LMFDB - Embedded newform 483.2.q.e.85.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.5
Character	$\chi$	$=$	483.85
Dual form			483.2.q.e.358.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.767372 - 0.885594i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0892119 + 0.620482i) q^{4} +(-1.61200 - 3.52979i) q^{5} +(-0.166766 + 1.15988i) q^{6} +(0.959493 - 0.281733i) q^{7} +(2.58953 + 1.66419i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.767372 - 0.885594i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0892119 + 0.620482i) q^{4} +(-1.61200 - 3.52979i) q^{5} +(-0.166766 + 1.15988i) q^{6} +(0.959493 - 0.281733i) q^{7} +(2.58953 + 1.66419i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-4.36297 - 1.28108i) q^{10} +(-2.08414 - 2.40523i) q^{11} +(-0.410508 - 0.473751i) q^{12} +(-3.15928 - 0.927649i) q^{13} +(0.486787 - 1.06592i) q^{14} +(3.26445 + 2.09794i) q^{15} +(2.25799 - 0.663006i) q^{16} +(0.340232 - 2.36637i) q^{17} +(-0.486787 - 1.06592i) q^{18} +(-0.774057 - 5.38368i) q^{19} +(2.04636 - 1.31512i) q^{20} +(-0.654861 + 0.755750i) q^{21} -3.72937 q^{22} +(4.56704 - 1.46361i) q^{23} -3.07818 q^{24} +(-6.58658 + 7.60132i) q^{25} +(-3.24587 + 2.08599i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.260408 + 0.570215i) q^{28} +(1.09115 - 7.58913i) q^{29} +(4.36297 - 1.28108i) q^{30} +(-1.80495 - 1.15997i) q^{31} +(-1.41188 + 3.09159i) q^{32} +(3.05366 + 0.896635i) q^{33} +(-1.83456 - 2.11719i) q^{34} +(-2.54116 - 2.93266i) q^{35} +(0.601471 + 0.176608i) q^{36} +(-1.69534 + 3.71228i) q^{37} +(-5.36175 - 3.44579i) q^{38} +(3.15928 - 0.927649i) q^{39} +(1.69992 - 11.8232i) q^{40} +(0.162074 + 0.354893i) q^{41} +(0.166766 + 1.15988i) q^{42} +(-1.82429 + 1.17240i) q^{43} +(1.30647 - 1.50775i) q^{44} -3.88046 q^{45} +(2.20845 - 5.16768i) q^{46} -0.212595 q^{47} +(-1.54109 + 1.77852i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.67733 + 11.6661i) q^{50} +(0.993133 + 2.17466i) q^{51} +(0.293744 - 2.04304i) q^{52} +(-0.155687 + 0.0457139i) q^{53} +(0.985789 + 0.633528i) q^{54} +(-5.13032 + 11.2338i) q^{55} +(2.95349 + 0.867224i) q^{56} +(3.56182 + 4.11056i) q^{57} +(-5.88357 - 6.79001i) q^{58} +(11.4444 + 3.36037i) q^{59} +(-1.01050 + 2.21270i) q^{60} +(9.82404 + 6.31353i) q^{61} +(-2.41233 + 0.708325i) q^{62} +(0.142315 - 0.989821i) q^{63} +(3.60966 + 7.90406i) q^{64} +(1.81836 + 12.6470i) q^{65} +(3.13735 - 2.01625i) q^{66} +(7.50573 - 8.66208i) q^{67} +1.49864 q^{68} +(-3.05075 + 3.70040i) q^{69} -4.54716 q^{70} +(-6.63561 + 7.65791i) q^{71} +(2.58953 - 1.66419i) q^{72} +(1.75073 + 12.1766i) q^{73} +(1.98661 + 4.35008i) q^{74} +(1.43140 - 9.95561i) q^{75} +(3.27143 - 0.960577i) q^{76} +(-2.67735 - 1.72063i) q^{77} +(1.60282 - 3.50970i) q^{78} +(1.88094 + 0.552294i) q^{79} +(-5.98016 - 6.90147i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(0.438663 + 0.128803i) q^{82} +(7.03938 - 15.4141i) q^{83} +(-0.527351 - 0.338908i) q^{84} +(-8.90124 + 2.61364i) q^{85} +(-0.361638 + 2.51525i) q^{86} +(3.18506 + 6.97431i) q^{87} +(-1.39419 - 9.69683i) q^{88} +(-12.7325 + 8.18270i) q^{89} +(-2.97776 + 3.43652i) q^{90} -3.29266 q^{91} +(1.31558 + 2.70320i) q^{92} +2.14555 q^{93} +(-0.163139 + 0.188273i) q^{94} +(-17.7555 + 11.4108i) q^{95} +(-0.483689 - 3.36413i) q^{96} +(5.34346 + 11.7005i) q^{97} +(0.166766 - 1.15988i) q^{98} +(-3.05366 + 0.896635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.767372	−	0.885594i	0.542614	−	0.626210i	−0.416532	−	0.909121i	$-0.636755\pi$
$2$	0.767372	−	0.885594i	0.542614	−	0.626210i	0.959146	+	0.282911i	$0.0913002\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	0.0892119	+	0.620482i	0.0446059	+	0.310241i
$5$	−1.61200	−	3.52979i	−0.720909	−	1.57857i	−0.812626	−	0.582786i	$-0.801963\pi$
$5$	−1.61200	−	3.52979i	−0.720909	−	1.57857i	0.0917163	−	0.995785i	$-0.470765\pi$
$6$	−0.166766	+	1.15988i	−0.0680819	+	0.473520i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	2.58953	+	1.66419i	0.915538	+	0.588380i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−4.36297	−	1.28108i	−1.37969	−	0.405114i
$11$	−2.08414	−	2.40523i	−0.628393	−	0.725204i	0.348885	−	0.937165i	$-0.386560\pi$
$11$	−2.08414	−	2.40523i	−0.628393	−	0.725204i	−0.977278	+	0.211962i	$0.932015\pi$
$12$	−0.410508	−	0.473751i	−0.118503	−	0.136760i
$13$	−3.15928	−	0.927649i	−0.876228	−	0.257284i	−0.187466	−	0.982271i	$-0.560027\pi$
$13$	−3.15928	−	0.927649i	−0.876228	−	0.257284i	−0.688762	+	0.724988i	$0.741846\pi$
$14$	0.486787	−	1.06592i	0.130099	−	0.284878i
$15$	3.26445	+	2.09794i	0.842878	+	0.541685i
$16$	2.25799	−	0.663006i	0.564498	−	0.165752i
$17$	0.340232	−	2.36637i	0.0825185	−	0.573929i	−0.906052	−	0.423167i	$-0.860918\pi$
$17$	0.340232	−	2.36637i	0.0825185	−	0.573929i	0.988570	−	0.150762i	$-0.0481726\pi$
$18$	−0.486787	−	1.06592i	−0.114737	−	0.251239i
$19$	−0.774057	−	5.38368i	−0.177581	−	1.23510i	−0.862339	−	0.506331i	$-0.831001\pi$
$19$	−0.774057	−	5.38368i	−0.177581	−	1.23510i	0.684758	−	0.728770i	$-0.259908\pi$
$20$	2.04636	−	1.31512i	0.457581	−	0.294069i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	−3.72937			−0.795104
$23$	4.56704	−	1.46361i	0.952293	−	0.305184i
$23$	4.56704	−	1.46361i	0.952293	−	0.305184i
$24$	−3.07818			−0.628331
$25$	−6.58658	+	7.60132i	−1.31732	+	1.52026i
$26$	−3.24587	+	2.08599i	−0.636567	+	0.409097i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	0.260408	+	0.570215i	0.0492125	+	0.107760i
$29$	1.09115	−	7.58913i	0.202622	−	1.40927i	−0.593843	−	0.804581i	$-0.702390\pi$
$29$	1.09115	−	7.58913i	0.202622	−	1.40927i	0.796465	−	0.604685i	$-0.206701\pi$
$30$	4.36297	−	1.28108i	0.796566	−	0.233893i
$31$	−1.80495	−	1.15997i	−0.324179	−	0.208337i	0.368421	−	0.929659i	$-0.379898\pi$
$31$	−1.80495	−	1.15997i	−0.324179	−	0.208337i	−0.692600	+	0.721322i	$0.743535\pi$
$32$	−1.41188	+	3.09159i	−0.249588	+	0.546521i
$33$	3.05366	+	0.896635i	0.531574	+	0.156084i
$34$	−1.83456	−	2.11719i	−0.314624	−	0.363095i
$35$	−2.54116	−	2.93266i	−0.429535	−	0.495710i
$36$	0.601471	+	0.176608i	0.100245	+	0.0294346i
$37$	−1.69534	+	3.71228i	−0.278712	+	0.610294i	−0.996278	−	0.0861960i	$-0.972529\pi$
$37$	−1.69534	+	3.71228i	−0.278712	+	0.610294i	0.717566	+	0.696490i	$0.245256\pi$
$38$	−5.36175	−	3.44579i	−0.869791	−	0.558981i
$39$	3.15928	−	0.927649i	0.505890	−	0.148543i
$40$	1.69992	−	11.8232i	0.268781	−	1.86941i
$41$	0.162074	+	0.354893i	0.0253118	+	0.0554250i	0.921866	−	0.387510i	$-0.126665\pi$
$41$	0.162074	+	0.354893i	0.0253118	+	0.0554250i	−0.896554	+	0.442935i	$0.853937\pi$
$42$	0.166766	+	1.15988i	0.0257325	+	0.178974i
$43$	−1.82429	+	1.17240i	−0.278202	+	0.178789i	−0.672300	−	0.740279i	$-0.734693\pi$
$43$	−1.82429	+	1.17240i	−0.278202	+	0.178789i	0.394098	+	0.919068i	$0.371057\pi$
$44$	1.30647	−	1.50775i	0.196958	−	0.227302i
$45$	−3.88046			−0.578465
$46$	2.20845	−	5.16768i	0.325618	−	0.761933i
$47$	−0.212595			−0.0310101			−0.0155051	−	0.999880i	$-0.504936\pi$
$47$	−0.212595			−0.0310101			−0.0155051	+	0.999880i	$0.504936\pi$
$48$	−1.54109	+	1.77852i	−0.222438	+	0.256707i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	1.67733	+	11.6661i	0.237210	+	1.64983i
$51$	0.993133	+	2.17466i	0.139067	+	0.304513i
$52$	0.293744	−	2.04304i	0.0407350	−	0.283318i
$53$	−0.155687	+	0.0457139i	−0.0213853	+	0.00627929i	−0.292408	−	0.956294i	$-0.594456\pi$
$53$	−0.155687	+	0.0457139i	−0.0213853	+	0.00627929i	0.271022	+	0.962573i	$0.412638\pi$
$54$	0.985789	+	0.633528i	0.134149	+	0.0862122i
$55$	−5.13032	+	11.2338i	−0.691772	+	1.51477i
$56$	2.95349	+	0.867224i	0.394677	+	0.115888i
$57$	3.56182	+	4.11056i	0.471774	+	0.544456i
$58$	−5.88357	−	6.79001i	−0.772551	−	0.891571i
$59$	11.4444	+	3.36037i	1.48993	+	0.437484i	0.922520	−	0.385950i	$-0.126126\pi$
$59$	11.4444	+	3.36037i	1.48993	+	0.437484i	0.567413	+	0.823434i	$0.307945\pi$
$60$	−1.01050	+	2.21270i	−0.130456	+	0.285658i
$61$	9.82404	+	6.31353i	1.25784	+	0.808364i	0.987987	−	0.154538i	$-0.0493888\pi$
$61$	9.82404	+	6.31353i	1.25784	+	0.808364i	0.269852	+	0.962902i	$0.413025\pi$
$62$	−2.41233	+	0.708325i	−0.306367	+	0.0899574i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	3.60966	+	7.90406i	0.451208	+	0.988007i
$65$	1.81836	+	12.6470i	0.225540	+	1.56867i
$66$	3.13735	−	2.01625i	0.386181	−	0.248183i
$67$	7.50573	−	8.66208i	0.916971	−	1.05824i	−0.0811333	−	0.996703i	$-0.525854\pi$
$67$	7.50573	−	8.66208i	0.916971	−	1.05824i	0.998105	−	0.0615382i	$-0.0196006\pi$
$68$	1.49864			0.181737
$69$	−3.05075	+	3.70040i	−0.367267	+	0.445475i
$70$	−4.54716			−0.543490
$71$	−6.63561	+	7.65791i	−0.787502	+	0.908826i	−0.997627	−	0.0688484i	$-0.978068\pi$
$71$	−6.63561	+	7.65791i	−0.787502	+	0.908826i	0.210125	+	0.977675i	$0.432613\pi$
$72$	2.58953	−	1.66419i	0.305179	−	0.196127i
$73$	1.75073	+	12.1766i	0.204907	+	1.42516i	0.789459	+	0.613803i	$0.210361\pi$
$73$	1.75073	+	12.1766i	0.204907	+	1.42516i	−0.584552	+	0.811356i	$0.698730\pi$
$74$	1.98661	+	4.35008i	0.230939	+	0.505686i
$75$	1.43140	−	9.95561i	0.165284	−	1.14958i
$76$	3.27143	−	0.960577i	0.375258	−	0.110186i
$77$	−2.67735	−	1.72063i	−0.305113	−	0.196084i
$78$	1.60282	−	3.50970i	0.181484	−	0.397395i
