LMFDB - Embedded newform 1155.2.l.e.1121.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.14
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71054 q^{2} +(-0.134822 + 1.72680i) q^{3} +0.925948 q^{4} -1.00000i q^{5} +(0.230619 - 2.95375i) q^{6} +1.00000i q^{7} +1.83721 q^{8} +(-2.96365 - 0.465620i) q^{9} +O(q^{10})$	\(q-1.71054 q^{2} +(-0.134822 + 1.72680i) q^{3} +0.925948 q^{4} -1.00000i q^{5} +(0.230619 - 2.95375i) q^{6} +1.00000i q^{7} +1.83721 q^{8} +(-2.96365 - 0.465620i) q^{9} +1.71054i q^{10} +(1.62703 + 2.89012i) q^{11} +(-0.124838 + 1.59892i) q^{12} -2.91265i q^{13} -1.71054i q^{14} +(1.72680 + 0.134822i) q^{15} -4.99452 q^{16} +2.59640 q^{17} +(5.06944 + 0.796462i) q^{18} -8.54218i q^{19} -0.925948i q^{20} +(-1.72680 - 0.134822i) q^{21} +(-2.78310 - 4.94366i) q^{22} +5.47708i q^{23} +(-0.247696 + 3.17248i) q^{24} -1.00000 q^{25} +4.98220i q^{26} +(1.20360 - 5.05483i) q^{27} +0.925948i q^{28} +3.64946 q^{29} +(-2.95375 - 0.230619i) q^{30} -0.818935 q^{31} +4.86890 q^{32} +(-5.21000 + 2.41989i) q^{33} -4.44125 q^{34} +1.00000 q^{35} +(-2.74418 - 0.431140i) q^{36} +7.87365 q^{37} +14.6118i q^{38} +(5.02954 + 0.392689i) q^{39} -1.83721i q^{40} -4.24521 q^{41} +(2.95375 + 0.230619i) q^{42} -7.69055i q^{43} +(1.50654 + 2.67610i) q^{44} +(-0.465620 + 2.96365i) q^{45} -9.36877i q^{46} -8.33635i q^{47} +(0.673371 - 8.62451i) q^{48} -1.00000 q^{49} +1.71054 q^{50} +(-0.350052 + 4.48346i) q^{51} -2.69696i q^{52} -8.95553i q^{53} +(-2.05880 + 8.64650i) q^{54} +(2.89012 - 1.62703i) q^{55} +1.83721i q^{56} +(14.7506 + 1.15167i) q^{57} -6.24254 q^{58} -6.09265i q^{59} +(1.59892 + 0.124838i) q^{60} +8.94663i q^{61} +1.40082 q^{62} +(0.465620 - 2.96365i) q^{63} +1.66058 q^{64} -2.91265 q^{65} +(8.91192 - 4.13933i) q^{66} +6.60766 q^{67} +2.40413 q^{68} +(-9.45781 - 0.738432i) q^{69} -1.71054 q^{70} +13.8063i q^{71} +(-5.44484 - 0.855442i) q^{72} +5.85007i q^{73} -13.4682 q^{74} +(0.134822 - 1.72680i) q^{75} -7.90962i q^{76} +(-2.89012 + 1.62703i) q^{77} +(-8.60324 - 0.671710i) q^{78} +5.16910i q^{79} +4.99452i q^{80} +(8.56640 + 2.75987i) q^{81} +7.26160 q^{82} +15.5613 q^{83} +(-1.59892 - 0.124838i) q^{84} -2.59640i q^{85} +13.1550i q^{86} +(-0.492027 + 6.30187i) q^{87} +(2.98919 + 5.30975i) q^{88} +1.96852i q^{89} +(0.796462 - 5.06944i) q^{90} +2.91265 q^{91} +5.07150i q^{92} +(0.110411 - 1.41413i) q^{93} +14.2597i q^{94} -8.54218 q^{95} +(-0.656436 + 8.40760i) q^{96} +1.84185 q^{97} +1.71054 q^{98} +(-3.47624 - 9.32286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.71054			−1.20953			−0.604767	−	0.796402i	$-0.706734\pi$
$2$	−1.71054			−1.20953			−0.604767	+	0.796402i	$0.706734\pi$
$3$	−0.134822	+	1.72680i	−0.0778396	+	0.996966i
$3$	−0.134822	+	1.72680i	−0.0778396	+	0.996966i
$4$	0.925948			0.462974
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.230619	−	2.95375i	0.0941496	−	1.20586i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.83721			0.649551
$9$	−2.96365	−	0.465620i	−0.987882	−	0.155207i
$10$			1.71054i			0.540920i
$11$	1.62703	+	2.89012i	0.490568	+	0.871403i
$11$	1.62703	+	2.89012i	0.490568	+	0.871403i
$12$	−0.124838	+	1.59892i	−0.0360377	+	0.461569i
$13$		−	2.91265i		−	0.807822i	−0.914798	−	0.403911i	$-0.867650\pi$
$13$		−	2.91265i		−	0.807822i	0.914798	−	0.403911i	$-0.132350\pi$
$14$		−	1.71054i		−	0.457161i
$15$	1.72680	+	0.134822i	0.445857	+	0.0348109i
$16$	−4.99452			−1.24863
$17$	2.59640			0.629720			0.314860	−	0.949138i	$-0.398042\pi$
$17$	2.59640			0.629720			0.314860	+	0.949138i	$0.398042\pi$
$18$	5.06944	+	0.796462i	1.19488	+	0.187728i
$19$		−	8.54218i		−	1.95971i	−0.199707	−	0.979856i	$-0.563999\pi$
$19$		−	8.54218i		−	1.95971i	0.199707	−	0.979856i	$-0.436001\pi$
$20$		−	0.925948i		−	0.207048i
$21$	−1.72680	−	0.134822i	−0.376818	−	0.0294206i
$22$	−2.78310	−	4.94366i	−0.593359	−	1.05399i
$23$			5.47708i			1.14205i	0.820932	+	0.571026i	$0.193454\pi$
$23$			5.47708i			1.14205i	−0.820932	+	0.571026i	$0.806546\pi$
$24$	−0.247696	+	3.17248i	−0.0505608	+	0.647581i
$25$	−1.00000			−0.200000
$26$			4.98220i			0.977089i
$27$	1.20360	−	5.05483i	0.231632	−	0.972803i
$28$			0.925948i			0.174988i
$29$	3.64946			0.677687			0.338844	−	0.940843i	$-0.389964\pi$
$29$	3.64946			0.677687			0.338844	+	0.940843i	$0.389964\pi$
$30$	−2.95375	−	0.230619i	−0.539279	−	0.0421050i
$31$	−0.818935			−0.147085			−0.0735426	−	0.997292i	$-0.523430\pi$
$31$	−0.818935			−0.147085			−0.0735426	+	0.997292i	$0.523430\pi$
$32$	4.86890			0.860709
$33$	−5.21000	+	2.41989i	−0.906945	+	0.421250i
$34$	−4.44125			−0.761668
$35$	1.00000			0.169031
$36$	−2.74418	−	0.431140i	−0.457364	−	0.0718567i
$37$	7.87365			1.29442			0.647210	−	0.762311i	$-0.275936\pi$
$37$	7.87365			1.29442			0.647210	+	0.762311i	$0.275936\pi$
$38$			14.6118i			2.37034i
$39$	5.02954	+	0.392689i	0.805371	+	0.0628805i
$40$		−	1.83721i		−	0.290488i
$41$	−4.24521			−0.662990			−0.331495	−	0.943457i	$-0.607553\pi$
$41$	−4.24521			−0.662990			−0.331495	+	0.943457i	$0.607553\pi$
$42$	2.95375	+	0.230619i	0.455774	+	0.0355852i
$43$		−	7.69055i		−	1.17280i	−0.810022	−	0.586399i	$-0.800545\pi$
$43$		−	7.69055i		−	1.17280i	0.810022	−	0.586399i	$-0.199455\pi$
$44$	1.50654	+	2.67610i	0.227120	+	0.403437i
$45$	−0.465620	+	2.96365i	−0.0694106	+	0.441794i
$46$		−	9.36877i		−	1.38135i
$47$		−	8.33635i		−	1.21598i	−0.793944	−	0.607991i	$-0.791976\pi$
$47$		−	8.33635i		−	1.21598i	0.793944	−	0.607991i	$-0.208024\pi$
$48$	0.673371	−	8.62451i	0.0971927	−	1.24484i
$49$	−1.00000			−0.142857
$50$	1.71054			0.241907
$51$	−0.350052	+	4.48346i	−0.0490171	+	0.627809i
$52$		−	2.69696i		−	0.374001i
$53$		−	8.95553i		−	1.23014i	−0.788474	−	0.615068i	$-0.789128\pi$
$53$		−	8.95553i		−	1.23014i	0.788474	−	0.615068i	$-0.210872\pi$
$54$	−2.05880	+	8.64650i	−0.280167	+	1.17664i
$55$	2.89012	−	1.62703i	0.389703	−	0.219388i
$56$			1.83721i			0.245507i
$57$	14.7506	+	1.15167i	1.95377	+	0.152543i
$58$	−6.24254			−0.819686
$59$		−	6.09265i		−	0.793195i	−0.917993	−	0.396598i	$-0.870191\pi$
$59$		−	6.09265i		−	0.793195i	0.917993	−	0.396598i	$-0.129809\pi$
$60$	1.59892	+	0.124838i	0.206420	+	0.0161165i
$61$			8.94663i			1.14550i	0.819730	+	0.572749i	$0.194123\pi$
$61$			8.94663i			1.14550i	−0.819730	+	0.572749i	$0.805877\pi$
$62$	1.40082			0.177905
$63$	0.465620	−	2.96365i	0.0586626	−	0.373384i
$64$	1.66058			0.207572
$65$	−2.91265			−0.361269
$66$	8.91192	−	4.13933i	1.09698	−	0.509516i
$67$	6.60766			0.807254			0.403627	−	0.914924i	$-0.367749\pi$
$67$	6.60766			0.807254			0.403627	+	0.914924i	$0.367749\pi$
$68$	2.40413			0.291544
$69$	−9.45781	−	0.738432i	−1.13859	−	0.0888968i
$70$	−1.71054			−0.204449
$71$			13.8063i			1.63850i	0.573434	+	0.819252i	$0.305611\pi$
$71$			13.8063i			1.63850i	−0.573434	+	0.819252i	$0.694389\pi$
$72$	−5.44484	−	0.855442i	−0.641680	−	0.100815i
$73$			5.85007i			0.684699i	0.939573	+	0.342349i	$0.111223\pi$
$73$			5.85007i			0.684699i	−0.939573	+	0.342349i	$0.888777\pi$
$74$	−13.4682			−1.56565
$75$	0.134822	−	1.72680i	0.0155679	−	0.199393i
$76$		−	7.90962i		−	0.907296i
$77$	−2.89012	+	1.62703i	−0.329359	+	0.185417i
$78$	−8.60324	−	0.671710i	−0.974125	−	0.0760562i
$79$			5.16910i			0.581569i	0.956789	+	0.290785i	$0.0939163\pi$
$79$			5.16910i			0.581569i	−0.956789	+	0.290785i	$0.906084\pi$
