LMFDB - Embedded newform 861.2.bk.a.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(16,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 18]))

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

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

chi := DirichletCharacter("861.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.bk (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	861.16
Dual form			861.2.bk.a.592.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07412 - 1.19293i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.0602948 + 0.573666i) q^{4} +(-1.90350 + 0.847493i) q^{5} +(-0.496049 + 1.52668i) q^{6} +(2.63290 - 0.260479i) q^{7} +(-1.84824 + 1.34282i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.07412 - 1.19293i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.0602948 + 0.573666i) q^{4} +(-1.90350 + 0.847493i) q^{5} +(-0.496049 + 1.52668i) q^{6} +(2.63290 - 0.260479i) q^{7} +(-1.84824 + 1.34282i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.05559 + 1.36044i) q^{10} +(-3.48746 - 1.55272i) q^{11} +(0.526957 - 0.234616i) q^{12} +(-0.660175 + 2.03181i) q^{13} +(-3.13879 - 2.86108i) q^{14} +(1.68570 + 1.22473i) q^{15} +(4.71558 + 1.00233i) q^{16} +(-1.63821 - 0.729376i) q^{17} +(1.57017 - 0.333750i) q^{18} +(2.10173 + 0.446737i) q^{19} +(-0.371407 - 1.14307i) q^{20} +(-1.54203 - 2.14992i) q^{21} +(1.89367 + 5.82810i) q^{22} +(3.67346 + 4.07979i) q^{23} +(2.08704 + 0.929210i) q^{24} +(-0.440584 + 0.489318i) q^{25} +(3.13292 - 1.39487i) q^{26} +1.00000 q^{27} +(-0.00932202 + 1.52611i) q^{28} +(3.50398 + 2.54579i) q^{29} +(-0.349623 - 3.32644i) q^{30} +(1.13870 + 0.506982i) q^{31} +(-1.58484 - 2.74503i) q^{32} +(0.399037 + 3.79658i) q^{33} +(0.889535 + 2.73771i) q^{34} +(-4.79097 + 2.72718i) q^{35} +(-0.466662 - 0.339050i) q^{36} +(-2.21544 + 0.986376i) q^{37} +(-1.72459 - 2.98708i) q^{38} +(2.08969 - 0.444177i) q^{39} +(2.38009 - 4.12244i) q^{40} +(5.99309 + 2.25453i) q^{41} +(-0.908379 + 4.14881i) q^{42} +(-0.829014 + 2.55144i) q^{43} +(1.10102 - 1.90702i) q^{44} +(0.217800 - 2.07223i) q^{45} +(0.921173 - 8.76437i) q^{46} +(3.66135 + 4.06634i) q^{47} +(-1.48975 - 4.58497i) q^{48} +(6.86430 - 1.37163i) q^{49} +1.05696 q^{50} +(0.187445 + 1.78342i) q^{51} +(-1.12578 - 0.501228i) q^{52} +(1.03816 - 9.87743i) q^{53} +(-1.07412 - 1.19293i) q^{54} +7.95429 q^{55} +(-4.51645 + 4.01695i) q^{56} +(-0.663981 - 2.04352i) q^{57} +(-0.726743 - 6.91449i) q^{58} +(10.4069 - 2.21205i) q^{59} +(-0.804227 + 0.893185i) q^{60} +(-6.25340 - 1.32920i) q^{61} +(-0.618307 - 1.90295i) q^{62} +(-1.09087 + 2.41040i) q^{63} +(1.40717 - 4.33083i) q^{64} +(-0.465301 - 4.42704i) q^{65} +(4.10045 - 4.55402i) q^{66} +(0.699275 - 6.65316i) q^{67} +(0.517194 - 0.895806i) q^{68} +(1.69647 - 5.22120i) q^{69} +(8.39943 + 2.78598i) q^{70} +(-10.7436 + 7.80565i) q^{71} +(-0.238800 - 2.27203i) q^{72} +(2.80012 + 4.84995i) q^{73} +(3.55633 + 1.58338i) q^{74} +(0.644054 + 0.136898i) q^{75} +(-0.383002 + 1.17876i) q^{76} +(-9.58656 - 3.17973i) q^{77} +(-2.77445 - 2.01576i) q^{78} +(-1.97595 + 3.42245i) q^{79} +(-9.82556 + 2.08849i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.74780 - 9.57099i) q^{82} +16.2245 q^{83} +(1.32631 - 0.754982i) q^{84} +3.73647 q^{85} +(3.93416 - 1.75160i) q^{86} +(0.452729 - 4.30743i) q^{87} +(8.53067 - 1.81325i) q^{88} +(-10.8974 - 2.31632i) q^{89} +(-2.70597 + 1.96600i) q^{90} +(-1.20893 + 5.52151i) q^{91} +(-2.56193 + 1.86135i) q^{92} +(-0.130291 - 1.23963i) q^{93} +(0.918136 - 8.73548i) q^{94} +(-4.37926 + 0.930840i) q^{95} +(-1.58484 + 2.74503i) q^{96} +(11.8293 + 8.59451i) q^{97} +(-9.00936 - 6.71536i) q^{98} +(3.08842 - 2.24387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 112 q^{3} + 28 q^{4} + 24 q^{8} - 112 q^{9}+O(q^{10}) $ 224 * q - 112 * q^3 + 28 * q^4 + 24 * q^8 - 112 * q^9	$ 224 q - 112 q^{3} + 28 q^{4} + 24 q^{8} - 112 q^{9} + 17 q^{10} + 28 q^{12} + 12 q^{14} + 28 q^{16} + 10 q^{17} - 10 q^{19} + 56 q^{20} + 32 q^{22} - 4 q^{23} - 12 q^{24} + 48 q^{25} - 26 q^{26} + 224 q^{27} + 15 q^{28} - 44 q^{29} + 17 q^{30} - 10 q^{31} + 66 q^{32} + 76 q^{34} - 7 q^{35} - 56 q^{36} + 19 q^{37} + 4 q^{38} - 70 q^{40} + 10 q^{41} + 6 q^{42} + 4 q^{43} - 2 q^{44} + 32 q^{46} - 44 q^{47} - 56 q^{48} - 16 q^{49} - 60 q^{50} + 10 q^{51} - 46 q^{52} + 53 q^{53} + 28 q^{55} - 13 q^{56} + 20 q^{57} - 32 q^{58} - 6 q^{59} - 28 q^{60} - 4 q^{61} + 18 q^{62} - 188 q^{64} + 46 q^{65} - 16 q^{66} - 6 q^{67} + 36 q^{68} + 8 q^{69} + 189 q^{70} - 34 q^{71} - 12 q^{72} - 102 q^{73} - 118 q^{74} + 48 q^{75} + 70 q^{76} - 18 q^{77} + 52 q^{78} - 66 q^{79} - 44 q^{80} - 112 q^{81} - 24 q^{82} + 52 q^{83} + 6 q^{84} + 128 q^{85} + 5 q^{86} + 22 q^{87} + 59 q^{88} + 52 q^{89} - 34 q^{90} + 126 q^{91} - 30 q^{92} - 10 q^{93} - 97 q^{94} + 53 q^{95} + 66 q^{96} + 112 q^{97} + 30 q^{98}+O(q^{100}) $ 224 * q - 112 * q^3 + 28 * q^4 + 24 * q^8 - 112 * q^9 + 17 * q^10 + 28 * q^12 + 12 * q^14 + 28 * q^16 + 10 * q^17 - 10 * q^19 + 56 * q^20 + 32 * q^22 - 4 * q^23 - 12 * q^24 + 48 * q^25 - 26 * q^26 + 224 * q^27 + 15 * q^28 - 44 * q^29 + 17 * q^30 - 10 * q^31 + 66 * q^32 + 76 * q^34 - 7 * q^35 - 56 * q^36 + 19 * q^37 + 4 * q^38 - 70 * q^40 + 10 * q^41 + 6 * q^42 + 4 * q^43 - 2 * q^44 + 32 * q^46 - 44 * q^47 - 56 * q^48 - 16 * q^49 - 60 * q^50 + 10 * q^51 - 46 * q^52 + 53 * q^53 + 28 * q^55 - 13 * q^56 + 20 * q^57 - 32 * q^58 - 6 * q^59 - 28 * q^60 - 4 * q^61 + 18 * q^62 - 188 * q^64 + 46 * q^65 - 16 * q^66 - 6 * q^67 + 36 * q^68 + 8 * q^69 + 189 * q^70 - 34 * q^71 - 12 * q^72 - 102 * q^73 - 118 * q^74 + 48 * q^75 + 70 * q^76 - 18 * q^77 + 52 * q^78 - 66 * q^79 - 44 * q^80 - 112 * q^81 - 24 * q^82 + 52 * q^83 + 6 * q^84 + 128 * q^85 + 5 * q^86 + 22 * q^87 + 59 * q^88 + 52 * q^89 - 34 * q^90 + 126 * q^91 - 30 * q^92 - 10 * q^93 - 97 * q^94 + 53 * q^95 + 66 * q^96 + 112 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.07412	−	1.19293i	−0.759519	−	0.843531i	0.232105	−	0.972691i	$-0.425439\pi$
$2$	−1.07412	−	1.19293i	−0.759519	−	0.843531i	−0.991624	+	0.129160i	$0.958772\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.0602948	+	0.573666i	−0.0301474	+	0.286833i
$5$	−1.90350	+	0.847493i	−0.851271	+	0.379010i	−0.785528	−	0.618826i	$-0.787609\pi$
$5$	−1.90350	+	0.847493i	−0.851271	+	0.379010i	−0.0657433	+	0.997837i	$0.520942\pi$
$6$	−0.496049	+	1.52668i	−0.202511	+	0.623266i
$7$	2.63290	−	0.260479i	0.995142	−	0.0984517i
$7$	2.63290	−	0.260479i	0.995142	−	0.0984517i
$8$	−1.84824	+	1.34282i	−0.653451	+	0.474760i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.05559	+	1.36044i	0.966263	+	0.430208i
$11$	−3.48746	−	1.55272i	−1.05151	−	0.468161i	−0.193126	−	0.981174i	$-0.561863\pi$
$11$	−3.48746	−	1.55272i	−1.05151	−	0.468161i	−0.858381	+	0.513013i	$0.828529\pi$
$12$	0.526957	−	0.234616i	0.152119	−	0.0677279i
$13$	−0.660175	+	2.03181i	−0.183100	+	0.563523i	−0.999910	−	0.0133829i	$-0.995740\pi$
$13$	−0.660175	+	2.03181i	−0.183100	+	0.563523i	0.816811	+	0.576906i	$0.195740\pi$
$14$	−3.13879	−	2.86108i	−0.838876	−	0.764657i
$15$	1.68570	+	1.22473i	0.435246	+	0.316225i
$16$	4.71558	+	1.00233i	1.17889	+	0.250582i
$17$	−1.63821	−	0.729376i	−0.397323	−	0.176900i	0.198341	−	0.980133i	$-0.436445\pi$
$17$	−1.63821	−	0.729376i	−0.397323	−	0.176900i	−0.595665	+	0.803233i	$0.703111\pi$
$18$	1.57017	−	0.333750i	0.370093	−	0.0786657i
$19$	2.10173	+	0.446737i	0.482171	+	0.102489i	0.442583	−	0.896728i	$-0.354062\pi$
$19$	2.10173	+	0.446737i	0.482171	+	0.102489i	0.0395877	+	0.999216i	$0.487396\pi$
$20$	−0.371407	−	1.14307i	−0.0830492	−	0.255599i
$21$	−1.54203	−	2.14992i	−0.336499	−	0.469150i
$22$	1.89367	+	5.82810i	0.403731	+	1.24256i
$23$	3.67346	+	4.07979i	0.765969	+	0.850694i	0.992364	−	0.123341i	$-0.0393609\pi$
$23$	3.67346	+	4.07979i	0.765969	+	0.850694i	−0.226396	+	0.974035i	$0.572694\pi$
$24$	2.08704	+	0.929210i	0.426015	+	0.189674i
$25$	−0.440584	+	0.489318i	−0.0881168	+	0.0978636i
$26$	3.13292	−	1.39487i	0.614416	−	0.273556i
$27$	1.00000			0.192450
$28$	−0.00932202	+	1.52611i	−0.00176170	+	0.288408i
$29$	3.50398	+	2.54579i	0.650672	+	0.472741i	0.863500	−	0.504349i	$-0.168267\pi$
$29$	3.50398	+	2.54579i	0.650672	+	0.472741i	−0.212828	+	0.977090i	$0.568267\pi$
$30$	−0.349623	−	3.32644i	−0.0638321	−	0.607322i
$31$	1.13870	+	0.506982i	0.204516	+	0.0910566i	0.506439	−	0.862276i	$-0.330962\pi$
$31$	1.13870	+	0.506982i	0.204516	+	0.0910566i	−0.301922	+	0.953333i	$0.597628\pi$
$32$	−1.58484	−	2.74503i	−0.280164	−	0.485258i
$33$	0.399037	+	3.79658i	0.0694634	+	0.660900i
$34$	0.889535	+	2.73771i	0.152554	+	0.469513i
$35$	−4.79097	+	2.72718i	−0.809821	+	0.460978i
$36$	−0.466662	−	0.339050i	−0.0777771	−	0.0565083i
$37$	−2.21544	+	0.986376i	−0.364215	+	0.162159i	−0.580681	−	0.814131i	$-0.697214\pi$
$37$	−2.21544	+	0.986376i	−0.364215	+	0.162159i	0.216466	+	0.976290i	$0.430547\pi$
$38$	−1.72459	−	2.98708i	−0.279765	−	0.484568i
$39$	2.08969	−	0.444177i	0.334618	−	0.0711252i
$40$	2.38009	−	4.12244i	0.376325	−	0.651814i
$41$	5.99309	+	2.25453i	0.935963	+	0.352099i
$41$	5.99309	+	2.25453i	0.935963	+	0.352099i
$42$	−0.908379	+	4.14881i	−0.140166	+	0.640175i
$43$	−0.829014	+	2.55144i	−0.126423	+	0.389091i	−0.994158	−	0.107937i	$-0.965575\pi$
$43$	−0.829014	+	2.55144i	−0.126423	+	0.389091i	0.867734	+	0.497028i	$0.165575\pi$
$44$	1.10102	−	1.90702i	0.165984	−	0.287493i
$45$	0.217800	−	2.07223i	0.0324677	−	0.308909i
$46$	0.921173	−	8.76437i	0.135820	−	1.29224i
$47$	3.66135	+	4.06634i	0.534062	+	0.593136i	0.948435	−	0.316971i	$-0.102666\pi$
$47$	3.66135	+	4.06634i	0.534062	+	0.593136i	−0.414373	+	0.910107i	$0.635999\pi$
$48$	−1.48975	−	4.58497i	−0.215027	−	0.661784i
$49$	6.86430	−	1.37163i	0.980615	−	0.195947i
$50$	1.05696			0.149477
$51$	0.187445	+	1.78342i	0.0262475	+	0.249728i
$52$	−1.12578	−	0.501228i	−0.156117	−	0.0695078i
