LMFDB - Embedded newform 98.2.g.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	98.37
Dual form			98.2.g.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826239 - 0.563320i) q^{2} +(-2.19243 + 2.03428i) q^{3} +(0.365341 - 0.930874i) q^{4} +(3.17919 + 0.980650i) q^{5} +(-0.665522 + 2.91584i) q^{6} +(-0.0867132 + 2.64433i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.444274 - 5.92843i) q^{9} +O(q^{10})$	\(q+(0.826239 - 0.563320i) q^{2} +(-2.19243 + 2.03428i) q^{3} +(0.365341 - 0.930874i) q^{4} +(3.17919 + 0.980650i) q^{5} +(-0.665522 + 2.91584i) q^{6} +(-0.0867132 + 2.64433i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.444274 - 5.92843i) q^{9} +(3.17919 - 0.980650i) q^{10} +(-0.138368 - 1.84640i) q^{11} +(1.09267 + 2.78408i) q^{12} +(-2.68880 - 1.29486i) q^{13} +(1.41796 + 2.23370i) q^{14} +(-8.96507 + 4.31735i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(-1.81295 - 0.273258i) q^{17} +(-2.97252 - 5.14856i) q^{18} +(2.91417 - 5.04749i) q^{19} +(2.07435 - 2.60115i) q^{20} +(-5.18919 - 5.97391i) q^{21} +(-1.15444 - 1.44762i) q^{22} +(-0.233672 + 0.0352204i) q^{23} +(2.47114 + 1.68479i) q^{24} +(5.01438 + 3.41875i) q^{25} +(-2.95101 + 0.444793i) q^{26} +(5.49178 + 6.88648i) q^{27} +(2.42986 + 1.04680i) q^{28} +(1.00936 - 1.26570i) q^{29} +(-4.97524 + 8.61737i) q^{30} +(-0.552111 - 0.956284i) q^{31} +(-0.988831 - 0.149042i) q^{32} +(4.05945 + 3.76662i) q^{33} +(-1.65186 + 0.795494i) q^{34} +(-2.86884 + 8.32179i) q^{35} +(-5.35630 - 2.57946i) q^{36} +(0.957619 + 2.43997i) q^{37} +(-0.435552 - 5.81204i) q^{38} +(8.52911 - 2.63088i) q^{39} +(0.248627 - 3.31770i) q^{40} +(2.45701 + 10.7649i) q^{41} +(-7.65274 - 2.01270i) q^{42} +(2.82733 - 12.3873i) q^{43} +(-1.76931 - 0.545761i) q^{44} +(7.22614 - 18.4119i) q^{45} +(-0.173229 + 0.160733i) q^{46} +(-5.91819 + 4.03495i) q^{47} +2.99083 q^{48} +(-6.98496 - 0.458597i) q^{49} +6.06893 q^{50} +(4.53065 - 3.08894i) q^{51} +(-2.18768 + 2.02987i) q^{52} +(-1.52956 + 3.89724i) q^{53} +(8.41681 + 2.59624i) q^{54} +(1.37077 - 6.00573i) q^{55} +(2.59733 - 0.503880i) q^{56} +(3.87889 + 16.9945i) q^{57} +(0.120980 - 1.61436i) q^{58} +(-9.88343 + 3.04864i) q^{59} +(0.743600 + 9.92266i) q^{60} +(-3.53111 - 8.99711i) q^{61} +(-0.994870 - 0.479104i) q^{62} +(15.6382 + 1.68888i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-7.27841 - 6.75337i) q^{65} +(5.47588 + 0.825357i) q^{66} +(3.11561 + 5.39640i) q^{67} +(-0.916713 + 1.58779i) q^{68} +(0.440662 - 0.552573i) q^{69} +(2.31749 + 8.49186i) q^{70} +(5.61436 + 7.04019i) q^{71} +(-5.87865 + 0.886064i) q^{72} +(1.05862 + 0.721752i) q^{73} +(2.16571 + 1.47655i) q^{74} +(-17.9484 + 2.70528i) q^{75} +(-3.63391 - 4.55678i) q^{76} +(4.89448 - 0.205784i) q^{77} +(5.56506 - 6.97836i) q^{78} +(-3.22298 + 5.58236i) q^{79} +(-1.66350 - 2.88127i) q^{80} +(-8.41343 - 1.26812i) q^{81} +(8.09415 + 7.51027i) q^{82} +(-3.35587 + 1.61610i) q^{83} +(-7.45678 + 2.64797i) q^{84} +(-5.49574 - 2.64661i) q^{85} +(-4.64199 - 11.8276i) q^{86} +(0.361829 + 4.82828i) q^{87} +(-1.76931 + 0.545761i) q^{88} +(0.736437 - 9.82707i) q^{89} +(-4.40128 - 19.2833i) q^{90} +(3.65719 - 6.99779i) q^{91} +(-0.0525843 + 0.230387i) q^{92} +(3.15582 + 0.973440i) q^{93} +(-2.61687 + 6.66767i) q^{94} +(14.2145 - 13.1891i) q^{95} +(2.47114 - 1.68479i) q^{96} +1.02034 q^{97} +(-6.02958 + 3.55586i) q^{98} -11.0077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

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 $

$2$	0.826239	−	0.563320i	0.584239	−	0.398327i
$2$	0.826239	−	0.563320i	0.584239	−	0.398327i
$3$	−2.19243	+	2.03428i	−1.26580	+	1.17449i	−0.289714	+	0.957113i	$0.593560\pi$
$3$	−2.19243	+	2.03428i	−1.26580	+	1.17449i	−0.976087	+	0.217378i	$0.930249\pi$
$4$	0.365341	−	0.930874i	0.182671	−	0.465437i
$5$	3.17919	+	0.980650i	1.42178	+	0.438560i	0.907858	−	0.419278i	$-0.137717\pi$
$5$	3.17919	+	0.980650i	1.42178	+	0.438560i	0.513919	+	0.857838i	$0.328193\pi$
$6$	−0.665522	+	2.91584i	−0.271698	+	1.19039i
$7$	−0.0867132	+	2.64433i	−0.0327745	+	0.999463i
$7$	−0.0867132	+	2.64433i	−0.0327745	+	0.999463i
$8$	−0.222521	−	0.974928i	−0.0786730	−	0.344689i
$9$	0.444274	−	5.92843i	0.148091	−	1.97614i
$10$	3.17919	−	0.980650i	1.00535	−	0.310109i
$11$	−0.138368	−	1.84640i	−0.0417196	−	0.556709i	−0.978427	−	0.206595i	$-0.933762\pi$
$11$	−0.138368	−	1.84640i	−0.0417196	−	0.556709i	0.936707	−	0.350114i	$-0.113857\pi$
$12$	1.09267	+	2.78408i	0.315427	+	0.803695i
$13$	−2.68880	−	1.29486i	−0.745739	−	0.359129i	0.0221136	−	0.999755i	$-0.492960\pi$
$13$	−2.68880	−	1.29486i	−0.745739	−	0.359129i	−0.767853	+	0.640626i	$0.778675\pi$
$14$	1.41796	+	2.23370i	0.378965	+	0.596980i
$15$	−8.96507	+	4.31735i	−2.31477	+	1.11474i
$16$	−0.733052	−	0.680173i	−0.183263	−	0.170043i
$17$	−1.81295	−	0.273258i	−0.439704	−	0.0662748i	−0.0745404	−	0.997218i	$-0.523749\pi$
$17$	−1.81295	−	0.273258i	−0.439704	−	0.0662748i	−0.365164	+	0.930943i	$0.618987\pi$
$18$	−2.97252	−	5.14856i	−0.700631	−	1.21353i
$19$	2.91417	−	5.04749i	0.668556	−	1.15797i	−0.309752	−	0.950817i	$-0.600246\pi$
$19$	2.91417	−	5.04749i	0.668556	−	1.15797i	0.978308	−	0.207156i	$-0.0664207\pi$
$20$	2.07435	−	2.60115i	0.463839	−	0.581636i
$21$	−5.18919	−	5.97391i	−1.13237	−	1.30361i
$22$	−1.15444	−	1.44762i	−0.246127	−	0.308633i
$23$	−0.233672	+	0.0352204i	−0.0487240	+	0.00734397i	−0.173359	−	0.984859i	$-0.555462\pi$
$23$	−0.233672	+	0.0352204i	−0.0487240	+	0.00734397i	0.124635	+	0.992203i	$0.460224\pi$
$24$	2.47114	+	1.68479i	0.504419	+	0.343907i
$25$	5.01438	+	3.41875i	1.00288	+	0.683750i
$26$	−2.95101	+	0.444793i	−0.578741	+	0.0872311i
$27$	5.49178	+	6.88648i	1.05689	+	1.32530i
$28$	2.42986	+	1.04680i	0.459200	+	0.197827i
$29$	1.00936	−	1.26570i	0.187433	−	0.235034i	−0.679232	−	0.733923i	$-0.737687\pi$
$29$	1.00936	−	1.26570i	0.187433	−	0.235034i	0.866666	+	0.498889i	$0.166259\pi$
$30$	−4.97524	+	8.61737i	−0.908351	+	1.57331i
$31$	−0.552111	−	0.956284i	−0.0991621	−	0.171754i	0.812176	−	0.583413i	$-0.198283\pi$
$31$	−0.552111	−	0.956284i	−0.0991621	−	0.171754i	−0.911338	+	0.411659i	$0.864950\pi$
$32$	−0.988831	−	0.149042i	−0.174802	−	0.0263472i
$33$	4.05945	+	3.76662i	0.706659	+	0.655684i
$34$	−1.65186	+	0.795494i	−0.283292	+	0.136426i
$35$	−2.86884	+	8.32179i	−0.484923	+	1.40664i
$36$	−5.35630	−	2.57946i	−0.892717	−	0.429910i
$37$	0.957619	+	2.43997i	0.157432	+	0.401129i	0.987726	−	0.156196i	$-0.0499230\pi$
$37$	0.957619	+	2.43997i	0.157432	+	0.401129i	−0.830295	+	0.557325i	$0.811828\pi$
$38$	−0.435552	−	5.81204i	−0.0706559	−	0.942838i
$39$	8.52911	−	2.63088i	1.36575	−	0.421279i
$40$	0.248627	−	3.31770i	0.0393114	−	0.524574i
$41$	2.45701	+	10.7649i	0.383721	+	1.68119i	0.685706	+	0.727879i	$0.259494\pi$
$41$	2.45701	+	10.7649i	0.383721	+	1.68119i	−0.301985	+	0.953313i	$0.597649\pi$
$42$	−7.65274	−	2.01270i	−1.18084	−	0.310567i
$43$	2.82733	−	12.3873i	0.431164	−	1.88905i	−0.0259885	−	0.999662i	$-0.508273\pi$
$43$	2.82733	−	12.3873i	0.431164	−	1.88905i	0.457152	−	0.889389i	$-0.348870\pi$
$44$	−1.76931	−	0.545761i	−0.266734	−	0.0822765i
$45$	7.22614	−	18.4119i	1.07721	−	2.74469i
$46$	−0.173229	+	0.160733i	−0.0255412	+	0.0236987i
$47$	−5.91819	+	4.03495i	−0.863257	+	0.588559i	−0.911971	−	0.410254i	$-0.865440\pi$
$47$	−5.91819	+	4.03495i	−0.863257	+	0.588559i	0.0487143	+	0.998813i	$0.484488\pi$
$48$	2.99083			0.431689
$49$	−6.98496	−	0.458597i	−0.997852	−	0.0655138i
$50$	6.06893			0.858276
$51$	4.53065	−	3.08894i	0.634417	−	0.432539i
$52$	−2.18768	+	2.02987i	−0.303376	+	0.281492i
$53$	−1.52956	+	3.89724i	−0.210101	+	0.535328i	−0.996612	−	0.0822484i	$-0.973790\pi$
$53$	−1.52956	+	3.89724i	−0.210101	+	0.535328i	0.786511	+	0.617576i	$0.211885\pi$
$54$	8.41681	+	2.59624i	1.14538	+	0.353304i
$55$	1.37077	−	6.00573i	0.184835	−	0.809813i
$56$	2.59733	−	0.503880i	0.347082	−	0.0673337i
$57$	3.87889	+	16.9945i	0.513771	+	2.25098i
$58$	0.120980	−	1.61436i	0.0158854	−	0.211976i
$59$	−9.88343	+	3.04864i	−1.28671	+	0.396898i	−0.861298	−	0.508100i	$-0.830348\pi$
$59$	−9.88343	+	3.04864i	−1.28671	+	0.396898i	−0.425415	+	0.904998i	$0.639872\pi$
$60$	0.743600	+	9.92266i	0.0959984	+	1.28101i
$61$	−3.53111	−	8.99711i	−0.452112	−	1.15196i	−0.957337	−	0.288975i	$-0.906686\pi$
$61$	−3.53111	−	8.99711i	−0.452112	−	1.15196i	0.505225	−	0.862988i	$-0.331410\pi$
$62$	−0.994870	−	0.479104i	−0.126349	−	0.0608463i
$63$	15.6382	+	1.68888i	1.97023	+	0.212779i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−7.27841	−	6.75337i	−0.902775	−	0.837653i
$66$	5.47588	+	0.825357i	0.674035	+	0.101594i
$67$	3.11561	+	5.39640i	0.380633	+	0.659275i	0.991153	−	0.132725i	$-0.0423728\pi$
$67$	3.11561	+	5.39640i	0.380633	+	0.659275i	−0.610520	+	0.792001i	$0.709040\pi$
$68$	−0.916713	+	1.58779i	−0.111168	+	0.192548i
$69$	0.440662	−	0.552573i	0.0530495	−	0.0665220i
$70$	2.31749	+	8.49186i	0.276992	+	1.01497i
$71$	5.61436	+	7.04019i	0.666302	+	0.835517i	0.994013	−	0.109261i	$-0.0348485\pi$
$71$	5.61436	+	7.04019i	0.666302	+	0.835517i	−0.327711	+	0.944778i	$0.606277\pi$
$72$	−5.87865	+	0.886064i	−0.692805	+	0.104424i
$73$	1.05862	+	0.721752i	0.123902	+	0.0844746i	0.623685	−	0.781676i	$-0.285635\pi$
$73$	1.05862	+	0.721752i	0.123902	+	0.0844746i	−0.499784	+	0.866150i	$0.666587\pi$
$74$	2.16571	+	1.47655i	0.251758	+	0.171646i
$75$	−17.9484	+	2.70528i	−2.07250	+	0.312379i
$76$	−3.63391	−	4.55678i	−0.416838	−	0.522698i
$77$	4.89448	−	0.205784i	0.557777	−	0.0234513i
