LMFDB - Embedded newform 49.2.g.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(2,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	49.23
Dual form			49.2.g.a.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.192191 - 2.56461i) q^{2} +(-0.776689 + 0.239577i) q^{3} +(-4.56263 - 0.687706i) q^{4} +(1.80872 + 1.67825i) q^{5} +(0.465149 + 2.03795i) q^{6} +(1.97351 - 1.76217i) q^{7} +(-1.49604 + 6.55456i) q^{8} +(-1.93287 + 1.31781i) q^{9} +O(q^{10})$	\(q+(0.192191 - 2.56461i) q^{2} +(-0.776689 + 0.239577i) q^{3} +(-4.56263 - 0.687706i) q^{4} +(1.80872 + 1.67825i) q^{5} +(0.465149 + 2.03795i) q^{6} +(1.97351 - 1.76217i) q^{7} +(-1.49604 + 6.55456i) q^{8} +(-1.93287 + 1.31781i) q^{9} +(4.65167 - 4.31612i) q^{10} +(-0.456097 - 0.310962i) q^{11} +(3.70850 - 0.558967i) q^{12} +(1.06432 - 0.512550i) q^{13} +(-4.13999 - 5.39997i) q^{14} +(-1.80688 - 0.870148i) q^{15} +(7.70403 + 2.37638i) q^{16} +(-2.74302 + 6.98911i) q^{17} +(3.00818 + 5.21032i) q^{18} +(-0.499767 + 0.865623i) q^{19} +(-7.09838 - 8.90108i) q^{20} +(-1.11063 + 1.84147i) q^{21} +(-0.885154 + 1.10995i) q^{22} +(-0.831710 - 2.11916i) q^{23} +(-0.408366 - 5.44927i) q^{24} +(0.0813043 + 1.08493i) q^{25} +(-1.10994 - 2.82807i) q^{26} +(2.70584 - 3.39301i) q^{27} +(-10.2163 + 6.68293i) q^{28} +(-3.55438 - 4.45705i) q^{29} +(-2.57886 + 4.46671i) q^{30} +(-2.90369 - 5.02934i) q^{31} +(2.66266 - 6.78436i) q^{32} +(0.428745 + 0.132250i) q^{33} +(17.3972 + 8.37803i) q^{34} +(6.52689 + 0.124775i) q^{35} +(9.72523 - 4.68342i) q^{36} +(3.63743 - 0.548254i) q^{37} +(2.12393 + 1.44807i) q^{38} +(-0.703851 + 0.653078i) q^{39} +(-13.7061 + 9.34464i) q^{40} +(-0.206089 + 0.902934i) q^{41} +(4.50919 + 3.20225i) q^{42} +(-0.949065 - 4.15812i) q^{43} +(1.86715 + 1.73247i) q^{44} +(-5.70762 - 0.860285i) q^{45} +(-5.59467 + 1.72573i) q^{46} +(-0.720789 + 9.61826i) q^{47} -6.55296 q^{48} +(0.789523 - 6.95533i) q^{49} +2.79805 q^{50} +(0.456047 - 6.08553i) q^{51} +(-5.20858 + 1.60664i) q^{52} +(7.73830 + 1.16636i) q^{53} +(-8.18172 - 7.59153i) q^{54} +(-0.303081 - 1.32789i) q^{55} +(8.59779 + 15.5718i) q^{56} +(0.180781 - 0.792052i) q^{57} +(-12.1137 + 8.25900i) q^{58} +(2.03470 - 1.88792i) q^{59} +(7.64573 + 5.21277i) q^{60} +(7.05098 - 1.06276i) q^{61} +(-13.4564 + 6.48024i) q^{62} +(-1.49235 + 6.00675i) q^{63} +(-2.35990 - 1.13647i) q^{64} +(2.78524 + 0.859133i) q^{65} +(0.421572 - 1.07415i) q^{66} +(-1.62615 - 2.81657i) q^{67} +(17.3219 - 30.0023i) q^{68} +(1.15368 + 1.44667i) q^{69} +(1.57441 - 16.7149i) q^{70} +(0.0286915 - 0.0359779i) q^{71} +(-5.74601 - 14.6406i) q^{72} +(0.624885 + 8.33852i) q^{73} +(-0.706977 - 9.43396i) q^{74} +(-0.323073 - 0.823175i) q^{75} +(2.87555 - 3.60582i) q^{76} +(-1.44808 + 0.190033i) q^{77} +(1.53962 + 1.93062i) q^{78} +(-2.93822 + 5.08914i) q^{79} +(9.94627 + 17.2275i) q^{80} +(1.27528 - 3.24937i) q^{81} +(2.27607 + 0.702073i) q^{82} +(-10.6979 - 5.15183i) q^{83} +(6.33379 - 7.63814i) q^{84} +(-16.6908 + 8.03787i) q^{85} +(-10.8464 + 1.63483i) q^{86} +(3.82845 + 2.61020i) q^{87} +(2.72056 - 2.52431i) q^{88} +(-3.72947 + 2.54271i) q^{89} +(-3.30325 + 14.4725i) q^{90} +(1.19725 - 2.88704i) q^{91} +(2.33743 + 10.2409i) q^{92} +(3.46017 + 3.21057i) q^{93} +(24.5286 + 3.69709i) q^{94} +(-2.35667 + 0.726935i) q^{95} +(-0.442687 + 5.90725i) q^{96} +1.37110 q^{97} +(-17.6860 - 3.36157i) q^{98} +1.29136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) $ 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

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 $

$2$	0.192191	−	2.56461i	0.135900	−	1.81345i	−0.347094	−	0.937830i	$-0.612832\pi$
$2$	0.192191	−	2.56461i	0.135900	−	1.81345i	0.482994	−	0.875624i	$-0.339549\pi$
$3$	−0.776689	+	0.239577i	−0.448422	+	0.138320i	−0.510737	−	0.859737i	$-0.670628\pi$
$3$	−0.776689	+	0.239577i	−0.448422	+	0.138320i	0.0623158	+	0.998056i	$0.480151\pi$
$4$	−4.56263	−	0.687706i	−2.28132	−	0.343853i
$5$	1.80872	+	1.67825i	0.808884	+	0.750534i	0.971724	−	0.236118i	$-0.0758752\pi$
$5$	1.80872	+	1.67825i	0.808884	+	0.750534i	−0.162841	+	0.986652i	$0.552066\pi$
$6$	0.465149	+	2.03795i	0.189896	+	0.831990i
$7$	1.97351	−	1.76217i	0.745919	−	0.666037i
$7$	1.97351	−	1.76217i	0.745919	−	0.666037i
$8$	−1.49604	+	6.55456i	−0.528928	+	2.31739i
$9$	−1.93287	+	1.31781i	−0.644289	+	0.439269i
$10$	4.65167	−	4.31612i	1.47099	−	1.36488i
$11$	−0.456097	−	0.310962i	−0.137519	−	0.0937586i	0.492607	−	0.870252i	$-0.336044\pi$
$11$	−0.456097	−	0.310962i	−0.137519	−	0.0937586i	−0.630125	+	0.776493i	$0.716996\pi$
$12$	3.70850	−	0.558967i	1.07055	−	0.161360i
$13$	1.06432	−	0.512550i	0.295189	−	0.142156i	−0.280428	−	0.959875i	$-0.590476\pi$
$13$	1.06432	−	0.512550i	0.295189	−	0.142156i	0.575617	+	0.817720i	$0.304762\pi$
$14$	−4.13999	−	5.39997i	−1.10646	−	1.44320i
$15$	−1.80688	−	0.870148i	−0.466535	−	0.224671i
$16$	7.70403	+	2.37638i	1.92601	+	0.594094i
$17$	−2.74302	+	6.98911i	−0.665281	+	1.69511i	0.0522984	+	0.998631i	$0.483345\pi$
$17$	−2.74302	+	6.98911i	−0.665281	+	1.69511i	−0.717579	+	0.696477i	$0.754750\pi$
$18$	3.00818	+	5.21032i	0.709035	+	1.22809i
$19$	−0.499767	+	0.865623i	−0.114655	+	0.198587i	−0.917642	−	0.397409i	$-0.869909\pi$
$19$	−0.499767	+	0.865623i	−0.114655	+	0.198587i	0.802987	+	0.595996i	$0.203243\pi$
$20$	−7.09838	−	8.90108i	−1.58725	−	1.99034i
$21$	−1.11063	+	1.84147i	−0.242360	+	0.401841i
$22$	−0.885154	+	1.10995i	−0.188716	+	0.236642i
$23$	−0.831710	−	2.11916i	−0.173424	−	0.441876i	0.817563	−	0.575840i	$-0.195325\pi$
$23$	−0.831710	−	2.11916i	−0.173424	−	0.441876i	−0.990986	+	0.133964i	$0.957229\pi$
$24$	−0.408366	−	5.44927i	−0.0833574	−	1.11233i
$25$	0.0813043	+	1.08493i	0.0162609	+	0.216986i
$26$	−1.10994	−	2.82807i	−0.217677	−	0.554631i
$27$	2.70584	−	3.39301i	0.520739	−	0.652986i
$28$	−10.2163	+	6.68293i	−1.93069	+	1.26295i
$29$	−3.55438	−	4.45705i	−0.660032	−	0.827654i	0.333315	−	0.942816i	$-0.391833\pi$
$29$	−3.55438	−	4.45705i	−0.660032	−	0.827654i	−0.993347	+	0.115162i	$0.963261\pi$
$30$	−2.57886	+	4.46671i	−0.470833	+	0.815506i
$31$	−2.90369	−	5.02934i	−0.521518	−	0.903295i	−0.999687	−	0.0250274i	$-0.992033\pi$
$31$	−2.90369	−	5.02934i	−0.521518	−	0.903295i	0.478169	−	0.878268i	$-0.341301\pi$
$32$	2.66266	−	6.78436i	0.470697	−	1.19932i
$33$	0.428745	+	0.132250i	0.0746350	+	0.0230218i
$34$	17.3972	+	8.37803i	2.98359	+	1.43682i
$35$	6.52689	+	0.124775i	1.10325	+	0.0210909i
$36$	9.72523	−	4.68342i	1.62087	−	0.780570i
$37$	3.63743	−	0.548254i	0.597989	−	0.0901324i	0.156929	−	0.987610i	$-0.449841\pi$
$37$	3.63743	−	0.548254i	0.597989	−	0.0901324i	0.441060	+	0.897477i	$0.354602\pi$
$38$	2.12393	+	1.44807i	0.344548	+	0.234909i
$39$	−0.703851	+	0.653078i	−0.112706	+	0.104576i
$40$	−13.7061	+	9.34464i	−2.16712	+	1.47752i
$41$	−0.206089	+	0.902934i	−0.0321857	+	0.141015i	−0.988468	−	0.151431i	$-0.951612\pi$
$41$	−0.206089	+	0.902934i	−0.0321857	+	0.141015i	0.956282	+	0.292446i	$0.0944690\pi$
$42$	4.50919	+	3.20225i	0.695783	+	0.494119i
$43$	−0.949065	−	4.15812i	−0.144731	−	0.634108i	−0.994299	−	0.106629i	$-0.965994\pi$
$43$	−0.949065	−	4.15812i	−0.144731	−	0.634108i	0.849568	−	0.527479i	$-0.176863\pi$
$44$	1.86715	+	1.73247i	0.281484	+	0.261179i
$45$	−5.70762	−	0.860285i	−0.850841	−	0.128244i
$46$	−5.59467	+	1.72573i	−0.824890	+	0.254445i
$47$	−0.720789	+	9.61826i	−0.105138	+	1.40297i	0.656188	+	0.754598i	$0.272168\pi$
$47$	−0.720789	+	9.61826i	−0.105138	+	1.40297i	−0.761326	+	0.648370i	$0.775451\pi$
$48$	−6.55296			−0.945838
$49$	0.789523	−	6.95533i	0.112789	−	0.993619i
$50$	2.79805			0.395704
$51$	0.456047	−	6.08553i	0.0638594	−	0.852145i
$52$	−5.20858	+	1.60664i	−0.722301	+	0.222800i
$53$	7.73830	+	1.16636i	1.06294	+	0.160212i	0.657153	−	0.753757i	$-0.271760\pi$
$53$	7.73830	+	1.16636i	1.06294	+	0.160212i	0.405784	+	0.913969i	$0.366998\pi$
$54$	−8.18172	−	7.59153i	−1.11339	−	1.03308i
$55$	−0.303081	−	1.32789i	−0.0408675	−	0.179052i
$56$	8.59779	+	15.5718i	1.14893	+	2.08087i
$57$	0.180781	−	0.792052i	0.0239450	−	0.104910i
$58$	−12.1137	+	8.25900i	−1.59061	+	1.08446i
$59$	2.03470	−	1.88792i	0.264895	−	0.245786i	−0.536531	−	0.843881i	$-0.680266\pi$
$59$	2.03470	−	1.88792i	0.264895	−	0.245786i	0.801426	+	0.598094i	$0.204075\pi$
$60$	7.64573	+	5.21277i	0.987059	+	0.672965i
$61$	7.05098	−	1.06276i	0.902786	−	0.136073i	0.318786	−	0.947827i	$-0.396725\pi$
$61$	7.05098	−	1.06276i	0.902786	−	0.136073i	0.584000	+	0.811754i	$0.301487\pi$
$62$	−13.4564	+	6.48024i	−1.70896	+	0.822991i
$63$	−1.49235	+	6.00675i	−0.188018	+	0.756779i
$64$	−2.35990	−	1.13647i	−0.294988	−	0.142059i
$65$	2.78524	+	0.859133i	0.345466	+	0.106562i
$66$	0.421572	−	1.07415i	0.0518919	−	0.132218i
$67$	−1.62615	−	2.81657i	−0.198665	−	0.344098i	0.749431	−	0.662083i	$-0.230327\pi$
$67$	−1.62615	−	2.81657i	−0.198665	−	0.344098i	−0.948096	+	0.317985i	$0.896994\pi$
$68$	17.3219	−	30.0023i	2.10058	−	3.63832i
$69$	1.15368	+	1.44667i	0.138887	+	0.174159i
$70$	1.57441	−	16.7149i	0.188178	−	1.99782i
$71$	0.0286915	−	0.0359779i	0.00340505	−	0.00426980i	−0.780126	−	0.625622i	$-0.784845\pi$
$71$	0.0286915	−	0.0359779i	0.00340505	−	0.00426980i	0.783531	+	0.621353i	$0.213417\pi$
$72$	−5.74601	−	14.6406i	−0.677173	−	1.72541i
$73$	0.624885	+	8.33852i	0.0731373	+	0.975950i	0.906221	+	0.422803i	$0.138954\pi$
$73$	0.624885	+	8.33852i	0.0731373	+	0.975950i	−0.833084	+	0.553146i	$0.813427\pi$
$74$	−0.706977	−	9.43396i	−0.0821844	−	1.09668i
