LMFDB - Embedded newform 43.2.g.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	43.23
Dual form			43.2.g.a.15.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0594739 - 0.0745779i) q^{2} +(-0.863608 - 2.20044i) q^{3} +(0.443017 - 1.94098i) q^{4} +(-0.284956 + 3.80248i) q^{5} +(-0.112742 + 0.195275i) q^{6} +(1.30981 + 2.26866i) q^{7} +(-0.342987 + 0.165174i) q^{8} +(-1.89695 + 1.76011i) q^{9} +O(q^{10})$	\(q+(-0.0594739 - 0.0745779i) q^{2} +(-0.863608 - 2.20044i) q^{3} +(0.443017 - 1.94098i) q^{4} +(-0.284956 + 3.80248i) q^{5} +(-0.112742 + 0.195275i) q^{6} +(1.30981 + 2.26866i) q^{7} +(-0.342987 + 0.165174i) q^{8} +(-1.89695 + 1.76011i) q^{9} +(0.300528 - 0.204897i) q^{10} +(-0.456380 - 1.99953i) q^{11} +(-4.65361 + 0.701419i) q^{12} +(-1.76837 - 1.20566i) q^{13} +(0.0912923 - 0.232609i) q^{14} +(8.61320 - 2.65682i) q^{15} +(-3.55476 - 1.71188i) q^{16} +(0.388739 + 5.18736i) q^{17} +(0.244084 + 0.0367898i) q^{18} +(-0.603144 - 0.559636i) q^{19} +(7.25431 + 2.23766i) q^{20} +(3.86088 - 4.84139i) q^{21} +(-0.121978 + 0.152956i) q^{22} +(-2.60979 - 0.805013i) q^{23} +(0.659661 + 0.612076i) q^{24} +(-9.43347 - 1.42187i) q^{25} +(0.0152567 + 0.203587i) q^{26} +(-0.878006 - 0.422825i) q^{27} +(4.98370 - 1.53727i) q^{28} +(1.43632 - 3.65969i) q^{29} +(-0.710401 - 0.484343i) q^{30} +(7.40600 - 1.11627i) q^{31} +(0.253169 + 1.10920i) q^{32} +(-4.00571 + 2.73104i) q^{33} +(0.363743 - 0.337504i) q^{34} +(-8.99976 + 4.33406i) q^{35} +(2.57597 + 4.46171i) q^{36} +(-0.431097 + 0.746681i) q^{37} +(-0.00586515 + 0.0782650i) q^{38} +(-1.12579 + 4.93241i) q^{39} +(-0.530334 - 1.35127i) q^{40} +(-2.40977 - 3.02176i) q^{41} -0.590682 q^{42} +(3.37563 + 5.62185i) q^{43} -4.08324 q^{44} +(-6.15223 - 7.71466i) q^{45} +(0.0951781 + 0.242510i) q^{46} +(-0.00195677 + 0.00857316i) q^{47} +(-0.696971 + 9.30043i) q^{48} +(0.0687935 - 0.119154i) q^{49} +(0.455006 + 0.788093i) q^{50} +(11.0787 - 5.33524i) q^{51} +(-3.12358 + 2.89826i) q^{52} +(3.12892 - 2.13326i) q^{53} +(0.0206850 + 0.0906269i) q^{54} +(7.73321 - 1.16559i) q^{55} +(-0.823971 - 0.561774i) q^{56} +(-0.710564 + 1.81049i) q^{57} +(-0.358356 + 0.110538i) q^{58} +(-3.54096 - 1.70524i) q^{59} +(-1.34105 - 17.8951i) q^{60} +(6.20973 + 0.935966i) q^{61} +(-0.523713 - 0.485935i) q^{62} +(-6.47773 - 1.99812i) q^{63} +(-4.85228 + 6.08457i) q^{64} +(5.08839 - 6.38064i) q^{65} +(0.441911 + 0.136311i) q^{66} +(-9.35418 - 8.67941i) q^{67} +(10.2408 + 1.54355i) q^{68} +(0.482453 + 6.43789i) q^{69} +(0.858476 + 0.413420i) q^{70} +(-0.220622 + 0.0680530i) q^{71} +(0.359905 - 0.917022i) q^{72} +(9.06930 + 6.18335i) q^{73} +(0.0813249 - 0.0122578i) q^{74} +(5.01809 + 21.9857i) q^{75} +(-1.35345 + 0.922766i) q^{76} +(3.93848 - 3.65437i) q^{77} +(0.434804 - 0.209390i) q^{78} +(-0.133642 - 0.231475i) q^{79} +(7.52235 - 13.0291i) q^{80} +(-0.752294 + 10.0387i) q^{81} +(-0.0820379 + 0.359432i) q^{82} +(-3.09474 - 7.88527i) q^{83} +(-7.68662 - 9.63872i) q^{84} -19.8356 q^{85} +(0.218504 - 0.586100i) q^{86} -9.29333 q^{87} +(0.486802 + 0.610431i) q^{88} +(5.18366 + 13.2077i) q^{89} +(-0.209446 + 0.917642i) q^{90} +(0.418989 - 5.59101i) q^{91} +(-2.71870 + 4.70892i) q^{92} +(-8.85217 - 15.3324i) q^{93} +(0.000755745 - 0.000363948i) q^{94} +(2.29987 - 2.13397i) q^{95} +(2.22210 - 1.51500i) q^{96} +(1.14326 + 5.00894i) q^{97} +(-0.0129777 + 0.00195607i) q^{98} +(4.38512 + 2.98973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{21}\right)$

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 $

$2$	−0.0594739	−	0.0745779i	−0.0420544	−	0.0527346i	0.760360	−	0.649502i	$-0.225023\pi$
$2$	−0.0594739	−	0.0745779i	−0.0420544	−	0.0527346i	−0.802414	+	0.596768i	$0.796451\pi$
$3$	−0.863608	−	2.20044i	−0.498604	−	1.27042i	−0.929767	−	0.368149i	$-0.879992\pi$
$3$	−0.863608	−	2.20044i	−0.498604	−	1.27042i	0.431163	−	0.902274i	$-0.358104\pi$
$4$	0.443017	−	1.94098i	0.221509	−	0.970492i
$5$	−0.284956	+	3.80248i	−0.127436	+	1.70052i	0.457313	+	0.889306i	$0.348812\pi$
$5$	−0.284956	+	3.80248i	−0.127436	+	1.70052i	−0.584750	+	0.811214i	$0.698807\pi$
$6$	−0.112742	+	0.195275i	−0.0460267	+	0.0797206i
$7$	1.30981	+	2.26866i	0.495062	+	0.857472i	0.999984	−	0.00569279i	$-0.00181208\pi$
$7$	1.30981	+	2.26866i	0.495062	+	0.857472i	−0.504922	+	0.863165i	$0.668479\pi$
$8$	−0.342987	+	0.165174i	−0.121264	+	0.0583978i
$9$	−1.89695	+	1.76011i	−0.632316	+	0.586704i
$10$	0.300528	−	0.204897i	0.0950354	−	0.0647940i
$11$	−0.456380	−	1.99953i	−0.137604	−	0.602881i	−0.995958	−	0.0898231i	$-0.971370\pi$
$11$	−0.456380	−	1.99953i	−0.137604	−	0.602881i	0.858354	−	0.513058i	$-0.171487\pi$
$12$	−4.65361	+	0.701419i	−1.34338	+	0.202482i
$13$	−1.76837	−	1.20566i	−0.490458	−	0.334389i	0.292707	−	0.956202i	$-0.405444\pi$
$13$	−1.76837	−	1.20566i	−0.490458	−	0.334389i	−0.783165	+	0.621813i	$0.786396\pi$
$14$	0.0912923	−	0.232609i	0.0243989	−	0.0621673i
$15$	8.61320	−	2.65682i	2.22392	−	0.685988i
$16$	−3.55476	−	1.71188i	−0.888691	−	0.427971i
$17$	0.388739	+	5.18736i	0.0942831	+	1.25812i	0.820898	+	0.571075i	$0.193473\pi$
$17$	0.388739	+	5.18736i	0.0942831	+	1.25812i	−0.726615	+	0.687045i	$0.758908\pi$
$18$	0.244084	+	0.0367898i	0.0575312	+	0.00867144i
$19$	−0.603144	−	0.559636i	−0.138371	−	0.128389i	0.607951	−	0.793974i	$-0.291992\pi$
$19$	−0.603144	−	0.559636i	−0.138371	−	0.128389i	−0.746322	+	0.665585i	$0.768182\pi$
$20$	7.25431	+	2.23766i	1.62211	+	0.500356i
$21$	3.86088	−	4.84139i	0.842512	−	1.05648i
$22$	−0.121978	+	0.152956i	−0.0260058	+	0.0326103i
$23$	−2.60979	−	0.805013i	−0.544178	−	0.167857i	0.0104646	−	0.999945i	$-0.496669\pi$
$23$	−2.60979	−	0.805013i	−0.544178	−	0.167857i	−0.554643	+	0.832088i	$0.687145\pi$
$24$	0.659661	+	0.612076i	0.134653	+	0.124940i
$25$	−9.43347	−	1.42187i	−1.88669	−	0.284373i
$26$	0.0152567	+	0.203587i	0.00299209	+	0.0399266i
$27$	−0.878006	−	0.422825i	−0.168972	−	0.0813728i
$28$	4.98370	−	1.53727i	0.941831	−	0.290516i
$29$	1.43632	−	3.65969i	0.266718	−	0.679587i	−0.733282	−	0.679925i	$-0.762012\pi$
$29$	1.43632	−	3.65969i	0.266718	−	0.679587i	1.00000		0.000337849i	$0.000107541\pi$
$30$	−0.710401	−	0.484343i	−0.129701	−	0.0884286i
$31$	7.40600	−	1.11627i	1.33016	−	0.200489i	0.554785	−	0.831994i	$-0.312801\pi$
$31$	7.40600	−	1.11627i	1.33016	−	0.200489i	0.775372	+	0.631505i	$0.217562\pi$
$32$	0.253169	+	1.10920i	0.0447543	+	0.196081i
$33$	−4.00571	+	2.73104i	−0.697304	+	0.475414i
$34$	0.363743	−	0.337504i	0.0623814	−	0.0578815i
$35$	−8.99976	+	4.33406i	−1.52124	+	0.732589i
$36$	2.57597	+	4.46171i	0.429328	+	0.743618i
$37$	−0.431097	+	0.746681i	−0.0708719	+	0.122754i	−0.899284	−	0.437366i	$-0.855911\pi$
$37$	−0.431097	+	0.746681i	−0.0708719	+	0.122754i	0.828412	+	0.560120i	$0.189245\pi$
$38$	−0.00586515	+	0.0782650i	−0.000951453	+	0.0126963i
$39$	−1.12579	+	4.93241i	−0.180271	+	0.789817i
$40$	−0.530334	−	1.35127i	−0.0838531	−	0.213654i
$41$	−2.40977	−	3.02176i	−0.376343	−	0.471920i	0.557203	−	0.830376i	$-0.311874\pi$
$41$	−2.40977	−	3.02176i	−0.376343	−	0.471920i	−0.933546	+	0.358457i	$0.883303\pi$
$42$	−0.590682			−0.0911442
$43$	3.37563	+	5.62185i	0.514778	+	0.857323i
$43$	3.37563	+	5.62185i	0.514778	+	0.857323i
$44$	−4.08324			−0.615572
$45$	−6.15223	−	7.71466i	−0.917121	−	1.15003i
$46$	0.0951781	+	0.242510i	0.0140332	+	0.0357561i
$47$	−0.00195677	+	0.00857316i	−0.000285424	+	0.00125052i	−0.975070	−	0.221896i	$-0.928776\pi$
$47$	−0.00195677	+	0.00857316i	−0.000285424	+	0.00125052i	0.974785	+	0.223146i	$0.0716327\pi$
$48$	−0.696971	+	9.30043i	−0.100599	+	1.34240i
$49$	0.0687935	−	0.119154i	0.00982764	−	0.0170220i
$50$	0.455006	+	0.788093i	0.0643475	+	0.111453i
$51$	11.0787	−	5.33524i	1.55133	−	0.747083i
$52$	−3.12358	+	2.89826i	−0.433163	+	0.401916i
$53$	3.12892	−	2.13326i	0.429790	−	0.293026i	−0.329038	−	0.944317i	$-0.606724\pi$
$53$	3.12892	−	2.13326i	0.429790	−	0.293026i	0.758828	+	0.651291i	$0.225772\pi$
$54$	0.0206850	+	0.0906269i	0.00281487	+	0.0123328i
$55$	7.73321	−	1.16559i	1.04275	−	0.157169i
$56$	−0.823971	−	0.561774i	−0.110108	−	0.0750702i
$57$	−0.710564	+	1.81049i	−0.0941165	+	0.239805i
$58$	−0.358356	+	0.110538i	−0.0470544	+	0.0145144i
$59$	−3.54096	−	1.70524i	−0.460993	−	0.222003i	0.188948	−	0.981987i	$-0.439492\pi$
$59$	−3.54096	−	1.70524i	−0.460993	−	0.222003i	−0.649941	+	0.759984i	$0.725207\pi$
$60$	−1.34105	−	17.8951i	−0.173129	−	2.31025i
$61$	6.20973	+	0.935966i	0.795075	+	0.119838i	0.534004	−	0.845482i	$-0.320687\pi$
$61$	6.20973	+	0.935966i	0.795075	+	0.119838i	0.261070	+	0.965320i	$0.415925\pi$
$62$	−0.523713	−	0.485935i	−0.0665117	−	0.0617138i
$63$	−6.47773	−	1.99812i	−0.816118	−	0.251739i
$64$	−4.85228	+	6.08457i	−0.606535	+	0.760571i
$65$	5.08839	−	6.38064i	0.631137	−	0.791420i
$66$	0.441911	+	0.136311i	0.0543954	+	0.0167788i
$67$	−9.35418	−	8.67941i	−1.14279	−	1.06036i	−0.997478	−	0.0709734i	$-0.977389\pi$
$67$	−9.35418	−	8.67941i	−1.14279	−	1.06036i	−0.145317	−	0.989385i	$-0.546420\pi$
$68$	10.2408	+	1.54355i	1.24188	+	0.187183i
$69$	0.482453	+	6.43789i	0.0580805	+	0.775031i
$70$	0.858476	+	0.413420i	0.102607	+	0.0494132i
$71$	−0.220622	+	0.0680530i	−0.0261830	+	0.00807640i	−0.307819	−	0.951445i	$-0.599599\pi$
$71$	−0.220622	+	0.0680530i	−0.0261830	+	0.00807640i	0.281636	+	0.959521i	$0.409123\pi$
$72$	0.359905	−	0.917022i	0.0424152	−	0.108072i
$73$	9.06930	+	6.18335i	1.06148	+	0.723706i	0.962472	−	0.271380i	$-0.0874801\pi$
$73$	9.06930	+	6.18335i	1.06148	+	0.723706i	0.0990097	+	0.995086i	$0.468433\pi$