$78$	5.56506	−	6.97836i	0.630119	−	0.790144i
$79$	−3.22298	+	5.58236i	−0.362613	+	0.628064i	−0.988390	−	0.151938i	$-0.951449\pi$
$79$	−3.22298	+	5.58236i	−0.362613	+	0.628064i	0.625777	+	0.780002i	$0.284782\pi$
$80$	−1.66350	−	2.88127i	−0.185985	−	0.322135i
$81$	−8.41343	−	1.26812i	−0.934825	−	0.140902i
$82$	8.09415	+	7.51027i	0.893849	+	0.829371i
$83$	−3.35587	+	1.61610i	−0.368354	+	0.177390i	−0.608899	−	0.793248i	$-0.708388\pi$
$83$	−3.35587	+	1.61610i	−0.368354	+	0.177390i	0.240544	+	0.970638i	$0.422674\pi$
$84$	−7.45678	+	2.64797i	−0.813602	+	0.288917i
$85$	−5.49574	−	2.64661i	−0.596096	−	0.287065i
$86$	−4.64199	−	11.8276i	−0.500558	−	1.27540i
$87$	0.361829	+	4.82828i	0.0387922	+	0.517645i
$88$	−1.76931	+	0.545761i	−0.188609	+	0.0581783i
$89$	0.736437	−	9.82707i	0.0780622	−	1.04167i	−0.811350	−	0.584561i	$-0.801267\pi$
$89$	0.736437	−	9.82707i	0.0780622	−	1.04167i	0.889412	−	0.457106i	$-0.151114\pi$
$90$	−4.40128	−	19.2833i	−0.463936	−	2.03264i
$91$	3.65719	−	6.99779i	0.383377	−	0.733568i
$92$	−0.0525843	+	0.230387i	−0.00548229	+	0.0240195i
$93$	3.15582	+	0.973440i	0.327243	+	0.100941i
$94$	−2.61687	+	6.66767i	−0.269909	+	0.687718i
$95$	14.2145	−	13.1891i	1.45838	−	1.35318i
$96$	2.47114	−	1.68479i	0.252209	−	0.171953i
$97$	1.02034			0.103600			0.0517999	−	0.998657i	$-0.483504\pi$
$97$	1.02034			0.103600			0.0517999	+	0.998657i	$0.483504\pi$
$98$	−6.02958	+	3.55586i	−0.609080	+	0.359196i
$99$	−11.0077			−1.10631
$100$	5.01438	−	3.41875i	0.501438	−	0.341875i
$101$	−7.52810	+	6.98506i	−0.749074	+	0.695039i	−0.959229	−	0.282629i	$-0.908794\pi$
$101$	−7.52810	+	6.98506i	−0.749074	+	0.695039i	0.210155	+	0.977668i	$0.432603\pi$
$102$	2.00333	−	5.10441i	0.198360	−	0.505412i
$103$	4.54830	+	1.40296i	0.448157	+	0.138238i	0.510615	−	0.859809i	$-0.329418\pi$
$103$	4.54830	+	1.40296i	0.448157	+	0.138238i	−0.0624578	+	0.998048i	$0.519894\pi$
$104$	−0.664079	+	2.90952i	−0.0651183	+	0.285302i
$105$	−10.6391	−	24.0810i	−1.03827	−	2.35006i
$106$	0.931617	+	4.08168i	0.0904867	+	0.396448i
$107$	−0.0497199	+	0.663466i	−0.00480661	+	0.0641397i	−0.999091	−	0.0426216i	$-0.986429\pi$
$107$	−0.0497199	+	0.663466i	−0.00480661	+	0.0641397i	0.994285	+	0.106761i	$0.0340481\pi$
$108$	8.41681	−	2.59624i	0.809908	−	0.249824i
$109$	0.311648	+	4.15866i	0.0298505	+	0.398327i	0.992038	+	0.125939i	$0.0401944\pi$
$109$	0.311648	+	4.15866i	0.0298505	+	0.398327i	−0.962187	+	0.272388i	$0.912187\pi$
$110$	−2.25057	−	5.73435i	−0.214583	−	0.546749i
$111$	−7.06310	−	3.40141i	−0.670400	−	0.322848i
$112$	1.86217	−	1.87945i	0.175958	−	0.177591i
$113$	−4.87459	+	2.34748i	−0.458562	+	0.220832i	−0.648880	−	0.760890i	$-0.724762\pi$
$113$	−4.87459	+	2.34748i	−0.458562	+	0.220832i	0.190318	+	0.981723i	$0.439048\pi$
$114$	12.7782	+	11.8565i	1.19679	+	1.11046i
$115$	−0.777427	−	0.117178i	−0.0724955	−	0.0109269i
$116$	−0.809444	−	1.40200i	−0.0751550	−	0.130172i
$117$	−8.87103	+	15.3651i	−0.820127	+	1.42050i
$118$	−6.44872	+	8.08644i	−0.593653	+	0.744417i
$119$	0.879791	−	4.77034i	0.0806503	−	0.437296i
$120$	6.20402	+	7.77960i	0.566347	+	0.710177i
$121$	7.48711	−	1.12850i	0.680646	−	0.102591i
$122$	−7.98579	−	5.44462i	−0.723000	−	0.492933i
$123$	−27.2856	−	18.6030i	−2.46026	−	1.67738i
$124$	−1.09189	+	0.164576i	−0.0980545	+	0.0147793i
$125$	2.21733	+	2.78045i	0.198324	+	0.248691i
$126$	13.8723	−	7.41389i	1.23584	−	0.660482i
$127$	−3.75193	+	4.70477i	−0.332930	+	0.417481i	−0.919916	−	0.392117i	$-0.871743\pi$
$127$	−3.75193	+	4.70477i	−0.332930	+	0.417481i	0.586986	+	0.809597i	$0.300314\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	19.0006	+	32.9100i	1.67291	+	2.89756i
$130$	−9.81801	−	1.47983i	−0.861097	−	0.129789i
$131$	8.69697	+	8.06961i	0.759858	+	0.705045i	0.961619	−	0.274390i	$-0.0884759\pi$
$131$	8.69697	+	8.06961i	0.759858	+	0.705045i	−0.201761	+	0.979435i	$0.564666\pi$
$132$	4.98933	−	2.40273i	0.434265	−	0.209131i
$133$	13.0945	+	8.14371i	1.13544	+	0.706149i
$134$	5.61414	+	2.70363i	0.484988	+	0.233558i
$135$	10.7062	+	27.2789i	0.921442	+	2.34780i
$136$	0.137012	+	1.82830i	0.0117487	+	0.156775i
$137$	−2.96609	+	0.914916i	−0.253410	+	0.0781666i	−0.418857	−	0.908052i	$-0.637569\pi$
$137$	−2.96609	+	0.914916i	−0.253410	+	0.0781666i	0.165448	+	0.986219i	$0.447093\pi$
$138$	0.0528168	−	0.704791i	0.00449606	−	0.0599958i
$139$	−3.29047	−	14.4165i	−0.279094	−	1.22279i	−0.898942	−	0.438068i	$-0.855663\pi$
$139$	−3.29047	−	14.4165i	−0.279094	−	1.22279i	0.619848	−	0.784722i	$-0.287194\pi$
$140$	6.69843	+	5.71082i	0.566121	+	0.482653i
$141$	4.76701	−	20.8856i	0.401454	−	1.75889i
$142$	8.60469	+	2.65419i	0.722089	+	0.222735i
$143$	−2.01878	+	5.14376i	−0.168819	+	0.430143i
$144$	−4.35803	+	4.04366i	−0.363169	+	0.336972i
$145$	4.45015	−	3.03406i	0.369565	−	0.251965i
$146$	1.28125			0.106037
$147$	16.2470	−	13.2039i	1.34003	−	1.08904i
$148$	2.62117			0.215458
$149$	−1.78070	+	1.21406i	−0.145881	+	0.0994597i	−0.634061	−	0.773283i	$-0.718613\pi$
$149$	−1.78070	+	1.21406i	−0.145881	+	0.0994597i	0.488180	+	0.872743i	$0.337661\pi$
$150$	−13.3057	+	12.3459i	−1.08641	+	1.00804i
$151$	−4.05831	+	10.3404i	−0.330261	+	0.841490i	0.665231	+	0.746638i	$0.268333\pi$
$151$	−4.05831	+	10.3404i	−0.330261	+	0.841490i	−0.995491	+	0.0948526i	$0.969762\pi$
$152$	−5.56940	−	1.71793i	−0.451738	−	0.139343i
$153$	−2.42543	+	10.6265i	−0.196085	+	0.859104i
$154$	3.92808	−	2.92718i	0.316534	−	0.235879i
$155$	−0.817486	−	3.58164i	−0.0656620	−	0.287684i
$156$	0.667015	−	8.90070i	0.0534040	−	0.712626i
$157$	22.9518	−	7.07969i	1.83175	−	0.565021i	0.831802	−	0.555073i	$-0.187309\pi$
$157$	22.9518	−	7.07969i	1.83175	−	0.565021i	0.999951	−	0.00994830i	$-0.00316669\pi$
$158$	0.481707	+	6.42793i	0.0383225	+	0.511378i
$159$	−4.57464	−	11.6560i	−0.362792	−	0.924380i
$160$	−2.99752	−	1.44353i	−0.236975	−	0.114121i
$161$	−0.0728719	−	0.620961i	−0.00574311	−	0.0489385i
$162$	−7.66586	+	3.69168i	−0.602287	+	0.290046i
$163$	−10.6045	−	9.83950i	−0.830605	−	0.770689i	0.145184	−	0.989405i	$-0.453623\pi$
$163$	−10.6045	−	9.83950i	−0.830605	−	0.770689i	−0.975789	+	0.218716i	$0.929813\pi$
$164$	10.9184	+	1.64568i	0.852583	+	0.128506i
$165$	9.21202	+	15.9557i	0.717155	+	1.24215i
$166$	−1.86237	+	3.22571i	−0.144548	+	0.250364i
$167$	13.8972	−	17.4265i	1.07539	−	1.34850i	0.141912	−	0.989879i	$-0.454675\pi$
$167$	13.8972	−	17.4265i	1.07539	−	1.34850i	0.933482	−	0.358623i	$-0.116754\pi$
$168$	−4.66943	+	6.38841i	−0.360254	+	0.492876i
$169$	−2.55238	−	3.20058i	−0.196337	−	0.246198i
$170$	−6.03168	+	0.909129i	−0.462609	+	0.0697270i
$171$	−28.6290	−	19.5189i	−2.18931	−	1.49265i
$172$	−10.4981	−	7.15749i	−0.800473	−	0.545753i
$173$	3.81152	−	0.574495i	0.289785	−	0.0436780i	−0.00254114	−	0.999997i	$-0.500809\pi$
$173$	3.81152	−	0.574495i	0.289785	−	0.0436780i	0.292326	+	0.956319i	$0.405571\pi$
$174$	3.01882	+	3.78548i	0.228856	+	0.286977i
$175$	−9.47511	+	12.9632i	−0.716251	+	0.979928i
$176$	−1.15444	+	1.44762i	−0.0870190	+	0.109118i
$177$	15.4670	−	26.7896i	1.16257	−	2.01363i
$178$	−4.92731	−	8.53435i	−0.369318	−	0.639677i
$179$	8.28582	+	1.24889i	0.619311	+	0.0933461i	0.451201	−	0.892422i	$-0.350996\pi$
$179$	8.28582	+	1.24889i	0.619311	+	0.0933461i	0.168110	+	0.985768i	$0.446234\pi$
$180$	−14.4992	−	13.4533i	−1.08070	−	1.00275i
$181$	−18.4967	+	8.90756i	−1.37485	+	0.662094i	−0.967895	−	0.251354i	$-0.919124\pi$
$181$	−18.4967	+	8.90756i	−1.37485	+	0.662094i	−0.406956	+	0.913448i	$0.633410\pi$
$182$	−0.920289	−	7.84202i	−0.0682163	−	0.581289i
$183$	26.0444	+	12.5423i	1.92525	+	0.927153i
$184$	0.0863343	+	0.219976i	0.00636465	+	0.0162169i
$185$	0.651692	+	8.69623i	0.0479134	+	0.639360i
$186$	3.15582	−	0.973440i	0.231396	−	0.0713761i
$187$	−0.253688	+	3.38523i	−0.0185515	+	0.247552i
$188$	1.59388	+	6.98322i	0.116245	+	0.509304i
$189$	−18.6863	+	13.9249i	−1.35923	+	1.01289i
$190$	4.31488	−	18.9047i	0.313034	−	1.37149i
$191$	7.51704	+	2.31870i	0.543914	+	0.167775i	0.554523	−	0.832168i	$-0.312901\pi$
$191$	7.51704	+	2.31870i	0.543914	+	0.167775i	−0.0106088	+	0.999944i	$0.503377\pi$
$192$	1.09267	−	2.78408i	0.0788568	−	0.200924i
$193$	−14.1501	+	13.1294i	−1.01855	+	0.945073i	−0.998501	−	0.0547265i	$-0.982571\pi$
$193$	−14.1501	+	13.1294i	−1.01855	+	0.945073i	−0.0200447	+	0.999799i	$0.506381\pi$
$194$	0.843044	−	0.574778i	0.0605271	−	0.0412666i
$195$	29.6957			2.12655
$196$	−2.97879	+	6.33457i	−0.212771	+	0.452470i
$197$	3.23620			0.230570			0.115285	−	0.993332i	$-0.463222\pi$
$197$	3.23620			0.230570			0.115285	+	0.993332i	$0.463222\pi$
$198$	−9.09498	+	6.20085i	−0.646352	+	0.440675i
$199$	−5.56382	+	5.16247i	−0.394409	+	0.365958i	−0.852303	−	0.523049i	$-0.824794\pi$
$199$	−5.56382	+	5.16247i	−0.394409	+	0.365958i	0.457894	+	0.889007i	$0.348604\pi$
$200$	2.21723	−	5.64941i	0.156782	−	0.399473i
$201$	−17.8086	−	5.49321i	−1.25612	−	0.387461i
$202$	−2.28519	+	10.0121i	−0.160785	+	0.704446i
$203$	3.25940	+	2.77883i	0.228765	+	0.195036i
$204$	−1.22018	−	5.34598i	−0.0854300	−	0.374293i
$205$	−2.74527	+	36.6331i	−0.191738	+	2.55856i
$206$	4.54830	−	1.40296i	0.316895	−	0.0977492i
$207$	0.104987	+	1.40096i	0.00729711	+	0.0973732i
$208$	1.09030	+	2.77805i	0.0755989	+	0.192623i
$209$	−9.72289	−	4.68230i	−0.672546	−	0.323881i
$210$	−22.3558	−	13.9034i	−1.54269	−	0.959427i
$211$	18.2188	−	8.77369i	1.25423	−	0.604006i	0.315588	−	0.948896i	$-0.397798\pi$
$211$	18.2188	−	8.77369i	1.25423	−	0.604006i	0.938643	+	0.344891i	$0.112084\pi$