$79$	1.88094	+	0.552294i	0.211622	+	0.0621379i	0.385825	−	0.922572i	$-0.373917\pi$
$79$	1.88094	+	0.552294i	0.211622	+	0.0621379i	−0.174203	+	0.984710i	$0.555735\pi$
$80$	−5.98016	−	6.90147i	−0.668602	−	0.771608i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	0.438663	+	0.128803i	0.0484422	+	0.0142239i
$83$	7.03938	−	15.4141i	0.772673	−	1.69192i	0.0519947	−	0.998647i	$-0.483442\pi$
$83$	7.03938	−	15.4141i	0.772673	−	1.69192i	0.720678	−	0.693270i	$-0.243831\pi$
$84$	−0.527351	−	0.338908i	−0.0575387	−	0.0369779i
$85$	−8.90124	+	2.61364i	−0.965475	+	0.283489i
$86$	−0.361638	+	2.51525i	−0.0389965	+	0.271226i
$87$	3.18506	+	6.97431i	0.341474	+	0.747724i
$88$	−1.39419	−	9.69683i	−0.148622	−	1.03369i
$89$	−12.7325	+	8.18270i	−1.34965	+	0.867365i	−0.997642	−	0.0686338i	$-0.978136\pi$
$89$	−12.7325	+	8.18270i	−1.34965	+	0.867365i	−0.352004	+	0.935999i	$0.614500\pi$
$90$	−2.97776	+	3.43652i	−0.313883	+	0.362241i
$91$	−3.29266			−0.345164
$92$	1.31558	+	2.70320i	0.137159	+	0.281828i
$93$	2.14555			0.222483
$94$	−0.163139	+	0.188273i	−0.0168265	+	0.0194189i
$95$	−17.7555	+	11.4108i	−1.82168	+	1.17072i
$96$	−0.483689	−	3.36413i	−0.0493663	−	0.343350i
$97$	5.34346	+	11.7005i	0.542546	+	1.18801i	0.960177	+	0.279393i	$0.0901331\pi$
$97$	5.34346	+	11.7005i	0.542546	+	1.18801i	−0.417631	+	0.908617i	$0.637140\pi$
$98$	0.166766	−	1.15988i	0.0168459	−	0.117166i
$99$	−3.05366	+	0.896635i	−0.306904	+	0.0901152i
$100$	−5.30409	−	3.40873i	−0.530409	−	0.340873i
$101$	−2.68428	+	5.87776i	−0.267096	+	0.584859i	−0.994893	−	0.100934i	$-0.967817\pi$
$101$	−2.68428	+	5.87776i	−0.267096	+	0.584859i	0.727797	+	0.685793i	$0.240544\pi$
$102$	2.68797	+	0.789259i	0.266149	+	0.0781483i
$103$	−10.6381	−	12.2770i	−1.04820	−	1.20969i	−0.977224	−	0.212208i	$-0.931935\pi$
$103$	−10.6381	−	12.2770i	−1.04820	−	1.20969i	−0.0709746	−	0.997478i	$-0.522611\pi$
$104$	−6.63728	−	7.65983i	−0.650839	−	0.751108i
$105$	3.72328	+	1.09325i	0.363355	+	0.106691i
$106$	−0.0789861	+	0.172955i	−0.00767181	+	0.0167989i
$107$	10.8397	+	6.96623i	1.04791	+	0.673451i	0.946931	−	0.321437i	$-0.104166\pi$
$107$	10.8397	+	6.96623i	1.04791	+	0.673451i	0.100979	+	0.994889i	$0.467802\pi$
$108$	−0.601471	+	0.176608i	−0.0578765	+	0.0169941i
$109$	−0.461106	+	3.20707i	−0.0441660	+	0.307181i	0.955750	+	0.294182i	$0.0950471\pi$
$109$	−0.461106	+	3.20707i	−0.0441660	+	0.307181i	−0.999916	+	0.0129995i	$0.995862\pi$
$110$	6.01175	+	13.1639i	0.573198	+	1.25513i
$111$	−0.580797	−	4.03954i	−0.0551269	−	0.383416i
$112$	1.97974	−	1.27230i	0.187067	−	0.120221i
$113$	7.28164	−	8.40346i	0.684999	−	0.790531i	−0.301645	−	0.953420i	$-0.597536\pi$
$113$	7.28164	−	8.40346i	0.684999	−	0.790531i	0.986644	+	0.162889i	$0.0520813\pi$
$114$	6.37352			0.596935
$115$	−12.5283	−	13.7614i	−1.16827	−	1.28325i
$116$	4.80627			0.446251
$117$	−2.15623	+	2.48843i	−0.199344	+	0.230055i
$118$	11.7580	−	7.55643i	1.08241	−	0.695625i
$119$	−0.340232	−	2.36637i	−0.0311890	−	0.216925i
$120$	4.96204	+	10.8653i	0.452970	+	0.991866i
$121$	0.123988	−	0.862353i	0.0112716	−	0.0783957i
$122$	13.1299	−	3.85529i	1.18873	−	0.349042i
$123$	−0.328215	−	0.210931i	−0.0295942	−	0.0190190i
$124$	0.558719	−	1.22342i	0.0501744	−	0.109867i
$125$	18.8323	+	5.52966i	1.68441	+	0.494588i
$126$	−0.767372	−	0.885594i	−0.0683629	−	0.0788950i
$127$	5.86858	+	6.77270i	0.520752	+	0.600980i	0.953819	−	0.300382i	$-0.0971141\pi$
$127$	5.86858	+	6.77270i	0.520752	+	0.600980i	−0.433067	+	0.901362i	$0.642569\pi$
$128$	3.24764	+	0.953592i	0.287053	+	0.0842864i
$129$	0.900844	−	1.97257i	0.0793149	−	0.173675i
$130$	12.5955	+	8.09461i	1.10470	+	0.709944i
$131$	−2.52707	+	0.742016i	−0.220791	+	0.0648302i	−0.390257	−	0.920706i	$-0.627614\pi$
$131$	−2.52707	+	0.742016i	−0.220791	+	0.0648302i	0.169466	+	0.985536i	$0.445796\pi$
$132$	−0.283923	+	1.97473i	−0.0247124	+	0.171878i
$133$	−2.25946	−	4.94753i	−0.195920	−	0.429005i
$134$	−1.91140	−	13.2941i	−0.165120	−	1.14843i
$135$	3.26445	−	2.09794i	0.280959	−	0.180562i
$136$	4.81913	−	5.56157i	0.413237	−	0.476901i
$137$	11.2038			0.957203			0.478601	−	0.878032i	$-0.341144\pi$
$137$	11.2038			0.957203			0.478601	+	0.878032i	$0.341144\pi$
$138$	0.935991	+	5.54131i	0.0796769	+	0.471707i
$139$	5.91591			0.501781			0.250891	−	0.968015i	$-0.419277\pi$
$139$	5.91591			0.501781			0.250891	+	0.968015i	$0.419277\pi$
$140$	1.59296	−	1.83837i	0.134630	−	0.155371i
$141$	0.178846	−	0.114937i	0.0150616	−	0.00967948i
$142$	1.68982	+	11.7529i	0.141806	+	0.986283i
$143$	4.35319	+	9.53216i	0.364032	+	0.797119i
$144$	0.334912	−	2.32936i	0.0279093	−	0.194114i
$145$	−28.5470	+	8.38216i	−2.37070	+	0.696100i
$146$	12.1270	+	7.79352i	1.00363	+	0.644996i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	−2.45465	−	0.720749i	−0.201771	−	0.0592452i
$149$	5.47221	+	6.31527i	0.448301	+	0.517367i	0.934249	−	0.356621i	$-0.116071\pi$
$149$	5.47221	+	6.31527i	0.448301	+	0.517367i	−0.485948	+	0.873988i	$0.661526\pi$
$150$	−7.71822	−	8.90730i	−0.630190	−	0.727278i
$151$	−2.57658	−	0.756553i	−0.209679	−	0.0615674i	0.175206	−	0.984532i	$-0.443941\pi$
$151$	−2.57658	−	0.756553i	−0.209679	−	0.0615674i	−0.384885	+	0.922964i	$0.625759\pi$
$152$	6.95503	−	15.2294i	0.564128	−	1.23527i
$153$	−2.01119	−	1.29251i	−0.162595	−	0.104493i
$154$	−3.57830	+	1.05069i	−0.288348	+	0.0846666i
$155$	−1.18487	+	8.24098i	−0.0951714	+	0.661931i
$156$	0.857436	+	1.87752i	0.0686498	+	0.150322i
$157$	−2.47067	−	17.1839i	−0.197181	−	1.37142i	−0.812416	−	0.583079i	$-0.801848\pi$
$157$	−2.47067	−	17.1839i	−0.197181	−	1.37142i	0.615235	−	0.788344i	$-0.289061\pi$
$158$	1.93249	−	1.24193i	0.153740	−	0.0988030i
$159$	0.106258	−	0.122628i	0.00842678	−	0.00972502i
$160$	13.1886			1.04265
$161$	3.96969	−	2.69101i	0.312856	−	0.212081i
$162$	−1.17181			−0.0920660
$163$	−5.65854	+	6.53030i	−0.443211	+	0.511493i	−0.932767	−	0.360479i	$-0.882613\pi$
$163$	−5.65854	+	6.53030i	−0.443211	+	0.511493i	0.489556	+	0.871972i	$0.337159\pi$
$164$	−0.205746	+	0.132225i	−0.0160661	+	0.0103250i
$165$	−1.75757	−	12.2242i	−0.136827	−	0.951649i
$166$	−8.24882	−	18.0624i	−0.640232	−	1.40191i
$167$	2.45876	−	17.1011i	0.190265	−	1.32332i	−0.641041	−	0.767506i	$-0.721497\pi$
$167$	2.45876	−	17.1011i	0.190265	−	1.32332i	0.831306	−	0.555815i	$-0.187594\pi$
$168$	−2.95349	+	0.867224i	−0.227867	+	0.0669078i
$169$	−1.81576	−	1.16692i	−0.139674	−	0.0897627i
$170$	−4.51594	+	9.88853i	−0.346357	+	0.758415i
$171$	−5.21873	−	1.53236i	−0.399086	−	0.117182i
$172$	−0.890202	−	1.02735i	−0.0678773	−	0.0783346i
$173$	−11.7977	−	13.6153i	−0.896962	−	1.03515i	−0.999184	−	0.0403878i	$-0.987141\pi$
$173$	−11.7977	−	13.6153i	−0.896962	−	1.03515i	0.102222	−	0.994762i	$-0.467405\pi$
$174$	8.62053	+	2.53122i	0.653521	+	0.191891i
$175$	−4.17824	+	9.14907i	−0.315845	+	0.691604i
$176$	−6.30066	−	4.04919i	−0.474930	−	0.305219i
$177$	−11.4444	+	3.36037i	−0.860213	+	0.252581i
$178$	−2.52403	+	17.5550i	−0.189184	+	1.31581i
$179$	−10.3697	−	22.7064i	−0.775067	−	1.69716i	−0.715165	−	0.698955i	$-0.753649\pi$
$179$	−10.3697	−	22.7064i	−0.775067	−	1.69716i	−0.0599015	−	0.998204i	$-0.519079\pi$
$180$	−0.346183	−	2.40776i	−0.0258030	−	0.179464i
$181$	14.3194	−	9.20254i	1.06436	−	0.684020i	0.113463	−	0.993542i	$-0.463806\pi$
$181$	14.3194	−	9.20254i	1.06436	−	0.684020i	0.950892	+	0.309522i	$0.100169\pi$
$182$	−2.52669	+	2.91596i	−0.187291	+	0.216145i
$183$	−11.6779			−0.863252
$184$	14.2622	+	3.81035i	1.05142	+	0.280903i
$185$	15.8365			1.16432
$186$	1.64643	−	1.90009i	0.120722	−	0.139321i
$187$	−6.40075	+	4.11351i	−0.468069	+	0.300810i
$188$	−0.0189660	−	0.131911i	−0.00138324	−	0.00962063i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	−3.51976	+	24.4805i	−0.255350	+	1.77600i
$191$	−9.75926	+	2.86558i	−0.706155	+	0.207346i	−0.615042	−	0.788495i	$-0.710861\pi$
$191$	−9.75926	+	2.86558i	−0.706155	+	0.207346i	−0.0911135	+	0.995841i	$0.529043\pi$
$192$	−7.30990	−	4.69779i	−0.527546	−	0.339034i
$193$	0.237978	−	0.521098i	0.0171300	−	0.0375095i	−0.900874	−	0.434081i	$-0.857073\pi$
$193$	0.237978	−	0.521098i	0.0171300	−	0.0375095i	0.918004	+	0.396572i	$0.129800\pi$
$194$	14.4623	+	4.24653i	1.03834	+	0.304883i
$195$	−8.36718	−	9.65624i	−0.599186	−	0.691498i
$196$	0.410508	+	0.473751i	0.0293220	+	0.0338394i
$197$	10.7824	+	3.16599i	0.768212	+	0.225567i	0.642279	−	0.766471i	$-0.277989\pi$
$197$	10.7824	+	3.16599i	0.768212	+	0.225567i	0.125934	+	0.992039i	$0.459807\pi$
$198$	−1.54924	+	3.39235i	−0.110099	+	0.241084i
$199$	−7.11131	−	4.57016i	−0.504108	−	0.323970i	0.263750	−	0.964591i	$-0.415041\pi$
$199$	−7.11131	−	4.57016i	−0.504108	−	0.323970i	−0.767857	+	0.640621i	$0.778677\pi$
$200$	−29.7062	+	8.72253i	−2.10055	+	0.616776i
$201$	−1.63115	+	11.3449i	−0.115053	+	0.800208i
$202$	3.14547	+	6.88761i	0.221314	+	0.484611i
$203$	−1.09115	−	7.58913i	−0.0765839	−	0.532653i
$204$	−1.26074	+	0.810227i	−0.0882693	+	0.0567273i
$205$	0.991435	−	1.14418i	0.0692448	−	0.0799128i
$206$	−19.0358			−1.32628
$207$	0.565868	−	4.76233i	0.0393305	−	0.331005i
$208$	−7.74867			−0.537274
$209$	−11.3357	+	13.0822i	−0.784110	+	0.904911i
$210$	3.82532	−	2.45838i	0.263972	−	0.169644i
