LMFDB - Embedded newform 349.2.e.a.123.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.12
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +O(q^{10})$	\(q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +2.64684i q^{10} -3.72216i q^{11} +(-1.71106 - 2.96364i) q^{12} +(3.22785 - 1.86360i) q^{13} +(-1.73228 + 3.00039i) q^{14} +(4.24877 + 7.35909i) q^{15} +(0.145481 + 0.251980i) q^{16} -5.36165 q^{17} +(4.38232 + 2.53014i) q^{18} +(1.62062 - 2.80699i) q^{19} +(1.69967 + 2.94391i) q^{20} +11.1228i q^{21} +(1.69549 + 2.93667i) q^{22} +(-2.39400 - 4.14653i) q^{23} +(7.31512 + 4.22339i) q^{24} +(-1.72049 - 2.97998i) q^{25} +(-1.69779 + 2.94065i) q^{26} +7.47134 q^{27} +4.44953i q^{28} +(-2.19135 + 3.79553i) q^{29} +(-6.70432 - 3.87074i) q^{30} +6.79620 q^{31} +(4.77257 + 2.75544i) q^{32} +(9.42805 + 5.44329i) q^{33} +(4.23019 - 2.44230i) q^{34} -11.0488i q^{35} +6.49892 q^{36} -7.48368 q^{37} +2.95285i q^{38} +10.9013i q^{39} +(-7.26644 - 4.19528i) q^{40} -2.38606 q^{41} +(-5.06657 - 8.77556i) q^{42} +(-1.70678 - 0.985410i) q^{43} +(3.77158 + 2.17752i) q^{44} -16.1376 q^{45} +(3.77759 + 2.18099i) q^{46} -7.30944i q^{47} -0.851005 q^{48} +(3.73109 - 6.46243i) q^{49} +(2.71484 + 1.56741i) q^{50} +(7.84088 - 13.5808i) q^{51} +4.36094i q^{52} +12.2676i q^{53} +(-5.89468 + 3.40329i) q^{54} +(-9.36530 - 5.40706i) q^{55} +(-5.49137 - 9.51134i) q^{56} +(4.73998 + 8.20989i) q^{57} -3.99275i q^{58} +(-7.06848 - 4.08099i) q^{59} -9.94240 q^{60} -4.05102i q^{61} +(-5.36201 + 3.09576i) q^{62} +(-18.2932 - 10.5616i) q^{63} -5.60248 q^{64} -10.8288i q^{65} -9.91795 q^{66} +15.3725 q^{67} +(3.13665 - 5.43284i) q^{68} +14.0039 q^{69} +(5.03285 + 8.71715i) q^{70} +(6.81338 - 3.93371i) q^{71} +(-13.8921 + 8.02061i) q^{72} +(-3.57439 + 6.19102i) q^{73} +(5.90441 - 3.40891i) q^{74} +10.0642 q^{75} +(1.89617 + 3.28427i) q^{76} +(-7.07752 - 12.2586i) q^{77} +(-4.96569 - 8.60082i) q^{78} +11.6997i q^{79} +0.845341 q^{80} +(-2.59439 + 4.49362i) q^{81} +(1.88253 - 1.08688i) q^{82} +(7.11627 + 12.3257i) q^{83} +(-11.2705 - 6.50701i) q^{84} +(-7.78870 + 13.4904i) q^{85} +1.79547 q^{86} +(-6.40927 - 11.1012i) q^{87} -10.7495 q^{88} +(12.8584 + 7.42383i) q^{89} +(12.7321 - 7.35090i) q^{90} +(7.08710 - 12.2752i) q^{91} +5.60211 q^{92} +(-9.93877 + 17.2145i) q^{93} +(3.32955 + 5.76694i) q^{94} +(-4.70844 - 8.15525i) q^{95} +(-13.9588 + 8.05913i) q^{96} +(-5.04200 + 2.91100i) q^{97} +6.79823i q^{98} +(-17.9048 + 10.3373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.788972	+	0.455513i	−0.557887	+	0.322096i	−0.752297	−	0.658824i	$-0.771054\pi$
$2$	−0.788972	+	0.455513i	−0.557887	+	0.322096i	0.194410	+	0.980920i	$0.437721\pi$
$3$	−1.46240	+	2.53295i	−0.844318	+	1.46240i	0.0418940	+	0.999122i	$0.486661\pi$
$3$	−1.46240	+	2.53295i	−0.844318	+	1.46240i	−0.886212	+	0.463280i	$0.846673\pi$
$4$	−0.585016	+	1.01328i	−0.292508	+	0.506639i
$5$	1.45267	−	2.51610i	0.649653	−	1.12523i	−0.333552	−	0.942732i	$-0.608247\pi$
$5$	1.45267	−	2.51610i	0.649653	−	1.12523i	0.983206	−	0.182501i	$-0.0584193\pi$
$6$		−	2.66457i		−	1.08781i
$7$	3.29342	−	1.90146i	1.24480	−	0.718684i	0.274730	−	0.961522i	$-0.411412\pi$
$7$	3.29342	−	1.90146i	1.24480	−	0.718684i	0.970067	+	0.242838i	$0.0780783\pi$
$8$		−	2.88798i		−	1.02106i
$9$	−2.77724	−	4.81032i	−0.925746	−	1.60344i
$10$			2.64684i			0.837004i
$11$		−	3.72216i		−	1.12227i	−0.827724	−	0.561136i	$-0.810364\pi$
$11$		−	3.72216i		−	1.12227i	0.827724	−	0.561136i	$-0.189636\pi$
$12$	−1.71106	−	2.96364i	−0.493940	−	0.855528i
$13$	3.22785	−	1.86360i	0.895243	−	0.516869i	0.0195893	−	0.999808i	$-0.493764\pi$
$13$	3.22785	−	1.86360i	0.895243	−	0.516869i	0.875654	+	0.482939i	$0.160431\pi$
$14$	−1.73228	+	3.00039i	−0.462971	+	0.801889i
$15$	4.24877	+	7.35909i	1.09703	+	1.90011i
$16$	0.145481	+	0.251980i	0.0363702	+	0.0629950i
$17$	−5.36165			−1.30039			−0.650195	−	0.759767i	$-0.725313\pi$
$17$	−5.36165			−1.30039			−0.650195	+	0.759767i	$0.725313\pi$
$18$	4.38232	+	2.53014i	1.03292	+	0.596359i
$19$	1.62062	−	2.80699i	0.371795	−	0.643968i	−0.618047	−	0.786141i	$-0.712076\pi$
$19$	1.62062	−	2.80699i	0.371795	−	0.643968i	0.989842	+	0.142174i	$0.0454091\pi$
$20$	1.69967	+	2.94391i	0.380058	+	0.658279i
$21$			11.1228i			2.42719i
$22$	1.69549	+	2.93667i	0.361480	+	0.626101i
$23$	−2.39400	−	4.14653i	−0.499183	−	0.864610i	0.500817	−	0.865553i	$-0.333033\pi$
$23$	−2.39400	−	4.14653i	−0.499183	−	0.864610i	−1.00000		0.000943088i	$0.999700\pi$
$24$	7.31512	+	4.22339i	1.49319	+	0.862096i
$25$	−1.72049	−	2.97998i	−0.344099	−	0.595997i
$26$	−1.69779	+	2.94065i	−0.332963	+	0.576709i
$27$	7.47134			1.43786
$28$			4.44953i			0.840883i
$29$	−2.19135	+	3.79553i	−0.406924	+	0.704812i	−0.994543	−	0.104325i	$-0.966732\pi$
$29$	−2.19135	+	3.79553i	−0.406924	+	0.704812i	0.587620	+	0.809137i	$0.300065\pi$
$30$	−6.70432	−	3.87074i	−1.22404	−	0.706697i
$31$	6.79620			1.22063			0.610317	−	0.792158i	$-0.291042\pi$
$31$	6.79620			1.22063			0.610317	+	0.792158i	$0.291042\pi$
$32$	4.77257	+	2.75544i	0.843679	+	0.487098i
$33$	9.42805	+	5.44329i	1.64121	+	0.947555i
$34$	4.23019	−	2.44230i	0.725471	−	0.418851i
$35$		−	11.0488i		−	1.86758i
$36$	6.49892			1.08315
$37$	−7.48368			−1.23031			−0.615155	−	0.788407i	$-0.710906\pi$
$37$	−7.48368			−1.23031			−0.615155	+	0.788407i	$0.710906\pi$
$38$			2.95285i			0.479015i
$39$			10.9013i			1.74561i
$40$	−7.26644	−	4.19528i	−1.14892	−	0.663332i
$41$	−2.38606			−0.372640			−0.186320	−	0.982489i	$-0.559656\pi$
$41$	−2.38606			−0.372640			−0.186320	+	0.982489i	$0.559656\pi$
$42$	−5.06657	−	8.77556i	−0.781789	−	1.35410i
$43$	−1.70678	−	0.985410i	−0.260282	−	0.150274i	0.364181	−	0.931328i	$-0.381349\pi$
$43$	−1.70678	−	0.985410i	−0.260282	−	0.150274i	−0.624463	+	0.781054i	$0.714682\pi$
$44$	3.77158	+	2.17752i	0.568587	+	0.328274i
$45$	−16.1376			−2.40566
$46$	3.77759	+	2.18099i	0.556976	+	0.321570i
$47$		−	7.30944i		−	1.06619i	−0.846055	−	0.533096i	$-0.821028\pi$
$47$		−	7.30944i		−	1.06619i	0.846055	−	0.533096i	$-0.178972\pi$
$48$	−0.851005			−0.122832
$49$	3.73109	−	6.46243i	0.533012	−	0.923204i
$50$	2.71484	+	1.56741i	0.383937	+	0.221666i
$51$	7.84088	−	13.5808i	1.09794	−	1.90169i
$52$			4.36094i			0.604753i
$53$			12.2676i			1.68508i	0.538634	+	0.842540i	$0.318941\pi$
$53$			12.2676i			1.68508i	−0.538634	+	0.842540i	$0.681059\pi$
$54$	−5.89468	+	3.40329i	−0.802164	+	0.463130i
$55$	−9.36530	−	5.40706i	−1.26282	−	0.729088i
$56$	−5.49137	−	9.51134i	−0.733816	−	1.27101i
$57$	4.73998	+	8.20989i	0.627826	+	1.08743i
$58$		−	3.99275i		−	0.524274i
$59$	−7.06848	−	4.08099i	−0.920238	−	0.531300i	−0.0365271	−	0.999333i	$-0.511630\pi$
$59$	−7.06848	−	4.08099i	−0.920238	−	0.531300i	−0.883711	+	0.468033i	$0.844963\pi$
$60$	−9.94240			−1.28356
$61$		−	4.05102i		−	0.518680i	−0.965786	−	0.259340i	$-0.916495\pi$
$61$		−	4.05102i		−	0.518680i	0.965786	−	0.259340i	$-0.0835050\pi$
$62$	−5.36201	+	3.09576i	−0.680976	+	0.393161i
$63$	−18.2932	−	10.5616i	−2.30473	−	1.33064i
$64$	−5.60248			−0.700311
$65$		−	10.8288i		−	1.34314i
$66$	−9.91795			−1.22082
$67$	15.3725			1.87805			0.939025	−	0.343849i	$-0.111731\pi$
$67$	15.3725			1.87805			0.939025	+	0.343849i	$0.111731\pi$
$68$	3.13665	−	5.43284i	0.380375	−	0.658828i
$69$	14.0039			1.68588
$70$	5.03285	+	8.71715i	0.601541	+	1.04190i
$71$	6.81338	−	3.93371i	0.808599	−	0.466845i	−0.0378699	−	0.999283i	$-0.512057\pi$
$71$	6.81338	−	3.93371i	0.808599	−	0.466845i	0.846469	+	0.532438i	$0.178724\pi$
$72$	−13.8921	+	8.02061i	−1.63720	+	0.945238i
$73$	−3.57439	+	6.19102i	−0.418350	+	0.724604i	−0.995774	−	0.0918407i	$-0.970725\pi$
$73$	−3.57439	+	6.19102i	−0.418350	+	0.724604i	0.577423	+	0.816445i	$0.304058\pi$
$74$	5.90441	−	3.40891i	0.686374	−	0.396278i
$75$	10.0642			1.16212
$76$	1.89617	+	3.28427i	0.217506	+	0.376731i
$77$	−7.07752	−	12.2586i	−0.806559	−	1.39700i
$78$	−4.96569	−	8.60082i	−0.562254	−	0.973852i
$79$			11.6997i			1.31632i	0.752877	+	0.658162i	$0.228666\pi$
$79$			11.6997i			1.31632i	−0.752877	+	0.658162i	$0.771334\pi$
$80$	0.845341			0.0945120
$81$	−2.59439	+	4.49362i	−0.288266	+	0.499291i
$82$	1.88253	−	1.08688i	0.207891	−	0.120026i
