LMFDB - Embedded newform 574.2.s.b.387.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.12
Character	$\chi$	$=$	574.387
Dual form			574.2.s.b.221.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(1.15441 + 1.99950i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0477161 - 0.453988i) q^{5} +(-0.713467 - 2.19582i) q^{6} +(0.841560 - 2.50834i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.16534 + 2.01843i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(1.15441 + 1.99950i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0477161 - 0.453988i) q^{5} +(-0.713467 - 2.19582i) q^{6} +(0.841560 - 2.50834i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.16534 + 2.01843i) q^{9} +(-0.0477161 + 0.453988i) q^{10} +(-0.408376 + 3.88544i) q^{11} +(0.241338 + 2.29618i) q^{12} +(1.68271 + 5.17884i) q^{13} +(-1.34468 + 2.27856i) q^{14} +(0.852667 - 0.619498i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.331864 - 3.15747i) q^{17} +(1.55953 - 1.73203i) q^{18} +(1.22323 + 1.35854i) q^{19} +(0.141063 - 0.434147i) q^{20} +(5.98694 - 1.21296i) q^{21} +(1.20728 - 3.71563i) q^{22} +(2.93973 + 0.624858i) q^{23} +(0.241338 - 2.29618i) q^{24} +(4.68691 - 0.996233i) q^{25} +(-0.569194 - 5.41552i) q^{26} +1.54534 q^{27} +(1.78904 - 1.94919i) q^{28} +(-5.36385 + 3.89707i) q^{29} +(-0.962835 + 0.428682i) q^{30} +(-0.0936936 + 0.891435i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.24038 + 3.66885i) q^{33} +(-0.981087 + 3.01948i) q^{34} +(-1.17891 - 0.262370i) q^{35} +(-1.88556 + 1.36994i) q^{36} +(0.0908725 + 0.864595i) q^{37} +(-0.914048 - 1.58318i) q^{38} +(-8.41256 + 9.34309i) q^{39} +(-0.228244 + 0.395331i) q^{40} +(5.36093 + 3.50150i) q^{41} +(-6.10830 - 0.0582991i) q^{42} +(1.44935 + 4.46064i) q^{43} +(-1.95342 + 3.38342i) q^{44} +(0.971948 + 0.432739i) q^{45} +(-2.74557 - 1.22241i) q^{46} +(-4.83996 - 1.02877i) q^{47} +(-0.713467 + 2.19582i) q^{48} +(-5.58356 - 4.22184i) q^{49} -4.79162 q^{50} +(6.69648 - 2.98147i) q^{51} +(-0.569194 + 5.41552i) q^{52} +(-5.93259 - 2.64136i) q^{53} +(-1.51157 - 0.321295i) q^{54} +1.78343 q^{55} +(-2.15520 + 1.53463i) q^{56} +(-1.30429 + 4.01418i) q^{57} +(6.05689 - 2.69670i) q^{58} +(0.593640 - 0.659304i) q^{59} +(1.03092 - 0.219129i) q^{60} +(-2.05375 - 2.28092i) q^{61} +(0.276986 - 0.852475i) q^{62} +(4.08220 + 4.62170i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.27084 - 1.01104i) q^{65} +(8.82310 - 1.87541i) q^{66} +(8.60212 + 3.82991i) q^{67} +(1.58743 - 2.74951i) q^{68} +(2.14425 + 6.59934i) q^{69} +(1.09860 + 0.501746i) q^{70} +(-5.76700 - 4.18997i) q^{71} +(2.12918 - 0.947973i) q^{72} +(-1.85231 - 3.20830i) q^{73} +(0.0908725 - 0.864595i) q^{74} +(7.40260 + 8.22142i) q^{75} +(0.564913 + 1.73862i) q^{76} +(9.40233 + 4.29417i) q^{77} +(10.1713 - 7.38985i) q^{78} +(6.00033 - 10.3929i) q^{79} +(0.305451 - 0.339237i) q^{80} +(5.27999 + 9.14520i) q^{81} +(-4.51578 - 4.53958i) q^{82} -0.383058 q^{83} +(5.96270 + 1.32701i) q^{84} -1.44929 q^{85} +(-0.490259 - 4.66450i) q^{86} +(-13.9843 - 6.22621i) q^{87} +(2.61419 - 2.90335i) q^{88} +(-9.47008 - 10.5176i) q^{89} +(-0.860737 - 0.625362i) q^{90} +(14.4064 + 0.137498i) q^{91} +(2.43142 + 1.76653i) q^{92} +(-1.89059 + 0.841744i) q^{93} +(4.52031 + 2.01257i) q^{94} +(0.558393 - 0.620158i) q^{95} +(1.15441 - 1.99950i) q^{96} +(-1.53797 + 1.11740i) q^{97} +(4.58377 + 5.29047i) q^{98} +(-7.36658 - 5.35213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{13} + 18 q^{14} - 2 q^{15} + 14 q^{16} + 17 q^{18} - 2 q^{19} - 8 q^{20} - 25 q^{21} + 16 q^{22} - 2 q^{23} + 3 q^{24} + 26 q^{25} - 2 q^{26} - 8 q^{27} + 4 q^{28} - 42 q^{29} + q^{30} + 13 q^{31} - 56 q^{32} + 17 q^{33} - 10 q^{34} + 8 q^{35} - 24 q^{36} + q^{37} - 2 q^{38} + 14 q^{39} - 16 q^{40} - 58 q^{41} - 62 q^{42} + 18 q^{43} + 12 q^{44} + 32 q^{45} + 3 q^{46} - 25 q^{47} + 4 q^{48} + 8 q^{49} + 88 q^{50} + 23 q^{51} - 2 q^{52} + 3 q^{53} - 6 q^{54} - 12 q^{55} + 8 q^{56} - 24 q^{57} + 21 q^{58} + 18 q^{59} + q^{60} - 6 q^{61} - 16 q^{62} - 71 q^{63} - 28 q^{64} + 2 q^{65} + 2 q^{66} + 9 q^{67} - 10 q^{68} + 38 q^{69} + 55 q^{70} - 10 q^{71} + 12 q^{72} - 78 q^{73} + q^{74} - 9 q^{75} + 4 q^{76} + 43 q^{77} + 22 q^{78} + 4 q^{80} - 80 q^{81} - 6 q^{82} + 156 q^{83} - 13 q^{84} + 44 q^{85} + 11 q^{86} - 8 q^{88} + 9 q^{89} - 64 q^{90} - 52 q^{91} - 6 q^{92} - 46 q^{93} + 20 q^{94} + 49 q^{95} - 2 q^{96} + 32 q^{97} - 21 q^{98} + 12 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9 + 4 * q^10 + 2 * q^11 + 3 * q^12 - 6 * q^13 + 18 * q^14 - 2 * q^15 + 14 * q^16 + 17 * q^18 - 2 * q^19 - 8 * q^20 - 25 * q^21 + 16 * q^22 - 2 * q^23 + 3 * q^24 + 26 * q^25 - 2 * q^26 - 8 * q^27 + 4 * q^28 - 42 * q^29 + q^30 + 13 * q^31 - 56 * q^32 + 17 * q^33 - 10 * q^34 + 8 * q^35 - 24 * q^36 + q^37 - 2 * q^38 + 14 * q^39 - 16 * q^40 - 58 * q^41 - 62 * q^42 + 18 * q^43 + 12 * q^44 + 32 * q^45 + 3 * q^46 - 25 * q^47 + 4 * q^48 + 8 * q^49 + 88 * q^50 + 23 * q^51 - 2 * q^52 + 3 * q^53 - 6 * q^54 - 12 * q^55 + 8 * q^56 - 24 * q^57 + 21 * q^58 + 18 * q^59 + q^60 - 6 * q^61 - 16 * q^62 - 71 * q^63 - 28 * q^64 + 2 * q^65 + 2 * q^66 + 9 * q^67 - 10 * q^68 + 38 * q^69 + 55 * q^70 - 10 * q^71 + 12 * q^72 - 78 * q^73 + q^74 - 9 * q^75 + 4 * q^76 + 43 * q^77 + 22 * q^78 + 4 * q^80 - 80 * q^81 - 6 * q^82 + 156 * q^83 - 13 * q^84 + 44 * q^85 + 11 * q^86 - 8 * q^88 + 9 * q^89 - 64 * q^90 - 52 * q^91 - 6 * q^92 - 46 * q^93 + 20 * q^94 + 49 * q^95 - 2 * q^96 + 32 * q^97 - 21 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	1.15441	+	1.99950i	0.666501	+	1.15441i	0.978876	+	0.204454i	$0.0655420\pi$
$3$	1.15441	+	1.99950i	0.666501	+	1.15441i	−0.312375	+	0.949959i	$0.601125\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.0477161	−	0.453988i	−0.0213393	−	0.203030i	0.978658	−	0.205497i	$-0.0658812\pi$
$5$	−0.0477161	−	0.453988i	−0.0213393	−	0.203030i	−0.999997	+	0.00246763i	$0.999215\pi$
$6$	−0.713467	−	2.19582i	−0.291272	−	0.896442i
$7$	0.841560	−	2.50834i	0.318080	−	0.948064i
$7$	0.841560	−	2.50834i	0.318080	−	0.948064i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−1.16534	+	2.01843i	−0.388447	+	0.672809i
$10$	−0.0477161	+	0.453988i	−0.0150892	+	0.143564i
$11$	−0.408376	+	3.88544i	−0.123130	+	1.17150i	0.742157	+	0.670226i	$0.233803\pi$
$11$	−0.408376	+	3.88544i	−0.123130	+	1.17150i	−0.865287	+	0.501277i	$0.832864\pi$
$12$	0.241338	+	2.29618i	0.0696683	+	0.662850i
$13$	1.68271	+	5.17884i	0.466699	+	1.43635i	0.856834	+	0.515593i	$0.172428\pi$
$13$	1.68271	+	5.17884i	0.466699	+	1.43635i	−0.390135	+	0.920758i	$0.627572\pi$
$14$	−1.34468	+	2.27856i	−0.359382	+	0.608970i
$15$	0.852667	−	0.619498i	0.220158	−	0.159954i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	0.331864	−	3.15747i	0.0804888	−	0.765799i	−0.877613	−	0.479370i	$-0.840865\pi$
$17$	0.331864	−	3.15747i	0.0804888	−	0.765799i	0.958101	−	0.286429i	$-0.0924683\pi$
$18$	1.55953	−	1.73203i	0.367585	−	0.408244i
$19$	1.22323	+	1.35854i	0.280629	+	0.311670i	0.866937	−	0.498418i	$-0.166086\pi$
$19$	1.22323	+	1.35854i	0.280629	+	0.311670i	−0.586307	+	0.810089i	$0.699419\pi$
$20$	0.141063	−	0.434147i	0.0315426	−	0.0970782i
$21$	5.98694	−	1.21296i	1.30646	−	0.264690i
$22$	1.20728	−	3.71563i	0.257393	−	0.792174i
$23$	2.93973	+	0.624858i	0.612975	+	0.130292i	0.503930	−	0.863745i	$-0.331887\pi$
$23$	2.93973	+	0.624858i	0.612975	+	0.130292i	0.109046	+	0.994037i	$0.465220\pi$
$24$	0.241338	−	2.29618i	0.0492629	−	0.468705i
$25$	4.68691	−	0.996233i	0.937382	−	0.199247i
$26$	−0.569194	−	5.41552i	−0.111628	−	1.06207i
$27$	1.54534			0.297402
$28$	1.78904	−	1.94919i	0.338096	−	0.368362i
$29$	−5.36385	+	3.89707i	−0.996043	+	0.723667i	−0.961236	−	0.275727i	$-0.911082\pi$
$29$	−5.36385	+	3.89707i	−0.996043	+	0.723667i	−0.0348067	+	0.999394i	$0.511082\pi$
$30$	−0.962835	+	0.428682i	−0.175789	+	0.0782662i
$31$	−0.0936936	+	0.891435i	−0.0168279	+	0.160106i	−0.999709	−	0.0241361i	$-0.992317\pi$
$31$	−0.0936936	+	0.891435i	−0.0168279	+	0.160106i	0.982881	+	0.184242i	$0.0589832\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−8.24038	+	3.66885i	−1.43447	+	0.638665i
$34$	−0.981087	+	3.01948i	−0.168255	+	0.517836i
$35$	−1.17891	−	0.262370i	−0.199273	−	0.0443486i
$36$	−1.88556	+	1.36994i	−0.314260	+	0.228323i
$37$	0.0908725	+	0.864595i	0.0149394	+	0.142138i	0.999449	−	0.0331920i	$-0.0105673\pi$
$37$	0.0908725	+	0.864595i	0.0149394	+	0.142138i	−0.984510	+	0.175330i	$0.943901\pi$
$38$	−0.914048	−	1.58318i	−0.148278	−	0.256825i
$39$	−8.41256	+	9.34309i	−1.34709	+	1.49609i
$40$	−0.228244	+	0.395331i	−0.0360886	+	0.0625073i
$41$	5.36093	+	3.50150i	0.837236	+	0.546842i
$41$	5.36093	+	3.50150i	0.837236	+	0.546842i
$42$	−6.10830	−	0.0582991i	−0.942532	−	0.00899574i
$43$	1.44935	+	4.46064i	0.221024	+	0.680241i	0.998671	+	0.0515402i	$0.0164130\pi$
$43$	1.44935	+	4.46064i	0.221024	+	0.680241i	−0.777647	+	0.628701i	$0.783587\pi$
$44$	−1.95342	+	3.38342i	−0.294489	+	0.510070i
$45$	0.971948	+	0.432739i	0.144889	+	0.0645089i
$46$	−2.74557	−	1.22241i	−0.404812	−	0.180234i
$47$	−4.83996	−	1.02877i	−0.705981	−	0.150061i	−0.159089	−	0.987264i	$-0.550856\pi$
$47$	−4.83996	−	1.02877i	−0.705981	−	0.150061i	−0.546892	+	0.837203i	$0.684189\pi$
$48$	−0.713467	+	2.19582i	−0.102980	+	0.316940i
$49$	−5.58356	−	4.22184i	−0.797651	−	0.603120i
$50$	−4.79162			−0.677637
$51$	6.69648	−	2.98147i	0.937695	−	0.417489i
$52$	−0.569194	+	5.41552i	−0.0789330	+	0.750998i
$53$	−5.93259	−	2.64136i	−0.814905	−	0.362819i	−0.0434120	−	0.999057i	$-0.513823\pi$
$53$	−5.93259	−	2.64136i	−0.814905	−	0.362819i	−0.771493	+	0.636238i	$0.780489\pi$
$54$	−1.51157	−	0.321295i	−0.205699	−	0.0437227i
$55$	1.78343			0.240478
$56$	−2.15520	+	1.53463i	−0.288001	+	0.205074i
$57$	−1.30429	+	4.01418i	−0.172757	+	0.531691i
