LMFDB - Embedded newform 115.2.l.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	115.17
Dual form			115.2.l.a.88.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0418710 - 0.0156171i) q^{2} +(2.62848 - 1.43526i) q^{3} +(-1.50999 + 1.30841i) q^{4} +(-0.593814 - 2.15578i) q^{5} +(0.0876426 - 0.101145i) q^{6} +(1.31081 + 1.75104i) q^{7} +(-0.0856252 + 0.156811i) q^{8} +(3.22702 - 5.02134i) q^{9} +O(q^{10})$	\(q+(0.0418710 - 0.0156171i) q^{2} +(2.62848 - 1.43526i) q^{3} +(-1.50999 + 1.30841i) q^{4} +(-0.593814 - 2.15578i) q^{5} +(0.0876426 - 0.101145i) q^{6} +(1.31081 + 1.75104i) q^{7} +(-0.0856252 + 0.156811i) q^{8} +(3.22702 - 5.02134i) q^{9} +(-0.0585306 - 0.0809910i) q^{10} +(-5.39993 + 2.46606i) q^{11} +(-2.09107 + 5.60637i) q^{12} +(1.18594 + 0.887787i) q^{13} +(0.0822312 + 0.0528468i) q^{14} +(-4.65493 - 4.81415i) q^{15} +(0.567555 - 3.94743i) q^{16} +(0.120040 + 1.67838i) q^{17} +(0.0566999 - 0.260645i) q^{18} +(3.35060 + 3.86680i) q^{19} +(3.71730 + 2.47825i) q^{20} +(5.95865 + 2.72122i) q^{21} +(-0.187588 + 0.187588i) q^{22} +(-3.92214 - 2.75986i) q^{23} +0.535068i q^{24} +(-4.29477 + 2.56026i) q^{25} +(0.0635213 + 0.0186515i) q^{26} +(0.634294 - 8.86858i) q^{27} +(-4.27040 - 0.928969i) q^{28} +(-1.20354 - 1.04288i) q^{29} +(-0.270090 - 0.128877i) q^{30} +(-0.807869 + 0.237212i) q^{31} +(-0.113839 - 0.523311i) q^{32} +(-10.6542 + 14.2323i) q^{33} +(0.0312376 + 0.0684007i) q^{34} +(2.99648 - 3.86562i) q^{35} +(1.69722 + 11.8045i) q^{36} +(-5.40713 + 1.17625i) q^{37} +(0.200681 + 0.109580i) q^{38} +(4.39144 + 0.631394i) q^{39} +(0.388895 + 0.0914725i) q^{40} +(6.12788 - 3.93815i) q^{41} +(0.291992 + 0.0208837i) q^{42} +(-0.360223 - 0.659699i) q^{43} +(4.92720 - 10.7891i) q^{44} +(-12.7412 - 3.97500i) q^{45} +(-0.207325 - 0.0543056i) q^{46} +(-1.16159 - 1.16159i) q^{47} +(-4.17378 - 11.1903i) q^{48} +(0.624212 - 2.12587i) q^{49} +(-0.139842 + 0.174273i) q^{50} +(2.72443 + 4.23930i) q^{51} +(-2.95236 + 0.211157i) q^{52} +(5.63313 - 4.21690i) q^{53} +(-0.111943 - 0.381242i) q^{54} +(8.52284 + 10.1767i) q^{55} +(-0.386821 + 0.0556164i) q^{56} +(14.3569 + 5.35483i) q^{57} +(-0.0666803 - 0.0248705i) q^{58} +(5.98982 - 0.861206i) q^{59} +(13.3278 + 1.17874i) q^{60} +(-2.24031 - 7.62978i) q^{61} +(-0.0301217 + 0.0225489i) q^{62} +(13.0226 - 0.931395i) q^{63} +(4.29924 + 6.68974i) q^{64} +(1.20964 - 3.08382i) q^{65} +(-0.223834 + 0.762308i) q^{66} +(1.40667 + 3.77142i) q^{67} +(-2.37727 - 2.37727i) q^{68} +(-14.2704 - 1.62494i) q^{69} +(0.0650960 - 0.208654i) q^{70} +(1.35921 - 2.97626i) q^{71} +(0.511087 + 0.935985i) q^{72} +(7.97697 + 0.570524i) q^{73} +(-0.208032 + 0.133694i) q^{74} +(-7.61408 + 12.8937i) q^{75} +(-10.1188 - 1.45486i) q^{76} +(-11.3965 - 6.22295i) q^{77} +(0.193734 - 0.0421444i) q^{78} +(-1.48088 - 10.2997i) q^{79} +(-8.84681 + 1.12052i) q^{80} +(-3.62280 - 7.93282i) q^{81} +(0.195078 - 0.260594i) q^{82} +(1.28200 + 5.89328i) q^{83} +(-12.5580 + 3.68736i) q^{84} +(3.54693 - 1.25542i) q^{85} +(-0.0253855 - 0.0219966i) q^{86} +(-4.66029 - 1.01378i) q^{87} +(0.0756642 - 1.05792i) q^{88} +(-1.16784 - 0.342910i) q^{89} +(-0.595563 + 0.0325423i) q^{90} +3.24036i q^{91} +(9.53343 - 0.964426i) q^{92} +(-1.78301 + 1.78301i) q^{93} +(-0.0667775 - 0.0304962i) q^{94} +(6.34634 - 9.51932i) q^{95} +(-1.05031 - 1.21212i) q^{96} +(-0.0478111 + 0.219784i) q^{97} +(-0.00706350 - 0.0987607i) q^{98} +(-5.04273 + 35.0729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	0.0418710	−	0.0156171i	0.0296073	−	0.0110429i	−0.334617	−	0.942354i	$-0.608607\pi$
$2$	0.0418710	−	0.0156171i	0.0296073	−	0.0110429i	0.364224	+	0.931311i	$0.381334\pi$
$3$	2.62848	−	1.43526i	1.51755	−	0.828647i	0.517913	−	0.855433i	$-0.326709\pi$
$3$	2.62848	−	1.43526i	1.51755	−	0.828647i	0.999641	+	0.0267858i	$0.00852722\pi$
$4$	−1.50999	+	1.30841i	−0.754995	+	0.654207i
$5$	−0.593814	−	2.15578i	−0.265562	−	0.964094i
$5$	−0.593814	−	2.15578i	−0.265562	−	0.964094i
$6$	0.0876426	−	0.101145i	0.0357799	−	0.0412922i
$7$	1.31081	+	1.75104i	0.495441	+	0.661832i	0.976666	−	0.214766i	$-0.0688988\pi$
$7$	1.31081	+	1.75104i	0.495441	+	0.661832i	−0.481225	+	0.876597i	$0.659808\pi$
$8$	−0.0856252	+	0.156811i	−0.0302731	+	0.0554410i
$9$	3.22702	−	5.02134i	1.07567	−	1.67378i
$10$	−0.0585306	−	0.0809910i	−0.0185090	−	0.0256116i
$11$	−5.39993	+	2.46606i	−1.62814	+	0.743546i	−0.999419	−	0.0340850i	$-0.989148\pi$
$11$	−5.39993	+	2.46606i	−1.62814	+	0.743546i	−0.628721	+	0.777631i	$0.716421\pi$
$12$	−2.09107	+	5.60637i	−0.603639	+	1.61842i
$13$	1.18594	+	0.887787i	0.328922	+	0.246228i	0.750956	−	0.660352i	$-0.229593\pi$
$13$	1.18594	+	0.887787i	0.328922	+	0.246228i	−0.422034	+	0.906580i	$0.638684\pi$
$14$	0.0822312	+	0.0528468i	0.0219772	+	0.0141239i
$15$	−4.65493	−	4.81415i	−1.20190	−	1.24301i
$16$	0.567555	−	3.94743i	0.141889	−	0.986857i
$17$	0.120040	+	1.67838i	0.0291140	+	0.407067i	0.991023	+	0.133695i	$0.0426843\pi$
$17$	0.120040	+	1.67838i	0.0291140	+	0.407067i	−0.961909	+	0.273371i	$0.911861\pi$
$18$	0.0566999	−	0.260645i	0.0133643	−	0.0614347i
$19$	3.35060	+	3.86680i	0.768681	+	0.887105i	0.996238	−	0.0866596i	$-0.0276192\pi$
$19$	3.35060	+	3.86680i	0.768681	+	0.887105i	−0.227557	+	0.973765i	$0.573074\pi$
$20$	3.71730	+	2.47825i	0.831215	+	0.554154i
$21$	5.95865	+	2.72122i	1.30028	+	0.593820i
$22$	−0.187588	+	0.187588i	−0.0399938	+	0.0399938i
$23$	−3.92214	−	2.75986i	−0.817823	−	0.575470i
$23$	−3.92214	−	2.75986i	−0.817823	−	0.575470i
$24$			0.535068i			0.109220i
$25$	−4.29477	+	2.56026i	−0.858954	+	0.512053i
$26$	0.0635213	+	0.0186515i	0.0124576	+	0.00365787i
$27$	0.634294	−	8.86858i	0.122070	−	1.70676i
$28$	−4.27040	−	0.928969i	−0.807030	−	0.175559i
$29$	−1.20354	−	1.04288i	−0.223493	−	0.193657i	0.535916	−	0.844271i	$-0.319966\pi$
$29$	−1.20354	−	1.04288i	−0.223493	−	0.193657i	−0.759409	+	0.650614i	$0.774512\pi$
$30$	−0.270090	−	0.128877i	−0.0493114	−	0.0235296i
$31$	−0.807869	+	0.237212i	−0.145098	+	0.0426045i	−0.353475	−	0.935444i	$-0.615000\pi$
$31$	−0.807869	+	0.237212i	−0.145098	+	0.0426045i	0.208377	+	0.978049i	$0.433182\pi$
$32$	−0.113839	−	0.523311i	−0.0201241	−	0.0925092i
$33$	−10.6542	+	14.2323i	−1.85465	+	2.47753i
$34$	0.0312376	+	0.0684007i	0.00535720	+	0.0117306i
$35$	2.99648	−	3.86562i	0.506498	−	0.653409i
$36$	1.69722	+	11.8045i	0.282871	+	1.96741i
$37$	−5.40713	+	1.17625i	−0.888927	+	0.193374i	−0.633766	−	0.773524i	$-0.718492\pi$
$37$	−5.40713	+	1.17625i	−0.888927	+	0.193374i	−0.255161	+	0.966899i	$0.582128\pi$
$38$	0.200681	+	0.109580i	0.0325548	+	0.0177763i
$39$	4.39144	+	0.631394i	0.703193	+	0.101104i
$40$	0.388895	+	0.0914725i	0.0614897	+	0.0144631i
$41$	6.12788	−	3.93815i	0.957015	−	0.615036i	0.0338444	−	0.999427i	$-0.489225\pi$
$41$	6.12788	−	3.93815i	0.957015	−	0.615036i	0.923170	+	0.384391i	$0.125589\pi$
$42$	0.291992	+	0.0208837i	0.0450554	+	0.00322242i
$43$	−0.360223	−	0.659699i	−0.0549335	−	0.100603i	0.848770	−	0.528763i	$-0.177344\pi$
$43$	−0.360223	−	0.659699i	−0.0549335	−	0.100603i	−0.903703	+	0.428160i	$0.859162\pi$
$44$	4.92720	−	10.7891i	0.742804	−	1.62651i
$45$	−12.7412	−	3.97500i	−1.89934	−	0.592558i
$46$	−0.207325	−	0.0543056i	−0.0305684	−	0.00800693i
$47$	−1.16159	−	1.16159i	−0.169435	−	0.169435i	0.617296	−	0.786731i	$-0.288228\pi$
$47$	−1.16159	−	1.16159i	−0.169435	−	0.169435i	−0.786731	+	0.617296i	$0.788228\pi$
$48$	−4.17378	−	11.1903i	−0.602433	−	1.61519i
$49$	0.624212	−	2.12587i	0.0891731	−	0.303696i
$50$	−0.139842	+	0.174273i	−0.0197767	+	0.0246459i
$51$	2.72443	+	4.23930i	0.381497	+	0.593620i
$52$	−2.95236	+	0.211157i	−0.409418	+	0.0292822i
$53$	5.63313	−	4.21690i	0.773769	−	0.579236i	−0.137763	−	0.990465i	$-0.543991\pi$
$53$	5.63313	−	4.21690i	0.773769	−	0.579236i	0.911532	+	0.411229i	$0.134900\pi$
$54$	−0.111943	−	0.381242i	−0.0152335	−	0.0518805i
$55$	8.52284	+	10.1767i	1.14922	+	1.37222i
$56$	−0.386821	+	0.0556164i	−0.0516911	+	0.00743206i
$57$	14.3569	+	5.35483i	1.90161	+	0.709265i
$58$	−0.0666803	−	0.0248705i	−0.00875555	−	0.00326565i
$59$	5.98982	−	0.861206i	0.779808	−	0.112120i	0.259096	−	0.965852i	$-0.416575\pi$
$59$	5.98982	−	0.861206i	0.779808	−	0.112120i	0.520712	+	0.853732i	$0.325666\pi$
$60$	13.3278	+	1.17874i	1.72061	+	0.152175i
$61$	−2.24031	−	7.62978i	−0.286842	−	0.976893i	−0.969282	−	0.245952i	$-0.920900\pi$
$61$	−2.24031	−	7.62978i	−0.286842	−	0.976893i	0.682440	−	0.730941i	$-0.260919\pi$
$62$	−0.0301217	+	0.0225489i	−0.00382547	+	0.00286371i
$63$	13.0226	−	0.931395i	1.64069	−	0.117345i
$64$	4.29924	+	6.68974i	0.537404	+	0.836218i
$65$	1.20964	−	3.08382i	0.150038	−	0.382500i
$66$	−0.223834	+	0.762308i	−0.0275520	+	0.0938336i
$67$	1.40667	+	3.77142i	0.171852	+	0.460753i	0.994112	−	0.108359i	$-0.0345597\pi$
$67$	1.40667	+	3.77142i	0.171852	+	0.460753i	−0.822260	+	0.569112i	$0.807287\pi$
$68$	−2.37727	−	2.37727i	−0.288287	−	0.288287i
$69$	−14.2704	−	1.62494i	−1.71795	−	0.195620i
$70$	0.0650960	−	0.208654i	0.00778046	−	0.0249389i
$71$	1.35921	−	2.97626i	0.161309	−	0.353217i	−0.811668	−	0.584119i	$-0.801440\pi$
$71$	1.35921	−	2.97626i	0.161309	−	0.353217i	0.972977	+	0.230902i	$0.0741676\pi$
$72$	0.511087	+	0.935985i	0.0602321	+	0.110307i
$73$	7.97697	+	0.570524i	0.933634	+	0.0667748i	0.529861	−	0.848084i	$-0.322244\pi$
$73$	7.97697	+	0.570524i	0.933634	+	0.0667748i	0.403773	+	0.914859i	$0.367699\pi$
$74$	−0.208032	+	0.133694i	−0.0241833	+	0.0155417i
$75$	−7.61408	+	12.8937i	−0.879198	+	1.48884i
$76$	−10.1188	−	1.45486i	−1.16070	−	0.166884i
$77$	−11.3965	−	6.22295i	−1.29875	−	0.709171i
