LMFDB - Embedded newform 722.2.i.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$16$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	722.11
Dual form			722.2.i.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.592235 + 0.805765i) q^{2} +(-0.271767 - 1.95984i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(3.51033 + 2.43401i) q^{5} +(1.41822 - 1.37967i) q^{6} +(1.70655 - 1.85381i) q^{7} +(-0.945817 + 0.324699i) q^{8} +(-0.880305 + 0.248926i) q^{9} +O(q^{10})$	\(q+(0.592235 + 0.805765i) q^{2} +(-0.271767 - 1.95984i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(3.51033 + 2.43401i) q^{5} +(1.41822 - 1.37967i) q^{6} +(1.70655 - 1.85381i) q^{7} +(-0.945817 + 0.324699i) q^{8} +(-0.880305 + 0.248926i) q^{9} +(0.117702 + 4.27001i) q^{10} +(-1.04103 - 4.11092i) q^{11} +(1.95161 + 0.325665i) q^{12} +(1.87412 + 0.761201i) q^{13} +(2.50441 + 0.277188i) q^{14} +(3.81627 - 7.54116i) q^{15} +(-0.821778 - 0.569808i) q^{16} +(-0.754125 - 2.41107i) q^{17} +(-0.721924 - 0.561896i) q^{18} +(-3.14348 + 3.01969i) q^{19} +(-3.37091 + 2.62369i) q^{20} +(-4.09695 - 2.84076i) q^{21} +(2.69591 - 3.27346i) q^{22} +(-0.820711 + 5.91854i) q^{23} +(0.893400 + 1.76541i) q^{24} +(4.64483 + 12.4058i) q^{25} +(0.496570 + 1.96091i) q^{26} +(-1.65728 - 3.77822i) q^{27} +(1.25985 + 2.18213i) q^{28} +(-0.503173 - 0.112764i) q^{29} +(8.33653 - 1.39112i) q^{30} +(0.256215 + 0.584110i) q^{31} +(-0.0275543 - 0.999620i) q^{32} +(-7.77383 + 3.15746i) q^{33} +(1.49614 - 2.03557i) q^{34} +(10.5027 - 2.35372i) q^{35} +(0.0252073 - 0.914476i) q^{36} +(-0.747656 - 2.95243i) q^{37} +(-4.29484 - 0.744542i) q^{38} +(0.982508 - 3.87984i) q^{39} +(-4.11045 - 1.16232i) q^{40} +(4.57194 - 0.252241i) q^{41} +(-0.137371 - 4.98358i) q^{42} +(0.167164 - 6.06440i) q^{43} +(4.23425 + 0.233610i) q^{44} +(-3.69605 - 1.26886i) q^{45} +(-5.25501 + 2.84387i) q^{46} +(8.10522 - 7.88488i) q^{47} +(-0.893400 + 1.76541i) q^{48} +(0.0537655 + 0.648853i) q^{49} +(-7.24532 + 11.0898i) q^{50} +(-4.52036 + 2.13321i) q^{51} +(-1.28595 + 1.56144i) q^{52} +(-2.49941 + 2.43146i) q^{53} +(2.06286 - 3.57297i) q^{54} +(6.35167 - 16.9646i) q^{55} +(-1.01215 + 2.30748i) q^{56} +(6.77239 + 5.34007i) q^{57} +(-0.207136 - 0.472222i) q^{58} +(-6.95180 + 0.383541i) q^{59} +(6.05811 + 5.89342i) q^{60} +(1.10213 + 5.64231i) q^{61} +(-0.318916 + 0.552379i) q^{62} +(-1.04082 + 2.05672i) q^{63} +(0.789141 - 0.614213i) q^{64} +(4.72600 + 7.23369i) q^{65} +(-7.14810 - 4.39392i) q^{66} +(-1.33139 - 1.15951i) q^{67} +2.52626 q^{68} +11.8224 q^{69} +(8.11664 + 7.06879i) q^{70} +(-3.21335 + 16.4505i) q^{71} +(0.751781 - 0.521273i) q^{72} +(0.633222 + 2.02452i) q^{73} +(1.93617 - 2.35097i) q^{74} +(23.0510 - 12.4746i) q^{75} +(-1.94363 - 3.90158i) q^{76} +(-9.39743 - 5.08563i) q^{77} +(3.70811 - 1.50611i) q^{78} +(0.278005 - 10.0855i) q^{79} +(-1.49779 - 4.00043i) q^{80} +(-9.29237 + 5.71200i) q^{81} +(2.91091 + 3.53452i) q^{82} +(0.767269 + 9.25956i) q^{83} +(3.93424 - 3.06214i) q^{84} +(3.22134 - 10.2992i) q^{85} +(4.98548 - 3.45686i) q^{86} +(-0.0842531 + 1.01678i) q^{87} +(2.31944 + 3.55016i) q^{88} +(-0.287942 + 0.920602i) q^{89} +(-1.16653 - 3.72961i) q^{90} +(4.60940 - 2.17523i) q^{91} +(-5.40369 - 2.55006i) q^{92} +(1.07513 - 0.660881i) q^{93} +(11.1536 + 1.86120i) q^{94} +(-18.3846 + 2.94884i) q^{95} +(-1.95161 + 0.325665i) q^{96} +(-9.08954 + 7.91609i) q^{97} +(-0.490982 + 0.427596i) q^{98} +(1.93974 + 3.35973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) $ 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{17}{57}\right)$

Coefficient data

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

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

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

$2$	0.592235	+	0.805765i	0.418774	+	0.569762i
$2$	0.592235	+	0.805765i	0.418774	+	0.569762i
$3$	−0.271767	−	1.95984i	−0.156904	−	1.13151i	−0.891504	−	0.453012i	$-0.850349\pi$
$3$	−0.271767	−	1.95984i	−0.156904	−	1.13151i	0.734600	−	0.678501i	$-0.237370\pi$
$4$	−0.298515	+	0.954405i	−0.149257	+	0.477203i
$5$	3.51033	+	2.43401i	1.56987	+	1.08852i	0.953639	+	0.300954i	$0.0973051\pi$
$5$	3.51033	+	2.43401i	1.56987	+	1.08852i	0.616228	+	0.787567i	$0.288660\pi$
$6$	1.41822	−	1.37967i	0.578986	−	0.563246i
$7$	1.70655	−	1.85381i	0.645016	−	0.700674i	−0.324449	−	0.945903i	$-0.605179\pi$
$7$	1.70655	−	1.85381i	0.645016	−	0.700674i	0.969465	+	0.245229i	$0.0788632\pi$
$8$	−0.945817	+	0.324699i	−0.334397	+	0.114799i
$9$	−0.880305	+	0.248926i	−0.293435	+	0.0829755i
$10$	0.117702	+	4.27001i	0.0372206	+	1.35029i
$11$	−1.04103	−	4.11092i	−0.313881	−	1.23949i	−0.902362	−	0.430979i	$-0.858168\pi$
$11$	−1.04103	−	4.11092i	−0.313881	−	1.23949i	0.588481	−	0.808511i	$-0.299726\pi$
$12$	1.95161	+	0.325665i	0.563380	+	0.0940115i
$13$	1.87412	+	0.761201i	0.519787	+	0.211119i	0.621094	−	0.783736i	$-0.286688\pi$
$13$	1.87412	+	0.761201i	0.519787	+	0.211119i	−0.101307	+	0.994855i	$0.532302\pi$
$14$	2.50441	+	0.277188i	0.669333	+	0.0740817i
$15$	3.81627	−	7.54116i	0.985357	−	1.94712i
$16$	−0.821778	−	0.569808i	−0.205444	−	0.142452i
$17$	−0.754125	−	2.41107i	−0.182902	−	0.584771i	−0.999966	−	0.00822385i	$-0.997382\pi$
$17$	−0.754125	−	2.41107i	−0.182902	−	0.584771i	0.817064	−	0.576547i	$-0.195600\pi$
$18$	−0.721924	−	0.561896i	−0.170159	−	0.132440i
$19$	−3.14348	+	3.01969i	−0.721164	+	0.692764i
$19$	−3.14348	+	3.01969i	−0.721164	+	0.692764i
$20$	−3.37091	+	2.62369i	−0.753760	+	0.586675i
$21$	−4.09695	−	2.84076i	−0.894027	−	0.619905i
$22$	2.69591	−	3.27346i	0.574769	−	0.697903i
$23$	−0.820711	+	5.91854i	−0.171130	+	1.23410i	0.689278	+	0.724497i	$0.257928\pi$
$23$	−0.820711	+	5.91854i	−0.171130	+	1.23410i	−0.860409	+	0.509605i	$0.829792\pi$
$24$	0.893400	+	1.76541i	0.182364	+	0.360362i
$25$	4.64483	+	12.4058i	0.928966	+	2.48116i
$26$	0.496570	+	1.96091i	0.0973853	+	0.384566i
$27$	−1.65728	−	3.77822i	−0.318944	−	0.727118i
$28$	1.25985	+	2.18213i	0.238090	+	0.412384i
$29$	−0.503173	−	0.112764i	−0.0934369	−	0.0209397i	0.171712	−	0.985147i	$-0.445070\pi$
$29$	−0.503173	−	0.112764i	−0.0934369	−	0.0209397i	−0.265149	+	0.964208i	$0.585421\pi$
$30$	8.33653	−	1.39112i	1.52204	−	0.253983i
$31$	0.256215	+	0.584110i	0.0460175	+	0.104909i	0.937279	−	0.348581i	$-0.113336\pi$
$31$	0.256215	+	0.584110i	0.0460175	+	0.104909i	−0.891261	+	0.453491i	$0.850179\pi$
$32$	−0.0275543	−	0.999620i	−0.00487097	−	0.176710i
$33$	−7.77383	+	3.15746i	−1.35325	+	0.549642i
$34$	1.49614	−	2.03557i	0.256586	−	0.349097i
$35$	10.5027	−	2.35372i	1.77529	−	0.397851i
$36$	0.0252073	−	0.914476i	0.00420122	−	0.152413i
$37$	−0.747656	−	2.95243i	−0.122914	−	0.485376i	−0.999987	−	0.00501988i	$-0.998402\pi$
$37$	−0.747656	−	2.95243i	−0.122914	−	0.485376i	0.877073	−	0.480356i	$-0.159493\pi$
$38$	−4.29484	−	0.744542i	−0.696715	−	0.120781i
$39$	0.982508	−	3.87984i	0.157327	−	0.621271i
$40$	−4.11045	−	1.16232i	−0.649919	−	0.183780i
$41$	4.57194	−	0.252241i	0.714017	−	0.0393934i	0.305562	−	0.952172i	$-0.401156\pi$
$41$	4.57194	−	0.252241i	0.714017	−	0.0393934i	0.408454	+	0.912779i	$0.366068\pi$
$42$	−0.137371	−	4.98358i	−0.0211969	−	0.768983i
$43$	0.167164	−	6.06440i	0.0254923	−	0.924813i	−0.873494	−	0.486835i	$-0.838151\pi$
$43$	0.167164	−	6.06440i	0.0254923	−	0.924813i	0.898986	−	0.437977i	$-0.144305\pi$
$44$	4.23425	+	0.233610i	0.638337	+	0.0352180i
$45$	−3.69605	−	1.26886i	−0.550974	−	0.189150i
$46$	−5.25501	+	2.84387i	−0.774809	+	0.419306i
$47$	8.10522	−	7.88488i	1.18227	−	1.15013i	0.196768	−	0.980450i	$-0.436955\pi$
$47$	8.10522	−	7.88488i	1.18227	−	1.15013i	0.985500	−	0.169678i	$-0.0542726\pi$
$48$	−0.893400	+	1.76541i	−0.128951	+	0.254814i
$49$	0.0537655	+	0.648853i	0.00768079	+	0.0926933i
$50$	−7.24532	+	11.0898i	−1.02464	+	1.56833i
$51$	−4.52036	+	2.13321i	−0.632978	+	0.298709i
$52$	−1.28595	+	1.56144i	−0.178329	+	0.216533i
$53$	−2.49941	+	2.43146i	−0.343320	+	0.333987i	−0.848665	−	0.528930i	$-0.822593\pi$
$53$	−2.49941	+	2.43146i	−0.343320	+	0.333987i	0.505345	+	0.862917i	$0.331365\pi$
$54$	2.06286	−	3.57297i	0.280719	−	0.486220i
$55$	6.35167	−	16.9646i	0.856459	−	2.28750i
$56$	−1.01215	+	2.30748i	−0.135255	+	0.308350i
$57$	6.77239	+	5.34007i	0.897026	+	0.707309i
$58$	−0.207136	−	0.472222i	−0.0271983	−	0.0620058i
$59$	−6.95180	+	0.383541i	−0.905047	+	0.0499328i	−0.501629	−	0.865083i	$-0.667266\pi$
$59$	−6.95180	+	0.383541i	−0.905047	+	0.0499328i	−0.403418	+	0.915016i	$0.632178\pi$
$60$	6.05811	+	5.89342i	0.782098	+	0.760837i
$61$	1.10213	+	5.64231i	0.141114	+	0.722424i	0.983121	+	0.182958i	$0.0585671\pi$
$61$	1.10213	+	5.64231i	0.141114	+	0.722424i	−0.842007	+	0.539467i	$0.818626\pi$
$62$	−0.318916	+	0.552379i	−0.0405024	+	0.0701523i
$63$	−1.04082	+	2.05672i	−0.131131	+	0.259123i
$64$	0.789141	−	0.614213i	0.0986426	−	0.0767766i
$65$	4.72600	+	7.23369i	0.586189	+	0.897228i
$66$	−7.14810	−	4.39392i	−0.879871	−	0.540854i
$67$	−1.33139	−	1.15951i	−0.162655	−	0.141657i	0.571594	−	0.820537i	$-0.306325\pi$
$67$	−1.33139	−	1.15951i	−0.162655	−	0.141657i	−0.734249	+	0.678880i	$0.762466\pi$
$68$	2.52626			0.306354
$69$	11.8224			1.42325
$70$	8.11664	+	7.06879i	0.970124	+	0.844882i
$71$	−3.21335	+	16.4505i	−0.381354	+	1.95232i	−0.0889013	+	0.996040i	$0.528336\pi$
$71$	−3.21335	+	16.4505i	−0.381354	+	1.95232i	−0.292453	+	0.956280i	$0.594471\pi$
$72$	0.751781	−	0.521273i	0.0885983	−	0.0614327i
$73$	0.633222	+	2.02452i	0.0741130	+	0.236952i	0.984079	−	0.177730i	$-0.0568752\pi$