$53$	1.03816	−	9.87743i	0.142602	−	1.35677i	−0.655932	−	0.754820i	$-0.727724\pi$
$53$	1.03816	−	9.87743i	0.142602	−	1.35677i	0.798534	−	0.601949i	$-0.205609\pi$
$54$	−1.07412	−	1.19293i	−0.146169	−	0.162338i
$55$	7.95429			1.07256
$56$	−4.51645	+	4.01695i	−0.603536	+	0.536787i
$57$	−0.663981	−	2.04352i	−0.0879464	−	0.270671i
$58$	−0.726743	−	6.91449i	−0.0954260	−	0.907918i
$59$	10.4069	−	2.21205i	1.35486	−	0.287984i	0.527450	−	0.849586i	$-0.323148\pi$
$59$	10.4069	−	2.21205i	1.35486	−	0.287984i	0.827407	+	0.561602i	$0.189815\pi$
$60$	−0.804227	+	0.893185i	−0.103825	+	0.115310i
$61$	−6.25340	−	1.32920i	−0.800666	−	0.170187i	−0.210632	−	0.977565i	$-0.567552\pi$
$61$	−6.25340	−	1.32920i	−0.800666	−	0.170187i	−0.590034	+	0.807378i	$0.700886\pi$
$62$	−0.618307	−	1.90295i	−0.0785250	−	0.241675i
$63$	−1.09087	+	2.41040i	−0.137436	+	0.303681i
$64$	1.40717	−	4.33083i	0.175897	−	0.541354i
$65$	−0.465301	−	4.42704i	−0.0577135	−	0.549107i
$66$	4.10045	−	4.55402i	0.504731	−	0.560561i
$67$	0.699275	−	6.65316i	0.0854301	−	0.812813i	−0.864979	−	0.501809i	$-0.832668\pi$
$67$	0.699275	−	6.65316i	0.0854301	−	0.812813i	0.950409	−	0.311004i	$-0.100665\pi$
$68$	0.517194	−	0.895806i	0.0627190	−	0.108632i
$69$	1.69647	−	5.22120i	0.204231	−	0.628559i
$70$	8.39943	+	2.78598i	1.00392	+	0.332988i
$71$	−10.7436	+	7.80565i	−1.27503	+	0.926360i	−0.999391	−	0.0349027i	$-0.988888\pi$
$71$	−10.7436	+	7.80565i	−1.27503	+	0.926360i	−0.275634	+	0.961263i	$0.588888\pi$
$72$	−0.238800	−	2.27203i	−0.0281429	−	0.267762i
$73$	2.80012	+	4.84995i	0.327729	+	0.567643i	0.982061	−	0.188564i	$-0.0603834\pi$
$73$	2.80012	+	4.84995i	0.327729	+	0.567643i	−0.654332	+	0.756207i	$0.727050\pi$
$74$	3.55633	+	1.58338i	0.413415	+	0.184064i
$75$	0.644054	+	0.136898i	0.0743689	+	0.0158076i
$76$	−0.383002	+	1.17876i	−0.0439333	+	0.135213i
$77$	−9.58656	−	3.17973i	−1.09249	−	0.362364i
$78$	−2.77445	−	2.01576i	−0.314145	−	0.228239i
$79$	−1.97595	+	3.42245i	−0.222312	+	0.385056i	−0.955510	−	0.294960i	$-0.904694\pi$
$79$	−1.97595	+	3.42245i	−0.222312	+	0.385056i	0.733198	+	0.680016i	$0.238027\pi$
$80$	−9.82556	+	2.08849i	−1.09853	+	0.233500i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.74780	−	9.57099i	−0.413875	−	1.05694i
$83$	16.2245			1.78087			0.890437	−	0.455106i	$-0.150399\pi$
$83$	16.2245			1.78087			0.890437	+	0.455106i	$0.150399\pi$
$84$	1.32631	−	0.754982i	0.144712	−	0.0823753i
$85$	3.73647			0.405277
$86$	3.93416	−	1.75160i	0.424231	−	0.188880i
$87$	0.452729	−	4.30743i	0.0485376	−	0.461805i
$88$	8.53067	−	1.81325i	0.909373	−	0.193293i
$89$	−10.8974	−	2.31632i	−1.15512	−	0.245529i	−0.409764	−	0.912192i	$-0.634389\pi$
$89$	−10.8974	−	2.31632i	−1.15512	−	0.245529i	−0.745360	+	0.666662i	$0.767722\pi$
$90$	−2.70597	+	1.96600i	−0.285234	+	0.207235i
$91$	−1.20893	+	5.52151i	−0.126730	+	0.578812i
$92$	−2.56193	+	1.86135i	−0.267099	+	0.194059i
$93$	−0.130291	−	1.23963i	−0.0135105	−	0.128544i
$94$	0.918136	−	8.73548i	0.0946985	−	0.900996i
$95$	−4.37926	+	0.930840i	−0.449302	+	0.0955021i
$96$	−1.58484	+	2.74503i	−0.161753	+	0.280164i
$97$	11.8293	+	8.59451i	1.20109	+	0.872641i	0.994391	−	0.105765i	$-0.0337290\pi$
$97$	11.8293	+	8.59451i	1.20109	+	0.872641i	0.206696	+	0.978405i	$0.433729\pi$
$98$	−9.00936	−	6.71536i	−0.910082	−	0.678353i
$99$	3.08842	−	2.24387i	0.310398	−	0.225517i
$100$	−0.254140	−	0.282252i	−0.0254140	−	0.0282252i
$101$	−2.87630	+	3.19445i	−0.286203	+	0.317860i	−0.869053	−	0.494720i	$-0.835271\pi$
$101$	−2.87630	+	3.19445i	−0.286203	+	0.317860i	0.582850	+	0.812580i	$0.301937\pi$
$102$	1.92616	−	2.13921i	0.190718	−	0.211814i
$103$	5.30023	+	1.12660i	0.522247	+	0.111007i	0.461490	−	0.887145i	$-0.347315\pi$
$103$	5.30023	+	1.12660i	0.522247	+	0.111007i	0.0607575	+	0.998153i	$0.480648\pi$
$104$	−1.50820	−	4.64177i	−0.147891	−	0.455163i
$105$	4.75729	+	2.78551i	0.464264	+	0.271838i
$106$	−12.8982	+	9.37111i	−1.25279	+	0.910202i
$107$	2.61481	+	0.555794i	0.252783	+	0.0537307i	0.332560	−	0.943082i	$-0.392088\pi$
$107$	2.61481	+	0.555794i	0.252783	+	0.0537307i	−0.0797772	+	0.996813i	$0.525421\pi$
$108$	−0.0602948	+	0.573666i	−0.00580187	+	0.0552011i
$109$	−2.62010	−	4.53814i	−0.250960	−	0.434675i	0.712831	−	0.701336i	$-0.247413\pi$
$109$	−2.62010	−	4.53814i	−0.250960	−	0.434675i	−0.963790	+	0.266661i	$0.914079\pi$
$110$	−8.54387	−	9.48893i	−0.814626	−	0.904734i
$111$	1.96194	+	1.42544i	0.186220	+	0.135296i
$112$	12.6767	+	1.41072i	1.19784	+	0.133300i
$113$	−9.17394	+	6.66526i	−0.863012	+	0.627015i	−0.928703	−	0.370825i	$-0.879075\pi$
$113$	−9.17394	+	6.66526i	−0.863012	+	0.627015i	0.0656907	+	0.997840i	$0.479075\pi$
$114$	−1.72459	+	2.98708i	−0.161523	+	0.279765i
$115$	−10.4500	−	4.65265i	−0.974469	−	0.433861i
$116$	−1.67170	+	1.85662i	−0.155214	+	0.172382i
$117$	−1.42951	−	1.58763i	−0.132158	−	0.146777i
$118$	−13.8171	−	10.0387i	−1.27196	−	0.924135i
$119$	−4.50321	−	1.49365i	−0.412809	−	0.136923i
$120$	−4.76018			−0.434543
$121$	2.39098	+	2.65545i	0.217362	+	0.241405i
$122$	5.13127	+	8.88762i	0.464563	+	0.804647i
$123$	−1.04406	−	6.31743i	−0.0941400	−	0.569624i
$124$	−0.359496	+	0.622665i	−0.0322837	+	0.0559170i
$125$	3.64336	−	11.2131i	0.325872	−	1.00293i
$126$	4.04717	−	1.28773i	0.360550	−	0.114720i
$127$	8.94958	+	6.50225i	0.794146	+	0.576981i	0.909191	−	0.416379i	$-0.136701\pi$
$127$	8.94958	+	6.50225i	0.794146	+	0.576981i	−0.115045	+	0.993360i	$0.536701\pi$
$128$	−12.4692	+	5.55164i	−1.10213	+	0.490700i
$129$	2.62412	−	0.557774i	0.231041	−	0.0491093i
$130$	−4.78138	+	5.31026i	−0.419355	+	0.465740i
$131$	0.342071	+	3.25459i	0.0298869	+	0.284354i	0.999250	+	0.0387225i	$0.0123288\pi$
$131$	0.342071	+	3.25459i	0.0298869	+	0.284354i	−0.969363	+	0.245632i	$0.921005\pi$
$132$	−2.20203			−0.191662
$133$	5.65001	+	0.628756i	0.489918	+	0.0545201i
$134$	−8.68788	+	6.31211i	−0.750518	+	0.545284i
$135$	−1.90350	+	0.847493i	−0.163827	+	0.0729406i
$136$	4.00722	−	0.851761i	0.343616	−	0.0730379i
$137$	9.34969	+	16.1941i	0.798798	+	1.38356i	0.920399	+	0.390980i	$0.127864\pi$
$137$	9.34969	+	16.1941i	0.798798	+	1.38356i	−0.121602	+	0.992579i	$0.538803\pi$
$138$	−8.05076	+	3.58443i	−0.685326	+	0.305127i
$139$	3.02549	+	9.31151i	0.256619	+	0.789792i	0.993506	+	0.113776i	$0.0362947\pi$
$139$	3.02549	+	9.31151i	0.256619	+	0.789792i	−0.736888	+	0.676015i	$0.763705\pi$
$140$	−1.27562	−	2.91285i	−0.107810	−	0.246181i
$141$	1.69088	−	5.20399i	0.142398	−	0.438255i
$142$	20.8515	+	4.43212i	1.74982	+	0.371935i
$143$	5.45715	−	6.06078i	0.456350	−	0.506828i
$144$	−3.22583	+	3.58264i	−0.268819	+	0.298554i
$145$	−8.82736	−	1.87631i	−0.733072	−	0.155819i
$146$	2.77799	−	8.54978i	0.229908	−	0.707585i
$147$	−4.62002	−	5.25885i	−0.381052	−	0.433742i
$148$	−0.432272	−	1.33039i	−0.0355325	−	0.109358i
$149$	16.2328	−	7.22730i	1.32984	−	0.592084i	0.386005	−	0.922497i	$-0.373855\pi$
$149$	16.2328	−	7.22730i	1.32984	−	0.592084i	0.943836	+	0.330413i	$0.107188\pi$
$150$	−0.528482	−	0.915358i	−0.0431504	−	0.0747387i
$151$	−16.0582	+	3.41327i	−1.30680	+	0.277768i	−0.808119	−	0.589020i	$-0.799514\pi$
$151$	−16.0582	+	3.41327i	−1.30680	+	0.277768i	−0.498677	+	0.866788i	$0.666181\pi$
$152$	−4.48439	+	1.99658i	−0.363732	+	0.161944i
$153$	1.45076	−	1.05404i	0.117287	−	0.0852140i
$154$	6.50393	+	14.8515i	0.524101	+	1.19677i
$155$	−2.59718			−0.208610
$156$	0.128812	+	1.22556i	0.0103132	+	0.0981237i
$157$	−1.59501	+	1.77144i	−0.127296	+	0.141376i	−0.803423	−	0.595408i	$-0.796990\pi$
$157$	−1.59501	+	1.77144i	−0.127296	+	0.141376i	0.676127	+	0.736785i	$0.263657\pi$
$158$	6.20517	−	1.31895i	0.493657	−	0.104930i
$159$	−9.07318	+	4.03964i	−0.719550	+	0.320364i
$160$	5.34315	+	3.88202i	0.422413	+	0.306901i
$161$	10.7345	+	9.78480i	0.846000	+	0.771150i
$162$	−0.496049	+	1.52668i	−0.0389733	+	0.119948i
$163$	−3.82110	+	6.61834i	−0.299292	+	0.518388i	−0.975974	−	0.217887i	$-0.930084\pi$
$163$	−3.82110	+	6.61834i	−0.299292	+	0.518388i	0.676683	+	0.736275i	$0.263417\pi$
$164$	−1.65470	+	3.30210i	−0.129210	+	0.257850i
$165$	−3.97714	−	6.88861i	−0.309620	−	0.536278i
$166$	−17.4271	−	19.3548i	−1.35261	−	1.50222i
$167$	8.77137			0.678749			0.339375	−	0.940651i	$-0.389785\pi$
$167$	8.77137			0.678749			0.339375	+	0.940651i	$0.389785\pi$
$168$	5.73700	+	1.90288i	0.442619	+	0.146811i
$169$	6.82480	+	4.95851i	0.524985	+	0.381424i
$170$	−4.01342	−	4.45735i	−0.307815	−	0.341863i
$171$	−1.43775	+	1.59679i	−0.109948	+	0.122109i
$172$	−1.41369	−	0.629416i	−0.107793	−	0.0479925i
$173$	5.79331	−	10.0343i	0.440457	−	0.762894i	−0.557266	−	0.830334i	$-0.688150\pi$
$173$	5.79331	−	10.0343i	0.440457	−	0.762894i	0.997723	+	0.0674401i	$0.0214832\pi$
$174$	−5.62476	+	4.08662i	−0.426412	+	0.309806i
$175$	−1.03256	+	1.40309i	−0.0780539	+	0.106063i
$176$	−14.8890	−	10.8175i	−1.12230	−	0.815401i
$177$	−7.11912	−	7.90658i	−0.535106	−	0.594295i
$178$	8.94194	+	15.4879i	0.670227	+	1.16087i
$179$	−2.22213	+	21.1421i	−0.166090	+	1.58024i	0.520931	+	0.853599i	$0.325585\pi$
$179$	−2.22213	+	21.1421i	−0.166090	+	1.58024i	−0.687021	+	0.726638i	$0.741082\pi$
$180$	1.17563	+	0.249889i	0.0876266	+	0.0186256i
$181$	1.08441	−	0.787870i	0.0806036	−	0.0585619i	−0.546754	−	0.837294i	$-0.684137\pi$
$181$	1.08441	−	0.787870i	0.0806036	−	0.0585619i	0.627357	+	0.778732i	$0.284137\pi$
$182$	7.88533	−	4.48860i	0.584499	−	0.332717i
$183$	1.97558	+	6.08021i	0.146039	+	0.449462i
$184$	−12.2679	−	2.60761i	−0.904399	−	0.192236i
$185$	3.38114	−	3.75513i	0.248586	−	0.276083i
$186$	−1.33885	+	1.48695i	−0.0981693	+	0.109028i
$187$	4.58065	+	5.08733i	0.334971	+	0.372023i
$188$	−2.55348	+	1.85521i	−0.186232	+	0.135305i
$189$	2.63290	−	0.260479i	0.191515	−	0.0189470i
$190$	5.81428	+	4.22432i	0.421812	+	0.306465i
$191$	−5.49727	+	9.52155i	−0.397769	+	0.688955i	−0.993450	−	0.114265i	$-0.963549\pi$
$191$	−5.49727	+	9.52155i	−0.397769	+	0.688955i	0.595682	+	0.803221i	$0.296882\pi$
