LMFDB - Embedded newform 151.2.g.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(2,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(30))

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

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

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

chi := DirichletCharacter("151.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.g (of order $15$, degree $8$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	151.2
Dual form			151.2.g.a.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.516346 - 0.894338i) q^{2} +(-1.72354 + 1.25222i) q^{3} +(0.466773 + 0.808475i) q^{4} +(-0.972803 - 1.08041i) q^{5} +(0.229968 + 2.18800i) q^{6} +(3.08940 + 3.43113i) q^{7} +3.02945 q^{8} +(0.475465 - 1.46333i) q^{9} +O(q^{10})$	\(q+(0.516346 - 0.894338i) q^{2} +(-1.72354 + 1.25222i) q^{3} +(0.466773 + 0.808475i) q^{4} +(-0.972803 - 1.08041i) q^{5} +(0.229968 + 2.18800i) q^{6} +(3.08940 + 3.43113i) q^{7} +3.02945 q^{8} +(0.475465 - 1.46333i) q^{9} +(-1.46855 + 0.312150i) q^{10} +(-0.346492 + 0.154268i) q^{11} +(-1.81689 - 0.808932i) q^{12} +(2.46793 + 1.09879i) q^{13} +(4.66378 - 0.991318i) q^{14} +(3.02957 + 0.643955i) q^{15} +(0.630699 - 1.09240i) q^{16} +(-5.92181 - 1.25872i) q^{17} +(-1.06321 - 1.18081i) q^{18} -2.65083 q^{19} +(0.419404 - 1.29079i) q^{20} +(-9.62122 - 2.04505i) q^{21} +(-0.0409419 + 0.389536i) q^{22} +(2.74636 - 4.75684i) q^{23} +(-5.22137 + 3.79355i) q^{24} +(0.301708 - 2.87056i) q^{25} +(2.25700 - 1.63981i) q^{26} +(-0.962063 - 2.96093i) q^{27} +(-1.33193 + 4.09926i) q^{28} +(-0.571518 - 0.415232i) q^{29} +(2.14022 - 2.37696i) q^{30} +(7.59551 + 1.61447i) q^{31} +(2.37813 + 4.11905i) q^{32} +(0.404013 - 0.699771i) q^{33} +(-4.18342 + 4.64616i) q^{34} +(0.701636 - 6.67562i) q^{35} +(1.40500 - 0.298642i) q^{36} +(-0.935769 - 8.90325i) q^{37} +(-1.36875 + 2.37074i) q^{38} +(-5.62951 + 1.19659i) q^{39} +(-2.94706 - 3.27304i) q^{40} +(-4.09894 + 2.97805i) q^{41} +(-6.79685 + 7.54867i) q^{42} +(-1.76755 + 1.96306i) q^{43} +(-0.286455 - 0.208122i) q^{44} +(-2.04353 + 0.909836i) q^{45} +(-2.83615 - 4.91235i) q^{46} +(5.50474 + 2.45087i) q^{47} +(0.280898 + 2.67257i) q^{48} +(-1.49653 + 14.2386i) q^{49} +(-2.41147 - 1.75203i) q^{50} +(11.7826 - 5.24597i) q^{51} +(0.263617 + 2.50815i) q^{52} +(3.84201 + 2.79138i) q^{53} +(-3.14482 - 0.668453i) q^{54} +(0.503741 + 0.224280i) q^{55} +(9.35918 + 10.3944i) q^{56} +(4.56880 - 3.31943i) q^{57} +(-0.666459 + 0.296727i) q^{58} -8.51517 q^{59} +(0.893501 + 2.74991i) q^{60} +(0.896599 - 8.53057i) q^{61} +(5.36580 - 5.95932i) q^{62} +(6.48977 - 2.88943i) q^{63} +7.43455 q^{64} +(-1.21367 - 3.73528i) q^{65} +(-0.417221 - 0.722648i) q^{66} +(-3.09044 - 9.51140i) q^{67} +(-1.74650 - 5.37517i) q^{68} +(1.22317 + 11.6376i) q^{69} +(-5.60797 - 4.07443i) q^{70} +(10.5572 - 2.24400i) q^{71} +(1.44040 - 4.43309i) q^{72} +(0.867652 - 2.67036i) q^{73} +(-8.44569 - 3.76026i) q^{74} +(3.07458 + 5.32532i) q^{75} +(-1.23734 - 2.14313i) q^{76} +(-1.59976 - 0.712261i) q^{77} +(-1.83662 + 5.65254i) q^{78} +(0.111575 - 0.343394i) q^{79} +(-1.79378 + 0.381281i) q^{80} +(9.10023 + 6.61171i) q^{81} +(0.546914 + 5.20354i) q^{82} +(-4.29637 - 13.2229i) q^{83} +(-2.83755 - 8.73309i) q^{84} +(4.40082 + 7.62245i) q^{85} +(0.842973 + 2.59440i) q^{86} +1.50499 q^{87} +(-1.04968 + 0.467348i) q^{88} +(-7.43935 + 8.26224i) q^{89} +(-0.241466 + 2.29739i) q^{90} +(3.85433 + 11.8624i) q^{91} +5.12772 q^{92} +(-15.1128 + 6.72866i) q^{93} +(5.03425 - 3.65760i) q^{94} +(2.57873 + 2.86397i) q^{95} +(-9.25676 - 4.12138i) q^{96} +(-8.10768 - 1.72334i) q^{97} +(11.9614 + 8.69044i) q^{98} +(0.0610005 + 0.580381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	0.516346	−	0.894338i	0.365112	−	0.632392i	−0.623682	−	0.781678i	$-0.714364\pi$
$2$	0.516346	−	0.894338i	0.365112	−	0.632392i	0.988794	+	0.149286i	$0.0476974\pi$
$3$	−1.72354	+	1.25222i	−0.995084	+	0.722971i	−0.961029	−	0.276449i	$-0.910842\pi$
$3$	−1.72354	+	1.25222i	−0.995084	+	0.722971i	−0.0340553	+	0.999420i	$0.510842\pi$
$4$	0.466773	+	0.808475i	0.233387	+	0.404238i
$5$	−0.972803	−	1.08041i	−0.435051	−	0.483173i	0.485255	−	0.874373i	$-0.338727\pi$
$5$	−0.972803	−	1.08041i	−0.435051	−	0.483173i	−0.920306	+	0.391200i	$0.872060\pi$
$6$	0.229968	+	2.18800i	0.0938842	+	0.893249i
$7$	3.08940	+	3.43113i	1.16768	+	1.29684i	0.946903	+	0.321520i	$0.104194\pi$
$7$	3.08940	+	3.43113i	1.16768	+	1.29684i	0.220780	+	0.975324i	$0.429140\pi$
$8$	3.02945			1.07107
$9$	0.475465	−	1.46333i	0.158488	−	0.487777i
$10$	−1.46855	+	0.312150i	−0.464397	+	0.0987106i
$11$	−0.346492	+	0.154268i	−0.104471	+	0.0465136i	−0.458307	−	0.888794i	$-0.651544\pi$
$11$	−0.346492	+	0.154268i	−0.104471	+	0.0465136i	0.353836	+	0.935308i	$0.384877\pi$
$12$	−1.81689	−	0.808932i	−0.524491	−	0.233519i
$13$	2.46793	+	1.09879i	0.684482	+	0.304751i	0.719357	−	0.694641i	$-0.244437\pi$
$13$	2.46793	+	1.09879i	0.684482	+	0.304751i	−0.0348751	+	0.999392i	$0.511103\pi$
$14$	4.66378	−	0.991318i	1.24645	−	0.264941i
$15$	3.02957	+	0.643955i	0.782232	+	0.166268i
$16$	0.630699	−	1.09240i	0.157675	−	0.273101i
$17$	−5.92181	−	1.25872i	−1.43625	−	0.305284i	−0.576959	−	0.816773i	$-0.695761\pi$
$17$	−5.92181	−	1.25872i	−1.43625	−	0.305284i	−0.859290	+	0.511489i	$0.829094\pi$
$18$	−1.06321	−	1.18081i	−0.250600	−	0.278320i
$19$	−2.65083			−0.608142			−0.304071	−	0.952649i	$-0.598346\pi$
$19$	−2.65083			−0.608142			−0.304071	+	0.952649i	$0.598346\pi$
$20$	0.419404	−	1.29079i	0.0937815	−	0.288630i
$21$	−9.62122	−	2.04505i	−2.09952	−	0.446267i
$22$	−0.0409419	+	0.389536i	−0.00872885	+	0.0830495i
$23$	2.74636	−	4.75684i	0.572656	−	0.991870i	−0.423635	−	0.905833i	$-0.639246\pi$
$23$	2.74636	−	4.75684i	0.572656	−	0.991870i	0.996292	−	0.0860374i	$-0.0274204\pi$
$24$	−5.22137	+	3.79355i	−1.06581	+	0.774354i
$25$	0.301708	−	2.87056i	0.0603417	−	0.574113i
$26$	2.25700	−	1.63981i	0.442635	−	0.321593i
$27$	−0.962063	−	2.96093i	−0.185149	−	0.569830i
$28$	−1.33193	+	4.09926i	−0.251711	+	0.774687i
$29$	−0.571518	−	0.415232i	−0.106128	−	0.0771067i	0.533455	−	0.845828i	$-0.320893\pi$
$29$	−0.571518	−	0.415232i	−0.106128	−	0.0771067i	−0.639584	+	0.768722i	$0.720893\pi$
$30$	2.14022	−	2.37696i	0.390749	−	0.433971i
$31$	7.59551	+	1.61447i	1.36419	+	0.289968i	0.831116	−	0.556099i	$-0.187702\pi$
$31$	7.59551	+	1.61447i	1.36419	+	0.289968i	0.533077	+	0.846067i	$0.321036\pi$
$32$	2.37813	+	4.11905i	0.420399	+	0.728152i
$33$	0.404013	−	0.699771i	0.0703297	−	0.121815i
$34$	−4.18342	+	4.64616i	−0.717451	+	0.796810i
$35$	0.701636	−	6.67562i	0.118598	−	1.12839i
$36$	1.40500	−	0.298642i	0.234167	−	0.0497737i
$37$	−0.935769	−	8.90325i	−0.153840	−	1.46369i	−0.750329	−	0.661064i	$-0.770105\pi$
$37$	−0.935769	−	8.90325i	−0.153840	−	1.46369i	0.596490	−	0.802621i	$-0.296562\pi$
$38$	−1.36875	+	2.37074i	−0.222040	+	0.384584i
$39$	−5.62951	+	1.19659i	−0.901443	+	0.191608i
$40$	−2.94706	−	3.27304i	−0.465971	−	0.517513i
$41$	−4.09894	+	2.97805i	−0.640146	+	0.465094i	−0.859901	−	0.510462i	$-0.829475\pi$
$41$	−4.09894	+	2.97805i	−0.640146	+	0.465094i	0.219754	+	0.975555i	$0.429475\pi$
$42$	−6.79685	+	7.54867i	−1.04878	+	1.16478i
$43$	−1.76755	+	1.96306i	−0.269548	+	0.299364i	−0.862689	−	0.505735i	$-0.831221\pi$
$43$	−1.76755	+	1.96306i	−0.269548	+	0.299364i	0.593140	+	0.805099i	$0.297888\pi$
$44$	−0.286455	−	0.208122i	−0.0431847	−	0.0313755i
$45$	−2.04353	+	0.909836i	−0.304631	+	0.135630i
$46$	−2.83615	−	4.91235i	−0.418167	−	0.724287i
$47$	5.50474	+	2.45087i	0.802948	+	0.357496i	0.766829	−	0.641852i	$-0.221834\pi$
$47$	5.50474	+	2.45087i	0.802948	+	0.357496i	0.0361198	+	0.999347i	$0.488500\pi$
$48$	0.280898	+	2.67257i	0.0405442	+	0.385752i
$49$	−1.49653	+	14.2386i	−0.213791	+	2.03408i
$50$	−2.41147	−	1.75203i	−0.341033	−	0.247775i
$51$	11.7826	−	5.24597i	1.64990	−	0.734583i
$52$	0.263617	+	2.50815i	0.0365571	+	0.347818i
$53$	3.84201	+	2.79138i	0.527741	+	0.383426i	0.819512	−	0.573062i	$-0.194245\pi$
$53$	3.84201	+	2.79138i	0.527741	+	0.383426i	−0.291771	+	0.956488i	$0.594245\pi$
$54$	−3.14482	−	0.668453i	−0.427956	−	0.0909649i
$55$	0.503741	+	0.224280i	0.0679244	+	0.0302419i
$56$	9.35918	+	10.3944i	1.25067	+	1.38901i
$57$	4.56880	−	3.31943i	0.605152	−	0.439669i
$58$	−0.666459	+	0.296727i	−0.0875104	+	0.0389621i
$59$	−8.51517			−1.10858			−0.554290	−	0.832323i	$-0.687010\pi$
$59$	−8.51517			−1.10858			−0.554290	+	0.832323i	$0.687010\pi$
$60$	0.893501	+	2.74991i	0.115350	+	0.355012i
$61$	0.896599	−	8.53057i	0.114798	−	1.09223i	−0.773765	−	0.633473i	$-0.781629\pi$
$61$	0.896599	−	8.53057i	0.114798	−	1.09223i	0.888563	−	0.458755i	$-0.151704\pi$
$62$	5.36580	−	5.95932i	0.681457	−	0.756834i
$63$	6.48977	−	2.88943i	0.817634	−	0.364034i
$64$	7.43455			0.929319
$65$	−1.21367	−	3.73528i	−0.150537	−	0.463305i
$66$	−0.417221	−	0.722648i	−0.0513564	−	0.0889519i
$67$	−3.09044	−	9.51140i	−0.377558	−	1.16200i	−0.941737	−	0.336350i	$-0.890807\pi$
$67$	−3.09044	−	9.51140i	−0.377558	−	1.16200i	0.564179	−	0.825652i	$-0.309193\pi$
$68$	−1.74650	−	5.37517i	−0.211794	−	0.651835i
$69$	1.22317	+	11.6376i	0.147252	+	1.40101i
$70$	−5.60797	−	4.07443i	−0.670281	−	0.486987i
$71$	10.5572	−	2.24400i	1.25291	−	0.266314i	0.466777	−	0.884375i	$-0.345415\pi$