$78$	0.193734	−	0.0421444i	0.0219361	−	0.00477191i
$79$	−1.48088	−	10.2997i	−0.166612	−	1.15881i	−0.885825	−	0.464020i	$-0.846407\pi$
$79$	−1.48088	−	10.2997i	−0.166612	−	1.15881i	0.719213	−	0.694789i	$-0.244502\pi$
$80$	−8.84681	+	1.12052i	−0.989103	+	0.125278i
$81$	−3.62280	−	7.93282i	−0.402533	−	0.881425i
$82$	0.195078	−	0.260594i	0.0215428	−	0.0287778i
$83$	1.28200	+	5.89328i	0.140718	+	0.646871i	0.992425	+	0.122853i	$0.0392042\pi$
$83$	1.28200	+	5.89328i	0.140718	+	0.646871i	−0.851707	+	0.524019i	$0.824432\pi$
$84$	−12.5580	+	3.68736i	−1.37019	+	0.402324i
$85$	3.54693	−	1.25542i	0.384719	−	0.136170i
$86$	−0.0253855	−	0.0219966i	−0.00273738	−	0.00237196i
$87$	−4.66029	−	1.01378i	−0.499636	−	0.108689i
$88$	0.0756642	−	1.05792i	0.00806583	−	0.112775i
$89$	−1.16784	−	0.342910i	−0.123791	−	0.0363484i	0.219250	−	0.975669i	$-0.429639\pi$
$89$	−1.16784	−	0.342910i	−0.123791	−	0.0363484i	−0.343041	+	0.939320i	$0.611457\pi$
$90$	−0.595563	+	0.0325423i	−0.0627779	+	0.00343026i
$91$			3.24036i			0.339682i
$92$	9.53343	−	0.964426i	0.993929	−	0.100548i
$93$	−1.78301	+	1.78301i	−0.184889	+	0.184889i
$94$	−0.0667775	−	0.0304962i	−0.00688757	−	0.00314545i
$95$	6.34634	−	9.51932i	0.651120	−	0.976662i
$96$	−1.05031	−	1.21212i	−0.107197	−	0.123712i
$97$	−0.0478111	+	0.219784i	−0.00485449	+	0.0223157i	−0.979510	−	0.201394i	$-0.935453\pi$
$97$	−0.0478111	+	0.219784i	−0.00485449	+	0.0223157i	0.974656	+	0.223709i	$0.0718166\pi$
$98$	−0.00706350	−	0.0987607i	−0.000713522	−	0.00997634i
$99$	−5.04273	+	35.0729i	−0.506813	+	3.52496i
$100$	3.13517	−	9.48531i	0.313517	−	0.948531i
$101$	−7.48411	−	4.80975i	−0.744697	−	0.478588i	0.112451	−	0.993657i	$-0.464130\pi$
$101$	−7.48411	−	4.80975i	−0.744697	−	0.478588i	−0.857148	+	0.515070i	$0.827766\pi$
$102$	0.180280	+	0.134956i	0.0178504	+	0.0133626i
$103$	−0.287717	+	0.771399i	−0.0283496	+	0.0760082i	−0.950353	−	0.311172i	$-0.899278\pi$
$103$	−0.287717	+	0.771399i	−0.0283496	+	0.0760082i	0.922004	+	0.387181i	$0.126551\pi$
$104$	−0.240761	+	0.109952i	−0.0236086	+	0.0107817i
$105$	2.32803	−	14.4614i	0.227192	−	1.41129i
$106$	0.170009	−	0.264539i	0.0165127	−	0.0256943i
$107$	−4.23577	+	7.75723i	−0.409487	+	0.749920i	−0.998296	−	0.0583526i	$-0.981415\pi$
$107$	−4.23577	+	7.75723i	−0.409487	+	0.749920i	0.588809	+	0.808272i	$0.299597\pi$
$108$	10.6460	+	14.2214i	1.02441	+	1.36845i
$109$	−1.73444	+	2.00165i	−0.166129	+	0.191723i	−0.832710	−	0.553710i	$-0.813212\pi$
$109$	−1.73444	+	2.00165i	−0.166129	+	0.191723i	0.666581	+	0.745433i	$0.267757\pi$
$110$	0.515790	+	0.293005i	0.0491786	+	0.0279370i
$111$	−12.5243	+	10.8524i	−1.18876	+	1.03006i
$112$	7.65607	−	4.18053i	0.723431	−	0.395023i
$113$	−7.76927	+	2.89779i	−0.730872	+	0.272601i	−0.687224	−	0.726446i	$-0.741171\pi$
$113$	−7.76927	+	2.89779i	−0.730872	+	0.272601i	−0.0436481	+	0.999047i	$0.513898\pi$
$114$	0.684763			0.0641339
$115$	−3.62062	+	10.0941i	−0.337625	+	0.941281i
$116$	3.18185			0.295428
$117$	8.28495	−	3.09013i	0.765944	−	0.285682i
$118$	0.237350	−	0.129603i	0.0218499	−	0.0119309i
$119$	−2.78156	+	2.41024i	−0.254985	+	0.220946i
$120$	1.15349	−	0.317731i	0.105299	−	0.0290048i
$121$	15.8743	−	18.3199i	1.44312	−	1.66544i
$122$	−0.212959	−	0.284479i	−0.0192804	−	0.0257556i
$123$	10.4548	−	19.1465i	0.942674	−	1.72638i
$124$	0.909503	−	1.41521i	0.0816758	−	0.127090i
$125$	8.06966	+	7.73826i	0.721772	+	0.692131i
$126$	0.530724	−	0.242374i	0.0472807	−	0.0215924i
$127$	−5.39997	+	14.4779i	−0.479170	+	1.28470i	0.442513	+	0.896762i	$0.354087\pi$
$127$	−5.39997	+	14.4779i	−0.479170	+	1.28470i	−0.921683	+	0.387943i	$0.873186\pi$
$128$	1.14195	+	0.854851i	0.100935	+	0.0755588i
$129$	−1.89368	−	1.21699i	−0.166729	−	0.107150i
$130$	0.00248876	−	0.148014i	0.000218279	−	0.0129816i
$131$	−1.61663	+	11.2439i	−0.141246	+	0.982386i	0.788723	+	0.614748i	$0.210742\pi$
$131$	−1.61663	+	11.2439i	−0.141246	+	0.982386i	−0.929969	+	0.367638i	$0.880167\pi$
$132$	−2.53405	−	35.4307i	−0.220561	−	3.08385i
$133$	−2.37892	+	10.9357i	−0.206278	+	0.948246i
$134$	0.117797	+	0.135945i	0.0101761	+	0.0117439i
$135$	−19.4954	+	3.89889i	−1.67789	+	0.335563i
$136$	−0.273466	−	0.124888i	−0.0234495	−	0.0107090i
$137$	−3.61310	+	3.61310i	−0.308688	+	0.308688i	−0.844401	−	0.535712i	$-0.820043\pi$
$137$	−3.61310	+	3.61310i	−0.308688	+	0.308688i	0.535712	+	0.844401i	$0.320043\pi$
$138$	−0.622892	+	0.154824i	−0.0530241	+	0.0131795i
$139$			13.8495i			1.17470i	0.809334	+	0.587348i	$0.199828\pi$
$139$			13.8495i			1.17470i	−0.809334	+	0.587348i	$0.800172\pi$
$140$	0.533172	+	9.75768i	0.0450613	+	0.824675i
$141$	−4.72039	−	1.38603i	−0.397529	−	0.116725i
$142$	0.0104311	−	0.145846i	0.000875358	−	0.0122391i
$143$	−8.59336	−	1.86937i	−0.718613	−	0.156325i
$144$	−17.9899	−	15.5883i	−1.49916	−	1.29903i
$145$	−1.53353	+	3.21385i	−0.127353	+	0.266896i
$146$	0.342914	−	0.100689i	0.0283797	−	0.00833304i
$147$	−1.41045	−	6.48372i	−0.116332	−	0.534768i
$148$	6.62569	−	8.85089i	0.544629	−	0.727539i
$149$	0.495437	+	1.08485i	0.0405877	+	0.0888748i	0.928840	−	0.370482i	$-0.120807\pi$
$149$	0.495437	+	1.08485i	0.0405877	+	0.0888748i	−0.888252	+	0.459356i	$0.848080\pi$
$150$	−0.117447	+	0.658782i	−0.00958951	+	0.0537894i
$151$	−2.31288	−	16.0864i	−0.188220	−	1.30910i	−0.836615	−	0.547792i	$-0.815469\pi$
$151$	−2.31288	−	16.0864i	−0.188220	−	1.30910i	0.648395	−	0.761304i	$-0.275441\pi$
$152$	−0.893252	+	0.194315i	−0.0724523	+	0.0157610i
$153$	8.81509	+	4.81340i	0.712658	+	0.389140i
$154$	−0.574366	−	0.0825814i	−0.0462838	−	0.00665460i
$155$	0.991101	+	1.60073i	0.0796071	+	0.128574i
$156$	−7.45715	+	4.79242i	−0.597050	+	0.383701i
$157$	−16.0284	−	1.14637i	−1.27920	−	0.0914904i	−0.584860	−	0.811134i	$-0.698851\pi$
$157$	−16.0284	−	1.14637i	−1.27920	−	0.0914904i	−0.694343	+	0.719644i	$0.744305\pi$
$158$	−0.222857	−	0.408133i	−0.0177296	−	0.0324693i
$159$	8.75421	−	19.1691i	0.694254	−	1.52020i
$160$	−1.06054	+	0.556162i	−0.0838433	+	0.0439684i
$161$	−0.308570	−	10.4855i	−0.0243187	−	0.826373i
$162$	−0.275578	−	0.275578i	−0.0216514	−	0.0216514i
$163$	5.04989	+	13.5393i	0.395538	+	1.06048i	0.970246	+	0.242120i	$0.0778427\pi$
$163$	5.04989	+	13.5393i	0.395538	+	1.06048i	−0.574708	+	0.818358i	$0.694885\pi$
$164$	−4.10031	+	13.9644i	−0.320181	+	1.09043i
$165$	37.0083	+	14.5167i	2.88109	+	1.13012i
$166$	0.145715	+	0.226736i	0.0113096	+	0.0175982i
$167$	17.3256	−	1.23915i	1.34070	−	0.0958886i	0.617522	−	0.786553i	$-0.288137\pi$
$167$	17.3256	−	1.23915i	1.34070	−	0.0958886i	0.723175	+	0.690665i	$0.242682\pi$
$168$	−0.936927	+	0.701375i	−0.0722855	+	0.0541123i
$169$	−3.04422	−	10.3677i	−0.234171	−	0.797513i
$170$	0.128908	−	0.107959i	0.00988676	−	0.00828005i
$171$	30.2290	−	4.34628i	2.31167	−	0.332368i
$172$	1.40709	+	0.524818i	0.107290	+	0.0400170i
$173$	−18.7219	−	6.98291i	−1.42340	−	0.530901i	−0.484408	−	0.874842i	$-0.660965\pi$
$173$	−18.7219	−	6.98291i	−1.42340	−	0.530901i	−0.938991	+	0.343941i	$0.888238\pi$
$174$	−0.210963	+	0.0303320i	−0.0159931	+	0.00229946i
$175$	−10.1128	−	4.16429i	−0.764454	−	0.314791i
$176$	6.66986	+	22.7155i	0.502760	+	1.71224i
$177$	14.5081	−	10.8606i	1.09049	−	0.816334i
$178$	−0.0542540	+	0.00388033i	−0.00406651	+	0.000290843i
$179$	8.23860	+	12.8195i	0.615782	+	0.958175i	0.999398	+	0.0346827i	$0.0110421\pi$
$179$	8.23860	+	12.8195i	0.615782	+	0.958175i	−0.383617	+	0.923492i	$0.625322\pi$
$180$	24.4400	−	10.6685i	1.82165	−	0.795183i
$181$	−1.30799	+	4.45462i	−0.0972224	+	0.331109i	−0.993714	−	0.111953i	$-0.964290\pi$
$181$	−1.30799	+	4.45462i	−0.0972224	+	0.331109i	0.896491	+	0.443062i	$0.146108\pi$
$182$	0.0506050	+	0.135677i	0.00375109	+	0.0100571i
$183$	−16.8393	−	16.8393i	−1.24480	−	1.24480i
$184$	0.768609	−	0.378721i	0.0566626	−	0.0279197i
$185$	5.74657	+	10.9581i	0.422496	+	0.805656i
$186$	−0.0468110	+	0.102502i	−0.00343235	+	0.00751579i
$187$	−4.78720	−	8.76710i	−0.350074	−	0.641114i
$188$	3.27382	+	0.234148i	0.238768	+	0.0170770i
$189$	16.3607	−	10.5144i	1.19007	−	0.764809i
$190$	0.117064	−	0.497695i	0.00849268	−	0.0361066i
$191$	0.657872	+	0.0945878i	0.0476020	+	0.00684413i	0.166075	−	0.986113i	$-0.446891\pi$
$191$	0.657872	+	0.0945878i	0.0476020	+	0.00684413i	−0.118473	+	0.992957i	$0.537800\pi$
$192$	20.9020	+	11.4133i	1.50847	+	0.823687i
$193$	−13.4353	+	2.92267i	−0.967093	+	0.210378i	−0.668260	−	0.743927i	$-0.732961\pi$
$193$	−13.4353	+	2.92267i	−0.967093	+	0.210378i	−0.298832	+	0.954306i	$0.596597\pi$
$194$	0.00143049	+	0.00994926i	0.000102703	+	0.000714315i
$195$	−1.24655	−	9.84190i	−0.0892675	−	0.704793i
$196$	1.83896	+	4.02677i	0.131355	+	0.287626i
$197$	−7.36976	+	9.84485i	−0.525074	+	0.701417i	−0.982169	−	0.188001i	$-0.939799\pi$
$197$	−7.36976	+	9.84485i	−0.525074	+	0.701417i	0.457095	+	0.889418i	$0.348890\pi$
$198$	0.336593	+	1.54729i	0.0239206	+	0.109961i
$199$	22.6293	−	6.64456i	1.60415	−	0.471021i	0.647452	−	0.762106i	$-0.275835\pi$
$199$	22.6293	−	6.64456i	1.60415	−	0.471021i	0.956697	+	0.291086i	$0.0940165\pi$
$200$	−0.0337366	−	0.892689i	−0.00238554	−	0.0631227i
$201$	9.11037	+	7.89418i	0.642596	+	0.556813i
$202$	−0.388481	−	0.0845090i	−0.0273335	−	0.00594603i
$203$	0.248499	−	3.47447i	0.0174412	−	0.243860i
$204$	−9.66062	−	2.83661i	−0.676379	−	0.198603i
$205$	−12.1286	−	10.8718i	−0.847099	−	0.759322i
$206$			0.0367925i			0.00256346i
$207$	−26.5150	+	10.7883i	−1.84292	+	0.749839i
$208$	4.17757	−	4.17757i	0.289662	−	0.289662i
$209$	−27.6288	−	12.6176i	−1.91112	−	0.872781i
$210$	−0.128368	−	0.641872i	−0.00885826	−	0.0442934i