$83$	7.11627	+	12.3257i	0.781112	+	1.35293i	0.931294	+	0.364267i	$0.118681\pi$
$83$	7.11627	+	12.3257i	0.781112	+	1.35293i	−0.150182	+	0.988658i	$0.547986\pi$
$84$	−11.2705	−	6.50701i	−1.22971	−	0.709973i
$85$	−7.78870	+	13.4904i	−0.844803	+	1.46324i
$86$	1.79547			0.193610
$87$	−6.40927	−	11.1012i	−0.687146	−	1.19017i
$88$	−10.7495			−1.14590
$89$	12.8584	+	7.42383i	1.36299	+	0.786924i	0.990021	−	0.140919i	$-0.0450056\pi$
$89$	12.8584	+	7.42383i	1.36299	+	0.786924i	0.372971	+	0.927843i	$0.378339\pi$
$90$	12.7321	−	7.35090i	1.34208	−	0.774853i
$91$	7.08710	−	12.2752i	0.742930	−	1.28679i
$92$	5.60211			0.584060
$93$	−9.93877	+	17.2145i	−1.03060	+	1.78506i
$94$	3.32955	+	5.76694i	0.343417	+	0.594815i
$95$	−4.70844	−	8.15525i	−0.483076	−	0.836711i
$96$	−13.9588	+	8.05913i	−1.42467	+	0.822532i
$97$	−5.04200	+	2.91100i	−0.511938	+	0.295568i	−0.733630	−	0.679549i	$-0.762175\pi$
$97$	−5.04200	+	2.91100i	−0.511938	+	0.295568i	0.221692	+	0.975117i	$0.428842\pi$
$98$			6.79823i			0.686725i
$99$	−17.9048	+	10.3373i	−1.79950	+	1.03894i
$100$	4.02607			0.402607
$101$		−	16.0750i		−	1.59952i	−0.600320	−	0.799760i	$-0.704960\pi$
$101$		−	16.0750i		−	1.59952i	0.600320	−	0.799760i	$-0.295040\pi$
$102$			14.2865i			1.41457i
$103$			19.7867i			1.94964i	0.222999	+	0.974819i	$0.428415\pi$
$103$			19.7867i			1.94964i	−0.222999	+	0.974819i	$0.571585\pi$
$104$	−5.38203	−	9.32196i	−0.527752	−	0.914093i
$105$	27.9860	+	16.1577i	2.73115	+	1.57683i
$106$	−5.58804	−	9.67876i	−0.542758	−	0.940084i
$107$	0.976050	−	0.563523i	0.0943583	−	0.0544778i	−0.452078	−	0.891978i	$-0.649317\pi$
$107$	0.976050	−	0.563523i	0.0943583	−	0.0544778i	0.546437	+	0.837500i	$0.315984\pi$
$108$	−4.37085	+	7.57054i	−0.420586	+	0.728476i
$109$	2.35788	−	4.08396i	0.225844	−	0.391173i	−0.730728	−	0.682668i	$-0.760819\pi$
$109$	2.35788	−	4.08396i	0.225844	−	0.391173i	0.956572	+	0.291495i	$0.0941528\pi$
$110$	9.85194			0.939346
$111$	10.9441	−	18.9558i	1.03877	−	1.79921i
$112$	0.958259	+	0.553251i	0.0905469	+	0.0522773i
$113$	0.355888	−	0.205472i	0.0334791	−	0.0193292i	−0.483167	−	0.875528i	$-0.660514\pi$
$113$	0.355888	−	0.205472i	0.0334791	−	0.0193292i	0.516646	+	0.856199i	$0.327180\pi$
$114$	−7.47943	−	4.31825i	−0.700512	−	0.404441i
$115$	−13.9107			−1.29718
$116$	−2.56395	−	4.44089i	−0.238057	−	0.412326i
$117$	−17.9290	−	10.3513i	−1.65754	−	0.956979i
$118$	7.43578			0.684519
$119$	−17.6582	+	10.1950i	−1.61872	+	0.934570i
$120$	21.2529	−	12.2704i	1.94012	−	1.12013i
$121$	−2.85444			−0.259495
$122$	1.84529	+	3.19614i	0.167065	+	0.289365i
$123$	3.48938	−	6.04378i	0.314626	−	0.544949i
$124$	−3.97588	+	6.88643i	−0.357045	+	0.618420i
$125$	4.52946			0.405127
$126$	19.2438			1.71437
$127$		−	3.07777i		−	0.273108i	−0.990633	−	0.136554i	$-0.956397\pi$
$127$		−	3.07777i		−	0.273108i	0.990633	−	0.136554i	$-0.0436027\pi$
$128$	−5.12494	+	2.95888i	−0.452985	+	0.261531i
$129$	4.99200	−	2.88213i	0.439521	−	0.253757i
$130$	4.93264	+	8.54358i	0.432621	+	0.749322i
$131$		−	9.13364i		−	0.798010i	−0.916949	−	0.399005i	$-0.869356\pi$
$131$		−	9.13364i		−	0.798010i	0.916949	−	0.399005i	$-0.130644\pi$
$132$	−11.0311	+	6.36882i	−0.960136	+	0.554335i
$133$		−	12.3261i		−	1.06881i
$134$	−12.1285	+	7.00237i	−1.04774	+	0.604913i
$135$	10.8534	−	18.7986i	0.934111	−	1.61793i
$136$			15.4843i			1.32777i
$137$	6.66936	+	3.85056i	0.569802	+	0.328975i	0.757070	−	0.653334i	$-0.226630\pi$
$137$	6.66936	+	3.85056i	0.569802	+	0.328975i	−0.187268	+	0.982309i	$0.559963\pi$
$138$	−11.0487	+	6.37898i	−0.940529	+	0.543015i
$139$	11.6995			0.992341			0.496170	−	0.868225i	$-0.334739\pi$
$139$	11.6995			0.992341			0.496170	+	0.868225i	$0.334739\pi$
$140$	11.1955	+	6.46370i	0.946189	+	0.546282i
$141$	18.5145	+	10.6893i	1.55920	+	0.900205i
$142$	−3.58371	+	6.20716i	−0.300738	+	0.520894i
$143$	−6.93660	−	12.0145i	−0.580068	−	1.00471i
$144$	0.808069	−	1.39962i	0.0673391	−	0.116635i
$145$	6.36661	+	11.0273i	0.528718	+	0.915767i
$146$		−	6.51272i		−	0.538997i
$147$	10.9127	+	18.9013i	0.900064	+	1.55896i
$148$	4.37807	−	7.58304i	0.359875	−	0.623322i
$149$	−2.15443	+	1.24386i	−0.176498	+	0.101901i	−0.585646	−	0.810567i	$-0.699159\pi$
$149$	−2.15443	+	1.24386i	−0.176498	+	0.101901i	0.409149	+	0.912468i	$0.365826\pi$
$150$	−7.94038	+	4.58438i	−0.648329	+	0.374313i
$151$	2.53021	−	4.38245i	0.205905	−	0.356638i	−0.744516	−	0.667605i	$-0.767319\pi$
$151$	2.53021	−	4.38245i	0.205905	−	0.356638i	0.950421	+	0.310967i	$0.100653\pi$
$152$	−8.10653	−	4.68031i	−0.657527	−	0.379623i
$153$	14.8906	+	25.7912i	1.20383	+	2.08510i
$154$	11.1679	+	6.44781i	0.899937	+	0.519579i
$155$	9.87263	−	17.0999i	0.792988	−	1.37350i
$156$	−11.0461	−	6.37744i	−0.884392	−	0.510604i
$157$	−4.39296	+	7.60883i	−0.350597	+	0.607251i	−0.986354	−	0.164638i	$-0.947354\pi$
$157$	−4.39296	+	7.60883i	−0.350597	+	0.607251i	0.635758	+	0.771889i	$0.280688\pi$
$158$	−5.32938	−	9.23076i	−0.423983	−	0.734360i
$159$	−31.0732	−	17.9401i	−2.46426	−	1.42274i
$160$	13.8659	−	8.00550i	1.09620	−	0.632890i
$161$	−15.7689	−	9.10417i	−1.24276	−	0.717509i
$162$		−	4.72711i		−	0.371397i
$163$		−	4.03054i		−	0.315697i	−0.987463	−	0.157848i	$-0.949544\pi$
$163$		−	4.03054i		−	0.315697i	0.987463	−	0.157848i	$-0.0504557\pi$
$164$	1.39588	−	2.41774i	0.109000	−	0.188794i
$165$	27.3917	−	15.8146i	2.13244	−	1.23116i
$166$	−11.2291	−	6.48311i	−0.871545	−	0.503187i
$167$			9.36911i			0.725003i	0.931983	+	0.362502i	$0.118077\pi$
$167$			9.36911i			0.725003i	−0.931983	+	0.362502i	$0.881923\pi$
$168$	32.1224			2.47830
$169$	0.445989	−	0.772476i	0.0343069	−	0.0594213i
$170$		−	14.1914i		−	1.08843i
$171$	−18.0034			−1.37675
$172$	1.99699	−	1.15296i	0.152269	−	0.0879125i
$173$	−1.70254	+	0.982963i	−0.129442	+	0.0747333i	−0.563323	−	0.826237i	$-0.690477\pi$
$173$	−1.70254	+	0.982963i	−0.129442	+	0.0747333i	0.433881	+	0.900970i	$0.357144\pi$
$174$	10.1135	+	5.83901i	0.766700	+	0.442654i
$175$	−11.3326	−	6.54289i	−0.856666	−	0.494596i
$176$	0.937909	−	0.541502i	0.0706975	−	0.0408172i
$177$	20.6739	−	11.9361i	1.55395	−	0.897172i
$178$	−13.5266			−1.01386
$179$		−	8.05262i		−	0.601881i	−0.953643	−	0.300941i	$-0.902699\pi$
$179$		−	8.05262i		−	0.601881i	0.953643	−	0.300941i	$-0.0973006\pi$
$180$	9.44077	−	16.3519i	0.703674	−	1.21880i
$181$	−15.5706			−1.15736			−0.578679	−	0.815556i	$-0.696431\pi$
$181$	−15.5706			−1.15736			−0.578679	+	0.815556i	$0.696431\pi$
$182$			12.9131i			0.957180i
$183$	10.2610	+	5.92422i	0.758518	+	0.437931i
$184$	−11.9751	+	6.91382i	−0.882815	+	0.509694i
$185$	−10.8713	+	18.8297i	−0.799274	+	1.38438i
$186$		−	18.1090i		−	1.32781i
$187$			19.9569i			1.45939i
$188$	7.40650	+	4.27614i	0.540174	+	0.311870i
$189$	24.6063	−	14.2064i	1.78984	−	1.03337i
$190$	7.42965	+	4.28951i	0.539003	+	0.311194i
$191$	7.60898	+	13.1791i	0.550566	+	0.953609i	0.998234	+	0.0594087i	$0.0189215\pi$
$191$	7.60898	+	13.1791i	0.550566	+	0.953609i	−0.447667	+	0.894200i	$0.647745\pi$
$192$	8.19308	−	14.1908i	0.591285	−	1.02414i
$193$	−12.2940	−	7.09792i	−0.884938	−	0.510919i	−0.0126549	−	0.999920i	$-0.504028\pi$
$193$	−12.2940	−	7.09792i	−0.884938	−	0.510919i	−0.872284	+	0.489000i	$0.837362\pi$
$194$	2.65200	−	4.59340i	0.190402	−	0.329787i
$195$	27.4288	+	15.8360i	1.96421	+	1.13404i
$196$	4.36549	+	7.56125i	0.311821	+	0.540089i
$197$	−8.79258	−	5.07640i	−0.626445	−	0.361678i	0.152929	−	0.988237i	$-0.451130\pi$
$197$	−8.79258	−	5.07640i	−0.626445	−	0.361678i	−0.779374	+	0.626559i	$0.784463\pi$
$198$	9.41756	−	16.3117i	0.669277	−	1.15922i
$199$	7.14996	−	4.12803i	0.506847	−	0.292628i	−0.224690	−	0.974430i	$-0.572137\pi$
$199$	7.14996	−	4.12803i	0.506847	−	0.292628i	0.731537	+	0.681802i	$0.238803\pi$
$200$	−8.60613	+	4.96875i	−0.608546	+	0.351344i
$201$	−22.4808	+	38.9378i	−1.58567	+	2.74646i
$202$	7.32236	+	12.6827i	0.515199	+	0.892351i
$203$			16.6670i			1.16980i
$204$	9.17409	+	15.8900i	0.642314	+	1.11252i
$205$	−3.46615	+	6.00355i	−0.242087	+	0.419306i
$206$	−9.01308	−	15.6111i	−0.627971	−	1.08768i
$207$	−13.2974	+	23.0318i	−0.924234	+	1.60082i
$208$	0.939178	+	0.542235i	0.0651203	+	0.0375972i
$209$	−10.4481	−	6.03219i	−0.722707	−	0.417255i
$210$	−29.4402			−2.03157
$211$	1.51078	−	0.872252i	0.104007	−	0.0600483i	−0.447094	−	0.894487i	$-0.647541\pi$
