LMFDB - Embedded newform 138.2.e.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	138.13
Dual form			138.2.e.b.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-1.61435 + 3.53494i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.99283 - 1.17240i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-1.61435 + 3.53494i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.99283 - 1.17240i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(3.72871 - 1.09485i) q^{10} +(-2.96537 + 3.42222i) q^{11} +(0.654861 - 0.755750i) q^{12} +(3.13097 - 0.919336i) q^{13} +(1.72871 + 3.78534i) q^{14} +(3.26921 - 2.10100i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.260239 + 1.81001i) q^{17} +(0.415415 - 0.909632i) q^{18} +(-0.194351 + 1.35174i) q^{19} +(-3.26921 - 2.10100i) q^{20} +(2.72514 + 3.14498i) q^{21} +4.52825 q^{22} +(-2.28185 - 4.21819i) q^{23} -1.00000 q^{24} +(-6.61537 - 7.63454i) q^{25} +(-2.74514 - 1.76419i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.72871 - 3.78534i) q^{28} +(-0.0798548 - 0.555402i) q^{29} +(-3.72871 - 1.09485i) q^{30} +(-3.90053 + 2.50672i) q^{31} +(0.415415 + 0.909632i) q^{32} +(4.34482 - 1.27576i) q^{33} +(1.19749 - 1.38198i) q^{34} +(10.5902 - 12.2218i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.04639 + 2.29127i) q^{37} +(1.14885 - 0.738323i) q^{38} +(-3.13097 - 0.919336i) q^{39} +(0.553053 + 3.84657i) q^{40} +(-2.54130 + 5.56467i) q^{41} +(0.592229 - 4.11904i) q^{42} +(8.28836 + 5.32661i) q^{43} +(-2.96537 - 3.42222i) q^{44} -3.88612 q^{45} +(-1.69360 + 4.48684i) q^{46} +2.38128 q^{47} +(0.654861 + 0.755750i) q^{48} +(8.67941 + 5.57792i) q^{49} +(-1.43766 + 9.99913i) q^{50} +(0.759635 - 1.66337i) q^{51} +(0.464395 + 3.22994i) q^{52} +(-10.1804 - 2.98924i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(-7.31020 - 16.0071i) q^{55} +(-3.99283 + 1.17240i) q^{56} +(0.894306 - 1.03208i) q^{57} +(-0.367451 + 0.424061i) q^{58} +(6.86289 - 2.01513i) q^{59} +(1.61435 + 3.53494i) q^{60} +(-2.73982 + 1.76078i) q^{61} +(4.44875 + 1.30627i) q^{62} +(-0.592229 - 4.11904i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-1.80470 + 12.5519i) q^{65} +(-3.80941 - 2.44816i) q^{66} +(4.11751 + 4.75186i) q^{67} -1.82862 q^{68} +(-0.360914 + 4.78223i) q^{69} -16.1717 q^{70} +(4.22647 + 4.87760i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.75805 + 12.2275i) q^{73} +(1.04639 - 2.29127i) q^{74} +(1.43766 + 9.99913i) q^{75} +(-1.31033 - 0.384746i) q^{76} +(15.8525 - 10.1878i) q^{77} +(1.35556 + 2.96827i) q^{78} +(-8.09543 + 2.37703i) q^{79} +(2.54487 - 2.93694i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.86969 - 1.72350i) q^{82} +(-0.156624 - 0.342959i) q^{83} +(-3.50079 + 2.24982i) q^{84} +(-6.81838 - 2.00206i) q^{85} +(-1.40214 - 9.75211i) q^{86} +(-0.233095 + 0.510407i) q^{87} +(-0.644437 + 4.48216i) q^{88} +(12.7912 + 8.22041i) q^{89} +(2.54487 + 2.93694i) q^{90} -13.5793 q^{91} +(4.50000 - 1.65831i) q^{92} +4.63657 q^{93} +(-1.55940 - 1.79965i) q^{94} +(-4.46458 - 2.86921i) q^{95} +(0.142315 - 0.989821i) q^{96} +(7.84133 - 17.1701i) q^{97} +(-1.46830 - 10.2122i) q^{98} +(-4.34482 - 1.27576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	−1.61435	+	3.53494i	−0.721961	+	1.58087i	0.0891748	+	0.996016i	$0.471577\pi$
$5$	−1.61435	+	3.53494i	−0.721961	+	1.58087i	−0.811136	+	0.584858i	$0.801150\pi$
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−3.99283	−	1.17240i	−1.50915	−	0.443126i	−0.580554	−	0.814222i	$-0.697164\pi$
$7$	−3.99283	−	1.17240i	−1.50915	−	0.443126i	−0.928595	+	0.371096i	$0.878982\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	3.72871	−	1.09485i	1.17912	−	0.346221i
$11$	−2.96537	+	3.42222i	−0.894094	+	1.03184i	0.105207	+	0.994450i	$0.466449\pi$
$11$	−2.96537	+	3.42222i	−0.894094	+	1.03184i	−0.999301	+	0.0373888i	$0.988096\pi$
$12$	0.654861	−	0.755750i	0.189042	−	0.218166i
$13$	3.13097	−	0.919336i	0.868376	−	0.254978i	0.182951	−	0.983122i	$-0.441435\pi$
$13$	3.13097	−	0.919336i	0.868376	−	0.254978i	0.685424	+	0.728144i	$0.259617\pi$
$14$	1.72871	+	3.78534i	0.462016	+	1.01167i
$15$	3.26921	−	2.10100i	0.844108	−	0.542475i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.260239	+	1.81001i	0.0631173	+	0.438991i	0.996737	+	0.0807238i	$0.0257232\pi$
$17$	0.260239	+	1.81001i	0.0631173	+	0.438991i	−0.933619	+	0.358267i	$0.883368\pi$
$18$	0.415415	−	0.909632i	0.0979143	−	0.214402i
$19$	−0.194351	+	1.35174i	−0.0445873	+	0.310111i	0.955308	+	0.295613i	$0.0955240\pi$
$19$	−0.194351	+	1.35174i	−0.0445873	+	0.310111i	−0.999895	+	0.0144978i	$0.995385\pi$
$20$	−3.26921	−	2.10100i	−0.731019	−	0.469797i
$21$	2.72514	+	3.14498i	0.594674	+	0.686290i
$22$	4.52825			0.965426
$23$	−2.28185	−	4.21819i	−0.475799	−	0.879554i
$23$	−2.28185	−	4.21819i	−0.475799	−	0.879554i
$24$	−1.00000			−0.204124
$25$	−6.61537	−	7.63454i	−1.32307	−	1.52691i
$26$	−2.74514	−	1.76419i	−0.538366	−	0.345987i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	1.72871	−	3.78534i	0.326695	−	0.715362i
$29$	−0.0798548	−	0.555402i	−0.0148287	−	0.103136i	0.981063	−	0.193689i	$-0.0620454\pi$
$29$	−0.0798548	−	0.555402i	−0.0148287	−	0.103136i	−0.995892	+	0.0905538i	$0.971136\pi$
$30$	−3.72871	−	1.09485i	−0.680766	−	0.199891i
$31$	−3.90053	+	2.50672i	−0.700556	+	0.450220i	−0.841824	−	0.539751i	$-0.818518\pi$
$31$	−3.90053	+	2.50672i	−0.700556	+	0.450220i	0.141269	+	0.989971i	$0.454882\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	4.34482	−	1.27576i	0.756337	−	0.222081i
$34$	1.19749	−	1.38198i	0.205368	−	0.237007i
$35$	10.5902	−	12.2218i	1.79007	−	2.06585i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	1.04639	+	2.29127i	0.172025	+	0.376682i	0.975933	−	0.218072i	$-0.0699767\pi$
$37$	1.04639	+	2.29127i	0.172025	+	0.376682i	−0.803908	+	0.594754i	$0.797249\pi$
$38$	1.14885	−	0.738323i	0.186369	−	0.119772i
$39$	−3.13097	−	0.919336i	−0.501357	−	0.147212i
$40$	0.553053	+	3.84657i	0.0874453	+	0.608196i
$41$	−2.54130	+	5.56467i	−0.396884	+	0.869055i	0.600693	+	0.799480i	$0.294892\pi$
$41$	−2.54130	+	5.56467i	−0.396884	+	0.869055i	−0.997577	+	0.0695749i	$0.977836\pi$
$42$	0.592229	−	4.11904i	0.0913829	−	0.635582i
$43$	8.28836	+	5.32661i	1.26396	+	0.812300i	0.988822	−	0.149104i	$-0.0476388\pi$
$43$	8.28836	+	5.32661i	1.26396	+	0.812300i	0.275142	+	0.961404i	$0.411275\pi$
$44$	−2.96537	−	3.42222i	−0.447047	−	0.515920i
$45$	−3.88612			−0.579309
$46$	−1.69360	+	4.48684i	−0.249708	+	0.661548i
$47$	2.38128			0.347345			0.173672	−	0.984803i	$-0.444437\pi$
$47$	2.38128			0.347345			0.173672	+	0.984803i	$0.444437\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	8.67941	+	5.57792i	1.23992	+	0.796846i
$50$	−1.43766	+	9.99913i	−0.203315	+	1.41409i
$51$	0.759635	−	1.66337i	0.106370	−	0.232918i
$52$	0.464395	+	3.22994i	0.0644000	+	0.447912i
$53$	−10.1804	−	2.98924i	−1.39839	−	0.410604i	−0.506259	−	0.862382i	$-0.668972\pi$
$53$	−10.1804	−	2.98924i	−1.39839	−	0.410604i	−0.892131	+	0.451777i	$0.850790\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	−7.31020	−	16.0071i	−0.985707	−	2.15840i
$56$	−3.99283	+	1.17240i	−0.533565	+	0.156669i
$57$	0.894306	−	1.03208i	0.118454	−	0.136703i
$58$	−0.367451	+	0.424061i	−0.0482487	+	0.0556820i
$59$	6.86289	−	2.01513i	0.893472	−	0.262347i	0.197404	−	0.980322i	$-0.436749\pi$
$59$	6.86289	−	2.01513i	0.893472	−	0.262347i	0.696069	+	0.717975i	$0.254931\pi$
$60$	1.61435	+	3.53494i	0.208412	+	0.456359i
$61$	−2.73982	+	1.76078i	−0.350799	+	0.225445i	−0.704158	−	0.710043i	$-0.748676\pi$
$61$	−2.73982	+	1.76078i	−0.350799	+	0.225445i	0.353360	+	0.935487i	$0.385039\pi$
$62$	4.44875	+	1.30627i	0.564992	+	0.165897i
$63$	−0.592229	−	4.11904i	−0.0746138	−	0.518950i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−1.80470	+	12.5519i	−0.223845	+	1.55688i
$66$	−3.80941	−	2.44816i	−0.468906	−	0.301347i
$67$	4.11751	+	4.75186i	0.503034	+	0.580532i	0.949301	−	0.314367i	$-0.101792\pi$
$67$	4.11751	+	4.75186i	0.503034	+	0.580532i	−0.446267	+	0.894900i	$0.647247\pi$
$68$	−1.82862			−0.221753
$69$	−0.360914	+	4.78223i	−0.0434489	+	0.575713i
$70$	−16.1717			−1.93289
$71$	4.22647	+	4.87760i	0.501589	+	0.578865i	0.948925	−	0.315501i	$-0.102173\pi$
$71$	4.22647	+	4.87760i	0.501589	+	0.578865i	−0.447336	+	0.894366i	$0.647627\pi$
$72$	0.841254	+	0.540641i	0.0991427	+	0.0637151i
$73$	−1.75805	+	12.2275i	−0.205765	+	1.43112i	0.581017	+	0.813892i	$0.302655\pi$
$73$	−1.75805	+	12.2275i	−0.205765	+	1.43112i	−0.786781	+	0.617232i	$0.788254\pi$
$74$	1.04639	−	2.29127i	0.121640	−	0.266355i
$75$	1.43766	+	9.99913i	0.166006	+	1.15460i
$76$	−1.31033	−	0.384746i	−0.150305	−	0.0441334i
$77$	15.8525	−	10.1878i	1.80656	−	1.16100i
$78$	1.35556	+	2.96827i	0.153487	+	0.336090i
$79$	−8.09543	+	2.37703i	−0.910807	+	0.267437i	−0.703381	−	0.710813i	$-0.748327\pi$
$79$	−8.09543	+	2.37703i	−0.910807	+	0.267437i	−0.207427	+	0.978251i	$0.566509\pi$
$80$	2.54487	−	2.93694i	0.284525	−	0.328359i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	5.86969	−	1.72350i	0.648199	−	0.190328i
$83$	−0.156624	−	0.342959i	−0.0171917	−	0.0376446i	0.900841	−	0.434148i	$-0.142951\pi$