$211$	−10.5202	−	12.1409i	−0.724238	−	0.835815i	0.267572	−	0.963538i	$-0.413779\pi$
$211$	−10.5202	−	12.1409i	−0.724238	−	0.835815i	−0.991810	+	0.127723i	$0.959233\pi$
$212$	−2.98851	+	13.7379i	−0.205251	+	0.943526i
$213$	−0.699040	−	9.77386i	−0.0478975	−	0.669694i
$214$	−0.0562106	+	0.390953i	−0.00384248	+	0.0267250i
$215$	−1.20826	+	1.16830i	−0.0824027	+	0.0796774i
$216$	1.33638	+	0.858838i	0.0909290	+	0.0584365i
$217$	−1.47433	−	1.10367i	−0.100084	−	0.0749222i
$218$	−0.0413628	+	0.110898i	−0.00280144	+	0.00751096i
$219$	21.7862	−	9.94941i	1.47217	−	0.672319i
$220$	−26.1847	−	4.21526i	−1.76537	−	0.284193i
$221$	−1.34768	+	2.09703i	−0.0906549	+	0.141062i
$222$	−0.354923	+	0.649994i	−0.0238209	+	0.0436247i
$223$	15.1684	+	20.2625i	1.01575	+	1.35688i	0.932827	+	0.360324i	$0.117334\pi$
$223$	15.1684	+	20.2625i	1.01575	+	1.35688i	0.0829210	+	0.996556i	$0.473575\pi$
$224$	0.767117	−	0.885300i	0.0512552	−	0.0591516i
$225$	−1.00335	+	29.8275i	−0.0668900	+	1.98850i
$226$	−0.280052	+	0.242667i	−0.0186288	+	0.0161419i
$227$	25.0432	−	13.6746i	1.66218	−	0.907618i	0.677022	−	0.735963i	$-0.263270\pi$
$227$	25.0432	−	13.6746i	1.66218	−	0.907618i	0.985157	−	0.171655i	$-0.0549115\pi$
$228$	−28.6850	+	10.6990i	−1.89971	+	0.708557i
$229$	2.70003			0.178423			0.0892116	−	0.996013i	$-0.471565\pi$
$229$	2.70003			0.178423			0.0892116	+	0.996013i	$0.471565\pi$
$230$	0.00604149	+	0.479194i	0.000398364	+	0.0315971i
$231$	−38.8870			−2.55858
$232$	0.266588	−	0.0994322i	0.0175024	−	0.00652804i
$233$	16.2143	−	8.85367i	1.06223	−	0.580023i	0.149576	−	0.988750i	$-0.452209\pi$
$233$	16.2143	−	8.85367i	1.06223	−	0.580023i	0.912657	+	0.408727i	$0.134027\pi$
$234$	0.298641	−	0.258774i	0.0195227	−	0.0169166i
$235$	−1.81436	+	3.19389i	−0.118356	+	0.208347i
$236$	−7.91776	+	9.13758i	−0.515402	+	0.594806i
$237$	−18.6752	−	24.9472i	−1.21309	−	1.62049i
$238$	−0.0788259	+	0.144359i	−0.00510952	+	0.00935740i
$239$	−10.4118	+	16.2011i	−0.673483	+	1.04796i	0.321402	+	0.946943i	$0.395846\pi$
$239$	−10.4118	+	16.2011i	−0.673483	+	1.04796i	−0.994885	+	0.101017i	$0.967790\pi$
$240$	−21.6454	+	15.6427i	−1.39721	+	1.00973i
$241$	9.26869	−	4.23287i	0.597049	−	0.272663i	−0.0938826	−	0.995583i	$-0.529928\pi$
$241$	9.26869	−	4.23287i	0.597049	−	0.272663i	0.690932	+	0.722920i	$0.257201\pi$
$242$	0.378569	−	1.01498i	0.0243353	−	0.0652455i
$243$	0.445291	+	0.333340i	0.0285654	+	0.0213838i
$244$	13.3657	+	8.58964i	0.855654	+	0.549896i
$245$	−4.95357	−	0.0832915i	−0.316472	−	0.00532130i
$246$	0.138739	−	0.964954i	0.00884571	−	0.0615232i
$247$	0.540733	+	7.56044i	0.0344060	+	0.481059i
$248$	0.0319766	−	0.146994i	0.00203051	−	0.00933412i
$249$	11.8281	+	13.6504i	0.749576	+	0.865057i
$250$	0.458734	+	0.197984i	0.0290129	+	0.0125216i
$251$	−2.32731	−	1.06285i	−0.146899	−	0.0670864i	0.340609	−	0.940205i	$-0.389367\pi$
$251$	−2.32731	−	1.06285i	−0.146899	−	0.0670864i	−0.487508	+	0.873119i	$0.662094\pi$
$252$	−18.4454	+	18.4454i	−1.16195	+	1.16195i
$253$	27.9853	+	5.23078i	1.75942	+	0.328856i
$254$			0.690536i			0.0433281i
$255$	7.52119	−	8.39063i	0.470995	−	0.525441i
$256$	−15.1988	−	4.46278i	−0.949926	−	0.278924i
$257$	0.402759	−	5.63131i	0.0251234	−	0.351271i	−0.969305	−	0.245860i	$-0.920930\pi$
$257$	0.402759	−	5.63131i	0.0251234	−	0.351271i	0.994429	−	0.105411i	$-0.0336159\pi$
$258$	−0.0982961	−	0.0213830i	−0.00611965	−	0.00133125i
$259$	−9.14741	−	7.92627i	−0.568392	−	0.492515i
$260$	2.20836	+	6.23924i	0.136957	+	0.386941i
$261$	−9.12051	+	2.67802i	−0.564545	+	0.165765i
$262$	0.107907	+	0.496041i	0.00666653	+	0.0306455i
$263$	5.49025	−	7.33412i	0.338543	−	0.452241i	−0.598671	−	0.800995i	$-0.704304\pi$
$263$	5.49025	−	7.33412i	0.338543	−	0.452241i	0.937214	+	0.348754i	$0.113395\pi$
$264$	−1.31951	−	2.88933i	−0.0812104	−	0.177826i
$265$	−12.4357	−	9.63972i	−0.763922	−	0.592163i
$266$	0.0711761	+	0.495041i	0.00436409	+	0.0303529i
$267$	−3.56182	+	0.774827i	−0.217980	+	0.0474186i
$268$	−7.05864	−	3.85431i	−0.431175	−	0.235439i
$269$	−21.8795	−	3.14580i	−1.33402	−	0.191803i	−0.561860	−	0.827232i	$-0.689914\pi$
$269$	−21.8795	−	3.14580i	−1.33402	−	0.191803i	−0.772159	+	0.635429i	$0.780823\pi$
$270$	−0.755401	+	0.467711i	−0.0459722	+	0.0284640i
$271$	7.89126	−	5.07140i	0.479360	−	0.308066i	−0.278554	−	0.960421i	$-0.589855\pi$
$271$	7.89126	−	5.07140i	0.479360	−	0.308066i	0.757914	+	0.652355i	$0.226219\pi$
$272$	6.69341	+	0.478722i	0.405848	+	0.0290268i
$273$	4.65076	+	8.51723i	0.281477	+	0.515486i
$274$	−0.0948582	+	0.207710i	−0.00573059	+	0.0125482i
$275$	16.8777	−	24.4164i	1.01776	−	1.47237i
$276$	23.6742	−	16.2179i	1.42502	−	0.976204i
$277$	22.2583	+	22.2583i	1.33737	+	1.33737i	0.898597	+	0.438775i	$0.144587\pi$
$277$	22.2583	+	22.2583i	1.33737	+	1.33737i	0.438775	+	0.898597i	$0.355413\pi$
$278$	0.216288	+	0.579891i	0.0129721	+	0.0347796i
$279$	−1.41589	+	4.82208i	−0.0847671	+	0.288690i
$280$	0.349596	+	0.800875i	0.0208924	+	0.0478614i
$281$	13.2888	+	20.6778i	0.792745	+	1.23354i	0.968478	+	0.249098i	$0.0801341\pi$
$281$	13.2888	+	20.6778i	0.792745	+	1.23354i	−0.175733	+	0.984438i	$0.556230\pi$
$282$	−0.219293	+	0.0156842i	−0.0130587	+	0.000933978i
$283$	−8.48373	+	6.35084i	−0.504305	+	0.377518i	−0.820927	−	0.571034i	$-0.806543\pi$
$283$	−8.48373	+	6.35084i	−0.504305	+	0.377518i	0.316621	+	0.948552i	$0.397452\pi$
$284$	1.84178	+	6.27253i	0.109290	+	0.372206i
$285$	3.01853	−	34.1300i	0.178802	−	2.02169i
$286$	−0.389007	+	0.0559307i	−0.0230024	+	0.00330725i
$287$	14.9284	+	5.56800i	0.881195	+	0.328669i
$288$	−2.99509	−	1.11711i	−0.176487	−	0.0658263i
$289$	14.0244	−	2.01641i	0.824966	−	0.118612i
$290$	−0.0140195	+	0.158516i	−0.000823256	+	0.00930841i
$291$	0.189777	+	0.646320i	0.0111249	+	0.0378880i
$292$	−12.7916	+	9.57569i	−0.748573	+	0.560375i
$293$	−3.71187	+	0.265478i	−0.216850	+	0.0155094i	−0.179341	−	0.983787i	$-0.557397\pi$
$293$	−3.71187	+	0.265478i	−0.216850	+	0.0155094i	−0.0375083	+	0.999296i	$0.511942\pi$
$294$	−0.160313	−	0.249453i	−0.00934967	−	0.0145484i
$295$	−5.41341	−	12.4013i	−0.315181	−	0.722034i
$296$	0.278538	−	0.948613i	0.0161897	−	0.0551370i
$297$	18.4454	+	49.4539i	1.07031	+	2.86961i
$298$	0.0376867	+	0.0376867i	0.00218313	+	0.00218313i
$299$	−2.20128	−	6.75506i	−0.127303	−	0.390655i
$300$	−5.37313	−	29.4317i	−0.310218	−	1.69924i
$301$	0.682976	−	1.49551i	0.0393661	−	0.0861996i
$302$	−0.348066	−	0.637435i	−0.0200289	−	0.0366803i
$303$	−26.5751	−	1.90069i	−1.52670	−	0.109192i
$304$	17.1656	−	11.0316i	0.984513	−	0.632708i
$305$	−15.1178	+	9.36027i	−0.865642	+	0.535968i
$306$	0.444268	+	0.0638761i	0.0253971	+	0.00365155i
$307$	−21.8784	−	11.9465i	−1.24867	−	0.681824i	−0.287497	−	0.957781i	$-0.592823\pi$
$307$	−21.8784	−	11.9465i	−1.24867	−	0.681824i	−0.961170	+	0.275957i	$0.911005\pi$
$308$	25.3508	−	5.51472i	1.44449	−	0.314230i
$309$	0.350899	+	2.44056i	0.0199619	+	0.138838i
$310$	0.0664971	+	0.0515460i	0.00377678	+	0.00292762i
$311$	2.57664	+	5.64206i	0.146108	+	0.319932i	0.968510	−	0.248975i	$-0.0800937\pi$
$311$	2.57664	+	5.64206i	0.146108	+	0.319932i	−0.822402	+	0.568907i	$0.807366\pi$
$312$	−0.475027	+	0.634562i	−0.0268931	+	0.0359250i
$313$	−4.23161	−	19.4524i	−0.239185	−	1.09951i	−0.927418	−	0.374025i	$-0.877977\pi$
$313$	−4.23161	−	19.4524i	−0.239185	−	1.09951i	0.688234	−	0.725489i	$-0.258386\pi$
$314$	−0.689027	+	0.202317i	−0.0388840	+	0.0114174i
$315$	−9.74089	−	27.5208i	−0.548837	−	1.55062i
$316$	15.7124	+	13.6149i	0.883892	+	0.765896i
$317$	−19.0233	−	4.13827i	−1.06846	−	0.232428i	−0.356244	−	0.934393i	$-0.615943\pi$
$317$	−19.0233	−	4.13827i	−1.06846	−	0.232428i	−0.712212	+	0.701965i	$0.752306\pi$
$318$	0.0671831	−	0.939343i	0.00376744	−	0.0526757i
$319$	9.07085	+	2.66344i	0.507870	+	0.149124i
$320$	11.8687	−	13.2407i	0.663478	−	0.740176i
$321$			26.4692i			1.47736i
$322$	−0.176673	−	0.434219i	−0.00984559	−	0.0241981i
$323$	−6.08775	+	6.08775i	−0.338731	+	0.338731i
$324$	15.8498	+	7.23836i	0.880545	+	0.402131i
$325$	−7.36633	−	0.776510i	−0.408610	−	0.0430730i
$326$	0.422888	+	0.488039i	0.0234216	+	0.0270300i
$327$	−1.68606	+	7.75067i	−0.0932391	+	0.428613i
$328$	0.0928436	+	1.29812i	0.00512643	+	0.0716769i
$329$	0.511364	−	3.55661i	0.0281924	−	0.196083i
$330$	1.77628	+	0.0298672i	0.0977811	+	0.00164413i
$331$	0.829437	+	0.533047i	0.0455900	+	0.0292989i	0.563237	−	0.826295i	$-0.309556\pi$
$331$	0.829437	+	0.533047i	0.0455900	+	0.0292989i	−0.517647	+	0.855594i	$0.673192\pi$
$332$	−9.64666	−	7.22140i	−0.529429	−	0.396326i
$333$	−11.5426	+	30.9469i	−0.632529	+	1.69588i
$334$	0.706089	−	0.322460i	0.0386355	−	0.0176442i
$335$	7.29506	−	5.27199i	0.398572	−	0.288040i
$336$	14.1237	−	21.9769i	0.770511	−	1.19894i
$337$	11.1544	−	20.4278i	0.607621	−	1.11277i	−0.374978	−	0.927034i	$-0.622350\pi$
$337$	11.1544	−	20.4278i	0.607621	−	1.11277i	0.982599	−	0.185741i	$-0.0594684\pi$
$338$	−0.289377	−	0.386563i	−0.0157401	−	0.0210263i
$339$	−16.2623	+	18.7677i	−0.883247	+	1.01932i
$340$	−3.71322	+	6.53653i	−0.201377	+	0.354493i
$341$	3.77746	−	3.27318i	0.204561	−	0.177253i
$342$	1.19784	−	0.654072i	0.0647719	−	0.0353681i
$343$	18.8866	−	7.04434i	1.01978	−	0.380358i
$344$	0.134292			0.00724054
$345$	4.97093	+	31.7287i	0.267626	+	1.70822i
$346$	−0.892957			−0.0480057
$347$	−17.3777	+	6.48157i	−0.932886	+	0.347949i	−0.769524	−	0.638617i	$-0.779507\pi$
$347$	−17.3777	+	6.48157i	−0.932886	+	0.347949i	−0.163362	+	0.986566i	$0.552234\pi$
$348$	8.36344	−	4.56679i	0.448328	−	0.244805i
$349$	4.17533	−	3.61794i	0.223500	−	0.193664i	−0.535912	−	0.844274i	$-0.680032\pi$