$80$			4.99452i			0.558404i
$81$	8.56640	+	2.75987i	0.951822	+	0.306652i
$82$	7.26160			0.801910
$83$	15.5613			1.70807			0.854037	−	0.520212i	$-0.174147\pi$
$83$	15.5613			1.70807			0.854037	+	0.520212i	$0.174147\pi$
$84$	−1.59892	−	0.124838i	−0.174457	−	0.0136210i
$85$		−	2.59640i		−	0.281619i
$86$			13.1550i			1.41854i
$87$	−0.492027	+	6.30187i	−0.0527509	+	0.675631i
$88$	2.98919	+	5.30975i	0.318649	+	0.566021i
$89$			1.96852i			0.208663i	0.994543	+	0.104331i	$0.0332703\pi$
$89$			1.96852i			0.208663i	−0.994543	+	0.104331i	$0.966730\pi$
$90$	0.796462	−	5.06944i	0.0839545	−	0.534365i
$91$	2.91265			0.305328
$92$			5.07150i			0.528740i
$93$	0.110411	−	1.41413i	0.0114490	−	0.146639i
$94$			14.2597i			1.47077i
$95$	−8.54218			−0.876410
$96$	−0.656436	+	8.40760i	−0.0669972	+	0.858097i
$97$	1.84185			0.187012			0.0935058	−	0.995619i	$-0.470193\pi$
$97$	1.84185			0.187012			0.0935058	+	0.995619i	$0.470193\pi$
$98$	1.71054			0.172791
$99$	−3.47624	−	9.32286i	−0.349375	−	0.936983i
$100$	−0.925948			−0.0925948
$101$	0.402680			0.0400682			0.0200341	−	0.999799i	$-0.493623\pi$
$101$	0.402680			0.0400682			0.0200341	+	0.999799i	$0.493623\pi$
$102$	0.598779	−	7.66913i	0.0592879	−	0.759357i
$103$	17.4242			1.71686			0.858429	−	0.512932i	$-0.171441\pi$
$103$	17.4242			1.71686			0.858429	+	0.512932i	$0.171441\pi$
$104$		−	5.35114i		−	0.524722i
$105$	−0.134822	+	1.72680i	−0.0131573	+	0.168518i
$106$			15.3188i			1.48789i
$107$	14.0557			1.35881			0.679406	−	0.733763i	$-0.262238\pi$
$107$	14.0557			1.35881			0.679406	+	0.733763i	$0.262238\pi$
$108$	1.11447	−	4.68052i	0.107240	−	0.450383i
$109$			10.8571i			1.03993i	0.854189	+	0.519963i	$0.174054\pi$
$109$			10.8571i			1.03993i	−0.854189	+	0.519963i	$0.825946\pi$
$110$	−4.94366	+	2.78310i	−0.471360	+	0.265358i
$111$	−1.06154	+	13.5962i	−0.100757	+	1.29049i
$112$		−	4.99452i		−	0.471937i
$113$			18.1520i			1.70760i	0.520603	+	0.853799i	$0.325707\pi$
$113$			18.1520i			1.70760i	−0.520603	+	0.853799i	$0.674293\pi$
$114$	−25.2315	−	1.96999i	−2.36315	−	0.184506i
$115$	5.47708			0.510741
$116$	3.37921			0.313752
$117$	−1.35619	+	8.63205i	−0.125380	+	0.798033i
$118$			10.4217i			0.959397i
$119$			2.59640i			0.238012i
$120$	3.17248	+	0.247696i	0.289607	+	0.0226115i
$121$	−5.70556	+	9.40461i	−0.518687	+	0.854964i
$122$		−	15.3036i		−	1.38552i
$123$	0.572348	−	7.33061i	0.0516069	−	0.660979i
$124$	−0.758292			−0.0680966
$125$			1.00000i			0.0894427i
$126$	−0.796462	+	5.06944i	−0.0709545	+	0.451621i
$127$		−	21.0203i		−	1.86525i	−0.360848	−	0.932625i	$-0.617513\pi$
$127$		−	21.0203i		−	1.86525i	0.360848	−	0.932625i	$-0.382487\pi$
$128$	−12.5783			−1.11177
$129$	13.2800	+	1.03686i	1.16924	+	0.0912901i
$130$	4.98220			0.436968
$131$	1.69649			0.148223			0.0741116	−	0.997250i	$-0.476388\pi$
$131$	1.69649			0.148223			0.0741116	+	0.997250i	$0.476388\pi$
$132$	−4.82419	+	2.24070i	−0.419892	+	0.195028i
$133$	8.54218			0.740701
$134$	−11.3027			−0.976401
$135$	−5.05483	−	1.20360i	−0.435051	−	0.103589i
$136$	4.77013			0.409036
$137$			22.8151i			1.94922i	0.223902	+	0.974612i	$0.428121\pi$
$137$			22.8151i			1.94922i	−0.223902	+	0.974612i	$0.571879\pi$
$138$	16.1780	+	1.26312i	1.37716	+	0.107524i
$139$		−	3.79771i		−	0.322118i	−0.986945	−	0.161059i	$-0.948509\pi$
$139$		−	3.79771i		−	0.322118i	0.986945	−	0.161059i	$-0.0514909\pi$
$140$	0.925948			0.0782569
$141$	14.3952	+	1.12392i	1.21229	+	0.0946514i
$142$		−	23.6162i		−	1.98183i
$143$	8.41789	−	4.73896i	0.703939	−	0.396292i
$144$	14.8020	+	2.32555i	1.23350	+	0.193796i
$145$		−	3.64946i		−	0.303071i
$146$		−	10.0068i		−	0.828167i
$147$	0.134822	−	1.72680i	0.0111199	−	0.142424i
$148$	7.29059			0.599283
$149$	0.0325137			0.00266363			0.00133181	−	0.999999i	$-0.499576\pi$
$149$	0.0325137			0.00266363			0.00133181	+	0.999999i	$0.499576\pi$
$150$	−0.230619	+	2.95375i	−0.0188299	+	0.241173i
$151$		−	13.1859i		−	1.07306i	−0.843882	−	0.536528i	$-0.819736\pi$
$151$		−	13.1859i		−	1.07306i	0.843882	−	0.536528i	$-0.180264\pi$
$152$		−	15.6938i		−	1.27293i
$153$	−7.69482	−	1.20894i	−0.622089	−	0.0977368i
$154$	4.94366	−	2.78310i	0.398372	−	0.224268i
$155$			0.818935i			0.0657785i
$156$	4.65710	+	0.363610i	0.372866	+	0.0291121i
$157$	−19.8296			−1.58258			−0.791289	−	0.611442i	$-0.790590\pi$
$157$	−19.8296			−1.58258			−0.791289	+	0.611442i	$0.790590\pi$
$158$		−	8.84195i		−	0.703428i
$159$	15.4644	+	1.20740i	1.22640	+	0.0957533i
$160$		−	4.86890i		−	0.384921i
$161$	−5.47708			−0.431655
$162$	−14.6532	−	4.72086i	−1.15126	−	0.370906i
$163$	4.95147			0.387829			0.193914	−	0.981018i	$-0.437882\pi$
$163$	4.95147			0.387829			0.193914	+	0.981018i	$0.437882\pi$
$164$	−3.93084			−0.306947
$165$	2.41989	+	5.21000i	0.188389	+	0.405598i
$166$	−26.6182			−2.06597
$167$	7.75939			0.600440			0.300220	−	0.953870i	$-0.402940\pi$
$167$	7.75939			0.600440			0.300220	+	0.953870i	$0.402940\pi$
$168$	−3.17248	−	0.247696i	−0.244762	−	0.0191102i
$169$	4.51650			0.347423
$170$			4.44125i			0.340628i
$171$	−3.97741	+	25.3160i	−0.304160	+	1.93596i
$172$		−	7.12105i		−	0.542975i
$173$	−8.65215			−0.657811			−0.328906	−	0.944363i	$-0.606680\pi$
$173$	−8.65215			−0.657811			−0.328906	+	0.944363i	$0.606680\pi$
$174$	0.841633	−	10.7796i	0.0638040	−	0.817199i
$175$		−	1.00000i		−	0.0755929i
$176$	−8.12622	−	14.4347i	−0.612537	−	1.08806i
$177$	10.5208	+	0.821423i	0.790788	+	0.0617420i
$178$		−	3.36724i		−	0.252385i
$179$		−	12.7222i		−	0.950902i	−0.879742	−	0.475451i	$-0.842285\pi$
$179$		−	12.7222i		−	0.950902i	0.879742	−	0.475451i	$-0.157715\pi$
$180$	−0.431140	+	2.74418i	−0.0321353	+	0.204539i
$181$	13.5316			1.00579			0.502897	−	0.864346i	$-0.332267\pi$
$181$	13.5316			1.00579			0.502897	+	0.864346i	$0.332267\pi$
$182$	−4.98220			−0.369305
$183$	−15.4490	−	1.20620i	−1.14202	−	0.0891651i
$184$			10.0625i			0.741821i
$185$		−	7.87365i		−	0.578883i
$186$	−0.188862	+	2.41893i	−0.0138480	+	0.177365i
$187$	4.22442	+	7.50391i	0.308920	+	0.548740i
$188$		−	7.71902i		−	0.562968i
$189$	5.05483	+	1.20360i	0.367685	+	0.0875487i
$190$	14.6118			1.06005
$191$			10.0545i			0.727521i	0.931492	+	0.363761i	$0.118507\pi$
$191$			10.0545i			0.727521i	−0.931492	+	0.363761i	$0.881493\pi$
$192$	−0.223882	+	2.86748i	−0.0161573	+	0.206942i
$193$		−	17.3464i		−	1.24862i	−0.781176	−	0.624311i	$-0.785380\pi$
$193$		−	17.3464i		−	1.24862i	0.781176	−	0.624311i	$-0.214620\pi$
$194$	−3.15056			−0.226197
$195$	0.392689	−	5.02954i	0.0281210	−	0.360173i
$196$	−0.925948			−0.0661392
$197$	12.3795			0.882003			0.441002	−	0.897506i	$-0.354623\pi$
$197$	12.3795			0.882003			0.441002	+	0.897506i	$0.354623\pi$
$198$	5.94625	+	15.9471i	0.422581	+	1.13331i
$199$	−0.184744			−0.0130961			−0.00654806	−	0.999979i	$-0.502084\pi$
$199$	−0.184744			−0.0130961			−0.00654806	+	0.999979i	$0.502084\pi$
$200$	−1.83721			−0.129910
$201$	−0.890858	+	11.4101i	−0.0628363	+	0.804804i
$202$	−0.688801			−0.0484639
$203$			3.64946i			0.256142i
$204$	−0.324130	+	4.15145i	−0.0226937	+	0.290660i
$205$			4.24521i			0.296498i
$206$	−29.8048			−2.07660
$207$	2.55024	−	16.2321i	0.177254	−	1.12821i
$208$			14.5473i			1.00867i
$209$	24.6879	−	13.8984i	1.70770	−	0.961371i
$210$	0.230619	−	2.95375i	0.0159142	−	0.203828i
$211$		−	6.43790i		−	0.443203i	−0.975137	−	0.221602i	$-0.928872\pi$
