LMFDB - Embedded newform 91.2.h.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$1.16700 + 2.02131i$ of defining polynomial
Character	$\chi$	$=$	91.16
Dual form			91.2.h.b.74.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90556 q^{2} +(-0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(0.736565 - 1.27577i) q^{5} +(0.408216 - 0.707051i) q^{6} +(1.58334 + 2.11968i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})$	\(q-1.90556 q^{2} +(-0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(0.736565 - 1.27577i) q^{5} +(0.408216 - 0.707051i) q^{6} +(1.58334 + 2.11968i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +(-1.40357 + 2.43105i) q^{10} +(2.19681 - 3.80498i) q^{11} +(-0.349433 + 0.605236i) q^{12} +(2.69752 + 2.39236i) q^{13} +(-3.01715 - 4.03917i) q^{14} +(0.315580 + 0.546600i) q^{15} -4.60164 q^{16} -1.20271 q^{17} +(-2.68344 - 4.64786i) q^{18} +(-1.62105 - 2.80773i) q^{19} +(1.20145 - 2.08098i) q^{20} +(-1.12569 + 0.133408i) q^{21} +(-4.18615 + 7.25062i) q^{22} -4.43710 q^{23} +(-0.150567 + 0.260790i) q^{24} +(1.41494 + 2.45075i) q^{25} +(-5.14029 - 4.55878i) q^{26} -2.49204 q^{27} +(2.58268 + 3.45753i) q^{28} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 - 1.04158i) q^{30} +(-2.62272 - 4.54268i) q^{31} +7.36300 q^{32} +(0.941217 + 1.63024i) q^{33} +2.29184 q^{34} +(3.87045 - 0.458697i) q^{35} +(2.29702 + 3.97856i) q^{36} +7.05055 q^{37} +(3.08900 + 5.35031i) q^{38} +(-1.46555 + 0.488407i) q^{39} +(0.517694 - 0.896672i) q^{40} +(-2.58195 - 4.47206i) q^{41} +(2.14507 - 0.254217i) q^{42} +(-0.0113752 + 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} +4.14897 q^{45} +8.45516 q^{46} +(-5.84178 + 10.1183i) q^{47} +(0.985780 - 1.70742i) q^{48} +(-1.98606 + 6.71235i) q^{49} +(-2.69626 - 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(4.40009 + 3.90231i) q^{52} +(0.0708929 + 0.122790i) q^{53} +4.74873 q^{54} +(-3.23618 - 5.60523i) q^{55} +(1.11285 + 1.48981i) q^{56} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} -5.34354 q^{59} +(0.514760 + 0.891591i) q^{60} +(-5.77287 - 9.99891i) q^{61} +(4.99774 + 8.65635i) q^{62} +(-2.94042 + 6.84690i) q^{63} -4.82736 q^{64} +(5.03899 - 1.67929i) q^{65} +(-1.79355 - 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} -1.96181 q^{68} +(0.950533 - 1.64637i) q^{69} +(-7.37537 + 0.874075i) q^{70} +(4.98486 - 8.63403i) q^{71} +(0.989763 + 1.71432i) q^{72} +(-7.62080 - 13.1996i) q^{73} -13.4352 q^{74} -1.21246 q^{75} +(-2.64418 - 4.57986i) q^{76} +(11.5436 - 1.36807i) q^{77} +(2.79269 - 0.930689i) q^{78} +(-0.387251 + 0.670738i) q^{79} +(-3.38941 + 5.87062i) q^{80} +(-3.69080 + 6.39265i) q^{81} +(4.92006 + 8.52179i) q^{82} -16.0186 q^{83} +(-1.83618 + 0.217610i) q^{84} +(-0.885875 + 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} +0.0717913 q^{87} +(1.54402 - 2.67433i) q^{88} +6.55760 q^{89} -7.90611 q^{90} +(-0.799921 + 9.50579i) q^{91} -7.23762 q^{92} +2.24739 q^{93} +(11.1319 - 19.2809i) q^{94} -4.77602 q^{95} +(-1.57733 + 2.73202i) q^{96} +(-1.74583 + 3.02387i) q^{97} +(3.78455 - 12.7908i) q^{98} +12.3743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20} - 9 q^{21} - 5 q^{22} + 2 q^{23} - 11 q^{24} + 7 q^{25} - 16 q^{26} - 8 q^{27} - q^{28} + 3 q^{29} - 5 q^{30} + 16 q^{31} - 16 q^{32} + 16 q^{33} + 32 q^{34} + 20 q^{35} - 21 q^{36} + 26 q^{37} - 17 q^{38} - 20 q^{39} - 5 q^{40} - 8 q^{41} + 50 q^{42} - 11 q^{43} + 21 q^{44} + 14 q^{45} - 32 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} + 41 q^{52} - 2 q^{53} + 36 q^{54} + 9 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} - 26 q^{59} + 20 q^{60} - 5 q^{61} + 5 q^{62} - 40 q^{63} - 30 q^{64} - 5 q^{65} + 18 q^{66} - 11 q^{67} - 58 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 6 q^{74} + 6 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} - 46 q^{84} - q^{85} - 7 q^{86} - 32 q^{87} - 8 q^{89} - 16 q^{90} - 23 q^{91} + 54 q^{92} + 14 q^{93} + 45 q^{94} + 12 q^{95} + 19 q^{96} - 35 q^{97} + 20 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.90556			−1.34743			−0.673717	−	0.738989i	$-0.735303\pi$
$2$	−1.90556			−1.34743			−0.673717	+	0.738989i	$0.735303\pi$
$3$	−0.214224	+	0.371047i	−0.123682	+	0.214224i	−0.921217	−	0.389049i	$-0.872804\pi$
$3$	−0.214224	+	0.371047i	−0.123682	+	0.214224i	0.797535	+	0.603273i	$0.206137\pi$
$4$	1.63116			0.815580
$5$	0.736565	−	1.27577i	0.329402	−	0.570541i	−0.652991	−	0.757365i	$-0.726486\pi$
$5$	0.736565	−	1.27577i	0.329402	−	0.570541i	0.982393	+	0.186825i	$0.0598196\pi$
$6$	0.408216	−	0.707051i	0.166654	−	0.288653i
$7$	1.58334	+	2.11968i	0.598447	+	0.801162i
$7$	1.58334	+	2.11968i	0.598447	+	0.801162i
$8$	0.702849			0.248495
$9$	1.40822	+	2.43910i	0.469405	+	0.813034i
$10$	−1.40357	+	2.43105i	−0.443847	+	0.768766i
$11$	2.19681	−	3.80498i	0.662362	−	1.14725i	−0.317631	−	0.948214i	$-0.602887\pi$
$11$	2.19681	−	3.80498i	0.662362	−	1.14725i	0.979993	−	0.199031i	$-0.0637794\pi$
$12$	−0.349433	+	0.605236i	−0.100873	+	0.174717i
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$14$	−3.01715	−	4.03917i	−0.806368	−	1.07951i
$15$	0.315580	+	0.546600i	0.0814823	+	0.141131i
$16$	−4.60164			−1.15041
$17$	−1.20271			−0.291700			−0.145850	−	0.989307i	$-0.546592\pi$
$17$	−1.20271			−0.291700			−0.145850	+	0.989307i	$0.546592\pi$
$18$	−2.68344	−	4.64786i	−0.632493	−	1.09551i
$19$	−1.62105	−	2.80773i	−0.371893	−	0.644138i	0.617963	−	0.786207i	$-0.287958\pi$
$19$	−1.62105	−	2.80773i	−0.371893	−	0.644138i	−0.989857	+	0.142068i	$0.954625\pi$
$20$	1.20145	−	2.08098i	0.268653	−	0.465321i
$21$	−1.12569	+	0.133408i	−0.245645	+	0.0291121i
$22$	−4.18615	+	7.25062i	−0.892490	+	1.54584i
$23$	−4.43710			−0.925200			−0.462600	−	0.886567i	$-0.653083\pi$
$23$	−4.43710			−0.925200			−0.462600	+	0.886567i	$0.653083\pi$
$24$	−0.150567	+	0.260790i	−0.0307343	+	0.0532334i
$25$	1.41494	+	2.45075i	0.282989	+	0.490151i
$26$	−5.14029	−	4.55878i	−1.00809	−	0.894050i
$27$	−2.49204			−0.479593
$28$	2.58268	+	3.45753i	0.488081	+	0.653412i
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	0.858142	−	0.513413i	$-0.171619\pi$
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	−0.873699	+	0.486466i	$0.838286\pi$
$30$	−0.601356	−	1.04158i	−0.109792	−	0.190165i
$31$	−2.62272	−	4.54268i	−0.471054	−	0.815889i	0.528398	−	0.848997i	$-0.322793\pi$
$31$	−2.62272	−	4.54268i	−0.471054	−	0.815889i	−0.999452	+	0.0331076i	$0.989460\pi$
$32$	7.36300			1.30161
$33$	0.941217	+	1.63024i	0.163845	+	0.283788i
$34$	2.29184			0.393047
$35$	3.87045	−	0.458697i	0.654225	−	0.0775340i
$36$	2.29702	+	3.97856i	0.382837	+	0.663094i
$37$	7.05055			1.15910			0.579552	−	0.814936i	$-0.303228\pi$
$37$	7.05055			1.15910			0.579552	+	0.814936i	$0.303228\pi$
$38$	3.08900	+	5.35031i	0.501102	+	0.867934i
$39$	−1.46555	+	0.488407i	−0.234676	+	0.0782077i
$40$	0.517694	−	0.896672i	0.0818546	−	0.141776i
$41$	−2.58195	−	4.47206i	−0.403233	−	0.698419i	0.590881	−	0.806758i	$-0.298780\pi$
$41$	−2.58195	−	4.47206i	−0.403233	−	0.698419i	−0.994114	+	0.108339i	$0.965447\pi$
$42$	2.14507	−	0.254217i	0.330991	−	0.0392266i
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	−0.866891	−	0.498497i	$-0.833886\pi$
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	0.865157	+	0.501502i	$0.167219\pi$
$44$	3.58334	−	6.20653i	0.540209	−	0.935670i
$45$	4.14897			0.618492
$46$	8.45516			1.24665
$47$	−5.84178	+	10.1183i	−0.852111	+	1.47590i	0.0271891	+	0.999630i	$0.491344\pi$
$47$	−5.84178	+	10.1183i	−0.852111	+	1.47590i	−0.879300	+	0.476269i	$0.841989\pi$
$48$	0.985780	−	1.70742i	0.142285	−	0.246445i
$49$	−1.98606	+	6.71235i	−0.283722	+	0.958906i
$50$	−2.69626	−	4.67006i	−0.381309	−	0.660446i
$51$	0.257649	−	0.446262i	0.0360781	−	0.0624892i
$52$	4.40009	+	3.90231i	0.610183	+	0.541154i
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	0.870853	−	0.491543i	$-0.163567\pi$
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	−0.861115	+	0.508410i	$0.830234\pi$
$54$	4.74873			0.646220
$55$	−3.23618	−	5.60523i	−0.436367	−	0.755809i
$56$	1.11285	+	1.48981i	0.148711	+	0.199084i
$57$	1.38907			0.183986
$58$	0.159649	+	0.276520i	0.0209630	+	0.0363089i
$59$	−5.34354			−0.695670			−0.347835	−	0.937556i	$-0.613083\pi$
$59$	−5.34354			−0.695670			−0.347835	+	0.937556i	$0.613083\pi$
$60$	0.514760	+	0.891591i	0.0664553	+	0.115104i
$61$	−5.77287	−	9.99891i	−0.739141	−	1.28023i	−0.952883	−	0.303339i	$-0.901898\pi$
$61$	−5.77287	−	9.99891i	−0.739141	−	1.28023i	0.213742	−	0.976890i	$-0.431435\pi$
$62$	4.99774	+	8.65635i	0.634714	+	1.09936i
$63$	−2.94042	+	6.84690i	−0.370458	+	0.862628i
$64$	−4.82736			−0.603420
$65$	5.03899	−	1.67929i	0.625010	−	0.208290i
$66$	−1.79355	−	3.10651i	−0.220770	−	0.382385i
$67$	−2.06773	+	3.58141i	−0.252613	+	0.437539i	−0.964245	−	0.265014i	$-0.914623\pi$
$67$	−2.06773	+	3.58141i	−0.252613	+	0.437539i	0.711631	+	0.702553i	$0.247957\pi$
$68$	−1.96181			−0.237905
$69$	0.950533	−	1.64637i	0.114431	−	0.198200i
