LMFDB - Embedded newform 43.2.g.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.1
Character	$\chi$	$=$	43.24
Dual form			43.2.g.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44188 + 1.80806i) q^{2} +(2.66973 - 0.402397i) q^{3} +(-0.745019 - 3.26414i) q^{4} +(-2.09843 + 1.43068i) q^{5} +(-3.12187 + 5.40724i) q^{6} +(-1.09365 - 1.89425i) q^{7} +(2.80884 + 1.35267i) q^{8} +(4.09883 - 1.26432i) q^{9} +O(q^{10})$	\(q+(-1.44188 + 1.80806i) q^{2} +(2.66973 - 0.402397i) q^{3} +(-0.745019 - 3.26414i) q^{4} +(-2.09843 + 1.43068i) q^{5} +(-3.12187 + 5.40724i) q^{6} +(-1.09365 - 1.89425i) q^{7} +(2.80884 + 1.35267i) q^{8} +(4.09883 - 1.26432i) q^{9} +(0.438918 - 5.85695i) q^{10} +(0.694710 - 3.04372i) q^{11} +(-3.30249 - 8.41460i) q^{12} +(0.257224 + 3.43242i) q^{13} +(5.00182 + 0.753903i) q^{14} +(-5.02653 + 4.66394i) q^{15} +(-0.462659 + 0.222805i) q^{16} +(-1.92873 - 1.31499i) q^{17} +(-3.62405 + 9.23392i) q^{18} +(-3.23214 - 0.996984i) q^{19} +(6.23332 + 5.78368i) q^{20} +(-3.68198 - 4.61706i) q^{21} +(4.50154 + 5.64475i) q^{22} +(4.82527 + 4.47719i) q^{23} +(8.04316 + 2.48099i) q^{24} +(0.529835 - 1.35000i) q^{25} +(-6.57690 - 4.48405i) q^{26} +(3.13647 - 1.51045i) q^{27} +(-5.36832 + 4.98107i) q^{28} +(-5.34977 - 0.806349i) q^{29} +(-1.18503 - 15.8131i) q^{30} +(0.778473 + 1.98352i) q^{31} +(-1.12320 + 4.92105i) q^{32} +(0.629903 - 8.40547i) q^{33} +(5.15856 - 1.59121i) q^{34} +(5.00501 + 2.41028i) q^{35} +(-7.18063 - 12.4372i) q^{36} +(-1.73964 + 3.01315i) q^{37} +(6.46296 - 4.40637i) q^{38} +(2.06792 + 9.06013i) q^{39} +(-7.82938 + 1.18009i) q^{40} +(1.33098 - 1.66900i) q^{41} +13.6569 q^{42} +(6.03879 + 2.55598i) q^{43} -10.4527 q^{44} +(-6.79225 + 8.51721i) q^{45} +(-15.0525 + 2.26880i) q^{46} +(0.260214 + 1.14007i) q^{47} +(-1.14552 + 0.781003i) q^{48} +(1.10788 - 1.91890i) q^{49} +(1.67692 + 2.90450i) q^{50} +(-5.67834 - 2.73454i) q^{51} +(11.0123 - 3.39683i) q^{52} +(0.777332 - 10.3728i) q^{53} +(-1.79144 + 7.84880i) q^{54} +(2.89680 + 7.38094i) q^{55} +(-0.509588 - 6.79998i) q^{56} +(-9.03014 - 1.36108i) q^{57} +(9.17165 - 8.51004i) q^{58} +(-5.53586 + 2.66593i) q^{59} +(18.9686 + 12.9326i) q^{60} +(0.913867 - 2.32849i) q^{61} +(-4.70878 - 1.45247i) q^{62} +(-6.87761 - 6.38149i) q^{63} +(-7.91838 - 9.92933i) q^{64} +(-5.45047 - 6.83467i) q^{65} +(14.2893 + 13.2586i) q^{66} +(9.87998 + 3.04757i) q^{67} +(-2.85536 + 7.27534i) q^{68} +(14.6838 + 10.0112i) q^{69} +(-11.5745 + 5.57401i) q^{70} +(8.30629 - 7.70711i) q^{71} +(13.2232 + 1.99307i) q^{72} +(0.624897 + 8.33868i) q^{73} +(-2.93960 - 7.48997i) q^{74} +(0.871282 - 3.81734i) q^{75} +(-0.846290 + 11.2930i) q^{76} +(-6.52534 + 2.01280i) q^{77} +(-19.3629 - 9.32469i) q^{78} +(-4.90787 - 8.50067i) q^{79} +(0.652093 - 1.12946i) q^{80} +(-2.86645 + 1.95431i) q^{81} +(1.09853 + 4.81298i) q^{82} +(-2.83709 + 0.427622i) q^{83} +(-12.3276 + 15.4583i) q^{84} +5.92862 q^{85} +(-13.3286 + 7.23307i) q^{86} -14.6069 q^{87} +(6.06847 - 7.60962i) q^{88} +(14.8273 - 2.23486i) q^{89} +(-5.60602 - 24.5616i) q^{90} +(6.22054 - 4.24110i) q^{91} +(11.0193 - 19.0860i) q^{92} +(2.87648 + 4.98220i) q^{93} +(-2.43652 - 1.17336i) q^{94} +(8.20879 - 2.53207i) q^{95} +(-1.01842 + 13.5899i) q^{96} +(0.939509 - 4.11626i) q^{97} +(1.87206 + 4.76993i) q^{98} +(-1.00075 - 13.3540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

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

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

$2$	−1.44188	+	1.80806i	−1.01956	+	1.27849i	−0.0596408	+	0.998220i	$0.518996\pi$
$2$	−1.44188	+	1.80806i	−1.01956	+	1.27849i	−0.959921	+	0.280270i	$0.909576\pi$
$3$	2.66973	−	0.402397i	1.54137	−	0.232324i	0.677305	−	0.735703i	$-0.263148\pi$
$3$	2.66973	−	0.402397i	1.54137	−	0.232324i	0.864066	+	0.503378i	$0.167910\pi$
$4$	−0.745019	−	3.26414i	−0.372510	−	1.63207i
$5$	−2.09843	+	1.43068i	−0.938445	+	0.639821i	−0.932889	−	0.360164i	$-0.882721\pi$
$5$	−2.09843	+	1.43068i	−0.938445	+	0.639821i	−0.00555574	+	0.999985i	$0.501768\pi$
$6$	−3.12187	+	5.40724i	−1.27450	+	2.20750i
$7$	−1.09365	−	1.89425i	−0.413359	−	0.715959i	0.581895	−	0.813264i	$-0.302311\pi$
$7$	−1.09365	−	1.89425i	−0.413359	−	0.715959i	−0.995255	+	0.0973044i	$0.968978\pi$
$8$	2.80884	+	1.35267i	0.993075	+	0.478240i
$9$	4.09883	−	1.26432i	1.36628	−	0.421440i
$10$	0.438918	−	5.85695i	0.138798	−	1.85213i
$11$	0.694710	−	3.04372i	0.209463	−	0.917717i	−0.755462	−	0.655192i	$-0.772588\pi$
$11$	0.694710	−	3.04372i	0.209463	−	0.917717i	0.964925	−	0.262525i	$-0.0845552\pi$
$12$	−3.30249	−	8.41460i	−0.953345	−	2.42908i
$13$	0.257224	+	3.43242i	0.0713411	+	0.951981i	0.911940	+	0.410323i	$0.134584\pi$
$13$	0.257224	+	3.43242i	0.0713411	+	0.951981i	−0.840599	+	0.541658i	$0.817797\pi$
$14$	5.00182	+	0.753903i	1.33679	+	0.201489i
$15$	−5.02653	+	4.66394i	−1.29785	+	1.20422i
$16$	−0.462659	+	0.222805i	−0.115665	+	0.0557012i
$17$	−1.92873	−	1.31499i	−0.467785	−	0.318931i	0.306385	−	0.951908i	$-0.400880\pi$
$17$	−1.92873	−	1.31499i	−0.467785	−	0.318931i	−0.774171	+	0.632977i	$0.781833\pi$
$18$	−3.62405	+	9.23392i	−0.854196	+	2.17646i
$19$	−3.23214	−	0.996984i	−0.741505	−	0.228724i	−0.0990872	−	0.995079i	$-0.531592\pi$
$19$	−3.23214	−	0.996984i	−0.741505	−	0.228724i	−0.642418	+	0.766355i	$0.722068\pi$
$20$	6.23332	+	5.78368i	1.39381	+	1.29327i
$21$	−3.68198	−	4.61706i	−0.803474	−	1.00753i
$22$	4.50154	+	5.64475i	0.959732	+	1.20347i
$23$	4.82527	+	4.47719i	1.00614	+	0.933560i	0.997793	−	0.0664056i	$-0.0211531\pi$
$23$	4.82527	+	4.47719i	1.00614	+	0.933560i	0.00834519	+	0.999965i	$0.497344\pi$
$24$	8.04316	+	2.48099i	1.64180	+	0.506429i
$25$	0.529835	−	1.35000i	0.105967	−	0.269999i
$26$	−6.57690	−	4.48405i	−1.28984	−	0.879395i
$27$	3.13647	−	1.51045i	0.603614	−	0.290685i
$28$	−5.36832	+	4.98107i	−1.01452	+	0.941334i
$29$	−5.34977	−	0.806349i	−0.993428	−	0.149735i	−0.367840	−	0.929889i	$-0.619903\pi$
$29$	−5.34977	−	0.806349i	−0.993428	−	0.149735i	−0.625588	+	0.780154i	$0.715141\pi$
$30$	−1.18503	−	15.8131i	−0.216356	−	2.88706i
$31$	0.778473	+	1.98352i	0.139818	+	0.356250i	0.983581	−	0.180465i	$-0.0577602\pi$
$31$	0.778473	+	1.98352i	0.139818	+	0.356250i	−0.843764	+	0.536715i	$0.819665\pi$
$32$	−1.12320	+	4.92105i	−0.198555	+	0.869928i
$33$	0.629903	−	8.40547i	0.109652	−	1.46321i
$34$	5.15856	−	1.59121i	0.884686	−	0.272890i
$35$	5.00501	+	2.41028i	0.846000	+	0.407412i
$36$	−7.18063	−	12.4372i	−1.19677	−	2.07287i
$37$	−1.73964	+	3.01315i	−0.285996	+	0.495359i	−0.972850	−	0.231436i	$-0.925658\pi$
$37$	−1.73964	+	3.01315i	−0.285996	+	0.495359i	0.686855	+	0.726795i	$0.258991\pi$
$38$	6.46296	−	4.40637i	1.04843	−	0.714808i
$39$	2.06792	+	9.06013i	0.331131	+	1.45078i
$40$	−7.82938	+	1.18009i	−1.23793	+	0.186588i
$41$	1.33098	−	1.66900i	0.207864	−	0.260653i	−0.666961	−	0.745093i	$-0.732405\pi$
$41$	1.33098	−	1.66900i	0.207864	−	0.260653i	0.874825	+	0.484440i	$0.160976\pi$
$42$	13.6569			2.10730
$43$	6.03879	+	2.55598i	0.920907	+	0.389783i
$43$	6.03879	+	2.55598i	0.920907	+	0.389783i
$44$	−10.4527			−1.57581
$45$	−6.79225	+	8.51721i	−1.01253	+	1.26967i
$46$	−15.0525	+	2.26880i	−2.21937	+	0.334516i
$47$	0.260214	+	1.14007i	0.0379561	+	0.166297i	0.990354	−	0.138562i	$-0.0442480\pi$
$47$	0.260214	+	1.14007i	0.0379561	+	0.166297i	−0.952398	+	0.304859i	$0.901391\pi$
$48$	−1.14552	+	0.781003i	−0.165342	+	0.112728i
$49$	1.10788	−	1.91890i	0.158268	−	0.274129i
$50$	1.67692	+	2.90450i	0.237152	+	0.410759i
$51$	−5.67834	−	2.73454i	−0.795126	−	0.382913i
$52$	11.0123	−	3.39683i	1.52713	−	0.471056i
$53$	0.777332	−	10.3728i	0.106775	−	1.42481i	−0.644391	−	0.764696i	$-0.722889\pi$
$53$	0.777332	−	10.3728i	0.106775	−	1.42481i	0.751166	−	0.660113i	$-0.229492\pi$
$54$	−1.79144	+	7.84880i	−0.243784	+	1.06809i
$55$	2.89680	+	7.38094i	0.390605	+	0.995245i
$56$	−0.509588	−	6.79998i	−0.0680966	−	0.908686i
$57$	−9.03014	−	1.36108i	−1.19607	−	0.180279i
$58$	9.17165	−	8.51004i	1.20430	−	1.11742i
$59$	−5.53586	+	2.66593i	−0.720708	+	0.347075i	−0.758022	−	0.652229i	$-0.773834\pi$
$59$	−5.53586	+	2.66593i	−0.720708	+	0.347075i	0.0373140	+	0.999304i	$0.488120\pi$
$60$	18.9686	+	12.9326i	2.44884	+	1.66959i
$61$	0.913867	−	2.32849i	0.117009	−	0.298133i	−0.860356	−	0.509693i	$-0.829759\pi$
$61$	0.913867	−	2.32849i	0.117009	−	0.298133i	0.977365	+	0.211560i	$0.0678543\pi$
$62$	−4.70878	−	1.45247i	−0.598015	−	0.184463i
$63$	−6.87761	−	6.38149i	−0.866497	−	0.803992i
$64$	−7.91838	−	9.92933i	−0.989797	−	1.24117i
$65$	−5.45047	−	6.83467i	−0.676047	−	0.847736i
$66$	14.2893	+	13.2586i	1.75890	+	1.63202i
$67$	9.87998	+	3.04757i	1.20703	+	0.372320i	0.832044	−	0.554710i	$-0.187171\pi$
$67$	9.87998	+	3.04757i	1.20703	+	0.372320i	0.374988	+	0.927030i	$0.377647\pi$
$68$	−2.85536	+	7.27534i	−0.346263	+	0.882264i
$69$	14.6838	+	10.0112i	1.76772	+	1.20521i
$70$	−11.5745	+	5.57401i	−1.38342	+	0.666221i
$71$	8.30629	−	7.70711i	0.985776	−	0.914666i	−0.0105816	−	0.999944i	$-0.503368\pi$
$71$	8.30629	−	7.70711i	0.985776	−	0.914666i	0.996357	+	0.0852780i	$0.0271778\pi$
$72$	13.2232	+	1.99307i	1.55836	+	0.234886i
$73$	0.624897	+	8.33868i	0.0731387	+	0.975968i	0.906217	+	0.422813i	$0.138957\pi$
$73$	0.624897	+	8.33868i	0.0731387	+	0.975968i	−0.833078	+	0.553155i	$0.813424\pi$
