LMFDB - Embedded newform 997.2.h.a.329.69

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [997,2,Mod(3,997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(997, base_ring=CyclotomicField(166))

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

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

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

chi := DirichletCharacter("997.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 997 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	997.h (of order $166$, degree $82$, 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:	$7.96108508152$
Analytic rank:	$0$
Dimension:	$6724$
Relative dimension:	$82$ over $\Q(\zeta_{166})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{166}]$

Embedding invariants

Embedding label			329.69
Character	$\chi$	$=$	997.329
Dual form			997.2.h.a.897.69

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17234 - 1.69315i) q^{2} +(0.792902 - 0.0601384i) q^{3} +(-0.788605 - 2.09778i) q^{4} +(-0.616092 + 1.39322i) q^{5} +(0.827724 - 1.41300i) q^{6} +(-4.03781 - 2.26379i) q^{7} +(-0.481595 - 0.120936i) q^{8} +(-2.34061 + 0.357105i) q^{9} +O(q^{10})$	\(q+(1.17234 - 1.69315i) q^{2} +(0.792902 - 0.0601384i) q^{3} +(-0.788605 - 2.09778i) q^{4} +(-0.616092 + 1.39322i) q^{5} +(0.827724 - 1.41300i) q^{6} +(-4.03781 - 2.26379i) q^{7} +(-0.481595 - 0.120936i) q^{8} +(-2.34061 + 0.357105i) q^{9} +(1.63665 + 2.67645i) q^{10} +(1.69153 - 0.635884i) q^{11} +(-0.751443 - 1.61591i) q^{12} +(-2.26654 - 4.04271i) q^{13} +(-8.56660 + 4.18267i) q^{14} +(-0.404714 + 1.14173i) q^{15} +(2.60289 - 2.27905i) q^{16} +(-0.456888 - 0.852351i) q^{17} +(-2.13935 + 4.38163i) q^{18} +(-4.10768 - 3.59661i) q^{19} +(3.40852 + 0.193729i) q^{20} +(-3.33773 - 1.55214i) q^{21} +(0.906394 - 3.60947i) q^{22} +(-3.55293 - 6.33718i) q^{23} +(-0.389130 - 0.0669280i) q^{24} +(1.80288 + 1.98210i) q^{25} +(-9.50205 - 0.901837i) q^{26} +(-4.15868 + 0.961027i) q^{27} +(-1.56471 + 10.2557i) q^{28} +(-4.65024 + 2.38051i) q^{29} +(1.45866 + 2.02374i) q^{30} +(8.27665 + 4.84840i) q^{31} +(-0.919816 - 8.06558i) q^{32} +(1.30297 - 0.605919i) q^{33} +(-1.97878 - 0.225664i) q^{34} +(5.64161 - 4.23084i) q^{35} +(2.59494 + 4.62846i) q^{36} +(6.49371 - 5.90658i) q^{37} +(-10.9052 + 2.73846i) q^{38} +(-2.04027 - 3.06917i) q^{39} +(0.465196 - 0.596458i) q^{40} +(-1.20534 - 1.48655i) q^{41} +(-6.54093 + 3.83163i) q^{42} +(-6.47698 + 6.85556i) q^{43} +(-2.66789 - 3.04699i) q^{44} +(0.944503 - 3.48098i) q^{45} +(-14.8950 - 1.41368i) q^{46} +(-1.82974 - 1.21635i) q^{47} +(1.92678 - 1.96359i) q^{48} +(7.52732 + 12.3096i) q^{49} +(5.46956 - 0.728859i) q^{50} +(-0.413526 - 0.648354i) q^{51} +(-6.69333 + 7.94282i) q^{52} +(6.98540 + 2.18232i) q^{53} +(-3.24821 + 8.16789i) q^{54} +(-0.156212 + 2.74842i) q^{55} +(1.67081 + 1.57855i) q^{56} +(-3.47328 - 2.60473i) q^{57} +(-1.42109 + 10.6643i) q^{58} +(-1.80306 - 2.94858i) q^{59} +(2.71427 - 0.0513743i) q^{60} +(4.85423 + 10.9772i) q^{61} +(17.9121 - 8.32961i) q^{62} +(10.2593 + 3.85672i) q^{63} +(-8.63614 - 4.62925i) q^{64} +(7.02877 - 0.667099i) q^{65} +(0.501613 - 2.91646i) q^{66} +(-1.24281 - 13.0947i) q^{67} +(-1.42774 + 1.63062i) q^{68} +(-3.19823 - 4.81109i) q^{69} +(-0.549550 - 14.5120i) q^{70} +(2.19068 + 0.871189i) q^{71} +(1.17041 + 0.111083i) q^{72} +(-1.46794 - 5.03134i) q^{73} +(-2.38788 - 17.9193i) q^{74} +(1.54871 + 1.46318i) q^{75} +(-4.30557 + 11.4533i) q^{76} +(-8.26957 - 1.26169i) q^{77} +(-7.58843 - 0.143630i) q^{78} +(6.84425 - 0.780533i) q^{79} +(1.57158 + 5.03049i) q^{80} +(3.54028 - 1.10602i) q^{81} +(-3.93001 + 0.298075i) q^{82} +(-1.09516 + 2.35505i) q^{83} +(-0.623897 + 8.22585i) q^{84} +(1.46899 - 0.111417i) q^{85} +(4.01426 + 19.0035i) q^{86} +(-3.54402 + 2.16717i) q^{87} +(-0.891531 + 0.101672i) q^{88} +(8.16478 - 7.71390i) q^{89} +(-4.78652 - 5.68006i) q^{90} +21.4547i q^{91} +(-10.4922 + 12.4508i) q^{92} +(6.85414 + 3.34656i) q^{93} +(-4.20453 + 1.67206i) q^{94} +(7.54156 - 3.50704i) q^{95} +(-1.21437 - 6.33990i) q^{96} +(1.19751 - 3.59278i) q^{97} +(29.6665 + 1.68615i) q^{98} +(-3.73212 + 2.09241i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6724 q - 83 q^{2} - 79 q^{3} - q^{4} - 83 q^{5} - 83 q^{6} - 83 q^{7} - 83 q^{8} - 165 q^{9}+O(q^{10}) $ 6724 * q - 83 * q^2 - 79 * q^3 - q^4 - 83 * q^5 - 83 * q^6 - 83 * q^7 - 83 * q^8 - 165 * q^9	\( 6724 q - 83 q^{2} - 79 q^{3} - q^{4} - 83 q^{5} - 83 q^{6} - 83 q^{7} - 83 q^{8} - 165 q^{9} - 77 q^{10} - 83 q^{11} - 83 q^{12} - 75 q^{13} - 75 q^{14} - 83 q^{15} - 161 q^{16} - 83 q^{17} - 83 q^{18} - 93 q^{19} - 83 q^{20} - 83 q^{21} - 97 q^{22} - 79 q^{23} - 83 q^{24} - q^{25} - 83 q^{26} - 73 q^{27} - 83 q^{28} - 83 q^{29} + 273 q^{30} - 55 q^{31} + 415 q^{32} - 83 q^{33} - 89 q^{34} - 39 q^{35} + 5 q^{36} - 83 q^{37} - 83 q^{38} - 35 q^{39} - 161 q^{40} + 166 q^{41} - 77 q^{42} - 83 q^{43} - 83 q^{44} - 83 q^{45} - 83 q^{46} - 83 q^{47} - 87 q^{48} + 7 q^{49} - 913 q^{50} - 83 q^{51} + 644 q^{52} - 87 q^{53} - 83 q^{54} + 352 q^{55} - 99 q^{56} - 93 q^{57} - 65 q^{58} + 519 q^{59} - 913 q^{60} - 83 q^{61} - 83 q^{62} + 830 q^{63} - 21 q^{64} - 83 q^{65} - 113 q^{66} - 85 q^{67} - 83 q^{68} - 75 q^{69} - 83 q^{70} - 97 q^{71} - 83 q^{72} - 47 q^{73} + 333 q^{74} - 53 q^{75} - 5 q^{76} - 121 q^{77} - 83 q^{78} - 87 q^{79} - 83 q^{80} - 157 q^{81} - 157 q^{82} - 403 q^{83} - 83 q^{84} + 177 q^{85} - 351 q^{86} - 83 q^{87} - 63 q^{88} - 59 q^{89} - 135 q^{90} - 9 q^{92} - 89 q^{93} + 129 q^{94} - 83 q^{95} + 747 q^{96} - 33 q^{97} - 83 q^{98} - 249 q^{99}+O(q^{100}) \) 6724 * q - 83 * q^2 - 79 * q^3 - q^4 - 83 * q^5 - 83 * q^6 - 83 * q^7 - 83 * q^8 - 165 * q^9 - 77 * q^10 - 83 * q^11 - 83 * q^12 - 75 * q^13 - 75 * q^14 - 83 * q^15 - 161 * q^16 - 83 * q^17 - 83 * q^18 - 93 * q^19 - 83 * q^20 - 83 * q^21 - 97 * q^22 - 79 * q^23 - 83 * q^24 - q^25 - 83 * q^26 - 73 * q^27 - 83 * q^28 - 83 * q^29 + 273 * q^30 - 55 * q^31 + 415 * q^32 - 83 * q^33 - 89 * q^34 - 39 * q^35 + 5 * q^36 - 83 * q^37 - 83 * q^38 - 35 * q^39 - 161 * q^40 + 166 * q^41 - 77 * q^42 - 83 * q^43 - 83 * q^44 - 83 * q^45 - 83 * q^46 - 83 * q^47 - 87 * q^48 + 7 * q^49 - 913 * q^50 - 83 * q^51 + 644 * q^52 - 87 * q^53 - 83 * q^54 + 352 * q^55 - 99 * q^56 - 93 * q^57 - 65 * q^58 + 519 * q^59 - 913 * q^60 - 83 * q^61 - 83 * q^62 + 830 * q^63 - 21 * q^64 - 83 * q^65 - 113 * q^66 - 85 * q^67 - 83 * q^68 - 75 * q^69 - 83 * q^70 - 97 * q^71 - 83 * q^72 - 47 * q^73 + 333 * q^74 - 53 * q^75 - 5 * q^76 - 121 * q^77 - 83 * q^78 - 87 * q^79 - 83 * q^80 - 157 * q^81 - 157 * q^82 - 403 * q^83 - 83 * q^84 + 177 * q^85 - 351 * q^86 - 83 * q^87 - 63 * q^88 - 59 * q^89 - 135 * q^90 - 9 * q^92 - 89 * q^93 + 129 * q^94 - 83 * q^95 + 747 * q^96 - 33 * q^97 - 83 * q^98 - 249 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/997\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{27}{166}\right)$

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 $

$2$	1.17234	−	1.69315i	0.828967	−	1.19723i	−0.149075	−	0.988826i	$-0.547630\pi$
$2$	1.17234	−	1.69315i	0.828967	−	1.19723i	0.978042	−	0.208408i	$-0.0668283\pi$
$3$	0.792902	−	0.0601384i	0.457782	−	0.0347209i	0.155282	−	0.987870i	$-0.450371\pi$
$3$	0.792902	−	0.0601384i	0.457782	−	0.0347209i	0.302500	+	0.953149i	$0.402179\pi$
$4$	−0.788605	−	2.09778i	−0.394303	−	1.04889i
$5$	−0.616092	+	1.39322i	−0.275525	+	0.623065i	−0.997637	−	0.0687113i	$-0.978111\pi$
$5$	−0.616092	+	1.39322i	−0.275525	+	0.623065i	0.722112	+	0.691776i	$0.243172\pi$
$6$	0.827724	−	1.41300i	0.337917	−	0.576855i
$7$	−4.03781	−	2.26379i	−1.52615	−	0.855633i	−0.999986	−	0.00524938i	$-0.998329\pi$
$7$	−4.03781	−	2.26379i	−1.52615	−	0.855633i	−0.526163	−	0.850384i	$-0.676370\pi$
$8$	−0.481595	−	0.120936i	−0.170269	−	0.0427573i
$9$	−2.34061	+	0.357105i	−0.780202	+	0.119035i
$10$	1.63665	+	2.67645i	0.517554	+	0.846368i
$11$	1.69153	−	0.635884i	0.510014	−	0.191726i	−0.0835642	−	0.996502i	$-0.526630\pi$
$11$	1.69153	−	0.635884i	0.510014	−	0.191726i	0.593578	+	0.804776i	$0.297715\pi$
$12$	−0.751443	−	1.61591i	−0.216923	−	0.466473i
$13$	−2.26654	−	4.04271i	−0.628626	−	1.12125i	−0.982554	−	0.185975i	$-0.940456\pi$
$13$	−2.26654	−	4.04271i	−0.628626	−	1.12125i	0.353929	−	0.935272i	$-0.384846\pi$