$211$	1.51078	−	0.872252i	0.104007	−	0.0600483i	0.551101	+	0.834438i	$0.314208\pi$
$212$	−12.4304	−	7.17672i	−0.853727	−	0.492899i
$213$			23.0106i			1.57666i
$214$	−0.513384	+	0.889207i	−0.0350942	+	0.0607849i
$215$	−4.95877	+	2.86295i	−0.338186	+	0.195252i
$216$		−	21.5771i		−	1.46814i
$217$	22.3828	−	12.9227i	1.51944	−	0.877249i
$218$			4.29618i			0.290974i
$219$	−10.4544	−	18.1075i	−0.706442	−	1.22359i
$220$	10.9577	−	6.32643i	0.738768	−	0.426528i
$221$	−17.3066	+	9.99195i	−1.16417	+	0.672132i
$222$			19.9408i			1.33834i
$223$	9.41521			0.630489			0.315245	−	0.949010i	$-0.397913\pi$
$223$	9.41521			0.630489			0.315245	+	0.949010i	$0.397913\pi$
$224$	20.9574			1.40028
$225$	−9.55644	+	16.5522i	−0.637096	+	1.10348i
$226$	−0.187190	+	0.324223i	−0.0124517	+	0.0215670i
$227$	−0.760430	−	1.31710i	−0.0504715	−	0.0874193i	0.839686	−	0.543072i	$-0.182739\pi$
$227$	−0.760430	−	1.31710i	−0.0504715	−	0.0874193i	−0.890157	+	0.455653i	$0.849406\pi$
$228$	−11.0919			−0.734577
$229$	11.9185	−	6.88117i	0.787599	−	0.454721i	−0.0515176	−	0.998672i	$-0.516406\pi$
$229$	11.9185	−	6.88117i	0.787599	−	0.454721i	0.839117	+	0.543952i	$0.183072\pi$
$230$	10.9752	−	6.33652i	0.723682	−	0.417818i
$231$	41.4007			2.72397
$232$	10.9614	+	6.32858i	0.719652	+	0.415492i
$233$	10.3133	+	17.8632i	0.675646	+	1.17025i	0.976280	+	0.216514i	$0.0694687\pi$
$233$	10.3133	+	17.8632i	0.675646	+	1.17025i	−0.300633	+	0.953740i	$0.597198\pi$
$234$	18.8606			1.23296
$235$	−18.3913	−	10.6182i	−1.19971	−	0.692655i
$236$	8.27035	−	4.77489i	0.538354	−	0.310819i
$237$	−29.6349	−	17.1097i	−1.92499	−	1.11140i
$238$	9.28786	−	16.0871i	0.602043	−	1.04277i
$239$	22.7370			1.47073			0.735367	−	0.677669i	$-0.237010\pi$
$239$	22.7370			1.47073			0.735367	+	0.677669i	$0.237010\pi$
$240$	−1.23623	+	2.14121i	−0.0797982	+	0.138215i
$241$	−0.999927	+	1.73192i	−0.0644110	+	0.111563i	−0.896433	−	0.443180i	$-0.853850\pi$
$241$	−0.999927	+	1.73192i	−0.0644110	+	0.111563i	0.832022	+	0.554743i	$0.187184\pi$
$242$	2.25208	−	1.30024i	0.144769	−	0.0835823i
$243$	3.61893	+	6.26817i	0.232155	+	0.402103i
$244$	4.10480	+	2.36991i	0.262783	+	0.151718i
$245$	−10.8401	−	18.7755i	−0.692546	−	1.19953i
$246$			6.35782i			0.405360i
$247$		−	12.0807i		−	0.768677i
$248$		−	19.6273i		−	1.24633i
$249$	−41.6274			−2.63803
$250$	−3.57361	+	2.06323i	−0.226015	+	0.130490i
$251$		−	4.54845i		−	0.287096i	−0.989643	−	0.143548i	$-0.954149\pi$
$251$		−	4.54845i		−	0.287096i	0.989643	−	0.143548i	$-0.0458511\pi$
$252$	21.4037	−	12.3574i	1.34830	−	0.778444i
$253$	−15.4340	+	8.91083i	−0.970328	+	0.560219i
$254$	1.40196	+	2.42827i	0.0879670	+	0.152363i
$255$	−22.7804	−	39.4568i	−1.42657	−	2.47088i
$256$	8.29810	−	14.3727i	0.518632	−	0.898296i
$257$	9.79450			0.610964			0.305482	−	0.952198i	$-0.401182\pi$
$257$	9.79450			0.610964			0.305482	+	0.952198i	$0.401182\pi$
$258$	−2.62570	+	4.54784i	−0.163469	+	0.283136i
$259$	−24.6469	+	14.2299i	−1.53148	+	0.884203i
$260$	10.9725	+	6.33500i	0.680488	+	0.392880i
$261$	24.3436			1.50683
$262$	4.16049	+	7.20618i	0.257036	+	0.445199i
$263$	5.11317			0.315291			0.157646	−	0.987496i	$-0.449610\pi$
$263$	5.11317			0.315291			0.157646	+	0.987496i	$0.449610\pi$
$264$	15.7201	−	27.2280i	0.967506	−	1.67577i
$265$	30.8664	+	17.8207i	1.89611	+	1.09472i
$266$	5.61471	+	9.72497i	0.344260	+	0.596276i
$267$	−37.6084	+	21.7132i	−2.30160	+	1.32883i
$268$	−8.99316	+	15.5766i	−0.549345	+	0.951493i
$269$	−15.8725			−0.967765			−0.483883	−	0.875133i	$-0.660774\pi$
$269$	−15.8725			−0.967765			−0.483883	+	0.875133i	$0.660774\pi$
$270$			19.7754i			1.20349i
$271$	−4.48554	−	7.76919i	−0.272477	−	0.471945i	0.697018	−	0.717053i	$-0.254510\pi$
$271$	−4.48554	−	7.76919i	−0.272477	−	0.471945i	−0.969496	+	0.245109i	$0.921176\pi$
$272$	−0.780016	−	1.35103i	−0.0472954	−	0.0819181i
$273$	20.7284	+	35.9026i	1.25454	+	2.17293i
$274$	−7.01591			−0.423847
$275$	−11.0920	+	6.40395i	−0.668870	+	0.386173i
$276$	−8.19253	+	14.1899i	−0.493133	+	0.854131i
$277$	−1.36761	+	0.789591i	−0.0821719	+	0.0474419i	−0.540523	−	0.841329i	$-0.681774\pi$
$277$	−1.36761	+	0.789591i	−0.0821719	+	0.0474419i	0.458351	+	0.888771i	$0.348440\pi$
$278$	−9.23059	+	5.32928i	−0.553614	+	0.319629i
$279$	−18.8747	−	32.6919i	−1.13000	−	1.95721i
$280$	−31.9086			−1.90690
$281$	10.7532	−	18.6250i	0.641480	−	1.11108i	−0.343622	−	0.939108i	$-0.611654\pi$
$281$	10.7532	−	18.6250i	0.641480	−	1.11108i	0.985102	−	0.171968i	$-0.0550127\pi$
$282$	−19.4765			−1.15981
$283$	−23.4411			−1.39343			−0.696715	−	0.717348i	$-0.745356\pi$
$283$	−23.4411			−1.39343			−0.696715	+	0.717348i	$0.745356\pi$
$284$			9.20512i			0.546224i
$285$	27.5425			1.63148
$286$	10.9456	+	6.31942i	0.647224	+	0.373675i
$287$	−7.85830	+	4.53699i	−0.463861	+	0.267810i
$288$		−	30.6101i		−	1.80372i
$289$	11.7473			0.691016
$290$	−10.0462	−	5.80015i	−0.589930	−	0.340597i
$291$		−	17.0282i		−	0.998212i
$292$	−4.18215	−	7.24369i	−0.244742	−	0.423905i
$293$	0.124522	+	0.215679i	0.00727467	+	0.0126001i	0.869640	−	0.493687i	$-0.164351\pi$
$293$	0.124522	+	0.215679i	0.00727467	+	0.0126001i	−0.862365	+	0.506287i	$0.831018\pi$
$294$	−17.2196	−	9.94175i	−1.00427	−	0.579814i
$295$	−20.5363	+	11.8567i	−1.19567	+	0.690321i
$296$			21.6127i			1.25621i
$297$		−	27.8095i		−	1.61367i
$298$	1.13319	−	1.96274i	0.0656438	−	0.113698i
$299$	−15.4549	−	8.92290i	−0.893780	−	0.516024i
$300$	−5.88773	+	10.1978i	−0.339928	+	0.588773i
$301$	−7.49486			−0.431997
$302$			4.61017i			0.265285i
$303$	40.7172	+	23.5081i	2.33914	+	1.35050i
$304$	0.943074			0.0540890
$305$	−10.1928	−	5.88479i	−0.583635	−	0.336962i
$306$	−23.4965	−	13.5657i	−1.34320	−	0.775499i
$307$	−4.15492	−	7.19653i	−0.237134	−	0.410728i	0.722757	−	0.691102i	$-0.242875\pi$
$307$	−4.15492	−	7.19653i	−0.237134	−	0.410728i	−0.959891	+	0.280375i	$0.909541\pi$
$308$	16.5619			0.943699
$309$	−50.1187	−	28.9360i	−2.85115	−	1.64611i
$310$			17.9884i			1.02167i
$311$			32.5143i			1.84372i	0.387528	+	0.921858i	$0.373329\pi$
$311$			32.5143i			1.84372i	−0.387528	+	0.921858i	$0.626671\pi$
$312$	31.4828			1.78236
$313$	26.1994			1.48088			0.740440	−	0.672123i	$-0.234617\pi$
$313$	26.1994			1.48088			0.740440	+	0.672123i	$0.234617\pi$
$314$		−	8.00420i		−	0.451703i
$315$	−53.1480	+	30.6850i	−2.99455	+	1.72891i
$316$	−11.8551	−	6.84453i	−0.666900	−	0.385035i
$317$	−1.93003	−	1.11430i	−0.108401	−	0.0625854i	0.444819	−	0.895620i	$-0.353268\pi$
$317$	−1.93003	−	1.11430i	−0.108401	−	0.0625854i	−0.553220	+	0.833035i	$0.686601\pi$
$318$	32.6878			1.83304
$319$	14.1276	+	8.15655i	0.790991	+	0.456679i
$320$	−8.13856	+	14.0964i	−0.454959	+	0.788012i
$321$			3.29639i			0.183986i
$322$	16.5883			0.924428
$323$	−8.68918	+	15.0501i	−0.483479	+	0.837410i
$324$	−3.03552	−	5.25767i	−0.168640	−	0.292093i
$325$	−11.1070	−	6.41262i	−0.616104	−	0.355708i
$326$	1.83596	+	3.17998i	0.101685	+	0.176123i
$327$	6.89633	+	11.9448i	0.381368	+	0.660549i
$328$			6.89089i			0.380486i
$329$	−13.8986	−	24.0731i	−0.766255	−	1.32719i
$330$	−14.4075	+	24.9545i	−0.793107	+	1.37370i
$331$	−14.5319	−	8.39000i	−0.798745	−	0.461156i	0.0442869	−	0.999019i	$-0.485898\pi$
$331$	−14.5319	−	8.39000i	−0.798745	−	0.461156i	−0.843032	+	0.537863i	$0.819232\pi$
$332$	−16.6525			−0.913926
$333$	20.7840	+	35.9989i	1.13895	+	1.97273i
$334$	−4.26775	−	7.39196i	−0.233521	−	0.404470i
$335$	22.3312	−	38.6787i	1.22008	−	2.11324i
$336$	−2.80272	+	1.61815i	−0.152901	+	0.0882773i
$337$	5.63262	+	9.75598i	0.306828	+	0.531442i	0.977667	−	0.210162i	$-0.0673990\pi$
$337$	5.63262	+	9.75598i	0.306828	+	0.531442i	−0.670839	+	0.741603i	$0.734066\pi$
$338$			0.812616i			0.0442005i
$339$			1.20193i			0.0652798i
$340$	−9.11303	−	15.7842i	−0.494223	−	0.856020i
$341$		−	25.2965i		−	1.36988i
$342$	14.2041	−	8.20076i	0.768071	−	0.443446i
$343$		−	1.75760i		−	0.0949016i
$344$	−2.84585	+	4.92915i	−0.153438	+	0.265762i
$345$	20.3431	−	35.2353i	1.09524	−	1.89700i
$346$	0.895504	−	1.55106i	0.0481426	−	0.0833855i
$347$	−20.0250	+	11.5615i	−1.07500	+	0.620651i	−0.929543	−	0.368713i	$-0.879798\pi$
$347$	−20.0250	+	11.5615i	−1.07500	+	0.620651i	−0.145457	+	0.989365i	$0.546465\pi$
$348$	14.9981			0.803983