$74$	−2.93960	−	7.48997i	−0.341721	−	0.870692i
$75$	0.871282	−	3.81734i	0.100607	−	0.440788i
$76$	−0.846290	+	11.2930i	−0.0970761	+	1.29539i
$77$	−6.52534	+	2.01280i	−0.743631	+	0.229380i
$78$	−19.3629	−	9.32469i	−2.19242	−	1.05581i
$79$	−4.90787	−	8.50067i	−0.552178	−	0.956400i	−0.998117	−	0.0613371i	$-0.980464\pi$
$79$	−4.90787	−	8.50067i	−0.552178	−	0.956400i	0.445939	−	0.895063i	$-0.352870\pi$
$80$	0.652093	−	1.12946i	0.0729062	−	0.126277i
$81$	−2.86645	+	1.95431i	−0.318495	+	0.217146i
$82$	1.09853	+	4.81298i	0.121312	+	0.531505i
$83$	−2.83709	+	0.427622i	−0.311411	+	0.0469376i	−0.302888	−	0.953026i	$-0.597951\pi$
$83$	−2.83709	+	0.427622i	−0.311411	+	0.0469376i	−0.00852244	+	0.999964i	$0.502713\pi$
$84$	−12.3276	+	15.4583i	−1.34505	+	1.68664i
$85$	5.92862			0.643049
$86$	−13.3286	+	7.23307i	−1.43726	+	0.779962i
$87$	−14.6069			−1.56603
$88$	6.06847	−	7.60962i	0.646901	−	0.811188i
$89$	14.8273	−	2.23486i	1.57169	−	0.236894i	0.695381	−	0.718641i	$-0.255236\pi$
$89$	14.8273	−	2.23486i	1.57169	−	0.236894i	0.876311	+	0.481747i	$0.159997\pi$
$90$	−5.60602	−	24.5616i	−0.590926	−	2.58902i
$91$	6.22054	−	4.24110i	0.652090	−	0.444588i
$92$	11.0193	−	19.0860i	1.14884	−	1.98985i
$93$	2.87648	+	4.98220i	0.298277	+	0.516630i
$94$	−2.43652	−	1.17336i	−0.251307	−	0.121023i
$95$	8.20879	−	2.53207i	0.842204	−	0.259785i
$96$	−1.01842	+	13.5899i	−0.103942	+	1.38701i
$97$	0.939509	−	4.11626i	0.0953927	−	0.417943i	−0.904572	−	0.426320i	$-0.859810\pi$
$97$	0.939509	−	4.11626i	0.0953927	−	0.417943i	0.999965	+	0.00837767i	$0.00266673\pi$
$98$	1.87206	+	4.76993i	0.189107	+	0.481836i
$99$	−1.00075	−	13.3540i	−0.100579	−	1.34213i
$100$	−4.80132	−	0.723683i	−0.480132	−	0.0723683i
$101$	−0.0681687	+	0.0632513i	−0.00678304	+	0.00629374i	−0.683557	−	0.729897i	$-0.739568\pi$
$101$	−0.0681687	+	0.0632513i	−0.00678304	+	0.00629374i	0.676774	+	0.736191i	$0.263377\pi$
$102$	13.1317	−	6.32388i	1.30023	−	0.626158i
$103$	−11.8798	−	8.09950i	−1.17055	−	0.798068i	−0.187655	−	0.982235i	$-0.560089\pi$
$103$	−11.8798	−	8.09950i	−1.17055	−	0.798068i	−0.982895	+	0.184167i	$0.941041\pi$
$104$	−3.92041	+	9.98905i	−0.384428	+	0.979507i
$105$	14.3319	+	4.42081i	1.39865	+	0.431427i
$106$	17.6338	+	16.3617i	1.71274	+	1.58919i
$107$	7.87307	+	9.87252i	0.761118	+	0.954412i	0.999861	−	0.0166707i	$-0.00530671\pi$
$107$	7.87307	+	9.87252i	0.761118	+	0.954412i	−0.238743	+	0.971083i	$0.576735\pi$
$108$	−7.26704	−	9.11258i	−0.699272	−	0.876859i
$109$	−10.5760	−	9.81311i	−1.01300	−	0.939926i	−0.0147987	−	0.999890i	$-0.504711\pi$
$109$	−10.5760	−	9.81311i	−1.01300	−	0.939926i	−0.998201	+	0.0599646i	$0.980901\pi$
$110$	−17.5220	−	5.40482i	−1.67066	−	0.515330i
$111$	−3.43190	+	8.74433i	−0.325741	+	0.829975i
$112$	0.928034	+	0.632723i	0.0876909	+	0.0597867i
$113$	−11.0000	+	5.29730i	−1.03479	+	0.498328i	−0.872602	−	0.488432i	$-0.837569\pi$
$113$	−11.0000	+	5.29730i	−1.03479	+	0.498328i	−0.162187	+	0.986760i	$0.551855\pi$
$114$	15.4813	−	14.3645i	1.44995	−	1.34536i
$115$	−16.5309	−	2.49163i	−1.54152	−	0.232346i
$116$	1.35365	+	18.0632i	0.125683	+	1.67712i
$117$	5.39400	+	13.7437i	0.498675	+	1.27060i
$118$	3.16188	−	13.8531i	0.291075	−	1.27528i
$119$	−0.381564	+	5.09162i	−0.0349779	+	0.466748i
$120$	−20.4275	+	6.30104i	−1.86477	+	0.575204i
$121$	1.12903	+	0.543713i	0.102639	+	0.0494284i
$122$	2.89237	+	5.00973i	0.261863	+	0.453560i
$123$	2.88176	−	4.99136i	0.259840	−	0.450055i
$124$	5.89451	−	4.01881i	0.529342	−	0.360899i
$125$	−2.00612	−	8.78939i	−0.179433	−	0.786147i
$126$	21.4548	−	3.23379i	1.91134	−	0.288089i
$127$	4.22668	−	5.30009i	0.375057	−	0.470307i	−0.558101	−	0.829773i	$-0.688470\pi$
$127$	4.22668	−	5.30009i	0.375057	−	0.470307i	0.933158	+	0.359466i	$0.117041\pi$
$128$	19.2749			1.70368
$129$	17.1505	+	4.39379i	1.51001	+	0.386852i
$130$	20.2164			1.77309
$131$	−1.63388	+	2.04883i	−0.142753	+	0.179007i	−0.848068	−	0.529887i	$-0.822234\pi$
$131$	−1.63388	+	2.04883i	−0.142753	+	0.179007i	0.705315	+	0.708894i	$0.250806\pi$
$132$	−27.9060	+	4.20615i	−2.42890	+	0.366098i
$133$	1.64628	+	7.21284i	0.142751	+	0.625432i
$134$	−19.7559	+	13.4694i	−1.70665	+	1.16357i
$135$	−4.42069	+	7.65686i	−0.380472	+	0.658997i
$136$	−3.63875	−	6.30251i	−0.312021	−	0.540436i
$137$	−3.39110	−	1.63307i	−0.289721	−	0.139522i	0.283378	−	0.959008i	$-0.408545\pi$
$137$	−3.39110	−	1.63307i	−0.289721	−	0.139522i	−0.573099	+	0.819486i	$0.694259\pi$
$138$	−39.2731	+	12.1142i	−3.34315	+	1.03123i
$139$	−1.36892	+	18.2669i	−0.116110	+	1.54938i	0.569854	+	0.821746i	$0.307000\pi$
$139$	−1.36892	+	18.2669i	−0.116110	+	1.54938i	−0.685964	+	0.727635i	$0.740619\pi$
$140$	4.13869	−	18.1328i	0.349783	−	1.53250i
$141$	1.15346	+	2.93898i	0.0971393	+	0.247507i
$142$	1.95825	+	26.1310i	0.164332	+	2.19286i
$143$	10.6260	+	1.60162i	0.888593	+	0.133934i
$144$	−1.61466	+	1.49819i	−0.134555	+	0.124849i
$145$	12.3797	−	5.96177i	1.02808	−	0.495098i
$146$	−15.9778	−	10.8935i	−1.32234	−	0.901553i
$147$	2.18558	−	5.56876i	0.180263	−	0.459304i
$148$	11.1314	+	3.43359i	0.914997	+	0.282239i
$149$	8.95319	+	8.30735i	0.733474	+	0.680564i	0.955671	−	0.294437i	$-0.0951322\pi$
$149$	8.95319	+	8.30735i	0.733474	+	0.680564i	−0.222197	+	0.975002i	$0.571323\pi$
$150$	5.64568	+	7.07946i	0.460968	+	0.578036i
$151$	−5.29170	−	6.63559i	−0.430633	−	0.539996i	0.518415	−	0.855129i	$-0.326522\pi$
$151$	−5.29170	−	6.63559i	−0.430633	−	0.539996i	−0.949048	+	0.315133i	$0.897951\pi$
$152$	−7.72999	−	7.17238i	−0.626985	−	0.581757i
$153$	−9.56809	−	2.95137i	−0.773535	−	0.238604i
$154$	5.76948	−	14.7004i	0.464918	−	1.18459i
$155$	−4.47135	−	3.04852i	−0.359148	−	0.244863i
$156$	28.0329	−	13.4999i	2.24443	−	1.08086i
$157$	−14.6338	+	13.5782i	−1.16791	+	1.08366i	−0.172789	+	0.984959i	$0.555278\pi$
$157$	−14.6338	+	13.5782i	−1.16791	+	1.08366i	−0.995117	+	0.0986994i	$0.968532\pi$
$158$	22.4463	+	3.38323i	1.78573	+	0.269155i
$159$	−2.09871	−	28.0053i	−0.166438	−	2.22097i
$160$	−4.68352	−	11.9334i	−0.370265	−	0.943419i
$161$	3.20379	−	14.0367i	0.252494	−	1.10625i
$162$	0.599561	−	8.00059i	0.0471060	−	0.628586i
$163$	−14.7466	+	4.54872i	−1.15504	+	0.356283i	−0.812353	−	0.583166i	$-0.801814\pi$
$163$	−14.7466	+	4.54872i	−1.15504	+	0.356283i	−0.342688	+	0.939449i	$0.611337\pi$
$164$	−6.43945	−	3.10108i	−0.502837	−	0.242153i
$165$	10.7038	+	18.5395i	0.833287	+	1.44330i
$166$	3.31757	−	5.74620i	0.257493	−	0.445991i
$167$	11.9849	−	8.17115i	0.927417	−	0.632302i	−0.00252959	−	0.999997i	$-0.500805\pi$
$167$	11.9849	−	8.17115i	0.927417	−	0.632302i	0.929947	+	0.367695i	$0.119853\pi$
$168$	−4.09676	−	17.9491i	−0.316072	−	1.38480i
$169$	1.13948	−	0.171748i	0.0876519	−	0.0132114i
$170$	−8.54835	+	10.7193i	−0.655629	+	0.822132i
$171$	−14.5085			−1.10949
$172$	3.84407	−	21.6157i	0.293108	−	1.64818i
$173$	−3.57561			−0.271849			−0.135924	−	0.990719i	$-0.543400\pi$
$173$	−3.57561			−0.271849			−0.135924	+	0.990719i	$0.543400\pi$
$174$	21.0614	−	26.4102i	1.59666	−	2.00215i
$175$	−3.13668	+	0.472779i	−0.237111	+	0.0357387i
$176$	0.356743	+	1.56299i	0.0268905	+	0.117815i
$177$	−13.7065	+	9.34494i	−1.03024	+	0.702409i
$178$	−17.3384	+	30.0310i	−1.29957	+	2.25092i
$179$	−1.18241	−	2.04800i	−0.0883776	−	0.153074i	0.818448	−	0.574581i	$-0.194835\pi$
$179$	−1.18241	−	2.04800i	−0.0883776	−	0.153074i	−0.906825	+	0.421506i	$0.861502\pi$
$180$	32.8618	+	15.8254i	2.44937	+	1.17955i
$181$	−12.4501	+	3.84036i	−0.925411	+	0.285451i	−0.720601	−	0.693350i	$-0.756134\pi$
$181$	−12.4501	+	3.84036i	−0.925411	+	0.285451i	−0.204810	+	0.978802i	$0.565658\pi$
$182$	−1.30112	+	17.3622i	−0.0964455	+	1.28698i
$183$	1.50280	−	6.58419i	0.111090	−	0.486718i
$184$	7.49726	+	19.1027i	0.552705	+	1.40827i
$185$	−0.660350	−	8.81175i	−0.0485499	−	0.647853i
$186$	−13.1556	−	1.98289i	−0.964618	−	0.145393i
$187$	−5.34236	+	4.95698i	−0.390672	+	0.362490i
$188$	3.52750	−	1.69875i	0.257269	−	0.123894i
$189$	−6.29135	−	4.28937i	−0.457628	−	0.312006i
$190$	−7.25793	+	18.4929i	−0.526546	+	1.34162i
$191$	3.57188	+	1.10178i	0.258452	+	0.0797220i	0.421274	−	0.906934i	$-0.361583\pi$
$191$	3.57188	+	1.10178i	0.258452	+	0.0797220i	−0.162821	+	0.986656i	$0.552059\pi$
$192$	−25.1355	−	23.3223i	−1.81400	−	1.68314i
$193$	−10.0175	−	12.5616i	−0.721078	−	0.904203i	0.277320	−	0.960777i	$-0.410554\pi$
$193$	−10.0175	−	12.5616i	−0.721078	−	0.904203i	−0.998398	+	0.0565743i	$0.981982\pi$
$194$	6.08778	+	7.63383i	0.437077	+	0.548077i
$195$	−17.3015	−	16.0535i	−1.23899	−	1.14961i
$196$	−7.08896	−	2.18665i	−0.506354	−	0.156190i
$197$	−7.38782	+	18.8239i	−0.526360	+	1.34114i	0.382466	+	0.923969i	$0.375075\pi$
$197$	−7.38782	+	18.8239i	−0.526360	+	1.34114i	−0.908826	+	0.417174i	$0.863020\pi$
$198$	25.5878	+	17.4455i	1.81845	+	1.23980i
$199$	8.36213	−	4.02699i	0.592776	−	0.285466i	−0.113347	−	0.993556i	$-0.536157\pi$
$199$	8.36213	−	4.02699i	0.592776	−	0.285466i	0.706123	+	0.708090i	$0.250443\pi$
$200$	3.31432	−	3.07524i	0.234358	−	0.217452i
$201$	27.6032	+	4.16052i	1.94698	+	0.293460i
$202$	−0.0160711	−	0.214454i	−0.00113076	−	0.0150889i
$203$	4.32333	+	11.0157i	0.303438	+	0.773148i
$204$	−4.69547	+	20.5722i	−0.328749	+	1.44034i
$205$	−0.405159	+	5.40648i	−0.0282976	+	0.377605i
$206$	31.7736	−	9.80085i	2.21377	−	0.682858i
$207$	25.4386	+	12.2506i	1.76810	+	0.851473i