$58$	6.05689	−	2.69670i	0.795308	−	0.354094i
$59$	0.593640	−	0.659304i	0.0772854	−	0.0858341i	−0.703262	−	0.710931i	$-0.748274\pi$
$59$	0.593640	−	0.659304i	0.0772854	−	0.0858341i	0.780547	+	0.625097i	$0.214941\pi$
$60$	1.03092	−	0.219129i	0.133092	−	0.0282895i
$61$	−2.05375	−	2.28092i	−0.262956	−	0.292042i	0.597180	−	0.802107i	$-0.296288\pi$
$61$	−2.05375	−	2.28092i	−0.262956	−	0.292042i	−0.860136	+	0.510065i	$0.829621\pi$
$62$	0.276986	−	0.852475i	0.0351772	−	0.108264i
$63$	4.08220	+	4.62170i	0.514309	+	0.582279i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.27084	−	1.01104i	0.281663	−	0.125404i
$66$	8.82310	−	1.87541i	1.08605	−	0.230847i
$67$	8.60212	+	3.82991i	1.05092	+	0.467898i	0.858178	−	0.513352i	$-0.171597\pi$
$67$	8.60212	+	3.82991i	1.05092	+	0.467898i	0.192738	+	0.981250i	$0.438263\pi$
$68$	1.58743	−	2.74951i	0.192504	−	0.333427i
$69$	2.14425	+	6.59934i	0.258138	+	0.794467i
$70$	1.09860	+	0.501746i	0.131308	+	0.0599702i
$71$	−5.76700	−	4.18997i	−0.684417	−	0.497258i	0.190403	−	0.981706i	$-0.439020\pi$
$71$	−5.76700	−	4.18997i	−0.684417	−	0.497258i	−0.874820	+	0.484448i	$0.839020\pi$
$72$	2.12918	−	0.947973i	0.250927	−	0.111720i
$73$	−1.85231	−	3.20830i	−0.216797	−	0.375503i	0.737030	−	0.675860i	$-0.236228\pi$
$73$	−1.85231	−	3.20830i	−0.216797	−	0.375503i	−0.953827	+	0.300357i	$0.902894\pi$
$74$	0.0908725	−	0.864595i	0.0105637	−	0.100507i
$75$	7.40260	+	8.22142i	0.854779	+	0.949328i
$76$	0.564913	+	1.73862i	0.0647999	+	0.199434i
$77$	9.40233	+	4.29417i	1.07150	+	0.489366i
$78$	10.1713	−	7.38985i	1.15167	−	0.836736i
$79$	6.00033	−	10.3929i	0.675090	−	1.16929i	−0.301353	−	0.953513i	$-0.597438\pi$
$79$	6.00033	−	10.3929i	0.675090	−	1.16929i	0.976443	−	0.215777i	$-0.0692284\pi$
$80$	0.305451	−	0.339237i	0.0341504	−	0.0379279i
$81$	5.27999	+	9.14520i	0.586665	+	1.01613i
$82$	−4.51578	−	4.53958i	−0.498684	−	0.501313i
$83$	−0.383058			−0.0420461			−0.0210230	−	0.999779i	$-0.506692\pi$
$83$	−0.383058			−0.0420461			−0.0210230	+	0.999779i	$0.506692\pi$
$84$	5.96270	+	1.32701i	0.650584	+	0.144789i
$85$	−1.44929			−0.157198
$86$	−0.490259	−	4.66450i	−0.0528660	−	0.502986i
$87$	−13.9843	−	6.22621i	−1.49927	−	0.667520i
$88$	2.61419	−	2.90335i	0.278673	−	0.309498i
$89$	−9.47008	−	10.5176i	−1.00383	−	1.11486i	−0.993375	−	0.114917i	$-0.963340\pi$
$89$	−9.47008	−	10.5176i	−1.00383	−	1.11486i	−0.0104512	−	0.999945i	$-0.503327\pi$
$90$	−0.860737	−	0.625362i	−0.0907297	−	0.0659190i
$91$	14.4064	+	0.137498i	1.51020	+	0.0144137i
$92$	2.43142	+	1.76653i	0.253493	+	0.184174i
$93$	−1.89059	+	0.841744i	−0.196045	+	0.0872847i
$94$	4.52031	+	2.01257i	0.466234	+	0.207581i
$95$	0.558393	−	0.620158i	0.0572899	−	0.0636269i
$96$	1.15441	−	1.99950i	0.117822	−	0.204073i
$97$	−1.53797	+	1.11740i	−0.156158	+	0.113455i	−0.663120	−	0.748513i	$-0.730768\pi$
$97$	−1.53797	+	1.11740i	−0.156158	+	0.113455i	0.506963	+	0.861968i	$0.330768\pi$
$98$	4.58377	+	5.29047i	0.463031	+	0.534418i
$99$	−7.36658	−	5.35213i	−0.740369	−	0.537910i
$100$	4.68691	+	0.996233i	0.468691	+	0.0996233i
$101$	−5.98331	+	1.27179i	−0.595362	+	0.126548i	−0.495731	−	0.868476i	$-0.665100\pi$
$101$	−5.98331	+	1.27179i	−0.595362	+	0.126548i	−0.0996312	+	0.995024i	$0.531766\pi$
$102$	−7.17003	+	1.52404i	−0.709939	+	0.150902i
$103$	−6.83734	−	7.59364i	−0.673703	−	0.748223i	0.305258	−	0.952270i	$-0.401257\pi$
$103$	−6.83734	−	7.59364i	−0.673703	−	0.748223i	−0.978961	+	0.204047i	$0.934591\pi$
$104$	1.68271	−	5.17884i	0.165003	−	0.507827i
$105$	−0.836344	−	2.66012i	−0.0816188	−	0.259601i
$106$	5.25378	+	3.81710i	0.510293	+	0.370749i
$107$	6.04361	+	6.71211i	0.584258	+	0.648884i	0.960711	−	0.277552i	$-0.0895229\pi$
$107$	6.04361	+	6.71211i	0.584258	+	0.648884i	−0.376453	+	0.926436i	$0.622856\pi$
$108$	1.41174	+	0.628548i	0.135845	+	0.0604821i
$109$	−1.79615	−	3.11102i	−0.172040	−	0.297982i	0.767093	−	0.641536i	$-0.221702\pi$
$109$	−1.79615	−	3.11102i	−0.172040	−	0.297982i	−0.939133	+	0.343554i	$0.888369\pi$
$110$	−1.74446	−	0.370796i	−0.166327	−	0.0353540i
$111$	−1.62385	+	1.17980i	−0.154129	+	0.111982i
$112$	2.42717	−	1.05301i	0.229346	−	0.0994999i
$113$	−9.45263	−	6.86774i	−0.889229	−	0.646063i	0.0464478	−	0.998921i	$-0.485210\pi$
$113$	−9.45263	−	6.86774i	−0.889229	−	0.646063i	−0.935677	+	0.352858i	$0.885210\pi$
$114$	2.11038	−	3.65528i	0.197655	−	0.342348i
$115$	0.143406	−	1.36442i	0.0133727	−	0.127233i
$116$	−6.48521	+	1.37847i	−0.602136	+	0.127988i
$117$	−12.4140	−	2.63868i	−1.14768	−	0.243946i
$118$	−0.717745	+	0.521472i	−0.0660738	+	0.0480054i
$119$	−7.64073	−	3.48963i	−0.700425	−	0.319894i
$120$	−1.05395			−0.0962124
$121$	−4.17023	−	0.886410i	−0.379112	−	0.0805827i
$122$	1.53464	+	2.65808i	0.138940	+	0.240651i
$123$	−0.812524	+	14.7614i	−0.0732629	+	1.33099i
$124$	−0.448172	+	0.776258i	−0.0402471	+	0.0697100i
$125$	−1.38123	−	4.25100i	−0.123541	−	0.380221i
$126$	−3.03209	−	5.36944i	−0.270120	−	0.478348i
$127$	17.0110	−	12.3592i	1.50948	−	1.09670i	0.543079	−	0.839682i	$-0.317258\pi$
$127$	17.0110	−	12.3592i	1.50948	−	1.09670i	0.966405	−	0.257023i	$-0.0827416\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	−7.24591	+	8.04740i	−0.637967	+	0.708534i
$130$	−2.43142	+	0.516815i	−0.213250	+	0.0453277i
$131$	16.5488	−	7.36798i	1.44587	−	0.643744i	0.474273	−	0.880378i	$-0.342711\pi$
$131$	16.5488	−	7.36798i	1.44587	−	0.643744i	0.971599	+	0.236634i	$0.0760443\pi$
$132$	−9.02022			−0.785109
$133$	4.43711	−	1.92500i	0.384746	−	0.166919i
$134$	−7.61786	−	5.53470i	−0.658083	−	0.478125i
$135$	−0.0737378	−	0.701568i	−0.00634634	−	0.0603814i
$136$	−2.12440	+	2.35938i	−0.182166	+	0.202315i
$137$	2.92839	+	5.07212i	0.250189	+	0.433340i	0.963578	−	0.267428i	$-0.0861738\pi$
$137$	2.92839	+	5.07212i	0.250189	+	0.433340i	−0.713389	+	0.700769i	$0.752841\pi$
$138$	−0.725318	−	6.90094i	−0.0617432	−	0.587447i
$139$	3.35711	−	10.3321i	0.284747	−	0.876360i	−0.701728	−	0.712445i	$-0.747588\pi$
$139$	3.35711	−	10.3321i	0.284747	−	0.876360i	0.986474	−	0.163915i	$-0.0524122\pi$
$140$	−0.970276	−	0.719194i	−0.0820033	−	0.0607830i
$141$	−3.53030	−	10.8651i	−0.297305	−	0.915010i
$142$	4.76983	+	5.29744i	0.400275	+	0.444551i
$143$	−20.8092	+	4.42314i	−1.74015	+	0.369881i
$144$	−2.27975	+	0.484576i	−0.189979	+	0.0403813i
$145$	2.02517	+	2.24917i	0.168181	+	0.186784i
$146$	1.14479	+	3.52331i	0.0947438	+	0.291591i
$147$	1.99584	−	16.0381i	0.164614	−	1.32280i
$148$	−0.268646	+	0.826808i	−0.0220826	+	0.0679632i
$149$	1.63595	+	15.5651i	0.134023	+	1.27514i	0.830280	+	0.557347i	$0.188181\pi$
$149$	1.63595	+	15.5651i	0.134023	+	1.27514i	−0.696257	+	0.717793i	$0.745153\pi$
$150$	−5.53151	−	9.58085i	−0.451646	−	0.782273i
$151$	15.6320	−	17.3611i	1.27212	−	1.41283i	0.405312	−	0.914179i	$-0.367163\pi$
$151$	15.6320	−	17.3611i	1.27212	−	1.41283i	0.866804	−	0.498649i	$-0.166170\pi$
$152$	−0.191088	−	1.81808i	−0.0154993	−	0.147466i
$153$	5.98640	+	4.34937i	0.483971	+	0.351626i
$154$	−8.30406	−	6.15519i	−0.669160	−	0.495999i
$155$	0.409172			0.0328655
$156$	−11.4854	+	5.11364i	−0.919571	+	0.409419i
$157$	−15.1974	+	3.23032i	−1.21289	+	0.257807i	−0.769573	−	0.638559i	$-0.779531\pi$
$157$	−15.1974	+	3.23032i	−1.21289	+	0.257807i	−0.443315	+	0.896366i	$0.646198\pi$
$158$	−8.03001	+	8.91823i	−0.638833	+	0.709496i
$159$	−1.56726	−	14.9115i	−0.124292	−	1.18256i
$160$	−0.369307	+	0.268317i	−0.0291963	+	0.0212124i
$161$	4.04131	−	6.84798i	0.318500	−	0.539697i
$162$	−3.26321	−	10.0431i	−0.256382	−	0.789063i
$163$	−5.06001	+	8.76420i	−0.396331	+	0.686465i	−0.993270	−	0.115821i	$-0.963050\pi$
$163$	−5.06001	+	8.76420i	−0.396331	+	0.686465i	0.596939	+	0.802286i	$0.296383\pi$
$164$	3.47326	+	5.37926i	0.271216	+	0.420050i
$165$	2.05881	+	3.56597i	0.160278	+	0.277610i
$166$	0.374687	+	0.0796422i	0.0290814	+	0.00618144i
$167$	−14.4988			−1.12195			−0.560977	−	0.827831i	$-0.689575\pi$
$167$	−14.4988			−1.12195			−0.560977	+	0.827831i	$0.689575\pi$
$168$	−5.55650	−	2.53773i	−0.428693	−	0.195790i
$169$	−13.4716	+	9.78771i	−1.03628	+	0.752901i
$170$	1.41762	+	0.301324i	0.108726	+	0.0231105i
$171$	−4.16760	+	0.885850i	−0.318704	+	0.0677427i
$172$	−0.490259	+	4.66450i	−0.0373819	+	0.355665i
$173$	8.43310	−	14.6066i	0.641157	−	1.11052i	−0.344018	−	0.938963i	$-0.611788\pi$
$173$	8.43310	−	14.6066i	0.641157	−	1.11052i	0.985175	−	0.171553i	$-0.0548785\pi$
$174$	12.3842	+	8.99766i	0.938845	+	0.682111i
$175$	1.44542	−	12.5948i	0.109263	−	0.952074i
$176$	−3.16070	+	2.29638i	−0.238247	+	0.173096i
$177$	2.00359	+	0.425875i	0.150599	+	0.0320108i
$178$	7.07641	+	12.2567i	0.530399	+	0.918678i
$179$	−16.2619	−	7.24027i	−1.21547	−	0.541163i	−0.304058	−	0.952654i	$-0.598342\pi$
$179$	−16.2619	−	7.24027i	−1.21547	−	0.541163i	−0.911414	+	0.411491i	$0.865008\pi$
$180$	0.711908	+	0.790654i	0.0530625	+	0.0589319i
$181$	−16.0056	−	11.6288i	−1.18969	−	0.864361i	−0.196459	−	0.980512i	$-0.562944\pi$
$181$	−16.0056	−	11.6288i	−1.18969	−	0.864361i	−0.993232	+	0.116151i	$0.962944\pi$
$182$	−14.0630	−	3.12975i	−1.04242	−	0.231993i
$183$	2.18983	−	6.73961i	0.161877	−	0.498206i
$184$	−2.01101	−	2.23345i	−0.148253	−	0.164652i
$185$	0.388180	−	0.0825101i	0.0285395	−	0.00606627i
$186$	2.02428	−	0.430274i	0.148428	−	0.0315492i
$187$	12.1326	+	2.57887i	0.887226	+	0.188586i
$188$	−4.00309	−	2.90841i	−0.291955	−	0.212118i
$189$	1.30050	−	3.87625i	0.0945974	−	0.281956i
$190$	−0.675129	+	0.490510i	−0.0489790	+	0.0355853i
$191$	7.01199	−	12.1451i	0.507369	−	0.878790i	−0.492594	−	0.870259i	$-0.663951\pi$
$191$	7.01199	−	12.1451i	0.507369	−	0.878790i	0.999964	−	0.00853051i	$-0.00271538\pi$
$192$	−1.54491	+	1.71579i	−0.111494	+	0.123827i
$193$	9.81815	+	4.37132i	0.706726	+	0.314655i	0.728440	−	0.685110i	$-0.240246\pi$
$193$	9.81815	+	4.37132i	0.706726	+	0.314655i	−0.0217141	+	0.999764i	$0.506912\pi$