$73$	0.633222	+	2.02452i	0.0741130	+	0.236952i	−0.909966	+	0.414682i	$0.863893\pi$
$74$	1.93617	−	2.35097i	0.225076	−	0.273294i
$75$	23.0510	−	12.4746i	2.66170	−	1.44044i
$76$	−1.94363	−	3.90158i	−0.222950	−	0.447542i
$77$	−9.39743	−	5.08563i	−1.07094	−	0.579562i
$78$	3.70811	−	1.50611i	0.419861	−	0.170533i
$79$	0.278005	−	10.0855i	0.0312780	−	1.13471i	−0.807374	−	0.590040i	$-0.799112\pi$
$79$	0.278005	−	10.0855i	0.0312780	−	1.13471i	0.838652	−	0.544668i	$-0.183344\pi$
$80$	−1.49779	−	4.00043i	−0.167458	−	0.447261i
$81$	−9.29237	+	5.71200i	−1.03249	+	0.634666i
$82$	2.91091	+	3.53452i	0.321456	+	0.390323i
$83$	0.767269	+	9.25956i	0.0842187	+	1.01637i	0.899390	+	0.437148i	$0.144011\pi$
$83$	0.767269	+	9.25956i	0.0842187	+	1.01637i	−0.815171	+	0.579221i	$0.803357\pi$
$84$	3.93424	−	3.06214i	0.429260	−	0.334107i
$85$	3.22134	−	10.2992i	0.349404	−	1.11711i
$86$	4.98548	−	3.45686i	0.537599	−	0.372763i
$87$	−0.0842531	+	1.01678i	−0.00903288	+	0.109011i
$88$	2.31944	+	3.55016i	0.247253	+	0.378448i
$89$	−0.287942	+	0.920602i	−0.0305218	+	0.0975837i	−0.968418	−	0.249333i	$-0.919789\pi$
$89$	−0.287942	+	0.920602i	−0.0305218	+	0.0975837i	0.937896	+	0.346916i	$0.112771\pi$
$90$	−1.16653	−	3.72961i	−0.122963	−	0.393135i
$91$	4.60940	−	2.17523i	0.483196	−	0.228026i
$92$	−5.40369	−	2.55006i	−0.563374	−	0.265863i
$93$	1.07513	−	0.660881i	0.111486	−	0.0685301i
$94$	11.1536	+	1.86120i	1.15040	+	0.191968i
$95$	−18.3846	+	2.94884i	−1.88622	+	0.302545i
$96$	−1.95161	+	0.325665i	−0.199185	+	0.0332381i
$97$	−9.08954	+	7.91609i	−0.922903	+	0.803757i	−0.980891	−	0.194560i	$-0.937672\pi$
$97$	−9.08954	+	7.91609i	−0.922903	+	0.803757i	0.0579873	+	0.998317i	$0.481532\pi$
$98$	−0.490982	+	0.427596i	−0.0495966	+	0.0431937i
$99$	1.93974	+	3.35973i	0.194951	+	0.337665i
$100$	−13.2267	+	0.729737i	−1.32267	+	0.0729737i
$101$	−9.64463	+	2.72724i	−0.959676	+	0.271371i	−0.715698	−	0.698410i	$-0.753891\pi$
$101$	−9.64463	+	2.72724i	−0.959676	+	0.271371i	−0.243978	+	0.969781i	$0.578453\pi$
$102$	−4.39599	−	2.37899i	−0.435268	−	0.235555i
$103$	−8.01618	−	8.70789i	−0.789858	−	0.858014i	0.202769	−	0.979227i	$-0.435006\pi$
$103$	−8.01618	−	8.70789i	−0.789858	−	0.858014i	−0.992627	+	0.121212i	$0.961322\pi$
$104$	−2.01974	−	0.111432i	−0.198051	−	0.0109268i
$105$	−7.46720	−	19.9440i	−0.728724	−	1.94634i
$106$	−3.43942	−	0.573938i	−0.334066	−	0.0557458i
$107$	−2.86060	+	6.52151i	−0.276545	+	0.630458i	−0.998081	−	0.0619181i	$-0.980278\pi$
$107$	−2.86060	+	6.52151i	−0.276545	+	0.630458i	0.721537	+	0.692376i	$0.243436\pi$
$108$	4.10067	−	0.453862i	0.394587	−	0.0436729i
$109$	−9.97090	−	9.69984i	−0.955039	−	0.929076i	0.0425070	−	0.999096i	$-0.486466\pi$
$109$	−9.97090	−	9.69984i	−0.955039	−	0.929076i	−0.997546	+	0.0700203i	$0.977694\pi$
$110$	17.4311	−	4.92906i	1.66199	−	0.469967i
$111$	−5.58309	+	2.26766i	−0.529924	+	0.215236i
$112$	−2.45872	+	0.551012i	−0.232327	+	0.0520658i
$113$	−5.82889	−	6.33186i	−0.548336	−	0.595652i	0.398580	−	0.917134i	$-0.369503\pi$
$113$	−5.82889	−	6.33186i	−0.548336	−	0.595652i	−0.946916	+	0.321482i	$0.895819\pi$
$114$	−0.291989	+	8.61953i	−0.0273473	+	0.807293i
$115$	−17.2867	+	18.7784i	−1.61200	+	1.75110i
$116$	0.257827	−	0.446569i	0.0239386	−	0.0414629i
$117$	−1.83928	−	0.203571i	−0.170041	−	0.0188202i
$118$	−4.42614	−	5.37437i	−0.407460	−	0.494751i
$119$	−5.75662	−	2.71661i	−0.527708	−	0.249032i
$120$	−1.16089	+	8.37170i	−0.105974	+	0.764228i
$121$	−6.14174	+	3.32374i	−0.558340	+	0.302158i
$122$	−3.89366	+	4.22964i	−0.352515	+	0.382934i
$123$	−1.73685	−	8.89171i	−0.156607	−	0.801738i
$124$	−0.633962	+	0.0701669i	−0.0569314	+	0.00630117i
$125$	−8.64779	+	34.1494i	−0.773482	+	3.05441i
$126$	−2.27365	+	0.379405i	−0.202553	+	0.0338001i
$127$	−1.69230	−	2.93115i	−0.150168	−	0.260098i	0.781121	−	0.624379i	$-0.214648\pi$
$127$	−1.69230	−	2.93115i	−0.150168	−	0.260098i	−0.931289	+	0.364281i	$0.881315\pi$
$128$	0.962268	+	0.272103i	0.0850533	+	0.0240508i
$129$	−11.9307	+	1.32049i	−1.05044	+	0.116262i
$130$	−3.02975	+	8.09209i	−0.265726	+	0.709723i
$131$	18.6739	+	2.06683i	1.63155	+	0.180580i	0.878621	−	0.477521i	$-0.158464\pi$
$131$	18.6739	+	2.06683i	1.63155	+	0.180580i	0.752930	+	0.658101i	$0.228640\pi$
$132$	−0.692889	−	8.36193i	−0.0603082	−	0.727812i
$133$	0.233411	+	10.9807i	0.0202393	+	0.952145i
$134$	0.145796	−	1.75949i	0.0125948	−	0.151997i
$135$	3.37861	−	17.2966i	0.290785	−	1.48866i
$136$	1.49614	+	2.03557i	0.128293	+	0.174549i
$137$	2.42458	+	2.11157i	0.207146	+	0.180404i	0.754101	−	0.656758i	$-0.228073\pi$
$137$	2.42458	+	2.11157i	0.207146	+	0.180404i	−0.546955	+	0.837162i	$0.684213\pi$
$138$	7.00166	+	9.52610i	0.596021	+	0.810915i
$139$	13.7419	+	8.44709i	1.16557	+	0.716473i	0.964753	−	0.263156i	$-0.0847633\pi$
$139$	13.7419	+	8.44709i	1.16557	+	0.716473i	0.200816	+	0.979629i	$0.435641\pi$
$140$	−0.888822	+	10.7265i	−0.0751192	+	0.906554i
$141$	−17.6558	−	13.7421i	−1.48689	−	1.15729i
$142$	−15.1583	+	7.15339i	−1.27206	+	0.600299i
$143$	1.17823	−	8.49679i	0.0985286	−	0.710537i
$144$	0.865255	+	0.297043i	0.0721046	+	0.0247535i
$145$	−1.49184	−	1.62057i	−0.123890	−	0.134581i
$146$	−1.25627	+	1.70922i	−0.103970	+	0.141456i
$147$	1.25704	−	0.281708i	0.103679	−	0.0232349i
$148$	3.04100	+	0.167777i	0.249969	+	0.0137911i
$149$	1.18247	+	2.33663i	0.0968720	+	0.191424i	0.935542	−	0.353216i	$-0.114912\pi$
$149$	1.18247	+	2.33663i	0.0968720	+	0.191424i	−0.838670	+	0.544640i	$0.816666\pi$
$150$	23.7032	+	11.1858i	1.93536	+	0.913318i
$151$	−5.71291	+	8.74427i	−0.464910	+	0.711598i	−0.990251	−	0.139294i	$-0.955517\pi$
$151$	−5.71291	+	8.74427i	−0.464910	+	0.711598i	0.525341	+	0.850892i	$0.323938\pi$
$152$	1.99267	−	3.87676i	0.161627	−	0.314447i
$153$	1.26404	+	1.93476i	0.102192	+	0.156416i
$154$	−1.46766	−	10.5840i	−0.118268	−	0.852884i
$155$	−0.522332	+	2.67405i	−0.0419547	+	0.214785i
$156$	3.40964	+	2.09590i	0.272990	+	0.167806i
$157$	−1.74392	−	12.5762i	−0.139180	−	1.00369i	−0.923572	−	0.383425i	$-0.874744\pi$
$157$	−1.74392	−	12.5762i	−0.139180	−	1.00369i	0.784392	−	0.620265i	$-0.212975\pi$
$158$	8.29119	−	5.74899i	0.659612	−	0.457365i
$159$	5.44453	+	4.23765i	0.431779	+	0.336067i
$160$	2.33636	−	3.57606i	0.184705	−	0.282713i
$161$	9.57126	+	11.6217i	0.754321	+	0.915921i
$162$	−10.1058	−	4.10462i	−0.793986	−	0.322489i
$163$	−4.40215	+	10.0359i	−0.344803	+	0.786072i	0.654740	+	0.755854i	$0.272778\pi$
$163$	−4.40215	+	10.0359i	−0.344803	+	0.786072i	−0.999543	+	0.0302178i	$0.990380\pi$
$164$	−1.12405	+	4.43878i	−0.0877736	+	0.346610i
$165$	−34.9740	−	7.83785i	−2.72272	−	0.610176i
$166$	−7.00663	+	6.10208i	−0.543820	+	0.473613i
$167$	−12.5591	−	2.81457i	−0.971855	−	0.217798i	−0.296290	−	0.955098i	$-0.595749\pi$
$167$	−12.5591	−	2.81457i	−0.971855	−	0.217798i	−0.675565	+	0.737300i	$0.736100\pi$
$168$	4.79736	+	1.35656i	0.370124	+	0.104661i
$169$	−6.38528	−	6.21170i	−0.491175	−	0.477823i
$170$	10.2065	−	3.50391i	0.782805	−	0.268737i
$171$	2.01554	−	3.44074i	0.154132	−	0.263120i
$172$	5.73800	+	1.96986i	0.437518	+	0.150200i
$173$	5.81708	+	11.4949i	0.442265	+	0.873939i	0.999063	+	0.0432908i	$0.0137842\pi$
$173$	5.81708	+	11.4949i	0.442265	+	0.873939i	−0.556798	+	0.830648i	$0.687970\pi$
$174$	−0.869186	+	0.534287i	−0.0658928	+	0.0405042i
$175$	30.9246	+	12.5605i	2.33768	+	0.949483i
$176$	−1.48694	+	3.97145i	−0.112083	+	0.299359i
$177$	2.64095	+	13.5202i	0.198506	+	1.01624i
$178$	−0.912319	+	0.313199i	−0.0683812	+	0.0234753i
$179$	7.90410	+	4.27749i	0.590780	+	0.319714i	0.743689	−	0.668526i	$-0.233074\pi$
$179$	7.90410	+	4.27749i	0.590780	+	0.319714i	−0.152908	+	0.988240i	$0.548864\pi$
$180$	2.31433	−	3.14876i	0.172500	−	0.234694i
$181$	9.82308	−	13.3648i	0.730144	−	0.993396i	−0.269395	−	0.963030i	$-0.586824\pi$
$181$	9.82308	−	13.3648i	0.730144	−	0.993396i	0.999539	−	0.0303665i	$-0.00966743\pi$
$182$	4.48257	+	2.42585i	0.332270	+	0.179816i
$183$	10.7585	−	3.69340i	0.795291	−	0.273024i
$184$	−1.14550	−	5.86434i	−0.0844477	−	0.432325i
$185$	4.56171	−	12.1838i	0.335384	−	0.895770i
$186$	1.16925	+	0.474906i	0.0857332	+	0.0348218i
$187$	−9.12667	+	5.61014i	−0.667408	+	0.410254i
$188$	5.10584	+	10.0894i	0.372382	+	0.735846i
$189$	−9.83233	−	3.37544i	−0.715196	−	0.245527i
$190$	−13.2641	−	13.0673i	−0.962278	−	0.947999i
$191$	−25.5822	+	8.78237i	−1.85106	+	0.635470i	−0.858640	+	0.512579i	$0.828690\pi$
$191$	−25.5822	+	8.78237i	−1.85106	+	0.635470i	−0.992420	+	0.122891i	$0.960783\pi$
$192$	−1.41822	−	1.37967i	−0.102351	−	0.0995688i
$193$	−3.17603	−	0.898096i	−0.228616	−	0.0646464i	0.155869	−	0.987778i	$-0.450182\pi$
$193$	−3.17603	−	0.898096i	−0.228616	−	0.0646464i	−0.384485	+	0.923131i	$0.625621\pi$
$194$	−11.7617	−	2.63585i	−0.844438	−	0.189243i
$195$	12.8925	−	11.2281i	0.923250	−	0.804059i
$196$	−0.635319	−	0.142378i	−0.0453799	−	0.0101699i
$197$	6.36068	−	25.1178i	0.453180	−	1.78957i	−0.146371	−	0.989230i	$-0.546759\pi$
$197$	6.36068	−	25.1178i	0.453180	−	1.78957i	0.599551	−	0.800337i	$-0.295346\pi$
$198$	−1.55837	+	3.55272i	−0.110748	+	0.252481i
$199$	−24.1681	−	9.81625i	−1.71323	−	0.695855i	−0.713247	−	0.700913i	$-0.752776\pi$
$199$	−24.1681	−	9.81625i	−1.71323	−	0.695855i	−0.999987	+	0.00505763i	$0.998390\pi$
$200$	−8.42131	−	10.2254i	−0.595477	−	0.723047i
$201$	−1.91063	+	2.92443i	−0.134765	+	0.206273i
$202$	−7.90940	−	6.15613i	−0.556504	−	0.433144i
$203$	−1.06773	+	0.740350i	−0.0749402	+	0.0519624i