$83$	−0.156624	−	0.342959i	−0.0171917	−	0.0376446i	−0.918033	+	0.396504i	$0.870223\pi$
$84$	−3.50079	+	2.24982i	−0.381968	+	0.245476i
$85$	−6.81838	−	2.00206i	−0.739557	−	0.217154i
$86$	−1.40214	−	9.75211i	−0.151197	−	1.05160i
$87$	−0.233095	+	0.510407i	−0.0249904	+	0.0547214i
$88$	−0.644437	+	4.48216i	−0.0686972	+	0.477800i
$89$	12.7912	+	8.22041i	1.35587	+	0.871362i	0.998049	−	0.0624300i	$-0.0198850\pi$
$89$	12.7912	+	8.22041i	1.35587	+	0.871362i	0.357816	+	0.933792i	$0.383521\pi$
$90$	2.54487	+	2.93694i	0.268253	+	0.309580i
$91$	−13.5793			−1.42350
$92$	4.50000	−	1.65831i	0.469157	−	0.172891i
$93$	4.63657			0.480790
$94$	−1.55940	−	1.79965i	−0.160840	−	0.185619i
$95$	−4.46458	−	2.86921i	−0.458056	−	0.294375i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	7.84133	−	17.1701i	0.796166	−	1.74336i	0.138075	−	0.990422i	$-0.455908\pi$
$97$	7.84133	−	17.1701i	0.796166	−	1.74336i	0.658091	−	0.752939i	$-0.271364\pi$
$98$	−1.46830	−	10.2122i	−0.148320	−	1.03159i
$99$	−4.34482	−	1.27576i	−0.436671	−	0.128218i
$100$	8.49830	−	5.46153i	0.849830	−	0.546153i
$101$	−0.458228	−	1.00338i	−0.0455954	−	0.0998399i	0.885464	−	0.464709i	$-0.153841\pi$
$101$	−0.458228	−	1.00338i	−0.0455954	−	0.0998399i	−0.931059	+	0.364869i	$0.881114\pi$
$102$	−1.75455	+	0.515181i	−0.173726	+	0.0510105i
$103$	−2.20457	+	2.54421i	−0.217223	+	0.250689i	−0.853894	−	0.520447i	$-0.825765\pi$
$103$	−2.20457	+	2.54421i	−0.217223	+	0.250689i	0.636671	+	0.771136i	$0.280311\pi$
$104$	2.13691	−	2.46613i	0.209541	−	0.241824i
$105$	−15.5166	+	4.55610i	−1.51427	+	0.444629i
$106$	4.40764	+	9.65139i	0.428108	+	0.937426i
$107$	−8.83179	+	5.67585i	−0.853802	+	0.548705i	−0.892758	−	0.450536i	$-0.851233\pi$
$107$	−8.83179	+	5.67585i	−0.853802	+	0.548705i	0.0389566	+	0.999241i	$0.487597\pi$
$108$	0.959493	+	0.281733i	0.0923273	+	0.0271097i
$109$	0.181690	+	1.26368i	0.0174028	+	0.121039i	0.996671	−	0.0815291i	$-0.0259803\pi$
$109$	0.181690	+	1.26368i	0.0174028	+	0.121039i	−0.979268	+	0.202568i	$0.935071\pi$
$110$	−7.31020	+	16.0071i	−0.697000	+	1.52622i
$111$	0.358476	−	2.49326i	0.0340251	−	0.236650i
$112$	3.50079	+	2.24982i	0.330794	+	0.212588i
$113$	−11.5853	−	13.3702i	−1.08985	−	1.25776i	−0.964055	−	0.265704i	$-0.914396\pi$
$113$	−11.5853	−	13.3702i	−1.08985	−	1.25776i	−0.125800	−	0.992056i	$-0.540150\pi$
$114$	−1.36564			−0.127904
$115$	18.5948	−	1.25655i	1.73397	−	0.117174i
$116$	0.561114			0.0520981
$117$	2.13691	+	2.46613i	0.197557	+	0.227993i
$118$	−6.01717	−	3.86700i	−0.553925	−	0.355986i
$119$	1.08296	−	7.53215i	0.0992748	−	0.690471i
$120$	1.61435	−	3.53494i	0.147370	−	0.322695i
$121$	−1.35271	−	9.40830i	−0.122974	−	0.855300i
$122$	3.12491	+	0.917557i	0.282916	+	0.0830717i
$123$	5.14636	−	3.30737i	0.464032	−	0.298215i
$124$	−1.92610	−	4.21757i	−0.172969	−	0.378749i
$125$	19.0237	−	5.58586i	1.70153	−	0.499614i
$126$	−2.72514	+	3.14498i	−0.242774	+	0.280177i
$127$	−6.61277	+	7.63154i	−0.586788	+	0.677190i	−0.969050	−	0.246864i	$-0.920600\pi$
$127$	−6.61277	+	7.63154i	−0.586788	+	0.677190i	0.382262	+	0.924054i	$0.375145\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	−4.09283	−	8.96205i	−0.360354	−	0.789065i
$130$	10.6679	−	6.85587i	0.935641	−	0.601300i
$131$	−7.21436	−	2.11833i	−0.630322	−	0.185079i	−0.0490599	−	0.998796i	$-0.515623\pi$
$131$	−7.21436	−	2.11833i	−0.630322	−	0.185079i	−0.581262	+	0.813717i	$0.697441\pi$
$132$	0.644437	+	4.48216i	0.0560911	+	0.390122i
$133$	2.36080	−	5.16943i	0.204707	−	0.448246i
$134$	0.894821	−	6.22362i	0.0773008	−	0.537639i
$135$	3.26921	+	2.10100i	0.281369	+	0.180825i
$136$	1.19749	+	1.38198i	0.102684	+	0.118504i
$137$	−14.3005			−1.22178			−0.610888	−	0.791717i	$-0.709188\pi$
$137$	−14.3005			−1.22178			−0.610888	+	0.791717i	$0.709188\pi$
$138$	3.85052	−	2.85894i	0.327778	−	0.243369i
$139$	21.8003			1.84907			0.924537	−	0.381092i	$-0.124452\pi$
$139$	21.8003			1.84907			0.924537	+	0.381092i	$0.124452\pi$
$140$	10.5902	+	12.2218i	0.895037	+	1.03293i
$141$	−2.00326	−	1.28741i	−0.168705	−	0.108420i
$142$	0.918499	−	6.38830i	0.0770787	−	0.536094i
$143$	−6.13833	+	13.4411i	−0.513313	+	1.12400i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	2.09223	+	0.614334i	0.173750	+	0.0510176i
$146$	10.3922	−	6.67868i	0.860067	−	0.552731i
$147$	−4.28594	−	9.38489i	−0.353498	−	0.774053i
$148$	−2.41686	+	0.709655i	−0.198665	+	0.0583333i
$149$	1.36272	−	1.57267i	0.111639	−	0.128838i	−0.697180	−	0.716896i	$-0.745562\pi$
$149$	1.36272	−	1.57267i	0.111639	−	0.128838i	0.808818	+	0.588058i	$0.200107\pi$
$150$	6.61537	−	7.63454i	0.540143	−	0.623358i
$151$	−18.0081	+	5.28767i	−1.46548	+	0.430304i	−0.914628	−	0.404297i	$-0.867516\pi$
$151$	−18.0081	+	5.28767i	−1.46548	+	0.430304i	−0.550854	+	0.834601i	$0.685698\pi$
$152$	0.567309	+	1.24223i	0.0460148	+	0.100758i
$153$	−1.53833	+	0.988626i	−0.124367	+	0.0799256i
$154$	−18.0805	−	5.30893i	−1.45697	−	0.427806i
$155$	−2.56427	−	17.8349i	−0.205967	−	1.43253i
$156$	1.35556	−	2.96827i	0.108532	−	0.237652i
$157$	0.283936	−	1.97482i	0.0226606	−	0.157608i	−0.975349	−	0.220667i	$-0.929177\pi$
$157$	0.283936	−	1.97482i	0.0226606	−	0.157608i	0.998010	+	0.0630593i	$0.0200857\pi$
$158$	7.09782	+	4.56149i	0.564672	+	0.362893i
$159$	6.94821	+	8.01867i	0.551029	+	0.635922i
$160$	−3.88612			−0.307225
$161$	4.16563	+	19.5178i	0.328297	+	1.53822i
$162$	1.00000			0.0785674
$163$	−0.457728	−	0.528246i	−0.0358520	−	0.0413754i	0.737540	−	0.675303i	$-0.235987\pi$
$163$	−0.457728	−	0.528246i	−0.0358520	−	0.0413754i	−0.773392	+	0.633928i	$0.781442\pi$
$164$	−5.14636	−	3.30737i	−0.401863	−	0.258262i
$165$	−2.50436	+	17.4182i	−0.194964	+	1.35601i
$166$	−0.156624	+	0.342959i	−0.0121564	+	0.0266188i
$167$	−0.715611	−	4.97718i	−0.0553756	−	0.385146i	−0.998596	−	0.0529775i	$-0.983129\pi$
$167$	−0.715611	−	4.97718i	−0.0553756	−	0.385146i	0.943220	−	0.332168i	$-0.107780\pi$
$168$	3.99283	+	1.17240i	0.308054	+	0.0904527i
$169$	−1.97849	+	1.27150i	−0.152191	+	0.0978074i
$170$	2.95204	+	6.46406i	0.226411	+	0.495771i
$171$	−1.31033	+	0.384746i	−0.100203	+	0.0294223i
$172$	−6.45195	+	7.44594i	−0.491956	+	0.567748i
$173$	5.68588	−	6.56186i	0.432289	−	0.498889i	−0.497252	−	0.867606i	$-0.665658\pi$
$173$	5.68588	−	6.56186i	0.432289	−	0.498889i	0.929542	+	0.368717i	$0.120203\pi$
$174$	0.538385	−	0.158084i	0.0408148	−	0.0119843i
$175$	17.4633	+	38.2393i	1.32010	+	2.89062i
$176$	3.80941	−	2.44816i	0.287145	−	0.184537i
$177$	−6.86289	−	2.01513i	−0.515847	−	0.151466i
$178$	−2.16389	−	15.0502i	−0.162190	−	1.12806i
$179$	−4.80854	+	10.5292i	−0.359407	+	0.786992i	0.640413	+	0.768031i	$0.278763\pi$
$179$	−4.80854	+	10.5292i	−0.359407	+	0.786992i	−0.999820	+	0.0189611i	$0.993964\pi$
$180$	0.553053	−	3.84657i	0.0412221	−	0.286706i
$181$	−2.19877	−	1.41307i	−0.163434	−	0.105032i	0.456367	−	0.889791i	$-0.349150\pi$
$181$	−2.19877	−	1.41307i	−0.163434	−	0.105032i	−0.619801	+	0.784759i	$0.712787\pi$
$182$	8.89254	+	10.2625i	0.659159	+	0.760710i
$183$	3.25684			0.240752
$184$	−4.20014	−	2.31491i	−0.309639	−	0.170657i
$185$	−9.78874			−0.719683
$186$	−3.03631	−	3.50408i	−0.222633	−	0.256932i
$187$	−6.96595	−	4.47674i	−0.509401	−	0.327372i
$188$	−0.338891	+	2.35704i	−0.0247162	+	0.171905i
$189$	−1.72871	+	3.78534i	−0.125745	+	0.275343i
$190$	0.755273	+	5.25304i	0.0547933	+	0.381096i
$191$	−5.90211	−	1.73302i	−0.427062	−	0.125397i	0.0611364	−	0.998129i	$-0.480528\pi$
$191$	−5.90211	−	1.73302i	−0.427062	−	0.125397i	−0.488198	+	0.872733i	$0.662346\pi$
$192$	−0.841254	+	0.540641i	−0.0607122	+	0.0390174i
$193$	3.54355	+	7.75930i	0.255071	+	0.558527i	0.993239	−	0.116090i	$-0.0370362\pi$
$193$	3.54355	+	7.75930i	0.255071	+	0.558527i	−0.738168	+	0.674617i	$0.764309\pi$
$194$	−18.1113	+	5.31795i	−1.30031	+	0.381807i
$195$	8.30430	−	9.58367i	0.594683	−	0.686301i
$196$	−6.75635	+	7.79725i	−0.482597	+	0.556946i
$197$	−3.15681	+	0.926923i	−0.224913	+	0.0660406i	−0.392248	−	0.919860i	$-0.628302\pi$
$197$	−3.15681	+	0.926923i	−0.224913	+	0.0660406i	0.167334	+	0.985900i	$0.446484\pi$
$198$	1.88110	+	4.11904i	0.133684	+	0.292728i
$199$	16.8471	−	10.8270i	1.19426	−	0.767505i	0.216307	−	0.976325i	$-0.430599\pi$
$199$	16.8471	−	10.8270i	1.19426	−	0.767505i	0.977954	+	0.208821i	$0.0669626\pi$
$200$	−9.69275	−	2.84605i	−0.685381	−	0.201246i
$201$	−0.894821	−	6.22362i	−0.0631158	−	0.438980i
$202$	−0.458228	+	1.00338i	−0.0322408	+	0.0705975i
$203$	−0.332308	+	2.31125i	−0.0233234	+	0.162218i
$204$	1.53833	+	0.988626i	0.107705	+	0.0692176i
$205$	−15.5682	−	17.9667i	−1.08733	−	1.25485i
$206$	3.36648			0.234554
$207$	2.88909	−	3.82794i	0.200806	−	0.266061i
$208$	−3.26315			−0.226259
$209$	−4.04964	−	4.67354i	−0.280120	−	0.323275i
$210$	13.6045	+	8.74308i	0.938800	+	0.603330i
$211$	−0.373327	+	2.59655i	−0.0257009	+	0.178754i	−0.998628	−	0.0523567i	$-0.983327\pi$
$211$	−0.373327	+	2.59655i	−0.0257009	+	0.178754i	0.972928	+	0.231110i	$0.0742358\pi$
$212$	4.40764	−	9.65139i	0.302718	−	0.662860i
$213$	−0.918499	−	6.38830i	−0.0629345	−	0.437719i
$214$	10.0731	+	2.95773i	0.688584	+	0.202186i
$215$	−32.2096	+	20.6998i	−2.19668	+	1.41172i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	18.5130	−	5.43592i	1.25675	−	0.369014i