$194$	1.73669	−	0.773222i	0.124687	−	0.0555141i
$195$	4.64307	+	3.37339i	0.332497	+	0.241573i
$196$	−3.38366	−	6.12788i	−0.241690	−	0.437706i
$197$	9.32839	+	6.77747i	0.664620	+	0.482875i	0.868220	−	0.496179i	$-0.165264\pi$
$197$	9.32839	+	6.77747i	0.664620	+	0.482875i	−0.203600	+	0.979054i	$0.565264\pi$
$198$	6.09283	+	6.76677i	0.432999	+	0.480894i
$199$	2.78729	−	3.09560i	0.197586	−	0.219441i	−0.636207	−	0.771518i	$-0.719498\pi$
$199$	2.78729	−	3.09560i	0.197586	−	0.219441i	0.833793	+	0.552077i	$0.186164\pi$
$200$	−4.37736	−	1.94893i	−0.309526	−	0.137810i
$201$	2.27248	+	21.6213i	0.160289	+	1.52505i
$202$	6.11698			0.430389
$203$	5.26118	+	16.7340i	0.369262	+	1.17450i
$204$	7.33021			0.513217
$205$	1.33384	−	2.60088i	0.0931591	−	0.181653i
$206$	5.10912	+	8.84926i	0.355969	+	0.616557i
$207$	−4.68701	+	5.20546i	−0.325770	+	0.361804i
$208$	−2.72268	+	4.71581i	−0.188784	+	0.326983i
$209$	−5.77806	+	4.19801i	−0.399677	+	0.290382i
$210$	0.264997	+	2.77588i	0.0182865	+	0.191554i
$211$	−8.32963	−	25.6360i	−0.573436	−	1.76485i	−0.641445	−	0.767169i	$-0.721665\pi$
$211$	−8.32963	−	25.6360i	−0.573436	−	1.76485i	0.0680093	−	0.997685i	$-0.478335\pi$
$212$	−4.34536	−	4.82601i	−0.298440	−	0.331452i
$213$	1.72036	−	16.3681i	0.117877	−	1.12152i
$214$	−4.51602	−	7.82197i	−0.308709	−	0.534699i
$215$	1.95592	−	0.870832i	0.133393	−	0.0593902i
$216$	−1.25021	−	0.908330i	−0.0850660	−	0.0618041i
$217$	2.15717	+	0.985211i	0.146439	+	0.0668805i
$218$	1.11008	+	3.41648i	0.0751842	+	0.231393i
$219$	4.27667	−	7.40742i	0.288991	−	0.500547i
$220$	1.62924	+	0.725386i	0.109844	+	0.0489055i
$221$	16.9105	−	3.59443i	1.13752	−	0.241787i
$222$	1.83366	−	0.816400i	0.123067	−	0.0547931i
$223$	3.52466	+	10.8478i	0.236029	+	0.726422i	0.996983	+	0.0776166i	$0.0247310\pi$
$223$	3.52466	+	10.8478i	0.236029	+	0.726422i	−0.760955	+	0.648805i	$0.775269\pi$
$224$	−2.59307	+	0.525359i	−0.173257	+	0.0351020i
$225$	−3.45102	+	10.6211i	−0.230068	+	0.708076i
$226$	7.81819	+	8.68298i	0.520058	+	0.577583i
$227$	−23.6908	+	5.03563i	−1.57241	+	0.334226i	−0.909901	−	0.414826i	$-0.863842\pi$
$227$	−23.6908	+	5.03563i	−1.57241	+	0.334226i	−0.662511	+	0.749052i	$0.730509\pi$
$228$	−2.82424	+	3.13663i	−0.187040	+	0.207729i
$229$	−9.38877	+	4.18015i	−0.620428	+	0.276232i	−0.692782	−	0.721147i	$-0.743615\pi$
$229$	−9.38877	+	4.18015i	−0.620428	+	0.276232i	0.0723547	+	0.997379i	$0.476949\pi$
$230$	−0.423951	+	1.30479i	−0.0279545	+	0.0860350i
$231$	2.26797	+	23.7572i	0.149221	+	1.56311i
$232$	6.63009			0.435287
$233$	7.26261	+	1.54372i	0.475790	+	0.101132i	0.439564	−	0.898211i	$-0.355133\pi$
$233$	7.26261	+	1.54372i	0.475790	+	0.101132i	0.0362259	+	0.999344i	$0.488466\pi$
$234$	11.5941	+	5.16205i	0.757933	+	0.337453i
$235$	−0.236103	+	2.24637i	−0.0154017	+	0.146537i
$236$	0.810480	−	0.360849i	0.0527578	−	0.0234893i
$237$	27.7074			1.79979
$238$	6.74823	+	5.00197i	0.437423	+	0.324230i
$239$	2.16771	−	6.67153i	0.140218	−	0.431545i	−0.856148	−	0.516731i	$-0.827149\pi$
$239$	2.16771	−	6.67153i	0.140218	−	0.431545i	0.996365	+	0.0851863i	$0.0271486\pi$
$240$	1.03092	+	0.219129i	0.0665458	+	0.0141447i
$241$	21.1528	+	9.41782i	1.36257	+	0.606655i	0.952259	−	0.305291i	$-0.0987538\pi$
$241$	21.1528	+	9.41782i	1.36257	+	0.606655i	0.410310	+	0.911946i	$0.365420\pi$
$242$	3.89481	+	1.73408i	0.250368	+	0.111471i
$243$	−9.87255	+	17.0998i	−0.633325	+	1.09695i
$244$	−0.948461	−	2.91906i	−0.0607190	−	0.186874i
$245$	−1.65024	+	2.73632i	−0.105430	+	0.174817i
$246$	3.86383	−	14.2699i	0.246349	−	0.909813i
$247$	−4.97731	+	8.62096i	−0.316699	+	0.548538i
$248$	0.599772	−	0.666114i	0.0380856	−	0.0422983i
$249$	−0.442207	−	0.765925i	−0.0280237	−	0.0485386i
$250$	0.467218	+	4.44528i	0.0295494	+	0.281144i
$251$	−17.4867	+	12.7048i	−1.10375	+	0.801920i	−0.981668	−	0.190600i	$-0.938957\pi$
$251$	−17.4867	+	12.7048i	−1.10375	+	0.801920i	−0.122081	+	0.992520i	$0.538957\pi$
$252$	1.84946	+	5.88251i	0.116505	+	0.370564i
$253$	−3.62836	+	11.1669i	−0.228113	+	0.702060i
$254$	−19.2089	+	8.55236i	−1.20527	+	0.536623i
$255$	−1.67308	−	2.89786i	−0.104772	−	0.181471i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	7.19853	−	3.20499i	0.449032	−	0.199922i	−0.169746	−	0.985488i	$-0.554295\pi$
$257$	7.19853	−	3.20499i	0.449032	−	0.199922i	0.618778	+	0.785566i	$0.287628\pi$
$258$	8.76072	−	6.36503i	0.545418	−	0.396270i
$259$	2.24517	+	0.499668i	0.139508	+	0.0310479i
$260$	2.48574			0.154159
$261$	−1.61524	−	15.3680i	−0.0999807	−	0.951253i
$262$	−17.7190	+	3.76629i	−1.09468	+	0.232682i
$263$	1.43805	−	13.6822i	0.0886742	−	0.843679i	−0.856288	−	0.516499i	$-0.827235\pi$
$263$	1.43805	−	13.6822i	0.0886742	−	0.843679i	0.944962	−	0.327180i	$-0.106098\pi$
$264$	8.82310	+	1.87541i	0.543024	+	0.115423i
$265$	−0.916067	+	2.81936i	−0.0562735	+	0.173192i
$266$	−4.74037	+	0.960406i	−0.290651	+	0.0588863i
$267$	10.0976	−	31.0771i	0.617961	−	1.90189i
$268$	6.30066	+	6.99759i	0.384874	+	0.427446i
$269$	−5.61112	+	6.23178i	−0.342116	+	0.379958i	−0.889509	−	0.456917i	$-0.848954\pi$
$269$	−5.61112	+	6.23178i	−0.342116	+	0.379958i	0.547393	+	0.836876i	$0.315620\pi$
$270$	−0.0737378	+	0.701568i	−0.00448754	+	0.0426961i
$271$	9.63270	+	10.6982i	0.585145	+	0.649869i	0.960915	−	0.276844i	$-0.0892885\pi$
$271$	9.63270	+	10.6982i	0.585145	+	0.649869i	−0.375770	+	0.926713i	$0.622622\pi$
$272$	2.56852	−	1.86614i	0.155739	−	0.113151i
$273$	16.3560	+	28.9643i	0.989910	+	1.75300i
$274$	−1.80984	−	5.57013i	−0.109337	−	0.336504i
$275$	1.95678	+	18.6175i	0.117998	+	1.12268i
$276$	−0.725318	+	6.90094i	−0.0436590	+	0.415388i
$277$	−2.95134	+	28.0802i	−0.177329	+	1.68717i	0.438056	+	0.898948i	$0.355667\pi$
$277$	−2.95134	+	28.0802i	−0.177329	+	1.68717i	−0.615385	+	0.788226i	$0.711000\pi$
$278$	−5.43192	+	9.40837i	−0.325785	+	0.564276i
$279$	−1.69011	−	1.22794i	−0.101184	−	0.0735147i
$280$	0.799544	+	0.905210i	0.0477819	+	0.0540966i
$281$	−4.45182	−	13.7013i	−0.265574	−	0.817351i	−0.991561	−	0.129643i	$-0.958617\pi$
$281$	−4.45182	−	13.7013i	−0.265574	−	0.817351i	0.725987	−	0.687708i	$-0.241383\pi$
$282$	1.19416	+	11.3617i	0.0711113	+	0.676579i
$283$	10.9929	+	4.89437i	0.653462	+	0.290940i	0.706564	−	0.707649i	$-0.250244\pi$
$283$	10.9929	+	4.89437i	0.653462	+	0.290940i	−0.0531019	+	0.998589i	$0.516911\pi$
$284$	−3.56420	−	6.17338i	−0.211496	−	0.366323i
$285$	1.88462	+	0.400589i	0.111636	+	0.0237289i
$286$	21.2741			1.25796
$287$	13.2945	−	10.5003i	0.784749	−	0.619814i
$288$	2.33068			0.137337
$289$	6.76902	+	1.43880i	0.398177	+	0.0846352i
$290$	−1.51328	−	2.62108i	−0.0888629	−	0.153915i
$291$	−4.00971	−	1.78524i	−0.235053	−	0.104652i
$292$	−0.387239	−	3.68434i	−0.0226615	−	0.215609i
$293$	−4.29542	−	13.2199i	−0.250941	−	0.772317i	−0.994602	−	0.103761i	$-0.966912\pi$
$293$	−4.29542	−	13.2199i	−0.250941	−	0.772317i	0.743661	−	0.668557i	$-0.233088\pi$
$294$	−5.28673	+	15.2726i	−0.308329	+	0.890719i
$295$	−0.327643	−	0.238046i	−0.0190761	−	0.0138596i
$296$	0.434678	−	0.752885i	0.0252652	−	0.0437606i
$297$	−0.631081	+	6.00434i	−0.0366191	+	0.348407i
$298$	1.63595	−	15.5651i	0.0947683	−	0.901660i
$299$	1.71066	+	16.2758i	0.0989299	+	0.941255i
$300$	3.41866	+	10.5216i	0.197376	+	0.607462i
$301$	12.4085	+	0.118430i	0.715215	+	0.00682618i
$302$	−18.9000	+	13.7317i	−1.08757	+	0.790168i
$303$	−9.45017	−	10.4955i	−0.542898	−	0.602949i
$304$	−0.191088	+	1.81808i	−0.0109596	+	0.104274i
$305$	−0.937515	+	1.04122i	−0.0536820	+	0.0596199i
$306$	−4.95129	−	5.49897i	−0.283047	−	0.314355i
$307$	1.81578	−	5.58840i	0.103632	−	0.318947i	−0.885775	−	0.464115i	$-0.846372\pi$
$307$	1.81578	−	5.58840i	0.103632	−	0.318947i	0.989407	+	0.145168i	$0.0463723\pi$
$308$	6.84286	+	7.74720i	0.389908	+	0.441437i
$309$	7.29038	−	22.4375i	0.414735	−	1.27642i
$310$	−0.400230	−	0.0850716i	−0.0227315	−	0.00483174i
$311$	3.05620	−	29.0778i	0.173301	−	1.64885i	−0.469582	−	0.882889i	$-0.655595\pi$
$311$	3.05620	−	29.0778i	0.173301	−	1.64885i	0.642883	−	0.765964i	$-0.277738\pi$
$312$	12.2976	−	2.61394i	0.696216	−	0.147985i
$313$	2.28131	+	21.7052i	0.128947	+	1.22685i	0.847278	+	0.531149i	$0.178240\pi$
$313$	2.28131	+	21.7052i	0.128947	+	1.22685i	−0.718331	+	0.695701i	$0.755094\pi$
$314$	15.5370			0.876802
$315$	1.90341	−	2.07380i	0.107245	−	0.116846i
$316$	9.70873	−	7.05381i	0.546159	−	0.396808i
$317$	9.43308	−	4.19988i	0.529814	−	0.235889i	−0.124353	−	0.992238i	$-0.539686\pi$
$317$	9.43308	−	4.19988i	0.529814	−	0.235889i	0.654168	+	0.756349i	$0.273019\pi$
$318$	−1.56726	+	14.9115i	−0.0878874	+	0.836193i
$319$	−12.9513	−	22.4324i	−0.725136	−	1.25597i
$320$	0.417023	−	0.185671i	0.0233123	−	0.0103793i
$321$	−6.44406	+	19.8328i	−0.359672	+	1.10696i
$322$	−5.37678	+	5.85810i	−0.299636	+	0.326459i
$323$	4.69550	−	3.41148i	0.261264	−	0.189820i
$324$	1.10382	+	10.5021i	0.0613232	+	0.583451i
$325$	13.0460	+	22.5964i	0.723663	+	1.25342i
$326$	6.77162	−	7.52065i	0.375045	−	0.416530i
$327$	4.14700	−	7.18281i	0.229329	−	0.397210i
$328$	−2.27895	−	5.98384i	−0.125834	−	0.330402i
$329$	−6.65361	+	11.2745i	−0.366826	+	0.621584i
$330$	−1.27242	−	3.91610i	−0.0700443	−	0.215574i
$331$	−2.22829	+	3.85952i	−0.122478	+	0.212138i	−0.920744	−	0.390166i	$-0.872417\pi$
$331$	−2.22829	+	3.85952i	−0.122478	+	0.212138i	0.798266	+	0.602305i	$0.205751\pi$
$332$	−0.349941	−	0.155804i	−0.0192055	−	0.00855084i
$333$	−1.85102	−	0.824127i	−0.101435	−	0.0451619i
$334$	14.1820	+	3.01448i	0.776005	+	0.164945i
$335$	1.32827	−	4.08801i	0.0725714	−	0.223352i
$336$	4.90745	+	3.63754i	0.267724	+	0.198444i
$337$	−27.8453			−1.51683			−0.758416	−	0.651771i	$-0.774026\pi$
$337$	−27.8453			−1.51683			−0.758416	+	0.651771i	$0.774026\pi$
$338$	15.2122	−	6.77292i	0.827436	−	0.368398i
$339$	2.81982	−	26.8288i	0.153151	−	1.45714i
$340$	−1.32399	−	0.589479i	−0.0718036	−	0.0319690i