$74$	0.0813249	−	0.0122578i	0.00945383	−	0.00142494i
$75$	5.01809	+	21.9857i	0.579439	+	2.53869i
$76$	−1.35345	+	0.922766i	−0.155251	+	0.105849i
$77$	3.93848	−	3.65437i	0.448831	−	0.416455i
$78$	0.434804	−	0.209390i	0.0492318	−	0.0237088i
$79$	−0.133642	−	0.231475i	−0.0150359	−	0.0260430i	0.858410	−	0.512965i	$-0.171453\pi$
$79$	−0.133642	−	0.231475i	−0.0150359	−	0.0260430i	−0.873445	+	0.486922i	$0.838120\pi$
$80$	7.52235	−	13.0291i	0.841024	−	1.45670i
$81$	−0.752294	+	10.0387i	−0.0835883	+	1.11541i
$82$	−0.0820379	+	0.359432i	−0.00905957	+	0.0396926i
$83$	−3.09474	−	7.88527i	−0.339692	−	0.865521i	−0.994009	−	0.109300i	$-0.965139\pi$
$83$	−3.09474	−	7.88527i	−0.339692	−	0.865521i	0.654317	−	0.756220i	$-0.272956\pi$
$84$	−7.68662	−	9.63872i	−0.838679	−	1.05167i
$85$	−19.8356			−2.15147
$86$	0.218504	−	0.586100i	0.0235619	−	0.0632008i
$87$	−9.29333			−0.996350
$88$	0.486802	+	0.610431i	0.0518933	+	0.0650722i
$89$	5.18366	+	13.2077i	0.549466	+	1.40002i	0.888340	+	0.459186i	$0.151859\pi$
$89$	5.18366	+	13.2077i	0.549466	+	1.40002i	−0.338874	+	0.940832i	$0.610046\pi$
$90$	−0.209446	+	0.917642i	−0.0220775	+	0.0967279i
$91$	0.418989	−	5.59101i	0.0439219	−	0.586097i
$92$	−2.71870	+	4.70892i	−0.283444	+	0.490939i
$93$	−8.85217	−	15.3324i	−0.917928	−	1.58990i
$94$	0.000755745	0	0.000363948i	7.79492e−5	0	3.75383e-5i
$95$	2.29987	−	2.13397i	0.235962	−	0.218941i
$96$	2.22210	−	1.51500i	0.226792	−	0.154624i
$97$	1.14326	+	5.00894i	0.116080	+	0.508581i	0.999221	+	0.0394720i	$0.0125676\pi$
$97$	1.14326	+	5.00894i	0.116080	+	0.508581i	−0.883140	+	0.469109i	$0.844575\pi$
$98$	−0.0129777	+	0.00195607i	−0.00131094	+	0.000197593i
$99$	4.38512	+	2.98973i	0.440721	+	0.300479i
$100$	−6.93901	+	17.6803i	−0.693901	+	1.76803i
$101$	−11.8407	+	3.65237i	−1.17819	+	0.363424i	−0.821177	−	0.570674i	$-0.806682\pi$
$101$	−11.8407	+	3.65237i	−1.17819	+	0.363424i	−0.357016	+	0.934098i	$0.616206\pi$
$102$	−1.05679	−	0.508922i	−0.104638	−	0.0503908i
$103$	0.430401	+	5.74330i	0.0424087	+	0.565904i	0.977423	+	0.211294i	$0.0677676\pi$
$103$	0.430401	+	5.74330i	0.0424087	+	0.565904i	−0.935014	+	0.354611i	$0.884613\pi$
$104$	0.805672	+	0.121436i	0.0790026	+	0.0119077i
$105$	17.3091	+	16.0605i	1.68919	+	1.56734i
$106$	−0.345183	−	0.106475i	−0.0335272	−	0.0103418i
$107$	7.57872	−	9.50341i	0.732663	−	0.918730i	−0.266317	−	0.963885i	$-0.585807\pi$
$107$	7.57872	−	9.50341i	0.732663	−	0.918730i	0.998980	+	0.0451556i	$0.0143784\pi$
$108$	−1.20967	+	1.51688i	−0.116400	+	0.145962i
$109$	16.9178	+	5.21845i	1.62043	+	0.499837i	0.966489	−	0.256707i	$-0.0826376\pi$
$109$	16.9178	+	5.21845i	1.62043	+	0.499837i	0.653943	+	0.756544i	$0.273114\pi$
$110$	−0.546852	−	0.507405i	−0.0521403	−	0.0483791i
$111$	2.01532	+	0.303761i	0.191286	+	0.0288317i
$112$	−0.772387	−	10.3068i	−0.0729837	−	0.973900i
$113$	−10.2255	−	4.92435i	−0.961935	−	0.463243i	−0.114080	−	0.993472i	$-0.536392\pi$
$113$	−10.2255	−	4.92435i	−0.961935	−	0.463243i	−0.847855	+	0.530228i	$0.822106\pi$
$114$	0.177282	−	0.0546844i	0.0166040	−	0.00512166i
$115$	3.80472	−	9.69426i	0.354792	−	0.903995i
$116$	−6.46709	−	4.40918i	−0.600454	−	0.409383i
$117$	5.47660	−	0.825465i	0.506312	−	0.0763142i
$118$	0.0834217	+	0.365494i	0.00767959	+	0.0336465i
$119$	−11.2592	+	7.67638i	−1.03213	+	0.703692i
$120$	−2.51538	+	2.33393i	−0.229622	+	0.213058i
$121$	6.12082	−	2.94763i	0.556438	−	0.267967i
$122$	−0.299515	−	0.518774i	−0.0271168	−	0.0469676i
$123$	−4.56809	+	7.91217i	−0.411891	+	0.713416i
$124$	1.11431	−	14.8695i	0.100068	−	1.33532i
$125$	3.85223	−	16.8777i	0.344554	−	1.50959i
$126$	0.236241	+	0.601932i	0.0210460	+	0.0536243i
$127$	−0.918776	−	1.15211i	−0.0815281	−	0.102233i	0.739395	−	0.673272i	$-0.235112\pi$
$127$	−0.918776	−	1.15211i	−0.0815281	−	0.102233i	−0.820923	+	0.571039i	$0.806540\pi$
$128$	3.01782			0.266740
$129$	9.45530	−	12.2829i	0.832493	−	1.08145i
$130$	−0.778481			−0.0682773
$131$	−8.27923	−	10.3818i	−0.723359	−	0.907064i	0.275163	−	0.961397i	$-0.411268\pi$
$131$	−8.27923	−	10.3818i	−0.723359	−	0.907064i	−0.998523	+	0.0543335i	$0.982697\pi$
$132$	3.52632	+	8.98491i	0.306927	+	0.782036i
$133$	0.479619	−	2.10135i	0.0415882	−	0.182210i
$134$	−0.0909628	+	1.21381i	−0.00785799	+	0.104858i
$135$	1.85798	−	3.21811i	0.159909	−	0.276971i
$136$	−0.990149	−	1.71499i	−0.0849046	−	0.147059i
$137$	1.72976	−	0.833009i	0.147783	−	0.0711688i	−0.358530	−	0.933518i	$-0.616722\pi$
$137$	1.72976	−	0.833009i	0.147783	−	0.0711688i	0.506314	+	0.862349i	$0.331008\pi$
$138$	0.451431	−	0.418867i	0.0384284	−	0.0356563i
$139$	−4.65402	+	3.17306i	−0.394749	+	0.269135i	−0.744386	−	0.667750i	$-0.767258\pi$
$139$	−4.65402	+	3.17306i	−0.394749	+	0.269135i	0.349636	+	0.936885i	$0.386305\pi$
$140$	4.42529	+	19.3885i	0.374005	+	1.63862i
$141$	0.0205546	−	0.00309811i	0.00173101	−	0.000260908i
$142$	0.0181965	+	0.0124062i	0.00152702	+	0.00104110i
$143$	−1.60370	+	4.08615i	−0.134108	+	0.341701i
$144$	9.75631	−	3.00942i	0.813026	−	0.250785i
$145$	13.5066	+	6.50443i	1.12166	+	0.540164i
$146$	−0.0782458	−	1.04412i	−0.00647567	−	0.0864118i
$147$	−0.321601	−	0.0484735i	−0.0265252	−	0.00399803i
$148$	1.25831	+	1.16754i	0.103433	+	0.0959716i
$149$	−2.22130	−	0.685179i	−0.181976	−	0.0561321i	0.202428	−	0.979297i	$-0.435117\pi$
$149$	−2.22130	−	0.685179i	−0.181976	−	0.0561321i	−0.384404	+	0.923165i	$0.625593\pi$
$150$	1.34120	−	1.68181i	0.109509	−	0.137320i
$151$	−3.04914	+	3.82350i	−0.248135	+	0.311152i	−0.890264	−	0.455445i	$-0.849480\pi$
$151$	−3.04914	+	3.82350i	−0.248135	+	0.311152i	0.642129	+	0.766597i	$0.278052\pi$
$152$	0.299308	+	0.0923243i	0.0242771	+	0.00748849i
$153$	−9.86775	−	9.15594i	−0.797760	−	0.740214i
$154$	−0.506772	−	0.0763836i	−0.0408369	−	0.00615517i
$155$	2.13422	+	28.4792i	0.171425	+	2.28751i
$156$	9.07498	+	4.37028i	0.726580	+	0.349903i
$157$	−17.4687	+	5.38839i	−1.39416	+	0.430040i	−0.898689	−	0.438587i	$-0.855479\pi$
$157$	−17.4687	+	5.38839i	−1.39416	+	0.430040i	−0.495467	+	0.868627i	$0.665003\pi$
$158$	−0.00931472	+	0.0237335i	−0.000741039	+	0.00188814i
$159$	−7.39627	−	5.04269i	−0.586562	−	0.399911i
$160$	−4.28986	+	0.646593i	−0.339144	+	0.0511177i
$161$	−1.59203	−	6.97513i	−0.125469	−	0.549717i
$162$	0.793405	−	0.540934i	0.0623358	−	0.0424998i
$163$	−7.38410	+	6.85144i	−0.578367	+	0.536646i	−0.914194	−	0.405278i	$-0.867175\pi$
$163$	−7.38410	+	6.85144i	−0.578367	+	0.536646i	0.335827	+	0.941924i	$0.390984\pi$
$164$	−6.93276	+	3.33864i	−0.541358	+	0.260704i
$165$	−9.24328	−	16.0098i	−0.719588	−	1.24636i
$166$	−0.404011	+	0.699767i	−0.0313573	+	0.0543125i
$167$	−0.122345	+	1.63258i	−0.00946733	+	0.126333i	−0.999935	−	0.0114137i	$-0.996367\pi$
$167$	−0.122345	+	1.63258i	−0.00946733	+	0.126333i	0.990468	+	0.137746i	$0.0439859\pi$
$168$	−0.524560	+	2.29825i	−0.0404707	+	0.177314i
$169$	−3.07590	−	7.83726i	−0.236608	−	0.602866i
$170$	1.17970	+	1.47930i	0.0904789	+	0.113457i
$171$	2.12916			0.162821
$172$	12.4074	−	4.06147i	0.946054	−	0.309684i
$173$	19.9781			1.51891			0.759453	−	0.650562i	$-0.225467\pi$
$173$	19.9781			1.51891			0.759453	+	0.650562i	$0.225467\pi$
$174$	0.552711	+	0.693078i	0.0419009	+	0.0525421i
$175$	−9.13033	−	23.2637i	−0.690188	−	1.75857i
$176$	−1.80064	+	7.88912i	−0.135728	+	0.594665i
$177$	−0.694264	+	9.26431i	−0.0521841	+	0.696348i
$178$	0.676714	−	1.17210i	0.0507218	−	0.0878528i
$179$	8.33106	+	14.4298i	0.622693	+	1.07854i	0.988982	+	0.148035i	$0.0472948\pi$
$179$	8.33106	+	14.4298i	0.622693	+	1.07854i	−0.366289	+	0.930501i	$0.619372\pi$
$180$	−17.6996	+	8.52367i	−1.31925	+	0.635317i
$181$	−19.0185	+	17.6466i	−1.41364	+	1.31166i	−0.526484	+	0.850185i	$0.676490\pi$
$181$	−19.0185	+	17.6466i	−1.41364	+	1.31166i	−0.887152	+	0.461478i	$0.847319\pi$
$182$	−0.441885	+	0.301272i	−0.0327547	+	0.0223318i
$183$	−3.30324	−	14.4724i	−0.244182	−	1.06983i
$184$	1.02809	−	0.154960i	0.0757919	−	0.0114238i
$185$	−2.71639	−	1.85201i	−0.199713	−	0.136162i
$186$	−0.616986	+	1.57206i	−0.0452396	+	0.115269i
$187$	10.1949	−	3.14470i	0.745523	−	0.229963i
$188$	0.0157735	+	0.00759612i	0.00115040	+	0.000554004i
$189$	−0.190775	−	2.54572i	−0.0138768	−	0.185174i
$190$	−0.295930	−	0.0446042i	−0.0214690	−	0.00323593i
$191$	−3.45551	−	3.20625i	−0.250032	−	0.231996i	0.545192	−	0.838311i	$-0.316457\pi$
$191$	−3.45551	−	3.20625i	−0.250032	−	0.231996i	−0.795225	+	0.606315i	$0.792647\pi$
$192$	17.5792	+	5.42246i	1.26867	+	0.391332i
$193$	9.91603	−	12.4343i	0.713772	−	0.895041i	−0.284196	−	0.958766i	$-0.591727\pi$
$193$	9.91603	−	12.4343i	0.713772	−	0.895041i	0.997968	+	0.0637249i	$0.0202980\pi$
$194$	0.305562	−	0.383163i	0.0219381	−	0.0275095i
$195$	−18.4346	−	5.68631i	−1.32013	−	0.407205i
$196$	−0.200799	−	0.186314i	−0.0143428	−	0.0133082i
$197$	23.4639	+	3.53661i	1.67173	+	0.251973i	0.915497	−	0.402326i	$-0.131798\pi$
$197$	23.4639	+	3.53661i	1.67173	+	0.251973i	0.756236	+	0.654299i	$0.227036\pi$
$198$	−0.0378328	−	0.504844i	−0.00268866	−	0.0358777i
$199$	5.32234	+	2.56311i	0.377291	+	0.181694i	0.612912	−	0.790151i	$-0.289998\pi$
$199$	5.32234	+	2.56311i	0.377291	+	0.181694i	−0.235621	+	0.971845i	$0.575712\pi$
$200$	3.47042	−	1.07048i	0.245395	−	0.0756945i
$201$	−11.0202	+	28.0789i	−0.777302	+	1.98053i
$202$	0.976599	+	0.665834i	0.0687132	+	0.0468479i
$203$	10.1839	−	1.53497i	0.714769	−	0.107734i
$204$	−5.44755	−	23.8673i	−0.381405	−	1.67104i
$205$	12.1768	−	8.30203i	0.850468	−	0.579839i
$206$	0.402726	−	0.373675i	0.0280592	−	0.0260352i
$207$	6.36755	−	3.06645i	0.442575	−	0.213133i
