LMFDB - Embedded newform 195.2.v.a.4.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(4,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("195.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.v (of order $6$, degree $2$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.16
Character	$\chi$	$=$	195.4
Dual form			195.2.v.a.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36408 - 2.36265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72141 - 4.71362i) q^{4} +(1.91068 - 1.16160i) q^{5} +(-2.36265 + 1.36408i) q^{6} +(1.86649 + 3.23285i) q^{7} -9.39252 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.36408 - 2.36265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72141 - 4.71362i) q^{4} +(1.91068 - 1.16160i) q^{5} +(-2.36265 + 1.36408i) q^{6} +(1.86649 + 3.23285i) q^{7} -9.39252 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.138139 - 6.09877i) q^{10} +(-2.02671 - 1.17012i) q^{11} +5.44282i q^{12} +(1.39527 + 3.32464i) q^{13} +10.1841 q^{14} +(-2.23549 + 0.0506345i) q^{15} +(-7.36930 + 12.7640i) q^{16} +(2.29853 - 1.32706i) q^{17} +2.72815 q^{18} +(-1.93887 + 1.11941i) q^{19} +(-10.6751 - 5.84502i) q^{20} -3.73298i q^{21} +(-5.52918 + 3.19227i) q^{22} +(0.387679 + 0.223827i) q^{23} +(8.13416 + 4.69626i) q^{24} +(2.30138 - 4.43888i) q^{25} +(9.75821 + 1.23852i) q^{26} -1.00000i q^{27} +(10.1590 - 17.5958i) q^{28} +(0.774666 - 1.34176i) q^{29} +(-2.92975 + 5.35076i) q^{30} -3.17845i q^{31} +(10.7121 + 18.5538i) q^{32} +(1.17012 + 2.02671i) q^{33} -7.24083i q^{34} +(7.32154 + 4.00883i) q^{35} +(2.72141 - 4.71362i) q^{36} +(0.797986 - 1.38215i) q^{37} +6.10781i q^{38} +(0.453977 - 3.57686i) q^{39} +(-17.9461 + 10.9103i) q^{40} +(-0.866750 - 0.500418i) q^{41} +(-8.81972 - 5.09207i) q^{42} +(-10.1144 + 5.83954i) q^{43} +12.7375i q^{44} +(1.96131 + 1.07390i) q^{45} +(1.05765 - 0.610634i) q^{46} +8.06550 q^{47} +(12.7640 - 7.36930i) q^{48} +(-3.46757 + 6.00600i) q^{49} +(-7.34826 - 11.4923i) q^{50} -2.65411 q^{51} +(11.8740 - 15.6245i) q^{52} +8.33803i q^{53} +(-2.36265 - 1.36408i) q^{54} +(-5.23161 + 0.118497i) q^{55} +(-17.5310 - 30.3647i) q^{56} +2.23881 q^{57} +(-2.11341 - 3.66053i) q^{58} +(-4.61091 + 2.66211i) q^{59} +(6.32236 + 10.3995i) q^{60} +(0.317815 + 0.550471i) q^{61} +(-7.50957 - 4.33565i) q^{62} +(-1.86649 + 3.23285i) q^{63} +28.9710 q^{64} +(6.52781 + 4.73156i) q^{65} +6.38455 q^{66} +(-5.06226 + 8.76809i) q^{67} +(-12.5105 - 7.22292i) q^{68} +(-0.223827 - 0.387679i) q^{69} +(19.4586 - 11.8299i) q^{70} +(3.28689 - 1.89769i) q^{71} +(-4.69626 - 8.13416i) q^{72} -0.0493999 q^{73} +(-2.17703 - 3.77072i) q^{74} +(-4.21249 + 2.69349i) q^{75} +(10.5529 + 6.09271i) q^{76} -8.73609i q^{77} +(-7.83160 - 5.95169i) q^{78} +1.93513 q^{79} +(0.746282 + 32.9481i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.36463 + 1.36522i) q^{82} -7.63279 q^{83} +(-17.5958 + 10.1590i) q^{84} +(2.85024 - 5.20555i) q^{85} +31.8623i q^{86} +(-1.34176 + 0.774666i) q^{87} +(19.0360 + 10.9904i) q^{88} +(-4.56030 - 2.63289i) q^{89} +(5.21262 - 3.16902i) q^{90} +(-8.14381 + 10.7161i) q^{91} -2.43650i q^{92} +(-1.58923 + 2.75262i) q^{93} +(11.0020 - 19.0559i) q^{94} +(-2.40425 + 4.39101i) q^{95} -21.4241i q^{96} +(-6.24133 - 10.8103i) q^{97} +(9.46005 + 16.3853i) q^{98} -2.34025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 20 * q^4 + 16 * q^9	$ 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) $ 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.36408	−	2.36265i	0.964547	−	1.67065i	0.253722	−	0.967277i	$-0.418345\pi$
$2$	1.36408	−	2.36265i	0.964547	−	1.67065i	0.710826	−	0.703368i	$-0.248321\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−2.72141	−	4.71362i	−1.36070	−	2.35681i
$5$	1.91068	−	1.16160i	0.854481	−	0.519482i
$5$	1.91068	−	1.16160i	0.854481	−	0.519482i
$6$	−2.36265	+	1.36408i	−0.964547	+	0.556882i
$7$	1.86649	+	3.23285i	0.705467	+	1.22190i	0.966523	+	0.256581i	$0.0825959\pi$
$7$	1.86649	+	3.23285i	0.705467	+	1.22190i	−0.261056	+	0.965324i	$0.584071\pi$
$8$	−9.39252			−3.32076
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.138139	−	6.09877i	−0.0436833	−	1.92860i
$11$	−2.02671	−	1.17012i	−0.611077	−	0.352805i	0.162310	−	0.986740i	$-0.448106\pi$
$11$	−2.02671	−	1.17012i	−0.611077	−	0.352805i	−0.773387	+	0.633934i	$0.781439\pi$
$12$			5.44282i			1.57121i
$13$	1.39527	+	3.32464i	0.386979	+	0.922088i
$13$	1.39527	+	3.32464i	0.386979	+	0.922088i
$14$	10.1841			2.72182
$15$	−2.23549	+	0.0506345i	−0.577202	+	0.0130738i
$16$	−7.36930	+	12.7640i	−1.84233	+	3.19100i
$17$	2.29853	−	1.32706i	0.557475	−	0.321859i	−0.194656	−	0.980872i	$-0.562359\pi$
$17$	2.29853	−	1.32706i	0.557475	−	0.321859i	0.752132	+	0.659013i	$0.229026\pi$
$18$	2.72815			0.643032
$19$	−1.93887	+	1.11941i	−0.444806	+	0.256809i	−0.705634	−	0.708576i	$-0.749338\pi$
$19$	−1.93887	+	1.11941i	−0.444806	+	0.256809i	0.260828	+	0.965385i	$0.416005\pi$
$20$	−10.6751	−	5.84502i	−2.38702	−	1.30699i
$21$		−	3.73298i		−	0.814603i
$22$	−5.52918	+	3.19227i	−1.17883	+	0.680595i
$23$	0.387679	+	0.223827i	0.0808367	+	0.0466711i	0.539874	−	0.841746i	$-0.318472\pi$
$23$	0.387679	+	0.223827i	0.0808367	+	0.0466711i	−0.459037	+	0.888417i	$0.651805\pi$
$24$	8.13416	+	4.69626i	1.66038	+	0.958620i
$25$	2.30138	−	4.43888i	0.460276	−	0.887776i
$26$	9.75821	+	1.23852i	1.91374	+	0.242893i
$27$		−	1.00000i		−	0.192450i
$28$	10.1590	−	17.5958i	1.91986	−	3.32530i
$29$	0.774666	−	1.34176i	0.143852	−	0.249159i	−0.785092	−	0.619379i	$-0.787384\pi$
$29$	0.774666	−	1.34176i	0.143852	−	0.249159i	0.928944	+	0.370220i	$0.120718\pi$
$30$	−2.92975	+	5.35076i	−0.534897	+	0.976910i
$31$		−	3.17845i		−	0.570867i	−0.958399	−	0.285433i	$-0.907862\pi$
$31$		−	3.17845i		−	0.570867i	0.958399	−	0.285433i	$-0.0921375\pi$
$32$	10.7121	+	18.5538i	1.89364	+	3.27988i
$33$	1.17012	+	2.02671i	0.203692	+	0.352805i
$34$		−	7.24083i		−	1.24179i
$35$	7.32154	+	4.00883i	1.23757	+	0.677617i
$36$	2.72141	−	4.71362i	0.453568	−	0.785603i
$37$	0.797986	−	1.38215i	0.131188	−	0.227224i	−0.792947	−	0.609291i	$-0.791454\pi$
$37$	0.797986	−	1.38215i	0.131188	−	0.227224i	0.924135	+	0.382067i	$0.124787\pi$
$38$			6.10781i			0.990818i
$39$	0.453977	−	3.57686i	0.0726945	−	0.572755i
$40$	−17.9461	+	10.9103i	−2.83753	+	1.72508i
$41$	−0.866750	−	0.500418i	−0.135364	−	0.0781522i	0.430789	−	0.902453i	$-0.358235\pi$
$41$	−0.866750	−	0.500418i	−0.135364	−	0.0781522i	−0.566153	+	0.824301i	$0.691569\pi$
$42$	−8.81972	−	5.09207i	−1.36091	−	0.785723i
$43$	−10.1144	+	5.83954i	−1.54243	+	0.890522i	−0.543744	+	0.839251i	$0.682994\pi$
$43$	−10.1144	+	5.83954i	−1.54243	+	0.890522i	−0.998685	+	0.0512703i	$0.983673\pi$
$44$			12.7375i			1.92026i
$45$	1.96131	+	1.07390i	0.292375	+	0.160087i
$46$	1.05765	−	0.610634i	0.155942	−	0.0900330i
$47$	8.06550			1.17647			0.588237	−	0.808689i	$-0.299822\pi$
$47$	8.06550			1.17647			0.588237	+	0.808689i	$0.299822\pi$
$48$	12.7640	−	7.36930i	1.84233	−	1.06367i
$49$	−3.46757	+	6.00600i	−0.495367	+	0.858000i
$50$	−7.34826	−	11.4923i	−1.03920	−	1.62526i
$51$	−2.65411			−0.371650
$52$	11.8740	−	15.6245i	1.64662	−	2.16672i
$53$			8.33803i			1.14532i	0.819794	+	0.572658i	$0.194088\pi$
$53$			8.33803i			1.14532i	−0.819794	+	0.572658i	$0.805912\pi$
$54$	−2.36265	−	1.36408i	−0.321516	−	0.185627i
$55$	−5.23161	+	0.118497i	−0.705430	+	0.0159782i
$56$	−17.5310	−	30.3647i	−2.34268	−	4.05765i
$57$	2.23881			0.296538
$58$	−2.11341	−	3.66053i	−0.277504	−	0.480651i
$59$	−4.61091	+	2.66211i	−0.600289	+	0.346577i	−0.769155	−	0.639062i	$-0.779323\pi$
$59$	−4.61091	+	2.66211i	−0.600289	+	0.346577i	0.168866	+	0.985639i	$0.445989\pi$
$60$	6.32236	+	10.3995i	0.816214	+	1.34257i
$61$	0.317815	+	0.550471i	0.0406920	+	0.0704806i	0.885654	−	0.464346i	$-0.153710\pi$
$61$	0.317815	+	0.550471i	0.0406920	+	0.0704806i	−0.844962	+	0.534826i	$0.820377\pi$
$62$	−7.50957	−	4.33565i	−0.953716	−	0.550628i
$63$	−1.86649	+	3.23285i	−0.235156	+	0.407301i
$64$	28.9710			3.62138
$65$	6.52781	+	4.73156i	0.809675	+	0.586878i
$66$	6.38455			0.785884
$67$	−5.06226	+	8.76809i	−0.618453	+	1.07119i	0.371315	+	0.928507i	$0.378907\pi$
$67$	−5.06226	+	8.76809i	−0.618453	+	1.07119i	−0.989768	+	0.142685i	$0.954426\pi$
$68$	−12.5105	−	7.22292i	−1.51712	−	0.875908i
$69$	−0.223827	−	0.387679i	−0.0269456	−	0.0466711i
$70$	19.4586	−	11.8299i	2.32575	−	1.41394i
$71$	3.28689	−	1.89769i	0.390082	−	0.225214i	−0.292114	−	0.956384i	$-0.594359\pi$
$71$	3.28689	−	1.89769i	0.390082	−	0.225214i	0.682196	+	0.731170i	$0.261025\pi$
$72$	−4.69626	−	8.13416i	−0.553460	−	0.958620i
$73$	−0.0493999			−0.00578182			−0.00289091	−	0.999996i	$-0.500920\pi$
$73$	−0.0493999			−0.00578182			−0.00289091	+	0.999996i	$0.500920\pi$
