LMFDB - Embedded newform 322.2.i.d.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	322.85
Dual form			322.2.i.d.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.863913 + 0.555203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415591 - 0.910017i) q^{5} +(0.146148 - 1.01648i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.808150 + 1.76960i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.863913 + 0.555203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415591 - 0.910017i) q^{5} +(0.146148 - 1.01648i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.808150 + 1.76960i) q^{9} +(0.959899 + 0.281852i) q^{10} +(2.43096 + 2.80548i) q^{11} +(0.672499 + 0.776106i) q^{12} +(-0.602728 - 0.176977i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(0.864279 + 0.555438i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.383528 + 2.66749i) q^{17} +(-0.808150 - 1.76960i) q^{18} +(0.863363 + 6.00482i) q^{19} +(-0.841610 + 0.540870i) q^{20} +(-0.672499 + 0.776106i) q^{21} -3.71218 q^{22} +(-0.450364 + 4.77464i) q^{23} -1.02693 q^{24} +(2.61889 - 3.02236i) q^{25} +(0.528453 - 0.339616i) q^{26} +(-0.722761 - 5.02692i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.803521 + 5.58861i) q^{29} +(-0.985754 + 0.289444i) q^{30} +(-6.41092 - 4.12005i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-3.65774 - 1.07401i) q^{33} +(-1.76480 - 2.03669i) q^{34} +(-0.655138 - 0.756070i) q^{35} +(1.86660 + 0.548084i) q^{36} +(-4.84949 + 10.6189i) q^{37} +(-5.10352 - 3.27983i) q^{38} +(0.618962 - 0.181744i) q^{39} +(0.142375 - 0.990241i) q^{40} +(0.800341 + 1.75250i) q^{41} +(-0.146148 - 1.01648i) q^{42} +(9.73977 - 6.25937i) q^{43} +(2.43096 - 2.80548i) q^{44} +1.94623 q^{45} +(-3.31351 - 3.46709i) q^{46} +8.85620 q^{47} +(0.672499 - 0.776106i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.569139 + 3.95845i) q^{50} +(-1.14967 - 2.51742i) q^{51} +(-0.0893984 + 0.621779i) q^{52} +(-3.99660 + 1.17351i) q^{53} +(4.27240 + 2.74570i) q^{54} +(1.54275 - 3.37814i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-4.07976 - 4.70830i) q^{57} +(-3.69740 - 4.26703i) q^{58} +(9.40573 + 2.76177i) q^{59} +(0.426785 - 0.934529i) q^{60} +(-5.57144 - 3.58055i) q^{61} +(7.31199 - 2.14699i) q^{62} +(-0.276860 + 1.92560i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.0894362 + 0.622043i) q^{65} +(3.20700 - 2.06101i) q^{66} +(8.45517 - 9.75779i) q^{67} +2.69492 q^{68} +(-2.26182 - 4.37491i) q^{69} +1.00042 q^{70} +(-7.10835 + 8.20348i) q^{71} +(-1.63658 + 1.05177i) q^{72} +(-0.505139 - 3.51332i) q^{73} +(-4.84949 - 10.6189i) q^{74} +(-0.584468 + 4.06507i) q^{75} +(5.82083 - 1.70915i) q^{76} +(3.12288 + 2.00695i) q^{77} +(-0.267981 + 0.586797i) q^{78} +(3.68292 + 1.08140i) q^{79} +(0.655138 + 0.756070i) q^{80} +(-0.406546 - 0.469180i) q^{81} +(-1.84857 - 0.542788i) q^{82} +(6.54061 - 14.3219i) q^{83} +(0.863913 + 0.555203i) q^{84} +(2.58686 - 0.759569i) q^{85} +(-1.64768 + 11.4598i) q^{86} +(-2.40864 - 5.27419i) q^{87} +(0.528298 + 3.67439i) q^{88} +(-3.53358 + 2.27089i) q^{89} +(-1.27451 + 1.47086i) q^{90} -0.628173 q^{91} +(4.79013 - 0.233722i) q^{92} +7.82594 q^{93} +(-5.79958 + 6.69307i) q^{94} +(5.10568 - 3.28122i) q^{95} +(0.146148 + 1.01648i) q^{96} +(-3.95761 - 8.66596i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-6.92916 + 2.03458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.863913	+	0.555203i	−0.498780	+	0.320547i	−0.765728	−	0.643164i	$-0.777621\pi$
$3$	−0.863913	+	0.555203i	−0.498780	+	0.320547i	0.266948	+	0.963711i	$0.413985\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.415591	−	0.910017i	−0.185858	−	0.406972i	0.793651	−	0.608373i	$-0.208178\pi$
$5$	−0.415591	−	0.910017i	−0.185858	−	0.406972i	−0.979509	+	0.201401i	$0.935450\pi$
$6$	0.146148	−	1.01648i	0.0596647	−	0.414977i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	−0.808150	+	1.76960i	−0.269383	+	0.589867i
$10$	0.959899	+	0.281852i	0.303547	+	0.0891294i
$11$	2.43096	+	2.80548i	0.732962	+	0.845883i	0.992802	−	0.119769i	$-0.0382153\pi$
$11$	2.43096	+	2.80548i	0.732962	+	0.845883i	−0.259840	+	0.965652i	$0.583670\pi$
$12$	0.672499	+	0.776106i	0.194134	+	0.224042i
$13$	−0.602728	−	0.176977i	−0.167167	−	0.0490845i	0.197078	−	0.980388i	$-0.436855\pi$
$13$	−0.602728	−	0.176977i	−0.167167	−	0.0490845i	−0.364245	+	0.931303i	$0.618673\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	0.864279	+	0.555438i	0.223156	+	0.143414i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.383528	+	2.66749i	−0.0930191	+	0.646962i	0.888962	+	0.457981i	$0.151427\pi$
$17$	−0.383528	+	2.66749i	−0.0930191	+	0.646962i	−0.981981	+	0.188981i	$0.939482\pi$
$18$	−0.808150	−	1.76960i	−0.190483	−	0.417099i
$19$	0.863363	+	6.00482i	0.198069	+	1.37760i	0.809880	+	0.586596i	$0.199532\pi$
$19$	0.863363	+	6.00482i	0.198069	+	1.37760i	−0.611811	+	0.791004i	$0.709559\pi$
$20$	−0.841610	+	0.540870i	−0.188190	+	0.120942i
$21$	−0.672499	+	0.776106i	−0.146751	+	0.169360i
$22$	−3.71218			−0.791439
$23$	−0.450364	+	4.77464i	−0.0939074	+	0.995581i
$23$	−0.450364	+	4.77464i	−0.0939074	+	0.995581i
$24$	−1.02693			−0.209622
$25$	2.61889	−	3.02236i	0.523778	−	0.604472i
$26$	0.528453	−	0.339616i	0.103638	−	0.0666042i
$27$	−0.722761	−	5.02692i	−0.139095	−	0.967430i
$28$	−0.415415	−	0.909632i	−0.0785061	−	0.171904i
$29$	−0.803521	+	5.58861i	−0.149210	+	1.03778i	0.768306	+	0.640082i	$0.221100\pi$
$29$	−0.803521	+	5.58861i	−0.149210	+	1.03778i	−0.917517	+	0.397697i	$0.869809\pi$
$30$	−0.985754	+	0.289444i	−0.179973	+	0.0528449i
$31$	−6.41092	−	4.12005i	−1.15144	−	0.739983i	−0.181511	−	0.983389i	$-0.558099\pi$
$31$	−6.41092	−	4.12005i	−1.15144	−	0.739983i	−0.969924	+	0.243406i	$0.921735\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−3.65774	−	1.07401i	−0.636732	−	0.186961i
$34$	−1.76480	−	2.03669i	−0.302661	−	0.349289i
$35$	−0.655138	−	0.756070i	−0.110739	−	0.127799i
$36$	1.86660	+	0.548084i	0.311100	+	0.0913473i
$37$	−4.84949	+	10.6189i	−0.797251	+	1.74574i	−0.142634	+	0.989776i	$0.545557\pi$
$37$	−4.84949	+	10.6189i	−0.797251	+	1.74574i	−0.654617	+	0.755960i	$0.727170\pi$
$38$	−5.10352	−	3.27983i	−0.827901	−	0.532059i
$39$	0.618962	−	0.181744i	0.0991133	−	0.0291023i
$40$	0.142375	−	0.990241i	0.0225115	−	0.156571i
$41$	0.800341	+	1.75250i	0.124992	+	0.273695i	0.961775	−	0.273840i	$-0.0882937\pi$
$41$	0.800341	+	1.75250i	0.124992	+	0.273695i	−0.836783	+	0.547535i	$0.815566\pi$
$42$	−0.146148	−	1.01648i	−0.0225511	−	0.156847i
$43$	9.73977	−	6.25937i	1.48530	−	0.954545i	0.488675	−	0.872466i	$-0.337480\pi$
$43$	9.73977	−	6.25937i	1.48530	−	0.954545i	0.996626	−	0.0820794i	$-0.0261561\pi$
$44$	2.43096	−	2.80548i	0.366481	−	0.422941i
$45$	1.94623			0.290127
$46$	−3.31351	−	3.46709i	−0.488550	−	0.511194i
$47$	8.85620			1.29181			0.645905	−	0.763418i	$-0.276480\pi$
$47$	8.85620			1.29181			0.645905	+	0.763418i	$0.276480\pi$
$48$	0.672499	−	0.776106i	0.0970669	−	0.112021i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.569139	+	3.95845i	0.0804884	+	0.559809i
$51$	−1.14967	−	2.51742i	−0.160985	−	0.352509i
$52$	−0.0893984	+	0.621779i	−0.0123973	+	0.0862253i
$53$	−3.99660	+	1.17351i	−0.548976	+	0.161194i	−0.544446	−	0.838796i	$-0.683260\pi$
$53$	−3.99660	+	1.17351i	−0.548976	+	0.161194i	−0.00452965	+	0.999990i	$0.501442\pi$
$54$	4.27240	+	2.74570i	0.581400	+	0.373643i
$55$	1.54275	−	3.37814i	0.208024	−	0.455509i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−4.07976	−	4.70830i	−0.540378	−	0.623629i
$58$	−3.69740	−	4.26703i	−0.485492	−	0.560288i
$59$	9.40573	+	2.76177i	1.22452	+	0.359552i	0.829180	−	0.558982i	$-0.188808\pi$
$59$	9.40573	+	2.76177i	1.22452	+	0.359552i	0.395342	+	0.918534i	$0.370626\pi$
$60$	0.426785	−	0.934529i	0.0550977	−	0.120647i
$61$	−5.57144	−	3.58055i	−0.713350	−	0.458442i	0.132968	−	0.991120i	$-0.457549\pi$
$61$	−5.57144	−	3.58055i	−0.713350	−	0.458442i	−0.846318	+	0.532678i	$0.821186\pi$
$62$	7.31199	−	2.14699i	0.928623	−	0.272668i
$63$	−0.276860	+	1.92560i	−0.0348811	+	0.242603i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.0894362	+	0.622043i	0.0110932	+	0.0771549i
$66$	3.20700	−	2.06101i	0.394754	−	0.253693i
$67$	8.45517	−	9.75779i	1.03296	−	1.19210i	0.0518530	−	0.998655i	$-0.483487\pi$
$67$	8.45517	−	9.75779i	1.03296	−	1.19210i	0.981110	−	0.193449i	$-0.0619673\pi$
$68$	2.69492			0.326807
$69$	−2.26182	−	4.37491i	−0.272291	−	0.526678i
$70$	1.00042			0.119573
$71$	−7.10835	+	8.20348i	−0.843606	+	0.973573i	−0.999900	−	0.0141372i	$-0.995500\pi$
$71$	−7.10835	+	8.20348i	−0.843606	+	0.973573i	0.156294	+	0.987711i	$0.450045\pi$
$72$	−1.63658	+	1.05177i	−0.192873	+	0.123952i
$73$	−0.505139	−	3.51332i	−0.0591221	−	0.411203i	−0.997794	−	0.0663907i	$-0.978852\pi$
$73$	−0.505139	−	3.51332i	−0.0591221	−	0.411203i	0.938672	−	0.344812i	$-0.112057\pi$
$74$	−4.84949	−	10.6189i	−0.563742	−	1.23442i
$75$	−0.584468	+	4.06507i	−0.0674886	+	0.469394i
$76$	5.82083	−	1.70915i	0.667695	−	0.196053i
$77$	3.12288	+	2.00695i	0.355885	+	0.228714i
$78$	−0.267981	+	0.586797i	−0.0303429	+	0.0664417i
$79$	3.68292	+	1.08140i	0.414361	+	0.121667i	0.482267	−	0.876024i	$-0.339814\pi$