$14$	−8.56660	+	4.18267i	−2.28952	+	1.11787i
$15$	−0.404714	+	1.14173i	−0.104497	+	0.294794i
$16$	2.60289	−	2.27905i	0.650723	−	0.569762i
$17$	−0.456888	−	0.852351i	−0.110812	−	0.206725i	0.819875	−	0.572542i	$-0.194043\pi$
$17$	−0.456888	−	0.852351i	−0.110812	−	0.206725i	−0.930687	+	0.365817i	$0.880790\pi$
$18$	−2.13935	+	4.38163i	−0.504249	+	1.03276i
$19$	−4.10768	−	3.59661i	−0.942366	−	0.825119i	0.0423825	−	0.999101i	$-0.486505\pi$
$19$	−4.10768	−	3.59661i	−0.942366	−	0.825119i	−0.984749	+	0.173982i	$0.944337\pi$
$20$	3.40852	+	0.193729i	0.762167	+	0.0433192i
$21$	−3.33773	−	1.55214i	−0.728352	−	0.338704i
$22$	0.906394	−	3.60947i	0.193244	−	0.769541i
$23$	−3.55293	−	6.33718i	−0.740837	−	1.32139i	−0.939915	−	0.341409i	$-0.889096\pi$
$23$	−3.55293	−	6.33718i	−0.740837	−	1.32139i	0.199078	−	0.979984i	$-0.436205\pi$
$24$	−0.389130	−	0.0669280i	−0.0794309	−	0.0136616i
$25$	1.80288	+	1.98210i	0.360576	+	0.396419i
$26$	−9.50205	−	0.901837i	−1.86351	−	0.176865i
$27$	−4.15868	+	0.961027i	−0.800338	+	0.184950i
$28$	−1.56471	+	10.2557i	−0.295702	+	1.93814i
$29$	−4.65024	+	2.38051i	−0.863528	+	0.442050i	−0.830247	−	0.557396i	$-0.811801\pi$
$29$	−4.65024	+	2.38051i	−0.863528	+	0.442050i	−0.0332814	+	0.999446i	$0.510596\pi$
$30$	1.45866	+	2.02374i	0.266313	+	0.369482i
$31$	8.27665	+	4.84840i	1.48653	+	0.870798i	0.999996	−	0.00286440i	$-0.000911770\pi$
$31$	8.27665	+	4.84840i	1.48653	+	0.870798i	0.486533	+	0.873662i	$0.338261\pi$
$32$	−0.919816	−	8.06558i	−0.162602	−	1.42581i
$33$	1.30297	−	0.605919i	0.226818	−	0.105477i
$34$	−1.97878	−	0.225664i	−0.339358	−	0.0387011i
$35$	5.64161	−	4.23084i	0.953607	−	0.715142i
$36$	2.59494	+	4.62846i	0.432490	+	0.771411i
$37$	6.49371	−	5.90658i	1.06756	−	0.971035i	0.0679147	−	0.997691i	$-0.478365\pi$
$37$	6.49371	−	5.90658i	1.06756	−	0.971035i	0.999645	+	0.0266561i	$0.00848592\pi$
$38$	−10.9052	+	2.73846i	−1.76905	+	0.444236i
$39$	−2.04027	−	3.06917i	−0.326704	−	0.491460i
$40$	0.465196	−	0.596458i	0.0735540	−	0.0943082i
$41$	−1.20534	−	1.48655i	−0.188242	−	0.232160i	0.673905	−	0.738818i	$-0.264616\pi$
$41$	−1.20534	−	1.48655i	−0.188242	−	0.232160i	−0.862147	+	0.506658i	$0.830881\pi$
$42$	−6.54093	+	3.83163i	−1.00929	+	0.591233i
$43$	−6.47698	+	6.85556i	−0.987730	+	1.04546i	0.0112332	+	0.999937i	$0.496424\pi$
$43$	−6.47698	+	6.85556i	−0.987730	+	1.04546i	−0.998963	+	0.0455266i	$0.985503\pi$
$44$	−2.66789	−	3.04699i	−0.402200	−	0.459351i
$45$	0.944503	−	3.48098i	0.140798	−	0.518913i
$46$	−14.8950	−	1.41368i	−2.19615	−	0.208436i
$47$	−1.82974	−	1.21635i	−0.266896	−	0.177422i	0.413000	−	0.910731i	$-0.364481\pi$
$47$	−1.82974	−	1.21635i	−0.266896	−	0.177422i	−0.679896	+	0.733309i	$0.737975\pi$
$48$	1.92678	−	1.96359i	0.278107	−	0.283420i
$49$	7.52732	+	12.3096i	1.07533	+	1.75851i
$50$	5.46956	−	0.728859i	0.773513	−	0.103076i
$51$	−0.413526	−	0.648354i	−0.0579053	−	0.0907877i
$52$	−6.69333	+	7.94282i	−0.928197	+	1.10147i
$53$	6.98540	+	2.18232i	0.959519	+	0.299765i	0.737553	−	0.675290i	$-0.235981\pi$
$53$	6.98540	+	2.18232i	0.959519	+	0.299765i	0.221966	+	0.975054i	$0.428752\pi$
$54$	−3.24821	+	8.16789i	−0.442025	+	1.11151i
$55$	−0.156212	+	2.74842i	−0.0210636	+	0.370597i
$56$	1.67081	+	1.57855i	0.223272	+	0.210942i
$57$	−3.47328	−	2.60473i	−0.460047	−	0.345005i
$58$	−1.42109	+	10.6643i	−0.186599	+	1.40029i
$59$	−1.80306	−	2.94858i	−0.234738	−	0.383873i	0.713894	−	0.700254i	$-0.246930\pi$
$59$	−1.80306	−	2.94858i	−0.234738	−	0.383873i	−0.948632	+	0.316381i	$0.897532\pi$
$60$	2.71427	−	0.0513743i	0.350410	−	0.00663240i
$61$	4.85423	+	10.9772i	0.621520	+	1.40549i	0.896068	+	0.443917i	$0.146412\pi$
$61$	4.85423	+	10.9772i	0.621520	+	1.40549i	−0.274548	+	0.961573i	$0.588528\pi$
$62$	17.9121	−	8.32961i	2.27483	−	1.05786i
$63$	10.2593	+	3.85672i	1.29255	+	0.485901i
$64$	−8.63614	−	4.62925i	−1.07952	−	0.578657i
$65$	7.02877	−	0.667099i	0.871812	−	0.0827434i
$66$	0.501613	−	2.91646i	0.0617443	−	0.358992i
$67$	−1.24281	−	13.0947i	−0.151834	−	1.59977i	−0.668586	−	0.743635i	$-0.733100\pi$
$67$	−1.24281	−	13.0947i	−0.151834	−	1.59977i	0.516753	−	0.856135i	$-0.327141\pi$
$68$	−1.42774	+	1.63062i	−0.173139	+	0.197742i
$69$	−3.19823	−	4.81109i	−0.385022	−	0.579187i
$70$	−0.549550	−	14.5120i	−0.0656838	−	1.73452i
$71$	2.19068	+	0.871189i	0.259985	+	0.103391i	0.495891	−	0.868385i	$-0.334842\pi$
$71$	2.19068	+	0.871189i	0.259985	+	0.103391i	−0.235905	+	0.971776i	$0.575806\pi$
$72$	1.17041	+	0.111083i	0.137934	+	0.0130913i
$73$	−1.46794	−	5.03134i	−0.171809	−	0.588873i	−0.999612	−	0.0278546i	$-0.991132\pi$
$73$	−1.46794	−	5.03134i	−0.171809	−	0.588873i	0.827803	−	0.561019i	$-0.189590\pi$
$74$	−2.38788	−	17.9193i	−0.277585	−	2.08307i
$75$	1.54871	+	1.46318i	0.178829	+	0.168954i
$76$	−4.30557	+	11.4533i	−0.493883	+	1.31379i
$77$	−8.26957	−	1.26169i	−0.942405	−	0.143782i
$78$	−7.58843	−	0.143630i	−0.859220	−	0.0162629i
$79$	6.84425	−	0.780533i	0.770039	−	0.0878168i	0.280565	−	0.959835i	$-0.409478\pi$
$79$	6.84425	−	0.780533i	0.770039	−	0.0878168i	0.489473	+	0.872018i	$0.337189\pi$
$80$	1.57158	+	5.03049i	0.175708	+	0.562426i
$81$	3.54028	−	1.10602i	0.393365	−	0.122892i
$82$	−3.93001	+	0.298075i	−0.433997	+	0.0329169i
$83$	−1.09516	+	2.35505i	−0.120210	+	0.258500i	−0.957598	−	0.288109i	$-0.906973\pi$
$83$	−1.09516	+	2.35505i	−0.120210	+	0.258500i	0.837388	+	0.546610i	$0.184082\pi$
$84$	−0.623897	+	8.22585i	−0.0680728	+	0.897514i
$85$	1.46899	−	0.111417i	0.159335	−	0.0120849i
$86$	4.01426	+	19.0035i	0.432869	+	2.04920i
$87$	−3.54402	+	2.16717i	−0.379959	+	0.232345i
$88$	−0.891531	+	0.101672i	−0.0950376	+	0.0108383i
$89$	8.16478	−	7.71390i	0.865465	−	0.817672i	−0.119065	−	0.992886i	$-0.537990\pi$
$89$	8.16478	−	7.71390i	0.865465	−	0.817672i	0.984530	+	0.175215i	$0.0560620\pi$
$90$	−4.78652	−	5.68006i	−0.504544	−	0.598731i
$91$			21.4547i			2.24906i
$92$	−10.4922	+	12.4508i	−1.09388	+	1.29809i
$93$	6.85414	+	3.34656i	0.710741	+	0.347022i
$94$	−4.20453	+	1.67206i	−0.433664	+	0.172460i
$95$	7.54156	−	3.50704i	0.773748	−	0.359815i
$96$	−1.21437	−	6.33990i	−0.123942	−	0.647063i
$97$	1.19751	−	3.59278i	0.121589	−	0.364792i	−0.870197	−	0.492704i	$-0.836008\pi$
$97$	1.19751	−	3.59278i	0.121589	−	0.364792i	0.991785	+	0.127913i	$0.0408277\pi$
$98$	29.6665	+	1.68615i	2.99677	+	0.170327i
$99$	−3.73212	+	2.09241i	−0.375092	+	0.210295i
$100$	2.73624	−	5.34514i	0.273624	−	0.534514i
$101$	0.769522	+	0.0291407i	0.0765703	+	0.00289961i	0.0760989	−	0.997100i	$-0.475754\pi$
$101$	0.769522	+	0.0291407i	0.0765703	+	0.00289961i	0.000471474		1.00000i	$0.499850\pi$
$102$	−1.58255	−	0.0599289i	−0.156696	−	0.00593385i
$103$	1.01969	−	8.94132i	0.100473	−	0.881015i	−0.840333	−	0.542070i	$-0.817641\pi$
$103$	1.01969	−	8.94132i	0.100473	−	0.881015i	0.940806	−	0.338945i	$-0.110070\pi$
$104$	0.602645	+	2.22106i	0.0590943	+	0.217793i
$105$	4.21881	−	3.69391i	0.411714	−	0.360489i
$106$	11.8842	−	9.26889i	1.15430	−	0.900274i
$107$	−2.18520	−	0.592915i	−0.211251	−	0.0573193i	0.154666	−	0.987967i	$-0.450570\pi$
$107$	−2.18520	−	0.592915i	−0.211251	−	0.0573193i	−0.365917	+	0.930648i	$0.619245\pi$
$108$	5.29558	+	7.96613i	0.509567	+	0.766541i
$109$	2.73608	−	1.74510i	0.262069	−	0.167150i	−0.400174	−	0.916439i	$-0.631050\pi$
$109$	2.73608	−	1.74510i	0.262069	−	0.167150i	0.662243	+	0.749289i	$0.269605\pi$
$110$	4.47035	+	3.48657i	0.426231	+	0.332431i
$111$	4.79366	−	5.07385i	0.454994	−	0.481589i
$112$	−15.6693	+	3.30995i	−1.48061	+	0.312761i
$113$	−2.87865	−	0.608081i	−0.270800	−	0.0572034i	0.0692885	−	0.997597i	$-0.477927\pi$
$113$	−2.87865	−	0.608081i	−0.270800	−	0.0572034i	−0.340089	+	0.940393i	$0.610457\pi$
$114$	−8.48204	+	2.82715i	−0.794416	+	0.264787i
$115$	11.0180	−	1.04571i	1.02743	−	0.0975133i
$116$	8.66100	+	7.87791i	0.804154	+	0.731445i
$117$	6.74876	+	8.65301i	0.623923	+	0.799971i
$118$	−7.10617	−	0.403892i	−0.654176	−	0.0371813i
$119$	−0.0847183	+	4.47593i	−0.00776611	+	0.410308i
$120$	0.332985	−	0.500908i	0.0303972	−	0.0457265i
$121$	−5.81904	+	5.09505i	−0.529004	+	0.463187i
$122$	24.2768	+	4.65010i	2.19792	+	0.421001i
$123$	−1.04511	−	1.10620i	−0.0942347	−	0.0997428i
$124$	3.64387	−	21.1861i	0.327229	−	1.90256i
$125$	−11.0982	+	3.69914i	−0.992653	+	0.330861i
