LMFDB - Embedded newform 483.2.q.e.127.4

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			127.4
Character	$\chi$	$=$	483.127
Dual form			483.2.q.e.232.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.486928 - 0.312930i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.691656 + 1.51452i) q^{4} +(-1.52427 + 0.447565i) q^{5} +(-0.240447 - 0.526506i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.301897 + 2.09974i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.486928 - 0.312930i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.691656 + 1.51452i) q^{4} +(-1.52427 + 0.447565i) q^{5} +(-0.240447 - 0.526506i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.301897 + 2.09974i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.602152 + 0.694921i) q^{10} +(0.0561151 + 0.0360630i) q^{11} +(1.40067 + 0.900154i) q^{12} +(-2.63455 + 3.04043i) q^{13} +(0.555367 + 0.163070i) q^{14} +(0.226084 + 1.57245i) q^{15} +(-1.37658 - 1.58866i) q^{16} +(2.45428 + 5.37412i) q^{17} +(-0.555367 + 0.163070i) q^{18} +(-1.69516 + 3.71187i) q^{19} +(0.376424 - 2.61809i) q^{20} +(0.841254 - 0.540641i) q^{21} +0.0386092 q^{22} +(4.58365 - 1.41074i) q^{23} +2.12133 q^{24} +(-2.08319 + 1.33879i) q^{25} +(-0.331395 + 2.30490i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.59753 + 0.469078i) q^{28} +(-0.547375 - 1.19858i) q^{29} +(0.602152 + 0.694921i) q^{30} +(1.17281 + 8.15708i) q^{31} +(-5.23824 - 1.53809i) q^{32} +(0.0436819 - 0.0504116i) q^{33} +(2.87678 + 1.84879i) q^{34} +(-1.33643 - 0.858872i) q^{35} +(1.09033 - 1.25830i) q^{36} +(0.0595107 + 0.0174739i) q^{37} +(0.336136 + 2.33788i) q^{38} +(2.63455 + 3.04043i) q^{39} +(-1.39994 - 3.06545i) q^{40} +(4.08789 - 1.20031i) q^{41} +(0.240447 - 0.526506i) q^{42} +(1.46849 - 10.2136i) q^{43} +(-0.0934302 + 0.0600440i) q^{44} +1.58862 q^{45} +(1.79045 - 2.12129i) q^{46} +3.35993 q^{47} +(-1.76840 + 1.13648i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-0.595418 + 1.30378i) q^{50} +(5.66870 - 1.66448i) q^{51} +(-2.78258 - 6.09300i) q^{52} +(-5.70745 - 6.58675i) q^{53} +(0.0823736 + 0.572921i) q^{54} +(-0.101675 - 0.0298544i) q^{55} +(-1.38918 + 1.60320i) q^{56} +(3.43285 + 2.20616i) q^{57} +(-0.641605 - 0.412334i) q^{58} +(1.34284 - 1.54972i) q^{59} +(-2.53787 - 0.745186i) q^{60} +(-0.107607 - 0.748421i) q^{61} +(3.12367 + 3.60490i) q^{62} +(-0.415415 - 0.909632i) q^{63} +(1.00193 - 0.294194i) q^{64} +(2.65497 - 5.81357i) q^{65} +(0.00549466 - 0.0382162i) q^{66} +(-11.8622 + 7.62340i) q^{67} -9.83671 q^{68} +(-0.744056 - 4.73776i) q^{69} -0.919512 q^{70} +(13.6224 - 8.75461i) q^{71} +(0.301897 - 2.09974i) q^{72} +(-0.0118936 + 0.0260434i) q^{73} +(0.0344455 - 0.0101141i) q^{74} +(1.02869 + 2.25252i) q^{75} +(-4.44922 - 5.13468i) q^{76} +(0.00949298 + 0.0660252i) q^{77} +(2.23428 + 0.656043i) q^{78} +(1.01149 - 1.16733i) q^{79} +(2.80931 + 1.80543i) q^{80} +(0.841254 + 0.540641i) q^{81} +(1.61489 - 1.86369i) q^{82} +(-0.373211 - 0.109585i) q^{83} +(0.236951 + 1.64803i) q^{84} +(-6.14625 - 7.09315i) q^{85} +(-2.48108 - 5.43280i) q^{86} +(-1.26428 + 0.371227i) q^{87} +(-0.0587819 + 0.128714i) q^{88} +(-1.25590 + 8.73497i) q^{89} +(0.773543 - 0.497126i) q^{90} -4.02307 q^{91} +(-1.03373 + 7.91775i) q^{92} +8.24096 q^{93} +(1.63605 - 1.05142i) q^{94} +(0.922565 - 6.41658i) q^{95} +(-2.26791 + 4.96603i) q^{96} +(-1.23771 + 0.363425i) q^{97} +(0.240447 + 0.526506i) q^{98} +(-0.0436819 - 0.0504116i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.486928	−	0.312930i	0.344310	−	0.221275i	−0.357044	−	0.934087i	$-0.616215\pi$
$2$	0.486928	−	0.312930i	0.344310	−	0.221275i	0.701354	+	0.712813i	$0.252579\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	−0.691656	+	1.51452i	−0.345828	+	0.757258i
$5$	−1.52427	+	0.447565i	−0.681673	+	0.200157i	−0.604195	−	0.796837i	$-0.706505\pi$
$5$	−1.52427	+	0.447565i	−0.681673	+	0.200157i	−0.0774785	+	0.996994i	$0.524687\pi$
$6$	−0.240447	−	0.526506i	−0.0981622	−	0.214945i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$8$	0.301897	+	2.09974i	0.106737	+	0.742371i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−0.602152	+	0.694921i	−0.190417	+	0.219753i
$11$	0.0561151	+	0.0360630i	0.0169193	+	0.0108734i	0.549073	−	0.835774i	$-0.314981\pi$
$11$	0.0561151	+	0.0360630i	0.0169193	+	0.0108734i	−0.532154	+	0.846648i	$0.678617\pi$
$12$	1.40067	+	0.900154i	0.404338	+	0.259852i
$13$	−2.63455	+	3.04043i	−0.730693	+	0.843265i	−0.992549	−	0.121842i	$-0.961120\pi$
$13$	−2.63455	+	3.04043i	−0.730693	+	0.843265i	0.261857	+	0.965107i	$0.415665\pi$
$14$	0.555367	+	0.163070i	0.148428	+	0.0435824i
$15$	0.226084	+	1.57245i	0.0583746	+	0.406004i
$16$	−1.37658	−	1.58866i	−0.344145	−	0.397165i
$17$	2.45428	+	5.37412i	0.595250	+	1.30342i	0.932217	+	0.361899i	$0.117872\pi$
$17$	2.45428	+	5.37412i	0.595250	+	1.30342i	−0.336967	+	0.941516i	$0.609401\pi$
$18$	−0.555367	+	0.163070i	−0.130901	+	0.0384360i
$19$	−1.69516	+	3.71187i	−0.388895	+	0.851562i	0.609381	+	0.792877i	$0.291418\pi$
$19$	−1.69516	+	3.71187i	−0.388895	+	0.851562i	−0.998277	+	0.0586847i	$0.981309\pi$
$20$	0.376424	−	2.61809i	0.0841710	−	0.585422i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	0.0386092			0.00823150
$23$	4.58365	−	1.41074i	0.955757	−	0.294159i
$23$	4.58365	−	1.41074i	0.955757	−	0.294159i
$24$	2.12133			0.433015
$25$	−2.08319	+	1.33879i	−0.416638	+	0.267757i
$26$	−0.331395	+	2.30490i	−0.0649919	+	0.452028i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−1.59753	+	0.469078i	−0.301905	+	0.0886474i
$29$	−0.547375	−	1.19858i	−0.101645	−	0.222571i	0.851976	−	0.523580i	$-0.175404\pi$
$29$	−0.547375	−	1.19858i	−0.101645	−	0.222571i	−0.953621	+	0.301009i	$0.902677\pi$
$30$	0.602152	+	0.694921i	0.109937	+	0.126875i
$31$	1.17281	+	8.15708i	0.210643	+	1.46506i	0.771017	+	0.636815i	$0.219749\pi$
$31$	1.17281	+	8.15708i	0.210643	+	1.46506i	−0.560373	+	0.828240i	$0.689342\pi$
$32$	−5.23824	−	1.53809i	−0.926000	−	0.271898i
$33$	0.0436819	−	0.0504116i	0.00760404	−	0.00877553i
$34$	2.87678	+	1.84879i	0.493364	+	0.317066i
$35$	−1.33643	−	0.858872i	−0.225898	−	0.145176i
$36$	1.09033	−	1.25830i	0.181721	−	0.209717i
$37$	0.0595107	+	0.0174739i	0.00978349	+	0.00287269i	0.286621	−	0.958044i	$-0.407468\pi$
$37$	0.0595107	+	0.0174739i	0.00978349	+	0.00287269i	−0.276837	+	0.960917i	$0.589286\pi$
$38$	0.336136	+	2.33788i	0.0545285	+	0.379254i
$39$	2.63455	+	3.04043i	0.421866	+	0.486859i
$40$	−1.39994	−	3.06545i	−0.221351	−	0.484690i
$41$	4.08789	−	1.20031i	0.638421	−	0.187457i	0.0535260	−	0.998566i	$-0.482954\pi$
$41$	4.08789	−	1.20031i	0.638421	−	0.187457i	0.584895	+	0.811109i	$0.301136\pi$
$42$	0.240447	−	0.526506i	0.0371018	−	0.0812417i
$43$	1.46849	−	10.2136i	0.223942	−	1.55755i	−0.498974	−	0.866617i	$-0.666290\pi$
$43$	1.46849	−	10.2136i	0.223942	−	1.55755i	0.722916	−	0.690936i	$-0.242801\pi$
$44$	−0.0934302	+	0.0600440i	−0.0140851	+	0.00905197i
$45$	1.58862			0.236817
$46$	1.79045	−	2.12129i	0.263987	−	0.312767i
$47$	3.35993			0.490097			0.245048	−	0.969511i	$-0.421196\pi$
$47$	3.35993			0.490097			0.245048	+	0.969511i	$0.421196\pi$
$48$	−1.76840	+	1.13648i	−0.255246	+	0.164037i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−0.595418	+	1.30378i	−0.0842049	+	0.184383i
$51$	5.66870	−	1.66448i	0.793777	−	0.233074i
$52$	−2.78258	−	6.09300i	−0.385875	−	0.844947i
$53$	−5.70745	−	6.58675i	−0.783979	−	0.904760i	0.213411	−	0.976962i	$-0.431543\pi$
$53$	−5.70745	−	6.58675i	−0.783979	−	0.904760i	−0.997390	+	0.0722029i	$0.976997\pi$
$54$	0.0823736	+	0.572921i	0.0112096	+	0.0779647i
$55$	−0.101675	−	0.0298544i	−0.0137098	−	0.00402557i
$56$	−1.38918	+	1.60320i	−0.185637	+	0.214236i
$57$	3.43285	+	2.20616i	0.454692	+	0.292213i
$58$	−0.641605	−	0.412334i	−0.0842468	−	0.0541421i
$59$	1.34284	−	1.54972i	0.174823	−	0.201757i	−0.661575	−	0.749879i	$-0.730112\pi$
$59$	1.34284	−	1.54972i	0.174823	−	0.201757i	0.836398	+	0.548122i	$0.184657\pi$
$60$	−2.53787	−	0.745186i	−0.327638	−	0.0962031i
$61$	−0.107607	−	0.748421i	−0.0137776	−	0.0958255i	0.981772	−	0.190061i	$-0.0608685\pi$
$61$	−0.107607	−	0.748421i	−0.0137776	−	0.0958255i	−0.995550	+	0.0942352i	$0.969959\pi$
$62$	3.12367	+	3.60490i	0.396706	+	0.457823i
$63$	−0.415415	−	0.909632i	−0.0523374	−	0.114603i
$64$	1.00193	−	0.294194i	0.125242	−	0.0367743i
$65$	2.65497	−	5.81357i	0.329308	−	0.721085i
$66$	0.00549466	−	0.0382162i	0.000676346	−	0.00470409i
$67$	−11.8622	+	7.62340i	−1.44920	+	0.931347i	−0.449937	+	0.893060i	$0.648554\pi$
$67$	−11.8622	+	7.62340i	−1.44920	+	0.931347i	−0.999267	+	0.0382865i	$0.987810\pi$
$68$	−9.83671			−1.19288
$69$	−0.744056	−	4.73776i	−0.0895738	−	0.570359i
$70$	−0.919512			−0.109903
$71$	13.6224	−	8.75461i	1.61669	−	1.03898i	0.658602	−	0.752491i	$-0.271148\pi$
$71$	13.6224	−	8.75461i	1.61669	−	1.03898i	0.958083	−	0.286489i	$-0.0924883\pi$
$72$	0.301897	−	2.09974i	0.0355789	−	0.247457i
$73$	−0.0118936	+	0.0260434i	−0.00139205	+	0.00304815i	−0.910327	−	0.413890i	$-0.864170\pi$
$73$	−0.0118936	+	0.0260434i	−0.00139205	+	0.00304815i	0.908935	+	0.416939i	$0.136897\pi$
$74$	0.0344455	−	0.0101141i	0.00400421	−	0.00117574i
$75$	1.02869	+	2.25252i	0.118783	+	0.260098i
$76$	−4.44922	−	5.13468i	−0.510361	−	0.588988i
$77$	0.00949298	+	0.0660252i	0.00108183	+	0.00752426i
