LMFDB - Embedded newform 350.2.u.a.179.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(9,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("350.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.u (of order $30$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			179.19
Character	$\chi$	$=$	350.179
Dual form			350.2.u.a.219.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 + 0.978148i) q^{2} +(0.927596 + 2.08342i) q^{3} +(-0.913545 + 0.406737i) q^{4} +(1.97118 - 1.05568i) q^{5} +(-1.84503 + 1.34049i) q^{6} +(-0.841740 + 2.50828i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.47279 + 1.63570i) q^{9} +O(q^{10})$	\(q+(0.207912 + 0.978148i) q^{2} +(0.927596 + 2.08342i) q^{3} +(-0.913545 + 0.406737i) q^{4} +(1.97118 - 1.05568i) q^{5} +(-1.84503 + 1.34049i) q^{6} +(-0.841740 + 2.50828i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.47279 + 1.63570i) q^{9} +(1.44244 + 1.70862i) q^{10} +(0.440408 + 0.489122i) q^{11} +(-1.69480 - 1.52601i) q^{12} +(-3.80785 + 1.23724i) q^{13} +(-2.62848 - 0.301845i) q^{14} +(4.02787 + 3.12754i) q^{15} +(0.669131 - 0.743145i) q^{16} +(6.49472 - 0.682623i) q^{17} +(-1.90617 - 1.10053i) q^{18} +(-2.11299 - 0.940765i) q^{19} +(-1.37138 + 1.76616i) q^{20} +(-6.00659 + 0.572977i) q^{21} +(-0.386868 + 0.532478i) q^{22} +(-0.0757367 - 0.356313i) q^{23} +(1.14029 - 1.97504i) q^{24} +(2.77109 - 4.16186i) q^{25} +(-2.00190 - 3.46740i) q^{26} +(1.73288 + 0.563048i) q^{27} +(-0.251242 - 2.63380i) q^{28} +(-4.46906 - 3.24696i) q^{29} +(-2.22175 + 4.59011i) q^{30} +(0.329077 + 3.13096i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.610524 + 1.37126i) q^{33} +(2.01803 + 6.21087i) q^{34} +(0.988716 + 5.83288i) q^{35} +(0.680163 - 2.09333i) q^{36} +(-1.86217 - 1.67671i) q^{37} +(0.480891 - 2.26242i) q^{38} +(-6.10984 - 6.78566i) q^{39} +(-2.01269 - 0.974205i) q^{40} +(-3.28018 - 10.0954i) q^{41} +(-1.80930 - 5.75620i) q^{42} -3.47345i q^{43} +(-0.601276 - 0.267705i) q^{44} +(-1.17636 + 4.77906i) q^{45} +(0.332780 - 0.148163i) q^{46} +(6.91225 + 0.726507i) q^{47} +(2.16896 + 0.704739i) q^{48} +(-5.58295 - 4.22264i) q^{49} +(4.64705 + 1.84524i) q^{50} +(7.44667 + 12.8980i) q^{51} +(2.97541 - 2.67907i) q^{52} +(4.29511 + 9.64697i) q^{53} +(-0.190457 + 1.81208i) q^{54} +(1.38448 + 0.499219i) q^{55} +(2.52400 - 0.793348i) q^{56} -5.27489i q^{57} +(2.24684 - 5.04648i) q^{58} +(-3.08830 - 0.656439i) q^{59} +(-4.95173 - 1.21887i) q^{60} +(7.15017 - 1.51981i) q^{61} +(-2.99412 + 0.972848i) q^{62} +(-2.86309 - 5.07101i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-6.19981 + 6.45869i) q^{65} +(-1.46823 - 0.312082i) q^{66} +(8.29701 - 0.872051i) q^{67} +(-5.65558 + 3.26525i) q^{68} +(0.672095 - 0.488306i) q^{69} +(-5.49985 + 2.17983i) q^{70} +(12.3215 + 8.95209i) q^{71} +(2.18900 + 0.230073i) q^{72} +(10.3927 - 9.35767i) q^{73} +(1.25290 - 2.17009i) q^{74} +(11.2413 + 1.91281i) q^{75} +2.31296 q^{76} +(-1.59756 + 0.692952i) q^{77} +(5.36707 - 7.38714i) q^{78} +(-0.900829 + 8.57081i) q^{79} +(0.534454 - 2.17126i) q^{80} +(1.12457 + 10.6996i) q^{81} +(9.19276 - 5.30744i) q^{82} +(-8.83852 - 12.1652i) q^{83} +(5.25424 - 2.96654i) q^{84} +(12.0816 - 8.20190i) q^{85} +(3.39755 - 0.722172i) q^{86} +(2.61929 - 12.3228i) q^{87} +(0.136843 - 0.643796i) q^{88} +(-11.0990 + 2.35916i) q^{89} +(-4.91920 - 0.157035i) q^{90} +(0.101862 - 10.5926i) q^{91} +(0.214115 + 0.294703i) q^{92} +(-6.21783 + 3.58987i) q^{93} +(0.726507 + 6.91225i) q^{94} +(-5.15823 + 0.376224i) q^{95} +(-0.238386 + 2.26809i) q^{96} +(-1.44169 + 1.98431i) q^{97} +(2.96961 - 6.33888i) q^{98} -1.44869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9}+O(q^{10}) $ 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9	$ 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9} - 2 q^{10} - 6 q^{11} - 16 q^{15} + 20 q^{16} - 20 q^{17} + 4 q^{19} - 4 q^{20} - 12 q^{21} + 40 q^{22} - 30 q^{23} - 16 q^{24} + 48 q^{26} - 120 q^{27} - 10 q^{28} + 24 q^{29} - 26 q^{30} - 6 q^{31} - 50 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} - 32 q^{39} + 2 q^{40} + 68 q^{41} + 10 q^{42} - 4 q^{44} + 16 q^{45} + 12 q^{46} + 24 q^{49} + 32 q^{50} + 12 q^{51} - 20 q^{53} + 16 q^{54} + 24 q^{55} + 24 q^{59} + 2 q^{60} - 8 q^{61} + 40 q^{64} + 2 q^{65} - 116 q^{69} - 118 q^{70} + 68 q^{71} - 40 q^{73} + 16 q^{74} + 196 q^{75} - 32 q^{76} - 80 q^{77} - 8 q^{79} - 2 q^{80} + 64 q^{81} - 160 q^{83} - 18 q^{84} + 12 q^{85} + 12 q^{86} - 10 q^{88} + 54 q^{89} + 44 q^{91} - 40 q^{92} - 16 q^{95} - 4 q^{96} - 20 q^{97} + 40 q^{98} - 24 q^{99}+O(q^{100}) $ 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9 - 2 * q^10 - 6 * q^11 - 16 * q^15 + 20 * q^16 - 20 * q^17 + 4 * q^19 - 4 * q^20 - 12 * q^21 + 40 * q^22 - 30 * q^23 - 16 * q^24 + 48 * q^26 - 120 * q^27 - 10 * q^28 + 24 * q^29 - 26 * q^30 - 6 * q^31 - 50 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 - 32 * q^39 + 2 * q^40 + 68 * q^41 + 10 * q^42 - 4 * q^44 + 16 * q^45 + 12 * q^46 + 24 * q^49 + 32 * q^50 + 12 * q^51 - 20 * q^53 + 16 * q^54 + 24 * q^55 + 24 * q^59 + 2 * q^60 - 8 * q^61 + 40 * q^64 + 2 * q^65 - 116 * q^69 - 118 * q^70 + 68 * q^71 - 40 * q^73 + 16 * q^74 + 196 * q^75 - 32 * q^76 - 80 * q^77 - 8 * q^79 - 2 * q^80 + 64 * q^81 - 160 * q^83 - 18 * q^84 + 12 * q^85 + 12 * q^86 - 10 * q^88 + 54 * q^89 + 44 * q^91 - 40 * q^92 - 16 * q^95 - 4 * q^96 - 20 * q^97 + 40 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.207912	+	0.978148i	0.147016	+	0.691655i
$2$	0.207912	+	0.978148i	0.147016	+	0.691655i
$3$	0.927596	+	2.08342i	0.535548	+	1.20286i	0.955413	+	0.295274i	$0.0954108\pi$
$3$	0.927596	+	2.08342i	0.535548	+	1.20286i	−0.419865	+	0.907587i	$0.637922\pi$
$4$	−0.913545	+	0.406737i	−0.456773	+	0.203368i
$5$	1.97118	−	1.05568i	0.881538	−	0.472113i
$5$	1.97118	−	1.05568i	0.881538	−	0.472113i
$6$	−1.84503	+	1.34049i	−0.753230	+	0.547254i
$7$	−0.841740	+	2.50828i	−0.318148	+	0.948041i
$7$	−0.841740	+	2.50828i	−0.318148	+	0.948041i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−1.47279	+	1.63570i	−0.490931	+	0.545234i
$10$	1.44244	+	1.70862i	0.456139	+	0.540312i
$11$	0.440408	+	0.489122i	0.132788	+	0.147476i	0.805871	−	0.592091i	$-0.201697\pi$
$11$	0.440408	+	0.489122i	0.132788	+	0.147476i	−0.673084	+	0.739566i	$0.735031\pi$
$12$	−1.69480	−	1.52601i	−0.489247	−	0.440520i
$13$	−3.80785	+	1.23724i	−1.05611	+	0.343150i	−0.785062	−	0.619417i	$-0.787369\pi$
$13$	−3.80785	+	1.23724i	−1.05611	+	0.343150i	−0.271045	+	0.962567i	$0.587369\pi$
$14$	−2.62848	−	0.301845i	−0.702490	−	0.0806716i
$15$	4.02787	+	3.12754i	1.03999	+	0.807528i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	6.49472	−	0.682623i	1.57520	−	0.165560i	0.723776	−	0.690035i	$-0.242405\pi$
$17$	6.49472	−	0.682623i	1.57520	−	0.165560i	0.851426	+	0.524475i	$0.175738\pi$
$18$	−1.90617	−	1.10053i	−0.449288	−	0.259397i
$19$	−2.11299	−	0.940765i	−0.484754	−	0.215826i	0.149783	−	0.988719i	$-0.452143\pi$
$19$	−2.11299	−	0.940765i	−0.484754	−	0.215826i	−0.634537	+	0.772893i	$0.718809\pi$
$20$	−1.37138	+	1.76616i	−0.306650	+	0.394925i
$21$	−6.00659	+	0.572977i	−1.31074	+	0.125034i
$22$	−0.386868	+	0.532478i	−0.0824805	+	0.113525i
$23$	−0.0757367	−	0.356313i	−0.0157922	−	0.0742964i	0.969546	−	0.244910i	$-0.0787584\pi$
$23$	−0.0757367	−	0.356313i	−0.0157922	−	0.0742964i	−0.985338	+	0.170613i	$0.945425\pi$
$24$	1.14029	−	1.97504i	0.232761	−	0.403154i
$25$	2.77109	−	4.16186i	0.554218	−	0.832372i
$26$	−2.00190	−	3.46740i	−0.392606	−	0.680013i
$27$	1.73288	+	0.563048i	0.333494	+	0.108359i
$28$	−0.251242	−	2.63380i	−0.0474802	−	0.497741i
$29$	−4.46906	−	3.24696i	−0.829883	−	0.602945i	0.0896431	−	0.995974i	$-0.471427\pi$
$29$	−4.46906	−	3.24696i	−0.829883	−	0.602945i	−0.919526	+	0.393029i	$0.871427\pi$
$30$	−2.22175	+	4.59011i	−0.405635	+	0.838035i
$31$	0.329077	+	3.13096i	0.0591039	+	0.562337i	0.983501	+	0.180904i	$0.0579024\pi$
$31$	0.329077	+	3.13096i	0.0591039	+	0.562337i	−0.924397	+	0.381432i	$0.875431\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.610524	+	1.37126i	−0.106279	+	0.238706i
$34$	2.01803	+	6.21087i	0.346090	+	1.06516i
$35$	0.988716	+	5.83288i	0.167123	+	0.985936i
$36$	0.680163	−	2.09333i	0.113361	−	0.348888i
$37$	−1.86217	−	1.67671i	−0.306140	−	0.275649i	0.501713	−	0.865034i	$-0.332703\pi$
$37$	−1.86217	−	1.67671i	−0.306140	−	0.275649i	−0.807852	+	0.589385i	$0.799370\pi$
$38$	0.480891	−	2.26242i	0.0780109	−	0.367012i
$39$	−6.10984	−	6.78566i	−0.978357	−	1.08658i
$40$	−2.01269	−	0.974205i	−0.318234	−	0.154035i
$41$	−3.28018	−	10.0954i	−0.512278	−	1.57663i	−0.788180	−	0.615444i	$-0.788977\pi$
$41$	−3.28018	−	10.0954i	−0.512278	−	1.57663i	0.275902	−	0.961186i	$-0.411023\pi$
$42$	−1.80930	−	5.75620i	−0.279180	−	0.888201i
$43$		−	3.47345i		−	0.529697i	−0.964290	−	0.264848i	$-0.914678\pi$
$43$		−	3.47345i		−	0.529697i	0.964290	−	0.264848i	$-0.0853219\pi$
$44$	−0.601276	−	0.267705i	−0.0906458	−	0.0403581i
$45$	−1.17636	+	4.77906i	−0.175362	+	0.712419i
$46$	0.332780	−	0.148163i	0.0490658	−	0.0218455i
$47$	6.91225	+	0.726507i	1.00826	+	0.105972i	0.594232	−	0.804294i	$-0.297456\pi$
$47$	6.91225	+	0.726507i	1.00826	+	0.105972i	0.414024	+	0.910266i	$0.364123\pi$
$48$	2.16896	+	0.704739i	0.313063	+	0.101720i
$49$	−5.58295	−	4.22264i	−0.797564	−	0.603235i
$50$	4.64705	+	1.84524i	0.657193	+	0.260956i
$51$	7.44667	+	12.8980i	1.04274	+	1.80608i
$52$	2.97541	−	2.67907i	0.412615	−	0.371520i
$53$	4.29511	+	9.64697i	0.589978	+	1.32511i	0.923944	+	0.382528i	$0.124946\pi$
$53$	4.29511	+	9.64697i	0.589978	+	1.32511i	−0.333965	+	0.942585i	$0.608387\pi$
$54$	−0.190457	+	1.81208i	−0.0259180	+	0.246593i
$55$	1.38448	+	0.499219i	0.186683	+	0.0673146i
$56$	2.52400	−	0.793348i	0.337284	−	0.106016i
$57$		−	5.27489i		−	0.698677i