$211$		−	6.43790i		−	0.443203i	0.975137	−	0.221602i	$-0.0711284\pi$
$212$		−	8.29236i		−	0.569522i
$213$	−23.8406	−	1.86139i	−1.63353	−	0.127540i
$214$	−24.0428			−1.64353
$215$	−7.69055			−0.524491
$216$	2.21126	−	9.28679i	0.150457	−	0.631886i
$217$		−	0.818935i		−	0.0555929i
$218$		−	18.5716i		−	1.25783i
$219$	−10.1019	−	0.788719i	−0.682621	−	0.0532967i
$220$	2.67610	−	1.50654i	0.180423	−	0.101571i
$221$		−	7.56240i		−	0.508702i
$222$	1.81581	−	23.2568i	0.121869	−	1.56090i
$223$	16.9239			1.13331			0.566654	−	0.823956i	$-0.308238\pi$
$223$	16.9239			1.13331			0.566654	+	0.823956i	$0.308238\pi$
$224$			4.86890i			0.325317i
$225$	2.96365	+	0.465620i	0.197576	+	0.0310414i
$226$		−	31.0498i		−	2.06540i
$227$	−6.92798			−0.459826			−0.229913	−	0.973211i	$-0.573844\pi$
$227$	−6.92798			−0.459826			−0.229913	+	0.973211i	$0.573844\pi$
$228$	13.6583	+	1.06639i	0.904543	+	0.0706235i
$229$	16.7741			1.10847			0.554233	−	0.832362i	$-0.313012\pi$
$229$	16.7741			1.10847			0.554233	+	0.832362i	$0.313012\pi$
$230$	−9.36877			−0.617759
$231$	−2.41989	−	5.21000i	−0.159217	−	0.342793i
$232$	6.70482			0.440193
$233$	5.44916			0.356986			0.178493	−	0.983941i	$-0.442878\pi$
$233$	5.44916			0.356986			0.178493	+	0.983941i	$0.442878\pi$
$234$	2.31981	−	14.7655i	0.151651	−	0.965249i
$235$	−8.33635			−0.543803
$236$		−	5.64148i		−	0.367229i
$237$	−8.92598	−	0.696909i	−0.579805	−	0.0452691i
$238$		−	4.44125i		−	0.287884i
$239$	−24.9896			−1.61644			−0.808221	−	0.588879i	$-0.799570\pi$
$239$	−24.9896			−1.61644			−0.808221	+	0.588879i	$0.799570\pi$
$240$	−8.62451	−	0.673371i	−0.556710	−	0.0434659i
$241$		−	7.00460i		−	0.451206i	−0.974219	−	0.225603i	$-0.927565\pi$
$241$		−	7.00460i		−	0.451206i	0.974219	−	0.225603i	$-0.0724352\pi$
$242$	9.75958	−	16.0870i	0.627370	−	1.03411i
$243$	−5.92067	+	14.4203i	−0.379811	+	0.925064i
$244$			8.28412i			0.530336i
$245$			1.00000i			0.0638877i
$246$	−0.979024	+	12.5393i	−0.0624203	+	0.799476i
$247$	−24.8804			−1.58310
$248$	−1.50456			−0.0955394
$249$	−2.09801	+	26.8712i	−0.132956	+	1.70289i
$250$		−	1.71054i		−	0.108184i
$251$		−	12.0660i		−	0.761602i	−0.924657	−	0.380801i	$-0.875648\pi$
$251$		−	12.0660i		−	0.761602i	0.924657	−	0.380801i	$-0.124352\pi$
$252$	0.431140	−	2.74418i	0.0271593	−	0.172867i
$253$	−15.8294	+	8.91137i	−0.995187	+	0.560253i
$254$			35.9561i			2.25608i
$255$	4.48346	+	0.350052i	0.280765	+	0.0219211i
$256$	18.1945			1.13716
$257$			7.07041i			0.441040i	0.975382	+	0.220520i	$0.0707754\pi$
$257$			7.07041i			0.441040i	−0.975382	+	0.220520i	$0.929225\pi$
$258$	−22.7160	−	1.77358i	−1.41424	−	0.110418i
$259$			7.87365i			0.489245i
$260$	−2.69696			−0.167258
$261$	−10.8157	−	1.69926i	−0.669475	−	0.105182i
$262$	−2.90192			−0.179281
$263$	−10.8435			−0.668641			−0.334320	−	0.942460i	$-0.608507\pi$
$263$	−10.8435			−0.668641			−0.334320	+	0.942460i	$0.608507\pi$
$264$	−9.57186	+	4.44585i	−0.589107	+	0.273623i
$265$	−8.95553			−0.550134
$266$	−14.6118			−0.895904
$267$	−3.39924	−	0.265400i	−0.208030	−	0.0162422i
$268$	6.11835			0.373738
$269$			0.498283i			0.0303808i	0.999885	+	0.0151904i	$0.00483545\pi$
$269$			0.498283i			0.0303808i	−0.999885	+	0.0151904i	$0.995165\pi$
$270$	8.64650	+	2.05880i	0.526209	+	0.125295i
$271$		−	2.79735i		−	0.169927i	−0.996384	−	0.0849635i	$-0.972923\pi$
$271$		−	2.79735i		−	0.169927i	0.996384	−	0.0849635i	$-0.0270774\pi$
$272$	−12.9678			−0.786287
$273$	−0.392689	+	5.02954i	−0.0237666	+	0.304402i
$274$		−	39.0261i		−	2.35765i
$275$	−1.62703	−	2.89012i	−0.0981135	−	0.174281i
$276$	−8.75744	−	0.683750i	−0.527136	−	0.0411569i
$277$		−	20.5396i		−	1.23410i	−0.786923	−	0.617052i	$-0.788327\pi$
$277$		−	20.5396i		−	1.23410i	0.786923	−	0.617052i	$-0.211673\pi$
$278$			6.49614i			0.389612i
$279$	2.42703	+	0.381313i	0.145303	+	0.0228286i
$280$	1.83721			0.109794
$281$	−11.6316			−0.693883			−0.346942	−	0.937887i	$-0.612780\pi$
$281$	−11.6316			−0.693883			−0.346942	+	0.937887i	$0.612780\pi$
$282$	−24.6235	−	1.92252i	−1.46631	−	0.114484i
$283$			17.6607i			1.04982i	0.851159	+	0.524909i	$0.175901\pi$
$283$			17.6607i			1.04982i	−0.851159	+	0.524909i	$0.824099\pi$
$284$			12.7839i			0.758585i
$285$	1.15167	−	14.7506i	0.0682193	−	0.873751i
$286$	−14.3991	+	8.10618i	−0.851439	+	0.479328i
$287$		−	4.24521i		−	0.250587i
$288$	−14.4297	−	2.26706i	−0.850279	−	0.133588i
$289$	−10.2587			−0.603453
$290$			6.24254i			0.366575i
$291$	−0.248322	+	3.18050i	−0.0145569	+	0.186444i
$292$			5.41686i			0.316998i
$293$	12.4626			0.728074			0.364037	−	0.931385i	$-0.381398\pi$
$293$	12.4626			0.728074			0.364037	+	0.931385i	$0.381398\pi$
$294$	−0.230619	+	2.95375i	−0.0134499	+	0.172266i
$295$	−6.09265			−0.354728
$296$	14.4655			0.840793
$297$	16.5674	−	4.74583i	0.961335	−	0.275381i
$298$	−0.0556160			−0.00322175
$299$	15.9528			0.922575
$300$	0.124838	−	1.59892i	0.00720754	−	0.0923139i
$301$	7.69055			0.443276
$302$			22.5551i			1.29790i
$303$	−0.0542902	+	0.695346i	−0.00311889	+	0.0399466i
$304$			42.6641i			2.44695i
$305$	8.94663			0.512283
$306$	13.1623	+	2.06794i	0.752438	+	0.118216i
$307$		−	32.3730i		−	1.84762i	−0.382847	−	0.923812i	$-0.625056\pi$
$307$		−	32.3730i		−	1.84762i	0.382847	−	0.923812i	$-0.374944\pi$
$308$	−2.67610	+	1.50654i	−0.152485	+	0.0858433i
$309$	−2.34917	+	30.0880i	−0.133639	+	1.71165i
$310$		−	1.40082i		−	0.0795613i
$311$		−	21.7486i		−	1.23325i	−0.787258	−	0.616624i	$-0.788500\pi$
$311$		−	21.7486i		−	1.23325i	0.787258	−	0.616624i	$-0.211500\pi$
$312$	9.24032	+	0.721451i	0.523130	+	0.0408441i
$313$	−25.1141			−1.41953			−0.709765	−	0.704438i	$-0.751199\pi$
$313$	−25.1141			−1.41953			−0.709765	+	0.704438i	$0.751199\pi$
$314$	33.9194			1.91418
$315$	−2.96365	−	0.465620i	−0.166983	−	0.0262347i
$316$			4.78632i			0.269251i
$317$		−	8.70505i		−	0.488924i	−0.969659	−	0.244462i	$-0.921389\pi$
$317$		−	8.70505i		−	0.488924i	0.969659	−	0.244462i	$-0.0786114\pi$
$318$	−26.4524	−	2.06531i	−1.48338	−	0.115817i
$319$	5.93777	+	10.5474i	0.332451	+	0.590539i
$320$		−	1.66058i		−	0.0928291i
$321$	−1.89501	+	24.2712i	−0.105769	+	1.35469i
$322$	9.36877			0.522101
$323$		−	22.1789i		−	1.23407i
$324$	7.93204	+	2.55549i	0.440669	+	0.141972i
$325$			2.91265i			0.161564i
$326$	−8.46968			−0.469092
$327$	−18.7481	−	1.46378i	−1.03677	−	0.0809474i
$328$	−7.79933			−0.430646
$329$	8.33635			0.459598
$330$	−4.13933	−	8.91192i	−0.227862	−	0.490585i
$331$	−0.0265806			−0.00146100			−0.000730501	−	1.00000i	$-0.500233\pi$
$331$	−0.0265806			−0.00146100			−0.000730501		1.00000i	$0.500233\pi$
$332$	14.4090			0.790794
$333$	−23.3347	−	3.66613i	−1.27873	−	0.200903i
$334$	−13.2728			−0.726253
$335$		−	6.60766i		−	0.361015i
$336$	8.62451	+	0.673371i	0.470506	+	0.0367354i
$337$		−	12.8940i		−	0.702383i	−0.936304	−	0.351192i	$-0.885777\pi$
$337$		−	12.8940i		−	0.702383i	0.936304	−	0.351192i	$-0.114223\pi$
$338$	−7.72565			−0.420220
$339$	−31.3448	−	2.44729i	−1.70242	−	0.132919i
$340$		−	2.40413i		−	0.130382i
$341$	−1.33243	−	2.36682i	−0.0721552	−	0.128170i
$342$	6.80353	−	43.3041i	0.367893	−	2.34162i
$343$		−	1.00000i		−	0.0539949i
$344$		−	14.1291i		−	0.761793i
$345$	−0.738432	+	9.45781i	−0.0397558	+	0.509191i
$346$	14.7999			0.795645
$347$	−11.2942			−0.606304			−0.303152	−	0.952942i	$-0.598039\pi$