$212$	3.06903	+	2.84765i	0.210782	+	0.195577i
$213$	−26.6308	−	4.01395i	−1.82471	−	0.275031i
$214$	0.332663	+	0.576190i	0.0227404	+	0.0393875i
$215$	21.1363	−	36.6091i	1.44148	−	2.49672i
$216$	5.49178	−	6.88648i	0.373668	−	0.468565i
$217$	2.57661	−	1.37704i	0.174911	−	0.0934797i
$218$	2.60015	+	3.26049i	0.176105	+	0.220828i
$219$	−3.78919	+	0.571128i	−0.256049	+	0.0385932i
$220$	−5.08978	−	3.47015i	−0.343153	−	0.233958i
$221$	4.52083	+	3.08225i	0.304104	+	0.207334i
$222$	−7.75189	+	1.16841i	−0.520273	+	0.0784185i
$223$	−3.17443	−	3.98061i	−0.212575	−	0.266561i	0.664100	−	0.747644i	$-0.268815\pi$
$223$	−3.17443	−	3.98061i	−0.212575	−	0.266561i	−0.876675	+	0.481083i	$0.840244\pi$
$224$	0.479862	−	2.60187i	0.0320621	−	0.173845i
$225$	22.4956	−	28.2085i	1.49970	−	1.88057i
$226$	−2.70519	+	4.68553i	−0.179947	+	0.311677i
$227$	−1.52022	−	2.63310i	−0.100901	−	0.174765i	0.811155	−	0.584831i	$-0.198839\pi$
$227$	−1.52022	−	2.63310i	−0.100901	−	0.174765i	−0.912056	+	0.410066i	$0.865506\pi$
$228$	17.2369	+	2.59804i	1.14154	+	0.172059i
$229$	−3.30610	−	3.06761i	−0.218473	−	0.202713i	0.563342	−	0.826224i	$-0.309515\pi$
$229$	−3.30610	−	3.06761i	−0.218473	−	0.202713i	−0.781815	+	0.623510i	$0.785706\pi$
$230$	−0.708350	+	0.341123i	−0.0467072	+	0.0224930i
$231$	−10.3122	+	10.4079i	−0.678492	+	0.684790i
$232$	−1.45857	−	0.702409i	−0.0957596	−	0.0461154i
$233$	−2.08940	−	5.32370i	−0.136881	−	0.348767i	0.845953	−	0.533257i	$-0.179032\pi$
$233$	−2.08940	−	5.32370i	−0.136881	−	0.348767i	−0.982834	+	0.184490i	$0.940937\pi$
$234$	1.32587	+	17.6925i	0.0866746	+	1.15659i
$235$	−22.7719	+	7.02421i	−1.48548	+	0.458209i
$236$	−0.772929	+	10.3140i	−0.0503134	+	0.671385i
$237$	−4.28992	−	18.7954i	−0.278660	−	1.22089i
$238$	−1.96031	−	4.43704i	−0.127068	−	0.287611i
$239$	−4.19539	+	18.3812i	−0.271377	+	1.18898i	0.637012	+	0.770854i	$0.280170\pi$
$239$	−4.19539	+	18.3812i	−0.271377	+	1.18898i	−0.908389	+	0.418126i	$0.862687\pi$
$240$	9.50841	+	2.93296i	0.613765	+	0.189322i
$241$	5.70637	−	14.5396i	0.367580	−	0.936578i	−0.620717	−	0.784035i	$-0.713158\pi$
$241$	5.70637	−	14.5396i	0.367580	−	0.936578i	0.988297	−	0.152543i	$-0.0487463\pi$
$242$	5.55043	−	5.15005i	0.356795	−	0.331058i
$243$	−0.807291	+	0.550402i	−0.0517877	+	0.0353083i
$244$	−9.66523			−0.618753
$245$	−21.7568	−	8.30777i	−1.38999	−	0.530764i
$246$	−33.0239			−2.10553
$247$	−14.3714	+	9.79826i	−0.914430	+	0.623448i
$248$	−0.809452	+	0.751062i	−0.0514003	+	0.0476925i
$249$	4.06991	−	10.3700i	0.257920	−	0.657170i
$250$	3.39833	+	1.04824i	0.214929	+	0.0662968i
$251$	0.986763	−	4.32329i	0.0622839	−	0.272884i	−0.934191	−	0.356773i	$-0.883877\pi$
$251$	0.986763	−	4.32329i	0.0622839	−	0.272884i	0.996475	+	0.0838891i	$0.0267342\pi$
$252$	7.28541	−	13.9402i	0.458937	−	0.878148i
$253$	0.0973636	+	0.426578i	0.00612120	+	0.0268187i
$254$	−0.449698	+	6.00080i	−0.0282165	+	0.376524i
$255$	17.4330	−	5.37736i	1.09169	−	0.336743i
$256$	0.0747301	+	0.997204i	0.00467063	+	0.0623252i
$257$	3.91804	+	9.98300i	0.244401	+	0.622722i	0.999457	−	0.0329369i	$-0.0104860\pi$
$257$	3.91804	+	9.98300i	0.244401	+	0.622722i	−0.755057	+	0.655659i	$0.772391\pi$
$258$	34.2379	+	16.4881i	2.13156	+	1.02650i
$259$	−6.53513	+	2.32068i	−0.406073	+	0.144200i
$260$	−8.94564	+	4.30799i	−0.554785	+	0.267170i
$261$	−7.05516	−	6.54623i	−0.436703	−	0.405202i
$262$	11.7315	+	1.76825i	0.724777	+	0.109243i
$263$	−6.95321	−	12.0433i	−0.428753	−	0.742622i	0.568010	−	0.823022i	$-0.307714\pi$
$263$	−6.95321	−	12.0433i	−0.428753	−	0.742622i	−0.996763	+	0.0803997i	$0.974380\pi$
$264$	2.76887	−	4.79582i	0.170412	−	0.295162i
$265$	−8.68458	+	10.8901i	−0.533490	+	0.668975i
$266$	15.4067	−	0.647763i	0.944647	−	0.0397169i
$267$	18.3764	+	23.0433i	1.12462	+	1.41023i
$268$	6.16163	−	0.928716i	0.376382	−	0.0567304i
$269$	13.1049	+	8.93479i	0.799022	+	0.544764i	0.892601	−	0.450848i	$-0.148878\pi$
$269$	13.1049	+	8.93479i	0.799022	+	0.544764i	−0.0935790	+	0.995612i	$0.529831\pi$
$270$	24.2126	+	16.5079i	1.47353	+	1.00464i
$271$	21.6307	−	3.26031i	1.31397	−	0.198049i	0.545596	−	0.838048i	$-0.316303\pi$
$271$	21.6307	−	3.26031i	1.31397	−	0.198049i	0.768376	+	0.639999i	$0.221065\pi$
$272$	1.14312	+	1.43343i	0.0693120	+	0.0869145i
$273$	6.21734	+	22.7819i	0.376290	+	1.37882i
$274$	−1.93530	+	2.42679i	−0.116916	+	0.146608i
$275$	5.61853	−	9.73158i	0.338810	−	0.586836i
$276$	−0.353384	−	0.612078i	−0.0212712	−	0.0368428i
$277$	24.5905	+	3.70642i	1.47750	+	0.222697i	0.837820	−	0.545946i	$-0.183830\pi$
$277$	24.5905	+	3.70642i	1.47750	+	0.222697i	0.639678	+	0.768643i	$0.279068\pi$
$278$	−10.8398	−	10.0579i	−0.650128	−	0.603231i
$279$	−5.91455	+	2.84830i	−0.354095	+	0.170523i
$280$	8.75153	+	0.945140i	0.523004	+	0.0564829i
$281$	−20.2525	−	9.75307i	−1.20816	−	0.581819i	−0.282169	−	0.959365i	$-0.591054\pi$
$281$	−20.2525	−	9.75307i	−1.20816	−	0.581819i	−0.925991	+	0.377545i	$0.876768\pi$
$282$	−7.82660	−	19.9419i	−0.466067	−	1.18752i
$283$	−0.213794	−	2.85288i	−0.0127087	−	0.169586i	−0.999947	−	0.0103335i	$-0.996711\pi$
$283$	−0.213794	−	2.85288i	−0.0127087	−	0.169586i	0.987238	−	0.159252i	$-0.0509084\pi$
$284$	8.60469	−	2.65419i	0.510594	−	0.157497i
$285$	−4.33396	+	57.8326i	−0.256721	+	3.42571i
$286$	1.22959	+	5.38719i	0.0727072	+	0.318551i
$287$	−28.6789	+	5.56370i	−1.69286	+	0.328415i
$288$	−1.32290	+	5.79599i	−0.0779525	+	0.341532i
$289$	−13.0326	−	4.02003i	−0.766625	−	0.236473i
$290$	1.96774	−	5.01372i	0.115550	−	0.294416i
$291$	−2.23703	+	2.07566i	−0.131137	+	0.121677i
$292$	1.05862	−	0.721752i	0.0619508	−	0.0422373i
$293$	8.33247			0.486788			0.243394	−	0.969927i	$-0.421739\pi$
$293$	8.33247			0.486788			0.243394	+	0.969927i	$0.421739\pi$
$294$	5.98584	−	20.0618i	0.349101	−	1.17003i
$295$	−34.4110			−2.00348
$296$	2.16571	−	1.47655i	0.125879	−	0.0858230i
$297$	11.9553	−	11.0929i	0.693715	−	0.643674i
$298$	−0.787378	+	2.00621i	−0.0456116	+	0.116216i
$299$	0.673903	+	0.207872i	0.0389728	+	0.0120215i
$300$	−4.03900	+	17.6960i	−0.233192	+	1.02168i
$301$	32.5110	+	8.55053i	1.87390	+	0.492845i
$302$	2.47183	+	10.8298i	0.142238	+	0.623183i
$303$	2.29529	−	30.6285i	0.131861	−	1.75956i
$304$	−5.56940	+	1.71793i	−0.319427	+	0.0985302i
$305$	−2.40304	−	32.0663i	−0.137598	−	1.83611i
$306$	3.98215	+	10.1463i	0.227644	+	0.580028i
$307$	−12.7514	−	6.14077i	−0.727763	−	0.350472i	0.0330409	−	0.999454i	$-0.489481\pi$
$307$	−12.7514	−	6.14077i	−0.727763	−	0.350472i	−0.760804	+	0.648982i	$0.775195\pi$
$308$	1.59659	−	4.63132i	0.0909744	−	0.263894i
$309$	−12.8259	+	6.17661i	−0.729638	+	0.351375i
$310$	−2.69305	−	2.49878i	−0.152955	−	0.141921i
$311$	27.0571	+	4.07821i	1.53427	+	0.231254i	0.861177	−	0.508305i	$-0.169728\pi$
$311$	27.0571	+	4.07821i	1.53427	+	0.231254i	0.673092	+	0.739559i	$0.264966\pi$
$312$	−4.46283	−	7.72985i	−0.252658	−	0.437616i
$313$	−10.1952	+	17.6586i	−0.576266	+	0.998122i	0.419637	+	0.907692i	$0.362158\pi$
$313$	−10.1952	+	17.6586i	−0.576266	+	0.998122i	−0.995903	+	0.0904301i	$0.971176\pi$
$314$	14.9755	−	18.7787i	0.845118	−	1.05974i
$315$	48.0606	+	20.7049i	2.70791	+	1.16659i
$316$	4.01898	+	5.03965i	0.226086	+	0.283502i
$317$	−15.6067	+	2.35233i	−0.876557	+	0.132120i	−0.571881	−	0.820336i	$-0.693786\pi$
$317$	−15.6067	+	2.35233i	−0.876557	+	0.132120i	−0.304676	+	0.952456i	$0.598548\pi$
$318$	−10.3458	−	7.05364i	−0.580163	−	0.395549i
$319$	−2.47664	−	1.68855i	−0.138665	−	0.0945404i
$320$	−3.28984	+	0.495864i	−0.183908	+	0.0277196i
$321$	−1.24067	−	1.55575i	−0.0692473	−	0.0868334i
$322$	−0.410009	−	0.472011i	−0.0228489	−	0.0263042i
$323$	−6.66250	+	8.35451i	−0.370712	+	0.464858i
$324$	−4.25423	+	7.36854i	−0.236346	+	0.409363i
$325$	−9.05588	−	15.6852i	−0.502330	−	0.870061i
$326$	−14.3046	−	2.15607i	−0.792258	−	0.119414i
$327$	−9.14314	−	8.48360i	−0.505617	−	0.469144i
$328$	9.94824	−	4.79082i	0.549300	−	0.264529i
$329$	−10.1566	−	15.9995i	−0.559950	−	0.882083i
$330$	16.5995	+	7.99389i	0.913772	+	0.440049i
$331$	1.63339	+	4.16180i	0.0897790	+	0.228753i	0.968710	−	0.248196i	$-0.0798378\pi$
$331$	1.63339	+	4.16180i	0.0897790	+	0.228753i	−0.878931	+	0.476949i	$0.841743\pi$
$332$	0.278350	+	3.71432i	0.0152764	+	0.203850i
$333$	14.8906	−	4.59316i	0.816002	−	0.251703i
$334$	1.66568	−	22.2270i	0.0911421	−	1.21621i
$335$	4.61315	+	20.2115i	0.252043	+	1.10427i
$336$	−0.259344	+	7.90873i	−0.0141484	+	0.431457i
$337$	−0.706740	+	3.09643i	−0.0384986	+	0.168673i	−0.990523	−	0.137350i	$-0.956141\pi$
$337$	−0.706740	+	3.09643i	−0.0384986	+	0.168673i	0.952024	+	0.306023i	$0.0989986\pi$
$338$	−3.91182	−	1.20664i	−0.212775	−	0.0656324i
$339$	5.91177	−	15.0630i	0.321083	−	0.818107i
$340$	−4.47147	+	4.14892i	−0.242500	+	0.225007i
$341$	−1.68928	+	1.15173i	−0.0914799	+	0.0623699i
$342$	−34.6498			−1.87364
$343$	1.81837	−	18.4308i	0.0981827	−	0.995168i
$344$	−12.7059			−0.685056
$345$	1.94283	−	1.32460i	0.104598	−	0.0713140i
$346$	2.82560	−	2.62178i	0.151905	−	0.140948i
$347$	−9.59627	+	24.4509i	−0.515155	+	1.31259i	0.402575	+	0.915387i	$0.368115\pi$
$347$	−9.59627	+	24.4509i	−0.515155	+	1.31259i	−0.917730	+	0.397206i	$0.869980\pi$
$348$	4.62671	+	1.42715i	0.248017	+	0.0765033i
$349$	1.22336	−	5.35990i	0.0654851	−	0.286909i	−0.931573	−	0.363553i	$-0.881563\pi$
$349$	1.22336	−	5.35990i	0.0654851	−	0.286909i	0.997059	+	0.0766443i	$0.0244206\pi$
$350$	−0.526256	+	16.0482i	−0.0281296	+	0.857815i
$351$	−5.84930	−	25.6274i	−0.312212	−	1.36789i