$218$	0.836047	−	0.964850i	0.0566242	−	0.0653479i
$219$	8.08967	−	9.33598i	0.546649	−	0.630867i
$220$	16.8845	−	4.95774i	1.13835	−	0.334251i
$221$	2.47881	+	5.42783i	0.166743	+	0.365115i
$222$	−2.11903	+	1.36182i	−0.142220	+	0.0913993i
$223$	−3.27091	−	0.960425i	−0.219036	−	0.0643148i	0.170373	−	0.985380i	$-0.445503\pi$
$223$	−3.27091	−	0.960425i	−0.219036	−	0.0643148i	−0.389409	+	0.921065i	$0.627321\pi$
$224$	−0.592229	−	4.11904i	−0.0395699	−	0.275215i
$225$	4.19650	−	9.18906i	0.279767	−	0.612604i
$226$	−2.51773	+	17.5112i	−0.167477	+	1.16483i
$227$	12.4561	+	8.00502i	0.826738	+	0.531312i	0.884240	−	0.467033i	$-0.154677\pi$
$227$	12.4561	+	8.00502i	0.826738	+	0.531312i	−0.0575021	+	0.998345i	$0.518314\pi$
$228$	0.894306	+	1.03208i	0.0592269	+	0.0683515i
$229$	9.79565			0.647315			0.323657	−	0.946174i	$-0.395088\pi$
$229$	9.79565			0.647315			0.323657	+	0.946174i	$0.395088\pi$
$230$	−13.1266	−	13.2301i	−0.865544	−	0.872369i
$231$	−18.8439			−1.23983
$232$	−0.367451	−	0.424061i	−0.0241244	−	0.0278410i
$233$	−3.32743	−	2.13841i	−0.217987	−	0.140092i	0.427090	−	0.904209i	$-0.359539\pi$
$233$	−3.32743	−	2.13841i	−0.217987	−	0.140092i	−0.645078	+	0.764117i	$0.723175\pi$
$234$	0.464395	−	3.22994i	0.0303585	−	0.211148i
$235$	−3.84422	+	8.41767i	−0.250769	+	0.549108i
$236$	1.01792	+	7.07982i	0.0662612	+	0.460857i
$237$	8.09543	+	2.37703i	0.525855	+	0.154405i
$238$	−6.40161	+	4.11406i	−0.414955	+	0.266675i
$239$	−4.08249	−	8.93942i	−0.264075	−	0.578243i	0.730424	−	0.682994i	$-0.239323\pi$
$239$	−4.08249	−	8.93942i	−0.264075	−	0.578243i	−0.994498	+	0.104751i	$0.966595\pi$
$240$	−3.72871	+	1.09485i	−0.240687	+	0.0706721i
$241$	−14.2018	+	16.3897i	−0.914818	+	1.05576i	0.0834259	+	0.996514i	$0.473414\pi$
$241$	−14.2018	+	16.3897i	−0.914818	+	1.05576i	−0.998244	+	0.0592420i	$0.981132\pi$
$242$	−6.22449	+	7.18344i	−0.400125	+	0.461769i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	−1.35294	−	2.96252i	−0.0866130	−	0.189656i
$245$	−33.7293	+	21.6765i	−2.15488	+	1.38486i
$246$	−5.86969	−	1.72350i	−0.374238	−	0.109886i
$247$	0.634198	+	4.41095i	0.0403531	+	0.280662i
$248$	−1.92610	+	4.21757i	−0.122307	+	0.267816i
$249$	−0.0536570	+	0.373193i	−0.00340038	+	0.0236501i
$250$	−16.6794	−	10.7192i	−1.05490	−	0.677940i
$251$	4.87930	+	5.63102i	0.307979	+	0.355427i	0.888547	−	0.458785i	$-0.151715\pi$
$251$	4.87930	+	5.63102i	0.307979	+	0.355427i	−0.580569	+	0.814211i	$0.697170\pi$
$252$	4.16140			0.262143
$253$	21.2021	+	4.69952i	1.33297	+	0.295456i
$254$	10.0980			0.633603
$255$	4.65359	+	5.37053i	0.291419	+	0.336316i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−0.583862	+	4.06085i	−0.0364203	+	0.253309i	−0.999895	−	0.0144905i	$-0.995387\pi$
$257$	−0.583862	+	4.06085i	−0.0364203	+	0.253309i	0.963475	+	0.267799i	$0.0862965\pi$
$258$	−4.09283	+	8.96205i	−0.254809	+	0.557953i
$259$	−1.49176	−	10.3754i	−0.0926936	−	0.644698i
$260$	−12.1673	−	3.57265i	−0.754587	−	0.221567i
$261$	0.472039	−	0.303361i	0.0292185	−	0.0187776i
$262$	3.12348	+	6.83946i	0.192969	+	0.422543i
$263$	25.7188	−	7.55172i	1.58589	−	0.465659i	0.634314	−	0.773076i	$-0.281283\pi$
$263$	25.7188	−	7.55172i	1.58589	−	0.465659i	0.951575	+	0.307417i	$0.0994645\pi$
$264$	2.96537	−	3.42222i	0.182506	−	0.210623i
$265$	27.0016	−	31.1615i	1.65870	−	1.91424i
$266$	−5.45279	+	1.60108i	−0.334332	+	0.0981687i
$267$	−6.31636	−	13.8309i	−0.386555	−	0.846437i
$268$	−5.28948	+	3.39934i	−0.323106	+	0.207648i
$269$	5.51035	+	1.61799i	0.335972	+	0.0986503i	0.445367	−	0.895348i	$-0.353073\pi$
$269$	5.51035	+	1.61799i	0.335972	+	0.0986503i	−0.109395	+	0.993998i	$0.534891\pi$
$270$	−0.553053	−	3.84657i	−0.0336577	−	0.234095i
$271$	2.88130	−	6.30917i	0.175027	−	0.383255i	−0.801705	−	0.597720i	$-0.796073\pi$
$271$	2.88130	−	6.30917i	0.175027	−	0.383255i	0.976732	+	0.214465i	$0.0688008\pi$
$272$	0.260239	−	1.81001i	0.0157793	−	0.109748i
$273$	11.4236	+	7.34151i	0.691389	+	0.444329i
$274$	9.36485	+	10.8076i	0.565752	+	0.652912i
$275$	45.7442			2.75848
$276$	−4.68219	−	1.03782i	−0.281835	−	0.0624696i
$277$	−3.81024			−0.228935			−0.114468	−	0.993427i	$-0.536516\pi$
$277$	−3.81024			−0.228935			−0.114468	+	0.993427i	$0.536516\pi$
$278$	−14.2761	−	16.4755i	−0.856226	−	0.988137i
$279$	−3.90053	−	2.50672i	−0.233519	−	0.150073i
$280$	2.30147	−	16.0071i	0.137539	−	0.956607i
$281$	7.54923	−	16.5305i	0.450349	−	0.986127i	−0.539233	−	0.842157i	$-0.681286\pi$
$281$	7.54923	−	16.5305i	0.450349	−	0.986127i	0.989582	−	0.143970i	$-0.0459870\pi$
$282$	0.338891	+	2.35704i	0.0201807	+	0.140360i
$283$	16.4044	+	4.81676i	0.975139	+	0.286327i	0.730217	−	0.683216i	$-0.239419\pi$
$283$	16.4044	+	4.81676i	0.975139	+	0.286327i	0.244923	+	0.969543i	$0.421237\pi$
$284$	−5.42945	+	3.48929i	−0.322178	+	0.207051i
$285$	2.20463	+	4.82747i	0.130591	+	0.285955i
$286$	14.1778	−	4.16299i	0.838353	−	0.246163i
$287$	16.6710	−	19.2394i	0.984058	−	1.13566i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	13.1030	−	3.84738i	0.770764	−	0.226317i
$290$	−0.905836	−	1.98350i	−0.0531925	−	0.116475i
$291$	−15.8794	+	10.2051i	−0.930867	+	0.598232i
$292$	−11.8529	−	3.48032i	−0.693637	−	0.203670i
$293$	1.85784	+	12.9216i	0.108536	+	0.754887i	0.969300	+	0.245882i	$0.0790776\pi$
$293$	1.85784	+	12.9216i	0.108536	+	0.754887i	−0.860763	+	0.509005i	$0.830013\pi$
$294$	−4.28594	+	9.38489i	−0.249961	+	0.547338i
$295$	−3.95578	+	27.5130i	−0.230314	+	1.60187i
$296$	2.11903	+	1.36182i	0.123166	+	0.0791541i
$297$	2.96537	+	3.42222i	0.172068	+	0.198578i
$298$	−2.08094			−0.120545
$299$	−11.0223	−	11.1093i	−0.637439	−	0.642465i
$300$	−10.1019			−0.583236
$301$	−26.8491	−	30.9855i	−1.54756	−	1.78598i
$302$	15.7890	+	10.1470i	0.908554	+	0.583892i
$303$	−0.156982	+	1.09183i	−0.00901837	+	0.0627241i
$304$	0.567309	−	1.24223i	0.0325374	−	0.0712470i
$305$	−1.80120	−	12.5276i	−0.103137	−	0.717331i
$306$	1.75455	+	0.515181i	0.100301	+	0.0294510i
$307$	−20.2621	+	13.0217i	−1.15642	+	0.743186i	−0.970907	−	0.239455i	$-0.923031\pi$
$307$	−20.2621	+	13.0217i	−1.15642	+	0.743186i	−0.185513	+	0.982642i	$0.559395\pi$
$308$	7.82802	+	17.1410i	0.446043	+	0.976698i
$309$	3.23011	−	0.948446i	0.183755	−	0.0539552i
$310$	−11.7995	+	13.6173i	−0.670164	+	0.773411i
$311$	−1.73347	+	2.00054i	−0.0982963	+	0.113440i	−0.802766	−	0.596294i	$-0.796639\pi$
$311$	−1.73347	+	2.00054i	−0.0982963	+	0.113440i	0.704470	+	0.709734i	$0.251185\pi$
$312$	−3.13097	+	0.919336i	−0.177256	+	0.0520472i
$313$	−10.3916	−	22.7544i	−0.587368	−	1.28616i	−0.937020	−	0.349277i	$-0.886427\pi$
$313$	−10.3916	−	22.7544i	−0.587368	−	1.28616i	0.349651	−	0.936880i	$-0.386300\pi$
$314$	−1.67841	+	1.07865i	−0.0947180	+	0.0608715i
$315$	15.5166	+	4.55610i	0.874263	+	0.256707i
$316$	−1.20074	−	8.35132i	−0.0675468	−	0.469798i
$317$	−1.22141	+	2.67452i	−0.0686012	+	0.150216i	−0.940826	−	0.338889i	$-0.889949\pi$
$317$	−1.22141	+	2.67452i	−0.0686012	+	0.150216i	0.872225	+	0.489104i	$0.162676\pi$
$318$	1.50999	−	10.5022i	0.0846761	−	0.588935i
$319$	2.13751	+	1.37369i	0.119678	+	0.0769121i
$320$	2.54487	+	2.93694i	0.142263	+	0.164180i
$321$	10.4984			0.585962
$322$	12.0227	−	15.9296i	0.669996	−	0.887722i
$323$	−2.49724			−0.138950
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	−27.7313	−	17.8218i	−1.53825	−	0.988575i
$326$	−0.0994738	+	0.691855i	−0.00550934	+	0.0383183i
$327$	0.530352	−	1.16131i	0.0293285	−	0.0642205i
$328$	0.870610	+	6.05523i	0.0480714	+	0.334344i
$329$	−9.50803	−	2.79181i	−0.524195	−	0.153917i
$330$	14.8038	−	9.51384i	0.814924	−	0.523720i
$331$	−0.506133	−	1.10828i	−0.0278196	−	0.0609164i	0.895212	−	0.445640i	$-0.147024\pi$
$331$	−0.506133	−	1.10828i	−0.0278196	−	0.0609164i	−0.923032	+	0.384724i	$0.874297\pi$
$332$	0.361758	−	0.106222i	0.0198540	−	0.00582967i
$333$	−1.64953	+	1.90366i	−0.0903935	+	0.104320i
$334$	−3.29288	+	3.80018i	−0.180178	+	0.207937i
$335$	−23.4447	+	6.88398i	−1.28092	+	0.376112i
$336$	−1.72871	−	3.78534i	−0.0943087	−	0.206507i
$337$	16.0373	−	10.3066i	0.873608	−	0.561434i	−0.0252465	−	0.999681i	$-0.508037\pi$
$337$	16.0373	−	10.3066i	0.873608	−	0.561434i	0.898854	+	0.438248i	$0.144401\pi$
$338$	2.25657	+	0.662588i	0.122741	+	0.0360400i
$339$	2.51773	+	17.5112i	0.136744	+	0.951077i
$340$	2.95204	−	6.46406i	0.160097	−	0.350563i
$341$	2.98798	−	20.7818i	0.161808	−	1.12540i
$342$	1.14885	+	0.738323i	0.0621228	+	0.0399239i
$343$	−9.03993	−	10.4326i	−0.488110	−	0.563309i
$344$	9.85240			0.531206
$345$	−16.3223	−	8.99602i	−0.878761	−	0.484330i
$346$	−8.68258			−0.466778
$347$	8.09188	+	9.33853i	0.434395	+	0.501319i	0.930168	−	0.367133i	$-0.119661\pi$
$347$	8.09188	+	9.33853i	0.434395	+	0.501319i	−0.495773	+	0.868452i	$0.665115\pi$
$348$	−0.472039	−	0.303361i	−0.0253039	−	0.0162619i
$349$	2.23168	−	15.5217i	0.119459	−	0.830856i	−0.838695	−	0.544602i	$-0.816681\pi$
$349$	2.23168	−	15.5217i	0.119459	−	0.830856i	0.958154	−	0.286254i	$-0.0924101\pi$
$350$	17.4633	−	38.2393i	0.933453	−	2.04398i
$351$	−0.464395	−	3.22994i	−0.0247876	−	0.172401i
$352$	−4.34482	−	1.27576i	−0.231580	−	0.0679980i