$211$	−0.113228	−	0.787520i	−0.00779496	−	0.0542151i	0.985553	−	0.169369i	$-0.0541730\pi$
$211$	−0.113228	−	0.787520i	−0.00779496	−	0.0542151i	−0.993348	+	0.115154i	$0.963264\pi$
$212$	−0.0422538	−	0.0925230i	−0.00290201	−	0.00635451i
$213$	1.44206	−	10.0297i	0.0988081	−	0.687225i
$214$	14.4873	−	4.25386i	0.990332	−	0.290788i
$215$	7.07909	+	4.54946i	0.482790	+	0.310270i
$216$	−1.27872	+	2.80001i	−0.0870061	+	0.190517i
$217$	−2.05864	−	0.604471i	−0.139750	−	0.0410342i
$218$	2.48632	+	2.86937i	0.168395	+	0.194338i
$219$	−8.05595	−	9.29707i	−0.544371	−	0.628237i
$220$	−7.42808	−	2.18108i	−0.500801	−	0.147048i
$221$	−3.27005	+	7.16041i	−0.219967	+	0.481661i
$222$	−4.02308	−	2.58547i	−0.270011	−	0.173526i
$223$	18.3485	−	5.38759i	1.22870	−	0.360780i	0.397943	−	0.917410i	$-0.369724\pi$
$223$	18.3485	−	5.38759i	1.22870	−	0.360780i	0.830760	+	0.556630i	$0.187906\pi$
$224$	−0.483689	+	3.36413i	−0.0323178	+	0.224776i
$225$	4.17824	+	9.14907i	0.278549	+	0.609938i
$226$	−1.85433	−	12.8972i	−0.123348	−	0.857906i
$227$	−15.4438	+	9.92510i	−1.02504	+	0.658752i	−0.941243	−	0.337731i	$-0.890341\pi$
$227$	−15.4438	+	9.92510i	−1.02504	+	0.658752i	−0.0837952	+	0.996483i	$0.526704\pi$
$228$	−2.23277	+	2.57676i	−0.147869	+	0.170650i
$229$	−10.7625			−0.711203			−0.355601	−	0.934638i	$-0.615724\pi$
$229$	−10.7625			−0.711203			−0.355601	+	0.934638i	$0.615724\pi$
$230$	−21.8009	+	0.534937i	−1.43751	+	0.0352727i
$231$	3.18257			0.209398
$232$	15.4553	−	17.8364i	1.01469	−	1.17102i
$233$	7.76507	−	4.99030i	0.508706	−	0.326926i	−0.260984	−	0.965343i	$-0.584047\pi$
$233$	7.76507	−	4.99030i	0.508706	−	0.326926i	0.769690	+	0.638417i	$0.220411\pi$
$234$	0.549103	+	3.81910i	0.0358960	+	0.249662i
$235$	0.342703	+	0.750416i	0.0223555	+	0.0489517i
$236$	−1.06408	+	7.40083i	−0.0692656	+	0.481753i
$237$	−1.88094	+	0.552294i	−0.122180	+	0.0358753i
$238$	−2.35673	−	1.51458i	−0.152764	−	0.0981754i
$239$	8.71797	−	19.0897i	0.563919	−	1.23481i	−0.386054	−	0.922476i	$-0.626162\pi$
$239$	8.71797	−	19.0897i	0.563919	−	1.23481i	0.949973	−	0.312333i	$-0.101111\pi$
$240$	8.76205	+	2.57277i	0.565588	+	0.166072i
$241$	8.89576	+	10.2663i	0.573026	+	0.661307i	0.966091	−	0.258204i	$-0.0831305\pi$
$241$	8.89576	+	10.2663i	0.573026	+	0.661307i	−0.393064	+	0.919511i	$0.628585\pi$
$242$	−0.668550	−	0.771548i	−0.0429760	−	0.0495970i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−3.04101	+	6.65888i	−0.194681	+	0.426291i
$245$	−3.26445	−	2.09794i	−0.208558	−	0.134032i
$246$	−0.438663	+	0.128803i	−0.0279681	+	0.00821218i
$247$	−2.54871	+	17.7266i	−0.162170	+	1.12792i
$248$	−2.74356	−	6.00757i	−0.174216	−	0.381481i
$249$	2.41159	+	16.7729i	0.152828	+	1.06294i
$250$	19.3484	−	12.4345i	1.22370	−	0.786424i
$251$	−19.3359	+	22.3148i	−1.22047	+	1.40850i	−0.336025	+	0.941853i	$0.609083\pi$
$251$	−19.3359	+	22.3148i	−1.22047	+	1.40850i	−0.884445	+	0.466644i	$0.845463\pi$
$252$	0.626863			0.0394887
$253$	−13.0387	−	7.93440i	−0.819735	−	0.498831i
$254$	10.5012			0.658907
$255$	6.07516	−	7.01111i	0.380441	−	0.439053i
$256$	−11.2832	+	7.25124i	−0.705197	+	0.453203i
$257$	1.06143	+	7.38242i	0.0662103	+	0.460502i	0.995774	+	0.0918404i	$0.0292750\pi$
$257$	1.06143	+	7.38242i	0.0662103	+	0.460502i	−0.929563	+	0.368662i	$0.879816\pi$
$258$	−1.05562	−	2.31148i	−0.0657198	−	0.143906i
$259$	−0.580797	+	4.03954i	−0.0360890	+	0.251005i
$260$	−7.68501	+	2.25652i	−0.476604	+	0.139944i
$261$	−6.45004	−	4.14519i	−0.399247	−	0.256581i
$262$	−1.28208	+	2.80736i	−0.0792072	+	0.173440i
$263$	−22.1982	−	6.51797i	−1.36880	−	0.401915i	−0.486942	−	0.873435i	$-0.661888\pi$
$263$	−22.1982	−	6.51797i	−1.36880	−	0.401915i	−0.881856	+	0.471519i	$0.843706\pi$
$264$	6.41537	+	7.40373i	0.394839	+	0.455668i
$265$	0.412329	+	0.475853i	0.0253292	+	0.0292314i
$266$	−6.11535	−	1.79563i	−0.374956	−	0.110097i
$267$	6.28739	−	13.7675i	0.384782	−	0.842555i
$268$	6.04427	+	3.88442i	0.369212	+	0.237278i
$269$	7.02157	−	2.06172i	0.428113	−	0.125705i	−0.0605757	−	0.998164i	$-0.519294\pi$
$269$	7.02157	−	2.06172i	0.428113	−	0.125705i	0.488688	+	0.872458i	$0.337475\pi$
$270$	0.647129	−	4.50088i	0.0393830	−	0.273915i
$271$	9.90580	+	21.6907i	0.601735	+	1.31762i	0.928086	+	0.372367i	$0.121454\pi$
$271$	9.90580	+	21.6907i	0.601735	+	1.31762i	−0.326351	+	0.945249i	$0.605819\pi$
$272$	−0.800675	−	5.56881i	−0.0485480	−	0.337659i
$273$	2.76996	−	1.78015i	0.167646	−	0.107739i
$274$	8.59746	−	9.92199i	0.519391	−	0.599410i
$275$	32.0103			1.93029
$276$	−2.56819	−	1.56282i	−0.154587	−	0.0940705i
$277$	12.7633			0.766874			0.383437	−	0.923567i	$-0.374740\pi$
$277$	12.7633			0.766874			0.383437	+	0.923567i	$0.374740\pi$
$278$	4.53970	−	5.23910i	0.272273	−	0.314220i
$279$	−1.80495	+	1.15997i	−0.108060	+	0.0694457i
$280$	−1.69992	−	11.8232i	−0.101590	−	0.706571i
$281$	−6.05413	−	13.2567i	−0.361159	−	0.790828i	−0.999773	−	0.0213006i	$-0.993219\pi$
$281$	−6.05413	−	13.2567i	−0.361159	−	0.790828i	0.638614	−	0.769527i	$-0.279508\pi$
$282$	0.0354536	−	0.246585i	0.00211123	−	0.0146839i
$283$	3.75312	−	1.10202i	0.223100	−	0.0655080i	−0.168272	−	0.985741i	$-0.553819\pi$
$283$	3.75312	−	1.10202i	0.223100	−	0.0655080i	0.391372	+	0.920233i	$0.372001\pi$
$284$	−5.34357	−	3.43410i	−0.317083	−	0.203777i
$285$	8.76775	−	19.1987i	0.519357	−	1.13723i
$286$	11.7821	+	3.45955i	0.696692	+	0.204567i
$287$	0.255494	+	0.294856i	0.0150813	+	0.0174048i
$288$	2.22569	+	2.56859i	0.131150	+	0.151355i
$289$	10.8274	+	3.17922i	0.636908	+	0.187013i
$290$	−14.4830	+	31.7133i	−0.850470	+	1.86227i
$291$	−10.8210	−	6.95423i	−0.634337	−	0.407664i
$292$	−7.39916	+	2.17259i	−0.433003	+	0.127141i
$293$	0.193438	−	1.34539i	0.0113008	−	0.0785986i	−0.983391	−	0.181502i	$-0.941904\pi$
$293$	0.193438	−	1.34539i	0.0113008	−	0.0785986i	0.994691	+	0.102903i	$0.0328132\pi$
$294$	0.486787	+	1.06592i	0.0283900	+	0.0621654i
$295$	−6.58695	−	45.8132i	−0.383507	−	2.66735i
$296$	−10.5681	+	6.79169i	−0.614257	+	0.394759i
$297$	2.08414	−	2.40523i	0.120934	−	0.139566i
$298$	9.79198			0.567234
$299$	−15.7863	+	0.387355i	−0.912945	+	0.0224013i
$300$	6.30498			0.364018
$301$	−1.42009	+	1.63887i	−0.0818527	+	0.0944630i
$302$	−2.64720	+	1.70125i	−0.152329	+	0.0978960i
$303$	−0.919594	−	6.39592i	−0.0528293	−	0.367436i
$304$	−5.31723	−	11.6431i	−0.304964	−	0.667778i
$305$	6.44907	−	44.8542i	0.369272	−	2.56835i
$306$	−2.68797	+	0.789259i	−0.153661	+	0.0451189i
$307$	8.26714	+	5.31297i	0.471830	+	0.303227i	0.754862	−	0.655884i	$-0.227704\pi$
$307$	8.26714	+	5.31297i	0.471830	+	0.303227i	−0.283032	+	0.959111i	$0.591340\pi$
$308$	0.828769	−	1.81475i	0.0472235	−	0.103405i
$309$	15.5867	+	4.57668i	0.886699	+	0.260358i
$310$	6.38893	+	7.37321i	0.362867	+	0.418770i
$311$	−8.27144	−	9.54575i	−0.469030	−	0.541290i	0.471111	−	0.882074i	$-0.343853\pi$
$311$	−8.27144	−	9.54575i	−0.469030	−	0.541290i	−0.940142	+	0.340784i	$0.889308\pi$
$312$	9.72485	+	2.85547i	0.550561	+	0.161659i
$313$	−6.58060	+	14.4095i	−0.371958	+	0.814474i	0.627402	+	0.778695i	$0.284118\pi$
$313$	−6.58060	+	14.4095i	−0.371958	+	0.814474i	−0.999360	+	0.0357783i	$0.988609\pi$
$314$	−17.1139	−	10.9984i	−0.965791	−	0.620676i
$315$	−3.72328	+	1.09325i	−0.209783	+	0.0615978i
$316$	−0.174886	+	1.21636i	−0.00983812	+	0.0684256i
$317$	4.19005	+	9.17493i	0.235337	+	0.515315i	0.990046	−	0.140744i	$-0.0449494\pi$
$317$	4.19005	+	9.17493i	0.235337	+	0.515315i	−0.754709	+	0.656059i	$0.772222\pi$
$318$	−0.0270594	−	0.188202i	−0.00151742	−	0.0105539i
$319$	−20.5277	+	13.1924i	−1.14933	+	0.738631i
$320$	22.0809	−	25.4827i	1.23436	−	1.42453i
$321$	−12.8851			−0.719178
$322$	0.663089	−	5.58054i	0.0369525	−	0.310992i
$323$	−13.0031			−0.723514
$324$	0.410508	−	0.473751i	0.0228060	−	0.0263195i
$325$	27.8602	−	17.9047i	1.54541	−	0.993173i
$326$	1.44100	+	10.0223i	0.0798094	+	0.555086i
$327$	−1.34596	−	2.94725i	−0.0744319	−	0.162983i
$328$	−0.170914	+	1.18873i	−0.00943712	+	0.0656366i
$329$	−0.203983	+	0.0598949i	−0.0112460	+	0.00330211i
$330$	−12.1744	−	7.82398i	−0.670176	−	0.430696i
$331$	2.33481	−	5.11253i	0.128333	−	0.281010i	−0.834549	−	0.550934i	$-0.814271\pi$
$331$	2.33481	−	5.11253i	0.128333	−	0.281010i	0.962882	+	0.269924i	$0.0869987\pi$
$332$	10.1922	+	2.99269i	0.559368	+	0.164245i
$333$	2.67254	+	3.08427i	0.146454	+	0.169017i
$334$	−13.2578	−	15.3004i	−0.725436	−	0.837198i
$335$	−42.6746	−	12.5304i	−2.33156	−	0.684609i
$336$	−0.977603	+	2.14065i	−0.0533326	+	0.116782i
$337$	23.2904	+	14.9678i	1.26871	+	0.815348i	0.989451	−	0.144869i	$-0.0462759\pi$
$337$	23.2904	+	14.9678i	1.26871	+	0.815348i	0.279256	+	0.960217i	$0.409912\pi$
$338$	−2.42677	+	0.712565i	−0.131999	+	0.0387584i
$339$	−1.58245	+	11.0062i	−0.0859470	+	0.597774i
$340$	−2.41582	−	5.28990i	−0.131016	−	0.286885i
$341$	0.971778	+	6.75887i	0.0526248	+	0.366013i
$342$	−5.36175	+	3.44579i	−0.289930	+	0.186327i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−6.67516			−0.359900
$345$	17.9794	+	4.80346i	0.967981	+	0.258610i
$346$	−21.1108			−1.13492
$347$	10.6380	−	12.2770i	0.571080	−	0.659062i	−0.394582	−	0.918861i	$-0.629111\pi$
$347$	10.6380	−	12.2770i	0.571080	−	0.659062i	0.965663	+	0.259799i	$0.0836562\pi$
