LMFDB - Embedded newform 354.2.e.c.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	354.7
Dual form			354.2.e.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-3.82834 + 1.77118i) q^{5} +(0.856857 - 0.515554i) q^{6} +(1.02375 - 3.68721i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})$	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-3.82834 + 1.77118i) q^{5} +(0.856857 - 0.515554i) q^{6} +(1.02375 - 3.68721i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(3.61440 + 2.17471i) q^{10} +(2.28614 - 2.16554i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(0.157798 - 0.0171616i) q^{13} +(-3.62637 + 1.22187i) q^{14} +(-1.56132 - 3.91861i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(-0.852814 - 3.07156i) q^{17} +(0.468408 + 0.883512i) q^{18} +(3.68227 - 2.79919i) q^{19} +(-0.228369 - 4.21202i) q^{20} +(3.62637 + 1.22187i) q^{21} +(-3.07535 - 0.676935i) q^{22} +(3.18679 - 6.01092i) q^{23} +(0.161782 + 0.986827i) q^{24} +(8.28217 - 9.75052i) q^{25} +(-0.102759 - 0.120977i) q^{26} +(0.161782 - 0.986827i) q^{27} +(3.04640 + 2.31581i) q^{28} +(-5.70871 + 8.41972i) q^{29} +(-2.36720 + 3.49136i) q^{30} +(-6.82976 - 5.19185i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(2.03860 + 2.40002i) q^{33} +(-2.06371 + 2.42958i) q^{34} +(2.61145 + 15.9291i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.961469 + 0.211635i) q^{37} +(-4.38330 - 1.47691i) q^{38} +(0.00859341 + 0.158496i) q^{39} +(-3.35808 + 2.55275i) q^{40} +(-1.41169 - 2.66272i) q^{41} +(-1.02375 - 3.68721i) q^{42} +(2.87079 + 2.71935i) q^{43} +(1.16555 + 2.92532i) q^{44} +(3.99739 - 1.34688i) q^{45} +(-6.76355 + 0.735581i) q^{46} +(-3.78931 - 1.75312i) q^{47} +(0.725995 - 0.687699i) q^{48} +(-6.54943 - 3.94066i) q^{49} +(-12.7182 - 1.38319i) q^{50} +(3.11322 - 0.685272i) q^{51} +(-0.0424645 + 0.152943i) q^{52} +(2.12195 - 1.27674i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(-4.91654 + 12.3396i) q^{55} +(0.207173 - 3.82108i) q^{56} +(2.59573 + 3.82841i) q^{57} +10.1726 q^{58} +(-6.17017 - 4.57483i) q^{59} +4.21820 q^{60} +(-5.03490 - 7.42592i) q^{61} +(-0.464463 + 8.56652i) q^{62} +(-1.41640 + 3.55490i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-0.573710 + 0.345190i) q^{65} +(0.842438 - 3.03419i) q^{66} +(-0.504961 + 0.111150i) q^{67} +(3.16906 + 0.344656i) q^{68} +(5.82957 + 3.50754i) q^{69} +(11.7188 - 11.1007i) q^{70} +(9.39506 + 4.34662i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(-2.34980 + 0.791740i) q^{73} +(-0.364396 - 0.914564i) q^{74} +(9.28784 + 8.79791i) q^{75} +(1.23743 + 4.45683i) q^{76} +(-5.64438 - 10.6464i) q^{77} +(0.126363 - 0.0960587i) q^{78} +(0.855561 + 15.7799i) q^{79} +(3.99739 + 1.34688i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-1.41169 + 2.66272i) q^{82} +(-0.0796732 - 0.485985i) q^{83} +(-2.47735 + 2.91656i) q^{84} +(8.70513 + 10.2485i) q^{85} +(0.639731 - 3.90219i) q^{86} +(-8.09831 - 6.15617i) q^{87} +(1.76716 - 2.60637i) q^{88} +(5.18600 - 7.64878i) q^{89} +(-3.35808 - 2.55275i) q^{90} +(0.0982674 - 0.599405i) q^{91} +(4.40445 + 5.18532i) q^{92} +(5.55399 - 6.53867i) q^{93} +(0.675472 + 4.12019i) q^{94} +(-9.13911 + 17.2382i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(4.86638 + 1.63968i) q^{97} +(0.413813 + 7.63234i) q^{98} +(-2.50687 + 1.90567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$4$	−0.370138	+	0.928977i	−0.185069	+	0.464488i
$5$	−3.82834	+	1.77118i	−1.71208	+	0.792095i	−0.716567	+	0.697518i	$0.754288\pi$
$5$	−3.82834	+	1.77118i	−1.71208	+	0.792095i	−0.995518	+	0.0945768i	$0.969850\pi$
$6$	0.856857	−	0.515554i	0.349810	−	0.210474i
$7$	1.02375	−	3.68721i	0.386940	−	1.39363i	−0.472019	−	0.881589i	$-0.656475\pi$
$7$	1.02375	−	3.68721i	0.386940	−	1.39363i	0.858959	−	0.512044i	$-0.171112\pi$
$8$	0.976621	−	0.214970i	0.345288	−	0.0760035i
$9$	−0.994138	−	0.108119i	−0.331379	−	0.0360397i
$10$	3.61440	+	2.17471i	1.14297	+	0.687704i
$11$	2.28614	−	2.16554i	0.689296	−	0.652936i	−0.260620	−	0.965441i	$-0.583927\pi$
$11$	2.28614	−	2.16554i	0.689296	−	0.652936i	0.949916	+	0.312506i	$0.101168\pi$
$12$	−0.907575	−	0.419889i	−0.261994	−	0.121212i
$13$	0.157798	−	0.0171616i	0.0437654	−	0.00475978i	−0.0862101	−	0.996277i	$-0.527476\pi$
$13$	0.157798	−	0.0171616i	0.0437654	−	0.00475978i	0.129976	+	0.991517i	$0.458510\pi$
$14$	−3.62637	+	1.22187i	−0.969189	+	0.326558i
$15$	−1.56132	−	3.91861i	−0.403131	−	1.01178i
$16$	−0.725995	−	0.687699i	−0.181499	−	0.171925i
$17$	−0.852814	−	3.07156i	−0.206838	−	0.744962i	−0.992062	−	0.125750i	$-0.959866\pi$
$17$	−0.852814	−	3.07156i	−0.206838	−	0.744962i	0.785224	−	0.619212i	$-0.212548\pi$
$18$	0.468408	+	0.883512i	0.110405	+	0.208246i
$19$	3.68227	−	2.79919i	0.844771	−	0.642178i	−0.0905842	−	0.995889i	$-0.528873\pi$
$19$	3.68227	−	2.79919i	0.844771	−	0.642178i	0.935355	+	0.353711i	$0.115080\pi$
$20$	−0.228369	−	4.21202i	−0.0510649	−	0.941836i
$21$	3.62637	+	1.22187i	0.791340	+	0.266633i
$22$	−3.07535	−	0.676935i	−0.655666	−	0.144323i
$23$	3.18679	−	6.01092i	0.664491	−	1.25336i	−0.290542	−	0.956862i	$-0.593836\pi$
$23$	3.18679	−	6.01092i	0.664491	−	1.25336i	0.955033	−	0.296500i	$-0.0958196\pi$
$24$	0.161782	+	0.986827i	0.0330236	+	0.201435i
$25$	8.28217	−	9.75052i	1.65643	−	1.95010i
$26$	−0.102759	−	0.120977i	−0.0201527	−	0.0237256i
$27$	0.161782	−	0.986827i	0.0311350	−	0.189915i
$28$	3.04640	+	2.31581i	0.575716	+	0.437648i
$29$	−5.70871	+	8.41972i	−1.06008	+	1.56350i	−0.258133	+	0.966109i	$0.583107\pi$
$29$	−5.70871	+	8.41972i	−1.06008	+	1.56350i	−0.801948	+	0.597394i	$0.796203\pi$
$30$	−2.36720	+	3.49136i	−0.432190	+	0.637432i
$31$	−6.82976	−	5.19185i	−1.22666	−	0.932484i	−0.227514	−	0.973775i	$-0.573060\pi$
$31$	−6.82976	−	5.19185i	−1.22666	−	0.932484i	−0.999147	+	0.0412908i	$0.986853\pi$
$32$	−0.161782	+	0.986827i	−0.0285993	+	0.174448i
$33$	2.03860	+	2.40002i	0.354874	+	0.417790i
$34$	−2.06371	+	2.42958i	−0.353923	+	0.416670i
$35$	2.61145	+	15.9291i	0.441415	+	2.69251i
$36$	0.468408	−	0.883512i	0.0780681	−	0.147252i
$37$	0.961469	+	0.211635i	0.158065	+	0.0347926i	0.293298	−	0.956021i	$-0.405247\pi$
$37$	0.961469	+	0.211635i	0.158065	+	0.0347926i	−0.135233	+	0.990814i	$0.543178\pi$
$38$	−4.38330	−	1.47691i	−0.711065	−	0.239586i
$39$	0.00859341	+	0.158496i	0.00137605	+	0.0253797i
$40$	−3.35808	+	2.55275i	−0.530960	+	0.403625i
$41$	−1.41169	−	2.66272i	−0.220468	−	0.415848i	0.748463	−	0.663176i	$-0.230792\pi$
$41$	−1.41169	−	2.66272i	−0.220468	−	0.415848i	−0.968932	+	0.247329i	$0.920447\pi$
$42$	−1.02375	−	3.68721i	−0.157968	−	0.568948i
$43$	2.87079	+	2.71935i	0.437791	+	0.414698i	0.874591	−	0.484861i	$-0.161130\pi$
$43$	2.87079	+	2.71935i	0.437791	+	0.414698i	−0.436800	+	0.899559i	$0.643888\pi$
$44$	1.16555	+	2.92532i	0.175714	+	0.441008i
$45$	3.99739	−	1.34688i	0.595896	−	0.200781i
$46$	−6.76355	+	0.735581i	−0.997231	+	0.108455i
$47$	−3.78931	−	1.75312i	−0.552727	−	0.255719i	0.123585	−	0.992334i	$-0.460561\pi$
$47$	−3.78931	−	1.75312i	−0.552727	−	0.255719i	−0.676312	+	0.736615i	$0.736423\pi$
$48$	0.725995	−	0.687699i	0.104788	−	0.0992609i
$49$	−6.54943	−	3.94066i	−0.935633	−	0.562951i
$50$	−12.7182	−	1.38319i	−1.79863	−	0.195613i
$51$	3.11322	−	0.685272i	0.435938	−	0.0959573i
$52$	−0.0424645	+	0.152943i	−0.00588877	+	0.0212094i
$53$	2.12195	−	1.27674i	0.291473	−	0.175373i	−0.362306	−	0.932059i	$-0.618010\pi$
$53$	2.12195	−	1.27674i	0.291473	−	0.175373i	0.653779	+	0.756686i	$0.273183\pi$
$54$	−0.907575	+	0.419889i	−0.123505	+	0.0571397i
$55$	−4.91654	+	12.3396i	−0.662946	+	1.66387i
$56$	0.207173	−	3.82108i	0.0276846	−	0.510613i
$57$	2.59573	+	3.82841i	0.343813	+	0.507086i
$58$	10.1726			1.33572
$59$	−6.17017	−	4.57483i	−0.803287	−	0.595592i
$59$	−6.17017	−	4.57483i	−0.803287	−	0.595592i
$60$	4.21820			0.544568
$61$	−5.03490	−	7.42592i	−0.644653	−	0.950792i	−0.999872	−	0.0160089i	$-0.994904\pi$
$61$	−5.03490	−	7.42592i	−0.644653	−	0.950792i	0.355219	−	0.934783i	$-0.384406\pi$
$62$	−0.464463	+	8.56652i	−0.0589869	+	1.08795i
$63$	−1.41640	+	3.55490i	−0.178450	+	0.447876i
$64$	0.907575	−	0.419889i	0.113447	−	0.0524861i
$65$	−0.573710	+	0.345190i	−0.0711599	+	0.0428155i
$66$	0.842438	−	3.03419i	0.103697	−	0.373483i
$67$	−0.504961	+	0.111150i	−0.0616908	+	0.0135792i	−0.245709	−	0.969344i	$-0.579021\pi$
$67$	−0.504961	+	0.111150i	−0.0616908	+	0.0135792i	0.184018	+	0.982923i	$0.441090\pi$
$68$	3.16906	+	0.344656i	0.384305	+	0.0417957i
$69$	5.82957	+	3.50754i	0.701798	+	0.422258i
$70$	11.7188	−	11.1007i	1.40067	−	1.32678i
$71$	9.39506	+	4.34662i	1.11499	+	0.515848i	0.888828	−	0.458242i	$-0.151521\pi$
$71$	9.39506	+	4.34662i	1.11499	+	0.515848i	0.226160	+	0.974090i	$0.427383\pi$
$72$	−0.994138	+	0.108119i	−0.117160	+	0.0127419i
$73$	−2.34980	+	0.791740i	−0.275023	+	0.0926661i	−0.453434	−	0.891290i	$-0.649801\pi$
$73$	−2.34980	+	0.791740i	−0.275023	+	0.0926661i	0.178410	+	0.983956i	$0.442905\pi$
$74$	−0.364396	−	0.914564i	−0.0423601	−	0.106316i
$75$	9.28784	+	8.79791i	1.07247	+	1.01589i
$76$	1.23743	+	4.45683i	0.141943	+	0.511233i
$77$	−5.64438	−	10.6464i	−0.643237	−	1.21327i
$78$	0.126363	−	0.0960587i	0.0143078	−	0.0108765i
$79$	0.855561	+	15.7799i	0.0962581	+	1.77538i	0.505380	+	0.862897i	$0.331352\pi$
$79$	0.855561	+	15.7799i	0.0962581	+	1.77538i	−0.409122	+	0.912480i	$0.634165\pi$
$80$	3.99739	+	1.34688i	0.446922	+	0.150586i