$349$	6.70238	−	17.4378i	0.358770	−	0.933426i
$349$	6.70238	−	17.4378i	0.358770	−	0.933426i
$350$	11.9215			0.637231
$351$	24.1163	−	13.9236i	1.28723	−	0.743185i
$352$	10.2562	−	17.7642i	0.546657	−	0.946838i
$353$	1.81411	−	3.14213i	0.0965552	−	0.167239i	−0.813701	−	0.581283i	$-0.802551\pi$
$353$	1.81411	−	3.14213i	0.0965552	−	0.167239i	0.910257	+	0.414045i	$0.135884\pi$
$354$	−10.8741	+	18.8345i	−0.577951	+	1.00104i
$355$		−	22.8575i		−	1.21315i
$356$	−15.0448	+	8.68612i	−0.797372	+	0.460363i
$357$		−	59.6365i		−	3.15630i
$358$	3.66807	+	6.35329i	0.193864	+	0.335782i
$359$		−	18.9391i		−	0.999569i	−0.866150	−	0.499784i	$-0.833413\pi$
$359$		−	18.9391i		−	0.999569i	0.866150	−	0.499784i	$-0.166587\pi$
$360$			46.6052i			2.45631i
$361$	4.24721	+	7.35638i	0.223537	+	0.387178i
$362$	12.2848	−	7.09263i	0.645675	−	0.372780i
$363$	4.17434	−	7.23018i	0.219096	−	0.379486i
$364$	8.29214	+	14.3624i	0.434626	+	0.752795i
$365$	10.3848	+	17.9870i	0.543566	+	0.941483i
$366$	−10.7942			−0.564223
$367$	−6.67162	−	3.85186i	−0.348256	−	0.201066i	0.315661	−	0.948872i	$-0.397774\pi$
$367$	−6.67162	−	3.85186i	−0.348256	−	0.201066i	−0.663917	+	0.747806i	$0.731107\pi$
$368$	0.696561	−	1.20648i	0.0363108	−	0.0628921i
$369$	6.62665	+	11.4777i	0.344970	+	0.597505i
$370$		−	19.8081i		−	1.02977i
$371$	23.3263	+	40.4023i	1.21104	+	2.09758i
$372$	−11.6287	−	20.1415i	−0.602919	−	1.04429i
$373$	−27.1246	−	15.6604i	−1.40446	−	0.810865i	−0.409613	−	0.912259i	$-0.634336\pi$
$373$	−27.1246	−	15.6604i	−1.40446	−	0.810865i	−0.994846	+	0.101395i	$0.967670\pi$
$374$	−9.09062	−	15.7454i	−0.470065	−	0.814176i
$375$	−6.62389	+	11.4729i	−0.342056	+	0.592458i
$376$	−21.1095			−1.08864
$377$			16.3352i			0.841305i
$378$	−12.9424	+	22.4170i	−0.665687	+	1.15300i
$379$	−3.25384	−	1.87860i	−0.167138	−	0.0964974i	0.414097	−	0.910233i	$-0.364097\pi$
$379$	−3.25384	−	1.87860i	−0.167138	−	0.0964974i	−0.581236	+	0.813735i	$0.697431\pi$
$380$	11.0180			0.565214
$381$	7.79585	+	4.50094i	0.399394	+	0.230590i
$382$	−12.0065	−	6.93198i	−0.614308	−	0.354671i
$383$	−27.7702	+	16.0331i	−1.41899	+	0.819255i	−0.996210	−	0.0869769i	$-0.972279\pi$
$383$	−27.7702	+	16.0331i	−1.41899	+	0.819255i	−0.422781	+	0.906232i	$0.638946\pi$
$384$		−	17.3083i		−	0.883261i
$385$	−41.1252			−2.09593
$386$	12.9328			0.658261
$387$			10.9469i			0.556461i
$388$		−	6.81193i		−	0.345823i
$389$	2.35547	+	1.35993i	0.119427	+	0.0689514i	0.558524	−	0.829489i	$-0.311368\pi$
$389$	2.35547	+	1.35993i	0.119427	+	0.0689514i	−0.439096	+	0.898440i	$0.644701\pi$
$390$	−28.8540			−1.46108
$391$	12.8358	+	22.2322i	0.649133	+	1.12433i
$392$	−18.6634	−	10.7753i	−0.942643	−	0.544235i
$393$	23.1351	+	13.3571i	1.16701	+	0.673774i
$394$	9.24946			0.465981
$395$	29.4377	+	16.9958i	1.48117	+	0.855154i
$396$		−	24.1900i		−	1.21559i
$397$	36.7920			1.84654			0.923269	−	0.384154i	$-0.125507\pi$
$397$	36.7920			1.84654			0.923269	+	0.384154i	$0.125507\pi$
$398$	−3.76074	+	6.51380i	−0.188509	+	0.326507i
$399$	31.2215	+	18.0258i	1.56303	+	0.902417i
$400$	0.500597	−	0.867060i	0.0250299	−	0.0433530i
$401$			10.6153i			0.530101i	0.964234	+	0.265051i	$0.0853887\pi$
$401$			10.6153i			0.530101i	−0.964234	+	0.265051i	$0.914611\pi$
$402$		−	40.9611i		−	2.04296i
$403$	21.9371	−	12.6654i	1.09276	−	0.630907i
$404$	16.2884	+	9.40412i	0.810378	+	0.467872i
$405$	7.53758	+	13.0555i	0.374545	+	0.648732i
$406$	−7.59205	−	13.1498i	−0.376787	−	0.652615i
$407$			27.8554i			1.38074i
$408$	−39.2211	−	22.6443i	−1.94173	−	1.12106i
$409$	−2.39326			−0.118339			−0.0591696	−	0.998248i	$-0.518845\pi$
$409$	−2.39326			−0.118339			−0.0591696	+	0.998248i	$0.518845\pi$
$410$		−	6.31551i		−	0.311901i
$411$	−19.5066	+	11.2621i	−0.962188	+	0.555520i
$412$	−20.0494	−	11.5755i	−0.987762	−	0.570284i
$413$	−31.0393			−1.52735
$414$		−	24.2286i		−	1.19077i
$415$	41.3503			2.02981
$416$	20.5402			1.00706
$417$	−17.1094	+	29.6344i	−0.837851	+	1.45120i
$418$	10.9910			0.537585
$419$	13.9701	+	24.1970i	0.682486	+	1.18210i	0.974220	+	0.225601i	$0.0724347\pi$
$419$	13.9701	+	24.1970i	0.682486	+	1.18210i	−0.291733	+	0.956500i	$0.594232\pi$
$420$	−32.7445	+	18.9051i	−1.59777	+	0.922472i
$421$	16.7426	−	9.66633i	0.815983	−	0.471108i	−0.0330460	−	0.999454i	$-0.510521\pi$
$421$	16.7426	−	9.66633i	0.815983	−	0.471108i	0.849029	+	0.528346i	$0.177187\pi$
$422$	−0.794644	+	1.37636i	−0.0386827	+	0.0670003i
$423$	−35.1608	+	20.3001i	−1.70957	+	0.987023i
$424$	35.4285			1.72056
$425$	9.22468	+	15.9776i	0.447463	+	0.775028i
$426$	−10.4816	−	18.1547i	−0.507837	−	0.879600i
$427$	−7.70284	−	13.3417i	−0.372767	−	0.645651i
$428$			1.31868i			0.0637408i
$429$	40.5764			1.95905
$430$	2.60822	−	4.51757i	0.125780	−	0.217857i
$431$	30.3276	−	17.5096i	1.46083	−	0.843410i	0.461779	−	0.886995i	$-0.347211\pi$
$431$	30.3276	−	17.5096i	1.46083	−	0.843410i	0.999050	+	0.0435847i	$0.0138778\pi$
$432$	1.08694	+	1.88263i	0.0522952	+	0.0905780i
$433$	3.33449	+	1.92517i	0.160245	+	0.0925177i	0.577978	−	0.816052i	$-0.303842\pi$
$433$	3.33449	+	1.92517i	0.160245	+	0.0925177i	−0.417733	+	0.908570i	$0.637175\pi$
$434$	−11.7729	+	20.3913i	−0.565117	+	0.978812i
$435$	−37.2422			−1.78563
$436$	2.75879	+	4.77837i	0.132122	+	0.228842i
$437$	−15.5190			−0.742375
$438$	16.4964	+	9.52421i	0.788230	+	0.455085i
$439$	−13.2961	+	7.67652i	−0.634589	+	0.366380i	−0.782527	−	0.622617i	$-0.786070\pi$
$439$	−13.2961	+	7.67652i	−0.634589	+	0.366380i	0.147938	+	0.988997i	$0.452736\pi$
$440$	−15.6155	+	27.0468i	−0.744439	+	1.28941i
$441$	−41.4485			−1.97374
$442$	9.10293	−	15.7667i	0.432982	−	0.749947i
$443$	−3.49833	−	6.05929i	−0.166211	−	0.287886i	0.770874	−	0.636988i	$-0.219820\pi$
$443$	−3.49833	−	6.05929i	−0.166211	−	0.287886i	−0.937085	+	0.349102i	$0.886487\pi$
$444$	12.8050	+	22.1789i	0.607698	+	1.05256i
$445$	37.3581	−	21.5687i	1.77095	−	1.02246i
$446$	−7.42834	+	4.28875i	−0.351742	+	0.203078i
$447$		−	7.27609i		−	0.344147i
$448$	−18.4513	+	10.6529i	−0.871744	+	0.503302i
$449$	15.9271			0.751648			0.375824	−	0.926691i	$-0.377360\pi$
$449$	15.9271			0.751648			0.375824	+	0.926691i	$0.377360\pi$
$450$		−	17.4123i		−	0.820825i
$451$			8.88128i			0.418203i
$452$			0.480817i			0.0226157i
$453$	7.40036	+	12.8178i	0.347699	+	0.602232i
$454$	1.19992	+	0.692772i	0.0563148	+	0.0325134i
$455$	−20.5904	−	35.6637i	−0.965294	−	1.67194i
$456$	23.7100	−	13.6890i	1.11032	−	0.641045i
$457$	−0.695814	+	1.20518i	−0.0325488	+	0.0563762i	−0.881841	−	0.471547i	$-0.843696\pi$
$457$	−0.695814	+	1.20518i	−0.0325488	+	0.0563762i	0.849292	+	0.527923i	$0.177029\pi$
$458$	−6.26892	+	10.8581i	−0.292928	+	0.507365i
$459$	−40.0587			−1.86978
$460$	8.13801	−	14.0954i	0.379437	−	0.657203i
$461$	−14.9319	−	8.62092i	−0.695446	−	0.401516i	0.110203	−	0.993909i	$-0.464850\pi$
$461$	−14.9319	−	8.62092i	−0.695446	−	0.401516i	−0.805649	+	0.592393i	$0.798183\pi$
$462$	−32.6640	+	18.8586i	−1.51967	+	0.877380i
$463$	−30.9321	−	17.8586i	−1.43753	−	0.829961i	−0.439856	−	0.898068i	$-0.644971\pi$
$463$	−30.9321	−	17.8586i	−1.43753	−	0.829961i	−0.997678	+	0.0681072i	$0.978304\pi$
$464$	−1.27520			−0.0591995
$465$	28.8755	+	50.0138i	1.33907	+	2.31934i
$466$	−16.2738	−	9.39568i	−0.753869	−	0.435246i
$467$	0.753312			0.0348591			0.0174296	−	0.999848i	$-0.494452\pi$
$467$	0.753312			0.0348591			0.0174296	+	0.999848i	$0.494452\pi$
$468$	20.9775	−	12.1114i	0.969685	−	0.559848i
$469$	50.6281	−	29.2302i	2.33779	−	1.34972i
$470$	19.3469			0.892407
$471$	−12.8486	−	22.2543i	−0.592030	−	1.02543i
$472$	−11.7858	+	20.4136i	−0.542486	+	0.939614i
$473$	−3.66785	+	6.35290i	−0.168648	+	0.292107i
$474$	31.1748			1.43191
$475$	−11.1530			−0.511737
$476$		−	23.8568i		−	1.09348i
$477$	59.0109	−	34.0700i	2.70192	−	1.55996i
$478$	−17.9388	+	10.3570i	−0.820503	+	0.473718i
$479$	15.0579	+	26.0810i	0.688013	+	1.19167i	0.972480	+	0.232987i	$0.0748500\pi$
$479$	15.0579	+	26.0810i	0.688013	+	1.19167i	−0.284467	+	0.958686i	$0.591817\pi$
$480$			46.8290i			2.13744i
$481$	−24.1562	+	13.9466i	−1.10143	+	0.635909i
$482$		−	1.82192i		−	0.0829861i
$483$	46.1209	−	26.6279i	2.09857	−	1.21161i
$484$	1.66990	−	2.89234i	0.0759043	−	0.131470i
$485$			16.9149i			0.768066i
$486$	−5.71047	−	3.29694i	−0.259032	−	0.149552i