$208$	−0.883767	−	1.53073i	−0.0612782	−	0.106137i
$209$	−5.27995	+	9.14514i	−0.365222	+	0.632582i
$210$	−28.6580	+	19.5387i	−1.97759	+	1.34830i
$211$	2.24730	+	9.84606i	0.154710	+	0.677831i	0.991478	+	0.130273i	$0.0415853\pi$
$211$	2.24730	+	9.84606i	0.154710	+	0.677831i	−0.836768	+	0.547558i	$0.815558\pi$
$212$	−34.4373	+	5.19059i	−2.36517	+	0.356491i
$213$	19.0743	−	23.9184i	1.30695	−	1.63886i
$214$	−29.2021			−1.99621
$215$	−16.3288	+	3.27606i	−1.11361	+	0.223425i
$216$	10.8530			0.738451
$217$	2.90590	−	3.64389i	0.197266	−	0.247363i
$218$	32.9920	−	4.97275i	2.23450	−	0.336797i
$219$	5.02377	+	22.0106i	0.339475	+	1.48734i
$220$	21.9343	−	14.9545i	1.47881	−	1.00823i
$221$	4.01746	−	6.95845i	0.270244	−	0.468076i
$222$	−10.8619	−	18.8133i	−0.729002	−	1.26267i
$223$	9.65689	+	4.65051i	0.646673	+	0.311421i	0.728317	−	0.685240i	$-0.240303\pi$
$223$	9.65689	+	4.65051i	0.646673	+	0.311421i	−0.0816442	+	0.996662i	$0.526017\pi$
$224$	10.5501	−	3.25427i	0.704907	−	0.217435i
$225$	0.464872	−	6.20329i	0.0309915	−	0.413553i
$226$	6.28278	−	27.5266i	0.417924	−	1.83105i
$227$	−6.20740	−	15.8162i	−0.412000	−	1.04976i	−0.974783	−	0.223154i	$-0.928365\pi$
$227$	−6.20740	−	15.8162i	−0.412000	−	1.04976i	0.562784	−	0.826604i	$-0.309730\pi$
$228$	2.28489	+	30.4897i	0.151320	+	2.01923i
$229$	1.15664	+	0.174336i	0.0764332	+	0.0115204i	0.187147	−	0.982332i	$-0.440076\pi$
$229$	1.15664	+	0.174336i	0.0764332	+	0.0115204i	−0.110714	+	0.993852i	$0.535314\pi$
$230$	28.3406	−	26.2962i	1.86872	−	1.73392i
$231$	−16.6110	+	7.99942i	−1.09292	+	0.526323i
$232$	−13.9359	−	9.50136i	−0.914939	−	0.623795i
$233$	6.82313	−	17.3850i	0.446998	−	1.13893i	−0.512867	−	0.858468i	$-0.671416\pi$
$233$	6.82313	−	17.3850i	0.446998	−	1.13893i	0.959865	−	0.280464i	$-0.0904883\pi$
$234$	−32.6269	−	10.0641i	−2.13288	−	0.657908i
$235$	−2.17712	−	2.02008i	−0.142020	−	0.131775i
$236$	12.8263	+	16.0837i	0.834922	+	1.04696i
$237$	−16.5233	−	20.7196i	−1.07331	−	1.34588i
$238$	−8.65578	−	8.03139i	−0.561071	−	0.520598i
$239$	15.1552	+	4.67477i	0.980310	+	0.302386i	0.743179	−	0.669092i	$-0.233317\pi$
$239$	15.1552	+	4.67477i	0.980310	+	0.302386i	0.237130	+	0.971478i	$0.423793\pi$
$240$	1.28642	−	3.27775i	0.0830383	−	0.211578i
$241$	−2.54236	−	1.73335i	−0.163768	−	0.111655i	0.478663	−	0.877999i	$-0.341122\pi$
$241$	−2.54236	−	1.73335i	−0.163768	−	0.111655i	−0.642431	+	0.766344i	$0.722074\pi$
$242$	−2.61099	+	1.25739i	−0.167841	+	0.0808279i
$243$	−14.5220	+	13.4744i	−0.931586	+	0.864386i
$244$	−8.28139	−	1.24822i	−0.530161	−	0.0799090i
$245$	0.420538	+	5.61170i	0.0268672	+	0.358518i
$246$	4.86951	+	12.4073i	0.310469	+	0.791062i
$247$	2.59068	−	11.3505i	0.164841	−	0.722216i
$248$	−0.496430	+	6.62439i	−0.0315233	+	0.420649i
$249$	−7.40219	+	2.28327i	−0.469095	+	0.144697i
$250$	18.7843	+	9.04605i	1.18802	+	0.572122i
$251$	5.80972	+	10.0627i	0.366706	+	0.635154i	0.989048	−	0.147592i	$-0.0471521\pi$
$251$	5.80972	+	10.0627i	0.366706	+	0.635154i	−0.622342	+	0.782745i	$0.713819\pi$
$252$	−15.7061	+	27.2038i	−0.989394	+	1.71368i
$253$	16.9795	−	11.5764i	1.06749	−	0.727804i
$254$	3.48851	+	15.2842i	0.218889	+	0.959014i
$255$	15.8278	−	2.38566i	0.991178	−	0.149396i
$256$	−11.9553	+	14.9915i	−0.747209	+	0.936970i
$257$	−24.8591			−1.55067			−0.775335	−	0.631550i	$-0.782419\pi$
$257$	−24.8591			−1.55067			−0.775335	+	0.631550i	$0.782419\pi$
$258$	−32.6731	+	24.6737i	−2.03414	+	1.53612i
$259$	7.61021			0.472876
$260$	−18.2486	+	22.8831i	−1.13173	+	1.41915i
$261$	−22.9473	+	3.45875i	−1.42040	+	0.214091i
$262$	−1.34853	−	5.90832i	−0.0833128	−	0.365017i
$263$	3.05043	−	2.07975i	0.188098	−	0.128243i	−0.465610	−	0.884990i	$-0.654165\pi$
$263$	3.05043	−	2.07975i	0.188098	−	0.128243i	0.653708	+	0.756747i	$0.273213\pi$
$264$	13.1391	−	22.7576i	0.808656	−	1.40063i
$265$	13.2090	+	22.8786i	0.811421	+	1.40542i
$266$	−15.4150	−	7.42346i	−0.945152	−	0.455161i
$267$	38.6856	−	11.9329i	2.36752	−	0.730284i
$268$	2.58693	−	34.5202i	0.158022	−	2.10866i
$269$	−4.94582	+	21.6690i	−0.301552	+	1.32118i	0.566233	+	0.824245i	$0.308400\pi$
$269$	−4.94582	+	21.6690i	−0.301552	+	1.32118i	−0.867785	+	0.496940i	$0.834457\pi$
$270$	−7.46995	−	19.0331i	−0.454606	−	1.15832i
$271$	0.545250	+	7.27585i	0.0331216	+	0.441977i	0.988970	+	0.148116i	$0.0473210\pi$
$271$	0.545250	+	7.27585i	0.0331216	+	0.441977i	−0.955848	+	0.293860i	$0.905060\pi$
$272$	1.18533	+	0.178660i	0.0718712	+	0.0108328i
$273$	14.9006	−	13.8257i	0.901824	−	0.836771i
$274$	7.84223	−	3.77662i	0.473766	−	0.228154i
$275$	−3.74094	−	2.55053i	−0.225587	−	0.153803i
$276$	21.7384	−	55.3885i	1.30850	−	3.33400i
$277$	7.04754	+	2.17388i	0.423446	+	0.130616i	0.499152	−	0.866514i	$-0.333645\pi$
$277$	7.04754	+	2.17388i	0.423446	+	0.130616i	−0.0757063	+	0.997130i	$0.524121\pi$
$278$	−31.0539	−	28.8138i	−1.86249	−	1.72814i
$279$	5.69863	+	7.14586i	0.341168	+	0.427811i
$280$	10.7980	+	13.5402i	0.645301	+	0.809182i
$281$	14.0185	+	13.0073i	0.836276	+	0.775951i	0.976806	−	0.214125i	$-0.0686901\pi$
$281$	14.0185	+	13.0073i	0.836276	+	0.775951i	−0.140530	+	0.990076i	$0.544881\pi$
$282$	−6.97700	−	2.15212i	−0.415474	−	0.128157i
$283$	7.23358	−	18.4309i	0.429992	−	1.09560i	−0.537627	−	0.843183i	$-0.680679\pi$
$283$	7.23358	−	18.4309i	0.429992	−	1.09560i	0.967618	−	0.252418i	$-0.0812257\pi$
$284$	−31.3455	−	21.3710i	−1.86001	−	1.26813i
$285$	20.8964	−	10.0632i	1.23779	−	0.596090i
$286$	−18.2172	+	16.9031i	−1.07721	+	0.999503i
$287$	−4.61712	−	0.695918i	−0.272540	−	0.0410788i
$288$	1.61799	+	21.5906i	0.0953413	+	1.27224i
$289$	−4.21999	−	10.7524i	−0.248235	−	0.632491i
$290$	−7.07085	+	30.9794i	−0.415215	+	1.81917i
$291$	0.851866	−	11.3674i	0.0499373	−	0.666367i
$292$	26.7531	−	8.25223i	1.56561	−	0.482925i
$293$	−9.89064	−	4.76308i	−0.577817	−	0.278262i	0.122063	−	0.992522i	$-0.461049\pi$
$293$	−9.89064	−	4.76308i	−0.577817	−	0.278262i	−0.699880	+	0.714260i	$0.746763\pi$
$294$	6.91731	+	11.9811i	0.403425	+	0.698753i
$295$	7.80250	−	13.5143i	0.454279	−	0.786835i
$296$	−8.96217	+	6.11030i	−0.520915	+	0.355154i
$297$	−2.41844	−	10.5959i	−0.140332	−	0.614835i
$298$	−27.9296	+	4.20971i	−1.61792	+	0.243862i
$299$	−14.1264	+	17.7140i	−0.816952	+	1.02443i
$300$	−13.1095			−0.756875
$301$	−1.76263	−	14.2343i	−0.101596	−	0.820452i
$302$	19.6275			1.12944
$303$	−0.156540	+	0.196295i	−0.00899299	+	0.0112769i
$304$	1.71751	−	0.258874i	0.0985062	−	0.0148474i
$305$	1.41365	+	6.19363i	0.0809456	+	0.354646i
$306$	19.1323	−	13.0442i	1.09372	−	0.745685i
$307$	0.404766	−	0.701075i	0.0231012	−	0.0400124i	−0.854244	−	0.519873i	$-0.825979\pi$
$307$	0.404766	−	0.701075i	0.0231012	−	0.0400124i	0.877345	+	0.479860i	$0.159313\pi$
$308$	11.4316	+	19.8001i	0.651374	+	1.12821i
$309$	−34.9751	−	16.8431i	−1.98966	−	0.958171i
$310$	11.9590	−	3.68888i	0.679228	−	0.209514i
$311$	−0.814411	+	10.8676i	−0.0461810	+	0.616243i	0.925317	+	0.379195i	$0.123799\pi$
$311$	−0.814411	+	10.8676i	−0.0461810	+	0.616243i	−0.971498	+	0.237048i	$0.923820\pi$
$312$	−6.44689	+	28.2457i	−0.364983	+	1.59910i
$313$	5.87609	+	14.9720i	0.332136	+	0.846269i	0.995214	+	0.0977190i	$0.0311546\pi$
$313$	5.87609	+	14.9720i	0.332136	+	0.846269i	−0.663078	+	0.748551i	$0.730750\pi$
$314$	−3.44999	−	46.0369i	−0.194694	−	2.59801i
$315$	23.5620	+	3.55141i	1.32757	+	0.200099i
$316$	−24.0910	+	22.3531i	−1.35522	+	1.25746i
$317$	1.20889	−	0.582170i	0.0678980	−	0.0326980i	−0.399627	−	0.916678i	$-0.630860\pi$
$317$	1.20889	−	0.582170i	0.0678980	−	0.0326980i	0.467525	+	0.883980i	$0.345146\pi$
$318$	53.6613	+	36.5857i	3.00918	+	2.05162i
$319$	−6.17084	+	15.7230i	−0.345501	+	0.880322i
$320$	30.8218	+	9.50728i	1.72299	+	0.531473i
$321$	24.9917	+	23.1889i	1.39490	+	1.29428i
$322$	20.7597	+	26.0319i	1.15690	+	1.45070i
$323$	4.92291	+	6.17313i	0.273918	+	0.343482i
$324$	8.51472	+	7.90051i	0.473040	+	0.438917i
$325$	4.77004	+	1.47136i	0.264594	+	0.0816165i
$326$	13.0384	−	33.2214i	0.722132	−	1.83996i
$327$	−32.1839	−	21.9426i	−1.77977	−	1.21343i
$328$	5.99610	−	2.88757i	0.331079	−	0.159439i
$329$	1.87500	−	1.73975i	0.103372	−	0.0959153i
$330$	−48.9540	−	7.37862i	−2.69483	−	0.406180i
$331$	−2.32022	−	30.9612i	−0.127531	−	1.70178i	−0.583766	−	0.811922i	$-0.698422\pi$
$331$	−2.32022	−	30.9612i	−0.127531	−	1.70178i	0.456235	−	0.889859i	$-0.349198\pi$
$332$	3.50950	+	8.94207i	0.192609	+	0.490760i
$333$	−3.32091	+	14.5499i	−0.181985	+	0.797327i
$334$	−2.50682	+	33.4511i	−0.137167	+	1.83036i
$335$	−25.0925	+	7.74002i	−1.37095	+	0.422882i
$336$	2.73221	+	1.31576i	0.149054	+	0.0717807i
$337$	−8.79414	−	15.2319i	−0.479047	−	0.829734i	0.520664	−	0.853762i	$-0.325684\pi$
$337$	−8.79414	−	15.2319i	−0.479047	−	0.829734i	−0.999711	+	0.0240275i	$0.992351\pi$
$338$	−1.33245	+	2.30788i	−0.0724759	+	0.125532i
$339$	−27.2353	+	18.5687i	−1.47922	+	1.00852i
$340$	−4.41694	−	19.3519i	−0.239542	−	1.04950i
$341$	6.57809	−	0.991487i	0.356223	−	0.0536920i
$342$	20.9195	−	26.2322i	1.13120	−	1.41848i
$343$	−20.1575			−1.08841
$344$	13.5046	+	15.3478i	0.728119	+	0.827498i
$345$	−45.1357			−2.43003
$346$	5.15560	−	6.46492i	0.277167	−	0.347556i
$347$	10.2678	−	1.54762i	0.551204	−	0.0830806i	0.132466	−	0.991188i	$-0.457711\pi$
$347$	10.2678	−	1.54762i	0.551204	−	0.0830806i	0.418738	+	0.908107i	$0.362472\pi$