$352$	−0.138368	+	1.84640i	−0.00737505	+	0.0984132i
$353$	−16.6489	+	5.13549i	−0.886129	+	0.273335i	−0.704221	−	0.709981i	$-0.748704\pi$
$353$	−16.6489	+	5.13549i	−0.886129	+	0.273335i	−0.181908	+	0.983315i	$0.558227\pi$
$354$	−2.31170	−	30.8475i	−0.122865	−	1.63952i
$355$	10.9452	+	27.8878i	0.580909	+	1.48013i
$356$	−8.87871	−	4.27576i	−0.470571	−	0.226615i
$357$	7.77532	+	12.2484i	0.411513	+	0.648253i
$358$	7.54959	−	3.63569i	0.399008	−	0.192152i
$359$	20.7165	+	19.2221i	1.09338	+	1.01450i	0.999822	+	0.0188899i	$0.00601321\pi$
$359$	20.7165	+	19.2221i	1.09338	+	1.01450i	0.0935539	+	0.995614i	$0.470177\pi$
$360$	−19.5583	−	2.94793i	−1.03081	−	0.155370i
$361$	−7.48476	−	12.9640i	−0.393935	−	0.682315i
$362$	−10.2649	+	17.7794i	−0.539512	+	0.934462i
$363$	−14.1193	+	17.7050i	−0.741070	+	0.929273i
$364$	−5.17794	−	5.96096i	−0.271398	−	0.312439i
$365$	2.65775	+	3.33272i	0.139113	+	0.174442i
$366$	28.5842	−	4.30837i	1.49412	−	0.225202i
$367$	−10.1053	−	6.88971i	−0.527495	−	0.359640i	0.270101	−	0.962832i	$-0.412943\pi$
$367$	−10.1053	−	6.88971i	−0.527495	−	0.359640i	−0.797596	+	0.603192i	$0.793895\pi$
$368$	0.195250	+	0.133119i	0.0101781	+	0.00693931i
$369$	64.9104	−	9.78366i	3.37910	−	0.509317i
$370$	5.43722	+	6.81805i	0.282667	+	0.354454i
$371$	−10.1730	−	4.38259i	−0.528154	−	0.227533i
$372$	2.05910	−	2.58203i	0.106759	−	0.133872i
$373$	17.6578	−	30.5841i	0.914285	−	1.58359i	0.106339	−	0.994330i	$-0.466087\pi$
$373$	17.6578	−	30.5841i	0.914285	−	1.58359i	0.807945	−	0.589257i	$-0.200580\pi$
$374$	1.69736	+	2.93991i	0.0877684	+	0.152019i
$375$	−10.5175	−	1.58527i	−0.543124	−	0.0818628i
$376$	5.25071	+	4.87195i	0.270785	+	0.251252i
$377$	−4.35287	+	2.09623i	−0.224184	+	0.107961i
$378$	−7.59517	+	22.0317i	−0.390653	+	1.13319i
$379$	−7.55027	−	3.63602i	−0.387831	−	0.186770i	0.229799	−	0.973238i	$-0.426193\pi$
$379$	−7.55027	−	3.63602i	−0.387831	−	0.186770i	−0.617631	+	0.786468i	$0.711907\pi$
$380$	−7.08428	−	18.0505i	−0.363416	−	0.925969i
$381$	−1.34497	−	17.9473i	−0.0689048	−	0.919471i
$382$	7.51704	−	2.31870i	0.384605	−	0.118635i
$383$	−0.420895	+	5.61645i	−0.0215067	+	0.286987i	0.976072	+	0.217446i	$0.0697726\pi$
$383$	−0.420895	+	5.61645i	−0.0215067	+	0.286987i	−0.997579	+	0.0695412i	$0.977846\pi$
$384$	−0.665522	−	2.91584i	−0.0339623	−	0.148798i
$385$	15.7623	+	4.14554i	0.803320	+	0.211276i
$386$	−4.29532	+	18.8190i	−0.218626	+	0.957863i
$387$	−72.1813	−	22.2650i	−3.66918	−	1.13179i
$388$	0.372772	−	0.949808i	0.0189246	−	0.0482192i
$389$	24.1455	−	22.4037i	1.22422	−	1.13591i	0.237867	−	0.971298i	$-0.423552\pi$
$389$	24.1455	−	22.4037i	1.22422	−	1.13591i	0.986358	−	0.164616i	$-0.0526386\pi$
$390$	24.5357	−	16.7282i	1.24241	−	0.847063i
$391$	0.433260			0.0219109
$392$	1.10720	+	6.91188i	0.0559221	+	0.349103i
$393$	−35.4833			−1.78990
$394$	2.67387	−	1.82302i	0.134708	−	0.0918422i
$395$	−15.7208	+	14.5868i	−0.790999	+	0.733940i
$396$	−4.02156	+	10.2468i	−0.202091	+	0.514920i
$397$	−2.30914	−	0.712277i	−0.115893	−	0.0357481i	0.236266	−	0.971688i	$-0.424076\pi$
$397$	−2.30914	−	0.712277i	−0.115893	−	0.0357481i	−0.352159	+	0.935940i	$0.614552\pi$
$398$	−1.68892	+	7.39965i	−0.0846580	+	0.370911i
$399$	−45.2754	+	8.78340i	−2.26661	+	0.439720i
$400$	−1.35046	−	5.91677i	−0.0675232	−	0.295838i
$401$	−2.28075	+	30.4345i	−0.113895	+	1.51983i	0.588767	+	0.808303i	$0.299614\pi$
$401$	−2.28075	+	30.4345i	−0.113895	+	1.51983i	−0.702662	+	0.711524i	$0.748005\pi$
$402$	−17.8086	+	5.49321i	−0.888210	+	0.273977i
$403$	0.246264	+	3.28616i	0.0122673	+	0.163695i
$404$	3.75188	+	9.55964i	0.186663	+	0.475610i
$405$	−25.5043	−	12.2822i	−1.26732	−	0.610309i
$406$	4.25841	+	0.459897i	0.211341	+	0.0228243i
$407$	4.37265	−	2.10576i	0.216744	−	0.104379i
$408$	−4.01966	−	3.72970i	−0.199003	−	0.184648i
$409$	20.3758	+	3.07116i	1.00752	+	0.151859i	0.632010	−	0.774960i	$-0.282230\pi$
$409$	20.3758	+	3.07116i	1.00752	+	0.151859i	0.375508	+	0.926819i	$0.377468\pi$
$410$	18.3679	+	31.8141i	0.907126	+	1.57119i
$411$	4.64174	−	8.03974i	0.228960	−	0.396571i
$412$	2.96766	−	3.72133i	0.146206	−	0.183337i
$413$	−7.20457	−	26.3994i	−0.354514	−	1.29903i
$414$	0.875931	+	1.09838i	0.0430497	+	0.0539826i
$415$	−12.2538	+	1.84696i	−0.601514	+	0.0906636i
$416$	2.46578	+	1.68114i	0.120895	+	0.0824247i
$417$	36.5413	+	24.9134i	1.78943	+	1.22002i
$418$	−10.6711	+	1.60840i	−0.521939	+	0.0786696i
$419$	20.5259	+	25.7386i	1.00275	+	1.25741i	0.966122	+	0.258085i	$0.0830916\pi$
$419$	20.5259	+	25.7386i	1.00275	+	1.25741i	0.0366322	+	0.999329i	$0.488337\pi$
$420$	−26.3033	+	1.10590i	−1.28347	+	0.0539624i
$421$	11.1361	−	13.9643i	0.542742	−	0.680576i	−0.432522	−	0.901624i	$-0.642376\pi$
$421$	11.1361	−	13.9643i	0.542742	−	0.680576i	0.975263	+	0.221047i	$0.0709475\pi$
$422$	10.1106	−	17.5122i	0.492179	−	0.852478i
$423$	21.2916	+	36.8782i	1.03523	+	1.79308i
$424$	4.13989	+	0.623988i	0.201051	+	0.0303035i
$425$	−8.15662	−	7.56823i	−0.395654	−	0.367113i
$426$	−24.2646	+	11.6852i	−1.17562	+	0.566150i
$427$	24.0975	−	8.55724i	1.16616	−	0.414114i
$428$	0.599438	+	0.288674i	0.0289750	+	0.0139536i
$429$	−6.03781	−	15.3841i	−0.291508	−	0.742751i
$430$	−3.15903	−	42.1543i	−0.152342	−	2.03286i
$431$	−12.8231	+	3.95540i	−0.617666	+	0.190525i	−0.587770	−	0.809028i	$-0.699994\pi$
$431$	−12.8231	+	3.95540i	−0.617666	+	0.190525i	−0.0298965	+	0.999553i	$0.509518\pi$
$432$	0.658233	−	8.78350i	0.0316692	−	0.422596i
$433$	−2.78017	−	12.1807i	−0.133606	−	0.585368i	−0.996760	−	0.0804274i	$-0.974371\pi$
$433$	−2.78017	−	12.1807i	−0.133606	−	0.585368i	0.863154	−	0.504941i	$-0.168486\pi$
$434$	1.35318	−	2.58922i	0.0649546	−	0.124287i
$435$	−3.58453	+	15.7048i	−0.171865	+	0.752989i
$436$	3.98505	+	1.22922i	0.190849	+	0.0588691i
$437$	−0.503186	+	1.28210i	−0.0240706	+	0.0613310i
$438$	−2.80904	+	2.60641i	−0.134221	+	0.124539i
$439$	18.4973	−	12.6112i	0.882826	−	0.601900i	−0.0347787	−	0.999395i	$-0.511073\pi$
$439$	18.4973	−	12.6112i	0.882826	−	0.601900i	0.917605	+	0.397495i	$0.130120\pi$
$440$	−6.16018			−0.293675
$441$	−5.82199	+	41.2061i	−0.277238	+	1.96219i
$442$	5.47157			0.260256
$443$	12.9260	−	8.81278i	0.614132	−	0.418708i	−0.215907	−	0.976414i	$-0.569271\pi$
$443$	12.9260	−	8.81278i	0.614132	−	0.418708i	0.830038	+	0.557706i	$0.188318\pi$
$444$	−5.74673	+	5.33218i	−0.272728	+	0.253054i
$445$	11.9782	−	30.5199i	0.567821	−	1.44678i
$446$	−4.86519	−	1.50071i	−0.230374	−	0.0710608i
$447$	1.43432	−	6.28418i	0.0678412	−	0.297232i
$448$	−1.06921	−	2.42008i	−0.0505152	−	0.114338i
$449$	−8.60198	−	37.6877i	−0.405952	−	1.77859i	−0.602521	−	0.798103i	$-0.705837\pi$
$449$	−8.60198	−	37.6877i	−0.405952	−	1.77859i	0.196568	−	0.980490i	$-0.437020\pi$
$450$	2.69627	−	35.9792i	0.127103	−	1.69608i
$451$	19.5363	−	6.02614i	0.919926	−	0.283760i
$452$	0.404318	+	5.39525i	0.0190175	+	0.253771i
$453$	−12.1377	−	30.9264i	−0.570279	−	1.45305i
$454$	−2.73935	−	1.31920i	−0.128564	−	0.0619131i
$455$	18.4893	−	18.6609i	0.866791	−	0.874837i
$456$	15.7053	−	7.56327i	0.735467	−	0.354182i
$457$	29.7768	+	27.6288i	1.39290	+	1.29242i	0.908692	+	0.417468i	$0.137082\pi$
$457$	29.7768	+	27.6288i	1.39290	+	1.29242i	0.484207	+	0.874953i	$0.339108\pi$
$458$	−4.45967	−	0.672188i	−0.208387	−	0.0314093i
$459$	−8.07453	−	13.9855i	−0.376887	−	0.652787i
$460$	−0.393104	+	0.680877i	−0.0183286	+	0.0317460i
$461$	18.3303	−	22.9855i	0.853728	−	1.07054i	−0.143001	−	0.989723i	$-0.545675\pi$
$461$	18.3303	−	22.9855i	0.853728	−	1.07054i	0.996729	−	0.0808185i	$-0.0257534\pi$
$462$	−2.65735	+	14.4085i	−0.123631	+	0.670343i
$463$	13.0356	+	16.3461i	0.605817	+	0.759670i	0.986272	−	0.165129i	$-0.0528042\pi$
$463$	13.0356	+	16.3461i	0.605817	+	0.759670i	−0.380455	+	0.924799i	$0.624233\pi$
$464$	−1.60081	+	0.241283i	−0.0743156	+	0.0112013i
$465$	9.07833	+	6.18950i	0.420998	+	0.287031i
$466$	−4.72529	−	3.22165i	−0.218895	−	0.149240i
$467$	−18.4212	+	2.77654i	−0.852430	+	0.128483i	−0.560701	−	0.828018i	$-0.689468\pi$
$467$	−18.4212	+	2.77654i	−0.852430	+	0.128483i	−0.291728	+	0.956501i	$0.594230\pi$
$468$	11.0620	+	13.8713i	0.511341	+	0.641201i
$469$	−14.5400	+	7.77077i	−0.671396	+	0.358821i
$470$	−14.8582	+	18.6316i	−0.685357	+	0.859410i
$471$	−35.9182	+	62.2121i	−1.65502	+	2.86658i
$472$	5.17147	+	8.95725i	0.238036	+	0.412291i
$473$	−23.2631	−	3.50635i	−1.06964	−	0.161222i
$474$	−14.1323	−	13.1129i	−0.649118	−	0.602294i
$475$	31.8689	−	15.3472i	1.46224	−	0.704179i
$476$	−4.11916	−	2.56177i	−0.188801	−	0.117419i
$477$	22.4250	+	10.7993i	1.02677	+	0.494466i
$478$	6.88810	+	17.5506i	0.315054	+	0.802746i
$479$	−1.48427	−	19.8062i	−0.0678180	−	0.904969i	−0.922545	−	0.385890i	$-0.873894\pi$
$479$	−1.48427	−	19.8062i	−0.0678180	−	0.904969i	0.854727	−	0.519078i	$-0.173725\pi$
$480$	9.50841	−	2.93296i	0.433998	−	0.133871i
$481$	0.584573	−	7.80058i	0.0266542	−	0.355676i
$482$	−3.47562	−	15.2277i	−0.158310	−	0.693602i
$483$	1.42297	+	1.21317i	0.0647476	+	0.0552012i
$484$	1.68486	−	7.38184i	0.0765844	−	0.335538i
$485$	3.24385	+	1.00060i	0.147296	+	0.0454348i
$486$	−0.356963	+	0.909526i	−0.0161922	+	0.0412570i
$487$	−1.12547	+	1.04428i	−0.0509998	+	0.0473209i	−0.705261	−	0.708948i	$-0.749170\pi$
$487$	−1.12547	+	1.04428i	−0.0509998	+	0.0473209i	0.654261	+	0.756269i	$0.272980\pi$
$488$	−7.98579	+	5.44462i	−0.361500	+	0.246466i
$489$	43.2658			1.95655
$490$	−22.6562	+	5.39184i	−1.02350	+	0.243578i
$491$	43.1713			1.94829			0.974147	−	0.225915i	$-0.0725370\pi$