$347$	−11.2942			−0.606304			−0.303152	+	0.952942i	$0.598039\pi$
$348$	−0.455592	+	5.83520i	−0.0244223	+	0.312800i
$349$		−	10.5462i		−	0.564527i	−0.959337	−	0.282264i	$-0.908915\pi$
$349$		−	10.5462i		−	0.564527i	0.959337	−	0.282264i	$-0.0910853\pi$
$350$			1.71054i			0.0914322i
$351$	−14.7229	−	3.50565i	−0.785852	−	0.187118i
$352$	7.92185	+	14.0717i	0.422236	+	0.750024i
$353$			17.2810i			0.919775i	0.887977	+	0.459887i	$0.152110\pi$
$353$			17.2810i			0.919775i	−0.887977	+	0.459887i	$0.847890\pi$
$354$	−17.9962	−	1.40508i	−0.956486	−	0.0746790i
$355$	13.8063			0.732761
$356$			1.82275i			0.0966055i
$357$	−4.48346	−	0.350052i	−0.237290	−	0.0185267i
$358$			21.7618i			1.15015i
$359$	23.7382			1.25285			0.626427	−	0.779480i	$-0.284517\pi$
$359$	23.7382			1.25285			0.626427	+	0.779480i	$0.284517\pi$
$360$	−0.855442	+	5.44484i	−0.0450857	+	0.286968i
$361$	−53.9689			−2.84047
$362$	−23.1463			−1.21654
$363$	−15.4706	−	11.1203i	−0.811996	−	0.583663i
$364$	2.69696			0.141359
$365$	5.85007			0.306207
$366$	26.4261	+	2.06326i	1.38132	+	0.107848i
$367$	10.3240			0.538908			0.269454	−	0.963013i	$-0.413157\pi$
$367$	10.3240			0.538908			0.269454	+	0.963013i	$0.413157\pi$
$368$		−	27.3554i		−	1.42600i
$369$	12.5813	+	1.97666i	0.654956	+	0.102901i
$370$			13.4682i			0.700178i
$371$	8.95553			0.464948
$372$	0.102234	−	1.30941i	0.00530061	−	0.0678900i
$373$			22.8858i			1.18498i	0.805578	+	0.592490i	$0.201855\pi$
$373$			22.8858i			1.18498i	−0.805578	+	0.592490i	$0.798145\pi$
$374$	−7.22604	−	12.8357i	−0.373650	−	0.663720i
$375$	−1.72680	−	0.134822i	−0.0891713	−	0.00696218i
$376$		−	15.3156i		−	0.789842i
$377$		−	10.6296i		−	0.547451i
$378$	−8.64650	−	2.05880i	−0.444728	−	0.105893i
$379$	−29.2649			−1.50324			−0.751618	−	0.659599i	$-0.770726\pi$
$379$	−29.2649			−1.50324			−0.751618	+	0.659599i	$0.770726\pi$
$380$	−7.90962			−0.405755
$381$	36.2977	+	2.83400i	1.85959	+	0.145190i
$382$		−	17.1987i		−	0.879962i
$383$			8.93135i			0.456371i	0.973618	+	0.228185i	$0.0732792\pi$
$383$			8.93135i			0.456371i	−0.973618	+	0.228185i	$0.926721\pi$
$384$	1.69583	−	21.7201i	0.0865400	−	1.10840i
$385$	1.62703	+	2.89012i	0.0829211	+	0.147294i
$386$			29.6717i			1.51025i
$387$	−3.58088	+	22.7921i	−0.182026	+	1.15859i
$388$	1.70546			0.0865815
$389$		−	28.9403i		−	1.46733i	−0.679509	−	0.733667i	$-0.737807\pi$
$389$		−	28.9403i		−	1.46733i	0.679509	−	0.733667i	$-0.262193\pi$
$390$	−0.671710	+	8.60324i	−0.0340134	+	0.435642i
$391$			14.2207i			0.719173i
$392$	−1.83721			−0.0927931
$393$	−0.228724	+	2.92949i	−0.0115376	+	0.147773i
$394$	−21.1756			−1.06681
$395$	5.16910			0.260086
$396$	−3.21882	−	8.63249i	−0.161752	−	0.433799i
$397$	6.85313			0.343949			0.171974	−	0.985101i	$-0.444985\pi$
$397$	6.85313			0.343949			0.171974	+	0.985101i	$0.444985\pi$
$398$	0.316011			0.0158402
$399$	−1.15167	+	14.7506i	−0.0576559	+	0.738454i
$400$	4.99452			0.249726
$401$		−	0.398644i		−	0.0199073i	−0.999950	−	0.00995367i	$-0.996832\pi$
$401$		−	0.398644i		−	0.0199073i	0.999950	−	0.00995367i	$-0.00316840\pi$
$402$	1.52385	−	19.5174i	0.0760026	−	0.973439i
$403$			2.38527i			0.118819i
$404$	0.372861			0.0185505
$405$	2.75987	−	8.56640i	0.137139	−	0.425668i
$406$		−	6.24254i		−	0.309812i
$407$	12.8107	+	22.7558i	0.635001	+	1.12796i
$408$	−0.643119	+	8.23705i	−0.0318391	+	0.407795i
$409$			10.3287i			0.510723i	0.966846	+	0.255362i	$0.0821945\pi$
$409$			10.3287i			0.510723i	−0.966846	+	0.255362i	$0.917806\pi$
$410$		−	7.26160i		−	0.358625i
$411$	−39.3970	−	3.07598i	−1.94331	−	0.151727i
$412$	16.1339			0.794861
$413$	6.09265			0.299800
$414$	−4.36229	+	27.7657i	−0.214395	+	1.36461i
$415$		−	15.5613i		−	0.763874i
$416$		−	14.1814i		−	0.695300i
$417$	6.55787	+	0.512015i	0.321140	+	0.0250735i
$418$	−42.2297	+	23.7737i	−2.06552	+	1.16281i
$419$			6.32231i			0.308865i	0.988003	+	0.154433i	$0.0493549\pi$
$419$			6.32231i			0.308865i	−0.988003	+	0.154433i	$0.950645\pi$
$420$	−0.124838	+	1.59892i	−0.00609148	+	0.0780195i
$421$	8.01906			0.390825			0.195413	−	0.980721i	$-0.437395\pi$
$421$	8.01906			0.390825			0.195413	+	0.980721i	$0.437395\pi$
$422$			11.0123i			0.536070i
$423$	−3.88157	+	24.7060i	−0.188728	+	1.20125i
$424$		−	16.4532i		−	0.799037i
$425$	−2.59640			−0.125944
$426$	40.7804	+	3.18398i	1.97581	+	0.154265i
$427$	−8.94663			−0.432958
$428$	13.0148			0.629095
$429$	7.04829	+	15.1749i	0.340295	+	0.732650i
$430$	13.1550			0.634390
$431$	−28.5527			−1.37534			−0.687668	−	0.726025i	$-0.741366\pi$
$431$	−28.5527			−1.37534			−0.687668	+	0.726025i	$0.741366\pi$
$432$	−6.01138	+	25.2465i	−0.289223	+	1.21467i
$433$	31.7984			1.52813			0.764067	−	0.645137i	$-0.223200\pi$
$433$	31.7984			1.52813			0.764067	+	0.645137i	$0.223200\pi$
$434$			1.40082i			0.0672416i
$435$	6.30187	+	0.492027i	0.302151	+	0.0235909i
$436$			10.0532i			0.481459i
$437$	46.7863			2.23809
$438$	17.2797	+	1.34913i	0.825654	+	0.0644642i
$439$		−	14.6351i		−	0.698495i	−0.937030	−	0.349248i	$-0.886437\pi$
$439$		−	14.6351i		−	0.698495i	0.937030	−	0.349248i	$-0.113563\pi$
$440$	5.30975	−	2.98919i	0.253132	−	0.142504i
$441$	2.96365	+	0.465620i	0.141126	+	0.0221724i
$442$			12.9358i			0.615293i
$443$			16.7640i			0.796480i	0.917281	+	0.398240i	$0.130379\pi$
$443$			16.7640i			0.796480i	−0.917281	+	0.398240i	$0.869621\pi$
$444$	−0.982933	+	12.5894i	−0.0466479	+	0.597465i
$445$	1.96852			0.0933169
$446$	−28.9490			−1.37078
$447$	−0.00438357	+	0.0561445i	−0.000207336	+	0.00265555i
$448$			1.66058i			0.0784549i
$449$		−	32.1984i		−	1.51954i	−0.650193	−	0.759769i	$-0.725312\pi$
$449$		−	32.1984i		−	1.51954i	0.650193	−	0.759769i	$-0.274688\pi$
$450$	−5.06944	−	0.796462i	−0.238976	−	0.0375456i
$451$	−6.90708	−	12.2691i	−0.325241	−	0.577732i
$452$			16.8078i			0.790574i
$453$	22.7694	+	1.77775i	1.06980	+	0.0835262i
$454$	11.8506			0.556175
$455$		−	2.91265i		−	0.136547i
$456$	27.0999	+	2.11587i	1.26907	+	0.0990846i
$457$			22.5048i			1.05273i	0.850258	+	0.526366i	$0.176446\pi$
$457$			22.5048i			1.05273i	−0.850258	+	0.526366i	$0.823554\pi$
$458$	−28.6928			−1.34073
$459$	3.12502	−	13.1244i	0.145863	−	0.612594i
$460$	5.07150			0.236460
$461$	12.4824			0.581364			0.290682	−	0.956820i	$-0.406118\pi$
$461$	12.4824			0.581364			0.290682	+	0.956820i	$0.406118\pi$
$462$	4.13933	+	8.91192i	0.192579	+	0.414620i
$463$	34.1226			1.58581			0.792906	−	0.609344i	$-0.208567\pi$
$463$	34.1226			1.58581			0.792906	+	0.609344i	$0.208567\pi$
$464$	−18.2273			−0.846180
$465$	−1.41413	−	0.110411i	−0.0655789	−	0.00512017i
$466$	−9.32101			−0.431787
$467$			9.38981i			0.434509i	0.976115	+	0.217254i	$0.0697101\pi$
$467$			9.38981i			0.434509i	−0.976115	+	0.217254i	$0.930290\pi$
$468$	−1.25576	+	7.99283i	−0.0580475	+	0.369469i
$469$			6.60766i			0.305113i
$470$	14.2597			0.657749
$471$	2.67347	−	34.2417i	0.123187	−	1.57778i
$472$		−	11.1935i		−	0.515221i
$473$	22.2266	−	12.5127i	1.02198	−	0.575337i
$474$	15.2682	+	1.19209i	0.701294	+	0.0547545i
$475$			8.54218i			0.391942i
$476$			2.40413i			0.110193i
$477$	−4.16988	+	26.5410i	−0.190926	+	1.21523i
$478$	42.7457			1.95514
$479$	−11.9555			−0.546259			−0.273129	−	0.961977i	$-0.588059\pi$
$479$	−11.9555			−0.546259			−0.273129	+	0.961977i	$0.588059\pi$
$480$	8.40760	+	0.656436i	0.383753	+	0.0299621i
$481$		−	22.9332i		−	1.04566i