$81$	0.976621	+	0.214970i	0.108513	+	0.0238856i
$82$	−1.41169	+	2.66272i	−0.155895	+	0.294049i
$83$	−0.0796732	−	0.485985i	−0.00874527	−	0.0533438i	0.982093	−	0.188395i	$-0.0603284\pi$
$83$	−0.0796732	−	0.485985i	−0.00874527	−	0.0533438i	−0.990839	+	0.135051i	$0.956880\pi$
$84$	−2.47735	+	2.91656i	−0.270301	+	0.318222i
$85$	8.70513	+	10.2485i	0.944204	+	1.11160i
$86$	0.639731	−	3.90219i	0.0689840	−	0.420784i
$87$	−8.09831	−	6.15617i	−0.868230	−	0.660011i
$88$	1.76716	−	2.60637i	0.188380	−	0.277840i
$89$	5.18600	−	7.64878i	0.549715	−	0.810770i	−0.446760	−	0.894654i	$-0.647422\pi$
$89$	5.18600	−	7.64878i	0.549715	−	0.810770i	0.996476	+	0.0838842i	$0.0267326\pi$
$90$	−3.35808	−	2.55275i	−0.353973	−	0.269083i
$91$	0.0982674	−	0.599405i	0.0103012	−	0.0628347i
$92$	4.40445	+	5.18532i	0.459196	+	0.540607i
$93$	5.55399	−	6.53867i	0.575922	−	0.678028i
$94$	0.675472	+	4.12019i	0.0696696	+	0.424966i
$95$	−9.13911	+	17.2382i	−0.937653	+	1.76860i
$96$	−0.976621	−	0.214970i	−0.0996759	−	0.0219403i
$97$	4.86638	+	1.63968i	0.494106	+	0.166484i	0.555313	−	0.831641i	$-0.312598\pi$
$97$	4.86638	+	1.63968i	0.494106	+	0.166484i	−0.0612069	+	0.998125i	$0.519495\pi$
$98$	0.413813	+	7.63234i	0.0418015	+	0.770982i
$99$	−2.50687	+	1.90567i	−0.251950	+	0.191527i
$100$	5.99246	+	11.3030i	0.599246	+	1.13030i
$101$	−4.35357	−	15.6801i	−0.433197	−	1.56023i	−0.782148	−	0.623092i	$-0.785876\pi$
$101$	−4.35357	−	15.6801i	−0.433197	−	1.56023i	0.348952	−	0.937141i	$-0.386538\pi$
$102$	−2.31429	−	2.19221i	−0.229149	−	0.217062i
$103$	−1.02888	−	2.58228i	−0.101378	−	0.254440i	0.869535	−	0.493871i	$-0.164418\pi$
$103$	−1.02888	−	2.58228i	−0.101378	−	0.254440i	−0.970913	+	0.239431i	$0.923039\pi$
$104$	0.150420	−	0.0506824i	0.0147499	−	0.00496982i
$105$	−16.0471	+	1.74523i	−1.56604	+	0.170317i
$106$	−2.24756	−	1.03983i	−0.218302	−	0.100997i
$107$	6.20784	−	5.88038i	0.600134	−	0.568477i	−0.326143	−	0.945321i	$-0.605749\pi$
$107$	6.20784	−	5.88038i	0.600134	−	0.568477i	0.926277	+	0.376843i	$0.122990\pi$
$108$	0.856857	+	0.515554i	0.0824511	+	0.0496092i
$109$	9.64809	+	1.04929i	0.924119	+	0.100504i	0.557791	−	0.829982i	$-0.311649\pi$
$109$	9.64809	+	1.04929i	0.924119	+	0.100504i	0.366328	+	0.930486i	$0.380615\pi$
$110$	12.9724	−	2.85545i	1.23687	−	0.272256i
$111$	−0.263378	+	0.948601i	−0.0249987	+	0.0900372i
$112$	−3.27893	+	1.97286i	−0.309829	+	0.186418i
$113$	−5.79526	+	2.68117i	−0.545172	+	0.252223i	−0.673089	−	0.739562i	$-0.735033\pi$
$113$	−5.79526	+	2.68117i	−0.545172	+	0.252223i	0.127917	+	0.991785i	$0.459171\pi$
$114$	1.71205	−	4.29691i	0.160348	−	0.402443i
$115$	−1.55369	+	28.6562i	−0.144883	+	2.67220i
$116$	−5.70871	−	8.41972i	−0.530041	−	0.781751i
$117$	−0.158729			−0.0146745
$118$	−0.323916	+	7.67431i	−0.0298189	+	0.706478i
$119$	−12.1985			−1.11824
$120$	−2.36720	−	3.49136i	−0.216095	−	0.318716i
$121$	−0.0586867	+	1.08241i	−0.00533516	+	0.0984012i
$122$	−3.32083	+	8.33466i	−0.300654	+	0.754585i
$123$	2.73525	−	1.26546i	0.246629	−	0.114103i
$124$	7.35106	−	4.42299i	0.660145	−	0.397196i
$125$	−8.79459	+	31.6753i	−0.786612	+	2.83312i
$126$	3.73722	−	0.822625i	0.332938	−	0.0732853i
$127$	−0.132883	−	0.0144518i	−0.0117914	−	0.00128239i	0.102221	−	0.994762i	$-0.467405\pi$
$127$	−0.132883	−	0.0144518i	−0.0117914	−	0.00128239i	−0.114013	+	0.993479i	$0.536370\pi$
$128$	−0.856857	−	0.515554i	−0.0757362	−	0.0455690i
$129$	−2.87079	+	2.71935i	−0.252759	+	0.239426i
$130$	0.607668	+	0.281137i	0.0532960	+	0.0246574i
$131$	18.6451	−	2.02778i	1.62903	−	0.177168i	0.752528	−	0.658560i	$-0.228834\pi$
$131$	18.6451	−	2.02778i	1.62903	−	0.177168i	0.876505	+	0.481392i	$0.159869\pi$
$132$	−2.98413	+	1.00547i	−0.259735	+	0.0875149i
$133$	−6.55147	−	16.4430i	−0.568085	−	1.42578i
$134$	0.375375	+	0.355574i	0.0324275	+	0.0307169i
$135$	1.12849	+	4.06445i	0.0971249	+	0.349812i
$136$	−1.49317	−	2.81642i	−0.128038	−	0.241506i
$137$	13.5163	−	10.2748i	1.15477	−	0.877834i	0.160747	−	0.986996i	$-0.448610\pi$
$137$	13.5163	−	10.2748i	1.15477	−	0.877834i	0.994024	+	0.109161i	$0.0348165\pi$
$138$	−0.368330	−	6.79346i	−0.0313544	−	0.578297i
$139$	−22.1275	−	7.45561i	−1.87683	−	0.632377i	−0.982893	−	0.184179i	$-0.941037\pi$
$139$	−22.1275	−	7.45561i	−1.87683	−	0.632377i	−0.893935	−	0.448197i	$-0.852066\pi$
$140$	−15.7644	−	3.47000i	−1.33233	−	0.293269i
$141$	1.95570	−	3.68884i	0.164699	−	0.310656i
$142$	−1.67474	−	10.2154i	−0.140541	−	0.857262i
$143$	0.323585	−	0.380953i	0.0270595	−	0.0318569i
$144$	0.647386	+	0.762162i	0.0539489	+	0.0635135i
$145$	6.94206	−	42.3447i	0.576507	−	3.51653i
$146$	1.97399	+	1.50059i	0.163369	+	0.124190i
$147$	4.28946	−	6.32648i	0.353789	−	0.521799i
$148$	−0.552481	+	0.814848i	−0.0454136	+	0.0669801i
$149$	−1.30783	−	0.994189i	−0.107142	−	0.0814472i	0.550232	−	0.835012i	$-0.314539\pi$
$149$	−1.30783	−	0.994189i	−0.107142	−	0.0814472i	−0.657373	+	0.753565i	$0.728333\pi$
$150$	2.06972	−	12.6247i	0.168992	−	1.03080i
$151$	6.12605	+	7.21214i	0.498531	+	0.586916i	0.952667	−	0.304017i	$-0.0983279\pi$
$151$	6.12605	+	7.21214i	0.498531	+	0.586916i	−0.454136	+	0.890932i	$0.650052\pi$
$152$	2.99444	−	3.52532i	0.242881	−	0.285942i
$153$	0.515721	+	3.14576i	0.0416935	+	0.254319i
$154$	−5.64438	+	10.6464i	−0.454837	+	0.857913i
$155$	35.3423	+	7.77944i	2.83876	+	0.624859i
$156$	−0.150420	−	0.0506824i	−0.0120432	−	0.00405784i
$157$	−0.102163	−	1.88428i	−0.00815346	−	0.150382i	−0.999775	−	0.0212056i	$-0.993250\pi$
$157$	−0.102163	−	1.88428i	−0.00815346	−	0.150382i	0.991622	−	0.129176i	$-0.0412332\pi$
$158$	12.5807	−	9.56361i	1.00087	−	0.760840i
$159$	1.15998	+	2.18796i	0.0919928	+	0.173517i
$160$	−1.12849	−	4.06445i	−0.0892149	−	0.321323i
$161$	−18.9010	−	17.9040i	−1.48961	−	1.41103i
$162$	−0.370138	−	0.928977i	−0.0290808	−	0.0729873i
$163$	2.64316	−	0.890586i	0.207029	−	0.0697561i	−0.213877	−	0.976861i	$-0.568609\pi$
$163$	2.64316	−	0.890586i	0.207029	−	0.0697561i	0.420905	+	0.907105i	$0.361712\pi$
$164$	2.99613	−	0.325849i	0.233958	−	0.0254445i
$165$	−12.0553	−	5.57738i	−0.938505	−	0.434199i
$166$	−0.357533	+	0.338673i	−0.0277499	+	0.0262861i
$167$	4.86926	+	2.92974i	0.376795	+	0.226710i	0.691335	−	0.722534i	$-0.257023\pi$
$167$	4.86926	+	2.92974i	0.376795	+	0.226710i	−0.314540	+	0.949244i	$0.601850\pi$
$168$	3.80426	+	0.413738i	0.293505	+	0.0319206i
$169$	−12.6715	+	2.78920i	−0.974728	+	0.214554i
$170$	3.59734	−	12.9565i	0.275904	−	0.993715i
$171$	−3.96333	+	2.38466i	−0.303083	+	0.182359i
$172$	−3.58881	+	1.66036i	−0.273644	+	0.126601i
$173$	−5.68523	+	14.2688i	−0.432240	+	1.08484i	0.538054	+	0.842910i	$0.319160\pi$
$173$	−5.68523	+	14.2688i	−0.432240	+	1.08484i	−0.970294	+	0.241930i	$0.922220\pi$
$174$	−0.550732	+	10.1576i	−0.0417509	+	0.770049i
$175$	−27.4733	−	40.5201i	−2.07679	−	3.06304i
$176$	−3.14897			−0.237362
$177$	4.90216	−	5.91344i	0.368469	−	0.444481i
$178$	−9.24113			−0.692652
$179$	−3.84340	−	5.66860i	−0.287270	−	0.423691i	0.656484	−	0.754340i	$-0.272043\pi$
$179$	−3.84340	−	5.66860i	−0.287270	−	0.423691i	−0.943754	+	0.330649i	$0.892732\pi$
$180$	−0.228369	+	4.21202i	−0.0170216	+	0.313945i
$181$	−6.02002	+	15.1091i	−0.447464	+	1.12305i	0.516327	+	0.856392i	$0.327299\pi$
$181$	−6.02002	+	15.1091i	−0.447464	+	1.12305i	−0.963791	+	0.266659i	$0.914080\pi$
$182$	−0.551267	+	0.255043i	−0.0408626	+	0.0189051i
$183$	7.68762	−	4.62549i	0.568285	−	0.341926i
$184$	1.82011	−	6.55545i	0.134180	−	0.483274i
$185$	−4.05567	+	0.892721i	−0.298179	+	0.0656341i
$186$	−8.52881	−	0.927564i	−0.625363	−	0.0680123i
$187$	−8.60124	−	5.17519i	−0.628985	−	0.378448i
$188$	3.03117	−	2.87128i	0.221071	−	0.209410i
$189$	−3.47301	−	1.60678i	−0.252624	−	0.116876i
$190$	19.3966	−	2.10951i	1.40718	−	0.153040i
$191$	−21.7715	+	7.33567i	−1.57533	+	0.530790i	−0.965200	−	0.261512i	$-0.915779\pi$
$191$	−21.7715	+	7.33567i	−1.57533	+	0.530790i	−0.610129	+	0.792302i	$0.708882\pi$
$192$	0.370138	+	0.928977i	0.0267124	+	0.0670431i
$193$	7.98342	+	7.56230i	0.574659	+	0.544346i	0.918877	−	0.394544i	$-0.129097\pi$
$193$	7.98342	+	7.56230i	0.574659	+	0.544346i	−0.344218	+	0.938890i	$0.611856\pi$
$194$	−1.37381	−	4.94802i	−0.0986338	−	0.355247i
$195$	−0.313623	−	0.591556i	−0.0224590	−	0.0423622i
$196$	6.08497	−	4.62568i	0.434641	−	0.330406i
$197$	−0.224062	−	4.13258i	−0.0159637	−	0.294434i	−0.995603	−	0.0936697i	$-0.970140\pi$
$197$	−0.224062	−	4.13258i	−0.0159637	−	0.294434i	0.979640	−	0.200764i	$-0.0643425\pi$
$198$	2.98413	+	1.00547i	0.212073	+	0.0714557i
$199$	−8.16372	−	1.79697i	−0.578711	−	0.127384i	−0.0840369	−	0.996463i	$-0.526781\pi$
$199$	−8.16372	−	1.79697i	−0.578711	−	0.127384i	−0.494674	+	0.869079i	$0.664712\pi$
$200$	5.99246	−	11.3030i	0.423731	−	0.799242i
$201$	−0.0836492	−	0.510238i	−0.00590016	−	0.0359894i
$202$	−10.5351	+	12.4029i	−0.741248	+	0.872665i
$203$	25.2010	+	29.6689i	1.76876	+	2.08235i
$204$	−0.515721	+	3.14576i	−0.0361077	+	0.220247i
$205$	10.1206	+	7.69346i	0.706851	+	0.537334i
$206$	−1.55993	+	2.30073i	−0.108686	+	0.160300i
$207$	−3.81800	+	5.63113i	−0.265369	+	0.391390i
$208$	−0.126363	−	0.0960587i	−0.00876170	−	0.00666047i
$209$	2.35641	−	14.3734i	0.162996	−	0.994232i
$210$	10.4499	+	12.3026i	0.721115	+	0.848962i
$211$	−2.88659	+	3.39835i	−0.198721	+	0.233952i	−0.852492	−	0.522740i	$-0.824910\pi$
$211$	−2.88659	+	3.39835i	−0.198721	+	0.233952i	0.653771	+	0.756692i	$0.273186\pi$
