LMFDB - Embedded newform 507.2.m.b.40.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.10
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.479187 + 0.118109i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.55524 - 0.816254i) q^{4} +(2.38960 - 3.46193i) q^{5} +(0.175008 - 0.461457i) q^{6} +(-0.109460 - 0.0969731i) q^{7} +(-1.38767 - 1.22937i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(0.479187 + 0.118109i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.55524 - 0.816254i) q^{4} +(2.38960 - 3.46193i) q^{5} +(0.175008 - 0.461457i) q^{6} +(-0.109460 - 0.0969731i) q^{7} +(-1.38767 - 1.22937i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.55395 - 1.37668i) q^{10} +(-1.10138 + 0.271465i) q^{11} +(-0.997766 + 1.44551i) q^{12} +(2.61201 + 2.48544i) q^{13} +(-0.0409984 - 0.0593965i) q^{14} +(-3.14865 - 2.78946i) q^{15} +(1.47578 + 2.13803i) q^{16} +(-3.06918 - 2.71906i) q^{17} +(-0.436998 - 0.229354i) q^{18} +0.0450389 q^{19} +(-6.54221 + 3.43362i) q^{20} +(-0.109460 + 0.0969731i) q^{21} -0.559828 q^{22} -6.46909 q^{23} +(-1.38767 + 1.22937i) q^{24} +(-4.50175 - 11.8701i) q^{25} +(0.958091 + 1.49949i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.0910821 + 0.240164i) q^{28} +(8.71311 + 2.14759i) q^{29} +(-1.17933 - 1.70856i) q^{30} +(0.113067 - 0.298134i) q^{31} +(1.76946 + 4.66568i) q^{32} +(0.136729 + 1.12607i) q^{33} +(-1.14957 - 1.66544i) q^{34} +(-0.597279 + 0.147216i) q^{35} +(1.31471 + 1.16473i) q^{36} +(-0.204895 + 0.540265i) q^{37} +(0.0215821 + 0.00531950i) q^{38} +(2.78216 - 2.29338i) q^{39} +(-7.57194 + 1.86632i) q^{40} +(1.14979 - 9.46941i) q^{41} +(-0.0639052 + 0.0335401i) q^{42} +(3.74663 + 9.87906i) q^{43} +(1.93449 + 0.476809i) q^{44} +(-3.14865 + 2.78946i) q^{45} +(-3.09991 - 0.764058i) q^{46} +(9.42126 - 4.94466i) q^{47} +(2.30033 - 1.20731i) q^{48} +(-0.841179 - 6.92773i) q^{49} +(-0.755211 - 6.21972i) q^{50} +(-3.06918 + 2.71906i) q^{51} +(-2.03356 - 5.99752i) q^{52} +(-2.59463 - 2.29865i) q^{53} +(-0.280356 + 0.406166i) q^{54} +(-1.69205 + 4.46157i) q^{55} +(0.0326786 + 0.269133i) q^{56} +(0.00542884 - 0.0447105i) q^{57} +(3.92156 + 2.05819i) q^{58} +(6.65022 - 9.63451i) q^{59} +(2.62001 + 6.90839i) q^{60} +(-4.37724 + 3.87789i) q^{61} +(0.0893929 - 0.129508i) q^{62} +(0.0830721 + 0.120351i) q^{63} +(-0.329442 - 2.71320i) q^{64} +(14.8461 - 3.10341i) q^{65} +(-0.0674798 + 0.555746i) q^{66} +(-5.03252 + 2.64127i) q^{67} +(2.55388 + 6.73402i) q^{68} +(-0.779763 + 6.42192i) q^{69} -0.303596 q^{70} +(-1.23862 + 10.2010i) q^{71} +(1.05314 + 1.52573i) q^{72} +(14.3942 - 3.54785i) q^{73} +(-0.161993 + 0.234688i) q^{74} +(-12.3262 + 3.03814i) q^{75} +(-0.0700463 - 0.0367631i) q^{76} +(0.146881 + 0.0770893i) q^{77} +(1.60404 - 0.770362i) q^{78} +(-4.85249 + 2.54678i) q^{79} +10.9282 q^{80} +(0.885456 + 0.464723i) q^{81} +(1.66939 - 4.40182i) q^{82} +(0.562264 + 4.63066i) q^{83} +(0.249391 - 0.0614694i) q^{84} +(-16.7473 + 4.12783i) q^{85} +(0.628533 + 5.17643i) q^{86} +(3.18218 - 8.39072i) q^{87} +(1.86207 + 0.977291i) q^{88} +2.15347 q^{89} +(-1.83826 + 0.964791i) q^{90} +(-0.0448906 - 0.525351i) q^{91} +(10.0610 + 5.28042i) q^{92} +(-0.282332 - 0.148179i) q^{93} +(5.09856 - 1.25668i) q^{94} +(0.107625 - 0.155921i) q^{95} +(4.84495 - 1.19417i) q^{96} +(1.41037 + 2.04328i) q^{97} +(0.415146 - 3.41903i) q^{98} +1.13434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	0.479187	+	0.118109i	0.338837	+	0.0835157i	0.405063	−	0.914289i	$-0.367250\pi$
$2$	0.479187	+	0.118109i	0.338837	+	0.0835157i	−0.0662261	+	0.997805i	$0.521096\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	−1.55524	−	0.816254i	−0.777621	−	0.408127i
$5$	2.38960	−	3.46193i	1.06866	−	1.54822i	0.254947	−	0.966955i	$-0.417942\pi$
$5$	2.38960	−	3.46193i	1.06866	−	1.54822i	0.813713	−	0.581267i	$-0.197443\pi$
$6$	0.175008	−	0.461457i	0.0714465	−	0.188389i
$7$	−0.109460	−	0.0969731i	−0.0413720	−	0.0366524i	0.642183	−	0.766551i	$-0.278029\pi$
$7$	−0.109460	−	0.0969731i	−0.0413720	−	0.0366524i	−0.683555	+	0.729899i	$0.739567\pi$
$8$	−1.38767	−	1.22937i	−0.490615	−	0.434647i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	1.55395	−	1.37668i	0.491402	−	0.435344i
$11$	−1.10138	+	0.271465i	−0.332077	+	0.0818497i	−0.401829	−	0.915715i	$-0.631625\pi$
$11$	−1.10138	+	0.271465i	−0.332077	+	0.0818497i	0.0697519	+	0.997564i	$0.477779\pi$
$12$	−0.997766	+	1.44551i	−0.288030	+	0.417284i
$13$	2.61201	+	2.48544i	0.724442	+	0.689336i
$13$	2.61201	+	2.48544i	0.724442	+	0.689336i
$14$	−0.0409984	−	0.0593965i	−0.0109573	−	0.0158744i
$15$	−3.14865	−	2.78946i	−0.812979	−	0.720236i
$16$	1.47578	+	2.13803i	0.368945	+	0.534508i
$17$	−3.06918	−	2.71906i	−0.744385	−	0.659468i	0.203140	−	0.979150i	$-0.434885\pi$
$17$	−3.06918	−	2.71906i	−0.744385	−	0.659468i	−0.947525	+	0.319682i	$0.896424\pi$
$18$	−0.436998	−	0.229354i	−0.103001	−	0.0540593i
$19$	0.0450389			0.0103326			0.00516631	−	0.999987i	$-0.498356\pi$
$19$	0.0450389			0.0103326			0.00516631	+	0.999987i	$0.498356\pi$
$20$	−6.54221	+	3.43362i	−1.46288	+	0.767780i
$21$	−0.109460	+	0.0969731i	−0.0238861	+	0.0211613i
$22$	−0.559828			−0.119356
$23$	−6.46909			−1.34890			−0.674449	−	0.738321i	$-0.735619\pi$
$23$	−6.46909			−1.34890			−0.674449	+	0.738321i	$0.735619\pi$
$24$	−1.38767	+	1.22937i	−0.283256	+	0.250943i
$25$	−4.50175	−	11.8701i	−0.900351	−	2.37403i
$26$	0.958091	+	1.49949i	0.187897	+	0.294075i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	0.0910821	+	0.240164i	0.0172129	+	0.0453867i
$29$	8.71311	+	2.14759i	1.61798	+	0.398797i	0.941325	−	0.337500i	$-0.109581\pi$
$29$	8.71311	+	2.14759i	1.61798	+	0.398797i	0.676658	+	0.736297i	$0.263428\pi$
$30$	−1.17933	−	1.70856i	−0.215316	−	0.311939i
$31$	0.113067	−	0.298134i	0.0203075	−	0.0535465i	−0.924479	−	0.381233i	$-0.875500\pi$
$31$	0.113067	−	0.298134i	0.0203075	−	0.0535465i	0.944787	+	0.327686i	$0.106269\pi$
$32$	1.76946	+	4.66568i	0.312799	+	0.824784i
$33$	0.136729	+	1.12607i	0.0238015	+	0.196023i
$34$	−1.14957	−	1.66544i	−0.197149	−	0.285620i
$35$	−0.597279	+	0.147216i	−0.100959	+	0.0248841i
$36$	1.31471	+	1.16473i	0.219118	+	0.194121i
$37$	−0.204895	+	0.540265i	−0.0336846	+	0.0888190i	−0.950803	−	0.309795i	$-0.899740\pi$
$37$	−0.204895	+	0.540265i	−0.0336846	+	0.0888190i	0.917119	+	0.398614i	$0.130509\pi$
$38$	0.0215821	+	0.00531950i	0.00350107	+	0.000862937i
$39$	2.78216	−	2.29338i	0.445502	−	0.367235i
$40$	−7.57194	+	1.86632i	−1.19723	+	0.295091i
$41$	1.14979	−	9.46941i	0.179568	−	1.47887i	−0.572563	−	0.819860i	$-0.694051\pi$
$41$	1.14979	−	9.46941i	0.179568	−	1.47887i	0.752131	−	0.659013i	$-0.229026\pi$
$42$	−0.0639052	+	0.0335401i	−0.00986079	+	0.00517534i
$43$	3.74663	+	9.87906i	0.571356	+	1.50654i	0.839608	+	0.543193i	$0.182785\pi$
$43$	3.74663	+	9.87906i	0.571356	+	1.50654i	−0.268251	+	0.963349i	$0.586446\pi$
$44$	1.93449	+	0.476809i	0.291635	+	0.0718816i
$45$	−3.14865	+	2.78946i	−0.469374	+	0.415829i
$46$	−3.09991	−	0.764058i	−0.457056	−	0.112654i
$47$	9.42126	−	4.94466i	1.37423	−	0.721252i	0.394001	−	0.919110i	$-0.371091\pi$
$47$	9.42126	−	4.94466i	1.37423	−	0.721252i	0.980231	+	0.197858i	$0.0633985\pi$
$48$	2.30033	−	1.20731i	0.332024	−	0.174260i
$49$	−0.841179	−	6.92773i	−0.120168	−	0.989676i
$50$	−0.755211	−	6.21972i	−0.106803	−	0.879602i
$51$	−3.06918	+	2.71906i	−0.429771	+	0.380744i
$52$	−2.03356	−	5.99752i	−0.282005	−	0.831706i
$53$	−2.59463	−	2.29865i	−0.356400	−	0.315743i	0.465856	−	0.884861i	$-0.345747\pi$
$53$	−2.59463	−	2.29865i	−0.356400	−	0.315743i	−0.822256	+	0.569117i	$0.807285\pi$
$54$	−0.280356	+	0.406166i	−0.0381516	+	0.0552722i
$55$	−1.69205	+	4.46157i	−0.228156	+	0.601599i
$56$	0.0326786	+	0.269133i	0.00436687	+	0.0359644i
$57$	0.00542884	−	0.0447105i	0.000719067	−	0.00592205i
$58$	3.92156	+	2.05819i	0.514926	+	0.270254i
$59$	6.65022	−	9.63451i	0.865785	−	1.25431i	−0.100006	−	0.994987i	$-0.531886\pi$
$59$	6.65022	−	9.63451i	0.865785	−	1.25431i	0.965792	−	0.259320i	$-0.0834983\pi$
$60$	2.62001	+	6.90839i	0.338241	+	0.891869i
$61$	−4.37724	+	3.87789i	−0.560448	+	0.496513i	−0.895122	−	0.445820i	$-0.852912\pi$
$61$	−4.37724	+	3.87789i	−0.560448	+	0.496513i	0.334675	+	0.942334i	$0.391374\pi$
$62$	0.0893929	−	0.129508i	0.0113529	−	0.0164475i
$63$	0.0830721	+	0.120351i	0.0104661	+	0.0151628i
$64$	−0.329442	−	2.71320i	−0.0411803	−	0.339150i
$65$	14.8461	−	3.10341i	1.84143	−	0.384931i
$66$	−0.0674798	+	0.555746i	−0.00830618	+	0.0684076i
$67$	−5.03252	+	2.64127i	−0.614820	+	0.322683i	−0.743227	−	0.669039i	$-0.766706\pi$
$67$	−5.03252	+	2.64127i	−0.614820	+	0.322683i	0.128407	+	0.991722i	$0.459014\pi$
$68$	2.55388	+	6.73402i	0.309703	+	0.816619i
$69$	−0.779763	+	6.42192i	−0.0938724	+	0.773109i
$70$	−0.303596			−0.0362867
$71$	−1.23862	+	10.2010i	−0.146998	+	1.21063i	0.713306	+	0.700853i	$0.247197\pi$
$71$	−1.23862	+	10.2010i	−0.146998	+	1.21063i	−0.860304	+	0.509782i	$0.829726\pi$
$72$	1.05314	+	1.52573i	0.124113	+	0.179809i
$73$	14.3942	−	3.54785i	1.68472	−	0.415245i	0.723341	−	0.690491i	$-0.242605\pi$
$73$	14.3942	−	3.54785i	1.68472	−	0.415245i	0.961374	+	0.275246i	$0.0887593\pi$
$74$	−0.161993	+	0.234688i	−0.0188314	+	0.0272819i
$75$	−12.3262	+	3.03814i	−1.42331	+	0.350814i
$76$	−0.0700463	−	0.0367631i	−0.00803486	−	0.00421702i
$77$	0.146881	+	0.0770893i	0.0167387	+	0.00878514i