$208$	4.22220	+	7.31307i	0.292757	+	0.507070i
$209$	−0.843746	+	1.46141i	−0.0583632	+	0.101088i
$210$	0.168319	−	2.24605i	0.0116151	−	0.154992i
$211$	−1.15048	+	5.04059i	−0.0792025	+	0.347009i	−0.998966	−	0.0454644i	$-0.985523\pi$
$211$	−1.15048	+	5.04059i	−0.0792025	+	0.347009i	0.919763	+	0.392473i	$0.128380\pi$
$212$	−2.75446	−	7.01826i	−0.189177	−	0.482016i
$213$	0.340277	+	0.426694i	0.0233154	+	0.0292366i
$214$	−1.15948			−0.0792605
$215$	−22.3388	+	11.2338i	−1.52350	+	0.766136i
$216$	0.370984			0.0252423
$217$	12.2329	+	15.3396i	0.830424	+	1.04132i
$218$	−0.616987	−	1.57206i	−0.0417876	−	0.106473i
$219$	5.77374	−	25.2964i	0.390153	−	1.70937i
$220$	1.16354	−	15.5264i	0.0784462	−	1.04679i
$221$	5.56674	−	9.64187i	0.374459	−	0.648583i
$222$	−0.0972053	−	0.168365i	−0.00652399	−	0.0112999i
$223$	−2.82436	+	1.36014i	−0.189133	+	0.0910818i	−0.526054	−	0.850451i	$-0.676329\pi$
$223$	−2.82436	+	1.36014i	−0.189133	+	0.0910818i	0.336920	+	0.941533i	$0.390615\pi$
$224$	−2.18480	+	2.02720i	−0.145978	+	0.135448i
$225$	20.3975	−	13.9068i	1.35983	−	0.927117i
$226$	0.240904	+	1.05547i	0.0160247	+	0.0702086i
$227$	−18.5881	+	2.80170i	−1.23374	+	0.185956i	−0.733352	−	0.679849i	$-0.762045\pi$
$227$	−18.5881	+	2.80170i	−1.23374	+	0.185956i	−0.500383	+	0.865804i	$0.666807\pi$
$228$	3.19934	+	2.18127i	0.211881	+	0.144458i
$229$	2.99489	−	7.63084i	0.197908	−	0.504260i	−0.797125	−	0.603815i	$-0.793647\pi$
$229$	2.99489	−	7.63084i	0.197908	−	0.504260i	0.995032	+	0.0995547i	$0.0317418\pi$
$230$	−0.949259	+	0.292808i	−0.0625923	+	0.0193072i
$231$	−11.4425	−	5.51043i	−0.752863	−	0.362559i
$232$	0.111845	+	1.49247i	0.00734299	+	0.0979854i
$233$	−6.36645	−	0.959587i	−0.417080	−	0.0628647i	−0.0628498	−	0.998023i	$-0.520019\pi$
$233$	−6.36645	−	0.959587i	−0.417080	−	0.0628647i	−0.354230	+	0.935158i	$0.615257\pi$
$234$	−0.387276	−	0.359340i	−0.0253170	−	0.0234908i
$235$	−0.0320417	−	0.00988354i	−0.00209017	−	0.000644731i
$236$	−4.87854	+	6.11750i	−0.317566	+	0.398215i
$237$	−0.393932	+	0.493976i	−0.0255887	+	0.0320872i
$238$	1.24212	+	0.383142i	0.0805144	+	0.0248354i
$239$	21.2757	+	19.7410i	1.37621	+	1.27694i	0.922612	+	0.385730i	$0.126051\pi$
$239$	21.2757	+	19.7410i	1.37621	+	1.27694i	0.453599	+	0.891206i	$0.350140\pi$
$240$	−35.1661	−	5.30043i	−2.26996	−	0.342141i
$241$	−0.934176	−	12.4657i	−0.0601756	−	0.802987i	−0.942896	−	0.333088i	$-0.891909\pi$
$241$	−0.934176	−	12.4657i	−0.0601756	−	0.802987i	0.882720	−	0.469899i	$-0.155710\pi$
$242$	−0.583858	−	0.281171i	−0.0375318	−	0.0180744i
$243$	19.9455	−	6.15237i	1.27950	−	0.394675i
$244$	4.56771	−	11.6383i	0.292418	−	0.745069i
$245$	0.433476	+	0.295539i	0.0276938	+	0.0188813i
$246$	0.861755	−	0.129889i	0.0549435	−	0.00828140i
$247$	0.391855	+	1.71683i	0.0249332	+	0.109239i
$248$	−2.35578	+	1.60615i	−0.149592	+	0.101990i
$249$	−14.6784	+	13.6196i	−0.930206	+	0.863105i
$250$	−1.48781	+	0.716493i	−0.0940975	+	0.0453150i
$251$	10.3646	+	17.9520i	0.654207	+	1.13312i	0.982092	+	0.188403i	$0.0603310\pi$
$251$	10.3646	+	17.9520i	0.654207	+	1.13312i	−0.327884	+	0.944718i	$0.606336\pi$
$252$	−6.74806	+	11.6880i	−0.425088	+	0.736274i
$253$	−0.418593	+	5.58574i	−0.0263167	+	0.351172i
$254$	−0.0312787	+	0.137041i	−0.00196260	+	0.00859870i
$255$	17.1302	+	43.6470i	1.07273	+	2.73328i
$256$	9.52508	+	11.9441i	0.595317	+	0.746504i
$257$	−13.3077			−0.830114			−0.415057	−	0.909795i	$-0.636238\pi$
$257$	−13.3077			−0.830114			−0.415057	+	0.909795i	$0.636238\pi$
$258$	−1.47838	+	0.0253568i	−0.0920398	+	0.00157865i
$259$	−2.25862			−0.140344
$260$	−10.1305	−	12.7032i	−0.628265	−	0.787820i
$261$	3.71683	+	9.47033i	0.230066	+	0.586199i
$262$	−0.281857	+	1.23490i	−0.0174132	+	0.0762921i
$263$	−0.267233	+	3.56598i	−0.0164783	+	0.219888i	0.982885	+	0.184218i	$0.0589753\pi$
$263$	−0.267233	+	3.56598i	−0.0164783	+	0.219888i	−0.999364	+	0.0356692i	$0.988644\pi$
$264$	0.922808	−	1.59835i	0.0567949	−	0.0983717i
$265$	7.22007	+	12.5055i	0.443526	+	0.768209i
$266$	−0.185239	+	0.0892063i	−0.0113577	+	0.00546959i
$267$	24.5862	−	22.8126i	1.50465	−	1.39611i
$268$	−20.9907	+	14.3112i	−1.28221	+	0.874195i
$269$	−4.97202	−	21.7839i	−0.303150	−	1.32818i	−0.865343	−	0.501179i	$-0.832900\pi$
$269$	−4.97202	−	21.7839i	−0.303150	−	1.32818i	0.562194	−	0.827006i	$-0.309957\pi$
$270$	−0.350501	+	0.0528295i	−0.0213308	+	0.00321510i
$271$	−24.3576	−	16.6067i	−1.47962	−	1.00879i	−0.990642	−	0.136489i	$-0.956418\pi$
$271$	−24.3576	−	16.6067i	−1.47962	−	1.00879i	−0.488976	−	0.872297i	$-0.662630\pi$
$272$	7.49828	−	19.1053i	0.454650	−	1.15843i
$273$	−12.6645	+	3.90649i	−0.766491	+	0.236431i
$274$	−0.165000	−	0.0794597i	−0.00996800	−	0.00480034i
$275$	1.46218	+	19.5114i	0.0881727	+	1.17658i
$276$	12.7096	+	1.91566i	0.765027	+	0.115309i
$277$	−12.8398	−	11.9136i	−0.771468	−	0.715817i	0.192657	−	0.981266i	$-0.438289\pi$
$277$	−12.8398	−	11.9136i	−0.771468	−	0.715817i	−0.964125	+	0.265449i	$0.914480\pi$
$278$	0.513433	+	0.158373i	0.0307937	+	0.00949859i
$279$	−12.0840	+	15.1529i	−0.723452	+	0.907181i
$280$	2.37093	−	2.97305i	0.141690	−	0.177674i
$281$	−16.1799	−	4.99085i	−0.965215	−	0.297729i	−0.228206	−	0.973613i	$-0.573286\pi$
$281$	−16.1799	−	4.99085i	−0.965215	−	0.297729i	−0.737009	+	0.675883i	$0.763762\pi$
$282$	−0.00145351	−	0.00134866i	−8.65554e−5	−	8.03117e-5i
$283$	−16.6158	−	2.50444i	−0.987709	−	0.148873i	−0.364732	−	0.931113i	$-0.618839\pi$
$283$	−16.6158	−	2.50444i	−0.987709	−	0.148873i	−0.622978	+	0.782239i	$0.714077\pi$
$284$	0.0343503	+	0.458373i	0.00203832	+	0.0271994i
$285$	−6.68186	−	3.21781i	−0.395799	−	0.190607i
$286$	0.400115	−	0.123419i	0.0236593	−	0.00729792i
$287$	3.69899	−	9.42488i	0.218345	−	0.556333i
$288$	−2.43257	−	1.65850i	−0.143341	−	0.0977280i
$289$	−9.94748	+	1.49934i	−0.585146	+	0.0881965i
$290$	−0.318203	−	1.39414i	−0.0186855	−	0.0818666i
$291$	10.0345	−	6.84143i	0.588235	−	0.401051i
$292$	16.0196	−	14.8641i	0.937479	−	0.869853i
$293$	14.4540	−	6.96069i	0.844413	−	0.406648i	0.0389122	−	0.999243i	$-0.487611\pi$
$293$	14.4540	−	6.96069i	0.844413	−	0.406648i	0.805501	+	0.592595i	$0.201896\pi$
$294$	0.0155118	+	0.0268672i	0.000904667	+	0.00156693i
$295$	7.49313	−	12.9785i	0.436267	−	0.755637i
$296$	0.0245283	−	0.327308i	0.00142568	−	0.0190244i
$297$	−0.444748	+	1.94857i	−0.0258069	+	0.113067i
$298$	0.0810099	+	0.206410i	0.00469278	+	0.0119570i
$299$	3.64451	+	4.57007i	0.210767	+	0.264294i
$300$	44.8970			2.59213
$301$	−8.33262	+	15.0217i	−0.480284	+	0.865836i
$302$	0.466493			0.0268436
$303$	18.2625	+	22.9005i	1.04915	+	1.31560i
$304$	1.18600	+	3.02189i	0.0680220	+	0.173317i
$305$	−5.32849	+	23.3456i	−0.305109	+	1.33677i
$306$	−0.0959569	+	1.28046i	−0.00548549	+	0.0731988i
$307$	−4.98469	+	8.63374i	−0.284491	+	0.492753i	−0.972486	−	0.232963i	$-0.925158\pi$
$307$	−4.98469	+	8.63374i	−0.284491	+	0.492753i	0.687994	+	0.725716i	$0.258491\pi$
$308$	−5.34827	−	9.26348i	−0.304746	−	0.527836i
$309$	12.2661	−	5.90703i	0.697793	−	0.336039i
$310$	1.99699	−	1.85294i	0.113422	−	0.105240i
$311$	−4.45615	+	3.03815i	−0.252685	+	0.172278i	−0.683038	−	0.730383i	$-0.739342\pi$
$311$	−4.45615	+	3.03815i	−0.252685	+	0.172278i	0.430353	+	0.902661i	$0.358389\pi$
$312$	−0.428574	−	1.87770i	−0.0242632	−	0.106304i
$313$	1.76937	−	0.266690i	0.100011	−	0.0150742i	−0.0988461	−	0.995103i	$-0.531515\pi$
$313$	1.76937	−	0.266690i	0.100011	−	0.0150742i	0.198857	+	0.980029i	$0.436277\pi$
$314$	1.44079	+	0.982312i	0.0813083	+	0.0554351i
$315$	9.44366	−	24.0621i	0.532090	−	1.35574i
$316$	−0.508496	+	0.156850i	−0.0286051	+	0.00882352i
$317$	8.19248	+	3.94529i	0.460136	+	0.221590i	0.649567	−	0.760304i	$-0.274950\pi$
$317$	8.19248	+	3.94529i	0.460136	+	0.221590i	−0.189431	+	0.981894i	$0.560664\pi$
$318$	0.0638116	+	0.851507i	0.00357838	+	0.0477501i
$319$	−7.97316	−	1.20176i	−0.446411	−	0.0672857i
$320$	−21.7537	−	20.1845i	−1.21607	−	1.12835i
$321$	−27.4567	−	8.46927i	−1.53248	−	0.472709i
$322$	−0.425507	+	0.533568i	−0.0237126	+	0.0297346i
$323$	2.66857	−	3.34628i	0.148483	−	0.186192i
$324$	19.1516	+	5.90749i	1.06398	+	0.328194i
$325$	14.9676	+	13.8879i	0.830254	+	0.770363i
$326$	0.950127	+	0.143209i	0.0526227	+	0.00793160i
$327$	−3.12748	−	41.7333i	−0.172950	−	2.30785i
$328$	1.32564	+	0.638393i	0.0731961	+	0.0352494i
$329$	−0.0220126	+	0.00678998i	−0.00121359	+	0.000374344i
$330$	−0.644246	+	1.64151i	−0.0354646	+	0.0903623i
$331$	18.2599	+	12.4494i	1.00365	+	0.684279i	0.949342	−	0.314245i	$-0.101751\pi$
$331$	18.2599	+	12.4494i	1.00365	+	0.684279i	0.0543114	+	0.998524i	$0.482704\pi$
$332$	−16.6762	+	2.51353i	−0.915226	+	0.137948i
$333$	−0.496474	−	2.17519i	−0.0272066	−	0.119200i
$334$	0.129031	−	0.0879716i	0.00706024	−	0.00481359i
$335$	35.6688	−	33.0958i	1.94879	−	1.80822i
$336$	−22.0124	+	10.6006i	−1.20087	+	0.578311i
$337$	−5.14845	−	8.91738i	−0.280454	−	0.485760i	0.691043	−	0.722814i	$-0.257152\pi$
$337$	−5.14845	−	8.91738i	−0.280454	−	0.485760i	−0.971497	+	0.237054i	$0.923818\pi$
$338$	−0.401551	+	0.695507i	−0.0218415	+	0.0378306i
$339$	−2.00488	+	26.7533i	−0.108890	+	1.45304i
$340$	−8.78751	+	38.5006i	−0.476570	+	2.08799i
$341$	−5.61197	−	14.2991i	−0.303905	−	0.774338i
$342$	−0.126629	−	0.158788i	−0.00684733	−	0.00858628i
$343$	18.6978			1.00958
$344$	−2.08638	−	1.37066i	−0.112490	−	0.0739008i
$345$	−24.6174			−1.32536
$346$	−1.18818	−	1.48992i	−0.0638767	−	0.0800989i
$347$	−11.4838	−	29.2603i	−0.616485	−	1.57078i	−0.807933	−	0.589275i	$-0.799414\pi$
$347$	−11.4838	−	29.2603i	−0.616485	−	1.57078i	0.191448	−	0.981503i	$-0.438682\pi$