$348$	−4.04329	+	2.59846i	−0.216743	+	0.139292i
$349$	3.89299	+	27.0763i	0.208387	+	1.44936i	0.778421	+	0.627742i	$0.216021\pi$
$349$	3.89299	+	27.0763i	0.208387	+	1.44936i	−0.570034	+	0.821621i	$0.693070\pi$
$350$	4.89610	+	10.7210i	0.261708	+	0.573060i
$351$	0.468594	−	3.25914i	0.0250117	−	0.173960i
$352$	10.3785	−	3.04742i	0.553178	−	0.162428i
$353$	8.00690	+	5.14572i	0.426164	+	0.273879i	0.736093	−	0.676881i	$-0.236669\pi$
$353$	8.00690	+	5.14572i	0.426164	+	0.273879i	−0.309929	+	0.950760i	$0.600305\pi$
$354$	−5.80617	+	12.7137i	−0.308595	+	0.675728i
$355$	37.7274	+	11.0778i	2.00236	+	0.587947i
$356$	−6.21312	−	7.17032i	−0.329294	−	0.380026i
$357$	1.56558	+	1.80677i	0.0828591	+	0.0956245i
$358$	−28.0661	−	8.24095i	−1.48334	−	0.435548i
$359$	−6.62948	+	14.5165i	−0.349890	+	0.766153i	0.650090	+	0.759857i	$0.274731\pi$
$359$	−6.62948	+	14.5165i	−0.349890	+	0.766153i	−0.999980	+	0.00629570i	$0.997996\pi$
$360$	−10.0486	−	6.45783i	−0.529607	−	0.340358i
$361$	−10.1545	+	2.98164i	−0.534449	+	0.156928i
$362$	2.83861	−	19.7430i	0.149194	−	1.03767i
$363$	0.361918	+	0.792490i	0.0189958	+	0.0415949i
$364$	−0.293744	−	2.04304i	−0.0153964	−	0.107084i
$365$	40.1586	−	25.8084i	2.10200	−	1.35087i
$366$	−8.96126	+	10.3418i	−0.468413	+	0.540577i
$367$	36.6856			1.91497			0.957485	−	0.288482i	$-0.0931507\pi$
$367$	36.6856			1.91497			0.957485	+	0.288482i	$0.0931507\pi$
$368$	9.34195	−	6.33280i	0.486983	−	0.330120i
$369$	0.390150			0.0203104
$370$	12.1525	−	14.0247i	0.631776	−	0.729108i
$371$	−0.136502	+	0.0877244i	−0.00708682	+	0.00455442i
$372$	0.191409	+	1.33128i	0.00992407	+	0.0690234i
$373$	−5.92722	−	12.9788i	−0.306900	−	0.672017i	0.691848	−	0.722043i	$-0.256797\pi$
$373$	−5.92722	−	12.9788i	−0.306900	−	0.672017i	−0.998748	+	0.0500263i	$0.984069\pi$
$374$	−1.26885	+	8.82506i	−0.0656108	+	0.456333i
$375$	−18.8323	+	5.52966i	−0.972495	+	0.285550i
$376$	−0.550521	−	0.353798i	−0.0283910	−	0.0182458i
$377$	−10.4873	+	22.9640i	−0.540124	+	1.18271i
$378$	1.12434	+	0.330137i	0.0578300	+	0.0169804i
$379$	3.21765	+	3.71336i	0.165279	+	0.190743i	0.832348	−	0.554254i	$-0.186996\pi$
$379$	3.21765	+	3.71336i	0.165279	+	0.190743i	−0.667068	+	0.744997i	$0.732451\pi$
$380$	−8.66418	−	9.99900i	−0.444463	−	0.512938i
$381$	−8.59856	−	2.52476i	−0.440518	−	0.129348i
$382$	−4.95124	+	10.8417i	−0.253328	+	0.554710i
$383$	−2.15282	−	1.38353i	−0.110004	−	0.0706951i	0.484482	−	0.874801i	$-0.339008\pi$
$383$	−2.15282	−	1.38353i	−0.110004	−	0.0706951i	−0.594486	+	0.804106i	$0.702644\pi$
$384$	−3.24764	+	0.953592i	−0.165730	+	0.0486628i
$385$	−1.75757	+	12.2242i	−0.0895740	+	0.623001i
$386$	−0.278864	−	0.610628i	−0.0141938	−	0.0310801i
$387$	0.308615	+	2.14647i	0.0156878	+	0.109111i
$388$	−6.78328	+	4.35935i	−0.344369	+	0.221312i
$389$	21.2217	−	24.4912i	1.07598	−	1.24175i	0.107097	−	0.994249i	$-0.465844\pi$
$389$	21.2217	−	24.4912i	1.07598	−	1.24175i	0.968887	−	0.247503i	$-0.0796101\pi$
$390$	−14.9723			−0.758150
$391$	−1.90959	−	11.3053i	−0.0965721	−	0.571732i
$392$	3.07818			0.155472
$393$	1.72475	−	1.99046i	0.0870019	−	0.100406i
$394$	11.0779	−	7.11932i	0.558095	−	0.358666i
$395$	−1.08260	−	7.52962i	−0.0544713	−	0.378857i
$396$	−0.828769	−	1.81475i	−0.0416472	−	0.0911946i
$397$	−2.76932	+	19.2611i	−0.138988	+	0.966685i	0.794292	+	0.607536i	$0.207842\pi$
$397$	−2.76932	+	19.2611i	−0.138988	+	0.966685i	−0.933280	+	0.359149i	$0.883067\pi$
$398$	−9.50433	+	2.79072i	−0.476409	+	0.139886i
$399$	4.57562	+	2.94057i	0.229067	+	0.147213i
$400$	−9.83272	+	21.5307i	−0.491636	+	1.07653i
$401$	25.8253	+	7.58300i	1.28966	+	0.378677i	0.853452	−	0.521171i	$-0.174505\pi$
$401$	25.8253	+	7.58300i	1.28966	+	0.378677i	0.436203	+	0.899848i	$0.356323\pi$
$402$	8.79529	+	10.1503i	0.438669	+	0.506251i
$403$	4.62631	+	5.33904i	0.230453	+	0.265957i
$404$	−3.88652	−	1.14118i	−0.193361	−	0.0567760i
$405$	−1.61200	+	3.52979i	−0.0801010	+	0.175397i
$406$	−7.55821	−	4.85737i	−0.375108	−	0.241067i
$407$	12.4622	−	3.65923i	0.617729	−	0.181381i
$408$	−1.04730	+	7.28411i	−0.0518489	+	0.360617i
$409$	3.26923	+	7.15861i	0.161653	+	0.353970i	0.973075	−	0.230491i	$-0.0740332\pi$
$409$	3.26923	+	7.15861i	0.161653	+	0.353970i	−0.811422	+	0.584461i	$0.801306\pi$
$410$	−0.252477	−	1.75602i	−0.0124690	−	0.0867236i
$411$	−9.42521	+	6.05721i	−0.464911	+	0.298780i
$412$	6.66861	−	7.69598i	0.328539	−	0.379154i
$413$	11.9275			0.586916
$414$	−3.78326	−	4.15561i	−0.185937	−	0.204237i
$415$	−65.7561			−3.22784
$416$	7.32845	−	8.45748i	0.359307	−	0.414662i
$417$	−4.97678	+	3.19838i	−0.243714	+	0.156626i
$418$	2.88674	+	20.0778i	0.141195	+	0.982035i
$419$	10.9742	+	24.0302i	0.536126	+	1.17395i	0.962965	+	0.269625i	$0.0868997\pi$
$419$	10.9742	+	24.0302i	0.536126	+	1.17395i	−0.426839	+	0.904327i	$0.640373\pi$
$420$	−0.346183	+	2.40776i	−0.0168920	+	0.117487i
$421$	−30.8577	+	9.06064i	−1.50391	+	0.441588i	−0.926951	−	0.375183i	$-0.877580\pi$
$421$	−30.8577	+	9.06064i	−1.50391	+	0.441588i	−0.576961	+	0.816772i	$0.695762\pi$
$422$	−0.784312	−	0.504046i	−0.0381797	−	0.0245366i
$423$	−0.0883151	+	0.193383i	−0.00429403	+	0.00940261i
$424$	−0.479234	−	0.140716i	−0.0232737	−	0.00683376i
$425$	15.7466	+	18.1725i	0.763820	+	0.881495i
$426$	−7.77567	−	8.97360i	−0.376733	−	0.434773i
$427$	11.2048	+	3.29003i	0.542239	+	0.159216i
$428$	−3.35540	+	7.34729i	−0.162189	+	0.355145i
$429$	−8.81561	−	5.66545i	−0.425622	−	0.273530i
$430$	9.46127	−	2.77808i	0.456263	−	0.133971i
$431$	1.35637	−	9.43375i	0.0653340	−	0.454408i	−0.930725	−	0.365719i	$-0.880823\pi$
$431$	1.35637	−	9.43375i	0.0653340	−	0.454408i	0.996059	−	0.0886891i	$-0.0282677\pi$
$432$	0.977603	+	2.14065i	0.0470350	+	0.102992i
$433$	0.590120	+	4.10437i	0.0283593	+	0.197244i	0.999076	−	0.0429849i	$-0.0136867\pi$
$433$	0.590120	+	4.10437i	0.0283593	+	0.197244i	−0.970716	+	0.240228i	$0.922778\pi$
$434$	−2.11506	+	1.35927i	−0.101526	+	0.0652468i
$435$	19.4835	−	22.4852i	0.934164	−	1.07808i
$436$	−2.03106			−0.0972703
$437$	−11.4148	−	23.4546i	−0.546043	−	1.12198i
$438$	−14.4153			−0.688792
$439$	0.729238	−	0.841586i	0.0348046	−	0.0401667i	−0.738080	−	0.674713i	$-0.764267\pi$
$439$	0.729238	−	0.841586i	0.0348046	−	0.0401667i	0.772885	+	0.634546i	$0.218813\pi$
$440$	−31.9804	+	20.5525i	−1.52460	+	0.979803i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	3.83188	+	8.39064i	0.182264	+	0.399102i
$443$	3.68460	−	25.6269i	0.175060	−	1.21757i	−0.692935	−	0.721000i	$-0.743683\pi$
$443$	3.68460	−	25.6269i	0.175060	−	1.21757i	0.867995	−	0.496572i	$-0.165408\pi$
$444$	2.45465	−	0.720749i	0.116492	−	0.0342052i
$445$	49.4081	+	31.7527i	2.34217	+	1.50522i
$446$	9.30887	−	20.3836i	0.440788	−	0.965191i
$447$	−8.01781	−	2.35424i	−0.379229	−	0.111352i
$448$	5.69028	+	6.56693i	0.268840	+	0.310258i
$449$	−12.6481	−	14.5966i	−0.596899	−	0.688858i	0.374251	−	0.927327i	$-0.377900\pi$
$449$	−12.6481	−	14.5966i	−0.596899	−	0.688858i	−0.971150	+	0.238470i	$0.923354\pi$
$450$	11.3086	+	3.32051i	0.533094	+	0.156530i
$451$	0.515813	−	1.12947i	0.0242887	−	0.0531849i
$452$	5.86381	+	3.76844i	0.275810	+	0.177253i
$453$	2.57658	−	0.756553i	0.121058	−	0.0355460i
$454$	−3.06149	+	21.2931i	−0.143683	+	0.999337i
$455$	5.30777	+	11.6224i	0.248832	+	0.544867i
$456$	2.38269	+	16.5720i	0.111580	+	0.776053i
$457$	−5.53161	+	3.55495i	−0.258758	+	0.166294i	−0.663588	−	0.748098i	$-0.730967\pi$
$457$	−5.53161	+	3.55495i	−0.258758	+	0.166294i	0.404830	+	0.914392i	$0.367331\pi$
$458$	−8.25880	+	9.53117i	−0.385909	+	0.445362i
$459$	2.39070			0.111588
$460$	7.42100	−	9.00128i	0.346006	−	0.419687i
$461$	−0.571967			−0.0266392			−0.0133196	−	0.999911i	$-0.504240\pi$
$461$	−0.571967			−0.0266392			−0.0133196	+	0.999911i	$0.504240\pi$
$462$	2.44222	−	2.81847i	0.113622	−	0.131127i
$463$	15.3464	−	9.86252i	0.713207	−	0.458350i	−0.133061	−	0.991108i	$-0.542481\pi$
$463$	15.3464	−	9.86252i	0.713207	−	0.458350i	0.846268	+	0.532758i	$0.178844\pi$
$464$	−2.56783	−	17.8596i	−0.119208	−	0.829113i
$465$	−3.45863	−	7.57334i	−0.160390	−	0.351205i
$466$	1.53931	−	10.7061i	0.0713070	−	0.495951i
$467$	11.1920	−	3.28626i	0.517903	−	0.152070i	−0.0123267	−	0.999924i	$-0.503924\pi$
$467$	11.1920	−	3.28626i	0.517903	−	0.152070i	0.530230	+	0.847854i	$0.322106\pi$
$468$	−1.73639	−	1.11591i	−0.0802645	−	0.0515828i
$469$	4.76131	−	10.4258i	0.219857	−	0.481419i
$470$	0.927545	+	0.272352i	0.0427845	+	0.0125627i
$471$	11.3688	+	13.1203i	0.523845	+	0.604549i
$472$	24.0433	+	27.7474i	1.10668	+	1.27718i
$473$	6.62198	+	1.94439i	0.304479	+	0.0894030i
$474$	−0.954272	+	2.08956i	−0.0438312	+	0.0959768i
$475$	46.0215	+	29.5762i	2.11161	+	1.35705i
$476$	1.43794	−	0.422216i	0.0659077	−	0.0193523i
$477$	−0.0230920	+	0.160608i	−0.00105731	+	0.00735375i
$478$	−10.2158	−	22.3695i	−0.467260	−	1.02316i
$479$	1.23121	+	8.56328i	0.0562556	+	0.391266i	0.998424	+	0.0561256i	$0.0178747\pi$
$479$	1.23121	+	8.56328i	0.0562556	+	0.391266i	−0.942168	+	0.335141i	$0.891216\pi$
$480$	−11.0950	+	7.13031i	−0.506414	+	0.325453i
$481$	8.79975	−	10.1555i	0.401234	−	0.463049i
$482$	15.9181			0.725049
$483$	−1.88465	+	4.41000i	−0.0857545	+	0.200662i
$484$	0.546136			0.0248244