$70$	−7.37537	+	0.874075i	−0.881526	+	0.104472i
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	−0.402424	−	0.915453i	$-0.631832\pi$
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	0.994018	−	0.109217i	$-0.0348344\pi$
$72$	0.989763	+	1.71432i	0.116645	+	0.202035i
$73$	−7.62080	−	13.1996i	−0.891947	−	1.54490i	−0.837539	−	0.546378i	$-0.816006\pi$
$73$	−7.62080	−	13.1996i	−0.891947	−	1.54490i	−0.0544080	−	0.998519i	$-0.517327\pi$
$74$	−13.4352			−1.56182
$75$	−1.21246			−0.140003
$76$	−2.64418	−	4.57986i	−0.303309	−	0.525346i
$77$	11.5436	−	1.36807i	1.31552	−	0.155906i
$78$	2.79269	−	0.930689i	0.316210	−	0.105380i
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	−0.886988	−	0.461793i	$-0.847206\pi$
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	0.843418	+	0.537257i	$0.180540\pi$
$80$	−3.38941	+	5.87062i	−0.378947	+	0.656356i
$81$	−3.69080	+	6.39265i	−0.410088	+	0.710294i
$82$	4.92006	+	8.52179i	0.543329	+	0.941074i
$83$	−16.0186			−1.75827			−0.879136	−	0.476571i	$-0.841879\pi$
$83$	−16.0186			−1.75827			−0.879136	+	0.476571i	$0.841879\pi$
$84$	−1.83618	+	0.217610i	−0.200343	+	0.0237432i
$85$	−0.885875	+	1.53438i	−0.0960866	+	0.166427i
$86$	0.0216761	−	0.0375441i	0.00233740	−	0.00404849i
$87$	0.0717913			0.00769683
$88$	1.54402	−	2.67433i	0.164593	−	0.285084i
$89$	6.55760			0.695104			0.347552	−	0.937661i	$-0.387013\pi$
$89$	6.55760			0.695104			0.347552	+	0.937661i	$0.387013\pi$
$90$	−7.90611			−0.833378
$91$	−0.799921	+	9.50579i	−0.0838545	+	0.996478i
$92$	−7.23762			−0.754574
$93$	2.24739			0.233044
$94$	11.1319	−	19.2809i	1.14816	−	1.98868i
$95$	−4.77602			−0.490010
$96$	−1.57733	+	2.73202i	−0.160986	+	0.278835i
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	−0.940942	−	0.338568i	$-0.890057\pi$
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	0.763680	+	0.645595i	$0.223391\pi$
$98$	3.78455	−	12.7908i	0.382297	−	1.29206i
$99$	12.3743			1.24367
$100$	2.30800	+	3.99757i	0.230800	+	0.399757i
$101$	−1.28890	+	2.23244i	−0.128250	+	0.222136i	−0.922999	−	0.384803i	$-0.874269\pi$
$101$	−1.28890	+	2.23244i	−0.128250	+	0.222136i	0.794749	+	0.606939i	$0.207603\pi$
$102$	−0.490966	+	0.850379i	−0.0486129	+	0.0842000i
$103$	8.43173	−	14.6042i	0.830803	−	1.43899i	−0.0665997	−	0.997780i	$-0.521215\pi$
$103$	8.43173	−	14.6042i	0.830803	−	1.43899i	0.897402	−	0.441213i	$-0.145452\pi$
$104$	1.89595	+	1.68146i	0.185913	+	0.164881i
$105$	−0.658944	+	1.53438i	−0.0643064	+	0.149740i
$106$	−0.135091	−	0.233984i	−0.0131212	−	0.0227265i
$107$	8.68265			0.839383			0.419692	−	0.907667i	$-0.362138\pi$
$107$	8.68265			0.839383			0.419692	+	0.907667i	$0.362138\pi$
$108$	−4.06491			−0.391146
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	0.995862	+	0.0908816i	$0.0289685\pi$
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	−0.419225	+	0.907882i	$0.637698\pi$
$110$	6.16674	+	10.6811i	0.587976	+	1.01840i
$111$	−1.51040	+	2.61608i	−0.143360	+	0.248307i
$112$	−7.28597	−	9.75398i	−0.688459	−	0.921665i
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	−0.997752	−	0.0670176i	$-0.978652\pi$
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	0.556915	+	0.830570i	$0.311985\pi$
$114$	−2.64695			−0.247910
$115$	−3.26821	+	5.66071i	−0.304763	+	0.527864i
$116$	−0.136660	−	0.236701i	−0.0126885	−	0.0219772i
$117$	−2.03651	+	9.94849i	−0.188275	+	0.919738i
$118$	10.1824			0.937369
$119$	−1.90430	−	2.54936i	−0.174567	−	0.233699i
$120$	0.221805	+	0.384177i	0.0202479	+	0.0350704i
$121$	−4.15192	−	7.19134i	−0.377448	−	0.653758i
$122$	11.0006	+	19.0535i	0.995944	+	1.72503i
$123$	2.21246			0.199491
$124$	−4.27807	−	7.40983i	−0.384182	−	0.665423i
$125$	11.5344			1.03167
$126$	5.60315	−	13.0472i	0.499168	−	1.16233i
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	−0.966764	−	0.255672i	$-0.917703\pi$
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	0.261964	−	0.965078i	$-0.415630\pi$
$128$	−5.52717			−0.488537
$129$	−0.00487367	−	0.00844145i	−0.000429103	−	0.000743228i
$130$	−9.60210	+	3.19998i	−0.842160	+	0.280657i
$131$	−0.928725	+	1.60860i	−0.0811430	+	0.140544i	−0.903741	−	0.428079i	$-0.859190\pi$
$131$	−0.928725	+	1.60860i	−0.0811430	+	0.140544i	0.822598	+	0.568623i	$0.192524\pi$
$132$	1.53527	+	2.65917i	0.133628	+	0.231451i
$133$	3.38482	−	7.88170i	0.293501	−	0.683430i
$134$	3.94018	−	6.82459i	0.340380	−	0.589555i
$135$	−1.83555	+	3.17926i	−0.157979	+	0.273627i
$136$	−0.845324			−0.0724859
$137$	−12.8002			−1.09360			−0.546798	−	0.837264i	$-0.684153\pi$
$137$	−12.8002			−1.09360			−0.546798	+	0.837264i	$0.684153\pi$
$138$	−1.81130	+	3.13726i	−0.154188	+	0.267061i
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	−0.858753	−	0.512389i	$-0.828761\pi$
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	0.873119	+	0.487508i	$0.162094\pi$
$140$	6.31332	−	0.748208i	0.533573	−	0.0632351i
$141$	−2.50290	−	4.33514i	−0.210782	−	0.365085i
$142$	−9.49894	+	16.4527i	−0.797134	+	1.38068i
$143$	15.0288	−	5.00848i	1.25677	−	0.418830i
$144$	−6.48010	−	11.2239i	−0.540009	−	0.935322i
$145$	−0.246840			−0.0204989
$146$	14.5219	+	25.1526i	1.20184	+	2.08165i
$147$	−2.06513	−	2.17486i	−0.170329	−	0.179380i
$148$	11.5006			0.945341
$149$	−1.96158	−	3.39756i	−0.160699	−	0.278339i	0.774421	−	0.632671i	$-0.218041\pi$
$149$	−1.96158	−	3.39756i	−0.160699	−	0.278339i	−0.935120	+	0.354332i	$0.884708\pi$
$150$	2.31041			0.188644
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	0.905907	−	0.423476i	$-0.139190\pi$
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	−0.819695	+	0.572800i	$0.805857\pi$
$152$	−1.13935	−	1.97341i	−0.0924135	−	0.160065i
$153$	−1.69368	−	2.93354i	−0.136926	−	0.237162i
$154$	−21.9971	+	2.60693i	−1.77257	+	0.210073i
$155$	−7.72721			−0.620664
$156$	−2.39054	+	0.796669i	−0.191397	+	0.0637846i
$157$	11.0564	+	19.1502i	0.882397	+	1.52836i	0.848668	+	0.528925i	$0.177405\pi$
$157$	11.0564	+	19.1502i	0.882397	+	1.52836i	0.0337285	+	0.999431i	$0.489262\pi$
$158$	0.737929	−	1.27813i	0.0587065	−	0.101683i
$159$	−0.0607478			−0.00481761
$160$	5.42333	−	9.39348i	0.428752	−	0.742620i
$161$	−7.02545	−	9.40522i	−0.553683	−	0.741235i
$162$	7.03303	−	12.1816i	0.552567	−	0.957074i
$163$	−1.92607	−	3.33605i	−0.150861	−	0.261299i	0.780683	−	0.624927i	$-0.214871\pi$
$163$	−1.92607	−	3.33605i	−0.150861	−	0.261299i	−0.931544	+	0.363628i	$0.881538\pi$
$164$	−4.21157	−	7.29465i	−0.328868	−	0.569616i
$165$	2.77307			0.215883
$166$	30.5244			2.36916
$167$	−1.06947	−	1.85238i	−0.0827582	−	0.143341i	0.821676	−	0.569956i	$-0.193040\pi$
$167$	−1.06947	−	1.85238i	−0.0827582	−	0.143341i	−0.904434	+	0.426614i	$0.859706\pi$
$168$	−0.791188	+	0.0937658i	−0.0610415	+	0.00723419i
$169$	1.55326	+	12.9069i	0.119482	+	0.992836i
$170$	1.68809	−	2.92385i	0.129470	−	0.224249i
$171$	4.56557	−	7.90779i	0.349138	−	0.604724i
$172$	−0.0185547	+	0.0321378i	−0.00141479	+	0.00245048i
$173$	8.30664	+	14.3875i	0.631542	+	1.09386i	0.987237	+	0.159260i	$0.0509110\pi$
$173$	8.30664	+	14.3875i	0.631542	+	1.09386i	−0.355695	+	0.934602i	$0.615756\pi$
$174$	−0.136803			−0.0103710
$175$	−2.95447	+	6.87961i	−0.223337	+	0.520049i
$176$	−10.1089	+	17.5091i	−0.761988	+	1.31980i
$177$	1.14471	−	1.98270i	0.0860419	−	0.149029i
$178$	−12.4959			−0.936607
$179$	0.269748	−	0.467217i	0.0201619	−	0.0349214i	−0.855768	−	0.517359i	$-0.826915\pi$
$179$	0.269748	−	0.467217i	0.0201619	−	0.0349214i	0.875930	+	0.482438i	$0.160248\pi$
$180$	6.76763			0.504430
$181$	2.77164			0.206014			0.103007	−	0.994681i	$-0.467154\pi$
$181$	2.77164			0.206014			0.103007	+	0.994681i	$0.467154\pi$
$182$	1.52430	−	18.1139i	0.112988	−	1.34269i
$183$	4.94675			0.365674
$184$	−3.11861			−0.229907
$185$	5.19319	−	8.99486i	0.381811	−	0.661316i
$186$	−4.28254			−0.314011
$187$	−2.64213	+	4.57629i	−0.193211	+	0.334652i
$188$	−9.52887	+	16.5045i	−0.694964	+	1.20371i
$189$	−3.94575	−	5.28231i	−0.287011	−	0.384232i
$190$	9.10100			0.660256
$191$	10.1204	+	17.5290i	0.732284	+	1.26835i	0.955905	+	0.293677i	$0.0948790\pi$
$191$	10.1204	+	17.5290i	0.732284	+	1.26835i	−0.223621	+	0.974676i	$0.571788\pi$
$192$	1.03414	−	1.79118i	0.0746323	−	0.129267i
$193$	8.18856	−	14.1830i	0.589425	−	1.02091i	−0.404882	−	0.914369i	$-0.632688\pi$
$193$	8.18856	−	14.1830i	0.589425	−	1.02091i	0.994308	−	0.106546i	$-0.0339791\pi$
$194$	3.32678	−	5.76216i	0.238849	−	0.413699i
$195$	−0.456378	+	2.22944i	−0.0326819	+	0.159654i
$196$	−3.23958	+	10.9489i	−0.231398	+	0.782064i
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	−0.967417	−	0.253190i	$-0.918520\pi$
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	0.264439	−	0.964402i	$-0.414813\pi$
$198$	−23.5800			−1.67576
$199$	−14.1175			−1.00076			−0.500380	−	0.865806i	$-0.666806\pi$
$199$	−14.1175			−1.00076			−0.500380	+	0.865806i	$0.666806\pi$
$200$	0.994491	+	1.72251i	0.0703212	+	0.121800i
$201$	−0.885913	−	1.53445i	−0.0624875	−	0.108232i
$202$	2.45607	−	4.25404i	0.172809	−	0.299313i