$341$	−3.42535	−	0.728081i	−0.185493	−	0.0394278i
$342$	4.26071			0.230393
$343$	−15.2887	+	10.4525i	−0.825512	+	0.564384i
$344$	1.44935	−	4.46064i	0.0781437	−	0.240502i
$345$	2.89371	−	1.28836i	0.155792	−	0.0693630i
$346$	−11.2857	+	12.5340i	−0.606723	+	0.673834i
$347$	17.5410	−	3.72845i	0.941648	−	0.200154i	0.288583	−	0.957455i	$-0.406816\pi$
$347$	17.5410	−	3.72845i	0.941648	−	0.200154i	0.653066	+	0.757301i	$0.273483\pi$
$348$	−10.2429	−	11.3759i	−0.549075	−	0.609810i
$349$	−3.73399	+	11.4920i	−0.199876	+	0.615155i	0.800009	+	0.599988i	$0.204828\pi$
$349$	−3.73399	+	11.4920i	−0.199876	+	0.615155i	−0.999885	+	0.0151668i	$0.995172\pi$
$350$	−4.03243	+	12.0190i	−0.215543	+	0.642443i
$351$	2.60036	+	8.00308i	0.138797	+	0.427173i
$352$	3.56908	−	1.58905i	0.190232	−	0.0846969i
$353$	−10.8283	+	2.30163i	−0.576333	+	0.122503i	−0.486851	−	0.873485i	$-0.661855\pi$
$353$	−10.8283	+	2.30163i	−0.576333	+	0.122503i	−0.0894821	+	0.995988i	$0.528521\pi$
$354$	−1.87126	−	0.833138i	−0.0994563	−	0.0442808i
$355$	−1.62702	+	2.81808i	−0.0863532	+	0.149568i
$356$	−4.37346	−	13.4601i	−0.231793	−	0.713385i
$357$	−1.84305	−	19.3061i	−0.0975443	−	1.02179i
$358$	14.4012	+	10.4631i	0.761128	+	0.552992i
$359$	26.4144	−	11.7604i	1.39410	−	0.620692i	0.434142	−	0.900844i	$-0.357052\pi$
$359$	26.4144	−	11.7604i	1.39410	−	0.620692i	0.959956	+	0.280152i	$0.0903849\pi$
$360$	−0.531965	−	0.921390i	−0.0280370	−	0.0485615i
$361$	1.63671	−	15.5723i	0.0861428	−	0.819594i
$362$	13.2381	+	14.7024i	0.695780	+	0.772742i
$363$	−3.04179	−	9.36167i	−0.159653	−	0.491360i
$364$	13.1050	+	5.98522i	0.686887	+	0.313711i
$365$	−1.36815	+	0.994017i	−0.0716121	+	0.0520292i
$366$	−3.54322	+	6.13704i	−0.185207	+	0.320788i
$367$	−24.4294	+	27.1316i	−1.27520	+	1.41626i	−0.412174	+	0.911105i	$0.635230\pi$
$367$	−24.4294	+	27.1316i	−1.27520	+	1.41626i	−0.863030	+	0.505152i	$0.831436\pi$
$368$	1.50270	+	2.60275i	0.0783337	+	0.135678i
$369$	−13.3148	+	6.74021i	−0.693142	+	0.350881i
$370$	−0.396852			−0.0206313
$371$	−11.6181	+	12.6581i	−0.603180	+	0.657176i
$372$	−2.06951			−0.107299
$373$	−0.258864	−	2.46292i	−0.0134034	−	0.127525i	0.985774	−	0.168076i	$-0.0537554\pi$
$373$	−0.258864	−	2.46292i	−0.0134034	−	0.127525i	−0.999177	+	0.0405508i	$0.987089\pi$
$374$	−11.3313	−	5.04503i	−0.585929	−	0.260872i
$375$	6.90537	−	7.66919i	0.356592	−	0.396035i
$376$	3.31092	+	3.67715i	0.170748	+	0.189634i
$377$	−29.2081	−	21.2209i	−1.50429	−	1.09293i
$378$	−2.07800	+	3.52116i	−0.106881	+	0.181109i
$379$	−22.4512	−	16.3118i	−1.15324	−	0.837879i	−0.164333	−	0.986405i	$-0.552547\pi$
$379$	−22.4512	−	16.3118i	−1.15324	−	0.837879i	−0.988908	+	0.148526i	$0.952547\pi$
$380$	0.762359	−	0.339424i	0.0391082	−	0.0174121i
$381$	44.3501	+	19.7459i	2.27212	+	1.01161i
$382$	−9.38387	+	10.4218i	−0.480120	+	0.533228i
$383$	−14.6981	+	25.4578i	−0.751038	+	1.30084i	0.196283	+	0.980547i	$0.437113\pi$
$383$	−14.6981	+	25.4578i	−0.751038	+	1.30084i	−0.947320	+	0.320288i	$0.896220\pi$
$384$	1.86788	−	1.35709i	0.0953198	−	0.0692539i
$385$	1.50086	−	4.47345i	0.0764910	−	0.227988i
$386$	−8.69475	−	6.31711i	−0.442551	−	0.321532i
$387$	−10.6925	−	2.27275i	−0.543528	−	0.115531i
$388$	−1.85950	+	0.395248i	−0.0944017	+	0.0200657i
$389$	−0.876647	+	0.186337i	−0.0444478	+	0.00944767i	−0.230082	−	0.973171i	$-0.573899\pi$
$389$	−0.876647	+	0.186337i	−0.0444478	+	0.00944767i	0.185634	+	0.982619i	$0.440566\pi$
$390$	−3.84024	−	4.26502i	−0.194458	−	0.215968i
$391$	2.94856	−	9.07474i	0.149115	−	0.458929i
$392$	2.03566	+	6.69747i	0.102816	+	0.338273i
$393$	33.8364	+	24.5836i	1.70682	+	1.24008i
$394$	−7.71542	−	8.56885i	−0.388697	−	0.431692i
$395$	−5.00455	−	2.22817i	−0.251806	−	0.112111i
$396$	−4.55280	−	7.88567i	−0.228787	−	0.396270i
$397$	−24.9762	−	5.30886i	−1.25352	−	0.266444i	−0.467138	−	0.884185i	$-0.654715\pi$
$397$	−24.9762	−	5.30886i	−1.25352	−	0.266444i	−0.786382	+	0.617741i	$0.788048\pi$
$398$	−3.36999	+	2.44844i	−0.168923	+	0.122729i
$399$	8.97129	+	6.64976i	0.449126	+	0.332904i
$400$	3.87650	+	2.81644i	0.193825	+	0.140822i
$401$	−5.58339	+	9.67072i	−0.278821	+	0.482933i	−0.971092	−	0.238705i	$-0.923277\pi$
$401$	−5.58339	+	9.67072i	−0.278821	+	0.482933i	0.692271	+	0.721638i	$0.256610\pi$
$402$	2.27248	−	21.6213i	0.113341	−	1.07837i
$403$	−4.77425	+	1.01480i	−0.237823	+	0.0505507i
$404$	−5.98331	−	1.27179i	−0.297681	−	0.0632740i
$405$	3.89987	−	2.83342i	0.193786	−	0.140794i
$406$	−1.66701	−	17.4622i	−0.0827325	−	0.866633i
$407$	−3.39644			−0.168355
$408$	−7.17003	−	1.52404i	−0.354969	−	0.0754510i
$409$	−7.79997	−	13.5099i	−0.385684	−	0.668024i	0.606180	−	0.795327i	$-0.292701\pi$
$409$	−7.79997	−	13.5099i	−0.385684	−	0.668024i	−0.991864	+	0.127304i	$0.959368\pi$
$410$	−1.84544	+	2.26672i	−0.0911398	+	0.111945i
$411$	−6.76114	+	11.7106i	−0.333503	+	0.577643i
$412$	−3.15761	−	9.71813i	−0.155564	−	0.478778i
$413$	−1.15418	−	2.04390i	−0.0567933	−	0.100574i
$414$	5.66687	−	4.11722i	0.278511	−	0.202350i
$415$	0.0182780	+	0.173904i	0.000897233	+	0.00853660i
$416$	3.64365	−	4.04668i	0.178645	−	0.198405i
$417$	24.5346	−	5.21499i	1.20147	−	0.255379i
$418$	6.52461	−	2.90494i	0.319129	−	0.142085i
$419$	−17.4093			−0.850502			−0.425251	−	0.905075i	$-0.639814\pi$
$419$	−17.4093			−0.850502			−0.425251	+	0.905075i	$0.639814\pi$
$420$	0.317931	−	2.77032i	0.0155135	−	0.135178i
$421$	−17.0939	−	12.4194i	−0.833105	−	0.605287i	0.0873308	−	0.996179i	$-0.472166\pi$
$421$	−17.0939	−	12.4194i	−0.833105	−	0.605287i	−0.920436	+	0.390893i	$0.872166\pi$
$422$	2.81759	+	26.8076i	0.137158	+	1.30497i
$423$	7.71669	−	8.57025i	0.375198	−	0.416700i
$424$	3.24702	+	5.62400i	0.157689	+	0.273125i
$425$	−1.59016	−	15.1294i	−0.0771343	−	0.733884i
$426$	−5.08588	+	15.6527i	−0.246412	+	0.758377i
$427$	−7.44969	+	3.23198i	−0.360516	+	0.156406i
$428$	2.79105	+	8.58998i	0.134911	+	0.415212i
$429$	−32.8665	−	36.5020i	−1.58681	−	1.76233i
$430$	−2.09423	+	0.445143i	−0.100993	+	0.0214667i
$431$	−18.3755	+	3.90584i	−0.885118	+	0.188138i	−0.627973	−	0.778235i	$-0.716115\pi$
$431$	−18.3755	+	3.90584i	−0.885118	+	0.188138i	−0.257145	+	0.966373i	$0.582782\pi$
$432$	1.03404	+	1.14841i	0.0497501	+	0.0552531i
$433$	5.79230	+	17.8269i	0.278360	+	0.856705i	0.988311	+	0.152453i	$0.0487173\pi$
$433$	5.79230	+	17.8269i	0.278360	+	0.856705i	−0.709950	+	0.704252i	$0.751283\pi$
$434$	−1.90520	−	1.41218i	−0.0914524	−	0.0677870i
$435$	−2.15935	+	6.64580i	−0.103533	+	0.318642i
$436$	−0.375497	−	3.57262i	−0.0179831	−	0.171097i
$437$	2.74708	+	4.75808i	0.131411	+	0.227610i
$438$	−5.72331	+	6.35638i	−0.273470	+	0.303719i
$439$	−2.85386	−	27.1527i	−0.136207	−	1.29593i	−0.822569	−	0.568665i	$-0.807460\pi$
$439$	−2.85386	−	27.1527i	−0.136207	−	1.29593i	0.686362	−	0.727260i	$-0.259207\pi$
$440$	−1.44282	−	1.04827i	−0.0687840	−	0.0499745i
$441$	15.0282	−	6.35013i	0.715629	−	0.302387i
$442$	−17.2882			−0.822318
$443$	25.3655	−	11.2934i	1.20515	−	0.536567i	0.296865	−	0.954919i	$-0.404059\pi$
$443$	25.3655	−	11.2934i	1.20515	−	0.536567i	0.908285	+	0.418352i	$0.137392\pi$
$444$	−1.96333	+	0.417319i	−0.0931756	+	0.0198051i
$445$	−4.32299	+	4.80116i	−0.204929	+	0.227597i
$446$	−1.19226	−	11.3436i	−0.0564550	−	0.537133i
$447$	−29.2338	+	21.2396i	−1.38271	+	1.00460i
$448$	2.64563	+	0.0252505i	0.124994	+	0.00119297i
$449$	4.69347	+	14.4450i	0.221498	+	0.681702i	0.998628	+	0.0523616i	$0.0166748\pi$
$449$	4.69347	+	14.4450i	0.221498	+	0.681702i	−0.777130	+	0.629340i	$0.783325\pi$
$450$	5.58386	−	9.67154i	0.263226	−	0.455921i
$451$	−15.7941	+	19.3996i	−0.743716	+	0.913492i
$452$	−5.84205	−	10.1187i	−0.274787	−	0.475945i
$453$	52.7594	+	11.2144i	2.47885	+	0.526896i
$454$	24.2200			1.13670
$455$	−0.624994	−	6.54689i	−0.0293002	−	0.306923i
$456$	3.41466	−	2.48090i	0.159906	−	0.116179i
$457$	−21.9335	−	4.66212i	−1.02601	−	0.218085i	−0.335981	−	0.941869i	$-0.609068\pi$
$457$	−21.9335	−	4.66212i	−1.02601	−	0.218085i	−0.690027	+	0.723784i	$0.742401\pi$
$458$	10.0527	−	2.13677i	0.469732	−	0.0998447i
$459$	0.512843	−	4.87938i	0.0239375	−	0.227750i
$460$	0.685966	−	1.18813i	0.0319834	−	0.0553968i
$461$	−0.115398	−	0.0838418i	−0.00537464	−	0.00390490i	0.585095	−	0.810965i	$-0.301057\pi$
$461$	−0.115398	−	0.0838418i	−0.00537464	−	0.00390490i	−0.590469	+	0.807060i	$0.701057\pi$
$462$	2.72100	−	23.7096i	0.126592	−	1.10307i
$463$	−3.42067	+	2.48526i	−0.158972	+	0.115500i	−0.664427	−	0.747353i	$-0.731324\pi$
$463$	−3.42067	+	2.48526i	−0.158972	+	0.115500i	0.505455	+	0.862853i	$0.331324\pi$
$464$	−6.48521	−	1.37847i	−0.301068	−	0.0639940i
$465$	0.472353	+	0.818140i	0.0219048	+	0.0379403i
$466$	−6.78295	−	3.01996i	−0.314214	−	0.139897i
$467$	−4.87163	−	5.41050i	−0.225432	−	0.250368i	0.619809	−	0.784753i	$-0.287210\pi$
$467$	−4.87163	−	5.41050i	−0.225432	−	0.250368i	−0.845241	+	0.534385i	$0.820543\pi$
$468$	−10.2675	−	7.45980i	−0.474617	−	0.344829i
$469$	16.8459	−	18.3539i	0.777872	−	0.847507i
$470$	0.697992	−	2.14820i	0.0321960	−	0.0990890i
$471$	−24.0032	−	26.6582i	−1.10601	−	1.22835i
$472$	−0.867794	+	0.184455i	−0.0399435	+	0.00849025i
$473$	−17.9234	+	3.80974i	−0.824119	+	0.175172i
$474$	−27.1020	−	5.76070i	−1.24483	−	0.264598i
$475$	7.08661	+	5.14873i	0.325156	+	0.236240i
$476$	−5.56080	−	6.29570i	−0.254879	−	0.288563i
$477$	12.2449	−	8.89643i	0.560655	−	0.407340i
$478$	−3.50743	+	6.07504i	−0.160426	+	0.277866i
$479$	−15.0790	+	16.7469i	−0.688977	+	0.765187i	−0.981581	−	0.191047i	$-0.938812\pi$
$479$	−15.0790	+	16.7469i	−0.688977	+	0.765187i	0.292604	+	0.956234i	$0.405478\pi$
$480$	−0.962835	−	0.428682i	−0.0439472	−	0.0195665i
$481$	−4.32468	+	1.92547i	−0.197189	+	0.0877940i
$482$	−18.7324	−	13.6099i	−0.853240	−	0.619915i
$483$	18.3579	+	0.175212i	0.835314	+	0.00797243i
$484$	−3.44916	−	2.50596i	−0.156780	−	0.113907i
$485$	0.580674	+	0.644904i	0.0263670	+	0.0292836i
