LMFDB - Embedded newform 122.2.i.b.77.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			77.1
Character	$\chi$	$=$	122.77
Dual form			122.2.i.b.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(-0.788472 - 2.42667i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0568473 - 0.540866i) q^{5} +(0.266710 + 2.53757i) q^{6} +(-0.858659 - 0.953638i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.83998 + 2.06337i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(-0.788472 - 2.42667i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0568473 - 0.540866i) q^{5} +(0.266710 + 2.53757i) q^{6} +(-0.858659 - 0.953638i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.83998 + 2.06337i) q^{9} +(-0.0568473 + 0.540866i) q^{10} -5.94516 q^{11} +(0.266710 - 2.53757i) q^{12} +(2.23911 - 3.87826i) q^{13} +(0.641623 + 1.11132i) q^{14} +(-1.26768 + 0.564407i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.34528 + 1.48941i) q^{17} +(3.20692 - 1.42781i) q^{18} +(-0.173753 + 0.192973i) q^{19} +(0.168057 - 0.517227i) q^{20} +(-1.63713 + 2.83560i) q^{21} +(5.81524 + 1.23607i) q^{22} +(3.74404 - 2.72020i) q^{23} +(-0.788472 + 2.42667i) q^{24} +(4.60143 - 0.978065i) q^{25} +(-2.99652 + 3.32797i) q^{26} +(1.05361 + 0.765492i) q^{27} +(-0.396545 - 1.22044i) q^{28} +(-0.939251 - 1.62683i) q^{29} +(1.35732 - 0.288508i) q^{30} +(6.97910 - 1.48345i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.68759 + 14.4269i) q^{33} +(-2.96251 - 2.15239i) q^{34} +(-0.466977 + 0.518631i) q^{35} +(-3.43370 + 0.729855i) q^{36} +(-2.98037 + 9.17263i) q^{37} +(0.210078 - 0.152630i) q^{38} +(-11.1767 - 2.37569i) q^{39} +(-0.271922 + 0.470983i) q^{40} +(0.966750 - 2.97535i) q^{41} +(2.19091 - 2.43325i) q^{42} +(7.11168 - 3.16632i) q^{43} +(-5.43117 - 2.41811i) q^{44} +(1.27745 + 1.41875i) q^{45} +(-4.22778 + 1.88233i) q^{46} +(1.31759 + 2.28213i) q^{47} +(1.27578 - 2.20971i) q^{48} +(0.559570 - 5.32395i) q^{49} -4.70423 q^{50} +(0.976654 - 9.29224i) q^{51} +(3.62296 - 2.63223i) q^{52} +(-8.27166 - 6.00971i) q^{53} +(-0.871430 - 0.967821i) q^{54} +(0.337966 + 3.21553i) q^{55} +(0.134136 + 1.27622i) q^{56} +(0.605281 + 0.269488i) q^{57} +(0.580489 + 1.78656i) q^{58} +(-1.84215 - 0.391562i) q^{59} -1.38765 q^{60} +(2.74935 + 7.31034i) q^{61} -7.13502 q^{62} +(4.40628 + 0.936583i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.22490 - 0.990591i) q^{65} +(-1.58563 - 15.0863i) q^{66} +(-0.0667527 - 0.635110i) q^{67} +(2.45026 + 2.72129i) q^{68} +(-9.55310 - 6.94073i) q^{69} +(0.564602 - 0.410208i) q^{70} +(-0.845478 + 8.04419i) q^{71} +3.51041 q^{72} +(0.845452 - 8.04394i) q^{73} +(4.82234 - 8.35253i) q^{74} +(-6.00154 - 10.3950i) q^{75} +(-0.237221 + 0.105617i) q^{76} +(5.10487 + 5.66953i) q^{77} +(10.4385 + 4.64754i) q^{78} +(-9.08816 + 4.04631i) q^{79} +(0.363903 - 0.404155i) q^{80} +(-2.22747 + 6.85546i) q^{81} +(-1.56423 + 2.70933i) q^{82} +(11.5364 + 2.45214i) q^{83} +(-2.64894 + 1.92457i) q^{84} +(0.615402 - 1.89401i) q^{85} +(-7.61459 + 1.61853i) q^{86} +(-3.20720 + 3.56196i) q^{87} +(4.80974 + 3.49448i) q^{88} +(4.78848 + 14.7374i) q^{89} +(-0.954559 - 1.65334i) q^{90} +(-5.62109 + 1.19480i) q^{91} +(4.52676 - 0.962192i) q^{92} +(-9.10268 - 15.7663i) q^{93} +(-0.814316 - 2.50621i) q^{94} +(0.114250 + 0.0830073i) q^{95} +(-1.70732 + 1.89617i) q^{96} +(-12.2043 + 2.59410i) q^{97} +(-1.65425 + 5.09127i) q^{98} +(16.8841 - 12.2670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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
$3$	−0.788472	−	2.42667i	−0.455225	−	1.40104i	−0.870871	−	0.491511i	$-0.836445\pi$
$3$	−0.788472	−	2.42667i	−0.455225	−	1.40104i	0.415646	−	0.909526i	$-0.363555\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.0568473	−	0.540866i	−0.0254229	−	0.241882i	−0.999852	−	0.0171885i	$-0.994528\pi$
$5$	−0.0568473	−	0.540866i	−0.0254229	−	0.241882i	0.974429	−	0.224694i	$-0.0721382\pi$
$6$	0.266710	+	2.53757i	0.108884	+	1.03596i
$7$	−0.858659	−	0.953638i	−0.324543	−	0.360441i	0.558690	−	0.829377i	$-0.311304\pi$
$7$	−0.858659	−	0.953638i	−0.324543	−	0.360441i	−0.883232	+	0.468936i	$0.844638\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−2.83998	+	2.06337i	−0.946660	+	0.687789i
$10$	−0.0568473	+	0.540866i	−0.0179767	+	0.171037i
$11$	−5.94516			−1.79253			−0.896267	−	0.443516i	$-0.853731\pi$
$11$	−5.94516			−1.79253			−0.896267	+	0.443516i	$0.853731\pi$
$12$	0.266710	−	2.53757i	0.0769924	−	0.732534i
$13$	2.23911	−	3.87826i	0.621018	−	1.07563i	−0.368278	−	0.929716i	$-0.620053\pi$
$13$	2.23911	−	3.87826i	0.621018	−	1.07563i	0.989297	−	0.145919i	$-0.0466140\pi$
$14$	0.641623	+	1.11132i	0.171481	+	0.297014i
$15$	−1.26768	+	0.564407i	−0.327313	+	0.145729i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	3.34528	+	1.48941i	0.811349	+	0.361236i	0.770108	−	0.637913i	$-0.220202\pi$
$17$	3.34528	+	1.48941i	0.811349	+	0.361236i	0.0412408	+	0.999149i	$0.486869\pi$
$18$	3.20692	−	1.42781i	0.755878	−	0.336538i
$19$	−0.173753	+	0.192973i	−0.0398618	+	0.0442710i	−0.762746	−	0.646698i	$-0.776149\pi$
$19$	−0.173753	+	0.192973i	−0.0398618	+	0.0442710i	0.722884	+	0.690969i	$0.242816\pi$
$20$	0.168057	−	0.517227i	0.0375788	−	0.115656i
$21$	−1.63713	+	2.83560i	−0.357252	+	0.618778i
$22$	5.81524	+	1.23607i	1.23981	+	0.263531i
$23$	3.74404	−	2.72020i	0.780686	−	0.567202i	−0.124499	−	0.992220i	$-0.539732\pi$
$23$	3.74404	−	2.72020i	0.780686	−	0.567202i	0.905185	+	0.425018i	$0.139732\pi$
$24$	−0.788472	+	2.42667i	−0.160946	+	0.495342i
$25$	4.60143	−	0.978065i	0.920287	−	0.195613i
$26$	−2.99652	+	3.32797i	−0.587665	+	0.652669i
$27$	1.05361	+	0.765492i	0.202767	+	0.147319i
$28$	−0.396545	−	1.22044i	−0.0749399	−	0.230641i
$29$	−0.939251	−	1.62683i	−0.174414	−	0.302095i	0.765544	−	0.643384i	$-0.222470\pi$
$29$	−0.939251	−	1.62683i	−0.174414	−	0.302095i	−0.939958	+	0.341289i	$0.889137\pi$
$30$	1.35732	−	0.288508i	0.247812	−	0.0526741i
$31$	6.97910	−	1.48345i	1.25348	−	0.266436i	0.467116	−	0.884196i	$-0.345293\pi$
$31$	6.97910	−	1.48345i	1.25348	−	0.266436i	0.786367	+	0.617760i	$0.211960\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	4.68759	+	14.4269i	0.816005	+	2.51141i
$34$	−2.96251	−	2.15239i	−0.508066	−	0.369132i
$35$	−0.466977	+	0.518631i	−0.0789336	+	0.0876646i
$36$	−3.43370	+	0.729855i	−0.572283	+	0.121642i
$37$	−2.98037	+	9.17263i	−0.489969	+	1.50797i	0.334683	+	0.942331i	$0.391371\pi$
$37$	−2.98037	+	9.17263i	−0.489969	+	1.50797i	−0.824652	+	0.565640i	$0.808629\pi$
$38$	0.210078	−	0.152630i	0.0340791	−	0.0247599i
$39$	−11.1767	−	2.37569i	−1.78971	−	0.380414i
$40$	−0.271922	+	0.470983i	−0.0429947	+	0.0744690i
$41$	0.966750	−	2.97535i	0.150981	−	0.464672i	−0.846751	−	0.531990i	$-0.821444\pi$
$41$	0.966750	−	2.97535i	0.150981	−	0.464672i	0.997732	+	0.0673184i	$0.0214443\pi$
$42$	2.19091	−	2.43325i	0.338065	−	0.375459i
$43$	7.11168	−	3.16632i	1.08452	−	0.482860i	0.214928	−	0.976630i	$-0.431048\pi$
$43$	7.11168	−	3.16632i	1.08452	−	0.482860i	0.869592	+	0.493770i	$0.164382\pi$
$44$	−5.43117	−	2.41811i	−0.818780	−	0.364544i
$45$	1.27745	+	1.41875i	0.190431	+	0.211495i
$46$	−4.22778	+	1.88233i	−0.623353	+	0.277535i
$47$	1.31759	+	2.28213i	0.192190	+	0.332884i	0.945976	−	0.324237i	$-0.105108\pi$
$47$	1.31759	+	2.28213i	0.192190	+	0.332884i	−0.753785	+	0.657121i	$0.771774\pi$
$48$	1.27578	−	2.20971i	0.184142	−	0.318944i
$49$	0.559570	−	5.32395i	0.0799386	−	0.760565i
$50$	−4.70423			−0.665279
$51$	0.976654	−	9.29224i	0.136759	−	1.30117i
$52$	3.62296	−	2.63223i	0.502414	−	0.365025i
$53$	−8.27166	−	6.00971i	−1.13620	−	0.825498i	−0.149615	−	0.988744i	$-0.547803\pi$
$53$	−8.27166	−	6.00971i	−1.13620	−	0.825498i	−0.986585	+	0.163247i	$0.947803\pi$
$54$	−0.871430	−	0.967821i	−0.118587	−	0.131704i
$55$	0.337966	+	3.21553i	0.0455713	+	0.433582i
$56$	0.134136	+	1.27622i	0.0179246	+	0.170542i
$57$	0.605281	+	0.269488i	0.0801714	+	0.0356946i
$58$	0.580489	+	1.78656i	0.0762219	+	0.234587i
$59$	−1.84215	−	0.391562i	−0.239828	−	0.0509770i	0.0864293	−	0.996258i	$-0.472454\pi$
$59$	−1.84215	−	0.391562i	−0.239828	−	0.0509770i	−0.326257	+	0.945281i	$0.605788\pi$
$60$	−1.38765			−0.179144
$61$	2.74935	+	7.31034i	0.352018	+	0.935993i
$61$	2.74935	+	7.31034i	0.352018	+	0.935993i
$62$	−7.13502			−0.906148
$63$	4.40628	+	0.936583i	0.555139	+	0.117998i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.22490	−	0.990591i	−0.275965	−	0.122868i
$66$	−1.58563	−	15.0863i	−0.195178	−	1.85699i
$67$	−0.0667527	−	0.635110i	−0.00815514	−	0.0775910i	0.989687	−	0.143244i	$-0.0457535\pi$
$67$	−0.0667527	−	0.635110i	−0.00815514	−	0.0775910i	−0.997842	+	0.0656534i	$0.979087\pi$
$68$	2.45026	+	2.72129i	0.297138	+	0.330005i
$69$	−9.55310	−	6.94073i	−1.15006	−	0.835566i
$70$	0.564602	−	0.410208i	0.0674829	−	0.0490292i
$71$	−0.845478	+	8.04419i	−0.100340	+	0.954669i	0.822312	+	0.569036i	$0.192684\pi$
$71$	−0.845478	+	8.04419i	−0.100340	+	0.954669i	−0.922652	+	0.385633i	$0.873983\pi$
$72$	3.51041			0.413706
$73$	0.845452	−	8.04394i	0.0989526	−	0.941471i	−0.826584	−	0.562813i	$-0.809719\pi$
$73$	0.845452	−	8.04394i	0.0989526	−	0.941471i	0.925537	−	0.378658i	$-0.123614\pi$
$74$	4.82234	−	8.35253i	0.560585	−	0.970962i
$75$	−6.00154	−	10.3950i	−0.692998	−	1.20031i
$76$	−0.237221	+	0.105617i	−0.0272111	+	0.0121152i