$203$	0.174938	−	0.407351i	0.0122782	−	0.0285904i
$204$	0.420267	−	0.727924i	0.0294246	−	0.0509649i
$205$	−7.60709			−0.531302
$206$	−16.0672	+	27.8291i	−1.11945	+	1.93895i
$207$	−6.24840	−	10.8225i	−0.434294	−	0.752219i
$208$	−12.4130	−	11.0088i	−0.860688	−	0.763320i
$209$	−14.2445			−0.985313
$210$	1.25566	−	2.92385i	0.0866486	−	0.201765i
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	0.934597	−	0.355709i	$-0.115761\pi$
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	−0.775352	+	0.631530i	$0.782427\pi$
$212$	0.115638	+	0.200290i	0.00794202	+	0.0137560i
$213$	2.13575	+	3.69923i	0.146339	+	0.253467i
$214$	−16.5453			−1.13101
$215$	0.0167571	+	0.0290242i	0.00114283	+	0.00197943i
$216$	−1.75152			−0.119176
$217$	5.47635	−	12.7519i	0.371759	−	0.865657i
$218$	−11.4720	−	19.8700i	−0.776980	−	1.34577i
$219$	6.53022			0.441272
$220$	−5.27873	−	9.14303i	−0.355892	−	0.616423i
$221$	−3.24434	−	2.87731i	−0.218238	−	0.193549i
$222$	2.87815	−	4.98510i	0.193169	−	0.334578i
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	0.962988	+	0.269545i	$0.0868732\pi$
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	−0.248061	+	0.968744i	$0.579793\pi$
$224$	11.6581	+	15.6072i	0.778943	+	1.04280i
$225$	−3.98509	+	6.90239i	−0.265673	+	0.460159i
$226$	8.92976	−	15.4668i	0.593999	−	1.02884i
$227$	−10.4490			−0.693526			−0.346763	−	0.937953i	$-0.612719\pi$
$227$	−10.4490			−0.693526			−0.346763	+	0.937953i	$0.612719\pi$
$228$	2.26579			0.150056
$229$	−7.22901	+	12.5210i	−0.477706	+	0.827412i	−0.999673	−	0.0255538i	$-0.991865\pi$
$229$	−7.22901	+	12.5210i	−0.477706	+	0.827412i	0.521967	+	0.852966i	$0.325198\pi$
$230$	6.22778	−	10.7868i	0.410648	−	0.711262i
$231$	−1.96530	+	4.57629i	−0.129307	+	0.301098i
$232$	−0.0588852	−	0.101992i	−0.00386600	−	0.00669611i
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	−0.672846	−	0.739783i	$-0.734928\pi$
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	0.977093	+	0.212811i	$0.0682617\pi$
$234$	3.88068	−	18.9574i	0.253688	−	1.23929i
$235$	8.60570	+	14.9055i	0.561374	+	0.972328i
$236$	−8.71616			−0.567374
$237$	−0.165917	−	0.287376i	−0.0107774	−	0.0186671i
$238$	3.62876	+	4.85796i	0.235218	+	0.314895i
$239$	19.6332			1.26997			0.634983	−	0.772526i	$-0.281007\pi$
$239$	19.6332			1.26997			0.634983	+	0.772526i	$0.281007\pi$
$240$	−1.45218	−	2.51525i	−0.0937380	−	0.162359i
$241$	7.31105			0.470946			0.235473	−	0.971881i	$-0.424336\pi$
$241$	7.31105			0.470946			0.235473	+	0.971881i	$0.424336\pi$
$242$	7.91174	+	13.7035i	0.508586	+	0.880897i
$243$	−5.31937	−	9.21341i	−0.341238	−	0.591041i
$244$	−9.41648	−	16.3098i	−0.602828	−	1.04413i
$245$	7.10053	+	7.47783i	0.453637	+	0.477741i
$246$	−4.21597			−0.268801
$247$	2.34429	−	11.4520i	0.149164	−	0.728676i
$248$	−1.84337	−	3.19282i	−0.117054	−	0.202744i
$249$	3.43157	−	5.94365i	0.217467	−	0.376664i
$250$	−21.9796			−1.39011
$251$	5.93191	−	10.2744i	0.374419	−	0.648512i	−0.615821	−	0.787886i	$-0.711176\pi$
$251$	5.93191	−	10.2744i	0.374419	−	0.648512i	0.990240	+	0.139374i	$0.0445089\pi$
$252$	−4.79629	+	11.1684i	−0.302138	+	0.703542i
$253$	−9.74746	+	16.8831i	−0.612817	+	1.06143i
$254$	15.1353	+	26.2151i	0.949672	+	1.64488i
$255$	−0.379551	−	0.657402i	−0.0237684	−	0.0411681i
$256$	20.1871			1.26169
$257$	−15.1722			−0.946413			−0.473206	−	0.880952i	$-0.656904\pi$
$257$	−15.1722			−0.946413			−0.473206	+	0.880952i	$0.656904\pi$
$258$	0.00928708	+	0.0160857i	0.000578188	+	0.00100145i
$259$	11.1634	+	14.9449i	0.693662	+	0.928630i
$260$	8.21940	−	2.73919i	0.509745	−	0.169877i
$261$	0.235963	−	0.408699i	0.0146057	−	0.0252979i
$262$	1.76974	−	3.06528i	0.109335	−	0.189374i
$263$	−8.59820	+	14.8925i	−0.530187	+	0.918312i	0.469192	+	0.883096i	$0.344545\pi$
$263$	−8.59820	+	14.8925i	−0.530187	+	0.918312i	−0.999380	+	0.0352156i	$0.988788\pi$
$264$	0.661533	+	1.14581i	0.0407145	+	0.0705196i
$265$	0.208869			0.0128307
$266$	−6.44997	+	15.0190i	−0.395473	+	0.920877i
$267$	−1.40479	+	2.43317i	−0.0859719	+	0.148908i
$268$	−3.37279	+	5.84185i	−0.206026	+	0.356848i
$269$	18.9220			1.15370			0.576849	−	0.816851i	$-0.304282\pi$
$269$	18.9220			1.15370			0.576849	+	0.816851i	$0.304282\pi$
$270$	3.49774	−	6.05827i	0.212866	−	0.368695i
$271$	32.1334			1.95196			0.975982	−	0.217853i	$-0.0699054\pi$
$271$	32.1334			1.95196			0.975982	+	0.217853i	$0.0699054\pi$
$272$	5.53444			0.335575
$273$	−3.35573	−	2.33318i	−0.203098	−	0.141210i
$274$	24.3916			1.47355
$275$	12.4334			0.749764
$276$	1.55047	−	2.68549i	0.0933273	−	0.161648i
$277$	18.4054			1.10587			0.552936	−	0.833224i	$-0.313507\pi$
$277$	18.4054			1.10587			0.552936	+	0.833224i	$0.313507\pi$
$278$	−0.322734	+	0.558992i	−0.0193563	+	0.0335261i
$279$	7.38671	−	12.7942i	0.442231	−	0.765966i
$280$	2.72034	−	0.322395i	0.162571	−	0.0192668i
$281$	−14.2252			−0.848603			−0.424302	−	0.905521i	$-0.639480\pi$
$281$	−14.2252			−0.848603			−0.424302	+	0.905521i	$0.639480\pi$
$282$	4.76942	+	8.26087i	0.284015	+	0.491928i
$283$	5.71446	−	9.89773i	0.339689	−	0.588359i	−0.644685	−	0.764448i	$-0.723011\pi$
$283$	5.71446	−	9.89773i	0.339689	−	0.588359i	0.984374	+	0.176089i	$0.0563448\pi$
$284$	8.13109	−	14.0835i	0.482492	−	0.835700i
$285$	1.02314	−	1.77213i	0.0606055	−	0.104972i
$286$	−28.6383	+	9.54396i	−1.69342	+	0.564346i
$287$	5.39123	−	12.5537i	0.318234	−	0.741022i
$288$	10.3687	+	17.9591i	0.610981	+	1.05825i
$289$	−15.5535			−0.914911
$290$	0.470368			0.0276210
$291$	−0.747997	−	1.29557i	−0.0438483	−	0.0759476i
$292$	−12.4307	−	21.5307i	−0.727453	−	1.25999i
$293$	6.60231	−	11.4355i	0.385711	−	0.668071i	−0.606156	−	0.795345i	$-0.707289\pi$
$293$	6.60231	−	11.4355i	0.385711	−	0.668071i	0.991868	+	0.127274i	$0.0406228\pi$
$294$	3.93523	+	4.14433i	0.229507	+	0.241702i
$295$	−3.93586	+	6.81712i	−0.229155	+	0.396908i
$296$	4.95547			0.288031
$297$	−5.47452	+	9.48215i	−0.317664	+	0.550210i
$298$	3.73791	+	6.47425i	0.216531	+	0.375043i
$299$	−11.9692	−	10.6151i	−0.692196	−	0.613889i
$300$	−1.97771			−0.114183
$301$	−0.0597736	+	0.00708392i	−0.00344529	+	0.000408310i
$302$	−2.01874	−	3.49656i	−0.116165	−	0.201204i
$303$	−0.552225	−	0.956482i	−0.0317245	−	0.0549484i
$304$	7.45947	+	12.9202i	0.427830	+	0.741023i
$305$	−17.0084			−0.973898
$306$	3.22740	+	5.59003i	0.184498	+	0.319561i
$307$	−6.65903			−0.380051			−0.190026	−	0.981779i	$-0.560857\pi$
$307$	−6.65903			−0.380051			−0.190026	+	0.981779i	$0.560857\pi$
$308$	18.8295	−	2.23153i	1.07291	−	0.127153i
$309$	3.61255	+	6.25713i	0.205511	+	0.355955i
$310$	14.7247			0.836304
$311$	1.02298	+	1.77186i	0.0580081	+	0.100473i	0.893571	−	0.448922i	$-0.148192\pi$
$311$	1.02298	+	1.77186i	0.0580081	+	0.100473i	−0.835563	+	0.549395i	$0.814858\pi$
$312$	−1.03006	+	0.343276i	−0.0583156	+	0.0194342i
$313$	−4.70883	+	8.15594i	−0.266159	+	0.461001i	−0.967867	−	0.251464i	$-0.919088\pi$
$313$	−4.70883	+	8.15594i	−0.266159	+	0.461001i	0.701708	+	0.712465i	$0.252421\pi$
$314$	−21.0686	−	36.4919i	−1.18897	−	2.05936i
$315$	6.56924	+	8.79448i	0.370135	+	0.495513i
$316$	−0.631667	+	1.09408i	−0.0355341	+	0.0615468i
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.166421	−	0.986055i	$-0.446779\pi$
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.770738	−	0.637153i	$-0.219888\pi$
$318$	0.115758			0.00649141
$319$	−0.736200			−0.0412193
$320$	−3.55567	+	6.15860i	−0.198768	+	0.344276i
$321$	−1.86003	+	3.22167i	−0.103817	+	0.179816i
$322$	13.3874	+	17.9222i	0.746051	+	0.998766i
$323$	1.94965	+	3.37689i	0.108481	+	0.187895i
$324$	−6.02027	+	10.4274i	−0.334460	+	0.579301i
$325$	−2.04624	+	9.99602i	−0.113505	+	0.554479i
$326$	3.67024	+	6.35704i	0.203276	+	0.352084i
$327$	−5.15873			−0.285279
$328$	−1.81472	−	3.14318i	−0.100201	−	0.173553i
$329$	−30.6970	+	3.63798i	−1.69238	+	0.200568i
$330$	−5.28425			−0.290888
$331$	−9.53298	−	16.5116i	−0.523980	−	0.907560i	−0.999610	−	0.0279144i	$-0.991113\pi$
$331$	−9.53298	−	16.5116i	−0.523980	−	0.907560i	0.475631	−	0.879645i	$-0.342220\pi$
$332$	−26.1289			−1.43401
$333$	9.92870	+	17.1970i	0.544089	+	0.942390i
$334$	2.03794	+	3.52982i	0.111511	+	0.193143i
$335$	3.04603	+	5.27588i	0.166423	+	0.288252i
$336$	5.18001	−	0.613897i	0.282593	−	0.0334908i
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$	−2.95983	−	24.5948i	−0.160994	−	1.33778i
$339$	−2.00777	−	3.47757i	−0.109047	−	0.188876i
$340$	−1.44500	+	2.50282i	−0.0783663	+	0.135734i
$341$	−23.0464			−1.24803
$342$	−8.69996	+	15.0688i	−0.470440	+	0.814826i
$343$	−17.3726	+	6.41814i	−0.938033	+	0.346547i
$344$	−0.00799504	+	0.0138478i	−0.000431064	+	0.000746624i
$345$	−1.40026	−	2.42532i	−0.0753874	−	0.130575i
$346$	−15.8288	−	27.4163i	−0.850961	−	1.47391i
$347$	11.6752			0.626757			0.313378	−	0.949628i	$-0.398539\pi$
$347$	11.6752			0.626757			0.313378	+	0.949628i	$0.398539\pi$
$348$	0.117103			0.00627738
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	−0.984966	−	0.172750i	$-0.944735\pi$