$78$	1.60404	−	0.770362i	0.181622	−	0.0872263i
$79$	−4.85249	+	2.54678i	−0.545948	+	0.286535i	−0.715062	−	0.699061i	$-0.753602\pi$
$79$	−4.85249	+	2.54678i	−0.545948	+	0.286535i	0.169114	+	0.985596i	$0.445909\pi$
$80$	10.9282			1.22181
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	1.66939	−	4.40182i	0.184353	−	0.486100i
$83$	0.562264	+	4.63066i	0.0617165	+	0.508281i	0.990485	+	0.137621i	$0.0439456\pi$
$83$	0.562264	+	4.63066i	0.0617165	+	0.508281i	−0.928768	+	0.370661i	$0.879131\pi$
$84$	0.249391	−	0.0614694i	0.0272108	−	0.00670687i
$85$	−16.7473	+	4.12783i	−1.81650	+	0.447726i
$86$	0.628533	+	5.17643i	0.0677764	+	0.558189i
$87$	3.18218	−	8.39072i	0.341165	−	0.899579i
$88$	1.86207	+	0.977291i	0.198498	+	0.104180i
$89$	2.15347			0.228267			0.114134	−	0.993465i	$-0.463591\pi$
$89$	2.15347			0.228267			0.114134	+	0.993465i	$0.463591\pi$
$90$	−1.83826	+	0.964791i	−0.193769	+	0.101698i
$91$	−0.0448906	−	0.525351i	−0.00470581	−	0.0550717i
$92$	10.0610	+	5.28042i	1.04893	+	0.550522i
$93$	−0.282332	−	0.148179i	−0.0292764	−	0.0153655i
$94$	5.09856	−	1.25668i	0.525876	−	0.129617i
$95$	0.107625	−	0.155921i	0.0110421	−	0.0159972i
$96$	4.84495	−	1.19417i	0.494486	−	0.121880i
$97$	1.41037	+	2.04328i	0.143202	+	0.207463i	0.888021	−	0.459803i	$-0.152080\pi$
$97$	1.41037	+	2.04328i	0.143202	+	0.207463i	−0.744820	+	0.667266i	$0.767464\pi$
$98$	0.415146	−	3.41903i	0.0419361	−	0.345374i
$99$	1.13434			0.114005
$100$	−2.68774	+	22.1355i	−0.268774	+	2.21355i
$101$	6.28497	+	16.5721i	0.625378	+	1.64899i	0.753673	+	0.657250i	$0.228280\pi$
$101$	6.28497	+	16.5721i	0.625378	+	1.64899i	−0.128295	+	0.991736i	$0.540950\pi$
$102$	−1.79186	+	0.940439i	−0.177420	+	0.0931174i
$103$	0.972560	−	8.00975i	0.0958292	−	0.789224i	−0.862993	−	0.505216i	$-0.831413\pi$
$103$	0.972560	−	8.00975i	0.0958292	−	0.789224i	0.958822	−	0.284008i	$-0.0916642\pi$
$104$	−0.569095	−	6.66008i	−0.0558044	−	0.653074i
$105$	0.0741487	+	0.610669i	0.00723617	+	0.0595952i
$106$	−0.971825	−	1.40793i	−0.0943920	−	0.136750i
$107$	8.22734	−	11.9194i	0.795367	−	1.15229i	−0.189990	−	0.981786i	$-0.560846\pi$
$107$	8.22734	−	11.9194i	0.795367	−	1.15229i	0.985357	−	0.170502i	$-0.0545391\pi$
$108$	1.31471	−	1.16473i	0.126508	−	0.112076i
$109$	0.836988	+	2.20696i	0.0801689	+	0.211388i	0.969108	−	0.246638i	$-0.0793259\pi$
$109$	0.836988	+	2.20696i	0.0801689	+	0.211388i	−0.888939	+	0.458026i	$0.848557\pi$
$110$	−1.33776	+	1.93808i	−0.127551	+	0.184789i
$111$	0.511628	+	0.268523i	0.0485616	+	0.0254871i
$112$	0.0457931	−	0.377140i	0.00432704	−	0.0356364i
$113$	1.07975	+	8.89257i	0.101575	+	0.836542i	0.951076	+	0.308956i	$0.0999797\pi$
$113$	1.07975	+	8.89257i	0.101575	+	0.836542i	−0.849502	+	0.527586i	$0.823097\pi$
$114$	0.00788215	−	0.0207835i	0.000738231	−	0.00194655i
$115$	−15.4585	+	22.3955i	−1.44151	+	2.08839i
$116$	−11.7980	−	10.4521i	−1.09542	−	0.970455i
$117$	−1.94131	−	3.03831i	−0.179474	−	0.280892i
$118$	4.32463	−	3.83128i	0.398114	−	0.352698i
$119$	0.0722771	+	0.595256i	0.00662563	+	0.0545670i
$120$	0.940012	+	7.74170i	0.0858110	+	0.706717i
$121$	−8.60068	+	4.51399i	−0.781880	+	0.410362i
$122$	−2.55553	+	1.34125i	−0.231367	+	0.121431i
$123$	−9.26178	−	2.28282i	−0.835106	−	0.205835i
$124$	−0.419200	+	0.371379i	−0.0376453	+	0.0333508i
$125$	−31.4294	−	7.74664i	−2.81113	−	0.692881i
$126$	0.0255926	+	0.0674821i	0.00227997	+	0.00601178i
$127$	−1.99467	+	1.04688i	−0.176998	+	0.0928959i	−0.550895	−	0.834574i	$-0.685714\pi$
$127$	−1.99467	+	1.04688i	−0.176998	+	0.0928959i	0.373897	+	0.927470i	$0.378021\pi$
$128$	1.36553	−	11.2462i	0.120697	−	0.994031i
$129$	10.2586	−	2.52853i	0.903223	−	0.222624i
$130$	7.48058	+	0.266338i	0.656091	+	0.0233593i
$131$	13.9028	+	3.42672i	1.21469	+	0.299394i	0.794061	−	0.607839i	$-0.207963\pi$
$131$	13.9028	+	3.42672i	1.21469	+	0.299394i	0.420629	+	0.907233i	$0.361809\pi$
$132$	0.706509	−	1.86291i	0.0614937	−	0.162146i
$133$	−0.00492996	−	0.00436756i	−0.000427481	−	0.000378715i
$134$	−2.72348	+	0.671277i	−0.235273	+	0.0579895i
$135$	2.38960	+	3.46193i	0.205664	+	0.297955i
$136$	0.916286	+	7.54629i	0.0785708	+	0.647089i
$137$	−2.17863	−	5.74457i	−0.186133	−	0.490792i	0.809173	−	0.587570i	$-0.199915\pi$
$137$	−2.17863	−	5.74457i	−0.186133	−	0.490792i	−0.995306	+	0.0967785i	$0.969146\pi$
$138$	−1.13214	+	2.98521i	−0.0963741	+	0.254118i
$139$	−1.45823	−	2.11262i	−0.123686	−	0.179190i	0.756249	−	0.654283i	$-0.227030\pi$
$139$	−1.45823	−	2.11262i	−0.123686	−	0.179190i	−0.879935	+	0.475093i	$0.842414\pi$
$140$	1.04908	+	0.258575i	0.0886633	+	0.0218536i
$141$	−3.77300	−	9.94858i	−0.317744	−	0.837821i
$142$	−1.79836	+	4.74189i	−0.150915	+	0.397931i
$143$	−3.55151	−	2.02833i	−0.296993	−	0.169617i
$144$	−0.921230	−	2.42908i	−0.0767691	−	0.202424i
$145$	28.2556	−	25.0323i	2.34650	−	2.07882i
$146$	7.31656			0.605523
$147$	−6.97861			−0.575586
$148$	0.759655	−	0.672995i	0.0624432	−	0.0553199i
$149$	11.6957	−	6.13838i	0.958149	−	0.502876i	0.0882465	−	0.996099i	$-0.471874\pi$
$149$	11.6957	−	6.13838i	0.958149	−	0.502876i	0.869903	+	0.493223i	$0.164181\pi$
$150$	−6.26540			−0.511568
$151$	−0.147504	−	0.0774161i	−0.0120037	−	0.00630004i	0.458711	−	0.888586i	$-0.348311\pi$
$151$	−0.147504	−	0.0774161i	−0.0120037	−	0.00630004i	−0.470714	+	0.882286i	$0.656004\pi$
$152$	−0.0624990	−	0.0553693i	−0.00506934	−	0.00449104i
$153$	2.32928	+	3.37455i	0.188311	+	0.272816i
$154$	0.0612787	+	0.0542882i	0.00493798	+	0.00437467i
$155$	−0.761934	−	1.10385i	−0.0612000	−	0.0886636i
$156$	−6.19891	+	1.29582i	−0.496310	+	0.103748i
$157$	11.7683	−	17.0493i	0.939211	−	1.36068i	0.00653118	−	0.999979i	$-0.497921\pi$
$157$	11.7683	−	17.0493i	0.939211	−	1.36068i	0.932680	−	0.360704i	$-0.117464\pi$
$158$	−2.62605	+	0.647263i	−0.208917	+	0.0514935i
$159$	−2.59463	+	2.29865i	−0.205768	+	0.182294i
$160$	20.3806	+	5.02336i	1.61122	+	0.397131i
$161$	0.708106	+	0.627328i	0.0558066	+	0.0494403i
$162$	0.369411	+	0.327270i	0.0290237	+	0.0257127i
$163$	−5.84865	+	15.4216i	−0.458102	+	1.20792i	0.484735	+	0.874661i	$0.338916\pi$
$163$	−5.84865	+	15.4216i	−0.458102	+	1.20792i	−0.942837	+	0.333254i	$0.891853\pi$
$164$	−9.51765	+	13.7887i	−0.743204	+	1.07672i
$165$	4.22509	+	2.21750i	0.328923	+	0.172632i
$166$	−0.277493	+	2.28536i	−0.0215377	+	0.177379i
$167$	−7.46379	−	1.83966i	−0.577565	−	0.142357i	−0.0602973	−	0.998180i	$-0.519205\pi$
$167$	−7.46379	−	1.83966i	−0.577565	−	0.142357i	−0.517268	+	0.855823i	$0.673051\pi$
$168$	0.271110			0.0209166
$169$	0.645222	+	12.9840i	0.0496325	+	0.998768i
$170$	−8.51262			−0.652888
$171$	−0.0437301	−	0.0107785i	−0.00334413	−	0.000824253i
$172$	2.23690	−	18.4225i	0.170562	−	1.40470i
$173$	8.34237	+	4.37841i	0.634258	+	0.332884i	0.751024	−	0.660275i	$-0.229560\pi$
$173$	8.34237	+	4.37841i	0.634258	+	0.332884i	−0.116765	+	0.993160i	$0.537253\pi$
$174$	2.51588	−	3.64488i	0.190728	−	0.276318i
$175$	−0.658323	+	1.73585i	−0.0497645	+	0.131218i
$176$	−2.20579	−	1.95416i	−0.166267	−	0.147300i
$177$	−8.76267	−	7.76305i	−0.658643	−	0.583506i
$178$	1.03192	+	0.254344i	0.0773453	+	0.0190639i
$179$	0.662820	−	0.587207i	0.0495415	−	0.0438899i	−0.637989	−	0.770046i	$-0.720233\pi$
$179$	0.662820	−	0.587207i	0.0495415	−	0.0438899i	0.687530	+	0.726156i	$0.258695\pi$
$180$	7.17383	−	1.76819i	0.534705	−	0.131793i
$181$	9.83844	−	14.2534i	0.731286	−	1.05945i	−0.264194	−	0.964470i	$-0.585106\pi$
$181$	9.83844	−	14.2534i	0.731286	−	1.05945i	0.995479	−	0.0949803i	$-0.0302788\pi$
$182$	0.0405377	−	0.257043i	0.00300485	−	0.0190533i
$183$	3.32200	+	4.81275i	0.245569	+	0.355769i
$184$	8.97695	+	7.95288i	0.661789	+	0.586294i
$185$	1.38074	+	2.00035i	0.101514	+	0.147069i
$186$	−0.117789	−	0.104352i	−0.00863668	−	0.00765143i
$187$	4.11845	+	2.16153i	0.301171	+	0.158067i
$188$	−18.6884			−1.36299
$189$	0.129486	−	0.0679597i	0.00941875	−	0.00494334i
$190$	0.0699882	−	0.0620041i	0.00507747	−	0.00449825i
$191$	−11.5597			−0.836428			−0.418214	−	0.908349i	$-0.637344\pi$
$191$	−11.5597			−0.836428			−0.418214	+	0.908349i	$0.637344\pi$
$192$	−2.73313			−0.197247
$193$	−12.4315	+	11.0134i	−0.894840	+	0.792760i	−0.979035	−	0.203690i	$-0.934707\pi$
$193$	−12.4315	+	11.0134i	−0.894840	+	0.792760i	0.0841950	+	0.996449i	$0.473168\pi$
$194$	0.434503	+	1.14569i	0.0311955	+	0.0822557i
$195$	−1.29129	−	15.1119i	−0.0924713	−	1.08218i
$196$	−4.34655	+	11.4609i	−0.310468	+	0.818637i
$197$	1.69285	+	4.46368i	0.120611	+	0.318024i	0.981701	−	0.190427i	$-0.0609874\pi$
$197$	1.69285	+	4.46368i	0.120611	+	0.318024i	−0.861091	+	0.508451i	$0.830218\pi$
$198$	0.543560	+	0.133976i	0.0386291	+	0.00952123i
$199$	0.423379	+	0.613371i	0.0300126	+	0.0434807i	0.837703	−	0.546126i	$-0.183898\pi$
$199$	0.423379	+	0.613371i	0.0300126	+	0.0434807i	−0.807690	+	0.589607i	$0.799283\pi$
$200$	−8.34582	+	22.0061i	−0.590139	+	1.55607i
$201$	2.01541	+	5.31420i	0.142156	+	0.374835i
$202$	1.05436	+	8.68346i	0.0741847	+	0.610966i
$203$	−0.745478	−	1.08001i	−0.0523223	−	0.0758020i
$204$	6.99275	−	1.72356i	0.489591	−	0.120673i
$205$	−30.0349	−	26.6086i	−2.09773	−	1.85842i
$206$	1.41206	−	3.72330i	0.0983831	−	0.259415i
$207$	6.28111	+	1.54815i	0.436567	+	0.107604i
$208$	−1.45919	+	9.25252i	−0.101177	+	0.641547i
$209$	−0.0496047	+	0.0122265i	−0.00343123	+	0.000845722i
$210$	−0.0365945	+	0.301383i	−0.00252526	+	0.0207974i