$204$	−0.686552	−	4.95105i	−0.0480683	−	0.346643i
$205$	16.6630	+	10.2427i	1.16379	+	0.715380i
$206$	2.26905	−	11.6163i	0.158092	−	0.809345i
$207$	−0.750806	−	5.41442i	−0.0521846	−	0.376328i
$208$	−1.10637	−	1.69343i	−0.0767130	−	0.117418i
$209$	15.6862	+	9.77904i	1.08503	+	0.676430i
$210$	11.6478	−	17.8284i	0.803778	−	1.23027i
$211$	−18.8888	−	8.91385i	−1.30036	−	0.613655i	−0.353540	−	0.935419i	$-0.615022\pi$
$211$	−18.8888	−	8.91385i	−1.30036	−	0.613655i	−0.946820	+	0.321765i	$0.895724\pi$
$212$	−1.57449	−	3.11127i	−0.108136	−	0.213683i
$213$	33.1137	+	1.82693i	2.26891	+	0.125179i
$214$	−6.94895	+	1.55730i	−0.475021	+	0.106455i
$215$	15.3476	−	20.8812i	1.04670	−	1.42408i
$216$	2.79427	+	3.03539i	0.190126	+	0.206532i
$217$	1.52007	+	0.521841i	0.103189	+	0.0354249i
$218$	1.91067	−	13.7788i	0.129407	−	0.933217i
$219$	3.79565	−	1.79121i	0.256486	−	0.121039i
$220$	14.2950	+	11.1262i	0.963768	+	0.750131i
$221$	0.421991	−	5.09267i	0.0283862	−	0.342570i
$222$	−5.13370	−	3.15568i	−0.344552	−	0.211795i
$223$	11.3081	+	15.3852i	0.757244	+	1.03027i	0.998214	+	0.0597352i	$0.0190256\pi$
$223$	11.3081	+	15.3852i	0.757244	+	1.03027i	−0.240970	+	0.970533i	$0.577466\pi$
$224$	−1.90013	−	1.65482i	−0.126958	−	0.110567i
$225$	−7.17699	−	9.76465i	−0.478466	−	0.650977i
$226$	1.64992	−	8.44667i	0.109751	−	0.561864i
$227$	−0.161627	+	1.95054i	−0.0107275	+	0.129462i	−0.999844	−	0.0176739i	$-0.994374\pi$
$227$	−0.161627	+	1.95054i	−0.0107275	+	0.129462i	0.989116	+	0.147136i	$0.0470055\pi$
$228$	−7.11825	+	4.86952i	−0.471417	+	0.322492i
$229$	−1.78659	−	21.5609i	−0.118061	−	1.42479i	−0.755936	−	0.654646i	$-0.772818\pi$
$229$	−1.78659	−	21.5609i	−0.118061	−	1.42479i	0.637875	−	0.770140i	$-0.279814\pi$
$230$	−25.3688	−	2.80782i	−1.67277	−	0.185142i
$231$	−7.41311	+	19.7995i	−0.487747	+	1.30271i
$232$	0.512524	−	0.0567262i	0.0336489	−	0.00372426i
$233$	15.7300	+	4.44801i	1.03050	+	0.291399i	0.745061	−	0.666997i	$-0.232421\pi$
$233$	15.7300	+	4.44801i	1.03050	+	0.291399i	0.285443	+	0.958396i	$0.407859\pi$
$234$	−0.925255	−	1.60259i	−0.0604858	−	0.104764i
$235$	47.6438	−	7.95035i	3.10794	−	0.518624i
$236$	1.70916	−	6.74932i	0.111257	−	0.439344i
$237$	−19.8415	+	2.19606i	−1.28884	+	0.142649i
$238$	−1.22032	−	6.24736i	−0.0791016	−	0.404956i
$239$	9.99907	−	10.8619i	0.646786	−	0.702597i	−0.323043	−	0.946384i	$-0.604706\pi$
$239$	9.99907	−	10.8619i	0.646786	−	0.702597i	0.969829	+	0.243787i	$0.0783899\pi$
$240$	−7.43314	+	4.02262i	−0.479807	+	0.259659i
$241$	0.0471631	−	0.340115i	0.00303804	−	0.0219088i	−0.988942	−	0.148300i	$-0.952620\pi$
$241$	0.0471631	−	0.340115i	0.00303804	−	0.0219088i	0.991981	+	0.126391i	$0.0403393\pi$
$242$	−6.31551	−	2.98036i	−0.405976	−	0.191585i
$243$	5.85151	+	7.10509i	0.375374	+	0.455792i
$244$	−5.71406	−	0.632432i	−0.365805	−	0.0404873i
$245$	−1.39058	+	2.40855i	−0.0888409	+	0.153877i
$246$	6.13600	−	6.66548i	0.391217	−	0.424975i
$247$	−8.18985	+	3.26643i	−0.521108	+	0.207838i
$248$	−0.431992	−	0.469269i	−0.0274315	−	0.0297986i
$249$	17.9387	−	4.02016i	1.13682	−	0.254767i
$250$	−32.6379	+	13.2564i	−2.06420	+	0.838406i
$251$	−10.4813	+	2.96383i	−0.661573	+	0.187075i	−0.586308	−	0.810088i	$-0.699419\pi$
$251$	−10.4813	+	2.96383i	−0.661573	+	0.187075i	−0.0752657	+	0.997164i	$0.523980\pi$
$252$	−1.65225	−	1.60733i	−0.104082	−	0.101252i
$253$	25.1851	−	2.78748i	1.58337	−	0.175247i
$254$	1.35958	−	3.09953i	0.0853077	−	0.194482i
$255$	−21.0602	−	3.51433i	−1.31884	−	0.220076i
$256$	0.350638	+	0.936511i	0.0219148	+	0.0585320i
$257$	11.8814	+	0.655515i	0.741141	+	0.0408899i	0.421724	−	0.906724i	$-0.361425\pi$
$257$	11.8814	+	0.655515i	0.741141	+	0.0408899i	0.319417	+	0.947614i	$0.396513\pi$
$258$	−8.12977	−	8.83128i	−0.506137	−	0.549812i
$259$	−6.74915	−	3.65246i	−0.419372	−	0.226953i
$260$	−8.31465	+	2.35116i	−0.515653	+	0.145813i
$261$	0.471016	−	0.0259867i	0.0291551	−	0.00160853i
$262$	9.39399	+	16.2709i	0.580363	+	1.00522i
$263$	−4.66750	+	4.06493i	−0.287810	+	0.250654i	−0.788588	−	0.614922i	$-0.789188\pi$
$263$	−4.66750	+	4.06493i	−0.287810	+	0.250654i	0.500778	+	0.865576i	$0.333047\pi$
$264$	6.32740	−	5.51053i	0.389424	−	0.339150i
$265$	−14.6919	+	2.45165i	−0.902519	+	0.150604i
$266$	−8.70960	+	6.69121i	−0.534020	+	0.410265i
$267$	1.88248	+	0.314131i	0.115206	+	0.0192245i
$268$	1.50408	−	0.924556i	0.0918765	−	0.0564763i
$269$	−18.2559	−	8.61517i	−1.11308	−	0.525276i	−0.220150	−	0.975466i	$-0.570655\pi$
$269$	−18.2559	−	8.61517i	−1.11308	−	0.525276i	−0.892933	+	0.450190i	$0.851356\pi$
$270$	15.9379	−	7.52130i	0.969953	−	0.457732i
$271$	4.98374	+	15.9339i	0.302741	+	0.967916i	0.973972	+	0.226668i	$0.0727832\pi$
$271$	4.98374	+	15.9339i	0.302741	+	0.967916i	−0.671231	+	0.741248i	$0.734234\pi$
$272$	−0.754125	+	2.41107i	−0.0457255	+	0.146193i
$273$	−5.51578	−	8.44252i	−0.333830	−	0.510965i
$274$	−0.265507	+	3.20419i	−0.0160398	+	0.193572i
$275$	46.1638	−	32.0093i	2.78378	−	1.93023i
$276$	−3.52917	+	11.2834i	−0.212431	+	0.679180i
$277$	−3.86007	+	3.00442i	−0.231929	+	0.180518i	−0.723509	−	0.690315i	$-0.757472\pi$
$277$	−3.86007	+	3.00442i	−0.231929	+	0.180518i	0.491580	+	0.870832i	$0.336420\pi$
$278$	1.33204	+	16.0754i	0.0798907	+	0.964137i
$279$	−0.370947	−	0.450417i	−0.0222080	−	0.0269657i
$280$	−9.16942	+	5.63642i	−0.547978	+	0.336841i
$281$	−8.64728	−	23.0959i	−0.515854	−	1.37778i	−0.892341	−	0.451362i	$-0.850938\pi$
$281$	−8.64728	−	23.0959i	−0.515854	−	1.37778i	0.376487	−	0.926422i	$-0.377132\pi$
$282$	0.616486	−	22.3650i	0.0367112	−	1.33181i
$283$	−6.27881	+	2.55023i	−0.373237	+	0.151596i	−0.555215	−	0.831707i	$-0.687364\pi$
$283$	−6.27881	+	2.55023i	−0.373237	+	0.151596i	0.181978	+	0.983303i	$0.441750\pi$
$284$	−14.7412	−	7.97757i	−0.874732	−	0.473381i
$285$	10.7756	+	35.2295i	0.638290	+	2.08681i
$286$	7.54420	−	4.08272i	0.446098	−	0.241416i
$287$	7.33464	−	8.90596i	0.432950	−	0.525702i
$288$	0.273088	+	0.873112i	0.0160919	+	0.0514486i
$289$	8.72566	−	6.05024i	0.513274	−	0.355896i
$290$	0.422278	−	2.16183i	0.0247970	−	0.126947i
$291$	17.9845	+	15.6627i	1.05427	+	0.918164i
$292$	−2.12124			−0.124136
$293$	−6.73028			−0.393187			−0.196594	−	0.980485i	$-0.562988\pi$
$293$	−6.73028			−0.393187			−0.196594	+	0.980485i	$0.562988\pi$
$294$	0.971452	+	0.846038i	0.0566562	+	0.0493419i
$295$	−25.3366	−	15.5744i	−1.47516	−	0.906775i
$296$	1.66580	+	2.54969i	0.0968225	+	0.148198i
$297$	−13.8067	+	10.7462i	−0.801145	+	0.623556i
$298$	−1.18247	+	2.33663i	−0.0684988	+	0.135357i
$299$	−6.04331	+	10.4673i	−0.349494	+	0.605341i
$300$	5.02474	+	25.7239i	0.290103	+	1.48517i
$301$	−10.9570	−	10.6591i	−0.631549	−	0.614380i
$302$	−10.4292	+	0.575396i	−0.600134	+	0.0331103i
$303$	7.96604	+	18.1607i	0.457637	+	1.04331i
$304$	4.30389	−	0.690331i	0.246845	−	0.0395932i
$305$	−9.86458	+	22.4890i	−0.564844	+	1.28772i
$306$	−0.810351	+	2.16435i	−0.0463247	+	0.123728i
$307$	7.62289	−	13.2032i	0.435061	−	0.753548i	−0.562239	−	0.826975i	$-0.690060\pi$
$307$	7.62289	−	13.2032i	0.435061	−	0.753548i	0.997301	+	0.0734263i	$0.0233934\pi$
$308$	7.65903	−	7.45082i	0.436414	−	0.424550i
$309$	−14.8875	+	18.0769i	−0.846922	+	1.02836i
$310$	−2.46400	+	1.16279i	−0.139946	+	0.0660420i
$311$	13.3624	−	20.4526i	0.757711	−	1.15976i	−0.224954	−	0.974369i	$-0.572223\pi$
$311$	13.3624	−	20.4526i	0.757711	−	1.15976i	0.982664	−	0.185393i	$-0.0593559\pi$
$312$	0.330508	+	3.98864i	0.0187113	+	0.225812i
$313$	−11.7703	+	23.2587i	−0.665296	+	1.31466i	0.270705	+	0.962662i	$0.412743\pi$
$313$	−11.7703	+	23.2587i	−0.665296	+	1.31466i	−0.936001	+	0.351998i	$0.885502\pi$
$314$	9.10066	−	8.85326i	0.513580	−	0.499618i
$315$	−8.65971	+	4.68640i	−0.487919	+	0.264049i
$316$	9.54267	+	3.27600i	0.536817	+	0.184290i
$317$	30.9151	+	1.70563i	1.73636	+	0.0957978i	0.895391	−	0.445281i	$-0.146896\pi$
$317$	30.9151	+	1.70563i	1.73636	+	0.0957978i	0.840972	+	0.541079i	$0.181984\pi$
$318$	−0.190106	+	6.89669i	−0.0106606	+	0.386747i
$319$	0.0602538	+	2.18590i	0.00337357	+	0.122387i
$320$	4.26514	−	0.235314i	0.238429	−	0.0131545i
$321$	13.5585	+	3.83398i	0.756763	+	0.213992i
$322$	−3.69595	+	14.5950i	−0.205967	+	0.813347i
$323$	9.65126	+	5.30194i	0.537011	+	0.295008i
$324$	−2.67765	−	10.5738i	−0.148758	−	0.587433i
$325$	−0.738339	+	26.7856i	−0.0409557	+	1.48580i
$326$	−10.6937	+	2.39651i	−0.592268	+	0.132730i
$327$	−16.3004	+	22.1774i	−0.901412	+	1.22641i
$328$	−4.24231	+	1.72308i	−0.234243	+	0.0951411i
$329$	−0.785086	−	28.4815i	−0.0432832	−	1.57023i
$330$	−14.3974	−	32.8227i	−0.792548	−	1.80683i
$331$	−8.31338	+	1.38726i	−0.456945	+	0.0762506i	−0.388591	−	0.921410i	$-0.627038\pi$
$331$	−8.31338	+	1.38726i	−0.456945	+	0.0762506i	−0.0683542	+	0.997661i	$0.521775\pi$
$332$	−9.06641	−	2.03183i	−0.497584	−	0.111511i
$333$	1.39310	+	2.41293i	0.0763416	+	0.132227i
$334$	−5.17008	−	11.7866i	−0.282894	−	0.644934i
$335$	−1.85137	−	7.31088i	−0.101151	−	0.399436i
$336$	1.74809	+	4.66895i	0.0953663	+	0.254712i
$337$	15.1056	+	29.8494i	0.822854	+	1.62600i	0.779049	+	0.626963i	$0.215702\pi$
$337$	15.1056	+	29.8494i	0.822854	+	1.62600i	0.0438045	+	0.999040i	$0.486052\pi$
$338$	1.22358	−	8.82382i	0.0665540	−	0.479953i
$339$	−10.8253	+	13.1445i	−0.587951	+	0.713910i
$340$	8.86799	+	6.14893i	0.480934	+	0.333473i
$341$	2.13451	−	1.66135i	0.115590	−	0.0899673i
$342$	3.96611	−	0.413675i	0.214462	−	0.0223690i
$343$	15.2134	+	11.8411i	0.821448	+	0.639358i
$344$	1.81100	+	5.79009i	0.0976427	+	0.312181i