$58$	2.24684	−	5.04648i	0.295024	−	0.662635i
$59$	−3.08830	−	0.656439i	−0.402063	−	0.0854611i	0.00244182	−	0.999997i	$-0.499223\pi$
$59$	−3.08830	−	0.656439i	−0.402063	−	0.0854611i	−0.404505	+	0.914536i	$0.632556\pi$
$60$	−4.95173	−	1.21887i	−0.639266	−	0.157355i
$61$	7.15017	−	1.51981i	0.915485	−	0.194592i	0.274002	−	0.961729i	$-0.411653\pi$
$61$	7.15017	−	1.51981i	0.915485	−	0.194592i	0.641483	+	0.767137i	$0.278319\pi$
$62$	−2.99412	+	0.972848i	−0.380254	+	0.123552i
$63$	−2.86309	−	5.07101i	−0.360716	−	0.638888i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−6.19981	+	6.45869i	−0.768992	+	0.801102i
$66$	−1.46823	−	0.312082i	−0.180727	−	0.0384146i
$67$	8.29701	−	0.872051i	1.01364	−	0.106538i	0.416884	−	0.908960i	$-0.363122\pi$
$67$	8.29701	−	0.872051i	1.01364	−	0.106538i	0.596757	+	0.802422i	$0.296456\pi$
$68$	−5.65558	+	3.26525i	−0.685839	+	0.395970i
$69$	0.672095	−	0.488306i	0.0809108	−	0.0587851i
$70$	−5.49985	+	2.17983i	−0.657358	+	0.260540i
$71$	12.3215	+	8.95209i	1.46229	+	1.06242i	0.982758	+	0.184895i	$0.0591946\pi$
$71$	12.3215	+	8.95209i	1.46229	+	1.06242i	0.479535	+	0.877523i	$0.340805\pi$
$72$	2.18900	+	0.230073i	0.257976	+	0.0271143i
$73$	10.3927	−	9.35767i	1.21638	−	1.09523i	0.223674	−	0.974664i	$-0.428195\pi$
$73$	10.3927	−	9.35767i	1.21638	−	1.09523i	0.992705	−	0.120568i	$-0.0384717\pi$
$74$	1.25290	−	2.17009i	0.145647	−	0.252268i
$75$	11.2413	+	1.91281i	1.29804	+	0.220872i
$76$	2.31296			0.265315
$77$	−1.59756	+	0.692952i	−0.182059	+	0.0789692i
$78$	5.36707	−	7.38714i	0.607701	−	0.836429i
$79$	−0.900829	+	8.57081i	−0.101351	+	0.964292i	0.819157	+	0.573569i	$0.194442\pi$
$79$	−0.900829	+	8.57081i	−0.101351	+	0.964292i	−0.920508	+	0.390723i	$0.872225\pi$
$80$	0.534454	−	2.17126i	0.0597538	−	0.242754i
$81$	1.12457	+	10.6996i	0.124952	+	1.18884i
$82$	9.19276	−	5.30744i	1.01517	−	0.586109i
$83$	−8.83852	−	12.1652i	−0.970154	−	1.33530i	−0.941969	−	0.335700i	$-0.891027\pi$
$83$	−8.83852	−	12.1652i	−0.970154	−	1.33530i	−0.0281850	−	0.999603i	$-0.508973\pi$
$84$	5.25424	−	2.96654i	0.573284	−	0.323676i
$85$	12.0816	−	8.20190i	1.31044	−	0.889621i
$86$	3.39755	−	0.722172i	0.366367	−	0.0778738i
$87$	2.61929	−	12.3228i	0.280817	−	1.32114i
$88$	0.136843	−	0.643796i	0.0145875	−	0.0686289i
$89$	−11.0990	+	2.35916i	−1.17649	+	0.250070i	−0.754357	−	0.656464i	$-0.772051\pi$
$89$	−11.0990	+	2.35916i	−1.17649	+	0.250070i	−0.422132	+	0.906534i	$0.638718\pi$
$90$	−4.91920	−	0.157035i	−0.518529	−	0.0165530i
$91$	0.101862	−	10.5926i	0.0106780	−	1.11041i
$92$	0.214115	+	0.294703i	0.0223230	+	0.0307250i
$93$	−6.21783	+	3.58987i	−0.644759	+	0.372252i
$94$	0.726507	+	6.91225i	0.0749335	+	0.712944i
$95$	−5.15823	+	0.376224i	−0.529224	+	0.0385997i
$96$	−0.238386	+	2.26809i	−0.0243301	+	0.231486i
$97$	−1.44169	+	1.98431i	−0.146381	+	0.201476i	−0.875911	−	0.482473i	$-0.839739\pi$
$97$	−1.44169	+	1.98431i	−0.146381	+	0.201476i	0.729530	+	0.683949i	$0.239739\pi$
$98$	2.96961	−	6.33888i	0.299976	−	0.640324i
$99$	−1.44869			−0.145599
$100$	−0.838736	+	4.92915i	−0.0838736	+	0.492915i
$101$	1.63784	−	2.83683i	0.162972	−	0.282275i	−0.772961	−	0.634453i	$-0.781225\pi$
$101$	1.63784	−	2.83683i	0.162972	−	0.282275i	0.935933	+	0.352178i	$0.114559\pi$
$102$	−11.0679	+	9.96559i	−1.09589	+	0.986740i
$103$	−6.34661	−	0.667055i	−0.625350	−	0.0657269i	−0.213447	−	0.976955i	$-0.568469\pi$
$103$	−6.34661	−	0.667055i	−0.625350	−	0.0657269i	−0.411903	+	0.911228i	$0.635136\pi$
$104$	3.23915	+	2.35338i	0.317625	+	0.230768i
$105$	−11.2352	+	7.47046i	−1.09644	+	0.729042i
$106$	−8.54316	+	6.20697i	−0.829785	+	0.602874i
$107$	−5.61421	+	3.24137i	−0.542747	+	0.313355i	−0.746191	−	0.665732i	$-0.768120\pi$
$107$	−5.61421	+	3.24137i	−0.542747	+	0.313355i	0.203445	+	0.979086i	$0.434786\pi$
$108$	−1.81208	+	0.190457i	−0.174367	+	0.0183268i
$109$	2.93066	+	0.622931i	0.280706	+	0.0596660i	0.346113	−	0.938193i	$-0.387501\pi$
$109$	2.93066	+	0.622931i	0.280706	+	0.0596660i	−0.0654070	+	0.997859i	$0.520835\pi$
$110$	−0.200460	+	1.45802i	−0.0191132	+	0.139016i
$111$	1.76594	−	5.43499i	0.167615	−	0.515867i
$112$	1.30078	+	2.30390i	0.122912	+	0.217698i
$113$	−7.56375	+	2.45761i	−0.711538	+	0.231193i	−0.642350	−	0.766411i	$-0.722041\pi$
$113$	−7.56375	+	2.45761i	−0.711538	+	0.231193i	−0.0691872	+	0.997604i	$0.522041\pi$
$114$	5.15963	−	1.09671i	0.483243	−	0.102717i
$115$	−0.525442	−	0.622403i	−0.0489978	−	0.0580394i
$116$	5.40335	+	1.14852i	0.501688	+	0.106637i
$117$	3.58441	−	8.05071i	0.331378	−	0.744288i
$118$		−	3.15730i		−	0.290653i
$119$	−3.75466	+	16.8652i	−0.344189	+	1.54603i
$120$	0.162709	−	5.09694i	0.0148533	−	0.465285i
$121$	1.10453	−	10.5089i	0.100412	−	0.955356i
$122$	2.97321	+	6.67793i	0.269181	+	0.604591i
$123$	17.9901	−	16.1984i	1.62212	−	1.46056i
$124$	−1.57410	−	2.72642i	−0.141359	−	0.244840i
$125$	1.06873	−	11.1291i	0.0955902	−	0.995421i
$126$	4.36493	−	3.85485i	0.388859	−	0.343417i
$127$	−5.91760	−	1.92275i	−0.525102	−	0.170616i	0.0344573	−	0.999406i	$-0.489030\pi$
$127$	−5.91760	−	1.92275i	−0.525102	−	0.170616i	−0.559560	+	0.828790i	$0.689030\pi$
$128$	−0.994522	−	0.104528i	−0.0879041	−	0.00923910i
$129$	7.23665	−	3.22196i	0.637151	−	0.283678i
$130$	−7.60657	−	4.72150i	−0.667140	−	0.414103i
$131$	−13.0776	−	5.82251i	−1.14259	−	0.508715i	−0.253906	−	0.967229i	$-0.581715\pi$
$131$	−13.0776	−	5.82251i	−1.14259	−	0.508715i	−0.888687	+	0.458514i	$0.848382\pi$
$132$		−	1.50103i		−	0.130648i
$133$	4.13830	−	4.50810i	0.358836	−	0.390902i
$134$	2.57804	+	7.93439i	0.222709	+	0.685427i
$135$	4.01022	−	0.719498i	0.345145	−	0.0619246i
$136$	−4.36976	−	4.85310i	−0.374703	−	0.416150i
$137$	−2.30646	+	10.8510i	−0.197054	+	0.927067i	0.762815	+	0.646617i	$0.223817\pi$
$137$	−2.30646	+	10.8510i	−0.197054	+	0.927067i	−0.959869	+	0.280450i	$0.909516\pi$
$138$	0.617372	+	0.555884i	0.0525542	+	0.0473200i
$139$	5.33581	−	16.4219i	0.452578	−	1.39289i	−0.421378	−	0.906885i	$-0.638453\pi$
$139$	5.33581	−	16.4219i	0.452578	−	1.39289i	0.873955	−	0.486006i	$-0.161547\pi$
$140$	−3.27568	−	4.92645i	−0.276846	−	0.416361i
$141$	4.89816	+	15.0750i	0.412500	+	1.26954i
$142$	−6.19469	+	13.9135i	−0.519846	+	1.16759i
$143$	−2.28217	−	1.31761i	−0.190845	−	0.110184i
$144$	0.230073	+	2.18900i	0.0191727	+	0.182416i
$145$	−12.2371	−	1.68245i	−1.01623	−	0.139720i
$146$	11.3140	+	8.22007i	0.936350	+	0.680298i
$147$	3.61880	−	15.5485i	0.298473	−	1.28242i
$148$	2.38316	+	0.774336i	0.195895	+	0.0636500i
$149$	−1.27584	−	2.20982i	−0.104521	−	0.181036i	0.809021	−	0.587779i	$-0.199998\pi$
$149$	−1.27584	−	2.20982i	−0.104521	−	0.181036i	−0.913542	+	0.406743i	$0.866664\pi$
$150$	0.466198	+	11.3934i	0.0380649	+	0.930265i
$151$	0.536456	−	0.929168i	0.0436561	−	0.0756146i	−0.843372	−	0.537331i	$-0.819433\pi$
$151$	0.536456	−	0.929168i	0.0436561	−	0.0756146i	0.887028	+	0.461716i	$0.152766\pi$
$152$	0.480891	+	2.26242i	0.0390054	+	0.183506i
$153$	−8.44881	+	11.6288i	−0.683046	+	0.940132i
$154$	−1.00996	−	1.41858i	−0.0813850	−	0.114313i
$155$	3.95395	+	5.82428i	0.317589	+	0.467817i
$156$	8.34159	+	3.71392i	0.667862	+	0.297351i
$157$	−12.8093	−	7.39546i	−1.02229	−	0.590222i	−0.107527	−	0.994202i	$-0.534293\pi$
$157$	−12.8093	−	7.39546i	−1.02229	−	0.590222i	−0.914768	+	0.403980i	$0.867627\pi$
$158$	−8.57081	+	0.900829i	−0.681857	+	0.0716661i
$159$	−16.1145	+	17.8970i	−1.27796	+	1.41932i
$160$	2.23493	+	0.0713455i	0.176687	+	0.00564036i
$161$	0.957484	+	0.109954i	0.0754603	+	0.00866561i
$162$	−10.2320	+	3.32457i	−0.803899	+	0.261203i
$163$	−4.83820	−	4.35634i	−0.378957	−	0.341215i	0.457537	−	0.889191i	$-0.348732\pi$
$163$	−4.83820	−	4.35634i	−0.378957	−	0.341215i	−0.836494	+	0.547976i	$0.815398\pi$
$164$	7.10275	+	7.88840i	0.554631	+	0.615981i
$165$	0.244156	+	3.34751i	0.0190075	+	0.260604i
$166$	10.0617	−	11.1747i	0.780940	−	0.867322i
$167$	1.02950	+	1.41699i	0.0796654	+	0.109650i	0.846990	−	0.531609i	$-0.178412\pi$
$167$	1.02950	+	1.41699i	0.0796654	+	0.109650i	−0.767324	+	0.641259i	$0.778412\pi$
$168$	3.99413	+	4.52264i	0.308154	+	0.348929i
$169$	2.45171	−	1.78127i	0.188593	−	0.137021i
$170$	10.5346	+	10.1123i	0.807966	+	0.775581i
$171$	4.65081	−	2.07068i	0.355657	−	0.158349i
$172$	1.41278	+	3.17316i	0.107724	+	0.241951i
$173$	5.19122	+	24.4228i	0.394681	+	1.85683i	0.505270	+	0.862961i	$0.331393\pi$
$173$	5.19122	+	24.4228i	0.394681	+	1.85683i	−0.110589	+	0.993866i	$0.535274\pi$
$174$	12.5981			0.955057
$175$	8.10657	+	10.4539i	0.612799	+	0.790239i
$176$	0.658179			0.0496121
$177$	−1.49706	−	7.04313i	−0.112526	−	0.529394i
$178$	−4.61521	−	10.3659i	−0.345925	−	0.776960i
$179$	−14.8502	+	6.61175i	−1.10996	+	0.494186i	−0.878058	−	0.478554i	$-0.841161\pi$
$179$	−14.8502	+	6.61175i	−1.10996	+	0.494186i	−0.231901	+	0.972739i	$0.574494\pi$
$180$	−0.869156	−	4.84435i	−0.0647830	−	0.361077i
$181$	−13.6600	+	9.92457i	−1.01534	+	0.737688i	−0.965322	−	0.261061i	$-0.915928\pi$
$181$	−13.6600	+	9.92457i	−1.01534	+	0.737688i	−0.0500175	+	0.998748i	$0.515928\pi$
$182$	10.3823	−	2.10269i	0.769587	−	0.155862i
$183$	9.79887	+	13.4870i	0.724353	+	0.996987i
$184$	−0.243747	+	0.270708i	−0.0179692	+	0.0199569i
$185$	−5.44074	−	1.33924i	−0.400011	−	0.0984627i
$186$	−4.80418	−	5.33558i	−0.352260	−	0.391224i
$187$	3.19421	+	2.87608i	0.233584	+	0.210320i
$188$	−6.61015	+	2.14777i	−0.482095	+	0.156642i
$189$	−2.87092	+	3.87262i	−0.208829	+	0.281692i
$190$	−1.44046	−	4.96729i	−0.104502	−	0.360365i
$191$	−2.12029	+	2.35482i	−0.153419	+	0.170389i	−0.814955	−	0.579525i	$-0.803238\pi$
$191$	−2.12029	+	2.35482i	−0.153419	+	0.170389i	0.661536	+	0.749914i	$0.269905\pi$
$192$	−2.26809	+	0.238386i	−0.163685	+	0.0172040i
$193$	−7.95278	−	4.59154i	−0.572454	−	0.330506i	0.185675	−	0.982611i	$-0.440553\pi$
$193$	−7.95278	−	4.59154i	−0.572454	−	0.330506i	−0.758129	+	0.652105i	$0.773886\pi$