$126$	18.5574	−	12.8492i	1.65322	−	1.14469i
$127$	3.17752	+	1.62661i	0.281959	+	0.144338i	0.590904	−	0.806742i	$-0.298771\pi$
$127$	3.17752	+	1.62661i	0.281959	+	0.144338i	−0.308945	+	0.951080i	$0.599976\pi$
$128$	−3.51030	+	1.79696i	−0.310270	+	0.158831i
$129$	−4.72332	+	5.82530i	−0.415865	+	0.512889i
$130$	7.11059	−	12.6828i	0.623640	−	1.11235i
$131$	3.46354	+	3.27227i	0.302611	+	0.285900i	0.823014	−	0.568021i	$-0.192291\pi$
$131$	3.46354	+	3.27227i	0.302611	+	0.285900i	−0.520403	+	0.853921i	$0.674218\pi$
$132$	−2.29862	−	2.25552i	−0.200069	−	0.196318i
$133$	8.44405	+	23.8214i	0.732192	+	2.06557i
$134$	−23.6282	−	13.2471i	−2.04116	−	1.14438i
$135$	1.22321	−	6.38601i	0.105277	−	0.549621i
$136$	0.116955	+	0.465742i	0.0100288	+	0.0399371i
$137$	−4.91397	+	4.64260i	−0.419828	+	0.396644i	−0.867406	−	0.497601i	$-0.834214\pi$
$137$	−4.91397	+	4.64260i	−0.419828	+	0.396644i	0.447578	+	0.894245i	$0.352287\pi$
$138$	−11.8953	−	0.225148i	−1.01259	−	0.0191659i
$139$	−14.0984	+	4.99753i	−1.19581	+	0.423885i	−0.856182	−	0.516674i	$-0.827170\pi$
$139$	−14.0984	+	4.99753i	−1.19581	+	0.423885i	−0.339632	+	0.940558i	$0.610303\pi$
$140$	−13.3244	−	8.49841i	−1.12612	−	0.718247i
$141$	−1.52396	−	0.854404i	−0.128340	−	0.0719538i
$142$	4.04326	−	2.68781i	0.339303	−	0.225556i
$143$	−6.40461	−	5.39710i	−0.535581	−	0.451328i
$144$	−5.27848	+	6.26385i	−0.439874	+	0.521988i
$145$	−0.451592	−	7.94540i	−0.0375026	−	0.659830i
$146$	−10.2397	−	3.41299i	−0.847443	−	0.282461i
$147$	6.70870	+	9.30762i	0.553324	+	0.767679i
$148$	−17.5117	−	8.96443i	−1.43945	−	0.736872i
$149$	10.7290	−	4.74446i	0.878955	−	0.388681i	0.0848008	−	0.996398i	$-0.472975\pi$
$149$	10.7290	−	4.74446i	0.878955	−	0.388681i	0.794154	+	0.607717i	$0.207914\pi$
$150$	4.29299	−	0.906844i	0.350521	−	0.0740435i
$151$	7.34997	−	4.30556i	0.598132	−	0.350381i	−0.175055	−	0.984559i	$-0.556010\pi$
$151$	7.34997	−	4.30556i	0.598132	−	0.350381i	0.773188	+	0.634177i	$0.218661\pi$
$152$	1.54328	+	2.22888i	0.125176	+	0.180786i
$153$	1.37377	+	1.83186i	0.111063	+	0.148097i
$154$	−11.8309	+	12.5225i	−0.953364	+	1.00909i
$155$	−11.8540	+	8.54409i	−0.952139	+	0.686278i
$156$	−4.82948	+	6.70040i	−0.386668	+	0.536461i
$157$	9.48800	−	4.85702i	0.757225	−	0.387632i	−0.0337901	−	0.999429i	$-0.510758\pi$
$157$	9.48800	−	4.85702i	0.757225	−	0.387632i	0.791015	+	0.611797i	$0.209553\pi$
$158$	6.70221	−	12.5034i	0.533199	−	0.994714i
$159$	5.66998	+	1.31027i	0.449659	+	0.103911i
$160$	11.8038	+	3.68764i	0.933171	+	0.291533i
$161$			33.6314i			2.65053i
$162$	2.27774	−	7.29085i	0.178956	−	0.572823i
$163$	2.29546	−	11.9840i	0.179795	−	0.938656i	−0.772854	−	0.634584i	$-0.781172\pi$
$163$	2.29546	−	11.9840i	0.179795	−	0.938656i	0.952649	−	0.304072i	$-0.0983464\pi$
$164$	−2.16792	+	3.70084i	−0.169286	+	0.288987i
$165$	0.0414252	+	2.18862i	0.00322495	+	0.170384i
$166$	2.70354	+	4.61518i	0.209835	+	0.358208i
$167$	−14.6840	+	1.67460i	−1.13629	+	0.129584i	−0.661098	−	0.750300i	$-0.729909\pi$
$167$	−14.6840	+	1.67460i	−1.13629	+	0.129584i	−0.475188	+	0.879884i	$0.657620\pi$
$168$	1.41972	+	1.15115i	0.109534	+	0.0888134i
$169$	−4.42434	+	7.23522i	−0.340334	+	0.556556i
$170$	1.53351	−	2.61784i	0.117615	−	0.200779i
$171$	10.8988	+	6.95138i	0.833454	+	0.531585i
$172$	19.4893	+	8.18096i	1.48604	+	0.623792i
$173$	−3.13733	+	8.34566i	−0.238527	+	0.634509i	−0.999905	−	0.0137990i	$-0.995607\pi$
$173$	−3.13733	+	8.34566i	−0.238527	+	0.634509i	0.761378	+	0.648308i	$0.224523\pi$
$174$	−0.485455	+	8.54120i	−0.0368022	+	0.647507i
$175$	−2.79264	−	12.0847i	−0.211104	−	0.913516i
$176$	2.95365	−	5.51020i	0.222640	−	0.415347i
$177$	−1.60697	−	2.22950i	−0.120787	−	0.167580i
$178$	−3.48888	−	22.8674i	−0.261502	−	1.71399i
$179$	−4.47065	−	11.2418i	−0.334152	−	0.840253i	−0.995894	−	0.0905219i	$-0.971146\pi$
$179$	−4.47065	−	11.2418i	−0.334152	−	0.840253i	0.661742	−	0.749732i	$-0.269817\pi$
$180$	−8.04717	+	0.763755i	−0.599801	+	0.0569269i
$181$	8.72266	+	2.54491i	0.648350	+	0.189162i	0.587804	−	0.809004i	$-0.299993\pi$
$181$	8.72266	+	2.54491i	0.648350	+	0.189162i	0.0605466	+	0.998165i	$0.480716\pi$
$182$	36.3259	+	25.1521i	2.69266	+	1.86440i
$183$	4.50908	+	8.41194i	0.333321	+	0.621829i
$184$	0.944680	+	3.48163i	0.0696427	+	0.256669i
$185$	4.22841	+	12.6861i	0.310879	+	0.932703i
$186$	13.7016	−	7.68176i	1.00465	−	0.563254i
$187$	−1.31483	−	1.15125i	−0.0961502	−	0.0841874i
$188$	−1.10868	+	4.79762i	−0.0808589	+	0.349903i
$189$	18.9675	+	5.53394i	1.37968	+	0.402535i
$190$	2.90332	−	16.8804i	0.210629	−	1.22463i
$191$	−4.94892	−	3.56706i	−0.358091	−	0.258103i	0.391254	−	0.920283i	$-0.372041\pi$
$191$	−4.94892	−	3.56706i	−0.358091	−	0.258103i	−0.749345	+	0.662179i	$0.769632\pi$
$192$	−7.12600	−	3.15118i	−0.514275	−	0.227417i
$193$	2.05229	−	1.20222i	0.147727	−	0.0865374i	−0.429734	−	0.902955i	$-0.641393\pi$
$193$	2.05229	−	1.20222i	0.147727	−	0.0865374i	0.577461	+	0.816418i	$0.304043\pi$
$194$	−4.67922	−	6.23951i	−0.335948	−	0.447971i
$195$	5.53300	−	0.951643i	0.396227	−	0.0681485i
$196$	19.8868	−	25.4981i	1.42048	−	1.82129i
$197$	−1.33718	+	1.52719i	−0.0952703	+	0.108808i	−0.798025	−	0.602624i	$-0.794122\pi$
$197$	−1.33718	+	1.52719i	−0.0952703	+	0.108808i	0.702755	+	0.711432i	$0.251953\pi$
$198$	−0.832550	+	8.77202i	−0.0591668	+	0.623400i
$199$	1.15729	+	0.221673i	0.0820380	+	0.0157140i	0.228980	−	0.973431i	$-0.426461\pi$
$199$	1.15729	+	0.221673i	0.0820380	+	0.0157140i	−0.146942	+	0.989145i	$0.546943\pi$
$200$	−0.628552	−	1.17260i	−0.0444454	−	0.0829154i
$201$	−1.77292	−	10.3080i	−0.125052	−	0.727074i
$202$	0.951479	−	1.26875i	0.0669458	−	0.0892690i
$203$	24.1658	+	0.915124i	1.69611	+	0.0642291i
$204$	−1.03400	+	1.37878i	−0.0723942	+	0.0965341i
$205$	2.81368	−	0.763445i	0.196516	−	0.0533213i
$206$	−13.9435	−	12.2087i	−0.971493	−	0.850622i
$207$	10.5790	+	13.5641i	0.735294	+	0.942767i
$208$	−15.1131	−	5.35719i	−1.04790	−	0.371455i
$209$	−9.23527	−	3.47175i	−0.638817	−	0.240146i
$210$	−1.30847	−	11.4736i	−0.0902930	−	0.791751i
$211$	−19.5735	+	5.71074i	−1.34750	+	0.393144i	−0.873260	−	0.487254i	$-0.837999\pi$
$211$	−19.5735	+	5.71074i	−1.34750	+	0.393144i	−0.474236	+	0.880398i	$0.657276\pi$
$212$	−0.930694	−	16.3748i	−0.0639204	−	1.12463i
$213$	1.78938	+	0.559023i	0.122606	+	0.0383036i
$214$	−3.56568	+	3.00476i	−0.243745	+	0.205401i
$215$	−5.56086	−	13.2475i	−0.379248	−	0.903471i
$216$	2.11902	+	0.0401078i	0.144181	+	0.00272899i
$217$	−22.4438	−	38.3135i	−1.52358	−	2.60089i
$218$	0.252902	−	6.67842i	0.0171287	−	0.452320i
$219$	−1.46650	−	3.90108i	−0.0990972	−	0.263610i
$220$	5.88878	−	1.83972i	0.397022	−	0.124034i
$221$	−2.41026	+	3.77896i	−0.162131	+	0.254200i
$222$	−2.97099	−	14.0646i	−0.199400	−	0.943956i
$223$	2.99781	+	7.97452i	0.200748	+	0.534013i	0.997529	−	0.0702548i	$-0.0223812\pi$
$223$	2.99781	+	7.97452i	0.200748	+	0.534013i	−0.796781	+	0.604268i	$0.793466\pi$
$224$	−14.5448	+	34.6496i	−0.971813	+	2.31512i
$225$	−4.92765	−	3.99548i	−0.328510	−	0.266366i
$226$	−4.40431	+	4.16109i	−0.292971	+	0.276792i
$227$	−10.6145	−	25.2866i	−0.704509	−	1.67833i	−0.734345	−	0.678777i	$-0.762510\pi$
$227$	−10.6145	−	25.2866i	−0.704509	−	1.67833i	0.0298356	−	0.999555i	$-0.490502\pi$
$228$	−2.72511	+	9.34029i	−0.180475	+	0.618576i
$229$	0.789729	−	13.8947i	0.0521868	−	0.918185i	−0.860481	−	0.509483i	$-0.829837\pi$
$229$	0.789729	−	13.8947i	0.0521868	−	0.918185i	0.912668	−	0.408703i	$-0.134019\pi$
$230$	11.1462	−	19.8810i	0.734961	−	1.31091i
$231$	−6.63283	−	0.503074i	−0.436408	−	0.0330998i
$232$	2.52742	−	0.584061i	0.165933	−	0.0383455i
$233$	5.69256	−	20.9800i	0.372932	−	1.37445i	−0.491141	−	0.871080i	$-0.663420\pi$
$233$	5.69256	−	20.9800i	0.372932	−	1.37445i	0.864073	−	0.503366i	$-0.167905\pi$
$234$	22.5626	−	1.28239i	1.47496	−	0.0838323i
$235$	2.82192	−	1.79985i	0.184082	−	0.117409i
$236$	−4.76358	+	6.10769i	−0.310083	+	0.397577i
$237$	5.37988	−	1.03049i	0.349461	−	0.0669374i
$238$	7.47908	+	5.39074i	0.484797	+	0.349430i
$239$	23.7161	−	7.90481i	1.53407	−	0.511319i	0.580954	−	0.813936i	$-0.302680\pi$
$239$	23.7161	−	7.90481i	1.53407	−	0.511319i	0.953112	+	0.302617i	$0.0978602\pi$
$240$	1.54864	+	3.89417i	0.0999640	+	0.251368i
$241$	1.89973	+	25.0472i	0.122372	+	1.61343i	0.647266	+	0.762264i	$0.275912\pi$