$74$	−2.17703	−	3.77072i	−0.253074	−	0.438338i
$75$	−4.21249	+	2.69349i	−0.486417	+	0.311018i
$76$	10.5529	+	6.09271i	1.21050	+	0.698882i
$77$		−	8.73609i		−	0.995570i
$78$	−7.83160	−	5.95169i	−0.886754	−	0.673897i
$79$	1.93513			0.217720			0.108860	−	0.994057i	$-0.465280\pi$
$79$	1.93513			0.217720			0.108860	+	0.994057i	$0.465280\pi$
$80$	0.746282	+	32.9481i	0.0834368	+	3.68371i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.36463	+	1.36522i	−0.261129	+	0.150763i
$83$	−7.63279			−0.837807			−0.418904	−	0.908031i	$-0.637585\pi$
$83$	−7.63279			−0.837807			−0.418904	+	0.908031i	$0.637585\pi$
$84$	−17.5958	+	10.1590i	−1.91986	+	1.10843i
$85$	2.85024	−	5.20555i	0.309152	−	0.564621i
$86$			31.8623i			3.43580i
$87$	−1.34176	+	0.774666i	−0.143852	+	0.0830529i
$88$	19.0360	+	10.9904i	2.02924	+	1.17158i
$89$	−4.56030	−	2.63289i	−0.483391	−	0.279086i	0.238438	−	0.971158i	$-0.423365\pi$
$89$	−4.56030	−	2.63289i	−0.483391	−	0.279086i	−0.721828	+	0.692072i	$0.756698\pi$
$90$	5.21262	−	3.16902i	0.549458	−	0.334044i
$91$	−8.14381	+	10.7161i	−0.853703	+	1.12335i
$92$		−	2.43650i		−	0.254022i
$93$	−1.58923	+	2.75262i	−0.164795	+	0.285433i
$94$	11.0020	−	19.0559i	1.13476	−	1.96547i
$95$	−2.40425	+	4.39101i	−0.246671	+	0.450508i
$96$		−	21.4241i		−	2.18659i
$97$	−6.24133	−	10.8103i	−0.633711	−	1.09762i	−0.986787	−	0.162025i	$-0.948197\pi$
$97$	−6.24133	−	10.8103i	−0.633711	−	1.09762i	0.353075	−	0.935595i	$-0.385136\pi$
$98$	9.46005	+	16.3853i	0.955609	+	1.65516i
$99$		−	2.34025i		−	0.235204i
$100$	−27.1862	+	1.23218i	−2.71862	+	0.123218i
$101$	0.348954	−	0.604407i	0.0347222	−	0.0601407i	−0.848142	−	0.529769i	$-0.822279\pi$
$101$	0.348954	−	0.604407i	0.0347222	−	0.0601407i	0.882864	+	0.469628i	$0.155612\pi$
$102$	−3.62041	+	6.27074i	−0.358474	+	0.620896i
$103$			3.92434i			0.386676i	0.981132	+	0.193338i	$0.0619315\pi$
$103$			3.92434i			0.386676i	−0.981132	+	0.193338i	$0.938069\pi$
$104$	−13.1051	−	31.2267i	−1.28506	−	3.06203i
$105$	−4.33622	−	7.13252i	−0.423172	−	0.696063i
$106$	19.6998	+	11.3737i	1.91342	+	1.10471i
$107$	−1.40633	−	0.811946i	−0.135955	−	0.0784938i	0.430480	−	0.902600i	$-0.358344\pi$
$107$	−1.40633	−	0.811946i	−0.135955	−	0.0784938i	−0.566435	+	0.824106i	$0.691678\pi$
$108$	−4.71362	+	2.72141i	−0.453568	+	0.261868i
$109$			17.6077i			1.68651i	0.537512	+	0.843256i	$0.319364\pi$
$109$			17.6077i			1.68651i	−0.537512	+	0.843256i	$0.680636\pi$
$110$	−6.85635	+	12.5221i	−0.653727	+	1.19394i
$111$	−1.38215	+	0.797986i	−0.131188	+	0.0757415i
$112$	−55.0189			−5.19880
$113$	16.2305	−	9.37069i	1.52684	−	0.881520i	0.527346	−	0.849651i	$-0.323187\pi$
$113$	16.2305	−	9.37069i	1.52684	−	0.881520i	0.999492	−	0.0318695i	$-0.0101461\pi$
$114$	3.05391	−	5.28952i	0.286025	−	0.495409i
$115$	1.00073	−	0.0226667i	0.0933183	−	0.00211368i
$116$	−8.43272			−0.782959
$117$	−2.18158	+	2.87066i	−0.201688	+	0.265393i
$118$			14.5253i			1.33716i
$119$	8.58036	+	4.95387i	0.786561	+	0.454121i
$120$	20.9969	−	0.475586i	1.91675	−	0.0434148i
$121$	−2.76162	−	4.78327i	−0.251057	−	0.434843i
$122$	1.73409			0.156997
$123$	0.500418	+	0.866750i	0.0451212	+	0.0781522i
$124$	−14.9820	+	8.64986i	−1.34542	+	0.776780i
$125$	−0.758998	−	11.1545i	−0.0678869	−	0.997693i
$126$	5.09207	+	8.81972i	0.453637	+	0.785723i
$127$	10.7726	+	6.21958i	0.955916	+	0.551898i	0.894914	−	0.446239i	$-0.147237\pi$
$127$	10.7726	+	6.21958i	0.955916	+	0.551898i	0.0610024	+	0.998138i	$0.480570\pi$
$128$	18.0946	−	31.3407i	1.59935	−	2.77016i
$129$	11.6791			1.02829
$130$	20.0835	−	8.96871i	1.76144	−	0.786608i
$131$	−5.54798			−0.484730			−0.242365	−	0.970185i	$-0.577923\pi$
$131$	−5.54798			−0.484730			−0.242365	+	0.970185i	$0.577923\pi$
$132$	6.36877	−	11.0310i	0.554330	−	0.960128i
$133$	−7.23775	−	4.17872i	−0.627592	−	0.362341i
$134$	13.8106	+	23.9207i	1.19305	+	2.06643i
$135$	−1.16160	−	1.91068i	−0.0999744	−	0.164445i
$136$	−21.5890	+	12.4644i	−1.85124	+	1.06881i
$137$	−6.77644	−	11.7371i	−0.578951	−	1.00277i	−0.995600	−	0.0937045i	$-0.970129\pi$
$137$	−6.77644	−	11.7371i	−0.578951	−	1.00277i	0.416650	−	0.909067i	$-0.363204\pi$
$138$	−1.22127			−0.103961
$139$	−2.70422	−	4.68385i	−0.229369	−	0.397279i	0.728252	−	0.685309i	$-0.240333\pi$
$139$	−2.70422	−	4.68385i	−0.229369	−	0.397279i	−0.957621	+	0.288030i	$0.907000\pi$
$140$	−1.02879	−	45.4206i	−0.0869484	−	3.83874i
$141$	−6.98492	−	4.03275i	−0.588237	−	0.339619i
$142$		−	10.3544i		−	0.868918i
$143$	1.06242	−	8.37073i	0.0888439	−	0.699995i
$144$	−14.7386			−1.22822
$145$	−0.0784496	−	3.46352i	−0.00651488	−	0.287630i
$146$	−0.0673852	+	0.116715i	−0.00557684	+	0.00965937i
$147$	6.00600	−	3.46757i	0.495367	−	0.286000i
$148$	−8.68658			−0.714033
$149$	12.7018	−	7.33339i	1.04057	−	0.600775i	0.120577	−	0.992704i	$-0.461525\pi$
$149$	12.7018	−	7.33339i	1.04057	−	0.600775i	0.919995	+	0.391929i	$0.128192\pi$
$150$	0.617616	+	13.6268i	0.0504282	+	1.11262i
$151$		−	12.3287i		−	1.00329i	−0.865073	−	0.501646i	$-0.832728\pi$
$151$		−	12.3287i		−	1.00329i	0.865073	−	0.501646i	$-0.167272\pi$
$152$	18.2108	−	10.5140i	1.47709	−	0.852801i
$153$	2.29853	+	1.32706i	0.185825	+	0.107286i
$154$	−20.6403	−	11.9167i	−1.66324	−	0.960275i
$155$	−3.69208	−	6.07300i	−0.296555	−	0.487795i
$156$	−18.0954	+	7.59421i	−1.44879	+	0.608024i
$157$		−	24.7850i		−	1.97806i	−0.147709	−	0.989031i	$-0.547190\pi$
$157$		−	24.7850i		−	1.97806i	0.147709	−	0.989031i	$-0.452810\pi$
$158$	2.63967	−	4.57204i	0.210001	−	0.363732i
$159$	4.16902	−	7.22095i	0.330625	−	0.572658i
$160$	42.0194	+	23.0073i	3.32192	+	1.81889i
$161$			1.67108i			0.131700i
$162$	1.36408	+	2.36265i	0.107172	+	0.185627i
$163$	7.96570	+	13.7970i	0.623922	+	1.08066i	0.988748	+	0.149589i	$0.0477949\pi$
$163$	7.96570	+	13.7970i	0.623922	+	1.08066i	−0.364827	+	0.931075i	$0.618872\pi$
$164$			5.44737i			0.425368i
$165$	4.58996	+	2.51318i	0.357328	+	0.195651i
$166$	−10.4117	+	18.0336i	−0.808105	+	1.39968i
$167$	−12.7158	+	22.0244i	−0.983977	+	1.70430i	−0.337578	+	0.941298i	$0.609608\pi$
$167$	−12.7158	+	22.0244i	−0.983977	+	1.70430i	−0.646399	+	0.763000i	$0.723726\pi$
$168$			35.0621i			2.70510i
$169$	−9.10643	+	9.27755i	−0.700494	+	0.713658i
$170$	−8.41093	−	13.8349i	−0.645089	−	1.06109i
$171$	−1.93887	−	1.11941i	−0.148269	−	0.0856030i
$172$	55.0507	+	31.7835i	4.19758	+	2.42347i
$173$	−11.7189	+	6.76594i	−0.890975	+	0.514405i	−0.874261	−	0.485456i	$-0.838654\pi$
$173$	−11.7189	+	6.76594i	−0.890975	+	0.514405i	−0.0167136	+	0.999860i	$0.505320\pi$
$174$			4.22681i			0.320434i
$175$	18.6458	−	0.845095i	1.40949	−	0.0638832i
$176$	29.8709	−	17.2460i	2.25161	−	1.29997i
$177$	5.32422			0.400193
$178$	−12.4412	+	7.18293i	−0.932507	+	0.538383i
$179$	5.88270	−	10.1891i	0.439694	−	0.761572i	−0.557972	−	0.829860i	$-0.688420\pi$
$179$	5.88270	−	10.1891i	0.439694	−	0.761572i	0.997666	+	0.0682881i	$0.0217537\pi$
$180$	−0.275594	−	12.1674i	−0.0205416	−	0.906903i
$181$	13.2944			0.988163			0.494081	−	0.869416i	$-0.335505\pi$
$181$	13.2944			0.988163			0.494081	+	0.869416i	$0.335505\pi$
$182$	14.2096	+	33.8586i	1.05329	+	2.50976i
$183$		−	0.635629i		−	0.0469871i
$184$	−3.64129	−	2.10230i	−0.268439	−	0.154984i
$185$	−0.0808112	−	3.56779i	−0.00594136	−	0.262309i
$186$	4.33565	+	7.50957i	0.317905	+	0.550628i
$187$	−6.21128			−0.454214
$188$	−21.9495	−	38.0177i	−1.60083	−	2.77272i
$189$	3.23285	−	1.86649i	0.235156	−	0.135767i
$190$	7.09483	+	11.6701i	0.514713	+	0.846636i
$191$	−8.30162	−	14.3788i	−0.600684	−	1.04042i	−0.992718	−	0.120465i	$-0.961562\pi$
$191$	−8.30162	−	14.3788i	−0.600684	−	1.04042i	0.392033	−	0.919951i	$-0.371772\pi$
$192$	−25.0896	−	14.4855i	−1.81069	−	1.04540i
$193$	−6.56697	+	11.3743i	−0.472701	+	0.818742i	−0.999512	−	0.0312407i	$-0.990054\pi$
$193$	−6.56697	+	11.3743i	−0.472701	+	0.818742i	0.526811	+	0.849982i	$0.323387\pi$
$194$	−34.0546			−2.44498
$195$	−3.28747	−	7.36156i	−0.235420	−	0.527172i
$196$	37.7467			2.69619
$197$	−8.29927	+	14.3748i	−0.591298	+	1.02416i	0.402759	+	0.915306i	$0.368051\pi$
$197$	−8.29927	+	14.3748i	−0.591298	+	1.02416i	−0.994058	+	0.108853i	$0.965282\pi$
$198$	−5.52918	−	3.19227i	−0.392942	−	0.226865i
$199$	−7.70000	−	13.3368i	−0.545839	−	0.945420i	−0.998554	−	0.0537648i	$-0.982878\pi$
$199$	−7.70000	−	13.3368i	−0.545839	−	0.945420i	0.452715	−	0.891655i	$-0.350455\pi$
$200$	−21.6158	+	41.6923i	−1.52847	+	2.94809i
$201$	8.76809	−	5.06226i	0.618453	−	0.357064i
$202$	−0.952000	−	1.64891i	−0.0669825	−	0.116017i
$203$	5.78362			0.405931
$204$	7.22292	+	12.5105i	0.505706	+	0.875908i
$205$	−2.23736	+	0.0506768i	−0.156264	+	0.00353942i
$206$	9.27183	+	5.35309i	0.645999	+	0.372968i
$207$			0.447654i			0.0311141i
$208$	−52.7179	−	6.69099i	−3.65533	−	0.463936i