$485$	32.6868	−	37.7226i	1.48423	−	1.71289i
$486$	0.985789	−	0.633528i	0.0447163	−	0.0287374i
$487$	−1.23157	−	8.56576i	−0.0558078	−	0.388152i	−0.998512	−	0.0545234i	$-0.982636\pi$
$487$	−1.23157	−	8.56576i	−0.0558078	−	0.388152i	0.942705	−	0.333628i	$-0.108273\pi$
$488$	14.9327	+	32.6982i	0.675974	+	1.48018i
$489$	1.22972	−	8.55288i	0.0556098	−	0.386775i
$490$	−4.36297	+	1.28108i	−0.197099	+	0.0578735i
$491$	−1.43715	−	0.923601i	−0.0648577	−	0.0416815i	0.507810	−	0.861469i	$-0.330455\pi$
$491$	−1.43715	−	0.923601i	−0.0648577	−	0.0416815i	−0.572668	+	0.819787i	$0.694092\pi$
$492$	0.101598	−	0.222469i	0.00458041	−	0.0100297i
$493$	−17.5874	−	5.16414i	−0.792098	−	0.232581i
$494$	13.7428	+	15.8600i	0.618318	+	0.713577i
$495$	8.08744	+	9.33340i	0.363503	+	0.419505i
$496$	−4.84463	−	1.42251i	−0.217530	−	0.0638727i
$497$	−4.20934	+	9.21717i	−0.188815	+	0.413447i
$498$	16.7046	+	10.7354i	0.748551	+	0.481065i
$499$	−34.3712	+	10.0923i	−1.53867	+	0.451794i	−0.937690	−	0.347472i	$-0.887040\pi$
$499$	−34.3712	+	10.0923i	−1.53867	+	0.451794i	−0.600978	+	0.799266i	$0.705222\pi$
$500$	−1.75099	+	12.1784i	−0.0783067	+	0.544635i
$501$	7.17710	+	15.7156i	0.320649	+	0.702123i
$502$	4.92405	+	34.2475i	0.219771	+	1.52854i
$503$	11.5264	−	7.40754i	0.513935	−	0.330286i	−0.257834	−	0.966189i	$-0.583009\pi$
$503$	11.5264	−	7.40754i	0.513935	−	0.330286i	0.771769	+	0.635903i	$0.219372\pi$
$504$	2.01578	−	2.32634i	0.0897900	−	0.103623i
$505$	25.0743			1.11579
$506$	−17.0322	+	5.45835i	−0.757173	+	0.242653i
$507$	2.15839			0.0958576
$508$	−3.67879	+	4.24555i	−0.163220	+	0.188366i
$509$	−36.7695	+	23.6303i	−1.62978	+	1.04740i	−0.680604	+	0.732652i	$0.738282\pi$
$509$	−36.7695	+	23.6303i	−1.62978	+	1.04740i	−0.949176	+	0.314744i	$0.898081\pi$
$510$	−1.54709	−	10.7603i	−0.0685064	−	0.476472i
$511$	5.11034	+	11.1901i	0.226068	+	0.495021i
$512$	−3.20011	+	22.2573i	−0.141426	+	0.983642i
$513$	5.21873	−	1.53236i	0.230412	−	0.0676552i
$514$	7.35234	+	4.72506i	0.324298	+	0.208414i
$515$	−26.1866	+	57.3407i	−1.15392	+	2.52673i
$516$	1.30431	+	0.382981i	0.0574192	+	0.0168598i
$517$	0.443078	+	0.511339i	0.0194866	+	0.0224887i
$518$	3.13170	+	3.61418i	0.137599	+	0.158798i
$519$	17.2858	+	5.07557i	0.758763	+	0.222793i
$520$	−16.3383	+	35.7759i	−0.716482	+	1.56888i
$521$	−2.69627	−	1.73279i	−0.118126	−	0.0759147i	0.480244	−	0.877135i	$-0.340548\pi$
$521$	−2.69627	−	1.73279i	−0.118126	−	0.0759147i	−0.598370	+	0.801220i	$0.704185\pi$
$522$	−8.62053	+	2.53122i	−0.377310	+	0.110788i
$523$	−0.00547230	+	0.0380607i	−0.000239287	+	0.00166428i	−0.989941	−	0.141483i	$-0.954813\pi$
$523$	−0.00547230	+	0.0380607i	−0.000239287	+	0.00166428i	0.989701	+	0.143147i	$0.0457221\pi$
$524$	−0.685853	−	1.50181i	−0.0299616	−	0.0656068i
$525$	−1.43140	−	9.95561i	−0.0624715	−	0.434499i
$526$	−22.8065	+	14.6569i	−0.994412	+	0.639069i
$527$	−3.35902	+	3.87652i	−0.146321	+	0.168864i
$528$	7.48961			0.325943
$529$	18.7157	−	13.3687i	0.813725	−	0.581250i
$530$	0.737822			0.0320490
$531$	7.81087	−	9.01423i	0.338963	−	0.391184i
$532$	2.86828	−	1.84333i	0.124356	−	0.0799187i
$533$	−0.182822	−	1.27156i	−0.00791891	−	0.0550772i
$534$	−7.36762	−	16.1328i	−0.318828	−	0.698136i
$535$	7.11578	−	49.4914i	0.307642	−	2.13970i
$536$	33.8517	−	9.93975i	1.46217	−	0.429332i
$537$	20.9996	+	13.4956i	0.906198	+	0.582378i
$538$	3.56231	−	7.80037i	0.153582	−	0.336298i
$539$	−3.05366	−	0.896635i	−0.131530	−	0.0386208i
$540$	1.59296	+	1.83837i	0.0685501	+	0.0791110i
$541$	−12.9076	−	14.8962i	−0.554942	−	0.640438i	0.407085	−	0.913390i	$-0.366545\pi$
$541$	−12.9076	−	14.8962i	−0.554942	−	0.640438i	−0.962027	+	0.272953i	$0.912000\pi$
$542$	26.8106	+	7.87230i	1.15161	+	0.338144i
$543$	−7.07101	+	15.4833i	−0.303446	+	0.664454i
$544$	6.83547	+	4.39289i	0.293068	+	0.188344i
$545$	12.0636	−	3.54219i	0.516747	−	0.151731i
$546$	0.549103	−	3.81910i	0.0234994	−	0.163442i
$547$	−7.97413	−	17.4609i	−0.340949	−	0.746575i	0.659035	−	0.752112i	$-0.270965\pi$
$547$	−7.97413	−	17.4609i	−0.340949	−	0.746575i	−0.999985	+	0.00553721i	$0.998237\pi$
$548$	0.999509	+	6.95174i	0.0426969	+	0.296964i
$549$	9.82404	−	6.31353i	0.419280	−	0.269455i
$550$	24.5638	−	28.3481i	1.04740	−	1.20877i
$551$	−41.7021			−1.77657
$552$	−14.0582	+	4.50526i	−0.598356	+	0.191757i
$553$	1.96035			0.0833624
$554$	9.79422	−	11.3031i	0.416116	−	0.480224i
$555$	−13.3225	+	8.56183i	−0.565508	+	0.363430i
$556$	0.527770	+	3.67072i	0.0223824	+	0.155673i
$557$	−13.7968	−	30.2107i	−0.584588	−	1.28007i	−0.938658	−	0.344851i	$-0.887930\pi$
$557$	−13.7968	−	30.2107i	−0.584588	−	1.28007i	0.354069	−	0.935219i	$-0.384798\pi$
$558$	−0.357804	+	2.48858i	−0.0151471	+	0.105350i
$559$	6.85103	−	2.01164i	0.289768	−	0.0850835i
$560$	−7.68229	−	4.93711i	−0.324636	−	0.208631i
$561$	3.16072	−	6.92101i	0.133446	−	0.292205i
$562$	−16.3858	−	4.81131i	−0.691194	−	0.202953i
$563$	−25.6428	−	29.5933i	−1.08071	−	1.24721i	−0.967293	−	0.253663i	$-0.918365\pi$
$563$	−25.6428	−	29.5933i	−1.08071	−	1.24721i	−0.113421	−	0.993547i	$-0.536181\pi$
$564$	0.0872719	+	0.100717i	0.00367481	+	0.00424096i
$565$	−41.4005	−	12.1563i	−1.74173	−	0.511419i
$566$	1.90410	−	4.16940i	0.0800353	−	0.175253i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−29.9273	+	8.78746i	−1.25572	+	0.368714i
$569$	−1.29843	+	9.03079i	−0.0544331	+	0.378590i	0.944336	+	0.328983i	$0.106706\pi$
$569$	−1.29843	+	9.03079i	−0.0544331	+	0.378590i	−0.998769	+	0.0496071i	$0.984203\pi$
$570$	−10.2741	−	22.4972i	−0.430336	−	0.942305i
$571$	3.81326	+	26.5218i	0.159580	+	1.10990i	0.899409	+	0.437108i	$0.143997\pi$
$571$	3.81326	+	26.5218i	0.159580	+	1.10990i	−0.739829	+	0.672795i	$0.765094\pi$
$572$	−5.52618	+	3.55146i	−0.231061	+	0.148494i
$573$	6.66076	−	7.68693i	0.278257	−	0.321126i
$574$	0.457182			0.0190824
$575$	−18.9558	+	44.3557i	−0.790511	+	1.84976i
$576$	8.68929			0.362054
$577$	−9.51807	+	10.9844i	−0.396242	+	0.457288i	−0.918454	−	0.395528i	$-0.870562\pi$
$577$	−9.51807	+	10.9844i	−0.396242	+	0.457288i	0.522212	+	0.852816i	$0.325107\pi$
$578$	11.1242	−	7.14907i	0.462705	−	0.297362i
$579$	0.0815275	+	0.567036i	0.00338817	+	0.0235652i
$580$	−7.74771	−	16.9651i	−0.321706	−	0.704438i
$581$	2.41159	−	16.7729i	0.100049	−	0.695859i
$582$	−14.4623	+	4.24653i	−0.599483	+	0.176024i
$583$	0.434427	+	0.279189i	0.0179921	+	0.0115628i
$584$	−15.7306	+	34.4451i	−0.650936	+	1.42535i
$585$	12.2595	+	3.59971i	0.506867	+	0.148830i
$586$	−1.04303	−	1.20372i	−0.0430873	−	0.0497253i
$587$	12.9967	+	14.9989i	0.536430	+	0.619073i	0.957667	−	0.287877i	$-0.0929496\pi$
$587$	12.9967	+	14.9989i	0.536430	+	0.619073i	−0.421238	+	0.906950i	$0.638404\pi$
$588$	−0.601471	−	0.176608i	−0.0248042	−	0.00728318i
$589$	−4.84779	+	10.6152i	−0.199750	+	0.437390i
$590$	−45.6266	−	29.3224i	−1.87842	−	1.20719i
$591$	−10.7824	+	3.16599i	−0.443528	+	0.130231i
$592$	−1.36680	+	9.50631i	−0.0561752	+	0.390707i
$593$	14.5513	+	31.8630i	0.597552	+	1.30846i	0.930769	+	0.365607i	$0.119139\pi$
$593$	14.5513	+	31.8630i	0.597552	+	1.30846i	−0.333217	+	0.942850i	$0.608134\pi$
$594$	−0.530745	−	3.69141i	−0.0217767	−	0.151460i
$595$	−7.80433	+	5.01554i	−0.319946	+	0.205617i
$596$	−3.43033	+	3.95881i	−0.140512	+	0.162159i
$597$	8.45323			0.345968
$598$	−11.7709	+	14.2775i	−0.481349	+	0.583850i
$599$	−38.6315			−1.57844			−0.789220	−	0.614110i	$-0.789515\pi$
$599$	−38.6315			−1.57844			−0.789220	+	0.614110i	$0.789515\pi$
$600$	20.2747	−	23.3982i	0.827711	−	0.955230i
$601$	−25.4096	+	16.3297i	−1.03648	+	0.666104i	−0.944113	−	0.329621i	$-0.893079\pi$
$601$	−25.4096	+	16.3297i	−1.03648	+	0.666104i	−0.0923652	+	0.995725i	$0.529443\pi$
$602$	0.361638	+	2.51525i	0.0147393	+	0.102514i
$603$	−4.76131	−	10.4258i	−0.193896	−	0.424572i
$604$	0.239566	−	1.66622i	0.00974781	−	0.0677975i
$605$	−3.24379	+	0.952464i	−0.131879	+	0.0387232i
$606$	−6.36986	−	4.09366i	−0.258758	−	0.166294i
$607$	19.2771	−	42.2110i	0.782434	−	1.71329i	0.0852933	−	0.996356i	$-0.472817\pi$
$607$	19.2771	−	42.2110i	0.782434	−	1.71329i	0.697140	−	0.716935i	$-0.254455\pi$
$608$	17.7370	+	5.20806i	0.719331	+	0.211215i
$609$	5.02093	+	5.79446i	0.203458	+	0.234803i
$610$	−34.7738	−	40.1311i	−1.40795	−	1.62486i
$611$	0.671648	+	0.197214i	0.0271719	+	0.00797840i
$612$	0.622559	−	1.36321i	0.0251654	−	0.0551046i
$613$	−27.7213	−	17.8154i	−1.11965	−	0.719558i	−0.156278	−	0.987713i	$-0.549949\pi$
$613$	−27.7213	−	17.8154i	−1.11965	−	0.719558i	−0.963376	+	0.268156i	$0.913586\pi$
$614$	11.0491	−	3.24431i	0.445905	−	0.130930i
$615$	−0.215459	+	1.49855i	−0.00868816	+	0.0604275i
$616$	−4.06963	−	8.91125i	−0.163970	−	0.359045i
$617$	2.57946	+	17.9405i	0.103845	+	0.722259i	0.973515	+	0.228624i	$0.0734228\pi$
$617$	2.57946	+	17.9405i	0.103845	+	0.722259i	−0.869670	+	0.493634i	$0.835668\pi$
$618$	16.0139	−	10.2915i	0.644174	−	0.413985i
$619$	−3.08608	+	3.56153i	−0.124040	+	0.143150i	−0.814373	−	0.580342i	$-0.802919\pi$
$619$	−3.08608	+	3.56153i	−0.124040	+	0.143150i	0.690333	+	0.723492i	$0.257464\pi$
$620$	−5.21909			−0.209604
$621$	2.09867	+	4.31226i	0.0842168	+	0.173045i
$622$	−14.8009			−0.593463
$623$	−9.91144	+	11.4384i	−0.397094	+	0.458270i