$192$	−4.45420	+	0.946769i	−0.321454	+	0.0683272i
$193$	−1.56350	+	14.8757i	−0.112543	+	1.07078i	0.781841	+	0.623478i	$0.214281\pi$
$193$	−1.56350	+	14.8757i	−0.112543	+	1.07078i	−0.894384	+	0.447299i	$0.852386\pi$
$194$	−2.45346	−	23.3432i	−0.176148	−	1.67594i
$195$	−3.60128	+	2.61649i	−0.257893	+	0.187370i
$196$	0.372976	+	4.02052i	0.0266411	+	0.287180i
$197$	−21.6783	+	15.7502i	−1.54452	+	1.12216i	−0.597094	+	0.802172i	$0.703678\pi$
$197$	−21.6783	+	15.7502i	−1.54452	+	1.12216i	−0.947423	+	0.319985i	$0.896322\pi$
$198$	−5.99412	−	1.27409i	−0.425984	−	0.0905456i
$199$	−11.2701	+	2.39553i	−0.798916	+	0.169815i	−0.589242	−	0.807956i	$-0.700574\pi$
$199$	−11.2701	+	2.39553i	−0.798916	+	0.169815i	−0.209674	+	0.977771i	$0.567240\pi$
$200$	0.157236	−	1.49600i	0.0111183	−	0.105783i
$201$	−6.11144	+	2.72099i	−0.431068	+	0.191924i
$202$	6.90027			0.485501
$203$	9.88873	+	5.79009i	0.694053	+	0.406384i
$204$	−1.03439			−0.0724216
$205$	−13.3185	+	0.787599i	−0.930207	+	0.0550083i
$206$	−4.34914	−	7.53293i	−0.303019	−	0.524844i
$207$	−5.36993	+	1.14141i	−0.373236	+	0.0793337i
$208$	−5.14964	+	8.91944i	−0.357063	+	0.618452i
$209$	−6.63604	−	4.82137i	−0.459025	−	0.333501i
$210$	−1.78699	−	8.66711i	−0.123314	−	0.598087i
$211$	−1.15676	+	3.56014i	−0.0796345	+	0.245090i	−0.982946	−	0.183896i	$-0.941129\pi$
$211$	−1.15676	+	3.56014i	−0.0796345	+	0.245090i	0.903311	+	0.428986i	$0.141129\pi$
$212$	5.60375	+	1.19111i	0.384867	+	0.0818061i
$213$	12.1317	+	5.40137i	0.831248	+	0.370095i
$214$	−2.14559	−	3.71628i	−0.146670	−	0.254040i
$215$	−0.584301	−	5.55925i	−0.0398490	−	0.379138i
$216$	−1.84824	+	1.34282i	−0.125757	+	0.0913676i
$217$	3.13014	+	1.03822i	0.212488	+	0.0704792i
$218$	−2.59939	+	8.00011i	−0.176053	+	0.541836i
$219$	2.80012	−	4.84995i	0.189214	−	0.327729i
$220$	−0.479602	+	4.56311i	−0.0323348	+	0.307645i
$221$	2.56346	−	2.84701i	0.172437	−	0.191510i
$222$	−0.406917	−	3.87156i	−0.0273105	−	0.259842i
$223$	−6.60852	+	20.3389i	−0.442539	+	1.36200i	0.442621	+	0.896709i	$0.354049\pi$
$223$	−6.60852	+	20.3389i	−0.442539	+	1.36200i	−0.885160	+	0.465287i	$0.845951\pi$
$224$	−4.88776	−	6.81457i	−0.326577	−	0.455317i
$225$	−0.203470	−	0.626216i	−0.0135647	−	0.0417477i
$226$	17.8051	+	3.78460i	1.18438	+	0.251748i
$227$	−4.69473	+	5.21402i	−0.311600	+	0.346067i	−0.878520	−	0.477706i	$-0.841468\pi$
$227$	−4.69473	+	5.21402i	−0.311600	+	0.346067i	0.566920	+	0.823773i	$0.308135\pi$
$228$	1.21234	−	0.257690i	0.0802888	−	0.0170659i
$229$	−0.332051	−	3.15925i	−0.0219425	−	0.208769i	−1.00000		0.000433502i	$-0.999862\pi$
$229$	−0.332051	−	3.15925i	−0.0219425	−	0.208769i	0.978057	−	0.208336i	$-0.0668047\pi$
$230$	5.67429	+	17.4637i	0.374152	+	1.15152i
$231$	2.03955	+	9.89207i	0.134193	+	0.650851i
$232$	−9.89473			−0.649621
$233$	18.0624	+	20.0603i	1.18331	+	1.31420i	0.938766	+	0.344556i	$0.111971\pi$
$233$	18.0624	+	20.0603i	1.18331	+	1.31420i	0.244541	+	0.969639i	$0.421363\pi$
$234$	−0.358471	+	3.41062i	−0.0234340	+	0.222959i
$235$	−10.4156	−	4.63731i	−0.679437	−	0.302505i
$236$	0.641497	+	6.10344i	0.0417579	+	0.397300i
$237$	3.95191			0.256704
$238$	3.05517	+	6.97640i	0.198037	+	0.452213i
$239$	−6.03657	−	18.5787i	−0.390473	−	1.20175i	−0.932431	−	0.361348i	$-0.882317\pi$
$239$	−6.03657	−	18.5787i	−0.390473	−	1.20175i	0.541958	−	0.840406i	$-0.317683\pi$
$240$	6.72147	+	7.46494i	0.433869	+	0.481860i
$241$	0.806179	−	7.67028i	0.0519305	−	0.494086i	−0.937385	−	0.348295i	$-0.886761\pi$
$241$	0.806179	−	7.67028i	0.0519305	−	0.494086i	0.989315	−	0.145791i	$-0.0465727\pi$
$242$	0.599574	−	5.70456i	0.0385421	−	0.366703i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.13957	−	3.50722i	0.0729533	−	0.224527i
$245$	−11.9038	+	8.42834i	−0.760503	+	0.538467i
$246$	−6.41482	+	8.03119i	−0.408994	+	0.512050i
$247$	−2.29520	+	3.97540i	−0.146040	+	0.252948i
$248$	−2.78538	+	0.592050i	−0.176872	+	0.0375952i
$249$	−8.11227	−	14.0509i	−0.514094	−	0.890437i
$250$	−17.2899	+	7.69796i	−1.09351	+	0.486862i
$251$	−13.1971	−	9.58824i	−0.832992	−	0.605204i	0.0874123	−	0.996172i	$-0.472140\pi$
$251$	−13.1971	−	9.58824i	−0.832992	−	0.605204i	−0.920404	+	0.390968i	$0.872140\pi$
$252$	−1.31699	−	0.771128i	−0.0829626	−	0.0485765i
$253$	−6.47627	−	19.9319i	−0.407159	−	1.25311i
$254$	−1.85619	−	17.6604i	−0.116468	−	1.10812i
$255$	−1.86823	−	3.23587i	−0.116993	−	0.202638i
$256$	11.6961	+	5.20744i	0.731007	+	0.325465i
$257$	1.79882	+	17.1146i	0.112207	+	1.06758i	0.895236	+	0.445593i	$0.147007\pi$
$257$	1.79882	+	17.1146i	0.112207	+	1.06758i	−0.783029	+	0.621986i	$0.786326\pi$
$258$	−3.48401	−	2.53128i	−0.216905	−	0.157591i
$259$	−5.57609	+	3.17410i	−0.346481	+	0.197229i
$260$	2.56770			0.159242
$261$	−3.95670	+	1.76164i	−0.244914	+	0.109043i
$262$	3.51508	−	3.90389i	0.217162	−	0.241183i
$263$	−16.5581	−	7.37214i	−1.02102	−	0.454586i	−0.173206	−	0.984886i	$-0.555413\pi$
$263$	−16.5581	−	7.37214i	−1.02102	−	0.454586i	−0.847810	+	0.530300i	$0.822079\pi$
$264$	−5.83566	−	6.48115i	−0.359160	−	0.398887i
$265$	6.39491	+	19.6815i	0.392836	+	1.20903i
$266$	−5.31874	−	7.41545i	−0.326113	−	0.454670i
$267$	3.44272	+	10.5956i	0.210691	+	0.648440i
$268$	3.77453	+	0.802301i	0.230566	+	0.0490084i
$269$	25.2789	−	5.37319i	1.54128	−	0.327609i	0.642595	−	0.766206i	$-0.277858\pi$
$269$	25.2789	−	5.37319i	1.54128	−	0.327609i	0.898684	+	0.438597i	$0.144524\pi$
$270$	3.05559	+	1.36044i	0.185957	+	0.0827936i
$271$	12.9846	+	2.75995i	0.788756	+	0.167655i	0.584641	−	0.811292i	$-0.301235\pi$
$271$	12.9846	+	2.75995i	0.788756	+	0.167655i	0.204114	+	0.978947i	$0.434569\pi$
$272$	−6.99401	−	5.08144i	−0.424074	−	0.308108i
$273$	5.38623	−	1.71379i	0.325990	−	0.103723i
$274$	9.27582	−	28.5480i	0.560373	−	1.72465i
$275$	2.29629	−	1.02237i	0.138471	−	0.0616514i
$276$	2.89294	+	1.28802i	0.174134	+	0.0775297i
$277$	−21.3564	−	9.50847i	−1.28318	−	0.571309i	−0.352045	−	0.935983i	$-0.614514\pi$
$277$	−21.3564	−	9.50847i	−1.28318	−	0.571309i	−0.931135	+	0.364674i	$0.881180\pi$
$278$	7.85826	−	13.6109i	0.471307	−	0.816328i
$279$	−1.00841	+	0.732652i	−0.0603718	+	0.0438627i
$280$	5.19272	−	11.4739i	0.310325	−	0.685698i
$281$	−0.533060	+	1.64059i	−0.0317997	+	0.0978695i	−0.965697	−	0.259673i	$-0.916385\pi$
$281$	−0.533060	+	1.64059i	−0.0317997	+	0.0978695i	0.933897	+	0.357542i	$0.116385\pi$
$282$	−8.02422	+	3.57261i	−0.477835	+	0.212746i
$283$	−0.147052	+	1.39911i	−0.00874136	+	0.0831685i	−0.998023	−	0.0628528i	$-0.979980\pi$
$283$	−0.147052	+	1.39911i	−0.00874136	+	0.0831685i	0.989281	+	0.146021i	$0.0466468\pi$
$284$	−3.83006	−	6.63386i	−0.227272	−	0.393647i
$285$	2.99576	+	3.32713i	0.177453	+	0.197082i
$286$	−13.0918			−0.774132
$287$	16.3664	+	4.37488i	0.966081	+	0.258241i
$288$	3.16969			0.186776
$289$	−9.22349	−	10.2437i	−0.542558	−	0.602572i
$290$	7.24334	+	12.5458i	0.425344	+	0.736717i
$291$	1.52840	−	14.5418i	0.0895964	−	0.852453i
$292$	−2.95108	+	1.31391i	−0.172699	+	0.0768906i
$293$	−1.67327	+	5.14981i	−0.0977537	+	0.300855i	−0.987962	−	0.154700i	$-0.950559\pi$
$293$	−1.67327	+	5.14981i	−0.0977537	+	0.300855i	0.890208	+	0.455555i	$0.150559\pi$
$294$	−1.31099	+	11.1600i	−0.0764586	+	0.650865i
$295$	−17.9348	+	13.0304i	−1.04420	+	0.758657i
$296$	2.77013	−	4.79800i	0.161010	−	0.278878i
$297$	−3.48746	−	1.55272i	−0.202363	−	0.0900977i
$298$	−26.0577	−	11.6016i	−1.50948	−	0.672064i
$299$	−10.7145	+	4.77039i	−0.619634	+	0.275879i
$300$	−0.117367	+	0.361218i	−0.00677618	+	0.0208549i
$301$	−1.51811	+	6.93363i	−0.0875025	+	0.399648i
$302$	21.3202	+	15.4901i	1.22684	+	0.891353i
$303$	4.20463	+	0.893721i	0.241550	+	0.0513430i
$304$	9.46310	+	4.21325i	0.542746	+	0.241646i
$305$	13.0298	−	2.76958i	0.746087	−	0.158586i
$306$	−2.81569	−	0.598494i	−0.160962	−	0.0342136i
$307$	−1.96108	−	6.03557i	−0.111924	−	0.344468i	0.879369	−	0.476142i	$-0.157965\pi$
$307$	−1.96108	−	6.03557i	−0.111924	−	0.344468i	−0.991293	+	0.131673i	$0.957965\pi$
$308$	2.40213	−	5.30777i	0.136874	−	0.302438i
$309$	−1.67445	−	5.15344i	−0.0952563	−	0.293169i
$310$	2.78968	+	3.09826i	0.158443	+	0.175969i
$311$	−1.74337	−	0.776201i	−0.0988577	−	0.0440143i	0.356712	−	0.934214i	$-0.383898\pi$
$311$	−1.74337	−	0.776201i	−0.0988577	−	0.0440143i	−0.455570	+	0.890200i	$0.650564\pi$
$312$	−3.26579	+	3.62703i	−0.184889	+	0.205340i
$313$	−4.14549	+	1.84569i	−0.234317	+	0.104325i	−0.520536	−	0.853839i	$-0.674268\pi$
$313$	−4.14549	+	1.84569i	−0.234317	+	0.104325i	0.286220	+	0.958164i	$0.407601\pi$
$314$	3.82645			0.215939
$315$	0.0336735	−	5.51269i	0.00189728	−	0.310605i
$316$	−1.84421	−	1.33989i	−0.103745	−	0.0753749i
$317$	1.22868	+	11.6901i	0.0690096	+	0.656582i	0.973280	+	0.229622i	$0.0737490\pi$
$317$	1.22868	+	11.6901i	0.0690096	+	0.656582i	−0.904270	+	0.426960i	$0.859584\pi$
$318$	14.5647	+	6.48463i	0.816749	+	0.363640i
$319$	−8.26708	−	14.3190i	−0.462867	−	0.801710i
$320$	0.991796	+	9.43631i	0.0554431	+	0.527506i
$321$	−0.826071	−	2.54239i	−0.0461068	−	0.141902i
$322$	0.142420	−	23.3156i	0.00793677	−	1.29933i
$323$	−3.11723	−	2.26480i	−0.173447	−	0.126017i
$324$	0.526957	−	0.234616i	0.0292754	−	0.0130342i
$325$	−0.703339	−	1.21822i	−0.0390142	−	0.0675746i
$326$	11.9996	−	2.55058i	0.664594	−	0.141264i
$327$	−2.62010	+	4.53814i	−0.144892	+	0.250960i
$328$	−14.1041	+	3.88075i	−0.778768	+	0.214279i
$329$	10.6991	+	9.75255i	0.589863	+	0.537675i
$330$	−3.94572	+	12.1437i	−0.217205	+	0.668487i
$331$	8.12554	−	14.0739i	0.446620	−	0.773569i	−0.551543	−	0.834146i	$-0.685961\pi$
$331$	8.12554	−	14.0739i	0.446620	−	0.773569i	0.998164	+	0.0605774i	$0.0192942\pi$
$332$	−0.978255	+	9.30747i	−0.0536887	+	0.510814i
$333$	0.253492	−	2.41181i	0.0138913	−	0.132166i
$334$	−9.42152	−	10.4637i	−0.515523	−	0.572546i
$335$	4.30743	+	13.2569i	0.235340	+	0.724303i
$336$	−5.11664	−	11.6837i	−0.279136	−	0.637399i
$337$	16.9482			0.923225			0.461612	−	0.887082i	$-0.347271\pi$
