12.0712i	1.61790	+	0.934096i	0.987462	+	0.157859i	$0.0504591\pi$
$167$	20.9079	+	12.0712i	1.61790	+	0.934096i	0.630441	+	0.776238i	$0.282874\pi$
$168$	2.91014	+	4.74598i	0.224522	+	0.366161i
$169$	−6.42325	+	11.3023i	−0.494096	+	0.869407i
$170$	0.806474	+	1.39685i	0.0618537	+	0.107134i
$171$	−1.32596	+	0.765541i	−0.101398	+	0.0585424i
$172$	−0.636708	−	1.10281i	−0.0485486	−	0.0840886i
$173$	9.59569	−	16.6202i	0.729547	−	1.26361i	−0.227528	−	0.973772i	$-0.573064\pi$
$173$	9.59569	−	16.6202i	0.729547	−	1.26361i	0.957075	−	0.289841i	$-0.0936024\pi$
$174$		−	0.244990i		−	0.0185727i
$175$	11.7026	+	6.34984i	0.884636	+	0.480002i
$176$	−0.653341	+	0.377206i	−0.0492474	+	0.0284330i
$177$	9.96812	−	5.75510i	0.749250	−	0.432580i
$178$	3.50222			0.262503
$179$	11.3937	+	19.7345i	0.851608	+	1.47503i	0.879756	+	0.475425i	$0.157706\pi$
$179$	11.3937	+	19.7345i	0.851608	+	1.47503i	−0.0281482	+	0.999604i	$0.508961\pi$
$180$		−	5.29445i		−	0.394625i
$181$	1.32420			0.0984270			0.0492135	−	0.998788i	$-0.484329\pi$
$181$	1.32420			0.0984270			0.0492135	+	0.998788i	$0.484329\pi$
$182$	−2.87367	−	4.65092i	−0.213011	−	0.344749i
$183$	−15.1561			−1.12037
$184$			9.53529i			0.702951i
$185$	−5.27394	−	9.13472i	−0.387747	−	0.671598i
$186$	−4.94797			−0.362803
$187$	0.271634	−	0.156828i	0.0198638	−	0.0114684i
$188$	14.2711	−	8.23942i	1.04083	−	0.600921i
$189$	0.0699870	+	2.64483i	0.00509080	+	0.192383i
$190$		−	2.77930i		−	0.201632i
$191$	3.88818	−	6.73453i	0.281339	−	0.487293i	−0.690376	−	0.723451i	$-0.742555\pi$
$191$	3.88818	−	6.73453i	0.281339	−	0.487293i	0.971715	+	0.236158i	$0.0758882\pi$
$192$	−0.580269	−	1.00506i	−0.0418773	−	0.0725336i
$193$	−9.50295	+	5.48653i	−0.684037	+	0.394929i	−0.801374	−	0.598163i	$-0.795897\pi$
$193$	−9.50295	+	5.48653i	−0.684037	+	0.394929i	0.117337	+	0.993092i	$0.462564\pi$
$194$	3.76442	+	6.52017i	0.270270	+	0.468121i
$195$	0.0388491	+	11.4201i	0.00278204	+	0.817812i
$196$	−11.6845	+	0.618818i	−0.834605	+	0.0442013i
$197$	5.20917	+	3.00752i	0.371138	+	0.214277i	0.673955	−	0.738772i	$-0.264594\pi$
$197$	5.20917	+	3.00752i	0.371138	+	0.214277i	−0.302818	+	0.953049i	$0.597927\pi$
$198$	0.202304			0.0143771
$199$	14.8254			1.05095			0.525473	−	0.850811i	$-0.323889\pi$
$199$	14.8254			1.05095			0.525473	+	0.850811i	$0.323889\pi$
$200$	9.17036	+	5.29451i	0.648443	+	0.374379i
$201$	−8.10167	−	4.67750i	−0.571448	−	0.329926i
$202$	−5.97917	+	3.45207i	−0.420693	+	0.242887i
$203$	0.994091	+	0.539392i	0.0697715	+	0.0378579i
$204$	0.742630	+	1.28627i	0.0519945	+	0.0900571i
$205$	17.3301			1.21039
$206$	−6.79510	+	3.92315i	−0.473437	+	0.273339i
$207$	−2.26579	+	3.92446i	−0.157483	+	0.272769i
$208$	3.87552	+	6.66017i	0.268719	+	0.461800i
$209$	−0.540466			−0.0373848
$210$	−4.22133	−	2.29049i	−0.291300	−	0.158059i
$211$	−10.3820	+	17.9821i	−0.714725	+	1.23794i	0.248340	+	0.968673i	$0.420115\pi$
$211$	−10.3820	+	17.9821i	−0.714725	+	1.23794i	−0.963065	+	0.269267i	$0.913218\pi$
$212$	3.45153	−	5.97823i	0.237052	−	0.410586i
$213$	−10.7783	−	6.22283i	−0.738514	−	0.426381i
$214$		−	2.94095i		−	0.201039i
$215$	2.08970	+	1.20649i	0.142516	+	0.0822818i
$216$			2.10419i			0.143172i
$217$	10.8939	−	20.0773i	0.739526	−	1.36293i
$218$	−0.286261	+	0.495819i	−0.0193880	+	0.0335811i
$219$			6.80007i			0.459506i
$220$	0.934459	−	1.61853i	0.0630012	−	0.109121i
$221$	−1.61129	−	2.76904i	−0.108387	−	0.186266i
$222$	0.954265	+	1.65284i	0.0640461	+	0.110931i
$223$	−6.16220	−	3.55775i	−0.412652	−	0.238244i	0.279277	−	0.960211i	$-0.409905\pi$
$223$	−6.16220	−	3.55775i	−0.412652	−	0.238244i	−0.691928	+	0.721966i	$0.743239\pi$
$224$	−14.3699	+	0.380254i	−0.960128	+	0.0254068i
$225$	2.51618	+	4.35815i	0.167745	+	0.290543i
$226$	1.45078	−	0.837607i	0.0965043	−	0.0557168i
$227$			3.70996i			0.246239i	0.992392	+	0.123119i	$0.0392898\pi$
$227$			3.70996i			0.246239i	−0.992392	+	0.123119i	$0.960710\pi$
$228$		−	2.55928i		−	0.169492i
$229$	11.3004	−	6.52429i	0.746751	−	0.431137i	−0.0777675	−	0.996972i	$-0.524779\pi$
$229$	11.3004	−	6.52429i	0.746751	−	0.431137i	0.824519	+	0.565834i	$0.191446\pi$
$230$	−4.11297	−	7.12388i	−0.271202	−	0.469735i
$231$	−0.445411	+	0.820885i	−0.0293059	+	0.0540102i
$232$	0.778985	+	0.449747i	0.0511429	+	0.0295273i
$233$	−8.10047	−	14.0304i	−0.530679	−	0.919164i	−0.999359	−	0.0357956i	$-0.988603\pi$
$233$	−8.10047	−	14.0304i	−0.530679	−	0.919164i	0.468680	−	0.883368i	$-0.344730\pi$
$234$	−0.00702935	−	2.06635i	−0.000459523	−	0.135082i
$235$	−15.6127	+	27.0421i	−1.01846	+	1.76403i
$236$			19.2399i			1.25241i
$237$	−3.48680	+	6.03932i	−0.226492	+	0.392296i
$238$	1.34684	−	0.0356399i	0.0873026	−	0.00231019i
$239$		−	14.4871i		−	0.937093i	−0.883439	−	0.468547i	$-0.844778\pi$
$239$		−	14.4871i		−	0.937093i	0.883439	−	0.468547i	$-0.155222\pi$
$240$	5.86235	+	3.38463i	0.378413	+	0.218477i
$241$		−	20.6501i		−	1.33019i	−0.746758	−	0.665096i	$-0.768391\pi$
$241$		−	20.6501i		−	1.33019i	0.746758	−	0.665096i	$-0.231609\pi$
$242$	−5.39773	−	3.11638i	−0.346979	−	0.200329i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	12.6670	−	21.9400i	0.810924	−	1.40456i
$245$	18.5881	−	12.0858i	1.18755	−	0.772136i
$246$	−3.13571			−0.199925
$247$	0.0187793	+	5.52036i	0.00119490	+	0.351252i
$248$	9.08336	−	15.7328i	0.576794	−	0.999037i
$249$	12.9786	−	7.49322i	0.822488	−	0.474864i
$250$	−0.0587300			−0.00371441
$251$	−12.9380	−	22.4093i	−0.816642	−	1.41447i	−0.908143	−	0.418660i	$-0.862500\pi$
$251$	−12.9380	−	22.4093i	−0.816642	−	1.41447i	0.0915012	−	0.995805i	$-0.470833\pi$
$252$	−3.88715	−	2.10916i	−0.244868	−	0.132865i
$253$	−1.38532	+	0.799814i	−0.0870942	+	0.0502838i
$254$	−7.74516	−	4.47167i	−0.485975	−	0.280578i
$255$	−2.43734	−	1.40720i	−0.152632	−	0.0881221i
$256$	−4.28772			−0.267982
$257$	−1.89069			−0.117938			−0.0589689	−	0.998260i	$-0.518781\pi$
$257$	−1.89069			−0.117938			−0.0589689	+	0.998260i	$0.518781\pi$
$258$	−0.378110	−	0.218302i	−0.0235401	−	0.0135909i
$259$	−8.80766	+	0.233067i	−0.547281	+	0.0144821i
$260$	−16.5643	−	9.48840i	−1.02727	−	0.588446i
$261$	0.213739	+	0.370207i	0.0132301	+	0.0229152i
$262$	2.71127	−	1.56535i	0.167503	−	0.0967077i
$263$	−3.04658	−	5.27683i	−0.187860	−	0.325384i	0.756676	−	0.653790i	$-0.226822\pi$
$263$	−3.04658	−	5.27683i	−0.187860	−	0.325384i	−0.944537	+	0.328406i	$0.893489\pi$
$264$	−0.371385	+	0.643258i	−0.0228572	+	0.0395898i
$265$			13.0805i			0.803529i
$266$	−2.04055	−	1.10720i	−0.125114	−	0.0678867i
$267$	−5.29223	+	3.05547i	−0.323879	+	0.186992i
$268$	13.5423	−	7.81868i	0.827230	−	0.477602i
$269$	−1.40409			−0.0856087			−0.0428043	−	0.999083i	$-0.513629\pi$
$269$	−1.40409			−0.0856087			−0.0428043	+	0.999083i	$0.513629\pi$
$270$	−0.907626	−	1.57205i	−0.0552364	−	0.0956722i
$271$		−	13.2620i		−	0.805608i	−0.915286	−	0.402804i	$-0.868036\pi$
$271$		−	13.2620i		−	0.805608i	0.915286	−	0.402804i	$-0.131964\pi$
