LMFDB - Embedded newform 430.2.q.d.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	430.101
Dual form			430.2.q.d.281.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 + 0.781831i) q^{2} +(-0.0969271 + 0.246966i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(-0.132653 - 0.229762i) q^{6} +(-2.60514 + 4.51223i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.14756 + 1.99264i) q^{9} +O(q^{10})$	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.0969271 + 0.246966i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(-0.132653 - 0.229762i) q^{6} +(-2.60514 + 4.51223i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.14756 + 1.99264i) q^{9} +(0.826239 + 0.563320i) q^{10} +(1.17841 - 5.16294i) q^{11} +(0.262343 + 0.0395418i) q^{12} +(-1.92404 + 1.31179i) q^{13} +(-1.90353 - 4.85011i) q^{14} +(0.253519 + 0.0782003i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.174935 + 2.33435i) q^{17} +(-2.89689 + 0.436636i) q^{18} +(-4.45924 + 4.13757i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.861860 - 1.08074i) q^{21} +(3.30182 + 4.14035i) q^{22} +(-5.46945 + 1.68710i) q^{23} +(-0.194483 + 0.180454i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.174022 - 2.32216i) q^{26} +(-1.41737 + 0.682569i) q^{27} +(4.97880 + 1.53576i) q^{28} +(3.34707 + 8.52821i) q^{29} +(-0.219206 + 0.149452i) q^{30} +(-1.24737 - 0.188011i) q^{31} +(0.222521 - 0.974928i) q^{32} +(1.16085 + 0.791455i) q^{33} +(-1.71600 - 1.59221i) q^{34} +(4.69429 + 2.26065i) q^{35} +(1.46481 - 2.53712i) q^{36} +(2.18014 + 3.77612i) q^{37} +(-0.454592 - 6.06610i) q^{38} +(-0.137475 - 0.602319i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-5.88034 + 7.37372i) q^{41} +1.38232 q^{42} +(-3.92451 - 5.25340i) q^{43} -5.29571 q^{44} +(1.82658 - 2.29046i) q^{45} +(2.09112 - 5.32808i) q^{46} +(-0.756925 - 3.31630i) q^{47} +(-0.0198263 - 0.264564i) q^{48} +(-10.0735 - 17.4478i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.559549 - 0.269465i) q^{51} +(1.70703 + 1.58390i) q^{52} +(5.37127 + 3.66207i) q^{53} +(0.350061 - 1.53372i) q^{54} +(-5.23656 - 0.789285i) q^{55} +(-4.30493 + 2.93505i) q^{56} +(-0.589619 - 1.50232i) q^{57} +(-8.75449 - 2.70040i) q^{58} +(5.27229 - 2.53900i) q^{59} +(0.0198263 - 0.264564i) q^{60} +(7.13286 - 1.07511i) q^{61} +(0.924719 - 0.858014i) q^{62} +(-14.5859 + 4.49917i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.45190 + 1.82063i) q^{65} +(-1.34256 + 0.414126i) q^{66} +(4.26191 - 3.95448i) q^{67} +(2.31475 - 0.348892i) q^{68} +(0.113481 - 1.51430i) q^{69} +(-4.69429 + 2.26065i) q^{70} +(8.04471 + 2.48146i) q^{71} +(1.07031 + 2.72710i) q^{72} +(7.18516 - 4.89876i) q^{73} +(-4.31159 - 0.649867i) q^{74} +(0.0590361 - 0.258654i) q^{75} +(5.02611 + 3.42674i) q^{76} +(20.2264 + 18.7674i) q^{77} +(0.556627 + 0.268057i) q^{78} +(-2.61954 + 4.53717i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.625601 + 8.34806i) q^{81} +(-2.09867 - 9.19488i) q^{82} +(0.820100 - 2.08958i) q^{83} +(-0.861860 + 1.08074i) q^{84} +2.34090 q^{85} +(6.55417 + 0.207131i) q^{86} -2.43060 q^{87} +(3.30182 - 4.14035i) q^{88} +(4.01516 - 10.2305i) q^{89} +(0.651900 + 2.85616i) q^{90} +(-0.906700 - 12.0991i) q^{91} +(2.86187 + 4.95691i) q^{92} +(0.167337 - 0.289836i) q^{93} +(3.06473 + 1.47589i) q^{94} +(4.45924 + 4.13757i) q^{95} +(0.219206 + 0.149452i) q^{96} +(0.0156549 - 0.0685885i) q^{97} +(19.9219 + 3.00275i) q^{98} +(12.8186 - 8.73956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$3$	−0.0969271	+	0.246966i	−0.0559609	+	0.142586i	−0.956120	−	0.292975i	$-0.905355\pi$
$3$	−0.0969271	+	0.246966i	−0.0559609	+	0.142586i	0.900159	+	0.435561i	$0.143450\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$6$	−0.132653	−	0.229762i	−0.0541553	−	0.0937998i
$7$	−2.60514	+	4.51223i	−0.984649	+	1.70546i	−0.341164	+	0.940004i	$0.610821\pi$
$7$	−2.60514	+	4.51223i	−0.984649	+	1.70546i	−0.643485	+	0.765458i	$0.722512\pi$
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	2.14756	+	1.99264i	0.715853	+	0.664214i
$10$	0.826239	+	0.563320i	0.261280	+	0.178137i
$11$	1.17841	−	5.16294i	0.355303	−	1.55668i	−0.409433	−	0.912340i	$-0.634273\pi$
$11$	1.17841	−	5.16294i	0.355303	−	1.55668i	0.764736	−	0.644344i	$-0.222869\pi$
$12$	0.262343	+	0.0395418i	0.0757318	+	0.0114147i
$13$	−1.92404	+	1.31179i	−0.533631	+	0.363824i	−0.799955	−	0.600060i	$-0.795143\pi$
$13$	−1.92404	+	1.31179i	−0.533631	+	0.363824i	0.266324	+	0.963884i	$0.414191\pi$
$14$	−1.90353	−	4.85011i	−0.508739	−	1.29625i
$15$	0.253519	+	0.0782003i	0.0654583	+	0.0201912i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.174935	+	2.33435i	−0.0424280	+	0.566163i	0.934966	+	0.354737i	$0.115430\pi$
$17$	−0.174935	+	2.33435i	−0.0424280	+	0.566163i	−0.977394	+	0.211426i	$0.932189\pi$
$18$	−2.89689	+	0.436636i	−0.682804	+	0.102916i
$19$	−4.45924	+	4.13757i	−1.02302	+	0.949223i	−0.998725	−	0.0504815i	$-0.983924\pi$
$19$	−4.45924	+	4.13757i	−1.02302	+	0.949223i	−0.0242945	+	0.999705i	$0.507734\pi$
$20$	−0.955573	+	0.294755i	−0.213673	+	0.0659093i
$21$	−0.861860	−	1.08074i	−0.188073	−	0.235836i
$22$	3.30182	+	4.14035i	0.703951	+	0.882726i
$23$	−5.46945	+	1.68710i	−1.14046	+	0.351785i	−0.806751	−	0.590891i	$-0.798776\pi$
$23$	−5.46945	+	1.68710i	−1.14046	+	0.351785i	−0.333708	+	0.942676i	$0.608300\pi$
$24$	−0.194483	+	0.180454i	−0.0396987	+	0.0368350i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	0.174022	−	2.32216i	0.0341284	−	0.455412i
$27$	−1.41737	+	0.682569i	−0.272773	+	0.131360i
$28$	4.97880	+	1.53576i	0.940904	+	0.290230i
$29$	3.34707	+	8.52821i	0.621536	+	1.58365i	0.800197	+	0.599737i	$0.204728\pi$
$29$	3.34707	+	8.52821i	0.621536	+	1.58365i	−0.178661	+	0.983911i	$0.557176\pi$
$30$	−0.219206	+	0.149452i	−0.0400213	+	0.0272861i
$31$	−1.24737	−	0.188011i	−0.224035	−	0.0337679i	0.0360653	−	0.999349i	$-0.488518\pi$
$31$	−1.24737	−	0.188011i	−0.224035	−	0.0337679i	−0.260100	+	0.965582i	$0.583756\pi$
$32$	0.222521	−	0.974928i	0.0393365	−	0.172345i
$33$	1.16085	+	0.791455i	0.202078	+	0.137775i
$34$	−1.71600	−	1.59221i	−0.294291	−	0.273062i
$35$	4.69429	+	2.26065i	0.793481	+	0.382120i
$36$	1.46481	−	2.53712i	0.244134	−	0.422853i
$37$	2.18014	+	3.77612i	0.358414	+	0.620791i	0.987696	−	0.156386i	$-0.0499844\pi$
$37$	2.18014	+	3.77612i	0.358414	+	0.620791i	−0.629282	+	0.777177i	$0.716651\pi$
$38$	−0.454592	−	6.06610i	−0.0737445	−	0.984052i
$39$	−0.137475	−	0.602319i	−0.0220137	−	0.0964483i
$40$	0.365341	−	0.930874i	0.0577655	−	0.147184i
$41$	−5.88034	+	7.37372i	−0.918355	+	1.15158i	0.0697132	+	0.997567i	$0.477792\pi$
$41$	−5.88034	+	7.37372i	−0.918355	+	1.15158i	−0.988069	+	0.154014i	$0.950780\pi$
$42$	1.38232			0.213296
$43$	−3.92451	−	5.25340i	−0.598483	−	0.801136i
$43$	−3.92451	−	5.25340i	−0.598483	−	0.801136i
$44$	−5.29571			−0.798359
$45$	1.82658	−	2.29046i	0.272291	−	0.341442i
$46$	2.09112	−	5.32808i	0.308319	−	0.785583i
$47$	−0.756925	−	3.31630i	−0.110409	−	0.483733i	−0.999654	−	0.0263018i	$-0.991627\pi$
$47$	−0.756925	−	3.31630i	−0.110409	−	0.483733i	0.889245	−	0.457431i	$-0.151230\pi$
$48$	−0.0198263	−	0.264564i	−0.00286168	−	0.0381865i
$49$	−10.0735	−	17.4478i	−1.43907	−	2.49254i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.559549	−	0.269465i	−0.0783526	−	0.0377326i
$52$	1.70703	+	1.58390i	0.236723	+	0.219647i
$53$	5.37127	+	3.66207i	0.737801	+	0.503024i	0.872955	−	0.487801i	$-0.162201\pi$
$53$	5.37127	+	3.66207i	0.737801	+	0.503024i	−0.135154	+	0.990825i	$0.543153\pi$
$54$	0.350061	−	1.53372i	0.0476373	−	0.208713i
$55$	−5.23656	−	0.789285i	−0.706098	−	0.106427i
$56$	−4.30493	+	2.93505i	−0.575270	+	0.392213i
$57$	−0.589619	−	1.50232i	−0.0780969	−	0.198988i
$58$	−8.75449	−	2.70040i	−1.14952	−	0.354580i
$59$	5.27229	−	2.53900i	0.686394	−	0.330550i	−0.0579752	−	0.998318i	$-0.518464\pi$
$59$	5.27229	−	2.53900i	0.686394	−	0.330550i	0.744370	+	0.667768i	$0.232750\pi$
$60$	0.0198263	−	0.264564i	0.00255957	−	0.0341551i
$61$	7.13286	−	1.07511i	0.913269	−	0.137653i	0.324436	−	0.945908i	$-0.394826\pi$
$61$	7.13286	−	1.07511i	0.913269	−	0.137653i	0.588833	+	0.808255i	$0.299587\pi$
$62$	0.924719	−	0.858014i	0.117439	−	0.108968i
$63$	−14.5859	+	4.49917i	−1.83766	+	0.566842i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	1.45190	+	1.82063i	0.180086	+	0.225821i
$66$	−1.34256	+	0.414126i	−0.165258	+	0.0509754i
$67$	4.26191	−	3.95448i	0.520676	−	0.483116i	−0.375496	−	0.926824i	$-0.622528\pi$
$67$	4.26191	−	3.95448i	0.520676	−	0.483116i	0.896172	+	0.443708i	$0.146337\pi$
$68$	2.31475	−	0.348892i	0.280705	−	0.0423094i
$69$	0.113481	−	1.51430i	0.0136615	−	0.182300i
$70$	−4.69429	+	2.26065i	−0.561075	+	0.270200i
$71$	8.04471	+	2.48146i	0.954731	+	0.294496i	0.732706	−	0.680545i	$-0.238257\pi$
$71$	8.04471	+	2.48146i	0.954731	+	0.294496i	0.222025	+	0.975041i	$0.428733\pi$
$72$	1.07031	+	2.72710i	0.126137	+	0.321392i
$73$	7.18516	−	4.89876i	0.840960	−	0.573357i	−0.0644376	−	0.997922i	$-0.520525\pi$
$73$	7.18516	−	4.89876i	0.840960	−	0.573357i	0.905397	+	0.424565i	$0.139573\pi$
$74$	−4.31159	−	0.649867i	−0.501212	−	0.0755456i
$75$	0.0590361	−	0.258654i	0.00681690	−	0.0298668i
$76$	5.02611	+	3.42674i	0.576534	+	0.393074i
$77$	20.2264	+	18.7674i	2.30502	+	2.13874i
$78$	0.556627	+	0.268057i	0.0630256	+	0.0303515i
$79$	−2.61954	+	4.53717i	−0.294721	+	0.510472i	−0.974920	−	0.222556i	$-0.928560\pi$