$194$	−2.24069	−	0.997620i	−0.160872	−	0.0716250i
$195$	−19.2071	−	6.92573i	−1.37545	−	0.495962i
$196$	6.81778	+	1.58679i	0.486984	+	0.113342i
$197$	−2.09879	+	2.88874i	−0.149533	+	0.205814i	−0.877212	−	0.480104i	$-0.840599\pi$
$197$	−2.09879	+	2.88874i	−0.149533	+	0.205814i	0.727679	+	0.685918i	$0.240599\pi$
$198$	−0.301199	−	1.41703i	−0.0214053	−	0.100704i
$199$	8.48664	−	14.6993i	0.601602	−	1.04201i	−0.390976	−	0.920401i	$-0.627863\pi$
$199$	8.48664	−	14.6993i	0.601602	−	1.04201i	0.992579	−	0.121605i	$-0.0388040\pi$
$200$	−4.99582	+	0.204421i	−0.353258	+	0.0144547i
$201$	9.51312	+	16.4772i	0.671004	+	1.16221i
$202$	3.11537	+	1.01224i	0.219196	+	0.0712212i
$203$	11.9061	−	8.47655i	0.835643	−	0.594937i
$204$	−12.0490	−	8.75408i	−0.843596	−	0.612908i
$205$	−17.1233	−	16.4369i	−1.19594	−	1.14801i
$206$	−0.667055	−	6.34661i	−0.0464760	−	0.442189i
$207$	0.694367	+	0.400893i	0.0482618	+	0.0278640i
$208$	−1.62850	+	3.65766i	−0.112916	+	0.253613i
$209$	−0.470429	−	1.44783i	−0.0325403	−	0.100149i
$210$	−9.64314	−	9.43646i	−0.665440	−	0.651178i
$211$	−8.65259	+	26.6299i	−0.595669	+	1.83328i	−0.0442995	+	0.999018i	$0.514106\pi$
$211$	−8.65259	+	26.6299i	−0.595669	+	1.83328i	−0.551369	+	0.834261i	$0.685894\pi$
$212$	−7.84755	−	7.06597i	−0.538972	−	0.485293i
$213$	−7.22155	+	33.9747i	−0.494813	+	2.32791i
$214$	−4.33780	−	4.81761i	−0.296526	−	0.329325i
$215$	−3.66685	−	6.84680i	−0.250077	−	0.466948i
$216$	−0.563048	−	1.73288i	−0.0383106	−	0.117908i
$217$	−8.13032	−	1.81004i	−0.551922	−	0.122873i
$218$			2.99613i			0.202924i
$219$	29.1362	+	12.9723i	1.96884	+	0.876584i
$220$	−1.46783	+	0.107059i	−0.0989613	+	0.00721790i
$221$	−23.8863	+	10.6349i	−1.60677	+	0.715380i
$222$	5.68338	+	0.597348i	0.381444	+	0.0400914i
$223$	−11.5704	−	3.75945i	−0.774812	−	0.251752i	−0.105188	−	0.994452i	$-0.533545\pi$
$223$	−11.5704	−	3.75945i	−0.774812	−	0.251752i	−0.669624	+	0.742701i	$0.733545\pi$
$224$	−1.98311	+	1.75136i	−0.132502	+	0.117018i
$225$	2.72632	+	10.6622i	0.181755	+	0.710815i
$226$	−3.97650	−	6.88750i	−0.264513	−	0.458149i
$227$	20.8920	−	18.8113i	1.38665	−	1.24855i	0.452459	−	0.891785i	$-0.350547\pi$
$227$	20.8920	−	18.8113i	1.38665	−	1.24855i	0.934195	−	0.356763i	$-0.116120\pi$
$228$	2.14549	+	4.81886i	0.142089	+	0.319137i
$229$	0.254989	−	2.42606i	0.0168501	−	0.160318i	−0.982861	−	0.184347i	$-0.940983\pi$
$229$	0.254989	−	2.42606i	0.0168501	−	0.160318i	0.999711	+	0.0240293i	$0.00764949\pi$
$230$	0.499557	−	0.643365i	0.0329398	−	0.0424222i
$231$	−2.92560	−	2.68561i	−0.192490	−	0.176700i
$232$			5.52406i			0.362672i
$233$	4.85366	−	10.9015i	0.317974	−	0.714181i	−0.681877	−	0.731467i	$-0.738836\pi$
$233$	4.85366	−	10.9015i	0.317974	−	0.714181i	0.999851	+	0.0172862i	$0.00550265\pi$
$234$	8.62002	+	1.83224i	0.563508	+	0.119777i
$235$	14.3922	−	5.86503i	0.938846	−	0.382593i
$236$	3.08830	−	0.656439i	0.201031	−	0.0427306i
$237$	−18.6922	+	6.07345i	−1.21419	+	0.394513i
$238$	−17.2773	−	0.166144i	−1.11992	−	0.0107695i
$239$	−1.55979	+	4.80054i	−0.100894	+	0.310521i	−0.988745	−	0.149611i	$-0.952198\pi$
$239$	−1.55979	+	4.80054i	−0.100894	+	0.310521i	0.887851	+	0.460132i	$0.152198\pi$
$240$	5.01939	−	0.900560i	0.324000	−	0.0581309i
$241$	−26.1201	−	5.55200i	−1.68254	−	0.357636i	−0.735199	−	0.677851i	$-0.762911\pi$
$241$	−26.1201	−	5.55200i	−1.68254	−	0.357636i	−0.947345	+	0.320216i	$0.896245\pi$
$242$	10.5089	−	1.10453i	0.675539	−	0.0710020i
$243$	−16.5147	+	9.53475i	−1.05942	+	0.611655i
$244$	−5.91384	+	4.29665i	−0.378595	+	0.275065i
$245$	−15.4627	−	2.42979i	−0.987878	−	0.155234i
$246$	19.5848	+	14.2292i	1.24868	+	0.907219i
$247$	9.20991	+	0.968001i	0.586013	+	0.0615924i
$248$	2.33957	−	2.10656i	0.148563	−	0.133767i
$249$	17.1466	−	29.6987i	1.08662	−	1.88208i
$250$	11.1081	−	1.26850i	0.702541	−	0.0802272i
$251$	0.542533			0.0342444			0.0171222	−	0.999853i	$-0.494550\pi$
$251$	0.542533			0.0342444			0.0171222	+	0.999853i	$0.494550\pi$
$252$	4.67813	+	3.46808i	0.294695	+	0.218468i
$253$	0.140926	−	0.193968i	0.00885992	−	0.0121946i
$254$	0.650390	−	6.18805i	0.0408091	−	0.388273i
$255$	28.2948	+	17.5630i	1.77189	+	1.09984i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	0.176988	−	0.102184i	0.0110402	−	0.00637406i	−0.494470	−	0.869195i	$-0.664638\pi$
$257$	0.176988	−	0.102184i	0.0110402	−	0.00637406i	0.505510	+	0.862821i	$0.331304\pi$
$258$	4.65614	+	6.40863i	0.289879	+	0.398984i
$259$	5.77313	−	3.25950i	0.358725	−	0.202536i
$260$	3.03683	−	8.42200i	0.188336	−	0.522310i
$261$	11.8931	−	2.52795i	0.736162	−	0.156476i
$262$	2.97630	−	14.0024i	0.183876	−	0.865069i
$263$	−5.15531	+	24.2538i	−0.317890	+	1.49556i	0.471611	+	0.881807i	$0.343673\pi$
$263$	−5.15531	+	24.2538i	−0.317890	+	1.49556i	−0.789501	+	0.613749i	$0.789661\pi$
$264$	1.46823	−	0.312082i	0.0903633	−	0.0192073i
$265$	18.6505	+	14.4817i	1.14569	+	0.889601i
$266$	5.26999	+	3.11058i	0.323124	+	0.190722i
$267$	−15.2105	−	20.9354i	−0.930866	−	1.28123i
$268$	−7.22500	+	4.17136i	−0.441337	+	0.254806i
$269$	−2.21327	−	21.0579i	−0.134946	−	1.28392i	−0.827052	−	0.562126i	$-0.809984\pi$
$269$	−2.21327	−	21.0579i	−0.134946	−	1.28392i	0.692106	−	0.721796i	$-0.256683\pi$
$270$	1.53755	+	3.77299i	0.0935721	+	0.229617i
$271$	2.56883	−	24.4408i	0.156045	−	1.48467i	−0.583801	−	0.811897i	$-0.698435\pi$
$271$	2.56883	−	24.4408i	0.156045	−	1.48467i	0.739847	−	0.672776i	$-0.234898\pi$
$272$	3.83853	−	5.28328i	0.232745	−	0.320346i
$273$	22.1632	−	9.61343i	1.34138	−	0.581831i
$274$	−11.0935			−0.670180
$275$	3.25607	−	0.477513i	0.196348	−	0.0287951i
$276$	−0.415378	+	0.719455i	−0.0250028	+	0.0433061i
$277$	−7.12548	+	6.41581i	−0.428128	+	0.385489i	−0.854834	−	0.518902i	$-0.826341\pi$
$277$	−7.12548	+	6.41581i	−0.428128	+	0.385489i	0.426705	+	0.904391i	$0.359674\pi$
$278$	17.1725	+	1.80490i	1.02994	+	0.108251i
$279$	−5.60597	−	4.07298i	−0.335621	−	0.243843i
$280$	4.13774	−	4.22837i	0.247277	−	0.252693i
$281$	7.52897	−	5.47012i	0.449141	−	0.326320i	−0.340116	−	0.940384i	$-0.610466\pi$
$281$	7.52897	−	5.47012i	0.449141	−	0.326320i	0.789256	+	0.614064i	$0.210466\pi$
$282$	−13.7272	+	7.92539i	−0.817442	+	0.471950i
$283$	5.47468	−	0.575412i	0.325436	−	0.0342047i	0.0595980	−	0.998222i	$-0.481018\pi$
$283$	5.47468	−	0.575412i	0.325436	−	0.0342047i	0.265838	+	0.964018i	$0.414351\pi$
$284$	−14.8974	−	3.16654i	−0.883998	−	0.187900i
$285$	−5.56859	−	10.3978i	−0.329855	−	0.615910i
$286$	0.814328	−	2.50624i	0.0481522	−	0.148197i
$287$	28.0831	+	0.270056i	1.65769	+	0.0159409i
$288$	−2.09333	+	0.680163i	−0.123350	+	0.0400790i
$289$	25.0869	−	5.33239i	1.47570	−	0.313670i
$290$	−0.898538	−	12.3194i	−0.0527640	−	0.723423i
$291$	−5.47144	−	1.16299i	−0.320742	−	0.0681758i
$292$	−5.68814	+	12.7758i	−0.332873	+	0.747645i
$293$		−	16.9861i		−	0.992336i	−0.868227	−	0.496168i	$-0.834740\pi$
$293$		−	16.9861i		−	0.992336i	0.868227	−	0.496168i	$-0.165260\pi$
$294$	15.9611	+	0.307004i	0.930872	+	0.0179048i
$295$	−6.78059	+	1.96629i	−0.394781	+	0.114482i
$296$	−0.261928	+	2.49208i	−0.0152242	+	0.144849i
$297$	0.487776	+	1.09556i	0.0283036	+	0.0635710i
$298$	1.89627	−	1.70741i	0.109848	−	0.0989077i
$299$	0.729240	+	1.26308i	0.0421731	+	0.0730459i
$300$	−11.0475	+	2.82483i	−0.637826	+	0.163091i
$301$	8.71240	+	2.92375i	0.502174	+	0.168522i
$302$	1.02040	+	0.331548i	0.0587174	+	0.0190784i
$303$	7.42955	+	0.780878i	0.426817	+	0.0448602i
$304$	−2.11299	+	0.940765i	−0.121189	+	0.0539566i
$305$	12.4898	−	10.5441i	0.715165	−	0.603753i
$306$	−13.1313	−	5.84642i	−0.750665	−	0.334218i
$307$			22.2416i			1.26940i	0.772760	+	0.634699i	$0.218876\pi$
$307$			22.2416i			1.26940i	−0.772760	+	0.634699i	$0.781124\pi$
$308$	1.17760	−	1.28283i	0.0670999	−	0.0730961i
$309$	−4.49734	−	13.8414i	−0.255845	−	0.787409i
$310$	−4.87493	+	5.07848i	−0.276877	+	0.288438i
$311$	1.98561	+	2.20524i	0.112594	+	0.125048i	0.796807	−	0.604234i	$-0.206521\pi$
$311$	1.98561	+	2.20524i	0.112594	+	0.125048i	−0.684213	+	0.729282i	$0.739854\pi$
$312$	−1.89844	+	8.93148i	−0.107478	+	0.505645i
$313$	22.8100	+	20.5382i	1.28930	+	1.16089i	0.977545	+	0.210725i	$0.0675825\pi$
$313$	22.8100	+	20.5382i	1.28930	+	1.16089i	0.311752	+	0.950164i	$0.399084\pi$
$314$	4.57065	−	14.0670i	0.257937	−	0.793847i
$315$	−10.9970	−	6.97337i	−0.619612	−	0.392905i
$316$	−2.66312	−	8.19623i	−0.149812	−	0.461074i
$317$	1.77369	−	3.98378i	0.0996205	−	0.223751i	−0.856859	−	0.515551i	$-0.827587\pi$
$317$	1.77369	−	3.98378i	0.0996205	−	0.223751i	0.956480	+	0.291799i	$0.0942540\pi$
$318$	−20.8563	−	12.0414i	−1.16956	−	0.675247i
$319$	−0.380047	−	3.61590i	−0.0212785	−	0.202452i
$320$	0.394882	+	2.20092i	0.0220745	+	0.123035i
$321$	−11.9608	−	8.69006i	−0.667589	−	0.485032i
$322$	0.0915207	+	0.959422i	0.00510025	+	0.0534665i
$323$	−14.3655	−	4.66763i	−0.799318	−	0.259714i
$324$	−5.37926	−	9.31715i	−0.298848	−	0.517620i
$325$	−5.40265	+	19.2762i	−0.299685	+	1.06925i
$326$	3.25522	−	5.63821i	0.180290	−	0.312271i
$327$	1.42065	+	6.68361i	0.0785619	+	0.369605i
$328$	−6.23928	+	8.58763i	−0.344506	+	0.474172i
$329$	−7.64060	+	16.7263i	−0.421240	+	0.922153i
$330$	−3.22360	+	0.934808i	−0.177453	+	0.0514595i
$331$	−8.35562	−	3.72016i	−0.459266	−	0.204479i	0.164044	−	0.986453i	$-0.447546\pi$
$331$	−8.35562	−	3.72016i	−0.459266	−	0.204479i	−0.623311	+	0.781974i	$0.714213\pi$
$332$	13.0224	+	7.51850i	0.714698	+	0.412631i
$333$	5.48519	−	0.576517i	0.300587	−	0.0315929i
$334$	−1.17198	+	1.30162i	−0.0641279	+	0.0712212i
$335$	15.4343	−	10.4779i	0.843265	−	0.572471i
$336$	−3.59339	+	4.84716i	−0.196035	+	0.264434i
$337$	23.4938	−	7.63360i	1.27979	−	0.415829i	0.411283	−	0.911508i	$-0.365081\pi$
$337$	23.4938	−	7.63360i	1.27979	−	0.415829i	0.868506	+	0.495679i	$0.165081\pi$
$338$	2.25208	+	2.02778i	0.122497	+	0.110297i
