LMFDB - Embedded newform 138.2.f.a.83.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, 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:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			83.2
Character	$\chi$	$=$	138.83
Dual form			138.2.f.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 - 0.959493i) q^{2} +(-1.37386 + 1.05476i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(-0.493501 - 3.43237i) q^{5} +(1.39909 + 1.02105i) q^{6} +(-1.02427 - 0.467769i) q^{7} +(0.755750 + 0.654861i) q^{8} +(0.774979 - 2.89817i) q^{9} +O(q^{10})$	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.37386 + 1.05476i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(-0.493501 - 3.43237i) q^{5} +(1.39909 + 1.02105i) q^{6} +(-1.02427 - 0.467769i) q^{7} +(0.755750 + 0.654861i) q^{8} +(0.774979 - 2.89817i) q^{9} +(-3.15430 + 1.44052i) q^{10} +(-5.23357 - 1.53672i) q^{11} +(0.585520 - 1.63008i) q^{12} +(-1.75336 - 3.83932i) q^{13} +(-0.160251 + 1.11457i) q^{14} +(4.29832 + 4.19508i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.62836 + 3.61713i) q^{17} +(-2.99911 + 0.0729229i) q^{18} +(0.292438 + 0.455042i) q^{19} +(2.27084 + 2.62069i) q^{20} +(1.90059 - 0.437708i) q^{21} +5.45452i q^{22} +(4.50939 - 1.63260i) q^{23} +(-1.72901 - 0.102555i) q^{24} +(-6.74018 + 1.97910i) q^{25} +(-3.18982 + 2.76400i) q^{26} +(1.99215 + 4.79910i) q^{27} +(1.11457 - 0.160251i) q^{28} +(-0.172034 + 0.267690i) q^{29} +(2.81417 - 5.30610i) q^{30} +(-0.725208 + 0.836935i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(8.81105 - 3.40891i) q^{33} +(1.88492 - 6.41944i) q^{34} +(-1.10008 + 3.74653i) q^{35} +(0.914917 + 2.85708i) q^{36} +(2.43391 + 0.349943i) q^{37} +(0.354220 - 0.408792i) q^{38} +(6.45841 + 3.42532i) q^{39} +(1.87476 - 2.91719i) q^{40} +(-4.67346 + 0.671942i) q^{41} +(-0.955435 - 1.70028i) q^{42} +(5.53903 - 4.79960i) q^{43} +(5.23357 - 1.53672i) q^{44} +(-10.3301 - 1.22977i) q^{45} +(-2.83691 - 3.86677i) q^{46} -4.17207i q^{47} +(0.388718 + 1.68787i) q^{48} +(-3.75370 - 4.33200i) q^{49} +(3.79786 + 5.90958i) q^{50} +(-11.5478 + 0.967124i) q^{51} +(3.55071 + 2.28190i) q^{52} +(3.81724 - 8.35859i) q^{53} +(4.04344 - 3.26352i) q^{54} +(-2.69181 + 18.7219i) q^{55} +(-0.467769 - 1.02427i) q^{56} +(-0.881726 - 0.316713i) q^{57} +(0.305314 + 0.0896482i) q^{58} +(-2.19802 + 1.00380i) q^{59} +(-5.88400 - 1.20528i) q^{60} +(1.32902 + 1.15160i) q^{61} +(1.00735 + 0.460040i) q^{62} +(-2.14947 + 2.60601i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-12.3127 + 7.91289i) q^{65} +(-5.75319 - 7.49374i) q^{66} +(1.38479 + 4.71615i) q^{67} -6.69045 q^{68} +(-4.47328 + 6.99927i) q^{69} +3.90470 q^{70} +(-2.57398 - 8.76616i) q^{71} +(2.48359 - 1.68279i) q^{72} +(-8.16392 + 5.24663i) q^{73} +(-0.349943 - 2.43391i) q^{74} +(7.17260 - 9.82825i) q^{75} +(-0.492028 - 0.224702i) q^{76} +(4.64177 + 4.02212i) q^{77} +(1.46702 - 7.16183i) q^{78} +(10.4223 - 4.75969i) q^{79} +(-3.32720 - 0.976955i) q^{80} +(-7.79882 - 4.49205i) q^{81} +(1.96139 + 4.29485i) q^{82} +(0.447423 - 3.11189i) q^{83} +(-1.36223 + 1.39576i) q^{84} +(9.63774 - 21.1037i) q^{85} +(-6.16571 - 3.96246i) q^{86} +(-0.0459972 - 0.549221i) q^{87} +(-2.94894 - 4.58863i) q^{88} +(1.93059 + 2.22803i) q^{89} +(1.73036 + 10.2581i) q^{90} +4.75268i q^{91} +(-2.91089 + 3.81139i) q^{92} +(0.113572 - 1.91475i) q^{93} +(-4.00307 + 1.17541i) q^{94} +(1.41756 - 1.22832i) q^{95} +(1.50998 - 0.848500i) q^{96} +(14.8791 - 2.13929i) q^{97} +(-3.09898 + 4.82211i) q^{98} +(-8.50958 + 13.9769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$3$	−1.37386	+	1.05476i	−0.793198	+	0.608964i
$3$	−1.37386	+	1.05476i	−0.793198	+	0.608964i
$4$	−0.841254	+	0.540641i	−0.420627	+	0.270320i
$5$	−0.493501	−	3.43237i	−0.220700	−	1.53500i	−0.735400	−	0.677634i	$-0.763006\pi$
$5$	−0.493501	−	3.43237i	−0.220700	−	1.53500i	0.514699	−	0.857371i	$-0.327904\pi$
$6$	1.39909	+	1.02105i	0.571177	+	0.416842i
$7$	−1.02427	−	0.467769i	−0.387138	−	0.176800i	0.212331	−	0.977198i	$-0.431894\pi$
$7$	−1.02427	−	0.467769i	−0.387138	−	0.176800i	−0.599470	+	0.800398i	$0.704622\pi$
$8$	0.755750	+	0.654861i	0.267198	+	0.231528i
$9$	0.774979	−	2.89817i	0.258326	−	0.966058i
$10$	−3.15430	+	1.44052i	−0.997478	+	0.455533i
$11$	−5.23357	−	1.53672i	−1.57798	−	0.463337i	−0.628669	−	0.777673i	$-0.716400\pi$
$11$	−5.23357	−	1.53672i	−1.57798	−	0.463337i	−0.949312	+	0.314335i	$0.898218\pi$
$12$	0.585520	−	1.63008i	0.169025	−	0.470564i
$13$	−1.75336	−	3.83932i	−0.486294	−	1.06484i	−0.980685	−	0.195596i	$-0.937336\pi$
$13$	−1.75336	−	3.83932i	−0.486294	−	1.06484i	0.494390	−	0.869240i	$-0.335391\pi$
$14$	−0.160251	+	1.11457i	−0.0428288	+	0.297881i
$15$	4.29832	+	4.19508i	1.10982	+	1.08316i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	5.62836	+	3.61713i	1.36508	+	0.877283i	0.998587	−	0.0531388i	$-0.0169226\pi$
$17$	5.62836	+	3.61713i	1.36508	+	0.877283i	0.366491	+	0.930421i	$0.380559\pi$
$18$	−2.99911	+	0.0729229i	−0.706898	+	0.0171881i
$19$	0.292438	+	0.455042i	0.0670898	+	0.104394i	0.873178	−	0.487402i	$-0.162055\pi$
$19$	0.292438	+	0.455042i	0.0670898	+	0.104394i	−0.806088	+	0.591796i	$0.798419\pi$
$20$	2.27084	+	2.62069i	0.507775	+	0.586004i
$21$	1.90059	−	0.437708i	0.414742	−	0.0955157i
$22$			5.45452i			1.16291i
$23$	4.50939	−	1.63260i	0.940273	−	0.340420i
$23$	4.50939	−	1.63260i	0.940273	−	0.340420i
$24$	−1.72901	−	0.102555i	−0.352933	−	0.0209340i
$25$	−6.74018	+	1.97910i	−1.34804	+	0.395819i
$26$	−3.18982	+	2.76400i	−0.625576	+	0.542064i
$27$	1.99215	+	4.79910i	0.383390	+	0.923586i
$28$	1.11457	−	0.160251i	0.210634	−	0.0302845i
$29$	−0.172034	+	0.267690i	−0.0319458	+	0.0497087i	−0.856859	−	0.515550i	$-0.827587\pi$
$29$	−0.172034	+	0.267690i	−0.0319458	+	0.0497087i	0.824913	+	0.565259i	$0.191224\pi$
$30$	2.81417	−	5.30610i	0.513795	−	0.968756i
$31$	−0.725208	+	0.836935i	−0.130251	+	0.150318i	−0.817129	−	0.576455i	$-0.804435\pi$
$31$	−0.725208	+	0.836935i	−0.130251	+	0.150318i	0.686877	+	0.726773i	$0.258981\pi$
$32$	−0.989821	−	0.142315i	−0.174977	−	0.0251579i
$33$	8.81105	−	3.40891i	1.53381	−	0.593415i
$34$	1.88492	−	6.41944i	0.323261	−	1.10092i
$35$	−1.10008	+	3.74653i	−0.185947	+	0.633279i
$36$	0.914917	+	2.85708i	0.152486	+	0.476181i
$37$	2.43391	+	0.349943i	0.400132	+	0.0575303i	0.339444	−	0.940626i	$-0.389761\pi$
$37$	2.43391	+	0.349943i	0.400132	+	0.0575303i	0.0606887	+	0.998157i	$0.480670\pi$
$38$	0.354220	−	0.408792i	0.0574621	−	0.0663148i
$39$	6.45841	+	3.42532i	1.03417	+	0.548490i
$40$	1.87476	−	2.91719i	0.296426	−	0.461248i
$41$	−4.67346	+	0.671942i	−0.729872	+	0.104940i	−0.497225	−	0.867621i	$-0.665648\pi$
$41$	−4.67346	+	0.671942i	−0.729872	+	0.104940i	−0.232647	+	0.972561i	$0.574739\pi$
$42$	−0.955435	−	1.70028i	−0.147427	−	0.262360i
$43$	5.53903	−	4.79960i	0.844694	−	0.731932i	−0.120710	−	0.992688i	$-0.538517\pi$
$43$	5.53903	−	4.79960i	0.844694	−	0.731932i	0.965405	+	0.260756i	$0.0839718\pi$
$44$	5.23357	−	1.53672i	0.788991	−	0.231669i
$45$	−10.3301	−	1.22977i	−1.53992	−	0.183323i
$46$	−2.83691	−	3.86677i	−0.418279	−	0.570125i
$47$		−	4.17207i		−	0.608558i	−0.952583	−	0.304279i	$-0.901584\pi$
$47$		−	4.17207i		−	0.608558i	0.952583	−	0.304279i	$-0.0984156\pi$
$48$	0.388718	+	1.68787i	0.0561066	+	0.243623i
$49$	−3.75370	−	4.33200i	−0.536243	−	0.618857i
$50$	3.79786	+	5.90958i	0.537098	+	0.835741i
$51$	−11.5478	+	0.967124i	−1.61701	+	0.135424i
$52$	3.55071	+	2.28190i	0.492395	+	0.316443i
$53$	3.81724	−	8.35859i	0.524338	−	1.14814i	−0.443432	−	0.896308i	$-0.646239\pi$
$53$	3.81724	−	8.35859i	0.524338	−	1.14814i	0.967771	−	0.251833i	$-0.0810334\pi$
$54$	4.04344	−	3.26352i	0.550243	−	0.444109i
$55$	−2.69181	+	18.7219i	−0.362964	+	2.52447i
$56$	−0.467769	−	1.02427i	−0.0625083	−	0.136874i
$57$	−0.881726	−	0.316713i	−0.116788	−	0.0419497i
$58$	0.305314	+	0.0896482i	0.0400897	+	0.0117714i
$59$	−2.19802	+	1.00380i	−0.286158	+	0.130684i	−0.553323	−	0.832967i	$-0.686641\pi$
$59$	−2.19802	+	1.00380i	−0.286158	+	0.130684i	0.267165	+	0.963651i	$0.413913\pi$
$60$	−5.88400	−	1.20528i	−0.759622	−	0.155600i
$61$	1.32902	+	1.15160i	0.170164	+	0.147448i	0.735779	−	0.677221i	$-0.236816\pi$
$61$	1.32902	+	1.15160i	0.170164	+	0.147448i	−0.565616	+	0.824669i	$0.691361\pi$
$62$	1.00735	+	0.460040i	0.127933	+	0.0584252i
$63$	−2.14947	+	2.60601i	−0.270807	+	0.328326i
$64$	0.142315	+	0.989821i	0.0177894	+	0.123728i
$65$	−12.3127	+	7.91289i	−1.52720	+	0.981473i
$66$	−5.75319	−	7.49374i	−0.708168	−	0.922416i
$67$	1.38479	+	4.71615i	0.169179	+	0.576170i	0.999813	+	0.0193510i	$0.00616001\pi$
$67$	1.38479	+	4.71615i	0.169179	+	0.576170i	−0.830634	+	0.556819i	$0.812022\pi$
$68$	−6.69045			−0.811336
$69$	−4.47328	+	6.99927i	−0.538520	+	0.842613i
$70$	3.90470			0.466701
$71$	−2.57398	−	8.76616i	−0.305475	−	1.04035i	−0.958990	−	0.283439i	$-0.908525\pi$
$71$	−2.57398	−	8.76616i	−0.305475	−	1.04035i	0.653516	−	0.756913i	$-0.273293\pi$
$72$	2.48359	−	1.68279i	0.292694	−	0.198319i
$73$	−8.16392	+	5.24663i	−0.955514	+	0.614072i	−0.922753	−	0.385392i	$-0.874066\pi$
$73$	−8.16392	+	5.24663i	−0.955514	+	0.614072i	−0.0327610	+	0.999463i	$0.510430\pi$
$74$	−0.349943	−	2.43391i	−0.0406801	−	0.282936i
$75$	7.17260	−	9.82825i	0.828220	−	1.13487i
$76$	−0.492028	−	0.224702i	−0.0564395	−	0.0257751i