$348$	−4.11711	+	18.0382i	−0.220700	+	0.966950i
$349$	0.303922	−	4.05556i	0.0162686	−	0.217089i	−0.983144	−	0.182831i	$-0.941474\pi$
$349$	0.303922	−	4.05556i	0.0162686	−	0.217089i	0.999413	−	0.0342584i	$-0.0109069\pi$
$350$	−1.19194	+	2.06450i	−0.0637120	+	0.110352i
$351$	1.04286	+	1.80629i	0.0556637	+	0.0964124i
$352$	2.10235	−	1.01244i	0.112055	−	0.0539630i
$353$	14.2465	−	13.2188i	0.758264	−	0.703566i	−0.203005	−	0.979178i	$-0.565071\pi$
$353$	14.2465	−	13.2188i	0.758264	−	0.703566i	0.961269	+	0.275612i	$0.0888804\pi$
$354$	0.732203	−	0.499208i	0.0389162	−	0.0265326i
$355$	−0.195902	−	0.858303i	−0.0103974	−	0.0455540i
$356$	27.9325	−	4.21014i	1.48042	−	0.223137i
$357$	26.6149	+	18.1457i	1.40861	+	0.960374i
$358$	0.580666	−	1.47951i	0.0306891	−	0.0781946i
$359$	0.236821	−	0.0730497i	0.0124990	−	0.00385542i	−0.288499	−	0.957480i	$-0.593156\pi$
$359$	0.236821	−	0.0730497i	0.0124990	−	0.00385542i	0.300998	+	0.953625i	$0.402680\pi$
$360$	3.38440	+	1.62984i	0.178373	+	0.0859001i
$361$	−1.36928	−	18.2718i	−0.0720674	−	0.961673i
$362$	2.44715	+	0.368849i	0.128620	+	0.0193863i
$363$	−11.7721	−	10.9229i	−0.617873	−	0.573303i
$364$	−10.6665	−	3.29017i	−0.559074	−	0.172452i
$365$	−26.0964	+	32.7238i	−1.36595	+	1.71284i
$366$	−0.882867	+	1.10708i	−0.0461482	+	0.0578680i
$367$	−1.51236	−	0.466502i	−0.0789447	−	0.0243512i	0.255031	−	0.966933i	$-0.417914\pi$
$367$	−1.51236	−	0.466502i	−0.0789447	−	0.0243512i	−0.333976	+	0.942582i	$0.608390\pi$
$368$	7.89909	+	7.32928i	0.411768	+	0.382065i
$369$	9.88985	+	1.49065i	0.514845	+	0.0776004i
$370$	0.0234358	+	0.312729i	0.00121837	+	0.0162580i
$371$	8.93793	+	4.30428i	0.464034	+	0.223467i
$372$	−33.6816	+	10.3894i	−1.74631	+	0.538666i
$373$	−3.98542	+	10.1547i	−0.206357	+	0.525790i	−0.996158	−	0.0875736i	$-0.972089\pi$
$373$	−3.98542	+	10.1547i	−0.206357	+	0.525790i	0.789801	+	0.613364i	$0.210184\pi$
$374$	−0.840854	−	0.573285i	−0.0434795	−	0.0296438i
$375$	−40.4652	+	6.09914i	−2.08961	+	0.314958i
$376$	−0.000744916	−	0.00326369i	−3.84161e−5	−	0.000168312i
$377$	−6.95228	+	4.73998i	−0.358061	+	0.244122i
$378$	−0.178508	+	0.165631i	−0.00918147	+	0.00851916i
$379$	−2.17682	+	1.04830i	−0.111816	+	0.0538476i	−0.488955	−	0.872309i	$-0.662622\pi$
$379$	−2.17682	+	1.04830i	−0.111816	+	0.0538476i	0.377140	+	0.926156i	$0.376908\pi$
$380$	−3.12312	−	5.40941i	−0.160213	−	0.277497i
$381$	−1.74168	+	3.01668i	−0.0892289	+	0.154549i
$382$	−0.0336024	+	0.448393i	−0.00171925	+	0.0229418i
$383$	3.65105	−	15.9963i	0.186560	−	0.817372i	−0.791853	−	0.610712i	$-0.790883\pi$
$383$	3.65105	−	15.9963i	0.186560	−	0.817372i	0.978413	−	0.206660i	$-0.0662594\pi$
$384$	−2.60621	−	6.64052i	−0.132998	−	0.338872i
$385$	12.7734	+	16.0173i	0.650992	+	0.816318i
$386$	−1.51707			−0.0772169
$387$	−16.2985	−	4.72288i	−0.828497	−	0.240077i
$388$	10.2288			0.519287
$389$	15.6280	+	19.5969i	0.792373	+	0.993604i	0.999882	+	0.0153710i	$0.00489293\pi$
$389$	15.6280	+	19.5969i	0.792373	+	0.993604i	−0.207509	+	0.978233i	$0.566536\pi$
$390$	0.672302	+	1.71300i	0.0340433	+	0.0867410i
$391$	3.16137	−	13.8509i	0.159877	−	0.700468i
$392$	−0.00391418	+	0.0522311i	−0.000197696	+	0.00263807i
$393$	−15.6945	+	27.1837i	−0.791685	+	1.37124i
$394$	−1.13174	−	1.96022i	−0.0570160	−	0.0987547i
$395$	0.918262	−	0.442212i	0.0462028	−	0.0222501i
$396$	7.74570	−	7.18696i	0.389236	−	0.361158i
$397$	−4.35664	+	2.97031i	−0.218653	+	0.149075i	−0.667694	−	0.744436i	$-0.732718\pi$
$397$	−4.35664	+	2.97031i	−0.218653	+	0.149075i	0.449040	+	0.893512i	$0.351766\pi$
$398$	−0.125389	−	0.549367i	−0.00628521	−	0.0275373i
$399$	−5.03808	+	0.759369i	−0.252220	+	0.0380160i
$400$	31.0997	+	21.2034i	1.55498	+	1.06017i
$401$	6.10988	−	15.5677i	0.305113	−	0.777415i	−0.693276	−	0.720672i	$-0.743833\pi$
$401$	6.10988	−	15.5677i	0.305113	−	0.777415i	0.998389	−	0.0567429i	$-0.0180715\pi$
$402$	2.74948	−	0.848101i	0.137131	−	0.0422994i
$403$	−14.4424	−	6.95510i	−0.719428	−	0.346458i
$404$	1.84357	+	24.6007i	0.0917208	+	1.22393i
$405$	−37.9574	−	5.72116i	−1.88612	−	0.284287i
$406$	−0.720151	−	0.668203i	−0.0357405	−	0.0331623i
$407$	1.68975	+	0.521220i	0.0837580	+	0.0258359i
$408$	−2.91862	+	3.65984i	−0.144493	+	0.181189i
$409$	−5.35968	+	6.72082i	−0.265019	+	0.332323i	−0.896480	−	0.443084i	$-0.853884\pi$
$409$	−5.35968	+	6.72082i	−0.265019	+	0.332323i	0.631461	+	0.775408i	$0.282456\pi$
$410$	−1.34335	−	0.414370i	−0.0663435	−	0.0204643i
$411$	−3.32682	−	3.08684i	−0.164100	−	0.152262i
$412$	11.3383	+	1.70898i	0.558600	+	0.0841954i
$413$	−0.769387	−	10.2668i	−0.0378591	−	0.505194i
$414$	−0.607392	−	0.292505i	−0.0298517	−	0.0143758i
$415$	30.8654	−	9.52072i	1.51512	−	0.467354i
$416$	0.889622	−	2.26672i	0.0436173	−	0.111135i
$417$	11.0014	+	7.50061i	0.538740	+	0.367306i
$418$	0.159170	−	0.0239910i	0.00778526	−	0.00117344i
$419$	4.09507	+	17.9417i	0.200057	+	0.876507i	0.970901	+	0.239483i	$0.0769779\pi$
$419$	4.09507	+	17.9417i	0.200057	+	0.876507i	−0.770843	+	0.637025i	$0.780165\pi$
$420$	38.8414	−	26.4816i	1.89526	−	1.29217i
$421$	−25.7002	+	23.8463i	−1.25255	+	1.16220i	−0.272782	+	0.962076i	$0.587944\pi$
$421$	−25.7002	+	23.8463i	−1.25255	+	1.16220i	−0.979771	+	0.200123i	$0.935866\pi$
$422$	0.444341	−	0.213983i	0.0216302	−	0.0104165i
$423$	−0.0113778	−	0.0197070i	−0.000553209	−	0.000958186i
$424$	−0.720820	+	1.24850i	−0.0350061	+	0.0606324i
$425$	3.70858	−	49.4876i	0.179893	−	2.40050i
$426$	0.0115844	−	0.0507544i	0.000561264	−	0.00245906i
$427$	6.01018	+	15.3137i	0.290853	+	0.741082i
$428$	−15.0885	−	18.9204i	−0.729329	−	0.914550i
$429$	10.3763			0.500971
$430$	2.16637	+	0.997869i	0.104472	+	0.0481215i
$431$	6.64041			0.319857			0.159929	−	0.987129i	$-0.448874\pi$
$431$	6.64041			0.319857			0.159929	+	0.987129i	$0.448874\pi$
$432$	2.39727	+	3.00609i	0.115339	+	0.144630i
$433$	2.91242	+	7.42073i	0.139962	+	0.356617i	0.983618	−	0.180267i	$-0.0576962\pi$
$433$	2.91242	+	7.42073i	0.139962	+	0.356617i	−0.843656	+	0.536885i	$0.819601\pi$
$434$	0.416455	−	1.82461i	0.0199905	−	0.0875840i
$435$	2.64819	−	35.3377i	0.126971	−	1.69431i
$436$	17.6238	−	30.5253i	0.844028	−	1.46190i
$437$	1.12356	+	1.94607i	0.0537474	+	0.0930932i
$438$	−2.22994	+	1.07388i	−0.106551	+	0.0513121i
$439$	19.3738	−	17.9763i	0.924661	−	0.857960i	−0.0655054	−	0.997852i	$-0.520866\pi$
$439$	19.3738	−	17.9763i	0.924661	−	0.857960i	0.990167	+	0.139892i	$0.0446755\pi$
$440$	−2.45987	+	1.67711i	−0.117270	+	0.0799530i
$441$	0.0792262	+	0.347113i	0.00377268	+	0.0165292i
$442$	−1.05015	+	0.158284i	−0.0499504	+	0.00752881i
$443$	−18.2951	−	12.4734i	−0.869228	−	0.592630i	0.0444757	−	0.999010i	$-0.485838\pi$
$443$	−18.2951	−	12.4734i	−0.869228	−	0.592630i	−0.913704	+	0.406381i	$0.866791\pi$
$444$	1.48242	−	3.77714i	0.0703525	−	0.179255i
$445$	−51.6992	+	15.9471i	−2.45078	+	0.755965i
$446$	0.269412	+	0.129742i	0.0127570	+	0.00614347i
$447$	0.410635	+	5.47955i	0.0194224	+	0.259174i
$448$	−20.1594	−	3.03854i	−0.952440	−	0.143557i
$449$	−3.86371	−	3.58500i	−0.182340	−	0.169186i	0.583722	−	0.811954i	$-0.301596\pi$
$449$	−3.86371	−	3.58500i	−0.182340	−	0.169186i	−0.766062	+	0.642767i	$0.777786\pi$
$450$	−2.25025	−	0.694111i	−0.106078	−	0.0327207i
$451$	−4.94233	+	6.19748i	−0.232725	+	0.291828i
$452$	−14.0882	+	17.6660i	−0.662651	+	0.830938i
$453$	11.0466	+	3.40743i	0.519016	+	0.160095i
$454$	1.31445	+	1.21963i	0.0616903	+	0.0572402i
$455$	21.1403	+	3.18639i	0.991073	+	0.149380i
$456$	−0.0553310	−	0.738341i	−0.00259111	−	0.0345760i
$457$	−7.71155	−	3.71369i	−0.360731	−	0.173719i	0.244735	−	0.969590i	$-0.421299\pi$
$457$	−7.71155	−	3.71369i	−0.360731	−	0.173719i	−0.605466	+	0.795871i	$0.707013\pi$
$458$	−0.747210	+	0.230484i	−0.0349148	+	0.0107698i
$459$	1.85203	−	4.71890i	0.0864455	−	0.220260i
$460$	−17.1309	−	11.6796i	−0.798731	−	0.544565i
$461$	26.0294	−	3.92330i	1.21231	−	0.182726i	0.488400	−	0.872620i	$-0.337581\pi$
$461$	26.0294	−	3.92330i	1.21231	−	0.182726i	0.723911	+	0.689893i	$0.242343\pi$
$462$	0.269575	+	1.18109i	0.0125418	+	0.0549491i
$463$	−0.386189	+	0.263300i	−0.0179477	+	0.0122366i	−0.572261	−	0.820072i	$-0.693933\pi$
$463$	−0.386189	+	0.263300i	−0.0179477	+	0.0122366i	0.554313	+	0.832308i	$0.312981\pi$
$464$	−11.3707	+	10.5505i	−0.527874	+	0.489795i
$465$	60.8236	−	29.2911i	2.82063	−	1.35834i
$466$	0.307073	+	0.531867i	0.0142249	+	0.0246383i
$467$	−8.33939	+	14.4443i	−0.385901	+	0.668400i	−0.991894	−	0.127070i	$-0.959443\pi$
$467$	−8.33939	+	14.4443i	−0.385901	+	0.668400i	0.605993	+	0.795470i	$0.292776\pi$
$468$	0.824013	−	10.9957i	0.0380900	−	0.508276i
$469$	7.43841	−	32.5898i	0.343474	−	1.50486i
$470$	0.00116855	+	0.00297741i	5.39011e−5	+	0.000137338i
$471$	26.9429	+	33.7854i	1.24146	+	1.55675i
$472$	1.49616			0.0688665
$473$	9.70048	−	9.31536i	0.446029	−	0.428321i
$474$	0.0602684			0.00276822
$475$	4.89402	+	6.13691i	0.224553	+	0.281581i
$476$	9.91172	+	25.2547i	0.454303	+	1.15755i
$477$	−2.18062	+	9.55394i	−0.0998439	+	0.437445i
$478$	0.206891	−	2.76077i	0.00946298	−	0.126275i
$479$	−16.6144	+	28.7771i	−0.759133	+	1.31486i	0.184160	+	0.982896i	$0.441044\pi$
$479$	−16.6144	+	28.7771i	−0.759133	+	1.31486i	−0.943293	+	0.331961i	$0.892290\pi$
$480$	5.12755	+	8.88117i	0.234039	+	0.405368i
$481$	1.66258	−	0.800656i	0.0758071	−	0.0365068i
$482$	−0.874108	+	0.811054i	−0.0398145	+	0.0369425i
$483$	−13.9734	+	9.52693i	−0.635814	+	0.433491i
$484$	−3.00968	−	13.1863i	−0.136804	−	0.599376i
$485$	−19.3722	+	2.91988i	−0.879644	+	0.132585i
