LMFDB - Embedded newform 690.2.m.c.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.1
Root			$1.74971 + 2.01927i$ of defining polynomial
Character	$\chi$	$=$	690.151
Dual form			690.2.m.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(0.170792 + 0.0501489i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(0.170792 + 0.0501489i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(-0.0281441 + 0.0324800i) q^{11} +(0.654861 - 0.755750i) q^{12} +(-4.70795 + 1.38238i) q^{13} +(-0.0739446 - 0.161916i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.635235 - 4.41816i) q^{17} +(0.415415 - 0.909632i) q^{18} +(0.832926 - 5.79313i) q^{19} +(0.841254 + 0.540641i) q^{20} +(-0.116566 - 0.134525i) q^{21} +0.0429772 q^{22} +(1.68276 - 4.49092i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(4.12779 + 2.65277i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-0.0739446 + 0.161916i) q^{28} +(0.802900 + 5.58429i) q^{29} +(0.959493 + 0.281733i) q^{30} +(-8.62178 + 5.54088i) q^{31} +(0.415415 + 0.909632i) q^{32} +(0.0412363 - 0.0121081i) q^{33} +(-2.92303 + 3.37336i) q^{34} +(0.116566 - 0.134525i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.965008 - 2.11307i) q^{37} +(-4.92360 + 3.16421i) q^{38} +(4.70795 + 1.38238i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(1.37136 - 3.00286i) q^{41} +(-0.0253323 + 0.176190i) q^{42} +(-4.26719 - 2.74236i) q^{43} +(-0.0281441 - 0.0324800i) q^{44} +1.00000 q^{45} +(-4.49598 + 1.66918i) q^{46} -9.19936 q^{47} +(0.654861 + 0.755750i) q^{48} +(-5.86212 - 3.76736i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(-1.85424 + 4.06022i) q^{51} +(-0.698298 - 4.85677i) q^{52} +(-10.0340 - 2.94625i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(0.0178534 + 0.0390934i) q^{55} +(0.170792 - 0.0501489i) q^{56} +(-3.83270 + 4.42318i) q^{57} +(3.69454 - 4.26372i) q^{58} +(12.6103 - 3.70271i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(-10.1136 + 6.49960i) q^{61} +(9.83359 + 2.88740i) q^{62} +(0.0253323 + 0.176190i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.698298 + 4.85677i) q^{65} +(-0.0361547 - 0.0232352i) q^{66} +(-6.02227 - 6.95007i) q^{67} +4.46359 q^{68} +(-3.84360 + 2.86823i) q^{69} -0.178002 q^{70} +(9.86179 + 11.3811i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.21575 + 8.45572i) q^{73} +(-0.965008 + 2.11307i) q^{74} +(0.142315 + 0.989821i) q^{75} +(5.61562 + 1.64890i) q^{76} +(-0.00643560 + 0.00413591i) q^{77} +(-2.03832 - 4.46330i) q^{78} +(6.03395 - 1.77173i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-3.16746 + 0.930052i) q^{82} +(-1.27425 - 2.79022i) q^{83} +(0.149745 - 0.0962351i) q^{84} +(-4.28278 - 1.25754i) q^{85} +(0.721880 + 5.02079i) q^{86} +(2.34365 - 5.13188i) q^{87} +(-0.00611629 + 0.0425397i) q^{88} +(-12.3038 - 7.90715i) q^{89} +(-0.654861 - 0.755750i) q^{90} -0.873404 q^{91} +(4.20572 + 2.30475i) q^{92} +10.2487 q^{93} +(6.02430 + 6.95241i) q^{94} +(-4.92360 - 3.16421i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-1.37544 + 3.01180i) q^{97} +(0.991695 + 6.89739i) q^{98} +(-0.0412363 - 0.0121081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	0.170792	+	0.0501489i	0.0645531	+	0.0189545i	0.313850	−	0.949473i	$-0.398381\pi$
$7$	0.170792	+	0.0501489i	0.0645531	+	0.0189545i	−0.249297	+	0.968427i	$0.580199\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−0.959493	+	0.281733i	−0.303418	+	0.0890917i
$11$	−0.0281441	+	0.0324800i	−0.00848575	+	0.00979308i	−0.759977	−	0.649950i	$-0.774790\pi$
$11$	−0.0281441	+	0.0324800i	−0.00848575	+	0.00979308i	0.751491	+	0.659744i	$0.229335\pi$
$12$	0.654861	−	0.755750i	0.189042	−	0.218166i
$13$	−4.70795	+	1.38238i	−1.30575	+	0.383403i	−0.859331	−	0.511420i	$-0.829120\pi$
$13$	−4.70795	+	1.38238i	−1.30575	+	0.383403i	−0.446421	+	0.894823i	$0.647301\pi$
$14$	−0.0739446	−	0.161916i	−0.0197625	−	0.0432739i
$15$	−0.841254	+	0.540641i	−0.217211	+	0.139593i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.635235	−	4.41816i	−0.154067	−	1.07156i	−0.909311	−	0.416117i	$-0.863391\pi$
$17$	−0.635235	−	4.41816i	−0.154067	−	1.07156i	0.755244	−	0.655444i	$-0.227518\pi$
$18$	0.415415	−	0.909632i	0.0979143	−	0.214402i
$19$	0.832926	−	5.79313i	0.191086	−	1.32903i	−0.638053	−	0.769993i	$-0.720260\pi$
$19$	0.832926	−	5.79313i	0.191086	−	1.32903i	0.829139	−	0.559042i	$-0.188831\pi$
$20$	0.841254	+	0.540641i	0.188110	+	0.120891i
$21$	−0.116566	−	0.134525i	−0.0254369	−	0.0293557i
$22$	0.0429772			0.00916276
$23$	1.68276	−	4.49092i	0.350879	−	0.936421i
$23$	1.68276	−	4.49092i	0.350879	−	0.936421i
$24$	−1.00000			−0.204124
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	4.12779	+	2.65277i	0.809526	+	0.520251i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	−0.0739446	+	0.161916i	−0.0139742	+	0.0305993i
$29$	0.802900	+	5.58429i	0.149095	+	1.03698i	0.917706	+	0.397260i	$0.130039\pi$
$29$	0.802900	+	5.58429i	0.149095	+	1.03698i	−0.768611	+	0.639716i	$0.779052\pi$
$30$	0.959493	+	0.281733i	0.175179	+	0.0514371i
$31$	−8.62178	+	5.54088i	−1.54852	+	0.995172i	−0.562834	+	0.826570i	$0.690289\pi$
$31$	−8.62178	+	5.54088i	−1.54852	+	0.995172i	−0.985684	+	0.168602i	$0.946075\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	0.0412363	−	0.0121081i	0.00717832	−	0.00210774i
$34$	−2.92303	+	3.37336i	−0.501295	+	0.578526i
$35$	0.116566	−	0.134525i	0.0197033	−	0.0227388i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−0.965008	−	2.11307i	−0.158646	−	0.347387i	0.813572	−	0.581465i	$-0.197520\pi$
$37$	−0.965008	−	2.11307i	−0.158646	−	0.347387i	−0.972218	+	0.234078i	$0.924793\pi$
$38$	−4.92360	+	3.16421i	−0.798714	+	0.513302i
$39$	4.70795	+	1.38238i	0.753876	+	0.221358i
$40$	−0.142315	−	0.989821i	−0.0225020	−	0.156505i
$41$	1.37136	−	3.00286i	0.214171	−	0.468969i	−0.771805	−	0.635860i	$-0.780646\pi$
$41$	1.37136	−	3.00286i	0.214171	−	0.468969i	0.985975	+	0.166891i	$0.0533729\pi$
$42$	−0.0253323	+	0.176190i	−0.00390886	+	0.0271867i
$43$	−4.26719	−	2.74236i	−0.650740	−	0.418205i	0.173196	−	0.984887i	$-0.444590\pi$
$43$	−4.26719	−	2.74236i	−0.650740	−	0.418205i	−0.823937	+	0.566682i	$0.808227\pi$
$44$	−0.0281441	−	0.0324800i	−0.00424288	−	0.00489654i
$45$	1.00000			0.149071
$46$	−4.49598	+	1.66918i	−0.662896	+	0.246107i
$47$	−9.19936			−1.34186			−0.670932	−	0.741519i	$-0.734106\pi$
$47$	−9.19936			−1.34186			−0.670932	+	0.741519i	$0.734106\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	−5.86212	−	3.76736i	−0.837446	−	0.538194i
$50$	−0.142315	+	0.989821i	−0.0201264	+	0.139982i
$51$	−1.85424	+	4.06022i	−0.259646	+	0.568545i
$52$	−0.698298	−	4.85677i	−0.0968365	−	0.673512i
$53$	−10.0340	−	2.94625i	−1.37828	−	0.404699i	−0.493108	−	0.869968i	$-0.664139\pi$
$53$	−10.0340	−	2.94625i	−1.37828	−	0.404699i	−0.885169	+	0.465269i	$0.845958\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	0.0178534	+	0.0390934i	0.00240735	+	0.00527135i
$56$	0.170792	−	0.0501489i	0.0228230	−	0.00670143i
$57$	−3.83270	+	4.42318i	−0.507654	+	0.585864i
$58$	3.69454	−	4.26372i	0.485117	−	0.559854i
$59$	12.6103	−	3.70271i	1.64172	−	0.482052i	0.674984	−	0.737832i	$-0.264150\pi$
$59$	12.6103	−	3.70271i	1.64172	−	0.482052i	0.966735	+	0.255780i	$0.0823321\pi$
$60$	−0.415415	−	0.909632i	−0.0536298	−	0.117433i
$61$	−10.1136	+	6.49960i	−1.29491	+	0.832188i	−0.992648	−	0.121036i	$-0.961378\pi$
$61$	−10.1136	+	6.49960i	−1.29491	+	0.832188i	−0.302262	+	0.953225i	$0.597742\pi$
$62$	9.83359	+	2.88740i	1.24887	+	0.366700i
$63$	0.0253323	+	0.176190i	0.00319157	+	0.0221979i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.698298	+	4.85677i	−0.0866132	+	0.602408i
$66$	−0.0361547	−	0.0232352i	−0.00445033	−	0.00286006i
$67$	−6.02227	−	6.95007i	−0.735737	−	0.849086i	0.257368	−	0.966314i	$-0.417145\pi$
$67$	−6.02227	−	6.95007i	−0.735737	−	0.849086i	−0.993105	+	0.117227i	$0.962599\pi$
$68$	4.46359			0.541290
$69$	−3.84360	+	2.86823i	−0.462715	+	0.345294i
$70$	−0.178002			−0.0212753
$71$	9.86179	+	11.3811i	1.17038	+	1.35069i	0.924404	+	0.381414i	$0.124563\pi$
$71$	9.86179	+	11.3811i	1.17038	+	1.35069i	0.245975	+	0.969276i	$0.420892\pi$
$72$	0.841254	+	0.540641i	0.0991427	+	0.0637151i
$73$	−1.21575	+	8.45572i	−0.142293	+	0.989667i	0.786109	+	0.618088i	$0.212092\pi$
$73$	−1.21575	+	8.45572i	−0.142293	+	0.989667i	−0.928401	+	0.371579i	$0.878817\pi$
$74$	−0.965008	+	2.11307i	−0.112180	+	0.245640i
$75$	0.142315	+	0.989821i	0.0164331	+	0.114295i
$76$	5.61562	+	1.64890i	0.644156	+	0.189141i
$77$	−0.00643560	+	0.00413591i	−0.000733405	+	0.000471331i
$78$	−2.03832	−	4.46330i	−0.230794	−	0.505369i
$79$	6.03395	−	1.77173i	0.678872	−	0.199335i	0.0759220	−	0.997114i	$-0.475810\pi$
$79$	6.03395	−	1.77173i	0.678872	−	0.199335i	0.602950	+	0.797779i	$0.293992\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−3.16746	+	0.930052i	−0.349788	+	0.102707i
$83$	−1.27425	−	2.79022i	−0.139867	−	0.306266i	0.826716	−	0.562619i	$-0.190206\pi$
$83$	−1.27425	−	2.79022i	−0.139867	−	0.306266i	−0.966583	+	0.256353i	$0.917479\pi$
$84$	0.149745	−	0.0962351i	0.0163385	−	0.0105001i
$85$	−4.28278	−	1.25754i	−0.464533	−	0.136399i
$86$	0.721880	+	5.02079i	0.0778423	+	0.541405i