$77$	4.64177	+	4.02212i	0.528979	+	0.458363i
$78$	1.46702	−	7.16183i	0.166108	−	0.810917i
$79$	10.4223	−	4.75969i	1.17260	−	0.535507i	0.268686	−	0.963228i	$-0.413411\pi$
$79$	10.4223	−	4.75969i	1.17260	−	0.535507i	0.903911	+	0.427721i	$0.140683\pi$
$80$	−3.32720	−	0.976955i	−0.371993	−	0.109227i
$81$	−7.79882	−	4.49205i	−0.866535	−	0.499116i
$82$	1.96139	+	4.29485i	0.216599	+	0.474286i
$83$	0.447423	−	3.11189i	0.0491110	−	0.341575i	−0.950420	−	0.310968i	$-0.899347\pi$
$83$	0.447423	−	3.11189i	0.0491110	−	0.341575i	0.999531	−	0.0306069i	$-0.00974400\pi$
$84$	−1.36223	+	1.39576i	−0.148632	+	0.152290i
$85$	9.63774	−	21.1037i	1.04536	−	2.28902i
$86$	−6.16571	−	3.96246i	−0.664865	−	0.427283i
$87$	−0.0459972	−	0.549221i	−0.00493142	−	0.0588827i
$88$	−2.94894	−	4.58863i	−0.314358	−	0.489150i
$89$	1.93059	+	2.22803i	0.204643	+	0.236170i	0.848789	−	0.528732i	$-0.177333\pi$
$89$	1.93059	+	2.22803i	0.204643	+	0.236170i	−0.644146	+	0.764903i	$0.722787\pi$
$90$	1.73036	+	10.2581i	0.182396	+	1.08130i
$91$			4.75268i			0.498216i
$92$	−2.91089	+	3.81139i	−0.303482	+	0.397365i
$93$	0.113572	−	1.91475i	0.0117768	−	0.198550i
$94$	−4.00307	+	1.17541i	−0.412885	+	0.121234i
$95$	1.41756	−	1.22832i	0.145438	−	0.126023i
$96$	1.50998	−	0.848500i	0.154112	−	0.0865996i
$97$	14.8791	−	2.13929i	1.51074	−	0.217212i	0.663402	−	0.748263i	$-0.269112\pi$
$97$	14.8791	−	2.13929i	1.51074	−	0.217212i	0.847340	+	0.531051i	$0.178203\pi$
$98$	−3.09898	+	4.82211i	−0.313045	+	0.487107i
$99$	−8.50958	+	13.9769i	−0.855245	+	1.40473i
$100$	4.60022	−	5.30894i	0.460022	−	0.530894i
$101$	12.0192	+	1.72810i	1.19596	+	0.171953i	0.711387	−	0.702800i	$-0.248067\pi$
$101$	12.0192	+	1.72810i	1.19596	+	0.171953i	0.484570	+	0.874753i	$0.338976\pi$
$102$	4.18133	+	10.8075i	0.414013	+	1.07011i
$103$	−0.612755	+	2.08685i	−0.0603766	+	0.205624i	−0.984157	−	0.177299i	$-0.943264\pi$
$103$	−0.612755	+	2.08685i	−0.0603766	+	0.205624i	0.923781	+	0.382922i	$0.125082\pi$
$104$	1.18912	−	4.04977i	0.116603	−	0.397113i
$105$	−2.44032	−	6.30752i	−0.238151	−	0.615551i
$106$	−9.09545	−	1.30773i	−0.883428	−	0.127018i
$107$	3.98158	−	4.59498i	0.384913	−	0.444214i	−0.529918	−	0.848049i	$-0.677777\pi$
$107$	3.98158	−	4.59498i	0.384913	−	0.444214i	0.914832	+	0.403835i	$0.132323\pi$
$108$	−4.27049	−	2.96022i	−0.410928	−	0.284847i
$109$	−4.62278	+	7.19318i	−0.442782	+	0.688982i	−0.988876	−	0.148742i	$-0.952478\pi$
$109$	−4.62278	+	7.19318i	−0.442782	+	0.688982i	0.546094	+	0.837724i	$0.316114\pi$
$110$	18.7219	−	2.69181i	1.78507	−	0.256654i
$111$	−3.71296	+	2.08641i	−0.352418	+	0.198033i
$112$	−0.850996	+	0.737392i	−0.0804116	+	0.0696770i
$113$	−2.36312	+	0.693874i	−0.222303	+	0.0652742i	−0.390988	−	0.920396i	$-0.627866\pi$
$113$	−2.36312	+	0.693874i	−0.222303	+	0.0652742i	0.168684	+	0.985670i	$0.446048\pi$
$114$	−0.0554730	+	0.935239i	−0.00519552	+	0.0875931i
$115$	−7.82907	−	14.6722i	−0.730065	−	1.36819i
$116$		−	0.318203i		−	0.0295444i
$117$	−12.4858	+	2.10614i	−1.15432	+	0.194713i
$118$	1.58240	+	1.82618i	0.145672	+	0.168114i
$119$	−4.07299	−	6.33770i	−0.373371	−	0.580976i
$120$	0.501262	+	5.98523i	0.0457587	+	0.546374i
$121$	15.7750	+	10.1380i	1.43409	+	0.921634i
$122$	0.730527	−	1.59963i	0.0661388	−	0.144824i
$123$	5.71194	−	5.85252i	0.515029	−	0.527704i
$124$	0.157603	−	1.09615i	0.0141531	−	0.0984373i
$125$	2.91667	+	6.38662i	0.260875	+	0.571237i
$126$	3.10602	+	1.32820i	0.276706	+	0.118326i
$127$	6.54035	+	1.92042i	0.580362	+	0.170410i	0.558720	−	0.829356i	$-0.311293\pi$
$127$	6.54035	+	1.92042i	0.580362	+	0.170410i	0.0216416	+	0.999766i	$0.493111\pi$
$128$	0.909632	−	0.415415i	0.0804009	−	0.0367178i
$129$	−2.54744	+	12.4363i	−0.224290	+	1.09496i
$130$	11.0612	+	9.58463i	0.970136	+	0.840627i
$131$	−16.0068	−	7.31006i	−1.39852	−	0.638683i	−0.433571	−	0.901119i	$-0.642747\pi$
$131$	−16.0068	−	7.31006i	−1.39852	−	0.638683i	−0.964949	+	0.262436i	$0.915474\pi$
$132$	−5.56933	+	7.63137i	−0.484748	+	0.664226i
$133$	−0.0866811	−	0.602880i	−0.00751620	−	0.0522763i
$134$	4.13498	−	2.65739i	0.357207	−	0.229563i
$135$	15.4892	−	9.20617i	1.33309	−	0.792341i
$136$	1.88492	+	6.41944i	0.161630	+	0.550462i
$137$	13.9061			1.18808			0.594041	−	0.804435i	$-0.297532\pi$
$137$	13.9061			1.18808			0.594041	+	0.804435i	$0.297532\pi$
$138$	7.97602	+	2.32016i	0.678964	+	0.197505i
$139$	−14.8405			−1.25875			−0.629377	−	0.777100i	$-0.716690\pi$
$139$	−14.8405			−1.25875			−0.629377	+	0.777100i	$0.716690\pi$
$140$	−1.10008	−	3.74653i	−0.0929737	−	0.316640i
$141$	4.40051	+	5.73183i	0.370590	+	0.482707i
$142$	−7.68589	+	4.93942i	−0.644986	+	0.414507i
$143$	3.27639	+	22.7878i	0.273985	+	1.90561i
$144$	−2.31433	−	1.90889i	−0.192861	−	0.159074i
$145$	1.00371	+	0.458379i	0.0833535	+	0.0380663i
$146$	7.33415	+	6.35507i	0.606978	+	0.525950i
$147$	9.72626	+	1.99232i	0.802208	+	0.164324i
$148$	−2.23673	+	1.02148i	−0.183858	+	0.0839651i
$149$	3.31083	+	0.972148i	0.271234	+	0.0796415i	0.414521	−	0.910040i	$-0.363949\pi$
$149$	3.31083	+	0.972148i	0.271234	+	0.0796415i	−0.143287	+	0.989681i	$0.545767\pi$
$150$	−11.4509	−	4.11312i	−0.934961	−	0.335835i
$151$	−1.88922	−	4.13680i	−0.153742	−	0.336648i	0.817051	−	0.576565i	$-0.195607\pi$
$151$	−1.88922	−	4.13680i	−0.153742	−	0.336648i	−0.970794	+	0.239917i	$0.922880\pi$
$152$	−0.0769794	+	0.535404i	−0.00624386	+	0.0434270i
$153$	14.8449	−	13.5088i	1.20014	−	1.09212i
$154$	2.55146	−	5.58691i	0.205602	−	0.450206i
$155$	3.23056	+	2.07616i	0.259485	+	0.166761i
$156$	−7.28503	+	0.610120i	−0.583269	+	0.0488487i
$157$	−8.68042	−	13.5070i	−0.692773	−	1.07798i	−0.992296	−	0.123887i	$-0.960464\pi$
$157$	−8.68042	−	13.5070i	−0.692773	−	1.07798i	0.299523	−	0.954089i	$-0.403172\pi$
$158$	−7.50318	−	8.65914i	−0.596921	−	0.688884i
$159$	3.57192	+	15.5098i	0.283272	+	1.23001i
$160$			3.46767i			0.274143i
$161$	−5.38252	−	0.437132i	−0.424202	−	0.0344508i
$162$	−2.11291	+	8.74846i	−0.166006	+	0.687344i
$163$	−6.19048	+	1.81769i	−0.484876	+	0.142372i	−0.515029	−	0.857173i	$-0.672219\pi$
$163$	−6.19048	+	1.81769i	−0.484876	+	0.142372i	0.0301527	+	0.999545i	$0.490401\pi$
$164$	3.56829	−	3.09194i	0.278636	−	0.241440i
$165$	−16.0489	−	28.5605i	−1.24941	−	2.22343i
$166$	−3.11189	+	0.447423i	−0.241530	+	0.0347267i
$167$	−5.40295	+	8.40716i	−0.418093	+	0.650565i	−0.984868	−	0.173307i	$-0.944555\pi$
$167$	−5.40295	+	8.40716i	−0.418093	+	0.650565i	0.566775	+	0.823873i	$0.308191\pi$
$168$	1.72301	+	0.913823i	0.132933	+	0.0705030i
$169$	−3.15292	+	3.63866i	−0.242532	+	0.279897i
$170$	−22.9641	−	3.30174i	−1.76127	−	0.253232i
$171$	1.54542	−	0.494887i	0.118181	−	0.0378450i
$172$	−2.06487	+	7.03231i	−0.157445	+	0.536208i
$173$	−6.48288	+	22.0787i	−0.492884	+	1.67861i	0.218525	+	0.975831i	$0.429875\pi$
$173$	−6.48288	+	22.0787i	−0.492884	+	1.67861i	−0.711409	+	0.702778i	$0.751943\pi$
$174$	−0.514015	+	0.198868i	−0.0389674	+	0.0150761i
$175$	7.82954	+	1.12572i	0.591858	+	0.0850963i
$176$	−3.57195	+	4.12225i	−0.269246	+	0.310726i
$177$	1.96101	−	3.69747i	0.147398	−	0.277919i
$178$	1.59386	−	2.48010i	0.119465	−	0.185891i
$179$	13.9699	−	2.00857i	1.04416	−	0.150127i	0.401170	−	0.916004i	$-0.368604\pi$
$179$	13.9699	−	2.00857i	1.04416	−	0.150127i	0.642988	+	0.765876i	$0.277694\pi$
$180$	9.35507	−	4.55031i	0.697285	−	0.339160i
$181$	−3.24823	+	2.81461i	−0.241439	+	0.209208i	−0.767172	−	0.641442i	$-0.778337\pi$
$181$	−3.24823	+	2.81461i	−0.241439	+	0.209208i	0.525733	+	0.850650i	$0.323791\pi$
$182$	4.56016	−	1.33898i	0.338021	−	0.0992520i
$183$	−3.04055	−	0.180348i	−0.224764	−	0.0133317i
$184$	4.47710	+	1.71919i	0.330056	+	0.126740i
$185$		−	8.52679i		−	0.626902i
$186$	−1.86918	+	0.430476i	−0.137055	+	0.0315640i
$187$	−23.8979	−	27.5797i	−1.74759	−	2.01683i
$188$	2.25559	+	3.50977i	0.164506	+	0.255976i
$189$	0.204362	−	5.84745i	0.0148652	−	0.425339i
$190$	−1.57793	−	1.01408i	−0.114475	−	0.0735689i
$191$	−3.52963	+	7.72880i	−0.255395	+	0.559237i	−0.993286	−	0.115683i	$-0.963094\pi$
$191$	−3.52963	+	7.72880i	−0.255395	+	0.559237i	0.737891	+	0.674919i	$0.235822\pi$
$192$	−1.23954	−	1.20977i	−0.0894562	−	0.0873075i
$193$	0.171980	−	1.19615i	0.0123794	−	0.0861006i	−0.982695	−	0.185230i	$-0.940697\pi$
$193$	0.171980	−	1.19615i	0.0123794	−	0.0861006i	0.995075	+	0.0991299i	$0.0316059\pi$
$194$	−6.24456	−	13.6737i	−0.448333	−	0.981712i
$195$	8.56974	−	23.8581i	0.613692	−	1.70851i
$196$	5.49987	+	1.61491i	0.392848	+	0.115351i
$197$	−0.0466277	+	0.0212941i	−0.00332208	+	0.00151714i	−0.417075	−	0.908872i	$-0.636945\pi$
$197$	−0.0466277	+	0.0212941i	−0.00332208	+	0.00151714i	0.413753	+	0.910389i	$0.364218\pi$
$198$	15.8081	+	4.22714i	1.12344	+	0.300410i
$199$	12.7882	+	11.0810i	0.906531	+	0.785514i	0.977274	−	0.211981i	$-0.0679914\pi$
$199$	12.7882	+	11.0810i	0.906531	+	0.785514i	−0.0707424	+	0.997495i	$0.522537\pi$
$200$	−6.38992	−	2.91818i	−0.451836	−	0.206346i
$201$	−6.87689	−	5.01872i	−0.485059	−	0.353993i
$202$	−1.72810	−	12.0192i	−0.121589	−	0.845669i
$203$	0.301426	−	0.193715i	0.0211560	−	0.0135961i
$204$	9.19173	−	7.05679i	0.643550	−	0.494074i
$205$	4.61271	+	15.7095i	0.322166	+	1.09720i
$206$	2.17495			0.151536
$207$	−1.23687	−	14.3342i	−0.0859682	−	0.996298i
$208$	−4.22074			−0.292656
$209$	−0.831224	−	2.83089i	−0.0574969	−	0.195817i
$210$	−5.36450	+	4.11850i	−0.370186	+	0.284204i