$353$	25.6703	−	16.4973i	1.36629	−	0.878063i	0.367640	−	0.929968i	$-0.380166\pi$
$353$	25.6703	−	16.4973i	1.36629	−	0.878063i	0.998652	+	0.0519054i	$0.0165294\pi$
$354$	2.97131	+	6.50625i	0.157923	+	0.345804i
$355$	−24.0651	+	7.06614i	−1.27724	+	0.375032i
$356$	−9.95712	+	11.4911i	−0.527726	+	0.609029i
$357$	−4.98323	+	5.75096i	−0.263741	+	0.304373i
$358$	11.1064	−	3.26113i	0.586991	−	0.172356i
$359$	6.85337	+	15.0068i	0.361707	+	0.792028i	0.999757	+	0.0220335i	$0.00701404\pi$
$359$	6.85337	+	15.0068i	0.361707	+	0.792028i	−0.638050	+	0.769995i	$0.720259\pi$
$360$	−3.26921	+	2.10100i	−0.172303	+	0.110732i
$361$	16.4409	+	4.82749i	0.865312	+	0.254079i
$362$	0.371967	+	2.58708i	0.0195501	+	0.135974i
$363$	−3.94854	+	8.64610i	−0.207245	+	0.453803i
$364$	1.93253	−	13.4411i	0.101292	−	0.704503i
$365$	−40.3855	−	25.9542i	−2.11387	−	1.35850i
$366$	−2.13277	−	2.46135i	−0.111482	−	0.128657i
$367$	−27.6912			−1.44547			−0.722736	−	0.691125i	$-0.757116\pi$
$367$	−27.6912			−1.44547			−0.722736	+	0.691125i	$0.757116\pi$
$368$	1.00102	+	4.69020i	0.0521816	+	0.244494i
$369$	−6.11749			−0.318464
$370$	6.41026	+	7.39784i	0.333254	+	0.384595i
$371$	37.1442	+	23.8711i	1.92843	+	1.23933i
$372$	−0.659852	+	4.58937i	−0.0342118	+	0.237948i
$373$	−8.45891	+	18.5224i	−0.437986	+	0.959055i	0.553978	+	0.832531i	$0.313109\pi$
$373$	−8.45891	+	18.5224i	−0.437986	+	0.959055i	−0.991964	+	0.126524i	$0.959618\pi$
$374$	1.17843	+	8.19616i	0.0609351	+	0.423813i
$375$	−19.0237	−	5.58586i	−0.982378	−	0.288452i
$376$	2.00326	−	1.28741i	0.103310	−	0.0663933i
$377$	−0.760625	−	1.66554i	−0.0391742	−	0.0857795i
$378$	3.99283	−	1.17240i	0.205369	−	0.0603018i
$379$	10.0383	−	11.5848i	0.515631	−	0.595070i	−0.436900	−	0.899510i	$-0.643924\pi$
$379$	10.0383	−	11.5848i	0.515631	−	0.595070i	0.952532	+	0.304440i	$0.0984692\pi$
$380$	3.47538	−	4.01081i	0.178283	−	0.205750i
$381$	9.68893	−	2.84493i	0.496379	−	0.145750i
$382$	2.55534	+	5.59540i	0.130742	+	0.286286i
$383$	−17.4189	+	11.1945i	−0.890065	+	0.572010i	−0.903828	−	0.427895i	$-0.859255\pi$
$383$	−17.4189	+	11.1945i	−0.890065	+	0.572010i	0.0137632	+	0.999905i	$0.495619\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	10.4216	+	72.4842i	0.531136	+	3.69413i
$386$	3.54355	−	7.75930i	0.180362	−	0.394938i
$387$	−1.40214	+	9.75211i	−0.0712749	+	0.495728i
$388$	15.8794	+	10.2051i	0.806155	+	0.518084i
$389$	22.5491	+	26.0230i	1.14328	+	1.31942i	0.940343	+	0.340227i	$0.110504\pi$
$389$	22.5491	+	26.0230i	1.14328	+	1.31942i	0.202939	+	0.979191i	$0.434951\pi$
$390$	−12.6810			−0.642128
$391$	7.04113	−	5.22790i	0.356085	−	0.264386i
$392$	10.3172			0.521099
$393$	4.92385	+	5.68243i	0.248375	+	0.286641i
$394$	2.76779	+	1.77875i	0.139439	+	0.0896123i
$395$	4.66622	−	32.4542i	0.234783	−	1.63295i
$396$	1.88110	−	4.11904i	0.0945290	−	0.206990i
$397$	3.76408	+	26.1797i	0.188914	+	1.31392i	0.834827	+	0.550513i	$0.185568\pi$
$397$	3.76408	+	26.1797i	0.188914	+	1.31392i	−0.645913	+	0.763411i	$0.723523\pi$
$398$	−19.2150	−	5.64203i	−0.963161	−	0.282810i
$399$	−4.78083	+	3.07246i	−0.239341	+	0.153815i
$400$	4.19650	+	9.18906i	0.209825	+	0.459453i
$401$	17.1744	−	5.04286i	0.857649	−	0.251829i	0.176795	−	0.984248i	$-0.443427\pi$
$401$	17.1744	−	5.04286i	0.857649	−	0.251829i	0.680854	+	0.732419i	$0.261609\pi$
$402$	−4.11751	+	4.75186i	−0.205363	+	0.237001i
$403$	−9.90793	+	11.4344i	−0.493549	+	0.569586i
$404$	1.05838	−	0.310768i	0.0526563	−	0.0154613i
$405$	−1.61435	−	3.53494i	−0.0802179	−	0.175653i
$406$	1.96434	−	1.26241i	0.0974886	−	0.0626522i
$407$	−10.9442	−	3.21350i	−0.542482	−	0.159287i
$408$	−0.260239	−	1.81001i	−0.0128838	−	0.0896086i
$409$	−3.93720	+	8.62128i	−0.194682	+	0.426295i	−0.981648	−	0.190702i	$-0.938924\pi$
$409$	−3.93720	+	8.62128i	−0.194682	+	0.426295i	0.786966	+	0.616997i	$0.211651\pi$
$410$	−3.38330	+	23.5313i	−0.167089	+	1.16213i
$411$	12.0304	+	7.73145i	0.593414	+	0.381364i
$412$	−2.20457	−	2.54421i	−0.108612	−	0.125344i
$413$	−29.7649			−1.46464
$414$	−4.78492	+	0.323343i	−0.235166	+	0.0158914i
$415$	1.46519			0.0719232
$416$	2.13691	+	2.46613i	0.104771	+	0.120912i
$417$	−18.3396	−	11.7861i	−0.898092	−	0.577169i
$418$	−0.880072	+	6.12103i	−0.0430457	+	0.299390i
$419$	−9.31071	+	20.3876i	−0.454858	+	0.996000i	0.533771	+	0.845629i	$0.320774\pi$
$419$	−9.31071	+	20.3876i	−0.454858	+	0.996000i	−0.988630	+	0.150372i	$0.951953\pi$
$420$	−2.30147	−	16.0071i	−0.112300	−	0.781067i
$421$	1.46821	+	0.431105i	0.0715561	+	0.0210108i	0.317315	−	0.948320i	$-0.397219\pi$
$421$	1.46821	+	0.431105i	0.0715561	+	0.0210108i	−0.245759	+	0.969331i	$0.579037\pi$
$422$	2.20682	−	1.41823i	0.107426	−	0.0690386i
$423$	0.989217	+	2.16608i	0.0480974	+	0.105319i
$424$	−10.1804	+	2.98924i	−0.494405	+	0.145171i
$425$	12.0970	−	13.9607i	0.586790	−	0.677192i
$426$	−4.22647	+	4.87760i	−0.204773	+	0.236321i
$427$	13.0040	−	3.81832i	0.629308	−	0.184781i
$428$	−4.36118	−	9.54966i	−0.210806	−	0.461600i
$429$	12.4307	−	7.98871i	0.600159	−	0.385699i
$430$	36.7367	+	10.7869i	1.77160	+	0.520189i
$431$	−0.0173124	−	0.120411i	−0.000833910	−	0.00579997i	0.989400	−	0.145214i	$-0.0463871\pi$
$431$	−0.0173124	−	0.120411i	−0.000833910	−	0.00579997i	−0.990234	+	0.139414i	$0.955478\pi$
$432$	−0.415415	+	0.909632i	−0.0199867	+	0.0437647i
$433$	−4.98003	+	34.6369i	−0.239325	+	1.66454i	0.416127	+	0.909306i	$0.363387\pi$
$433$	−4.98003	+	34.6369i	−0.239325	+	1.66454i	−0.655452	+	0.755236i	$0.727522\pi$
$434$	−16.2317	−	10.4315i	−0.779144	−	0.500726i
$435$	−1.42796	−	1.64795i	−0.0684655	−	0.0790134i
$436$	−1.27668			−0.0611418
$437$	6.14540	−	2.26466i	0.293974	−	0.108334i
$438$	−12.3533			−0.590262
$439$	14.1236	+	16.2995i	0.674082	+	0.777932i	0.985009	−	0.172502i	$-0.0551850\pi$
$439$	14.1236	+	16.2995i	0.674082	+	0.777932i	−0.310927	+	0.950434i	$0.600640\pi$
$440$	−14.8038	−	9.51384i	−0.705745	−	0.453554i
$441$	−1.46830	+	10.2122i	−0.0699189	+	0.486296i
$442$	2.47881	−	5.42783i	0.117905	−	0.258176i
$443$	0.470047	+	3.26925i	0.0223326	+	0.155327i	0.997936	−	0.0642127i	$-0.0204536\pi$
$443$	0.470047	+	3.26925i	0.0223326	+	0.155327i	−0.975604	+	0.219539i	$0.929545\pi$
$444$	2.41686	+	0.709655i	0.114699	+	0.0336787i
$445$	−49.7082	+	31.9455i	−2.35640	+	1.51436i
$446$	1.41615	+	3.10093i	0.0670566	+	0.146833i
$447$	−1.99665	+	0.586268i	−0.0944381	+	0.0277295i
$448$	−2.72514	+	3.14498i	−0.128751	+	0.148586i
$449$	−14.5964	+	16.8451i	−0.688846	+	0.794971i	−0.987200	−	0.159484i	$-0.949017\pi$
$449$	−14.5964	+	16.8451i	−0.688846	+	0.794971i	0.298354	+	0.954455i	$0.403562\pi$
$450$	−9.69275	+	2.84605i	−0.456921	+	0.134164i
$451$	−11.5076	−	25.1982i	−0.541873	−	1.18654i
$452$	14.8828	−	9.56462i	0.700030	−	0.449882i
$453$	18.0081	+	5.28767i	0.846097	+	0.248436i
$454$	−2.10719	−	14.6558i	−0.0988954	−	0.687832i
$455$	21.9218	−	48.0020i	1.02771	−	2.25037i
$456$	0.194351	−	1.35174i	0.00910134	−	0.0633012i
$457$	−30.3801	−	19.5241i	−1.42112	−	0.913299i	−0.999980	−	0.00630408i	$-0.997993\pi$
$457$	−30.3801	−	19.5241i	−1.42112	−	0.913299i	−0.421141	−	0.906995i	$-0.638370\pi$
$458$	−6.41479	−	7.40306i	−0.299743	−	0.345922i
$459$	1.82862			0.0853526
$460$	−1.40255	+	18.5843i	−0.0653944	+	0.866499i
$461$	31.5662			1.47018			0.735091	−	0.677968i	$-0.237139\pi$
$461$	31.5662			1.47018			0.735091	+	0.677968i	$0.237139\pi$
$462$	12.3401	+	14.2412i	0.574113	+	0.662562i
$463$	−23.4268	−	15.0555i	−1.08874	−	0.699688i	−0.132177	−	0.991226i	$-0.542197\pi$
$463$	−23.4268	−	15.0555i	−1.08874	−	0.699688i	−0.956559	+	0.291538i	$0.905833\pi$
$464$	−0.0798548	+	0.555402i	−0.00370717	+	0.0257839i
$465$	−7.48506	+	16.3900i	−0.347111	+	0.760068i
$466$	0.562901	+	3.91507i	0.0260759	+	0.181362i
$467$	−0.565960	−	0.166181i	−0.0261895	−	0.00768994i	0.268612	−	0.963249i	$-0.413435\pi$
$467$	−0.565960	−	0.166181i	−0.0261895	−	0.00768994i	−0.294801	+	0.955559i	$0.595253\pi$
$468$	−2.74514	+	1.76419i	−0.126894	+	0.0815499i
$469$	−10.8694	−	23.8008i	−0.501904	−	1.09902i
$470$	8.87908	−	2.60713i	0.409561	−	0.120258i
$471$	−1.30653	+	1.50782i	−0.0602017	+	0.0694765i
$472$	4.68397	−	5.40559i	0.215597	−	0.248813i
$473$	−42.8069	+	12.5692i	−1.96826	+	0.577935i
$474$	−3.50494	−	7.67474i	−0.160987	−	0.352513i
$475$	11.6057	−	7.45850i	0.532504	−	0.342219i
$476$	7.30137	+	2.14387i	0.334658	+	0.0982643i
$477$	−1.50999	−	10.5022i	−0.0691378	−	0.480864i
$478$	−4.08249	+	8.93942i	−0.186729	+	0.408879i
$479$	1.46379	−	10.1809i	0.0668823	−	0.465177i	−0.928665	−	0.370918i	$-0.879043\pi$
$479$	1.46379	−	10.1809i	0.0668823	−	0.465177i	0.995548	−	0.0942583i	$-0.0300480\pi$
$480$	3.26921	+	2.10100i	0.149219	+	0.0958969i
$481$	5.38266	+	6.21192i	0.245428	+	0.283239i
$482$	21.6867			0.987804
$483$	7.04776	−	18.6715i	0.320684	−	0.849583i
$484$	9.50505			0.432048
$485$	48.0367	+	55.4373i	2.18123	+	2.51728i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	3.91425	−	27.2242i	0.177372	−	1.23365i	−0.685443	−	0.728127i	$-0.740391\pi$
$487$	3.91425	−	27.2242i	0.177372	−	1.23365i	0.862814	−	0.505521i	$-0.168700\pi$
$488$	−1.35294	+	2.96252i	−0.0612446	+	0.134107i
$489$	0.0994738	+	0.691855i	0.00449836	+	0.0312868i