$78$	2.23428	+	0.656043i	0.252982	+	0.0742823i
$79$	1.01149	−	1.16733i	0.113802	−	0.131334i	−0.695990	−	0.718051i	$-0.745034\pi$
$79$	1.01149	−	1.16733i	0.113802	−	0.131334i	0.809792	+	0.586717i	$0.199580\pi$
$80$	2.80931	+	1.80543i	0.314090	+	0.201853i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	1.61489	−	1.86369i	0.178335	−	0.205810i
$83$	−0.373211	−	0.109585i	−0.0409652	−	0.0120285i	0.261186	−	0.965289i	$-0.415886\pi$
$83$	−0.373211	−	0.109585i	−0.0409652	−	0.0120285i	−0.302151	+	0.953260i	$0.597705\pi$
$84$	0.236951	+	1.64803i	0.0258535	+	0.179815i
$85$	−6.14625	−	7.09315i	−0.666654	−	0.769360i
$86$	−2.48108	−	5.43280i	−0.267541	−	0.585834i
$87$	−1.26428	+	0.371227i	−0.135545	+	0.0397997i
$88$	−0.0587819	+	0.128714i	−0.00626617	+	0.0137210i
$89$	−1.25590	+	8.73497i	−0.133125	+	0.925905i	0.808321	+	0.588742i	$0.200376\pi$
$89$	−1.25590	+	8.73497i	−0.133125	+	0.925905i	−0.941446	+	0.337163i	$0.890533\pi$
$90$	0.773543	−	0.497126i	0.0815386	−	0.0524017i
$91$	−4.02307			−0.421732
$92$	−1.03373	+	7.91775i	−0.107773	+	0.825482i
$93$	8.24096			0.854548
$94$	1.63605	−	1.05142i	0.168745	−	0.108446i
$95$	0.922565	−	6.41658i	0.0946532	−	0.658327i
$96$	−2.26791	+	4.96603i	−0.231468	+	0.506844i
$97$	−1.23771	+	0.363425i	−0.125671	+	0.0369002i	−0.343963	−	0.938983i	$-0.611769\pi$
$97$	−1.23771	+	0.363425i	−0.125671	+	0.0369002i	0.218293	+	0.975883i	$0.429951\pi$
$98$	0.240447	+	0.526506i	0.0242889	+	0.0531852i
$99$	−0.0436819	−	0.0504116i	−0.00439020	−	0.00506656i
$100$	−0.586760	−	4.08100i	−0.0586760	−	0.408100i
$101$	−1.41970	−	0.416861i	−0.141265	−	0.0414792i	0.210336	−	0.977629i	$-0.432544\pi$
$101$	−1.41970	−	0.416861i	−0.141265	−	0.0414792i	−0.351601	+	0.936150i	$0.614363\pi$
$102$	2.23938	−	2.58439i	0.221732	−	0.255892i
$103$	−6.42355	−	4.12817i	−0.632931	−	0.406760i	0.184462	−	0.982840i	$-0.440946\pi$
$103$	−6.42355	−	4.12817i	−0.632931	−	0.406760i	−0.817394	+	0.576079i	$0.804582\pi$
$104$	−7.17949	−	4.61398i	−0.704007	−	0.452438i
$105$	−1.04032	+	1.20060i	−0.101525	+	0.117166i
$106$	−4.84031	−	1.42124i	−0.470132	−	0.138043i
$107$	1.88632	+	13.1196i	0.182357	+	1.26832i	0.851170	+	0.524891i	$0.175894\pi$
$107$	1.88632	+	13.1196i	0.182357	+	1.26832i	−0.668812	+	0.743431i	$0.733197\pi$
$108$	−1.09033	−	1.25830i	−0.104917	−	0.121080i
$109$	4.02334	+	8.80988i	0.385366	+	0.843834i	0.998547	+	0.0538911i	$0.0171624\pi$
$109$	4.02334	+	8.80988i	0.385366	+	0.843834i	−0.613181	+	0.789943i	$0.710110\pi$
$110$	−0.0588507	+	0.0172801i	−0.00561120	+	0.00164760i
$111$	0.0257653	−	0.0564181i	0.00244553	−	0.00535497i
$112$	0.299160	−	2.08070i	0.0282679	−	0.196608i
$113$	−1.27426	+	0.818914i	−0.119872	+	0.0770370i	−0.599203	−	0.800597i	$-0.704516\pi$
$113$	−1.27426	+	0.818914i	−0.119872	+	0.0770370i	0.479331	+	0.877634i	$0.340879\pi$
$114$	2.36192			0.221214
$115$	−6.35531	+	4.20182i	−0.592636	+	0.391822i
$116$	2.19387			0.203696
$117$	3.38442	−	2.17504i	0.312890	−	0.201082i
$118$	0.168914	−	1.17482i	0.0155498	−	0.108151i
$119$	−2.45428	+	5.37412i	−0.224983	+	0.492645i
$120$	−3.23348	+	0.949436i	−0.295175	+	0.0866712i
$121$	−4.56772	−	10.0019i	−0.415247	−	0.909264i
$122$	−0.286600	−	0.330754i	−0.0259475	−	0.0299451i
$123$	−0.606327	−	4.21710i	−0.0546707	−	0.380243i
$124$	−13.1652	−	3.86565i	−1.18227	−	0.347146i
$125$	7.77776	−	8.97602i	0.695664	−	0.802839i
$126$	−0.486928	−	0.312930i	−0.0433790	−	0.0278780i
$127$	4.80373	+	3.08717i	0.426262	+	0.273942i	0.736133	−	0.676837i	$-0.236650\pi$
$127$	4.80373	+	3.08717i	0.426262	+	0.273942i	−0.309872	+	0.950778i	$0.600286\pi$
$128$	7.54609	−	8.70865i	0.666986	−	0.769743i
$129$	−9.90061	−	2.90708i	−0.871700	−	0.255954i
$130$	−0.526460	−	3.66161i	−0.0461736	−	0.321144i
$131$	−1.27283	−	1.46892i	−0.111207	−	0.128340i	0.697417	−	0.716666i	$-0.254333\pi$
$131$	−1.27283	−	1.46892i	−0.111207	−	0.128340i	−0.808624	+	0.588326i	$0.799787\pi$
$132$	0.0461363	+	0.101024i	0.00401565	+	0.00879305i
$133$	−3.91534	+	1.14965i	−0.339503	+	0.0996870i
$134$	−3.39047	+	7.42410i	−0.292892	+	0.641344i
$135$	0.226084	−	1.57245i	0.0194582	−	0.135335i
$136$	−10.5433	+	6.77579i	−0.904083	+	0.581019i
$137$	17.3646			1.48356			0.741781	−	0.670642i	$-0.233981\pi$
$137$	17.3646			1.48356			0.741781	+	0.670642i	$0.233981\pi$
$138$	−1.84489	−	2.07411i	−0.157047	−	0.176560i
$139$	16.3046			1.38294			0.691470	−	0.722405i	$-0.256963\pi$
$139$	16.3046			1.38294			0.691470	+	0.722405i	$0.256963\pi$
$140$	2.22512	−	1.43000i	0.188057	−	0.120857i
$141$	0.478169	−	3.32574i	0.0402691	−	0.280077i
$142$	3.89357	−	8.52573i	0.326741	−	0.715463i
$143$	−0.257485	+	0.0756044i	−0.0215320	+	0.00632236i
$144$	0.873243	+	1.91214i	0.0727702	+	0.159345i
$145$	1.37079	+	1.58198i	0.113838	+	0.131376i
$146$	0.00235842	+	0.0164032i	0.000195184	+	0.00135754i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	−0.0676254	+	0.0780439i	−0.00555878	+	0.00641517i
$149$	2.56996	+	1.65162i	0.210540	+	0.135306i	0.641661	−	0.766988i	$-0.278246\pi$
$149$	2.56996	+	1.65162i	0.210540	+	0.135306i	−0.431121	+	0.902294i	$0.641882\pi$
$150$	1.20578	+	0.774906i	0.0984512	+	0.0632708i
$151$	−11.7315	+	13.5388i	−0.954694	+	1.10178i	0.0400315	+	0.999198i	$0.487254\pi$
$151$	−11.7315	+	13.5388i	−0.954694	+	1.10178i	−0.994725	+	0.102577i	$0.967291\pi$
$152$	−8.30574	−	2.43878i	−0.673684	−	0.197812i
$153$	−0.840799	−	5.84788i	−0.0679745	−	0.472773i
$154$	0.0252836	+	0.0291789i	0.00203741	+	0.00235130i
$155$	−5.43851	−	11.9087i	−0.436831	−	0.956527i
$156$	−6.42699	+	1.88713i	−0.514571	+	0.151092i
$157$	3.35681	−	7.35038i	0.267902	−	0.586625i	−0.727094	−	0.686538i	$-0.759129\pi$
$157$	3.35681	−	7.35038i	0.267902	−	0.586625i	0.994996	+	0.0999137i	$0.0318567\pi$
$158$	0.127234	−	0.884930i	0.0101222	−	0.0704012i
$159$	−7.33196	+	4.71196i	−0.581462	+	0.373683i
$160$	8.67288			0.685652
$161$	4.06781	+	2.54025i	0.320589	+	0.200200i
$162$	0.578813			0.0454758
$163$	11.1556	−	7.16924i	0.873771	−	0.561538i	−0.0251333	−	0.999684i	$-0.508001\pi$
$163$	11.1556	−	7.16924i	0.873771	−	0.561538i	0.898904	+	0.438146i	$0.144365\pi$
$164$	−1.00952	+	7.02137i	−0.0788303	+	0.548277i
$165$	−0.0440204	+	0.0963913i	−0.00342699	+	0.00750405i
$166$	−0.216019	+	0.0634289i	−0.0167663	+	0.00492304i
$167$	−4.90732	−	10.7455i	−0.379739	−	0.831513i	−0.998929	−	0.0462718i	$-0.985266\pi$
$167$	−4.90732	−	10.7455i	−0.379739	−	0.831513i	0.619189	−	0.785242i	$-0.287461\pi$
$168$	1.38918	+	1.60320i	0.107177	+	0.123689i
$169$	−0.453286	−	3.15268i	−0.0348682	−	0.242514i
$170$	−5.21244	−	1.53051i	−0.399776	−	0.117385i
$171$	2.67225	−	3.08394i	0.204352	−	0.235834i
$172$	14.4529	+	9.28831i	1.10202	+	0.708227i
$173$	13.6560	+	8.77618i	1.03825	+	0.667241i	0.944553	−	0.328360i	$-0.106496\pi$
$173$	13.6560	+	8.77618i	1.03825	+	0.667241i	0.0936946	+	0.995601i	$0.470132\pi$
$174$	−0.499447	+	0.576393i	−0.0378630	+	0.0436962i
$175$	−2.37599	−	0.697652i	−0.179608	−	0.0527376i
$176$	−0.0199552	−	0.138791i	−0.00150418	−	0.0104618i
$177$	−1.34284	−	1.54972i	−0.100934	−	0.116484i
$178$	2.12190	+	4.64631i	0.159043	+	0.348256i
$179$	10.1367	−	2.97642i	0.757656	−	0.222468i	0.119984	−	0.992776i	$-0.461716\pi$
$179$	10.1367	−	2.97642i	0.757656	−	0.222468i	0.637672	+	0.770308i	$0.279898\pi$
$180$	−1.09878	+	2.40599i	−0.0818980	+	0.179332i
$181$	2.47541	−	17.2168i	0.183996	−	1.27972i	−0.663202	−	0.748440i	$-0.730803\pi$
$181$	2.47541	−	17.2168i	0.183996	−	1.27972i	0.847198	−	0.531277i	$-0.178288\pi$
$182$	−1.95895	+	1.25894i	−0.145207	+	0.0933187i
$183$	−0.756118			−0.0558938
$184$	4.34597	+	9.19858i	0.320389	+	0.678128i
$185$	−0.0985309			−0.00724414
$186$	4.01276	−	2.57884i	0.294230	−	0.189090i
$187$	−0.0560847	+	0.390078i	−0.00410132	+	0.0285253i
$188$	−2.32392	+	5.08867i	−0.169489	+	0.371130i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−1.55872	−	3.41311i	−0.113081	−	0.247613i
$191$	−1.63118	−	1.88249i	−0.118028	−	0.136212i	0.693660	−	0.720302i	$-0.255997\pi$
$191$	−1.63118	−	1.88249i	−0.118028	−	0.136212i	−0.811689	+	0.584090i	$0.801451\pi$
$192$	−0.148610	−	1.03360i	−0.0107250	−	0.0745939i
$193$	19.5873	+	5.75136i	1.40993	+	0.413992i	0.896081	−	0.443891i	$-0.146402\pi$
$193$	19.5873	+	5.75136i	1.40993	+	0.413992i	0.513846	+	0.857883i	$0.328220\pi$
$194$	−0.488950	+	0.564278i	−0.0351046	+	0.0405128i
$195$	−5.37655	−	3.45530i	−0.385023	−	0.247439i
$196$	−1.40067	−	0.900154i	−0.100048	−	0.0642967i
$197$	10.5694	−	12.1978i	0.753040	−	0.869055i	−0.241819	−	0.970321i	$-0.577744\pi$
$197$	10.5694	−	12.1978i	0.753040	−	0.869055i	0.994859	+	0.101267i	$0.0322895\pi$
$198$	−0.0370452	−	0.0108775i	−0.00263269	−	0.000773027i
$199$	2.63037	+	18.2946i	0.186462	+	1.29687i	0.841080	+	0.540910i	$0.181920\pi$
$199$	2.63037	+	18.2946i	0.186462	+	1.29687i	−0.654618	+	0.755959i	$0.727171\pi$
$200$	−3.44001	−	3.96999i	−0.243246	−	0.280720i
$201$	5.85763	+	12.8264i	0.413166	+	0.904706i
$202$	−0.821738	+	0.241284i	−0.0578173	+	0.0169767i
$203$	0.547375	−	1.19858i	0.0384182	−	0.0841241i
$204$	−1.39991	+	9.73658i	−0.0980133	+	0.681697i
$205$	−5.69382	+	3.65919i	−0.397673	+	0.255569i
$206$	−4.41963			−0.307930
$207$	−4.79543	+	0.0622284i	−0.333305	+	0.00432517i
$208$	8.45689			0.586380
$209$	−0.228985	+	0.147160i	−0.0158392	+	0.0101792i
$210$	−0.130860	+	0.910153i	−0.00903021	+	0.0628065i