$75$	−0.323073	−	0.823175i	−0.0373052	−	0.0950521i
$76$	2.87555	−	3.60582i	0.329848	−	0.413616i
$77$	−1.44808	+	0.190033i	−0.165024	+	0.0216562i
$78$	1.53962	+	1.93062i	0.174327	+	0.218600i
$79$	−2.93822	+	5.08914i	−0.330575	+	0.572573i	−0.982625	−	0.185603i	$-0.940576\pi$
$79$	−2.93822	+	5.08914i	−0.330575	+	0.572573i	0.652049	+	0.758176i	$0.273909\pi$
$80$	9.94627	+	17.2275i	1.11203	+	1.92609i
$81$	1.27528	−	3.24937i	0.141698	−	0.361041i
$82$	2.27607	+	0.702073i	0.251349	+	0.0775310i
$83$	−10.6979	−	5.15183i	−1.17425	−	0.565487i	−0.258016	−	0.966141i	$-0.583069\pi$
$83$	−10.6979	−	5.15183i	−1.17425	−	0.565487i	−0.916230	+	0.400654i	$0.868783\pi$
$84$	6.33379	−	7.63814i	0.691074	−	0.833389i
$85$	−16.6908	+	8.03787i	−1.81037	+	0.871829i
$86$	−10.8464	+	1.63483i	−1.16959	+	0.176288i
$87$	3.82845	+	2.61020i	0.410453	+	0.279842i
$88$	2.72056	−	2.52431i	0.290012	−	0.269092i
$89$	−3.72947	+	2.54271i	−0.395323	+	0.269527i	−0.744624	−	0.667484i	$-0.767371\pi$
$89$	−3.72947	+	2.54271i	−0.395323	+	0.269527i	0.349301	+	0.937011i	$0.386419\pi$
$90$	−3.30325	+	14.4725i	−0.348193	+	1.52553i
$91$	1.19725	−	2.88704i	0.125506	−	0.302644i
$92$	2.33743	+	10.2409i	0.243693	+	1.06769i
$93$	3.46017	+	3.21057i	0.358803	+	0.332921i
$94$	24.5286	+	3.69709i	2.52993	+	0.381325i
$95$	−2.35667	+	0.726935i	−0.241789	+	0.0745820i
$96$	−0.442687	+	5.90725i	−0.0451816	+	0.602906i
$97$	1.37110			0.139214			0.0696070	−	0.997574i	$-0.477825\pi$
$97$	1.37110			0.139214			0.0696070	+	0.997574i	$0.477825\pi$
$98$	−17.6860	−	3.36157i	−1.78655	−	0.339570i
$99$	1.29136			0.129787
$100$	0.375152	−	5.00605i	0.0375152	−	0.500605i
$101$	−0.292681	+	0.0902801i	−0.0291228	+	0.00898321i	−0.309282	−	0.950970i	$-0.600089\pi$
$101$	−0.292681	+	0.0902801i	−0.0291228	+	0.00898321i	0.280160	+	0.959953i	$0.409613\pi$
$102$	−15.5194	−	2.33917i	−1.53665	−	0.231612i
$103$	−0.602550	−	0.559085i	−0.0593710	−	0.0550882i	0.649929	−	0.759995i	$-0.274798\pi$
$103$	−0.602550	−	0.559085i	−0.0593710	−	0.0550882i	−0.709300	+	0.704906i	$0.750989\pi$
$104$	1.76728	+	7.74294i	0.173296	+	0.759258i
$105$	−5.09925	+	1.46678i	−0.497636	+	0.143143i
$106$	4.47850	−	19.6216i	0.434990	−	1.90582i
$107$	4.93082	−	3.36177i	0.476680	−	0.324995i	−0.301034	−	0.953613i	$-0.597332\pi$
$107$	4.93082	−	3.36177i	0.476680	−	0.324995i	0.777714	+	0.628619i	$0.216379\pi$
$108$	−14.6791	+	13.6202i	−1.41250	+	1.31061i
$109$	−4.92510	−	3.35788i	−0.471739	−	0.321626i	0.304009	−	0.952669i	$-0.401675\pi$
$109$	−4.92510	−	3.35788i	−0.471739	−	0.321626i	−0.775748	+	0.631043i	$0.782627\pi$
$110$	−3.46376	+	0.522078i	−0.330257	+	0.0497782i
$111$	−2.69380	+	1.29727i	−0.255684	+	0.123131i
$112$	19.3916	−	8.88598i	1.83233	−	0.839646i
$113$	9.88796	+	4.76179i	0.930181	+	0.447951i	0.836695	−	0.547669i	$-0.184485\pi$
$113$	9.88796	+	4.76179i	0.930181	+	0.447951i	0.0934859	+	0.995621i	$0.470199\pi$
$114$	−1.99656	−	0.615858i	−0.186995	−	0.0576804i
$115$	2.05215	−	5.22878i	0.191364	−	0.487586i
$116$	13.1522	+	22.7802i	1.22115	+	2.11509i
$117$	−1.38175	+	2.39326i	−0.127743	+	0.221257i
$118$	−4.45074	−	5.58105i	−0.409723	−	0.513777i
$119$	6.90259	+	18.6268i	0.632760	+	1.70751i
$120$	8.40660	−	10.5415i	0.767414	−	0.962306i
$121$	−3.90742	−	9.95595i	−0.355220	−	0.905087i
$122$	−1.37044	−	18.2873i	−0.124074	−	1.65565i
$123$	−0.0562552	−	0.750673i	−0.00507236	−	0.0676859i
$124$	9.78975	+	24.9439i	0.879146	+	2.24003i
$125$	6.01821	−	7.54660i	0.538285	−	0.674988i
$126$	15.1182	+	4.98173i	1.34683	+	0.443808i
$127$	12.7459	+	15.9829i	1.13102	+	1.41825i	0.894752	+	0.446563i	$0.147352\pi$
$127$	12.7459	+	15.9829i	1.13102	+	1.41825i	0.236265	+	0.971689i	$0.424077\pi$
$128$	3.92001	−	6.78965i	0.346483	−	0.600126i
$129$	1.73332	+	3.00220i	0.152610	+	0.264329i
$130$	2.73864	−	6.97794i	0.240195	−	0.612006i
$131$	−12.1691	−	3.75368i	−1.06322	−	0.327961i	−0.286680	−	0.958026i	$-0.592552\pi$
$131$	−12.1691	−	3.75368i	−1.06322	−	0.327961i	−0.776542	+	0.630066i	$0.783028\pi$
$132$	−1.86526	−	0.898260i	−0.162350	−	0.0781835i
$133$	0.539075	+	2.58899i	0.0467437	+	0.224494i
$134$	−7.53593	+	3.62911i	−0.651005	+	0.313507i
$135$	10.5884	−	1.59595i	0.911305	−	0.137357i
$136$	−41.7069	−	28.4353i	−3.57634	−	2.43830i
$137$	6.88438	−	6.38777i	0.588172	−	0.545744i	−0.328952	−	0.944347i	$-0.606695\pi$
$137$	6.88438	−	6.38777i	0.588172	−	0.545744i	0.917124	+	0.398603i	$0.130505\pi$
$138$	3.93188	−	2.68071i	0.334704	−	0.228197i
$139$	−2.74110	+	12.0095i	−0.232497	+	1.01864i	0.715063	+	0.699060i	$0.246398\pi$
$139$	−2.74110	+	12.0095i	−0.232497	+	1.01864i	−0.947560	+	0.319577i	$0.896459\pi$
$140$	−29.6940	−	5.05788i	−2.50960	−	0.427469i
$141$	−1.74448	−	7.64308i	−0.146912	−	0.643663i
$142$	−0.0867552	−	0.0804971i	−0.00728034	−	0.00675516i
$143$	−0.644817	−	0.0971905i	−0.0539223	−	0.00812748i
$144$	−18.0225	+	5.55920i	−1.50187	+	0.463266i
$145$	1.05115	−	14.0267i	0.0872936	−	1.16485i
$146$	21.5052			1.77978
$147$	1.05312	+	5.59128i	0.0868601	+	0.461161i
$148$	−16.9733			−1.39519
$149$	−1.37609	+	18.3627i	−0.112734	+	1.50433i	0.598356	+	0.801230i	$0.295821\pi$
$149$	−1.37609	+	18.3627i	−0.112734	+	1.50433i	−0.711090	+	0.703101i	$0.751798\pi$
$150$	−2.17322	+	0.670348i	−0.177442	+	0.0547337i
$151$	−11.6661	−	1.75838i	−0.949375	−	0.143095i	−0.343941	−	0.938991i	$-0.611762\pi$
$151$	−11.6661	−	1.75838i	−0.949375	−	0.143095i	−0.605433	+	0.795896i	$0.707000\pi$
$152$	−4.92611	−	4.57076i	−0.399560	−	0.370737i
$153$	−3.90840	−	17.1238i	−0.315975	−	1.38438i
$154$	0.209051	+	3.75029i	0.0168458	+	0.302207i
$155$	3.18851	−	13.9698i	0.256107	−	1.12208i
$156$	3.66054	−	2.49571i	0.293078	−	0.199817i
$157$	14.3558	−	13.3202i	1.14572	−	1.06307i	0.148470	−	0.988917i	$-0.452565\pi$
$157$	14.3558	−	13.3202i	1.14572	−	1.06307i	0.997247	−	0.0741526i	$-0.0236252\pi$
$158$	12.4870	+	8.51347i	0.993410	+	0.677296i
$159$	−6.28969	+	0.948018i	−0.498805	+	0.0751827i
$160$	16.2018	−	7.80239i	1.28087	−	0.616833i
$161$	−5.37571	−	2.71659i	−0.423666	−	0.214097i
$162$	−8.08826	−	3.89510i	−0.635474	−	0.306028i
$163$	6.90684	+	2.13048i	0.540986	+	0.166872i	0.553192	−	0.833054i	$-0.313409\pi$
$163$	6.90684	+	2.13048i	0.540986	+	0.166872i	−0.0122067	+	0.999925i	$0.503886\pi$
$164$	1.56126	−	3.97803i	0.121914	−	0.310632i
$165$	0.553531	+	0.958744i	0.0430923	+	0.0746381i
$166$	−15.2685	+	26.4458i	−1.18506	+	2.05259i
$167$	11.4043	+	14.3005i	0.882489	+	1.10661i	0.993618	+	0.112801i	$0.0359821\pi$
$167$	11.4043	+	14.3005i	0.882489	+	1.10661i	−0.111128	+	0.993806i	$0.535446\pi$
$168$	−10.4085	−	10.0346i	−0.803029	−	0.774187i
$169$	−7.23530	+	9.07278i	−0.556561	+	0.697906i
$170$	17.4062	+	44.3502i	1.33499	+	3.40151i
$171$	−0.174739	−	2.33173i	−0.0133626	−	0.178312i
$172$	1.47067	+	19.6247i	0.112137	+	1.49637i
$173$	−3.98146	−	10.1446i	−0.302705	−	0.771279i	−0.998588	−	0.0531238i	$-0.983082\pi$
$173$	−3.98146	−	10.1446i	−0.302705	−	0.771279i	0.695883	−	0.718155i	$-0.255013\pi$
$174$	7.42993	−	9.31684i	0.563262	−	0.706308i
$175$	2.07229	+	1.99786i	0.156650	+	0.151024i
$176$	−2.77482	−	3.47952i	−0.209160	−	0.262279i
$177$	−1.12802	+	1.95379i	−0.0847874	+	0.146856i
$178$	5.80430	+	10.0533i	0.435050	+	0.753529i
$179$	5.26170	−	13.4066i	0.393278	−	1.00206i	−0.587897	−	0.808936i	$-0.700044\pi$
$179$	5.26170	−	13.4066i	0.393278	−	1.00206i	0.981175	−	0.193120i	$-0.0618607\pi$
$180$	25.4501	+	7.85033i	1.89694	+	0.585129i
$181$	−16.2838	−	7.84185i	−1.21036	−	0.582880i	−0.283751	−	0.958898i	$-0.591579\pi$
$181$	−16.2838	−	7.84185i	−1.21036	−	0.582880i	−0.926613	+	0.376017i	$0.877293\pi$
$182$	−7.17402	−	3.62535i	−0.531774	−	0.268729i
$183$	−5.22181	+	2.51469i	−0.386007	+	0.185891i
$184$	15.1344	−	2.28115i	1.11573	−	0.168169i
$185$	7.49919	+	5.11286i	0.551351	+	0.375905i
$186$	8.89889	−	8.25696i	0.652498	−	0.605430i
$187$	3.42443	−	2.33474i	0.250419	−	0.170733i
$188$	9.90323	−	43.3889i	0.722267	−	3.16446i
$189$	−0.639051	−	11.4643i	−0.0464841	−	0.833905i
$190$	1.41138	+	6.18364i	0.102392	+	0.448609i
$191$	0.531050	+	0.492742i	0.0384254	+	0.0356536i	0.699152	−	0.714973i	$-0.253561\pi$
$191$	0.531050	+	0.492742i	0.0384254	+	0.0356536i	−0.660726	+	0.750627i	$0.729752\pi$
$192$	2.10518	+	0.317305i	0.151928	+	0.0228995i
$193$	10.9094	−	3.36510i	0.785275	−	0.242225i	0.123914	−	0.992293i	$-0.460455\pi$
$193$	10.9094	−	3.36510i	0.785275	−	0.242225i	0.661361	+	0.750068i	$0.269979\pi$
$194$	0.263513	−	3.51634i	0.0189191	−	0.252458i
$195$	−2.36909			−0.169654
$196$	−8.38552	+	31.1917i	−0.598966	+	2.22798i
$197$	−0.639392			−0.0455548			−0.0227774	−	0.999741i	$-0.507251\pi$
$197$	−0.639392			−0.0455548			−0.0227774	+	0.999741i	$0.507251\pi$
$198$	0.248189	−	3.31185i	0.0176380	−	0.235363i
$199$	−17.3966	+	5.36613i	−1.23321	+	0.380395i	−0.841783	−	0.539815i	$-0.818494\pi$
$199$	−17.3966	+	5.36613i	−1.23321	+	0.380395i	−0.391425	+	0.920210i	$0.628018\pi$
$200$	−7.23288	−	1.09018i	−0.511442	−	0.0770875i
$201$	1.93779	+	1.79801i	0.136681	+	0.126822i
$202$	0.175283	+	0.767964i	0.0123328	+	0.0540337i
$203$	−14.8687	−	2.53264i	−1.04358	−	0.177756i
$204$	−6.26583	+	27.4524i	−0.438696	+	1.92205i
$205$	−1.88810	+	1.28729i	−0.131871	+	0.0899079i
$206$	−1.54964	+	1.43785i	−0.107968	+	0.100180i
$207$	4.40023	+	3.00003i	0.305837	+	0.208516i
$208$	9.41756	−	1.41947i	0.652990	−	0.0984225i
$209$	0.497118	−	0.239400i	0.0343864	−	0.0165596i
$210$	2.78169	+	13.3595i	0.191955	+	0.921894i
$211$	20.9321	+	10.0804i	1.44102	+	0.693960i	0.981011	−	0.193952i	$-0.0621306\pi$
