LMFDB - Embedded newform 1183.2.e.h.508.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (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:	$9.44630255912$
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:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.5
Root			$1.16700 - 2.02131i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.h.170.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.952780 + 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(0.736565 + 1.27577i) q^{5} -0.816433 q^{6} +(1.04402 + 2.43105i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})$	\(q+(0.952780 + 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(0.736565 + 1.27577i) q^{5} -0.816433 q^{6} +(1.04402 + 2.43105i) 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} +(-3.01715 + 4.03917i) q^{14} -0.631159 q^{15} +(2.30082 + 3.98514i) q^{16} +(0.601356 - 1.04158i) q^{17} +(-2.68344 + 4.64786i) q^{18} +(-1.62105 - 2.80773i) q^{19} -2.40291 q^{20} +(-1.12569 - 0.133408i) q^{21} +8.37230 q^{22} +(2.21855 + 3.84264i) q^{23} +(-0.150567 + 0.260790i) q^{24} +(1.41494 - 2.45075i) q^{25} -2.49204 q^{27} +(-4.28565 - 0.507904i) q^{28} +0.167561 q^{29} +(-0.601356 - 1.04158i) q^{30} +(-2.62272 + 4.54268i) q^{31} +(-3.68150 + 6.37655i) q^{32} +(0.941217 + 1.63024i) q^{33} +2.29184 q^{34} +(-2.33247 + 3.12256i) q^{35} -4.59405 q^{36} +(-3.52527 - 6.10595i) q^{37} +(3.08900 - 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +5.16390 q^{41} +(-0.852374 - 1.98479i) q^{42} +0.0227504 q^{43} +(3.58334 + 6.20653i) q^{44} +(-2.07449 + 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +(-5.84178 - 10.1183i) q^{47} -1.97156 q^{48} +(-4.82003 + 5.07615i) q^{49} +5.39252 q^{50} +(0.257649 + 0.446262i) q^{51} +(0.0708929 - 0.122790i) q^{53} +(-2.37436 - 4.11252i) q^{54} +6.47236 q^{55} +(0.733790 + 1.70866i) q^{56} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} +(2.67177 - 4.62764i) q^{59} +(0.514760 - 0.891591i) q^{60} +(-5.77287 - 9.99891i) q^{61} -9.99549 q^{62} +(-4.45938 + 5.96993i) q^{63} -4.82736 q^{64} +(-1.79355 + 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} +(0.980907 + 1.69898i) q^{68} -1.90107 q^{69} +(-7.37537 - 0.874075i) q^{70} -9.96971 q^{71} +(0.989763 + 1.71432i) q^{72} +(-7.62080 + 13.1996i) q^{73} +(6.71762 - 11.6353i) q^{74} +(0.606229 + 1.05002i) q^{75} +5.28837 q^{76} +(11.5436 + 1.36807i) q^{77} +(-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} +(1.10654 - 1.48137i) q^{84} +1.77175 q^{85} +(0.0216761 + 0.0375441i) q^{86} +(-0.0358956 + 0.0621731i) q^{87} +(1.54402 - 2.67433i) q^{88} +(-3.27880 - 5.67904i) q^{89} -7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +(11.1319 - 19.2809i) q^{94} +(2.38801 - 4.13616i) q^{95} +(-1.57733 - 2.73202i) q^{96} +3.49166 q^{97} +(-12.9694 - 3.11787i) q^{98} +12.3743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{14} + 4 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 9 q^{21} + 10 q^{22} - q^{23} - 11 q^{24} + 7 q^{25} - 8 q^{27} + 8 q^{28} - 6 q^{29} - 5 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} + 32 q^{34} - 28 q^{35} + 42 q^{36} - 13 q^{37} - 17 q^{38} - 5 q^{40} + 16 q^{41} - 52 q^{42} + 22 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} - 42 q^{48} + 6 q^{49} - 12 q^{50} - 20 q^{51} - 2 q^{53} - 18 q^{54} - 18 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} + 13 q^{59} + 20 q^{60} - 5 q^{61} - 10 q^{62} + 8 q^{63} - 30 q^{64} + 18 q^{66} - 11 q^{67} + 29 q^{68} - 46 q^{69} - 39 q^{70} - 12 q^{71} + 25 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} + 18 q^{76} + 11 q^{77} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} + 41 q^{84} + 2 q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} + 54 q^{92} - 7 q^{93} + 45 q^{94} - 6 q^{95} + 19 q^{96} + 70 q^{97} - 82 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^14 + 4 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 9 * q^21 + 10 * q^22 - q^23 - 11 * q^24 + 7 * q^25 - 8 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 28 * q^35 + 42 * q^36 - 13 * q^37 - 17 * q^38 - 5 * q^40 + 16 * q^41 - 52 * q^42 + 22 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 42 * q^48 + 6 * q^49 - 12 * q^50 - 20 * q^51 - 2 * q^53 - 18 * q^54 - 18 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 - 5 * q^61 - 10 * q^62 + 8 * q^63 - 30 * q^64 + 18 * q^66 - 11 * q^67 + 29 * q^68 - 46 * q^69 - 39 * q^70 - 12 * q^71 + 25 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 + 18 * q^76 + 11 * q^77 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 + 41 * q^84 + 2 * q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 + 19 * q^96 + 70 * q^97 - 82 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.952780	+	1.65026i	0.673717	+	1.16691i	0.976842	+	0.213962i	$0.0686367\pi$
$2$	0.952780	+	1.65026i	0.673717	+	1.16691i	−0.303125	+	0.952951i	$0.598030\pi$
$3$	−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	$0.206137\pi$
$4$	−0.815580	+	1.41263i	−0.407790	+	0.706313i
$5$	0.736565	+	1.27577i	0.329402	+	0.570541i	0.982393	−	0.186825i	$-0.0598196\pi$
$5$	0.736565	+	1.27577i	0.329402	+	0.570541i	−0.652991	+	0.757365i	$0.726486\pi$
$6$	−0.816433			−0.333307
$7$	1.04402	+	2.43105i	0.394604	+	0.918851i
$7$	1.04402	+	2.43105i	0.394604	+	0.918851i
$8$	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
$13$		0			0
$13$		0			0
$14$	−3.01715	+	4.03917i	−0.806368	+	1.07951i
$15$	−0.631159			−0.162965
$16$	2.30082	+	3.98514i	0.575205	+	0.996284i
$17$	0.601356	−	1.04158i	0.145850	−	0.252620i	−0.783840	−	0.620963i	$-0.786742\pi$
$17$	0.601356	−	1.04158i	0.145850	−	0.252620i	0.929690	+	0.368343i	$0.120075\pi$
$18$	−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	$0.954625\pi$
$20$	−2.40291			−0.537307
$21$	−1.12569	−	0.133408i	−0.245645	−	0.0291121i
$22$	8.37230			1.78498
$23$	2.21855	+	3.84264i	0.462600	+	0.801246i	0.999090	−	0.0426603i	$-0.0135833\pi$
$23$	2.21855	+	3.84264i	0.462600	+	0.801246i	−0.536490	+	0.843907i	$0.680250\pi$
$24$	−0.150567	+	0.260790i	−0.0307343	+	0.0532334i
$25$	1.41494	−	2.45075i	0.282989	−	0.490151i
$26$		0			0
$27$	−2.49204			−0.479593
$28$	−4.28565	−	0.507904i	−0.809912	−	0.0959848i
$29$	0.167561			0.0311154			0.0155577	−	0.999879i	$-0.495048\pi$
$29$	0.167561			0.0311154			0.0155577	+	0.999879i	$0.495048\pi$
$30$	−0.601356	−	1.04158i	−0.109792	−	0.190165i
$31$	−2.62272	+	4.54268i	−0.471054	+	0.815889i	−0.999452	−	0.0331076i	$-0.989460\pi$
$31$	−2.62272	+	4.54268i	−0.471054	+	0.815889i	0.528398	+	0.848997i	$0.322793\pi$
$32$	−3.68150	+	6.37655i	−0.650803	+	1.12722i
$33$	0.941217	+	1.63024i	0.163845	+	0.283788i
$34$	2.29184			0.393047
$35$	−2.33247	+	3.12256i	−0.394259	+	0.527809i
$36$	−4.59405			−0.765675
$37$	−3.52527	−	6.10595i	−0.579552	−	1.00381i	−0.995531	−	0.0944386i	$-0.969894\pi$
$37$	−3.52527	−	6.10595i	−0.579552	−	1.00381i	0.415979	−	0.909374i	$-0.363439\pi$
$38$	3.08900	−	5.35031i	0.501102	−	0.867934i
$39$		0			0
$40$	0.517694	+	0.896672i	0.0818546	+	0.141776i
$41$	5.16390			0.806465			0.403233	−	0.915098i	$-0.367887\pi$
$41$	5.16390			0.806465			0.403233	+	0.915098i	$0.367887\pi$
$42$	−0.852374	−	1.98479i	−0.131524	−	0.306260i
$43$	0.0227504			0.00346940			0.00173470	−	0.999998i	$-0.499448\pi$
$43$	0.0227504			0.00346940			0.00173470	+	0.999998i	$0.499448\pi$
$44$	3.58334	+	6.20653i	0.540209	+	0.935670i
$45$	−2.07449	+	3.59311i	−0.309246	+	0.535630i