$87$	2.34365	−	5.13188i	0.251266	−	0.550196i
$88$	−0.00611629	+	0.0425397i	−0.000651999	+	0.00453475i
$89$	−12.3038	−	7.90715i	−1.30420	−	0.838156i	−0.310534	−	0.950562i	$-0.600508\pi$
$89$	−12.3038	−	7.90715i	−1.30420	−	0.838156i	−0.993662	+	0.112406i	$0.964144\pi$
$90$	−0.654861	−	0.755750i	−0.0690284	−	0.0796630i
$91$	−0.873404			−0.0915576
$92$	4.20572	+	2.30475i	0.438477	+	0.240287i
$93$	10.2487			1.06274
$94$	6.02430	+	6.95241i	0.621359	+	0.717087i
$95$	−4.92360	−	3.16421i	−0.505151	−	0.324641i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−1.37544	+	3.01180i	−0.139655	+	0.305802i	−0.966517	−	0.256603i	$-0.917397\pi$
$97$	−1.37544	+	3.01180i	−0.139655	+	0.305802i	0.826862	+	0.562405i	$0.190124\pi$
$98$	0.991695	+	6.89739i	0.100176	+	0.696741i
$99$	−0.0412363	−	0.0121081i	−0.00414440	−	0.00121691i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	0.610309	+	1.33639i	0.0607281	+	0.132976i	0.937563	−	0.347816i	$-0.113077\pi$
$101$	0.610309	+	1.33639i	0.0607281	+	0.132976i	−0.876835	+	0.480792i	$0.840349\pi$
$102$	4.28278	−	1.25754i	0.424059	−	0.124515i
$103$	9.91658	−	11.4443i	0.977110	−	1.12764i	−0.0146965	−	0.999892i	$-0.504678\pi$
$103$	9.91658	−	11.4443i	0.977110	−	1.12764i	0.991806	−	0.127753i	$-0.0407763\pi$
$104$	−3.21321	+	3.70824i	−0.315081	+	0.363623i
$105$	−0.170792	+	0.0501489i	−0.0166675	+	0.00489403i
$106$	4.34425	+	9.51258i	0.421951	+	0.923944i
$107$	16.1511	−	10.3797i	1.56138	−	1.00344i	0.579273	−	0.815134i	$-0.303337\pi$
$107$	16.1511	−	10.3797i	1.56138	−	1.00344i	0.982110	−	0.188307i	$-0.0602999\pi$
$108$	0.959493	+	0.281733i	0.0923273	+	0.0271097i
$109$	−0.747726	−	5.20055i	−0.0716191	−	0.498122i	−0.993784	−	0.111325i	$-0.964491\pi$
$109$	−0.747726	−	5.20055i	−0.0716191	−	0.498122i	0.922165	−	0.386797i	$-0.126419\pi$
$110$	0.0178534	−	0.0390934i	0.00170225	−	0.00372741i
$111$	−0.330597	+	2.29935i	−0.0313789	+	0.218245i
$112$	−0.149745	−	0.0962351i	−0.0141495	−	0.00909336i
$113$	2.54892	+	2.94162i	0.239783	+	0.276724i	0.862867	−	0.505430i	$-0.168666\pi$
$113$	2.54892	+	2.94162i	0.239783	+	0.276724i	−0.623085	+	0.782154i	$0.714121\pi$
$114$	5.85270			0.548156
$115$	−3.38604	−	3.39628i	−0.315750	−	0.316705i
$116$	−5.64172			−0.523820
$117$	−3.21321	−	3.70824i	−0.297062	−	0.342827i
$118$	−11.0563	−	7.10546i	−1.01782	−	0.654110i
$119$	0.113073	−	0.786440i	0.0103654	−	0.0720929i
$120$	−0.415415	+	0.909632i	−0.0379220	+	0.0830377i
$121$	1.56520	+	10.8862i	0.142291	+	0.989655i
$122$	11.5351	+	3.38700i	1.04433	+	0.306644i
$123$	−2.77713	+	1.78476i	−0.250406	+	0.160926i
$124$	−4.25748	−	9.32258i	−0.382333	−	0.837192i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	0.116566	−	0.134525i	0.0103846	−	0.0119844i
$127$	6.94161	−	8.01104i	0.615968	−	0.710865i	−0.358968	−	0.933350i	$-0.616871\pi$
$127$	6.94161	−	8.01104i	0.615968	−	0.710865i	0.974936	+	0.222485i	$0.0714168\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	2.10716	+	4.61403i	0.185525	+	0.406243i
$130$	4.12779	−	2.65277i	0.362031	−	0.232663i
$131$	−8.94559	−	2.62666i	−0.781580	−	0.229493i	−0.133484	−	0.991051i	$-0.542616\pi$
$131$	−8.94559	−	2.62666i	−0.781580	−	0.229493i	−0.648096	+	0.761558i	$0.724435\pi$
$132$	0.00611629	+	0.0425397i	0.000532355	+	0.00370261i
$133$	0.432776	−	0.947647i	0.0375264	−	0.0821714i
$134$	−1.30876	+	9.10265i	−0.113060	+	0.786350i
$135$	−0.841254	−	0.540641i	−0.0724036	−	0.0465310i
$136$	−2.92303	−	3.37336i	−0.250648	−	0.289263i
$137$	20.3195			1.73601			0.868007	−	0.496552i	$-0.165401\pi$
$137$	20.3195			1.73601			0.868007	+	0.496552i	$0.165401\pi$
$138$	4.68469	+	1.02651i	0.398787	+	0.0873820i
$139$	−1.79719			−0.152436			−0.0762179	−	0.997091i	$-0.524284\pi$
$139$	−1.79719			−0.152436			−0.0762179	+	0.997091i	$0.524284\pi$
$140$	0.116566	+	0.134525i	0.00985166	+	0.0113694i
$141$	7.73899	+	4.97355i	0.651741	+	0.418848i
$142$	2.14317	−	14.9061i	0.179851	−	1.25089i
$143$	0.0876013	−	0.191820i	0.00732559	−	0.0160408i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	5.41319	+	1.58945i	0.449541	+	0.131997i
$146$	7.18655	−	4.61851i	0.594763	−	0.382231i
$147$	2.89474	+	6.33860i	0.238754	+	0.522799i
$148$	2.22890	−	0.654464i	0.183214	−	0.0537966i
$149$	5.13346	−	5.92433i	0.420549	−	0.485340i	−0.505455	−	0.862853i	$-0.668675\pi$
$149$	5.13346	−	5.92433i	0.420549	−	0.485340i	0.926004	+	0.377513i	$0.123221\pi$
$150$	0.654861	−	0.755750i	0.0534692	−	0.0617067i
$151$	9.95586	−	2.92330i	0.810196	−	0.237895i	0.149707	−	0.988730i	$-0.452167\pi$
$151$	9.95586	−	2.92330i	0.810196	−	0.237895i	0.660489	+	0.750835i	$0.270349\pi$
$152$	−2.43130	−	5.32380i	−0.197204	−	0.431817i
$153$	3.75501	−	2.41320i	0.303575	−	0.195096i
$154$	0.00734014	+	0.00215526i	0.000591485	+	0.000173676i
$155$	1.45855	+	10.1444i	0.117153	+	0.814819i
$156$	−2.03832	+	4.46330i	−0.163196	+	0.357350i
$157$	−0.556411	+	3.86992i	−0.0444064	+	0.308854i	0.955498	+	0.294999i	$0.0953193\pi$
$157$	−0.556411	+	3.86992i	−0.0444064	+	0.308854i	−0.999904	+	0.0138547i	$0.995590\pi$
$158$	−5.29038	−	3.39992i	−0.420880	−	0.270483i
$159$	6.84828	+	7.90334i	0.543104	+	0.626776i
$160$	1.00000			0.0790569
$161$	0.512615	−	0.682622i	0.0403998	−	0.0537981i
$162$	1.00000			0.0785674
$163$	−6.33198	−	7.30749i	−0.495959	−	0.572367i	0.451489	−	0.892277i	$-0.350893\pi$
$163$	−6.33198	−	7.30749i	−0.495959	−	0.572367i	−0.947448	+	0.319909i	$0.896347\pi$
$164$	2.77713	+	1.78476i	0.216858	+	0.139366i
$165$	0.00611629	−	0.0425397i	0.000476152	−	0.00331171i
$166$	−1.27425	+	2.79022i	−0.0989010	+	0.216563i
$167$	0.212772	+	1.47986i	0.0164648	+	0.114515i	0.996396	−	0.0848190i	$-0.0270312\pi$
$167$	0.212772	+	1.47986i	0.0164648	+	0.114515i	−0.979932	+	0.199334i	$0.936122\pi$
$168$	−0.170792	−	0.0501489i	−0.0131769	−	0.00386907i
$169$	9.31756	−	5.98803i	0.716735	−	0.460618i
$170$	1.85424	+	4.06022i	0.142214	+	0.311405i
$171$	5.61562	−	1.64890i	0.429438	−	0.126094i
$172$	3.32173	−	3.83348i	0.253279	−	0.292300i
$173$	0.570037	−	0.657858i	0.0433391	−	0.0500160i	−0.733666	−	0.679510i	$-0.762192\pi$
$173$	0.570037	−	0.657858i	0.0433391	−	0.0500160i	0.777005	+	0.629494i	$0.216738\pi$
$174$	−5.41319	+	1.58945i	−0.410373	+	0.120496i
$175$	−0.0739446	−	0.161916i	−0.00558969	−	0.0122397i
$176$	0.0361547	−	0.0232352i	0.00272526	−	0.00175142i
$177$	−12.6103	−	3.70271i	−0.947847	−	0.278313i
$178$	2.08143	+	14.4766i	0.156010	+	1.08507i
$179$	8.14852	−	17.8428i	0.609049	−	1.33363i	−0.314173	−	0.949366i	$-0.601727\pi$
$179$	8.14852	−	17.8428i	0.609049	−	1.33363i	0.923222	−	0.384266i	$-0.125545\pi$
$180$	−0.142315	+	0.989821i	−0.0106075	+	0.0737769i
$181$	−13.2081	−	8.48836i	−0.981754	−	0.630935i	−0.0518177	−	0.998657i	$-0.516501\pi$
$181$	−13.2081	−	8.48836i	−0.981754	−	0.630935i	−0.929936	+	0.367722i	$0.880138\pi$
$182$	0.571958	+	0.660074i	0.0423963	+	0.0489280i
$183$	12.0220			0.888694
$184$	−1.01235	−	4.68777i	−0.0746311	−	0.345587i
$185$	−2.32300			−0.170790
$186$	−6.71149	−	7.74548i	−0.492111	−	0.567926i
$187$	0.161380	+	0.103712i	0.0118013	+	0.00758421i
$188$	1.30921	−	9.10572i	0.0954836	−	0.664103i
$189$	0.0739446	−	0.161916i	0.00537868	−	0.0117777i
$190$	0.832926	+	5.79313i	0.0604268	+	0.420278i
$191$	7.87268	+	2.31163i	0.569647	+	0.167264i	0.553857	−	0.832612i	$-0.313155\pi$
$191$	7.87268	+	2.31163i	0.569647	+	0.167264i	0.0157903	+	0.999875i	$0.494974\pi$
$192$	−0.841254	+	0.540641i	−0.0607122	+	0.0390174i
$193$	0.582156	+	1.27474i	0.0419045	+	0.0917580i	0.929427	−	0.369007i	$-0.120302\pi$
$193$	0.582156	+	1.27474i	0.0419045	+	0.0917580i	−0.887522	+	0.460765i	$0.847575\pi$
$194$	3.17689	−	0.932819i	0.228087	−	0.0669725i
$195$	3.21321	−	3.70824i	0.230103	−	0.265553i
$196$	4.56328	−	5.26630i	0.325948	−	0.376164i
$197$	−10.4918	+	3.08068i	−0.747512	+	0.219489i	−0.633235	−	0.773960i	$-0.718273\pi$
$197$	−10.4918	+	3.08068i	−0.747512	+	0.219489i	−0.114277	+	0.993449i	$0.536455\pi$
$198$	0.0178534	+	0.0390934i	0.00126878	+	0.00277825i
$199$	2.65133	−	1.70391i	0.187948	−	0.120787i	−0.443283	−	0.896382i	$-0.646186\pi$
$199$	2.65133	−	1.70391i	0.187948	−	0.120787i	0.631231	+	0.775595i	$0.282550\pi$
$200$	−0.959493	−	0.281733i	−0.0678464	−	0.0199215i
$201$	1.30876	+	9.10265i	0.0923131	+	0.642052i
$202$	0.610309	−	1.33639i	0.0429412	−	0.0940282i
$203$	−0.142918	+	0.994014i	−0.0100309	+	0.0697661i
$204$	−3.75501	−	2.41320i	−0.262903	−	0.168958i
$205$	−2.16182	−	2.49487i	−0.150988	−	0.174249i
$206$	−15.1430			−1.05507
$207$	4.78412	−	0.334903i	0.332520	−	0.0232774i
$208$	4.90671			0.340219
$209$	0.164719	+	0.190096i	0.0113938	+	0.0131492i
$210$	0.149745	+	0.0962351i	0.0103334	+	0.00664085i
$211$	−2.67467	+	18.6028i	−0.184132	+	1.28067i	0.662732	+	0.748857i	$0.269397\pi$
$211$	−2.67467	+	18.6028i	−0.184132	+	1.28067i	−0.846864	+	0.531810i	$0.821512\pi$
$212$	4.34425	−	9.51258i	0.298364	−	0.653327i
$213$	−2.14317	−	14.9061i	−0.146848	−	1.02135i
$214$	−18.4211	−	5.40893i	−1.25924	−	0.369747i
$215$	−4.26719	+	2.74236i	−0.291020	+	0.187027i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−1.75040	+	0.513963i	−0.118825	+	0.0348901i
$218$	−3.44065	+	3.97073i	−0.233031	+	0.268932i
$219$	5.59426	−	6.45612i	0.378025	−	0.436264i