$71$	10.5572	−	2.24400i	1.25291	−	0.266314i	0.786130	+	0.618062i	$0.212082\pi$
$72$	1.44040	−	4.43309i	0.169752	−	0.522444i
$73$	0.867652	−	2.67036i	0.101551	−	0.312542i	−0.887355	−	0.461088i	$-0.847459\pi$
$73$	0.867652	−	2.67036i	0.101551	−	0.312542i	0.988905	+	0.148546i	$0.0474593\pi$
$74$	−8.44569	−	3.76026i	−0.981792	−	0.437122i
$75$	3.07458	+	5.32532i	0.355022	+	0.614915i
$76$	−1.23734	−	2.14313i	−0.141932	−	0.245834i
$77$	−1.59976	−	0.712261i	−0.182310	−	0.0811697i
$78$	−1.83662	+	5.65254i	−0.207956	+	0.640024i
$79$	0.111575	−	0.343394i	0.0125532	−	0.0386348i	−0.944584	−	0.328271i	$-0.893534\pi$
$79$	0.111575	−	0.343394i	0.0125532	−	0.0386348i	0.957137	+	0.289636i	$0.0935342\pi$
$80$	−1.79378	+	0.381281i	−0.200551	+	0.0426285i
$81$	9.10023	+	6.61171i	1.01114	+	0.734634i
$82$	0.546914	+	5.20354i	0.0603966	+	0.574635i
$83$	−4.29637	−	13.2229i	−0.471588	−	1.45140i	−0.850504	−	0.525968i	$-0.823703\pi$
$83$	−4.29637	−	13.2229i	−0.471588	−	1.45140i	0.378916	−	0.925431i	$-0.376297\pi$
$84$	−2.83755	−	8.73309i	−0.309603	−	0.952859i
$85$	4.40082	+	7.62245i	0.477336	+	0.826771i
$86$	0.842973	+	2.59440i	0.0909001	+	0.279762i
$87$	1.50499			0.161352
$88$	−1.04968	+	0.467348i	−0.111896	+	0.0498194i
$89$	−7.43935	+	8.26224i	−0.788570	+	0.875795i	−0.994710	−	0.102727i	$-0.967243\pi$
$89$	−7.43935	+	8.26224i	−0.788570	+	0.875795i	0.206140	+	0.978523i	$0.433910\pi$
$90$	−0.241466	+	2.29739i	−0.0254527	+	0.242166i
$91$	3.85433	+	11.8624i	0.404044	+	1.24352i
$92$	5.12772			0.534602
$93$	−15.1128	+	6.72866i	−1.56713	+	0.697729i
$94$	5.03425	−	3.65760i	0.519244	−	0.377253i
$95$	2.57873	+	2.86397i	0.264573	+	0.293838i
$96$	−9.25676	−	4.12138i	−0.944764	−	0.420636i
$97$	−8.10768	−	1.72334i	−0.823211	−	0.174979i	−0.222998	−	0.974819i	$-0.571584\pi$
$97$	−8.10768	−	1.72334i	−0.823211	−	0.174979i	−0.600213	+	0.799840i	$0.704918\pi$
$98$	11.9614	+	8.69044i	1.20828	+	0.877867i
$99$	0.0610005	+	0.580381i	0.00613078	+	0.0583305i
$100$	2.46161	−	1.09598i	0.246161	−	0.109598i
$101$	−1.73799	−	1.26272i	−0.172937	−	0.125646i	0.497950	−	0.867206i	$-0.334086\pi$
$101$	−1.73799	−	1.26272i	−0.172937	−	0.125646i	−0.670887	+	0.741560i	$0.734086\pi$
$102$	1.39225	−	13.2464i	0.137854	−	1.31159i
$103$	−0.771734	−	7.34256i	−0.0760412	−	0.723484i	−0.964420	−	0.264373i	$-0.914835\pi$
$103$	−0.771734	−	7.34256i	−0.0760412	−	0.723484i	0.888379	−	0.459110i	$-0.151832\pi$
$104$	7.47648	+	3.32875i	0.733130	+	0.326410i
$105$	7.15006	+	12.3843i	0.697775	+	1.20858i
$106$	4.48025	−	1.99473i	0.435160	−	0.193746i
$107$	12.6395	+	9.18310i	1.22190	+	0.887764i	0.996257	−	0.0864457i	$-0.0275509\pi$
$107$	12.6395	+	9.18310i	1.22190	+	0.887764i	0.225645	+	0.974209i	$0.427551\pi$
$108$	1.94477	−	2.15988i	0.187135	−	0.207835i
$109$	−13.3658	+	14.8442i	−1.28021	+	1.42182i	−0.423607	+	0.905846i	$0.639236\pi$
$109$	−13.3658	+	14.8442i	−1.28021	+	1.42182i	−0.856605	+	0.515974i	$0.827430\pi$
$110$	0.460686	−	0.334708i	0.0439247	−	0.0319132i
$111$	12.7617	+	14.1733i	1.21128	+	1.34527i
$112$	5.69665	−	1.21086i	0.538283	−	0.114416i
$113$	5.68329	−	9.84375i	0.534639	−	0.926022i	−0.464542	−	0.885551i	$-0.653781\pi$
$113$	5.68329	−	9.84375i	0.534639	−	0.926022i	0.999181	−	0.0404708i	$-0.0128858\pi$
$114$	−0.609607	−	5.80002i	−0.0570949	−	0.543222i
$115$	−7.81100	+	1.66028i	−0.728379	+	0.154822i
$116$	0.0689355	−	0.655878i	0.00640050	−	0.0608967i
$117$	2.78131	−	3.08896i	0.257133	−	0.285575i
$118$	−4.39677	+	7.61544i	−0.404756	+	0.701058i
$119$	−13.9760	−	24.2072i	−1.28118	−	2.21907i
$120$	9.17794	+	1.95083i	0.837827	+	0.178086i
$121$	−7.26418	+	8.06769i	−0.660380	+	0.733426i
$122$	−7.16626	−	5.20659i	−0.648802	−	0.471383i
$123$	3.33548	−	10.2656i	0.300750	−	0.925614i
$124$	2.24012	+	6.89437i	0.201168	+	0.619133i
$125$	−9.27575	+	6.73923i	−0.829648	+	0.602775i
$126$	0.766839	−	7.29599i	0.0683155	−	0.649978i
$127$	−7.52435	+	5.46676i	−0.667678	+	0.485097i	−0.869247	−	0.494378i	$-0.835396\pi$
$127$	−7.52435	+	5.46676i	−0.667678	+	0.485097i	0.201569	+	0.979474i	$0.435396\pi$
$128$	−0.917463	+	1.58909i	−0.0810930	+	0.140457i
$129$	0.588244	−	5.59677i	0.0517920	−	0.492768i
$130$	−3.96728	−	0.843271i	−0.347953	−	0.0739598i
$131$	−3.18805	+	9.81182i	−0.278541	+	0.857262i	0.709719	+	0.704485i	$0.248822\pi$
$131$	−3.18805	+	9.81182i	−0.278541	+	0.857262i	−0.988261	+	0.152778i	$0.951178\pi$
$132$	0.754330			0.0656560
$133$	−8.18947	−	9.09532i	−0.710117	−	0.788665i
$134$	−10.1021	−	2.14728i	−0.872692	−	0.185496i
$135$	−2.26311	+	3.91982i	−0.194777	+	0.337364i
$136$	−17.9398	−	3.81323i	−1.53833	−	0.326982i
$137$	10.7729	−	2.28985i	0.920392	−	0.195635i	0.276732	−	0.960947i	$-0.410749\pi$
$137$	10.7729	−	2.28985i	0.920392	−	0.195635i	0.643660	+	0.765312i	$0.277415\pi$
$138$	11.0396	+	4.91513i	0.939750	+	0.418404i
$139$	5.87142	+	2.61412i	0.498007	+	0.221727i	0.640340	−	0.768092i	$-0.278794\pi$
$139$	5.87142	+	2.61412i	0.498007	+	0.221727i	−0.142333	+	0.989819i	$0.545460\pi$
$140$	5.72458	−	2.54875i	0.483815	−	0.215408i
$141$	−12.5566	+	2.66900i	−1.05746	+	0.224770i
$142$	3.44427	−	10.6004i	0.289036	−	0.889563i
$143$	−1.02463			−0.0856837
$144$	−1.29867	−	1.44232i	−0.108222	−	0.120193i
$145$	0.107355	+	1.02141i	0.00891532	+	0.0848236i
$146$	−1.94019	−	2.15480i	−0.160572	−	0.178333i
$147$	−15.2505	−	26.4147i	−1.25784	−	2.17865i
$148$	6.76126	−	4.91235i	0.555772	−	0.403792i
$149$	−1.81047	+	3.13583i	−0.148320	+	0.256897i	−0.930607	−	0.366021i	$-0.880720\pi$
$149$	−1.81047	+	3.13583i	−0.148320	+	0.256897i	0.782287	+	0.622918i	$0.214053\pi$
$150$	6.35018			0.518490
$151$	−3.51691	+	11.7742i	−0.286202	+	0.958169i
$151$	−3.51691	+	11.7742i	−0.286202	+	0.958169i
$152$	−8.03055			−0.651364
$153$	−4.65753	+	8.06708i	−0.376539	+	0.652185i
$154$	−1.46303	+	1.06296i	−0.117895	+	0.0856555i
$155$	−5.64464	−	9.77681i	−0.453388	−	0.785292i
$156$	−3.59512	−	3.99278i	−0.287840	−	0.319678i
$157$	−0.655840	−	6.23990i	−0.0523417	−	0.497998i	−0.989017	−	0.147800i	$-0.952781\pi$
$157$	−0.655840	−	6.23990i	−0.0523417	−	0.497998i	0.936676	−	0.350198i	$-0.113886\pi$
$158$	−0.249499	−	0.277096i	−0.0198490	−	0.0220446i
$159$	−10.1173			−0.802352
$160$	2.13679	−	6.57637i	0.168928	−	0.519908i
$161$	24.8059	−	5.27266i	1.95498	−	0.415544i
$162$	10.6120	−	4.72475i	0.833755	−	0.371212i
$163$	4.94285	+	2.20070i	0.387154	+	0.172372i	0.591077	−	0.806615i	$-0.298703\pi$
$163$	4.94285	+	2.20070i	0.387154	+	0.172372i	−0.203924	+	0.978987i	$0.565369\pi$
$164$	−4.32096	−	1.92381i	−0.337410	−	0.150225i
$165$	−1.14906	+	0.244241i	−0.0894545	+	0.0190141i
$166$	−14.0441	−	2.98517i	−1.09004	−	0.231694i
$167$	−0.563488	+	0.975990i	−0.0436040	+	0.0755244i	−0.887004	−	0.461762i	$-0.847217\pi$
$167$	−0.563488	+	0.975990i	−0.0436040	+	0.0755244i	0.843400	+	0.537287i	$0.180551\pi$
$168$	−29.1470	−	6.19539i	−2.24874	−	0.477985i
$169$	−3.81535	−	4.23738i	−0.293489	−	0.325952i
$170$	9.08939			0.697125
$171$	−1.26038	+	3.87904i	−0.0963833	+	0.296637i
$172$	−2.41213	−	0.512714i	−0.183923	−	0.0390941i
$173$	0.0742142	−	0.706101i	0.00564240	−	0.0536838i	−0.991338	−	0.131332i	$-0.958075\pi$
$173$	0.0742142	−	0.706101i	0.00564240	−	0.0536838i	0.996981	+	0.0776485i	$0.0247412\pi$
$174$	0.777098	−	1.34597i	0.0589117	−	0.102038i
$175$	10.7814	−	7.83311i	0.814994	−	0.592128i
$176$	−0.0500091	+	0.475805i	−0.00376958	+	0.0358652i
$177$	14.6762	−	10.6629i	1.10313	−	0.801471i
$178$	3.54795	+	10.9195i	0.265930	+	0.818449i
$179$	−6.94329	+	21.3693i	−0.518966	+	1.59721i	0.256982	+	0.966416i	$0.417272\pi$
$179$	−6.94329	+	21.3693i	−0.518966	+	1.59721i	−0.775948	+	0.630797i	$0.782728\pi$
$180$	−1.68944	−	1.22745i	−0.125924	−	0.0914889i
$181$	15.4406	−	17.1485i	1.14769	−	1.27464i	0.191632	−	0.981467i	$-0.438622\pi$
$181$	15.4406	−	17.1485i	1.14769	−	1.27464i	0.956059	−	0.293174i	$-0.0947114\pi$
$182$	12.5992	+	2.67804i	0.933912	+	0.198509i
$183$	9.13685	+	15.8255i	0.675415	+	1.16985i
$184$	8.31998	−	14.4106i	0.613357	−	1.06237i
$185$	−8.70882	+	9.67212i	−0.640285	+	0.711108i
$186$	−1.78575	+	16.9903i	−0.130937	+	1.24579i
$187$	2.24604	−	0.477410i	0.164247	−	0.0349117i
$188$	0.588000	+	5.59444i	0.0428843	+	0.408017i
$189$	7.18711	−	12.4484i	0.522785	−	0.905491i
$190$	3.89288	−	0.827457i	0.282419	−	0.0600300i
$191$	8.46023	+	9.39603i	0.612161	+	0.679873i	0.966919	−	0.255085i	$-0.0821034\pi$
$191$	8.46023	+	9.39603i	0.612161	+	0.679873i	−0.354758	+	0.934958i	$0.615437\pi$
$192$	−12.8137	+	9.30971i	−0.924751	+	0.671871i
$193$	0.496040	−	0.550908i	0.0357057	−	0.0396552i	−0.725027	−	0.688720i	$-0.758173\pi$
$193$	0.496040	−	0.550908i	0.0357057	−	0.0396552i	0.760733	+	0.649065i	$0.224840\pi$
$194$	−5.72762	+	6.36117i	−0.411219	+	0.456705i
$195$	6.76921	+	4.91812i	0.484753	+	0.352194i
$196$	−12.2101	+	5.43628i	−0.872148	+	0.388305i
$197$	−7.68045	−	13.3029i	−0.547209	−	0.947794i	−0.998464	−	0.0553992i	$-0.982357\pi$
$197$	−7.68045	−	13.3029i	−0.547209	−	0.947794i	0.451255	−	0.892395i	$-0.350976\pi$
$198$	0.550554	+	0.245122i	0.0391262	+	0.0174201i
$199$	1.67988	+	15.9829i	0.119083	+	1.13300i	0.876947	+	0.480588i	$0.159577\pi$
$199$	1.67988	+	15.9829i	0.119083	+	1.13300i	−0.757863	+	0.652413i	$0.773757\pi$
$200$	0.914010	−	8.69623i	0.0646303	−	0.614916i
$201$	17.2369	+	12.5233i	1.21580	+	0.883327i