$211$	20.9321	+	10.0804i	1.44102	+	0.693960i	0.460013	+	0.887912i	$0.347845\pi$
$212$	−34.5049	−	10.6434i	−2.36981	−	0.730989i
$213$	−0.0136649	+	0.0348175i	−0.000936301	+	0.00238565i
$214$	−7.67398	−	13.2917i	−0.524583	−	0.908604i
$215$	5.26176	−	9.11364i	0.358849	−	0.621545i
$216$	18.1917	+	22.8116i	1.23779	+	1.55214i
$217$	−14.5930	−	4.80868i	−0.990638	−	0.326434i
$218$	−9.55821	+	11.9856i	−0.647364	+	0.811768i
$219$	−2.48306	−	6.32673i	−0.167789	−	0.427521i
$220$	0.469653	+	6.26709i	0.0316640	+	0.422527i
$221$	0.662810	+	8.84459i	0.0445854	+	0.594951i
$222$	2.80926	+	7.15787i	0.188545	+	0.480405i
$223$	−17.3419	+	21.7461i	−1.16130	+	1.45622i	−0.295847	+	0.955235i	$0.595602\pi$
$223$	−17.3419	+	21.7461i	−1.16130	+	1.45622i	−0.865453	+	0.500990i	$0.832969\pi$
$224$	−6.70038	−	18.0811i	−0.447688	−	1.20809i
$225$	−1.58688	−	1.98988i	−0.105792	−	0.132659i
$226$	14.1125	−	24.4436i	0.938751	−	1.62596i
$227$	−11.7659	−	20.3791i	−0.780930	−	1.35261i	−0.931401	−	0.363996i	$-0.881412\pi$
$227$	−11.7659	−	20.3791i	−0.780930	−	1.35261i	0.150471	−	0.988614i	$-0.451921\pi$
$228$	−1.36954	+	3.48952i	−0.0906997	+	0.231099i
$229$	5.92387	+	1.82727i	0.391460	+	0.120750i	0.484236	−	0.874938i	$-0.339098\pi$
$229$	5.92387	+	1.82727i	0.391460	+	0.120750i	−0.0927755	+	0.995687i	$0.529574\pi$
$230$	−13.0154	−	6.26788i	−0.858209	−	0.413292i
$231$	1.07918	−	0.494523i	0.0710050	−	0.0325372i
$232$	34.5315	−	16.6295i	2.26710	−	1.09178i
$233$	−20.1050	+	3.03035i	−1.31712	+	0.198525i	−0.769740	−	0.638357i	$-0.779614\pi$
$233$	−20.1050	+	3.03035i	−1.31712	+	0.198525i	−0.547384	+	0.836882i	$0.684376\pi$
$234$	5.87222	+	4.00361i	0.383879	+	0.261724i
$235$	−17.4455	+	16.1871i	−1.13802	+	1.05593i
$236$	−10.5819	+	7.21462i	−0.688823	+	0.469632i
$237$	1.06284	−	4.65661i	0.0690389	−	0.302479i
$238$	49.0971	−	14.1226i	3.18249	−	0.915430i
$239$	−2.07422	−	9.08775i	−0.134170	−	0.587838i	−0.996653	−	0.0817510i	$-0.973949\pi$
$239$	−2.07422	−	9.08775i	−0.134170	−	0.587838i	0.862483	−	0.506087i	$-0.168908\pi$
$240$	−11.8525	−	10.9975i	−0.765073	−	0.709884i
$241$	4.03795	+	0.608623i	0.260107	+	0.0392049i	0.277801	−	0.960639i	$-0.410394\pi$
$241$	4.03795	+	0.608623i	0.260107	+	0.0392049i	−0.0176939	+	0.999843i	$0.505632\pi$
$242$	−26.2841	+	8.10758i	−1.68961	+	0.521175i
$243$	−1.18497	+	15.8123i	−0.0760160	+	1.01436i
$244$	−32.9019			−2.10633
$245$	13.1008	−	11.2552i	0.836978	−	0.719070i
$246$	−1.93600			−0.123435
$247$	−0.0882381	+	1.17746i	−0.00561445	+	0.0749197i
$248$	37.3091	−	11.5083i	2.36913	−	0.730780i
$249$	9.54319	+	1.43840i	0.604775	+	0.0911552i
$250$	−18.1974	−	16.8848i	−1.15091	−	1.06789i
$251$	1.62926	+	7.13827i	0.102838	+	0.450563i	0.999961	+	0.00878312i	$0.00279579\pi$
$251$	1.62926	+	7.13827i	0.102838	+	0.450563i	−0.897123	+	0.441780i	$0.854347\pi$
$252$	10.9399	−	26.3803i	0.689149	−	1.66180i
$253$	−0.279638	+	1.22517i	−0.0175807	+	0.0770261i
$254$	43.4395	−	29.6166i	2.72564	−	1.85831i
$255$	11.0379	−	10.2417i	0.691219	−	0.641357i
$256$	−20.9878	−	14.3092i	−1.31173	−	0.894325i
$257$	4.97304	−	0.749565i	0.310210	−	0.0467566i	0.00790750	−	0.999969i	$-0.497483\pi$
$257$	4.97304	−	0.749565i	0.310210	−	0.0467566i	0.302302	+	0.953212i	$0.402245\pi$
$258$	8.03259	−	3.86829i	0.500087	−	0.240829i
$259$	6.21240	−	7.49175i	0.386020	−	0.465515i
$260$	−12.1172	−	5.83533i	−0.751476	−	0.361892i
$261$	12.7437	+	3.93090i	0.788814	+	0.243317i
$262$	−11.9655	+	30.4877i	−0.739233	+	1.88353i
$263$	−8.22314	−	14.2429i	−0.507061	−	0.878255i	−0.999967	−	0.00817206i	$-0.997399\pi$
$263$	−8.22314	−	14.2429i	−0.507061	−	0.878255i	0.492906	−	0.870083i	$-0.335935\pi$
$264$	−1.50826	+	2.61239i	−0.0928271	+	0.160781i
$265$	12.0390	+	15.0964i	0.739548	+	0.927364i
$266$	6.74337	−	0.884935i	0.413462	−	0.0542589i
$267$	2.28747	−	2.86839i	0.139991	−	0.175543i
$268$	5.48253	+	13.9693i	0.334899	+	0.853308i
$269$	0.490517	+	6.54550i	0.0299074	+	0.399086i	0.991989	+	0.126324i	$0.0403180\pi$
$269$	0.490517	+	6.54550i	0.0299074	+	0.399086i	−0.962082	+	0.272762i	$0.912063\pi$
$270$	−2.05798	−	27.4619i	−0.125245	−	1.67128i
$271$	1.62902	+	4.15068i	0.0989561	+	0.252136i	0.971776	−	0.235907i	$-0.0758061\pi$
$271$	1.62902	+	4.15068i	0.0989561	+	0.252136i	−0.872820	+	0.488043i	$0.837711\pi$
$272$	−37.7411	+	47.3258i	−2.28839	+	2.86955i
$273$	−0.238226	+	2.52916i	−0.0144181	+	0.153072i
$274$	−15.0590	−	18.8834i	−0.909749	−	1.14079i
$275$	0.300290	−	0.520117i	0.0181081	−	0.0313642i
$276$	−4.26894	−	7.39402i	−0.256960	−	0.445068i
$277$	−9.56689	+	24.3760i	−0.574819	+	1.46461i	0.287267	+	0.957851i	$0.407253\pi$
$277$	−9.56689	+	24.3760i	−0.574819	+	1.46461i	−0.862085	+	0.506763i	$0.830842\pi$
$278$	30.2730	+	9.33798i	1.81565	+	0.560055i
$279$	12.2401	+	5.89454i	0.732798	+	0.352897i
$280$	−10.5823	+	42.5942i	−0.632414	+	2.54549i
$281$	−0.748290	+	0.360358i	−0.0446393	+	0.0214971i	−0.456070	−	0.889944i	$-0.650743\pi$
$281$	−0.748290	+	0.360358i	−0.0446393	+	0.0214971i	0.411431	+	0.911441i	$0.365029\pi$
$282$	−19.9368	+	3.00499i	−1.18722	+	0.178945i
$283$	24.5639	+	16.7474i	1.46017	+	0.995528i	0.993829	+	0.110923i	$0.0353808\pi$
$283$	24.5639	+	16.7474i	1.46017	+	0.995528i	0.466342	+	0.884604i	$0.345572\pi$
$284$	−0.155651	+	0.144423i	−0.00923618	+	0.00856992i
$285$	1.65624	−	1.12921i	0.0981072	−	0.0668883i
$286$	−0.373184	+	1.63503i	−0.0220668	+	0.0966811i
$287$	1.18440	+	2.14512i	0.0699131	+	0.126622i
$288$	3.79390	+	16.6221i	0.223557	+	0.979469i
$289$	−28.8616	−	26.7797i	−1.69774	−	1.57527i
$290$	−35.7709	−	5.39160i	−2.10054	−	0.316606i
$291$	−1.06492	+	0.328484i	−0.0624266	+	0.0192561i
$292$	2.88333	−	38.4753i	0.168734	−	2.25160i
$293$	13.1758			0.769740			0.384870	−	0.922971i	$-0.374246\pi$
$293$	13.1758			0.769740			0.384870	+	0.922971i	$0.374246\pi$
$294$	14.5419	−	1.62626i	0.848099	−	0.0948452i
$295$	6.84859			0.398740
$296$	−1.84816	+	24.6619i	−0.107422	+	1.43345i
$297$	−2.28922	+	0.706132i	−0.132834	+	0.0409739i
$298$	46.8287	+	7.05829i	2.71271	+	0.408876i
$299$	−1.97138	−	1.82917i	−0.114008	−	0.105784i
$300$	0.907958	+	3.97802i	0.0524210	+	0.229671i
$301$	−9.20031	−	6.53371i	−0.530297	−	0.376597i
$302$	−6.75169	+	29.5811i	−0.388516	+	1.70220i
$303$	0.205693	−	0.140239i	0.0118168	−	0.00805653i
$304$	−5.90727	+	5.48114i	−0.338805	+	0.314365i
$305$	14.5368	+	9.91104i	0.832376	+	0.567505i
$306$	−44.6670	+	6.73247i	−2.55344	+	0.384870i
$307$	16.6155	−	8.00162i	0.948299	−	0.456677i	0.105210	−	0.994450i	$-0.466449\pi$
$307$	16.6155	−	8.00162i	0.948299	−	0.456677i	0.843089	+	0.537773i	$0.180734\pi$
$308$	6.73775	+	0.128807i	0.383919	+	0.00733944i
$309$	0.601938	+	0.289878i	0.0342430	+	0.0164906i
$310$	−35.2142	−	10.8621i	−2.00003	−	0.616928i
$311$	−2.87398	+	7.32277i	−0.162968	+	0.415236i	−0.988909	−	0.148520i	$-0.952549\pi$
$311$	−2.87398	+	7.32277i	−0.162968	+	0.415236i	0.825941	+	0.563756i	$0.190644\pi$
$312$	−3.22765	−	5.59046i	−0.182730	−	0.316497i
$313$	7.71392	−	13.3609i	0.436017	−	0.755203i	−0.561361	−	0.827571i	$-0.689722\pi$
$313$	7.71392	−	13.3609i	0.436017	−	0.755203i	0.997378	+	0.0723677i	$0.0230555\pi$
$314$	−31.4021	−	39.3770i	−1.77213	−	2.22217i
$315$	−12.7800	+	8.36000i	−0.720073	+	0.471033i
$316$	16.9058	−	21.1992i	0.951028	−	1.19255i
$317$	3.22329	+	8.21280i	0.181038	+	0.461277i	0.992368	−	0.123311i	$-0.0393514\pi$
$317$	3.22329	+	8.21280i	0.181038	+	0.461277i	−0.811330	+	0.584588i	$0.801256\pi$
$318$	1.22248	+	16.3128i	0.0685530	+	0.914777i
$319$	0.235170	+	3.13813i	0.0131670	+	0.175701i
$320$	−2.36113	−	6.01605i	−0.131991	−	0.336307i
$321$	−3.02431	+	3.79236i	−0.168800	+	0.211669i
$322$	−8.00015	+	13.2645i	−0.445831	+	0.739202i
$323$	−4.67906	−	5.86735i	−0.260350	−	0.326468i
$324$	−8.05325	+	13.9486i	−0.447403	+	0.774924i
$325$	0.642615	+	1.11304i	0.0356459	+	0.0617404i
$326$	6.79128	−	17.3039i	0.376134	−	0.958375i
$327$	4.62974	+	1.42809i	0.256025	+	0.0789733i
$328$	−5.61002	−	2.70164i	−0.309761	−	0.149173i
$329$	15.5265	+	20.2519i	0.856004	+	1.11652i
$330$	2.56519	−	1.23533i	0.141209	−	0.0680027i
$331$	8.06498	−	1.21560i	0.443291	−	0.0668154i	0.0763958	−	0.997078i	$-0.475659\pi$
$331$	8.06498	−	1.21560i	0.443291	−	0.0668154i	0.366895	+	0.930262i	$0.380421\pi$
$332$	45.2676	+	30.8629i	2.48438	+	1.69382i
$333$	−6.30817	+	5.85313i	−0.345686	+	0.320749i
$334$	38.8670	−	26.4991i	2.12671	−	1.44997i
$335$	1.78565	−	7.82345i	0.0975605	−	0.427441i
$336$	−12.9324	+	11.5474i	−0.705518	+	0.629963i
$337$	−3.49358	−	15.3064i	−0.190307	−	0.833791i	−0.976450	−	0.215745i	$-0.930782\pi$
$337$	−3.49358	−	15.3064i	−0.190307	−	0.833791i	0.786142	−	0.618046i	$-0.212075\pi$
$338$	21.8776	+	20.2994i	1.18998	+	1.10414i
$339$	−8.82068	−	1.32950i	−0.479074	−	0.0722088i
$340$	81.6817	−	25.1955i	4.42981	−	1.36642i
$341$	−0.239567	+	3.19680i	−0.0129733	+	0.173117i
$342$	−6.01357			−0.325176
$343$	−10.6983	−	15.1177i	−0.577656	−	0.816280i
$344$	28.6745			1.54603
$345$	−0.341184	+	4.55278i	−0.0183687	+	0.245114i
$346$	−26.7821	+	8.26119i	−1.43982	+	0.444124i
$347$	−16.6538	−	2.51016i	−0.894023	−	0.134752i	−0.314068	−	0.949401i	$-0.601692\pi$
$347$	−16.6538	−	2.51016i	−0.894023	−	0.134752i	−0.579955	+	0.814648i	$0.696930\pi$
$348$	−15.6728	−	14.5422i	−0.840149	−	0.779544i
$349$	−3.59731	−	15.7608i	−0.192559	−	0.843658i	−0.975225	−	0.221215i	$-0.928998\pi$
$349$	−3.59731	−	15.7608i	−0.192559	−	0.843658i	0.782666	−	0.622443i	$-0.213860\pi$
$350$	5.52200	−	4.93064i	0.295163	−	0.263554i