$272$	−1.89899			−0.115143
$273$	8.40006	+	4.52094i	0.508395	+	0.273620i
$274$	9.04177			0.546233
$275$			1.77640i			0.107121i
$276$	−3.78737	−	6.55992i	−0.227973	−	0.394861i
$277$	16.8899			1.01481			0.507407	−	0.861706i	$-0.330604\pi$
$277$	16.8899			1.01481			0.507407	+	0.861706i	$0.330604\pi$
$278$	−4.62803	+	2.67199i	−0.277571	+	0.160256i
$279$	7.47692	−	4.31680i	0.447631	−	0.258440i
$280$	15.0324	−	9.21755i	0.898356	−	0.550854i
$281$		−	22.5550i		−	1.34552i	−0.739860	−	0.672761i	$-0.765108\pi$
$281$		−	22.5550i		−	1.34552i	0.739860	−	0.672761i	$-0.234892\pi$
$282$	2.82497	−	4.89298i	0.168224	−	0.291373i
$283$	−0.399128	−	0.691311i	−0.0237257	−	0.0410941i	0.853919	−	0.520406i	$-0.174220\pi$
$283$	−0.399128	−	0.691311i	−0.0237257	−	0.0410941i	−0.877644	+	0.479312i	$0.840886\pi$
$284$	18.0164	−	10.4018i	1.06908	−	0.617231i
$285$	2.42477	+	4.19982i	0.143631	+	0.248776i
$286$	0.362558	−	0.632932i	0.0214385	−	0.0374261i
$287$	6.90385	−	12.7237i	0.407521	−	0.751054i
$288$	−4.70529	−	2.71660i	−0.277262	−	0.160077i
$289$	−16.2105			−0.953557
$290$	−0.775980			−0.0455671
$291$	−11.3769	−	6.56845i	−0.666925	−	0.385049i
$292$	−9.84380	−	5.68332i	−0.576065	−	0.332591i
$293$	−26.6711	+	15.3986i	−1.55814	+	0.899593i	−0.560706	+	0.828015i	$0.689470\pi$
$293$	−26.6711	+	15.3986i	−1.55814	+	0.899593i	−0.997435	+	0.0715779i	$0.977197\pi$
$294$	−3.36333	+	2.18681i	−0.196153	+	0.127537i
$295$	−18.2286	−	31.5729i	−1.06131	−	1.83825i
$296$	−7.00726			−0.407289
$297$	−0.305703	+	0.176498i	−0.0177387	+	0.0102414i
$298$	0.803774	−	1.39218i	0.0465614	−	0.0806467i
$299$	8.21750	+	14.1220i	0.475230	+	0.816694i
$300$	−8.41182			−0.485657
$301$	1.71828	−	1.05361i	0.0990398	−	0.0607292i
$302$	5.79490	−	10.0371i	0.333459	−	0.577568i
$303$	6.02344	−	10.4329i	0.346037	−	0.599355i
$304$	2.83380	+	1.63609i	0.162529	+	0.0938364i
$305$			48.0051i			2.74877i
$306$	0.441011	+	0.254618i	0.0252109	+	0.0145555i
$307$			21.4161i			1.22228i	0.791522	+	0.611140i	$0.209289\pi$
$307$			21.4161i			1.22228i	−0.791522	+	0.611140i	$0.790711\pi$
$308$	−0.816052	−	1.33085i	−0.0464989	−	0.0758324i
$309$	6.84541	−	11.8566i	0.389422	−	0.674498i
$310$			15.6722i			0.890119i
$311$	−9.69378	+	16.7901i	−0.549684	+	0.952081i	0.448612	+	0.893727i	$0.351919\pi$
$311$	−9.69378	+	16.7901i	−0.549684	+	0.952081i	−0.998296	+	0.0583541i	$0.981415\pi$
$312$	6.58320	+	3.77101i	0.372700	+	0.213491i
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	0.954104	−	0.299476i	$-0.0968117\pi$
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	−0.736405	+	0.676540i	$0.763478\pi$
$314$	2.30435	+	1.33041i	0.130042	+	0.0750796i
$315$	8.37719	−	0.221676i	0.472001	−	0.0124900i
$316$	−5.82836	−	10.0950i	−0.327871	−	0.567889i
$317$	−12.7818	+	7.37956i	−0.717896	+	0.414477i	−0.813978	−	0.580896i	$-0.802702\pi$
$317$	−12.7818	+	7.37956i	−0.717896	+	0.414477i	0.0960819	+	0.995373i	$0.469369\pi$
$318$		−	2.36678i		−	0.132723i
$319$			0.150898i			0.00844866i
$320$	−3.18340	+	1.83794i	−0.177958	+	0.102744i
$321$	2.56579	+	4.44409i	0.143209	+	0.248045i
$322$	−6.86881	+	0.181761i	−0.382784	+	0.0101292i
$323$	−1.17818	−	0.680224i	−0.0655558	−	0.0378487i
$324$	−0.835774	−	1.44760i	−0.0464319	−	0.0804224i
$325$	18.1443	−	0.0617235i	1.00646	−	0.00342381i
$326$	−0.935102	+	1.61964i	−0.0517905	+	0.0897038i
$327$		−	0.998980i		−	0.0552437i
$328$	5.75645	−	9.97046i	0.317847	−	0.550527i
$329$	13.6344	+	22.2356i	0.751691	+	1.22589i
$330$		−	0.640776i		−	0.0352736i
$331$	1.43371	+	0.827754i	0.0788040	+	0.0454975i	0.538884	−	0.842380i	$-0.318846\pi$
$331$	1.43371	+	0.827754i	0.0788040	+	0.0454975i	−0.460080	+	0.887877i	$0.652179\pi$
$332$			25.0506i			1.37483i
$333$	−2.88399	−	1.66507i	−0.158042	−	0.0912455i
$334$	−6.91808	+	11.9825i	−0.378540	+	0.655651i
$335$	−14.8155	+	25.6612i	−0.809456	+	1.40202i
$336$	4.82038	−	2.95576i	0.262973	−	0.161250i
$337$	−2.88666			−0.157246			−0.0786231	−	0.996904i	$-0.525052\pi$
$337$	−2.88666			−0.157246			−0.0786231	+	0.996904i	$0.525052\pi$
$338$	−6.47742	−	3.68121i	−0.352325	−	0.200231i
$339$	−1.46152	+	2.53143i	−0.0793789	+	0.137488i
$340$	4.07413	−	2.35220i	0.220950	−	0.127566i
$341$	3.04762			0.165038
$342$	−0.438737	−	0.759914i	−0.0237242	−	0.0410915i
$343$	−1.46836	−	18.4620i	−0.0792837	−	0.996852i
$344$	1.38825	−	0.801505i	0.0748493	−	0.0432143i
$345$	12.4303	+	7.17663i	0.669224	+	0.386377i
$346$	9.52517	+	5.49936i	0.512076	+	0.295647i
$347$	−29.0876			−1.56151			−0.780753	−	0.624840i	$-0.785164\pi$
$347$	−29.0876			−1.56151			−0.780753	+	0.624840i	$0.785164\pi$
$348$	−0.714550			−0.0383039
$349$	−15.8747	−	9.16529i	−0.849756	−	0.490607i	0.0108128	−	0.999942i	$-0.496558\pi$
$349$	−15.8747	−	9.16529i	−0.849756	−	0.490607i	−0.860568	+	0.509335i	$0.829891\pi$
$350$	−3.63913	+	6.70686i	−0.194520	+	0.358497i
$351$	1.81339	+	3.11635i	0.0967915	+	0.166338i
$352$	−0.958950	−	1.66095i	−0.0511122	−	0.0885289i
$353$	6.19062	−	3.57415i	0.329493	−	0.190233i	−0.326123	−	0.945327i	$-0.605742\pi$
$353$	6.19062	−	3.57415i	0.329493	−	0.190233i	0.655616	+	0.755094i	$0.272409\pi$
$354$	3.29829	+	5.71280i	0.175302	+	0.303632i
$355$	−19.7101	+	34.1389i	−1.04610	+	1.81191i
$356$		−	10.2147i		−	0.541380i
$357$	−2.00412	+	1.22889i	−0.106070	+	0.0650397i
$358$	−11.3100	+	6.52983i	−0.597752	+	0.345112i
$359$	13.0092	−	7.51088i	0.686601	−	0.396409i	−0.115737	−	0.993280i	$-0.536923\pi$
$359$	13.0092	−	7.51088i	0.686601	−	0.396409i	0.802337	+	0.596871i	$0.203590\pi$
$360$	6.66479			0.351265
$361$	−8.32789	−	14.4243i	−0.438310	−	0.759175i
$362$			0.758908i			0.0398873i
$363$	10.8754			0.570810
$364$	−13.5651	+	8.38147i	−0.711004	+	0.439309i
$365$	21.5385			1.12737
$366$		−	8.68604i		−	0.454026i
$367$	2.02451	+	3.50655i	0.105678	+	0.183040i	0.914015	−	0.405680i	$-0.132965\pi$
$367$	2.02451	+	3.50655i	0.105678	+	0.183040i	−0.808337	+	0.588720i	$0.799632\pi$
$368$	9.68476			0.504853
$369$	4.73839	−	2.73571i	0.246671	−	0.142415i
$370$	5.23517	−	3.02253i	0.272164	−	0.157134i
$371$	9.60363	+	5.21092i	0.498596	+	0.270537i
$372$			14.4315i			0.748237i
$373$	−9.50471	+	16.4626i	−0.492135	+	0.852403i	−0.999959	−	0.00905764i	$-0.997117\pi$
$373$	−9.50471	+	16.4626i	−0.492135	+	0.852403i	0.507824	+	0.861461i	$0.330450\pi$
$374$	0.0898790	+	0.155675i	0.00464753	+	0.00804977i
$375$	0.0887474	−	0.0512383i	0.00458289	−	0.00264593i
$376$	10.3720	+	17.9648i	0.534895	+	0.926465i
$377$	1.54128	−	0.00524316i	0.0793802	−	0.000270037i
$378$	−1.51577	+	0.0401100i	−0.0779627	+	0.00206304i
$379$	14.4405	+	8.33722i	0.741758	+	0.428254i	0.822708	−	0.568464i	$-0.192462\pi$
$379$	14.4405	+	8.33722i	0.741758	+	0.428254i	−0.0809502	+	0.996718i	$0.525795\pi$
$380$	−8.10623			−0.415841
$381$	15.6050			0.799469
$382$	3.85960	+	2.22834i	0.197474	+	0.114012i
$383$	7.48326	+	4.32046i	0.382377	+	0.220765i	0.678852	−	0.734275i	$-0.262478\pi$