$486$	−1.64507	−	1.12159i	−0.0746218	−	0.0508763i
$487$	−6.75202	+	17.2039i	−0.305963	+	0.779582i	0.692352	+	0.721560i	$0.256575\pi$
$487$	−6.75202	+	17.2039i	−0.305963	+	0.779582i	−0.998315	+	0.0580220i	$0.981521\pi$
$488$	−2.28446	+	0.704661i	−0.103412	+	0.0318985i
$489$	21.4531	+	10.3313i	0.970144	+	0.467197i
$490$	−0.00373984	−	0.0499046i	−0.000168949	−	0.00225446i
$491$	32.4622	+	4.89288i	1.46500	+	0.220813i	0.832618	−	0.553847i	$-0.186841\pi$
$491$	32.4622	+	4.89288i	1.46500	+	0.220813i	0.632378	+	0.774660i	$0.282079\pi$
$492$	13.3337	+	12.3718i	0.601128	+	0.557765i
$493$	19.5425	+	6.02806i	0.880149	+	0.271490i
$494$	0.104732	−	0.131330i	0.00471214	−	0.00590883i
$495$	−12.6179	+	15.8224i	−0.567134	+	0.711163i
$496$	−28.2375	−	8.71012i	−1.26790	−	0.391096i
$497$	−0.443362	−	0.411380i	−0.0198875	−	0.0184529i
$498$	1.88870	+	0.284676i	0.0846347	+	0.0127566i
$499$	0.813521	+	10.8557i	0.0364182	+	0.485967i	0.985357	+	0.170506i	$0.0545401\pi$
$499$	0.813521	+	10.8557i	0.0364182	+	0.485967i	−0.948938	+	0.315461i	$0.897841\pi$
$500$	−31.0528	−	14.9542i	−1.38872	−	0.668774i
$501$	3.69804	−	1.14070i	0.165216	−	0.0509625i
$502$	0.722400	−	1.84065i	0.0322423	−	0.0821520i
$503$	−23.3239	−	15.9020i	−1.03996	−	0.709034i	−0.0822059	−	0.996615i	$-0.526197\pi$
$503$	−23.3239	−	15.9020i	−1.03996	−	0.709034i	−0.957756	+	0.287581i	$0.907149\pi$
$504$	2.55182	−	0.384624i	0.113667	−	0.0171325i
$505$	−10.5140	−	46.0647i	−0.467866	−	2.04985i
$506$	0.441468	−	0.300988i	0.0196257	−	0.0133805i
$507$	−14.5890	+	13.5366i	−0.647922	+	0.601183i
$508$	−2.64326	+	1.27293i	−0.117276	+	0.0564770i
$509$	−5.59692	−	9.69414i	−0.248079	−	0.429685i	0.714914	−	0.699213i	$-0.246466\pi$
$509$	−5.59692	−	9.69414i	−0.248079	−	0.429685i	−0.962993	+	0.269527i	$0.913133\pi$
$510$	2.23630	−	3.87339i	0.0990251	−	0.171517i
$511$	−2.14883	+	28.6742i	−0.0950587	+	1.26847i
$512$	1.66733	−	7.30503i	0.0736861	−	0.322840i
$513$	0.292936	+	0.746389i	0.0129334	+	0.0329539i
$514$	0.791463	+	0.992463i	0.0349099	+	0.0437757i
$515$	−21.9614			−0.967736
$516$	−19.6521	−	23.7941i	−0.865136	−	1.04748i
$517$	0.0180353			0.000793193
$518$	0.134329	+	0.168443i	0.00590207	+	0.00740097i
$519$	−17.2532	−	43.9605i	−0.757333	−	1.92965i
$520$	−0.691337	+	3.02895i	−0.0303171	+	0.132828i
$521$	3.10988	−	41.4985i	0.136246	−	1.81808i	−0.341827	−	0.939763i	$-0.611046\pi$
$521$	3.10988	−	41.4985i	0.136246	−	1.81808i	0.478074	−	0.878320i	$-0.341335\pi$
$522$	0.485223	−	0.840431i	0.0212376	−	0.0367847i
$523$	−3.42717	−	5.93602i	−0.149859	−	0.259564i	0.781316	−	0.624136i	$-0.214549\pi$
$523$	−3.42717	−	5.93602i	−0.149859	−	0.259564i	−0.931175	+	0.364572i	$0.881215\pi$
$524$	−23.8188	+	11.4705i	−1.04053	+	0.501092i
$525$	−43.3053	+	40.1814i	−1.89000	+	1.75366i
$526$	0.281837	−	0.192153i	0.0122887	−	0.00837826i
$527$	8.66952	+	37.9837i	0.377650	+	1.65459i
$528$	18.9146	−	2.85091i	0.823151	−	0.124070i
$529$	−12.8405	−	8.75454i	−0.558285	−	0.380632i
$530$	0.503231	−	1.28221i	0.0218589	−	0.0556957i
$531$	9.71842	−	2.99773i	0.421743	−	0.130091i
$532$	−3.86620	−	1.86186i	−0.167621	−	0.0807221i
$533$	0.618174	+	8.24895i	0.0267761	+	0.357302i
$534$	−3.16355	−	0.476829i	−0.136900	−	0.0206344i
$535$	33.9769	+	31.5260i	1.46895	+	1.36299i
$536$	4.64198	+	1.43186i	0.200503	+	0.0618469i
$537$	24.5572	−	30.7937i	1.05972	−	1.32885i
$538$	−1.32889	+	1.66637i	−0.0572925	+	0.0718425i
$539$	−0.269647	−	0.0831752i	−0.0116145	−	0.00358261i
$540$	−5.42319	−	5.03198i	−0.233377	−	0.216542i
$541$	15.2983	+	2.30585i	0.657727	+	0.0991363i	0.469421	−	0.882974i	$-0.344462\pi$
$541$	15.2983	+	2.30585i	0.657727	+	0.0991363i	0.188305	+	0.982111i	$0.439701\pi$
$542$	0.210146	+	2.80420i	0.00902655	+	0.120451i
$543$	55.2548	+	26.6093i	2.37121	+	1.14192i
$544$	−5.65543	+	1.74447i	−0.242474	+	0.0747934i
$545$	−24.6639	+	62.8425i	−1.05648	+	2.69188i
$546$	1.04455	+	0.712159i	0.0447024	+	0.0304776i
$547$	−15.2020	+	2.29134i	−0.649993	+	0.0979706i	−0.465759	−	0.884912i	$-0.654218\pi$
$547$	−15.2020	+	2.29134i	−0.649993	+	0.0979706i	−0.184234	+	0.982882i	$0.558980\pi$
$548$	−0.850544	−	3.72648i	−0.0363334	−	0.159187i
$549$	−13.4269	+	9.15434i	−0.573048	+	0.390698i
$550$	1.36816	−	1.26947i	0.0583385	−	0.0541302i
$551$	−2.91440	+	1.40350i	−0.124158	+	0.0597912i
$552$	−1.22885	−	2.12842i	−0.0523032	−	0.0905918i
$553$	0.350092	−	0.606378i	0.0148874	−	0.0257858i
$554$	−0.124858	+	1.66611i	−0.00530470	+	0.0707863i
$555$	−1.72932	+	7.57666i	−0.0734057	+	0.321611i
$556$	4.09705	+	10.4391i	0.173754	+	0.442717i
$557$	19.3868	+	24.3103i	0.821445	+	1.03006i	0.998944	+	0.0459389i	$0.0146279\pi$
$557$	19.3868	+	24.3103i	0.821445	+	1.03006i	−0.177499	+	0.984121i	$0.556801\pi$
$558$	1.84876			0.0782641
$559$	0.808647	−	14.0114i	0.0342021	−	0.592617i
$560$	39.4114			1.66544
$561$	−15.7241	−	19.7174i	−0.663871	−	0.832468i
$562$	0.590077	+	1.50349i	0.0248909	+	0.0634210i
$563$	−0.0465986	+	0.204162i	−0.00196390	+	0.00860439i	−0.975900	−	0.218217i	$-0.929976\pi$
$563$	−0.0465986	+	0.204162i	−0.00196390	+	0.00860439i	0.973936	+	0.226821i	$0.0728332\pi$
$564$	0.00309266	−	0.0412687i	0.000130224	−	0.00173772i
$565$	21.6385	−	37.4790i	0.910340	−	1.57675i
$566$	0.801434	+	1.38812i	0.0336868	+	0.0583472i
$567$	−23.7597	+	11.4421i	−0.997812	+	0.480521i
$568$	0.0644300	−	0.0597823i	0.00270342	−	0.00250841i
$569$	10.2124	−	6.96269i	0.428126	−	0.291891i	−0.330023	−	0.943973i	$-0.607056\pi$
$569$	10.2124	−	6.96269i	0.428126	−	0.291891i	0.758149	+	0.652082i	$0.226104\pi$
$570$	0.157418	+	0.689695i	0.00659353	+	0.0288881i
$571$	28.3573	−	4.27418i	1.18672	−	0.178869i	0.474132	−	0.880454i	$-0.342762\pi$
$571$	28.3573	−	4.27418i	1.18672	−	0.178869i	0.712586	+	0.701585i	$0.247524\pi$
$572$	7.22069	+	4.92298i	0.301912	+	0.205840i
$573$	−4.07094	+	10.3726i	−0.170066	+	0.433321i
$574$	−0.922882	+	0.284671i	−0.0385203	+	0.0118820i
$575$	23.4747	+	11.3048i	0.978964	+	0.471444i
$576$	−1.50499	−	20.0827i	−0.0627078	−	0.836777i
$577$	−21.1891	−	3.19374i	−0.882112	−	0.132957i	−0.307661	−	0.951496i	$-0.599546\pi$
$577$	−21.1891	−	3.19374i	−0.882112	−	0.132957i	−0.574451	+	0.818539i	$0.694784\pi$
$578$	0.703433	+	0.652691i	0.0292590	+	0.0271484i
$579$	−35.9245	−	11.0812i	−1.49297	−	0.460520i
$580$	18.6087	−	23.3345i	0.772682	−	0.968913i
$581$	13.8355	−	17.3491i	0.573992	−	0.719763i
$582$	−1.10701	−	0.341468i	−0.0458871	−	0.0141543i
$583$	−5.69350	−	5.28279i	−0.235800	−	0.218791i
$584$	−4.13198	−	0.622796i	−0.170983	−	0.0257715i
$585$	1.57822	+	21.0599i	0.0652513	+	0.870718i
$586$	−1.37875	−	0.663971i	−0.0569557	−	0.0274284i
$587$	−35.5182	+	10.9559i	−1.46599	+	0.452199i	−0.922099	−	0.386954i	$-0.873527\pi$
$587$	−35.5182	+	10.9559i	−1.46599	+	0.452199i	−0.543895	+	0.839153i	$0.683051\pi$
$588$	−0.236561	+	0.602748i	−0.00975562	+	0.0248569i
$589$	−5.09160	−	3.47139i	−0.209796	−	0.143036i
$590$	−1.41355	+	0.213059i	−0.0581951	+	0.00877150i
$591$	−12.4815	−	54.6850i	−0.513421	−	2.24944i
$592$	2.81068	−	1.91629i	0.115518	−	0.0787589i
$593$	16.3786	−	15.1971i	0.672588	−	0.624071i	−0.268081	−	0.963397i	$-0.586389\pi$
$593$	16.3786	−	15.1971i	0.672588	−	0.624071i	0.940669	+	0.339326i	$0.110199\pi$
$594$	0.171771	−	0.0827206i	0.00704785	−	0.00339407i
$595$	−25.9809	−	45.0002i	−1.06511	−	1.84483i
$596$	−2.31400	+	4.00796i	−0.0947849	+	0.164172i
$597$	1.04353	−	13.9250i	0.0427090	−	0.569912i
$598$	0.124073	−	0.543600i	0.00507373	−	0.0222294i
$599$	−7.67327	−	19.5512i	−0.313521	−	0.798839i	−0.997588	−	0.0694191i	$-0.977885\pi$
$599$	−7.67327	−	19.5512i	−0.313521	−	0.798839i	0.684066	−	0.729420i	$-0.260210\pi$
$600$	−5.35261	−	6.71196i	−0.218519	−	0.274014i
$601$	25.2099			1.02833			0.514167	−	0.857690i	$-0.328101\pi$
$601$	25.2099			1.02833			0.514167	+	0.857690i	$0.328101\pi$
$602$	1.61586	−	0.271970i	0.0658575	−	0.0110847i
$603$	33.0211			1.34472
$604$	6.07053	+	7.61221i	0.247006	+	0.309736i
$605$	9.46414	+	24.1142i	0.384772	+	0.980383i
$606$	0.621727	−	2.72396i	0.0252559	−	0.110653i
$607$	−2.51010	+	33.4949i	−0.101882	+	1.35952i	0.678678	+	0.734436i	$0.262553\pi$
$607$	−2.51010	+	33.4949i	−0.101882	+	1.35952i	−0.780559	+	0.625082i	$0.785066\pi$
$608$	0.468054	−	0.810693i	0.0189821	−	0.0328779i
$609$	−12.1725	−	21.0834i	−0.493255	−	0.854342i
$610$	2.05798	−	0.991069i	0.0833250	−	0.0401272i
$611$	0.0137966	−	0.0128014i	0.000558150	−	0.000517887i
$612$	−22.1431	+	15.0969i	−0.895082	+	0.610257i
$613$	−0.400141	−	1.75313i	−0.0161615	−	0.0708083i	0.966204	−	0.257778i	$-0.0829904\pi$
$613$	−0.400141	−	1.75313i	−0.0161615	−	0.0708083i	−0.982366	+	0.186970i	$0.940133\pi$
$614$	0.940345	−	0.141734i	0.0379492	−	0.00571993i
$615$	−28.7841	−	19.6247i	−1.16069	−	0.791344i
$616$	−0.747240	+	1.90394i	−0.0301072	+	0.0767118i
$617$	32.6145	−	10.0602i	1.31301	−	0.405009i	0.442326	−	0.896854i	$-0.354154\pi$
$617$	32.6145	−	10.0602i	1.31301	−	0.405009i	0.870683	+	0.491845i	$0.163677\pi$
$618$	−1.17005	−	0.563464i	−0.0470661	−	0.0226659i
$619$	0.351580	+	4.69151i	0.0141312	+	0.188568i	0.999802	+	0.0198885i	$0.00633113\pi$
$619$	0.351580	+	4.69151i	0.0141312	+	0.188568i	−0.985671	+	0.168679i	$0.946050\pi$
$620$	56.2233	+	8.47429i	2.25798	+	0.340336i
$621$	1.95103	+	1.81029i	0.0782921	+	0.0726444i
$622$	0.491604	+	0.151640i	0.0197115	+	0.00608020i
$623$	−23.1742	+	29.0596i	−0.928456	+	1.16425i
$624$	12.4456	−	15.6063i	0.498223	−	0.624752i
$625$	17.4985	+	5.39756i	0.699938	+	0.215902i
$626$	−0.125121	−	0.116095i	−0.00500083	−	0.00464010i