$202$	−2.02671	+	0.902348i	−0.142599	+	0.0634890i
$203$	−0.340934	−	3.24377i	−0.0239289	−	0.227668i
$204$	9.74106	+	7.07730i	0.682011	+	0.495510i
$205$	7.20497	+	1.53146i	0.503217	+	0.106962i
$206$	−6.96521	−	3.10111i	−0.485289	−	0.216065i
$207$	−5.65503	−	6.28055i	−0.393052	−	0.436528i
$208$	2.75685	−	2.00297i	0.191153	−	0.138881i
$209$	0.918490	−	0.408938i	0.0635333	−	0.0282869i
$210$	14.7676			1.01906
$211$	−7.01159	−	21.5794i	−0.482698	−	1.48559i	−0.835288	−	0.549813i	$-0.814699\pi$
$211$	−7.01159	−	21.5794i	−0.482698	−	1.48559i	0.352590	−	0.935778i	$-0.385301\pi$
$212$	−0.463417	+	4.40911i	−0.0318276	+	0.302819i
$213$	−15.3857	+	17.0875i	−1.05421	+	1.17082i
$214$	14.7391	−	6.56228i	1.00755	−	0.448588i
$215$	3.84038			0.261912
$216$	−2.91452	−	8.96998i	−0.198308	−	0.610330i
$217$	17.9261	+	31.0489i	1.21690	+	2.10774i
$218$	6.37437	+	19.6183i	0.431727	+	1.32872i
$219$	1.84845	+	5.68895i	0.124907	+	0.384424i
$220$	0.0538081	+	0.511950i	0.00362774	+	0.0345156i
$221$	−13.2316	−	9.61329i	−0.890051	−	0.646660i
$222$	19.2651	−	4.09493i	1.29299	−	0.274834i
$223$	−7.58390	+	23.3408i	−0.507856	+	1.56302i	0.288061	+	0.957612i	$0.406989\pi$
$223$	−7.58390	+	23.3408i	−0.507856	+	1.56302i	−0.795916	+	0.605406i	$0.793011\pi$
$224$	−6.78597	+	20.8851i	−0.453406	+	1.39544i
$225$	−4.05713	−	1.80635i	−0.270475	−	0.120423i
$226$	−5.86909	−	10.1656i	−0.390406	−	0.676203i
$227$	2.70189	+	4.67982i	0.179331	+	0.310611i	0.941652	−	0.336589i	$-0.109273\pi$
$227$	2.70189	+	4.67982i	0.179331	+	0.310611i	−0.762321	+	0.647200i	$0.775940\pi$
$228$	4.81627	+	2.14434i	0.318965	+	0.142012i
$229$	1.51938	−	4.67618i	0.100404	−	0.309011i	−0.888221	−	0.459417i	$-0.848058\pi$
$229$	1.51938	−	4.67618i	0.100404	−	0.309011i	0.988624	+	0.150406i	$0.0480582\pi$
$230$	−2.54833	+	7.84295i	−0.168032	+	0.517149i
$231$	3.64916	−	0.775653i	0.240097	−	0.0510342i
$232$	−1.73139	−	1.25793i	−0.113671	−	0.0825869i
$233$	−1.08708	−	10.3428i	−0.0712167	−	0.677581i	−0.970646	−	0.240514i	$-0.922684\pi$
$233$	−1.08708	−	10.3428i	−0.0712167	−	0.677581i	0.899429	−	0.437067i	$-0.143983\pi$
$234$	−1.32645	−	4.08241i	−0.0867131	−	0.266875i
$235$	−2.70709	−	8.33157i	−0.176591	−	0.543492i
$236$	−3.97465	−	6.88430i	−0.258728	−	0.448130i
$237$	0.237701	+	0.731569i	0.0154403	+	0.0475205i
$238$	−28.8658			−1.87109
$239$	−8.54091	+	3.80266i	−0.552465	+	0.245973i	−0.663930	−	0.747795i	$-0.731113\pi$
$239$	−8.54091	+	3.80266i	−0.552465	+	0.245973i	0.111464	+	0.993768i	$0.464446\pi$
$240$	2.61420	−	2.90337i	0.168746	−	0.187412i
$241$	2.14817	−	20.4385i	0.138376	−	1.31656i	−0.676293	−	0.736632i	$-0.736415\pi$
$241$	2.14817	−	20.4385i	0.138376	−	1.31656i	0.814669	−	0.579926i	$-0.196918\pi$
$242$	3.46441	+	10.6623i	0.222701	+	0.685402i
$243$	−14.6240			−0.938130
$244$	7.31526	−	3.25697i	0.468312	−	0.208506i
$245$	16.8393	−	12.2345i	1.07582	−	0.781631i
$246$	−7.45861	−	8.28363i	−0.475544	−	0.528145i
$247$	−6.54207	−	2.91272i	−0.416262	−	0.185332i
$248$	23.0102	+	4.89097i	1.46115	+	0.310577i
$249$	23.9629	+	17.4101i	1.51859	+	1.10332i
$250$	1.23765	+	11.7754i	0.0782757	+	0.744743i
$251$	−4.23781	+	1.88680i	−0.267488	+	0.119093i	−0.536098	−	0.844156i	$-0.680102\pi$
$251$	−4.23781	+	1.88680i	−0.267488	+	0.119093i	0.268610	+	0.963249i	$0.413436\pi$
$252$	5.36528	+	3.89811i	0.337981	+	0.245558i
$253$	−0.217764	+	2.07188i	−0.0136907	+	0.130258i
$254$	1.00396	+	9.55205i	0.0629941	+	0.599349i
$255$	−17.1300	−	7.62676i	−1.07272	−	0.477606i
$256$	8.38201	+	14.5181i	0.523876	+	0.907379i
$257$	−9.96729	+	4.43772i	−0.621742	+	0.276818i	−0.693334	−	0.720616i	$-0.743859\pi$
$257$	−9.96729	+	4.43772i	−0.621742	+	0.276818i	0.0715915	+	0.997434i	$0.477192\pi$
$258$	−4.70166	−	3.41596i	−0.292713	−	0.212668i
$259$	27.6572	−	30.7164i	1.71853	−	1.90863i
$260$	2.45338	−	2.72475i	0.152152	−	0.168982i
$261$	−0.879358	+	0.638891i	−0.0544309	+	0.0395464i
$262$	7.12894	+	7.91749i	0.440427	+	0.489144i
$263$	−14.7338	+	3.13177i	−0.908525	+	0.193113i	−0.638393	−	0.769710i	$-0.720401\pi$
$263$	−14.7338	+	3.13177i	−0.908525	+	0.193113i	−0.270132	+	0.962823i	$0.587067\pi$
$264$	1.22394	−	2.11992i	0.0753282	−	0.130472i
$265$	−0.721688	−	6.86640i	−0.0443329	−	0.421800i
$266$	−12.3629	+	2.62781i	−0.758018	+	0.161122i
$267$	2.47583	−	23.5560i	0.151519	−	1.44160i
$268$	6.24720	−	6.93821i	0.381608	−	0.423819i
$269$	8.17095	−	14.1525i	0.498192	−	0.862894i	−0.501806	−	0.864980i	$-0.667331\pi$
$269$	8.17095	−	14.1525i	0.498192	−	0.862894i	0.999998	+	0.00208659i	$0.000664182\pi$
$270$	2.33709	+	4.04796i	0.142231	+	0.246351i
$271$	19.2629	+	4.09446i	1.17014	+	0.248721i	0.751688	−	0.659519i	$-0.229240\pi$
$271$	19.2629	+	4.09446i	1.17014	+	0.248721i	0.418451	+	0.908239i	$0.362573\pi$
$272$	−5.10990	+	5.67512i	−0.309833	+	0.344105i
$273$	−21.4974	−	15.6188i	−1.30108	−	0.945293i
$274$	3.51465	−	10.8170i	0.212328	−	0.653477i
$275$	0.338297	+	1.04117i	0.0204001	+	0.0627849i
$276$	−8.83781	+	6.42104i	−0.531973	+	0.386501i
$277$	−1.26797	+	12.0639i	−0.0761850	+	0.724852i	0.888040	+	0.459766i	$0.152067\pi$
$277$	−1.26797	+	12.0639i	−0.0761850	+	0.724852i	−0.964225	+	0.265085i	$0.914600\pi$
$278$	5.36959	−	3.90124i	0.322047	−	0.233981i
$279$	5.97390	−	10.3471i	0.357648	−	0.619465i
$280$	2.12557	−	20.2235i	0.127027	−	1.20858i
$281$	−14.0299	−	2.98214i	−0.836953	−	0.177900i	−0.230553	−	0.973060i	$-0.574053\pi$
$281$	−14.0299	−	2.98214i	−0.836953	−	0.177900i	−0.606400	+	0.795160i	$0.707387\pi$
$282$	−4.09659	+	12.6080i	−0.243948	+	0.750796i
$283$	−7.16360			−0.425832			−0.212916	−	0.977071i	$-0.568296\pi$
$283$	−7.16360			−0.425832			−0.212916	+	0.977071i	$0.568296\pi$
$284$	6.74203	+	7.48778i	0.400066	+	0.444318i
$285$	−8.03087	−	1.70701i	−0.475708	−	0.101115i
$286$	−0.529063	+	0.916364i	−0.0312841	+	0.0541857i
$287$	−22.8813	−	4.86358i	−1.35064	−	0.287088i
$288$	7.15824	−	1.52153i	0.421804	−	0.0896571i
$289$	17.9532	+	7.99326i	1.05607	+	0.470192i
$290$	0.968919	+	0.431391i	0.0568969	+	0.0253321i
$291$	16.1319	−	7.18238i	0.945668	−	0.421039i
$292$	2.56391	−	0.544977i	0.150042	−	0.0318924i
$293$	−4.71952	+	14.5252i	−0.275717	+	0.848571i	0.713311	+	0.700847i	$0.247195\pi$
$293$	−4.71952	+	14.5252i	−0.275717	+	0.848571i	−0.989029	+	0.147723i	$0.952805\pi$
$294$	−31.4982			−1.83701
$295$	8.28358	+	9.19985i	0.482289	+	0.535636i
$296$	−2.83487	−	26.9720i	−0.164773	−	1.56771i
$297$	0.790123	+	0.877521i	0.0458476	+	0.0509189i
$298$	1.86966	+	3.23835i	0.108307	+	0.187592i
$299$	12.0046	−	8.72188i	0.694246	−	0.504399i
$300$	−2.87026	+	4.97144i	−0.165715	+	0.287026i
$301$	−12.1962			−0.702975
$302$	8.71415	+	9.22486i	0.501443	+	0.530831i
$303$	4.57670			0.262925
$304$	−1.67187	+	2.89577i	−0.0958886	+	0.166084i
$305$	−10.0887	+	7.32987i	−0.577678	+	0.419707i
$306$	4.80980	+	8.33081i	0.274958	+	0.476241i
$307$	22.3503	+	24.8225i	1.27560	+	1.41669i	0.862541	+	0.505988i	$0.168872\pi$
$307$	22.3503	+	24.8225i	1.27560	+	1.41669i	0.413056	+	0.910706i	$0.364461\pi$
$308$	−0.170882	−	1.62583i	−0.00973691	−	0.0926405i
$309$	10.5246	+	11.6888i	0.598725	+	0.664951i
$310$	−11.6584			−0.662150
$311$	3.33886	−	10.2759i	0.189329	−	0.582696i	−0.810667	−	0.585508i	$-0.800895\pi$
$311$	3.33886	−	10.2759i	0.189329	−	0.582696i	0.999996	+	0.00281219i	$0.000895148\pi$
$312$	−17.0543	+	3.62501i	−0.965511	+	0.205226i
$313$	20.1597	−	8.97569i	1.13949	−	0.507336i	0.251805	−	0.967778i	$-0.418976\pi$
$313$	20.1597	−	8.97569i	1.13949	−	0.507336i	0.887690	+	0.460442i	$0.152309\pi$
$314$	−5.91922	−	2.63541i	−0.334041	−	0.148725i
$315$	−9.43503	−	4.20074i	−0.531604	−	0.236685i
$316$	0.329706	−	0.0700811i	0.0185474	−	0.00394237i
$317$	−29.3288	−	6.23403i	−1.64727	−	0.350138i	−0.711482	−	0.702704i	$-0.751976\pi$
$317$	−29.3288	−	6.23403i	−1.64727	−	0.350138i	−0.935787	+	0.352567i	$0.885309\pi$
$318$	−5.22402	+	9.04826i	−0.292948	+	0.507401i
$319$	0.262083	+	0.0557076i	0.0146739	+	0.00311902i
$320$	−7.23236	−	8.03235i	−0.404301	−	0.449022i
$321$	−33.2838			−1.85772
$322$	8.09291	−	24.9074i	0.451000	−	1.38804i
$323$	15.6977	+	3.33665i	0.873443	+	0.185656i
$324$	−1.09765	+	10.4435i	−0.0609808	+	0.580193i
$325$	3.89876	−	6.75284i	0.216264	−	0.374580i
$326$	4.52039	−	3.28426i	0.250361	−	0.181898i
$327$	4.44817	−	42.3215i	0.245984	−	2.34039i
$328$	−12.4175	+	9.02186i	−0.685643	+	0.498149i
$329$	8.59710	+	26.4592i	0.473973	+	1.45874i
$330$	−0.374881	+	1.15376i	−0.0206365	+	0.0635126i
$331$	−9.08167	−	6.59822i	−0.499174	−	0.362671i	0.309528	−	0.950890i	$-0.399829\pi$
$331$	−9.08167	−	6.59822i	−0.499174	−	0.362671i	−0.808701	+	0.588220i	$0.799829\pi$
$332$	8.68494	−	9.64560i	0.476648	−	0.529371i
$333$	−13.4733	−	2.86384i	−0.738333	−	0.156938i
$334$	0.581910	+	1.00790i	0.0318407	+	0.0551497i
$335$	−7.26980	+	12.5917i	−0.397191	+	0.687956i
$336$	−8.30211	+	9.22043i	−0.452917	+	0.503016i
$337$	2.53614	−	24.1297i	0.138152	−	1.31443i	−0.677343	−	0.735667i	$-0.736869\pi$
$337$	2.53614	−	24.1297i	0.138152	−	1.31443i	0.815496	−	0.578763i	$-0.196464\pi$
$338$	−5.75969	+	1.22426i	−0.313286	+	0.0665909i
$339$	2.53120	+	24.0828i	0.137476	+	1.30800i
$340$	−4.10837	+	7.11591i	−0.222808	+	0.385915i
$341$	−2.88084	+	0.612342i	−0.156006	+	0.0331602i
$342$	2.81838	+	3.13013i	0.152400	+	0.169258i
$343$	−27.3309	+	19.8571i	−1.47573	+	1.07218i