$345$	41.5006	+	28.7759i	2.23432	+	1.54924i
$346$	−5.81708	+	11.4949i	−0.312728	+	0.617968i
$347$	23.0183	+	2.54767i	1.23569	+	0.136766i	0.704016	−	0.710184i	$-0.251388\pi$
$347$	23.0183	+	2.54767i	1.23569	+	0.136766i	0.531672	+	0.846950i	$0.321564\pi$
$348$	−0.945273	−	0.383937i	−0.0506719	−	0.0205812i
$349$	−10.4329	−	1.74095i	−0.558463	−	0.0931910i	−0.121370	−	0.992607i	$-0.538729\pi$
$349$	−10.4329	−	1.74095i	−0.558463	−	0.0931910i	−0.437093	+	0.899416i	$0.643992\pi$
$350$	8.19383	+	32.3567i	0.437979	+	1.72954i
$351$	−0.229955	−	8.34235i	−0.0122741	−	0.445282i
$352$	−4.08068	+	1.15391i	−0.217501	+	0.0615034i
$353$	22.0235	−	7.56068i	1.17219	−	0.402415i	0.331253	−	0.943542i	$-0.392529\pi$
$353$	22.0235	−	7.56068i	1.17219	−	0.402415i	0.840941	+	0.541127i	$0.182002\pi$
$354$	−9.33002	+	10.1351i	−0.495885	+	0.538674i
$355$	−51.3207	+	49.9255i	−2.72382	+	2.64977i
$356$	−0.792673	−	0.549627i	−0.0420116	−	0.0291302i
$357$	−3.75967	+	12.0203i	−0.198983	+	0.636183i
$358$	1.23444	+	8.90213i	0.0652421	+	0.470492i
$359$	19.1832	+	26.0997i	1.01245	+	1.37749i	0.924423	+	0.381370i	$0.124548\pi$
$359$	19.1832	+	26.0997i	1.01245	+	1.37749i	0.0880275	+	0.996118i	$0.471944\pi$
$360$	3.90778			0.205958
$361$	0.762963	−	18.9847i	0.0401560	−	0.999193i
$362$	16.5864			0.871764
$363$	8.18311	+	11.1335i	0.429502	+	0.584359i
$364$	0.700075	+	5.04857i	0.0366939	+	0.264617i
$365$	−2.70489	+	8.64801i	−0.141580	+	0.452657i
$366$	9.34757	+	6.48146i	0.488605	+	0.338792i
$367$	−13.5440	+	13.1758i	−0.706993	+	0.687773i	−0.960097	−	0.279665i	$-0.909776\pi$
$367$	−13.5440	+	13.1758i	−0.706993	+	0.687773i	0.253104	+	0.967439i	$0.418548\pi$
$368$	4.04688	−	4.39608i	0.210958	−	0.229161i
$369$	−3.96191	+	1.36013i	−0.206249	+	0.0708053i
$370$	12.5189	−	3.54000i	0.650826	−	0.184036i
$371$	0.242097	+	8.78284i	0.0125691	+	0.455982i
$372$	0.309805	+	1.22339i	0.0160627	+	0.0634300i
$373$	−27.9324	−	4.66109i	−1.44628	−	0.241342i	−0.611205	−	0.791472i	$-0.709315\pi$
$373$	−27.9324	−	4.66109i	−1.44628	−	0.241342i	−0.835079	+	0.550130i	$0.814578\pi$
$374$	−9.92559	−	4.03143i	−0.513240	−	0.208460i
$375$	69.2774	+	7.66762i	3.57747	+	0.395954i
$376$	−5.10584	+	10.0894i	−0.263314	+	0.520322i
$377$	−0.857170	−	0.594349i	−0.0441465	−	0.0306105i
$378$	−3.10324	−	9.92160i	−0.159613	−	0.510312i
$379$	−28.9497	−	22.5324i	−1.48704	−	1.15741i	−0.949328	−	0.314287i	$-0.898235\pi$
$379$	−28.9497	−	22.5324i	−1.48704	−	1.15741i	−0.537716	−	0.843126i	$-0.680713\pi$
$380$	2.67369	−	18.4266i	0.137157	−	0.945266i
$381$	−5.28468	+	4.11323i	−0.270742	+	0.210727i
$382$	−22.2272	−	15.4120i	−1.13724	−	0.788546i
$383$	11.7512	−	14.2687i	0.600460	−	0.729098i	−0.380181	−	0.924912i	$-0.624138\pi$
$383$	11.7512	−	14.2687i	0.600460	−	0.729098i	0.980641	+	0.195814i	$0.0627350\pi$
$384$	0.271767	−	1.95984i	0.0138685	−	0.100013i
$385$	−20.6096	−	40.7257i	−1.05036	−	2.07557i
$386$	−1.15730	−	3.09102i	−0.0589052	−	0.157329i
$387$	1.36244	+	5.38013i	0.0692565	+	0.273488i
$388$	−4.84179	−	11.0382i	−0.245805	−	0.560378i
$389$	8.28991	+	14.3586i	0.420315	+	0.728008i	0.995970	−	0.0896853i	$-0.0285861\pi$
$389$	8.28991	+	14.3586i	0.420315	+	0.728008i	−0.575655	+	0.817693i	$0.695253\pi$
$390$	16.6826	+	3.73865i	0.844755	+	0.189314i
$391$	14.8890	−	2.48453i	0.752967	−	0.125648i
$392$	−0.261535	−	0.596239i	−0.0132095	−	0.0301146i
$393$	−1.02430	−	37.1596i	−0.0516690	−	1.87445i
$394$	24.0060	−	9.75041i	1.20941	−	0.491219i
$395$	25.5241	−	34.7268i	1.28426	−	1.74729i
$396$	−3.78558	+	0.848368i	−0.190233	+	0.0426321i
$397$	0.315805	−	11.4568i	0.0158498	−	0.575001i	−0.949459	−	0.313891i	$-0.898367\pi$
$397$	0.315805	−	11.4568i	0.0158498	−	0.575001i	0.965309	−	0.261110i	$-0.0840887\pi$
$398$	−6.40363	−	25.2874i	−0.320985	−	1.26754i
$399$	21.4569	−	3.44163i	1.07419	−	0.172297i
$400$	3.25190	−	12.8415i	0.162595	−	0.642073i
$401$	−2.41812	−	0.683780i	−0.120755	−	0.0341463i	0.211190	−	0.977445i	$-0.432266\pi$
$401$	−2.41812	−	0.683780i	−0.120755	−	0.0341463i	−0.331945	+	0.943299i	$0.607705\pi$
$402$	−3.48794	+	0.192435i	−0.173963	+	0.00959779i
$403$	0.0355510	+	1.28972i	0.00177092	+	0.0642457i
$404$	0.276172	−	10.0190i	0.0137401	−	0.498464i
$405$	−46.5223	−	2.56671i	−2.31171	−	0.127541i
$406$	−1.22890	−	0.421881i	−0.0609891	−	0.0209376i
$407$	−11.3589	+	6.14711i	−0.563038	+	0.304701i
$408$	3.58279	−	3.48539i	0.177374	−	0.172552i
$409$	11.1529	−	22.0387i	0.551474	−	1.08974i	−0.430827	−	0.902435i	$-0.641778\pi$
$409$	11.1529	−	22.0387i	0.551474	−	1.08974i	0.982301	−	0.187308i	$-0.0599763\pi$
$410$	1.61520	+	19.4925i	0.0797688	+	0.962667i
$411$	3.47941	−	5.32564i	0.171627	−	0.262694i
$412$	10.7038	−	5.05125i	0.527339	−	0.248857i
$413$	−11.1526	+	13.5418i	−0.548783	+	0.666350i
$414$	3.91810	−	3.81158i	0.192564	−	0.187329i
$415$	−19.8445	+	34.3716i	−0.974127	+	1.68724i
$416$	0.709272	−	1.89438i	0.0347749	−	0.0928797i
$417$	12.8204	−	29.2275i	0.627816	−	1.43128i
$418$	1.41029	+	18.4308i	0.0689795	+	0.901482i
$419$	4.07379	+	9.28732i	0.199018	+	0.453715i	0.986739	−	0.162317i	$-0.0518969\pi$
$419$	4.07379	+	9.28732i	0.199018	+	0.453715i	−0.787721	+	0.616033i	$0.788739\pi$
$420$	21.2637	−	1.17315i	1.03756	−	0.0572440i
$421$	9.73503	+	9.47038i	0.474456	+	0.461558i	0.895228	−	0.445608i	$-0.147013\pi$
$421$	9.73503	+	9.47038i	0.474456	+	0.461558i	−0.420772	+	0.907167i	$0.638241\pi$
$422$	−4.00416	−	20.4990i	−0.194919	−	0.997878i
$423$	−5.17231	+	8.95870i	−0.251486	+	0.435587i
$424$	1.57449	−	3.11127i	0.0764639	−	0.151097i
$425$	26.4085	−	20.5545i	1.28100	−	0.997041i
$426$	18.1390	+	27.7638i	0.878838	+	1.34516i
$427$	12.3406	+	7.58575i	0.597204	+	0.367100i
$428$	−5.37023	−	4.67694i	−0.259580	−	0.226068i
$429$	−16.9725			−0.819441
$430$	25.9147			1.24972
$431$	−3.66212	−	3.18934i	−0.176398	−	0.153625i	0.564046	−	0.825744i	$-0.309244\pi$
$431$	−3.66212	−	3.18934i	−0.176398	−	0.153625i	−0.740444	+	0.672118i	$0.765385\pi$
$432$	−0.790943	+	4.04919i	−0.0380543	+	0.194817i
$433$	−1.16782	+	0.809750i	−0.0561219	+	0.0389141i	−0.597537	−	0.801842i	$-0.703854\pi$
$433$	−1.16782	+	0.809750i	−0.0561219	+	0.0389141i	0.541415	+	0.840756i	$0.317889\pi$
$434$	0.479759	+	1.53387i	0.0230292	+	0.0736283i
$435$	−2.77062	+	3.36417i	−0.132841	+	0.161300i
$436$	12.2340	−	6.62073i	0.585904	−	0.317075i
$437$	−15.2923	−	21.0831i	−0.731528	−	1.00854i
$438$	3.69121	+	1.99758i	0.176373	+	0.0954482i
$439$	−4.65834	+	1.89205i	−0.222330	+	0.0903027i	−0.484756	−	0.874649i	$-0.661092\pi$
$439$	−4.65834	+	1.89205i	−0.222330	+	0.0903027i	0.262426	+	0.964952i	$0.415478\pi$
$440$	−0.499137	+	18.1078i	−0.0237954	+	0.863254i
$441$	−0.208847	−	0.557805i	−0.00994509	−	0.0265622i
$442$	4.35342	−	2.67604i	0.207071	−	0.127286i
$443$	10.4462	+	12.6841i	0.496313	+	0.602639i	0.958833	−	0.283969i	$-0.0916514\pi$
$443$	10.4462	+	12.6841i	0.496313	+	0.602639i	−0.462521	+	0.886609i	$0.653055\pi$
$444$	−0.497627	−	6.00546i	−0.0236163	−	0.285007i
$445$	−3.25153	+	2.53076i	−0.154137	+	0.119970i
$446$	−5.69980	+	18.2233i	−0.269894	+	0.862898i
$447$	4.25806	−	2.95247i	0.201399	−	0.139647i
$448$	0.208076	−	2.51110i	0.00983065	−	0.118638i
$449$	9.05725	+	13.8632i	0.427438	+	0.654243i	0.984329	−	0.176343i	$-0.0564268\pi$
$449$	9.05725	+	13.8632i	0.427438	+	0.654243i	−0.556891	+	0.830586i	$0.688006\pi$
$450$	3.61755	−	11.5659i	0.170533	−	0.545224i
$451$	−5.79645	−	18.5323i	−0.272944	−	0.872651i
$452$	7.78317	−	3.67297i	0.366090	−	0.172762i
$453$	18.6899	+	8.81999i	0.878129	+	0.414399i
$454$	−1.66740	+	1.02495i	−0.0782550	+	0.0481032i
$455$	21.4750	+	3.58355i	1.00677	+	0.167999i
$456$	−8.13936	−	2.85173i	−0.381161	−	0.133545i
$457$	24.3085	−	4.05638i	1.13711	−	0.189749i	0.434053	−	0.900887i	$-0.357083\pi$
$457$	24.3085	−	4.05638i	1.13711	−	0.189749i	0.703053	+	0.711138i	$0.251820\pi$
$458$	16.3150	−	14.2087i	0.762348	−	0.663930i
$459$	−7.85976	+	6.84507i	−0.366862	+	0.319500i
$460$	−12.7619	−	22.1042i	−0.595025	−	1.03061i
$461$	−12.4064	+	0.684478i	−0.577822	+	0.0318793i	−0.341642	−	0.939830i	$-0.610983\pi$
$461$	−12.4064	+	0.684478i	−0.577822	+	0.0318793i	−0.236180	+	0.971709i	$0.575895\pi$
$462$	−20.3441	+	5.75276i	−0.946493	+	0.267643i
$463$	24.7930	+	13.4173i	1.15223	+	0.623555i	0.935726	−	0.352727i	$-0.114745\pi$
$463$	24.7930	+	13.4173i	1.15223	+	0.623555i	0.216503	+	0.976282i	$0.430535\pi$
$464$	0.349243	+	0.379379i	0.0162132	+	0.0176122i
$465$	5.38265	+	0.296969i	0.249615	+	0.0137716i
$466$	5.73179	+	15.3089i	0.265520	+	0.709172i
$467$	−38.2472	−	6.38233i	−1.76987	−	0.295339i	−0.812235	−	0.583330i	$-0.801750\pi$
$467$	−38.2472	−	6.38233i	−1.76987	−	0.295339i	−0.957633	+	0.287991i	$0.907013\pi$
$468$	0.743341	−	1.69465i	0.0343610	−	0.0783351i
$469$	−4.42160	+	0.489382i	−0.204170	+	0.0225976i
$470$	34.6225	+	33.6813i	1.59702	+	1.55360i
$471$	−24.1734	+	6.83558i	−1.11385	+	0.314967i
$472$	6.45059	−	2.62001i	0.296913	−	0.120596i
$473$	−25.1043	+	5.62601i	−1.15430	+	0.258684i
$474$	−13.5204	−	14.6870i	−0.621010	−	0.674597i
$475$	−52.0625	−	24.9714i	−2.38879	−	1.14577i
$476$	4.31119	−	4.68320i	0.197603	−	0.214654i
$477$	1.59499	−	2.76260i	0.0730294	−	0.126491i
$478$	14.6739	+	1.62411i	0.671170	+	0.0742851i
$479$	15.1506	+	18.3963i	0.692247	+	0.840549i	0.993599	−	0.112964i	$-0.0360345\pi$
$479$	15.1506	+	18.3963i	0.692247	+	0.840549i	−0.301352	+	0.953513i	$0.597438\pi$
$480$	−7.64345	−	3.60703i	−0.348874	−	0.164638i
$481$	0.846195	−	6.10232i	0.0385832	−	0.278242i