$624$	6.51860	−	4.18925i	0.260953	−	0.167704i
$625$	−3.68214	−	25.6098i	−0.147285	−	1.02439i
$626$	7.71121	+	16.8852i	0.308202	+	0.674868i
$627$	2.46349	−	17.1340i	0.0983825	−	0.684265i
$628$	10.4419	−	3.06601i	0.416676	−	0.122347i
$629$	8.20780	+	5.27483i	0.327266	+	0.210321i
$630$	−1.88896	+	4.13624i	−0.0752579	+	0.164792i
$631$	34.4534	+	10.1164i	1.37157	+	0.402729i	0.882827	−	0.469699i	$-0.155637\pi$
$631$	34.4534	+	10.1164i	1.37157	+	0.402729i	0.488743	+	0.872428i	$0.337456\pi$
$632$	3.95163	+	4.56042i	0.157187	+	0.181404i
$633$	0.521019	+	0.601288i	0.0207087	+	0.0238991i
$634$	11.3406	+	3.32990i	0.450392	+	0.132247i
$635$	14.4461	−	31.6325i	0.573275	−	1.25530i
$636$	0.0855679	+	0.0549911i	0.00339299	+	0.00218054i
$637$	−3.15928	+	0.927649i	−0.125175	+	0.0367548i
$638$	−4.06931	+	28.3027i	−0.161106	+	1.12051i
$639$	4.20934	+	9.21717i	0.166519	+	0.364626i
$640$	−1.86921	−	13.0007i	−0.0738872	−	0.513897i
$641$	17.6866	−	11.3665i	0.698578	−	0.448949i	−0.142548	−	0.989788i	$-0.545530\pi$
$641$	17.6866	−	11.3665i	0.698578	−	0.448949i	0.841126	+	0.540839i	$0.181893\pi$
$642$	−9.88769	+	11.4110i	−0.390236	+	0.450356i
$643$	−8.69700			−0.342976			−0.171488	−	0.985186i	$-0.554858\pi$
$643$	−8.69700			−0.342976			−0.171488	+	0.985186i	$0.554858\pi$
$644$	2.02387	+	2.22306i	0.0797516	+	0.0876006i
$645$	−8.41493			−0.331338
$646$	−9.97824	+	11.5155i	−0.392589	+	0.453071i
$647$	−1.73142	+	1.11271i	−0.0680690	+	0.0437453i	−0.574233	−	0.818692i	$-0.694700\pi$
$647$	−1.73142	+	1.11271i	−0.0680690	+	0.0437453i	0.506164	+	0.862437i	$0.331063\pi$
$648$	−0.438071	−	3.04685i	−0.0172091	−	0.119692i
$649$	−15.7693	−	34.5299i	−0.618998	−	1.35542i
$650$	5.52287	−	38.4124i	0.216625	−	1.50666i
$651$	2.05864	−	0.604471i	0.0806844	−	0.0236911i
$652$	−4.55675	−	2.92844i	−0.178456	−	0.114687i
$653$	−19.1666	+	41.9690i	−0.750046	+	1.64237i	0.0162362	+	0.999868i	$0.494832\pi$
$653$	−19.1666	+	41.9690i	−0.750046	+	1.64237i	−0.766282	+	0.642504i	$0.777896\pi$
$654$	−3.64292	−	1.06966i	−0.142449	−	0.0418269i
$655$	6.69281	+	7.72392i	0.261510	+	0.301798i
$656$	0.601259	+	0.693889i	0.0234752	+	0.0270918i
$657$	11.8035	+	3.46581i	0.460497	+	0.135214i
$658$	−0.103488	+	0.226608i	−0.00403440	+	0.00883410i
$659$	8.60592	+	5.53069i	0.335239	+	0.215445i	0.697420	−	0.716663i	$-0.254331\pi$
$659$	8.60592	+	5.53069i	0.335239	+	0.215445i	−0.362181	+	0.932108i	$0.617968\pi$
$660$	7.42808	−	2.18108i	0.289138	−	0.0848984i
$661$	2.89453	−	20.1319i	0.112584	−	0.783041i	−0.852805	−	0.522229i	$-0.825101\pi$
$661$	2.89453	−	20.1319i	0.112584	−	0.783041i	0.965390	−	0.260812i	$-0.0839903\pi$
$662$	−2.73596	−	5.99091i	−0.106336	−	0.232843i
$663$	−1.12027	−	7.79164i	−0.0435077	−	0.302602i
$664$	43.8807	−	28.2004i	1.70290	−	1.09439i
$665$	−13.8215	+	15.9509i	−0.535975	+	0.618548i
$666$	4.78224			0.185308
$667$	−6.12421	−	36.2569i	−0.237130	−	1.40387i
$668$	10.8303			0.419036
$669$	−12.5230	+	14.4523i	−0.484165	+	0.558757i
$670$	−43.8441	+	28.1769i	−1.69385	+	1.08857i
$671$	−5.28922	−	36.7874i	−0.204188	−	1.42016i
$672$	−1.41188	−	3.09159i	−0.0544645	−	0.119261i
$673$	−2.64746	+	18.4135i	−0.102052	+	0.709787i	0.872985	+	0.487746i	$0.162181\pi$
$673$	−2.64746	+	18.4135i	−0.102052	+	0.709787i	−0.975037	+	0.222041i	$0.928728\pi$
$674$	31.1278	−	9.13994i	1.19900	−	0.352057i
$675$	−8.46132	−	5.43776i	−0.325676	−	0.209299i
$676$	0.562064	−	1.23075i	0.0216178	−	0.0473364i
$677$	−1.70750	−	0.501366i	−0.0656244	−	0.0192691i	0.248756	−	0.968566i	$-0.419978\pi$
$677$	−1.70750	−	0.501366i	−0.0656244	−	0.0192691i	−0.314380	+	0.949297i	$0.601797\pi$
$678$	8.53269	+	9.84725i	0.327696	+	0.378181i
$679$	8.42343	+	9.72116i	0.323262	+	0.373064i
$680$	−27.3997	−	8.04526i	−1.05073	−	0.308522i
$681$	7.62620	−	16.6990i	0.292237	−	0.639909i
$682$	6.73133	+	4.32596i	0.257756	+	0.165650i
$683$	40.5063	−	11.8937i	1.54993	−	0.455100i	0.608850	−	0.793286i	$-0.291631\pi$
$683$	40.5063	−	11.8937i	1.54993	−	0.455100i	0.941080	+	0.338185i	$0.109813\pi$
$684$	0.485228	−	3.37483i	0.0185531	−	0.129040i
$685$	−18.0605	−	39.5470i	−0.690056	−	1.51101i
$686$	−0.166766	−	1.15988i	−0.00636715	−	0.0442845i
$687$	9.05395	−	5.81862i	0.345430	−	0.221994i
$688$	−3.34192	+	3.85679i	−0.127410	+	0.147039i
$689$	0.534267			0.0203539
$690$	18.0508	−	12.2365i	0.687184	−	0.465834i
$691$	−9.12494			−0.347129			−0.173565	−	0.984822i	$-0.555529\pi$
$691$	−9.12494			−0.347129			−0.173565	+	0.984822i	$0.555529\pi$
$692$	7.39554	−	8.53490i	0.281136	−	0.324448i
$693$	−2.67735	+	1.72063i	−0.101704	+	0.0653613i
$694$	−2.70907	−	18.8420i	−0.102835	−	0.715232i
$695$	−9.53646	−	20.8819i	−0.361739	−	0.792097i
$696$	−3.35877	+	23.3607i	−0.127314	+	0.885486i
$697$	0.894951	−	0.262781i	0.0338987	−	0.00995355i
$698$	26.9660	+	17.3300i	1.02068	+	0.655950i
$699$	−3.83443	+	8.39622i	−0.145031	+	0.317574i
$700$	−6.04958	−	1.77632i	−0.228653	−	0.0671385i
$701$	−18.8621	−	21.7681i	−0.712413	−	0.822168i	0.277960	−	0.960593i	$-0.410342\pi$
$701$	−18.8621	−	21.7681i	−0.712413	−	0.822168i	−0.990373	+	0.138424i	$0.955796\pi$
$702$	−2.52669	−	2.91596i	−0.0953639	−	0.110056i
$703$	21.2980	+	6.25366i	0.803270	+	0.235861i
$704$	11.4880	−	25.1553i	0.432971	−	0.948074i
$705$	−0.694006	−	0.446011i	−0.0261378	−	0.0167977i
$706$	10.7013	−	3.14218i	0.402748	−	0.118258i
$707$	−0.919594	+	6.39592i	−0.0345849	+	0.240543i
$708$	−3.10603	−	6.80125i	−0.116732	−	0.255607i
$709$	0.585469	+	4.07203i	0.0219877	+	0.152928i	0.997857	−	0.0654255i	$-0.0208405\pi$
$709$	0.585469	+	4.07203i	0.0219877	+	0.152928i	−0.975870	+	0.218354i	$0.929931\pi$
$710$	38.7614	−	24.9104i	1.45469	−	0.934872i
$711$	1.28375	−	1.48153i	0.0481446	−	0.0555618i
$712$	−46.5889			−1.74599
$713$	−9.94103	−	2.65589i	−0.372294	−	0.0994637i
$714$	2.80145			0.104842
$715$	26.6292	−	30.7317i	0.995875	−	1.14930i
$716$	13.1639	−	8.45989i	0.491956	−	0.316161i
$717$	2.98664	+	20.7726i	0.111538	+	0.775766i
$718$	7.76848	+	17.0106i	0.289917	+	0.634830i
$719$	0.296976	−	2.06552i	0.0110754	−	0.0770308i	−0.983534	−	0.180722i	$-0.942156\pi$
$719$	0.296976	−	2.06552i	0.0110754	−	0.0770308i	0.994609	+	0.103692i	$0.0330655\pi$
$720$	−8.76205	+	2.57277i	−0.326542	+	0.0958815i
$721$	−13.6660	−	8.78258i	−0.508947	−	0.327080i
$722$	−5.15177	+	11.2808i	−0.191729	+	0.419828i
$723$	−13.0339	−	3.82711i	−0.484737	−	0.142332i
$724$	6.98748	+	8.06398i	0.259688	+	0.299696i
$725$	50.5005	+	58.2806i	1.87554	+	2.16449i
$726$	0.979551	+	0.287622i	0.0363545	+	0.0106747i
$727$	14.4619	−	31.6672i	0.536364	−	1.17447i	−0.426501	−	0.904487i	$-0.640254\pi$
$727$	14.4619	−	31.6672i	0.536364	−	1.17447i	0.962864	−	0.269985i	$-0.0870188\pi$
$728$	−8.52645	−	5.47961i	−0.316011	−	0.203088i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	7.96083	−	55.3688i	0.294644	−	2.04929i
$731$	2.15365	+	4.71583i	0.0796556	+	0.174421i
$732$	−1.04180	−	7.24590i	−0.0385062	−	0.267816i
$733$	0.756996	−	0.486492i	0.0279603	−	0.0179690i	−0.526586	−	0.850122i	$-0.676528\pi$
$733$	0.756996	−	0.486492i	0.0279603	−	0.0179690i	0.554546	+	0.832153i	$0.312892\pi$
$734$	28.1515	−	32.4885i	1.03909	−	1.19917i
$735$	3.88046			0.143133
$736$	−1.92323	+	16.1859i	−0.0708912	+	0.596619i
$737$	−36.4773			−1.34366
$738$	0.299390	−	0.345515i	0.0110207	−	0.0127186i
$739$	6.17363	−	3.96755i	0.227101	−	0.145949i	−0.422143	−	0.906529i	$-0.638722\pi$
$739$	6.17363	−	3.96755i	0.227101	−	0.145949i	0.649244	+	0.760581i	$0.275086\pi$
$740$	1.41280	+	9.82624i	0.0519356	+	0.361220i
$741$	−7.43964	−	16.2905i	−0.273302	−	0.598448i
$742$	−0.0270594	+	0.188202i	−0.000993383	+	0.00690913i
$743$	33.3688	−	9.79797i	1.22418	−	0.359453i	0.395132	−	0.918624i	$-0.370699\pi$
$743$	33.3688	−	9.79797i	1.22418	−	0.359453i	0.829052	+	0.559172i	$0.188881\pi$
$744$	5.55597	+	3.57060i	0.203692	+	0.130905i
$745$	13.4704	−	29.4960i	0.493516	−	1.08065i
$746$	−16.0423	−	4.71045i	−0.587351	−	0.172462i
$747$	−11.0969	−	12.8065i	−0.406014	−	0.468565i
$748$	−3.12339	−	3.60458i	−0.114202	−	0.131796i
$749$	12.3632	+	3.63016i	0.451741	+	0.132643i
$750$	−9.55433	+	20.9211i	−0.348875	+	0.763929i
$751$	5.13733	+	3.30156i	0.187464	+	0.120476i	0.631006	−	0.775778i	$-0.282642\pi$
$751$	5.13733	+	3.30156i	0.187464	+	0.120476i	−0.443543	+	0.896253i	$0.646279\pi$
$752$	−0.480037	+	0.140952i	−0.0175052	+	0.00513998i
$753$	4.20209	−	29.2262i	0.153133	−	1.06506i
$754$	12.2891	+	26.9094i	0.447544	+	0.979984i
$755$	1.48298	+	10.3144i	0.0539713	+	0.375379i
$756$	−0.527351	+	0.338908i	−0.0191796	+	0.0123260i
$757$	−30.8232	+	35.5718i	−1.12029	+	1.29288i	−0.168642	+	0.985677i	$0.553938\pi$
$757$	−30.8232	+	35.5718i	−1.12029	+	1.29288i	−0.951644	+	0.307202i	$0.900607\pi$
$758$	5.75767			0.209128
$759$	15.2585	−	0.374404i	0.553848	−	0.0135900i
$760$	−64.9682			−2.35664
$761$	−0.398804	+	0.460245i	−0.0144566	+	0.0166839i	−0.762932	−	0.646479i	$-0.776241\pi$
$761$	−0.398804	+	0.460245i	−0.0144566	+	0.0166839i	0.748475	+	0.663163i	$0.230786\pi$
$762$	−8.83421	+	5.67740i	−0.320030	+	0.205671i
$763$	0.461106	+	3.20707i	0.0166932	+	0.116104i
$764$	−2.64868	−	5.79980i	−0.0958259	−	0.209830i
$765$	−1.32026	+	9.18260i	−0.0477341	+	0.331998i
$766$	−2.87726	+	0.844839i	−0.103960	+	0.0305253i