$212$	0.400643	+	2.44382i	0.0275163	+	0.167842i
$213$	−4.84888	+	9.14596i	−0.332240	+	0.626671i
$214$	−8.35088	−	1.83817i	−0.570855	−	0.125655i
$215$	−15.8068	−	5.32593i	−1.07802	−	0.363226i
$216$	−0.0541389	−	0.998533i	−0.00368369	−	0.0679416i
$217$	−26.1354	+	19.8676i	−1.77418	+	1.34870i
$218$	−4.54589	−	8.57446i	−0.307887	−	0.580736i
$219$	−0.663363	−	2.38922i	−0.0448259	−	0.161448i
$220$	−9.64339	−	9.13470i	−0.650157	−	0.615862i
$221$	−0.187286	−	0.470051i	−0.0125982	−	0.0316191i
$222$	0.932951	−	0.314348i	0.0626156	−	0.0210976i
$223$	−0.912719	+	0.0992642i	−0.0611202	+	0.00664722i	−0.138628	−	0.990345i	$-0.544269\pi$
$223$	−0.912719	+	0.0992642i	−0.0611202	+	0.00664722i	0.0775078	+	0.996992i	$0.475304\pi$
$224$	3.47301	+	1.60678i	0.232050	+	0.107358i
$225$	−9.28784	+	8.79791i	−0.619189	+	0.586527i
$226$	5.47140	+	3.29203i	0.363952	+	0.218983i
$227$	19.7255	+	2.14528i	1.30923	+	0.142387i	0.735984	−	0.676999i	$-0.236720\pi$
$227$	19.7255	+	2.14528i	1.30923	+	0.142387i	0.573243	+	0.819386i	$0.305685\pi$
$228$	−4.51729	+	0.994330i	−0.299165	+	0.0658511i
$229$	1.28531	−	4.62927i	0.0849358	−	0.305911i	−0.908864	−	0.417092i	$-0.863049\pi$
$229$	1.28531	−	4.62927i	0.0849358	−	0.305911i	0.993800	+	0.111181i	$0.0354632\pi$
$230$	24.5903	−	14.7955i	1.62144	−	0.975587i
$231$	10.9364	−	5.05971i	0.719562	−	0.332905i
$232$	−3.76525	+	9.45008i	−0.247201	+	0.620428i
$233$	0.170444	−	3.14365i	0.0111661	−	0.205947i	−0.987627	−	0.156824i	$-0.949875\pi$
$233$	0.170444	−	3.14365i	0.0111661	−	0.205947i	0.998793	−	0.0491233i	$-0.0156427\pi$
$234$	0.0890766	+	0.131378i	0.00582312	+	0.00858846i
$235$	17.6118			1.14887
$236$	6.53372	−	4.03862i	0.425309	−	0.262892i
$237$	−15.8031			−1.02652
$238$	6.84566	+	10.0966i	0.443738	+	0.654465i
$239$	0.927697	−	17.1104i	0.0600077	−	1.10678i	−0.801158	−	0.598453i	$-0.795782\pi$
$239$	0.927697	−	17.1104i	0.0600077	−	1.10678i	0.861166	−	0.508324i	$-0.169735\pi$
$240$	−1.56132	+	3.91861i	−0.100783	+	0.252945i
$241$	−0.699244	+	0.323505i	−0.0450423	+	0.0208388i	−0.442281	−	0.896877i	$-0.645831\pi$
$241$	−0.699244	+	0.323505i	−0.0450423	+	0.0208388i	0.397239	+	0.917715i	$0.369969\pi$
$242$	0.928836	−	0.558862i	0.0597078	−	0.0359250i
$243$	−0.267528	+	0.963550i	−0.0171620	+	0.0618118i
$244$	8.76212	−	1.92869i	0.560937	−	0.123472i
$245$	32.0530	+	3.48598i	2.04779	+	0.222711i
$246$	−2.58239	−	1.55377i	−0.164647	−	0.0990650i
$247$	0.533018	−	0.504901i	0.0339151	−	0.0321261i
$248$	−7.78618	−	3.60227i	−0.494423	−	0.228744i
$249$	0.489585	−	0.0532456i	0.0310262	−	0.00337430i
$250$	31.1527	−	10.4966i	1.97027	−	0.663860i
$251$	4.89741	+	12.2916i	0.309122	+	0.775837i	0.998668	+	0.0515952i	$0.0164305\pi$
$251$	4.89741	+	12.2916i	0.309122	+	0.775837i	−0.689547	+	0.724241i	$0.742190\pi$
$252$	−2.77816	−	2.63161i	−0.175008	−	0.165776i
$253$	−5.73147	−	20.6429i	−0.360335	−	1.29781i
$254$	0.0626103	+	0.118096i	0.00392852	+	0.00740998i
$255$	−10.7047	+	8.13752i	−0.670356	+	0.509592i
$256$	0.0541389	+	0.998533i	0.00338368	+	0.0624083i
$257$	21.2942	+	7.17484i	1.32829	+	0.447554i	0.891913	−	0.452208i	$-0.149363\pi$
$257$	21.2942	+	7.17484i	1.32829	+	0.447554i	0.436381	+	0.899762i	$0.356260\pi$
$258$	3.86183	+	0.850053i	0.240427	+	0.0529220i
$259$	1.76464	−	3.32847i	0.109650	−	0.206821i
$260$	−0.108321	−	0.660731i	−0.00671780	−	0.0409768i
$261$	6.58558	−	7.75314i	0.407637	−	0.479908i
$262$	−12.1418	−	14.2944i	−0.750122	−	0.883112i
$263$	1.58307	−	9.65628i	0.0976161	−	0.595432i	−0.892038	−	0.451960i	$-0.850725\pi$
$263$	1.58307	−	9.65628i	0.0976161	−	0.595432i	0.989654	−	0.143472i	$-0.0458267\pi$
$264$	2.50687	+	1.90567i	0.154287	+	0.117286i
$265$	−5.86223	+	8.64614i	−0.360114	+	0.531128i
$266$	−9.93305	+	14.6502i	−0.609034	+	0.898258i
$267$	7.35680	+	5.59250i	0.450229	+	0.342255i
$268$	0.0836492	−	0.510238i	0.00510969	−	0.0311677i
$269$	0.516368	+	0.607915i	0.0314835	+	0.0370652i	0.777678	−	0.628662i	$-0.216397\pi$
$269$	0.516368	+	0.607915i	0.0314835	+	0.0370652i	−0.746195	+	0.665727i	$0.768121\pi$
$270$	2.73081	−	3.21495i	0.166192	−	0.195656i
$271$	−3.51352	−	21.4315i	−0.213431	−	1.30187i	−0.848409	−	0.529342i	$-0.822439\pi$
$271$	−3.51352	−	21.4315i	−0.213431	−	1.30187i	0.634977	−	0.772531i	$-0.281009\pi$
$272$	−1.49317	+	2.81642i	−0.0905367	+	0.170770i
$273$	0.593206	+	0.130574i	0.0359024	+	0.00790272i
$274$	−16.0895	−	5.42117i	−0.972001	−	0.327505i
$275$	−2.18101	−	40.2264i	−0.131520	−	2.42574i
$276$	−5.41617	+	4.11726i	−0.326015	+	0.247830i
$277$	9.84876	+	18.5767i	0.591755	+	1.11617i	0.980812	+	0.194954i	$0.0624558\pi$
$277$	9.84876	+	18.5767i	0.591755	+	1.11617i	−0.389058	+	0.921213i	$0.627199\pi$
$278$	6.24672	+	22.4987i	0.374653	+	1.34938i
$279$	6.22839	+	5.89984i	0.372884	+	0.353214i
$280$	5.97468	+	14.9953i	0.357055	+	0.896141i
$281$	−24.8167	+	8.36172i	−1.48044	+	0.498819i	−0.939591	−	0.342300i	$-0.888794\pi$
$281$	−24.8167	+	8.36172i	−1.48044	+	0.498819i	−0.540850	+	0.841119i	$0.681897\pi$
$282$	−4.15072	+	0.451418i	−0.247172	+	0.0268816i
$283$	17.3460	+	8.02512i	1.03111	+	0.477044i	0.861120	−	0.508402i	$-0.169763\pi$
$283$	17.3460	+	8.02512i	1.03111	+	0.477044i	0.169993	+	0.985445i	$0.445626\pi$
$284$	−7.51537	+	7.11894i	−0.445955	+	0.422431i
$285$	−16.7181	−	10.0590i	−0.990297	−	0.595842i
$286$	−0.496902	−	0.0540414i	−0.0293825	−	0.00319553i
$287$	−11.2632	+	2.47922i	−0.664847	+	0.146344i
$288$	0.267528	−	0.963550i	0.0157643	−	0.0567777i
$289$	5.85940	−	3.52548i	0.344671	−	0.207381i
$290$	−38.9440	+	18.0174i	−2.28687	+	1.05802i
$291$	−1.90073	+	4.77048i	−0.111423	+	0.279650i
$292$	0.134243	−	2.47596i	0.00785596	−	0.144895i
$293$	8.35441	+	12.3218i	0.488070	+	0.719849i	0.989369	−	0.145425i	$-0.0464549\pi$
$293$	8.35441	+	12.3218i	0.488070	+	0.719849i	−0.501300	+	0.865274i	$0.667145\pi$
$294$	−7.64355			−0.445781
$295$	31.7243	+	6.58552i	1.84706	+	0.383424i
$296$	0.984486			0.0572221
$297$	−1.76716	−	2.60637i	−0.102541	−	0.151237i
$298$	−0.0889402	+	1.64041i	−0.00515217	+	0.0950262i
$299$	0.399713	−	1.00320i	0.0231160	−	0.0580168i
$300$	−11.6108	+	5.37174i	−0.670352	+	0.310138i
$301$	12.9658	−	7.80125i	0.747335	−	0.449657i
$302$	2.53155	−	9.11782i	0.145674	−	0.524672i
$303$	15.8928	−	3.49828i	0.913020	−	0.200971i
$304$	−4.59831	−	0.500097i	−0.263731	−	0.0286825i
$305$	32.4279	+	19.5112i	1.85682	+	1.11721i
$306$	2.31429	−	2.19221i	0.132299	−	0.125321i
$307$	8.44322	+	3.90625i	0.481880	+	0.222941i	0.645762	−	0.763538i	$-0.276540\pi$
$307$	8.44322	+	3.90625i	0.481880	+	0.222941i	−0.163882	+	0.986480i	$0.552402\pi$
$308$	11.9795	−	1.30285i	0.682594	−	0.0742366i
$309$	2.63420	−	0.887564i	0.149854	−	0.0504918i
$310$	−13.3947	−	33.6182i	−0.760768	−	1.90938i
$311$	2.48290	+	2.35193i	0.140792	+	0.133366i	0.754855	−	0.655892i	$-0.227707\pi$
$311$	2.48290	+	2.35193i	0.140792	+	0.133366i	−0.614063	+	0.789257i	$0.710466\pi$
$312$	0.0424645	+	0.152943i	0.00240408	+	0.00865871i
$313$	15.4861	+	29.2098i	0.875325	+	1.65104i	0.752483	+	0.658612i	$0.228856\pi$
$313$	15.4861	+	29.2098i	0.875325	+	1.65104i	0.122842	+	0.992426i	$0.460799\pi$
$314$	−1.50226	+	1.14199i	−0.0847776	+	0.0644463i
$315$	−0.873897	−	16.1181i	−0.0492385	−	0.908151i
$316$	−14.9758	−	5.04595i	−0.842456	−	0.283857i
$317$	−5.72643	−	1.26048i	−0.321629	−	0.0707958i	0.0512217	−	0.998687i	$-0.483688\pi$
$317$	−5.72643	−	1.26048i	−0.321629	−	0.0707958i	−0.372850	+	0.927891i	$0.621620\pi$
$318$	1.15998	−	2.18796i	0.0650487	−	0.122695i
$319$	5.18238	+	31.6111i	0.290157	+	1.76988i
$320$	−2.73081	+	3.21495i	−0.152657	+	0.179721i
$321$	5.53567	+	6.51709i	0.308971	+	0.363749i
$322$	−4.21193	+	25.6917i	−0.234722	+	1.43174i
$323$	−11.7382	−	8.92312i	−0.653129	−	0.496495i
$324$	−0.561187	+	0.827689i	−0.0311771	+	0.0459827i
$325$	1.13958	−	1.68075i	0.0632125	−	0.0932314i
$326$	−2.22044	−	1.68793i	−0.122979	−	0.0934860i
$327$	−1.57009	+	9.57713i	−0.0868262	+	0.529616i
$328$	−1.95109	−	2.29700i	−0.107731	−	0.126831i
$329$	−10.3434	+	12.1772i	−0.570250	+	0.671351i
$330$	2.14895	+	13.1080i	0.118296	+	0.721572i
$331$	−2.22384	+	4.19461i	−0.122233	+	0.230557i	−0.937076	−	0.349126i	$-0.886479\pi$
$331$	−2.22384	+	4.19461i	−0.122233	+	0.230557i	0.814842	+	0.579683i	$0.196823\pi$
$332$	0.480959	+	0.105867i	0.0263960	+	0.00581021i
$333$	−0.932951	−	0.314348i	−0.0511254	−	0.0172262i
$334$	−0.307655	−	5.67437i	−0.0168341	−	0.310487i
$335$	1.73629	−	1.31990i	0.0948639	−	0.0721136i
$336$	−1.79245	−	3.38093i	−0.0977863	−	0.184445i
$337$	−6.87388	−	24.7575i	−0.374444	−	1.34862i	−0.875503	−	0.483212i	$-0.839470\pi$
$337$	−6.87388	−	24.7575i	−0.374444	−	1.34862i	0.501060	−	0.865413i	$-0.332944\pi$
$338$	9.41965	+	8.92277i	0.512361	+	0.485335i
$339$	−2.36349	−	5.93191i	−0.128367	−	0.322177i
$340$	−12.7427	+	4.29351i	−0.691070	+	0.232849i
$341$	−26.8569	+	2.92087i	−1.45439	+	0.158174i
$342$	4.19792	+	1.94217i	0.226998	+	0.105020i
$343$	−1.78787	+	1.69357i	−0.0965362	+	0.0914439i
$344$	3.38825	+	2.03864i	0.182682	+	0.109916i
$345$	−28.5300	−	3.10283i	−1.53601	−	0.167051i
$346$	15.0006	−	3.30189i	0.806439	−	0.177511i
$347$	−6.35081	+	22.8735i	−0.340929	+	1.22792i	0.572155	+	0.820146i	$0.306108\pi$
$347$	−6.35081	+	22.8735i	−0.340929	+	1.22792i	−0.913084	+	0.407771i	$0.866306\pi$
$348$	8.71644	−	5.24451i	0.467250	−	0.281135i