$482$	0.301985	−	0.163426i	0.0137550	−	0.00744385i
$483$	20.1756	−	21.9165i	0.918021	−	0.997236i
$484$	−1.33880	−	6.85389i	−0.0608544	−	0.311540i
$485$	−51.1751	+	5.66406i	−2.32374	+	0.257192i
$486$	−2.25957	+	8.92282i	−0.102496	+	0.404748i
$487$	8.17488	−	1.36415i	0.370439	−	0.0618154i	0.0235530	−	0.999723i	$-0.492502\pi$
$487$	8.17488	−	1.36415i	0.370439	−	0.0618154i	0.346886	+	0.937907i	$0.387239\pi$
$488$	−2.87447	−	4.97874i	−0.130121	−	0.225377i
$489$	20.8651	+	5.90008i	0.943552	+	0.266811i
$490$	−2.76428	+	0.305950i	−0.124877	+	0.0138214i
$491$	0.476262	−	1.27204i	0.0214934	−	0.0574063i	−0.925325	−	0.379176i	$-0.876207\pi$
$491$	0.476262	−	1.27204i	0.0214934	−	0.0574063i	0.946818	+	0.321770i	$0.104278\pi$
$492$	9.00477	+	0.996647i	0.405966	+	0.0449323i
$493$	0.107574	+	1.29822i	0.00484489	+	0.0584691i
$494$	−7.48229	−	4.66460i	−0.336644	−	0.209870i
$495$	−1.36848	+	16.5151i	−0.0615086	+	0.742298i
$496$	0.122279	−	0.626002i	0.00549050	−	0.0281083i
$497$	25.0124	+	34.0306i	1.12196	+	1.52648i
$498$	13.8632	+	12.0735i	0.621227	+	0.541027i
$499$	−3.01206	−	4.09806i	−0.134839	−	0.183454i	0.733108	−	0.680112i	$-0.238069\pi$
$499$	−3.01206	−	4.09806i	−0.134839	−	0.183454i	−0.867946	+	0.496658i	$0.834560\pi$
$500$	−30.0108	−	18.4476i	−1.34212	−	0.825001i
$501$	−2.10295	+	25.3788i	−0.0939527	+	1.13384i
$502$	−8.59554	−	6.69018i	−0.383638	−	0.298597i
$503$	27.5182	−	12.9861i	1.22698	−	0.579023i	0.299926	−	0.953963i	$-0.403038\pi$
$503$	27.5182	−	12.9861i	1.22698	−	0.579023i	0.927049	+	0.374939i	$0.122336\pi$
$504$	0.316612	−	2.28324i	0.0141030	−	0.101704i
$505$	−40.4939	−	13.9016i	−1.80196	−	0.618612i
$506$	17.1615	+	18.6424i	0.762923	+	0.828755i
$507$	−10.4386	+	14.2022i	−0.463595	+	0.630744i
$508$	3.30269	−	0.740149i	0.146533	−	0.0328388i
$509$	41.5196	+	2.29070i	1.84033	+	0.101534i	0.941549	−	0.336875i	$-0.109370\pi$
$509$	41.5196	+	2.29070i	1.84033	+	0.101534i	0.898776	+	0.438409i	$0.144458\pi$
$510$	−9.64088	−	19.0509i	−0.426905	−	0.843588i
$511$	4.83370	+	2.28108i	0.213830	+	0.100909i
$512$	−0.546948	+	0.837166i	−0.0241719	+	0.0369979i
$513$	16.6187	+	6.87229i	0.733732	+	0.303419i
$514$	6.50839	+	9.96184i	0.287073	+	0.439398i
$515$	−6.94435	−	50.0790i	−0.306005	−	2.20675i
$516$	2.30120	−	11.7809i	0.101305	−	0.518624i
$517$	−40.8519	−	25.1116i	−1.79666	−	1.10440i
$518$	−1.05406	−	7.60134i	−0.0463128	−	0.333984i
$519$	20.9472	−	14.5245i	0.919480	−	0.637553i
$520$	−6.81871	−	5.30721i	−0.299020	−	0.232737i
$521$	−12.0655	+	18.4676i	−0.528600	+	0.809082i	−0.997235	−	0.0743097i	$-0.976325\pi$
$521$	−12.0655	+	18.4676i	−0.528600	+	0.809082i	0.468636	+	0.883392i	$0.344746\pi$
$522$	0.299891	+	0.364138i	0.0131259	+	0.0159379i
$523$	13.4202	+	5.45081i	0.586824	+	0.238347i	0.650352	−	0.759633i	$-0.274621\pi$
$523$	13.4202	+	5.45081i	0.586824	+	0.238347i	−0.0635282	+	0.997980i	$0.520235\pi$
$524$	−7.54705	+	17.2055i	−0.329694	+	0.751627i
$525$	16.2122	−	64.0207i	0.707560	−	2.79409i
$526$	−6.03963	−	1.35351i	−0.263340	−	0.0590160i
$527$	1.21511	−	1.05824i	0.0529312	−	0.0460978i
$528$	8.18750	+	1.83486i	0.356315	+	0.0798521i
$529$	−12.2234	−	3.45645i	−0.531453	−	0.150281i
$530$	−10.6765	−	10.3863i	−0.463759	−	0.451152i
$531$	6.02423	−	2.06812i	0.261429	−	0.0897488i
$532$	−10.5497	−	3.05512i	−0.457387	−	0.132456i
$533$	8.76036	+	3.00743i	0.379453	+	0.130266i
$534$	0.861758	+	1.70288i	0.0372919	+	0.0736908i
$535$	−25.9151	+	15.9299i	−1.12041	+	0.688711i
$536$	1.63575	+	0.664383i	0.0706535	+	0.0286970i
$537$	6.23511	−	16.6532i	0.269065	−	0.718640i
$538$	−3.86999	−	19.8122i	−0.166847	−	0.854164i
$539$	2.61141	−	0.896500i	0.112482	−	0.0386150i
$540$	15.4994	+	8.38786i	0.666989	+	0.360956i
$541$	14.7042	−	20.0058i	0.632183	−	0.860116i	−0.365310	−	0.930886i	$-0.619037\pi$
$541$	14.7042	−	20.0058i	0.632183	−	0.860116i	0.997493	+	0.0707700i	$0.0225456\pi$
$542$	−9.88744	+	13.4523i	−0.424702	+	0.577828i
$543$	−28.8624	−	15.6195i	−1.23860	−	0.670299i
$544$	−2.38938	+	0.820274i	−0.102444	+	0.0351690i
$545$	−11.3916	−	58.3189i	−0.487964	−	2.49811i
$546$	3.53605	−	9.44438i	0.151329	−	0.404182i
$547$	12.2334	+	4.96876i	0.523061	+	0.212449i	0.622536	−	0.782591i	$-0.286102\pi$
$547$	12.2334	+	4.96876i	0.523061	+	0.212449i	−0.0994753	+	0.995040i	$0.531716\pi$
$548$	−2.73907	+	1.68370i	−0.117007	+	0.0719240i
$549$	−2.37474	−	4.69261i	−0.101351	−	0.200276i
$550$	53.1318	+	18.2402i	2.26555	+	0.777764i
$551$	1.92223	−	1.16496i	0.0818897	−	0.0496288i
$552$	−11.1819	+	3.83874i	−0.475931	+	0.163387i
$553$	−18.2222	−	17.7268i	−0.774886	−	0.753820i
$554$	−4.70693	−	1.33099i	−0.199978	−	0.0565484i
$555$	−25.1180	−	5.62907i	−1.06620	−	0.238941i
$556$	−12.1641	+	10.5937i	−0.515873	+	0.449274i
$557$	18.4352	+	4.13143i	0.781125	+	0.175054i	0.590963	−	0.806698i	$-0.298748\pi$
$557$	18.4352	+	4.13143i	0.781125	+	0.175054i	0.190162	+	0.981753i	$0.439099\pi$
$558$	0.143242	−	0.565649i	0.00606391	−	0.0239458i
$559$	4.92952	−	11.2382i	0.208496	−	0.475324i
$560$	−9.97209	−	4.05031i	−0.421398	−	0.171157i
$561$	13.4753	+	16.3621i	0.568927	+	0.690810i
$562$	13.4886	−	20.6459i	0.568983	−	0.870893i
$563$	8.15360	+	6.34620i	0.343633	+	0.267460i	0.771294	−	0.636479i	$-0.219610\pi$
$563$	8.15360	+	6.34620i	0.343633	+	0.267460i	−0.427661	+	0.903939i	$0.640662\pi$
$564$	18.3860	−	12.7486i	0.774191	−	0.536812i
$565$	−5.04952	−	36.4145i	−0.212435	−	1.53197i
$566$	−5.77343	−	3.54891i	−0.242675	−	0.149172i
$567$	−5.26895	+	26.9741i	−0.221275	+	1.13281i
$568$	−2.30224	−	16.6026i	−0.0966000	−	0.696629i
$569$	20.8520	+	31.9163i	0.874160	+	1.33800i	0.940355	+	0.340194i	$0.110493\pi$
$569$	20.8520	+	31.9163i	0.874160	+	1.33800i	−0.0661957	+	0.997807i	$0.521086\pi$
$570$	−22.0050	+	29.5467i	−0.921688	+	1.23758i
$571$	21.8414	−	33.4307i	0.914033	−	1.39903i	−0.00290250	−	0.999996i	$-0.500924\pi$
$571$	21.8414	−	33.4307i	0.914033	−	1.39903i	0.916935	−	0.399036i	$-0.130655\pi$
$572$	7.75766	+	3.66093i	0.324364	+	0.153071i
$573$	24.1644	+	47.7501i	1.00948	+	1.99479i
$574$	11.5199	+	0.635573i	0.480833	+	0.0265283i
$575$	−77.2362	+	17.3090i	−3.22097	+	0.721837i
$576$	−0.541790	+	0.737132i	−0.0225746	+	0.0307139i
$577$	5.69694	+	6.18853i	0.237167	+	0.257632i	0.842942	−	0.538004i	$-0.180821\pi$
$577$	5.69694	+	6.18853i	0.237167	+	0.257632i	−0.605776	+	0.795635i	$0.707137\pi$
$578$	10.0427	+	3.44767i	0.417722	+	0.143404i
$579$	−0.896984	+	6.46858i	−0.0372774	+	0.268825i
$580$	1.99201	−	0.940053i	0.0827138	−	0.0390336i
$581$	18.4748	+	14.3795i	0.766465	+	0.596564i
$582$	−1.96941	+	23.7673i	−0.0816348	+	0.985185i
$583$	12.5975	+	7.74365i	0.521735	+	0.320709i
$584$	−1.25627	−	1.70922i	−0.0519850	−	0.0707281i
$585$	−5.96098	−	5.19142i	−0.246456	−	0.214639i
$586$	−3.98591	−	5.42303i	−0.164656	−	0.224023i
$587$	−2.16286	+	11.0726i	−0.0892706	+	0.457016i	0.909844	+	0.414950i	$0.136201\pi$
$587$	−2.16286	+	11.0726i	−0.0892706	+	0.457016i	−0.999115	+	0.0420658i	$0.986606\pi$
$588$	−0.106380	+	1.28382i	−0.00438704	+	0.0529437i
$589$	−2.56924	−	1.06245i	−0.105864	−	0.0437776i
$590$	−2.45596	−	29.6391i	−0.101110	−	1.22022i
$591$	−50.9554	−	5.63974i	−2.09602	−	0.231988i
$592$	−1.06791	+	2.85226i	−0.0438908	+	0.117227i
$593$	−17.4946	+	1.93630i	−0.718415	+	0.0795142i	−0.461780	−	0.886994i	$-0.652789\pi$
$593$	−17.4946	+	1.93630i	−0.718415	+	0.0795142i	−0.256635	+	0.966508i	$0.582614\pi$
$594$	−16.8357	−	4.76068i	−0.690777	−	0.195333i
$595$	−13.5954	−	23.5479i	−0.557356	−	0.965368i
$596$	−2.58308	+	0.431040i	−0.105807	+	0.0176561i
$597$	−12.6702	+	50.0334i	−0.518556	+	2.04773i
$598$	−12.0133	+	1.32963i	−0.491259	+	0.0543725i
$599$	−1.61445	−	8.26510i	−0.0659648	−	0.337703i	0.933835	−	0.357704i	$-0.116440\pi$
$599$	−1.61445	−	8.26510i	−0.0659648	−	0.337703i	−0.999800	+	0.0200006i	$0.993633\pi$
$600$	−17.7516	+	19.2833i	−0.724705	+	0.787239i
$601$	6.19754	−	3.35394i	0.252803	−	0.136810i	−0.344605	−	0.938748i	$-0.611987\pi$
$601$	6.19754	−	3.35394i	0.252803	−	0.136810i	0.597407	+	0.801938i	$0.296198\pi$
$602$	2.09963	−	15.1414i	0.0855746	−	0.617119i
$603$	1.46066	+	0.689304i	0.0594828	+	0.0280706i
$604$	−6.64018	−	8.06273i	−0.270185	−	0.328068i
$605$	−29.6495	−	3.28161i	−1.20542	−	0.133416i
$606$	−9.91552	+	17.1742i	−0.402790	+	0.697653i
$607$	9.57764	−	10.4041i	0.388744	−	0.422289i	−0.510403	−	0.859936i	$-0.670504\pi$
$607$	9.57764	−	10.4041i	0.388744	−	0.422289i	0.899147	+	0.437646i	$0.144188\pi$
$608$	3.10516	+	3.05908i	0.125931	+	0.124062i
$609$	1.74114	+	1.89138i	0.0705546	+	0.0766427i
$610$	−23.9630	+	5.37023i	−0.970233	+	0.217434i
$611$	21.1921	−	8.60749i	0.857341	−	0.348222i
$612$	−2.22388	+	0.628852i	−0.0898949	+	0.0254198i
$613$	−18.6323	−	18.1258i	−0.752551	−	0.732093i	0.217217	−	0.976123i	$-0.430302\pi$
$613$	−18.6323	−	18.1258i	−0.752551	−	0.732093i	−0.969768	+	0.244031i	$0.921530\pi$
$614$	15.1532	−	1.67716i	0.611535	−	0.0676847i
$615$	15.5456	−	35.4403i	0.626858	−	1.42909i
$616$	10.5396	+	1.75874i	0.424651	+	0.0708617i
$617$	12.4725	+	33.3125i	0.502123	+	1.34111i	0.904826	+	0.425781i	$0.140001\pi$
$617$	12.4725	+	33.3125i	0.502123	+	1.34111i	−0.402703	+	0.915331i	$0.631929\pi$
$618$	−23.3827	−	1.29006i	−0.940589	−	0.0518938i
$619$	−23.4735	−	25.4990i	−0.943481	−	1.02489i	−0.999650	−	0.0264718i	$-0.991573\pi$
$619$	−23.4735	−	25.4990i	−0.943481	−	1.02489i	0.0561690	−	0.998421i	$-0.482111\pi$
$620$	−2.39620	−	1.29676i	−0.0962337	−	0.0520791i
$621$	23.7217	−	6.70786i	0.951919	−	0.269177i