$220$	−0.0412363	+	0.0121081i	−0.00278015	+	0.000816326i
$221$	9.09823	+	19.9223i	0.612013	+	1.34012i
$222$	1.95423	−	1.25591i	0.131159	−	0.0842909i
$223$	26.3495	+	7.73691i	1.76449	+	0.518102i	0.992998	−	0.118133i	$-0.0376910\pi$
$223$	26.3495	+	7.73691i	1.76449	+	0.518102i	0.771495	+	0.636235i	$0.219509\pi$
$224$	0.0253323	+	0.176190i	0.00169259	+	0.0117722i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	0.553934	−	3.85270i	0.0368472	−	0.256278i
$227$	−18.4663	−	11.8675i	−1.22565	−	0.787676i	−0.242441	−	0.970166i	$-0.577948\pi$
$227$	−18.4663	−	11.8675i	−1.22565	−	0.787676i	−0.983208	+	0.182490i	$0.941584\pi$
$228$	−3.83270	−	4.42318i	−0.253827	−	0.292932i
$229$	23.2857			1.53876			0.769382	−	0.638789i	$-0.220564\pi$
$229$	23.2857			1.53876			0.769382	+	0.638789i	$0.220564\pi$
$230$	−0.349358	+	4.78309i	−0.0230360	+	0.315388i
$231$	0.00765001			0.000503334
$232$	3.69454	+	4.26372i	0.242558	+	0.279927i
$233$	2.40075	+	1.54287i	0.157278	+	0.101077i	0.616913	−	0.787032i	$-0.288383\pi$
$233$	2.40075	+	1.54287i	0.157278	+	0.101077i	−0.459634	+	0.888108i	$0.652020\pi$
$234$	−0.698298	+	4.85677i	−0.0456491	+	0.317497i
$235$	−3.82155	+	8.36803i	−0.249291	+	0.545870i
$236$	1.87040	+	13.0089i	0.121752	+	0.846806i
$237$	−6.03395	−	1.77173i	−0.391947	−	0.115086i
$238$	−0.668399	+	0.429554i	−0.0433259	+	0.0278438i
$239$	−6.36935	−	13.9469i	−0.411999	−	0.902151i	−0.995911	−	0.0903350i	$-0.971206\pi$
$239$	−6.36935	−	13.9469i	−0.411999	−	0.902151i	0.583913	−	0.811816i	$-0.301521\pi$
$240$	0.959493	−	0.281733i	0.0619350	−	0.0181858i
$241$	−10.4302	+	12.0371i	−0.671870	+	0.775379i	−0.984668	−	0.174441i	$-0.944188\pi$
$241$	−10.4302	+	12.0371i	−0.671870	+	0.775379i	0.312798	+	0.949820i	$0.398734\pi$
$242$	7.20226	−	8.31185i	0.462979	−	0.534306i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	−4.99413	−	10.9356i	−0.319716	−	0.700081i
$245$	−5.86212	+	3.76736i	−0.374517	+	0.240688i
$246$	3.16746	+	0.930052i	0.201950	+	0.0592979i
$247$	4.08693	+	28.4252i	0.260045	+	1.80865i
$248$	−4.25748	+	9.32258i	−0.270350	+	0.591984i
$249$	−0.436539	+	3.03619i	−0.0276645	+	0.192411i
$250$	0.841254	+	0.540641i	0.0532055	+	0.0341931i
$251$	−14.8450	−	17.1320i	−0.937008	−	1.08136i	−0.996538	−	0.0831383i	$-0.973506\pi$
$251$	−14.8450	−	17.1320i	−0.937008	−	1.08136i	0.0595300	−	0.998227i	$-0.481040\pi$
$252$	−0.178002			−0.0112131
$253$	0.0985052	+	0.181049i	0.00619297	+	0.0113824i
$254$	−10.6001			−0.665111
$255$	2.92303	+	3.37336i	0.183047	+	0.211248i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−0.305179	+	2.12257i	−0.0190366	+	0.132402i	−0.997123	−	0.0757951i	$-0.975851\pi$
$257$	−0.305179	+	2.12257i	−0.0190366	+	0.132402i	0.978087	+	0.208197i	$0.0667596\pi$
$258$	2.10716	−	4.61403i	0.131186	−	0.287257i
$259$	−0.0588469	−	0.409289i	−0.00365657	−	0.0254320i
$260$	−4.70795	−	1.38238i	−0.291975	−	0.0857316i
$261$	−4.74611	+	3.05014i	−0.293777	+	0.188799i
$262$	3.87302	+	8.48073i	0.239276	+	0.523941i
$263$	−10.3304	+	3.03327i	−0.636997	+	0.187039i	−0.584257	−	0.811569i	$-0.698614\pi$
$263$	−10.3304	+	3.03327i	−0.636997	+	0.187039i	−0.0527406	+	0.998608i	$0.516796\pi$
$264$	0.0281441	−	0.0324800i	0.00173215	−	0.00199900i
$265$	−6.84828	+	7.90334i	−0.420687	+	0.485498i
$266$	−0.999592	+	0.293507i	−0.0612889	+	0.0179960i
$267$	6.07566	+	13.3038i	0.371824	+	0.814181i
$268$	7.73639	−	4.97187i	0.472575	−	0.303705i
$269$	16.4006	+	4.81565i	0.999962	+	0.293615i	0.740441	−	0.672122i	$-0.234617\pi$
$269$	16.4006	+	4.81565i	0.999962	+	0.293615i	0.259522	+	0.965737i	$0.416435\pi$
$270$	0.142315	+	0.989821i	0.00866101	+	0.0602386i
$271$	2.51486	−	5.50677i	0.152767	−	0.334513i	−0.817739	−	0.575589i	$-0.804773\pi$
$271$	2.51486	−	5.50677i	0.152767	−	0.334513i	0.970506	+	0.241076i	$0.0775003\pi$
$272$	−0.635235	+	4.41816i	−0.0385168	+	0.267890i
$273$	0.734754	+	0.472198i	0.0444693	+	0.0285787i
$274$	−13.3065	−	15.3565i	−0.803872	−	0.927718i
$275$	0.0429772			0.00259162
$276$	−2.29204	−	4.21267i	−0.137964	−	0.253573i
$277$	−17.3834			−1.04447			−0.522233	−	0.852803i	$-0.674901\pi$
$277$	−17.3834			−1.04447			−0.522233	+	0.852803i	$0.674901\pi$
$278$	1.17691	+	1.35823i	0.0705864	+	0.0814610i
$279$	−8.62178	−	5.54088i	−0.516173	−	0.331724i
$280$	0.0253323	−	0.176190i	0.00151389	−	0.0105294i
$281$	10.2212	−	22.3813i	0.609746	−	1.33516i	−0.313002	−	0.949753i	$-0.601335\pi$
$281$	10.2212	−	22.3813i	0.609746	−	1.33516i	0.922748	−	0.385405i	$-0.125938\pi$
$282$	−1.30921	−	9.10572i	−0.0779620	−	0.542238i
$283$	4.44304	+	1.30459i	0.264111	+	0.0775500i	0.411107	−	0.911587i	$-0.365142\pi$
$283$	4.44304	+	1.30459i	0.264111	+	0.0775500i	−0.146996	+	0.989137i	$0.546960\pi$
$284$	−12.6688	+	8.14171i	−0.751752	+	0.483122i
$285$	2.43130	+	5.32380i	0.144018	+	0.315355i
$286$	−0.202335	+	0.0594108i	−0.0119643	+	0.00351303i
$287$	0.384807	−	0.444091i	0.0227145	−	0.0262139i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−2.80521	+	0.823684i	−0.165012	+	0.0484520i
$290$	−2.34365	−	5.13188i	−0.137624	−	0.301355i
$291$	2.78540	−	1.79007i	0.163283	−	0.104936i
$292$	−8.19663	−	2.40675i	−0.479671	−	0.140844i
$293$	0.815608	+	5.67268i	0.0476483	+	0.331401i	0.999678	+	0.0253941i	$0.00808406\pi$
$293$	0.815608	+	5.67268i	0.0476483	+	0.331401i	−0.952029	+	0.306007i	$0.901007\pi$
$294$	2.89474	−	6.33860i	0.168825	−	0.369675i
$295$	1.87040	−	13.0089i	0.108899	−	0.757407i
$296$	−1.95423	−	1.25591i	−0.113587	−	0.0729981i
$297$	0.0281441	+	0.0324800i	0.00163308	+	0.00188468i
$298$	−7.83901			−0.454102
$299$	−1.71420	+	23.4692i	−0.0991346	+	1.35726i
$300$	−1.00000			−0.0577350
$301$	−0.591273	−	0.682366i	−0.0340804	−	0.0393309i
$302$	−8.72898	−	5.60978i	−0.502297	−	0.322806i
$303$	0.209083	−	1.45420i	0.0120115	−	0.0835417i
$304$	−2.43130	+	5.32380i	−0.139445	+	0.305341i
$305$	1.71091	+	11.8997i	0.0979666	+	0.681373i
$306$	−4.28278	−	1.25754i	−0.244830	−	0.0718887i
$307$	1.73414	−	1.11446i	0.0989726	−	0.0636058i	−0.490218	−	0.871600i	$-0.663083\pi$
$307$	1.73414	−	1.11446i	0.0989726	−	0.0636058i	0.589191	+	0.807994i	$0.299447\pi$
$308$	−0.00317793	−	0.00695870i	−0.000181079	−	0.000396509i
$309$	−14.5296	+	4.26629i	−0.826562	+	0.242701i
$310$	6.71149	−	7.74548i	0.381187	−	0.439913i
$311$	11.5240	−	13.2994i	0.653464	−	0.754138i	−0.328231	−	0.944598i	$-0.606452\pi$
$311$	11.5240	−	13.2994i	0.653464	−	0.754138i	0.981695	+	0.190460i	$0.0609978\pi$
$312$	4.70795	−	1.38238i	0.266535	−	0.0782619i
$313$	13.8188	+	30.2589i	0.781083	+	1.71033i	0.700574	+	0.713580i	$0.252928\pi$
$313$	13.8188	+	30.2589i	0.781083	+	1.71033i	0.0805098	+	0.996754i	$0.474345\pi$
$314$	3.28907	−	2.11375i	0.185613	−	0.119286i
$315$	0.170792	+	0.0501489i	0.00962301	+	0.00282557i
$316$	0.894973	+	6.22467i	0.0503462	+	0.350165i
$317$	−3.75040	+	8.21223i	−0.210643	+	0.461245i	−0.985233	−	0.171220i	$-0.945229\pi$
$317$	−3.75040	+	8.21223i	−0.210643	+	0.461245i	0.774589	+	0.632464i	$0.217957\pi$
$318$	1.48827	−	10.3512i	0.0834583	−	0.580465i
$319$	−0.203974	−	0.131086i	−0.0114204	−	0.00733943i
$320$	−0.654861	−	0.755750i	−0.0366078	−	0.0422477i
$321$	−19.1988			−1.07157
$322$	−0.851583	+	0.0596134i	−0.0474569	+	0.00332212i
$323$	−26.1241			−1.45358
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	4.12779	+	2.65277i	0.228968	+	0.147149i
$326$	−1.37607	+	9.57078i	−0.0762135	+	0.530077i
$327$	−2.18260	+	4.77923i	−0.120698	+	0.264292i
$328$	−0.469808	−	3.26758i	−0.0259408	−	0.180422i
$329$	−1.57117	−	0.461338i	−0.0866216	−	0.0254344i
$330$	−0.0361547	+	0.0232352i	−0.00199025	+	0.00127906i
$331$	13.2741	+	29.0661i	0.729608	+	1.59762i	0.799929	+	0.600094i	$0.204870\pi$
$331$	13.2741	+	29.0661i	0.729608	+	1.59762i	−0.0703215	+	0.997524i	$0.522403\pi$
$332$	2.94316	−	0.864190i	0.161527	−	0.0474286i
$333$	1.52124	−	1.75560i	0.0833634	−	0.0962065i
$334$	0.979068	−	1.12990i	0.0535722	−	0.0618256i
$335$	−8.82375	+	2.59089i	−0.482093	+	0.141555i
$336$	0.0739446	+	0.161916i	0.00403401	+	0.00883325i
$337$	0.0442525	−	0.0284393i	0.00241058	−	0.00154919i	−0.539435	−	0.842027i	$-0.681362\pi$
$337$	0.0442525	−	0.0284393i	0.00241058	−	0.00154919i	0.541846	+	0.840478i	$0.317726\pi$
$338$	−10.6272	−	3.12042i	−0.578041	−	0.169728i
$339$	−0.553934	−	3.85270i	−0.0300856	−	0.209250i
$340$	1.85424	−	4.06022i	0.100560	−	0.220197i
$341$	0.0626842	−	0.435978i	0.00339454	−	0.0236095i
$342$	−4.92360	−	3.16421i	−0.266238	−	0.171101i
$343$	−1.62824	−	1.87909i	−0.0879165	−	0.101461i
$344$	−5.07242			−0.273486
$345$	1.01235	+	4.68777i	0.0545029	+	0.252381i
$346$	−0.870471			−0.0467968
$347$	−2.69859	−	3.11434i	−0.144868	−	0.167186i	0.678678	−	0.734436i	$-0.262553\pi$
$347$	−2.69859	−	3.11434i	−0.144868	−	0.167186i	−0.823546	+	0.567249i	$0.808008\pi$
$348$	4.74611	+	3.05014i	0.254418	+	0.163505i
$349$	2.35752	−	16.3969i	0.126195	−	0.877708i	−0.824119	−	0.566416i	$-0.808329\pi$
$349$	2.35752	−	16.3969i	0.126195	−	0.877708i	0.950315	−	0.311291i	$-0.100762\pi$
$350$	−0.0739446	+	0.161916i	−0.00395251	+	0.00865478i
$351$	0.698298	+	4.85677i	0.0372724	+	0.259235i
$352$	−0.0412363	−	0.0121081i	−0.00219790	−	0.000645362i