$79$	−2.61954	+	4.53717i	−0.294721	+	0.510472i	0.680199	+	0.733027i	$0.261893\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	0.625601	+	8.34806i	0.0695112	+	0.927562i
$82$	−2.09867	−	9.19488i	−0.231759	−	1.01540i
$83$	0.820100	−	2.08958i	0.0900176	−	0.229361i	−0.878774	−	0.477239i	$-0.841638\pi$
$83$	0.820100	−	2.08958i	0.0900176	−	0.229361i	0.968791	+	0.247877i	$0.0797330\pi$
$84$	−0.861860	+	1.08074i	−0.0940366	+	0.117918i
$85$	2.34090			0.253906
$86$	6.55417	+	0.207131i	0.706754	+	0.0223355i
$87$	−2.43060			−0.260588
$88$	3.30182	−	4.14035i	0.351975	−	0.441363i
$89$	4.01516	−	10.2305i	0.425606	−	1.08443i	−0.543855	−	0.839179i	$-0.683036\pi$
$89$	4.01516	−	10.2305i	0.425606	−	1.08443i	0.969461	−	0.245247i	$-0.0788691\pi$
$90$	0.651900	+	2.85616i	0.0687163	+	0.301066i
$91$	−0.906700	−	12.0991i	−0.0950480	−	1.26833i
$92$	2.86187	+	4.95691i	0.298371	+	0.516793i
$93$	0.167337	−	0.289836i	0.0173520	−	0.0300546i
$94$	3.06473	+	1.47589i	0.316102	+	0.152227i
$95$	4.45924	+	4.13757i	0.457508	+	0.424506i
$96$	0.219206	+	0.149452i	0.0223726	+	0.0152534i
$97$	0.0156549	−	0.0685885i	0.00158951	−	0.00696411i	−0.974127	−	0.226002i	$-0.927435\pi$
$97$	0.0156549	−	0.0685885i	0.00158951	−	0.00696411i	0.975716	+	0.219037i	$0.0702917\pi$
$98$	19.9219	+	3.00275i	2.01242	+	0.303323i
$99$	12.8186	−	8.73956i	1.28832	−	0.878359i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	−13.9031	−	4.28854i	−1.38341	−	0.426726i	−0.488342	−	0.872652i	$-0.662398\pi$
$101$	−13.9031	−	4.28854i	−1.38341	−	0.426726i	−0.895070	+	0.445927i	$0.852874\pi$
$102$	0.559549	−	0.269465i	0.0554037	−	0.0266810i
$103$	0.101990	−	1.36096i	0.0100494	−	0.134099i	−0.989922	−	0.141611i	$-0.954772\pi$
$103$	0.101990	−	1.36096i	0.0100494	−	0.134099i	0.999972	+	0.00751132i	$0.00239095\pi$
$104$	−2.30266	+	0.347070i	−0.225794	+	0.0340330i
$105$	−1.01331	+	0.940213i	−0.0988888	+	0.0917554i
$106$	−6.21205	+	1.91616i	−0.603368	+	0.186114i
$107$	8.96328	+	11.2396i	0.866513	+	1.08657i	0.995484	+	0.0949245i	$0.0302610\pi$
$107$	8.96328	+	11.2396i	0.866513	+	1.08657i	−0.128972	+	0.991648i	$0.541168\pi$
$108$	0.980850	+	1.22995i	0.0943823	+	0.118352i
$109$	11.4960	−	3.54603i	1.10111	−	0.339648i	0.309641	−	0.950854i	$-0.399791\pi$
$109$	11.4960	−	3.54603i	1.10111	−	0.339648i	0.791472	+	0.611205i	$0.209315\pi$
$110$	3.88203	−	3.60200i	0.370137	−	0.343437i
$111$	−1.14389	+	0.172414i	−0.108573	+	0.0163648i
$112$	0.389364	−	5.19570i	0.0367915	−	0.490948i
$113$	5.22842	−	2.51787i	0.491848	−	0.236861i	−0.171484	−	0.985187i	$-0.554856\pi$
$113$	5.22842	−	2.51787i	0.491848	−	0.236861i	0.663332	+	0.748325i	$0.269142\pi$
$114$	1.54219	+	0.475701i	0.144439	+	0.0445535i
$115$	2.09112	+	5.32808i	0.194998	+	0.496846i
$116$	7.56959	−	5.16086i	0.702819	−	0.479174i
$117$	−6.74590	−	1.01678i	−0.623658	−	0.0940014i
$118$	−1.30215	+	5.70509i	−0.119873	+	0.525196i
$119$	−10.0774	−	6.87065i	−0.923793	−	0.629831i
$120$	0.194483	+	0.180454i	0.0177538	+	0.0164731i
$121$	−15.3566	−	7.39536i	−1.39606	−	0.672305i
$122$	−3.60671	+	6.24701i	−0.326536	+	0.565578i
$123$	−1.25109	−	2.16696i	−0.112807	−	0.195388i
$124$	0.0942693	+	1.25794i	0.00846564	+	0.112966i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	5.57660	−	14.2089i	0.496803	−	1.26583i
$127$	−8.30612	+	10.4155i	−0.737049	+	0.924230i	−0.999167	−	0.0408061i	$-0.987007\pi$
$127$	−8.30612	+	10.4155i	−0.737049	+	0.924230i	0.262119	+	0.965036i	$0.415579\pi$
$128$	−1.00000			−0.0883883
$129$	1.67780	−	0.460026i	0.147722	−	0.0405030i
$130$	−2.32867			−0.204238
$131$	−4.30713	+	5.40097i	−0.376316	+	0.471885i	−0.933538	−	0.358478i	$-0.883296\pi$
$131$	−4.30713	+	5.40097i	−0.376316	+	0.471885i	0.557222	+	0.830363i	$0.311867\pi$
$132$	0.513298	−	1.30786i	0.0446768	−	0.113835i
$133$	−7.05273	−	30.9000i	−0.611549	−	2.67937i
$134$	0.434476	+	5.79768i	0.0375330	+	0.500843i
$135$	0.786580	+	1.36240i	0.0676981	+	0.117256i
$136$	−1.17045	+	2.02727i	−0.100365	+	0.173837i
$137$	2.92859	+	1.41034i	0.250207	+	0.120493i	0.554784	−	0.831994i	$-0.312801\pi$
$137$	2.92859	+	1.41034i	0.250207	+	0.120493i	−0.304577	+	0.952488i	$0.598515\pi$
$138$	1.11317	+	1.03287i	0.0947593	+	0.0879238i
$139$	−4.38410	−	2.98903i	−0.371855	−	0.253526i	0.362945	−	0.931811i	$-0.381771\pi$
$139$	−4.38410	−	2.98903i	−0.371855	−	0.253526i	−0.734800	+	0.678284i	$0.762724\pi$
$140$	1.15939	−	5.07964i	0.0979868	−	0.429308i
$141$	0.892381	+	0.134505i	0.0751521	+	0.0113274i
$142$	−6.95588	+	4.74244i	−0.583725	+	0.397977i
$143$	4.50537	+	11.4795i	0.376758	+	0.959963i
$144$	−2.79946	−	0.863519i	−0.233288	−	0.0719599i
$145$	8.25423	−	3.97503i	0.685477	−	0.330108i
$146$	−0.649870	+	8.67192i	−0.0537836	+	0.717693i
$147$	5.28540	−	0.796646i	0.435933	−	0.0657063i
$148$	3.19632	−	2.96575i	0.262736	−	0.243783i
$149$	−5.20528	+	1.60562i	−0.426433	+	0.131537i	−0.500541	−	0.865713i	$-0.666865\pi$
$149$	−5.20528	+	1.60562i	−0.426433	+	0.131537i	0.0741075	+	0.997250i	$0.476389\pi$
$150$	0.165415	+	0.207424i	0.0135061	+	0.0169361i
$151$	13.1114	+	16.4411i	1.06699	+	1.33796i	0.938124	+	0.346299i	$0.112562\pi$
$151$	13.1114	+	16.4411i	1.06699	+	1.33796i	0.128864	+	0.991662i	$0.458867\pi$
$152$	−5.81286	+	1.79303i	−0.471485	+	0.145434i
$153$	−5.02721	+	4.66457i	−0.406426	+	0.377108i
$154$	−27.2839	+	4.11239i	−2.19860	+	0.331386i
$155$	−0.0942693	+	1.25794i	−0.00757190	+	0.101040i
$156$	−0.556627	+	0.268057i	−0.0445658	+	0.0214618i
$157$	8.26161	+	2.54837i	0.659348	+	0.203382i	0.606332	−	0.795212i	$-0.292640\pi$
$157$	8.26161	+	2.54837i	0.659348	+	0.203382i	0.0530163	+	0.998594i	$0.483116\pi$
$158$	−1.91405	−	4.87692i	−0.152274	−	0.387987i
$159$	−1.42503	+	0.971568i	−0.113012	+	0.0770504i
$160$	−0.988831	−	0.149042i	−0.0781739	−	0.0117828i
$161$	6.63608	−	29.0746i	0.522996	−	2.29140i
$162$	−6.91683	−	4.71582i	−0.543438	−	0.370510i
$163$	4.08687	+	3.79206i	0.320108	+	0.297017i	0.823816	−	0.566857i	$-0.191841\pi$
$163$	4.08687	+	3.79206i	0.320108	+	0.297017i	−0.503708	+	0.863874i	$0.668031\pi$
$164$	8.49734	+	4.09210i	0.663531	+	0.319540i
$165$	0.702491	−	1.21675i	0.0546889	−	0.0947239i
$166$	1.12238	+	1.94401i	0.0871132	+	0.150885i
$167$	−0.619551	−	8.26734i	−0.0479423	−	0.639746i	−0.968480	−	0.249092i	$-0.919868\pi$
$167$	−0.619551	−	8.26734i	−0.0479423	−	0.639746i	0.920538	−	0.390654i	$-0.127751\pi$
$168$	−0.307594	−	1.34766i	−0.0237314	−	0.103974i
$169$	−2.76830	+	7.05352i	−0.212946	+	0.542578i
$170$	−1.45952	+	1.83019i	−0.111940	+	0.140369i
$171$	−17.8212			−1.36282
$172$	−4.24840	+	4.99511i	−0.323937	+	0.380874i
$173$	16.1954			1.23131			0.615656	−	0.788015i	$-0.288891\pi$
$173$	16.1954			1.23131			0.615656	+	0.788015i	$0.288891\pi$
$174$	1.51545	−	1.90032i	0.114886	−	0.144063i
$175$	1.90353	−	4.85011i	0.143893	−	0.366634i
$176$	1.17841	+	5.16294i	0.0888257	+	0.389171i
$177$	0.116020	+	1.54818i	0.00872058	+	0.116368i
$178$	5.49508	+	9.51777i	0.411874	+	0.713387i
$179$	0.0410631	−	0.0711234i	0.00306920	−	0.00531601i	−0.864487	−	0.502656i	$-0.832356\pi$
$179$	0.0410631	−	0.0711234i	0.00306920	−	0.00531601i	0.867556	+	0.497340i	$0.165690\pi$
$180$	−2.63949	−	1.27111i	−0.196736	−	0.0947430i
$181$	5.67278	+	5.26357i	0.421655	+	0.391238i	0.862263	−	0.506461i	$-0.169047\pi$
$181$	5.67278	+	5.26357i	0.421655	+	0.391238i	−0.440608	+	0.897700i	$0.645237\pi$
$182$	10.0248	+	6.83476i	0.743084	+	0.506626i
$183$	−0.425853	+	1.86578i	−0.0314799	+	0.137923i
$184$	−5.65981	−	0.853080i	−0.417247	−	0.0628899i
$185$	3.60264	−	2.45624i	0.264871	−	0.180586i
$186$	0.122270	+	0.311539i	0.00896528	+	0.0228431i
$187$	11.8460	+	3.65399i	0.866262	+	0.267206i
$188$	−3.06473	+	1.47589i	−0.223518	+	0.107641i
$189$	0.612532	−	8.17368i	0.0445552	−	0.594548i
$190$	−6.01517	+	0.906641i	−0.436386	+	0.0657747i
$191$	10.6774	−	9.90721i	0.772592	−	0.716861i	−0.191772	−	0.981440i	$-0.561423\pi$
$191$	10.6774	−	9.90721i	0.772592	−	0.716861i	0.964364	+	0.264579i	$0.0852329\pi$
$192$	−0.253519	+	0.0782003i	−0.0182962	+	0.00564362i
$193$	−13.7726	−	17.2703i	−0.991371	−	1.24314i	−0.969934	−	0.243370i	$-0.921747\pi$
$193$	−13.7726	−	17.2703i	−0.991371	−	1.24314i	−0.0214377	−	0.999770i	$-0.506824\pi$
$194$	0.0438640	+	0.0550037i	0.00314925	+	0.00394904i
$195$	−0.590362	+	0.182102i	−0.0422767	+	0.0130406i
$196$	−14.7688	+	13.7034i	−1.05491	+	0.978815i
$197$	−7.99093	+	1.20444i	−0.569330	+	0.0858127i	−0.427398	−	0.904064i	$-0.640570\pi$
$197$	−7.99093	+	1.20444i	−0.569330	+	0.0858127i	−0.141932	+	0.989876i	$0.545332\pi$
$198$	−1.15939	+	15.4710i	−0.0823944	+	1.09948i
$199$	−9.45861	+	4.55503i	−0.670503	+	0.322897i	−0.737979	−	0.674824i	$-0.764220\pi$
$199$	−9.45861	+	4.55503i	−0.670503	+	0.322897i	0.0674761	+	0.997721i	$0.478505\pi$
$200$	−0.955573	−	0.294755i	−0.0675692	−	0.0208423i
$201$	0.563528	+	1.43584i	0.0397482	+	0.101277i
$202$	12.0214	−	8.19603i	0.845820	−	0.576671i
$203$	−47.2008	−	7.11438i	−3.31285	−	0.499331i
$204$	−0.138197	+	0.605482i	−0.00967575	+	0.0423922i
$205$	7.79254	+	5.31286i	0.544255	+	0.371066i
$206$	1.00045	+	0.928283i	0.0697047	+	0.0646766i
$207$	−15.1078	−	7.27552i	−1.05006	−	0.505683i
$208$	1.16433	−	2.01669i	0.0807320	−	0.139832i
$209$	16.1072	+	27.8985i	1.11416	+	1.92978i
$210$	−0.103301	−	1.37845i	−0.00712842	−	0.0951221i
$211$	1.01598	+	4.45131i	0.0699431	+	0.306441i	0.997784	−	0.0665354i	$-0.0211945\pi$