$627$	3.94441	+	0.594524i	0.157525	+	0.0237430i
$628$	2.71983	+	36.2937i	0.108533	+	1.44827i
$629$	−4.04089	−	1.94599i	−0.161121	−	0.0775917i
$630$	−2.35615	+	0.726776i	−0.0938713	+	0.0289554i
$631$	−0.362038	+	0.922458i	−0.0144125	+	0.0367225i	−0.937899	−	0.346909i	$-0.887231\pi$
$631$	−0.362038	+	0.922458i	−0.0144125	+	0.0367225i	0.923486	+	0.383631i	$0.125327\pi$
$632$	0.0840713	+	0.0573189i	0.00334418	+	0.00228002i
$633$	12.0851	−	1.82153i	0.480339	−	0.0723994i
$634$	−0.193007	−	0.845620i	−0.00766530	−	0.0335839i
$635$	4.64268	−	3.16532i	0.184239	−	0.125612i
$636$	−13.0645	+	12.1220i	−0.518040	+	0.480670i
$637$	−0.265311	+	0.127767i	−0.0105120	+	0.00506231i
$638$	0.384570	+	0.666095i	0.0152253	+	0.0263710i
$639$	0.298728	−	0.517413i	0.0118175	−	0.0204685i
$640$	−0.859946	+	11.4752i	−0.0339923	+	0.453596i
$641$	−1.41414	+	6.19574i	−0.0558551	+	0.244717i	−0.995147	−	0.0984029i	$-0.968627\pi$
$641$	−1.41414	+	6.19574i	−0.0558551	+	0.244717i	0.939292	+	0.343120i	$0.111484\pi$
$642$	1.00134	+	2.55137i	0.0395196	+	0.100694i
$643$	−25.4227	−	31.8790i	−1.00257	−	1.25719i	−0.966185	−	0.257849i	$-0.916986\pi$
$643$	−25.4227	−	31.8790i	−1.00257	−	1.25719i	−0.0363877	−	0.999338i	$-0.511585\pi$
$644$	−14.2439			−0.561289
$645$	44.0112	+	39.4537i	1.73294	+	1.55349i
$646$	−0.408269			−0.0160631
$647$	−15.8901	−	19.9255i	−0.624704	−	0.783354i	0.364294	−	0.931284i	$-0.381310\pi$
$647$	−15.8901	−	19.9255i	−0.624704	−	0.783354i	−0.988998	+	0.147930i	$0.952739\pi$
$648$	−1.40010	−	3.56739i	−0.0550011	−	0.140140i
$649$	−1.79365	+	7.85848i	−0.0704068	+	0.308472i
$650$	0.145549	−	1.94222i	0.00570892	−	0.0761802i
$651$	23.1893	−	40.1651i	0.908862	−	1.57419i
$652$	10.0273	+	17.3677i	0.392698	+	0.680173i
$653$	−30.6683	+	14.7691i	−1.20015	+	0.577959i	−0.923717	−	0.383075i	$-0.874865\pi$
$653$	−30.6683	+	14.7691i	−1.20015	+	0.577959i	−0.276428	+	0.961035i	$0.589151\pi$
$654$	−2.92638	+	2.71528i	−0.114430	+	0.106176i
$655$	41.8359	−	28.5232i	1.63466	−	1.11449i
$656$	3.39327	+	14.8669i	0.132485	+	0.580454i
$657$	−28.0874	+	4.23349i	−1.09579	+	0.165164i
$658$	0.00181556	+	0.00123783i	7.07778e−5	+	4.82555e-5i
$659$	−13.9249	+	35.4800i	−0.542437	+	1.38211i	0.352458	+	0.935828i	$0.385346\pi$
$659$	−13.9249	+	35.4800i	−0.542437	+	1.38211i	−0.894894	+	0.446278i	$0.852749\pi$
$660$	−35.1698	+	10.8484i	−1.36898	+	0.422275i
$661$	−18.3116	−	8.81838i	−0.712237	−	0.342995i	0.0424334	−	0.999099i	$-0.486489\pi$
$661$	−18.3116	−	8.81838i	−0.712237	−	0.342995i	−0.754671	+	0.656104i	$0.772203\pi$
$662$	−0.157538	−	2.10220i	−0.00612288	−	0.0817042i
$663$	−26.0238	−	3.92246i	−1.01068	−	0.152336i
$664$	2.36390	+	2.19338i	0.0917370	+	0.0851195i
$665$	7.85365	+	2.42253i	0.304551	+	0.0939417i
$666$	−0.132694	+	0.166393i	−0.00514180	+	0.00644761i
$667$	−6.69459	+	8.39475i	−0.259216	+	0.325046i
$668$	3.11461	+	0.960730i	0.120508	+	0.0371718i
$669$	5.43205	+	5.04020i	0.210015	+	0.194866i
$670$	−4.58958	−	0.691768i	−0.177311	−	0.0267253i
$671$	−0.962502	−	12.8437i	−0.0371570	−	0.495825i
$672$	6.34754	+	3.05681i	0.244862	+	0.117919i
$673$	−31.2428	+	9.63712i	−1.20432	+	0.371484i	−0.831029	−	0.556230i	$-0.812247\pi$
$673$	−31.2428	+	9.63712i	−1.20432	+	0.371484i	−0.373293	+	0.927714i	$0.621771\pi$
$674$	−0.358841	+	0.914312i	−0.0138220	+	0.0352180i
$675$	7.68144	+	5.23712i	0.295659	+	0.201577i
$676$	−16.5747	+	2.49823i	−0.637488	+	0.0960858i
$677$	2.99152	+	13.1067i	0.114973	+	0.503732i	0.999319	+	0.0368987i	$0.0117479\pi$
$677$	2.99152	+	13.1067i	0.114973	+	0.503732i	−0.884346	+	0.466833i	$0.845395\pi$
$678$	2.11444	−	1.44160i	0.0812047	−	0.0553644i
$679$	−9.86612	+	9.15442i	−0.378627	+	0.351314i
$680$	6.80335	−	3.27632i	0.260897	−	0.125641i
$681$	22.2178	+	38.4824i	0.851388	+	1.47465i
$682$	−0.732629	+	1.26895i	−0.0280538	+	0.0485906i
$683$	1.41269	−	18.8510i	0.0540551	−	0.721315i	−0.902672	−	0.430329i	$-0.858398\pi$
$683$	1.41269	−	18.8510i	0.0540551	−	0.721315i	0.956727	−	0.290986i	$-0.0939833\pi$
$684$	0.943253	−	4.13266i	0.0360662	−	0.158016i
$685$	2.67459	+	6.81475i	0.102191	+	0.260378i
$686$	−1.11203	−	1.39444i	−0.0424575	−	0.0532400i
$687$	−19.3776			−0.739301
$688$	−2.37560	−	25.7630i	−0.0905691	−	0.982205i
$689$	−8.10508			−0.308779
$690$	1.46409	+	1.83591i	0.0557371	+	0.0698921i
$691$	11.9747	+	30.5111i	0.455540	+	1.16070i	0.955590	+	0.294700i	$0.0952198\pi$
$691$	11.9747	+	30.5111i	0.455540	+	1.16070i	−0.500050	+	0.865997i	$0.666685\pi$
$692$	8.85064	−	38.7772i	0.336451	−	1.47409i
$693$	−1.03899	+	13.8643i	−0.0394679	+	0.526662i
$694$	−1.49919	+	2.59667i	−0.0569084	+	0.0985682i
$695$	−10.7393	−	18.6010i	−0.407365	−	0.705576i
$696$	3.18749	−	1.53502i	0.120822	−	0.0581846i
$697$	14.7382	−	13.6750i	0.558249	−	0.517979i
$698$	−0.320530	+	0.218534i	−0.0121323	+	0.00827163i
$699$	3.38660	+	14.8377i	0.128093	+	0.561212i
$700$	−49.1994	+	7.41562i	−1.85956	+	0.280284i
$701$	−2.39258	−	1.63123i	−0.0903666	−	0.0616109i	0.517294	−	0.855808i	$-0.326939\pi$
$701$	−2.39258	−	1.63123i	−0.0903666	−	0.0616109i	−0.607660	+	0.794197i	$0.707892\pi$
$702$	0.0726861	−	0.185201i	0.00274336	−	0.00698997i
$703$	0.677884	−	0.209099i	0.0255669	−	0.00788633i
$704$	14.3807	+	6.92540i	0.541995	+	0.261011i
$705$	0.00592332	+	0.0790412i	0.000223085	+	0.00297686i
$706$	−1.83312	−	0.276299i	−0.0689906	−	0.0103987i
$707$	−23.7950	−	22.0786i	−0.894905	−	0.830350i
$708$	17.6743	+	5.45180i	0.664241	+	0.204891i
$709$	17.2331	−	21.6097i	0.647204	−	0.811568i	−0.344680	−	0.938720i	$-0.612012\pi$
$709$	17.2331	−	21.6097i	0.647204	−	0.811568i	0.991883	+	0.127153i	$0.0405838\pi$
$710$	−0.0523594	+	0.0656566i	−0.00196501	+	0.00246405i
$711$	0.660935	+	0.203872i	0.0247870	+	0.00764578i
$712$	−3.95950	−	3.67388i	−0.148389	−	0.137684i
$713$	−20.2267	−	3.04868i	−0.757496	−	0.114174i
$714$	−0.229621	−	3.06408i	−0.00859336	−	0.114670i
$715$	−15.0805	−	7.26239i	−0.563979	−	0.271598i
$716$	31.6989	−	9.77781i	1.18464	−	0.365414i
$717$	25.0649	−	63.8643i	0.936065	−	2.38505i
$718$	−0.0195326	−	0.0133171i	−0.000728950	−	0.000496990i
$719$	13.9296	−	2.09955i	0.519486	−	0.0782999i	0.115934	−	0.993257i	$-0.463014\pi$
$719$	13.9296	−	2.09955i	0.519486	−	0.0782999i	0.403551	+	0.914957i	$0.367776\pi$
$720$	8.66314	+	37.9557i	0.322856	+	1.41452i
$721$	−12.4658	+	8.49907i	−0.464252	+	0.316522i
$722$	−1.28124	+	1.18881i	−0.0476827	+	0.0442430i
$723$	−26.6233	+	12.8211i	−0.990129	+	0.476821i
$724$	25.8263	+	44.7324i	0.959826	+	1.66247i
$725$	−18.7531	+	32.4813i	−0.696473	+	1.20633i
$726$	−0.114475	+	1.52756i	−0.00424857	+	0.0566932i
$727$	9.48127	−	41.5401i	0.351641	−	1.54064i	−0.421752	−	0.906711i	$-0.638585\pi$
$727$	9.48127	−	41.5401i	0.351641	−	1.54064i	0.773393	−	0.633927i	$-0.218558\pi$
$728$	0.779782	+	1.98685i	0.0289006	+	0.0736376i
$729$	−11.9333	−	14.9639i	−0.441974	−	0.554218i
$730$	3.99253			0.147770
$731$	−27.8503	+	19.6960i	−1.03008	+	0.728484i
$732$	−29.5542			−1.09235
$733$	22.9376	+	28.7628i	0.847218	+	1.06238i	0.997280	+	0.0737016i	$0.0234812\pi$
$733$	22.9376	+	28.7628i	0.847218	+	1.06238i	−0.150062	+	0.988677i	$0.547947\pi$
$734$	0.0551554	+	0.140534i	0.00203582	+	0.00518719i
$735$	0.275962	−	1.20907i	0.0101790	−	0.0445971i
$736$	0.232207	−	3.09859i	0.00855927	−	0.114216i
$737$	−13.0857	+	22.6651i	−0.482017	+	0.834878i
$738$	−0.477018	−	0.826219i	−0.0175593	−	0.0304136i
$739$	20.2360	−	9.74515i	0.744394	−	0.358481i	−0.0229335	−	0.999737i	$-0.507301\pi$
$739$	20.2360	−	9.74515i	0.744394	−	0.358481i	0.767327	+	0.641256i	$0.221586\pi$
$740$	−4.79813	+	4.45201i	−0.176383	+	0.163659i
$741$	3.43937	−	2.34492i	0.126348	−	0.0861428i
$742$	−0.210569	−	0.922565i	−0.00773025	−	0.0338684i
$743$	34.6409	−	5.22128i	1.27085	−	0.191550i	0.521230	−	0.853416i	$-0.325473\pi$
$743$	34.6409	−	5.22128i	1.27085	−	0.191550i	0.749622	+	0.661866i	$0.230235\pi$
$744$	5.56870	+	3.79667i	0.204158	+	0.139193i
$745$	3.23835	−	8.25118i	0.118644	−	0.302300i
$746$	0.994345	−	0.306715i	0.0364055	−	0.0112296i
$747$	19.7495	+	9.51087i	0.722597	+	0.347984i
$748$	−1.58731	−	21.1812i	−0.0580380	−	0.774463i
$749$	31.4867	+	4.74585i	1.15050	+	0.173410i
$750$	2.86148	+	2.65507i	0.104487	+	0.0969494i
$751$	20.8142	+	6.42033i	0.759521	+	0.234281i	0.650239	−	0.759730i	$-0.274669\pi$
$751$	20.8142	+	6.42033i	0.759521	+	0.234281i	0.109282	+	0.994011i	$0.465145\pi$
$752$	0.0216321	−	0.0271258i	0.000788842	−	0.000989176i
$753$	30.5513	−	38.3101i	1.11335	−	1.39610i
$754$	0.766977	+	0.236581i	0.0279317	+	0.00861578i
$755$	−13.6699	−	12.6838i	−0.497498	−	0.461611i
$756$	−5.02571	−	0.757504i	−0.182783	−	0.0275502i
$757$	−1.77819	−	23.7283i	−0.0646294	−	0.862420i	−0.931466	−	0.363828i	$-0.881470\pi$
$757$	−1.77819	−	23.7283i	−0.0646294	−	0.862420i	0.866837	−	0.498592i	$-0.166149\pi$
$758$	0.207644	+	0.0999962i	0.00754198	+	0.00363203i
$759$	12.6526	−	3.90280i	0.459259	−	0.141663i
$760$	−0.436351	+	1.11180i	−0.0158281	+	0.0403294i
$761$	−15.0749	−	10.2779i	−0.546463	−	0.372572i	0.258395	−	0.966039i	$-0.416806\pi$
$761$	−15.0749	−	10.2779i	−0.546463	−	0.372572i	−0.804858	+	0.593467i	$0.797759\pi$
$762$	0.328562	−	0.0495228i	0.0119025	−	0.00179402i
$763$	10.3202	+	45.2159i	0.373618	+	1.63693i
$764$	−7.75413	+	5.28668i	−0.280535	+	0.191265i
$765$	37.6271	−	34.9129i	1.36041	−	1.26228i
$766$	−1.41011	+	0.679074i	−0.0509494	+	0.0245359i
$767$	4.20580	+	7.28467i	0.151863	+	0.263034i
$768$	18.0562	−	31.2743i	0.651548	−	1.12851i
$769$	−2.88919	+	38.5536i	−0.104187	+	1.39028i	0.662887	+	0.748719i	$0.269331\pi$