$344$	−5.35470	+	5.94699i	−0.288706	+	0.320640i
$345$	11.3835	−	12.6427i	0.612867	−	0.680658i
$346$	−0.593172	−	0.430965i	−0.0318891	−	0.0231688i
$347$	−8.11736	+	3.61408i	−0.435763	+	0.194014i	−0.612880	−	0.790176i	$-0.709989\pi$
$347$	−8.11736	+	3.61408i	−0.435763	+	0.194014i	0.177118	+	0.984190i	$0.443323\pi$
$348$	0.702491	+	1.21675i	0.0376575	+	0.0652247i
$349$	−8.85278	−	3.94151i	−0.473878	−	0.210984i	0.155879	−	0.987776i	$-0.450179\pi$
$349$	−8.85278	−	3.94151i	−0.473878	−	0.210984i	−0.629757	+	0.776792i	$0.716846\pi$
$350$	−1.43854	−	13.6868i	−0.0768931	−	0.731589i
$351$	0.879142	−	8.36448i	0.0469251	−	0.446463i
$352$	−1.45944	−	1.06035i	−0.0777885	−	0.0565166i
$353$	6.02959	−	2.68455i	0.320923	−	0.142884i	−0.239952	−	0.970785i	$-0.577132\pi$
$353$	6.02959	−	2.68455i	0.320923	−	0.142884i	0.560875	+	0.827901i	$0.310465\pi$
$354$	−1.95822	−	18.6312i	−0.104078	−	0.990238i
$355$	−12.6945	−	9.22308i	−0.673753	−	0.489510i
$356$	−10.1523	−	2.15794i	−0.538071	−	0.114371i
$357$	54.4009	+	24.2208i	2.87920	+	1.28190i
$358$	15.5262	+	17.2436i	0.820585	+	0.911352i
$359$	−1.68471	+	1.22401i	−0.0889157	+	0.0646010i	−0.631355	−	0.775494i	$-0.717501\pi$
$359$	−1.68471	+	1.22401i	−0.0889157	+	0.0646010i	0.542439	+	0.840095i	$0.317501\pi$
$360$	−6.19076	+	2.75630i	−0.326282	+	0.145270i
$361$	−11.9731			−0.630164
$362$	−7.36388	−	22.6637i	−0.387037	−	1.19118i
$363$	2.41754	−	23.0013i	0.126888	−	1.20726i
$364$	−7.79136	+	8.65318i	−0.408378	+	0.453550i
$365$	−3.72913	+	1.66032i	−0.195192	+	0.0869049i
$366$	18.8711			0.986409
$367$	−3.94499	−	12.1414i	−0.205927	−	0.633778i	−0.999674	−	0.0255302i	$-0.991873\pi$
$367$	−3.94499	−	12.1414i	−0.205927	−	0.633778i	0.793747	−	0.608248i	$-0.208127\pi$
$368$	−3.46426	−	6.00027i	−0.180587	−	0.312786i
$369$	2.40897	+	7.41406i	0.125406	+	0.385960i
$370$	4.15338	+	12.7828i	0.215924	+	0.664545i
$371$	2.29192	+	21.8061i	0.118990	+	1.13212i
$372$	−12.4942	−	9.07757i	−0.647794	−	0.470650i
$373$	6.60032	−	1.40294i	0.341752	−	0.0726416i	−0.0338388	−	0.999427i	$-0.510773\pi$
$373$	6.60032	−	1.40294i	0.341752	−	0.0726416i	0.375590	+	0.926786i	$0.377440\pi$
$374$	0.732767	−	2.25523i	0.0378905	−	0.116615i
$375$	7.54808	−	23.2306i	0.389781	−	1.19962i
$376$	16.6763	+	7.42478i	0.860016	+	0.382904i
$377$	−0.954214	−	1.65275i	−0.0491445	−	0.0851208i
$378$	−7.42207	−	12.8554i	−0.381750	−	0.661211i
$379$	−7.18269	−	3.19794i	−0.368950	−	0.164267i	0.213883	−	0.976859i	$-0.431389\pi$
$379$	−7.18269	−	3.19794i	−0.368950	−	0.164267i	−0.582833	+	0.812592i	$0.698056\pi$
$380$	−1.11177	+	3.42167i	−0.0570325	+	0.175528i
$381$	6.12289	−	18.8443i	0.313685	−	0.965424i
$382$	12.7716	−	2.71469i	0.653454	−	0.138896i
$383$	1.26537	+	0.919349i	0.0646576	+	0.0469765i	0.619645	−	0.784883i	$-0.287277\pi$
$383$	1.26537	+	0.919349i	0.0646576	+	0.0469765i	−0.554987	+	0.831859i	$0.687277\pi$
$384$	−0.408616	−	3.88772i	−0.0208521	−	0.198395i
$385$	0.786724	+	2.42129i	0.0400952	+	0.123400i
$386$	−0.236570	−	0.728086i	−0.0120411	−	0.0370586i
$387$	2.03220	+	3.51987i	0.103302	+	0.178925i
$388$	−2.39117	−	7.35927i	−0.121393	−	0.373610i
$389$	−8.40610			−0.426206			−0.213103	−	0.977030i	$-0.568357\pi$
$389$	−8.40610			−0.426206			−0.213103	+	0.977030i	$0.568357\pi$
$390$	7.89371	−	3.51451i	0.399714	−	0.177964i
$391$	−22.2510	+	24.7122i	−1.12528	+	1.24975i
$392$	−4.53368	+	43.1351i	−0.228985	+	2.17865i
$393$	−6.79185	−	20.9032i	−0.342603	−	1.05443i
$394$	−15.8631			−0.799170
$395$	−0.479546	+	0.213508i	−0.0241286	+	0.0107427i
$396$	−0.440750	+	0.320224i	−0.0221485	+	0.0160918i
$397$	24.4548	+	27.1598i	1.22735	+	1.36311i	0.909895	+	0.414838i	$0.136162\pi$
$397$	24.4548	+	27.1598i	1.22735	+	1.36311i	0.317456	+	0.948273i	$0.397171\pi$
$398$	15.1616	+	6.75036i	0.759980	+	0.338365i
$399$	25.5042	+	5.42109i	1.27681	+	0.271394i
$400$	−2.94552	−	2.14005i	−0.147276	−	0.107002i
$401$	2.18011	+	20.7424i	0.108870	+	1.03582i	0.903458	+	0.428677i	$0.141020\pi$
$401$	2.18011	+	20.7424i	0.108870	+	1.03582i	−0.794588	+	0.607148i	$0.792313\pi$
$402$	20.1003	−	8.94922i	1.00251	−	0.446346i
$403$	16.9712	+	12.3303i	0.845397	+	0.614217i
$404$	0.209633	−	1.99453i	0.0104297	−	0.0992315i
$405$	−1.70940	−	16.2638i	−0.0849407	−	0.808157i
$406$	−3.07706	−	1.37000i	−0.152712	−	0.0679918i
$407$	1.69772	+	2.94054i	0.0841530	+	0.145757i
$408$	35.6949	−	15.8924i	1.76716	−	0.786792i
$409$	−23.4085	−	17.0073i	−1.15748	−	0.840956i	−0.168019	−	0.985784i	$-0.553737\pi$
$409$	−23.4085	−	17.0073i	−1.15748	−	0.840956i	−0.989457	+	0.144828i	$0.953737\pi$
$410$	5.08990	−	5.65291i	0.251372	−	0.279177i
$411$	−15.7001	+	17.4367i	−0.774428	+	0.860090i
$412$	5.57605	−	4.05124i	0.274712	−	0.199590i
$413$	−26.3068	−	29.2166i	−1.29447	−	1.43766i
$414$	−8.53688	+	1.81457i	−0.419565	+	0.0891813i
$415$	−10.1066	+	17.5051i	−0.496112	+	0.859291i
$416$	1.34309	+	12.7786i	0.0658503	+	0.626523i
$417$	−13.3931	+	2.84678i	−0.655861	+	0.139408i
$418$	0.108530	−	1.03259i	0.00530838	−	0.0505058i
$419$	−2.42656	+	2.69497i	−0.118545	+	0.131658i	−0.799496	−	0.600671i	$-0.794900\pi$
$419$	−2.42656	+	2.69497i	−0.118545	+	0.131658i	0.680951	+	0.732329i	$0.261567\pi$
$420$	−6.67492	+	11.5613i	−0.325703	+	0.564133i
$421$	−9.56069	−	16.5596i	−0.465959	−	0.807065i	0.533285	−	0.845936i	$-0.320957\pi$
$421$	−9.56069	−	16.5596i	−0.465959	−	0.807065i	−0.999244	+	0.0388703i	$0.987624\pi$
$422$	−22.9197	−	4.87174i	−1.11571	−	0.237152i
$423$	6.20373	−	6.88995i	0.301636	−	0.335001i
$424$	11.6392	+	8.45636i	0.565249	+	0.410677i
$425$	−5.39989	+	16.6192i	−0.261933	+	0.806147i
$426$	7.33769	+	22.5831i	0.355512	+	1.09415i
$427$	32.0394	−	23.2780i	1.55050	−	1.12650i
$428$	−1.52455	+	14.5051i	−0.0736918	+	0.701131i
$429$	1.76598	−	1.28306i	0.0852625	−	0.0619468i
$430$	1.98297	−	3.43460i	0.0956271	−	0.165631i
$431$	−1.66378	+	15.8299i	−0.0801417	+	0.762497i	0.878473	+	0.477792i	$0.158563\pi$
$431$	−1.66378	+	15.8299i	−0.0801417	+	0.762497i	−0.958615	+	0.284706i	$0.908104\pi$
$432$	−3.84129	−	0.816492i	−0.184814	−	0.0392835i
$433$	−3.51380	+	10.8144i	−0.168862	+	0.519705i	−0.999300	−	0.0374063i	$-0.988090\pi$
$433$	−3.51380	+	10.8144i	−0.168862	+	0.519705i	0.830438	+	0.557112i	$0.188090\pi$
$434$	37.0243			1.77722
$435$	−1.46406	−	1.62601i	−0.0701965	−	0.0779611i
$436$	−18.2400	−	3.87703i	−0.873537	−	0.185676i
$437$	−7.28014	+	12.6096i	−0.348256	+	0.603198i
$438$	6.04228	+	1.28433i	0.288712	+	0.0613675i
$439$	−1.11446	+	0.236887i	−0.0531905	+	0.0113060i	−0.234430	−	0.972133i	$-0.575322\pi$
$439$	−1.11446	+	0.236887i	−0.0531905	+	0.0113060i	0.181240	+	0.983439i	$0.441989\pi$
$440$	1.52606	+	0.679445i	0.0727520	+	0.0323913i
$441$	20.1242	+	8.95986i	0.958294	+	0.426660i
$442$	−15.4296	+	6.86970i	−0.733911	+	0.326758i
$443$	2.85276	−	0.606374i	0.135539	−	0.0288097i	−0.139643	−	0.990202i	$-0.544595\pi$
$443$	2.85276	−	0.606374i	0.135539	−	0.0288097i	0.275182	+	0.961392i	$0.411262\pi$
$444$	−5.50193	+	16.9332i	−0.261110	+	0.803614i
$445$	16.1636			0.766228
$446$	16.9587	+	18.8345i	0.803017	+	0.891841i
$447$	−0.806341	−	7.67183i	−0.0381386	−	0.362865i
$448$	22.9683	+	25.5089i	1.08515	+	1.20518i
$449$	−10.6978	−	18.5292i	−0.504862	−	0.874446i	−0.999984	−	0.00562292i	$-0.998210\pi$
$449$	−10.6978	−	18.5292i	−0.504862	−	0.874446i	0.495123	−	0.868823i	$-0.335123\pi$
$450$	−3.71037	+	2.69574i	−0.174908	+	0.127078i
$451$	0.960830	−	1.66421i	0.0452437	−	0.0783644i
$452$	10.6112			0.499111
$453$	−8.68236	−	24.6972i	−0.407933	−	1.16037i
$454$	5.58045			0.261904
$455$	9.06673	−	15.7040i	0.425055	−	0.736216i
$456$	13.8409	−	10.0560i	0.648162	−	0.470917i
$457$	3.81853	+	6.61388i	0.178623	+	0.309384i	0.941409	−	0.337267i	$-0.109502\pi$
$457$	3.81853	+	6.61388i	0.178623	+	0.309384i	−0.762786	+	0.646651i	$0.776169\pi$
$458$	−3.39756	−	3.77337i	−0.158757	−	0.176318i
$459$	1.97018	+	18.7450i	0.0919601	+	0.874942i
$460$	−4.98826	−	5.54002i	−0.232579	−	0.258305i
$461$	−7.51250			−0.349892			−0.174946	−	0.984578i	$-0.555975\pi$
$461$	−7.51250			−0.349892			−0.174946	+	0.984578i	$0.555975\pi$
$462$	1.19053	−	3.66409i	0.0553887	−	0.170469i
$463$	31.7144	−	6.74109i	1.47389	−	0.313285i	0.600233	−	0.799825i	$-0.295075\pi$
$463$	31.7144	−	6.74109i	1.47389	−	0.313285i	0.873658	+	0.486540i	$0.161741\pi$
$464$	−0.814056	+	0.362441i	−0.0377916	+	0.0168259i
$465$	21.9715	+	9.78233i	1.01890	+	0.453645i
$466$	−9.81129	−	4.36827i	−0.454499	−	0.202356i
$467$	−22.0482	+	4.68648i	−1.02027	+	0.216865i	−0.687531	−	0.726155i	$-0.741305\pi$
$467$	−22.0482	+	4.68648i	−1.02027	+	0.216865i	−0.332737	+	0.943020i	$0.607972\pi$
$468$	3.79559	+	0.806778i	0.175451	+	0.0372933i
$469$	23.0872	−	39.9882i	1.06607	−	1.84648i
$470$	−8.84903	−	1.88092i	−0.408175	−	0.0867604i
$471$	8.94410	+	9.93343i	0.412123	+	0.457708i
$472$	−25.7963			−1.18737
$473$	0.309603	−	0.952860i	0.0142356	−	0.0438126i
$474$	0.777006	+	0.165158i	0.0356891	+	0.00758594i
$475$	−0.799777	+	7.60937i	−0.0366963	+	0.349142i
$476$	13.0473	−	22.5985i	0.598020	−	1.03580i
$477$	5.91146	−	4.29492i	0.270667	−	0.196651i
$478$	−1.00921	+	9.60194i	−0.0461600	+	0.439183i
$479$	20.1130	−	14.6130i	0.918987	−	0.667683i	−0.0242845	−	0.999705i	$-0.507731\pi$
$479$	20.1130	−	14.6130i	0.918987	−	0.667683i	0.943272	+	0.332022i	$0.107731\pi$