$383$	7.48326	+	4.32046i	0.382377	+	0.220765i	−0.296475	+	0.955041i	$0.595811\pi$
$384$	9.98659	−	5.76576i	0.509626	−	0.294233i
$385$	2.60006	+	1.41079i	0.132511	+	0.0719005i
$386$	−3.14437	−	5.44620i	−0.160044	−	0.277204i
$387$	0.761819			0.0387254
$388$	19.0170	−	10.9795i	0.965443	−	0.557399i
$389$	3.54047	−	6.13227i	0.179509	−	0.310918i	−0.762204	−	0.647337i	$-0.775883\pi$
$389$	3.54047	−	6.13227i	0.179509	−	0.310918i	0.941712	+	0.336419i	$0.109216\pi$
$390$	−6.54495	+	0.0222647i	−0.331416	+	0.00112742i
$391$	−4.02654			−0.203631
$392$	−0.778985	−	14.7087i	−0.0393447	−	0.742902i
$393$	−2.73134	+	4.73083i	−0.137778	+	0.238639i
$394$	−1.72363	+	2.98541i	−0.0868351	+	0.150403i
$395$	19.1289	+	11.0441i	0.962478	+	0.555687i
$396$		−	0.590050i		−	0.0296511i
$397$	−18.7486	−	10.8245i	−0.940964	−	0.543266i	−0.0507018	−	0.998714i	$-0.516146\pi$
$397$	−18.7486	−	10.8245i	−0.940964	−	0.543266i	−0.890262	+	0.455448i	$0.849479\pi$
$398$			8.49654i			0.425893i
$399$	4.04945	−	0.107156i	0.202726	−	0.00536450i
$400$	5.37750	−	9.31411i	0.268875	−	0.465705i
$401$			14.7595i			0.737053i	0.929617	+	0.368527i	$0.120138\pi$
$401$			14.7595i			0.737053i	−0.929617	+	0.368527i	$0.879862\pi$
$402$	2.68071	−	4.64312i	0.133702	−	0.231578i
$403$	−0.105894	−	31.1287i	−0.00527496	−	1.55063i
$404$	10.0685	+	17.4391i	0.500925	+	0.867628i
$405$	2.74304	+	1.58369i	0.136303	+	0.0786944i
$406$	−0.309129	+	0.569720i	−0.0153418	+	0.0282747i
$407$	−0.587764	−	1.01804i	−0.0291344	−	0.0504622i
$408$	−1.61919	+	0.934842i	−0.0801620	+	0.0462816i
$409$		−	17.5127i		−	0.865948i	−0.901406	−	0.432974i	$-0.857464\pi$
$409$		−	17.5127i		−	0.865948i	0.901406	−	0.432974i	$-0.142536\pi$
$410$			9.93200i			0.490507i
$411$	−13.6631	+	7.88838i	−0.673950	+	0.389105i
$412$	11.4424	+	19.8189i	0.563729	+	0.976406i
$413$	−30.4425	+	0.805564i	−1.49798	+	0.0396392i
$414$	−2.24913	−	1.29854i	−0.110539	−	0.0638197i
$415$	−23.7340	−	41.1084i	−1.16505	−	2.01793i
$416$	−16.9318	+	9.85251i	−0.830148	+	0.483059i
$417$	4.66230	−	8.07533i	0.228314	−	0.395451i
$418$		−	0.309745i		−	0.0151501i
$419$	15.4087	−	26.6887i	0.752764	−	1.30383i	−0.193714	−	0.981058i	$-0.562053\pi$
$419$	15.4087	−	26.6887i	0.752764	−	1.30383i	0.946478	−	0.322768i	$-0.104613\pi$
$420$	−6.68054	+	12.3121i	−0.325977	+	0.600770i
$421$		−	29.3681i		−	1.43131i	−0.698452	−	0.715657i	$-0.746127\pi$
$421$		−	29.3681i		−	1.43131i	0.698452	−	0.715657i	$-0.253873\pi$
$422$	−10.3057	−	5.94998i	−0.501672	−	0.289641i
$423$			9.85843i			0.479333i
$424$	7.52555	+	4.34488i	0.365473	+	0.211006i
$425$	−2.23576	+	3.87244i	−0.108450	+	0.187841i
$426$	3.56634	−	6.17709i	0.172790	−	0.299281i
$427$	35.2451	+	19.1239i	1.70563	+	0.925473i
$428$	−8.57770			−0.414619
$429$	0.00432961	+	1.27274i	0.000209036	+	0.0614483i
$430$	−0.691446	+	1.19762i	−0.0333445	+	0.0577544i
$431$	−18.4400	+	10.6463i	−0.888224	+	0.512816i	−0.873361	−	0.487073i	$-0.838064\pi$
$431$	−18.4400	+	10.6463i	−0.888224	+	0.512816i	−0.0148626	+	0.999890i	$0.504731\pi$
$432$	2.13717			0.102825
$433$	8.80166	+	15.2449i	0.422981	+	0.732624i	0.996229	−	0.0867574i	$-0.0276505\pi$
$433$	8.80166	+	15.2449i	0.422981	+	0.732624i	−0.573249	+	0.819381i	$0.694317\pi$
$434$	11.5064	+	6.24336i	0.552325	+	0.299691i
$435$	1.17259	−	0.676994i	0.0562213	−	0.0324594i
$436$	1.44613	+	0.834922i	0.0692569	+	0.0399855i
$437$	6.00867	+	3.46911i	0.287434	+	0.165950i
$438$	−3.89716			−0.186214
$439$	22.8133			1.08882			0.544409	−	0.838820i	$-0.316754\pi$
$439$	22.8133			1.08882			0.544409	+	0.838820i	$0.316754\pi$
$440$	2.03745	+	1.17632i	0.0971315	+	0.0560789i
$441$	3.17449	−	6.23880i	0.151166	−	0.297086i
$442$	1.58696	−	0.923442i	0.0754838	−	0.0439236i
$443$	−19.5291	−	33.8254i	−0.927857	−	1.60709i	−0.786901	−	0.617079i	$-0.788316\pi$
$443$	−19.5291	−	33.8254i	−0.927857	−	1.60709i	−0.140955	−	0.990016i	$-0.545017\pi$
$444$	4.82073	−	2.78325i	0.228782	−	0.132087i
$445$	9.67787	+	16.7626i	0.458775	+	0.794621i
$446$	2.03897	−	3.53160i	0.0965480	−	0.167226i
$447$			2.80497i			0.132671i
$448$	0.0812225	+	3.06942i	0.00383740	+	0.145016i
$449$	−10.3848	+	5.99568i	−0.490090	+	0.282954i	−0.724612	−	0.689157i	$-0.757981\pi$
$449$	−10.3848	+	5.99568i	−0.490090	+	0.282954i	0.234522	+	0.972111i	$0.424648\pi$
$450$	−2.49768	+	1.44204i	−0.117742	+	0.0679783i
$451$	1.93139			0.0909455
$452$	−2.44300	−	4.23140i	−0.114909	−	0.199029i
$453$			20.2228i			0.950148i
$454$	−2.12620			−0.0997876
$455$	14.3196	−	26.6063i	0.671313	−	1.24732i
$456$	3.22169			0.150869
$457$		−	2.49129i		−	0.116538i	−0.998301	−	0.0582689i	$-0.981442\pi$
$457$		−	2.49129i		−	0.116538i	0.998301	−	0.0582689i	$-0.0185581\pi$
$458$	3.73911	+	6.47633i	0.174717	+	0.302619i
$459$	−0.888553			−0.0414741
$460$	−20.7778	+	11.9961i	−0.968771	+	0.559320i
$461$	−28.0132	+	16.1734i	−1.30471	+	0.753273i	−0.981207	−	0.192956i	$-0.938193\pi$
$461$	−28.0132	+	16.1734i	−1.30471	+	0.753273i	−0.323499	+	0.946228i	$0.604859\pi$
$462$	−0.470454	−	0.255268i	−0.0218875	−	0.0118761i
$463$			23.4856i			1.09147i	0.837958	+	0.545735i	$0.183749\pi$
$463$			23.4856i			1.09147i	−0.837958	+	0.545735i	$0.816251\pi$
$464$	0.456797	−	0.791195i	0.0212063	−	0.0367303i
$465$	−13.6730	−	23.6823i	−0.634069	−	1.09824i
$466$	8.04093	−	4.64243i	0.372489	−	0.215057i
$467$	−1.27155	−	2.20240i	−0.0588405	−	0.101915i	0.835105	−	0.550091i	$-0.185407\pi$
$467$	−1.27155	−	2.20240i	−0.0588405	−	0.101915i	−0.893945	+	0.448176i	$0.852074\pi$
$468$	−6.02682	+	0.0205021i	−0.278590	+	0.000947711i
$469$	12.9382	+	21.1002i	0.597430	+	0.974314i
$470$	−15.4980	−	8.94776i	−0.714869	−	0.412730i
$471$	−4.64282			−0.213930
$472$	−24.2196			−1.11480
$473$	0.232891	+	0.134459i	0.0107083	+	0.00618245i
$474$	−3.46117	−	1.99831i	−0.158977	−	0.0917854i
$475$	6.67268	−	3.85247i	0.306164	−	0.176764i
$476$	−0.103949	−	3.92825i	−0.00476449	−	0.180051i
$477$	2.06487	+	3.57646i	0.0945439	+	0.163755i
$478$	8.30266			0.379755
$479$	−16.9874	+	9.80768i	−0.776174	+	0.448124i	−0.835073	−	0.550140i	$-0.814574\pi$
$479$	−16.9874	+	9.80768i	−0.776174	+	0.448124i	0.0588986	+	0.998264i	$0.481241\pi$
$480$	−8.60454	+	14.9035i	−0.392742	+	0.680249i
$481$	−10.3779	+	6.03885i	−0.473191	+	0.275348i
$482$	11.8347			0.539057
$483$	10.2209	−	6.26727i	0.465069	−	0.285171i
$484$	−9.08938	+	15.7433i	−0.413153	+	0.715603i
$485$	−20.8048	+	36.0350i	−0.944699	+	1.63627i
$486$	−0.496325	−	0.286553i	−0.0225138	−	0.0129983i
$487$			3.52506i			0.159736i	0.996805	+	0.0798678i	$0.0254498\pi$
$487$			3.52506i			0.159736i	−0.996805	+	0.0798678i	$0.974550\pi$
$488$	27.6186	+	15.9456i	1.25024	+	0.721824i
$489$		−	3.26327i		−	0.147570i
$490$	6.92648	+	10.6530i	0.312906	+	0.481252i
$491$	−8.85905	+	15.3443i	−0.399803	+	0.692480i	−0.993701	−	0.112061i	$-0.964255\pi$
$491$	−8.85905	+	15.3443i	−0.399803	+	0.692480i	0.593898	+	0.804540i	$0.297588\pi$