$486$	13.2121	−	14.6735i	0.599311	−	0.665602i
$487$	23.2803	+	10.3651i	1.05493	+	0.469686i	0.859556	−	0.511042i	$-0.170740\pi$
$487$	23.2803	+	10.3651i	1.05493	+	0.469686i	0.195377	+	0.980728i	$0.437407\pi$
$488$	0.320828	+	3.05247i	0.0145232	+	0.138179i
$489$	−23.3654			−1.05662
$490$	2.18309	−	2.33342i	0.0986220	−	0.105413i
$491$	17.2880			0.780198			0.390099	−	0.920773i	$-0.372441\pi$
$491$	17.2880			0.780198			0.390099	+	0.920773i	$0.372441\pi$
$492$	−6.74626	+	13.1547i	−0.304145	+	0.593059i
$493$	10.5248	+	18.2295i	0.474014	+	0.821016i
$494$	6.66094	−	7.39773i	0.299690	−	0.332839i
$495$	−2.07830	+	3.59972i	−0.0934127	+	0.161796i
$496$	−0.725158	+	0.526858i	−0.0325606	+	0.0236566i
$497$	−15.3631	+	10.9395i	−0.689131	+	0.490703i
$498$	0.273299	+	0.841128i	0.0122468	+	0.0376919i
$499$	−13.0355	−	14.4774i	−0.583549	−	0.648097i	0.376998	−	0.926214i	$-0.376956\pi$
$499$	−13.0355	−	14.4774i	−0.583549	−	0.648097i	−0.960547	+	0.278117i	$0.910290\pi$
$500$	0.467218	−	4.44528i	0.0208946	−	0.198799i
$501$	−16.7377	−	28.9905i	−0.747784	−	1.29520i
$502$	19.7460	−	8.79149i	0.881308	−	0.392383i
$503$	28.6423	+	20.8099i	1.27710	+	0.927866i	0.999461	−	0.0328203i	$-0.0104489\pi$
$503$	28.6423	+	20.8099i	1.27710	+	0.927866i	0.277637	+	0.960686i	$0.410449\pi$
$504$	−0.586006	−	6.13849i	−0.0261028	−	0.273430i
$505$	0.862879	+	2.65567i	0.0383976	+	0.118176i
$506$	5.87081	−	10.1685i	0.260989	−	0.452047i
$507$	−35.1224	−	15.6375i	−1.55984	−	0.694485i
$508$	20.5673	−	4.37171i	0.912526	−	0.193963i
$509$	−8.08091	+	3.59785i	−0.358180	+	0.159472i	−0.577935	−	0.816083i	$-0.696141\pi$
$509$	−8.08091	+	3.59785i	−0.358180	+	0.159472i	0.219754	+	0.975555i	$0.429474\pi$
$510$	1.03402	+	3.18239i	0.0457872	+	0.140918i
$511$	−9.60635	+	1.94626i	−0.424960	+	0.0860975i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	1.89032	+	2.09941i	0.0834596	+	0.0926913i
$514$	−7.70758	+	1.63830i	−0.339967	+	0.0722622i
$515$	−3.12117	+	3.46641i	−0.137535	+	0.152748i
$516$	−9.89264	+	4.40449i	−0.435499	+	0.193897i
$517$	5.97373	−	18.3852i	0.262724	−	0.808582i
$518$	−2.09222	−	0.955547i	−0.0919270	−	0.0419843i
$519$	38.9411			1.70933
$520$	−2.43142	−	0.516815i	−0.106625	−	0.0226638i
$521$	20.2382	+	9.01063i	0.886652	+	0.394763i	0.798960	−	0.601385i	$-0.205384\pi$
$521$	20.2382	+	9.01063i	0.886652	+	0.394763i	0.0876924	+	0.996148i	$0.472051\pi$
$522$	−1.61524	+	15.3680i	−0.0706971	+	0.672638i
$523$	5.34978	−	2.38188i	0.233930	−	0.104152i	−0.286424	−	0.958103i	$-0.592467\pi$
$523$	5.34978	−	2.38188i	0.233930	−	0.104152i	0.520354	+	0.853951i	$0.325800\pi$
$524$	18.1149			0.791352
$525$	26.8519	−	11.6494i	1.17191	−	0.508423i
$526$	−4.25131	+	13.0842i	−0.185366	+	0.570498i
$527$	2.78359	+	0.591670i	0.121255	+	0.0257735i
$528$	−8.24038	−	3.66885i	−0.358616	−	0.159666i
$529$	−12.7600	−	5.68112i	−0.554783	−	0.247005i
$530$	1.48223	−	2.56729i	0.0643838	−	0.111516i
$531$	0.638965	+	1.96653i	0.0277287	+	0.0853403i
$532$	4.83647	+	0.0461604i	0.209687	+	0.00200131i
$533$	−9.11281	+	33.6553i	−0.394720	+	1.45778i
$534$	−16.3382	+	28.2986i	−0.707023	+	1.22460i
$535$	2.75884	−	3.06400i	0.119275	−	0.132468i
$536$	−4.70809	−	8.15466i	−0.203359	−	0.352228i
$537$	−4.29603	−	40.8740i	−0.185387	−	1.76384i
$538$	6.78416	−	4.92898i	0.292486	−	0.212504i
$539$	18.6839	−	19.9705i	0.804772	−	0.860189i
$540$	0.217991	−	0.670906i	0.00938082	−	0.0288712i
$541$	−6.45572	+	2.87427i	−0.277553	+	0.123575i	−0.540793	−	0.841156i	$-0.681876\pi$
$541$	−6.45572	+	2.87427i	−0.277553	+	0.123575i	0.263240	+	0.964730i	$0.415209\pi$
$542$	−7.19792	−	12.4672i	−0.309177	−	0.535511i
$543$	4.77465	−	45.4278i	0.204900	−	1.94949i
$544$	−2.90038	+	1.29133i	−0.124353	+	0.0553655i
$545$	−1.32666	+	0.963876i	−0.0568280	+	0.0412879i
$546$	−9.97656	−	31.7320i	−0.426957	−	1.35800i
$547$	20.0281			0.856338			0.428169	−	0.903699i	$-0.359159\pi$
$547$	20.0281			0.856338			0.428169	+	0.903699i	$0.359159\pi$
$548$	0.612200	+	5.82470i	0.0261519	+	0.248819i
$549$	6.99720	−	1.48730i	0.298633	−	0.0634764i
$550$	1.95678	−	18.6175i	0.0834374	−	0.793854i
$551$	−11.8556	−	2.51998i	−0.505065	−	0.107355i
$552$	2.14425	−	6.59934i	0.0912655	−	0.280886i
$553$	−21.0192	−	23.7971i	−0.893829	−	1.01196i
$554$	8.72505	−	26.8529i	0.370692	−	1.14087i
$555$	0.613099	+	0.680915i	0.0260246	+	0.0289032i
$556$	7.26933	−	8.07341i	0.308288	−	0.342389i
$557$	−2.95512	+	28.1161i	−0.125212	+	1.19132i	0.733802	+	0.679364i	$0.237744\pi$
$557$	−2.95512	+	28.1161i	−0.125212	+	1.19132i	−0.859014	+	0.511952i	$0.828923\pi$
$558$	1.39788	+	1.55250i	0.0591768	+	0.0657225i
$559$	−20.6621	+	15.0119i	−0.873913	+	0.634935i
$560$	−0.593868	−	1.05166i	−0.0250955	−	0.0444409i
$561$	8.84961	+	27.2363i	0.373631	+	1.14992i
$562$	1.50588	+	14.3275i	0.0635217	+	0.604369i
$563$	1.28254	−	12.2025i	0.0540525	−	0.514276i	−0.933679	−	0.358112i	$-0.883421\pi$
$563$	1.28254	−	12.2025i	0.0540525	−	0.514276i	0.987731	−	0.156164i	$-0.0499127\pi$
$564$	1.19416	−	11.3617i	0.0502833	−	0.478414i
$565$	−2.66683	+	4.61909i	−0.112194	+	0.194326i
$566$	−9.73512	−	7.07298i	−0.409198	−	0.297299i
$567$	27.3827	−	5.54777i	1.14997	−	0.232985i
$568$	2.20280	+	6.77951i	0.0924273	+	0.284462i
$569$	3.91593	+	37.2576i	0.164164	+	1.56192i	0.697855	+	0.716239i	$0.254138\pi$
$569$	3.91593	+	37.2576i	0.164164	+	1.56192i	−0.533690	+	0.845680i	$0.679195\pi$
$570$	−1.76015	−	0.783671i	−0.0737247	−	0.0328244i
$571$	17.9294	+	31.0547i	0.750324	+	1.29960i	0.947666	+	0.319264i	$0.103436\pi$
$571$	17.9294	+	31.0547i	0.750324	+	1.29960i	−0.197342	+	0.980335i	$0.563231\pi$
$572$	−20.8092	−	4.42314i	−0.870077	−	0.184941i
$573$	32.3789			1.35265
$574$	−15.1871	+	7.50678i	−0.633898	+	0.313327i
$575$	14.4007			0.600552
$576$	−2.27975	−	0.484576i	−0.0949895	−	0.0201907i
$577$	−13.5652	−	23.4956i	−0.564727	−	0.978136i	−0.997075	−	0.0764288i	$-0.975648\pi$
$577$	−13.5652	−	23.4956i	−0.564727	−	0.978136i	0.432348	−	0.901707i	$-0.357685\pi$
$578$	−6.32195	−	2.81471i	−0.262959	−	0.117077i
$579$	2.59373	+	24.6777i	0.107792	+	1.02557i
$580$	0.935259	+	2.87843i	0.0388345	+	0.119520i
$581$	−0.322366	+	0.960840i	−0.0133740	+	0.0398624i
$582$	3.55091	+	2.57989i	0.147190	+	0.106940i
$583$	12.6856	−	21.9721i	0.525383	−	0.909990i
$584$	−0.387239	+	3.68434i	−0.0160241	+	0.152459i
$585$	−0.605583	+	5.76173i	−0.0250378	+	0.238218i
$586$	1.45297	+	13.8241i	0.0600218	+	0.571069i
$587$	−1.67616	−	5.15870i	−0.0691826	−	0.212922i	0.910488	−	0.413536i	$-0.135706\pi$
$587$	−1.67616	−	5.15870i	−0.0691826	−	0.212922i	−0.979670	+	0.200614i	$0.935706\pi$
$588$	8.34657	−	13.8397i	0.344207	−	0.570741i
$589$	−1.32566	+	0.963147i	−0.0546228	+	0.0396858i
$590$	0.270990	+	0.300965i	0.0111565	+	0.0123905i
$591$	−2.78275	+	26.4761i	−0.114467	+	1.08908i
$592$	−0.581713	+	0.646058i	−0.0239083	+	0.0265528i
$593$	3.30037	+	3.66543i	0.135530	+	0.150521i	0.807089	−	0.590430i	$-0.201042\pi$
$593$	3.30037	+	3.66543i	0.135530	+	0.150521i	−0.671559	+	0.740951i	$0.734375\pi$
$594$	1.86566	−	5.74192i	0.0765491	−	0.235594i
$595$	−1.21966	+	3.63532i	−0.0500014	+	0.149033i
$596$	−4.83636	+	14.8848i	−0.198105	+	0.609705i
$597$	9.40735	+	1.99959i	0.385017	+	0.0818379i
$598$	1.71066	−	16.2758i	0.0699540	−	0.665568i
$599$	31.4811	−	6.69152i	1.28628	−	0.273408i	0.486492	−	0.873685i	$-0.338276\pi$
$599$	31.4811	−	6.69152i	1.28628	−	0.273408i	0.799792	+	0.600277i	$0.204943\pi$
$600$	−1.15640	−	11.0024i	−0.0472098	−	0.449172i
$601$	−45.2695			−1.84658			−0.923291	−	0.384102i	$-0.874511\pi$
$601$	−45.2695			−1.84658			−0.923291	+	0.384102i	$0.874511\pi$
$602$	−12.1127	−	2.69572i	−0.493678	−	0.109869i
$603$	−17.7548	+	12.8996i	−0.723031	+	0.525313i
$604$	21.3420	−	9.50205i	0.868392	−	0.386633i
$605$	−0.203433	+	1.93553i	−0.00827071	+	0.0786906i
$606$	7.06153	+	12.2309i	0.286855	+	0.496847i
$607$	39.6251	−	17.6422i	1.60833	−	0.716076i	0.611181	−	0.791491i	$-0.290695\pi$
$607$	39.6251	−	17.6422i	1.60833	−	0.716076i	0.997152	+	0.0754143i	$0.0240279\pi$
$608$	0.564913	−	1.73862i	0.0229102	−	0.0705104i
$609$	−27.3861	+	29.8377i	−1.10974	+	1.20908i
$610$	1.13351	−	0.823543i	0.0458944	−	0.0333443i
$611$	−2.81642	−	26.7965i	−0.113940	−	1.08407i
$612$	3.69980	+	6.40823i	0.149555	+	0.259038i
$613$	−22.1523	+	24.6026i	−0.894722	+	0.993690i	−1.00000		0.000752952i	$-0.999760\pi$
$613$	−22.1523	+	24.6026i	−0.894722	+	0.993690i	0.105277	+	0.994443i	$0.466427\pi$
$614$	−2.93800	+	5.08876i	−0.118568	+	0.205366i
$615$	6.74025	−	0.335478i	0.271793	−	0.0135278i
$616$	−5.08259	−	9.00061i	−0.204784	−	0.362645i
$617$	13.0288	+	40.0986i	0.524520	+	1.61431i	0.765262	+	0.643719i	$0.222609\pi$
$617$	13.0288	+	40.0986i	0.524520	+	1.61431i	−0.240742	+	0.970589i	$0.577391\pi$
$618$	−11.7961	+	20.4314i	−0.474508	+	0.821872i
$619$	31.8261	+	14.1699i	1.27920	+	0.569536i	0.930016	−	0.367519i	$-0.119793\pi$
$619$	31.8261	+	14.1699i	1.27920	+	0.569536i	0.349183	+	0.937055i	$0.386459\pi$
$620$	0.373797	+	0.166425i	0.0150120	+	0.00668379i
$621$	4.54289	+	0.965621i	0.182300	+	0.0387490i
$622$	−9.03504	+	27.8070i	−0.362272	+	1.11496i
$623$	−34.3513	+	14.9030i	−1.37626	+	0.597077i
$624$	−12.5724			−0.503298
$625$	20.0228	−	8.91473i	0.800912	−	0.356589i
$626$	2.28131	−	21.7052i	0.0911794	−	0.867514i
$627$	−15.0642	−	6.70701i	−0.601606	−	0.267852i
$628$	−15.1974	−	3.23032i	−0.606444	−	0.128904i
$629$	2.76009			0.110052
$630$	−2.29298	+	1.63274i	−0.0913546	+	0.0650500i
$631$	−6.42858	+	19.7851i	−0.255918	+	0.787634i	0.737730	+	0.675096i	$0.235898\pi$
$631$	−6.42858	+	19.7851i	−0.255918	+	0.787634i	−0.993647	+	0.112538i	$0.964102\pi$
$632$	−10.9631	+	4.88111i	−0.436090	+	0.194160i
$633$	41.6434	−	46.2496i	1.65518	−	1.83826i
$634$	−10.1001	+	2.14685i	−0.401128	+	0.0852624i
$635$	−6.42265	−	7.13307i	−0.254875	−	0.283067i