$491$	43.1713			1.94829			0.974147	+	0.225915i	$0.0725370\pi$
$492$	−27.2856	+	18.6030i	−1.23013	+	0.838688i
$493$	−2.17578	+	2.01883i	−0.0979921	+	0.0909234i
$494$	−6.35466	+	16.1914i	−0.285909	+	0.728485i
$495$	−34.9955	−	10.7947i	−1.57293	−	0.485186i
$496$	−0.245713	+	1.07654i	−0.0110328	+	0.0483379i
$497$	−19.1034	+	14.2358i	−0.856906	+	0.638561i
$498$	−2.47889	−	10.8607i	−0.111082	−	0.486681i
$499$	−2.08693	+	27.8482i	−0.0934240	+	1.24666i	0.731669	+	0.681660i	$0.238742\pi$
$499$	−2.08693	+	27.8482i	−0.0934240	+	1.24666i	−0.825093	+	0.564997i	$0.808877\pi$
$500$	3.39833	−	1.04824i	0.151978	−	0.0468789i
$501$	4.98177	+	66.4771i	0.222569	+	2.96998i
$502$	−1.62009	−	4.12793i	−0.0723084	−	0.184239i
$503$	22.7653	+	10.9632i	1.01505	+	0.488824i	0.866020	−	0.500009i	$-0.166670\pi$
$503$	22.7653	+	10.9632i	1.01505	+	0.488824i	0.149032	+	0.988832i	$0.452384\pi$
$504$	−1.83329	−	15.6219i	−0.0816611	−	0.695855i
$505$	−30.7832	+	14.8244i	−1.36983	+	0.659677i
$506$	0.320746	+	0.297608i	0.0142589	+	0.0132303i
$507$	12.1068	+	1.82480i	0.537681	+	0.0810424i
$508$	3.00881	+	5.21142i	0.133494	+	0.231219i
$509$	−20.2550	+	35.0828i	−0.897789	+	1.55502i	−0.0674748	+	0.997721i	$0.521494\pi$
$509$	−20.2550	+	35.0828i	−0.897789	+	1.55502i	−0.830314	+	0.557295i	$0.811839\pi$
$510$	11.3746	−	14.2633i	0.503677	−	0.631590i
$511$	−2.00035	+	2.73674i	−0.0884901	+	0.121066i
$512$	0.623490	+	0.781831i	0.0275546	+	0.0345524i
$513$	50.7634	−	7.65135i	2.24126	−	0.337815i
$514$	8.86086	+	6.04123i	0.390836	+	0.266467i
$515$	13.0841	+	8.92058i	0.576554	+	0.393088i
$516$	37.5767	−	5.66378i	1.65422	−	0.249334i
$517$	8.26901	+	10.3690i	0.363671	+	0.456029i
$518$	−4.09229	+	5.59881i	−0.179805	+	0.245998i
$519$	−7.18782	+	9.01325i	−0.315510	+	0.395638i
$520$	−4.96446	+	8.59869i	−0.217706	+	0.377077i
$521$	−3.91779	−	6.78581i	−0.171641	−	0.297292i	0.767352	−	0.641226i	$-0.221574\pi$
$521$	−3.91779	−	6.78581i	−0.171641	−	0.297292i	−0.938994	+	0.343934i	$0.888240\pi$
$522$	−9.51687	−	1.43444i	−0.416542	−	0.0627836i
$523$	11.1528	+	10.3483i	0.487676	+	0.452498i	0.885279	−	0.465060i	$-0.153967\pi$
$523$	11.1528	+	10.3483i	0.487676	+	0.452498i	−0.397603	+	0.917558i	$0.630158\pi$
$524$	10.6891	−	5.14762i	0.466958	−	0.224875i
$525$	−5.59730	−	47.6960i	−0.244286	−	2.08163i
$526$	−12.5292	−	6.03377i	−0.546301	−	0.263085i
$527$	0.739636	+	1.88456i	0.0322191	+	0.0820928i
$528$	−0.413835	−	5.52225i	−0.0180099	−	0.240325i
$529$	−21.9248	+	6.76291i	−0.953253	+	0.294040i
$530$	−1.04091	+	13.8900i	−0.0452144	+	0.603345i
$531$	13.6827	+	59.9476i	0.593777	+	2.60151i
$532$	12.3647	−	9.21412i	0.536079	−	0.399483i
$533$	7.33257	−	32.1261i	0.317609	−	1.39154i
$534$	28.1641	+	8.68746i	1.21878	+	0.375943i
$535$	−0.808697	+	2.06053i	−0.0349630	+	0.0890844i
$536$	4.56781	−	4.23831i	0.197299	−	0.183067i
$537$	−20.7067	+	14.1176i	−0.893559	+	0.609218i
$538$	15.8609			0.683814
$539$	0.119746	+	12.9605i	0.00515781	+	0.558246i
$540$	29.3047			1.26107
$541$	20.2540	−	13.8090i	0.870789	−	0.593694i	−0.0433658	−	0.999059i	$-0.513808\pi$
$541$	20.2540	−	13.8090i	0.870789	−	0.593694i	0.914155	+	0.405365i	$0.132856\pi$
$542$	16.0355	−	14.8788i	0.688785	−	0.639099i
$543$	22.4324	−	57.1567i	0.962665	−	2.45283i
$544$	1.75197	+	0.540412i	0.0751152	+	0.0231700i
$545$	−3.08740	+	13.5268i	−0.132250	+	0.579424i
$546$	17.9705	+	15.3210i	0.769067	+	0.655677i
$547$	−6.70718	−	29.3861i	−0.286778	−	1.25646i	−0.888918	−	0.458067i	$-0.848542\pi$
$547$	−6.70718	−	29.3861i	−0.286778	−	1.25646i	0.602140	−	0.798391i	$-0.294315\pi$
$548$	−0.231961	+	3.09531i	−0.00990889	+	0.132225i
$549$	−54.9075	+	16.9367i	−2.34339	+	0.722842i
$550$	−0.839747	−	11.2056i	−0.0358069	−	0.477810i
$551$	−3.44715	−	8.78319i	−0.146853	−	0.374176i
$552$	−0.636775	−	0.306655i	−0.0271030	−	0.0130521i
$553$	−14.4821	−	9.00667i	−0.615842	−	0.383003i
$554$	22.4055	−	10.7899i	0.951919	−	0.458420i
$555$	−19.1194	−	17.7402i	−0.811571	−	0.753028i
$556$	−14.6221	−	2.20392i	−0.620114	−	0.0934671i
$557$	−16.2996	−	28.2318i	−0.690638	−	1.19622i	−0.971629	−	0.236510i	$-0.923997\pi$
$557$	−16.2996	−	28.2318i	−0.690638	−	1.19622i	0.280991	−	0.959710i	$-0.409337\pi$
$558$	−3.28233	+	5.68516i	−0.138952	+	0.240672i
$559$	−23.6420	+	29.6461i	−0.999949	+	1.25390i
$560$	7.76327	−	4.14900i	0.328058	−	0.175327i
$561$	−6.33031	−	7.93796i	−0.267266	−	0.335141i
$562$	−22.2275	+	3.35025i	−0.937609	+	0.141322i
$563$	−25.3438	−	17.2791i	−1.06811	−	0.728227i	−0.104229	−	0.994553i	$-0.533238\pi$
$563$	−25.3438	−	17.2791i	−1.06811	−	0.728227i	−0.963883	+	0.266327i	$0.914190\pi$
$564$	−17.7003	−	12.0679i	−0.745317	−	0.508148i
$565$	−17.7993	+	2.68281i	−0.748822	+	0.112867i
$566$	−1.78373	−	2.23672i	−0.0749757	−	0.0940165i
$567$	4.08288	−	22.1379i	0.171465	−	0.929705i
$568$	5.61436	−	7.04019i	0.235573	−	0.295400i
$569$	1.38627	−	2.40110i	0.0581157	−	0.100659i	−0.835504	−	0.549485i	$-0.814824\pi$
$569$	1.38627	−	2.40110i	0.0581157	−	0.100659i	0.893620	+	0.448825i	$0.148157\pi$
$570$	28.9974	+	50.2249i	1.21457	+	2.10369i
$571$	−9.10135	−	1.37181i	−0.380880	−	0.0574084i	−0.0441877	−	0.999023i	$-0.514070\pi$
$571$	−9.10135	−	1.37181i	−0.380880	−	0.0574084i	−0.336692	+	0.941615i	$0.609308\pi$
$572$	4.05065	+	3.75845i	0.169366	+	0.157149i
$573$	−21.1975	+	10.2082i	−0.885538	+	0.426452i
$574$	−20.5615	+	20.7524i	−0.858221	+	0.866187i
$575$	−1.29213	−	0.622258i	−0.0538856	−	0.0259499i
$576$	2.17197	+	5.53409i	0.0904988	+	0.230587i
$577$	−1.32538	−	17.6860i	−0.0551764	−	0.736278i	−0.954351	−	0.298688i	$-0.903451\pi$
$577$	−1.32538	−	17.6860i	−0.0551764	−	0.736278i	0.899174	−	0.437590i	$-0.144168\pi$
$578$	−13.0326	+	4.02003i	−0.542086	+	0.167211i
$579$	4.31431	−	57.5705i	0.179297	−	2.39255i
$580$	−1.19851	−	5.25100i	−0.0497653	−	0.218036i
$581$	−3.98250	−	9.01416i	−0.165222	−	0.373970i
$582$	−0.679058	+	2.97515i	−0.0281479	+	0.123324i
$583$	7.40749	+	2.28491i	0.306787	+	0.0946313i
$584$	0.468092	−	1.19268i	0.0193698	−	0.0493534i
$585$	−43.2705	+	40.1491i	−1.78901	+	1.65996i
$586$	6.88461	−	4.69385i	0.284401	−	0.193901i
$587$	−31.6825			−1.30768			−0.653838	−	0.756634i	$-0.726842\pi$
$587$	−31.6825			−1.30768			−0.653838	+	0.756634i	$0.726842\pi$
$588$	−6.35550	−	19.9478i	−0.262096	−	0.822634i
$589$	−6.43578			−0.265182
$590$	−28.4317	+	19.3844i	−1.17051	+	0.798042i
$591$	−7.09514	+	6.58333i	−0.291855	+	0.270802i
$592$	0.957619	−	2.43997i	0.0393579	−	0.100282i
$593$	2.25593	+	0.695862i	0.0926399	+	0.0285756i	0.340729	−	0.940162i	$-0.389326\pi$
$593$	2.25593	+	0.695862i	0.0926399	+	0.0285756i	−0.248089	+	0.968737i	$0.579802\pi$
$594$	3.62907	−	15.9000i	0.148903	−	0.652385i
$595$	7.47506	−	14.3030i	0.306447	−	0.586368i
$596$	0.479574	+	2.10115i	0.0196441	+	0.0860665i
$597$	1.69639	−	22.6367i	0.0694286	−	0.926460i
$598$	0.673903	−	0.207872i	0.0275580	−	0.00850051i
$599$	−0.717375	−	9.57270i	−0.0293111	−	0.391130i	−0.992495	−	0.122286i	$-0.960977\pi$
$599$	−0.717375	−	9.57270i	−0.0293111	−	0.391130i	0.963184	−	0.268844i	$-0.0866416\pi$
$600$	6.63135	+	16.8964i	0.270724	+	0.689793i
$601$	−8.07962	−	3.89094i	−0.329575	−	0.158715i	0.261777	−	0.965128i	$-0.415691\pi$
$601$	−8.07962	−	3.89094i	−0.329575	−	0.158715i	−0.591352	+	0.806414i	$0.701406\pi$
$602$	31.6786	−	11.2493i	1.29112	−	0.458489i
$603$	33.3764	−	16.0732i	1.35919	−	0.654551i
$604$	8.14295	+	7.55555i	0.331332	+	0.307431i
$605$	24.9096	+	3.75452i	1.01272	+	0.152643i
$606$	−15.3572	−	26.5995i	−0.623844	−	1.08053i
$607$	1.85540	−	3.21365i	0.0753084	−	0.130438i	−0.825912	−	0.563799i	$-0.809339\pi$
$607$	1.85540	−	3.21365i	0.0753084	−	0.130438i	0.901220	+	0.433361i	$0.142673\pi$
$608$	−3.63391	+	4.55678i	−0.147374	+	0.184802i
$609$	−12.7989	+	0.538120i	−0.518639	+	0.0218057i
$610$	−20.0491	−	25.1408i	−0.811764	−	1.01792i
$611$	21.1375	−	3.18597i	0.855133	−	0.128891i
$612$	9.00584	+	6.14008i	0.364040	+	0.248198i
$613$	−17.5058	−	11.9353i	−0.707053	−	0.482060i	0.155624	−	0.987816i	$-0.450261\pi$
$613$	−17.5058	−	11.9353i	−0.707053	−	0.482060i	−0.862677	+	0.505756i	$0.831214\pi$
$614$	−13.9950	+	2.10940i	−0.564790	+	0.0851284i
$615$	−68.5031	−	85.9001i	−2.76231	−	3.46383i
$616$	−1.28975	−	4.72597i	−0.0519654	−	0.190415i
$617$	10.9428	−	13.7218i	0.440539	−	0.552419i	−0.511146	−	0.859494i	$-0.670779\pi$
$617$	10.9428	−	13.7218i	0.440539	−	0.552419i	0.951685	+	0.307075i	$0.0993503\pi$
$618$	−7.11782	+	12.3284i	−0.286321	+	0.495922i
$619$	−10.9209	−	18.9156i	−0.438948	−	0.760281i	0.558660	−	0.829396i	$-0.311316\pi$
$619$	−10.9209	−	18.9156i	−0.438948	−	0.760281i	−0.997609	+	0.0691159i	$0.977982\pi$
$620$	−3.63271	−	0.547544i	−0.145893	−	0.0219899i
$621$	−1.52582	−	1.41576i	−0.0612291	−	0.0568123i
$622$	24.6530	−	11.8723i	0.988495	−	0.476034i
$623$	25.9222	+	2.79952i	1.03855	+	0.112160i
$624$	−8.04174	−	3.87270i	−0.321927	−	0.155032i
$625$	−6.76347	−	17.2330i	−0.270539	−	0.689321i
$626$	1.52377	+	20.3334i	0.0609023	+	0.812685i
$627$	30.8419	−	9.51346i	1.23171	−	0.379931i
$628$	1.79493	−	23.9517i	0.0716256	−	0.955778i
$629$	−1.06937	−	4.68522i	−0.0426386	−	0.186812i
$630$	51.3730	−	9.96632i	2.04675	−	0.397068i
$631$	−8.45139	+	37.0280i	−0.336445	+	1.47406i	0.469956	+	0.882690i	$0.344270\pi$
$631$	−8.45139	+	37.0280i	−0.336445	+	1.47406i	−0.806400	+	0.591370i	$0.798587\pi$
$632$	6.15958	+	1.89998i	0.245015	+	0.0755770i
$633$	−22.0952	+	56.2977i	−0.878207	+	2.23763i
$634$	−11.5697	+	10.7351i	−0.459492	+	0.426346i
$635$	−16.5418	+	11.2780i	−0.656442	+	0.447555i