$492$			9.14574i			0.412322i
$493$	−0.189918	+	0.328948i	−0.00855349	+	0.0148151i
$494$	−3.16376	+	0.0107625i	−0.142344	+	0.000484228i
$495$	0.559038	+	0.968281i	0.0251269	+	0.0435210i
$496$	−15.9795	−	9.22574i	−0.717499	−	0.414248i
$497$	17.2126	+	28.0711i	0.772092	+	1.25916i
$498$	4.29442	+	7.43815i	0.192437	+	0.333311i
$499$	10.2757	−	5.93271i	0.460006	−	0.265584i	−0.252041	−	0.967717i	$-0.581102\pi$
$499$	10.2757	−	5.93271i	0.460006	−	0.265584i	0.712047	+	0.702132i	$0.247768\pi$
$500$			0.171295i			0.00766053i
$501$		−	24.1424i		−	1.07860i
$502$	12.8429	−	7.41488i	0.573209	−	0.330942i
$503$	−12.6878	−	21.9759i	−0.565722	−	0.979858i	−0.996982	−	0.0776311i	$-0.975264\pi$
$503$	−12.6878	−	21.9759i	−0.565722	−	0.979858i	0.431261	−	0.902227i	$-0.358069\pi$
$504$	2.65507	−	4.89325i	0.118266	−	0.217963i
$505$	−33.0451	−	19.0786i	−1.47049	−	0.848985i
$506$	−0.458378	−	0.793935i	−0.0203774	−	0.0352947i
$507$	12.9997	−	0.0884461i	0.577337	−	0.00392803i
$508$	−13.0423	+	22.5899i	−0.578657	+	1.00226i
$509$			12.9314i			0.573174i	0.958054	+	0.286587i	$0.0925208\pi$
$509$			12.9314i			0.573174i	−0.958054	+	0.286587i	$0.907479\pi$
$510$	0.806474	−	1.39685i	0.0357113	−	0.0618537i
$511$	8.58034	−	15.8134i	0.379572	−	0.699544i
$512$			20.6057i			0.910653i
$513$	1.32596	+	0.765541i	0.0585424	+	0.0337995i
$514$		−	1.08357i		−	0.0477940i
$515$	−37.5545	−	21.6821i	−1.65485	−	0.955427i
$516$	−0.636708	+	1.10281i	−0.0280295	+	0.0485486i
$517$	−1.73999	+	3.01375i	−0.0765247	+	0.132545i
$518$	−0.133572	−	5.04773i	−0.00586883	−	0.221784i
$519$	−19.1914			−0.842408
$520$	11.9443	−	20.8515i	0.523790	−	0.914401i
$521$	11.6491	−	20.1769i	0.510357	−	0.883964i	−0.489571	−	0.871963i	$-0.662847\pi$
$521$	11.6491	−	20.1769i	0.510357	−	0.883964i	0.999928	−	0.0120008i	$-0.00382005\pi$
$522$	−0.212168	+	0.122495i	−0.00928634	+	0.00536147i
$523$	15.3596			0.671627			0.335813	−	0.941929i	$-0.390989\pi$
$523$	15.3596			0.671627			0.335813	+	0.941929i	$0.390989\pi$
$524$	−4.56557	−	7.90781i	−0.199448	−	0.345454i
$525$	−0.352199	−	13.3097i	−0.0153712	−	0.580883i
$526$	3.02419	−	1.74602i	0.131861	−	0.0761299i
$527$	6.64364	+	3.83571i	0.289401	+	0.167086i
$528$	0.653341	+	0.377206i	0.0284330	+	0.0164158i
$529$	−2.46483			−0.107167
$530$	−7.49652			−0.325628
$531$	−9.96812	−	5.75510i	−0.432580	−	0.249750i
$532$	−3.22930	+	5.95155i	−0.140008	+	0.258032i
$533$	−0.0671088	−	19.7274i	−0.00290681	−	0.854487i
$534$	−1.75111	−	3.03301i	−0.0757780	−	0.131251i
$535$	14.0762	−	8.12687i	0.608565	−	0.351355i
$536$	9.84235	+	17.0475i	0.425125	+	0.736338i
$537$	11.3937	−	19.7345i	0.491676	−	0.851608i
$538$		−	0.804692i		−	0.0346927i
$539$	2.07159	−	1.34693i	0.0892296	−	0.0580164i
$540$	−4.58512	+	2.64722i	−0.197312	+	0.113918i
$541$	27.6990	−	15.9920i	1.19087	−	0.687551i	0.232368	−	0.972628i	$-0.425353\pi$
$541$	27.6990	−	15.9920i	1.19087	−	0.687551i	0.958505	+	0.285077i	$0.0920193\pi$
$542$	7.60053			0.326471
$543$	−0.662100	−	1.14679i	−0.0284134	−	0.0492135i
$544$		−	4.82769i		−	0.206986i
$545$	−3.16416			−0.135538
$546$	−2.59098	+	4.81413i	−0.110884	+	0.206026i
$547$	−3.77706			−0.161496			−0.0807478	−	0.996735i	$-0.525731\pi$
$547$	−3.77706			−0.161496			−0.0807478	+	0.996735i	$0.525731\pi$
$548$		−	26.3716i		−	1.12654i
$549$	7.57803	+	13.1255i	0.323422	+	0.560184i
$550$	−1.01807			−0.0434105
$551$	0.566817	−	0.327252i	0.0241472	−	0.0139414i
$552$	8.25780	−	4.76765i	0.351475	−	0.202924i
$553$	15.7289	−	9.64465i	0.668861	−	0.410132i
$554$			9.67971i			0.411251i
$555$	−5.27394	+	9.13472i	−0.223866	+	0.387747i
$556$	7.79326	+	13.4983i	0.330508	+	0.572456i
$557$	4.77707	−	2.75804i	0.202411	−	0.116862i	−0.395369	−	0.918523i	$-0.629383\pi$
$557$	4.77707	−	2.75804i	0.202411	−	0.116862i	0.597780	+	0.801661i	$0.296050\pi$
$558$	2.47399	+	4.28507i	0.104732	+	0.181401i
$559$	1.36529	−	2.38344i	0.0577455	−	0.100809i
$560$	−9.36204	−	15.2680i	−0.395618	−	0.645191i
$561$	−0.271634	−	0.156828i	−0.0114684	−	0.00662127i
$562$	12.9264			0.545269
$563$	2.65222			0.111778			0.0558888	−	0.998437i	$-0.482201\pi$
$563$	2.65222			0.111778			0.0558888	+	0.998437i	$0.482201\pi$
$564$	−14.2711	−	8.23942i	−0.600921	−	0.346942i
$565$	8.01802	+	4.62920i	0.337321	+	0.194752i
$566$	0.396195	−	0.228743i	0.0166533	−	0.00961479i
$567$	2.25549	−	1.38302i	0.0947218	−	0.0580815i
$568$	13.0940	+	22.6795i	0.549412	+	0.951610i
$569$	29.6363			1.24242			0.621210	−	0.783644i	$-0.286641\pi$
$569$	29.6363			1.24242			0.621210	+	0.783644i	$0.286641\pi$
$570$	−2.40694	+	1.38965i	−0.100816	+	0.0582060i
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	−0.449854	−	0.893102i	$-0.648524\pi$
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	0.998376	−	0.0569662i	$-0.0181427\pi$
$572$	−1.84604	−	1.05745i	−0.0771867	−	0.0442144i
$573$	−7.77636			−0.324862
$574$	7.29202	+	3.95664i	0.304363	+	0.165147i
$575$	11.4022	−	19.7493i	0.475506	−	0.823601i
$576$	−0.580269	+	1.00506i	−0.0241779	+	0.0418773i
$577$	−24.6222	−	14.2157i	−1.02504	−	0.591806i	−0.109478	−	0.993989i	$-0.534918\pi$
$577$	−24.6222	−	14.2157i	−1.02504	−	0.591806i	−0.915559	+	0.402183i	$0.868251\pi$
$578$		−	9.29033i		−	0.386427i
$579$	9.50295	+	5.48653i	0.394929	+	0.228012i
$580$			2.26326i			0.0939767i
$581$	−39.6365	+	1.04886i	−1.64440	+	0.0435139i
$582$	3.76442	−	6.52017i	0.156040	−	0.270270i
$583$			1.45778i			0.0603751i
$584$	7.15431	−	12.3916i	0.296048	−	0.512769i
$585$	9.87069	−	5.74370i	0.408103	−	0.237473i
$586$	−8.82501	−	15.2854i	−0.364558	−	0.631433i
$587$	0.721765	+	0.416711i	0.0297904	+	0.0171995i	0.514821	−	0.857298i	$-0.327858\pi$
$587$	0.721765	+	0.416711i	0.0297904	+	0.0171995i	−0.485031	+	0.874497i	$0.661192\pi$
$588$	6.37815	+	9.80963i	0.263030	+	0.404543i
$589$	−6.60938	−	11.4478i	−0.272335	−	0.471697i
$590$	18.0947	−	10.4470i	0.744945	−	0.430094i
$591$		−	6.01503i		−	0.247425i
$592$			7.11710i			0.292511i
$593$	−23.9758	+	13.8424i	−0.984566	+	0.568440i	−0.903646	−	0.428281i	$-0.859119\pi$
$593$	−23.9758	+	13.8424i	−0.984566	+	0.568440i	−0.0809207	+	0.996721i	$0.525786\pi$
$594$	−0.101152	−	0.175201i	−0.00415032	−	0.00718857i
$595$	3.89237	+	6.34784i	0.159572	+	0.260236i
$596$	−4.06049	−	2.34432i	−0.166324	−	0.0960272i
$597$	−7.41270	−	12.8392i	−0.303382	−	0.525473i
$598$	−8.09339	+	4.70950i	−0.330963	+	0.192586i
$599$	12.4488	−	21.5620i	0.508645	−	0.881000i	−0.491304	−	0.870988i	$-0.663480\pi$
$599$	12.4488	−	21.5620i	0.508645	−	0.881000i	0.999950	−	0.0100118i	$-0.00318692\pi$
$600$		−	10.5890i		−	0.432295i
$601$	15.3339	−	26.5592i	0.625485	−	1.08337i	−0.362962	−	0.931804i	$-0.618235\pi$
$601$	15.3339	−	26.5592i	0.625485	−	1.08337i	0.988447	−	0.151568i	$-0.0484321\pi$
$602$	0.603833	+	0.984756i	0.0246104	+	0.0401356i
$603$			9.35501i			0.380965i
$604$	−29.2746	−	16.9017i	−1.19116	−	0.687719i
$605$		−	34.4466i		−	1.40045i
$606$	5.97917	+	3.45207i	0.242887	+	0.140231i