$339$	−12.1363	−	13.4788i	−0.659155	−	0.732066i
$340$	−7.70110	+	12.4069i	−0.417651	+	0.672856i
$341$	−1.38649	+	1.53986i	−0.0750828	+	0.0833879i
$342$	2.99239	+	4.11866i	0.161810	+	0.222712i
$343$	15.2910	−	10.4492i	0.825635	−	0.564205i
$344$	−2.81008	+	2.04164i	−0.151510	+	0.110078i
$345$	0.809326	−	1.67205i	0.0435727	−	0.0900204i
$346$	−22.8097	+	10.1556i	−1.22626	+	0.545966i
$347$	−3.66174	−	8.22440i	−0.196572	−	0.441509i	0.788186	−	0.615437i	$-0.211021\pi$
$347$	−3.66174	−	8.22440i	−0.196572	−	0.441509i	−0.984758	+	0.173928i	$0.944354\pi$
$348$	2.61929	+	12.3228i	0.140408	+	0.660570i
$349$	−4.88619			−0.261552			−0.130776	−	0.991412i	$-0.541747\pi$
$349$	−4.88619			−0.261552			−0.130776	+	0.991412i	$0.541747\pi$
$350$	−8.53998	+	10.1029i	−0.456481	+	0.540023i
$351$	−7.29518			−0.389388
$352$	0.136843	+	0.643796i	0.00729376	+	0.0343144i
$353$	15.0334	+	33.7655i	0.800145	+	1.79715i	0.564768	+	0.825250i	$0.308966\pi$
$353$	15.0334	+	33.7655i	0.800145	+	1.79715i	0.235377	+	0.971904i	$0.424368\pi$
$354$	6.57796	−	2.92870i	0.349615	−	0.155659i
$355$	33.7384	+	4.63864i	1.79065	+	0.246194i
$356$	9.17986	−	6.66956i	0.486532	−	0.353486i
$357$	−38.6200	+	7.82156i	−2.04399	+	0.413961i
$358$	−9.55481	−	13.1511i	−0.504987	−	0.695055i
$359$	−10.7673	+	11.9583i	−0.568275	+	0.631133i	−0.956954	−	0.290240i	$-0.906265\pi$
$359$	−10.7673	+	11.9583i	−0.568275	+	0.631133i	0.388679	+	0.921373i	$0.372932\pi$
$360$	4.55779	−	1.85736i	0.240216	−	0.0978915i
$361$	−9.13378	−	10.1441i	−0.480725	−	0.533899i
$362$	−12.5478	−	11.2981i	−0.659496	−	0.593813i
$363$	22.9190	−	7.44683i	1.20294	−	0.390857i
$364$	4.21534	+	9.71824i	0.220944	+	0.509374i
$365$	10.6073	−	29.4170i	0.555210	−	1.53976i
$366$	−11.1550	+	12.3888i	−0.583079	+	0.647575i
$367$	−9.91207	+	1.04180i	−0.517406	+	0.0543816i	−0.359633	−	0.933094i	$-0.617098\pi$
$367$	−9.91207	+	1.04180i	−0.517406	+	0.0543816i	−0.157773	+	0.987475i	$0.550431\pi$
$368$	−0.315470	−	0.182137i	−0.0164450	−	0.00949453i
$369$	21.3440	+	9.50297i	1.11113	+	0.494705i
$370$	0.178778	−	5.60029i	0.00929422	−	0.291145i
$371$	−27.8127	+	2.65309i	−1.44396	+	0.137742i
$372$	4.22014	−	5.80853i	0.218804	−	0.301158i
$373$	1.01912	+	4.79459i	0.0527681	+	0.248255i	0.996624	−	0.0821035i	$-0.0261638\pi$
$373$	1.01912	+	4.79459i	0.0527681	+	0.248255i	−0.943856	+	0.330358i	$0.892830\pi$
$374$	−2.14912	+	3.72238i	−0.111128	+	0.192480i
$375$	24.1780	−	8.09674i	1.24855	−	0.418114i
$376$	−3.47516	−	6.01916i	−0.179218	−	0.310414i
$377$	21.0348	+	6.83461i	1.08335	+	0.352000i
$378$	−4.38489	−	2.00302i	−0.225534	−	0.103024i
$379$	−6.41239	−	4.65888i	−0.329383	−	0.239310i	0.410786	−	0.911732i	$-0.365254\pi$
$379$	−6.41239	−	4.65888i	−0.329383	−	0.239310i	−0.740169	+	0.672421i	$0.765254\pi$
$380$	4.55926	−	2.44174i	0.233885	−	0.125259i
$381$	−1.48327	−	14.1124i	−0.0759901	−	0.722998i
$382$	−2.74420	−	1.58436i	−0.140405	−	0.0810630i
$383$	−8.96320	+	20.1317i	−0.457998	+	1.02868i	0.525997	+	0.850486i	$0.323692\pi$
$383$	−8.96320	+	20.1317i	−0.457998	+	1.02868i	−0.983995	+	0.178194i	$0.942974\pi$
$384$	−0.704739	−	2.16896i	−0.0359635	−	0.110684i
$385$	−2.41755	+	3.05245i	−0.123210	+	0.155567i
$386$	2.83773	−	8.73363i	0.144437	−	0.444530i
$387$	5.68154	+	5.11568i	0.288809	+	0.260044i
$388$	0.509954	−	2.39914i	0.0258890	−	0.121798i
$389$	19.7268	+	21.9088i	1.00019	+	1.11082i	0.993838	+	0.110842i	$0.0353547\pi$
$389$	19.7268	+	21.9088i	1.00019	+	1.11082i	0.00635028	+	0.999980i	$0.497979\pi$
$390$	2.78102	−	20.2273i	0.140822	−	1.02425i
$391$	−0.735116	−	2.26246i	−0.0371764	−	0.114417i
$392$	−0.134616	+	6.99871i	−0.00679916	+	0.353488i
$393$		−	32.6470i		−	1.64682i
$394$	−3.26198	−	1.45233i	−0.164336	−	0.0731671i
$395$	7.27232	+	17.8456i	0.365910	+	0.897909i
$396$	1.32344	−	0.589234i	0.0665054	−	0.0296101i
$397$	−24.8015	−	2.60674i	−1.24475	−	0.130829i	−0.540845	−	0.841122i	$-0.681895\pi$
$397$	−24.8015	−	2.60674i	−1.24475	−	0.130829i	−0.703905	+	0.710294i	$0.748562\pi$
$398$	16.1426	+	5.24503i	0.809153	+	0.262910i
$399$	13.2309	+	4.44009i	0.662374	+	0.222283i
$400$	−1.23864	−	4.84415i	−0.0619321	−	0.242207i
$401$	−14.5124	−	25.1362i	−0.724715	−	1.25524i	−0.959091	−	0.283098i	$-0.908638\pi$
$401$	−14.5124	−	25.1362i	−0.724715	−	1.25524i	0.234376	−	0.972146i	$-0.424695\pi$
$402$	−14.1392	+	12.7310i	−0.705202	+	0.634966i
$403$	−5.12683	−	11.5151i	−0.255386	−	0.573606i
$404$	−0.342403	+	3.25774i	−0.0170352	+	0.162079i
$405$	13.5120	+	19.9036i	0.671419	+	0.989018i
$406$	10.7667	+	9.88352i	0.534344	+	0.490511i
$407$		−	1.64927i		−	0.0817511i
$408$	6.05766	−	13.6057i	0.299899	−	0.673584i
$409$	31.3656	+	6.66696i	1.55093	+	0.329660i	0.902185	−	0.431348i	$-0.141962\pi$
$409$	31.3656	+	6.66696i	1.55093	+	0.329660i	0.648742	+	0.761008i	$0.275295\pi$
$410$	12.5176	−	20.1665i	0.618202	−	0.995953i
$411$	−24.7467	+	5.26007i	−1.22066	+	0.259460i
$412$	6.06923	−	1.97201i	0.299010	−	0.0971541i
$413$	4.24608	−	7.19378i	0.208936	−	0.353983i
$414$	−0.247765	+	0.762543i	−0.0121770	+	0.0374770i
$415$	−30.2648	−	14.6491i	−1.48564	−	0.719097i
$416$	−3.91631	−	0.832438i	−0.192013	−	0.0408136i
$417$	39.1632	−	4.11622i	1.91783	−	0.201572i
$418$	1.31839	−	0.761170i	0.0644844	−	0.0372301i
$419$	−14.6138	+	10.6175i	−0.713930	+	0.518701i	−0.884439	−	0.466655i	$-0.845459\pi$
$419$	−14.6138	+	10.6175i	−0.713930	+	0.518701i	0.170509	+	0.985356i	$0.445459\pi$
$420$	7.22533	−	11.3944i	0.352560	−	0.555988i
$421$	7.35700	+	5.34517i	0.358558	+	0.260508i	0.752450	−	0.658649i	$-0.228872\pi$
$421$	7.35700	+	5.34517i	0.358558	+	0.260508i	−0.393892	+	0.919157i	$0.628872\pi$
$422$	−27.8470	−	2.92683i	−1.35557	−	0.142476i
$423$	−11.3687	+	10.2364i	−0.552763	+	0.497710i
$424$	5.27996	−	9.14516i	0.256418	−	0.444128i
$425$	15.1565	−	28.9217i	0.735197	−	1.40291i
$426$	−34.7337			−1.68286
$427$	−2.20646	+	19.2139i	−0.106778	+	0.929826i
$428$	3.81046	−	5.24464i	0.184185	−	0.253509i
$429$	0.628199	−	5.97692i	0.0303297	−	0.288568i
$430$	5.93480	−	5.01025i	0.286201	−	0.241616i
$431$	−2.39074	−	22.7463i	−0.115158	−	1.09565i	−0.887615	−	0.460586i	$-0.847639\pi$
$431$	−2.39074	−	22.7463i	−0.115158	−	1.09565i	0.772457	−	0.635067i	$-0.219027\pi$
$432$	1.57795	−	0.911031i	0.0759192	−	0.0438320i
$433$	14.7683	+	20.3268i	0.709718	+	0.976843i	0.999803	+	0.0198420i	$0.00631632\pi$
$433$	14.7683	+	20.3268i	0.709718	+	0.976843i	−0.290085	+	0.957001i	$0.593684\pi$
$434$	0.0800944	−	8.32898i	0.00384465	−	0.399804i
$435$	−7.84580	−	27.0555i	−0.376177	−	1.29721i
$436$	−2.93066	+	0.622931i	−0.140353	+	0.0298330i
$437$	−0.175176	+	0.824138i	−0.00837980	+	0.0394239i
$438$	−6.63104	+	31.1966i	−0.316843	+	1.49063i
$439$	8.87450	−	1.88633i	0.423557	−	0.0900297i	0.00879817	−	0.999961i	$-0.497199\pi$
$439$	8.87450	−	1.88633i	0.423557	−	0.0900297i	0.414758	+	0.909932i	$0.363866\pi$
$440$	−0.409899	−	1.41350i	−0.0195412	−	0.0673859i
$441$	15.1295	−	2.91296i	0.720453	−	0.138712i
$442$	−15.3687	−	21.1532i	−0.731016	−	1.00616i
$443$	−0.705410	+	0.407268i	−0.0335150	+	0.0193499i	−0.516664	−	0.856188i	$-0.672826\pi$
$443$	−0.705410	+	0.407268i	−0.0335150	+	0.0193499i	0.483149	+	0.875538i	$0.339493\pi$
$444$	0.597348	+	5.68338i	0.0283489	+	0.269721i
$445$	−19.3875	+	16.3673i	−0.919058	+	0.775883i
$446$	1.27168	−	12.0992i	0.0602157	−	0.572914i
$447$	3.42052	−	4.70794i	0.161785	−	0.222678i
$448$	−2.12540	−	1.57564i	−0.100416	−	0.0744422i
$449$	−19.6554			−0.927595			−0.463797	−	0.885941i	$-0.653513\pi$
$449$	−19.6554			−0.927595			−0.463797	+	0.885941i	$0.653513\pi$
$450$	−9.86240	+	4.88355i	−0.464918	+	0.230213i
$451$	3.49325	−	6.05048i	0.164491	−	0.284906i
$452$	5.91023	−	5.32159i	0.277994	−	0.250307i
$453$	2.43346	+	0.255767i	0.114334	+	0.0120170i
$454$	22.7439	+	16.5244i	1.06742	+	0.775529i
$455$	−10.9816	−	20.9874i	−0.514824	−	0.983905i
$456$	−4.26748	+	3.10050i	−0.199843	+	0.145194i
$457$	−3.55478	+	2.05235i	−0.166285	+	0.0960049i	−0.580833	−	0.814023i	$-0.697273\pi$
$457$	−3.55478	+	2.05235i	−0.166285	+	0.0960049i	0.414548	+	0.910028i	$0.363940\pi$
$458$	2.42606	−	0.254989i	0.113362	−	0.0119148i
$459$	11.6389	+	2.47393i	0.543259	+	0.115473i
$460$	0.733170	+	0.354877i	0.0341842	+	0.0165462i
$461$	−1.79745	+	5.53200i	−0.0837158	+	0.257651i	−0.984149	−	0.177344i	$-0.943250\pi$
$461$	−1.79745	+	5.53200i	−0.0837158	+	0.257651i	0.900433	+	0.434994i	$0.143250\pi$
$462$	2.01866	−	3.42004i	0.0939164	−	0.159115i
$463$	22.0433	−	7.16230i	1.02444	−	0.332860i	0.251849	−	0.967766i	$-0.418961\pi$
$463$	22.0433	−	7.16230i	1.02444	−	0.332860i	0.772589	+	0.634906i	$0.218961\pi$
$464$	−5.40335	+	1.14852i	−0.250844	+	0.0533185i
$465$	−8.46672	+	13.6403i	−0.392635	+	0.632554i
$466$	11.6724	+	2.48105i	0.540714	+	0.114932i
$467$	−10.6949	+	24.0212i	−0.494901	+	1.11157i	0.477580	+	0.878588i	$0.341514\pi$
$467$	−10.6949	+	24.0212i	−0.494901	+	1.11157i	−0.972482	+	0.232979i	$0.925153\pi$
$468$			8.81260i			0.407362i
$469$	−4.79658	+	21.5453i	−0.221485	+	0.994868i
$470$	8.72918	+	12.8583i	0.402647	+	0.593110i
$471$	3.52595	−	33.5471i	0.162467	−	1.54577i
$472$	1.28419	+	2.88434i	0.0591096	+	0.132762i
$473$	1.69894	−	1.52974i	0.0781175	−	0.0703373i
$474$	−9.82706	−	17.0210i	−0.451372	−	0.781799i
$475$	−9.77063	+	6.18704i	−0.448307	+	0.283881i
$476$	−3.42963	−	16.9343i	−0.157197	−	0.776181i
$477$	−22.1054	−	7.18247i	−1.01214	−	0.328863i
$478$	−5.01993	−	0.527616i	−0.229606	−	0.0241326i
$479$	−27.1201	+	12.0747i	−1.23915	+	0.551705i	−0.918473	−	0.395484i	$-0.870577\pi$
$479$	−27.1201	+	12.0747i	−1.23915	+	0.551705i	−0.320677	+	0.947189i	$0.603910\pi$
$480$	1.92447	+	4.72247i	0.0878396	+	0.215550i
$481$	9.16538	+	4.08069i	0.417905	+	0.186063i
$482$		−	26.7036i		−	1.21632i
$483$	0.659078	+	2.09683i	0.0299891	+	0.0954091i
$484$	3.26532	+	10.0496i	0.148424	+	0.456801i