$482$			11.9817i			0.545749i
$483$	0.738432	−	9.45781i	0.0335998	−	0.430345i
$484$	−5.28305	+	8.70818i	−0.240139	+	0.395826i
$485$		−	1.84185i		−	0.0836341i
$486$	10.1275	−	24.6665i	0.459394	−	1.11890i
$487$	25.6053			1.16029			0.580144	−	0.814514i	$-0.302996\pi$
$487$	25.6053			1.16029			0.580144	+	0.814514i	$0.302996\pi$
$488$			16.4368i			0.744061i
$489$	−0.667567	+	8.55017i	−0.0301884	+	0.386652i
$490$		−	1.71054i		−	0.0772743i
$491$	2.06697			0.0932810			0.0466405	−	0.998912i	$-0.485148\pi$
$491$	2.06697			0.0932810			0.0466405	+	0.998912i	$0.485148\pi$
$492$	0.529964	−	6.78776i	0.0238926	−	0.306016i
$493$	9.47546			0.426753
$494$	42.5588			1.91481
$495$	−9.32286	+	3.47624i	−0.419031	+	0.156245i
$496$	4.09019			0.183655
$497$	−13.8063			−0.619296
$498$	3.58872	−	45.9642i	0.160815	−	2.05971i
$499$	−0.887583			−0.0397337			−0.0198668	−	0.999803i	$-0.506324\pi$
$499$	−0.887583			−0.0397337			−0.0198668	+	0.999803i	$0.506324\pi$
$500$			0.925948i			0.0414097i
$501$	−1.04614	+	13.3989i	−0.0467380	+	0.598618i
$502$			20.6394i			0.921184i
$503$	7.72462			0.344424			0.172212	−	0.985060i	$-0.444909\pi$
$503$	7.72462			0.344424			0.172212	+	0.985060i	$0.444909\pi$
$504$	0.855442	−	5.44484i	0.0381044	−	0.242532i
$505$		−	0.402680i		−	0.0179190i
$506$	27.0769	−	15.2433i	1.20371	−	0.677646i
$507$	−0.608924	+	7.79907i	−0.0270432	+	0.346369i
$508$		−	19.4637i		−	0.863562i
$509$			21.9715i			0.973869i	0.873439	+	0.486934i	$0.161885\pi$
$509$			21.9715i			0.973869i	−0.873439	+	0.486934i	$0.838115\pi$
$510$	−7.66913	−	0.598779i	−0.339595	−	0.0265144i
$511$	−5.85007			−0.258792
$512$	−5.96588			−0.263657
$513$	−43.1793	−	10.2813i	−1.90641	−	0.453932i
$514$		−	12.0942i		−	0.533453i
$515$		−	17.4242i		−	0.767802i
$516$	12.2966	+	0.960075i	0.541328	+	0.0422649i
$517$	24.0930	−	13.5635i	1.05961	−	0.596521i
$518$		−	13.4682i		−	0.591759i
$519$	1.16650	−	14.9405i	0.0512037	−	0.655815i
$520$	−5.35114			−0.234663
$521$		−	38.9745i		−	1.70750i	−0.520680	−	0.853752i	$-0.674321\pi$
$521$		−	38.9745i		−	1.70750i	0.520680	−	0.853752i	$-0.325679\pi$
$522$	18.5007	+	2.90666i	0.809753	+	0.127221i
$523$		−	15.5404i		−	0.679534i	−0.940510	−	0.339767i	$-0.889652\pi$
$523$		−	15.5404i		−	0.679534i	0.940510	−	0.339767i	$-0.110348\pi$
$524$	1.57086			0.0686235
$525$	1.72680	+	0.134822i	0.0753635	+	0.00588412i
$526$	18.5483			0.808744
$527$	−2.12629			−0.0926225
$528$	26.0214	−	12.0862i	1.13244	−	0.525984i
$529$	−6.99846			−0.304281
$530$	15.3188			0.665406
$531$	−2.83686	+	18.0564i	−0.123109	+	0.783583i
$532$	7.90962			0.342926
$533$			12.3648i			0.535578i
$534$	5.81453	+	0.453978i	0.251619	+	0.0196455i
$535$		−	14.0557i		−	0.607679i
$536$	12.1396			0.524353
$537$	21.9686	+	1.71523i	0.948017	+	0.0740178i
$538$		−	0.852333i		−	0.0367467i
$539$	−1.62703	−	2.89012i	−0.0700811	−	0.124486i
$540$	−4.68052	−	1.11447i	−0.201417	−	0.0479590i
$541$		−	4.83648i		−	0.207937i	−0.994581	−	0.103968i	$-0.966846\pi$
$541$		−	4.83648i		−	0.207937i	0.994581	−	0.103968i	$-0.0331540\pi$
$542$			4.78498i			0.205533i
$543$	−1.82436	+	23.3663i	−0.0782906	+	1.00274i
$544$	12.6416			0.542006
$545$	10.8571			0.465069
$546$	0.671710	−	8.60324i	0.0287465	−	0.368185i
$547$			32.1846i			1.37611i	0.725657	+	0.688056i	$0.241536\pi$
$547$			32.1846i			1.37611i	−0.725657	+	0.688056i	$0.758464\pi$
$548$			21.1256i			0.902440i
$549$	4.16573	−	26.5147i	0.177789	−	1.13162i
$550$	2.78310	+	4.94366i	0.118672	+	0.210798i
$551$		−	31.1743i		−	1.32807i
$552$	−17.3760	−	1.35665i	−0.739570	−	0.0577430i
$553$	−5.16910			−0.219812
$554$			35.1338i			1.49269i
$555$	13.5962	+	1.06154i	0.577126	+	0.0450600i
$556$		−	3.51648i		−	0.149132i
$557$	14.1257			0.598526			0.299263	−	0.954171i	$-0.403259\pi$
$557$	14.1257			0.598526			0.299263	+	0.954171i	$0.403259\pi$
$558$	−4.15154	−	0.652251i	−0.175749	−	0.0276120i
$559$	−22.3998			−0.947412
$560$	−4.99452			−0.211057
$561$	−13.5273	+	6.28302i	−0.571121	+	0.265269i
$562$	19.8963			0.839276
$563$	−33.0423			−1.39257			−0.696284	−	0.717766i	$-0.745165\pi$
$563$	−33.0423			−1.39257			−0.696284	+	0.717766i	$0.745165\pi$
$564$	13.3292	+	1.04069i	0.561260	+	0.0438212i
$565$	18.1520			0.763661
$566$		−	30.2093i		−	1.26979i
$567$	−2.75987	+	8.56640i	−0.115904	+	0.359755i
$568$			25.3650i			1.06429i
$569$	34.4220			1.44305			0.721524	−	0.692390i	$-0.243442\pi$
$569$	34.4220			1.44305			0.721524	+	0.692390i	$0.243442\pi$
$570$	−1.96999	+	25.2315i	−0.0825137	+	1.05683i
$571$			11.9937i			0.501919i	0.967998	+	0.250960i	$0.0807462\pi$
$571$			11.9937i			0.501919i	−0.967998	+	0.250960i	$0.919254\pi$
$572$	7.79453	−	4.38803i	0.325906	−	0.183473i
$573$	−17.3621	−	1.35557i	−0.725314	−	0.0566299i
$574$			7.26160i			0.303093i
$575$		−	5.47708i		−	0.228410i
$576$	−4.92136	−	0.773198i	−0.205057	−	0.0322166i
$577$	−14.7633			−0.614606			−0.307303	−	0.951612i	$-0.599426\pi$
$577$	−14.7633			−0.614606			−0.307303	+	0.951612i	$0.599426\pi$
$578$	17.5479			0.729897
$579$	29.9537	+	2.33868i	1.24483	+	0.0971922i
$580$		−	3.37921i		−	0.140314i
$581$			15.5613i			0.645591i
$582$	0.424765	−	5.44037i	0.0176071	−	0.225511i
$583$	25.8825	−	14.5709i	1.07195	−	0.603465i
$584$			10.7478i			0.444747i
$585$	8.63205	+	1.35619i	0.356891	+	0.0560714i
$586$	−21.3178			−0.880630
$587$			11.2721i			0.465250i	0.972567	+	0.232625i	$0.0747315\pi$
$587$			11.2721i			0.465250i	−0.972567	+	0.232625i	$0.925269\pi$
$588$	0.124838	−	1.59892i	0.00514824	−	0.0659385i
$589$			6.99550i			0.288244i
$590$	10.4217			0.429055
$591$	−1.66903	+	21.3769i	−0.0686547	+	0.879327i
$592$	−39.3251			−1.61625
$593$	−26.2019			−1.07598			−0.537992	−	0.842950i	$-0.680817\pi$
$593$	−26.2019			−1.07598			−0.537992	+	0.842950i	$0.680817\pi$
$594$	−28.3391	+	8.11793i	−1.16277	+	0.333083i
$595$	2.59640			0.106442
$596$	0.0301060			0.00123319
$597$	0.0249075	−	0.319014i	0.00101940	−	0.0130564i
$598$	−27.2879			−1.11589
$599$			18.7545i			0.766287i	0.923689	+	0.383143i	$0.125158\pi$
$599$			18.7545i			0.766287i	−0.923689	+	0.383143i	$0.874842\pi$
$600$	0.247696	−	3.17248i	0.0101122	−	0.129516i
$601$			18.1986i			0.742335i	0.928566	+	0.371168i	$0.121042\pi$
$601$			18.1986i			0.742335i	−0.928566	+	0.371168i	$0.878958\pi$
$602$	−13.1550			−0.536158
$603$	−19.5828	−	3.07666i	−0.797471	−	0.125291i
$604$		−	12.2095i		−	0.496797i
$605$	9.40461	+	5.70556i	0.382352	+	0.231964i
$606$	0.0928655	−	1.18942i	0.00377240	−	0.0483168i
$607$		−	20.5455i		−	0.833915i	−0.908926	−	0.416958i	$-0.863096\pi$
$607$		−	20.5455i		−	0.833915i	0.908926	−	0.416958i	$-0.136904\pi$
$608$		−	41.5911i		−	1.68674i
$609$	−6.30187	−	0.492027i	−0.255365	−	0.0199380i
$610$	−15.3036			−0.619624
$611$	−24.2808			−0.982297
$612$	−7.12500	−	1.11941i	−0.288011	−	0.0452496i
$613$		−	4.32183i		−	0.174557i	−0.996184	−	0.0872785i	$-0.972183\pi$
$613$		−	4.32183i		−	0.174557i	0.996184	−	0.0872785i	$-0.0278170\pi$
$614$			55.3753i			2.23477i
$615$	−7.33061	−	0.572348i	−0.295599	−	0.0230793i
$616$	−5.30975	+	2.98919i	−0.213936	+	0.120438i
$617$			31.0643i			1.25060i	0.780383	+	0.625301i	$0.215024\pi$
$617$			31.0643i			1.25060i	−0.780383	+	0.625301i	$0.784976\pi$
$618$	4.01835	−	51.4668i	0.161642	−	2.07030i
$619$	10.2674			0.412680			0.206340	−	0.978480i	$-0.433845\pi$
$619$	10.2674			0.412680			0.206340	+	0.978480i	$0.433845\pi$