$353$	−17.5599	+	11.2851i	−0.934619	+	0.600643i	−0.916864	−	0.399199i	$-0.869288\pi$
$353$	−17.5599	+	11.2851i	−0.934619	+	0.600643i	−0.0177549	+	0.999842i	$0.505652\pi$
$354$	5.45966	+	11.9550i	0.290178	+	0.635400i
$355$	14.4494	−	4.24272i	0.766893	−	0.225180i
$356$	9.57767	−	11.0532i	0.507616	−	0.585820i
$357$	−0.520305	+	0.600464i	−0.0275374	+	0.0317799i
$358$	−18.8208	+	5.52629i	−0.994711	+	0.292074i
$359$	−1.65518	−	3.62435i	−0.0873573	−	0.191286i	0.860911	−	0.508755i	$-0.169894\pi$
$359$	−1.65518	−	3.62435i	−0.0873573	−	0.191286i	−0.948269	+	0.317469i	$0.897167\pi$
$360$	0.841254	−	0.540641i	0.0443380	−	0.0284943i
$361$	−14.6362	−	4.29757i	−0.770326	−	0.226188i
$362$	2.23442	+	15.5407i	0.117439	+	0.816803i
$363$	4.56880	−	10.0043i	0.239800	−	0.525088i
$364$	0.124298	−	0.864514i	0.00651500	−	0.0453128i
$365$	7.18655	+	4.61851i	0.376161	+	0.241744i
$366$	−7.87275	−	9.08564i	−0.411515	−	0.474914i
$367$	9.26597			0.483680			0.241840	−	0.970316i	$-0.422249\pi$
$367$	9.26597			0.483680			0.241840	+	0.970316i	$0.422249\pi$
$368$	−2.87983	+	3.83491i	−0.150122	+	0.199909i
$369$	3.30119			0.171853
$370$	1.52124	+	1.75560i	0.0790855	+	0.0912695i
$371$	−1.56597	−	1.00639i	−0.0813013	−	0.0522491i
$372$	−1.45855	+	10.1444i	−0.0756221	+	0.525963i
$373$	−9.06422	+	19.8479i	−0.469327	+	1.02768i	0.515934	+	0.856628i	$0.327445\pi$
$373$	−9.06422	+	19.8479i	−0.469327	+	1.02768i	−0.985261	+	0.171055i	$0.945282\pi$
$374$	−0.0273006	−	0.189880i	−0.00141168	−	0.00981845i
$375$	0.959493	+	0.281733i	0.0495480	+	0.0145486i
$376$	−7.73899	+	4.97355i	−0.399108	+	0.256491i
$377$	−11.4996	−	25.1807i	−0.592261	−	1.29687i
$378$	−0.170792	+	0.0501489i	−0.00878457	+	0.00257938i
$379$	−4.48868	+	5.18022i	−0.230568	+	0.266090i	−0.859231	−	0.511588i	$-0.829057\pi$
$379$	−4.48868	+	5.18022i	−0.230568	+	0.266090i	0.628662	+	0.777678i	$0.283603\pi$
$380$	3.83270	−	4.42318i	0.196614	−	0.226904i
$381$	−10.1707	+	2.98640i	−0.521063	+	0.152998i
$382$	−3.40850	−	7.46357i	−0.174394	−	0.381870i
$383$	−10.9595	+	7.04326i	−0.560006	+	0.359894i	−0.789818	−	0.613341i	$-0.789825\pi$
$383$	−10.9595	+	7.04326i	−0.560006	+	0.359894i	0.229812	+	0.973235i	$0.426189\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	0.00108871	+	0.00757215i	5.54858e−5	+	0.000385912i
$386$	0.582156	−	1.27474i	0.0296309	−	0.0648827i
$387$	0.721880	−	5.02079i	0.0366952	−	0.255221i
$388$	−2.78540	−	1.79007i	−0.141407	−	0.0908769i
$389$	−3.74016	−	4.31637i	−0.189634	−	0.218849i	0.652969	−	0.757385i	$-0.273523\pi$
$389$	−3.74016	−	4.31637i	−0.189634	−	0.218849i	−0.842603	+	0.538536i	$0.818978\pi$
$390$	−4.90671			−0.248461
$391$	−20.9105	−	4.58190i	−1.05749	−	0.231717i
$392$	−6.96832			−0.351953
$393$	6.10543	+	7.04604i	0.307978	+	0.355426i
$394$	9.19891	+	5.91178i	0.463435	+	0.297831i
$395$	0.894973	−	6.22467i	0.0450310	−	0.313197i
$396$	0.0178534	−	0.0390934i	0.000897165	−	0.00196452i
$397$	−3.01072	−	20.9400i	−0.151104	−	1.05095i	−0.914374	−	0.404870i	$-0.867317\pi$
$397$	−3.01072	−	20.9400i	−0.151104	−	1.05095i	0.763271	−	0.646079i	$-0.223592\pi$
$398$	−3.02398	−	0.887920i	−0.151578	−	0.0445074i
$399$	−0.876411	+	0.563235i	−0.0438754	+	0.0281970i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	30.4725	−	8.94753i	1.52172	−	0.446818i	0.589218	−	0.807974i	$-0.299436\pi$
$401$	30.4725	−	8.94753i	1.52172	−	0.446818i	0.932505	+	0.361156i	$0.117618\pi$
$402$	6.02227	−	6.95007i	0.300363	−	0.346638i
$403$	32.9314	−	38.0048i	1.64043	−	1.89315i
$404$	−1.40964	+	0.413909i	−0.0701325	+	0.0205927i
$405$	0.415415	+	0.909632i	0.0206421	+	0.0452000i
$406$	0.844817	−	0.542931i	0.0419276	−	0.0269452i
$407$	0.0957918	+	0.0281270i	0.00474822	+	0.00139420i
$408$	0.635235	+	4.41816i	0.0314488	+	0.218731i
$409$	0.584986	−	1.28094i	0.0289257	−	0.0633384i	−0.894618	−	0.446832i	$-0.852552\pi$
$409$	0.584986	−	1.28094i	0.0289257	−	0.0633384i	0.923543	+	0.383494i	$0.125279\pi$
$410$	−0.469808	+	3.26758i	−0.0232021	+	0.161374i
$411$	−17.0939	−	10.9856i	−0.843178	−	0.541878i
$412$	9.91658	+	11.4443i	0.488555	+	0.563822i
$413$	2.33942			0.115115
$414$	−3.38604	−	3.39628i	−0.166415	−	0.166918i
$415$	−3.06741			−0.150573
$416$	−3.21321	−	3.70824i	−0.157541	−	0.181812i
$417$	1.51189	+	0.971635i	0.0740378	+	0.0475812i
$418$	0.0357968	−	0.248972i	0.00175088	−	0.0121776i
$419$	−8.73060	+	19.1173i	−0.426518	+	0.933943i	0.567361	+	0.823469i	$0.307964\pi$
$419$	−8.73060	+	19.1173i	−0.426518	+	0.933943i	−0.993879	+	0.110474i	$0.964763\pi$
$420$	−0.0253323	−	0.176190i	−0.00123609	−	0.00859719i
$421$	−6.37116	−	1.87074i	−0.310511	−	0.0911743i	0.122764	−	0.992436i	$-0.460824\pi$
$421$	−6.37116	−	1.87074i	−0.310511	−	0.0911743i	−0.433275	+	0.901262i	$0.642642\pi$
$422$	15.8106	−	10.1608i	0.769646	−	0.494622i
$423$	−3.82155	−	8.36803i	−0.185810	−	0.406868i
$424$	−10.0340	+	2.94625i	−0.487295	+	0.143083i
$425$	−2.92303	+	3.37336i	−0.141788	+	0.163632i
$426$	−9.86179	+	11.3811i	−0.477806	+	0.551417i
$427$	−2.05326	+	0.602892i	−0.0993642	+	0.0291760i
$428$	7.97548	+	17.4639i	0.385509	+	0.844148i
$429$	−0.177401	+	0.114008i	−0.00856498	+	0.00550438i
$430$	4.86695	+	1.42906i	0.234705	+	0.0689156i
$431$	−3.64327	−	25.3395i	−0.175490	−	1.22056i	−0.867042	−	0.498234i	$-0.833982\pi$
$431$	−3.64327	−	25.3395i	−0.175490	−	1.22056i	0.691552	−	0.722326i	$-0.256927\pi$
$432$	−0.415415	+	0.909632i	−0.0199867	+	0.0437647i
$433$	−2.87940	+	20.0267i	−0.138375	+	0.962420i	0.795788	+	0.605575i	$0.207057\pi$
$433$	−2.87940	+	20.0267i	−0.138375	+	0.962420i	−0.934163	+	0.356845i	$0.883852\pi$
$434$	1.53469	+	0.986288i	0.0736676	+	0.0473433i
$435$	−3.69454	−	4.26372i	−0.177140	−	0.204430i
$436$	5.25403			0.251622
$437$	−24.6148	−	13.4890i	−1.17749	−	0.645268i
$438$	−8.54267			−0.408184
$439$	5.64129	+	6.51039i	0.269244	+	0.310724i	0.874230	−	0.485512i	$-0.161367\pi$
$439$	5.64129	+	6.51039i	0.269244	+	0.310724i	−0.604986	+	0.796236i	$0.706821\pi$
$440$	0.0361547	+	0.0232352i	0.00172361	+	0.00110770i
$441$	0.991695	−	6.89739i	0.0472236	−	0.328447i
$442$	9.09823	−	19.9223i	0.432759	−	0.947609i
$443$	2.10373	+	14.6318i	0.0999511	+	0.695175i	0.976760	+	0.214336i	$0.0687588\pi$
$443$	2.10373	+	14.6318i	0.0999511	+	0.695175i	−0.876809	+	0.480839i	$0.840332\pi$
$444$	−2.22890	−	0.654464i	−0.105779	−	0.0310595i
$445$	−12.3038	+	7.90715i	−0.583254	+	0.374835i
$446$	−11.4081	−	24.9802i	−0.540188	−	1.18285i
$447$	−7.52148	+	2.20850i	−0.355754	+	0.104459i
$448$	0.116566	−	0.134525i	0.00550725	−	0.00635570i
$449$	7.65173	−	8.83057i	0.361108	−	0.416740i	−0.545903	−	0.837848i	$-0.683813\pi$
$449$	7.65173	−	8.83057i	0.361108	−	0.416740i	0.907010	+	0.421108i	$0.138359\pi$
$450$	−0.959493	+	0.281733i	−0.0452309	+	0.0132810i
$451$	0.0589373	+	0.129055i	0.00277525	+	0.00607694i
$452$	−3.27442	+	2.10434i	−0.154016	+	0.0989800i
$453$	−9.95586	−	2.92330i	−0.467767	−	0.137349i
$454$	3.12394	+	21.7274i	0.146614	+	1.01972i
$455$	−0.362825	+	0.794476i	−0.0170095	+	0.0372456i
$456$	−0.832926	+	5.79313i	−0.0390053	+	0.271288i
$457$	−8.45151	−	5.43146i	−0.395345	−	0.254073i	0.327831	−	0.944736i	$-0.393682\pi$
$457$	−8.45151	−	5.43146i	−0.395345	−	0.254073i	−0.723176	+	0.690663i	$0.757319\pi$
$458$	−15.2489	−	17.5982i	−0.712535	−	0.822309i
$459$	−4.46359			−0.208343
$460$	3.84360	−	2.86823i	0.179209	−	0.133732i
$461$	−10.0371			−0.467476			−0.233738	−	0.972300i	$-0.575096\pi$
$461$	−10.0371			−0.467476			−0.233738	+	0.972300i	$0.575096\pi$
$462$	−0.00500969	−	0.00578150i	−0.000233072	−	0.000268980i
$463$	12.8039	+	8.22858i	0.595048	+	0.382414i	0.803224	−	0.595677i	$-0.203116\pi$
$463$	12.8039	+	8.22858i	0.595048	+	0.382414i	−0.208176	+	0.978091i	$0.566753\pi$
$464$	0.802900	−	5.58429i	0.0372737	−	0.259244i
$465$	4.25748	−	9.32258i	0.197436	−	0.432324i
$466$	−0.406135	−	2.82473i	−0.0188138	−	0.130853i
$467$	−2.03439	−	0.597350i	−0.0941402	−	0.0276421i	0.234323	−	0.972159i	$-0.424713\pi$
$467$	−2.03439	−	0.597350i	−0.0941402	−	0.0276421i	−0.328463	+	0.944517i	$0.606531\pi$
$468$	4.12779	−	2.65277i	0.190807	−	0.122624i
$469$	−0.680014	−	1.48902i	−0.0314001	−	0.0687567i
$470$	8.82672	−	2.59176i	0.407146	−	0.119549i
$471$	2.56032	−	2.95477i	0.117973	−	0.136149i
$472$	8.60661	−	9.93256i	0.396151	−	0.457183i
$473$	0.209168	−	0.0614172i	0.00961754	−	0.00282396i
$474$	2.61241	+	5.72039i	0.119992	+	0.262746i
$475$	−4.92360	+	3.16421i	−0.225910	+	0.145184i
$476$	0.762343	+	0.223844i	0.0349420	+	0.0102599i
$477$	−1.48827	−	10.3512i	−0.0681434	−	0.473948i
$478$	−6.36935	+	13.9469i	−0.291327	+	0.637917i
$479$	−2.93436	+	20.4089i	−0.134074	+	0.932509i	0.806091	+	0.591791i	$0.201579\pi$
$479$	−2.93436	+	20.4089i	−0.134074	+	0.932509i	−0.940166	+	0.340717i	$0.889330\pi$
$480$	−0.841254	−	0.540641i	−0.0383978	−	0.0246768i
$481$	7.46428	+	8.61424i	0.340342	+	0.392775i
$482$	15.9274			0.725473
$483$	−0.800293	+	0.297117i	−0.0364146	+	0.0135193i
$484$	−10.9982			−0.499916
$485$	2.16825	+	2.50229i	0.0984552	+	0.113623i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−4.58505	+	31.8897i	−0.207768	+	1.44506i	0.572648	+	0.819801i	$0.305916\pi$
$487$	−4.58505	+	31.8897i	−0.207768	+	1.44506i	−0.780417	+	0.625260i	$0.784993\pi$