$211$	1.01598	+	4.45131i	0.0699431	+	0.306441i	−0.927841	+	0.372976i	$0.878337\pi$
$212$	2.37503	−	6.05149i	0.163118	−	0.415618i
$213$	−1.39259	+	1.74625i	−0.0954186	+	0.119651i
$214$	−14.3760			−0.982722
$215$	−4.94543	+	4.30613i	−0.337275	+	0.293675i
$216$	−1.57316			−0.107040
$217$	4.09793	−	5.13864i	0.278186	−	0.348834i
$218$	−4.39521	+	11.1988i	−0.297681	+	0.758480i
$219$	0.513392	+	2.24932i	0.0346918	+	0.151995i
$220$	0.395749	+	5.28090i	0.0266814	+	0.356038i
$221$	−2.72558	−	4.72085i	−0.183343	−	0.317559i
$222$	0.578405	−	1.00183i	0.0388200	−	0.0672382i
$223$	−16.8352	−	8.10739i	−1.12737	−	0.542911i	−0.225206	−	0.974311i	$-0.572306\pi$
$223$	−16.8352	−	8.10739i	−1.12737	−	0.542911i	−0.902161	+	0.431400i	$0.858020\pi$
$224$	3.81940	+	3.54389i	0.255194	+	0.236786i
$225$	−2.42056	−	1.65031i	−0.161371	−	0.110021i
$226$	−1.29131	+	5.65761i	−0.0858968	+	0.376338i
$227$	−14.4187	−	2.17326i	−0.957000	−	0.144245i	−0.348070	−	0.937469i	$-0.613163\pi$
$227$	−14.4187	−	2.17326i	−0.957000	−	0.144245i	−0.608930	+	0.793224i	$0.708401\pi$
$228$	−1.33345	+	0.909134i	−0.0883102	+	0.0602089i
$229$	−2.69416	−	6.86460i	−0.178035	−	0.453626i	0.813801	−	0.581143i	$-0.197394\pi$
$229$	−2.69416	−	6.86460i	−0.178035	−	0.453626i	−0.991836	+	0.127518i	$0.959299\pi$
$230$	−5.46945	−	1.68710i	−0.360645	−	0.111244i
$231$	−6.59540	+	3.17618i	−0.433946	+	0.208977i
$232$	−0.684640	+	9.13589i	−0.0449488	+	0.599800i
$233$	4.98321	−	0.751098i	0.326461	−	0.0492061i	0.0162329	−	0.999868i	$-0.494833\pi$
$233$	4.98321	−	0.751098i	0.326461	−	0.0492061i	0.310228	+	0.950662i	$0.399595\pi$
$234$	5.00095	−	4.64020i	0.326922	−	0.303340i
$235$	−3.25047	+	1.00264i	−0.212037	+	0.0654047i
$236$	−3.64854	−	4.57513i	−0.237500	−	0.297815i
$237$	−0.866624	−	1.08671i	−0.0562933	−	0.0705895i
$238$	11.6548	−	3.59504i	0.755471	−	0.233032i
$239$	20.6883	−	19.1960i	1.33822	−	1.24168i	0.391278	−	0.920272i	$-0.372033\pi$
$239$	20.6883	−	19.1960i	1.33822	−	1.24168i	0.946939	−	0.321412i	$-0.104157\pi$
$240$	−0.262343	+	0.0395418i	−0.0169341	+	0.00255241i
$241$	−0.514799	+	6.86951i	−0.0331611	+	0.442504i	0.955769	+	0.294119i	$0.0950264\pi$
$241$	−0.514799	+	6.86951i	−0.0331611	+	0.442504i	−0.988930	+	0.148384i	$0.952593\pi$
$242$	15.3566	−	7.39536i	0.987161	−	0.475392i
$243$	−6.63214	−	2.04574i	−0.425452	−	0.131234i
$244$	−2.63536	−	6.71479i	−0.168712	−	0.429870i
$245$	−16.6462	+	11.3492i	−1.06349	+	0.725073i
$246$	2.47424	+	0.372932i	0.157752	+	0.0237773i
$247$	3.15213	−	13.8104i	0.200565	−	0.878734i
$248$	−1.04227	−	0.710608i	−0.0661843	−	0.0451237i
$249$	0.436566	+	0.405074i	0.0276662	+	0.0256705i
$250$	−0.900969	−	0.433884i	−0.0569823	−	0.0274412i
$251$	0.218010	−	0.377604i	0.0137607	−	0.0238342i	−0.859063	−	0.511870i	$-0.828953\pi$
$251$	0.218010	−	0.377604i	0.0137607	−	0.0238342i	0.872824	+	0.488036i	$0.162286\pi$
$252$	7.63204	+	13.2191i	0.480773	+	0.832724i
$253$	2.26517	+	30.2265i	0.142410	+	1.90033i
$254$	−2.96442	−	12.9880i	−0.186004	−	0.814937i
$255$	−0.226896	+	0.578122i	−0.0142088	+	0.0362034i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−8.28980			−0.517104			−0.258552	−	0.965997i	$-0.583245\pi$
$257$	−8.28980			−0.517104			−0.258552	+	0.965997i	$0.583245\pi$
$258$	−0.686431	+	1.59858i	−0.0427353	+	0.0995233i
$259$	−22.7183			−1.41165
$260$	1.45190	−	1.82063i	0.0900431	−	0.112910i
$261$	−9.80563	+	24.9843i	−0.606953	+	1.54649i
$262$	−1.53720	−	6.73490i	−0.0949684	−	0.416084i
$263$	1.28446	+	17.1400i	0.0792034	+	1.05690i	0.885272	+	0.465074i	$0.153972\pi$
$263$	1.28446	+	17.1400i	0.0792034	+	1.05690i	−0.806068	+	0.591822i	$0.798409\pi$
$264$	0.702491	+	1.21675i	0.0432354	+	0.0748858i
$265$	3.25043	−	5.62992i	0.199673	−	0.345843i
$266$	28.5559	+	13.7518i	1.75088	+	0.843178i
$267$	2.13740	+	1.98322i	0.130807	+	0.121371i
$268$	−4.80370	−	3.27510i	−0.293432	−	0.200059i
$269$	−0.640574	+	2.80654i	−0.0390565	+	0.171118i	−0.990695	−	0.136104i	$-0.956542\pi$
$269$	−0.640574	+	2.80654i	−0.0390565	+	0.171118i	0.951638	+	0.307221i	$0.0993992\pi$
$270$	−1.55559	−	0.234467i	−0.0946702	−	0.0142692i
$271$	−20.5552	+	14.0143i	−1.24864	+	0.851310i	−0.993303	−	0.115541i	$-0.963140\pi$
$271$	−20.5552	+	14.0143i	−1.24864	+	0.851310i	−0.255340	+	0.966851i	$0.582187\pi$
$272$	−0.855225	−	2.17908i	−0.0518556	−	0.132126i
$273$	3.07594	+	0.948803i	0.186165	+	0.0574242i
$274$	−2.92859	+	1.41034i	−0.176923	+	0.0852015i
$275$	−0.395749	+	5.28090i	−0.0238646	+	0.318450i
$276$	−1.50158	+	0.226327i	−0.0903846	+	0.0136233i
$277$	2.84714	−	2.64176i	0.171068	−	0.158728i	−0.589993	−	0.807409i	$-0.700869\pi$
$277$	2.84714	−	2.64176i	0.171068	−	0.158728i	0.761061	+	0.648681i	$0.224679\pi$
$278$	5.07036	−	1.56400i	0.304100	−	0.0938025i
$279$	−2.30417	−	2.88934i	−0.137947	−	0.172980i
$280$	3.24855	+	4.07356i	0.194138	+	0.243442i
$281$	8.04727	−	2.48226i	0.480060	−	0.148079i	−0.0452746	−	0.998975i	$-0.514416\pi$
$281$	8.04727	−	2.48226i	0.480060	−	0.148079i	0.525335	+	0.850896i	$0.323940\pi$
$282$	−0.661551	+	0.613829i	−0.0393948	+	0.0365530i
$283$	5.89480	−	0.888498i	0.350409	−	0.0528157i	0.0285207	−	0.999593i	$-0.490920\pi$
$283$	5.89480	−	0.888498i	0.350409	−	0.0528157i	0.321889	+	0.946777i	$0.395682\pi$
$284$	0.629132	−	8.39519i	0.0373321	−	0.498163i
$285$	−1.45406	+	0.700239i	−0.0861311	+	0.0414786i
$286$	−11.7841	−	3.63491i	−0.696807	−	0.214937i
$287$	−17.9528	−	45.7430i	−1.05972	−	2.70012i
$288$	2.42056	−	1.65031i	0.142633	−	0.0972454i
$289$	11.3915	+	1.71700i	0.670091	+	0.101000i
$290$	−2.03863	+	8.93181i	−0.119712	+	0.524494i
$291$	0.0154217	+	0.0105143i	0.000904034	+	0.000616360i
$292$	−6.37479	−	5.91494i	−0.373056	−	0.346146i
$293$	8.87549	+	4.27421i	0.518512	+	0.249702i	0.674788	−	0.738011i	$-0.264235\pi$
$293$	8.87549	+	4.27421i	0.518512	+	0.249702i	−0.156277	+	0.987713i	$0.549949\pi$
$294$	−2.67255	+	4.62899i	−0.155866	+	0.269968i
$295$	−2.92590	−	5.06781i	−0.170353	−	0.295059i
$296$	0.325845	+	4.34810i	0.0189393	+	0.252728i
$297$	1.85382	+	8.12213i	0.107570	+	0.471294i
$298$	1.99012	−	5.07074i	0.115284	−	0.293740i
$299$	8.31031	−	10.4208i	0.480597	−	0.602650i
$300$	−0.265306			−0.0153174
$301$	33.9284	−	4.02249i	1.95560	−	0.231853i
$302$	−21.0290			−1.21008
$303$	2.40671	−	3.01792i	0.138262	−	0.173375i
$304$	2.22241	−	5.66261i	0.127464	−	0.324773i
$305$	−1.60514	−	7.03257i	−0.0919100	−	0.402684i
$306$	−0.512493	−	6.83874i	−0.0292973	−	0.390945i
$307$	0.689061	+	1.19349i	0.0393268	+	0.0681160i	0.885019	−	0.465555i	$-0.154145\pi$
$307$	0.689061	+	1.19349i	0.0393268	+	0.0681160i	−0.845692	+	0.533671i	$0.820812\pi$
$308$	13.7961	−	23.8955i	0.786103	−	1.36157i
$309$	0.326225	+	0.157102i	0.0185583	+	0.00893721i
$310$	−0.924719	−	0.858014i	−0.0525205	−	0.0487319i
$311$	14.5774	+	9.93873i	0.826611	+	0.563574i	0.901082	−	0.433650i	$-0.142774\pi$
$311$	14.5774	+	9.93873i	0.826611	+	0.563574i	−0.0744709	+	0.997223i	$0.523727\pi$
$312$	0.137475	−	0.602319i	0.00778301	−	0.0340996i
$313$	−19.5338	−	2.94424i	−1.10411	−	0.166418i	−0.428405	−	0.903587i	$-0.640924\pi$
$313$	−19.5338	−	2.94424i	−1.10411	−	0.166418i	−0.675709	+	0.737169i	$0.736162\pi$
$314$	−7.14343	+	4.87030i	−0.403127	+	0.274847i
$315$	5.57660	+	14.2089i	0.314206	+	0.800583i
$316$	5.00632	+	1.54424i	0.281627	+	0.0868705i
$317$	13.2540	−	6.38281i	0.744421	−	0.358494i	−0.0229168	−	0.999737i	$-0.507295\pi$
$317$	13.2540	−	6.38281i	0.744421	−	0.358494i	0.767338	+	0.641243i	$0.221581\pi$
$318$	0.128888	−	1.71990i	0.00722770	−	0.0964469i
$319$	47.9748	−	7.23104i	2.68607	−	0.404860i
$320$	0.733052	−	0.680173i	0.0409788	−	0.0380228i
$321$	−3.64459	+	1.12421i	−0.203421	+	0.0627470i
$322$	18.5939	+	23.3160i	1.03620	+	1.29935i
$323$	−8.87845	−	11.1332i	−0.494010	−	0.619469i
$324$	7.99955	−	2.46753i	0.444419	−	0.137085i
$325$	1.70703	−	1.58390i	0.0946892	−	0.0878588i
$326$	−5.51287	+	0.830931i	−0.305330	+	0.0460210i
$327$	−0.238519	+	3.18282i	−0.0131902	+	0.176010i
$328$	−8.49734	+	4.09210i	−0.469187	+	0.225949i
$329$	16.9358	+	5.22401i	0.933702	+	0.288009i
$330$	0.513298	+	1.30786i	0.0282561	+	0.0719954i
$331$	−26.1223	+	17.8099i	−1.43581	+	0.978919i	−0.439053	+	0.898461i	$0.644686\pi$
$331$	−26.1223	+	17.8099i	−1.43581	+	0.978919i	−0.996758	+	0.0804578i	$0.974362\pi$
$332$	−2.21968	−	0.334563i	−0.121821	−	0.0183615i
$333$	−2.84247	+	12.4537i	−0.155767	+	0.682458i
$334$	6.84995	+	4.67021i	0.374812	+	0.255543i
$335$	−4.26191	−	3.95448i	−0.232853	−	0.216056i
$336$	1.24542	+	0.599764i	0.0679434	+	0.0327198i
$337$	−2.13560	+	3.69896i	−0.116333	+	0.201495i	−0.918312	−	0.395857i	$-0.870447\pi$
$337$	−2.13560	+	3.69896i	−0.116333	+	0.201495i	0.801979	+	0.597353i	$0.203781\pi$
$338$	−3.78865	−	6.56214i	−0.206076	−	0.356933i
$339$	0.115054	+	1.53529i	0.00624889	+	0.0833856i
$340$	−0.520898	−	2.28220i	−0.0282497	−	0.123770i
$341$	−2.44061	+	6.21856i	−0.132166	+	0.336754i
$342$	11.1113	−	13.9332i	0.600831	−	0.753419i
$343$	68.4992			3.69861
$344$	−1.25650	−	6.43593i	−0.0677460	−	0.347002i
$345$	−1.51854			−0.0817556
$346$	−10.0977	+	12.6621i	−0.542853	+	0.680717i
$347$	5.05940	−	12.8911i	0.271603	−	0.692032i	−0.728374	−	0.685180i	$-0.759724\pi$
$347$	5.05940	−	12.8911i	0.271603	−	0.692032i	0.999977	−	0.00685239i	$-0.00218120\pi$
$348$	0.540860	+	2.36966i	0.0289931	+	0.127027i