$79$	3.68292	+	1.08140i	0.414361	+	0.121667i	−0.0679061	+	0.997692i	$0.521632\pi$
$80$	0.655138	+	0.756070i	0.0732467	+	0.0845312i
$81$	−0.406546	−	0.469180i	−0.0451718	−	0.0521311i
$82$	−1.84857	−	0.542788i	−0.204140	−	0.0599409i
$83$	6.54061	−	14.3219i	0.717925	−	1.57204i	−0.0988652	−	0.995101i	$-0.531521\pi$
$83$	6.54061	−	14.3219i	0.717925	−	1.57204i	0.816790	−	0.576935i	$-0.195751\pi$
$84$	0.863913	+	0.555203i	0.0942606	+	0.0605776i
$85$	2.58686	−	0.759569i	0.280584	−	0.0823869i
$86$	−1.64768	+	11.4598i	−0.177674	+	1.23575i
$87$	−2.40864	−	5.27419i	−0.258234	−	0.565453i
$88$	0.528298	+	3.67439i	0.0563167	+	0.391691i
$89$	−3.53358	+	2.27089i	−0.374558	+	0.240714i	−0.714353	−	0.699786i	$-0.753279\pi$
$89$	−3.53358	+	2.27089i	−0.374558	+	0.240714i	0.339795	+	0.940500i	$0.389642\pi$
$90$	−1.27451	+	1.47086i	−0.134345	+	0.155042i
$91$	−0.628173			−0.0658504
$92$	4.79013	−	0.233722i	0.499406	−	0.0243672i
$93$	7.82594			0.811512
$94$	−5.79958	+	6.69307i	−0.598181	+	0.690337i
$95$	5.10568	−	3.28122i	0.523832	−	0.336646i
$96$	0.146148	+	1.01648i	0.0149162	+	0.103744i
$97$	−3.95761	−	8.66596i	−0.401835	−	0.879895i	−0.997081	−	0.0763517i	$-0.975673\pi$
$97$	−3.95761	−	8.66596i	−0.401835	−	0.879895i	0.595246	−	0.803543i	$-0.297054\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	−6.92916	+	2.03458i	−0.696406	+	0.204483i
$100$	−3.36430	−	2.16211i	−0.336430	−	0.216211i
$101$	−0.102628	+	0.224723i	−0.0102118	+	0.0223608i	−0.914669	−	0.404203i	$-0.867549\pi$
$101$	−0.102628	+	0.224723i	−0.0102118	+	0.0223608i	0.904457	+	0.426564i	$0.140276\pi$
$102$	2.65541	+	0.779698i	0.262924	+	0.0772016i
$103$	−10.0089	−	11.5509i	−0.986206	−	1.13814i	−0.990411	−	0.138151i	$-0.955884\pi$
$103$	−10.0089	−	11.5509i	−0.986206	−	1.13814i	0.00420554	−	0.999991i	$-0.498661\pi$
$104$	−0.411366	−	0.474742i	−0.0403377	−	0.0465522i
$105$	0.985754	+	0.289444i	0.0961998	+	0.0282468i
$106$	1.73034	−	3.78891i	0.168065	−	0.368012i
$107$	7.97532	+	5.12543i	0.771004	+	0.495494i	0.866037	−	0.499980i	$-0.166659\pi$
$107$	7.97532	+	5.12543i	0.771004	+	0.495494i	−0.0950332	+	0.995474i	$0.530296\pi$
$108$	−4.87289	+	1.43081i	−0.468894	+	0.137680i
$109$	−1.03921	+	7.22786i	−0.0995383	+	0.692304i	0.877552	+	0.479481i	$0.159175\pi$
$109$	−1.03921	+	7.22786i	−0.0995383	+	0.692304i	−0.977091	+	0.212823i	$0.931734\pi$
$110$	1.54275	+	3.37814i	0.147095	+	0.322093i
$111$	−1.70611	−	11.8662i	−0.161937	−	1.12629i
$112$	−0.841254	+	0.540641i	−0.0794910	+	0.0510858i
$113$	1.63373	−	1.88543i	0.153688	−	0.177366i	−0.673684	−	0.739019i	$-0.735289\pi$
$113$	1.63373	−	1.88543i	0.153688	−	0.177366i	0.827373	+	0.561654i	$0.189835\pi$
$114$	6.22997			0.583490
$115$	4.53217	−	1.57446i	0.422627	−	0.146819i
$116$	5.64608			0.524226
$117$	0.800273	−	0.923565i	0.0739853	−	0.0853836i
$118$	−8.24665	+	5.29980i	−0.759166	+	0.487886i
$119$	0.383528	+	2.66749i	0.0351579	+	0.244529i
$120$	0.426785	+	0.934529i	0.0389600	+	0.0853104i
$121$	−0.395671	+	2.75195i	−0.0359701	+	0.250178i
$122$	6.35452	−	1.86585i	0.575311	−	0.168927i
$123$	−1.66442	−	1.06966i	−0.150076	−	0.0964478i
$124$	−3.16574	+	6.93201i	−0.284292	+	0.622513i
$125$	−8.63828	−	2.53643i	−0.772631	−	0.226865i
$126$	−1.27397	−	1.47024i	−0.113494	−	0.130979i
$127$	−2.68268	−	3.09598i	−0.238049	−	0.274723i	0.624137	−	0.781315i	$-0.285451\pi$
$127$	−2.68268	−	3.09598i	−0.238049	−	0.274723i	−0.862186	+	0.506592i	$0.830905\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	−4.93909	+	10.8151i	−0.434863	+	0.952216i
$130$	−0.528677	−	0.339760i	−0.0463680	−	0.0297989i
$131$	−20.0289	+	5.88100i	−1.74993	+	0.513826i	−0.990589	−	0.136868i	$-0.956296\pi$
$131$	−20.0289	+	5.88100i	−1.74993	+	0.513826i	−0.759340	+	0.650694i	$0.774478\pi$
$132$	−0.542527	+	3.77336i	−0.0472210	+	0.328429i
$133$	2.52014	+	5.51834i	0.218524	+	0.478501i
$134$	1.83748	+	12.7800i	0.158734	+	1.10402i
$135$	−4.27421	+	2.74687i	−0.367865	+	0.236413i
$136$	−1.76480	+	2.03669i	−0.151330	+	0.174644i
$137$	−6.96097			−0.594716			−0.297358	−	0.954766i	$-0.596106\pi$
$137$	−6.96097			−0.594716			−0.297358	+	0.954766i	$0.596106\pi$
$138$	4.78752	+	1.15559i	0.407540	+	0.0983705i
$139$	13.6054			1.15400			0.576998	−	0.816746i	$-0.304224\pi$
$139$	13.6054			1.15400			0.576998	+	0.816746i	$0.304224\pi$
$140$	−0.655138	+	0.756070i	−0.0553693	+	0.0638996i
$141$	−7.65098	+	4.91699i	−0.644329	+	0.414085i
$142$	−1.54479	−	10.7443i	−0.129636	−	0.901639i
$143$	−0.968702	−	2.12116i	−0.0810069	−	0.177380i
$144$	0.276860	−	1.92560i	0.0230717	−	0.160467i
$145$	5.41967	−	1.59136i	0.450079	−	0.132155i
$146$	2.98599	+	1.91898i	0.247122	+	0.158816i
$147$	−0.426604	+	0.934133i	−0.0351857	+	0.0770460i
$148$	11.2010	+	3.28890i	0.920714	+	0.270346i
$149$	3.06316	+	3.53508i	0.250944	+	0.289605i	0.867220	−	0.497926i	$-0.165905\pi$
$149$	3.06316	+	3.53508i	0.250944	+	0.289605i	−0.616276	+	0.787530i	$0.711359\pi$
$150$	−2.68943	−	3.10376i	−0.219591	−	0.253421i
$151$	−0.109257	−	0.0320808i	−0.00889123	−	0.00261070i	0.277284	−	0.960788i	$-0.410566\pi$
$151$	−0.109257	−	0.0320808i	−0.00889123	−	0.00261070i	−0.286175	+	0.958177i	$0.592384\pi$
$152$	−2.52014	+	5.51834i	−0.204411	+	0.447597i
$153$	−4.41045	−	2.83443i	−0.356564	−	0.229150i
$154$	−3.56181	+	1.04584i	−0.287019	+	0.0842763i
$155$	−1.08499	+	7.54631i	−0.0871489	+	0.606134i
$156$	−0.267981	−	0.586797i	−0.0214557	−	0.0469814i
$157$	0.893472	+	6.21423i	0.0713068	+	0.495950i	0.993910	+	0.110198i	$0.0351486\pi$
$157$	0.893472	+	6.21423i	0.0713068	+	0.495950i	−0.922603	+	0.385751i	$0.873942\pi$
$158$	−3.22907	+	2.07520i	−0.256891	+	0.165094i
$159$	2.80118	−	3.23273i	0.222148	−	0.256372i
$160$	−1.00042			−0.0790904
$161$	0.913050	+	4.70811i	0.0719584	+	0.371051i
$162$	0.620814			0.0487757
$163$	−1.90951	+	2.20369i	−0.149565	+	0.172607i	−0.825588	−	0.564273i	$-0.809156\pi$
$163$	−1.90951	+	2.20369i	−0.149565	+	0.172607i	0.676023	+	0.736880i	$0.263702\pi$
$164$	1.62076	−	1.04160i	0.126560	−	0.0813355i
$165$	0.542757	+	3.77496i	0.0422536	+	0.293880i
$166$	6.54061	+	14.3219i	0.507649	+	1.11160i
$167$	0.472372	−	3.28542i	0.0365533	−	0.254234i	−0.963348	−	0.268253i	$-0.913554\pi$
$167$	0.472372	−	3.28542i	0.0365533	−	0.254234i	0.999902	+	0.0140196i	$0.00446273\pi$
$168$	−0.985337	+	0.289321i	−0.0760204	+	0.0223216i
$169$	−10.6043	−	6.81499i	−0.815718	−	0.524230i
$170$	−1.11999	+	2.45243i	−0.0858990	+	0.188093i
$171$	−11.3239	−	3.32499i	−0.865958	−	0.254268i
$172$	−7.58177	−	8.74983i	−0.578105	−	0.667169i
$173$	−0.795134	−	0.917633i	−0.0604529	−	0.0697664i	0.724718	−	0.689046i	$-0.241970\pi$
$173$	−0.795134	−	0.917633i	−0.0604529	−	0.0697664i	−0.785171	+	0.619280i	$0.787425\pi$
$174$	5.56329	+	1.63353i	0.421752	+	0.123838i
$175$	1.66131	−	3.63776i	0.125583	−	0.274989i
$176$	−3.12288	−	2.00695i	−0.235396	−	0.151280i
$177$	−9.65907	+	2.83616i	−0.726020	+	0.213179i
$178$	0.597775	−	4.15762i	0.0448051	−	0.311627i
$179$	7.09306	+	15.5316i	0.530160	+	1.16089i	0.965448	+	0.260597i	$0.0839195\pi$
$179$	7.09306	+	15.5316i	0.530160	+	1.16089i	−0.435287	+	0.900292i	$0.643353\pi$
$180$	−0.276977	−	1.92642i	−0.0206447	−	0.143587i
$181$	7.53564	−	4.84286i	0.560120	−	0.359967i	−0.229743	−	0.973251i	$-0.573788\pi$
$181$	7.53564	−	4.84286i	0.560120	−	0.359967i	0.789862	+	0.613284i	$0.210152\pi$
$182$	0.411366	−	0.474742i	0.0304925	−	0.0351902i
$183$	6.80117			0.502757
$184$	−2.96023	+	3.77320i	−0.218231	+	0.278164i
$185$	11.6788			0.858641
$186$	−5.12490	+	5.91445i	−0.375776	+	0.433669i
$187$	−8.41593	+	5.40859i	−0.615433	+	0.395515i
$188$	−1.26037	−	8.76605i	−0.0919218	−	0.639330i
$189$	−2.10973	−	4.61966i	−0.153460	−	0.336031i
$190$	−0.863728	+	6.00736i	−0.0626614	+	0.435820i
$191$	9.87341	−	2.89910i	0.714415	−	0.209771i	0.0957266	−	0.995408i	$-0.469483\pi$
$191$	9.87341	−	2.89910i	0.714415	−	0.209771i	0.618688	+	0.785636i	$0.287664\pi$
$192$	−0.863913	−	0.555203i	−0.0623475	−	0.0400683i
$193$	3.28284	−	7.18842i	0.236304	−	0.517434i	−0.753912	−	0.656975i	$-0.771836\pi$
$193$	3.28284	−	7.18842i	0.236304	−	0.517434i	0.990216	+	0.139541i	$0.0445629\pi$
$194$	9.14098	+	2.68403i	0.656284	+	0.192702i
$195$	−0.422625	−	0.487735i	−0.0302648	−	0.0349274i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	4.79203	+	1.40707i	0.341418	+	0.100249i	0.447947	−	0.894060i	$-0.352155\pi$
$197$	4.79203	+	1.40707i	0.341418	+	0.100249i	−0.106529	+	0.994310i	$0.533974\pi$
$198$	3.00000	−	6.56908i	0.213200	−	0.466844i
$199$	−1.27408	−	0.818800i	−0.0903170	−	0.0580432i	0.494703	−	0.869062i	$-0.335277\pi$
$199$	−1.27408	−	0.818800i	−0.0903170	−	0.0580432i	−0.585020	+	0.811019i	$0.698913\pi$
$200$	3.83716	−	1.12669i	0.271328	−	0.0796691i
$201$	−1.88698	+	13.1242i	−0.133097	+	0.925710i
$202$	−0.102628	−	0.224723i	−0.00722085	−	0.0158115i
$203$	0.803521	+	5.58861i	0.0563962	+	0.392244i
$204$	−2.32818	+	1.49623i	−0.163005	+	0.104757i
$205$	1.26219	−	1.45665i	0.0881554	−	0.101737i
$206$	15.2840			1.06489
$207$	−8.08525	−	4.65559i	−0.561964	−	0.323586i
$208$	0.628173			0.0435560
$209$	−14.7476	+	17.0196i	−1.02011	+	1.17727i
$210$	−0.864279	+	0.555438i	−0.0596409	+	0.0383289i
$211$	1.65544	+	11.5138i	0.113965	+	0.792646i	0.963997	+	0.265914i	$0.0856737\pi$