$337$	16.9482			0.923225			0.461612	+	0.887082i	$0.347271\pi$
$338$	−1.41550	−	13.4676i	−0.0769930	−	0.732539i
$339$	10.3593	+	4.61224i	0.562638	+	0.250502i
$340$	−0.225289	+	2.14349i	−0.0122180	+	0.116247i
$341$	−3.18396	−	3.53615i	−0.172421	−	0.191493i
$342$	3.44918			0.186510
$343$	17.7157	−	5.39936i	0.956559	−	0.291538i
$344$	−1.89392	−	5.82889i	−0.102113	−	0.314273i
$345$	1.19570	+	11.3763i	0.0643742	+	0.612479i
$346$	−18.1930	+	3.86703i	−0.978060	+	0.207893i
$347$	−11.4885	+	12.7593i	−0.616737	+	0.684956i	−0.967893	−	0.251361i	$-0.919122\pi$
$347$	−11.4885	+	12.7593i	−0.616737	+	0.684956i	0.351156	+	0.936317i	$0.385789\pi$
$348$	2.44373	+	0.519431i	0.130998	+	0.0278444i
$349$	8.49353	+	26.1404i	0.454648	+	1.39926i	0.871548	+	0.490310i	$0.163117\pi$
$349$	8.49353	+	26.1404i	0.454648	+	1.39926i	−0.416900	+	0.908952i	$0.636883\pi$
$350$	2.78288	−	0.275317i	0.148751	−	0.0147163i
$351$	−0.660175	+	2.03181i	−0.0352375	+	0.108450i
$352$	1.26482	+	12.0340i	0.0674153	+	0.641414i
$353$	17.9946	−	19.9851i	0.957758	−	1.06370i	−0.0401593	−	0.999193i	$-0.512787\pi$
$353$	17.9946	−	19.9851i	0.957758	−	1.06370i	0.997917	−	0.0645049i	$-0.0205468\pi$
$354$	−1.78522	+	16.9853i	−0.0948835	+	0.902756i
$355$	13.8351	−	23.9631i	0.734292	−	1.27183i
$356$	1.98585	−	6.11182i	0.105250	−	0.323926i
$357$	0.958064	+	4.64673i	0.0507061	+	0.245931i
$358$	27.6080	−	20.0584i	1.45913	−	1.06012i
$359$	−0.306454	−	2.91572i	−0.0161740	−	0.153886i	0.983454	−	0.181158i	$-0.0579846\pi$
$359$	−0.306454	−	2.91572i	−0.0161740	−	0.153886i	−0.999628	+	0.0272723i	$0.991318\pi$
$360$	2.38009	+	4.12244i	0.125442	+	0.217271i
$361$	−13.1397	−	5.85015i	−0.691561	−	0.307903i
$362$	−2.10466	−	0.447360i	−0.110619	−	0.0235127i
$363$	1.10420	−	3.39838i	0.0579555	−	0.178369i
$364$	−3.09461	−	1.02644i	−0.162202	−	0.0538001i
$365$	−9.44032	−	6.85879i	−0.494129	−	0.359006i
$366$	5.13127	−	8.88762i	0.268216	−	0.464563i
$367$	14.9199	−	3.17133i	0.778814	−	0.165542i	0.198682	−	0.980064i	$-0.436334\pi$
$367$	14.9199	−	3.17133i	0.778814	−	0.165542i	0.580133	+	0.814522i	$0.303001\pi$
$368$	13.2332	+	22.9205i	0.689827	+	1.19482i
$369$	−4.94902	+	4.06290i	−0.257636	+	0.211506i
$370$	−8.11137			−0.421690
$371$	0.160507	−	26.2767i	0.00833312	−	1.36422i
$372$	0.718992			0.0372780
$373$	6.06697	−	2.70119i	0.314136	−	0.139862i	−0.243612	−	0.969873i	$-0.578332\pi$
$373$	6.06697	−	2.70119i	0.314136	−	0.139862i	0.557748	+	0.830010i	$0.311666\pi$
$374$	1.14867	−	10.9288i	0.0593961	−	0.565116i
$375$	−11.5325	+	2.45131i	−0.595537	+	0.126585i
$376$	−12.2274	−	2.59902i	−0.630581	−	0.134034i
$377$	−7.48580	+	5.43875i	−0.385538	+	0.280110i
$378$	−3.13879	−	2.86108i	−0.161442	−	0.147158i
$379$	27.5229	−	19.9966i	1.41376	−	1.02715i	0.420993	−	0.907064i	$-0.361682\pi$
$379$	27.5229	−	19.9966i	1.41376	−	1.02715i	0.992763	−	0.120090i	$-0.0383183\pi$
$380$	−0.269945	−	2.56836i	−0.0138479	−	0.131754i
$381$	1.15632	−	11.0017i	0.0592402	−	0.563633i
$382$	17.2633	−	3.66943i	0.883268	−	0.187744i
$383$	9.71372	−	16.8247i	0.496348	−	0.859700i	−0.503643	−	0.863912i	$-0.668007\pi$
$383$	9.71372	−	16.8247i	0.496348	−	0.859700i	0.999991	+	0.00421167i	$0.00134062\pi$
$384$	11.0424	+	8.02281i	0.563507	+	0.409412i
$385$	20.9428	−	2.07192i	1.06735	−	0.105595i
$386$	19.4251	−	14.1132i	0.988712	−	0.718341i
$387$	−1.79511	−	1.99367i	−0.0912504	−	0.101344i
$388$	−5.64363	+	6.26789i	−0.286512	+	0.318204i
$389$	−5.75335	+	6.38974i	−0.291706	+	0.323973i	−0.871129	−	0.491055i	$-0.836612\pi$
$389$	−5.75335	+	6.38974i	−0.291706	+	0.323973i	0.579422	+	0.815027i	$0.303278\pi$
$390$	6.98951	+	1.48567i	0.353927	+	0.0752296i
$391$	−3.04218	−	9.36286i	−0.153850	−	0.473500i
$392$	−10.8450	+	11.7526i	−0.547756	+	0.593598i
$393$	2.64752	−	1.92353i	0.133550	−	0.0970295i
$394$	42.0741	+	8.94313i	2.11966	+	0.450548i
$395$	0.860724	−	8.18924i	0.0433077	−	0.412046i
$396$	1.10102	+	1.90702i	0.0553281	+	0.0958311i
$397$	6.90972	+	7.67402i	0.346789	+	0.385148i	0.891155	−	0.453700i	$-0.149896\pi$
$397$	6.90972	+	7.67402i	0.346789	+	0.385148i	−0.544366	+	0.838848i	$0.683230\pi$
$398$	14.9632	+	10.8714i	0.750036	+	0.544933i
$399$	−2.28049	−	5.20743i	−0.114167	−	0.260698i
$400$	−2.56806	+	1.86581i	−0.128403	+	0.0932904i
$401$	13.4127	−	23.2314i	0.669797	−	1.16012i	−0.308163	−	0.951334i	$-0.599714\pi$
$401$	13.4127	−	23.2314i	0.669797	−	1.16012i	0.977961	−	0.208790i	$-0.0669524\pi$
$402$	9.81039	+	4.36787i	0.489298	+	0.217849i
$403$	−1.78183	+	1.97892i	−0.0887593	+	0.0985772i
$404$	−1.65913	−	1.84265i	−0.0825446	−	0.0916750i
$405$	1.68570	+	1.22473i	0.0837631	+	0.0608575i
$406$	−3.71452	−	18.0159i	−0.184348	−	0.894112i
$407$	9.25780			0.458892
$408$	−2.74126	−	3.04447i	−0.135712	−	0.150724i
$409$	−13.9511	−	24.1640i	−0.689838	−	1.19483i	−0.971890	−	0.235435i	$-0.924349\pi$
$409$	−13.9511	−	24.1640i	−0.689838	−	1.19483i	0.282052	−	0.959399i	$-0.408985\pi$
$410$	15.2453	+	15.0422i	0.752911	+	0.742879i
$411$	9.34969	−	16.1941i	0.461186	−	0.798798i
$412$	−0.965869	+	2.97264i	−0.0475849	+	0.146451i
$413$	26.8240	−	8.53486i	1.31992	−	0.419973i
$414$	7.12958	+	5.17995i	0.350400	+	0.254580i
$415$	−30.8834	+	13.7502i	−1.51601	+	0.674970i
$416$	6.62366	−	1.40790i	0.324751	−	0.0690281i
$417$	6.55126	−	7.27591i	0.320816	−	0.356303i
$418$	1.37635	+	13.0951i	0.0673195	+	0.640502i
$419$	5.15817			0.251993			0.125997	−	0.992031i	$-0.459787\pi$
$419$	5.15817			0.251993			0.125997	+	0.992031i	$0.459787\pi$
$420$	−1.88479	+	2.56115i	−0.0919685	+	0.124971i
$421$	−4.73370	+	3.43923i	−0.230706	+	0.167618i	−0.697133	−	0.716942i	$-0.745541\pi$
$421$	−4.73370	+	3.43923i	−0.230706	+	0.167618i	0.466426	+	0.884560i	$0.345541\pi$
$422$	5.48950	−	2.44408i	0.267225	−	0.118976i
$423$	−5.35223	+	1.13765i	−0.260234	+	0.0553145i
$424$	11.3449	+	19.6499i	0.550956	+	0.954284i
$425$	1.07866	−	0.480252i	0.0523229	−	0.0232957i
$426$	−6.58742	−	20.2740i	−0.319161	−	0.982278i
$427$	−16.8108	−	1.87077i	−0.813532	−	0.0905331i
$428$	−0.476500	+	1.46652i	−0.0230325	+	0.0708867i
$429$	−7.97737	−	1.69564i	−0.385151	−	0.0818664i
$430$	−6.00421	+	6.66835i	−0.289548	+	0.321576i
$431$	−11.8393	+	13.1489i	−0.570279	+	0.633359i	−0.957433	−	0.288656i	$-0.906792\pi$
$431$	−11.8393	+	13.1489i	−0.570279	+	0.633359i	0.387154	+	0.922015i	$0.373458\pi$
$432$	4.71558	+	1.00233i	0.226878	+	0.0482245i
$433$	9.42539	−	29.0084i	0.452956	−	1.39405i	−0.420563	−	0.907263i	$-0.638168\pi$
$433$	9.42539	−	29.0084i	0.452956	−	1.39405i	0.873519	−	0.486790i	$-0.161832\pi$
$434$	−2.12362	−	4.84922i	−0.101937	−	0.232770i
$435$	2.78874	+	8.58287i	0.133710	+	0.411517i
$436$	2.76136	−	1.22944i	0.132245	−	0.0588793i
$437$	5.89803	+	10.2157i	0.282141	+	0.488683i
$438$	−8.79333	+	1.86908i	−0.420161	+	0.0893081i
$439$	−35.1261	+	15.6392i	−1.67648	+	0.746417i	−0.676530	+	0.736415i	$0.736517\pi$
$439$	−35.1261	+	15.6392i	−1.67648	+	0.746417i	−0.999950	+	0.0100014i	$0.996816\pi$
$440$	−14.7014	+	10.6812i	−0.700863	+	0.509207i
$441$	−2.24429	+	6.63047i	−0.106871	+	0.315737i
$442$	−6.14975			−0.292514
$443$	−0.160276	−	1.52493i	−0.00761495	−	0.0724514i	0.990054	−	0.140685i	$-0.0449304\pi$
$443$	−0.160276	−	1.52493i	−0.00761495	−	0.0724514i	−0.997669	+	0.0682334i	$0.978264\pi$
$444$	−0.936020	+	1.03956i	−0.0444215	+	0.0493351i
$445$	22.7063	−	4.82637i	1.07638	−	0.228792i
$446$	31.3613	−	13.9630i	1.48500	−	0.661166i
$447$	−14.3754	−	10.4444i	−0.679934	−	0.494001i
$448$	2.57685	−	11.7692i	0.121745	−	0.556041i
$449$	−1.44759	+	4.45522i	−0.0683160	+	0.210255i	−0.979386	−	0.201996i	$-0.935257\pi$
$449$	−1.44759	+	4.45522i	−0.0683160	+	0.210255i	0.911070	+	0.412251i	$0.135257\pi$
$450$	−0.528482	+	0.915358i	−0.0249129	+	0.0431504i
$451$	−17.4000	−	17.1681i	−0.819333	−	0.808416i
$452$	−3.27050	−	5.66466i	−0.153831	−	0.266443i
$453$	10.9851	+	12.2002i	0.516124	+	0.573213i
$454$	11.2627			0.528584
$455$	−2.37824	−	11.5348i	−0.111494	−	0.540758i
$456$	3.97129	+	2.88531i	0.185973	+	0.135117i
$457$	13.0093	+	14.4483i	0.608552	+	0.675865i	0.966141	−	0.258014i	$-0.0830680\pi$
$457$	13.0093	+	14.4483i	0.608552	+	0.675865i	−0.357590	+	0.933879i	$0.616401\pi$
$458$	−3.41211	+	3.78953i	−0.159438	+	0.177073i
$459$	−1.63821	−	0.729376i	−0.0764649	−	0.0340444i
$460$	3.29915	−	5.71429i	0.153824	−	0.266430i
$461$	−4.33754	+	3.15141i	−0.202019	+	0.146776i	−0.684195	−	0.729299i	$-0.739846\pi$
$461$	−4.33754	+	3.15141i	−0.202019	+	0.146776i	0.482176	+	0.876074i	$0.339846\pi$
$462$	9.60985	−	13.0583i	0.447091	−	0.607529i
$463$	−14.2803	−	10.3752i	−0.663661	−	0.482178i	0.204237	−	0.978922i	$-0.434529\pi$
$463$	−14.2803	−	10.3752i	−0.663661	−	0.482178i	−0.867897	+	0.496744i	$0.834529\pi$
$464$	13.9716	+	15.5170i	0.648613	+	0.720358i
$465$	1.29859	+	2.24922i	0.0602206	+	0.104305i
$466$	4.52941	−	43.0945i	0.209821	−	1.99631i
$467$	−5.87778	−	1.24936i	−0.271991	−	0.0578135i	0.0698968	−	0.997554i	$-0.477733\pi$
$467$	−5.87778	−	1.24936i	−0.271991	−	0.0578135i	−0.341888	+	0.939741i	$0.611066\pi$
$468$	0.996964	−	0.724337i	0.0460847	−	0.0334825i
$469$	0.108113	−	17.6992i	0.00499220	−	0.817275i
$470$	5.65559	+	17.4061i	0.260873	+	0.802884i
$471$	2.33162	+	0.495601i	0.107435	+	0.0228361i
$472$	−16.2640	+	18.0630i	−0.748610	+	0.831415i
$473$	6.85281	−	7.61082i	0.315093	−	0.349946i
$474$	−4.24483	−	4.71436i	−0.194971	−	0.216538i
$475$	−1.14459	+	0.831591i	−0.0525172	+	0.0381560i
$476$	1.12838	−	2.49328i	0.0517192	−	0.114279i
$477$	8.03502	+	5.83779i	0.367898	+	0.267294i
$478$	−15.6791	+	27.1570i	−0.717145	+	1.24213i
$479$	23.9971	−	5.10073i	1.09645	−	0.233058i	0.376040	−	0.926603i	$-0.377285\pi$
$479$	23.9971	−	5.10073i	1.09645	−	0.233058i	0.720413	+	0.693545i	$0.243952\pi$
$480$	0.690357	−	6.56831i	0.0315104	−	0.299801i
$481$	−0.541552	−	5.15253i	−0.0246927	−	0.234935i
$482$	−10.0161	+	7.27710i	−0.456219	+	0.331463i
$483$	3.10662	−	14.1888i	0.141356	−	0.645612i