$241$	1.89973	+	25.0472i	0.122372	+	1.61343i	−0.524893	+	0.851168i	$0.675895\pi$
$242$	1.80478	+	15.8256i	0.116016	+	1.01731i
$243$	14.6391	−	5.82167i	0.939096	−	0.373460i
$244$	19.1998	−	18.8398i	1.22914	−	1.20610i
$245$	−21.7874	+	2.90333i	−1.39195	+	0.185487i
$246$	−3.09818	+	0.472689i	−0.197533	+	0.0301375i
$247$	−5.22985	+	24.7580i	−0.332767	+	1.57532i
$248$	−3.39964	−	3.33591i	−0.215878	−	0.211830i
$249$	−0.726729	+	1.93318i	−0.0460546	+	0.122511i
$250$	−6.74765	+	23.1275i	−0.426759	+	1.46271i
$251$	11.3738	−	9.58455i	0.717906	−	0.604972i	−0.210037	−	0.977693i	$-0.567359\pi$
$251$	11.3738	−	9.58455i	0.717906	−	0.604972i	0.927943	+	0.372722i	$0.121575\pi$
$252$		−	24.5633i		−	1.54734i
$253$	−10.0396	−	8.46025i	−0.631183	−	0.531891i
$254$	6.47921	−	3.47307i	0.406542	−	0.217920i
$255$	1.15807	−	0.176686i	0.0725210	−	0.0110645i
$256$	1.51586	−	11.3754i	0.0947411	−	0.710964i
$257$	−19.4724	+	15.7888i	−1.21466	+	0.984879i	−0.214690	+	0.976682i	$0.568874\pi$
$257$	−19.4724	+	15.7888i	−1.21466	+	0.984879i	−0.999966	+	0.00819686i	$0.997391\pi$
$258$	4.32576	+	14.8265i	0.269310	+	0.923057i
$259$	−39.5916	+	9.14922i	−2.46010	+	0.568505i
$260$	−6.94235	−	14.2188i	−0.430546	−	0.881809i
$261$	10.0343	−	7.23247i	0.621107	−	0.447678i
$262$	9.60087	−	2.02807i	0.593144	−	0.125295i
$263$	2.39324	+	1.05831i	0.147574	+	0.0652583i	0.476899	−	0.878958i	$-0.341761\pi$
$263$	2.39324	+	1.05831i	0.147574	+	0.0652583i	−0.329325	+	0.944217i	$0.606821\pi$
$264$	−0.700782	+	0.134231i	−0.0431302	+	0.00826136i
$265$	−7.34409	+	8.38766i	−0.451144	+	0.515250i
$266$	50.2323	+	13.6297i	3.07994	+	0.835689i
$267$	6.00997	−	6.60738i	0.367804	−	0.404365i
$268$	−26.4897	+	12.9337i	−1.61812	+	0.790050i
$269$	0.0767506	−	0.305639i	0.00467957	−	0.0186351i	−0.967503	−	0.252860i	$-0.918629\pi$
$269$	0.0767506	−	0.305639i	0.00467957	−	0.0186351i	0.972182	+	0.234225i	$0.0752553\pi$
$270$	−9.37844	−	9.55763i	−0.570753	−	0.581659i
$271$	−5.19684	−	27.1312i	−0.315686	−	1.64810i	−0.692210	−	0.721697i	$-0.743363\pi$
$271$	−5.19684	−	27.1312i	−0.315686	−	1.64810i	0.376524	−	0.926407i	$-0.377119\pi$
$272$	−3.13178	−	1.17731i	−0.189892	−	0.0713848i
$273$	1.29025	+	17.0115i	0.0780895	+	1.02958i
$274$	2.09978	+	13.7627i	0.126852	+	0.831438i
$275$	4.31000	+	2.20634i	0.259903	+	0.133047i
$276$	−7.57048	+	10.5032i	−0.455689	+	0.632221i
$277$	1.36026	+	2.78597i	0.0817301	+	0.167393i	0.935568	−	0.353145i	$-0.114888\pi$
$277$	1.36026	+	2.78597i	0.0817301	+	0.167393i	−0.853838	+	0.520538i	$0.825731\pi$
$278$	−8.06658	+	29.7295i	−0.483802	+	1.78306i
$279$	−21.1037	−	8.39255i	−1.26345	−	0.502449i
$280$	−3.22863	+	1.35527i	−0.192948	+	0.0809932i
$281$	−19.3154	+	17.5690i	−1.15226	+	1.04808i	−0.154063	+	0.988061i	$0.549236\pi$
$281$	−19.3154	+	17.5690i	−1.15226	+	1.04808i	−0.998197	+	0.0600164i	$0.980885\pi$
$282$	−3.23322	+	1.57863i	−0.192535	+	0.0940061i
$283$	4.92416	+	3.01112i	0.292711	+	0.178993i	0.660313	−	0.750990i	$-0.270424\pi$
$283$	4.92416	+	3.01112i	0.292711	+	0.178993i	−0.367602	+	0.929983i	$0.619821\pi$
$284$	0.0999862	−	5.28258i	0.00593309	−	0.313464i
$285$	5.76881	−	3.23427i	0.341715	−	0.191582i
$286$	−16.6464	+	4.51672i	−0.984324	+	0.267079i
$287$	1.50169	+	8.73105i	0.0886417	+	0.515377i
$288$	5.03319	+	18.5499i	0.296583	+	1.09306i
$289$	8.89347	−	13.3784i	0.523146	−	0.786966i
$290$	−13.9821	−	8.55008i	−0.821059	−	0.502078i
$291$	0.733443	−	2.92074i	0.0429952	−	0.171217i
$292$	−9.39702	+	7.04715i	−0.549919	+	0.412403i
$293$	−17.7033	−	2.35910i	−1.03424	−	0.137820i	−0.404429	−	0.914569i	$-0.632530\pi$
$293$	−17.7033	−	2.35910i	−1.03424	−	0.137820i	−0.629810	+	0.776749i	$0.716867\pi$
$294$	23.6240	−	0.447144i	1.37778	−	0.0260779i
$295$	5.21886	−	0.695451i	0.303854	−	0.0404907i
$296$	−3.84165	+	2.05925i	−0.223292	+	0.119692i
$297$	−6.42341	+	4.27004i	−0.372724	+	0.247773i
$298$	4.54495	−	23.7279i	0.263282	−	1.37452i
$299$	−17.5665	+	28.7270i	−1.01590	+	1.66132i
$300$	1.84812	−	4.40273i	0.106701	−	0.254192i
$301$	41.6724	−	13.0189i	2.40196	−	0.750398i
$302$	1.32671	−	17.4921i	0.0763434	−	1.00656i
$303$	0.611908	−	0.0231721i	0.0351532	−	0.00133120i
$304$	−18.8887			−1.08334
$305$	−18.2843			−1.04696
$306$	4.71213	−	0.178442i	0.269375	−	0.0102008i
$307$	8.74170	−	18.7982i	0.498915	−	1.07287i	−0.481594	−	0.876395i	$-0.659942\pi$
$307$	8.74170	−	18.7982i	0.498915	−	1.07287i	0.980509	−	0.196476i	$-0.0629496\pi$
$308$	3.87469	+	18.3427i	0.220781	+	1.04517i
$309$	0.270795	−	7.15091i	0.0154050	−	0.406801i
$310$	0.569475	+	30.0871i	0.0323440	+	1.70884i
$311$	−17.7465	−	11.3189i	−1.00631	−	0.641837i	−0.0716726	−	0.997428i	$-0.522834\pi$
$311$	−17.7465	−	11.3189i	−1.00631	−	0.641837i	−0.934641	+	0.355591i	$0.884279\pi$
$312$	0.611409	+	1.72484i	0.0346142	+	0.0976497i
$313$	3.20091	−	15.1531i	0.180926	−	0.856502i	−0.789245	−	0.614079i	$-0.789528\pi$
$313$	3.20091	−	15.1531i	0.180926	−	0.856502i	0.970171	−	0.242423i	$-0.0779422\pi$
$314$	2.89949	−	21.7586i	0.163628	−	1.22791i
$315$	−11.6939	+	11.9174i	−0.658879	+	0.671468i
$316$	−7.03480	−	13.7422i	−0.395738	−	0.773060i
$317$	−17.0049	−	2.92474i	−0.955092	−	0.164270i	−0.329270	−	0.944236i	$-0.606803\pi$
$317$	−17.0049	−	2.92474i	−0.955092	−	0.164270i	−0.625822	+	0.779966i	$0.715236\pi$
$318$	8.86561	−	8.06401i	0.497158	−	0.452207i
$319$	−6.35227	+	6.98371i	−0.355659	+	0.391013i
$320$	11.7702	−	9.17996i	0.657974	−	0.513175i
$321$	−1.76830	−	0.338709i	−0.0986970	−	0.0189049i
$322$	56.9429	+	39.4273i	3.17330	+	2.19720i
$323$	−1.18883	+	5.14443i	−0.0661480	+	0.286244i
$324$	−5.11208	−	6.55453i	−0.284005	−	0.364140i
$325$	3.92674	−	11.7810i	0.217816	−	0.653495i
$326$	−17.5995	−	17.9358i	−0.974747	−	0.993371i
$327$	2.06449	−	1.54823i	0.114167	−	0.0856175i
$328$	0.400707	+	0.861684i	0.0221254	+	0.0475785i
$329$	4.63461	+	9.05354i	0.255514	+	0.499138i
$330$	3.75422	+	2.49566i	0.206663	+	0.137382i
$331$	−7.13460	−	24.4538i	−0.392153	−	1.34410i	−0.881571	−	0.472052i	$-0.843513\pi$
$331$	−7.13460	−	24.4538i	−0.392153	−	1.34410i	0.489417	−	0.872050i	$-0.337209\pi$
$332$	5.80403	+	0.440212i	0.318538	+	0.0241598i
$333$	−13.0899	+	16.1439i	−0.717324	+	0.884680i
$334$	−14.3793	+	26.8254i	−0.786800	+	1.46782i
$335$	19.0094	+	6.33602i	1.03859	+	0.346174i
$336$	−12.2251	+	3.56679i	−0.666936	+	0.194584i
$337$	−4.29047	+	1.70624i	−0.233717	+	0.0929447i	−0.483456	−	0.875368i	$-0.660619\pi$
$337$	−4.29047	+	1.70624i	−0.233717	+	0.0929447i	0.249740	+	0.968313i	$0.419655\pi$
$338$	7.06347	+	15.9732i	0.384202	+	0.868825i
$339$	−2.31905	−	0.309031i	−0.125954	−	0.0167842i
$340$	−1.39218	−	2.99376i	−0.0755018	−	0.162360i
$341$	17.0832	+	2.93820i	0.925106	+	0.159112i
$342$	24.5468	−	10.3039i	1.32734	−	0.557173i
$343$	−1.30130	−	34.3635i	−0.0702635	−	1.85546i
$344$	3.94836	−	2.51830i	0.212881	−	0.135778i
$345$	8.67329	−	1.49175i	0.466954	−	0.0803132i
$346$	10.4524	+	15.0959i	0.561925	+	0.811560i
$347$	13.0113	+	17.3499i	0.698481	+	0.931390i	0.999755	−	0.0221473i	$-0.00705029\pi$
$347$	13.0113	+	17.3499i	0.698481	+	0.931390i	−0.301274	+	0.953538i	$0.597412\pi$
$348$	7.34109	+	5.72555i	0.393524	+	0.306922i
$349$	10.9511	−	0.622426i	0.586199	−	0.0333177i	0.238855	−	0.971055i	$-0.423228\pi$
$349$	10.9511	−	0.622426i	0.586199	−	0.0333177i	0.347345	+	0.937738i	$0.387083\pi$
$350$	−23.7350	−	9.43896i	−1.26869	−	0.504533i
$351$	13.3110	+	14.6341i	0.710487	+	0.781112i
$352$	−6.68467	−	13.0582i	−0.356294	−	0.696007i
$353$	−17.7720	+	6.68093i	−0.945911	+	0.355590i	−0.776615	−	0.629975i	$-0.783065\pi$
$353$	−17.7720	+	6.68093i	−0.945911	+	0.355590i	−0.169296	+	0.985565i	$0.554149\pi$
$354$	−5.65878	+	0.107107i	−0.300761	+	0.00569266i
$355$	−2.56341	+	2.51535i	−0.136052	+	0.133501i
$356$	−22.6209	−	11.0447i	−1.19890	−	0.585369i
$357$	0.202002	+	3.55407i	0.0106911	+	0.188101i
$358$	−24.2752	−	5.60974i	−1.28298	−	0.296484i
$359$	3.03323	+	13.1258i	0.160088	+	0.692752i	0.990719	+	0.135929i	$0.0434018\pi$
$359$	3.03323	+	13.1258i	0.160088	+	0.692752i	−0.830631	+	0.556824i	$0.812020\pi$
$360$	−0.875843	+	1.56220i	−0.0461610	+	0.0823350i
$361$	1.42771	+	10.7139i	0.0751426	+	0.563892i
$362$	14.5348	−	11.7852i	0.763932	−	0.619418i
$363$	−4.30752	+	4.38982i	−0.226086	+	0.230406i
$364$	45.0073	−	16.9193i	2.35902	−	0.886811i