$351$	1.14079	−	4.99813i	0.0608909	−	0.266780i
$352$	−3.32411	+	2.26634i	−0.177176	+	0.120796i
$353$	0.337701	−	0.313341i	0.0179740	−	0.0166775i	−0.671135	−	0.741336i	$-0.734193\pi$
$353$	0.337701	−	0.313341i	0.0179740	−	0.0166775i	0.689109	+	0.724658i	$0.258002\pi$
$354$	4.79393	+	3.26844i	0.254794	+	0.173716i
$355$	0.112275	−	0.0169227i	0.00595892	−	0.000898162i
$356$	18.7649	−	9.03668i	0.994535	−	0.478943i
$357$	−9.82371	−	12.8135i	−0.519926	−	0.678163i
$358$	−33.3714	−	16.0708i	−1.76374	−	0.849370i
$359$	−23.3998	−	7.21788i	−1.23499	−	0.380945i	−0.392551	−	0.919730i	$-0.628407\pi$
$359$	−23.3998	−	7.21788i	−1.23499	−	0.380945i	−0.842443	+	0.538785i	$0.818883\pi$
$360$	14.1776	−	36.1239i	0.747225	−	1.90390i
$361$	9.00047	+	15.5893i	0.473709	+	0.820488i
$362$	−23.2409	+	40.2544i	−1.22151	+	2.11573i
$363$	5.42007	+	6.79655i	0.284480	+	0.356726i
$364$	−7.44806	+	12.3491i	−0.390384	+	0.647270i
$365$	−12.8638	+	16.1307i	−0.673324	+	0.844322i
$366$	5.44562	+	13.8752i	0.284647	+	0.725269i
$367$	−1.17692	−	15.7049i	−0.0614346	−	0.819788i	−0.939784	−	0.341769i	$-0.888974\pi$
$367$	−1.17692	−	15.7049i	−0.0614346	−	0.819788i	0.878349	−	0.478019i	$-0.158645\pi$
$368$	−1.37159	−	18.3025i	−0.0714989	−	0.954086i
$369$	−0.791550	−	2.01684i	−0.0412065	−	0.104992i
$370$	14.5538	−	18.2499i	0.756615	−	0.948765i
$371$	17.3270	−	11.3344i	0.899572	−	0.588451i
$372$	−13.5796	−	17.0282i	−0.704068	−	0.882873i
$373$	−13.3984	+	23.2067i	−0.693744	+	1.20160i	0.276858	+	0.960911i	$0.410707\pi$
$373$	−13.3984	+	23.2067i	−0.693744	+	1.20160i	−0.970602	+	0.240689i	$0.922627\pi$
$374$	−5.32955	−	9.23106i	−0.275585	−	0.477327i
$375$	−2.86629	+	7.30319i	−0.148015	+	0.377135i
$376$	−61.9651	−	19.1137i	−3.19561	−	0.985714i
$377$	−6.06746	−	2.92193i	−0.312490	−	0.150487i
$378$	−29.5243	−	0.564420i	−1.51857	−	0.0290306i
$379$	21.1837	−	10.2015i	1.08813	−	0.524018i	0.198226	−	0.980156i	$-0.436482\pi$
$379$	21.1837	−	10.2015i	1.08813	−	0.524018i	0.889909	+	0.456139i	$0.150768\pi$
$380$	11.2525	−	1.69604i	0.577242	−	0.0870052i
$381$	−13.7287	−	9.36010i	−0.703345	−	0.479532i
$382$	1.36575	−	1.26724i	0.0698781	−	0.0648374i
$383$	−19.9742	+	13.6182i	−1.02064	+	0.695857i	−0.953347	−	0.301876i	$-0.902387\pi$
$383$	−19.9742	+	13.6182i	−1.02064	+	0.695857i	−0.0672882	+	0.997734i	$0.521435\pi$
$384$	−1.41798	+	6.21259i	−0.0723612	+	0.317035i
$385$	−2.93810	−	2.08652i	−0.149739	−	0.106339i
$386$	−6.53349	−	28.6251i	−0.332546	−	1.45698i
$387$	7.31402	+	6.78642i	0.371793	+	0.344973i
$388$	−6.25582	−	0.942913i	−0.317591	−	0.0478692i
$389$	−9.32181	+	2.87540i	−0.472635	+	0.145788i	−0.521917	−	0.852996i	$-0.674783\pi$
$389$	−9.32181	+	2.87540i	−0.472635	+	0.145788i	0.0492822	+	0.998785i	$0.484307\pi$
$390$	−0.455319	+	6.07580i	−0.0230560	+	0.307660i
$391$	17.0925			0.864403
$392$	44.4080	+	15.5804i	2.24294	+	0.786929i
$393$	10.3509			0.522135
$394$	−0.122885	+	1.63979i	−0.00619088	+	0.0826115i
$395$	−13.8552	+	4.27378i	−0.697133	+	0.215037i
$396$	−5.89202	−	0.888079i	−0.296085	−	0.0446276i
$397$	21.7416	+	20.1733i	1.09118	+	1.01247i	0.999861	+	0.0166470i	$0.00529915\pi$
$397$	21.7416	+	20.1733i	1.09118	+	1.01247i	0.0913202	+	0.995822i	$0.470891\pi$
$398$	10.4186	+	45.6467i	0.522235	+	2.28806i
$399$	−1.03896	−	1.88169i	−0.0520129	−	0.0942025i
$400$	−1.95183	+	8.55155i	−0.0975917	+	0.427577i
$401$	−15.0542	+	10.2638i	−0.751770	+	0.512548i	−0.877535	−	0.479512i	$-0.840814\pi$
$401$	−15.0542	+	10.2638i	−0.751770	+	0.512548i	0.125765	+	0.992060i	$0.459861\pi$
$402$	4.98362	−	4.62412i	0.248560	−	0.230630i
$403$	−5.66824	−	3.86454i	−0.282355	−	0.192506i
$404$	1.39748	−	0.210636i	0.0695273	−	0.0104796i
$405$	7.75986	−	3.73695i	0.385591	−	0.185691i
$406$	−9.35287	+	37.6457i	−0.464175	+	1.86832i
$407$	−1.82951	−	0.881044i	−0.0906853	−	0.0436718i
$408$	39.2057	+	12.0934i	1.94097	+	0.598711i
$409$	−10.2588	+	26.1390i	−0.507264	+	1.29249i	0.416364	+	0.909198i	$0.363304\pi$
$409$	−10.2588	+	26.1390i	−0.507264	+	1.29249i	−0.923628	+	0.383290i	$0.874791\pi$
$410$	2.93851	+	5.08965i	0.145123	+	0.251360i
$411$	−3.81666	+	6.61065i	−0.188262	+	0.326079i
$412$	2.36473	+	2.96527i	0.116502	+	0.146089i
$413$	0.688666	−	7.31132i	0.0338870	−	0.359767i
$414$	8.53959	−	10.7083i	0.419698	−	0.526284i
$415$	−10.7034	−	27.2719i	−0.525411	−	1.33873i
$416$	−0.643392	−	8.58548i	−0.0315449	−	0.420938i
$417$	−0.748226	−	9.98439i	−0.0366408	−	0.488938i
$418$	−0.518425	−	1.32093i	−0.0253570	−	0.0646086i
$419$	−5.06020	+	6.34529i	−0.247207	+	0.309988i	−0.889918	−	0.456121i	$-0.849238\pi$
$419$	−5.06020	+	6.34529i	−0.247207	+	0.309988i	0.642711	+	0.766109i	$0.277810\pi$
$420$	24.2747	−	3.18558i	1.18449	−	0.155441i
$421$	4.02881	+	5.05197i	0.196352	+	0.246218i	0.870254	−	0.492603i	$-0.163954\pi$
$421$	4.02881	+	5.05197i	0.196352	+	0.246218i	−0.673902	+	0.738821i	$0.735383\pi$
$422$	29.8752	−	51.7453i	1.45430	−	2.51892i
$423$	−11.2818	−	19.5407i	−0.548541	−	0.950100i
$424$	−19.2218	+	48.9763i	−0.933491	+	2.37850i
$425$	−7.80572	−	2.40775i	−0.378633	−	0.116793i
$426$	0.0866671	+	0.0417367i	0.00419903	+	0.00202215i
$427$	12.0425	−	14.5224i	0.582775	−	0.702789i
$428$	−24.8094	+	11.9476i	−1.19921	+	0.577508i
$429$	0.524107	−	0.0789964i	0.0253041	−	0.00381398i
$430$	−22.3617	−	15.2459i	−1.07838	−	0.735224i
$431$	19.2279	−	17.8409i	0.926177	−	0.859367i	−0.0641754	−	0.997939i	$-0.520442\pi$
$431$	19.2279	−	17.8409i	0.926177	−	0.859367i	0.990352	+	0.138572i	$0.0442512\pi$
$432$	28.9089	−	19.7098i	1.39088	−	0.948287i
$433$	−0.0249686	+	0.109395i	−0.00119992	+	0.00525717i	−0.975524	−	0.219892i	$-0.929430\pi$
$433$	−0.0249686	+	0.109395i	−0.00119992	+	0.00525717i	0.974324	+	0.225149i	$0.0722868\pi$
$434$	−15.1370	+	36.5012i	−0.726601	+	1.75211i
$435$	2.54405	+	11.1462i	0.121978	+	0.534419i
$436$	20.1622	+	18.7078i	0.965594	+	0.895940i
$437$	2.25006	+	0.339141i	0.107635	+	0.0162233i
$438$	−16.7028	+	5.15214i	−0.798091	+	0.246179i
$439$	2.20823	−	29.4667i	0.105393	−	1.40637i	−0.654372	−	0.756173i	$-0.727067\pi$
$439$	2.20823	−	29.4667i	0.105393	−	1.40637i	0.759765	−	0.650198i	$-0.225314\pi$
$440$	9.15713			0.436549
$441$	7.63974	+	14.4842i	0.363797	+	0.689723i
$442$	22.8103			1.08498
$443$	1.77675	−	23.7091i	0.0844161	−	1.12646i	−0.780708	−	0.624897i	$-0.785141\pi$
$443$	1.77675	−	23.7091i	0.0844161	−	1.12646i	0.865124	−	0.501559i	$-0.167240\pi$
$444$	13.1830	−	4.06640i	0.625636	−	0.192983i
$445$	−11.0129	−	1.65992i	−0.522060	−	0.0786879i
$446$	52.4373	+	48.6547i	2.48298	+	2.30387i
$447$	−3.33048	−	14.5918i	−0.157526	−	0.690168i
$448$	−6.65995	+	1.91571i	−0.314653	+	0.0905087i
$449$	6.76384	−	29.6343i	0.319205	−	1.39853i	−0.519745	−	0.854321i	$-0.673973\pi$
$449$	6.76384	−	29.6343i	0.319205	−	1.39853i	0.838950	−	0.544208i	$-0.183170\pi$
$450$	−5.40826	+	3.68729i	−0.254948	+	0.173821i
$451$	0.374775	−	0.347740i	0.0176475	−	0.0163744i
$452$	−41.8404	−	28.5263i	−1.96801	−	1.34176i
$453$	9.48221	−	1.42921i	0.445513	−	0.0671503i
$454$	−54.5258	+	26.2583i	−2.55902	+	1.23236i
$455$	7.01065	−	3.21255i	0.328664	−	0.150607i
$456$	4.92110	+	2.36988i	0.230452	+	0.110980i
$457$	18.4118	+	5.67930i	0.861269	+	0.265666i	0.693762	−	0.720205i	$-0.255952\pi$
$457$	18.4118	+	5.67930i	0.861269	+	0.265666i	0.167507	+	0.985871i	$0.446428\pi$
$458$	5.82476	−	14.8412i	0.272173	−	0.693485i
$459$	16.2920	+	28.2185i	0.760444	+	1.31713i
$460$	−12.9591	+	22.4457i	−0.604219	+	1.04654i
$461$	11.4345	+	14.3384i	0.532558	+	0.667807i	0.973223	−	0.229865i	$-0.0738285\pi$
$461$	11.4345	+	14.3384i	0.532558	+	0.667807i	−0.440664	+	0.897672i	$0.645257\pi$
$462$	−1.06085	−	2.86273i	−0.0493552	−	0.133186i
$463$	4.26160	−	5.34387i	0.198053	−	0.248351i	−0.672881	−	0.739751i	$-0.734943\pi$
$463$	4.26160	−	5.34387i	0.198053	−	0.248351i	0.870934	+	0.491400i	$0.163515\pi$
$464$	−16.7914	−	42.7838i	−0.779521	−	1.98619i
$465$	0.870353	+	11.6140i	0.0403616	+	0.538589i
$466$	3.90765	+	52.1440i	0.181018	+	2.41552i
$467$	−7.38059	−	18.8054i	−0.341533	−	0.870212i	−0.993693	−	0.112131i	$-0.964232\pi$
$467$	−7.38059	−	18.8054i	−0.341533	−	0.870212i	0.652160	−	0.758081i	$-0.273863\pi$
$468$	7.95027	−	9.96932i	0.367501	−	0.460832i
$469$	−8.17249	−	2.69299i	−0.377370	−	0.124351i
$470$	38.1607	+	47.8520i	1.76022	+	2.20725i
$471$	−7.95876	+	13.7850i	−0.366721	+	0.635179i
$472$	9.33052	+	16.1609i	0.429472	+	0.743867i
$473$	−0.860153	+	2.19163i	−0.0395499	+	0.100771i
$474$	−11.7381	−	3.62073i	−0.539150	−	0.166306i
$475$	−0.979774	−	0.471834i	−0.0449551	−	0.0216492i
$476$	−18.6842	−	89.7341i	−0.856391	−	4.11296i
$477$	−16.4942	+	7.94317i	−0.755215	+	0.363693i
$478$	−23.7052	+	3.57298i	−1.08425	+	0.163424i
$479$	−1.59466	−	1.08722i	−0.0728619	−	0.0496764i	0.526341	−	0.850273i	$-0.323563\pi$
$479$	−1.59466	−	1.08722i	−0.0728619	−	0.0496764i	−0.599203	+	0.800597i	$0.704516\pi$
$480$	−10.7145	+	9.94162i	−0.489048	+	0.453771i
$481$	3.59038	−	2.44788i	0.163707	−	0.111614i
$482$	2.33694	−	10.2388i	0.106445	−	0.466365i
$483$	4.82609	+	0.822046i	0.219595	+	0.0374044i
$484$	10.9814	+	48.1125i	0.499153	+	2.18693i
$485$	2.47993	+	2.30104i	0.112608	+	0.104485i
$486$	40.3248	+	6.07798i	1.82917	+	0.275703i
$487$	−9.71429	+	2.99646i	−0.440196	+	0.135783i	−0.506928	−	0.861988i	$-0.669219\pi$
$487$	−9.71429	+	2.99646i	−0.440196	+	0.135783i	0.0667317	+	0.997771i	$0.478743\pi$
$488$	−3.58257	+	47.8060i	−0.162175	+	2.16408i
$489$	−5.87488			−0.265671
$490$	−26.3474	−	35.7616i	−1.19026	−	1.61554i