$488$	−4.99413	+	10.9356i	−0.226074	+	0.495032i
$489$	1.37607	+	9.57078i	0.0622281	+	0.432806i
$490$	6.68605	+	1.96320i	0.302045	+	0.0886884i
$491$	−17.0648	+	10.9669i	−0.770125	+	0.494929i	−0.865743	−	0.500489i	$-0.833154\pi$
$491$	−17.0648	+	10.9669i	−0.770125	+	0.494929i	0.0956179	+	0.995418i	$0.469517\pi$
$492$	−1.37136	−	3.00286i	−0.0618258	−	0.135380i
$493$	24.1622	−	7.09467i	1.08821	−	0.319528i
$494$	18.8060	−	21.7032i	0.846120	−	0.976475i
$495$	−0.0281441	+	0.0324800i	−0.00126498	+	0.00145987i
$496$	9.83359	−	2.88740i	0.441541	−	0.129648i
$497$	1.11356	+	2.43836i	0.0499500	+	0.109375i
$498$	2.58047	−	1.65837i	0.115634	−	0.0743133i
$499$	34.1188	+	10.0182i	1.52737	+	0.448476i	0.934244	−	0.356636i	$-0.116076\pi$
$499$	34.1188	+	10.0182i	1.52737	+	0.448476i	0.593124	+	0.805111i	$0.297894\pi$
$500$	−0.142315	−	0.989821i	−0.00636451	−	0.0442662i
$501$	0.621078	−	1.35997i	0.0277477	−	0.0607590i
$502$	−3.22613	+	22.4382i	−0.143989	+	1.00147i
$503$	13.5163	+	8.68638i	0.602661	+	0.387307i	0.806099	−	0.591781i	$-0.201575\pi$
$503$	13.5163	+	8.68638i	0.602661	+	0.387307i	−0.203438	+	0.979088i	$0.565211\pi$
$504$	0.116566	+	0.134525i	0.00519228	+	0.00599221i
$505$	1.46916			0.0653766
$506$	0.0723202	−	0.193007i	0.00321502	−	0.00858020i
$507$	−11.0758			−0.491894
$508$	6.94161	+	8.01104i	0.307984	+	0.355432i
$509$	−17.2356	−	11.0766i	−0.763955	−	0.490964i	0.0997187	−	0.995016i	$-0.468206\pi$
$509$	−17.2356	−	11.0766i	−0.763955	−	0.490964i	−0.863673	+	0.504052i	$0.831842\pi$
$510$	0.635235	−	4.41816i	0.0281287	−	0.195639i
$511$	−0.631685	+	1.38320i	−0.0279441	+	0.0611890i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−5.61562	−	1.64890i	−0.247936	−	0.0728005i
$514$	1.80398	−	1.15935i	0.0795701	−	0.0511366i
$515$	−6.29064	−	13.7746i	−0.277199	−	0.606981i
$516$	−4.86695	+	1.42906i	−0.214255	+	0.0629111i
$517$	0.258907	−	0.298795i	0.0113867	−	0.0131410i
$518$	−0.270783	+	0.312501i	−0.0118975	+	0.0137305i
$519$	−0.835211	+	0.245240i	−0.0366617	+	0.0107648i
$520$	2.03832	+	4.46330i	0.0893863	+	0.195729i
$521$	21.6606	−	13.9204i	0.948968	−	0.609865i	0.0280440	−	0.999607i	$-0.491072\pi$
$521$	21.6606	−	13.9204i	0.948968	−	0.609865i	0.920924	+	0.389742i	$0.127436\pi$
$522$	5.41319	+	1.58945i	0.236929	+	0.0695685i
$523$	−4.63877	−	32.2634i	−0.202839	−	1.41078i	−0.795806	−	0.605551i	$-0.792953\pi$
$523$	−4.63877	−	32.2634i	−0.202839	−	1.41078i	0.592967	−	0.805227i	$-0.297956\pi$
$524$	3.87302	−	8.48073i	0.169194	−	0.370482i
$525$	−0.0253323	+	0.176190i	−0.00110559	+	0.00768956i
$526$	9.05734	+	5.82080i	0.394919	+	0.253799i
$527$	29.9574	+	34.5726i	1.30496	+	1.50601i
$528$	−0.0429772			−0.00187034
$529$	−17.3366	−	15.1143i	−0.753767	−	0.657141i
$530$	10.4576			0.454250
$531$	8.60661	+	9.93256i	0.373495	+	0.431036i
$532$	0.876411	+	0.563235i	0.0379972	+	0.0244193i
$533$	−2.30521	+	16.0331i	−0.0998497	+	0.694470i
$534$	6.07566	−	13.3038i	0.262919	−	0.575713i
$535$	−2.73228	−	19.0034i	−0.118127	−	0.821589i
$536$	−8.82375	−	2.59089i	−0.381128	−	0.111909i
$537$	−16.5015	+	10.6049i	−0.712092	+	0.457634i
$538$	−7.10068	−	15.5483i	−0.306132	−	0.670336i
$539$	0.287347	−	0.0843728i	0.0123769	−	0.00363419i
$540$	0.654861	−	0.755750i	0.0281807	−	0.0325223i
$541$	28.5766	−	32.9792i	1.22860	−	1.41789i	0.352467	−	0.935824i	$-0.385343\pi$
$541$	28.5766	−	32.9792i	1.22860	−	1.41789i	0.876138	−	0.482061i	$-0.160112\pi$
$542$	−5.80862	+	1.70557i	−0.249502	+	0.0732603i
$543$	6.52224	+	14.2817i	0.279896	+	0.612887i
$544$	3.75501	−	2.41320i	0.160995	−	0.103465i
$545$	−5.04120	−	1.48023i	−0.215941	−	0.0634061i
$546$	−0.124298	−	0.864514i	−0.00531948	−	0.0369978i
$547$	−2.17668	+	4.76627i	−0.0930683	+	0.203791i	−0.950441	−	0.310905i	$-0.899368\pi$
$547$	−2.17668	+	4.76627i	−0.0930683	+	0.203791i	0.857373	+	0.514696i	$0.172095\pi$
$548$	−2.89177	+	20.1127i	−0.123530	+	0.859172i
$549$	−10.1136	−	6.49960i	−0.431637	−	0.277396i
$550$	−0.0281441	−	0.0324800i	−0.00120007	−	0.00138495i
$551$	33.0193			1.40667
$552$	−1.68276	+	4.49092i	−0.0716230	+	0.191146i
$553$	1.11940			0.0476016
$554$	11.3837	+	13.1375i	0.483647	+	0.558158i
$555$	1.95423	+	1.25591i	0.0829524	+	0.0533103i
$556$	0.255767	−	1.77890i	0.0108469	−	0.0754421i
$557$	−5.04431	+	11.0455i	−0.213734	+	0.468012i	−0.985884	−	0.167428i	$-0.946454\pi$
$557$	−5.04431	+	11.0455i	−0.213734	+	0.468012i	0.772150	+	0.635440i	$0.219181\pi$
$558$	1.45855	+	10.1444i	0.0617452	+	0.429447i
$559$	23.8807	+	7.01201i	1.01005	+	0.296576i
$560$	−0.149745	+	0.0962351i	−0.00632787	+	0.00406667i
$561$	−0.0796901	−	0.174497i	−0.00336452	−	0.00736727i
$562$	−23.6081	+	6.93197i	−0.995849	+	0.292408i
$563$	5.02324	−	5.79713i	0.211704	−	0.244320i	−0.639959	−	0.768409i	$-0.721049\pi$
$563$	5.02324	−	5.79713i	0.211704	−	0.244320i	0.851663	+	0.524089i	$0.175594\pi$
$564$	−6.02430	+	6.95241i	−0.253669	+	0.292749i
$565$	3.73465	−	1.09659i	0.157118	−	0.0461340i
$566$	−1.92362	−	4.21215i	−0.0808560	−	0.177050i
$567$	−0.149745	+	0.0962351i	−0.00628869	+	0.00404149i
$568$	14.4494	+	4.24272i	0.606282	+	0.178020i
$569$	1.39172	+	9.67964i	0.0583440	+	0.405792i	0.997975	+	0.0636029i	$0.0202591\pi$
$569$	1.39172	+	9.67964i	0.0583440	+	0.405792i	−0.939631	+	0.342189i	$0.888832\pi$
$570$	2.43130	−	5.32380i	0.101836	−	0.222990i
$571$	5.71483	−	39.7475i	0.239158	−	1.66338i	−0.417112	−	0.908855i	$-0.636958\pi$
$571$	5.71483	−	39.7475i	0.239158	−	1.66338i	0.656270	−	0.754526i	$-0.272133\pi$
$572$	0.177401	+	0.114008i	0.00741749	+	0.00476693i
$573$	−5.37316	−	6.20096i	−0.224467	−	0.259049i
$574$	−0.587617			−0.0245267
$575$	−4.49598	+	1.66918i	−0.187495	+	0.0696096i
$576$	1.00000			0.0416667
$577$	18.8113	+	21.7094i	0.783125	+	0.903775i	0.997331	−	0.0730137i	$-0.0232617\pi$
$577$	18.8113	+	21.7094i	0.783125	+	0.903775i	−0.214206	+	0.976789i	$0.568716\pi$
$578$	2.45952	+	1.58064i	0.102303	+	0.0657458i
$579$	0.199438	−	1.38712i	0.00828834	−	0.0576467i
$580$	−2.34365	+	5.13188i	−0.0973149	+	0.213090i
$581$	−0.0777047	−	0.540448i	−0.00322373	−	0.0224216i
$582$	−3.17689	−	0.932819i	−0.131686	−	0.0386666i
$583$	0.378092	−	0.242985i	0.0156590	−	0.0100634i
$584$	3.54875	+	7.77068i	0.146848	+	0.321553i
$585$	−4.70795	+	1.38238i	−0.194650	+	0.0571544i
$586$	3.75301	−	4.33121i	0.155036	−	0.178921i
$587$	−9.39502	+	10.8424i	−0.387774	+	0.447515i	−0.915753	−	0.401743i	$-0.868405\pi$
$587$	−9.39502	+	10.8424i	−0.387774	+	0.447515i	0.527979	+	0.849258i	$0.322950\pi$
$588$	−6.68605	+	1.96320i	−0.275728	+	0.0809611i
$589$	24.9177	+	54.5622i	1.02672	+	2.24820i
$590$	−11.0563	+	7.10546i	−0.455181	+	0.292527i
$591$	10.4918	+	3.08068i	0.431576	+	0.126722i
$592$	0.330597	+	2.29935i	0.0135874	+	0.0945028i
$593$	17.9256	−	39.2516i	0.736116	−	1.61187i	−0.0537243	−	0.998556i	$-0.517109\pi$
$593$	17.9256	−	39.2516i	0.736116	−	1.61187i	0.789840	−	0.613313i	$-0.210164\pi$
$594$	0.00611629	−	0.0425397i	0.000250954	−	0.00174543i
$595$	−0.668399	−	0.429554i	−0.0274017	−	0.0176100i
$596$	5.13346	+	5.92433i	0.210275	+	0.242670i
$597$	−3.15164			−0.128988
$598$	18.8594	−	14.0736i	0.771219	−	0.575511i
$599$	13.6793			0.558920			0.279460	−	0.960157i	$-0.409844\pi$
$599$	13.6793			0.558920			0.279460	+	0.960157i	$0.409844\pi$
$600$	0.654861	+	0.755750i	0.0267346	+	0.0308533i
$601$	−31.9544	−	20.5359i	−1.30345	−	0.837675i	−0.309865	−	0.950781i	$-0.600284\pi$
$601$	−31.9544	−	20.5359i	−1.30345	−	0.837675i	−0.993583	+	0.113105i	$0.963920\pi$
$602$	−0.128496	+	0.893709i	−0.00523711	+	0.0364249i
$603$	3.82026	−	8.36521i	0.155573	−	0.340658i
$604$	1.47668	+	10.2705i	0.0600853	+	0.417903i
$605$	10.5527	+	3.09854i	0.429026	+	0.125973i
$606$	−1.23593	+	0.794286i	−0.0502063	+	0.0322657i
$607$	0.361622	+	0.791843i	0.0146778	+	0.0321399i	0.916829	−	0.399280i	$-0.130740\pi$
$607$	0.361622	+	0.791843i	0.0146778	+	0.0321399i	−0.902151	+	0.431420i	$0.858013\pi$
$608$	5.61562	−	1.64890i	0.227744	−	0.0668716i
$609$	0.657635	−	0.758951i	0.0266487	−	0.0307542i
$610$	7.87275	−	9.08564i	0.318759	−	0.367867i
$611$	43.3102	−	12.7170i	1.75214	−	0.514475i
$612$	1.85424	+	4.06022i	0.0749533	+	0.164125i
$613$	−29.6589	+	19.0606i	−1.19791	+	0.769851i	−0.978594	−	0.205802i	$-0.934020\pi$
$613$	−29.6589	+	19.0606i	−1.19791	+	0.769851i	−0.219318	+	0.975653i	$0.570383\pi$
$614$	−1.97788	−	0.580757i	−0.0798206	−	0.0234374i
$615$	0.469808	+	3.26758i	0.0189445	+	0.131762i
$616$	−0.00317793	+	0.00695870i	−0.000128042	+	0.000280374i
$617$	4.54465	−	31.6087i	0.182961	−	1.27252i	−0.666754	−	0.745278i	$-0.732317\pi$
$617$	4.54465	−	31.6087i	0.182961	−	1.27252i	0.849715	−	0.527242i	$-0.176774\pi$
$618$	12.7391	+	8.18694i	0.512443	+	0.329327i
$619$	−12.8217	−	14.7971i	−0.515348	−	0.594744i	0.437112	−	0.899407i	$-0.356001\pi$
$619$	−12.8217	−	14.7971i	−0.515348	−	0.594744i	−0.952460	+	0.304664i	$0.901456\pi$
$620$	−10.2487			−0.411599
$621$	−4.20572	−	2.30475i	−0.168770	−	0.0924866i
$622$	−17.5976			−0.705599
$623$	−1.70484	−	1.96749i	−0.0683031	−	0.0788260i
$624$	−4.12779	−	2.65277i	−0.165244	−	0.106196i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	13.8188	−	30.2589i	0.552309	−	1.20939i
$627$	−0.0357968	−	0.248972i	−0.00142959	−	0.00994299i