$211$	9.41085	−	6.04799i	0.647870	−	0.416361i	−0.175018	−	0.984565i	$-0.555998\pi$
$211$	9.41085	−	6.04799i	0.647870	−	0.416361i	0.822887	+	0.568205i	$0.192362\pi$
$212$	1.30773	+	9.09545i	0.0898152	+	0.624678i
$213$	12.7824	+	9.32855i	0.875838	+	0.639182i
$214$	−5.53059	−	2.52574i	−0.378064	−	0.172656i
$215$	−19.2075	−	16.6434i	−1.30994	−	1.13507i
$216$	−1.63717	+	4.93150i	−0.111395	+	0.335546i
$217$	1.13430	−	0.518019i	0.0770015	−	0.0351654i
$218$	8.20419	+	2.40897i	0.555658	+	0.163156i
$219$	5.68216	−	15.8191i	0.383965	−	1.06895i
$220$	−7.85735	−	17.2052i	−0.529743	−	1.15997i
$221$	4.01878	−	27.9512i	0.270332	−	1.88020i
$222$	3.04795	+	2.97475i	0.204565	+	0.199652i
$223$	−6.16749	+	13.5049i	−0.413006	+	0.904356i	0.582779	+	0.812631i	$0.301965\pi$
$223$	−6.16749	+	13.5049i	−0.413006	+	0.904356i	−0.995784	+	0.0917254i	$0.970762\pi$
$224$	0.947276	+	0.608777i	0.0632925	+	0.0406756i
$225$	0.512264	+	21.0680i	0.0341509	+	1.40453i
$226$	1.33153	+	2.07191i	0.0885724	+	0.137821i
$227$	4.69859	+	5.42246i	0.311856	+	0.359901i	0.889941	−	0.456075i	$-0.150745\pi$
$227$	4.69859	+	5.42246i	0.311856	+	0.359901i	−0.578085	+	0.815977i	$0.696200\pi$
$228$	0.912984	−	0.210261i	0.0604638	−	0.0139249i
$229$			8.31850i			0.549702i	0.961487	+	0.274851i	$0.0886285\pi$
$229$			8.31850i			0.549702i	−0.961487	+	0.274851i	$0.911371\pi$
$230$	−11.8722	+	11.6456i	−0.782830	+	0.767887i
$231$	−10.6195	−	0.629887i	−0.698712	−	0.0414435i
$232$	−0.305314	+	0.0896482i	−0.0200448	+	0.00588569i
$233$	0.846742	−	0.733706i	0.0554719	−	0.0480667i	−0.626684	−	0.779274i	$-0.715588\pi$
$233$	0.846742	−	0.733706i	0.0554719	−	0.0480667i	0.682156	+	0.731207i	$0.261043\pi$
$234$	5.53850	+	11.3867i	0.362063	+	0.744372i
$235$	−14.3201	+	2.05892i	−0.934140	+	0.134309i
$236$	1.30640	−	2.03280i	0.0850393	−	0.132324i
$237$	−9.29842	+	17.5321i	−0.603997	+	1.13883i
$238$	−4.93348	+	5.69354i	−0.319790	+	0.369058i
$239$	−5.10519	−	0.734016i	−0.330227	−	0.0474795i	−0.0247928	−	0.999693i	$-0.507893\pi$
$239$	−5.10519	−	0.734016i	−0.330227	−	0.0474795i	−0.305434	+	0.952213i	$0.598802\pi$
$240$	5.60156	−	2.16719i	0.361579	−	0.139892i
$241$	−2.93330	+	9.98989i	−0.188950	+	0.643506i	0.809462	+	0.587173i	$0.199759\pi$
$241$	−2.93330	+	9.98989i	−0.188950	+	0.643506i	−0.998412	+	0.0563329i	$0.982059\pi$
$242$	5.28298	−	17.9922i	0.339603	−	1.15658i
$243$	15.4525	−	2.05441i	0.991278	−	0.131790i
$244$	−1.74065	−	0.250267i	−0.111434	−	0.0160217i
$245$	−13.0166	+	15.0219i	−0.831600	+	0.959717i
$246$	−7.22469	−	3.83173i	−0.460629	−	0.244302i
$247$	1.23430	−	1.92061i	0.0785368	−	0.122206i
$248$	−1.09615	+	0.157603i	−0.0696057	+	0.0100078i
$249$	2.66759	+	4.74722i	0.169052	+	0.300843i
$250$	5.30620	−	4.59784i	0.335593	−	0.290793i
$251$	−22.5777	+	6.62941i	−1.42509	+	0.418445i	−0.901224	−	0.433354i	$-0.857330\pi$
$251$	−22.5777	+	6.62941i	−1.42509	+	0.418445i	−0.523869	+	0.851799i	$0.675512\pi$
$252$	0.399332	−	3.35440i	0.0251556	−	0.211307i
$253$	−26.1091	+	1.61466i	−1.64146	+	0.101513i
$254$		−	6.81646i		−	0.427703i
$255$	9.01836	+	39.1590i	0.564752	+	2.45223i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	13.2691	+	20.6471i	0.827702	+	1.28793i	0.955161	+	0.296086i	$0.0956816\pi$
$257$	13.2691	+	20.6471i	0.827702	+	1.28793i	−0.127459	+	0.991844i	$0.540682\pi$
$258$	12.6502	−	1.05946i	0.787570	−	0.0659588i
$259$	−2.32929	−	1.49695i	−0.144735	−	0.0930157i
$260$	6.08007	−	13.3135i	0.377070	−	0.825668i
$261$	0.642488	+	0.706037i	0.0397690	+	0.0437026i
$262$	−2.50431	+	17.4179i	−0.154717	+	1.07608i
$263$	−6.38077	−	13.9719i	−0.393455	−	0.861547i	−0.997892	−	0.0648938i	$-0.979329\pi$
$263$	−6.38077	−	13.9719i	−0.393455	−	0.861547i	0.604437	−	0.796653i	$-0.293398\pi$
$264$	8.89131	+	3.19373i	0.547222	+	0.196560i
$265$	−30.5736	−	8.97723i	−1.87812	−	0.551467i
$266$	−0.554038	+	0.253021i	−0.0339703	+	0.0155137i
$267$	−5.00239	−	1.02469i	−0.306141	−	0.0627098i
$268$	−3.71470	−	3.21881i	−0.226912	−	0.196620i
$269$	18.9814	+	8.66850i	1.15731	+	0.528528i	0.899179	−	0.437581i	$-0.144165\pi$
$269$	18.9814	+	8.66850i	1.15731	+	0.528528i	0.258136	+	0.966109i	$0.416892\pi$
$270$	−13.1971	−	12.2681i	−0.803148	−	0.746610i
$271$	−3.37020	−	23.4402i	−0.204725	−	1.42389i	−0.790024	−	0.613076i	$-0.789932\pi$
$271$	−3.37020	−	23.4402i	−0.204725	−	1.42389i	0.585299	−	0.810818i	$-0.300977\pi$
$272$	5.62836	−	3.61713i	0.341270	−	0.219321i
$273$	−5.01291	−	6.52951i	−0.303395	−	0.395184i
$274$	−3.91781	−	13.3429i	−0.236684	−	0.806071i
$275$	38.3165			2.31057
$276$	−0.0209289	−	8.30660i	−0.00125977	−	0.499998i
$277$	33.1250			1.99029			0.995145	−	0.0984225i	$-0.0313797\pi$
$277$	33.1250			1.99029			0.995145	+	0.0984225i	$0.0313797\pi$
$278$	4.18105	+	14.2393i	0.250763	+	0.854019i
$279$	1.86356	+	2.75039i	0.111568	+	0.164661i
$280$	−3.28484	+	2.11104i	−0.196307	+	0.126159i
$281$	−2.41184	−	16.7747i	−0.143878	−	1.00070i	−0.925988	−	0.377554i	$-0.876765\pi$
$281$	−2.41184	−	16.7747i	−0.143878	−	1.00070i	0.782109	−	0.623141i	$-0.214144\pi$
$282$	4.25989	−	5.83711i	0.253672	−	0.347595i
$283$	20.1373	+	9.19639i	1.19704	+	0.546669i	0.911341	−	0.411652i	$-0.135048\pi$
$283$	20.1373	+	9.19639i	1.19704	+	0.546669i	0.285696	+	0.958320i	$0.407775\pi$
$284$	6.90471	+	5.98296i	0.409719	+	0.355024i
$285$	−0.651945	+	3.18271i	−0.0386179	+	0.188528i
$286$	20.9416	−	9.56373i	1.23831	−	0.565515i
$287$	5.10121	+	1.49785i	0.301115	+	0.0884153i
$288$	−1.17954	+	2.75838i	−0.0695053	+	0.162539i
$289$	11.5328	+	25.2533i	0.678399	+	1.48549i
$290$	0.157034	−	1.09219i	0.00922133	−	0.0641357i
$291$	−18.1853	+	18.6329i	−1.06604	+	1.09228i
$292$	4.03138	−	8.82749i	0.235919	−	0.516590i
$293$	22.7630	+	14.6289i	1.32983	+	0.854631i	0.996117	−	0.0880433i	$-0.0280614\pi$
$293$	22.7630	+	14.6289i	1.32983	+	0.854631i	0.333715	+	0.942674i	$0.391698\pi$
$294$	−0.828586	−	9.89358i	−0.0483241	−	0.577005i
$295$	4.53016	+	7.04906i	0.263756	+	0.410412i
$296$	1.61026	+	1.85834i	0.0935946	+	0.108014i
$297$	−3.05124	−	28.1778i	−0.177051	−	1.63504i
$298$		−	3.45061i		−	0.199888i
$299$	−14.1746	−	14.4505i	−0.819741	−	0.835692i
$300$	−0.720422	+	12.1458i	−0.0415936	+	0.701241i
$301$	−7.91858	+	2.32510i	−0.456419	+	0.134017i
$302$	−3.43698	+	2.97816i	−0.197776	+	0.171374i
$303$	−18.3354	+	10.3032i	−1.05334	+	0.591902i
$304$	0.535404	−	0.0769794i	0.0307075	−	0.00441507i
$305$	3.29686	−	5.13001i	0.188778	−	0.293744i
$306$	−17.1439	−	10.4377i	−0.980050	−	0.596686i
$307$	15.3903	−	17.7613i	0.878369	−	1.01369i	−0.121408	−	0.992603i	$-0.538741\pi$
$307$	15.3903	−	17.7613i	0.878369	−	1.01369i	0.999778	−	0.0210896i	$-0.00671352\pi$
$308$	−6.07943	−	0.874090i	−0.346408	−	0.0498059i
$309$	−1.35928	−	3.51335i	−0.0773268	−	0.199868i
$310$	1.08190	−	3.68462i	0.0614480	−	0.209273i
$311$	−5.36040	+	18.2559i	−0.303961	+	1.03519i	0.655930	+	0.754821i	$0.272276\pi$
$311$	−5.36040	+	18.2559i	−0.303961	+	1.03519i	−0.959891	+	0.280373i	$0.909542\pi$
$312$	2.63784	+	6.81804i	0.149338	+	0.385996i
$313$	−30.0771	−	4.32443i	−1.70006	−	0.244431i	−0.777111	−	0.629363i	$-0.783316\pi$
$313$	−30.0771	−	4.32443i	−1.70006	−	0.244431i	−0.922945	+	0.384932i	$0.874225\pi$
$314$	−10.5143	+	12.1342i	−0.593357	+	0.684770i
$315$	10.0056	+	6.09170i	0.563749	+	0.343229i
$316$	−6.19449	+	9.63881i	−0.348467	+	0.542226i
$317$	−21.3003	+	3.06252i	−1.19634	+	0.172008i	−0.711559	−	0.702626i	$-0.752011\pi$
$317$	−21.3003	+	3.06252i	−1.19634	+	0.172008i	−0.484784	+	0.874634i	$0.661102\pi$
$318$	13.8752	−	7.79685i	0.778083	−	0.437226i
$319$	1.31171	−	1.13661i	0.0734418	−	0.0636377i
$320$	3.32720	−	0.976955i	0.185996	−	0.0546135i
$321$	−0.623538	+	10.5125i	−0.0348025	+	0.586748i
$322$	1.09701	+	5.28765i	0.0611338	+	0.294669i
$323$			3.61893i			0.201362i
$324$	8.98936	−	0.437408i	0.499409	−	0.0243005i
$325$	19.4163	+	22.4076i	1.07702	+	1.24295i
$326$	3.48812	+	5.42762i	0.193189	+	0.300608i
$327$	−1.23601	−	14.7583i	−0.0683513	−	0.816137i
$328$	−3.97200	−	2.55265i	−0.219317	−	0.140946i
$329$	−1.95157	+	4.27333i	−0.107593	+	0.235596i
$330$	−22.8821	+	23.4453i	−1.25962	+	1.29062i
$331$	3.52974	−	24.5499i	0.194012	−	1.34938i	−0.627244	−	0.778823i	$-0.715817\pi$
$331$	3.52974	−	24.5499i	0.194012	−	1.34938i	0.821256	−	0.570560i	$-0.193274\pi$
$332$	1.30602	+	2.85979i	0.0716772	+	0.156951i
$333$	2.90043	−	6.78269i	0.158942	−	0.371689i
$334$	9.58880	+	2.81552i	0.524676	+	0.154059i
$335$	15.5042	−	7.08053i	0.847085	−	0.386851i
$336$	0.391380	−	1.91067i	0.0213515	−	0.104235i
$337$	11.4915	+	9.95745i	0.625982	+	0.542417i	0.909052	−	0.416683i	$-0.136807\pi$
$337$	11.4915	+	9.95745i	0.625982	+	0.542417i	−0.283070	+	0.959099i	$0.591353\pi$
$338$	4.37955	+	2.00007i	0.238216	+	0.108790i
$339$	2.51472	−	3.44580i	0.136581	−	0.187150i
$340$	3.30174	+	22.9641i	0.179062	+	1.24540i
$341$	5.08156	−	3.26572i	0.275182	−	0.176849i
$342$	−0.910237	−	1.34340i	−0.0492200	−	0.0726426i
$343$	4.03911	+	13.7559i	0.218091	+	0.742751i
$344$	7.32919			0.395163
$345$	26.2317	+	11.8998i	1.41227	+	0.640665i
$346$	23.0108			1.23707
$347$	−1.31185	−	4.46777i	−0.0704241	−	0.239842i	0.916757	−	0.399445i	$-0.130797\pi$
$347$	−1.31185	−	4.46777i	−0.0704241	−	0.239842i	−0.987181	+	0.159602i	$0.948979\pi$
$348$	0.335627	+	0.437166i	0.0179915	+	0.0234346i