$349$	4.17533	−	3.61794i	0.223500	−	0.193664i	0.759412	+	0.650610i	$0.225487\pi$
$350$	−0.488466	−	0.0164312i	−0.0261096	−	0.000878285i
$351$	8.62565	−	9.95453i	0.460403	−	0.531334i
$352$	1.90524	+	2.54511i	0.101550	+	0.135655i
$353$	−5.50397	+	10.0798i	−0.292947	+	0.536492i	−0.982155	−	0.188071i	$-0.939776\pi$
$353$	−5.50397	+	10.0798i	−0.292947	+	0.536492i	0.689209	+	0.724563i	$0.257958\pi$
$354$	0.437857	−	0.681318i	0.0232718	−	0.0362117i
$355$	−7.22328	−	1.16282i	−0.383372	−	0.0617159i
$356$	2.21210	−	1.01023i	0.117241	−	0.0535422i
$357$	−3.85197	+	10.3275i	−0.203868	+	0.546590i
$358$	0.545162	+	0.408103i	0.0288127	+	0.0215689i
$359$	9.54503	+	6.13422i	0.503767	+	0.323752i	0.767722	−	0.640784i	$-0.221390\pi$
$359$	9.54503	+	6.13422i	0.503767	+	0.323752i	−0.263954	+	0.964535i	$0.585027\pi$
$360$	1.71429	−	1.65759i	0.0903509	−	0.0873627i
$361$	−1.02163	+	7.10563i	−0.0537703	+	0.373980i
$362$	0.0148011	+	0.206946i	0.000777928	+	0.0108769i
$363$	15.4314	−	70.9372i	0.809941	−	3.72324i
$364$	−4.23974	−	4.89292i	−0.222223	−	0.256458i
$365$	−3.50691	−	17.5354i	−0.183560	−	0.917844i
$366$	−0.968060	−	0.442098i	−0.0506013	−	0.0231088i
$367$	17.6394	−	17.6394i	0.920767	−	0.920767i	−0.0763165	−	0.997084i	$-0.524316\pi$
$367$	17.6394	−	17.6394i	0.920767	−	0.920767i	0.997084	+	0.0763165i	$0.0243159\pi$
$368$	−13.1204	+	13.9160i	−0.683947	+	0.725422i
$369$		−	43.4787i		−	2.26341i
$370$	0.411748	+	0.369083i	0.0214058	+	0.0191877i
$371$	14.7680	+	4.33626i	0.766714	+	0.225128i
$372$	0.359412	−	5.02524i	0.0186347	−	0.260546i
$373$	−14.1852	−	3.08579i	−0.734479	−	0.159776i	−0.170258	−	0.985400i	$-0.554460\pi$
$373$	−14.1852	−	3.08579i	−0.734479	−	0.159776i	−0.564222	+	0.825623i	$0.690824\pi$
$374$	−0.337361	−	0.292325i	−0.0174445	−	0.0151158i
$375$	32.3174	+	8.75781i	1.66886	+	0.452251i
$376$	0.281611	−	0.0826883i	0.0145230	−	0.00426433i
$377$	−0.501484	−	2.30529i	−0.0258278	−	0.118728i
$378$	0.520835	−	0.695754i	0.0267889	−	0.0357857i
$379$	−13.3596	−	29.2533i	−0.686234	−	1.50264i	−0.855900	−	0.517141i	$-0.826996\pi$
$379$	−13.3596	−	29.2533i	−0.686234	−	1.50264i	0.169666	−	0.985502i	$-0.445731\pi$
$380$	2.87231	+	22.6777i	0.147346	+	1.16334i
$381$	6.58580	+	45.8052i	0.337401	+	2.34667i
$382$	0.0290230	−	0.00631356i	0.00148494	−	0.000323030i
$383$	−11.4771	−	6.26696i	−0.586451	−	0.320226i	0.158486	−	0.987361i	$-0.449339\pi$
$383$	−11.4771	−	6.26696i	−0.586451	−	0.320226i	−0.744937	+	0.667135i	$0.767521\pi$
$384$	4.22852	+	0.607969i	0.215786	+	0.0310253i
$385$	−6.64792	+	28.2636i	−0.338809	+	1.44045i
$386$	−0.516905	+	0.332195i	−0.0263098	+	0.0169083i
$387$	−4.47502	−	0.320060i	−0.227478	−	0.0162696i
$388$	−0.215374	−	0.394429i	−0.0109340	−	0.0200241i
$389$	6.26784	−	13.7247i	0.317792	−	0.695868i	−0.681564	−	0.731759i	$-0.738700\pi$
$389$	6.26784	−	13.7247i	0.317792	−	0.695868i	0.999356	+	0.0358913i	$0.0114270\pi$
$390$	−0.205896	−	0.392623i	−0.0104260	−	0.0198812i
$391$	4.16127	−	6.91413i	0.210445	−	0.349663i
$392$	0.279911	+	0.279911i	0.0141376	+	0.0141376i
$393$	11.8887	+	31.8747i	0.599703	+	1.60787i
$394$	−0.154832	+	0.527308i	−0.00780030	+	0.0265654i
$395$	−21.3246	+	9.30856i	−1.07295	+	0.468364i
$396$	−38.2754	−	59.5578i	−1.92341	−	2.99289i
$397$	9.04417	−	0.646852i	0.453914	−	0.0324646i	0.157489	−	0.987521i	$-0.449660\pi$
$397$	9.04417	−	0.646852i	0.453914	−	0.0324646i	0.296425	+	0.955056i	$0.404206\pi$
$398$	0.843743	−	0.631618i	0.0422930	−	0.0316602i
$399$	9.44263	+	32.1587i	0.472723	+	1.60995i
$400$	7.66894	+	18.4064i	0.383447	+	0.920319i
$401$	−32.2293	+	4.63388i	−1.60946	+	0.231405i	−0.887592	−	0.460630i	$-0.847623\pi$
$401$	−32.2293	+	4.63388i	−1.60946	+	0.231405i	−0.721864	+	0.692035i	$0.756714\pi$
$402$	0.504745	+	0.188260i	0.0251744	+	0.00938956i
$403$	−1.16868	−	0.435896i	−0.0582162	−	0.0217135i
$404$	17.5941	−	2.52965i	0.875338	−	0.125855i
$405$	−14.9501	+	12.5206i	−0.742879	+	0.622152i
$406$	−0.0438562	−	0.149361i	−0.00217655	−	0.00741264i
$407$	26.2974	−	19.6860i	1.30351	−	0.975799i
$408$	−0.898047	+	0.0642296i	−0.0444600	+	0.00317984i
$409$	1.95774	+	3.04630i	0.0968039	+	0.150630i	0.886277	−	0.463155i	$-0.153283\pi$
$409$	1.95774	+	3.04630i	0.0968039	+	0.150630i	−0.789473	+	0.613785i	$0.789646\pi$
$410$	−0.677623	−	0.265801i	−0.0334654	−	0.0131270i
$411$	−4.31123	+	14.6827i	−0.212658	+	0.724245i
$412$	−0.574859	−	1.54126i	−0.0283213	−	0.0759323i
$413$	9.35955	+	9.35955i	0.460553	+	0.460553i
$414$	−0.941729	+	0.865804i	−0.0462835	+	0.0425519i
$415$	11.9433	−	6.26323i	0.586275	−	0.307450i
$416$	0.329582	−	0.721683i	0.0161591	−	0.0353834i
$417$	19.8776	+	36.4031i	0.973409	+	1.78267i
$418$	−1.35390	−	0.0968326i	−0.0662212	−	0.00473624i
$419$	−8.34513	+	5.36309i	−0.407686	+	0.262004i	−0.728372	−	0.685181i	$-0.759723\pi$
$419$	−8.34513	+	5.36309i	−0.407686	+	0.262004i	0.320686	+	0.947186i	$0.396087\pi$
$420$	15.4062	+	24.8826i	0.751747	+	1.21415i
$421$	29.8515	+	4.29200i	1.45488	+	0.209179i	0.823949	−	0.566664i	$-0.191766\pi$
$421$	29.8515	+	4.29200i	1.45488	+	0.209179i	0.630926	+	0.775843i	$0.282675\pi$
$422$	−0.630095	−	0.344058i	−0.0306726	−	0.0167485i
$423$	−9.58120	+	2.08426i	−0.465854	+	0.101340i
$424$	0.178919	+	1.24441i	0.00868907	+	0.0604338i
$425$	−4.81264	−	6.90091i	−0.233447	−	0.334744i
$426$	−0.181909	−	0.398324i	−0.00881350	−	0.0192989i
$427$	10.4234	−	13.9241i	0.504426	−	0.673834i
$428$	−3.75370	−	17.2555i	−0.181442	−	0.834075i
$429$	−25.2705	+	7.42009i	−1.22007	+	0.358245i
$430$	−0.0323456	+	0.0677874i	−0.00155985	+	0.00326900i
$431$	−16.4952	−	14.2932i	−0.794546	−	0.688478i	0.159811	−	0.987148i	$-0.448912\pi$
$431$	−16.4952	−	14.2932i	−0.794546	−	0.688478i	−0.954357	+	0.298670i	$0.903457\pi$
$432$	−34.6481	−	7.53724i	−1.66701	−	0.362635i
$433$	−1.60973	+	22.5070i	−0.0773588	+	1.08162i	0.799435	+	0.600752i	$0.205132\pi$
$433$	−1.60973	+	22.5070i	−0.0773588	+	1.08162i	−0.876794	+	0.480866i	$0.840322\pi$
$434$	−0.0789680	−	0.0231871i	−0.00379058	−	0.00111302i
$435$	0.581851	+	10.6486i	0.0278976	+	0.510560i
$436$		−	5.29184i		−	0.253433i
$437$	−2.46972	−	24.4133i	−0.118143	−	1.16785i
$438$	0.756828	−	0.756828i	0.0361626	−	0.0361626i
$439$	−10.4846	−	4.78816i	−0.500403	−	0.228526i	0.149190	−	0.988809i	$-0.452333\pi$
$439$	−10.4846	−	4.78816i	−0.500403	−	0.228526i	−0.649593	+	0.760282i	$0.725061\pi$
$440$	−2.32558	+	0.465095i	−0.110868	+	0.0221725i
$441$	−8.66038	−	9.99461i	−0.412399	−	0.475934i
$442$	−0.0236793	+	0.108852i	−0.00112631	+	0.00517755i
$443$	2.02567	+	28.3225i	0.0962423	+	1.34564i	0.784478	+	0.620156i	$0.212931\pi$
$443$	2.02567	+	28.3225i	0.0962423	+	1.34564i	−0.688236	+	0.725487i	$0.741615\pi$
$444$	4.71219	−	32.7740i	0.223631	−	1.55538i
$445$	−0.0457561	+	2.72124i	−0.00216905	+	0.128999i
$446$	0.951556	+	0.611528i	0.0450575	+	0.0289567i
$447$	2.85929	+	2.14044i	0.135240	+	0.101239i
$448$	−6.07852	+	16.2971i	−0.287183	+	0.769968i
$449$	6.67352	−	3.04769i	0.314943	−	0.143830i	−0.251671	−	0.967813i	$-0.580980\pi$
$449$	6.67352	−	3.04769i	0.314943	−	0.143830i	0.566614	+	0.823983i	$0.308253\pi$
$450$	0.423808	+	1.26458i	0.0199785	+	0.0596128i
$451$	−23.3784	+	36.3775i	−1.10085	+	1.71295i
$452$	7.94002	−	14.5411i	0.373467	−	0.683954i
$453$	−29.1676	−	38.9633i	−1.37041	−	1.83066i
$454$	0.835028	−	0.963673i	0.0391898	−	0.0452274i
$455$	6.98551	−	1.92417i	0.327486	−	0.0902066i
$456$	−2.06900	+	1.79280i	−0.0968900	+	0.0839556i
$457$	−18.7730	+	10.2508i	−0.878164	+	0.479514i	−0.854047	−	0.520195i	$-0.825859\pi$
$457$	−18.7730	+	10.2508i	−0.878164	+	0.479514i	−0.0241170	+	0.999709i	$0.507677\pi$
$458$	0.113053	−	0.0421666i	0.00528262	−	0.00197032i
$459$	14.9610			0.698319
$460$	−7.74017	−	19.9793i	−0.360887	−	0.931539i
$461$	23.7566			1.10645			0.553227	−	0.833030i	$-0.313396\pi$
$461$	23.7566			1.10645			0.553227	+	0.833030i	$0.313396\pi$
$462$	−1.62824	+	0.607301i	−0.0757524	+	0.0282542i
$463$	−23.8152	+	13.0041i	−1.10679	+	0.604351i	−0.925374	−	0.379056i	$-0.876249\pi$
$463$	−23.8152	+	13.0041i	−1.10679	+	0.604351i	−0.181413	+	0.983407i	$0.558067\pi$
$464$	−4.79976	+	4.15902i	−0.222823	+	0.193077i
$465$	4.90255	+	2.78500i	0.227350	+	0.129151i
$466$	0.540640	−	0.623931i	0.0250446	−	0.0289031i
$467$	−16.0689	−	21.4656i	−0.743582	−	0.993310i	−0.999645	−	0.0266494i	$-0.991516\pi$
$467$	−16.0689	−	21.4656i	−0.743582	−	0.993310i	0.256063	−	0.966660i	$-0.417575\pi$
$468$	−8.46703	+	15.5062i	−0.391389	+	0.716775i
$469$	−4.76004	+	7.40677i	−0.219798	+	0.342013i
$470$	−0.0260898	+	0.162067i	−0.00120343	+	0.00747557i
$471$	−43.7756	+	19.9917i	−2.01707	+	0.921167i
$472$	−0.377833	+	1.01301i	−0.0173912	+	0.0466275i
$473$	3.57204	+	2.67399i	0.164242	+	0.122950i
$474$	−1.17155	−	0.752911i	−0.0538112	−	0.0345823i
$475$	−24.2901	−	8.02860i	−1.11451	−	0.368377i
$476$	1.04654	−	7.27887i	0.0479682	−	0.333626i
$477$	−2.99631	−	41.8939i	−0.137192	−	1.91819i
$478$	−0.182939	+	0.840956i	−0.00836743	+	0.0384644i
$479$	2.13637	+	2.46550i	0.0976133	+	0.112652i	0.802454	−	0.596714i	$-0.203527\pi$
$479$	2.13637	+	2.46550i	0.0976133	+	0.112652i	−0.704841	+	0.709365i	$0.748982\pi$
$480$	−1.98938	+	2.98402i	−0.0908024	+	0.136201i
$481$	−7.45682	−	3.40542i	−0.340002	−	0.155274i
$482$	0.321984	−	0.321984i	0.0146660	−	0.0146660i
$483$	−15.8605	−	27.1180i	−0.721676	−	1.23391i
$484$			48.4330i			2.20150i
$485$	0.502197	−	0.0274407i	0.0228036	−	0.00124602i
$486$	0.0238506	+	0.00700316i	0.00108188	+	0.000317670i
$487$	−1.56693	+	21.9086i	−0.0710044	+	0.992772i	0.829664	+	0.558264i	$0.188532\pi$