$636$	4.63328	−	14.2598i	0.183721	−	0.565436i
$637$	12.4687	−	36.0204i	0.494029	−	1.42718i
$638$	8.00437	+	24.6349i	0.316896	+	0.975306i
$639$	15.1777	−	6.75753i	0.600419	−	0.267324i
$640$	−0.446514	+	0.0949094i	−0.0176500	+	0.00375162i
$641$	1.19531	+	0.532188i	0.0472121	+	0.0210202i	0.430207	−	0.902730i	$-0.358441\pi$
$641$	1.19531	+	0.532188i	0.0472121	+	0.0210202i	−0.382995	+	0.923750i	$0.625107\pi$
$642$	10.4267	−	18.0596i	0.411509	−	0.712755i
$643$	9.38756	+	28.8919i	0.370209	+	1.13939i	0.946654	+	0.322251i	$0.104439\pi$
$643$	9.38756	+	28.8919i	0.370209	+	1.13939i	−0.576445	+	0.817136i	$0.695561\pi$
$644$	6.47725	−	4.61219i	0.255239	−	0.181746i
$645$	3.99917	+	2.90557i	0.157467	+	0.114407i
$646$	−5.30218	+	2.36068i	−0.208611	+	0.0928798i
$647$	15.8215	+	27.4037i	0.622009	+	1.07735i	0.989111	+	0.147171i	$0.0470167\pi$
$647$	15.8215	+	27.4037i	0.622009	+	1.07735i	−0.367102	+	0.930181i	$0.619650\pi$
$648$	1.10382	−	10.5021i	0.0433620	−	0.412562i
$649$	2.31926	+	2.57580i	0.0910388	+	0.101109i
$650$	−8.06288	−	24.8150i	−0.316252	−	0.973325i
$651$	0.520339	+	5.45062i	0.0203937	+	0.213626i
$652$	−8.18727	+	5.94840i	−0.320638	+	0.232957i
$653$	24.2250	−	41.9589i	0.947997	−	1.64198i	0.198362	−	0.980129i	$-0.436438\pi$
$653$	24.2250	−	41.9589i	0.947997	−	1.64198i	0.749635	−	0.661851i	$-0.230229\pi$
$654$	−5.54976	+	6.16364i	−0.217013	+	0.241017i
$655$	−4.13462	−	7.16137i	−0.161553	−	0.279818i
$656$	0.985042	+	6.32690i	0.0384594	+	0.247024i
$657$	8.63431			0.336856
$658$	8.85232	−	9.64477i	0.345099	−	0.375992i
$659$	21.3023			0.829822			0.414911	−	0.909862i	$-0.363813\pi$
$659$	21.3023			0.829822			0.414911	+	0.909862i	$0.363813\pi$
$660$	0.430409	+	4.09507i	0.0167537	+	0.159400i
$661$	−5.96000	−	2.65356i	−0.231817	−	0.103212i	0.287541	−	0.957768i	$-0.407162\pi$
$661$	−5.96000	−	2.65356i	−0.231817	−	0.103212i	−0.519358	+	0.854557i	$0.673829\pi$
$662$	2.98204	−	3.31189i	0.115900	−	0.128720i
$663$	26.7087	+	29.6630i	1.03728	+	1.15202i
$664$	0.309900	+	0.225156i	0.0120265	+	0.00873774i
$665$	−1.08565	−	1.92254i	−0.0420996	−	0.0745529i
$666$	1.63922	+	1.19097i	0.0635187	+	0.0461490i
$667$	−18.2034	+	8.10467i	−0.704838	+	0.313814i
$668$	−13.2454	−	5.89721i	−0.512478	−	0.228170i
$669$	−17.6213	+	19.5704i	−0.681278	+	0.756635i
$670$	−2.14919	+	3.72251i	−0.0830306	+	0.143813i
$671$	9.70109	−	7.04825i	0.374506	−	0.272095i
$672$	−4.04393	−	4.57836i	−0.155998	−	0.176614i
$673$	−7.84083	−	5.69670i	−0.302242	−	0.219591i	0.426319	−	0.904573i	$-0.359810\pi$
$673$	−7.84083	−	5.69670i	−0.302242	−	0.219591i	−0.728560	+	0.684982i	$0.759810\pi$
$674$	27.2368	+	5.78937i	1.04912	+	0.222998i
$675$	7.24289	−	1.53952i	0.278779	−	0.0592563i
$676$	−16.2880	+	3.46211i	−0.626460	+	0.133158i
$677$	−4.98117	−	5.53215i	−0.191442	−	0.212618i	0.639781	−	0.768558i	$-0.279025\pi$
$677$	−4.98117	−	5.53215i	−0.191442	−	0.212618i	−0.831223	+	0.555940i	$0.812359\pi$
$678$	−8.33621	+	25.6562i	−0.320150	+	0.985322i
$679$	1.50853	+	4.79812i	0.0578922	+	0.184135i
$680$	1.17250	+	0.851871i	0.0449633	+	0.0326678i
$681$	−37.4177	−	41.5566i	−1.43385	−	1.59245i
$682$	3.19912	+	1.42434i	0.122501	+	0.0545408i
$683$	11.4736	+	19.8729i	0.439026	+	0.760415i	0.997615	−	0.0690295i	$-0.0219903\pi$
$683$	11.4736	+	19.8729i	0.439026	+	0.760415i	−0.558589	+	0.829445i	$0.688657\pi$
$684$	−4.16760	−	0.885850i	−0.159352	−	0.0338713i
$685$	2.16295	−	1.57148i	0.0826421	−	0.0600430i
$686$	17.1278	−	7.04542i	0.653943	−	0.268995i
$687$	−19.1967	−	13.9473i	−0.732402	−	0.532121i
$688$	−2.34510	+	4.06183i	−0.0894060	+	0.154856i
$689$	3.69637	−	35.1686i	0.140820	−	1.33982i
$690$	−3.09834	+	0.658572i	−0.117952	+	0.0250714i
$691$	−41.6823	−	8.85984i	−1.58567	−	0.337044i	−0.671066	−	0.741398i	$-0.734163\pi$
$691$	−41.6823	−	8.85984i	−1.58567	−	0.337044i	−0.914603	+	0.404354i	$0.867496\pi$
$692$	13.6450	−	9.91370i	0.518707	−	0.376862i
$693$	−19.6244	+	13.9738i	−0.745469	+	0.530819i
$694$	−17.9328			−0.680721
$695$	−4.85085	−	1.03108i	−0.184003	−	0.0391111i
$696$	7.65386	+	13.2569i	0.290119	+	0.502501i
$697$	12.8350	−	15.7650i	0.486159	−	0.597140i
$698$	6.04172	−	10.4646i	0.228683	−	0.396090i
$699$	5.29739	+	16.3037i	0.200366	+	0.616662i
$700$	6.44321	−	10.9180i	0.243530	−	0.412661i
$701$	−10.1662	+	7.38616i	−0.383971	+	0.278971i	−0.762981	−	0.646421i	$-0.776265\pi$
$701$	−10.1662	+	7.38616i	−0.383971	+	0.278971i	0.379009	+	0.925393i	$0.376265\pi$
$702$	−0.879601	−	8.36884i	−0.0331984	−	0.315862i
$703$	−1.06343	+	1.18106i	−0.0401079	+	0.0445444i
$704$	−3.82147	+	0.812278i	−0.144027	+	0.0306139i
$705$	−4.76419	+	2.12116i	−0.179430	+	0.0798873i
$706$	11.0702			0.416633
$707$	−1.84522	+	16.0785i	−0.0693968	+	0.604693i
$708$	1.65715	+	1.20399i	0.0622794	+	0.0452487i
$709$	−2.49457	−	23.7343i	−0.0936857	−	0.891360i	−0.935912	−	0.352235i	$-0.885422\pi$
$709$	−2.49457	−	23.7343i	−0.0936857	−	0.891360i	0.842226	−	0.539125i	$-0.181245\pi$
$710$	2.17738	−	2.41822i	0.0817155	−	0.0907542i
$711$	13.9848	+	24.2225i	0.524473	+	0.908413i
$712$	1.47937	+	14.0753i	0.0554418	+	0.527493i
$713$	−0.832454	+	2.56203i	−0.0311756	+	0.0959488i
$714$	−2.21120	+	19.2674i	−0.0827521	+	0.721066i
$715$	3.00099	+	9.23609i	0.112231	+	0.345410i
$716$	−11.9111	−	13.2286i	−0.445139	−	0.494377i
$717$	15.8422	−	3.36736i	0.591637	−	0.125756i
$718$	−28.2823	+	6.01159i	−1.05549	+	0.224350i
$719$	7.04018	+	7.81891i	0.262554	+	0.291596i	0.859980	−	0.510329i	$-0.170476\pi$
$719$	7.04018	+	7.81891i	0.262554	+	0.291596i	−0.597425	+	0.801925i	$0.703810\pi$
$720$	0.328772	+	1.01186i	0.0122526	+	0.0377097i
$721$	−24.8015	+	10.7599i	−0.923655	+	0.400719i
$722$	−4.83861	+	14.8917i	−0.180074	+	0.554212i
$723$	5.58808	+	53.1670i	0.207823	+	1.97730i
$724$	−9.89203	−	17.1335i	−0.367635	−	0.636762i
$725$	−21.2575	+	23.6089i	−0.789484	+	0.876811i
$726$	1.02892	+	9.78952i	0.0381868	+	0.363323i
$727$	−9.48661	−	6.89243i	−0.351839	−	0.255626i	0.397801	−	0.917472i	$-0.369773\pi$
$727$	−9.48661	−	6.89243i	−0.351839	−	0.255626i	−0.749640	+	0.661846i	$0.769773\pi$
$728$	−11.5742	−	8.57910i	−0.428968	−	0.317963i
$729$	−13.9081			−0.515116
$730$	1.54492	−	0.687841i	0.0571800	−	0.0254582i
$731$	14.5653	−	3.09596i	0.538718	−	0.114508i
$732$	4.74176	−	5.26626i	0.175260	−	0.194646i
$733$	−3.96545	−	37.7287i	−0.146467	−	1.39354i	−0.782870	−	0.622185i	$-0.786245\pi$
$733$	−3.96545	−	37.7287i	−0.146467	−	1.39354i	0.636403	−	0.771356i	$-0.280421\pi$
$734$	29.5365	−	21.4595i	1.09021	−	0.792086i
$735$	−7.37633	−	0.140816i	−0.272080	−	0.00519407i
$736$	−0.928720	−	2.85831i	−0.0342331	−	0.105359i
$737$	−18.3938	+	31.8589i	−0.677543	+	1.17354i
$738$	14.4252	−	3.82461i	0.531000	−	0.140786i
$739$	5.19538	+	8.99866i	0.191115	+	0.331021i	0.945620	−	0.325273i	$-0.105456\pi$
$739$	5.19538	+	8.99866i	0.191115	+	0.331021i	−0.754505	+	0.656294i	$0.772123\pi$
$740$	0.388180	+	0.0825101i	0.0142698	+	0.00303313i
$741$	−22.9835			−0.844320
$742$	13.9960	−	9.96597i	0.513808	−	0.365862i
$743$	6.74366	−	4.89956i	0.247401	−	0.179747i	−0.457173	−	0.889378i	$-0.651138\pi$
$743$	6.74366	−	4.89956i	0.247401	−	0.179747i	0.704574	+	0.709630i	$0.251138\pi$
$744$	2.02428	+	0.430274i	0.0742138	+	0.0157746i
$745$	6.98830	−	1.48541i	0.256031	−	0.0544211i
$746$	−0.258864	+	2.46292i	−0.00947767	+	0.0901740i
$747$	0.446393	−	0.773175i	0.0163327	−	0.0282890i
$748$	10.0348	+	7.29070i	0.366908	+	0.266574i
$749$	21.9223	−	9.51080i	0.801024	−	0.347517i
$750$	−8.34898	+	6.06589i	−0.304862	+	0.221495i
$751$	−21.3532	−	4.53877i	−0.779190	−	0.165622i	−0.198887	−	0.980022i	$-0.563733\pi$
$751$	−21.3532	−	4.53877i	−0.779190	−	0.165622i	−0.580303	+	0.814401i	$0.697066\pi$
$752$	−2.47404	−	4.28517i	−0.0902191	−	0.156264i
$753$	−45.5901	−	20.2980i	−1.66140	−	0.739701i
$754$	24.1577	+	26.8299i	0.879773	+	0.977087i
$755$	−8.62764	−	6.26835i	−0.313992	−	0.228129i
$756$	2.76468	−	3.01217i	0.100550	−	0.109552i
$757$	−11.4947	+	35.3772i	−0.417783	+	1.28581i	0.491954	+	0.870621i	$0.336283\pi$
$757$	−11.4947	+	35.3772i	−0.417783	+	1.28581i	−0.909737	+	0.415184i	$0.863717\pi$
$758$	18.5692	+	20.6232i	0.674463	+	0.749067i
$759$	−26.5170	+	5.63636i	−0.962505	+	0.204587i
$760$	−0.816269	+	0.173503i	−0.0296092	+	0.00629363i
$761$	−14.8125	−	3.14848i	−0.536951	−	0.114132i	−0.0685487	−	0.997648i	$-0.521837\pi$
$761$	−14.8125	−	3.14848i	−0.536951	−	0.114132i	−0.468402	+	0.883515i	$0.655170\pi$
$762$	−39.2755	−	28.5353i	−1.42280	−	1.03373i
$763$	−9.31507	+	1.88725i	−0.337228	+	0.0683229i
$764$	11.3456	−	8.24308i	0.410471	−	0.298224i
$765$	1.68892	−	2.92529i	0.0610629	−	0.105764i
$766$	19.6699	−	21.8456i	0.710702	−	0.789315i
$767$	4.41335	+	1.96495i	0.159357	+	0.0709502i
$768$	−2.10922	+	0.939084i	−0.0761098	+	0.0338863i
$769$	7.78360	+	5.65512i	0.280684	+	0.203929i	0.719216	−	0.694787i	$-0.244501\pi$
$769$	7.78360	+	5.65512i	0.280684	+	0.203929i	−0.438532	+	0.898716i	$0.644501\pi$
$770$	−2.39815	+	4.06365i	−0.0864232	+	0.146444i
$771$	14.7185	+	10.6936i	0.530073	+	0.385121i
$772$	7.19135	+	7.98680i	0.258822	+	0.287451i
$773$	13.7609	−	15.2831i	0.494946	−	0.549694i	−0.442978	−	0.896532i	$-0.646078\pi$
$773$	13.7609	−	15.2831i	0.494946	−	0.549694i	0.937925	+	0.346839i	$0.112745\pi$
$774$	9.98628	+	4.44618i	0.358949	+	0.159815i
$775$	0.448944	+	4.27141i	0.0161265	+	0.153434i
$776$	1.90104			0.0682433
$777$	1.59277	+	5.06605i	0.0571403	+	0.181744i
$778$	0.896232			0.0321315
$779$	1.80075	+	11.5662i	0.0645186	+	0.414401i
$780$	2.86957	+	4.97025i	0.102747	+	0.177963i
$781$	18.6350	−	20.6962i	0.666812	−	0.740569i
$782$	−4.77087	+	8.26339i	−0.170606	+	0.295498i
$783$	−8.28900	+	6.02231i	−0.296225	+	0.215220i
$784$	−0.598691	−	6.97435i	−0.0213818	−	0.249084i
$785$	2.19169	+	6.74532i	0.0782247	+	0.240751i
$786$	−27.9858	−	31.0814i	−0.998220	−	1.10864i