$485$	−0.747028	+	5.43339i	−0.0339208	+	0.246717i
$486$	−12.7600	−	14.1714i	−0.578805	−	0.642828i
$487$	−6.89507	+	32.4388i	−0.312446	+	1.46994i	0.489216	+	0.872163i	$0.337283\pi$
$487$	−6.89507	+	32.4388i	−0.312446	+	1.46994i	−0.801661	+	0.597778i	$0.796050\pi$
$488$	−5.43232	−	4.89128i	−0.245909	−	0.221418i
$489$	4.58816	−	14.1209i	0.207484	−	0.638569i
$490$	−0.838189	−	15.6300i	−0.0378655	−	0.706092i
$491$	9.13814	+	28.1243i	0.412398	+	1.26923i	0.914557	+	0.404456i	$0.132539\pi$
$491$	9.13814	+	28.1243i	0.412398	+	1.26923i	−0.502159	+	0.864775i	$0.667461\pi$
$492$	−9.84633	+	22.1152i	−0.443907	+	0.997031i
$493$	−31.2417	−	18.0374i	−1.40706	−	0.812365i
$494$	0.968001	+	9.20991i	0.0435524	+	0.414374i
$495$	−2.85562	+	1.52935i	−0.128351	+	0.0687390i
$496$	2.54695	+	1.85047i	0.114361	+	0.0830884i
$497$	−32.8259	+	23.3704i	−1.47244	+	1.04831i
$498$	32.6147	+	10.5972i	1.46150	+	0.474870i
$499$	3.90044	+	6.75576i	0.174608	+	0.302429i	0.940025	−	0.341104i	$-0.110801\pi$
$499$	3.90044	+	6.75576i	0.174608	+	0.302429i	−0.765418	+	0.643534i	$0.777468\pi$
$500$	3.55030	+	10.6017i	0.158774	+	0.474121i
$501$	−1.99722	+	3.45928i	−0.0892290	+	0.154549i
$502$	0.112799	+	0.530677i	0.00503446	+	0.0236853i
$503$	−8.18531	+	11.2661i	−0.364965	+	0.502331i	−0.951524	−	0.307576i	$-0.900482\pi$
$503$	−8.18531	+	11.2661i	−0.364965	+	0.502331i	0.586559	+	0.809907i	$0.300482\pi$
$504$	−2.41965	+	5.29696i	−0.107780	+	0.235945i
$505$	0.233706	−	7.32093i	0.0103998	−	0.325777i
$506$	0.219029	+	0.0975180i	0.00973703	+	0.00433520i
$507$	5.98531	+	3.45562i	0.265817	+	0.153470i
$508$	6.18805	−	0.650390i	0.274550	−	0.0288564i
$509$	26.5486	−	29.4852i	1.17675	−	1.30691i	0.234449	−	0.972128i	$-0.424671\pi$
$509$	26.5486	−	29.4852i	1.17675	−	1.30691i	0.942296	−	0.334780i	$-0.108662\pi$
$510$	−11.2964	+	31.3281i	−0.500212	+	1.38723i
$511$	14.7237	+	33.9447i	0.651337	+	1.50162i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−3.13188	−	2.81995i	−0.138276	−	0.124504i
$514$	0.136749	+	0.151875i	0.00603173	+	0.00669892i
$515$	−13.2145	+	5.38509i	−0.582300	+	0.237295i
$516$	−5.30052	+	5.88682i	−0.233342	+	0.259153i
$517$	2.68886	+	3.70089i	0.118256	+	0.162765i
$518$	4.38858	+	4.96928i	0.192823	+	0.218338i
$519$	−46.0674	+	33.4699i	−2.02213	+	1.46917i
$520$	8.86935	+	1.21943i	0.388947	+	0.0534757i
$521$	26.2640	−	11.6935i	1.15065	−	0.512301i	0.259377	−	0.965776i	$-0.416483\pi$
$521$	26.2640	−	11.6935i	1.15065	−	0.512301i	0.891269	+	0.453475i	$0.149816\pi$
$522$	4.94541	+	11.1076i	0.216455	+	0.486165i
$523$	−6.27695	−	29.5307i	−0.274472	−	1.29129i	−0.872026	−	0.489459i	$-0.837194\pi$
$523$	−6.27695	−	29.5307i	−0.274472	−	1.29129i	0.597554	−	0.801828i	$-0.296139\pi$
$524$	14.3152			0.625362
$525$	−14.2601	+	26.5863i	−0.622363	+	1.16032i
$526$	−24.7957			−1.08114
$527$	4.27453	+	20.1101i	0.186201	+	0.876008i
$528$	0.610524	+	1.37126i	0.0265697	+	0.0596764i
$529$	20.8903	−	9.30097i	0.908275	−	0.404390i
$530$	−10.2875	+	21.2539i	−0.446862	+	0.923209i
$531$	5.62217	−	4.08475i	0.243981	−	0.177263i
$532$	−1.94691	+	5.80155i	−0.0844093	+	0.251529i
$533$	24.9809	+	34.3832i	1.08204	+	1.48930i
$534$	17.3155	−	19.2308i	0.749315	−	0.832199i
$535$	−7.64478	+	12.3161i	−0.330513	+	0.532472i
$536$	−5.58236	−	6.19984i	−0.241121	−	0.267792i
$537$	−27.5501	−	24.8062i	−1.18887	−	1.07047i
$538$	20.1376	−	6.54309i	0.868192	−	0.282093i
$539$	−0.393384	−	4.59043i	−0.0169442	−	0.197724i
$540$	−3.37087	+	2.28840i	−0.145059	+	0.0984770i
$541$	3.66417	−	4.06947i	0.157535	−	0.174960i	−0.659211	−	0.751958i	$-0.729109\pi$
$541$	3.66417	−	4.06947i	0.157535	−	0.174960i	0.816745	+	0.576998i	$0.195776\pi$
$542$	24.4408	−	2.56883i	1.04982	−	0.110341i
$543$	−33.3480	−	19.2535i	−1.43110	−	0.826245i
$544$	5.96591	+	2.65619i	0.255786	+	0.113883i
$545$	6.43447	−	1.86593i	0.275622	−	0.0799275i
$546$	14.0113	+	19.6802i	0.599630	+	0.842234i
$547$	−18.4932	+	25.4538i	−0.790714	+	1.08832i	0.203305	+	0.979116i	$0.434832\pi$
$547$	−18.4932	+	25.4538i	−0.790714	+	1.08832i	−0.994019	+	0.109209i	$0.965168\pi$
$548$	−2.30646	−	10.8510i	−0.0985271	−	0.463533i
$549$	−8.04475	+	13.9339i	−0.343341	+	0.594685i
$550$	1.14405	+	3.08563i	0.0487825	+	0.131572i
$551$	6.38846	+	11.0651i	0.272158	+	0.471391i
$552$	−0.790095	−	0.256718i	−0.0336287	−	0.0109266i
$553$	−20.7397	−	9.47393i	−0.881944	−	0.402873i
$554$	−7.75708	−	5.63585i	−0.329567	−	0.239444i
$555$	−2.25663	−	12.5776i	−0.0957884	−	0.533889i
$556$	1.80490	+	17.1725i	0.0765448	+	0.728275i
$557$	4.42676	+	2.55579i	0.187568	+	0.108292i	0.590843	−	0.806786i	$-0.298795\pi$
$557$	4.42676	+	2.55579i	0.187568	+	0.108292i	−0.403276	+	0.915079i	$0.632128\pi$
$558$	2.81843	−	6.33029i	0.119314	−	0.267983i
$559$	4.29751	+	13.2264i	0.181765	+	0.559416i
$560$	4.99625	+	3.16820i	0.211130	+	0.133881i
$561$	−3.02913	+	9.32271i	−0.127890	+	0.393605i
$562$	6.91594	+	6.22714i	0.291731	+	0.262676i
$563$	−3.52012	+	16.5609i	−0.148355	+	0.697957i	0.839598	+	0.543208i	$0.182790\pi$
$563$	−3.52012	+	16.5609i	−0.148355	+	0.697957i	−0.987954	+	0.154749i	$0.950543\pi$
$564$	−10.6062	−	11.7794i	−0.446604	−	0.496004i
$565$	−12.3151	+	12.8293i	−0.518098	+	0.539731i
$566$	1.70109	+	5.23541i	0.0715020	+	0.220061i
$567$	−27.7842	−	6.18553i	−1.16683	−	0.259768i
$568$		−	15.2302i		−	0.639045i
$569$	10.3398	+	4.60359i	0.433468	+	0.192992i	0.611858	−	0.790967i	$-0.290422\pi$
$569$	10.3398	+	4.60359i	0.433468	+	0.192992i	−0.178390	+	0.983960i	$0.557089\pi$
$570$	9.01277	−	7.60872i	0.377503	−	0.318694i
$571$	−13.8029	+	6.14546i	−0.577635	+	0.257180i	−0.674692	−	0.738099i	$-0.735724\pi$
$571$	−13.8029	+	6.14546i	−0.577635	+	0.257180i	0.0970573	+	0.995279i	$0.469057\pi$
$572$	2.62079	+	0.275456i	0.109581	+	0.0115174i
$573$	−6.87285	−	2.23312i	−0.287117	−	0.0932901i
$574$	5.57464	+	27.5255i	0.232681	+	1.14889i
$575$	−1.69280	−	0.672170i	−0.0705946	−	0.0280314i
$576$	−1.10053	−	1.90617i	−0.0458553	−	0.0794237i
$577$	−13.9776	+	12.5855i	−0.581896	+	0.523942i	−0.906665	−	0.421852i	$-0.861380\pi$
$577$	−13.9776	+	12.5855i	−0.581896	+	0.523942i	0.324769	+	0.945793i	$0.394714\pi$
$578$	10.4317	+	23.4301i	0.433903	+	0.974562i
$579$	2.18912	−	20.8280i	0.0909765	−	0.865584i
$580$	11.8634	−	3.44026i	0.492602	−	0.142849i
$581$	37.9534	−	11.9296i	1.57457	−	0.494922i
$582$		−	5.59368i		−	0.231865i
$583$	−2.82695	+	6.34943i	−0.117080	+	0.262967i
$584$	−13.6792	−	2.90761i	−0.566050	−	0.120318i
$585$	−1.43345	−	19.6534i	−0.0592658	−	0.812566i
$586$	16.6149	−	3.53160i	0.686354	−	0.145889i
$587$	−17.1361	+	5.56787i	−0.707285	+	0.229811i	−0.640502	−	0.767957i	$-0.721274\pi$
$587$	−17.1361	+	5.56787i	−0.707285	+	0.229811i	−0.0667829	+	0.997768i	$0.521274\pi$
$588$	3.01821	+	15.6762i	0.124469	+	0.646474i
$589$	2.25016	−	6.92528i	0.0927162	−	0.285351i
$590$	−3.33309	−	6.22360i	−0.137221	−	0.256221i
$591$	−7.96528	−	1.69307i	−0.327648	−	0.0696437i
$592$	−2.49208	+	0.261928i	−0.102424	+	0.0107652i
$593$	17.2667	−	9.96891i	0.709056	−	0.409374i	−0.101655	−	0.994820i	$-0.532414\pi$
$593$	17.2667	−	9.96891i	0.709056	−	0.409374i	0.810712	+	0.585446i	$0.199080\pi$
$594$	−0.970207	+	0.704897i	−0.0398081	+	0.0289223i
$595$	10.4031	+	37.2080i	0.426485	+	1.52538i
$596$	2.06436	+	1.49984i	0.0845594	+	0.0614360i
$597$	38.4969	+	4.04619i	1.57557	+	0.165599i
$598$	−1.08386	+	0.975914i	−0.0443224	+	0.0399081i
$599$	−3.36397	+	5.82656i	−0.137448	+	0.238067i	−0.926530	−	0.376221i	$-0.877223\pi$
$599$	−3.36397	+	5.82656i	−0.137448	+	0.238067i	0.789082	+	0.614288i	$0.210557\pi$
$600$	−5.06000	−	10.2187i	−0.206573	−	0.417179i
$601$	32.1654			1.31206			0.656028	−	0.754737i	$-0.272235\pi$
$601$	32.1654			1.31206			0.656028	+	0.754737i	$0.272235\pi$
$602$	−1.04845	+	9.12989i	−0.0427315	+	0.372107i
$603$	−10.7934	+	14.8558i	−0.439540	+	0.604974i
$604$	−0.112150	+	1.06703i	−0.00456331	+	0.0434170i
$605$	−8.91680	−	21.8810i	−0.362519	−	0.889588i
$606$	0.780878	+	7.42955i	0.0317210	+	0.301805i
$607$	18.6144	−	10.7470i	0.755537	−	0.436209i	−0.0721543	−	0.997393i	$-0.522987\pi$
$607$	18.6144	−	10.7470i	0.755537	−	0.436209i	0.827691	+	0.561184i	$0.189654\pi$
$608$	−1.35952	−	1.87122i	−0.0551360	−	0.0758881i
$609$	28.7042	+	16.9425i	1.16315	+	0.686544i
$610$	12.9105	+	10.0246i	0.522729	+	0.405886i
$611$	−27.2197	+	5.78572i	−1.10119	+	0.234065i
$612$	2.98852	−	14.0599i	0.120804	−	0.568337i
$613$	0.185175	−	0.871179i	0.00747914	−	0.0351866i	−0.974250	−	0.225471i	$-0.927608\pi$
$613$	0.185175	−	0.871179i	0.00747914	−	0.0351866i	0.981729	+	0.190285i	$0.0609411\pi$
$614$	−21.7556	+	4.62430i	−0.877985	+	0.186621i
$615$	18.3615	−	50.9217i	0.740407	−	2.05336i
$616$	1.49963	+	0.885150i	0.0604220	+	0.0356637i
$617$	3.94755	+	5.43334i	0.158922	+	0.218738i	0.881051	−	0.473020i	$-0.156836\pi$
$617$	3.94755	+	5.43334i	0.158922	+	0.218738i	−0.722129	+	0.691758i	$0.756836\pi$
$618$	12.6039	−	7.27684i	0.507002	−	0.292718i
$619$	−0.927795	−	8.82738i	−0.0372912	−	0.354802i	−0.997217	−	0.0745492i	$-0.976248\pi$
$619$	−0.927795	−	8.82738i	−0.0372912	−	0.354802i	0.959926	−	0.280253i	$-0.0904185\pi$
$620$	−5.98106	−	3.71252i	−0.240205	−	0.149099i
$621$	0.0693785	−	0.660093i	0.00278406	−	0.0264886i
$622$	−1.74422	+	2.40071i	−0.0699369	+	0.0962599i
$623$	3.42502	−	29.8251i	0.137221	−	1.19492i
$624$	−9.13101			−0.365533
$625$	−9.64213	−	23.0658i	−0.385685	−	0.922630i
$626$	−15.3469	+	26.5817i	−0.613387	+	1.06242i
$627$	2.58007	−	2.32310i	0.103038	−	0.0927758i
$628$	14.7099	+	1.54607i	0.586989	+	0.0616950i
$629$	−13.2389	−	9.61860i	−0.527868	−	0.383519i
$630$	4.53458	−	12.2066i	0.180662	−	0.486321i
$631$	26.9301	−	19.5658i	1.07207	−	0.778903i	0.0957857	−	0.995402i	$-0.469464\pi$
$631$	26.9301	−	19.5658i	1.07207	−	0.778903i	0.976283	+	0.216499i	$0.0694637\pi$
$632$	7.46343	−	4.30901i	0.296879	−	0.171403i