$211$	1.65544	+	11.5138i	0.113965	+	0.792646i	−0.850032	+	0.526732i	$0.823417\pi$
$212$	1.73034	+	3.78891i	0.118840	+	0.260224i
$213$	1.58640	−	11.0337i	0.108698	−	0.756014i
$214$	−9.09627	+	2.67091i	−0.621808	+	0.182579i
$215$	−9.74390	−	6.26202i	−0.664528	−	0.427066i
$216$	2.10973	−	4.61966i	0.143549	−	0.314328i
$217$	−7.31199	−	2.14699i	−0.496370	−	0.145747i
$218$	−4.78192	−	5.51863i	−0.323872	−	0.373769i
$219$	2.38700	+	2.75475i	0.161299	+	0.186149i
$220$	−3.56332	−	1.04628i	−0.240239	−	0.0705405i
$221$	0.703247	−	1.53990i	0.0473055	−	0.103585i
$222$	10.0852	+	6.48135i	0.676873	+	0.435000i
$223$	−22.6402	+	6.64777i	−1.51610	+	0.445168i	−0.930764	−	0.365622i	$-0.880856\pi$
$223$	−22.6402	+	6.64777i	−1.51610	+	0.445168i	−0.585338	+	0.810789i	$0.699038\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	3.23192	+	7.07691i	0.215461	+	0.471794i
$226$	0.355044	+	2.46938i	0.0236171	+	0.164261i
$227$	10.3377	−	6.64362i	0.686136	−	0.440953i	−0.150574	−	0.988599i	$-0.548112\pi$
$227$	10.3377	−	6.64362i	0.686136	−	0.440953i	0.836710	+	0.547646i	$0.184476\pi$
$228$	−4.07976	+	4.70830i	−0.270189	+	0.311815i
$229$	14.2463			0.941420			0.470710	−	0.882288i	$-0.343998\pi$
$229$	14.2463			0.941420			0.470710	+	0.882288i	$0.343998\pi$
$230$	−1.77805	+	4.45624i	−0.117241	+	0.293836i
$231$	−3.81216			−0.250822
$232$	−3.69740	+	4.26703i	−0.242746	+	0.280144i
$233$	13.3690	−	8.59174i	0.875833	−	0.562864i	−0.0236988	−	0.999719i	$-0.507544\pi$
$233$	13.3690	−	8.59174i	0.875833	−	0.562864i	0.899532	+	0.436856i	$0.143908\pi$
$234$	0.173916	+	1.20961i	0.0113692	+	0.0790748i
$235$	−3.68056	−	8.05929i	−0.240093	−	0.525730i
$236$	1.39509	−	9.70303i	0.0908123	−	0.631614i
$237$	−3.78212	+	1.11053i	−0.245675	+	0.0721366i
$238$	−2.26711	−	1.45699i	−0.146955	−	0.0944423i
$239$	4.34784	−	9.52044i	0.281238	−	0.615826i	−0.715313	−	0.698804i	$-0.753716\pi$
$239$	4.34784	−	9.52044i	0.281238	−	0.615826i	0.996551	+	0.0829781i	$0.0264431\pi$
$240$	−0.985754	−	0.289444i	−0.0636302	−	0.0186835i
$241$	7.18777	+	8.29513i	0.463005	+	0.534336i	0.938453	−	0.345408i	$-0.112259\pi$
$241$	7.18777	+	8.29513i	0.463005	+	0.534336i	−0.475448	+	0.879744i	$0.657714\pi$
$242$	−1.82068	−	2.10118i	−0.117038	−	0.135069i
$243$	15.2304	+	4.47204i	0.977029	+	0.286882i
$244$	−2.75120	+	6.02430i	−0.176128	+	0.385666i
$245$	−0.841610	−	0.540870i	−0.0537685	−	0.0345549i
$246$	1.89836	−	0.557408i	0.121035	−	0.0355390i
$247$	0.542341	−	3.77207i	0.0345083	−	0.240011i
$248$	−3.16574	−	6.93201i	−0.201025	−	0.440183i
$249$	2.30107	+	16.0043i	0.145824	+	1.01423i
$250$	7.57378	−	4.86737i	0.479008	−	0.307840i
$251$	11.7293	−	13.5363i	0.740346	−	0.854405i	−0.253249	−	0.967401i	$-0.581499\pi$
$251$	11.7293	−	13.5363i	0.740346	−	0.854405i	0.993595	+	0.112996i	$0.0360448\pi$
$252$	1.94540			0.122549
$253$	−14.4899	+	10.3435i	−0.910975	+	0.650288i
$254$	4.09656			0.257041
$255$	−1.81310	+	2.09243i	−0.113541	+	0.131033i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−3.68492	−	25.6292i	−0.229859	−	1.59870i	−0.698696	−	0.715419i	$-0.746236\pi$
$257$	−3.68492	−	25.6292i	−0.229859	−	1.59870i	0.468837	−	0.883285i	$-0.344673\pi$
$258$	−4.93909	−	10.8151i	−0.307494	−	0.673319i
$259$	−1.66136	+	11.5550i	−0.103232	+	0.717994i
$260$	0.602983	−	0.177052i	0.0373954	−	0.0109803i
$261$	−9.24026	−	5.93835i	−0.571958	−	0.367575i
$262$	8.67155	−	18.9880i	0.535730	−	1.17308i
$263$	1.89958	+	0.557766i	0.117133	+	0.0343933i	0.339774	−	0.940507i	$-0.389650\pi$
$263$	1.89958	+	0.557766i	0.117133	+	0.0343933i	−0.222641	+	0.974901i	$0.571468\pi$
$264$	−2.49644	−	2.88104i	−0.153645	−	0.177316i
$265$	2.72886	+	3.14928i	0.167633	+	0.193459i
$266$	−5.82083	−	1.70915i	−0.356898	−	0.104795i
$267$	1.79190	−	3.92370i	0.109662	−	0.240127i
$268$	−10.8618	−	6.98043i	−0.663488	−	0.426398i
$269$	2.96321	−	0.870077i	0.180670	−	0.0530495i	−0.190146	−	0.981756i	$-0.560896\pi$
$269$	2.96321	−	0.870077i	0.180670	−	0.0530495i	0.370816	+	0.928706i	$0.379078\pi$
$270$	0.723068	−	5.02905i	0.0440045	−	0.306058i
$271$	−4.96415	−	10.8700i	−0.301551	−	0.660304i	0.696827	−	0.717239i	$-0.254594\pi$
$271$	−4.96415	−	10.8700i	−0.301551	−	0.660304i	−0.998378	+	0.0569350i	$0.981867\pi$
$272$	−0.383528	−	2.66749i	−0.0232548	−	0.161741i
$273$	0.542687	−	0.348764i	0.0328449	−	0.0211081i
$274$	4.55847	−	5.26075i	0.275387	−	0.317814i
$275$	14.8456			0.895221
$276$	−4.00849	+	2.86141i	−0.241283	+	0.172237i
$277$	23.7183			1.42509			0.712547	−	0.701624i	$-0.247542\pi$
$277$	23.7183			1.42509			0.712547	+	0.701624i	$0.247542\pi$
$278$	−8.90965	+	10.2823i	−0.534365	+	0.616690i
$279$	12.4718	−	8.01516i	0.746669	−	0.479855i
$280$	−0.142375	−	0.990241i	−0.00850854	−	0.0591782i
$281$	−12.5007	−	27.3728i	−0.745732	−	1.63293i	−0.773889	−	0.633322i	$-0.781691\pi$
$281$	−12.5007	−	27.3728i	−0.745732	−	1.63293i	0.0281566	−	0.999604i	$-0.491036\pi$
$282$	1.29432	−	9.00217i	0.0770754	−	0.536071i
$283$	−15.2336	+	4.47298i	−0.905541	+	0.265891i	−0.701163	−	0.713001i	$-0.747335\pi$
$283$	−15.2336	+	4.47298i	−0.905541	+	0.265891i	−0.204378	+	0.978892i	$0.565517\pi$
$284$	9.13160	+	5.86852i	0.541861	+	0.348233i
$285$	−2.58912	+	5.66938i	−0.153366	+	0.335825i
$286$	2.23743	+	0.656969i	0.132302	+	0.0388474i
$287$	1.26166	+	1.45603i	0.0744734	+	0.0859469i
$288$	1.27397	+	1.47024i	0.0750694	+	0.0866347i
$289$	9.34296	+	2.74334i	0.549586	+	0.161373i
$290$	−2.34646	+	5.13803i	−0.137789	+	0.301716i
$291$	8.23040	+	5.28935i	0.482474	+	0.310067i
$292$	−3.40567	+	0.999995i	−0.199302	+	0.0585203i
$293$	−4.35297	+	30.2756i	−0.254303	+	1.76872i	0.317434	+	0.948280i	$0.397179\pi$
$293$	−4.35297	+	30.2756i	−0.254303	+	1.76872i	−0.571738	+	0.820437i	$0.693730\pi$
$294$	−0.426604	−	0.934133i	−0.0248801	−	0.0544797i
$295$	−1.39568	−	9.70714i	−0.0812594	−	0.565172i
$296$	−9.82066	+	6.31135i	−0.570814	+	0.366840i
$297$	12.3459	−	14.2479i	0.716381	−	0.826748i
$298$	−4.67758			−0.270965
$299$	1.11645	−	2.79810i	0.0645658	−	0.161818i
$300$	4.10687			0.237110
$301$	7.58177	−	8.74983i	0.437006	−	0.504332i
$302$	0.0957933	−	0.0615626i	0.00551229	−	0.00354253i
$303$	−0.0361056	−	0.251120i	−0.00207421	−	0.0144265i
$304$	−2.52014	−	5.51834i	−0.144540	−	0.316499i
$305$	−0.942920	+	6.55815i	−0.0539914	+	0.375519i
$306$	5.03035	−	1.47704i	0.287566	−	0.0844370i
$307$	26.4435	+	16.9942i	1.50921	+	0.969911i	0.993584	+	0.113097i	$0.0360772\pi$
$307$	26.4435	+	16.9942i	1.50921	+	0.969911i	0.515627	+	0.856813i	$0.327559\pi$
$308$	1.54209	−	3.37671i	0.0878690	−	0.192406i
$309$	15.0599	+	4.42198i	0.856727	+	0.251558i
$310$	−4.99260	−	5.76176i	−0.283560	−	0.327246i
$311$	12.5433	+	14.4758i	0.711266	+	0.820845i	0.990228	−	0.139457i	$-0.0445357\pi$
$311$	12.5433	+	14.4758i	0.711266	+	0.820845i	−0.278962	+	0.960302i	$0.589990\pi$
$312$	0.618962	+	0.181744i	0.0350418	+	0.0102892i
$313$	10.4896	−	22.9691i	0.592909	−	1.29829i	−0.340759	−	0.940151i	$-0.610684\pi$
$313$	10.4896	−	22.9691i	0.592909	−	1.29829i	0.933668	−	0.358139i	$-0.116589\pi$
$314$	−5.28150	−	3.39422i	−0.298052	−	0.191547i
$315$	1.86739	−	0.548316i	0.105216	−	0.0308941i
$316$	0.546261	−	3.79933i	0.0307296	−	0.213729i
$317$	−6.42647	−	14.0720i	−0.360946	−	0.790362i	−0.999779	−	0.0210165i	$-0.993310\pi$
$317$	−6.42647	−	14.0720i	−0.360946	−	0.790362i	0.638833	−	0.769346i	$-0.279418\pi$
$318$	0.608755	+	4.23398i	0.0341373	+	0.237430i
$319$	−17.6321	+	11.3314i	−0.987205	+	0.634438i
$320$	0.655138	−	0.756070i	0.0366233	−	0.0422656i
$321$	−9.73564			−0.543390
$322$	−4.15608	−	2.39312i	−0.231609	−	0.133363i
$323$	−16.3489			−0.909679
$324$	−0.406546	+	0.469180i	−0.0225859	+	0.0260655i
$325$	−2.11336	+	1.35818i	−0.117228	+	0.0753381i
$326$	−0.414977	−	2.88623i	−0.0229834	−	0.159853i
$327$	−3.11514	−	6.82122i	−0.172268	−	0.377214i
$328$	−0.274185	+	1.90700i	−0.0151393	+	0.105296i
$329$	8.49746	−	2.49508i	0.468480	−	0.137558i
$330$	−3.20835	−	2.06188i	−0.176614	−	0.113503i
$331$	4.57503	−	10.0179i	0.251466	−	0.550634i	−0.741233	−	0.671247i	$-0.765759\pi$
$331$	4.57503	−	10.0179i	0.251466	−	0.550634i	0.992700	+	0.120613i	$0.0384861\pi$
$332$	−15.1070	−	4.43581i	−0.829103	−	0.243447i
$333$	−14.8721	−	17.1633i	−0.814987	−	0.940545i
$334$	2.17362	+	2.50849i	0.118935	+	0.137258i
$335$	−12.3936	−	3.63910i	−0.677137	−	0.198825i
$336$	0.426604	−	0.934133i	0.0232732	−	0.0509611i
$337$	6.55608	+	4.21334i	0.357133	+	0.229515i	0.706887	−	0.707326i	$-0.250099\pi$
$337$	6.55608	+	4.21334i	0.357133	+	0.229515i	−0.349755	+	0.936841i	$0.613735\pi$
$338$	12.0948	−	3.55135i	0.657870	−	0.193168i
$339$	−0.364607	+	2.53589i	−0.0198027	+	0.137731i
$340$	−1.11999	−	2.45243i	−0.0607398	−	0.133002i
$341$	−4.02599	−	28.0014i	−0.218019	−	1.51636i
$342$	9.92841	−	6.38060i	0.536867	−	0.345024i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	11.5777			0.624227
$345$	−3.04126	+	3.87647i	−0.163736	+	0.208702i
$346$	1.21420			0.0652759
$347$	−6.33124	+	7.30664i	−0.339879	+	0.392241i	−0.899798	−	0.436306i	$-0.856287\pi$
$347$	−6.33124	+	7.30664i	−0.339879	+	0.392241i	0.559920	+	0.828547i	$0.310832\pi$
$348$	−4.87772	+	3.13472i	−0.261473	+	0.168039i
$349$	4.09504	+	28.4816i	0.219202	+	1.52459i	0.740993	+	0.671513i	$0.234355\pi$