$349$	5.79333	−	3.72315i	0.310110	−	0.199296i	−0.376323	−	0.926488i	$-0.622812\pi$
$349$	5.79333	−	3.72315i	0.310110	−	0.199296i	0.686433	+	0.727193i	$0.259175\pi$
$350$	−1.12572	−	7.82954i	−0.0601722	−	0.418507i
$351$	14.9323	−	16.0631i	0.797027	−	0.857382i
$352$	4.96160	+	2.26589i	0.264454	+	0.120772i
$353$	−26.4583	−	22.9262i	−1.40823	−	1.22024i	−0.942016	−	0.335568i	$-0.891072\pi$
$353$	−26.4583	−	22.9262i	−1.40823	−	1.22024i	−0.466215	−	0.884671i	$-0.654383\pi$
$354$	−4.10017	−	0.839877i	−0.217922	−	0.0446390i
$355$	−28.8185	+	13.1610i	−1.52953	+	0.698511i
$356$	−2.82868	−	0.830576i	−0.149920	−	0.0440204i
$357$	12.2804	+	4.41109i	0.649950	+	0.233460i
$358$	−5.86298	−	12.8381i	−0.309868	−	0.678516i
$359$	0.132119	−	0.918905i	0.00697295	−	0.0484979i	−0.986038	−	0.166521i	$-0.946747\pi$
$359$	0.132119	−	0.918905i	0.00697295	−	0.0484979i	0.993011	+	0.118023i	$0.0376557\pi$
$360$	−7.00162	−	7.69415i	−0.369018	−	0.405517i
$361$	7.77134	−	17.0169i	0.409018	−	0.895624i
$362$	3.61573	+	2.32369i	0.190038	+	0.122130i
$363$	−32.3657	+	2.71062i	−1.69876	+	0.142271i
$364$	−2.56949	−	3.99820i	−0.134678	−	0.209563i
$365$	22.0373	+	25.4324i	1.15348	+	1.33119i
$366$	0.683579	+	2.96819i	0.0357313	+	0.155150i
$367$		−	12.4382i		−	0.649268i	−0.945840	−	0.324634i	$-0.894759\pi$
$367$		−	12.4382i		−	0.649268i	0.945840	−	0.324634i	$-0.105241\pi$
$368$	0.388206	−	4.78009i	0.0202367	−	0.249180i
$369$	−1.67443	+	14.0652i	−0.0871673	+	0.732207i
$370$	−8.18139	+	2.40227i	−0.425330	+	0.124888i
$371$	−7.81979	+	6.77589i	−0.405983	+	0.351786i
$372$	0.939648	+	1.67219i	0.0487185	+	0.0866990i
$373$	4.16743	−	0.599187i	0.215782	−	0.0310247i	−0.0335761	−	0.999436i	$-0.510690\pi$
$373$	4.16743	−	0.599187i	0.215782	−	0.0310247i	0.249358	+	0.968411i	$0.419781\pi$
$374$	−19.7297	+	30.7000i	−1.02020	+	1.58746i
$375$	−10.7434	−	5.69794i	−0.554788	−	0.294240i
$376$	2.73212	−	3.15304i	0.140898	−	0.162606i
$377$	1.32938	+	0.191136i	0.0684667	+	0.00984402i
$378$	−5.66816	+	1.45133i	−0.291539	+	0.0746485i
$379$	2.31115	−	7.87107i	0.118716	−	0.404310i	−0.878597	−	0.477563i	$-0.841520\pi$
$379$	2.31115	−	7.87107i	0.118716	−	0.404310i	0.997313	+	0.0732537i	$0.0233383\pi$
$380$	−0.528444	+	1.79972i	−0.0271086	+	0.0923235i
$381$	−11.0111	+	4.26009i	−0.564115	+	0.218251i
$382$	8.41014	+	1.20920i	0.430300	+	0.0618679i
$383$	22.1774	−	25.5940i	1.13321	−	1.30779i	0.187691	−	0.982228i	$-0.439900\pi$
$383$	22.1774	−	25.5940i	1.13321	−	1.30779i	0.945519	−	0.325566i	$-0.105555\pi$
$384$	−0.811545	+	1.53016i	−0.0414140	+	0.0780857i
$385$	11.5147	−	17.9172i	0.586843	−	0.913146i
$386$	−1.19615	+	0.171980i	−0.0608823	+	0.00875356i
$387$	−9.61743	−	19.7727i	−0.488882	−	1.00510i
$388$	−11.3605	+	9.84393i	−0.576742	+	0.499750i
$389$	2.08019	−	0.610799i	0.105470	−	0.0309687i	−0.228572	−	0.973527i	$-0.573406\pi$
$389$	2.08019	−	0.610799i	0.105470	−	0.0309687i	0.334042	+	0.942558i	$0.391587\pi$
$390$	−25.3060	−	1.50101i	−1.28142	−	0.0760065i
$391$	31.2858	+	7.12220i	1.58219	+	0.360185i
$392$		−	5.73206i		−	0.289513i
$393$	29.7014	−	6.84027i	1.49824	−	0.345046i
$394$	0.0335681	+	0.0387397i	0.00169114	+	0.00195168i
$395$	−21.4804	−	33.4242i	−1.08080	−	1.68175i
$396$	−0.397759	−	16.3587i	−0.0199882	−	0.822057i
$397$	−24.3971	−	15.6791i	−1.22446	−	0.786911i	−0.241438	−	0.970416i	$-0.577619\pi$
$397$	−24.3971	−	15.6791i	−1.22446	−	0.786911i	−0.983019	+	0.183505i	$0.941255\pi$
$398$	7.02933	−	15.3921i	0.352348	−	0.771535i
$399$	0.754979	+	0.736845i	0.0377962	+	0.0368884i
$400$	−0.999724	+	6.95323i	−0.0499862	+	0.347662i
$401$	−13.6290	−	29.8434i	−0.680600	−	1.49031i	−0.862006	−	0.506898i	$-0.830792\pi$
$401$	−13.6290	−	29.8434i	−0.680600	−	1.49031i	0.181406	−	0.983408i	$-0.441935\pi$
$402$	−2.87798	+	8.01227i	−0.143541	+	0.399616i
$403$	4.48481	+	1.31686i	0.223404	+	0.0655974i
$404$	−11.0455	+	5.04431i	−0.549534	+	0.250964i
$405$	−11.5697	+	28.9853i	−0.574901	+	1.44029i
$406$	−0.270790	−	0.234641i	−0.0134391	−	0.0116450i
$407$	−12.2003	−	5.57168i	−0.604745	−	0.276178i
$408$	−9.36055	−	6.83128i	−0.463416	−	0.338199i
$409$	0.956843	+	6.65499i	0.0473128	+	0.329068i	0.999707	+	0.0241991i	$0.00770357\pi$
$409$	0.956843	+	6.65499i	0.0473128	+	0.329068i	−0.952394	+	0.304869i	$0.901387\pi$
$410$	13.7736	−	8.85173i	0.680228	−	0.437156i
$411$	−19.1051	+	14.6676i	−0.942385	+	0.723499i
$412$	−0.612755	−	2.08685i	−0.0301883	−	0.102812i
$413$	2.72092			0.133888
$414$	−13.4051	+	5.22518i	−0.658826	+	0.256804i
$415$	−10.9020			−0.535157
$416$	1.18912	+	4.04977i	0.0583014	+	0.198556i
$417$	20.3887	−	15.6531i	0.998441	−	0.766535i
$418$	−2.48203	+	1.59511i	−0.121400	+	0.0780192i
$419$	−0.634594	−	4.41370i	−0.0310019	−	0.215623i	0.968432	−	0.249280i	$-0.0801938\pi$
$419$	−0.634594	−	4.41370i	−0.0310019	−	0.215623i	−0.999433	+	0.0336566i	$0.989285\pi$
$420$	5.46303	+	3.98689i	0.266569	+	0.194540i
$421$	4.31204	+	1.96924i	0.210156	+	0.0959750i	0.517712	−	0.855555i	$-0.326784\pi$
$421$	4.31204	+	1.96924i	0.210156	+	0.0959750i	−0.307556	+	0.951530i	$0.599511\pi$
$422$	−8.45434	−	7.32573i	−0.411551	−	0.356611i
$423$	−12.0914	−	3.23326i	−0.587903	−	0.157207i
$424$	8.35859	−	3.81724i	0.405929	−	0.185382i
$425$	−45.0948	−	13.2410i	−2.18742	−	0.642285i
$426$	5.34945	−	14.8928i	0.259182	−	0.721559i
$427$	−0.822594	−	1.80123i	−0.0398081	−	0.0871676i
$428$	−0.865279	+	6.01815i	−0.0418248	+	0.290898i
$429$	−28.5368	−	27.8514i	−1.37777	−	1.34468i
$430$	−10.5579	+	23.1185i	−0.509145	+	1.11487i
$431$	23.8818	+	15.3479i	1.15035	+	0.739282i	0.969708	−	0.244268i	$-0.0785476\pi$
$431$	23.8818	+	15.3479i	1.15035	+	0.739282i	0.180638	+	0.983550i	$0.442184\pi$
$432$	5.19298	+	0.181490i	0.249847	+	0.00873192i
$433$	5.81783	+	9.05272i	0.279587	+	0.435046i	0.952438	−	0.304732i	$-0.0985669\pi$
$433$	5.81783	+	9.05272i	0.279587	+	0.435046i	−0.672851	+	0.739778i	$0.734931\pi$
$434$	−0.816605	−	0.942413i	−0.0391983	−	0.0452373i
$435$	−1.86243	+	0.428921i	−0.0892968	+	0.0205652i
$436$		−	8.55055i		−	0.409497i
$437$	2.06162	+	1.57453i	0.0986205	+	0.0753200i
$438$	−16.7791	−	0.995242i	−0.801738	−	0.0475545i
$439$	0.155517	−	0.0456639i	0.00742242	−	0.00217942i	−0.278019	−	0.960576i	$-0.589678\pi$
$439$	0.155517	−	0.0456639i	0.00742242	−	0.00217942i	0.285442	+	0.958396i	$0.407860\pi$
$440$	−14.2946	+	12.3863i	−0.681468	+	0.590496i
$441$	−15.4639	+	7.52166i	−0.736377	+	0.358174i
$442$	−27.9512	+	4.01878i	−1.32950	+	0.191154i
$443$	−12.3664	+	19.2424i	−0.587543	+	0.914236i	0.412451	+	0.910980i	$0.364673\pi$
$443$	−12.3664	+	19.2424i	−0.587543	+	0.914236i	−0.999995	+	0.00325581i	$0.998964\pi$
$444$	1.99554	−	3.76257i	0.0947041	−	0.178564i
$445$	6.69466	−	7.72606i	0.317358	−	0.366250i
$446$	14.6955	+	2.11289i	0.695850	+	0.100048i
$447$	−5.57400	+	2.15653i	−0.263641	+	0.102000i
$448$	0.317239	−	1.08042i	0.0149881	−	0.0510449i
$449$	−0.00112074	+	0.00381690i	−5.28911e−5	+	0.000180131i	−0.959519	−	0.281642i	$-0.909121\pi$
$449$	−0.00112074	+	0.00381690i	−5.28911e−5	+	0.000180131i	0.959467	+	0.281823i	$0.0909390\pi$
$450$	20.0702	−	6.42705i	0.946121	−	0.302974i
$451$	25.4915	+	3.66512i	1.20035	+	0.172584i
$452$	1.61285	−	1.86132i	0.0758619	−	0.0875492i
$453$	6.95884	+	3.69073i	0.326955	+	0.173405i
$454$	3.87907	−	6.03595i	0.182054	−	0.283281i
$455$	16.3130	−	2.34545i	0.764763	−	0.109956i
$456$	−0.458961	−	0.816764i	−0.0214928	−	0.0382485i
$457$	−2.60575	+	2.25790i	−0.121892	+	0.105620i	−0.713674	−	0.700478i	$-0.752970\pi$
$457$	−2.60575	+	2.25790i	−0.121892	+	0.105620i	0.591782	+	0.806098i	$0.298425\pi$
$458$	7.98154	−	2.34359i	0.372953	−	0.109509i
$459$	−6.14638	+	34.2169i	−0.286889	+	1.59711i
$460$	14.5186	+	8.11035i	0.676935	+	0.378147i
$461$			18.0351i			0.839979i	0.907529	+	0.419989i	$0.137966\pi$
$461$			18.0351i			0.839979i	−0.907529	+	0.419989i	$0.862034\pi$
$462$	2.38749	+	10.3668i	0.111076	+	0.482307i
$463$	5.02851	+	5.80321i	0.233695	+	0.269698i	0.860469	−	0.509503i	$-0.170171\pi$
$463$	5.02851	+	5.80321i	0.233695	+	0.269698i	−0.626774	+	0.779201i	$0.715625\pi$
$464$	0.172034	+	0.267690i	0.00798646	+	0.0124272i
$465$	−6.62818	+	0.555109i	−0.307374	+	0.0257426i
$466$	−0.942540	−	0.605734i	−0.0436623	−	0.0280601i
$467$	−6.12689	+	13.4160i	−0.283519	+	0.620820i	−0.996789	−	0.0800692i	$-0.974486\pi$
$467$	−6.12689	+	13.4160i	−0.283519	+	0.620820i	0.713270	+	0.700889i	$0.247213\pi$
$468$	9.36508	−	8.52215i	0.432901	−	0.393937i
$469$	0.787673	−	5.47838i	0.0363713	−	0.252968i
$470$	6.00995	+	13.1600i	0.277219	+	0.607024i
$471$	26.1723	+	9.40099i	1.20595	+	0.433175i
$472$	−2.31851	−	0.680775i	−0.106718	−	0.0313352i
$473$	−36.3645	+	16.6071i	−1.67204	+	0.763597i
$474$	19.4416	+	3.98241i	0.892982	+	0.182918i
$475$	−2.87165	−	2.48830i	−0.131761	−	0.114171i
$476$	6.85284	+	3.12959i	0.314099	+	0.143444i
$477$	−21.2664	−	17.5408i	−0.973720	−	0.803136i
$478$	0.734016	+	5.10519i	0.0335731	+	0.233506i
$479$	2.02491	−	1.30133i	0.0925203	−	0.0594592i	−0.493563	−	0.869710i	$-0.664306\pi$
$479$	2.02491	−	1.30133i	0.0925203	−	0.0594592i	0.586083	+	0.810251i	$0.300669\pi$
$480$	−3.65755	−	4.76409i	−0.166943	−	0.217450i
$481$	−2.92397	−	9.95813i	−0.133322	−	0.454052i
$482$	10.4116			0.474237
$483$	7.85590	−	5.07669i	0.357456	−	0.230998i
$484$	−18.7518			−0.852353
$485$	−14.6857	−	50.0148i	−0.666843	−	2.27106i