$209$	5.23937			0.362415
$210$	−22.7666	+	0.515669i	−1.57104	+	0.0355845i
$211$	2.80652	−	4.86103i	0.193209	−	0.334647i	−0.753103	−	0.657902i	$-0.771444\pi$
$211$	2.80652	−	4.86103i	0.193209	−	0.334647i	0.946312	+	0.323255i	$0.104777\pi$
$212$	39.3023	−	22.6912i	2.69929	−	1.55844i
$213$	−3.79537			−0.260055
$214$	−3.83669	+	2.21511i	−0.262271	+	0.151422i
$215$	−12.5421	+	22.9063i	−0.855366	+	1.56220i
$216$			9.39252i			0.639080i
$217$	10.2755	−	5.93255i	0.697544	−	0.402727i
$218$	41.6008	+	24.0182i	2.81756	+	1.62672i
$219$	0.0427816	+	0.0246999i	0.00289091	+	0.00166907i
$220$	14.7959	+	24.3373i	0.997539	+	1.64082i
$221$	7.61906	+	5.79017i	0.512513	+	0.389489i
$222$			4.35406i			0.292225i
$223$	9.04102	−	15.6595i	0.605431	−	1.04864i	−0.386552	−	0.922268i	$-0.626334\pi$
$223$	9.04102	−	15.6595i	0.605431	−	1.04864i	0.991983	−	0.126370i	$-0.0403327\pi$
$224$	−39.9879	+	69.2610i	−2.67180	+	4.62770i
$225$	4.99487	−	0.226386i	0.332991	−	0.0150924i
$226$		−	51.1293i		−	3.40107i
$227$	−4.23521	−	7.33560i	−0.281101	−	0.486881i	0.690555	−	0.723280i	$-0.257366\pi$
$227$	−4.23521	−	7.33560i	−0.281101	−	0.486881i	−0.971656	+	0.236399i	$0.924033\pi$
$228$	−6.09271	−	10.5529i	−0.403500	−	0.698882i
$229$			23.6883i			1.56537i	0.622419	+	0.782684i	$0.286150\pi$
$229$			23.6883i			1.56537i	−0.622419	+	0.782684i	$0.713850\pi$
$230$	1.31151	−	2.39529i	0.0864787	−	0.157941i
$231$	−4.36805	+	7.56568i	−0.287396	+	0.497785i
$232$	−7.27606	+	12.6025i	−0.477697	+	0.827396i
$233$		−	4.75242i		−	0.311341i	−0.987809	−	0.155671i	$-0.950246\pi$
$233$		−	4.75242i		−	0.311341i	0.987809	−	0.155671i	$-0.0497539\pi$
$234$	3.80652	+	9.07012i	0.248840	+	0.592932i
$235$	15.4106	−	9.36886i	1.00527	−	0.611157i
$236$	25.0963	+	14.4894i	1.63363	+	0.943177i
$237$	−1.67588	−	0.967567i	−0.108860	−	0.0628502i
$238$	23.4085	−	13.5149i	1.51735	−	0.876042i
$239$		−	13.2798i		−	0.859002i	−0.903066	−	0.429501i	$-0.858690\pi$
$239$		−	13.2798i		−	0.859002i	0.903066	−	0.429501i	$-0.141310\pi$
$240$	15.8277	−	28.9070i	1.02168	−	1.86594i
$241$	8.62590	−	4.98016i	0.555643	−	0.320801i	−0.195752	−	0.980653i	$-0.562715\pi$
$241$	8.62590	−	4.98016i	0.555643	−	0.320801i	0.751395	+	0.659853i	$0.229381\pi$
$242$	−15.0683			−0.968624
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.72981	−	2.99611i	0.110739	−	0.191806i
$245$	0.351157	+	15.5035i	0.0224346	+	0.990479i
$246$	2.73043			0.174086
$247$	−6.42686	−	4.88415i	−0.408932	−	0.310771i
$248$			29.8537i			1.89571i
$249$	6.61019	+	3.81639i	0.418904	+	0.241854i
$250$	−27.3896	−	13.4224i	−1.73227	−	0.848907i
$251$	−9.95334	−	17.2397i	−0.628249	−	1.08816i	−0.987903	−	0.155073i	$-0.950439\pi$
$251$	−9.95334	−	17.2397i	−0.628249	−	1.08816i	0.359654	−	0.933086i	$-0.382895\pi$
$252$	20.3179			1.27991
$253$	−0.523810	−	0.907266i	−0.0329317	−	0.0570393i
$254$	29.3894	−	16.9680i	1.84405	−	1.06466i
$255$	−5.07116	+	3.08301i	−0.317568	+	0.193066i
$256$	−20.3937	−	35.3230i	−1.27461	−	2.20769i
$257$	15.9957	+	9.23510i	0.997782	+	0.576070i	0.907591	−	0.419855i	$-0.137919\pi$
$257$	15.9957	+	9.23510i	0.997782	+	0.576070i	0.0901908	+	0.995925i	$0.471252\pi$
$258$	15.9312	−	27.5936i	0.991830	−	1.71790i
$259$	5.95773			0.370195
$260$	4.53795	−	43.6461i	0.281432	−	2.70682i
$261$	1.54933			0.0959012
$262$	−7.56787	+	13.1079i	−0.467545	+	0.809811i
$263$	−8.70446	−	5.02552i	−0.536740	−	0.309887i	0.207017	−	0.978337i	$-0.433625\pi$
$263$	−8.70446	−	5.02552i	−0.536740	−	0.309887i	−0.743757	+	0.668450i	$0.766958\pi$
$264$	−10.9904	−	19.0360i	−0.676413	−	1.17158i
$265$	9.68544	+	15.9313i	0.594972	+	0.978652i
$266$	−19.7457	+	11.4002i	−1.21069	+	0.698989i
$267$	2.63289	+	4.56030i	0.161130	+	0.279086i
$268$	55.1059			3.36613
$269$	−11.1969	−	19.3936i	−0.682688	−	1.18245i	−0.974157	−	0.225870i	$-0.927477\pi$
$269$	−11.1969	−	19.3936i	−0.682688	−	1.18245i	0.291469	−	0.956580i	$-0.405856\pi$
$270$	−6.09877	+	0.138139i	−0.371159	+	0.00840685i
$271$	13.0612	+	7.54088i	0.793410	+	0.458076i	0.841162	−	0.540784i	$-0.181872\pi$
$271$	13.0612	+	7.54088i	0.793410	+	0.458076i	−0.0477516	+	0.998859i	$0.515206\pi$
$272$			39.1179i			2.37187i
$273$	12.4108	−	5.20852i	0.751136	−	0.315234i
$274$	−36.9743			−2.23370
$275$	−9.85827	+	6.30344i	−0.594476	+	0.380112i
$276$	−1.21825	+	2.11007i	−0.0733299	+	0.127011i
$277$	−11.0406	+	6.37430i	−0.663366	+	0.382994i	−0.793558	−	0.608494i	$-0.791774\pi$
$277$	−11.0406	+	6.37430i	−0.663366	+	0.382994i	0.130192	+	0.991489i	$0.458441\pi$
$278$	−14.7551			−0.884950
$279$	2.75262	−	1.58923i	0.164795	−	0.0951445i
$280$	−68.7677	−	37.6531i	−4.10966	−	2.25020i
$281$		−	2.48331i		−	0.148142i	−0.997253	−	0.0740709i	$-0.976401\pi$
$281$		−	2.48331i		−	0.148142i	0.997253	−	0.0740709i	$-0.0235991\pi$
$282$	−19.0559	+	11.0020i	−1.13476	+	0.655157i
$283$	−6.72924	−	3.88513i	−0.400012	−	0.230947i	0.286477	−	0.958087i	$-0.407516\pi$
$283$	−6.72924	−	3.88513i	−0.400012	−	0.230947i	−0.686489	+	0.727140i	$0.740849\pi$
$284$	−17.8899	−	10.3288i	−1.06157	−	0.612899i
$285$	4.27764	−	2.60060i	0.253386	−	0.154046i
$286$	−18.3279	−	13.9284i	−1.08375	−	0.823605i
$287$		−	3.73610i		−	0.220535i
$288$	−10.7121	+	18.5538i	−0.631214	+	1.09329i
$289$	−4.97784	+	8.62187i	−0.292814	+	0.507169i
$290$	−8.29010	−	4.53916i	−0.486811	−	0.266549i
$291$			12.4827i			0.731747i
$292$	0.134437	+	0.232852i	0.00786734	+	0.0136266i
$293$	−7.69740	−	13.3323i	−0.449687	−	0.778881i	0.548678	−	0.836034i	$-0.315131\pi$
$293$	−7.69740	−	13.3323i	−0.449687	−	0.778881i	−0.998365	+	0.0571527i	$0.981798\pi$
$294$		−	18.9201i		−	1.10344i
$295$	−5.71766	+	10.4425i	−0.332895	+	0.607983i
$296$	−7.49510	+	12.9819i	−0.435644	+	0.754558i
$297$	−1.17012	+	2.02671i	−0.0678974	+	0.117602i
$298$		−	40.0132i		−	2.31790i
$299$	−0.203224	+	1.60119i	−0.0117528	+	0.0925994i
$300$	24.1600	+	12.5260i	1.39488	+	0.723188i
$301$	−37.7568	−	21.7989i	−2.17626	−	1.25647i
$302$	−29.1283	−	16.8172i	−1.67614	−	0.967722i
$303$	−0.604407	+	0.348954i	−0.0347222	+	0.0200469i
$304$		−	32.9969i		−	1.89250i
$305$	1.24667	+	0.682600i	0.0713840	+	0.0390856i
$306$	6.27074	−	3.62041i	0.358474	−	0.206965i
$307$	26.0526			1.48690			0.743451	−	0.668790i	$-0.233188\pi$
$307$	26.0526			1.48690			0.743451	+	0.668790i	$0.233188\pi$
$308$	−41.1786	+	23.7745i	−2.34637	+	1.35468i
$309$	1.96217	−	3.39858i	0.111624	−	0.193338i
$310$	−19.3846	+	0.439067i	−1.10097	+	0.0249373i
$311$	−10.6032			−0.601255			−0.300627	−	0.953742i	$-0.597196\pi$
$311$	−10.6032			−0.601255			−0.300627	+	0.953742i	$0.597196\pi$
$312$	−4.26399	+	33.5957i	−0.241401	+	1.90198i
$313$		−	1.86028i		−	0.105149i	−0.998617	−	0.0525745i	$-0.983257\pi$
$313$		−	1.86028i		−	0.105149i	0.998617	−	0.0525745i	$-0.0167427\pi$
$314$	−58.5584	−	33.8087i	−3.30464	−	1.90793i
$315$	0.189018	+	8.34505i	0.0106499	+	0.470191i
$316$	−5.26629	−	9.12148i	−0.296252	−	0.513123i
$317$	8.78399			0.493358			0.246679	−	0.969097i	$-0.420661\pi$
$317$	8.78399			0.493358			0.246679	+	0.969097i	$0.420661\pi$
$318$	−11.3737	−	19.6998i	−0.637806	−	1.10471i
$319$	−3.14005	+	1.81291i	−0.175809	+	0.101503i
$320$	55.3543	−	33.6527i	3.09440	−	1.88124i
$321$	0.811946	+	1.40633i	0.0453184	+	0.0784938i
$322$	3.94818	+	2.27948i	0.220023	+	0.127031i
$323$	−2.97103	+	5.14597i	−0.165312	+	0.286329i
$324$	5.44282			0.302379
$325$	17.9687	+	1.45781i	0.996725	+	0.0808645i
$326$	43.4633			2.40721
$327$	8.80385	−	15.2487i	0.486854	−	0.843256i
$328$	8.14097	+	4.70019i	0.449510	+	0.259525i
$329$	15.0542	+	26.0746i	0.829963	+	1.43754i
$330$	12.1988	−	7.41628i	0.671523	−	0.408253i
$331$	13.6130	−	7.85944i	0.748235	−	0.431994i	−0.0768205	−	0.997045i	$-0.524477\pi$
$331$	13.6130	−	7.85944i	0.748235	−	0.431994i	0.825056	+	0.565051i	$0.191144\pi$
$332$	20.7719	+	35.9780i	1.14001	+	1.97455i
$333$	1.59597			0.0874587
$334$	34.6906	+	60.0859i	1.89818	+	3.28775i
$335$	0.512650	+	22.6333i	0.0280090	+	1.23659i
$336$	47.6478	+	27.5095i	2.59940	+	1.50076i
$337$			23.7835i			1.29557i	0.761824	+	0.647784i	$0.224304\pi$
$337$			23.7835i			1.29557i	−0.761824	+	0.647784i	$0.775696\pi$
$338$	9.49774	+	34.1706i	0.516609	+	1.85863i
$339$	−18.7414			−1.01789
$340$	−32.2936	+	0.731458i	−1.75137	+	0.0396689i
$341$	−3.71918	+	6.44181i	−0.201405	+	0.348844i
$342$	−5.28952	+	3.05391i	−0.286025	+	0.165136i
$343$	0.242143			0.0130745
$344$	94.9996	−	54.8480i	5.12203	−	2.95721i
$345$	−0.877989	−	0.480734i	−0.0472693	−	0.0258818i
$346$			36.9170i			1.98467i
$347$	−25.4580	+	14.6982i	−1.36666	+	0.789039i	−0.990499	−	0.137517i	$-0.956088\pi$
$347$	−25.4580	+	14.6982i	−1.36666	+	0.789039i	−0.376157	+	0.926556i	$0.622755\pi$
$348$	7.30295	+	4.21636i	0.391479	+	0.226021i
$349$	−17.1537	−	9.90370i	−0.918217	−	0.530133i	−0.0351512	−	0.999382i	$-0.511191\pi$