$607$	−4.11638	+	7.12977i	−0.167079	+	0.289388i	−0.937391	−	0.348278i	$-0.886767\pi$
$607$	−4.11638	+	7.12977i	−0.167079	+	0.289388i	0.770313	+	0.637666i	$0.220100\pi$
$608$	−4.15934	+	7.20419i	−0.168684	+	0.292169i
$609$	−0.0299179	−	1.13060i	−0.00121233	−	0.0458144i
$610$	−27.5121			−1.11393
$611$	30.8432	+	17.6677i	1.24778	+	0.714759i
$612$	0.742630	−	1.28627i	0.0300190	−	0.0519945i
$613$	−33.7573	+	19.4898i	−1.36344	+	0.787184i	−0.990080	−	0.140502i	$-0.955128\pi$
$613$	−33.7573	+	19.4898i	−1.36344	+	0.787184i	−0.373362	+	0.927686i	$0.621795\pi$
$614$	−12.2737			−0.495326
$615$	−8.66505	−	15.0083i	−0.349409	−	0.605194i
$616$	1.67531	−	1.02727i	0.0675003	−	0.0413898i
$617$	−39.3193	+	22.7010i	−1.58293	+	0.913907i	−0.588506	+	0.808493i	$0.700284\pi$
$617$	−39.3193	+	22.7010i	−1.58293	+	0.913907i	−0.994428	+	0.105414i	$0.966383\pi$
$618$	6.79510	+	3.92315i	0.273339	+	0.157812i
$619$	−20.2395	−	11.6853i	−0.813495	−	0.469672i	0.0346730	−	0.999399i	$-0.488961\pi$
$619$	−20.2395	−	11.6853i	−0.813495	−	0.469672i	−0.848168	+	0.529727i	$0.822294\pi$
$620$	45.7101			1.83576
$621$	4.53157			0.181846
$622$	−9.62253	−	5.55557i	−0.385828	−	0.222758i
$623$	16.1624	−	0.427686i	0.647532	−	0.0171349i
$624$	3.83012	−	6.68639i	0.153327	−	0.267670i
$625$	12.4186	+	21.5096i	0.496744	+	0.860385i
$626$	−3.82317	+	2.20731i	−0.152805	+	0.0882218i
$627$	0.270233	+	0.468057i	0.0107921	+	0.0186924i
$628$	3.88035	−	6.72096i	0.154843	−	0.268195i
$629$		−	2.95901i		−	0.117984i
$630$	0.127044	+	4.80102i	0.00506155	+	0.191277i
$631$	27.7776	−	16.0374i	1.10581	−	0.638439i	0.168069	−	0.985775i	$-0.446247\pi$
$631$	27.7776	−	16.0374i	1.10581	−	0.638439i	0.937741	+	0.347336i	$0.112914\pi$
$632$	12.7079	−	7.33689i	0.505492	−	0.291846i
$633$	20.7640			0.825293
$634$	−4.22927	−	7.32532i	−0.167966	−	0.290926i
$635$		−	49.4272i		−	1.96146i
$636$	−6.90306			−0.273724
$637$	−13.8296	−	21.1126i	−0.547950	−	0.836511i
$638$	−0.0864806			−0.00342380
$639$			12.4457i			0.492343i
$640$	−18.2624	−	31.6314i	−0.721885	−	1.25034i
$641$	−31.2142			−1.23289			−0.616444	−	0.787399i	$-0.711427\pi$
$641$	−31.2142			−1.23289			−0.616444	+	0.787399i	$0.711427\pi$
$642$	−2.54694	+	1.47047i	−0.100520	+	0.0580350i
$643$	−6.24367	+	3.60479i	−0.246226	+	0.142159i	−0.618035	−	0.786150i	$-0.712071\pi$
$643$	−6.24367	+	3.60479i	−0.246226	+	0.142159i	0.371809	+	0.928309i	$0.378738\pi$
$644$	0.530134	+	20.0339i	0.0208902	+	0.789446i
$645$		−	2.41298i		−	0.0950108i
$646$	0.389841	−	0.675224i	0.0153381	−	0.0265663i
$647$	11.5276	+	19.9664i	0.453196	+	0.784959i	0.998583	−	0.0532257i	$-0.0169503\pi$
$647$	11.5276	+	19.9664i	0.453196	+	0.784959i	−0.545386	+	0.838185i	$0.683617\pi$
$648$	1.82228	−	1.05209i	0.0715860	−	0.0413302i
$649$	−2.03153	−	3.51871i	−0.0797444	−	0.138121i
$650$	0.0353742	+	10.3986i	0.00138749	+	0.407868i
$651$	−22.8344	+	0.604239i	−0.894949	+	0.0236820i
$652$	4.72393	+	2.72736i	0.185003	+	0.106812i
$653$	−17.4861			−0.684284			−0.342142	−	0.939648i	$-0.611152\pi$
$653$	−17.4861			−0.684284			−0.342142	+	0.939648i	$0.611152\pi$
$654$	0.572522			0.0223874
$655$	14.9844	+	8.65123i	0.585488	+	0.338031i
$656$	−10.1267	−	5.84668i	−0.395383	−	0.228275i
$657$	5.88903	−	3.40003i	0.229753	−	0.132648i
$658$	−12.7434	+	7.81398i	−0.496789	+	0.304621i
$659$	20.2279	+	35.0357i	0.787967	+	1.36480i	0.927211	+	0.374540i	$0.122199\pi$
$659$	20.2279	+	35.0357i	0.787967	+	1.36480i	−0.139244	+	0.990258i	$0.544467\pi$
$660$	−1.86892			−0.0727475
$661$	−38.7038	+	22.3457i	−1.50540	+	0.869146i	−0.505424	+	0.862871i	$0.668664\pi$
$661$	−38.7038	+	22.3457i	−1.50540	+	0.869146i	−0.999980	+	0.00627497i	$0.998003\pi$
$662$	−0.474392	+	0.821670i	−0.0184378	+	0.0319351i
$663$	−1.59241	+	2.77994i	−0.0618442	+	0.107964i
$664$	−31.5343			−1.22377
$665$	−0.339404	−	12.8262i	−0.0131615	−	0.497378i
$666$	0.954265	−	1.65284i	0.0369770	−	0.0640461i
$667$	0.968574	−	1.67762i	0.0375033	−	0.0649577i
$668$	34.9486	+	20.1776i	1.35220	+	0.780694i
$669$			7.11550i			0.275101i
$670$	−14.7066	−	8.49085i	−0.568165	−	0.328030i
$671$			5.35002i			0.206535i
$672$	7.51425	+	12.2546i	0.289869	+	0.472730i
$673$	6.76618	−	11.7194i	0.260817	−	0.451748i	−0.705642	−	0.708568i	$-0.749341\pi$
$673$	6.76618	−	11.7194i	0.260817	−	0.451748i	0.966459	+	0.256820i	$0.0826748\pi$
$674$		−	1.65436i		−	0.0637237i
$675$	2.51618	−	4.35815i	0.0968477	−	0.167745i
$676$	−10.7368	+	18.8923i	−0.412953	+	0.726628i
$677$	16.7974	+	29.0939i	0.645575	+	1.11817i	0.984168	+	0.177237i	$0.0567158\pi$
$677$	16.7974	+	29.0939i	0.645575	+	1.11817i	−0.338593	+	0.940933i	$0.609951\pi$
$678$	−1.45078	−	0.837607i	−0.0557168	−	0.0321681i
$679$	18.1686	+	29.6302i	0.697249	+	1.13710i
$680$	2.96101	+	5.12862i	0.113549	+	0.196673i
$681$	3.21292	−	1.85498i	0.123119	−	0.0710829i
$682$			1.74661i			0.0668813i
$683$		−	41.2155i		−	1.57707i	−0.614992	−	0.788533i	$-0.710841\pi$
$683$		−	41.2155i		−	1.57707i	0.614992	−	0.788533i	$-0.289159\pi$
$684$	−2.21640	+	1.27964i	−0.0847462	+	0.0489282i
$685$	24.9856	+	43.2763i	0.954650	+	1.65350i
$686$	10.5807	−	0.841524i	0.403972	−	0.0321295i
$687$	−11.3004	−	6.52429i	−0.431137	−	0.248917i
$688$	−0.814069	−	1.41001i	−0.0310361	−	0.0537561i
$689$	14.8899	−	0.0506527i	0.567260	−	0.00192971i
$690$	−4.11297	+	7.12388i	−0.156578	+	0.271202i
$691$			4.37493i			0.166430i	0.996532	+	0.0832152i	$0.0265189\pi$
$691$			4.37493i			0.166430i	−0.996532	+	0.0832152i	$0.973481\pi$
$692$	16.0397	−	27.7815i	0.609737	−	1.05610i
$693$	0.933612	−	0.0247051i	0.0354650	−	0.000938470i
$694$		−	16.6703i		−	0.632796i
$695$	−25.5777	−	14.7673i	−0.970218	−	0.560156i
$696$		−	0.899494i		−	0.0340952i
$697$	4.21031	+	2.43082i	0.159477	+	0.0920740i
$698$	5.25269	−	9.09792i	0.198817	−	0.344361i
$699$	−8.10047	+	14.0304i	−0.306388	+	0.530679i
$700$	19.5615	+	10.6141i	0.739356	+	0.401174i
$701$	41.1220			1.55316			0.776579	−	0.630020i	$-0.216953\pi$
$701$	41.1220			1.55316			0.776579	+	0.630020i	$0.216953\pi$
$702$	−1.78600	+	1.03926i	−0.0674082	+	0.0392245i
$703$	−2.54936	+	4.41563i	−0.0961511	+	0.166539i
$704$	−0.354780	+	0.204832i	−0.0133713	+	0.00771991i
$705$	31.2255			1.17602
$706$	2.04837	+	3.54788i	0.0770915	+	0.133526i
$707$	−27.1716	+	16.6611i	−1.02189	+	0.626606i
$708$	16.6622	−	9.61993i	0.626204	−	0.361539i
$709$	16.5571	+	9.55925i	0.621815	+	0.359005i	0.777575	−	0.628790i	$-0.216449\pi$
$709$	16.5571	+	9.55925i	0.621815	+	0.359005i	−0.155760	+	0.987795i	$0.549783\pi$
$710$	−19.5652	−	11.2960i	−0.734271	−	0.423931i
$711$	6.97360			0.261530
$712$	12.8586			0.481896
$713$	−33.8822	−	19.5619i	−1.26890	−	0.732599i
$714$	−0.704285	−	1.14858i	−0.0263572	−	0.0429844i
$715$	4.03125	−	0.0137136i	0.150760	−	0.000512859i
$716$	19.0452	+	32.9872i	0.711752	+	1.23279i
$717$	−12.5462	+	7.24355i	−0.468547	+	0.270516i
$718$	4.30454	+	7.45568i	0.160644	+	0.278243i