$46$	−4.22758	+	7.32239i	−0.623323	+	1.07963i
$47$	−5.84178	−	10.1183i	−0.852111	−	1.47590i	−0.879300	−	0.476269i	$-0.841989\pi$
$47$	−5.84178	−	10.1183i	−0.852111	−	1.47590i	0.0271891	−	0.999630i	$-0.491344\pi$
$48$	−1.97156			−0.284570
$49$	−4.82003	+	5.07615i	−0.688576	+	0.725164i
$50$	5.39252			0.762618
$51$	0.257649	+	0.446262i	0.0360781	+	0.0624892i
$52$		0			0
$53$	0.0708929	−	0.122790i	0.00973788	−	0.0168665i	−0.861115	−	0.508410i	$-0.830234\pi$
$53$	0.0708929	−	0.122790i	0.00973788	−	0.0168665i	0.870853	+	0.491543i	$0.163567\pi$
$54$	−2.37436	−	4.11252i	−0.323110	−	0.559643i
$55$	6.47236			0.872734
$56$	0.733790	+	1.70866i	0.0980568	+	0.228330i
$57$	1.38907			0.183986
$58$	0.159649	+	0.276520i	0.0209630	+	0.0363089i
$59$	2.67177	−	4.62764i	0.347835	−	0.602468i	−0.638030	−	0.770012i	$-0.720250\pi$
$59$	2.67177	−	4.62764i	0.347835	−	0.602468i	0.985865	+	0.167544i	$0.0535837\pi$
$60$	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	$-0.431435\pi$
$62$	−9.99549			−1.26943
$63$	−4.45938	+	5.96993i	−0.561829	+	0.752140i
$64$	−4.82736			−0.603420
$65$		0			0
$66$	−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	$0.247957\pi$
$68$	0.980907	+	1.69898i	0.118952	+	0.206032i
$69$	−1.90107			−0.228861
$70$	−7.37537	−	0.874075i	−0.881526	−	0.104472i
$71$	−9.96971			−1.18319			−0.591594	−	0.806236i	$-0.701501\pi$
$71$	−9.96971			−1.18319			−0.591594	+	0.806236i	$0.701501\pi$
$72$	0.989763	+	1.71432i	0.116645	+	0.202035i
$73$	−7.62080	+	13.1996i	−0.891947	+	1.54490i	−0.0544080	+	0.998519i	$0.517327\pi$
$73$	−7.62080	+	13.1996i	−0.891947	+	1.54490i	−0.837539	+	0.546378i	$0.816006\pi$
$74$	6.71762	−	11.6353i	0.780908	−	1.35257i
$75$	0.606229	+	1.05002i	0.0700013	+	0.121246i
$76$	5.28837			0.606617
$77$	11.5436	+	1.36807i	1.31552	+	0.155906i
$78$		0			0
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	0.843418	−	0.537257i	$-0.180540\pi$
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	−0.886988	+	0.461793i	$0.847206\pi$
$80$	−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	$0.841879\pi$
$84$	1.10654	−	1.48137i	0.120734	−	0.161631i
$85$	1.77175			0.192173
$86$	0.0216761	+	0.0375441i	0.00233740	+	0.00404849i
$87$	−0.0358956	+	0.0621731i	−0.00384842	+	0.00666565i
$88$	1.54402	−	2.67433i	0.164593	−	0.285084i
$89$	−3.27880	−	5.67904i	−0.347552	−	0.601977i	0.638262	−	0.769819i	$-0.279654\pi$
$89$	−3.27880	−	5.67904i	−0.347552	−	0.601977i	−0.985814	+	0.167842i	$0.946320\pi$
$90$	−7.90611			−0.833378
$91$		0			0
$92$	−7.23762			−0.754574
$93$	−1.12370	−	1.94630i	−0.116522	−	0.201822i
$94$	11.1319	−	19.2809i	1.14816	−	1.98868i
$95$	2.38801	−	4.13616i	0.245005	−	0.424361i
$96$	−1.57733	−	2.73202i	−0.160986	−	0.278835i
$97$	3.49166			0.354524			0.177262	−	0.984164i	$-0.443276\pi$
$97$	3.49166			0.354524			0.177262	+	0.984164i	$0.443276\pi$
$98$	−12.9694	−	3.11787i	−1.31011	−	0.314952i
$99$	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	0.897402	+	0.441213i	$0.145452\pi$
$103$	8.43173	+	14.6042i	0.830803	+	1.43899i	−0.0665997	+	0.997780i	$0.521215\pi$
$104$		0			0
$105$	−0.658944	−	1.53438i	−0.0643064	−	0.149740i
$106$	0.270181			0.0262423
$107$	−4.34132	−	7.51939i	−0.419692	−	0.726927i	0.576217	−	0.817297i	$-0.304528\pi$
$107$	−4.34132	−	7.51939i	−0.419692	−	0.726927i	−0.995908	+	0.0903697i	$0.971195\pi$
$108$	2.03245	−	3.52031i	0.195573	−	0.338742i
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	−0.419225	−	0.907882i	$-0.637698\pi$
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	0.995862	−	0.0908816i	$-0.0289685\pi$
$110$	6.16674	+	10.6811i	0.587976	+	1.01840i
$111$	3.02079			0.286721
$112$	−7.28597	+	9.75398i	−0.688459	+	0.921665i
$113$	9.37232			0.881674			0.440837	−	0.897587i	$-0.354682\pi$
$113$	9.37232			0.881674			0.440837	+	0.897587i	$0.354682\pi$
$114$	1.32348	+	2.29233i	0.123955	+	0.214696i
$115$	−3.26821	+	5.66071i	−0.304763	+	0.527864i
$116$	−0.136660	+	0.236701i	−0.0126885	+	0.0219772i
$117$		0			0
$118$	10.1824			0.937369
$119$	3.15996	+	0.374495i	0.289673	+	0.0343299i
$120$	−0.443609			−0.0404958
$121$	−4.15192	−	7.19134i	−0.377448	−	0.653758i
$122$	11.0006	−	19.0535i	0.995944	−	1.72503i
$123$	−1.10623	+	1.91605i	−0.0997453	+	0.172764i
$124$	−4.27807	−	7.40983i	−0.384182	−	0.665423i
$125$	11.5344			1.03167
$126$	−14.1008	−	1.67112i	−1.25620	−	0.148875i
$127$	15.8854			1.40960			0.704800	−	0.709406i	$-0.251037\pi$
$127$	15.8854			1.40960			0.704800	+	0.709406i	$0.251037\pi$
$128$	2.76359	+	4.78667i	0.244269	+	0.423086i
$129$	−0.00487367	+	0.00844145i	−0.000429103	+	0.000743228i
$130$		0			0
$131$	−0.928725	−	1.60860i	−0.0811430	−	0.140544i	0.822598	−	0.568623i	$-0.192524\pi$
$131$	−0.928725	−	1.60860i	−0.0811430	−	0.140544i	−0.903741	+	0.428079i	$0.859190\pi$
$132$	−3.07055			−0.267257
$133$	5.13334	−	6.87219i	0.445117	−	0.595894i
$134$	−7.88036			−0.680759
$135$	−1.83555	−	3.17926i	−0.157979	−	0.273627i
$136$	0.422662	−	0.732072i	0.0362430	−	0.0627747i
$137$	6.40011	−	11.0853i	0.546798	−	0.947082i	−0.451693	−	0.892173i	$-0.649180\pi$
$137$	6.40011	−	11.0853i	0.546798	−	0.947082i	0.998491	−	0.0549088i	$-0.0174868\pi$
$138$	−1.81130	−	3.13726i	−0.154188	−	0.267061i
$139$	−0.338729			−0.0287306			−0.0143653	−	0.999897i	$-0.504573\pi$
$139$	−0.338729			−0.0287306			−0.0143653	+	0.999897i	$0.504573\pi$
$140$	−2.50869	−	5.84160i	−0.212023	−	0.493705i
$141$	5.00579			0.421564
$142$	−9.49894	−	16.4527i	−0.797134	−	1.38068i
$143$		0			0
$144$	−6.48010	+	11.2239i	−0.540009	+	0.935322i
$145$	0.123420	+	0.213769i	0.0102495	+	0.0177526i
$146$	−29.0438			−2.40368
$147$	−0.850922	−	2.87589i	−0.0701828	−	0.237199i
$148$	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	$0.884708\pi$
$150$	−1.15521	+	2.00088i	−0.0943222	+	0.163371i
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	−0.819695	−	0.572800i	$-0.805857\pi$
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	0.905907	+	0.423476i	$0.139190\pi$
$152$	−1.13935	−	1.97341i	−0.0924135	−	0.160065i
$153$	3.38736			0.273851
$154$	8.74087	+	20.3535i	0.704359	+	1.64013i
$155$	−7.72721			−0.620664
$156$		0			0
$157$	11.0564	−	19.1502i	0.882397	−	1.52836i	0.0337285	−	0.999431i	$-0.489262\pi$
$157$	11.0564	−	19.1502i	0.882397	−	1.52836i	0.848668	−	0.528925i	$-0.177405\pi$
$158$	0.737929	−	1.27813i	0.0587065	−	0.101683i
$159$	0.0303739	+	0.0526091i	0.00240881	+	0.00417217i
$160$	−10.8467			−0.857504
$161$	−7.02545	+	9.40522i	−0.553683	+	0.741235i
$162$	−14.0661			−1.10513
$163$	−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
$165$	−1.38653	+	2.40155i	−0.107942	+	0.186960i
$166$	−15.2622	−	26.4349i	−1.18458	−	2.05175i
$167$	2.13894			0.165516			0.0827582	−	0.996570i	$-0.473627\pi$
$167$	2.13894			0.165516			0.0827582	+	0.996570i	$0.473627\pi$
$168$	−0.791188	−	0.0937658i	−0.0610415	−	0.00723419i
$169$		0			0
$170$	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
$175$	7.43515	+	0.881159i	0.562044	+	0.0666094i
$176$	20.2178			1.52398
$177$	1.14471	+	1.98270i	0.0860419	+	0.149029i
$178$	6.24795	−	10.8218i	0.468303	−	0.811125i
$179$	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	$0.160248\pi$
$180$	−3.38382	−	5.86094i	−0.252215	−	0.436849i
$181$	2.77164			0.206014			0.103007	−	0.994681i	$-0.467154\pi$
$181$	2.77164			0.206014			0.103007	+	0.994681i	$0.467154\pi$
$182$		0			0
$183$	4.94675			0.365674
$184$	1.55931	+	2.70080i	0.114954	+	0.199105i