$633$	−63.5073	+	6.67489i	−2.52419	+	0.265303i
$634$	4.26550	+	0.906659i	0.169405	+	0.0360080i
$635$	−13.6945	+	2.45701i	−0.543448	+	0.0975033i
$636$	7.44199	−	22.9041i	0.295094	−	0.908206i
$637$	26.4834	+	9.17171i	1.04931	+	0.363396i
$638$	3.45787	−	1.12353i	0.136898	−	0.0444810i
$639$	−32.7900	+	6.96972i	−1.29715	+	0.275718i
$640$	−2.07073	+	0.843850i	−0.0818527	+	0.0333561i
$641$	38.1850	+	8.11647i	1.50822	+	0.320581i	0.886525	−	0.462681i	$-0.153112\pi$
$641$	38.1850	+	8.11647i	1.50822	+	0.320581i	0.621692	+	0.783262i	$0.286446\pi$
$642$	6.01336	−	13.5062i	0.237328	−	0.533048i
$643$			0.308081i			0.0121495i	0.999982	+	0.00607477i	$0.00193367\pi$
$643$			0.308081i			0.0121495i	−0.999982	+	0.00607477i	$0.998066\pi$
$644$	−0.919428	+	0.288996i	−0.0362305	+	0.0113880i
$645$	10.8634	−	13.9906i	0.427745	−	0.550881i
$646$	1.57888	−	15.0220i	0.0621202	−	0.591034i
$647$	17.4632	+	39.2229i	0.686548	+	1.54201i	0.833290	+	0.552836i	$0.186455\pi$
$647$	17.4632	+	39.2229i	0.686548	+	1.54201i	−0.146742	+	0.989175i	$0.546879\pi$
$648$	7.99514	−	7.19886i	0.314079	−	0.282798i
$649$	−1.03903	−	1.79966i	−0.0407856	−	0.0706428i
$650$	−19.9783	−	1.27683i	−0.783612	−	0.0500815i
$651$	−3.77060	−	18.6178i	−0.147781	−	0.729690i
$652$	6.19180	+	2.01184i	0.242490	+	0.0787896i
$653$	−4.89111	−	0.514076i	−0.191404	−	0.0201173i	0.00834148	−	0.999965i	$-0.497345\pi$
$653$	−4.89111	−	0.514076i	−0.191404	−	0.0201173i	−0.199745	+	0.979848i	$0.564011\pi$
$654$	−6.24219	+	2.77920i	−0.244089	+	0.108675i
$655$	−31.9249	+	2.32850i	−1.24741	+	0.0909818i
$656$	−9.69718	−	4.31746i	−0.378611	−	0.168569i
$657$			30.7813i			1.20089i
$658$	−17.9494	−	3.99604i	−0.699740	−	0.155782i
$659$	5.05781	+	15.5663i	0.197024	+	0.606379i	0.999947	+	0.0102954i	$0.00327720\pi$
$659$	5.05781	+	15.5663i	0.197024	+	0.606379i	−0.802923	+	0.596083i	$0.796723\pi$
$660$	−1.58460	−	2.95880i	−0.0616806	−	0.115171i
$661$	2.94846	+	3.27460i	0.114682	+	0.127367i	0.797752	−	0.602986i	$-0.206022\pi$
$661$	2.94846	+	3.27460i	0.114682	+	0.127367i	−0.683070	+	0.730353i	$0.739356\pi$
$662$	1.90164	−	8.94650i	0.0739092	−	0.347715i
$663$	−44.3138	−	39.9003i	−1.72100	−	1.54960i
$664$	−4.64669	+	14.3010i	−0.180326	+	0.554988i
$665$	3.39822	−	13.2550i	0.131777	−	0.514006i
$666$	1.70435	+	5.24546i	0.0660424	+	0.203258i
$667$	−0.818463	+	1.83830i	−0.0316910	+	0.0711792i
$668$	−1.51684	−	0.875748i	−0.0586883	−	0.0338837i
$669$	−2.90017	−	27.5932i	−0.112127	−	1.06682i
$670$	13.4579	+	12.9185i	0.519925	+	0.499086i
$671$	3.89236	+	2.82797i	0.150263	+	0.109172i
$672$	−5.48834	−	2.50708i	−0.211717	−	0.0967127i
$673$	29.9446	+	9.72959i	1.15428	+	0.375048i	0.822754	−	0.568398i	$-0.192437\pi$
$673$	29.9446	+	9.72959i	1.15428	+	0.375048i	0.331526	+	0.943446i	$0.392437\pi$
$674$	12.3514	+	21.3933i	0.475759	+	0.824039i
$675$	7.14530	−	5.65176i	0.275023	−	0.217536i
$676$	−1.51524	+	2.62447i	−0.0582784	+	0.100941i
$677$	−8.99347	−	42.3110i	−0.345647	−	1.62614i	−0.716596	−	0.697489i	$-0.754301\pi$
$677$	−8.99347	−	42.3110i	−0.345647	−	1.62614i	0.370948	−	0.928653i	$-0.379033\pi$
$678$	10.6609	−	14.6735i	0.409431	−	0.563533i
$679$	−3.76368	−	5.28643i	−0.144437	−	0.202874i
$680$	−13.7369	−	4.95328i	−0.526785	−	0.189950i
$681$	58.5711	+	26.0775i	2.24445	+	0.999293i
$682$	−1.79447	−	1.03604i	−0.0687140	−	0.0396720i
$683$	48.9380	−	5.14359i	1.87256	−	0.196814i	0.901035	−	0.433747i	$-0.142809\pi$
$683$	48.9380	−	5.14359i	1.87256	−	0.196814i	0.971526	+	0.236932i	$0.0761420\pi$
$684$	−3.40651	+	3.78331i	−0.130251	+	0.144659i
$685$	6.90876	+	23.8242i	0.263970	+	0.910276i
$686$	13.4001	+	12.7843i	0.511617	+	0.488107i
$687$	5.29101	−	1.71915i	0.201865	−	0.0655898i
$688$	−2.58128	−	2.32419i	−0.0984103	−	0.0886091i
$689$	−28.2908	−	31.4201i	−1.07779	−	1.19701i
$690$	1.80378	+	0.444001i	0.0686689	+	0.0169028i
$691$	−21.3017	+	23.6580i	−0.810356	+	0.899991i	−0.996590	−	0.0825143i	$-0.973705\pi$
$691$	−21.3017	+	23.6580i	−0.810356	+	0.899991i	0.186234	+	0.982505i	$0.440372\pi$
$692$	−14.6760	−	20.1998i	−0.557899	−	0.767883i
$693$	1.21942	−	3.63371i	0.0463219	−	0.138033i
$694$	7.28336	−	5.29167i	0.276473	−	0.200869i
$695$	−6.81844	−	38.0035i	−0.258638	−	1.44155i
$696$	−11.5089	+	5.12410i	−0.436244	+	0.194228i
$697$	−28.1952	−	63.3274i	−1.06797	−	2.39870i
$698$	−1.01590	−	4.77942i	−0.0384522	−	0.180904i
$699$	27.2146			1.02935
$700$	−11.6577	−	6.25285i	−0.440619	−	0.236336i
$701$	−30.3225			−1.14526			−0.572632	−	0.819813i	$-0.694078\pi$
$701$	−30.3225			−1.14526			−0.572632	+	0.819813i	$0.694078\pi$
$702$	−1.51675	−	7.13577i	−0.0572462	−	0.269322i
$703$	2.35737	+	5.29475i	0.0889100	+	0.199695i
$704$	−0.601276	+	0.267705i	−0.0226615	+	0.0100895i
$705$	25.5695	+	24.5446i	0.963003	+	0.924404i
$706$	−29.9020	+	21.7251i	−1.12538	+	0.817634i
$707$	5.73693	+	6.49605i	0.215759	+	0.244309i
$708$	4.23233	+	5.82531i	0.159061	+	0.218929i
$709$	−7.08499	+	7.86867i	−0.266082	+	0.295514i	−0.861349	−	0.508014i	$-0.830380\pi$
$709$	−7.08499	+	7.86867i	−0.266082	+	0.295514i	0.595267	+	0.803528i	$0.297046\pi$
$710$	2.47733	+	33.9656i	0.0929726	+	1.27470i
$711$	−12.6926	−	14.0965i	−0.476008	−	0.528661i
$712$	8.43241	+	7.59258i	0.316018	+	0.284544i
$713$	1.09068	−	0.354383i	0.0408462	−	0.0132717i
$714$	−15.6802	−	36.1498i	−0.586816	−	1.35287i
$715$	−5.88953	−	0.188011i	−0.220256	−	0.00703122i
$716$	10.8771	−	12.0803i	0.406497	−	0.451461i
$717$	−11.4484	+	1.20327i	−0.427547	+	0.0449370i
$718$	−13.9356	−	8.04572i	−0.520072	−	0.300264i
$719$	−3.07057	−	1.36711i	−0.114513	−	0.0509845i	0.348680	−	0.937242i	$-0.386630\pi$
$719$	−3.07057	−	1.36711i	−0.114513	−	0.0509845i	−0.463194	+	0.886257i	$0.653297\pi$
$720$	2.76439	+	4.07202i	0.103023	+	0.151755i
$721$	7.01536	−	15.3576i	0.261266	−	0.571946i
$722$	8.02340	−	11.0433i	0.298600	−	0.410988i
$723$	−12.6618	−	59.5690i	−0.470897	−	2.21540i
$724$	8.44235	−	14.6226i	0.313757	−	0.543444i
$725$	−25.8975	+	9.60197i	−0.961811	+	0.356608i
$726$	12.0492	+	20.8699i	0.447189	+	0.774554i
$727$	−3.12748	−	1.01618i	−0.115992	−	0.0376880i	0.250446	−	0.968131i	$-0.419423\pi$
$727$	−3.12748	−	1.01618i	−0.115992	−	0.0376880i	−0.366438	+	0.930443i	$0.619423\pi$
$728$	−8.62946	+	6.14376i	−0.319829	+	0.227703i
$729$	−9.07232	−	6.59143i	−0.336012	−	0.244127i
$730$	30.9796	+	4.25933i	1.14661	+	0.157645i
$731$	−2.37106	−	22.5591i	−0.0876968	−	0.834379i
$732$	−14.4374	−	8.33542i	−0.533620	−	0.308086i
$733$	4.83862	−	10.8677i	0.178719	−	0.401409i	−0.801866	−	0.597503i	$-0.796159\pi$
$733$	4.83862	−	10.8677i	0.178719	−	0.401409i	0.980585	+	0.196095i	$0.0628261\pi$
$734$	−3.07987	−	9.47887i	−0.113680	−	0.349871i
$735$	−9.28091	−	34.4692i	−0.342332	−	1.27141i
$736$	0.112567	−	0.346445i	0.00414926	−	0.0127701i
$737$	4.08060	+	3.67419i	0.150311	+	0.135341i
$738$	−4.85764	+	22.8534i	−0.178812	+	0.841245i
$739$	2.73909	+	3.04207i	0.100759	+	0.111904i	0.791415	−	0.611279i	$-0.209345\pi$
$739$	2.73909	+	3.04207i	0.100759	+	0.111904i	−0.690656	+	0.723183i	$0.742678\pi$
$740$	5.51508	−	0.989495i	0.202738	−	0.0363746i
$741$	6.52633	+	20.0860i	0.239751	+	0.737877i
$742$	−8.37770	−	26.6533i	−0.307555	−	0.978473i
$743$		−	10.3969i		−	0.381426i	−0.981646	−	0.190713i	$-0.938920\pi$
$743$		−	10.3969i		−	0.381426i	0.981646	−	0.190713i	$-0.0610800\pi$
$744$	6.55901	+	2.92026i	0.240465	+	0.107062i
$745$	−4.84778	−	3.00908i	−0.177609	−	0.110244i
$746$	−4.47793	+	1.99370i	−0.163949	+	0.0729947i
$747$	32.9159	+	3.45960i	1.20433	+	0.126580i
$748$	−4.08786	−	1.32823i	−0.149467	−	0.0485648i
$749$	−3.40455	−	16.8104i	−0.124400	−	0.614239i
$750$	12.9467	+	21.9662i	0.472746	+	0.802093i
$751$	0.253712	+	0.439442i	0.00925809	+	0.0160355i	0.870617	−	0.491961i	$-0.163720\pi$
$751$	0.253712	+	0.439442i	0.00925809	+	0.0160355i	−0.861359	+	0.507996i	$0.830386\pi$
$752$	5.16510	−	4.65068i	0.188352	−	0.169593i
$753$	0.503251	+	1.13032i	0.0183395	+	0.0411912i
$754$	−2.31188	+	21.9961i	−0.0841939	+	0.801051i
$755$	0.0765474	−	2.39788i	0.00278585	−	0.0872678i
$756$	1.04758	−	4.70552i	0.0381001	−	0.171138i
$757$		−	36.2335i		−	1.31693i	−0.752612	−	0.658464i	$-0.771207\pi$
$757$		−	36.2335i		−	1.31693i	0.752612	−	0.658464i	$-0.228793\pi$
$758$	3.22386	−	7.24090i	0.117096	−	0.263001i
$759$	0.534837	+	0.113683i	0.0194134	+	0.00412644i
$760$	3.33630	+	3.95196i	0.121020	+	0.143353i
$761$	−34.6603	+	7.36727i	−1.25643	+	0.267063i	−0.787580	−	0.616212i	$-0.788666\pi$
$761$	−34.6603	+	7.36727i	−1.25643	+	0.267063i	−0.468854	+	0.883276i	$0.655333\pi$
$762$	13.4956	−	4.38498i	0.488893	−	0.158851i
$763$	−4.02934	+	6.82658i	−0.145872	+	0.247139i
$764$	0.979190	−	3.01364i	0.0354259	−	0.109030i
$765$	−4.37786	+	31.8416i	−0.158282	+	1.15124i
$766$	−21.5553	−	4.58172i	−0.778825	−	0.165544i
$767$	12.5720	−	1.32137i	0.453947	−	0.0477118i
$768$	1.97504	−	1.14029i	0.0712682	−	0.0411467i
$769$	3.44193	−	2.50071i	0.124119	−	0.0901777i	−0.523994	−	0.851722i	$-0.675559\pi$
$769$	3.44193	−	2.50071i	0.124119	−	0.0901777i	0.648113	+	0.761544i	$0.275559\pi$
$770$	−3.48838	−	1.73008i	−0.125712	−	0.0623478i
$771$	0.377065	+	0.273954i	0.0135797	+	0.00986620i
$772$	9.13278	+	0.959893i	0.328696	+	0.0345473i
$773$	−10.3893	+	9.35454i	−0.373676	+	0.336460i	−0.834476	−	0.551045i	$-0.814229\pi$
$773$	−10.3893	+	9.35454i	−0.373676	+	0.336460i	0.460800	+	0.887504i	$0.347563\pi$
$774$	−3.82263	+	6.62099i	−0.137402	+	0.237987i
$775$	13.9425	+	7.30659i	0.500829	+	0.262460i
$776$	2.45274			0.0880483
$777$	12.1460	+	9.00432i	0.435736	+	0.323028i
$778$	−17.3286	+	23.8508i	−0.621262	+	0.855093i
$779$	−2.56636	+	24.4173i	−0.0919495	+	0.874841i
$780$	20.3635	−	1.48524i	0.729129	−	0.0531802i
$781$	1.04781	+	9.96929i	0.0374937	+	0.356729i
$782$	2.06018	−	1.18944i	0.0736718	−	0.0425344i
$783$	−5.91616	−	8.14290i	−0.211426	−	0.291003i