$348$	10.8825	+	47.6791i	0.583361	+	2.55587i
$349$	2.49302	−	1.69971i	0.133448	−	0.0909834i	−0.494756	−	0.869032i	$-0.664743\pi$
$349$	2.49302	−	1.69971i	0.133448	−	0.0909834i	0.628204	+	0.778048i	$0.283790\pi$
$350$	3.66790	−	6.35300i	0.196058	−	0.339582i
$351$	5.99126	+	10.3772i	0.319790	+	0.553892i
$352$	14.1980	+	6.83741i	0.756757	+	0.364435i
$353$	−26.0698	+	8.04147i	−1.38756	+	0.428004i	−0.896469	−	0.443106i	$-0.853876\pi$
$353$	−26.0698	+	8.04147i	−1.38756	+	0.428004i	−0.491087	+	0.871111i	$0.663400\pi$
$354$	2.86692	−	38.2564i	0.152375	−	2.03331i
$355$	−6.40371	+	28.0565i	−0.339874	+	1.48908i
$356$	−18.3415	−	46.7335i	−0.972099	−	2.47687i
$357$	1.03018	+	13.7468i	0.0545230	+	0.727558i
$358$	5.40779	+	0.815093i	0.285811	+	0.0430790i
$359$	8.13180	−	7.54521i	0.429180	−	0.398221i	−0.435787	−	0.900050i	$-0.643530\pi$
$359$	8.13180	−	7.54521i	0.429180	−	0.398221i	0.864967	+	0.501829i	$0.167339\pi$
$360$	−30.5993	+	14.7358i	−1.61272	+	0.776647i
$361$	−6.24576	−	4.25829i	−0.328724	−	0.224120i
$362$	11.0080	−	28.0479i	0.578567	−	1.47416i
$363$	3.23300	+	0.997248i	0.169688	+	0.0523420i
$364$	−18.4780	−	17.1451i	−0.968509	−	0.898645i
$365$	−13.2413	−	16.6041i	−0.693082	−	0.869097i
$366$	9.73775	+	12.2108i	0.509000	+	0.638266i
$367$	20.0449	+	18.5989i	1.04633	+	0.970855i	0.999606	−	0.0280524i	$-0.00893051\pi$
$367$	20.0449	+	18.5989i	1.04633	+	0.970855i	0.0467268	+	0.998908i	$0.485121\pi$
$368$	−3.23000	−	0.996322i	−0.168375	−	0.0519369i
$369$	3.34531	−	8.52372i	0.174150	−	0.443727i
$370$	16.8843	+	11.5115i	0.877773	+	0.598456i
$371$	−20.4987	+	9.87167i	−1.06424	+	0.512512i
$372$	14.1196	−	13.1011i	0.732067	−	0.679259i
$373$	−1.06601	−	0.160675i	−0.0551958	−	0.00831943i	0.121386	−	0.992605i	$-0.461266\pi$
$373$	−1.06601	−	0.160675i	−0.0551958	−	0.00831943i	−0.176582	+	0.984286i	$0.556504\pi$
$374$	−1.25948	−	16.8067i	−0.0651264	−	0.869052i
$375$	−8.89263	−	22.6581i	−0.459214	−	1.17006i
$376$	−0.811238	+	3.55427i	−0.0418364	+	0.183297i
$377$	1.39163	−	18.5701i	0.0716728	−	0.956407i
$378$	16.8268	−	5.19038i	0.865477	−	0.266964i
$379$	2.72408	+	1.31185i	0.139927	+	0.0673851i	0.502537	−	0.864556i	$-0.332400\pi$
$379$	2.72408	+	1.31185i	0.139927	+	0.0673851i	−0.362610	+	0.931941i	$0.618114\pi$
$380$	−14.3808	−	24.9082i	−0.737717	−	1.27776i
$381$	9.15136	−	15.8506i	0.468839	−	0.812052i
$382$	−7.14231	+	4.86954i	−0.365432	+	0.249147i
$383$	−4.48641	−	19.6562i	−0.229245	−	1.00439i	−0.950258	−	0.311465i	$-0.899180\pi$
$383$	−4.48641	−	19.6562i	−0.229245	−	1.00439i	0.721013	−	0.692922i	$-0.243677\pi$
$384$	51.4589	−	7.75618i	2.62600	−	0.395806i
$385$	10.8133	−	13.5594i	0.551095	−	0.691051i
$386$	37.1562			1.89120
$387$	27.9835	+	2.84155i	1.42248	+	0.144444i
$388$	−14.1360			−0.717647
$389$	−5.67821	+	7.12025i	−0.287897	+	0.361011i	−0.904657	−	0.426140i	$-0.859873\pi$
$389$	−5.67821	+	7.12025i	−0.287897	+	0.361011i	0.616761	+	0.787151i	$0.288445\pi$
$390$	53.9724	−	8.13502i	2.73300	−	0.411933i
$391$	−3.41919	−	14.9804i	−0.172916	−	0.757594i
$392$	5.70748	−	3.89130i	0.288271	−	0.196540i
$393$	−3.53759	+	6.12729i	−0.178448	+	0.309081i
$394$	−23.3823	−	40.4993i	−1.17798	−	2.04033i
$395$	22.4606	+	10.8164i	1.13011	+	0.544234i
$396$	−42.8439	+	13.2156i	−2.15299	+	0.664109i
$397$	−1.77959	+	23.7470i	−0.0893152	+	1.19183i	0.754906	+	0.655834i	$0.227683\pi$
$397$	−1.77959	+	23.7470i	−0.0893152	+	1.19183i	−0.844221	+	0.535996i	$0.819936\pi$
$398$	−4.77614	+	20.9257i	−0.239406	+	1.04891i
$399$	7.29756	+	18.5939i	0.365335	+	0.930858i
$400$	0.0556531	+	0.742639i	0.00278265	+	0.0371319i
$401$	−5.83102	−	0.878885i	−0.291187	−	0.0438894i	0.00182424	−	0.999998i	$-0.499419\pi$
$401$	−5.83102	−	0.878885i	−0.291187	−	0.0438894i	−0.293011	+	0.956109i	$0.594657\pi$
$402$	−47.3230	+	43.9093i	−2.36025	+	2.19000i
$403$	−6.60802	+	3.18225i	−0.329169	+	0.158519i
$404$	0.257248	+	0.175389i	0.0127986	+	0.00872593i
$405$	3.21903	−	8.20196i	0.159955	−	0.407559i
$406$	−26.1507	−	8.06642i	−1.29784	−	0.400330i
$407$	7.96265	+	7.38826i	0.394694	+	0.366222i
$408$	−12.2506	−	15.3618i	−0.606496	−	0.760522i
$409$	17.4884	+	21.9297i	0.864744	+	1.08435i	0.995670	+	0.0929626i	$0.0296337\pi$
$409$	17.4884	+	21.9297i	0.864744	+	1.08435i	−0.130925	+	0.991392i	$0.541795\pi$
$410$	−9.19103	−	8.52803i	−0.453913	−	0.421170i
$411$	−9.71046	−	2.99528i	−0.478982	−	0.147746i
$412$	−17.5873	+	44.8116i	−0.866462	+	2.20771i
$413$	11.1042	+	7.57073i	0.546403	+	0.372531i
$414$	−58.8290	+	28.3306i	−2.89129	+	1.39237i
$415$	5.34163	−	4.95630i	0.262210	−	0.243295i
$416$	−17.1800	−	2.58947i	−0.842320	−	0.126959i
$417$	3.69592	+	49.3187i	0.180990	+	2.41515i
$418$	−8.92190	−	22.7326i	−0.436384	−	1.11189i
$419$	4.15386	−	18.1993i	0.202930	−	0.889092i	−0.766212	−	0.642588i	$-0.777861\pi$
$419$	4.15386	−	18.1993i	0.202930	−	0.889092i	0.969142	−	0.246505i	$-0.0792821\pi$
$420$	3.75260	−	50.0750i	0.183108	−	2.44341i
$421$	28.4499	−	8.77563i	1.38656	−	0.427698i	0.490429	−	0.871481i	$-0.336840\pi$
$421$	28.4499	−	8.77563i	1.38656	−	0.427698i	0.896134	+	0.443783i	$0.146364\pi$
$422$	−21.0426	−	10.1336i	−1.02434	−	0.493295i
$423$	2.50799	+	4.34397i	0.121943	+	0.211211i
$424$	16.2143	−	28.0840i	0.787436	−	1.36388i
$425$	−2.79713	+	1.90705i	−0.135681	+	0.0925057i
$426$	15.7430	+	68.9747i	0.762752	+	3.34184i
$427$	−5.41020	+	0.815456i	−0.261818	+	0.0394627i
$428$	26.3597	−	33.0540i	1.27415	−	1.59773i
$429$	29.0131			1.40077
$430$	17.6208	−	34.2470i	0.849749	−	1.65154i
$431$	−5.00624			−0.241142			−0.120571	−	0.992705i	$-0.538473\pi$
$431$	−5.00624			−0.241142			−0.120571	+	0.992705i	$0.538473\pi$
$432$	−1.11458	+	1.39764i	−0.0536254	+	0.0672441i
$433$	11.5286	−	1.73766i	0.554031	−	0.0835068i	0.133941	−	0.990989i	$-0.457237\pi$
$433$	11.5286	−	1.73766i	0.554031	−	0.0835068i	0.420090	+	0.907482i	$0.361999\pi$
$434$	2.39840	+	10.5081i	0.115127	+	0.504404i
$435$	30.6516	−	20.8979i	1.46963	−	1.00198i
$436$	−24.1521	+	41.8326i	−1.15667	+	2.00342i
$437$	−11.1323	−	19.2817i	−0.532529	−	0.922367i
$438$	−47.0401	−	22.6533i	−2.24766	−	1.08242i
$439$	−1.49477	+	0.461075i	−0.0713414	+	0.0220059i	−0.330220	−	0.943904i	$-0.607123\pi$
$439$	−1.49477	+	0.461075i	−0.0713414	+	0.0220059i	0.258879	+	0.965910i	$0.416647\pi$
$440$	−1.84728	+	24.6503i	−0.0880658	+	1.17516i
$441$	2.11490	−	9.26596i	0.100709	−	0.441236i
$442$	6.78859	+	17.2970i	0.322900	+	0.822736i
$443$	−0.829554	−	11.0696i	−0.0394133	−	0.525934i	−0.981613	−	0.190882i	$-0.938865\pi$
$443$	−0.829554	−	11.0696i	−0.0394133	−	0.525934i	0.942200	−	0.335052i	$-0.108754\pi$
$444$	31.0996	+	4.68751i	1.47592	+	0.222459i
$445$	−27.9166	+	25.9029i	−1.32338	+	1.22791i
$446$	−22.3324	+	10.7547i	−1.05747	+	0.509252i
$447$	27.2455	+	18.5757i	1.28867	+	0.878598i
$448$	−10.1487	+	25.8585i	−0.479483	+	1.22170i
$449$	−26.5331	−	8.18438i	−1.25217	−	0.386245i	−0.403412	−	0.915019i	$-0.632176\pi$
$449$	−26.5331	−	8.18438i	−1.25217	−	0.386245i	−0.848763	+	0.528774i	$0.822652\pi$
$450$	10.5456	+	9.78490i	0.497125	+	0.461265i
$451$	−4.15532	−	5.21060i	−0.195666	−	0.245358i
$452$	25.4863	+	31.9589i	1.19878	+	1.50322i
$453$	−16.7976	−	15.5859i	−0.789219	−	0.732288i
$454$	37.5469	+	11.5817i	1.76216	+	0.543556i
$455$	−6.98569	+	17.7993i	−0.327494	+	0.834442i
$456$	−23.5231	−	16.0378i	−1.10157	−	0.751039i
$457$	24.3111	−	11.7076i	1.13722	−	0.547658i	0.232051	−	0.972704i	$-0.425456\pi$
$457$	24.3111	−	11.7076i	1.13722	−	0.547658i	0.905172	+	0.425046i	$0.139742\pi$
$458$	−1.98295	+	1.83991i	−0.0926571	+	0.0859732i
$459$	−8.03562	−	1.21117i	−0.375071	−	0.0565328i
$460$	4.18280	+	55.8156i	0.195024	+	2.60242i
$461$	9.46767	+	24.1232i	0.440953	+	1.12353i	0.962734	+	0.270451i	$0.0871728\pi$
$461$	9.46767	+	24.1232i	0.440953	+	1.12353i	−0.521780	+	0.853080i	$0.674732\pi$
$462$	9.48757	−	41.5678i	0.441402	−	1.93391i
$463$	0.770586	−	10.2828i	0.0358122	−	0.477880i	−0.950248	−	0.311493i	$-0.899171\pi$
$463$	0.770586	−	10.2828i	0.0358122	−	0.477880i	0.986061	−	0.166387i	$-0.0532101\pi$
$464$	2.65478	−	0.818891i	0.123245	−	0.0380161i
$465$	−13.1640	−	6.33946i	−0.610467	−	0.293985i
$466$	21.5951	+	37.4037i	1.00037	+	1.73269i
$467$	3.41277	−	5.91110i	0.157924	−	0.273533i	−0.776196	−	0.630492i	$-0.782853\pi$
$467$	3.41277	−	5.91110i	0.157924	−	0.273533i	0.934120	+	0.356959i	$0.116186\pi$
$468$	40.8427	−	27.8461i	1.88795	−	1.28719i
$469$	−5.03234	−	22.0481i	−0.232372	−	1.01809i
$470$	6.79156	−	1.02366i	0.313271	−	0.0472181i
$471$	−33.6045	+	42.1388i	−1.54842	+	1.94165i
$472$	−19.1555			−0.881702
$473$	11.9749	−	16.6047i	0.550606	−	0.763486i
$474$	61.2869			2.81500
$475$	−3.05843	+	3.83515i	−0.140330	+	0.175969i
$476$	16.9041	−	2.54788i	0.774796	−	0.116782i
$477$	−9.92836	−	43.4990i	−0.454589	−	1.99168i
$478$	−30.3042	+	20.6611i	−1.38608	+	0.945016i
$479$	−7.24872	+	12.5552i	−0.331203	+	0.573660i	−0.982748	−	0.184950i	$-0.940788\pi$
$479$	−7.24872	+	12.5552i	−0.331203	+	0.573660i	0.651545	+	0.758610i	$0.274121\pi$
$480$	−17.3057	−	29.9744i	−0.789894	−	1.36814i
$481$	−10.7899	−	5.19613i	−0.491976	−	0.236923i
$482$	6.79976	−	2.09745i	0.309721	−	0.0955362i
$483$	2.90492	−	38.7635i	0.132179	−	1.76380i
$484$	0.933606	−	4.09040i	0.0424366	−	0.185927i
$485$	3.91757	+	9.98181i	0.177888	+	0.453251i
$486$	−3.42363	−	45.6851i	−0.155299	−	2.07232i