$349$	−17.1537	−	9.90370i	−0.918217	−	0.530133i	−0.883066	+	0.469249i	$0.844525\pi$
$350$	23.4376	−	45.2062i	1.25279	−	2.41637i
$351$	3.32464	−	1.39527i	0.177456	−	0.0744742i
$352$		−	50.1377i		−	2.67235i
$353$	0.734126	−	1.27154i	0.0390736	−	0.0676775i	−0.845827	−	0.533457i	$-0.820893\pi$
$353$	0.734126	−	1.27154i	0.0390736	−	0.0676775i	0.884901	+	0.465779i	$0.154226\pi$
$354$	7.26264	−	12.5793i	0.386005	−	0.668580i
$355$	4.07584	−	7.44391i	0.216323	−	0.395082i
$356$			28.6607i			1.51901i
$357$	−4.95387	−	8.58036i	−0.262187	−	0.454121i
$358$	−16.0489	−	27.7975i	−0.848211	−	1.46914i
$359$			35.9295i			1.89629i	0.317840	+	0.948144i	$0.397043\pi$
$359$			35.9295i			1.89629i	−0.317840	+	0.948144i	$0.602957\pi$
$360$	−18.4217	−	10.0866i	−0.970907	−	0.531610i
$361$	−6.99386	+	12.1137i	−0.368098	+	0.637565i
$362$	18.1345	−	31.4099i	0.953130	−	1.65087i
$363$			5.52324i			0.289895i
$364$	72.6743	+	9.22386i	3.80917	+	0.483462i
$365$	−0.0943873	+	0.0573828i	−0.00494046	+	0.00300355i
$366$	−1.50177	−	0.867047i	−0.0784987	−	0.0453213i
$367$	−19.7705	−	11.4145i	−1.03201	−	0.595833i	−0.114453	−	0.993429i	$-0.536512\pi$
$367$	−19.7705	−	11.4145i	−1.03201	−	0.595833i	−0.917561	+	0.397595i	$0.869845\pi$
$368$	−5.71385	+	3.29889i	−0.297855	+	0.171967i
$369$		−	1.00084i		−	0.0521015i
$370$	−8.53966	−	4.67581i	−0.443956	−	0.243084i
$371$	−26.9557	+	15.5629i	−1.39947	+	0.807983i
$372$	17.2997			0.896949
$373$	17.8144	−	10.2851i	0.922394	−	0.532545i	0.0379961	−	0.999278i	$-0.487903\pi$
$373$	17.8144	−	10.2851i	0.922394	−	0.532545i	0.884398	+	0.466733i	$0.154569\pi$
$374$	−8.47266	+	14.6751i	−0.438111	+	0.758830i
$375$	−4.91996	+	10.0396i	−0.254066	+	0.518444i
$376$	−75.7554			−3.90678
$377$	5.54174	+	0.703360i	0.285414	+	0.0362249i
$378$		−	10.1841i		−	0.523815i
$379$	22.4067	+	12.9365i	1.15096	+	0.664505i	0.949120	−	0.314914i	$-0.101976\pi$
$379$	22.4067	+	12.9365i	1.15096	+	0.664505i	0.201836	+	0.979419i	$0.435309\pi$
$380$	27.2405	−	0.617003i	1.39741	−	0.0316516i
$381$	−6.21958	−	10.7726i	−0.318639	−	0.551898i
$382$	−45.2962			−2.31755
$383$	−5.90514	−	10.2280i	−0.301739	−	0.522627i	0.674791	−	0.738009i	$-0.264234\pi$
$383$	−5.90514	−	10.2280i	−0.301739	−	0.522627i	−0.976530	+	0.215382i	$0.930900\pi$
$384$	−31.3407	+	18.0946i	−1.59935	+	0.923385i
$385$	−10.1478	−	16.6919i	−0.517181	−	0.850696i
$386$	17.9157	+	31.0309i	0.911885	+	1.57943i
$387$	−10.1144	−	5.83954i	−0.514143	−	0.296841i
$388$	−33.9704	+	58.8385i	−1.72459	+	2.98707i
$389$	4.31443			0.218750			0.109375	−	0.994001i	$-0.465115\pi$
$389$	4.31443			0.218750			0.109375	+	0.994001i	$0.465115\pi$
$390$	−21.8771	−	2.27460i	−1.10779	−	0.115179i
$391$	1.18812			0.0600860
$392$	32.5692	−	56.4115i	1.64499	−	2.84921i
$393$	4.80470	+	2.77399i	0.242365	+	0.139929i
$394$	22.6417	+	39.2165i	1.14067	+	1.97570i
$395$	3.69742	−	2.24785i	0.186037	−	0.113102i
$396$	−11.0310	+	6.36877i	−0.554330	+	0.320043i
$397$	8.29714	+	14.3711i	0.416421	+	0.721263i	0.995577	−	0.0939544i	$-0.0299508\pi$
$397$	8.29714	+	14.3711i	0.416421	+	0.721263i	−0.579155	+	0.815217i	$0.696617\pi$
$398$	−42.0135			−2.10595
$399$	4.17872	+	7.23775i	0.209197	+	0.362341i
$400$	39.6983	+	62.0863i	1.98492	+	3.10431i
$401$	−1.05626	−	0.609829i	−0.0527469	−	0.0304534i	0.473395	−	0.880850i	$-0.343028\pi$
$401$	−1.05626	−	0.609829i	−0.0527469	−	0.0304534i	−0.526142	+	0.850397i	$0.676362\pi$
$402$		−	27.6212i		−	1.37762i
$403$	10.5672	−	4.43481i	0.526390	−	0.220913i
$404$	−3.79859			−0.188987
$405$	0.0506345	+	2.23549i	0.00251605	+	0.111083i
$406$	7.88930	−	13.6647i	0.391539	−	0.678166i
$407$	−3.23458	+	1.86748i	−0.160332	+	0.0925678i
$408$	24.9288			1.23416
$409$	−22.0397	+	12.7246i	−1.08979	+	0.629191i	−0.933521	−	0.358523i	$-0.883280\pi$
$409$	−22.0397	+	12.7246i	−1.08979	+	0.629191i	−0.156270	+	0.987714i	$0.549947\pi$
$410$	−2.93220	+	5.35523i	−0.144811	+	0.264476i
$411$			13.5529i			0.668514i
$412$	18.4978	−	10.6797i	0.911322	−	0.526152i
$413$	−17.2124	−	9.93759i	−0.846968	−	0.488997i
$414$	1.05765	+	0.610634i	0.0519806	+	0.0300110i
$415$	−14.5838	+	8.86623i	−0.715891	+	0.435226i
$416$	−46.7385	+	61.5014i	−2.29154	+	3.01535i
$417$			5.40844i			0.264853i
$418$	7.14690	−	12.3788i	0.349566	−	0.605466i
$419$	16.0653	−	27.8259i	0.784840	−	1.35938i	−0.144255	−	0.989541i	$-0.546079\pi$
$419$	16.0653	−	27.8259i	0.784840	−	1.35938i	0.929095	−	0.369842i	$-0.120588\pi$
$420$	−21.8193	+	39.8498i	−1.06467	+	1.94447i
$421$		−	11.6222i		−	0.566433i	−0.959056	−	0.283217i	$-0.908598\pi$
$421$		−	11.6222i		−	0.566433i	0.959056	−	0.283217i	$-0.0914016\pi$
$422$	−7.65660	−	13.2616i	−0.372718	−	0.645566i
$423$	4.03275	+	6.98492i	0.196079	+	0.339619i
$424$		−	78.3152i		−	3.80332i
$425$	−0.600855	−	13.2570i	−0.0291457	−	0.643057i
$426$	−5.17718	+	8.96713i	−0.250835	+	0.434459i
$427$	−1.18640	+	2.05490i	−0.0574137	+	0.0994434i
$428$			8.83855i			0.427227i
$429$	−5.10545	+	6.71805i	−0.246493	+	0.324351i
$430$	37.0112	+	60.8786i	1.78484	+	2.93583i
$431$	18.2332	+	10.5269i	0.878260	+	0.507064i	0.870084	−	0.492903i	$-0.164064\pi$
$431$	18.2332	+	10.5269i	0.878260	+	0.507064i	0.00817569	+	0.999967i	$0.497398\pi$
$432$	12.7640	+	7.36930i	0.614109	+	0.354556i
$433$	14.4642	−	8.35090i	0.695105	−	0.401319i	−0.110417	−	0.993885i	$-0.535219\pi$
$433$	14.4642	−	8.35090i	0.695105	−	0.401319i	0.805522	+	0.592566i	$0.201885\pi$
$434$		−	32.3698i		−	1.55380i
$435$	−1.66382	+	3.03872i	−0.0797741	+	0.145696i
$436$	82.9959	−	47.9177i	3.97478	−	2.29484i
$437$	−1.00221			−0.0479423
$438$	0.116715	−	0.0673852i	0.00557684	−	0.00321979i
$439$	8.72877	−	15.1187i	0.416601	−	0.721575i	−0.578994	−	0.815332i	$-0.696554\pi$
$439$	8.72877	−	15.1187i	0.416601	−	0.721575i	0.995595	+	0.0937572i	$0.0298877\pi$
$440$	49.1380	−	1.11299i	2.34256	−	0.0530596i
$441$	−6.93513			−0.330244
$442$	24.0731	−	10.1029i	1.14504	−	0.480547i
$443$		−	15.4536i		−	0.734220i	−0.930177	−	0.367110i	$-0.880347\pi$
$443$		−	15.4536i		−	0.734220i	0.930177	−	0.367110i	$-0.119653\pi$
$444$	7.52280	+	4.34329i	0.357016	+	0.206123i
$445$	−11.7716	+	0.266630i	−0.558029	+	0.0126395i
$446$	−24.6653	−	42.7215i	−1.16793	−	2.02292i
$447$	−14.6668			−0.693715
$448$	54.0741	+	93.6591i	2.55476	+	4.42498i
$449$	−15.5420	+	8.97319i	−0.733473	+	0.423471i	−0.819691	−	0.572805i	$-0.805855\pi$
$449$	−15.5420	+	8.97319i	−0.733473	+	0.423471i	0.0862182	+	0.996276i	$0.472522\pi$
$450$	6.27851	−	12.1099i	0.295972	−	0.570868i
$451$	1.17110	+	2.02841i	0.0551451	+	0.0955140i
$452$	−88.3397	−	51.0029i	−4.15515	−	2.39898i
$453$	−6.16433	+	10.6769i	−0.289625	+	0.501646i
$454$	−23.1086			−1.08454
$455$	−3.11237	+	29.9349i	−0.145910	+	1.40337i
$456$	−21.0281			−0.984730
$457$	−11.5720	+	20.0433i	−0.541315	+	0.937586i	0.457514	+	0.889203i	$0.348740\pi$
$457$	−11.5720	+	20.0433i	−0.541315	+	0.937586i	−0.998829	+	0.0483830i	$0.984593\pi$
$458$	55.9672	+	32.3127i	2.61518	+	1.50987i
$459$	−1.32706	−	2.29853i	−0.0619417	−	0.107286i
$460$	−2.83023	−	4.65536i	−0.131960	−	0.217057i
$461$	−12.0519	+	6.95814i	−0.561311	+	0.324073i	−0.753671	−	0.657251i	$-0.771719\pi$
$461$	−12.0519	+	6.95814i	−0.561311	+	0.324073i	0.192361	+	0.981324i	$0.438386\pi$
$462$	11.9167	+	20.6403i	0.554415	+	0.960275i
$463$	7.46187			0.346783			0.173391	−	0.984853i	$-0.444527\pi$
$463$	7.46187			0.346783			0.173391	+	0.984853i	$0.444527\pi$
$464$	11.4175	+	19.7757i	0.530044	+	0.918063i
$465$	0.160939	+	7.10541i	0.00746338	+	0.329506i
$466$	−11.2283	−	6.48266i	−0.520141	−	0.300304i
$467$		−	6.50590i		−	0.301057i	−0.988606	−	0.150529i	$-0.951902\pi$
$467$		−	6.50590i		−	0.301057i	0.988606	−	0.150529i	$-0.0480975\pi$
$468$	19.4682	+	2.47091i	0.899916	+	0.114218i
$469$	−37.7946			−1.74519
$470$	−1.11416	−	49.1896i	−0.0513922	−	2.26895i
$471$	−12.3925	+	21.4645i	−0.571017	+	0.989031i
$472$	43.3081	−	25.0039i	1.99341	−	1.15090i
$473$	27.3319			1.25672
$474$	−4.57204	+	2.63967i	−0.210001	+	0.121244i
$475$	0.506836	+	11.1826i	0.0232552	+	0.513092i
$476$		−	53.9260i		−	2.47170i
$477$	−7.22095	+	4.16902i	−0.330625	+	0.190886i
$478$	−31.3756	−	18.1147i	−1.43509	−	0.828548i
$479$	−2.56069	−	1.47842i	−0.117001	−	0.0675506i	0.440357	−	0.897823i	$-0.354852\pi$
$479$	−2.56069	−	1.47842i	−0.117001	−	0.0675506i	−0.557358	+	0.830272i	$0.688185\pi$
$480$	−24.8862	−	40.9346i	−1.13589	−	1.86840i
$481$	5.70856	+	0.724534i	0.260288	+	0.0330359i
$482$		−	27.1733i		−	1.23771i
$483$	0.835541	−	1.44720i	0.0380184	−	0.0658498i
$484$	−15.0310	+	26.0345i	−0.683227	+	1.18338i
$485$	−24.4824	−	13.4051i	−1.11169	−	0.608694i
$486$		−	2.72815i		−	0.123752i
$487$	7.61819	+	13.1951i	0.345213	+	0.597927i	0.985392	−	0.170299i	$-0.0544732\pi$