$211$	−7.20037	+	15.7666i	−0.495694	+	1.08542i	0.482151	+	0.876088i	$0.339856\pi$
$211$	−7.20037	+	15.7666i	−0.495694	+	1.08542i	−0.977845	+	0.209330i	$0.932872\pi$
$212$	13.9233	−	4.08826i	0.956258	−	0.280783i
$213$	−6.72682	−	14.7297i	−0.460914	−	1.00926i
$214$	5.02402	+	5.79803i	0.343435	+	0.396345i
$215$	2.33287	+	16.2254i	0.159100	+	1.10657i
$216$	−2.03541	−	0.597649i	−0.138492	−	0.0406649i
$217$	−5.39668	+	6.22810i	−0.366351	+	0.422791i
$218$	4.71595	+	3.03076i	0.319404	+	0.205269i
$219$	0.0240857	+	0.0154790i	0.00162756	+	0.00104597i
$220$	0.115539	−	0.133339i	0.00778964	−	0.00898973i
$221$	−22.8056	−	6.69632i	−1.53407	−	0.450443i
$222$	−0.00510906	−	0.0355343i	−0.000342898	−	0.00238491i
$223$	18.8323	+	21.7336i	1.26110	+	1.45539i	0.834551	+	0.550931i	$0.185727\pi$
$223$	18.8323	+	21.7336i	1.26110	+	1.45539i	0.426554	+	0.904462i	$0.359727\pi$
$224$	−2.26791	−	4.96603i	−0.151531	−	0.331807i
$225$	2.37599	−	0.697652i	0.158399	−	0.0465102i
$226$	−0.364208	+	0.797505i	−0.0242268	+	0.0530492i
$227$	−3.71576	+	25.8437i	−0.246624	+	1.71531i	0.370831	+	0.928700i	$0.379073\pi$
$227$	−3.71576	+	25.8437i	−0.246624	+	1.71531i	−0.617455	+	0.786606i	$0.711836\pi$
$228$	−5.71561	+	3.67320i	−0.378525	+	0.243263i
$229$	−11.0288			−0.728801			−0.364401	−	0.931242i	$-0.618726\pi$
$229$	−11.0288			−0.728801			−0.364401	+	0.931242i	$0.618726\pi$
$230$	−1.77970	+	4.03475i	−0.117350	+	0.266044i
$231$	0.0667041			0.00438881
$232$	2.35147	−	1.51120i	0.154381	−	0.0992148i
$233$	0.0923843	−	0.642547i	0.00605230	−	0.0420946i	−0.986571	−	0.163330i	$-0.947776\pi$
$233$	0.0923843	−	0.642547i	0.00605230	−	0.0420946i	0.992624	+	0.121235i	$0.0386856\pi$
$234$	0.967337	−	2.11817i	0.0632368	−	0.138469i
$235$	−5.12144	+	1.50379i	−0.334086	+	0.0980965i
$236$	1.41830	+	3.10564i	0.0923232	+	0.202160i
$237$	−1.01149	−	1.16733i	−0.0657035	−	0.0758259i
$238$	0.486665	+	3.38483i	0.0315458	+	0.219406i
$239$	−5.34387	−	1.56910i	−0.345666	−	0.101497i	0.104291	−	0.994547i	$-0.466743\pi$
$239$	−5.34387	−	1.56910i	−0.345666	−	0.101497i	−0.449957	+	0.893050i	$0.648561\pi$
$240$	2.18686	−	2.52377i	0.141161	−	0.162909i
$241$	−14.2886	−	9.18274i	−0.920411	−	0.591512i	−0.00763420	−	0.999971i	$-0.502430\pi$
$241$	−14.2886	−	9.18274i	−0.920411	−	0.591512i	−0.912777	+	0.408459i	$0.866066\pi$
$242$	−5.35404	−	3.44083i	−0.344171	−	0.221185i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	1.20792	+	0.354678i	0.0773293	+	0.0227059i
$245$	−0.226084	−	1.57245i	−0.0144440	−	0.100460i
$246$	−1.61489	−	1.86369i	−0.102962	−	0.118824i
$247$	−6.81973	−	14.9331i	−0.433929	−	0.950172i
$248$	−16.7737	+	4.92520i	−1.06513	+	0.312751i
$249$	−0.161583	+	0.353817i	−0.0102399	+	0.0224222i
$250$	0.978349	−	6.80457i	0.0618762	−	0.430359i
$251$	−22.0526	+	14.1723i	−1.39195	+	0.894549i	−0.999680	−	0.0253022i	$-0.991945\pi$
$251$	−22.0526	+	14.1723i	−1.39195	+	0.894549i	−0.392266	+	0.919852i	$0.628309\pi$
$252$	1.66498			0.104884
$253$	0.308087	+	0.0861364i	0.0193693	+	0.00541535i
$254$	3.30513			0.207383
$255$	−7.89565	+	5.07423i	−0.494445	+	0.317761i
$256$	0.651987	−	4.53467i	0.0407492	−	0.283417i
$257$	−0.0568229	+	0.124425i	−0.00354452	+	0.00776141i	−0.911396	−	0.411531i	$-0.864994\pi$
$257$	−0.0568229	+	0.124425i	−0.00354452	+	0.00776141i	0.907851	+	0.419292i	$0.137722\pi$
$258$	−5.73060	+	1.68265i	−0.356771	+	0.104758i
$259$	0.0257653	+	0.0564181i	0.00160098	+	0.00350565i
$260$	6.96842	+	8.04198i	0.432163	+	0.498742i
$261$	0.187522	+	1.30425i	0.0116073	+	0.0807308i
$262$	−1.07944	−	0.316954i	−0.0666883	−	0.0195815i
$263$	−16.1991	+	18.6948i	−0.998882	+	1.15277i	−0.0106295	+	0.999944i	$0.503384\pi$
$263$	−16.1991	+	18.6948i	−0.998882	+	1.15277i	−0.988253	+	0.152828i	$0.951162\pi$
$264$	0.119039	+	0.0765016i	0.00732633	+	0.00470835i
$265$	11.6477	+	7.48551i	0.715512	+	0.459831i
$266$	−1.54673	+	1.78502i	−0.0948360	+	0.109447i
$267$	8.46733	+	2.48623i	0.518192	+	0.152155i
$268$	−3.34117	−	23.2383i	−0.204094	−	1.41951i
$269$	−4.05150	−	4.67568i	−0.247024	−	0.285081i	0.618674	−	0.785648i	$-0.287670\pi$
$269$	−4.05150	−	4.67568i	−0.247024	−	0.285081i	−0.865698	+	0.500567i	$0.833125\pi$
$270$	−0.381979	−	0.836418i	−0.0232465	−	0.0509027i
$271$	30.7539	−	9.03015i	1.86816	−	0.548543i	0.869673	−	0.493628i	$-0.164329\pi$
$271$	30.7539	−	9.03015i	1.86816	−	0.548543i	0.998491	−	0.0549148i	$-0.0174887\pi$
$272$	5.15913	−	11.2969i	0.312818	−	0.684977i
$273$	−0.572543	+	3.98212i	−0.0346519	+	0.241009i
$274$	8.45533	−	5.43391i	0.510805	−	0.328275i
$275$	−0.165179			−0.00996066
$276$	7.69004	+	2.15002i	0.462886	+	0.129416i
$277$	14.8240			0.890687			0.445343	−	0.895360i	$-0.353082\pi$
$277$	14.8240			0.890687			0.445343	+	0.895360i	$0.353082\pi$
$278$	7.93918	−	5.10220i	0.476161	−	0.306010i
$279$	1.17281	−	8.15708i	0.0702144	−	0.488352i
$280$	1.39994	−	3.06545i	0.0836627	−	0.183196i
$281$	−0.691551	+	0.203058i	−0.0412545	+	0.0121134i	−0.302295	−	0.953215i	$-0.597753\pi$
$281$	−0.691551	+	0.203058i	−0.0412545	+	0.0121134i	0.261040	+	0.965328i	$0.415934\pi$
$282$	−0.807888	−	1.76903i	−0.0481090	−	0.105344i
$283$	3.08760	+	3.56328i	0.183539	+	0.211815i	0.840061	−	0.542491i	$-0.182519\pi$
$283$	3.08760	+	3.56328i	0.183539	+	0.211815i	−0.656523	+	0.754306i	$0.727973\pi$
$284$	3.83695	+	26.6866i	0.227681	+	1.58356i
$285$	−6.21998	−	1.82635i	−0.368440	−	0.108184i
$286$	−0.101718	+	0.117389i	−0.00601470	+	0.00694133i
$287$	3.58413	+	2.30338i	0.211565	+	0.135964i
$288$	4.59273	+	2.95157i	0.270629	+	0.173923i
$289$	−11.7251	+	13.5314i	−0.689710	+	0.795967i
$290$	1.16252	+	0.341348i	0.0682658	+	0.0200446i
$291$	0.183581	+	1.27683i	0.0107617	+	0.0748493i
$292$	−0.0312169	−	0.0360262i	−0.00182683	−	0.00210827i
$293$	−6.99926	−	15.3262i	−0.408901	−	0.895369i	−0.996290	−	0.0860637i	$-0.972571\pi$
$293$	−6.99926	−	15.3262i	−0.408901	−	0.895369i	0.587388	−	0.809305i	$-0.300156\pi$
$294$	0.555367	−	0.163070i	0.0323896	−	0.00951045i
$295$	−1.35325	+	2.96321i	−0.0787893	+	0.172525i
$296$	−0.0187246	+	0.130232i	−0.00108834	+	0.00756960i
$297$	−0.0561151	+	0.0360630i	−0.00325613	+	0.00209259i
$298$	1.76823			0.102431
$299$	−7.78660	+	17.6529i	−0.450311	+	1.02090i
$300$	−4.12297			−0.238040
$301$	8.68054	−	5.57865i	0.500338	−	0.321548i
$302$	−1.47568	+	10.2636i	−0.0849157	+	0.590602i
$303$	−0.614661	+	1.34592i	−0.0353114	+	0.0773211i
$304$	8.23042	−	2.41667i	0.472047	−	0.138606i
$305$	0.498989	+	1.09263i	0.0285720	+	0.0625640i
$306$	−2.23938	−	2.58439i	−0.128017	−	0.147740i
$307$	4.86564	+	33.8413i	0.277697	+	1.93143i	0.355979	+	0.934494i	$0.384147\pi$
$307$	4.86564	+	33.8413i	0.277697	+	1.93143i	−0.0782821	+	0.996931i	$0.524943\pi$
$308$	−0.106562	−	0.0312894i	−0.00607193	−	0.00178288i
$309$	−5.00031	+	5.77067i	−0.284458	+	0.328282i
$310$	−6.37474	−	4.09679i	−0.362061	−	0.232682i
$311$	−24.5173	−	15.7563i	−1.39025	−	0.893458i	−0.390615	−	0.920554i	$-0.627737\pi$
$311$	−24.5173	−	15.7563i	−1.39025	−	0.893458i	−0.999633	+	0.0270966i	$0.991374\pi$
$312$	−5.58876	+	6.44978i	−0.316401	+	0.365147i
$313$	3.75660	+	1.10304i	0.212336	+	0.0623474i	0.386170	−	0.922427i	$-0.373798\pi$
$313$	3.75660	+	1.10304i	0.212336	+	0.0623474i	−0.173835	+	0.984775i	$0.555616\pi$
$314$	−0.665629	−	4.62955i	−0.0375636	−	0.261261i
$315$	1.04032	+	1.20060i	0.0586156	+	0.0676460i
$316$	1.06833	+	2.33931i	0.0600981	+	0.131596i
$317$	32.4675	−	9.53333i	1.82356	−	0.535445i	0.824042	−	0.566528i	$-0.191714\pi$
$317$	32.4675	−	9.53333i	1.82356	−	0.535445i	0.999517	+	0.0310830i	$0.00989562\pi$
$318$	−2.09562	+	4.58878i	−0.117517	+	0.257326i
$319$	0.0125085	−	0.0869986i	0.000700342	−	0.00487099i
$320$	−1.39554	+	0.896862i	−0.0780133	+	0.0501361i
$321$	13.2545			0.739796
$322$	2.77565	−	0.0360186i	0.154681	−	0.00200724i
$323$	−24.1084			−1.34143
$324$	−1.40067	+	0.900154i	−0.0778148	+	0.0500086i
$325$	1.41778	−	9.86090i	0.0786445	−	0.546984i
$326$	3.18849	−	6.98181i	0.176594	−	0.386687i
$327$	9.29279	−	2.72861i	0.513892	−	0.150892i
$328$	3.75447	+	8.22114i	0.207306	+	0.453936i
$329$	2.20029	+	2.53927i	0.121306	+	0.139994i
$330$	0.00872891	+	0.0607109i	0.000480511	+	0.00334203i
$331$	−2.39862	−	0.704297i	−0.131840	−	0.0387117i	0.215147	−	0.976582i	$-0.430977\pi$
$331$	−2.39862	−	0.704297i	−0.131840	−	0.0387117i	−0.346987	+	0.937870i	$0.612795\pi$
$332$	0.424101	−	0.489439i	0.0232756	−	0.0268614i
$333$	−0.0521771	−	0.0335322i	−0.00285929	−	0.00183755i
$334$	−5.75210	−	3.69665i	−0.314741	−	0.202272i
$335$	14.6693	−	16.9292i	0.801468	−	0.924943i
$336$	−2.01695	−	0.592229i	−0.110034	−	0.0323088i
$337$	−0.668808	−	4.65166i	−0.0364323	−	0.253392i	0.963463	−	0.267840i	$-0.0863099\pi$
$337$	−0.668808	−	4.65166i	−0.0364323	−	0.253392i	−0.999896	+	0.0144482i	$0.995401\pi$
$338$	−1.20728	−	1.39328i	−0.0656676	−	0.0757844i
$339$	0.629233	+	1.37783i	0.0341753	+	0.0748334i
$340$	14.9938	−	4.40257i	0.813152	−	0.238763i
$341$	−0.228356	+	0.500030i	−0.0123662	+	0.0270782i
$342$	0.336136	−	2.33788i	0.0181762	−	0.126418i
$343$	−0.841254	+	0.540641i	−0.0454234	+	0.0291919i
$344$	21.8892			1.18018
$345$	3.25460	+	6.88860i	0.175222	+	0.370870i
$346$	9.39582			0.505123
$347$	−3.53575	+	2.27229i	−0.189809	+	0.121983i	−0.632094	−	0.774892i	$-0.717804\pi$
$347$	−3.53575	+	2.27229i	−0.189809	+	0.121983i	0.442285	+	0.896875i	$0.354168\pi$