$487$	34.0607	−	19.6649i	1.54344	−	0.891104i	0.544819	−	0.838554i	$-0.316598\pi$
$487$	34.0607	−	19.6649i	1.54344	−	0.891104i	0.998618	−	0.0525499i	$-0.0167349\pi$
$488$	−11.6993			−0.529601
$489$	10.2092	+	5.89428i	0.461675	+	0.266548i
$490$	17.1050	+	9.87558i	0.772725	+	0.446133i
$491$	4.90674	−	8.49873i	0.221438	−	0.383542i	−0.733807	−	0.679358i	$-0.762258\pi$
$491$	4.90674	−	8.49873i	0.221438	−	0.383542i	0.955245	+	0.295816i	$0.0955916\pi$
$492$	4.08268	+	7.07141i	0.184061	+	0.318804i
$493$	11.7493	−	20.3503i	0.529160	−	0.916531i
$494$	5.50292	+	9.53133i	0.247588	+	0.428835i
$495$			60.0668i			2.69980i
$496$	0.988716	+	1.71251i	0.0443946	+	0.0768938i
$497$	14.9596	−	25.9107i	0.671028	−	1.16225i
$498$	32.8428	−	18.9618i	1.47172	−	0.849699i
$499$	34.1585	−	19.7214i	1.52914	−	0.882852i	0.529747	−	0.848156i	$-0.322287\pi$
$499$	34.1585	−	19.7214i	1.52914	−	0.882852i	0.999398	−	0.0346962i	$-0.0110464\pi$
$500$	−2.64980	+	4.58960i	−0.118503	+	0.205253i
$501$	−23.7315	−	13.7014i	−1.06025	−	0.612133i
$502$	2.07188	+	3.58860i	0.0924725	+	0.160167i
$503$	−3.36988	−	1.94560i	−0.150255	−	0.0867500i	0.422987	−	0.906136i	$-0.360981\pi$
$503$	−3.36988	−	1.94560i	−0.150255	−	0.0867500i	−0.573243	+	0.819386i	$0.694315\pi$
$504$	−30.5017	+	52.8305i	−1.35865	+	2.35326i
$505$	−40.4462	−	23.3516i	−1.79983	−	1.03913i
$506$	8.11800	−	14.0608i	0.360889	−	0.625078i
$507$	1.30443	+	2.25934i	0.0579318	+	0.100341i
$508$	3.11863	+	1.80054i	0.138367	+	0.0798862i
$509$	−22.2139	+	12.8252i	−0.984614	+	0.568467i	−0.903660	−	0.428251i	$-0.859130\pi$
$509$	−22.2139	+	12.8252i	−0.984614	+	0.568467i	−0.0809538	+	0.996718i	$0.525797\pi$
$510$	35.9462	+	20.7536i	1.59172	+	0.918983i
$511$			27.1862i			1.20265i
$512$			3.28404i			0.145135i
$513$	12.1082	−	20.9720i	0.534589	−	0.925936i
$514$	−7.72758	+	4.46152i	−0.340849	+	0.196789i
$515$	49.7851	+	28.7435i	2.19380	+	1.26659i
$516$			6.74437i			0.296904i
$517$	−27.2069			−1.19656
$518$	12.9638	−	22.4540i	0.569597	−	0.986571i
$519$		−	5.74995i		−	0.252395i
$520$	−31.2733			−1.37142
$521$	22.2314	−	12.8353i	0.973976	−	0.562325i	0.0735299	−	0.997293i	$-0.476574\pi$
$521$	22.2314	−	12.8353i	0.973976	−	0.562325i	0.900446	+	0.434968i	$0.143240\pi$
$522$	−19.2064	+	11.0888i	−0.840642	+	0.485345i
$523$	7.06674	+	4.07998i	0.309007	+	0.178405i	0.646482	−	0.762929i	$-0.276240\pi$
$523$	7.06674	+	4.07998i	0.309007	+	0.178405i	−0.337475	+	0.941334i	$0.609573\pi$
$524$	9.25491	+	5.34333i	0.404303	+	0.233424i
$525$	33.1457	−	19.1367i	1.44660	−	0.835193i
$526$	−4.03414	+	2.32911i	−0.175897	+	0.101554i
$527$	−36.4388			−1.58730
$528$			3.16757i			0.137851i
$529$	0.0375495	−	0.0650376i	0.00163259	−	0.00282772i
$530$	−32.4703			−1.41042
$531$			45.3355i			1.96739i
$532$	12.4898	+	7.21099i	0.541501	+	0.312636i
$533$	−7.70183	+	4.44665i	−0.333603	+	0.192606i
$534$	19.7813	−	34.2623i	0.856021	−	1.48267i
$535$		−	3.27445i		−	0.141567i
$536$		−	44.3955i		−	1.91759i
$537$	20.3969	+	11.7762i	0.880193	+	0.508179i
$538$	12.5230	−	7.23014i	0.539904	−	0.311714i
$539$	−24.0542	−	13.8877i	−1.03609	−	0.598185i
$540$	12.6988	+	21.9950i	0.546470	+	0.946513i
$541$	−15.2487	+	26.4115i	−0.655592	+	1.13552i	0.326153	+	0.945317i	$0.394248\pi$
$541$	−15.2487	+	26.4115i	−0.655592	+	1.13552i	−0.981745	+	0.190202i	$0.939086\pi$
$542$	7.07793	+	4.08645i	0.304023	+	0.175528i
$543$	22.7705	−	39.4397i	0.977178	−	1.69252i
$544$	−25.5888	−	14.7737i	−1.09711	−	0.633418i
$545$	−6.85043	−	11.8653i	−0.293440	−	0.508253i
$546$	−32.7082	−	18.8841i	−1.39978	−	0.808165i
$547$	22.3286	−	38.6743i	0.954702	−	1.65359i	0.219652	−	0.975578i	$-0.429508\pi$
$547$	22.3286	−	38.6743i	0.954702	−	1.65359i	0.735050	−	0.678013i	$-0.237159\pi$
$548$	−7.80336	+	4.50527i	−0.333343	+	0.192456i
$549$	−19.4867	+	11.2506i	−0.831671	+	0.480166i
$550$	5.83416	−	10.1051i	0.248769	−	0.430881i
$551$	7.10268	+	12.3022i	0.302584	+	0.524091i
$552$		−	40.4431i		−	1.72137i
$553$	22.2466	+	38.5322i	0.946020	+	1.63856i
$554$	0.719338	−	1.24593i	0.0305617	−	0.0529345i
$555$	−31.7964	−	55.0730i	−1.34968	−	2.33772i
$556$	−6.84441	+	11.8549i	−0.290268	+	0.502758i
$557$	−2.01623	−	1.16407i	−0.0854305	−	0.0493233i	0.456676	−	0.889633i	$-0.349040\pi$
$557$	−2.01623	−	1.16407i	−0.0854305	−	0.0493233i	−0.542107	+	0.840310i	$0.682373\pi$
$558$	29.7831	+	17.1953i	1.26082	+	0.727935i
$559$	−7.34563			−0.310687
$560$	2.78407	−	1.60738i	0.117648	−	0.0679242i
$561$	−50.5499	−	29.1850i	−2.13422	−	1.23219i
$562$			19.5928i			0.826473i
$563$	−4.70331	+	8.14636i	−0.198221	+	0.343328i	−0.947952	−	0.318415i	$-0.896850\pi$
$563$	−4.70331	+	8.14636i	−0.198221	+	0.343328i	0.749731	+	0.661743i	$0.230183\pi$
$564$	−21.6625	+	12.5069i	−0.912158	+	0.526634i
$565$		−	1.19393i		−	0.0502290i
$566$	18.4944	−	10.6777i	0.777377	−	0.448819i
$567$			19.7325i			0.828687i
$568$	−11.3605	−	19.6769i	−0.476675	−	0.825625i
$569$	21.1710	−	12.2231i	0.887533	−	0.512418i	0.0143986	−	0.999896i	$-0.495417\pi$
$569$	21.1710	−	12.2231i	0.887533	−	0.512418i	0.873135	+	0.487479i	$0.162083\pi$
$570$	−21.7303	+	12.5460i	−0.910180	+	0.525493i
$571$			2.92557i			0.122431i	0.998125	+	0.0612157i	$0.0194978\pi$
$571$			2.92557i			0.122431i	−0.998125	+	0.0612157i	$0.980502\pi$
$572$	16.2321			0.678698
$573$	−44.5095			−1.85941
$574$	4.13331	−	7.15911i	0.172521	−	0.298816i
$575$	−8.23772	+	14.2681i	−0.343537	+	0.595023i
$576$	15.5594	+	26.9497i	0.648310	+	1.12291i
$577$	−2.15971			−0.0899101			−0.0449550	−	0.998989i	$-0.514314\pi$
$577$	−2.15971			−0.0899101			−0.0449550	+	0.998989i	$0.514314\pi$
$578$	−9.26827	+	5.35104i	−0.385509	+	0.222574i
$579$	35.9574	−	20.7600i	1.49434	−	0.862757i
$580$	−14.8983			−0.618618
$581$	46.8738	+	27.0626i	1.94465	+	1.12274i
$582$	7.75657	+	13.4348i	0.321520	+	0.556890i
$583$	45.6618			1.89112
$584$	17.8796	+	10.3228i	0.739861	+	0.427159i
$585$	−52.0898	+	30.0740i	−2.15365	+	1.24341i
$586$	−0.196489	−	0.113443i	−0.00811689	−	0.00468629i
$587$	−5.29823	+	9.17680i	−0.218681	+	0.378767i	−0.954405	−	0.298515i	$-0.903509\pi$
$587$	−5.29823	+	9.17680i	−0.218681	+	0.378767i	0.735724	+	0.677282i	$0.236842\pi$
$588$	−25.5364			−1.05310
$589$	11.0140	−	19.0769i	0.453825	−	0.786048i
$590$	10.8017	−	18.7091i	0.444700	−	0.770243i
$591$	25.7166	−	14.8475i	1.05784	−	0.610743i
$592$	−1.08873	−	1.88574i	−0.0447466	−	0.0775033i
$593$	−12.3358	−	7.12210i	−0.506572	−	0.292470i	0.224851	−	0.974393i	$-0.427810\pi$
$593$	−12.3358	−	7.12210i	−0.506572	−	0.292470i	−0.731424	+	0.681923i	$0.761144\pi$
$594$	12.6676	+	21.9409i	0.519757	+	0.900246i
$595$			59.2395i			2.42858i
$596$		−	2.91071i		−	0.119227i
$597$			24.1474i			0.988285i
$598$	16.2580			0.664838
$599$	17.7884	−	10.2701i	0.726813	−	0.419626i	−0.0904421	−	0.995902i	$-0.528828\pi$
$599$	17.7884	−	10.2701i	0.726813	−	0.419626i	0.817255	+	0.576276i	$0.195495\pi$
$600$		−	29.0653i		−	1.18658i
$601$	−35.3644	+	20.4176i	−1.44254	+	0.832853i	−0.998019	−	0.0629143i	$-0.979961\pi$
$601$	−35.3644	+	20.4176i	−1.44254	+	0.832853i	−0.444524	+	0.895767i	$0.646627\pi$
$602$	5.91323	−	3.41401i	0.241005	−	0.139145i
$603$	−42.6931	−	73.9466i	−1.73860	−	3.01134i
$604$	2.96042	+	5.12760i	0.120458	+	0.208639i
$605$	−4.14656	+	7.18206i	−0.168582	+	0.291992i
$606$	−42.8329			−1.73997
$607$	−11.8656	+	20.5518i	−0.481609	+	0.834172i	−0.999777	−	0.0211070i	$-0.993281\pi$
$607$	−11.8656	+	20.5518i	−0.481609	+	0.834172i	0.518168	+	0.855279i	$0.326614\pi$
$608$	15.4690	−	8.93104i	0.627351	−	0.362201i
$609$	−42.2169	−	24.3739i	−1.71071	−	0.987681i
$610$	10.7224			0.434137
$611$	−13.6219	−	23.5938i	−0.551082	−	0.954501i
$612$	−34.8449			−1.40852
$613$	8.86221	−	15.3498i	0.357941	−	0.619972i	−0.629676	−	0.776858i	$-0.716812\pi$
$613$	8.86221	−	15.3498i	0.357941	−	0.619972i	0.987617	+	0.156886i	$0.0501455\pi$
$614$	6.55623	+	3.78524i	0.264588	+	0.152760i
$615$	−10.1378	−	17.5592i	−0.408796	−	0.708056i
$616$	−35.4027	+	20.4398i	−1.42642	+	0.823541i
$617$	−6.80941	+	11.7943i	−0.274137	+	0.474819i	−0.969917	−	0.243436i	$-0.921725\pi$
$617$	−6.80941	+	11.7943i	−0.274137	+	0.474819i	0.695780	+	0.718255i	$0.255059\pi$
$618$	52.7230			2.12083
$619$			0.984228i			0.0395595i	0.999804	+	0.0197797i	$0.00629650\pi$