$491$	−39.8079			−1.79650			−0.898252	−	0.439481i	$-0.855162\pi$
$491$	−39.8079			−1.79650			−0.898252	+	0.439481i	$0.855162\pi$
$492$	−0.259571	+	3.46373i	−0.0117024	+	0.156157i
$493$	40.9006	−	12.6162i	1.84207	−	0.568203i
$494$	3.00276	+	0.452593i	0.135100	+	0.0203631i
$495$	2.33571	+	2.16723i	0.104983	+	0.0974096i
$496$	−10.4185	−	45.6464i	−0.467804	−	2.04958i
$497$	−0.00677620	−	0.121562i	−0.000303954	−	0.00545281i
$498$	5.52307	−	24.1981i	0.247494	−	1.08434i
$499$	−0.431953	+	0.294501i	−0.0193369	+	0.0131837i	−0.572950	−	0.819590i	$-0.694201\pi$
$499$	−0.431953	+	0.294501i	−0.0193369	+	0.0131837i	0.553613	+	0.832774i	$0.313249\pi$
$500$	−32.6487	+	30.2936i	−1.46010	+	1.35477i
$501$	−12.2836	−	8.37485i	−0.548793	−	0.374161i
$502$	18.6200	−	2.80651i	0.831052	−	0.125261i
$503$	−8.65152	+	4.16635i	−0.385752	+	0.185768i	−0.616701	−	0.787197i	$-0.711531\pi$
$503$	−8.65152	+	4.16635i	−0.385752	+	0.185768i	0.230949	+	0.972966i	$0.425817\pi$
$504$	−37.1390	−	18.7680i	−1.65430	−	0.835992i
$505$	−0.680890	−	0.327899i	−0.0302992	−	0.0145913i
$506$	3.08835	+	0.952631i	0.137294	+	0.0423496i
$507$	3.44595	−	8.78014i	0.153040	−	0.389939i
$508$	−47.1634	−	81.6894i	−2.09254	−	3.62438i
$509$	7.64275	−	13.2376i	0.338759	−	0.586747i	−0.645441	−	0.763810i	$-0.723326\pi$
$509$	7.64275	−	13.2376i	0.338759	−	0.586747i	0.984200	+	0.177063i	$0.0566596\pi$
$510$	−24.1445	−	30.2762i	−1.06914	−	1.34065i
$511$	15.9271	+	15.3550i	0.704573	+	0.679267i
$512$	−30.9549	+	38.8162i	−1.36803	+	1.71545i
$513$	1.58478	+	4.03795i	0.0699697	+	0.178280i
$514$	−0.966569	−	12.8980i	−0.0426335	−	0.568905i
$515$	−0.151562	−	2.02245i	−0.00667862	−	0.0891199i
$516$	−5.84387	−	14.8899i	−0.257262	−	0.655492i
$517$	3.31966	−	4.16273i	0.145999	−	0.183076i
$518$	−18.0195	−	17.3722i	−0.791729	−	0.763292i
$519$	5.52276	+	6.92532i	0.242422	+	0.303988i
$520$	−9.79806	+	16.9707i	−0.429673	+	0.744216i
$521$	15.8646	+	27.4783i	0.695041	+	1.20385i	0.970167	+	0.242439i	$0.0779473\pi$
$521$	15.8646	+	27.4783i	0.695041	+	1.20385i	−0.275125	+	0.961408i	$0.588719\pi$
$522$	12.5305	−	31.9271i	0.548443	−	1.39741i
$523$	−14.7458	−	4.54848i	−0.644790	−	0.198891i	−0.0449220	−	0.998990i	$-0.514304\pi$
$523$	−14.7458	−	4.54848i	−0.644790	−	0.198891i	−0.599868	+	0.800099i	$0.704780\pi$
$524$	52.9418	+	25.4954i	2.31278	+	1.11377i
$525$	−2.08816	−	1.05524i	−0.0911349	−	0.0460545i
$526$	−38.1079	+	18.3518i	−1.66158	+	0.800176i
$527$	43.1155	−	6.49861i	1.87814	−	0.283084i
$528$	2.98879	+	2.03772i	0.130070	+	0.0886804i
$529$	13.0611	−	12.1189i	0.567873	−	0.526909i
$530$	41.0302	−	27.9739i	1.78224	−	1.21511i
$531$	−1.44488	+	6.33044i	−0.0627025	+	0.274718i
$532$	−0.679132	−	12.1833i	−0.0294441	−	0.528215i
$533$	0.243454	+	1.06664i	0.0105452	+	0.0462014i
$534$	−6.91668	−	6.41774i	−0.299314	−	0.277723i
$535$	14.5603	+	2.19462i	0.629499	+	0.0948816i
$536$	20.8941	−	6.44498i	0.902489	−	0.278381i
$537$	−0.874796	+	11.6733i	−0.0377502	+	0.503742i
$538$	16.8809			0.727789
$539$	−2.52294	+	2.92680i	−0.108671	+	0.126066i
$540$	−49.4085			−2.12621
$541$	1.09498	−	14.6115i	0.0470769	−	0.628197i	−0.922906	−	0.385025i	$-0.874193\pi$
$541$	1.09498	−	14.6115i	0.0470769	−	0.628197i	0.969983	−	0.243172i	$-0.0781880\pi$
$542$	10.9580	−	3.38009i	0.470685	−	0.145187i
$543$	14.5262	+	2.18947i	0.623377	+	0.0939590i
$544$	40.1129	+	37.2193i	1.71983	+	1.59576i
$545$	−3.27278	−	14.3390i	−0.140190	−	0.614215i
$546$	6.44053	+	1.09704i	0.275629	+	0.0469490i
$547$	−7.66606	+	33.5872i	−0.327777	+	1.43608i	0.495581	+	0.868562i	$0.334955\pi$
$547$	−7.66606	+	33.5872i	−0.327777	+	1.43608i	−0.823358	+	0.567523i	$0.807902\pi$
$548$	−35.8038	+	24.4106i	−1.52946	+	1.04277i
$549$	−12.2281	+	11.3460i	−0.521883	+	0.484236i
$550$	−1.27618	−	0.870088i	−0.0544167	−	0.0371007i
$551$	5.63449	−	0.849262i	0.240037	−	0.0361798i
$552$	−11.2082	+	5.39761i	−0.477055	+	0.229737i
$553$	3.16931	+	15.2211i	0.134773	+	0.647268i
$554$	60.6764	+	29.2202i	2.57789	+	1.24145i
$555$	−7.04946	−	2.17447i	−0.299233	−	0.0923011i
$556$	20.7657	−	52.9101i	0.880660	−	2.24389i
$557$	−2.52513	−	4.37365i	−0.106993	−	0.185318i	0.807558	−	0.589789i	$-0.200789\pi$
$557$	−2.52513	−	4.37365i	−0.106993	−	0.185318i	−0.914551	+	0.404471i	$0.867456\pi$
$558$	17.4696	−	30.2583i	0.739549	−	1.28094i
$559$	−3.14135	−	3.93913i	−0.132865	−	0.166608i
$560$	49.9868	+	16.4716i	2.11233	+	0.696053i
$561$	−2.10037	+	2.63378i	−0.0886777	+	0.111198i
$562$	0.780363	+	1.98833i	0.0329176	+	0.0838727i
$563$	1.26441	+	16.8723i	0.0532884	+	0.711085i	0.958312	+	0.285723i	$0.0922339\pi$
$563$	1.26441	+	16.8723i	0.0532884	+	0.711085i	−0.905024	+	0.425361i	$0.860147\pi$
$564$	2.70324	+	36.0722i	0.113827	+	1.51892i
$565$	9.89308	+	25.2072i	0.416205	+	1.06047i
$566$	47.6714	−	59.7781i	2.00378	−	2.51266i
$567$	−3.20914	−	8.65994i	−0.134771	−	0.363683i
$568$	0.192896	+	0.241884i	0.00809374	+	0.0101492i
$569$	−5.08278	+	8.80364i	−0.213081	+	0.369068i	−0.952677	−	0.303983i	$-0.901683\pi$
$569$	−5.08278	+	8.80364i	−0.213081	+	0.369068i	0.739596	+	0.673051i	$0.235017\pi$
$570$	−2.57766	−	4.46463i	−0.107966	−	0.187003i
$571$	0.574829	−	1.46464i	0.0240558	−	0.0612933i	−0.918341	−	0.395790i	$-0.870471\pi$
$571$	0.574829	−	1.46464i	0.0240558	−	0.0612933i	0.942397	+	0.334496i	$0.108566\pi$
$572$	2.87522	+	0.886889i	0.120219	+	0.0370827i
$573$	−0.530510	−	0.255480i	−0.0221624	−	0.0106728i
$574$	5.72902	−	2.62526i	0.239125	−	0.109576i
$575$	2.23152	−	1.07464i	0.0930610	−	0.0448158i
$576$	6.05903	−	0.913251i	0.252459	−	0.0380521i
$577$	−25.3112	−	17.2569i	−1.05372	−	0.718413i	−0.0929230	−	0.995673i	$-0.529621\pi$
$577$	−25.3112	−	17.2569i	−1.05372	−	0.718413i	−0.960795	+	0.277261i	$0.910573\pi$
$578$	−74.2263	+	68.8720i	−3.08741	+	2.86470i
$579$	−7.66700	+	5.22727i	−0.318630	+	0.217238i
$580$	−14.4423	+	63.2757i	−0.599682	+	2.62738i
$581$	−30.1908	+	8.68427i	−1.25253	+	0.360284i
$582$	0.637765	+	2.79423i	0.0264362	+	0.115825i
$583$	−3.16673	−	2.93829i	−0.131152	−	0.121692i
$584$	−55.5902	−	8.37887i	−2.30034	−	0.346720i
$585$	−6.51567	+	2.00982i	−0.269390	+	0.0830958i
$586$	2.53228	−	33.7909i	0.104607	−	1.39589i
$587$	−39.4658			−1.62893			−0.814463	−	0.580215i	$-0.802968\pi$
$587$	−39.4658			−1.62893			−0.814463	+	0.580215i	$0.802968\pi$
$588$	−0.959854	−	26.2352i	−0.0395837	−	1.08192i
$589$	5.80467			0.239177
$590$	1.31624	−	17.5640i	0.0541886	−	0.723097i
$591$	0.496609	−	0.153183i	0.0204278	−	0.00630113i
$592$	29.3257	+	4.42014i	1.20528	+	0.181667i
$593$	−19.9140	−	18.4775i	−0.817772	−	0.758781i	0.155647	−	0.987813i	$-0.450254\pi$
$593$	−19.9140	−	18.4775i	−0.817772	−	0.758781i	−0.973419	+	0.229031i	$0.926444\pi$
$594$	1.37099	+	6.00668i	0.0562522	+	0.246457i
$595$	−18.7755	+	45.2749i	−0.769719	+	1.85609i
$596$	18.9067	−	82.8359i	0.774450	−	3.39309i
$597$	12.2261	−	8.33562i	0.500381	−	0.341154i
$598$	−5.07000	+	4.70428i	−0.207328	+	0.192372i
$599$	11.4154	+	7.78290i	0.466421	+	0.318001i	0.773626	−	0.633643i	$-0.218441\pi$
$599$	11.4154	+	7.78290i	0.466421	+	0.318001i	−0.307204	+	0.951644i	$0.599394\pi$
$600$	5.87888	−	0.886099i	0.240004	−	0.0361748i
$601$	−27.6964	+	13.3379i	−1.12976	+	0.544063i	−0.902894	−	0.429864i	$-0.858562\pi$
$601$	−27.6964	+	13.3379i	−1.12976	+	0.544063i	−0.226864	+	0.973926i	$0.572847\pi$
$602$	−18.5246	+	22.3395i	−0.755008	+	0.910490i
$603$	6.85481	+	3.30110i	0.279150	+	0.134431i
$604$	52.0189	+	16.0457i	2.11662	+	0.652891i
$605$	9.64111	−	24.5651i	0.391967	−	0.998715i
$606$	−0.320126	−	0.554475i	−0.0130042	−	0.0225240i
$607$	−4.20387	+	7.28132i	−0.170630	+	0.295540i	−0.938640	−	0.344898i	$-0.887914\pi$
$607$	−4.20387	+	7.28132i	−0.170630	+	0.295540i	0.768010	+	0.640437i	$0.221247\pi$
$608$	4.54198	+	5.69546i	0.184202	+	0.230982i
$609$	12.1551	−	1.59512i	0.492550	−	0.0646376i
$610$	28.2118	−	35.3765i	1.14226	−	1.43235i
$611$	4.16268	+	10.6063i	0.168404	+	0.429087i
$612$	6.05643	+	80.8174i	0.244817	+	3.26685i
$613$	−3.04303	−	40.6065i	−0.122907	−	1.64008i	−0.628860	−	0.777518i	$-0.716478\pi$
$613$	−3.04303	−	40.6065i	−0.122907	−	1.64008i	0.505953	−	0.862561i	$-0.331141\pi$
$614$	−17.3277	−	44.1502i	−0.699289	−	1.78176i
$615$	1.15806	−	1.45217i	0.0466976	−	0.0585570i
$616$	0.920803	−	9.77584i	0.0371002	−	0.393880i
$617$	−12.6776	−	15.8972i	−0.510381	−	0.639997i	0.458155	−	0.888872i	$-0.348511\pi$
$617$	−12.6776	−	15.8972i	−0.510381	−	0.639997i	−0.968536	+	0.248875i	$0.919939\pi$
$618$	0.859111	−	1.48802i	0.0345585	−	0.0598571i
$619$	0.831657	+	1.44047i	0.0334271	+	0.0578975i	0.882255	−	0.470772i	$-0.156024\pi$
$619$	0.831657	+	1.44047i	0.0334271	+	0.0578975i	−0.848828	+	0.528669i	$0.822691\pi$
$620$	−24.1551	+	61.5461i	−0.970091	+	2.47175i
$621$	−9.44082	−	2.91211i	−0.378847	−	0.116859i
$622$	18.2277	+	8.77800i	0.730865	+	0.351966i
$623$	−2.87948	+	11.5900i	−0.115364	+	0.464345i
$624$	−6.97445	+	3.35872i	−0.279201	+	0.134456i
$625$	28.9294	−	4.36041i	1.15718	−	0.174416i
$626$	−32.7830	−	22.3511i	−1.31027	−	0.893328i
$627$	−0.328752	+	0.305037i	−0.0131291	+	0.0121820i
$628$	−74.6606	+	50.9027i	−2.97928	+	2.03124i
$629$	−6.14574	+	26.9263i	−0.245047	+	1.07362i
$630$	18.9839	+	34.3825i	0.756338	+	1.36983i
$631$	5.45794	+	23.9128i	0.217277	+	0.951953i	0.959480	+	0.281778i	$0.0909240\pi$
$631$	5.45794	+	23.9128i	0.217277	+	0.951953i	−0.742203	+	0.670176i	$0.766219\pi$
$632$	−28.9614	−	26.8723i	−1.15202	−	1.06892i
$633$	−18.6727	−	2.81446i	−0.742175	−	0.111865i