$620$			0.758292i			0.0304537i
$621$	27.6858	+	6.59220i	1.11099	+	0.264536i
$622$			37.2018i			1.49166i
$623$	−1.96852			−0.0788672
$624$	−25.1201	−	1.96129i	−1.00561	−	0.0785145i
$625$	1.00000			0.0400000
$626$	42.9586			1.71697
$627$	20.6712	+	44.5048i	0.825528	+	1.77735i
$628$	−18.3612			−0.732693
$629$	20.4432			0.815123
$630$	5.06944	+	0.796462i	0.201971	+	0.0317318i
$631$	−12.8542			−0.511716			−0.255858	−	0.966714i	$-0.582358\pi$
$631$	−12.8542			−0.511716			−0.255858	+	0.966714i	$0.582358\pi$
$632$			9.49672i			0.377759i
$633$	11.1169	+	0.867971i	0.441858	+	0.0344987i
$634$			14.8903i			0.591371i
$635$	−21.0203			−0.834165
$636$	14.3192	+	1.11799i	0.567794	+	0.0443313i
$637$			2.91265i			0.115403i
$638$	−10.1568	−	18.0417i	−0.402112	−	0.714277i
$639$	6.42848	−	40.9169i	0.254307	−	1.61865i
$640$			12.5783i			0.497201i
$641$			15.9428i			0.629703i	0.949141	+	0.314852i	$0.101955\pi$
$641$			15.9428i			0.629703i	−0.949141	+	0.314852i	$0.898045\pi$
$642$	3.24150	−	41.5169i	0.127932	−	1.63854i
$643$	5.34522			0.210795			0.105398	−	0.994430i	$-0.466389\pi$
$643$	5.34522			0.210795			0.105398	+	0.994430i	$0.466389\pi$
$644$	−5.07150			−0.199845
$645$	1.03686	−	13.2800i	0.0408262	−	0.522900i
$646$			37.9380i			1.49265i
$647$		−	32.4011i		−	1.27382i	−0.770939	−	0.636908i	$-0.780213\pi$
$647$		−	32.4011i		−	1.27382i	0.770939	−	0.636908i	$-0.219787\pi$
$648$	15.7383	+	5.07045i	0.618257	+	0.199186i
$649$	17.6085	−	9.91291i	0.691193	−	0.389116i
$650$		−	4.98220i		−	0.195418i
$651$	1.41413	+	0.110411i	0.0554243	+	0.00432733i
$652$	4.58480			0.179555
$653$			28.9888i			1.13442i	0.823573	+	0.567210i	$0.191977\pi$
$653$			28.9888i			1.13442i	−0.823573	+	0.567210i	$0.808023\pi$
$654$	32.0693	+	2.50386i	1.25401	+	0.0979086i
$655$		−	1.69649i		−	0.0662874i
$656$	21.2028			0.827829
$657$	2.72391	−	17.3375i	0.106270	−	0.676402i
$658$	−14.2597			−0.555899
$659$	−33.6615			−1.31127			−0.655633	−	0.755080i	$-0.727598\pi$
$659$	−33.6615			−1.31127			−0.655633	+	0.755080i	$0.727598\pi$
$660$	2.24070	+	4.82419i	0.0872190	+	0.187781i
$661$	−30.4149			−1.18300			−0.591501	−	0.806304i	$-0.701464\pi$
$661$	−30.4149			−1.18300			−0.591501	+	0.806304i	$0.701464\pi$
$662$	0.0454672			0.00176713
$663$	13.0587	+	1.01958i	0.507159	+	0.0395971i
$664$	28.5893			1.10948
$665$		−	8.54218i		−	0.331252i
$666$	39.9150	+	6.27107i	1.54667	+	0.242999i
$667$			19.9884i			0.773954i
$668$	7.18480			0.277988
$669$	−2.28172	+	29.2241i	−0.0882162	+	1.12987i
$670$			11.3027i			0.436660i
$671$	−25.8568	+	14.5564i	−0.998191	+	0.561945i
$672$	−8.40760	−	0.656436i	−0.324330	−	0.0253226i
$673$		−	31.6621i		−	1.22049i	−0.792215	−	0.610243i	$-0.791072\pi$
$673$		−	31.6621i		−	1.22049i	0.792215	−	0.610243i	$-0.208928\pi$
$674$			22.0558i			0.849557i
$675$	−1.20360	+	5.05483i	−0.0463264	+	0.194561i
$676$	4.18204			0.160848
$677$	−34.7954			−1.33730			−0.668649	−	0.743578i	$-0.733127\pi$
$677$	−34.7954			−1.33730			−0.668649	+	0.743578i	$0.733127\pi$
$678$	53.6166	+	4.18619i	2.05913	+	0.160770i
$679$			1.84185i			0.0706838i
$680$		−	4.77013i		−	0.182926i
$681$	0.934044	−	11.9632i	0.0357926	−	0.458431i
$682$	2.27918	+	4.04854i	0.0872742	+	0.155027i
$683$		−	4.59620i		−	0.175869i	−0.996126	−	0.0879343i	$-0.971973\pi$
$683$		−	4.59620i		−	0.175869i	0.996126	−	0.0879343i	$-0.0280265\pi$
$684$	−3.68288	+	23.4413i	−0.140818	+	0.896301i
$685$	22.8151			0.871719
$686$			1.71054i			0.0653087i
$687$	−2.26152	+	28.9655i	−0.0862825	+	1.10510i
$688$			38.4106i			1.46439i
$689$	−26.0843			−0.993732
$690$	1.26312	−	16.1780i	0.0480861	−	0.615884i
$691$	5.17549			0.196885			0.0984425	−	0.995143i	$-0.468614\pi$
$691$	5.17549			0.196885			0.0984425	+	0.995143i	$0.468614\pi$
$692$	−8.01145			−0.304549
$693$	9.32286	−	3.47624i	0.354146	−	0.132051i
$694$	19.3192			0.733346
$695$	−3.79771			−0.144055
$696$	−0.903957	+	11.5778i	−0.0342644	+	0.438857i
$697$	−11.0223			−0.417498
$698$			18.0398i			0.682815i
$699$	−0.734667	+	9.40958i	−0.0277877	+	0.355903i
$700$		−	0.925948i		−	0.0349976i
$701$	−1.26582			−0.0478095			−0.0239047	−	0.999714i	$-0.507610\pi$
$701$	−1.26582			−0.0478095			−0.0239047	+	0.999714i	$0.507610\pi$
$702$	25.1842	+	5.99655i	0.950516	+	0.226325i
$703$		−	67.2582i		−	2.53669i
$704$	2.70181	+	4.79926i	0.101828	+	0.180879i
$705$	1.12392	−	14.3952i	0.0423294	−	0.542153i
$706$		−	29.5599i		−	1.11250i
$707$			0.402680i			0.0151443i
$708$	9.74168	+	0.760595i	0.366115	+	0.0285849i
$709$	−32.6689			−1.22690			−0.613452	−	0.789732i	$-0.710220\pi$
$709$	−32.6689			−1.22690			−0.613452	+	0.789732i	$0.710220\pi$
$710$	−23.6162			−0.886300
$711$	2.40684	−	15.3194i	0.0902635	−	0.574522i
$712$			3.61659i			0.135537i
$713$		−	4.48538i		−	0.167979i
$714$	7.66913	+	0.598779i	0.287010	+	0.0224087i
$715$	−4.73896	−	8.41789i	−0.177227	−	0.314811i
$716$		−	11.7801i		−	0.440243i
$717$	3.36915	−	43.1519i	0.125823	−	1.61154i
$718$	−40.6051			−1.51537
$719$		−	48.6735i		−	1.81521i	−0.419821	−	0.907607i	$-0.637907\pi$
$719$		−	48.6735i		−	1.81521i	0.419821	−	0.907607i	$-0.362093\pi$
$720$	2.32555	−	14.8020i	0.0866681	−	0.551637i
$721$			17.4242i			0.648911i
$722$	92.3160			3.43565
$723$	12.0955	+	0.944375i	0.449837	+	0.0351217i
$724$	12.5295			0.465657
$725$	−3.64946			−0.135537
$726$	26.4631	+	19.0217i	0.982137	+	0.705961i
$727$	−23.5262			−0.872539			−0.436269	−	0.899816i	$-0.643700\pi$
$727$	−23.5262			−0.872539			−0.436269	+	0.899816i	$0.643700\pi$
$728$	5.35114			0.198326
$729$	−24.1027	−	12.1680i	−0.892693	−	0.450665i
$730$	−10.0068			−0.370368
$731$		−	19.9678i		−	0.738534i
$732$	−14.3050	−	1.11688i	−0.528727	−	0.0412811i
$733$		−	21.2743i		−	0.785784i	−0.919585	−	0.392892i	$-0.871475\pi$
$733$		−	21.2743i		−	0.785784i	0.919585	−	0.392892i	$-0.128525\pi$
$734$	−17.6596			−0.651828
$735$	−1.72680	−	0.134822i	−0.0636938	−	0.00497299i
$736$			26.6674i			0.982973i
$737$	10.7508	+	19.0969i	0.396012	+	0.703443i
$738$	−21.5208	−	3.38115i	−0.792192	−	0.124462i
$739$			36.0309i			1.32542i	0.748878	+	0.662708i	$0.230593\pi$
$739$			36.0309i			1.32542i	−0.748878	+	0.662708i	$0.769407\pi$
$740$		−	7.29059i		−	0.268008i
$741$	3.35442	−	42.9633i	0.123228	−	1.57830i
$742$	−15.3188			−0.562371
$743$	20.7055			0.759610			0.379805	−	0.925066i	$-0.375991\pi$
$743$	20.7055			0.759610			0.379805	+	0.925066i	$0.375991\pi$
$744$	0.202847	−	2.59806i	0.00743674	−	0.0952495i
$745$		−	0.0325137i		−	0.00119121i
$746$		−	39.1470i		−	1.43327i
$747$	−46.1182	−	7.24565i	−1.68738	−	0.265105i
$748$	3.91160	+	6.94823i	0.143022	+	0.254052i
$749$			14.0557i			0.513583i
$750$	2.95375	+	0.230619i	0.107856	+	0.00842100i
$751$	39.2898			1.43371			0.716853	−	0.697225i	$-0.245582\pi$
$751$	39.2898			1.43371			0.716853	+	0.697225i	$0.245582\pi$
$752$			41.6360i			1.51831i
$753$	20.8356	+	1.62677i	0.759291	+	0.0592827i
$754$			18.1823i			0.662161i
$755$	−13.1859			−0.479885
$756$	4.68052	+	1.11447i	0.170229	+	0.0405328i
$757$	−1.72547			−0.0627134			−0.0313567	−	0.999508i	$-0.509983\pi$
$757$	−1.72547			−0.0627134			−0.0313567	+	0.999508i	$0.509983\pi$
$758$	50.0587			1.81822
$759$	−13.2540	−	28.5356i	−0.481089	−	1.03578i
$760$	−15.6938			−0.569273
$761$	28.6641			1.03907			0.519537	−	0.854448i	$-0.326105\pi$
$761$	28.6641			1.03907			0.519537	+	0.854448i	$0.326105\pi$