$211$	−12.3912	+	6.50341i	−0.853046	+	0.447713i	−0.833777	−	0.552101i	$-0.813826\pi$
$211$	−12.3912	+	6.50341i	−0.853046	+	0.447713i	−0.0192692	+	0.999814i	$0.506134\pi$
$212$	2.15900	+	5.69283i	0.148281	+	0.390985i
$213$	9.97731	+	2.45919i	0.683634	+	0.168501i
$214$	5.35022	−	4.73988i	0.365734	−	0.324012i
$215$	43.1535	+	10.6364i	2.94305	+	0.725396i
$216$	1.64155	−	0.861552i	0.111693	−	0.0586212i
$217$	−0.0412874	+	0.0216693i	−0.00280277	+	0.00147101i
$218$	0.140413	+	1.15640i	0.00950994	+	0.0783214i
$219$	−1.78696	−	14.7169i	−0.120751	−	0.994476i
$220$	6.27332	−	5.55768i	0.422947	−	0.374699i
$221$	−1.25870	−	14.7305i	−0.0846692	−	0.990878i
$222$	0.213451	+	0.189101i	0.0143259	+	0.0126916i
$223$	−11.8509	+	17.1691i	−0.793598	+	1.14973i	0.192128	+	0.981370i	$0.438461\pi$
$223$	−11.8509	+	17.1691i	−0.793598	+	1.14973i	−0.985726	+	0.168355i	$0.946154\pi$
$224$	0.258761	−	0.682296i	0.0172892	−	0.0455878i
$225$	1.53023	+	12.6026i	0.102015	+	0.840171i
$226$	−0.532889	+	4.38873i	−0.0354472	+	0.291934i
$227$	10.9943	+	5.77028i	0.729721	+	0.382987i	0.788296	−	0.615296i	$-0.210964\pi$
$227$	10.9943	+	5.77028i	0.729721	+	0.382987i	−0.0585755	+	0.998283i	$0.518656\pi$
$228$	−0.0449383	+	0.0651043i	−0.00297611	+	0.00431164i
$229$	−1.03996	−	2.74214i	−0.0687223	−	0.181206i	0.896255	−	0.443539i	$-0.146277\pi$
$229$	−1.03996	−	2.74214i	−0.0687223	−	0.181206i	−0.964977	+	0.262333i	$0.915508\pi$
$230$	−10.0526	+	8.90586i	−0.662851	+	0.587235i
$231$	0.0942318	−	0.136518i	0.00620000	−	0.00898224i
$232$	−9.45073	−	13.6917i	−0.620471	−	0.898907i
$233$	0.503276	+	4.14485i	0.0329707	+	0.271538i	0.999866	+	0.0163652i	$0.00520943\pi$
$233$	0.503276	+	4.14485i	0.0329707	+	0.271538i	−0.966895	+	0.255173i	$0.917867\pi$
$234$	−0.571399	−	1.68521i	−0.0373535	−	0.110165i
$235$	5.39495	−	44.4315i	0.351928	−	2.89839i
$236$	−18.2069	+	9.55572i	−1.18517	+	0.622024i
$237$	1.94331	+	5.12409i	0.126232	+	0.332845i
$238$	−0.0356708	+	0.293776i	−0.00231220	+	0.0190426i
$239$	0.439311			0.0284167			0.0142083	−	0.999899i	$-0.495477\pi$
$239$	0.439311			0.0284167			0.0142083	+	0.999899i	$0.495477\pi$
$240$	1.31725	−	10.8486i	0.0850283	−	0.700271i
$241$	2.77718	+	4.02344i	0.178894	+	0.259173i	0.902165	−	0.431392i	$-0.141977\pi$
$241$	2.77718	+	4.02344i	0.178894	+	0.259173i	−0.723271	+	0.690565i	$0.757362\pi$
$242$	−4.65448	+	1.14723i	−0.299201	+	0.0737465i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	9.97300	−	2.45812i	0.638456	−	0.157365i
$245$	−25.9934	−	13.6424i	−1.66066	−	0.871580i
$246$	−4.16850	−	2.18780i	−0.265774	−	0.139489i
$247$	0.117642	+	0.111941i	0.00748539	+	0.00712265i
$248$	−0.523416	+	0.274710i	−0.0332370	+	0.0174441i
$249$	4.66468			0.295612
$250$	−14.1456	−	7.42419i	−0.894647	−	0.469547i
$251$	4.12049	−	10.8648i	0.260083	−	0.685783i	−0.739833	−	0.672791i	$-0.765095\pi$
$251$	4.12049	−	10.8648i	0.260083	−	0.685783i	0.999916	−	0.0129916i	$-0.00413546\pi$
$252$	−0.0309605	−	0.254982i	−0.00195033	−	0.0160624i
$253$	7.12490	−	1.75613i	0.447938	−	0.110407i
$254$	−1.07947	+	0.266065i	−0.0677318	+	0.0166944i
$255$	2.07908	+	17.1227i	0.130197	+	1.07227i
$256$	0.0442605	−	0.116705i	0.00276628	−	0.00729408i
$257$	−5.36998	−	2.81839i	−0.334970	−	0.175806i	0.288849	−	0.957375i	$-0.406728\pi$
$257$	−5.36998	−	2.81839i	−0.334970	−	0.175806i	−0.623819	+	0.781569i	$0.714420\pi$
$258$	5.21445			0.324638
$259$	0.0748190	−	0.0392680i	0.00464903	−	0.00244000i
$260$	−25.6224	−	7.29159i	−1.58903	−	0.452205i
$261$	−7.94597	−	4.17037i	−0.491843	−	0.258139i
$262$	6.25730	+	3.28408i	0.386577	+	0.202891i
$263$	0.281008	−	0.0692623i	0.0173277	−	0.00427089i	−0.230642	−	0.973039i	$-0.574083\pi$
$263$	0.281008	−	0.0692623i	0.0173277	−	0.00427089i	0.247970	+	0.968768i	$0.420237\pi$
$264$	1.19461	−	1.73070i	0.0735234	−	0.106517i
$265$	−14.1579	+	3.48960i	−0.869711	+	0.214365i
$266$	−0.00184652	−	0.00267515i	−0.000113218	−	0.000164024i
$267$	0.259572	−	2.13777i	0.0158855	−	0.130829i
$268$	9.98273			0.609792
$269$	1.93920	−	15.9707i	0.118235	−	0.973752i	−0.805997	−	0.591920i	$-0.798370\pi$
$269$	1.93920	−	15.9707i	0.118235	−	0.973752i	0.924232	−	0.381832i	$-0.124707\pi$
$270$	0.736179	+	1.94115i	0.0448025	+	0.118134i
$271$	9.06204	−	4.75612i	0.550480	−	0.288914i	−0.166461	−	0.986048i	$-0.553234\pi$
$271$	9.06204	−	4.75612i	0.550480	−	0.288914i	0.716941	+	0.697134i	$0.245542\pi$
$272$	1.28400	−	10.5747i	0.0778542	−	0.641187i
$273$	−0.526931	−	0.0187608i	−0.0318913	−	0.00113545i
$274$	−0.365485	−	3.01004i	−0.0220798	−	0.181843i
$275$	8.18044	+	11.8514i	0.493299	+	0.714668i
$276$	6.45464	−	9.35116i	0.388523	−	0.562873i
$277$	10.4032	−	9.21639i	0.625065	−	0.553759i	−0.290020	−	0.957021i	$-0.593662\pi$
$277$	10.4032	−	9.21639i	0.625065	−	0.553759i	0.915085	+	0.403261i	$0.132123\pi$
$278$	−0.449248	−	1.18457i	−0.0269441	−	0.0710458i
$279$	−0.181130	+	0.262412i	−0.0108440	+	0.0157102i
$280$	1.00981	+	0.529988i	0.0603475	+	0.0316728i
$281$	0.926776	−	7.63269i	0.0552868	−	0.455328i	−0.938607	−	0.344988i	$-0.887883\pi$
$281$	0.926776	−	7.63269i	0.0552868	−	0.455328i	0.993894	−	0.110340i	$-0.0351939\pi$
$282$	−0.632955	−	5.21286i	−0.0376920	−	0.310421i
$283$	−2.52688	+	6.66282i	−0.150207	+	0.396064i	−0.988908	−	0.148528i	$-0.952546\pi$
$283$	−2.52688	+	6.66282i	−0.150207	+	0.396064i	0.838701	+	0.544592i	$0.183316\pi$
$284$	10.2530	−	14.8540i	0.608401	−	0.881421i
$285$	−0.141812	−	0.125634i	−0.00840021	−	0.00744193i
$286$	−1.46228	−	1.39142i	−0.0864662	−	0.0822761i
$287$	−1.04413	+	0.925023i	−0.0616333	+	0.0546024i
$288$	−0.601472	−	4.95357i	−0.0354421	−	0.291892i
$289$	−0.0225253	−	0.185512i	−0.00132502	−	0.0109125i
$290$	16.4963	−	8.65791i	0.968695	−	0.508410i
$291$	2.19838	−	1.15380i	0.128871	−	0.0676369i
$292$	−25.2824	−	6.23156i	−1.47954	−	0.364674i
$293$	−13.4925	+	11.9533i	−0.788239	+	0.698318i	−0.957874	−	0.287188i	$-0.907279\pi$
$293$	−13.4925	+	11.9533i	−0.788239	+	0.698318i	0.169636	+	0.985507i	$0.445741\pi$
$294$	−3.34406	−	0.824238i	−0.195030	−	0.0480705i
$295$	−17.4626	−	46.0452i	−1.01671	−	2.68085i
$296$	0.948510	−	0.497816i	0.0551310	−	0.0289350i
$297$	0.136729	−	1.12607i	0.00793383	−	0.0653410i
$298$	6.32943	−	1.56006i	0.366654	−	0.0903721i
$299$	−16.8973	−	16.0785i	−0.977199	−	0.929844i
$300$	21.6501	+	5.33628i	1.24997	+	0.308090i
$301$	0.547896	−	1.44468i	0.0315802	−	0.0832702i
$302$	−0.0615386	−	0.0545184i	−0.00354115	−	0.00313718i
$303$	17.2088	−	4.24160i	0.988622	−	0.243674i
$304$	0.0664674	+	0.0962946i	0.00381217	+	0.00552288i
$305$	2.96516	+	24.4203i	0.169785	+	1.39830i
$306$	0.717598	+	1.89215i	0.0410223	+	0.108167i
$307$	−9.17186	+	24.1842i	−0.523466	+	1.38027i	0.369117	+	0.929383i	$0.379660\pi$
$307$	−9.17186	+	24.1842i	−0.523466	+	1.38027i	−0.892583	+	0.450883i	$0.851109\pi$
$308$	−0.165511	−	0.239785i	−0.00943089	−	0.0136630i
$309$	−7.83412	−	1.93094i	−0.445668	−	0.109847i
$310$	−0.234734	−	0.618943i	−0.0133320	−	0.0351536i
$311$	−5.35689	+	14.1250i	−0.303761	+	0.800953i	0.693030	+	0.720909i	$0.256275\pi$
$311$	−5.35689	+	14.1250i	−0.303761	+	0.800953i	−0.996791	+	0.0800442i	$0.974494\pi$
$312$	−6.68012	−	0.237838i	−0.378187	−	0.0134649i
$313$	0.164086	+	0.432659i	0.00927469	+	0.0244553i	0.939574	−	0.342347i	$-0.111222\pi$
$313$	0.164086	+	0.432659i	0.00927469	+	0.0244553i	−0.930299	+	0.366802i	$0.880453\pi$
$314$	7.65289	−	6.77987i	0.431878	−	0.382610i
$315$	0.615154			0.0346600
$316$	9.62561			0.541483
$317$	−10.8448	+	9.60768i	−0.609106	+	0.539621i	−0.910304	−	0.413941i	$-0.864152\pi$
$317$	−10.8448	+	9.60768i	−0.609106	+	0.539621i	0.301198	+	0.953562i	$0.402614\pi$
$318$	−1.51481	+	0.795032i	−0.0849461	+	0.0445832i
$319$	−10.1794			−0.569937
$320$	−10.1801	−	5.34295i	−0.569087	−	0.298680i
$321$	−10.8408	−	9.60408i	−0.605072	−	0.536047i
$322$	0.265223	+	0.384241i	0.0147803	+	0.0214129i
$323$	−0.138232	−	0.122463i	−0.00769146	−	0.00681404i
$324$	−0.997766	−	1.44551i	−0.0554314	−	0.0803063i
$325$	17.7438	−	42.1938i	0.984251	−	2.34049i
$326$	−4.62403	+	6.69907i	−0.256102	+	0.371027i
$327$	2.29175	−	0.564866i	0.126734	−	0.0312372i
$328$	−13.2369	+	11.7269i	−0.730886	+	0.647509i
$329$	−1.51075	−	0.372366i	−0.0832903	−	0.0205292i
$330$	1.76270	+	1.56162i	0.0970336	+	0.0859643i
$331$	2.54231	+	2.25229i	0.139738	+	0.123797i	0.730096	−	0.683344i	$-0.239475\pi$
$331$	2.54231	+	2.25229i	0.139738	+	0.123797i	−0.590359	+	0.807141i	$0.701014\pi$
$332$	2.90534	−	7.66075i	0.159451	−	0.420438i
$333$	0.328235	−	0.475531i	0.0179872	−	0.0260589i
$334$	−3.35927	−	1.76308i	−0.183811	−	0.0964716i
$335$	−2.88181	+	23.7338i	−0.157450	+	1.29672i
$336$	−0.368870	−	0.0909184i	−0.0201235	−	0.00496000i
$337$	−15.4710			−0.842761			−0.421381	−	0.906884i	$-0.638454\pi$
$337$	−15.4710			−0.842761			−0.421381	+	0.906884i	$0.638454\pi$
$338$	−1.22434	+	6.29796i	−0.0665955	+	0.342564i
$339$	8.95788			0.486525
$340$	29.4154	+	7.25025i	1.59527	+	0.393200i
$341$	−0.0435968	+	0.359052i	−0.00236090	+	0.0194437i
$342$	−0.0196819	−	0.0103299i	−0.00106427	−	0.000558574i
$343$	−1.16123	+	1.68234i	−0.0627007	+	0.0908376i
$344$	6.94590	−	18.3148i	0.374498	−	0.987470i
$345$	20.3689	+	18.0453i	1.09663	+	0.971526i
$346$	3.48043	+	3.08339i	0.187109	+	0.165764i
$347$	17.2106	+	4.24204i	0.923916	+	0.227725i	0.672451	−	0.740142i	$-0.265242\pi$
$347$	17.2106	+	4.24204i	0.923916	+	0.227725i	0.251465	+	0.967866i	$0.419088\pi$