$349$	4.09504	+	28.4816i	0.219202	+	1.52459i	−0.521790	+	0.853074i	$0.674736\pi$
$350$	1.66131	+	3.63776i	0.0888007	+	0.194446i
$351$	−0.454019	+	3.15777i	−0.0242338	+	0.168549i
$352$	3.56181	−	1.04584i	0.189845	−	0.0557435i
$353$	−10.9900	−	7.06285i	−0.584939	−	0.375918i	0.214447	−	0.976736i	$-0.431205\pi$
$353$	−10.9900	−	7.06285i	−0.584939	−	0.375918i	−0.799386	+	0.600818i	$0.794842\pi$
$354$	4.18192	−	9.15713i	0.222267	−	0.486696i
$355$	10.4195	+	3.05943i	0.553008	+	0.162378i
$356$	2.75066	+	3.17443i	0.145785	+	0.168244i
$357$	−1.81233	−	2.09155i	−0.0959189	−	0.110696i
$358$	−16.3830	−	4.81048i	−0.865868	−	0.254242i
$359$	−6.25561	+	13.6979i	−0.330158	+	0.722946i	−0.999805	−	0.0197336i	$-0.993718\pi$
$359$	−6.25561	+	13.6979i	−0.330158	+	0.722946i	0.669647	+	0.742680i	$0.266445\pi$
$360$	1.63727	+	1.05221i	0.0862918	+	0.0554564i
$361$	−17.0821	+	5.01575i	−0.899057	+	0.263987i
$362$	−1.27480	+	8.86645i	−0.0670022	+	0.466010i
$363$	−1.18607	−	2.59713i	−0.0622524	−	0.136314i
$364$	0.0893984	+	0.621779i	0.00468575	+	0.0325901i
$365$	−2.98725	+	1.91979i	−0.156360	+	0.100486i
$366$	−4.45382	+	5.13998i	−0.232805	+	0.268671i
$367$	33.2066			1.73337			0.866685	−	0.498857i	$-0.166247\pi$
$367$	33.2066			1.73337			0.866685	+	0.498857i	$0.166247\pi$
$368$	−0.913050	−	4.70811i	−0.0475960	−	0.245427i
$369$	−3.74803			−0.195115
$370$	−7.64798	+	8.82624i	−0.397599	+	0.458854i
$371$	−3.50410	+	2.25195i	−0.181924	+	0.116915i
$372$	−1.11375	−	7.74628i	−0.0577451	−	0.401626i
$373$	−10.1245	−	22.1695i	−0.524226	−	1.14790i	−0.967815	−	0.251664i	$-0.919022\pi$
$373$	−10.1245	−	22.1695i	−0.524226	−	1.14790i	0.443588	−	0.896231i	$-0.353705\pi$
$374$	1.42372	−	9.90220i	0.0736189	−	0.512031i
$375$	8.87095	−	2.60475i	0.458094	−	0.134509i
$376$	7.45031	+	4.78802i	0.384220	+	0.246923i
$377$	1.47336	−	3.22621i	0.0758819	−	0.166158i
$378$	4.87289	+	1.43081i	0.250634	+	0.0735929i
$379$	−0.487499	−	0.562603i	−0.0250411	−	0.0288990i	0.743091	−	0.669191i	$-0.233359\pi$
$379$	−0.487499	−	0.562603i	−0.0250411	−	0.0288990i	−0.768132	+	0.640292i	$0.778814\pi$
$380$	−3.97444	−	4.58675i	−0.203884	−	0.235295i
$381$	4.03649	+	1.18522i	0.206796	+	0.0607207i
$382$	−4.27472	+	9.36033i	−0.218714	+	0.478916i
$383$	3.33902	+	2.14586i	0.170616	+	0.109648i	0.623162	−	0.782093i	$-0.285848\pi$
$383$	3.33902	+	2.14586i	0.170616	+	0.109648i	−0.452546	+	0.891741i	$0.649484\pi$
$384$	0.985337	−	0.289321i	0.0502828	−	0.0147644i
$385$	0.528522	−	3.67595i	0.0269360	−	0.187344i
$386$	3.28284	+	7.18842i	0.167092	+	0.365881i
$387$	3.20540	+	22.2940i	0.162940	+	1.13327i
$388$	−8.01453	+	5.15062i	−0.406876	+	0.261483i
$389$	2.95708	−	3.41266i	0.149930	−	0.173029i	−0.675816	−	0.737070i	$-0.736209\pi$
$389$	2.95708	−	3.41266i	0.149930	−	0.173029i	0.825746	+	0.564041i	$0.190754\pi$
$390$	0.645366			0.0326794
$391$	−12.5636	−	3.03255i	−0.635368	−	0.153363i
$392$	1.00000			0.0505076
$393$	14.0380	−	16.2008i	0.708125	−	0.817220i
$394$	−4.20150	+	2.70014i	−0.211669	+	0.136031i
$395$	−0.546493	−	3.80094i	−0.0274970	−	0.191246i
$396$	3.00000	+	6.56908i	0.150756	+	0.330108i
$397$	−4.49133	+	31.2379i	−0.225413	+	1.56779i	0.491660	+	0.870787i	$0.336390\pi$
$397$	−4.49133	+	31.2379i	−0.225413	+	1.56779i	−0.717073	+	0.696998i	$0.754519\pi$
$398$	1.45315	−	0.426684i	0.0728399	−	0.0213877i
$399$	−5.24098	−	3.36818i	−0.262377	−	0.168620i
$400$	−1.66131	+	3.63776i	−0.0830654	+	0.181888i
$401$	−6.18685	−	1.81662i	−0.308957	−	0.0907179i	0.123579	−	0.992335i	$-0.460563\pi$
$401$	−6.18685	−	1.81662i	−0.308957	−	0.0907179i	−0.432536	+	0.901617i	$0.642381\pi$
$402$	−8.68291	−	10.0206i	−0.433064	−	0.499783i
$403$	3.13489	+	3.61785i	0.156160	+	0.180218i
$404$	0.237041	+	0.0696016i	0.0117932	+	0.00346281i
$405$	−0.258005	+	0.564951i	−0.0128203	+	0.0280726i
$406$	−4.74979	−	3.05250i	−0.235728	−	0.151493i
$407$	−41.5800	+	12.2090i	−2.06104	+	0.605177i
$408$	0.393858	−	2.73934i	0.0194989	−	0.135618i
$409$	11.5919	+	25.3828i	0.573183	+	1.25510i	0.945085	+	0.326824i	$0.105979\pi$
$409$	11.5919	+	25.3828i	0.573183	+	1.25510i	−0.371902	+	0.928272i	$0.621294\pi$
$410$	0.274301	+	1.90780i	0.0135468	+	0.0942197i
$411$	6.01367	−	3.86475i	0.296633	−	0.190634i
$412$	−10.0089	+	11.5509i	−0.493103	+	0.569071i
$413$	9.80281			0.482365
$414$	8.81317	−	3.06166i	0.433144	−	0.150472i
$415$	−15.7514			−0.773207
$416$	−0.411366	+	0.474742i	−0.0201689	+	0.0232761i
$417$	−11.7539	+	7.55376i	−0.575590	+	0.369909i
$418$	−3.20495	−	22.2909i	−0.156759	−	1.09029i
$419$	0.456772	+	1.00019i	0.0223148	+	0.0488625i	0.920461	−	0.390834i	$-0.127813\pi$
$419$	0.456772	+	1.00019i	0.0223148	+	0.0488625i	−0.898146	+	0.439696i	$0.855086\pi$
$420$	0.146210	−	1.01691i	0.00713432	−	0.0496203i
$421$	19.8417	−	5.82605i	0.967025	−	0.283944i	0.240167	−	0.970732i	$-0.422798\pi$
$421$	19.8417	−	5.82605i	0.967025	−	0.283944i	0.726858	+	0.686787i	$0.240980\pi$
$422$	−9.78566	−	6.28886i	−0.476359	−	0.306137i
$423$	−7.15714	+	15.6719i	−0.347992	+	0.761996i
$424$	−3.99660	−	1.17351i	−0.194092	−	0.0569906i
$425$	7.05770	+	8.14502i	0.342349	+	0.395092i
$426$	7.29981	+	8.42444i	0.353677	+	0.408165i
$427$	−6.35452	−	1.86585i	−0.307517	−	0.0902950i
$428$	3.93825	−	8.62357i	0.190363	−	0.416836i
$429$	2.01455	+	1.29467i	0.0972633	+	0.0625074i
$430$	11.1134	−	3.26319i	0.535937	−	0.157365i
$431$	3.57624	−	24.8733i	0.172261	−	1.19810i	−0.701831	−	0.712343i	$-0.747634\pi$
$431$	3.57624	−	24.8733i	0.172261	−	1.19810i	0.874092	−	0.485760i	$-0.161457\pi$
$432$	2.10973	+	4.61966i	0.101504	+	0.222264i
$433$	4.75882	+	33.0983i	0.228694	+	1.59060i	0.703619	+	0.710577i	$0.251566\pi$
$433$	4.75882	+	33.0983i	0.228694	+	1.59060i	−0.474925	+	0.880026i	$0.657525\pi$
$434$	6.41092	−	4.12005i	0.307734	−	0.197769i
$435$	−3.79860	+	4.38381i	−0.182129	+	0.210188i
$436$	7.30219			0.349711
$437$	−29.0597	+	1.41789i	−1.39011	+	0.0678268i
$438$	−3.64505			−0.174167
$439$	−2.83105	+	3.26721i	−0.135119	+	0.155935i	−0.819276	−	0.573399i	$-0.805625\pi$
$439$	−2.83105	+	3.26721i	−0.135119	+	0.155935i	0.684158	+	0.729334i	$0.260170\pi$
$440$	3.12420	−	2.00780i	0.148941	−	0.0957183i
$441$	0.276860	+	1.92560i	0.0131838	+	0.0916954i
$442$	0.703247	+	1.53990i	0.0334501	+	0.0732454i
$443$	−3.58098	+	24.9062i	−0.170137	+	1.18333i	0.708454	+	0.705757i	$0.249393\pi$
$443$	−3.58098	+	24.9062i	−0.170137	+	1.18333i	−0.878591	+	0.477574i	$0.841516\pi$
$444$	−11.5027	+	3.37749i	−0.545892	+	0.160288i
$445$	3.53507	+	2.27185i	0.167579	+	0.107696i
$446$	9.80215	−	21.4637i	0.464145	−	1.01634i
$447$	−4.60899	−	1.35332i	−0.217998	−	0.0640099i
$448$	0.654861	+	0.755750i	0.0309393	+	0.0357058i
$449$	17.5896	+	20.2995i	0.830107	+	0.957994i	0.999621	−	0.0275337i	$-0.00876535\pi$
$449$	17.5896	+	20.2995i	0.830107	+	0.957994i	−0.169514	+	0.985528i	$0.554220\pi$
$450$	−7.46483	−	2.19187i	−0.351895	−	0.103326i
$451$	−2.97101	+	6.50560i	−0.139899	+	0.306337i
$452$	−2.09874	−	1.34878i	−0.0987163	−	0.0634411i
$453$	0.112200	−	0.0329449i	0.00527162	−	0.00154789i
$454$	−1.74883	+	12.1633i	−0.0820764	+	0.570854i
$455$	0.261063	+	0.571648i	0.0122388	+	0.0267993i
$456$	−0.886617	−	6.16656i	−0.0415197	−	0.288776i
$457$	10.3411	−	6.64585i	0.483738	−	0.310880i	−0.275945	−	0.961174i	$-0.588991\pi$
$457$	10.3411	−	6.64585i	0.483738	−	0.310880i	0.759683	+	0.650294i	$0.225354\pi$
$458$	−9.32932	+	10.7666i	−0.435931	+	0.503091i
$459$	13.6865			0.638829
$460$	−2.20343	−	4.26197i	−0.102735	−	0.198715i
$461$	−18.3750			−0.855810			−0.427905	−	0.903824i	$-0.640748\pi$
$461$	−18.3750			−0.855810			−0.427905	+	0.903824i	$0.640748\pi$
$462$	2.49644	−	2.88104i	0.116145	−	0.134038i
$463$	23.1000	−	14.8454i	1.07355	−	0.689926i	0.120488	−	0.992715i	$-0.461554\pi$
$463$	23.1000	−	14.8454i	1.07355	−	0.689926i	0.953058	+	0.302788i	$0.0979176\pi$
$464$	−0.803521	−	5.58861i	−0.0373025	−	0.259445i
$465$	−3.25239	−	7.12174i	−0.150826	−	0.330263i
$466$	−2.26163	+	15.7300i	−0.104768	+	0.728679i
$467$	−30.0494	+	8.82331i	−1.39052	+	0.408294i	−0.889419	−	0.457093i	$-0.848891\pi$
$467$	−30.0494	+	8.82331i	−1.39052	+	0.408294i	−0.501103	+	0.865387i	$0.667072\pi$
$468$	−1.02805	−	0.660691i	−0.0475218	−	0.0305404i
$469$	5.36359	−	11.7446i	0.247668	−	0.542316i
$470$	8.50106	+	2.49614i	0.392125	+	0.115138i
$471$	−4.22204	−	4.87250i	−0.194541	−	0.224513i
$472$	6.41948	+	7.40847i	0.295480	+	0.341002i
$473$	41.2375	+	12.1084i	1.89610	+	0.556746i
$474$	1.63748	−	3.58557i	0.0752118	−	0.164691i
$475$	20.4098	+	13.1166i	0.936464	+	0.601829i
$476$	2.58576	−	0.759248i	0.118518	−	0.0348001i
$477$	1.15321	−	8.02077i	0.0528020	−	0.367246i
$478$	4.34784	+	9.52044i	0.198866	+	0.435455i
$479$	−1.74572	−	12.1418i	−0.0797641	−	0.554771i	−0.990042	−	0.140773i	$-0.955041\pi$
$479$	−1.74572	−	12.1418i	−0.0797641	−	0.554771i	0.910278	−	0.413998i	$-0.135868\pi$
$480$	0.864279	−	0.555438i	0.0394487	−	0.0253522i
$481$	4.80222	−	5.54206i	0.218962	−	0.252696i
$482$	−10.9760			−0.499945
$483$	−3.40275	−	3.56047i	−0.154831	−	0.162007i
$484$	2.78025			0.126375
$485$	−6.24143	+	7.20299i	−0.283409	+	0.327071i
$486$	−13.3535	+	8.58179i	−0.605728	+	0.389278i
$487$	0.158295	+	1.10097i	0.00717303	+	0.0498895i	0.993094	−	0.117325i	$-0.0374319\pi$