$719$	7.49690	−	12.9850i	0.279587	−	0.484259i	−0.691695	−	0.722190i	$-0.743136\pi$
$719$	7.49690	−	12.9850i	0.279587	−	0.484259i	0.971282	+	0.237931i	$0.0764691\pi$
$720$		−	6.76926i		−	0.252275i
$721$	−30.8796	+	18.9347i	−1.15001	+	0.705166i
$722$	8.26668	−	4.77277i	0.307654	−	0.177624i
$723$	−17.8835	+	10.3251i	−0.665096	+	0.383993i
$724$	2.21346			0.0822628
$725$	−1.07561	−	1.86301i	−0.0399471	−	0.0691905i
$726$			6.23276i			0.231319i
$727$	18.8699			0.699847			0.349923	−	0.936778i	$-0.386208\pi$
$727$	18.8699			0.699847			0.349923	+	0.936778i	$0.386208\pi$
$728$	−10.5508	−	17.0761i	−0.391039	−	0.632882i
$729$	1.00000			0.0370370
$730$			12.3438i			0.456866i
$731$	0.338458	+	0.586227i	0.0125183	+	0.0216824i
$732$	−25.3341			−0.936375
$733$	22.4233	−	12.9461i	0.828225	−	0.478176i	−0.0250198	−	0.999687i	$-0.507965\pi$
$733$	22.4233	−	12.9461i	0.828225	−	0.478176i	0.853244	+	0.521511i	$0.174632\pi$
$734$	−2.00962	+	1.16026i	−0.0741766	+	0.0428259i
$735$	−19.7607	−	10.0549i	−0.728884	−	0.370879i
$736$			24.6210i			0.907541i
$737$	−1.65114	+	2.85986i	−0.0608205	+	0.105344i
$738$	1.56785	+	2.71560i	0.0577135	+	0.0999627i
$739$	34.6057	−	19.9796i	1.27299	−	0.734962i	0.297442	−	0.954740i	$-0.403867\pi$
$739$	34.6057	−	19.9796i	1.27299	−	0.734962i	0.975550	+	0.219778i	$0.0705332\pi$
$740$	−8.81564	−	15.2691i	−0.324069	−	0.561305i
$741$	4.77139	−	2.77645i	0.175281	−	0.101995i
$742$	−2.98641	+	5.50391i	−0.109635	+	0.202055i
$743$	−10.9942	−	6.34749i	−0.403337	−	0.232867i	0.284586	−	0.958651i	$-0.408144\pi$
$743$	−10.9942	−	6.34749i	−0.403337	−	0.232867i	−0.687923	+	0.725784i	$0.741477\pi$
$744$	−18.1667			−0.666024
$745$	8.88444			0.325501
$746$	−9.43485	−	5.44721i	−0.345434	−	0.199437i
$747$	−12.9786	−	7.49322i	−0.474864	−	0.274163i
$748$	0.454049	−	0.262145i	0.0166017	−	0.00958498i
$749$	−0.359144	−	13.5722i	−0.0131229	−	0.495916i
$750$	0.0293650	+	0.0508617i	0.00107226	+	0.00185721i
$751$	−37.3088			−1.36142			−0.680709	−	0.732554i	$-0.738328\pi$
$751$	−37.3088			−1.36142			−0.680709	+	0.732554i	$0.738328\pi$
$752$	18.2464	−	10.5346i	0.665379	−	0.384157i
$753$	−12.9380	+	22.4093i	−0.471488	+	0.816642i
$754$	0.00300489	+	0.883320i	0.000109432	+	0.0321686i
$755$	64.0534			2.33114
$756$	0.116987	+	4.42095i	0.00425476	+	0.160789i
$757$	12.2949	−	21.2953i	0.446864	−	0.773992i	−0.551316	−	0.834297i	$-0.685874\pi$
$757$	12.2949	−	21.2953i	0.446864	−	0.773992i	0.998180	+	0.0603051i	$0.0192074\pi$
$758$	−4.77812	+	8.27594i	−0.173549	+	0.300596i
$759$	1.38532	+	0.799814i	0.0502838	+	0.0290314i
$760$		−	10.2043i		−	0.370150i
$761$	12.4784	+	7.20440i	0.452341	+	0.261159i	0.708818	−	0.705391i	$-0.249229\pi$
$761$	12.4784	+	7.20440i	0.452341	+	0.261159i	−0.256477	+	0.966550i	$0.582562\pi$
$762$			8.94334i			0.323983i
$763$	−1.26052	+	2.32311i	−0.0456337	+	0.0841021i
$764$	6.49928	−	11.2571i	0.235136	−	0.407267i
$765$			2.81439i			0.101755i
$766$	−2.47609	+	4.28871i	−0.0894646	+	0.154957i
$767$	−35.8698	+	20.8724i	−1.29518	+	0.753660i
$768$	2.14386	+	3.71327i	0.0773599	+	0.133991i
$769$	−22.7651	−	13.1435i	−0.820932	−	0.473965i	0.0298056	−	0.999556i	$-0.490511\pi$
$769$	−22.7651	−	13.1435i	−0.820932	−	0.473965i	−0.850738	+	0.525590i	$0.823845\pi$
$770$	−0.808533	+	1.49011i	−0.0291375	+	0.0536999i
$771$	0.945343	+	1.63738i	0.0340457	+	0.0589689i
$772$	−15.8846	+	9.17100i	−0.571701	+	0.330071i
$773$		−	43.6593i		−	1.57032i	−0.619295	−	0.785158i	$-0.712582\pi$
$773$		−	43.6593i		−	1.57032i	0.619295	−	0.785158i	$-0.287418\pi$
$774$			0.436603i			0.0156934i
$775$	−37.6265	+	21.7237i	−1.35158	+	0.780337i
$776$	13.8213	+	23.9391i	0.496155	+	0.859365i
$777$	4.60567	+	7.51112i	0.165228	+	0.269460i
$778$	3.51444	+	2.02906i	0.125999	+	0.0727455i
$779$	−4.18860	−	7.25486i	−0.150072	−	0.259932i
$780$	0.0649382	+	19.0893i	0.00232516	+	0.683506i
$781$	−2.19663	+	3.80468i	−0.0786017	+	0.136142i
$782$		−	2.30764i		−	0.0825210i
$783$	0.213739	−	0.370207i	0.00763841	−	0.0132301i
$784$	−14.9393	+	0.791195i	−0.533545	+	0.0282570i
$785$			14.7056i			0.524866i
$786$	−2.71127	−	1.56535i	−0.0967077	−	0.0558342i
$787$			15.8702i			0.565710i	0.959163	+	0.282855i	$0.0912815\pi$
$787$			15.8702i			0.565710i	−0.959163	+	0.282855i	$0.908718\pi$
$788$	8.70738	+	5.02721i	0.310188	+	0.179087i
$789$	−3.04658	+	5.27683i	−0.108461	+	0.187860i
$790$	−6.32942	+	10.9629i	−0.225191	+	0.390042i
$791$	6.59290	−	4.04263i	0.234416	−	0.143740i
$792$	0.742770			0.0263932
$793$	54.6456	−	0.185894i	1.94052	−	0.00660130i
$794$	6.20359	−	10.7449i	0.220157	−	0.381324i
$795$	11.3280	−	6.54025i	0.401764	−	0.231959i
$796$	24.7814			0.878353
$797$	14.7381	+	25.5272i	0.522051	+	0.904219i	0.999671	+	0.0256525i	$0.00816634\pi$
$797$	14.7381	+	25.5272i	0.522051	+	0.904219i	−0.477620	+	0.878567i	$0.658500\pi$
$798$	0.0614117	+	2.32076i	0.00217395	+	0.0821542i
$799$	−7.58615	+	4.37987i	−0.268379	+	0.154949i
$800$	23.6787	+	13.6709i	0.837169	+	0.483340i
$801$	5.29223	+	3.05547i	0.186992	+	0.107960i
$802$	−8.45876			−0.298689
$803$	2.40040			0.0847081
$804$	−13.5423	−	7.81868i	−0.477602	−	0.275743i
$805$	−19.8509	−	32.3737i	−0.699652	−	1.14102i
$806$	17.8401	−	0.0606886i	0.628390	−	0.00213766i
$807$	0.702043	+	1.21597i	0.0247131	+	0.0428043i
$808$	−21.9528	+	12.6745i	−0.772297	+	0.445886i
$809$	−3.24854	−	5.62663i	−0.114212	−	0.197822i	0.803252	−	0.595639i	$-0.203101\pi$
$809$	−3.24854	−	5.62663i	−0.114212	−	0.197822i	−0.917465	+	0.397817i	$0.869768\pi$
$810$	−0.907626	+	1.57205i	−0.0318907	+	0.0552364i
$811$			20.7305i			0.727945i	0.931410	+	0.363972i	$0.118580\pi$
$811$			20.7305i			0.727945i	−0.931410	+	0.363972i	$0.881420\pi$
$812$	1.66167	+	0.901621i	0.0583132	+	0.0316407i
$813$	−11.4852	+	6.63099i	−0.402804	+	0.232559i
$814$	0.583444	−	0.336851i	0.0204497	−	0.0118066i
$815$	−10.3361			−0.362056
$816$	0.949496	+	1.64457i	0.0332390	+	0.0575716i
$817$		−	1.16641i		−	0.0408074i
$818$	10.0367			0.350924
$819$	−0.284780	−	9.53514i	−0.00995101	−	0.333185i
$820$	28.9681			1.01161
$821$			25.1122i			0.876420i	0.898873	+	0.438210i	$0.144387\pi$
$821$			25.1122i			0.876420i	−0.898873	+	0.438210i	$0.855613\pi$
$822$	−4.52089	−	7.83040i	−0.157684	−	0.273117i
$823$	50.5413			1.76176			0.880880	−	0.473339i	$-0.156952\pi$
$823$	50.5413			1.76176			0.880880	+	0.473339i	$0.156952\pi$
$824$	−24.9485	+	14.4040i	−0.869123	+	0.501789i
$825$	1.53841	−	0.888200i	0.0535605	−	0.0309232i
$826$	−0.461674	−	17.4468i	−0.0160637	−	0.607051i
$827$			7.58852i			0.263879i	0.991258	+	0.131939i	$0.0421204\pi$
$827$			7.58852i			0.263879i	−0.991258	+	0.131939i	$0.957880\pi$
$828$	−3.78737	+	6.55992i	−0.131620	+	0.227973i
$829$	19.4095	+	33.6183i	0.674120	+	1.16761i	0.976725	+	0.214495i	$0.0688104\pi$
$829$	19.4095	+	33.6183i	0.674120	+	1.16761i	−0.302605	+	0.953116i	$0.597856\pi$
$830$	23.5595	−	13.6021i	0.817763	−	0.472135i