$634$	21.6821	−	6.68805i	0.861107	−	0.265616i
$635$	−3.76941	+	50.2993i	−0.149585	+	1.99607i
$636$	29.3495			1.16378
$637$	−2.72465	−	7.80737i	−0.107954	−	0.309339i
$638$	8.09327			0.320416
$639$	−0.00804480	+	0.107350i	−0.000318247	+	0.00424672i
$640$	18.4849	−	5.70184i	0.730680	−	0.225385i
$641$	13.4951	+	2.03406i	0.533024	+	0.0803405i	0.410039	−	0.912068i	$-0.365515\pi$
$641$	13.4951	+	2.03406i	0.533024	+	0.0803405i	0.122985	+	0.992408i	$0.460753\pi$
$642$	9.14469	+	8.48503i	0.360912	+	0.334877i
$643$	0.0325384	+	0.142560i	0.00128319	+	0.00562202i	0.975565	−	0.219709i	$-0.0705108\pi$
$643$	0.0325384	+	0.142560i	0.00128319	+	0.00562202i	−0.974282	+	0.225331i	$0.927654\pi$
$644$	22.6592	+	16.0917i	0.892897	+	0.634101i
$645$	−1.90334	+	8.33906i	−0.0749438	+	0.328350i
$646$	−15.9468	+	10.8723i	−0.627417	+	0.427765i
$647$	−0.0705631	+	0.0654730i	−0.00277412	+	0.00257401i	−0.681559	−	0.731764i	$-0.738698\pi$
$647$	−0.0705631	+	0.0654730i	−0.00277412	+	0.00257401i	0.678784	+	0.734338i	$0.262507\pi$
$648$	19.3903	+	13.2201i	0.761723	+	0.519334i
$649$	−1.51509	+	0.228363i	−0.0594725	+	0.00896404i
$650$	2.97802	−	1.43414i	0.116808	−	0.0562516i
$651$	12.4863	+	0.238702i	0.489376	+	0.00935547i
$652$	−30.0482	−	14.4705i	−1.17678	−	0.566707i
$653$	28.3547	+	8.74628i	1.10961	+	0.342268i	0.794790	−	0.606884i	$-0.207581\pi$
$653$	28.3547	+	8.74628i	1.10961	+	0.342268i	0.314816	+	0.949153i	$0.398057\pi$
$654$	4.55228	−	11.5990i	0.178008	−	0.453558i
$655$	−15.7109	−	27.2122i	−0.613877	−	1.06327i
$656$	−3.73343	+	6.46648i	−0.145766	+	0.252474i
$657$	−12.1964	−	15.2938i	−0.475826	−	0.596667i
$658$	54.9224	−	35.9272i	2.14110	−	1.40059i
$659$	22.4578	−	28.1612i	0.874833	−	1.09701i	−0.119723	−	0.992807i	$-0.538201\pi$
$659$	22.4578	−	28.1612i	0.874833	−	1.09701i	0.994556	−	0.104199i	$-0.0332279\pi$
$660$	−1.86622	−	4.75506i	−0.0726427	−	0.185090i
$661$	−2.09756	−	27.9900i	−0.0815856	−	1.08868i	−0.876321	−	0.481728i	$-0.840009\pi$
$661$	−2.09756	−	27.9900i	−0.0815856	−	1.08868i	0.794735	−	0.606956i	$-0.207610\pi$
$662$	−1.56752	−	20.9172i	−0.0609236	−	0.812968i
$663$	−2.63376	−	6.71070i	−0.102287	−	0.260622i
$664$	49.7724	−	62.4126i	1.93154	−	2.42208i
$665$	−3.36993	+	5.58746i	−0.130680	+	0.216672i
$666$	13.7986	+	17.3029i	0.534686	+	0.670475i
$667$	−6.48900	+	11.2393i	−0.251255	+	0.435187i
$668$	−42.1990	−	73.0907i	−1.63273	−	2.82797i
$669$	8.25942	−	21.0447i	0.319328	−	0.813634i
$670$	−19.7209	−	6.08310i	−0.761885	−	0.235011i
$671$	−3.54642	−	1.70786i	−0.136908	−	0.0659314i
$672$	9.53592	+	12.4381i	0.367856	+	0.479811i
$673$	10.1804	−	4.90261i	0.392425	−	0.188982i	−0.227257	−	0.973835i	$-0.572976\pi$
$673$	10.1804	−	4.90261i	0.392425	−	0.188982i	0.619682	+	0.784853i	$0.287262\pi$
$674$	−39.9263	+	6.01792i	−1.53790	+	0.231802i
$675$	3.90118	+	2.65978i	0.150157	+	0.102375i
$676$	39.2514	−	36.4200i	1.50967	−	1.40077i
$677$	−14.1411	+	9.64122i	−0.543486	+	0.370542i	−0.803724	−	0.595002i	$-0.797151\pi$
$677$	−14.1411	+	9.64122i	−0.543486	+	0.370542i	0.260238	+	0.965544i	$0.416199\pi$
$678$	−5.10492	+	22.3661i	−0.196053	+	0.858965i
$679$	2.70589	−	2.41611i	0.103842	−	0.0927217i
$680$	−27.7147	−	121.426i	−1.06281	−	4.65647i
$681$	14.0208	+	13.0094i	0.537278	+	0.498522i
$682$	8.15252	+	1.22879i	0.312176	+	0.0470530i
$683$	33.3593	−	10.2900i	1.27646	−	0.393735i	0.418858	−	0.908052i	$-0.362430\pi$
$683$	33.3593	−	10.2900i	1.27646	−	0.393735i	0.857601	+	0.514316i	$0.171954\pi$
$684$	−0.806275	+	10.7590i	−0.0308287	+	0.411380i
$685$	23.1721			0.885362
$686$	−40.8272	+	24.5316i	−1.55879	+	0.936620i
$687$	−5.03878			−0.192241
$688$	2.56965	−	34.2896i	0.0979671	−	1.30728i
$689$	8.83385	−	2.72488i	0.336543	−	0.103810i
$690$	11.6106	+	1.75001i	0.442006	+	0.0666217i
$691$	0.513219	+	0.476197i	0.0195238	+	0.0181154i	0.689874	−	0.723929i	$-0.257666\pi$
$691$	0.513219	+	0.476197i	0.0195238	+	0.0181154i	−0.670351	+	0.742045i	$0.733856\pi$
$692$	11.1894	+	49.0241i	0.425358	+	1.86362i
$693$	2.54853	−	2.27560i	0.0968105	−	0.0864429i
$694$	−9.63829	+	42.2281i	−0.365864	+	1.60296i
$695$	−25.1129	+	17.1217i	−0.952585	+	0.649461i
$696$	−22.8362	+	21.1889i	−0.865603	+	0.803163i
$697$	−5.74540	−	3.91715i	−0.217622	−	0.148372i
$698$	−41.1118	+	6.19660i	−1.55610	+	0.234545i
$699$	14.8894	−	7.17034i	0.563167	−	0.271207i
$700$	−8.08114	−	10.5406i	−0.305439	−	0.398397i
$701$	−4.92502	−	2.37177i	−0.186016	−	0.0895803i	0.338558	−	0.940946i	$-0.390061\pi$
$701$	−4.92502	−	2.37177i	−0.186016	−	0.0895803i	−0.524573	+	0.851365i	$0.675775\pi$
$702$	−12.5990	−	3.88628i	−0.475519	−	0.146678i
$703$	−1.34329	+	3.42264i	−0.0506630	+	0.129087i
$704$	0.722947	+	1.25218i	0.0272471	+	0.0471933i
$705$	9.67169	−	16.7519i	0.364257	−	0.630911i
$706$	−0.738695	−	0.926294i	−0.0278011	−	0.0348615i
$707$	−0.418521	+	0.693922i	−0.0157401	+	0.0260976i
$708$	6.49039	−	8.13869i	0.243924	−	0.305871i
$709$	−1.69008	−	4.30624i	−0.0634722	−	0.161724i	0.895619	−	0.444822i	$-0.146733\pi$
$709$	−1.69008	−	4.30624i	−0.0634722	−	0.161724i	−0.959091	+	0.283098i	$0.908638\pi$
$710$	−0.0218219	−	0.291193i	−0.000818962	−	0.0109283i
$711$	−1.02732	−	13.7086i	−0.0385275	−	0.514114i
$712$	−11.0869	−	28.2490i	−0.415500	−	1.05868i
$713$	−8.24295	+	10.3363i	−0.308701	+	0.387099i
$714$	−34.7497	+	22.7314i	−1.30048	+	0.850700i
$715$	−1.00318	−	1.25795i	−0.0375169	−	0.0470447i
$716$	−33.2270	+	57.5508i	−1.24175	+	2.15078i
$717$	3.78824	+	6.56142i	0.141474	+	0.245041i
$718$	−23.0083	+	58.6242i	−0.858662	+	2.18783i
$719$	8.29735	+	2.55939i	0.309439	+	0.0954493i	0.445585	−	0.895239i	$-0.352996\pi$
$719$	8.29735	+	2.55939i	0.309439	+	0.0954493i	−0.136146	+	0.990689i	$0.543472\pi$
$720$	−41.9273	−	20.1911i	−1.56254	−	0.752478i
$721$	−2.17434	−	0.0415672i	−0.0809767	−	0.00154804i
$722$	41.7102	−	20.0866i	1.55229	−	0.747545i
$723$	−3.28205	+	0.494689i	−0.122061	+	0.0183977i
$724$	68.9040	+	46.9779i	2.56080	+	1.74592i
$725$	4.54661	−	4.21863i	0.168857	−	0.156676i
$726$	18.4722	−	12.5941i	0.685568	−	0.467412i
$727$	11.7882	−	51.6473i	0.437199	−	1.91549i	0.0363767	−	0.999338i	$-0.488418\pi$
$727$	11.7882	−	51.6473i	0.437199	−	1.91549i	0.400822	−	0.916156i	$-0.368724\pi$
$728$	17.1321	+	12.1666i	0.634959	+	0.450923i
$729$	−0.537682	−	2.35574i	−0.0199141	−	0.0872495i
$730$	38.8968	+	36.0909i	1.43963	+	1.33579i
$731$	31.6649	+	4.77272i	1.17117	+	0.176525i
$732$	25.5546	−	7.88254i	0.944524	−	0.291347i
$733$	−0.896448	+	11.9623i	−0.0331111	+	0.441836i	0.955870	+	0.293791i	$0.0949171\pi$
$733$	−0.896448	+	11.9623i	−0.0331111	+	0.441836i	−0.988981	+	0.148045i	$0.952702\pi$
$734$	−40.5031			−1.49500
$735$	−7.47874	+	11.8805i	−0.275858	+	0.438217i
$736$	−16.5917			−0.611579
$737$	−0.134164	+	1.79030i	−0.00494200	+	0.0659465i
$738$	−5.32453	+	1.64240i	−0.195999	+	0.0604576i
$739$	5.88797	+	0.887468i	0.216592	+	0.0326460i	0.256442	−	0.966560i	$-0.417450\pi$
$739$	5.88797	+	0.887468i	0.216592	+	0.0326460i	−0.0398496	+	0.999206i	$0.512688\pi$
$740$	−30.6999	−	28.4853i	−1.12855	−	1.04714i
$741$	−0.213557	−	0.935656i	−0.00784523	−	0.0343722i
$742$	−25.7381	−	46.6153i	−0.944877	−	1.71130i
$743$	−2.49333	+	10.9240i	−0.0914713	+	0.400762i	−0.999849	−	0.0173892i	$-0.994465\pi$
$743$	−2.49333	+	10.9240i	−0.0914713	+	0.400762i	0.908378	+	0.418151i	$0.137322\pi$
$744$	−26.2204	+	17.8768i	−0.961288	+	0.655395i
$745$	−33.3061	+	30.9035i	−1.22024	+	1.13222i
$746$	56.9412	+	38.8219i	2.08477	+	1.42137i
$747$	27.4667	−	4.13994i	1.00495	−	0.151473i
$748$	−17.2300	+	8.29755i	−0.629993	+	0.303389i
$749$	3.80703	−	15.3234i	0.139106	−	0.559906i
$750$	18.1790	+	8.75452i	0.663802	+	0.319670i
$751$	28.4014	+	8.76067i	1.03638	+	0.319681i	0.765843	−	0.643028i	$-0.222322\pi$
$751$	28.4014	+	8.76067i	1.03638	+	0.319681i	0.270539	+	0.962709i	$0.412798\pi$
$752$	−28.4096	+	72.3865i	−1.03599	+	2.63966i
$753$	−2.97559	−	5.15388i	−0.108437	−	0.187818i
$754$	−8.65973	+	14.9991i	−0.315369	+	0.546235i
$755$	−18.1497	−	22.7590i	−0.660536	−	0.828286i
$756$	−4.96832	+	52.7469i	−0.180696	+	1.91839i
$757$	−21.0101	+	26.3458i	−0.763626	+	0.957556i	−0.999900	−	0.0141302i	$-0.995502\pi$
$757$	−21.0101	+	26.3458i	−0.763626	+	0.957556i	0.236275	+	0.971686i	$0.424074\pi$
$758$	−22.0917	−	56.2886i	−0.802405	−	2.04450i
$759$	−0.0763316	−	1.01857i	−0.00277066	−	0.0369719i
$760$	−1.23908	−	16.5344i	−0.0449463	−	0.599767i
$761$	−14.4598	−	36.8429i	−0.524167	−	1.33555i	−0.910620	−	0.413246i	$-0.864395\pi$
$761$	−14.4598	−	36.8429i	−0.524167	−	1.33555i	0.386453	−	0.922309i	$-0.373700\pi$
$762$	−26.6436	+	33.4100i	−0.965194	+	1.21032i
$763$	−15.6369	+	2.05204i	−0.566094	+	0.0742888i
$764$	−2.08412	−	2.61341i	−0.0754009	−	0.0945497i
$765$	21.6688	−	37.5314i	0.783436	−	1.35695i
$766$	31.0865	+	53.8434i	1.12320	+	1.94544i
$767$	1.19791	−	3.05224i	0.0432542	−	0.110210i
$768$	19.7291	+	6.08563i	0.711913	+	0.219596i
$769$	−24.4950	−	11.7962i	−0.883313	−	0.425381i	−0.0634795	−	0.997983i	$-0.520220\pi$
$769$	−24.4950	−	11.7962i	−0.883313	−	0.425381i	−0.819833	+	0.572602i	$0.805934\pi$
$770$	−5.91580	+	7.13406i	−0.213191	+	0.257094i
$771$	−3.68293	+	1.77360i	−0.132637	+	0.0638748i
$772$	−52.0897	+	7.85126i	−1.87475	+	0.282573i
$773$	1.56880	+	1.06959i	0.0564260	+	0.0384706i	0.591205	−	0.806522i	$-0.298653\pi$
$773$	1.56880	+	1.06959i	0.0564260	+	0.0384706i	−0.534779	+	0.844992i	$0.679605\pi$
$774$	18.8102	−	17.4533i	0.676119	−	0.627347i
$775$	5.22040	−	3.55921i	0.187522	−	0.127851i
$776$	−2.05121	+	8.98695i	−0.0736343	+	0.322613i