$628$	−3.75135	−	1.10150i	−0.149695	−	0.0439545i
$629$	−8.72288	+	5.60585i	−0.347804	+	0.223520i
$630$	−0.0739446	−	0.161916i	−0.00294603	−	0.00645090i
$631$	−44.6916	+	13.1226i	−1.77915	+	0.522404i	−0.995151	−	0.0983636i	$-0.968639\pi$
$631$	−44.6916	+	13.1226i	−1.77915	+	0.522404i	−0.783995	+	0.620768i	$0.786821\pi$
$632$	4.11821	−	4.75267i	0.163814	−	0.189051i
$633$	12.3075	−	14.2036i	0.489179	−	0.564542i
$634$	8.66238	−	2.54350i	0.344027	−	0.101015i
$635$	−4.40345	−	9.64221i	−0.174746	−	0.382640i
$636$	−8.79751	+	5.65381i	−0.348844	+	0.224188i
$637$	32.8065	+	9.63286i	1.29984	+	0.381668i
$638$	0.0345064	+	0.239997i	0.00136612	+	0.00950157i
$639$	−6.25589	+	13.6985i	−0.247479	+	0.541904i
$640$	−0.142315	+	0.989821i	−0.00562549	+	0.0391261i
$641$	−0.497077	−	0.319452i	−0.0196334	−	0.0126176i	0.530787	−	0.847505i	$-0.321896\pi$
$641$	−0.497077	−	0.319452i	−0.0196334	−	0.0126176i	−0.550421	+	0.834887i	$0.685533\pi$
$642$	12.5726	+	14.5095i	0.496199	+	0.572644i
$643$	4.24217			0.167295			0.0836474	−	0.996495i	$-0.473343\pi$
$643$	4.24217			0.167295			0.0836474	+	0.996495i	$0.473343\pi$
$644$	0.602721	+	0.604545i	0.0237505	+	0.0238224i
$645$	5.07242			0.199726
$646$	17.1076	+	19.7432i	0.673090	+	0.776787i
$647$	−31.9764	−	20.5500i	−1.25712	−	0.807902i	−0.269233	−	0.963075i	$-0.586770\pi$
$647$	−31.9764	−	20.5500i	−1.25712	−	0.807902i	−0.987887	+	0.155172i	$0.950407\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	−0.234641	+	0.513791i	−0.00921045	+	0.0201681i
$650$	−0.698298	−	4.85677i	−0.0273895	−	0.190498i
$651$	1.75040	+	0.513963i	0.0686035	+	0.0201438i
$652$	8.13425	−	5.22756i	0.318562	−	0.204727i
$653$	−3.35850	−	7.35408i	−0.131428	−	0.287788i	0.832465	−	0.554078i	$-0.186929\pi$
$653$	−3.35850	−	7.35408i	−0.131428	−	0.287788i	−0.963893	+	0.266291i	$0.914202\pi$
$654$	5.04120	−	1.48023i	0.197127	−	0.0578816i
$655$	−6.10543	+	7.04604i	−0.238559	+	0.275312i
$656$	−2.16182	+	2.49487i	−0.0844048	+	0.0974083i
$657$	−8.19663	+	2.40675i	−0.319781	+	0.0938962i
$658$	0.680243	+	1.48953i	0.0265186	+	0.0580677i
$659$	4.46395	−	2.86881i	0.173891	−	0.111753i	−0.450800	−	0.892625i	$-0.648861\pi$
$659$	4.46395	−	2.86881i	0.173891	−	0.111753i	0.624691	+	0.780872i	$0.285225\pi$
$660$	0.0412363	+	0.0121081i	0.00160512	+	0.000471306i
$661$	−0.717146	−	4.98786i	−0.0278938	−	0.194005i	0.971110	−	0.238632i	$-0.0766991\pi$
$661$	−0.717146	−	4.98786i	−0.0278938	−	0.194005i	−0.999004	+	0.0446271i	$0.985790\pi$
$662$	13.2741	−	29.0661i	0.515911	−	1.12969i
$663$	3.11691	−	21.6786i	0.121051	−	0.841928i
$664$	−2.58047	−	1.65837i	−0.100142	−	0.0643572i
$665$	−0.682228	−	0.787333i	−0.0264557	−	0.0305315i
$666$	−2.32300			−0.0900143
$667$	26.4297	+	5.79126i	1.02336	+	0.224238i
$668$	−1.49508			−0.0578463
$669$	−17.9837	−	20.7543i	−0.695291	−	0.802408i
$670$	7.73639	+	4.97187i	0.298883	+	0.192080i
$671$	0.0735302	−	0.511414i	0.00283860	−	0.0197429i
$672$	0.0739446	−	0.161916i	0.00285248	−	0.00624605i
$673$	−3.36559	−	23.4082i	−0.129734	−	0.902319i	−0.945890	−	0.324488i	$-0.894808\pi$
$673$	−3.36559	−	23.4082i	−0.129734	−	0.902319i	0.816156	−	0.577832i	$-0.196101\pi$
$674$	−0.0504722	−	0.0148200i	−0.00194412	−	0.000570844i
$675$	−0.841254	+	0.540641i	−0.0323799	+	0.0208093i
$676$	4.60106	+	10.0749i	0.176964	+	0.387496i
$677$	31.3117	−	9.19395i	1.20341	−	0.353352i	0.382253	−	0.924058i	$-0.375148\pi$
$677$	31.3117	−	9.19395i	1.20341	−	0.353352i	0.821155	+	0.570706i	$0.193330\pi$
$678$	−2.54892	+	2.94162i	−0.0978909	+	0.112972i
$679$	−0.385953	+	0.445413i	−0.0148115	+	0.0170934i
$680$	−4.28278	+	1.25754i	−0.164237	+	0.0482244i
$681$	9.11872	+	19.9672i	0.349430	+	0.765146i
$682$	−0.370540	+	0.238131i	−0.0141887	+	0.00911852i
$683$	−45.1194	−	13.2482i	−1.72644	−	0.506930i	−0.740224	−	0.672361i	$-0.765280\pi$
$683$	−45.1194	−	13.2482i	−1.72644	−	0.506930i	−0.986221	+	0.165431i	$0.947099\pi$
$684$	0.832926	+	5.79313i	0.0318477	+	0.221506i
$685$	8.44103	−	18.4833i	0.322515	−	0.706210i
$686$	−0.353850	+	2.46108i	−0.0135100	+	0.0939644i
$687$	−19.5892	−	12.5892i	−0.747375	−	0.480309i
$688$	3.32173	+	3.83348i	0.126640	+	0.146150i
$689$	51.3125			1.95485
$690$	2.87983	−	3.83491i	0.109633	−	0.145993i
$691$	−21.4937			−0.817659			−0.408829	−	0.912611i	$-0.634063\pi$
$691$	−21.4937			−0.817659			−0.408829	+	0.912611i	$0.634063\pi$
$692$	0.570037	+	0.657858i	0.0216696	+	0.0250080i
$693$	−0.00643560	−	0.00413591i	−0.000244468	−	0.000157110i
$694$	−0.586459	+	4.07891i	−0.0222617	+	0.154833i
$695$	−0.746581	+	1.63478i	−0.0283194	+	0.0620109i
$696$	−0.802900	−	5.58429i	−0.0304338	−	0.211672i
$697$	−14.1383	−	4.15137i	−0.535525	−	0.157244i
$698$	−13.9358	+	8.95601i	−0.527479	+	0.338990i
$699$	−1.18550	−	2.59589i	−0.0448398	−	0.0981855i
$700$	0.170792	−	0.0501489i	0.00645531	−	0.00189545i
$701$	28.8521	−	33.2971i	1.08973	−	1.25761i	0.125629	−	0.992077i	$-0.459905\pi$
$701$	28.8521	−	33.2971i	1.08973	−	1.25761i	0.964101	−	0.265537i	$-0.0855493\pi$
$702$	3.21321	−	3.70824i	0.121275	−	0.139959i
$703$	−13.0451	+	3.83038i	−0.492004	+	0.144466i
$704$	0.0178534	+	0.0390934i	0.000672874	+	0.00147339i
$705$	7.73899	−	4.97355i	0.291467	−	0.187315i
$706$	20.0280	+	5.88074i	0.753763	+	0.221325i
$707$	0.0372171	+	0.258851i	0.00139969	+	0.00973508i
$708$	5.45966	−	11.9550i	0.205186	−	0.449296i
$709$	2.84279	−	19.7721i	0.106763	−	0.742555i	−0.864169	−	0.503202i	$-0.832155\pi$
$709$	2.84279	−	19.7721i	0.106763	−	0.742555i	0.970932	−	0.239354i	$-0.0769356\pi$
$710$	−12.6688	−	8.14171i	−0.475450	−	0.305553i
$711$	4.11821	+	4.75267i	0.154445	+	0.178239i
$712$	−14.6255			−0.548114
$713$	10.3753	+	48.0437i	0.388557	+	1.79925i
$714$	0.794527			0.0297344
$715$	−0.138095	−	0.159370i	−0.00516445	−	0.00596009i
$716$	16.5015	+	10.6049i	0.616690	+	0.396323i
$717$	−2.18204	+	15.1764i	−0.0814898	+	0.566774i
$718$	−1.65518	+	3.62435i	−0.0617709	+	0.135260i
$719$	0.833551	+	5.79747i	0.0310862	+	0.216209i	0.999443	−	0.0333589i	$-0.0106204\pi$
$719$	0.833551	+	5.79747i	0.0310862	+	0.216209i	−0.968357	+	0.249568i	$0.919711\pi$
$720$	−0.959493	−	0.281733i	−0.0357582	−	0.0104996i
$721$	2.26759	−	1.45729i	0.0844494	−	0.0542724i
$722$	6.33678	+	13.8756i	0.235831	+	0.516397i
$723$	15.2822	−	4.48726i	0.568352	−	0.166883i
$724$	10.2817	−	11.8657i	0.382115	−	0.440985i
$725$	3.69454	−	4.26372i	0.137212	−	0.158351i
$726$	−10.5527	+	3.09854i	−0.391646	+	0.114998i
$727$	13.9276	+	30.4973i	0.516548	+	1.13108i	0.970730	+	0.240173i	$0.0772043\pi$
$727$	13.9276	+	30.4973i	0.516548	+	1.13108i	−0.454182	+	0.890909i	$0.650068\pi$
$728$	−0.734754	+	0.472198i	−0.0272318	+	0.0175008i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−1.21575	−	8.45572i	−0.0449969	−	0.312960i
$731$	−9.40549	+	20.5951i	−0.347875	+	0.761739i
$732$	−1.71091	+	11.8997i	−0.0632372	+	0.439824i
$733$	26.9636	+	17.3284i	0.995923	+	0.640041i	0.933713	−	0.358022i	$-0.116549\pi$
$733$	26.9636	+	17.3284i	0.995923	+	0.640041i	0.0622097	+	0.998063i	$0.480185\pi$
$734$	−6.06792	−	7.00275i	−0.223971	−	0.258476i
$735$	6.96832			0.257030
$736$	4.78412	−	0.334903i	0.176345	−	0.0123447i
$737$	0.395229			0.0145585
$738$	−2.16182	−	2.49487i	−0.0795776	−	0.0918374i
$739$	0.170922	+	0.109845i	0.00628746	+	0.00404070i	0.543781	−	0.839227i	$-0.316992\pi$
$739$	0.170922	+	0.109845i	0.00628746	+	0.00404070i	−0.537493	+	0.843268i	$0.680629\pi$
$740$	0.330597	−	2.29935i	0.0121530	−	0.0845259i
$741$	11.9297	−	26.1224i	0.438248	−	0.959629i
$742$	0.264916	+	1.84253i	0.00972536	+	0.0676413i
$743$	−2.49263	−	0.731903i	−0.0914459	−	0.0268509i	0.235690	−	0.971828i	$-0.424265\pi$
$743$	−2.49263	−	0.731903i	−0.0914459	−	0.0268509i	−0.327135	+	0.944977i	$0.606083\pi$
$744$	8.62178	−	5.54088i	0.316090	−	0.203139i
$745$	−3.25644	−	7.13061i	−0.119307	−	0.261245i
$746$	20.9358	−	6.14731i	0.766515	−	0.225069i
$747$	2.00873	−	2.31820i	0.0734956	−	0.0848184i
$748$	−0.125624	+	0.144977i	−0.00459325	+	0.00530089i
$749$	3.27900	−	0.962800i	0.119812	−	0.0351799i
$750$	−0.415415	−	0.909632i	−0.0151688	−	0.0332151i
$751$	16.5591	−	10.6419i	0.604252	−	0.388329i	−0.202446	−	0.979293i	$-0.564889\pi$
$751$	16.5591	−	10.6419i	0.604252	−	0.388329i	0.806698	+	0.590965i	$0.201253\pi$
$752$	8.82672	+	2.59176i	0.321877	+	0.0945117i
$753$	3.22613	+	22.4382i	0.117567	+	0.817694i
$754$	−11.4996	+	25.1807i	−0.418792	+	0.917026i
$755$	1.47668	−	10.2705i	0.0537420	−	0.373784i
$756$	0.149745	+	0.0962351i	0.00544616	+	0.00350004i
$757$	−3.34963	−	3.86568i	−0.121744	−	0.140501i	0.691605	−	0.722276i	$-0.256904\pi$
$757$	−3.34963	−	3.86568i	−0.121744	−	0.140501i	−0.813350	+	0.581775i	$0.802358\pi$
$758$	6.85441			0.248963
$759$	0.0150144	−	0.205564i	0.000544988	−	0.00746149i
$760$	−5.85270			−0.212300
$761$	−1.08051	−	1.24698i	−0.0391685	−	0.0452029i	0.735827	−	0.677169i	$-0.236794\pi$
$761$	−1.08051	−	1.24698i	−0.0391685	−	0.0452029i	−0.774996	+	0.631966i	$0.782248\pi$
$762$	8.91739	+	5.73086i	0.323043	+	0.207607i
$763$	0.133097	−	0.925707i	0.00481842	−	0.0335128i
$764$	−3.40850	+	7.46357i	−0.123315	+	0.270023i
$765$	−0.635235	−	4.41816i	−0.0229670	−	0.159739i
$766$	12.4999	+	3.67030i	0.451640	+	0.132613i