$487$	−1.56693	+	21.9086i	−0.0710044	+	0.992772i	−0.900668	+	0.434508i	$0.856922\pi$
$488$	1.38826	+	0.301997i	0.0628435	+	0.0136708i
$489$	32.7059	+	28.3398i	1.47901	+	1.28157i
$490$	−0.208712	+	0.0738728i	−0.00942864	+	0.00333723i
$491$	1.00676	−	0.295612i	0.0454345	−	0.0133408i	−0.258936	−	0.965894i	$-0.583372\pi$
$491$	1.00676	−	0.295612i	0.0454345	−	0.0133408i	0.304371	+	0.952554i	$0.401554\pi$
$492$	9.26491	+	42.5901i	0.417695	+	1.92011i
$493$	1.60587	−	2.14519i	0.0723247	−	0.0966145i
$494$	0.140713	+	0.308118i	0.00633097	+	0.0138629i
$495$	78.6040	−	9.95579i	3.53299	−	0.447480i
$496$	0.477867	+	3.32364i	0.0214569	+	0.149236i
$497$	6.99323	−	1.52128i	0.313689	−	0.0682389i
$498$	0.708433	+	0.386834i	0.0317457	+	0.0173344i
$499$	−36.2908	−	5.21782i	−1.62460	−	0.233582i	−0.730976	−	0.682403i	$-0.760935\pi$
$499$	−36.2908	−	5.21782i	−1.62460	−	0.233582i	−0.893621	+	0.448822i	$0.851844\pi$
$500$	−22.3099	−	1.12624i	−0.997731	−	0.0503668i
$501$	43.7616	−	28.1239i	1.95512	−	1.25648i
$502$	−0.114046	−	0.00815670i	−0.00509010	−	0.000364051i
$503$	10.6538	+	19.5111i	0.475031	+	0.869955i	0.999825	+	0.0187251i	$0.00596075\pi$
$503$	10.6538	+	19.5111i	0.475031	+	0.869955i	−0.524793	+	0.851230i	$0.675857\pi$
$504$	−0.969010	+	2.12184i	−0.0431631	+	0.0945141i
$505$	−5.92458	+	18.9902i	−0.263640	+	0.845052i
$506$	1.25346	−	0.218030i	0.0557231	−	0.00969262i
$507$	−22.8820	−	22.8820i	−1.01622	−	1.01622i
$508$	−10.7892	−	28.9269i	−0.478692	−	1.28342i
$509$	0.873199	−	2.97384i	0.0387039	−	0.131813i	−0.937875	−	0.346974i	$-0.887209\pi$
$509$	0.873199	−	2.97384i	0.0387039	−	0.131813i	0.976579	+	0.215161i	$0.0690275\pi$
$510$	0.183882	−	0.468783i	0.00814245	−	0.0207581i
$511$	9.45731	+	14.7159i	0.418367	+	0.650992i
$512$	−3.55175	+	0.254026i	−0.156967	+	0.0112265i
$513$	36.4183	−	27.2624i	1.60791	−	1.20367i
$514$	−0.0710807	−	0.242078i	−0.00313523	−	0.0106776i
$515$	1.83382	+	0.162187i	0.0808076	+	0.00714680i
$516$	4.45177	−	0.640067i	0.195978	−	0.0281774i
$517$	9.13704	+	3.40794i	0.401847	+	0.149881i
$518$	−0.506796	−	0.189025i	−0.0222673	−	0.00830529i
$519$	−59.2324	+	8.51634i	−2.60002	+	0.373826i
$520$	0.380000	+	0.453737i	0.0166641	+	0.0198977i
$521$	−2.88814	−	9.83609i	−0.126532	−	0.430927i	0.871722	−	0.490001i	$-0.163003\pi$
$521$	−2.88814	−	9.83609i	−0.126532	−	0.430927i	−0.998254	+	0.0590737i	$0.981185\pi$
$522$	−0.340062	+	0.254567i	−0.0148841	+	0.0111421i
$523$	32.1283	−	2.29786i	1.40487	−	0.100479i	0.651788	−	0.758401i	$-0.274019\pi$
$523$	32.1283	−	2.29786i	1.40487	−	0.100479i	0.753085	+	0.657923i	$0.228565\pi$
$524$	−12.2706	−	19.0934i	−0.536044	−	0.834100i
$525$	−32.5581	+	3.56868i	−1.42095	+	0.155750i
$526$	0.115345	−	0.392828i	0.00502927	−	0.0171281i
$527$	−0.495108	−	1.32744i	−0.0215672	−	0.0578240i
$528$	50.1342	+	50.1342i	2.18181	+	2.18181i
$529$	7.76638	+	21.6491i	0.337669	+	0.941265i
$530$	−0.671241	−	0.209415i	−0.0291569	−	0.00909639i
$531$	15.0049	−	32.8561i	0.651156	−	1.42583i
$532$	−10.7163	−	19.6254i	−0.464610	−	0.850869i
$533$	10.7636	+	0.769826i	0.466222	+	0.0333449i
$534$	−0.137036	+	0.0880680i	−0.00593015	+	0.00381107i
$535$	19.2381	+	4.52503i	0.831737	+	0.195634i
$536$	−0.711846	−	0.102348i	−0.0307471	−	0.00442076i
$537$	40.0543	+	21.8713i	1.72847	+	0.943817i
$538$	−0.965247	+	0.209977i	−0.0416147	+	0.00905273i
$539$	1.87183	+	13.0189i	0.0806256	+	0.560763i
$540$	24.3364	−	31.3953i	1.04727	−	1.35104i
$541$	−10.3639	−	22.6937i	−0.445578	−	0.975679i	−0.990541	−	0.137219i	$-0.956184\pi$
$541$	−10.3639	−	22.6937i	−0.445578	−	0.975679i	0.544963	−	0.838460i	$-0.316544\pi$
$542$	0.251214	−	0.335583i	0.0107906	−	0.0144145i
$543$	2.95549	+	13.5862i	0.126832	+	0.583039i
$544$	0.864648	−	0.253884i	0.0370715	−	0.0108852i
$545$	5.34505	+	2.55046i	0.228957	+	0.109250i
$546$	0.327746	+	0.283994i	0.0140262	+	0.0121538i
$547$	3.86146	+	0.840010i	0.165104	+	0.0359162i	0.294357	−	0.955695i	$-0.404894\pi$
$547$	3.86146	+	0.840010i	0.165104	+	0.0359162i	−0.129253	+	0.991612i	$0.541258\pi$
$548$	0.728316	−	10.1832i	0.0311121	−	0.435004i
$549$	−45.5413	−	13.3721i	−1.94365	−	0.570708i
$550$	0.325372	−	1.28592i	0.0138739	−	0.0548318i
$551$		−	8.14813i		−	0.347122i
$552$	1.47671	−	2.09861i	0.0628531	−	0.0893229i
$553$	16.0941	−	16.0941i	0.684390	−	0.684390i
$554$	1.27959	+	0.584368i	0.0543644	+	0.0248274i
$555$	30.8325	+	20.5554i	1.30877	+	0.872527i
$556$	−18.1208	−	20.9126i	−0.768495	−	0.886890i
$557$	−4.89683	+	22.5104i	−0.207485	+	0.953795i	0.749126	+	0.662428i	$0.230474\pi$
$557$	−4.89683	+	22.5104i	−0.207485	+	0.953795i	−0.956611	+	0.291367i	$0.905890\pi$
$558$	0.0160220	+	0.224017i	0.000678267	+	0.00948341i
$559$	0.158468	−	1.10217i	0.00670247	−	0.0466167i
$560$	−13.5586	−	14.0223i	−0.572955	−	0.592552i
$561$	−25.1661	−	16.1733i	−1.06251	−	0.682836i
$562$	0.879344	+	0.658269i	0.0370929	+	0.0277674i
$563$	12.0876	−	32.4081i	0.509431	−	1.36584i	−0.386764	−	0.922179i	$-0.626407\pi$
$563$	12.0876	−	32.4081i	0.509431	−	1.36584i	0.896195	−	0.443660i	$-0.146320\pi$
$564$	8.94125	−	4.08333i	0.376494	−	0.171939i
$565$	10.8605	+	15.0281i	0.456905	+	0.632237i
$566$	−0.256041	+	0.398407i	−0.0107622	+	0.0167463i
$567$	9.14189	−	16.7421i	0.383923	−	0.703103i
$568$	0.350327	+	0.467982i	0.0146994	+	0.0196361i
$569$	6.43749	−	7.42926i	0.269874	−	0.311451i	−0.604595	−	0.796533i	$-0.706665\pi$
$569$	6.43749	−	7.42926i	0.269874	−	0.311451i	0.874468	+	0.485082i	$0.161210\pi$
$570$	−0.406622	−	1.47620i	−0.0170315	−	0.0618311i
$571$	12.5200	−	10.8487i	0.523947	−	0.454003i	−0.352285	−	0.935893i	$-0.614595\pi$
$571$	12.5200	−	10.8487i	0.523947	−	0.454003i	0.876232	+	0.481890i	$0.160050\pi$
$572$	15.4218	−	8.42094i	0.644818	−	0.352097i
$573$	1.86496	−	0.695595i	0.0779100	−	0.0290589i
$574$	0.712022			0.0297192
$575$	23.9107	+	1.81124i	0.997143	+	0.0755337i
$576$	47.4652			1.97772
$577$	14.0263	−	5.23153i	0.583921	−	0.217791i	−0.0401041	−	0.999196i	$-0.512769\pi$
$577$	14.0263	−	5.23153i	0.583921	−	0.217791i	0.624025	+	0.781404i	$0.285496\pi$
$578$	0.555726	−	0.303449i	0.0231152	−	0.0126218i
$579$	−31.1196	+	26.9653i	−1.29329	+	1.12064i
$580$	−1.88943	−	6.85938i	−0.0784543	−	0.284820i
$581$	−8.63891	+	9.96983i	−0.358402	+	0.413618i
$582$	0.0180398	+	0.0240983i	0.000747773	+	0.000998907i
$583$	−20.0193	+	36.6626i	−0.829115	+	1.51841i
$584$	−0.772494	+	1.20202i	−0.0319660	+	0.0497401i
$585$	−11.5814	−	16.0256i	−0.478830	−	0.662576i
$586$	−0.151274	+	0.0690843i	−0.00624905	+	0.00285385i
$587$	−12.8477	+	34.4461i	−0.530283	+	1.42174i	0.345215	+	0.938524i	$0.387806\pi$
$587$	−12.8477	+	34.4461i	−0.530283	+	1.42174i	−0.875498	+	0.483221i	$0.839467\pi$
$588$	10.6131	+	7.94490i	0.437679	+	0.327642i
$589$	−3.62410	−	2.32907i	−0.149328	−	0.0959676i
$590$	−0.420338	−	0.434715i	−0.0173050	−	0.0178969i
$591$	−5.24137	+	36.4545i	−0.215601	+	1.49954i
$592$	1.57432	+	22.0119i	0.0647041	+	0.904682i
$593$	3.52820	−	16.2189i	0.144886	−	0.666029i	−0.846207	−	0.532854i	$-0.821119\pi$
$593$	3.52820	−	16.2189i	0.144886	−	0.666029i	0.991093	−	0.133174i	$-0.0425171\pi$
$594$	1.54465	+	1.78262i	0.0633778	+	0.0731419i
$595$	6.84767	+	4.56520i	0.280727	+	0.187155i
$596$	−2.16754	−	0.989884i	−0.0887860	−	0.0405472i
$597$	49.9440	−	49.9440i	2.04407	−	2.04407i
$598$	−0.197664	−	0.248464i	−0.00808308	−	0.0101604i
$599$		−	21.8343i		−	0.892124i	−0.895002	−	0.446062i	$-0.852826\pi$
$599$		−	21.8343i		−	0.892124i	0.895002	−	0.446062i	$-0.147174\pi$
$600$	−1.36992	−	2.29800i	−0.0559266	−	0.0938153i
$601$	−32.6812	−	9.59607i	−1.33309	−	0.391432i	−0.463894	−	0.885891i	$-0.653548\pi$
$601$	−32.6812	−	9.59607i	−1.33309	−	0.391432i	−0.869201	+	0.494459i	$0.835366\pi$
$602$	0.00524141	−	0.0732845i	0.000213624	−	0.00298685i
$603$	23.4770	+	5.10710i	0.956056	+	0.207977i
$604$	24.5401	+	21.2642i	0.998524	+	0.865226i
$605$	−48.9200	−	23.3428i	−1.98888	−	0.949021i
$606$	−1.14241	+	0.335441i	−0.0464072	+	0.0136264i
$607$	0.775667	+	3.56569i	0.0314834	+	0.144727i	0.990205	−	0.139618i	$-0.0445875\pi$
$607$	0.775667	+	3.56569i	0.0314834	+	0.144727i	−0.958722	+	0.284345i	$0.908224\pi$
$608$	1.64211	−	2.19360i	0.0665963	−	0.0889623i
$609$	−4.33360	−	9.48925i	−0.175606	−	0.384524i
$610$	−0.486817	+	0.628020i	−0.0197106	+	0.0254278i
$611$	−0.346336	−	2.40882i	−0.0140113	−	0.0974505i
$612$	−19.6086	+	4.26559i	−0.792631	+	0.172426i
$613$	27.3561	+	14.9376i	1.10490	+	0.603323i	0.924849	−	0.380334i	$-0.124191\pi$
$613$	27.3561	+	14.9376i	1.10490	+	0.603323i	0.180054	+	0.983657i	$0.442373\pi$
$614$	−1.10264	−	0.158536i	−0.0444990	−	0.00639799i
$615$	−47.4837	−	11.1687i	−1.91473	−	0.450366i
$616$	1.95165	−	1.25425i	0.0786343	−	0.0505352i
$617$	−13.1926	−	0.943555i	−0.531115	−	0.0379861i	−0.196793	−	0.980445i	$-0.563053\pi$
$617$	−13.1926	−	0.943555i	−0.531115	−	0.0379861i	−0.334322	+	0.942459i	$0.608507\pi$
$618$	0.0528068	+	0.0967085i	0.00212420	+	0.00389019i
$619$	−17.1411	+	37.5338i	−0.688960	+	1.50861i	0.163902	+	0.986477i	$0.447592\pi$
$619$	−17.1411	+	37.5338i	−0.688960	+	1.50861i	−0.852862	+	0.522136i	$0.825135\pi$
$620$	−3.59097	−	1.12031i	−0.144217	−	0.0449929i
$621$	−26.9638	+	33.0333i	−1.08202	+	1.32558i
$622$	0.195999	+	0.195999i	0.00785885	+	0.00785885i
$623$	−0.930376	−	2.49443i	−0.0372747	−	0.0999374i
$624$	4.98476	−	16.9765i	0.199550	−	0.679606i
$625$	11.8901	−	21.9915i	0.475604	−	0.879660i
$626$	−0.480971	−	0.748406i	−0.0192235	−	0.0299123i
$627$	−90.7314	+	6.48924i	−3.62346	+	0.259155i
$628$	25.7026	−	19.2407i	1.02565	−	0.767789i
$629$	−2.62326	−	8.93402i	−0.104596	−	0.356223i
$630$	−0.837655	−	1.00020i	−0.0333730	−	0.0398489i