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	0.342877	−	0.939380i	$-0.388599\pi$
$350$	5.62992	−	13.1095i	0.300932	−	0.700732i
$351$	−6.72233	−	5.96184i	−0.358811	−	0.318219i
$352$	16.1751	−	28.0161i	0.862135	−	1.49326i
$353$	−6.39668	+	11.0794i	−0.340461	+	0.589696i	−0.984518	−	0.175282i	$-0.943916\pi$
$353$	−6.39668	+	11.0794i	−0.340461	+	0.589696i	0.644057	+	0.764977i	$0.277250\pi$
$354$	−2.18132	+	3.77816i	−0.115936	+	0.200807i
$355$	−7.34334	−	12.7190i	−0.389744	−	0.675057i
$356$	10.6965			0.566912
$357$	1.35388	−	0.160452i	0.0716548	−	0.00849200i
$358$	−0.514021	+	0.890310i	−0.0271668	+	0.0470544i
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	−0.981640	−	0.190742i	$-0.938911\pi$
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	0.656008	+	0.754754i	$0.272244\pi$
$360$	2.91610			0.153692
$361$	4.24442	−	7.35155i	0.223390	−	0.386924i
$362$	−5.28152			−0.277591
$363$	3.55776			0.186734
$364$	−1.30480	+	15.5055i	−0.0683900	+	0.812707i
$365$	−22.4528			−1.17524
$366$	−9.42633			−0.492722
$367$	−1.01538	+	1.75870i	−0.0530026	+	0.0918032i	−0.891309	−	0.453396i	$-0.850212\pi$
$367$	−1.01538	+	1.75870i	−0.0530026	+	0.0918032i	0.838307	+	0.545199i	$0.183546\pi$
$368$	20.4179			1.06436
$369$	7.27188	−	12.5953i	0.378559	−	0.655684i
$370$	−9.89593	+	17.1403i	−0.514465	+	0.891079i
$371$	−0.148028	+	0.344689i	−0.00768521	+	0.0178953i
$372$	3.66586			0.190066
$373$	1.93700	+	3.35498i	0.100294	+	0.173714i	0.911806	−	0.410622i	$-0.134688\pi$
$373$	1.93700	+	3.35498i	0.100294	+	0.173714i	−0.811512	+	0.584336i	$0.801355\pi$
$374$	5.03473	−	8.72040i	0.260340	−	0.450921i
$375$	−2.47095	+	4.27981i	−0.127599	+	0.221009i
$376$	−4.10588	+	7.11160i	−0.211745	+	0.366753i
$377$	0.121160	−	0.591877i	0.00624007	−	0.0304832i
$378$	7.51886	+	10.0658i	0.386728	+	0.517727i
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	0.990200	−	0.139659i	$-0.0446006\pi$
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	−0.616048	+	0.787709i	$0.711267\pi$
$380$	−7.79045			−0.399642
$381$	6.80606			0.348685
$382$	−19.2850	−	33.4025i	−0.986705	−	1.70902i
$383$	13.3909	+	23.1937i	0.684243	+	1.18514i	0.973674	+	0.227945i	$0.0732008\pi$
$383$	13.3909	+	23.1937i	0.684243	+	1.18514i	−0.289430	+	0.957199i	$0.593466\pi$
$384$	1.18405	−	2.05084i	0.0604234	−	0.104656i
$385$	6.75730	−	15.7347i	0.344384	−	0.801912i
$386$	−15.6038	+	27.0266i	−0.794212	+	1.37562i
$387$	−0.0640749			−0.00325711
$388$	−2.84773	+	4.93241i	−0.144571	+	0.250405i
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	0.672583	−	0.740022i	$-0.265185\pi$
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	−0.977169	+	0.212463i	$0.931852\pi$
$390$	0.869656	−	4.24834i	0.0440368	−	0.215123i
$391$	5.33655			0.269881
$392$	−1.39590	+	4.71776i	−0.0705035	+	0.238283i
$393$	−0.397910	−	0.689200i	−0.0200719	−	0.0347655i
$394$	18.8017	+	32.5655i	0.947216	+	1.64063i
$395$	0.570470	+	0.988084i	0.0287035	+	0.0497159i
$396$	20.1845			1.01431
$397$	0.828825	+	1.43557i	0.0415975	+	0.0720491i	0.886075	−	0.463543i	$-0.153422\pi$
$397$	0.828825	+	1.43557i	0.0415975	+	0.0720491i	−0.844477	+	0.535592i	$0.820089\pi$
$398$	26.9017			1.34846
$399$	2.19937	+	2.94437i	0.110106	+	0.147403i
$400$	−6.51106	−	11.2775i	−0.325553	−	0.563874i
$401$	−20.4828			−1.02286			−0.511430	−	0.859325i	$-0.670884\pi$
$401$	−20.4828			−1.02286			−0.511430	+	0.859325i	$0.670884\pi$
$402$	1.68816	+	2.92398i	0.0841978	+	0.145835i
$403$	3.79287	−	18.5285i	0.188936	−	0.922968i
$404$	−2.10240	+	3.64146i	−0.104598	+	0.181169i
$405$	5.43702	+	9.41720i	0.270168	+	0.467944i
$406$	−0.333355	+	0.776231i	−0.0165441	+	0.0385237i
$407$	15.4887	−	26.8272i	0.767746	−	1.32978i
$408$	0.181089	−	0.313655i	0.00896522	−	0.0155282i
$409$	14.8659			0.735070			0.367535	−	0.930010i	$-0.380202\pi$
$409$	14.8659			0.735070			0.367535	+	0.930010i	$0.380202\pi$
$410$	14.4958			0.715895
$411$	2.74211	−	4.74948i	0.135258	−	0.234274i
$412$	13.7535	−	23.8217i	0.677586	−	1.17361i
$413$	−8.46065	−	11.3266i	−0.416321	−	0.557344i
$414$	11.9067	+	20.6230i	0.585182	+	1.01357i
$415$	−11.7988	+	20.4360i	−0.579178	+	1.00317i
$416$	19.8619	+	17.6149i	0.973808	+	0.863643i
$417$	0.0725639	+	0.125684i	0.00355347	+	0.00615479i
$418$	27.1438			1.32764
$419$	11.8087	+	20.4533i	0.576895	+	0.999211i	0.995833	+	0.0911962i	$0.0290690\pi$
$419$	11.8087	+	20.4533i	0.576895	+	0.999211i	−0.418938	+	0.908015i	$0.637598\pi$
$420$	−1.07484	+	2.50282i	−0.0524470	+	0.122125i
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	−4.40788	−	7.63467i	−0.214572	−	0.371650i
$423$	−32.9059			−1.59994
$424$	0.0498269	+	0.0863028i	0.00241981	+	0.00419123i
$425$	−1.70177	−	2.94755i	−0.0825479	−	0.142977i
$426$	−4.06980	−	7.04910i	−0.197182	−	0.341530i
$427$	12.0540	−	28.0683i	0.583335	−	1.35832i
$428$	14.1628			0.684584
$429$	−1.36115	+	6.64932i	−0.0657169	+	0.321032i
$430$	−0.0319317	−	0.0553074i	−0.00153988	−	0.00266716i
$431$	6.65859	−	11.5330i	0.320733	−	0.555526i	−0.659906	−	0.751348i	$-0.729404\pi$
$431$	6.65859	−	11.5330i	0.320733	−	0.555526i	0.980640	+	0.195822i	$0.0627374\pi$
$432$	11.4675			0.551728
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	−0.999943	−	0.0106929i	$-0.996596\pi$
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	0.509232	+	0.860629i	$0.329930\pi$
$434$	−10.4355	+	24.2996i	−0.500921	+	1.16642i
$435$	0.0528790	−	0.0915890i	0.00253535	−	0.00439136i
$436$	9.82001	+	17.0087i	0.470293	+	0.814571i
$437$	7.19275	+	12.4582i	0.344076	+	0.595957i
$438$	−12.4437			−0.594585
$439$	−9.77074			−0.466332			−0.233166	−	0.972437i	$-0.574909\pi$
$439$	−9.77074			−0.466332			−0.233166	+	0.972437i	$0.574909\pi$
$440$	−2.27455	−	3.93963i	−0.108435	−	0.187814i
$441$	−19.1689	+	4.60824i	−0.912804	+	0.219440i
$442$	6.18229	+	5.48290i	0.294061	+	0.260795i
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	0.497232	+	0.867618i	$0.334350\pi$
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	−0.999995	+	0.00319331i	$0.998984\pi$
$444$	−2.46370	+	4.26725i	−0.116922	+	0.202514i
$445$	4.83010	−	8.36597i	0.228968	−	0.396585i
$446$	−20.3440	−	35.2368i	−0.963317	−	1.66851i
$447$	1.68087			0.0795023
$448$	−7.64337	−	10.2324i	−0.361115	−	0.483438i
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	−0.568522	−	0.822668i	$-0.692484\pi$
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	0.996712	+	0.0810200i	$0.0258178\pi$
$450$	7.59384	−	13.1529i	0.357977	−	0.620034i
$451$	−22.6882			−1.06834
$452$	−7.64387	+	13.2396i	−0.359538	+	0.622737i
$453$	−0.907789			−0.0426517
$454$	19.9112			0.934480
$455$	11.5380	+	8.02215i	0.540910	+	0.376084i
$456$	0.976304			0.0457196
$457$	−18.0198			−0.842932			−0.421466	−	0.906844i	$-0.638484\pi$
$457$	−18.0198			−0.842932			−0.421466	+	0.906844i	$0.638484\pi$
$458$	13.7753	−	23.8595i	0.643678	−	1.11488i
$459$	2.99720			0.139897
$460$	−5.33098	+	9.23352i	−0.248558	+	0.430515i
$461$	14.8873	−	25.7855i	0.693370	−	1.20095i	−0.277357	−	0.960767i	$-0.589458\pi$
$461$	14.8873	−	25.7855i	0.693370	−	1.20095i	0.970727	−	0.240185i	$-0.0772082\pi$
$462$	3.74500	−	8.72040i	0.174233	−	0.405710i
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	0.385529	+	0.667755i	0.0178977	+	0.0309997i
$465$	1.65535	−	2.86715i	0.0767651	−	0.132961i
$466$	−8.84968	+	15.3281i	−0.409953	+	0.710060i
$467$	2.91461	−	5.04825i	0.134872	−	0.233605i	−0.790677	−	0.612234i	$-0.790271\pi$
$467$	2.91461	−	5.04825i	0.134872	−	0.233605i	0.925549	+	0.378629i	$0.123604\pi$
$468$	−3.32186	+	16.2276i	−0.153553	+	0.750120i
$469$	−10.8654	+	1.28768i	−0.501715	+	0.0594596i
$470$	−16.3987	−	28.4033i	−0.756414	−	1.31015i
$471$	−9.47418			−0.436547
$472$	−3.75570			−0.172870
$473$	0.0499782	+	0.0865648i	0.00229800	+	0.00398025i
$474$	0.316164	+	0.547612i	0.0145219	+	0.0251527i
$475$	4.58738	−	7.94557i	0.210483	−	0.364568i
$476$	−3.10622	−	4.15841i	−0.142373	−	0.190600i
$477$	−0.199665	+	0.345830i	−0.00914203	+	0.0158345i
$478$	−37.4122			−1.71120
$479$	−7.24565	+	12.5498i	−0.331062	+	0.573417i	−0.982720	−	0.185096i	$-0.940740\pi$
$479$	−7.24565	+	12.5498i	−0.331062	+	0.573417i	0.651658	+	0.758513i	$0.274074\pi$
$480$	2.32361	+	4.02461i	0.106058	+	0.183698i
$481$	19.0190	+	16.8674i	0.867193	+	0.769088i
$482$	−13.9316			−0.634569
$483$	4.99479	−	0.591946i	0.227271	−	0.0269345i
$484$	−6.77245	−	11.7302i	−0.307839	−	0.533192i
$485$	2.57183	+	4.45455i	0.116781	+	0.202271i
$486$	10.1364	+	17.5567i	0.459795	+	0.796389i
$487$	−17.9601			−0.813851			−0.406926	−	0.913461i	$-0.633399\pi$
$487$	−17.9601			−0.813851			−0.406926	+	0.913461i	$0.633399\pi$
$488$	−4.05746	−	7.02772i	−0.183672	−	0.318130i
$489$	1.65044			0.0746354
$490$	−13.5305	−	14.2494i	−0.611245	−	0.643724i
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	0.906332	+	0.422566i	$0.138870\pi$
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	−0.0872134	+	0.996190i	$0.527796\pi$
$492$	3.60887			0.162701
$493$	0.100764	+	0.174528i	0.00453818	+	0.00786036i
$494$	−4.46719	+	21.8226i	−0.200988	+	0.981844i