$490$	38.4700	+	11.2958i	1.73790	+	0.510292i
$491$	7.39546	−	4.75278i	0.333753	−	0.214490i	−0.363021	−	0.931781i	$-0.618255\pi$
$491$	7.39546	−	4.75278i	0.333753	−	0.214490i	0.696773	+	0.717291i	$0.254618\pi$
$492$	2.54130	+	5.56467i	0.114571	+	0.250875i
$493$	0.984500	−	0.289075i	0.0443396	−	0.0130193i
$494$	2.91826	−	3.36785i	0.131299	−	0.151527i
$495$	11.5238	−	13.2992i	0.517957	−	0.597754i
$496$	4.44875	−	1.30627i	0.199755	−	0.0586534i
$497$	−11.1571	−	24.4306i	−0.500463	−	1.09586i
$498$	0.317178	−	0.203838i	0.0142131	−	0.00913420i
$499$	−22.5980	−	6.63537i	−1.01163	−	0.297040i	−0.266407	−	0.963861i	$-0.585837\pi$
$499$	−22.5980	−	6.63537i	−1.01163	−	0.297040i	−0.745218	+	0.666821i	$0.767655\pi$
$500$	2.82165	+	19.6250i	0.126188	+	0.877656i
$501$	−2.08886	+	4.57396i	−0.0933233	+	0.204349i
$502$	1.06037	−	7.37506i	0.0473268	−	0.329165i
$503$	5.74416	+	3.69155i	0.256119	+	0.164598i	0.662400	−	0.749151i	$-0.269538\pi$
$503$	5.74416	+	3.69155i	0.256119	+	0.164598i	−0.406280	+	0.913748i	$0.633174\pi$
$504$	−2.72514	−	3.14498i	−0.121387	−	0.140088i
$505$	4.28663			0.190752
$506$	−10.3328	−	19.1010i	−0.459348	−	0.849145i
$507$	2.35183			0.104449
$508$	−6.61277	−	7.63154i	−0.293394	−	0.338595i
$509$	15.7629	+	10.1302i	0.698680	+	0.449014i	0.841162	−	0.540783i	$-0.181872\pi$
$509$	15.7629	+	10.1302i	0.698680	+	0.449014i	−0.142482	+	0.989797i	$0.545508\pi$
$510$	1.01132	−	7.03390i	0.0447821	−	0.311466i
$511$	21.3552	−	46.7613i	0.944698	−	2.06860i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	1.31033	+	0.384746i	0.0578523	+	0.0169870i
$514$	3.45133	−	2.21804i	0.152232	−	0.0978335i
$515$	−5.43469	−	11.9003i	−0.239481	−	0.524390i
$516$	9.45330	−	2.77574i	0.416158	−	0.122195i
$517$	−7.06137	+	8.14926i	−0.310559	+	0.358404i
$518$	−6.86434	+	7.92187i	−0.301602	+	0.348067i
$519$	−8.33087	+	2.44617i	−0.365685	+	0.107375i
$520$	5.26788	+	11.5351i	0.231012	+	0.505846i
$521$	26.2821	−	16.8905i	1.15144	−	0.739986i	0.181516	−	0.983388i	$-0.441900\pi$
$521$	26.2821	−	16.8905i	1.15144	−	0.739986i	0.969926	+	0.243402i	$0.0782633\pi$
$522$	−0.538385	−	0.158084i	−0.0235645	−	0.00691915i
$523$	−1.94917	−	13.5568i	−0.0852312	−	0.592796i	−0.987017	−	0.160613i	$-0.948653\pi$
$523$	−1.94917	−	13.5568i	−0.0852312	−	0.592796i	0.901786	−	0.432182i	$-0.142256\pi$
$524$	3.12348	−	6.83946i	0.136450	−	0.298783i
$525$	5.98267	−	41.6103i	0.261105	−	1.81602i
$526$	−22.5494	−	14.4916i	−0.983202	−	0.631866i
$527$	−5.55224	−	6.40763i	−0.241860	−	0.279121i
$528$	−4.52825			−0.197067
$529$	−12.5863	+	19.2506i	−0.547231	+	0.836981i
$530$	−41.2326			−1.79103
$531$	4.68397	+	5.40559i	0.203267	+	0.234583i
$532$	4.78083	+	3.07246i	0.207275	+	0.133208i
$533$	−2.84093	+	19.7591i	−0.123054	+	0.855863i
$534$	−6.31636	+	13.8309i	−0.273336	+	0.598522i
$535$	−5.80616	−	40.3827i	−0.251022	−	1.74590i
$536$	6.03292	+	1.77143i	0.260583	+	0.0765139i
$537$	9.73773	−	6.25806i	0.420214	−	0.270055i
$538$	−2.38572	−	5.22400i	−0.102856	−	0.225223i
$539$	−44.8266	+	13.1623i	−1.93082	+	0.566939i
$540$	−2.54487	+	2.93694i	−0.109514	+	0.126386i
$541$	−15.6006	+	18.0041i	−0.670723	+	0.774055i	−0.984489	−	0.175445i	$-0.943864\pi$
$541$	−15.6006	+	18.0041i	−0.670723	+	0.774055i	0.313766	+	0.949500i	$0.398409\pi$
$542$	−6.65501	+	1.95409i	−0.285857	+	0.0839352i
$543$	1.08577	+	2.37749i	0.0465947	+	0.102028i
$544$	−1.53833	+	0.988626i	−0.0659554	+	0.0423870i
$545$	−4.76036	−	1.39777i	−0.203912	−	0.0598738i
$546$	−1.93253	−	13.4411i	−0.0827048	−	0.575224i
$547$	−9.15200	+	20.0401i	−0.391311	+	0.856852i	0.606766	+	0.794880i	$0.292466\pi$
$547$	−9.15200	+	20.0401i	−0.391311	+	0.856852i	−0.998078	+	0.0619723i	$0.980261\pi$
$548$	2.03518	−	14.1550i	0.0869385	−	0.604670i
$549$	−2.73982	−	1.76078i	−0.116933	−	0.0751482i
$550$	−29.9561	−	34.5711i	−1.27733	−	1.47412i
$551$	0.766281			0.0326447
$552$	2.28185	+	4.21819i	0.0971220	+	0.179538i
$553$	35.1105			1.49305
$554$	2.49518	+	2.87959i	0.106010	+	0.122342i
$555$	8.23481	+	5.29219i	0.349548	+	0.224641i
$556$	−3.10250	+	21.5784i	−0.131575	+	0.915127i
$557$	4.15715	−	9.10289i	0.176144	−	0.385702i	−0.800882	−	0.598822i	$-0.795636\pi$
$557$	4.15715	−	9.10289i	0.176144	−	0.385702i	0.977026	+	0.213121i	$0.0683628\pi$
$558$	0.659852	+	4.58937i	0.0279338	+	0.194284i
$559$	30.8476	+	9.05767i	1.30471	+	0.383098i
$560$	−13.6045	+	8.74308i	−0.574895	+	0.369463i
$561$	3.43982	+	7.53215i	0.145229	+	0.318008i
$562$	−17.4366	+	5.11985i	−0.735519	+	0.215968i
$563$	−8.93843	+	10.3155i	−0.376710	+	0.434747i	−0.912169	−	0.409815i	$-0.865593\pi$
$563$	−8.93843	+	10.3155i	−0.376710	+	0.434747i	0.535459	+	0.844561i	$0.320139\pi$
$564$	1.55940	−	1.79965i	0.0656627	−	0.0757788i
$565$	65.9655	−	19.3692i	2.77519	−	0.814870i
$566$	−7.10232	−	15.5519i	−0.298533	−	0.653696i
$567$	3.50079	−	2.24982i	0.147019	−	0.0944836i
$568$	6.19256	+	1.81830i	0.259834	+	0.0762942i
$569$	−2.92081	−	20.3147i	−0.122447	−	0.851637i	−0.954770	−	0.297346i	$-0.903899\pi$
$569$	−2.92081	−	20.3147i	−0.122447	−	0.851637i	0.832323	−	0.554291i	$-0.187011\pi$
$570$	2.20463	−	4.82747i	0.0923419	−	0.202200i
$571$	1.46949	−	10.2205i	0.0614963	−	0.427716i	−0.935694	−	0.352812i	$-0.885226\pi$
$571$	1.46949	−	10.2205i	0.0614963	−	0.427716i	0.997191	−	0.0749046i	$-0.0238652\pi$
$572$	−12.4307	−	7.98871i	−0.519753	−	0.334025i
$573$	4.02823	+	4.64883i	0.168282	+	0.194208i
$574$	−25.4573			−1.06257
$575$	−17.1087	+	45.3258i	−0.713482	+	1.89022i
$576$	1.00000			0.0416667
$577$	−26.7283	−	30.8461i	−1.11271	−	1.28414i	−0.954984	−	0.296656i	$-0.904129\pi$
$577$	−26.7283	−	30.8461i	−1.11271	−	1.28414i	−0.157728	−	0.987483i	$-0.550417\pi$
$578$	−11.4883	−	7.38308i	−0.477850	−	0.307095i
$579$	1.21397	−	8.44333i	0.0504508	−	0.350893i
$580$	−0.905836	+	1.98350i	−0.0376128	+	0.0823605i
$581$	0.223288	+	1.55300i	0.00926356	+	0.0644295i
$582$	18.1113	+	5.31795i	0.750737	+	0.220436i
$583$	40.4186	−	25.9755i	1.67397	−	1.07579i
$584$	5.13173	+	11.2369i	0.212353	+	0.464987i
$585$	−12.1673	+	3.57265i	−0.503058	+	0.147711i
$586$	8.54886	−	9.86591i	0.353150	−	0.407557i
$587$	−28.1493	+	32.4861i	−1.16185	+	1.34084i	−0.232079	+	0.972697i	$0.574553\pi$
$587$	−28.1493	+	32.4861i	−1.16185	+	1.34084i	−0.929768	+	0.368146i	$0.879993\pi$
$588$	9.89932	−	2.90670i	0.408241	−	0.119870i
$589$	−2.63037	−	5.75970i	−0.108382	−	0.237324i
$590$	23.3835	−	15.0276i	0.962682	−	0.618678i
$591$	3.15681	+	0.926923i	0.129854	+	0.0381285i
$592$	−0.358476	−	2.49326i	−0.0147333	−	0.102472i
$593$	−10.3634	+	22.6928i	−0.425576	+	0.931881i	0.568448	+	0.822719i	$0.307544\pi$
$593$	−10.3634	+	22.6928i	−0.425576	+	0.931881i	−0.994024	+	0.109162i	$0.965183\pi$
$594$	0.644437	−	4.48216i	0.0264416	−	0.183905i
$595$	24.8774	+	15.9878i	1.01988	+	0.655434i
$596$	1.36272	+	1.57267i	0.0558194	+	0.0644190i
$597$	−20.0262			−0.819618
$598$	−1.17772	+	15.6052i	−0.0481604	+	0.638142i
$599$	33.7284			1.37811			0.689053	−	0.724711i	$-0.258027\pi$
$599$	33.7284			1.37811			0.689053	+	0.724711i	$0.258027\pi$
$600$	6.61537	+	7.63454i	0.270071	+	0.311679i
$601$	33.5327	+	21.5502i	1.36783	+	0.879049i	0.998732	−	0.0503423i	$-0.0160312\pi$
$601$	33.5327	+	21.5502i	1.36783	+	0.879049i	0.369095	+	0.929392i	$0.379668\pi$
$602$	−5.83487	+	40.5824i	−0.237812	+	1.65402i
$603$	−2.61197	+	5.71942i	−0.106368	+	0.232913i
$604$	−2.67102	−	18.5774i	−0.108682	−	0.755902i
$605$	35.4416	+	10.4066i	1.44090	+	0.423088i
$606$	0.927953	−	0.596359i	0.0376955	−	0.0242254i
$607$	11.9674	+	26.2049i	0.485741	+	1.06362i	0.980845	+	0.194790i	$0.0624027\pi$
$607$	11.9674	+	26.2049i	0.485741	+	1.06362i	−0.495104	+	0.868834i	$0.664870\pi$
$608$	−1.31033	+	0.384746i	−0.0531407	+	0.0156035i
$609$	1.52911	−	1.76469i	0.0619627	−	0.0715088i
$610$	−8.28822	+	9.56512i	−0.335580	+	0.387280i
$611$	7.45571	−	2.18919i	0.301626	−	0.0885653i
$612$	−0.759635	−	1.66337i	−0.0307064	−	0.0672377i
$613$	−24.3644	+	15.6581i	−0.984070	+	0.632423i	−0.930558	−	0.366144i	$-0.880678\pi$
$613$	−24.3644	+	15.6581i	−0.984070	+	0.632423i	−0.0535115	+	0.998567i	$0.517041\pi$
$614$	23.1100	+	6.78571i	0.932644	+	0.273849i
$615$	3.38330	+	23.5313i	0.136428	+	0.948876i
$616$	7.82802	−	17.1410i	0.315400	−	0.690629i
$617$	3.70256	−	25.7519i	0.149060	−	1.03673i	−0.768704	−	0.639605i	$-0.779098\pi$
$617$	3.70256	−	25.7519i	0.149060	−	1.03673i	0.917764	−	0.397127i	$-0.129993\pi$
$618$	−2.83206	−	1.82006i	−0.113922	−	0.0732134i
$619$	−13.9138	−	16.0574i	−0.559244	−	0.645402i	0.403768	−	0.914862i	$-0.367700\pi$
$619$	−13.9138	−	16.0574i	−0.559244	−	0.645402i	−0.963012	+	0.269459i	$0.913155\pi$
$620$	18.0183			0.723631
$621$	−4.50000	+	1.65831i	−0.180579	+	0.0665458i
$622$	2.64709			0.106139
$623$	−41.4355	−	47.8192i	−1.66008	−	1.91583i
$624$	2.74514	+	1.76419i	0.109894	+	0.0706243i
$625$	−3.77698	+	26.2695i	−0.151079	+	1.05078i
$626$	−10.3916	+	22.7544i	−0.415332	+	0.909450i
$627$	0.880072	+	6.12103i	0.0351467	+	0.244451i
$628$	1.91431	+	0.562092i	0.0763892	+	0.0224299i
$629$	−3.87490	+	2.49025i	−0.154502	+	0.0992926i
$630$	−6.71797	−	14.7103i	−0.267650	−	0.586072i
$631$	−16.4814	+	4.83937i	−0.656113	+	0.192652i	−0.592810	−	0.805342i	$-0.701982\pi$