$77$	5.10487	+	5.66953i	0.581754	+	0.646103i
$78$	10.4385	+	4.64754i	1.18193	+	0.526230i
$79$	−9.08816	+	4.04631i	−1.02250	+	0.455246i	−0.848329	−	0.529470i	$-0.822391\pi$
$79$	−9.08816	+	4.04631i	−1.02250	+	0.455246i	−0.174170	+	0.984716i	$0.555724\pi$
$80$	0.363903	−	0.404155i	0.0406856	−	0.0451860i
$81$	−2.22747	+	6.85546i	−0.247497	+	0.761718i
$82$	−1.56423	+	2.70933i	−0.172741	+	0.299196i
$83$	11.5364	+	2.45214i	1.26628	+	0.269157i	0.791622	−	0.611011i	$-0.209237\pi$
$83$	11.5364	+	2.45214i	1.26628	+	0.269157i	0.474662	+	0.880168i	$0.342570\pi$
$84$	−2.64894	+	1.92457i	−0.289023	+	0.209987i
$85$	0.615402	−	1.89401i	0.0667498	−	0.205435i
$86$	−7.61459	+	1.61853i	−0.821102	+	0.174531i
$87$	−3.20720	+	3.56196i	−0.343848	+	0.381882i
$88$	4.80974	+	3.49448i	0.512720	+	0.372513i
$89$	4.78848	+	14.7374i	0.507578	+	1.56216i	0.796394	+	0.604779i	$0.206738\pi$
$89$	4.78848	+	14.7374i	0.507578	+	1.56216i	−0.288816	+	0.957385i	$0.593262\pi$
$90$	−0.954559	−	1.65334i	−0.100619	−	0.174278i
$91$	−5.62109	+	1.19480i	−0.589250	+	0.125249i
$92$	4.52676	−	0.962192i	0.471947	−	0.100315i
$93$	−9.10268	−	15.7663i	−0.943904	−	1.63489i
$94$	−0.814316	−	2.50621i	−0.0839903	−	0.258496i
$95$	0.114250	+	0.0830073i	0.0117218	+	0.00851637i
$96$	−1.70732	+	1.89617i	−0.174253	+	0.193527i
$97$	−12.2043	+	2.59410i	−1.23916	+	0.263391i	−0.780463	−	0.625202i	$-0.785017\pi$
$97$	−12.2043	+	2.59410i	−1.23916	+	0.263391i	−0.458696	+	0.888593i	$0.651683\pi$
$98$	−1.65425	+	5.09127i	−0.167105	+	0.514296i
$99$	16.8841	−	12.2670i	1.69692	−	1.23288i
$100$	4.60143	+	0.978065i	0.460143	+	0.0978065i
$101$	−4.33458	+	7.50772i	−0.431307	+	0.747046i	−0.996986	−	0.0775798i	$-0.975281\pi$
$101$	−4.33458	+	7.50772i	−0.431307	+	0.747046i	0.565679	+	0.824625i	$0.308614\pi$
$102$	−2.88728	+	8.88612i	−0.285883	+	0.879857i
$103$	−12.3052	+	13.6663i	−1.21247	+	1.34658i	−0.291681	+	0.956516i	$0.594215\pi$
$103$	−12.3052	+	13.6663i	−1.21247	+	1.34658i	−0.920787	+	0.390066i	$0.872452\pi$
$104$	−4.09106	+	1.82146i	−0.401162	+	0.178609i
$105$	1.62674	+	0.724273i	0.158754	+	0.0706818i
$106$	6.84142	+	7.59816i	0.664497	+	0.737999i
$107$	17.9662	−	7.99906i	1.73686	−	0.773298i	0.742186	−	0.670194i	$-0.233789\pi$
$107$	17.9662	−	7.99906i	1.73686	−	0.773298i	0.994670	−	0.103105i	$-0.0328777\pi$
$108$	0.651166	+	1.12785i	0.0626585	+	0.108528i
$109$	−0.0606462	+	0.105042i	−0.00580885	+	0.0100612i	−0.868915	−	0.494961i	$-0.835182\pi$
$109$	−0.0606462	+	0.105042i	−0.00580885	+	0.0100612i	0.863106	+	0.505022i	$0.168516\pi$
$110$	0.337966	−	3.21553i	0.0322238	−	0.306589i
$111$	24.6089			2.33577
$112$	0.134136	−	1.27622i	0.0126746	−	0.120591i
$113$	7.48953	−	5.44146i	0.704555	−	0.511889i	−0.176857	−	0.984237i	$-0.556593\pi$
$113$	7.48953	−	5.44146i	0.704555	−	0.511889i	0.881413	+	0.472347i	$0.156593\pi$
$114$	−0.536024	−	0.389444i	−0.0502033	−	0.0364748i
$115$	−1.68410	−	1.87039i	−0.157043	−	0.174414i
$116$	−0.196357	−	1.86821i	−0.0182313	−	0.173459i
$117$	1.64323	+	15.6343i	0.151917	+	1.44539i
$118$	1.72049	+	0.766011i	0.158384	+	0.0705170i
$119$	−1.45209	−	4.46908i	−0.133113	−	0.409680i
$120$	1.35732	+	0.288508i	0.123906	+	0.0263371i
$121$	24.3449			2.21318
$122$	−1.16936	−	7.72221i	−0.105869	−	0.699136i
$123$	−7.98245			−0.719753
$124$	6.97910	+	1.48345i	0.626742	+	0.133218i
$125$	−1.63087	−	5.01929i	−0.145869	−	0.448939i
$126$	−4.11526	−	1.83223i	−0.366617	−	0.163228i
$127$	−1.35130	−	12.8567i	−0.119908	−	1.14085i	−0.874625	−	0.484800i	$-0.838892\pi$
$127$	−1.35130	−	12.8567i	−0.119908	−	1.14085i	0.754717	−	0.656051i	$-0.227774\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	−13.2910	−	14.7611i	−1.17021	−	1.29964i
$130$	1.97033	+	1.43153i	0.172809	+	0.125553i
$131$	−1.60165	+	1.16367i	−0.139937	+	0.101670i	−0.655551	−	0.755151i	$-0.727564\pi$
$131$	−1.60165	+	1.16367i	−0.139937	+	0.101670i	0.515614	+	0.856821i	$0.327564\pi$
$132$	−1.58563	+	15.0863i	−0.138011	+	1.31309i
$133$	0.333221			0.0288939
$134$	−0.0667527	+	0.635110i	−0.00576656	+	0.0548651i
$135$	0.354133	−	0.613377i	0.0304789	−	0.0527911i
$136$	−1.83093	−	3.17127i	−0.157001	−	0.271934i
$137$	11.4452	−	5.09574i	0.977831	−	0.435358i	0.145331	−	0.989383i	$-0.453575\pi$
$137$	11.4452	−	5.09574i	0.977831	−	0.435358i	0.832500	+	0.554025i	$0.186909\pi$
$138$	7.90128	+	8.77526i	0.672602	+	0.747000i
$139$	−7.26506	−	3.23461i	−0.616214	−	0.274356i	0.0747989	−	0.997199i	$-0.476169\pi$
$139$	−7.26506	−	3.23461i	−0.616214	−	0.274356i	−0.691013	+	0.722843i	$0.742835\pi$
$140$	−0.637551	+	0.283856i	−0.0538829	+	0.0239902i
$141$	4.49910	−	4.99676i	0.378893	−	0.420803i
$142$	2.49948	−	7.69262i	0.209752	−	0.645550i
$143$	−13.3119	+	23.0569i	−1.11320	+	1.92811i
$144$	−3.43370	−	0.729855i	−0.286141	−	0.0608212i
$145$	−0.826502	+	0.600489i	−0.0686373	+	0.0498679i
$146$	−2.49940	+	7.69238i	−0.206852	+	0.636626i
$147$	−13.3607	+	2.83990i	−1.10197	+	0.234231i
$148$	−6.45355	+	7.16739i	−0.530478	+	0.589156i
$149$	−6.39892	−	4.64908i	−0.524220	−	0.380868i	0.293972	−	0.955814i	$-0.405023\pi$
$149$	−6.39892	−	4.64908i	−0.524220	−	0.380868i	−0.818191	+	0.574946i	$0.805023\pi$
$150$	3.70916	+	11.4156i	0.302851	+	0.932081i
$151$	−2.56120	−	4.43613i	−0.208428	−	0.361007i	0.742792	−	0.669523i	$-0.233501\pi$
$151$	−2.56120	−	4.43613i	−0.208428	−	0.361007i	−0.951219	+	0.308515i	$0.900168\pi$
$152$	0.253996	−	0.0539885i	0.0206018	−	0.00437905i
$153$	−12.5737	+	2.67263i	−1.01653	+	0.216069i
$154$	−3.81455	−	6.60700i	−0.307385	−	0.532407i
$155$	−1.19909	−	3.69042i	−0.0963133	−	0.296422i
$156$	−9.24416	−	6.71628i	−0.740125	−	0.537733i
$157$	5.21456	−	5.79135i	0.416167	−	0.462200i	−0.498215	−	0.867054i	$-0.666011\pi$
$157$	5.21456	−	5.79135i	0.416167	−	0.462200i	0.914382	+	0.404853i	$0.132677\pi$
$158$	9.73084	−	2.06835i	0.774144	−	0.164549i
$159$	−8.06161	+	24.8111i	−0.639327	+	1.96765i
$160$	−0.439980	+	0.319664i	−0.0347834	+	0.0252717i
$161$	−5.80894	−	1.23473i	−0.457809	−	0.0973102i
$162$	3.60413	−	6.24254i	0.283167	−	0.490460i
$163$	−4.63061	+	14.2516i	−0.362698	+	1.11627i	0.588713	+	0.808342i	$0.299635\pi$
$163$	−4.63061	+	14.2516i	−0.362698	+	1.11627i	−0.951410	+	0.307926i	$0.900365\pi$
$164$	2.09335	−	2.32491i	0.163464	−	0.181545i
$165$	7.53655	−	3.35549i	0.586720	−	0.261225i
$166$	−10.7745	−	4.79710i	−0.836261	−	0.372328i
$167$	−8.24277	−	9.15452i	−0.637845	−	0.708398i	0.334382	−	0.942437i	$-0.391472\pi$
$167$	−8.24277	−	9.15452i	−0.637845	−	0.708398i	−0.972227	+	0.234039i	$0.924806\pi$
$168$	2.99119	−	1.33176i	0.230775	−	0.102748i
$169$	−3.52725	−	6.10937i	−0.271327	−	0.469952i
$170$	−0.995742	+	1.72468i	−0.0763699	+	0.132277i
$171$	0.0952829	−	0.906556i	0.00728646	−	0.0693261i
$172$	7.78470			0.593578
$173$	1.20871	−	11.5001i	0.0918963	−	0.874334i	−0.847337	−	0.531055i	$-0.821796\pi$
$173$	1.20871	−	11.5001i	0.0918963	−	0.874334i	0.939233	−	0.343279i	$-0.111538\pi$
$174$	3.87769	−	2.81731i	0.293967	−	0.213580i
$175$	−4.88378	−	3.54828i	−0.369179	−	0.268224i
$176$	−3.97809	−	4.41812i	−0.299860	−	0.333028i
$177$	0.502297	+	4.77903i	0.0377549	+	0.359214i
$178$	−1.61976	−	15.4110i	−0.121406	−	1.15510i
$179$	2.93742	+	1.30782i	0.219553	+	0.0977514i	0.513566	−	0.858050i	$-0.328324\pi$
$179$	2.93742	+	1.30782i	0.219553	+	0.0977514i	−0.294013	+	0.955801i	$0.594991\pi$
$180$	0.589950	+	1.81568i	0.0439723	+	0.135333i
$181$	11.3119	+	2.40441i	0.840806	+	0.178719i	0.608132	−	0.793836i	$-0.291919\pi$
$181$	11.3119	+	2.40441i	0.840806	+	0.178719i	0.232674	+	0.972555i	$0.425253\pi$
$182$	5.74666			0.425971
$183$	15.5720	−	12.4358i	1.15111	−	0.919278i
$184$	−4.62789			−0.341172
$185$	5.13058	+	1.09054i	0.377208	+	0.0801781i
$186$	5.62576	+	17.3143i	0.412501	+	1.26955i
$187$	−19.8882	−	8.85480i	−1.45437	−	0.647527i
$188$	0.275452	+	2.62075i	0.0200894	+	0.191138i
$189$	−0.174689	−	1.66206i	−0.0127068	−	0.120897i
$190$	−0.0944949	−	0.104947i	−0.00685538	−	0.00761367i
$191$	20.7861	+	15.1020i	1.50403	+	1.09274i	0.968741	+	0.248073i	$0.0797973\pi$
$191$	20.7861	+	15.1020i	1.50403	+	1.09274i	0.535289	+	0.844669i	$0.320203\pi$
$192$	2.06425	−	1.49976i	0.148974	−	0.108236i
$193$	−0.407953	+	3.88141i	−0.0293651	+	0.279390i	0.969979	+	0.243187i	$0.0781929\pi$
$193$	−0.407953	+	3.88141i	−0.0293651	+	0.279390i	−0.999344	+	0.0362029i	$0.988474\pi$
$194$	12.4770			0.895793
$195$	−0.649560	+	6.18015i	−0.0465160	+	0.442570i
$196$	2.67664	−	4.63608i	0.191189	−	0.331148i
$197$	−8.60083	−	14.8971i	−0.612783	−	1.06137i	−0.990769	−	0.135561i	$-0.956716\pi$
$197$	−8.60083	−	14.8971i	−0.612783	−	1.06137i	0.377986	−	0.925811i	$-0.376617\pi$
$198$	−19.0656	+	8.48857i	−1.35494	+	0.603256i
$199$	4.50930	+	5.00808i	0.319656	+	0.355014i	0.881462	−	0.472255i	$-0.156560\pi$
$199$	4.50930	+	5.00808i	0.319656	+	0.355014i	−0.561806	+	0.827269i	$0.689893\pi$
$200$	−4.29753	−	1.91338i	−0.303881	−	0.135297i
$201$	−1.48857	+	0.662753i	−0.104995	+	0.0467470i
$202$	5.80080	−	6.44244i	0.408143	−	0.453289i
$203$	−0.744910	+	2.29260i	−0.0522824	+	0.160909i
$204$	4.67171	−	8.09164i	0.327085	−	0.566528i
$205$	−1.66422	−	0.353741i	−0.116234	−	0.0247064i
$206$	14.8777	−	10.8093i	1.03658	−	0.753118i
$207$	−5.02022	+	15.4506i	−0.348929	+	1.07389i
$208$	4.38036	−	0.931075i	0.303724	−	0.0645585i
$209$	1.03299	−	1.14725i	0.0714536	−	0.0793572i