$495$	9.11449	−	15.7868i	0.409666	−	0.709562i
$496$	12.0688	+	20.9038i	0.541905	+	0.938607i
$497$	26.1941	−	3.10433i	1.17496	−	0.139248i
$498$	−6.53906	+	11.3260i	−0.293022	+	0.507530i
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	0.468711	+	0.883352i	$0.344719\pi$
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	−0.999360	+	0.0357602i	$0.988615\pi$
$500$	18.8145			0.841410
$501$	0.916426			0.0409429
$502$	−11.3036	+	19.5784i	−0.504505	+	0.873828i
$503$	−13.8876	+	24.0540i	−0.619217	+	1.07252i	0.370411	+	0.928868i	$0.379217\pi$
$503$	−13.8876	+	24.0540i	−0.619217	+	1.07252i	−0.989629	+	0.143648i	$0.954117\pi$
$504$	−2.06667	+	4.81233i	−0.0920568	+	0.214358i
$505$	1.89871	+	3.28867i	0.0844916	+	0.146344i
$506$	18.5744	−	32.1717i	0.825731	−	1.43021i
$507$	−5.12180	−	2.18863i	−0.227467	−	0.0972003i
$508$	−12.9558	−	22.4401i	−0.574820	−	0.995618i
$509$	8.70416			0.385805			0.192902	−	0.981218i	$-0.438210\pi$
$509$	8.70416			0.385805			0.192902	+	0.981218i	$0.438210\pi$
$510$	0.723257	+	1.25272i	0.0320264	+	0.0554713i
$511$	15.9126	−	37.0531i	0.703931	−	1.63913i
$512$	−27.4134			−1.21151
$513$	4.03971	+	6.99698i	0.178357	+	0.308924i
$514$	28.9114			1.27523
$515$	−12.4210	−	21.5139i	−0.547336	−	0.948014i
$516$	−0.00794974	−	0.0137693i	−0.000349968	−	0.000606162i
$517$	25.6665	+	44.4557i	1.12881	+	1.95516i
$518$	−21.2726	−	28.4784i	−0.934664	−	1.25127i
$519$	−7.11792			−0.312442
$520$	3.54165	−	1.18028i	0.155312	−	0.0517589i
$521$	4.28573	+	7.42310i	0.187761	+	0.325212i	0.944504	−	0.328501i	$-0.106544\pi$
$521$	4.28573	+	7.42310i	0.187761	+	0.325212i	−0.756742	+	0.653713i	$0.773210\pi$
$522$	−0.449641	+	0.778801i	−0.0196803	+	0.0340872i
$523$	29.9493			1.30959			0.654796	−	0.755806i	$-0.272755\pi$
$523$	29.9493			1.30959			0.654796	+	0.755806i	$0.272755\pi$
$524$	−1.51490	+	2.62388i	−0.0661786	+	0.114625i
$525$	−1.91974	−	2.57002i	−0.0837842	−	0.112165i
$526$	16.3844	−	28.3786i	0.714393	−	1.23736i
$527$	3.15437	+	5.46353i	0.137407	+	0.237995i
$528$	−4.33114	−	7.50175i	−0.188489	−	0.326472i
$529$	−3.31212			−0.144005
$530$	−0.398012			−0.0172885
$531$	−7.52486	−	13.0334i	−0.326551	−	0.565603i
$532$	5.52118	−	12.8563i	0.239373	−	0.557391i
$533$	3.73391	−	18.2404i	0.161734	−	0.790081i
$534$	2.67692	−	4.63656i	0.115842	−	0.200643i
$535$	6.39534	−	11.0770i	0.276494	−	0.478902i
$536$	−1.45330	+	2.51719i	−0.0627730	+	0.108726i
$537$	0.115573	+	0.200178i	0.00498734	+	0.00863832i
$538$	−36.0571			−1.55453
$539$	21.1774	+	22.3026i	0.912174	+	0.960643i
$540$	−2.99407	+	5.18588i	−0.128844	+	0.223165i
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	−0.956417	−	0.292003i	$-0.905678\pi$
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	0.731091	+	0.682280i	$0.239011\pi$
$542$	−61.2321			−2.63014
$543$	−0.593751	+	1.02841i	−0.0254803	+	0.0441331i
$544$	−8.85557			−0.379679
$545$	17.7373			0.759781
$546$	6.39454	+	4.44601i	0.273661	+	0.190271i
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	−20.8792			−0.891915
$549$	16.2589	−	28.1613i	0.693914	−	1.20189i
$550$	−23.6927			−1.01026
$551$	−0.271625	+	0.470468i	−0.0115716	+	0.0200426i
$552$	0.668081	−	1.15715i	0.0284354	−	0.0492516i
$553$	−2.03490	+	0.241161i	−0.0865326	+	0.0102552i
$554$	−35.0726			−1.49009
$555$	2.22501	+	3.85383i	0.0944464	+	0.163586i
$556$	0.276261	−	0.478497i	0.0117161	−	0.0202928i
$557$	−5.92986	+	10.2708i	−0.251256	+	0.435189i	−0.963872	−	0.266366i	$-0.914177\pi$
$557$	−5.92986	+	10.2708i	−0.251256	+	0.435189i	0.712616	+	0.701555i	$0.247510\pi$
$558$	−14.0758	+	24.3800i	−0.595877	+	1.03209i
$559$	−0.0778200	+	0.0259342i	−0.00329144	+	0.00109690i
$560$	−17.8104	+	2.11076i	−0.752627	+	0.0891958i
$561$	−1.13201	−	1.96070i	−0.0477936	−	0.0827809i
$562$	27.1069			1.14344
$563$	7.69349			0.324242			0.162121	−	0.986771i	$-0.448166\pi$
$563$	7.69349			0.324242			0.162121	+	0.986771i	$0.448166\pi$
$564$	−4.08262	−	7.07131i	−0.171909	−	0.297756i
$565$	6.90332	+	11.9569i	0.290425	+	0.503031i
$566$	−10.8892	+	18.8607i	−0.457709	+	0.792775i
$567$	−19.3941	+	2.29845i	−0.814477	+	0.0965258i
$568$	3.50360	−	6.06841i	0.147008	−	0.254625i
$569$	37.4196			1.56871			0.784355	−	0.620312i	$-0.212994\pi$
$569$	37.4196			1.56871			0.784355	+	0.620312i	$0.212994\pi$
$570$	−1.94965	+	3.37689i	−0.0816619	+	0.141443i
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	0.678903	−	0.734228i	$-0.262456\pi$
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	−0.975311	+	0.220834i	$0.929122\pi$
$572$	24.5144	−	8.16963i	1.02500	−	0.341589i
$573$	−8.67209			−0.362282
$574$	−10.2733	+	23.9218i	−0.428799	+	0.998478i
$575$	−6.27825	−	10.8742i	−0.261821	−	0.453488i
$576$	−6.79797	−	11.7744i	−0.283249	−	0.490601i
$577$	7.48776	+	12.9692i	0.311720	+	0.539914i	0.978735	−	0.205130i	$-0.0657617\pi$
$577$	7.48776	+	12.9692i	0.311720	+	0.539914i	−0.667015	+	0.745044i	$0.732428\pi$
$578$	29.6381			1.23278
$579$	3.50837	+	6.07667i	0.145803	+	0.252538i
$580$	−0.402635			−0.0167185
$581$	−25.3629	−	33.9543i	−1.05223	−	1.40866i
$582$	1.42535	+	2.46878i	0.0590828	+	0.102334i
$583$	0.622952			0.0258000
$584$	−5.35627	−	9.27732i	−0.221644	−	0.383898i
$585$	11.1919	+	9.92582i	0.462730	+	0.410382i
$586$	−12.5811	+	21.7911i	−0.519720	+	0.900182i
$587$	6.58821	+	11.4111i	0.271925	+	0.470987i	0.969355	−	0.245666i	$-0.0790066\pi$
$587$	6.58821	+	11.4111i	0.271925	+	0.470987i	−0.697430	+	0.716653i	$0.745673\pi$
$588$	−3.36856	−	3.54755i	−0.138917	−	0.146298i
$589$	−8.50309	+	14.7278i	−0.350364	+	0.606848i
$590$	7.50003	−	12.9904i	0.308771	−	0.534807i
$591$	8.45478			0.347783
$592$	−32.4441			−1.33344
$593$	22.0663	−	38.2200i	0.906156	−	1.56951i	0.0867989	−	0.996226i	$-0.472336\pi$
$593$	22.0663	−	38.2200i	0.906156	−	1.56951i	0.819357	−	0.573283i	$-0.194330\pi$
$594$	10.4320	−	18.0688i	0.428032	−	0.741372i
$595$	−4.65503	+	0.551680i	−0.190838	+	0.0226167i
$596$	−3.19965	−	5.54195i	−0.131063	−	0.227007i
$597$	3.02429	−	5.23823i	0.123776	−	0.214387i
$598$	22.8080	+	20.2278i	0.932689	+	0.827175i
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	0.921000	−	0.389564i	$-0.127374\pi$
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	−0.797872	+	0.602827i	$0.794041\pi$
$600$	−0.852175			−0.0347899
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	0.825534	−	0.564353i	$-0.190874\pi$
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	−0.901511	+	0.432757i	$0.857541\pi$
$602$	0.113902	−	0.0134988i	0.00464230	−	0.000550172i
$603$	−11.6472			−0.474312
$604$	1.72804	+	2.99305i	0.0703129	+	0.121786i
$605$	−12.2326			−0.497328
$606$	1.05230	+	1.82263i	0.0427467	+	0.0740394i
$607$	3.00825	+	5.21045i	0.122101	+	0.211486i	0.920596	−	0.390516i	$-0.127703\pi$
$607$	3.00825	+	5.21045i	0.122101	+	0.211486i	−0.798495	+	0.602002i	$0.794370\pi$
$608$	−11.9358	−	20.6733i	−0.484059	−	0.838415i
$609$	0.113670	+	0.152174i	0.00460615	+	0.00616641i
$610$	32.4105			1.31226
$611$	−39.9648	+	13.3186i	−1.61680	+	0.538813i
$612$	−2.76266	−	4.78506i	−0.111674	−	0.193425i
$613$	−4.90413	+	8.49420i	−0.198076	+	0.343077i	−0.947904	−	0.318555i	$-0.896803\pi$
$613$	−4.90413	+	8.49420i	−0.198076	+	0.343077i	0.749829	+	0.661632i	$0.230136\pi$
$614$	12.6892			0.512094
$615$	1.62962	−	2.82258i	0.0657126	−	0.113818i
$616$	8.11342	−	0.961543i	0.326899	−	0.0387417i
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	0.295350	+	0.955389i	$0.404564\pi$
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	−0.975066	+	0.221914i	$0.928770\pi$
$618$	−6.88394	−	11.9233i	−0.276913	−	0.479627i
$619$	−2.04671	−	3.54501i	−0.0822644	−	0.142486i	0.821958	−	0.569548i	$-0.192882\pi$
$619$	−2.04671	−	3.54501i	−0.0822644	−	0.142486i	−0.904222	+	0.427062i	$0.859549\pi$
$620$	−12.6043			−0.506201
$621$	11.0574			0.443719
$622$	−1.94936	−	3.37639i	−0.0781621	−	0.135381i
$623$	10.3829	+	13.9000i	0.415983	+	0.556891i
$624$	6.74393	−	2.24747i	0.269973	−	0.0899709i
$625$	1.42115	−	2.46150i	0.0568459	−	0.0984599i
$626$	8.97297	−	15.5416i	0.358632	−	0.621169i
$627$	3.05151	−	5.28537i	0.121866	−	0.211077i
$628$	18.0347	+	31.2371i	0.719665	+	1.24650i
$629$	−8.47978			−0.338111
$630$	−12.5181	−	16.7584i	−0.498732	−	0.667671i
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	−0.466340	−	0.884605i	$-0.654428\pi$
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	0.999261	−	0.0384402i	$-0.0122389\pi$
$632$	−0.272179	+	0.471427i	−0.0108267	+	0.0187524i
$633$	−1.98214			−0.0787831
$634$	−31.7955	+	55.0714i	−1.26276	+	2.18717i
$635$	−23.4012			−0.928650
$636$	−0.0990892			−0.00392914
$637$	−21.4158	+	13.3553i	−0.848523	+	0.529158i
$638$	1.40287			0.0555403
$639$	28.0790			1.11079
$640$	−4.07112	+	7.05139i	−0.160925	+	0.278731i
$641$	−18.5722			−0.733558			−0.366779	−	0.930308i	$-0.619539\pi$
$641$	−18.5722			−0.733558			−0.366779	+	0.930308i	$0.619539\pi$
$642$	3.54440	−	6.13908i	0.139886	−	0.242290i
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	−0.824632	−	0.565670i	$-0.808618\pi$