$484$	−1.66751	+	1.21152i	−0.0757959	+	0.0550689i
$485$	−29.8009	−	6.33438i	−1.35319	−	0.287629i
$486$	1.57017	−	0.333750i	0.0712244	−	0.0151392i
$487$	−2.75549	+	26.2167i	−0.124863	+	1.18799i	0.735216	+	0.677833i	$0.237081\pi$
$487$	−2.75549	+	26.2167i	−0.124863	+	1.18799i	−0.860079	+	0.510160i	$0.829586\pi$
$488$	13.3427	−	5.94054i	0.603994	−	0.268916i
$489$	7.64220			0.345592
$490$	22.8405	+	5.14732i	1.03183	+	0.232532i
$491$	−20.8748			−0.942069			−0.471034	−	0.882115i	$-0.656119\pi$
$491$	−20.8748			−0.942069			−0.471034	+	0.882115i	$0.656119\pi$
$492$	3.68705	−	0.218036i	0.166225	−	0.00982981i
$493$	−3.88340	−	6.72624i	−0.174899	−	0.302935i
$494$	7.20770	−	1.53204i	0.324290	−	0.0689299i
$495$	−3.97714	+	6.88861i	−0.178759	+	0.309620i
$496$	4.86146	+	3.53206i	0.218286	+	0.158594i
$497$	−26.2535	+	23.3499i	−1.17763	+	1.04739i
$498$	−8.04817	+	24.7697i	−0.360647	+	1.10996i
$499$	−20.7478	−	4.41008i	−0.928798	−	0.197422i	−0.281414	−	0.959586i	$-0.590804\pi$
$499$	−20.7478	−	4.41008i	−0.928798	−	0.197422i	−0.647384	+	0.762164i	$0.724137\pi$
$500$	6.21291	+	2.76617i	0.277850	+	0.123707i
$501$	−4.38569	−	7.59623i	−0.195938	−	0.339375i
$502$	2.73714	+	26.0422i	0.122165	+	1.16232i
$503$	9.13435	−	6.63649i	0.407281	−	0.295907i	−0.365219	−	0.930921i	$-0.619006\pi$
$503$	9.13435	−	6.63649i	0.407281	−	0.295907i	0.772500	+	0.635015i	$0.219006\pi$
$504$	−1.22055	−	5.91983i	−0.0543678	−	0.263690i
$505$	2.76776	−	8.51829i	0.123164	−	0.379059i
$506$	−16.8211	+	29.1350i	−0.747790	+	1.29521i
$507$	0.881793	−	8.38970i	0.0391618	−	0.372600i
$508$	−4.26973	+	4.74202i	−0.189439	+	0.210393i
$509$	−3.00406	−	28.5817i	−0.133152	−	1.26686i	−0.833283	−	0.552846i	$-0.813542\pi$
$509$	−3.00406	−	28.5817i	−0.133152	−	1.26686i	0.700131	−	0.714014i	$-0.253125\pi$
$510$	−1.85347	+	5.70440i	−0.0820731	+	0.252595i
$511$	8.63573	+	12.0400i	0.382022	+	0.532620i
$512$	2.08477	+	6.41625i	0.0921345	+	0.283561i
$513$	2.10173	+	0.446737i	0.0927938	+	0.0197239i
$514$	18.4844	−	20.5290i	0.815312	−	0.905496i
$515$	−11.0438	+	2.34743i	−0.486647	+	0.103440i
$516$	0.161755	+	1.53900i	0.00712089	+	0.0677507i
$517$	−6.45492	−	19.8662i	−0.283887	−	0.873715i
$518$	9.77589	+	3.24253i	0.429528	+	0.142468i
$519$	−11.5866			−0.508596
$520$	6.80473	+	7.55742i	0.298407	+	0.331415i
$521$	2.23902	−	21.3029i	0.0980934	−	0.933296i	−0.829198	−	0.558955i	$-0.811202\pi$
$521$	2.23902	−	21.3029i	0.0980934	−	0.933296i	0.927291	−	0.374341i	$-0.122131\pi$
$522$	6.35150	+	2.82787i	0.277998	+	0.123772i
$523$	−1.79637	−	17.0913i	−0.0785496	−	0.747350i	−0.960926	−	0.276806i	$-0.910724\pi$
$523$	−1.79637	−	17.0913i	−0.0785496	−	0.747350i	0.882376	−	0.470544i	$-0.155942\pi$
$524$	−1.88767			−0.0824633
$525$	1.73139	+	0.192676i	0.0755639	+	0.00840906i
$526$	8.99094	+	27.6713i	0.392024	+	1.20653i
$527$	−1.49564	−	1.66108i	−0.0651512	−	0.0723578i
$528$	−1.92373	+	18.3030i	−0.0837194	+	0.796537i
$529$	−0.746222	+	7.09983i	−0.0324444	+	0.308688i
$530$	16.6098	−	28.7691i	0.721484	−	1.24965i
$531$	−3.28774	+	10.1186i	−0.142676	+	0.439111i
$532$	−0.701363	+	3.20331i	−0.0304079	+	0.138881i
$533$	−8.53727	+	10.6884i	−0.369790	+	0.462967i
$534$	8.94194	−	15.4879i	0.386956	−	0.670227i
$535$	−5.44832	+	1.15808i	−0.235551	+	0.0500680i
$536$	7.64159	+	13.2356i	0.330067	+	0.571692i
$537$	19.4207	−	8.64665i	0.838064	−	0.373130i
$538$	−33.5624	−	24.3845i	−1.44698	−	1.05129i
$539$	−26.0687	−	5.87481i	−1.12286	−	0.253046i
$540$	−0.371407	−	1.14307i	−0.0159828	−	0.0491901i
$541$	−3.64385	−	34.6689i	−0.156661	−	1.49053i	−0.736853	−	0.676053i	$-0.763689\pi$
$541$	−3.64385	−	34.6689i	−0.156661	−	1.49053i	0.580192	−	0.814480i	$-0.302978\pi$
$542$	−10.6546	−	18.4542i	−0.457652	−	0.792677i
$543$	−1.22452	−	0.545192i	−0.0525492	−	0.0233964i
$544$	0.594141	+	5.65287i	0.0254736	+	0.242365i
$545$	8.83339	+	6.41784i	0.378381	+	0.274910i
$546$	−7.82991	−	4.58460i	−0.335089	−	0.196203i
$547$	−25.3805			−1.08519			−0.542596	−	0.839994i	$-0.682559\pi$
$547$	−25.3805			−1.08519			−0.542596	+	0.839994i	$0.682559\pi$
$548$	−9.85377	+	4.38718i	−0.420932	+	0.187411i
$549$	4.27783	−	4.75101i	0.182573	−	0.202768i
$550$	−3.68612	−	1.64116i	−0.157177	−	0.0699795i
$551$	6.22712	+	6.91592i	0.265284	+	0.294628i
$552$	3.87567	+	11.9281i	0.164959	+	0.507693i
$553$	−4.31101	+	9.52566i	−0.183323	+	0.405072i
$554$	11.5964	+	35.6900i	0.492683	+	1.51632i
$555$	−4.94261	−	1.05058i	−0.209802	−	0.0445948i
$556$	−5.52412	+	1.17419i	−0.234275	+	0.0497967i
$557$	11.9907	+	5.33859i	0.508061	+	0.226203i	0.644725	−	0.764414i	$-0.276972\pi$
$557$	11.9907	+	5.33859i	0.508061	+	0.226203i	−0.136665	+	0.990617i	$0.543638\pi$
$558$	1.95716	+	0.416007i	0.0828531	+	0.0176110i
$559$	−4.63675	−	3.36880i	−0.196114	−	0.142485i
$560$	−25.3257	+	8.05813i	−1.07021	+	0.340518i
$561$	2.11543	−	6.51063i	0.0893136	−	0.274879i
$562$	2.52969	−	1.12629i	0.106708	−	0.0475096i
$563$	−20.7179	−	9.22421i	−0.873156	−	0.388754i	−0.0792935	−	0.996851i	$-0.525266\pi$
$563$	−20.7179	−	9.22421i	−0.873156	−	0.388754i	−0.793863	+	0.608097i	$0.791933\pi$
$564$	2.88340	+	1.28377i	0.121413	+	0.0540566i
$565$	11.8138	−	20.4622i	0.497012	−	0.860850i
$566$	1.82700	−	1.32739i	0.0767944	−	0.0557944i
$567$	−1.54203	−	2.14992i	−0.0647592	−	0.0902880i
$568$	9.37504	−	28.8534i	0.393368	−	1.21066i
$569$	−15.4474	+	6.87764i	−0.647590	+	0.288326i	−0.704126	−	0.710075i	$-0.748661\pi$
$569$	−15.4474	+	6.87764i	−0.647590	+	0.288326i	0.0565360	+	0.998401i	$0.481994\pi$
$570$	0.751230	−	7.14748i	0.0314656	−	0.299375i
$571$	2.99836	+	5.19331i	0.125477	+	0.217333i	0.921919	−	0.387382i	$-0.126620\pi$
$571$	2.99836	+	5.19331i	0.125477	+	0.217333i	−0.796442	+	0.604715i	$0.793287\pi$
$572$	3.14783	+	3.49602i	0.131617	+	0.146176i
$573$	10.9945			0.459304
$574$	−12.3606	−	24.2232i	−0.515922	−	1.01106i
$575$	−3.61478			−0.150747
$576$	3.04702	+	3.38406i	0.126959	+	0.141003i
$577$	17.0965	+	29.6120i	0.711736	+	1.23276i	0.964205	+	0.265157i	$0.0854239\pi$
$577$	17.0965	+	29.6120i	0.711736	+	1.23276i	−0.252470	+	0.967605i	$0.581243\pi$
$578$	−2.31293	+	22.0060i	−0.0962050	+	0.915330i
$579$	13.6645	−	6.08382i	0.567877	−	0.252835i
$580$	1.60862	−	4.95083i	0.0667944	−	0.205572i
$581$	42.7176	−	4.22615i	1.77222	−	0.175330i
$582$	−18.9890	+	13.7963i	−0.787121	+	0.571877i
$583$	−18.9574	+	32.8351i	−0.785134	+	1.35989i
$584$	−11.6879	−	5.20379i	−0.483649	−	0.215334i
$585$	4.06658	+	1.81056i	0.168133	+	0.0748574i
$586$	7.94067	−	3.53541i	0.328026	−	0.146047i
$587$	1.92110	−	5.91253i	0.0792922	−	0.244036i	−0.903551	−	0.428481i	$-0.859049\pi$
$587$	1.92110	−	5.91253i	0.0792922	−	0.244036i	0.982843	+	0.184445i	$0.0590488\pi$
$588$	3.29539	−	2.33327i	0.135899	−	0.0962223i
$589$	2.16675	+	1.57424i	0.0892796	+	0.0648654i
$590$	34.8085	+	7.39877i	1.43304	+	0.304602i
$591$	24.4792	+	10.8989i	1.00694	+	0.448319i
$592$	−11.4357	+	2.43074i	−0.470006	+	0.0999028i
$593$	45.2926	+	9.62724i	1.85994	+	0.395343i	0.994417	−	0.105520i	$-0.0336508\pi$
$593$	45.2926	+	9.62724i	1.85994	+	0.395343i	0.865526	+	0.500863i	$0.166984\pi$
$594$	1.89367	+	5.82810i	0.0776981	+	0.239130i
$595$	9.83773	−	0.973270i	0.403308	−	0.0399002i
$596$	3.16731	+	9.74797i	0.129738	+	0.399293i
$597$	7.70965	+	8.56243i	0.315535	+	0.350437i
$598$	17.1994	+	7.65767i	0.703336	+	0.313145i
$599$	−19.4088	+	21.5557i	−0.793024	+	0.880742i	−0.995125	−	0.0986227i	$-0.968556\pi$
$599$	−19.4088	+	21.5557i	−0.793024	+	0.880742i	0.202101	+	0.979365i	$0.435223\pi$
$600$	−1.37420	+	0.611831i	−0.0561013	+	0.0249779i
$601$	−10.5488			−0.430295			−0.215148	−	0.976582i	$-0.569023\pi$
$601$	−10.5488			−0.430295			−0.215148	+	0.976582i	$0.569023\pi$
$602$	9.90199	−	5.63655i	0.403575	−	0.229729i
$603$	5.41217	+	3.93217i	0.220400	+	0.160130i
$604$	−0.989855	−	9.41784i	−0.0402766	−	0.383207i
$605$	−6.80171	−	3.02832i	−0.276529	−	0.123119i
$606$	−3.45013	−	5.97581i	−0.140152	−	0.242751i
$607$	1.56031	+	14.8454i	0.0633312	+	0.602556i	0.979455	+	0.201661i	$0.0646340\pi$
$607$	1.56031	+	14.8454i	0.0633312	+	0.602556i	−0.916124	+	0.400895i	$0.868699\pi$
$608$	−2.10461	−	6.47733i	−0.0853533	−	0.262690i
$609$	0.0699952	−	11.4589i	0.00283635	−	0.464340i
$610$	−17.2996	−	12.5689i	−0.700439	−	0.508899i
$611$	−10.6792	+	4.75467i	−0.432032	+	0.192353i
$612$	0.517194	+	0.895806i	0.0209063	+	0.0362108i
$613$	7.72885	−	1.64282i	0.312165	−	0.0663528i	−0.0491649	−	0.998791i	$-0.515656\pi$
$613$	7.72885	−	1.64282i	0.312165	−	0.0663528i	0.361330	+	0.932438i	$0.382323\pi$
$614$	−5.09360	+	8.82237i	−0.205561	+	0.356042i
$615$	7.34135	+	11.1404i	0.296032	+	0.449224i
$616$	21.9881	−	6.99616i	0.885925	−	0.281883i
$617$	−0.158456	+	0.487677i	−0.00637920	+	0.0196331i	−0.954195	−	0.299184i	$-0.903286\pi$
$617$	−0.158456	+	0.487677i	−0.00637920	+	0.0196331i	0.947816	+	0.318817i	$0.103286\pi$
$618$	−4.34914	+	7.53293i	−0.174948	+	0.303019i
$619$	−4.28020	+	40.7233i	−0.172036	+	1.63681i	0.479038	+	0.877794i	$0.340986\pi$
$619$	−4.28020	+	40.7233i	−0.172036	+	1.63681i	−0.651073	+	0.759015i	$0.725681\pi$
$620$	0.156596	−	1.48991i	0.00628906	−	0.0598364i
$621$	3.67346	+	4.07979i	0.147411	+	0.163716i
$622$	0.946642	+	2.91346i	0.0379569	+	0.116819i
$623$	−29.2951	−	3.26008i	−1.17368	−	0.130612i
$624$	10.2993			0.412301
$625$	2.22376	+	21.1577i	0.0889506	+	0.846308i
$626$	6.65455	+	2.96279i	0.265969	+	0.118417i
$627$	−0.857405	+	8.15767i	−0.0342415	+	0.325786i
$628$	−0.920045	−	1.02181i	−0.0367138	−	0.0407748i
$629$	4.34878			0.173397
$630$	−6.61244	+	5.88113i	−0.263446	+	0.234310i
$631$	4.13978	+	12.7409i	0.164802	+	0.507208i	0.999022	−	0.0442241i	$-0.0140816\pi$
$631$	4.13978	+	12.7409i	0.164802	+	0.507208i	−0.834220	+	0.551432i	$0.814082\pi$
$632$	−0.943717	−	8.97886i	−0.0375390	−	0.357160i
$633$	3.66155	−	0.778286i	0.145533	−	0.0309341i
$634$	12.6258	−	14.0223i	0.501434	−	0.556898i