$831$	−8.44494	−	14.6271i	−0.292952	−	0.507407i
$832$	2.10450	+	3.61664i	0.0729606	+	0.125384i
$833$	6.21117	−	0.328948i	0.215204	−	0.0113974i
$834$	4.62803	+	2.67199i	0.160256	+	0.0925236i
$835$	−76.4683			−2.64629
$836$	−0.903415			−0.0312453
$837$	−7.47692	−	4.31680i	−0.258440	−	0.149210i
$838$	15.2954	+	8.83083i	0.528373	+	0.305056i
$839$	−0.124870	+	0.0720936i	−0.00431098	+	0.00248895i	−0.502154	−	0.864778i	$-0.667459\pi$
$839$	−0.124870	+	0.0720936i	−0.00431098	+	0.00248895i	0.497843	+	0.867267i	$0.334126\pi$
$840$	−15.4988	−	8.40964i	−0.534760	−	0.290160i
$841$	14.4086	+	24.9565i	0.496849	+	0.860568i
$842$	16.8311			0.580037
$843$	−19.5332	+	11.2775i	−0.672761	+	0.388418i
$844$	−17.3540	+	30.0580i	−0.597349	+	1.03464i
$845$	−0.280143	−	41.1751i	−0.00963722	−	1.41647i
$846$	−5.64993			−0.194249
$847$	−25.2905	−	13.7226i	−0.868992	−	0.471514i
$848$	4.41299	−	7.64351i	0.151543	−	0.262479i
$849$	−0.399128	+	0.691311i	−0.0136980	+	0.0237257i
$850$	−2.21932	−	1.28133i	−0.0761222	−	0.0439492i
$851$			15.0908i			0.517306i
$852$	−18.0164	−	10.4018i	−0.617231	−	0.356358i
$853$			2.84303i			0.0973435i	0.998815	+	0.0486718i	$0.0154988\pi$
$853$			2.84303i			0.0973435i	−0.998815	+	0.0486718i	$0.984501\pi$
$854$	−10.9601	+	20.1992i	−0.375046	+	0.691202i
$855$	2.42477	−	4.19982i	0.0829253	−	0.143631i
$856$		−	10.7978i		−	0.369062i
$857$	−16.0653	+	27.8259i	−0.548779	+	0.950513i	0.449580	+	0.893240i	$0.351574\pi$
$857$	−16.0653	+	27.8259i	−0.548779	+	0.950513i	−0.998359	+	0.0572728i	$0.981760\pi$
$858$	−0.729414	+	0.00248133i	−0.0249018	+	8.47113e-5i
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	−0.999998	−	0.00189479i	$-0.999397\pi$
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	0.498358	−	0.866971i	$-0.333936\pi$
$860$	3.49303	+	2.01670i	0.119111	+	0.0687690i
$861$	−14.4709	+	0.382928i	−0.493168	+	0.0130501i
$862$	−6.10149	−	10.5681i	−0.207818	−	0.359951i
$863$	36.9726	−	21.3461i	1.25856	−	0.726631i	0.285767	−	0.958299i	$-0.407752\pi$
$863$	36.9726	−	21.3461i	1.25856	−	0.726631i	0.972795	+	0.231669i	$0.0744185\pi$
$864$			5.43321i			0.184841i
$865$			60.7866i			2.06681i
$866$	−8.73696	+	5.04429i	−0.296894	+	0.171412i
$867$	8.10524	+	14.0387i	0.275268	+	0.476779i
$868$	18.2097	−	33.5601i	0.618077	−	1.13910i
$869$	2.13185	+	1.23083i	0.0723182	+	0.0417529i
$870$	0.387990	+	0.672018i	0.0131541	+	0.0227836i
$871$	29.2682	+	16.7655i	0.991715	+	0.568078i
$872$	−1.05102	+	1.82042i	−0.0355921	+	0.0616473i
$873$			13.1369i			0.444617i
$874$	−1.98817	+	3.44361i	−0.0672508	+	0.116482i
$875$	−0.271033	+	0.00717203i	−0.00916258	+	0.000242459i
$876$			11.3666i			0.384043i
$877$	−11.3481	−	6.55181i	−0.383197	−	0.221239i	0.296011	−	0.955184i	$-0.404343\pi$
$877$	−11.3481	−	6.55181i	−0.383197	−	0.221239i	−0.679208	+	0.733945i	$0.737677\pi$
$878$			13.0744i			0.441241i
$879$	26.6711	+	15.3986i	0.899593	+	0.519380i
$880$	1.19476	−	2.06938i	0.0402753	−	0.0697589i
$881$	−18.9666	+	32.8512i	−0.639002	+	1.10678i	0.346650	+	0.937995i	$0.387319\pi$
$881$	−18.9666	+	32.8512i	−0.639002	+	1.10678i	−0.985652	+	0.168790i	$0.946014\pi$
$882$	3.57550	+	1.81932i	0.120393	+	0.0612598i
$883$	15.9034			0.535194			0.267597	−	0.963531i	$-0.413770\pi$
$883$	15.9034			0.535194			0.267597	+	0.963531i	$0.413770\pi$
$884$	−2.69335	−	4.62859i	−0.0905872	−	0.155676i
$885$	−18.2286	+	31.5729i	−0.612749	+	1.06131i
$886$	19.3856	−	11.1923i	0.651271	−	0.376012i
$887$	−10.1640			−0.341275			−0.170637	−	0.985334i	$-0.554583\pi$
$887$	−10.1640			−0.341275			−0.170637	+	0.985334i	$0.554583\pi$
$888$	3.50363	+	6.06846i	0.117574	+	0.203644i
$889$	−36.2892	−	19.6905i	−1.21710	−	0.660397i
$890$	−9.60673	+	5.54645i	−0.322018	+	0.185917i
$891$	0.305703	+	0.176498i	0.0102414	+	0.00591290i
$892$	−10.3004	−	5.94695i	−0.344884	−	0.199119i
$893$	15.0941			0.505104
$894$	−1.60755			−0.0537645
$895$	−62.5070	−	36.0884i	−2.08938	−	1.20630i
$896$	−30.4989	+	0.807057i	−1.01890	+	0.0269619i
$897$	8.12123	−	14.1775i	0.271160	−	0.473374i
$898$	−3.43616	−	5.95161i	−0.114666	−	0.198608i
$899$	−3.19622	+	1.84534i	−0.106600	+	0.0615454i
$900$	4.20591	+	7.28485i	0.140197	+	0.242828i
$901$	−1.83475	+	3.17788i	−0.0611243	+	0.105870i
$902$			1.10689i			0.0368554i
$903$	−1.77159	−	0.961265i	−0.0589549	−	0.0319889i
$904$	5.32660	−	3.07532i	0.177160	−	0.102283i
$905$	−3.63233	+	2.09713i	−0.120743	+	0.0697109i
$906$	−11.5898			−0.385045
$907$	−14.4751	−	25.0717i	−0.480639	−	0.832492i	0.519114	−	0.854705i	$-0.326262\pi$
$907$	−14.4751	−	25.0717i	−0.480639	−	0.832492i	−0.999753	+	0.0222132i	$0.992929\pi$
$908$			6.20138i			0.205800i
$909$	−12.0469			−0.399570
$910$	15.2482	+	8.20665i	0.505474	+	0.272048i
$911$	2.42075			0.0802032			0.0401016	−	0.999196i	$-0.487232\pi$
$911$	2.42075			0.0802032			0.0401016	+	0.999196i	$0.487232\pi$
$912$		−	3.27219i		−	0.108353i
$913$	−2.64508	−	4.58141i	−0.0875393	−	0.151622i
$914$	1.42778			0.0472267
$915$	41.5737	−	24.0026i	1.37438	−	0.793500i
$916$	18.8892	−	10.9057i	0.624116	−	0.360333i
$917$	12.3211	−	7.55502i	0.406877	−	0.249489i
$918$		−	0.509236i		−	0.0168073i
$919$	−1.55235	+	2.68875i	−0.0512074	+	0.0886937i	−0.890493	−	0.454997i	$-0.849640\pi$
$919$	−1.55235	+	2.68875i	−0.0512074	+	0.0886937i	0.839286	+	0.543691i	$0.182974\pi$
$920$	−15.1010	−	26.1557i	−0.497865	−	0.862327i
$921$	18.5469	−	10.7080i	0.611140	−	0.352842i
$922$	−9.26911	−	16.0546i	−0.305262	−	0.528729i
$923$	38.9377	+	22.3044i	1.28165	+	0.734158i
$924$	−0.744526	+	1.37215i	−0.0244931	+	0.0451404i
$925$	14.5133	+	8.37924i	0.477193	+	0.275508i
$926$	−13.4598			−0.442316
$927$	−13.6908			−0.449666
$928$	2.01141	+	1.16129i	0.0660277	+	0.0381211i
$929$	7.09737	+	4.09767i	0.232857	+	0.134440i	0.611889	−	0.790943i	$-0.290410\pi$
$929$	7.09737	+	4.09767i	0.232857	+	0.134440i	−0.379032	+	0.925383i	$0.623743\pi$
$930$	13.5725	−	7.83608i	0.445059	−	0.256955i
$931$	−9.55211	−	4.86041i	−0.313058	−	0.159294i
$932$	−13.5403	−	23.4525i	−0.443528	−	0.768214i
$933$	19.3876			0.634721
$934$	1.26221	−	0.728736i	0.0413007	−	0.0238450i
$935$	−0.496735	+	0.860369i	−0.0162450	+	0.0281371i
$936$	−0.0258086	−	7.58672i	−0.000843581	−	0.247980i
$937$	53.8795			1.76017			0.880084	−	0.474819i	$-0.157486\pi$
$937$	53.8795			1.76017			0.880084	+	0.474819i	$0.157486\pi$
$938$	−12.0926	+	7.41497i	−0.394839	+	0.242107i
$939$	3.85148	−	6.67096i	0.125688	−	0.217699i
$940$	−26.0974	+	45.2021i	−0.851205	+	1.47433i
$941$	−2.93824	−	1.69639i	−0.0957838	−	0.0553008i	0.451343	−	0.892351i	$-0.350945\pi$
$941$	−2.93824	−	1.69639i	−0.0957838	−	0.0553008i	−0.547127	+	0.837050i	$0.684278\pi$
$942$		−	2.66083i		−	0.0866945i
$943$	−21.4724	−	12.3971i	−0.699236	−	0.403704i
$944$			24.5993i			0.800638i
$945$	−4.38057	−	7.14402i	−0.142500	−	0.232395i
$946$	−0.0770596	+	0.133471i	−0.00250542	+	0.00433952i
$947$			44.1524i			1.43476i	0.696681	+	0.717381i	$0.254659\pi$