$349$	4.47007	−	2.06807i	0.239277	−	0.110701i	−0.296586	−	0.955006i	$-0.595848\pi$
$349$	4.47007	−	2.06807i	0.239277	−	0.110701i	0.535863	+	0.844305i	$0.319986\pi$
$350$	−18.1204	+	45.4788i	−0.968576	+	2.43094i
$351$	0.00859341	−	0.158496i	0.000458682	−	0.00845990i
$352$	1.76716	+	2.60637i	0.0941899	+	0.138920i
$353$	24.1709			1.28649			0.643245	−	0.765661i	$-0.277588\pi$
$353$	24.1709			1.28649			0.643245	+	0.765661i	$0.277588\pi$
$354$	−7.64552	−	0.738920i	−0.406355	−	0.0392732i
$355$	−43.6661			−2.31756
$356$	5.18600	+	7.64878i	0.274858	+	0.405385i
$357$	0.660415	−	12.1806i	0.0349529	−	0.644668i
$358$	−2.53497	+	6.36229i	−0.133977	+	0.336257i
$359$	14.1905	−	6.56524i	0.748947	−	0.346500i	−0.00800687	−	0.999968i	$-0.502549\pi$
$359$	14.1905	−	6.56524i	0.748947	−	0.346500i	0.756954	+	0.653468i	$0.226687\pi$
$360$	3.61440	−	2.17471i	0.190496	−	0.114617i
$361$	0.640615	−	2.30729i	0.0337166	−	0.121436i
$362$	15.8840	−	3.49633i	0.834844	−	0.183763i
$363$	−1.07765	−	0.117201i	−0.0565619	−	0.00615147i
$364$	0.520460	+	0.313151i	0.0272795	+	0.0164136i
$365$	7.59352	−	7.19296i	0.397463	−	0.376497i
$366$	−8.14265	−	3.76719i	−0.425623	−	0.196914i
$367$	12.3398	−	1.34203i	0.644132	−	0.0700536i	0.219778	−	0.975550i	$-0.429467\pi$
$367$	12.3398	−	1.34203i	0.644132	−	0.0700536i	0.424354	+	0.905496i	$0.360501\pi$
$368$	−6.44730	+	2.17235i	−0.336089	+	0.113241i
$369$	1.11552	+	2.79975i	0.0580717	+	0.145749i
$370$	3.01489	+	2.85585i	0.156736	+	0.148469i
$371$	−2.53525	−	9.13114i	−0.131624	−	0.474065i
$372$	4.01852	+	7.57974i	0.208351	+	0.392991i
$373$	10.0581	−	7.64597i	0.520789	−	0.395894i	−0.311491	−	0.950249i	$-0.600828\pi$
$373$	10.0581	−	7.64597i	0.520789	−	0.395894i	0.832280	+	0.554356i	$0.187035\pi$
$374$	0.543453	+	10.0234i	0.0281013	+	0.518298i
$375$	−31.1527	−	10.4966i	−1.60872	−	0.542040i
$376$	−4.07758	−	0.897544i	−0.210285	−	0.0462873i
$377$	−0.756330	+	1.42659i	−0.0389530	+	0.0734731i
$378$	0.619089	+	3.77628i	0.0318425	+	0.194231i
$379$	−5.07554	+	5.97538i	−0.260713	+	0.306935i	−0.876908	−	0.480659i	$-0.840398\pi$
$379$	−5.07554	+	5.97538i	−0.260713	+	0.306935i	0.616195	+	0.787594i	$0.288673\pi$
$380$	−12.6311	−	14.8705i	−0.647964	−	0.762842i
$381$	0.0216248	−	0.131905i	0.00110787	−	0.00675771i
$382$	18.2895	+	13.9033i	0.935774	+	0.711357i
$383$	−16.5332	+	24.3847i	−0.844809	+	1.24600i	0.122518	+	0.992466i	$0.460903\pi$
$383$	−16.5332	+	24.3847i	−0.844809	+	1.24600i	−0.967327	+	0.253533i	$0.918407\pi$
$384$	0.561187	−	0.827689i	0.0286380	−	0.0422378i
$385$	40.4653	+	30.7609i	2.06230	+	1.56772i
$386$	1.77904	−	10.8517i	0.0905507	−	0.552335i
$387$	−2.55995	−	3.01380i	−0.130129	−	0.153200i
$388$	−3.32445	+	3.91385i	−0.168774	+	0.198696i
$389$	−0.798744	−	4.87212i	−0.0404979	−	0.247026i	0.958817	−	0.284023i	$-0.0916692\pi$
$389$	−0.798744	−	4.87212i	−0.0404979	−	0.247026i	−0.999315	+	0.0369966i	$0.988221\pi$
$390$	−0.313623	+	0.591556i	−0.0158809	+	0.0299546i
$391$	−21.1806	−	4.66220i	−1.07115	−	0.235778i
$392$	−7.24343	−	2.44060i	−0.365849	−	0.123269i
$393$	1.01538	+	18.7276i	0.0512191	+	0.944681i
$394$	−3.29475	+	2.50460i	−0.165987	+	0.126180i
$395$	−31.2244	−	58.8954i	−1.57107	−	2.96335i
$396$	−0.842438	−	3.03419i	−0.0423341	−	0.152474i
$397$	−9.61860	−	9.11122i	−0.482744	−	0.457279i	0.407207	−	0.913336i	$-0.366503\pi$
$397$	−9.61860	−	9.11122i	−0.482744	−	0.457279i	−0.889951	+	0.456057i	$0.849261\pi$
$398$	3.09404	+	7.76546i	0.155090	+	0.389247i
$399$	16.7735	−	5.65166i	0.839727	−	0.282937i
$400$	−12.7182	+	1.38319i	−0.635912	+	0.0691596i
$401$	23.5639	+	10.9018i	1.17672	+	0.544410i	0.908066	−	0.418826i	$-0.137558\pi$
$401$	23.5639	+	10.9018i	1.17672	+	0.544410i	0.268656	+	0.963236i	$0.413420\pi$
$402$	−0.375375	+	0.355574i	−0.0187220	+	0.0177344i
$403$	−1.16683	−	0.702056i	−0.0581238	−	0.0349719i
$404$	16.1779	+	1.75945i	0.804881	+	0.0875361i
$405$	−4.11958	+	0.906789i	−0.204704	+	0.0450587i
$406$	10.4141	−	37.5083i	0.516845	−	1.86151i
$407$	2.65635	−	1.59828i	0.131671	−	0.0792236i
$408$	2.89312	−	1.33850i	0.143231	−	0.0662657i
$409$	−6.48963	+	16.2877i	−0.320891	+	0.805377i	0.676716	+	0.736244i	$0.263402\pi$
$409$	−6.48963	+	16.2877i	−0.320891	+	0.805377i	−0.997607	+	0.0691326i	$0.977977\pi$
$410$	0.688257	−	12.6942i	0.0339906	−	0.626920i
$411$	9.52796	+	14.0527i	0.469980	+	0.693168i
$412$	2.77971			0.136946
$413$	−23.1850	+	18.0672i	−1.14086	+	0.889029i
$414$	6.80343			0.334371
$415$	1.16578	+	1.71940i	0.0572260	+	0.0844020i
$416$	−0.00859341	+	0.158496i	−0.000421327	+	0.00777091i
$417$	8.64263	−	21.6914i	0.423232	−	1.06223i
$418$	−13.2191	+	6.11582i	−0.646569	+	0.299134i
$419$	9.50811	−	5.72084i	0.464501	−	0.279481i	−0.264004	−	0.964522i	$-0.585043\pi$
$419$	9.50811	−	5.72084i	0.464501	−	0.279481i	0.728505	+	0.685040i	$0.240215\pi$
$420$	4.31838	−	15.5534i	0.210715	−	0.758928i
$421$	31.6148	−	6.95894i	1.54081	−	0.339158i	0.638287	−	0.769799i	$-0.279643\pi$
$421$	31.6148	−	6.95894i	1.54081	−	0.339158i	0.902524	+	0.430641i	$0.141712\pi$
$422$	4.43269	+	0.482084i	0.215780	+	0.0234675i
$423$	3.57755	+	2.15254i	0.173946	+	0.104660i
$424$	1.79788	−	1.70305i	0.0873129	−	0.0827072i
$425$	−37.0124	−	17.1238i	−1.79537	−	0.830625i
$426$	10.2911	−	1.11923i	0.498607	−	0.0542268i
$427$	−32.5354	+	10.9624i	−1.57450	+	0.530510i
$428$	3.16498	+	7.94349i	0.152985	+	0.383963i
$429$	0.362876	+	0.343734i	0.0175198	+	0.0165957i
$430$	4.46236	+	16.0720i	0.215194	+	0.775059i
$431$	−5.50679	−	10.3869i	−0.265253	−	0.500320i	0.714731	−	0.699400i	$-0.246549\pi$
$431$	−5.50679	−	10.3869i	−0.265253	−	0.500320i	−0.979983	+	0.199080i	$0.936205\pi$
$432$	−0.796093	+	0.605174i	−0.0383020	+	0.0291165i
$433$	−1.29447	−	23.8752i	−0.0622085	−	1.14737i	−0.848390	−	0.529372i	$-0.822428\pi$
$433$	−1.29447	−	23.8752i	−0.0622085	−	1.14737i	0.786181	−	0.617996i	$-0.212055\pi$
$434$	31.1110	+	10.4825i	1.49338	+	0.503177i
$435$	41.9067	+	9.22437i	2.00927	+	0.442275i
$436$	−4.54589	+	8.57446i	−0.217709	+	0.410642i
$437$	−5.09108	−	31.0542i	−0.243540	−	1.48553i
$438$	−1.60526	+	1.88986i	−0.0767022	+	0.0903008i
$439$	−7.79452	−	9.17642i	−0.372012	−	0.437966i	0.544020	−	0.839073i	$-0.316902\pi$
$439$	−7.79452	−	9.17642i	−0.372012	−	0.437966i	−0.916032	+	0.401106i	$0.868626\pi$
$440$	−2.14895	+	13.1080i	−0.102447	+	0.624900i
$441$	6.08497	+	4.62568i	0.289761	+	0.220270i
$442$	−0.283954	+	0.418801i	−0.0135063	+	0.0199203i
$443$	3.57536	−	5.27327i	0.169871	−	0.250540i	−0.733219	−	0.679993i	$-0.761983\pi$
$443$	3.57536	−	5.27327i	0.169871	−	0.250540i	0.903090	+	0.429452i	$0.141293\pi$
$444$	−0.783742	−	0.595785i	−0.0371948	−	0.0282747i
$445$	−6.30642	+	38.4675i	−0.298953	+	1.82353i
$446$	0.594366	+	0.699742i	0.0281441	+	0.0331337i
$447$	1.06354	−	1.25209i	0.0503035	−	0.0592219i
$448$	−0.619089	−	3.77628i	−0.0292492	−	0.178412i
$449$	18.7735	−	35.4105i	0.885974	−	1.67112i	0.155883	−	0.987776i	$-0.450178\pi$
$449$	18.7735	−	35.4105i	0.885974	−	1.67112i	0.730092	−	0.683349i	$-0.239477\pi$
$450$	12.4941	+	2.75017i	0.588980	+	0.129644i
$451$	−8.99355	−	3.03028i	−0.423490	−	0.142690i
$452$	−0.345700	−	6.37606i	−0.0162604	−	0.299905i
$453$	−7.53322	+	5.72660i	−0.353942	+	0.269059i
$454$	−9.29407	−	17.5305i	−0.436192	−	0.822746i
$455$	0.685451	+	2.46877i	0.0321345	+	0.115738i
$456$	3.35804	+	3.18090i	0.157255	+	0.148959i
$457$	−14.0646	−	35.2995i	−0.657915	−	1.65124i	−0.754807	−	0.655947i	$-0.772270\pi$
$457$	−14.0646	−	35.2995i	−0.657915	−	1.65124i	0.0968927	−	0.995295i	$-0.469110\pi$
$458$	−4.55290	+	1.53405i	−0.212743	+	0.0716815i
$459$	−3.16906	+	0.344656i	−0.147919	+	0.0160872i
$460$	−26.0458	−	12.0501i	−1.21439	−	0.561838i
$461$	−7.92465	+	7.50663i	−0.369088	+	0.349618i	−0.849655	−	0.527340i	$-0.823190\pi$
$461$	−7.92465	+	7.50663i	−0.369088	+	0.349618i	0.480567	+	0.876958i	$0.340431\pi$
$462$	−10.3252	−	6.21249i	−0.480373	−	0.289031i
$463$	7.96223	+	0.865944i	0.370036	+	0.0402438i	0.291248	−	0.956648i	$-0.405929\pi$
$463$	7.96223	+	0.865944i	0.370036	+	0.0402438i	0.0787879	+	0.996891i	$0.474895\pi$
$464$	9.93474	−	2.18680i	0.461209	−	0.101520i
$465$	−9.68142	+	34.8693i	−0.448965	+	1.61703i
$466$	−2.69761	+	1.62310i	−0.124965	+	0.0751887i
$467$	−6.99760	+	3.23743i	−0.323810	+	0.149811i	−0.575059	−	0.818112i	$-0.695021\pi$
$467$	−6.99760	+	3.23743i	−0.323810	+	0.149811i	0.251249	+	0.967923i	$0.419159\pi$
$468$	0.0587516	−	0.147456i	0.00271580	−	0.00681613i
$469$	−0.107118	+	1.97568i	−0.00494627	+	0.0912286i
$470$	−9.88353	−	14.5771i	−0.455893	−	0.672392i
$471$	1.88704			0.0869504
$472$	−7.00936	−	3.14147i	−0.322632	−	0.144598i
$473$	12.4519			0.572539
$474$	8.86848	+	13.0800i	0.407343	+	0.600786i
$475$	3.20363	−	59.0874i	0.146992	−	2.71112i
$476$	4.51514	−	11.3322i	0.206951	−	0.519408i
$477$	−2.24756	+	1.03983i	−0.102908	+	0.0476105i
$478$	−14.6827	+	8.83427i	−0.671570	+	0.404070i
$479$	−1.88141	+	6.77623i	−0.0859638	+	0.309614i	−0.994015	−	0.109246i	$-0.965156\pi$
$479$	−1.88141	+	6.77623i	−0.0859638	+	0.309614i	0.908051	+	0.418860i	$0.137570\pi$
$480$	4.11958	−	0.906789i	0.188032	−	0.0413891i
$481$	0.155350	+	0.0168954i	0.00708337	+	0.000770362i
$482$	0.660168	+	0.397210i	0.0300698	+	0.0180924i
$483$	18.9010	−	17.9040i	0.860026	−	0.814660i
$484$	−0.983814	−	0.455161i	−0.0447188	−	0.0206891i
$485$	−21.5343	+	2.34200i	−0.977823	+	0.106345i
$486$	0.947653	−	0.319302i	0.0429864	−	0.0144838i