$487$	7.61819	+	13.1951i	0.345213	+	0.597927i	−0.640179	+	0.768226i	$0.721140\pi$
$488$	−2.98508	−	5.17031i	−0.135128	−	0.234049i
$489$		−	15.9314i		−	0.720443i
$490$	37.1082	+	20.3182i	1.67638	+	0.917884i
$491$	8.42838	−	14.5984i	0.380367	−	0.658816i	−0.610747	−	0.791826i	$-0.709131\pi$
$491$	8.42838	−	14.5984i	0.380367	−	0.658816i	0.991115	+	0.133010i	$0.0424642\pi$
$492$	2.72368	−	4.71756i	0.122793	−	0.212684i
$493$		−	4.11210i		−	0.185200i
$494$	−20.3063	+	8.52207i	−0.913622	+	0.383426i
$495$	−2.71843	−	4.47146i	−0.122184	−	0.200977i
$496$	40.5698	+	23.4230i	1.82164	+	1.05172i
$497$	12.2699	+	7.08402i	0.550380	+	0.317762i
$498$	18.0336	−	10.4117i	0.808105	−	0.466560i
$499$			5.35532i			0.239737i	0.992790	+	0.119869i	$0.0382473\pi$
$499$			5.35532i			0.239737i	−0.992790	+	0.119869i	$0.961753\pi$
$500$	−50.5127	+	33.9337i	−2.25900	+	1.51756i
$501$	22.0244	−	12.7158i	0.983977	−	0.568099i
$502$	−54.3084			−2.42390
$503$	35.1282	−	20.2812i	1.56629	−	0.904296i	0.569691	−	0.821859i	$-0.307063\pi$
$503$	35.1282	−	20.2812i	1.56629	−	0.904296i	0.996596	−	0.0824369i	$-0.0262703\pi$
$504$	17.5310	−	30.3647i	0.780895	−	1.35255i
$505$	−0.0353382	−	1.56017i	−0.00157253	−	0.0694267i
$506$	−2.85807			−0.127057
$507$	12.5252	−	3.48138i	0.556262	−	0.154614i
$508$		−	67.7040i		−	3.00388i
$509$	29.6048	+	17.0923i	1.31221	+	0.757605i	0.982462	−	0.186464i	$-0.0597027\pi$
$509$	29.6048	+	17.0923i	1.31221	+	0.757605i	0.329748	+	0.944069i	$0.393036\pi$
$510$	0.366635	+	16.1868i	0.0162349	+	0.716765i
$511$	−0.0922044	−	0.159703i	−0.00407888	−	0.00706483i
$512$	−38.8961			−1.71898
$513$	1.11941	+	1.93887i	0.0494229	+	0.0856030i
$514$	43.6386	−	25.1948i	1.92482	−	1.11129i
$515$	4.55850	+	7.49814i	0.200872	+	0.330408i
$516$	−31.7835	−	55.0507i	−1.39919	−	2.42347i
$517$	−16.3464	−	9.43763i	−0.718916	−	0.415066i
$518$	8.12680	−	14.0760i	0.357071	−	0.618465i
$519$	13.5319			0.593983
$520$	−61.3126	−	44.4413i	−2.68874	−	1.94888i
$521$	41.1861			1.80440			0.902198	−	0.431321i	$-0.141952\pi$
$521$	41.1861			1.80440			0.902198	+	0.431321i	$0.141952\pi$
$522$	2.11341	−	3.66053i	0.0925013	−	0.160217i
$523$	3.27850	+	1.89284i	0.143359	+	0.0827682i	0.569964	−	0.821670i	$-0.306957\pi$
$523$	3.27850	+	1.89284i	0.143359	+	0.0827682i	−0.426605	+	0.904438i	$0.640291\pi$
$524$	15.0983	+	26.1511i	0.659573	+	1.14241i
$525$	−16.5702	−	8.59100i	−0.723185	−	0.374942i
$526$	−23.7471	+	13.7104i	−1.03542	+	0.597802i
$527$	−4.21798	−	7.30576i	−0.183738	−	0.318244i
$528$	−34.4920			−1.50107
$529$	−11.3998	−	19.7450i	−0.495644	−	0.858480i
$530$	50.8517	−	1.15180i	2.20886	−	0.0500312i
$531$	−4.61091	−	2.66211i	−0.200096	−	0.115526i
$532$			45.4880i			1.97215i
$533$	0.454357	−	3.57985i	0.0196804	−	0.155060i
$534$	14.3659			0.621671
$535$	−3.63020	+	0.0822250i	−0.156947	+	0.00355489i
$536$	47.5474	−	82.3545i	2.05373	−	3.55717i
$537$	−10.1891	+	5.88270i	−0.439694	+	0.253857i
$538$	−61.0938			−2.63394
$539$	14.0555	−	8.11496i	0.605414	−	0.349536i
$540$	−5.84502	+	10.6751i	−0.251530	+	0.459381i
$541$		−	3.22373i		−	0.138599i	−0.997596	−	0.0692995i	$-0.977924\pi$
$541$		−	3.22373i		−	0.138599i	0.997596	−	0.0692995i	$-0.0220764\pi$
$542$	35.6329	−	20.5727i	1.53056	−	0.883671i
$543$	−11.5133	−	6.64718i	−0.494081	−	0.285258i
$544$	49.2440	+	28.4310i	2.11132	+	1.21897i
$545$	20.4531	+	33.6426i	0.876113	+	1.44109i
$546$	4.62336	−	36.4272i	0.197862	−	1.55894i
$547$			3.95250i			0.168997i	0.996424	+	0.0844983i	$0.0269288\pi$
$547$			3.95250i			0.168997i	−0.996424	+	0.0844983i	$0.973071\pi$
$548$	−36.8829	+	63.8831i	−1.57556	+	2.72895i
$549$	−0.317815	+	0.550471i	−0.0135640	+	0.0234935i
$550$	1.44537	+	31.8900i	0.0616310	+	1.35979i
$551$			3.46866i			0.147770i
$552$	2.10230	+	3.64129i	0.0894798	+	0.154984i
$553$	3.61191	+	6.25601i	0.153594	+	0.266033i
$554$			34.7801i			1.47767i
$555$	−1.71391	+	3.13020i	−0.0727514	+	0.132870i
$556$	−14.7186	+	25.4933i	−0.624207	+	1.08116i
$557$	10.9335	−	18.9374i	0.463268	−	0.802404i	−0.535853	−	0.844311i	$-0.680010\pi$
$557$	10.9335	−	18.9374i	0.463268	−	0.802404i	0.999122	+	0.0419069i	$0.0133433\pi$
$558$		−	8.67130i		−	0.367085i
$559$	−33.5267	−	25.4789i	−1.41803	−	1.07764i
$560$	−105.123	+	63.9099i	−4.44227	+	2.70068i
$561$	5.37913	+	3.10564i	0.227107	+	0.131120i
$562$	−5.86719	−	3.38742i	−0.247492	−	0.142890i
$563$	18.0807	−	10.4389i	0.762013	−	0.439948i	−0.0680053	−	0.997685i	$-0.521663\pi$
$563$	18.0807	−	10.4389i	0.762013	−	0.439948i	0.830018	+	0.557737i	$0.188330\pi$
$564$			43.8990i			1.84848i
$565$	20.1263	−	36.7577i	0.846720	−	1.54641i
$566$	−18.3584	+	10.5992i	−0.771661	+	0.445519i
$567$	−3.73298			−0.156770
$568$	−30.8722	+	17.8241i	−1.29537	+	0.747881i
$569$	−8.19610	+	14.1961i	−0.343599	+	0.595130i	−0.985098	−	0.171993i	$-0.944979\pi$
$569$	−8.19610	+	14.1961i	−0.343599	+	0.595130i	0.641500	+	0.767123i	$0.278313\pi$
$570$	−0.309266	−	13.6540i	−0.0129537	−	0.571903i
$571$	43.2862			1.81147			0.905735	−	0.423843i	$-0.139319\pi$
$571$	43.2862			1.81147			0.905735	+	0.423843i	$0.139319\pi$
$572$	−42.3477	+	17.7723i	−1.77065	+	0.743099i
$573$			16.6032i			0.693610i
$574$	−8.82710	−	5.09633i	−0.368436	−	0.212717i
$575$	1.88574	−	1.20575i	0.0786407	−	0.0502833i
$576$	14.4855	+	25.0896i	0.603563	+	1.04540i
$577$	20.6414			0.859311			0.429656	−	0.902993i	$-0.358635\pi$
$577$	20.6414			0.859311			0.429656	+	0.902993i	$0.358635\pi$
$578$	13.5803	+	23.5218i	0.564866	+	0.978377i
$579$	11.3743	−	6.56697i	0.472701	−	0.272914i
$580$	−16.1122	+	9.79543i	−0.669023	+	0.406733i
$581$	−14.2465	−	24.6757i	−0.591045	−	1.02372i
$582$	29.4922	+	17.0273i	1.22249	+	0.705805i
$583$	9.75653	−	16.8988i	0.404074	−	0.699877i
$584$	0.463990			0.0192000
$585$	−0.833751	+	8.01903i	−0.0344713	+	0.331546i
$586$	−41.9994			−1.73498
$587$	4.86133	−	8.42007i	0.200649	−	0.347534i	−0.748089	−	0.663598i	$-0.769028\pi$
$587$	4.86133	−	8.42007i	0.200649	−	0.347534i	0.948738	+	0.316065i	$0.102362\pi$
$588$	−32.6896	−	18.8733i	−1.34809	−	0.778323i
$589$	3.55797	+	6.16259i	0.146604	+	0.253925i
$590$	16.8725	+	27.7531i	0.694631	+	1.14258i
$591$	14.3748	−	8.29927i	0.591298	−	0.341386i
$592$	11.7612	+	20.3710i	0.483382	+	0.837243i
$593$	−6.32051			−0.259552			−0.129776	−	0.991543i	$-0.541426\pi$
$593$	−6.32051			−0.259552			−0.129776	+	0.991543i	$0.541426\pi$
$594$	3.19227	+	5.52918i	0.130981	+	0.226865i
$595$	22.1487	−	0.501674i	0.908009	−	0.0205666i
$596$	−69.1336	−	39.9143i	−2.83182	−	1.63495i
$597$			15.4000i			0.630280i
$598$	3.50584	+	2.66430i	0.143365	+	0.108951i
$599$	−7.45206			−0.304483			−0.152241	−	0.988343i	$-0.548649\pi$
$599$	−7.45206			−0.304483			−0.152241	+	0.988343i	$0.548649\pi$
$600$	39.5659	−	25.2987i	1.61527	−	1.03281i
$601$	3.05867	−	5.29776i	0.124766	−	0.216100i	−0.796876	−	0.604143i	$-0.793515\pi$
$601$	3.05867	−	5.29776i	0.124766	−	0.216100i	0.921641	+	0.388043i	$0.126849\pi$
$602$	−103.006	+	59.4707i	−4.19822	+	2.42384i
$603$	−10.1245			−0.412302
$604$	−58.1125	+	33.5513i	−2.36457	+	1.36518i
$605$	−10.8328	−	5.93139i	−0.440416	−	0.241145i
$606$			1.90400i			0.0773447i
$607$	35.6944	−	20.6082i	1.44879	−	0.836460i	0.450382	−	0.892836i	$-0.351288\pi$
$607$	35.6944	−	20.6082i	1.44879	−	0.836460i	0.998410	+	0.0563759i	$0.0179545\pi$
$608$	−41.5385	−	23.9823i	−1.68461	−	0.972609i
$609$	−5.00876	−	2.89181i	−0.202965	−	0.117182i
$610$	3.31329	−	2.01432i	0.134151	−	0.0815574i
$611$	11.2536	+	26.8148i	0.455271	+	1.08481i
$612$		−	14.4458i		−	0.583939i
$613$	−12.7973	+	22.1655i	−0.516877	+	0.895257i	0.482931	+	0.875658i	$0.339572\pi$
$613$	−12.7973	+	22.1655i	−0.516877	+	0.895257i	−0.999808	+	0.0195987i	$0.993761\pi$
$614$	35.5378	−	61.5532i	1.43419	−	2.48409i
$615$	1.96295	+	1.07479i	0.0791539	+	0.0433399i
$616$			82.0540i			3.30605i
$617$	16.0897	+	27.8683i	0.647749	+	1.12193i	0.983659	+	0.180040i	$0.0576227\pi$
$617$	16.0897	+	27.8683i	0.647749	+	1.12193i	−0.335910	+	0.941894i	$0.609044\pi$
$618$	−5.35309	−	9.27183i	−0.215333	−	0.372968i
$619$		−	19.8298i		−	0.797028i	−0.917162	−	0.398514i	$-0.869526\pi$
$619$		−	19.8298i		−	0.797028i	0.917162	−	0.398514i	$-0.130474\pi$
$620$	−18.5781	+	33.9302i	−0.746115	+	1.36267i
$621$	0.223827	−	0.387679i	0.00898186	−	0.0155570i
$622$	−14.4636	+	25.0517i	−0.579939	+	1.00448i
$623$		−	19.6570i		−	0.787543i
$624$	42.3095	+	32.1535i	1.69374	+	1.28717i
$625$	−14.4073	−	20.4311i	−0.576292	−	0.817244i
$626$	−4.39518	−	2.53756i	−0.175667	−	0.101421i
$627$	−4.53743	−	2.61968i	−0.181207	−	0.104620i
$628$	−116.827	+	67.4502i	−4.66191	+	2.69156i
$629$		−	4.23589i		−	0.168896i
$630$	19.9743	+	10.9367i	0.795794	+	0.435729i
$631$	−19.0859	+	11.0192i	−0.759797	+	0.438669i	−0.829223	−	0.558918i	$-0.811217\pi$