$619$			0.984228i			0.0395595i	−0.999804	+	0.0197797i	$0.993704\pi$
$620$	11.5513	+	20.0074i	0.463911	+	0.803517i
$621$	−17.8864	−	30.9801i	−0.717756	−	1.24319i
$622$	−14.8107	−	25.6528i	−0.593854	−	1.02859i
$623$	56.4644			2.26220
$624$	−2.74691	+	1.58593i	−0.109965	+	0.0634880i
$625$	15.1823	−	26.2965i	0.607291	−	1.05186i
$626$	−20.6706	+	11.9342i	−0.826164	+	0.476986i
$627$	30.5585	−	17.6430i	1.22039	−	0.704592i
$628$	−5.13991	−	8.90258i	−0.205105	−	0.355252i
$629$	40.1249			1.59988
$630$	27.9549	−	48.4192i	1.11375	−	1.92907i
$631$	−12.9590			−0.515890			−0.257945	−	0.966160i	$-0.583045\pi$
$631$	−12.9590			−0.515890			−0.257945	+	0.966160i	$0.583045\pi$
$632$	33.7886			1.34404
$633$			5.10233i			0.202799i
$634$	2.03032			0.0806342
$635$	−7.74397	−	4.47098i	−0.307310	−	0.177425i
$636$	36.3566	−	20.9905i	1.44163	−	0.832328i
$637$		−	27.8130i		−	1.10199i
$638$	−14.8617			−0.588378
$639$	−37.8448	−	21.8497i	−1.49712	−	0.864360i
$640$			17.1931i			0.679618i
$641$	−5.80317	−	10.0514i	−0.229211	−	0.397006i	0.728363	−	0.685191i	$-0.240281\pi$
$641$	−5.80317	−	10.0514i	−0.229211	−	0.397006i	−0.957575	+	0.288186i	$0.906948\pi$
$642$	−1.50155	−	2.60075i	−0.0592613	−	0.102644i
$643$	4.72188	+	2.72618i	0.186213	+	0.107510i	0.590208	−	0.807251i	$-0.299046\pi$
$643$	4.72188	+	2.72618i	0.186213	+	0.107510i	−0.403996	+	0.914761i	$0.632379\pi$
$644$	18.4501	−	10.6522i	0.727036	−	0.419754i
$645$		−	16.7471i		−	0.659418i
$646$		−	15.8321i		−	0.622907i
$647$	5.53347	−	9.58426i	0.217543	−	0.376796i	−0.736513	−	0.676423i	$-0.763529\pi$
$647$	5.53347	−	9.58426i	0.217543	−	0.376796i	0.954056	+	0.299627i	$0.0968623\pi$
$648$	12.9775	+	7.49255i	0.509803	+	0.294335i
$649$	−15.1901	+	26.3100i	−0.596263	+	1.03276i
$650$	11.6841			0.458289
$651$			75.5926i			2.96271i
$652$	4.08406	+	2.35793i	0.159944	+	0.0923438i
$653$	−42.9590			−1.68111			−0.840557	−	0.541723i	$-0.817772\pi$
$653$	−42.9590			−1.68111			−0.840557	+	0.541723i	$0.817772\pi$
$654$	−10.8820	−	6.28273i	−0.425521	−	0.245674i
$655$	−22.9811	−	13.2682i	−0.897947	−	0.518430i
$656$	−0.347125	−	0.601239i	−0.0135530	−	0.0234744i
$657$	39.7077			1.54915
$658$	21.9312	+	12.6620i	0.854967	+	0.493616i
$659$		−	27.2028i		−	1.05967i	−0.848101	−	0.529835i	$-0.822254\pi$
$659$		−	27.2028i		−	1.05967i	0.848101	−	0.529835i	$-0.177746\pi$
$660$			37.0071i			1.44050i
$661$	−46.1146			−1.79365			−0.896825	−	0.442386i	$-0.854132\pi$
$661$	−46.1146			−1.79365			−0.896825	+	0.442386i	$0.854132\pi$
$662$	15.2870			0.594146
$663$		−	58.4490i		−	2.26997i
$664$	35.5965	−	20.5516i	1.38141	−	0.797559i
$665$	−31.0137	−	17.9058i	−1.20266	−	0.694357i
$666$	−32.7959	−	18.9347i	−1.27082	−	0.733706i
$667$	20.9844			0.812517
$668$	−9.49351	−	5.48108i	−0.367315	−	0.212069i
$669$	−13.7688	+	23.8483i	−0.532334	+	0.922029i
$670$			40.6885i			1.57193i
$671$	−15.0785			−0.582100
$672$	−30.6482	+	53.0843i	−1.18228	+	2.04777i
$673$	19.0750	+	33.0389i	0.735287	+	1.27355i	0.954597	+	0.297899i	$0.0962860\pi$
$673$	19.0750	+	33.0389i	0.735287	+	1.27355i	−0.219310	+	0.975655i	$0.570381\pi$
$674$	−8.88795	−	5.13146i	−0.342351	−	0.197656i
$675$	−12.8544	−	22.2645i	−0.494766	−	0.856960i
$676$	0.521822	+	0.903822i	0.0200701	+	0.0347624i
$677$			18.3343i			0.704646i	0.935878	+	0.352323i	$0.114608\pi$
$677$			18.3343i			0.704646i	−0.935878	+	0.352323i	$0.885392\pi$
$678$	−0.547494	−	0.948288i	−0.0210264	−	0.0364188i
$679$	−11.0703	+	19.1743i	−0.424839	+	0.735843i
$680$	38.9601	+	22.4936i	1.49405	+	0.862591i
$681$	4.44822			0.170456
$682$	11.5229	+	19.9582i	0.441234	+	0.764240i
$683$	−7.10692	−	12.3095i	−0.271939	−	0.471012i	0.697420	−	0.716663i	$-0.254331\pi$
$683$	−7.10692	−	12.3095i	−0.271939	−	0.471012i	−0.969358	+	0.245651i	$0.920998\pi$
$684$	10.5322	−	18.2424i	0.402711	−	0.697515i
$685$	19.3767	−	11.1872i	0.740347	−	0.427440i
$686$	0.800611	+	1.38670i	0.0305675	+	0.0529444i
$687$			40.2521i			1.53572i
$688$		−	0.573433i		−	0.0218619i
$689$	22.8618	+	39.5978i	0.870965	+	1.50856i
$690$			37.0662i			1.41109i
$691$	−24.7831	+	14.3085i	−0.942794	+	0.544322i	−0.890835	−	0.454327i	$-0.849880\pi$
$691$	−24.7831	+	14.3085i	−0.942794	+	0.544322i	−0.0519587	+	0.998649i	$0.516546\pi$
$692$		−	2.30020i		−	0.0874403i
$693$	−39.3119	+	68.0903i	−1.49334	+	2.58654i
$694$	10.5328	−	18.2433i	0.399819	−	0.692507i
$695$	16.9955	−	29.4371i	0.644677	−	1.11661i
$696$	−32.0600	+	18.5099i	−1.21523	+	0.701614i
$697$	12.7932			0.484577
$698$	2.65517	+	16.8110i	0.100500	+	0.636305i
$699$	−60.3287			−2.28184
$700$	13.2595	−	7.65540i	0.501163	−	0.289347i
$701$	−7.70203	+	13.3403i	−0.290901	+	0.503856i	−0.974023	−	0.226448i	$-0.927289\pi$
$701$	−7.70203	+	13.3403i	−0.290901	+	0.503856i	0.683122	+	0.730305i	$0.260622\pi$
$702$	−12.6847	+	21.9706i	−0.478754	+	0.829227i
$703$	−12.1282	+	21.0066i	−0.457423	+	0.792279i
$704$			20.8533i			0.785939i
$705$	53.7908	−	31.0562i	2.02588	−	1.16964i
$706$			3.30540i			0.124400i
$707$	−30.5659	−	52.9417i	−1.14955	−	1.99108i
$708$			27.9312i			1.04972i
$709$			11.6766i			0.438525i	0.975666	+	0.219263i	$0.0703651\pi$
$709$			11.6766i			0.438525i	−0.975666	+	0.219263i	$0.929635\pi$
$710$	10.4119	+	18.0339i	0.390751	+	0.676801i
$711$	56.2795	−	32.4930i	2.11064	−	1.21858i
$712$	21.4399	−	37.1349i	0.803493	−	1.39169i
$713$	−16.2701	−	28.1806i	−0.609319	−	1.05537i
$714$	27.1652	+	47.0515i	1.01663	+	1.76086i
$715$	−40.3063			−1.50737
$716$	8.15954	+	4.71091i	0.304936	+	0.176055i
$717$	−33.2506	+	57.5918i	−1.24177	+	2.15080i
$718$	8.62702	+	14.9424i	0.321957	+	0.557646i
$719$			41.5665i			1.55017i	0.631859	+	0.775084i	$0.282292\pi$
$719$			41.5665i			1.55017i	−0.631859	+	0.775084i	$0.717708\pi$
$720$	−2.34771	−	4.06636i	−0.0874941	−	0.151544i
$721$	37.6235	+	65.1658i	1.40117	+	2.42690i
$722$	−6.70185	−	3.86931i	−0.249417	−	0.144001i
$723$	−2.92459	−	5.06554i	−0.108767	−	0.188389i
$724$	9.10908	−	15.7774i	0.338536	−	0.586362i
$725$	15.0808			0.560088
$726$			7.60587i			0.282280i
$727$	−13.1180	+	22.7210i	−0.486519	+	0.842676i	−0.999880	−	0.0154971i	$-0.995067\pi$
$727$	−13.1180	+	22.7210i	−0.486519	+	0.842676i	0.513361	+	0.858173i	$0.328400\pi$
$728$	−35.4506	−	20.4674i	−1.31389	−	0.758573i
$729$	−36.7357			−1.36058
$730$	−16.3866	−	9.46083i	−0.606496	−	0.350161i
$731$	9.15116	+	5.28342i	0.338468	+	0.195414i
$732$	−12.0057	+	6.93152i	−0.443745	+	0.256196i
$733$			27.5520i			1.01766i	0.860868	+	0.508828i	$0.169921\pi$
$733$			27.5520i			1.01766i	−0.860868	+	0.508828i	$0.830079\pi$
$734$	7.01829			0.259050
$735$	63.4101			2.33892
$736$		−	26.3861i		−	0.972605i
$737$		−	57.2188i		−	2.10768i
$738$	−10.4565	−	6.03705i	−0.384908	−	0.222227i
$739$	18.3318			0.674347			0.337173	−	0.941443i	$-0.390529\pi$
$739$	18.3318			0.674347			0.337173	+	0.941443i	$0.390529\pi$
$740$	−12.7198	−	22.0313i	−0.467588	−	0.809887i
$741$	30.5999	+	17.6668i	1.12411	+	0.649008i
$742$	−36.8075	−	21.2508i	−1.35125	−	0.780143i
$743$	19.8630			0.728704			0.364352	−	0.931261i	$-0.381290\pi$
$743$	19.8630			0.728704			0.364352	+	0.931261i	$0.381290\pi$
$744$	49.7150	+	28.7030i	1.82264	+	1.05230i
$745$			7.22766i			0.264801i
$746$	28.5341			1.04471
$747$	39.5272	−	68.4630i	1.44622	−	2.50493i
$748$	−20.2219	−	11.6751i	−0.739385	−	0.426884i
$749$	2.14303	−	3.71184i	0.0783046	−	0.135628i
$750$		−	12.0691i		−	0.440700i
$751$			28.9486i			1.05635i	0.849136	+	0.528175i	$0.177123\pi$
$751$			28.9486i			1.05635i	−0.849136	+	0.528175i	$0.822877\pi$
$752$	1.84183	−	1.06338i	0.0671648	−	0.0387776i
$753$	11.5210	+	6.65167i	0.419850	+	0.242400i
$754$	−7.44089	−	12.8880i	−0.270981	−	0.469353i
$755$	−7.35110	−	12.7325i	−0.267534	−	0.463383i
$756$			33.2440i			1.20907i
$757$	−1.32465	−	0.764787i	−0.0481452	−	0.0277967i	0.475734	−	0.879589i	$-0.342182\pi$
$757$	−1.32465	−	0.764787i	−0.0481452	−	0.0277967i	−0.523879	+	0.851792i	$0.675516\pi$
$758$	3.42291			0.124326
$759$		−	52.1249i		−	1.89201i
$760$	−23.5522	+	13.5979i	−0.854329	+	0.493247i
$761$	−3.68255	−	2.12612i	−0.133492	−	0.0770719i	0.431767	−	0.901985i	$-0.357890\pi$
$761$	−3.68255	−	2.12612i	−0.133492	−	0.0770719i	−0.565259	+	0.824914i	$0.691224\pi$
$762$	−8.20094			−0.297089
$763$		−	17.9336i		−	0.649241i