$349$	1.37423	+	18.3378i	0.0735608	+	0.981600i	0.904842	+	0.425748i	$0.139989\pi$
$349$	1.37423	+	18.3378i	0.0735608	+	0.981600i	−0.831281	+	0.555852i	$0.812392\pi$
$350$	2.60514	+	4.51223i	0.139250	+	0.241189i
$351$	1.83168	−	3.17257i	0.0977681	−	0.169339i
$352$	−4.77127	−	2.29772i	−0.254310	−	0.122469i
$353$	21.8184	+	20.2445i	1.16128	+	1.07751i	0.995824	+	0.0912906i	$0.0290992\pi$
$353$	21.8184	+	20.2445i	1.16128	+	1.07751i	0.165453	+	0.986218i	$0.447091\pi$
$354$	−1.28275	−	0.874564i	−0.0681774	−	0.0464826i
$355$	1.87334	−	8.20765i	0.0994268	−	0.435617i
$356$	−10.8674	−	1.63800i	−0.575972	−	0.0868138i
$357$	2.67359	−	1.82282i	0.141501	−	0.0964740i
$358$	0.0300041	+	0.0764492i	0.00158577	+	0.00404046i
$359$	−3.21042	−	0.990284i	−0.169440	−	0.0522652i	0.208875	−	0.977942i	$-0.433020\pi$
$359$	−3.21042	−	0.990284i	−0.169440	−	0.0522652i	−0.378314	+	0.925677i	$0.623496\pi$
$360$	2.63949	−	1.27111i	0.139113	−	0.0669935i
$361$	1.34546	−	17.9539i	0.0708138	−	0.944944i
$362$	−7.65215	+	1.15338i	−0.402188	+	0.0606201i
$363$	3.31488	−	3.07576i	0.173986	−	0.161435i
$364$	−11.5940	+	3.57626i	−0.607689	+	0.187447i
$365$	−5.42201	−	6.79899i	−0.283801	−	0.355875i
$366$	−1.19321	−	1.49624i	−0.0623702	−	0.0782098i
$367$	−8.54630	+	2.63618i	−0.446113	+	0.137608i	−0.509669	−	0.860371i	$-0.670232\pi$
$367$	−8.54630	+	2.63618i	−0.446113	+	0.137608i	0.0635558	+	0.997978i	$0.479756\pi$
$368$	4.19580	−	3.89313i	0.218721	−	0.202944i
$369$	−27.3216	+	4.11806i	−1.42230	+	0.214378i
$370$	−0.325845	+	4.34810i	−0.0169399	+	0.226047i
$371$	−30.5170	+	14.6962i	−1.58436	+	0.762989i
$372$	−0.319805	−	0.0986468i	−0.0165811	−	0.00511460i
$373$	−11.4440	−	29.1588i	−0.592548	−	1.50979i	−0.840940	−	0.541128i	$-0.817997\pi$
$373$	−11.4440	−	29.1588i	−0.592548	−	1.50979i	0.248392	−	0.968660i	$-0.420098\pi$
$374$	−10.2426	+	6.98331i	−0.529634	+	0.361098i
$375$	−0.262343	−	0.0395418i	−0.0135473	−	0.00204193i
$376$	0.756925	−	3.31630i	0.0390354	−	0.171025i
$377$	−17.6271	−	12.0179i	−0.907840	−	0.618955i
$378$	6.00853	+	5.57510i	0.309045	+	0.286752i
$379$	31.3049	+	15.0757i	1.60803	+	0.774384i	0.999812	−	0.0193889i	$-0.00617207\pi$
$379$	31.3049	+	15.0757i	1.60803	+	0.774384i	0.608214	+	0.793773i	$0.291886\pi$
$380$	3.04156	−	5.26813i	0.156029	−	0.270249i
$381$	−1.76720	−	3.06088i	−0.0905363	−	0.156814i
$382$	1.08850	+	14.5250i	0.0556924	+	0.743164i
$383$	3.37840	+	14.8017i	0.172628	+	0.756333i	0.984910	+	0.173068i	$0.0553680\pi$
$383$	3.37840	+	14.8017i	0.172628	+	0.756333i	−0.812282	+	0.583265i	$0.801775\pi$
$384$	0.0969271	−	0.246966i	0.00494629	−	0.0126029i
$385$	17.2034	−	21.5724i	0.876766	−	1.09943i
$386$	22.0895			1.12433
$387$	2.04002	−	19.1021i	0.103700	−	0.971016i
$388$	−0.0703524			−0.00357160
$389$	−15.9598	+	20.0130i	−0.809195	+	1.01470i	0.190262	+	0.981733i	$0.439066\pi$
$389$	−15.9598	+	20.0130i	−0.809195	+	1.01470i	−0.999457	+	0.0329646i	$0.989505\pi$
$390$	0.225711	−	0.575102i	0.0114293	−	0.0291214i
$391$	−2.98149	−	13.0627i	−0.150780	−	0.660612i
$392$	−1.50558	−	20.0906i	−0.0760434	−	1.01473i
$393$	−0.916380	−	1.58722i	−0.0462252	−	0.0800645i
$394$	4.04059	−	6.99851i	0.203562	−	0.352580i
$395$	4.72024	+	2.27315i	0.237501	+	0.114375i
$396$	−11.3728	−	10.5525i	−0.571507	−	0.530281i
$397$	−19.6792	−	13.4171i	−0.987673	−	0.673384i	−0.0422085	−	0.999109i	$-0.513439\pi$
$397$	−19.6792	−	13.4171i	−0.987673	−	0.673384i	−0.945465	+	0.325725i	$0.894392\pi$
$398$	2.33608	−	10.2350i	0.117097	−	0.513037i
$399$	8.31487	+	1.25326i	0.416264	+	0.0627417i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	−8.76067	−	22.3218i	−0.437487	−	1.11470i	−0.964322	−	0.264731i	$-0.914717\pi$
$401$	−8.76067	−	22.3218i	−0.437487	−	1.11470i	0.526836	−	0.849967i	$-0.323378\pi$
$402$	−1.47394	−	0.454651i	−0.0735136	−	0.0226759i
$403$	2.64662	−	1.27455i	0.131838	−	0.0634897i
$404$	−1.08729	+	14.5088i	−0.0540945	+	0.721841i
$405$	8.27797	−	1.24770i	0.411336	−	0.0619989i
$406$	34.9915	−	32.4673i	1.73660	−	1.61133i
$407$	22.0650	−	6.80614i	1.09372	−	0.337368i
$408$	−0.387220	−	0.485559i	−0.0191703	−	0.0240387i
$409$	10.0821	+	12.6426i	0.498529	+	0.625136i	0.965897	−	0.258927i	$-0.0833689\pi$
$409$	10.0821	+	12.6426i	0.498529	+	0.625136i	−0.467368	+	0.884063i	$0.654798\pi$
$410$	−9.01233	+	2.77994i	−0.445087	+	0.137291i
$411$	−0.632165	+	0.586564i	−0.0311824	+	0.0289331i
$412$	−1.34953	+	0.203409i	−0.0664867	+	0.0100213i
$413$	−2.27848	+	30.4043i	−0.112117	+	1.49610i
$414$	15.1078	−	7.27552i	0.742506	−	0.357572i
$415$	−2.14502	−	0.661652i	−0.105295	−	0.0324792i
$416$	0.850758	+	2.16770i	0.0417118	+	0.106280i
$417$	1.16313	−	0.793007i	0.0569586	−	0.0388337i
$418$	−31.8546	−	4.80131i	−1.55806	−	0.234840i
$419$	−6.85941	+	30.0530i	−0.335104	+	1.46819i	0.474002	+	0.880524i	$0.342809\pi$
$419$	−6.85941	+	30.0530i	−0.335104	+	1.46819i	−0.809106	+	0.587663i	$0.800048\pi$
$420$	1.14212	+	0.778686i	0.0557299	+	0.0379960i
$421$	−4.57676	−	4.24661i	−0.223058	−	0.206967i	0.560726	−	0.828002i	$-0.310522\pi$
$421$	−4.57676	−	4.24661i	−0.223058	−	0.206967i	−0.783783	+	0.621034i	$0.786713\pi$
$422$	−4.11363	−	1.98102i	−0.200248	−	0.0964344i
$423$	4.98267	−	8.63024i	0.242266	−	0.419616i
$424$	3.25043	+	5.62992i	0.157855	+	0.273413i
$425$	−0.174935	−	2.33435i	−0.00848561	−	0.113233i
$426$	−0.497009	−	2.17754i	−0.0240802	−	0.105502i
$427$	−13.7309	+	34.9859i	−0.664487	+	1.69309i
$428$	8.96328	−	11.2396i	0.433256	−	0.543286i
$429$	−3.27174			−0.157961
$430$	−0.283242	−	6.55132i	−0.0136591	−	0.315933i
$431$	18.8366			0.907329			0.453665	−	0.891173i	$-0.350116\pi$
$431$	18.8366			0.907329			0.453665	+	0.891173i	$0.350116\pi$
$432$	0.980850	−	1.22995i	0.0471911	−	0.0591758i
$433$	−13.8626	+	35.3214i	−0.666196	+	1.69744i	0.0492627	+	0.998786i	$0.484313\pi$
$433$	−13.8626	+	35.3214i	−0.666196	+	1.69744i	−0.715459	+	0.698655i	$0.753782\pi$
$434$	1.46254	+	6.40779i	0.0702039	+	0.307584i
$435$	0.181639	+	2.42380i	0.00870892	+	0.116213i
$436$	−6.01522	−	10.4187i	−0.288077	−	0.498964i
$437$	17.4091	−	30.1534i	0.832790	−	1.44243i
$438$	−2.07868	−	1.00104i	−0.0993232	−	0.0478315i
$439$	−16.9818	−	15.7568i	−0.810498	−	0.752033i	0.161537	−	0.986867i	$-0.448355\pi$
$439$	−16.9818	−	15.7568i	−0.810498	−	0.752033i	−0.972035	+	0.234834i	$0.924545\pi$
$440$	−4.37552	−	2.98318i	−0.208595	−	0.142218i
$441$	13.1338	−	57.5429i	0.625419	−	2.74014i
$442$	5.39028	+	0.812454i	0.256390	+	0.0386445i
$443$	−0.0765827	+	0.0522132i	−0.00363855	+	0.00248072i	−0.565138	−	0.824996i	$-0.691177\pi$
$443$	−0.0765827	+	0.0522132i	−0.00363855	+	0.00248072i	0.561499	+	0.827477i	$0.310225\pi$
$444$	0.422630	+	1.07684i	0.0200571	+	0.0511048i
$445$	−10.5019	−	3.23941i	−0.497838	−	0.153563i
$446$	16.8352	−	8.10739i	0.797169	−	0.383896i
$447$	0.108000	−	1.44116i	0.00510821	−	0.0681643i
$448$	−5.15208	+	0.776551i	−0.243413	+	0.0366886i
$449$	24.0596	−	22.3240i	1.13544	−	1.05353i	0.137429	−	0.990512i	$-0.456116\pi$
$449$	24.0596	−	22.3240i	1.13544	−	1.05353i	0.998012	−	0.0630233i	$-0.0200742\pi$
$450$	2.79946	−	0.863519i	0.131968	−	0.0407067i
$451$	31.1406	+	39.0491i	1.46635	+	1.83875i
$452$	−3.61818	−	4.53705i	−0.170185	−	0.213405i
$453$	−5.33125	+	1.64447i	−0.250484	+	0.0772641i
$454$	10.6890	−	9.91795i	0.501660	−	0.465473i
$455$	−11.9975	+	1.80833i	−0.562451	+	0.0847758i
$456$	0.120606	−	1.60937i	0.00564788	−	0.0753658i
$457$	−13.9528	+	6.71932i	−0.652685	+	0.314316i	−0.730763	−	0.682631i	$-0.760836\pi$
$457$	−13.9528	+	6.71932i	−0.652685	+	0.314316i	0.0780788	+	0.996947i	$0.475121\pi$
$458$	7.04674	+	2.17363i	0.329273	+	0.101567i
$459$	−1.34541	−	3.42804i	−0.0627982	−	0.160007i
$460$	4.72918	−	3.22430i	0.220499	−	0.150334i
$461$	28.8911	+	4.35464i	1.34559	+	0.202816i	0.782022	−	0.623251i	$-0.214188\pi$
$461$	28.8911	+	4.35464i	1.34559	+	0.202816i	0.563573	+	0.826066i	$0.309426\pi$
$462$	1.62893	−	7.13681i	0.0757847	−	0.332034i
$463$	1.96392	+	1.33898i	0.0912711	+	0.0622276i	0.608096	−	0.793864i	$-0.291934\pi$
$463$	1.96392	+	1.33898i	0.0912711	+	0.0622276i	−0.516825	+	0.856091i	$0.672886\pi$
$464$	−6.71586	−	6.23141i	−0.311776	−	0.289286i
$465$	−0.301531	−	0.145210i	−0.0139831	−	0.00673393i
$466$	−2.51975	+	4.36433i	−0.116725	+	0.202174i
$467$	17.0853	+	29.5927i	0.790615	+	1.36939i	0.925587	+	0.378536i	$0.123572\pi$
$467$	17.0853	+	29.5927i	0.790615	+	1.36939i	−0.134971	+	0.990849i	$0.543094\pi$
$468$	0.509816	+	6.80302i	0.0235662	+	0.314470i
$469$	6.74064	+	29.5327i	0.311254	+	1.36369i
$470$	1.24274	−	3.16645i	0.0573233	−	0.146057i
$471$	−1.43013	+	1.79333i	−0.0658971	+	0.0826324i
$472$	5.85181			0.269351
$473$	−31.7476	+	14.0714i	−1.45976	+	0.647003i
$474$	1.38996			0.0638428
$475$	3.79276	−	4.75597i	0.174024	−	0.218219i
$476$	−4.45596	+	11.3536i	−0.204238	+	0.520391i
$477$	4.23792	+	18.5675i	0.194041	+	0.850149i
$478$	2.10905	+	28.1433i	0.0964656	+	1.28724i
$479$	6.72009	+	11.6395i	0.307049	+	0.531824i	0.977715	−	0.209935i	$-0.0673252\pi$
$479$	6.72009	+	11.6395i	0.307049	+	0.531824i	−0.670667	+	0.741759i	$0.733992\pi$
$480$	0.132653	−	0.229762i	0.00605475	−	0.0104871i
$481$	−9.14814	−	4.40551i	−0.417119	−	0.200874i
$482$	−5.04983	−	4.68555i	−0.230013	−	0.213421i
$483$	6.53722	+	4.45700i	0.297454	+	0.202801i
$484$	−3.79277	+	16.6172i	−0.172399	+	0.755328i
$485$	−0.0695667	−	0.0104855i	−0.00315886	−	0.000476121i