$631$	−19.0859	+	11.0192i	−0.759797	+	0.438669i	0.0694258	+	0.997587i	$0.477883\pi$
$632$	−18.1758			−0.722994
$633$	−4.86103	+	2.80652i	−0.193209	+	0.111549i
$634$	11.9820	−	20.7535i	0.475867	−	0.824227i
$635$	27.8077	−	0.629851i	1.10351	−	0.0249949i
$636$	−45.3824			−1.79953
$637$	−24.8060	−	3.14839i	−0.982849	−	0.124744i
$638$			9.89178i			0.391619i
$639$	3.28689	+	1.89769i	0.130027	+	0.0750713i
$640$	−1.83242	−	80.9007i	−0.0724328	−	3.19788i
$641$	22.1778	+	38.4131i	0.875970	+	1.51723i	0.855725	+	0.517430i	$0.173111\pi$
$641$	22.1778	+	38.4131i	0.875970	+	1.51723i	0.0202450	+	0.999795i	$0.493555\pi$
$642$	4.43023			0.174847
$643$	23.6894	+	41.0312i	0.934218	+	1.61811i	0.776022	+	0.630706i	$0.217235\pi$
$643$	23.6894	+	41.0312i	0.934218	+	1.61811i	0.158197	+	0.987408i	$0.449432\pi$
$644$	7.87684	−	4.54769i	0.310391	−	0.179204i
$645$	22.3150	−	13.5664i	0.878651	−	0.534176i
$646$	8.10542	+	14.0390i	0.318903	+	0.552357i
$647$	22.5781	+	13.0355i	0.887637	+	0.512478i	0.873169	−	0.487418i	$-0.162061\pi$
$647$	22.5781	+	13.0355i	0.887637	+	0.512478i	0.0144683	+	0.999895i	$0.495394\pi$
$648$	4.69626	−	8.13416i	0.184487	−	0.319540i
$649$	12.4600			0.489097
$650$	27.9550	−	40.4652i	1.09648	−	1.58718i
$651$	−11.8651			−0.465030
$652$	43.3558	−	75.0945i	1.69795	−	2.94093i
$653$	−20.0320	−	11.5655i	−0.783913	−	0.452592i	0.0539022	−	0.998546i	$-0.482834\pi$
$653$	−20.0320	−	11.5655i	−0.783913	−	0.452592i	−0.837815	+	0.545954i	$0.816167\pi$
$654$	−24.0182	−	41.6008i	−0.939188	−	1.62672i
$655$	−10.6004	+	6.44453i	−0.414192	+	0.251809i
$656$	12.7747	−	7.37547i	0.498768	−	0.287964i
$657$	−0.0246999	−	0.0427816i	−0.000963637	−	0.00166907i
$658$	82.1401			3.20215
$659$	−23.7412	−	41.1210i	−0.924828	−	1.60185i	−0.791838	−	0.610731i	$-0.790876\pi$
$659$	−23.7412	−	41.1210i	−0.924828	−	1.60185i	−0.132990	−	0.991117i	$-0.542458\pi$
$660$	−0.644958	−	28.4747i	−0.0251050	−	1.10838i
$661$	−6.14537	−	3.54803i	−0.239027	−	0.138002i	0.375702	−	0.926740i	$-0.377401\pi$
$661$	−6.14537	−	3.54803i	−0.239027	−	0.138002i	−0.614729	+	0.788738i	$0.710735\pi$
$662$		−	42.8835i		−	1.66671i
$663$	−3.70321	−	8.82396i	−0.143821	−	0.342694i
$664$	71.6911			2.78216
$665$	−18.6830	+	0.423174i	−0.724495	+	0.0164100i
$666$	2.17703	−	3.77072i	0.0843581	−	0.146113i
$667$	0.600644	−	0.346782i	0.0232570	−	0.0134274i
$668$	138.419			5.35560
$669$	−15.6595	+	9.04102i	−0.605431	+	0.349546i
$670$	54.1738	+	29.6623i	2.09292	+	1.14596i
$671$		−	1.48753i		−	0.0574254i
$672$	69.2610	−	39.9879i	2.67180	−	1.54257i
$673$	−20.3750	−	11.7635i	−0.785398	−	0.453450i	0.0529421	−	0.998598i	$-0.483140\pi$
$673$	−20.3750	−	11.7635i	−0.785398	−	0.453450i	−0.838340	+	0.545148i	$0.816473\pi$
$674$	56.1920	+	32.4424i	2.16443	+	1.24964i
$675$	−4.43888	−	2.30138i	−0.170853	−	0.0885802i
$676$	68.5131	+	17.6762i	2.63512	+	0.679854i
$677$			39.9097i			1.53385i	0.641735	+	0.766927i	$0.278215\pi$
$677$			39.9097i			1.53385i	−0.641735	+	0.766927i	$0.721785\pi$
$678$	−25.5647	+	44.2793i	−0.981805	+	1.70054i
$679$	23.2988	−	40.3546i	0.894125	−	1.54867i
$680$	−26.7710	+	48.8932i	−1.02662	+	1.87497i
$681$			8.47042i			0.324587i
$682$	10.1465	+	17.5742i	0.388529	+	0.672952i
$683$	−17.6681	−	30.6020i	−0.676051	−	1.17095i	−0.976161	−	0.217050i	$-0.930357\pi$
$683$	−17.6681	−	30.6020i	−0.676051	−	1.17095i	0.300110	−	0.953905i	$-0.402977\pi$
$684$			12.1854i			0.465922i
$685$	−26.5814	−	14.5544i	−1.01562	−	0.556095i
$686$	0.330302	−	0.572099i	0.0126110	−	0.0218429i
$687$	11.8442	−	20.5147i	0.451883	−	0.782684i
$688$		−	172.133i		−	6.56252i
$689$	−27.7209	+	11.6338i	−1.05608	+	0.443214i
$690$	−2.33345	+	1.41862i	−0.0888329	+	0.0540060i
$691$	8.44945	+	4.87829i	0.321432	+	0.185579i	0.652031	−	0.758192i	$-0.273917\pi$
$691$	8.44945	+	4.87829i	0.321432	+	0.185579i	−0.330599	+	0.943771i	$0.607251\pi$
$692$	63.7841	+	36.8257i	2.42471	+	1.39990i
$693$	7.56568	−	4.36805i	0.287396	−	0.165928i
$694$			80.1977i			3.04426i
$695$	−10.6076	−	5.80811i	−0.402371	−	0.220314i
$696$	12.6025	−	7.27606i	0.477697	−	0.275799i
$697$	−2.65633			−0.100616
$698$	−46.7979	+	27.0188i	−1.77133	+	1.02268i
$699$	−2.37621	+	4.11572i	−0.0898765	+	0.155671i
$700$	−54.7262	−	85.5891i	−2.06845	−	3.23496i
$701$	−26.4004			−0.997128			−0.498564	−	0.866853i	$-0.666139\pi$
$701$	−26.4004			−0.997128			−0.498564	+	0.866853i	$0.666139\pi$
$702$	1.23852	−	9.75821i	0.0467449	−	0.368300i
$703$			3.57308i			0.134761i
$704$	−58.7160	−	33.8997i	−2.21294	−	1.27764i
$705$	−18.0304	+	0.408392i	−0.679063	+	0.0153809i
$706$	−2.00281	−	3.46897i	−0.0753767	−	0.130556i
$707$	2.60528			0.0979816
$708$	−14.4894	−	25.0963i	−0.544544	−	0.943177i
$709$	7.54818	−	4.35794i	0.283478	−	0.163666i	−0.351519	−	0.936181i	$-0.614335\pi$
$709$	7.54818	−	4.35794i	0.283478	−	0.163666i	0.634997	+	0.772515i	$0.281001\pi$
$710$	−12.0276	−	19.7838i	−0.451388	−	0.742474i
$711$	0.967567	+	1.67588i	0.0362866	+	0.0628502i
$712$	42.8327	+	24.7295i	1.60522	+	0.926777i
$713$	0.711423	−	1.23222i	0.0266430	−	0.0461470i
$714$	−27.0299			−1.01157
$715$	−7.69348	−	17.2279i	−0.287720	−	0.644286i
$716$	−64.0369			−2.39317
$717$	−6.63992	+	11.5007i	−0.247972	+	0.429501i
$718$	84.8889	+	49.0106i	3.16803	+	1.82906i
$719$	3.21941	+	5.57618i	0.120064	+	0.207956i	0.919793	−	0.392405i	$-0.128357\pi$
$719$	3.21941	+	5.57618i	0.120064	+	0.207956i	−0.799729	+	0.600361i	$0.795023\pi$
$720$	−28.1607	+	17.1203i	−1.04949	+	0.638037i
$721$	−12.6868	+	7.32473i	−0.472482	+	0.272787i
$722$	19.0803	+	33.0481i	0.710096	+	1.22992i
$723$	−9.96033			−0.370429
$724$	−36.1794	−	62.6645i	−1.34460	−	2.32891i
$725$	−4.17311	−	6.52655i	−0.154985	−	0.242390i
$726$	13.0495	+	7.53413i	0.484312	+	0.279618i
$727$		−	14.6296i		−	0.542580i	−0.962498	−	0.271290i	$-0.912550\pi$
$727$		−	14.6296i		−	0.542580i	0.962498	−	0.271290i	$-0.0874502\pi$
$728$	76.4909	−	100.651i	2.83494	−	3.73039i
$729$	−1.00000			−0.0370370
$730$	0.00682403	+	0.301279i	0.000252569	+	0.0111508i
$731$	−15.4988	+	26.8447i	−0.573244	+	0.992888i
$732$	−2.99611	+	1.72981i	−0.110739	+	0.0639355i
$733$	3.51568			0.129854			0.0649272	−	0.997890i	$-0.479318\pi$
$733$	3.51568			0.129854			0.0649272	+	0.997890i	$0.479318\pi$
$734$	−53.9370	+	31.1406i	−1.99085	+	1.14942i
$735$	7.44762	−	13.6020i	0.274709	−	0.501716i
$736$			9.59058i			0.353514i
$737$	20.5195	−	11.8469i	0.755845	−	0.436387i
$738$	−2.36463	−	1.36522i	−0.0870431	−	0.0502543i
$739$	14.3874	+	8.30656i	0.529249	+	0.305562i	0.740710	−	0.671824i	$-0.234489\pi$
$739$	14.3874	+	8.30656i	0.529249	+	0.305562i	−0.211462	+	0.977386i	$0.567822\pi$
$740$	−16.5973	+	10.0903i	−0.610127	+	0.370927i
$741$	3.12375	+	7.44323i	0.114754	+	0.273434i
$742$			84.9157i			3.11735i
$743$	7.04435	−	12.2012i	0.258432	−	0.447618i	−0.707390	−	0.706824i	$-0.750127\pi$
$743$	7.04435	−	12.2012i	0.258432	−	0.447618i	0.965822	+	0.259206i	$0.0834608\pi$
$744$	14.9268	−	25.8540i	0.547244	−	0.947855i
$745$	15.7506	−	28.7661i	0.577058	−	1.05391i
$746$		−	56.1189i		−	2.05466i
$747$	−3.81639	−	6.61019i	−0.139635	−	0.241854i
$748$	16.9034	+	29.2776i	0.618050	+	1.07049i
$749$		−	6.06196i		−	0.221499i
$750$	17.0089	+	25.3190i	0.621077	+	0.924517i
$751$	3.79642	−	6.57560i	0.138533	−	0.239947i	−0.788408	−	0.615152i	$-0.789095\pi$
$751$	3.79642	−	6.57560i	0.138533	−	0.239947i	0.926942	+	0.375205i	$0.122428\pi$
$752$	−59.4371	+	102.948i	−2.16745	+	3.75413i
$753$			19.9067i			0.725439i
$754$	9.22114	−	12.1337i	0.335814	−	0.441885i
$755$	−14.3209	−	23.5561i	−0.521192	−	0.857294i
$756$	−17.5958	−	10.1590i	−0.639954	−	0.369478i
$757$	−40.9906	−	23.6659i	−1.48983	−	0.860152i	−0.489895	−	0.871782i	$-0.662965\pi$
$757$	−40.9906	−	23.6659i	−1.48983	−	0.860152i	−0.999932	+	0.0116295i	$0.996298\pi$
$758$	61.1290	−	35.2928i	2.22030	−	1.28189i
$759$			1.04762i			0.0380262i
$760$	22.5820	−	41.2426i	0.819134	−	1.49603i
$761$	9.59232	−	5.53813i	0.347721	−	0.200757i	−0.315960	−	0.948773i	$-0.602327\pi$
$761$	9.59232	−	5.53813i	0.347721	−	0.200757i	0.663681	+	0.748016i	$0.268993\pi$
$762$	−33.9359			−1.22937
$763$	−56.9231	+	32.8646i	−2.06076	+	1.18978i
$764$	−45.1842	+	78.2613i	−1.63471	+	2.83139i
$765$	5.93326	−	0.134390i	0.214517	−	0.00485887i
$766$	−32.2203			−1.16417
$767$	−15.2840	−	11.6152i	−0.551874	−	0.419401i
$768$			40.7875i			1.47179i
$769$	36.9061	+	21.3078i	1.33087	+	0.768378i	0.985433	−	0.170065i	$-0.0543976\pi$
$769$	36.9061	+	21.3078i	1.33087	+	0.768378i	0.345436	+	0.938442i	$0.387731\pi$
$770$	−53.2794	+	1.20679i	−1.92006	+	0.0434898i
$771$	−9.23510	−	15.9957i	−0.332594	−	0.576070i
$772$	71.4856			2.57282
$773$	3.03622	+	5.25888i	0.109205	+	0.189149i	0.915448	−	0.402435i	$-0.131836\pi$
$773$	3.03622	+	5.25888i	0.109205	+	0.189149i	−0.806243	+	0.591584i	$0.798503\pi$