$487$	0.158295	+	1.10097i	0.00717303	+	0.0498895i	−0.985921	+	0.167214i	$0.946523\pi$
$488$	−2.75120	−	6.02430i	−0.124541	−	0.272707i
$489$	0.426154	−	2.96397i	0.0192713	−	0.134035i
$490$	0.959899	−	0.281852i	0.0433638	−	0.0127328i
$491$	−9.95291	−	6.39635i	−0.449169	−	0.288663i	0.296435	−	0.955053i	$-0.404202\pi$
$491$	−9.95291	−	6.39635i	−0.449169	−	0.288663i	−0.745603	+	0.666390i	$0.767839\pi$
$492$	−0.821898	+	1.79971i	−0.0370540	+	0.0811370i
$493$	−14.5994	−	4.28678i	−0.657525	−	0.193067i
$494$	2.49558	+	2.88005i	0.112281	+	0.129580i
$495$	4.73120	+	5.46010i	0.212652	+	0.245413i
$496$	7.31199	+	2.14699i	0.328318	+	0.0964028i
$497$	−4.50923	+	9.87383i	−0.202266	+	0.442902i
$498$	−13.6021	−	8.74153i	−0.609524	−	0.391717i
$499$	−0.981830	+	0.288291i	−0.0439528	+	0.0129057i	−0.303635	−	0.952788i	$-0.598200\pi$
$499$	−0.981830	+	0.288291i	−0.0439528	+	0.0129057i	0.259682	+	0.965694i	$0.416382\pi$
$500$	−1.28126	+	8.91133i	−0.0572995	+	0.398527i
$501$	1.41599	+	3.10058i	0.0632616	+	0.138524i
$502$	2.54902	+	17.7288i	0.113768	+	0.791275i
$503$	−1.06207	+	0.682553i	−0.0473555	+	0.0304335i	−0.564104	−	0.825703i	$-0.690778\pi$
$503$	−1.06207	+	0.682553i	−0.0473555	+	0.0304335i	0.516749	+	0.856137i	$0.327142\pi$
$504$	−1.27397	+	1.47024i	−0.0567471	+	0.0654896i
$505$	0.247153			0.0109982
$506$	1.67183	−	17.7243i	0.0743220	−	0.787941i
$507$	12.9449			0.574904
$508$	−2.68268	+	3.09598i	−0.119025	+	0.137362i
$509$	−1.88986	+	1.21454i	−0.0837666	+	0.0538335i	−0.581854	−	0.813294i	$-0.697672\pi$
$509$	−1.88986	+	1.21454i	−0.0837666	+	0.0538335i	0.498087	+	0.867127i	$0.334036\pi$
$510$	−0.394025	−	2.74050i	−0.0174477	−	0.121351i
$511$	−1.47449	−	3.22869i	−0.0652278	−	0.142829i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	29.5617	−	8.68010i	1.30518	−	0.383236i
$514$	21.7823	+	13.9987i	0.960778	+	0.617454i
$515$	−6.35189	+	13.9087i	−0.279898	+	0.612891i
$516$	11.4079	+	3.34967i	0.502206	+	0.147461i
$517$	21.5290	+	24.8458i	0.946847	+	1.09272i
$518$	−7.64474	−	8.82250i	−0.335891	−	0.387638i
$519$	1.19640	+	0.351294i	0.0525161	+	0.0154201i
$520$	−0.261063	+	0.571648i	−0.0114484	+	0.0250684i
$521$	9.05508	+	5.81935i	0.396710	+	0.254950i	0.723753	−	0.690059i	$-0.242416\pi$
$521$	9.05508	+	5.81935i	0.396710	+	0.254950i	−0.327042	+	0.945010i	$0.606052\pi$
$522$	10.5390	−	3.09453i	0.461279	−	0.135444i
$523$	3.09639	−	21.5359i	0.135396	−	0.941697i	−0.802962	−	0.596031i	$-0.796744\pi$
$523$	3.09639	−	21.5359i	0.135396	−	0.941697i	0.938357	−	0.345667i	$-0.112347\pi$
$524$	8.67155	+	18.9880i	0.378818	+	0.829496i
$525$	0.584468	+	4.06507i	0.0255083	+	0.177414i
$526$	−1.66549	+	1.07034i	−0.0726188	+	0.0466692i
$527$	13.4490	−	15.5209i	0.585846	−	0.676103i
$528$	3.81216			0.165903
$529$	−22.5943	−	4.30065i	−0.982363	−	0.186985i
$530$	−4.16709			−0.181007
$531$	−12.4885	+	14.4125i	−0.541954	+	0.625448i
$532$	5.10352	−	3.27983i	0.221266	−	0.142199i
$533$	−0.172235	−	1.19792i	−0.00746035	−	0.0518879i
$534$	1.79190	+	3.92370i	0.0775429	+	0.169795i
$535$	1.34976	−	9.38777i	0.0583551	−	0.405868i
$536$	12.3884	−	3.63756i	0.535097	−	0.157119i
$537$	−14.7510	−	9.47989i	−0.636552	−	0.409087i
$538$	−1.28293	+	2.80922i	−0.0553110	+	0.121114i
$539$	3.56181	+	1.04584i	0.153418	+	0.0450476i
$540$	3.32719	+	3.83978i	0.143179	+	0.165238i
$541$	−14.4588	−	16.6863i	−0.621631	−	0.717401i	0.354385	−	0.935100i	$-0.384690\pi$
$541$	−14.4588	−	16.6863i	−0.621631	−	0.717401i	−0.976016	+	0.217699i	$0.930145\pi$
$542$	11.4658	+	3.36667i	0.492499	+	0.144611i
$543$	−3.82136	+	8.36762i	−0.163990	+	0.359089i
$544$	2.26711	+	1.45699i	0.0972017	+	0.0624677i
$545$	7.00937	−	2.05814i	0.300248	−	0.0881609i
$546$	−0.0918063	+	0.638527i	−0.00392895	+	0.0273264i
$547$	−11.4728	−	25.1220i	−0.490543	−	1.07414i	−0.979428	−	0.201792i	$-0.935324\pi$
$547$	−11.4728	−	25.1220i	−0.490543	−	1.07414i	0.488885	−	0.872348i	$-0.337404\pi$
$548$	0.990650	+	6.89012i	0.0423185	+	0.294331i
$549$	10.8387	−	6.96562i	0.462585	−	0.297285i
$550$	−9.72177	+	11.2195i	−0.414538	+	0.478402i
$551$	−34.2523			−1.45920
$552$	0.462495	−	4.90324i	0.0196851	−	0.208696i
$553$	3.83840			0.163225
$554$	−15.5322	+	17.9251i	−0.659899	+	0.761564i
$555$	−10.0894	+	6.48410i	−0.428273	+	0.275235i
$556$	−1.93625	−	13.4669i	−0.0821153	−	0.571125i
$557$	−5.32676	−	11.6640i	−0.225702	−	0.494218i	0.762573	−	0.646902i	$-0.223936\pi$
$557$	−5.32676	−	11.6640i	−0.225702	−	0.494218i	−0.988275	+	0.152684i	$0.951208\pi$
$558$	−2.10986	+	14.6744i	−0.0893175	+	0.621217i
$559$	−6.97819	+	2.04898i	−0.295146	+	0.0866627i
$560$	0.841610	+	0.540870i	0.0355645	+	0.0228559i
$561$	4.26776	−	9.34509i	0.180185	−	0.394550i
$562$	28.8732	+	8.47795i	1.21794	+	0.357621i
$563$	12.2000	+	14.0796i	0.514169	+	0.593383i	0.952161	−	0.305596i	$-0.0988557\pi$
$563$	12.2000	+	14.0796i	0.514169	+	0.593383i	−0.437992	+	0.898979i	$0.644310\pi$
$564$	5.95579	+	6.87334i	0.250784	+	0.289420i
$565$	−2.39473	−	0.703157i	−0.100747	−	0.0295820i
$566$	6.59541	−	14.4419i	0.277226	−	0.607040i
$567$	−0.522262	−	0.335637i	−0.0219329	−	0.0140954i
$568$	−10.4151	+	3.05814i	−0.437006	+	0.128317i
$569$	1.70241	−	11.8405i	0.0713688	−	0.496381i	−0.922516	−	0.385959i	$-0.873871\pi$
$569$	1.70241	−	11.8405i	0.0713688	−	0.496381i	0.993885	−	0.110422i	$-0.0352202\pi$
$570$	−2.58912	−	5.66938i	−0.108446	−	0.237464i
$571$	1.00355	+	6.97985i	0.0419973	+	0.292098i	0.999986	+	0.00529173i	$0.00168442\pi$
$571$	1.00355	+	6.97985i	0.0419973	+	0.292098i	−0.957989	+	0.286806i	$0.907406\pi$
$572$	−1.96171	+	1.26071i	−0.0820232	+	0.0527131i
$573$	−6.92018	+	7.98631i	−0.289095	+	0.333633i
$574$	−1.92661			−0.0804150
$575$	13.2512	+	13.8654i	0.552614	+	0.578227i
$576$	−1.94540			−0.0810585
$577$	−28.1179	+	32.4498i	−1.17057	+	1.35090i	−0.246281	+	0.969198i	$0.579209\pi$
$577$	−28.1179	+	32.4498i	−1.17057	+	1.35090i	−0.924284	+	0.381706i	$0.875337\pi$
$578$	−8.19161	+	5.26443i	−0.340726	+	0.218971i
$579$	1.15494	+	8.03281i	0.0479978	+	0.333832i
$580$	−2.34646	−	5.13803i	−0.0974315	−	0.213345i
$581$	2.24071	−	15.5845i	0.0929604	−	0.646554i
$582$	−9.38719	+	2.75633i	−0.389112	+	0.114253i
$583$	−13.0078	−	8.35962i	−0.538729	−	0.346220i
$584$	1.47449	−	3.22869i	0.0610150	−	0.133604i
$585$	−1.17305	−	0.344437i	−0.0484995	−	0.0142407i
$586$	−20.0302	−	23.1160i	−0.827438	−	0.954914i
$587$	1.83068	+	2.11271i	0.0755601	+	0.0872010i	0.792271	−	0.610170i	$-0.208899\pi$
$587$	1.83068	+	2.11271i	0.0755601	+	0.0872010i	−0.716711	+	0.697371i	$0.754353\pi$
$588$	0.985337	+	0.289321i	0.0406346	+	0.0119314i
$589$	19.2052	−	42.0535i	0.791336	−	1.73279i
$590$	8.25014	+	5.30204i	0.339653	+	0.218282i
$591$	−4.92110	+	1.44497i	−0.202427	+	0.0594379i
$592$	1.66136	−	11.5550i	0.0682815	−	0.474908i
$593$	−19.0533	−	41.7210i	−0.782426	−	1.71327i	−0.697159	−	0.716916i	$-0.745553\pi$
$593$	−19.0533	−	41.7210i	−0.782426	−	1.71327i	−0.0852666	−	0.996358i	$-0.527174\pi$
$594$	2.68302	+	18.6608i	0.110086	+	0.765662i
$595$	2.26807	−	1.45760i	0.0929820	−	0.0597559i
$596$	3.06316	−	3.53508i	0.125472	−	0.144802i
$597$	1.55529			0.0636539
$598$	1.38355	+	2.67612i	0.0565775	+	0.109435i
$599$	−19.8978			−0.813002			−0.406501	−	0.913650i	$-0.633251\pi$
$599$	−19.8978			−0.813002			−0.406501	+	0.913650i	$0.633251\pi$
$600$	−2.68943	+	3.10376i	−0.109795	+	0.126711i
$601$	−12.1247	+	7.79206i	−0.494576	+	0.317845i	−0.764043	−	0.645165i	$-0.776789\pi$
$601$	−12.1247	+	7.79206i	−0.494576	+	0.317845i	0.269468	+	0.963009i	$0.413152\pi$
$602$	1.64768	+	11.4598i	0.0671543	+	0.467068i
$603$	10.4344	+	22.8480i	0.424920	+	0.930444i
$604$	−0.0162054	+	0.112711i	−0.000659386	+	0.00458613i
$605$	2.66876	−	0.783620i	0.108501	−	0.0318587i
$606$	0.213428	+	0.137162i	0.00866993	+	0.00557182i
$607$	0.546813	−	1.19735i	0.0221944	−	0.0485990i	−0.898210	−	0.439566i	$-0.855132\pi$
$607$	0.546813	−	1.19735i	0.0221944	−	0.0485990i	0.920405	+	0.390967i	$0.127859\pi$
$608$	5.82083	+	1.70915i	0.236066	+	0.0693152i
$609$	−3.79699	−	4.38196i	−0.153862	−	0.177566i
$610$	−4.33884	−	5.00729i	−0.175674	−	0.202739i
$611$	−5.33788	−	1.56734i	−0.215947	−	0.0634079i
$612$	−2.17790	+	4.76894i	−0.0880365	+	0.192773i
$613$	17.9213	+	11.5173i	0.723833	+	0.465179i	0.849968	−	0.526834i	$-0.176621\pi$
$613$	17.9213	+	11.5173i	0.723833	+	0.465179i	−0.126135	+	0.992013i	$0.540257\pi$
$614$	−30.1602	+	8.85583i	−1.21717	+	0.357392i
$615$	−0.281689	+	1.95919i	−0.0113588	+	0.0790022i
$616$	1.54209	+	3.37671i	0.0621327	+	0.136052i
$617$	−5.33517	−	37.1069i	−0.214786	−	1.49387i	−0.756882	−	0.653551i	$-0.773278\pi$
$617$	−5.33517	−	37.1069i	−0.214786	−	1.49387i	0.542096	−	0.840316i	$-0.317631\pi$
$618$	−13.2040	+	8.48572i	−0.531145	+	0.341346i
$619$	−11.2084	+	12.9351i	−0.450502	+	0.519907i	−0.934886	−	0.354948i	$-0.884498\pi$
$619$	−11.2084	+	12.9351i	−0.450502	+	0.519907i	0.484384	+	0.874856i	$0.339044\pi$
$620$	7.62391			0.306183
$621$	24.3272	−	1.18698i	0.976217	−	0.0476319i
$622$	−19.1542			−0.768013
$623$	−2.75066	+	3.17443i	−0.110203	+	0.127181i
$624$	−0.542687	+	0.348764i	−0.0217249	+	0.0139617i
$625$	−1.56390	−	10.8771i	−0.0625558	−	0.435085i
$626$	10.4896	+	22.9691i	0.419250	+	0.918030i
$627$	3.29128	−	22.8914i	0.131441	−	0.914193i