$486$	5.73449	−	3.90971i	0.260122	−	0.177348i
$487$	−7.22555	−	18.4104i	−0.327421	−	0.834255i	−0.995895	−	0.0905192i	$-0.971147\pi$
$487$	−7.22555	−	18.4104i	−0.327421	−	0.834255i	0.668474	−	0.743736i	$-0.266948\pi$
$488$	6.89295	+	2.12619i	0.312029	+	0.0962483i
$489$	−1.33264	+	0.641765i	−0.0602640	+	0.0290216i
$490$	1.50558	−	20.0906i	0.0680153	−	0.907601i
$491$	26.8837	−	4.05207i	1.21324	−	0.182867i	0.488921	−	0.872328i	$-0.337391\pi$
$491$	26.8837	−	4.05207i	1.21324	−	0.182867i	0.724323	+	0.689461i	$0.242152\pi$
$492$	−1.83423	+	1.70192i	−0.0826937	+	0.0767285i
$493$	−20.4933	+	6.32136i	−0.922973	+	0.284700i
$494$	8.83208	+	11.0751i	0.397374	+	0.498291i
$495$	−9.67306	−	12.1296i	−0.434772	−	0.545187i
$496$	1.20542	−	0.371823i	0.0541250	−	0.0166953i
$497$	−32.1545	+	29.8350i	−1.44233	+	1.33828i
$498$	−0.588894	+	0.0887614i	−0.0263890	+	0.00397750i
$499$	2.49522	−	33.2964i	0.111701	−	1.49055i	−0.606705	−	0.794927i	$-0.707509\pi$
$499$	2.49522	−	33.2964i	0.111701	−	1.49055i	0.718406	−	0.695624i	$-0.244872\pi$
$500$	0.900969	−	0.433884i	0.0402926	−	0.0194039i
$501$	2.10180	+	0.648321i	0.0939017	+	0.0289648i
$502$	0.159296	+	0.405880i	0.00710973	+	0.0181153i
$503$	8.06448	−	5.49827i	0.359577	−	0.245156i	−0.370033	−	0.929019i	$-0.620654\pi$
$503$	8.06448	−	5.49827i	0.359577	−	0.245156i	0.729611	+	0.683863i	$0.239701\pi$
$504$	−15.0936	−	2.27499i	−0.672322	−	0.101336i
$505$	−3.23757	+	14.1847i	−0.144070	+	0.631212i
$506$	−25.0444	−	17.0750i	−1.11336	−	0.759075i
$507$	−1.47366	−	1.36735i	−0.0654474	−	0.0607263i
$508$	12.0027	+	5.78019i	0.532533	+	0.256454i
$509$	3.96240	−	6.86308i	0.175630	−	0.304201i	−0.764749	−	0.644328i	$-0.777137\pi$
$509$	3.96240	−	6.86308i	0.175630	−	0.304201i	0.940379	+	0.340128i	$0.110470\pi$
$510$	−0.310527	−	0.537848i	−0.0137503	−	0.0238163i
$511$	3.38600	+	45.1831i	0.149788	+	1.99878i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	3.49621	−	8.90820i	0.154361	−	0.393307i
$514$	5.16861	−	6.48123i	0.227978	−	0.285875i
$515$	−1.36478			−0.0601392
$516$	−0.821839	−	1.53337i	−0.0361794	−	0.0675029i
$517$	−18.0138			−0.792247
$518$	14.1646	−	17.7619i	0.622358	−	0.780412i
$519$	−1.56977	+	3.99971i	−0.0689053	+	0.175568i
$520$	0.518177	+	2.27028i	0.0227236	+	0.0995585i
$521$	−2.67418	−	35.6845i	−0.117158	−	1.56337i	−0.677762	−	0.735281i	$-0.737050\pi$
$521$	−2.67418	−	35.6845i	−0.117158	−	1.56337i	0.560604	−	0.828084i	$-0.310569\pi$
$522$	−13.4198	−	23.2438i	−0.587370	−	1.01735i
$523$	14.2715	−	24.7190i	0.624051	−	1.08089i	−0.364673	−	0.931136i	$-0.618819\pi$
$523$	14.2715	−	24.7190i	0.624051	−	1.08089i	0.988724	−	0.149752i	$-0.0478474\pi$
$524$	6.22399	+	2.99731i	0.271896	+	0.130938i
$525$	1.01331	+	0.940213i	0.0442244	+	0.0410343i
$526$	−14.2014	−	9.68237i	−0.619211	−	0.422171i
$527$	0.657094	−	2.87892i	0.0286235	−	0.125408i
$528$	−1.38929	−	0.209402i	−0.0604611	−	0.00911305i
$529$	8.06511	−	5.49870i	0.350657	−	0.239074i
$530$	2.37503	+	6.05149i	0.103165	+	0.262860i
$531$	16.3819	+	5.05314i	0.710913	+	0.219288i
$532$	−28.5559	+	13.7518i	−1.23806	+	0.596217i
$533$	1.64126	−	21.9010i	0.0710907	−	0.948640i
$534$	−2.88319	+	0.434571i	−0.124768	+	0.0188057i
$535$	10.5383	−	9.77815i	0.455612	−	0.422746i
$536$	5.55564	−	1.71369i	0.239967	−	0.0740200i
$537$	0.0135850	+	0.0170350i	0.000586234	+	0.000735114i
$538$	−1.79485	−	2.25067i	−0.0773815	−	0.0970333i
$539$	−101.952	+	31.4481i	−4.39140	+	1.35457i
$540$	1.15321	−	1.07002i	0.0496262	−	0.0460464i
$541$	−29.0247	+	4.37477i	−1.24787	+	0.188086i	−0.739561	−	0.673089i	$-0.764967\pi$
$541$	−29.0247	+	4.37477i	−1.24787	+	0.188086i	−0.508308	+	0.861175i	$0.669729\pi$
$542$	1.85914	−	24.8085i	0.0798570	−	1.06562i
$543$	−1.84977	+	0.890803i	−0.0793813	+	0.0382280i
$544$	2.23690	+	0.689991i	0.0959061	+	0.0295831i
$545$	−4.39521	−	11.1988i	−0.188270	−	0.479705i
$546$	−2.65962	+	1.81330i	−0.113821	+	0.0776021i
$547$	2.65031	+	0.399470i	0.113319	+	0.0170801i	0.205457	−	0.978666i	$-0.434132\pi$
$547$	2.65031	+	0.399470i	0.113319	+	0.0170801i	−0.0921379	+	0.995746i	$0.529370\pi$
$548$	0.723303	−	3.16900i	0.0308980	−	0.135373i
$549$	17.4605	+	11.9044i	0.745197	+	0.508067i
$550$	−3.88203	−	3.60200i	−0.165530	−	0.153590i
$551$	−50.2114	−	24.1806i	−2.13908	−	1.03013i
$552$	0.759271	−	1.31510i	0.0323167	−	0.0559742i
$553$	−13.6485	−	23.6399i	−0.580393	−	1.00527i
$554$	0.290248	+	3.87309i	0.0123315	+	0.164552i
$555$	0.257414	+	1.12781i	0.0109266	+	0.0478727i
$556$	−1.93854	+	4.93931i	−0.0822122	+	0.209473i
$557$	−15.9614	+	20.0149i	−0.676304	+	0.848059i	−0.995008	−	0.0997956i	$-0.968181\pi$
$557$	−15.9614	+	20.0149i	−0.676304	+	0.848059i	0.318704	+	0.947854i	$0.396753\pi$
$558$	3.69560			0.156447
$559$	14.4422	+	4.95960i	0.610841	+	0.209769i
$560$	−5.21027			−0.220174
$561$	−2.05061	+	2.57138i	−0.0865767	+	0.108564i
$562$	−3.07669	+	7.83927i	−0.129782	+	0.330680i
$563$	4.00073	+	17.5284i	0.168611	+	0.738732i	0.986554	+	0.163434i	$0.0522569\pi$
$563$	4.00073	+	17.5284i	0.168611	+	0.738732i	−0.817944	+	0.575298i	$0.804886\pi$
$564$	−0.0674410	−	0.899938i	−0.00283978	−	0.0378942i
$565$	−2.90155	−	5.02563i	−0.122069	−	0.211430i
$566$	−2.98069	+	5.16271i	−0.125288	+	0.217005i
$567$	−39.2981	−	18.9250i	−1.65037	−	0.794775i
$568$	6.17137	+	5.72619i	0.258945	+	0.240266i
$569$	9.59555	+	6.54214i	0.402266	+	0.274261i	0.747507	−	0.664253i	$-0.231250\pi$
$569$	9.59555	+	6.54214i	0.402266	+	0.274261i	−0.345241	+	0.938514i	$0.612203\pi$
$570$	0.359123	−	1.57342i	0.0150420	−	0.0659034i
$571$	−11.6916	−	1.76223i	−0.489279	−	0.0737469i	−0.100230	−	0.994964i	$-0.531958\pi$
$571$	−11.6916	−	1.76223i	−0.489279	−	0.0737469i	−0.389048	+	0.921217i	$0.627196\pi$
$572$	10.1891	−	6.94684i	0.426029	−	0.290462i
$573$	1.41181	+	3.59724i	0.0589794	+	0.150277i
$574$	46.9567	+	14.4842i	1.95994	+	0.604560i
$575$	5.15691	−	2.48344i	0.215058	−	0.103567i
$576$	−0.218930	+	2.92142i	−0.00912209	+	0.121726i
$577$	8.95983	−	1.35048i	0.373003	−	0.0562211i	0.0401340	−	0.999194i	$-0.487222\pi$
$577$	8.95983	−	1.35048i	0.373003	−	0.0562211i	0.332869	+	0.942973i	$0.391983\pi$
$578$	−8.44491	+	7.83573i	−0.351262	+	0.325924i
$579$	5.60010	−	1.72740i	0.232732	−	0.0717884i
$580$	−5.71211	−	7.16275i	−0.237182	−	0.297417i
$581$	7.29219	+	9.14412i	0.302531	+	0.379362i
$582$	−0.0178357	+	0.00550158i	−0.000739313	+	0.000228048i
$583$	25.2366	−	23.4161i	1.04519	−	0.969797i
$584$	8.59910	−	1.29611i	0.355833	−	0.0536333i
$585$	−0.509816	+	6.80302i	−0.0210783	+	0.281270i
$586$	−8.87549	+	4.27421i	−0.366643	+	0.176566i
$587$	11.9338	+	3.68108i	0.492559	+	0.151934i	0.531077	−	0.847323i	$-0.321787\pi$
$587$	11.9338	+	3.68108i	0.492559	+	0.151934i	−0.0385177	+	0.999258i	$0.512264\pi$
$588$	−1.95279	−	4.97562i	−0.0805315	−	0.205191i
$589$	6.34025	−	4.32271i	0.261246	−	0.178114i
$590$	5.78645	+	0.872166i	0.238224	+	0.0359065i
$591$	0.477082	−	2.09023i	0.0196245	−	0.0859807i
$592$	−3.60264	−	2.45624i	−0.148068	−	0.100951i
$593$	−20.8003	−	19.2998i	−0.854164	−	0.792549i	0.125730	−	0.992064i	$-0.459873\pi$
$593$	−20.8003	−	19.2998i	−0.854164	−	0.792549i	−0.979895	+	0.199516i	$0.936063\pi$
$594$	−7.50598	−	3.61469i	−0.307974	−	0.148312i
$595$	−6.09835	+	10.5627i	−0.250008	+	0.433027i
$596$	2.72364	+	4.71749i	0.111565	+	0.193236i
$597$	−0.208142	−	2.77746i	−0.00851868	−	0.113674i
$598$	2.96591	+	12.9945i	0.121285	+	0.531385i
$599$	−8.40988	+	21.4280i	−0.343618	+	0.875525i	0.649708	+	0.760184i	$0.274891\pi$
$599$	−8.40988	+	21.4280i	−0.343618	+	0.875525i	−0.993326	+	0.115341i	$0.963204\pi$
$600$	0.165415	−	0.207424i	0.00675306	−	0.00846807i
$601$	−2.99510			−0.122172			−0.0610862	−	0.998132i	$-0.519456\pi$
$601$	−2.99510			−0.122172			−0.0610862	+	0.998132i	$0.519456\pi$
$602$	−18.0091	+	29.0343i	−0.733997	+	1.18335i
$603$	17.0326			0.693620
$604$	13.1114	−	16.4411i	0.533494	−	0.668980i
$605$	−6.22708	+	15.8663i	−0.253167	+	0.645058i
$606$	0.858946	+	3.76329i	0.0348923	+	0.152873i
$607$	1.41141	+	18.8339i	0.0572873	+	0.764446i	0.949687	+	0.313200i	$0.101401\pi$
$607$	1.41141	+	18.8339i	0.0572873	+	0.764446i	−0.892400	+	0.451246i	$0.850980\pi$
$608$	3.04156	+	5.26813i	0.123351	+	0.213651i
$609$	6.33205	−	10.9674i	0.256587	−	0.444423i
$610$	6.49907	+	3.12979i	0.263140	+	0.126721i
$611$	5.80663	+	5.38776i	0.234911	+	0.217966i
$612$	5.66628	+	3.86320i	0.229046	+	0.156161i
$613$	2.24090	−	9.81801i	0.0905089	−	0.396546i	−0.909299	−	0.416143i	$-0.863381\pi$
$613$	2.24090	−	9.81801i	0.0905089	−	0.396546i	0.999808	+	0.0195978i	$0.00623858\pi$
$614$	−1.36273	−	0.205398i	−0.0549953	−	0.00828921i
$615$	−2.06741	+	1.40953i	−0.0833658	+	0.0568379i
$616$	10.0805	+	25.6848i	0.406156	+	1.03487i
$617$	25.2559	+	7.79042i	1.01676	+	0.313630i	0.757961	−	0.652300i	$-0.226196\pi$
$617$	25.2559	+	7.79042i	1.01676	+	0.313630i	0.258804	+	0.965930i	$0.416672\pi$
$618$	−0.326225	+	0.157102i	−0.0131227	+	0.00631956i
$619$	1.13408	−	15.1332i	0.0455824	−	0.608255i	−0.926905	−	0.375297i	$-0.877541\pi$
$619$	1.13408	−	15.1332i	0.0455824	−	0.608255i	0.972487	−	0.232957i	$-0.0748403\pi$
$620$	1.24737	−	0.188011i	0.0500958	−	0.00755072i
$621$	6.60067	−	6.12453i	0.264876	−	0.245769i
$622$	−16.8593	+	5.20040i	−0.675996	+	0.208517i
$623$	35.7021	+	44.7691i	1.43038	+	1.79363i
$624$	0.385198	+	0.483023i	0.0154202	+	0.0193364i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	14.4810	−	13.4364i	0.578777	−	0.537027i