$635$	−22.5461	−	4.79233i	−0.894716	−	0.190178i
$636$	−1.77034	−	5.44855i	−0.0701986	−	0.216049i
$637$	−1.74475	+	14.8525i	−0.0691296	+	0.588476i
$638$	−8.20176	+	25.2424i	−0.324711	+	0.999357i
$639$	−1.38811	−	13.2070i	−0.0549129	−	0.522461i
$640$	19.0301	−	21.1351i	0.752231	−	0.835437i
$641$	0.899513	−	8.55830i	0.0355286	−	0.338032i	−0.962290	−	0.272024i	$-0.912307\pi$
$641$	0.899513	−	8.55830i	0.0355286	−	0.338032i	0.997819	−	0.0660083i	$-0.0210264\pi$
$642$	−2.14559	+	3.71628i	−0.0846799	+	0.146670i
$643$	4.78131	−	14.7154i	0.188557	−	0.580318i	−0.811435	−	0.584443i	$-0.801313\pi$
$643$	4.78131	−	14.7154i	0.188557	−	0.580318i	0.999991	+	0.00412530i	$0.00131313\pi$
$644$	−6.26045	+	5.56807i	−0.246696	+	0.219413i
$645$	−4.52230	+	3.28565i	−0.178066	+	0.129372i
$646$	0.646530	+	6.15132i	0.0254374	+	0.242020i
$647$	−3.04641	−	5.27654i	−0.119767	−	0.207442i	0.799908	−	0.600122i	$-0.204881\pi$
$647$	−3.04641	−	5.27654i	−0.119767	−	0.207442i	−0.919675	+	0.392680i	$0.871548\pi$
$648$	2.08704	+	0.929210i	0.0819866	+	0.0365028i
$649$	−39.7281	−	8.44447i	−1.55947	−	0.331475i
$650$	−0.697782	+	2.14755i	−0.0273692	+	0.0842339i
$651$	−0.665940	−	3.22989i	−0.0261003	−	0.126589i
$652$	−3.56633	−	2.59109i	−0.139668	−	0.101475i
$653$	12.9118	−	22.3640i	0.505279	−	0.875169i	−0.494702	−	0.869063i	$-0.664723\pi$
$653$	12.9118	−	22.3640i	0.505279	−	0.875169i	0.999981	−	0.00610675i	$-0.00194385\pi$
$654$	8.22800	−	1.74891i	0.321740	−	0.0683880i
$655$	−3.40937	−	5.90520i	−0.133215	−	0.230735i
$656$	26.0011	+	16.6384i	1.01517	+	0.649622i
$657$	−5.60023			−0.218486
$658$	0.141951	−	23.2388i	0.00553382	−	0.905942i
$659$	−24.1528			−0.940861			−0.470430	−	0.882437i	$-0.655901\pi$
$659$	−24.1528			−0.940861			−0.470430	+	0.882437i	$0.655901\pi$
$660$	4.19157	−	1.86621i	0.163157	−	0.0726420i
$661$	4.55704	−	43.3573i	0.177248	−	1.68640i	−0.438713	−	0.898627i	$-0.644565\pi$
$661$	4.55704	−	43.3573i	0.177248	−	1.68640i	0.615961	−	0.787777i	$-0.288768\pi$
$662$	−25.5170	+	5.42380i	−0.991746	+	0.210802i
$663$	−3.74731	−	0.796515i	−0.145533	−	0.0309341i
$664$	−29.9868	+	21.7867i	−1.16371	+	0.845488i
$665$	−11.2877	+	3.59151i	−0.437717	+	0.139273i
$666$	−3.14941	+	2.28818i	−0.122037	+	0.0886652i
$667$	2.48543	+	23.6473i	0.0962363	+	0.915628i
$668$	−0.528868	+	5.03184i	−0.0204625	+	0.194688i
$669$	20.9183	−	4.44632i	0.808748	−	0.171905i
$670$	11.1879	−	19.3780i	0.432227	−	0.748638i
$671$	19.7446	+	14.3453i	0.762232	+	0.553794i
$672$	−3.45771	+	7.64020i	−0.133384	+	0.294727i
$673$	32.5046	−	23.6160i	1.25296	−	0.910328i	0.254570	−	0.967054i	$-0.418066\pi$
$673$	32.5046	−	23.6160i	1.25296	−	0.910328i	0.998390	+	0.0567263i	$0.0180662\pi$
$674$	−18.2044	−	20.2180i	−0.701206	−	0.778769i
$675$	−0.440584	+	0.489318i	−0.0169581	+	0.0188339i
$676$	−3.25603	+	3.61619i	−0.125232	+	0.139084i
$677$	1.34337	+	0.285542i	0.0516299	+	0.0109743i	0.233654	−	0.972320i	$-0.424932\pi$
$677$	1.34337	+	0.285542i	0.0516299	+	0.0109743i	−0.182024	+	0.983294i	$0.558265\pi$
$678$	−5.62501	−	17.3120i	−0.216027	−	0.664863i
$679$	33.3841	+	19.5472i	1.28116	+	0.750152i
$680$	−6.90588	+	5.01742i	−0.264828	+	0.192409i
$681$	6.86284	+	1.45874i	0.262985	+	0.0558991i
$682$	−0.798426	+	7.59651i	−0.0305733	+	0.290885i
$683$	5.51916	+	9.55946i	0.211185	+	0.365783i	0.952086	−	0.305832i	$-0.0989345\pi$
$683$	5.51916	+	9.55946i	0.211185	+	0.365783i	−0.740901	+	0.671614i	$0.765601\pi$
$684$	−0.829333	−	0.921068i	−0.0317104	−	0.0352179i
$685$	−31.5216	−	22.9017i	−1.20438	−	0.875031i
$686$	−25.4699	−	15.3341i	−0.972446	−	0.585459i
$687$	−2.56997	+	1.86719i	−0.0980503	+	0.0712377i
$688$	−6.46665	+	11.2006i	−0.246539	+	0.427018i
$689$	19.3837	+	8.63018i	0.738460	+	0.328784i
$690$	12.2868	−	13.6459i	0.467752	−	0.519491i
$691$	−17.3833	−	19.3061i	−0.661293	−	0.734441i	0.315429	−	0.948949i	$-0.397852\pi$
$691$	−17.3833	−	19.3061i	−0.661293	−	0.734441i	−0.976722	+	0.214509i	$0.931185\pi$
$692$	5.40703	+	3.92844i	0.205545	+	0.149337i
$693$	7.54701	−	6.71234i	0.286687	−	0.254981i
$694$	27.5611			1.04620
$695$	−13.6505	−	15.1604i	−0.517791	−	0.575066i
$696$	4.94737	+	8.56909i	0.187529	+	0.324810i
$697$	−8.17351	−	8.06460i	−0.309594	−	0.305468i
$698$	22.0606	−	38.2102i	0.835008	−	1.44628i
$699$	8.34155	−	25.6727i	0.315506	−	0.971029i
$700$	−0.742646	−	0.676941i	−0.0280694	−	0.0255860i
$701$	7.11662	+	5.17052i	0.268791	+	0.195288i	0.714014	−	0.700132i	$-0.246875\pi$
$701$	7.11662	+	5.17052i	0.268791	+	0.195288i	−0.445223	+	0.895420i	$0.646875\pi$
$702$	3.13292	−	1.39487i	0.118245	−	0.0526458i
$703$	−5.09691	+	1.08338i	−0.192233	+	0.0408605i
$704$	−11.6320	+	12.9186i	−0.438397	+	0.486890i
$705$	1.19176	+	11.3388i	0.0448841	+	0.427044i
$706$	−43.1693			−1.62470
$707$	−6.74092	+	9.15989i	−0.253518	+	0.344493i
$708$	4.96499	−	3.60727i	0.186596	−	0.135570i
$709$	−4.79685	+	2.13570i	−0.180150	+	0.0802077i	−0.494829	−	0.868990i	$-0.664769\pi$
$709$	−4.79685	+	2.13570i	−0.180150	+	0.0802077i	0.314680	+	0.949198i	$0.398103\pi$
$710$	−43.4470	+	9.23495i	−1.63054	+	0.346581i
$711$	−1.97595	−	3.42245i	−0.0741040	−	0.128352i
$712$	23.2514	−	10.3522i	0.871384	−	0.387965i
$713$	2.11459	+	6.50802i	0.0791918	+	0.243727i
$714$	4.51415	−	6.13405i	0.168938	−	0.229561i
$715$	−5.25122	+	16.1616i	−0.196385	+	0.604410i
$716$	−11.9945	−	2.54952i	−0.448257	−	0.0952800i
$717$	−13.0713	+	14.5172i	−0.488157	+	0.542153i
$718$	−3.14909	+	3.49742i	−0.117523	+	0.130522i
$719$	−5.50804	−	1.17077i	−0.205415	−	0.0436624i	0.104055	−	0.994572i	$-0.466818\pi$
$719$	−5.50804	−	1.17077i	−0.205415	−	0.0436624i	−0.309470	+	0.950909i	$0.600152\pi$
$720$	3.10410	−	9.55343i	0.115683	−	0.356035i
$721$	14.2484	+	1.58562i	0.530639	+	0.0590517i
$722$	7.13475	+	21.9585i	0.265528	+	0.817211i
$723$	−7.04575	+	3.13697i	−0.262034	+	0.116665i
$724$	0.386590	+	0.669594i	0.0143675	+	0.0248853i
$725$	−2.78950	+	0.592926i	−0.103599	+	0.0220207i
$726$	−5.24008	+	2.33304i	−0.194478	+	0.0865871i
$727$	−23.2240	+	16.8732i	−0.861332	+	0.625794i	−0.928247	−	0.371965i	$-0.878684\pi$
$727$	−23.2240	+	16.8732i	−0.861332	+	0.625794i	0.0669153	+	0.997759i	$0.478684\pi$
$728$	−5.18003	−	11.8284i	−0.191985	−	0.438392i
$729$	1.00000			0.0370370
$730$	1.95797	+	18.6288i	0.0724677	+	0.689484i
$731$	3.21905	−	3.57512i	0.119061	−	0.132231i
$732$	−3.60713	+	0.766719i	−0.133323	+	0.0283387i
$733$	−28.3780	+	12.6347i	−1.04817	+	0.466673i	−0.857232	−	0.514930i	$-0.827818\pi$
$733$	−28.3780	+	12.6347i	−1.04817	+	0.466673i	−0.190933	+	0.981603i	$0.561151\pi$
$734$	−19.8090	−	14.3921i	−0.731164	−	0.531222i
$735$	13.2510	+	6.09478i	0.488772	+	0.224809i
$736$	5.37728	−	16.5496i	0.198209	−	0.610026i
$737$	−12.7691	+	22.1168i	−0.470358	+	0.814683i
$738$	10.1626	+	1.53981i	0.374091	+	0.0566810i
$739$	−4.49987	−	7.79400i	−0.165530	−	0.286707i	0.771313	−	0.636456i	$-0.219600\pi$
$739$	−4.49987	−	7.79400i	−0.165530	−	0.286707i	−0.936844	+	0.349749i	$0.886267\pi$
$740$	1.95033	+	2.16606i	0.0716955	+	0.0796259i
$741$	4.59039			0.168632
$742$	−31.5187	+	28.0329i	−1.15709	+	1.02912i
$743$	1.50386	+	1.09262i	0.0551712	+	0.0400843i	0.615029	−	0.788504i	$-0.289144\pi$
$743$	1.50386	+	1.09262i	0.0551712	+	0.0400843i	−0.559858	+	0.828589i	$0.689144\pi$
$744$	1.90542	+	2.11618i	0.0698560	+	0.0775830i
$745$	−24.7740	+	27.5143i	−0.907650	+	1.00805i
$746$	−9.73901	−	4.33609i	−0.356570	−	0.158755i
$747$	−8.11227	+	14.0509i	−0.296812	+	0.514094i
$748$	−3.19462	+	2.32103i	−0.116807	+	0.0848652i
$749$	7.02929	+	0.782248i	0.256845	+	0.0285827i
$750$	15.3116	+	11.1245i	0.559100	+	0.406210i
$751$	22.0459	+	24.4845i	0.804468	+	0.893452i	0.996119	−	0.0880111i	$-0.0280511\pi$
$751$	22.0459	+	24.4845i	0.804468	+	0.893452i	−0.191652	+	0.981463i	$0.561384\pi$
$752$	13.1896	+	22.8450i	0.480974	+	0.833071i
$753$	−1.70512	+	16.2231i	−0.0621380	+	0.591203i
$754$	14.5287	+	3.08817i	0.529105	+	0.112465i
$755$	27.6740	−	20.1064i	1.00716	−	0.731745i
$756$	−0.00932202	+	1.52611i	−0.000339039	+	0.0555041i
$757$	3.18061	+	9.78890i	0.115601	+	0.355784i	0.992072	−	0.125671i	$-0.0401085\pi$
$757$	3.18061	+	9.78890i	0.115601	+	0.355784i	−0.876471	+	0.481455i	$0.840108\pi$
$758$	−53.4175	−	11.3542i	−1.94021	−	0.412404i
$759$	−14.0234	+	15.5746i	−0.509017	+	0.565321i
$760$	6.84396	−	7.60098i	0.248256	−	0.275717i
$761$	9.28631	+	10.3135i	0.336629	+	0.373864i	0.887564	−	0.460684i	$-0.152396\pi$
$761$	9.28631	+	10.3135i	0.336629	+	0.373864i	−0.550936	+	0.834548i	$0.685729\pi$
$762$	−14.3663	+	10.4377i	−0.520436	+	0.378119i
$763$	−8.08053	−	11.2660i	−0.292535	−	0.407856i
$764$	−5.13074	−	3.72770i	−0.185624	−	0.134863i
$765$	−1.86823	+	3.23587i	−0.0675461	+	0.116993i
$766$	−30.5044	+	6.48391i	−1.10217	+	0.234273i
$767$	−2.37589	+	22.6051i	−0.0857885	+	0.816223i
$768$	−1.33828	−	12.7328i	−0.0482909	−	0.459457i
$769$	−12.9733	+	9.42568i	−0.467831	+	0.339899i	−0.796595	−	0.604513i	$-0.793368\pi$
$769$	−12.9733	+	9.42568i	−0.467831	+	0.339899i	0.328765	+	0.944412i	$0.393368\pi$
$770$	−24.9668	−	22.7579i	−0.899741	−	0.820137i
$771$	13.9223	−	10.1151i	0.501398	−	0.364287i
$772$	−8.43942	−	1.79385i	−0.303742	−	0.0645623i
$773$	−12.7895	+	2.71850i	−0.460007	+	0.0977775i	−0.432086	−	0.901833i	$-0.642222\pi$
$773$	−12.7895	+	2.71850i	−0.460007	+	0.0977775i	−0.0279215	+	0.999610i	$0.508889\pi$
$774$	−0.450149	+	4.28288i	−0.0161803	+	0.153945i
$775$	−0.749768	+	0.333818i	−0.0269325	+	0.0119911i
$776$	−33.4044			−1.19915
$777$	5.53690	+	3.24198i	0.198635	+	0.116305i
$778$	13.8023			0.494837
$779$	11.5887	+	7.41576i	0.415208	+	0.265697i
$780$	−1.28385	−	2.22370i	−0.0459692	−	0.0796211i
$781$	49.5876	−	10.5402i	1.77438	−	0.377157i
$782$	−7.90159	+	13.6860i	−0.282560	+	0.489409i
$783$	3.50398	+	2.54579i	0.125222	+	0.0909790i
$784$	33.7440	+	0.412255i	1.20514	+	0.0147234i
$785$	1.53482	−	4.72370i	0.0547802	−	0.168596i
$786$	−5.13841	−	1.09220i	−0.183281	−	0.0389575i