$486$	−6.32466	−	14.2478i	−0.286892	−	0.646292i
$487$	18.7222	−	12.0320i	0.848385	−	0.545224i	−0.0426858	−	0.999089i	$-0.513591\pi$
$487$	18.7222	−	12.0320i	0.848385	−	0.545224i	0.891071	+	0.453865i	$0.149955\pi$
$488$	0.250267	+	1.74065i	0.0113291	+	0.0787954i
$489$	6.58763	−	9.02670i	0.297903	−	0.408202i
$490$	18.0807	+	8.25716i	0.816801	+	0.373020i
$491$	26.4667	+	22.9335i	1.19442	+	1.03497i	0.998522	+	0.0543513i	$0.0173091\pi$
$491$	26.4667	+	22.9335i	1.19442	+	1.03497i	0.195903	+	0.980623i	$0.437236\pi$
$492$	−1.64108	+	8.01156i	−0.0739858	+	0.361189i
$493$	−1.93654	+	0.884386i	−0.0872172	+	0.0398307i
$494$	−2.19056	−	0.643206i	−0.0985579	−	0.0289392i
$495$	52.1733	+	22.3104i	2.34502	+	1.00278i
$496$	0.460040	+	1.00735i	0.0206564	+	0.0452312i
$497$	−1.46409	+	10.1830i	−0.0656733	+	0.456768i
$498$	3.80338	−	3.89698i	0.170434	−	0.174628i
$499$	−13.5846	+	29.7461i	−0.608129	+	1.33162i	0.315717	+	0.948853i	$0.397755\pi$
$499$	−13.5846	+	29.7461i	−0.608129	+	1.33162i	−0.923846	+	0.382764i	$0.874972\pi$
$500$	−5.90653	−	3.79589i	−0.264148	−	0.169758i
$501$	−1.44460	−	17.2490i	−0.0645402	−	0.770631i
$502$	12.7218	+	19.7954i	0.567800	+	0.883513i
$503$	3.18224	+	3.67250i	0.141889	+	0.163749i	0.822246	−	0.569132i	$-0.192721\pi$
$503$	3.18224	+	3.67250i	0.141889	+	0.163749i	−0.680357	+	0.732881i	$0.738175\pi$
$504$	−3.33103	+	0.561887i	−0.148376	+	0.0250285i
$505$		−	42.1073i		−	1.87375i
$506$	8.90503	+	24.5966i	0.395877	+	1.09345i
$507$	0.493765	−	8.32457i	0.0219289	−	0.369707i
$508$	−6.54035	+	1.92042i	−0.290181	+	0.0852048i
$509$	17.6690	−	15.3103i	0.783164	−	0.678616i	−0.168519	−	0.985698i	$-0.553898\pi$
$509$	17.6690	−	15.3103i	0.783164	−	0.678616i	0.951683	+	0.307083i	$0.0993529\pi$
$510$	35.0320	−	19.6854i	1.55124	−	0.871685i
$511$	10.8163	−	1.55515i	0.478484	−	0.0687957i
$512$	−0.540641	+	0.841254i	−0.0238932	+	0.0371785i
$513$	−1.60121	+	2.30995i	−0.0706951	+	0.101987i
$514$	16.0724	−	18.5485i	0.708924	−	0.818141i
$515$	7.46526	+	1.07334i	0.328958	+	0.0472971i
$516$	−4.58052	−	11.8393i	−0.201646	−	0.521198i
$517$	−6.41128	+	21.8348i	−0.281968	+	0.960294i
$518$	−0.780071	+	2.65668i	−0.0342744	+	0.116728i
$519$	−14.3810	−	37.1708i	−0.631257	−	1.63162i
$520$	−14.4872	−	2.08294i	−0.635304	−	0.0913429i
$521$	6.62077	−	7.64077i	0.290061	−	0.334748i	−0.591952	−	0.805973i	$-0.701643\pi$
$521$	6.62077	−	7.64077i	0.290061	−	0.334748i	0.882013	+	0.471225i	$0.156188\pi$
$522$	0.496428	−	0.815377i	0.0217280	−	0.0356881i
$523$	−11.0228	+	17.1518i	−0.481994	+	0.749997i	−0.994046	−	0.108957i	$-0.965249\pi$
$523$	−11.0228	+	17.1518i	−0.481994	+	0.749997i	0.512052	+	0.858954i	$0.328885\pi$
$524$	17.4179	−	2.50431i	0.760904	−	0.109401i
$525$	−11.9440	+	6.71168i	−0.521281	+	0.292922i
$526$	−11.6083	+	10.0587i	−0.506146	+	0.438578i
$527$	−7.10903	+	2.08740i	−0.309674	+	0.0909286i
$528$	0.559388	−	9.43093i	0.0243442	−	0.410428i
$529$	17.6692	−	14.7240i	0.768228	−	0.640176i
$530$			31.8644i			1.38410i
$531$	1.20578	+	7.14818i	0.0523262	+	0.310205i
$532$	0.398862	+	0.460312i	0.0172929	+	0.0199570i
$533$	10.7741	+	16.7648i	0.466676	+	0.726162i
$534$	0.426156	+	5.08844i	0.0184416	+	0.220199i
$535$	−17.7366	−	11.3986i	−0.766821	−	0.492806i
$536$	−2.04187	+	4.47107i	−0.0881954	+	0.193121i
$537$	−17.0741	+	17.4943i	−0.736802	+	0.754935i
$538$	2.96970	−	20.6547i	0.128033	−	0.890487i
$539$	12.9882	+	28.4402i	0.559442	+	1.22501i
$540$	−8.05308	+	16.1188i	−0.346549	+	0.693643i
$541$	2.46769	+	0.724579i	0.106094	+	0.0311521i	0.334349	−	0.942449i	$-0.391484\pi$
$541$	2.46769	+	0.724579i	0.106094	+	0.0311521i	−0.228255	+	0.973601i	$0.573302\pi$
$542$	−21.5413	+	9.83756i	−0.925276	+	0.422559i
$543$	1.49389	−	7.29296i	0.0641088	−	0.312971i
$544$	−5.05630	−	4.38131i	−0.216787	−	0.187847i
$545$	26.9710	+	12.3173i	1.15531	+	0.527613i
$546$	−4.85272	+	6.64943i	−0.207677	+	0.284569i
$547$	5.56535	+	38.7079i	0.237957	+	1.65503i	0.662087	+	0.749427i	$0.269671\pi$
$547$	5.56535	+	38.7079i	0.237957	+	1.65503i	−0.424130	+	0.905601i	$0.639420\pi$
$548$	−11.6986	+	7.51823i	−0.499739	+	0.321163i
$549$	4.36751	−	2.95926i	0.186401	−	0.126298i
$550$	−10.7950	−	36.7644i	−0.460301	−	1.56764i
$551$	−0.172119			−0.00733252
$552$	−7.96423	+	2.36032i	−0.338980	+	0.100462i
$553$	−12.9017			−0.548635
$554$	−9.33240	−	31.7832i	−0.396496	−	1.35034i
$555$	8.99368	+	11.7146i	0.381760	+	0.497257i
$556$	12.4846	−	8.02337i	0.529465	−	0.340267i
$557$	−2.58495	−	17.9787i	−0.109528	−	0.761783i	−0.968366	−	0.249535i	$-0.919722\pi$
$557$	−2.58495	−	17.9787i	−0.109528	−	0.761783i	0.858838	−	0.512247i	$-0.171187\pi$
$558$	2.11395	−	2.56295i	0.0894906	−	0.108498i
$559$	−28.1391	−	12.8507i	−1.19016	−	0.543526i
$560$	2.95097	+	2.55703i	0.124701	+	0.108054i
$561$	61.9223	+	12.6841i	2.61436	+	0.535524i
$562$	−15.4157	+	7.04013i	−0.650273	+	0.296970i
$563$	8.47052	+	2.48717i	0.356990	+	0.104822i	0.455310	−	0.890333i	$-0.349529\pi$
$563$	8.47052	+	2.48717i	0.356990	+	0.104822i	−0.0983196	+	0.995155i	$0.531347\pi$
$564$	−6.80081	−	2.44283i	−0.286366	−	0.102862i
$565$	3.54784	+	7.76868i	0.149259	+	0.326831i
$566$	3.15054	−	21.9125i	0.132427	−	0.921051i
$567$	5.88687	+	8.24912i	0.247225	+	0.346431i
$568$	3.79533	−	8.31062i	0.159249	−	0.348706i
$569$	5.93908	+	3.81682i	0.248979	+	0.160009i	0.659178	−	0.751987i	$-0.270904\pi$
$569$	5.93908	+	3.81682i	0.248979	+	0.160009i	−0.410199	+	0.911996i	$0.634541\pi$
$570$	3.23746	−	0.271137i	0.135602	−	0.0113567i
$571$	2.96871	+	4.61940i	0.124237	+	0.193316i	0.897801	−	0.440402i	$-0.145164\pi$
$571$	2.96871	+	4.61940i	0.124237	+	0.193316i	−0.773564	+	0.633718i	$0.781528\pi$
$572$	−15.0763	−	17.3989i	−0.630370	−	0.727486i
$573$	−3.30279	−	14.3412i	−0.137976	−	0.599112i
$574$		−	5.31657i		−	0.221909i
$575$	−27.1631	+	19.9285i	−1.13278	+	0.831077i
$576$	2.97896	+	0.354638i	0.124124	+	0.0147766i
$577$	29.4154	−	8.63714i	1.22458	−	0.359569i	0.395377	−	0.918519i	$-0.370614\pi$
$577$	29.4154	−	8.63714i	1.22458	−	0.359569i	0.829201	+	0.558950i	$0.188796\pi$
$578$	20.9812	−	18.1803i	0.872702	−	0.756201i
$579$	1.02537	+	1.82474i	0.0426128	+	0.0758335i
$580$	−1.09219	+	0.157034i	−0.0453508	+	0.00652046i
$581$	−1.91393	+	2.97813i	−0.0794032	+	0.123554i
$582$	23.0015	+	12.1992i	0.953444	+	0.505674i
$583$	−32.8226	+	37.8793i	−1.35937	+	1.56880i
$584$	−9.60569	−	1.38109i	−0.397486	−	0.0571499i
$585$	13.3908	+	41.8166i	0.553643	+	1.72891i
$586$	7.62326	−	25.9624i	0.314914	−	1.07250i
$587$	0.278923	−	0.949924i	0.0115124	−	0.0392076i	−0.953536	−	0.301278i	$-0.902587\pi$
$587$	0.278923	−	0.949924i	0.0115124	−	0.0392076i	0.965049	+	0.262070i	$0.0844051\pi$
$588$	−9.25938	+	3.58237i	−0.381850	+	0.147734i
$589$	−0.592919	−	0.0852488i	−0.0244308	−	0.00351262i
$590$	5.48723	−	6.33261i	0.225906	−	0.260709i
$591$	0.0415997	−	0.0784360i	0.00171118	−	0.00322642i
$592$	1.32940	−	2.06859i	0.0546381	−	0.0850186i
$593$	31.7713	−	4.56802i	1.30469	−	0.187586i	0.545310	−	0.838234i	$-0.316412\pi$
$593$	31.7713	−	4.56802i	1.30469	−	0.187586i	0.759379	+	0.650648i	$0.225503\pi$
$594$	−26.1768	+	10.8662i	−1.07405	+	0.445847i
$595$	−19.7433	+	17.1077i	−0.809398	+	0.701347i
$596$	−3.31083	+	0.972148i	−0.135617	+	0.0398208i
$597$	−29.2570	−	1.73536i	−1.19741	−	0.0710234i
$598$	−9.87167	+	17.6716i	−0.403682	+	0.722647i
$599$		−	24.9640i		−	1.02000i	−0.860174	−	0.510000i	$-0.829645\pi$
$599$		−	24.9640i		−	1.02000i	0.860174	−	0.510000i	$-0.170355\pi$
$600$	11.8568	−	2.73064i	0.484053	−	0.111478i
$601$	−1.43270	−	1.65343i	−0.0584412	−	0.0674447i	0.725776	−	0.687931i	$-0.241481\pi$
$601$	−1.43270	−	1.65343i	−0.0584412	−	0.0674447i	−0.784217	+	0.620486i	$0.786935\pi$
$602$	4.46184	+	6.94276i	0.181851	+	0.282966i
$603$	14.7414	−	0.358435i	0.600317	−	0.0145966i
$604$	3.82583	+	2.45871i	0.155671	+	0.100044i
$605$	27.0123	−	59.1488i	1.09821	−	2.40474i
$606$	15.0515	+	14.6900i	0.611426	+	0.596740i
$607$	2.04248	−	14.2058i	0.0829017	−	0.576594i	−0.905455	−	0.424442i	$-0.860470\pi$
$607$	2.04248	−	14.2058i	0.0829017	−	0.576594i	0.988357	−	0.152152i	$-0.0486205\pi$
$608$	−0.224702	−	0.492028i	−0.00911286	−	0.0199544i
$609$	−0.209795	+	0.584068i	−0.00850133	+	0.0236676i
$610$	−5.85105	−	1.71802i	−0.236902	−	0.0695607i
$611$	−16.0179	+	7.31513i	−0.648015	+	0.295938i
$612$	−5.18496	+	19.3901i	−0.209589	+	0.783797i
$613$	−34.8471	−	30.1952i	−1.40746	−	1.21957i	−0.942485	−	0.334249i	$-0.891517\pi$
$613$	−34.8471	−	30.1952i	−1.40746	−	1.21957i	−0.464976	−	0.885323i	$-0.653937\pi$
$614$	−21.3778	−	9.76292i	−0.862738	−	0.393999i
$615$	−22.9069	−	16.7173i	−0.923694	−	0.674107i
$616$	0.874090	+	6.07943i	0.0352181	+	0.244947i
$617$	−28.1178	+	18.0702i	−1.13198	+	0.727479i	−0.965972	−	0.258645i	$-0.916724\pi$
$617$	−28.1178	+	18.0702i	−1.13198	+	0.727479i	−0.166008	+	0.986124i	$0.553088\pi$
$618$	−2.98808	+	2.29405i	−0.120198	+	0.0922801i
$619$	−4.48251	−	15.2660i	−0.180167	−	0.613593i	−0.999206	−	0.0398542i	$-0.987311\pi$
$619$	−4.48251	−	15.2660i	−0.180167	−	0.613593i	0.819038	−	0.573739i	$-0.194508\pi$
$620$	−3.84018			−0.154225
$621$	16.8184	+	18.3886i	0.674899	+	0.737910i
$622$	19.0266			0.762896
$623$	−0.935252	−	3.18518i	−0.0374701	−	0.127611i
$624$	5.79870	−	4.45185i	0.232134	−	0.178217i
$625$	−9.06602	+	5.82638i	−0.362641	+	0.233055i
$626$	4.32443	+	30.0771i	0.172839	+	1.20212i