$787$	2.40070	−	22.8411i	0.0855755	−	0.814197i	−0.864596	−	0.502468i	$-0.832425\pi$
$787$	2.40070	−	22.8411i	0.0855755	−	0.814197i	0.950171	−	0.311729i	$-0.100908\pi$
$788$	5.76526	+	9.98572i	0.205379	+	0.355727i
$789$	29.0176	−	12.9195i	1.03306	−	0.459946i
$790$	4.43193	+	3.21999i	0.157681	+	0.114562i
$791$	−25.1816	+	17.9308i	−0.895354	+	0.637547i
$792$	2.81378	+	8.65993i	0.0999834	+	0.307717i
$793$	8.35667	−	14.4742i	0.296754	−	0.513993i
$794$	23.3266	+	10.3857i	0.827831	+	0.368574i
$795$	−6.69484	+	1.42303i	−0.237442	+	0.0504698i
$796$	3.80541	−	1.69428i	0.134879	−	0.0600521i
$797$	−15.0865	−	46.4314i	−0.534390	−	1.64468i	−0.744964	−	0.667105i	$-0.767533\pi$
$797$	−15.0865	−	46.4314i	−0.534390	−	1.64468i	0.210574	−	0.977578i	$-0.432467\pi$
$798$	−7.39269	−	8.36969i	−0.261698	−	0.296284i
$799$	−4.85451	+	14.9406i	−0.171740	+	0.528562i
$800$	−3.20622	−	3.56087i	−0.113357	−	0.125896i
$801$	32.2649	−	6.85811i	1.14002	−	0.242319i
$802$	7.47204	−	8.29854i	0.263847	−	0.293032i
$803$	13.2221	−	5.88686i	0.466598	−	0.207743i
$804$	−6.71814	+	20.6763i	−0.236930	+	0.729197i
$805$	−3.30174	−	1.50795i	−0.116371	−	0.0531482i
$806$	4.88091			0.171923
$807$	−18.9380	−	4.02540i	−0.666650	−	0.141701i
$808$	5.58814	+	2.48800i	0.196590	+	0.0875276i
$809$	1.96058	−	18.6536i	0.0689302	−	0.655827i	−0.904442	−	0.426597i	$-0.859712\pi$
$809$	1.96058	−	18.6536i	0.0689302	−	0.655827i	0.973372	−	0.229231i	$-0.0736210\pi$
$810$	−4.40375	+	1.96068i	−0.154732	+	0.0688912i
$811$	4.43043			0.155574			0.0777868	−	0.996970i	$-0.475215\pi$
$811$	4.43043			0.155574			0.0777868	+	0.996970i	$0.475215\pi$
$812$	−2.00001	+	17.4272i	−0.0701864	+	0.611574i
$813$	−10.2710	+	31.6107i	−0.360218	+	1.10864i
$814$	3.32222	+	0.706159i	0.116444	+	0.0247509i
$815$	4.22029	+	1.87899i	0.147830	+	0.0658183i
$816$	6.69648	+	2.98147i	0.234424	+	0.104372i
$817$	−4.28706	+	7.42541i	−0.149985	+	0.259782i
$818$	4.82065	+	14.8364i	0.168550	+	0.518744i
$819$	−17.0659	+	28.9180i	−0.596330	+	1.01048i
$820$	2.27639	−	1.83350i	0.0794950	−	0.0640285i
$821$	−9.23297	+	15.9920i	−0.322233	+	0.558124i	−0.980948	−	0.194268i	$-0.937767\pi$
$821$	−9.23297	+	15.9920i	−0.322233	+	0.558124i	0.658716	+	0.752392i	$0.271100\pi$
$822$	9.04818	−	10.0490i	0.315591	−	0.350500i
$823$	25.1020	+	43.4779i	0.875000	+	1.51554i	0.856763	+	0.515710i	$0.172472\pi$
$823$	25.1020	+	43.4779i	0.875000	+	1.51554i	0.0182367	+	0.999834i	$0.494195\pi$
$824$	1.06810	+	10.1623i	0.0372089	+	0.354019i
$825$	−34.9669	+	25.4049i	−1.21739	+	0.884486i
$826$	0.704005	+	2.23920i	0.0244955	+	0.0779117i
$827$	11.0126	−	33.8934i	0.382946	−	1.17859i	−0.555013	−	0.831842i	$-0.687287\pi$
$827$	11.0126	−	33.8934i	0.382946	−	1.17859i	0.937959	−	0.346746i	$-0.112713\pi$
$828$	−6.39905	+	2.84904i	−0.222382	+	0.0990110i
$829$	−15.8023	−	27.3704i	−0.548837	−	0.950614i	−0.998355	−	0.0573423i	$-0.981737\pi$
$829$	−15.8023	−	27.3704i	−0.548837	−	0.950614i	0.449517	−	0.893272i	$-0.351596\pi$
$830$	0.0182780	−	0.173904i	0.000634440	−	0.00603629i
$831$	−59.5534	+	26.5149i	−2.06589	+	0.919792i
$832$	−4.40538	+	3.20070i	−0.152729	+	0.110964i
$833$	−15.1833	+	16.2288i	−0.526071	+	0.562296i
$834$	−25.0827			−0.868544
$835$	0.691828	+	6.58231i	0.0239417	+	0.227790i
$836$	−6.98600	+	1.48492i	−0.241616	+	0.0513571i
$837$	−0.144789	+	1.37757i	−0.00500463	+	0.0476159i
$838$	17.0289	+	3.61961i	0.588254	+	0.125037i
$839$	5.10871	−	15.7230i	0.176372	−	0.542818i	−0.823321	−	0.567576i	$-0.807881\pi$
$839$	5.10871	−	15.7230i	0.176372	−	0.542818i	0.999693	+	0.0247576i	$0.00788138\pi$
$840$	−0.886965	+	2.64368i	−0.0306032	+	0.0912155i
$841$	4.62230	−	14.2260i	0.159390	−	0.490551i
$842$	14.1382	+	15.7021i	0.487235	+	0.541129i
$843$	22.2566	−	24.7184i	0.766556	−	0.851347i
$844$	2.81759	−	26.8076i	0.0969855	−	0.922756i
$845$	5.08632	+	5.64893i	0.174975	+	0.194329i
$846$	−9.32992	+	6.77858i	−0.320769	+	0.233052i
$847$	−5.73292	+	9.71440i	−0.196985	+	0.333791i
$848$	−2.00677	−	6.17619i	−0.0689126	−	0.212091i
$849$	2.90409	+	27.6305i	0.0996680	+	0.948277i
$850$	−1.59016	+	15.1294i	−0.0545422	+	0.518934i
$851$	−0.273109	+	2.59845i	−0.00936204	+	0.0890739i
$852$	8.22912	−	14.2533i	0.281925	−	0.488309i
$853$	−23.0245	−	16.7283i	−0.788345	−	0.572766i	0.119127	−	0.992879i	$-0.461990\pi$
$853$	−23.0245	−	16.7283i	−0.788345	−	0.572766i	−0.907472	+	0.420113i	$0.861990\pi$
$854$	7.95886	−	1.61248i	0.272347	−	0.0551778i
$855$	0.601027	+	1.84977i	0.0205547	+	0.0632609i
$856$	−0.944105	−	8.98256i	−0.0322688	−	0.307018i
$857$	23.7328	+	10.5665i	0.810698	+	0.360946i	0.769854	−	0.638219i	$-0.220329\pi$
$857$	23.7328	+	10.5665i	0.810698	+	0.360946i	0.0408437	+	0.999166i	$0.486995\pi$
$858$	24.5591	+	42.5376i	0.838435	+	1.45221i
$859$	−37.4900	−	7.96874i	−1.27914	−	0.271890i	−0.482261	−	0.876028i	$-0.660184\pi$
$859$	−37.4900	−	7.96874i	−1.27914	−	0.271890i	−0.796880	+	0.604138i	$0.793518\pi$
$860$	2.14102			0.0730082
$861$	36.3427	+	14.4607i	1.23856	+	0.492818i
$862$	18.7861			0.639855
$863$	25.8066	+	5.48537i	0.878468	+	0.186724i	0.625005	−	0.780621i	$-0.285097\pi$
$863$	25.8066	+	5.48537i	0.878468	+	0.186724i	0.253463	+	0.967345i	$0.418430\pi$
$864$	−0.772672	−	1.33831i	−0.0262868	−	0.0455301i
$865$	−7.03360	−	3.13156i	−0.239150	−	0.106476i
$866$	−1.95931	−	18.6416i	−0.0665801	−	0.633467i
$867$	4.93736	+	15.1956i	0.167682	+	0.516071i
$868$	1.56996	+	1.77744i	0.0532878	+	0.0603301i
$869$	37.9305	+	27.5581i	1.28670	+	0.934844i
$870$	3.49390	−	6.05162i	0.118454	−	0.205169i
$871$	−5.35964	+	50.9936i	−0.181604	+	1.72785i
$872$	−0.375497	+	3.57262i	−0.0127159	+	0.120984i
$873$	−0.463136	−	4.40644i	−0.0156748	−	0.149135i
$874$	−1.69779	−	5.22526i	−0.0574286	−	0.176747i
$875$	−11.8253	−	0.112864i	−0.399770	−	0.00381550i
$876$	6.91980	−	5.02753i	0.233798	−	0.169865i
$877$	−3.35047	−	3.72107i	−0.113137	−	0.125652i	0.683916	−	0.729561i	$-0.260276\pi$
$877$	−3.35047	−	3.72107i	−0.113137	−	0.125652i	−0.797053	+	0.603909i	$0.793609\pi$
$878$	−2.85386	+	27.1527i	−0.0963131	+	0.916358i
$879$	21.4746	−	23.8500i	0.724321	−	0.804440i
$880$	1.19335	+	1.32535i	0.0402277	+	0.0446774i
$881$	16.9965	−	52.3098i	0.572626	−	1.76236i	−0.0714995	−	0.997441i	$-0.522778\pi$
$881$	16.9965	−	52.3098i	0.572626	−	1.76236i	0.644125	−	0.764920i	$-0.277222\pi$
$882$	−16.0201	+	3.08682i	−0.539424	+	0.103939i
$883$	10.0723	−	30.9993i	0.338959	−	1.04321i	−0.625780	−	0.780000i	$-0.715219\pi$
$883$	10.0723	−	30.9993i	0.338959	−	1.04321i	0.964739	−	0.263209i	$-0.0847810\pi$
$884$	16.9105	+	3.59443i	0.568760	+	0.120894i
$885$	0.0977391	−	0.929926i	0.00328547	−	0.0312591i
$886$	−27.1592	+	5.77287i	−0.912432	+	0.193943i
$887$	−3.86940	−	36.8148i	−0.129922	−	1.23612i	−0.844111	−	0.536169i	$-0.819871\pi$
$887$	−3.86940	−	36.8148i	−0.129922	−	1.23612i	0.714189	−	0.699953i	$-0.246796\pi$
$888$	2.00719			0.0673570
$889$	−16.6854	−	53.0705i	−0.559610	−	1.77993i
$890$	5.22674	−	3.79745i	0.175201	−	0.127291i
$891$	−37.6893	+	16.7804i	−1.26264	+	0.562164i
$892$	−1.19226	+	11.3436i	−0.0399197	+	0.379810i
$893$	−4.52279	−	7.83370i	−0.151349	−	0.262145i
$894$	33.0110	−	14.6974i	1.10405	−	0.491555i
$895$	−2.51104	+	7.72819i	−0.0839349	+	0.258325i
$896$	−2.58257	−	0.574756i	−0.0862775	−	0.0192013i
$897$	−30.5687	+	22.2095i	−1.02066	+	0.741553i
$898$	−1.58762	−	15.1052i	−0.0529795	−	0.504066i
$899$	−2.97142	−	5.14666i	−0.0991025	−	0.171651i
$900$	−7.47267	+	8.29924i	−0.249089	+	0.276641i
$901$	−10.3088	+	17.8554i	−0.343437	+	0.594851i
$902$	19.4824	−	15.6919i	0.648692	−	0.522483i
$903$	14.0878	+	24.9476i	0.468811	+	0.830204i
$904$	3.61059	+	11.1122i	0.120086	+	0.369588i
$905$	−4.51560	+	7.82126i	−0.150104	+	0.259987i
$906$	−49.2749	−	21.9386i	−1.63705	−	0.728861i
$907$	29.0167	+	12.9191i	0.963483	+	0.428970i	0.827329	−	0.561717i	$-0.189859\pi$
$907$	29.0167	+	12.9191i	0.963483	+	0.428970i	0.136154	+	0.990688i	$0.456526\pi$
$908$	−23.6908	−	5.03563i	−0.786206	−	0.167113i
$909$	4.40557	−	13.5590i	0.146124	−	0.449722i
$910$	−0.749839	+	6.53377i	−0.0248569	+	0.216592i
$911$	32.0606			1.06221			0.531107	−	0.847305i	$-0.321776\pi$
$911$	32.0606			1.06221			0.531107	+	0.847305i	$0.321776\pi$
$912$	−3.85585	+	1.71674i	−0.127680	+	0.0568468i
$913$	0.156432	−	1.48835i	0.00517713	−	0.0492571i
$914$	20.4849	+	9.12048i	0.677581	+	0.301679i
$915$	−3.16419	−	0.672570i	−0.104605	−	0.0222345i
$916$	−10.2773			−0.339571
$917$	−4.55465	−	47.7105i	−0.150408	−	1.57554i
$918$	−1.51612	+	4.66613i	−0.0500393	+	0.154005i
$919$	−8.67408	+	3.86195i	−0.286132	+	0.127394i	−0.544784	−	0.838577i	$-0.683388\pi$
$919$	−8.67408	+	3.86195i	−0.286132	+	0.127394i	0.258652	+	0.965971i	$0.416722\pi$
$920$	−0.918002	+	1.01954i	−0.0302656	+	0.0336134i
$921$	13.2702	−	2.82067i	0.437268	−	0.0929441i
$922$	0.0954449	+	0.106002i	0.00314331	+	0.00349100i
$923$	11.9950	−	36.9168i	0.394820	−	1.21513i
$924$	−7.59105	+	22.6258i	−0.249727	+	0.744334i
$925$	1.28725	+	3.96175i	0.0423245	+	0.130261i
$926$	3.86263	−	1.71975i	0.126934	−	0.0565147i
$927$	23.2950	−	4.95151i	0.765109	−	0.162629i
$928$	6.05689	+	2.69670i	0.198827	+	0.0885235i
$929$	−23.8591	+	41.3252i	−0.782792	+	1.35584i	0.147517	+	0.989060i	$0.452872\pi$
$929$	−23.8591	+	41.3252i	−0.782792	+	1.35584i	−0.930309	+	0.366776i	$0.880461\pi$
$930$	−0.291930	−	0.898469i	−0.00957277	−	0.0294620i
$931$	−1.09446	−	12.7498i	−0.0358696	−	0.417857i
$932$	6.00684	+	4.36422i	0.196761	+	0.142955i
$933$	61.6693	−	27.4570i	2.01896	−	0.898901i
$934$	3.64027	+	6.30513i	0.119113	+	0.206310i
$935$	0.591855	−	5.63113i	0.0193557	−	0.184158i
$936$	8.49218	+	9.43153i	0.277576	+	0.308279i
$937$	2.09669	+	6.45293i	0.0684957	+	0.210808i	0.979445	−	0.201709i	$-0.0646496\pi$
$937$	2.09669	+	6.45293i	0.0684957	+	0.210808i	−0.910950	+	0.412517i	$0.864650\pi$
$938$	−20.2938	+	14.4504i	−0.662616	+	0.471823i