$185$	5.19319	−	8.99486i	0.381811	−	0.661316i
$186$	2.14127	−	3.70879i	0.157006	−	0.271942i
$187$	−2.64213	−	4.57629i	−0.193211	−	0.334652i
$188$	19.0577			1.38993
$189$	−2.60174	−	6.05827i	−0.189249	−	0.440674i
$190$	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			0
$196$	−3.23958	−	10.9489i	−0.231398	−	0.782064i
$197$	19.7335			1.40595			0.702977	−	0.711212i	$-0.251854\pi$
$197$	19.7335			1.40595			0.702977	+	0.711212i	$0.251854\pi$
$198$	11.7900	+	20.4209i	0.837879	+	1.45125i
$199$	7.05873	−	12.2261i	0.500380	−	0.866683i	−0.499620	−	0.866245i	$-0.666527\pi$
$199$	7.05873	−	12.2261i	0.500380	−	0.866683i	1.00000		0.000438630i	$-0.000139620\pi$
$200$	0.994491	−	1.72251i	0.0703212	−	0.121800i
$201$	−0.885913	−	1.53445i	−0.0624875	−	0.108232i
$202$	−4.91214			−0.345617
$203$	0.174938	+	0.407351i	0.0122782	+	0.0285904i
$204$	−0.840534			−0.0588492
$205$	3.80354	+	6.58793i	0.265651	+	0.460121i
$206$	−16.0672	+	27.8291i	−1.11945	+	1.93895i
$207$	−6.24840	+	10.8225i	−0.434294	+	0.752219i
$208$		0			0
$209$	−14.2445			−0.985313
$210$	1.90430	−	2.54936i	0.131409	−	0.175922i
$211$	−4.62634			−0.318490			−0.159245	−	0.987239i	$-0.550906\pi$
$211$	−4.62634			−0.318490			−0.159245	+	0.987239i	$0.550906\pi$
$212$	0.115638	+	0.200290i	0.00794202	+	0.0137560i
$213$	2.13575	−	3.69923i	0.146339	−	0.253467i
$214$	8.27265	−	14.3287i	0.565507	−	0.979487i
$215$	0.0167571	+	0.0290242i	0.00114283	+	0.00197943i
$216$	−1.75152			−0.119176
$217$	−13.7817	−	1.63330i	−0.935561	−	0.110876i
$218$	22.9439			1.55396
$219$	−3.26511	−	5.65534i	−0.220636	−	0.382152i
$220$	−5.27873	+	9.14303i	−0.355892	+	0.616423i
$221$		0			0
$222$	2.87815	+	4.98510i	0.193169	+	0.334578i
$223$	−21.3523			−1.42985			−0.714926	−	0.699200i	$-0.753540\pi$
$223$	−21.3523			−1.42985			−0.714926	+	0.699200i	$0.753540\pi$
$224$	−19.3453	−	2.29266i	−1.29256	−	0.153185i
$225$	7.97019			0.531346
$226$	8.92976	+	15.4668i	0.593999	+	1.02884i
$227$	5.22451	−	9.04911i	0.346763	−	0.600611i	−0.638910	−	0.769282i	$-0.720614\pi$
$227$	5.22451	−	9.04911i	0.346763	−	0.600611i	0.985672	+	0.168671i	$0.0539476\pi$
$228$	−1.13289	+	1.96223i	−0.0750278	+	0.129952i
$229$	−7.22901	−	12.5210i	−0.477706	−	0.827412i	0.521967	−	0.852966i	$-0.325198\pi$
$229$	−7.22901	−	12.5210i	−0.477706	−	0.827412i	−0.999673	+	0.0255538i	$0.991865\pi$
$230$	−12.4556			−0.821295
$231$	−2.98054	+	3.99015i	−0.196105	+	0.262533i
$232$	0.117770			0.00773200
$233$	4.64413	+	8.04388i	0.304247	+	0.526972i	0.977093	−	0.212811i	$-0.0682617\pi$
$233$	4.64413	+	8.04388i	0.304247	+	0.526972i	−0.672846	+	0.739783i	$0.734928\pi$
$234$		0			0
$235$	8.60570	−	14.9055i	0.561374	−	0.972328i
$236$	4.35808	+	7.54842i	0.283687	+	0.491360i
$237$	0.331833			0.0215549
$238$	2.39273	+	5.57158i	0.155098	+	0.361152i
$239$	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
$241$	−3.65552	+	6.33155i	−0.235473	+	0.407851i	−0.959410	−	0.282015i	$-0.908997\pi$
$241$	−3.65552	+	6.33155i	−0.235473	+	0.407851i	0.723937	+	0.689866i	$0.242331\pi$
$242$	7.91174	−	13.7035i	0.508586	−	0.880897i
$243$	−5.31937	−	9.21341i	−0.341238	−	0.591041i
$244$	18.8330			1.20566
$245$	−10.0263	−	2.41033i	−0.640554	−	0.153990i
$246$	−4.21597			−0.268801
$247$		0			0
$248$	−1.84337	+	3.19282i	−0.117054	+	0.202744i
$249$	3.43157	−	5.94365i	0.217467	−	0.376664i
$250$	10.9898	+	19.0349i	0.695055	+	1.20387i
$251$	−11.8638			−0.748837			−0.374419	−	0.927260i	$-0.622158\pi$
$251$	−11.8638			−0.748837			−0.374419	+	0.927260i	$0.622158\pi$
$252$	−4.79629	−	11.1684i	−0.302138	−	0.703542i
$253$	19.4949			1.22563
$254$	15.1353	+	26.2151i	0.949672	+	1.64488i
$255$	−0.379551	+	0.657402i	−0.0237684	+	0.0411681i
$256$	−10.0935	+	17.4825i	−0.630846	+	1.09266i
$257$	7.58608	+	13.1395i	0.473206	+	0.819618i	0.999530	−	0.0306670i	$-0.00976315\pi$
$257$	7.58608	+	13.1395i	0.473206	+	0.819618i	−0.526323	+	0.850285i	$0.676430\pi$
$258$	−0.0185742			−0.00115638
$259$	11.1634	−	14.9449i	0.693662	−	0.928630i
$260$		0			0
$261$	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
$266$	16.2319	+	1.92368i	0.995239	+	0.117948i
$267$	2.80959			0.171944
$268$	−3.37279	−	5.84185i	−0.206026	−	0.356848i
$269$	−9.46102	+	16.3870i	−0.576849	+	0.999131i	0.418989	+	0.907991i	$0.362384\pi$
$269$	−9.46102	+	16.3870i	−0.576849	+	0.999131i	−0.995838	+	0.0911401i	$0.970949\pi$
$270$	3.49774	−	6.05827i	0.212866	−	0.368695i
$271$	−16.0667	−	27.8283i	−0.975982	−	1.69045i	−0.676657	−	0.736298i	$-0.736572\pi$
$271$	−16.0667	−	27.8283i	−0.975982	−	1.69045i	−0.299324	−	0.954151i	$-0.596761\pi$
$272$	5.53444			0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	−6.21672	−	10.7677i	−0.374882	−	0.649315i
$276$	1.55047	−	2.68549i	0.0933273	−	0.161648i
$277$	−9.20269	+	15.9395i	−0.552936	+	0.957714i	0.445125	+	0.895469i	$0.353159\pi$
$277$	−9.20269	+	15.9395i	−0.552936	+	0.957714i	−0.998061	+	0.0622450i	$0.980174\pi$
$278$	−0.322734	−	0.558992i	−0.0193563	−	0.0335261i
$279$	−14.7734			−0.884461
$280$	−1.63937	+	2.19469i	−0.0979712	+	0.131158i
$281$	−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
$286$		0			0
$287$	5.39123	+	12.5537i	0.318234	+	0.741022i
$288$	−20.7374			−1.22196
$289$	7.77674	+	13.4697i	0.457455	+	0.792336i
$290$	−0.235184	+	0.407351i	−0.0138105	+	0.0239205i
$291$	−0.747997	+	1.29557i	−0.0438483	+	0.0759476i
$292$	−12.4307	−	21.5307i	−0.727453	−	1.25999i
$293$	−13.2046			−0.771422			−0.385711	−	0.922620i	$-0.626044\pi$
$293$	−13.2046			−0.771422			−0.385711	+	0.922620i	$0.626044\pi$
$294$	3.93523	−	4.14433i	0.229507	−	0.241702i
$295$	7.87173			0.458310
$296$	−2.47773	−	4.29156i	−0.144015	−	0.249442i
$297$	−5.47452	+	9.48215i	−0.317664	+	0.550210i
$298$	3.73791	−	6.47425i	0.216531	−	0.375043i
$299$		0			0
$300$	−1.97771			−0.114183
$301$	0.0237519	+	0.0553074i	0.00136904	+	0.00318786i
$302$	4.03748			0.232331
$303$	−0.552225	−	0.956482i	−0.0317245	−	0.0549484i
$304$	7.45947	−	12.9202i	0.427830	−	0.741023i
$305$	8.50420	−	14.7297i	0.486949	−	0.843420i
$306$	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	$0.560857\pi$
$308$	−11.3473	+	15.1911i	−0.646573	+	0.865590i
$309$	−7.22511			−0.411022
$310$	−7.36233	−	12.7519i	−0.418152	−	0.724261i
$311$	1.02298	−	1.77186i	0.0580081	−	0.100473i	−0.835563	−	0.549395i	$-0.814858\pi$
$311$	1.02298	−	1.77186i	0.0580081	−	0.100473i	0.893571	+	0.448922i	$0.148192\pi$
$312$		0			0
$313$	−4.70883	−	8.15594i	−0.266159	−	0.461001i	0.701708	−	0.712465i	$-0.252421\pi$
$313$	−4.70883	−	8.15594i	−0.266159	−	0.461001i	−0.967867	+	0.251464i	$0.919088\pi$
$314$	42.1373			2.37794
$315$	−10.9009	−	1.29189i	−0.614194	−	0.0727897i
$316$	1.26333			0.0710681
$317$	16.6856	+	28.9004i	0.937159	+	1.62321i	0.770738	+	0.637153i	$0.219888\pi$
$317$	16.6856	+	28.9004i	0.937159	+	1.62321i	0.166421	+	0.986055i	$0.446779\pi$
$318$	−0.0578792	+	0.100250i	−0.00324571	+	0.00562173i
$319$	0.368100	−	0.637568i	0.0206097	−	0.0356970i
$320$	−3.55567	−	6.15860i	−0.198768	−	0.344276i
$321$	3.72006			0.207634
$322$	−22.2148	−	2.63273i	−1.23798	−	0.146717i
$323$	−3.89930			−0.216963
$324$	−6.02027	−	10.4274i	−0.334460	−	0.579301i
$325$		0			0
$326$	3.67024	−	6.35704i	0.203276	−	0.352084i
$327$	2.57937	+	4.46760i	0.142639	+	0.247059i
$328$	3.62944			0.200402
$329$	18.4991	−	24.7654i	1.01989	−	1.36536i
$330$	−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	$-0.342220\pi$
$332$	13.0645	−	22.6283i	0.717005	−	1.24189i