$365$	7.91412	+	1.05461i	0.414244	+	0.0552010i
$366$	19.5288	+	2.22710i	1.02079	+	0.116413i
$367$	3.66783	+	19.1487i	0.191459	+	0.999553i	0.941207	+	0.337830i	$0.109693\pi$
$367$	3.66783	+	19.1487i	0.191459	+	0.999553i	−0.749748	+	0.661724i	$0.769825\pi$
$368$	−23.6906	−	8.39769i	−1.23496	−	0.437760i
$369$	3.35208	+	3.04900i	0.174502	+	0.158724i
$370$	26.4366	+	7.71310i	1.37437	+	0.400985i
$371$	−23.2654	−	24.6253i	−1.20788	−	1.27848i
$372$	1.61514	−	17.0176i	0.0837409	−	0.882322i
$373$	22.4515	+	6.09183i	1.16250	+	0.315423i	0.790293	−	0.612729i	$-0.209928\pi$
$373$	22.4515	+	6.09183i	1.16250	+	0.315423i	0.372202	+	0.928152i	$0.378603\pi$
$374$	−3.49065	+	0.876558i	−0.180497	+	0.0453257i
$375$	−8.57732	+	3.60048i	−0.442931	+	0.185928i
$376$	0.734096	+	0.807068i	0.0378581	+	0.0416213i
$377$	20.1637	+	13.4041i	1.03848	+	0.690345i
$378$	31.6061	−	25.6271i	1.62564	−	1.31812i
$379$	8.81965	+	6.61415i	0.453035	+	0.339746i	0.801932	−	0.597415i	$-0.203805\pi$
$379$	8.81965	+	6.61415i	0.453035	+	0.339746i	−0.348898	+	0.937161i	$0.613444\pi$
$380$	−13.3043	−	13.0549i	−0.682497	−	0.669701i
$381$	2.61728	+	1.09865i	0.134088	+	0.0562856i
$382$	−11.8413	+	4.19744i	−0.605856	+	0.214760i
$383$	13.8014	+	23.5602i	0.705219	+	1.20387i	0.970825	+	0.239791i	$0.0770788\pi$
$383$	13.8014	+	23.5602i	0.705219	+	1.20387i	−0.265605	+	0.964082i	$0.585572\pi$
$384$	−2.67526	+	1.63592i	−0.136521	+	0.0834826i
$385$	6.85261	−	10.7440i	0.349242	−	0.547564i
$386$	0.370449	−	4.88423i	0.0188554	−	0.248601i
$387$	12.7119	−	18.3591i	0.646182	−	0.933247i
$388$	−8.48124	+	0.321173i	−0.430570	+	0.0163051i
$389$	11.0171	−	15.9114i	0.558587	−	0.806739i	−0.437110	−	0.899408i	$-0.643998\pi$
$389$	11.0171	−	15.9114i	0.558587	−	0.806739i	0.995697	+	0.0926693i	$0.0295400\pi$
$390$	4.87527	−	10.4838i	0.246869	−	0.530869i
$391$	−3.77821	+	5.92372i	−0.191072	+	0.299576i
$392$	−2.13644	−	6.83856i	−0.107907	−	0.345399i
$393$	2.94304	+	2.38630i	0.148457	+	0.120373i
$394$	1.01813	+	4.05442i	0.0512926	+	0.204259i
$395$	−3.12924	+	10.0164i	−0.157449	+	0.503980i
$396$	7.33258	+	6.17909i	0.368476	+	0.310511i
$397$	−9.19678	−	14.4193i	−0.461573	−	0.723685i	0.530727	−	0.847543i	$-0.321919\pi$
$397$	−9.19678	−	14.4193i	−0.461573	−	0.723685i	−0.992300	+	0.123858i	$0.960473\pi$
$398$	1.73206	−	1.69958i	0.0868201	−	0.0851923i
$399$	8.12788	+	18.3802i	0.406903	+	0.920161i
$400$	9.21000	+	1.05033i	0.460500	+	0.0525164i
$401$	−0.418097	−	0.426085i	−0.0208788	−	0.0212777i	0.703247	−	0.710945i	$-0.251733\pi$
$401$	−0.418097	−	0.426085i	−0.0208788	−	0.0212777i	−0.724126	+	0.689667i	$0.757757\pi$
$402$	−19.5315	−	9.08269i	−0.974142	−	0.453003i
$403$	0.841313	−	44.4492i	0.0419088	−	2.21417i
$404$	−0.545718	−	1.63727i	−0.0271505	−	0.0814573i
$405$	−0.640209	+	5.61379i	−0.0318122	+	0.278951i
$406$	29.8799	−	39.8433i	1.48291	−	1.97739i
$407$	7.22838	−	14.1204i	0.358298	−	0.699921i
$408$	0.120743	+	0.362254i	0.00597766	+	0.0179343i
$409$	−1.00081	+	1.50552i	−0.0494871	+	0.0744433i	−0.856693	−	0.515827i	$-0.827485\pi$
$409$	−1.00081	+	1.50552i	−0.0494871	+	0.0744433i	0.807206	+	0.590270i	$0.200979\pi$
$410$	2.00596	−	5.65899i	0.0990674	−	0.279478i
$411$	−3.61709	+	3.97664i	−0.178418	+	0.196153i
$412$	−19.5611	+	4.91209i	−0.963705	+	0.242001i
$413$	0.605427	+	15.9876i	0.0297911	+	0.786697i
$414$	35.3681	−	2.01021i	1.73825	−	0.0987966i
$415$	−2.60637	−	2.97673i	−0.127942	−	0.146122i
$416$	−30.5220	+	21.9995i	−1.49647	+	1.07862i
$417$	−10.8781	+	4.81040i	−0.532705	+	0.235566i
$418$	−16.7050	+	11.5666i	−0.817070	+	0.565741i
$419$	−3.99949	−	10.0571i	−0.195388	−	0.491319i	0.798463	−	0.602044i	$-0.205647\pi$
$419$	−3.99949	−	10.0571i	−0.195388	−	0.491319i	−0.993851	+	0.110724i	$0.964683\pi$
$420$	−11.0760	−	5.93710i	−0.540453	−	0.289701i
$421$	29.5591	+	10.4779i	1.44062	+	0.510663i	0.935791	−	0.352555i	$-0.114687\pi$
$421$	29.5591	+	10.4779i	1.44062	+	0.510663i	0.504831	+	0.863218i	$0.331555\pi$
$422$	−13.2776	+	39.8357i	−0.646345	+	1.93917i
$423$	4.71707	+	2.19357i	0.229352	+	0.106655i
$424$	−3.10021	−	1.89578i	−0.150560	−	0.0920672i
$425$	0.865725	−	2.44228i	0.0419938	−	0.118468i
$426$	3.04427	−	2.37432i	0.147495	−	0.115036i
$427$	5.24974	−	55.3130i	0.254053	−	2.67678i
$428$	0.479450	+	5.05164i	0.0231751	+	0.244180i
$429$	−5.40280	−	3.89421i	−0.260850	−	0.188014i
$430$	−28.9491	−	6.11516i	−1.39605	−	0.294899i
$431$	37.7019	−	16.6721i	1.81604	−	0.803067i	0.859699	−	0.510801i	$-0.170651\pi$
$431$	37.7019	−	16.6721i	1.81604	−	0.803067i	0.956337	−	0.292266i	$-0.0944091\pi$
$432$	−8.63436	+	11.9793i	−0.415421	+	0.576353i
$433$	1.96813	−	12.8999i	0.0945822	−	0.619928i	−0.891418	−	0.453182i	$-0.850289\pi$
$433$	1.96813	−	12.8999i	0.0945822	−	0.619928i	0.986000	−	0.166746i	$-0.0533258\pi$
$434$	−91.1820	−	6.91579i	−4.37687	−	0.331968i
$435$	−0.835891	−	6.27276i	−0.0400779	−	0.300756i
$436$	−5.81852	−	4.36350i	−0.278657	−	0.208974i
$437$	−8.19807	+	38.8096i	−0.392167	+	1.85651i
$438$	−8.32432	−	2.09037i	−0.397752	−	0.0998816i
$439$	−34.8016	+	23.1348i	−1.66099	+	1.10416i	−0.789506	+	0.613743i	$0.789663\pi$
$439$	−34.8016	+	23.1348i	−1.66099	+	1.10416i	−0.871486	+	0.490421i	$0.836843\pi$
$440$	0.407614	−	1.30473i	0.0194322	−	0.0622008i
$441$	−22.0143	−	26.1239i	−1.04830	−	1.24399i
$442$	3.57269	+	8.51112i	0.169936	+	0.404833i
$443$	19.3857	+	2.95766i	0.921041	+	0.140523i	0.593980	−	0.804480i	$-0.297556\pi$
$443$	19.3857	+	2.95766i	0.921041	+	0.140523i	0.327062	+	0.945003i	$0.393942\pi$
$444$	−14.4241	−	6.05479i	−0.684540	−	0.287348i
$445$	5.71687	+	16.1278i	0.271006	+	0.764530i
$446$	17.0165	+	4.27310i	0.805753	+	0.202337i
$447$	8.22173	−	4.40711i	0.388874	−	0.208449i
$448$	24.3914	+	38.2425i	1.15239	+	1.80679i
$449$	25.0990	+	12.2547i	1.18450	+	0.578334i	0.922223	−	0.386659i	$-0.126371\pi$
$449$	25.0990	+	12.2547i	1.18450	+	0.578334i	0.262274	+	0.964994i	$0.415528\pi$
$450$	−12.5418	+	3.65918i	−0.591226	+	0.172495i
$451$	−2.98414	−	1.74808i	−0.140517	−	0.0823140i
$452$	0.994496	+	6.51831i	0.0467772	+	0.306596i
$453$	5.56887	−	3.85590i	0.261649	−	0.181166i
$454$	−55.2577	−	11.6725i	−2.59337	−	0.547819i
$455$	−29.8910	−	13.2181i	−1.40131	−	0.619672i
$456$	1.35771	+	1.67447i	0.0635805	+	0.0784142i
$457$	−2.01055	+	0.345803i	−0.0940498	+	0.0161760i	−0.216337	−	0.976319i	$-0.569411\pi$
$457$	−2.01055	+	0.345803i	−0.0940498	+	0.0161760i	0.122287	+	0.992495i	$0.460977\pi$
$458$	−22.5999	−	17.6263i	−1.05602	−	0.823625i
$459$	2.71918	+	3.10557i	0.126921	+	0.144956i
$460$	−10.8825	−	22.2887i	−0.507400	−	1.03921i
$461$	−3.70641	+	24.2932i	−0.172625	+	1.13145i	0.724371	+	0.689410i	$0.242130\pi$
$461$	−3.70641	+	24.2932i	−0.172625	+	1.13145i	−0.896996	+	0.442039i	$0.854255\pi$
$462$	−8.62769	+	10.6406i	−0.401396	+	0.495044i
$463$	1.46756	+	6.35061i	0.0682034	+	0.295138i	0.997184	−	0.0749894i	$-0.0238923\pi$
$463$	1.46756	+	6.35061i	0.0682034	+	0.295138i	−0.928981	+	0.370127i	$0.879314\pi$
$464$	−6.67878	+	16.7943i	−0.310054	+	0.779657i
$465$	−8.88525	+	7.48751i	−0.412044	+	0.347225i
$466$	−28.8486	−	34.2340i	−1.33639	−	1.58586i
$467$	6.85226	+	27.2873i	0.317085	+	1.26270i	0.894800	+	0.446467i	$0.147318\pi$
$467$	6.85226	+	27.2873i	0.317085	+	1.26270i	−0.577715	+	0.816238i	$0.696056\pi$
$468$	12.8300	−	20.9812i	0.593068	−	0.969857i
$469$	−24.6254	+	55.6873i	−1.13710	+	2.57140i
$470$	0.260837	−	6.88795i	0.0120315	−	0.317717i
$471$	7.23096	−	4.42173i	0.333185	−	0.203743i
$472$	0.511754	+	1.63808i	0.0235554	+	0.0753986i
$473$	−6.59663	+	15.7150i	−0.303314	+	0.722575i
$474$	4.56226	−	10.3170i	0.209552	−	0.473875i
$475$	−0.276835	−	14.6261i	−0.0127021	−	0.671091i
$476$	9.45634	−	3.35202i	0.433431	−	0.153640i
$477$	−17.1294	−	2.61342i	−0.784301	−	0.119660i
$478$	14.4193	−	49.4219i	0.659522	−	2.26050i
$479$	−13.1624	+	33.0980i	−0.601407	+	1.51229i	0.239383	+	0.970925i	$0.423055\pi$
$479$	−13.1624	+	33.0980i	−0.601407	+	1.51229i	−0.840790	+	0.541361i	$0.817909\pi$
$480$	9.58101	+	2.21407i	0.437311	+	0.101058i
$481$	−38.5969	−	12.8647i	−1.75987	−	0.586580i
$482$	44.6357	+	26.1472i	2.03310	+	1.19097i
$483$	2.02254	+	26.6664i	0.0920287	+	1.21336i
$484$	15.2772	+	8.18910i	0.694420	+	0.372232i
$485$	4.26774	+	3.88187i	0.193788	+	0.176267i
$486$	7.30497	−	31.6110i	0.331360	−	1.43390i