$947$			44.1524i			1.43476i	−0.696681	+	0.717381i	$0.745341\pi$
$948$	−5.82836	+	10.0950i	−0.189296	+	0.327871i
$949$	−0.0834051	−	24.5178i	−0.00270745	−	0.795883i
$950$	2.20788	+	3.82416i	0.0716331	+	0.124072i
$951$	12.7818	+	7.37956i	0.414477	+	0.239299i
$952$	4.94499	−	0.130854i	0.160268	−	0.00424099i
$953$	8.43489	+	14.6097i	0.273233	+	0.473253i	0.969688	−	0.244347i	$-0.0785737\pi$
$953$	8.43489	+	14.6097i	0.273233	+	0.473253i	−0.696455	+	0.717601i	$0.745240\pi$
$954$	−2.04969	+	1.18339i	−0.0663613	+	0.0383137i
$955$			24.6308i			0.797033i
$956$		−	24.2159i		−	0.783198i
$957$	0.130681	−	0.0754489i	0.00422433	−	0.00243892i
$958$	−5.62085	−	9.73559i	−0.181601	−	0.314543i
$959$	41.7268	−	1.10417i	1.34743	−	0.0356555i
$960$	3.18340	+	1.83794i	0.102744	+	0.0593192i
$961$	21.7695	+	37.7059i	0.702242	+	1.21632i
$962$	−3.46090	−	5.94764i	−0.111584	−	0.191760i
$963$	2.56579	−	4.44409i	0.0826816	−	0.143209i
$964$		−	34.5177i		−	1.11174i
$965$	17.3780	−	30.0995i	0.559417	−	0.968938i
$966$	3.59182	+	5.85769i	0.115565	+	0.188468i
$967$		−	21.6217i		−	0.695308i	−0.937623	−	0.347654i	$-0.886978\pi$
$967$		−	21.6217i		−	0.695308i	0.937623	−	0.347654i	$-0.113022\pi$
$968$	−19.8180	−	11.4419i	−0.636976	−	0.367758i
$969$			1.36045i			0.0437039i
$970$	−20.6519	−	11.9234i	−0.663093	−	0.382837i
$971$	−18.1828	+	31.4936i	−0.583515	+	1.01068i	0.411544	+	0.911390i	$0.364990\pi$
$971$	−18.1828	+	31.4936i	−0.583515	+	1.01068i	−0.995059	+	0.0992873i	$0.968344\pi$
$972$	−0.835774	+	1.44760i	−0.0268075	+	0.0464319i
$973$	−21.0315	+	12.8961i	−0.674241	+	0.413431i
$974$	−2.02023			−0.0647325
$975$	−9.12561	−	15.6826i	−0.292253	−	0.502244i
$976$	16.1956	−	28.0515i	0.518407	−	0.897907i
$977$	10.4549	−	6.03614i	0.334482	−	0.193113i	−0.323347	−	0.946280i	$-0.604808\pi$
$977$	10.4549	−	6.03614i	0.334482	−	0.193113i	0.657829	+	0.753167i	$0.271475\pi$
$978$	1.87020			0.0598025
$979$	1.07857	+	1.86814i	0.0344712	+	0.0597059i
$980$	31.0709	−	20.2021i	0.992524	−	0.645331i
$981$	−0.865142	+	0.499490i	−0.0276219	+	0.0159475i
$982$	−8.79393	−	5.07718i	−0.280626	−	0.162019i
$983$	10.8771	+	6.27988i	0.346925	+	0.200297i	0.663330	−	0.748327i	$-0.269143\pi$
$983$	10.8771	+	6.27988i	0.346925	+	0.200297i	−0.316405	+	0.948624i	$0.602476\pi$
$984$	−11.5129			−0.367018
$985$	−19.0519			−0.607045
$986$	−0.188522	−	0.108843i	−0.00600378	−	0.00346628i
$987$	12.4394	−	22.9256i	0.395950	−	0.729729i
$988$	0.0313904	+	9.22756i	0.000998663	+	0.293568i
$989$	−1.72612	−	2.98973i	−0.0548874	−	0.0950678i
$990$	−0.554929	+	0.320388i	−0.0176368	+	0.0101826i
$991$	4.56723	+	7.91068i	0.145083	+	0.251291i	0.929404	−	0.369064i	$-0.120322\pi$
$991$	4.56723	+	7.91068i	0.145083	+	0.251291i	−0.784321	+	0.620355i	$0.786988\pi$
$992$	23.4541	−	40.6236i	0.744667	−	1.28980i
$993$		−	1.65551i		−	0.0525360i
$994$	−16.0877	+	9.86468i	−0.510272	+	0.312888i
$995$	−40.6667	+	23.4789i	−1.28922	+	0.744332i
$996$	21.6944	−	12.5253i	0.687415	−	0.396879i
$997$	−14.9919			−0.474798			−0.237399	−	0.971412i	$-0.576295\pi$
$997$	−14.9919			−0.474798			−0.237399	+	0.971412i	$0.576295\pi$
$998$	3.40007	+	5.88910i	0.107627	+	0.186416i
$999$			3.33015i			0.105361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.4.4	✓	12
3.2	odd	2		819.2.bm.e.550.3		12
7.2	even	3		273.2.bl.c.121.4	yes	12
13.10	even	6		273.2.bl.c.88.4	yes	12
21.2	odd	6		819.2.do.f.667.3		12
39.23	odd	6		819.2.do.f.361.3		12
91.23	even	6	inner	273.2.t.c.205.3	yes	12
273.23	odd	6		819.2.bm.e.478.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.4	✓	12	1.1	even	1	trivial
273.2.t.c.205.3	yes	12	91.23	even	6	inner
273.2.bl.c.88.4	yes	12	13.10	even	6
273.2.bl.c.121.4	yes	12	7.2	even	3
819.2.bm.e.478.4		12	273.23	odd	6
819.2.bm.e.550.3		12	3.2	odd	2
819.2.do.f.361.3		12	39.23	odd	6
819.2.do.f.667.3		12	21.2	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.573107i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.67155 q^{4} +(-2.74304 + 1.58369i) q^{5} +(0.496325 - 0.286553i) q^{6} +(0.0699870 + 2.64483i) q^{7} +2.10419i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+0.573107i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.67155 q^{4} +(-2.74304 + 1.58369i) q^{5} +(0.496325 - 0.286553i) q^{6} +(0.0699870 + 2.64483i) q^{7} +2.10419i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.907626 - 1.57205i) q^{10} +(-0.305703 + 0.176498i) q^{11} +(-0.835774 - 1.44760i) q^{12} +(1.81339 + 3.11635i) q^{13} +(-1.51577 + 0.0401100i) q^{14} +(2.74304 + 1.58369i) q^{15} +2.13717 q^{16} -0.888553 q^{17} +(-0.496325 - 0.286553i) q^{18} +(1.32596 + 0.765541i) q^{19} +(-4.58512 + 2.64722i) q^{20} +(2.25549 - 1.38302i) q^{21} +(-0.101152 - 0.175201i) q^{22} +4.53157 q^{23} +(1.82228 - 1.05209i) q^{24} +(2.51618 - 4.35815i) q^{25} +(-1.78600 + 1.03926i) q^{26} +1.00000 q^{27} +(0.116987 + 4.42095i) q^{28} +(0.213739 - 0.370207i) q^{29} +(-0.907626 + 1.57205i) q^{30} +(-7.47692 - 4.31680i) q^{31} +5.43321i q^{32} +(0.305703 + 0.176498i) q^{33} -0.509236i q^{34} +(-4.38057 - 7.14402i) q^{35} +(-0.835774 + 1.44760i) q^{36} +3.33015i q^{37} +(-0.438737 + 0.759914i) q^{38} +(1.79214 - 3.12861i) q^{39} +(-3.33239 - 5.77187i) q^{40} +(-4.73839 - 2.73571i) q^{41} +(0.792620 + 1.29264i) q^{42} +(-0.380909 - 0.659754i) q^{43} +(-0.510998 + 0.295025i) q^{44} -3.16739i q^{45} +2.59708i q^{46} +(8.53765 - 4.92921i) q^{47} +(-1.06859 - 1.85085i) q^{48} +(-6.99020 + 0.370207i) q^{49} +(2.49768 + 1.44204i) q^{50} +(0.444277 + 0.769510i) q^{51} +(3.03117 + 5.20913i) q^{52} +(2.06487 - 3.57646i) q^{53} +0.573107i q^{54} +(0.559038 - 0.968281i) q^{55} +(-5.56521 + 0.147266i) q^{56} -1.53108i q^{57} +(0.212168 + 0.122495i) q^{58} +11.5102i q^{59} +(4.58512 + 2.64722i) q^{60} +(7.57803 - 13.1255i) q^{61} +(2.47399 - 4.28507i) q^{62} +(-2.32548 - 1.26180i) q^{63} +1.16054 q^{64} +(-9.90954 - 5.67641i) q^{65} +(-0.101152 + 0.175201i) q^{66} +(8.10167 - 4.67750i) q^{67} -1.48526 q^{68} +(-2.26579 - 3.92446i) q^{69} +(4.09429 - 2.51054i) q^{70} +(10.7783 - 6.22283i) q^{71} +(-1.82228 - 1.05209i) q^{72} +(-5.88903 - 3.40003i) q^{73} -1.90853 q^{74} -5.03235 q^{75} +(2.21640 + 1.27964i) q^{76} +(-0.488201 - 0.796179i) q^{77} +(1.79303 + 1.02709i) q^{78} +(-3.48680 - 6.03932i) q^{79} +(-5.86235 + 3.38463i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.56785 - 2.71560i) q^{82} +14.9864i q^{83} +(3.77017 - 2.31179i) q^{84} +(2.43734 - 1.40720i) q^{85} +(0.378110 - 0.218302i) q^{86} -0.427478 q^{87} +(-0.371385 - 0.643258i) q^{88} -6.11094i q^{89} +1.81525 q^{90} +(-8.11528 + 5.01420i) q^{91} +7.57475 q^{92} +8.63360i q^{93} +(2.82497 + 4.89298i) q^{94} -4.84953 q^{95} +(4.70529 - 2.71660i) q^{96} +(11.3769 - 6.56845i) q^{97} +(-0.212168 - 4.00613i) q^{98} -0.352996i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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