$628$	6.02383	−	1.76875i	0.240377	−	0.0705810i
$629$	−26.4659	−	17.0086i	−1.05527	−	0.678178i
$630$	−0.808493	+	1.77035i	−0.0322111	+	0.0705325i
$631$	22.1774	+	6.51188i	0.882869	+	0.259234i	0.691580	−	0.722300i	$-0.256915\pi$
$631$	22.1774	+	6.51188i	0.882869	+	0.259234i	0.191289	+	0.981534i	$0.438733\pi$
$632$	2.51362	+	2.90087i	0.0999863	+	0.115390i
$633$	−7.82268	−	9.02785i	−0.310923	−	0.358825i
$634$	14.8433	+	4.35840i	0.589505	+	0.173094i
$635$	−1.70249	+	3.72794i	−0.0675614	+	0.147939i
$636$	−3.59848	−	2.31260i	−0.142689	−	0.0917006i
$637$	−0.602728	+	0.176977i	−0.0238809	+	0.00701208i
$638$	2.98281	−	20.7459i	0.118091	−	0.821339i
$639$	−8.77227	−	19.2086i	−0.347026	−	0.759880i
$640$	0.142375	+	0.990241i	0.00562787	+	0.0391427i
$641$	−13.0833	+	8.40815i	−0.516761	+	0.332102i	−0.772889	−	0.634541i	$-0.781189\pi$
$641$	−13.0833	+	8.40815i	−0.516761	+	0.332102i	0.256129	+	0.966643i	$0.417553\pi$
$642$	6.37549	−	7.35770i	0.251620	−	0.290385i
$643$	17.4059			0.686422			0.343211	−	0.939258i	$-0.388485\pi$
$643$	17.4059			0.686422			0.343211	+	0.939258i	$0.388485\pi$
$644$	4.53025	−	1.57379i	0.178517	−	0.0620160i
$645$	11.8946			0.468348
$646$	10.7063	−	12.3557i	0.421233	−	0.486129i
$647$	−20.0950	+	12.9143i	−0.790017	+	0.507713i	−0.872344	−	0.488892i	$-0.837401\pi$
$647$	−20.0950	+	12.9143i	−0.790017	+	0.507713i	0.0823270	+	0.996605i	$0.473765\pi$
$648$	−0.0883510	−	0.614495i	−0.00347075	−	0.0241396i
$649$	15.1169	+	33.1013i	0.593388	+	1.29934i
$650$	0.357518	−	2.48659i	0.0140230	−	0.0975321i
$651$	7.50893	−	2.20482i	0.294298	−	0.0864138i
$652$	2.45302	+	1.57646i	0.0960675	+	0.0617388i
$653$	1.02980	−	2.25494i	0.0402990	−	0.0882425i	−0.888412	−	0.459047i	$-0.848191\pi$
$653$	1.02980	−	2.25494i	0.0402990	−	0.0882425i	0.928711	+	0.370805i	$0.120918\pi$
$654$	7.19512	+	2.11268i	0.281351	+	0.0826122i
$655$	13.6756	+	15.7825i	0.534351	+	0.616674i
$656$	−1.26166	−	1.45603i	−0.0492595	−	0.0568485i
$657$	6.62541	+	1.94540i	0.258482	+	0.0758971i
$658$	−3.67900	+	8.05588i	−0.143422	+	0.314051i
$659$	−31.6977	−	20.3709i	−1.23477	−	0.793537i	−0.250141	−	0.968209i	$-0.580477\pi$
$659$	−31.6977	−	20.3709i	−1.23477	−	0.793537i	−0.984627	+	0.174672i	$0.944113\pi$
$660$	3.65929	−	1.07447i	0.142438	−	0.0418235i
$661$	1.95312	−	13.5842i	0.0759674	−	0.528365i	−0.915931	−	0.401335i	$-0.868546\pi$
$661$	1.95312	−	13.5842i	0.0759674	−	0.528365i	0.991899	−	0.127030i	$-0.0405445\pi$
$662$	4.57503	+	10.0179i	0.177813	+	0.389357i
$663$	0.247411	+	1.72078i	0.00960864	+	0.0668296i
$664$	13.2453	−	8.51225i	0.514018	−	0.330340i
$665$	3.97444	−	4.58675i	0.154122	−	0.177866i
$666$	22.7103			0.880008
$667$	−26.3217	−	6.35344i	−1.01918	−	0.246006i
$668$	−3.31921			−0.128424
$669$	15.8683	−	18.3130i	0.613505	−	0.708022i
$670$	10.8664	−	6.98339i	0.419804	−	0.269792i
$671$	−3.49880	−	24.3347i	−0.135070	−	0.939431i
$672$	0.426604	+	0.934133i	0.0164566	+	0.0360350i
$673$	−1.73063	+	12.0368i	−0.0667108	+	0.463983i	0.928895	+	0.370343i	$0.120760\pi$
$673$	−1.73063	+	12.0368i	−0.0667108	+	0.463983i	−0.995606	+	0.0936410i	$0.970149\pi$
$674$	−7.47755	+	2.19561i	−0.288025	+	0.0845716i
$675$	−17.0860	−	10.9805i	−0.657639	−	0.422639i
$676$	−5.23647	+	11.4663i	−0.201403	+	0.441011i
$677$	−10.1483	−	2.97981i	−0.390030	−	0.114523i	0.0808369	−	0.996727i	$-0.474241\pi$
$677$	−10.1483	−	2.97981i	−0.390030	−	0.114523i	−0.470867	+	0.882204i	$0.656059\pi$
$678$	−1.67773	−	1.93621i	−0.0644330	−	0.0743597i
$679$	−6.23878	−	7.19994i	−0.239423	−	0.276308i
$680$	2.58686	+	0.759569i	0.0992014	+	0.0291282i
$681$	−5.24229	+	11.4790i	−0.200885	+	0.439877i
$682$	23.7985	+	15.2944i	0.911291	+	0.585651i
$683$	22.0094	−	6.46254i	0.842166	−	0.247282i	0.167930	−	0.985799i	$-0.446292\pi$
$683$	22.0094	−	6.46254i	0.842166	−	0.247282i	0.674235	+	0.738517i	$0.264473\pi$
$684$	−1.67959	+	11.6818i	−0.0642207	+	0.446665i
$685$	2.89292	+	6.33461i	0.110533	+	0.242033i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	−12.3075	+	7.90957i	−0.469562	+	0.301769i
$688$	−7.58177	+	8.74983i	−0.289052	+	0.333584i
$689$	2.61655			0.0996825
$690$	−0.938040	−	4.83697i	−0.0357106	−	0.184140i
$691$	23.3886			0.889743			0.444871	−	0.895595i	$-0.353249\pi$
$691$	23.3886			0.889743			0.444871	+	0.895595i	$0.353249\pi$
$692$	−0.795134	+	0.917633i	−0.0302264	+	0.0348832i
$693$	−6.07527	+	3.90434i	−0.230780	+	0.148314i
$694$	−1.37591	−	9.56966i	−0.0522288	−	0.363260i
$695$	−5.65428	−	12.3812i	−0.214479	−	0.469644i
$696$	0.825164	−	5.73914i	0.0312778	−	0.217542i
$697$	−4.98174	+	1.46277i	−0.188697	+	0.0554064i
$698$	−24.2067	−	15.5567i	−0.916236	−	0.588829i
$699$	−6.77950	+	14.8450i	−0.256424	+	0.561490i
$700$	−3.83716	−	1.12669i	−0.145031	−	0.0425849i
$701$	−23.0268	−	26.5743i	−0.869709	−	1.00370i	−0.999925	−	0.0122125i	$-0.996113\pi$
$701$	−23.0268	−	26.5743i	−0.869709	−	1.00370i	0.130216	−	0.991486i	$-0.458433\pi$
$702$	−2.08917	−	2.41103i	−0.0788505	−	0.0909983i
$703$	−67.9514	−	19.9523i	−2.56284	−	0.752517i
$704$	−1.54209	+	3.37671i	−0.0581198	+	0.127265i
$705$	7.65422	+	4.91907i	0.288275	+	0.185263i
$706$	12.5347	−	3.68051i	0.471749	−	0.138518i
$707$	−0.0351586	+	0.244534i	−0.00132228	+	0.00919664i
$708$	4.18192	+	9.15713i	0.157166	+	0.344146i
$709$	−4.61634	−	32.1074i	−0.173370	−	1.20582i	−0.871700	−	0.490040i	$-0.836982\pi$
$709$	−4.61634	−	32.1074i	−0.173370	−	1.20582i	0.698329	−	0.715777i	$-0.253927\pi$
$710$	−9.13547	+	5.87101i	−0.342848	+	0.220335i
$711$	−4.89000	+	5.64336i	−0.183389	+	0.211643i
$712$	−4.20037			−0.157416
$713$	22.5590	−	28.7543i	0.844841	−	1.07686i
$714$	2.76751			0.103571
$715$	−1.52771	+	1.76307i	−0.0571331	+	0.0659351i
$716$	14.3641	−	9.23124i	0.536811	−	0.344988i
$717$	1.52962	+	10.6388i	0.0571248	+	0.397312i
$718$	−6.25561	−	13.6979i	−0.233457	−	0.511200i
$719$	−5.02540	+	34.9524i	−0.187416	+	1.30351i	0.651252	+	0.758862i	$0.274244\pi$
$719$	−5.02540	+	34.9524i	−0.187416	+	1.30351i	−0.838667	+	0.544644i	$0.816665\pi$
$720$	−1.86739	+	0.548316i	−0.0695936	+	0.0204345i
$721$	−12.8577	−	8.26316i	−0.478847	−	0.307736i
$722$	7.39573	−	16.1944i	0.275241	−	0.602693i
$723$	−10.8151	−	3.17560i	−0.402217	−	0.118102i
$724$	−5.86600	−	6.76973i	−0.218008	−	0.251595i
$725$	14.7865	+	17.0645i	0.549155	+	0.633759i
$726$	2.73949	+	0.804386i	0.101672	+	0.0298536i
$727$	21.6538	−	47.4152i	0.803094	−	1.75853i	0.168476	−	0.985706i	$-0.446115\pi$
$727$	21.6538	−	47.4152i	0.803094	−	1.75853i	0.634619	−	0.772826i	$-0.281157\pi$
$728$	−0.528453	−	0.339616i	−0.0195858	−	0.0125870i
$729$	−13.8536	+	4.06779i	−0.513097	+	0.150659i
$730$	0.505353	−	3.51481i	0.0187040	−	0.130089i
$731$	12.9614	+	28.3814i	0.479393	+	1.04972i
$732$	−0.967907	−	6.73194i	−0.0357749	−	0.248820i
$733$	33.5604	−	21.5680i	1.23958	−	0.796631i	0.254227	−	0.967145i	$-0.418179\pi$
$733$	33.5604	−	21.5680i	1.23958	−	0.796631i	0.985355	+	0.170513i	$0.0545426\pi$
$734$	−21.7457	+	25.0959i	−0.802648	+	0.926305i
$735$	1.02737			0.0378951
$736$	4.15608	+	2.39312i	0.153195	+	0.0882117i
$737$	47.9294			1.76550
$738$	2.45444	−	2.83257i	0.0903491	−	0.104268i
$739$	34.4345	−	22.1297i	1.26669	−	0.814055i	0.277508	−	0.960723i	$-0.410492\pi$
$739$	34.4345	−	22.1297i	1.26669	−	0.814055i	0.989186	+	0.146669i	$0.0468552\pi$
$740$	−1.66206	−	11.5599i	−0.0610987	−	0.424951i
$741$	1.62573	+	3.55984i	0.0597226	+	0.130774i
$742$	0.592788	−	4.12293i	0.0217619	−	0.151358i
$743$	18.5260	−	5.43973i	0.679654	−	0.199564i	0.0763562	−	0.997081i	$-0.475671\pi$
$743$	18.5260	−	5.43973i	0.679654	−	0.199564i	0.603297	+	0.797516i	$0.293853\pi$
$744$	6.58360	+	4.23102i	0.241366	+	0.155117i
$745$	1.94396	−	4.25668i	0.0712211	−	0.155953i
$746$	23.3847	+	6.86638i	0.856176	+	0.251396i
$747$	20.0583	+	23.1485i	0.733896	+	0.846961i
$748$	6.55125	+	7.56054i	0.239537	+	0.276441i
$749$	9.09627	+	2.67091i	0.332370	+	0.0975928i
$750$	−3.84070	+	8.40996i	−0.140243	+	0.307089i
$751$	24.5950	+	15.8063i	0.897485	+	0.576779i	0.906043	−	0.423185i	$-0.139088\pi$
$751$	24.5950	+	15.8063i	0.897485	+	0.576779i	−0.00855847	+	0.999963i	$0.502724\pi$
$752$	−8.49746	+	2.49508i	−0.309870	+	0.0909862i
$753$	−2.61768	+	18.2063i	−0.0953934	+	0.663476i
$754$	1.47336	+	3.22621i	0.0536566	+	0.117492i
$755$	0.0162122	+	0.112758i	0.000590023	+	0.00410370i
$756$	−4.27240	+	2.74570i	−0.155386	+	0.0998603i
$757$	11.9747	−	13.8196i	0.435230	−	0.502282i	−0.495186	−	0.868787i	$-0.664900\pi$
$757$	11.9747	−	13.8196i	0.435230	−	0.502282i	0.930416	+	0.366505i	$0.119446\pi$
$758$	0.744431			0.0270389
$759$	6.77533	−	16.9807i	0.245929	−	0.616361i
$760$	6.06914			0.220151
$761$	22.0621	−	25.4611i	0.799752	−	0.922963i	−0.198616	−	0.980077i	$-0.563645\pi$
$761$	22.0621	−	25.4611i	0.799752	−	0.922963i	0.998368	+	0.0571147i	$0.0181901\pi$
$762$	−3.53907	+	2.27442i	−0.128207	+	0.0823937i
$763$	1.03921	+	7.22786i	0.0376219	+	0.261666i
$764$	−4.27472	−	9.36033i	−0.154654	−	0.338645i
$765$	−0.746432	+	5.19155i	−0.0269873	+	0.187701i
$766$	−3.80832	+	1.11822i	−0.137600	+	0.0404031i
$767$	−5.18032	−	3.32919i	−0.187051	−	0.120210i
$768$	−0.426604	+	0.934133i	−0.0153938	+	0.0337076i
$769$	−21.1550	−	6.21166i	−0.762868	−	0.223998i	−0.122920	−	0.992417i	$-0.539226\pi$