$487$	7.33325	−	15.0194i	0.332301	−	0.680592i	−0.665533	−	0.746368i	$-0.731796\pi$
$487$	7.33325	−	15.0194i	0.332301	−	0.680592i	0.997834	+	0.0657764i	$0.0209524\pi$
$488$	−1.01023	−	5.87363i	−0.0457309	−	0.265887i
$489$	1.09938	−	9.64014i	0.0497158	−	0.435942i
$490$	−20.6264	+	40.2930i	−0.931808	+	1.82025i
$491$	0.601798	−	0.163287i	0.0271588	−	0.00736906i	−0.248259	−	0.968694i	$-0.579858\pi$
$491$	0.601798	−	0.163287i	0.0271588	−	0.00736906i	0.275418	+	0.961325i	$0.411184\pi$
$492$	−1.49639	+	3.06478i	−0.0674623	+	0.138171i
$493$	4.15367	+	2.87601i	0.187072	+	0.129529i
$494$	35.7878	+	37.8797i	1.61017	+	1.70429i
$495$	−0.615846	−	6.48876i	−0.0276802	−	0.291648i
$496$	32.5929	−	6.24301i	1.46347	−	0.280319i
$497$	−6.87334	−	8.47693i	−0.308312	−	0.380242i
$498$	2.42119	+	3.49680i	0.108496	+	0.156695i
$499$	15.6178	+	22.5559i	0.699147	+	1.00974i	0.998454	+	0.0555848i	$0.0177023\pi$
$499$	15.6178	+	22.5559i	0.699147	+	1.00974i	−0.299307	+	0.954157i	$0.596756\pi$
$500$	16.5121	+	20.3644i	0.738443	+	0.910725i
$501$	−11.5423	+	2.21087i	−0.515672	+	0.0987743i
$502$	−2.89415	−	30.4938i	−0.129172	−	1.36100i
$503$	17.2989	+	18.3100i	0.771320	+	0.816405i	0.987111	−	0.160035i	$-0.0511607\pi$
$503$	17.2989	+	18.3100i	0.771320	+	0.816405i	−0.215791	+	0.976440i	$0.569233\pi$
$504$	−4.47443	−	3.09810i	−0.199307	−	0.138000i
$505$	−0.514696	+	1.05416i	−0.0229037	+	0.0469094i
$506$	−26.0942	+	7.08021i	−1.16003	+	0.314754i
$507$	−3.07295	+	6.00289i	−0.136475	+	0.266598i
$508$	0.906464	−	7.94850i	0.0402178	−	0.352658i
$509$	5.64761	+	32.8361i	0.250326	+	1.45544i	0.789764	+	0.613411i	$0.210203\pi$
$509$	5.64761	+	32.8361i	0.250326	+	1.45544i	−0.539438	+	0.842026i	$0.681363\pi$
$510$	1.05849	−	2.16791i	0.0468707	−	0.0959967i
$511$	−5.46266	+	23.6387i	−0.241654	+	1.04571i
$512$	−23.3176	−	21.2094i	−1.03050	−	0.937330i
$513$	20.5390	+	11.0096i	0.906817	+	0.486084i
$514$	3.90451	+	51.4794i	0.172220	+	2.27066i
$515$	11.8290	+	6.92932i	0.521247	+	0.305342i
$516$	15.9451	+	5.31464i	0.701942	+	0.233964i
$517$	−3.86852	−	0.893974i	−0.170137	−	0.0393169i
$518$	−30.9238	+	77.7603i	−1.35871	+	3.41659i
$519$	−1.98570	+	6.80596i	−0.0871625	+	0.298749i
$520$	−3.46570	−	0.528760i	−0.151981	−	0.0231877i
$521$	−28.0172	+	9.93135i	−1.22745	+	0.435100i	−0.867297	−	0.497791i	$-0.834145\pi$
$521$	−28.0172	+	9.93135i	−1.22745	+	0.435100i	−0.360158	+	0.932891i	$0.617277\pi$
$522$	−0.482053	−	25.4684i	−0.0210989	−	1.11472i
$523$	4.94114	−	11.1738i	0.216061	−	0.488596i	−0.773306	−	0.634033i	$-0.781399\pi$
$523$	4.94114	−	11.1738i	0.216061	−	0.488596i	0.989368	+	0.145437i	$0.0464588\pi$
$524$	4.13315	−	9.84629i	0.180558	−	0.430137i
$525$	−2.94105	−	9.41402i	−0.128358	−	0.410861i
$526$	4.59756	−	2.81141i	0.200463	−	0.122583i
$527$	0.351034	−	9.26978i	0.0152913	−	0.403798i
$528$	2.01058	−	4.54668i	0.0874992	−	0.197869i
$529$	−15.5376	+	25.4090i	−0.675547	+	1.10474i
$530$	5.59178	+	22.2678i	0.242892	+	0.967250i
$531$	5.27320	+	6.25759i	0.228837	+	0.271556i
$532$	43.3130	−	36.4994i	1.87786	−	1.58245i
$533$	−3.27775	+	8.24217i	−0.141975	+	0.357008i
$534$	−4.14155	−	17.9218i	−0.179222	−	0.775553i
$535$	2.17234	−	2.67916i	0.0939185	−	0.115830i
$536$	−0.985085	+	6.45663i	−0.0425492	+	0.278884i
$537$	−4.22085	−	8.64480i	−0.182143	−	0.373051i
$538$	−0.427513	−	0.488261i	−0.0184314	−	0.0210504i
$539$	20.5601	+	16.0355i	0.885587	+	0.690698i
$540$	−14.3611	+	2.47002i	−0.618003	+	0.106293i
$541$	−17.0772	−	21.0614i	−0.734206	−	0.905500i	0.264052	−	0.964508i	$-0.414941\pi$
$541$	−17.0772	−	21.0614i	−0.734206	−	0.905500i	−0.998257	+	0.0590087i	$0.981206\pi$
$542$	−52.0295	−	23.0079i	−2.23486	−	0.988274i
$543$	7.06926	+	1.49330i	0.303371	+	0.0640835i
$544$	−6.45445	+	4.46907i	−0.276732	+	0.191610i
$545$	0.745621	+	4.88709i	0.0319389	+	0.209340i
$546$	30.3155	+	17.7586i	1.29738	+	0.759997i
$547$	−28.4083	+	8.28836i	−1.21465	+	0.354385i	−0.824232	−	0.566253i	$-0.808393\pi$
$547$	−28.4083	+	8.28836i	−1.21465	+	0.354385i	−0.390419	+	0.920637i	$0.627670\pi$
$548$	13.6143	+	6.64725i	0.581576	+	0.283956i
$549$	−15.2819	−	23.9599i	−0.652214	−	1.02258i
$550$	8.78843	−	4.71089i	0.374740	−	0.200873i
$551$	27.6635	+	6.94673i	1.17850	+	0.295941i
$552$	0.958418	+	2.70378i	0.0407930	+	0.115080i
$553$	−29.4028	−	12.3423i	−1.25033	−	0.524849i
$554$	6.31174	+	0.962979i	0.268160	+	0.0409131i
$555$	4.11564	+	9.80456i	0.174699	+	0.416180i
$556$	21.6018	+	25.6344i	0.916121	+	1.08714i
$557$	−5.81880	+	18.6254i	−0.246550	+	0.789185i	0.745848	+	0.666117i	$0.232045\pi$
$557$	−5.81880	+	18.6254i	−0.246550	+	0.789185i	−0.992398	+	0.123069i	$0.960726\pi$
$558$	−38.9505	+	25.8928i	−1.64891	+	1.09613i
$559$	42.3954	+	10.6462i	1.79314	+	0.450284i
$560$	5.04224	−	23.8699i	0.213073	−	1.00869i
$561$	−1.11177	−	0.833753i	−0.0469389	−	0.0352011i
$562$	7.10268	+	53.3005i	0.299609	+	2.24835i
$563$	12.6997	+	0.963222i	0.535229	+	0.0405950i	0.340469	−	0.940256i	$-0.389414\pi$
$563$	12.6997	+	0.963222i	0.535229	+	0.0405950i	0.194760	+	0.980851i	$0.437607\pi$
$564$	−0.590554	+	3.87072i	−0.0248668	+	0.162987i
$565$	2.62070	−	3.63594i	0.110254	−	0.152965i
$566$	10.8710	−	4.80727i	0.456944	−	0.202065i
$567$	−16.7988	−	3.54855i	−0.705484	−	0.149025i
$568$	−0.949660	−	0.684492i	−0.0398469	−	0.0287206i
$569$	0.0696941	+	0.734320i	0.00292173	+	0.0307843i	0.996868	−	0.0790817i	$-0.0251988\pi$
$569$	0.0696941	+	0.734320i	0.00292173	+	0.0307843i	−0.993946	+	0.109866i	$0.964958\pi$
$570$	1.28689	−	13.5591i	0.0539019	−	0.567928i
$571$	30.9177	−	24.1137i	1.29387	−	1.00913i	0.295311	−	0.955401i	$-0.404577\pi$
$571$	30.9177	−	24.1137i	1.29387	−	1.00913i	0.998556	−	0.0537266i	$-0.0171099\pi$
$572$	−6.27123	+	17.6917i	−0.262213	+	0.739725i
$573$	−4.13852	−	2.53071i	−0.172889	−	0.105722i
$574$	16.5434	+	7.69315i	0.690509	+	0.321106i
$575$	6.15537	−	18.4674i	0.256697	−	0.770145i
$576$	21.8669	+	7.75125i	0.911122	+	0.322969i
$577$	−37.7054	−	20.2114i	−1.56970	−	0.841410i	−0.999806	−	0.0196904i	$-0.993732\pi$
$577$	−37.7054	−	20.2114i	−1.56970	−	0.841410i	−0.569892	−	0.821719i	$-0.693015\pi$
$578$	−12.2255	−	30.7420i	−0.508513	−	1.27870i
$579$	1.55496	−	1.07666i	0.0646221	−	0.0447445i
$580$	−16.3116	+	7.21313i	−0.677302	+	0.299509i
$581$	9.75341	−	7.03002i	0.404640	−	0.291654i
$582$	−4.08539	−	4.66592i	−0.169345	−	0.193408i
$583$	13.2037	−	0.750456i	0.546841	−	0.0310807i
$584$	0.0984808	+	2.60059i	0.00407516	+	0.107613i
$585$	−16.2134	+	4.07143i	−0.670340	+	0.168333i
$586$	−24.7485	+	27.2086i	−1.02235	+	1.12398i
$587$	−14.2106	+	40.0893i	−0.586534	+	1.65466i	0.158285	+	0.987393i	$0.449404\pi$
$587$	−14.2106	+	40.0893i	−0.586534	+	1.65466i	−0.744818	+	0.667267i	$0.767464\pi$
$588$	14.2348	−	21.4134i	0.587035	−	0.883075i
$589$	−16.5600	−	49.6835i	−0.682343	−	2.04717i
$590$	4.94076	−	9.65159i	0.203408	−	0.397350i
$591$	−0.968411	+	1.29133i	−0.0398351	+	0.0531182i
$592$	3.44107	−	30.1736i	0.141427	−	1.24013i
$593$	−7.56294	−	22.6904i	−0.310573	−	0.931784i	−0.981699	−	0.190440i	$-0.939008\pi$
$593$	−7.56294	−	22.6904i	−0.310573	−	0.931784i	0.671126	−	0.741343i	$-0.265811\pi$
$594$	−0.300601	+	15.8817i	−0.0123338	+	0.651633i
$595$	−6.18374	−	2.87562i	−0.253509	−	0.117889i
$596$	−18.4138	−	18.7656i	−0.754258	−	0.768670i
$597$	0.930947	+	0.106167i	0.0381011	+	0.00434513i
$598$	28.0450	+	63.4203i	1.14685	+	2.59345i
$599$	27.2202	−	26.7099i	1.11219	−	1.09134i	0.117022	−	0.993129i	$-0.462665\pi$
$599$	27.2202	−	26.7099i	1.11219	−	1.09134i	0.995166	−	0.0982065i	$-0.0313106\pi$
$600$	−0.568898	−	0.891956i	−0.0232252	−	0.0364140i
$601$	9.08106	+	7.65252i	0.370424	+	0.312153i	0.810422	−	0.585846i	$-0.199238\pi$
$601$	9.08106	+	7.65252i	0.370424	+	0.312153i	−0.439998	+	0.897999i	$0.645021\pi$
$602$	26.8111	−	85.8200i	1.09274	−	3.49776i
$603$	7.58511	+	30.2057i	0.308890	+	1.23007i
$604$	−14.8283	−	12.0233i	−0.603357	−	0.489219i
$605$	−3.51344	−	11.2462i	−0.142842	−	0.457223i
$606$	0.678128	−	1.06321i	0.0275471	−	0.0431901i
$607$	−2.40323	+	5.16793i	−0.0975442	+	0.209760i	−0.949438	−	0.313955i	$-0.898346\pi$
$607$	−2.40323	+	5.16793i	−0.0975442	+	0.209760i	0.851894	+	0.523715i	$0.175454\pi$
$608$	−25.2305	+	36.4390i	−1.02323	+	1.47780i
$609$	19.2161	−	0.727688i	0.778677	−	0.0294874i
$610$	−21.4354	+	30.9580i	−0.867892	+	1.25345i