$622$	24.3937	−	1.34584i	0.978098	−	0.0539632i
$623$	1.21523	+	2.10484i	0.0486873	+	0.0843288i
$624$	−3.01817	+	2.62852i	−0.120823	+	0.105225i
$625$	−63.5289	+	55.3274i	−2.54116	+	2.21309i
$626$	−25.7118	+	4.29055i	−1.02765	+	0.171485i
$627$	14.9024	−	33.3999i	0.595143	−	1.33387i
$628$	12.5234	+	2.08978i	0.499737	+	0.0833914i
$629$	−6.55469	+	4.02915i	−0.261353	+	0.160653i
$630$	−8.90473	−	4.20224i	−0.354773	−	0.167421i
$631$	15.1984	−	7.17231i	0.605039	−	0.285525i	−0.0996706	−	0.995020i	$-0.531779\pi$
$631$	15.1984	−	7.17231i	0.605039	−	0.285525i	0.704710	+	0.709496i	$0.251077\pi$
$632$	3.01182	+	9.62931i	0.119804	+	0.383034i
$633$	−12.3364	+	39.4415i	−0.490326	+	1.56766i
$634$	16.9347	+	25.9204i	0.672561	+	1.02943i
$635$	1.19391	−	14.4084i	0.0473790	−	0.571780i
$636$	−5.66970	+	3.93128i	−0.224818	+	0.155886i
$637$	−0.393145	+	1.25695i	−0.0155770	+	0.0498023i
$638$	−1.72563	+	1.34312i	−0.0683185	+	0.0531744i
$639$	−1.26625	−	15.2814i	−0.0500921	−	0.604522i
$640$	2.71558	+	3.29734i	0.107343	+	0.130339i
$641$	−25.5034	+	15.6769i	−1.00733	+	0.619200i	−0.926014	−	0.377488i	$-0.876788\pi$
$641$	−25.5034	+	15.6769i	−1.00733	+	0.619200i	−0.0813107	+	0.996689i	$0.525911\pi$
$642$	4.94054	+	13.1956i	0.194988	+	0.520789i
$643$	−0.319200	+	11.5800i	−0.0125880	+	0.456670i	0.966899	+	0.255161i	$0.0821285\pi$
$643$	−0.319200	+	11.5800i	−0.0125880	+	0.456670i	−0.979487	+	0.201509i	$0.935415\pi$
$644$	−13.9490	+	5.66560i	−0.549668	+	0.223256i
$645$	−45.0947	−	24.4040i	−1.77560	−	0.960907i
$646$	1.44370	+	10.9166i	0.0568017	+	0.429510i
$647$	5.28693	−	2.86114i	0.207851	−	0.112483i	−0.368687	−	0.929553i	$-0.620193\pi$
$647$	5.28693	−	2.86114i	0.207851	−	0.112483i	0.576538	+	0.817070i	$0.304403\pi$
$648$	6.93420	−	8.41973i	0.272401	−	0.330758i
$649$	8.81372	+	28.1790i	0.345969	+	1.10612i
$650$	−22.0201	+	15.2684i	−0.863701	+	0.598877i
$651$	0.609620	−	3.12091i	0.0238929	−	0.122318i
$652$	−8.26420	−	7.19730i	−0.323651	−	0.281868i
$653$	18.7746			0.734709			0.367354	−	0.930081i	$-0.380264\pi$
$653$	18.7746			0.734709			0.367354	+	0.930081i	$0.380264\pi$
$654$	−27.5234			−1.07625
$655$	60.5210	+	52.7078i	2.36475	+	2.05946i
$656$	−3.90085	−	2.39784i	−0.152302	−	0.0936200i
$657$	−1.06139	−	1.62457i	−0.0414086	−	0.0633806i
$658$	22.4844	−	17.5003i	0.876534	−	0.682234i
$659$	21.1490	−	41.7917i	0.823850	−	1.62797i	0.0464871	−	0.998919i	$-0.485197\pi$
$659$	21.1490	−	41.7917i	0.823850	−	1.62797i	0.777363	−	0.629053i	$-0.216557\pi$
$660$	17.9207	−	31.0396i	0.697563	−	1.20822i
$661$	−7.78595	−	39.8597i	−0.302839	−	1.55036i	−0.753366	−	0.657602i	$-0.771571\pi$
$661$	−7.78595	−	39.8597i	−0.302839	−	1.55036i	0.450527	−	0.892763i	$-0.351236\pi$
$662$	−6.04128	−	5.87705i	−0.234801	−	0.228418i
$663$	−10.0955	+	0.556984i	−0.392077	+	0.0216315i
$664$	−3.73227	−	8.50872i	−0.144840	−	0.330202i
$665$	−25.9077	+	39.1139i	−1.00466	+	1.51677i
$666$	−1.11921	+	2.55153i	−0.0433684	+	0.0988699i
$667$	1.08036	−	2.88551i	0.0418316	−	0.111727i
$668$	6.43533	−	11.1463i	0.248990	−	0.431264i
$669$	27.0793	−	26.3432i	1.04695	−	1.01849i
$670$	4.79441	−	5.82153i	0.185224	−	0.224905i
$671$	22.0478	−	10.4046i	0.851144	−	0.401665i
$672$	−2.72679	+	4.17367i	−0.105188	+	0.161003i
$673$	3.72544	+	44.9594i	0.143605	+	1.73306i	0.564051	+	0.825740i	$0.309242\pi$
$673$	3.72544	+	44.9594i	0.143605	+	1.73306i	−0.420446	+	0.907318i	$0.638126\pi$
$674$	−15.1056	+	29.8494i	−0.581845	+	1.14976i
$675$	39.1740	−	38.1090i	1.50781	−	1.46682i
$676$	7.83457	−	4.23986i	0.301330	−	0.163072i
$677$	8.78946	+	3.01742i	0.337806	+	0.115969i	0.488383	−	0.872629i	$-0.337587\pi$
$677$	8.78946	+	3.01742i	0.337806	+	0.115969i	−0.150577	+	0.988598i	$0.548113\pi$
$678$	−17.0025	−	0.938054i	−0.652977	−	0.0360257i
$679$	−0.836853	+	30.3595i	−0.0321155	+	1.16509i
$680$	0.297345	+	10.7871i	0.0114027	+	0.413668i
$681$	3.86667	−	0.213330i	0.148171	−	0.00817483i
$682$	2.60279	+	0.735999i	0.0996660	+	0.0281829i
$683$	9.01743	−	35.6090i	0.345042	−	1.36254i	−0.517121	−	0.855912i	$-0.672996\pi$
$683$	9.01743	−	35.6090i	0.345042	−	1.36254i	0.862164	−	0.506630i	$-0.169109\pi$
$684$	2.68219	+	2.95076i	0.102556	+	0.112825i
$685$	3.37150	+	13.3138i	0.128818	+	0.508692i
$686$	−0.531206	+	19.2712i	−0.0202815	+	0.735776i
$687$	−41.7704	+	9.36096i	−1.59364	+	0.357143i
$688$	−3.59292	+	4.88834i	−0.136979	+	0.186366i
$689$	−6.53502	+	2.65429i	−0.248964	+	0.101121i
$690$	1.39152	+	50.4818i	0.0529743	+	1.92181i
$691$	−0.446888	−	1.01880i	−0.0170004	−	0.0387571i	0.907068	−	0.420984i	$-0.138315\pi$
$691$	−0.446888	−	1.01880i	−0.0170004	−	0.0387571i	−0.924068	+	0.382227i	$0.875157\pi$
$692$	−12.7072	+	2.12046i	−0.483057	+	0.0806080i
$693$	9.53855	+	2.13764i	0.362340	+	0.0812022i
$694$	11.5794	+	20.0562i	0.439550	+	0.761322i
$695$	27.6782	+	63.0999i	1.04989	+	2.39352i
$696$	−0.250461	−	0.989048i	−0.00949370	−	0.0374898i
$697$	−4.05598	−	10.8330i	−0.153631	−	0.410331i
$698$	−4.77596	−	9.43756i	−0.180773	−	0.357217i
$699$	4.44250	−	32.0370i	0.168031	−	1.21175i
$700$	−21.2192	+	25.7651i	−0.802012	+	0.973829i
$701$	25.3149	+	17.5529i	0.956129	+	0.662965i	0.941530	−	0.336928i	$-0.109388\pi$
$701$	25.3149	+	17.5529i	0.956129	+	0.662965i	0.0145989	+	0.999893i	$0.495353\pi$
$702$	6.58579	−	5.12592i	0.248565	−	0.193466i
$703$	11.2657	+	7.02322i	0.424892	+	0.264886i
$704$	−3.34650	−	2.60468i	−0.126126	−	0.0981677i
$705$	−28.5294	−	91.2136i	−1.07448	−	3.43530i
$706$	19.1352	+	13.2681i	0.720164	+	0.499351i
$707$	−11.4033	+	22.5335i	−0.428864	+	0.847458i
$708$	−13.6921	−	1.51544i	−0.514580	−	0.0569537i
$709$	21.3060	+	8.65376i	0.800164	+	0.324999i	0.739497	−	0.673159i	$-0.235063\pi$
$709$	21.3060	+	8.65376i	0.800164	+	0.324999i	0.0606669	+	0.998158i	$0.480677\pi$
$710$	−70.6221	−	11.7848i	−2.65040	−	0.442274i
$711$	2.26582	+	8.94752i	0.0849749	+	0.335558i
$712$	−0.0265784	−	0.964216i	−0.000996069	−	0.0361355i
$713$	−3.66736	+	1.03703i	−0.137344	+	0.0388371i
$714$	−11.9122	+	4.08945i	−0.445802	+	0.153044i
$715$	24.8172	−	26.9587i	0.928112	−	1.00820i
$716$	−6.44195	+	6.26682i	−0.240747	+	0.234202i
$717$	−24.0049	−	16.6447i	−0.896481	−	0.621606i
$718$	−9.66924	+	30.9143i	−0.360853	+	1.15371i
$719$	−4.24097	−	30.5836i	−0.158161	−	1.14058i	−0.888960	−	0.457985i	$-0.848572\pi$
$719$	−4.24097	−	30.5836i	−0.158161	−	1.14058i	0.730799	−	0.682593i	$-0.239148\pi$
$720$	2.31433	+	3.14876i	0.0862499	+	0.117347i
$721$	−29.8228			−1.11066
$722$	15.7490	−	10.6286i	0.586119	−	0.395556i
$723$	−0.679388			−0.0252667
$724$	9.82308	+	13.3648i	0.365072	+	0.496698i
$725$	−0.938230	−	6.76603i	−0.0348450	−	0.251284i
$726$	−4.12468	+	13.1873i	−0.153081	+	0.489428i
$727$	8.43107	+	5.84597i	0.312691	+	0.216815i	0.715746	−	0.698361i	$-0.246087\pi$
$727$	8.43107	+	5.84597i	0.312691	+	0.216815i	−0.403055	+	0.915176i	$0.632052\pi$
$728$	−3.65335	+	3.55404i	−0.135402	+	0.131721i
$729$	−9.82790	+	10.6759i	−0.363996	+	0.395405i
$730$	−8.57019	+	2.94215i	−0.317197	+	0.108894i
$731$	−14.7478	+	4.17027i	−0.545466	+	0.154243i
$732$	0.313426	+	11.3705i	0.0115845	+	0.420266i
$733$	−3.76374	−	14.8627i	−0.139017	−	0.548965i	−0.999238	−	0.0390430i	$-0.987569\pi$
$733$	−3.76374	−	14.8627i	−0.139017	−	0.548965i	0.860221	−	0.509922i	$-0.170326\pi$
$734$	−18.6379	−	3.11011i	−0.687937	−	0.114796i
$735$	5.09829	+	2.07075i	0.188053	+	0.0763807i
$736$	5.93891	+	0.657318i	0.218911	+	0.0242291i
$737$	−3.38064	+	6.68033i	−0.124528	+	0.246073i
$738$	−3.44232	−	2.38685i	−0.126714	−	0.0878613i
$739$	−7.42097	−	23.7262i	−0.272985	−	0.872781i	−0.985287	−	0.170908i	$-0.945330\pi$
$739$	−7.42097	−	23.7262i	−0.272985	−	0.872781i	0.712302	−	0.701873i	$-0.247653\pi$
$740$	10.2665	+	7.99077i	0.377405	+	0.293746i
$741$	8.62740	+	15.1631i	0.316936	+	0.557029i
$742$	−6.93352	+	5.39658i	−0.254538	+	0.198115i
$743$	40.3288	+	27.9634i	1.47952	+	1.02588i	0.987904	+	0.155066i	$0.0495591\pi$
$743$	40.3288	+	27.9634i	1.47952	+	1.02588i	0.491618	+	0.870811i	$0.336406\pi$
$744$	−0.802290	+	0.974167i	−0.0294134	+	0.0357147i
$745$	−1.53651	+	11.0805i	−0.0562933	+	0.405958i
$746$	−12.7868	−	25.2674i	−0.468158	−	0.925105i
$747$	−2.98038	−	7.96024i	−0.109046	−	0.291250i
$748$	−2.62990	−	10.3852i	−0.0961587	−	0.379722i
$749$	7.20787	+	16.4323i	0.263370	+	0.600423i
$750$	34.8502	+	60.3623i	1.27255	+	2.20412i
$751$	−14.0080	−	3.13928i	−0.511161	−	0.114554i	−0.0445335	−	0.999008i	$-0.514180\pi$
$751$	−14.0080	−	3.13928i	−0.511161	−	0.114554i	−0.466627	+	0.884454i	$0.654531\pi$
$752$	−11.1536	+	1.86120i	−0.406728	+	0.0678710i
$753$	8.65709	+	19.7362i	0.315482	+	0.719226i
$754$	−0.0287411	−	1.04267i	−0.00104669	−	0.0379719i
$755$	−41.3378	+	16.7900i	−1.50444	+	0.611050i
$756$	6.15663	−	8.37640i	0.223915	−	0.304647i
$757$	−30.3128	+	6.79327i	−1.10174	+	0.246905i	−0.731371	−	0.681980i	$-0.761119\pi$
$757$	−30.3128	+	6.79327i	−1.10174	+	0.246905i	−0.370368	+	0.928885i	$0.620768\pi$
$758$	1.01083	−	36.6711i	0.0367151	−	1.33195i
$759$	−12.3075	−	48.6011i	−0.446733	−	1.76411i
$760$	16.4310	−	8.75853i	0.596015	−	0.317705i
$761$	6.25243	−	24.6903i	0.226650	−	0.895022i	−0.746600	−	0.665274i	$-0.768315\pi$
$761$	6.25243	−	24.6903i	0.226650	−	0.895022i	0.973250	−	0.229749i	$-0.0737904\pi$
$762$	−6.44407	−	1.82221i	−0.233444	−	0.0660117i
$763$	−34.9975	+	1.93086i	−1.26699	+	0.0699020i
$764$	−0.745281	−	27.0374i	−0.0269633	−	0.978179i
$765$	−0.272018	+	9.86832i	−0.00983484	+	0.356790i
$766$	18.4567	+	1.01829i	0.666869	+	0.0367922i