$636$	−12.5216			−0.496512
$637$	18.1874	+	10.2776i	0.720609	+	0.407214i
$638$	−2.99749			−0.118672
$639$	44.2316	−	30.1566i	1.74977	−	1.19298i
$640$	−2.43886	+	2.26293i	−0.0964045	+	0.0894503i
$641$	−14.1185	+	35.9735i	−0.557649	+	1.42087i	0.322682	+	0.946507i	$0.395415\pi$
$641$	−14.1185	+	35.9735i	−0.557649	+	1.42087i	−0.880331	+	0.474359i	$0.842680\pi$
$642$	−1.90147	−	0.586526i	−0.0750451	−	0.0231484i
$643$	9.13136	−	40.0071i	0.360106	−	1.57773i	−0.392817	−	0.919617i	$-0.628499\pi$
$643$	9.13136	−	40.0071i	0.360106	−	1.57773i	0.752923	−	0.658109i	$-0.228643\pi$
$644$	−0.604659	−	0.159028i	−0.0238269	−	0.00626657i
$645$	28.1333	+	123.260i	1.10775	+	4.85336i
$646$	−0.798553	+	10.6559i	−0.0314186	+	0.419253i
$647$	−17.0986	+	5.27423i	−0.672216	+	0.207351i	−0.612028	−	0.790836i	$-0.709646\pi$
$647$	−17.0986	+	5.27423i	−0.672216	+	0.207351i	−0.0601878	+	0.998187i	$0.519170\pi$
$648$	0.635838	+	8.48467i	0.0249781	+	0.333309i
$649$	6.99654	+	17.8269i	0.274638	+	0.699767i
$650$	−16.3181	−	7.85840i	−0.640050	−	0.308232i
$651$	−2.84775	+	8.26061i	−0.111612	+	0.323759i
$652$	−13.0336	+	6.27664i	−0.510434	+	0.245812i
$653$	8.15318	+	7.56504i	0.319058	+	0.296043i	0.823400	−	0.567461i	$-0.192074\pi$
$653$	8.15318	+	7.56504i	0.319058	+	0.296043i	−0.504342	+	0.863504i	$0.668265\pi$
$654$	−12.3334	−	1.85896i	−0.482274	−	0.0726911i
$655$	19.7359	+	34.1835i	0.771144	+	1.33566i
$656$	5.52086	−	9.56241i	0.215553	−	0.373349i
$657$	4.74917	−	5.95526i	0.185283	−	0.232337i
$658$	−17.4046	−	7.49804i	−0.678502	−	0.292304i
$659$	−2.37967	−	2.98401i	−0.0926988	−	0.116241i	0.733319	−	0.679885i	$-0.237970\pi$
$659$	−2.37967	−	2.98401i	−0.0926988	−	0.116241i	−0.826018	+	0.563644i	$0.809399\pi$
$660$	18.2183	−	2.74596i	0.709145	−	0.106886i
$661$	23.0201	+	15.6949i	0.895379	+	0.610459i	0.921150	−	0.389209i	$-0.127251\pi$
$661$	23.0201	+	15.6949i	0.895379	+	0.610459i	−0.0257703	+	0.999668i	$0.508204\pi$
$662$	3.69399	+	2.51852i	0.143571	+	0.0978851i
$663$	−16.1817	+	2.43901i	−0.628447	+	0.0947232i
$664$	2.32233	+	2.91211i	0.0901240	+	0.113012i
$665$	33.6439	+	38.7316i	1.30465	+	1.50195i
$666$	9.71581	−	12.1832i	0.376480	−	0.472091i
$667$	−0.191281	+	0.331308i	−0.00740643	+	0.0128283i
$668$	−11.1447	−	19.3031i	−0.431200	−	0.746860i
$669$	15.0574	+	2.26954i	0.582152	+	0.0877453i
$670$	15.1971	+	14.1009i	0.587116	+	0.544764i
$671$	−16.1236	+	7.76473i	−0.622446	+	0.299754i
$672$	4.24087	+	6.68060i	0.163595	+	0.257710i
$673$	1.88559	+	0.908055i	0.0726843	+	0.0350029i	0.469873	−	0.882734i	$-0.344300\pi$
$673$	1.88559	+	0.908055i	0.0726843	+	0.0350029i	−0.397188	+	0.917737i	$0.630014\pi$
$674$	1.16034	+	2.95651i	0.0446948	+	0.113881i
$675$	3.99477	+	53.3064i	0.153759	+	2.05177i
$676$	−3.91182	+	1.20664i	−0.150455	+	0.0464091i
$677$	0.309925	−	4.13567i	0.0119114	−	0.158947i	−0.988076	−	0.153966i	$-0.950795\pi$
$677$	0.309925	−	4.13567i	0.0119114	−	0.158947i	0.999988	−	0.00498092i	$-0.00158548\pi$
$678$	−3.60073	−	15.7758i	−0.138285	−	0.605867i
$679$	−0.0884770	+	2.69812i	−0.00339543	+	0.103544i
$680$	−1.35733	+	5.94687i	−0.0520514	+	0.228052i
$681$	8.68945	+	2.68034i	0.332981	+	0.102711i
$682$	−0.746957	+	1.90322i	−0.0286025	+	0.0728779i
$683$	−26.5127	+	24.6002i	−1.01448	+	0.941300i	−0.998283	−	0.0585689i	$-0.981346\pi$
$683$	−26.5127	+	24.6002i	−1.01448	+	0.941300i	−0.0161967	+	0.999869i	$0.505156\pi$
$684$	−28.6290	+	19.5189i	−1.09466	+	0.746324i
$685$	−10.3270			−0.394573
$686$	−8.88002	−	16.2525i	−0.339041	−	0.620525i
$687$	13.4888			0.514629
$688$	−10.4981	+	7.15749i	−0.400237	+	0.272877i
$689$	9.15905	−	8.49835i	0.348932	−	0.323761i
$690$	0.859068	−	2.18887i	0.0327042	−	0.0833289i
$691$	−0.624644	−	0.192677i	−0.0237626	−	0.00732979i	0.282851	−	0.959164i	$-0.408720\pi$
$691$	−0.624644	−	0.192677i	−0.0237626	−	0.00732979i	−0.306614	+	0.951834i	$0.599196\pi$
$692$	0.857724	−	3.75793i	0.0326058	−	0.142855i
$693$	0.954512	−	29.1080i	0.0362589	−	1.10572i
$694$	5.84487	+	25.6081i	0.221868	+	0.972068i
$695$	3.67650	−	49.0595i	0.139458	−	1.86093i
$696$	4.62671	−	1.42715i	0.175375	−	0.0540960i
$697$	−1.51285	−	20.1876i	−0.0573032	−	0.764658i
$698$	−2.00855	−	5.11771i	−0.0760248	−	0.193708i
$699$	15.4108	+	7.42143i	0.582889	+	0.280704i
$700$	8.60549	+	13.5561i	0.325257	+	0.512374i
$701$	−17.3914	+	8.37528i	−0.656866	+	0.316330i	−0.732461	−	0.680809i	$-0.761628\pi$
$701$	−17.3914	+	8.37528i	−0.656866	+	0.316330i	0.0755956	+	0.997139i	$0.475914\pi$
$702$	−19.2694	−	17.8794i	−0.727275	−	0.674813i
$703$	15.1064	+	2.27692i	0.569749	+	0.0858758i
$704$	0.925786	+	1.60351i	0.0348919	+	0.0604345i
$705$	35.6367	−	61.7246i	1.34216	−	2.32468i
$706$	−10.8630	+	13.6218i	−0.408835	+	0.512663i
$707$	−17.8180	−	20.5125i	−0.670115	−	0.771451i
$708$	−19.2870	−	24.1851i	−0.724850	−	0.908933i
$709$	−36.5709	+	5.51218i	−1.37345	+	0.207014i	−0.793963	−	0.607967i	$-0.791985\pi$
$709$	−36.5709	+	5.51218i	−1.37345	+	0.207014i	−0.579488	+	0.814981i	$0.696747\pi$
$710$	24.7531	+	16.8764i	0.928967	+	0.633359i
$711$	31.6627	+	21.5873i	1.18744	+	0.809586i
$712$	−9.74456	+	1.46876i	−0.365193	+	0.0550439i
$713$	0.162694	+	0.204012i	0.00609293	+	0.00764029i
$714$	13.3240	+	5.74009i	0.498639	+	0.214818i
$715$	−11.4623	+	14.3733i	−0.428666	+	0.537530i
$716$	4.18970	−	7.25678i	0.156577	−	0.271199i
$717$	−28.1944	−	48.8341i	−1.05294	−	1.82374i
$718$	27.9450	+	4.21203i	1.04290	+	0.157191i
$719$	18.9075	+	17.5436i	0.705131	+	0.654266i	0.948904	−	0.315566i	$-0.102194\pi$
$719$	18.9075	+	17.5436i	0.705131	+	0.654266i	−0.243772	+	0.969833i	$0.578385\pi$
$720$	−17.8204	+	8.58186i	−0.664128	+	0.319827i
$721$	−4.10430	+	11.9056i	−0.152852	+	0.443386i
$722$	−13.4871	−	6.49503i	−0.501937	−	0.241720i
$723$	17.0668	+	43.4854i	0.634720	+	1.61724i
$724$	1.53420	+	20.4724i	0.0570179	+	0.760851i
$725$	9.38842	−	2.89594i	0.348677	−	0.107553i
$726$	−1.69231	+	22.5823i	−0.0628074	+	0.838106i
$727$	−8.75369	−	38.3524i	−0.324656	−	1.42241i	−0.829164	−	0.559005i	$-0.811183\pi$
$727$	−8.75369	−	38.3524i	−0.324656	−	1.42241i	0.504508	−	0.863407i	$-0.331674\pi$
$728$	−7.63615	−	2.00834i	−0.283014	−	0.0744339i
$729$	6.33019	−	27.7344i	0.234451	−	1.02720i
$730$	4.07332	+	1.25645i	0.150761	+	0.0465035i
$731$	−8.51074	+	21.6850i	−0.314781	+	0.802049i
$732$	21.1904	−	19.6618i	0.783218	−	0.726721i
$733$	1.56371	−	1.06612i	0.0577571	−	0.0393781i	−0.534097	−	0.845423i	$-0.679348\pi$
$733$	1.56371	−	1.06612i	0.0577571	−	0.0393781i	0.591854	+	0.806045i	$0.298396\pi$
$734$	−12.2305			−0.451437
$735$	64.6006	−	26.0452i	2.38283	−	0.960691i
$736$	0.236312			0.00871056
$737$	9.53279	−	6.49935i	0.351145	−	0.239407i
$738$	48.1201	−	44.6490i	1.77133	−	1.64355i
$739$	−6.33905	+	16.1516i	−0.233186	+	0.594148i	−0.998791	−	0.0491633i	$-0.984345\pi$
$739$	−6.33905	+	16.1516i	−0.233186	+	0.594148i	0.765605	+	0.643311i	$0.222440\pi$
$740$	8.33318	+	2.57045i	0.306334	+	0.0944915i
$741$	11.5759	−	50.7175i	0.425252	−	1.86315i
$742$	−10.8741	+	2.10957i	−0.399201	+	0.0774447i
$743$	0.204751	+	0.897071i	0.00751157	+	0.0329104i	0.978545	−	0.206034i	$-0.0660558\pi$
$743$	0.204751	+	0.897071i	0.00751157	+	0.0329104i	−0.971033	+	0.238944i	$0.923199\pi$
$744$	0.246799	−	3.29330i	0.00904809	−	0.120738i
$745$	−6.85175	+	2.11348i	−0.251029	+	0.0774321i
$746$	−2.63913	−	35.2168i	−0.0966255	−	1.28938i
$747$	8.09001	+	20.6130i	0.295998	+	0.754190i
$748$	3.05854	+	1.47291i	0.111831	+	0.0538551i
$749$	−1.75011	−	0.189007i	−0.0639477	−	0.00690617i
$750$	−9.58302	+	4.61494i	−0.349922	+	0.168514i
$751$	−23.5269	−	21.8298i	−0.858508	−	0.796579i	0.122108	−	0.992517i	$-0.461034\pi$
$751$	−23.5269	−	21.8298i	−0.858508	−	0.796579i	−0.980616	+	0.195938i	$0.937225\pi$
$752$	7.08281	+	1.06756i	0.258283	+	0.0389300i
$753$	6.63137	+	11.4859i	0.241661	+	0.418568i
$754$	−2.41566	+	4.18404i	−0.0879731	+	0.152374i
$755$	−23.0425	+	28.8943i	−0.838601	+	1.05157i
$756$	6.13547	+	22.4820i	0.223145	+	0.817661i
$757$	7.47753	+	9.37653i	0.271775	+	0.340796i	0.898924	−	0.438104i	$-0.144350\pi$
$757$	7.47753	+	9.37653i	0.271775	+	0.340796i	−0.627149	+	0.778899i	$0.715778\pi$
$758$	−8.28657	+	1.24900i	−0.300982	+	0.0453657i
$759$	−1.08124	−	0.737178i	−0.0392466	−	0.0267579i
$760$	−16.0215	−	10.9233i	−0.581161	−	0.396229i
$761$	6.06620	−	0.914333i	0.219900	−	0.0331445i	−0.0381682	−	0.999271i	$-0.512152\pi$
$761$	6.06620	−	0.914333i	0.219900	−	0.0331445i	0.258068	+	0.966127i	$0.416914\pi$
$762$	−11.2214	−	14.0711i	−0.406507	−	0.509744i
$763$	−11.0239	+	0.463491i	−0.399092	+	0.0167795i
$764$	4.90470	−	6.15030i	0.177446	−	0.222510i
$765$	−18.1318	+	31.4052i	−0.655557	+	1.13546i
$766$	2.81610	+	4.87763i	0.101750	+	0.176236i
$767$	30.5221	+	4.60047i	1.10209	+	0.166113i
$768$	−2.19243	−	2.03428i	−0.0791126	−	0.0734057i
$769$	23.8203	−	11.4712i	0.858981	−	0.413664i	0.0480779	−	0.998844i	$-0.484690\pi$
$769$	23.8203	−	11.4712i	0.858981	−	0.413664i	0.810903	+	0.585180i	$0.198976\pi$
$770$	15.3587	−	5.45400i	0.553488	−	0.196548i
$771$	−28.8982	−	13.9167i	−1.04074	−	0.501196i
$772$	7.05217	+	17.9686i	0.253813	+	0.646706i
$773$	1.45921	+	19.4718i	0.0524841	+	0.700351i	0.959940	+	0.280204i	$0.0904023\pi$
$773$	1.45921	+	19.4718i	0.0524841	+	0.700351i	−0.907456	+	0.420147i	$0.861979\pi$
$774$	−72.1813	+	22.2650i	−2.59450	+	0.800298i
$775$	0.500800	−	6.68271i	0.0179893	−	0.240050i
$776$	−0.227047	−	0.994758i	−0.00815051	−	0.0357097i
$777$	9.60692	−	18.3822i	0.344646	−	0.659459i