$333$	9.92870	−	17.1970i	0.544089	−	0.942390i
$334$	2.03794	+	3.52982i	0.111511	+	0.193143i
$335$	−6.09207			−0.332845
$336$	−2.05835	−	4.79297i	−0.112292	−	0.261478i
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$		0			0
$339$	−2.00777	+	3.47757i	−0.109047	+	0.188876i
$340$	−1.44500	+	2.50282i	−0.0783663	+	0.135734i
$341$	11.5232	+	19.9588i	0.624017	+	1.08083i
$342$	17.3999			0.940880
$343$	−17.3726	−	6.41814i	−0.938033	−	0.346547i
$344$	0.0159901			0.000862127
$345$	−1.40026	−	2.42532i	−0.0753874	−	0.130575i
$346$	−15.8288	+	27.4163i	−0.850961	+	1.47391i
$347$	−5.83759	+	10.1110i	−0.313378	+	0.542787i	−0.979091	−	0.203420i	$-0.934794\pi$
$347$	−5.83759	+	10.1110i	−0.313378	+	0.542787i	0.665713	+	0.746208i	$0.268128\pi$
$348$	−0.0585515	−	0.101414i	−0.00313869	−	0.00543637i
$349$	23.9904			1.28418			0.642089	−	0.766631i	$-0.278068\pi$
$349$	23.9904			1.28418			0.642089	+	0.766631i	$0.278068\pi$
$350$	5.62992	+	13.1095i	0.300932	+	0.700732i
$351$		0			0
$352$	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
$357$	−0.815894	+	1.09227i	−0.0431817	+	0.0578089i
$358$	1.02804			0.0543337
$359$	−6.16986	−	10.6865i	−0.325633	−	0.564012i	0.656008	−	0.754754i	$-0.272244\pi$
$359$	−6.16986	−	10.6865i	−0.325633	−	0.564012i	−0.981640	+	0.190742i	$0.938911\pi$
$360$	−1.45805	+	2.52542i	−0.0768460	+	0.133101i
$361$	4.24442	−	7.35155i	0.223390	−	0.386924i
$362$	2.64076	+	4.57393i	0.138795	+	0.240401i
$363$	3.55776			0.186734
$364$		0			0
$365$	−22.4528			−1.17524
$366$	4.71316	+	8.16344i	0.246361	+	0.426710i
$367$	−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	$0.183546\pi$
$368$	−10.2090	+	17.6825i	−0.532179	+	0.921762i
$369$	7.27188	+	12.5953i	0.378559	+	0.655684i
$370$	19.7919			1.02893
$371$	0.372523	+	0.0441487i	0.0193404	+	0.00229208i
$372$	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			0
$378$	7.51886	−	10.0658i	0.386728	−	0.517727i
$379$	−14.5679			−0.748303			−0.374152	−	0.927368i	$-0.622066\pi$
$379$	−14.5679			−0.748303			−0.374152	+	0.927368i	$0.622066\pi$
$380$	3.89523	+	6.74673i	0.199821	+	0.346100i
$381$	−3.40303	+	5.89422i	−0.174342	+	0.301970i
$382$	−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	$0.593466\pi$
$384$	−2.36810			−0.120847
$385$	6.75730	+	15.7347i	0.344384	+	0.801912i
$386$	31.2076			1.58842
$387$	0.0320375	+	0.0554905i	0.00162856	+	0.00282074i
$388$	−2.84773	+	4.93241i	−0.144571	+	0.250405i
$389$	−6.00738	+	10.4051i	−0.304586	+	0.527559i	−0.977169	−	0.212463i	$-0.931852\pi$
$389$	−6.00738	+	10.4051i	−0.304586	+	0.527559i	0.672583	+	0.740022i	$0.265185\pi$
$390$		0			0
$391$	5.33655			0.269881
$392$	−3.38775	+	3.56776i	−0.171107	+	0.180199i
$393$	0.795820			0.0401438
$394$	18.8017	+	32.5655i	0.947216	+	1.64063i
$395$	0.570470	−	0.988084i	0.0287035	−	0.0497159i
$396$	−10.0922	+	17.4803i	−0.507154	+	0.878417i
$397$	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
$399$	1.45022	+	3.37689i	0.0726017	+	0.169056i
$400$	13.0221			0.651106
$401$	10.2414	+	17.7386i	0.511430	+	0.885823i	0.999912	+	0.0132488i	$0.00421735\pi$
$401$	10.2414	+	17.7386i	0.511430	+	0.885823i	−0.488482	+	0.872574i	$0.662449\pi$
$402$	1.68816	−	2.92398i	0.0841978	−	0.145835i
$403$		0			0
$404$	−2.10240	−	3.64146i	−0.104598	−	0.181169i
$405$	−10.8740			−0.540336
$406$	−0.505558	+	0.676809i	−0.0250904	+	0.0335895i
$407$	−30.9774			−1.53549
$408$	0.181089	+	0.313655i	0.00896522	+	0.0155282i
$409$	−7.43293	+	12.8742i	−0.367535	+	0.636589i	−0.989180	−	0.146710i	$-0.953131\pi$
$409$	−7.43293	+	12.8742i	−0.367535	+	0.636589i	0.621645	+	0.783299i	$0.286465\pi$
$410$	−7.24788	+	12.5537i	−0.357947	+	0.619983i
$411$	2.74211	+	4.74948i	0.135258	+	0.234274i
$412$	−27.5070			−1.35517
$413$	14.0394	+	1.66385i	0.690835	+	0.0818727i
$414$	−23.8134			−1.17036
$415$	−11.7988	−	20.4360i	−0.579178	−	1.00317i
$416$		0			0
$417$	0.0725639	−	0.125684i	0.00355347	−	0.00615479i
$418$	−13.5719	−	23.5072i	−0.663822	−	1.14977i
$419$	−23.6175			−1.15379			−0.576895	−	0.816819i	$-0.695736\pi$
$419$	−23.6175			−1.15379			−0.576895	+	0.816819i	$0.695736\pi$
$420$	2.70493	+	0.320568i	0.131987	+	0.0156421i
$421$	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
$423$	16.4530	−	28.4974i	0.799971	−	1.38559i
$424$	0.0498269	−	0.0863028i	0.00241981	−	0.00419123i
$425$	−1.70177	−	2.94755i	−0.0825479	−	0.142977i
$426$	8.13960			0.394365
$427$	18.2809	−	24.4733i	0.884673	−	1.18434i
$428$	14.1628			0.684584
$429$		0			0
$430$	−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	$0.0627374\pi$
$432$	−5.73373	−	9.93110i	−0.275864	−	0.477810i
$433$	20.4221			0.981422			0.490711	−	0.871322i	$-0.336737\pi$
$433$	20.4221			0.981422			0.490711	+	0.871322i	$0.336737\pi$
$434$	−10.4355	−	24.2996i	−0.500921	−	1.16642i
$435$	−0.105758			−0.00507070
$436$	9.82001	+	17.0087i	0.470293	+	0.814571i
$437$	7.19275	−	12.4582i	0.344076	−	0.595957i
$438$	6.22187	−	10.7766i	0.297292	−	0.514925i
$439$	4.88537	+	8.46171i	0.233166	+	0.403855i	0.958738	−	0.284291i	$-0.0917581\pi$
$439$	4.88537	+	8.46171i	0.233166	+	0.403855i	−0.725572	+	0.688146i	$0.758425\pi$
$440$	4.54909			0.216869
$441$	−19.1689	−	4.60824i	−0.912804	−	0.219440i
$442$		0			0
$443$	−10.5819	−	18.3285i	−0.502763	−	0.870811i	−0.999995	−	0.00319331i	$-0.998984\pi$
$443$	−10.5819	−	18.3285i	−0.502763	−	0.870811i	0.497232	−	0.867618i	$-0.334350\pi$
$444$	−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
$448$	−5.03988	−	11.7356i	−0.238112	−	0.554454i
$449$	−18.1464			−0.856382			−0.428191	−	0.903688i	$-0.640849\pi$
$449$	−18.1464			−0.856382			−0.428191	+	0.903688i	$0.640849\pi$
$450$	7.59384	+	13.1529i	0.357977	+	0.620034i
$451$	11.3441	−	19.6485i	0.534172	−	0.925213i
$452$	−7.64387	+	13.2396i	−0.359538	+	0.622737i
$453$	0.453895	+	0.786168i	0.0213258	+	0.0369374i
$454$	19.9112			0.934480
$455$		0			0
$456$	0.976304			0.0457196
$457$	9.00991	+	15.6056i	0.421466	+	0.730000i	0.996083	−	0.0884220i	$-0.0281824\pi$
$457$	9.00991	+	15.6056i	0.421466	+	0.730000i	−0.574617	+	0.818422i	$0.694849\pi$
$458$	13.7753	−	23.8595i	0.643678	−	1.11488i
$459$	−1.49860	+	2.59565i	−0.0699487	+	0.121155i
$460$	−5.33098	−	9.23352i	−0.248558	−	0.430515i
$461$	−29.7746			−1.38674			−0.693370	−	0.720582i	$-0.743875\pi$
$461$	−29.7746			−1.38674			−0.693370	+	0.720582i	$0.743875\pi$
$462$	−9.42459	−	1.11693i	−0.438472	−	0.0519645i
$463$	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	0.925549	−	0.378629i	$-0.123604\pi$
$467$	2.91461	+	5.04825i	0.134872	+	0.233605i	−0.790677	+	0.612234i	$0.790271\pi$
$468$		0			0
$469$	−10.8654	−	1.28768i	−0.501715	−	0.0594596i
$470$	32.7973			1.51283
$471$	4.73709	+	8.20488i	0.218274	+	0.378061i
$472$	1.87785	−	3.25253i	0.0864350	−	0.149710i
$473$	0.0499782	−	0.0865648i	0.00229800	−	0.00398025i
$474$	0.316164	+	0.547612i	0.0145219	+	0.0251527i
$475$	−9.17476			−0.420967
$476$	−3.10622	+	4.15841i	−0.142373	+	0.190600i
$477$	0.399330			0.0182841
$478$	18.7061	+	32.4000i	0.855598	+	1.48194i
$479$	−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
$481$		0			0
$482$	−13.9316			−0.634569
$483$	−1.98476	−	4.62159i	−0.0903095	−	0.210290i
$484$	13.5449			0.615677
$485$	2.57183	+	4.45455i	0.116781	+	0.202271i
$486$	10.1364	−	17.5567i	0.459795	−	0.796389i
$487$	8.98006	−	15.5539i	0.406926	−	0.704816i	−0.587618	−	0.809139i	$-0.699934\pi$
$487$	8.98006	−	15.5539i	0.406926	−	0.704816i	0.994543	+	0.104323i	$0.0332675\pi$