$348$	0.312220	−	2.17154i	0.0167368	−	0.116407i
$349$	−4.96545	+	10.8728i	−0.265795	+	0.582009i	−0.994725	−	0.102579i	$-0.967291\pi$
$349$	−4.96545	+	10.8728i	−0.265795	+	0.582009i	0.728930	+	0.684588i	$0.240018\pi$
$350$	−1.37525	+	0.403810i	−0.0735102	+	0.0215845i
$351$	−1.67124	−	3.65951i	−0.0892044	−	0.195330i
$352$	−0.238476	−	0.275216i	−0.0127108	−	0.0146691i
$353$	0.0339852	+	0.236372i	0.00180885	+	0.0125808i	0.990706	−	0.136022i	$-0.0434316\pi$
$353$	0.0339852	+	0.236372i	0.00180885	+	0.0125808i	−0.988897	+	0.148602i	$0.952523\pi$
$354$	−1.13882	−	0.334389i	−0.0605278	−	0.0177726i
$355$	−16.8460	+	19.4413i	−0.894092	+	1.03184i
$356$	−12.3606	−	7.94367i	−0.655110	−	0.421014i
$357$	4.97014	+	3.19412i	0.263048	+	0.169051i
$358$	4.00446	−	4.62139i	0.211642	−	0.244248i
$359$	−1.94039	−	0.569751i	−0.102410	−	0.0300703i	0.230126	−	0.973161i	$-0.426086\pi$
$359$	−1.94039	−	0.569751i	−0.102410	−	0.0300703i	−0.332536	+	0.943091i	$0.607904\pi$
$360$	0.479599	+	3.33569i	0.0252771	+	0.175806i
$361$	1.53790	+	1.77484i	0.0809423	+	0.0934124i
$362$	−4.18231	−	9.15799i	−0.219818	−	0.481333i
$363$	−10.5502	+	3.09780i	−0.553739	+	0.162593i
$364$	2.78258	−	6.09300i	0.145847	−	0.319360i
$365$	0.00647295	−	0.0450204i	0.000338810	−	0.00235647i
$366$	−0.368175	+	0.236612i	−0.0192448	+	0.0123679i
$367$	8.92363			0.465810			0.232905	−	0.972500i	$-0.425177\pi$
$367$	8.92363			0.465810			0.232905	+	0.972500i	$0.425177\pi$
$368$	−8.55094	−	5.33986i	−0.445749	−	0.278360i
$369$	−4.26047			−0.221791
$370$	−0.0479775	+	0.0308332i	−0.00249423	+	0.00160294i
$371$	1.24035	−	8.62681i	0.0643956	−	0.447881i
$372$	−5.69991	+	12.4811i	−0.295527	+	0.647113i
$373$	30.0910	−	8.83550i	1.55805	−	0.457485i	0.614556	−	0.788873i	$-0.289335\pi$
$373$	30.0910	−	8.83550i	1.55805	−	0.457485i	0.943495	+	0.331388i	$0.107517\pi$
$374$	0.0947577	+	0.207490i	0.00489980	+	0.0107291i
$375$	−7.77776	−	8.97602i	−0.401642	−	0.463520i
$376$	1.01436	+	7.05500i	0.0523114	+	0.363834i
$377$	5.08630	+	1.49347i	0.261958	+	0.0769178i
$378$	−0.379042	+	0.437437i	−0.0194958	+	0.0224993i
$379$	−11.4184	−	7.33813i	−0.586521	−	0.376934i	0.213467	−	0.976950i	$-0.431525\pi$
$379$	−11.4184	−	7.33813i	−0.586521	−	0.376934i	−0.799988	+	0.600016i	$0.795161\pi$
$380$	9.07991	+	5.83531i	0.465790	+	0.299345i
$381$	3.73939	−	4.31548i	0.191575	−	0.221089i
$382$	−1.38336	−	0.406190i	−0.0707786	−	0.0207825i
$383$	−3.29539	−	22.9200i	−0.168387	−	1.17115i	−0.882219	−	0.470839i	$-0.843951\pi$
$383$	−3.29539	−	22.9200i	−0.168387	−	1.17115i	0.713833	−	0.700316i	$-0.246958\pi$
$384$	−7.54609	−	8.70865i	−0.385085	−	0.444411i
$385$	−0.0440204	−	0.0963913i	−0.00224349	−	0.00491255i
$386$	11.3374	−	3.32896i	0.577058	−	0.169440i
$387$	−4.28649	+	9.38611i	−0.217895	+	0.477123i
$388$	0.305658	−	2.12590i	0.0155174	−	0.107926i
$389$	−7.25333	+	4.66143i	−0.367758	+	0.236344i	−0.711447	−	0.702740i	$-0.751960\pi$
$389$	−7.25333	+	4.66143i	−0.367758	+	0.236344i	0.343689	+	0.939084i	$0.388323\pi$
$390$	−3.69926			−0.187319
$391$	18.8310	+	21.1707i	0.952325	+	1.07065i
$392$	−2.12133			−0.107144
$393$	−1.63511	+	1.05082i	−0.0824805	+	0.0530070i
$394$	1.32951	−	9.24692i	0.0669796	−	0.465853i
$395$	−1.01933	+	2.23203i	−0.0512881	+	0.112305i
$396$	0.106562	−	0.0312894i	0.00535494	−	0.00157235i
$397$	−9.15674	−	20.0505i	−0.459564	−	1.00630i	−0.987587	−	0.157074i	$-0.949794\pi$
$397$	−9.15674	−	20.0505i	−0.459564	−	1.00630i	0.528023	−	0.849230i	$-0.322933\pi$
$398$	7.00572	+	8.08504i	0.351165	+	0.405266i
$399$	0.580734	+	4.03910i	0.0290731	+	0.202208i
$400$	4.99455	+	1.46653i	0.249728	+	0.0733267i
$401$	−16.8690	+	19.4679i	−0.842399	+	0.972180i	−0.999882	−	0.0153416i	$-0.995116\pi$
$401$	−16.8690	+	19.4679i	−0.842399	+	0.972180i	0.157483	+	0.987522i	$0.449662\pi$
$402$	6.86602	+	4.41252i	0.342446	+	0.220077i
$403$	−27.8909	−	17.9244i	−1.38934	−	0.892878i
$404$	1.61328	−	1.86183i	0.0802638	−	0.0926294i
$405$	−1.52427	−	0.447565i	−0.0757415	−	0.0222397i
$406$	−0.108540	−	0.754914i	−0.00538676	−	0.0374658i
$407$	0.00270928	+	0.00312668i	0.000134294	+	0.000154984i
$408$	5.20635	+	11.4003i	0.257753	+	0.564399i
$409$	6.99848	−	2.05494i	0.346053	−	0.101610i	−0.104087	−	0.994568i	$-0.533192\pi$
$409$	6.99848	−	2.05494i	0.346053	−	0.101610i	0.450140	+	0.892958i	$0.351374\pi$
$410$	−1.62741	+	3.56353i	−0.0803720	+	0.175990i
$411$	2.47125	−	17.1879i	0.121898	−	0.847817i
$412$	10.6951	−	6.87330i	0.526908	−	0.338623i
$413$	2.05058			0.100902
$414$	−2.31556	+	1.53093i	−0.113803	+	0.0752412i
$415$	0.617920			0.0303325
$416$	18.4769	−	11.8744i	0.905903	−	0.582189i
$417$	2.32039	−	16.1387i	0.113630	−	0.790314i
$418$	−0.0654486	+	0.143312i	−0.00320119	+	0.00700964i
$419$	−15.5644	+	4.57012i	−0.760371	+	0.223265i	−0.638858	−	0.769325i	$-0.720593\pi$
$419$	−15.5644	+	4.57012i	−0.760371	+	0.223265i	−0.121513	+	0.992590i	$0.538775\pi$
$420$	−1.09878	−	2.40599i	−0.0536148	−	0.117400i
$421$	−16.9309	−	19.5394i	−0.825164	−	0.952290i	0.174311	−	0.984691i	$-0.444230\pi$
$421$	−16.9309	−	19.5394i	−0.825164	−	0.952290i	−0.999475	+	0.0324008i	$0.989685\pi$
$422$	1.42778	+	9.93041i	0.0695031	+	0.483405i
$423$	−3.22383	−	0.946603i	−0.156748	−	0.0460254i
$424$	12.1074	−	13.9727i	0.587988	−	0.678574i
$425$	−12.3075	−	7.90957i	−0.597003	−	0.383670i
$426$	−7.88484	−	5.06728i	−0.382022	−	0.245510i
$427$	0.495152	−	0.571436i	0.0239621	−	0.0276537i
$428$	−21.1746	−	6.21741i	−1.02351	−	0.300530i
$429$	0.0381909	+	0.265624i	0.00184388	+	0.0128244i
$430$	6.21336	+	7.17060i	0.299635	+	0.345797i
$431$	−6.95286	−	15.2246i	−0.334908	−	0.733346i	0.665001	−	0.746842i	$-0.268431\pi$
$431$	−6.95286	−	15.2246i	−0.334908	−	0.733346i	−0.999909	+	0.0134967i	$0.995704\pi$
$432$	2.01695	−	0.592229i	0.0970404	−	0.0284936i
$433$	4.49466	−	9.84193i	0.216000	−	0.472973i	−0.770353	−	0.637617i	$-0.779920\pi$
$433$	4.49466	−	9.84193i	0.216000	−	0.472973i	0.986353	+	0.164644i	$0.0526475\pi$
$434$	−0.678838	+	4.72142i	−0.0325853	+	0.226635i
$435$	1.76096	−	1.13170i	0.0844315	−	0.0542608i
$436$	−16.1255			−0.772270
$437$	−2.53352	+	19.4053i	−0.121195	+	0.928283i
$438$	0.0165718			0.000791833
$439$	−15.6652	+	10.0674i	−0.747662	+	0.480493i	−0.858159	−	0.513383i	$-0.828392\pi$
$439$	−15.6652	+	10.0674i	−0.747662	+	0.480493i	0.110498	+	0.993876i	$0.464755\pi$
$440$	0.0319913	−	0.222504i	0.00152512	−	0.0106075i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−13.2002	+	3.87592i	−0.627867	+	0.184359i
$443$	−1.72698	−	3.78156i	−0.0820513	−	0.179667i	0.864160	−	0.503218i	$-0.167851\pi$
$443$	−1.72698	−	3.78156i	−0.0820513	−	0.179667i	−0.946211	+	0.323551i	$0.895123\pi$
$444$	0.0676254	+	0.0780439i	0.00320936	+	0.00370380i
$445$	−1.99514	−	13.8765i	−0.0945789	−	0.657810i
$446$	15.9711	+	4.68953i	0.756253	+	0.222056i
$447$	2.00055	−	2.30876i	0.0946227	−	0.109200i
$448$	0.878464	+	0.564555i	0.0415035	+	0.0266727i
$449$	5.87869	+	3.77801i	0.277433	+	0.178295i	0.671957	−	0.740590i	$-0.265454\pi$
$449$	5.87869	+	3.77801i	0.277433	+	0.178295i	−0.394524	+	0.918886i	$0.629090\pi$
$450$	0.938618	−	1.08322i	0.0442469	−	0.0510636i
$451$	0.272679	+	0.0800657i	0.0128399	+	0.00377015i
$452$	−0.358912	−	2.49629i	−0.0168818	−	0.117415i
$453$	11.7315	+	13.5388i	0.551193	+	0.636110i
$454$	6.27795	+	13.7468i	0.294639	+	0.645169i
$455$	6.13224	−	1.80059i	0.287484	−	0.0844128i
$456$	−3.59599	+	7.87412i	−0.168398	+	0.368740i
$457$	−1.19204	+	8.29084i	−0.0557614	+	0.387829i	0.942760	+	0.333472i	$0.108220\pi$
$457$	−1.19204	+	8.29084i	−0.0557614	+	0.387829i	−0.998522	+	0.0543575i	$0.982689\pi$
$458$	−5.37021	+	3.45123i	−0.250934	+	0.161265i
$459$	−5.90802			−0.275763
$460$	−1.96804	−	12.5314i	−0.0917601	−	0.584281i
$461$	−16.5576			−0.771164			−0.385582	−	0.922674i	$-0.625999\pi$
$461$	−16.5576			−0.771164			−0.385582	+	0.922674i	$0.625999\pi$
$462$	0.0324801	−	0.0208737i	0.00151111	−	0.000971132i
$463$	3.95401	−	27.5007i	0.183758	−	1.27807i	−0.664019	−	0.747715i	$-0.731151\pi$
$463$	3.95401	−	27.5007i	0.183758	−	1.27807i	0.847778	−	0.530352i	$-0.177940\pi$
$464$	−1.15064	+	2.51954i	−0.0534169	+	0.116967i
$465$	−12.5614	+	3.68837i	−0.582523	+	0.171044i
$466$	−0.156087	−	0.341784i	−0.00723061	−	0.0158328i
$467$	5.80748	+	6.70218i	0.268738	+	0.310140i	0.874038	−	0.485857i	$-0.161492\pi$
$467$	5.80748	+	6.70218i	0.268738	+	0.310140i	−0.605300	+	0.795997i	$0.706947\pi$
$468$	0.953270	+	6.63014i	0.0440649	+	0.306478i
$469$	−13.5295	−	3.97262i	−0.624734	−	0.183439i
$470$	−2.02319	+	2.33489i	−0.0933229	+	0.107700i
$471$	−6.79784	−	4.36871i	−0.313228	−	0.201300i
$472$	3.65942	+	2.35177i	0.168439	+	0.108249i
$473$	0.450735	−	0.520176i	0.0207248	−	0.0239177i
$474$	−0.857815	−	0.251877i	−0.0394007	−	0.0115691i
$475$	−1.43807	−	10.0020i	−0.0659831	−	0.458923i
$476$	−6.44167	−	7.43409i	−0.295254	−	0.340741i
$477$	3.62056	+	7.92791i	0.165774	+	0.362994i
$478$	−3.09310	+	0.908216i	−0.141475	+	0.0415408i
$479$	17.1011	−	37.4461i	0.781367	−	1.71096i	0.0815100	−	0.996673i	$-0.474026\pi$
$479$	17.1011	−	37.4461i	0.781367	−	1.71096i	0.699857	−	0.714283i	$-0.253247\pi$
$480$	1.23428	−	8.58461i	0.0563369	−	0.391832i
$481$	−0.209912	+	0.134902i	−0.00957117	+	0.00615102i
$482$	−9.83108			−0.447794
$483$	3.09331	−	3.66489i	0.140750	−	0.166758i
$484$	18.3073			0.832151
$485$	1.72395	−	1.10791i	0.0782804	−	0.0503078i