$778$	7.32946	−	32.1125i	0.262774	−	1.15129i
$779$	61.4958	+	18.9689i	2.20331	+	0.679632i
$780$	10.8490	−	27.6429i	0.388458	−	0.989775i
$781$	12.2221	−	11.3405i	0.437342	−	0.405794i
$782$	0.357976	−	0.244064i	0.0128012	−	0.00872771i
$783$	14.2594			0.509589
$784$	4.80841	+	5.08716i	0.171729	+	0.181684i
$785$	79.9108			2.85214
$786$	−29.3177	+	19.9885i	−1.04573	+	0.712966i
$787$	−29.9109	+	27.7533i	−1.06621	+	0.989298i	−0.999964	−	0.00850570i	$-0.997293\pi$
$787$	−29.9109	+	27.7533i	−1.06621	+	0.989298i	−0.0662455	+	0.997803i	$0.521102\pi$
$788$	1.18232	−	3.01249i	0.0421183	−	0.107316i
$789$	39.7439	+	12.2594i	1.41492	+	0.436445i
$790$	−4.77211	+	20.9080i	−0.169784	+	0.743873i
$791$	−5.78481	−	13.0936i	−0.205684	−	0.465554i
$792$	2.44944	+	10.7317i	0.0870371	+	0.381335i
$793$	−2.15554	+	28.7637i	−0.0765456	+	1.02143i
$794$	−2.30914	+	0.712277i	−0.0819485	+	0.0252778i
$795$	−3.11320	−	41.5427i	−0.110414	−	1.47337i
$796$	2.77292	+	7.06528i	0.0982834	+	0.250422i
$797$	6.18508	+	2.97858i	0.219087	+	0.105507i	0.540208	−	0.841531i	$-0.318345\pi$
$797$	6.18508	+	2.97858i	0.219087	+	0.105507i	−0.321121	+	0.947038i	$0.604060\pi$
$798$	−32.4605	+	32.7618i	−1.14909	+	1.15975i
$799$	11.8320	−	5.69797i	0.418584	−	0.201580i
$800$	−4.44884	−	4.12792i	−0.157290	−	0.145944i
$801$	−57.9319	−	8.73182i	−2.04692	−	0.308524i
$802$	15.2599	+	26.4310i	0.538847	+	0.933310i
$803$	1.18616	−	2.05449i	0.0418587	−	0.0725014i
$804$	−11.6197	+	14.5706i	−0.409795	+	0.513866i
$805$	0.377271	−	2.04561i	0.0132971	−	0.0720984i
$806$	2.05463	+	2.57643i	0.0723714	+	0.0907509i
$807$	−46.9075	+	7.07017i	−1.65122	+	0.248882i
$808$	8.48509	+	5.78503i	0.298504	+	0.203517i
$809$	−23.9672	−	16.3406i	−0.842643	−	0.574504i	0.0632566	−	0.997997i	$-0.479851\pi$
$809$	−23.9672	−	16.3406i	−0.842643	−	0.574504i	−0.905899	+	0.423493i	$0.860804\pi$
$810$	−27.9915	+	4.21903i	−0.983520	+	0.148242i
$811$	22.1175	+	27.7345i	0.776652	+	0.973891i	1.00000		0.000848054i	$-0.000269944\pi$
$811$	22.1175	+	27.7345i	0.776652	+	0.973891i	−0.223348	+	0.974739i	$0.571699\pi$
$812$	3.77753	−	2.01886i	0.132565	−	0.0708483i
$813$	−40.7915	+	51.1509i	−1.43062	+	1.79394i
$814$	2.42664	−	4.20306i	0.0850537	−	0.147317i
$815$	−24.0645	−	41.6809i	−0.842942	−	1.46002i
$816$	−5.42221	−	0.817267i	−0.189815	−	0.0286101i
$817$	−54.2856	−	50.3697i	−1.89921	−	1.76221i
$818$	18.5653	−	8.94059i	0.649121	−	0.312600i
$819$	−39.8611	−	24.7903i	−1.39286	−	0.866243i
$820$	33.0978	+	15.9391i	1.15583	+	0.556616i
$821$	0.0286915	+	0.0731049i	0.00100134	+	0.00255138i	0.931374	−	0.364065i	$-0.118611\pi$
$821$	0.0286915	+	0.0731049i	0.00100134	+	0.00255138i	−0.930372	+	0.366616i	$0.880516\pi$
$822$	−0.693756	−	9.25753i	−0.0241975	−	0.322893i
$823$	−4.99098	+	1.53951i	−0.173974	+	0.0536640i	−0.380519	−	0.924773i	$-0.624254\pi$
$823$	−4.99098	+	1.53951i	−0.173974	+	0.0536640i	0.206544	+	0.978437i	$0.433778\pi$
$824$	0.355698	−	4.74645i	0.0123913	−	0.165351i
$825$	7.47851	+	32.7655i	0.260368	+	1.14075i
$826$	−20.8240	−	17.7537i	−0.724560	−	0.617732i
$827$	0.807896	−	3.53962i	0.0280933	−	0.123085i	−0.958937	−	0.283620i	$-0.908465\pi$
$827$	0.807896	−	3.53962i	0.0280933	−	0.123085i	0.987030	+	0.160535i	$0.0513219\pi$
$828$	1.34247	+	0.414097i	0.0466540	+	0.0143909i
$829$	−12.0660	+	30.7435i	−0.419068	+	1.06777i	0.553024	+	0.833165i	$0.313474\pi$
$829$	−12.0660	+	30.7435i	−0.419068	+	1.06777i	−0.972092	+	0.234602i	$0.924621\pi$
$830$	−9.08411	+	8.42882i	−0.315314	+	0.292569i
$831$	−61.4528	+	41.8978i	−2.13177	+	1.45342i
$832$	2.98434			0.103463
$833$	12.5381	+	2.74011i	0.434418	+	0.0949391i
$834$	44.2260			1.53142
$835$	61.2710	−	41.7739i	2.12037	−	1.44564i
$836$	−7.91080	+	7.34015i	−0.273601	+	0.253864i
$837$	3.55336	−	9.05380i	0.122822	−	0.312945i
$838$	31.4584	+	9.70362i	1.08671	+	0.335206i
$839$	−4.09299	+	17.9326i	−0.141306	+	0.619101i	0.853827	+	0.520557i	$0.174276\pi$
$839$	−4.09299	+	17.9326i	−0.141306	+	0.619101i	−0.995133	+	0.0985441i	$0.968581\pi$
$840$	−21.1098	+	15.7309i	−0.728357	+	0.542767i
$841$	5.86992	+	25.7178i	0.202411	+	0.886821i
$842$	1.33475	−	17.8110i	0.0459986	−	0.613808i
$843$	64.2426	−	19.8162i	2.21263	−	0.682507i
$844$	−1.51114	−	20.1647i	−0.0520155	−	0.694099i
$845$	−4.97584	−	12.6782i	−0.171174	−	0.436145i
$846$	38.3662	+	18.4762i	1.31906	+	0.635224i
$847$	2.33490	+	19.8962i	0.0802279	+	0.683643i
$848$	3.77204	−	1.81652i	0.129532	−	0.0623795i
$849$	6.27228	+	5.81982i	0.215264	+	0.199736i
$850$	−11.0026	−	1.65838i	−0.377388	−	0.0568821i
$851$	−0.309706	−	0.536426i	−0.0106166	−	0.0183885i
$852$	−13.4658	+	23.3235i	−0.461331	+	0.799049i
$853$	−26.6033	+	33.3594i	−0.910879	+	1.14221i	0.0785102	+	0.996913i	$0.474984\pi$
$853$	−26.6033	+	33.3594i	−0.910879	+	1.14221i	−0.989389	+	0.145292i	$0.953588\pi$
$854$	15.0898	−	20.6449i	0.516364	−	0.706456i
$855$	−71.8757	−	90.1293i	−2.45810	−	3.08236i
$856$	0.657895	−	0.0991618i	0.0224864	−	0.00338928i
$857$	8.17235	+	5.57181i	0.279162	+	0.190329i	0.694805	−	0.719199i	$-0.255491\pi$
$857$	8.17235	+	5.57181i	0.279162	+	0.190329i	−0.415642	+	0.909528i	$0.636443\pi$
$858$	−13.6548	−	9.30971i	−0.466169	−	0.317828i
$859$	−50.1132	+	7.55336i	−1.70984	+	0.257717i	−0.929814	−	0.368029i	$-0.880033\pi$
$859$	−50.1132	+	7.55336i	−1.70984	+	0.257717i	−0.780027	+	0.625746i	$0.784795\pi$
$860$	−26.3565	−	33.0500i	−0.898749	−	1.12700i
$861$	51.5585	−	70.5390i	1.75711	−	2.40396i
$862$	−8.36678	+	10.4916i	−0.284974	+	0.357346i
$863$	6.11098	−	10.5845i	0.208020	−	0.360302i	−0.743071	−	0.669213i	$-0.766631\pi$
$863$	6.11098	−	10.5845i	0.208020	−	0.360302i	0.951091	+	0.308911i	$0.0999647\pi$
$864$	−4.40407	−	7.62807i	−0.149829	−	0.259512i
$865$	12.6809	+	1.91134i	0.431165	+	0.0649877i
$866$	−9.15873	−	8.49806i	−0.311226	−	0.288776i
$867$	36.7510	−	17.6984i	1.24813	−	0.601068i
$868$	−0.340511	−	2.90159i	−0.0115577	−	0.0984862i
$869$	10.7532	+	5.17847i	0.364777	+	0.175667i
$870$	5.88517	+	14.9952i	0.199526	+	0.508384i
$871$	−1.38969	−	18.5441i	−0.0470879	−	0.628344i
$872$	3.98505	−	1.22922i	0.134951	−	0.0416268i
$873$	0.453311	−	6.04901i	0.0153422	−	0.204728i
$874$	0.306479	+	1.34277i	0.0103668	+	0.0454199i
$875$	−7.54469	+	5.62225i	−0.255057	+	0.190067i
$876$	−0.852697	+	3.73591i	−0.0288100	+	0.126225i
$877$	−53.3623	−	16.4601i	−1.80192	−	0.555817i	−0.802737	−	0.596333i	$-0.796624\pi$
$877$	−53.3623	−	16.4601i	−1.80192	−	0.555817i	−0.999179	+	0.0405157i	$0.987100\pi$
$878$	8.17900	−	20.8397i	0.276028	−	0.703307i
$879$	−18.2684	+	16.9506i	−0.616177	+	0.571729i
$880$	−5.08978	+	3.47015i	−0.171577	+	0.116979i
$881$	31.8418			1.07278			0.536389	−	0.843971i	$-0.319788\pi$
$881$	31.8418			1.07278			0.536389	+	0.843971i	$0.319788\pi$
$882$	18.4019	+	37.3257i	0.619623	+	1.25682i
$883$	−3.53415			−0.118934			−0.0594668	−	0.998230i	$-0.518940\pi$
$883$	−3.53415			−0.118934			−0.0594668	+	0.998230i	$0.518940\pi$
$884$	4.52083	−	3.08225i	0.152052	−	0.103667i
$885$	75.4437	−	70.0015i	2.53601	−	2.35307i
$886$	5.71553	−	14.5629i	0.192017	−	0.489251i
$887$	−23.2236	−	7.16352i	−0.779771	−	0.240527i	−0.120781	−	0.992679i	$-0.538540\pi$
$887$	−23.2236	−	7.16352i	−0.779771	−	0.240527i	−0.658990	+	0.752152i	$0.729016\pi$
$888$	−1.74444	+	7.64290i	−0.0585397	+	0.256479i
$889$	−12.1156	−	10.3293i	−0.406345	−	0.346434i
$890$	−7.29564	−	31.9643i	−0.244551	−	1.07145i
$891$	−1.17730	+	15.7100i	−0.0394410	+	0.526304i
$892$	−4.86519	+	1.50071i	−0.162899	+	0.0502476i
$893$	3.11978	+	41.6305i	0.104399	+	1.39311i
$894$	−2.35491	−	6.00022i	−0.0787600	−	0.200677i
$895$	25.1175	+	12.0959i	0.839584	+	0.404323i
$896$	−2.24670	−	1.39726i	−0.0750570	−	0.0466792i
$897$	−1.90036	+	0.915163i	−0.0634511	+	0.0305564i
$898$	−28.3375	−	26.2934i	−0.945636	−	0.877422i
$899$	−1.76765	−	0.266430i	−0.0589543	−	0.00888593i
$900$	−18.0400	−	31.2463i	−0.601335	−	1.04154i
$901$	3.83796	−	6.64754i	0.127861	−	0.221462i
$902$	12.7470	−	15.9842i	0.424428	−	0.532215i
$903$	−88.6724	+	47.3901i	−2.95083	+	1.57704i
$904$	3.37332	+	4.23001i	0.112195	+	0.140688i
$905$	−67.5398	+	10.1800i	−2.24510	+	0.338394i
$906$	−27.4501	−	18.7152i	−0.911968	−	0.621769i
$907$	29.3893	+	20.0373i	0.975854	+	0.665326i	0.942531	−	0.334119i	$-0.108439\pi$
$907$	29.3893	+	20.0373i	0.975854	+	0.665326i	0.0333231	+	0.999445i	$0.489391\pi$
$908$	−3.00649	+	0.453155i	−0.0997738	+	0.0150385i
$909$	38.0658	+	47.7331i	1.26256	+	1.58321i
$910$	4.76450	−	25.8337i	0.157942	−	0.856380i
$911$	−12.2597	+	15.3732i	−0.406183	+	0.509337i	−0.942283	−	0.334817i	$-0.891325\pi$
$911$	−12.2597	+	15.3732i	−0.406183	+	0.509337i	0.536100	+	0.844154i	$0.319897\pi$
$912$	8.71578	−	15.0962i	0.288608	−	0.499884i
$913$	3.44831	+	5.97264i	0.114122	+	0.197666i
$914$	40.1666	+	6.05414i	1.32859	+	0.200253i
$915$	70.5003	+	65.4148i	2.33067	+	2.16255i
$916$	−4.06341	+	1.95684i	−0.134259	+	0.0646557i
$917$	−22.0928	+	22.2979i	−0.729570	+	0.736342i
$918$	−14.5498	−	7.00681i	−0.480215	−	0.231259i
$919$	−14.6835	−	37.4129i	−0.484363	−	1.23414i	−0.939141	−	0.343532i	$-0.888377\pi$
$919$	−14.6835	−	37.4129i	−0.484363	−	1.23414i	0.454778	−	0.890605i	$-0.349719\pi$
$920$	0.0587535	+	0.784010i	0.00193704	+	0.0258481i
$921$	40.4487	−	12.4768i	1.33283	−	0.411124i
$922$	2.19703	−	29.3173i	0.0723554	−	0.965515i
$923$	−5.97986	−	26.1995i	−0.196829	−	0.862366i
$924$	5.92098	+	13.4018i	0.194786	+	0.440886i
$925$	−3.53979	+	15.5088i	−0.116388	+	0.509927i
$926$	19.9786	+	6.16260i	0.656539	+	0.202515i