$487$	3.03944	+	0.458123i	0.137730	+	0.0207595i	0.217546	−	0.976050i	$-0.430195\pi$
$487$	3.03944	+	0.458123i	0.137730	+	0.0207595i	−0.0798152	+	0.996810i	$0.525433\pi$
$488$	5.71658	−	5.30421i	0.258777	−	0.240110i
$489$	−37.5390	+	18.0778i	−1.69757	+	0.817508i
$490$	−10.7526	−	7.33102i	−0.485755	−	0.331182i
$491$	0.599753	−	1.52815i	0.0270665	−	0.0689643i	−0.916702	−	0.399572i	$-0.869159\pi$
$491$	0.599753	−	1.52815i	0.0270665	−	0.0689643i	0.943768	+	0.330608i	$0.107254\pi$
$492$	−18.4395	−	5.68782i	−0.831316	−	0.256427i
$493$	9.25793	+	8.59010i	0.416956	+	0.386879i
$494$	16.7869	+	21.0502i	0.755280	+	0.947092i
$495$	21.2054	+	26.5907i	0.953111	+	1.19516i
$496$	−0.802105	−	0.744245i	−0.0360156	−	0.0334176i
$497$	−23.6833	−	7.30534i	−1.06234	−	0.327689i
$498$	6.54476	−	16.6758i	0.293278	−	0.747260i
$499$	28.2528	+	19.2624i	1.26477	+	0.862305i	0.994927	−	0.100599i	$-0.0320760\pi$
$499$	28.2528	+	19.2624i	1.26477	+	0.862305i	0.269843	+	0.962904i	$0.413028\pi$
$500$	−27.1952	+	13.0965i	−1.21621	+	0.585695i
$501$	28.7083	−	26.6375i	1.28259	−	1.19007i
$502$	−26.5709	−	4.00492i	−1.18592	−	0.178748i
$503$	−1.88051	−	25.0937i	−0.0838478	−	1.11887i	−0.867422	−	0.497573i	$-0.834225\pi$
$503$	−1.88051	−	25.0937i	−0.0838478	−	1.11887i	0.783574	−	0.621298i	$-0.213394\pi$
$504$	−10.6861	−	27.2277i	−0.475996	−	1.21282i
$505$	0.0525544	−	0.230256i	0.00233864	−	0.0102463i
$506$	−3.55152	+	47.3917i	−0.157884	+	2.10682i
$507$	2.97298	−	0.917044i	0.132035	−	0.0407273i
$508$	−20.4492	−	9.84782i	−0.907287	−	0.436926i
$509$	−2.57282	−	4.45626i	−0.114038	−	0.197520i	0.803357	−	0.595498i	$-0.203045\pi$
$509$	−2.57282	−	4.45626i	−0.114038	−	0.197520i	−0.917395	+	0.397978i	$0.869712\pi$
$510$	−18.5084	+	32.0575i	−0.819566	+	1.41953i
$511$	15.1121	−	10.3033i	0.668521	−	0.455790i
$512$	−1.28925	−	5.64858i	−0.0569774	−	0.249634i
$513$	−11.6434	+	1.75496i	−0.514070	+	0.0774835i
$514$	35.8438	−	44.9468i	1.58100	−	1.98252i
$515$	36.5167			1.60912
$516$	1.56452	−	59.2551i	0.0688743	−	2.60856i
$517$	3.65084			0.160564
$518$	−10.9730	+	13.7597i	−0.482126	+	0.604567i
$519$	−9.54593	+	1.43882i	−0.419020	+	0.0631571i
$520$	−6.06446	−	26.5702i	−0.265944	−	1.16518i
$521$	−19.7648	+	13.4754i	−0.865910	+	0.590367i	−0.912742	−	0.408535i	$-0.866040\pi$
$521$	−19.7648	+	13.4754i	−0.865910	+	0.590367i	0.0468326	+	0.998903i	$0.485087\pi$
$522$	26.8336	−	46.4771i	1.17447	−	2.03425i
$523$	15.5493	+	26.9322i	0.679925	+	1.17766i	0.975003	+	0.222192i	$0.0713211\pi$
$523$	15.5493	+	26.9322i	0.679925	+	1.17766i	−0.295078	+	0.955473i	$0.595346\pi$
$524$	7.90494	+	3.80682i	0.345329	+	0.166302i
$525$	−8.18386	+	2.52439i	−0.357173	+	0.110173i
$526$	−0.638044	+	8.51411i	−0.0278200	+	0.371233i
$527$	1.10683	−	4.84935i	0.0482143	−	0.211241i
$528$	1.58135	+	4.02922i	0.0688195	+	0.175349i
$529$	1.51915	+	20.2716i	0.0660500	+	0.881375i
$530$	−60.4116	−	9.10558i	−2.62411	−	0.395521i
$531$	−19.3200	+	17.9263i	−0.838415	+	0.777935i
$532$	22.3172	−	10.7474i	0.967574	−	0.465959i
$533$	6.07105	+	4.13917i	0.262966	+	0.179288i
$534$	−34.2045	+	87.1518i	−1.48018	+	3.77143i
$535$	−30.6455	−	9.45288i	−1.32492	−	0.408684i
$536$	23.6289	+	21.9244i	1.02061	+	0.946992i
$537$	−3.98083	−	4.99180i	−0.171786	−	0.215412i
$538$	−32.0476	−	40.1864i	−1.38167	−	1.73256i
$539$	−5.07095	−	4.70515i	−0.218421	−	0.202665i
$540$	28.2866	+	8.72525i	1.21726	+	0.375475i
$541$	14.4954	−	36.9338i	0.623208	−	1.58791i	−0.174363	−	0.984681i	$-0.555787\pi$
$541$	14.4954	−	36.9338i	0.623208	−	1.58791i	0.797571	−	0.603226i	$-0.206118\pi$
$542$	−13.9414	−	9.50505i	−0.598832	−	0.408277i
$543$	−31.6932	+	15.2626i	−1.36008	+	0.654982i
$544$	8.63746	−	8.01439i	0.370328	−	0.343614i
$545$	36.2325	+	5.46116i	1.55203	+	0.233931i
$546$	3.51288	+	46.8761i	0.150337	+	2.00611i
$547$	−11.8825	−	30.2760i	−0.508057	−	1.29451i	−0.923049	−	0.384683i	$-0.874311\pi$
$547$	−11.8825	−	30.2760i	−0.508057	−	1.29451i	0.414991	−	0.909825i	$-0.363785\pi$
$548$	−2.80413	+	12.2857i	−0.119786	+	0.524819i
$549$	0.801818	−	10.6995i	0.0342208	−	0.456644i
$550$	10.0055	−	3.08628i	0.426635	−	0.131599i
$551$	16.4873	+	7.93987i	0.702383	+	0.338250i
$552$	27.7025	+	47.9822i	1.17910	+	2.04226i
$553$	−10.7349	+	18.5935i	−0.456496	+	0.790674i
$554$	−14.0922	+	9.60789i	−0.598720	+	0.408200i
$555$	−5.30878	−	23.2593i	−0.225345	−	0.987302i
$556$	60.6458	−	9.14088i	2.57195	−	0.387660i
$557$	1.95247	−	2.44832i	0.0827289	−	0.103739i	−0.738745	−	0.673986i	$-0.764581\pi$
$557$	1.95247	−	2.44832i	0.0827289	−	0.103739i	0.821473	+	0.570247i	$0.193152\pi$
$558$	−21.1369			−0.894794
$559$	−7.21987	+	21.3851i	−0.305368	+	0.904493i
$560$	−2.85264			−0.120546
$561$	−12.2680	+	15.3836i	−0.517955	+	0.649495i
$562$	−43.7310	+	6.59139i	−1.84468	+	0.278041i
$563$	6.72355	+	29.4578i	0.283364	+	1.24150i	0.893450	+	0.449163i	$0.148278\pi$
$563$	6.72355	+	29.4578i	0.283364	+	1.24150i	−0.610086	+	0.792335i	$0.708865\pi$
$564$	8.73390	−	5.95467i	0.367764	−	0.250737i
$565$	15.5039	−	26.8535i	0.652252	−	1.12973i
$566$	22.8941	+	39.6538i	0.962312	+	1.66677i
$567$	6.83684	+	3.29245i	0.287120	+	0.138270i
$568$	33.7562	−	10.4124i	1.41638	−	0.436895i
$569$	0.616751	−	8.22997i	0.0258555	−	0.345018i	−0.969241	−	0.246112i	$-0.920847\pi$
$569$	0.616751	−	8.22997i	0.0258555	−	0.345018i	0.995097	−	0.0989057i	$-0.0315342\pi$
$570$	−11.9352	+	52.2917i	−0.499912	+	2.19026i
$571$	−10.6006	−	27.0098i	−0.443620	−	1.13033i	−0.961484	−	0.274862i	$-0.911368\pi$
$571$	−10.6006	−	27.0098i	−0.443620	−	1.13033i	0.517864	−	0.855463i	$-0.326727\pi$
$572$	−2.68869	−	35.8781i	−0.112420	−	1.50014i
$573$	9.97933	+	1.50414i	0.416892	+	0.0628364i
$574$	7.91558	−	7.34459i	0.330390	−	0.306557i
$575$	8.60080	−	4.14192i	0.358678	−	0.172730i
$576$	−45.0099	−	30.6872i	−1.87541	−	1.27864i
$577$	−5.97389	+	15.2212i	−0.248696	+	0.633668i	−0.999644	−	0.0266942i	$-0.991502\pi$
$577$	−5.97389	+	15.2212i	−0.248696	+	0.633668i	0.750947	+	0.660362i	$0.229597\pi$
$578$	25.5256	+	7.87360i	1.06172	+	0.327499i
$579$	−31.7989	−	29.5051i	−1.32152	−	1.22619i
$580$	−28.6832	−	35.9676i	−1.19101	−	1.49347i
$581$	3.91279	+	4.90648i	0.162330	+	0.203555i
$582$	19.3246	+	17.9306i	0.801029	+	0.743247i
$583$	−31.0318	−	9.57205i	−1.28521	−	0.396434i
$584$	−9.52421	+	24.2673i	−0.394115	+	1.00419i
$585$	−30.9818	−	21.1230i	−1.28094	−	0.873329i
$586$	22.8730	−	11.0151i	0.944876	−	0.455028i
$587$	17.5967	−	16.3274i	0.726294	−	0.673902i	−0.227699	−	0.973732i	$-0.573120\pi$
$587$	17.5967	−	16.3274i	0.726294	−	0.673902i	0.953993	+	0.299830i	$0.0969298\pi$
$588$	−19.8055	−	2.98520i	−0.816766	−	0.123108i
$589$	−0.538601	−	7.18714i	−0.0221927	−	0.296141i
$590$	13.1844	+	33.5934i	0.542795	+	1.38302i
$591$	−12.1488	+	53.2275i	−0.499736	+	2.18949i
$592$	0.133517	−	1.78166i	0.00548752	−	0.0732259i
$593$	39.7443	−	12.2595i	1.63210	−	0.503438i	0.662695	−	0.748889i	$-0.269412\pi$
$593$	39.7443	−	12.2595i	1.63210	−	0.503438i	0.969409	+	0.245451i	$0.0789362\pi$
$594$	22.6450	+	10.9053i	0.929138	+	0.447449i
$595$	−6.48381	−	11.2303i	−0.265810	−	0.460397i
$596$	20.4461	−	35.4136i	0.837504	−	1.45060i
$597$	20.7042	−	14.1159i	0.847367	−	0.577725i
$598$	−11.6593	−	51.0828i	−0.476785	−	2.08893i
$599$	16.5902	−	2.50057i	0.677856	−	0.102170i	0.198914	−	0.980017i	$-0.436259\pi$
$599$	16.5902	−	2.50057i	0.677856	−	0.102170i	0.478942	+	0.877847i	$0.341020\pi$
$600$	7.61087	−	9.54373i	0.310713	−	0.389621i
$601$	3.26297			0.133099			0.0665496	−	0.997783i	$-0.478801\pi$
$601$	3.26297			0.133099			0.0665496	+	0.997783i	$0.478801\pi$
$602$	28.2780	+	17.3372i	1.15252	+	0.706612i
$603$	44.3495			1.80605
$604$	−17.7171	+	22.2165i	−0.720898	+	0.903978i
$605$	−3.14707	+	0.474344i	−0.127947	+	0.0192848i
$606$	−0.129201	−	0.566067i	−0.00524844	−	0.0229949i
$607$	29.4413	−	20.0727i	1.19499	−	0.814728i	0.208412	−	0.978041i	$-0.433171\pi$
$607$	29.4413	−	20.0727i	1.19499	−	0.814728i	0.986574	+	0.163314i	$0.0522182\pi$
$608$	8.53655	−	14.7857i	0.346203	−	0.599641i
$609$	15.9748	+	27.6692i	0.647332	+	1.12121i
$610$	−13.2368	−	6.37449i	−0.535941	−	0.258095i
$611$	−3.84627	+	1.18642i	−0.155604	+	0.0479973i
$612$	−2.50527	+	33.4305i	−0.101269	+	1.35135i
$613$	−4.85086	+	21.2530i	−0.195924	+	0.858400i	0.777407	+	0.628997i	$0.216534\pi$
$613$	−4.85086	+	21.2530i	−0.195924	+	0.858400i	−0.973332	+	0.229403i	$0.926323\pi$
$614$	0.683961	+	1.74270i	0.0276024	+	0.0703298i
$615$	1.09389	+	14.5969i	0.0441097	+	0.588603i
$616$	−21.0513	−	3.17297i	−0.848180	−	0.127843i
$617$	−7.66377	+	7.11094i	−0.308532	+	0.286276i	−0.819207	−	0.573498i	$-0.805586\pi$
$617$	−7.66377	+	7.11094i	−0.308532	+	0.286276i	0.510675	+	0.859774i	$0.329396\pi$
$618$	80.8831	−	38.9512i	3.25360	−	1.56685i
$619$	−29.4072	−	20.0495i	−1.18197	−	0.805856i	−0.197313	−	0.980340i	$-0.563222\pi$
$619$	−29.4072	−	20.0495i	−1.18197	−	0.805856i	−0.984660	+	0.174485i	$0.944174\pi$
$620$	−6.61955	+	16.8663i	−0.265848	+	0.677368i
$621$	21.8969	+	6.75429i	0.878691	+	0.271040i
$622$	−18.4749	−	17.1422i	−0.740776	−	0.687340i
$623$	−20.4492	−	25.6425i	−0.819280	−	1.02734i
$624$	−2.97538	−	3.73101i	−0.119111	−	0.149360i
$625$	22.1001	+	20.5059i	0.884002	+	0.820234i
$626$	−35.5429	−	10.9635i	−1.42058	−	0.438191i
$627$	−10.4161	+	26.5397i	−0.415978	+	1.05989i