$767$	−13.3204	−	4.57291i	−0.480973	−	0.165118i
$768$	1.74012	−	0.941705i	0.0627911	−	0.0339809i
$769$	4.62228	−	4.49662i	0.166684	−	0.162152i	−0.609226	−	0.792997i	$-0.708520\pi$
$769$	4.62228	−	4.49662i	0.166684	−	0.162152i	0.775909	+	0.630845i	$0.217292\pi$
$770$	20.6096	−	40.7257i	0.742718	−	1.46765i
$771$	−1.94426	−	23.4638i	−0.0700209	−	0.845027i
$772$	1.80524	−	2.76313i	0.0649720	−	0.0994471i
$773$	−21.2879	+	10.0460i	−0.765671	+	0.361329i	−0.769486	−	0.638664i	$-0.779488\pi$
$773$	−21.2879	+	10.0460i	−0.765671	+	0.361329i	0.00381459	+	0.999993i	$0.498786\pi$
$774$	−3.52824	+	4.28411i	−0.126820	+	0.153989i
$775$	−6.05627	+	5.89164i	−0.217548	+	0.211634i
$776$	6.02670	−	10.4385i	0.216346	−	0.374722i
$777$	−5.32403	+	14.2199i	−0.190999	+	0.510135i
$778$	−6.66004	+	15.1834i	−0.238774	+	0.544350i
$779$	−13.6101	+	14.5987i	−0.487633	+	0.523054i
$780$	6.86753	+	15.6564i	0.245897	+	0.560589i
$781$	70.9721	−	3.91564i	2.53958	−	0.140113i
$782$	10.8197	+	10.5256i	0.386912	+	0.376394i
$783$	0.407853	+	2.08798i	0.0145755	+	0.0746183i
$784$	0.325539	−	0.563849i	0.0116264	−	0.0201375i
$785$	24.4889	−	48.3913i	0.874045	−	1.72716i
$786$	29.3353	−	22.8326i	1.04636	−	0.814411i
$787$	−5.96005	−	9.12254i	−0.212453	−	0.325183i	0.714999	−	0.699125i	$-0.246427\pi$
$787$	−5.96005	−	9.12254i	−0.212453	−	0.325183i	−0.927452	+	0.373942i	$0.878006\pi$
$788$	22.0738	+	13.5687i	0.786345	+	0.483365i
$789$	9.23507	+	8.04283i	0.328777	+	0.286332i
$790$	43.0979			1.53335
$791$	−21.6854			−0.771043
$792$	−2.92554	−	2.54785i	−0.103955	−	0.0905341i
$793$	−2.22941	+	11.4133i	−0.0791685	+	0.405299i
$794$	9.41853	−	6.53066i	0.334251	−	0.231765i
$795$	8.79762	+	28.1276i	0.312019	+	0.997582i
$796$	16.5832	−	20.1359i	0.587777	−	0.713698i
$797$	−14.3494	+	7.76552i	−0.508283	+	0.275069i	−0.709784	−	0.704419i	$-0.751207\pi$
$797$	−14.3494	+	7.76552i	−0.508283	+	0.275069i	0.201501	+	0.979488i	$0.435418\pi$
$798$	15.4807	+	15.2510i	0.548010	+	0.539878i
$799$	−25.1234	−	13.5961i	−0.888800	−	0.480995i
$800$	12.2731	−	4.98490i	0.433919	−	0.176243i
$801$	0.0243146	−	0.882087i	0.000859113	−	0.0311670i
$802$	−0.881132	−	2.35340i	−0.0311138	−	0.0831014i
$803$	7.66345	−	4.71071i	0.270437	−	0.166237i
$804$	−2.22074	−	2.69650i	−0.0783195	−	0.0950981i
$805$	5.31087	+	64.0926i	0.187184	+	2.25897i
$806$	−1.01816	+	0.792465i	−0.0358631	+	0.0279134i
$807$	−11.9230	+	38.1200i	−0.419710	+	1.34189i
$808$	8.23652	−	5.71108i	0.289760	−	0.200915i
$809$	−1.75686	+	21.2022i	−0.0617680	+	0.745429i	0.893380	+	0.449301i	$0.148327\pi$
$809$	−1.75686	+	21.2022i	−0.0617680	+	0.745429i	−0.955148	+	0.296128i	$0.904305\pi$
$810$	−25.4840	−	39.0062i	−0.895416	−	1.37054i
$811$	−16.4648	+	52.6407i	−0.578156	+	1.84847i	−0.0509987	+	0.998699i	$0.516240\pi$
$811$	−16.4648	+	52.6407i	−0.578156	+	1.84847i	−0.527157	+	0.849768i	$0.676742\pi$
$812$	−0.387859	−	1.24006i	−0.0136112	−	0.0435174i
$813$	29.8735	−	14.0976i	1.04771	−	0.494425i
$814$	−11.6803	−	5.51204i	−0.409393	−	0.193197i
$815$	−39.8804	+	24.5144i	−1.39695	+	0.858703i
$816$	4.93026	+	0.822714i	0.172594	+	0.0288008i
$817$	17.7871	+	19.5681i	0.622293	+	0.684602i
$818$	24.3631	−	4.06549i	0.851837	−	0.142146i
$819$	−3.51621	+	3.06227i	−0.122866	+	0.107004i
$820$	−14.7498	+	12.8456i	−0.515086	+	0.448589i
$821$	−12.1218	−	20.9956i	−0.423054	−	0.732752i	0.573182	−	0.819428i	$-0.305709\pi$
$821$	−12.1218	−	20.9956i	−0.423054	−	0.732752i	−0.996237	+	0.0866763i	$0.972375\pi$
$822$	6.35185	−	0.350441i	0.221546	−	0.0122230i
$823$	17.2742	−	4.88467i	0.602140	−	0.170269i	0.0426276	−	0.999091i	$-0.486427\pi$
$823$	17.2742	−	4.88467i	0.602140	−	0.170269i	0.559512	+	0.828822i	$0.310988\pi$
$824$	10.4093	+	5.63323i	0.362625	+	0.196243i
$825$	−75.2788	−	81.7746i	−2.62087	−	2.84703i
$826$	−17.5165	−	0.966412i	−0.609477	−	0.0336258i
$827$	−1.28291	−	3.42650i	−0.0446112	−	0.119151i	0.912309	−	0.409503i	$-0.134298\pi$
$827$	−1.28291	−	3.42650i	−0.0446112	−	0.119151i	−0.956920	+	0.290352i	$0.906228\pi$
$828$	5.39167	+	0.899711i	0.187374	+	0.0312671i
$829$	21.6165	−	49.2807i	0.750772	−	1.71159i	0.0494150	−	0.998778i	$-0.484264\pi$
$829$	21.6165	−	49.2807i	0.750772	−	1.71159i	0.701357	−	0.712810i	$-0.252578\pi$
$830$	−39.4481	+	4.36611i	−1.36926	+	0.151550i
$831$	6.93721	+	6.74862i	0.240649	+	0.234107i
$832$	1.94648	−	0.550413i	0.0674821	−	0.0190821i
$833$	1.52389	−	0.618949i	0.0527995	−	0.0214453i
$834$	31.1431	−	6.97934i	1.07840	−	0.241675i
$835$	−37.2360	−	40.4491i	−1.28861	−	1.39980i
$836$	−14.0157	+	12.0518i	−0.484743	+	0.416819i
$837$	1.78228	−	1.93607i	0.0616045	−	0.0669203i
$838$	−5.07075	+	8.78280i	−0.175166	+	0.303397i
$839$	−50.8569	−	5.62884i	−1.75577	−	0.194329i	−0.826304	−	0.563225i	$-0.809561\pi$
$839$	−50.8569	−	5.62884i	−1.75577	−	0.194329i	−0.929471	+	0.368896i	$0.879736\pi$
$840$	13.5384	+	16.4388i	0.467120	+	0.567192i
$841$	−25.9859	−	12.2630i	−0.896065	−	0.422863i
$842$	−1.86548	+	13.4528i	−0.0642885	+	0.463615i
$843$	−42.9141	+	23.2240i	−1.47804	+	0.799876i
$844$	14.1460	−	15.3667i	0.486926	−	0.528943i
$845$	−7.29512	−	37.3469i	−0.250960	−	1.28477i
$846$	−10.2818	+	1.13799i	−0.353497	+	0.0391250i
$847$	−4.31961	+	17.0577i	−0.148423	+	0.586111i
$848$	3.43942	−	0.573938i	0.118110	−	0.0197091i
$849$	6.70442	+	11.6124i	0.230095	+	0.398536i
$850$	32.2021	+	9.10590i	1.10452	+	0.312330i
$851$	18.0877	−	2.00194i	0.620038	−	0.0686258i
$852$	−11.6286	+	31.0585i	−0.398388	+	1.06405i
$853$	−42.3439	−	4.68662i	−1.44983	−	0.160467i	−0.649652	−	0.760232i	$-0.725085\pi$
$853$	−42.3439	−	4.68662i	−1.44983	−	0.160467i	−0.800176	+	0.599765i	$0.795261\pi$
$854$	1.19622	+	14.4362i	0.0409337	+	0.493996i
$855$	15.4500	−	7.17229i	0.528379	−	0.245287i
$856$	0.588074	−	7.09699i	0.0200999	−	0.242570i
$857$	4.96078	−	25.3964i	0.169457	−	0.867525i	−0.795668	−	0.605734i	$-0.792880\pi$
$857$	4.96078	−	25.3964i	0.169457	−	0.867525i	0.965124	−	0.261791i	$-0.0843132\pi$
$858$	−10.0517	−	13.6759i	−0.343160	−	0.466887i
$859$	2.58374	+	2.25018i	0.0881561	+	0.0767752i	0.699707	−	0.714430i	$-0.253314\pi$
$859$	2.58374	+	2.25018i	0.0881561	+	0.0767752i	−0.611551	+	0.791205i	$0.709454\pi$
$860$	15.3476	+	20.8812i	0.523349	+	0.712042i
$861$	−19.4475	−	11.9544i	−0.662771	−	0.407404i
$862$	0.401024	−	4.83965i	0.0136589	−	0.164839i
$863$	−12.8722	−	10.0188i	−0.438175	−	0.341046i	0.370979	−	0.928641i	$-0.379022\pi$
$863$	−12.8722	−	10.0188i	−0.438175	−	0.341046i	−0.809155	+	0.587596i	$0.800075\pi$
$864$	−3.73112	+	1.76076i	−0.126935	+	0.0599022i
$865$	−7.55873	+	54.5096i	−0.257005	+	1.85338i
$866$	−1.34409	−	0.461428i	−0.0456741	−	0.0156800i
$867$	−14.2288	−	15.4566i	−0.483236	−	0.524935i
$868$	−0.951812	+	1.29499i	−0.0323066	+	0.0439547i
$869$	−41.7502	+	9.35643i	−1.41628	+	0.317395i
$870$	−4.35159	−	0.240084i	−0.147533	−	0.00813961i
$871$	−1.61257	−	3.18652i	−0.0546397	−	0.107971i
$872$	12.5802	+	5.93673i	0.426019	+	0.201043i
$873$	6.03104	−	9.23120i	0.204120	−	0.312429i
$874$	7.93143	−	24.8081i	0.268285	−	0.839148i
$875$	48.5485	+	74.3090i	1.64124	+	2.51210i
$876$	0.576482	+	4.15729i	0.0194775	+	0.140462i
$877$	−2.07755	+	10.6359i	−0.0701539	+	0.359149i	−0.999960	−	0.00889989i	$-0.997167\pi$
$877$	−2.07755	+	10.6359i	−0.0701539	+	0.359149i	0.929806	+	0.368049i	$0.119974\pi$
$878$	−4.28338	−	2.63298i	−0.144557	−	0.0888589i
$879$	1.82907	+	13.1903i	0.0616928	+	0.444897i
$880$	−14.8862	+	10.3219i	−0.501814	+	0.347950i
$881$	−21.9707	−	17.1005i	−0.740213	−	0.576131i	0.172365	−	0.985033i	$-0.444859\pi$
$881$	−21.9707	−	17.1005i	−0.740213	−	0.576131i	−0.912578	+	0.408902i	$0.865912\pi$
$882$	0.325773	−	0.498633i	0.0109694	−	0.0167899i
$883$	−11.9084	−	14.4595i	−0.400749	−	0.486602i	0.532196	−	0.846621i	$-0.321367\pi$
$883$	−11.9084	−	14.4595i	−0.400749	−	0.486602i	−0.932945	+	0.360019i	$0.882770\pi$
$884$	4.73450	+	1.92299i	0.159239	+	0.0646771i
$885$	−23.6376	+	53.8883i	−0.794569	+	1.81144i
$886$	−4.03380	+	15.9291i	−0.135518	+	0.535150i
$887$	−23.1821	−	5.19523i	−0.778379	−	0.174439i	−0.188655	−	0.982043i	$-0.560413\pi$
$887$	−23.1821	−	5.19523i	−0.778379	−	0.174439i	−0.589724	+	0.807605i	$0.700764\pi$
$888$	4.54428	−	3.95762i	0.152496	−	0.132809i
$889$	−8.32180	−	1.86496i	−0.279104	−	0.0625487i
$890$	−3.96487	−	1.12116i	−0.132903	−	0.0375813i
$891$	33.1552	+	32.2539i	1.11074	+	1.08055i
$892$	−18.0593	+	6.19977i	−0.604671	+	0.207584i
$893$	−1.66874	+	49.2612i	−0.0558421	+	1.64846i
$894$	4.90078	+	1.68244i	0.163906	+	0.0562692i
$895$	17.3346	+	34.2540i	0.579431	+	1.14499i
$896$	2.14659	−	1.31950i	0.0717124	−	0.0440815i
$897$	22.1566	+	8.99925i	0.739788	+	0.300476i
$898$	−5.80643	+	15.5083i	−0.193763	+	0.517518i
$899$	−0.0630538	−	0.322800i	−0.00210296	−	0.0107660i
$900$	11.4619	−	3.93487i	0.382062	−	0.131162i
$901$	7.74729	+	4.19263i	0.258100	+	0.139677i
$902$	11.4998	−	15.6461i	0.382902	−	0.520957i
$903$	−17.9124	+	24.3707i	−0.596087	+	0.811005i
$904$	7.56902	+	4.09615i	0.251742	+	0.136236i
$905$	67.0122	−	23.0053i	2.22756	−	0.764723i
$906$	3.96199	+	20.2832i	0.131628	+	0.673864i
$907$	13.3878	−	35.7572i	0.444535	−	1.18730i	−0.502048	−	0.864839i	$-0.667420\pi$
$907$	13.3878	−	35.7572i	0.444535	−	1.18730i	0.946583	−	0.322460i	$-0.104510\pi$
$908$	−1.81336	−	0.736523i	−0.0601785	−	0.0244424i
$909$	7.81133	−	4.80161i	0.259085	−	0.159259i
$910$	9.83077	+	19.4261i	0.325887	+	0.643970i
$911$	27.9883	+	9.60840i	0.927295	+	0.318341i	0.746657	−	0.665209i	$-0.231658\pi$