$348$	−11.7980	+	10.4521i	−0.632440	+	0.560293i
$349$	−10.6897	+	2.63477i	−0.572206	+	0.141036i	−0.514793	−	0.857314i	$-0.672131\pi$
$349$	−10.6897	+	2.63477i	−0.572206	+	0.141036i	−0.0574131	+	0.998351i	$0.518285\pi$
$350$	−0.520480	+	0.754046i	−0.0278208	+	0.0403054i
$351$	−3.25015	+	1.56093i	−0.173480	+	0.0833161i
$352$	−3.21541	−	4.65832i	−0.171382	−	0.248289i
$353$	−11.2405	−	9.95825i	−0.598274	−	0.530024i	0.308729	−	0.951150i	$-0.400097\pi$
$353$	−11.2405	−	9.95825i	−0.598274	−	0.530024i	−0.907002	+	0.421126i	$0.861635\pi$
$354$	−3.28207	−	4.75490i	−0.174440	−	0.252720i
$355$	32.3553	+	28.6643i	1.71724	+	1.52134i
$356$	−3.34916	−	1.75778i	−0.177505	−	0.0931620i
$357$	0.599628			0.0317357
$358$	0.386970	−	0.203097i	0.0204520	−	0.0107340i
$359$	−20.9411	+	18.5522i	−1.10523	+	0.979148i	−0.999883	−	0.0152878i	$-0.995134\pi$
$359$	−20.9411	+	18.5522i	−1.10523	+	0.979148i	−0.105346	+	0.994436i	$0.533595\pi$
$360$	7.79856			0.411020
$361$	−18.9980			−0.999893
$362$	6.39792	−	5.66806i	0.336267	−	0.297907i
$363$	3.44438	+	9.08207i	0.180783	+	0.476685i
$364$	−0.359004	+	0.853689i	−0.0188169	+	0.0447455i
$365$	22.1139	−	58.3097i	1.15750	−	3.05207i
$366$	1.02343	+	2.69857i	0.0534956	+	0.141056i
$367$	32.9710	+	8.12662i	1.72107	+	0.424206i	0.971370	−	0.237570i	$-0.0763509\pi$
$367$	32.9710	+	8.12662i	1.72107	+	0.424206i	0.749701	+	0.661776i	$0.230197\pi$
$368$	−9.54694	−	13.8311i	−0.497669	−	0.720998i
$369$	−3.38256	+	8.91908i	−0.176089	+	0.464309i
$370$	0.425374	+	1.12162i	0.0221142	+	0.0583102i
$371$	0.0611019	+	0.503219i	0.00317225	+	0.0261258i
$372$	0.318142	+	0.460909i	0.0164949	+	0.0238970i
$373$	−14.5169	+	3.57810i	−0.751658	+	0.185267i	−0.596489	−	0.802621i	$-0.703438\pi$
$373$	−14.5169	+	3.57810i	−0.751658	+	0.185267i	−0.155168	+	0.987888i	$0.549592\pi$
$374$	1.71821	+	1.52220i	0.0888466	+	0.0787112i
$375$	−11.4786	+	30.2665i	−0.592750	+	1.56295i
$376$	−19.1524	−	4.72063i	−0.987708	−	0.243448i
$377$	17.4211	+	27.2654i	0.897230	+	1.40424i
$378$	0.0700749	−	0.0172719i	0.00360427	−	0.000888372i
$379$	−0.622054	+	5.12307i	−0.0319528	+	0.263155i	0.967974	+	0.251051i	$0.0807760\pi$
$379$	−0.622054	+	5.12307i	−0.0319528	+	0.263155i	−0.999927	+	0.0121041i	$0.996147\pi$
$380$	−0.294654	+	0.154646i	−0.0151154	+	0.00793319i
$381$	0.798820	+	2.10631i	0.0409248	+	0.107910i
$382$	−5.53924	−	1.36530i	−0.283412	−	0.0698549i
$383$	−22.6879	+	20.0998i	−1.15930	+	1.02705i	−0.160098	+	0.987101i	$0.551181\pi$
$383$	−22.6879	+	20.0998i	−1.15930	+	1.02705i	−0.999202	+	0.0399484i	$0.987281\pi$
$384$	−10.9996	−	2.71115i	−0.561320	−	0.138353i
$385$	0.617865	−	0.324280i	0.0314893	−	0.0165269i
$386$	−7.25781	+	3.80919i	−0.369413	+	0.193883i
$387$	−1.27355	−	10.4886i	−0.0647381	−	0.533166i
$388$	−0.525637	−	4.32901i	−0.0266852	−	0.219772i
$389$	−12.1091	+	10.7277i	−0.613953	+	0.543915i	−0.911766	−	0.410709i	$-0.865281\pi$
$389$	−12.1091	+	10.7277i	−0.613953	+	0.543915i	0.297813	+	0.954624i	$0.403743\pi$
$390$	1.16608	−	7.39394i	0.0590468	−	0.374407i
$391$	19.8548	+	17.5898i	1.00410	+	0.889555i
$392$	−7.34944	+	10.6475i	−0.371203	+	0.537780i
$393$	5.07753	−	13.3883i	0.256127	−	0.675353i
$394$	0.283992	+	2.33888i	0.0143073	+	0.117831i
$395$	−2.77871	+	22.8848i	−0.139812	+	1.15146i
$396$	−1.76417	−	0.925907i	−0.0886528	−	0.0465286i
$397$	−7.31932	+	10.6039i	−0.367346	+	0.532193i	−0.962451	−	0.271455i	$-0.912495\pi$
$397$	−7.31932	+	10.6039i	−0.367346	+	0.532193i	0.595105	+	0.803648i	$0.297111\pi$
$398$	0.130433	+	0.343924i	0.00653803	+	0.0172394i
$399$	−0.00492996	+	0.00436756i	−0.000246806	+	0.000218651i
$400$	18.7352	−	27.1426i	0.936759	−	1.35713i
$401$	−0.944352	−	1.36813i	−0.0471587	−	0.0683212i	0.798695	−	0.601736i	$-0.205524\pi$
$401$	−0.944352	−	1.36813i	−0.0471587	−	0.0683212i	−0.845854	+	0.533415i	$0.820909\pi$
$402$	0.338104	+	2.78454i	0.0168631	+	0.138880i
$403$	1.03633	−	0.497709i	0.0516231	−	0.0247926i
$404$	3.75240	−	30.9038i	0.186689	−	1.53752i
$405$	3.72472	−	1.95488i	0.185083	−	0.0971390i
$406$	−0.229665	−	0.605576i	−0.0113981	−	0.0300542i
$407$	0.0790040	−	0.650656i	0.00391608	−	0.0322518i
$408$	7.60172			0.376341
$409$	3.79473	−	31.2524i	0.187638	−	1.54533i	−0.529444	−	0.848345i	$-0.677599\pi$
$409$	3.79473	−	31.2524i	0.187638	−	1.54533i	0.717082	−	0.696989i	$-0.245477\pi$
$410$	−11.2496	−	16.2979i	−0.555579	−	0.804895i
$411$	−5.96529	+	1.47031i	−0.294246	+	0.0725251i
$412$	−8.05055	+	11.6632i	−0.396622	+	0.574607i
$413$	−1.66222	+	0.409701i	−0.0817926	+	0.0201601i
$414$	2.82698	+	1.48371i	0.138938	+	0.0729205i
$415$	17.3746	+	9.11890i	0.852886	+	0.447629i
$416$	−6.97440	+	16.5847i	−0.341948	+	0.813132i
$417$	−2.27298	+	1.19295i	−0.111309	+	0.0584192i
$418$	−0.0252140			−0.00123326
$419$	−2.38435	−	1.25140i	−0.116483	−	0.0611351i	0.405475	−	0.914106i	$-0.367106\pi$
$419$	−2.38435	−	1.25140i	−0.116483	−	0.0611351i	−0.521958	+	0.852971i	$0.674798\pi$
$420$	0.383142	−	1.01026i	0.0186954	−	0.0492957i
$421$	4.21116	+	34.6820i	0.205239	+	1.69030i	0.623382	+	0.781917i	$0.285758\pi$
$421$	4.21116	+	34.6820i	0.205239	+	1.69030i	−0.418143	+	0.908381i	$0.637319\pi$
$422$	−6.70583	+	1.65284i	−0.326434	+	0.0804589i
$423$	−10.3308	+	2.54632i	−0.502302	+	0.123806i
$424$	0.774613	+	6.37951i	0.0376185	+	0.309816i
$425$	−18.4589	+	48.6721i	−0.895388	+	2.36094i
$426$	4.49055	+	2.35682i	0.217568	+	0.114188i
$427$	0.855184			0.0413852
$428$	−22.5247	+	11.8219i	−1.08877	+	0.571433i
$429$	−2.44163	+	3.28113i	−0.117883	+	0.158415i
$430$	19.4224	+	10.1936i	0.936630	+	0.491581i
$431$	24.5745	+	12.8977i	1.18371	+	0.621261i	0.937510	−	0.347958i	$-0.113125\pi$
$431$	24.5745	+	12.8977i	1.18371	+	0.621261i	0.246203	+	0.969218i	$0.420817\pi$
$432$	−2.52241	+	0.621719i	−0.121360	+	0.0299125i
$433$	0.237010	−	0.343368i	0.0113900	−	0.0165012i	−0.817248	−	0.576287i	$-0.804501\pi$
$433$	0.237010	−	0.343368i	0.0113900	−	0.0165012i	0.828637	+	0.559786i	$0.189117\pi$
$434$	−0.0223437	+	0.00550723i	−0.00107253	+	0.000264356i
$435$	−21.4439	−	31.0669i	−1.02816	−	1.48954i
$436$	0.499718	−	4.11554i	0.0239321	−	0.197099i
$437$	−0.291361			−0.0139377
$438$	0.881914	−	7.26321i	0.0421395	−	0.347050i
$439$	3.05246	+	8.04868i	0.145686	+	0.384143i	0.987919	−	0.154971i	$-0.0495285\pi$
$439$	3.05246	+	8.04868i	0.145686	+	0.384143i	−0.842233	+	0.539114i	$0.818759\pi$
$440$	7.83291	−	4.11103i	0.373420	−	0.195986i
$441$	−0.841179	+	6.92773i	−0.0400561	+	0.329892i
$442$	1.13665	−	7.20731i	0.0540648	−	0.342817i
$443$	1.70753	+	14.0627i	0.0811271	+	0.668141i	0.975372	+	0.220564i	$0.0707899\pi$
$443$	1.70753	+	14.0627i	0.0811271	+	0.668141i	−0.894245	+	0.447577i	$0.852287\pi$
$444$	−0.576522	−	0.835237i	−0.0273605	−	0.0396386i
$445$	5.14592	−	7.45516i	0.243940	−	0.353408i
$446$	−7.70664	+	6.82749i	−0.364920	+	0.323291i
$447$	−4.68386	−	12.3503i	−0.221539	−	0.584151i
$448$	−0.227047	+	0.328934i	−0.0107269	+	0.0155407i
$449$	29.1338	+	15.2906i	1.37491	+	0.721607i	0.980350	−	0.197264i	$-0.0632057\pi$
$449$	29.1338	+	15.2906i	1.37491	+	0.721607i	0.394557	+	0.918871i	$0.370898\pi$
$450$	−0.755211	+	6.21972i	−0.0356010	+	0.293201i
$451$	1.30426	+	10.7415i	0.0614150	+	0.505798i
$452$	5.57931	−	14.7114i	0.262429	−	0.691968i
$453$	−0.0946314	+	0.137097i	−0.00444617	+	0.00644139i
$454$	4.58683	+	4.06358i	0.215271	+	0.190713i
$455$	−1.92600	−	1.09997i	−0.0902921	−	0.0515673i
$456$	−0.0624990	+	0.0553693i	−0.00292678	+	0.00259290i
$457$	1.96950	+	16.2203i	0.0921291	+	0.758752i	0.963422	+	0.267988i	$0.0863589\pi$
$457$	1.96950	+	16.2203i	0.0921291	+	0.758752i	−0.871293	+	0.490763i	$0.836718\pi$
$458$	−0.174463	−	1.43683i	−0.00815210	−	0.0671386i
$459$	3.63071	−	1.90554i	0.169467	−	0.0889431i
$460$	42.3222	−	22.2124i	1.97328	−	1.03566i
$461$	3.83002	+	0.944014i	0.178382	+	0.0439671i	0.327495	−	0.944853i	$-0.393796\pi$
$461$	3.83002	+	0.944014i	0.178382	+	0.0439671i	−0.149113	+	0.988820i	$0.547642\pi$
$462$	0.0612787	−	0.0542882i	0.00285094	−	0.00252572i
$463$	22.2215	+	5.47710i	1.03272	+	0.254542i	0.719027	−	0.694982i	$-0.244588\pi$
$463$	22.2215	+	5.47710i	1.03272	+	0.254542i	0.313692	+	0.949525i	$0.398434\pi$
$464$	8.26700	+	21.7983i	0.383786	+	1.01196i
$465$	−1.18765	+	0.623324i	−0.0550757	+	0.0289060i
$466$	−0.248381	+	2.04560i	−0.0115060	+	0.0947607i
$467$	20.1460	−	4.96554i	0.932245	−	0.229778i	0.256188	−	0.966627i	$-0.417533\pi$
$467$	20.1460	−	4.96554i	0.932245	−	0.229778i	0.676057	+	0.736849i	$0.263687\pi$
$468$	0.539173	+	6.30990i	0.0249233	+	0.291675i
$469$	0.806992	+	0.198906i	0.0372634	+	0.00918461i
$470$	7.83295	−	20.6538i	0.361307	−	0.952689i
$471$	−15.5065	−	13.7375i	−0.714501	−	0.632993i
$472$	−21.0726	+	5.19394i	−0.969947	+	0.239070i
$473$	−6.80826	−	9.86347i	−0.313044	−	0.453523i
$474$	0.326009	+	2.68492i	0.0149741	+	0.123323i
$475$	−0.202754	−	0.534618i	−0.00930299	−	0.0245300i
$476$	0.373471	−	0.984762i	0.0171180	−	0.0451365i
$477$	1.96914	+	2.85279i	0.0901606	+	0.130620i
$478$	0.210512	+	0.0518866i	0.00962861	+	0.00237324i
$479$	−10.3534	−	27.2997i	−0.473060	−	1.24736i	−0.933151	−	0.359485i	$-0.882952\pi$
$479$	−10.3534	−	27.2997i	−0.473060	−	1.24736i	0.460091	−	0.887872i	$-0.347817\pi$
$480$	7.44334	−	19.6265i	0.339740	−	0.895821i
$481$	−1.87798	+	0.901924i	−0.0856286	+	0.0411242i
$482$	0.855585	+	2.25599i	0.0389708	+	0.102758i
$483$	0.708106	−	0.627328i	0.0322200	−	0.0285444i