$210$	−1.44061	−	1.04667i	−0.0994116	−	0.0722268i
$211$	−4.19677	−	12.9163i	−0.288918	−	0.889197i	−0.985197	−	0.171426i	$-0.945162\pi$
$211$	−4.19677	−	12.9163i	−0.288918	−	0.889197i	0.696279	−	0.717771i	$-0.254838\pi$
$212$	−5.11217	−	8.85454i	−0.351105	−	0.608132i
$213$	20.1872	−	4.29092i	1.38321	−	0.294009i
$214$	−19.2367	+	4.08888i	−1.31499	+	0.279510i
$215$	−2.11683	−	3.66647i	−0.144367	−	0.250051i
$216$	−0.402443	−	1.23859i	−0.0273828	−	0.0842755i
$217$	−7.40735	−	5.38175i	−0.502843	−	0.365337i
$218$	0.0811604	−	0.0901378i	0.00549688	−	0.00610490i
$219$	−20.1866	+	4.29079i	−1.36408	+	0.289945i
$220$	−0.999127	+	3.07500i	−0.0673612	+	0.207316i
$221$	13.2668	−	9.63888i	0.892420	−	0.648381i
$222$	−24.0711	−	5.11647i	−1.61555	−	0.343395i
$223$	−4.90093	+	8.48865i	−0.328190	+	0.568442i	−0.982153	−	0.188085i	$-0.939772\pi$
$223$	−4.90093	+	8.48865i	−0.328190	+	0.568442i	0.653963	+	0.756527i	$0.273105\pi$
$224$	−0.396545	+	1.22044i	−0.0264953	+	0.0815440i
$225$	−11.0499	+	12.2721i	−0.736658	+	0.818142i
$226$	−8.45720	+	3.76539i	−0.562565	+	0.250470i
$227$	24.8697	+	11.0727i	1.65066	+	0.734921i	0.999707	−	0.0241975i	$-0.00770305\pi$
$227$	24.8697	+	11.0727i	1.65066	+	0.734921i	0.650952	+	0.759118i	$0.274370\pi$
$228$	0.443341	+	0.492380i	0.0293610	+	0.0326086i
$229$	−1.93377	+	0.860971i	−0.127787	+	0.0568946i	−0.469634	−	0.882861i	$-0.655614\pi$
$229$	−1.93377	+	0.860971i	−0.127787	+	0.0568946i	0.341847	+	0.939756i	$0.388948\pi$
$230$	1.25843	+	2.17966i	0.0829781	+	0.143722i
$231$	9.73302	−	16.8581i	0.640386	−	1.10918i
$232$	−0.196357	+	1.86821i	−0.0128915	+	0.122654i
$233$	−16.1005			−1.05478			−0.527390	−	0.849623i	$-0.676829\pi$
$233$	−16.1005			−1.05478			−0.527390	+	0.849623i	$0.676829\pi$
$234$	1.64323	−	15.6343i	0.107421	−	1.02204i
$235$	1.15943	−	0.842373i	0.0756327	−	0.0549503i
$236$	−1.52363	−	1.10698i	−0.0991798	−	0.0720584i
$237$	16.9848	+	18.8636i	1.10328	+	1.22532i
$238$	0.491187	+	4.67333i	0.0318389	+	0.302927i
$239$	1.83172	+	17.4277i	0.118484	+	1.12730i	0.878614	+	0.477532i	$0.158469\pi$
$239$	1.83172	+	17.4277i	0.118484	+	1.12730i	−0.760130	+	0.649771i	$0.774865\pi$
$240$	−1.26768	−	0.564407i	−0.0818283	−	0.0364323i
$241$	2.68532	+	8.26458i	0.172977	+	0.532368i	0.999535	−	0.0304828i	$-0.00970449\pi$
$241$	2.68532	+	8.26458i	0.172977	+	0.532368i	−0.826558	+	0.562851i	$0.809704\pi$
$242$	−23.8129	−	5.06160i	−1.53075	−	0.325372i
$243$	22.2992			1.43050
$244$	−0.461727	+	7.79659i	−0.0295590	+	0.499125i
$245$	−2.91135			−0.186000
$246$	7.80801	+	1.65964i	0.497821	+	0.105815i
$247$	0.359344	+	1.10595i	0.0228645	+	0.0703698i
$248$	−6.51816	−	2.90207i	−0.413904	−	0.184282i
$249$	−3.14561	−	29.9285i	−0.199345	−	1.89664i
$250$	0.551659	+	5.24869i	0.0348900	+	0.331956i
$251$	12.0250	+	13.3551i	0.759010	+	0.842966i	0.991564	−	0.129617i	$-0.0413748\pi$
$251$	12.0250	+	13.3551i	0.759010	+	0.842966i	−0.232554	+	0.972584i	$0.574708\pi$
$252$	3.64439	+	2.64781i	0.229575	+	0.166796i
$253$	−22.2589	+	16.1720i	−1.39941	+	1.01673i
$254$	−1.35130	+	12.8567i	−0.0847880	+	0.806704i
$255$	−5.08137			−0.318208
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	0.488507	−	0.846118i	0.0304722	−	0.0527794i	−0.850387	−	0.526158i	$-0.823632\pi$
$257$	0.488507	−	0.846118i	0.0304722	−	0.0527794i	0.880859	+	0.473378i	$0.156966\pi$
$258$	9.93153	+	17.2019i	0.618310	+	1.07094i
$259$	11.3065	−	5.03397i	0.702551	−	0.312796i
$260$	−1.62964	−	1.80990i	−0.101066	−	0.112245i
$261$	6.02420	+	2.68215i	0.372888	+	0.166021i
$262$	1.80859	−	0.805236i	0.111735	−	0.0497477i
$263$	6.38810	−	7.09470i	0.393907	−	0.437478i	−0.513270	−	0.858227i	$-0.671566\pi$
$263$	6.38810	−	7.09470i	0.393907	−	0.437478i	0.907177	+	0.420749i	$0.138233\pi$
$264$	4.68759	−	14.4269i	0.288501	−	0.887916i
$265$	−2.78023	+	4.81549i	−0.170788	+	0.295813i
$266$	−0.325939	−	0.0692806i	−0.0199846	−	0.00424786i
$267$	31.9872	−	23.2401i	1.95759	−	1.42227i
$268$	0.197341	−	0.607352i	0.0120545	−	0.0370999i
$269$	−2.17184	+	0.461639i	−0.132419	+	0.0281466i	−0.273645	−	0.961831i	$-0.588229\pi$
$269$	−2.17184	+	0.461639i	−0.132419	+	0.0281466i	0.141225	+	0.989978i	$0.454896\pi$
$270$	−0.473923	+	0.526345i	−0.0288420	+	0.0320323i
$271$	−11.0608	−	8.03617i	−0.671898	−	0.488162i	0.198762	−	0.980048i	$-0.436308\pi$
$271$	−11.0608	−	8.03617i	−0.671898	−	0.488162i	−0.870660	+	0.491885i	$0.836308\pi$
$272$	1.13158	+	3.48264i	0.0686120	+	0.211166i
$273$	7.33145	+	12.6984i	0.443720	+	0.768545i
$274$	−12.2546	+	2.60479i	−0.740326	+	0.157361i
$275$	−27.3563	+	5.81475i	−1.64964	+	0.350643i
$276$	−5.90414	−	10.2263i	−0.355388	−	0.615549i
$277$	7.24484	+	22.2973i	0.435300	+	1.33972i	0.892778	+	0.450496i	$0.148753\pi$
$277$	7.24484	+	22.2973i	0.435300	+	1.33972i	−0.457478	+	0.889221i	$0.651247\pi$
$278$	6.43378	+	4.67442i	0.385873	+	0.280353i
$279$	−16.7596	+	18.6134i	−1.00337	+	1.11436i
$280$	0.682636	−	0.145099i	0.0407953	−	0.00867131i
$281$	6.07244	−	18.6890i	0.362251	−	1.11489i	−0.589433	−	0.807817i	$-0.700649\pi$
$281$	6.07244	−	18.6890i	0.362251	−	1.11489i	0.951684	−	0.307078i	$-0.0993511\pi$
$282$	−5.43967	+	3.95215i	−0.323928	+	0.235347i
$283$	21.2436	+	4.51547i	1.26280	+	0.268417i	0.790195	−	0.612856i	$-0.209979\pi$
$283$	21.2436	+	4.51547i	1.26280	+	0.268417i	0.472608	+	0.881273i	$0.343313\pi$
$284$	−4.04425	+	7.00484i	−0.239982	+	0.415661i
$285$	0.111348	−	0.342695i	0.00659571	−	0.0202995i
$286$	17.8148	−	19.7853i	1.05341	−	1.16993i
$287$	−3.66752	+	1.63288i	−0.216487	+	0.0963861i
$288$	3.20692	+	1.42781i	0.188969	+	0.0841346i
$289$	−2.40269	−	2.66846i	−0.141335	−	0.156968i
$290$	0.933290	−	0.415527i	0.0548047	−	0.0244006i
$291$	15.9178	+	27.5704i	0.933117	+	1.61621i
$292$	4.04412	−	7.00462i	0.236664	−	0.409915i
$293$	−1.75362	+	16.6846i	−0.102448	+	0.974724i	0.815697	+	0.578479i	$0.196354\pi$
$293$	−1.75362	+	16.6846i	−0.102448	+	0.974724i	−0.918145	+	0.396245i	$0.870313\pi$
$294$	13.6592			0.796618
$295$	−0.107061	+	1.01862i	−0.00623333	+	0.0593062i
$296$	7.80270	−	5.66900i	0.453523	−	0.329504i
$297$	−6.26387	−	4.55097i	−0.363467	−	0.264074i
$298$	5.29248	+	5.87790i	0.306585	+	0.340498i
$299$	−2.16632	−	20.6112i	−0.125282	−	1.19198i
$300$	−1.25466	−	11.9373i	−0.0724381	−	0.689202i
$301$	−9.12603	−	4.06317i	−0.526016	−	0.234197i
$302$	1.58291	+	4.87170i	0.0910863	+	0.280335i
$303$	21.6364	+	4.59897i	1.24298	+	0.264204i
$304$	−0.259670			−0.0148931
$305$	3.79762	−	1.90260i	0.217451	−	0.108943i
$306$	12.8546			0.734850
$307$	−9.20242	−	1.95603i	−0.525210	−	0.111637i	−0.0623262	−	0.998056i	$-0.519852\pi$
$307$	−9.20242	−	1.95603i	−0.525210	−	0.111637i	−0.462884	+	0.886419i	$0.653185\pi$
$308$	2.35752	+	7.25571i	0.134332	+	0.413432i
$309$	42.8659	+	19.0851i	2.43856	+	1.08572i
$310$	0.405606	+	3.85908i	0.0230369	+	0.219181i
$311$	1.05323	+	10.0208i	0.0597230	+	0.568226i	0.982937	+	0.183941i	$0.0588855\pi$
$311$	1.05323	+	10.0208i	0.0597230	+	0.568226i	−0.923214	+	0.384285i	$0.874448\pi$
$312$	7.64576	+	8.49148i	0.432856	+	0.480735i
$313$	−24.6330	−	17.8969i	−1.39234	−	1.01159i	−0.995604	−	0.0936598i	$-0.970143\pi$
$313$	−24.6330	−	17.8969i	−1.39234	−	1.01159i	−0.396734	−	0.917933i	$-0.629857\pi$
$314$	−6.30470	+	4.58063i	−0.355795	+	0.258500i
$315$	0.256081	−	2.43645i	0.0144285	−	0.137278i
$316$	−9.94823			−0.559632
$317$	0.101923	−	0.969734i	0.00572457	−	0.0544657i	−0.991287	−	0.131722i	$-0.957949\pi$
$317$	0.101923	−	0.969734i	0.00572457	−	0.0544657i	0.997011	+	0.0772564i	$0.0246160\pi$
$318$	13.0440	−	22.5928i	0.731469	−	1.26694i
$319$	5.58399	+	9.67176i	0.312644	+	0.541515i
$320$	0.496827	−	0.221202i	0.0277735	−	0.0123655i
$321$	−33.5769	−	37.2909i	−1.87408	−	2.08138i
$322$	5.42529	+	2.41549i	0.302339	+	0.134610i
$323$	−0.868670	+	0.386757i	−0.0483341	+	0.0215197i
$324$	−4.82327	+	5.35678i	−0.267959	+	0.297599i
$325$	6.50994	−	20.0355i	0.361107	−	1.11137i
$326$	7.49249	−	12.9774i	0.414971	−	0.718750i
$327$	0.302720	+	0.0643452i	0.0167405	+	0.00355830i
$328$	−2.53098	+	1.83887i	−0.139750	+	0.101535i
$329$	1.04497	−	3.21608i	0.0576109	−	0.177308i
$330$	−8.06951	+	1.71523i	−0.444212	+	0.0944201i
$331$	−4.00676	+	4.44995i	−0.220231	+	0.244592i	−0.843129	−	0.537712i	$-0.819289\pi$
$331$	−4.00676	+	4.44995i	−0.220231	+	0.244592i	0.622897	+	0.782304i	$0.285955\pi$
$332$	9.54165	+	6.93241i	0.523666	+	0.380466i
$333$	−10.4623	−	32.1997i	−0.573331	−	1.76453i
$334$	6.15931	+	10.6682i	0.337023	+	0.583740i
$335$	−0.339714	+	0.0722085i	−0.0185606	+	0.00394517i
$336$	−3.20272	+	0.680758i	−0.174722	+	0.0371384i
$337$	−13.8515	−	23.9914i	−0.754537	−	1.30690i	−0.945604	−	0.325319i	$-0.894528\pi$
$337$	−13.8515	−	23.9914i	−0.754537	−	1.30690i	0.191067	−	0.981577i	$-0.438805\pi$
$338$	2.17996	+	6.70923i	0.118574	+	0.364934i
$339$	−19.1099	−	13.8842i	−1.03791	−	0.754084i
$340$	1.33256	−	1.47996i	0.0722684	−	0.0802622i
$341$	−41.4919	+	8.81937i	−2.24691	+	0.477596i
$342$	−0.281684	+	0.866935i	−0.0152317	+	0.0468785i
$343$	−12.8248	+	9.31775i	−0.692473	+	0.503111i
$344$	−7.61459	−	1.61853i	−0.410551	−	0.0872653i
$345$	−3.21094	+	5.56151i	−0.172871	+	0.299421i
$346$	−3.57329	+	10.9975i	−0.192101	+	0.591227i
$347$	−4.62875	+	5.14075i	−0.248485	+	0.275970i	−0.854464	−	0.519510i	$-0.826115\pi$
$347$	−4.62875	+	5.14075i	−0.248485	+	0.275970i	0.605980	+	0.795480i	$0.292781\pi$