$627$	4.12788	+	3.01250i	0.164852	+	0.120308i
$628$	14.6049	+	6.66982i	0.582798	+	0.266155i
$629$	12.4331	+	10.7734i	0.495742	+	0.429563i
$630$	3.02606	−	11.3165i	0.120561	−	0.450860i
$631$	−24.9128	+	11.3773i	−0.991763	+	0.452923i	−0.844141	−	0.536121i	$-0.819889\pi$
$631$	−24.9128	+	11.3773i	−0.991763	+	0.452923i	−0.147622	+	0.989044i	$0.547162\pi$
$632$	10.9936	+	3.22800i	0.437300	+	0.128403i
$633$	−6.55003	+	18.2352i	−0.260340	+	0.724786i
$634$	8.93945	+	19.5747i	0.355031	+	0.777409i
$635$	3.36393	−	23.3966i	0.133493	−	0.928467i
$636$	−11.3901	−	11.1165i	−0.451648	−	0.440799i
$637$	−10.0504	+	22.0072i	−0.398209	+	0.871957i
$638$	−1.46012	−	0.938361i	−0.0578066	−	0.0371501i
$639$	−27.4006	+	0.666241i	−1.08395	+	0.0263561i
$640$	−1.87476	−	2.91719i	−0.0741065	−	0.115312i
$641$	−8.21721	−	9.48316i	−0.324560	−	0.374562i	0.569897	−	0.821716i	$-0.306983\pi$
$641$	−8.21721	−	9.48316i	−0.324560	−	0.374562i	−0.894457	+	0.447154i	$0.852438\pi$
$642$	10.2623	−	2.36342i	0.405020	−	0.0932767i
$643$		−	6.52422i		−	0.257290i	−0.991691	−	0.128645i	$-0.958937\pi$
$643$		−	6.52422i		−	0.257290i	0.991691	−	0.128645i	$-0.0410628\pi$
$644$	4.76440	−	2.54227i	0.187744	−	0.100180i
$645$	43.9432	+	2.60646i	1.73026	+	0.102629i
$646$	3.47233	−	1.01957i	0.136617	−	0.0401144i
$647$	13.1388	−	11.3849i	0.516541	−	0.447585i	−0.357164	−	0.934042i	$-0.616256\pi$
$647$	13.1388	−	11.3849i	0.516541	−	0.447585i	0.873705	+	0.486457i	$0.161711\pi$
$648$	−2.95229	−	8.50200i	−0.115977	−	0.333990i
$649$	13.0461	−	1.87574i	0.512104	−	0.0736294i
$650$	16.0298	−	24.9428i	0.628739	−	0.978337i
$651$	−1.01199	+	1.90810i	−0.0396630	+	0.0747842i
$652$	4.22505	−	4.87597i	0.165466	−	0.190958i
$653$	−24.6073	−	3.53800i	−0.962958	−	0.138453i	−0.357136	−	0.934052i	$-0.616247\pi$
$653$	−24.6073	−	3.53800i	−0.962958	−	0.138453i	−0.605822	+	0.795600i	$0.707156\pi$
$654$	−13.8123	+	5.34384i	−0.540103	+	0.208961i
$655$	−17.1915	+	58.5488i	−0.671727	+	2.28769i
$656$	−1.33021	+	4.53027i	−0.0519358	+	0.176877i
$657$	8.87878	+	27.7265i	0.346394	+	1.08171i
$658$	4.65005	+	0.668576i	0.181278	+	0.0260638i
$659$	−1.15555	+	1.33358i	−0.0450140	+	0.0519489i	−0.777810	−	0.628499i	$-0.783669\pi$
$659$	−1.15555	+	1.33358i	−0.0450140	+	0.0519489i	0.732796	+	0.680448i	$0.238215\pi$
$660$	28.9422	+	15.3499i	1.12657	+	0.597496i
$661$	−9.56182	+	14.8785i	−0.371912	+	0.578706i	−0.975881	−	0.218301i	$-0.929948\pi$
$661$	−9.56182	+	14.8785i	−0.371912	+	0.578706i	0.603970	+	0.797007i	$0.293585\pi$
$662$	−24.5499	+	3.52974i	−0.954158	+	0.137187i
$663$	23.9605	+	42.6399i	0.930548	+	1.65599i
$664$	2.37600	−	2.05881i	0.0922065	−	0.0798974i
$665$	−2.02653	+	0.595044i	−0.0785856	+	0.0230748i
$666$	−7.32509	−	0.872032i	−0.283842	−	0.0337906i
$667$	−0.338738	+	1.48798i	−0.0131160	+	0.0576148i
$668$		−	9.99361i		−	0.386664i
$669$	−5.77113	−	25.0591i	−0.223125	−	0.968839i
$670$	−11.1618	−	12.8814i	−0.431216	−	0.497650i
$671$	−5.18584	−	8.06933i	−0.200197	−	0.311513i
$672$	−1.94354	+	0.162771i	−0.0749735	+	0.00627902i
$673$	−26.4183	−	16.9780i	−1.01835	−	0.654453i	−0.0788082	−	0.996890i	$-0.525111\pi$
$673$	−26.4183	−	16.9780i	−1.01835	−	0.654453i	−0.939541	+	0.342437i	$0.888748\pi$
$674$	6.31657	−	13.8314i	0.243305	−	0.532764i
$675$	−22.9253	−	28.4041i	−0.882397	−	1.09327i
$676$	0.685195	−	4.76563i	0.0263536	−	0.183294i
$677$	−0.624956	−	1.36846i	−0.0240190	−	0.0525943i	0.897242	−	0.441539i	$-0.145567\pi$
$677$	−0.624956	−	1.36846i	−0.0240190	−	0.0525943i	−0.921261	+	0.388944i	$0.872840\pi$
$678$	−4.01470	−	1.44207i	−0.154184	−	0.0553822i
$679$	−16.2409	−	4.76877i	−0.623270	−	0.183008i
$680$	21.1037	−	9.63774i	0.809290	−	0.369590i
$681$	−12.1746	−	2.49383i	−0.466531	−	0.0955639i
$682$	−4.56508	−	3.95566i	−0.174806	−	0.151470i
$683$	−19.3713	−	8.84656i	−0.741221	−	0.338504i	0.00876169	−	0.999962i	$-0.497211\pi$
$683$	−19.3713	−	8.84656i	−0.741221	−	0.338504i	−0.749983	+	0.661457i	$0.769938\pi$
$684$	−1.03254	+	1.25184i	−0.0394800	+	0.0478655i
$685$	−6.86270	−	47.7311i	−0.262210	−	1.82371i
$686$	12.0608	−	7.75099i	0.460482	−	0.295934i
$687$	−8.77399	−	11.4285i	−0.334749	−	0.436023i
$688$	−2.06487	−	7.03231i	−0.0787225	−	0.268104i
$689$	−38.7843			−1.47756
$690$	4.02748	−	28.5217i	0.153323	−	1.08580i
$691$	7.45907			0.283756			0.141878	−	0.989884i	$-0.454686\pi$
$691$	7.45907			0.283756			0.141878	+	0.989884i	$0.454686\pi$
$692$	−6.48288	−	22.0787i	−0.246442	−	0.839305i
$693$	15.2541	−	10.3356i	0.579454	−	0.392617i
$694$	−3.91720	+	2.51743i	−0.148695	+	0.0955604i
$695$	7.32379	+	50.9381i	0.277807	+	1.93219i
$696$	0.324901	−	0.445196i	0.0123153	−	0.0168751i
$697$	−28.7344	−	13.1226i	−1.08839	−	0.497053i
$698$	−5.20451	−	4.50973i	−0.196993	−	0.170696i
$699$	−0.389423	+	1.90111i	−0.0147293	+	0.0719068i
$700$	−7.19524	+	3.28595i	−0.271954	+	0.124197i
$701$	−7.24645	−	2.12775i	−0.273695	−	0.0803640i	0.142005	−	0.989866i	$-0.454645\pi$
$701$	−7.24645	−	2.12775i	−0.273695	−	0.0803640i	−0.415700	+	0.909502i	$0.636463\pi$
$702$	−19.6193	−	9.80195i	−0.740483	−	0.369951i
$703$	0.552528	+	1.20987i	0.0208390	+	0.0456310i
$704$	0.776259	−	5.39900i	0.0292564	−	0.203482i
$705$	17.5021	−	17.9329i	0.659169	−	0.675391i
$706$	−14.5434	+	31.8456i	−0.547348	+	1.19852i
$707$	−11.5026	−	7.39227i	−0.432600	−	0.278015i
$708$	0.349296	+	4.17071i	0.0131273	+	0.156745i
$709$	2.93580	+	4.56820i	0.110256	+	0.171562i	0.891997	−	0.452042i	$-0.149304\pi$
$709$	2.93580	+	4.56820i	0.110256	+	0.171562i	−0.781740	+	0.623604i	$0.785668\pi$
$710$	20.7469	+	23.9433i	0.778619	+	0.898574i
$711$	−5.71737	−	33.8942i	−0.214418	−	1.27113i
$712$			2.94810i			0.110485i
$713$	−1.90387	+	4.95804i	−0.0713005	+	0.185680i
$714$	0.772612	−	13.0258i	0.0289143	−	0.487476i
$715$	76.5992	−	22.4916i	2.86465	−	0.841137i
$716$	−10.6663	+	9.24240i	−0.398618	+	0.345405i
$717$	7.78802	−	4.37630i	0.290849	−	0.163436i
$718$	−0.918905	+	0.132119i	−0.0342932	+	0.00493062i
$719$	−7.29869	+	11.3570i	−0.272195	+	0.423544i	−0.950260	−	0.311458i	$-0.899183\pi$
$719$	−7.29869	+	11.3570i	−0.272195	+	0.423544i	0.678065	+	0.735002i	$0.262819\pi$
$720$	−5.40990	+	8.88570i	−0.201615	+	0.331150i
$721$	1.60379	−	1.85088i	0.0597284	−	0.0689303i
$722$	−18.5170	−	2.66234i	−0.689131	−	0.0990821i
$723$	−6.50696	−	16.8186i	−0.241997	−	0.625491i
$724$	1.21089	−	4.12392i	0.0450025	−	0.153264i
$725$	0.629755	−	2.14475i	0.0233885	−	0.0796539i
$726$	11.7193	+	30.2910i	0.434944	+	1.12420i
$727$	−1.04977	−	0.150933i	−0.0389336	−	0.00559781i	0.122820	−	0.992429i	$-0.460806\pi$
$727$	−1.04977	−	0.150933i	−0.0389336	−	0.00559781i	−0.161754	+	0.986831i	$0.551715\pi$
$728$	−3.11234	+	3.59183i	−0.115351	+	0.133122i
$729$	−19.0626	+	19.1211i	−0.706024	+	0.708188i
$730$	18.1936	−	28.3098i	0.673375	−	1.04779i
$731$	48.5364	−	6.97849i	1.79519	−	0.258109i
$732$	2.65538	−	1.49213i	0.0981455	−	0.0551506i
$733$	25.8250	−	22.3775i	0.953869	−	0.826532i	−0.0310556	−	0.999518i	$-0.509887\pi$
$733$	25.8250	−	22.3775i	0.953869	−	0.826532i	0.984924	+	0.172986i	$0.0553414\pi$
$734$	−11.9344	+	3.50424i	−0.440505	+	0.129344i
$735$	2.03847	−	34.3674i	0.0751903	−	1.26766i
$736$	−4.69584	+	0.974227i	−0.173091	+	0.0359105i
$737$		−	26.8103i		−	0.987572i
$738$	13.9672	−	2.35603i	0.514141	−	0.0867268i
$739$	29.0748	+	33.5541i	1.06953	+	1.23431i	0.970976	+	0.239176i	$0.0768774\pi$
$739$	29.0748	+	33.5541i	1.06953	+	1.23431i	0.0985575	+	0.995131i	$0.468577\pi$
$740$	4.60993	+	7.17319i	0.169464	+	0.263692i
$741$	0.330020	+	3.94054i	0.0121236	+	0.144759i
$742$	8.70450	+	5.59404i	0.319552	+	0.205364i
$743$	−15.5165	+	33.9765i	−0.569247	+	1.24648i	0.377951	+	0.925826i	$0.376629\pi$
$743$	−15.5165	+	33.9765i	−0.569247	+	1.24648i	−0.947198	+	0.320650i	$0.896099\pi$
$744$	1.33973	−	1.37270i	0.0491167	−	0.0503255i
$745$	1.70288	−	11.8438i	0.0623886	−	0.433922i
$746$	−1.74902	−	3.82981i	−0.0640361	−	0.140219i
$747$	−8.67206	−	3.70836i	−0.317294	−	0.135682i
$748$	35.0149	+	10.2813i	1.28027	+	0.375922i
$749$	−6.22761	+	2.84405i	−0.227552	+	0.103919i
$750$	−2.44036	+	11.9135i	−0.0891094	+	0.435021i
$751$	−21.7132	−	18.8146i	−0.792327	−	0.686556i	0.161513	−	0.986871i	$-0.448363\pi$
$751$	−21.7132	−	18.8146i	−0.792327	−	0.686556i	−0.953840	+	0.300315i	$0.902908\pi$
$752$	−3.79505	−	1.73314i	−0.138391	−	0.0632011i
$753$	24.0262	−	32.9219i	0.875563	−	1.19974i
$754$	−0.191136	−	1.32938i	−0.00696077	−	0.0484132i
$755$	−13.2667	+	8.52601i	−0.482826	+	0.310293i
$756$	2.98945	+	5.02967i	0.108725	+	0.182927i
$757$	6.18376	+	21.0600i	0.224753	+	0.765437i	0.992236	+	0.124368i	$0.0396905\pi$
$757$	6.18376	+	21.0600i	0.224753	+	0.765437i	−0.767483	+	0.641069i	$0.778491\pi$
$758$	−8.20336			−0.297960
$759$	34.1671	−	29.7570i	1.24019	−	1.08011i
$760$	1.87569			0.0680386
$761$	10.5126	+	35.8025i	0.381080	+	1.29784i	0.897315	+	0.441391i	$0.145515\pi$
$761$	10.5126	+	35.8025i	0.381080	+	1.29784i	−0.516235	+	0.856447i	$0.672667\pi$
$762$	7.18970	+	9.36486i	0.260456	+	0.339253i
$763$	8.09973	−	5.20538i	0.293230	−	0.188447i
$764$	−1.20920	−	8.41014i	−0.0437472	−	0.304268i
$765$	−53.6931	−	44.2868i	−1.94128	−	1.60119i
$766$	−30.8054	−	14.0683i	−1.11304	−	0.508310i
$767$	7.70785	+	6.67889i	0.278314	+	0.241161i
$768$	1.69682	+	0.347575i	0.0612286	+	0.0125420i
$769$	32.5205	−	14.8516i	1.17272	−	0.535563i	0.268771	−	0.963204i	$-0.413383\pi$