$777$	−3.03025	+	7.30711i	−0.108710	+	0.262141i
$778$	5.58271	+	24.4594i	0.200150	+	0.876914i
$779$	−0.678603	−	0.629652i	−0.0243135	−	0.0225596i
$780$	10.8093	+	1.62924i	0.387035	+	0.0583361i
$781$	−0.0242739	+	0.00748750i	−0.000868588	+	0.000267924i
$782$	3.28502	−	43.8355i	0.117472	−	1.56755i
$783$	−24.7404			−0.884150
$784$	22.6110	−	51.7079i	0.807536	−	1.84671i
$785$	48.3202			1.72462
$786$	1.98936	−	26.5461i	0.0709580	−	0.946868i
$787$	−29.1284	+	8.98492i	−1.03832	+	0.320278i	−0.766617	−	0.642105i	$-0.778061\pi$
$787$	−29.1284	+	8.98492i	−1.03832	+	0.320278i	−0.271698	+	0.962383i	$0.587585\pi$
$788$	2.91731	+	0.439714i	0.103925	+	0.0156642i
$789$	9.79909	+	9.09223i	0.348857	+	0.323692i
$790$	8.29772	+	36.3547i	0.295220	+	1.29344i
$791$	27.9051	−	8.02679i	0.992192	−	0.285400i
$792$	−1.93193	+	8.46432i	−0.0686480	+	0.300767i
$793$	6.95979	−	4.74510i	0.247149	−	0.168503i
$794$	55.9152	−	51.8817i	1.98436	−	1.84121i
$795$	−12.9673	−	8.84094i	−0.459902	−	0.313556i
$796$	83.0644	−	12.5199i	2.94414	−	0.443757i
$797$	38.6850	−	18.6297i	1.37029	−	0.659899i	0.403387	−	0.915030i	$-0.367833\pi$
$797$	38.6850	−	18.6297i	1.37029	−	0.659899i	0.966906	+	0.255131i	$0.0821186\pi$
$798$	−5.02549	+	2.30287i	−0.177900	+	0.0815209i
$799$	−65.2459	−	31.4208i	−2.30824	−	1.11159i
$800$	7.57705	+	2.33721i	0.267889	+	0.0826328i
$801$	3.85778	−	9.82945i	0.136308	−	0.347307i
$802$	23.4293	+	40.5807i	0.827317	+	1.43296i
$803$	2.30795	−	3.99749i	0.0814459	−	0.141068i
$804$	−7.60493	−	9.53628i	−0.268205	−	0.336319i
$805$	−5.16406	−	13.9353i	−0.182009	−	0.491155i
$806$	−11.0004	+	13.7941i	−0.387473	+	0.485876i
$807$	−1.94913	−	4.96630i	−0.0686126	−	0.174822i
$808$	−0.153885	−	2.05346i	−0.00541367	−	0.0722404i
$809$	2.35366	+	31.4075i	0.0827504	+	1.10423i	0.871788	+	0.489883i	$0.162960\pi$
$809$	2.35366	+	31.4075i	0.0827504	+	1.10423i	−0.789038	+	0.614345i	$0.789420\pi$
$810$	−8.09246	−	20.6192i	−0.284340	−	0.724486i
$811$	−9.32495	+	11.6931i	−0.327443	+	0.410601i	−0.918117	−	0.396310i	$-0.870291\pi$
$811$	−9.32495	+	11.6931i	−0.327443	+	0.410601i	0.590674	+	0.806911i	$0.298862\pi$
$812$	66.0987	+	21.7808i	2.31961	+	0.764356i
$813$	−2.25965	−	2.83351i	−0.0792495	−	0.0993757i
$814$	−2.61115	+	4.52265i	−0.0915208	+	0.158519i
$815$	8.91707	+	15.4448i	0.312351	+	0.541008i
$816$	17.9749	−	45.7993i	0.629248	−	1.60330i
$817$	4.07368	+	1.25656i	0.142520	+	0.0439616i
$818$	65.0646	+	31.3335i	2.27493	+	1.09555i
$819$	1.49042	+	7.15801i	0.0520796	+	0.250121i
$820$	9.49999	−	4.57495i	0.331754	−	0.159764i
$821$	−3.05863	+	0.461015i	−0.106747	+	0.0160895i	−0.202198	−	0.979345i	$-0.564809\pi$
$821$	−3.05863	+	0.461015i	−0.106747	+	0.0160895i	0.0954515	+	0.995434i	$0.469571\pi$
$822$	16.2202	+	11.0588i	0.565745	+	0.385718i
$823$	−13.4039	+	12.4370i	−0.467229	+	0.433525i	−0.878323	−	0.478068i	$-0.841337\pi$
$823$	−13.4039	+	12.4370i	−0.467229	+	0.433525i	0.411094	+	0.911593i	$0.365147\pi$
$824$	4.56599	−	3.11304i	0.159064	−	0.108448i
$825$	−0.108624	+	0.475912i	−0.00378179	+	0.0165691i
$826$	−18.6183	−	3.17133i	−0.647815	−	0.110345i
$827$	6.82739	+	29.9127i	0.237412	+	1.04017i	0.943325	+	0.331870i	$0.107680\pi$
$827$	6.82739	+	29.9127i	0.237412	+	1.04017i	−0.705913	+	0.708298i	$0.749463\pi$
$828$	−18.0135	−	16.7141i	−0.626012	−	0.580855i
$829$	−6.21676	−	0.937026i	−0.215917	−	0.0325443i	0.0401928	−	0.999192i	$-0.487203\pi$
$829$	−6.21676	−	0.937026i	−0.215917	−	0.0325443i	−0.256110	+	0.966648i	$0.582441\pi$
$830$	−71.9989	+	22.2087i	−2.49912	+	0.770876i
$831$	1.59056	−	21.2246i	0.0551761	−	0.736273i
$832$	−3.09419			−0.107272
$833$	46.4459	+	24.5967i	1.60926	+	0.852225i
$834$	−25.7499			−0.891645
$835$	−3.37264	+	45.0048i	−0.116715	+	1.55745i
$836$	−2.43280	+	0.750421i	−0.0841403	+	0.0259538i
$837$	−24.9215	−	3.75631i	−0.861413	−	0.129837i
$838$	15.3007	+	14.1970i	0.528553	+	0.490426i
$839$	5.38717	+	23.6027i	0.185986	+	0.814857i	0.978705	+	0.205270i	$0.0658073\pi$
$839$	5.38717	+	23.6027i	0.185986	+	0.814857i	−0.792720	+	0.609586i	$0.791336\pi$
$840$	−1.98543	−	35.6177i	−0.0685037	−	1.22893i
$841$	−0.778582	+	3.41119i	−0.0268477	+	0.117627i
$842$	13.7306	−	9.36139i	0.473189	−	0.322615i
$843$	0.494856	−	0.459159i	0.0170437	−	0.0158143i
$844$	−88.5730	−	60.3881i	−3.04881	−	2.07864i
$845$	−28.3130	+	4.26749i	−0.973996	+	0.146806i
$846$	−52.2825	+	25.1779i	−1.79751	+	0.865635i
$847$	−25.2554	−	12.7627i	−0.867787	−	0.438531i
$848$	56.8444	+	27.3748i	1.95204	+	0.940055i
$849$	−23.0908	−	7.12256i	−0.792473	−	0.244446i
$850$	−7.67512	+	19.5559i	−0.263255	+	0.670762i
$851$	−4.18712	−	7.25231i	−0.143533	−	0.248606i
$852$	0.0862919	−	0.149462i	0.00295631	−	0.00512048i
$853$	2.13074	+	2.67187i	0.0729553	+	0.0914830i	0.816970	−	0.576680i	$-0.195652\pi$
$853$	2.13074	+	2.67187i	0.0729553	+	0.0914830i	−0.744015	+	0.668163i	$0.767081\pi$
$854$	−34.9299	−	33.6753i	−1.19528	−	1.15234i
$855$	3.59716	−	4.51070i	0.123020	−	0.154263i
$856$	14.6583	+	37.3487i	0.501009	+	1.27655i
$857$	−2.80983	−	37.4946i	−0.0959820	−	1.28079i	−0.812392	−	0.583111i	$-0.801835\pi$
$857$	−2.80983	−	37.4946i	−0.0959820	−	1.28079i	0.716410	−	0.697679i	$-0.245784\pi$
$858$	−0.101866	−	1.35931i	−0.00347766	−	0.0464062i
$859$	5.73058	+	14.6013i	0.195525	+	0.498190i	0.994689	−	0.102923i	$-0.0328195\pi$
$859$	5.73058	+	14.6013i	0.195525	+	0.498190i	−0.799164	+	0.601113i	$0.794724\pi$
$860$	−30.2750	+	37.9636i	−1.03237	+	1.29455i
$861$	−1.43383	−	1.38233i	−0.0488649	−	0.0471098i
$862$	−42.0596	−	52.7410i	−1.43255	−	1.79637i
$863$	7.37672	−	12.7769i	0.251107	−	0.434929i	−0.712724	−	0.701444i	$-0.752539\pi$
$863$	7.37672	−	12.7769i	0.251107	−	0.434929i	0.963831	+	0.266515i	$0.0858722\pi$
$864$	−15.8147	−	27.3918i	−0.538026	−	0.931889i
$865$	9.82377	−	25.0306i	0.334018	−	0.851065i
$866$	0.275756	+	0.0850595i	0.00937058	+	0.00289044i
$867$	28.8323	+	13.8849i	0.979195	+	0.471556i
$868$	63.2756	+	31.9759i	2.14771	+	1.08533i
$869$	2.92264	−	1.40747i	0.0991439	−	0.0477452i
$870$	29.0746	−	4.38229i	0.985721	−	0.148574i
$871$	−3.17437	−	2.16425i	−0.107559	−	0.0733327i
$872$	29.3775	−	27.2584i	0.994849	−	0.923085i
$873$	−2.65015	+	1.80684i	−0.0896941	+	0.0611524i
$874$	1.30221	−	5.70534i	0.0440478	−	0.192986i
$875$	−1.42135	−	25.4984i	−0.0480504	−	0.862004i
$876$	6.97835	+	30.5741i	0.235776	+	1.03300i
$877$	−14.8941	−	13.8197i	−0.502939	−	0.466659i	0.387430	−	0.921899i	$-0.373363\pi$
$877$	−14.8941	−	13.8197i	−0.502939	−	0.466659i	−0.890369	+	0.455240i	$0.849553\pi$
$878$	−75.1463	−	11.3265i	−2.53607	−	0.382250i
$879$	−10.2335	+	3.15662i	−0.345168	+	0.106470i
$880$	0.820612	−	10.9503i	0.0276628	−	0.369135i
$881$	−35.6191			−1.20004			−0.600019	−	0.799986i	$-0.704840\pi$
$881$	−35.6191			−1.20004			−0.600019	+	0.799986i	$0.704840\pi$
$882$	38.6146	−	16.8092i	1.30022	−	0.565997i
$883$	−33.7765			−1.13667			−0.568335	−	0.822797i	$-0.692412\pi$
$883$	−33.7765			−1.13667			−0.568335	+	0.822797i	$0.692412\pi$
$884$	3.05832	−	40.8104i	0.102862	−	1.37260i
$885$	−5.31922	+	1.64076i	−0.178804	+	0.0551537i
$886$	−60.4632	−	9.11337i	−2.03130	−	0.306170i
$887$	10.3527	+	9.60591i	0.347610	+	0.322535i	0.834583	−	0.550882i	$-0.185709\pi$
$887$	10.3527	+	9.60591i	0.347610	+	0.322535i	−0.486973	+	0.873417i	$0.661899\pi$
$888$	−4.47299	−	19.5974i	−0.150104	−	0.657647i
$889$	53.3188	+	9.08199i	1.78826	+	0.304600i
$890$	−6.37363	+	27.9247i	−0.213645	+	0.936038i
$891$	−1.59208	+	1.08546i	−0.0533368	+	0.0363644i
$892$	94.0797	−	87.2932i	3.15002	−	2.92279i
$893$	−7.96555	−	5.43082i	−0.266557	−	0.181736i
$894$	−38.0623	+	5.73698i	−1.27300	+	0.191873i
$895$	32.0165	−	15.4183i	1.07019	−	0.515378i
$896$	−4.22832	−	20.3072i	−0.141258	−	0.678416i
$897$	1.96938	+	0.948402i	0.0657556	+	0.0316662i
$898$	−74.7005	−	23.0421i	−2.49279	−	0.768923i
$899$	−12.0952	+	30.8181i	−0.403397	+	1.02784i
$900$	5.87189	+	10.1704i	0.195730	+	0.339014i
$901$	−29.3782	+	50.8845i	−0.978729	+	1.69521i
$902$	−0.819790	−	1.02798i	−0.0272960	−	0.0342281i
$903$	8.71111	+	2.87048i	0.289887	+	0.0955235i
$904$	−46.0042	+	57.6874i	−1.53008	+	1.91865i
$905$	−16.2922	−	41.5119i	−0.541572	−	1.37990i
$906$	−1.84298	−	24.5929i	−0.0612289	−	0.817043i
$907$	4.09246	+	54.6101i	0.135888	+	1.81330i	0.483157	+	0.875534i	$0.339490\pi$
$907$	4.09246	+	54.6101i	0.135888	+	1.81330i	−0.347269	+	0.937765i	$0.612891\pi$
$908$	39.6686	+	101.074i	1.31645	+	3.35426i
$909$	0.446742	−	0.560196i	0.0148175	−	0.0185805i
$910$	−6.89156	−	18.5970i	−0.228453	−	0.616485i
$911$	−4.83611	−	6.06430i	−0.160228	−	0.200919i	0.695237	−	0.718781i	$-0.255300\pi$
$911$	−4.83611	−	6.06430i	−0.160228	−	0.200919i	−0.855464	+	0.517862i	$0.826728\pi$
$912$	3.27496	−	5.67239i	0.108445	−	0.187832i
$913$	3.27726	+	5.67637i	0.108461	+	0.187861i
$914$	18.1038	−	46.1277i	0.598820	−	1.52577i
$915$	−13.6651	−	4.21511i	−0.451753	−	0.139347i
$916$	−25.7718	−	12.4110i	−0.851525	−	0.410073i
$917$	−30.6306	+	14.0361i	−1.01151	+	0.463514i
$918$	75.5007	−	36.3592i	2.49189	−	1.20003i
$919$	−3.92654	+	0.591830i	−0.129525	+	0.0195227i	−0.213485	−	0.976946i	$-0.568481\pi$
$919$	−3.92654	+	0.591830i	−0.129525	+	0.0195227i	0.0839600	+	0.996469i	$0.473243\pi$
$920$	31.2023	+	21.2734i	1.02871	+	0.701362i
$921$	−10.9881	+	10.1955i	−0.362070	+	0.335952i
$922$	38.9701	−	26.5694i	1.28341	−	0.875015i
$923$	0.0120964	−	0.0529978i	0.000398158	−	0.00174445i
$924$	−5.26400	+	1.51417i	−0.173173	+	0.0498124i
$925$	0.890556	+	3.90178i	0.0292813	+	0.128290i