$767$	−33.0388	−	21.2328i	−1.19296	−	0.766670i
$768$	5.57168	−	12.2003i	0.201051	−	0.440239i
$769$	5.94987	+	1.74704i	0.214558	+	0.0629999i	0.387245	−	0.921977i	$-0.373427\pi$
$769$	5.94987	+	1.74704i	0.214558	+	0.0629999i	−0.172687	+	0.984977i	$0.555245\pi$
$770$	9.47694	+	10.9370i	0.341525	+	0.394141i
$771$	−4.88417	−	5.63663i	−0.175899	−	0.202998i
$772$	0.344563	+	0.101173i	0.0124011	+	0.00364129i
$773$	3.61398	−	7.91351i	0.129986	−	0.284629i	−0.833437	−	0.552614i	$-0.813630\pi$
$773$	3.61398	−	7.91351i	0.129986	−	0.284629i	0.963423	+	0.267985i	$0.0863577\pi$
$774$	2.13772	+	1.37383i	0.0768388	+	0.0493813i
$775$	20.7058	−	6.07976i	0.743773	−	0.218392i
$776$	−5.63488	+	39.1914i	−0.202280	+	1.40689i
$777$	−1.69534	−	3.71228i	−0.0608200	−	0.133177i
$778$	−5.40429	−	37.5877i	−0.193753	−	1.34758i
$779$	1.78518	−	1.14726i	0.0639606	−	0.0411050i
$780$	5.24508	−	6.05314i	0.187804	−	0.216737i
$781$	32.2486			1.15394
$782$	−11.4772	−	6.98422i	−0.410425	−	0.249755i
$783$	7.66717			0.274002
$784$	1.54109	−	1.77852i	0.0550391	−	0.0635185i
$785$	−56.6728	+	36.4214i	−2.02274	+	1.29994i
$786$	−0.439221	−	3.05485i	−0.0156665	−	0.108963i
$787$	11.5945	+	25.3884i	0.413299	+	0.904998i	0.995747	+	0.0921301i	$0.0293676\pi$
$787$	11.5945	+	25.3884i	0.413299	+	0.904998i	−0.582448	+	0.812868i	$0.697905\pi$
$788$	−1.00253	+	6.97272i	−0.0357135	+	0.248393i
$789$	22.1982	−	6.51797i	0.790275	−	0.232046i
$790$	−7.49895	−	4.81928i	−0.266801	−	0.171462i
$791$	4.61915	−	10.1145i	0.164238	−	0.359631i
$792$	−9.39972	−	2.76001i	−0.334004	−	0.0980725i
$793$	−25.1802	−	29.0595i	−0.894175	−	1.03193i
$794$	14.9324	+	17.2329i	0.529931	+	0.611573i
$795$	−0.604139	−	0.177391i	−0.0214266	−	0.00629141i
$796$	2.20129	−	4.82016i	0.0780227	−	0.170846i
$797$	−21.1222	−	13.5744i	−0.748185	−	0.480829i	0.110153	−	0.993915i	$-0.464866\pi$
$797$	−21.1222	−	13.5744i	−0.748185	−	0.480829i	−0.858338	+	0.513085i	$0.828502\pi$
$798$	6.11535	−	1.79563i	0.216481	−	0.0635646i
$799$	−0.0723317	+	0.503078i	−0.00255891	+	0.0177976i
$800$	−14.2007	−	31.0952i	−0.502070	−	1.09938i
$801$	2.15396	+	14.9811i	0.0761065	+	0.529332i
$802$	26.5331	−	17.0518i	0.936916	−	0.602119i
$803$	25.6387	−	29.5886i	0.904769	−	1.04416i
$804$	−7.18484			−0.253390
$805$	−15.8979	−	9.67428i	−0.560326	−	0.340974i
$806$	8.27832			0.291591
$807$	−4.79227	+	5.53058i	−0.168696	+	0.194686i
$808$	−16.7327	+	10.7535i	−0.588656	+	0.378306i
$809$	6.00638	+	41.7753i	0.211173	+	1.46874i	0.769248	+	0.638951i	$0.220631\pi$
$809$	6.00638	+	41.7753i	0.211173	+	1.46874i	−0.558074	+	0.829791i	$0.688460\pi$
$810$	1.88896	+	4.13624i	0.0663713	+	0.145333i
$811$	0.812865	−	5.65360i	0.0285436	−	0.198525i	−0.970560	−	0.240860i	$-0.922571\pi$
$811$	0.812865	−	5.65360i	0.0285436	−	0.198525i	0.999103	+	0.0423350i	$0.0134797\pi$
$812$	4.61158	−	1.35408i	0.161835	−	0.0475190i
$813$	−20.0602	−	12.8919i	−0.703541	−	0.452138i
$814$	6.32255	−	13.8445i	0.221605	−	0.485248i
$815$	32.1722	+	9.44661i	1.12694	+	0.330900i
$816$	3.68430	+	4.25191i	0.128976	+	0.148847i
$817$	7.72394	+	8.91390i	0.270226	+	0.311858i
$818$	8.84834	+	2.59811i	0.309375	+	0.0908407i
$819$	−1.36782	+	2.99511i	−0.0477955	+	0.104658i
$820$	0.798390	+	0.513094i	0.0278810	+	0.0179180i
$821$	−20.7576	+	6.09498i	−0.724445	+	0.212716i	−0.623108	−	0.782136i	$-0.714130\pi$
$821$	−20.7576	+	6.09498i	−0.724445	+	0.212716i	−0.101337	+	0.994852i	$0.532312\pi$
$822$	−1.86841	+	12.9950i	−0.0651681	+	0.453254i
$823$	2.10938	+	4.61889i	0.0735282	+	0.161004i	0.942827	−	0.333283i	$-0.108156\pi$
$823$	2.10938	+	4.61889i	0.0735282	+	0.161004i	−0.869299	+	0.494287i	$0.835429\pi$
$824$	−7.11636	−	49.4954i	−0.247910	−	1.72425i
$825$	−26.9288	+	17.3061i	−0.937540	+	0.602520i
$826$	9.15286	−	10.5630i	0.318469	−	0.367532i
$827$	27.2660			0.948130			0.474065	−	0.880490i	$-0.342786\pi$
$827$	27.2660			0.948130			0.474065	+	0.880490i	$0.342786\pi$
$828$	3.00542	−	0.0737454i	0.104446	−	0.00256283i
$829$	6.79931			0.236150			0.118075	−	0.993005i	$-0.462328\pi$
$829$	6.79931			0.236150			0.118075	+	0.993005i	$0.462328\pi$
$830$	−50.4594	+	58.2332i	−1.75147	+	2.02130i
$831$	−10.7372	+	6.90037i	−0.372469	+	0.239371i
$832$	−4.07175	−	28.3197i	−0.141163	−	0.981808i
$833$	−0.993133	−	2.17466i	−0.0344100	−	0.0753475i
$834$	−0.986572	+	6.86176i	−0.0341622	+	0.237603i
$835$	−64.3268	+	18.8880i	−2.22612	+	0.653648i
$836$	−9.12853	−	5.86655i	−0.315717	−	0.202899i
$837$	0.891293	−	1.95166i	0.0308076	−	0.0674593i
$838$	29.7023	+	8.72139i	1.02605	+	0.301275i
$839$	−30.3725	−	35.0517i	−1.04857	−	1.21012i	−0.977123	−	0.212674i	$-0.931783\pi$
$839$	−30.3725	−	35.0517i	−1.04857	−	1.21012i	−0.0714506	−	0.997444i	$-0.522763\pi$
$840$	7.82216	+	9.02726i	0.269890	+	0.311470i
$841$	−28.5790	−	8.39156i	−0.985484	−	0.289364i
$842$	−15.6553	+	34.2803i	−0.539516	+	1.18138i
$843$	12.2602	+	7.87913i	0.422262	+	0.271372i
$844$	0.478541	−	0.140512i	0.0164721	−	0.00483663i
$845$	−1.19197	+	8.29031i	−0.0410049	+	0.285195i
$846$	0.103488	+	0.226608i	0.00355801	+	0.00779095i
$847$	−0.123988	−	0.862353i	−0.00426026	−	0.0296308i
$848$	−0.321232	+	0.206443i	−0.0110311	+	0.00708929i
$849$	−2.56153	+	2.95616i	−0.0879115	+	0.101455i
$850$	28.1769			0.966460
$851$	−2.30935	+	19.4354i	−0.0791635	+	0.666238i
$852$	6.35191			0.217613
$853$	−24.3558	+	28.1081i	−0.833928	+	0.962405i	−0.999718	−	0.0237565i	$-0.992437\pi$
$853$	−24.3558	+	28.1081i	−0.833928	+	0.962405i	0.165789	+	0.986161i	$0.446983\pi$
$854$	11.5119	−	7.39825i	0.393929	−	0.253163i
$855$	3.00370	+	20.8912i	0.102724	+	0.714463i
$856$	16.4765	+	36.0786i	0.563156	+	1.23314i
$857$	3.88013	−	26.9869i	0.132543	−	0.921856i	−0.809681	−	0.586871i	$-0.800360\pi$
$857$	3.88013	−	26.9869i	0.132543	−	0.921856i	0.942223	−	0.334985i	$-0.108731\pi$
$858$	−11.7821	+	3.45955i	−0.402236	+	0.118107i
$859$	3.73812	+	2.40235i	0.127543	+	0.0819670i	0.602857	−	0.797849i	$-0.294029\pi$
$859$	3.73812	+	2.40235i	0.127543	+	0.0819670i	−0.475314	+	0.879816i	$0.657665\pi$
$860$	−2.19132	+	4.79832i	−0.0747233	+	0.163621i
$861$	−0.374346	−	0.109918i	−0.0127577	−	0.00374600i
$862$	−7.31364	−	8.44039i	−0.249104	−	0.287481i
$863$	5.92523	+	6.83808i	0.201697	+	0.232771i	0.847583	−	0.530663i	$-0.178057\pi$
$863$	5.92523	+	6.83808i	0.201697	+	0.232771i	−0.645885	+	0.763434i	$0.723512\pi$
$864$	−3.26105	−	0.957532i	−0.110943	−	0.0325759i
$865$	−29.0412	+	63.5913i	−0.987429	+	2.16217i
$866$	4.08765	+	2.62697i	0.138904	+	0.0892682i
$867$	−10.8274	+	3.17922i	−0.367719	+	0.107972i
$868$	0.191409	−	1.33128i	0.00649683	−	0.0451864i
$869$	−2.59175	−	5.67515i	−0.0879192	−	0.192516i
$870$	−4.96165	−	34.5090i	−0.168216	−	1.16997i
$871$	−31.7481	+	20.4033i	−1.07574	+	0.691339i
$872$	−6.53122	+	7.53743i	−0.221175	+	0.255250i
$873$	12.8629			0.435344
$874$	−29.5306	−	7.88952i	−0.998888	−	0.266867i
$875$	19.6273			0.663525
$876$	5.04998	−	5.82799i	0.170623	−	0.196909i
$877$	14.3065	−	9.19426i	0.483098	−	0.310468i	−0.276327	−	0.961064i	$-0.589117\pi$
$877$	14.3065	−	9.19426i	0.483098	−	0.310468i	0.759424	+	0.650596i	$0.225481\pi$
$878$	−0.185707	−	1.29162i	−0.00626730	−	0.0435900i
$879$	0.564643	+	1.23640i	0.0190449	+	0.0417026i
$880$	−4.13612	+	28.7673i	−0.139428	+	0.969746i
$881$	−31.3942	+	9.21818i	−1.05770	+	0.310568i	−0.763924	−	0.645306i	$-0.776730\pi$
$881$	−31.3942	+	9.21818i	−1.05770	+	0.310568i	−0.293775	+	0.955875i	$0.594912\pi$
$882$	−0.985789	−	0.633528i	−0.0331932	−	0.0213320i
$883$	−19.6871	+	43.1088i	−0.662524	+	1.45073i	0.217626	+	0.976032i	$0.430169\pi$
$883$	−19.6871	+	43.1088i	−0.662524	+	1.45073i	−0.880151	+	0.474694i	$0.842559\pi$
$884$	−4.73464	−	1.39021i	−0.159243	−	0.0467580i
$885$	30.3098	+	34.9794i	1.01885	+	1.17582i
$886$	−19.8676	−	22.9284i	−0.667465	−	0.770296i
$887$	16.8246	+	4.94015i	0.564915	+	0.165874i	0.551706	−	0.834039i	$-0.313977\pi$
$887$	16.8246	+	4.94015i	0.564915	+	0.165874i	0.0132093	+	0.999913i	$0.495795\pi$
$888$	5.21856	−	11.4271i	0.175124	−	0.383467i
$889$	7.53895	+	4.84499i	0.252848	+	0.162496i
$890$	66.0344	−	19.3894i	2.21348	−	0.649936i
$891$	−0.452928	+	3.15018i	−0.0151736	+	0.105535i
$892$	4.97981	+	10.9043i	0.166736	+	0.365102i
$893$	0.164561	+	1.14454i	0.00550681	+	0.0383007i
$894$	−8.23754	+	5.29395i	−0.275505	+	0.177056i
$895$	−63.4331	+	73.2057i	−2.12033	+	2.44700i
$896$	3.38474			0.113076
$897$	13.0709	−	8.86058i	0.436423	−	0.295846i
$898$	−22.6325			−0.755255
$899$	−10.7727	+	12.4323i	−0.359288	+	0.414641i
$900$	−5.30409	+	3.40873i	−0.176803	+	0.113624i
$901$	0.0552061	+	0.383967i	0.00183918	+	0.0127918i
$902$	−0.604435	−	1.32353i	−0.0201255	−	0.0440687i
$903$	0.308615	−	2.14647i	0.0102701	−	0.0714299i
$904$	32.8410	−	9.64299i	1.09228	−	0.320721i
$905$	−55.5660	−	35.7101i	−1.84708	−	1.18704i
$906$	1.30720	−	2.86237i	0.0434288	−	0.0950958i
$907$	−45.0741	−	13.2349i	−1.49666	−	0.439459i	−0.572000	−	0.820253i	$-0.693832\pi$
$907$	−45.0741	−	13.2349i	−1.49666	−	0.439459i	−0.924660	+	0.380794i	$0.875651\pi$
$908$	−7.53611	−	8.69714i	−0.250095	−	0.288625i
$909$	4.23151	+	4.88342i	0.140350	+	0.161973i
$910$	14.3658	+	4.21817i	0.476221	+	0.139831i