$488$	−4.05746	−	7.02772i	−0.183672	−	0.318130i
$489$	1.65044			0.0746354
$490$	−5.57514	−	18.8425i	−0.251859	−	0.851216i
$491$	−36.3009			−1.63824			−0.819119	−	0.573624i	$-0.805537\pi$
$491$	−36.3009			−1.63824			−0.819119	+	0.573624i	$0.805537\pi$
$492$	−1.80444	−	3.12537i	−0.0813503	−	0.140903i
$493$	0.100764	−	0.174528i	0.00453818	−	0.00786036i
$494$		0			0
$495$	9.11449	+	15.7868i	0.409666	+	0.709562i
$496$	−24.1376			−1.08381
$497$	−10.4086	−	24.2369i	−0.466890	−	1.08717i
$498$	13.0781			0.586045
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	−0.999360	−	0.0357602i	$-0.988615\pi$
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	0.468711	−	0.883352i	$-0.344719\pi$
$500$	−9.40726	+	16.2938i	−0.420705	+	0.728683i
$501$	−0.458213	+	0.793648i	−0.0204714	+	0.0354576i
$502$	−11.3036	−	19.5784i	−0.504505	−	0.873828i
$503$	27.7752			1.23843			0.619217	−	0.785220i	$-0.287450\pi$
$503$	27.7752			1.23843			0.619217	+	0.785220i	$0.287450\pi$
$504$	−3.13427	+	4.19595i	−0.139611	+	0.186903i
$505$	−3.79743			−0.168983
$506$	18.5744	+	32.1717i	0.825731	+	1.43021i
$507$		0			0
$508$	−12.9558	+	22.4401i	−0.574820	+	0.995618i
$509$	−4.35208	−	7.53802i	−0.192902	−	0.334117i	0.753308	−	0.657667i	$-0.228457\pi$
$509$	−4.35208	−	7.53802i	−0.192902	−	0.334117i	−0.946211	+	0.323551i	$0.895123\pi$
$510$	−1.44651			−0.0640527
$511$	−40.0452	−	4.74586i	−1.77150	−	0.209945i
$512$	−27.4134			−1.21151
$513$	4.03971	+	6.99698i	0.178357	+	0.308924i
$514$	−14.4557	+	25.0380i	−0.637615	+	1.10438i
$515$	−12.4210	+	21.5139i	−0.547336	+	0.948014i
$516$	−0.00794974	−	0.0137693i	−0.000349968	−	0.000606162i
$517$	−51.3330			−2.25762
$518$	35.2993	+	4.18341i	1.55096	+	0.183809i
$519$	−7.11792			−0.312442
$520$		0			0
$521$	4.28573	−	7.42310i	0.187761	−	0.325212i	−0.756742	−	0.653713i	$-0.773210\pi$
$521$	4.28573	−	7.42310i	0.187761	−	0.325212i	0.944504	+	0.328501i	$0.106544\pi$
$522$	−0.449641	+	0.778801i	−0.0196803	+	0.0340872i
$523$	−14.9746	−	25.9369i	−0.654796	−	1.13414i	−0.981945	−	0.189167i	$-0.939421\pi$
$523$	−14.9746	−	25.9369i	−0.654796	−	1.13414i	0.327149	−	0.944973i	$-0.393912\pi$
$524$	3.02980			0.132357
$525$	−1.91974	+	2.57002i	−0.0837842	+	0.112165i
$526$	−32.7688			−1.42879
$527$	3.15437	+	5.46353i	0.137407	+	0.237995i
$528$	−4.33114	+	7.50175i	−0.188489	+	0.326472i
$529$	1.65606	−	2.86838i	0.0720027	−	0.124712i
$530$	0.199006	+	0.344689i	0.00864427	+	0.0149723i
$531$	15.0497			0.653102
$532$	5.52118	+	12.8563i	0.239373	+	0.557391i
$533$		0			0
$534$	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
$539$	8.72597	+	29.4915i	0.375854	+	1.27029i
$540$	5.98814			0.257688
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	0.731091	−	0.682280i	$-0.239011\pi$
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	−0.956417	+	0.292003i	$0.905678\pi$
$542$	30.6160	−	53.0285i	1.31507	−	2.27777i
$543$	−0.593751	+	1.02841i	−0.0254803	+	0.0441331i
$544$	4.42778	+	7.66914i	0.189840	+	0.328812i
$545$	17.7373			0.759781
$546$		0			0
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	10.4396	+	18.0819i	0.445957	+	0.772421i
$549$	16.2589	−	28.1613i	0.693914	−	1.20189i
$550$	11.8463	−	20.5184i	0.505129	−	0.874909i
$551$	−0.271625	−	0.470468i	−0.0115716	−	0.0200426i
$552$	−1.33616			−0.0568708
$553$	1.22630	−	1.64169i	0.0521476	−	0.0698118i
$554$	−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			0
$560$	−17.8104	−	2.11076i	−0.752627	−	0.0891958i
$561$	2.26402			0.0955872
$562$	−13.5535	−	23.4753i	−0.571719	−	0.990246i
$563$	−3.84675	+	6.66276i	−0.162121	+	0.280802i	−0.935629	−	0.352985i	$-0.885167\pi$
$563$	−3.84675	+	6.66276i	−0.162121	+	0.280802i	0.773508	+	0.633786i	$0.218500\pi$
$564$	−4.08262	+	7.07131i	−0.171909	+	0.297756i
$565$	6.90332	+	11.9569i	0.290425	+	0.503031i
$566$	21.7785			0.915418
$567$	−19.3941	−	2.29845i	−0.814477	−	0.0965258i
$568$	−7.00720			−0.294016
$569$	−18.7098	−	32.4063i	−0.784355	−	1.35854i	−0.929384	−	0.369115i	$-0.879661\pi$
$569$	−18.7098	−	32.4063i	−0.784355	−	1.35854i	0.145029	−	0.989427i	$-0.453673\pi$
$570$	−1.94965	+	3.37689i	−0.0816619	+	0.141443i
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	−0.975311	−	0.220834i	$-0.929122\pi$
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	0.678903	+	0.734228i	$0.262456\pi$
$572$		0			0
$573$	−8.67209			−0.362282
$574$	−15.5803	+	20.8579i	−0.650308	+	0.870590i
$575$	12.5565			0.523642
$576$	−6.79797	−	11.7744i	−0.283249	−	0.490601i
$577$	7.48776	−	12.9692i	0.311720	−	0.539914i	−0.667015	−	0.745044i	$-0.732428\pi$
$577$	7.48776	−	12.9692i	0.311720	−	0.539914i	0.978735	+	0.205130i	$0.0657617\pi$
$578$	−14.8190	+	25.6673i	−0.616391	+	1.06762i
$579$	3.50837	+	6.07667i	0.145803	+	0.252538i
$580$	−0.402635			−0.0167185
$581$	−16.7238	−	38.9421i	−0.693820	−	1.61559i
$582$	−2.85071			−0.118166
$583$	−0.311476	−	0.539492i	−0.0129000	−	0.0223435i
$584$	−5.35627	+	9.27732i	−0.221644	+	0.383898i
$585$		0			0
$586$	−12.5811	−	21.7911i	−0.519720	−	0.900182i
$587$	−13.1764			−0.543849			−0.271925	−	0.962319i	$-0.587660\pi$
$587$	−13.1764			−0.543849			−0.271925	+	0.962319i	$0.587660\pi$
$588$	4.75655	+	1.14348i	0.196157	+	0.0471564i
$589$	17.0062			0.700728
$590$	7.50003	+	12.9904i	0.308771	+	0.534807i
$591$	−4.22739	+	7.32205i	−0.173892	+	0.301189i
$592$	16.2220	−	28.0974i	0.666722	−	1.15480i
$593$	22.0663	+	38.2200i	0.906156	+	1.56951i	0.819357	+	0.573283i	$0.194330\pi$
$593$	22.0663	+	38.2200i	0.906156	+	1.56951i	0.0867989	+	0.996226i	$0.472336\pi$
$594$	−20.8641			−0.856063
$595$	1.84975	+	4.30722i	0.0758323	+	0.176579i
$596$	6.39930			0.262125
$597$	3.02429	+	5.23823i	0.123776	+	0.214387i
$598$		0			0
$599$	3.01349	−	5.21952i	0.123128	−	0.213264i	−0.797872	−	0.602827i	$-0.794041\pi$
$599$	3.01349	−	5.21952i	0.123128	−	0.213264i	0.921000	+	0.389564i	$0.127374\pi$
$600$	0.426087	+	0.738005i	0.0173949	+	0.0301289i
$601$	3.72520			0.151954			0.0759770	−	0.997110i	$-0.475792\pi$
$601$	3.72520			0.151954			0.0759770	+	0.997110i	$0.475792\pi$
$602$	−0.0686414	+	0.0918927i	−0.00279761	+	0.00374527i
$603$	−11.6472			−0.474312
$604$	1.72804	+	2.99305i	0.0703129	+	0.121786i
$605$	6.11632	−	10.5938i	0.248664	−	0.430698i
$606$	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	$0.794370\pi$
$608$	23.8715			0.968118
$609$	−0.188622	−	0.0223541i	−0.00764335	−	0.000905833i
$610$	32.4105			1.31226
$611$		0			0
$612$	−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	$0.230136\pi$
$614$	−6.34459	−	10.9892i	−0.256047	−	0.443486i
$615$	−3.25924			−0.131425
$616$	8.11342	+	0.961543i	0.326899	+	0.0387417i
$617$	33.7676			1.35943			0.679716	−	0.733475i	$-0.262103\pi$
$617$	33.7676			1.35943			0.679716	+	0.733475i	$0.262103\pi$
$618$	−6.88394	−	11.9233i	−0.276913	−	0.479627i
$619$	−2.04671	+	3.54501i	−0.0822644	+	0.142486i	−0.904222	−	0.427062i	$-0.859549\pi$
$619$	−2.04671	+	3.54501i	−0.0822644	+	0.142486i	0.821958	+	0.569548i	$0.192882\pi$
$620$	6.30215	−	10.9156i	0.253100	−	0.438383i
$621$	−5.52871	−	9.57601i	−0.221860	−	0.384272i
$622$	3.89871			0.156324
$623$	10.3829	−	13.9000i	0.415983	−	0.556891i
$624$		0			0
$625$	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
$630$	−8.25416	−	19.2202i	−0.328854	−	0.765750i
$631$	−26.7736			−1.06584			−0.532921	−	0.846165i	$-0.678906\pi$
$631$	−26.7736			−1.06584			−0.532921	+	0.846165i	$0.678906\pi$
$632$	−0.272179	−	0.471427i	−0.0108267	−	0.0187524i
$633$	0.991071	−	1.71659i	0.0393915	−	0.0682282i