$762$	−62.0888	−	4.84767i	−2.24924	−	0.175613i
$763$	−10.8571			−0.393055
$764$			9.30999i			0.336824i
$765$	−1.20894	+	7.69482i	−0.0437092	+	0.278207i
$766$		−	15.2774i		−	0.551996i
$767$	−17.7457			−0.640761
$768$	−2.45302	+	31.4182i	−0.0885158	+	1.13371i
$769$			4.80487i			0.173268i	0.996240	+	0.0866340i	$0.0276111\pi$
$769$			4.80487i			0.173268i	−0.996240	+	0.0866340i	$0.972389\pi$
$770$	−2.78310	−	4.94366i	−0.100296	−	0.178157i
$771$	−12.2092	−	0.953247i	−0.439702	−	0.0343304i
$772$		−	16.0619i		−	0.578079i
$773$			11.6765i			0.419974i	0.977704	+	0.209987i	$0.0673422\pi$
$773$			11.6765i			0.419974i	−0.977704	+	0.209987i	$0.932658\pi$
$774$	6.12523	−	38.9868i	0.220167	−	1.40135i
$775$	0.818935			0.0294170
$776$	3.38387			0.121474
$777$	−13.5962	−	1.06154i	−0.487761	−	0.0380826i
$778$			49.5036i			1.77479i
$779$			36.2634i			1.29927i
$780$	0.363610	−	4.65710i	0.0130193	−	0.166751i
$781$	−39.9018	+	22.4632i	−1.42780	+	0.803797i
$782$		−	24.3251i		−	0.869864i
$783$	4.39247	−	18.4474i	0.156974	−	0.659257i
$784$	4.99452			0.178376
$785$			19.8296i			0.707750i
$786$	0.391242	−	5.01102i	0.0139552	−	0.178737i
$787$			27.5108i			0.980655i	0.871538	+	0.490328i	$0.163123\pi$
$787$			27.5108i			0.980655i	−0.871538	+	0.490328i	$0.836877\pi$
$788$	11.4628			0.408345
$789$	1.46195	−	18.7246i	0.0520467	−	0.666612i
$790$	−8.84195			−0.314583
$791$	−18.1520			−0.645411
$792$	−6.38658	−	17.1280i	−0.226937	−	0.608619i
$793$	26.0584			0.925360
$794$	−11.7225			−0.416018
$795$	1.20740	−	15.4644i	0.0428222	−	0.548465i
$796$	−0.171063			−0.00606317
$797$		−	19.0409i		−	0.674463i	−0.941422	−	0.337232i	$-0.890509\pi$
$797$		−	19.0409i		−	0.674463i	0.941422	−	0.337232i	$-0.109491\pi$
$798$	1.96999	−	25.2315i	0.0697368	−	0.893186i
$799$		−	21.6445i		−	0.765728i
$800$	−4.86890			−0.172142
$801$	0.916584	−	5.83400i	0.0323859	−	0.206134i
$802$			0.681897i			0.0240786i
$803$	−16.9074	+	9.51823i	−0.596649	+	0.335891i
$804$	−0.824888	+	10.5651i	−0.0290916	+	0.372604i
$805$			5.47708i			0.193042i
$806$		−	4.08010i		−	0.143715i
$807$	−0.860433	−	0.0671795i	−0.0302887	−	0.00236483i
$808$	0.739808			0.0260263
$809$	12.0598			0.423998			0.211999	−	0.977270i	$-0.432003\pi$
$809$	12.0598			0.423998			0.211999	+	0.977270i	$0.432003\pi$
$810$	−4.72086	+	14.6532i	−0.165874	+	0.514860i
$811$			53.4376i			1.87645i	0.346028	+	0.938224i	$0.387530\pi$
$811$			53.4376i			1.87645i	−0.346028	+	0.938224i	$0.612470\pi$
$812$			3.37921i			0.118587i
$813$	4.83045	+	0.377145i	0.169411	+	0.0132270i
$814$	−21.9131	−	38.9247i	−0.768055	−	1.36431i
$815$		−	4.95147i		−	0.173442i
$816$	1.74834	−	22.3927i	0.0612042	−	0.783901i
$817$	−65.6941			−2.29835
$818$		−	17.6677i		−	0.617737i
$819$	−8.63205	−	1.35619i	−0.301628	−	0.0473890i
$820$			3.93084i			0.137271i
$821$	13.3909			0.467345			0.233672	−	0.972315i	$-0.424926\pi$
$821$	13.3909			0.467345			0.233672	+	0.972315i	$0.424926\pi$
$822$	67.3901	+	5.26158i	2.35050	+	0.183519i
$823$	7.85539			0.273822			0.136911	−	0.990583i	$-0.456283\pi$
$823$	7.85539			0.273822			0.136911	+	0.990583i	$0.456283\pi$
$824$	32.0119			1.11519
$825$	5.21000	−	2.41989i	0.181389	−	0.0842499i
$826$	−10.4217			−0.362618
$827$	31.1193			1.08212			0.541062	−	0.840983i	$-0.318023\pi$
$827$	31.1193			1.08212			0.541062	+	0.840983i	$0.318023\pi$
$828$	2.36139	−	15.0301i	0.0820640	−	0.522333i
$829$	2.70996			0.0941206			0.0470603	−	0.998892i	$-0.485015\pi$
$829$	2.70996			0.0941206			0.0470603	+	0.998892i	$0.485015\pi$
$830$			26.6182i			0.923932i
$831$	35.4676	+	2.76919i	1.23036	+	0.0960621i
$832$		−	4.83667i		−	0.167681i
$833$	−2.59640			−0.0899600
$834$	−11.2175	−	0.875823i	−0.388430	−	0.0303273i
$835$		−	7.75939i		−	0.268525i
$836$	22.8597	−	12.8692i	0.790620	−	0.445090i
$837$	−0.985667	+	4.13958i	−0.0340696	+	0.143085i
$838$		−	10.8146i		−	0.373583i
$839$			33.7490i			1.16514i	0.812779	+	0.582572i	$0.197954\pi$
$839$			33.7490i			1.16514i	−0.812779	+	0.582572i	$0.802046\pi$
$840$	−0.247696	+	3.17248i	−0.00854633	+	0.109461i
$841$	−15.6815			−0.540740
$842$	−13.7169			−0.472717
$843$	1.56820	−	20.0854i	0.0540116	−	0.691778i
$844$		−	5.96116i		−	0.205192i
$845$		−	4.51650i		−	0.155372i
$846$	6.63959	−	42.2606i	0.228274	−	1.45295i
$847$	−9.40461	−	5.70556i	−0.323146	−	0.196045i
$848$			44.7286i			1.53598i
$849$	−30.4964	−	2.38105i	−1.04663	−	0.0817173i
$850$	4.44125			0.152334
$851$			43.1247i			1.47829i
$852$	−22.0752	−	1.72355i	−0.756283	−	0.0590479i
$853$			49.4243i			1.69226i	0.532980	+	0.846128i	$0.321072\pi$
$853$			49.4243i			1.69226i	−0.532980	+	0.846128i	$0.678928\pi$
$854$	15.3036			0.523678
$855$	25.3160	+	3.97741i	0.865789	+	0.136025i
$856$	25.8232			0.882618
$857$	−22.1799			−0.757652			−0.378826	−	0.925468i	$-0.623672\pi$
$857$	−22.1799			−0.757652			−0.378826	+	0.925468i	$0.623672\pi$
$858$	−12.0564	−	25.9573i	−0.411598	−	0.886166i
$859$	20.6685			0.705201			0.352600	−	0.935774i	$-0.385297\pi$
$859$	20.6685			0.705201			0.352600	+	0.935774i	$0.385297\pi$
$860$	−7.12105			−0.242826
$861$	7.33061	+	0.572348i	0.249826	+	0.0195056i
$862$	48.8406			1.66352
$863$		−	34.0925i		−	1.16052i	−0.814431	−	0.580261i	$-0.802951\pi$
$863$		−	34.0925i		−	1.16052i	0.814431	−	0.580261i	$-0.197049\pi$
$864$	5.86019	−	24.6115i	0.199368	−	0.837300i
$865$			8.65215i			0.294182i
$866$	−54.3925			−1.84833
$867$	1.38310	−	17.7147i	0.0469725	−	0.601622i
$868$		−	0.758292i		−	0.0257381i
$869$	−14.9393	+	8.41027i	−0.506781	+	0.285299i
$870$	−10.7796	−	0.841633i	−0.365463	−	0.0285340i
$871$		−	19.2458i		−	0.652118i
$872$			19.9468i			0.675485i
$873$	−5.45859	−	0.857603i	−0.184745	−	0.0290255i
$874$	−80.0298			−2.70705
$875$	−1.00000			−0.0338062
$876$	−9.35381	−	0.730312i	−0.316036	−	0.0246750i
$877$		−	51.0814i		−	1.72489i	−0.506147	−	0.862447i	$-0.668931\pi$
$877$		−	51.0814i		−	1.72489i	0.506147	−	0.862447i	$-0.331069\pi$
$878$			25.0339i			0.844854i
$879$	−1.68024	+	21.5204i	−0.0566729	+	0.725865i
$880$	−14.4347	+	8.12622i	−0.486595	+	0.273935i
$881$			10.7228i			0.361260i	0.983551	+	0.180630i	$0.0578137\pi$
$881$			10.7228i			0.361260i	−0.983551	+	0.180630i	$0.942186\pi$
$882$	−5.06944	−	0.796462i	−0.170697	−	0.0268183i
$883$	2.83011			0.0952408			0.0476204	−	0.998866i	$-0.484836\pi$
$883$	2.83011			0.0952408			0.0476204	+	0.998866i	$0.484836\pi$
$884$		−	7.00239i		−	0.235516i
$885$	0.821423	−	10.5208i	0.0276118	−	0.353651i
$886$		−	28.6754i		−	0.963370i
$887$	19.4199			0.652058			0.326029	−	0.945360i	$-0.394289\pi$
$887$	19.4199			0.652058			0.326029	+	0.945360i	$0.394289\pi$
$888$	−1.95027	+	24.9790i	−0.0654469	+	0.838242i
$889$	21.0203			0.704998
$890$	−3.36724			−0.112870
$891$	5.96143	+	29.2483i	0.199715	+	0.979854i
$892$	15.6707			0.524692
$893$	−71.2106			−2.38297
$894$	0.00749827	−	0.0960375i	0.000250779	−	0.00321197i
$895$	−12.7222			−0.425256
$896$		−	12.5783i		−	0.420211i
$897$	−2.15079	+	27.5472i	−0.0718128	+	0.919775i
$898$			55.0767i			1.83793i
$899$	−2.98867			−0.0996777
$900$	2.74418	+	0.431140i	0.0914728	+	0.0143713i
$901$		−	23.2522i		−	0.774642i
$902$	11.8148	+	20.9869i	0.393391	+	0.698786i
$903$	−1.03686	+	13.2800i	−0.0345044	+	0.441931i
$904$			33.3490i			1.10917i
$905$		−	13.5316i		−	0.449805i
$906$	−38.9480	−	3.04092i	−1.29396	−	0.101028i