$926$	−12.8859	−	11.9564i	−0.423458	−	0.392911i
$927$	1.90141	+	0.286592i	0.0624506	+	0.00941292i
$928$	−39.7024	+	12.2466i	−1.30329	+	0.402013i
$929$	0.179373	−	2.39356i	0.00588503	−	0.0785303i	−0.993488	−	0.113937i	$-0.963654\pi$
$929$	0.179373	−	2.39356i	0.00588503	−	0.0785303i	0.999373	+	0.0354070i	$0.0112728\pi$
$930$	29.9528			0.982191
$931$	5.62612	+	4.15948i	0.184388	+	0.136321i
$932$	93.8158			3.07304
$933$	0.477819	−	6.37606i	0.0156431	−	0.208743i
$934$	−49.6471	+	15.3141i	−1.62450	+	0.501093i
$935$	10.1121	+	1.52415i	0.330701	+	0.0498452i
$936$	−13.6196	−	12.6372i	−0.445171	−	0.413058i
$937$	8.08320	+	35.4148i	0.264067	+	1.15695i	0.916795	+	0.399359i	$0.130767\pi$
$937$	8.08320	+	35.4148i	0.264067	+	1.15695i	−0.652728	+	0.757592i	$0.726376\pi$
$938$	−8.47716	+	20.4417i	−0.276789	+	0.667444i
$939$	−2.79036	+	12.2253i	−0.0910598	+	0.398959i
$940$	90.7294	−	61.8582i	2.95927	−	2.01759i
$941$	−25.9278	+	24.0575i	−0.845222	+	0.784251i	−0.978374	−	0.206845i	$-0.933681\pi$
$941$	−25.9278	+	24.0575i	−0.845222	+	0.784251i	0.133152	+	0.991096i	$0.457490\pi$
$942$	33.8235	+	23.0605i	1.10203	+	0.751351i
$943$	2.08487	−	0.314244i	0.0678927	−	0.0102332i
$944$	20.1618	−	9.70940i	0.656210	−	0.316014i
$945$	18.0841	−	21.8082i	0.588274	−	0.709420i
$946$	5.45537	+	2.62717i	0.177369	+	0.0854166i
$947$	15.6140	+	4.81629i	0.507387	+	0.156508i	0.537871	−	0.843027i	$-0.319229\pi$
$947$	15.6140	+	4.81629i	0.507387	+	0.156508i	−0.0304839	+	0.999535i	$0.509705\pi$
$948$	−8.05173	+	20.5155i	−0.261508	+	0.666312i
$949$	4.93898	+	8.55457i	0.160326	+	0.277693i
$950$	−1.39838	+	2.42206i	−0.0453693	+	0.0785819i
$951$	−4.47109	−	5.60657i	−0.144985	−	0.181805i
$952$	−132.417	+	17.3771i	−4.29166	+	0.563196i
$953$	25.4951	−	31.9699i	0.825869	−	1.03561i	−0.172847	−	0.984949i	$-0.555297\pi$
$953$	25.4951	−	31.9699i	0.825869	−	1.03561i	0.998716	−	0.0506581i	$-0.0161319\pi$
$954$	17.2011	+	43.8277i	0.556906	+	1.41897i
$955$	0.133577	+	1.78246i	0.00432246	+	0.0576792i
$956$	3.21420	+	42.8905i	0.103955	+	1.38718i
$957$	−0.934477	−	2.38101i	−0.0302073	−	0.0769670i
$958$	−3.09478	+	3.88073i	−0.0999877	+	0.125381i
$959$	2.33010	−	24.7378i	0.0752427	−	0.798825i
$960$	3.27517	+	4.10693i	0.105706	+	0.132551i
$961$	−1.36281	+	2.36045i	−0.0439616	+	0.0761437i
$962$	−5.58782	−	9.67839i	−0.180159	−	0.312044i
$963$	−5.10045	+	12.9957i	−0.164360	+	0.418781i
$964$	−18.0051	−	5.55385i	−0.579906	−	0.178877i
$965$	25.3795	+	12.2221i	0.816994	+	0.393444i
$966$	3.03576	−	12.2191i	0.0976739	−	0.393142i
$967$	34.8489	−	16.7823i	1.12066	−	0.539683i	0.220566	−	0.975372i	$-0.429209\pi$
$967$	34.8489	−	16.7823i	1.12066	−	0.539683i	0.900097	+	0.435689i	$0.143495\pi$
$968$	71.1025	−	10.7170i	2.28532	−	0.344457i
$969$	5.03985	+	3.43611i	0.161903	+	0.110384i
$970$	6.37790	−	5.91783i	0.204782	−	0.190010i
$971$	48.3246	−	32.9471i	1.55081	−	1.05732i	0.580864	−	0.814001i	$-0.302715\pi$
$971$	48.3246	−	32.9471i	1.55081	−	1.05732i	0.969945	−	0.243323i	$-0.0782374\pi$
$972$	16.2808	−	71.3310i	0.522208	−	2.28794i
$973$	15.7532	+	28.5313i	0.505026	+	0.914671i
$974$	5.81776	+	25.4893i	0.186413	+	0.816729i
$975$	−0.765771	−	0.710531i	−0.0245243	−	0.0227552i
$976$	56.8465	+	8.56823i	1.81961	+	0.274262i
$977$	−12.6343	+	3.89716i	−0.404206	+	0.124681i	−0.490190	−	0.871615i	$-0.663073\pi$
$977$	−12.6343	+	3.89716i	−0.404206	+	0.124681i	0.0859843	+	0.996296i	$0.472597\pi$
$978$	−1.12910	+	15.0668i	−0.0361046	+	0.481783i
$979$	2.49169			0.0796348
$980$	−67.5143	+	42.3440i	−2.15667	+	1.35263i
$981$	13.9446			0.445217
$982$	−7.65071	+	102.092i	−0.244144	+	3.25788i
$983$	−13.0627	+	4.02931i	−0.416635	+	0.128515i	−0.495983	−	0.868332i	$-0.665192\pi$
$983$	−13.0627	+	4.02931i	−0.416635	+	0.128515i	0.0793480	+	0.996847i	$0.474716\pi$
$984$	5.00449	+	0.754306i	0.159537	+	0.0240464i
$985$	−1.15648	−	1.07306i	−0.0368485	−	0.0341904i
$986$	−24.4948	−	107.319i	−0.780074	−	3.41773i
$987$	−16.9112	−	12.0097i	−0.538288	−	0.382272i
$988$	1.21234	−	5.31161i	0.0385697	−	0.168985i
$989$	−8.02239	+	5.46958i	−0.255097	+	0.173922i
$990$	6.00700	−	5.57368i	0.190915	−	0.177143i
$991$	22.6269	+	15.4268i	0.718767	+	0.490047i	0.866624	−	0.498962i	$-0.166285\pi$
$991$	22.6269	+	15.4268i	0.718767	+	0.490047i	−0.147857	+	0.989009i	$0.547238\pi$
$992$	−41.8524	+	6.30823i	−1.32881	+	0.200286i
$993$	−5.97275	+	2.87632i	−0.189539	+	0.0912774i
$994$	−0.313062	−	0.00598485i	−0.00992973	−	0.000189828i
$995$	−40.4711	−	19.4899i	−1.28302	−	0.617871i
$996$	−42.5529	−	13.1258i	−1.34834	−	0.415908i
$997$	12.9555	−	33.0101i	0.410305	−	1.04544i	−0.565101	−	0.825022i	$-0.691163\pi$
$997$	12.9555	−	33.0101i	0.410305	−	1.04544i	0.975406	−	0.220418i	$-0.0707421\pi$
$998$	0.672262	+	1.16439i	0.0212801	+	0.0368582i
$999$	7.98205	−	13.8253i	0.252541	−	0.437414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.23.4	✓	48
3.2	odd	2		441.2.bb.d.415.1		48
4.3	odd	2		784.2.bg.c.513.3		48
7.2	even	3		343.2.e.d.148.1		48
7.3	odd	6		343.2.g.h.263.4		48
7.4	even	3		343.2.g.i.263.4		48
7.5	odd	6		343.2.e.c.148.1		48
7.6	odd	2		343.2.g.g.275.4		48
49.9	even	21		2401.2.a.h.1.23		24
49.12	odd	42		343.2.e.c.197.1		48
49.17	odd	42		343.2.g.g.116.4		48
49.20	odd	14		343.2.g.h.30.4		48
49.29	even	7		343.2.g.i.30.4		48
49.32	even	21	inner	49.2.g.a.32.4	yes	48
49.37	even	21		343.2.e.d.197.1		48
49.40	odd	42		2401.2.a.i.1.23		24
147.32	odd	42		441.2.bb.d.424.1		48
196.179	odd	42		784.2.bg.c.81.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.4	✓	48	1.1	even	1	trivial
49.2.g.a.32.4	yes	48	49.32	even	21	inner
343.2.e.c.148.1		48	7.5	odd	6
343.2.e.c.197.1		48	49.12	odd	42
343.2.e.d.148.1		48	7.2	even	3
343.2.e.d.197.1		48	49.37	even	21
343.2.g.g.116.4		48	49.17	odd	42
343.2.g.g.275.4		48	7.6	odd	2
343.2.g.h.30.4		48	49.20	odd	14
343.2.g.h.263.4		48	7.3	odd	6
343.2.g.i.30.4		48	49.29	even	7
343.2.g.i.263.4		48	7.4	even	3
441.2.bb.d.415.1		48	3.2	odd	2
441.2.bb.d.424.1		48	147.32	odd	42
784.2.bg.c.81.3		48	196.179	odd	42
784.2.bg.c.513.3		48	4.3	odd	2
2401.2.a.h.1.23		24	49.9	even	21
2401.2.a.i.1.23		24	49.40	odd	42

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.192191 - 2.56461i) q^{2} +(-0.776689 + 0.239577i) q^{3} +(-4.56263 - 0.687706i) q^{4} +(1.80872 + 1.67825i) q^{5} +(0.465149 + 2.03795i) q^{6} +(1.97351 - 1.76217i) q^{7} +(-1.49604 + 6.55456i) q^{8} +(-1.93287 + 1.31781i) q^{9} +O(q^{10})\)	\(q+(0.192191 - 2.56461i) q^{2} +(-0.776689 + 0.239577i) q^{3} +(-4.56263 - 0.687706i) q^{4} +(1.80872 + 1.67825i) q^{5} +(0.465149 + 2.03795i) q^{6} +(1.97351 - 1.76217i) q^{7} +(-1.49604 + 6.55456i) q^{8} +(-1.93287 + 1.31781i) q^{9} +(4.65167 - 4.31612i) q^{10} +(-0.456097 - 0.310962i) q^{11} +(3.70850 - 0.558967i) q^{12} +(1.06432 - 0.512550i) q^{13} +(-4.13999 - 5.39997i) q^{14} +(-1.80688 - 0.870148i) q^{15} +(7.70403 + 2.37638i) q^{16} +(-2.74302 + 6.98911i) q^{17} +(3.00818 + 5.21032i) q^{18} +(-0.499767 + 0.865623i) q^{19} +(-7.09838 - 8.90108i) q^{20} +(-1.11063 + 1.84147i) q^{21} +(-0.885154 + 1.10995i) q^{22} +(-0.831710 - 2.11916i) q^{23} +(-0.408366 - 5.44927i) q^{24} +(0.0813043 + 1.08493i) q^{25} +(-1.10994 - 2.82807i) q^{26} +(2.70584 - 3.39301i) q^{27} +(-10.2163 + 6.68293i) q^{28} +(-3.55438 - 4.45705i) q^{29} +(-2.57886 + 4.46671i) q^{30} +(-2.90369 - 5.02934i) q^{31} +(2.66266 - 6.78436i) q^{32} +(0.428745 + 0.132250i) q^{33} +(17.3972 + 8.37803i) q^{34} +(6.52689 + 0.124775i) q^{35} +(9.72523 - 4.68342i) q^{36} +(3.63743 - 0.548254i) q^{37} +(2.12393 + 1.44807i) q^{38} +(-0.703851 + 0.653078i) q^{39} +(-13.7061 + 9.34464i) q^{40} +(-0.206089 + 0.902934i) q^{41} +(4.50919 + 3.20225i) q^{42} +(-0.949065 - 4.15812i) q^{43} +(1.86715 + 1.73247i) q^{44} +(-5.70762 - 0.860285i) q^{45} +(-5.59467 + 1.72573i) q^{46} +(-0.720789 + 9.61826i) q^{47} -6.55296 q^{48} +(0.789523 - 6.95533i) q^{49} +2.79805 q^{50} +(0.456047 - 6.08553i) q^{51} +(-5.20858 + 1.60664i) q^{52} +(7.73830 + 1.16636i) q^{53} +(-8.18172 - 7.59153i) q^{54} +(-0.303081 - 1.32789i) q^{55} +(8.59779 + 15.5718i) q^{56} +(0.180781 - 0.792052i) q^{57} +(-12.1137 + 8.25900i) q^{58} +(2.03470 - 1.88792i) q^{59} +(7.64573 + 5.21277i) q^{60} +(7.05098 - 1.06276i) q^{61} +(-13.4564 + 6.48024i) q^{62} +(-1.49235 + 6.00675i) q^{63} +(-2.35990 - 1.13647i) q^{64} +(2.78524 + 0.859133i) q^{65} +(0.421572 - 1.07415i) q^{66} +(-1.62615 - 2.81657i) q^{67} +(17.3219 - 30.0023i) q^{68} +(1.15368 + 1.44667i) q^{69} +(1.57441 - 16.7149i) q^{70} +(0.0286915 - 0.0359779i) q^{71} +(-5.74601 - 14.6406i) q^{72} +(0.624885 + 8.33852i) q^{73} +(-0.706977 - 9.43396i) q^{74} +(-0.323073 - 0.823175i) q^{75} +(2.87555 - 3.60582i) q^{76} +(-1.44808 + 0.190033i) q^{77} +(1.53962 + 1.93062i) q^{78} +(-2.93822 + 5.08914i) q^{79} +(9.94627 + 17.2275i) q^{80} +(1.27528 - 3.24937i) q^{81} +(2.27607 + 0.702073i) q^{82} +(-10.6979 - 5.15183i) q^{83} +(6.33379 - 7.63814i) q^{84} +(-16.6908 + 8.03787i) q^{85} +(-10.8464 + 1.63483i) q^{86} +(3.82845 + 2.61020i) q^{87} +(2.72056 - 2.52431i) q^{88} +(-3.72947 + 2.54271i) q^{89} +(-3.30325 + 14.4725i) q^{90} +(1.19725 - 2.88704i) q^{91} +(2.33743 + 10.2409i) q^{92} +(3.46017 + 3.21057i) q^{93} +(24.5286 + 3.69709i) q^{94} +(-2.35667 + 0.726935i) q^{95} +(-0.442687 + 5.90725i) q^{96} +1.37110 q^{97} +(-17.6860 - 3.36157i) q^{98} +1.29136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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