$486$	0.0823736	−	0.572921i	0.00373654	−	0.0259882i
$487$	−11.6906	+	25.5989i	−0.529752	+	1.16000i	0.435862	+	0.900014i	$0.356444\pi$
$487$	−11.6906	+	25.5989i	−0.529752	+	1.16000i	−0.965614	+	0.259982i	$0.916284\pi$
$488$	1.53901	−	0.451893i	0.0696675	−	0.0204562i
$489$	−5.50867	−	12.0623i	−0.249111	−	0.545476i
$490$	−0.602152	−	0.694921i	−0.0272025	−	0.0313933i
$491$	−5.64136	−	39.2365i	−0.254591	−	1.77072i	−0.569885	−	0.821725i	$-0.693012\pi$
$491$	−5.64136	−	39.2365i	−0.254591	−	1.77072i	0.315294	−	0.948994i	$-0.397897\pi$
$492$	6.80623	+	1.99849i	0.306849	+	0.0900989i
$493$	5.09793	−	5.88332i	0.229599	−	0.264971i
$494$	−7.99374	−	5.13726i	−0.359655	−	0.231136i
$495$	0.0891454	+	0.0572903i	0.00400679	+	0.00257501i
$496$	11.3444	−	13.0921i	0.509377	−	0.587852i
$497$	15.5371	+	4.56210i	0.696934	+	0.204638i
$498$	0.0320406	+	0.222847i	0.00143577	+	0.00998603i
$499$	−4.45845	−	5.14533i	−0.199588	−	0.230337i	0.647129	−	0.762381i	$-0.275970\pi$
$499$	−4.45845	−	5.14533i	−0.199588	−	0.230337i	−0.846717	+	0.532044i	$0.821424\pi$
$500$	8.21478	+	17.9879i	0.367376	+	0.804442i
$501$	−11.3345	+	3.32812i	−0.506390	+	0.148689i
$502$	−6.30308	+	13.8018i	−0.281320	+	0.616005i
$503$	1.90284	−	13.2345i	0.0848434	−	0.590099i	−0.902402	−	0.430894i	$-0.858198\pi$
$503$	1.90284	−	13.2345i	0.0848434	−	0.590099i	0.987246	−	0.159204i	$-0.0508928\pi$
$504$	1.78458	−	1.14688i	0.0794915	−	0.0510861i
$505$	2.35057			0.104599
$506$	0.176971	−	0.0544673i	0.00786731	−	0.00242137i
$507$	−3.18510			−0.141455
$508$	−7.99809	+	5.14006i	−0.354858	+	0.228053i
$509$	3.79867	−	26.4204i	0.168373	−	1.17106i	−0.713874	−	0.700274i	$-0.753061\pi$
$509$	3.79867	−	26.4204i	0.168373	−	1.17106i	0.882247	−	0.470787i	$-0.156030\pi$
$510$	−2.25674	+	4.94157i	−0.0999301	+	0.218816i
$511$	−0.0274710	+	0.00806621i	−0.00121525	+	0.000356828i
$512$	8.47225	+	18.5516i	0.374424	+	0.819875i
$513$	−2.67225	−	3.08394i	−0.117983	−	0.136159i
$514$	0.0112676	+	0.0783676i	0.000496990	+	0.00345664i
$515$	11.6388	+	3.41747i	0.512869	+	0.150592i
$516$	11.2506	−	12.9839i	0.495282	−	0.571585i
$517$	0.188543	+	0.121169i	0.00829211	+	0.00532902i
$518$	0.0302008	+	0.0194088i	0.00132695	+	0.000852776i
$519$	10.6303	−	12.2680i	0.466619	−	0.538507i
$520$	13.0085	+	3.81965i	0.570461	+	0.167503i
$521$	−2.92397	−	20.3367i	−0.128102	−	0.890966i	−0.947958	−	0.318396i	$-0.896856\pi$
$521$	−2.92397	−	20.3367i	−0.128102	−	0.890966i	0.819856	−	0.572570i	$-0.194053\pi$
$522$	0.499447	+	0.576393i	0.0218602	+	0.0252280i
$523$	11.0213	+	24.1332i	0.481927	+	1.05527i	0.981929	+	0.189248i	$0.0606051\pi$
$523$	11.0213	+	24.1332i	0.481927	+	1.05527i	−0.500002	+	0.866024i	$0.666668\pi$
$524$	3.10506	−	0.911729i	0.135645	−	0.0398291i
$525$	−1.02869	+	2.25252i	−0.0448957	+	0.0983078i
$526$	−2.03766	+	14.1722i	−0.0888461	+	0.617938i
$527$	−40.9587	+	26.3226i	−1.78419	+	1.14663i
$528$	−0.140219			−0.00610223
$529$	19.0196	−	12.9326i	0.826941	−	0.562288i
$530$	8.01402			0.348107
$531$	−1.72506	+	1.10863i	−0.0748611	+	0.0481103i
$532$	0.966909	−	6.72500i	0.0419208	−	0.291566i
$533$	−7.12028	+	15.5912i	−0.308413	+	0.675331i
$534$	4.90099	−	1.43906i	0.212087	−	0.0622743i
$535$	−8.74714	−	19.1536i	−0.378172	−	0.828081i
$536$	−19.5884	−	22.6062i	−0.846088	−	0.976438i
$537$	−1.50351	−	10.4572i	−0.0648813	−	0.451260i
$538$	−3.43595	−	1.00889i	−0.148134	−	0.0434961i
$539$	−0.0436819	+	0.0504116i	−0.00188151	+	0.00217138i
$540$	2.22512	+	1.43000i	0.0957541	+	0.0615374i
$541$	−21.3077	−	13.6936i	−0.916091	−	0.588736i	−0.00456983	−	0.999990i	$-0.501455\pi$
$541$	−21.3077	−	13.6936i	−0.916091	−	0.588736i	−0.911521	+	0.411254i	$0.865091\pi$
$542$	12.1491	−	14.0208i	0.521849	−	0.602246i
$543$	−16.6893	−	4.90042i	−0.716207	−	0.210297i
$544$	−4.59025	−	31.9259i	−0.196805	−	1.36881i
$545$	−10.0756	−	11.6279i	−0.431593	−	0.498085i
$546$	0.967337	+	2.11817i	0.0413982	+	0.0906494i
$547$	−32.0821	+	9.42017i	−1.37173	+	0.402777i	−0.882884	−	0.469591i	$-0.844401\pi$
$547$	−32.0821	+	9.42017i	−1.37173	+	0.402777i	−0.488849	+	0.872368i	$0.662583\pi$
$548$	−12.0104	+	26.2990i	−0.513057	+	1.12344i
$549$	−0.107607	+	0.748421i	−0.00459254	+	0.0319418i
$550$	−0.0804302	+	0.0516894i	−0.00342956	+	0.00220404i
$551$	5.37688			0.229063
$552$	9.72345	−	2.99264i	0.413857	−	0.127375i
$553$	1.54459			0.0656828
$554$	7.21821	−	4.63886i	0.306673	−	0.197086i
$555$	−0.0140224	+	0.0975280i	−0.000595218	+	0.00413983i
$556$	−11.2772	+	24.6936i	−0.478260	+	1.04724i
$557$	39.8147	−	11.6906i	1.68700	−	0.495348i	0.709222	−	0.704985i	$-0.249046\pi$
$557$	39.8147	−	11.6906i	1.68700	−	0.495348i	0.977779	+	0.209637i	$0.0672282\pi$
$558$	−1.98152	−	4.33892i	−0.0838844	−	0.183681i
$559$	27.1848	+	31.3730i	1.14980	+	1.32694i
$560$	0.475250	+	3.30544i	0.0200830	+	0.139680i
$561$	0.378126	+	0.111028i	0.0159645	+	0.00468759i
$562$	−0.273193	+	0.315281i	−0.0115239	+	0.0132993i
$563$	−17.3549	−	11.1533i	−0.731420	−	0.470055i	0.121172	−	0.992631i	$-0.461335\pi$
$563$	−17.3549	−	11.1533i	−0.731420	−	0.470055i	−0.852593	+	0.522576i	$0.824971\pi$
$564$	4.70615	+	3.02446i	0.198165	+	0.127353i
$565$	1.57579	−	1.81856i	0.0662939	−	0.0765073i
$566$	2.61849	+	0.768858i	0.110063	+	0.0323175i
$567$	0.142315	+	0.989821i	0.00597666	+	0.0415686i
$568$	22.4950	+	25.9606i	0.943869	+	1.08928i
$569$	1.96094	+	4.29387i	0.0822070	+	0.180008i	0.946272	−	0.323372i	$-0.104817\pi$
$569$	1.96094	+	4.29387i	0.0822070	+	0.180008i	−0.864065	+	0.503381i	$0.832089\pi$
$570$	−3.60020	+	1.05711i	−0.150796	+	0.0442776i
$571$	−15.2297	+	33.3484i	−0.637343	+	1.39559i	0.264865	+	0.964285i	$0.414672\pi$
$571$	−15.2297	+	33.3484i	−0.637343	+	1.39559i	−0.902208	+	0.431301i	$0.858055\pi$
$572$	0.0635870	−	0.442257i	0.00265871	−	0.0184917i
$573$	−2.09547	+	1.34668i	−0.0875394	+	0.0562582i
$574$	2.46601			0.102929
$575$	−7.65994	+	9.07535i	−0.319441	+	0.378468i
$576$	−1.04423			−0.0435097
$577$	21.1816	−	13.6126i	0.881800	−	0.566698i	−0.0195410	−	0.999809i	$-0.506220\pi$
$577$	21.1816	−	13.6126i	0.881800	−	0.566698i	0.901341	+	0.433111i	$0.142584\pi$
$578$	−1.47487	+	10.2580i	−0.0613466	+	0.426675i
$579$	8.48039	−	18.5695i	0.352433	−	0.771720i
$580$	−3.34404	+	0.981900i	−0.138854	+	0.0407712i
$581$	−0.161583	−	0.353817i	−0.00670358	−	0.0146788i
$582$	0.488950	+	0.564278i	0.0202676	+	0.0233901i
$583$	−0.0827363	−	0.575443i	−0.00342659	−	0.0238324i
$584$	−0.0582752	−	0.0171111i	−0.00241144	−	0.000708064i
$585$	−4.18529	+	4.83009i	−0.173041	+	0.199700i
$586$	−8.20418	−	5.27250i	−0.338911	−	0.217805i
$587$	−2.27673	−	1.46316i	−0.0939706	−	0.0603913i	0.492812	−	0.870136i	$-0.335969\pi$
$587$	−2.27673	−	1.46316i	−0.0939706	−	0.0603913i	−0.586782	+	0.809745i	$0.699606\pi$
$588$	−1.09033	+	1.25830i	−0.0449643	+	0.0518916i
$589$	−32.2662	−	9.47420i	−1.32950	−	0.390378i
$590$	0.268339	+	1.86634i	0.0110474	+	0.0768360i
$591$	−10.5694	−	12.1978i	−0.434768	−	0.501749i
$592$	−0.0541612	−	0.118596i	−0.00222601	−	0.00487428i
$593$	31.6719	−	9.29972i	1.30061	−	0.381894i	0.443152	−	0.896446i	$-0.353860\pi$
$593$	31.6719	−	9.29972i	1.30061	−	0.381894i	0.857459	+	0.514553i	$0.172042\pi$
$594$	−0.0160388	+	0.0351201i	−0.000658081	+	0.00144100i
$595$	1.33571	−	9.29005i	0.0547587	−	0.380855i
$596$	−4.27893	+	2.74990i	−0.175272	+	0.112640i
$597$	18.4827			0.756448
$598$	1.73261	+	11.0324i	0.0708517	+	0.451147i
$599$	16.8054			0.686649			0.343325	−	0.939217i	$-0.388447\pi$
$599$	16.8054			0.686649			0.343325	+	0.939217i	$0.388447\pi$
$600$	−4.41914	+	2.84001i	−0.180411	+	0.115943i
$601$	−4.09919	+	28.5105i	−0.167210	+	1.16297i	0.717409	+	0.696652i	$0.245328\pi$
$601$	−4.09919	+	28.5105i	−0.167210	+	1.16297i	−0.884618	+	0.466316i	$0.845581\pi$
$602$	2.48108	−	5.43280i	0.101121	−	0.221424i
$603$	13.5295	−	3.97262i	0.550964	−	0.161778i
$604$	−12.3906	−	27.1317i	−0.504168	−	1.10397i
$605$	11.4389	+	13.2012i	0.465059	+	0.536706i
$606$	0.121883	+	0.847712i	0.00495114	+	0.0344360i
$607$	19.1034	+	5.60927i	0.775384	+	0.227673i	0.645402	−	0.763843i	$-0.276690\pi$
$607$	19.1034	+	5.60927i	0.775384	+	0.227673i	0.129982	+	0.991516i	$0.458508\pi$
$608$	14.5888	−	16.8364i	0.591655	−	0.682806i
$609$	−1.10848	−	0.712380i	−0.0449181	−	0.0288671i
$610$	0.584889	+	0.375885i	0.0236815	+	0.0152192i
$611$	−8.85192	+	10.2157i	−0.358110	+	0.413281i
$612$	9.43825	+	2.77132i	0.381519	+	0.112024i
$613$	−2.69759	−	18.7622i	−0.108955	−	0.757797i	−0.968907	−	0.247423i	$-0.920416\pi$
$613$	−2.69759	−	18.7622i	−0.108955	−	0.757797i	0.859953	−	0.510374i	$-0.170493\pi$
$614$	12.9592	+	14.9557i	0.522989	+	0.603562i
$615$	2.81163	+	6.15662i	0.113376	+	0.248259i
$616$	−0.135770	+	0.0398656i	−0.00547032	+	0.00160623i
$617$	−9.33660	+	20.4443i	−0.375877	+	0.823056i	0.623280	+	0.781999i	$0.285800\pi$
$617$	−9.33660	+	20.4443i	−0.375877	+	0.823056i	−0.999157	+	0.0410572i	$0.986927\pi$
$618$	−0.628979	+	4.37465i	−0.0253013	+	0.175974i
$619$	29.3283	−	18.8482i	1.17880	−	0.757572i	0.203638	−	0.979046i	$-0.434723\pi$
$619$	29.3283	−	18.8482i	1.17880	−	0.757572i	0.975166	+	0.221474i	$0.0710869\pi$
$620$	21.7974			0.875406
$621$	−0.620866	+	4.75547i	−0.0249145	+	0.190831i
$622$	−16.8688			−0.676376
$623$	−7.42389	+	4.77104i	−0.297432	+	0.191148i
$624$	1.20354	−	8.37081i	0.0481802	−	0.335100i
$625$	−2.69459	+	5.90034i	−0.107784	+	0.236013i