$628$	55.2237	+	37.6509i	2.20366	+	1.50243i
$629$	7.31755	−	3.52395i	0.291770	−	0.140509i
$630$	−40.3947	+	37.4808i	−1.60936	+	1.49327i
$631$	2.47757	+	0.373434i	0.0986307	+	0.0148662i	0.198172	−	0.980167i	$-0.436499\pi$
$631$	2.47757	+	0.373434i	0.0986307	+	0.0148662i	−0.0995415	+	0.995033i	$0.531738\pi$
$632$	−2.28684	−	30.5157i	−0.0909655	−	1.21385i
$633$	9.96172	+	25.3820i	0.395943	+	1.00885i
$634$	−0.690473	+	3.02516i	−0.0274222	+	0.120145i
$635$	−1.28663	+	17.1689i	−0.0510584	+	0.681327i
$636$	−89.8498	+	27.7150i	−3.56278	+	1.09897i
$637$	6.87144	+	3.30911i	0.272256	+	0.131112i
$638$	−19.5306	−	33.8280i	−0.773223	−	1.33926i
$639$	24.3018	−	42.0920i	0.961365	−	1.66513i
$640$	−40.4470	+	27.5763i	−1.59881	+	1.09005i
$641$	4.07453	+	17.8517i	0.160934	+	0.705099i	0.989419	+	0.145087i	$0.0463462\pi$
$641$	4.07453	+	17.8517i	0.160934	+	0.705099i	−0.828485	+	0.560012i	$0.810797\pi$
$642$	−77.9618	+	11.7508i	−3.07691	+	0.463769i
$643$	−24.5104	+	30.7351i	−0.966596	+	1.21207i	0.0106459	+	0.999943i	$0.496611\pi$
$643$	−24.5104	+	30.7351i	−0.966596	+	1.21207i	−0.977242	+	0.212129i	$0.931960\pi$
$644$	−48.2048			−1.89953
$645$	−42.2751	+	15.3168i	−1.66458	+	0.603100i
$646$	−18.2596			−0.718415
$647$	−12.5557	+	15.7443i	−0.493615	+	0.618973i	−0.964776	−	0.263074i	$-0.915264\pi$
$647$	−12.5557	+	15.7443i	−0.493615	+	0.618973i	0.471161	+	0.882047i	$0.343835\pi$
$648$	−10.6949	+	1.61200i	−0.420137	+	0.0633254i
$649$	4.26854	+	18.7017i	0.167555	+	0.734105i
$650$	−9.53813	+	6.50298i	−0.374116	+	0.255068i
$651$	6.29169	−	10.8975i	0.246591	−	0.427108i
$652$	25.8342	+	44.7461i	1.01174	+	1.75239i
$653$	15.7461	+	7.58290i	0.616191	+	0.296742i	0.715822	−	0.698283i	$-0.246052\pi$
$653$	15.7461	+	7.58290i	0.616191	+	0.296742i	−0.0996314	+	0.995024i	$0.531766\pi$
$654$	86.0788	−	26.5518i	3.36595	−	1.03826i
$655$	0.497366	−	6.63688i	0.0194337	−	0.259324i
$656$	−0.243930	+	1.06873i	−0.00952385	+	0.0417267i
$657$	13.1041	+	33.3887i	0.511240	+	1.30262i
$658$	0.442040	+	5.89861i	0.0172325	+	0.229952i
$659$	−21.9925	−	3.31483i	−0.856705	−	0.129128i	−0.294021	−	0.955799i	$-0.594993\pi$
$659$	−21.9925	−	3.31483i	−0.856705	−	0.129128i	−0.562685	+	0.826672i	$0.690231\pi$
$660$	52.5410	−	48.7509i	2.04515	−	1.89763i
$661$	32.1228	−	15.4695i	1.24943	−	0.601695i	0.312073	−	0.950058i	$-0.398977\pi$
$661$	32.1228	−	15.4695i	1.24943	−	0.601695i	0.937360	+	0.348364i	$0.113263\pi$
$662$	59.3251	+	40.4472i	2.30574	+	1.57202i
$663$	7.92549	−	20.1938i	0.307800	−	0.784263i
$664$	−8.54735	−	2.63651i	−0.331702	−	0.102316i
$665$	−13.7739	−	12.7803i	−0.534128	−	0.495599i
$666$	−21.5186	−	26.9835i	−0.833830	−	1.04559i
$667$	−22.2039	−	27.8428i	−0.859739	−	1.07808i
$668$	−35.6008	−	33.0327i	−1.37743	−	1.27807i
$669$	27.6527	+	8.52971i	1.06911	+	0.329778i
$670$	22.1860	−	56.5289i	0.857118	−	2.18390i
$671$	−6.45242	−	4.39918i	−0.249093	−	0.169829i
$672$	26.8564	−	12.9334i	1.03601	−	0.498915i
$673$	−36.7476	+	34.0968i	−1.41652	+	1.31434i	−0.532858	+	0.846205i	$0.678882\pi$
$673$	−36.7476	+	34.0968i	−1.41652	+	1.31434i	−0.883659	+	0.468131i	$0.844927\pi$
$674$	40.2202	+	6.06222i	1.54923	+	0.233508i
$675$	−0.377285	−	5.03452i	−0.0145217	−	0.193779i
$676$	−1.40954	−	3.59145i	−0.0542132	−	0.138133i
$677$	−4.39828	+	19.2701i	−0.169040	+	0.740611i	0.817344	+	0.576150i	$0.195446\pi$
$677$	−4.39828	+	19.2701i	−0.169040	+	0.740611i	−0.986384	+	0.164461i	$0.947412\pi$
$678$	5.69668	−	76.0169i	0.218780	−	2.91941i
$679$	−8.82471	+	2.72206i	−0.338661	+	0.104463i
$680$	16.6526	+	8.01945i	0.638596	+	0.307532i
$681$	−22.9365	−	39.7272i	−0.878928	−	1.52235i
$682$	−7.69214	+	13.3232i	−0.294547	+	0.510171i
$683$	−29.2387	+	19.9346i	−1.11879	+	0.762776i	−0.973969	−	0.226682i	$-0.927212\pi$
$683$	−29.2387	+	19.9346i	−1.11879	+	0.762776i	−0.144819	+	0.989458i	$0.546260\pi$
$684$	10.8091	+	47.3579i	0.413297	+	1.81077i
$685$	9.45237	−	1.42471i	0.361156	−	0.0544356i
$686$	29.0647	−	36.4460i	1.10970	−	1.39152i
$687$	3.15808			0.120488
$688$	−3.36339	+	0.162924i	−0.128228	+	0.00621143i
$689$	35.8036			1.36401
$690$	65.0803	−	81.6081i	2.47756	−	3.10677i
$691$	3.92945	−	0.592270i	0.149484	−	0.0225310i	−0.0738741	−	0.997268i	$-0.523536\pi$
$691$	3.92945	−	0.592270i	0.149484	−	0.0225310i	0.223358	+	0.974737i	$0.428298\pi$
$692$	2.66390	+	11.6713i	0.101266	+	0.443677i
$693$	−24.2014	+	16.5002i	−0.919336	+	0.626793i
$694$	−12.0067	+	20.7962i	−0.455769	+	0.789415i
$695$	−23.2616	−	40.2903i	−0.882363	−	1.52830i
$696$	−41.0285	−	19.7583i	−1.55518	−	0.748937i
$697$	−4.76181	+	1.46882i	−0.180366	+	0.0556356i
$698$	−0.521452	+	6.95830i	−0.0197373	+	0.263375i
$699$	11.2202	−	49.1590i	0.424388	−	1.85937i
$700$	3.88011	+	9.88636i	0.146654	+	0.373669i
$701$	3.47305	+	46.3446i	0.131175	+	1.75041i	0.543532	+	0.839389i	$0.317087\pi$
$701$	3.47305	+	46.3446i	0.131175	+	1.75041i	−0.412356	+	0.911023i	$0.635294\pi$
$702$	−27.4012	−	4.13006i	−1.03419	−	0.155879i
$703$	8.62684	−	8.00454i	0.325368	−	0.301897i
$704$	−35.7231	+	17.2033i	−1.34636	+	0.648375i
$705$	−6.62521	−	4.51699i	−0.249520	−	0.170120i
$706$	23.0500	−	58.7305i	0.867500	−	2.21035i
$707$	0.194366	+	0.0599540i	0.00730989	+	0.00225480i
$708$	40.7148	+	37.7779i	1.53016	+	1.41978i
$709$	−3.25494	−	4.08156i	−0.122242	−	0.153286i	0.716945	−	0.697130i	$-0.245540\pi$
$709$	−3.25494	−	4.08156i	−0.122242	−	0.153286i	−0.839187	+	0.543844i	$0.816968\pi$
$710$	−41.4944	−	52.0323i	−1.55726	−	1.95274i
$711$	−30.8641	−	28.6377i	−1.15749	−	1.07400i
$712$	44.6706	+	13.7790i	1.67410	+	0.516391i
$713$	−5.12425	+	13.0564i	−0.191905	+	0.488965i
$714$	−26.3404	−	17.9586i	−0.985766	−	0.672084i
$715$	−24.5893	+	11.8416i	−0.919589	+	0.442851i
$716$	−5.80404	+	5.38536i	−0.216907	+	0.201260i
$717$	42.3415	+	6.38195i	1.58127	+	0.238338i
$718$	1.91711	+	25.5820i	0.0715459	+	0.954713i
$719$	−12.3995	−	31.5934i	−0.462424	−	1.17824i	−0.951951	−	0.306249i	$-0.900926\pi$
$719$	−12.3995	−	31.5934i	−0.462424	−	1.17824i	0.489528	−	0.871988i	$-0.337169\pi$
$720$	1.24482	−	5.45391i	0.0463917	−	0.203255i
$721$	−2.35020	+	31.3613i	−0.0875261	+	1.16795i
$722$	16.7049	−	5.15277i	0.621690	−	0.191766i
$723$	−7.48491	−	3.60454i	−0.278367	−	0.134054i
$724$	21.8111	+	37.7779i	0.810602	+	1.40400i
$725$	−3.92306	+	6.79495i	−0.145699	+	0.252358i
$726$	−6.46467	+	4.40754i	−0.239927	+	0.163579i
$727$	−2.58485	−	11.3250i	−0.0958667	−	0.420020i	0.904107	−	0.427307i	$-0.140538\pi$
$727$	−2.58485	−	11.3250i	−0.0958667	−	0.420020i	−0.999973	+	0.00728718i	$0.997680\pi$
$728$	23.2093	−	3.49824i	0.860194	−	0.129653i
$729$	−26.8586	+	33.6796i	−0.994762	+	1.24739i
$730$	49.1135			1.81777
$731$	−8.28611	−	12.8707i	−0.306473	−	0.476040i
$732$	−22.6114			−0.835740
$733$	−15.6208	+	19.5879i	−0.576969	+	0.723496i	−0.981592	−	0.190987i	$-0.938831\pi$
$733$	−15.6208	+	19.5879i	−0.576969	+	0.723496i	0.404624	+	0.914483i	$0.367402\pi$
$734$	−62.5302	+	9.42491i	−2.30803	+	0.347880i
$735$	3.38086	+	14.8125i	0.124705	+	0.546367i
$736$	−27.4522	+	18.7166i	−1.01190	+	0.689904i
$737$	16.1397	−	27.9547i	0.594513	−	1.02973i
$738$	10.5878	+	18.3387i	0.389744	+	0.675056i
$739$	34.3378	+	16.5362i	1.26314	+	0.608294i	0.941002	−	0.338400i	$-0.109886\pi$
$739$	34.3378	+	16.5362i	1.26314	+	0.608294i	0.322134	+	0.946694i	$0.395600\pi$
$740$	−28.2709	+	8.72040i	−1.03926	+	0.320568i
$741$	2.34901	−	31.3453i	0.0862929	−	1.15150i
$742$	11.7081	−	51.2967i	0.429819	−	1.88316i
$743$	11.6235	+	29.6163i	0.426426	+	1.08652i	0.969121	+	0.246586i	$0.0793089\pi$
$743$	11.6235	+	29.6163i	0.426426	+	1.08652i	−0.542694	+	0.839930i	$0.682596\pi$
$744$	1.34030	+	17.8851i	0.0491380	+	0.655700i
$745$	−30.6728	−	4.62318i	−1.12376	−	0.169380i
$746$	1.82756	−	1.69573i	0.0669118	−	0.0620851i
$747$	−11.0881	+	5.33974i	−0.405692	+	0.195371i
$748$	20.1605	+	13.7452i	0.737140	+	0.502573i
$749$	10.0907	−	25.7106i	0.368705	−	0.939445i
$750$	53.7892	+	16.5918i	1.96410	+	0.605846i
$751$	4.15240	+	3.85286i	0.151523	+	0.140593i	0.752292	−	0.658830i	$-0.228948\pi$
$751$	4.15240	+	3.85286i	0.151523	+	0.140593i	−0.600769	+	0.799423i	$0.705139\pi$
$752$	−0.374405	−	0.469488i	−0.0136531	−	0.0171205i
$753$	19.5596	+	24.5270i	0.712792	+	0.893813i
$754$	31.5692	+	29.2919i	1.14968	+	1.06675i
$755$	20.5977	+	6.35354i	0.749626	+	0.231229i
$756$	−9.31394	+	23.7315i	−0.338745	+	0.863108i
$757$	−28.1860	−	19.2169i	−1.02444	−	0.698450i	−0.0702110	−	0.997532i	$-0.522367\pi$
$757$	−28.1860	−	19.2169i	−1.02444	−	0.698450i	−0.954227	+	0.299082i	$0.903320\pi$
$758$	−6.29969	+	3.03377i	−0.228815	+	0.110192i
$759$	40.6724	−	37.7385i	1.47631	−	1.36982i
$760$	26.4822	+	3.99155i	0.960611	+	0.144789i
$761$	−0.366937	−	4.89643i	−0.0133014	−	0.177495i	−0.999898	−	0.0143142i	$-0.995443\pi$
$761$	−0.366937	−	4.89643i	−0.0133014	−	0.177495i	0.986596	−	0.163181i	$-0.0521756\pi$
$762$	15.4637	+	39.4009i	0.560191	+	1.42734i
$763$	−7.02207	+	30.7657i	−0.254216	+	1.11379i
$764$	0.935246	−	12.4800i	0.0338360	−	0.451510i
$765$	24.3004	−	7.49568i	0.878583	−	0.271007i
$766$	42.0085	+	20.2302i	1.51783	+	0.730948i
$767$	−10.5745	−	18.3157i	−0.381825	−	0.661340i
$768$	−25.8850	+	44.8342i	−0.934045	+	1.61781i
$769$	−25.1259	+	17.1305i	−0.906062	+	0.617742i	−0.924123	−	0.382095i	$-0.875203\pi$
$769$	−25.1259	+	17.1305i	−0.906062	+	0.617742i	0.0180616	+	0.999837i	$0.494250\pi$