$634$	−31.7955	+	55.0714i	−1.26276	+	2.18717i
$635$	11.7006	+	20.2661i	0.464325	+	0.804234i
$636$	−0.0990892			−0.00392914
$637$		0			0
$638$	1.40287			0.0555403
$639$	−14.0395	−	24.3172i	−0.555395	−	0.961972i
$640$	−4.07112	+	7.05139i	−0.160925	+	0.278731i
$641$	9.28610	−	16.0840i	0.366779	−	0.635279i	−0.622281	−	0.782794i	$-0.713794\pi$
$641$	9.28610	−	16.0840i	0.366779	−	0.635279i	0.989060	+	0.147514i	$0.0471273\pi$
$642$	3.54440	+	6.13908i	0.139886	+	0.242290i
$643$	−3.93390			−0.155138			−0.0775690	−	0.996987i	$-0.524716\pi$
$643$	−3.93390			−0.155138			−0.0775690	+	0.996987i	$0.524716\pi$
$644$	−7.55624	−	17.5950i	−0.297758	−	0.693341i
$645$	−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
$650$		0			0
$651$	3.55839	−	4.76375i	0.139464	−	0.186706i
$652$	6.28345			0.246079
$653$	7.23363	+	12.5290i	0.283074	+	0.490298i	0.972140	−	0.234400i	$-0.0753125\pi$
$653$	7.23363	+	12.5290i	0.283074	+	0.490298i	−0.689066	+	0.724698i	$0.741979\pi$
$654$	−4.91514	+	8.51327i	−0.192197	+	0.332895i
$655$	1.36813	−	2.36967i	0.0534573	−	0.0925908i
$656$	11.8812	+	20.5788i	0.463883	+	0.803468i
$657$	−42.9269			−1.67474
$658$	58.4949	+	6.93238i	2.28037	+	0.270252i
$659$	−23.4132			−0.912048			−0.456024	−	0.889967i	$-0.650727\pi$
$659$	−23.4132			−0.912048			−0.456024	+	0.889967i	$0.650727\pi$
$660$	−2.26166	−	3.91731i	−0.0880349	−	0.152481i
$661$	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
$663$		0			0
$664$	−11.2587			−0.436921
$665$	12.5484	+	1.48714i	0.486604	+	0.0576688i
$666$	37.8395			1.46625
$667$	0.371744	+	0.643879i	0.0143940	+	0.0249311i
$668$	−1.74448	+	3.02153i	−0.0674959	+	0.116906i
$669$	4.57416	−	7.92268i	0.176847	−	0.306309i
$670$	−5.80440	−	10.0535i	−0.224243	−	0.388401i
$671$	−50.7276			−1.95832
$672$	4.99491	−	6.68686i	0.192683	−	0.257951i
$673$	7.29407			0.281166			0.140583	−	0.990069i	$-0.455102\pi$
$673$	7.29407			0.281166			0.140583	+	0.990069i	$0.455102\pi$
$674$	−29.8076	−	51.6283i	−1.14815	−	1.98865i
$675$	−3.52609	+	6.10737i	−0.135719	+	0.235073i
$676$		0			0
$677$	7.87553	+	13.6408i	0.302681	+	0.524259i	0.976742	−	0.214416i	$-0.0687849\pi$
$677$	7.87553	+	13.6408i	0.302681	+	0.524259i	−0.674061	+	0.738676i	$0.735452\pi$
$678$	−7.65187			−0.293868
$679$	3.64537	+	8.48841i	0.139897	+	0.325755i
$680$	1.24527			0.0477540
$681$	2.23843	+	3.87707i	0.0857767	+	0.148570i
$682$	−21.9582	+	38.0327i	−0.840822	+	1.45635i
$683$	−20.7427	+	35.9274i	−0.793697	+	1.37472i	0.129967	+	0.991518i	$0.458513\pi$
$683$	−20.7427	+	35.9274i	−0.793697	+	1.37472i	−0.923664	+	0.383204i	$0.874820\pi$
$684$	7.44717	+	12.8989i	0.284750	+	0.493201i
$685$	18.8564			0.720465
$686$	−5.96066	−	34.7845i	−0.227579	−	1.32808i
$687$	6.19450			0.236335
$688$	0.0523445	+	0.0906634i	0.00199562	+	0.00345651i
$689$		0			0
$690$	2.66828	−	4.62159i	0.101580	−	0.175941i
$691$	23.4108	+	40.5487i	0.890589	+	1.54255i	0.839171	+	0.543868i	$0.183041\pi$
$691$	23.4108	+	40.5487i	0.890589	+	1.54255i	0.0514184	+	0.998677i	$0.483626\pi$
$692$	−27.0989			−1.03015
$693$	12.9191	+	30.0826i	0.490755	+	1.14274i
$694$	−22.2478			−0.844514
$695$	−0.249496	−	0.432140i	−0.00946392	−	0.0163920i
$696$	−0.0252292	+	0.0436983i	−0.000956311	+	0.00165638i
$697$	3.10534	−	5.37860i	0.117623	−	0.203729i
$698$	22.8576	+	39.5905i	0.865172	+	1.49852i
$699$	−3.97954			−0.150520
$700$	−7.30870	+	9.78442i	−0.276243	+	0.369816i
$701$	29.8626			1.12790			0.563948	−	0.825810i	$-0.309282\pi$
$701$	29.8626			1.12790			0.563948	+	0.825810i	$0.309282\pi$
$702$		0			0
$703$	−11.4293	+	19.7961i	−0.431063	+	0.746623i
$704$	−10.6048	+	18.3680i	−0.399683	+	0.692271i
$705$	3.68709	+	6.38623i	0.138864	+	0.240519i
$706$	−24.3785			−0.917497
$707$	−6.77281	−	0.802663i	−0.254718	−	0.0301873i
$708$	−3.73442			−0.140348
$709$	−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
$711$	1.09067	−	1.88909i	0.0409031	−	0.0708463i
$712$	−2.30450	−	3.99151i	−0.0863647	−	0.149588i
$713$	−23.2745			−0.871638
$714$	−2.57990	−	0.305750i	−0.0965502	−	0.0114424i
$715$		0			0
$716$	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
$721$	−26.7006	+	35.7451i	−0.994383	+	1.33122i
$722$	16.1760			0.602008
$723$	−1.56620	−	2.71274i	−0.0582476	−	0.100888i
$724$	−2.26049	+	3.91528i	−0.0840105	+	0.145510i
$725$	0.237090	−	0.410652i	0.00880530	−	0.0152512i
$726$	3.38977	+	5.87125i	0.125806	+	0.217902i
$727$	−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			0
$729$	−17.5866			−0.651357
$730$	−21.3926	−	37.0531i	−0.791776	−	1.37140i
$731$	0.0136811	−	0.0236963i	0.000506013	−	0.000876440i
$732$	−4.03447	+	6.98790i	−0.149118	+	0.258280i
$733$	5.99189	+	10.3783i	0.221316	+	0.383330i	0.955208	−	0.295936i	$-0.0956316\pi$
$733$	5.99189	+	10.3783i	0.221316	+	0.383330i	−0.733892	+	0.679266i	$0.762298\pi$
$734$	−3.86975			−0.142835
$735$	3.04221	−	3.20386i	0.112213	−	0.118176i
$736$	−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
$741$		0			0
$742$	0.282075	+	0.656825i	0.0103553	+	0.0241128i
$743$	−38.4598			−1.41095			−0.705477	−	0.708733i	$-0.749267\pi$
$743$	−38.4598			−1.41095			−0.705477	+	0.708733i	$0.749267\pi$
$744$	−0.789789	−	1.36795i	−0.0289551	−	0.0501516i
$745$	2.88966	−	5.00504i	0.105869	−	0.183371i
$746$	−3.69107	+	6.39312i	−0.135140	+	0.234069i
$747$	−22.5577	−	39.0710i	−0.825342	−	1.42953i
$748$	8.61945			0.315158
$749$	13.7476	−	18.4044i	0.502326	−	0.672482i
$750$	−9.41710			−0.343864
$751$	−5.85573	−	10.1424i	−0.213679	−	0.370102i	0.739184	−	0.673503i	$-0.235211\pi$
$751$	−5.85573	−	10.1424i	−0.213679	−	0.370102i	−0.952863	+	0.303401i	$0.901878\pi$
$752$	26.8817	−	46.5605i	0.980276	−	1.69789i
$753$	2.54151	−	4.40203i	0.0926178	−	0.160419i
$754$		0			0
$755$	3.12125			0.113594
$756$	10.6800	+	1.26571i	0.388428	+	0.0460336i
$757$	9.31582			0.338589			0.169295	−	0.985566i	$-0.445851\pi$
$757$	9.31582			0.338589			0.169295	+	0.985566i	$0.445851\pi$
$758$	−13.8800	−	24.0409i	−0.504145	−	0.873205i
$759$	−4.17627	+	7.23352i	−0.151589	+	0.262560i
$760$	1.67841	−	2.90709i	0.0608824	−	0.105451i
$761$	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
$763$	31.6349	+	3.74913i	1.14526	+	0.135728i
$764$	−33.0159			−1.19447
$765$	2.49501	+	4.32148i	0.0902072	+	0.156243i
$766$	−25.5172	+	44.1971i	−0.921973	+	1.59690i
$767$		0			0
$768$	−4.32455	−	7.49035i	−0.156049	−	0.270285i
$769$	25.3542			0.914294			0.457147	−	0.889391i	$-0.348871\pi$
$769$	25.3542			0.914294			0.457147	+	0.889391i	$0.348871\pi$
$770$	−19.5281	+	26.1430i	−0.703744	+	0.942128i
$771$	−6.50047			−0.234109
$772$	13.3568	+	23.1347i	0.480723	+	0.832637i
$773$	11.5542	−	20.0125i	0.415576	−	0.719798i	−0.579913	−	0.814678i	$-0.696913\pi$
$773$	11.5542	−	20.0125i	0.415576	−	0.719798i	0.995489	+	0.0948801i	$0.0302468\pi$
$774$	−0.0610493	+	0.105741i	−0.00219437	+	0.00380076i
$775$	7.42200	+	12.8553i	0.266606	+	0.461775i
$776$	2.45411			0.0880974
$777$	3.15377	+	7.34370i	0.113141	+	0.263454i
$778$	−22.8949			−0.820820
$779$	−8.37091	−	14.4988i	−0.299919	−	0.519475i
$780$		0			0
$781$	−21.9015	+	37.9346i	−0.783699	+	1.35741i
$782$	5.08456	+	8.80672i	0.181824	+	0.314928i
$783$	−0.417569			−0.0149227
$784$	−31.3192	−	7.52918i	−1.11854	−	0.268899i
$785$	32.5750			1.16265
$786$	0.758241	+	1.31331i	0.0270456	+	0.0468443i
$787$	12.3346	−	21.3642i	0.439682	−	0.761551i	−0.557983	−	0.829852i	$-0.688425\pi$
$787$	12.3346	−	21.3642i	0.439682	−	0.761551i	0.997665	+	0.0683012i	$0.0217579\pi$