$769$	32.5205	−	14.8516i	1.17272	−	0.535563i	0.903949	+	0.427641i	$0.140655\pi$
$770$	−20.4355	−	6.00041i	−0.736445	−	0.216240i
$771$	−40.0075	−	14.3706i	−1.44083	−	0.517543i
$772$	0.502008	+	1.09924i	0.0180676	+	0.0395626i
$773$	−4.54681	+	31.6238i	−0.163537	+	1.13743i	0.728361	+	0.685193i	$0.240282\pi$
$773$	−4.54681	+	31.6238i	−0.163537	+	1.13743i	−0.891899	+	0.452235i	$0.850627\pi$
$774$	−16.2622	+	14.7985i	−0.584532	+	0.531920i
$775$	3.23166	−	7.07635i	0.116085	−	0.254190i
$776$	12.6458	+	8.12696i	0.453958	+	0.291741i
$777$	4.77903	−	0.400243i	0.171447	−	0.0143587i
$778$	−1.17211	−	1.82385i	−0.0420223	−	0.0653881i
$779$	−1.67246	−	1.93012i	−0.0599220	−	0.0691537i
$780$	5.68933	+	24.7039i	0.203711	+	0.884540i
$781$			49.8338i			1.78319i
$782$	−1.98053	−	32.0251i	−0.0708235	−	1.14521i
$783$	−1.62739	−	0.292327i	−0.0581580	−	0.0104469i
$784$	−5.49987	+	1.61491i	−0.196424	+	0.0576753i
$785$	−42.0773	+	36.4602i	−1.50180	+	1.30132i
$786$	−14.9311	−	26.5712i	−0.532573	−	0.947762i
$787$	12.7089	−	1.82727i	0.453025	−	0.0651351i	0.0879740	−	0.996123i	$-0.471961\pi$
$787$	12.7089	−	1.82727i	0.453025	−	0.0651351i	0.365051	+	0.930988i	$0.381052\pi$
$788$	0.0277132	−	0.0431226i	0.000987242	−	0.00153618i
$789$	23.5033	+	12.4653i	0.836739	+	0.443777i
$790$	−26.0186	+	30.0270i	−0.925699	+	1.06831i
$791$	2.74505	+	0.394679i	0.0976027	+	0.0140332i
$792$	−15.5840	+	4.99043i	−0.553754	+	0.177327i
$793$	2.09112	−	7.12171i	0.0742579	−	0.252899i
$794$	−8.17051	+	27.8262i	−0.289960	+	0.987514i
$795$	51.4726	−	19.9143i	1.82555	−	0.706287i
$796$	−16.7490	−	2.40814i	−0.593652	−	0.0853542i
$797$	15.3096	−	17.6682i	0.542293	−	0.625839i	−0.416777	−	0.909009i	$-0.636840\pi$
$797$	15.3096	−	17.6682i	0.542293	−	0.625839i	0.959070	+	0.283169i	$0.0913859\pi$
$798$	0.494295	−	0.931990i	0.0174979	−	0.0329921i
$799$	15.0909	−	23.4819i	0.533878	−	0.830730i
$800$	6.95323	−	0.999724i	0.245834	−	0.0353456i
$801$	7.95337	−	3.86853i	0.281019	−	0.136688i
$802$	−24.7948	+	21.4848i	−0.875533	+	0.758654i
$803$	50.7890	−	14.9130i	1.79231	−	0.526268i
$804$	8.49853	+	0.504084i	0.299720	+	0.0177777i
$805$	1.15588	+	18.6906i	0.0407394	+	0.658756i
$806$		−	4.67414i		−	0.164640i
$807$	−35.2209	+	8.11142i	−1.23983	+	0.285535i
$808$	7.95185	+	9.17693i	0.279745	+	0.322843i
$809$	11.2758	+	17.5455i	0.396437	+	0.616868i	0.980891	−	0.194559i	$-0.0623276\pi$
$809$	11.2758	+	17.5455i	0.396437	+	0.616868i	−0.584454	+	0.811427i	$0.698691\pi$
$810$	31.0707	+	2.93491i	1.09171	+	0.103122i
$811$	−8.00639	−	5.14540i	−0.281143	−	0.180679i	0.392468	−	0.919766i	$-0.371621\pi$
$811$	−8.00639	−	5.14540i	−0.281143	−	0.180679i	−0.673611	+	0.739086i	$0.735258\pi$
$812$	−0.148846	+	0.325927i	−0.00522346	+	0.0114378i
$813$	29.3539	+	28.6489i	1.02949	+	1.00476i
$814$	−1.90877	+	13.2758i	−0.0669025	+	0.465317i
$815$	9.29400	+	20.3510i	0.325555	+	0.712865i
$816$	−3.91739	+	10.9060i	−0.137136	+	0.381786i
$817$	3.80384	+	1.11691i	0.133079	+	0.0390757i
$818$	6.11584	−	2.79301i	0.213835	−	0.0976554i
$819$	13.7741	+	3.68322i	0.481305	+	0.128702i
$820$	−12.3736	−	10.7218i	−0.432106	−	0.374422i
$821$	20.9659	+	9.57479i	0.731713	+	0.334162i	0.746190	−	0.665733i	$-0.231881\pi$
$821$	20.9659	+	9.57479i	0.731713	+	0.334162i	−0.0144767	+	0.999895i	$0.504608\pi$
$822$	19.4560	+	14.1989i	0.678605	+	0.495242i
$823$	−2.32111	−	16.1437i	−0.0809087	−	0.562733i	−0.989443	−	0.144922i	$-0.953707\pi$
$823$	−2.32111	−	16.1437i	−0.0809087	−	0.562733i	0.908534	−	0.417810i	$-0.137202\pi$
$824$	−1.82969	+	1.17587i	−0.0637402	+	0.0409633i
$825$	−52.6415	+	40.4146i	−1.83274	+	1.40706i
$826$	−0.766573	−	2.61071i	−0.0266725	−	0.0908381i
$827$	31.5338			1.09654			0.548269	−	0.836302i	$-0.315287\pi$
$827$	31.5338			1.09654			0.548269	+	0.836302i	$0.315287\pi$
$828$	8.79019	+	11.3900i	0.305480	+	0.395831i
$829$	−37.5470			−1.30406			−0.652030	−	0.758193i	$-0.726082\pi$
$829$	−37.5470			−1.30406			−0.652030	+	0.758193i	$0.726082\pi$
$830$	3.07144	+	10.4604i	0.106611	+	0.363085i
$831$	−45.5091	+	34.9388i	−1.57869	+	1.21201i
$832$	3.55071	−	2.28190i	0.123099	−	0.0791108i
$833$	−5.45778	−	37.9597i	−0.189101	−	1.31523i
$834$	−20.7632	−	15.1529i	−0.718971	−	0.524701i
$835$	31.5229	+	14.3960i	1.09089	+	0.498194i
$836$	2.22976	+	1.93210i	0.0771180	+	0.0668231i
$837$	−5.46126	−	1.81304i	−0.188769	−	0.0626678i
$838$	−4.05612	+	1.85237i	−0.140116	+	0.0639890i
$839$	26.4189	+	7.75730i	0.912083	+	0.267812i	0.703917	−	0.710282i	$-0.251432\pi$
$839$	26.4189	+	7.75730i	0.912083	+	0.267812i	0.208166	+	0.978094i	$0.433251\pi$
$840$	2.28628	−	6.36498i	0.0788841	−	0.219613i
$841$	12.0050	+	26.2872i	0.413965	+	0.906456i
$842$	0.674633	−	4.69217i	0.0232494	−	0.161703i
$843$	21.0068	+	20.5022i	0.723511	+	0.706133i
$844$	−4.64712	+	10.1758i	−0.159961	+	0.350265i
$845$	14.0452	+	9.02631i	0.483170	+	0.310515i
$846$	0.304239	+	12.5125i	0.0104600	+	0.430189i
$847$	−11.4157	−	17.7631i	−0.392246	−	0.610347i
$848$	−6.01750	−	6.94457i	−0.206642	−	0.238478i
$849$	−37.3657	+	8.60538i	−1.28239	+	0.295336i
$850$			46.9986i			1.61204i
$851$	11.5468	−	2.39556i	0.395818	−	0.0821189i
$852$	−15.7967	−	0.936967i	−0.541185	−	0.0321000i
$853$	1.20632	−	0.354208i	0.0413037	−	0.0121278i	−0.261015	−	0.965335i	$-0.584057\pi$
$853$	1.20632	−	0.354208i	0.0413037	−	0.0121278i	0.302319	+	0.953207i	$0.402239\pi$
$854$	−1.49652	+	1.29674i	−0.0512097	+	0.0443735i
$855$	−2.46131	−	5.06024i	−0.0841749	−	0.173057i
$856$	6.01815	−	0.865279i	0.205696	−	0.0295746i
$857$	−21.0640	+	32.7762i	−0.719533	+	1.11961i	0.268185	+	0.963367i	$0.413576\pi$
$857$	−21.0640	+	32.7762i	−0.719533	+	1.11961i	−0.987718	+	0.156247i	$0.950060\pi$
$858$	−18.6835	+	35.2275i	−0.637843	+	1.20265i
$859$	−23.5208	+	27.1444i	−0.802519	+	0.926156i	−0.998517	−	0.0544482i	$-0.982660\pi$
$859$	−23.5208	+	27.1444i	−0.802519	+	0.926156i	0.195998	+	0.980604i	$0.437205\pi$
$860$	25.1565	+	3.61696i	0.857830	+	0.123337i
$861$	−8.58821	+	3.32270i	−0.292686	+	0.113237i
$862$	7.99792	−	27.2384i	0.272410	−	0.927744i
$863$	12.3529	−	42.0700i	0.420496	−	1.43208i	−0.428434	−	0.903573i	$-0.640935\pi$
$863$	12.3529	−	42.0700i	0.420496	−	1.43208i	0.848930	−	0.528505i	$-0.177247\pi$
$864$	−1.28889	−	5.03376i	−0.0438491	−	0.171252i
$865$	78.9815	+	11.3558i	2.68545	+	0.386110i
$866$	7.04695	−	8.13261i	0.239465	−	0.276357i
$867$	−42.4805	−	22.5302i	−1.44271	−	0.765165i
$868$	−0.674174	+	1.04904i	−0.0228830	+	0.0356066i
$869$	−61.8600	+	8.89413i	−2.09846	+	0.301713i
$870$	0.936254	+	1.66615i	0.0317420	+	0.0564878i
$871$	15.6788	−	13.5857i	0.531255	−	0.460335i
$872$	−8.20419	+	2.40897i	−0.277829	+	0.0815780i
$873$	5.33095	−	44.7801i	0.180425	−	1.51558i
$874$	0.929926	−	2.42170i	0.0314552	−	0.0819153i
$875$		−	7.90597i		−	0.267270i
$876$	3.77230	+	16.3799i	0.127454	+	0.553424i
$877$	−17.3719	−	20.0483i	−0.586608	−	0.676982i	0.382404	−	0.923995i	$-0.375096\pi$
$877$	−17.3719	−	20.0483i	−0.586608	−	0.676982i	−0.969012	+	0.247013i	$0.920551\pi$
$878$	−0.0876284	−	0.136352i	−0.00295731	−	0.00460167i
$879$	−46.7032	+	3.91138i	−1.57526	+	0.131928i
$880$	15.9119	+	10.2259i	0.536389	+	0.344716i
$881$	8.43060	−	18.4604i	0.284034	−	0.621948i	−0.712808	−	0.701359i	$-0.752577\pi$
$881$	8.43060	−	18.4604i	0.284034	−	0.621948i	0.996842	+	0.0794115i	$0.0253041\pi$
$882$	11.5737	+	12.7184i	0.389706	+	0.428252i
$883$	3.27780	−	22.7976i	0.110307	−	0.767201i	−0.857314	−	0.514793i	$-0.827869\pi$
$883$	3.27780	−	22.7976i	0.110307	−	0.767201i	0.967621	−	0.252407i	$-0.0812223\pi$
$884$	11.7308	+	25.6868i	0.394548	+	0.863939i
$885$	−13.6588	−	4.90621i	−0.459137	−	0.164920i
$886$	21.9470	+	6.44422i	0.737323	+	0.216498i
$887$	33.6760	−	15.3793i	1.13073	−	0.516386i	0.239932	−	0.970790i	$-0.422875\pi$
$887$	33.6760	−	15.3793i	1.13073	−	0.516386i	0.890796	+	0.454404i	$0.150148\pi$
$888$	−4.17237	−	0.854666i	−0.140016	−	0.0286807i
$889$	−5.80078	−	5.02641i	−0.194552	−	0.168580i
$890$	−9.29920	−	4.24680i	−0.311710	−	0.142353i
$891$	33.9127	+	35.4940i	1.13612	+	1.18909i
$892$	−2.11289	−	14.6955i	−0.0707447	−	0.492040i
$893$	1.89847	−	1.22007i	0.0635297	−	0.0408281i
$894$	3.63955	+	4.74065i	0.121725	+	0.158551i
$895$	−13.7883	−	46.9586i	−0.460892	−	1.56965i
$896$	−1.12603			−0.0376180
$897$	34.7157	+	4.90212i	1.15912	+	0.163677i
$898$	0.00397804			0.000132749
$899$	−0.0992785	−	0.338112i	−0.00331112	−	0.0112767i
$900$	−11.8211	−	17.4466i	−0.394038	−	0.581552i
$901$	51.7189	−	33.2377i	1.72301	−	1.10731i
$902$	−3.66512	−	25.4915i	−0.122035	−	0.848774i
$903$	8.42660	−	11.5465i	0.280420	−	0.384245i
$904$	−2.24032	−	1.02312i	−0.0745118	−	0.0340284i
$905$	11.2638	+	9.76012i	0.374421	+	0.324437i
$906$	1.58069	−	7.71675i	0.0525151	−	0.256372i
$907$	−17.1488	+	7.83159i	−0.569416	+	0.260044i	−0.679251	−	0.733906i	$-0.737695\pi$
$907$	−17.1488	+	7.83159i	−0.569416	+	0.260044i	0.109835	+	0.993950i	$0.464968\pi$
$908$	−6.88431	−	2.02142i	−0.228464	−	0.0670830i
$909$	14.3230	−	33.4945i	0.475063	−	1.11094i
$910$	−6.84633	−	14.9914i	−0.226954	−	0.496959i
$911$	5.16512	−	35.9242i	0.171128	−	1.19022i	−0.705378	−	0.708832i	$-0.749223\pi$
$911$	5.16512	−	35.9242i	0.171128	−	1.19022i	0.876506	−	0.481391i	$-0.159868\pi$
$912$	−0.654375	+	0.670479i	−0.0216685	+	0.0222018i
$913$	−7.12371	+	15.5988i	−0.235760	+	0.516243i