$770$	8.92478	+	39.1020i	0.321627	+	1.40914i
$771$	−66.3672	+	10.0032i	−2.39016	+	0.360258i
$772$	−33.5396	+	42.0573i	−1.20712	+	1.51368i
$773$	−30.0965			−1.08250			−0.541248	−	0.840863i	$-0.682048\pi$
$773$	−30.0965			−1.08250			−0.541248	+	0.840863i	$0.682048\pi$
$774$	−45.4866	+	46.4987i	−1.63498	+	1.67136i
$775$	3.09020			0.111003
$776$	8.20686	−	10.2911i	0.294609	−	0.369428i
$777$	20.3172	−	3.06233i	0.728877	−	0.109860i
$778$	−4.68654	−	20.5331i	−0.168020	−	0.736146i
$779$	−5.96588	+	4.06747i	−0.213750	+	0.145732i
$780$	−39.5109	+	68.4349i	−1.41472	+	2.45036i
$781$	−17.6879	−	30.6363i	−0.632921	−	1.09625i
$782$	32.0156	+	15.4179i	1.14487	+	0.551343i
$783$	−17.9974	+	5.55145i	−0.643173	+	0.198393i
$784$	−0.0850294	+	1.13464i	−0.00303676	+	0.0405228i
$785$	11.2819	−	49.4292i	0.402668	−	1.76420i
$786$	−5.97772	−	15.2310i	−0.213218	−	0.543271i
$787$	−1.07726	−	14.3750i	−0.0384001	−	0.512413i	−0.982929	−	0.183985i	$-0.941100\pi$
$787$	−1.07726	−	14.3750i	−0.0384001	−	0.512413i	0.944529	−	0.328428i	$-0.106519\pi$
$788$	66.9478	+	10.0908i	2.38492	+	0.359468i
$789$	7.30695	−	6.77986i	0.260134	−	0.241370i
$790$	−51.9421	+	25.0140i	−1.84802	+	0.889959i
$791$	22.0645	+	15.0433i	0.784523	+	0.534878i
$792$	15.2526	−	38.8630i	0.541978	−	1.38094i
$793$	8.22743	+	2.53783i	0.292165	+	0.0901209i
$794$	−40.3700	−	37.4579i	−1.43268	−	1.32933i
$795$	44.4707	+	55.7645i	1.57721	+	1.97776i
$796$	−19.3746	−	24.2950i	−0.686715	−	0.861114i
$797$	−24.4960	−	22.7290i	−0.867695	−	0.805103i	0.114411	−	0.993433i	$-0.463502\pi$
$797$	−24.4960	−	22.7290i	−0.867695	−	0.805103i	−0.982106	+	0.188331i	$0.939692\pi$
$798$	−44.1410	−	13.6157i	−1.56258	−	0.481991i
$799$	0.997296	−	2.54107i	0.0352818	−	0.0898966i
$800$	6.04830	+	4.12366i	0.213840	+	0.145793i
$801$	57.9490	−	27.9068i	2.04753	−	0.986038i
$802$	9.99670	−	9.27558i	0.352996	−	0.327532i
$803$	25.8147	+	3.89095i	0.910982	+	0.137309i
$804$	−6.98442	−	93.2006i	−0.246321	−	3.28693i
$805$	13.3592	+	34.0387i	0.470849	+	1.19970i
$806$	3.77426	−	16.5361i	0.132943	−	0.582459i
$807$	−4.48444	+	59.8407i	−0.157860	+	2.10649i
$808$	−0.277033	+	0.0854533i	−0.00974598	+	0.00300624i
$809$	−3.32419	−	1.60085i	−0.116872	−	0.0562828i	0.374534	−	0.927213i	$-0.377803\pi$
$809$	−3.32419	−	1.60085i	−0.116872	−	0.0562828i	−0.491406	+	0.870930i	$0.663517\pi$
$810$	10.1882	+	17.6464i	0.357976	+	0.620033i
$811$	−5.57112	+	9.64946i	−0.195628	+	0.338838i	−0.947106	−	0.320920i	$-0.896008\pi$
$811$	−5.57112	+	9.64946i	−0.195628	+	0.338838i	0.751478	+	0.659758i	$0.229341\pi$
$812$	32.7358	−	22.3189i	1.14880	−	0.783238i
$813$	4.38346	+	19.2052i	0.153735	+	0.673555i
$814$	−24.8396	+	3.74396i	−0.870626	+	0.131226i
$815$	24.4368	−	30.6428i	0.855985	−	1.07337i
$816$	3.23641			0.113297
$817$	−16.9700	−	14.2819i	−0.593704	−	0.499659i
$818$	−64.8663			−2.26800
$819$	20.1348	−	25.2483i	0.703568	−	0.882247i
$820$	17.9494	−	2.70543i	0.626819	−	0.0944778i
$821$	−4.85328	−	21.2636i	−0.169381	−	0.742105i	−0.986247	−	0.165278i	$-0.947148\pi$
$821$	−4.85328	−	21.2636i	−0.169381	−	0.742105i	0.816866	−	0.576827i	$-0.195709\pi$
$822$	19.4169	−	13.2382i	0.677244	−	0.461737i
$823$	1.16937	−	2.02540i	0.0407616	−	0.0706011i	−0.844925	−	0.534885i	$-0.820355\pi$
$823$	1.16937	−	2.02540i	0.0407616	−	0.0706011i	0.885686	+	0.464284i	$0.153688\pi$
$824$	−22.4125	−	38.8196i	−0.780776	−	1.35234i
$825$	−11.0136	−	5.30388i	−0.383445	−	0.184657i
$826$	−29.6992	+	9.16100i	−1.03337	+	0.318752i
$827$	−0.0250877	+	0.334773i	−0.000872386	+	0.0116412i	−0.997623	−	0.0689082i	$-0.978048\pi$
$827$	−0.0250877	+	0.334773i	−0.000872386	+	0.0116412i	0.996751	+	0.0805494i	$0.0256675\pi$
$828$	21.0354	−	92.1620i	0.731030	−	3.20285i
$829$	−17.8696	−	45.5310i	−0.620637	−	1.58136i	−0.801595	−	0.597867i	$-0.796015\pi$
$829$	−17.8696	−	45.5310i	−0.620637	−	1.58136i	0.180958	−	0.983491i	$-0.442080\pi$
$830$	1.25931	+	16.8044i	0.0437114	+	0.583288i
$831$	19.6898	+	2.96776i	0.683032	+	0.102950i
$832$	32.0448	−	29.7332i	1.11095	−	1.03081i
$833$	−4.66012	+	2.24420i	−0.161464	+	0.0777568i
$834$	−94.5001	−	64.4291i	−3.27227	−	2.23100i
$835$	−13.4590	+	34.2931i	−0.465770	+	1.18676i
$836$	33.7847	+	10.4212i	1.16847	+	0.360425i
$837$	5.43765	+	5.04540i	0.187953	+	0.174395i
$838$	26.9160	+	33.7516i	0.929797	+	1.16593i
$839$	5.83338	+	7.31482i	0.201391	+	0.252536i	0.872263	−	0.489037i	$-0.162652\pi$
$839$	5.83338	+	7.31482i	0.201391	+	0.252536i	−0.670873	+	0.741573i	$0.734080\pi$
$840$	34.2762	+	31.8037i	1.18264	+	1.09733i
$841$	0.258262	+	0.0796631i	0.00890557	+	0.00274701i
$842$	−25.1544	+	64.0924i	−0.866879	+	2.20877i
$843$	42.6599	+	29.0850i	1.46928	+	1.00174i
$844$	30.4647	−	14.6710i	1.04864	−	0.504997i
$845$	−2.14539	+	1.99063i	−0.0738036	+	0.0684797i
$846$	−11.4704	−	1.72888i	−0.394359	−	0.0594401i
$847$	−0.204832	−	2.73330i	−0.00703812	−	0.0939172i
$848$	1.95146	+	4.97225i	0.0670136	+	0.170748i
$849$	11.8952	−	52.1162i	0.408242	−	1.78862i
$850$	0.585063	−	7.80712i	0.0200675	−	0.267782i
$851$	−21.8847	+	6.75054i	−0.750198	+	0.231405i
$852$	−92.2837	−	44.4415i	−3.16159	−	1.52254i
$853$	−0.941402	−	1.63056i	−0.0322330	−	0.0558292i	0.849459	−	0.527655i	$-0.176929\pi$
$853$	−0.941402	−	1.63056i	−0.0322330	−	0.0558292i	−0.881692	+	0.471826i	$0.843595\pi$
$854$	6.32645	−	10.9577i	0.216487	−	0.374966i
$855$	30.4451	−	20.7571i	1.04120	−	0.709877i
$856$	8.75997	+	38.3799i	0.299410	+	1.31180i
$857$	46.5499	−	7.01627i	1.59011	−	0.239671i	0.706440	−	0.707773i	$-0.250300\pi$
$857$	46.5499	−	7.01627i	1.59011	−	0.239671i	0.883674	+	0.468102i	$0.155062\pi$
$858$	−41.8334	+	52.4574i	−1.42817	+	1.79087i
$859$	22.8236			0.778731			0.389365	−	0.921083i	$-0.372694\pi$
$859$	22.8236			0.778731			0.389365	+	0.921083i	$0.372694\pi$
$860$	22.8588	+	50.8587i	0.779477	+	1.73427i
$861$	−12.6065			−0.429628
$862$	7.21838	−	9.05157i	0.245859	−	0.308298i
$863$	5.87122	−	0.884945i	0.199859	−	0.0301239i	−0.0483498	−	0.998830i	$-0.515396\pi$
$863$	5.87122	−	0.884945i	0.199859	−	0.0301239i	0.248209	+	0.968707i	$0.420158\pi$
$864$	3.91010	+	17.1313i	0.133024	+	0.582818i
$865$	7.50316	−	5.11557i	0.255115	−	0.173935i
$866$	−13.4811	+	23.3500i	−0.458107	+	0.793464i
$867$	−15.5930	−	27.0078i	−0.529565	−	0.917233i
$868$	−14.0591	−	6.77052i	−0.477198	−	0.229806i
$869$	−29.2832	+	9.03268i	−0.993366	+	0.306413i
$870$	−6.41124	+	85.5521i	−0.217361	+	2.90049i
$871$	−7.91916	+	34.6961i	−0.268331	+	1.17563i
$872$	−16.4325	−	41.8693i	−0.556474	−	1.41787i
$873$	−1.35339	−	18.0597i	−0.0458052	−	0.611228i
$874$	50.9137	+	7.67401i	1.72218	+	0.259577i
$875$	−14.4553	+	13.4126i	−0.488679	+	0.453428i
$876$	68.1029	−	32.7966i	2.30098	−	1.10810i
$877$	−0.815608	−	0.556072i	−0.0275411	−	0.0187772i	0.549471	−	0.835513i	$-0.314829\pi$
$877$	−0.815608	−	0.556072i	−0.0275411	−	0.0187772i	−0.577012	+	0.816735i	$0.695782\pi$
$878$	1.32162	−	3.36744i	0.0446026	−	0.113646i
$879$	−28.3220	−	8.73618i	−0.955278	−	0.294664i
$880$	−2.98474	−	2.76944i	−0.100616	−	0.0933577i
$881$	12.4472	+	15.6083i	0.419357	+	0.525857i	0.945973	−	0.324247i	$-0.105111\pi$
$881$	12.4472	+	15.6083i	0.419357	+	0.525857i	−0.526616	+	0.850103i	$0.676539\pi$
$882$	13.7040	+	17.1842i	0.461437	+	0.578624i
$883$	−0.936091	−	0.868565i	−0.0315020	−	0.0292296i	0.664265	−	0.747497i	$-0.268745\pi$
$883$	−0.936091	−	0.868565i	−0.0315020	−	0.0292296i	−0.695767	+	0.718268i	$0.744935\pi$
$884$	−25.7065	−	7.92939i	−0.864602	−	0.266694i
$885$	15.3925	−	39.2193i	0.517412	−	1.31834i
$886$	21.2106	+	14.4612i	0.712586	+	0.485833i
$887$	6.00791	−	2.89326i	0.201726	−	0.0971460i	−0.330293	−	0.943878i	$-0.607148\pi$
$887$	6.00791	−	2.89326i	0.201726	−	0.0971460i	0.532019	+	0.846732i	$0.321433\pi$
$888$	−21.4678	+	19.9192i	−0.720413	+	0.668445i
$889$	−14.6622	−	2.20997i	−0.491754	−	0.0741200i
$890$	−6.58148	−	87.8237i	−0.220612	−	2.94386i
$891$	3.95704	+	10.0824i	0.132566	+	0.337772i
$892$	7.98537	−	34.9862i	0.267370	−	1.17142i
$893$	0.295585	−	3.94431i	0.00989138	−	0.131991i
$894$	−72.8705	+	22.4776i	−2.43716	+	0.751763i
$895$	5.41124	+	2.60591i	0.180878	+	0.0871061i
$896$	−21.0799	−	36.5115i	−0.704231	−	1.21976i
$897$	−30.5857	+	52.9760i	−1.02123	+	1.76882i
$898$	53.0553	−	36.1725i	1.77048	−	1.20709i
$899$	−2.56525	−	11.2391i	−0.0855558	−	0.374844i
$900$	−20.5948	+	3.10416i	−0.686492	+	0.103472i
$901$	−15.1393	+	18.9841i	−0.504363	+	0.632451i
$902$	15.4125			0.513181
$903$	−10.4336	−	37.2925i	−0.347209	−	1.24102i
$904$	−38.0626			−1.26594
$905$	20.6314	−	25.8709i	0.685809	−	0.859978i
$906$	52.4002	−	7.89806i	1.74088	−	0.262396i
$907$	1.34368	+	5.88707i	0.0446163	+	0.195477i	0.992324	−	0.123661i	$-0.0394637\pi$
$907$	1.34368	+	5.88707i	0.0446163	+	0.195477i	−0.947708	+	0.319138i	$0.896607\pi$
$908$	−47.0017	+	32.0452i	−1.55981	+	1.06346i
$909$	−0.199442	+	0.345444i	−0.00661507	+	0.0114576i
$910$	−22.1096	−	38.2949i	−0.732925	−	1.26946i
$911$	38.9508	+	18.7577i	1.29050	+	0.621471i	0.948067	−	0.318072i	$-0.103035\pi$
$911$	38.9508	+	18.7577i	1.29050	+	0.621471i	0.342431	+	0.939543i	$0.388750\pi$
$912$	4.48113	−	1.38225i	0.148385	−	0.0457708i
$913$	−0.669389	+	8.93238i	−0.0221536	+	0.295619i
$914$	−13.8856	+	60.8367i	−0.459294	+	2.01230i
$915$	6.26638	+	15.9665i	0.207160	+	0.527835i