$487$	1.94667	+	4.88578i	0.0882122	+	0.221396i	0.966464	−	0.256803i	$-0.0826691\pi$
$487$	1.94667	+	4.88578i	0.0882122	+	0.221396i	−0.878252	+	0.478199i	$0.841290\pi$
$488$	−6.51354	−	6.16995i	−0.294854	−	0.279301i
$489$	0.746182	+	2.68750i	0.0337435	+	0.121533i
$490$	−15.1024	−	28.4862i	−0.682259	−	1.28688i
$491$	−6.96842	+	5.29725i	−0.314480	+	0.239062i	−0.750492	−	0.660879i	$-0.770184\pi$
$491$	−6.96842	+	5.29725i	−0.314480	+	0.239062i	0.436012	+	0.899941i	$0.356390\pi$
$492$	0.163164	+	3.00937i	0.00735598	+	0.135673i
$493$	30.7301	+	10.3542i	1.38402	+	0.466329i
$494$	−0.717024	−	0.157829i	−0.0322604	−	0.00710106i
$495$	6.22186	−	11.7357i	0.279652	−	0.527480i
$496$	1.38794	+	8.46608i	0.0623205	+	0.380138i
$497$	25.6450	−	30.1917i	1.15034	−	1.35428i
$498$	−0.318820	−	0.375344i	−0.0142867	−	0.0168196i
$499$	−2.37916	+	14.5122i	−0.106506	+	0.649657i	0.878580	+	0.477595i	$0.158491\pi$
$499$	−2.37916	+	14.5122i	−0.106506	+	0.649657i	−0.985086	+	0.172062i	$0.944957\pi$
$500$	−26.1704	−	19.8942i	−1.17037	−	0.889695i
$501$	−3.18906	+	4.70351i	−0.142477	+	0.210137i
$502$	7.42523	−	10.9514i	0.331404	−	0.488785i
$503$	25.4105	+	19.3165i	1.13300	+	0.861282i	0.991686	−	0.128683i	$-0.0410750\pi$
$503$	25.4105	+	19.3165i	1.13300	+	0.861282i	0.141311	+	0.989965i	$0.454868\pi$
$504$	−0.619089	+	3.77628i	−0.0275764	+	0.168209i
$505$	44.4393	+	52.3180i	1.97752	+	2.32812i
$506$	−13.8695	+	16.3284i	−0.616573	+	0.725886i
$507$	−2.09909	−	12.8039i	−0.0932239	−	0.568640i
$508$	0.0626103	−	0.118096i	0.00277788	−	0.00523964i
$509$	39.8663	+	8.77524i	1.76704	+	0.388955i	0.975122	−	0.221669i	$-0.0711504\pi$
$509$	39.8663	+	8.77524i	1.76704	+	0.388955i	0.791920	+	0.610624i	$0.209081\pi$
$510$	12.7427	+	4.29351i	0.564256	+	0.190120i
$511$	0.513705	+	9.47474i	0.0227250	+	0.419138i
$512$	0.796093	−	0.605174i	0.0351827	−	0.0267452i
$513$	−2.16659	−	4.08662i	−0.0956572	−	0.180429i
$514$	−6.01148	−	21.6514i	−0.265155	−	0.955001i
$515$	8.51256	+	8.06353i	0.375108	+	0.355321i
$516$	−1.46363	−	3.67343i	−0.0644327	−	0.161714i
$517$	−12.4593	+	4.19804i	−0.547961	+	0.184629i
$518$	−3.74524	+	0.407319i	−0.164556	+	0.0178966i
$519$	−13.9401	−	6.44939i	−0.611904	−	0.283097i
$520$	−0.486091	+	0.460450i	−0.0213165	+	0.0201921i
$521$	−13.7423	−	8.26847i	−0.602061	−	0.362248i	0.181660	−	0.983361i	$-0.441853\pi$
$521$	−13.7423	−	8.26847i	−0.602061	−	0.362248i	−0.783721	+	0.621113i	$0.786681\pi$
$522$	−10.1129	−	1.09985i	−0.442631	−	0.0481390i
$523$	22.1820	−	4.88263i	0.969952	−	0.213503i	0.298385	−	0.954446i	$-0.403552\pi$
$523$	22.1820	−	4.88263i	0.969952	−	0.213503i	0.671568	+	0.740943i	$0.265621\pi$
$524$	−5.01752	+	18.0715i	−0.219191	+	0.789455i
$525$	41.9481	−	25.2393i	1.83076	−	1.10153i
$526$	−8.88079	+	4.10869i	−0.387221	+	0.179147i
$527$	−10.1226	+	25.4057i	−0.440945	+	1.10669i
$528$	0.170482	−	3.14435i	0.00741926	−	0.136840i
$529$	−13.0682	−	19.2742i	−0.568183	−	0.838007i
$530$	10.4461			0.453751
$531$	5.63937	+	5.21512i	0.244728	+	0.226317i
$532$	17.7001			0.767395
$533$	−0.268459	−	0.395947i	−0.0116282	−	0.0171504i
$534$	0.500305	−	9.22758i	0.0216503	−	0.399316i
$535$	−13.3505	+	33.5073i	−0.577193	+	1.44864i
$536$	−0.469261	+	0.217103i	−0.0202690	+	0.00937743i
$537$	5.86836	−	3.53088i	0.253238	−	0.152369i
$538$	0.213386	−	0.768546i	0.00919971	−	0.0331344i
$539$	−23.5066	+	5.17418i	−1.01250	+	0.222868i
$540$	−4.19348	−	0.456068i	−0.180458	−	0.0196260i
$541$	−6.51483	−	3.91984i	−0.280094	−	0.168527i	0.368574	−	0.929598i	$-0.379846\pi$
$541$	−6.51483	−	3.91984i	−0.280094	−	0.168527i	−0.648668	+	0.761071i	$0.724674\pi$
$542$	−15.7669	+	14.9352i	−0.677246	+	0.641522i
$543$	−14.7610	−	6.82918i	−0.633456	−	0.293068i
$544$	3.16906	−	0.344656i	0.135872	−	0.0147770i
$545$	−38.7946	+	13.0714i	−1.66178	+	0.559919i
$546$	−0.224824	−	0.564266i	−0.00962159	−	0.0241484i
$547$	6.16791	+	5.84256i	0.263721	+	0.249810i	0.808122	−	0.589016i	$-0.200484\pi$
$547$	6.16791	+	5.84256i	0.263721	+	0.249810i	−0.544401	+	0.838825i	$0.683243\pi$
$548$	4.54216	+	16.3594i	0.194031	+	0.698838i
$549$	4.20250	+	7.92676i	0.179358	+	0.338306i
$550$	−32.0710	+	24.3798i	−1.36751	+	1.03956i
$551$	2.54737	+	46.9834i	0.108522	+	2.00156i
$552$	6.44730	+	2.17235i	0.274415	+	0.0924612i
$553$	59.0596	+	13.0000i	2.51147	+	0.552816i
$554$	9.84876	−	18.5767i	0.418434	−	0.789250i
$555$	−0.671842	−	4.09805i	−0.0285181	−	0.173953i
$556$	15.1163	−	17.7963i	0.641074	−	0.754731i
$557$	−16.4104	−	19.3198i	−0.695330	−	0.818605i	0.295268	−	0.955415i	$-0.404591\pi$
$557$	−16.4104	−	19.3198i	−0.695330	−	0.818605i	−0.990597	+	0.136809i	$0.956315\pi$
$558$	1.38794	−	8.46608i	0.0587564	−	0.358398i
$559$	0.499675	+	0.379843i	0.0211340	+	0.0160656i
$560$	9.05854	−	13.3604i	0.382793	−	0.564578i
$561$	5.63327	−	8.30844i	0.237837	−	0.350783i
$562$	20.8477	+	15.8480i	0.879408	+	0.668509i
$563$	1.65399	−	10.0889i	0.0697073	−	0.425195i	−0.928800	−	0.370581i	$-0.879159\pi$
$563$	1.65399	−	10.0889i	0.0697073	−	0.425195i	0.998508	−	0.0546147i	$-0.0173931\pi$
$564$	2.70296	+	3.18218i	0.113815	+	0.133994i
$565$	17.4374	−	20.5289i	0.733596	−	0.863656i
$566$	−3.09205	−	18.8607i	−0.129969	−	0.792774i
$567$	1.79245	−	3.38093i	0.0752760	−	0.141986i
$568$	10.1098	+	2.22534i	0.424198	+	0.0933730i
$569$	−18.0913	−	6.09568i	−0.758428	−	0.255544i	−0.0865920	−	0.996244i	$-0.527598\pi$
$569$	−18.0913	−	6.09568i	−0.758428	−	0.255544i	−0.671836	+	0.740700i	$0.734494\pi$
$570$	1.05630	+	19.4824i	0.0442437	+	0.816027i
$571$	−27.0472	+	20.5607i	−1.13189	+	0.860440i	−0.991558	−	0.129665i	$-0.958610\pi$
$571$	−27.0472	+	20.5607i	−1.13189	+	0.860440i	−0.140331	+	0.990105i	$0.544817\pi$
$572$	0.234126	+	0.441608i	0.00978929	+	0.0184646i
$573$	−6.14623	−	22.1367i	−0.256762	−	0.924774i
$574$	8.37280	+	7.93114i	0.349474	+	0.331039i
$575$	−32.2161	−	80.8563i	−1.34350	−	3.37194i
$576$	−0.947653	+	0.319302i	−0.0394855	+	0.0133042i
$577$	26.4154	−	2.87284i	1.09969	−	0.119598i	0.459766	−	0.888040i	$-0.347933\pi$
$577$	26.4154	−	2.87284i	1.09969	−	0.119598i	0.639919	+	0.768442i	$0.278968\pi$
$578$	−6.20622	−	2.87130i	−0.258145	−	0.119431i
$579$	−7.98342	+	7.56230i	−0.331780	+	0.314278i
$580$	36.7677	+	22.1224i	1.52670	+	0.918582i
$581$	−1.87349	−	0.203754i	−0.0777255	−	0.00845316i
$582$	5.01514	−	1.10392i	0.207884	−	0.0457587i
$583$	2.08625	−	7.51398i	0.0864035	−	0.311197i
$584$	−2.12466	+	1.27837i	−0.0879191	+	0.0528992i
$585$	0.607668	−	0.281137i	0.0251240	−	0.0116236i
$586$	5.51026	−	13.8297i	0.227627	−	0.571300i
$587$	−0.860856	+	15.8775i	−0.0355313	+	0.655337i	0.925475	+	0.378809i	$0.123666\pi$
$587$	−0.860856	+	15.8775i	−0.0355313	+	0.655337i	−0.961006	+	0.276527i	$0.910816\pi$
$588$	4.28946	+	6.32648i	0.176894	+	0.260900i
$589$	−39.6820			−1.63507
$590$	−12.3525	−	29.9536i	−0.508545	−	1.23317i
$591$	4.13865			0.170241
$592$	−0.552481	−	0.814848i	−0.0227068	−	0.0334900i
$593$	−0.290773	+	5.36299i	−0.0119406	+	0.220232i	0.986473	+	0.163924i	$0.0524153\pi$
$593$	−0.290773	+	5.36299i	−0.0119406	+	0.220232i	−0.998413	+	0.0563071i	$0.982067\pi$
$594$	−1.16555	+	2.92532i	−0.0478232	+	0.120027i
$595$	46.7001	−	21.6058i	1.91452	−	0.885750i
$596$	1.40766	−	0.846960i	0.0576599	−	0.0346928i
$597$	2.23631	−	8.05446i	0.0915261	−	0.329647i
$598$	−1.05465	+	0.232147i	−0.0431280	+	0.00949320i
$599$	0.888213	+	0.0965990i	0.0362914	+	0.00394693i	0.126247	−	0.991999i	$-0.459707\pi$
$599$	0.888213	+	0.0965990i	0.0362914	+	0.00394693i	−0.0899553	+	0.995946i	$0.528672\pi$
$600$	10.9620	+	6.59561i	0.447521	+	0.269264i
$601$	−34.7123	+	32.8812i	−1.41594	+	1.34125i	−0.555686	+	0.831392i	$0.687544\pi$
$601$	−34.7123	+	32.8812i	−1.41594	+	1.34125i	−0.860257	+	0.509860i	$0.829697\pi$
$602$	−13.7332	−	6.35367i	−0.559725	−	0.258956i
$603$	0.514018	−	0.0559028i	0.0209324	−	0.00227654i
$604$	−8.96739	+	3.02147i	−0.364878	+	0.122942i
$605$	−1.69247	−	4.24779i	−0.0688088	−	0.172697i
$606$	−11.8143	−	11.1911i	−0.479925	−	0.454609i
$607$	−1.21891	−	4.39011i	−0.0494740	−	0.178189i	0.934685	−	0.355477i	$-0.115682\pi$
$607$	−1.21891	−	4.39011i	−0.0494740	−	0.178189i	−0.984159	+	0.177288i	$0.943268\pi$
$608$	2.16659	+	4.08662i	0.0878668	+	0.165734i
$609$	−30.9897	+	23.5578i	−1.25577	+	0.954609i
$610$	−2.04890	−	37.7897i	−0.0829575	−	1.53006i
$611$	−0.628033	−	0.211609i	−0.0254075	−	0.00856078i
$612$	−3.11322	−	0.685272i	−0.125845	−	0.0277005i
$613$	6.08705	−	11.4814i	0.245854	−	0.463729i	−0.729618	−	0.683855i	$-0.760302\pi$
$613$	6.08705	−	11.4814i	0.245854	−	0.463729i	0.975471	+	0.220126i	$0.0706469\pi$
$614$	−1.50507	−	9.18050i	−0.0607395	−	0.370495i
$615$	−8.23009	+	9.68921i	−0.331869	+	0.390707i
$616$	−7.80108	−	9.18414i	−0.314315	−	0.370040i
$617$	−7.45062	+	45.4467i	−0.299951	+	1.82962i	0.220095	+	0.975479i	$0.429363\pi$
$617$	−7.45062	+	45.4467i	−0.299951	+	1.82962i	−0.520045	+	0.854139i	$0.674085\pi$
$618$	−2.21290	−	1.68221i	−0.0890161	−	0.0676683i
$619$	14.2995	−	21.0902i	0.574745	−	0.847686i	−0.423561	−	0.905868i	$-0.639220\pi$
$619$	14.2995	−	21.0902i	0.574745	−	0.847686i	0.998306	+	0.0581819i	$0.0185303\pi$
$620$	−20.3085	+	29.9527i	−0.815607	+	1.20293i
$621$	−5.41617	−	4.11726i	−0.217343	−	0.165220i
$622$	0.553294	−	3.37494i	0.0221851	−	0.135323i
$623$	−22.8935	−	26.9523i	−0.917208	−	1.07982i
$624$	0.102759	−	0.120977i	0.00411365	−	0.00484296i
$625$	−12.0853	−	73.7168i	−0.483410	−	2.94867i