$480$	4.55224	+	14.0104i	0.207780	+	0.639482i
$481$	7.47343	−	23.0008i	0.340759	−	1.04875i
$482$	−17.1697	−	12.4745i	−0.782059	−	0.568199i
$483$	−36.1514	+	40.1502i	−1.64494	+	1.82690i
$484$	−9.91325	−	2.10713i	−0.450602	−	0.0957785i
$485$	6.02527	+	10.4361i	0.273593	+	0.473878i
$486$	−7.55105	+	13.0788i	−0.342522	+	0.593266i
$487$	−17.3070	+	19.2213i	−0.784253	+	0.871001i	−0.994292	−	0.106692i	$-0.965974\pi$
$487$	−17.3070	+	19.2213i	−0.784253	+	0.871001i	0.210039	+	0.977693i	$0.432641\pi$
$488$	2.71620	−	25.8430i	0.122957	−	1.16986i
$489$	−11.2749	+	2.39656i	−0.509871	+	0.108376i
$490$	−2.24684	−	21.3772i	−0.101502	−	0.965725i
$491$	4.81660	−	8.34260i	0.217370	−	0.376496i	−0.736633	−	0.676293i	$-0.763585\pi$
$491$	4.81660	−	8.34260i	0.217370	−	0.376496i	0.954003	+	0.299796i	$0.0969188\pi$
$492$	9.85636	−	2.09503i	0.444359	−	0.0944515i
$493$	2.86176	+	3.17831i	0.128887	+	0.143144i
$494$	−5.98292	+	4.34685i	−0.269185	+	0.195574i
$495$	0.567706	−	0.630502i	0.0255165	−	0.0283389i
$496$	6.55413	−	7.27910i	0.294289	−	0.326841i
$497$	40.3148	+	29.2904i	1.80836	+	1.31385i
$498$	27.9437	−	12.4413i	1.25219	−	0.557509i
$499$	0.811445	+	1.40546i	0.0363253	+	0.0629172i	0.883616	−	0.468211i	$-0.155101\pi$
$499$	0.811445	+	1.40546i	0.0363253	+	0.0629172i	−0.847291	+	0.531129i	$0.821768\pi$
$500$	−9.77817	−	4.35352i	−0.437293	−	0.194695i
$501$	−0.250964	−	2.38777i	−0.0112123	−	0.106678i
$502$	−0.500745	+	4.76428i	−0.0223494	+	0.212640i
$503$	−32.2354	−	23.4204i	−1.43730	−	1.04426i	−0.988597	−	0.150585i	$-0.951884\pi$
$503$	−32.2354	−	23.4204i	−1.43730	−	1.04426i	−0.448708	−	0.893679i	$-0.648116\pi$
$504$	19.6604	−	8.75339i	0.875745	−	0.389907i
$505$	0.326466	+	3.10612i	0.0145276	+	0.138221i
$506$	1.74052	+	1.26456i	0.0773756	+	0.0562167i
$507$	11.8820	+	2.52560i	0.527699	+	0.112166i
$508$	−7.93191	−	3.53151i	−0.351921	−	0.156686i
$509$	2.96430	+	3.29219i	0.131390	+	0.145924i	0.805250	−	0.592936i	$-0.202031\pi$
$509$	2.96430	+	3.29219i	0.131390	+	0.145924i	−0.673859	+	0.738860i	$0.735365\pi$
$510$	−15.6659	+	11.3819i	−0.693697	+	0.504001i
$511$	11.8429	−	5.27278i	0.523897	−	0.233254i
$512$	13.6422			0.602907
$513$	2.55026	+	7.84890i	0.112597	+	0.346538i
$514$	−1.17775	+	11.2055i	−0.0519482	+	0.494255i
$515$	−7.18221	+	7.97665i	−0.316486	+	0.351493i
$516$	4.79942	−	2.13684i	0.211283	−	0.0940692i
$517$	−2.28544			−0.100513
$518$	−13.1902	−	40.5952i	−0.579543	−	1.78365i
$519$	0.756284	+	1.30992i	0.0331972	+	0.0574992i
$520$	−3.67675	−	11.3159i	−0.161236	−	0.496233i
$521$	13.5151	+	41.5953i	0.592108	+	1.82232i	0.568624	+	0.822598i	$0.307476\pi$
$521$	13.5151	+	41.5953i	0.592108	+	1.82232i	0.0234843	+	0.999724i	$0.492524\pi$
$522$	0.117331	+	1.11633i	0.00513545	+	0.0488605i
$523$	13.3335	+	9.68733i	0.583032	+	0.423597i	0.839816	−	0.542871i	$-0.182663\pi$
$523$	13.3335	+	9.68733i	0.583032	+	0.423597i	−0.256784	+	0.966469i	$0.582663\pi$
$524$	−9.42071	+	2.00243i	−0.411545	+	0.0874767i
$525$	−8.77326	+	27.0013i	−0.382896	+	1.17843i
$526$	−4.80688	+	14.7941i	−0.209590	+	0.645052i
$527$	−42.9470	−	19.1212i	−1.87080	−	0.832933i
$528$	−0.509621	−	0.882690i	−0.0221784	−	0.0384141i
$529$	−3.58503	−	6.20946i	−0.155871	−	0.269976i
$530$	−6.51352	−	2.90001i	−0.282929	−	0.125968i
$531$	−4.04866	+	12.4605i	−0.175697	+	0.540740i
$532$	3.53072	−	10.8664i	0.153076	−	0.471120i
$533$	−13.3882	+	2.84574i	−0.579906	+	0.123263i
$534$	−19.7886	−	14.3773i	−0.856337	−	0.622165i
$535$	−2.37421	−	22.5891i	−0.102646	−	0.976612i
$536$	−9.36234	−	28.8143i	−0.404392	−	1.24459i
$537$	−14.7920	−	45.5252i	−0.638324	−	1.96456i
$538$	−8.43808	−	14.6152i	−0.363792	−	0.630105i
$539$	−1.67802	−	5.16442i	−0.0722775	−	0.222447i
$540$	−4.22543			−0.181834
$541$	4.01889	−	1.78932i	0.172786	−	0.0769291i	−0.318521	−	0.947916i	$-0.603186\pi$
$541$	4.01889	−	1.78932i	0.172786	−	0.0769291i	0.491307	+	0.870987i	$0.336519\pi$
$542$	13.6082	−	15.1134i	0.584521	−	0.649176i
$543$	−5.13867	+	48.8912i	−0.220521	+	2.09812i
$544$	−8.89812	−	27.3856i	−0.381504	−	1.17415i
$545$	29.0401			1.24394
$546$	−25.0686	+	11.1613i	−1.07284	+	0.477658i
$547$	−25.7955	+	18.7415i	−1.10293	+	0.801329i	−0.981537	−	0.191275i	$-0.938738\pi$
$547$	−25.7955	+	18.7415i	−1.10293	+	0.801329i	−0.121398	+	0.992604i	$0.538738\pi$
$548$	6.87980	+	7.64079i	0.293890	+	0.326398i
$549$	−12.0567	−	5.36801i	−0.514569	−	0.229101i
$550$	1.10584	+	0.235053i	0.0471530	+	0.0100227i
$551$	1.51500	+	1.10071i	0.0645410	+	0.0468918i
$552$	3.70552	+	35.2557i	0.157717	+	1.50058i
$553$	1.52293	−	0.678051i	0.0647615	−	0.0288337i
$554$	10.1345	+	7.36316i	0.430575	+	0.312831i
$555$	2.89831	−	27.5756i	0.123027	−	1.17052i
$556$	0.627167	+	5.96710i	0.0265978	+	0.253061i
$557$	24.6572	+	10.9781i	1.04476	+	0.465157i	0.856059	−	0.516878i	$-0.172906\pi$
$557$	24.6572	+	10.9781i	1.04476	+	0.465157i	0.188701	+	0.982035i	$0.439572\pi$
$558$	−6.16920	−	10.6854i	−0.261163	−	0.452348i
$559$	−6.51919	+	2.90253i	−0.275732	+	0.122764i
$560$	−6.84994	−	4.97677i	−0.289463	−	0.210307i
$561$	−3.27330	+	3.63537i	−0.138199	+	0.153486i
$562$	−9.91132	+	11.0076i	−0.418084	+	0.464329i
$563$	−8.06341	+	5.85841i	−0.339832	+	0.246902i	−0.744591	−	0.667521i	$-0.767355\pi$
$563$	−8.06341	+	5.85841i	−0.339832	+	0.246902i	0.404759	+	0.914423i	$0.367355\pi$
$564$	−8.01892	−	8.90592i	−0.337658	−	0.375007i
$565$	−16.1640	+	3.43576i	−0.680024	+	0.144544i
$566$	−3.69890	+	6.40668i	−0.155476	+	0.269293i
$567$	5.42866	+	51.6502i	0.227982	+	2.16911i
$568$	31.9825	−	6.79808i	1.34195	−	0.285241i
$569$	0.336867	−	3.20508i	0.0141222	−	0.134364i	−0.985189	−	0.171472i	$-0.945148\pi$
$569$	0.336867	−	3.20508i	0.0141222	−	0.134364i	0.999311	+	0.0371078i	$0.0118145\pi$
$570$	−5.67336	+	6.30090i	−0.237631	+	0.263916i
$571$	−3.60255	+	6.23981i	−0.150762	+	0.261128i	−0.931508	−	0.363721i	$-0.881506\pi$
$571$	−3.60255	+	6.23981i	−0.150762	+	0.261128i	0.780746	+	0.624849i	$0.214839\pi$
$572$	−0.478269	−	0.828386i	−0.0199974	−	0.0346366i
$573$	−26.3474	−	5.60032i	−1.10068	−	0.233957i
$574$	−16.1644	+	17.9523i	−0.674687	+	0.749316i
$575$	−12.8262	−	9.31879i	−0.534890	−	0.388620i
$576$	3.53487	−	10.8792i	0.147286	−	0.453300i
$577$	4.64147	+	14.2850i	0.193227	+	0.594691i	0.999993	+	0.00382000i	$0.00121595\pi$
$577$	4.64147	+	14.2850i	0.193227	+	0.594691i	−0.806766	+	0.590871i	$0.798784\pi$
$578$	16.4187	−	11.9289i	0.682929	−	0.496177i
$579$	−0.165083	+	1.57066i	−0.00686062	+	0.0652745i
$580$	−0.775675	+	0.563561i	−0.0322082	+	0.0234006i
$581$	32.0961	−	55.5922i	1.33157	−	2.30635i
$582$	1.90617	−	18.1360i	0.0790131	−	0.751760i
$583$	−1.76185	−	0.374492i	−0.0729683	−	0.0155099i
$584$	2.62851	−	8.08972i	0.108768	−	0.334755i
$585$	−6.04301			−0.249848
$586$	10.5535	+	11.7209i	0.435962	+	0.484185i
$587$	26.8212	+	5.70101i	1.10703	+	0.235306i	0.724934	−	0.688818i	$-0.241870\pi$
$587$	26.8212	+	5.70101i	1.10703	+	0.235306i	0.382093	+	0.924124i	$0.375203\pi$
$588$	14.2371	−	24.6593i	0.587127	−	1.01693i
$589$	−20.1344	−	4.27970i	−0.829623	−	0.176342i
$590$	12.5050	−	2.65801i	0.514821	−	0.109429i
$591$	29.8957	+	13.3104i	1.22975	+	0.547518i
$592$	−10.3161	−	4.59303i	−0.423990	−	0.188772i
$593$	16.1081	−	7.17180i	0.661481	−	0.294510i	−0.0484040	−	0.998828i	$-0.515414\pi$
$593$	16.1081	−	7.17180i	0.661481	−	0.294510i	0.709885	+	0.704317i	$0.248747\pi$
$594$	1.19278	−	0.253533i	0.0489402	−	0.0104026i
$595$	−12.5577	+	38.6486i	−0.514815	+	1.58444i
$596$	−3.38032			−0.138463
$597$	−22.9095	−	25.4436i	−0.937625	−	1.04134i
$598$	−1.60176	−	15.2397i	−0.0655008	−	0.623198i
$599$	−18.3109	−	20.3363i	−0.748162	−	0.830918i	0.242083	−	0.970256i	$-0.422169\pi$
$599$	−18.3109	−	20.3363i	−0.748162	−	0.830918i	−0.990245	+	0.139337i	$0.955503\pi$
$600$	9.31428	+	16.1328i	0.380254	+	0.658619i
$601$	−38.0085	+	27.6148i	−1.55040	+	1.12643i	−0.607030	+	0.794679i	$0.707639\pi$
$601$	−38.0085	+	27.6148i	−1.55040	+	1.12643i	−0.943367	+	0.331751i	$0.892361\pi$
$602$	−6.29744	+	10.9075i	−0.256665	+	0.444556i
$603$	−15.3877			−0.626636
$604$	−11.1607	+	2.65254i	−0.454124	+	0.107930i
$605$	15.7830			0.641670
$606$	2.36316	−	4.09312i	0.0959969	−	0.166271i
$607$	−7.70529	+	5.59822i	−0.312748	+	0.227225i	−0.733075	−	0.680148i	$-0.761915\pi$
$607$	−7.70529	+	5.59822i	−0.312748	+	0.227225i	0.420327	+	0.907373i	$0.361915\pi$
$608$	−6.30402	−	10.9189i	−0.255662	−	0.442819i
$609$	4.64953	+	5.16383i	0.188408	+	0.209249i
$610$	1.34612	+	12.8075i	0.0545028	+	0.518559i
$611$	10.8923	+	12.0972i	0.440656	+	0.489399i
$612$	−8.69605			−0.351517
$613$	4.92917	−	15.1704i	0.199087	−	0.612728i	−0.800817	−	0.598909i	$-0.795601\pi$
$613$	4.92917	−	15.1704i	0.199087	−	0.612728i	0.999905	−	0.0138188i	$-0.00439880\pi$
$614$	33.7401	−	7.17169i	1.36164	−	0.289426i
$615$	−14.3358	+	6.38269i	−0.578073	+	0.257375i
$616$	−4.84641	−	2.15776i	−0.195267	−	0.0869386i
$617$	44.3269	+	19.7356i	1.78454	+	0.794526i	0.979541	+	0.201244i	$0.0644984\pi$
$617$	44.3269	+	19.7356i	1.78454	+	0.794526i	0.804994	+	0.593282i	$0.202168\pi$
$618$	15.8881	−	3.37711i	0.639112	−	0.135847i
$619$	31.6801	+	6.73381i	1.27333	+	0.270655i	0.794506	−	0.607256i	$-0.207730\pi$
$619$	31.6801	+	6.73381i	1.27333	+	0.270655i	0.478824	+	0.877911i	$0.341063\pi$
$620$	5.26954	−	9.12710i	0.211630	−	0.366553i