$784$	−6.87376	+	1.32344i	−0.245491	+	0.0472656i
$785$	−33.0567	−	1.05527i	−1.17984	−	0.0376641i
$786$	31.9336	−	6.78769i	1.13903	−	0.242109i
$787$	0.589704	−	2.77434i	0.0210207	−	0.0988946i	−0.966387	−	0.257093i	$-0.917235\pi$
$787$	0.589704	−	2.77434i	0.0210207	−	0.0988946i	0.987407	+	0.158199i	$0.0505686\pi$
$788$	0.742386	−	3.49265i	0.0264464	−	0.124421i
$789$	−55.3129	+	11.7571i	−1.96919	+	0.418564i
$790$	−15.9436	+	10.8237i	−0.567249	+	0.385090i
$791$	0.202334	−	21.0407i	0.00719419	−	0.748120i
$792$	0.851517	+	1.17201i	0.0302573	+	0.0416457i
$793$	−25.3464	+	14.6337i	−0.900075	+	0.519659i
$794$	−2.60674	−	24.8015i	−0.0925098	−	0.880172i
$795$	−12.8711	+	52.2899i	−0.456492	+	1.85453i
$796$	−1.77419	+	16.8803i	−0.0628845	+	0.598306i
$797$	15.9513	−	21.9551i	0.565025	−	0.777691i	−0.426929	−	0.904285i	$-0.640405\pi$
$797$	15.9513	−	21.9551i	0.565025	−	0.777691i	0.991955	+	0.126594i	$0.0404047\pi$
$798$	−1.59220	+	13.8649i	−0.0563634	+	0.490813i
$799$	45.3891			1.60575
$800$	4.48076	−	2.21873i	0.158419	−	0.0784440i
$801$	12.4876	−	21.6292i	0.441228	−	0.764229i
$802$	21.5697	−	19.4214i	0.761651	−	0.685794i
$803$	9.15409	+	0.962133i	0.323041	+	0.0339529i
$804$	−15.3925	−	11.1833i	−0.542853	−	0.394406i
$805$	2.00345	−	0.794055i	0.0706123	−	0.0279868i
$806$	10.1975	−	7.40892i	0.359192	−	0.260968i
$807$	41.8193	−	24.1444i	1.47211	−	0.849922i
$808$	−3.25774	+	0.342403i	−0.114607	+	0.0120457i
$809$	12.0546	+	2.56229i	0.423818	+	0.0900853i	0.414883	−	0.909875i	$-0.363823\pi$
$809$	12.0546	+	2.56229i	0.423818	+	0.0900853i	0.00893498	+	0.999960i	$0.497156\pi$
$810$	−16.6594	+	17.3550i	−0.585350	+	0.609791i
$811$	14.9260	−	45.9375i	0.524123	−	1.61308i	−0.241922	−	0.970296i	$-0.577778\pi$
$811$	14.9260	−	45.9375i	0.524123	−	1.61308i	0.766044	−	0.642788i	$-0.222222\pi$
$812$	−7.42902	+	12.5864i	−0.260707	+	0.441694i
$813$	53.3031	−	17.3192i	1.86942	−	0.607412i
$814$	1.61323	−	0.342902i	0.0565435	−	0.0120187i
$815$	−14.1358	−	3.47953i	−0.495157	−	0.121883i
$816$	14.5679	+	3.09650i	0.509978	+	0.108399i
$817$	−3.26771	+	7.33939i	−0.114323	+	0.256773i
$818$			32.0663i			1.12117i
$819$	17.1763	+	15.7673i	0.600188	+	0.550954i
$820$	22.3284	+	8.05123i	0.779741	+	0.281161i
$821$	3.14928	−	29.9634i	0.109911	−	1.04573i	−0.791026	−	0.611782i	$-0.790453\pi$
$821$	3.14928	−	29.9634i	0.109911	−	1.04573i	0.900937	−	0.433949i	$-0.142880\pi$
$822$	−10.2902	−	23.1123i	−0.358914	−	0.806133i
$823$	−10.4708	+	9.42797i	−0.364990	+	0.328638i	−0.831136	−	0.556069i	$-0.812309\pi$
$823$	−10.4708	+	9.42797i	−0.364990	+	0.328638i	0.466146	+	0.884708i	$0.345642\pi$
$824$	3.19078	+	5.52660i	0.111156	+	0.192528i
$825$	4.01517	+	6.34080i	0.139790	+	0.220758i
$826$	7.91939	+	2.65763i	0.275551	+	0.0924706i
$827$	−31.1026	−	10.1058i	−1.08154	−	0.351415i	−0.286570	−	0.958059i	$-0.592515\pi$
$827$	−31.1026	−	10.1058i	−1.08154	−	0.351415i	−0.794973	+	0.606645i	$0.792515\pi$
$828$	−0.797393	−	0.0838094i	−0.0277113	−	0.00291258i
$829$	−17.9824	+	8.00627i	−0.624554	+	0.278069i	−0.694512	−	0.719481i	$-0.744380\pi$
$829$	−17.9824	+	8.00627i	−0.624554	+	0.278069i	0.0699588	+	0.997550i	$0.477713\pi$
$830$	8.03659	−	32.6492i	0.278954	−	1.13327i
$831$	−19.9764	−	8.89405i	−0.692972	−	0.308531i
$832$		−	4.00381i		−	0.138807i
$833$	−39.1422	−	23.6138i	−1.35620	−	0.818171i
$834$	12.1688	+	37.4516i	0.421370	+	1.29684i
$835$	3.52522	+	1.70632i	0.121995	+	0.0590495i
$836$	1.01864	+	1.13132i	0.0352306	+	0.0391275i
$837$	−1.19263	+	5.61087i	−0.0412232	+	0.193940i
$838$	−13.4239	−	12.0869i	−0.463721	−	0.417536i
$839$	8.88342	−	27.3403i	0.306690	−	0.943894i	−0.672352	−	0.740232i	$-0.734716\pi$
$839$	8.88342	−	27.3403i	0.306690	−	0.943894i	0.979041	−	0.203662i	$-0.0652843\pi$
$840$	12.6476	+	4.69842i	0.436384	+	0.162111i
$841$	0.468232	+	1.44107i	0.0161459	+	0.0496921i
$842$	−3.69876	+	8.30755i	−0.127468	+	0.286297i
$843$	18.3804	+	10.6119i	0.633053	+	0.365494i
$844$	−2.92683	−	27.8470i	−0.100746	−	0.958532i
$845$	2.95230	−	6.09941i	0.101562	−	0.209826i
$846$	−12.3764	−	8.99196i	−0.425509	−	0.309150i
$847$	25.4296	+	11.6163i	0.873771	+	0.399139i
$848$	10.0431	+	3.26320i	0.344881	+	0.112059i
$849$	6.27711	+	10.8723i	0.215430	+	0.373136i
$850$	31.4409	+	8.81211i	1.07841	+	0.302253i
$851$	−0.456399	+	0.790506i	−0.0156451	+	0.0270982i
$852$	−7.22155	−	33.9747i	−0.247406	−	1.16396i
$853$	−22.9079	+	31.5300i	−0.784351	+	1.07957i	0.210438	+	0.977607i	$0.432511\pi$
$853$	−22.9079	+	31.5300i	−0.784351	+	1.07957i	−0.994789	+	0.101959i	$0.967489\pi$
$854$	−19.2528	+	1.83655i	−0.658817	+	0.0628455i
$855$	6.98162	−	8.99143i	0.238766	−	0.307500i
$856$	5.92227	+	2.63677i	0.202419	+	0.0901228i
$857$	30.9097	+	17.8457i	1.05586	+	0.609599i	0.924283	−	0.381707i	$-0.124664\pi$
$857$	30.9097	+	17.8457i	1.05586	+	0.609599i	0.131573	+	0.991306i	$0.457997\pi$
$858$	5.97692	−	0.628199i	0.204049	−	0.0214464i
$859$	34.5518	−	38.3737i	1.17889	−	1.30929i	0.237732	−	0.971331i	$-0.423596\pi$
$859$	34.5518	−	38.3737i	1.17889	−	1.30929i	0.941160	−	0.337962i	$-0.109737\pi$
$860$	6.13468	+	4.76342i	0.209191	+	0.162431i
$861$	25.4871	+	58.7592i	0.868598	+	2.00251i
$862$	21.7522	−	7.06773i	0.740884	−	0.240728i
$863$	23.2127	+	20.9008i	0.790170	+	0.711472i	0.961819	−	0.273686i	$-0.0882429\pi$
$863$	23.2127	+	20.9008i	0.790170	+	0.711472i	−0.171649	+	0.985158i	$0.554910\pi$
$864$	1.21920	+	1.35406i	0.0414779	+	0.0460659i
$865$	36.0154	+	42.6614i	1.22456	+	1.45053i
$866$	−16.8121	+	18.6717i	−0.571298	+	0.634491i
$867$	34.3801	+	47.3202i	1.16761	+	1.60708i
$868$	8.16362	−	1.65335i	0.277091	−	0.0561183i
$869$	−4.58891	+	3.33404i	−0.155668	+	0.113099i
$870$	24.8330	−	13.2995i	0.841919	−	0.450895i
$871$	−30.5148	+	13.5861i	−1.03395	+	0.460346i
$872$	−1.21864	−	2.73710i	−0.0412683	−	0.0926901i
$873$	−1.12244	−	5.28065i	−0.0379887	−	0.178723i
$874$	−0.842550			−0.0284997
$875$	27.0154	+	12.0485i	0.913288	+	0.407314i
$876$	−31.8935			−1.07758
$877$	0.600338	+	2.82437i	0.0202720	+	0.0953722i	0.987121	−	0.159978i	$-0.0511425\pi$
$877$	0.600338	+	2.82437i	0.0202720	+	0.0953722i	−0.966849	+	0.255351i	$0.917809\pi$
$878$	3.69022	+	8.28838i	0.124539	+	0.279719i
$879$	35.3890	−	15.7562i	1.19364	−	0.531443i
$880$	1.29739	−	0.694825i	0.0437349	−	0.0234225i
$881$	31.3716	−	22.7928i	1.05694	−	0.767910i	0.0834180	−	0.996515i	$-0.473416\pi$
$881$	31.3716	−	22.7928i	1.05694	−	0.767910i	0.973519	+	0.228605i	$0.0734163\pi$
$882$	5.99490	+	14.1933i	0.201859	+	0.477912i
$883$	20.1128	+	27.6829i	0.676849	+	0.931603i	0.999891	−	0.0147820i	$-0.00470543\pi$
$883$	20.1128	+	27.6829i	0.676849	+	0.931603i	−0.323042	+	0.946385i	$0.604705\pi$
$884$	17.4957	−	19.4309i	0.588443	−	0.653532i
$885$	−10.3863	−	12.3028i	−0.349130	−	0.413556i
$886$	−0.545031	−	0.605319i	−0.0183107	−	0.0203361i
$887$	−13.5184	−	12.1720i	−0.453904	−	0.408697i	0.410211	−	0.911990i	$-0.365455\pi$
$887$	−13.5184	−	12.1720i	−0.453904	−	0.408697i	−0.864116	+	0.503293i	$0.832122\pi$
$888$	−5.43499	+	1.76594i	−0.182386	+	0.0592609i
$889$	9.80387	−	13.2246i	0.328811	−	0.443537i
$890$	−20.0405	−	15.5609i	−0.671759	−	0.521604i
$891$	−4.73813	+	5.26223i	−0.158733	+	0.176291i
$892$	12.0992	−	1.27168i	0.405111	−	0.0425789i
$893$	−13.9221	−	8.03791i	−0.465884	−	0.268978i
$894$	5.31622	+	2.36693i	0.177801	+	0.0791621i
$895$	−22.2926	+	28.7100i	−0.745159	+	0.959670i
$896$	1.09932	−	2.40655i	0.0367256	−	0.0803973i
$897$	−1.95508	+	2.69094i	−0.0652783	+	0.0898479i
$898$	−4.08658	−	19.2259i	−0.136371	−	0.641575i
$899$	8.69543	−	15.0609i	0.290009	−	0.502310i
$900$	−6.82734	−	8.63154i	−0.227578	−	0.287718i
$901$	34.4808	+	59.7225i	1.14872	+	1.98964i
$902$	6.64455	+	2.15895i	0.221239	+	0.0718850i
$903$	1.99021	+	20.8636i	0.0662300	+	0.694297i
$904$	6.43411	+	4.67465i	0.213995	+	0.155477i
$905$	−16.4492	+	33.9837i	−0.546788	+	1.12966i
$906$	0.255767	+	2.43346i	0.00849728	+	0.0808462i
$907$	−31.2896	−	18.0651i	−1.03895	−	0.599840i	−0.119417	−	0.992844i	$-0.538103\pi$
$907$	−31.2896	−	18.0651i	−1.03895	−	0.599840i	−0.919537	+	0.393004i	$0.871436\pi$
$908$	−11.4346	+	25.6825i	−0.379470	+	0.852304i
$909$	2.22800	+	6.85709i	0.0738982	+	0.227435i
$910$	18.2456	−	15.1051i	0.604836	−	0.500730i
$911$	−1.03816	+	3.19512i	−0.0343957	+	0.105859i	−0.966780	−	0.255609i	$-0.917724\pi$
$911$	−1.03816	+	3.19512i	−0.0343957	+	0.105859i	0.932385	+	0.361468i	$0.117724\pi$
$912$	−3.92001	−	3.52959i	−0.129805	−	0.116877i
$913$	2.05771	−	9.68076i	0.0681002	−	0.320386i
$914$	−2.74658	−	3.05039i	−0.0908489	−	0.100898i
$915$	33.5532	+	16.2408i	1.10924	+	0.536905i
$916$	0.753822	+	2.32002i	0.0249070	+	0.0766558i
$917$	25.6124	−	27.9012i	0.845797	−	0.921379i
$918$			11.8990i			0.392724i
$919$	−18.9477	−	8.43608i	−0.625029	−	0.278281i	0.0696829	−	0.997569i	$-0.477801\pi$
$919$	−18.9477	−	8.43608i	−0.625029	−	0.278281i	−0.694711	+	0.719289i	$0.744468\pi$
$920$	−0.194688	+	0.790931i	−0.00641866	+	0.0260762i
$921$	−46.3386	+	20.6313i	−1.52691	+	0.679823i
$922$	−5.78482	−	0.608009i	−0.190513	−	0.0200237i
$923$	−57.9943	−	18.8435i	−1.90891	−	0.620241i
$924$	3.76501	+	1.26348i	0.123860	+	0.0415654i
$925$	−12.1385	+	3.10380i	−0.399111	+	0.102052i
$926$	11.5888	+	20.0725i	0.380833	+	0.659622i
$927$	10.4383	−	9.39873i	0.342840	−	0.308695i
$928$	−2.24684	−	5.04648i	−0.0737560	−	0.165659i
$929$	−2.21739	+	21.0970i	−0.0727501	+	0.692171i	0.895987	+	0.444081i	$0.146470\pi$
$929$	−2.21739	+	21.0970i	−0.0727501	+	0.692171i	−0.968737	+	0.248090i	$0.920197\pi$
$930$	−15.1026	−	5.44572i	−0.495232	−	0.178572i
$931$	7.82421	+	14.1747i	0.256428	+	0.464556i
$932$			11.9332i			0.390884i
$933$	−2.75259	+	6.18242i	−0.0901158	+	0.202403i
$934$	−25.7198	−	5.46692i	−0.841579	−	0.178883i
$935$	9.33257	+	2.29721i	0.305208	+	0.0751268i
$936$	−8.62002	+	1.83224i	−0.281754	+	0.0598887i