$916$	−0.292664	−	3.90533i	−0.00966990	−	0.129036i
$917$	5.66788	+	0.854295i	0.187170	+	0.0282113i
$918$	13.7763	−	12.7825i	0.454684	−	0.421885i
$919$	12.2540	−	5.90124i	0.404224	−	0.194664i	−0.220714	−	0.975339i	$-0.570839\pi$
$919$	12.2540	−	5.90124i	0.404224	−	0.194664i	0.624938	+	0.780675i	$0.285124\pi$
$920$	−43.0623	−	29.3594i	−1.41972	−	0.967951i
$921$	0.798505	−	2.03456i	0.0263116	−	0.0670410i
$922$	−57.2674	−	17.6647i	−1.88600	−	0.581755i
$923$	28.5906	+	26.5282i	0.941071	+	0.873187i
$924$	38.4867	+	48.2608i	1.26612	+	1.58767i
$925$	3.14602	+	3.94499i	0.103441	+	0.129710i
$926$	17.4807	+	16.2198i	0.574453	+	0.533014i
$927$	−58.9336	−	18.1786i	−1.93563	−	0.597064i
$928$	9.97694	−	25.4208i	0.327509	−	0.834480i
$929$	8.47948	+	5.78121i	0.278203	+	0.189675i	0.694381	−	0.719608i	$-0.255678\pi$
$929$	8.47948	+	5.78121i	0.278203	+	0.189675i	−0.416178	+	0.909283i	$0.636631\pi$
$930$	30.4430	−	14.6606i	0.998267	−	0.480740i
$931$	−5.49394	+	5.09763i	−0.180056	+	0.167068i
$932$	−61.8307	−	9.31947i	−2.02533	−	0.305269i
$933$	2.19882	+	29.3412i	0.0719861	+	0.960588i
$934$	5.76680	+	14.6936i	0.188696	+	0.480788i
$935$	4.11867	−	18.0451i	0.134695	−	0.590137i
$936$	−3.43973	+	45.9001i	−0.112431	+	1.50029i
$937$	−44.1491	+	13.6182i	−1.44229	+	0.444887i	−0.914534	−	0.404509i	$-0.867443\pi$
$937$	−44.1491	+	13.6182i	−1.44229	+	0.444887i	−0.527756	+	0.849396i	$0.676966\pi$
$938$	47.1203	+	22.6919i	1.53853	+	0.740918i
$939$	21.7123	+	37.6068i	0.708554	+	1.22725i
$940$	−4.97182	+	8.61144i	−0.162163	+	0.280874i
$941$	−19.4037	+	13.2292i	−0.632542	+	0.431260i	−0.836687	−	0.547681i	$-0.815511\pi$
$941$	−19.4037	+	13.2292i	−0.632542	+	0.431260i	0.204145	+	0.978941i	$0.434559\pi$
$942$	−27.7357	−	121.518i	−0.903677	−	3.95927i
$943$	13.8948	−	2.09430i	0.452476	−	0.0681997i
$944$	1.96724	−	2.46684i	0.0640281	−	0.0802887i
$945$	19.3387			0.629087
$946$	12.7560	+	45.5933i	0.414733	+	1.48237i
$947$	−39.6686			−1.28906			−0.644528	−	0.764580i	$-0.722946\pi$
$947$	−39.6686			−1.28906			−0.644528	+	0.764580i	$0.722946\pi$
$948$	−55.3216	+	69.3711i	−1.79676	+	2.25307i
$949$	−28.4611	+	4.28982i	−0.923886	+	0.139253i
$950$	−2.52429	−	11.0596i	−0.0818988	−	0.358822i
$951$	2.99315	−	2.04069i	0.0970595	−	0.0661740i
$952$	−7.95902	+	13.7854i	−0.257953	+	0.446788i
$953$	−11.2928	−	19.5597i	−0.365809	−	0.633600i	0.623096	−	0.782145i	$-0.285874\pi$
$953$	−11.2928	−	19.5597i	−0.365809	−	0.633600i	−0.988906	+	0.148545i	$0.952541\pi$
$954$	92.9642	+	44.7692i	3.00983	+	1.44946i
$955$	−9.07163	+	2.79823i	−0.293551	+	0.0905486i
$956$	3.96817	−	52.9516i	0.128340	−	1.71258i
$957$	−10.1476	+	44.4595i	−0.328025	+	1.43717i
$958$	−12.2487	−	31.2091i	−0.395737	−	1.00832i
$959$	0.615223	+	8.20958i	0.0198666	+	0.265101i
$960$	86.1118	+	12.9793i	2.77925	+	0.418904i
$961$	19.3963	−	17.9971i	0.625687	−	0.580552i
$962$	24.9526	−	12.0165i	0.804503	−	0.387428i
$963$	44.7524	+	30.5117i	1.44213	+	0.983225i
$964$	−3.76380	+	9.58999i	−0.121224	+	0.308873i
$965$	38.9927	+	12.0277i	1.25522	+	0.387184i
$966$	65.8981	+	61.1445i	2.12024	+	1.96729i
$967$	27.2629	+	34.1866i	0.876716	+	1.09937i	0.994333	+	0.106308i	$0.0339029\pi$
$967$	27.2629	+	34.1866i	0.876716	+	1.09937i	−0.117618	+	0.993059i	$0.537526\pi$
$968$	2.43581	+	3.05440i	0.0782898	+	0.0981723i
$969$	15.6269	+	14.4996i	0.502009	+	0.465796i
$970$	−23.6963	−	7.30936i	−0.760844	−	0.234689i
$971$	−0.637644	+	1.62469i	−0.0204630	+	0.0521388i	−0.940740	−	0.339128i	$-0.889868\pi$
$971$	−0.637644	+	1.62469i	−0.0204630	+	0.0521388i	0.920277	+	0.391267i	$0.127963\pi$
$972$	54.8017	+	37.3632i	1.75776	+	1.19842i
$973$	36.0992	−	17.3845i	1.15729	−	0.557321i
$974$	−5.21082	+	4.83494i	−0.166965	+	0.154921i
$975$	13.3268	+	2.00869i	0.426799	+	0.0643296i
$976$	0.0959912	+	1.28091i	0.00307260	+	0.0410010i
$977$	−11.5658	−	29.4693i	−0.370024	−	0.942806i	−0.987698	−	0.156372i	$-0.950020\pi$
$977$	−11.5658	−	29.4693i	−0.370024	−	0.942806i	0.617674	−	0.786434i	$-0.288075\pi$
$978$	21.4409	−	93.9388i	0.685605	−	3.00383i
$979$	3.49839	−	46.6828i	0.111809	−	1.49199i
$980$	18.0041	−	5.55352i	0.575119	−	0.177401i
$981$	−55.7562	−	26.8508i	−1.78016	−	0.857280i
$982$	1.89821	+	3.28779i	0.0605742	+	0.104918i
$983$	0.979597	−	1.69671i	0.0312443	−	0.0541167i	−0.849980	−	0.526814i	$-0.823386\pi$
$983$	0.979597	−	1.69671i	0.0312443	−	0.0541167i	0.881225	+	0.472698i	$0.156720\pi$
$984$	14.8460	−	10.1219i	0.473275	−	0.322673i
$985$	−11.4282	−	50.0701i	−0.364132	−	1.59537i
$986$	−28.8802	+	4.35299i	−0.919733	+	0.138627i
$987$	4.30568	−	5.39915i	0.137051	−	0.171857i
$988$	−38.9798			−1.24011
$989$	17.6952	+	39.3701i	0.562673	+	1.25190i
$990$	−78.6531			−2.49976
$991$	37.6576	−	47.2211i	1.19623	−	1.50003i	0.377345	−	0.926073i	$-0.376837\pi$
$991$	37.6576	−	47.2211i	1.19623	−	1.50003i	0.818887	−	0.573954i	$-0.194591\pi$
$992$	−10.6354	+	1.60302i	−0.337673	+	0.0508961i
$993$	−18.6531	−	81.7244i	−0.591937	−	2.59345i
$994$	47.3570	−	32.2874i	1.50207	−	1.02410i
$995$	−11.7860	+	20.4139i	−0.373640	+	0.647164i
$996$	12.9677	+	22.4607i	0.410897	+	0.711695i
$997$	3.94108	+	1.89792i	0.124815	+	0.0601079i	0.495249	−	0.868751i	$-0.335077\pi$
$997$	3.94108	+	1.89792i	0.124815	+	0.0601079i	−0.370434	+	0.928859i	$0.620791\pi$
$998$	−75.5647	+	23.3086i	−2.39196	+	0.737822i
$999$	−0.905143	+	12.0783i	−0.0286375	+	0.382140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.24.1	yes	36
3.2	odd	2		387.2.y.c.325.3		36
4.3	odd	2		688.2.bg.c.497.1		36
43.3	odd	42		1849.2.a.o.1.16		18
43.9	even	21	inner	43.2.g.a.9.1	✓	36
43.40	even	21		1849.2.a.n.1.3		18
129.95	odd	42		387.2.y.c.181.3		36
172.95	odd	42		688.2.bg.c.353.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.1	✓	36	43.9	even	21	inner
43.2.g.a.24.1	yes	36	1.1	even	1	trivial
387.2.y.c.181.3		36	129.95	odd	42
387.2.y.c.325.3		36	3.2	odd	2
688.2.bg.c.353.1		36	172.95	odd	42
688.2.bg.c.497.1		36	4.3	odd	2
1849.2.a.n.1.3		18	43.40	even	21
1849.2.a.o.1.16		18	43.3	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44188 + 1.80806i) q^{2} +(2.66973 - 0.402397i) q^{3} +(-0.745019 - 3.26414i) q^{4} +(-2.09843 + 1.43068i) q^{5} +(-3.12187 + 5.40724i) q^{6} +(-1.09365 - 1.89425i) q^{7} +(2.80884 + 1.35267i) q^{8} +(4.09883 - 1.26432i) q^{9} +O(q^{10})\)	\(q+(-1.44188 + 1.80806i) q^{2} +(2.66973 - 0.402397i) q^{3} +(-0.745019 - 3.26414i) q^{4} +(-2.09843 + 1.43068i) q^{5} +(-3.12187 + 5.40724i) q^{6} +(-1.09365 - 1.89425i) q^{7} +(2.80884 + 1.35267i) q^{8} +(4.09883 - 1.26432i) q^{9} +(0.438918 - 5.85695i) q^{10} +(0.694710 - 3.04372i) q^{11} +(-3.30249 - 8.41460i) q^{12} +(0.257224 + 3.43242i) q^{13} +(5.00182 + 0.753903i) q^{14} +(-5.02653 + 4.66394i) q^{15} +(-0.462659 + 0.222805i) q^{16} +(-1.92873 - 1.31499i) q^{17} +(-3.62405 + 9.23392i) q^{18} +(-3.23214 - 0.996984i) q^{19} +(6.23332 + 5.78368i) q^{20} +(-3.68198 - 4.61706i) q^{21} +(4.50154 + 5.64475i) q^{22} +(4.82527 + 4.47719i) q^{23} +(8.04316 + 2.48099i) q^{24} +(0.529835 - 1.35000i) q^{25} +(-6.57690 - 4.48405i) q^{26} +(3.13647 - 1.51045i) q^{27} +(-5.36832 + 4.98107i) q^{28} +(-5.34977 - 0.806349i) q^{29} +(-1.18503 - 15.8131i) q^{30} +(0.778473 + 1.98352i) q^{31} +(-1.12320 + 4.92105i) q^{32} +(0.629903 - 8.40547i) q^{33} +(5.15856 - 1.59121i) q^{34} +(5.00501 + 2.41028i) q^{35} +(-7.18063 - 12.4372i) q^{36} +(-1.73964 + 3.01315i) q^{37} +(6.46296 - 4.40637i) q^{38} +(2.06792 + 9.06013i) q^{39} +(-7.82938 + 1.18009i) q^{40} +(1.33098 - 1.66900i) q^{41} +13.6569 q^{42} +(6.03879 + 2.55598i) q^{43} -10.4527 q^{44} +(-6.79225 + 8.51721i) q^{45} +(-15.0525 + 2.26880i) q^{46} +(0.260214 + 1.14007i) q^{47} +(-1.14552 + 0.781003i) q^{48} +(1.10788 - 1.91890i) q^{49} +(1.67692 + 2.90450i) q^{50} +(-5.67834 - 2.73454i) q^{51} +(11.0123 - 3.39683i) q^{52} +(0.777332 - 10.3728i) q^{53} +(-1.79144 + 7.84880i) q^{54} +(2.89680 + 7.38094i) q^{55} +(-0.509588 - 6.79998i) q^{56} +(-9.03014 - 1.36108i) q^{57} +(9.17165 - 8.51004i) q^{58} +(-5.53586 + 2.66593i) q^{59} +(18.9686 + 12.9326i) q^{60} +(0.913867 - 2.32849i) q^{61} +(-4.70878 - 1.45247i) q^{62} +(-6.87761 - 6.38149i) q^{63} +(-7.91838 - 9.92933i) q^{64} +(-5.45047 - 6.83467i) q^{65} +(14.2893 + 13.2586i) q^{66} +(9.87998 + 3.04757i) q^{67} +(-2.85536 + 7.27534i) q^{68} +(14.6838 + 10.0112i) q^{69} +(-11.5745 + 5.57401i) q^{70} +(8.30629 - 7.70711i) q^{71} +(13.2232 + 1.99307i) q^{72} +(0.624897 + 8.33868i) q^{73} +(-2.93960 - 7.48997i) q^{74} +(0.871282 - 3.81734i) q^{75} +(-0.846290 + 11.2930i) q^{76} +(-6.52534 + 2.01280i) q^{77} +(-19.3629 - 9.32469i) q^{78} +(-4.90787 - 8.50067i) q^{79} +(0.652093 - 1.12946i) q^{80} +(-2.86645 + 1.95431i) q^{81} +(1.09853 + 4.81298i) q^{82} +(-2.83709 + 0.427622i) q^{83} +(-12.3276 + 15.4583i) q^{84} +5.92862 q^{85} +(-13.3286 + 7.23307i) q^{86} -14.6069 q^{87} +(6.06847 - 7.60962i) q^{88} +(14.8273 - 2.23486i) q^{89} +(-5.60602 - 24.5616i) q^{90} +(6.22054 - 4.24110i) q^{91} +(11.0193 - 19.0860i) q^{92} +(2.87648 + 4.98220i) q^{93} +(-2.43652 - 1.17336i) q^{94} +(8.20879 - 2.53207i) q^{95} +(-1.01842 + 13.5899i) q^{96} +(0.939509 - 4.11626i) q^{97} +(1.87206 + 4.76993i) q^{98} +(-1.00075 - 13.3540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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