$621$	−16.7268	−	3.55540i	−0.671225	−	0.142673i
$622$	−7.46616	−	8.29201i	−0.299366	−	0.332479i
$623$	−51.3319			−2.05657
$624$	−2.24337	+	6.90437i	−0.0898066	+	0.276396i
$625$	2.18809	+	0.465092i	0.0875235	+	0.0186037i
$626$	2.38210	−	22.6642i	0.0952078	−	0.905842i
$627$	−1.07097	+	1.85497i	−0.0427704	+	0.0740805i
$628$	4.73868	−	3.44285i	0.189094	−	0.137385i
$629$	−5.66524	+	53.9012i	−0.225888	+	2.14918i
$630$	−8.62862	+	6.26906i	−0.343773	+	0.249765i
$631$	−11.1156	−	34.2102i	−0.442504	−	1.36189i	−0.885198	−	0.465214i	$-0.845977\pi$
$631$	−11.1156	−	34.2102i	−0.442504	−	1.36189i	0.442694	−	0.896673i	$-0.354023\pi$
$632$	0.338012	−	1.04029i	0.0134454	−	0.0413807i
$633$	39.1070	+	28.4129i	1.55436	+	1.12931i
$634$	−20.7191	+	23.0109i	−0.822862	+	0.913881i
$635$	13.2260	+	2.81128i	0.524859	+	0.111562i
$636$	−4.72247	−	8.17957i	−0.187258	−	0.324341i
$637$	−19.3386	+	33.4955i	−0.766224	+	1.32714i
$638$	0.185147	−	0.205627i	0.00733005	−	0.00814084i
$639$	1.73586	−	16.5156i	0.0686694	−	0.653346i
$640$	2.60938	−	0.554640i	0.103145	−	0.0219241i
$641$	−0.291092	−	2.76956i	−0.0114974	−	0.109391i	0.987268	−	0.159066i	$-0.0508482\pi$
$641$	−0.291092	−	2.76956i	−0.0114974	−	0.109391i	−0.998765	+	0.0496748i	$0.984182\pi$
$642$	−17.1860	+	29.7670i	−0.678276	+	1.17481i
$643$	−24.5484	+	5.21792i	−0.968094	+	0.205775i	−0.664716	−	0.747096i	$-0.731448\pi$
$643$	−24.5484	+	5.21792i	−0.968094	+	0.205775i	−0.303377	+	0.952870i	$0.598114\pi$
$644$	15.8416	+	17.5938i	0.624245	+	0.693295i
$645$	−6.61903	+	4.80901i	−0.260624	+	0.189355i
$646$	11.0895	−	12.3162i	0.436312	−	0.484574i
$647$	26.7548	−	29.7142i	1.05184	−	1.16819i	0.0664644	−	0.997789i	$-0.478828\pi$
$647$	26.7548	−	29.7142i	1.05184	−	1.16819i	0.985375	−	0.170398i	$-0.0545052\pi$
$648$	27.5687	+	20.0298i	1.08300	+	0.786846i
$649$	2.95044	−	1.31362i	0.115815	−	0.0515641i
$650$	−4.02622	−	6.97361i	−0.157921	−	0.273527i
$651$	−69.7763	−	31.0664i	−2.73475	−	1.21759i
$652$	0.527980	+	5.02340i	0.0206773	+	0.196731i
$653$	−0.915798	+	8.71323i	−0.0358379	+	0.340975i	0.961881	+	0.273469i	$0.0881710\pi$
$653$	−0.915798	+	8.71323i	−0.0358379	+	0.340975i	−0.997719	+	0.0675065i	$0.978496\pi$
$654$	−35.5529	−	25.8307i	−1.39023	−	1.01006i
$655$	13.7021	−	6.10057i	0.535385	−	0.238369i
$656$	0.668036	+	6.35594i	0.0260824	+	0.248158i
$657$	−3.49508	−	2.53932i	−0.136356	−	0.0990684i
$658$	28.1025	+	5.97337i	1.09555	+	0.232866i
$659$	−13.5420	−	6.02929i	−0.527521	−	0.234868i	0.125654	−	0.992074i	$-0.459897\pi$
$659$	−13.5420	−	6.02929i	−0.527521	−	0.234868i	−0.653176	+	0.757206i	$0.726564\pi$
$660$	−0.733815	−	0.814984i	−0.0285637	−	0.0317232i
$661$	−4.98733	+	3.62351i	−0.193985	+	0.140938i	−0.680538	−	0.732713i	$-0.738254\pi$
$661$	−4.98733	+	3.62351i	−0.193985	+	0.140938i	0.486553	+	0.873651i	$0.338254\pi$
$662$	−10.5903	+	4.71511i	−0.411604	+	0.183258i
$663$	34.8430			1.35319
$664$	−13.0157	−	40.0581i	−0.505105	−	1.55455i
$665$	−1.85992	+	17.6959i	−0.0721244	+	0.686218i
$666$	−9.51814	+	10.5710i	−0.368820	+	0.409616i
$667$	−3.54479	+	1.57824i	−0.137255	+	0.0611098i
$668$	−1.05208			−0.0407064
$669$	−16.1568	−	49.7255i	−0.624658	−	1.92250i
$670$	7.50746	+	13.0033i	0.290039	+	0.502362i
$671$	1.00533	+	3.09409i	0.0388104	+	0.119446i
$672$	−14.4569	−	44.4937i	−0.557686	−	1.71638i
$673$	−3.77009	−	35.8700i	−0.145326	−	1.38269i	−0.787589	−	0.616201i	$-0.788671\pi$
$673$	−3.77009	−	35.8700i	−0.145326	−	1.38269i	0.642263	−	0.766485i	$-0.277996\pi$
$674$	−20.2706	−	14.7275i	−0.780795	−	0.567281i
$675$	−8.78978	+	1.86833i	−0.338319	+	0.0719119i
$676$	1.64491	−	5.06251i	0.0632657	−	0.194712i
$677$	12.8315	−	39.4913i	0.493155	−	1.51777i	−0.326658	−	0.945143i	$-0.605922\pi$
$677$	12.8315	−	39.4913i	0.493155	−	1.51777i	0.819812	−	0.572632i	$-0.194078\pi$
$678$	22.8451	+	10.1713i	0.877362	+	0.390627i
$679$	−19.1349	−	33.1426i	−0.734329	−	1.27190i
$680$	13.3321	+	23.0918i	0.511262	+	0.885532i
$681$	−10.5170	−	4.68246i	−0.403012	−	0.179432i
$682$	−0.939871	+	2.89263i	−0.0359895	+	0.110764i
$683$	10.3014	−	31.7046i	0.394174	−	1.21314i	−0.535429	−	0.844580i	$-0.679850\pi$
$683$	10.3014	−	31.7046i	0.394174	−	1.21314i	0.929603	−	0.368562i	$-0.120150\pi$
$684$	−3.72441	+	0.791649i	−0.142407	+	0.0302694i
$685$	−12.9539	−	9.41155i	−0.494943	−	0.359597i
$686$	3.64672	+	34.6962i	0.139232	+	1.32471i
$687$	3.23691	+	9.96217i	0.123496	+	0.380081i
$688$	1.02966	+	3.16897i	0.0392555	+	0.120816i
$689$	6.41467	+	11.1105i	0.244379	+	0.423278i
$690$	−5.42898	−	16.7087i	−0.206678	−	0.636088i
$691$	35.9587			1.36793			0.683966	−	0.729514i	$-0.260253\pi$
$691$	35.9587			1.36793			0.683966	+	0.729514i	$0.260253\pi$
$692$	0.605506	−	0.269589i	0.0230179	−	0.0102482i
$693$	−1.80290	+	2.00233i	−0.0684867	+	0.0760622i
$694$	−0.959158	+	9.12578i	−0.0364091	+	0.346410i
$695$	−2.88741	−	8.88655i	−0.109526	−	0.337086i
$696$	4.55931			0.172820
$697$	28.0217	−	12.4760i	1.06140	−	0.472564i
$698$	−8.09614	+	5.88219i	−0.306443	+	0.222644i
$699$	14.8251	+	16.4650i	0.560738	+	0.622763i
$700$	11.3653	+	5.06017i	0.429569	+	0.191256i
$701$	30.3992	+	6.46155i	1.14816	+	0.244049i	0.742418	−	0.669937i	$-0.233679\pi$
$701$	30.3992	+	6.46155i	1.14816	+	0.244049i	0.405744	+	0.913987i	$0.367012\pi$
$702$	−7.02673	−	5.10522i	−0.265207	−	0.192684i
$703$	2.48056	+	23.6010i	0.0935562	+	0.890128i
$704$	−2.57601	+	1.14691i	−0.0970871	+	0.0432260i
$705$	15.0987	+	10.9699i	0.568652	+	0.413150i
$706$	0.712465	−	6.77865i	0.0268140	−	0.255118i
$707$	−1.03678	−	9.86432i	−0.0389922	−	0.370986i
$708$	15.4711	+	6.88819i	0.581441	+	0.258874i
$709$	−8.37329	−	14.5030i	−0.314466	−	0.544670i	0.664858	−	0.746970i	$-0.268492\pi$
$709$	−8.37329	−	14.5030i	−0.314466	−	0.544670i	−0.979324	+	0.202299i	$0.935159\pi$
$710$	−14.8033	+	6.59085i	−0.555558	+	0.247350i
$711$	−0.449448	−	0.326543i	−0.0168556	−	0.0122463i
$712$	−22.5371	+	25.0300i	−0.844615	+	0.938040i
$713$	28.5398	−	31.6967i	1.06882	−	1.18705i
$714$	49.7513	−	36.1464i	1.86190	−	1.35275i
$715$	0.996761	+	1.10702i	0.0372768	+	0.0414000i
$716$	−20.5175	+	4.36112i	−0.766773	+	0.162983i
$717$	9.95879	−	17.2491i	0.371918	−	0.644181i
$718$	0.224788	+	2.13872i	0.00838902	+	0.0798162i
$719$	33.1768	−	7.05194i	1.23728	−	0.262993i	0.457596	−	0.889160i	$-0.348711\pi$
$719$	33.1768	−	7.05194i	1.23728	−	0.262993i	0.779689	+	0.626168i	$0.215377\pi$
$720$	−0.294942	+	2.80618i	−0.0109918	+	0.104580i
$721$	22.8090	−	25.3320i	0.849453	−	0.943413i
$722$	−6.18227	+	10.7080i	−0.230080	+	0.398511i
$723$	21.8911	+	37.9164i	0.814137	+	1.41013i
$724$	21.0714	+	4.47887i	0.783113	+	0.166456i
$725$	−1.36438	+	1.51530i	−0.0506719	+	0.0562768i
$726$	−19.3227	−	14.0387i	−0.717131	−	0.521026i
$727$	6.33633	−	19.5012i	0.235002	−	0.723260i	−0.762120	−	0.647436i	$-0.775841\pi$
$727$	6.33633	−	19.5012i	0.235002	−	0.723260i	0.997121	−	0.0758242i	$-0.0241588\pi$
$728$	11.6765	+	35.9366i	0.432760	+	1.33190i
$729$	−2.09571	+	1.52262i	−0.0776189	+	0.0563935i
$730$	−0.440639	+	4.19240i	−0.0163088	+	0.155168i
$731$	12.9380	−	9.40002i	0.478530	−	0.347672i
$732$	−8.52968	+	14.7738i	−0.315266	+	0.546057i
$733$	1.59489	−	15.1744i	0.0589086	−	0.560478i	−0.924768	−	0.380532i	$-0.875741\pi$
$733$	1.59489	−	15.1744i	0.0589086	−	0.560478i	0.983676	−	0.179946i	$-0.0575923\pi$
$734$	−12.8955	−	2.74103i	−0.475983	−	0.101173i
$735$	−13.7029	+	42.1731i	−0.505438	+	1.55558i
$736$	26.1249			0.962976
$737$	2.53812	+	2.81887i	0.0934928	+	0.103834i
$738$	7.87453	+	1.67378i	0.289866	+	0.0616128i
$739$	−15.8529	+	27.4580i	−0.583158	+	1.01006i	0.411945	+	0.911209i	$0.364850\pi$
$739$	−15.8529	+	27.4580i	−0.583158	+	1.01006i	−0.995102	+	0.0988501i	$0.968484\pi$
$740$	−11.8847	−	2.52617i	−0.436891	−	0.0928640i
$741$	14.9229	−	3.17195i	0.548205	−	0.116525i
$742$	20.6855	+	9.20976i	0.759387	+	0.338101i
$743$	−22.7535	−	10.1305i	−0.834744	−	0.371652i	−0.0555663	−	0.998455i	$-0.517696\pi$
$743$	−22.7535	−	10.1305i	−0.834744	−	0.371652i	−0.779178	+	0.626803i	$0.784363\pi$
$744$	−45.7835	+	20.3841i	−1.67850	+	0.747318i
$745$	5.14920	−	1.09450i	0.188652	−	0.0400993i
$746$	2.15335	−	6.62732i	0.0788396	−	0.242643i
$747$	−21.3922			−0.782700
$748$	1.43437	+	1.59302i	0.0524456	+	0.0582467i
$749$	7.53995	+	71.7378i	0.275504	+	2.62124i
$750$	−16.8786	−	18.7456i	−0.616319	−	0.684491i
$751$	23.6170	+	40.9059i	0.861798	+	1.49268i	0.870192	+	0.492713i	$0.163995\pi$
$751$	23.6170	+	40.9059i	0.861798	+	1.49268i	−0.00839348	+	0.999965i	$0.502672\pi$
$752$	6.14916	−	4.46763i	0.224237	−	0.162918i
$753$	4.94133	−	8.55864i	0.180072	−	0.311894i
$754$	−1.97082			−0.0717730
$755$	16.1422	−	7.65426i	0.587474	−	0.278567i
$756$	13.4190			0.488044
$757$	−13.7162	+	23.7572i	−0.498525	+	0.863470i	−0.999999	−	0.00170278i	$-0.999458\pi$
$757$	−13.7162	+	23.7572i	−0.498525	+	0.863470i	0.501474	+	0.865173i	$0.332791\pi$
$758$	−6.56879	+	4.77251i	−0.238589	+	0.173345i
$759$	−2.21913	−	3.84365i	−0.0805495	−	0.139516i
$760$	7.81215	+	8.67627i	0.283376	+	0.314721i
$761$	2.79610	+	26.6031i	0.101358	+	0.964361i	0.920493	+	0.390759i	$0.127787\pi$
$761$	2.79610	+	26.6031i	0.101358	+	0.964361i	−0.819135	+	0.573601i	$0.805546\pi$
$762$	−13.6917	−	15.2061i	−0.495996	−	0.550860i
$763$	−92.2247			−3.33876
$764$	−3.64745	+	11.2257i	−0.131960	+	0.406132i
$765$	13.2466	−	2.81565i	0.478932	−	0.101800i