$631$	−16.4814	+	4.83937i	−0.656113	+	0.192652i	−0.0633031	+	0.997994i	$0.520163\pi$
$632$	−5.52519	+	6.37641i	−0.219780	+	0.253640i
$633$	1.71786	−	1.98252i	0.0682789	−	0.0787980i
$634$	2.82112	−	0.828355i	0.112041	−	0.0328982i
$635$	−16.3017	−	35.6957i	−0.646913	−	1.41654i
$636$	−8.92588	+	5.73632i	−0.353934	+	0.227460i
$637$	32.3030	+	9.48501i	1.27989	+	0.375810i
$638$	−0.361603	−	2.51500i	−0.0143160	−	0.0995698i
$639$	−2.68109	+	5.87076i	−0.106062	+	0.232244i
$640$	0.553053	−	3.84657i	0.0218613	−	0.152049i
$641$	−1.99719	−	1.28351i	−0.0788841	−	0.0506957i	0.500604	−	0.865676i	$-0.333111\pi$
$641$	−1.99719	−	1.28351i	−0.0788841	−	0.0506957i	−0.579488	+	0.814981i	$0.696748\pi$
$642$	−6.87497	−	7.93414i	−0.271334	−	0.313136i
$643$	46.5640			1.83630			0.918152	−	0.396229i	$-0.129681\pi$
$643$	46.5640			1.83630			0.918152	+	0.396229i	$0.129681\pi$
$644$	−19.9120	+	1.34556i	−0.784641	+	0.0530224i
$645$	38.2876			1.50757
$646$	1.63534	+	1.88729i	0.0643418	+	0.0742544i
$647$	−8.05133	−	5.17427i	−0.316530	−	0.203422i	0.372722	−	0.927943i	$-0.378425\pi$
$647$	−8.05133	−	5.17427i	−0.316530	−	0.203422i	−0.689252	+	0.724521i	$0.742061\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	−13.4548	+	29.4620i	−0.528148	+	1.15648i
$650$	4.69130	+	32.6287i	0.184008	+	1.27980i
$651$	−18.5130	−	5.43592i	−0.725583	−	0.213050i
$652$	0.588011	−	0.377892i	0.0230283	−	0.0147994i
$653$	−13.3634	−	29.2618i	−0.522951	−	1.14510i	−0.968310	−	0.249751i	$-0.919651\pi$
$653$	−13.3634	−	29.2618i	−0.522951	−	1.14510i	0.445359	−	0.895352i	$-0.353076\pi$
$654$	−1.22496	+	0.359682i	−0.0478999	+	0.0140647i
$655$	19.1347	−	22.0826i	0.747654	−	0.862839i
$656$	4.00611	−	4.62329i	0.156412	−	0.180509i
$657$	−11.8529	+	3.48032i	−0.462425	+	0.135780i
$658$	4.11653	+	9.01394i	0.160479	+	0.351400i
$659$	1.52992	−	0.983217i	0.0595970	−	0.0383007i	−0.510503	−	0.859876i	$-0.670541\pi$
$659$	1.52992	−	0.983217i	0.0595970	−	0.0383007i	0.570100	+	0.821575i	$0.306904\pi$
$660$	−16.8845	−	4.95774i	−0.657229	−	0.192980i
$661$	−5.79394	−	40.2978i	−0.225358	−	1.56740i	−0.717295	−	0.696770i	$-0.754620\pi$
$661$	−5.79394	−	40.2978i	−0.225358	−	1.56740i	0.491936	−	0.870631i	$-0.336289\pi$
$662$	−0.506133	+	1.10828i	−0.0196714	+	0.0430744i
$663$	0.849201	−	5.90632i	0.0329802	−	0.229383i
$664$	−0.317178	−	0.203838i	−0.0123089	−	0.00791045i
$665$	14.4625	+	16.6906i	0.560830	+	0.647233i
$666$	2.51890			0.0976053
$667$	−2.16058	+	1.60419i	−0.0836579	+	0.0621144i
$668$	5.02836			0.194553
$669$	2.23242	+	2.57635i	0.0863103	+	0.0996074i
$670$	20.5556	+	13.2103i	0.794131	+	0.510357i
$671$	2.09883	−	14.5977i	0.0810243	−	0.563536i
$672$	−1.72871	+	3.78534i	−0.0666863	+	0.146023i
$673$	1.83983	+	12.7963i	0.0709204	+	0.493262i	0.994063	+	0.108805i	$0.0347024\pi$
$673$	1.83983	+	12.7963i	0.0709204	+	0.493262i	−0.923143	+	0.384457i	$0.874389\pi$
$674$	−18.2914	−	5.37083i	−0.704557	−	0.206877i
$675$	−8.49830	+	5.46153i	−0.327100	+	0.210214i
$676$	−0.976986	−	2.13930i	−0.0375764	−	0.0822808i
$677$	−6.54833	+	1.92276i	−0.251673	+	0.0738978i	−0.405136	−	0.914257i	$-0.632776\pi$
$677$	−6.54833	+	1.92276i	−0.251673	+	0.0738978i	0.153463	+	0.988154i	$0.450958\pi$
$678$	11.5853	−	13.3702i	0.444931	−	0.513478i
$679$	−51.4394	+	59.3642i	−1.97406	+	2.27819i
$680$	−6.81838	+	2.00206i	−0.261473	+	0.0767754i
$681$	−6.15086	−	13.4685i	−0.235702	−	0.516114i
$682$	−17.6626	+	11.3510i	−0.676335	+	0.434654i
$683$	−1.81814	−	0.533855i	−0.0695693	−	0.0204274i	0.246763	−	0.969076i	$-0.420633\pi$
$683$	−1.81814	−	0.533855i	−0.0695693	−	0.0204274i	−0.316332	+	0.948649i	$0.602451\pi$
$684$	−0.194351	−	1.35174i	−0.00743121	−	0.0516852i
$685$	23.0861	−	50.5515i	0.882075	−	1.93147i
$686$	−1.96456	+	13.6638i	−0.0750074	+	0.521688i
$687$	−8.24062	−	5.29593i	−0.314399	−	0.202052i
$688$	−6.45195	−	7.44594i	−0.245978	−	0.283874i
$689$	−34.6228			−1.31902
$690$	3.89007	+	18.2267i	0.148093	+	0.693878i
$691$	−14.4219			−0.548635			−0.274317	−	0.961639i	$-0.588452\pi$
$691$	−14.4219			−0.548635			−0.274317	+	0.961639i	$0.588452\pi$
$692$	5.68588	+	6.56186i	0.216145	+	0.249444i
$693$	15.8525	+	10.1878i	0.602185	+	0.387001i
$694$	1.75853	−	12.2309i	0.0667530	−	0.464278i
$695$	−35.1933	+	77.0627i	−1.33496	+	2.92315i
$696$	0.0798548	+	0.555402i	0.00302689	+	0.0210525i
$697$	−10.7334	−	3.15162i	−0.406557	−	0.119376i
$698$	−13.1919	+	8.47794i	−0.499322	+	0.320895i
$699$	1.64310	+	3.59789i	0.0621478	+	0.136085i
$700$	−40.3354	+	11.8435i	−1.52453	+	0.447644i
$701$	−23.6742	+	27.3215i	−0.894164	+	1.03192i	0.105134	+	0.994458i	$0.466473\pi$
$701$	−23.6742	+	27.3215i	−0.894164	+	1.03192i	−0.999298	+	0.0374621i	$0.988073\pi$
$702$	−2.13691	+	2.46613i	−0.0806525	+	0.0930779i
$703$	−3.30057	+	0.969136i	−0.124484	+	0.0365517i
$704$	1.88110	+	4.11904i	0.0708967	+	0.155242i
$705$	7.78490	−	5.00305i	0.293196	−	0.188426i
$706$	−29.2783	−	8.59688i	−1.10190	−	0.323548i
$707$	0.653264	+	4.54355i	0.0245685	+	0.170878i
$708$	2.97131	−	6.50625i	0.111669	−	0.244520i
$709$	−2.70692	+	18.8271i	−0.101661	+	0.707066i	0.873703	+	0.486461i	$0.161712\pi$
$709$	−2.70692	+	18.8271i	−0.101661	+	0.707066i	−0.975363	+	0.220605i	$0.929197\pi$
$710$	21.0995	+	13.5598i	0.791850	+	0.508891i
$711$	−5.52519	−	6.37641i	−0.207211	−	0.239134i
$712$	15.2049			0.569829
$713$	19.4742	+	10.7332i	0.729316	+	0.401963i
$714$	7.60961			0.284782
$715$	−37.6039	−	43.3973i	−1.40631	−	1.62297i
$716$	−9.73773	−	6.25806i	−0.363916	−	0.233875i
$717$	−1.39860	+	9.72748i	−0.0522317	+	0.363279i
$718$	6.85337	−	15.0068i	0.255766	−	0.560049i
$719$	1.57451	+	10.9509i	0.0587192	+	0.408401i	0.997889	+	0.0649469i	$0.0206878\pi$
$719$	1.57451	+	10.9509i	0.0587192	+	0.408401i	−0.939170	+	0.343454i	$0.888403\pi$
$720$	3.72871	+	1.09485i	0.138961	+	0.0408025i
$721$	11.7853	−	7.57398i	0.438909	−	0.282070i
$722$	−7.11814	−	15.5866i	−0.264910	−	0.580072i
$723$	20.8083	−	6.10986i	0.773868	−	0.227228i
$724$	1.71160	−	1.97529i	0.0636112	−	0.0734112i
$725$	−3.71197	+	4.28385i	−0.137859	+	0.159098i
$726$	9.12003	−	2.67788i	0.338476	−	0.0993855i
$727$	−2.40641	−	5.26930i	−0.0892488	−	0.195428i	0.859744	−	0.510725i	$-0.170623\pi$
$727$	−2.40641	−	5.26930i	−0.0892488	−	0.195428i	−0.948993	+	0.315297i	$0.897896\pi$
$728$	−11.4236	+	7.34151i	−0.423387	+	0.272095i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	6.83201	+	47.5177i	0.252864	+	1.75871i
$731$	−7.48423	+	16.3882i	−0.276814	+	0.606138i
$732$	−0.463496	+	3.22369i	−0.0171313	+	0.119151i
$733$	−12.4548	−	8.00421i	−0.460028	−	0.295642i	0.290026	−	0.957019i	$-0.406336\pi$
$733$	−12.4548	−	8.00421i	−0.460028	−	0.295642i	−0.750054	+	0.661377i	$0.769972\pi$
$734$	18.1339	+	20.9276i	0.669335	+	0.772453i
$735$	40.0941			1.47889
$736$	2.88909	−	3.82794i	0.106493	−	0.141100i
$737$	−28.4719			−1.04878
$738$	4.00611	+	4.62329i	0.147467	+	0.170186i
$739$	3.09958	+	1.99198i	0.114020	+	0.0732762i	0.596408	−	0.802681i	$-0.296594\pi$
$739$	3.09958	+	1.99198i	0.114020	+	0.0732762i	−0.482388	+	0.875958i	$0.660230\pi$
$740$	1.39308	−	9.68911i	0.0512108	−	0.356179i
$741$	1.85122	−	4.05360i	0.0680061	−	0.148913i
$742$	−6.28368	−	43.7039i	−0.230681	−	1.60442i
$743$	38.9084	+	11.4245i	1.42741	+	0.419125i	0.902004	−	0.431727i	$-0.142096\pi$
$743$	38.9084	+	11.4245i	1.42741	+	0.419125i	0.525405	+	0.850852i	$0.323914\pi$
$744$	3.90053	−	2.50672i	0.143000	−	0.0919007i
$745$	3.35937	+	7.35599i	0.123078	+	0.269503i
$746$	19.5377	−	5.73680i	0.715327	−	0.210039i
$747$	0.246902	−	0.284941i	0.00903369	−	0.0104254i
$748$	5.42254	−	6.25794i	0.198268	−	0.228813i
$749$	41.9182	−	12.3083i	1.53166	−	0.449736i
$750$	8.23635	+	18.0351i	0.300749	+	0.658548i
$751$	13.5084	−	8.68135i	0.492930	−	0.316787i	−0.270453	−	0.962733i	$-0.587173\pi$
$751$	13.5084	−	8.68135i	0.492930	−	0.316787i	0.763383	+	0.645946i	$0.223537\pi$
$752$	−2.28482	−	0.670883i	−0.0833187	−	0.0244646i
$753$	−1.06037	−	7.37506i	−0.0386422	−	0.268762i
$754$	−0.760625	+	1.66554i	−0.0277003	+	0.0606552i
$755$	10.3799	−	72.1939i	0.377764	−	2.62741i
$756$	−3.50079	−	2.24982i	−0.127323	−	0.0818252i
$757$	30.5222	+	35.2245i	1.10935	+	1.28026i	0.956412	+	0.292021i	$0.0943277\pi$
$757$	30.5222	+	35.2245i	1.10935	+	1.28026i	0.152937	+	0.988236i	$0.451127\pi$
$758$	−15.3289			−0.556769
$759$	−15.2956	−	15.4162i	−0.555196	−	0.559574i
$760$	−5.30706			−0.192507
$761$	15.9058	+	18.3562i	0.576584	+	0.665413i	0.966867	−	0.255282i	$-0.0821683\pi$
$761$	15.9058	+	18.3562i	0.576584	+	0.665413i	−0.390283	+	0.920695i	$0.627623\pi$
$762$	−8.49496	−	5.45938i	−0.307740	−	0.197772i
$763$	0.756086	−	5.25869i	0.0273722	−	0.190377i
$764$	2.55534	−	5.59540i	0.0924488	−	0.202435i
$765$	−1.01132	−	7.03390i	−0.0365644	−	0.254311i
$766$	19.8672	+	5.83353i	0.717830	+	0.210774i
$767$	19.6349	−	12.6186i	0.708977	−	0.455632i
$768$	−0.415415	−	0.909632i	−0.0149900	−	0.0328235i
$769$	−17.6741	+	5.18957i	−0.637343	+	0.187141i	−0.584412	−	0.811457i	$-0.698675\pi$
$769$	−17.6741	+	5.18957i	−0.637343	+	0.187141i	−0.0529313	+	0.998598i	$0.516856\pi$
$770$	47.9551	−	55.3432i	1.72818	−	1.99443i