$611$	−0.770143	+	10.1540i	−0.0311566	+	0.410788i
$612$	2.75948	−	4.32649i	0.111545	−	0.174888i
$613$	−24.0381	+	14.6993i	−0.970891	+	0.593700i	−0.914447	−	0.404706i	$-0.867374\pi$
$613$	−24.0381	+	14.6993i	−0.970891	+	0.593700i	−0.0564441	+	0.998406i	$0.517976\pi$
$614$	−21.5799	−	36.8388i	−0.870893	−	1.48669i
$615$	2.18506	−	0.774547i	0.0881102	−	0.0312327i
$616$	3.83000	+	1.60771i	0.154315	+	0.0647765i
$617$	16.6867	+	16.3738i	0.671781	+	0.659186i	0.953876	−	0.300200i	$-0.0970535\pi$
$617$	16.6867	+	16.3738i	0.671781	+	0.659186i	−0.282095	+	0.959386i	$0.591029\pi$
$618$	−11.7901	−	8.84177i	−0.474266	−	0.355668i
$619$	−9.07158	+	7.35550i	−0.364618	+	0.295643i	−0.794526	−	0.607230i	$-0.792281\pi$
$619$	−9.07158	+	7.35550i	−0.364618	+	0.295643i	0.429909	+	0.902872i	$0.358546\pi$
$620$	27.2718	+	18.1293i	1.09526	+	0.728089i
$621$	20.8657	+	22.9398i	0.837311	+	0.920543i
$622$	−39.9695	+	16.7779i	−1.60263	+	0.672732i
$623$	−50.4305	+	12.6639i	−2.02046	+	0.507368i
$624$	−12.3054	−	3.33885i	−0.492609	−	0.133661i
$625$	0.418003	−	4.40421i	0.0167201	−	0.176169i
$626$	−21.9038	−	23.1841i	−0.875452	−	0.926622i
$627$	−7.53145	−	2.19737i	−0.300777	−	0.0877543i
$628$	−17.6713	−	16.0735i	−0.705160	−	0.641402i
$629$	−8.00137	−	2.83628i	−0.319036	−	0.113090i
$630$	6.46860	+	33.7707i	0.257715	+	1.34546i
$631$	−10.3297	−	1.17802i	−0.411218	−	0.0468962i	−0.0947541	−	0.995501i	$-0.530206\pi$
$631$	−10.3297	−	1.17802i	−0.411218	−	0.0468962i	−0.316464	+	0.948605i	$0.602496\pi$
$632$	−3.39055	−	0.451816i	−0.134869	−	0.0179723i
$633$	−15.1764	+	5.70518i	−0.603209	+	0.226760i
$634$	−24.8875	+	25.3630i	−0.988409	+	1.00729i
$635$	−4.22386	+	3.42483i	−0.167619	+	0.135910i
$636$	−1.72271	−	12.9277i	−0.0683097	−	0.512615i
$637$	32.7032	−	58.3310i	1.29575	−	2.31116i
$638$	4.37744	+	18.9426i	0.173304	+	0.749944i
$639$	−5.43861	−	1.25681i	−0.215148	−	0.0497185i
$640$	−0.340890	−	5.99770i	−0.0134749	−	0.237080i
$641$	28.8900	+	14.1056i	1.14108	+	0.557138i	0.909511	−	0.415679i	$-0.136456\pi$
$641$	28.8900	+	14.1056i	1.14108	+	0.557138i	0.231574	+	0.972817i	$0.425613\pi$
$642$	−2.64653	+	2.59691i	−0.104450	+	0.102492i
$643$	−6.03578	+	0.114242i	−0.238028	+	0.00450527i	−0.137803	−	0.990460i	$-0.544004\pi$
$643$	−6.03578	+	0.114242i	−0.238028	+	0.00450527i	−0.100224	+	0.994965i	$0.531956\pi$
$644$	70.5514	−	26.5219i	2.78011	−	1.04511i
$645$	−5.20590	−	10.1695i	−0.204982	−	0.400425i
$646$	7.31657	+	8.04386i	0.287867	+	0.316482i
$647$	−32.3862	−	12.8793i	−1.27323	−	0.506339i	−0.367434	−	0.930050i	$-0.619764\pi$
$647$	−32.3862	−	12.8793i	−1.27323	−	0.506339i	−0.905798	+	0.423710i	$0.860728\pi$
$648$	−1.83874	+	0.104508i	−0.0722325	+	0.00410547i
$649$	−4.92488	−	3.84107i	−0.193318	−	0.150775i
$650$	−15.3436	−	20.4599i	−0.601824	−	0.802503i
$651$	−20.0998	−	29.0291i	−0.787774	−	1.13774i
$652$	−26.9499	+	4.63522i	−1.05544	+	0.181529i
$653$	35.1559	−	22.4228i	1.37576	−	0.877471i	0.376946	−	0.926235i	$-0.376974\pi$
$653$	35.1559	−	22.4228i	1.37576	−	0.877471i	0.998810	+	0.0487645i	$0.0155284\pi$
$654$	−0.201103	−	5.31054i	−0.00786374	−	0.207658i
$655$	−6.69284	+	2.80944i	−0.261511	+	0.109774i
$656$	−6.52528	−	1.12231i	−0.254770	−	0.0438188i
$657$	5.23257	+	11.2522i	0.204142	+	0.438989i
$658$	20.7623	+	2.76672i	0.809398	+	0.107858i
$659$	1.27910	+	2.89253i	0.0498268	+	0.112677i	0.937745	−	0.347324i	$-0.112909\pi$
$659$	1.27910	+	2.89253i	0.0498268	+	0.112677i	−0.887919	+	0.460001i	$0.847849\pi$
$660$	4.55859	−	1.81286i	0.177443	−	0.0705655i
$661$	35.8657	−	10.4641i	1.39501	−	0.407007i	0.505070	−	0.863078i	$-0.331467\pi$
$661$	35.8657	−	10.4641i	1.39501	−	0.407007i	0.889943	+	0.456071i	$0.150744\pi$
$662$	−49.7680	−	16.5882i	−1.93429	−	0.644717i
$663$	−1.68384	+	3.14129i	−0.0653947	+	0.121998i
$664$	0.812236	−	1.00173i	0.0315209	−	0.0388748i
$665$	−38.3906	−	2.91177i	−1.48872	−	0.112914i
$666$	11.9881	+	41.0893i	0.464531	+	1.59218i
$667$	31.6077	+	21.0116i	1.22386	+	0.813573i
$668$	15.0929	+	29.4833i	0.583960	+	1.14074i
$669$	2.85654	+	6.14273i	0.110440	+	0.237491i
$670$	33.0132	−	24.7577i	1.27541	−	0.956474i
$671$	15.1913	+	15.4816i	0.586453	+	0.597659i
$672$	−9.44880	+	28.3484i	−0.364495	+	1.09356i
$673$	−22.9060	−	29.3692i	−0.882961	−	1.13210i	−0.990447	−	0.137894i	$-0.955967\pi$
$673$	−22.9060	−	29.3692i	−0.882961	−	1.13210i	0.107486	−	0.994207i	$-0.465720\pi$
$674$	−2.14097	+	9.26468i	−0.0824671	+	0.356862i
$675$	−9.40245	−	6.51027i	−0.361901	−	0.250581i
$676$	18.6670	+	3.57556i	0.717961	+	0.137522i
$677$	−5.99314	+	4.67424i	−0.230335	+	0.179646i	−0.723571	−	0.690250i	$-0.757501\pi$
$677$	−5.99314	+	4.67424i	−0.230335	+	0.179646i	0.493236	+	0.869895i	$0.335814\pi$
$678$	−3.24195	+	3.56421i	−0.124506	+	0.136883i
$679$	−12.9686	+	11.7961i	−0.497690	+	0.452691i
$680$	−0.720934	−	0.123996i	−0.0276466	−	0.00475504i
$681$	−9.93695	−	19.4115i	−0.380785	−	0.743849i
$682$	25.0020	−	25.4797i	0.957377	−	0.975670i
$683$	4.64190	−	34.8342i	0.177618	−	1.33289i	−0.644950	−	0.764225i	$-0.723122\pi$
$683$	4.64190	−	34.8342i	0.177618	−	1.33289i	0.822568	−	0.568667i	$-0.192541\pi$
$684$	5.98760	−	28.3453i	0.228942	−	1.08381i
$685$	−3.44069	−	9.70648i	−0.131462	−	0.370866i
$686$	−59.7080	−	38.0823i	−2.27966	−	1.45399i
$687$	−0.209425	−	11.0646i	−0.00799007	−	0.422141i
$688$	−1.23473	+	32.6056i	−0.0470736	+	1.24308i
$689$	−7.01022	−	33.1863i	−0.267068	−	1.26430i
$690$	7.64226	−	16.4340i	0.290936	−	0.625630i
$691$	2.73123	−	0.103428i	0.103901	−	0.00393457i	0.0141600	−	0.999900i	$-0.495493\pi$
$691$	2.73123	−	0.103428i	0.103901	−	0.00393457i	0.0897407	+	0.995965i	$0.471396\pi$
$692$	19.9815			0.759583
$693$	19.8064			0.752381
$694$	44.6294	−	1.69005i	1.69411	−	0.0641536i
$695$	1.72330	−	22.7211i	0.0653686	−	0.861861i
$696$	1.96887	−	0.615098i	0.0746299	−	0.0233152i
$697$	−0.716358	+	1.70656i	−0.0271340	+	0.0646405i
$698$	11.7845	−	19.2715i	0.446051	−	0.729437i
$699$	3.25194	−	16.9774i	0.123000	−	0.642145i
$700$	−23.1487	+	15.3884i	−0.874940	+	0.581627i
$701$	−18.9541	+	10.1600i	−0.715885	+	0.383738i	−0.789666	−	0.613537i	$-0.789746\pi$
$701$	−18.9541	+	10.1600i	−0.715885	+	0.383738i	0.0737815	+	0.997274i	$0.476493\pi$
$702$	40.3827	−	5.38128i	1.52415	−	0.203103i
$703$	−47.9177	+	0.906964i	−1.80725	+	0.0342068i
$704$	−17.5519	−	2.33892i	−0.661513	−	0.0881514i
$705$	2.12927	−	1.59681i	0.0801928	−	0.0601393i
$706$	−9.52304	+	37.9230i	−0.358404	+	1.42725i
$707$	−3.04122	−	1.85970i	−0.114377	−	0.0699414i
$708$	−3.40975	+	5.12927i	−0.128146	+	0.192770i
$709$	−2.36299	−	8.70884i	−0.0887441	−	0.327067i	0.906777	−	0.421611i	$-0.138535\pi$
$709$	−2.36299	−	8.70884i	−0.0887441	−	0.327067i	−0.995521	+	0.0945440i	$0.969861\pi$
$710$	1.25367	+	7.28906i	0.0470495	+	0.273554i
$711$	−15.7410	+	4.27104i	−0.590332	+	0.160176i
$712$	−4.86501	+	2.72756i	−0.182324	+	0.102220i
$713$	1.31880	−	69.6766i	0.0493896	−	2.60941i
$714$	6.25437	+	3.82455i	0.234064	+	0.143130i
$715$	11.4651	−	5.59790i	0.428772	−	0.209349i
$716$	−20.0573	+	18.2438i	−0.749577	+	0.681804i
$717$	18.3291	−	7.69398i	0.684514	−	0.287337i
$718$	25.7798	+	10.2521i	0.962095	+	0.382606i
$719$	5.04427	−	18.5907i	0.188120	−	0.693317i	−0.806637	−	0.591047i	$-0.798715\pi$
$719$	5.04427	−	18.5907i	0.188120	−	0.693317i	0.994757	−	0.102270i	$-0.0326105\pi$
$720$	−5.47487	−	11.2132i	−0.204036	−	0.417890i
$721$	−24.3586	+	33.7950i	−0.907162	+	1.25859i
$722$	19.8140	+	10.1430i	0.737401	+	0.377484i
$723$	3.01260	+	19.7457i	0.112040	+	0.734351i
$724$	−1.54007	−	20.3052i	−0.0572361	−	0.754636i
$725$	−13.1022	−	4.92544i	−0.486605	−	0.182926i
$726$	2.38274	+	12.4396i	0.0884319	+	0.461677i
$727$	15.8930	+	16.1967i	0.589439	+	0.600701i	0.942216	−	0.335006i	$-0.108738\pi$
$727$	15.8930	+	16.1967i	0.589439	+	0.600701i	−0.352777	+	0.935707i	$0.614763\pi$
$728$	2.59464	−	10.3325i	0.0961639	−	0.382947i
$729$	1.25832	−	0.614377i	0.0466043	−	0.0227547i
$730$	11.0636	−	12.1634i	0.409483	−	0.450187i
$731$	8.80260	+	2.38843i	0.325576	+	0.0883394i
$732$	14.0905	−	16.0928i	0.520801	−	0.594806i
$733$	−4.99850	+	0.957437i	−0.184624	+	0.0353637i	−0.279604	−	0.960115i	$-0.590203\pi$
$733$	−4.99850	+	0.957437i	−0.184624	+	0.0353637i	0.0949802	+	0.995479i	$0.469721\pi$
$734$	36.7214	+	16.2385i	1.35541	+	0.599375i