$767$	−54.2501	+	34.8644i	−1.95886	+	1.25888i
$768$	−0.415415	−	0.909632i	−0.0149900	−	0.0328235i
$769$	−35.9157	+	10.5458i	−1.29515	+	0.380291i	−0.855466	−	0.517860i	$-0.826729\pi$
$769$	−35.9157	+	10.5458i	−1.29515	+	0.380291i	−0.439687	+	0.898151i	$0.644911\pi$
$770$	0.00500969	−	0.00578150i	0.000180537	−	0.000208351i
$771$	1.40428	−	1.62063i	0.0505739	−	0.0583654i
$772$	−1.34462	+	0.394815i	−0.0483938	+	0.0142097i
$773$	7.43954	+	16.2903i	0.267582	+	0.585922i	0.994955	−	0.100320i	$-0.0319866\pi$
$773$	7.43954	+	16.2903i	0.267582	+	0.585922i	−0.727374	+	0.686242i	$0.759259\pi$
$774$	−4.26719	+	2.74236i	−0.153381	+	0.0985719i
$775$	9.83359	+	2.88740i	0.353233	+	0.103719i
$776$	0.471206	+	3.27731i	0.0169153	+	0.117649i
$777$	−0.171773	+	0.376131i	−0.00616233	+	0.0134936i
$778$	−0.812814	+	5.65324i	−0.0291408	+	0.202679i
$779$	−16.2537	−	10.4456i	−0.582350	−	0.374254i
$780$	3.21321	+	3.70824i	0.115051	+	0.132776i
$781$	−0.647209			−0.0231590
$782$	10.2307	+	18.8036i	0.365849	+	0.672416i
$783$	5.64172			0.201618
$784$	4.56328	+	5.26630i	0.162974	+	0.188082i
$785$	3.28907	+	2.11375i	0.117392	+	0.0754431i
$786$	1.32684	−	9.22835i	0.0473267	−	0.329164i
$787$	9.03064	−	19.7743i	0.321907	−	0.704879i	−0.677627	−	0.735406i	$-0.736991\pi$
$787$	9.03064	−	19.7743i	0.321907	−	0.704879i	0.999534	+	0.0305273i	$0.00971866\pi$
$788$	−1.55618	−	10.8235i	−0.0554366	−	0.385570i
$789$	10.3304	+	3.03327i	0.367770	+	0.107987i
$790$	−5.29038	+	3.39992i	−0.188223	+	0.120964i
$791$	0.287816	+	0.630229i	0.0102336	+	0.0224084i
$792$	−0.0412363	+	0.0121081i	−0.00146527	+	0.000430241i
$793$	38.6293	−	44.5806i	1.37177	−	1.58310i
$794$	−13.8538	+	15.9881i	−0.491653	+	0.567398i
$795$	10.0340	−	2.94625i	0.355870	−	0.104493i
$796$	1.30924	+	2.86684i	0.0464048	+	0.101612i
$797$	−17.7177	+	11.3865i	−0.627593	+	0.403330i	−0.815418	−	0.578873i	$-0.803493\pi$
$797$	−17.7177	+	11.3865i	−0.627593	+	0.403330i	0.187825	+	0.982203i	$0.439856\pi$
$798$	0.999592	+	0.293507i	0.0353852	+	0.0103900i
$799$	5.84376	+	40.6442i	0.206737	+	1.43789i
$800$	0.415415	−	0.909632i	0.0146871	−	0.0321603i
$801$	2.08143	−	14.4766i	0.0735436	−	0.511507i
$802$	−26.7173	−	17.1702i	−0.943422	−	0.606300i
$803$	−0.240425	−	0.277466i	−0.00848443	−	0.00979155i
$804$	−9.19626			−0.324327
$805$	−0.407987	−	0.749863i	−0.0143796	−	0.0264292i
$806$	−50.2876			−1.77130
$807$	−11.1935	−	12.9180i	−0.394031	−	0.454736i
$808$	1.23593	+	0.794286i	0.0434800	+	0.0279429i
$809$	−5.85105	+	40.6950i	−0.205712	+	1.43076i	0.581234	+	0.813737i	$0.302570\pi$
$809$	−5.85105	+	40.6950i	−0.205712	+	1.43076i	−0.786946	+	0.617022i	$0.788339\pi$
$810$	0.415415	−	0.909632i	0.0145962	−	0.0319612i
$811$	−5.85070	−	40.6925i	−0.205446	−	1.42891i	−0.787779	−	0.615958i	$-0.788769\pi$
$811$	−5.85070	−	40.6925i	−0.205446	−	1.42891i	0.582333	−	0.812950i	$-0.302140\pi$
$812$	−0.963557	−	0.282926i	−0.0338142	−	0.00992875i
$813$	−5.09282	+	3.27296i	−0.178613	+	0.114788i
$814$	−0.0414733	−	0.0908138i	−0.00145364	−	0.00318302i
$815$	−9.27753	+	2.72413i	−0.324978	+	0.0954221i
$816$	2.92303	−	3.37336i	0.102327	−	0.118091i
$817$	−19.4411	+	22.4362i	−0.680157	+	0.784943i
$818$	−1.35115	+	0.396735i	−0.0472420	+	0.0138715i
$819$	−0.362825	−	0.794476i	−0.0126781	−	0.0277612i
$820$	2.77713	−	1.78476i	0.0969817	−	0.0623264i
$821$	−1.95442	−	0.573871i	−0.0682099	−	0.0200282i	0.247450	−	0.968901i	$-0.420408\pi$
$821$	−1.95442	−	0.573871i	−0.0682099	−	0.0200282i	−0.315659	+	0.948873i	$0.602226\pi$
$822$	2.89177	+	20.1127i	0.100862	+	0.701511i
$823$	−12.7706	+	27.9638i	−0.445157	+	0.974757i	0.545466	+	0.838133i	$0.316353\pi$
$823$	−12.7706	+	27.9638i	−0.445157	+	0.974757i	−0.990623	+	0.136625i	$0.956375\pi$
$824$	2.15508	−	14.9889i	0.0750757	−	0.522163i
$825$	−0.0361547	−	0.0232352i	−0.00125874	−	0.000808946i
$826$	−1.53199	−	1.76801i	−0.0533048	−	0.0615171i
$827$	19.1360			0.665423			0.332711	−	0.943029i	$-0.392036\pi$
$827$	19.1360			0.665423			0.332711	+	0.943029i	$0.392036\pi$
$828$	−0.349358	+	4.78309i	−0.0121410	+	0.166224i
$829$	−54.0985			−1.87892			−0.939459	−	0.342661i	$-0.888672\pi$
$829$	−54.0985			−1.87892			−0.939459	+	0.342661i	$0.888672\pi$
$830$	2.00873	+	2.31820i	0.0697240	+	0.0804658i
$831$	14.6238	+	9.39816i	0.507295	+	0.326019i
$832$	−0.698298	+	4.85677i	−0.0242091	+	0.168378i
$833$	−12.9209	+	28.2929i	−0.447684	+	0.980292i
$834$	−0.255767	−	1.77890i	−0.00885649	−	0.0615982i
$835$	1.43452	+	0.421212i	0.0496435	+	0.0145766i
$836$	−0.211603	+	0.135989i	−0.00731843	+	0.00470327i
$837$	4.25748	+	9.32258i	0.147160	+	0.322235i
$838$	20.1652	−	5.92105i	0.696597	−	0.204539i
$839$	7.83386	−	9.04076i	0.270455	−	0.312122i	−0.604233	−	0.796807i	$-0.706521\pi$
$839$	7.83386	−	9.04076i	0.270455	−	0.312122i	0.874688	+	0.484686i	$0.161066\pi$
$840$	−0.116566	+	0.134525i	−0.00402192	+	0.00464155i
$841$	−2.71436	+	0.797007i	−0.0935985	+	0.0274830i
$842$	2.75841	+	6.04007i	0.0950611	+	0.208155i
$843$	−20.6989	+	13.3024i	−0.712907	+	0.458158i
$844$	−18.0328	−	5.29490i	−0.620713	−	0.182258i
$845$	−1.57625	−	10.9631i	−0.0542247	−	0.377141i
$846$	−3.82155	+	8.36803i	−0.131388	+	0.287699i
$847$	−0.278609	+	1.93777i	−0.00957310	+	0.0665824i
$848$	8.79751	+	5.65381i	0.302108	+	0.194153i
$849$	−3.03240	−	3.49958i	−0.104072	−	0.120105i
$850$	4.46359			0.153100
$851$	−11.1135	+	0.777979i	−0.380966	+	0.0266688i
$852$	15.0594			0.515926
$853$	−27.3235	−	31.5330i	−0.935539	−	1.07967i	−0.996670	−	0.0815394i	$-0.974016\pi$
$853$	−27.3235	−	31.5330i	−0.935539	−	1.07967i	0.0611315	−	0.998130i	$-0.480529\pi$
$854$	1.80023	+	1.15694i	0.0616028	+	0.0395897i
$855$	0.832926	−	5.79313i	0.0284855	−	0.198121i
$856$	7.97548	−	17.4639i	0.272596	−	0.596902i
$857$	0.478268	+	3.32643i	0.0163373	+	0.113629i	0.996358	−	0.0852659i	$-0.0271740\pi$
$857$	0.478268	+	3.32643i	0.0163373	+	0.113629i	−0.980021	+	0.198894i	$0.936265\pi$
$858$	0.202335	+	0.0594108i	0.00690759	+	0.00202825i
$859$	−10.7977	+	6.93928i	−0.368414	+	0.236765i	−0.711728	−	0.702456i	$-0.752087\pi$
$859$	−10.7977	+	6.93928i	−0.368414	+	0.236765i	0.343314	+	0.939221i	$0.388451\pi$
$860$	−2.10716	−	4.61403i	−0.0718535	−	0.157337i
$861$	−0.563815	+	0.165551i	−0.0192147	+	0.00564196i
$862$	−16.7645	+	19.3472i	−0.571000	+	0.658970i
$863$	2.32028	−	2.67775i	0.0789833	−	0.0911516i	−0.714882	−	0.699245i	$-0.753520\pi$
$863$	2.32028	−	2.67775i	0.0789833	−	0.0911516i	0.793866	+	0.608093i	$0.208065\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	−0.361607	−	0.791808i	−0.0122950	−	0.0269223i
$866$	17.0208	−	10.9386i	0.578389	−	0.371708i
$867$	2.80521	+	0.823684i	0.0952699	+	0.0279738i
$868$	−0.259624	−	1.80572i	−0.00881221	−	0.0612903i
$869$	−0.112274	+	0.245846i	−0.00380864	+	0.00833975i
$870$	−0.802900	+	5.58429i	−0.0272209	+	0.189325i
$871$	37.9602	+	24.3955i	1.28623	+	0.826611i
$872$	−3.44065	−	3.97073i	−0.116515	−	0.134466i
$873$	−3.31101			−0.112061
$874$	5.92496	+	27.4361i	0.200415	+	0.928040i
$875$	−0.178002			−0.00601756
$876$	5.59426	+	6.45612i	0.189012	+	0.218132i
$877$	−28.7423	−	18.4715i	−0.970557	−	0.623739i	−0.0436570	−	0.999047i	$-0.513901\pi$
$877$	−28.7423	−	18.4715i	−0.970557	−	0.623739i	−0.926900	+	0.375307i	$0.877537\pi$
$878$	1.22597	−	8.52680i	0.0413744	−	0.287765i
$879$	2.38075	−	5.21311i	0.0803006	−	0.175834i
$880$	−0.00611629	−	0.0425397i	−0.000206180	−	0.00143401i
$881$	−5.65713	−	1.66108i	−0.190594	−	0.0559633i	0.185043	−	0.982730i	$-0.440758\pi$
$881$	−5.65713	−	1.66108i	−0.190594	−	0.0559633i	−0.375636	+	0.926767i	$0.622576\pi$
$882$	−5.86212	+	3.76736i	−0.197388	+	0.126853i
$883$	−11.7317	−	25.6889i	−0.394804	−	0.864500i	−0.997771	−	0.0667340i	$-0.978742\pi$
$883$	−11.7317	−	25.6889i	−0.394804	−	0.864500i	0.602967	−	0.797766i	$-0.293985\pi$
$884$	−21.0144	+	6.17038i	−0.706790	+	0.207532i
$885$	−8.60661	+	9.93256i	−0.289308	+	0.333879i
$886$	9.68029	−	11.1717i	0.325216	−	0.375319i
$887$	44.7238	−	13.1321i	1.50168	−	0.440932i	0.575431	−	0.817850i	$-0.304834\pi$
$887$	44.7238	−	13.1321i	1.50168	−	0.440932i	0.926247	+	0.376918i	$0.123016\pi$
$888$	0.965008	+	2.11307i	0.0323835	+	0.0709101i
$889$	1.58731	−	1.02010i	0.0532368	−	0.0342132i
$890$	14.0331	+	4.12048i	0.470390	+	0.138119i
$891$	−0.00611629	−	0.0425397i	−0.000204903	−	0.00142513i
$892$	−11.4081	+	24.9802i	−0.381971	+	0.836400i
$893$	−7.66239	+	53.2931i	−0.256412	+	1.78338i
$894$	6.59459	+	4.23809i	0.220556	+	0.141743i
$895$	−12.8453	−	14.8243i	−0.429372	−	0.495522i
$896$	−0.178002			−0.00594662
$897$	14.1305	−	18.8168i	0.471804	−	0.628275i
$898$	−11.6845			−0.389917
$899$	−37.8643	−	43.6978i	−1.26285	−	1.45740i
$900$	0.841254	+	0.540641i	0.0280418	+	0.0180214i
$901$	−6.64305	+	46.2034i	−0.221312	+	1.53926i
$902$	0.0589373	−	0.129055i	0.00196240	−	0.00429705i
$903$	0.128496	+	0.893709i	0.00427608	+	0.0297408i
$904$	3.73465	+	1.09659i	0.124213	+	0.0364721i
$905$	−13.2081	+	8.48836i	−0.439054	+	0.282163i
$906$	4.31041	+	9.43849i	0.143204	+	0.313573i
$907$	16.8208	−	4.93903i	0.558525	−	0.163998i	0.00972691	−	0.999953i	$-0.496904\pi$
$907$	16.8208	−	4.93903i	0.558525	−	0.163998i	0.548798	+	0.835955i	$0.315086\pi$
$908$	14.3748	−	16.5894i	0.477043	−	0.550537i