$788$	−16.0943	+	27.8761i	−0.573334	+	0.993044i
$789$	−3.68388	−	6.38066i	−0.131149	−	0.227158i
$790$	2.17413			0.0773521
$791$	9.78492	+	22.7846i	0.347912	+	0.810127i
$792$	8.69727			0.309044
$793$		0			0
$794$	−1.57938	+	2.73556i	−0.0560500	+	0.0970814i
$795$	−0.0447447	+	0.0775000i	−0.00158693	+	0.00274864i
$796$	11.5139	+	19.9427i	0.408100	+	0.706849i
$797$	11.3137			0.400752			0.200376	−	0.979719i	$-0.435784\pi$
$797$	11.3137			0.400752			0.200376	+	0.979719i	$0.435784\pi$
$798$	−4.19103	+	5.61068i	−0.148361	+	0.198616i
$799$	−14.0519			−0.497122
$800$	10.4182	+	18.0449i	0.368340	+	0.637984i
$801$	9.23451	−	15.9946i	0.326285	−	0.565143i
$802$	−19.5156	+	33.8019i	−0.689118	+	1.19359i
$803$	33.4828	+	57.9940i	1.18158	+	2.04656i
$804$	2.89013			0.101927
$805$	−17.1736	−	2.03529i	−0.605289	−	0.0717344i
$806$		0			0
$807$	−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	$0.670313\pi$
$812$	−0.718110	−	0.0851051i	−0.0252007	−	0.00298660i
$813$	13.7675			0.482846
$814$	−29.5146	−	51.1209i	−1.03449	−	1.79179i
$815$	2.83735	−	4.91443i	0.0993880	−	0.172145i
$816$	−1.18561	+	2.05354i	−0.0415046	+	0.0718881i
$817$	−0.0368794	−	0.0638770i	−0.00129025	−	0.00223477i
$818$	−28.3278			−0.990458
$819$		0			0
$820$	−12.4084			−0.433319
$821$	6.87589	+	11.9094i	0.239970	+	0.415640i	0.960705	−	0.277570i	$-0.0895290\pi$
$821$	6.87589	+	11.9094i	0.239970	+	0.415640i	−0.720735	+	0.693210i	$0.756196\pi$
$822$	−5.22526	+	9.05041i	−0.182252	+	0.315669i
$823$	14.5577	−	25.2146i	0.507448	−	0.878926i	−0.492515	−	0.870304i	$-0.663922\pi$
$823$	14.5577	−	25.2146i	0.507448	−	0.878926i	0.999963	−	0.00862197i	$-0.00274449\pi$
$824$	5.92623	+	10.2645i	0.206450	+	0.357582i
$825$	5.32708			0.185465
$826$	10.6307	+	24.7540i	0.369889	+	0.861303i
$827$	−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
$832$		0			0
$833$	2.38865	+	8.07301i	0.0827620	+	0.279713i
$834$	0.276550			0.00957613
$835$	1.57547	+	2.72880i	0.0545214	+	0.0944339i
$836$	11.6175	−	20.1221i	0.401801	−	0.695939i
$837$	6.53591	−	11.3205i	0.225914	−	0.391295i
$838$	−22.5023	−	38.9751i	−0.777328	−	1.34637i
$839$	0.734337			0.0253521			0.0126761	−	0.999920i	$-0.495965\pi$
$839$	0.734337			0.0253521			0.0126761	+	0.999920i	$0.495965\pi$
$840$	−0.463138	−	1.07844i	−0.0159798	−	0.0372096i
$841$	−28.9719			−0.999032
$842$	24.8506	+	43.0426i	0.856409	+	1.48334i
$843$	3.04737	−	5.27820i	0.104957	−	0.181791i
$844$	3.77314	−	6.53528i	0.129877	−	0.224954i
$845$		0			0
$846$	62.7042			2.15582
$847$	13.1478	−	17.6015i	0.451765	−	0.604794i
$848$	0.652447			0.0224051
$849$	2.44834	+	4.24066i	0.0840270	+	0.145539i
$850$	3.24282	−	5.61674i	0.111228	−	0.192652i
$851$	15.6420	−	27.0927i	0.536201	−	0.928727i
$852$	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	$0.119313\pi$
$854$	57.8050	+	6.85062i	1.97805	+	0.234423i
$855$	13.4513			0.460026
$856$	−3.05129	−	5.28500i	−0.104291	−	0.180637i
$857$	10.5106	−	18.2048i	0.359034	−	0.621864i	−0.628766	−	0.777595i	$-0.716440\pi$
$857$	10.5106	−	18.2048i	0.359034	−	0.621864i	0.987800	+	0.155730i	$0.0497730\pi$
$858$		0			0
$859$	25.6814	+	44.4816i	0.876240	+	1.51769i	0.855436	+	0.517908i	$0.173289\pi$
$859$	25.6814	+	44.4816i	0.876240	+	1.51769i	0.0208035	+	0.999784i	$0.493378\pi$
$860$	−0.0546671			−0.00186413
$861$	−5.81294	−	0.688906i	−0.198104	−	0.0234779i
$862$	25.3767			0.864334
$863$	−3.55660	−	6.16021i	−0.121068	−	0.209696i	0.799121	−	0.601170i	$-0.205299\pi$
$863$	−3.55660	−	6.16021i	−0.121068	−	0.209696i	−0.920189	+	0.391474i	$0.871965\pi$
$864$	9.17443	−	15.8906i	0.312121	−	0.540609i
$865$	−12.2368	+	21.1947i	−0.416062	+	0.720641i
$866$	19.4577	+	33.7018i	0.661201	+	1.14523i
$867$	−6.66385			−0.226316
$868$	13.5473	−	18.1362i	0.459825	−	0.615584i
$869$	−3.40286			−0.115434
$870$	−0.100764	−	0.174528i	−0.00341622	−	0.00591707i
$871$		0			0
$872$	4.23133	−	7.32888i	0.143291	−	0.248187i
$873$	4.91701	+	8.51652i	0.166416	+	0.288240i
$874$	27.4124			0.927239
$875$	12.0422	+	28.0408i	0.407101	+	0.947953i
$876$	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	$0.836088\pi$
$878$	−9.30937	+	16.1243i	−0.314176	+	0.544169i
$879$	2.82874	−	4.89953i	0.0954112	−	0.165257i
$880$	14.8917	+	25.7933i	0.502000	+	0.869490i
$881$	−37.0927			−1.24969			−0.624843	−	0.780751i	$-0.714837\pi$
$881$	−37.0927			−1.24969			−0.624843	+	0.780751i	$0.714837\pi$
$882$	−10.6589	−	36.0244i	−0.358905	−	1.21300i
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$		0			0
$885$	−1.68631	+	2.92078i	−0.0566847	+	0.0981809i
$886$	20.1645	−	34.9260i	0.677440	−	1.17336i
$887$	−13.7900	−	23.8849i	−0.463022	−	0.801977i	0.536088	−	0.844162i	$-0.319901\pi$
$887$	−13.7900	−	23.8849i	−0.463022	−	0.801977i	−0.999110	+	0.0421849i	$0.986568\pi$
$888$	2.12316			0.0712485
$889$	16.5847	+	38.6182i	0.556233	+	1.29521i
$890$	18.4081			0.617040
$891$	16.2159	+	28.0868i	0.543254	+	0.940944i
$892$	17.4145	−	30.1627i	0.583079	−	1.00992i
$893$	−18.9396	+	32.8043i	−0.633789	+	1.09775i
$894$	1.60150	+	2.77388i	0.0535621	+	0.0927723i
$895$	0.794748			0.0265655
$896$	−8.75140	+	11.7158i	−0.292364	+	0.391398i
$897$		0			0
$898$	−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
$903$	−0.0256098	−	0.00303509i	−0.000852242	−	0.000101001i
$904$	6.58732			0.219091
$905$	2.04149	+	3.53597i	0.0678615	+	0.117539i
$906$	−0.864923	+	1.49809i	−0.0287352	+	0.0497707i
$907$	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	$-0.102263\pi$
$908$	8.52200	+	14.7605i	0.282813	+	0.489846i
$909$	−7.26019			−0.240805
$910$		0			0
$911$	35.4678			1.17510			0.587550	−	0.809188i	$-0.300093\pi$
$911$	35.4678			1.17510			0.587550	+	0.809188i	$0.300093\pi$
$912$	3.19599	+	5.53562i	0.105830	+	0.183303i
$913$	−35.1898	+	60.9505i	−1.16461	+	2.01717i
$914$	−17.1689	+	29.7375i	−0.567898	+	0.983627i
$915$	3.64360	+	6.31090i	0.120454	+	0.208632i
$916$	23.5833			0.779215
$917$	2.94098	−	3.93719i	0.0971196	−	0.130018i
$918$	−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
$923$		0			0
$924$	−3.20572	−	7.46466i	−0.105461	−	0.245569i
$925$	−19.9523			−0.656026
$926$	16.8706	+	29.2207i	0.554402	+	0.960252i
$927$	−23.7474	+	41.1317i	−0.779967	+	1.35094i
$928$	−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	$0.889815\pi$
$930$	6.30874			0.206872
$931$	22.0660	+	5.30470i	0.723183	+	0.173854i
$932$	−15.1506			−0.496276
$933$	0.438295	+	0.759149i	0.0143491	+	0.0248534i
$934$	−5.55396	+	9.61975i	−0.181731	+	0.314768i
$935$	3.89219	−	6.74148i	0.127288	−	0.220470i
$936$		0			0
$937$	−10.9816			−0.358755			−0.179377	−	0.983780i	$-0.557408\pi$
$937$	−10.9816			−0.358755			−0.179377	+	0.983780i	$0.557408\pi$
$938$	−8.22728	−	19.1576i	−0.268630	−	0.625517i
$939$	4.03498			0.131677
$940$	14.0373	+	24.3132i	0.457845	+	0.793011i
$941$	−4.08897	+	7.08231i	−0.133297	+	0.230877i	−0.924946	−	0.380100i	$-0.875890\pi$
$941$	−4.08897	+	7.08231i	−0.133297	+	0.230877i	0.791649	+	0.610976i	$0.209223\pi$
$942$	−9.02681	+	15.6349i	−0.294109	+	0.509412i
$943$	11.4564	+	19.8430i	0.373071	+	0.646177i
$944$	24.5890			0.800305
$945$	5.81260	−	7.78153i	0.189084	−	0.253133i
$946$	0.190473			0.00619281
$947$	2.29689	+	3.97833i	0.0746389	+	0.129278i	0.900929	−	0.433966i	$-0.142886\pi$
$947$	2.29689	+	3.97833i	0.0746389	+	0.129278i	−0.826290	+	0.563244i	$0.809553\pi$
$948$	−0.270636	+	0.468756i	−0.00878986	+	0.0152245i
$949$		0			0
$950$	−8.74153	−	15.1408i	−0.283613	−	0.491231i