$627$	−8.45121	+	1.27382i	−0.337509	+	0.0508713i
$628$	0.646095	−	8.62154i	0.0257820	−	0.344037i
$629$	−9.19617	+	4.42864i	−0.366675	+	0.176582i
$630$	−14.5859	−	4.49917i	−0.581118	−	0.179251i
$631$	17.2717	+	44.0076i	0.687576	+	1.75192i	0.658787	+	0.752330i	$0.271070\pi$
$631$	17.2717	+	44.0076i	0.687576	+	1.75192i	0.0287894	+	0.999586i	$0.490835\pi$
$632$	−4.32873	+	2.95128i	−0.172187	+	0.117395i
$633$	−1.19780	−	0.180539i	−0.0476082	−	0.00717578i
$634$	−3.27348	+	14.3420i	−0.130006	+	0.569595i
$635$	11.0071	+	7.50454i	0.436805	+	0.297808i
$636$	1.26431	+	1.17311i	0.0501331	+	0.0465167i
$637$	42.2694	+	20.3559i	1.67478	+	0.806530i
$638$	−24.2583	+	42.0167i	−0.960397	+	1.66346i
$639$	12.3318	+	21.3593i	0.487839	+	0.844962i
$640$	0.0747301	+	0.997204i	0.00295397	+	0.0394179i
$641$	−0.169944	−	0.744571i	−0.00671237	−	0.0294088i	0.971461	−	0.237200i	$-0.0762297\pi$
$641$	−0.169944	−	0.744571i	−0.00671237	−	0.0294088i	−0.978173	+	0.207791i	$0.933373\pi$
$642$	1.39342	−	3.55038i	0.0549940	−	0.140122i
$643$	25.3011	−	31.7266i	0.997779	−	1.25118i	0.0299543	−	0.999551i	$-0.490464\pi$
$643$	25.3011	−	31.7266i	0.997779	−	1.25118i	0.967825	−	0.251624i	$-0.0809647\pi$
$644$	−29.8223			−1.17516
$645$	−0.584122	−	1.63873i	−0.0229998	−	0.0645251i
$646$	14.2399			0.560263
$647$	−22.2795	+	27.9377i	−0.875899	+	1.09834i	0.118531	+	0.992950i	$0.462181\pi$
$647$	−22.2795	+	27.9377i	−0.875899	+	1.09834i	−0.994431	+	0.105393i	$0.966390\pi$
$648$	−3.05844	+	7.79278i	−0.120147	+	0.306129i
$649$	−6.89581	−	30.2125i	−0.270684	−	1.18594i
$650$	0.174022	+	2.32216i	0.00682569	+	0.0910825i
$651$	0.871871	+	1.51012i	0.0341713	+	0.0591865i
$652$	2.78757	−	4.82821i	0.109170	−	0.189087i
$653$	9.98501	+	4.80853i	0.390744	+	0.188172i	0.618932	−	0.785445i	$-0.287566\pi$
$653$	9.98501	+	4.80853i	0.390744	+	0.188172i	−0.228188	+	0.973617i	$0.573280\pi$
$654$	−2.33971	−	2.17094i	−0.0914901	−	0.0848904i
$655$	5.70774	+	3.89147i	0.223020	+	0.152052i
$656$	2.09867	−	9.19488i	0.0819393	−	0.359000i
$657$	25.1920	+	3.79709i	0.982835	+	0.148139i
$658$	−14.6436	+	9.98384i	−0.570867	+	0.389210i
$659$	0.356072	+	0.907256i	0.0138706	+	0.0353417i	0.937641	−	0.347604i	$-0.113005\pi$
$659$	0.356072	+	0.907256i	0.0138706	+	0.0353417i	−0.923771	+	0.382946i	$0.874910\pi$
$660$	−1.34256	−	0.414126i	−0.0522592	−	0.0161198i
$661$	−25.7598	+	12.4053i	−1.00194	+	0.482509i	−0.861596	−	0.507594i	$-0.830535\pi$
$661$	−25.7598	+	12.4053i	−1.00194	+	0.482509i	−0.140343	+	0.990103i	$0.544821\pi$
$662$	2.36266	−	31.5275i	0.0918274	−	1.22535i
$663$	1.43007	−	0.215549i	0.0555394	−	0.00837122i
$664$	1.64552	−	1.52682i	0.0638585	−	0.0592520i
$665$	−30.2866	+	9.34217i	−1.17446	+	0.362274i
$666$	−7.96443	−	9.98708i	−0.308616	−	0.386992i
$667$	−32.6946	−	40.9978i	−1.26594	−	1.58744i
$668$	−7.92219	+	2.44367i	−0.306519	+	0.0945485i
$669$	3.63404	−	3.37189i	0.140500	−	0.130365i
$670$	5.74900	−	0.866522i	0.222103	−	0.0334767i
$671$	2.85471	−	38.0934i	0.110205	−	1.47058i
$672$	−1.24542	+	0.599764i	−0.0480433	+	0.0231364i
$673$	−3.22633	−	0.995191i	−0.124366	−	0.0383618i	0.231947	−	0.972728i	$-0.425490\pi$
$673$	−3.22633	−	0.995191i	−0.124366	−	0.0383618i	−0.356313	+	0.934367i	$0.615966\pi$
$674$	−1.56044	−	3.97594i	−0.0601060	−	0.153148i
$675$	1.29981	−	0.886193i	0.0500296	−	0.0341096i
$676$	7.49267	+	1.12934i	0.288180	+	0.0434361i
$677$	−5.03664	+	22.0670i	−0.193574	+	0.848102i	0.781088	+	0.624420i	$0.214665\pi$
$677$	−5.03664	+	22.0670i	−0.193574	+	0.848102i	−0.974662	+	0.223682i	$0.928192\pi$
$678$	−1.27207	−	0.867286i	−0.0488537	−	0.0333079i
$679$	0.268704	+	0.249321i	0.0103119	+	0.00956806i
$680$	2.10907	+	1.01568i	0.0808793	+	0.0389494i
$681$	1.93428	−	3.35027i	0.0741218	−	0.128383i
$682$	−3.34018	−	5.78535i	−0.127902	−	0.221533i
$683$	−2.02423	−	27.0114i	−0.0774548	−	1.03356i	−0.891577	−	0.452869i	$-0.850400\pi$
$683$	−2.02423	−	27.0114i	−0.0774548	−	1.03356i	0.814122	−	0.580694i	$-0.197219\pi$
$684$	3.96558	+	17.3744i	0.151628	+	0.664325i
$685$	1.18754	−	3.02580i	0.0453735	−	0.115610i
$686$	−42.7085	+	53.5548i	−1.63062	+	2.04473i
$687$	1.95646			0.0746436
$688$	5.81523	+	3.03036i	0.221704	+	0.115532i
$689$	−15.1384			−0.576726
$690$	0.946796	−	1.18724i	0.0360439	−	0.0451976i
$691$	9.83889	−	25.0691i	0.374289	−	0.953673i	−0.612326	−	0.790606i	$-0.709766\pi$
$691$	9.83889	−	25.0691i	0.374289	−	0.953673i	0.986615	−	0.163068i	$-0.0521388\pi$
$692$	−3.60381	−	15.7893i	−0.136996	−	0.600220i
$693$	6.04075	+	80.6082i	0.229469	+	3.06205i
$694$	6.92421	+	11.9931i	0.262839	+	0.455251i
$695$	−2.65305	+	4.59522i	−0.100636	+	0.174306i
$696$	−2.18990	−	1.05460i	−0.0830078	−	0.0399744i
$697$	−16.1842	−	15.0167i	−0.613019	−	0.568798i
$698$	−15.1939	−	10.3590i	−0.575097	−	0.392095i
$699$	−0.297512	+	1.30349i	−0.0112529	+	0.0493024i
$700$	−5.15208	−	0.776551i	−0.194730	−	0.0293509i
$701$	−18.0633	+	12.3154i	−0.682242	+	0.465145i	−0.854190	−	0.519961i	$-0.825946\pi$
$701$	−18.0633	+	12.3154i	−0.682242	+	0.465145i	0.171947	+	0.985106i	$0.444994\pi$
$702$	1.33838	+	3.41013i	0.0505139	+	0.128707i
$703$	−25.3457	−	7.81813i	−0.955933	−	0.294866i
$704$	4.77127	−	2.29772i	0.179824	−	0.0865987i
$705$	0.0674410	−	0.899938i	0.00253998	−	0.0338936i
$706$	−29.4314	+	4.43607i	−1.10766	+	0.166954i
$707$	55.5704	−	51.5618i	2.08994	−	1.93918i
$708$	1.48354	−	0.457613i	0.0557550	−	0.0171981i
$709$	9.05587	+	11.3557i	0.340100	+	0.426472i	0.922241	−	0.386616i	$-0.126356\pi$
$709$	9.05587	+	11.3557i	0.340100	+	0.426472i	−0.582140	+	0.813088i	$0.697785\pi$
$710$	5.24899	+	6.58203i	0.196991	+	0.247019i
$711$	−14.6666	+	4.52404i	−0.550039	+	0.169665i
$712$	8.05636	−	7.47521i	0.301925	−	0.280145i
$713$	7.13965	−	1.07613i	0.267382	−	0.0403014i
$714$	−0.241816	+	3.22681i	−0.00904973	+	0.120760i
$715$	11.1107	−	5.35063i	0.415517	−	0.200102i
$716$	−0.0784776	−	0.0242071i	−0.00293285	−	0.000904663i
$717$	2.73550	+	6.96993i	0.102159	+	0.260297i
$718$	2.77590	−	1.89258i	0.103596	−	0.0706304i
$719$	−20.1886	−	3.04295i	−0.752909	−	0.113483i	−0.238636	−	0.971109i	$-0.576700\pi$
$719$	−20.1886	−	3.04295i	−0.752909	−	0.113483i	−0.514273	+	0.857626i	$0.671938\pi$
$720$	−0.651900	+	2.85616i	−0.0242949	+	0.106443i
$721$	5.87526	+	4.00569i	0.218806	+	0.149180i
$722$	13.1981	+	12.2460i	0.491181	+	0.455750i
$723$	−1.64664	−	0.792979i	−0.0612392	−	0.0294912i
$724$	3.86929	−	6.70181i	0.143801	−	0.249071i
$725$	−4.58075	−	7.93410i	−0.170125	−	0.294665i
$726$	0.337931	+	4.50938i	0.0125418	+	0.167359i
$727$	−9.92616	−	43.4893i	−0.368141	−	1.61293i	−0.731883	−	0.681430i	$-0.761358\pi$
$727$	−9.92616	−	43.4893i	−0.368141	−	1.61293i	0.363742	−	0.931500i	$-0.381499\pi$
$728$	4.43268	−	11.2943i	0.164286	−	0.418594i
$729$	−14.5105	+	18.1956i	−0.537426	+	0.673912i
$730$	8.69623			0.321862
$731$	12.9498	−	8.24218i	0.478966	−	0.304848i
$732$	1.91376			0.0707347
$733$	−9.99689	+	12.5357i	−0.369244	+	0.463017i	−0.931391	−	0.364020i	$-0.881404\pi$
$733$	−9.99689	+	12.5357i	−0.369244	+	0.463017i	0.562147	+	0.827037i	$0.309975\pi$
$734$	3.26748	−	8.32540i	0.120605	−	0.307296i
$735$	−1.18940	−	5.21109i	−0.0438716	−	0.192214i
$736$	0.427736	+	5.70774i	0.0157666	+	0.210390i
$737$	−15.3945	−	26.6640i	−0.567062	−	0.982180i
$738$	13.8151	−	23.9284i	0.508540	−	0.880818i
$739$	18.3525	+	8.83809i	0.675107	+	0.325114i	0.739835	−	0.672789i	$-0.234904\pi$
$739$	18.3525	+	8.83809i	0.675107	+	0.325114i	−0.0647279	+	0.997903i	$0.520618\pi$
$740$	−3.19632	−	2.96575i	−0.117499	−	0.109023i
$741$	3.10517	+	2.11707i	0.114071	+	0.0777726i
$742$	7.53707	−	33.0221i	0.276695	−	1.21228i
$743$	−18.9534	−	2.85676i	−0.695332	−	0.104804i	−0.208140	−	0.978099i	$-0.566741\pi$
$743$	−18.9534	−	2.85676i	−0.695332	−	0.104804i	−0.487193	+	0.873295i	$0.661979\pi$
$744$	0.276520	−	0.188528i	0.0101377	−	0.00691179i
$745$	1.99012	+	5.07074i	0.0729123	+	0.185777i
$746$	29.9325	+	9.23296i	1.09591	+	0.338043i
$747$	5.92500	−	2.85333i	0.216784	−	0.104398i
$748$	0.926407	−	12.3620i	0.0338728	−	0.452001i
$749$	−74.0662	+	11.1637i	−2.70632	+	0.407912i
$750$	0.194483	−	0.180454i	0.00710151	−	0.00658924i
$751$	1.57319	−	0.485266i	0.0574067	−	0.0177076i	−0.265919	−	0.963995i	$-0.585675\pi$
$751$	1.57319	−	0.485266i	0.0574067	−	0.0177076i	0.323326	+	0.946288i	$0.395199\pi$
$752$	2.12086	+	2.65947i	0.0773397	+	0.0969809i
$753$	0.0721245	+	0.0904412i	0.00262836	+	0.00329586i
$754$	20.3863	−	6.28834i	0.742425	−	0.229008i
$755$	15.4154	−	14.3034i	0.561022	−	0.520552i
$756$	−8.10505	+	1.22164i	−0.294778	+	0.0444306i
$757$	−1.56914	+	20.9388i	−0.0570315	+	0.761032i	0.893234	+	0.449592i	$0.148431\pi$
$757$	−1.56914	+	20.9388i	−0.0570315	+	0.761032i	−0.950266	+	0.311441i	$0.899189\pi$
$758$	−31.3049	+	15.0757i	−1.13705	+	0.547572i
$759$	−7.68449	−	2.37035i	−0.278929	−	0.0860383i
$760$	2.22241	+	5.66261i	0.0806153	+	0.205405i
$761$	2.48811	−	1.69636i	0.0901938	−	0.0614931i	−0.517383	−	0.855754i	$-0.673094\pi$
$761$	2.48811	−	1.69636i	0.0901938	−	0.0614931i	0.607577	+	0.794261i	$0.292142\pi$
$762$	3.49492	+	0.526775i	0.126608	+	0.0190830i
$763$	−13.9480	+	61.1103i	−0.504953	+	2.21234i
$764$	−12.0348	−	8.20517i	−0.435403	−	0.296853i
$765$	5.02721	+	4.66457i	0.181759	+	0.168648i
$766$	−13.6789	−	6.58739i	−0.494237	−	0.238012i
$767$	−6.81346	+	11.8013i	−0.246020	+	0.426118i