$911$	16.8039	−	36.7954i	0.556738	−	1.21909i	−0.396825	−	0.917894i	$-0.629888\pi$
$911$	16.8039	−	36.7954i	0.556738	−	1.21909i	0.953563	−	0.301192i	$-0.0973846\pi$
$912$	10.7679	+	6.92009i	0.356560	+	0.229147i
$913$	−51.7455	+	15.1939i	−1.71253	+	0.502843i
$914$	−1.09656	+	7.62673i	−0.0362709	+	0.252270i
$915$	18.8247	+	41.2204i	0.622326	+	1.36270i
$916$	−0.960139	−	6.67791i	−0.0317239	−	0.220644i
$917$	−2.21566	+	1.42392i	−0.0731675	+	0.0470219i
$918$	1.83456	−	2.11719i	0.0605494	−	0.0698778i
$919$	36.0789			1.19013			0.595067	−	0.803676i	$-0.297125\pi$
$919$	36.0789			1.19013			0.595067	+	0.803676i	$0.297125\pi$
$920$	−9.54097	−	56.4850i	−0.314557	−	1.86225i
$921$	−9.82716			−0.323816
$922$	−0.438911	+	0.506531i	−0.0144548	+	0.0166817i
$923$	28.0676	−	18.0380i	0.923857	−	0.593727i
$924$	0.283923	+	1.97473i	0.00934040	+	0.0649639i
$925$	−17.0517	−	37.3380i	−0.560657	−	1.22767i
$926$	3.04219	−	21.1589i	0.0999726	−	0.695324i
$927$	−15.5867	+	4.57668i	−0.511936	+	0.150318i
$928$	21.9219	+	14.0884i	0.719622	+	0.462473i
$929$	−18.8838	+	41.3498i	−0.619558	+	1.35664i	0.296283	+	0.955100i	$0.404253\pi$
$929$	−18.8838	+	41.3498i	−0.619558	+	1.35664i	−0.915841	+	0.401542i	$0.868474\pi$
$930$	−9.36097	−	2.74863i	−0.306958	−	0.0901311i
$931$	−3.56182	−	4.11056i	−0.116734	−	0.134718i
$932$	3.78913	+	4.37289i	0.124117	+	0.143239i
$933$	12.1192	+	3.55852i	0.396765	+	0.116501i
$934$	5.67812	−	12.4333i	0.185794	−	0.406831i
$935$	24.8379	+	15.9623i	0.812285	+	0.522024i
$936$	−9.72485	+	2.85547i	−0.317867	+	0.0933341i
$937$	3.49492	−	24.3077i	0.114174	−	0.794099i	−0.849609	−	0.527413i	$-0.823162\pi$
$937$	3.49492	−	24.3077i	0.114174	−	0.794099i	0.963783	−	0.266686i	$-0.0859287\pi$
$938$	−5.57935	−	12.2171i	−0.182172	−	0.398901i
$939$	−2.25441	−	15.6798i	−0.0735700	−	0.511691i
$940$	−0.435047	+	0.279587i	−0.0141897	+	0.00911914i
$941$	−26.4099	+	30.4786i	−0.860937	+	0.993574i	0.139058	+	0.990284i	$0.455593\pi$
$941$	−26.4099	+	30.4786i	−0.860937	+	0.993574i	−0.999995	+	0.00328975i	$0.998953\pi$
$942$	20.3433			0.662820
$943$	1.25963	+	1.38360i	0.0410190	+	0.0450561i
$944$	28.0693			0.913577
$945$	2.54116	−	2.93266i	0.0826640	−	0.0953994i
$946$	6.80346	−	4.37232i	0.221199	−	0.142156i
$947$	5.01681	+	34.8927i	0.163024	+	1.13386i	0.892892	+	0.450271i	$0.148672\pi$
$947$	5.01681	+	34.8927i	0.163024	+	1.13386i	−0.729868	+	0.683588i	$0.760418\pi$
$948$	−0.510491	−	1.11782i	−0.0165800	−	0.0363051i
$949$	5.76454	−	40.0933i	0.187125	−	1.30148i
$950$	61.5081	−	18.0604i	1.99559	−	0.585957i
$951$	−8.48523	−	5.45313i	−0.275153	−	0.176830i
$952$	3.05705	−	6.69400i	0.0990794	−	0.216954i
$953$	55.8741	+	16.4061i	1.80994	+	0.531446i	0.998589	−	0.0531119i	$-0.0169140\pi$
$953$	55.8741	+	16.4061i	1.80994	+	0.531446i	0.811352	+	0.584558i	$0.198732\pi$
$954$	0.124514	+	0.143697i	0.00403128	+	0.00465235i
$955$	25.8468	+	29.8288i	0.836384	+	0.965239i
$956$	12.6226	+	3.70632i	0.408243	+	0.119871i
$957$	10.1367	−	22.1962i	0.327673	−	0.717503i
$958$	8.52839	+	5.48086i	0.275540	+	0.177079i
$959$	10.7499	−	3.15647i	0.347134	−	0.101928i
$960$	−4.79864	+	33.3753i	−0.154875	+	1.07718i
$961$	−10.9656	−	24.0112i	−0.353727	−	0.774555i
$962$	−2.24093	−	15.5860i	−0.0722505	−	0.502513i
$963$	10.8397	−	6.96623i	0.349303	−	0.224484i
$964$	−5.57642	+	6.43553i	−0.179604	+	0.207275i
$965$	−2.22299			−0.0715606
$966$	2.45924	+	5.05315i	0.0791249	+	0.162582i
$967$	53.5735			1.72281			0.861404	−	0.507920i	$-0.169585\pi$
$967$	53.5735			1.72281			0.861404	+	0.507920i	$0.169585\pi$
$968$	1.75619	−	2.02675i	0.0564461	−	0.0651422i
$969$	10.9389	−	7.03003i	0.351409	−	0.225837i
$970$	−8.32397	−	57.8945i	−0.267267	−	1.85888i
$971$	−1.54058	−	3.37341i	−0.0494397	−	0.108258i	0.883300	−	0.468808i	$-0.155316\pi$
$971$	−1.54058	−	3.37341i	−0.0494397	−	0.108258i	−0.932740	+	0.360550i	$0.882589\pi$
$972$	−0.0892119	+	0.620482i	−0.00286147	+	0.0199020i
$973$	5.67628	−	1.66671i	0.181973	−	0.0534321i
$974$	−8.53086	−	5.48245i	−0.273346	−	0.175669i
$975$	−13.7575	+	30.1248i	−0.440593	+	0.964765i
$976$	26.3685	+	7.74249i	0.844035	+	0.247831i
$977$	−7.83814	−	9.04569i	−0.250764	−	0.289397i	0.616386	−	0.787444i	$-0.288596\pi$
$977$	−7.83814	−	9.04569i	−0.250764	−	0.289397i	−0.867150	+	0.498047i	$0.834051\pi$
$978$	−6.63073	−	7.65227i	−0.212027	−	0.244693i
$979$	46.2177	+	13.5707i	1.47712	+	0.433723i
$980$	1.01050	−	2.21270i	0.0322794	−	0.0706820i
$981$	2.72570	+	1.75170i	0.0870249	+	0.0559275i
$982$	−1.92077	+	0.563988i	−0.0612941	+	0.0179976i
$983$	−4.47135	+	31.0989i	−0.142614	+	0.991902i	0.785302	+	0.619113i	$0.212508\pi$
$983$	−4.47135	+	31.0989i	−0.142614	+	0.991902i	−0.927916	+	0.372789i	$0.878401\pi$
$984$	−0.498894	−	1.09243i	−0.0159042	−	0.0348253i
$985$	−6.20592	−	43.1631i	−0.197737	−	1.37529i
$986$	−18.0694	+	11.6125i	−0.575448	+	0.369818i
$987$	0.139220	−	0.160668i	0.00443142	−	0.00511413i
$988$	−11.2264			−0.357161
$989$	−6.61567	+	8.02445i	−0.210366	+	0.255163i
$990$	14.4717			0.459940
$991$	2.11373	−	2.43937i	0.0671448	−	0.0774892i	−0.721183	−	0.692744i	$-0.756401\pi$
$991$	2.11373	−	2.43937i	0.0671448	−	0.0774892i	0.788328	+	0.615255i	$0.210947\pi$
$992$	6.13453	−	3.94243i	0.194772	−	0.125172i
$993$	0.799872	+	5.56323i	0.0253832	+	0.176544i
$994$	4.93255	+	10.8008i	0.156451	+	0.342580i
$995$	−4.66828	+	32.4686i	−0.147994	+	1.02932i
$996$	−10.1922	+	2.99269i	−0.322951	+	0.0948271i
$997$	7.53071	+	4.83969i	0.238500	+	0.153275i	0.654431	−	0.756121i	$-0.272908\pi$
$997$	7.53071	+	4.83969i	0.238500	+	0.153275i	−0.415931	+	0.909396i	$0.636544\pi$
$998$	−17.4378	+	38.1835i	−0.551985	+	1.20868i
$999$	−3.91576	−	1.14977i	−0.123889	−	0.0363772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.e.85.5	✓	60
23.13	even	11	inner	483.2.q.e.358.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.e.85.5	✓	60	1.1	even	1	trivial
483.2.q.e.358.5	yes	60	23.13	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.767372 - 0.885594i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0892119 + 0.620482i) q^{4} +(-1.61200 - 3.52979i) q^{5} +(-0.166766 + 1.15988i) q^{6} +(0.959493 - 0.281733i) q^{7} +(2.58953 + 1.66419i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.767372 - 0.885594i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0892119 + 0.620482i) q^{4} +(-1.61200 - 3.52979i) q^{5} +(-0.166766 + 1.15988i) q^{6} +(0.959493 - 0.281733i) q^{7} +(2.58953 + 1.66419i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-4.36297 - 1.28108i) q^{10} +(-2.08414 - 2.40523i) q^{11} +(-0.410508 - 0.473751i) q^{12} +(-3.15928 - 0.927649i) q^{13} +(0.486787 - 1.06592i) q^{14} +(3.26445 + 2.09794i) q^{15} +(2.25799 - 0.663006i) q^{16} +(0.340232 - 2.36637i) q^{17} +(-0.486787 - 1.06592i) q^{18} +(-0.774057 - 5.38368i) q^{19} +(2.04636 - 1.31512i) q^{20} +(-0.654861 + 0.755750i) q^{21} -3.72937 q^{22} +(4.56704 - 1.46361i) q^{23} -3.07818 q^{24} +(-6.58658 + 7.60132i) q^{25} +(-3.24587 + 2.08599i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.260408 + 0.570215i) q^{28} +(1.09115 - 7.58913i) q^{29} +(4.36297 - 1.28108i) q^{30} +(-1.80495 - 1.15997i) q^{31} +(-1.41188 + 3.09159i) q^{32} +(3.05366 + 0.896635i) q^{33} +(-1.83456 - 2.11719i) q^{34} +(-2.54116 - 2.93266i) q^{35} +(0.601471 + 0.176608i) q^{36} +(-1.69534 + 3.71228i) q^{37} +(-5.36175 - 3.44579i) q^{38} +(3.15928 - 0.927649i) q^{39} +(1.69992 - 11.8232i) q^{40} +(0.162074 + 0.354893i) q^{41} +(0.166766 + 1.15988i) q^{42} +(-1.82429 + 1.17240i) q^{43} +(1.30647 - 1.50775i) q^{44} -3.88046 q^{45} +(2.20845 - 5.16768i) q^{46} -0.212595 q^{47} +(-1.54109 + 1.77852i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.67733 + 11.6661i) q^{50} +(0.993133 + 2.17466i) q^{51} +(0.293744 - 2.04304i) q^{52} +(-0.155687 + 0.0457139i) q^{53} +(0.985789 + 0.633528i) q^{54} +(-5.13032 + 11.2338i) q^{55} +(2.95349 + 0.867224i) q^{56} +(3.56182 + 4.11056i) q^{57} +(-5.88357 - 6.79001i) q^{58} +(11.4444 + 3.36037i) q^{59} +(-1.01050 + 2.21270i) q^{60} +(9.82404 + 6.31353i) q^{61} +(-2.41233 + 0.708325i) q^{62} +(0.142315 - 0.989821i) q^{63} +(3.60966 + 7.90406i) q^{64} +(1.81836 + 12.6470i) q^{65} +(3.13735 - 2.01625i) q^{66} +(7.50573 - 8.66208i) q^{67} +1.49864 q^{68} +(-3.05075 + 3.70040i) q^{69} -4.54716 q^{70} +(-6.63561 + 7.65791i) q^{71} +(2.58953 - 1.66419i) q^{72} +(1.75073 + 12.1766i) q^{73} +(1.98661 + 4.35008i) q^{74} +(1.43140 - 9.95561i) q^{75} +(3.27143 - 0.960577i) q^{76} +(-2.67735 - 1.72063i) q^{77} +(1.60282 - 3.50970i) q^{78} +(1.88094 + 0.552294i) q^{79} +(-5.98016 - 6.90147i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(0.438663 + 0.128803i) q^{82} +(7.03938 - 15.4141i) q^{83} +(-0.527351 - 0.338908i) q^{84} +(-8.90124 + 2.61364i) q^{85} +(-0.361638 + 2.51525i) q^{86} +(3.18506 + 6.97431i) q^{87} +(-1.39419 - 9.69683i) q^{88} +(-12.7325 + 8.18270i) q^{89} +(-2.97776 + 3.43652i) q^{90} -3.29266 q^{91} +(1.31558 + 2.70320i) q^{92} +2.14555 q^{93} +(-0.163139 + 0.188273i) q^{94} +(-17.7555 + 11.4108i) q^{95} +(-0.483689 - 3.36413i) q^{96} +(5.34346 + 11.7005i) q^{97} +(0.166766 - 1.15988i) q^{98} +(-3.05366 + 0.896635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more