$631$	10.7192	−	1.54119i	0.426726	−	0.0613539i	0.0743938	−	0.997229i	$-0.476298\pi$
$631$	10.7192	−	1.54119i	0.426726	−	0.0613539i	0.352332	+	0.935875i	$0.385389\pi$
$632$	1.74191	+	0.649698i	0.0692893	+	0.0258436i
$633$	−45.0774	−	16.8130i	−1.79167	−	0.668257i
$634$	−0.861153	+	0.123815i	−0.0342007	+	0.00491732i
$635$	34.4177	+	3.04398i	1.36583	+	0.120797i
$636$	11.8623	+	40.3992i	0.470370	+	1.60193i
$637$	2.62760	−	1.96700i	0.104109	−	0.0779353i
$638$	0.421401	−	0.0301392i	0.0166834	−	0.00119322i
$639$	−10.5586	−	16.4295i	−0.417692	−	0.649942i
$640$	1.16477	−	2.96941i	0.0460414	−	0.117376i
$641$	4.17670	−	14.2245i	0.164970	−	0.561835i	−0.834964	−	0.550305i	$-0.814512\pi$
$641$	4.17670	−	14.2245i	0.164970	−	0.561835i	0.999934	−	0.0115302i	$-0.00367024\pi$
$642$	0.413371	+	1.10829i	0.0163144	+	0.0437407i
$643$	−3.85951	−	3.85951i	−0.152204	−	0.152204i	0.626898	−	0.779102i	$-0.284324\pi$
$643$	−3.85951	−	3.85951i	−0.152204	−	0.152204i	−0.779102	+	0.626898i	$0.784324\pi$
$644$	14.1853	+	15.4293i	0.558979	+	0.607998i
$645$	−1.49908	+	4.80502i	−0.0590261	+	0.189197i
$646$	−0.159827	+	0.349973i	−0.00628832	+	0.0137695i
$647$	3.24763	+	5.94759i	0.127677	+	0.233824i	0.933696	−	0.358066i	$-0.116564\pi$
$647$	3.24763	+	5.94759i	0.127677	+	0.233824i	−0.806019	+	0.591890i	$0.798382\pi$
$648$	1.55415	+	0.111155i	0.0610530	+	0.00436659i
$649$	−30.2208	+	19.4217i	−1.18627	+	0.762370i
$650$	−0.320562	+	0.0825273i	−0.0125735	+	0.00323699i
$651$	−5.45932	−	0.784931i	−0.213967	−	0.0307639i
$652$	−25.3403	−	13.8368i	−0.992401	−	0.541892i
$653$	−0.440016	+	0.0957197i	−0.0172192	+	0.00374580i	−0.221167	−	0.975236i	$-0.570986\pi$
$653$	−0.440016	+	0.0957197i	−0.0172192	+	0.00374580i	0.203947	+	0.978982i	$0.434623\pi$
$654$	0.0504460	+	0.350860i	0.00197259	+	0.0137197i
$655$	25.1994	−	3.19170i	0.984622	−	0.124710i
$656$	−12.0677	−	26.4245i	−0.471163	−	1.03170i
$657$	28.6067	−	38.2140i	1.11605	−	1.49087i
$658$	−0.0341326	−	0.156905i	−0.00133063	−	0.00611679i
$659$	29.4135	−	8.63659i	1.14579	−	0.336434i	0.346893	−	0.937905i	$-0.387237\pi$
$659$	29.4135	−	8.63659i	1.14579	−	0.336434i	0.798895	+	0.601471i	$0.205418\pi$
$660$	−74.8760	+	26.5021i	−2.91454	+	1.03159i
$661$	11.3717	+	9.85364i	0.442308	+	0.383262i	0.847349	−	0.531036i	$-0.178197\pi$
$661$	11.3717	+	9.85364i	0.442308	+	0.383262i	−0.405041	+	0.914299i	$0.632743\pi$
$662$	0.0430540	+	0.00936582i	0.00167334	+	0.000364013i
$663$	−0.532569	+	7.44629i	−0.0206833	+	0.289190i
$664$	−1.03390	−	0.303581i	−0.0401232	−	0.0117812i
$665$	24.9876	−	1.36535i	0.968978	−	0.0529462i
$666$			1.47604i			0.0571953i
$667$	1.84228	+	7.41192i	0.0713333	+	0.286991i
$668$	−24.5402	+	24.5402i	−0.949489	+	0.949489i
$669$	68.9517	+	31.4892i	2.66583	+	1.21744i
$670$	0.223118	−	0.334671i	0.00861981	−	0.0129295i
$671$	30.9130	+	35.6755i	1.19338	+	1.37724i
$672$	0.745717	−	3.42801i	0.0287667	−	0.132238i
$673$	−2.05084	−	28.6744i	−0.0790539	−	1.10532i	−0.869875	−	0.493272i	$-0.835801\pi$
$673$	−2.05084	−	28.6744i	−0.0790539	−	1.10532i	0.790821	−	0.612047i	$-0.209654\pi$
$674$	0.148024	−	1.02953i	0.00570169	−	0.0396561i
$675$	19.9818	+	39.7125i	0.769099	+	1.52853i
$676$	18.1620	+	11.6720i	0.698537	+	0.448922i
$677$	−0.415205	−	0.310819i	−0.0159576	−	0.0119457i	0.591269	−	0.806474i	$-0.298627\pi$
$677$	−0.415205	−	0.310819i	−0.0159576	−	0.0119457i	−0.607227	+	0.794529i	$0.707718\pi$
$678$	−0.387822	+	1.03979i	−0.0148942	+	0.0399330i
$679$	−0.447523	+	0.204377i	−0.0171744	+	0.00784326i
$680$	−0.106843	+	0.663693i	−0.00409723	+	0.0254515i
$681$	46.1990	−	71.8871i	1.77035	−	2.75472i
$682$	0.107048	−	0.196044i	0.00409909	−	0.00750693i
$683$	−3.30134	−	4.41007i	−0.126322	−	0.168747i	0.732921	−	0.680313i	$-0.238156\pi$
$683$	−3.30134	−	4.41007i	−0.126322	−	0.168747i	−0.859244	+	0.511567i	$0.829065\pi$
$684$	−39.9588	+	46.1149i	−1.52786	+	1.76325i
$685$	9.93457	+	5.64354i	0.379580	+	0.215629i
$686$	0.680789	−	0.589907i	0.0259926	−	0.0225227i
$687$	7.09698	−	3.87525i	0.270767	−	0.147850i
$688$	−2.80856	+	1.04754i	−0.107075	+	0.0399371i
$689$	10.4243			0.397134
$690$	0.703648	+	1.25088i	0.0267874	+	0.0476202i
$691$	−7.80935			−0.297082			−0.148541	−	0.988906i	$-0.547458\pi$
$691$	−7.80935			−0.297082			−0.148541	+	0.988906i	$0.547458\pi$
$692$	37.4064	−	13.9519i	1.42198	−	0.530370i
$693$	−68.0243	+	37.1441i	−2.58403	+	1.41099i
$694$	−0.626401	+	0.542779i	−0.0237778	+	0.0206036i
$695$	29.8564	−	8.22401i	1.13252	−	0.311954i
$696$	0.558011	−	0.643979i	0.0211513	−	0.0244099i
$697$	7.34530	+	9.81217i	0.278223	+	0.371663i
$698$	0.118323	−	0.216693i	0.00447861	−	0.00820196i
$699$	29.9116	−	46.5434i	1.13136	−	1.76043i
$700$	20.7188	−	6.94365i	0.783097	−	0.262445i
$701$	−25.7129	+	11.7427i	−0.971164	+	0.443516i	−0.836856	−	0.547424i	$-0.815609\pi$
$701$	−25.7129	+	11.7427i	−0.971164	+	0.443516i	−0.134309	+	0.990940i	$0.542881\pi$
$702$	0.205704	−	0.551514i	0.00776380	−	0.0208155i
$703$	−22.6655	−	16.9672i	−0.854845	−	0.639929i
$704$	−39.7129	−	25.5219i	−1.49674	−	0.961894i
$705$	−0.184945	+	10.9992i	−0.00696542	+	0.414253i
$706$	−0.0730402	+	0.508006i	−0.00274890	+	0.0191190i
$707$	−1.38821	−	19.4097i	−0.0522089	−	0.729976i
$708$	−7.69688	+	35.3820i	−0.289266	+	1.32974i
$709$	−21.8668	−	25.2356i	−0.821223	−	0.947742i	0.178119	−	0.984009i	$-0.442999\pi$
$709$	−21.8668	−	25.2356i	−0.821223	−	0.947742i	−0.999342	+	0.0362670i	$0.988453\pi$
$710$	−0.320606	+	0.0641181i	−0.0120321	+	0.00240631i
$711$	−56.4972	−	25.8014i	−2.11881	−	0.967629i
$712$	0.153769	−	0.153769i	0.00576273	−	0.00576273i
$713$	3.82325	+	1.29923i	0.143182	+	0.0486564i
$714$			0.492580i			0.0184344i
$715$	1.07291	+	19.6354i	0.0401244	+	0.734324i
$716$	−29.2134	−	8.57783i	−1.09176	−	0.320569i
$717$	−4.11447	+	57.5278i	−0.153658	+	2.14842i
$718$	0.495458	+	0.107780i	0.0184903	+	0.00402233i
$719$	−1.63113	−	1.41338i	−0.0608307	−	0.0527101i	0.623915	−	0.781492i	$-0.285541\pi$
$719$	−1.63113	−	1.41338i	−0.0608307	−	0.0527101i	−0.684746	+	0.728782i	$0.740087\pi$
$720$	−22.9223	+	48.0388i	−0.854265	+	1.79030i
$721$	−1.72790	+	0.507356i	−0.0643502	+	0.0188949i
$722$	0.0681922	+	0.313475i	0.00253785	+	0.0116663i
$723$	18.2873	−	24.4290i	0.680113	−	0.908524i
$724$	−3.85342	−	8.43782i	−0.143211	−	0.313589i
$725$	7.83899	+	1.39753i	0.291133	+	0.0519028i
$726$	−0.461702	−	3.21121i	−0.0171354	−	0.119179i
$727$	−46.3952	+	10.0927i	−1.72070	+	0.374316i	−0.961128	−	0.276105i	$-0.910956\pi$
$727$	−46.3952	+	10.0927i	−1.72070	+	0.374316i	−0.759574	+	0.650421i	$0.774593\pi$
$728$	−0.508124	−	0.277457i	−0.0188323	−	0.0102832i
$729$	27.5453	+	3.96042i	1.02020	+	0.146682i
$730$	−0.420689	−	0.679456i	−0.0155704	−	0.0251478i
$731$	1.06398	−	0.683781i	0.0393528	−	0.0252905i
$732$	47.4600	+	3.39440i	1.75417	+	0.125461i
$733$	7.02744	+	12.8698i	0.259564	+	0.475357i	0.974666	−	0.223663i	$-0.0718016\pi$
$733$	7.02744	+	12.8698i	0.259564	+	0.475357i	−0.715102	+	0.699020i	$0.753620\pi$
$734$	0.463102	−	1.01405i	0.0170934	−	0.0374294i
$735$	−13.1399	+	6.89073i	−0.484673	+	0.254169i
$736$	−0.997769	+	2.36668i	−0.0367783	+	0.0872369i
$737$	−16.8965	−	16.8965i	−0.622390	−	0.622390i
$738$	−0.679010	−	1.82050i	−0.0249947	−	0.0670134i
$739$	13.1249	−	44.6992i	0.482806	−	1.64429i	−0.253276	−	0.967394i	$-0.581508\pi$
$739$	13.1249	−	44.6992i	0.482806	−	1.64429i	0.736082	−	0.676893i	$-0.236674\pi$
$740$	−23.0150	−	9.02775i	−0.846048	−	0.331867i
$741$	12.2725	+	19.0964i	0.450841	+	0.701523i
$742$	0.686069	−	0.0490686i	0.0251864	−	0.00180137i
$743$	−9.78705	+	7.32649i	−0.359052	+	0.268783i	−0.763540	−	0.645760i	$-0.776541\pi$
$743$	−9.78705	+	7.32649i	−0.359052	+	0.268783i	0.404488	+	0.914543i	$0.367450\pi$
$744$	−0.126925	−	0.432265i	−0.00465328	−	0.0158476i
$745$	2.04451	−	1.71225i	0.0749051	−	0.0627321i
$746$	−0.642138	+	0.0923254i	−0.0235103	+	0.00338027i
$747$	33.7292	+	12.5804i	1.23409	+	0.460291i
$748$	18.6996	+	6.97459i	0.683725	+	0.255016i
$749$	−19.1355	+	2.75127i	−0.699197	+	0.100529i
$750$	1.48993	−	0.138004i	0.0544046	−	0.00503921i
$751$	−5.31519	−	18.1019i	−0.193954	−	0.660546i	−0.997836	−	0.0657572i	$-0.979054\pi$
$751$	−5.31519	−	18.1019i	−0.193954	−	0.660546i	0.803882	−	0.594789i	$-0.202764\pi$
$752$	−5.24455	+	3.92602i	−0.191249	+	0.143167i
$753$	−7.64277	+	0.546621i	−0.278518	+	0.0199200i
$754$	−0.0569995	−	0.0886929i	−0.00207580	−	0.00323001i
$755$	−33.3054	+	14.5384i	−1.21211	+	0.529107i
$756$	−10.9473	+	37.2832i	−0.398151	+	1.35598i
$757$	−1.13147	−	3.03359i	−0.0411240	−	0.110258i	0.914764	−	0.403988i	$-0.132376\pi$
$757$	−1.13147	−	3.03359i	−0.0411240	−	0.110258i	−0.955888	+	0.293730i	$0.905103\pi$
$758$	−1.01623	−	1.01623i	−0.0369111	−	0.0369111i
$759$	81.0663	−	26.4171i	2.94252	−	0.958880i
$760$	0.949326	+	1.81027i	0.0344357	+	0.0656653i
$761$	−20.5867	+	45.0787i	−0.746269	+	1.63410i	0.0266896	+	0.999644i	$0.491503\pi$
$761$	−20.5867	+	45.0787i	−0.746269	+	1.63410i	−0.772958	+	0.634457i	$0.781224\pi$
$762$	0.991098	+	1.81506i	0.0359037	+	0.0657527i
$763$	−5.77850	−	0.413287i	−0.209196	−	0.0149620i
$764$	−1.11714	+	0.717943i	−0.0404167	+	0.0259743i
$765$	5.14211	−	21.8616i	0.185913	−	0.790410i
$766$	−0.578428	−	0.0831654i	−0.0208995	−	0.00300489i
$767$	7.86817	+	4.29634i	0.284103	+	0.155132i
$768$	−46.3551	+	10.0839i	−1.67269	+	0.363872i
$769$	−0.0646542	−	0.449680i	−0.00233149	−	0.0162159i	0.988622	−	0.150418i	$-0.0480619\pi$
$769$	−0.0646542	−	0.449680i	−0.00233149	−	0.0162159i	−0.990954	+	0.134202i	$0.957153\pi$
$770$	0.163039	+	1.28725i	0.00587553	+	0.0463891i