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	0.902201	+	0.431317i	$0.141951\pi$
$644$	−11.4596	−	15.3414i	−0.451572	−	0.604536i
$645$	−0.0143591			−0.000565389
$646$	−3.71518	−	6.43487i	−0.146172	−	0.253177i
$647$	0.0985378	−	0.170672i	0.00387392	−	0.00670983i	−0.864082	−	0.503351i	$-0.832100\pi$
$647$	0.0985378	−	0.170672i	0.00387392	−	0.00670983i	0.867956	+	0.496641i	$0.165434\pi$
$648$	−2.59407	+	4.49306i	−0.101905	+	0.176504i
$649$	−11.7387	+	20.3321i	−0.460785	+	0.798104i
$650$	3.89922	−	19.0480i	0.152940	−	0.747125i
$651$	3.55839	+	4.76375i	0.139464	+	0.186706i
$652$	−3.14172	−	5.44163i	−0.123039	−	0.213110i
$653$	−14.4673			−0.566148			−0.283074	−	0.959098i	$-0.591354\pi$
$653$	−14.4673			−0.566148			−0.283074	+	0.959098i	$0.591354\pi$
$654$	9.83028			0.384394
$655$	1.36813	+	2.36967i	0.0534573	+	0.0925908i
$656$	11.8812	+	20.5788i	0.463883	+	0.803468i
$657$	21.4635	−	37.1758i	0.837369	−	1.45037i
$658$	58.4949	−	6.93238i	2.28037	−	0.270252i
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	−0.542722	−	0.839912i	$-0.682606\pi$
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	0.998746	+	0.0500552i	$0.0159397\pi$
$660$	4.52332			0.176070
$661$	2.02409	−	3.50582i	0.0787278	−	0.136361i	−0.823973	−	0.566628i	$-0.808248\pi$
$661$	2.02409	−	3.50582i	0.0787278	−	0.136361i	0.902701	+	0.430268i	$0.141581\pi$
$662$	18.1657	+	31.4638i	0.706028	+	1.22288i
$663$	1.76263	−	0.587412i	0.0684550	−	0.0228132i
$664$	−11.2587			−0.436921
$665$	−7.56208	−	10.1236i	−0.293245	−	0.392577i
$666$	−18.9197	−	32.7699i	−0.733125	−	1.26981i
$667$	0.371744	+	0.643879i	0.0143940	+	0.0249311i
$668$	−1.74448	−	3.02153i	−0.0674959	−	0.116906i
$669$	−9.14832			−0.353695
$670$	−5.80440	−	10.0535i	−0.224243	−	0.388401i
$671$	−50.7276			−1.95832
$672$	−8.28844	+	0.982285i	−0.319734	+	0.0378925i
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	0.787133	−	0.616783i	$-0.211564\pi$
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	−0.927716	+	0.373286i	$0.878231\pi$
$674$	59.6152			2.29629
$675$	−3.52609	−	6.10737i	−0.135719	−	0.235073i
$676$	2.53362	+	21.0532i	0.0974468	+	0.809737i
$677$	7.87553	−	13.6408i	0.302681	−	0.524259i	−0.674061	−	0.738676i	$-0.735452\pi$
$677$	7.87553	−	13.6408i	0.302681	−	0.524259i	0.976742	+	0.214416i	$0.0687849\pi$
$678$	3.82593	+	6.62671i	0.146934	+	0.254497i
$679$	−9.17387	+	1.08722i	−0.352061	+	0.0417236i
$680$	−0.622636	+	1.07844i	−0.0238770	+	0.0413562i
$681$	2.23843	−	3.87707i	0.0857767	−	0.148570i
$682$	43.9163			1.68164
$683$	41.4854			1.58739			0.793697	−	0.608314i	$-0.208154\pi$
$683$	41.4854			1.58739			0.793697	+	0.608314i	$0.208154\pi$
$684$	7.44717	−	12.8989i	0.284750	−	0.493201i
$685$	−9.42819	+	16.3301i	−0.360233	+	0.623941i
$686$	33.1045	−	12.2301i	1.26394	−	0.466949i
$687$	−3.09725	−	5.36460i	−0.118168	−	0.204672i
$688$	0.0523445	−	0.0906634i	0.00199562	−	0.00345651i
$689$	−0.102522	+	0.500830i	−0.00390579	+	0.0190801i
$690$	2.66828	+	4.62159i	0.101580	+	0.175941i
$691$	−46.8216			−1.78118			−0.890589	−	0.454809i	$-0.849708\pi$
$691$	−46.8216			−1.78118			−0.890589	+	0.454809i	$0.849708\pi$
$692$	13.5494	+	23.4683i	0.515073	+	0.892132i
$693$	19.5928	+	26.2296i	0.744268	+	0.996378i
$694$	−22.2478			−0.844514
$695$	−0.249496	−	0.432140i	−0.00946392	−	0.0163920i
$696$	0.0504584			0.00191262
$697$	3.10534	+	5.37860i	0.117623	+	0.203729i
$698$	22.8576	+	39.5905i	0.865172	+	1.49852i
$699$	1.98977	+	3.44638i	0.0752600	+	0.130354i
$700$	−4.81921	+	11.2217i	−0.182149	+	0.424142i
$701$	29.8626			1.12790			0.563948	−	0.825810i	$-0.309282\pi$
$701$	29.8626			1.12790			0.563948	+	0.825810i	$0.309282\pi$
$702$	12.8098	+	11.3606i	0.483475	+	0.428780i
$703$	−11.4293	−	19.7961i	−0.431063	−	0.746623i
$704$	−10.6048	+	18.3680i	−0.399683	+	0.692271i
$705$	−7.37418			−0.277728
$706$	12.1893	−	21.1124i	0.458749	−	0.794576i
$707$	−6.77281	+	0.802663i	−0.254718	+	0.0301873i
$708$	1.86721	−	3.23410i	0.0701740	−	0.121545i
$709$	−13.4666	−	23.3249i	−0.505750	−	0.875984i	−0.999978	−	0.00665185i	$-0.997883\pi$
$709$	−13.4666	−	23.3249i	−0.505750	−	0.875984i	0.494228	−	0.869332i	$-0.335451\pi$
$710$	13.9932	+	24.2369i	0.525155	+	0.909595i
$711$	−2.18133			−0.0818063
$712$	4.60900			0.172729
$713$	11.6373	+	20.1563i	0.435819	+	0.754861i
$714$	−2.57990	+	0.305750i	−0.0965502	+	0.0114424i
$715$	4.68004	−	22.8623i	0.175023	−	0.855003i
$716$	0.440002	−	0.762105i	0.0164436	−	0.0284812i
$717$	−4.20590	+	7.28483i	−0.157072	+	0.272057i
$718$	11.7570	−	20.3638i	0.438769	−	0.759969i
$719$	7.24938	+	12.5563i	0.270356	+	0.468271i	0.968953	−	0.247245i	$-0.0795252\pi$
$719$	7.24938	+	12.5563i	0.270356	+	0.468271i	−0.698597	+	0.715516i	$0.746192\pi$
$720$	−19.0921			−0.711519
$721$	44.3064	−	5.25087i	1.65006	−	0.195553i
$722$	−8.08799	+	14.0088i	−0.301004	+	0.521354i
$723$	−1.56620	+	2.71274i	−0.0582476	+	0.100888i
$724$	4.52098			0.168021
$725$	0.237090	−	0.410652i	0.00880530	−	0.0152512i
$726$	−6.77953			−0.251612
$727$	−6.26424			−0.232328			−0.116164	−	0.993230i	$-0.537060\pi$
$727$	−6.26424			−0.232328			−0.116164	+	0.993230i	$0.537060\pi$
$728$	−0.562223	+	6.68113i	−0.0208374	+	0.247619i
$729$	−17.5866			−0.651357
$730$	42.7852			1.58355
$731$	0.0136811	−	0.0236963i	0.000506013	−	0.000876440i
$732$	8.06893			0.298236
$733$	5.99189	−	10.3783i	0.221316	−	0.383330i	−0.733892	−	0.679266i	$-0.762298\pi$
$733$	5.99189	−	10.3783i	0.221316	−	0.383330i	0.955208	+	0.295936i	$0.0956316\pi$
$734$	1.93487	−	3.35130i	0.0714175	−	0.123699i
$735$	−4.29573	+	1.03270i	−0.158450	+	0.0380917i
$736$	−32.6704			−1.20425
$737$	9.08480	+	15.7353i	0.334643	+	0.579619i
$738$	−13.8570	+	24.0010i	−0.510084	+	0.883491i
$739$	−6.76269	+	11.7133i	−0.248770	+	0.430882i	−0.963185	−	0.268840i	$-0.913360\pi$
$739$	−6.76269	+	11.7133i	−0.248770	+	0.430882i	0.714415	+	0.699722i	$0.246693\pi$
$740$	8.47091	−	14.6721i	0.311397	−	0.539355i
$741$	3.74704	+	3.32314i	0.137651	+	0.122079i
$742$	0.282075	−	0.656825i	0.0103553	−	0.0241128i
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	0.966519	+	0.256594i	$0.0826003\pi$
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	−0.261043	+	0.965327i	$0.584066\pi$
$744$	1.57958			0.0579101
$745$	−5.77932			−0.211738
$746$	−3.69107	−	6.39312i	−0.135140	−	0.234069i
$747$	−22.5577	−	39.0710i	−0.825342	−	1.42953i
$748$	−4.30973	+	7.46466i	−0.157579	+	0.272935i
$749$	13.7476	+	18.4044i	0.502326	+	0.672482i
$750$	4.70855	−	8.15544i	0.171932	−	0.297795i
$751$	11.7115			0.427357			0.213679	−	0.976904i	$-0.431455\pi$
$751$	11.7115			0.427357			0.213679	+	0.976904i	$0.431455\pi$
$752$	26.8817	−	46.5605i	0.980276	−	1.69789i
$753$	2.54151	+	4.40203i	0.0926178	+	0.160419i
$754$	−0.230878	+	1.12786i	−0.00840809	+	0.0410742i
$755$	3.12125			0.113594
$756$	−6.43614	−	8.61629i	−0.234080	−	0.313371i
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	0.768877	−	0.639396i	$-0.220816\pi$
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	−0.938172	+	0.346169i	$0.887482\pi$
$758$	−13.8800	−	24.0409i	−0.504145	−	0.873205i
$759$	−4.17627	−	7.23352i	−0.151589	−	0.262560i
$760$	−3.35682			−0.121765
$761$	21.9691	+	38.0515i	0.796378	+	1.37937i	0.921960	+	0.387284i	$0.126587\pi$
$761$	21.9691	+	38.0515i	0.796378	+	1.37937i	−0.125582	+	0.992083i	$0.540080\pi$
$762$	−12.9693			−0.469830
$763$	−12.5706	+	29.2712i	−0.455086	+	1.05969i
$764$	16.5079	+	28.5926i	0.597236	+	1.03444i
$765$	−4.99002			−0.180414
$766$	−25.5172	−	44.1971i	−0.921973	−	1.59690i
$767$	−14.4143	−	12.7837i	−0.520471	−	0.461591i
$768$	−4.32455	+	7.49035i	−0.156049	+	0.270285i
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	0.541662	−	0.840597i	$-0.317795\pi$
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	−0.998809	+	0.0487946i	$0.984462\pi$
$770$	−12.8764	+	29.9833i	−0.464035	+	1.08052i
$771$	3.25024	−	5.62957i	0.117054	−	0.202744i
$772$	13.3568	−	23.1347i	0.480723	−	0.832637i
$773$	−23.1084			−0.831152			−0.415576	−	0.909559i	$-0.636420\pi$
$773$	−23.1084			−0.831152			−0.415576	+	0.909559i	$0.636420\pi$
$774$	0.122099			0.00438874
$775$	7.42200	−	12.8553i	0.266606	−	0.461775i
$776$	−1.22705	+	2.12532i	−0.0440487	+	0.0762946i
$777$	−7.93672	+	0.940602i	−0.284728	+	0.0337439i
$778$	11.4474	+	19.8275i	0.410410	+	0.710851i
$779$	−8.37091	+	14.4988i	−0.299919	+	0.519475i
$780$	−0.744426	+	3.63658i	−0.0266547	+	0.130210i
$781$	−21.9015	−	37.9346i	−0.783699	−	1.35741i
$782$	−10.1691			−0.363647
$783$	0.208785	+	0.361626i	0.00746135	+	0.0129234i
$784$	9.13912	−	30.8878i	0.326397	−	1.10314i
$785$	32.5750			1.16265
$786$	0.758241	+	1.31331i	0.0270456	+	0.0468443i
$787$	−24.6692			−0.879364			−0.439682	−	0.898154i	$-0.644909\pi$
$787$	−24.6692			−0.879364			−0.439682	+	0.898154i	$0.644909\pi$
$788$	−16.0943	−	27.8761i	−0.573334	−	0.993044i
$789$	−3.68388	−	6.38066i	−0.131149	−	0.227158i
$790$	−1.08707	−	1.88285i	−0.0386761	−	0.0669889i