$626$	2.17437	−	0.638452i	0.0869052	−	0.0255177i
$627$	0.113074	+	0.247597i	0.00451573	+	0.00988808i
$628$	8.81051	+	10.1679i	0.351578	+	0.405742i
$629$	0.0521489	+	0.362703i	0.00207931	+	0.0144619i
$630$	0.882265	+	0.259056i	0.0351503	+	0.0103211i
$631$	−11.4376	+	13.1997i	−0.455323	+	0.525471i	−0.936271	−	0.351278i	$-0.885747\pi$
$631$	−11.4376	+	13.1997i	−0.455323	+	0.525471i	0.480948	+	0.876749i	$0.340293\pi$
$632$	2.75645	+	1.77146i	0.109646	+	0.0704650i
$633$	14.5814	+	9.37090i	0.579559	+	0.372460i
$634$	12.8261	−	14.8021i	0.509389	−	0.587867i
$635$	−8.70387	−	2.55569i	−0.345403	−	0.101419i
$636$	−2.06515	−	14.3634i	−0.0818885	−	0.569547i
$637$	−2.63455	−	3.04043i	−0.104385	−	0.120466i
$638$	−0.0211337	−	0.0462763i	−0.000836691	−	0.00183210i
$639$	−15.5371	+	4.56210i	−0.614638	+	0.180474i
$640$	−7.60457	+	16.6517i	−0.300597	+	0.658215i
$641$	−4.12078	+	28.6607i	−0.162761	+	1.13203i	0.730638	+	0.682765i	$0.239223\pi$
$641$	−4.12078	+	28.6607i	−0.162761	+	1.13203i	−0.893399	+	0.449264i	$0.851686\pi$
$642$	6.45401	−	4.14774i	0.254719	−	0.163698i
$643$	2.62597			0.103558			0.0517791	−	0.998659i	$-0.483511\pi$
$643$	2.62597			0.103558			0.0517791	+	0.998659i	$0.483511\pi$
$644$	−6.66078	+	4.40378i	−0.262472	+	0.173533i
$645$	16.3923			0.645446
$646$	−11.7391	+	7.54425i	−0.461868	+	0.296824i
$647$	−2.36120	+	16.4225i	−0.0928282	+	0.645634i	0.889286	+	0.457351i	$0.151202\pi$
$647$	−2.36120	+	16.4225i	−0.0928282	+	0.645634i	−0.982115	+	0.188284i	$0.939708\pi$
$648$	−0.881234	+	1.92963i	−0.0346181	+	0.0758032i
$649$	0.131241	−	0.0385360i	0.00515168	−	0.00151267i
$650$	−2.39541	−	5.24521i	−0.0939557	−	0.205734i
$651$	5.39668	+	6.22810i	0.211513	+	0.244099i
$652$	3.14212	+	21.8539i	0.123055	+	0.855865i
$653$	5.12885	+	1.50597i	0.200707	+	0.0589330i	0.380541	−	0.924764i	$-0.375738\pi$
$653$	5.12885	+	1.50597i	0.200707	+	0.0589330i	−0.179834	+	0.983697i	$0.557556\pi$
$654$	3.67106	−	4.23663i	0.143550	−	0.165665i
$655$	2.59757	+	1.66936i	0.101495	+	0.0652271i
$656$	−7.53419	−	4.84193i	−0.294161	−	0.189046i
$657$	0.0187492	−	0.0216377i	0.000731474	−	0.000844166i
$658$	1.86600	+	0.547906i	0.0727441	+	0.0213596i
$659$	0.763396	+	5.30954i	0.0297377	+	0.206830i	0.999273	−	0.0381209i	$-0.0121372\pi$
$659$	0.763396	+	5.30954i	0.0297377	+	0.206830i	−0.969535	+	0.244951i	$0.921228\pi$
$660$	−0.115539	−	0.133339i	−0.00449735	−	0.00519022i
$661$	2.96840	+	6.49989i	0.115457	+	0.252816i	0.958535	−	0.284976i	$-0.0919857\pi$
$661$	2.96840	+	6.49989i	0.115457	+	0.252816i	−0.843077	+	0.537792i	$0.819258\pi$
$662$	−1.38835	+	0.407656i	−0.0539597	+	0.0158440i
$663$	−9.87374	+	21.6205i	−0.383464	+	0.839669i
$664$	0.117428	−	0.816730i	0.00455709	−	0.0316953i
$665$	5.45348	−	3.50474i	0.211477	−	0.135908i
$666$	−0.0358997			−0.00139109
$667$	−4.19986	−	4.72169i	−0.162619	−	0.182824i
$668$	19.6684			0.760995
$669$	24.1925	−	15.5476i	0.935338	−	0.601105i
$670$	1.84522	−	12.8338i	0.0712870	−	0.495812i
$671$	0.0209519	−	0.0458783i	0.000808840	−	0.00177111i
$672$	−5.23824	+	1.53809i	−0.202070	+	0.0593330i
$673$	−19.8767	−	43.5239i	−0.766190	−	1.67772i	−0.734866	−	0.678212i	$-0.762755\pi$
$673$	−19.8767	−	43.5239i	−0.766190	−	1.67772i	−0.0313236	−	0.999509i	$-0.509972\pi$
$674$	−1.78130	−	2.05573i	−0.0686132	−	0.0791839i
$675$	−0.352413	−	2.45109i	−0.0135644	−	0.0943424i
$676$	5.08830	+	1.49406i	0.195704	+	0.0574638i
$677$	10.5783	−	12.2080i	0.406558	−	0.469193i	−0.515137	−	0.857108i	$-0.672259\pi$
$677$	10.5783	−	12.2080i	0.406558	−	0.469193i	0.921695	+	0.387915i	$0.126805\pi$
$678$	0.737555	+	0.473998i	0.0283256	+	0.0182038i
$679$	−1.08519	−	0.697407i	−0.0416456	−	0.0267640i
$680$	13.0382	−	15.0469i	0.499994	−	0.577024i
$681$	25.0518	+	7.35588i	0.959988	+	0.281878i
$682$	0.0452813	+	0.314938i	0.00173391	+	0.0120596i
$683$	−14.8886	−	17.1824i	−0.569697	−	0.657465i	0.395661	−	0.918397i	$-0.370516\pi$
$683$	−14.8886	−	17.1824i	−0.569697	−	0.657465i	−0.965357	+	0.260932i	$0.915970\pi$
$684$	2.82239	+	6.18018i	0.107917	+	0.236305i
$685$	−26.4684	+	7.77181i	−1.01130	+	0.296946i
$686$	−0.240447	+	0.526506i	−0.00918032	+	0.0201021i
$687$	−1.56956	+	10.9165i	−0.0598823	+	0.416491i
$688$	−18.2473	+	11.7269i	−0.695674	+	0.447082i
$689$	35.0631			1.33580
$690$	3.74040	+	2.33579i	0.142395	+	0.0889222i
$691$	−21.9973			−0.836815			−0.418407	−	0.908259i	$-0.637412\pi$
$691$	−21.9973			−0.836815			−0.418407	+	0.908259i	$0.637412\pi$
$692$	−22.7369	+	14.6121i	−0.864328	+	0.555470i
$693$	0.00949298	−	0.0660252i	0.000360609	−	0.00250809i
$694$	−1.01059	+	2.21288i	−0.0383614	+	0.0839998i
$695$	−24.8526	+	7.29739i	−0.942714	+	0.276806i
$696$	−1.16117	−	2.54260i	−0.0440139	−	0.0963769i
$697$	16.4834	+	19.0229i	0.624355	+	0.720544i
$698$	0.984611	+	6.84812i	0.0372681	+	0.259205i
$699$	−0.622859	−	0.182888i	−0.0235587	−	0.00691746i
$700$	2.69997	−	3.11593i	0.102049	−	0.117771i
$701$	−21.0030	−	13.4978i	−0.793271	−	0.509805i	0.0801424	−	0.996783i	$-0.474462\pi$
$701$	−21.0030	−	13.4978i	−0.793271	−	0.509805i	−0.873414	+	0.486979i	$0.838099\pi$
$702$	−1.95895	−	1.25894i	−0.0739357	−	0.0475156i
$703$	−0.165741	+	0.191275i	−0.00625103	+	0.00721408i
$704$	0.0668331	+	0.0196240i	0.00251887	+	0.000739606i
$705$	0.759627	+	5.28332i	0.0286092	+	0.198981i
$706$	0.0905162	+	0.104461i	0.00340662	+	0.00393145i
$707$	−0.614661	−	1.34592i	−0.0231167	−	0.0506186i
$708$	3.27587	−	0.961882i	0.123115	−	0.0361497i
$709$	−14.8006	+	32.4089i	−0.555850	+	1.21714i	0.398146	+	0.917322i	$0.369654\pi$
$709$	−14.8006	+	32.4089i	−0.555850	+	1.21714i	−0.953996	+	0.299819i	$0.903074\pi$
$710$	−2.11902	+	14.7381i	−0.0795255	+	0.553112i
$711$	−1.29939	+	0.835070i	−0.0487311	+	0.0313176i
$712$	−18.7203			−0.701574
$713$	16.8832	+	35.7347i	0.632282	+	1.33827i
$714$	3.41963			0.127977
$715$	0.358638	−	0.230483i	0.0134123	−	0.00861957i
$716$	−2.50331	+	17.4109i	−0.0935531	+	0.650676i
$717$	−2.31364	+	5.06617i	−0.0864046	+	0.189200i
$718$	−1.12312	+	0.329779i	−0.0419146	+	0.0123073i
$719$	15.9449	+	34.9144i	0.594644	+	1.30209i	0.932595	+	0.360924i	$0.117539\pi$
$719$	15.9449	+	34.9144i	0.594644	+	1.30209i	−0.337952	+	0.941164i	$0.609734\pi$
$720$	−2.18686	−	2.52377i	−0.0814995	−	0.0940555i
$721$	−1.08667	−	7.55797i	−0.0404698	−	0.281474i
$722$	1.30425	+	0.382962i	0.0485391	+	0.0142524i
$723$	−11.1228	+	12.8363i	−0.413660	+	0.477389i
$724$	24.3630	+	15.6572i	0.905445	+	0.581894i
$725$	2.74493	+	1.76406i	0.101944	+	0.0655156i
$726$	−4.16777	+	4.80986i	−0.154680	+	0.178511i
$727$	−23.1846	−	6.80761i	−0.859869	−	0.252480i	−0.178068	−	0.984018i	$-0.556985\pi$
$727$	−23.1846	−	6.80761i	−0.859869	−	0.252480i	−0.681801	+	0.731538i	$0.738803\pi$
$728$	−1.21455	−	8.44741i	−0.0450144	−	0.313082i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−0.0109363	−	0.0239473i	−0.000404772	−	0.000886328i
$731$	58.4930	−	17.1751i	2.16344	−	0.635243i
$732$	0.522973	−	1.14515i	0.0193296	−	0.0423260i
$733$	1.83100	−	12.7349i	0.0676295	−	0.470374i	−0.927660	−	0.373426i	$-0.878183\pi$
$733$	1.83100	−	12.7349i	0.0676295	−	0.470374i	0.995289	−	0.0969476i	$-0.0309079\pi$
$734$	4.34517	−	2.79247i	0.160383	−	0.103072i
$735$	−1.58862			−0.0585971
$736$	−26.1801	+	0.339729i	−0.965011	+	0.0125226i
$737$	−0.940573			−0.0346465
$738$	−2.07454	+	1.33323i	−0.0763649	+	0.0490767i
$739$	1.09793	−	7.63625i	0.0403879	−	0.280904i	−0.959612	−	0.281327i	$-0.909225\pi$
$739$	1.09793	−	7.63625i	0.0403879	−	0.280904i	1.00000		0.000422829i	$0.000134591\pi$
$740$	0.0681495	−	0.149227i	0.00250523	−	0.00548568i
$741$	−15.7517	+	4.62511i	−0.578652	+	0.169908i
$742$	−2.09562	−	4.58878i	−0.0769328	−	0.168459i
$743$	16.3231	+	18.8379i	0.598836	+	0.691094i	0.971545	−	0.236854i	$-0.0761164\pi$
$743$	16.3231	+	18.8379i	0.598836	+	0.691094i	−0.372709	+	0.927948i	$0.621571\pi$
$744$	2.48792	+	17.3039i	0.0912117	+	0.634392i
$745$	−4.65652	−	1.36728i	−0.170602	−	0.0500932i
$746$	11.8872	−	13.7186i	0.435223	−	0.502274i
$747$	0.327220	+	0.210291i	0.0119723	+	0.00769416i
$748$	−0.551987	−	0.354741i	−0.0201827	−	0.0129706i
$749$	−8.67988	+	10.0171i	−0.317156	+	0.366017i
$750$	−6.59607	−	1.93678i	−0.240855	−	0.0707213i
$751$	−1.88668	−	13.1221i	−0.0688458	−	0.478833i	−0.994853	−	0.101328i	$-0.967691\pi$
$751$	−1.88668	−	13.1221i	−0.0688458	−	0.478833i	0.926007	−	0.377506i	$-0.123218\pi$
$752$	−4.62522	−	5.33779i	−0.168665	−	0.194649i
$753$	10.8897	+	23.8450i	0.396842	+	0.868962i
$754$	2.94402	−	0.864441i	0.107215	−	0.0314811i
$755$	11.8224	−	25.8874i	0.430261	−	0.942140i
$756$	0.236951	−	1.64803i	0.00861782	−	0.0599382i
$757$	−24.8142	+	15.9471i	−0.901887	+	0.579608i	−0.907349	−	0.420377i	$-0.861898\pi$
$757$	−24.8142	+	15.9471i	−0.901887	+	0.579608i	0.00546216	+	0.999985i	$0.498261\pi$
$758$	−7.85624			−0.285351
$759$	0.129105	−	0.292693i	0.00468621	−	0.0106241i
$760$	13.7517			0.498826
$761$	−29.6475	+	19.0533i	−1.07472	+	0.690682i	−0.953332	−	0.301923i	$-0.902372\pi$
$761$	−29.6475	+	19.0533i	−1.07472	+	0.690682i	−0.121390	+	0.992605i	$0.538735\pi$
$762$	0.470370	−	3.27149i	0.0170397	−	0.118514i
$763$	−4.02334	+	8.80988i	−0.145655	+	0.318939i
$764$	3.97927	−	1.16842i	0.143965	−	0.0422720i
$765$	3.89891	+	8.53743i	0.140965	+	0.308671i
$766$	−8.77695	−	10.1291i	−0.317124	−	0.365981i