$764$	−17.8055			−0.644180
$765$	86.5243			3.12829
$766$	14.6066	−	25.2994i	0.527758	−	0.914104i
$767$	−30.4213			−1.09845
$768$	24.2703	+	42.0374i	0.875780	+	1.51690i
$769$	−16.1205	+	9.30717i	−0.581320	+	0.335625i	−0.761658	−	0.647980i	$-0.775614\pi$
$769$	−16.1205	+	9.30717i	−0.581320	+	0.335625i	0.180338	+	0.983605i	$0.442281\pi$
$770$	32.4466	−	18.7331i	1.16929	−	0.675093i
$771$	−14.3235	+	24.8090i	−0.515848	+	0.893475i
$772$	14.3843	−	8.30479i	0.517703	−	0.298896i
$773$	23.7953			0.855857			0.427929	−	0.903813i	$-0.359243\pi$
$773$	23.7953			0.855857			0.427929	+	0.903813i	$0.359243\pi$
$774$	−4.98644	−	8.63677i	−0.179234	−	0.310442i
$775$	−11.6928	−	20.2526i	−0.420018	−	0.727493i
$776$	8.40692	+	14.5612i	0.301791	+	0.522717i
$777$		−	83.2393i		−	2.98619i
$778$	−2.47787			−0.0888359
$779$	−3.86688	+	6.69764i	−0.138546	+	0.239968i
$780$	−32.0925	+	18.5286i	−1.14910	+	0.663431i
$781$	−14.6419	−	25.3605i	−0.523927	−	0.907469i
$782$	−20.2541	−	11.6937i	−0.724286	−	0.418167i
$783$	−16.3723	+	28.3577i	−0.585099	+	1.01342i
$784$	2.17120			0.0775430
$785$	12.7630	+	22.1062i	0.455532	+	0.789005i
$786$	−24.3372			−0.868081
$787$	−34.2072	−	19.7495i	−1.21936	−	0.703995i	−0.254575	−	0.967053i	$-0.581936\pi$
$787$	−34.2072	−	19.7495i	−1.21936	−	0.703995i	−0.964780	+	0.263058i	$0.915269\pi$
$788$	10.2876	−	5.93955i	0.366481	−	0.211588i
$789$	−7.47750	+	12.9514i	−0.266206	+	0.461083i
$790$	−30.9673			−1.10177
$791$	0.781392	−	1.35341i	0.0277831	−	0.0481217i
$792$	29.8540	+	51.7086i	1.06081	+	1.83738i
$793$	−7.54947	−	13.0761i	−0.268089	−	0.464344i
$794$	−29.0278	+	16.7592i	−1.03016	+	0.594763i
$795$	−90.2781	+	52.1221i	−3.20183	+	1.84858i
$796$			9.65985i			0.342384i
$797$	−27.2316	+	15.7222i	−0.964593	+	0.556908i	−0.897584	−	0.440844i	$-0.854679\pi$
$797$	−27.2316	+	15.7222i	−0.964593	+	0.556908i	−0.0670096	+	0.997752i	$0.521346\pi$
$798$	−32.8439			−1.16266
$799$			39.1907i			1.38647i
$800$		−	18.9629i		−	0.670440i
$801$		−	82.4710i		−	2.91397i
$802$	−4.83539	−	8.37515i	−0.170744	−	0.295737i
$803$	23.0439	+	13.3044i	0.813203	+	0.469503i
$804$	−26.3032	−	45.5585i	−0.927643	−	1.60672i
$805$	−45.8140	+	26.4507i	−1.61473	+	0.932265i
$806$	−11.5385	+	19.9852i	−0.406426	+	0.703950i
$807$	23.2120	−	40.2044i	0.817102	−	1.41526i
$808$	−46.4242			−1.63320
$809$	−14.7568	+	25.5596i	−0.518822	+	0.898627i	0.480938	+	0.876754i	$0.340296\pi$
$809$	−14.7568	+	25.5596i	−0.518822	+	0.898627i	−0.999761	+	0.0218724i	$0.993037\pi$
$810$	−11.8939	−	6.86693i	−0.417908	−	0.241279i
$811$	27.3251	−	15.7762i	0.959515	−	0.553976i	0.0634915	−	0.997982i	$-0.479776\pi$
$811$	27.3251	−	15.7762i	0.959515	−	0.553976i	0.896024	+	0.444006i	$0.146443\pi$
$812$	−16.8883	−	9.75049i	−0.592665	−	0.342175i
$813$	26.2387			0.920230
$814$	−12.6885	−	21.9771i	−0.444732	−	0.770298i
$815$	−10.1412	−	5.85505i	−0.355232	−	0.205093i
$816$	4.56279			0.159730
$817$	−5.53207	+	3.19394i	−0.193543	+	0.111742i
$818$	1.88822	−	1.09016i	0.0660200	−	0.0381166i
$819$	−78.7303			−2.75106
$820$	−4.05551	−	7.02435i	−0.141625	−	0.245301i
$821$	−17.7100	+	30.6747i	−0.618085	+	1.07055i	0.371750	+	0.928333i	$0.378758\pi$
$821$	−17.7100	+	30.6747i	−0.618085	+	1.07055i	−0.989835	+	0.142221i	$0.954576\pi$
$822$	10.2601	−	17.7710i	0.357862	−	0.619834i
$823$	−38.1303			−1.32914			−0.664569	−	0.747227i	$-0.731385\pi$
$823$	−38.1303			−1.32914			−0.664569	+	0.747227i	$0.731385\pi$
$824$	57.1435			1.99069
$825$		−	37.4606i		−	1.30421i
$826$	24.4891	−	14.1388i	0.852086	−	0.491952i
$827$	1.90616	−	1.10052i	0.0662839	−	0.0382690i	−0.466492	−	0.884526i	$-0.654482\pi$
$827$	1.90616	−	1.10052i	0.0662839	−	0.0382690i	0.532776	+	0.846257i	$0.321149\pi$
$828$	−15.5584	−	26.9479i	−0.540691	−	0.936505i
$829$			36.8094i			1.27844i	0.769023	+	0.639221i	$0.220743\pi$
$829$			36.8094i			1.27844i	−0.769023	+	0.639221i	$0.779257\pi$
$830$	−32.6242	+	18.8356i	−1.13240	+	0.653794i
$831$		−	4.61880i		−	0.160224i
$832$	−18.0840	+	10.4408i	−0.626948	+	0.361969i
$833$	−20.0048	+	34.6493i	−0.693124	+	1.20053i
$834$		−	31.1742i		−	1.07947i
$835$	23.5736	+	13.6102i	0.815797	+	0.471001i
$836$	12.2246	−	7.05785i	0.422795	−	0.244101i
$837$	50.7767			1.75510
$838$	−22.0441	−	12.7272i	−0.761501	−	0.439653i
$839$	−37.2741	−	21.5202i	−1.28685	−	0.742961i	−0.308755	−	0.951142i	$-0.599912\pi$
$839$	−37.2741	−	21.5202i	−1.28685	−	0.742961i	−0.978090	+	0.208181i	$0.933246\pi$
$840$	46.6632	−	80.8230i	1.61003	−	2.78866i
$841$	4.89597	+	8.48006i	0.168826	+	0.292416i
$842$	−8.80628	+	15.2529i	−0.303484	+	0.525650i
$843$	31.4509	+	54.4746i	1.08323	+	1.87620i
$844$			2.04112i			0.0702584i
$845$	−1.29575	−	2.24430i	−0.0445751	−	0.0772064i
$846$	18.4939	−	32.0324i	0.635833	−	1.10130i
$847$	−9.40089	+	5.42761i	−0.323018	+	0.186495i
$848$	−3.09118	+	1.78469i	−0.106152	+	0.0612867i
$849$	34.2803	−	59.3753i	1.17650	−	2.03775i
$850$	−14.5560	−	8.40393i	−0.499268	−	0.288252i
$851$	17.9159	+	31.0313i	0.614149	+	1.06374i
$852$	−23.3162	−	13.4616i	−0.798798	−	0.461186i
$853$	13.2264	−	22.9088i	0.452864	−	0.784383i	−0.545699	−	0.837981i	$-0.683736\pi$
$853$	13.2264	−	22.9088i	0.452864	−	0.784383i	0.998563	+	0.0535985i	$0.0170691\pi$
$854$	12.1546	+	7.01749i	0.415923	+	0.240133i
$855$	−26.1529	+	45.2982i	−0.894411	+	1.54916i
$856$	−1.62744	−	2.81881i	−0.0556248	−	0.0963451i
$857$	−6.73916	−	3.89086i	−0.230205	−	0.132909i	0.380461	−	0.924797i	$-0.375765\pi$
$857$	−6.73916	−	3.89086i	−0.230205	−	0.132909i	−0.610667	+	0.791888i	$0.709099\pi$
$858$	−32.0136	+	18.4831i	−1.09293	+	0.631001i
$859$	−6.88188	−	3.97325i	−0.234807	−	0.135566i	0.377981	−	0.925813i	$-0.376619\pi$
$859$	−6.88188	−	3.97325i	−0.234807	−	0.135566i	−0.612787	+	0.790248i	$0.709952\pi$
$860$		−	6.69948i		−	0.228451i
$861$		−	26.5396i		−	0.904467i
$862$	−15.9517	+	27.6292i	−0.543319	+	0.941055i
$863$	−38.0159	+	21.9485i	−1.29408	+	0.747135i	−0.979374	−	0.202056i	$-0.935238\pi$
$863$	−38.0159	+	21.9485i	−1.29408	+	0.747135i	−0.314701	+	0.949191i	$0.601904\pi$
$864$	35.6575	+	20.5869i	1.21309	+	0.700379i
$865$			5.71168i			0.194203i
$866$	−3.50776			−0.119198
$867$	−17.1792	+	29.7553i	−0.583437	+	1.01054i
$868$			30.2399i			1.02641i
$869$	43.5483			1.47727
$870$	29.3830	−	16.9643i	0.996178	−	0.575144i
$871$	49.6200	−	28.6481i	1.68131	−	0.970705i
$872$	−11.7944	−	6.80951i	−0.399409	−	0.230599i
$873$	28.0057	+	16.1691i	0.947849	+	0.547241i
$874$	12.2441	−	7.06911i	0.414161	−	0.239116i
$875$	14.9174	−	8.61257i	0.504301	−	0.291158i
$876$	24.4639			0.826559
$877$			35.5173i			1.19934i	0.800249	+	0.599668i	$0.204701\pi$
$877$			35.5173i			1.19934i	−0.800249	+	0.599668i	$0.795299\pi$
$878$	6.99350	−	12.1131i	0.236019	−	0.408797i
$879$	−0.728406			−0.0245685
$880$		−	3.14649i		−	0.106068i
$881$	−40.8367	−	23.5771i	−1.37582	−	0.794331i	−0.384169	−	0.923263i	$-0.625512\pi$
$881$	−40.8367	−	23.5771i	−1.37582	−	0.794331i	−0.991654	+	0.128931i	$0.958845\pi$
$882$	32.7017	−	18.8803i	1.10112	−	0.635733i
$883$	17.6590	−	30.5862i	0.594271	−	1.02931i	−0.399378	−	0.916786i	$-0.630774\pi$
$883$	17.6590	−	30.5862i	0.594271	−	1.02931i	0.993649	−	0.112522i	$-0.0358928\pi$
$884$		−	23.3818i		−	0.786415i
$885$		−	69.3568i		−	2.33140i
$886$	5.52017	+	3.18707i	0.185454	+	0.107072i
$887$	13.9607	−	8.06021i	0.468754	−	0.270635i	−0.246964	−	0.969025i	$-0.579433\pi$
$887$	13.9607	−	8.06021i	0.468754	−	0.270635i	0.715718	+	0.698389i	$0.246100\pi$
$888$	−54.7440	−	31.6065i	−1.83709	−	1.06064i
$889$	−5.85225	−	10.1364i	−0.196278	−	0.339964i
$890$	−19.6497	+	34.0342i	−0.658658	+	1.14083i
$891$	16.7259	+	9.65673i	0.560340	+	0.323512i
$892$	−5.50805	+	9.54022i	−0.184423	+	0.319430i
$893$	−20.5175	−	11.8458i	−0.686593	−	0.396405i
$894$	3.31435	+	5.74063i	0.110849	+	0.191995i
$895$	−20.2612	−	11.6978i	−0.677257	−	0.391014i
$896$	−11.2524	+	19.4897i	−0.375916	+	0.651106i
$897$	45.2026	−	26.0977i	1.50927	−	0.871377i
$898$	−12.5660	+	7.25501i	−0.419334	+	0.242103i
$899$	−14.8929	+	25.7952i	−0.496704	+	0.860317i
$900$	−11.1813	−	19.3667i	−0.372711	−	0.645555i
$901$		−	65.7744i		−	2.19126i
$902$	−4.04554	−	7.00708i	−0.134702	−	0.233310i
$903$	10.9605	−	18.9841i	0.364743	−	0.631753i