$626$	15.4861	−	29.2098i	0.618948	−	1.16746i
$627$	14.2248	+	3.13111i	0.568083	+	0.125045i
$628$	1.78826	+	0.602536i	0.0713595	+	0.0240438i
$629$	−0.169904	−	3.13369i	−0.00677451	−	0.124948i
$630$	−12.8503	+	9.76857i	−0.511970	+	0.389189i
$631$	6.94836	+	13.1060i	0.276610	+	0.521742i	0.982426	−	0.186654i	$-0.0597642\pi$
$631$	6.94836	+	13.1060i	0.276610	+	0.521742i	−0.705816	+	0.708395i	$0.749419\pi$
$632$	4.22777	+	15.2270i	0.168172	+	0.605700i
$633$	−3.23709	−	3.06634i	−0.128663	−	0.121876i
$634$	2.17031	+	5.44707i	0.0861941	+	0.216331i
$635$	0.534316	−	0.180032i	0.0212037	−	0.00714435i
$636$	−2.46192	+	0.267750i	−0.0976216	+	0.0106170i
$637$	−1.10112	−	0.509431i	−0.0436279	−	0.0201844i
$638$	23.2559	−	22.0291i	0.920709	−	0.872142i
$639$	−8.87003	−	5.33692i	−0.350893	−	0.211125i
$640$	4.19348	+	0.456068i	0.165762	+	0.0180277i
$641$	−20.4074	+	4.49200i	−0.806043	+	0.177423i	−0.598834	−	0.800873i	$-0.704369\pi$
$641$	−20.4074	+	4.49200i	−0.806043	+	0.177423i	−0.207209	+	0.978297i	$0.566438\pi$
$642$	2.28758	−	8.23912i	0.0902836	−	0.325172i
$643$	6.76352	−	4.06948i	0.266727	−	0.160485i	−0.375907	−	0.926657i	$-0.622669\pi$
$643$	6.76352	−	4.06948i	0.266727	−	0.160485i	0.642635	+	0.766173i	$0.277841\pi$
$644$	23.6284	−	10.9317i	0.931089	−	0.430768i
$645$	6.17389	−	15.4953i	0.243097	−	0.610126i
$646$	−0.798262	+	14.7231i	−0.0314072	+	0.579272i
$647$	−22.3554	−	32.9718i	−0.878882	−	1.29625i	−0.954223	−	0.299096i	$-0.903315\pi$
$647$	−22.3554	−	32.9718i	−0.878882	−	1.29625i	0.0753410	−	0.997158i	$-0.475995\pi$
$648$	1.00000			0.0392837
$649$	−24.0128	+	2.90308i	−0.942586	+	0.113956i
$650$	−2.03066			−0.0796490
$651$	−18.4235	−	27.1727i	−0.722075	−	1.06498i
$652$	−0.151003	+	2.78508i	−0.00591372	+	0.109072i
$653$	3.43563	−	8.62279i	0.134447	−	0.337436i	−0.846304	−	0.532700i	$-0.821177\pi$
$653$	3.43563	−	8.62279i	0.134447	−	0.337436i	0.980751	+	0.195265i	$0.0625565\pi$
$654$	8.80800	−	4.07501i	0.344420	−	0.159346i
$655$	−67.7883	+	40.7869i	−2.64871	+	1.59368i
$656$	−0.806275	+	2.90394i	−0.0314798	+	0.113380i
$657$	2.42163	−	0.533040i	0.0944767	−	0.0207959i
$658$	15.8835	+	1.72744i	0.619204	+	0.0673425i
$659$	16.4082	+	9.87247i	0.639172	+	0.384577i	0.797938	−	0.602739i	$-0.205924\pi$
$659$	16.4082	+	9.87247i	0.639172	+	0.384577i	−0.158767	+	0.987316i	$0.550752\pi$
$660$	9.64339	−	9.13470i	0.375368	−	0.355568i
$661$	−6.32086	−	2.92434i	−0.245853	−	0.113744i	0.293093	−	0.956084i	$-0.405315\pi$
$661$	−6.32086	−	2.92434i	−0.245853	−	0.113744i	−0.538946	+	0.842340i	$0.681177\pi$
$662$	4.71983	−	0.513312i	0.183441	−	0.0199504i
$663$	0.479501	−	0.161563i	0.0186223	−	0.00627458i
$664$	−0.182283	−	0.457495i	−0.00707394	−	0.0177543i
$665$	54.2046	+	51.3454i	2.10197	+	1.99109i
$666$	0.263378	+	0.948601i	0.0102057	+	0.0367575i
$667$	32.4178	+	61.1464i	1.25522	+	2.36760i
$668$	−4.52396	+	3.43902i	−0.175037	+	0.133060i
$669$	−0.0497050	−	0.916755i	−0.00192171	−	0.0354438i
$670$	−2.06685	−	0.696402i	−0.0798493	−	0.0269044i
$671$	−27.5916	−	6.07338i	−1.06516	−	0.234460i
$672$	−1.79245	+	3.38093i	−0.0691454	+	0.130422i
$673$	−4.70967	−	28.7277i	−0.181545	−	1.10737i	−0.907631	−	0.419769i	$-0.862111\pi$
$673$	−4.70967	−	28.7277i	−0.181545	−	1.10737i	0.726086	−	0.687604i	$-0.241337\pi$
$674$	−16.6339	+	19.5830i	−0.640716	+	0.754309i
$675$	−8.28217	−	9.75052i	−0.318781	−	0.375298i
$676$	2.09909	−	12.8039i	0.0807342	−	0.492457i
$677$	−19.7068	−	14.9807i	−0.757392	−	0.575755i	0.153622	−	0.988130i	$-0.450906\pi$
$677$	−19.7068	−	14.9807i	−0.757392	−	0.575755i	−0.911014	+	0.412375i	$0.864699\pi$
$678$	−3.58342	+	5.28515i	−0.137620	+	0.202975i
$679$	11.0278	−	16.2647i	0.423207	−	0.624184i
$680$	10.7047	+	8.13752i	0.410508	+	0.312060i
$681$	−3.21005	+	19.5804i	−0.123009	+	0.750323i
$682$	17.4893	+	20.5900i	0.669701	+	0.788434i
$683$	−9.38596	+	11.0500i	−0.359144	+	0.422817i	−0.911827	−	0.410575i	$-0.865328\pi$
$683$	−9.38596	+	11.0500i	−0.359144	+	0.422817i	0.552683	+	0.833391i	$0.313604\pi$
$684$	−0.748311	−	4.56449i	−0.0286124	−	0.174528i
$685$	−33.5463	+	63.2750i	−1.28174	+	2.41762i
$686$	2.40508	+	0.529398i	0.0918263	+	0.0202125i
$687$	4.55290	+	1.53405i	0.173704	+	0.0585277i
$688$	−0.214080	−	3.94848i	−0.00816173	−	0.150534i
$689$	0.312930	−	0.237883i	0.0119217	−	0.00906264i
$690$	13.4425	+	25.3553i	0.511748	+	0.965259i
$691$	3.12850	+	11.2678i	0.119014	+	0.428648i	0.998918	−	0.0465022i	$-0.0148074\pi$
$691$	3.12850	+	11.2678i	0.119014	+	0.428648i	−0.879905	+	0.475150i	$0.842394\pi$
$692$	−11.1511	−	10.5629i	−0.423901	−	0.401541i
$693$	4.46021	+	11.1943i	0.169429	+	0.425236i
$694$	22.4962	−	7.57984i	0.853943	−	0.287727i
$695$	97.9166	−	10.6491i	3.71419	−	0.403942i
$696$	−9.23237	−	4.27135i	−0.349952	−	0.161905i
$697$	−6.97480	+	6.60688i	−0.264189	+	0.250254i
$698$	−4.22026	−	2.53925i	−0.159739	−	0.0961120i
$699$	3.12981	+	0.340387i	0.118380	+	0.0128746i
$700$	47.8112	−	10.5240i	1.80709	−	0.397771i
$701$	−5.39057	+	19.4151i	−0.203599	+	0.733298i	0.789266	+	0.614052i	$0.210461\pi$
$701$	−5.39057	+	19.4151i	−0.203599	+	0.733298i	−0.992865	+	0.119246i	$0.961952\pi$
$702$	−0.136008	+	0.0818333i	−0.00513329	+	0.00308860i
$703$	4.13279	−	1.91203i	0.155871	−	0.0721137i
$704$	1.16555	−	2.92532i	0.0439284	−	0.110252i
$705$	−0.953485	+	17.5860i	−0.0359103	+	0.662327i
$706$	−13.5644	−	20.0060i	−0.510504	−	0.752937i
$707$	−62.2729			−2.34201
$708$	3.67897	+	6.74279i	0.138264	+	0.253409i
$709$	−6.54222			−0.245698			−0.122849	−	0.992425i	$-0.539203\pi$
$709$	−6.54222			−0.245698			−0.122849	+	0.992425i	$0.539203\pi$
$710$	24.5048	+	36.1419i	0.919650	+	1.35638i
$711$	0.855561	−	15.7799i	0.0320860	−	0.591792i
$712$	3.42050	−	8.58480i	0.128189	−	0.321729i
$713$	−52.9728	+	24.5078i	−1.98385	+	0.917825i
$714$	−10.4524	+	6.28900i	−0.391171	+	0.235360i
$715$	−0.564055	+	2.03154i	−0.0210945	+	0.0759754i
$716$	6.68859	−	1.47227i	0.249964	−	0.0550213i
$717$	17.0350	+	1.85267i	0.636185	+	0.0691893i
$718$	−13.3975	−	8.06102i	−0.499991	−	0.300834i
$719$	36.0457	−	34.1443i	1.34428	−	1.27337i	0.412210	−	0.911089i	$-0.364757\pi$
$719$	36.0457	−	34.1443i	1.34428	−	1.27337i	0.932069	−	0.362280i	$-0.118002\pi$
$720$	−3.82834	−	1.77118i	−0.142674	−	0.0660079i
$721$	−10.5747	+	1.15007i	−0.393823	+	0.0428308i
$722$	−2.26922	+	0.764590i	−0.0844517	+	0.0284551i
$723$	−0.285174	−	0.715733i	−0.0106057	−	0.0266184i
$724$	−11.8078	−	11.1849i	−0.438832	−	0.415684i
$725$	34.8162	+	125.397i	1.29304	+	4.65711i
$726$	0.507756	+	0.957730i	0.0188446	+	0.0355447i
$727$	41.5818	−	31.6097i	1.54218	−	1.17234i	0.620621	−	0.784110i	$-0.286880\pi$
$727$	41.5818	−	31.6097i	1.54218	−	1.17234i	0.921563	−	0.388228i	$-0.126913\pi$
$728$	−0.0328843	−	0.606516i	−0.00121877	−	0.0224790i
$729$	−0.947653	−	0.319302i	−0.0350983	−	0.0118260i
$730$	−10.2149	−	2.24847i	−0.378071	−	0.0832197i
$731$	5.90441	−	11.1369i	0.218382	−	0.411913i
$732$	1.45149	+	8.85369i	0.0536485	+	0.327242i
$733$	−20.6431	+	24.3029i	−0.762470	+	0.897649i	−0.997228	−	0.0744047i	$-0.976294\pi$
$733$	−20.6431	+	24.3029i	−0.762470	+	0.897649i	0.234758	+	0.972054i	$0.424570\pi$
$734$	−8.03572	−	9.46038i	−0.296604	−	0.349189i
$735$	−5.21618	+	31.8173i	−0.192402	+	1.17360i
$736$	5.41617	+	4.11726i	0.199643	+	0.151764i
$737$	−0.913708	+	1.34762i	−0.0336569	+	0.0496402i
$738$	1.69130	−	2.49448i	0.0622577	−	0.0918232i
$739$	24.5437	+	18.6576i	0.902853	+	0.686331i	0.949898	−	0.312561i	$-0.101187\pi$
$739$	24.5437	+	18.6576i	0.902853	+	0.686331i	−0.0470441	+	0.998893i	$0.514980\pi$
$740$	0.671842	−	4.09805i	0.0246974	−	0.150647i
$741$	0.475304	+	0.559571i	0.0174607	+	0.0205564i
$742$	−6.13500	+	7.22268i	−0.225223	+	0.265153i
$743$	0.508881	+	3.10403i	0.0186690	+	0.113876i	0.994517	−	0.104574i	$-0.0333481\pi$
$743$	0.508881	+	3.10403i	0.0186690	+	0.113876i	−0.975848	+	0.218450i	$0.929900\pi$
$744$	4.01852	−	7.57974i	0.147326	−	0.277887i
$745$	6.76772	+	1.48969i	0.247950	+	0.0545779i
$746$	−11.9730	−	4.03416i	−0.438362	−	0.147701i
$747$	0.0266619	+	0.491750i	0.000975508	+	0.0179922i
$748$	7.99128	−	6.07481i	0.292190	−	0.222117i
$749$	−15.3269	−	28.9096i	−0.560033	−	1.05633i
$750$	8.79459	+	31.6753i	0.321133	+	1.15662i
$751$	−12.1924	−	11.5492i	−0.444906	−	0.421437i	0.432168	−	0.901793i	$-0.357749\pi$
$751$	−12.1924	−	11.5492i	−0.444906	−	0.421437i	−0.877074	+	0.480356i	$0.840507\pi$
$752$	1.54540	+	3.87866i	0.0563549	+	0.141440i
$753$	−12.5387	+	4.22477i	−0.456935	+	0.153959i
$754$	1.60522	−	0.174578i	0.0584585	−	0.00635775i
$755$	−36.2266	−	16.7602i	−1.31842	−	0.609966i
$756$	2.77816	−	2.63161i	0.101041	−	0.0957108i
$757$	−18.5831	−	11.1811i	−0.675413	−	0.406383i	0.136117	−	0.990693i	$-0.456538\pi$
$757$	−18.5831	−	11.1811i	−0.675413	−	0.406383i	−0.811530	+	0.584310i	$0.801365\pi$
$758$	7.79408	+	0.847658i	0.283094	+	0.0307883i
$759$	20.9229	−	4.60548i	0.759454	−	0.167168i
$760$	−5.21974	+	18.7998i	−0.189340	+	0.681941i
$761$	6.58993	−	3.96503i	0.238885	−	0.143732i	−0.391078	−	0.920358i	$-0.627898\pi$
$761$	6.58993	−	3.96503i	0.238885	−	0.143732i	0.629963	+	0.776625i	$0.283070\pi$
$762$	−0.121312	+	0.0561249i	−0.00439467	+	0.00203319i
$763$	13.7462	−	34.5003i	0.497645	−	1.24899i
$764$	1.24379	−	22.9404i	0.0449989	−	0.829955i
$765$	−7.54605	−	11.1296i	−0.272828	−	0.402391i
$766$	29.4612			1.06448
$767$	−1.05215	−	0.616011i	−0.0379911	−	0.0222429i