$769$	−21.1550	−	6.21166i	−0.762868	−	0.223998i	−0.639948	+	0.768418i	$0.721044\pi$
$770$	2.43199	+	2.80666i	0.0876428	+	0.101145i
$771$	17.4128	+	20.0955i	0.627108	+	0.723721i
$772$	−7.58245	−	2.22641i	−0.272898	−	0.0801302i
$773$	8.68963	−	19.0276i	0.312544	−	0.684376i	−0.686543	−	0.727089i	$-0.740873\pi$
$773$	8.68963	−	19.0276i	0.312544	−	0.684376i	0.999087	+	0.0427127i	$0.0136000\pi$
$774$	−18.9478	−	12.1770i	−0.681064	−	0.437694i
$775$	−29.2418	+	8.58615i	−1.05039	+	0.308424i
$776$	1.35582	−	9.42992i	0.0486710	−	0.338514i
$777$	−4.98011	−	10.9049i	−0.178660	−	0.391212i
$778$	0.642636	+	4.46963i	0.0230396	+	0.160244i
$779$	−9.83248	+	6.31895i	−0.352285	+	0.226400i
$780$	−0.422625	+	0.487735i	−0.0151324	+	0.0174637i
$781$	−40.2948			−1.44186
$782$	10.5192	−	7.50903i	0.376168	−	0.268522i
$783$	28.6743			1.02473
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	5.28374	−	3.39565i	0.188585	−	0.121196i
$786$	3.05076	+	21.2185i	0.108817	+	0.756838i
$787$	−9.36923	−	20.5157i	−0.333977	−	0.731307i	0.665915	−	0.746028i	$-0.268041\pi$
$787$	−9.36923	−	20.5157i	−0.333977	−	0.731307i	−0.999892	+	0.0147205i	$0.995314\pi$
$788$	0.710768	−	4.94350i	0.0253200	−	0.176105i
$789$	−1.95074	+	0.572789i	−0.0694482	+	0.0203918i
$790$	3.23043	+	2.07607i	0.114934	+	0.0738634i
$791$	1.03637	−	2.26933i	0.0368490	−	0.0806880i
$792$	−6.92916	−	2.03458i	−0.246217	−	0.0722958i
$793$	2.72439	+	3.14411i	0.0967459	+	0.111651i
$794$	−20.6668	−	23.8508i	−0.733438	−	0.846433i
$795$	−4.10599	−	1.20563i	−0.145624	−	0.0427592i
$796$	−0.629146	+	1.37764i	−0.0222995	+	0.0488291i
$797$	12.7540	+	8.19652i	0.451771	+	0.290336i	0.746672	−	0.665192i	$-0.231650\pi$
$797$	12.7540	+	8.19652i	0.451771	+	0.290336i	−0.294901	+	0.955528i	$0.595287\pi$
$798$	5.97761	−	1.75519i	0.211605	−	0.0621329i
$799$	−3.39660	+	23.6238i	−0.120163	+	0.835752i
$800$	−1.66131	−	3.63776i	−0.0587361	−	0.128614i
$801$	−1.16291	−	8.08825i	−0.0410896	−	0.285784i
$802$	5.42444	−	3.48608i	0.191544	−	0.123098i
$803$	8.62856	−	9.95789i	0.304495	−	0.351406i
$804$	13.2592			0.467615
$805$	3.90501	−	2.78754i	0.137634	−	0.0982479i
$806$	−4.78711			−0.168619
$807$	−2.07689	+	2.39685i	−0.0731098	+	0.0843733i
$808$	−0.207830	+	0.133564i	−0.00731144	+	0.00469878i
$809$	−5.05798	−	35.1791i	−0.177829	−	1.23683i	−0.861773	−	0.507295i	$-0.830646\pi$
$809$	−5.05798	−	35.1791i	−0.177829	−	1.23683i	0.683943	−	0.729535i	$-0.260264\pi$
$810$	−0.258005	−	0.564951i	−0.00906535	−	0.0198504i
$811$	2.99269	−	20.8146i	0.105087	−	0.730899i	−0.867344	−	0.497710i	$-0.834175\pi$
$811$	2.99269	−	20.8146i	0.105087	−	0.730899i	0.972431	−	0.233190i	$-0.0749163\pi$
$812$	5.41738	−	1.59069i	0.190113	−	0.0558221i
$813$	10.3236	+	6.63460i	0.362066	+	0.232686i
$814$	18.0022	−	39.4192i	0.630975	−	1.38164i
$815$	2.79898	+	0.821854i	0.0980439	+	0.0287883i
$816$	1.81233	+	2.09155i	0.0634444	+	0.0732187i
$817$	45.9953	+	53.0815i	1.60917	+	1.85708i
$818$	−26.7741	−	7.86159i	−0.936134	−	0.274874i
$819$	0.507658	−	1.11162i	0.0177390	−	0.0388430i
$820$	−1.62145	−	1.04204i	−0.0566235	−	0.0363897i
$821$	44.1702	−	12.9695i	1.54155	−	0.452640i	0.602987	−	0.797751i	$-0.293977\pi$
$821$	44.1702	−	12.9695i	1.54155	−	0.452640i	0.938562	+	0.345111i	$0.112159\pi$
$822$	−1.01733	+	7.07571i	−0.0354836	+	0.246794i
$823$	−0.240829	−	0.527342i	−0.00839477	−	0.0183820i	0.905388	−	0.424585i	$-0.139580\pi$
$823$	−0.240829	−	0.527342i	−0.00839477	−	0.0183820i	−0.913783	+	0.406203i	$0.866853\pi$
$824$	−2.17514	−	15.1284i	−0.0757746	−	0.527024i
$825$	−12.8253	+	8.24230i	−0.446518	+	0.286960i
$826$	−6.41948	+	7.40847i	−0.223362	+	0.257774i
$827$	10.5425			0.366600			0.183300	−	0.983057i	$-0.441322\pi$
$827$	10.5425			0.366600			0.183300	+	0.983057i	$0.441322\pi$
$828$	−3.45755	+	8.66551i	−0.120158	+	0.301147i
$829$	−30.1186			−1.04606			−0.523032	−	0.852313i	$-0.675199\pi$
$829$	−30.1186			−1.04606			−0.523032	+	0.852313i	$0.675199\pi$
$830$	10.3150	−	11.9041i	0.358038	−	0.413198i
$831$	−20.4905	+	13.1685i	−0.710809	+	0.456809i
$832$	−0.0893984	−	0.621779i	−0.00309933	−	0.0215563i
$833$	1.11951	+	2.45139i	0.0387888	+	0.0849356i
$834$	1.98840	−	13.8297i	0.0688528	−	0.478882i
$835$	−3.18610	+	0.935524i	−0.110260	+	0.0323752i
$836$	18.9452	+	12.1753i	0.655232	+	0.421092i
$837$	−16.0776	+	35.2050i	−0.555722	+	1.21686i
$838$	−1.05502	−	0.309780i	−0.0364449	−	0.0107012i
$839$	24.7472	+	28.5598i	0.854369	+	0.985995i	0.999994	−	0.00334517i	$-0.00106480\pi$
$839$	24.7472	+	28.5598i	0.854369	+	0.985995i	−0.145625	+	0.989340i	$0.546519\pi$
$840$	0.672784	+	0.776434i	0.0232133	+	0.0267895i
$841$	−2.76167	−	0.810900i	−0.0952301	−	0.0279621i
$842$	−8.59052	+	18.8106i	−0.296049	+	0.648256i
$843$	25.9970	+	16.7073i	0.895385	+	0.575429i
$844$	11.1611	−	3.27718i	0.384179	−	0.112805i
$845$	−1.79470	+	12.4824i	−0.0617394	+	0.429407i
$846$	−7.15714	−	15.6719i	−0.246068	−	0.538813i
$847$	0.395671	+	2.75195i	0.0135954	+	0.0945583i
$848$	3.50410	−	2.25195i	0.120331	−	0.0773321i
$849$	10.6771	−	12.3220i	0.366436	−	0.422889i
$850$	−10.7774			−0.369662
$851$	−48.5174	−	27.9369i	−1.66315	−	0.957665i
$852$	−11.1471			−0.381894
$853$	6.13839	−	7.08408i	0.210175	−	0.242554i	−0.640868	−	0.767651i	$-0.721425\pi$
$853$	6.13839	−	7.08408i	0.210175	−	0.242554i	0.851043	+	0.525097i	$0.175971\pi$
$854$	5.57144	−	3.58055i	0.190651	−	0.122524i
$855$	1.68030	+	11.6868i	0.0574651	+	0.399678i
$856$	3.93825	+	8.62357i	0.134607	+	0.294748i
$857$	−3.91887	+	27.2563i	−0.133866	+	0.931058i	0.806582	+	0.591122i	$0.201315\pi$
$857$	−3.91887	+	27.2563i	−0.133866	+	0.931058i	−0.940448	+	0.339936i	$0.889594\pi$
$858$	−2.29770	+	0.674665i	−0.0784421	+	0.0230327i
$859$	25.7986	+	16.5798i	0.880237	+	0.565694i	0.900868	−	0.434093i	$-0.142931\pi$
$859$	25.7986	+	16.5798i	0.880237	+	0.565694i	−0.0206310	+	0.999787i	$0.506568\pi$
$860$	−4.81158	+	10.5359i	−0.164074	+	0.359271i
$861$	−1.89836	−	0.557408i	−0.0646958	−	0.0189964i
$862$	16.4560	+	18.9913i	0.560494	+	0.646845i
$863$	−16.1923	−	18.6869i	−0.551193	−	0.636111i	0.409967	−	0.912100i	$-0.365540\pi$
$863$	−16.1923	−	18.6869i	−0.551193	−	0.636111i	−0.961161	+	0.275989i	$0.910995\pi$
$864$	−4.87289	−	1.43081i	−0.165779	−	0.0486771i
$865$	−0.504612	+	1.10495i	−0.0171573	+	0.0375693i
$866$	−28.1304	−	18.0783i	−0.955910	−	0.614326i
$867$	−9.59461	+	2.81723i	−0.325850	+	0.0956782i
$868$	−1.08454	+	7.54311i	−0.0368115	+	0.256030i
$869$	5.91917	+	12.9612i	0.200794	+	0.439678i
$870$	−0.825514	−	5.74157i	−0.0279875	−	0.194658i
$871$	−6.82307	+	4.38492i	−0.231191	+	0.148577i
$872$	−4.78192	+	5.51863i	−0.161936	+	0.186884i
$873$	18.5336			0.627269
$874$	17.9585	−	22.8903i	0.607454	−	0.774278i
$875$	−9.00296			−0.304356
$876$	2.38700	−	2.75475i	0.0806493	−	0.0930743i
$877$	−30.3963	+	19.5345i	−1.02641	+	0.659633i	−0.941589	−	0.336763i	$-0.890668\pi$
$877$	−30.3963	+	19.5345i	−1.02641	+	0.659633i	−0.0848199	+	0.996396i	$0.527032\pi$
$878$	−0.615246	−	4.27913i	−0.0207635	−	0.144414i
$879$	−13.0485	−	28.5722i	−0.440115	−	0.963717i
$880$	−0.528522	+	3.67595i	−0.0178165	+	0.123916i
$881$	−31.0327	+	9.11202i	−1.04552	+	0.306992i	−0.759005	−	0.651084i	$-0.774314\pi$
$881$	−31.0327	+	9.11202i	−1.04552	+	0.306992i	−0.286513	+	0.958076i	$0.592496\pi$
$882$	−1.63658	−	1.05177i	−0.0551065	−	0.0354148i
$883$	−9.51214	+	20.8287i	−0.320109	+	0.700941i	−0.999460	−	0.0328728i	$-0.989534\pi$
$883$	−9.51214	+	20.8287i	−0.320109	+	0.700941i	0.679350	+	0.733814i	$0.262262\pi$
$884$	−1.62431	−	0.476939i	−0.0546313	−	0.0160412i
$885$	6.59518	+	7.61124i	0.221694	+	0.255849i
$886$	−16.4778	−	19.0164i	−0.553584	−	0.638870i
$887$	−5.94613	−	1.74594i	−0.199651	−	0.0586229i	0.180378	−	0.983597i	$-0.442268\pi$
$887$	−5.94613	−	1.74594i	−0.199651	−	0.0586229i	−0.380029	+	0.924974i	$0.624086\pi$
$888$	4.98011	−	10.9049i	0.167121	−	0.365945i
$889$	−3.44625	−	2.21477i	−0.115583	−	0.0742810i
$890$	−4.03193	+	1.18388i	−0.135151	+	0.0396838i
$891$	0.327974	−	2.28111i	0.0109876	−	0.0764201i
$892$	9.80215	+	21.4637i	0.328200	+	0.718658i
$893$	7.64611	+	53.1799i	0.255867	+	1.77960i
$894$	4.04102	−	2.59700i	0.135152	−	0.0868568i
$895$	11.1862	−	12.9096i	0.373915	−	0.431521i
$896$	−1.00000			−0.0334077
$897$	0.589002	+	3.03717i	0.0196662	+	0.101408i
$898$	−26.8601			−0.896334
$899$	28.1767	−	32.5176i	0.939745	−	1.08452i
$900$	6.54493	−	4.20617i	0.218164	−	0.140206i
$901$	−1.59752	−	11.1110i	−0.0532210	−	0.370160i
$902$	−2.97101	−	6.50560i	−0.0989238	−	0.216613i
$903$	−1.69206	+	11.7685i	−0.0563081	+	0.391632i
$904$	2.39372	−	0.702859i	0.0796139	−	0.0233768i
$905$	−7.53883	−	4.84491i	−0.250599	−	0.161050i
$906$	−0.0485773	+	0.106369i	−0.00161387	+	0.00353389i
$907$	−37.2784	−	10.9459i	−1.23781	−	0.363453i	−0.403617	−	0.914928i	$-0.632247\pi$
$907$	−37.2784	−	10.9459i	−1.23781	−	0.363453i	−0.834192	+	0.551475i	$0.814065\pi$
$908$	−8.04721	−	9.28697i	−0.267056	−	0.308199i
$909$	−0.314732	−	0.363220i	−0.0104390	−	0.0120472i
$910$	−0.602983	−	0.177052i	−0.0199887	−	0.00586921i
$911$	−13.0563	+	28.5892i	−0.432573	+	0.947203i	0.560329	+	0.828270i	$0.310675\pi$
$911$	−13.0563	+	28.5892i	−0.432573	+	0.947203i	−0.992902	+	0.118933i	$0.962053\pi$
$912$	5.24098	+	3.36818i	0.173546	+	0.111531i