$904$	−0.593399	−	1.02780i	−0.0197361	−	0.0341840i
$905$	−22.6190	+	39.1772i	−0.751881	+	1.30230i
$906$	−11.6773	−	6.74192i	−0.387954	−	0.223985i
$907$	−40.8862	−	23.6057i	−1.35760	−	0.783813i	−0.368304	−	0.929705i	$-0.620061\pi$
$907$	−40.8862	−	23.6057i	−1.35760	−	0.783813i	−0.989301	+	0.145892i	$0.953395\pi$
$908$	1.77946			0.0590533
$909$	−77.3257	+	44.6440i	−2.56473	+	1.48075i
$910$	32.4905	+	18.7584i	1.07705	+	0.621835i
$911$		−	25.1654i		−	0.833766i	−0.908960	−	0.416883i	$-0.863122\pi$
$911$		−	25.1654i		−	0.833766i	0.908960	−	0.416883i	$-0.136878\pi$
$912$	−1.37915	+	2.38876i	−0.0456683	+	0.0790998i
$913$	45.8783	−	26.4879i	1.51835	−	0.876620i
$914$		−	1.26781i		−	0.0419354i
$915$	29.8118	−	17.2118i	0.985548	−	0.569006i
$916$			16.1024i			0.532038i
$917$	−17.3672	−	30.0809i	−0.573517	−	0.993360i
$918$	31.6052	−	18.2473i	1.04313	−	0.602249i
$919$	41.9351	−	24.2112i	1.38331	−	0.798655i	0.390761	−	0.920492i	$-0.372212\pi$
$919$	41.9351	−	24.2112i	1.38331	−	0.798655i	0.992550	+	0.121837i	$0.0388786\pi$
$920$			40.1740i			1.32450i
$921$	24.3046			0.800865
$922$	15.7078			0.517307
$923$	14.6617	−	25.3948i	0.482595	−	0.835880i
$924$	−24.2201	+	41.9504i	−0.796782	+	1.38007i
$925$	12.8756	+	22.3012i	0.423348	+	0.733260i
$926$	32.5393			1.06931
$927$	95.1801	−	54.9523i	3.12612	−	1.80487i
$928$	−20.9167	+	12.0763i	−0.686626	+	0.396424i
$929$	−25.4929			−0.836395			−0.418197	−	0.908356i	$-0.637338\pi$
$929$	−25.4929			−0.836395			−0.418197	+	0.908356i	$0.637338\pi$
$930$	−45.5639	−	26.3063i	−1.49410	−	0.862618i
$931$	−12.0933	−	20.9462i	−0.396342	−	0.686485i
$932$	−24.1338			−0.790528
$933$	−82.3572	−	47.5489i	−2.69625	−	1.55668i
$934$	−0.594341	+	0.343143i	−0.0194474	+	0.0112280i
$935$	50.2135	+	28.9908i	1.64216	+	0.948099i
$936$	−29.8944	+	51.7786i	−0.977128	+	1.69244i
$937$	0.740836			0.0242021			0.0121010	−	0.999927i	$-0.496148\pi$
$937$	0.740836			0.0242021			0.0121010	+	0.999927i	$0.496148\pi$
$938$	−26.6294	+	46.1235i	−0.869482	+	1.50599i
$939$	−38.3141	+	66.3620i	−1.25033	+	2.16564i
$940$	21.5184	−	12.4236i	0.701852	−	0.405214i
$941$	12.1635	+	21.0678i	0.396518	+	0.686790i	0.993294	−	0.115618i	$-0.0368849\pi$
$941$	12.1635	+	21.0678i	0.396518	+	0.686790i	−0.596775	+	0.802408i	$0.703552\pi$
$942$	20.2743	+	11.7054i	0.660572	+	0.381381i
$943$	5.71222	+	9.89385i	0.186015	+	0.322188i
$944$		−	2.37482i		−	0.0772939i
$945$		−	82.5490i		−	2.68532i
$946$		−	6.68301i		−	0.217283i
$947$	40.5244			1.31686			0.658432	−	0.752640i	$-0.271220\pi$
$947$	40.5244			1.31686			0.658432	+	0.752640i	$0.271220\pi$
$948$	34.6738	−	20.0189i	1.12615	−	0.650184i
$949$			26.6449i			0.864929i
$950$	8.79943	−	5.08035i	0.285491	−	0.164828i
$951$	5.64495	−	3.25912i	0.183050	−	0.105684i
$952$	29.4428	+	50.9965i	0.954247	+	1.65280i
$953$	−6.34907	−	10.9969i	−0.205667	−	0.356225i	0.744678	−	0.667424i	$-0.232603\pi$
$953$	−6.34907	−	10.9969i	−0.205667	−	0.356225i	−0.950345	+	0.311199i	$0.899270\pi$
$954$	−31.0386	+	53.7605i	−1.00491	+	1.74056i
$955$	44.2133			1.43071
$956$	−13.3015	+	23.0389i	−0.430201	+	0.745131i
$957$	−41.3203	+	23.8563i	−1.33570	+	0.771165i
$958$	−23.7605	−	13.7181i	−0.767667	−	0.443213i
$959$	29.2867			0.945717
$960$	−23.8037	−	41.2292i	−0.768260	−	1.33067i
$961$	15.1883			0.489946
$962$	12.7057	−	22.0069i	0.409648	−	0.709530i
$963$	−5.42145	−	3.13007i	−0.174704	−	0.100865i
$964$	−1.16995	−	2.02641i	−0.0376814	−	0.0652662i
$965$	−35.7181	+	20.6219i	−1.14981	+	0.663841i
$966$	−24.2587	+	42.0173i	−0.780512	+	1.35189i
$967$	25.9709			0.835167			0.417584	−	0.908639i	$-0.362877\pi$
$967$	25.9709			0.835167			0.417584	+	0.908639i	$0.362877\pi$
$968$			8.24358i			0.264959i
$969$	−25.4141	−	44.0186i	−0.816420	−	1.41408i
$970$	−7.70495	−	13.3454i	−0.247391	−	0.428494i
$971$	29.3701	+	50.8705i	0.942531	+	1.63251i	0.760621	+	0.649196i	$0.224895\pi$
$971$	29.3701	+	50.8705i	0.942531	+	1.63251i	0.181910	+	0.983315i	$0.441772\pi$
$972$	−8.46853			−0.271628
$973$	38.5315	−	22.2462i	1.23526	−	0.713179i
$974$	−17.9153	+	31.0302i	−0.574042	+	0.994271i
$975$	32.4857	−	18.7556i	1.04038	−	0.600661i
$976$	1.02078	−	0.589345i	0.0326742	−	0.0188645i
$977$	8.10364	+	14.0359i	0.259258	+	0.449049i	0.966043	−	0.258380i	$-0.0831885\pi$
$977$	8.10364	+	14.0359i	0.259258	+	0.449049i	−0.706785	+	0.707428i	$0.749855\pi$
$978$	−10.7397			−0.343417
$979$	27.6326	−	47.8611i	0.883143	−	1.52965i
$980$	25.3664			0.810301
$981$	−26.1936			−0.836296
$982$			8.94034i			0.285298i
$983$	−10.8142			−0.344920			−0.172460	−	0.985017i	$-0.555172\pi$
$983$	−10.8142			−0.344920			−0.172460	+	0.985017i	$0.555172\pi$
$984$	−17.4543	−	10.0773i	−0.556423	−	0.321251i
$985$	−25.5454	+	14.7487i	−0.813945	+	0.469931i
$986$			21.4077i			0.681761i
$987$	81.3014			2.58785
$988$	12.2411	+	7.06741i	0.389441	+	0.224844i
$989$			9.43628i			0.300056i
$990$	−27.3612	−	47.3910i	−0.869596	−	1.50618i
$991$	−4.67928	−	8.10476i	−0.148642	−	0.257456i	0.782084	−	0.623174i	$-0.214157\pi$
$991$	−4.67928	−	8.10476i	−0.148642	−	0.257456i	−0.930726	+	0.365717i	$0.880824\pi$
$992$	32.4353	+	18.7265i	1.02982	+	0.594568i
$993$	42.5030	−	24.5391i	1.34879	−	0.778725i
$994$			27.2571i			0.864542i
$995$		−	23.9866i		−	0.760428i
$996$	24.3527	−	42.1801i	0.771644	−	1.33653i
$997$	16.9018	+	9.75824i	0.535284	+	0.309046i	0.743166	−	0.669108i	$-0.233323\pi$
$997$	16.9018	+	9.75824i	0.535284	+	0.309046i	−0.207881	+	0.978154i	$0.566657\pi$
$998$	−17.9667	+	31.1193i	−0.568727	+	0.985064i
$999$	−55.9131			−1.76901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.12	✓	58
349.227	even	6	inner	349.2.e.a.227.12	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.12	✓	58	1.1	even	1	trivial
349.2.e.a.227.12	yes	58	349.227	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +O(q^{10})\)	\(q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +2.64684i q^{10} -3.72216i q^{11} +(-1.71106 - 2.96364i) q^{12} +(3.22785 - 1.86360i) q^{13} +(-1.73228 + 3.00039i) q^{14} +(4.24877 + 7.35909i) q^{15} +(0.145481 + 0.251980i) q^{16} -5.36165 q^{17} +(4.38232 + 2.53014i) q^{18} +(1.62062 - 2.80699i) q^{19} +(1.69967 + 2.94391i) q^{20} +11.1228i q^{21} +(1.69549 + 2.93667i) q^{22} +(-2.39400 - 4.14653i) q^{23} +(7.31512 + 4.22339i) q^{24} +(-1.72049 - 2.97998i) q^{25} +(-1.69779 + 2.94065i) q^{26} +7.47134 q^{27} +4.44953i q^{28} +(-2.19135 + 3.79553i) q^{29} +(-6.70432 - 3.87074i) q^{30} +6.79620 q^{31} +(4.77257 + 2.75544i) q^{32} +(9.42805 + 5.44329i) q^{33} +(4.23019 - 2.44230i) q^{34} -11.0488i q^{35} +6.49892 q^{36} -7.48368 q^{37} +2.95285i q^{38} +10.9013i q^{39} +(-7.26644 - 4.19528i) q^{40} -2.38606 q^{41} +(-5.06657 - 8.77556i) q^{42} +(-1.70678 - 0.985410i) q^{43} +(3.77158 + 2.17752i) q^{44} -16.1376 q^{45} +(3.77759 + 2.18099i) q^{46} -7.30944i q^{47} -0.851005 q^{48} +(3.73109 - 6.46243i) q^{49} +(2.71484 + 1.56741i) q^{50} +(7.84088 - 13.5808i) q^{51} +4.36094i q^{52} +12.2676i q^{53} +(-5.89468 + 3.40329i) q^{54} +(-9.36530 - 5.40706i) q^{55} +(-5.49137 - 9.51134i) q^{56} +(4.73998 + 8.20989i) q^{57} -3.99275i q^{58} +(-7.06848 - 4.08099i) q^{59} -9.94240 q^{60} -4.05102i q^{61} +(-5.36201 + 3.09576i) q^{62} +(-18.2932 - 10.5616i) q^{63} -5.60248 q^{64} -10.8288i q^{65} -9.91795 q^{66} +15.3725 q^{67} +(3.13665 - 5.43284i) q^{68} +14.0039 q^{69} +(5.03285 + 8.71715i) q^{70} +(6.81338 - 3.93371i) q^{71} +(-13.8921 + 8.02061i) q^{72} +(-3.57439 + 6.19102i) q^{73} +(5.90441 - 3.40891i) q^{74} +10.0642 q^{75} +(1.89617 + 3.28427i) q^{76} +(-7.07752 - 12.2586i) q^{77} +(-4.96569 - 8.60082i) q^{78} +11.6997i q^{79} +0.845341 q^{80} +(-2.59439 + 4.49362i) q^{81} +(1.88253 - 1.08688i) q^{82} +(7.11627 + 12.3257i) q^{83} +(-11.2705 - 6.50701i) q^{84} +(-7.78870 + 13.4904i) q^{85} +1.79547 q^{86} +(-6.40927 - 11.1012i) q^{87} -10.7495 q^{88} +(12.8584 + 7.42383i) q^{89} +(12.7321 - 7.35090i) q^{90} +(7.08710 - 12.2752i) q^{91} +5.60211 q^{92} +(-9.93877 + 17.2145i) q^{93} +(3.32955 + 5.76694i) q^{94} +(-4.70844 - 8.15525i) q^{95} +(-13.9588 + 8.05913i) q^{96} +(-5.04200 + 2.91100i) q^{97} +6.79823i q^{98} +(-17.9048 + 10.3373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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