$768$	0.132653	+	0.229762i	0.00478670	+	0.00829081i
$769$	2.27330	+	30.3351i	0.0819772	+	1.09391i	0.874809	+	0.484469i	$0.160987\pi$
$769$	2.27330	+	30.3351i	0.0819772	+	1.09391i	−0.792831	+	0.609441i	$0.791394\pi$
$770$	6.13982	+	26.9003i	0.221264	+	0.969420i
$771$	0.803507	−	2.04730i	0.0289376	−	0.0737318i
$772$	−13.7726	+	17.2703i	−0.495686	+	0.621570i
$773$	28.3894			1.02109			0.510547	−	0.859850i	$-0.329443\pi$
$773$	28.3894			1.02109			0.510547	+	0.859850i	$0.329443\pi$
$774$	13.6627	+	13.5049i	0.491096	+	0.485425i
$775$	1.26146			0.0453131
$776$	0.0438640	−	0.0550037i	0.00157463	−	0.00197452i
$777$	2.20202	−	5.61065i	0.0789970	−	0.201281i
$778$	−5.69599	−	24.9558i	−0.204211	−	0.894708i
$779$	−4.28741	−	57.2115i	−0.153612	−	2.04981i
$780$	0.308905	+	0.535038i	0.0110606	+	0.0191574i
$781$	22.2916	−	38.6102i	0.797656	−	1.38158i
$782$	12.0718	+	5.81347i	0.431687	+	0.207889i
$783$	−10.5651	−	9.80300i	−0.377567	−	0.350331i
$784$	16.6462	+	11.3492i	0.594507	+	0.405328i
$785$	1.92385	−	8.42895i	0.0686652	−	0.300842i
$786$	1.81229	+	0.273159i	0.0646422	+	0.00974325i
$787$	−24.1705	+	16.4792i	−0.861585	+	0.587419i	−0.911484	−	0.411335i	$-0.865063\pi$
$787$	−24.1705	+	16.4792i	−0.861585	+	0.587419i	0.0498987	+	0.998754i	$0.484110\pi$
$788$	2.95239	+	7.52257i	0.105175	+	0.267980i
$789$	−4.35749	−	1.34411i	−0.155131	−	0.0478515i
$790$	−4.72024	+	2.27315i	−0.167939	+	0.0808750i
$791$	−2.25952	+	30.1512i	−0.0803393	+	1.07205i
$792$	15.3411	−	2.31230i	0.545122	−	0.0821640i
$793$	−12.3136	+	11.4253i	−0.437268	+	0.405725i
$794$	22.7597	−	7.02044i	0.807712	−	0.249146i
$795$	1.07534	+	1.34844i	0.0381385	+	0.0478242i
$796$	6.54556	+	8.20787i	0.232001	+	0.290920i
$797$	−39.1890	+	12.0882i	−1.38815	+	0.428187i	−0.896668	−	0.442703i	$-0.854020\pi$
$797$	−39.1890	+	12.0882i	−1.38815	+	0.428187i	−0.491479	+	0.870890i	$0.663543\pi$
$798$	−6.16408	+	5.71943i	−0.218206	+	0.202465i
$799$	7.87382	−	1.18679i	0.278556	−	0.0419855i
$800$	−0.0747301	+	0.997204i	−0.00264211	+	0.0352565i
$801$	29.0084	−	13.9697i	1.02496	−	0.493596i
$802$	22.9141	+	7.06806i	0.809124	+	0.249582i
$803$	−16.8250	−	42.8693i	−0.593740	−	1.51282i
$804$	1.27445	−	0.868904i	0.0449463	−	0.0306439i
$805$	−29.4892	−	4.44478i	−1.03936	−	0.156658i
$806$	−0.653662	+	2.86388i	−0.0230243	+	0.100876i
$807$	−0.631032	−	0.430230i	−0.0222134	−	0.0151448i
$808$	−10.6655	−	9.89618i	−0.375212	−	0.348146i
$809$	−31.3999	−	15.1214i	−1.10396	−	0.531639i	−0.209059	−	0.977903i	$-0.567040\pi$
$809$	−31.3999	−	15.1214i	−1.10396	−	0.531639i	−0.894902	+	0.446264i	$0.852754\pi$
$810$	−4.18573	+	7.24991i	−0.147072	+	0.254736i
$811$	6.92522	+	11.9948i	0.243177	+	0.421195i	0.961618	−	0.274393i	$-0.0884770\pi$
$811$	6.92522	+	11.9948i	0.243177	+	0.421195i	−0.718440	+	0.695589i	$0.755144\pi$
$812$	3.56716	+	47.6005i	0.125183	+	1.67045i
$813$	−1.46871	−	6.43482i	−0.0515098	−	0.225679i
$814$	−8.43603	+	21.4947i	−0.295683	+	0.753387i
$815$	3.47604	−	4.35882i	0.121760	−	0.152683i
$816$	0.621053			0.0217412
$817$	39.2366	+	7.18820i	1.37272	+	0.251483i
$818$	−16.1705			−0.565388
$819$	22.1619	−	27.7902i	0.774401	−	0.971068i
$820$	3.44566	−	8.77939i	0.120328	−	0.306589i
$821$	−12.2196	−	53.5375i	−0.426466	−	1.86847i	−0.491961	−	0.870617i	$-0.663720\pi$
$821$	−12.2196	−	53.5375i	−0.426466	−	1.86847i	0.0654950	−	0.997853i	$-0.479137\pi$
$822$	−0.0644453	−	0.859963i	−0.00224779	−	0.0299947i
$823$	−7.25920	−	12.5733i	−0.253040	−	0.438278i	0.711321	−	0.702867i	$-0.248097\pi$
$823$	−7.25920	−	12.5733i	−0.253040	−	0.438278i	−0.964361	+	0.264589i	$0.914764\pi$
$824$	0.682388	−	1.18193i	0.0237721	−	0.0411745i
$825$	−1.26585	−	0.609599i	−0.0440711	−	0.0212235i
$826$	−22.3504	−	20.7381i	−0.777670	−	0.721572i
$827$	5.45867	+	3.72166i	0.189816	+	0.129415i	0.654500	−	0.756062i	$-0.272879\pi$
$827$	5.45867	+	3.72166i	0.189816	+	0.129415i	−0.464683	+	0.885477i	$0.653832\pi$
$828$	−3.73131	+	16.3479i	−0.129672	+	0.568130i
$829$	−14.5124	−	2.18739i	−0.504036	−	0.0759713i	−0.107898	−	0.994162i	$-0.534412\pi$
$829$	−14.5124	−	2.18739i	−0.504036	−	0.0759713i	−0.396139	+	0.918191i	$0.629650\pi$
$830$	1.85470	−	1.26451i	0.0643776	−	0.0438919i
$831$	0.376460	+	0.959206i	0.0130593	+	0.0332745i
$832$	−2.22521	−	0.686387i	−0.0771453	−	0.0237962i
$833$	42.4914	−	20.4628i	1.47224	−	0.708993i
$834$	−0.105200	+	1.40380i	−0.00364279	+	0.0486097i
$835$	−8.19792	+	1.23564i	−0.283701	+	0.0427610i
$836$	23.6148	−	21.9114i	0.816736	−	0.757821i
$837$	1.89632	−	0.584937i	0.0655464	−	0.0202184i
$838$	−19.2196	−	24.1007i	−0.663931	−	0.832543i
$839$	5.75389	+	7.21515i	0.198646	+	0.249095i	0.871171	−	0.490980i	$-0.163361\pi$
$839$	5.75389	+	7.21515i	0.198646	+	0.249095i	−0.672524	+	0.740075i	$0.734790\pi$
$840$	−1.32090	+	0.407445i	−0.0455755	+	0.0140582i
$841$	−40.2689	+	37.3641i	−1.38858	+	1.28842i
$842$	6.17370	−	0.930535i	0.212760	−	0.0320684i
$843$	−0.166966	+	2.22800i	−0.00575060	+	0.0767365i
$844$	4.11363	−	1.98102i	0.141597	−	0.0681894i
$845$	7.24067	+	2.23345i	0.249087	+	0.0768330i
$846$	3.64075	+	9.27647i	0.125171	+	0.318932i
$847$	73.3756	−	50.0267i	2.52122	−	1.71894i
$848$	−6.42826	−	0.968904i	−0.220747	−	0.0332723i
$849$	−0.351937	+	1.54194i	−0.0120784	+	0.0529191i
$850$	1.93414	+	1.31867i	0.0663404	+	0.0452301i
$851$	−18.2949	−	16.9752i	−0.627141	−	0.581902i
$852$	2.01235	+	0.969096i	0.0689419	+	0.0332007i
$853$	23.8423	−	41.2960i	0.816344	−	1.41395i	−0.0920155	−	0.995758i	$-0.529331\pi$
$853$	23.8423	−	41.2960i	0.816344	−	1.41395i	0.908359	−	0.418191i	$-0.137336\pi$
$854$	−18.7920	−	32.5486i	−0.643048	−	1.11379i
$855$	1.33178	+	17.7713i	0.0455458	+	0.607767i
$856$	3.19896	+	14.0155i	0.109338	+	0.479042i
$857$	4.38168	−	11.1643i	0.149675	−	0.381366i	−0.836297	−	0.548277i	$-0.815284\pi$
$857$	4.38168	−	11.1643i	0.149675	−	0.381366i	0.985972	+	0.166911i	$0.0533792\pi$
$858$	2.03990	−	2.55795i	0.0696409	−	0.0873269i
$859$	33.3044			1.13633			0.568166	−	0.822914i	$-0.307653\pi$
$859$	33.3044			1.13633			0.568166	+	0.822914i	$0.307653\pi$
$860$	5.29863	+	3.86323i	0.180682	+	0.131735i
$861$	13.0371			0.444303
$862$	−11.7445	+	14.7271i	−0.400018	+	0.501606i
$863$	2.14133	−	5.45602i	0.0728917	−	0.185725i	−0.889784	−	0.456381i	$-0.849145\pi$
$863$	2.14133	−	5.45602i	0.0728917	−	0.185725i	0.962676	+	0.270656i	$0.0872406\pi$
$864$	0.350061	+	1.53372i	0.0119093	+	0.0521782i
$865$	−1.21028	−	16.1501i	−0.0411508	−	0.549120i
$866$	−18.9722	−	32.8608i	−0.644702	−	1.11666i
$867$	−1.52819	+	2.64690i	−0.0519000	+	0.0898935i
$868$	−5.92168	−	2.85173i	−0.200995	−	0.0967941i
$869$	20.3382	+	18.8711i	0.689928	+	0.640159i
$870$	−2.00826	−	1.36921i	−0.0680863	−	0.0464204i
$871$	−3.01265	+	13.1993i	−0.102080	+	0.447240i
$872$	11.8961	+	1.79304i	0.402852	+	0.0607201i
$873$	0.170292	−	0.116103i	0.00576352	−	0.00392950i
$874$	12.7205	+	32.4113i	0.430278	+	1.09633i
$875$	−4.97880	−	1.53576i	−0.168314	−	0.0519180i
$876$	2.07868	−	1.00104i	0.0702321	−	0.0338220i
$877$	−1.50381	+	20.0670i	−0.0507801	+	0.677614i	0.912493	+	0.409092i	$0.134154\pi$
$877$	−1.50381	+	20.0670i	−0.0507801	+	0.677614i	−0.963273	+	0.268522i	$0.913465\pi$
$878$	22.9072	−	3.45270i	0.773080	−	0.116523i
$879$	−1.91586	+	1.77766i	−0.0646204	+	0.0599589i
$880$	5.06044	−	1.56094i	0.170587	−	0.0526192i
$881$	2.54732	+	3.19424i	0.0858215	+	0.107617i	0.822888	−	0.568203i	$-0.192361\pi$
$881$	2.54732	+	3.19424i	0.0858215	+	0.107617i	−0.737067	+	0.675820i	$0.763790\pi$
$882$	36.8001	+	46.1459i	1.23912	+	1.55381i
$883$	−22.4482	+	6.92437i	−0.755444	+	0.233023i	−0.648472	−	0.761239i	$-0.724592\pi$
$883$	−22.4482	+	6.92437i	−0.755444	+	0.233023i	−0.106972	+	0.994262i	$0.534115\pi$
$884$	−3.99599	+	3.70774i	−0.134400	+	0.124705i
$885$	1.53518	−	0.231391i	0.0516044	−	0.00777812i
$886$	0.00692661	−	0.0924292i	0.000232704	−	0.00310522i
$887$	−46.9398	+	22.6050i	−1.57608	+	0.759002i	−0.998361	−	0.0572308i	$-0.981773\pi$
$887$	−46.9398	+	22.6050i	−1.57608	+	0.759002i	−0.577723	+	0.816233i	$0.696059\pi$
$888$	−1.10542	−	0.340976i	−0.0370953	−	0.0114424i
$889$	−25.3587	−	64.6130i	−0.850505	−	2.16705i
$890$	9.08050	−	6.19098i	0.304379	−	0.207522i
$891$	43.8377	+	6.60747i	1.46862	+	0.221359i
$892$	−4.15795	+	18.2171i	−0.139218	+	0.609955i
$893$	17.0967	+	11.6564i	0.572121	+	0.390065i
$894$	1.05940	+	0.982984i	0.0354318	+	0.0328759i
$895$	−0.0739932	−	0.0356332i	−0.00247332	−	0.00119109i
$896$	2.60514	−	4.51223i	0.0870315	−	0.150743i
$897$	1.76809	+	3.06242i	0.0590348	+	0.102251i
$898$	2.45272	+	32.7293i	0.0818484	+	1.09219i
$899$	−2.57165	−	11.2672i	−0.0857695	−	0.375781i
$900$	−1.07031	+	2.72710i	−0.0356769	+	0.0909033i
$901$	−9.48818	+	11.8978i	−0.316097	+	0.396373i
$902$	−49.9457			−1.66301
$903$	−2.29516	+	8.76906i	−0.0763783	+	0.291816i
$904$	5.80310			0.193008
$905$	4.82493	−	6.05027i	0.160386	−	0.201118i
$906$	2.03828	−	5.19345i	0.0677173	−	0.172541i
$907$	−2.56126	−	11.2216i	−0.0850453	−	0.372608i	0.914439	−	0.404724i	$-0.132632\pi$
$907$	−2.56126	−	11.2216i	−0.0850453	−	0.372608i	−0.999484	+	0.0321162i	$0.989775\pi$
$908$	1.08968	+	14.5407i	0.0361622	+	0.482552i
$909$	−21.3122	−	36.9138i	−0.706881	−	1.22435i
$910$	6.06650	−	10.5075i	0.201102	−	0.348320i
$911$	21.6050	+	10.4044i	0.715806	+	0.344714i	0.756084	−	0.654474i	$-0.227110\pi$