$951$	−14.2978			−0.463640
$952$	2.22097	+	0.263214i	0.0719822	+	0.00853080i
$953$	21.1428			0.684883			0.342442	−	0.939539i	$-0.388746\pi$
$953$	21.1428			0.684883			0.342442	+	0.939539i	$0.388746\pi$
$954$	0.380474	+	0.659000i	0.0123183	+	0.0213359i
$955$	−14.9086	+	25.8225i	−0.482432	+	0.835596i
$956$	−16.0124	+	27.7344i	−0.517879	+	0.896993i
$957$	0.157712	+	0.273165i	0.00509809	+	0.00883016i
$958$	−27.6141			−0.892170
$959$	33.6308	+	3.98568i	1.08600	+	0.128704i
$960$	3.04683			0.0983361
$961$	1.74271	+	3.01846i	0.0562164	+	0.0973697i
$962$		0			0
$963$	12.2270	−	21.1779i	0.394011	−	0.682447i
$964$	−5.96274	−	10.3278i	−0.192047	−	0.332635i
$965$	24.1256			0.776631
$966$	5.73581	−	7.67873i	0.184547	−	0.247059i
$967$	−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
$969$	0.835323	−	1.44682i	0.0268344	−	0.0464786i
$970$	−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	$0.518384\pi$
$972$	17.3535			0.556613
$973$	−0.353641	−	0.823468i	−0.0113372	−	0.0263992i
$974$	34.2241			1.09661
$975$		0			0
$976$	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	$0.266346\pi$
$978$	1.57251	+	2.72366i	0.0502832	+	0.0870930i
$979$	−28.8115			−0.920821
$980$	11.5821	−	12.1975i	0.369977	−	0.389636i
$981$	33.9113			1.08271
$982$	−34.5868	−	59.9061i	−1.10371	−	1.91168i
$983$	8.03657	−	13.9197i	0.256327	−	0.443971i	−0.708928	−	0.705280i	$-0.750821\pi$
$983$	8.03657	−	13.9197i	0.256327	−	0.443971i	0.965255	+	0.261310i	$0.0841544\pi$
$984$	−0.777512	+	1.34669i	−0.0247862	+	0.0429309i
$985$	14.5350	+	25.1754i	0.463124	+	0.802155i
$986$	0.384024			0.0122298
$987$	5.22616	+	12.1693i	0.166350	+	0.387354i
$988$		0			0
$989$	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
$994$	30.0802	−	40.2694i	0.954084	−	1.27727i
$995$	20.7968			0.659304
$996$	5.59743	+	9.69504i	0.177362	+	0.307199i
$997$	8.47687	−	14.6824i	0.268465	−	0.464996i	−0.700000	−	0.714142i	$-0.746817\pi$
$997$	8.47687	−	14.6824i	0.268465	−	0.464996i	0.968466	+	0.249147i	$0.0801502\pi$
$998$	22.5881	−	39.1238i	0.715015	−	1.23844i
$999$	8.78511	+	15.2163i	0.277949	+	0.481421i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	91.16	even	3
91.2.g.b.81.5	yes	12	13.9	even	3
91.2.h.b.16.2	yes	12	91.9	even	3
91.2.h.b.74.2	yes	12	13.3	even	3
637.2.f.j.295.5		12	91.3	odd	6
637.2.f.j.393.5		12	91.87	odd	6
637.2.f.k.295.5		12	91.81	even	3
637.2.f.k.393.5		12	91.74	even	3
637.2.g.l.263.5		12	91.48	odd	6
637.2.g.l.373.5		12	91.68	odd	6
637.2.h.l.165.2		12	91.55	odd	6
637.2.h.l.471.2		12	91.61	odd	6
819.2.n.d.100.2		12	273.107	odd	6
819.2.n.d.172.2		12	39.35	odd	6
819.2.s.d.289.5		12	273.191	odd	6
819.2.s.d.802.5		12	39.29	odd	6
1183.2.e.g.170.2		12	91.51	even	6
1183.2.e.g.508.2		12	13.12	even	2
1183.2.e.h.170.5		12	7.2	even	3	inner
1183.2.e.h.508.5		12	1.1	even	1	trivial
8281.2.a.bz.1.2		6	7.4	even	3
8281.2.a.ca.1.2		6	7.3	odd	6
8281.2.a.ce.1.5		6	91.25	even	6
8281.2.a.cf.1.5		6	91.38	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.952780 + 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(0.736565 + 1.27577i) q^{5} -0.816433 q^{6} +(1.04402 + 2.43105i) q^{7} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})\)	\(q+(0.952780 + 1.65026i) q^{2} +(-0.214224 + 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} +(0.736565 + 1.27577i) q^{5} -0.816433 q^{6} +(1.04402 + 2.43105i) 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} +(-3.01715 + 4.03917i) q^{14} -0.631159 q^{15} +(2.30082 + 3.98514i) q^{16} +(0.601356 - 1.04158i) q^{17} +(-2.68344 + 4.64786i) q^{18} +(-1.62105 - 2.80773i) q^{19} -2.40291 q^{20} +(-1.12569 - 0.133408i) q^{21} +8.37230 q^{22} +(2.21855 + 3.84264i) q^{23} +(-0.150567 + 0.260790i) q^{24} +(1.41494 - 2.45075i) q^{25} -2.49204 q^{27} +(-4.28565 - 0.507904i) q^{28} +0.167561 q^{29} +(-0.601356 - 1.04158i) q^{30} +(-2.62272 + 4.54268i) q^{31} +(-3.68150 + 6.37655i) q^{32} +(0.941217 + 1.63024i) q^{33} +2.29184 q^{34} +(-2.33247 + 3.12256i) q^{35} -4.59405 q^{36} +(-3.52527 - 6.10595i) q^{37} +(3.08900 - 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +5.16390 q^{41} +(-0.852374 - 1.98479i) q^{42} +0.0227504 q^{43} +(3.58334 + 6.20653i) q^{44} +(-2.07449 + 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +(-5.84178 - 10.1183i) q^{47} -1.97156 q^{48} +(-4.82003 + 5.07615i) q^{49} +5.39252 q^{50} +(0.257649 + 0.446262i) q^{51} +(0.0708929 - 0.122790i) q^{53} +(-2.37436 - 4.11252i) q^{54} +6.47236 q^{55} +(0.733790 + 1.70866i) q^{56} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} +(2.67177 - 4.62764i) q^{59} +(0.514760 - 0.891591i) q^{60} +(-5.77287 - 9.99891i) q^{61} -9.99549 q^{62} +(-4.45938 + 5.96993i) q^{63} -4.82736 q^{64} +(-1.79355 + 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} +(0.980907 + 1.69898i) q^{68} -1.90107 q^{69} +(-7.37537 - 0.874075i) q^{70} -9.96971 q^{71} +(0.989763 + 1.71432i) q^{72} +(-7.62080 + 13.1996i) q^{73} +(6.71762 - 11.6353i) q^{74} +(0.606229 + 1.05002i) q^{75} +5.28837 q^{76} +(11.5436 + 1.36807i) q^{77} +(-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} +(1.10654 - 1.48137i) q^{84} +1.77175 q^{85} +(0.0216761 + 0.0375441i) q^{86} +(-0.0358956 + 0.0621731i) q^{87} +(1.54402 - 2.67433i) q^{88} +(-3.27880 - 5.67904i) q^{89} -7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +(11.1319 - 19.2809i) q^{94} +(2.38801 - 4.13616i) q^{95} +(-1.57733 - 2.73202i) q^{96} +3.49166 q^{97} +(-12.9694 - 3.11787i) q^{98} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{14} + 4 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 9 q^{21} + 10 q^{22} - q^{23} - 11 q^{24} + 7 q^{25} - 8 q^{27} + 8 q^{28} - 6 q^{29} - 5 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} + 32 q^{34} - 28 q^{35} + 42 q^{36} - 13 q^{37} - 17 q^{38} - 5 q^{40} + 16 q^{41} - 52 q^{42} + 22 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} - 42 q^{48} + 6 q^{49} - 12 q^{50} - 20 q^{51} - 2 q^{53} - 18 q^{54} - 18 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} + 13 q^{59} + 20 q^{60} - 5 q^{61} - 10 q^{62} + 8 q^{63} - 30 q^{64} + 18 q^{66} - 11 q^{67} + 29 q^{68} - 46 q^{69} - 39 q^{70} - 12 q^{71} + 25 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} + 18 q^{76} + 11 q^{77} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} + 41 q^{84} + 2 q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} + 54 q^{92} - 7 q^{93} + 45 q^{94} - 6 q^{95} + 19 q^{96} + 70 q^{97} - 82 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^14 + 4 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 9 * q^21 + 10 * q^22 - q^23 - 11 * q^24 + 7 * q^25 - 8 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 28 * q^35 + 42 * q^36 - 13 * q^37 - 17 * q^38 - 5 * q^40 + 16 * q^41 - 52 * q^42 + 22 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 42 * q^48 + 6 * q^49 - 12 * q^50 - 20 * q^51 - 2 * q^53 - 18 * q^54 - 18 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 - 5 * q^61 - 10 * q^62 + 8 * q^63 - 30 * q^64 + 18 * q^66 - 11 * q^67 + 29 * q^68 - 46 * q^69 - 39 * q^70 - 12 * q^71 + 25 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 + 18 * q^76 + 11 * q^77 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 + 41 * q^84 + 2 * q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 + 19 * q^96 + 70 * q^97 - 82 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

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