$735$	−17.1007	+	3.61232i	−0.630768	+	0.133242i
$736$	−47.8450	+	34.4855i	−1.76359	+	1.27115i
$737$	−10.4289	−	21.3597i	−0.384155	−	0.786795i
$738$	9.09215	−	2.10110i	0.334687	−	0.0773427i
$739$	1.99899	+	6.85151i	0.0735340	+	0.252037i	0.988436	−	0.151639i	$-0.0484552\pi$
$739$	1.99899	+	6.85151i	0.0735340	+	0.252037i	−0.914902	+	0.403676i	$0.867732\pi$
$740$	23.2782	−	18.8746i	0.855723	−	0.693845i
$741$	−2.65784	+	19.9452i	−0.0976384	+	0.732706i
$742$	−68.9691	+	10.5226i	−2.53194	+	0.386296i
$743$	15.0272	−	8.05508i	0.551295	−	0.295512i	−0.173092	−	0.984906i	$-0.555376\pi$
$743$	15.0272	−	8.05508i	0.551295	−	0.295512i	0.724387	+	0.689393i	$0.242123\pi$
$744$	−2.89620	−	2.44060i	−0.106180	−	0.0894766i
$745$			17.8708i			0.654737i
$746$	36.6351	−	30.8720i	1.34131	−	1.13030i
$747$	1.72235	−	5.90333i	0.0630174	−	0.215992i
$748$	−1.37818	+	3.66611i	−0.0503912	+	0.134046i
$749$	7.48117	+	7.34091i	0.273356	+	0.268231i
$750$	−3.95937	+	18.7436i	−0.144576	+	0.684420i
$751$	36.7821	−	5.61183i	1.34220	−	0.204779i	0.560354	−	0.828253i	$-0.310665\pi$
$751$	36.7821	−	5.61183i	1.34220	−	0.204779i	0.781843	+	0.623475i	$0.214280\pi$
$752$	−7.53474	+	1.00406i	−0.274764	+	0.0366142i
$753$	8.44188	−	8.28361i	0.307639	−	0.301871i
$754$	46.3337	−	18.4260i	1.68737	−	0.671035i
$755$	1.47031	+	12.8927i	0.0535101	+	0.469214i
$756$	−3.34889	−	44.1538i	−0.121798	−	1.60586i
$757$	−8.20278	−	20.6266i	−0.298135	−	0.749685i	−0.999326	−	0.0367113i	$-0.988312\pi$
$757$	−8.20278	−	20.6266i	−0.298135	−	0.749685i	0.701191	−	0.712974i	$-0.252652\pi$
$758$	21.5383	−	7.17893i	0.782307	−	0.260750i
$759$	−8.46918	−	6.10438i	−0.307412	−	0.221575i
$760$	−4.05610	+	0.776926i	−0.147130	+	0.0281821i
$761$	0.955149	−	1.22466i	0.0346241	−	0.0443938i	−0.770904	−	0.636952i	$-0.780195\pi$
$761$	0.955149	−	1.22466i	0.0346241	−	0.0443938i	0.805528	+	0.592558i	$0.201882\pi$
$762$	4.92851	−	3.14345i	0.178541	−	0.113875i
$763$	−14.9983	+	0.852457i	−0.542975	+	0.0308610i
$764$	−3.58017	+	13.1947i	−0.129526	+	0.477369i
$765$	−3.39855	+	0.785369i	−0.122875	+	0.0283951i
$766$	56.0708	+	4.25275i	2.02592	+	0.153658i

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:	\( N \)	\(=\)	\( 997 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	997.h (of order \(166\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17234 - 1.69315i) q^{2} +(0.792902 - 0.0601384i) q^{3} +(-0.788605 - 2.09778i) q^{4} +(-0.616092 + 1.39322i) q^{5} +(0.827724 - 1.41300i) q^{6} +(-4.03781 - 2.26379i) q^{7} +(-0.481595 - 0.120936i) q^{8} +(-2.34061 + 0.357105i) q^{9} +O(q^{10})\)	\(q+(1.17234 - 1.69315i) q^{2} +(0.792902 - 0.0601384i) q^{3} +(-0.788605 - 2.09778i) q^{4} +(-0.616092 + 1.39322i) q^{5} +(0.827724 - 1.41300i) q^{6} +(-4.03781 - 2.26379i) q^{7} +(-0.481595 - 0.120936i) q^{8} +(-2.34061 + 0.357105i) q^{9} +(1.63665 + 2.67645i) q^{10} +(1.69153 - 0.635884i) q^{11} +(-0.751443 - 1.61591i) q^{12} +(-2.26654 - 4.04271i) q^{13} +(-8.56660 + 4.18267i) q^{14} +(-0.404714 + 1.14173i) q^{15} +(2.60289 - 2.27905i) q^{16} +(-0.456888 - 0.852351i) q^{17} +(-2.13935 + 4.38163i) q^{18} +(-4.10768 - 3.59661i) q^{19} +(3.40852 + 0.193729i) q^{20} +(-3.33773 - 1.55214i) q^{21} +(0.906394 - 3.60947i) q^{22} +(-3.55293 - 6.33718i) q^{23} +(-0.389130 - 0.0669280i) q^{24} +(1.80288 + 1.98210i) q^{25} +(-9.50205 - 0.901837i) q^{26} +(-4.15868 + 0.961027i) q^{27} +(-1.56471 + 10.2557i) q^{28} +(-4.65024 + 2.38051i) q^{29} +(1.45866 + 2.02374i) q^{30} +(8.27665 + 4.84840i) q^{31} +(-0.919816 - 8.06558i) q^{32} +(1.30297 - 0.605919i) q^{33} +(-1.97878 - 0.225664i) q^{34} +(5.64161 - 4.23084i) q^{35} +(2.59494 + 4.62846i) q^{36} +(6.49371 - 5.90658i) q^{37} +(-10.9052 + 2.73846i) q^{38} +(-2.04027 - 3.06917i) q^{39} +(0.465196 - 0.596458i) q^{40} +(-1.20534 - 1.48655i) q^{41} +(-6.54093 + 3.83163i) q^{42} +(-6.47698 + 6.85556i) q^{43} +(-2.66789 - 3.04699i) q^{44} +(0.944503 - 3.48098i) q^{45} +(-14.8950 - 1.41368i) q^{46} +(-1.82974 - 1.21635i) q^{47} +(1.92678 - 1.96359i) q^{48} +(7.52732 + 12.3096i) q^{49} +(5.46956 - 0.728859i) q^{50} +(-0.413526 - 0.648354i) q^{51} +(-6.69333 + 7.94282i) q^{52} +(6.98540 + 2.18232i) q^{53} +(-3.24821 + 8.16789i) q^{54} +(-0.156212 + 2.74842i) q^{55} +(1.67081 + 1.57855i) q^{56} +(-3.47328 - 2.60473i) q^{57} +(-1.42109 + 10.6643i) q^{58} +(-1.80306 - 2.94858i) q^{59} +(2.71427 - 0.0513743i) q^{60} +(4.85423 + 10.9772i) q^{61} +(17.9121 - 8.32961i) q^{62} +(10.2593 + 3.85672i) q^{63} +(-8.63614 - 4.62925i) q^{64} +(7.02877 - 0.667099i) q^{65} +(0.501613 - 2.91646i) q^{66} +(-1.24281 - 13.0947i) q^{67} +(-1.42774 + 1.63062i) q^{68} +(-3.19823 - 4.81109i) q^{69} +(-0.549550 - 14.5120i) q^{70} +(2.19068 + 0.871189i) q^{71} +(1.17041 + 0.111083i) q^{72} +(-1.46794 - 5.03134i) q^{73} +(-2.38788 - 17.9193i) q^{74} +(1.54871 + 1.46318i) q^{75} +(-4.30557 + 11.4533i) q^{76} +(-8.26957 - 1.26169i) q^{77} +(-7.58843 - 0.143630i) q^{78} +(6.84425 - 0.780533i) q^{79} +(1.57158 + 5.03049i) q^{80} +(3.54028 - 1.10602i) q^{81} +(-3.93001 + 0.298075i) q^{82} +(-1.09516 + 2.35505i) q^{83} +(-0.623897 + 8.22585i) q^{84} +(1.46899 - 0.111417i) q^{85} +(4.01426 + 19.0035i) q^{86} +(-3.54402 + 2.16717i) q^{87} +(-0.891531 + 0.101672i) q^{88} +(8.16478 - 7.71390i) q^{89} +(-4.78652 - 5.68006i) q^{90} +21.4547i q^{91} +(-10.4922 + 12.4508i) q^{92} +(6.85414 + 3.34656i) q^{93} +(-4.20453 + 1.67206i) q^{94} +(7.54156 - 3.50704i) q^{95} +(-1.21437 - 6.33990i) q^{96} +(1.19751 - 3.59278i) q^{97} +(29.6665 + 1.68615i) q^{98} +(-3.73212 + 2.09241i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6724 q - 83 q^{2} - 79 q^{3} - q^{4} - 83 q^{5} - 83 q^{6} - 83 q^{7} - 83 q^{8} - 165 q^{9}+O(q^{10}) \) 6724 * q - 83 * q^2 - 79 * q^3 - q^4 - 83 * q^5 - 83 * q^6 - 83 * q^7 - 83 * q^8 - 165 * q^9	\( 6724 q - 83 q^{2} - 79 q^{3} - q^{4} - 83 q^{5} - 83 q^{6} - 83 q^{7} - 83 q^{8} - 165 q^{9} - 77 q^{10} - 83 q^{11} - 83 q^{12} - 75 q^{13} - 75 q^{14} - 83 q^{15} - 161 q^{16} - 83 q^{17} - 83 q^{18} - 93 q^{19} - 83 q^{20} - 83 q^{21} - 97 q^{22} - 79 q^{23} - 83 q^{24} - q^{25} - 83 q^{26} - 73 q^{27} - 83 q^{28} - 83 q^{29} + 273 q^{30} - 55 q^{31} + 415 q^{32} - 83 q^{33} - 89 q^{34} - 39 q^{35} + 5 q^{36} - 83 q^{37} - 83 q^{38} - 35 q^{39} - 161 q^{40} + 166 q^{41} - 77 q^{42} - 83 q^{43} - 83 q^{44} - 83 q^{45} - 83 q^{46} - 83 q^{47} - 87 q^{48} + 7 q^{49} - 913 q^{50} - 83 q^{51} + 644 q^{52} - 87 q^{53} - 83 q^{54} + 352 q^{55} - 99 q^{56} - 93 q^{57} - 65 q^{58} + 519 q^{59} - 913 q^{60} - 83 q^{61} - 83 q^{62} + 830 q^{63} - 21 q^{64} - 83 q^{65} - 113 q^{66} - 85 q^{67} - 83 q^{68} - 75 q^{69} - 83 q^{70} - 97 q^{71} - 83 q^{72} - 47 q^{73} + 333 q^{74} - 53 q^{75} - 5 q^{76} - 121 q^{77} - 83 q^{78} - 87 q^{79} - 83 q^{80} - 157 q^{81} - 157 q^{82} - 403 q^{83} - 83 q^{84} + 177 q^{85} - 351 q^{86} - 83 q^{87} - 63 q^{88} - 59 q^{89} - 135 q^{90} - 9 q^{92} - 89 q^{93} + 129 q^{94} - 83 q^{95} + 747 q^{96} - 33 q^{97} - 83 q^{98} - 249 q^{99}+O(q^{100}) \) 6724 * q - 83 * q^2 - 79 * q^3 - q^4 - 83 * q^5 - 83 * q^6 - 83 * q^7 - 83 * q^8 - 165 * q^9 - 77 * q^10 - 83 * q^11 - 83 * q^12 - 75 * q^13 - 75 * q^14 - 83 * q^15 - 161 * q^16 - 83 * q^17 - 83 * q^18 - 93 * q^19 - 83 * q^20 - 83 * q^21 - 97 * q^22 - 79 * q^23 - 83 * q^24 - q^25 - 83 * q^26 - 73 * q^27 - 83 * q^28 - 83 * q^29 + 273 * q^30 - 55 * q^31 + 415 * q^32 - 83 * q^33 - 89 * q^34 - 39 * q^35 + 5 * q^36 - 83 * q^37 - 83 * q^38 - 35 * q^39 - 161 * q^40 + 166 * q^41 - 77 * q^42 - 83 * q^43 - 83 * q^44 - 83 * q^45 - 83 * q^46 - 83 * q^47 - 87 * q^48 + 7 * q^49 - 913 * q^50 - 83 * q^51 + 644 * q^52 - 87 * q^53 - 83 * q^54 + 352 * q^55 - 99 * q^56 - 93 * q^57 - 65 * q^58 + 519 * q^59 - 913 * q^60 - 83 * q^61 - 83 * q^62 + 830 * q^63 - 21 * q^64 - 83 * q^65 - 113 * q^66 - 85 * q^67 - 83 * q^68 - 75 * q^69 - 83 * q^70 - 97 * q^71 - 83 * q^72 - 47 * q^73 + 333 * q^74 - 53 * q^75 - 5 * q^76 - 121 * q^77 - 83 * q^78 - 87 * q^79 - 83 * q^80 - 157 * q^81 - 157 * q^82 - 403 * q^83 - 83 * q^84 + 177 * q^85 - 351 * q^86 - 83 * q^87 - 63 * q^88 - 59 * q^89 - 135 * q^90 - 9 * q^92 - 89 * q^93 + 129 * q^94 - 83 * q^95 + 747 * q^96 - 33 * q^97 - 83 * q^98 - 249 * q^99

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