$787$	−3.07166	−	1.36759i	−0.109493	−	0.0487494i	0.351259	−	0.936278i	$-0.385754\pi$
$787$	−3.07166	−	1.36759i	−0.109493	−	0.0487494i	−0.460752	+	0.887529i	$0.652420\pi$
$788$	−7.72828	−	13.3858i	−0.275309	−	0.476849i
$789$	1.89459	+	18.0258i	0.0674491	+	0.641736i
$790$	−10.6937	+	7.76946i	−0.380466	+	0.276425i
$791$	−22.4179	+	19.9386i	−0.797089	+	0.708934i
$792$	−2.69502	+	8.29441i	−0.0957632	+	0.294729i
$793$	6.82903	−	11.8282i	0.242506	−	0.420033i
$794$	1.73271	−	16.4857i	0.0614917	−	0.585055i
$795$	13.8472	−	15.3789i	0.491111	−	0.545434i
$796$	−0.694709	−	6.60972i	−0.0246233	−	0.234275i
$797$	−5.15276	+	15.8586i	−0.182520	+	0.561739i	−0.999897	−	0.0143642i	$-0.995428\pi$
$797$	−5.15276	+	15.8586i	−0.182520	+	0.561739i	0.817377	+	0.576104i	$0.195428\pi$
$798$	−3.76260	+	8.31389i	−0.133195	+	0.294308i
$799$	−3.03215	−	9.33200i	−0.107270	−	0.330142i
$800$	2.04145	+	0.433924i	0.0721762	+	0.0153415i
$801$	7.45470	−	8.27928i	0.263399	−	0.292534i
$802$	−42.1204	+	8.95297i	−1.48732	+	0.316140i
$803$	−2.23470	−	21.2617i	−0.0788608	−	0.750311i
$804$	−1.19245	−	3.66999i	−0.0420545	−	0.129431i
$805$	−28.7257	−	9.52793i	−1.01245	−	0.335816i
$806$	4.27463			0.150567
$807$	−17.2927	−	19.2055i	−0.608733	−	0.676067i
$808$	1.02650	−	9.76648i	0.0361121	−	0.343584i
$809$	−2.75624	−	1.22716i	−0.0969043	−	0.0431446i	0.357712	−	0.933832i	$-0.383557\pi$
$809$	−2.75624	−	1.22716i	−0.0969043	−	0.0431446i	−0.454616	+	0.890687i	$0.650224\pi$
$810$	−0.349623	−	3.32644i	−0.0122845	−	0.116879i
$811$	13.1027			0.460097			0.230048	−	0.973179i	$-0.426112\pi$
$811$	13.1027			0.460097			0.230048	+	0.973179i	$0.426112\pi$
$812$	−3.91782	+	5.32372i	−0.137488	+	0.186826i
$813$	−4.10209	−	12.6249i	−0.143867	−	0.442776i
$814$	−9.94400	−	11.0439i	−0.348537	−	0.387090i
$815$	1.66447	−	15.8364i	0.0583038	−	0.554723i
$816$	−0.903656	+	8.59771i	−0.0316343	+	0.300980i
$817$	−2.88219	+	4.99210i	−0.100835	+	0.174651i
$818$	−13.8409	+	42.5978i	−0.483935	+	1.48940i
$819$	−4.17730	−	3.80772i	−0.145967	−	0.133052i
$820$	0.351219	−	7.68789i	0.0122651	−	0.268473i
$821$	5.85629	−	10.1434i	0.204386	−	0.354007i	−0.745551	−	0.666449i	$-0.767814\pi$
$821$	5.85629	−	10.1434i	0.204386	−	0.354007i	0.949937	+	0.312442i	$0.101147\pi$
$822$	−29.3612	+	6.24092i	−1.02409	+	0.217677i
$823$	13.5319	+	23.4379i	0.471691	+	0.816992i	0.999475	−	0.0323860i	$-0.0103106\pi$
$823$	13.5319	+	23.4379i	0.471691	+	0.816992i	−0.527785	+	0.849378i	$0.676977\pi$
$824$	−11.3089	+	5.03506i	−0.393965	+	0.175404i
$825$	−2.03355	−	1.47746i	−0.0707990	−	0.0514385i
$826$	−38.9938	−	22.8318i	−1.35677	−	0.794419i
$827$	−8.23187	−	25.3351i	−0.286250	−	0.880987i	−0.986021	−	0.166620i	$-0.946715\pi$
$827$	−8.23187	−	25.3351i	−0.286250	−	0.880987i	0.699771	−	0.714367i	$-0.253285\pi$
$828$	−0.331012	−	3.14937i	−0.0115035	−	0.109448i
$829$	27.4210	+	47.4946i	0.952371	+	1.64956i	0.740273	+	0.672307i	$0.234696\pi$
$829$	27.4210	+	47.4946i	0.952371	+	1.64956i	0.212098	+	0.977248i	$0.431970\pi$
$830$	49.5756	+	22.0725i	1.72079	+	0.766147i
$831$	2.44361	+	23.2494i	0.0847679	+	0.806513i
$832$	7.87045	+	5.71822i	0.272859	+	0.198243i
$833$	−12.2456	−	2.75965i	−0.424284	−	0.0956162i
$834$	−15.7165			−0.544218
$835$	−16.6963	+	7.43368i	−0.577800	+	0.257253i
$836$	3.16598	−	3.51617i	0.109498	−	0.121609i
$837$	1.13870	+	0.506982i	0.0393592	+	0.0175238i
$838$	−5.54050	−	6.15335i	−0.191393	−	0.212564i
$839$	−3.89136	−	11.9764i	−0.134345	−	0.413471i	0.861143	−	0.508363i	$-0.169749\pi$
$839$	−3.89136	−	11.9764i	−0.134345	−	0.413471i	−0.995488	+	0.0948924i	$0.969749\pi$
$840$	−12.5331	+	1.23993i	−0.432432	+	0.0427815i
$841$	−3.16468	−	9.73988i	−0.109127	−	0.335858i
$842$	9.18735	+	1.95283i	0.316617	+	0.0672990i
$843$	1.68732	−	0.358652i	0.0581145	−	0.0123526i
$844$	−1.97258	−	0.878251i	−0.0678992	−	0.0302307i
$845$	−17.1933	−	3.65455i	−0.591468	−	0.125720i
$846$	7.10608	+	5.16287i	0.244312	+	0.177503i
$847$	6.98690	+	6.36874i	0.240073	+	0.218833i
$848$	14.7959	−	45.5372i	0.508094	−	1.56375i
$849$	1.28519	−	0.572204i	0.0441077	−	0.0196380i
$850$	−1.73152	−	0.770925i	−0.0593908	−	0.0264425i
$851$	−12.1625	−	5.41510i	−0.416925	−	0.185627i
$852$	−3.83006	+	6.63386i	−0.131216	+	0.227272i
$853$	−3.69243	+	2.68271i	−0.126426	+	0.0918541i	−0.649201	−	0.760617i	$-0.724897\pi$
$853$	−3.69243	+	2.68271i	−0.126426	+	0.0918541i	0.522775	+	0.852471i	$0.324897\pi$
$854$	15.8251	+	22.0636i	0.541525	+	0.755001i
$855$	1.38350	−	4.25797i	0.0473146	−	0.145619i
$856$	−5.57912	+	2.48398i	−0.190690	+	0.0849009i
$857$	−5.66699	+	53.9178i	−0.193581	+	1.84180i	0.278736	+	0.960368i	$0.410085\pi$
$857$	−5.66699	+	53.9178i	−0.193581	+	1.84180i	−0.472316	+	0.881429i	$0.656582\pi$
$858$	6.54588	+	11.3378i	0.223473	+	0.387066i
$859$	−19.9325	−	22.1373i	−0.680088	−	0.755314i	0.299987	−	0.953943i	$-0.403018\pi$
$859$	−19.9325	−	22.1373i	−0.680088	−	0.755314i	−0.980075	+	0.198629i	$0.936351\pi$
$860$	3.22439			0.109951
$861$	−4.39447	−	16.3612i	−0.149763	−	0.557588i
$862$	28.4026			0.967396
$863$	−8.48397	−	9.42240i	−0.288798	−	0.320742i	0.581236	−	0.813735i	$-0.302569\pi$
$863$	−8.48397	−	9.42240i	−0.288798	−	0.320742i	−0.870033	+	0.492993i	$0.835903\pi$
$864$	−1.58484	−	2.74503i	−0.0539175	−	0.0933879i
$865$	−2.52356	+	24.0101i	−0.0858036	+	0.816367i
$866$	−44.7291	+	19.9147i	−1.51996	+	0.676728i
$867$	−4.25958	+	13.1096i	−0.144663	+	0.445227i
$868$	−0.784325	+	1.73306i	−0.0266217	+	0.0588237i
$869$	12.2051	−	8.86755i	0.414031	−	0.300811i
$870$	7.24334	−	12.5458i	0.245572	−	0.425344i
$871$	13.0563	+	5.81304i	0.442396	+	0.196967i
$872$	10.9365	+	4.86924i	0.370356	+	0.164893i
$873$	−13.3577	+	5.94725i	−0.452091	+	0.201284i
$874$	5.85143	−	18.0089i	0.197928	−	0.609158i
$875$	6.67182	−	30.4720i	0.225549	−	1.03014i
$876$	2.61342	+	1.89876i	0.0882992	+	0.0641531i
$877$	10.3697	+	2.20414i	0.350159	+	0.0744285i	0.379633	−	0.925137i	$-0.376050\pi$
$877$	10.3697	+	2.20414i	0.350159	+	0.0744285i	−0.0294748	+	0.999566i	$0.509383\pi$
$878$	56.3862	+	25.1048i	1.90294	+	0.847245i
$879$	5.29650	−	1.12581i	0.178646	−	0.0379725i
$880$	37.5090	+	7.97279i	1.26443	+	0.268763i
$881$	−10.6524	−	32.7847i	−0.358888	−	1.10454i	−0.953720	−	0.300695i	$-0.902781\pi$
$881$	−10.6524	−	32.7847i	−0.358888	−	1.10454i	0.594832	−	0.803850i	$-0.297219\pi$
$882$	10.3203	−	4.44465i	0.347504	−	0.149659i
$883$	6.93417	+	21.3412i	0.233354	+	0.718188i	0.997336	+	0.0729508i	$0.0232416\pi$
$883$	6.93417	+	21.3412i	0.233354	+	0.718188i	−0.763982	+	0.645238i	$0.776758\pi$
$884$	1.47867	+	1.64223i	0.0497330	+	0.0552341i
$885$	20.2520	+	9.01678i	0.680764	+	0.303096i
$886$	−1.64698	+	1.82916i	−0.0553313	+	0.0614517i
$887$	5.25904	−	2.34148i	0.176581	−	0.0786191i	−0.316542	−	0.948579i	$-0.602522\pi$
$887$	5.25904	−	2.34148i	0.176581	−	0.0786191i	0.493123	+	0.869959i	$0.335855\pi$
$888$	−5.54025			−0.185919
$889$	25.2570	+	14.7886i	0.847093	+	0.495993i
$890$	−30.1469	−	21.9030i	−1.01053	−	0.734190i
$891$	0.399037	+	3.79658i	0.0133682	+	0.127190i
$892$	−11.2693	−	5.01742i	−0.377324	−	0.167996i
$893$	5.87859	+	10.1820i	0.196720	+	0.340728i
$894$	2.98154	+	28.3674i	0.0997175	+	0.948748i
$895$	−13.6880	−	42.1273i	−0.457539	−	1.40816i
$896$	−31.3840	+	17.8648i	−1.04847	+	0.596823i
$897$	9.48852	+	6.89381i	0.316812	+	0.230178i
$898$	6.86967	−	3.05857i	0.229244	−	0.102066i
$899$	2.69931	+	4.67534i	0.0900269	+	0.155931i
$900$	0.371507	−	0.0789663i	0.0123836	−	0.00263221i
$901$	−8.90508	+	15.4240i	−0.296671	+	0.513850i
$902$	−1.79074	+	39.1977i	−0.0596250	+	1.30514i
$903$	6.76375	−	2.15209i	0.225084	−	0.0716170i
$904$	8.00537	−	24.6380i	0.266255	−	0.819447i
$905$	−1.39646	+	2.41874i	−0.0464199	+	0.0804017i
$906$	2.75467	−	26.2089i	0.0915177	−	0.870733i
$907$	−1.91287	+	18.1997i	−0.0635158	+	0.604312i	0.915752	+	0.401743i	$0.131596\pi$
$907$	−1.91287	+	18.1997i	−0.0635158	+	0.604312i	−0.979268	+	0.202569i	$0.935071\pi$
$908$	−2.70804	−	3.00759i	−0.0898696	−	0.0998103i
$909$	−1.32833	−	4.08818i	−0.0440579	−	0.135596i
$910$	−11.2057	+	15.2268i	−0.371464	+	0.504764i
$911$	−51.8792			−1.71883			−0.859417	−	0.511276i	$-0.829173\pi$
$911$	−51.8792			−1.71883			−0.859417	+	0.511276i	$0.829173\pi$
$912$	−1.08277	−	10.3019i	−0.0358542	−	0.341130i
$913$	−56.5824	−	25.1921i	−1.87260	−	0.833736i
$914$	3.26228	−	31.0386i	0.107907	−	1.02666i
$915$	−8.91345	−	9.89939i	−0.294670	−	0.327264i
$916$	1.83238			0.0605435
$917$	1.74839	+	8.47989i	0.0577369	+	0.280031i
$918$	0.889535	+	2.73771i	0.0293590	+	0.0903578i
$919$	−4.58548	−	43.6279i	−0.151261	−	1.43915i	−0.762132	−	0.647422i	$-0.775847\pi$
$919$	−4.58548	−	43.6279i	−0.151261	−	1.43915i	0.610871	−	0.791730i	$-0.290819\pi$
$920$	25.5618	−	5.43333i	0.842748	−	0.179132i
$921$	−4.24642	+	4.71613i	−0.139924	+	0.155402i
$922$	8.41846	+	1.78940i	0.277247	+	0.0589307i
$923$	−8.76697	−	26.9820i	−0.288568	−	0.888122i
$924$	−5.79772	+	0.573583i	−0.190731	+	0.0188695i
$925$	0.493434	−	1.51863i	0.0162240	−	0.0499324i
$926$	2.96180	+	28.1797i	0.0973309	+	0.926041i
$927$	−3.62578	+	4.02684i	−0.119086	+	0.132259i
$928$	1.43501	−	13.6532i	0.0471065	−	0.448188i
$929$	−6.54214	+	11.3313i	−0.214641	+	0.371769i	−0.953161	−	0.302462i	$-0.902191\pi$
$929$	−6.54214	+	11.3313i	−0.214641	+	0.371769i	0.738521	+	0.674231i	$0.235525\pi$
$930$	1.28833	−	3.96507i	0.0422460	−	0.130020i
$931$	15.0397	+	0.183742i	0.492906	+	0.00602191i
$932$	−12.5970	+	9.15226i	−0.412629	+	0.299792i
$933$	0.199478	+	1.89791i	0.00653062	+	0.0621347i
$934$	4.82305	+	8.35376i	0.157815	+	0.273343i
$935$	−13.0308	−	5.80167i	−0.426151	−	0.189735i
$936$	4.77399	+	1.01474i	0.156043	+	0.0331679i
$937$	16.1969	−	49.8490i	0.529130	−	1.62849i	−0.226871	−	0.973925i	$-0.572850\pi$
$937$	16.1969	−	49.8490i	0.529130	−	1.62849i	0.756001	−	0.654570i	$-0.227150\pi$
$938$	−21.2301	+	18.8822i	−0.693188	+	0.616524i
$939$	3.67116	+	2.66725i	0.119804	+	0.0870425i