$939$	−40.7660	+	29.6182i	−1.33035	+	0.966555i
$940$	−1.12937	+	1.95613i	−0.0368361	+	0.0638020i
$941$	12.0408	−	13.3726i	0.392517	−	0.435935i	−0.514202	−	0.857669i	$-0.671912\pi$
$941$	12.0408	−	13.3726i	0.392517	−	0.435935i	0.906719	+	0.421734i	$0.138579\pi$
$942$	17.9361	+	31.0662i	0.584389	+	1.01219i
$943$	13.5717	+	13.6433i	0.441956	+	0.444286i
$944$	0.887181			0.0288753
$945$	−1.82183	−	0.405452i	−0.0592640	−	0.0131893i
$946$	18.3238			0.595759
$947$	1.80871	+	17.2088i	0.0587753	+	0.559210i	0.983796	+	0.179293i	$0.0573809\pi$
$947$	1.80871	+	17.2088i	0.0587753	+	0.559210i	−0.925020	+	0.379917i	$0.875952\pi$
$948$	25.3120	+	11.2696i	0.822095	+	0.366020i
$949$	13.4984	−	14.9915i	0.438176	−	0.486644i
$950$	−5.86127	−	6.50960i	−0.190165	−	0.211199i
$951$	19.2873	+	14.0131i	0.625434	+	0.454405i
$952$	4.13033	+	7.31428i	0.133865	+	0.237057i
$953$	−10.8078	−	7.85234i	−0.350100	−	0.254362i	0.398811	−	0.917033i	$-0.369423\pi$
$953$	−10.8078	−	7.85234i	−0.350100	−	0.254362i	−0.748911	+	0.662671i	$0.769423\pi$
$954$	−13.8270	+	6.15617i	−0.447665	+	0.199313i
$955$	−5.84832	−	2.60384i	−0.189247	−	0.0842583i
$956$	4.69386	−	5.21305i	0.151810	−	0.168602i
$957$	29.9024	−	51.7925i	0.966608	−	1.67421i
$958$	18.2314	−	13.2459i	0.589029	−	0.427955i
$959$	15.1870	−	3.07691i	0.490415	−	0.0993586i
$960$	0.852667	+	0.619498i	0.0275197	+	0.0199942i
$961$	29.5367	+	6.27822i	0.952797	+	0.202523i
$962$	4.63051	−	0.984244i	0.149294	−	0.0317333i
$963$	−20.5908	+	4.37670i	−0.663528	+	0.141037i
$964$	15.4934	+	17.2072i	0.499010	+	0.554207i
$965$	1.51605	−	4.66591i	0.0488032	−	0.150201i
$966$	−17.9203	−	3.98821i	−0.576577	−	0.128318i
$967$	−4.00339	−	2.90864i	−0.128740	−	0.0935354i	0.521552	−	0.853220i	$-0.325353\pi$
$967$	−4.00339	−	2.90864i	−0.128740	−	0.0935354i	−0.650292	+	0.759684i	$0.725353\pi$
$968$	2.85277	+	3.16832i	0.0916915	+	0.101834i
$969$	12.2418	+	5.45040i	0.393263	+	0.175092i
$970$	−0.433902	−	0.751540i	−0.0139317	−	0.0241305i
$971$	1.81015	+	0.384759i	0.0580904	+	0.0123475i	0.236865	−	0.971543i	$-0.423880\pi$
$971$	1.81015	+	0.384759i	0.0580904	+	0.0123475i	−0.178775	+	0.983890i	$0.557213\pi$
$972$	−15.9741	+	11.6059i	−0.512370	+	0.372259i
$973$	−23.0913	−	17.1159i	−0.740273	−	0.548710i
$974$	−20.6166	−	14.9788i	−0.660598	−	0.479953i
$975$	−30.1210	+	52.1711i	−0.964644	+	1.67081i
$976$	0.320828	−	3.05247i	0.0102694	−	0.0977072i
$977$	56.9672	−	12.1087i	1.82254	−	0.387393i	0.835713	−	0.549166i	$-0.185055\pi$
$977$	56.9672	−	12.1087i	1.82254	−	0.387393i	0.986828	+	0.161773i	$0.0517213\pi$
$978$	22.8548	+	4.85794i	0.730816	+	0.155340i
$979$	44.7328	−	32.5003i	1.42967	−	1.03871i
$980$	−2.62053	+	1.82854i	−0.0837097	+	0.0584105i
$981$	8.37250			0.267313
$982$	−16.9102	−	3.59438i	−0.539628	−	0.114701i
$983$	−8.06083	−	13.9618i	−0.257100	−	0.445311i	0.708363	−	0.705848i	$-0.249434\pi$
$983$	−8.06083	−	13.9618i	−0.257100	−	0.445311i	−0.965464	+	0.260537i	$0.916100\pi$
$984$	9.33385	−	11.4646i	0.297552	−	0.365478i
$985$	2.63178	−	4.55837i	0.0838554	−	0.145242i
$986$	−6.50469	−	20.0194i	−0.207152	−	0.637547i
$987$	−30.2244	−	0.288469i	−0.962054	−	0.00918207i
$988$	−8.05346	+	5.85118i	−0.256215	+	0.186151i
$989$	1.47342	+	14.0187i	0.0468522	+	0.445769i
$990$	2.78131	−	3.08896i	0.0883958	−	0.0981735i
$991$	−31.9872	+	6.79908i	−1.01611	+	0.215980i	−0.685719	−	0.727866i	$-0.740512\pi$
$991$	−31.9872	+	6.79908i	−1.01611	+	0.215980i	−0.330386	+	0.943846i	$0.607179\pi$
$992$	0.818852	−	0.364576i	0.0259986	−	0.0115753i
$993$	−10.2895			−0.326527
$994$	17.3019	−	7.50626i	0.548782	−	0.238084i
$995$	−1.53837	−	1.11769i	−0.0487695	−	0.0354331i
$996$	−0.0924465	−	0.879570i	−0.00292928	−	0.0278702i
$997$	13.2653	−	14.7326i	0.420117	−	0.466587i	−0.495518	−	0.868598i	$-0.665022\pi$
$997$	13.2653	−	14.7326i	0.420117	−	0.466587i	0.915635	+	0.402010i	$0.131688\pi$
$998$	9.74062	+	16.8713i	0.308334	+	0.534050i
$999$	0.140429	+	1.33610i	0.00444299	+	0.0422722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.b.387.12	yes	112
7.4	even	3	inner	574.2.s.b.305.12	yes	112
41.16	even	5	inner	574.2.s.b.303.12	yes	112
287.221	even	15	inner	574.2.s.b.221.12	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.b.221.12	✓	112	287.221	even	15	inner
574.2.s.b.303.12	yes	112	41.16	even	5	inner
574.2.s.b.305.12	yes	112	7.4	even	3	inner
574.2.s.b.387.12	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(1.15441 + 1.99950i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0477161 - 0.453988i) q^{5} +(-0.713467 - 2.19582i) q^{6} +(0.841560 - 2.50834i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.16534 + 2.01843i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(1.15441 + 1.99950i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0477161 - 0.453988i) q^{5} +(-0.713467 - 2.19582i) q^{6} +(0.841560 - 2.50834i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.16534 + 2.01843i) q^{9} +(-0.0477161 + 0.453988i) q^{10} +(-0.408376 + 3.88544i) q^{11} +(0.241338 + 2.29618i) q^{12} +(1.68271 + 5.17884i) q^{13} +(-1.34468 + 2.27856i) q^{14} +(0.852667 - 0.619498i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.331864 - 3.15747i) q^{17} +(1.55953 - 1.73203i) q^{18} +(1.22323 + 1.35854i) q^{19} +(0.141063 - 0.434147i) q^{20} +(5.98694 - 1.21296i) q^{21} +(1.20728 - 3.71563i) q^{22} +(2.93973 + 0.624858i) q^{23} +(0.241338 - 2.29618i) q^{24} +(4.68691 - 0.996233i) q^{25} +(-0.569194 - 5.41552i) q^{26} +1.54534 q^{27} +(1.78904 - 1.94919i) q^{28} +(-5.36385 + 3.89707i) q^{29} +(-0.962835 + 0.428682i) q^{30} +(-0.0936936 + 0.891435i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.24038 + 3.66885i) q^{33} +(-0.981087 + 3.01948i) q^{34} +(-1.17891 - 0.262370i) q^{35} +(-1.88556 + 1.36994i) q^{36} +(0.0908725 + 0.864595i) q^{37} +(-0.914048 - 1.58318i) q^{38} +(-8.41256 + 9.34309i) q^{39} +(-0.228244 + 0.395331i) q^{40} +(5.36093 + 3.50150i) q^{41} +(-6.10830 - 0.0582991i) q^{42} +(1.44935 + 4.46064i) q^{43} +(-1.95342 + 3.38342i) q^{44} +(0.971948 + 0.432739i) q^{45} +(-2.74557 - 1.22241i) q^{46} +(-4.83996 - 1.02877i) q^{47} +(-0.713467 + 2.19582i) q^{48} +(-5.58356 - 4.22184i) q^{49} -4.79162 q^{50} +(6.69648 - 2.98147i) q^{51} +(-0.569194 + 5.41552i) q^{52} +(-5.93259 - 2.64136i) q^{53} +(-1.51157 - 0.321295i) q^{54} +1.78343 q^{55} +(-2.15520 + 1.53463i) q^{56} +(-1.30429 + 4.01418i) q^{57} +(6.05689 - 2.69670i) q^{58} +(0.593640 - 0.659304i) q^{59} +(1.03092 - 0.219129i) q^{60} +(-2.05375 - 2.28092i) q^{61} +(0.276986 - 0.852475i) q^{62} +(4.08220 + 4.62170i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.27084 - 1.01104i) q^{65} +(8.82310 - 1.87541i) q^{66} +(8.60212 + 3.82991i) q^{67} +(1.58743 - 2.74951i) q^{68} +(2.14425 + 6.59934i) q^{69} +(1.09860 + 0.501746i) q^{70} +(-5.76700 - 4.18997i) q^{71} +(2.12918 - 0.947973i) q^{72} +(-1.85231 - 3.20830i) q^{73} +(0.0908725 - 0.864595i) q^{74} +(7.40260 + 8.22142i) q^{75} +(0.564913 + 1.73862i) q^{76} +(9.40233 + 4.29417i) q^{77} +(10.1713 - 7.38985i) q^{78} +(6.00033 - 10.3929i) q^{79} +(0.305451 - 0.339237i) q^{80} +(5.27999 + 9.14520i) q^{81} +(-4.51578 - 4.53958i) q^{82} -0.383058 q^{83} +(5.96270 + 1.32701i) q^{84} -1.44929 q^{85} +(-0.490259 - 4.66450i) q^{86} +(-13.9843 - 6.22621i) q^{87} +(2.61419 - 2.90335i) q^{88} +(-9.47008 - 10.5176i) q^{89} +(-0.860737 - 0.625362i) q^{90} +(14.4064 + 0.137498i) q^{91} +(2.43142 + 1.76653i) q^{92} +(-1.89059 + 0.841744i) q^{93} +(4.52031 + 2.01257i) q^{94} +(0.558393 - 0.620158i) q^{95} +(1.15441 - 1.99950i) q^{96} +(-1.53797 + 1.11740i) q^{97} +(4.58377 + 5.29047i) q^{98} +(-7.36658 - 5.35213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{13} + 18 q^{14} - 2 q^{15} + 14 q^{16} + 17 q^{18} - 2 q^{19} - 8 q^{20} - 25 q^{21} + 16 q^{22} - 2 q^{23} + 3 q^{24} + 26 q^{25} - 2 q^{26} - 8 q^{27} + 4 q^{28} - 42 q^{29} + q^{30} + 13 q^{31} - 56 q^{32} + 17 q^{33} - 10 q^{34} + 8 q^{35} - 24 q^{36} + q^{37} - 2 q^{38} + 14 q^{39} - 16 q^{40} - 58 q^{41} - 62 q^{42} + 18 q^{43} + 12 q^{44} + 32 q^{45} + 3 q^{46} - 25 q^{47} + 4 q^{48} + 8 q^{49} + 88 q^{50} + 23 q^{51} - 2 q^{52} + 3 q^{53} - 6 q^{54} - 12 q^{55} + 8 q^{56} - 24 q^{57} + 21 q^{58} + 18 q^{59} + q^{60} - 6 q^{61} - 16 q^{62} - 71 q^{63} - 28 q^{64} + 2 q^{65} + 2 q^{66} + 9 q^{67} - 10 q^{68} + 38 q^{69} + 55 q^{70} - 10 q^{71} + 12 q^{72} - 78 q^{73} + q^{74} - 9 q^{75} + 4 q^{76} + 43 q^{77} + 22 q^{78} + 4 q^{80} - 80 q^{81} - 6 q^{82} + 156 q^{83} - 13 q^{84} + 44 q^{85} + 11 q^{86} - 8 q^{88} + 9 q^{89} - 64 q^{90} - 52 q^{91} - 6 q^{92} - 46 q^{93} + 20 q^{94} + 49 q^{95} - 2 q^{96} + 32 q^{97} - 21 q^{98} + 12 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9 + 4 * q^10 + 2 * q^11 + 3 * q^12 - 6 * q^13 + 18 * q^14 - 2 * q^15 + 14 * q^16 + 17 * q^18 - 2 * q^19 - 8 * q^20 - 25 * q^21 + 16 * q^22 - 2 * q^23 + 3 * q^24 + 26 * q^25 - 2 * q^26 - 8 * q^27 + 4 * q^28 - 42 * q^29 + q^30 + 13 * q^31 - 56 * q^32 + 17 * q^33 - 10 * q^34 + 8 * q^35 - 24 * q^36 + q^37 - 2 * q^38 + 14 * q^39 - 16 * q^40 - 58 * q^41 - 62 * q^42 + 18 * q^43 + 12 * q^44 + 32 * q^45 + 3 * q^46 - 25 * q^47 + 4 * q^48 + 8 * q^49 + 88 * q^50 + 23 * q^51 - 2 * q^52 + 3 * q^53 - 6 * q^54 - 12 * q^55 + 8 * q^56 - 24 * q^57 + 21 * q^58 + 18 * q^59 + q^60 - 6 * q^61 - 16 * q^62 - 71 * q^63 - 28 * q^64 + 2 * q^65 + 2 * q^66 + 9 * q^67 - 10 * q^68 + 38 * q^69 + 55 * q^70 - 10 * q^71 + 12 * q^72 - 78 * q^73 + q^74 - 9 * q^75 + 4 * q^76 + 43 * q^77 + 22 * q^78 + 4 * q^80 - 80 * q^81 - 6 * q^82 + 156 * q^83 - 13 * q^84 + 44 * q^85 + 11 * q^86 - 8 * q^88 + 9 * q^89 - 64 * q^90 - 52 * q^91 - 6 * q^92 - 46 * q^93 + 20 * q^94 + 49 * q^95 - 2 * q^96 + 32 * q^97 - 21 * q^98 + 12 * q^99

Introduction

L-functions

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