$767$	1.17404	+	8.16566i	0.0423923	+	0.294845i
$768$	−4.39573	−	1.29070i	−0.158617	−	0.0465742i
$769$	−35.2290	+	40.6564i	−1.27039	+	1.46611i	−0.451377	+	0.892333i	$0.649067\pi$
$769$	−35.2290	+	40.6564i	−1.27039	+	1.46611i	−0.819013	+	0.573775i	$0.805478\pi$
$770$	−0.0515985	−	0.0331603i	−0.00185948	−	0.00119502i
$771$	0.115072	+	0.0739521i	0.00414420	+	0.00266332i
$772$	−22.2582	+	25.6874i	−0.801091	+	0.924508i
$773$	−46.4182	−	13.6296i	−1.66955	−	0.490223i	−0.695872	−	0.718166i	$-0.744982\pi$
$773$	−46.4182	−	13.6296i	−1.66955	−	0.490223i	−0.973675	+	0.227943i	$0.926800\pi$
$774$	0.849979	+	5.91173i	0.0305519	+	0.212493i
$775$	−13.3638	−	15.4226i	−0.480041	−	0.553997i
$776$	−1.13676	−	2.48916i	−0.0408073	−	0.0893555i
$777$	0.0595107	−	0.0174739i	0.00213493	−	0.000626873i
$778$	−2.07315	+	4.53956i	−0.0743260	+	0.162751i
$779$	−2.47420	+	17.2084i	−0.0886474	+	0.616556i
$780$	8.95183	−	5.75299i	0.320527	−	0.205990i
$781$	1.08014			0.0386505
$782$	15.7943	+	4.41584i	0.564803	+	0.157910i
$783$	1.31766			0.0470893
$784$	1.76840	−	1.13648i	0.0631570	−	0.0405886i
$785$	−1.82690	+	12.7063i	−0.0652047	+	0.453509i
$786$	−0.467348	+	1.02335i	−0.0166698	+	0.0365017i
$787$	−0.530750	+	0.155842i	−0.0189192	+	0.00555517i	−0.291178	−	0.956669i	$-0.594047\pi$
$787$	−0.530750	+	0.155842i	−0.0189192	+	0.00555517i	0.272259	+	0.962224i	$0.412229\pi$
$788$	11.1633	+	24.4442i	0.397676	+	0.870789i
$789$	16.1991	+	18.6948i	0.576705	+	0.665553i
$790$	0.202126	+	1.40581i	0.00719131	+	0.0500167i
$791$	−1.45335	−	0.426743i	−0.0516753	−	0.0151732i
$792$	0.0926639	−	0.106940i	0.00329267	−	0.00379994i
$793$	2.55902	+	1.64458i	0.0908735	+	0.0584009i
$794$	−10.7331	−	6.89772i	−0.380902	−	0.244791i
$795$	9.06696	−	10.4638i	0.321572	−	0.371114i
$796$	−29.5268	−	8.66984i	−1.04655	−	0.307294i
$797$	0.0181330	+	0.126118i	0.000642306	+	0.00446733i	0.990140	−	0.140081i	$-0.0447362\pi$
$797$	0.0181330	+	0.126118i	0.000642306	+	0.00446733i	−0.989498	+	0.144548i	$0.953827\pi$
$798$	1.54673	+	1.78502i	0.0547536	+	0.0631890i
$799$	8.24622	+	18.0567i	0.291730	+	0.638800i
$800$	12.9714	−	3.80875i	0.458609	−	0.134660i
$801$	3.66595	−	8.02731i	0.129530	−	0.283631i
$802$	−2.12192	+	14.7583i	−0.0749276	+	0.521133i
$803$	−0.00160662	+	0.00103251i	−5.66963e−5	+	3.64365e-5i
$804$	−23.4773			−0.827980
$805$	−7.33737	−	2.05141i	−0.258608	−	0.0723029i
$806$	−19.1899			−0.675937
$807$	−5.20468	+	3.34484i	−0.183213	+	0.117744i
$808$	0.446697	−	3.10685i	0.0157147	−	0.109298i
$809$	20.6959	−	45.3178i	0.727630	−	1.59329i	−0.0752627	−	0.997164i	$-0.523980\pi$
$809$	20.6959	−	45.3178i	0.727630	−	1.59329i	0.802893	−	0.596124i	$-0.203293\pi$
$810$	−0.882265	+	0.259056i	−0.0309996	+	0.00910232i
$811$	1.73613	+	3.80160i	0.0609638	+	0.133492i	0.937662	−	0.347549i	$-0.112986\pi$
$811$	1.73613	+	3.80160i	0.0609638	+	0.133492i	−0.876698	+	0.481041i	$0.840259\pi$
$812$	1.43668	+	1.65802i	0.0504175	+	0.0581849i
$813$	−4.56150	−	31.7260i	−0.159979	−	1.11268i
$814$	0.00229766		0.000674653i	8.05328e−5		2.36466e-5i
$815$	−13.7954	+	15.9207i	−0.483230	+	0.557677i
$816$	−10.4477	−	6.71434i	−0.365743	−	0.235049i
$817$	35.4221	+	22.7644i	1.23926	+	0.796426i
$818$	2.76471	−	3.19064i	0.0966657	−	0.111558i
$819$	3.86011	+	1.13343i	0.134883	+	0.0396052i
$820$	−1.60374	−	11.1543i	−0.0560051	−	0.389524i
$821$	32.9213	+	37.9932i	1.14896	+	1.32597i	0.937258	+	0.348636i	$0.113355\pi$
$821$	32.9213	+	37.9932i	1.14896	+	1.32597i	0.211702	+	0.977334i	$0.432099\pi$
$822$	−4.17528	−	9.14260i	−0.145630	−	0.318885i
$823$	36.1628	−	10.6184i	1.26056	−	0.370133i	0.417855	−	0.908514i	$-0.362782\pi$
$823$	36.1628	−	10.6184i	1.26056	−	0.370133i	0.842702	+	0.538381i	$0.180964\pi$
$824$	6.72883	−	14.7341i	0.234410	−	0.513286i
$825$	−0.0235074	+	0.163498i	−0.000818423	+	0.00569226i
$826$	0.998485	−	0.641687i	0.0347417	−	0.0223272i
$827$	39.0025			1.35625			0.678125	−	0.734947i	$-0.262793\pi$
$827$	39.0025			1.35625			0.678125	+	0.734947i	$0.262793\pi$
$828$	3.22254	−	7.30579i	0.111991	−	0.253894i
$829$	−8.91284			−0.309556			−0.154778	−	0.987949i	$-0.549466\pi$
$829$	−8.91284			−0.309556			−0.154778	+	0.987949i	$0.549466\pi$
$830$	0.300882	−	0.193365i	0.0104438	−	0.00671181i
$831$	2.10967	−	14.6731i	0.0731837	−	0.509004i
$832$	−1.74517	+	3.82138i	−0.0605028	+	0.132483i
$833$	−5.66870	+	1.66448i	−0.196409	+	0.0576708i
$834$	−3.92041	−	8.58449i	−0.135753	−	0.297257i
$835$	12.2894	+	14.1827i	0.425292	+	0.490813i
$836$	−0.0644968	−	0.448585i	−0.00223067	−	0.0155146i
$837$	−7.90715	−	2.32175i	−0.273311	−	0.0802513i
$838$	−6.14862	+	7.09589i	−0.212401	+	0.245123i
$839$	12.3960	+	7.96642i	0.427957	+	0.275031i	0.736838	−	0.676069i	$-0.236318\pi$
$839$	12.3960	+	7.96642i	0.427957	+	0.275031i	−0.308881	+	0.951101i	$0.599954\pi$
$840$	−2.83502	−	1.82195i	−0.0978173	−	0.0628634i
$841$	17.8540	−	20.6046i	0.615654	−	0.710503i
$842$	−14.3586	−	4.21606i	−0.494830	−	0.145295i
$843$	0.102573	+	0.713410i	0.00353280	+	0.0245711i
$844$	−18.8986	−	21.8101i	−0.650516	−	0.750736i
$845$	2.10196	+	4.60265i	0.0723096	+	0.158336i
$846$	−1.86600	+	0.547906i	−0.0641542	+	0.0188374i
$847$	4.56772	−	10.0019i	0.156949	−	0.343670i
$848$	−2.60733	+	18.1344i	−0.0895361	+	0.622737i
$849$	3.96642	−	2.54906i	0.136127	−	0.0874836i
$850$	−8.46802			−0.290451
$851$	0.297427	−	0.00385959i	0.0101957	−	0.000132305i
$852$	26.9610			0.923668
$853$	3.25912	−	2.09451i	0.111590	−	0.0717147i	−0.483655	−	0.875259i	$-0.660691\pi$
$853$	3.25912	−	2.09451i	0.111590	−	0.0717147i	0.595246	+	0.803544i	$0.297055\pi$
$854$	0.0622841	−	0.433196i	0.00213132	−	0.0148237i
$855$	−2.69295	+	5.89675i	−0.0920971	+	0.201665i
$856$	−26.9784	+	7.92156i	−0.922101	+	0.270753i
$857$	−10.2358	−	22.4133i	−0.349649	−	0.765624i	−0.999982	−	0.00597483i	$-0.998098\pi$
$857$	−10.2358	−	22.4133i	−0.349649	−	0.765624i	0.650334	−	0.759649i	$-0.274629\pi$
$858$	0.101718	+	0.117389i	0.00347259	+	0.00400758i
$859$	2.56785	+	17.8598i	0.0876139	+	0.609368i	0.985568	+	0.169279i	$0.0541440\pi$
$859$	2.56785	+	17.8598i	0.0876139	+	0.609368i	−0.897954	+	0.440089i	$0.854947\pi$
$860$	−26.1872	−	7.68926i	−0.892977	−	0.262202i
$861$	2.79001	−	3.21984i	0.0950833	−	0.109732i
$862$	−8.14979	−	5.23755i	−0.277583	−	0.178392i
$863$	16.8234	+	10.8117i	0.572675	+	0.368036i	0.794697	−	0.607006i	$-0.207629\pi$
$863$	16.8234	+	10.8117i	0.572675	+	0.368036i	−0.222023	+	0.975042i	$0.571266\pi$
$864$	3.57514	−	4.12593i	0.121629	−	0.140367i
$865$	−24.7433	−	7.26530i	−0.841299	−	0.247028i
$866$	−0.891257	−	6.19883i	−0.0302861	−	0.210645i
$867$	11.7251	+	13.5314i	0.398204	+	0.459552i
$868$	−5.69991	−	12.4811i	−0.193468	−	0.423635i
$869$	0.0988572	−	0.0290271i	0.00335350	−	0.000984677i
$870$	0.503318	−	1.10211i	0.0170641	−	0.0373651i
$871$	8.07324	−	56.1506i	0.273551	−	1.90259i
$872$	−17.2838	+	11.1077i	−0.585305	+	0.376153i
$873$	1.28996			0.0436587
$874$	4.83886	+	10.2418i	0.163677	+	0.346435i
$875$	11.8770			0.401515
$876$	−0.0401021	+	0.0257721i	−0.00135493	+	0.000870758i
$877$	0.820653	−	5.70776i	0.0277115	−	0.192737i	−0.971263	−	0.238007i	$-0.923506\pi$
$877$	0.820653	−	5.70776i	0.0277115	−	0.192737i	0.998975	+	0.0452700i	$0.0144148\pi$
$878$	−4.47745	+	9.80424i	−0.151107	+	0.330877i
$879$	−16.1663	+	4.74687i	−0.545277	+	0.160108i
$880$	0.0925352	+	0.202624i	0.00311936	+	0.00683045i
$881$	8.21997	+	9.48635i	0.276938	+	0.319603i	0.877130	−	0.480252i	$-0.159455\pi$
$881$	8.21997	+	9.48635i	0.276938	+	0.319603i	−0.600193	+	0.799855i	$0.704909\pi$
$882$	−0.0823736	−	0.572921i	−0.00277366	−	0.0192913i
$883$	37.8422	+	11.1115i	1.27349	+	0.373931i	0.847499	−	0.530797i	$-0.178107\pi$
$883$	37.8422	+	11.1115i	1.27349	+	0.373931i	0.425991	+	0.904727i	$0.359925\pi$
$884$	25.9153	−	29.9079i	0.871626	−	1.00591i
$885$	2.74046	+	1.76119i	0.0921195	+	0.0592016i
$886$	−2.02428	−	1.30092i	−0.0680070	−	0.0437054i
$887$	−1.88167	+	2.17156i	−0.0631801	+	0.0729138i	−0.786460	−	0.617641i	$-0.788088\pi$
$887$	−1.88167	+	2.17156i	−0.0631801	+	0.0729138i	0.723280	+	0.690555i	$0.242634\pi$
$888$	0.126242	+	0.0370680i	0.00423640	+	0.00124392i
$889$	0.812646	+	5.65208i	0.0272553	+	0.189565i
$890$	−5.31387	−	6.13253i	−0.178121	−	0.205563i
$891$	0.0277099	+	0.0606762i	0.000928316	+	0.00203273i
$892$	−45.9414	+	13.4896i	−1.53823	+	0.451666i
$893$	−5.69561	+	12.4717i	−0.190596	+	0.417348i
$894$	0.251645	−	1.75023i	0.00841627	−	0.0585364i
$895$	−14.1190	+	9.07371i	−0.471945	+	0.303301i
$896$	11.5232			0.384963
$897$	16.3651	+	10.2196i	0.546415	+	0.341223i
$898$	4.04475			0.134975
$899$	9.13498	−	5.87070i	0.304669	−	0.195799i
$900$	−0.586760	+	4.08100i	−0.0195587	+	0.136033i
$901$	21.3903	−	46.8383i	0.712615	−	1.56041i
$902$	0.157830	−	0.0463430i	0.00525516	−	0.00154305i
$903$	−4.28649	−	9.38611i	−0.142646	−	0.312350i
$904$	−2.10420	−	2.42838i	−0.0699847	−	0.0807667i
$905$	3.93248	+	27.3510i	0.130720	+	0.909177i
$906$	9.94909	+	2.92132i	0.330536	+	0.0970542i
$907$	34.3390	−	39.6293i	1.14021	−	1.31587i	0.198246	−	0.980152i	$-0.436475\pi$
$907$	34.3390	−	39.6293i	1.14021	−	1.31587i	0.941962	−	0.335719i	$-0.108979\pi$
$908$	−36.5706	−	23.5025i	−1.21364	−	0.779959i
$909$	1.24475	+	0.799949i	0.0412856	+	0.0265326i
$910$	2.42250	−	2.79572i	0.0803051	−	0.0926771i
$911$	41.4885	+	12.1821i	1.37458	+	0.403612i	0.883878	−	0.467717i	$-0.154924\pi$