$771$	−7.02374	−	15.3799i	−0.252954	−	0.553892i
$772$	16.4631	−	21.9921i	0.592519	−	0.791513i
$773$	−3.81878	−	17.5547i	−0.137352	−	0.631397i	−0.993419	−	0.114533i	$-0.963463\pi$
$773$	−3.81878	−	17.5547i	−0.137352	−	0.631397i	0.856067	−	0.516864i	$-0.172901\pi$
$774$	−0.192372	+	0.0564855i	−0.00691467	+	0.00203033i
$775$	2.86229	−	3.08713i	0.102816	−	0.110893i
$776$	−0.0303707	−	0.0263164i	−0.00109024	−	0.000944702i
$777$	−35.4200	−	7.70516i	−1.27069	−	0.276421i
$778$	0.0481017	−	0.672550i	0.00172453	−	0.0241121i
$779$	35.7602	+	10.5001i	1.28124	+	0.376206i
$780$	14.7596	+	13.2302i	0.528477	+	0.473716i
$781$			19.4235i			0.695027i
$782$	0.0662581	−	0.354488i	0.00236938	−	0.0126765i
$783$	−10.0122	+	10.0122i	−0.357808	+	0.357808i
$784$	−8.03745	−	3.67058i	−0.287052	−	0.131092i
$785$	7.04655	+	35.2344i	0.251502	+	1.25757i
$786$	0.995580	+	1.14896i	0.0355112	+	0.0409821i
$787$	8.53364	−	39.2285i	0.304192	−	1.39835i	−0.530527	−	0.847668i	$-0.678006\pi$
$787$	8.53364	−	39.2285i	0.304192	−	1.39835i	0.834718	−	0.550677i	$-0.185631\pi$
$788$	−1.75287	−	24.5083i	−0.0624434	−	0.873073i
$789$	3.90466	−	27.1575i	0.139010	−	0.966833i
$790$	−0.747508	+	0.722786i	−0.0265951	+	0.0257156i
$791$	−15.2582	−	9.80586i	−0.542520	−	0.348656i
$792$	−5.06803	−	3.79388i	−0.180085	−	0.134810i
$793$	4.11674	−	11.0374i	0.146190	−	0.391950i
$794$	0.368586	−	0.168328i	0.0130806	−	0.00597373i
$795$	−46.5226	−	7.48930i	−1.64999	−	0.265618i
$796$	−25.4762	+	39.6417i	−0.902979	+	1.40506i
$797$	−22.2020	+	40.6599i	−0.786434	+	1.44025i	0.108522	+	0.994094i	$0.465388\pi$
$797$	−22.2020	+	40.6599i	−0.786434	+	1.44025i	−0.894957	+	0.446153i	$0.852794\pi$
$798$	0.897597	+	1.19905i	0.0317746	+	0.0424459i
$799$	1.81015	−	2.08902i	0.0640384	−	0.0739042i
$800$	1.82873	+	1.95604i	0.0646553	+	0.0691565i
$801$	−5.49053	+	4.75757i	−0.193998	+	0.168100i
$802$	−1.27711	+	0.697353i	−0.0450962	+	0.0246244i
$803$	−44.4820	+	16.5909i	−1.56974	+	0.585481i
$804$	−24.0854			−0.849428
$805$	−22.4212	+	6.89164i	−0.790243	+	0.242898i
$806$	−0.0557413			−0.00196340
$807$	−62.0250	+	23.1341i	−2.18338	+	0.814360i
$808$	1.39505	−	0.761754i	0.0490776	−	0.0267984i
$809$	21.1056	−	18.2881i	0.742034	−	0.642976i	−0.199499	−	0.979898i	$-0.563931\pi$
$809$	21.1056	−	18.2881i	0.742034	−	0.642976i	0.941532	+	0.336922i	$0.109386\pi$
$810$	−0.430443	+	0.757727i	−0.0151242	+	0.0266238i
$811$	20.4907	−	23.6475i	0.719525	−	0.830376i	−0.271725	−	0.962375i	$-0.587594\pi$
$811$	20.4907	−	23.6475i	0.719525	−	0.830376i	0.991250	+	0.131999i	$0.0421396\pi$
$812$	4.17082	+	5.57156i	0.146367	+	0.195523i
$813$	13.4632	−	24.6561i	0.472177	−	0.864727i
$814$	0.793661	−	1.23496i	0.0278178	−	0.0432854i
$815$	26.1890	−	18.9263i	0.917361	−	0.662958i
$816$	18.2806	−	8.34847i	0.639949	−	0.292255i
$817$	1.34396	−	3.60330i	0.0470193	−	0.126064i
$818$	0.129547	+	0.0969775i	0.00452950	+	0.00339074i
$819$	16.2710	+	10.4567i	0.568554	+	0.365387i
$820$	32.5389	+	0.547124i	1.13631	+	0.0191064i
$821$	0.329249	−	2.28997i	0.0114909	−	0.0799207i	−0.983269	−	0.182159i	$-0.941691\pi$
$821$	0.329249	−	2.28997i	0.0114909	−	0.0799207i	0.994760	+	0.102238i	$0.0326005\pi$
$822$	0.0487854	+	0.682109i	0.00170159	+	0.0237913i
$823$	−4.65086	+	21.3796i	−0.162119	+	0.745247i	0.822250	+	0.569127i	$0.192719\pi$
$823$	−4.65086	+	21.3796i	−0.162119	+	0.745247i	−0.984369	+	0.176121i	$0.943645\pi$
$824$	−0.0963279	−	0.111168i	−0.00335574	−	0.00387273i
$825$	9.31875	−	88.4019i	0.324437	−	3.07776i
$826$	0.538062	+	0.245725i	0.0187216	+	0.00854986i
$827$	−20.5161	+	20.5161i	−0.713415	+	0.713415i	−0.967248	−	0.253833i	$-0.918309\pi$
$827$	−20.5161	+	20.5161i	−0.713415	+	0.713415i	0.253833	+	0.967248i	$0.418309\pi$
$828$	25.9219	−	50.9828i	0.900847	−	1.77178i
$829$		−	48.6278i		−	1.68891i	−0.535623	−	0.844457i	$-0.679923\pi$
$829$		−	48.6278i		−	1.68891i	0.535623	−	0.844457i	$-0.320077\pi$
$830$	0.402266	−	0.448768i	0.0139629	−	0.0155770i
$831$	90.4520	+	26.5591i	3.13774	+	0.921325i
$832$	−0.840410	+	11.7505i	−0.0291360	+	0.407374i
$833$	3.64295	+	0.792474i	0.126221	+	0.0274576i
$834$	1.40080	+	1.21380i	0.0485059	+	0.0420306i
$835$	−12.9595	−	36.6144i	−0.448483	−	1.26709i
$836$	58.2283	−	17.0974i	2.01387	−	0.591325i
$837$	1.59131	+	7.31512i	0.0550036	+	0.252848i
$838$	−0.265663	+	0.354884i	−0.00917718	+	0.0122593i
$839$	3.33719	+	7.30742i	0.115212	+	0.252280i	0.958450	−	0.285261i	$-0.0920804\pi$
$839$	3.33719	+	7.30742i	0.115212	+	0.252280i	−0.843237	+	0.537541i	$0.819353\pi$
$840$	2.06837	+	1.60332i	0.0713656	+	0.0553199i
$841$	−3.76620	−	26.1945i	−0.129869	−	0.903259i
$842$	1.31694	−	0.286483i	0.0453848	−	0.00987287i
$843$	64.6075	+	35.2784i	2.22520	+	1.21505i
$844$	31.7707	+	4.56793i	1.09359	+	0.157235i
$845$	−20.5427	+	12.7191i	−0.706691	+	0.437552i
$846$	−0.368624	+	0.236901i	−0.0126736	+	0.00814481i
$847$	52.8871	+	3.78256i	1.81722	+	0.129970i
$848$	−13.4488	−	24.6297i	−0.461835	−	0.845787i
$849$	−13.1842	+	28.8694i	−0.452481	+	0.990796i
$850$	−0.309282	−	0.213789i	−0.0106083	−	0.00733290i
$851$	24.4538	+	10.3095i	0.838266	+	0.353405i
$852$	13.8438	+	13.8438i	0.474281	+	0.474281i
$853$	−12.9217	−	34.6444i	−0.442431	−	1.18620i	−0.946547	−	0.322566i	$-0.895454\pi$
$853$	−12.9217	−	34.6444i	−0.442431	−	1.18620i	0.504116	−	0.863636i	$-0.331818\pi$
$854$	0.218986	−	0.745799i	0.00749356	−	0.0255207i
$855$	−27.3200	−	62.5862i	−0.934325	−	2.14040i
$856$	−0.853729	−	1.32843i	−0.0291798	−	0.0454047i
$857$	22.3780	−	1.60051i	0.764418	−	0.0546723i	0.316315	−	0.948654i	$-0.397554\pi$
$857$	22.3780	−	1.60051i	0.764418	−	0.0546723i	0.448103	+	0.893982i	$0.352100\pi$
$858$	−0.942221	+	0.705338i	−0.0321669	+	0.0240798i
$859$	3.83663	+	13.0664i	0.130904	+	0.445819i	0.998693	−	0.0511149i	$-0.0162775\pi$
$859$	3.83663	+	13.0664i	0.130904	+	0.445819i	−0.867789	+	0.496933i	$0.834459\pi$
$860$	0.295841	−	3.34502i	0.0100881	−	0.114064i
$861$	47.2305	−	6.79072i	1.60961	−	0.231427i
$862$	−0.913888	−	0.340863i	−0.0311272	−	0.0116098i
$863$	47.2121	+	17.6092i	1.60712	+	0.599425i	0.983276	−	0.182124i	$-0.0582972\pi$
$863$	47.2121	+	17.6092i	1.60712	+	0.599425i	0.623844	+	0.781549i	$0.285570\pi$
$864$	−4.71323	+	0.677661i	−0.160347	+	0.0230545i
$865$	−3.93628	+	44.5068i	−0.133838	+	1.51328i
$866$	0.284092	+	0.967530i	0.00965386	+	0.0328780i
$867$	33.9689	−	25.4288i	1.15364	−	0.863606i
$868$	3.67029	−	0.262504i	0.124578	−	0.00890998i
$869$	33.3964	+	51.9658i	1.13289	+	1.76282i
$870$	0.190662	+	0.436779i	0.00646405	+	0.0148082i
$871$	−1.67999	+	5.72152i	−0.0569243	+	0.193866i
$872$	−0.165369	−	0.443370i	−0.00560009	−	0.0150144i
$873$	0.949325	+	0.949325i	0.0321298	+	0.0321298i
$874$	−0.484674	−	0.983641i	−0.0163944	−	0.0332721i
$875$	−2.97219	+	24.2737i	−0.100478	+	0.820602i
$876$	−19.8790	+	43.5288i	−0.671648	+	1.47070i
$877$	7.13275	+	13.0627i	0.240856	+	0.441095i	0.969945	−	0.243324i	$-0.0782379\pi$
$877$	7.13275	+	13.0627i	0.240856	+	0.441095i	−0.729089	+	0.684419i	$0.760056\pi$
$878$	−0.513778	−	0.0367461i	−0.0173392	−	0.00124012i
$879$	−9.37554	+	6.02529i	−0.316229	+	0.203228i
$880$	45.0089	−	27.8675i	1.51725	−	0.939413i
$881$	54.5686	+	7.84578i	1.83846	+	0.264331i	0.972012	−	0.234931i	$-0.0754864\pi$
$881$	54.5686	+	7.84578i	1.83846	+	0.264331i	0.866451	+	0.499262i	$0.166395\pi$
$882$	−0.518705	−	0.283235i	−0.0174657	−	0.00953701i
$883$	−32.6101	+	7.09389i	−1.09742	+	0.238729i	−0.724595	−	0.689174i	$-0.757973\pi$
$883$	−32.6101	+	7.09389i	−1.09742	+	0.238729i	−0.372822	+	0.927903i	$0.621610\pi$
$884$	−0.708802	−	4.92983i	−0.0238396	−	0.165808i
$885$	−32.0282	−	24.8270i	−1.07662	−	0.834552i
$886$	0.527131	+	1.15426i	0.0177093	+	0.0387780i
$887$	−13.4777	+	18.0042i	−0.452538	+	0.604520i	−0.967555	−	0.252660i	$-0.918695\pi$
$887$	−13.4777	+	18.0042i	−0.452538	+	0.604520i	0.515017	+	0.857180i	$0.327786\pi$
$888$	−0.629374	−	2.89319i	−0.0211204	−	0.0970890i
$889$	−32.4298	+	9.52224i	−1.08766	+	0.319366i
$890$	0.0405819	+	0.114656i	0.00136031	+	0.00384326i
$891$	39.1257	+	33.9026i	1.31076	+	1.13578i
$892$	−49.4159	−	10.7498i	−1.65457	−	0.359929i
$893$	0.599610	−	8.38365i	0.0200652	−	0.280548i
$894$	0.153149	+	0.0449686i	0.00512207	+	0.00150397i
$895$	22.7438	−	25.3730i	0.760243	−	0.848126i
$896$			3.12015i			0.104237i
$897$	−15.4813	−	14.5962i	−0.516905	−	0.487352i
$898$	0.231831	−	0.231831i	0.00773630	−	0.00773630i
$899$	1.21969	+	0.557013i	0.0406789	+	0.0185774i
$900$	−37.5117	−	46.3521i	−1.25039	−	1.54507i
$901$	7.75376	+	8.94832i	0.258315	+	0.298112i
$902$	−0.410767	+	1.88826i	−0.0136770	+	0.0628723i
$903$	−0.351253	−	4.91116i	−0.0116890	−	0.163433i
$904$	0.210841	−	1.46643i	0.00701246	−	0.0487727i
$905$	10.3799	+	0.174532i	0.345039	+	0.00580163i
$906$	−1.82977	−	1.17592i	−0.0607900	−	0.0390674i
$907$	−15.7177	−	11.7661i	−0.521899	−	0.390688i	0.305597	−	0.952161i	$-0.401144\pi$
$907$	−15.7177	−	11.7661i	−0.521899	−	0.390688i	−0.827495	+	0.561473i	$0.810235\pi$
$908$	−19.9230	+	53.4155i	−0.661166	+	1.77266i
$909$	−48.3028	+	22.0591i	−1.60210	+	0.731656i
$910$	0.262440	−	0.189660i	0.00869981	−	0.00628718i
$911$	20.6964	−	32.2042i	0.685702	−	1.06697i	−0.307610	−	0.951513i	$-0.599529\pi$
$911$	20.6964	−	32.2042i	0.685702	−	1.06697i	0.993312	−	0.115461i	$-0.0368344\pi$
$912$	29.2861	−	53.6335i	0.969760	−	1.77598i
$913$	−21.4559	−	28.6618i	−0.710088	−	0.948566i
$914$	−0.625957	+	0.722392i	−0.0207048	+	0.0238946i
$915$	−26.3024	+	46.3013i	−0.869531	+	1.53067i
$916$	−4.07702	+	3.53276i	−0.134709	+	0.116726i
$917$	−21.8077	+	11.9079i	−0.720153	+	0.393233i