$348$	−4.37871	+	1.94953i	−0.234723	+	0.104506i
$349$	13.9035	+	6.19023i	0.744236	+	0.331355i	0.743582	−	0.668645i	$-0.233125\pi$
$349$	13.9035	+	6.19023i	0.744236	+	0.331355i	0.000653801		1.00000i	$0.499792\pi$
$350$	4.03933	+	4.48613i	0.215911	+	0.239794i
$351$	5.32792	−	2.37214i	0.284383	−	0.126616i
$352$	2.97258	+	5.14866i	0.158439	+	0.274424i
$353$	−3.17099	+	5.49231i	−0.168775	+	0.292326i	−0.937989	−	0.346664i	$-0.887314\pi$
$353$	−3.17099	+	5.49231i	−0.168775	+	0.292326i	0.769215	+	0.638990i	$0.220648\pi$
$354$	0.502297	−	4.77903i	0.0266968	−	0.254003i
$355$	4.39889			0.233469
$356$	−1.61976	+	15.4110i	−0.0858469	+	0.816779i
$357$	−9.70004	+	7.04749i	−0.513381	+	0.372993i
$358$	−2.60132	−	1.88997i	−0.137484	−	0.0998880i
$359$	−0.434014	−	0.482021i	−0.0229064	−	0.0254401i	0.731583	−	0.681753i	$-0.238782\pi$
$359$	−0.434014	−	0.482021i	−0.0229064	−	0.0254401i	−0.754489	+	0.656313i	$0.772115\pi$
$360$	−0.199557	−	1.89866i	−0.0105176	−	0.100068i
$361$	1.97899	+	18.8289i	0.104158	+	0.990992i
$362$	−10.5648	−	4.70375i	−0.555273	−	0.247223i
$363$	−19.1953	−	59.0771i	−1.00749	−	3.10074i
$364$	−5.62109	−	1.19480i	−0.294625	−	0.0626245i
$365$	−4.39875			−0.230241
$366$	−17.8172	+	8.92641i	−0.931322	+	0.466591i
$367$	16.4398			0.858149			0.429074	−	0.903269i	$-0.358840\pi$
$367$	16.4398			0.858149			0.429074	+	0.903269i	$0.358840\pi$
$368$	4.52676	+	0.962192i	0.235973	+	0.0501577i
$369$	3.39369	+	10.4447i	0.176668	+	0.543729i
$370$	−4.79173	−	2.13342i	−0.249110	−	0.110911i
$371$	1.37145	+	13.0485i	0.0712021	+	0.677443i
$372$	−1.90298	−	18.1056i	−0.0986648	−	0.938733i
$373$	−1.62242	−	1.80188i	−0.0840055	−	0.0932976i	0.699677	−	0.714460i	$-0.253327\pi$
$373$	−1.62242	−	1.80188i	−0.0840055	−	0.0932976i	−0.783682	+	0.621162i	$0.786661\pi$
$374$	17.6126	+	12.7963i	0.910725	+	0.661681i
$375$	−10.8943	+	7.91515i	−0.562577	+	0.408736i
$376$	0.275452	−	2.62075i	0.0142053	−	0.135155i
$377$	−8.41235			−0.433258
$378$	−0.174689	+	1.66206i	−0.00898505	+	0.0854870i
$379$	2.04520	−	3.54240i	0.105055	−	0.181961i	−0.808706	−	0.588214i	$-0.799831\pi$
$379$	2.04520	−	3.54240i	0.105055	−	0.181961i	0.913761	+	0.406253i	$0.133165\pi$
$380$	0.0706102	+	0.122300i	0.00362223	+	0.00627388i
$381$	−30.1336	+	13.4163i	−1.54379	+	0.687340i
$382$	−17.1920	−	19.0937i	−0.879620	−	0.976916i
$383$	−14.6574	−	6.52588i	−0.748957	−	0.333457i	−0.00348484	−	0.999994i	$-0.501109\pi$
$383$	−14.6574	−	6.52588i	−0.748957	−	0.333457i	−0.745472	+	0.666537i	$0.767776\pi$
$384$	−2.33096	+	1.03781i	−0.118951	+	0.0529605i
$385$	2.77626	−	3.08334i	0.141491	−	0.157142i
$386$	1.20603	−	3.71177i	0.0613852	−	0.188924i
$387$	−13.6637	+	23.6663i	−0.694567	+	1.20303i
$388$	−12.2043	−	2.59410i	−0.619579	−	0.131696i
$389$	10.2763	−	7.46615i	0.521027	−	0.378549i	−0.295963	−	0.955199i	$-0.595641\pi$
$389$	10.2763	−	7.46615i	0.521027	−	0.378549i	0.816991	+	0.576651i	$0.195641\pi$
$390$	1.92029	−	5.91005i	0.0972378	−	0.299267i
$391$	16.5764	−	3.52341i	0.838302	−	0.178187i
$392$	−3.58204	+	3.97826i	−0.180920	+	0.200933i
$393$	4.08669	+	2.96915i	0.206146	+	0.149774i
$394$	5.31560	+	16.3597i	0.267796	+	0.824192i
$395$	2.70515	+	4.68545i	0.136111	+	0.235751i
$396$	20.4139	−	4.33910i	1.02584	−	0.218048i
$397$	−5.12068	+	1.08843i	−0.257000	+	0.0546270i	−0.334610	−	0.942357i	$-0.608604\pi$
$397$	−5.12068	+	1.08843i	−0.257000	+	0.0546270i	0.0776100	+	0.996984i	$0.475271\pi$
$398$	−3.36952	−	5.83618i	−0.168899	−	0.292541i
$399$	−0.262736	−	0.808617i	−0.0131532	−	0.0404815i
$400$	3.80580	+	2.76508i	0.190290	+	0.138254i
$401$	15.2557	−	16.9431i	0.761831	−	0.846099i	−0.230062	−	0.973176i	$-0.573893\pi$
$401$	15.2557	−	16.9431i	0.761831	−	0.846099i	0.991893	+	0.127077i	$0.0405594\pi$
$402$	1.59383	−	0.338780i	0.0794932	−	0.0168968i
$403$	9.87378	−	30.3884i	0.491848	−	1.51375i
$404$	−7.01350	+	5.09561i	−0.348935	+	0.253516i
$405$	3.83451	+	0.815050i	0.190538	+	0.0405002i
$406$	1.20529	−	2.08762i	0.0598175	−	0.103607i
$407$	17.7188	−	54.5327i	0.878286	−	2.70309i
$408$	−6.25197	+	6.94352i	−0.309519	+	0.343755i
$409$	33.3951	−	14.8684i	1.65128	−	0.735197i	0.651554	−	0.758603i	$-0.274118\pi$
$409$	33.3951	−	14.8684i	1.65128	−	0.735197i	0.999726	+	0.0234056i	$0.00745093\pi$
$410$	1.55431	+	0.692022i	0.0767618	+	0.0341766i
$411$	−21.3899	−	23.7559i	−1.05509	−	1.17179i
$412$	−16.8000	+	7.47982i	−0.827674	+	0.368504i
$413$	1.20837	+	2.09297i	0.0594602	+	0.102988i
$414$	8.12288	−	14.0692i	0.399218	−	0.691466i
$415$	0.670464	−	6.37904i	0.0329118	−	0.313135i
$416$	−4.47822			−0.219563
$417$	−2.12103	+	20.1803i	−0.103867	+	0.988233i
$418$	−1.24895	+	0.907413i	−0.0610880	+	0.0443830i
$419$	−0.355583	−	0.258346i	−0.0173714	−	0.0126210i	0.579066	−	0.815281i	$-0.303417\pi$
$419$	−0.355583	−	0.258346i	−0.0173714	−	0.0126210i	−0.596437	+	0.802660i	$0.703417\pi$
$420$	1.19152	+	1.32331i	0.0581400	+	0.0645711i
$421$	1.23727	+	11.7718i	0.0603006	+	0.573722i	0.982403	+	0.186775i	$0.0598036\pi$
$421$	1.23727	+	11.7718i	0.0603006	+	0.573722i	−0.922102	+	0.386947i	$0.873530\pi$
$422$	1.41961	+	13.5066i	0.0691053	+	0.657493i
$423$	−8.45081	−	3.76254i	−0.410893	−	0.182941i
$424$	3.15949	+	9.72392i	0.153439	+	0.472235i
$425$	16.8498	+	3.58154i	0.817336	+	0.173730i
$426$	−20.6382			−0.999924
$427$	4.61066	−	8.89898i	0.223126	−	0.430652i
$428$	19.6664			0.950613
$429$	66.4474	+	14.1238i	3.20811	+	0.681905i
$430$	1.30828	+	4.02646i	0.0630907	+	0.194173i
$431$	−23.4073	−	10.4216i	−1.12749	−	0.501990i	−0.243688	−	0.969854i	$-0.578357\pi$
$431$	−23.4073	−	10.4216i	−1.12749	−	0.501990i	−0.883801	+	0.467863i	$0.845024\pi$
$432$	0.136131	+	1.29520i	0.00654960	+	0.0623152i
$433$	3.33307	+	31.7120i	0.160177	+	1.52398i	0.719184	+	0.694820i	$0.244516\pi$
$433$	3.33307	+	31.7120i	0.160177	+	1.52398i	−0.559007	+	0.829163i	$0.688817\pi$
$434$	6.12655	+	6.80422i	0.294084	+	0.326613i
$435$	2.10886	+	1.53218i	0.101112	+	0.0734623i
$436$	−0.0981275	+	0.0712938i	−0.00469946	+	0.00341436i
$437$	−0.125615	+	1.19514i	−0.00600896	+	0.0571714i
$438$	20.6376			0.986101
$439$	−1.18628	+	11.2867i	−0.0566182	+	0.538686i	0.929046	+	0.369965i	$0.120630\pi$
$439$	−1.18628	+	11.2867i	−0.0566182	+	0.538686i	−0.985664	+	0.168721i	$0.946036\pi$
$440$	1.61662	−	2.80007i	0.0770694	−	0.133488i
$441$	9.39610	+	16.2745i	0.447433	+	0.774977i
$442$	−14.9809	+	6.66993i	−0.712569	+	0.317256i
$443$	−3.82346	−	4.24638i	−0.181658	−	0.201752i	0.645438	−	0.763813i	$-0.276675\pi$
$443$	−3.82346	−	4.24638i	−0.181658	−	0.201752i	−0.827095	+	0.562062i	$0.810008\pi$
$444$	22.4813	+	10.0093i	1.06692	+	0.475022i
$445$	7.69875	−	3.42770i	0.364956	−	0.162489i
$446$	6.55872	−	7.28419i	0.310564	−	0.344917i
$447$	−6.23642	+	19.1937i	−0.294972	+	0.907832i
$448$	0.641623	−	1.11132i	0.0303138	−	0.0525051i
$449$	−16.6250	−	3.53376i	−0.784584	−	0.166769i	−0.201834	−	0.979420i	$-0.564690\pi$
$449$	−16.6250	−	3.53376i	−0.784584	−	0.166769i	−0.582750	+	0.812651i	$0.698023\pi$
$450$	13.3599	−	9.70655i	0.629793	−	0.457571i
$451$	−5.74748	+	17.6889i	−0.270638	+	0.832940i
$452$	9.05526	−	1.92476i	0.425924	−	0.0905329i
$453$	−8.74559	+	9.71296i	−0.410904	+	0.456355i
$454$	−22.0241	−	16.0014i	−1.03364	−	0.750985i
$455$	0.965769	+	2.97233i	0.0452759	+	0.139345i
$456$	−0.331281	−	0.573796i	−0.0155137	−	0.0268704i
$457$	12.0242	−	2.55582i	0.562468	−	0.119556i	0.0821012	−	0.996624i	$-0.473837\pi$
$457$	12.0242	−	2.55582i	0.562468	−	0.119556i	0.480367	+	0.877068i	$0.340504\pi$
$458$	2.07052	−	0.440103i	0.0967491	−	0.0205647i
$459$	2.38448	+	4.13004i	0.111298	+	0.192774i
$460$	−0.777750	−	2.39367i	−0.0362628	−	0.111605i
$461$	−6.24226	−	4.53527i	−0.290731	−	0.211228i	0.432853	−	0.901464i	$-0.357507\pi$
$461$	−6.24226	−	4.53527i	−0.290731	−	0.211228i	−0.723584	+	0.690236i	$0.757507\pi$
$462$	−13.0253	+	14.4661i	−0.605993	+	0.673023i
$463$	26.2779	−	5.58554i	1.22124	−	0.259582i	0.448194	−	0.893936i	$-0.352067\pi$
$463$	26.2779	−	5.58554i	1.22124	−	0.259582i	0.773042	+	0.634354i	$0.218734\pi$
$464$	0.580489	−	1.78656i	0.0269485	−	0.0829390i
$465$	−8.00999	+	5.81959i	−0.371454	+	0.269877i
$466$	15.7487	+	3.34748i	0.729543	+	0.155069i
$467$	−4.43991	+	7.69015i	−0.205455	+	0.355858i	−0.950277	−	0.311404i	$-0.899201\pi$
$467$	−4.43991	+	7.69015i	−0.205455	+	0.355858i	0.744823	+	0.667262i	$0.232534\pi$
$468$	−4.85787	+	14.9510i	−0.224555	+	0.691110i
$469$	−0.548347	+	0.609001i	−0.0253203	+	0.0281210i
$470$	−1.30923	+	0.582907i	−0.0603903	+	0.0268875i
$471$	−18.1652	−	8.08768i	−0.837010	−	0.372661i
$472$	1.26018	+	1.39957i	0.0580045	+	0.0644205i
$473$	−42.2801	+	18.8243i	−1.94404	+	0.865542i
$474$	−12.6917	−	21.9827i	−0.582949	−	1.00970i
$475$	−0.610775	+	1.05789i	−0.0280243	+	0.0485395i
$476$	0.491187	−	4.67333i	0.0225135	−	0.214202i
$477$	35.8916			1.64336
$478$	1.83172	−	17.4277i	0.0837811	−	0.797124i
$479$	6.50980	−	4.72964i	0.297440	−	0.216103i	−0.429048	−	0.903282i	$-0.641151\pi$
$479$	6.50980	−	4.72964i	0.297440	−	0.216103i	0.726489	+	0.687179i	$0.241151\pi$
$480$	1.12263	+	0.815639i	0.0512408	+	0.0372286i
$481$	28.9004	+	32.0972i	1.31775	+	1.46351i
$482$	−0.908341	−	8.64228i	−0.0413738	−	0.393645i
$483$	1.58391	+	15.0699i	0.0720705	+	0.685705i
$484$	22.2402	+	9.90198i	1.01092	+	0.450090i
$485$	2.09684	+	6.45342i	0.0952127	+	0.293035i