$484$	17.0607			0.775486
$485$	10.4439			0.474233
$486$	0.369411	−	0.327270i	0.0167568	−	0.0148453i
$487$	−18.3245	+	9.61743i	−0.830361	+	0.435807i	−0.825651	−	0.564182i	$-0.809192\pi$
$487$	−18.3245	+	9.61743i	−0.830361	+	0.435807i	−0.00471053	+	0.999989i	$0.501499\pi$
$488$	10.8415			0.490772
$489$	14.6042	+	7.66488i	0.660425	+	0.346618i
$490$	−10.8444	−	9.60732i	−0.489901	−	0.434014i
$491$	−7.36116	−	10.6645i	−0.332205	−	0.481281i	0.620914	−	0.783879i	$-0.286762\pi$
$491$	−7.36116	−	10.6645i	−0.332205	−	0.481281i	−0.953118	+	0.302597i	$0.902146\pi$
$492$	12.5409	+	11.1103i	0.565389	+	0.500891i
$493$	−20.9027	−	30.2828i	−0.941409	−	1.36387i
$494$	0.0431513	+	0.0675354i	0.00194147	+	0.00303856i
$495$	2.71061	−	3.92699i	0.121833	−	0.176505i
$496$	0.804284	−	0.198238i	0.0361134	−	0.00890116i
$497$	1.12480	−	0.996487i	0.0504542	−	0.0446985i
$498$	2.23525	+	0.550940i	0.100164	+	0.0246882i
$499$	10.2799	+	9.10721i	0.460192	+	0.407695i	0.861109	−	0.508420i	$-0.169770\pi$
$499$	10.2799	+	9.10721i	0.460192	+	0.407695i	−0.400917	+	0.916114i	$0.631309\pi$
$500$	42.5570	+	37.7022i	1.90321	+	1.68609i
$501$	−2.72591	+	7.18762i	−0.121785	+	0.321119i
$502$	3.25772	−	4.71963i	0.145399	−	0.210647i
$503$	−28.9713	−	15.2053i	−1.29177	−	0.677971i	−0.327989	−	0.944681i	$-0.606371\pi$
$503$	−28.9713	−	15.2053i	−1.29177	−	0.677971i	−0.963777	+	0.266710i	$0.914063\pi$
$504$	0.0326786	−	0.269133i	0.00145562	−	0.0119881i
$505$	72.3900	+	17.8425i	3.22131	+	0.793982i
$506$	3.62157			0.160999
$507$	12.9671	+	0.924528i	0.575888	+	0.0410597i
$508$	3.95672			0.175551
$509$	−14.9445	−	3.68350i	−0.662405	−	0.163268i	−0.106240	−	0.994340i	$-0.533881\pi$
$509$	−14.9445	−	3.68350i	−0.662405	−	0.163268i	−0.556164	+	0.831072i	$0.687727\pi$
$510$	−1.02608	+	8.45055i	−0.0454357	+	0.374197i
$511$	−1.91964	−	1.00750i	−0.0849197	−	0.0445693i
$512$	−12.8360	+	18.5961i	−0.567275	+	0.821839i
$513$	−0.0159710	+	0.0421121i	−0.000705137	+	0.00185929i
$514$	−2.24035	−	1.98478i	−0.0988177	−	0.0875448i
$515$	−25.4052	−	22.5070i	−1.11949	−	0.991777i
$516$	−18.0186	−	4.44118i	−0.793223	−	0.195512i
$517$	−9.03404	+	8.00346i	−0.397317	+	0.351992i
$518$	0.0404902	−	0.00997994i	0.00177904	−	0.000438494i
$519$	5.35205	−	7.75378i	0.234929	−	0.340353i
$520$	−24.4166	−	13.9447i	−1.07074	−	0.611517i
$521$	−17.8703	−	25.8896i	−0.782911	−	1.13424i	−0.987841	−	0.155466i	$-0.950312\pi$
$521$	−17.8703	−	25.8896i	−0.782911	−	1.13424i	0.204930	−	0.978777i	$-0.434303\pi$
$522$	−3.31505	−	2.93688i	−0.145096	−	0.128544i
$523$	8.71595	+	12.6272i	0.381122	+	0.552150i	0.965858	−	0.259074i	$-0.0834172\pi$
$523$	8.71595	+	12.6272i	0.381122	+	0.552150i	−0.584736	+	0.811224i	$0.698802\pi$
$524$	−18.8251	−	16.6776i	−0.822377	−	0.728562i
$525$	1.64385	+	0.862757i	0.0717433	+	0.0376538i
$526$	0.142836			0.00622795
$527$	−1.15767	+	0.607591i	−0.0504288	+	0.0264671i
$528$	−2.20579	+	1.95416i	−0.0959945	+	0.0850437i
$529$	18.8491			0.819527
$530$	−7.19643			−0.312593
$531$	−8.76267	+	7.76305i	−0.380267	+	0.336888i
$532$	0.00410223	+	0.0108167i	0.000177854	+	0.000468963i
$533$	26.5389	−	21.8765i	1.14953	−	0.947576i
$534$	0.376873	−	0.993734i	0.0163089	−	0.0430031i
$535$	−21.6040	−	56.9649i	−0.934020	−	2.46281i
$536$	10.2306	+	2.52161i	0.441893	+	0.108917i
$537$	−0.503032	−	0.728767i	−0.0217074	−	0.0314486i
$538$	2.81553	−	7.42393i	0.121386	−	0.320068i
$539$	2.80709	+	7.40168i	0.120910	+	0.318813i
$540$	−0.890588	−	7.33465i	−0.0383248	−	0.315633i
$541$	23.3446	+	33.8204i	1.00366	+	1.45405i	0.887491	+	0.460824i	$0.152446\pi$
$541$	23.3446	+	33.8204i	1.00366	+	1.45405i	0.116170	+	0.993229i	$0.462938\pi$
$542$	4.90416	−	1.20877i	0.210651	−	0.0519209i
$543$	−12.9636	−	11.4848i	−0.556322	−	0.492859i
$544$	7.25546	−	19.1311i	0.311075	−	0.820238i
$545$	9.64039	+	2.37614i	0.412949	+	0.101783i
$546$	−0.250283	−	0.0712253i	−0.0107111	−	0.00304816i
$547$	−39.1833	+	9.65782i	−1.67536	+	0.412939i	−0.958685	−	0.284470i	$-0.908182\pi$
$547$	−39.1833	+	9.65782i	−1.67536	+	0.412939i	−0.716673	+	0.697409i	$0.754336\pi$
$548$	−1.30073	+	10.7125i	−0.0555646	+	0.457615i
$549$	5.17808	−	2.71767i	0.220995	−	0.115987i
$550$	2.52021	+	6.64524i	0.107462	+	0.283354i
$551$	0.392429	+	0.0967250i	0.0167180	+	0.00412062i
$552$	8.97695	−	7.95288i	0.382084	−	0.338497i
$553$	0.778123	+	0.191790i	0.0330891	+	0.00815574i
$554$	6.07360	−	3.18767i	0.258043	−	0.135431i
$555$	2.15219	−	1.12956i	0.0913555	−	0.0479471i
$556$	0.543475	+	4.47592i	0.0230485	+	0.189821i
$557$	2.29339	+	18.8878i	0.0971742	+	0.800302i	0.957075	+	0.289840i	$0.0936022\pi$
$557$	2.29339	+	18.8878i	0.0971742	+	0.800302i	−0.859901	+	0.510461i	$0.829475\pi$
$558$	−0.117789	+	0.104352i	−0.00498639	+	0.00441755i
$559$	−14.7675	+	35.1162i	−0.624599	+	1.48526i
$560$	−1.19620	−	1.05974i	−0.0505489	−	0.0447824i
$561$	2.64219	−	3.82787i	0.111553	−	0.161613i
$562$	1.34559	−	3.54803i	0.0567602	−	0.149664i
$563$	1.03594	+	8.53177i	0.0436599	+	0.359571i	0.998123	+	0.0612423i	$0.0195062\pi$
$563$	1.03594	+	8.53177i	0.0436599	+	0.359571i	−0.954463	+	0.298329i	$0.903571\pi$
$564$	−2.25264	+	18.5522i	−0.0948533	+	0.781187i
$565$	33.3656	+	17.5116i	1.40370	+	0.736719i
$566$	−1.99779	+	2.89429i	−0.0839733	+	0.121656i
$567$	−0.0518564	−	0.136734i	−0.00217776	−	0.00574229i
$568$	14.2596	−	12.6329i	0.598317	−	0.530063i
$569$	24.4722	−	35.4542i	1.02593	−	1.48632i	0.159384	−	0.987217i	$-0.449049\pi$
$569$	24.4722	−	35.4542i	1.02593	−	1.48632i	0.866545	−	0.499099i	$-0.166336\pi$
$570$	−0.0531159	−	0.0769516i	−0.00222478	−	0.00322315i
$571$	−1.95389	−	16.0918i	−0.0817679	−	0.673419i	−0.974746	−	0.223318i	$-0.928311\pi$
$571$	−1.95389	−	16.0918i	−0.0817679	−	0.673419i	0.892978	−	0.450101i	$-0.148612\pi$
$572$	3.86783	+	6.05348i	0.161722	+	0.253109i
$573$	−1.39336	+	11.4754i	−0.0582086	+	0.479391i
$574$	−0.609590	+	0.319937i	−0.0254438	+	0.0133539i
$575$	29.1222	+	76.7890i	1.21448	+	3.20232i
$576$	−0.329442	+	2.71320i	−0.0137268	+	0.113050i
$577$	−5.45668			−0.227165			−0.113582	−	0.993529i	$-0.536233\pi$
$577$	−5.45668			−0.227165			−0.113582	+	0.993529i	$0.536233\pi$
$578$	0.0111169	−	0.0915556i	0.000462401	−	0.00380821i
$579$	9.43461	+	13.6684i	0.392089	+	0.568039i
$580$	−64.3770	+	15.8675i	−2.67311	+	0.658862i
$581$	0.387504	−	0.561397i	0.0160764	−	0.0232907i
$582$	1.18971	−	0.293237i	0.0493151	−	0.0121551i
$583$	3.48167	+	1.82732i	0.144196	+	0.0756799i
$584$	−24.3360	−	12.7725i	−1.00703	−	0.528530i
$585$	−15.1574	−	0.539660i	−0.626679	−	0.0223122i
$586$	−7.87721	+	4.13428i	−0.325405	+	0.170786i
$587$	−29.8035			−1.23012			−0.615060	−	0.788480i	$-0.710868\pi$
$587$	−29.8035			−1.23012			−0.615060	+	0.788480i	$0.710868\pi$
$588$	10.8534	+	5.69632i	0.447588	+	0.234912i
$589$	0.00509243	−	0.0134276i	0.000209830	−	0.000553276i
$590$	−2.92952	−	24.1268i	−0.120606	−	0.993283i
$591$	4.63519	−	1.14247i	0.190666	−	0.0469950i
$592$	−1.45748	+	0.359238i	−0.0599022	+	0.0147646i
$593$	−0.543562	−	4.47664i	−0.0223214	−	0.183834i	0.977284	−	0.211936i	$-0.0679767\pi$
$593$	−0.543562	−	4.47664i	−0.0223214	−	0.183834i	−0.999605	+	0.0281021i	$0.991054\pi$
$594$	0.198518	−	0.523448i	0.00814528	−	0.0214773i
$595$	2.23345	+	1.17220i	0.0915623	+	0.0480556i
$596$	−23.2001			−0.950314
$597$	0.659931	−	0.346359i	0.0270092	−	0.0141755i
$598$	−6.19798	−	9.70035i	−0.253454	−	0.396677i
$599$	31.2779	+	16.4159i	1.27798	+	0.670736i	0.960698	−	0.277594i	$-0.0895371\pi$
$599$	31.2779	+	16.4159i	1.27798	+	0.670736i	0.317283	+	0.948331i	$0.397229\pi$
$600$	20.8397	+	10.9375i	0.850777	+	0.446522i
$601$	8.96799	−	2.21041i	0.365812	−	0.0901646i	−0.0521250	−	0.998641i	$-0.516599\pi$
$601$	8.96799	−	2.21041i	0.365812	−	0.0901646i	0.417937	+	0.908476i	$0.362753\pi$
$602$	0.433175	−	0.627563i	0.0176549	−	0.0255776i
$603$	5.51838	−	1.36016i	0.224726	−	0.0553900i
$604$	0.166213	+	0.240802i	0.00676312	+	0.00979808i
$605$	−4.92506	+	40.5616i	−0.200232	+	1.64906i
$606$	8.74723			0.355332
$607$	1.20050	−	9.88699i	0.0487267	−	0.401301i	−0.947856	−	0.318699i	$-0.896754\pi$
$607$	1.20050	−	9.88699i	0.0487267	−	0.401301i	0.996583	−	0.0826015i	$-0.0263229\pi$
$608$	0.0796945	+	0.210137i	0.00323204	+	0.00852219i
$609$	−1.16199	+	0.609862i	−0.0470864	+	0.0247129i
$610$	−1.46339	+	12.0521i	−0.0592509	+	0.487975i
$611$	36.8981	+	10.5004i	1.49274	+	0.424801i
$612$	−0.868109	−	7.14952i	−0.0350912	−	0.289002i
$613$	9.72788	+	14.0933i	0.392905	+	0.569222i	0.968657	−	0.248403i	$-0.0799058\pi$
$613$	9.72788	+	14.0933i	0.392905	+	0.569222i	−0.575751	+	0.817625i	$0.695290\pi$
$614$	−7.25142	+	10.5055i	−0.292643	+	0.423967i
$615$	−30.0349	+	26.6086i	−1.21112	+	1.07296i
$616$	−0.109051	−	0.287545i	−0.00439381	−	0.0115855i
$617$	−7.37490	+	10.6844i	−0.296902	+	0.430137i	−0.942836	−	0.333256i	$-0.891853\pi$
$617$	−7.37490	+	10.6844i	−0.296902	+	0.430137i	0.645934	+	0.763393i	$0.276468\pi$
$618$	−3.52595	−	1.85056i	−0.141835	−	0.0744405i
$619$	1.54453	−	12.7203i	0.0620797	−	0.511273i	−0.928189	−	0.372108i	$-0.878635\pi$
$619$	1.54453	−	12.7203i	0.0620797	−	0.511273i	0.990269	−	0.139165i	$-0.0444418\pi$
$620$	0.283968	+	2.33869i	0.0114044	+	0.0939240i
$621$	2.29397	−	6.04870i	0.0920539	−	0.242726i
$622$	−4.23524	+	6.13581i	−0.169818	+	0.246023i
$623$	−0.235719	−	0.208829i	−0.00944387	−	0.00836654i
$624$	9.00918	+	2.56382i	0.360656	+	0.102635i