$940$	3.28827	−	5.69546i	0.107252	−	0.185765i
$941$	56.6966	−	12.0512i	1.84826	−	0.392859i	0.855990	−	0.516993i	$-0.172949\pi$
$941$	56.6966	−	12.0512i	1.84826	−	0.392859i	0.992265	+	0.124134i	$0.0396152\pi$
$942$	−1.91322	−	3.31380i	−0.0623362	−	0.107969i
$943$	12.8173	+	32.7324i	0.417390	+	1.06591i
$944$	51.2915			1.66940
$945$	−4.79097	+	2.72718i	−0.155850	+	0.0887153i
$946$	−16.4399			−0.534509
$947$	46.7771	−	20.8265i	1.52005	−	0.676771i	0.534350	−	0.845263i	$-0.320556\pi$
$947$	46.7771	−	20.8265i	1.52005	−	0.676771i	0.985703	+	0.168492i	$0.0538898\pi$
$948$	−0.238279	+	2.26708i	−0.00773895	+	0.0736312i
$949$	−11.7027	+	2.48749i	−0.379887	+	0.0807474i
$950$	2.22146	+	0.472185i	0.0720736	+	0.0153197i
$951$	9.50960	−	6.90913i	0.308370	−	0.224044i
$952$	10.3287	−	3.28639i	0.334756	−	0.106513i
$953$	35.6565	−	25.9060i	1.15503	−	0.839177i	0.165886	−	0.986145i	$-0.446951\pi$
$953$	35.6565	−	25.9060i	1.15503	−	0.839177i	0.989141	+	0.146968i	$0.0469515\pi$
$954$	−1.66651	−	15.8557i	−0.0539551	−	0.513348i
$955$	2.39461	−	22.7832i	0.0774877	−	0.737246i
$956$	11.0219	−	2.34278i	0.356475	−	0.0757710i
$957$	−8.26708	+	14.3190i	−0.267237	+	0.462867i
$958$	−31.8606	−	23.1481i	−1.02937	−	0.747880i
$959$	28.8350	+	40.2021i	0.931131	+	1.29819i
$960$	7.67619	−	5.57707i	0.247748	−	0.179999i
$961$	−19.7034	−	21.8829i	−0.635595	−	0.705900i
$962$	−5.56493	+	6.18048i	−0.179420	+	0.199267i
$963$	−1.78874	+	1.98659i	−0.0576412	+	0.0640170i
$964$	4.35157	+	0.924956i	0.140155	+	0.0297908i
$965$	−9.63093	−	29.6410i	−0.310031	−	0.954177i
$966$	−20.2632	+	11.5345i	−0.651956	+	0.371116i
$967$	13.9849	−	10.1606i	0.449725	−	0.326744i	−0.339762	−	0.940511i	$-0.610347\pi$
$967$	13.9849	−	10.1606i	0.449725	−	0.326744i	0.789487	+	0.613767i	$0.210347\pi$
$968$	−7.98491	−	1.69725i	−0.256645	−	0.0545516i
$969$	−0.402760	+	3.83200i	−0.0129385	+	0.123102i
$970$	24.4533	+	42.3544i	0.785149	+	1.35992i
$971$	4.05591	+	4.50454i	0.130160	+	0.144558i	0.804702	−	0.593679i	$-0.202325\pi$
$971$	4.05591	+	4.50454i	0.130160	+	0.144558i	−0.674541	+	0.738237i	$0.735659\pi$
$972$	−0.466662	−	0.339050i	−0.0149682	−	0.0108750i
$973$	10.3913	+	23.7282i	0.333129	+	0.760690i
$974$	34.2345	−	24.8728i	1.09694	−	0.796977i
$975$	−0.703339	+	1.21822i	−0.0225249	+	0.0390142i
$976$	−28.1561	−	12.5359i	−0.901255	−	0.401265i
$977$	37.6412	−	41.8048i	1.20425	−	1.33745i	0.277981	−	0.960587i	$-0.410335\pi$
$977$	37.6412	−	41.8048i	1.20425	−	1.33745i	0.926267	−	0.376867i	$-0.122999\pi$
$978$	−8.20865	−	9.11663i	−0.262484	−	0.291518i
$979$	34.4077	+	24.9986i	1.09967	+	0.798960i
$980$	−4.11732	−	7.33697i	−0.131523	−	0.234371i
$981$	5.24019			0.167306
$982$	22.4221	+	24.9023i	0.715519	+	0.794664i
$983$	−17.1164	−	29.6465i	−0.545928	−	0.945575i	−0.998548	−	0.0538715i	$-0.982844\pi$
$983$	−17.1164	−	29.6465i	−0.545928	−	0.945575i	0.452620	−	0.891704i	$-0.350489\pi$
$984$	10.4129	+	10.2741i	0.331950	+	0.327527i
$985$	27.9165	−	48.3528i	0.889493	−	1.54065i
$986$	−3.85271	+	11.8574i	−0.122695	+	0.377618i
$987$	3.09638	−	14.1420i	0.0985589	−	0.450145i
$988$	−2.14216	−	1.55637i	−0.0681513	−	0.0495148i
$989$	−13.4547	+	5.99041i	−0.427834	+	0.190484i
$990$	12.4896	−	2.65474i	0.396945	−	0.0843733i
$991$	14.9662	−	16.6217i	0.475417	−	0.528005i	−0.456962	−	0.889486i	$-0.651062\pi$
$991$	14.9662	−	16.6217i	0.475417	−	0.528005i	0.932379	+	0.361482i	$0.117729\pi$
$992$	−0.412981	−	3.92925i	−0.0131122	−	0.124754i
$993$	−16.2511			−0.515713
$994$	56.0543	+	6.23795i	1.77794	+	0.197856i
$995$	19.4224	−	14.1112i	0.615733	−	0.447356i
$996$	8.54964	−	3.80654i	0.270906	−	0.120615i
$997$	−42.2377	+	8.97791i	−1.33768	+	0.284333i	−0.820551	−	0.571573i	$-0.806333\pi$
$997$	−42.2377	+	8.97791i	−1.33768	+	0.284333i	−0.517131	+	0.855906i	$0.673000\pi$
$998$	17.0247	+	29.4877i	0.538908	+	0.933416i
$999$	−2.21544	+	0.986376i	−0.0700933	+	0.0312075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.bk.a.16.7	✓	224
7.4	even	3	inner	861.2.bk.a.508.22	yes	224
41.18	even	5	inner	861.2.bk.a.100.22	yes	224
287.18	even	15	inner	861.2.bk.a.592.7	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.bk.a.16.7	✓	224	1.1	even	1	trivial
861.2.bk.a.100.22	yes	224	41.18	even	5	inner
861.2.bk.a.508.22	yes	224	7.4	even	3	inner
861.2.bk.a.592.7	yes	224	287.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07412 - 1.19293i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.0602948 + 0.573666i) q^{4} +(-1.90350 + 0.847493i) q^{5} +(-0.496049 + 1.52668i) q^{6} +(2.63290 - 0.260479i) q^{7} +(-1.84824 + 1.34282i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.07412 - 1.19293i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.0602948 + 0.573666i) q^{4} +(-1.90350 + 0.847493i) q^{5} +(-0.496049 + 1.52668i) q^{6} +(2.63290 - 0.260479i) q^{7} +(-1.84824 + 1.34282i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.05559 + 1.36044i) q^{10} +(-3.48746 - 1.55272i) q^{11} +(0.526957 - 0.234616i) q^{12} +(-0.660175 + 2.03181i) q^{13} +(-3.13879 - 2.86108i) q^{14} +(1.68570 + 1.22473i) q^{15} +(4.71558 + 1.00233i) q^{16} +(-1.63821 - 0.729376i) q^{17} +(1.57017 - 0.333750i) q^{18} +(2.10173 + 0.446737i) q^{19} +(-0.371407 - 1.14307i) q^{20} +(-1.54203 - 2.14992i) q^{21} +(1.89367 + 5.82810i) q^{22} +(3.67346 + 4.07979i) q^{23} +(2.08704 + 0.929210i) q^{24} +(-0.440584 + 0.489318i) q^{25} +(3.13292 - 1.39487i) q^{26} +1.00000 q^{27} +(-0.00932202 + 1.52611i) q^{28} +(3.50398 + 2.54579i) q^{29} +(-0.349623 - 3.32644i) q^{30} +(1.13870 + 0.506982i) q^{31} +(-1.58484 - 2.74503i) q^{32} +(0.399037 + 3.79658i) q^{33} +(0.889535 + 2.73771i) q^{34} +(-4.79097 + 2.72718i) q^{35} +(-0.466662 - 0.339050i) q^{36} +(-2.21544 + 0.986376i) q^{37} +(-1.72459 - 2.98708i) q^{38} +(2.08969 - 0.444177i) q^{39} +(2.38009 - 4.12244i) q^{40} +(5.99309 + 2.25453i) q^{41} +(-0.908379 + 4.14881i) q^{42} +(-0.829014 + 2.55144i) q^{43} +(1.10102 - 1.90702i) q^{44} +(0.217800 - 2.07223i) q^{45} +(0.921173 - 8.76437i) q^{46} +(3.66135 + 4.06634i) q^{47} +(-1.48975 - 4.58497i) q^{48} +(6.86430 - 1.37163i) q^{49} +1.05696 q^{50} +(0.187445 + 1.78342i) q^{51} +(-1.12578 - 0.501228i) q^{52} +(1.03816 - 9.87743i) q^{53} +(-1.07412 - 1.19293i) q^{54} +7.95429 q^{55} +(-4.51645 + 4.01695i) q^{56} +(-0.663981 - 2.04352i) q^{57} +(-0.726743 - 6.91449i) q^{58} +(10.4069 - 2.21205i) q^{59} +(-0.804227 + 0.893185i) q^{60} +(-6.25340 - 1.32920i) q^{61} +(-0.618307 - 1.90295i) q^{62} +(-1.09087 + 2.41040i) q^{63} +(1.40717 - 4.33083i) q^{64} +(-0.465301 - 4.42704i) q^{65} +(4.10045 - 4.55402i) q^{66} +(0.699275 - 6.65316i) q^{67} +(0.517194 - 0.895806i) q^{68} +(1.69647 - 5.22120i) q^{69} +(8.39943 + 2.78598i) q^{70} +(-10.7436 + 7.80565i) q^{71} +(-0.238800 - 2.27203i) q^{72} +(2.80012 + 4.84995i) q^{73} +(3.55633 + 1.58338i) q^{74} +(0.644054 + 0.136898i) q^{75} +(-0.383002 + 1.17876i) q^{76} +(-9.58656 - 3.17973i) q^{77} +(-2.77445 - 2.01576i) q^{78} +(-1.97595 + 3.42245i) q^{79} +(-9.82556 + 2.08849i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.74780 - 9.57099i) q^{82} +16.2245 q^{83} +(1.32631 - 0.754982i) q^{84} +3.73647 q^{85} +(3.93416 - 1.75160i) q^{86} +(0.452729 - 4.30743i) q^{87} +(8.53067 - 1.81325i) q^{88} +(-10.8974 - 2.31632i) q^{89} +(-2.70597 + 1.96600i) q^{90} +(-1.20893 + 5.52151i) q^{91} +(-2.56193 + 1.86135i) q^{92} +(-0.130291 - 1.23963i) q^{93} +(0.918136 - 8.73548i) q^{94} +(-4.37926 + 0.930840i) q^{95} +(-1.58484 + 2.74503i) q^{96} +(11.8293 + 8.59451i) q^{97} +(-9.00936 - 6.71536i) q^{98} +(3.08842 - 2.24387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 112 q^{3} + 28 q^{4} + 24 q^{8} - 112 q^{9}+O(q^{10}) \) 224 * q - 112 * q^3 + 28 * q^4 + 24 * q^8 - 112 * q^9	\( 224 q - 112 q^{3} + 28 q^{4} + 24 q^{8} - 112 q^{9} + 17 q^{10} + 28 q^{12} + 12 q^{14} + 28 q^{16} + 10 q^{17} - 10 q^{19} + 56 q^{20} + 32 q^{22} - 4 q^{23} - 12 q^{24} + 48 q^{25} - 26 q^{26} + 224 q^{27} + 15 q^{28} - 44 q^{29} + 17 q^{30} - 10 q^{31} + 66 q^{32} + 76 q^{34} - 7 q^{35} - 56 q^{36} + 19 q^{37} + 4 q^{38} - 70 q^{40} + 10 q^{41} + 6 q^{42} + 4 q^{43} - 2 q^{44} + 32 q^{46} - 44 q^{47} - 56 q^{48} - 16 q^{49} - 60 q^{50} + 10 q^{51} - 46 q^{52} + 53 q^{53} + 28 q^{55} - 13 q^{56} + 20 q^{57} - 32 q^{58} - 6 q^{59} - 28 q^{60} - 4 q^{61} + 18 q^{62} - 188 q^{64} + 46 q^{65} - 16 q^{66} - 6 q^{67} + 36 q^{68} + 8 q^{69} + 189 q^{70} - 34 q^{71} - 12 q^{72} - 102 q^{73} - 118 q^{74} + 48 q^{75} + 70 q^{76} - 18 q^{77} + 52 q^{78} - 66 q^{79} - 44 q^{80} - 112 q^{81} - 24 q^{82} + 52 q^{83} + 6 q^{84} + 128 q^{85} + 5 q^{86} + 22 q^{87} + 59 q^{88} + 52 q^{89} - 34 q^{90} + 126 q^{91} - 30 q^{92} - 10 q^{93} - 97 q^{94} + 53 q^{95} + 66 q^{96} + 112 q^{97} + 30 q^{98}+O(q^{100}) \) 224 * q - 112 * q^3 + 28 * q^4 + 24 * q^8 - 112 * q^9 + 17 * q^10 + 28 * q^12 + 12 * q^14 + 28 * q^16 + 10 * q^17 - 10 * q^19 + 56 * q^20 + 32 * q^22 - 4 * q^23 - 12 * q^24 + 48 * q^25 - 26 * q^26 + 224 * q^27 + 15 * q^28 - 44 * q^29 + 17 * q^30 - 10 * q^31 + 66 * q^32 + 76 * q^34 - 7 * q^35 - 56 * q^36 + 19 * q^37 + 4 * q^38 - 70 * q^40 + 10 * q^41 + 6 * q^42 + 4 * q^43 - 2 * q^44 + 32 * q^46 - 44 * q^47 - 56 * q^48 - 16 * q^49 - 60 * q^50 + 10 * q^51 - 46 * q^52 + 53 * q^53 + 28 * q^55 - 13 * q^56 + 20 * q^57 - 32 * q^58 - 6 * q^59 - 28 * q^60 - 4 * q^61 + 18 * q^62 - 188 * q^64 + 46 * q^65 - 16 * q^66 - 6 * q^67 + 36 * q^68 + 8 * q^69 + 189 * q^70 - 34 * q^71 - 12 * q^72 - 102 * q^73 - 118 * q^74 + 48 * q^75 + 70 * q^76 - 18 * q^77 + 52 * q^78 - 66 * q^79 - 44 * q^80 - 112 * q^81 - 24 * q^82 + 52 * q^83 + 6 * q^84 + 128 * q^85 + 5 * q^86 + 22 * q^87 + 59 * q^88 + 52 * q^89 - 34 * q^90 + 126 * q^91 - 30 * q^92 - 10 * q^93 - 97 * q^94 + 53 * q^95 + 66 * q^96 + 112 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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