$486$	−21.8119	−	4.63627i	−0.989410	−	0.210306i
$487$	−17.6814			−0.801221			−0.400611	−	0.916248i	$-0.631202\pi$
$487$	−17.6814			−0.801221			−0.400611	+	0.916248i	$0.631202\pi$
$488$	2.07264	−	7.53022i	0.0938240	−	0.340877i
$489$	38.2349			1.72904
$490$	2.84773	+	0.605304i	0.128647	+	0.0273449i
$491$	10.0192	+	30.8360i	0.452161	+	1.39161i	0.874436	+	0.485141i	$0.161232\pi$
$491$	10.0192	+	30.8360i	0.452161	+	1.39161i	−0.422275	+	0.906468i	$0.638768\pi$
$492$	−7.29233	−	3.24675i	−0.328764	−	0.146375i
$493$	−0.719032	−	6.84113i	−0.0323836	−	0.308109i
$494$	−0.121552	−	1.15649i	−0.00546889	−	0.0520331i
$495$	−7.59464	−	8.43470i	−0.341354	−	0.379112i
$496$	5.77235	+	4.19386i	0.259186	+	0.188310i
$497$	8.39722	−	6.10094i	0.376667	−	0.273664i
$498$	−3.14561	+	29.9285i	−0.140958	+	1.34113i
$499$	7.21776			0.323111			0.161556	−	0.986864i	$-0.448349\pi$
$499$	7.21776			0.323111			0.161556	+	0.986864i	$0.448349\pi$
$500$	0.551659	−	5.24869i	0.0246709	−	0.234728i
$501$	−15.7158	+	27.2206i	−0.702130	+	1.21612i
$502$	−8.98553	−	15.5634i	−0.401044	−	0.694628i
$503$	−9.25285	+	4.11963i	−0.412564	+	0.183685i	−0.602514	−	0.798108i	$-0.705834\pi$
$503$	−9.25285	+	4.11963i	−0.412564	+	0.183685i	0.189950	+	0.981794i	$0.439167\pi$
$504$	−3.01424	−	3.34766i	−0.134265	−	0.149117i
$505$	4.30707	+	1.91763i	0.191662	+	0.0853335i
$506$	25.1349	−	11.1908i	1.11738	−	0.497490i
$507$	−12.0443	+	13.3765i	−0.534906	+	0.594073i
$508$	3.99484	−	12.2948i	0.177242	−	0.545495i
$509$	4.17484	−	7.23103i	0.185046	−	0.320510i	−0.758546	−	0.651620i	$-0.774090\pi$
$509$	4.17484	−	7.23103i	0.185046	−	0.320510i	0.943592	+	0.331110i	$0.107423\pi$
$510$	4.97033	+	1.05648i	0.220090	+	0.0467816i
$511$	−8.39696	+	6.10075i	−0.371459	+	0.269881i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.330787	+	0.0703110i	−0.0146046	+	0.00310431i
$514$	−0.653750	+	0.726062i	−0.0288357	+	0.0320252i
$515$	8.09116	+	5.87857i	0.356539	+	0.259041i
$516$	−6.13802	−	18.8909i	−0.270211	−	0.831625i
$517$	−7.83329	−	13.5677i	−0.344508	−	0.596705i
$518$	−12.1060	+	2.57322i	−0.531909	+	0.113061i
$519$	−28.8599	+	6.13436i	−1.26681	+	0.269269i
$520$	1.21773	+	2.10917i	0.0534010	+	0.0924932i
$521$	−2.78238	−	8.56329i	−0.121898	−	0.375164i	0.871425	−	0.490529i	$-0.163196\pi$
$521$	−2.78238	−	8.56329i	−0.121898	−	0.375164i	−0.993323	+	0.115364i	$0.963196\pi$
$522$	−5.33491	−	3.87604i	−0.233502	−	0.169649i
$523$	19.7034	−	21.8828i	0.861569	−	0.956870i	−0.137867	−	0.990451i	$-0.544025\pi$
$523$	19.7034	−	21.8828i	0.861569	−	0.956870i	0.999436	+	0.0335810i	$0.0106912\pi$
$524$	−1.93649	+	0.411613i	−0.0845958	+	0.0179814i
$525$	−4.75976	+	14.6490i	−0.207733	+	0.639337i
$526$	−7.72357	+	5.61150i	−0.336764	+	0.244673i
$527$	25.5565	+	5.43220i	1.11326	+	0.236630i
$528$	−7.58469	+	13.1371i	−0.330081	+	0.571717i
$529$	−0.489072	+	1.50521i	−0.0212640	+	0.0654439i
$530$	3.72067	−	4.13222i	0.161616	−	0.179492i
$531$	6.03962	−	2.68901i	0.262097	−	0.116693i
$532$	0.304413	+	0.135533i	0.0131980	+	0.00587611i
$533$	−9.37451	−	10.4115i	−0.406055	−	0.450970i
$534$	−36.1201	+	16.0817i	−1.56307	+	0.695924i
$535$	−5.34775	−	9.26257i	−0.231203	−	0.400456i
$536$	−0.319304	+	0.553051i	−0.0137918	+	0.0238882i
$537$	0.857581	−	8.15933i	0.0370073	−	0.352101i
$538$	2.22036			0.0957266
$539$	−3.32673	+	31.6518i	−0.143293	+	1.36334i
$540$	0.573000	−	0.416309i	0.0246580	−	0.0179151i
$541$	−8.09348	−	5.88025i	−0.347966	−	0.252812i	0.400049	−	0.916494i	$-0.368993\pi$
$541$	−8.09348	−	5.88025i	−0.347966	−	0.252812i	−0.748015	+	0.663682i	$0.768993\pi$
$542$	9.14832	+	10.1602i	0.392954	+	0.436419i
$543$	−3.08439	−	29.3460i	−0.132364	−	1.25936i
$544$	−0.382769	−	3.64180i	−0.0164111	−	0.156141i
$545$	0.0602613	+	0.0268301i	0.00258131	+	0.00114927i
$546$	−4.53109	−	13.9452i	−0.193913	−	0.596802i
$547$	−37.8665	−	8.04877i	−1.61905	−	0.344140i	−0.692826	−	0.721105i	$-0.743634\pi$
$547$	−37.8665	−	8.04877i	−1.61905	−	0.344140i	−0.926228	+	0.376965i	$0.876968\pi$
$548$	12.5284			0.535185
$549$	−22.8920	−	15.0883i	−0.977007	−	0.643953i
$550$	27.9674			1.19253
$551$	0.477132	+	0.101418i	0.0203265	+	0.00432053i
$552$	3.64896	+	11.2303i	0.155310	+	0.477995i
$553$	11.6623	+	5.19241i	0.495934	+	0.220804i
$554$	−2.45065	−	23.3164i	−0.104118	−	0.990618i
$555$	−1.39895	−	13.3101i	−0.0593820	−	0.564982i
$556$	−5.32132	−	5.90993i	−0.225674	−	0.250637i
$557$	−7.52226	−	5.46524i	−0.318729	−	0.231570i	0.416904	−	0.908950i	$-0.363115\pi$
$557$	−7.52226	−	5.46524i	−0.318729	−	0.231570i	−0.735633	+	0.677381i	$0.763115\pi$
$558$	20.2633	−	14.7222i	0.857814	−	0.623238i
$559$	3.64403	−	34.6707i	0.154126	−	1.46641i
$560$	−0.697887			−0.0294911
$561$	−5.80636	+	55.2438i	−0.245145	+	2.33240i
$562$	−9.82541	+	17.0181i	−0.414460	+	0.717866i
$563$	−11.9112	−	20.6307i	−0.501996	−	0.869482i	−0.999997	−	0.00230616i	$-0.999266\pi$
$563$	−11.9112	−	20.6307i	−0.501996	−	0.869482i	0.498001	−	0.867176i	$-0.334067\pi$
$564$	6.14250	−	2.73482i	0.258646	−	0.115157i
$565$	−3.36886	−	3.74149i	−0.141729	−	0.157406i
$566$	−19.8406	−	8.83360i	−0.833962	−	0.371304i
$567$	8.45027	−	3.76230i	0.354878	−	0.158002i
$568$	5.41226	−	6.01093i	0.227093	−	0.252213i
$569$	1.08798	−	3.34845i	0.0456104	−	0.140374i	−0.925658	−	0.378362i	$-0.876488\pi$
$569$	1.08798	−	3.34845i	0.0456104	−	0.140374i	0.971268	+	0.237987i	$0.0764876\pi$
$570$	−0.180166	+	0.312056i	−0.00754630	+	0.0130706i
$571$	2.96398	+	0.630012i	0.124038	+	0.0263652i	0.269513	−	0.962997i	$-0.413137\pi$
$571$	2.96398	+	0.630012i	0.124038	+	0.0263652i	−0.145474	+	0.989362i	$0.546471\pi$
$572$	−21.5391	+	15.6491i	−0.900594	+	0.654320i
$573$	20.2583	−	62.3485i	0.846301	−	2.60465i
$574$	3.92687	−	0.834681i	0.163904	−	0.0348389i
$575$	14.5674	−	16.1787i	0.607503	−	0.674700i
$576$	−2.83998	−	2.06337i	−0.118332	−	0.0859736i
$577$	12.0088	+	36.9593i	0.499932	+	1.53863i	0.809126	+	0.587635i	$0.199941\pi$
$577$	12.0088	+	36.9593i	0.499932	+	1.53863i	−0.309194	+	0.950999i	$0.600059\pi$
$578$	1.79539	+	3.10970i	0.0746782	+	0.129346i
$579$	9.74055	−	2.07042i	0.404804	−	0.0860437i
$580$	−0.999288	+	0.212405i	−0.0414932	+	0.00881965i
$581$	−7.56738	−	13.1071i	−0.313948	−	0.543774i
$582$	−9.83773	−	30.2774i	−0.407787	−	1.25504i
$583$	49.1764	+	35.7287i	2.03668	+	1.47973i
$584$	−5.41209	+	6.01074i	−0.223954	+	0.248726i
$585$	8.36263	−	1.77753i	0.345752	−	0.0734919i
$586$	5.18422	−	15.9554i	0.214158	−	0.659111i
$587$	−2.81911	+	2.04820i	−0.116357	+	0.0845383i	−0.644442	−	0.764653i	$-0.722910\pi$
$587$	−2.81911	+	2.04820i	−0.116357	+	0.0845383i	0.528085	+	0.849192i	$0.322910\pi$
$588$	−13.3607	−	2.83990i	−0.550985	−	0.117115i
$589$	−0.926377	+	1.60453i	−0.0381707	+	0.0661136i
$590$	0.316504	−	0.974099i	0.0130303	−	0.0401030i
$591$	−29.3687	+	32.6173i	−1.20807	+	1.34170i
$592$	−8.81085	+	3.92284i	−0.362124	+	0.161228i
$593$	2.80646	+	1.24952i	0.115248	+	0.0513115i	0.463551	−	0.886070i	$-0.346575\pi$
$593$	2.80646	+	1.24952i	0.115248	+	0.0513115i	−0.348303	+	0.937382i	$0.613242\pi$
$594$	5.18079	+	5.75385i	0.212571	+	0.236083i
$595$	−2.33462	+	1.03944i	−0.0957103	+	0.0426130i
$596$	−3.95475	−	6.84982i	−0.161993	−	0.280580i
$597$	8.59750	−	14.8913i	0.351872	−	0.609461i
$598$	−2.16632	+	20.6112i	−0.0885875	+	0.842854i
$599$	28.7073			1.17295			0.586474	−	0.809968i	$-0.300516\pi$
$599$	28.7073			1.17295			0.586474	+	0.809968i	$0.300516\pi$
$600$	−1.25466	+	11.9373i	−0.0512214	+	0.487340i
$601$	−14.0655	+	10.2192i	−0.573742	+	0.416848i	−0.836463	−	0.548024i	$-0.815380\pi$
$601$	−14.0655	+	10.2192i	−0.573742	+	0.416848i	0.262720	+	0.964872i	$0.415380\pi$
$602$	8.08183	+	5.87179i	0.329391	+	0.239316i
$603$	1.50004	+	1.66596i	0.0610863	+	0.0678433i
$604$	−0.535437	−	5.09434i	−0.0217866	−	0.207286i
$605$	−1.38394	−	13.1673i	−0.0562653	−	0.535328i
$606$	−20.2074	−	8.99694i	−0.820871	−	0.365476i
$607$	−2.45326	−	7.55036i	−0.0995748	−	0.306460i	0.888844	−	0.458210i	$-0.151509\pi$
$607$	−2.45326	−	7.55036i	−0.0995748	−	0.306460i	−0.988419	+	0.151750i	$0.951509\pi$
$608$	0.253996	+	0.0539885i	0.0103009	+	0.00218952i
$609$	6.15071			0.249239
$610$	−4.11020	+	1.07146i	−0.166417	+	0.0433820i
$611$	11.8009			0.477415
$612$	−12.5737	−	2.67263i	−0.508263	−	0.108035i
$613$	1.56738	+	4.82391i	0.0633060	+	0.194836i	0.977707	−	0.209974i	$-0.0673378\pi$
$613$	1.56738	+	4.82391i	0.0633060	+	0.194836i	−0.914401	+	0.404810i	$0.867338\pi$
$614$	8.59464	+	3.82658i	0.346852	+	0.154428i
$615$	0.453780	+	4.31743i	0.0182982	+	0.174096i
$616$	−0.797458	−	7.58731i	−0.0321305	−	0.305701i
$617$	−6.57413	−	7.30131i	−0.264664	−	0.293940i	0.596135	−	0.802884i	$-0.296702\pi$
$617$	−6.57413	−	7.30131i	−0.264664	−	0.293940i	−0.860799	+	0.508945i	$0.830036\pi$
$618$	−37.9612	−	27.5804i	−1.52702	−	1.10945i
$619$	−17.7139	+	12.8699i	−0.711981	+	0.517285i	−0.883812	−	0.467842i	$-0.845032\pi$
$619$	−17.7139	+	12.8699i	−0.711981	+	0.517285i	0.171831	+	0.985126i	$0.445032\pi$
$620$	0.405606	−	3.85908i	0.0162895	−	0.154985i
$621$	6.02704			0.241857
$622$	1.05323	−	10.0208i	0.0422305	−	0.401797i
$623$	9.94249	−	17.2209i	0.398337	−	0.689941i
$624$	−5.71321	−	9.89557i	−0.228711	−	0.396140i
$625$	18.8656	−	8.39951i	0.754624	−	0.335980i
$626$	20.3737	+	22.6273i	0.814298	+	0.904369i
$627$	−3.59849	−	1.60215i	−0.143710	−	0.0639838i
$628$	7.11929	−	3.16971i	0.284091	−	0.126485i