$625$	−54.4097	+	48.2027i	−2.17639	+	1.92811i
$626$	0.0275270	+	0.226705i	0.00110020	+	0.00906095i
$627$	0.00615813	+	0.0507168i	0.000245932	+	0.00202543i
$628$	−32.2191	+	16.9099i	−1.28568	+	0.674778i
$629$	2.09787	−	1.10105i	0.0836476	−	0.0439016i
$630$	0.294774	+	0.0726553i	0.0117441	+	0.00289466i
$631$	11.4016	−	10.1009i	0.453890	−	0.402111i	−0.404963	−	0.914333i	$-0.632716\pi$
$631$	11.4016	−	10.1009i	0.453890	−	0.402111i	0.858853	+	0.512221i	$0.171177\pi$
$632$	9.86457	+	2.43140i	0.392392	+	0.0967158i
$633$	4.96240	+	13.0848i	0.197238	+	0.520073i
$634$	−6.33146	+	3.32301i	−0.251454	+	0.131973i
$635$	−1.14222	+	9.40704i	−0.0453277	+	0.373307i
$636$	5.91156	−	1.45707i	0.234409	−	0.0577765i
$637$	15.0213	−	20.1860i	0.595164	−	0.799799i
$638$	−4.87784	−	1.20228i	−0.193115	−	0.0475987i
$639$	3.64389	−	9.60814i	0.144150	−	0.380092i
$640$	−35.6704	−	31.6012i	−1.41000	−	1.24915i
$641$	11.5965	−	2.85828i	0.458034	−	0.112895i	−0.00354618	−	0.999994i	$-0.501129\pi$
$641$	11.5965	−	2.85828i	0.458034	−	0.112895i	0.461580	+	0.887098i	$0.347283\pi$
$642$	−4.06043	−	5.88254i	−0.160252	−	0.232166i
$643$	5.65771	+	46.5954i	0.223118	+	1.83754i	0.487497	+	0.873125i	$0.337910\pi$
$643$	5.65771	+	46.5954i	0.223118	+	1.83754i	−0.264379	+	0.964419i	$0.585167\pi$
$644$	−0.589218	−	1.55364i	−0.0232184	−	0.0612220i
$645$	15.7604	−	41.5568i	0.620566	−	1.63630i
$646$	−0.0517752	−	0.0750093i	−0.00203707	−	0.00295120i
$647$	45.5410	+	11.2249i	1.79040	+	0.441295i	0.987866	−	0.155308i	$-0.0496370\pi$
$647$	45.5410	+	11.2249i	1.79040	+	0.441295i	0.802537	+	0.596603i	$0.203483\pi$
$648$	−0.657404	−	1.73343i	−0.0258253	−	0.0680956i
$649$	−4.70896	+	12.4165i	−0.184843	+	0.487391i
$650$	13.4861	−	18.1230i	0.528968	−	0.710843i
$651$	0.0165346	+	0.0435983i	0.000648044	+	0.00170875i
$652$	21.6840	−	19.2104i	0.849212	−	0.752336i
$653$	27.0970			1.06039			0.530193	−	0.847877i	$-0.322119\pi$
$653$	27.0970			1.06039			0.530193	+	0.847877i	$0.322119\pi$
$654$	1.16489			0.0455510
$655$	45.0851	−	39.9419i	1.76162	−	1.56066i
$656$	21.9428	−	11.5165i	0.856721	−	0.449642i
$657$	−14.8250			−0.578378
$658$	−0.679952	−	0.356866i	−0.0265073	−	0.0139121i
$659$	−32.8512	−	29.1037i	−1.27970	−	1.13372i	−0.983948	−	0.178454i	$-0.942891\pi$
$659$	−32.8512	−	29.1037i	−1.27970	−	1.13372i	−0.295754	−	0.955264i	$-0.595571\pi$
$660$	−4.76099	−	6.89749i	−0.185321	−	0.268484i
$661$	2.00789	+	1.77883i	0.0780978	+	0.0691886i	0.701269	−	0.712897i	$-0.252617\pi$
$661$	2.00789	+	1.77883i	0.0780978	+	0.0691886i	−0.623171	+	0.782086i	$0.714156\pi$
$662$	0.952225	+	1.37954i	0.0370093	+	0.0536172i
$663$	−14.7748	−	0.526039i	−0.573805	−	0.0204296i
$664$	4.91255	−	7.11705i	0.190644	−	0.276195i
$665$	−0.0269008	+	0.00663045i	−0.00104317	+	0.000257118i
$666$	0.213451	−	0.189101i	0.00827105	−	0.00732751i
$667$	−56.3659	−	13.8929i	−2.18250	−	0.537937i
$668$	10.1064	+	8.95346i	0.391027	+	0.346420i
$669$	15.6154	+	13.8340i	0.603726	+	0.534855i
$670$	−4.18410	+	11.0326i	−0.161646	+	0.426225i
$671$	3.76827	−	5.45928i	0.145472	−	0.210753i
$672$	−0.646131	−	0.339116i	−0.0249250	−	0.0130817i
$673$	−3.77184	+	31.0639i	−0.145394	+	1.19742i	0.719146	+	0.694859i	$0.244533\pi$
$673$	−3.77184	+	31.0639i	−0.145394	+	1.19742i	−0.864539	+	0.502565i	$0.832390\pi$
$674$	−7.41353	−	1.82727i	−0.285558	−	0.0703838i
$675$	12.6951			0.488636
$676$	9.59474	−	20.7199i	0.369029	−	0.796919i
$677$	−27.7996			−1.06842			−0.534212	−	0.845350i	$-0.679392\pi$
$677$	−27.7996			−1.06842			−0.534212	+	0.845350i	$0.679392\pi$
$678$	4.29250	+	1.05801i	0.164853	+	0.0406325i
$679$	0.0437635	−	0.360425i	0.00167949	−	0.0138318i
$680$	28.3143	+	14.8605i	1.08580	+	0.569873i
$681$	7.05343	−	10.2187i	0.270288	−	0.391580i
$682$	−0.0632983	+	0.166904i	−0.00242382	+	0.00639108i
$683$	−28.5036	−	25.2520i	−1.09066	−	0.966240i	−0.0910982	−	0.995842i	$-0.529038\pi$
$683$	−28.5036	−	25.2520i	−1.09066	−	0.966240i	−0.999562	+	0.0296015i	$0.990576\pi$
$684$	0.0592129	+	0.0524581i	0.00226406	+	0.00200578i
$685$	−25.0933	−	6.18495i	−0.958767	−	0.236315i
$686$	−0.755147	+	0.669002i	−0.0288317	+	0.0255426i
$687$	−2.84750	+	0.701846i	−0.108639	+	0.0267771i
$688$	−15.5926	+	22.5897i	−0.594461	+	0.861225i
$689$	−1.06408	−	12.4529i	−0.0405384	−	0.474417i
$690$	7.62922	+	11.0528i	0.290439	+	0.420774i
$691$	−38.0402	−	33.7007i	−1.44712	−	1.28204i	−0.893347	−	0.449367i	$-0.851649\pi$
$691$	−38.0402	−	33.7007i	−1.44712	−	1.28204i	−0.553772	−	0.832668i	$-0.686812\pi$
$692$	−9.40050	−	13.6190i	−0.357353	−	0.517716i
$693$	−0.124165	−	0.110000i	−0.00471662	−	0.00417856i
$694$	7.74610	+	4.06547i	0.294038	+	0.154323i
$695$	−10.7983			−0.409604
$696$	−14.7311	+	7.73146i	−0.558380	+	0.293060i
$697$	−29.2768	+	25.9370i	−1.10894	+	0.982433i
$698$	−5.43356			−0.205663
$699$	4.17530			0.157924
$700$	2.44075	−	2.16231i	0.0922516	−	0.0817278i
$701$	4.19686	+	11.0662i	0.158513	+	0.417965i	0.990619	−	0.136652i	$-0.0436341\pi$
$701$	4.19686	+	11.0662i	0.158513	+	0.417965i	−0.832106	+	0.554617i	$0.812865\pi$
$702$	−1.74179	+	0.364104i	−0.0657397	+	0.0137422i
$703$	−0.00922826	+	0.0243329i	−0.000348050	+	0.000917733i
$704$	1.09938	+	2.89882i	0.0414343	+	0.109253i
$705$	−43.4572	−	10.7112i	−1.63669	−	0.403409i
$706$	−4.21016	−	6.09948i	−0.158452	−	0.229557i
$707$	0.919095	−	2.42346i	0.0345661	−	0.0911434i
$708$	7.29145	+	19.2260i	0.274029	+	0.722556i
$709$	−4.04117	−	33.2820i	−0.151769	−	1.24993i	−0.847175	−	0.531315i	$-0.821698\pi$
$709$	−4.04117	−	33.2820i	−0.151769	−	1.24993i	0.695405	−	0.718618i	$-0.255225\pi$
$710$	12.1187	+	17.5570i	0.454808	+	0.658903i
$711$	5.32097	−	1.31150i	0.199552	−	0.0491851i
$712$	−2.98830	−	2.64740i	−0.111991	−	0.0992156i
$713$	−0.731443	+	1.92866i	−0.0273928	+	0.0722288i
$714$	0.287334	+	0.0708215i	0.0107532	+	0.00265043i
$715$	−15.5086	+	7.44820i	−0.579989	+	0.278547i
$716$	−1.51016	+	0.372220i	−0.0564372	+	0.0139105i
$717$	0.0529531	−	0.436108i	0.00197757	−	0.0162868i
$718$	−12.2259	+	6.41665i	−0.456266	+	0.239467i
$719$	−1.69126	−	4.45949i	−0.0630734	−	0.166311i	0.899774	−	0.436355i	$-0.143731\pi$
$719$	−1.69126	−	4.45949i	−0.0630734	−	0.166311i	−0.962848	+	0.270044i	$0.912962\pi$
$720$	−10.6107	−	2.61530i	−0.395437	−	0.0974664i
$721$	−0.883187	+	0.782435i	−0.0328916	+	0.0291394i
$722$	−9.10359	−	2.24383i	−0.338800	−	0.0835068i
$723$	4.32886	−	2.27196i	0.160992	−	0.0844951i
$724$	−26.9356	+	14.1369i	−1.00105	+	0.525393i
$725$	−13.7321	−	113.094i	−0.509996	−	4.20020i
$726$	0.577826	+	4.75883i	0.0214451	+	0.176617i
$727$	6.47375	−	5.73524i	0.240098	−	0.212708i	−0.534489	−	0.845175i	$-0.679496\pi$
$727$	6.47375	−	5.73524i	0.240098	−	0.212708i	0.774587	+	0.632467i	$0.217958\pi$
$728$	−0.583555	+	0.784199i	−0.0216280	+	0.0290643i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	17.4836	−	25.3294i	0.647098	−	0.937483i
$731$	15.3626	−	40.5079i	0.568207	−	1.49824i
$732$	−1.23809	−	10.1966i	−0.0457611	−	0.376877i
$733$	2.04575	−	16.8483i	0.0755615	−	0.622305i	−0.904904	−	0.425615i	$-0.860058\pi$
$733$	2.04575	−	16.8483i	0.0755615	−	0.622305i	0.980466	−	0.196690i	$-0.0630192\pi$
$734$	14.8395	+	7.78835i	0.547734	+	0.287473i
$735$	−16.6761	+	24.1595i	−0.615106	+	0.891135i
$736$	−11.4468	−	30.1827i	−0.421935	−	1.11255i
$737$	4.82568	−	4.27518i	0.177756	−	0.157478i
$738$	−2.67431	+	3.87440i	−0.0984426	+	0.142619i
$739$	−12.0786	−	17.4989i	−0.444319	−	0.643708i	0.535278	−	0.844676i	$-0.320207\pi$
$739$	−12.0786	−	17.4989i	−0.444319	−	0.643708i	−0.979598	+	0.200968i	$0.935591\pi$
$740$	−0.514593	−	4.23806i	−0.0189168	−	0.155794i
$741$	0.125305	−	0.103291i	0.00460320	−	0.00379450i
$742$	−0.0301555	+	0.248353i	−0.00110704	+	0.00911733i
$743$	0.175994	−	0.0923689i	0.00645660	−	0.00338868i	−0.461492	−	0.887144i	$-0.652686\pi$
$743$	0.175994	−	0.0923689i	0.00645660	−	0.00338868i	0.467948	+	0.883756i	$0.344993\pi$
$744$	0.209616	+	0.552713i	0.00768491	+	0.0202634i
$745$	6.69739	−	55.1579i	0.245373	−	2.02083i
$746$	−7.37893			−0.270162
$747$	0.562264	−	4.63066i	0.0205722	−	0.169427i
$748$	−4.64082	−	6.72339i	−0.169685	−	0.245832i
$749$	−2.05642	+	0.506863i	−0.0751400	+	0.0185204i
$750$	−9.07512	+	13.1476i	−0.331377	+	0.480082i
$751$	−11.4040	+	2.81083i	−0.416137	+	0.102568i	−0.441824	−	0.897102i	$-0.645669\pi$
$751$	−11.4040	+	2.81083i	−0.416137	+	0.102568i	0.0256877	+	0.999670i	$0.491822\pi$
$752$	24.4755	+	12.8457i	0.892531	+	0.468436i
$753$	−10.2890	−	5.40006i	−0.374950	−	0.196789i
$754$	5.12766	+	15.1228i	0.186738	+	0.550741i
$755$	−0.620485	+	0.325655i	−0.0225817	+	0.0118518i
$756$	−0.256855			−0.00934173
$757$	41.2970	+	21.6744i	1.50097	+	0.787768i	0.997106	−	0.0760175i	$-0.0242205\pi$
$757$	41.2970	+	21.6744i	1.50097	+	0.787768i	0.503860	+	0.863785i	$0.331913\pi$
$758$	−0.903162	+	2.38144i	−0.0328043	+	0.0864979i
$759$	−0.884514	−	7.28463i	−0.0321058	−	0.264415i
$760$	−0.341032	+	0.0840568i	−0.0123705	+	0.00304906i
$761$	−12.7407	+	3.14030i	−0.461849	+	0.113836i	−0.463373	−	0.886163i	$-0.653361\pi$
$761$	−12.7407	+	3.14030i	−0.461849	+	0.113836i	0.00152388	+	0.999999i	$0.499515\pi$
$762$	0.134009	+	1.10367i	0.00485465	+	0.0399816i
$763$	0.122399	−	0.322739i	0.00443113	−	0.0116839i
$764$	17.9781	+	9.43562i	0.650424	+	0.341369i
$765$	17.2485			0.623620
$766$	−13.2457	+	6.95190i	−0.478588	+	0.251182i
$767$	41.3164	−	8.63677i	1.49185	−	0.311856i