$771$	2.68664	−	3.10055i	0.0967569	−	0.111663i
$772$	−8.18462	+	2.40322i	−0.294571	+	0.0864938i
$773$	0.380004	+	0.832092i	0.0136678	+	0.0299283i	0.916343	−	0.400395i	$-0.131127\pi$
$773$	0.380004	+	0.832092i	0.0136678	+	0.0299283i	−0.902675	+	0.430323i	$0.858400\pi$
$774$	8.28836	−	5.32661i	0.297919	−	0.191461i
$775$	44.9411	+	13.1959i	1.61433	+	0.474011i
$776$	−2.68632	−	18.6838i	−0.0964332	−	0.670708i
$777$	−4.35444	+	9.53488i	−0.156214	+	0.342062i
$778$	4.90038	−	34.0829i	0.175687	−	1.22193i
$779$	−7.02810	−	4.51668i	−0.251808	−	0.161827i
$780$	8.30430	+	9.58367i	0.297342	+	0.343150i
$781$	−29.2253			−1.04576
$782$	−8.56194	−	1.89778i	−0.306174	−	0.0678645i
$783$	−0.561114			−0.0200526
$784$	−6.75635	−	7.79725i	−0.241298	−	0.278473i
$785$	6.52249	+	4.19175i	0.232798	+	0.149610i
$786$	1.07006	−	7.44240i	0.0381676	−	0.265462i
$787$	−9.92451	+	21.7317i	−0.353771	+	0.774650i	0.646164	+	0.763199i	$0.276372\pi$
$787$	−9.92451	+	21.7317i	−0.353771	+	0.774650i	−0.999934	+	0.0114510i	$0.996355\pi$
$788$	−0.468228	−	3.25659i	−0.0166799	−	0.116011i
$789$	−25.7188	−	7.55172i	−0.915613	−	0.268848i
$790$	−27.5830	+	17.7265i	−0.981359	+	0.630681i
$791$	30.5830	+	66.9675i	1.08741	+	2.38109i
$792$	−4.34482	+	1.27576i	−0.154387	+	0.0453320i
$793$	−6.95957	+	8.03177i	−0.247141	+	0.285216i
$794$	17.3204	−	19.9888i	0.614677	−	0.709376i
$795$	−39.5624	+	11.6166i	−1.40313	+	0.411997i
$796$	8.31919	+	18.2165i	0.294866	+	0.645666i
$797$	−27.0265	+	17.3689i	−0.957327	+	0.615237i	−0.923257	−	0.384183i	$-0.874483\pi$
$797$	−27.0265	+	17.3689i	−0.957327	+	0.615237i	−0.0340698	+	0.999419i	$0.510847\pi$
$798$	5.45279	+	1.60108i	0.193027	+	0.0566777i
$799$	0.619702	+	4.31012i	0.0219235	+	0.152481i
$800$	4.19650	−	9.18906i	0.148369	−	0.324882i
$801$	−2.16389	+	15.0502i	−0.0764573	+	0.531772i
$802$	−15.0580	−	9.67718i	−0.531716	−	0.341713i
$803$	−36.6320	−	42.2756i	−1.29272	−	1.49187i
$804$	6.28762			0.221747
$805$	−75.7190	−	16.7834i	−2.66875	−	0.591536i
$806$	15.1298			0.532926
$807$	−3.76086	−	4.34026i	−0.132388	−	0.152784i
$808$	−0.927953	−	0.596359i	−0.0326453	−	0.0209798i
$809$	7.44818	−	51.8032i	0.261864	−	1.82130i	−0.256959	−	0.966422i	$-0.582720\pi$
$809$	7.44818	−	51.8032i	0.261864	−	1.82130i	0.518823	−	0.854882i	$-0.326371\pi$
$810$	−1.61435	+	3.53494i	−0.0567226	+	0.124205i
$811$	6.61378	+	45.9998i	0.232241	+	1.61527i	0.688371	+	0.725359i	$0.258326\pi$
$811$	6.61378	+	45.9998i	0.232241	+	1.61527i	−0.456130	+	0.889913i	$0.650765\pi$
$812$	−2.24043	−	0.657850i	−0.0786238	−	0.0230860i
$813$	−5.83490	+	3.74986i	−0.204639	+	0.131513i
$814$	4.73830	+	10.3754i	0.166077	+	0.363659i
$815$	2.60625	−	0.765265i	0.0912931	−	0.0268061i
$816$	−1.19749	+	1.38198i	−0.0419205	+	0.0483789i
$817$	−8.81106	+	10.1685i	−0.308260	+	0.355751i
$818$	9.09385	−	2.67019i	0.317959	−	0.0933612i
$819$	−5.64104	−	12.3521i	−0.197114	−	0.431619i
$820$	19.9994	−	12.8528i	0.698409	−	0.448840i
$821$	15.3678	+	4.51238i	0.536338	+	0.157483i	0.538674	−	0.842514i	$-0.318925\pi$
$821$	15.3678	+	4.51238i	0.536338	+	0.157483i	−0.00233589	+	0.999997i	$0.500744\pi$
$822$	−2.03518	−	14.1550i	−0.0709850	−	0.493711i
$823$	20.3184	−	44.4912i	0.708257	−	1.55087i	−0.121408	−	0.992603i	$-0.538741\pi$
$823$	20.3184	−	44.4912i	0.708257	−	1.55087i	0.829664	−	0.558263i	$-0.188532\pi$
$824$	−0.479100	+	3.33221i	−0.0166902	+	0.116083i
$825$	−38.4824	−	24.7312i	−1.33979	−	0.861028i
$826$	19.4919	+	22.4948i	0.678209	+	0.782695i
$827$	10.4217			0.362400			0.181200	−	0.983446i	$-0.442002\pi$
$827$	10.4217			0.362400			0.181200	+	0.983446i	$0.442002\pi$
$828$	3.37782	+	3.40446i	0.117387	+	0.118313i
$829$	−0.753780			−0.0261799			−0.0130899	−	0.999914i	$-0.504167\pi$
$829$	−0.753780			−0.0261799			−0.0130899	+	0.999914i	$0.504167\pi$
$830$	−0.959493	−	1.10731i	−0.0333045	−	0.0384354i
$831$	3.20538	+	2.05997i	0.111193	+	0.0714596i
$832$	0.464395	−	3.22994i	0.0161000	−	0.111978i
$833$	−7.83734	+	17.1614i	−0.271548	+	0.594607i
$834$	3.10250	+	21.5784i	0.107431	+	0.747198i
$835$	18.7493	+	5.50529i	0.648846	+	0.190518i
$836$	5.20229	−	3.34331i	0.179925	−	0.115631i
$837$	1.92610	+	4.21757i	0.0665758	+	0.145781i
$838$	21.5052	−	6.31448i	0.742883	−	0.218130i
$839$	−6.01932	+	6.94666i	−0.207810	+	0.239825i	−0.850081	−	0.526652i	$-0.823447\pi$
$839$	−6.01932	+	6.94666i	−0.207810	+	0.239825i	0.642271	+	0.766478i	$0.277992\pi$
$840$	−10.5902	+	12.2218i	−0.365397	+	0.421691i
$841$	27.5232	−	8.08154i	0.949076	−	0.278674i
$842$	−0.635664	−	1.39191i	−0.0219064	−	0.0479684i
$843$	−15.2879	+	9.82492i	−0.526542	+	0.338388i
$844$	−2.51699	−	0.739054i	−0.0866383	−	0.0254393i
$845$	−1.30069	−	9.04648i	−0.0447450	−	0.311208i
$846$	0.989217	−	2.16608i	0.0340100	−	0.0744715i
$847$	−5.62917	+	39.1517i	−0.193420	+	1.34527i
$848$	8.92588	+	5.73632i	0.306516	+	0.196986i
$849$	−11.1961	−	12.9210i	−0.384249	−	0.443447i
$850$	−18.4726			−0.633605
$851$	7.27732	−	9.64220i	0.249463	−	0.330530i
$852$	6.45399			0.221110
$853$	24.6118	+	28.4036i	0.842693	+	0.972520i	0.999887	−	0.0150481i	$-0.00479013\pi$
$853$	24.6118	+	28.4036i	0.842693	+	0.972520i	−0.157194	+	0.987568i	$0.550245\pi$
$854$	−11.4015	−	7.32730i	−0.390151	−	0.250735i
$855$	0.755273	−	5.25304i	0.0258298	−	0.179650i
$856$	−4.36118	+	9.54966i	−0.149062	+	0.326401i
$857$	−5.58420	−	38.8390i	−0.190753	−	1.32671i	−0.830022	−	0.557731i	$-0.811672\pi$
$857$	−5.58420	−	38.8390i	−0.190753	−	1.32671i	0.639269	−	0.768983i	$-0.279237\pi$
$858$	−14.1778	−	4.16299i	−0.484023	−	0.142122i
$859$	21.7427	−	13.9732i	0.741853	−	0.476760i	−0.114324	−	0.993444i	$-0.536470\pi$
$859$	21.7427	−	13.9732i	0.741853	−	0.476760i	0.856176	+	0.516684i	$0.172834\pi$
$860$	−15.9053	−	34.8276i	−0.542365	−	1.18761i
$861$	−24.4261	+	7.17216i	−0.832440	+	0.244426i
$862$	−0.0796630	+	0.0919360i	−0.00271333	+	0.00313135i
$863$	35.7028	−	41.2032i	1.21534	−	1.40257i	0.325971	−	0.945380i	$-0.394309\pi$
$863$	35.7028	−	41.2032i	1.21534	−	1.40257i	0.889367	−	0.457195i	$-0.151146\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	14.0168	+	30.6924i	0.476584	+	1.04357i
$866$	29.4380	−	18.9187i	1.00035	−	0.642883i
$867$	−13.1030	−	3.84738i	−0.445001	−	0.130664i
$868$	2.74591	+	19.0982i	0.0932022	+	0.648236i
$869$	15.8712	−	34.7532i	0.538395	−	1.17892i
$870$	−0.310326	+	2.15836i	−0.0105210	+	0.0731753i
$871$	17.2604	+	11.0926i	0.584846	+	0.375857i
$872$	0.836047	+	0.964850i	0.0283121	+	0.0326739i
$873$	18.8759			0.638852
$874$	−5.73590	−	3.16134i	−0.194020	−	0.106934i
$875$	−82.5072			−2.78925
$876$	8.08967	+	9.33598i	0.273325	+	0.315433i
$877$	−20.1908	−	12.9758i	−0.681795	−	0.438163i	0.153365	−	0.988170i	$-0.450989\pi$
$877$	−20.1908	−	12.9758i	−0.681795	−	0.438163i	−0.835160	+	0.550007i	$0.814625\pi$
$878$	3.06935	−	21.3478i	0.103586	−	0.720453i
$879$	5.42302	−	11.8748i	0.182914	−	0.400526i
$880$	2.50436	+	17.4182i	0.0844220	+	0.587168i
$881$	−18.5735	−	5.45368i	−0.625758	−	0.183739i	−0.0465459	−	0.998916i	$-0.514821\pi$
$881$	−18.5735	−	5.45368i	−0.625758	−	0.183739i	−0.579212	+	0.815177i	$0.696640\pi$
$882$	8.67941	−	5.57792i	0.292251	−	0.187818i
$883$	−15.6656	−	34.3029i	−0.527190	−	1.15438i	−0.966645	−	0.256120i	$-0.917556\pi$
$883$	−15.6656	−	34.3029i	−0.527190	−	1.15438i	0.439456	−	0.898264i	$-0.355171\pi$
$884$	−5.72535	+	1.68112i	−0.192564	+	0.0565420i
$885$	18.2025	−	21.0068i	0.611870	−	0.706136i
$886$	2.16292	−	2.49614i	0.0726647	−	0.0838595i
$887$	−4.87305	+	1.43086i	−0.163621	+	0.0480435i	−0.362517	−	0.931977i	$-0.618083\pi$
$887$	−4.87305	+	1.43086i	−0.163621	+	0.0480435i	0.198896	+	0.980021i	$0.436264\pi$
$888$	−1.04639	−	2.29127i	−0.0351145	−	0.0768900i
$889$	35.3509	−	22.7186i	1.18563	−	0.761959i
$890$	56.6948	+	16.6471i	1.90041	+	0.558012i
$891$	−0.644437	−	4.48216i	−0.0215895	−	0.150158i
$892$	1.41615	−	3.10093i	0.0474162	−	0.103827i
$893$	−0.462804	+	3.21887i	−0.0154871	+	0.107715i
$894$	1.75060	+	1.12504i	0.0585487	+	0.0376270i
$895$	−29.4575	−	33.9958i	−0.984657	−	1.13635i
$896$	4.16140			0.139023
$897$	3.26647	+	15.3048i	0.109064	+	0.511014i
$898$	22.2893			0.743804
$899$	1.70371	+	1.96619i	0.0568220	+	0.0655761i
$900$	8.49830	+	5.46153i	0.283277	+	0.182051i
$901$	2.76120	−	19.2045i	0.0919888	−	0.639796i
$902$	−11.5076	+	25.1982i	−0.383162	+	0.839008i
$903$	5.83487	+	40.5824i	0.194172	+	1.35050i
$904$	−16.9746	−	4.98421i	−0.564568	−	0.165772i
$905$	8.54471	−	5.49135i	0.284036	−	0.182539i
$906$	−7.79668	−	17.0723i	−0.259027	−	0.567190i
$907$	35.0870	−	10.3025i	1.16504	−	0.342088i	0.358654	−	0.933471i	$-0.383236\pi$
$907$	35.0870	−	10.3025i	1.16504	−	0.342088i	0.806391	+	0.591383i	$0.201418\pi$
$908$	−9.69622	+	11.1900i	−0.321781	+	0.371355i
$909$	0.722351	−	0.833637i	0.0239589	−	0.0276500i
$910$	−50.6332	+	14.8672i	−1.67847	+	0.492844i
$911$	11.9149	+	26.0901i	0.394759	+	0.864402i	0.997775	+	0.0666729i	$0.0212384\pi$
$911$	11.9149	+	26.0901i	0.394759	+	0.864402i	−0.603016	+	0.797729i	$0.706034\pi$
$912$	−1.14885	+	0.738323i	−0.0380423	+	0.0244483i
$913$	1.63813	+	0.480999i	0.0542142	+	0.0159187i
$914$	5.13940	+	35.7453i	0.169996	+	1.18235i
$915$	−5.25768	+	11.5127i	−0.173814	+	0.380599i