$629$	−23.6320	+	26.2460i	−0.942269	+	1.04650i
$630$	−0.757051	+	2.32996i	−0.0301616	+	0.0928279i
$631$	3.87283	−	6.70794i	0.154175	−	0.267039i	−0.778583	−	0.627541i	$-0.784061\pi$
$631$	3.87283	−	6.70794i	0.154175	−	0.267039i	0.932758	+	0.360502i	$0.117395\pi$
$632$	9.73084	+	2.06835i	0.387072	+	0.0822747i
$633$	−28.0346	+	20.3683i	−1.11428	+	0.809569i
$634$	−0.301315	+	0.927352i	−0.0119667	+	0.0368298i
$635$	−6.87695	+	1.46174i	−0.272903	+	0.0580074i
$636$	−17.4562	+	19.3871i	−0.692184	+	0.768748i
$637$	−19.3947	−	14.0911i	−0.768447	−	0.558309i
$638$	−3.45110	−	10.6214i	−0.136630	−	0.420505i
$639$	−14.1970	−	24.5899i	−0.561623	−	0.972760i
$640$	−0.531960	+	0.113072i	−0.0210276	+	0.00446955i
$641$	6.34083	−	1.34778i	0.250448	−	0.0532343i	−0.0809770	−	0.996716i	$-0.525804\pi$
$641$	6.34083	−	1.34778i	0.250448	−	0.0532343i	0.331425	+	0.943482i	$0.392471\pi$
$642$	25.0900	+	43.4571i	0.990221	+	1.71511i
$643$	−3.58008	−	11.0183i	−0.141184	−	0.434521i	0.855316	−	0.518106i	$-0.173363\pi$
$643$	−3.58008	−	11.0183i	−0.141184	−	0.434521i	−0.996501	+	0.0835854i	$0.973363\pi$
$644$	−4.80452	−	3.49069i	−0.189325	−	0.137552i
$645$	−7.22823	+	8.02776i	−0.284611	+	0.316093i
$646$	0.930098	−	0.197699i	0.0365942	−	0.00777834i
$647$	12.6281	−	38.8652i	0.496461	−	1.52795i	−0.318207	−	0.948021i	$-0.603081\pi$
$647$	12.6281	−	38.8652i	0.496461	−	1.52795i	0.814668	−	0.579928i	$-0.196919\pi$
$648$	5.83160	−	4.23691i	0.229087	−	0.166441i
$649$	10.9519	+	2.32790i	0.429900	+	0.0913780i
$650$	−10.5333	+	18.2442i	−0.413150	+	0.715597i
$651$	−7.21924	+	22.2185i	−0.282944	+	0.870813i
$652$	−10.0269	+	11.1360i	−0.392684	+	0.436120i
$653$	−30.8098	+	13.7174i	−1.20568	+	0.536804i	−0.908447	−	0.418000i	$-0.862731\pi$
$653$	−30.8098	+	13.7174i	−1.20568	+	0.536804i	−0.297235	+	0.954804i	$0.596064\pi$
$654$	−0.282727	−	0.125878i	−0.0110555	−	0.00492223i
$655$	0.720437	+	0.800126i	0.0281498	+	0.0312635i
$656$	2.85800	−	1.27246i	0.111586	−	0.0496813i
$657$	14.1965	+	24.5891i	0.553859	+	0.959312i
$658$	−1.69079	+	2.92854i	−0.0659140	+	0.114166i
$659$	−0.445046	+	4.23433i	−0.0173365	+	0.164946i	−0.999765	−	0.0216955i	$-0.993094\pi$
$659$	−0.445046	+	4.23433i	−0.0173365	+	0.164946i	0.982428	+	0.186641i	$0.0597602\pi$
$660$	8.24979			0.321122
$661$	−0.282834	+	2.69099i	−0.0110010	+	0.104667i	−0.998644	−	0.0520500i	$-0.983424\pi$
$661$	−0.282834	+	2.69099i	−0.0110010	+	0.104667i	0.987644	+	0.156717i	$0.0500911\pi$
$662$	4.84440	−	3.51966i	0.188283	−	0.136796i
$663$	−33.8508	−	24.5941i	−1.31466	−	0.955155i
$664$	−7.89181	−	8.76475i	−0.306262	−	0.340138i
$665$	−0.0189427	−	0.180228i	−0.000734567	−	0.00698894i
$666$	3.53899	+	33.6713i	0.137133	+	1.30474i
$667$	−7.94190	−	3.53596i	−0.307511	−	0.136913i
$668$	−3.80666	−	11.7157i	−0.147284	−	0.453294i
$669$	24.4634	+	5.19985i	0.945809	+	0.201038i
$670$	0.347304			0.0134175
$671$	−16.3453	−	43.4611i	−0.631004	−	1.67780i
$672$	3.27427			0.126308
$673$	3.85745	+	0.819927i	0.148694	+	0.0316059i	0.281657	−	0.959515i	$-0.409116\pi$
$673$	3.85745	+	0.819927i	0.148694	+	0.0316059i	−0.132963	+	0.991121i	$0.542449\pi$
$674$	8.56067	+	26.3470i	0.329745	+	1.01485i
$675$	5.59681	+	2.49186i	0.215421	+	0.0959118i
$676$	−0.737396	−	7.01585i	−0.0283614	−	0.269840i
$677$	5.18506	+	49.3326i	0.199278	+	1.89600i	0.400247	+	0.916407i	$0.368924\pi$
$677$	5.18506	+	49.3326i	0.199278	+	1.89600i	−0.200969	+	0.979598i	$0.564409\pi$
$678$	15.8056	+	17.5539i	0.607011	+	0.674154i
$679$	12.9532	+	9.41103i	0.497097	+	0.361162i
$680$	−1.61114	+	1.17057i	−0.0617846	+	0.0448891i
$681$	7.26071	−	69.0810i	0.278231	−	2.64719i
$682$	42.4188			1.62430
$683$	−3.62035	+	34.4454i	−0.138529	+	1.31802i	0.675573	+	0.737293i	$0.263896\pi$
$683$	−3.62035	+	34.4454i	−0.138529	+	1.31802i	−0.814102	+	0.580722i	$0.802770\pi$
$684$	0.455775	−	0.789425i	0.0174270	−	0.0301844i
$685$	−3.40674	−	5.90065i	−0.130165	−	0.225452i
$686$	14.4818	−	6.44771i	0.552917	−	0.246175i
$687$	3.61402	+	4.01377i	0.137883	+	0.153135i
$688$	7.11168	+	3.16632i	0.271130	+	0.120715i
$689$	−41.8284	+	18.6232i	−1.59354	+	0.709488i
$690$	4.29707	−	4.77238i	0.163587	−	0.181681i
$691$	10.3659	−	31.9029i	0.394337	−	1.21364i	−0.535140	−	0.844763i	$-0.679741\pi$
$691$	10.3659	−	31.9029i	0.394337	−	1.21364i	0.929477	−	0.368880i	$-0.120259\pi$
$692$	5.78171	−	10.0142i	0.219788	−	0.380683i
$693$	−26.1960	−	5.56814i	−0.995105	−	0.211516i
$694$	5.59643	−	4.06604i	0.212437	−	0.154345i
$695$	−1.33649	+	4.11330i	−0.0506960	+	0.156026i
$696$	4.68835	−	0.996539i	0.177711	−	0.0377737i
$697$	7.66557	−	8.51348i	0.290354	−	0.322471i
$698$	−12.3126	−	8.94565i	−0.466040	−	0.338598i
$699$	12.6948	+	39.0706i	0.480162	+	1.47779i
$700$	−3.01834	−	5.22793i	−0.114083	−	0.197597i
$701$	−35.6188	+	7.57101i	−1.34530	+	0.285953i	−0.823599	−	0.567173i	$-0.808037\pi$
$701$	−35.6188	+	7.57101i	−1.34530	+	0.285953i	−0.521705	+	0.853126i	$0.674704\pi$
$702$	−5.70469	+	1.21257i	−0.215310	+	0.0457655i
$703$	−1.25222	−	2.16891i	−0.0472283	−	0.0818018i
$704$	−1.83716	−	5.65418i	−0.0692404	−	0.213100i
$705$	−2.95834	−	2.14936i	−0.111417	−	0.0809494i
$706$	4.24361	−	4.71301i	0.159710	−	0.177376i
$707$	10.8816	−	2.31295i	0.409244	−	0.0869874i
$708$	−1.48494	+	4.57017i	−0.0558074	+	0.171757i
$709$	−37.2598	+	27.0709i	−1.39932	+	1.01667i	−0.404554	+	0.914514i	$0.632573\pi$
$709$	−37.2598	+	27.0709i	−1.39932	+	1.01667i	−0.994769	+	0.102153i	$0.967427\pi$
$710$	−4.30276	−	0.914580i	−0.161480	−	0.0343236i
$711$	17.4612	−	30.2436i	0.654845	−	1.13423i
$712$	4.78848	−	14.7374i	0.179456	−	0.552308i
$713$	22.0947	−	24.5387i	0.827454	−	0.918981i
$714$	10.9533	−	4.87674i	0.409918	−	0.182507i
$715$	13.2274	+	5.88922i	0.494677	+	0.220244i
$716$	2.15153	+	2.38951i	0.0804064	+	0.0893004i
$717$	40.8470	−	18.1862i	1.52546	−	0.679177i
$718$	0.324312	+	0.561725i	0.0121032	+	0.0209634i
$719$	1.35930	−	2.35438i	0.0506934	−	0.0878036i	−0.839565	−	0.543259i	$-0.817190\pi$
$719$	1.35930	−	2.35438i	0.0506934	−	0.0878036i	0.890259	+	0.455455i	$0.150524\pi$
$720$	−0.199557	+	1.89866i	−0.00743705	+	0.0707588i
$721$	23.5987			0.878861
$722$	1.97899	−	18.8289i	0.0736505	−	0.700737i
$723$	17.9381	−	13.0328i	0.667124	−	0.484694i
$724$	9.35596	+	6.79750i	0.347711	+	0.252627i
$725$	−5.91304	−	6.56710i	−0.219605	−	0.243896i
$726$	6.49303	+	61.7770i	0.240979	+	2.29276i
$727$	2.86318	+	27.2414i	0.106190	+	1.01033i	0.909765	+	0.415123i	$0.136262\pi$
$727$	2.86318	+	27.2414i	0.106190	+	1.01033i	−0.803576	+	0.595203i	$0.797072\pi$
$728$	5.24984	+	2.33738i	0.194572	+	0.0866290i
$729$	−10.8999	−	33.5465i	−0.403700	−	1.24246i
$730$	4.30263	+	0.914551i	0.159247	+	0.0338491i
$731$	28.5065			1.05435
$732$	19.2838	−	5.02694i	0.712750	−	0.185801i
$733$	−7.89088			−0.291456			−0.145728	−	0.989325i	$-0.546552\pi$
$733$	−7.89088			−0.291456			−0.145728	+	0.989325i	$0.546552\pi$
$734$	−16.0805	−	3.41802i	−0.593543	−	0.126161i
$735$	2.29552	+	7.06489i	0.0846716	+	0.260592i
$736$	−4.22778	−	1.88233i	−0.155838	−	0.0693836i
$737$	0.396856	+	3.77583i	0.0146184	+	0.139084i
$738$	−1.14795	−	10.9220i	−0.0422567	−	0.402046i
$739$	17.6301	+	19.5802i	0.648534	+	0.720270i	0.974319	−	0.225174i	$-0.0722951\pi$
$739$	17.6301	+	19.5802i	0.648534	+	0.720270i	−0.325785	+	0.945444i	$0.605628\pi$
$740$	4.24346	+	3.08305i	0.155993	+	0.113335i
$741$	2.40044	−	1.74402i	0.0881822	−	0.0640681i
$742$	1.37145	−	13.0485i	0.0503475	−	0.479024i
$743$	−34.2856			−1.25782			−0.628908	−	0.777480i	$-0.716498\pi$
$743$	−34.2856			−1.25782			−0.628908	+	0.777480i	$0.716498\pi$
$744$	−1.90298	+	18.1056i	−0.0697665	+	0.663784i
$745$	−2.15077	+	3.72524i	−0.0787981	+	0.136482i
$746$	1.21233	+	2.09982i	0.0443866	+	0.0768798i
$747$	−37.8228	+	16.8398i	−1.38386	+	0.616136i
$748$	−14.5672	−	16.1785i	−0.532630	−	0.591545i
$749$	−23.0550	−	10.2648i	−0.842413	−	0.375066i
$750$	12.3019	−	5.47714i	0.449200	−	0.199997i
$751$	−19.6241	+	21.7947i	−0.716093	+	0.795302i	−0.985851	−	0.167627i	$-0.946390\pi$
$751$	−19.6241	+	21.7947i	−0.716093	+	0.795302i	0.269758	+	0.962928i	$0.413056\pi$
$752$	−0.814316	+	2.50621i	−0.0296951	+	0.0913920i
$753$	22.9270	−	39.7108i	0.835507	−	1.44714i
$754$	8.22852	+	1.74903i	0.299665	+	0.0636958i
$755$	−2.25375	+	1.63745i	−0.0820225	+	0.0595929i
$756$	0.516433	−	1.58942i	0.0187825	−	0.0578066i
$757$	1.53035	−	0.325287i	0.0556217	−	0.0118228i	−0.180017	−	0.983664i	$-0.557615\pi$
$757$	1.53035	−	0.325287i	0.0556217	−	0.0118228i	0.235638	+	0.971841i	$0.424282\pi$
$758$	−2.73702	+	3.03977i	−0.0994129	+	0.110409i
$759$	56.7947	+	41.2638i	2.06152	+	1.49778i
$760$	−0.0436395	−	0.134309i	−0.00158297	−	0.00487189i
$761$	0.873817	+	1.51350i	0.0316759	+	0.0548642i	0.881429	−	0.472317i	$-0.156582\pi$
$761$	0.873817	+	1.51350i	0.0316759	+	0.0548642i	−0.849753	+	0.527181i	$0.823249\pi$
$762$	32.2645	−	6.85803i	1.16882	−	0.248440i
$763$	0.152247	−	0.0323610i	0.00551170	−	0.00117155i
$764$	12.8465	+	22.2508i	0.464771	+	0.805007i
$765$	2.16031	+	6.64876i	0.0781063	+	0.240387i
$766$	12.9803	+	9.43072i	0.468996	+	0.340746i
$767$	−5.64337	+	6.26760i	−0.203770	+	0.226310i
$768$	2.49579	−	0.530497i	0.0900592	−	0.0191427i
$769$	−12.8832	+	39.6506i	−0.464582	+	1.42984i	0.394926	+	0.918713i	$0.370770\pi$
$769$	−12.8832	+	39.6506i	−0.464582	+	1.42984i	−0.859508	+	0.511123i	$0.829230\pi$