$766$	1.47558	−	0.656970i	0.0533149	−	0.0237373i
$767$	−21.0149	−	9.35643i	−0.758803	−	0.337841i
$768$	−32.6265	−	14.5263i	−1.17731	−	0.524172i
$769$	8.55044	−	1.81745i	0.308337	−	0.0655390i	−0.0511446	−	0.998691i	$-0.516287\pi$
$769$	8.55044	−	1.81745i	0.308337	−	0.0655390i	0.359481	+	0.933152i	$0.382954\pi$
$770$	2.57167	+	0.546625i	0.0926766	+	0.0196990i
$771$	11.6220	−	20.1298i	0.418555	−	0.724958i
$772$	0.676933	+	0.143887i	0.0243634	+	0.00517859i
$773$	32.4887	+	36.0824i	1.16854	+	1.29779i	0.946481	+	0.322759i	$0.104610\pi$
$773$	32.4887	+	36.0824i	1.16854	+	1.29779i	0.222057	+	0.975034i	$0.428723\pi$
$774$	4.19727			0.150868
$775$	6.92608	−	21.3163i	0.248792	−	0.765703i
$776$	−24.5618	−	5.22078i	−0.881718	−	0.187415i
$777$	−9.20438	+	87.5738i	−0.330205	+	3.14169i
$778$	−4.34046	+	7.51789i	−0.155613	+	0.269530i
$779$	10.8656	−	7.89431i	0.389300	−	0.282843i
$780$	−0.816490	+	7.76838i	−0.0292350	+	0.278153i
$781$	−3.31180	+	2.40616i	−0.118505	+	0.0860993i
$782$	10.6119	+	32.6599i	0.379479	+	1.16792i
$783$	−0.679635	+	2.09170i	−0.0242882	+	0.0747513i
$784$	14.6104	+	10.6151i	0.521800	+	0.379110i
$785$	−6.10363	+	6.77877i	−0.217848	+	0.241945i
$786$	−22.2014	−	4.71906i	−0.791899	−	0.168323i
$787$	4.58124	+	7.93494i	0.163304	+	0.282850i	0.936052	−	0.351863i	$-0.114452\pi$
$787$	4.58124	+	7.93494i	0.163304	+	0.282850i	−0.772748	+	0.634713i	$0.781118\pi$
$788$	7.17006	−	12.4189i	0.255423	−	0.442405i
$789$	21.4726	−	23.8477i	0.764443	−	0.849000i
$790$	−0.0566638	+	0.539120i	−0.00201601	+	0.0191810i
$791$	51.3331	−	10.9112i	1.82519	−	0.387957i
$792$	0.184798	+	1.75824i	0.00656651	+	0.0624762i
$793$	11.5861	−	20.0677i	0.411434	−	0.712625i
$794$	36.9172	−	7.84699i	1.31014	−	0.278479i
$795$	9.84212	+	10.9308i	0.349064	+	0.387675i
$796$	−12.1377	+	8.81855i	−0.430209	+	0.312565i
$797$	2.57349	−	2.85815i	0.0911576	−	0.101241i	−0.695840	−	0.718197i	$-0.744968\pi$
$797$	2.57349	−	2.85815i	0.0911576	−	0.101241i	0.786998	+	0.616956i	$0.211634\pi$
$798$	18.0173	−	20.0102i	0.637805	−	0.708354i
$799$	−29.5130	−	21.4425i	−1.04410	−	0.758581i
$800$	12.5415	−	5.58383i	0.443409	−	0.197418i
$801$	8.55323	+	14.8146i	0.302213	+	0.523449i
$802$	19.6764	+	8.76049i	0.694797	+	0.309344i
$803$	0.111317	+	1.05911i	0.00392828	+	0.0373751i
$804$	−2.07908	+	19.7811i	−0.0733235	+	0.697627i
$805$	−29.8279	−	21.6712i	−1.05130	−	0.763811i
$806$	19.7905	−	8.81130i	0.697091	−	0.310365i
$807$	3.63915	+	34.6242i	0.128104	+	1.21883i
$808$	−5.26516	−	3.82536i	−0.185228	−	0.134576i
$809$	3.41151	+	0.725139i	0.119942	+	0.0254945i	0.267492	−	0.963560i	$-0.413805\pi$
$809$	3.41151	+	0.725139i	0.119942	+	0.0254945i	−0.147549	+	0.989055i	$0.547139\pi$
$810$	−15.4280	−	6.86899i	−0.542085	−	0.241352i
$811$	6.63324	+	7.36696i	0.232925	+	0.258689i	0.848264	−	0.529573i	$-0.177648\pi$
$811$	6.63324	+	7.36696i	0.232925	+	0.258689i	−0.615340	+	0.788262i	$0.710981\pi$
$812$	2.46337	−	1.78974i	0.0864472	−	0.0628076i
$813$	−38.3275	+	17.0645i	−1.34420	+	0.598478i
$814$	3.50645			0.122901
$815$	−2.43077	−	7.48114i	−0.0851461	−	0.262053i
$816$	1.70059	−	16.1800i	0.0595325	−	0.566414i
$817$	4.68546	−	5.20374i	0.163924	−	0.182056i
$818$	−27.2971	+	12.1535i	−0.954422	+	0.424936i
$819$	19.1912			0.670595
$820$	2.12494	+	6.53988i	0.0742060	+	0.228383i
$821$	8.80305	+	15.2473i	0.307229	+	0.532136i	0.977755	−	0.209750i	$-0.0672650\pi$
$821$	8.80305	+	15.2473i	0.307229	+	0.532136i	−0.670526	+	0.741886i	$0.733932\pi$
$822$	7.48763	+	23.0446i	0.261161	+	0.803772i
$823$	3.82149	+	11.7613i	0.133209	+	0.409974i	0.995307	−	0.0967666i	$-0.0308500\pi$
$823$	3.82149	+	11.7613i	0.133209	+	0.409974i	−0.862098	+	0.506741i	$0.830850\pi$
$824$	−2.33793	−	22.2439i	−0.0814456	−	0.774903i
$825$	−1.88684	−	1.37087i	−0.0656915	−	0.0477276i
$826$	−39.7129	+	8.44124i	−1.38179	+	0.293708i
$827$	−15.6009	+	48.0146i	−0.542496	+	1.66963i	0.184374	+	0.982856i	$0.440974\pi$
$827$	−15.6009	+	48.0146i	−0.542496	+	1.66963i	−0.726870	+	0.686775i	$0.759026\pi$
$828$	2.43805	−	7.50354i	0.0847280	−	0.260766i
$829$	20.0849	+	8.94238i	0.697578	+	0.310582i	0.724714	−	0.689050i	$-0.241972\pi$
$829$	20.0849	+	8.94238i	0.697578	+	0.310582i	−0.0271361	+	0.999632i	$0.508639\pi$
$830$	10.4370	+	18.0774i	0.362273	+	0.627475i
$831$	−12.9213	−	22.3804i	−0.448236	−	0.776368i
$832$	18.3480	+	8.16905i	0.636102	+	0.283211i
$833$	26.7846	−	82.4344i	0.928030	−	2.85618i
$834$	−4.36947	+	13.4478i	−0.151302	+	0.465661i
$835$	1.60263	−	0.340649i	0.0554613	−	0.0117887i
$836$	0.759343	+	0.551695i	0.0262624	+	0.0190808i
$837$	−2.52702	−	24.0430i	−0.0873464	−	0.831046i
$838$	1.15727	+	3.56170i	0.0399771	+	0.123037i
$839$	−7.25932	−	22.3419i	−0.250619	−	0.771327i	−0.994661	−	0.103194i	$-0.967094\pi$
$839$	−7.25932	−	22.3419i	−0.250619	−	0.771327i	0.744042	−	0.668133i	$-0.232906\pi$
$840$	21.6608	+	37.5175i	0.747367	+	1.29448i
$841$	−8.80728	−	27.1060i	−0.303699	−	0.934690i
$842$	−19.7465			−0.680509
$843$	27.9153	−	12.4287i	0.961454	−	0.428067i
$844$	14.1736	−	15.7414i	0.487876	−	0.541841i
$845$	−0.866507	+	8.24426i	−0.0298088	+	0.283611i
$846$	−2.95866	−	9.10583i	−0.101721	−	0.313065i
$847$	−50.1232			−1.72225
$848$	5.47247	−	2.43650i	0.187925	−	0.0836697i
$849$	12.3467	−	8.97042i	0.423738	−	0.307864i
$850$	12.0749	+	13.4106i	0.414167	+	0.459979i
$851$	−44.9213	−	20.0003i	−1.53988	−	0.685600i
$852$	−20.9965	−	4.46294i	−0.719328	−	0.152898i
$853$	2.98561	+	2.16917i	0.102225	+	0.0742711i	0.637724	−	0.770265i	$-0.279876\pi$
$853$	2.98561	+	2.16917i	0.102225	+	0.0742711i	−0.535498	+	0.844536i	$0.679876\pi$
$854$	−4.27496	−	40.6736i	−0.146286	−	1.39182i
$855$	5.41704	−	2.41182i	0.185259	−	0.0824825i
$856$	38.2906	+	27.8198i	1.30875	+	0.950860i
$857$	2.32322	−	22.1039i	0.0793596	−	0.755056i	−0.880400	−	0.474232i	$-0.842726\pi$
$857$	2.32322	−	22.1039i	0.0793596	−	0.755056i	0.959759	−	0.280824i	$-0.0906076\pi$
$858$	−0.235632	−	2.24189i	−0.00804435	−	0.0765368i
$859$	36.6582	+	16.3213i	1.25076	+	0.556875i	0.921873	−	0.387493i	$-0.126659\pi$
$859$	36.6582	+	16.3213i	1.25076	+	0.556875i	0.328890	+	0.944368i	$0.393326\pi$
$860$	1.79259	+	3.10485i	0.0611267	+	0.105875i
$861$	45.5271	−	20.2700i	1.55156	−	0.690798i
$862$	13.2981	+	9.66167i	0.452937	+	0.329078i
$863$	32.8200	−	36.4503i	1.11721	−	1.24078i	0.149483	−	0.988764i	$-0.452239\pi$
$863$	32.8200	−	36.4503i	1.11721	−	1.24078i	0.967723	−	0.252018i	$-0.0810942\pi$
$864$	9.90828	−	11.0043i	0.337086	−	0.374372i
$865$	−0.835072	+	0.606715i	−0.0283933	+	0.0206289i
$866$	7.85736	+	8.72648i	0.267004	+	0.296538i
$867$	−40.9523	+	8.70467i	−1.39081	+	0.295626i
$868$	−16.7348	+	28.9856i	−0.568017	+	0.983835i
$869$	0.0143147	+	0.136196i	0.000485594	+	0.00462012i
$870$	−2.21016	+	0.469785i	−0.0749316	+	0.0159272i
$871$	2.82407	−	26.8693i	0.0956901	−	0.910431i
$872$	−40.4911	+	44.9699i	−1.37120	+	1.52287i
$873$	−6.37673	+	11.0448i	−0.215820	+	0.373811i
$874$	7.51814	+	13.0218i	0.254305	+	0.440469i
$875$	−51.7796	−	11.0061i	−1.75047	−	0.372074i
$876$	−3.73657	+	4.14988i	−0.126247	+	0.140211i
$877$	−7.96436	−	5.78645i	−0.268937	−	0.195394i	0.445141	−	0.895461i	$-0.353154\pi$
$877$	−7.96436	−	5.78645i	−0.268937	−	0.195394i	−0.714078	+	0.700066i	$0.753154\pi$
$878$	−0.363593	+	1.11902i	−0.0122707	+	0.0377652i
$879$	−10.0545	−	30.9446i	−0.339130	−	1.04373i
$880$	0.562712	−	0.408834i	0.0189690	−	0.0137818i
$881$	4.64505	−	44.1947i	0.156496	−	1.48896i	−0.581165	−	0.813786i	$-0.697403\pi$
$881$	4.64505	−	44.1947i	0.156496	−	1.48896i	0.737661	−	0.675171i	$-0.235930\pi$
$882$	18.4042	−	13.3714i	0.619701	−	0.450239i
$883$	−13.0463	+	22.5969i	−0.439043	+	0.760445i	−0.997616	−	0.0690103i	$-0.978016\pi$
$883$	−13.0463	+	22.5969i	−0.439043	+	0.760445i	0.558573	+	0.829456i	$0.311349\pi$
$884$	1.59597	−	15.1846i	0.0536782	−	0.510714i
$885$	−25.7973	−	5.48339i	−0.867167	−	0.184322i
$886$	0.930711	−	2.86443i	0.0312678	−	0.0962325i
$887$	−0.325820			−0.0109400			−0.00546998	−	0.999985i	$-0.501741\pi$
$887$	−0.325820			−0.0109400			−0.00546998	+	0.999985i	$0.501741\pi$
$888$	38.6609	+	42.9373i	1.29737	+	1.44088i
$889$	−42.0029	−	8.92799i	−1.40873	−	0.299435i
$890$	8.34601	−	14.4557i	0.279759	−	0.484557i
$891$	−4.17313	−	0.887027i	−0.139805	−	0.0297165i
$892$	−22.4105	+	4.76349i	−0.750358	+	0.159493i
$893$	−14.5921	−	6.49683i	−0.488306	−	0.217408i
$894$	−7.27755	−	3.24018i	−0.243398	−	0.108368i
$895$	29.8420	−	13.2865i	0.997506	−	0.444119i
$896$	−8.28678	+	1.76141i	−0.276842	+	0.0588446i
$897$	−9.76869	+	30.0649i	−0.326167	+	1.00384i
$898$	−22.0951			−0.737324
$899$	−3.67059	−	4.07660i	−0.122421	−	0.135962i
$900$	−0.433370	−	4.12324i	−0.0144457	−	0.137441i
$901$	−19.2381	−	21.3661i	−0.640913	−	0.711807i
$902$	−0.992242	−	1.71861i	−0.0330380	−	0.0572236i
$903$	21.0205	−	15.2723i	0.699519	−	0.508231i
$904$	17.2173	−	29.8212i	0.572637	−	0.991837i
$905$	−33.5481			−1.11518
$906$	−26.5707	−	4.98733i	−0.882753	−	0.165693i
$907$	−32.7901			−1.08878			−0.544389	−	0.838833i	$-0.683238\pi$
$907$	−32.7901			−1.08878			−0.544389	+	0.838833i	$0.683238\pi$
$908$	−2.52234	+	4.36883i	−0.0837070	+	0.144985i
$909$	−2.67414	+	1.94287i	−0.0886955	+	0.0644410i
$910$	−9.36314	−	16.2174i	−0.310385	−	0.537603i
$911$	−24.1091	−	26.7758i	−0.798769	−	0.887123i	0.196868	−	0.980430i	$-0.436923\pi$