$791$	−24.6245	+	2.91832i	−0.875547	+	0.103763i
$792$	8.69727			0.309044
$793$	8.34850	−	40.7831i	0.296464	−	1.44825i
$794$	−1.57938	−	2.73556i	−0.0560500	−	0.0970814i
$795$	−0.0447447	+	0.0775000i	−0.00158693	+	0.00274864i
$796$	−23.0278			−0.816199
$797$	−5.65686	+	9.79797i	−0.200376	+	0.347062i	−0.948650	−	0.316329i	$-0.897550\pi$
$797$	−5.65686	+	9.79797i	−0.200376	+	0.347062i	0.748273	+	0.663390i	$0.230883\pi$
$798$	−4.19103	−	5.61068i	−0.148361	−	0.198616i
$799$	7.02597	−	12.1693i	0.248561	−	0.430520i
$800$	10.4182	+	18.0449i	0.368340	+	0.637984i
$801$	9.23451	+	15.9946i	0.326285	+	0.565143i
$802$	39.0311			1.37824
$803$	−66.9657			−2.36317
$804$	−1.44507	−	2.50293i	−0.0509635	−	0.0882714i
$805$	−17.1736	+	2.03529i	−0.605289	+	0.0717344i
$806$	−7.22754	+	35.3071i	−0.254579	+	1.24364i
$807$	−4.05355	+	7.02096i	−0.142692	+	0.247149i
$808$	−0.905900	+	1.56906i	−0.0318694	+	0.0551995i
$809$	−8.18540	+	14.1775i	−0.287783	+	0.498455i	−0.973280	−	0.229620i	$-0.926252\pi$
$809$	−8.18540	+	14.1775i	−0.287783	+	0.498455i	0.685497	+	0.728075i	$0.259585\pi$
$810$	−10.3606	−	17.9450i	−0.364033	−	0.630524i
$811$	−29.0412			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$811$	−29.0412			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$812$	0.285352	−	0.664454i	0.0100139	−	0.0233178i
$813$	−6.88373	+	11.9230i	−0.241423	+	0.418157i
$814$	−29.5146	+	51.1209i	−1.03449	+	1.79179i
$815$	−5.67470			−0.198776
$816$	−1.18561	+	2.05354i	−0.0415046	+	0.0718881i
$817$	0.0737588			0.00258050
$818$	−28.3278			−0.990458
$819$	−24.3121	+	11.4351i	−0.849532	+	0.399576i
$820$	−12.4084			−0.433319
$821$	−13.7518			−0.479940			−0.239970	−	0.970780i	$-0.577138\pi$
$821$	−13.7518			−0.479940			−0.239970	+	0.970780i	$0.577138\pi$
$822$	−5.22526	+	9.05041i	−0.182252	+	0.315669i
$823$	−29.1153			−1.01490			−0.507448	−	0.861682i	$-0.669411\pi$
$823$	−29.1153			−1.01490			−0.507448	+	0.861682i	$0.669411\pi$
$824$	5.92623	−	10.2645i	0.206450	−	0.357582i
$825$	−2.66354	+	4.61338i	−0.0927325	+	0.160617i
$826$	16.1223	+	21.5835i	0.560966	+	0.750985i
$827$	−22.9118			−0.796722			−0.398361	−	0.917229i	$-0.630421\pi$
$827$	−22.9118			−0.796722			−0.398361	+	0.917229i	$0.630421\pi$
$828$	−10.1921	−	17.6533i	−0.354201	−	0.613494i
$829$	11.6914	−	20.2502i	0.406061	−	0.703317i	−0.588384	−	0.808582i	$-0.700236\pi$
$829$	11.6914	−	20.2502i	0.406061	−	0.703317i	0.994444	+	0.105264i	$0.0335689\pi$
$830$	22.4832	−	38.9421i	0.780404	−	1.35170i
$831$	−3.94287	+	6.82925i	−0.136777	+	0.236904i
$832$	−13.0219	−	11.5488i	−0.451454	−	0.400382i
$833$	2.38865	−	8.07301i	0.0827620	−	0.279713i
$834$	−0.138275	−	0.239499i	−0.00478806	−	0.00829317i
$835$	−3.15094			−0.109043
$836$	−23.2350			−0.803601
$837$	6.53591	+	11.3205i	0.225914	+	0.391295i
$838$	−22.5023	−	38.9751i	−0.777328	−	1.34637i
$839$	−0.367168	+	0.635954i	−0.0126761	+	0.0219556i	−0.872294	−	0.488982i	$-0.837368\pi$
$839$	−0.367168	+	0.635954i	−0.0126761	+	0.0219556i	0.859618	+	0.510938i	$0.170702\pi$
$840$	−0.463138	+	1.07844i	−0.0159798	+	0.0372096i
$841$	14.4860	−	25.0904i	0.499516	−	0.865187i
$842$	−49.7013			−1.71282
$843$	3.04737	−	5.27820i	0.104957	−	0.181791i
$844$	3.77314	+	6.53528i	0.129877	+	0.224954i
$845$	17.6103	+	7.52515i	0.605811	+	0.258873i
$846$	62.7042			2.15582
$847$	8.66941	−	20.1871i	0.297884	−	0.693637i
$848$	−0.326223	−	0.565035i	−0.0112026	−	0.0194034i
$849$	2.44834	+	4.24066i	0.0840270	+	0.145539i
$850$	3.24282	+	5.61674i	0.111228	+	0.192652i
$851$	−31.2840			−1.07240
$852$	3.48375	+	6.03403i	0.119351	+	0.206722i
$853$	54.3567			1.86114			0.930569	−	0.366118i	$-0.119313\pi$
$853$	54.3567			1.86114			0.930569	+	0.366118i	$0.119313\pi$
$854$	−22.9697	+	53.4859i	−0.786006	+	1.83025i
$855$	−6.72567	−	11.6492i	−0.230013	−	0.398395i
$856$	6.10259			0.208582
$857$	10.5106	+	18.2048i	0.359034	+	0.621864i	0.987800	−	0.155730i	$-0.0497730\pi$
$857$	10.5106	+	18.2048i	0.359034	+	0.621864i	−0.628766	+	0.777595i	$0.716440\pi$
$858$	2.59375	−	12.6707i	0.0885493	−	0.432570i
$859$	25.6814	−	44.4816i	0.876240	−	1.51769i	0.0208035	−	0.999784i	$-0.493378\pi$
$859$	25.6814	−	44.4816i	0.876240	−	1.51769i	0.855436	−	0.517908i	$-0.173289\pi$
$860$	0.0273336	+	0.0473431i	0.000932066	+	0.00161439i
$861$	3.50308	+	4.68970i	0.119385	+	0.159824i
$862$	−12.6884	+	21.9769i	−0.432167	+	0.748535i
$863$	−3.55660	+	6.16021i	−0.121068	+	0.209696i	−0.920189	−	0.391474i	$-0.871965\pi$
$863$	−3.55660	+	6.16021i	−0.121068	+	0.209696i	0.799121	+	0.601170i	$0.205299\pi$
$864$	−18.3489			−0.624241
$865$	24.4735			0.832124
$866$	19.4577	−	33.7018i	0.661201	−	1.14523i
$867$	3.33193	−	5.77107i	0.113158	−	0.195996i
$868$	8.93280	−	20.8004i	0.303199	−	0.706012i
$869$	1.70143	+	2.94696i	0.0577171	+	0.0999689i
$870$	−0.100764	+	0.174528i	−0.00341622	+	0.00591707i
$871$	−14.1458	+	4.71419i	−0.479311	+	0.159734i
$872$	4.23133	+	7.32888i	0.143291	+	0.248187i
$873$	−9.83403			−0.332831
$874$	−13.7062	−	23.7399i	−0.463620	−	0.803013i
$875$	18.2630	+	24.4493i	0.617401	+	0.826537i
$876$	10.6518			0.359892
$877$	−0.256238	−	0.443818i	−0.00865255	−	0.0149867i	0.861667	−	0.507475i	$-0.169421\pi$
$877$	−0.256238	−	0.443818i	−0.00865255	−	0.0149867i	−0.870319	+	0.492488i	$0.836088\pi$
$878$	18.6187			0.628352
$879$	2.82874	+	4.89953i	0.0954112	+	0.165257i
$880$	14.8917	+	25.7933i	0.502000	+	0.869490i
$881$	18.5464	+	32.1232i	0.624843	+	1.08226i	0.988571	+	0.150754i	$0.0481702\pi$
$881$	18.5464	+	32.1232i	0.624843	+	1.08226i	−0.363729	+	0.931505i	$0.618497\pi$
$882$	36.5275	−	8.78127i	1.22994	−	0.295681i
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$	−5.29204	−	4.69336i	−0.177990	−	0.157855i
$885$	−1.68631	−	2.92078i	−0.0566847	−	0.0981809i
$886$	20.1645	−	34.9260i	0.677440	−	1.17336i
$887$	27.5799			0.926043			0.463022	−	0.886347i	$-0.346765\pi$
$887$	27.5799			0.926043			0.463022	+	0.886347i	$0.346765\pi$
$888$	−1.06158	+	1.83871i	−0.0356243	+	0.0617030i
$889$	16.5847	−	38.6182i	0.556233	−	1.29521i
$890$	−9.20404	+	15.9419i	−0.308520	+	0.534372i
$891$	16.2159	+	28.0868i	0.543254	+	0.940944i
$892$	17.4145	+	30.1627i	0.583079	+	1.00992i
$893$	37.8792			1.26758
$894$	−3.20300			−0.107124
$895$	−0.397374	−	0.688272i	−0.0132827	−	0.0230064i
$896$	−8.75140	−	11.7158i	−0.292364	−	0.391398i
$897$	6.50279	−	2.16711i	0.217122	−	0.0723577i
$898$	−17.2895	+	29.9463i	−0.576959	+	0.999323i
$899$	−0.439466	+	0.761178i	−0.0146570	+	0.0253867i
$900$	−6.50032	+	11.2589i	−0.216677	+	0.375296i
$901$	−0.0852637	−	0.147681i	−0.00284054	−	0.00491997i
$902$	43.2337			1.43952
$903$	0.0101765	−	0.0236963i	0.000338651	−	0.000788564i
$904$	−3.29366	+	5.70479i	−0.109546	+	0.189738i
$905$	2.04149	−	3.53597i	0.0678615	−	0.117539i
$906$	1.72985			0.0574703
$907$	22.5236	−	39.0119i	0.747882	−	1.29537i	−0.200954	−	0.979601i	$-0.564404\pi$
$907$	22.5236	−	39.0119i	0.747882	−	1.29537i	0.948836	−	0.315769i	$-0.102263\pi$
$908$	−17.0440			−0.565625
$909$	−7.26019			−0.240805
$910$	−21.9863	−	15.2867i	−0.728840	−	0.506749i
$911$	35.4678			1.17510			0.587550	−	0.809188i	$-0.300093\pi$
$911$	35.4678			1.17510			0.587550	+	0.809188i	$0.300093\pi$
$912$	−6.39198			−0.211660
$913$	−35.1898	+	60.9505i	−1.16461	+	2.01717i
$914$	34.3379			1.13580
$915$	3.64360	−	6.31090i	0.120454	−	0.208632i
$916$	−11.7917	+	20.4238i	−0.389608	+	0.674820i
$917$	−4.88020	+	0.578365i	−0.161158	+	0.0190993i
$918$	−5.71135			−0.188503
$919$	−8.68622	−	15.0450i	−0.286532	−	0.496288i	0.686447	−	0.727179i	$-0.259169\pi$
$919$	−8.68622	−	15.0450i	−0.286532	−	0.496288i	−0.972980	+	0.230891i	$0.925836\pi$
$920$	−2.29706	+	3.97862i	−0.0757318	+	0.131171i
$921$	1.42652	−	2.47081i	0.0470056	−	0.0814160i
$922$	−28.3686	+	49.1359i	−0.934271	+	1.61820i
$923$	34.1024	−	11.3649i	1.12250	−	0.374081i
$924$	−3.20572	+	7.46466i	−0.105461	+	0.245569i
$925$	9.97613	+	17.2792i	0.328013	+	0.568136i
$926$	−33.7412			−1.10880
$927$	47.4948			1.55993
$928$	−0.616877	−	1.06846i	−0.0202500	−	0.0350740i
$929$	−5.38001	−	9.31845i	−0.176512	−	0.305729i	0.764171	−	0.645013i	$-0.223148\pi$
$929$	−5.38001	−	9.31845i	−0.176512	−	0.305729i	−0.940684	+	0.339285i	$0.889815\pi$
$930$	−3.15437	+	5.46353i	−0.103436	+	0.179156i
$931$	22.0660	−	5.30470i	0.723183	−	0.173854i
$932$	7.57532	−	13.1208i	0.248138	−	0.429788i
$933$	−0.876590			−0.0286983
$934$	−5.55396	+	9.61975i	−0.181731	+	0.314768i
$935$	3.89219	+	6.74148i	0.127288	+	0.220470i
$936$	−1.43136	+	6.99228i	−0.0467853	+	0.228550i
$937$	−10.9816			−0.358755			−0.179377	−	0.983780i	$-0.557408\pi$
$937$	−10.9816			−0.358755			−0.179377	+	0.983780i	$0.557408\pi$
$938$	20.7046	−	2.45375i	0.676029	−	0.0801179i
$939$	−2.01749	−	3.49439i	−0.0658383	−	0.114035i
$940$	14.0373	+	24.3132i	0.457845	+	0.793011i
$941$	−4.08897	−	7.08231i	−0.133297	−	0.230877i	0.791649	−	0.610976i	$-0.209223\pi$
$941$	−4.08897	−	7.08231i	−0.133297	−	0.230877i	−0.924946	+	0.380100i	$0.875890\pi$
$942$	18.0536			0.588219
$943$	11.4564	+	19.8430i	0.373071	+	0.646177i