$909$	−0.962093	+	1.11031i	−0.0319106	+	0.0368268i
$910$	0.838025	−	0.246066i	0.0277802	−	0.00815702i
$911$	11.7150	+	25.6522i	0.388134	+	0.849894i	0.998337	+	0.0576494i	$0.0183605\pi$
$911$	11.7150	+	25.6522i	0.388134	+	0.849894i	−0.610203	+	0.792245i	$0.708912\pi$
$912$	4.92360	−	3.16421i	0.163037	−	0.104777i
$913$	0.126489	+	0.0371405i	0.00418617	+	0.00122917i
$914$	1.42974	+	9.94407i	0.0472917	+	0.328921i
$915$	4.99413	−	10.9356i	0.165101	−	0.361521i
$916$	−3.31391	+	23.0487i	−0.109495	+	0.761551i
$917$	−1.39611	−	0.897223i	−0.0461035	−	0.0296289i
$918$	2.92303	+	3.37336i	0.0964744	+	0.111337i
$919$	−31.1814			−1.02858			−0.514289	−	0.857617i	$-0.671944\pi$
$919$	−31.1814			−1.02858			−0.514289	+	0.857617i	$0.671944\pi$
$920$	−4.68469	−	1.02651i	−0.154450	−	0.0338429i
$921$	−2.06138			−0.0679247
$922$	6.57293	+	7.58556i	0.216468	+	0.249817i
$923$	−62.1619	−	39.9490i	−2.04608	−	1.31494i
$924$	−0.00108871	+	0.00757215i	−3.58160e−5	+	0.000249105i
$925$	−0.965008	+	2.11307i	−0.0317293	+	0.0694774i
$926$	−2.16604	−	15.0651i	−0.0711804	−	0.495071i
$927$	14.5296	+	4.26629i	0.477216	+	0.140123i
$928$	−4.74611	+	3.05014i	−0.155799	+	0.100126i
$929$	19.7451	+	43.2357i	0.647815	+	1.41852i	0.893454	+	0.449155i	$0.148275\pi$
$929$	19.7451	+	43.2357i	0.647815	+	1.41852i	−0.245640	+	0.969361i	$0.578998\pi$
$930$	−9.83359	+	2.88740i	−0.322456	+	0.0946816i
$931$	−26.7075	+	30.8221i	−0.875302	+	1.01015i
$932$	−1.86883	+	2.15674i	−0.0612155	+	0.0706464i
$933$	−16.8848	+	4.95781i	−0.552782	+	0.162311i
$934$	0.880793	+	1.92867i	0.0288204	+	0.0631079i
$935$	0.161380	−	0.103712i	0.00527768	−	0.00339176i
$936$	−4.70795	−	1.38238i	−0.153884	−	0.0451845i
$937$	−0.0368350	−	0.256193i	−0.00120335	−	0.00836946i	0.989211	−	0.146498i	$-0.0468003\pi$
$937$	−0.0368350	−	0.256193i	−0.00120335	−	0.00836946i	−0.990414	+	0.138129i	$0.955891\pi$
$938$	−0.680014	+	1.48902i	−0.0222032	+	0.0486183i
$939$	4.73410	−	32.9264i	0.154492	−	1.07451i
$940$	−7.73899	−	4.97355i	−0.252418	−	0.162219i
$941$	10.8304	+	12.4989i	0.353060	+	0.407453i	0.904303	−	0.426892i	$-0.140392\pi$
$941$	10.8304	+	12.4989i	0.353060	+	0.407453i	−0.551243	+	0.834345i	$0.685846\pi$
$942$	−3.90972			−0.127386
$943$	−11.1779	−	11.2118i	−0.364004	−	0.365105i
$944$	−13.1427			−0.427757
$945$	−0.116566	−	0.134525i	−0.00379191	−	0.00437609i
$946$	−0.183392	−	0.117859i	−0.00596258	−	0.00383192i
$947$	−2.31893	+	16.1285i	−0.0753553	+	0.524107i	0.916825	+	0.399290i	$0.130743\pi$
$947$	−2.31893	+	16.1285i	−0.0753553	+	0.524107i	−0.992180	+	0.124817i	$0.960166\pi$
$948$	2.61241	−	5.72039i	0.0848472	−	0.185790i
$949$	−5.96533	−	41.4897i	−0.193643	−	1.34681i
$950$	5.61562	+	1.64890i	0.182195	+	0.0534973i
$951$	7.59491	−	4.88095i	0.246282	−	0.158276i
$952$	−0.330059	−	0.722727i	−0.0106973	−	0.0234237i
$953$	22.6494	−	6.65046i	0.733685	−	0.215429i	0.106514	−	0.994311i	$-0.466031\pi$
$953$	22.6494	−	6.65046i	0.733685	−	0.215429i	0.627171	+	0.778882i	$0.284213\pi$
$954$	−6.84828	+	7.90334i	−0.221721	+	0.255880i
$955$	5.37316	−	6.20096i	0.173871	−	0.200658i
$956$	14.7114	−	4.31966i	0.475801	−	0.139708i
$957$	0.100724	+	0.220554i	0.00325593	+	0.00712949i
$958$	17.3457	−	11.1474i	0.560413	−	0.360155i
$959$	3.47040	+	1.01900i	0.112065	+	0.0329053i
$960$	0.142315	+	0.989821i	0.00459319	+	0.0319463i
$961$	30.7559	−	67.3460i	0.992125	−	2.17245i
$962$	1.62214	−	11.2823i	0.0523000	−	0.363754i
$963$	16.1511	+	10.3797i	0.520461	+	0.334480i
$964$	−10.4302	−	12.0371i	−0.335935	−	0.387690i
$965$	1.40138			0.0451121
$966$	0.748627	+	0.410251i	0.0240867	+	0.0131996i
$967$	−9.28016			−0.298430			−0.149215	−	0.988805i	$-0.547675\pi$
$967$	−9.28016			−0.298430			−0.149215	+	0.988805i	$0.547675\pi$
$968$	7.20226	+	8.31185i	0.231489	+	0.267153i
$969$	21.9770	+	14.1237i	0.706001	+	0.453720i
$970$	0.471206	−	3.27731i	0.0151295	−	0.105228i
$971$	−1.18497	+	2.59473i	−0.0380276	+	0.0832688i	−0.927692	−	0.373345i	$-0.878211\pi$
$971$	−1.18497	+	2.59473i	−0.0380276	+	0.0832688i	0.889665	+	0.456614i	$0.150938\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	−0.306945	−	0.0901272i	−0.00984021	−	0.00288935i
$974$	27.1032	−	17.4182i	0.868443	−	0.558114i
$975$	−2.03832	−	4.46330i	−0.0652785	−	0.142940i
$976$	11.5351	−	3.38700i	0.369228	−	0.108415i
$977$	4.49321	−	5.18544i	0.143751	−	0.165897i	−0.679308	−	0.733853i	$-0.737720\pi$
$977$	4.49321	−	5.18544i	0.143751	−	0.165897i	0.823059	+	0.567956i	$0.192266\pi$
$978$	6.33198	−	7.30749i	0.202474	−	0.233668i
$979$	0.603102	−	0.177087i	0.0192752	−	0.00565971i
$980$	−2.89474	−	6.33860i	−0.0924692	−	0.202479i
$981$	4.41997	−	2.84054i	0.141119	−	0.0906915i
$982$	19.4633	+	5.71495i	0.621100	+	0.182371i
$983$	−1.04067	−	7.23803i	−0.0331923	−	0.230857i	0.966472	−	0.256773i	$-0.0826591\pi$
$983$	−1.04067	−	7.23803i	−0.0331923	−	0.230857i	−0.999664	+	0.0259152i	$0.991750\pi$
$984$	−1.37136	+	3.00286i	−0.0437174	+	0.0957278i
$985$	−1.55618	+	10.8235i	−0.0495840	+	0.344864i
$986$	−21.1847	−	13.6146i	−0.674658	−	0.433577i
$987$	1.07234	+	1.23754i	0.0341328	+	0.0393914i
$988$	−28.7175			−0.913625
$989$	−19.4963	+	14.5489i	−0.619947	+	0.462627i
$990$	0.0429772			0.00136590
$991$	−2.58305	−	2.98100i	−0.0820533	−	0.0946945i	0.713238	−	0.700922i	$-0.247228\pi$
$991$	−2.58305	−	2.98100i	−0.0820533	−	0.0946945i	−0.795292	+	0.606227i	$0.792682\pi$
$992$	−8.62178	−	5.54088i	−0.273742	−	0.175923i
$993$	4.54749	−	31.6285i	0.144310	−	1.00370i
$994$	1.11356	−	2.43836i	0.0353200	−	0.0773400i
$995$	−0.448526	−	3.11956i	−0.0142192	−	0.0988968i
$996$	−2.94316	−	0.864190i	−0.0932577	−	0.0273829i
$997$	−11.3916	+	7.32091i	−0.360774	+	0.231855i	−0.708453	−	0.705758i	$-0.750606\pi$
$997$	−11.3916	+	7.32091i	−0.360774	+	0.231855i	0.347678	+	0.937614i	$0.386970\pi$
$998$	−14.7718	−	32.3458i	−0.467594	−	1.02389i
$999$	−2.22890	+	0.654464i	−0.0705192	+	0.0207063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.151.1	✓	20
23.16	even	11	inner	690.2.m.c.361.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.151.1	✓	20	1.1	even	1	trivial
690.2.m.c.361.1	yes	20	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(0.170792 + 0.0501489i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.142315 + 0.989821i) q^{6} +(0.170792 + 0.0501489i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(-0.0281441 + 0.0324800i) q^{11} +(0.654861 - 0.755750i) q^{12} +(-4.70795 + 1.38238i) q^{13} +(-0.0739446 - 0.161916i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.635235 - 4.41816i) q^{17} +(0.415415 - 0.909632i) q^{18} +(0.832926 - 5.79313i) q^{19} +(0.841254 + 0.540641i) q^{20} +(-0.116566 - 0.134525i) q^{21} +0.0429772 q^{22} +(1.68276 - 4.49092i) q^{23} -1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(4.12779 + 2.65277i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-0.0739446 + 0.161916i) q^{28} +(0.802900 + 5.58429i) q^{29} +(0.959493 + 0.281733i) q^{30} +(-8.62178 + 5.54088i) q^{31} +(0.415415 + 0.909632i) q^{32} +(0.0412363 - 0.0121081i) q^{33} +(-2.92303 + 3.37336i) q^{34} +(0.116566 - 0.134525i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.965008 - 2.11307i) q^{37} +(-4.92360 + 3.16421i) q^{38} +(4.70795 + 1.38238i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(1.37136 - 3.00286i) q^{41} +(-0.0253323 + 0.176190i) q^{42} +(-4.26719 - 2.74236i) q^{43} +(-0.0281441 - 0.0324800i) q^{44} +1.00000 q^{45} +(-4.49598 + 1.66918i) q^{46} -9.19936 q^{47} +(0.654861 + 0.755750i) q^{48} +(-5.86212 - 3.76736i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(-1.85424 + 4.06022i) q^{51} +(-0.698298 - 4.85677i) q^{52} +(-10.0340 - 2.94625i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(0.0178534 + 0.0390934i) q^{55} +(0.170792 - 0.0501489i) q^{56} +(-3.83270 + 4.42318i) q^{57} +(3.69454 - 4.26372i) q^{58} +(12.6103 - 3.70271i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(-10.1136 + 6.49960i) q^{61} +(9.83359 + 2.88740i) q^{62} +(0.0253323 + 0.176190i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.698298 + 4.85677i) q^{65} +(-0.0361547 - 0.0232352i) q^{66} +(-6.02227 - 6.95007i) q^{67} +4.46359 q^{68} +(-3.84360 + 2.86823i) q^{69} -0.178002 q^{70} +(9.86179 + 11.3811i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.21575 + 8.45572i) q^{73} +(-0.965008 + 2.11307i) q^{74} +(0.142315 + 0.989821i) q^{75} +(5.61562 + 1.64890i) q^{76} +(-0.00643560 + 0.00413591i) q^{77} +(-2.03832 - 4.46330i) q^{78} +(6.03395 - 1.77173i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-3.16746 + 0.930052i) q^{82} +(-1.27425 - 2.79022i) q^{83} +(0.149745 - 0.0962351i) q^{84} +(-4.28278 - 1.25754i) q^{85} +(0.721880 + 5.02079i) q^{86} +(2.34365 - 5.13188i) q^{87} +(-0.00611629 + 0.0425397i) q^{88} +(-12.3038 - 7.90715i) q^{89} +(-0.654861 - 0.755750i) q^{90} -0.873404 q^{91} +(4.20572 + 2.30475i) q^{92} +10.2487 q^{93} +(6.02430 + 6.95241i) q^{94} +(-4.92360 - 3.16421i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-1.37544 + 3.01180i) q^{97} +(0.991695 + 6.89739i) q^{98} +(-0.0412363 - 0.0121081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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