$770$	−3.35665	+	2.43875i	−0.120965	+	0.0878864i
$771$	−2.43842	−	0.518303i	−0.0878177	−	0.0186662i
$772$	−1.95139	+	3.37992i	−0.0702322	+	0.121646i
$773$	−9.15723	+	28.1830i	−0.329363	+	1.01367i	0.640070	+	0.768316i	$0.278905\pi$
$773$	−9.15723	+	28.1830i	−0.329363	+	1.01367i	−0.969433	+	0.245357i	$0.921095\pi$
$774$	18.2857	−	20.3083i	0.657264	−	0.729966i
$775$	30.6630	−	13.6520i	1.10145	−	0.490395i
$776$	11.3983	+	5.07483i	0.409174	+	0.182176i
$777$	−21.1306	−	23.4679i	−0.758057	−	0.841908i
$778$	−11.6040	+	5.16644i	−0.416024	+	0.185226i
$779$	0.406186	+	0.703534i	0.0145531	+	0.0252067i
$780$	−3.10710	+	5.38165i	−0.111252	+	0.192694i
$781$	5.02650	−	47.8240i	0.179862	−	1.71128i
$782$	−16.9467			−0.606012
$783$	0.255722	−	2.43303i	0.00913875	−	0.0869494i
$784$	4.33089	−	3.14658i	0.154675	−	0.112378i
$785$	−3.42878	−	2.49115i	−0.122378	−	0.0889130i
$786$	−3.38006	−	3.75394i	−0.120563	−	0.133899i
$787$	−2.30698	−	21.9495i	−0.0822351	−	0.782414i	−0.955465	−	0.295105i	$-0.904645\pi$
$787$	−2.30698	−	21.9495i	−0.0822351	−	0.782414i	0.873230	−	0.487309i	$-0.162021\pi$
$788$	−1.79806	−	17.1074i	−0.0640533	−	0.609427i
$789$	−22.2533	−	9.90782i	−0.792239	−	0.352728i
$790$	−1.67187	−	5.14550i	−0.0594826	−	0.183069i
$791$	−11.6201	−	2.46994i	−0.413164	−	0.0878208i
$792$	−20.8699			−0.741581
$793$	34.5075	+	5.70599i	1.22540	+	0.202626i
$794$	5.23508			0.185786
$795$	13.8777	+	2.94980i	0.492193	+	0.104619i
$796$	2.08248	+	6.40921i	0.0738115	+	0.227168i
$797$	22.5870	+	10.0564i	0.800074	+	0.356216i	0.765704	−	0.643193i	$-0.222391\pi$
$797$	22.5870	+	10.0564i	0.800074	+	0.356216i	0.0343700	+	0.999409i	$0.489058\pi$
$798$	0.0888733	+	0.845573i	0.00314608	+	0.0299330i
$799$	1.00867	+	9.59681i	0.0356840	+	0.339511i
$800$	−3.14775	−	3.49593i	−0.111290	−	0.123600i
$801$	−44.0079	−	31.9736i	−1.55494	−	1.12973i
$802$	−18.4450	+	13.4010i	−0.651314	+	0.473208i
$803$	−5.02635	+	47.8225i	−0.177376	+	1.68762i
$804$	−1.62944			−0.0574659
$805$	−0.337600	+	3.21205i	−0.0118988	+	0.113210i
$806$	−15.9761	+	27.6714i	−0.562734	+	0.974684i
$807$	2.83268	+	4.90635i	0.0997151	+	0.172712i
$808$	7.91967	−	3.52607i	0.278613	−	0.124047i
$809$	−13.8349	−	15.3652i	−0.486409	−	0.540212i	0.449115	−	0.893474i	$-0.351739\pi$
$809$	−13.8349	−	15.3652i	−0.486409	−	0.540212i	−0.935525	+	0.353262i	$0.885073\pi$
$810$	−3.58126	−	1.59448i	−0.125833	−	0.0560243i
$811$	−17.7297	+	7.89377i	−0.622574	+	0.277188i	−0.693683	−	0.720281i	$-0.744013\pi$
$811$	−17.7297	+	7.89377i	−0.622574	+	0.277188i	0.0711085	+	0.997469i	$0.477346\pi$
$812$	−1.61299	+	1.79141i	−0.0566049	+	0.0628661i
$813$	−10.7799	+	33.1773i	−0.378069	+	1.16358i
$814$	−28.6696	+	49.6571i	−1.00487	+	1.74048i
$815$	7.97141	+	1.69438i	0.279226	+	0.0593514i
$816$	7.55899	−	5.49193i	0.264618	−	0.192256i
$817$	−0.624665	+	1.92252i	−0.0218542	+	0.0672605i
$818$	−35.7566	+	7.60030i	−1.25020	+	0.265738i
$819$	13.4985	−	14.9916i	0.471675	−	0.523848i
$820$	−1.37646	−	1.00006i	−0.0480682	−	0.0349236i
$821$	−11.4869	−	35.3530i	−0.400895	−	1.23383i	−0.924274	−	0.381729i	$-0.875329\pi$
$821$	−11.4869	−	35.3530i	−0.400895	−	1.23383i	0.523379	−	0.852100i	$-0.324671\pi$
$822$	15.9834	+	27.6840i	0.557484	+	0.965590i
$823$	−47.1647	+	10.0252i	−1.64406	+	0.349455i	−0.934712	−	0.355405i	$-0.884343\pi$
$823$	−47.1647	+	10.0252i	−1.64406	+	0.349455i	−0.709346	+	0.704860i	$0.751010\pi$
$824$	17.9880	−	3.82346i	0.626641	−	0.133197i
$825$	35.6801	+	61.7998i	1.24222	+	2.15159i
$826$	−0.746817	−	2.29847i	−0.0259851	−	0.0799739i
$827$	15.5150	+	11.2723i	0.539508	+	0.391976i	0.823902	−	0.566732i	$-0.191792\pi$
$827$	15.5150	+	11.2723i	0.539508	+	0.391976i	−0.284394	+	0.958707i	$0.591792\pi$
$828$	−10.8705	+	12.0730i	−0.377777	+	0.419564i
$829$	25.6382	−	5.44956i	0.890450	−	0.189271i	0.260100	−	0.965582i	$-0.416245\pi$
$829$	25.6382	−	5.44956i	0.890450	−	0.189271i	0.630350	+	0.776311i	$0.282911\pi$
$830$	−1.98209	+	6.10024i	−0.0687993	+	0.211743i
$831$	48.3959	−	35.1617i	1.67883	−	1.21974i
$832$	4.38036	+	0.931075i	0.151862	+	0.0322792i
$833$	9.80148	−	16.9767i	0.339601	−	0.588207i
$834$	6.27040	−	19.2983i	0.217126	−	0.668246i
$835$	−4.48279	+	4.97864i	−0.155133	+	0.172293i
$836$	1.41032	−	0.627913i	0.0487768	−	0.0217168i
$837$	8.48881	+	3.77946i	0.293416	+	0.130637i
$838$	0.294099	+	0.326630i	0.0101595	+	0.0112833i
$839$	−29.8798	+	13.3033i	−1.03156	+	0.459282i	−0.851490	−	0.524371i	$-0.824300\pi$
$839$	−29.8798	+	13.3033i	−1.03156	+	0.459282i	−0.180074	+	0.983653i	$0.557634\pi$
$840$	−0.890346	−	1.54213i	−0.0307199	−	0.0532084i
$841$	12.7356	−	22.0587i	0.439159	−	0.760646i
$842$	1.23727	−	11.7718i	0.0426390	−	0.405683i
$843$	−50.1401			−1.72692
$844$	1.41961	−	13.5066i	0.0488648	−	0.464918i
$845$	−3.10384	+	2.25507i	−0.106775	+	0.0775767i
$846$	7.48386	+	5.43735i	0.257301	+	0.186940i
$847$	−20.9040	−	23.2162i	−0.718270	−	0.797720i
$848$	−1.06873	−	10.1683i	−0.0367005	−	0.349182i
$849$	−5.79246	−	55.1116i	−0.198797	−	1.89142i
$850$	−15.7370	−	7.00655i	−0.539773	−	0.240323i
$851$	13.7928	+	42.4499i	0.472811	+	1.45516i
$852$	20.1872	+	4.29092i	0.691603	+	0.147005i
$853$	−8.07341			−0.276428			−0.138214	−	0.990402i	$-0.544136\pi$
$853$	−8.07341			−0.276428			−0.138214	+	0.990402i	$0.544136\pi$
$854$	−6.36011	+	7.74590i	−0.217638	+	0.265059i
$855$	−0.495741			−0.0169540
$856$	−19.2367	−	4.08888i	−0.657496	−	0.139755i
$857$	−0.428545	−	1.31892i	−0.0146388	−	0.0450536i	0.943470	−	0.331457i	$-0.107540\pi$
$857$	−0.428545	−	1.31892i	−0.0146388	−	0.0450536i	−0.958109	+	0.286403i	$0.907540\pi$
$858$	−62.0589	−	27.6304i	−2.11865	−	0.943286i
$859$	5.34513	+	50.8555i	0.182373	+	1.73517i	0.577368	+	0.816484i	$0.304080\pi$
$859$	5.34513	+	50.8555i	0.182373	+	1.73517i	−0.394994	+	0.918684i	$0.629253\pi$
$860$	−0.442539	−	4.21048i	−0.0150905	−	0.143576i
$861$	6.85420	+	7.61236i	0.233591	+	0.259429i
$862$	20.7290	+	15.0605i	0.706032	+	0.512963i
$863$	25.1739	−	18.2899i	0.856929	−	0.622595i	−0.0701187	−	0.997539i	$-0.522338\pi$
$863$	25.1739	−	18.2899i	0.856929	−	0.622595i	0.927048	+	0.374943i	$0.122338\pi$
$864$	0.136131	−	1.29520i	0.00463126	−	0.0440635i
$865$	−6.28871			−0.213822
$866$	3.33307	−	31.7120i	0.113262	−	1.07762i
$867$	−4.58102	+	7.93455i	−0.155579	+	0.269472i
$868$	−4.57799	−	7.92931i	−0.155387	−	0.269138i
$869$	54.0306	−	24.0560i	1.83286	−	0.816043i
$870$	−1.74422	−	1.93715i	−0.0591346	−	0.0656756i
$871$	−2.61258	−	1.16320i	−0.0885240	−	0.0394134i
$872$	0.110806	−	0.0493340i	0.00375237	−	0.00167066i
$873$	29.3074	−	32.5491i	0.991905	−	1.10162i
$874$	0.371354	−	1.14291i	0.0125612	−	0.0386595i
$875$	−3.38623	+	5.86512i	−0.114475	+	0.198277i
$876$	−20.1866	−	4.29079i	−0.682041	−	0.144972i
$877$	−8.32715	+	6.05003i	−0.281188	+	0.204295i	−0.719435	−	0.694559i	$-0.755599\pi$
$877$	−8.32715	+	6.05003i	−0.281188	+	0.204295i	0.438248	+	0.898854i	$0.355599\pi$
$878$	3.50700	−	10.7934i	0.118356	−	0.364261i
$879$	41.8706	−	8.89988i	1.41226	−	0.300185i
$880$	−2.16346	+	2.40277i	−0.0729303	+	0.0809973i
$881$	29.3456	+	21.3209i	0.988680	+	0.718318i	0.959632	−	0.281260i	$-0.0907523\pi$
$881$	29.3456	+	21.3209i	0.988680	+	0.718318i	0.0290483	+	0.999578i	$0.490752\pi$
$882$	−5.80711	−	17.8724i	−0.195535	−	0.601796i
$883$	−3.86737	−	6.69848i	−0.130147	−	0.225422i	0.793586	−	0.608458i	$-0.208212\pi$
$883$	−3.86737	−	6.69848i	−0.130147	−	0.225422i	−0.923733	+	0.383036i	$0.874878\pi$
$884$	16.0403	−	3.40947i	0.539493	−	0.114673i
$885$	2.55626	−	0.543350i	0.0859278	−	0.0182645i
$886$	2.85703	+	4.94853i	0.0959839	+	0.166249i
$887$	1.74191	+	5.36105i	0.0584876	+	0.180006i	0.976032	−	0.217627i	$-0.0698316\pi$
$887$	1.74191	+	5.36105i	0.0584876	+	0.180006i	−0.917544	+	0.397633i	$0.869832\pi$
$888$	−19.9090	−	14.4647i	−0.668102	−	0.485404i
$889$	−11.1004	+	12.3282i	−0.372294	+	0.413475i
$890$	−8.24317	+	1.75214i	−0.276312	+	0.0587319i
$891$	13.2427	−	40.7568i	0.443647	−	1.36540i
$892$	−7.92986	+	5.76138i	−0.265511	+	0.192905i
$893$	−0.669326	−	0.142270i	−0.0223981	−	0.00476087i
$894$	10.0907	−	17.4777i	0.337485	−	0.584541i
$895$	0.540373	−	1.66310i	0.0180627	−	0.0555912i
$896$	−0.858659	+	0.953638i	−0.0286858	+	0.0318588i
$897$	−48.3084	+	21.5083i	−1.61297	+	0.718141i
$898$	15.5270	+	6.91308i	0.518144	+	0.230692i
$899$	−8.96845	−	9.96047i	−0.299115	−	0.332200i
$900$	−15.0861	+	6.71676i	−0.502870	+	0.223892i
$901$	−18.7201	−	32.4241i	−0.623655	−	1.08020i
$902$	9.29963	−	16.1074i	0.309644	−	0.536319i
$903$	−2.66435	+	25.3496i	−0.0886639	+	0.843580i
$904$	−9.25756			−0.307902
$905$	0.657416	−	6.25489i	0.0218532	−	0.207920i
$906$	10.5739	−	7.68240i	0.351295	−	0.255231i
$907$	7.18536	+	5.22047i	0.238586	+	0.173343i	0.700653	−	0.713502i	$-0.252892\pi$
$907$	7.18536	+	5.22047i	0.238586	+	0.173343i	−0.462067	+	0.886845i	$0.652892\pi$
$908$	18.2159	+	20.2308i	0.604517	+	0.671384i
$909$	−3.18104	−	30.2656i	−0.105508	−	1.00385i
$910$	−0.326682	−	3.10817i	−0.0108294	−	0.103035i
$911$	−13.1554	−	5.85716i	−0.435857	−	0.194056i	0.177065	−	0.984199i	$-0.443340\pi$
$911$	−13.1554	−	5.85716i	−0.435857	−	0.194056i	−0.612923	+	0.790143i	$0.710006\pi$
$912$	0.204743	+	0.630134i	0.00677972	+	0.0208658i
$913$	−68.5857	−	14.5783i	−2.26986	−	0.482473i
$914$	−12.2928			−0.406610
$915$	−7.61130	−	7.71541i	−0.251622	−	0.255064i