$937$	−17.7738	+	5.77506i	−0.580645	+	0.188663i	−0.584589	−	0.811329i	$-0.698744\pi$
$937$	−17.7738	+	5.77506i	−0.580645	+	0.188663i	0.00394473	+	0.999992i	$0.498744\pi$
$938$	−22.0717	−	0.212249i	−0.720667	−	0.00693019i
$939$	−21.6312	+	66.5739i	−0.705906	+	2.17256i
$940$	−10.7624	+	11.2118i	−0.351032	+	0.365689i
$941$	−15.2929	−	3.25061i	−0.498534	−	0.105967i	−0.0482197	−	0.998837i	$-0.515355\pi$
$941$	−15.2929	−	3.25061i	−0.498534	−	0.105967i	−0.450314	+	0.892870i	$0.648688\pi$
$942$	33.5471	−	3.52595i	1.09302	−	0.114882i
$943$	−3.34868	+	1.93336i	−0.109048	+	0.0629589i
$944$	−2.55431	+	1.85581i	−0.0831356	+	0.0604016i
$945$	−1.57086	+	10.6644i	−0.0511001	+	0.346913i
$946$	1.84954	+	1.34377i	0.0601336	+	0.0436896i
$947$	−45.4639	−	4.77845i	−1.47738	−	0.155279i	−0.668701	−	0.743531i	$-0.733150\pi$
$947$	−45.4639	−	4.77845i	−1.47738	−	0.155279i	−0.808677	+	0.588252i	$0.799816\pi$
$948$	14.6059	−	13.1512i	0.474376	−	0.427130i
$949$	−27.9963	+	48.4909i	−0.908797	+	1.57408i
$950$	−8.08326	−	8.27076i	−0.262256	−	0.268339i
$951$	9.94514			0.322493
$952$	15.8512	−	6.87552i	0.513739	−	0.222837i
$953$	−30.7438	+	42.3152i	−0.995888	+	1.37072i	−0.0680735	+	0.997680i	$0.521685\pi$
$953$	−30.7438	+	42.3152i	−0.995888	+	1.37072i	−0.927814	+	0.373042i	$0.878315\pi$
$954$	2.42955	−	23.1156i	0.0786596	−	0.748396i
$955$	−1.69354	+	6.88012i	−0.0548016	+	0.222635i
$956$	−0.527616	−	5.01993i	−0.0170643	−	0.162356i
$957$	7.18089	−	4.14589i	0.232125	−	0.134018i
$958$	−17.4494	−	24.0170i	−0.563764	−	0.775955i
$959$	−25.2760	−	14.9190i	−0.816205	−	0.481760i
$960$	−4.21915	+	2.86427i	−0.136172	+	0.0924440i
$961$	20.6280	−	4.38461i	0.665419	−	0.141439i
$962$	−2.08593	+	9.81351i	−0.0672530	+	0.316400i
$963$	2.96666	−	13.9570i	0.0955993	−	0.449759i
$964$	26.1201	−	5.55200i	0.841272	−	0.178818i
$965$	−20.5235	−	0.655172i	−0.660676	−	0.0210907i
$966$	−1.91398	+	1.08063i	−0.0615813	+	0.0347687i
$967$	−33.0972	−	45.5544i	−1.06433	−	1.46493i	−0.875683	−	0.482886i	$-0.839589\pi$
$967$	−33.0972	−	45.5544i	−1.06433	−	1.46493i	−0.188651	−	0.982044i	$-0.560411\pi$
$968$	−9.15112	+	5.28340i	−0.294128	+	0.169815i
$969$	−3.60076	−	34.2590i	−0.115673	−	1.10056i
$970$	−5.46997	+	0.398961i	−0.175630	+	0.0128099i
$971$	0.647067	−	6.15644i	0.0207654	−	0.197569i	−0.979221	−	0.202796i	$-0.934997\pi$
$971$	0.647067	−	6.15644i	0.0207654	−	0.197569i	0.999986	+	0.00522683i	$0.00166376\pi$
$972$	11.2088	−	15.4276i	0.359522	−	0.494839i
$973$	36.6995	+	27.2067i	1.17653	+	0.872208i
$974$	−33.1635			−1.06263
$975$	−45.1719	+	6.62461i	−1.44666	+	0.212157i
$976$	3.65495	−	6.33056i	0.116992	−	0.202636i
$977$	23.2379	−	20.9235i	0.743445	−	0.669401i	−0.207683	−	0.978196i	$-0.566592\pi$
$977$	23.2379	−	20.9235i	0.743445	−	0.669401i	0.951129	+	0.308795i	$0.0999257\pi$
$978$	14.7663	+	1.55200i	0.472173	+	0.0496274i
$979$	−6.04199	−	4.38976i	−0.193103	−	0.140297i
$980$	15.1142	−	4.06954i	0.482805	−	0.129997i
$981$	−5.33519	+	3.87624i	−0.170339	+	0.123759i
$982$	−25.6098	+	14.7858i	−0.817241	+	0.471834i
$983$	21.8449	−	2.29599i	0.696745	−	0.0732309i	0.250467	−	0.968125i	$-0.419416\pi$
$983$	21.8449	−	2.29599i	0.696745	−	0.0732309i	0.446278	+	0.894894i	$0.352749\pi$
$984$	−23.6791	−	5.03315i	−0.754863	−	0.160451i
$985$	−1.08752	+	7.90987i	−0.0346511	+	0.252029i
$986$	11.1477	−	34.3092i	0.355016	−	1.09263i
$987$	−41.9353	−	0.403265i	−1.33482	−	0.0128361i
$988$	−8.80740	+	2.86170i	−0.280201	+	0.0910427i
$989$	−1.23764	+	0.263068i	−0.0393546	+	0.00836507i
$990$	−2.08964	−	2.47525i	−0.0664132	−	0.0786686i
$991$	−1.39927	−	0.297425i	−0.0444494	−	0.00944800i	0.185633	−	0.982619i	$-0.440566\pi$
$991$	−1.39927	−	0.297425i	−0.0444494	−	0.00944800i	−0.230083	+	0.973171i	$0.573900\pi$
$992$	−1.28049	+	2.87603i	−0.0406556	+	0.0913139i
$993$		−	20.8590i		−	0.661942i
$994$	−29.6846	−	27.2496i	−0.941539	−	0.864303i
$995$	1.21097	−	37.9341i	0.0383903	−	1.20259i
$996$	−3.58461	+	34.1052i	−0.113583	+	1.08067i
$997$	13.5716	+	30.4822i	0.429816	+	0.965382i	0.990520	+	0.137366i	$0.0438637\pi$
$997$	13.5716	+	30.4822i	0.429816	+	0.965382i	−0.560704	+	0.828016i	$0.689470\pi$
$998$	−5.79718	+	5.21981i	−0.183507	+	0.165230i
$999$	−2.28286	−	3.95404i	−0.0722266	−	0.125100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.u.a.179.19	yes	160
7.2	even	3	inner	350.2.u.a.79.12	✓	160
25.19	even	10	inner	350.2.u.a.319.12	yes	160
175.44	even	30	inner	350.2.u.a.219.19	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.u.a.79.12	✓	160	7.2	even	3	inner
350.2.u.a.179.19	yes	160	1.1	even	1	trivial
350.2.u.a.219.19	yes	160	175.44	even	30	inner
350.2.u.a.319.12	yes	160	25.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 + 0.978148i) q^{2} +(0.927596 + 2.08342i) q^{3} +(-0.913545 + 0.406737i) q^{4} +(1.97118 - 1.05568i) q^{5} +(-1.84503 + 1.34049i) q^{6} +(-0.841740 + 2.50828i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.47279 + 1.63570i) q^{9} +O(q^{10})\)	\(q+(0.207912 + 0.978148i) q^{2} +(0.927596 + 2.08342i) q^{3} +(-0.913545 + 0.406737i) q^{4} +(1.97118 - 1.05568i) q^{5} +(-1.84503 + 1.34049i) q^{6} +(-0.841740 + 2.50828i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.47279 + 1.63570i) q^{9} +(1.44244 + 1.70862i) q^{10} +(0.440408 + 0.489122i) q^{11} +(-1.69480 - 1.52601i) q^{12} +(-3.80785 + 1.23724i) q^{13} +(-2.62848 - 0.301845i) q^{14} +(4.02787 + 3.12754i) q^{15} +(0.669131 - 0.743145i) q^{16} +(6.49472 - 0.682623i) q^{17} +(-1.90617 - 1.10053i) q^{18} +(-2.11299 - 0.940765i) q^{19} +(-1.37138 + 1.76616i) q^{20} +(-6.00659 + 0.572977i) q^{21} +(-0.386868 + 0.532478i) q^{22} +(-0.0757367 - 0.356313i) q^{23} +(1.14029 - 1.97504i) q^{24} +(2.77109 - 4.16186i) q^{25} +(-2.00190 - 3.46740i) q^{26} +(1.73288 + 0.563048i) q^{27} +(-0.251242 - 2.63380i) q^{28} +(-4.46906 - 3.24696i) q^{29} +(-2.22175 + 4.59011i) q^{30} +(0.329077 + 3.13096i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.610524 + 1.37126i) q^{33} +(2.01803 + 6.21087i) q^{34} +(0.988716 + 5.83288i) q^{35} +(0.680163 - 2.09333i) q^{36} +(-1.86217 - 1.67671i) q^{37} +(0.480891 - 2.26242i) q^{38} +(-6.10984 - 6.78566i) q^{39} +(-2.01269 - 0.974205i) q^{40} +(-3.28018 - 10.0954i) q^{41} +(-1.80930 - 5.75620i) q^{42} -3.47345i q^{43} +(-0.601276 - 0.267705i) q^{44} +(-1.17636 + 4.77906i) q^{45} +(0.332780 - 0.148163i) q^{46} +(6.91225 + 0.726507i) q^{47} +(2.16896 + 0.704739i) q^{48} +(-5.58295 - 4.22264i) q^{49} +(4.64705 + 1.84524i) q^{50} +(7.44667 + 12.8980i) q^{51} +(2.97541 - 2.67907i) q^{52} +(4.29511 + 9.64697i) q^{53} +(-0.190457 + 1.81208i) q^{54} +(1.38448 + 0.499219i) q^{55} +(2.52400 - 0.793348i) q^{56} -5.27489i q^{57} +(2.24684 - 5.04648i) q^{58} +(-3.08830 - 0.656439i) q^{59} +(-4.95173 - 1.21887i) q^{60} +(7.15017 - 1.51981i) q^{61} +(-2.99412 + 0.972848i) q^{62} +(-2.86309 - 5.07101i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-6.19981 + 6.45869i) q^{65} +(-1.46823 - 0.312082i) q^{66} +(8.29701 - 0.872051i) q^{67} +(-5.65558 + 3.26525i) q^{68} +(0.672095 - 0.488306i) q^{69} +(-5.49985 + 2.17983i) q^{70} +(12.3215 + 8.95209i) q^{71} +(2.18900 + 0.230073i) q^{72} +(10.3927 - 9.35767i) q^{73} +(1.25290 - 2.17009i) q^{74} +(11.2413 + 1.91281i) q^{75} +2.31296 q^{76} +(-1.59756 + 0.692952i) q^{77} +(5.36707 - 7.38714i) q^{78} +(-0.900829 + 8.57081i) q^{79} +(0.534454 - 2.17126i) q^{80} +(1.12457 + 10.6996i) q^{81} +(9.19276 - 5.30744i) q^{82} +(-8.83852 - 12.1652i) q^{83} +(5.25424 - 2.96654i) q^{84} +(12.0816 - 8.20190i) q^{85} +(3.39755 - 0.722172i) q^{86} +(2.61929 - 12.3228i) q^{87} +(0.136843 - 0.643796i) q^{88} +(-11.0990 + 2.35916i) q^{89} +(-4.91920 - 0.157035i) q^{90} +(0.101862 - 10.5926i) q^{91} +(0.214115 + 0.294703i) q^{92} +(-6.21783 + 3.58987i) q^{93} +(0.726507 + 6.91225i) q^{94} +(-5.15823 + 0.376224i) q^{95} +(-0.238386 + 2.26809i) q^{96} +(-1.44169 + 1.98431i) q^{97} +(2.96961 - 6.33888i) q^{98} -1.44869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9}+O(q^{10}) \) 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9	\( 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9} - 2 q^{10} - 6 q^{11} - 16 q^{15} + 20 q^{16} - 20 q^{17} + 4 q^{19} - 4 q^{20} - 12 q^{21} + 40 q^{22} - 30 q^{23} - 16 q^{24} + 48 q^{26} - 120 q^{27} - 10 q^{28} + 24 q^{29} - 26 q^{30} - 6 q^{31} - 50 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} - 32 q^{39} + 2 q^{40} + 68 q^{41} + 10 q^{42} - 4 q^{44} + 16 q^{45} + 12 q^{46} + 24 q^{49} + 32 q^{50} + 12 q^{51} - 20 q^{53} + 16 q^{54} + 24 q^{55} + 24 q^{59} + 2 q^{60} - 8 q^{61} + 40 q^{64} + 2 q^{65} - 116 q^{69} - 118 q^{70} + 68 q^{71} - 40 q^{73} + 16 q^{74} + 196 q^{75} - 32 q^{76} - 80 q^{77} - 8 q^{79} - 2 q^{80} + 64 q^{81} - 160 q^{83} - 18 q^{84} + 12 q^{85} + 12 q^{86} - 10 q^{88} + 54 q^{89} + 44 q^{91} - 40 q^{92} - 16 q^{95} - 4 q^{96} - 20 q^{97} + 40 q^{98} - 24 q^{99}+O(q^{100}) \) 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9 - 2 * q^10 - 6 * q^11 - 16 * q^15 + 20 * q^16 - 20 * q^17 + 4 * q^19 - 4 * q^20 - 12 * q^21 + 40 * q^22 - 30 * q^23 - 16 * q^24 + 48 * q^26 - 120 * q^27 - 10 * q^28 + 24 * q^29 - 26 * q^30 - 6 * q^31 - 50 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 - 32 * q^39 + 2 * q^40 + 68 * q^41 + 10 * q^42 - 4 * q^44 + 16 * q^45 + 12 * q^46 + 24 * q^49 + 32 * q^50 + 12 * q^51 - 20 * q^53 + 16 * q^54 + 24 * q^55 + 24 * q^59 + 2 * q^60 - 8 * q^61 + 40 * q^64 + 2 * q^65 - 116 * q^69 - 118 * q^70 + 68 * q^71 - 40 * q^73 + 16 * q^74 + 196 * q^75 - 32 * q^76 - 80 * q^77 - 8 * q^79 - 2 * q^80 + 64 * q^81 - 160 * q^83 - 18 * q^84 + 12 * q^85 + 12 * q^86 - 10 * q^88 + 54 * q^89 + 44 * q^91 - 40 * q^92 - 16 * q^95 - 4 * q^96 - 20 * q^97 + 40 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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