$944$	24.5890			0.800305
$945$	−9.64530	+	1.14309i	−0.313762	+	0.0371847i
$946$	−0.0952365	−	0.164954i	−0.00309640	−	0.00536313i
$947$	−4.59378			−0.149278			−0.0746389	−	0.997211i	$-0.523780\pi$
$947$	−4.59378			−0.149278			−0.0746389	+	0.997211i	$0.523780\pi$
$948$	−0.270636	−	0.468756i	−0.00878986	−	0.0152245i
$949$	11.0209	−	53.8379i	0.357753	−	1.74765i
$950$	−8.74153	+	15.1408i	−0.283613	+	0.491231i
$951$	7.14892	+	12.3823i	0.231820	+	0.401524i
$952$	−1.33844	−	1.79181i	−0.0433790	−	0.0580730i
$953$	−10.5714	+	18.3102i	−0.342442	+	0.593126i	−0.984886	−	0.173206i	$-0.944587\pi$
$953$	−10.5714	+	18.3102i	−0.342442	+	0.593126i	0.642444	+	0.766333i	$0.277921\pi$
$954$	0.380474	−	0.659000i	0.0123183	−	0.0213359i
$955$	29.8172			0.964863
$956$	32.0249			1.03576
$957$	0.157712	−	0.273165i	0.00509809	−	0.00883016i
$958$	13.8070	−	23.9145i	0.446085	−	0.772641i
$959$	−20.2671	−	27.1323i	−0.654459	−	0.876148i
$960$	−1.52342	−	2.63864i	−0.0491681	−	0.0851616i
$961$	1.74271	−	3.01846i	0.0562164	−	0.0973697i
$962$	−36.2419	−	32.1419i	−1.16849	−	1.03630i
$963$	12.2270	+	21.1779i	0.394011	+	0.682447i
$964$	11.9255			0.384094
$965$	−12.0628	−	20.8934i	−0.388316	−	0.672582i
$966$	−9.51788	+	1.12799i	−0.306233	+	0.0362924i
$967$	−32.0750			−1.03146			−0.515731	−	0.856750i	$-0.672480\pi$
$967$	−32.0750			−1.03146			−0.515731	+	0.856750i	$0.672480\pi$
$968$	−2.91817	−	5.05442i	−0.0937936	−	0.162455i
$969$	−1.67065			−0.0536689
$970$	−4.90079	−	8.48841i	−0.157355	−	0.272546i
$971$	26.0417	+	45.1056i	0.835719	+	1.44751i	0.893444	+	0.449175i	$0.148282\pi$
$971$	26.0417	+	45.1056i	0.835719	+	1.44751i	−0.0577245	+	0.998333i	$0.518384\pi$
$972$	−8.67673	−	15.0285i	−0.278306	−	0.482041i
$973$	0.889965	−	0.105472i	0.0285310	−	0.00338128i
$974$	34.2241			1.09661
$975$	−3.27064	−	2.90063i	−0.104744	−	0.0928946i
$976$	26.5647	+	46.0114i	0.850315	+	1.47279i
$977$	−9.62898	+	16.6779i	−0.308058	+	0.533573i	−0.977938	−	0.208897i	$-0.933013\pi$
$977$	−9.62898	+	16.6779i	−0.308058	+	0.533573i	0.669879	+	0.742470i	$0.266346\pi$
$978$	−3.14501			−0.100566
$979$	14.4058	−	24.9515i	0.460410	−	0.797454i
$980$	11.5821	+	12.1975i	0.369977	+	0.389636i
$981$	−16.9557	+	29.3681i	−0.541353	+	0.937650i
$982$	−34.5868	−	59.9061i	−1.10371	−	1.91168i
$983$	8.03657	+	13.9197i	0.256327	+	0.443971i	0.965255	−	0.261310i	$-0.0841544\pi$
$983$	8.03657	+	13.9197i	0.256327	+	0.443971i	−0.708928	+	0.705280i	$0.750821\pi$
$984$	1.55502			0.0495723
$985$	−29.0700			−0.926248
$986$	−0.192012	−	0.332574i	−0.00611490	−	0.0105913i
$987$	5.22616	−	12.1693i	0.166350	−	0.387354i
$988$	3.82391	−	18.6801i	0.121655	−	0.594294i
$989$	0.0504729	−	0.0874216i	0.00160494	−	0.00277985i
$990$	−17.3682	+	30.0826i	−0.551998	+	0.956088i
$991$	−10.7132	+	18.5559i	−0.340317	+	0.589447i	−0.984492	−	0.175432i	$-0.943868\pi$
$991$	−10.7132	+	18.5559i	−0.340317	+	0.589447i	0.644174	+	0.764879i	$0.277201\pi$
$992$	−19.3111	−	33.4478i	−0.613127	−	1.06197i
$993$	8.16876			0.259228
$994$	−49.9144	+	5.91549i	−1.58319	+	0.187628i
$995$	−10.3984	+	18.0106i	−0.329652	+	0.570974i
$996$	5.59743	−	9.69504i	0.177362	−	0.307199i
$997$	−16.9537			−0.536931			−0.268465	−	0.963289i	$-0.586516\pi$
$997$	−16.9537			−0.536931			−0.268465	+	0.963289i	$0.586516\pi$
$998$	22.5881	−	39.1238i	0.715015	−	1.23844i
$999$	−17.5702			−0.555897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.h.b.16.2	yes	12
3.2	odd	2		819.2.s.d.289.5		12
7.2	even	3		637.2.f.k.393.5		12
7.3	odd	6		637.2.g.l.263.5		12
7.4	even	3		91.2.g.b.81.5	yes	12
7.5	odd	6		637.2.f.j.393.5		12
7.6	odd	2		637.2.h.l.471.2		12
13.3	even	3		1183.2.e.h.170.5		12
13.9	even	3		91.2.g.b.9.5	✓	12
13.10	even	6		1183.2.e.g.170.2		12
21.11	odd	6		819.2.n.d.172.2		12
39.35	odd	6		819.2.n.d.100.2		12
91.9	even	3		637.2.f.k.295.5		12
91.16	even	3		8281.2.a.bz.1.2		6
91.23	even	6		8281.2.a.ce.1.5		6
91.48	odd	6		637.2.g.l.373.5		12
91.61	odd	6		637.2.f.j.295.5		12
91.68	odd	6		8281.2.a.ca.1.2		6
91.74	even	3	inner	91.2.h.b.74.2	yes	12
91.75	odd	6		8281.2.a.cf.1.5		6
91.81	even	3		1183.2.e.h.508.5		12
91.87	odd	6		637.2.h.l.165.2		12
91.88	even	6		1183.2.e.g.508.2		12
273.74	odd	6		819.2.s.d.802.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	13.9	even	3
91.2.g.b.81.5	yes	12	7.4	even	3
91.2.h.b.16.2	yes	12	1.1	even	1	trivial
91.2.h.b.74.2	yes	12	91.74	even	3	inner
637.2.f.j.295.5		12	91.61	odd	6
637.2.f.j.393.5		12	7.5	odd	6
637.2.f.k.295.5		12	91.9	even	3
637.2.f.k.393.5		12	7.2	even	3
637.2.g.l.263.5		12	7.3	odd	6
637.2.g.l.373.5		12	91.48	odd	6
637.2.h.l.165.2		12	91.87	odd	6
637.2.h.l.471.2		12	7.6	odd	2
819.2.n.d.100.2		12	39.35	odd	6
819.2.n.d.172.2		12	21.11	odd	6
819.2.s.d.289.5		12	3.2	odd	2
819.2.s.d.802.5		12	273.74	odd	6
1183.2.e.g.170.2		12	13.10	even	6
1183.2.e.g.508.2		12	91.88	even	6
1183.2.e.h.170.5		12	13.3	even	3
1183.2.e.h.508.5		12	91.81	even	3
8281.2.a.bz.1.2		6	91.16	even	3
8281.2.a.ca.1.2		6	91.68	odd	6
8281.2.a.ce.1.5		6	91.23	even	6
8281.2.a.cf.1.5		6	91.75	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.90556 q^{2} +(-0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(0.736565 - 1.27577i) q^{5} +(0.408216 - 0.707051i) q^{6} +(1.58334 + 2.11968i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})\)	\(q-1.90556 q^{2} +(-0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(0.736565 - 1.27577i) q^{5} +(0.408216 - 0.707051i) q^{6} +(1.58334 + 2.11968i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +(-1.40357 + 2.43105i) q^{10} +(2.19681 - 3.80498i) q^{11} +(-0.349433 + 0.605236i) q^{12} +(2.69752 + 2.39236i) q^{13} +(-3.01715 - 4.03917i) q^{14} +(0.315580 + 0.546600i) q^{15} -4.60164 q^{16} -1.20271 q^{17} +(-2.68344 - 4.64786i) q^{18} +(-1.62105 - 2.80773i) q^{19} +(1.20145 - 2.08098i) q^{20} +(-1.12569 + 0.133408i) q^{21} +(-4.18615 + 7.25062i) q^{22} -4.43710 q^{23} +(-0.150567 + 0.260790i) q^{24} +(1.41494 + 2.45075i) q^{25} +(-5.14029 - 4.55878i) q^{26} -2.49204 q^{27} +(2.58268 + 3.45753i) q^{28} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 - 1.04158i) q^{30} +(-2.62272 - 4.54268i) q^{31} +7.36300 q^{32} +(0.941217 + 1.63024i) q^{33} +2.29184 q^{34} +(3.87045 - 0.458697i) q^{35} +(2.29702 + 3.97856i) q^{36} +7.05055 q^{37} +(3.08900 + 5.35031i) q^{38} +(-1.46555 + 0.488407i) q^{39} +(0.517694 - 0.896672i) q^{40} +(-2.58195 - 4.47206i) q^{41} +(2.14507 - 0.254217i) q^{42} +(-0.0113752 + 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} +4.14897 q^{45} +8.45516 q^{46} +(-5.84178 + 10.1183i) q^{47} +(0.985780 - 1.70742i) q^{48} +(-1.98606 + 6.71235i) q^{49} +(-2.69626 - 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(4.40009 + 3.90231i) q^{52} +(0.0708929 + 0.122790i) q^{53} +4.74873 q^{54} +(-3.23618 - 5.60523i) q^{55} +(1.11285 + 1.48981i) q^{56} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} -5.34354 q^{59} +(0.514760 + 0.891591i) q^{60} +(-5.77287 - 9.99891i) q^{61} +(4.99774 + 8.65635i) q^{62} +(-2.94042 + 6.84690i) q^{63} -4.82736 q^{64} +(5.03899 - 1.67929i) q^{65} +(-1.79355 - 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} -1.96181 q^{68} +(0.950533 - 1.64637i) q^{69} +(-7.37537 + 0.874075i) q^{70} +(4.98486 - 8.63403i) q^{71} +(0.989763 + 1.71432i) q^{72} +(-7.62080 - 13.1996i) q^{73} -13.4352 q^{74} -1.21246 q^{75} +(-2.64418 - 4.57986i) q^{76} +(11.5436 - 1.36807i) q^{77} +(2.79269 - 0.930689i) q^{78} +(-0.387251 + 0.670738i) q^{79} +(-3.38941 + 5.87062i) q^{80} +(-3.69080 + 6.39265i) q^{81} +(4.92006 + 8.52179i) q^{82} -16.0186 q^{83} +(-1.83618 + 0.217610i) q^{84} +(-0.885875 + 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} +0.0717913 q^{87} +(1.54402 - 2.67433i) q^{88} +6.55760 q^{89} -7.90611 q^{90} +(-0.799921 + 9.50579i) q^{91} -7.23762 q^{92} +2.24739 q^{93} +(11.1319 - 19.2809i) q^{94} -4.77602 q^{95} +(-1.57733 + 2.73202i) q^{96} +(-1.74583 + 3.02387i) q^{97} +(3.78455 - 12.7908i) q^{98} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20} - 9 q^{21} - 5 q^{22} + 2 q^{23} - 11 q^{24} + 7 q^{25} - 16 q^{26} - 8 q^{27} - q^{28} + 3 q^{29} - 5 q^{30} + 16 q^{31} - 16 q^{32} + 16 q^{33} + 32 q^{34} + 20 q^{35} - 21 q^{36} + 26 q^{37} - 17 q^{38} - 20 q^{39} - 5 q^{40} - 8 q^{41} + 50 q^{42} - 11 q^{43} + 21 q^{44} + 14 q^{45} - 32 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} + 41 q^{52} - 2 q^{53} + 36 q^{54} + 9 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} - 26 q^{59} + 20 q^{60} - 5 q^{61} + 5 q^{62} - 40 q^{63} - 30 q^{64} - 5 q^{65} + 18 q^{66} - 11 q^{67} - 58 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 6 q^{74} + 6 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} - 46 q^{84} - q^{85} - 7 q^{86} - 32 q^{87} - 8 q^{89} - 16 q^{90} - 23 q^{91} + 54 q^{92} + 14 q^{93} + 45 q^{94} + 12 q^{95} + 19 q^{96} - 35 q^{97} + 20 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

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