$916$	−2.11678			−0.0699403
$917$	2.48499	+	0.528201i	0.0820615	+	0.0174427i
$918$	−1.47369	−	4.53555i	−0.0486390	−	0.149695i
$919$	4.77643	+	2.12660i	0.157560	+	0.0701502i	0.484001	−	0.875067i	$-0.339183\pi$
$919$	4.77643	+	2.12660i	0.157560	+	0.0701502i	−0.326442	+	0.945217i	$0.605850\pi$
$920$	0.263083	+	2.50306i	0.00867358	+	0.0825236i
$921$	2.50921	+	23.8735i	0.0826811	+	0.786659i
$922$	5.16292	+	5.73400i	0.170032	+	0.188839i
$923$	29.3043	+	21.2908i	0.964563	+	0.700796i
$924$	15.7484	−	11.4419i	0.518083	−	0.376409i
$925$	−4.74254	+	45.1222i	−0.155934	+	1.48361i
$926$	−26.8649			−0.882837
$927$	6.74792	−	64.2022i	0.221631	−	2.10868i
$928$	−0.939251	+	1.62683i	−0.0308324	+	0.0534033i
$929$	28.8126	+	49.9048i	0.945310	+	1.63732i	0.755130	+	0.655575i	$0.227574\pi$
$929$	28.8126	+	49.9048i	0.945310	+	1.63732i	0.190180	+	0.981749i	$0.439093\pi$
$930$	9.04491	−	4.02705i	0.296594	−	0.132052i
$931$	0.930151	+	1.03304i	0.0304845	+	0.0338564i
$932$	−14.7085	−	6.54867i	−0.481795	−	0.214509i
$933$	23.4867	−	10.4569i	0.768919	−	0.342345i
$934$	5.94176	−	6.59899i	0.194420	−	0.215926i
$935$	−3.65867	+	11.2602i	−0.119651	+	0.368248i
$936$	7.86020	−	13.6143i	0.256919	−	0.444996i
$937$	43.6811	+	9.28471i	1.42700	+	0.303318i	0.855721	−	0.517438i	$-0.173114\pi$
$937$	43.6811	+	9.28471i	1.42700	+	0.303318i	0.571279	+	0.820756i	$0.306447\pi$
$938$	0.662982	−	0.481685i	0.0216471	−	0.0157276i
$939$	−24.0074	+	73.8873i	−0.783453	+	2.41122i
$940$	1.40181	−	0.297965i	0.0457221	−	0.00971853i
$941$	21.3816	−	23.7467i	0.697020	−	0.774119i	−0.285879	−	0.958266i	$-0.592285\pi$
$941$	21.3816	−	23.7467i	0.697020	−	0.774119i	0.982899	+	0.184147i	$0.0589522\pi$
$942$	16.0868	+	11.6877i	0.524135	+	0.380806i
$943$	−4.47401	−	13.7696i	−0.145694	−	0.448399i
$944$	−0.941655	−	1.63099i	−0.0306483	−	0.0530843i
$945$	−0.889019	+	0.188967i	−0.0289198	+	0.00614709i
$946$	45.2699	−	9.62242i	1.47185	−	0.312852i
$947$	−21.3076	−	36.9059i	−0.692405	−	1.19928i	−0.971048	−	0.238885i	$-0.923218\pi$
$947$	−21.3076	−	36.9059i	−0.692405	−	1.19928i	0.278643	−	0.960395i	$-0.410115\pi$
$948$	7.84391	+	24.1411i	0.254758	+	0.784065i
$949$	−29.3034	−	21.2902i	−0.951228	−	0.691108i
$950$	0.817377	−	0.907789i	0.0265192	−	0.0294526i
$951$	−2.43359	+	0.517275i	−0.0789144	+	0.0167738i
$952$	−1.45209	+	4.46908i	−0.0470626	+	0.144844i
$953$	−29.5849	+	21.4947i	−0.958347	+	0.696280i	−0.952766	−	0.303704i	$-0.901777\pi$
$953$	−29.5849	+	21.4947i	−0.958347	+	0.696280i	−0.00558109	+	0.999984i	$0.501777\pi$
$954$	−35.1073	−	7.46228i	−1.13664	−	0.241600i
$955$	6.98652	−	12.1010i	0.226078	−	0.391579i
$956$	−5.41512	+	16.6660i	−0.175137	+	0.539017i
$957$	19.0673	−	21.1764i	0.616359	−	0.684537i
$958$	−7.35089	+	3.27283i	−0.237497	+	0.105740i
$959$	−14.6870	−	6.53909i	−0.474269	−	0.211158i
$960$	−0.928517	−	1.03122i	−0.0299678	−	0.0332826i
$961$	18.1873	−	8.09750i	0.586686	−	0.261210i
$962$	−21.5955	−	37.4045i	−0.696267	−	1.20597i
$963$	−34.5186	+	59.7880i	−1.11235	+	1.92664i
$964$	−0.908341	+	8.64228i	−0.0292557	+	0.278349i
$965$	2.12251			0.0683261
$966$	1.58391	−	15.0699i	0.0509616	−	0.484867i
$967$	18.2784	−	13.2800i	0.587793	−	0.427057i	−0.253732	−	0.967274i	$-0.581658\pi$
$967$	18.2784	−	13.2800i	0.587793	−	0.427057i	0.841525	+	0.540218i	$0.181658\pi$
$968$	−19.6955	−	14.3096i	−0.633036	−	0.459928i
$969$	1.62345	+	1.80303i	0.0521528	+	0.0579215i
$970$	−0.709280	−	6.74835i	−0.0227736	−	0.216677i
$971$	−1.63282	−	15.5352i	−0.0523996	−	0.498549i	−0.988975	−	0.148083i	$-0.952690\pi$
$971$	−1.63282	−	15.5352i	−0.0523996	−	0.498549i	0.936575	−	0.350466i	$-0.113977\pi$
$972$	20.3714	+	9.06991i	0.653412	+	0.290918i
$973$	3.15356	+	9.70566i	0.101098	+	0.311149i
$974$	17.2950	+	3.67617i	0.554169	+	0.117792i
$975$	−53.7525			−1.72146
$976$	−3.59297	+	6.93474i	−0.115008	+	0.221976i
$977$	−42.7792			−1.36863			−0.684315	−	0.729187i	$-0.739898\pi$
$977$	−42.7792			−1.36863			−0.684315	+	0.729187i	$0.739898\pi$
$978$	−37.3994	−	7.94949i	−1.19590	−	0.254197i
$979$	−28.4683	−	87.6163i	−0.909850	−	2.80023i
$980$	−2.65965	−	1.18415i	−0.0849595	−	0.0378264i
$981$	−0.0445067	−	0.423453i	−0.00142099	−	0.0135198i
$982$	−3.38911	−	32.2453i	−0.108151	−	1.02899i
$983$	2.28194	+	2.53436i	0.0727827	+	0.0808334i	0.778436	−	0.627724i	$-0.216013\pi$
$983$	2.28194	+	2.53436i	0.0727827	+	0.0808334i	−0.705654	+	0.708557i	$0.749347\pi$
$984$	6.45793	+	4.69196i	0.205871	+	0.149574i
$985$	−7.56838	+	5.49875i	−0.241149	+	0.175205i
$986$	−0.719032	+	6.84113i	−0.0228986	+	0.217866i
$987$	−8.62829			−0.274641
$988$	−0.121552	+	1.15649i	−0.00386709	+	0.0367929i
$989$	18.0134	−	31.2000i	0.572791	−	0.992104i
$990$	5.67500	+	9.82940i	0.180363	+	0.312399i
$991$	−20.1842	+	8.98658i	−0.641172	+	0.285468i	−0.701456	−	0.712713i	$-0.747466\pi$
$991$	−20.1842	+	8.98658i	−0.641172	+	0.285468i	0.0602838	+	0.998181i	$0.480799\pi$
$992$	−4.77426	−	5.30235i	−0.151583	−	0.168350i
$993$	13.9578	+	6.21441i	0.442937	+	0.197208i
$994$	−9.48218	+	4.22174i	−0.300756	+	0.133905i
$995$	2.45236	−	2.72362i	0.0777450	−	0.0863445i
$996$	9.29934	−	28.6204i	0.294661	−	0.906873i
$997$	−13.8476	+	23.9848i	−0.438558	+	0.759606i	−0.997579	−	0.0695486i	$-0.977844\pi$
$997$	−13.8476	+	23.9848i	−0.438558	+	0.759606i	0.559020	+	0.829154i	$0.311177\pi$
$998$	−7.06003	−	1.50066i	−0.223481	−	0.0475025i
$999$	−10.1617	+	7.38292i	−0.321502	+	0.233585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.b.77.1	✓	24
4.3	odd	2		976.2.bw.b.321.3		24
61.15	even	15		7442.2.a.w.1.3		12
61.42	even	15	inner	122.2.i.b.103.1	yes	24
61.46	even	30		7442.2.a.u.1.3		12
244.103	odd	30		976.2.bw.b.225.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.b.77.1	✓	24	1.1	even	1	trivial
122.2.i.b.103.1	yes	24	61.42	even	15	inner
976.2.bw.b.225.3		24	244.103	odd	30
976.2.bw.b.321.3		24	4.3	odd	2
7442.2.a.u.1.3		12	61.46	even	30
7442.2.a.w.1.3		12	61.15	even	15

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-0.788472 - 2.42667i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0568473 - 0.540866i) q^{5} +(0.266710 + 2.53757i) q^{6} +(-0.858659 - 0.953638i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.83998 + 2.06337i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-0.788472 - 2.42667i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0568473 - 0.540866i) q^{5} +(0.266710 + 2.53757i) q^{6} +(-0.858659 - 0.953638i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.83998 + 2.06337i) q^{9} +(-0.0568473 + 0.540866i) q^{10} -5.94516 q^{11} +(0.266710 - 2.53757i) q^{12} +(2.23911 - 3.87826i) q^{13} +(0.641623 + 1.11132i) q^{14} +(-1.26768 + 0.564407i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.34528 + 1.48941i) q^{17} +(3.20692 - 1.42781i) q^{18} +(-0.173753 + 0.192973i) q^{19} +(0.168057 - 0.517227i) q^{20} +(-1.63713 + 2.83560i) q^{21} +(5.81524 + 1.23607i) q^{22} +(3.74404 - 2.72020i) q^{23} +(-0.788472 + 2.42667i) q^{24} +(4.60143 - 0.978065i) q^{25} +(-2.99652 + 3.32797i) q^{26} +(1.05361 + 0.765492i) q^{27} +(-0.396545 - 1.22044i) q^{28} +(-0.939251 - 1.62683i) q^{29} +(1.35732 - 0.288508i) q^{30} +(6.97910 - 1.48345i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.68759 + 14.4269i) q^{33} +(-2.96251 - 2.15239i) q^{34} +(-0.466977 + 0.518631i) q^{35} +(-3.43370 + 0.729855i) q^{36} +(-2.98037 + 9.17263i) q^{37} +(0.210078 - 0.152630i) q^{38} +(-11.1767 - 2.37569i) q^{39} +(-0.271922 + 0.470983i) q^{40} +(0.966750 - 2.97535i) q^{41} +(2.19091 - 2.43325i) q^{42} +(7.11168 - 3.16632i) q^{43} +(-5.43117 - 2.41811i) q^{44} +(1.27745 + 1.41875i) q^{45} +(-4.22778 + 1.88233i) q^{46} +(1.31759 + 2.28213i) q^{47} +(1.27578 - 2.20971i) q^{48} +(0.559570 - 5.32395i) q^{49} -4.70423 q^{50} +(0.976654 - 9.29224i) q^{51} +(3.62296 - 2.63223i) q^{52} +(-8.27166 - 6.00971i) q^{53} +(-0.871430 - 0.967821i) q^{54} +(0.337966 + 3.21553i) q^{55} +(0.134136 + 1.27622i) q^{56} +(0.605281 + 0.269488i) q^{57} +(0.580489 + 1.78656i) q^{58} +(-1.84215 - 0.391562i) q^{59} -1.38765 q^{60} +(2.74935 + 7.31034i) q^{61} -7.13502 q^{62} +(4.40628 + 0.936583i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.22490 - 0.990591i) q^{65} +(-1.58563 - 15.0863i) q^{66} +(-0.0667527 - 0.635110i) q^{67} +(2.45026 + 2.72129i) q^{68} +(-9.55310 - 6.94073i) q^{69} +(0.564602 - 0.410208i) q^{70} +(-0.845478 + 8.04419i) q^{71} +3.51041 q^{72} +(0.845452 - 8.04394i) q^{73} +(4.82234 - 8.35253i) q^{74} +(-6.00154 - 10.3950i) q^{75} +(-0.237221 + 0.105617i) q^{76} +(5.10487 + 5.66953i) q^{77} +(10.4385 + 4.64754i) q^{78} +(-9.08816 + 4.04631i) q^{79} +(0.363903 - 0.404155i) q^{80} +(-2.22747 + 6.85546i) q^{81} +(-1.56423 + 2.70933i) q^{82} +(11.5364 + 2.45214i) q^{83} +(-2.64894 + 1.92457i) q^{84} +(0.615402 - 1.89401i) q^{85} +(-7.61459 + 1.61853i) q^{86} +(-3.20720 + 3.56196i) q^{87} +(4.80974 + 3.49448i) q^{88} +(4.78848 + 14.7374i) q^{89} +(-0.954559 - 1.65334i) q^{90} +(-5.62109 + 1.19480i) q^{91} +(4.52676 - 0.962192i) q^{92} +(-9.10268 - 15.7663i) q^{93} +(-0.814316 - 2.50621i) q^{94} +(0.114250 + 0.0830073i) q^{95} +(-1.70732 + 1.89617i) q^{96} +(-12.2043 + 2.59410i) q^{97} +(-1.65425 + 5.09127i) q^{98} +(16.8841 - 12.2670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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