$914$	2.90056	+	1.86408i	0.0959421	+	0.0616582i
$915$	0.881492	+	10.5253i	0.0291412	+	0.347956i
$916$	−4.49732	−	6.99797i	−0.148596	−	0.231219i
$917$	12.9759	+	14.9750i	0.428502	+	0.494517i
$918$	34.5625	−	3.74261i	1.14073	−	0.123525i
$919$		−	53.2873i		−	1.75779i	−0.477019	−	0.878893i	$-0.658283\pi$
$919$		−	53.2873i		−	1.75779i	0.477019	−	0.878893i	$-0.341717\pi$
$920$	3.69145	−	16.2155i	0.121703	−	0.534609i
$921$	−2.41021	+	40.6345i	−0.0794190	+	1.33895i
$922$	17.3046	−	5.08108i	0.569895	−	0.167336i
$923$	−29.1430	+	25.2525i	−0.959253	+	0.831197i
$924$	9.27423	−	5.21144i	0.305100	−	0.171444i
$925$	−17.0976	+	2.45826i	−0.562165	+	0.0808271i
$926$	4.15145	−	6.45978i	0.136425	−	0.212281i
$927$	5.57319	+	3.39314i	0.183048	+	0.111445i
$928$	0.208379	−	0.240482i	0.00684037	−	0.00789421i
$929$	−12.5666	−	1.80681i	−0.412298	−	0.0592795i	−0.0669551	−	0.997756i	$-0.521328\pi$
$929$	−12.5666	−	1.80681i	−0.412298	−	0.0592795i	−0.345343	+	0.938476i	$0.612238\pi$
$930$	2.40000	+	6.20330i	0.0786990	+	0.203414i
$931$	0.873519	−	2.97493i	0.0286284	−	0.0974994i
$932$	−0.315653	+	1.07502i	−0.0103396	+	0.0352133i
$933$	−11.8910	−	30.7349i	−0.389295	−	1.00622i
$934$	14.5987	+	2.09898i	0.477685	+	0.0686807i
$935$	−82.8702	+	95.6373i	−2.71014	+	3.12767i
$936$	−10.8154	−	6.58476i	−0.353512	−	0.215230i
$937$	−11.0898	+	17.2560i	−0.362287	+	0.563730i	−0.973772	−	0.227526i	$-0.926936\pi$
$937$	−11.0898	+	17.2560i	−0.362287	+	0.563730i	0.611484	+	0.791256i	$0.290573\pi$
$938$	−5.47838	+	0.787673i	−0.178876	+	0.0257184i
$939$	45.8829	−	25.7828i	1.49733	−	0.841390i
$940$	10.9337	−	9.47410i	0.356618	−	0.309011i
$941$	15.2789	−	4.48630i	0.498079	−	0.146249i	−0.0230380	−	0.999735i	$-0.507334\pi$
$941$	15.2789	−	4.48630i	0.498079	−	0.146249i	0.521117	+	0.853486i	$0.325516\pi$
$942$	1.64660	−	27.7607i	0.0536492	−	0.904492i
$943$	−19.9775	+	10.6599i	−0.650556	+	0.347135i
$944$			2.41639i			0.0786468i
$945$	−20.1715	+	2.18427i	−0.656178	+	0.0710544i
$946$	26.1795	+	30.2127i	0.851169	+	0.982301i
$947$	9.60324	+	14.9429i	0.312064	+	0.485580i	0.961488	−	0.274845i	$-0.0886267\pi$
$947$	9.60324	+	14.9429i	0.312064	+	0.485580i	−0.649425	+	0.760426i	$0.724990\pi$
$948$	−1.65624	−	19.7760i	−0.0537922	−	0.642296i
$949$	34.4578	+	22.1447i	1.11855	+	0.718846i
$950$	−1.57847	+	3.45637i	−0.0512123	+	0.112139i
$951$	26.0334	−	26.6741i	0.844190	−	0.864966i
$952$	1.07215	−	7.45696i	0.0347485	−	0.241681i
$953$	−14.8344	−	32.4827i	−0.480532	−	1.05222i	−0.982317	−	0.187226i	$-0.940050\pi$
$953$	−14.8344	−	32.4827i	−0.480532	−	1.05222i	0.501785	−	0.864992i	$-0.332677\pi$
$954$	−10.8388	+	25.3467i	−0.350919	+	0.820631i
$955$	28.2700	+	8.30083i	0.914796	+	0.268608i
$956$	4.69160	−	2.14258i	0.151737	−	0.0692960i
$957$	−0.603267	+	2.94507i	−0.0195009	+	0.0952007i
$958$	−1.81910	−	1.57626i	−0.0587724	−	0.0509265i
$959$	−14.2437	−	6.50487i	−0.459952	−	0.210053i
$960$	−3.54066	+	4.85159i	−0.114274	+	0.156584i
$961$	4.23723	+	29.4706i	0.136685	+	0.950663i
$962$	−8.73098	+	5.61106i	−0.281498	+	0.180908i
$963$	−10.2314	−	15.1003i	−0.329703	−	0.486601i
$964$	−2.93330	−	9.98989i	−0.0944751	−	0.321753i
$965$	−4.19050			−0.134897
$966$	−7.08431	−	6.10741i	−0.227934	−	0.196503i
$967$	19.5352			0.628210			0.314105	−	0.949388i	$-0.398296\pi$
$967$	19.5352			0.628210			0.314105	+	0.949388i	$0.398296\pi$
$968$	5.28298	+	17.9922i	0.169802	+	0.578291i
$969$	−3.81708	−	4.97189i	−0.122622	−	0.159720i
$970$	−43.8515	+	28.1816i	−1.40799	+	0.904857i
$971$	6.53113	+	45.4250i	0.209594	+	1.45776i	0.774485	+	0.632592i	$0.218009\pi$
$971$	6.53113	+	45.4250i	0.209594	+	1.45776i	−0.564891	+	0.825165i	$0.691082\pi$
$972$	−11.8888	+	10.0825i	−0.381332	+	0.323397i
$973$	15.2007	+	6.94192i	0.487312	+	0.222548i
$974$	−16.8193	−	14.5740i	−0.538926	−	0.466982i
$975$	−50.3099	−	10.3055i	−1.61121	−	0.330039i
$976$	1.59963	−	0.730527i	0.0512029	−	0.0233836i
$977$	−29.5224	−	8.66855i	−0.944504	−	0.277331i	−0.227007	−	0.973893i	$-0.572894\pi$
$977$	−29.5224	−	8.66855i	−0.944504	−	0.277331i	−0.717497	+	0.696562i	$0.754712\pi$
$978$	−10.5170	−	3.77767i	−0.336297	−	0.120797i
$979$	−6.68007	−	14.6273i	−0.213496	−	0.467491i
$980$	2.82878	−	19.6746i	0.0903619	−	0.628481i
$981$	17.2645	+	18.9722i	0.551214	+	0.605735i
$982$	14.5480	−	31.8557i	0.464246	−	1.01656i
$983$	−12.5808	−	8.08517i	−0.401264	−	0.257877i	0.324408	−	0.945917i	$-0.394835\pi$
$983$	−12.5808	−	8.08517i	−0.401264	−	0.257877i	−0.725672	+	0.688040i	$0.758471\pi$
$984$	8.14938	−	0.682509i	0.259793	−	0.0217576i
$985$	0.0961002	+	0.149535i	0.00306201	+	0.00476458i
$986$	1.39415	+	1.60893i	0.0443987	+	0.0512388i
$987$	−1.82615	−	7.92938i	−0.0581269	−	0.252395i
$988$			2.28304i			0.0726331i
$989$	17.1419	−	30.6863i	0.545079	−	0.975767i
$990$	6.70778	−	56.3455i	0.213187	−	1.79078i
$991$	2.38165	−	0.699316i	0.0756557	−	0.0222145i	−0.243686	−	0.969854i	$-0.578357\pi$
$991$	2.38165	−	0.699316i	0.0756557	−	0.0222145i	0.319341	+	0.947640i	$0.396538\pi$
$992$	0.836935	−	0.725208i	0.0265727	−	0.0230254i
$993$	21.0448	+	37.4511i	0.667835	+	1.18847i
$994$	10.1830	−	1.46409i	0.322984	−	0.0464381i
$995$	31.7233	−	49.3624i	1.00570	−	1.56489i
$996$	−4.81066	−	2.55141i	−0.152432	−	0.0808445i
$997$	−21.5919	+	24.9184i	−0.683823	+	0.789173i	−0.986472	−	0.163929i	$-0.947583\pi$
$997$	−21.5919	+	24.9184i	−0.683823	+	0.789173i	0.302650	+	0.953102i	$0.402129\pi$
$998$	32.3684	+	4.65387i	1.02460	+	0.147316i
$999$	3.16931	+	12.3777i	0.100273	+	0.391613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.83.2	yes	80
3.2	odd	2	inner	138.2.f.a.83.7	yes	80
23.5	odd	22	inner	138.2.f.a.5.7	yes	80
69.5	even	22	inner	138.2.f.a.5.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.2	✓	80	69.5	even	22	inner
138.2.f.a.5.7	yes	80	23.5	odd	22	inner
138.2.f.a.83.2	yes	80	1.1	even	1	trivial
138.2.f.a.83.7	yes	80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.37386 + 1.05476i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(-0.493501 - 3.43237i) q^{5} +(1.39909 + 1.02105i) q^{6} +(-1.02427 - 0.467769i) q^{7} +(0.755750 + 0.654861i) q^{8} +(0.774979 - 2.89817i) q^{9} +O(q^{10})\)	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.37386 + 1.05476i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(-0.493501 - 3.43237i) q^{5} +(1.39909 + 1.02105i) q^{6} +(-1.02427 - 0.467769i) q^{7} +(0.755750 + 0.654861i) q^{8} +(0.774979 - 2.89817i) q^{9} +(-3.15430 + 1.44052i) q^{10} +(-5.23357 - 1.53672i) q^{11} +(0.585520 - 1.63008i) q^{12} +(-1.75336 - 3.83932i) q^{13} +(-0.160251 + 1.11457i) q^{14} +(4.29832 + 4.19508i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.62836 + 3.61713i) q^{17} +(-2.99911 + 0.0729229i) q^{18} +(0.292438 + 0.455042i) q^{19} +(2.27084 + 2.62069i) q^{20} +(1.90059 - 0.437708i) q^{21} +5.45452i q^{22} +(4.50939 - 1.63260i) q^{23} +(-1.72901 - 0.102555i) q^{24} +(-6.74018 + 1.97910i) q^{25} +(-3.18982 + 2.76400i) q^{26} +(1.99215 + 4.79910i) q^{27} +(1.11457 - 0.160251i) q^{28} +(-0.172034 + 0.267690i) q^{29} +(2.81417 - 5.30610i) q^{30} +(-0.725208 + 0.836935i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(8.81105 - 3.40891i) q^{33} +(1.88492 - 6.41944i) q^{34} +(-1.10008 + 3.74653i) q^{35} +(0.914917 + 2.85708i) q^{36} +(2.43391 + 0.349943i) q^{37} +(0.354220 - 0.408792i) q^{38} +(6.45841 + 3.42532i) q^{39} +(1.87476 - 2.91719i) q^{40} +(-4.67346 + 0.671942i) q^{41} +(-0.955435 - 1.70028i) q^{42} +(5.53903 - 4.79960i) q^{43} +(5.23357 - 1.53672i) q^{44} +(-10.3301 - 1.22977i) q^{45} +(-2.83691 - 3.86677i) q^{46} -4.17207i q^{47} +(0.388718 + 1.68787i) q^{48} +(-3.75370 - 4.33200i) q^{49} +(3.79786 + 5.90958i) q^{50} +(-11.5478 + 0.967124i) q^{51} +(3.55071 + 2.28190i) q^{52} +(3.81724 - 8.35859i) q^{53} +(4.04344 - 3.26352i) q^{54} +(-2.69181 + 18.7219i) q^{55} +(-0.467769 - 1.02427i) q^{56} +(-0.881726 - 0.316713i) q^{57} +(0.305314 + 0.0896482i) q^{58} +(-2.19802 + 1.00380i) q^{59} +(-5.88400 - 1.20528i) q^{60} +(1.32902 + 1.15160i) q^{61} +(1.00735 + 0.460040i) q^{62} +(-2.14947 + 2.60601i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-12.3127 + 7.91289i) q^{65} +(-5.75319 - 7.49374i) q^{66} +(1.38479 + 4.71615i) q^{67} -6.69045 q^{68} +(-4.47328 + 6.99927i) q^{69} +3.90470 q^{70} +(-2.57398 - 8.76616i) q^{71} +(2.48359 - 1.68279i) q^{72} +(-8.16392 + 5.24663i) q^{73} +(-0.349943 - 2.43391i) q^{74} +(7.17260 - 9.82825i) q^{75} +(-0.492028 - 0.224702i) q^{76} +(4.64177 + 4.02212i) q^{77} +(1.46702 - 7.16183i) q^{78} +(10.4223 - 4.75969i) q^{79} +(-3.32720 - 0.976955i) q^{80} +(-7.79882 - 4.49205i) q^{81} +(1.96139 + 4.29485i) q^{82} +(0.447423 - 3.11189i) q^{83} +(-1.36223 + 1.39576i) q^{84} +(9.63774 - 21.1037i) q^{85} +(-6.16571 - 3.96246i) q^{86} +(-0.0459972 - 0.549221i) q^{87} +(-2.94894 - 4.58863i) q^{88} +(1.93059 + 2.22803i) q^{89} +(1.73036 + 10.2581i) q^{90} +4.75268i q^{91} +(-2.91089 + 3.81139i) q^{92} +(0.113572 - 1.91475i) q^{93} +(-4.00307 + 1.17541i) q^{94} +(1.41756 - 1.22832i) q^{95} +(1.50998 - 0.848500i) q^{96} +(14.8791 - 2.13929i) q^{97} +(-3.09898 + 4.82211i) q^{98} +(-8.50958 + 13.9769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

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Database

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