$916$	−1.39407	+	9.69594i	−0.0460612	+	0.320363i
$917$	26.3222	+	16.9163i	0.869236	+	0.558624i
$918$	−1.19749	−	1.38198i	−0.0395231	−	0.0456120i
$919$	−16.5221			−0.545013			−0.272507	−	0.962154i	$-0.587853\pi$
$919$	−16.5221			−0.545013			−0.272507	+	0.962154i	$0.587853\pi$
$920$	14.9636	−	11.1102i	0.493335	−	0.366292i
$921$	24.0856			0.793649
$922$	−20.6714	−	23.8561i	−0.680777	−	0.785659i
$923$	17.7171	+	11.3861i	0.583166	+	0.374778i
$924$	2.68176	−	18.6521i	0.0882234	−	0.613607i
$925$	10.5706	−	23.1463i	0.347558	−	0.761045i
$926$	3.96311	+	27.5641i	0.130236	+	0.905811i
$927$	−3.23011	−	0.948446i	−0.106091	−	0.0311511i
$928$	0.472039	−	0.303361i	0.0154954	−	0.00995831i
$929$	−1.47887	−	3.23827i	−0.0485201	−	0.106244i	0.883819	−	0.467828i	$-0.154963\pi$
$929$	−1.47887	−	3.23827i	−0.0485201	−	0.106244i	−0.932340	+	0.361584i	$0.882236\pi$
$930$	17.2884	−	5.07633i	0.566909	−	0.166460i
$931$	−9.22677	+	10.6483i	−0.302395	+	0.348983i
$932$	2.59019	−	2.98924i	0.0848444	−	0.0979157i
$933$	2.53986	−	0.745771i	0.0831514	−	0.0244154i
$934$	0.245034	+	0.536550i	0.00801776	+	0.0175564i
$935$	27.0705	−	17.3972i	0.885301	−	0.568949i
$936$	3.13097	+	0.919336i	0.102339	+	0.0300495i
$937$	7.19018	+	50.0088i	0.234893	+	1.63372i	0.676454	+	0.736485i	$0.263516\pi$
$937$	7.19018	+	50.0088i	0.234893	+	1.63372i	−0.441561	+	0.897231i	$0.645575\pi$
$938$	−10.8694	+	23.8008i	−0.354900	+	0.777123i
$939$	−3.56000	+	24.7604i	−0.116176	+	0.808024i
$940$	−7.78490	−	5.00305i	−0.253915	−	0.163182i
$941$	−39.2974	−	45.3517i	−1.28106	−	1.47842i	−0.797770	−	0.602961i	$-0.793987\pi$
$941$	−39.2974	−	45.3517i	−1.28106	−	1.47842i	−0.483290	−	0.875461i	$-0.660558\pi$
$942$	1.99513			0.0650047
$943$	29.2717	−	1.97805i	0.953218	−	0.0644140i
$944$	−7.15262			−0.232798
$945$	−10.5902	−	12.2218i	−0.344500	−	0.397574i
$946$	37.5318	+	24.1202i	1.22026	+	0.784216i
$947$	−1.46743	+	10.2062i	−0.0476850	+	0.331656i	0.951989	+	0.306131i	$0.0990347\pi$
$947$	−1.46743	+	10.2062i	−0.0476850	+	0.331656i	−0.999674	+	0.0255247i	$0.991874\pi$
$948$	−3.50494	+	7.67474i	−0.113835	+	0.249264i
$949$	5.73680	+	39.9003i	0.186224	+	1.29522i
$950$	−13.2368	−	3.88669i	−0.429460	−	0.126101i
$951$	2.47347	−	1.58960i	0.0802077	−	0.0515463i
$952$	−3.16115	−	6.92194i	−0.102453	−	0.224341i
$953$	−40.5703	+	11.9125i	−1.31420	+	0.385884i	−0.862397	−	0.506233i	$-0.831038\pi$
$953$	−40.5703	+	11.9125i	−1.31420	+	0.385884i	−0.451805	+	0.892117i	$0.649220\pi$
$954$	−6.94821	+	8.01867i	−0.224957	+	0.259614i
$955$	15.6542	−	18.0659i	0.506558	−	0.584600i
$956$	9.42942	−	2.76873i	0.304969	−	0.0895471i
$957$	−1.05551	−	2.31125i	−0.0341199	−	0.0747121i
$958$	−8.65278	+	5.56081i	−0.279559	+	0.179661i
$959$	57.0996	+	16.7660i	1.84384	+	0.541401i
$960$	−0.553053	−	3.84657i	−0.0178497	−	0.124147i
$961$	−3.94737	+	8.64354i	−0.127335	+	0.278824i
$962$	1.16976	−	8.13588i	0.0377147	−	0.262311i
$963$	−8.83179	−	5.67585i	−0.284601	−	0.182902i
$964$	−14.2018	−	16.3897i	−0.457409	−	0.527878i
$965$	−33.1492			−1.06711
$966$	−18.7263	+	6.90090i	−0.602509	+	0.222033i
$967$	−18.6393			−0.599399			−0.299700	−	0.954034i	$-0.596886\pi$
$967$	−18.6393			−0.599399			−0.299700	+	0.954034i	$0.596886\pi$
$968$	−6.22449	−	7.18344i	−0.200063	−	0.230884i
$969$	2.10081	+	1.35011i	0.0674878	+	0.0433718i
$970$	10.4394	−	72.6074i	0.335188	−	2.33128i
$971$	3.15485	−	6.90816i	0.101244	−	0.221693i	−0.852231	−	0.523166i	$-0.824751\pi$
$971$	3.15485	−	6.90816i	0.101244	−	0.221693i	0.953475	+	0.301472i	$0.0974781\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	−87.0448	−	25.5587i	−2.79053	−	0.819373i
$974$	−23.1380	+	14.8699i	−0.741389	+	0.476462i
$975$	13.6938	+	29.9853i	0.438553	+	0.960298i
$976$	3.12491	−	0.917557i	0.100026	−	0.0293703i
$977$	−8.48096	+	9.78755i	−0.271330	+	0.313131i	−0.875019	−	0.484088i	$-0.839151\pi$
$977$	−8.48096	+	9.78755i	−0.271330	+	0.313131i	0.603689	+	0.797220i	$0.293697\pi$
$978$	0.457728	−	0.528246i	0.0146365	−	0.0168914i
$979$	−66.0628	+	19.3978i	−2.11138	+	0.619956i
$980$	−16.6557	−	36.4708i	−0.532046	−	1.16502i
$981$	−1.07401	+	0.690225i	−0.0342905	+	0.0220372i
$982$	−8.43491	−	2.47671i	−0.269169	−	0.0790351i
$983$	5.17713	+	36.0077i	0.165125	+	1.14847i	0.888789	+	0.458316i	$0.151547\pi$
$983$	5.17713	+	36.0077i	0.165125	+	1.14847i	−0.723665	+	0.690152i	$0.757544\pi$
$984$	2.54130	−	5.56467i	0.0810136	−	0.177395i
$985$	1.81959	−	12.6555i	0.0579770	−	0.403239i
$986$	−0.863179	−	0.554731i	−0.0274892	−	0.0176662i
$987$	6.48930	+	7.48905i	0.206557	+	0.238379i
$988$	−4.45630			−0.141774
$989$	3.55586	−	47.1164i	0.113070	−	1.49822i
$990$	−17.5973			−0.559280
$991$	20.5079	+	23.6674i	0.651456	+	0.751820i	0.981357	−	0.192195i	$-0.0615607\pi$
$991$	20.5079	+	23.6674i	0.651456	+	0.751820i	−0.329901	+	0.944016i	$0.607015\pi$
$992$	−3.90053	−	2.50672i	−0.123842	−	0.0795884i
$993$	−0.173394	+	1.20598i	−0.00550248	+	0.0382706i
$994$	−11.1571	+	24.4306i	−0.353881	+	0.774891i
$995$	11.0756	+	77.0322i	0.351119	+	2.44208i
$996$	−0.361758	−	0.106222i	−0.0114627	−	0.00336576i
$997$	−16.3606	+	10.5143i	−0.518144	+	0.332991i	−0.773438	−	0.633872i	$-0.781464\pi$
$997$	−16.3606	+	10.5143i	−0.518144	+	0.332991i	0.255293	+	0.966864i	$0.417828\pi$
$998$	9.78386	+	21.4237i	0.309703	+	0.678154i
$999$	2.41686	−	0.709655i	0.0764662	−	0.0224525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.b.13.1	✓	10
3.2	odd	2		414.2.i.e.289.1		10
23.4	even	11		3174.2.a.ba.1.1		5
23.16	even	11	inner	138.2.e.b.85.1	yes	10
23.19	odd	22		3174.2.a.bb.1.5		5
69.50	odd	22		9522.2.a.bs.1.5		5
69.62	odd	22		414.2.i.e.361.1		10
69.65	even	22		9522.2.a.br.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.13.1	✓	10	1.1	even	1	trivial
138.2.e.b.85.1	yes	10	23.16	even	11	inner
414.2.i.e.289.1		10	3.2	odd	2
414.2.i.e.361.1		10	69.62	odd	22
3174.2.a.ba.1.1		5	23.4	even	11
3174.2.a.bb.1.5		5	23.19	odd	22
9522.2.a.br.1.1		5	69.65	even	22
9522.2.a.bs.1.5		5	69.50	odd	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-1.61435 + 3.53494i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.99283 - 1.17240i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-1.61435 + 3.53494i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.99283 - 1.17240i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(3.72871 - 1.09485i) q^{10} +(-2.96537 + 3.42222i) q^{11} +(0.654861 - 0.755750i) q^{12} +(3.13097 - 0.919336i) q^{13} +(1.72871 + 3.78534i) q^{14} +(3.26921 - 2.10100i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.260239 + 1.81001i) q^{17} +(0.415415 - 0.909632i) q^{18} +(-0.194351 + 1.35174i) q^{19} +(-3.26921 - 2.10100i) q^{20} +(2.72514 + 3.14498i) q^{21} +4.52825 q^{22} +(-2.28185 - 4.21819i) q^{23} -1.00000 q^{24} +(-6.61537 - 7.63454i) q^{25} +(-2.74514 - 1.76419i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.72871 - 3.78534i) q^{28} +(-0.0798548 - 0.555402i) q^{29} +(-3.72871 - 1.09485i) q^{30} +(-3.90053 + 2.50672i) q^{31} +(0.415415 + 0.909632i) q^{32} +(4.34482 - 1.27576i) q^{33} +(1.19749 - 1.38198i) q^{34} +(10.5902 - 12.2218i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.04639 + 2.29127i) q^{37} +(1.14885 - 0.738323i) q^{38} +(-3.13097 - 0.919336i) q^{39} +(0.553053 + 3.84657i) q^{40} +(-2.54130 + 5.56467i) q^{41} +(0.592229 - 4.11904i) q^{42} +(8.28836 + 5.32661i) q^{43} +(-2.96537 - 3.42222i) q^{44} -3.88612 q^{45} +(-1.69360 + 4.48684i) q^{46} +2.38128 q^{47} +(0.654861 + 0.755750i) q^{48} +(8.67941 + 5.57792i) q^{49} +(-1.43766 + 9.99913i) q^{50} +(0.759635 - 1.66337i) q^{51} +(0.464395 + 3.22994i) q^{52} +(-10.1804 - 2.98924i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(-7.31020 - 16.0071i) q^{55} +(-3.99283 + 1.17240i) q^{56} +(0.894306 - 1.03208i) q^{57} +(-0.367451 + 0.424061i) q^{58} +(6.86289 - 2.01513i) q^{59} +(1.61435 + 3.53494i) q^{60} +(-2.73982 + 1.76078i) q^{61} +(4.44875 + 1.30627i) q^{62} +(-0.592229 - 4.11904i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-1.80470 + 12.5519i) q^{65} +(-3.80941 - 2.44816i) q^{66} +(4.11751 + 4.75186i) q^{67} -1.82862 q^{68} +(-0.360914 + 4.78223i) q^{69} -16.1717 q^{70} +(4.22647 + 4.87760i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.75805 + 12.2275i) q^{73} +(1.04639 - 2.29127i) q^{74} +(1.43766 + 9.99913i) q^{75} +(-1.31033 - 0.384746i) q^{76} +(15.8525 - 10.1878i) q^{77} +(1.35556 + 2.96827i) q^{78} +(-8.09543 + 2.37703i) q^{79} +(2.54487 - 2.93694i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(5.86969 - 1.72350i) q^{82} +(-0.156624 - 0.342959i) q^{83} +(-3.50079 + 2.24982i) q^{84} +(-6.81838 - 2.00206i) q^{85} +(-1.40214 - 9.75211i) q^{86} +(-0.233095 + 0.510407i) q^{87} +(-0.644437 + 4.48216i) q^{88} +(12.7912 + 8.22041i) q^{89} +(2.54487 + 2.93694i) q^{90} -13.5793 q^{91} +(4.50000 - 1.65831i) q^{92} +4.63657 q^{93} +(-1.55940 - 1.79965i) q^{94} +(-4.46458 - 2.86921i) q^{95} +(0.142315 - 0.989821i) q^{96} +(7.84133 - 17.1701i) q^{97} +(-1.46830 - 10.2122i) q^{98} +(-4.34482 - 1.27576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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