$769$	−2.88919	+	38.5536i	−0.104187	+	1.39028i	−0.767074	+	0.641558i	$0.778288\pi$
$770$	0.434855	−	1.90522i	0.0156711	−	0.0686595i
$771$	11.4927	+	29.2828i	0.413898	+	1.05460i
$772$	−19.7418	−	24.7555i	−0.710524	−	0.890969i
$773$	−25.0975			−0.902696			−0.451348	−	0.892348i	$-0.649057\pi$
$773$	−25.0975			−0.902696			−0.451348	+	0.892348i	$0.649057\pi$
$774$	0.617111	+	1.49639i	0.0221816	+	0.0537868i
$775$	−71.4515			−2.56661
$776$	−1.21947	−	1.52917i	−0.0437764	−	0.0548938i
$777$	1.95056	+	4.96995i	0.0699760	+	0.178296i
$778$	0.532038	−	2.33101i	0.0190745	−	0.0835709i
$779$	−0.237645	+	3.17115i	−0.00851452	+	0.113618i
$780$	−19.2039	+	33.2621i	−0.687609	+	1.19097i
$781$	0.236761	+	0.410083i	0.00847199	+	0.0146739i
$782$	−1.22099	+	0.587996i	−0.0436624	+	0.0210267i
$783$	−2.80851	+	2.60592i	−0.100368	+	0.0931278i
$784$	−0.448522	+	0.305797i	−0.0160186	+	0.0109213i
$785$	−15.5114	−	67.9598i	−0.553625	−	2.42559i
$786$	2.96072	−	0.446257i	0.105605	−	0.0159175i
$787$	38.6848	+	26.3748i	1.37896	+	0.940161i	0.999891	+	0.0147940i	$0.00470924\pi$
$787$	38.6848	+	26.3748i	1.37896	+	0.940161i	0.379072	+	0.925367i	$0.376243\pi$
$788$	17.2594	−	43.9763i	0.614841	−	1.56659i
$789$	8.07749	−	2.49158i	0.287566	−	0.0887025i
$790$	−0.0875919	−	0.0421820i	−0.00311638	−	0.00150077i
$791$	−2.22182	−	29.6481i	−0.0789989	−	1.05417i
$792$	−1.99787	−	0.301130i	−0.0709911	−	0.0107002i
$793$	−9.85266	−	9.14194i	−0.349878	−	0.324640i
$794$	0.480626	+	0.148253i	0.0170568	+	0.00526132i
$795$	21.2823	−	26.6872i	0.754806	−	0.946497i
$796$	7.33284	−	9.19509i	0.259906	−	0.325911i
$797$	34.1768	+	10.5421i	1.21060	+	0.373422i	0.833380	−	0.552700i	$-0.186403\pi$
$797$	34.1768	+	10.5421i	1.21060	+	0.373422i	0.377224	+	0.926122i	$0.376879\pi$
$798$	0.356267	+	0.330567i	0.0126117	+	0.0117019i
$799$	−0.0452328	−	0.00681774i	−0.00160022	−	0.000241194i
$800$	−0.811118	−	10.8236i	−0.0286774	−	0.382673i
$801$	−33.0802	−	15.9306i	−1.16883	−	0.562880i
$802$	−1.52439	+	0.470211i	−0.0538280	+	0.0166037i
$803$	8.22474	−	20.9563i	0.290245	−	0.739532i
$804$	49.6186	+	33.8294i	1.74991	+	1.19307i
$805$	26.9764	−	4.06604i	0.950794	−	0.143309i
$806$	0.340250	+	1.49073i	0.0119848	+	0.0525088i
$807$	−43.6401	+	29.7533i	−1.53620	+	1.04737i
$808$	3.45793	−	3.20849i	0.121650	−	0.112874i
$809$	−16.9543	+	8.16477i	−0.596082	+	0.287058i	−0.707497	−	0.706716i	$-0.750176\pi$
$809$	−16.9543	+	8.16477i	−0.596082	+	0.287058i	0.111415	+	0.993774i	$0.464462\pi$
$810$	1.83080	+	3.17105i	0.0643279	+	0.111419i
$811$	9.73642	−	16.8640i	0.341892	−	0.592174i	−0.642892	−	0.765957i	$-0.722266\pi$
$811$	9.73642	−	16.8640i	0.341892	−	0.592174i	0.984784	+	0.173783i	$0.0555990\pi$
$812$	1.53228	−	20.4468i	0.0537723	−	0.717542i
$813$	−15.5066	+	67.9390i	−0.543842	+	2.38273i
$814$	−0.0616248	−	0.157017i	−0.00215995	−	0.00550346i
$815$	−23.9483	−	30.0302i	−0.838872	−	1.05191i
$816$	−48.5156			−1.69839
$817$	1.11020	−	5.27991i	0.0388409	−	0.184721i
$818$	0.819986			0.0286701
$819$	9.04601	+	11.3433i	0.316093	+	0.396368i
$820$	−10.7196	−	27.3130i	−0.374344	−	0.953812i
$821$	−5.71556	+	25.0415i	−0.199475	+	0.873955i	0.771776	+	0.635895i	$0.219369\pi$
$821$	−5.71556	+	25.0415i	−0.199475	+	0.873955i	−0.971250	+	0.238060i	$0.923488\pi$
$822$	−0.0323510	+	0.431694i	−0.00112837	+	0.0150570i
$823$	−15.9442	+	27.6162i	−0.555780	+	0.962639i	0.442062	+	0.896984i	$0.354247\pi$
$823$	−15.9442	+	27.6162i	−0.555780	+	0.962639i	−0.997842	+	0.0656550i	$0.979086\pi$
$824$	−1.09627	−	1.89879i	−0.0381902	−	0.0661474i
$825$	41.6709	−	20.0677i	1.45079	−	0.698666i
$826$	−0.719915	+	0.667983i	−0.0250490	+	0.0232421i
$827$	−0.792811	+	0.540529i	−0.0275687	+	0.0187960i	−0.577026	−	0.816726i	$-0.695787\pi$
$827$	−0.792811	+	0.540529i	−0.0275687	+	0.0187960i	0.549457	+	0.835522i	$0.314835\pi$
$828$	−3.13100	−	13.7178i	−0.108810	−	0.476726i
$829$	−32.7066	+	4.92973i	−1.13595	+	0.171217i	−0.689977	−	0.723831i	$-0.742380\pi$
$829$	−32.7066	+	4.92973i	−1.13595	+	0.171217i	−0.445971	+	0.895048i	$0.647141\pi$
$830$	−2.54572	−	1.73564i	−0.0883633	−	0.0602451i
$831$	−15.1265	+	38.5418i	−0.524734	+	1.33700i
$832$	15.9165	−	4.90960i	0.551806	−	0.170210i
$833$	0.644836	+	0.310537i	0.0223423	+	0.0107595i
$834$	−0.0949148	−	1.26655i	−0.00328663	−	0.0438570i
$835$	−6.17298	−	0.930427i	−0.213625	−	0.0321988i
$836$	2.46278	+	2.28513i	0.0851772	+	0.0790329i
$837$	−6.97450	−	2.15135i	−0.241074	−	0.0743615i
$838$	1.09450	−	1.37246i	0.0378089	−	0.0474109i
$839$	−15.4494	+	19.3729i	−0.533373	+	0.668828i	−0.973388	−	0.229162i	$-0.926401\pi$
$839$	−15.4494	+	19.3729i	−0.533373	+	0.668828i	0.440016	+	0.897990i	$0.354973\pi$
$840$	−8.58956	−	2.64953i	−0.296368	−	0.0914175i
$841$	9.92820	+	9.21202i	0.342352	+	0.317656i
$842$	3.30690	+	0.498436i	0.113963	+	0.0171772i
$843$	2.99107	+	39.9131i	0.103018	+	1.37468i
$844$	9.27403	+	4.46614i	0.319225	+	0.153731i
$845$	30.6775	−	9.46276i	1.05534	−	0.325529i
$846$	−0.000793022		0.00202059i	−2.72646e−5		6.94692e-5i
$847$	14.7043	+	10.0252i	0.505245	+	0.344470i
$848$	−14.7745	+	2.22689i	−0.507357	+	0.0764718i
$849$	8.83872	+	38.7250i	0.303344	+	1.32904i
$850$	−3.91124	+	2.66664i	−0.134155	+	0.0914651i
$851$	1.72616	−	1.60164i	0.0591720	−	0.0549036i
$852$	0.978956	−	0.471440i	0.0335385	−	0.0161513i
$853$	−16.3009	−	28.2341i	−0.558133	−	0.966716i	−0.997652	−	0.0684822i	$-0.978184\pi$
$853$	−16.3009	−	28.2341i	−0.558133	−	0.966716i	0.439519	−	0.898233i	$-0.355149\pi$
$854$	0.784615	−	1.35899i	0.0268490	−	0.0465038i
$855$	−0.606716	+	8.09607i	−0.0207493	+	0.276880i
$856$	−1.02969	+	4.51136i	−0.0351940	+	0.154195i
$857$	−16.6207	−	42.3489i	−0.567753	−	1.44661i	−0.869841	−	0.493332i	$-0.835779\pi$
$857$	−16.6207	−	42.3489i	−0.567753	−	1.44661i	0.302088	−	0.953280i	$-0.402316\pi$
$858$	−0.617118	−	0.773841i	−0.0210681	−	0.0264185i
$859$	39.0901			1.33374			0.666868	−	0.745176i	$-0.267635\pi$
$859$	39.0901			1.33374			0.666868	+	0.745176i	$0.267635\pi$
$860$	11.9081	+	48.3361i	0.406062	+	1.64825i
$861$	−23.9333			−0.815646
$862$	−0.394931	−	0.495228i	−0.0134514	−	0.0168675i
$863$	1.66521	+	4.24289i	0.0566845	+	0.144430i	0.956411	−	0.292025i	$-0.0943291\pi$
$863$	1.66521	+	4.24289i	0.0566845	+	0.144430i	−0.899726	+	0.436455i	$0.856234\pi$
$864$	0.246716	−	1.08093i	0.00839345	−	0.0367741i
$865$	−5.69288	+	75.9662i	−0.193564	+	2.58293i
$866$	0.380209	−	0.658542i	0.0129200	−	0.0223782i
$867$	11.8899	+	20.5940i	0.403803	+	0.699407i
$868$	35.1933	−	16.9482i	1.19454	−	0.575259i
$869$	−0.401850	+	0.372863i	−0.0136318	+	0.0126485i
$870$	−2.79291	+	1.90417i	−0.0946885	+	0.0645575i
$871$	6.07729	+	26.6263i	0.205921	+	0.902199i
$872$	−6.66454	+	1.00452i	−0.225690	+	0.0340173i
$873$	−10.9850	−	7.48944i	−0.371786	−	0.253479i
$874$	0.0783111	−	0.199534i	0.00264891	−	0.00674932i
$875$	43.3355	−	13.3672i	1.46501	−	0.451895i
$876$	−46.5421	−	22.4135i	−1.57251	−	0.757282i
$877$	0.204644	+	2.73079i	0.00691034	+	0.0922121i	0.999593	−	0.0285441i	$-0.00908712\pi$
$877$	0.204644	+	2.73079i	0.00691034	+	0.0922121i	−0.992682	+	0.120756i	$0.961468\pi$
$878$	−2.49287	−	0.375740i	−0.0841303	−	0.0126806i
$879$	−27.7992	−	25.7939i	−0.937643	−	0.870005i
$880$	−29.4851	−	9.09495i	−0.993942	−	0.306591i
$881$	−27.4554	+	34.4279i	−0.924995	+	1.15991i	0.0618258	+	0.998087i	$0.480308\pi$
$881$	−27.4554	+	34.4279i	−0.924995	+	1.15991i	−0.986820	+	0.161820i	$0.948264\pi$
$882$	0.0211751	−	0.0265527i	0.000713001	−	0.000894075i
$883$	−20.8371	−	6.42741i	−0.701226	−	0.216299i	−0.0764153	−	0.997076i	$-0.524347\pi$
$883$	−20.8371	−	6.42741i	−0.701226	−	0.216299i	−0.624810	+	0.780777i	$0.714824\pi$
$884$	−16.2486	−	15.0765i	−0.546499	−	0.507077i
$885$	−35.0295	−	5.27984i	−1.17750	−	0.177480i
$886$	0.157842	+	2.10626i	0.00530281	+	0.0707610i
$887$	27.5679	+	13.2760i	0.925638	+	0.445764i	0.835081	−	0.550127i	$-0.185421\pi$
$887$	27.5679	+	13.2760i	0.925638	+	0.445764i	0.0905573	+	0.995891i	$0.471135\pi$
$888$	−0.741404	+	0.228693i	−0.0248799	+	0.00767443i
$889$	1.41032	−	3.59343i	0.0473005	−	0.120520i
$890$	4.26406	+	2.90719i	0.142932	+	0.0974491i
$891$	20.4159	−	3.07721i	0.683960	−	0.103090i
$892$	1.38877	+	6.08461i	0.0464996	+	0.203728i
$893$	0.00597807	−	0.00407578i	0.000200048	−	0.000136391i
$894$	0.384231	−	0.356515i	0.0128506	−	0.0119236i
$895$	−57.2431	+	27.5668i	−1.91342	+	0.921457i
$896$	3.95277	+	6.84639i	0.132053	+	0.228722i
$897$	6.90872	−	11.9663i	0.230676	−	0.399542i
$898$	−0.0375718	+	0.501361i	−0.00125379	+	0.0167306i
$899$	6.55218	−	28.7070i	0.218528	−	0.957432i
$900$	−17.9564	−	45.7521i	−0.598546	−	1.52507i
$901$	12.2823	+	15.4016i	0.409184	+	0.513100i
$902$	0.756135			0.0251765
$903$	40.2504	+	5.36254i	1.33945	+	0.178454i
$904$	4.32059			0.143701
$905$	−61.6814	−	77.3460i	−2.05036	−	2.57107i
$906$	−0.402867	−	1.02649i	−0.0133844	−	0.0341028i
$907$	−2.53741	+	11.1171i	−0.0842534	+	0.369138i	−0.999424	−	0.0339277i	$-0.989198\pi$
$907$	−2.53741	+	11.1171i	−0.0842534	+	0.369138i	0.915171	+	0.403066i	$0.132056\pi$
$908$	−2.79678	+	37.3204i	−0.0928143	+	1.23852i
$909$	16.0326	−	27.7693i	0.531768	−	0.921049i
$910$	−1.01966	−	1.76611i	−0.0338015	−	0.0585459i
$911$	45.7889	−	22.0508i	1.51706	−	0.730575i	0.524391	−	0.851478i	$-0.324293\pi$
$911$	45.7889	−	22.0508i	1.51706	−	0.730575i	0.992664	+	0.120903i	$0.0385789\pi$
$912$	5.62523	−	5.21945i	0.186270	−	0.172833i
$913$	−14.3545	+	9.78670i	−0.475063	+	0.323892i
$914$	0.181677	+	0.795979i	0.00600934	+	0.0263287i
$915$	55.9724	−	8.43647i	1.85039	−	0.278901i