$911$	41.4885	+	12.1821i	1.37458	+	0.403612i	0.490698	+	0.871330i	$0.336742\pi$
$912$	−1.22076	−	8.49058i	−0.0404234	−	0.281151i
$913$	−0.0169908	−	0.0196084i	−0.000562314	−	0.000648945i
$914$	2.01401	+	4.41007i	0.0666175	+	0.145872i
$915$	1.15253	−	0.338412i	0.0381013	−	0.0111876i
$916$	7.62811	−	16.7032i	0.252040	−	0.551890i
$917$	0.276612	−	1.92388i	0.00913453	−	0.0635320i
$918$	−2.87678	+	1.84879i	−0.0949479	+	0.0610193i
$919$	−8.30530			−0.273967			−0.136983	−	0.990573i	$-0.543741\pi$
$919$	−8.30530			−0.273967			−0.136983	+	0.990573i	$0.543741\pi$
$920$	−10.7414	−	12.0760i	−0.354133	−	0.398134i
$921$	34.1893			1.12658
$922$	−8.06236	+	5.18136i	−0.265520	+	0.170639i
$923$	−9.27119	+	64.4826i	−0.305165	+	2.12247i
$924$	−0.0461363	+	0.101024i	−0.00151777	+	0.00332346i
$925$	−0.147366	+	0.0432705i	−0.00484536	+	0.00142273i
$926$	−6.68048	−	14.6282i	−0.219534	−	0.480713i
$927$	5.00031	+	5.77067i	0.164232	+	0.189534i
$928$	1.02376	+	7.12039i	0.0336065	+	0.233738i
$929$	5.05470	+	1.48419i	0.165839	+	0.0486948i	0.363598	−	0.931556i	$-0.381548\pi$
$929$	5.05470	+	1.48419i	0.165839	+	0.0486948i	−0.197759	+	0.980251i	$0.563366\pi$
$930$	−4.96231	+	5.72682i	−0.162721	+	0.187790i
$931$	−3.43285	−	2.20616i	−0.112507	−	0.0723038i
$932$	0.909249	+	0.584339i	0.0297834	+	0.0191407i
$933$	−19.0851	+	22.0254i	−0.624818	+	0.721078i
$934$	4.92514	+	1.44615i	0.161155	+	0.0473195i
$935$	−0.0890972	−	0.619685i	−0.00291379	−	0.0202659i
$936$	5.58876	+	6.44978i	0.182674	+	0.210818i
$937$	−9.22720	−	20.2047i	−0.301439	−	0.660060i	0.696930	−	0.717139i	$-0.254549\pi$
$937$	−9.22720	−	20.2047i	−0.301439	−	0.660060i	−0.998370	+	0.0570787i	$0.981821\pi$
$938$	−7.83104	+	2.29940i	−0.255693	+	0.0750781i
$939$	1.62643	−	3.56139i	0.0530765	−	0.116221i
$940$	1.26476	−	8.79661i	0.0412520	−	0.286914i
$941$	28.4395	−	18.2770i	0.927102	−	0.595812i	0.0123920	−	0.999923i	$-0.496055\pi$
$941$	28.4395	−	18.2770i	0.927102	−	0.595812i	0.914710	+	0.404111i	$0.132419\pi$
$942$	−4.67716			−0.152390
$943$	17.0441	−	11.2687i	0.555033	−	0.366960i
$944$	−4.31052			−0.140295
$945$	1.33643	−	0.858872i	0.0434741	−	0.0279391i
$946$	0.0566971	−	0.394337i	0.00184338	−	0.0128210i
$947$	−7.82681	+	17.1383i	−0.254337	+	0.556921i	−0.993131	−	0.117011i	$-0.962669\pi$
$947$	−7.82681	+	17.1383i	−0.254337	+	0.556921i	0.738793	+	0.673932i	$0.235396\pi$
$948$	2.46754	−	0.724534i	0.0801419	−	0.0235318i
$949$	−0.0478490	−	0.104775i	−0.00155324	−	0.00340113i
$950$	−3.83015	−	4.42023i	−0.124267	−	0.143411i
$951$	−4.81568	−	33.4938i	−0.156159	−	1.08611i
$952$	−12.0252	−	3.53092i	−0.389739	−	0.114438i
$953$	8.54336	−	9.85956i	0.276747	−	0.319383i	−0.600312	−	0.799766i	$-0.704957\pi$
$953$	8.54336	−	9.85956i	0.276747	−	0.319383i	0.877059	+	0.480383i	$0.159502\pi$
$954$	4.24383	+	2.72734i	0.137399	+	0.0883010i
$955$	3.32890	+	2.13935i	0.107721	+	0.0692278i
$956$	6.07255	−	7.00810i	0.196400	−	0.226658i
$957$	−0.0843329	−	0.0247624i	−0.00272610	−	0.000800454i
$958$	−3.39101	−	23.5850i	−0.109558	−	0.761996i
$959$	11.3714	+	13.1233i	0.367202	+	0.423774i
$960$	0.689126	+	1.50898i	0.0222415	+	0.0487020i
$961$	−35.4182	+	10.3997i	−1.14252	+	0.335475i
$962$	−0.0599972	+	0.131375i	−0.00193439	+	0.00423572i
$963$	1.88632	−	13.1196i	0.0607857	−	0.422774i
$964$	23.7902	−	15.2890i	0.766231	−	0.492427i
$965$	−32.4304			−1.04397
$966$	0.359365	−	2.75253i	0.0115624	−	0.0885611i
$967$	−16.5932			−0.533600			−0.266800	−	0.963752i	$-0.585966\pi$
$967$	−16.5932			−0.533600			−0.266800	+	0.963752i	$0.585966\pi$
$968$	19.6224	−	12.6106i	0.630689	−	0.405319i
$969$	−3.43099	+	23.8631i	−0.110219	+	0.766592i
$970$	0.492739	−	1.07895i	0.0158209	−	0.0346429i
$971$	31.0969	−	9.13088i	0.997948	−	0.293024i	0.258334	−	0.966056i	$-0.416826\pi$
$971$	31.0969	−	9.13088i	0.997948	−	0.293024i	0.739614	+	0.673032i	$0.235008\pi$
$972$	0.691656	+	1.51452i	0.0221849	+	0.0485781i
$973$	10.6773	+	12.3222i	0.342297	+	0.395032i
$974$	2.31816	+	16.1231i	0.0742786	+	0.516619i
$975$	−9.55876	−	2.80670i	−0.306125	−	0.0898865i
$976$	−1.04086	+	1.20121i	−0.0333170	+	0.0384499i
$977$	9.84746	+	6.32858i	0.315048	+	0.202469i	0.688602	−	0.725139i	$-0.258225\pi$
$977$	9.84746	+	6.32858i	0.315048	+	0.202469i	−0.373554	+	0.927608i	$0.621861\pi$
$978$	−6.45698	−	4.14965i	−0.206471	−	0.132691i
$979$	−0.385484	+	0.444872i	−0.0123201	+	0.0142182i
$980$	2.53787	+	0.745186i	0.0810693	+	0.0238041i
$981$	−1.37833	−	9.58652i	−0.0440068	−	0.306074i
$982$	−15.0252	−	17.3400i	−0.479474	−	0.553342i
$983$	−23.1459	−	50.6825i	−0.738241	−	1.61652i	−0.786427	−	0.617684i	$-0.788071\pi$
$983$	−23.1459	−	50.6825i	−0.738241	−	1.61652i	0.0481859	−	0.998838i	$-0.484656\pi$
$984$	8.67177	−	2.54626i	0.276446	−	0.0811719i
$985$	−10.6513	+	23.3232i	−0.339380	+	0.743138i
$986$	0.641258	−	4.46005i	0.0204218	−	0.142037i
$987$	2.82656	−	1.81652i	0.0899703	−	0.0578204i
$988$	27.3334			0.869590
$989$	−7.67760	−	48.8870i	−0.244133	−	1.55452i
$990$	0.0613352			0.00194936
$991$	0.571383	−	0.367206i	0.0181506	−	0.0116647i	−0.531534	−	0.847037i	$-0.678384\pi$
$991$	0.571383	−	0.367206i	0.0181506	−	0.0116647i	0.549685	+	0.835372i	$0.314748\pi$
$992$	6.40283	−	44.5327i	0.203290	−	1.41391i
$993$	−1.03849	+	2.27397i	−0.0329554	+	0.0721622i
$994$	8.99306	−	2.64060i	0.285243	−	0.0837548i
$995$	−12.1974	−	26.7086i	−0.386684	−	0.846720i
$996$	−0.424101	−	0.489439i	−0.0134382	−	0.0155085i
$997$	−1.40007	−	9.73767i	−0.0443405	−	0.308395i	−0.999907	−	0.0136202i	$-0.995664\pi$
$997$	−1.40007	−	9.73767i	−0.0443405	−	0.308395i	0.955567	−	0.294775i	$-0.0952447\pi$
$998$	−3.78107	−	1.11022i	−0.119688	−	0.0351435i
$999$	−0.0406164	+	0.0468739i	−0.00128505	+	0.00148302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.e.127.4	✓	60
23.2	even	11	inner	483.2.q.e.232.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.e.127.4	✓	60	1.1	even	1	trivial
483.2.q.e.232.4	yes	60	23.2	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)

\(f(q)\)	\(=\)	\(q+(0.486928 - 0.312930i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.691656 + 1.51452i) q^{4} +(-1.52427 + 0.447565i) q^{5} +(-0.240447 - 0.526506i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.301897 + 2.09974i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.486928 - 0.312930i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.691656 + 1.51452i) q^{4} +(-1.52427 + 0.447565i) q^{5} +(-0.240447 - 0.526506i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.301897 + 2.09974i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.602152 + 0.694921i) q^{10} +(0.0561151 + 0.0360630i) q^{11} +(1.40067 + 0.900154i) q^{12} +(-2.63455 + 3.04043i) q^{13} +(0.555367 + 0.163070i) q^{14} +(0.226084 + 1.57245i) q^{15} +(-1.37658 - 1.58866i) q^{16} +(2.45428 + 5.37412i) q^{17} +(-0.555367 + 0.163070i) q^{18} +(-1.69516 + 3.71187i) q^{19} +(0.376424 - 2.61809i) q^{20} +(0.841254 - 0.540641i) q^{21} +0.0386092 q^{22} +(4.58365 - 1.41074i) q^{23} +2.12133 q^{24} +(-2.08319 + 1.33879i) q^{25} +(-0.331395 + 2.30490i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.59753 + 0.469078i) q^{28} +(-0.547375 - 1.19858i) q^{29} +(0.602152 + 0.694921i) q^{30} +(1.17281 + 8.15708i) q^{31} +(-5.23824 - 1.53809i) q^{32} +(0.0436819 - 0.0504116i) q^{33} +(2.87678 + 1.84879i) q^{34} +(-1.33643 - 0.858872i) q^{35} +(1.09033 - 1.25830i) q^{36} +(0.0595107 + 0.0174739i) q^{37} +(0.336136 + 2.33788i) q^{38} +(2.63455 + 3.04043i) q^{39} +(-1.39994 - 3.06545i) q^{40} +(4.08789 - 1.20031i) q^{41} +(0.240447 - 0.526506i) q^{42} +(1.46849 - 10.2136i) q^{43} +(-0.0934302 + 0.0600440i) q^{44} +1.58862 q^{45} +(1.79045 - 2.12129i) q^{46} +3.35993 q^{47} +(-1.76840 + 1.13648i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-0.595418 + 1.30378i) q^{50} +(5.66870 - 1.66448i) q^{51} +(-2.78258 - 6.09300i) q^{52} +(-5.70745 - 6.58675i) q^{53} +(0.0823736 + 0.572921i) q^{54} +(-0.101675 - 0.0298544i) q^{55} +(-1.38918 + 1.60320i) q^{56} +(3.43285 + 2.20616i) q^{57} +(-0.641605 - 0.412334i) q^{58} +(1.34284 - 1.54972i) q^{59} +(-2.53787 - 0.745186i) q^{60} +(-0.107607 - 0.748421i) q^{61} +(3.12367 + 3.60490i) q^{62} +(-0.415415 - 0.909632i) q^{63} +(1.00193 - 0.294194i) q^{64} +(2.65497 - 5.81357i) q^{65} +(0.00549466 - 0.0382162i) q^{66} +(-11.8622 + 7.62340i) q^{67} -9.83671 q^{68} +(-0.744056 - 4.73776i) q^{69} -0.919512 q^{70} +(13.6224 - 8.75461i) q^{71} +(0.301897 - 2.09974i) q^{72} +(-0.0118936 + 0.0260434i) q^{73} +(0.0344455 - 0.0101141i) q^{74} +(1.02869 + 2.25252i) q^{75} +(-4.44922 - 5.13468i) q^{76} +(0.00949298 + 0.0660252i) q^{77} +(2.23428 + 0.656043i) q^{78} +(1.01149 - 1.16733i) q^{79} +(2.80931 + 1.80543i) q^{80} +(0.841254 + 0.540641i) q^{81} +(1.61489 - 1.86369i) q^{82} +(-0.373211 - 0.109585i) q^{83} +(0.236951 + 1.64803i) q^{84} +(-6.14625 - 7.09315i) q^{85} +(-2.48108 - 5.43280i) q^{86} +(-1.26428 + 0.371227i) q^{87} +(-0.0587819 + 0.128714i) q^{88} +(-1.25590 + 8.73497i) q^{89} +(0.773543 - 0.497126i) q^{90} -4.02307 q^{91} +(-1.03373 + 7.91775i) q^{92} +8.24096 q^{93} +(1.63605 - 1.05142i) q^{94} +(0.922565 - 6.41658i) q^{95} +(-2.26791 + 4.96603i) q^{96} +(-1.23771 + 0.363425i) q^{97} +(0.240447 + 0.526506i) q^{98} +(-0.0436819 - 0.0504116i) 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