$768$	−1.00000			−0.0360844
$769$	15.1954	+	22.4115i	0.547959	+	0.808180i	0.996323	−	0.0856714i	$-0.0273035\pi$
$769$	15.1954	+	22.4115i	0.547959	+	0.808180i	−0.448364	+	0.893851i	$0.647993\pi$
$770$	2.75187	−	50.7553i	0.0991706	−	1.82909i
$771$	−8.31716	+	20.8745i	−0.299535	+	0.751777i
$772$	−9.98017	+	4.61732i	−0.359194	+	0.166181i
$773$	−32.1300	+	19.3320i	−1.15564	+	0.695323i	−0.958511	−	0.285056i	$-0.907988\pi$
$773$	−32.1300	+	19.3320i	−1.15564	+	0.695323i	−0.197124	+	0.980378i	$0.563160\pi$
$774$	−1.05788	+	3.81014i	−0.0380248	+	0.136953i
$775$	−107.189	+	23.5940i	−3.85033	+	0.847521i
$776$	5.10509	+	0.555212i	0.183262	+	0.0199310i
$777$	3.22806	+	1.94226i	0.115806	+	0.0696781i
$778$	−3.58436	+	3.39528i	−0.128505	+	0.121727i
$779$	−12.6517	−	5.85329i	−0.453293	−	0.209716i
$780$	0.665626	−	0.0723912i	0.0238332	−	0.00259202i
$781$	30.8912	−	10.4084i	1.10537	−	0.372443i
$782$	8.02743	+	20.1473i	0.287060	+	0.720467i
$783$	7.38524	+	6.99567i	0.263927	+	0.250005i
$784$	2.04487	+	7.36494i	0.0730309	+	0.263034i
$785$	3.72850	+	7.03270i	0.133076	+	0.251008i
$786$	14.9308	−	11.3501i	0.532564	−	0.404844i
$787$	−0.997022	−	18.3890i	−0.0355400	−	0.655497i	−0.960983	−	0.276609i	$-0.910789\pi$
$787$	−0.997022	−	18.3890i	−0.0355400	−	0.655497i	0.925443	−	0.378888i	$-0.123693\pi$
$788$	3.92200	+	1.32148i	0.139716	+	0.0470756i
$789$	9.55641	+	2.10353i	0.340217	+	0.0748875i
$790$	−31.2244	+	58.8954i	−1.11091	+	2.09541i
$791$	3.95315	+	24.1131i	0.140558	+	0.857365i
$792$	−2.03860	+	2.40002i	−0.0724384	+	0.0852811i
$793$	−0.921941	−	1.08539i	−0.0327391	−	0.0385434i
$794$	−2.14342	+	13.0743i	−0.0760672	+	0.463990i
$795$	−8.31609	−	6.32173i	−0.294941	−	0.224208i
$796$	4.69105	−	6.91878i	0.166270	−	0.245230i
$797$	15.9052	−	23.4585i	0.563392	−	0.830941i	−0.434162	−	0.900835i	$-0.642956\pi$
$797$	15.9052	−	23.4585i	0.563392	−	0.830941i	0.997554	+	0.0698936i	$0.0222660\pi$
$798$	−14.0909	−	10.7116i	−0.498812	−	0.379187i
$799$	−2.15324	+	13.1342i	−0.0761760	+	0.464653i
$800$	8.28217	+	9.75052i	0.292819	+	0.344733i
$801$	−5.98258	+	7.04324i	−0.211384	+	0.248861i
$802$	−4.20043	−	25.6215i	−0.148322	−	0.904726i
$803$	−3.65742	+	6.89862i	−0.129067	+	0.243447i
$804$	0.504961	+	0.111150i	0.0178086	+	0.00391997i
$805$	104.071	+	35.0655i	3.66801	+	1.23590i
$806$	0.0737238	+	1.35975i	0.00259681	+	0.0478953i
$807$	−0.634979	+	0.482699i	−0.0223523	+	0.0169918i
$808$	−7.62256	−	14.3777i	−0.268161	−	0.505804i
$809$	8.03050	+	28.9233i	0.282337	+	1.01689i	0.959651	+	0.281193i	$0.0907302\pi$
$809$	8.03050	+	28.9233i	0.282337	+	1.01689i	−0.677314	+	0.735694i	$0.736856\pi$
$810$	3.06240	+	2.90086i	0.107602	+	0.101926i
$811$	−2.62065	−	6.57734i	−0.0920235	−	0.230962i	0.875759	−	0.482748i	$-0.160361\pi$
$811$	−2.62065	−	6.57734i	−0.0920235	−	0.230962i	−0.967783	+	0.251786i	$0.918982\pi$
$812$	−36.8895	+	12.4295i	−1.29457	+	0.436191i
$813$	21.5903	−	2.34809i	0.757205	−	0.0823510i
$814$	−2.81359	−	1.30170i	−0.0986162	−	0.0456247i
$815$	−8.54154	+	8.09098i	−0.299197	+	0.283415i
$816$	−2.73145	−	1.64346i	−0.0956198	−	0.0575325i
$817$	18.1830	+	1.97752i	0.636143	+	0.0691847i
$818$	17.1231	−	3.76907i	0.598694	−	0.131783i
$819$	−0.162498	+	0.585266i	−0.00567815	+	0.0204509i
$820$	−10.8931	+	6.55413i	−0.380402	+	0.228880i
$821$	3.43975	−	1.59140i	0.120048	−	0.0555402i	−0.358946	−	0.933358i	$-0.616864\pi$
$821$	3.43975	−	1.59140i	0.120048	−	0.0555402i	0.478994	+	0.877818i	$0.341002\pi$
$822$	6.28429	−	15.7724i	0.219190	−	0.550125i
$823$	2.06979	−	38.1750i	0.0721483	−	1.33070i	−0.708493	−	0.705718i	$-0.750625\pi$
$823$	2.06979	−	38.1750i	0.0721483	−	1.33070i	0.780641	−	0.624979i	$-0.214893\pi$
$824$	−1.55993	−	2.30073i	−0.0543429	−	0.0801498i
$825$	40.2855			1.40256
$826$	27.9652	+	9.05091i	0.973032	+	0.314921i
$827$	−2.63341			−0.0915727			−0.0457863	−	0.998951i	$-0.514579\pi$
$827$	−2.63341			−0.0915727			−0.0457863	+	0.998951i	$0.514579\pi$
$828$	−3.81800	−	5.63113i	−0.132685	−	0.195695i
$829$	−0.258688	+	4.77121i	−0.00898459	+	0.165711i	0.990598	+	0.136808i	$0.0436843\pi$
$829$	−0.258688	+	4.77121i	−0.00898459	+	0.165711i	−0.999582	+	0.0289033i	$0.990799\pi$
$830$	0.768906	−	1.92981i	0.0266891	−	0.0669846i
$831$	−19.0827	+	8.82859i	−0.661971	+	0.306260i
$832$	0.136008	−	0.0818333i	0.00471523	−	0.00283706i
$833$	−6.51852	+	23.4776i	−0.225853	+	0.813450i
$834$	−22.8038	+	5.01951i	−0.789633	+	0.173811i
$835$	−23.8303	−	2.59170i	−0.824680	−	0.0896894i
$836$	12.4804	+	7.50921i	0.431644	+	0.259711i
$837$	−6.22839	+	5.89984i	−0.215285	+	0.203928i
$838$	−10.0709	−	4.65930i	−0.347894	−	0.160953i
$839$	−20.9637	+	2.27994i	−0.723747	+	0.0787123i	−0.462575	−	0.886580i	$-0.653075\pi$
$839$	−20.9637	+	2.27994i	−0.723747	+	0.0787123i	−0.261172	+	0.965292i	$0.584109\pi$
$840$	−15.2968	+	5.15409i	−0.527789	+	0.177833i
$841$	−27.5683	−	69.1912i	−0.950631	−	2.38590i
$842$	−23.5016	−	22.2619i	−0.809920	−	0.767197i
$843$	−7.00591	−	25.2330i	−0.241296	−	0.869071i
$844$	−2.08855	−	3.93943i	−0.0718910	−	0.135601i
$845$	43.5705	−	33.1214i	1.49887	−	1.13941i
$846$	−0.226041	−	4.16907i	−0.00777144	−	0.143336i
$847$	3.93100	+	1.32451i	0.135071	+	0.0455106i
$848$	−2.41854	−	0.532361i	−0.0830531	−	0.0182814i
$849$	−8.95244	+	16.8861i	−0.307247	+	0.579529i
$850$	6.59774	+	40.2444i	0.226301	+	1.38037i
$851$	4.33612	−	5.10487i	0.148640	−	0.174993i
$852$	−6.70163	−	7.88976i	−0.229594	−	0.270299i
$853$	−4.39057	+	26.7813i	−0.150330	+	0.916975i	0.798686	+	0.601748i	$0.205529\pi$
$853$	−4.39057	+	26.7813i	−0.150330	+	0.916975i	−0.949016	+	0.315227i	$0.897919\pi$
$854$	27.3319	+	20.7772i	0.935279	+	0.710981i
$855$	10.9493	−	16.1490i	0.374459	−	0.552285i
$856$	4.79860	−	7.07740i	0.164013	−	0.241900i
$857$	10.6129	+	8.06769i	0.362529	+	0.275587i	0.770542	−	0.637389i	$-0.219985\pi$
$857$	10.6129	+	8.06769i	0.362529	+	0.275587i	−0.408014	+	0.912976i	$0.633779\pi$
$858$	0.0808639	−	0.493248i	0.00276065	−	0.0168392i
$859$	−22.2567	−	26.2026i	−0.759388	−	0.894020i	0.237617	−	0.971359i	$-0.423634\pi$
$859$	−22.2567	−	26.2026i	−0.759388	−	0.894020i	−0.997005	+	0.0773385i	$0.975358\pi$
$860$	10.7984	−	12.7128i	0.368221	−	0.433504i
$861$	−1.86581	−	11.3809i	−0.0635866	−	0.387861i
$862$	−5.50679	+	10.3869i	−0.187562	+	0.353779i
$863$	39.6243	+	8.72197i	1.34883	+	0.296899i	0.829897	−	0.557917i	$-0.188399\pi$
$863$	39.6243	+	8.72197i	1.34883	+	0.296899i	0.518930	+	0.854817i	$0.326330\pi$
$864$	0.947653	+	0.319302i	0.0322398	+	0.0108629i
$865$	−3.50769	−	64.6955i	−0.119265	−	2.19971i
$866$	−19.0348	+	14.4699i	−0.646828	+	0.491706i
$867$	3.20309	+	6.04167i	0.108783	+	0.205186i
$868$	−8.78283	−	31.6329i	−0.298109	−	1.07369i
$869$	36.1280	+	34.2222i	1.22556	+	1.16091i
$870$	−15.8826	−	39.8624i	−0.538471	−	1.35146i
$871$	−0.0777745	+	0.0262053i	−0.00263529	+	0.000887932i
$872$	9.64809	−	1.04929i	0.326725	−	0.0355335i
$873$	−4.66058	−	2.15621i	−0.157737	−	0.0729767i
$874$	−22.8462	+	21.6411i	−0.772784	+	0.732020i
$875$	107.790	+	64.8549i	3.64396	+	2.19250i
$876$	2.46506	+	0.268092i	0.0832868	+	0.00905798i
$877$	−14.0182	+	3.08564i	−0.473361	+	0.104195i	−0.445243	−	0.895410i	$-0.646883\pi$
$877$	−14.0182	+	3.08564i	−0.473361	+	0.104195i	−0.0281186	+	0.999605i	$0.508952\pi$
$878$	−3.22104	+	11.6011i	−0.108705	+	0.391519i
$879$	−12.7561	+	7.67506i	−0.430251	+	0.258874i
$880$	12.0553	−	5.57738i	0.406385	−	0.188013i
$881$	−18.3837	+	46.1396i	−0.619362	+	1.55448i	0.199135	+	0.979972i	$0.436187\pi$
$881$	−18.3837	+	46.1396i	−0.619362	+	1.55448i	−0.818497	+	0.574510i	$0.805193\pi$
$882$	0.413813	−	7.63234i	0.0139338	−	0.256994i
$883$	−12.8951	−	19.0189i	−0.433955	−	0.640036i	0.546342	−	0.837562i	$-0.316020\pi$
$883$	−12.8951	−	19.0189i	−0.433955	−	0.640036i	−0.980298	+	0.197526i	$0.936709\pi$
$884$	0.505988			0.0170182
$885$	−8.29338	+	31.3213i	−0.278779	+	1.05285i
$886$	−6.37107			−0.214040
$887$	−17.3336	−	25.5651i	−0.582005	−	0.858393i	0.416712	−	0.909039i	$-0.363182\pi$
$887$	−17.3336	−	25.5651i	−0.582005	−	0.858393i	−0.998717	+	0.0506455i	$0.983872\pi$
$888$	−0.0532990	+	0.983042i	−0.00178860	+	0.0329887i
$889$	−0.189325	+	0.475170i	−0.00634976	+	0.0159367i
$890$	35.3782	−	16.3677i	1.18588	−	0.548646i
$891$	2.69822	−	1.62346i	0.0903936	−	0.0543880i
$892$	0.245618	−	0.884637i	0.00822390	−	0.0296198i
$893$	−18.8606	+	4.15152i	−0.631145	+	0.138925i
$894$	−1.63318	−	0.177620i	−0.0546219	−	0.00594049i
$895$	24.7539	+	14.8940i	0.827433	+	0.497850i
$896$	−2.77816	+	2.63161i	−0.0928118	+	0.0879160i
$897$	0.980093	+	0.453439i	0.0327243	+	0.0151399i
$898$	−39.8443	+	4.33333i	−1.32962	+	0.144605i
$899$	82.7031	−	27.8659i	2.75830	−	0.929380i
$900$	−4.73527	−	11.8846i	−0.157842	−	0.396154i
$901$	−5.73120	−	5.42889i	−0.190934	−	0.180862i
$902$	2.53894	+	9.14442i	0.0845373	+	0.304476i
$903$	7.08786	+	13.3691i	0.235869	+	0.444896i
$904$	−5.08339	+	3.86430i	−0.169071	+	0.128525i
$905$	−3.71425	−	68.5053i	−0.123466	−	2.27719i
$906$	8.96739	+	3.02147i	0.297922	+	0.100382i
$907$	17.4859	+	3.84895i	0.580611	+	0.127802i	0.495559	−	0.868574i	$-0.334963\pi$
$907$	17.4859	+	3.84895i	0.580611	+	0.127802i	0.0850522	+	0.996377i	$0.472894\pi$
$908$	−9.29407	+	17.5305i	−0.308434	+	0.581769i
$909$	2.63273	+	16.0589i	0.0873221	+	0.532641i
$910$	1.65871	−	1.95278i	0.0549857	−	0.0647342i
$911$	−9.38764	−	11.0520i	−0.311026	−	0.366168i	0.584332	−	0.811515i	$-0.301357\pi$