$916$	−13.4846	−	9.19362i	−0.445543	−	0.303766i
$917$	12.7086	−	32.3810i	0.419675	−	1.06931i
$918$	−0.462074	+	0.142531i	−0.0152507	+	0.00470422i
$919$	−14.7924	−	7.12364i	−0.487956	−	0.234987i	0.173695	−	0.984800i	$-0.444429\pi$
$919$	−14.7924	−	7.12364i	−0.487956	−	0.234987i	−0.661651	+	0.749812i	$0.730144\pi$
$920$	0.296270	+	3.95345i	0.00976773	+	0.130341i
$921$	23.3028	+	3.51233i	0.767854	+	0.115735i
$922$	−1.84066	−	1.70789i	−0.0606190	−	0.0562462i
$923$	0.472191	+	0.145652i	0.0155424	+	0.00479418i
$924$	−15.7649	+	19.7685i	−0.518627	+	0.650337i
$925$	5.12842	−	6.43084i	0.168621	−	0.211445i
$926$	0.0426045	+	0.0131418i	0.00140007	+	0.000431865i
$927$	−10.9253	−	10.1372i	−0.358834	−	0.332949i
$928$	4.42297	+	0.666656i	0.145191	+	0.0218841i
$929$	−1.64742	−	21.9833i	−0.0540500	−	0.721247i	−0.956738	−	0.290951i	$-0.906028\pi$
$929$	−1.64742	−	21.9833i	−0.0540500	−	0.721247i	0.902688	−	0.430296i	$-0.141591\pi$
$930$	−5.80189	−	2.79404i	−0.190251	−	0.0916203i
$931$	−0.108175	+	0.0333676i	−0.00354530	+	0.00109358i
$932$	−4.68299	+	11.9321i	−0.153396	+	0.390848i
$933$	10.5336	+	7.18171i	0.344856	+	0.235119i
$934$	1.57320	−	0.237122i	0.0514766	−	0.00775886i
$935$	9.05256	+	39.6619i	0.296050	+	1.29708i
$936$	−1.74206	+	1.18772i	−0.0569410	+	0.0388217i
$937$	15.9976	−	14.8436i	0.522619	−	0.484920i	−0.374181	−	0.927356i	$-0.622076\pi$
$937$	15.9976	−	14.8436i	0.522619	−	0.484920i	0.896800	+	0.442436i	$0.145886\pi$
$938$	−2.87287	+	1.38350i	−0.0938026	+	0.0451730i
$939$	−2.11488	−	3.66308i	−0.0690165	−	0.119540i
$940$	−0.0333788	+	0.0578138i	−0.00108870	+	0.00188568i
$941$	−2.53842	+	33.8728i	−0.0827500	+	1.10422i	0.789040	+	0.614342i	$0.210579\pi$
$941$	−2.53842	+	33.8728i	−0.0827500	+	1.10422i	−0.871790	+	0.489880i	$0.837041\pi$
$942$	0.917241	−	4.01869i	0.0298853	−	0.130936i
$943$	3.85644	+	9.82605i	0.125583	+	0.319980i
$944$	9.66810	+	12.1234i	0.314670	+	0.394583i
$945$	9.73439			0.316660
$946$	−1.27165	−	0.169421i	−0.0413448	−	0.00550834i
$947$	39.0671			1.26951			0.634756	−	0.772713i	$-0.281101\pi$
$947$	39.0671			1.26951			0.634756	+	0.772713i	$0.281101\pi$
$948$	0.784280	+	0.983457i	0.0254722	+	0.0319412i
$949$	−8.58292	−	21.8689i	−0.278613	−	0.709895i
$950$	0.166611	−	0.729972i	0.00540558	−	0.0236834i
$951$	1.60627	−	21.4342i	0.0520870	−	0.695052i
$952$	2.59382	−	4.49262i	0.0840661	−	0.145607i
$953$	−4.03686	−	6.99204i	−0.130767	−	0.226494i	0.793206	−	0.608954i	$-0.208411\pi$
$953$	−4.03686	−	6.99204i	−0.130767	−	0.226494i	−0.923972	+	0.382459i	$0.875077\pi$
$954$	0.842203	−	0.405584i	0.0272673	−	0.0131313i
$955$	13.1764	−	12.2259i	0.426377	−	0.395620i
$956$	47.7424	−	32.5502i	1.54410	−	1.05275i
$957$	4.24129	+	18.5823i	0.137101	+	0.600680i
$958$	3.13426	−	0.472414i	0.101263	−	0.0152630i
$959$	4.15547	+	2.83315i	0.134187	+	0.0914873i
$960$	−25.6281	+	65.2992i	−0.827142	+	2.10752i
$961$	23.9800	−	7.39686i	0.773549	−	0.238608i
$962$	−0.158591	−	0.0763736i	−0.00511319	−	0.00246238i
$963$	2.35062	+	31.3669i	0.0757478	+	1.01078i
$964$	−24.6096	−	3.70930i	−0.792622	−	0.119469i
$965$	44.4555	+	41.2487i	1.43107	+	1.32784i
$966$	1.54155	+	0.475507i	0.0495987	+	0.0152992i
$967$	8.24855	−	10.3434i	0.265255	−	0.332620i	−0.631310	−	0.775530i	$-0.717483\pi$
$967$	8.24855	−	10.3434i	0.265255	−	0.332620i	0.896566	+	0.442910i	$0.146054\pi$
$968$	−1.61249	+	2.02200i	−0.0518274	+	0.0649895i
$969$	−9.66788	−	2.98215i	−0.310577	−	0.0958003i
$970$	1.36990	+	1.27108i	0.0439847	+	0.0408119i
$971$	−35.5621	−	5.36012i	−1.14124	−	0.172014i	−0.448898	−	0.893583i	$-0.648183\pi$
$971$	−35.5621	−	5.36012i	−1.14124	−	0.172014i	−0.692343	+	0.721568i	$0.743422\pi$
$972$	−3.10546	−	41.4395i	−0.0996077	−	1.32917i
$973$	−13.2945	−	6.40228i	−0.426201	−	0.205248i
$974$	1.68460	−	0.519630i	0.0539780	−	0.0166500i
$975$	17.6333	−	44.9290i	0.564719	−	1.43888i
$976$	−20.4719	−	13.9575i	−0.655288	−	0.446768i
$977$	−15.3762	+	2.31759i	−0.491928	+	0.0741462i	−0.390322	−	0.920678i	$-0.627636\pi$
$977$	−15.3762	+	2.31759i	−0.491928	+	0.0741462i	−0.101606	+	0.994825i	$0.532398\pi$
$978$	−0.505416	−	2.21437i	−0.0161614	−	0.0708078i
$979$	24.0436	−	16.3926i	0.768435	−	0.523910i
$980$	0.765674	−	0.710442i	0.0244586	−	0.0226942i
$981$	−41.2773	+	19.8781i	−1.31788	+	0.634658i
$982$	−1.56575	−	2.71196i	−0.0499651	−	0.0865421i
$983$	12.6302	−	21.8761i	0.402840	−	0.697739i	−0.591227	−	0.806505i	$-0.701356\pi$
$983$	12.6302	−	21.8761i	0.402840	−	0.697739i	0.994067	+	0.108766i	$0.0346898\pi$
$984$	0.259913	−	3.46830i	0.00828573	−	0.110565i
$985$	−20.1341	+	88.2131i	−0.641525	+	2.81070i
$986$	−0.712708	−	1.81595i	−0.0226972	−	0.0578316i
$987$	0.0339512	+	0.0425734i	0.00108068	+	0.00135513i
$988$	3.50594			0.111539
$989$	−4.28401	−	17.3892i	−0.136224	−	0.552946i
$990$	1.93044			0.0613534
$991$	−36.8301	−	46.1835i	−1.16995	−	1.46707i	−0.855507	−	0.517790i	$-0.826755\pi$
$991$	−36.8301	−	46.1835i	−1.16995	−	1.46707i	−0.314440	−	0.949277i	$-0.601817\pi$
$992$	3.11314	+	7.93216i	0.0988424	+	0.251846i
$993$	11.6247	−	50.9311i	0.368898	−	1.61625i
$994$	−0.00431138	+	0.0575314i	−0.000136749	+	0.00182479i
$995$	−11.2628	+	19.5077i	−0.357054	+	0.618436i
$996$	19.9326	+	34.5242i	0.631588	+	1.09394i
$997$	33.8868	−	16.3190i	1.07321	−	0.516829i	0.188067	−	0.982156i	$-0.439778\pi$
$997$	33.8868	−	16.3190i	1.07321	−	0.516829i	0.885139	+	0.465327i	$0.154063\pi$
$998$	0.761211	−	0.706300i	0.0240957	−	0.0223575i
$999$	0.694221	−	0.473312i	0.0219642	−	0.0149749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.23.3	yes	36
3.2	odd	2		387.2.y.c.109.1		36
4.3	odd	2		688.2.bg.c.625.3		36
43.12	odd	42		1849.2.a.o.1.8		18
43.15	even	21	inner	43.2.g.a.15.3	✓	36
43.31	even	21		1849.2.a.n.1.11		18
129.101	odd	42		387.2.y.c.316.1		36
172.15	odd	42		688.2.bg.c.273.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.15.3	✓	36	43.15	even	21	inner
43.2.g.a.23.3	yes	36	1.1	even	1	trivial
387.2.y.c.109.1		36	3.2	odd	2
387.2.y.c.316.1		36	129.101	odd	42
688.2.bg.c.273.3		36	172.15	odd	42
688.2.bg.c.625.3		36	4.3	odd	2
1849.2.a.n.1.11		18	43.31	even	21
1849.2.a.o.1.8		18	43.12	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0594739 - 0.0745779i) q^{2} +(-0.863608 - 2.20044i) q^{3} +(0.443017 - 1.94098i) q^{4} +(-0.284956 + 3.80248i) q^{5} +(-0.112742 + 0.195275i) q^{6} +(1.30981 + 2.26866i) q^{7} +(-0.342987 + 0.165174i) q^{8} +(-1.89695 + 1.76011i) q^{9} +O(q^{10})\)	\(q+(-0.0594739 - 0.0745779i) q^{2} +(-0.863608 - 2.20044i) q^{3} +(0.443017 - 1.94098i) q^{4} +(-0.284956 + 3.80248i) q^{5} +(-0.112742 + 0.195275i) q^{6} +(1.30981 + 2.26866i) q^{7} +(-0.342987 + 0.165174i) q^{8} +(-1.89695 + 1.76011i) q^{9} +(0.300528 - 0.204897i) q^{10} +(-0.456380 - 1.99953i) q^{11} +(-4.65361 + 0.701419i) q^{12} +(-1.76837 - 1.20566i) q^{13} +(0.0912923 - 0.232609i) q^{14} +(8.61320 - 2.65682i) q^{15} +(-3.55476 - 1.71188i) q^{16} +(0.388739 + 5.18736i) q^{17} +(0.244084 + 0.0367898i) q^{18} +(-0.603144 - 0.559636i) q^{19} +(7.25431 + 2.23766i) q^{20} +(3.86088 - 4.84139i) q^{21} +(-0.121978 + 0.152956i) q^{22} +(-2.60979 - 0.805013i) q^{23} +(0.659661 + 0.612076i) q^{24} +(-9.43347 - 1.42187i) q^{25} +(0.0152567 + 0.203587i) q^{26} +(-0.878006 - 0.422825i) q^{27} +(4.98370 - 1.53727i) q^{28} +(1.43632 - 3.65969i) q^{29} +(-0.710401 - 0.484343i) q^{30} +(7.40600 - 1.11627i) q^{31} +(0.253169 + 1.10920i) q^{32} +(-4.00571 + 2.73104i) q^{33} +(0.363743 - 0.337504i) q^{34} +(-8.99976 + 4.33406i) q^{35} +(2.57597 + 4.46171i) q^{36} +(-0.431097 + 0.746681i) q^{37} +(-0.00586515 + 0.0782650i) q^{38} +(-1.12579 + 4.93241i) q^{39} +(-0.530334 - 1.35127i) q^{40} +(-2.40977 - 3.02176i) q^{41} -0.590682 q^{42} +(3.37563 + 5.62185i) q^{43} -4.08324 q^{44} +(-6.15223 - 7.71466i) q^{45} +(0.0951781 + 0.242510i) q^{46} +(-0.00195677 + 0.00857316i) q^{47} +(-0.696971 + 9.30043i) q^{48} +(0.0687935 - 0.119154i) q^{49} +(0.455006 + 0.788093i) q^{50} +(11.0787 - 5.33524i) q^{51} +(-3.12358 + 2.89826i) q^{52} +(3.12892 - 2.13326i) q^{53} +(0.0206850 + 0.0906269i) q^{54} +(7.73321 - 1.16559i) q^{55} +(-0.823971 - 0.561774i) q^{56} +(-0.710564 + 1.81049i) q^{57} +(-0.358356 + 0.110538i) q^{58} +(-3.54096 - 1.70524i) q^{59} +(-1.34105 - 17.8951i) q^{60} +(6.20973 + 0.935966i) q^{61} +(-0.523713 - 0.485935i) q^{62} +(-6.47773 - 1.99812i) q^{63} +(-4.85228 + 6.08457i) q^{64} +(5.08839 - 6.38064i) q^{65} +(0.441911 + 0.136311i) q^{66} +(-9.35418 - 8.67941i) q^{67} +(10.2408 + 1.54355i) q^{68} +(0.482453 + 6.43789i) q^{69} +(0.858476 + 0.413420i) q^{70} +(-0.220622 + 0.0680530i) q^{71} +(0.359905 - 0.917022i) q^{72} +(9.06930 + 6.18335i) q^{73} +(0.0813249 - 0.0122578i) q^{74} +(5.01809 + 21.9857i) q^{75} +(-1.35345 + 0.922766i) q^{76} +(3.93848 - 3.65437i) q^{77} +(0.434804 - 0.209390i) q^{78} +(-0.133642 - 0.231475i) q^{79} +(7.52235 - 13.0291i) q^{80} +(-0.752294 + 10.0387i) q^{81} +(-0.0820379 + 0.359432i) q^{82} +(-3.09474 - 7.88527i) q^{83} +(-7.68662 - 9.63872i) q^{84} -19.8356 q^{85} +(0.218504 - 0.586100i) q^{86} -9.29333 q^{87} +(0.486802 + 0.610431i) q^{88} +(5.18366 + 13.2077i) q^{89} +(-0.209446 + 0.917642i) q^{90} +(0.418989 - 5.59101i) q^{91} +(-2.71870 + 4.70892i) q^{92} +(-8.85217 - 15.3324i) q^{93} +(0.000755745 - 0.000363948i) q^{94} +(2.29987 - 2.13397i) q^{95} +(2.22210 - 1.51500i) q^{96} +(1.14326 + 5.00894i) q^{97} +(-0.0129777 + 0.00195607i) q^{98} +(4.38512 + 2.98973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

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