$774$	−27.5936	+	15.9312i	−0.991830	+	0.572634i
$775$	−14.1088	−	7.31482i	−0.506802	−	0.262756i
$776$	58.6219	+	101.536i	2.10440	+	3.64493i
$777$	−5.15955	−	2.97887i	−0.185098	−	0.106866i
$778$	5.88520	−	10.1935i	0.210995	−	0.365454i
$779$	2.24068			0.0802808
$780$	−25.7530	+	35.5297i	−0.922106	+	1.27217i
$781$	−8.88211			−0.317827
$782$	1.62069	−	2.80712i	0.0579558	−	0.100382i
$783$	−1.34176	−	0.774666i	−0.0479506	−	0.0276843i
$784$	−51.1071	−	88.5201i	−1.82525	−	3.16143i
$785$	−28.7903	−	47.3562i	−1.02757	−	1.69022i
$786$	13.1079	−	7.56787i	0.467545	−	0.269937i
$787$	−14.8576	−	25.7341i	−0.529616	−	0.917323i	−0.999403	−	0.0345427i	$-0.989003\pi$
$787$	−14.8576	−	25.7341i	−0.529616	−	0.917323i	0.469787	−	0.882780i	$-0.344331\pi$
$788$	90.3428			3.21833
$789$	5.02552	+	8.70446i	0.178913	+	0.309887i
$790$	−0.267317	−	11.8019i	−0.00951070	−	0.419894i
$791$	60.5882	+	34.9806i	2.15427	+	1.24377i
$792$			21.9808i			0.781055i
$793$	−1.38668	+	1.82468i	−0.0492424	+	0.0647961i
$794$	45.2717			1.60663
$795$	−0.422192	−	18.6396i	−0.0149736	−	0.661079i
$796$	−41.9097	+	72.5897i	−1.48545	+	2.57287i
$797$	4.57027	−	2.63865i	0.161887	−	0.0934656i	−0.416868	−	0.908967i	$-0.636872\pi$
$797$	4.57027	−	2.63865i	0.161887	−	0.0934656i	0.578755	+	0.815502i	$0.303539\pi$
$798$	22.8003			0.807123
$799$	18.5388	−	10.7034i	0.655855	−	0.378658i
$800$	107.011	−	4.85012i	3.78340	−	0.171478i
$801$		−	5.26578i		−	0.186057i
$802$	−2.88163	+	1.66371i	−0.101754	+	0.0587476i
$803$	0.100119	+	0.0578040i	0.00353314	+	0.00203986i
$804$	−47.7231	−	27.5529i	−1.68306	−	0.971717i
$805$	1.94113	+	3.19290i	0.0684157	+	0.112535i
$806$	3.93657	−	31.0160i	0.138660	−	1.09249i
$807$			22.3938i			0.788300i
$808$	−3.27756	+	5.67690i	−0.115304	+	0.199713i
$809$	−3.85539	+	6.67773i	−0.135548	+	0.234777i	−0.925807	−	0.377997i	$-0.876613\pi$
$809$	−3.85539	+	6.67773i	−0.135548	+	0.234777i	0.790258	+	0.612774i	$0.209946\pi$
$810$	5.35076	+	2.92975i	0.188007	+	0.102941i
$811$			19.8702i			0.697739i	0.937171	+	0.348869i	$0.113434\pi$
$811$			19.8702i			0.697739i	−0.937171	+	0.348869i	$0.886566\pi$
$812$	−15.7396	−	27.2618i	−0.552351	−	0.956701i
$813$	−7.54088	−	13.0612i	−0.264470	−	0.458076i
$814$			10.1896i			0.357144i
$815$	31.2464	+	17.1087i	1.09452	+	0.599291i
$816$	19.5590	−	33.8771i	0.684701	−	1.18594i
$817$	13.0736	−	22.6442i	0.457388	−	0.792219i
$818$			69.4293i			2.42754i
$819$	−13.3523	−	1.69469i	−0.466568	−	0.0592171i
$820$	6.32765	+	10.4082i	0.220971	+	0.363469i
$821$	−9.92947	−	5.73278i	−0.346541	−	0.200076i	0.316620	−	0.948553i	$-0.397452\pi$
$821$	−9.92947	−	5.73278i	−0.346541	−	0.200076i	−0.663161	+	0.748477i	$0.730785\pi$
$822$	32.0207	+	18.4872i	1.11685	+	0.644814i
$823$	−16.7495	+	9.67033i	−0.583851	+	0.337087i	−0.762662	−	0.646797i	$-0.776108\pi$
$823$	−16.7495	+	9.67033i	−0.583851	+	0.337087i	0.178811	+	0.983883i	$0.442775\pi$
$824$		−	36.8594i		−	1.28406i
$825$	11.6892	−	0.529800i	0.406967	−	0.0184453i
$826$	−46.9581	+	27.1113i	−1.63388	+	0.943322i
$827$	−23.2829			−0.809624			−0.404812	−	0.914400i	$-0.632663\pi$
$827$	−23.2829			−0.809624			−0.404812	+	0.914400i	$0.632663\pi$
$828$	2.11007	−	1.21825i	0.0733299	−	0.0423370i
$829$	−10.2008	+	17.6683i	−0.354289	+	0.613647i	−0.986996	−	0.160745i	$-0.948610\pi$
$829$	−10.2008	+	17.6683i	−0.354289	+	0.613647i	0.632707	+	0.774391i	$0.281944\pi$
$830$	1.05438	+	46.5506i	0.0365982	+	1.61580i
$831$	12.7486			0.442244
$832$	40.4225	+	96.3182i	1.40140	+	3.33923i
$833$			18.4066i			0.637752i
$834$	12.7783	+	7.37753i	0.442475	+	0.255463i
$835$	1.28771	+	56.8521i	0.0445632	+	1.96745i
$836$	−14.2585	−	24.6964i	−0.493139	−	0.854142i
$837$	−3.17845			−0.109863
$838$	−43.8285	−	75.9132i	−1.51403	−	2.62238i
$839$	0.271188	−	0.156570i	0.00936244	−	0.00540541i	−0.495311	−	0.868715i	$-0.664946\pi$
$839$	0.271188	−	0.156570i	0.00936244	−	0.00540541i	0.504674	+	0.863310i	$0.331613\pi$
$840$	40.7281	+	66.9924i	1.40525	+	2.31146i
$841$	13.2998	+	23.0359i	0.458613	+	0.794342i
$842$	−27.4593	−	15.8536i	−0.946309	−	0.546352i
$843$	−1.24165	+	2.15061i	−0.0427649	+	0.0740709i
$844$	−30.5507			−1.05160
$845$	−6.62266	+	28.3044i	−0.227826	+	0.973702i
$846$	22.0039			0.756510
$847$	10.3091	−	17.8558i	0.354224	−	0.613534i
$848$	−106.427	−	61.4455i	−3.65471	−	2.11005i
$849$	3.88513	+	6.72924i	0.133337	+	0.230947i
$850$	−32.1412	−	16.6639i	−1.10243	−	0.571567i
$851$	0.618726	−	0.357221i	0.0212096	−	0.0122454i
$852$	10.3288	+	17.8899i	0.353857	+	0.612899i
$853$	−24.8887			−0.852173			−0.426087	−	0.904682i	$-0.640108\pi$
$853$	−24.8887			−0.852173			−0.426087	+	0.904682i	$0.640108\pi$
$854$	3.23667	+	5.60607i	0.110756	+	0.191836i
$855$	−5.00485	+	0.113361i	−0.171162	+	0.00387686i
$856$	13.2090	+	7.62622i	0.451475	+	0.260659i
$857$		−	21.1571i		−	0.722714i	−0.932428	−	0.361357i	$-0.882314\pi$
$857$		−	21.1571i		−	0.722714i	0.932428	−	0.361357i	$-0.117686\pi$
$858$	8.90819	+	21.2263i	0.304121	+	0.724654i
$859$	22.8178			0.778535			0.389267	−	0.921125i	$-0.372728\pi$
$859$	22.8178			0.778535			0.389267	+	0.921125i	$0.372728\pi$
$860$	142.104	−	3.21869i	4.84570	−	0.109756i
$861$	−1.86805	+	3.23556i	−0.0636630	+	0.110268i
$862$	49.7428	−	28.7190i	1.69425	−	0.978174i
$863$	−41.2937			−1.40565			−0.702826	−	0.711362i	$-0.748079\pi$
$863$	−41.2937			−1.40565			−0.702826	+	0.711362i	$0.748079\pi$
$864$	18.5538	−	10.7121i	0.631214	−	0.364432i
$865$	−14.5318	+	26.5402i	−0.494097	+	0.902395i
$866$		−	45.5651i		−	1.54836i
$867$	8.62187	−	4.97784i	0.292814	−	0.169056i
$868$	−55.9275	−	32.2898i	−1.89830	−	1.09599i
$869$	−3.92196	−	2.26435i	−0.133043	−	0.0768127i
$870$	4.90986	+	8.07607i	0.166460	+	0.273805i
$871$	−36.2139	−	4.59630i	−1.22706	−	0.155740i
$872$		−	165.381i		−	5.60050i
$873$	6.24133	−	10.8103i	0.211237	−	0.365873i
$874$	−1.36709	+	2.36787i	−0.0462426	+	0.0800945i
$875$	34.6444	−	23.2736i	1.17119	−	0.786791i
$876$		−	0.268874i		−	0.00908443i
$877$	23.1812	+	40.1510i	0.782773	+	1.35580i	0.930320	+	0.366748i	$0.119529\pi$
$877$	23.1812	+	40.1510i	0.782773	+	1.35580i	−0.147547	+	0.989055i	$0.547138\pi$
$878$	−23.8134	−	41.2460i	−0.803664	−	1.39199i
$879$			15.3948i			0.519254i
$880$	37.0408	−	67.6495i	1.24865	−	2.28047i
$881$	15.4598	−	26.7772i	0.520855	−	0.902147i	−0.478851	−	0.877896i	$-0.658947\pi$
$881$	15.4598	−	26.7772i	0.520855	−	0.902147i	0.999706	−	0.0242508i	$-0.00772003\pi$
$882$	−9.46005	+	16.3853i	−0.318536	+	0.551721i
$883$		−	22.2922i		−	0.750193i	−0.926986	−	0.375097i	$-0.877610\pi$
$883$		−	22.2922i		−	0.750193i	0.926986	−	0.375097i	$-0.122390\pi$
$884$	6.55808	−	51.6707i	0.220572	−	1.73787i
$885$	10.1729	−	6.18460i	0.341957	−	0.207893i
$886$	−36.5113	−	21.0798i	−1.22662	−	0.708190i
$887$	21.2844	+	12.2886i	0.714662	+	0.412610i	0.812785	−	0.582564i	$-0.197951\pi$
$887$	21.2844	+	12.2886i	0.714662	+	0.412610i	−0.0981229	+	0.995174i	$0.531284\pi$
$888$	12.9819	−	7.49510i	0.435644	−	0.251519i
$889$			46.4351i			1.55738i
$890$	−15.4274	+	28.1759i	−0.517129	+	0.944459i
$891$	2.02671	−	1.17012i	0.0678974	−	0.0392006i
$892$	−98.4172			−3.29525
$893$	−15.6379	+	9.02856i	−0.523303	+	0.302129i
$894$	−20.0066	+	34.6525i	−0.669121	+	1.15895i
$895$	−0.595735	−	26.3015i	−0.0199132	−	0.879162i
$896$	135.093			4.51315
$897$	0.976594	−	1.28506i	0.0326075	−	0.0429070i
$898$			48.9605i			1.63383i
$899$	−4.26472	−	2.46224i	−0.142236	−	0.0821202i
$900$	−14.6602	−	22.9278i	−0.488673	−	0.764261i
$901$	11.0650	+	19.1652i	0.368630	+	0.638486i
$902$	6.38989			0.212760
$903$	21.7989	+	37.7568i	0.725421	+	1.25647i
$904$	−152.445	+	88.0144i	−5.07026	+	2.92732i
$905$	25.4013	−	15.4427i	0.844366	−	0.513333i
$906$	16.8172	+	29.1283i	0.558715	+	0.967722i
$907$	−6.54797	−	3.78047i	−0.217422	−	0.125529i	0.387334	−	0.921939i	$-0.373396\pi$
$907$	−6.54797	−	3.78047i	−0.217422	−	0.125529i	−0.604756	+	0.796411i	$0.706729\pi$
$908$	−23.0515	+	39.9263i	−0.764990	+	1.32500i
$909$	0.697909			0.0231482
$910$	66.4801	+	48.1869i	2.20379	+	1.59738i
$911$	−30.4986			−1.01046			−0.505232	−	0.862984i	$-0.668593\pi$
$911$	−30.4986			−1.01046			−0.505232	+	0.862984i	$0.668593\pi$
$912$	−16.4985	+	28.5762i	−0.546319	+	0.946252i
$913$	15.4695	+	8.93130i	0.511965	+	0.295583i
$914$	31.5702	+	54.6812i	1.04425	+	1.80869i
$915$	−0.738346	−	1.21448i	−0.0244090	−	0.0401496i
$916$	111.658	−	64.4656i	3.68927	−	2.13000i
$917$	−10.3553	−	17.9358i	−0.341961	−	0.592293i
$918$	−7.24083			−0.238983
$919$	6.09823	+	10.5624i	0.201162	+	0.348423i	0.948903	−	0.315568i	$-0.102195\pi$
$919$	6.09823	+	10.5624i	0.201162	+	0.348423i	−0.747741	+	0.663990i	$0.768862\pi$
$920$	−9.39935	+	0.212898i	−0.309888	+	0.00701903i
$921$	−22.5622	−	13.0263i	−0.743451	−	0.429232i