$918$	0.626431	−	0.233647i	0.0206753	−	0.00771149i
$919$	−17.9248			−0.591286			−0.295643	−	0.955298i	$-0.595534\pi$
$919$	−17.9248			−0.591286			−0.295643	+	0.955298i	$0.595534\pi$
$920$	−1.27285	−	1.43206i	−0.0419646	−	0.0472137i
$921$	−74.6534			−2.45991
$922$	0.994712	−	0.371008i	0.0327591	−	0.0122185i
$923$	4.25423	−	2.32299i	0.140030	−	0.0764621i
$924$	58.7190	−	50.8803i	1.93171	−	1.67384i
$925$	20.2109	−	18.8954i	0.664530	−	0.621277i
$926$	−0.794081	+	0.916418i	−0.0260951	+	0.0301154i
$927$	2.94499	+	3.93405i	0.0967262	+	0.129211i
$928$	−0.408738	+	0.748548i	−0.0134175	+	0.0245723i
$929$	−13.6568	+	21.2504i	−0.448065	+	0.697203i	−0.989659	−	0.143437i	$-0.954185\pi$
$929$	−13.6568	+	21.2504i	−0.448065	+	0.697203i	0.541594	+	0.840640i	$0.317821\pi$
$930$	0.248768	+	0.0400472i	0.00815743	+	0.00131320i
$931$	10.3118	−	4.70924i	0.337956	−	0.154339i
$932$	−12.8991	+	34.5839i	−0.422525	+	1.13283i
$933$	14.8705	+	11.1319i	0.486838	+	0.364442i
$934$	−1.00805	−	0.647836i	−0.0329845	−	0.0211978i
$935$	−16.0572	+	15.5262i	−0.525127	+	0.507760i
$936$	−0.224835	+	1.56376i	−0.00734897	+	0.0511132i
$937$	2.40915	+	33.6843i	0.0787034	+	1.10042i	0.871326	+	0.490705i	$0.163261\pi$
$937$	2.40915	+	33.6843i	0.0787034	+	1.10042i	−0.792623	+	0.609713i	$0.791285\pi$
$938$	−0.0836357	+	0.384467i	−0.00273080	+	0.0125533i
$939$	−39.0419	−	45.0568i	−1.27409	−	1.47037i
$940$	−1.43927	−	7.19668i	−0.0469438	−	0.234730i
$941$	−32.9888	−	15.0655i	−1.07540	−	0.491121i	−0.202635	−	0.979254i	$-0.564951\pi$
$941$	−32.9888	−	15.0655i	−1.07540	−	0.491121i	−0.872769	+	0.488134i	$0.837678\pi$
$942$	−1.52072	+	1.52072i	−0.0495477	+	0.0495477i
$943$	−34.9032	−	1.46610i	−1.13660	−	0.0477427i
$944$		−	24.1332i		−	0.785468i
$945$	−32.3819	−	29.0265i	−1.05338	−	0.944232i
$946$	0.191325	+	0.0561780i	0.00622050	+	0.00182650i
$947$	−3.59928	+	50.3244i	−0.116961	+	1.63532i	0.512781	+	0.858520i	$0.328615\pi$
$947$	−3.59928	+	50.3244i	−0.116961	+	1.63532i	−0.629741	+	0.776805i	$0.716839\pi$
$948$	60.8406	+	13.2351i	1.97601	+	0.429855i
$949$	8.95374	+	7.75846i	0.290651	+	0.251850i
$950$	−1.14243	+	0.0431750i	−0.0370655	+	0.00140078i
$951$	−55.9419	+	16.4260i	−1.81404	+	0.532650i
$952$	−0.139779	−	0.642556i	−0.00453028	−	0.0208253i
$953$	14.0537	−	18.7736i	0.455244	−	0.608135i	−0.512924	−	0.858434i	$-0.671438\pi$
$953$	14.0537	−	18.7736i	0.455244	−	0.608135i	0.968169	+	0.250298i	$0.0805288\pi$
$954$	−0.779719	−	1.70735i	−0.0252443	−	0.0552774i
$955$	−0.186743	−	1.47440i	−0.00604288	−	0.0477103i
$956$	−5.47599	−	38.0864i	−0.177106	−	1.23180i
$957$	27.6653	−	6.01822i	0.894292	−	0.194541i
$958$	0.127956	+	0.0698692i	0.00413407	+	0.00225737i
$959$	−11.0628	−	1.59059i	−0.357237	−	0.0513629i
$960$	12.1928	−	51.8374i	0.393520	−	1.67305i
$961$	−25.4825	+	16.3766i	−0.822015	+	0.528277i
$962$	−0.365407	−	0.0261344i	−0.0117812	−	0.000842608i
$963$	25.2828	+	46.3020i	0.814727	+	1.49206i
$964$	−8.45729	+	18.5189i	−0.272391	+	0.596453i
$965$	14.2787	+	27.2280i	0.459647	+	0.876500i
$966$	−1.08760	−	0.887765i	−0.0349929	−	0.0285634i
$967$	24.8528	+	24.8528i	0.799211	+	0.799211i	0.982971	−	0.183760i	$-0.0588270\pi$
$967$	24.8528	+	24.8528i	0.799211	+	0.799211i	−0.183760	+	0.982971i	$0.558827\pi$
$968$	1.51352	+	4.05790i	0.0486463	+	0.130426i
$969$	−7.26404	+	24.7390i	−0.233354	+	0.794732i
$970$	0.0205990	−	0.00899182i	0.000661393	−	0.000288710i
$971$	−28.9994	−	45.1239i	−0.930634	−	1.44809i	−0.893643	−	0.448779i	$-0.851859\pi$
$971$	−28.9994	−	45.1239i	−0.930634	−	1.44809i	−0.0369909	−	0.999316i	$-0.511777\pi$
$972$	−1.10853	+	0.0792837i	−0.0355562	+	0.00254303i
$973$	−24.2510	+	18.1541i	−0.777452	+	0.581993i
$974$	0.276539	+	0.941804i	0.00886087	+	0.0301773i
$975$	−20.4768	+	8.53155i	−0.655781	+	0.273228i
$976$	−31.3895	+	4.51313i	−1.00475	+	0.144462i
$977$	−34.5894	−	12.9012i	−1.10661	−	0.412745i	−0.271286	−	0.962499i	$-0.587449\pi$
$977$	−34.5894	−	12.9012i	−1.10661	−	0.412745i	−0.835327	+	0.549754i	$0.814722\pi$
$978$	1.81201	+	0.675847i	0.0579418	+	0.0216112i
$979$	7.15191	−	1.02829i	0.228576	−	0.0328643i
$980$	7.58883	−	6.35555i	0.242416	−	0.203021i
$981$	4.45390	+	15.1686i	0.142202	+	0.484296i
$982$	0.0375375	−	0.0281003i	0.00119787	−	0.000896715i
$983$	10.0797	−	0.720914i	0.321492	−	0.0229936i	0.0903394	−	0.995911i	$-0.471205\pi$
$983$	10.0797	−	0.720914i	0.321492	−	0.0229936i	0.231153	+	0.972917i	$0.425750\pi$
$984$	2.10718	+	3.27884i	0.0671745	+	0.104526i
$985$	25.5996	+	10.0416i	0.815671	+	0.319951i
$986$	0.0337377	−	0.114900i	0.00107443	−	0.00365917i
$987$	−3.76055	−	10.0824i	−0.119700	−	0.320927i
$988$	−10.7087	−	10.7087i	−0.340688	−	0.340688i
$989$	−0.407830	+	3.58160i	−0.0129682	+	0.113888i
$990$	3.13575	−	1.64442i	0.0996605	−	0.0522632i
$991$	−7.79005	+	17.0578i	−0.247459	+	0.541860i	−0.992077	−	0.125631i	$-0.959904\pi$
$991$	−7.79005	+	17.0578i	−0.247459	+	0.541860i	0.744618	+	0.667491i	$0.232632\pi$
$992$	0.216103	+	0.395763i	0.00686127	+	0.0125655i
$993$	2.94522	+	0.210646i	0.0934637	+	0.00668466i
$994$	0.269055	−	0.172911i	0.00853392	−	0.00548442i
$995$	−27.7618	−	44.8382i	−0.880109	−	1.42147i
$996$	−35.7206	−	5.13585i	−1.13185	−	0.162736i
$997$	10.2896	+	5.61854i	0.325875	+	0.177941i	0.633855	−	0.773452i	$-0.281471\pi$
$997$	10.2896	+	5.61854i	0.325875	+	0.177941i	−0.307981	+	0.951393i	$0.599653\pi$
$998$	−1.60102	+	0.348280i	−0.0506793	+	0.0110246i
$999$	7.00196	+	48.6997i	0.221532	+	1.54079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.17.6	✓	200
5.2	odd	4		575.2.r.b.293.6		200
5.3	odd	4	inner	115.2.l.a.63.5	yes	200
5.4	even	2		575.2.r.b.132.5		200
23.19	odd	22	inner	115.2.l.a.42.5	yes	200
115.19	odd	22		575.2.r.b.157.6		200
115.42	even	44		575.2.r.b.318.5		200
115.88	even	44	inner	115.2.l.a.88.6	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.17.6	✓	200	1.1	even	1	trivial
115.2.l.a.42.5	yes	200	23.19	odd	22	inner
115.2.l.a.63.5	yes	200	5.3	odd	4	inner
115.2.l.a.88.6	yes	200	115.88	even	44	inner
575.2.r.b.132.5		200	5.4	even	2
575.2.r.b.157.6		200	115.19	odd	22
575.2.r.b.293.6		200	5.2	odd	4
575.2.r.b.318.5		200	115.42	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0418710 - 0.0156171i) q^{2} +(2.62848 - 1.43526i) q^{3} +(-1.50999 + 1.30841i) q^{4} +(-0.593814 - 2.15578i) q^{5} +(0.0876426 - 0.101145i) q^{6} +(1.31081 + 1.75104i) q^{7} +(-0.0856252 + 0.156811i) q^{8} +(3.22702 - 5.02134i) q^{9} +O(q^{10})\)	\(q+(0.0418710 - 0.0156171i) q^{2} +(2.62848 - 1.43526i) q^{3} +(-1.50999 + 1.30841i) q^{4} +(-0.593814 - 2.15578i) q^{5} +(0.0876426 - 0.101145i) q^{6} +(1.31081 + 1.75104i) q^{7} +(-0.0856252 + 0.156811i) q^{8} +(3.22702 - 5.02134i) q^{9} +(-0.0585306 - 0.0809910i) q^{10} +(-5.39993 + 2.46606i) q^{11} +(-2.09107 + 5.60637i) q^{12} +(1.18594 + 0.887787i) q^{13} +(0.0822312 + 0.0528468i) q^{14} +(-4.65493 - 4.81415i) q^{15} +(0.567555 - 3.94743i) q^{16} +(0.120040 + 1.67838i) q^{17} +(0.0566999 - 0.260645i) q^{18} +(3.35060 + 3.86680i) q^{19} +(3.71730 + 2.47825i) q^{20} +(5.95865 + 2.72122i) q^{21} +(-0.187588 + 0.187588i) q^{22} +(-3.92214 - 2.75986i) q^{23} +0.535068i q^{24} +(-4.29477 + 2.56026i) q^{25} +(0.0635213 + 0.0186515i) q^{26} +(0.634294 - 8.86858i) q^{27} +(-4.27040 - 0.928969i) q^{28} +(-1.20354 - 1.04288i) q^{29} +(-0.270090 - 0.128877i) q^{30} +(-0.807869 + 0.237212i) q^{31} +(-0.113839 - 0.523311i) q^{32} +(-10.6542 + 14.2323i) q^{33} +(0.0312376 + 0.0684007i) q^{34} +(2.99648 - 3.86562i) q^{35} +(1.69722 + 11.8045i) q^{36} +(-5.40713 + 1.17625i) q^{37} +(0.200681 + 0.109580i) q^{38} +(4.39144 + 0.631394i) q^{39} +(0.388895 + 0.0914725i) q^{40} +(6.12788 - 3.93815i) q^{41} +(0.291992 + 0.0208837i) q^{42} +(-0.360223 - 0.659699i) q^{43} +(4.92720 - 10.7891i) q^{44} +(-12.7412 - 3.97500i) q^{45} +(-0.207325 - 0.0543056i) q^{46} +(-1.16159 - 1.16159i) q^{47} +(-4.17378 - 11.1903i) q^{48} +(0.624212 - 2.12587i) q^{49} +(-0.139842 + 0.174273i) q^{50} +(2.72443 + 4.23930i) q^{51} +(-2.95236 + 0.211157i) q^{52} +(5.63313 - 4.21690i) q^{53} +(-0.111943 - 0.381242i) q^{54} +(8.52284 + 10.1767i) q^{55} +(-0.386821 + 0.0556164i) q^{56} +(14.3569 + 5.35483i) q^{57} +(-0.0666803 - 0.0248705i) q^{58} +(5.98982 - 0.861206i) q^{59} +(13.3278 + 1.17874i) q^{60} +(-2.24031 - 7.62978i) q^{61} +(-0.0301217 + 0.0225489i) q^{62} +(13.0226 - 0.931395i) q^{63} +(4.29924 + 6.68974i) q^{64} +(1.20964 - 3.08382i) q^{65} +(-0.223834 + 0.762308i) q^{66} +(1.40667 + 3.77142i) q^{67} +(-2.37727 - 2.37727i) q^{68} +(-14.2704 - 1.62494i) q^{69} +(0.0650960 - 0.208654i) q^{70} +(1.35921 - 2.97626i) q^{71} +(0.511087 + 0.935985i) q^{72} +(7.97697 + 0.570524i) q^{73} +(-0.208032 + 0.133694i) q^{74} +(-7.61408 + 12.8937i) q^{75} +(-10.1188 - 1.45486i) q^{76} +(-11.3965 - 6.22295i) q^{77} +(0.193734 - 0.0421444i) q^{78} +(-1.48088 - 10.2997i) q^{79} +(-8.84681 + 1.12052i) q^{80} +(-3.62280 - 7.93282i) q^{81} +(0.195078 - 0.260594i) q^{82} +(1.28200 + 5.89328i) q^{83} +(-12.5580 + 3.68736i) q^{84} +(3.54693 - 1.25542i) q^{85} +(-0.0253855 - 0.0219966i) q^{86} +(-4.66029 - 1.01378i) q^{87} +(0.0756642 - 1.05792i) q^{88} +(-1.16784 - 0.342910i) q^{89} +(-0.595563 + 0.0325423i) q^{90} +3.24036i q^{91} +(9.53343 - 0.964426i) q^{92} +(-1.78301 + 1.78301i) q^{93} +(-0.0667775 - 0.0304962i) q^{94} +(6.34634 - 9.51932i) q^{95} +(-1.05031 - 1.21212i) q^{96} +(-0.0478111 + 0.219784i) q^{97} +(-0.00706350 - 0.0987607i) q^{98} +(-5.04273 + 35.0729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

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