$768$	−0.110519	−	0.0580050i	−0.00398802	−	0.00209308i
$769$	14.3387	+	7.52555i	0.517068	+	0.271378i	0.703007	−	0.711183i	$-0.251840\pi$
$769$	14.3387	+	7.52555i	0.517068	+	0.271378i	−0.185939	+	0.982561i	$0.559533\pi$
$770$	0.334373	−	0.0824156i	0.0120500	−	0.00297005i
$771$	−3.44512	+	4.99111i	−0.124073	+	0.179751i
$772$	28.3237	−	6.98117i	1.01939	−	0.251258i
$773$	−12.6824	−	18.3736i	−0.456154	−	0.660853i	0.525661	−	0.850694i	$-0.323818\pi$
$773$	−12.6824	−	18.3736i	−0.456154	−	0.660853i	−0.981815	+	0.189841i	$0.939203\pi$
$774$	0.628533	−	5.17643i	0.0225921	−	0.186063i
$775$	−4.04790			−0.145405
$776$	0.554808	−	4.56925i	0.0199164	−	0.164027i
$777$	−0.0299633	−	0.0790067i	−0.00107493	−	0.00283435i
$778$	−7.06954	+	3.71038i	−0.253455	+	0.133024i
$779$	0.0517855	−	0.426492i	0.00185541	−	0.0152807i
$780$	−10.3269	+	24.5567i	−0.369761	+	0.879269i
$781$	−1.40502	−	11.5714i	−0.0502755	−	0.414056i
$782$	7.43665	+	10.7738i	0.265934	+	0.385272i
$783$	−5.09774	+	7.38535i	−0.182178	+	0.263931i
$784$	13.5703	−	12.0223i	0.484655	−	0.429367i
$785$	−30.9020	−	81.4819i	−1.10294	−	2.90821i
$786$	4.01437	−	5.81582i	0.143188	−	0.207444i
$787$	−27.8278	−	14.6052i	−0.991956	−	0.520618i	−0.111001	−	0.993820i	$-0.535406\pi$
$787$	−27.8278	−	14.6052i	−0.991956	−	0.520618i	−0.880954	+	0.473202i	$0.843098\pi$
$788$	1.01070	−	8.32390i	0.0360048	−	0.296527i
$789$	−0.0348855	−	0.287308i	−0.00124196	−	0.0102284i
$790$	−4.03442	+	10.6379i	−0.143538	+	0.378479i
$791$	0.744150	−	1.07809i	0.0264589	−	0.0383324i
$792$	−1.57408	−	1.39452i	−0.0559326	−	0.0495520i
$793$	−21.0717	−	0.750232i	−0.748276	−	0.0266415i
$794$	−4.75974	+	4.21676i	−0.168917	+	0.149647i
$795$	1.75762	+	14.4753i	0.0623362	+	0.513385i
$796$	−0.157791	−	1.29952i	−0.00559275	−	0.0460604i
$797$	43.3566	−	22.7553i	1.53577	−	0.806034i	0.536486	−	0.843909i	$-0.319751\pi$
$797$	43.3566	−	22.7553i	1.53577	−	0.806034i	0.999282	+	0.0378755i	$0.0120590\pi$
$798$	−0.00287822	+	0.00151061i	−0.000101888	+	5.34749e-5i
$799$	−42.3603	−	10.4409i	−1.49860	−	0.369372i
$800$	47.4167	−	42.0075i	1.67643	−	1.48519i
$801$	−2.09089	−	0.515359i	−0.0738781	−	0.0182093i
$802$	−0.290933	−	0.767127i	−0.0102732	−	0.0270882i
$803$	−14.8903	+	7.81504i	−0.525468	+	0.275787i
$804$	1.20329	−	9.90995i	0.0424366	−	0.349497i
$805$	3.86385	−	0.952354i	0.136183	−	0.0335661i
$806$	0.555379	−	0.116096i	0.0195624	−	0.00408931i
$807$	−15.6205	−	3.85012i	−0.549869	−	0.135530i
$808$	11.6517	−	30.7231i	0.409907	−	1.08084i
$809$	−26.2690	−	23.2723i	−0.923571	−	0.818212i	0.0600996	−	0.998192i	$-0.480858\pi$
$809$	−26.2690	−	23.2723i	−0.923571	−	0.818212i	−0.983670	+	0.179980i	$0.942397\pi$
$810$	2.01573	−	0.496833i	0.0708255	−	0.0174569i
$811$	−13.6201	−	19.7322i	−0.478267	−	0.692890i	0.507377	−	0.861724i	$-0.330615\pi$
$811$	−13.6201	−	19.7322i	−0.478267	−	0.692890i	−0.985644	+	0.168834i	$0.946000\pi$
$812$	0.277835	+	2.28818i	0.00975010	+	0.0802993i
$813$	−3.62914	−	9.56925i	−0.127279	−	0.335608i
$814$	0.114706	−	0.302455i	0.00402045	−	0.0106010i
$815$	39.4127	+	57.0991i	1.38057	+	2.00009i
$816$	−10.3429	−	2.54929i	−0.362073	−	0.0892429i
$817$	0.168744	+	0.444942i	0.00590361	+	0.0155665i
$818$	5.50959	−	14.5276i	0.192638	−	0.507945i
$819$	−0.0821385	+	0.520828i	−0.00287015	+	0.0181992i
$820$	24.9921	+	65.8989i	0.872763	+	2.30129i
$821$	−9.26309	+	8.20638i	−0.323284	+	0.286405i	−0.809118	−	0.587647i	$-0.800055\pi$
$821$	−9.26309	+	8.20638i	−0.323284	+	0.286405i	0.485834	+	0.874051i	$0.338516\pi$
$822$	−3.03215			−0.105758
$823$	−57.0247			−1.98776			−0.993878	−	0.110488i	$-0.964759\pi$
$823$	−57.0247			−1.98776			−0.993878	+	0.110488i	$0.964759\pi$
$824$	−11.1965	+	9.91924i	−0.390049	+	0.345553i
$825$	12.7511	−	6.69227i	0.443935	−	0.232995i
$826$	−0.844905			−0.0293980
$827$	1.61419	+	0.847193i	0.0561309	+	0.0294598i	0.492555	−	0.870281i	$-0.336063\pi$
$827$	1.61419	+	0.847193i	0.0561309	+	0.0294598i	−0.436424	+	0.899741i	$0.643755\pi$
$828$	−8.50495	−	7.53473i	−0.295568	−	0.261850i
$829$	−4.68087	−	6.78140i	−0.162573	−	0.235528i	0.733228	−	0.679983i	$-0.238013\pi$
$829$	−4.68087	−	6.78140i	−0.162573	−	0.235528i	−0.895801	+	0.444455i	$0.853397\pi$
$830$	7.24867	+	6.42176i	0.251605	+	0.222903i
$831$	−7.89523	−	11.4382i	−0.273883	−	0.396787i
$832$	5.88298	−	7.90572i	0.203956	−	0.274082i
$833$	−16.2552	+	23.5497i	−0.563208	+	0.815948i
$834$	−1.23008	+	0.303189i	−0.0425943	+	0.0104986i
$835$	−24.2042	+	21.4431i	−0.837622	+	0.742068i
$836$	0.0871272	+	0.0214749i	0.00301336	+	0.000742726i
$837$	0.238666	+	0.211440i	0.00824951	+	0.00730843i
$838$	−0.994749	−	0.881271i	−0.0343630	−	0.0304430i
$839$	0.983846	−	2.59419i	0.0339661	−	0.0895613i	−0.916960	−	0.398979i	$-0.869365\pi$
$839$	0.983846	−	2.59419i	0.0339661	−	0.0895613i	0.950926	+	0.309417i	$0.100134\pi$
$840$	0.647842	−	0.938562i	0.0223527	−	0.0323835i
$841$	45.6279	+	23.9474i	1.57338	+	0.825771i
$842$	−2.07833	+	17.1166i	−0.0716239	+	0.589876i
$843$	−7.46532	−	1.84004i	−0.257119	−	0.0633743i
$844$	24.5798			0.846070
$845$	46.4914	+	28.7928i	1.59935	+	0.990501i
$846$	−5.25114			−0.180538
$847$	1.37917	+	0.339934i	0.0473887	+	0.0116803i
$848$	1.08548	−	8.93971i	0.0372754	−	0.306991i
$849$	6.30966	+	3.31157i	0.216547	+	0.113653i
$850$	−14.5939	+	21.1429i	−0.500566	+	0.725196i
$851$	1.32549	−	3.49502i	0.0454371	−	0.119808i
$852$	−13.5098	−	11.9686i	−0.462838	−	0.410039i
$853$	30.3875	+	26.9210i	1.04045	+	0.921757i	0.997008	−	0.0772987i	$-0.0246295\pi$
$853$	30.3875	+	26.9210i	1.04045	+	0.921757i	0.0434409	+	0.999056i	$0.486168\pi$
$854$	0.409793	+	0.101005i	0.0140228	+	0.00345632i
$855$	−0.141812	+	0.125634i	−0.00484986	+	0.00429660i
$856$	−26.0701	+	6.42570i	−0.891057	+	0.219626i
$857$	−22.7771	+	32.9983i	−0.778050	+	1.12720i	0.210689	+	0.977553i	$0.432429\pi$
$857$	−22.7771	+	32.9983i	−0.778050	+	1.12720i	−0.988739	+	0.149647i	$0.952186\pi$
$858$	−1.55753	+	1.28390i	−0.0531731	+	0.0438316i
$859$	18.9376	+	27.4358i	0.646141	+	0.936097i	1.00000		0.000798336i	$0.000254118\pi$
$859$	18.9376	+	27.4358i	0.646141	+	0.936097i	−0.353858	+	0.935299i	$0.615130\pi$
$860$	−58.4322	−	51.7664i	−1.99252	−	1.76522i
$861$	0.792422	+	1.14802i	0.0270057	+	0.0391244i
$862$	10.2525	+	9.08289i	0.349200	+	0.309364i
$863$	−14.1191	−	7.41028i	−0.480620	−	0.252249i	0.206971	−	0.978347i	$-0.433639\pi$
$863$	−14.1191	−	7.41028i	−0.480620	−	0.252249i	−0.687591	+	0.726098i	$0.741332\pi$
$864$	−4.98995			−0.169762
$865$	35.0926	−	18.4180i	1.19319	−	0.626232i
$866$	0.154127	−	0.136545i	0.00523745	−	0.00463997i
$867$	−0.186875			−0.00634660
$868$	0.0818995			0.00277985
$869$	4.65305	−	4.12224i	0.157844	−	0.139838i
$870$	−6.60638	−	17.4196i	−0.223977	−	0.590580i
$871$	−19.7097	−	5.60897i	−0.667838	−	0.190053i
$872$	1.55170	−	4.09149i	0.0525471	−	0.138555i
$873$	−0.880401	−	2.32143i	−0.0297971	−	0.0785684i
$874$	−0.139616	−	0.0344123i	−0.00472259	−	0.00116401i
$875$	2.68904	+	3.89575i	0.0909062	+	0.131700i
$876$	−9.23358	+	24.3470i	−0.311974	+	0.822607i
$877$	−11.7374	−	30.9491i	−0.396345	−	1.04508i	−0.973550	−	0.228476i	$-0.926626\pi$
$877$	−11.7374	−	30.9491i	−0.396345	−	1.04508i	0.577205	−	0.816600i	$-0.304143\pi$
$878$	0.512079	+	4.21735i	0.0172818	+	0.142329i
$879$	10.2398	+	14.8349i	0.345380	+	0.500369i
$880$	−12.0361	+	2.96663i	−0.405736	+	0.100005i
$881$	8.08854	+	7.16582i	0.272510	+	0.241423i	0.788298	−	0.615293i	$-0.210962\pi$
$881$	8.08854	+	7.16582i	0.272510	+	0.241423i	−0.515788	+	0.856716i	$0.672501\pi$
$882$	−1.22131	+	3.22033i	−0.0411237	+	0.108434i
$883$	25.2653	+	6.22733i	0.850244	+	0.209566i	0.640279	−	0.768143i	$-0.278819\pi$
$883$	25.2653	+	6.22733i	0.850244	+	0.209566i	0.209965	+	0.977709i	$0.432665\pi$
$884$	−10.0662	+	23.9368i	−0.338563	+	0.805083i
$885$	−47.8144	+	11.7852i	−1.60726	+	0.396155i
$886$	−0.842713	+	6.94037i	−0.0283115	+	0.233166i
$887$	16.0398	−	8.41834i	0.538564	−	0.282660i	−0.173430	−	0.984846i	$-0.555485\pi$
$887$	16.0398	−	8.41834i	0.538564	−	0.282660i	0.711993	+	0.702186i	$0.247793\pi$
$888$	−0.379857	−	1.00160i	−0.0127472	−	0.0336115i
$889$	0.319856	+	0.0788374i	0.0107276	+	0.00264412i
$890$	3.34638	−	2.96464i	0.112171	−	0.0993748i
$891$	−1.10138	−	0.271465i	−0.0368975	−	0.00909441i
$892$	32.4454	−	17.0287i	1.08635	−	0.570161i
$893$	0.424323	−	0.222702i	0.0141994	−	0.00745243i
$894$	−0.785762	−	6.47133i	−0.0262798	−	0.216434i
$895$	−0.448997	−	3.69782i	−0.0150083	−	0.123605i
$896$	−1.24005	+	1.09859i	−0.0414271	+	0.0367012i
$897$	−17.9980	+	14.8361i	−0.600937	+	0.495363i
$898$	12.1546	+	10.7680i	0.405603	+	0.359333i
$899$	1.62544	−	2.35485i	0.0542114	−	0.0785388i
$900$	7.90701	−	20.8491i	0.263567	−	0.694969i
$901$	1.71325	+	14.1099i	0.0570767	+	0.470069i
$902$	−0.643687	+	5.30124i	−0.0214324	+	0.176512i
$903$	−1.36811	−	0.718039i	−0.0455278	−	0.0238948i
$904$	9.43388	−	13.6673i	0.313766	−	0.454569i
$905$	−25.8345	−	68.1200i	−0.858768	−	2.26438i
$906$	−0.0615386	+	0.0545184i	−0.00204448	+	0.00181125i
$907$	−22.8318	+	33.0776i	−0.758118	+	1.09832i	0.233904	+	0.972260i	$0.424850\pi$
$907$	−22.8318	+	33.0776i	−0.758118	+	1.09832i	−0.992022	+	0.126064i	$0.959766\pi$
$908$	−12.3889	−	17.9484i	−0.411139	−	0.595637i
$909$	−2.13638	−	17.5946i	−0.0708591	−	0.583577i
$910$	−0.792997	−	0.754569i	−0.0262876	−	0.0250137i
$911$	6.43070	−	52.9616i	0.213059	−	1.75470i	−0.357940	−	0.933745i	$-0.616521\pi$