$911$	27.9883	+	9.60840i	0.927295	+	0.318341i	0.180637	+	0.983550i	$0.442184\pi$
$912$	−2.52259	−	8.24731i	−0.0835313	−	0.273096i
$913$	37.2666	−	12.7936i	1.23334	−	0.423407i
$914$	17.6649	+	17.1846i	0.584302	+	0.568418i
$915$	46.7556	+	13.2212i	1.54569	+	0.437081i
$916$	21.1112	+	4.73113i	0.697533	+	0.156321i
$917$	35.6996	−	31.0908i	1.17890	−	1.02671i
$918$	−10.1703	−	2.27923i	−0.335671	−	0.0752257i
$919$	−2.95875	+	11.6838i	−0.0976000	+	0.385414i	−0.998853	−	0.0478792i	$-0.984754\pi$
$919$	−2.95875	+	11.6838i	−0.0976000	+	0.385414i	0.901253	+	0.433293i	$0.142648\pi$
$920$	10.2528	−	23.3739i	0.338024	−	0.770616i
$921$	−27.9478	−	11.3514i	−0.920913	−	0.374042i
$922$	−7.89901	−	9.59124i	−0.260140	−	0.315871i
$923$	−18.5444	+	28.3843i	−0.610395	+	0.934279i
$924$	−16.6839	−	12.9856i	−0.548859	−	0.427194i
$925$	33.1544	−	22.9888i	1.09011	−	0.755867i
$926$	3.87210	+	27.9236i	0.127245	+	0.917625i
$927$	9.22431	+	5.67016i	0.302966	+	0.186233i
$928$	−0.0988563	+	0.506089i	−0.00324512	+	0.0166132i
$929$	−6.65566	−	47.9972i	−0.218365	−	1.57474i	−0.710170	−	0.704030i	$-0.751382\pi$
$929$	−6.65566	−	47.9972i	−0.218365	−	1.57474i	0.491805	−	0.870705i	$-0.336337\pi$
$930$	2.94851	+	4.51303i	0.0966855	+	0.147988i
$931$	−2.12835	−	1.87730i	−0.0697537	−	0.0615262i
$932$	−8.94083	+	13.6850i	−0.292867	+	0.448266i
$933$	−43.7153	−	20.6298i	−1.43117	−	0.675388i
$934$	−17.5087	−	34.5981i	−0.572901	−	1.13208i
$935$	−45.6927	−	2.52094i	−1.49431	−	0.0824435i
$936$	1.80572	−	0.404672i	0.0590218	−	0.0132271i
$937$	−2.56526	+	3.49016i	−0.0838033	+	0.114019i	−0.845647	−	0.533742i	$-0.820785\pi$
$937$	−2.56526	+	3.49016i	−0.0838033	+	0.114019i	0.761844	+	0.647760i	$0.224294\pi$
$938$	−3.01295	−	3.27294i	−0.0983764	−	0.106865i
$939$	48.7821	+	16.7469i	1.59194	+	0.546515i
$940$	−6.63454	+	47.8448i	−0.216395	+	1.56053i
$941$	0.236352	−	0.111537i	0.00770484	−	0.00363600i	−0.422920	−	0.906167i	$-0.638995\pi$
$941$	0.236352	−	0.111537i	0.00770484	−	0.00363600i	0.430625	+	0.902531i	$0.358293\pi$
$942$	−19.8242	−	15.4298i	−0.645908	−	0.502730i
$943$	−2.25934	+	27.2662i	−0.0735744	+	0.887910i
$944$	5.93138	+	3.64600i	0.193050	+	0.118667i
$945$	−26.2988	−	35.7809i	−0.855502	−	1.16395i
$946$	−19.4009	−	16.8963i	−0.630778	−	0.549345i
$947$	−14.8410	−	20.1919i	−0.482268	−	0.656150i	0.494817	−	0.868997i	$-0.335235\pi$
$947$	−14.8410	−	20.1919i	−0.482268	−	0.656150i	−0.977085	+	0.212847i	$0.931726\pi$
$948$	3.82706	−	19.5924i	0.124297	−	0.636331i
$949$	−0.354336	+	4.27620i	−0.0115022	+	0.138811i
$950$	−10.7122	−	56.7391i	−0.347549	−	1.84086i
$951$	−5.05892	−	61.0521i	−0.164047	−	1.97975i
$952$	6.32679	+	0.700249i	0.205053	+	0.0226952i
$953$	8.16580	−	21.8099i	0.264516	−	0.706491i	−0.735077	−	0.677983i	$-0.762854\pi$
$953$	8.16580	−	21.8099i	0.264516	−	0.706491i	0.999594	−	0.0285082i	$-0.00907567\pi$
$954$	3.17061	−	0.350923i	0.102652	−	0.0113616i
$955$	−111.178	−	31.4382i	−3.59764	−	1.01732i
$956$	7.38177	+	12.7856i	0.238743	+	0.413516i
$957$	4.26763	−	0.712141i	0.137953	−	0.0230203i
$958$	−5.85041	+	23.1027i	−0.189018	+	0.746415i
$959$	8.05212	−	0.891208i	0.260016	−	0.0287786i
$960$	−1.62030	−	8.29504i	−0.0522950	−	0.267721i
$961$	20.7202	−	22.5081i	0.668393	−	0.726069i
$962$	5.41818	−	2.93217i	0.174689	−	0.0945370i
$963$	0.894823	−	6.45300i	0.0288353	−	0.207945i
$964$	0.310529	+	0.146542i	0.0100015	+	0.00471980i
$965$	−8.96295	−	10.8831i	−0.288527	−	0.350339i
$966$	29.6083	+	3.27704i	0.952630	+	0.105437i
$967$	15.5559	−	26.9437i	0.500245	−	0.866450i	−0.499755	−	0.866167i	$-0.666577\pi$
$967$	15.5559	−	26.9437i	0.500245	−	0.866450i	1.00000		0.000282918i	$-9.00556e-5\pi$
$968$	4.72974	−	5.13787i	0.152020	−	0.165137i
$969$	7.76805	−	20.3558i	0.249546	−	0.653923i
$970$	−34.8716	−	37.8807i	−1.11966	−	1.21627i
$971$	30.8621	−	6.91635i	0.990411	−	0.221956i	0.306777	−	0.951781i	$-0.400749\pi$
$971$	30.8621	−	6.91635i	0.990411	−	0.221956i	0.683634	+	0.729825i	$0.260399\pi$
$972$	−8.52789	+	3.46373i	−0.273532	+	0.111099i
$973$	39.1105	−	11.0594i	1.25382	−	0.354548i
$974$	5.94063	+	5.77914i	0.190350	+	0.185176i
$975$	52.6960	−	5.83239i	1.68762	−	0.186786i
$976$	2.30933	−	5.26473i	0.0739197	−	0.168520i
$977$	44.9836	+	7.50644i	1.43915	+	0.240152i	0.832152	−	0.554548i	$-0.187109\pi$
$977$	44.9836	+	7.50644i	1.43915	+	0.240152i	0.607002	+	0.794700i	$0.292372\pi$
$978$	7.60296	+	20.3066i	0.243116	+	0.649333i
$979$	4.08428	+	0.225336i	0.130534	+	0.00720177i
$980$	−1.88363	−	2.04617i	−0.0601703	−	0.0653624i
$981$	11.1920	+	6.05679i	0.357332	+	0.193379i
$982$	1.30702	−	0.369591i	0.0417088	−	0.0117941i
$983$	−50.5165	+	2.78707i	−1.61123	+	0.0888939i	−0.838158	−	0.545428i	$-0.816367\pi$
$983$	−50.5165	+	2.78707i	−1.61123	+	0.0888939i	−0.773069	+	0.634322i	$0.781280\pi$
$984$	4.52988	+	7.84598i	0.144407	+	0.250121i
$985$	83.4649	−	72.6897i	2.65941	−	2.31609i
$986$	−0.982355	+	0.855534i	−0.0312846	+	0.0272457i
$987$	−55.6057	+	9.27895i	−1.76995	+	0.295352i
$988$	−0.672707	−	8.79151i	−0.0214017	−	0.279695i
$989$	35.7552	+	5.96649i	1.13695	+	0.189723i
$990$	−14.1177	+	8.67814i	−0.448691	+	0.275809i
$991$	25.8364	+	12.1925i	0.820721	+	0.387308i	0.790672	−	0.612241i	$-0.209732\pi$
$991$	25.8364	+	12.1925i	0.820721	+	0.387308i	0.0300499	+	0.999548i	$0.490433\pi$
$992$	0.576829	−	0.272212i	0.0183143	−	0.00864274i
$993$	4.97810	+	15.9159i	0.157975	+	0.505075i
$994$	−12.6075	+	40.3083i	−0.399884	+	1.27850i
$995$	−60.9453	−	93.2837i	−1.93210	−	2.95729i
$996$	−1.51811	+	18.3209i	−0.0481032	+	0.580519i
$997$	0.685383	−	0.475234i	0.0217063	−	0.0150508i	−0.558905	−	0.829232i	$-0.688778\pi$
$997$	0.685383	−	0.475234i	0.0217063	−	0.0150508i	0.580612	+	0.814181i	$0.302814\pi$
$998$	1.51822	−	4.85403i	0.0480585	−	0.153652i
$999$	−9.91584	+	7.71781i	−0.313723	+	0.244181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.a.11.4	✓	576
361.197	even	57	inner	722.2.i.a.197.4	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.a.11.4	✓	576	1.1	even	1	trivial
722.2.i.a.197.4	yes	576	361.197	even	57	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.592235 + 0.805765i) q^{2} +(-0.271767 - 1.95984i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(3.51033 + 2.43401i) q^{5} +(1.41822 - 1.37967i) q^{6} +(1.70655 - 1.85381i) q^{7} +(-0.945817 + 0.324699i) q^{8} +(-0.880305 + 0.248926i) q^{9} +O(q^{10})\)	\(q+(0.592235 + 0.805765i) q^{2} +(-0.271767 - 1.95984i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(3.51033 + 2.43401i) q^{5} +(1.41822 - 1.37967i) q^{6} +(1.70655 - 1.85381i) q^{7} +(-0.945817 + 0.324699i) q^{8} +(-0.880305 + 0.248926i) q^{9} +(0.117702 + 4.27001i) q^{10} +(-1.04103 - 4.11092i) q^{11} +(1.95161 + 0.325665i) q^{12} +(1.87412 + 0.761201i) q^{13} +(2.50441 + 0.277188i) q^{14} +(3.81627 - 7.54116i) q^{15} +(-0.821778 - 0.569808i) q^{16} +(-0.754125 - 2.41107i) q^{17} +(-0.721924 - 0.561896i) q^{18} +(-3.14348 + 3.01969i) q^{19} +(-3.37091 + 2.62369i) q^{20} +(-4.09695 - 2.84076i) q^{21} +(2.69591 - 3.27346i) q^{22} +(-0.820711 + 5.91854i) q^{23} +(0.893400 + 1.76541i) q^{24} +(4.64483 + 12.4058i) q^{25} +(0.496570 + 1.96091i) q^{26} +(-1.65728 - 3.77822i) q^{27} +(1.25985 + 2.18213i) q^{28} +(-0.503173 - 0.112764i) q^{29} +(8.33653 - 1.39112i) q^{30} +(0.256215 + 0.584110i) q^{31} +(-0.0275543 - 0.999620i) q^{32} +(-7.77383 + 3.15746i) q^{33} +(1.49614 - 2.03557i) q^{34} +(10.5027 - 2.35372i) q^{35} +(0.0252073 - 0.914476i) q^{36} +(-0.747656 - 2.95243i) q^{37} +(-4.29484 - 0.744542i) q^{38} +(0.982508 - 3.87984i) q^{39} +(-4.11045 - 1.16232i) q^{40} +(4.57194 - 0.252241i) q^{41} +(-0.137371 - 4.98358i) q^{42} +(0.167164 - 6.06440i) q^{43} +(4.23425 + 0.233610i) q^{44} +(-3.69605 - 1.26886i) q^{45} +(-5.25501 + 2.84387i) q^{46} +(8.10522 - 7.88488i) q^{47} +(-0.893400 + 1.76541i) q^{48} +(0.0537655 + 0.648853i) q^{49} +(-7.24532 + 11.0898i) q^{50} +(-4.52036 + 2.13321i) q^{51} +(-1.28595 + 1.56144i) q^{52} +(-2.49941 + 2.43146i) q^{53} +(2.06286 - 3.57297i) q^{54} +(6.35167 - 16.9646i) q^{55} +(-1.01215 + 2.30748i) q^{56} +(6.77239 + 5.34007i) q^{57} +(-0.207136 - 0.472222i) q^{58} +(-6.95180 + 0.383541i) q^{59} +(6.05811 + 5.89342i) q^{60} +(1.10213 + 5.64231i) q^{61} +(-0.318916 + 0.552379i) q^{62} +(-1.04082 + 2.05672i) q^{63} +(0.789141 - 0.614213i) q^{64} +(4.72600 + 7.23369i) q^{65} +(-7.14810 - 4.39392i) q^{66} +(-1.33139 - 1.15951i) q^{67} +2.52626 q^{68} +11.8224 q^{69} +(8.11664 + 7.06879i) q^{70} +(-3.21335 + 16.4505i) q^{71} +(0.751781 - 0.521273i) q^{72} +(0.633222 + 2.02452i) q^{73} +(1.93617 - 2.35097i) q^{74} +(23.0510 - 12.4746i) q^{75} +(-1.94363 - 3.90158i) q^{76} +(-9.39743 - 5.08563i) q^{77} +(3.70811 - 1.50611i) q^{78} +(0.278005 - 10.0855i) q^{79} +(-1.49779 - 4.00043i) q^{80} +(-9.29237 + 5.71200i) q^{81} +(2.91091 + 3.53452i) q^{82} +(0.767269 + 9.25956i) q^{83} +(3.93424 - 3.06214i) q^{84} +(3.22134 - 10.2992i) q^{85} +(4.98548 - 3.45686i) q^{86} +(-0.0842531 + 1.01678i) q^{87} +(2.31944 + 3.55016i) q^{88} +(-0.287942 + 0.920602i) q^{89} +(-1.16653 - 3.72961i) q^{90} +(4.60940 - 2.17523i) q^{91} +(-5.40369 - 2.55006i) q^{92} +(1.07513 - 0.660881i) q^{93} +(11.1536 + 1.86120i) q^{94} +(-18.3846 + 2.94884i) q^{95} +(-1.95161 + 0.325665i) q^{96} +(-9.08954 + 7.91609i) q^{97} +(-0.490982 + 0.427596i) q^{98} +(1.93974 + 3.35973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Introduction

L-functions

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