$927$	10.3381	−	26.3410i	0.339547	−	0.865151i
$928$	−1.18673	+	1.10112i	−0.0389563	+	0.0361461i
$929$	−6.70254	+	4.56971i	−0.219903	+	0.149927i	−0.668261	−	0.743926i	$-0.732961\pi$
$929$	−6.70254	+	4.56971i	−0.219903	+	0.149927i	0.448358	+	0.893854i	$0.352009\pi$
$930$	10.9875			0.360296
$931$	−22.6701	+	33.9201i	−0.742983	+	1.11169i
$932$	−5.71904			−0.187333
$933$	−67.6171	+	46.1006i	−2.21368	+	1.50926i
$934$	−13.6562	+	12.6711i	−0.446844	+	0.414611i
$935$	−4.12625	+	10.5135i	−0.134943	+	0.343829i
$936$	16.9538	+	5.22957i	0.554154	+	0.170934i
$937$	−5.01856	+	21.9877i	−0.163949	+	0.718308i	0.824388	+	0.566025i	$0.191520\pi$
$937$	−5.01856	+	21.9877i	−0.163949	+	0.718308i	−0.988337	+	0.152283i	$0.951338\pi$
$938$	−7.63611	+	14.6112i	−0.249328	+	0.477073i
$939$	−13.5702	−	59.4551i	−0.442848	−	1.94024i
$940$	−1.78087	+	23.7640i	−0.0580855	+	0.775097i
$941$	37.6051	−	11.5996i	1.22589	−	0.378137i	0.386818	−	0.922156i	$-0.373574\pi$
$941$	37.6051	−	11.5996i	1.22589	−	0.378137i	0.839073	+	0.544019i	$0.183098\pi$
$942$	5.36834	+	71.6355i	0.174910	+	2.33401i
$943$	−0.953279	−	2.42892i	−0.0310430	−	0.0790964i
$944$	9.31867	+	4.48763i	0.303297	+	0.146060i
$945$	−73.0629	+	25.9453i	−2.37674	+	0.843999i
$946$	−21.1961	+	10.2075i	−0.689145	+	0.331875i
$947$	5.76718	+	5.35116i	0.187408	+	0.173889i	0.768297	−	0.640094i	$-0.221104\pi$
$947$	5.76718	+	5.35116i	0.187408	+	0.173889i	−0.580889	+	0.813983i	$0.697295\pi$
$948$	−19.0634	−	2.87335i	−0.619150	−	0.0933219i
$949$	−1.91184	−	3.31140i	−0.0620609	−	0.107493i
$950$	17.6859	−	30.6328i	0.573806	−	0.993861i
$951$	29.4312	−	36.9056i	0.954374	−	1.19675i
$952$	−4.84651	+	0.203767i	−0.157076	+	0.00660414i
$953$	−34.9481	−	43.8235i	−1.13208	−	1.41958i	−0.893846	−	0.448374i	$-0.852003\pi$
$953$	−34.9481	−	43.8235i	−1.13208	−	1.41958i	−0.238233	−	0.971208i	$-0.576568\pi$
$954$	24.6118	−	3.70964i	0.796838	−	0.120104i
$955$	21.6243	+	14.7432i	0.699745	+	0.477078i
$956$	15.5778	+	10.6208i	0.503823	+	0.343501i
$957$	8.86484	−	1.33616i	0.286560	−	0.0431919i
$958$	−12.3836	−	15.5285i	−0.400096	−	0.501704i
$959$	−2.16214	−	7.92264i	−0.0698192	−	0.255836i
$960$	6.20402	−	7.77960i	0.200234	−	0.251086i
$961$	14.8903	−	25.7908i	0.480334	−	0.831962i
$962$	−3.91123	−	6.77445i	−0.126103	−	0.218417i
$963$	3.91122	+	0.589522i	0.126037	+	0.0189971i
$964$	−11.4498	−	10.6238i	−0.368772	−	0.342170i
$965$	−57.8612	+	27.8645i	−1.86262	+	0.896989i
$966$	1.85912	+	0.200780i	0.0598162	+	0.00645998i
$967$	20.3084	+	9.78002i	0.653075	+	0.314504i	0.730922	−	0.682461i	$-0.239090\pi$
$967$	20.3084	+	9.78002i	0.653075	+	0.314504i	−0.0778473	+	0.996965i	$0.524805\pi$
$968$	−2.76624	−	7.04828i	−0.0889105	−	0.226540i
$969$	−2.38833	−	31.8701i	−0.0767243	−	1.02381i
$970$	3.24385	−	1.00060i	0.104154	−	0.0321272i
$971$	2.88857	−	38.5452i	0.0926985	−	1.23698i	−0.735884	−	0.677108i	$-0.763233\pi$
$971$	2.88857	−	38.5452i	0.0926985	−	1.23698i	0.828582	−	0.559867i	$-0.189148\pi$
$972$	0.217418	+	0.952570i	0.00697368	+	0.0305537i
$973$	38.4073	−	7.45098i	1.23128	−	0.238867i
$974$	−0.341640	+	1.49682i	−0.0109469	+	0.0479613i
$975$	51.7626	+	15.9666i	1.65773	+	0.511342i
$976$	−3.53111	+	8.99711i	−0.113028	+	0.287991i
$977$	30.3053	−	28.1192i	0.969552	−	0.899613i	−0.0254290	−	0.999677i	$-0.508095\pi$
$977$	30.3053	−	28.1192i	0.969552	−	0.899613i	0.994981	+	0.100064i	$0.0319047\pi$
$978$	35.7479	−	24.3725i	1.14309	−	0.779347i
$979$	−18.2466			−0.583162
$980$	−15.6821	+	17.2177i	−0.500948	+	0.549998i
$981$	24.7928			0.791572
$982$	35.6698	−	24.3193i	1.13827	−	0.776059i
$983$	−5.72568	+	5.31265i	−0.182621	+	0.169447i	−0.766186	−	0.642619i	$-0.777848\pi$
$983$	−5.72568	+	5.31265i	−0.182621	+	0.169447i	0.583565	+	0.812066i	$0.301657\pi$
$984$	−12.0650	+	30.7411i	−0.384617	+	0.979989i
$985$	10.2885	+	3.17358i	0.327819	+	0.101119i
$986$	−0.660467	+	2.89369i	−0.0210335	+	0.0921540i
$987$	54.8151	+	14.4166i	1.74478	+	0.458885i
$988$	3.87048	+	16.9577i	0.123136	+	0.539495i
$989$	−0.224381	+	2.99416i	−0.00713490	+	0.0952086i
$990$	−34.9955	+	10.7947i	−1.11223	+	0.343078i
$991$	−2.10636	−	28.1074i	−0.0669107	−	0.892861i	−0.925148	−	0.379608i	$-0.876059\pi$
$991$	−2.10636	−	28.1074i	−0.0669107	−	0.892861i	0.858237	−	0.513254i	$-0.171560\pi$
$992$	0.403418	+	1.02789i	0.0128085	+	0.0326356i
$993$	−12.0473	−	5.80170i	−0.382311	−	0.184111i
$994$	−7.76471	+	22.5235i	−0.246281	+	0.714401i
$995$	−22.7510	+	10.9563i	−0.721256	+	0.347339i
$996$	−8.16622	−	7.57714i	−0.258757	−	0.240091i
$997$	−32.9804	−	4.97100i	−1.04450	−	0.157433i	−0.395690	−	0.918384i	$-0.629495\pi$
$997$	−32.9804	−	4.97100i	−1.04450	−	0.157433i	−0.648809	+	0.760951i	$0.724733\pi$
$998$	13.9631	+	24.1849i	0.441996	+	0.765559i
$999$	−11.5438	+	19.9944i	−0.365229	+	0.632596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.37.1	✓	24
3.2	odd	2		882.2.z.b.37.1		24
4.3	odd	2		784.2.bg.b.625.2		24
7.2	even	3		686.2.e.c.197.1		24
7.3	odd	6		686.2.g.d.459.1		24
7.4	even	3		686.2.g.f.459.2		24
7.5	odd	6		686.2.e.d.197.4		24
7.6	odd	2		686.2.g.e.373.2		24
49.2	even	21		4802.2.a.o.1.12		12
49.4	even	21	inner	98.2.g.b.53.1	yes	24
49.22	even	7		686.2.g.f.275.2		24
49.23	even	21		686.2.e.c.491.1		24
49.26	odd	42		686.2.e.d.491.4		24
49.27	odd	14		686.2.g.d.275.1		24
49.45	odd	42		686.2.g.e.263.2		24
49.47	odd	42		4802.2.a.l.1.1		12
147.53	odd	42		882.2.z.b.739.1		24
196.151	odd	42		784.2.bg.b.641.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.37.1	✓	24	1.1	even	1	trivial
98.2.g.b.53.1	yes	24	49.4	even	21	inner
686.2.e.c.197.1		24	7.2	even	3
686.2.e.c.491.1		24	49.23	even	21
686.2.e.d.197.4		24	7.5	odd	6
686.2.e.d.491.4		24	49.26	odd	42
686.2.g.d.275.1		24	49.27	odd	14
686.2.g.d.459.1		24	7.3	odd	6
686.2.g.e.263.2		24	49.45	odd	42
686.2.g.e.373.2		24	7.6	odd	2
686.2.g.f.275.2		24	49.22	even	7
686.2.g.f.459.2		24	7.4	even	3
784.2.bg.b.625.2		24	4.3	odd	2
784.2.bg.b.641.2		24	196.151	odd	42
882.2.z.b.37.1		24	3.2	odd	2
882.2.z.b.739.1		24	147.53	odd	42
4802.2.a.l.1.1		12	49.47	odd	42
4802.2.a.o.1.12		12	49.2	even	21

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826239 - 0.563320i) q^{2} +(-2.19243 + 2.03428i) q^{3} +(0.365341 - 0.930874i) q^{4} +(3.17919 + 0.980650i) q^{5} +(-0.665522 + 2.91584i) q^{6} +(-0.0867132 + 2.64433i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.444274 - 5.92843i) q^{9} +O(q^{10})\)	\(q+(0.826239 - 0.563320i) q^{2} +(-2.19243 + 2.03428i) q^{3} +(0.365341 - 0.930874i) q^{4} +(3.17919 + 0.980650i) q^{5} +(-0.665522 + 2.91584i) q^{6} +(-0.0867132 + 2.64433i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.444274 - 5.92843i) q^{9} +(3.17919 - 0.980650i) q^{10} +(-0.138368 - 1.84640i) q^{11} +(1.09267 + 2.78408i) q^{12} +(-2.68880 - 1.29486i) q^{13} +(1.41796 + 2.23370i) q^{14} +(-8.96507 + 4.31735i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(-1.81295 - 0.273258i) q^{17} +(-2.97252 - 5.14856i) q^{18} +(2.91417 - 5.04749i) q^{19} +(2.07435 - 2.60115i) q^{20} +(-5.18919 - 5.97391i) q^{21} +(-1.15444 - 1.44762i) q^{22} +(-0.233672 + 0.0352204i) q^{23} +(2.47114 + 1.68479i) q^{24} +(5.01438 + 3.41875i) q^{25} +(-2.95101 + 0.444793i) q^{26} +(5.49178 + 6.88648i) q^{27} +(2.42986 + 1.04680i) q^{28} +(1.00936 - 1.26570i) q^{29} +(-4.97524 + 8.61737i) q^{30} +(-0.552111 - 0.956284i) q^{31} +(-0.988831 - 0.149042i) q^{32} +(4.05945 + 3.76662i) q^{33} +(-1.65186 + 0.795494i) q^{34} +(-2.86884 + 8.32179i) q^{35} +(-5.35630 - 2.57946i) q^{36} +(0.957619 + 2.43997i) q^{37} +(-0.435552 - 5.81204i) q^{38} +(8.52911 - 2.63088i) q^{39} +(0.248627 - 3.31770i) q^{40} +(2.45701 + 10.7649i) q^{41} +(-7.65274 - 2.01270i) q^{42} +(2.82733 - 12.3873i) q^{43} +(-1.76931 - 0.545761i) q^{44} +(7.22614 - 18.4119i) q^{45} +(-0.173229 + 0.160733i) q^{46} +(-5.91819 + 4.03495i) q^{47} +2.99083 q^{48} +(-6.98496 - 0.458597i) q^{49} +6.06893 q^{50} +(4.53065 - 3.08894i) q^{51} +(-2.18768 + 2.02987i) q^{52} +(-1.52956 + 3.89724i) q^{53} +(8.41681 + 2.59624i) q^{54} +(1.37077 - 6.00573i) q^{55} +(2.59733 - 0.503880i) q^{56} +(3.87889 + 16.9945i) q^{57} +(0.120980 - 1.61436i) q^{58} +(-9.88343 + 3.04864i) q^{59} +(0.743600 + 9.92266i) q^{60} +(-3.53111 - 8.99711i) q^{61} +(-0.994870 - 0.479104i) q^{62} +(15.6382 + 1.68888i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-7.27841 - 6.75337i) q^{65} +(5.47588 + 0.825357i) q^{66} +(3.11561 + 5.39640i) q^{67} +(-0.916713 + 1.58779i) q^{68} +(0.440662 - 0.552573i) q^{69} +(2.31749 + 8.49186i) q^{70} +(5.61436 + 7.04019i) q^{71} +(-5.87865 + 0.886064i) q^{72} +(1.05862 + 0.721752i) q^{73} +(2.16571 + 1.47655i) q^{74} +(-17.9484 + 2.70528i) q^{75} +(-3.63391 - 4.55678i) q^{76} +(4.89448 - 0.205784i) q^{77} +(5.56506 - 6.97836i) q^{78} +(-3.22298 + 5.58236i) q^{79} +(-1.66350 - 2.88127i) q^{80} +(-8.41343 - 1.26812i) q^{81} +(8.09415 + 7.51027i) q^{82} +(-3.35587 + 1.61610i) q^{83} +(-7.45678 + 2.64797i) q^{84} +(-5.49574 - 2.64661i) q^{85} +(-4.64199 - 11.8276i) q^{86} +(0.361829 + 4.82828i) q^{87} +(-1.76931 + 0.545761i) q^{88} +(0.736437 - 9.82707i) q^{89} +(-4.40128 - 19.2833i) q^{90} +(3.65719 - 6.99779i) q^{91} +(-0.0525843 + 0.230387i) q^{92} +(3.15582 + 0.973440i) q^{93} +(-2.61687 + 6.66767i) q^{94} +(14.2145 - 13.1891i) q^{95} +(2.47114 - 1.68479i) q^{96} +1.02034 q^{97} +(-6.02958 + 3.55586i) q^{98} -11.0077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

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