$922$			37.9657i			1.25033i
$923$	10.8952	+	8.27992i	0.358621	+	0.272537i
$924$	47.5489			1.56425
$925$	−4.29874	−	6.72302i	−0.141342	−	0.221052i
$926$	10.1786	−	17.6298i	0.334488	−	0.579351i
$927$	−3.39858	+	1.96217i	−0.111624	+	0.0644461i
$928$	33.1930			1.08962
$929$	−43.7395	+	25.2530i	−1.43505	+	0.828524i	−0.997500	−	0.0706712i	$-0.977486\pi$
$929$	−43.7395	+	25.2530i	−1.43505	+	0.828524i	−0.437547	+	0.899196i	$0.644153\pi$
$930$	17.0071	+	9.31208i	0.557686	+	0.305355i
$931$		−	15.5264i		−	0.508859i
$932$	−22.4011	+	12.9333i	−0.733772	+	0.423643i
$933$	9.18268	+	5.30162i	0.300627	+	0.173567i
$934$	−15.3712	−	8.87454i	−0.502960	−	0.290384i
$935$	−11.8678	+	7.21501i	−0.388117	+	0.235956i
$936$	20.4906	−	26.9627i	0.669756	−	0.881305i
$937$		−	9.97732i		−	0.325945i	−0.986631	−	0.162972i	$-0.947892\pi$
$937$		−	9.97732i		−	0.325945i	0.986631	−	0.162972i	$-0.0521082\pi$
$938$	−51.5547	+	89.2954i	−1.68332	+	2.91560i
$939$	−0.930138	+	1.61105i	−0.0303539	+	0.0525745i
$940$	−86.0997	−	47.1430i	−2.80826	−	1.53763i
$941$		−	51.3470i		−	1.67387i	−0.547305	−	0.836933i	$-0.684346\pi$
$941$		−	51.3470i		−	1.67387i	0.547305	−	0.836933i	$-0.315654\pi$
$942$	33.8087	+	58.5584i	1.10155	+	1.90793i
$943$	−0.224014	−	0.388004i	−0.00729490	−	0.0126351i
$944$		−	78.4715i		−	2.55403i
$945$	4.00883	−	7.32154i	0.130407	−	0.238170i
$946$	37.2828	−	64.5758i	1.21217	−	2.09954i
$947$	−25.2810	+	43.7880i	−0.821522	+	1.42292i	0.0830260	+	0.996547i	$0.473542\pi$
$947$	−25.2810	+	43.7880i	−0.821522	+	1.42292i	−0.904548	+	0.426371i	$0.859792\pi$
$948$			10.5326i			0.342082i
$949$	−0.0689263	−	0.164237i	−0.00223744	−	0.00533135i
$950$	27.1119	+	14.0564i	0.879625	+	0.456050i
$951$	−7.60716	−	4.39200i	−0.246679	−	0.142420i
$952$	−80.5913	−	46.5294i	−2.61198	−	1.50803i
$953$	−30.8855	+	17.8318i	−1.00048	+	0.577627i	−0.908390	−	0.418123i	$-0.862688\pi$
$953$	−30.8855	+	17.8318i	−1.00048	+	0.577627i	−0.0920897	+	0.995751i	$0.529355\pi$
$954$			22.7474i			0.736475i
$955$	−32.5641	−	17.8302i	−1.05375	−	0.576971i
$956$	−62.5961	+	36.1399i	−2.02450	+	1.16885i
$957$	3.62582			0.117206
$958$	−6.98596	+	4.03334i	−0.225706	+	0.130311i
$959$	25.2963	−	43.8145i	0.816861	−	1.41484i
$960$	−64.7646	+	1.46693i	−2.09027	+	0.0473451i
$961$	20.8974			0.674111
$962$	9.49874	−	12.4990i	0.306252	−	0.402984i
$963$		−	1.62389i		−	0.0523292i
$964$	−46.9492	−	27.1061i	−1.51213	−	0.873029i
$965$	0.665030	+	29.3608i	0.0214081	+	0.945159i
$966$	−2.27948	−	3.94818i	−0.0733412	−	0.127031i
$967$	7.79539			0.250683			0.125341	−	0.992114i	$-0.459997\pi$
$967$	7.79539			0.250683			0.125341	+	0.992114i	$0.459997\pi$
$968$	25.9386	+	44.9270i	0.833698	+	1.44401i
$969$	5.14597	−	2.97103i	0.165312	−	0.0954432i
$970$	−65.0674	+	39.5578i	−2.08919	+	1.27012i
$971$	5.58454	+	9.67270i	0.179216	+	0.310412i	0.941612	−	0.336699i	$-0.109310\pi$
$971$	5.58454	+	9.67270i	0.179216	+	0.310412i	−0.762396	+	0.647111i	$0.775977\pi$
$972$	−4.71362	−	2.72141i	−0.151189	−	0.0872892i
$973$	10.0948	−	17.4847i	0.323625	−	0.560534i
$974$	41.5672			1.33190
$975$	−14.8325	−	10.2469i	−0.475019	−	0.328162i
$976$	−9.36829			−0.299872
$977$	17.4149	−	30.1634i	0.557151	−	0.965014i	−0.440582	−	0.897712i	$-0.645228\pi$
$977$	17.4149	−	30.1634i	0.557151	−	0.965014i	0.997733	−	0.0673013i	$-0.0214389\pi$
$978$	−37.6403	−	21.7316i	−1.20360	−	0.694901i
$979$	6.16161	+	10.6722i	0.196926	+	0.341086i
$980$	72.1217	−	43.8464i	2.30384	−	1.40062i
$981$	−15.2487	+	8.80385i	−0.486854	+	0.281085i
$982$	−22.9939	−	39.8266i	−0.733765	−	1.27092i
$983$	−20.6364			−0.658199			−0.329099	−	0.944295i	$-0.606745\pi$
$983$	−20.6364			−0.658199			−0.329099	+	0.944295i	$0.606745\pi$
$984$	−4.70019	−	8.14097i	−0.149837	−	0.259525i
$985$	0.840458	+	37.1059i	0.0267792	+	1.18229i
$986$	−9.71545	−	5.60922i	−0.309403	−	0.178634i
$987$		−	30.1083i		−	0.958359i
$988$	−5.53190	+	43.5855i	−0.175993	+	1.38664i
$989$	−5.22818			−0.166247
$990$	−14.2726	+	0.323278i	−0.453614	+	0.0102745i
$991$	−20.5680	+	35.6249i	−0.653365	+	1.13166i	0.328936	+	0.944352i	$0.393310\pi$
$991$	−20.5680	+	35.6249i	−0.653365	+	1.13166i	−0.982301	+	0.187310i	$0.940023\pi$
$992$	58.9724	−	34.0477i	1.87238	−	1.08102i
$993$	−15.7189			−0.498824
$994$	33.4741	−	19.3263i	1.06173	−	0.612993i
$995$	−30.2042	−	16.5380i	−0.957538	−	0.524290i
$996$		−	41.5439i		−	1.31637i
$997$	−44.2553	+	25.5508i	−1.40158	+	0.809202i	−0.994555	−	0.104216i	$-0.966767\pi$
$997$	−44.2553	+	25.5508i	−1.40158	+	0.809202i	−0.407024	+	0.913418i	$0.633433\pi$
$998$	12.6527	+	7.30507i	0.400516	+	0.231238i
$999$	−1.38215	−	0.797986i	−0.0437294	−	0.0252472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.4.16	yes	32
3.2	odd	2		585.2.bf.c.199.1		32
5.2	odd	4		975.2.bc.m.901.8		16
5.3	odd	4		975.2.bc.n.901.1		16
5.4	even	2	inner	195.2.v.a.4.1	✓	32
13.10	even	6	inner	195.2.v.a.49.1	yes	32
15.14	odd	2		585.2.bf.c.199.16		32
39.23	odd	6		585.2.bf.c.244.16		32
65.23	odd	12		975.2.bc.n.751.1		16
65.49	even	6	inner	195.2.v.a.49.16	yes	32
65.62	odd	12		975.2.bc.m.751.8		16
195.179	odd	6		585.2.bf.c.244.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.1	✓	32	5.4	even	2	inner
195.2.v.a.4.16	yes	32	1.1	even	1	trivial
195.2.v.a.49.1	yes	32	13.10	even	6	inner
195.2.v.a.49.16	yes	32	65.49	even	6	inner
585.2.bf.c.199.1		32	3.2	odd	2
585.2.bf.c.199.16		32	15.14	odd	2
585.2.bf.c.244.1		32	195.179	odd	6
585.2.bf.c.244.16		32	39.23	odd	6
975.2.bc.m.751.8		16	65.62	odd	12
975.2.bc.m.901.8		16	5.2	odd	4
975.2.bc.n.751.1		16	65.23	odd	12
975.2.bc.n.901.1		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36408 - 2.36265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72141 - 4.71362i) q^{4} +(1.91068 - 1.16160i) q^{5} +(-2.36265 + 1.36408i) q^{6} +(1.86649 + 3.23285i) q^{7} -9.39252 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.36408 - 2.36265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72141 - 4.71362i) q^{4} +(1.91068 - 1.16160i) q^{5} +(-2.36265 + 1.36408i) q^{6} +(1.86649 + 3.23285i) q^{7} -9.39252 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.138139 - 6.09877i) q^{10} +(-2.02671 - 1.17012i) q^{11} +5.44282i q^{12} +(1.39527 + 3.32464i) q^{13} +10.1841 q^{14} +(-2.23549 + 0.0506345i) q^{15} +(-7.36930 + 12.7640i) q^{16} +(2.29853 - 1.32706i) q^{17} +2.72815 q^{18} +(-1.93887 + 1.11941i) q^{19} +(-10.6751 - 5.84502i) q^{20} -3.73298i q^{21} +(-5.52918 + 3.19227i) q^{22} +(0.387679 + 0.223827i) q^{23} +(8.13416 + 4.69626i) q^{24} +(2.30138 - 4.43888i) q^{25} +(9.75821 + 1.23852i) q^{26} -1.00000i q^{27} +(10.1590 - 17.5958i) q^{28} +(0.774666 - 1.34176i) q^{29} +(-2.92975 + 5.35076i) q^{30} -3.17845i q^{31} +(10.7121 + 18.5538i) q^{32} +(1.17012 + 2.02671i) q^{33} -7.24083i q^{34} +(7.32154 + 4.00883i) q^{35} +(2.72141 - 4.71362i) q^{36} +(0.797986 - 1.38215i) q^{37} +6.10781i q^{38} +(0.453977 - 3.57686i) q^{39} +(-17.9461 + 10.9103i) q^{40} +(-0.866750 - 0.500418i) q^{41} +(-8.81972 - 5.09207i) q^{42} +(-10.1144 + 5.83954i) q^{43} +12.7375i q^{44} +(1.96131 + 1.07390i) q^{45} +(1.05765 - 0.610634i) q^{46} +8.06550 q^{47} +(12.7640 - 7.36930i) q^{48} +(-3.46757 + 6.00600i) q^{49} +(-7.34826 - 11.4923i) q^{50} -2.65411 q^{51} +(11.8740 - 15.6245i) q^{52} +8.33803i q^{53} +(-2.36265 - 1.36408i) q^{54} +(-5.23161 + 0.118497i) q^{55} +(-17.5310 - 30.3647i) q^{56} +2.23881 q^{57} +(-2.11341 - 3.66053i) q^{58} +(-4.61091 + 2.66211i) q^{59} +(6.32236 + 10.3995i) q^{60} +(0.317815 + 0.550471i) q^{61} +(-7.50957 - 4.33565i) q^{62} +(-1.86649 + 3.23285i) q^{63} +28.9710 q^{64} +(6.52781 + 4.73156i) q^{65} +6.38455 q^{66} +(-5.06226 + 8.76809i) q^{67} +(-12.5105 - 7.22292i) q^{68} +(-0.223827 - 0.387679i) q^{69} +(19.4586 - 11.8299i) q^{70} +(3.28689 - 1.89769i) q^{71} +(-4.69626 - 8.13416i) q^{72} -0.0493999 q^{73} +(-2.17703 - 3.77072i) q^{74} +(-4.21249 + 2.69349i) q^{75} +(10.5529 + 6.09271i) q^{76} -8.73609i q^{77} +(-7.83160 - 5.95169i) q^{78} +1.93513 q^{79} +(0.746282 + 32.9481i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.36463 + 1.36522i) q^{82} -7.63279 q^{83} +(-17.5958 + 10.1590i) q^{84} +(2.85024 - 5.20555i) q^{85} +31.8623i q^{86} +(-1.34176 + 0.774666i) q^{87} +(19.0360 + 10.9904i) q^{88} +(-4.56030 - 2.63289i) q^{89} +(5.21262 - 3.16902i) q^{90} +(-8.14381 + 10.7161i) q^{91} -2.43650i q^{92} +(-1.58923 + 2.75262i) q^{93} +(11.0020 - 19.0559i) q^{94} +(-2.40425 + 4.39101i) q^{95} -21.4241i q^{96} +(-6.24133 - 10.8103i) q^{97} +(9.46005 + 16.3853i) q^{98} -2.34025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 20 * q^4 + 16 * q^9	\( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Introduction

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