$911$	6.43070	−	52.9616i	0.213059	−	1.75470i	0.570999	−	0.820951i	$-0.306556\pi$
$912$	0.103604	−	0.0543757i	0.00343068	−	0.00180056i
$913$	−1.87633	−	4.94746i	−0.0620973	−	0.163737i
$914$	−0.972002	+	8.00516i	−0.0321510	+	0.264787i
$915$	24.5996			0.813239
$916$	−0.620899	+	5.11356i	−0.0205151	+	0.168957i
$917$	−1.18950	−	1.72328i	−0.0392806	−	0.0569078i
$918$	1.96485	−	0.484292i	0.0648497	−	0.0159840i
$919$	32.1723	−	46.6096i	1.06126	−	1.53751i	0.236829	−	0.971551i	$-0.423892\pi$
$919$	32.1723	−	46.6096i	1.06126	−	1.53751i	0.824435	−	0.565956i	$-0.191493\pi$
$920$	48.9836	−	12.0734i	1.61494	−	0.398047i
$921$	22.9023	+	12.0201i	0.754658	+	0.396075i
$922$	1.72380	+	0.904719i	0.0567703	+	0.0297953i
$923$	−28.5892	+	23.5666i	−0.941025	+	0.775704i
$924$	−0.257987	+	0.135402i	−0.00848714	+	0.00445439i
$925$	7.33541			0.241187
$926$	10.0013	+	5.24911i	0.328665	+	0.172497i
$927$	−2.86116	+	7.54425i	−0.0939728	+	0.247786i
$928$	5.39753	+	44.4527i	0.177183	+	1.45923i
$929$	0.654542	−	0.161330i	0.0214748	−	0.00529307i	−0.228564	−	0.973529i	$-0.573403\pi$
$929$	0.654542	−	0.161330i	0.0214748	−	0.00529307i	0.250038	+	0.968236i	$0.419557\pi$
$930$	−0.642725	+	0.158417i	−0.0210758	+	0.00519471i
$931$	−0.0378858	−	0.312017i	−0.00124166	−	0.0102260i
$932$	2.60054	−	6.85705i	0.0851834	−	0.224610i
$933$	13.3763	+	7.02041i	0.437919	+	0.229838i
$934$	10.2402			0.335069
$935$	17.3245	−	9.09259i	0.566571	−	0.297359i
$936$	−1.04130	+	6.60274i	−0.0340360	+	0.215817i
$937$	27.0859	+	14.2158i	0.884858	+	0.464409i	0.844982	−	0.534795i	$-0.179611\pi$
$937$	27.0859	+	14.2158i	0.884858	+	0.464409i	0.0398762	+	0.999205i	$0.487304\pi$
$938$	0.363208	+	0.190626i	0.0118592	+	0.00622416i
$939$	0.449283	−	0.110738i	0.0146618	−	0.00361381i
$940$	−44.6578	+	64.6980i	−1.45658	+	2.11022i
$941$	−3.78807	+	0.933675i	−0.123488	+	0.0304369i	−0.300575	−	0.953758i	$-0.597179\pi$
$941$	−3.78807	+	0.933675i	−0.123488	+	0.0304369i	0.177088	+	0.984195i	$0.443332\pi$
$942$	−5.80798	−	8.41432i	−0.189234	−	0.274153i
$943$	−7.43813	+	61.2585i	−0.242219	+	1.99485i
$944$	30.4132			0.989864
$945$	0.0741487	−	0.610669i	0.00241206	−	0.0198651i
$946$	−2.09747	−	5.53057i	−0.0681946	−	0.179814i
$947$	−1.54794	+	0.812419i	−0.0503012	+	0.0264001i	−0.489686	−	0.871899i	$-0.662889\pi$
$947$	−1.54794	+	0.812419i	−0.0503012	+	0.0264001i	0.439385	+	0.898299i	$0.355196\pi$
$948$	1.16024	−	9.55543i	0.0376828	−	0.310346i
$949$	46.4158	+	26.5088i	1.50672	+	0.860513i
$950$	−0.0340139	−	0.280129i	−0.00110356	−	0.00908859i
$951$	8.23043	+	11.9238i	0.266890	+	0.386657i
$952$	0.631490	−	0.914872i	0.0204667	−	0.0296512i
$953$	16.9366	−	15.0045i	0.548631	−	0.486045i	−0.342671	−	0.939456i	$-0.611331\pi$
$953$	16.9366	−	15.0045i	0.548631	−	0.486045i	0.891302	+	0.453411i	$0.149793\pi$
$954$	0.606645	+	1.59959i	0.0196409	+	0.0517887i
$955$	−27.6229	+	40.0187i	−0.893857	+	1.29498i
$956$	−0.683235	−	0.358589i	−0.0220974	−	0.0115976i
$957$	−1.22699	+	10.1052i	−0.0396630	+	0.326654i
$958$	−1.73688	−	14.3045i	−0.0561162	−	0.462158i
$959$	−0.318596	+	0.840069i	−0.0102880	+	0.0271272i
$960$	−6.53107	+	9.46189i	−0.210790	+	0.305381i
$961$	23.1277	+	20.4894i	0.746056	+	0.660948i
$962$	−1.00643	+	0.210384i	−0.0324486	+	0.00678305i
$963$	−10.8408	+	9.60408i	−0.349339	+	0.309487i
$964$	−1.03504	−	8.52431i	−0.0333363	−	0.274550i
$965$	8.42117	+	69.3545i	0.271087	+	2.23260i
$966$	0.413409	−	0.216974i	0.0133012	−	0.00698101i
$967$	5.01002	−	2.62946i	0.161112	−	0.0845579i	−0.382240	−	0.924063i	$-0.624847\pi$
$967$	5.01002	−	2.62946i	0.161112	−	0.0845579i	0.543352	+	0.839505i	$0.317155\pi$
$968$	17.4842	+	4.30948i	0.561964	+	0.138512i
$969$	−0.138232	+	0.122463i	−0.00444066	+	0.00393409i
$970$	5.00458	+	1.23352i	0.160687	+	0.0396059i
$971$	−0.0975977	−	0.257344i	−0.00313206	−	0.00825856i	0.933441	−	0.358731i	$-0.116790\pi$
$971$	−0.0975977	−	0.257344i	−0.00313206	−	0.00825856i	−0.936573	+	0.350472i	$0.886021\pi$
$972$	−1.55524	+	0.816254i	−0.0498844	+	0.0261813i
$973$	−0.0452487	+	0.372657i	−0.00145061	+	0.0119468i
$974$	−9.91676	+	2.44426i	−0.317754	+	0.0783192i
$975$	−39.7474	−	22.7004i	−1.27293	−	0.726994i
$976$	−14.7509	−	3.63577i	−0.472165	−	0.116378i
$977$	−15.1994	+	40.0775i	−0.486272	+	1.28219i	0.437489	+	0.899224i	$0.355868\pi$
$977$	−15.1994	+	40.0775i	−0.486272	+	1.28219i	−0.923761	+	0.382970i	$0.874901\pi$
$978$	6.09286	+	5.39780i	0.194828	+	0.172603i
$979$	−2.37178	+	0.584591i	−0.0758023	+	0.0186836i
$980$	29.2904	+	42.4344i	0.935646	+	1.35552i
$981$	−0.284508	−	2.34313i	−0.00908363	−	0.0748104i
$982$	−2.26780	−	5.97971i	−0.0723685	−	0.190820i
$983$	−1.55447	+	4.09881i	−0.0495800	+	0.130732i	−0.957519	−	0.288371i	$-0.906886\pi$
$983$	−1.55447	+	4.09881i	−0.0495800	+	0.130732i	0.907939	+	0.419103i	$0.137655\pi$
$984$	10.0458	+	14.5539i	0.320250	+	0.463962i
$985$	19.4982	+	4.80587i	0.621264	+	0.153128i
$986$	−6.43963	−	16.9799i	−0.205080	−	0.540751i
$987$	−0.551752	+	1.45485i	−0.0175625	+	0.0463084i
$988$	−0.0915895	−	0.270121i	−0.00291385	−	0.00859371i
$989$	−24.2373	−	63.9085i	−0.770701	−	2.03217i
$990$	1.76270	−	1.56162i	0.0560224	−	0.0496315i
$991$	52.2928			1.66114			0.830568	−	0.556917i	$-0.188016\pi$
$991$	52.2928			1.66114			0.830568	+	0.556917i	$0.188016\pi$
$992$	1.59107			0.0505165
$993$	2.54231	−	2.25229i	0.0806776	−	0.0714742i
$994$	0.656685	−	0.344655i	0.0208288	−	0.0109318i
$995$	3.13515			0.0993910
$996$	−7.25470	−	3.80756i	−0.229874	−	0.120647i
$997$	6.50765	+	5.76527i	0.206099	+	0.182588i	0.759858	−	0.650089i	$-0.225268\pi$
$997$	6.50765	+	5.76527i	0.206099	+	0.182588i	−0.553759	+	0.832677i	$0.686807\pi$
$998$	3.85036	+	5.57821i	0.121881	+	0.176575i
$999$	−0.432499	−	0.383161i	−0.0136837	−	0.0121227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.10	✓	204
169.131	even	13	inner	507.2.m.b.469.10	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.10	✓	204	1.1	even	1	trivial
507.2.m.b.469.10	yes	204	169.131	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.479187 + 0.118109i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.55524 - 0.816254i) q^{4} +(2.38960 - 3.46193i) q^{5} +(0.175008 - 0.461457i) q^{6} +(-0.109460 - 0.0969731i) q^{7} +(-1.38767 - 1.22937i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(0.479187 + 0.118109i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.55524 - 0.816254i) q^{4} +(2.38960 - 3.46193i) q^{5} +(0.175008 - 0.461457i) q^{6} +(-0.109460 - 0.0969731i) q^{7} +(-1.38767 - 1.22937i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.55395 - 1.37668i) q^{10} +(-1.10138 + 0.271465i) q^{11} +(-0.997766 + 1.44551i) q^{12} +(2.61201 + 2.48544i) q^{13} +(-0.0409984 - 0.0593965i) q^{14} +(-3.14865 - 2.78946i) q^{15} +(1.47578 + 2.13803i) q^{16} +(-3.06918 - 2.71906i) q^{17} +(-0.436998 - 0.229354i) q^{18} +0.0450389 q^{19} +(-6.54221 + 3.43362i) q^{20} +(-0.109460 + 0.0969731i) q^{21} -0.559828 q^{22} -6.46909 q^{23} +(-1.38767 + 1.22937i) q^{24} +(-4.50175 - 11.8701i) q^{25} +(0.958091 + 1.49949i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.0910821 + 0.240164i) q^{28} +(8.71311 + 2.14759i) q^{29} +(-1.17933 - 1.70856i) q^{30} +(0.113067 - 0.298134i) q^{31} +(1.76946 + 4.66568i) q^{32} +(0.136729 + 1.12607i) q^{33} +(-1.14957 - 1.66544i) q^{34} +(-0.597279 + 0.147216i) q^{35} +(1.31471 + 1.16473i) q^{36} +(-0.204895 + 0.540265i) q^{37} +(0.0215821 + 0.00531950i) q^{38} +(2.78216 - 2.29338i) q^{39} +(-7.57194 + 1.86632i) q^{40} +(1.14979 - 9.46941i) q^{41} +(-0.0639052 + 0.0335401i) q^{42} +(3.74663 + 9.87906i) q^{43} +(1.93449 + 0.476809i) q^{44} +(-3.14865 + 2.78946i) q^{45} +(-3.09991 - 0.764058i) q^{46} +(9.42126 - 4.94466i) q^{47} +(2.30033 - 1.20731i) q^{48} +(-0.841179 - 6.92773i) q^{49} +(-0.755211 - 6.21972i) q^{50} +(-3.06918 + 2.71906i) q^{51} +(-2.03356 - 5.99752i) q^{52} +(-2.59463 - 2.29865i) q^{53} +(-0.280356 + 0.406166i) q^{54} +(-1.69205 + 4.46157i) q^{55} +(0.0326786 + 0.269133i) q^{56} +(0.00542884 - 0.0447105i) q^{57} +(3.92156 + 2.05819i) q^{58} +(6.65022 - 9.63451i) q^{59} +(2.62001 + 6.90839i) q^{60} +(-4.37724 + 3.87789i) q^{61} +(0.0893929 - 0.129508i) q^{62} +(0.0830721 + 0.120351i) q^{63} +(-0.329442 - 2.71320i) q^{64} +(14.8461 - 3.10341i) q^{65} +(-0.0674798 + 0.555746i) q^{66} +(-5.03252 + 2.64127i) q^{67} +(2.55388 + 6.73402i) q^{68} +(-0.779763 + 6.42192i) q^{69} -0.303596 q^{70} +(-1.23862 + 10.2010i) q^{71} +(1.05314 + 1.52573i) q^{72} +(14.3942 - 3.54785i) q^{73} +(-0.161993 + 0.234688i) q^{74} +(-12.3262 + 3.03814i) q^{75} +(-0.0700463 - 0.0367631i) q^{76} +(0.146881 + 0.0770893i) q^{77} +(1.60404 - 0.770362i) q^{78} +(-4.85249 + 2.54678i) q^{79} +10.9282 q^{80} +(0.885456 + 0.464723i) q^{81} +(1.66939 - 4.40182i) q^{82} +(0.562264 + 4.63066i) q^{83} +(0.249391 - 0.0614694i) q^{84} +(-16.7473 + 4.12783i) q^{85} +(0.628533 + 5.17643i) q^{86} +(3.18218 - 8.39072i) q^{87} +(1.86207 + 0.977291i) q^{88} +2.15347 q^{89} +(-1.83826 + 0.964791i) q^{90} +(-0.0448906 - 0.525351i) q^{91} +(10.0610 + 5.28042i) q^{92} +(-0.282332 - 0.148179i) q^{93} +(5.09856 - 1.25668i) q^{94} +(0.107625 - 0.155921i) q^{95} +(4.84495 - 1.19417i) q^{96} +(1.41037 + 2.04328i) q^{97} +(0.415146 - 3.41903i) q^{98} +1.13434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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