$911$	−24.1091	−	26.7758i	−0.798769	−	0.887123i	−0.995637	+	0.0933072i	$0.970256\pi$
$912$	−0.744613	−	7.08452i	−0.0246566	−	0.234592i
$913$	3.52853	+	3.91883i	0.116777	+	0.129694i
$914$	7.88672			0.260870
$915$	8.20962	−	25.2666i	0.271402	−	0.835288i
$916$	4.48979	−	0.954333i	0.148347	−	0.0315321i
$917$	−43.5147	+	19.3740i	−1.43698	+	0.639786i
$918$	17.7817	+	7.91690i	0.586882	+	0.261297i
$919$	−0.312300	−	0.139045i	−0.0103018	−	0.00458667i	0.401579	−	0.915824i	$-0.368461\pi$
$919$	−0.312300	−	0.139045i	−0.0103018	−	0.00458667i	−0.411881	+	0.911238i	$0.635128\pi$
$920$	−23.6630	+	5.02973i	−0.780147	+	0.165825i
$921$	−69.6047	−	14.7949i	−2.29355	−	0.487510i
$922$	−3.87905	+	6.71871i	−0.127750	+	0.221269i
$923$	28.5201	+	6.06214i	0.938751	+	0.199538i
$924$	2.33043	+	2.58820i	0.0766654	+	0.0851456i
$925$	−25.8397			−0.849603
$926$	10.3468	−	31.8441i	0.340016	−	1.04646i
$927$	−11.1115	−	2.36182i	−0.364950	−	0.0775725i
$928$	0.351215	−	3.34159i	0.0115292	−	0.109693i
$929$	−7.37316	+	12.7707i	−0.241906	+	0.418993i	−0.961257	−	0.275653i	$-0.911106\pi$
$929$	−7.37316	+	12.7707i	−0.241906	+	0.418993i	0.719351	+	0.694646i	$0.244439\pi$
$930$	20.0936	−	14.5988i	0.658895	−	0.478715i
$931$	3.96706	−	37.7440i	0.130015	−	1.23701i
$932$	7.85450	−	5.70663i	0.257283	−	0.186927i
$933$	7.11313	+	21.8920i	0.232873	+	0.716711i
$934$	−7.19319	+	22.1384i	−0.235368	+	0.724389i
$935$	−2.70075	−	1.96221i	−0.0883240	−	0.0641711i
$936$	8.42586	−	9.35786i	0.275408	−	0.305871i
$937$	28.8017	+	6.12200i	0.940912	+	0.199997i	0.652740	−	0.757582i	$-0.273619\pi$
$937$	28.8017	+	6.12200i	0.940912	+	0.199997i	0.288172	+	0.957579i	$0.406953\pi$
$938$	−23.8420	−	41.2955i	−0.778468	−	1.34835i
$939$	−23.5064	+	40.7144i	−0.767104	+	1.32866i
$940$	5.47227	−	6.07757i	0.178486	−	0.198228i
$941$	−0.917778	+	8.73207i	−0.0299187	+	0.284657i	0.969325	+	0.245781i	$0.0790445\pi$
$941$	−0.917778	+	8.73207i	−0.0299187	+	0.284657i	−0.999244	+	0.0388762i	$0.987622\pi$
$942$	13.5021	−	2.86996i	0.439922	−	0.0935083i
$943$	2.90895	+	27.6768i	0.0947285	+	0.901281i
$944$	−5.37051	+	9.30199i	−0.174795	+	0.302754i
$945$	−20.4410	+	4.34487i	−0.664947	+	0.141339i
$946$	−0.692317	−	0.768896i	−0.0225092	−	0.0249990i
$947$	31.3078	−	22.7464i	1.01737	−	0.739160i	0.0516247	−	0.998667i	$-0.483560\pi$
$947$	31.3078	−	22.7464i	1.01737	−	0.739160i	0.965741	+	0.259507i	$0.0835600\pi$
$948$	−0.480503	+	0.533652i	−0.0156060	+	0.0173322i
$949$	5.07548	−	5.63690i	0.164757	−	0.182981i
$950$	6.39238	+	4.64434i	0.207396	+	0.150682i
$951$	58.3556	−	25.9816i	1.89231	−	0.842511i
$952$	−42.3396	−	73.3344i	−1.37224	−	2.37678i
$953$	−51.8132	−	23.0687i	−1.67839	−	0.747269i	−0.999920	−	0.0126453i	$-0.995975\pi$
$953$	−51.8132	−	23.0687i	−1.67839	−	0.747269i	−0.678474	−	0.734624i	$-0.737359\pi$
$954$	−0.788755	−	7.50451i	−0.0255369	−	0.242967i
$955$	1.92141	−	18.2810i	0.0621753	−	0.591559i
$956$	−7.06102	−	5.13013i	−0.228370	−	0.165920i
$957$	−0.521468	+	0.232173i	−0.0168567	+	0.00750508i
$958$	−2.68365	−	25.5332i	−0.0867046	−	0.824940i
$959$	41.1386	+	29.8889i	1.32843	+	0.965164i
$960$	22.5235	+	4.78752i	0.726943	+	0.154517i
$961$	26.7653	+	11.9167i	0.863396	+	0.384409i
$962$	−16.7117	−	18.5602i	−0.538805	−	0.598404i
$963$	19.4475	−	14.1294i	0.626687	−	0.455315i
$964$	17.5267	−	7.80339i	0.564497	−	0.251330i
$965$	−1.07775			−0.0346941
$966$	17.2412	+	53.0629i	0.554726	+	1.70727i
$967$	1.09493	−	10.4176i	0.0352106	−	0.335006i	−0.962709	−	0.270538i	$-0.912798\pi$
$967$	1.09493	−	10.4176i	0.0352106	−	0.335006i	0.997920	−	0.0644678i	$-0.0205350\pi$
$968$	−22.0065	+	24.4407i	−0.707315	+	0.785553i
$969$	−31.2338	+	13.9062i	−1.00337	+	0.446731i
$970$	12.4445			0.399569
$971$	15.0448	+	46.3032i	0.482811	+	1.48594i	0.835126	+	0.550059i	$0.185395\pi$
$971$	15.0448	+	46.3032i	0.482811	+	1.48594i	−0.352314	+	0.935882i	$0.614605\pi$
$972$	−6.82609	−	11.8231i	−0.218947	−	0.379227i
$973$	9.16976	+	28.2216i	0.293969	+	0.904744i
$974$	8.25397	+	25.4031i	0.264474	+	0.813968i
$975$	1.73641	+	16.5209i	0.0556098	+	0.529091i
$976$	−8.75333	−	6.35967i	−0.280187	−	0.203568i
$977$	26.6122	−	5.65659i	0.851399	−	0.180970i	0.238510	−	0.971140i	$-0.423341\pi$
$977$	26.6122	−	5.65659i	0.851399	−	0.180970i	0.612888	+	0.790170i	$0.290008\pi$
$978$	−3.67844	+	11.3211i	−0.117623	+	0.362008i
$979$	1.30307	−	4.01045i	0.0416465	−	0.128175i
$980$	17.7514	+	7.90343i	0.567047	+	0.252466i
$981$	15.3670	+	26.6165i	0.490632	+	0.849799i
$982$	−4.97407	−	8.61534i	−0.158729	−	0.274927i
$983$	−28.9869	−	12.9058i	−0.924539	−	0.411631i	−0.111450	−	0.993770i	$-0.535549\pi$
$983$	−28.9869	−	12.9058i	−0.924539	−	0.411631i	−0.813090	+	0.582139i	$0.802216\pi$
$984$	10.1047	−	31.0990i	0.322125	−	0.991400i
$985$	−6.90101	+	21.2391i	−0.219885	+	0.676735i
$986$	4.32014	−	0.918274i	0.137581	−	0.0292438i
$987$	−47.9501	−	34.8378i	−1.52627	−	1.10890i
$988$	−0.698804	−	6.64868i	−0.0222319	−	0.211523i
$989$	4.48364	+	13.7992i	0.142571	+	0.438790i
$990$	−0.270748	−	0.833278i	−0.00860495	−	0.0264833i
$991$	17.1864	+	29.7677i	0.545944	+	0.945603i	0.998547	+	0.0538905i	$0.0171622\pi$
$991$	17.1864	+	29.7677i	0.545944	+	0.945603i	−0.452603	+	0.891712i	$0.649504\pi$
$992$	11.4130	+	35.1257i	0.362364	+	1.11524i
$993$	23.9150			0.758920
$994$	47.0119	−	20.9310i	1.49113	−	0.663892i
$995$	15.6339	−	17.3632i	0.495628	−	0.550451i
$996$	−2.89037	+	27.5000i	−0.0915848	+	0.871371i
$997$	4.67681	+	14.3937i	0.148116	+	0.455854i	0.997399	−	0.0720845i	$-0.0229651\pi$
$997$	4.67681	+	14.3937i	0.148116	+	0.455854i	−0.849283	+	0.527939i	$0.822965\pi$
$998$	1.67595			0.0530511
$999$	−25.4616	+	11.3362i	−0.805569	+	0.358662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.2.8	✓	96
151.76	even	15	inner	151.2.g.a.76.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.2.8	✓	96	1.1	even	1	trivial
151.2.g.a.76.8	yes	96	151.76	even	15	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.516346 - 0.894338i) q^{2} +(-1.72354 + 1.25222i) q^{3} +(0.466773 + 0.808475i) q^{4} +(-0.972803 - 1.08041i) q^{5} +(0.229968 + 2.18800i) q^{6} +(3.08940 + 3.43113i) q^{7} +3.02945 q^{8} +(0.475465 - 1.46333i) q^{9} +O(q^{10})\)	\(q+(0.516346 - 0.894338i) q^{2} +(-1.72354 + 1.25222i) q^{3} +(0.466773 + 0.808475i) q^{4} +(-0.972803 - 1.08041i) q^{5} +(0.229968 + 2.18800i) q^{6} +(3.08940 + 3.43113i) q^{7} +3.02945 q^{8} +(0.475465 - 1.46333i) q^{9} +(-1.46855 + 0.312150i) q^{10} +(-0.346492 + 0.154268i) q^{11} +(-1.81689 - 0.808932i) q^{12} +(2.46793 + 1.09879i) q^{13} +(4.66378 - 0.991318i) q^{14} +(3.02957 + 0.643955i) q^{15} +(0.630699 - 1.09240i) q^{16} +(-5.92181 - 1.25872i) q^{17} +(-1.06321 - 1.18081i) q^{18} -2.65083 q^{19} +(0.419404 - 1.29079i) q^{20} +(-9.62122 - 2.04505i) q^{21} +(-0.0409419 + 0.389536i) q^{22} +(2.74636 - 4.75684i) q^{23} +(-5.22137 + 3.79355i) q^{24} +(0.301708 - 2.87056i) q^{25} +(2.25700 - 1.63981i) q^{26} +(-0.962063 - 2.96093i) q^{27} +(-1.33193 + 4.09926i) q^{28} +(-0.571518 - 0.415232i) q^{29} +(2.14022 - 2.37696i) q^{30} +(7.59551 + 1.61447i) q^{31} +(2.37813 + 4.11905i) q^{32} +(0.404013 - 0.699771i) q^{33} +(-4.18342 + 4.64616i) q^{34} +(0.701636 - 6.67562i) q^{35} +(1.40500 - 0.298642i) q^{36} +(-0.935769 - 8.90325i) q^{37} +(-1.36875 + 2.37074i) q^{38} +(-5.62951 + 1.19659i) q^{39} +(-2.94706 - 3.27304i) q^{40} +(-4.09894 + 2.97805i) q^{41} +(-6.79685 + 7.54867i) q^{42} +(-1.76755 + 1.96306i) q^{43} +(-0.286455 - 0.208122i) q^{44} +(-2.04353 + 0.909836i) q^{45} +(-2.83615 - 4.91235i) q^{46} +(5.50474 + 2.45087i) q^{47} +(0.280898 + 2.67257i) q^{48} +(-1.49653 + 14.2386i) q^{49} +(-2.41147 - 1.75203i) q^{50} +(11.7826 - 5.24597i) q^{51} +(0.263617 + 2.50815i) q^{52} +(3.84201 + 2.79138i) q^{53} +(-3.14482 - 0.668453i) q^{54} +(0.503741 + 0.224280i) q^{55} +(9.35918 + 10.3944i) q^{56} +(4.56880 - 3.31943i) q^{57} +(-0.666459 + 0.296727i) q^{58} -8.51517 q^{59} +(0.893501 + 2.74991i) q^{60} +(0.896599 - 8.53057i) q^{61} +(5.36580 - 5.95932i) q^{62} +(6.48977 - 2.88943i) q^{63} +7.43455 q^{64} +(-1.21367 - 3.73528i) q^{65} +(-0.417221 - 0.722648i) q^{66} +(-3.09044 - 9.51140i) q^{67} +(-1.74650 - 5.37517i) q^{68} +(1.22317 + 11.6376i) q^{69} +(-5.60797 - 4.07443i) q^{70} +(10.5572 - 2.24400i) q^{71} +(1.44040 - 4.43309i) q^{72} +(0.867652 - 2.67036i) q^{73} +(-8.44569 - 3.76026i) q^{74} +(3.07458 + 5.32532i) q^{75} +(-1.23734 - 2.14313i) q^{76} +(-1.59976 - 0.712261i) q^{77} +(-1.83662 + 5.65254i) q^{78} +(0.111575 - 0.343394i) q^{79} +(-1.79378 + 0.381281i) q^{80} +(9.10023 + 6.61171i) q^{81} +(0.546914 + 5.20354i) q^{82} +(-4.29637 - 13.2229i) q^{83} +(-2.83755 - 8.73309i) q^{84} +(4.40082 + 7.62245i) q^{85} +(0.842973 + 2.59440i) q^{86} +1.50499 q^{87} +(-1.04968 + 0.467348i) q^{88} +(-7.43935 + 8.26224i) q^{89} +(-0.241466 + 2.29739i) q^{90} +(3.85433 + 11.8624i) q^{91} +5.12772 q^{92} +(-15.1128 + 6.72866i) q^{93} +(5.03425 - 3.65760i) q^{94} +(2.57873 + 2.86397i) q^{95} +(-9.25676 - 4.12138i) q^{96} +(-8.10768 - 1.72334i) q^{97} +(11.9614 + 8.69044i) q^{98} +(0.0610005 + 0.580381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

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Database

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