$913$	56.0798	−	16.4665i	1.85597	−	0.544962i
$914$	−1.74941	+	12.1674i	−0.0578654	+	0.402462i
$915$	−2.82651	−	6.18918i	−0.0934414	−	0.204608i
$916$	−2.02746	−	14.1013i	−0.0669890	−	0.465919i
$917$	−17.5607	+	11.2856i	−0.579905	+	0.372682i
$918$	−8.96273	+	10.3435i	−0.295814	+	0.341388i
$919$	−34.5539			−1.13983			−0.569913	−	0.821705i	$-0.693023\pi$
$919$	−34.5539			−1.13983			−0.569913	+	0.821705i	$0.693023\pi$
$920$	4.66392	+	1.12576i	0.153765	+	0.0371152i
$921$	−32.2801			−1.06367
$922$	12.0331	−	13.8869i	0.396288	−	0.457341i
$923$	5.73623	−	3.68645i	0.188810	−	0.121341i
$924$	0.542527	+	3.77336i	0.0178478	+	0.124134i
$925$	19.3938	+	42.4666i	0.637666	+	1.39629i
$926$	−3.90782	+	27.1795i	−0.128419	+	0.893173i
$927$	28.5292	−	8.37692i	0.937020	−	0.275134i
$928$	4.74979	+	3.05250i	0.155919	+	0.100203i
$929$	−18.2613	+	39.9866i	−0.599133	+	1.31192i	0.330630	+	0.943760i	$0.392739\pi$
$929$	−18.2613	+	39.9866i	−0.599133	+	1.31192i	−0.929763	+	0.368158i	$0.879989\pi$
$930$	7.51212	+	2.20576i	0.246332	+	0.0723296i
$931$	3.97276	+	4.58481i	0.130202	+	0.150261i
$932$	−10.4069	−	12.0102i	−0.340889	−	0.393407i
$933$	−18.8733	−	5.54171i	−0.617885	−	0.181427i
$934$	13.0100	−	28.4879i	0.425700	−	0.932152i
$935$	8.41949	+	5.41088i	0.275347	+	0.176955i
$936$	1.17255	−	0.344292i	0.0383260	−	0.0112535i
$937$	−1.29493	+	9.00642i	−0.0423034	+	0.294227i	0.957676	+	0.287848i	$0.0929397\pi$
$937$	−1.29493	+	9.00642i	−0.0423034	+	0.294227i	−0.999980	+	0.00637917i	$0.997969\pi$
$938$	5.36359	+	11.7446i	0.175127	+	0.383476i
$939$	3.69038	+	25.6672i	0.120431	+	0.837616i
$940$	−7.45346	+	4.79005i	−0.243105	+	0.156234i
$941$	−11.9684	+	13.8122i	−0.390157	+	0.450266i	−0.916517	−	0.399997i	$-0.869011\pi$
$941$	−11.9684	+	13.8122i	−0.390157	+	0.450266i	0.526359	+	0.850262i	$0.323557\pi$
$942$	6.44724			0.210062
$943$	−8.72801	+	3.03208i	−0.284223	+	0.0987380i
$944$	−9.80281			−0.319054
$945$	−3.32719	+	3.83978i	−0.108234	+	0.124908i
$946$	−36.1557	+	23.2359i	−1.17552	+	0.755464i
$947$	6.15410	+	42.8027i	0.199981	+	1.39090i	0.804331	+	0.594181i	$0.202524\pi$
$947$	6.15410	+	42.8027i	0.199981	+	1.39090i	−0.604350	+	0.796719i	$0.706567\pi$
$948$	1.63748	+	3.58557i	0.0531828	+	0.116454i
$949$	−0.317315	+	2.20697i	−0.0103005	+	0.0716414i
$950$	−23.2784	+	6.83515i	−0.755250	+	0.221762i
$951$	13.3647	+	8.58898i	0.433381	+	0.278517i
$952$	−1.11951	+	2.45139i	−0.0362836	+	0.0794500i
$953$	−32.7251	−	9.60895i	−1.06007	−	0.311264i	−0.295190	−	0.955438i	$-0.595383\pi$
$953$	−32.7251	−	9.60895i	−1.06007	−	0.311264i	−0.764879	+	0.644174i	$0.777201\pi$
$954$	5.30650	+	6.12403i	0.171804	+	0.198273i
$955$	−6.74153	−	7.78014i	−0.218151	−	0.251759i
$956$	−10.0423	−	2.94868i	−0.324791	−	0.0953673i
$957$	8.94131	−	19.5787i	0.289031	−	0.632891i
$958$	10.3193	+	6.63183i	0.333403	+	0.214265i
$959$	−6.67901	+	1.96113i	−0.215676	+	0.0633283i
$960$	−0.146210	+	1.01691i	−0.00471891	+	0.0328207i
$961$	11.2472	+	24.6280i	0.362815	+	0.794453i
$962$	1.04362	+	7.25855i	0.0336477	+	0.234025i
$963$	−15.5152	+	9.97103i	−0.499971	+	0.321312i
$964$	7.18777	−	8.29513i	0.231503	−	0.267168i
$965$	−7.90591			−0.254500
$966$	4.91915	−	0.240017i	0.158271	−	0.00772242i
$967$	−36.9752			−1.18904			−0.594521	−	0.804080i	$-0.702658\pi$
$967$	−36.9752			−1.18904			−0.594521	+	0.804080i	$0.702658\pi$
$968$	−1.82068	+	2.10118i	−0.0585188	+	0.0675343i
$969$	14.1241	−	9.07698i	0.453730	−	0.291594i
$970$	−1.35639	−	9.43391i	−0.0435511	−	0.302905i
$971$	15.4415	+	33.8121i	0.495541	+	1.08508i	0.977893	+	0.209106i	$0.0670553\pi$
$971$	15.4415	+	33.8121i	0.495541	+	1.08508i	−0.482352	+	0.875977i	$0.660217\pi$
$972$	2.25901	−	15.7118i	0.0724579	−	0.503956i
$973$	13.0543	−	3.83309i	0.418501	−	0.122883i
$974$	−0.935716	−	0.601348i	−0.0299823	−	0.0192684i
$975$	1.07170	−	2.34669i	0.0343218	−	0.0751543i
$976$	6.35452	+	1.86585i	0.203403	+	0.0597245i
$977$	9.34404	+	10.7836i	0.298942	+	0.344998i	0.885271	−	0.465075i	$-0.153973\pi$
$977$	9.34404	+	10.7836i	0.298942	+	0.344998i	−0.586329	+	0.810073i	$0.699427\pi$
$978$	1.96094	+	2.26305i	0.0627041	+	0.0723644i
$979$	−14.9609	−	4.39292i	−0.478153	−	0.140398i
$980$	−0.415591	+	0.910017i	−0.0132756	+	0.0290694i
$981$	−11.9506	−	7.68019i	−0.381554	−	0.245210i
$982$	11.3518	−	3.33319i	0.362251	−	0.106366i
$983$	4.78523	−	33.2820i	0.152625	−	1.06153i	−0.759172	−	0.650890i	$-0.774396\pi$
$983$	4.78523	−	33.2820i	0.152625	−	1.06153i	0.911797	−	0.410641i	$-0.134695\pi$
$984$	−0.821898	−	1.79971i	−0.0262012	−	0.0573726i
$985$	−0.711069	−	4.94559i	−0.0226565	−	0.157580i
$986$	12.8003	−	8.22626i	0.407645	−	0.261978i
$987$	−5.95579	+	6.87334i	−0.189575	+	0.218781i
$988$	−3.81086			−0.121239
$989$	25.4998	+	49.3229i	0.810846	+	1.56838i
$990$	−7.22474			−0.229617
$991$	−6.54828	+	7.55712i	−0.208013	+	0.240060i	−0.850163	−	0.526519i	$-0.823497\pi$
$991$	−6.54828	+	7.55712i	−0.208013	+	0.240060i	0.642150	+	0.766579i	$0.278042\pi$
$992$	−6.41092	+	4.12005i	−0.203547	+	0.130812i
$993$	1.60955	+	11.1947i	0.0510775	+	0.355252i
$994$	−4.50923	−	9.87383i	−0.143024	−	0.313179i
$995$	−0.215627	+	1.49972i	−0.00683584	+	0.0475443i
$996$	15.5139	−	4.55529i	0.491576	−	0.144340i
$997$	−28.1654	−	18.1008i	−0.892008	−	0.573259i	0.0124018	−	0.999923i	$-0.496052\pi$
$997$	−28.1654	−	18.1008i	−0.892008	−	0.573259i	−0.904410	+	0.426664i	$0.859689\pi$
$998$	0.425086	−	0.930808i	0.0134559	−	0.0294642i
$999$	56.8853	+	16.7030i	1.79977	+	0.528461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.85.1	✓	40
23.6	even	11		7406.2.a.bu.1.6		20
23.13	even	11	inner	322.2.i.d.197.1	yes	40
23.17	odd	22		7406.2.a.bv.1.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.85.1	✓	40	1.1	even	1	trivial
322.2.i.d.197.1	yes	40	23.13	even	11	inner
7406.2.a.bu.1.6		20	23.6	even	11
7406.2.a.bv.1.6		20	23.17	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.863913 + 0.555203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415591 - 0.910017i) q^{5} +(0.146148 - 1.01648i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.808150 + 1.76960i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.863913 + 0.555203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415591 - 0.910017i) q^{5} +(0.146148 - 1.01648i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.808150 + 1.76960i) q^{9} +(0.959899 + 0.281852i) q^{10} +(2.43096 + 2.80548i) q^{11} +(0.672499 + 0.776106i) q^{12} +(-0.602728 - 0.176977i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(0.864279 + 0.555438i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.383528 + 2.66749i) q^{17} +(-0.808150 - 1.76960i) q^{18} +(0.863363 + 6.00482i) q^{19} +(-0.841610 + 0.540870i) q^{20} +(-0.672499 + 0.776106i) q^{21} -3.71218 q^{22} +(-0.450364 + 4.77464i) q^{23} -1.02693 q^{24} +(2.61889 - 3.02236i) q^{25} +(0.528453 - 0.339616i) q^{26} +(-0.722761 - 5.02692i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.803521 + 5.58861i) q^{29} +(-0.985754 + 0.289444i) q^{30} +(-6.41092 - 4.12005i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-3.65774 - 1.07401i) q^{33} +(-1.76480 - 2.03669i) q^{34} +(-0.655138 - 0.756070i) q^{35} +(1.86660 + 0.548084i) q^{36} +(-4.84949 + 10.6189i) q^{37} +(-5.10352 - 3.27983i) q^{38} +(0.618962 - 0.181744i) q^{39} +(0.142375 - 0.990241i) q^{40} +(0.800341 + 1.75250i) q^{41} +(-0.146148 - 1.01648i) q^{42} +(9.73977 - 6.25937i) q^{43} +(2.43096 - 2.80548i) q^{44} +1.94623 q^{45} +(-3.31351 - 3.46709i) q^{46} +8.85620 q^{47} +(0.672499 - 0.776106i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.569139 + 3.95845i) q^{50} +(-1.14967 - 2.51742i) q^{51} +(-0.0893984 + 0.621779i) q^{52} +(-3.99660 + 1.17351i) q^{53} +(4.27240 + 2.74570i) q^{54} +(1.54275 - 3.37814i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-4.07976 - 4.70830i) q^{57} +(-3.69740 - 4.26703i) q^{58} +(9.40573 + 2.76177i) q^{59} +(0.426785 - 0.934529i) q^{60} +(-5.57144 - 3.58055i) q^{61} +(7.31199 - 2.14699i) q^{62} +(-0.276860 + 1.92560i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.0894362 + 0.622043i) q^{65} +(3.20700 - 2.06101i) q^{66} +(8.45517 - 9.75779i) q^{67} +2.69492 q^{68} +(-2.26182 - 4.37491i) q^{69} +1.00042 q^{70} +(-7.10835 + 8.20348i) q^{71} +(-1.63658 + 1.05177i) q^{72} +(-0.505139 - 3.51332i) q^{73} +(-4.84949 - 10.6189i) q^{74} +(-0.584468 + 4.06507i) q^{75} +(5.82083 - 1.70915i) q^{76} +(3.12288 + 2.00695i) q^{77} +(-0.267981 + 0.586797i) q^{78} +(3.68292 + 1.08140i) q^{79} +(0.655138 + 0.756070i) q^{80} +(-0.406546 - 0.469180i) q^{81} +(-1.84857 - 0.542788i) q^{82} +(6.54061 - 14.3219i) q^{83} +(0.863913 + 0.555203i) q^{84} +(2.58686 - 0.759569i) q^{85} +(-1.64768 + 11.4598i) q^{86} +(-2.40864 - 5.27419i) q^{87} +(0.528298 + 3.67439i) q^{88} +(-3.53358 + 2.27089i) q^{89} +(-1.27451 + 1.47086i) q^{90} -0.628173 q^{91} +(4.79013 - 0.233722i) q^{92} +7.82594 q^{93} +(-5.79958 + 6.69307i) q^{94} +(5.10568 - 3.28122i) q^{95} +(0.146148 + 1.01648i) q^{96} +(-3.95761 - 8.66596i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-6.92916 + 2.03458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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