$911$	−9.38764	−	11.0520i	−0.311026	−	0.366168i	−0.895358	+	0.445346i	$0.853081\pi$
$912$	0.748311	−	4.56449i	0.0247790	−	0.151145i
$913$	−1.23456	−	0.938492i	−0.0408581	−	0.0310595i
$914$	−21.3241	+	31.4507i	−0.705340	+	1.04030i
$915$	−21.2382	+	31.3241i	−0.702115	+	1.03554i
$916$	3.82475	+	2.90750i	0.126373	+	0.0960664i
$917$	11.6111	−	70.8244i	0.383431	−	2.33883i
$918$	2.06371	+	2.42958i	0.0681124	+	0.0801882i
$919$	−6.07130	+	7.14768i	−0.200274	+	0.235780i	−0.853126	−	0.521705i	$-0.825296\pi$
$919$	−6.07130	+	7.14768i	−0.200274	+	0.235780i	0.652853	+	0.757485i	$0.273572\pi$
$920$	4.64286	+	28.3202i	0.153071	+	0.933690i
$921$	−4.35763	+	8.21936i	−0.143589	+	0.270837i
$922$	10.6604	+	2.34652i	0.351080	+	0.0772786i
$923$	1.55712	+	0.524655i	0.0512533	+	0.0172692i
$924$	0.652380	+	12.0324i	0.0214617	+	0.395838i
$925$	10.0266	−	7.62203i	0.329673	−	0.250611i
$926$	−3.75157	−	7.07620i	−0.123284	−	0.232538i
$927$	0.743650	+	2.67839i	0.0244247	+	0.0879697i
$928$	−7.38524	−	6.99567i	−0.242432	−	0.229644i
$929$	3.50827	+	8.80510i	0.115103	+	0.288886i	0.975230	−	0.221194i	$-0.0709953\pi$
$929$	3.50827	+	8.80510i	0.115103	+	0.288886i	−0.860127	+	0.510079i	$0.829616\pi$
$930$	34.2940	−	11.5550i	1.12455	−	0.378904i
$931$	−35.1474	+	3.82251i	−1.15191	+	0.125278i
$932$	2.85729	+	1.32192i	0.0935936	+	0.0433010i
$933$	−2.48290	+	2.35193i	−0.0812866	+	0.0769987i
$934$	6.60655	+	3.97503i	0.216173	+	0.130067i
$935$	42.0946	+	4.57807i	1.37664	+	0.149719i
$936$	−0.155018	+	0.0341220i	−0.00506692	+	0.00111531i
$937$	3.03528	−	10.9321i	0.0991583	−	0.357136i	−0.897280	−	0.441462i	$-0.854460\pi$
$937$	3.03528	−	10.9321i	0.0991583	−	0.357136i	0.996438	+	0.0843262i	$0.0268738\pi$
$938$	1.69537	−	1.02007i	0.0553556	−	0.0333064i
$939$	−30.0054	+	13.8820i	−0.979189	+	0.453021i
$940$	−6.51881	+	16.3610i	−0.212620	+	0.533636i
$941$	1.58455	−	29.2252i	0.0516547	−	0.952716i	−0.851756	−	0.523939i	$-0.824462\pi$
$941$	1.58455	−	29.2252i	0.0516547	−	0.952716i	0.903411	−	0.428777i	$-0.141055\pi$
$942$	−1.05898	−	1.56189i	−0.0345036	−	0.0508890i
$943$	−20.5042			−0.667707
$944$	1.33341	+	7.56452i	0.0433987	+	0.246204i
$945$	16.1418			0.525091
$946$	−6.98784	−	10.3063i	−0.227194	−	0.335087i
$947$	−0.278680	+	5.13994i	−0.00905587	+	0.167026i	0.990507	+	0.137462i	$0.0438945\pi$
$947$	−0.278680	+	5.13994i	−0.00905587	+	0.167026i	−0.999563	+	0.0295636i	$0.990588\pi$
$948$	5.84932	−	14.6807i	0.189977	−	0.476807i
$949$	−0.357207	+	0.165262i	−0.0115954	+	0.00536462i
$950$	−50.7038	+	30.5075i	−1.64505	+	0.989794i
$951$	1.56866	−	5.64979i	0.0508672	−	0.183207i
$952$	−11.9133	+	2.62232i	−0.386113	+	0.0849900i
$953$	7.90408	+	0.859621i	0.256038	+	0.0278458i	0.235238	−	0.971938i	$-0.424413\pi$
$953$	7.90408	+	0.859621i	0.256038	+	0.0278458i	0.0208003	+	0.999784i	$0.493379\pi$
$954$	2.12195	+	1.27674i	0.0687008	+	0.0413359i
$955$	70.3558	−	66.6446i	2.27666	−	2.15657i
$956$	15.5518	+	7.19501i	0.502980	+	0.232703i
$957$	−31.8453	+	3.46339i	−1.02941	+	0.111955i
$958$	6.66443	−	2.24551i	0.215318	−	0.0725491i
$959$	−24.0480	−	60.3560i	−0.776551	−	1.94900i
$960$	−3.06240	−	2.90086i	−0.0988384	−	0.0936247i
$961$	11.3970	+	41.0482i	0.367644	+	1.32413i
$962$	−0.0731965	−	0.138063i	−0.00235995	−	0.00445134i
$963$	−6.80723	+	5.17472i	−0.219360	+	0.166753i
$964$	−0.0417115	−	0.769323i	−0.00134344	−	0.0247782i
$965$	−43.9574	−	14.8110i	−1.41504	−	0.476782i
$966$	−25.4259	−	5.59667i	−0.818067	−	0.180070i
$967$	−10.1776	+	19.1970i	−0.327290	+	0.617335i	−0.991484	−	0.130225i	$-0.958430\pi$
$967$	−10.1776	+	19.1970i	−0.327290	+	0.617335i	0.664194	+	0.747560i	$0.268775\pi$
$968$	0.175372	+	1.06972i	0.00563667	+	0.0343822i
$969$	9.54552	−	11.2379i	0.306646	−	0.361012i
$970$	14.0232	+	16.5094i	0.450259	+	0.530085i
$971$	−5.16313	+	31.4937i	−0.165693	+	1.01068i	0.764773	+	0.644300i	$0.222851\pi$
$971$	−5.16313	+	31.4937i	−0.165693	+	1.01068i	−0.930465	+	0.366380i	$0.880597\pi$
$972$	−0.796093	−	0.605174i	−0.0255347	−	0.0194110i
$973$	−50.1433	+	73.9559i	−1.60752	+	2.37092i
$974$	2.95146	−	4.35308i	0.0945709	−	0.139482i
$975$	1.61659	+	1.22890i	0.0517724	+	0.0393564i
$976$	−1.45149	+	8.85369i	−0.0464610	+	0.283400i
$977$	−29.2034	−	34.3809i	−0.934299	−	1.09994i	−0.994808	−	0.101774i	$-0.967548\pi$
$977$	−29.2034	−	34.3809i	−0.934299	−	1.09994i	0.0605090	−	0.998168i	$-0.480728\pi$
$978$	1.80567	−	2.12580i	0.0577389	−	0.0679755i
$979$	−4.70786	−	28.7167i	−0.150464	−	0.917789i
$980$	−15.1024	+	28.4862i	−0.482430	+	0.909959i
$981$	−9.47808	−	2.08628i	−0.302612	−	0.0666099i
$982$	8.29506	+	2.79493i	0.264706	+	0.0891899i
$983$	2.91074	+	53.6855i	0.0928383	+	1.71230i	0.560301	+	0.828289i	$0.310685\pi$
$983$	2.91074	+	53.6855i	0.0928383	+	1.71230i	−0.467463	+	0.884013i	$0.654832\pi$
$984$	2.39926	−	1.82387i	0.0764856	−	0.0581429i
$985$	8.17731	+	15.4241i	0.260551	+	0.491451i
$986$	−8.67530	−	31.2456i	−0.276278	−	0.995063i
$987$	−11.5994	−	10.9875i	−0.369212	−	0.349736i
$988$	0.271751	+	0.682045i	0.00864556	+	0.0216987i
$989$	25.4944	−	8.59006i	0.810675	−	0.273148i
$990$	−13.2051	+	1.43614i	−0.419686	+	0.0456436i
$991$	40.7571	+	18.8562i	1.29469	+	0.598988i	0.941642	−	0.336617i	$-0.109283\pi$
$991$	40.7571	+	18.8562i	1.29469	+	0.598988i	0.353049	+	0.935605i	$0.385145\pi$
$992$	6.22839	−	5.89984i	0.197752	−	0.187320i
$993$	−4.06806	−	2.44767i	−0.129096	−	0.0776746i
$994$	−39.3810	−	4.28294i	−1.24909	−	0.135847i
$995$	34.4362	−	7.57999i	1.09170	−	0.240302i
$996$	−0.131750	+	0.474522i	−0.00417467	+	0.0150358i
$997$	−39.0661	+	23.5053i	−1.23724	+	0.744421i	−0.975347	−	0.220677i	$-0.929173\pi$
$997$	−39.0661	+	23.5053i	−1.23724	+	0.744421i	−0.261890	+	0.965098i	$0.584346\pi$
$998$	13.3468	−	6.17488i	0.422485	−	0.195462i
$999$	0.364396	−	0.914564i	0.0115290	−	0.0289355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.7.1	✓	84
59.17	even	29	inner	354.2.e.c.253.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.7.1	✓	84	1.1	even	1	trivial
354.2.e.c.253.1	yes	84	59.17	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-3.82834 + 1.77118i) q^{5} +(0.856857 - 0.515554i) q^{6} +(1.02375 - 3.68721i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})\)	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-3.82834 + 1.77118i) q^{5} +(0.856857 - 0.515554i) q^{6} +(1.02375 - 3.68721i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(3.61440 + 2.17471i) q^{10} +(2.28614 - 2.16554i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(0.157798 - 0.0171616i) q^{13} +(-3.62637 + 1.22187i) q^{14} +(-1.56132 - 3.91861i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(-0.852814 - 3.07156i) q^{17} +(0.468408 + 0.883512i) q^{18} +(3.68227 - 2.79919i) q^{19} +(-0.228369 - 4.21202i) q^{20} +(3.62637 + 1.22187i) q^{21} +(-3.07535 - 0.676935i) q^{22} +(3.18679 - 6.01092i) q^{23} +(0.161782 + 0.986827i) q^{24} +(8.28217 - 9.75052i) q^{25} +(-0.102759 - 0.120977i) q^{26} +(0.161782 - 0.986827i) q^{27} +(3.04640 + 2.31581i) q^{28} +(-5.70871 + 8.41972i) q^{29} +(-2.36720 + 3.49136i) q^{30} +(-6.82976 - 5.19185i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(2.03860 + 2.40002i) q^{33} +(-2.06371 + 2.42958i) q^{34} +(2.61145 + 15.9291i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.961469 + 0.211635i) q^{37} +(-4.38330 - 1.47691i) q^{38} +(0.00859341 + 0.158496i) q^{39} +(-3.35808 + 2.55275i) q^{40} +(-1.41169 - 2.66272i) q^{41} +(-1.02375 - 3.68721i) q^{42} +(2.87079 + 2.71935i) q^{43} +(1.16555 + 2.92532i) q^{44} +(3.99739 - 1.34688i) q^{45} +(-6.76355 + 0.735581i) q^{46} +(-3.78931 - 1.75312i) q^{47} +(0.725995 - 0.687699i) q^{48} +(-6.54943 - 3.94066i) q^{49} +(-12.7182 - 1.38319i) q^{50} +(3.11322 - 0.685272i) q^{51} +(-0.0424645 + 0.152943i) q^{52} +(2.12195 - 1.27674i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(-4.91654 + 12.3396i) q^{55} +(0.207173 - 3.82108i) q^{56} +(2.59573 + 3.82841i) q^{57} +10.1726 q^{58} +(-6.17017 - 4.57483i) q^{59} +4.21820 q^{60} +(-5.03490 - 7.42592i) q^{61} +(-0.464463 + 8.56652i) q^{62} +(-1.41640 + 3.55490i) q^{63} +(0.907575 - 0.419889i) q^{64} +(-0.573710 + 0.345190i) q^{65} +(0.842438 - 3.03419i) q^{66} +(-0.504961 + 0.111150i) q^{67} +(3.16906 + 0.344656i) q^{68} +(5.82957 + 3.50754i) q^{69} +(11.7188 - 11.1007i) q^{70} +(9.39506 + 4.34662i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(-2.34980 + 0.791740i) q^{73} +(-0.364396 - 0.914564i) q^{74} +(9.28784 + 8.79791i) q^{75} +(1.23743 + 4.45683i) q^{76} +(-5.64438 - 10.6464i) q^{77} +(0.126363 - 0.0960587i) q^{78} +(0.855561 + 15.7799i) q^{79} +(3.99739 + 1.34688i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-1.41169 + 2.66272i) q^{82} +(-0.0796732 - 0.485985i) q^{83} +(-2.47735 + 2.91656i) q^{84} +(8.70513 + 10.2485i) q^{85} +(0.639731 - 3.90219i) q^{86} +(-8.09831 - 6.15617i) q^{87} +(1.76716 - 2.60637i) q^{88} +(5.18600 - 7.64878i) q^{89} +(-3.35808 - 2.55275i) q^{90} +(0.0982674 - 0.599405i) q^{91} +(4.40445 + 5.18532i) q^{92} +(5.55399 - 6.53867i) q^{93} +(0.675472 + 4.12019i) q^{94} +(-9.13911 + 17.2382i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(4.86638 + 1.63968i) q^{97} +(0.413813 + 7.63234i) q^{98} +(-2.50687 + 1.90567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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