$911$	21.6050	+	10.4044i	0.715806	+	0.344714i	−0.0402780	+	0.999189i	$0.512824\pi$
$912$	1.18306	+	1.09772i	0.0391751	+	0.0363492i
$913$	−9.82196	−	6.69650i	−0.325059	−	0.221622i
$914$	3.44606	−	15.0982i	0.113985	−	0.499403i
$915$	1.89239	+	0.285232i	0.0625604	+	0.00942947i
$916$	−6.09298	+	4.15413i	−0.201318	+	0.137256i
$917$	−13.1498	−	33.5050i	−0.434243	−	1.10643i
$918$	3.51900	+	1.08547i	0.116144	+	0.0358257i
$919$	32.2444	−	15.5281i	1.06365	−	0.512225i	0.181592	−	0.983374i	$-0.441875\pi$
$919$	32.2444	−	15.5281i	1.06365	−	0.512225i	0.882054	+	0.471149i	$0.156161\pi$
$920$	−0.427736	+	5.70774i	−0.0141020	+	0.188179i
$921$	−0.361540	+	0.0544934i	−0.0119132	+	0.00179562i
$922$	−21.4179	+	19.8729i	−0.705362	+	0.654480i
$923$	−18.7335	+	5.77851i	−0.616619	+	0.190202i
$924$	4.56416	+	5.72328i	0.150150	+	0.188282i
$925$	−2.71860	−	3.40901i	−0.0893869	−	0.112088i
$926$	−2.27134	+	0.700616i	−0.0746409	+	0.0230237i
$927$	2.93093	−	2.71951i	0.0962645	−	0.0893204i
$928$	9.05918	−	1.36545i	0.297382	−	0.0448231i
$929$	0.767767	−	10.2451i	0.0251896	−	0.336132i	−0.970344	−	0.241727i	$-0.922286\pi$
$929$	0.767767	−	10.2451i	0.0251896	−	0.336132i	0.995534	−	0.0944050i	$-0.0300949\pi$
$930$	0.301531	−	0.145210i	0.00988758	−	0.00476161i
$931$	117.111	+	36.1241i	3.83817	+	1.18392i
$932$	−1.84113	−	4.69114i	−0.0603084	−	0.153663i
$933$	−3.86748	+	2.63680i	−0.126616	+	0.0863250i
$934$	−33.7890	−	5.09287i	−1.10561	−	0.166644i
$935$	2.75853	−	12.0859i	0.0902135	−	0.395251i
$936$	−5.63668	−	3.84302i	−0.184241	−	0.125613i
$937$	14.5503	+	13.5007i	0.475336	+	0.441048i	0.881100	−	0.472931i	$-0.156804\pi$
$937$	14.5503	+	13.5007i	0.475336	+	0.441048i	−0.405763	+	0.913978i	$0.632994\pi$
$938$	−27.2923	−	13.1433i	−0.891125	−	0.429143i
$939$	2.62048	−	4.53880i	0.0855161	−	0.148118i
$940$	1.70079	+	2.94586i	0.0554738	+	0.0960834i
$941$	−2.96378	−	39.5489i	−0.0966166	−	1.28926i	−0.809142	−	0.587613i	$-0.800068\pi$
$941$	−2.96378	−	39.5489i	−0.0966166	−	1.28926i	0.712526	−	0.701646i	$-0.247551\pi$
$942$	−0.510409	−	2.23625i	−0.0166300	−	0.0728609i
$943$	19.7220	−	50.2510i	0.642238	−	1.63640i
$944$	−3.64854	+	4.57513i	−0.118750	+	0.148908i
$945$	−8.19660			−0.266635
$946$	8.79288	−	33.5947i	0.285881	−	1.09226i
$947$	55.5197			1.80415			0.902073	−	0.431583i	$-0.142045\pi$
$947$	55.5197			1.80415			0.902073	+	0.431583i	$0.142045\pi$
$948$	−0.866624	+	1.08671i	−0.0281466	+	0.0352948i
$949$	−7.39839	+	18.8508i	−0.240162	+	0.611922i
$950$	1.35362	+	5.93060i	0.0439172	+	0.192414i
$951$	0.291663	+	3.89197i	0.00945781	+	0.126206i
$952$	−6.09835	−	10.5627i	−0.197649	−	0.342338i
$953$	5.51753	−	9.55665i	0.178730	−	0.309570i	−0.762716	−	0.646734i	$-0.776134\pi$
$953$	5.51753	−	9.55665i	0.178730	−	0.309570i	0.941446	+	0.337164i	$0.109468\pi$
$954$	−17.1590	−	8.26333i	−0.555542	−	0.267535i
$955$	−10.6774	−	9.90721i	−0.345514	−	0.320590i
$956$	−23.3183	−	15.8981i	−0.754167	−	0.514182i
$957$	−2.86424	+	12.5490i	−0.0925876	+	0.405653i
$958$	−13.2901	−	2.00315i	−0.429382	−	0.0647190i
$959$	−13.9931	+	9.54036i	−0.451862	+	0.308074i
$960$	0.0969271	+	0.246966i	0.00312831	+	0.00797080i
$961$	−28.1022	−	8.66837i	−0.906521	−	0.279625i
$962$	9.14814	−	4.40551i	0.294948	−	0.142039i
$963$	−3.14734	+	41.9983i	−0.101422	+	1.35338i
$964$	6.81183	−	1.02672i	0.219394	−	0.0330684i
$965$	−16.1927	+	15.0247i	−0.521263	+	0.483661i
$966$	−7.56051	+	2.33211i	−0.243255	+	0.0750344i
$967$	1.23340	+	1.54663i	0.0396634	+	0.0497363i	0.801268	−	0.598306i	$-0.204159\pi$
$967$	1.23340	+	1.54663i	0.0396634	+	0.0497363i	−0.761604	+	0.648042i	$0.775588\pi$
$968$	−10.6271	−	13.3260i	−0.341568	−	0.428313i
$969$	3.61009	−	1.11357i	0.115973	−	0.0357729i
$970$	0.0515720	−	0.0478518i	0.00165588	−	0.00153643i
$971$	0.539257	−	0.0812800i	0.0173056	−	0.00260840i	−0.140384	−	0.990097i	$-0.544834\pi$
$971$	0.539257	−	0.0812800i	0.0173056	−	0.00260840i	0.157689	+	0.987489i	$0.449596\pi$
$972$	−0.518663	+	6.92107i	−0.0166361	+	0.221994i
$973$	24.9084	−	11.9952i	0.798526	−	0.384550i
$974$	18.8989	+	5.82953i	0.605559	+	0.186790i
$975$	0.225711	+	0.575102i	0.00722854	+	0.0184180i
$976$	−5.96001	+	4.06347i	−0.190775	+	0.130068i
$977$	22.6107	+	3.40801i	0.723380	+	0.109032i	0.500404	−	0.865792i	$-0.333185\pi$
$977$	22.6107	+	3.40801i	0.723380	+	0.109032i	0.222976	+	0.974824i	$0.428423\pi$
$978$	0.329134	−	1.44203i	0.0105246	−	0.0461111i
$979$	−48.0877	−	32.7857i	−1.53689	−	1.04783i
$980$	14.7688	+	13.7034i	0.471771	+	0.437739i
$981$	31.7542	+	15.2920i	1.01383	+	0.488237i
$982$	−13.5937	+	23.5449i	−0.433792	+	0.751349i
$983$	19.6526	+	34.0394i	0.626822	+	1.08569i	0.988186	+	0.153262i	$0.0489780\pi$
$983$	19.6526	+	34.0394i	0.626822	+	1.08569i	−0.361364	+	0.932425i	$0.617689\pi$
$984$	−0.186989	−	2.49519i	−0.00596099	−	0.0795438i
$985$	1.79823	+	7.87858i	0.0572965	+	0.251032i
$986$	7.83515	−	19.9636i	0.249522	−	0.635772i
$987$	−2.93169	+	3.67623i	−0.0933168	+	0.117016i
$988$	−14.1656			−0.450666
$989$	30.3280	+	22.1122i	0.964373	+	0.703126i
$990$	15.5144			0.493080
$991$	11.8728	−	14.8880i	0.377151	−	0.472933i	−0.556639	−	0.830755i	$-0.687909\pi$
$991$	11.8728	−	14.8880i	0.377151	−	0.472933i	0.933790	+	0.357822i	$0.116481\pi$
$992$	−0.460865	+	1.17426i	−0.0146325	+	0.0372829i
$993$	−1.86648	−	8.17758i	−0.0592309	−	0.259508i
$994$	−3.27795	−	43.7412i	−0.103970	−	1.38739i
$995$	5.24913	+	9.09176i	0.166409	+	0.288228i
$996$	0.297773	−	0.515758i	0.00943529	−	0.0163424i
$997$	53.4996	+	25.7640i	1.69435	+	0.815956i	0.994854	+	0.101318i	$0.0323060\pi$
$997$	53.4996	+	25.7640i	1.69435	+	0.815956i	0.699495	+	0.714637i	$0.253408\pi$
$998$	24.4764	+	22.7108i	0.774787	+	0.718898i
$999$	−5.66753	−	3.86406i	−0.179313	−	0.122253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.101.3	✓	60
43.23	even	21	inner	430.2.q.d.281.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.101.3	✓	60	1.1	even	1	trivial
430.2.q.d.281.3	yes	60	43.23	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.0969271 + 0.246966i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(-0.132653 - 0.229762i) q^{6} +(-2.60514 + 4.51223i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.14756 + 1.99264i) q^{9} +O(q^{10})\)	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.0969271 + 0.246966i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(-0.132653 - 0.229762i) q^{6} +(-2.60514 + 4.51223i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.14756 + 1.99264i) q^{9} +(0.826239 + 0.563320i) q^{10} +(1.17841 - 5.16294i) q^{11} +(0.262343 + 0.0395418i) q^{12} +(-1.92404 + 1.31179i) q^{13} +(-1.90353 - 4.85011i) q^{14} +(0.253519 + 0.0782003i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.174935 + 2.33435i) q^{17} +(-2.89689 + 0.436636i) q^{18} +(-4.45924 + 4.13757i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.861860 - 1.08074i) q^{21} +(3.30182 + 4.14035i) q^{22} +(-5.46945 + 1.68710i) q^{23} +(-0.194483 + 0.180454i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.174022 - 2.32216i) q^{26} +(-1.41737 + 0.682569i) q^{27} +(4.97880 + 1.53576i) q^{28} +(3.34707 + 8.52821i) q^{29} +(-0.219206 + 0.149452i) q^{30} +(-1.24737 - 0.188011i) q^{31} +(0.222521 - 0.974928i) q^{32} +(1.16085 + 0.791455i) q^{33} +(-1.71600 - 1.59221i) q^{34} +(4.69429 + 2.26065i) q^{35} +(1.46481 - 2.53712i) q^{36} +(2.18014 + 3.77612i) q^{37} +(-0.454592 - 6.06610i) q^{38} +(-0.137475 - 0.602319i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-5.88034 + 7.37372i) q^{41} +1.38232 q^{42} +(-3.92451 - 5.25340i) q^{43} -5.29571 q^{44} +(1.82658 - 2.29046i) q^{45} +(2.09112 - 5.32808i) q^{46} +(-0.756925 - 3.31630i) q^{47} +(-0.0198263 - 0.264564i) q^{48} +(-10.0735 - 17.4478i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.559549 - 0.269465i) q^{51} +(1.70703 + 1.58390i) q^{52} +(5.37127 + 3.66207i) q^{53} +(0.350061 - 1.53372i) q^{54} +(-5.23656 - 0.789285i) q^{55} +(-4.30493 + 2.93505i) q^{56} +(-0.589619 - 1.50232i) q^{57} +(-8.75449 - 2.70040i) q^{58} +(5.27229 - 2.53900i) q^{59} +(0.0198263 - 0.264564i) q^{60} +(7.13286 - 1.07511i) q^{61} +(0.924719 - 0.858014i) q^{62} +(-14.5859 + 4.49917i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.45190 + 1.82063i) q^{65} +(-1.34256 + 0.414126i) q^{66} +(4.26191 - 3.95448i) q^{67} +(2.31475 - 0.348892i) q^{68} +(0.113481 - 1.51430i) q^{69} +(-4.69429 + 2.26065i) q^{70} +(8.04471 + 2.48146i) q^{71} +(1.07031 + 2.72710i) q^{72} +(7.18516 - 4.89876i) q^{73} +(-4.31159 - 0.649867i) q^{74} +(0.0590361 - 0.258654i) q^{75} +(5.02611 + 3.42674i) q^{76} +(20.2264 + 18.7674i) q^{77} +(0.556627 + 0.268057i) q^{78} +(-2.61954 + 4.53717i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.625601 + 8.34806i) q^{81} +(-2.09867 - 9.19488i) q^{82} +(0.820100 - 2.08958i) q^{83} +(-0.861860 + 1.08074i) q^{84} +2.34090 q^{85} +(6.55417 + 0.207131i) q^{86} -2.43060 q^{87} +(3.30182 - 4.14035i) q^{88} +(4.01516 - 10.2305i) q^{89} +(0.651900 + 2.85616i) q^{90} +(-0.906700 - 12.0991i) q^{91} +(2.86187 + 4.95691i) q^{92} +(0.167337 - 0.289836i) q^{93} +(3.06473 + 1.47589i) q^{94} +(4.45924 + 4.13757i) q^{95} +(0.219206 + 0.149452i) q^{96} +(0.0156549 - 0.0685885i) q^{97} +(19.9219 + 3.00275i) q^{98} +(12.8186 - 8.73956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

L-functions

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