$907$	−50.4480			−1.67510			−0.837549	−	0.546362i	$-0.816012\pi$
$907$	−50.4480			−1.67510			−0.837549	+	0.546362i	$0.816012\pi$
$908$	−6.41495			−0.212888
$909$	−1.19340	−	0.187496i	−0.0395826	−	0.00621885i
$910$			4.98220i			0.165158i
$911$		−	10.7240i		−	0.355301i	−0.984094	−	0.177651i	$-0.943150\pi$
$911$		−	10.7240i		−	0.355301i	0.984094	−	0.177651i	$-0.0568497\pi$
$912$	−73.6721	−	5.75206i	−2.43953	−	0.190470i
$913$	25.3187	+	44.9740i	0.837926	+	1.48842i
$914$		−	38.4954i		−	1.27331i
$915$	−1.20620	+	15.4490i	−0.0398759	+	0.510728i
$916$	15.5320			0.513191
$917$			1.69649i			0.0560231i
$918$	−5.34547	+	22.4498i	−0.176427	+	0.740954i
$919$		−	10.3108i		−	0.340122i	−0.985434	−	0.170061i	$-0.945603\pi$
$919$		−	10.3108i		−	0.340122i	0.985434	−	0.170061i	$-0.0543965\pi$
$920$	10.0625			0.331752
$921$	55.9015	+	4.36459i	1.84202	+	0.143818i
$922$	−21.3517			−0.703180
$923$	40.2128			1.32362
$924$	−2.24070	−	4.82419i	−0.0737135	−	0.158704i
$925$	−7.87365			−0.258884
$926$	−58.3681			−1.91809
$927$	−51.6392	−	8.11306i	−1.69605	−	0.266468i
$928$	17.7689			0.583291
$929$		−	10.2851i		−	0.337443i	−0.985664	−	0.168721i	$-0.946036\pi$
$929$		−	10.2851i		−	0.337443i	0.985664	−	0.168721i	$-0.0539638\pi$
$930$	2.41893	+	0.188862i	0.0793199	+	0.00619302i
$931$			8.54218i			0.279959i
$932$	5.04564			0.165275
$933$	37.5553	+	2.93219i	1.22951	+	0.0959955i
$934$		−	16.0616i		−	0.525553i
$935$	7.50391	−	4.22442i	0.245404	−	0.138153i
$936$	−2.49160	+	15.8589i	−0.0814404	+	0.518364i
$937$			4.40061i			0.143762i	0.997413	+	0.0718808i	$0.0229001\pi$
$937$			4.40061i			0.143762i	−0.997413	+	0.0718808i	$0.977100\pi$
$938$		−	11.3027i		−	0.369045i
$939$	3.38593	−	43.3668i	0.110496	−	1.41522i
$940$	−7.71902			−0.251767
$941$	−43.4308			−1.41580			−0.707902	−	0.706311i	$-0.750358\pi$
$941$	−43.4308			−1.41580			−0.707902	+	0.706311i	$0.750358\pi$
$942$	−4.57309	+	58.5719i	−0.148999	+	1.90838i
$943$		−	23.2514i		−	0.757169i
$944$			30.4298i			0.990406i
$945$	1.20360	−	5.05483i	0.0391530	−	0.164434i
$946$	−38.0195	+	21.4036i	−1.23612	+	0.695890i
$947$		−	21.8772i		−	0.710914i	−0.934693	−	0.355457i	$-0.884325\pi$
$947$		−	21.8772i		−	0.710914i	0.934693	−	0.355457i	$-0.115675\pi$
$948$	−8.26499	−	0.645301i	−0.268435	−	0.0209584i
$949$	17.0392			0.553115
$950$		−	14.6118i		−	0.474068i
$951$	15.0318	+	1.17363i	0.487441	+	0.0380577i
$952$			4.77013i			0.154601i
$953$	−27.5519			−0.892492			−0.446246	−	0.894910i	$-0.647239\pi$
$953$	−27.5519			−0.892492			−0.446246	+	0.894910i	$0.647239\pi$
$954$	7.13274	−	45.3995i	0.230931	−	1.46986i
$955$	10.0545			0.325357
$956$	−23.1391			−0.748371
$957$	−19.0137	+	8.83130i	−0.614625	+	0.285475i
$958$	20.4503			0.660719
$959$	−22.8151			−0.736737
$960$	2.86748	+	0.223882i	0.0925474	+	0.00722577i
$961$	−30.3293			−0.978366
$962$			39.2281i			1.26476i
$963$	−41.6560	−	6.54460i	−1.34235	−	0.210897i
$964$		−	6.48590i		−	0.208897i
$965$	−17.3464			−0.558401
$966$	−1.26312	+	16.1780i	−0.0406401	+	0.520517i
$967$		−	1.30033i		−	0.0418159i	−0.999781	−	0.0209080i	$-0.993344\pi$
$967$		−	1.30033i		−	0.0418159i	0.999781	−	0.0209080i	$-0.00665570\pi$
$968$	−10.4823	+	17.2782i	−0.336914	+	0.555343i
$969$	38.2985	+	2.99021i	1.23033	+	0.0960594i
$970$			3.15056i			0.101158i
$971$		−	7.59328i		−	0.243680i	−0.992550	−	0.121840i	$-0.961121\pi$
$971$		−	7.59328i		−	0.243680i	0.992550	−	0.121840i	$-0.0388795\pi$
$972$	−5.48223	+	13.3525i	−0.175843	+	0.428281i
$973$	3.79771			0.121749
$974$	−43.7989			−1.40341
$975$	−5.02954	−	0.392689i	−0.161074	−	0.0125761i
$976$		−	44.6841i		−	1.43030i
$977$			30.4832i			0.975244i	0.873055	+	0.487622i	$0.162136\pi$
$977$			30.4832i			0.975244i	−0.873055	+	0.487622i	$0.837864\pi$
$978$	1.14190	−	14.6254i	0.0365139	−	0.467669i
$979$	−5.68926	+	3.20284i	−0.181830	+	0.102363i
$980$			0.925948i			0.0295783i
$981$	5.05531	−	32.1767i	0.161404	−	1.02732i
$982$	−3.53563			−0.112827
$983$		−	24.0207i		−	0.766142i	−0.923719	−	0.383071i	$-0.874866\pi$
$983$		−	24.0207i		−	0.766142i	0.923719	−	0.383071i	$-0.125134\pi$
$984$	1.05152	−	13.4679i	0.0335213	−	0.429340i
$985$		−	12.3795i		−	0.394444i
$986$	−16.2082			−0.516173
$987$	−1.12392	+	14.3952i	−0.0357749	+	0.458203i
$988$	−23.0379			−0.732934
$989$	42.1218			1.33940
$990$	15.9471	−	5.94625i	0.506833	−	0.188984i
$991$	−53.3161			−1.69364			−0.846820	−	0.531879i	$-0.821486\pi$
$991$	−53.3161			−1.69364			−0.846820	+	0.531879i	$0.821486\pi$
$992$	−3.98732			−0.126597
$993$	0.00358365	−	0.0458993i	0.000113724	−	0.00145657i
$994$	23.6162			0.749060
$995$			0.184744i			0.00585677i
$996$	−1.94264	+	24.8813i	−0.0615550	+	0.788395i
$997$		−	33.7889i		−	1.07010i	−0.844819	−	0.535052i	$-0.820292\pi$
$997$		−	33.7889i		−	1.07010i	0.844819	−	0.535052i	$-0.179708\pi$
$998$	1.51825			0.0480593
$999$	9.47670	−	39.8000i	0.299829	−	1.25922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.14	yes	40
3.2	odd	2		1155.2.l.f.1121.27	yes	40
11.10	odd	2		1155.2.l.f.1121.28	yes	40
33.32	even	2	inner	1155.2.l.e.1121.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.13	✓	40	33.32	even	2	inner
1155.2.l.e.1121.14	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.27	yes	40	3.2	odd	2
1155.2.l.f.1121.28	yes	40	11.10	odd	2

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.71054 q^{2} +(-0.134822 + 1.72680i) q^{3} +0.925948 q^{4} -1.00000i q^{5} +(0.230619 - 2.95375i) q^{6} +1.00000i q^{7} +1.83721 q^{8} +(-2.96365 - 0.465620i) q^{9} +O(q^{10})\)	\(q-1.71054 q^{2} +(-0.134822 + 1.72680i) q^{3} +0.925948 q^{4} -1.00000i q^{5} +(0.230619 - 2.95375i) q^{6} +1.00000i q^{7} +1.83721 q^{8} +(-2.96365 - 0.465620i) q^{9} +1.71054i q^{10} +(1.62703 + 2.89012i) q^{11} +(-0.124838 + 1.59892i) q^{12} -2.91265i q^{13} -1.71054i q^{14} +(1.72680 + 0.134822i) q^{15} -4.99452 q^{16} +2.59640 q^{17} +(5.06944 + 0.796462i) q^{18} -8.54218i q^{19} -0.925948i q^{20} +(-1.72680 - 0.134822i) q^{21} +(-2.78310 - 4.94366i) q^{22} +5.47708i q^{23} +(-0.247696 + 3.17248i) q^{24} -1.00000 q^{25} +4.98220i q^{26} +(1.20360 - 5.05483i) q^{27} +0.925948i q^{28} +3.64946 q^{29} +(-2.95375 - 0.230619i) q^{30} -0.818935 q^{31} +4.86890 q^{32} +(-5.21000 + 2.41989i) q^{33} -4.44125 q^{34} +1.00000 q^{35} +(-2.74418 - 0.431140i) q^{36} +7.87365 q^{37} +14.6118i q^{38} +(5.02954 + 0.392689i) q^{39} -1.83721i q^{40} -4.24521 q^{41} +(2.95375 + 0.230619i) q^{42} -7.69055i q^{43} +(1.50654 + 2.67610i) q^{44} +(-0.465620 + 2.96365i) q^{45} -9.36877i q^{46} -8.33635i q^{47} +(0.673371 - 8.62451i) q^{48} -1.00000 q^{49} +1.71054 q^{50} +(-0.350052 + 4.48346i) q^{51} -2.69696i q^{52} -8.95553i q^{53} +(-2.05880 + 8.64650i) q^{54} +(2.89012 - 1.62703i) q^{55} +1.83721i q^{56} +(14.7506 + 1.15167i) q^{57} -6.24254 q^{58} -6.09265i q^{59} +(1.59892 + 0.124838i) q^{60} +8.94663i q^{61} +1.40082 q^{62} +(0.465620 - 2.96365i) q^{63} +1.66058 q^{64} -2.91265 q^{65} +(8.91192 - 4.13933i) q^{66} +6.60766 q^{67} +2.40413 q^{68} +(-9.45781 - 0.738432i) q^{69} -1.71054 q^{70} +13.8063i q^{71} +(-5.44484 - 0.855442i) q^{72} +5.85007i q^{73} -13.4682 q^{74} +(0.134822 - 1.72680i) q^{75} -7.90962i q^{76} +(-2.89012 + 1.62703i) q^{77} +(-8.60324 - 0.671710i) q^{78} +5.16910i q^{79} +4.99452i q^{80} +(8.56640 + 2.75987i) q^{81} +7.26160 q^{82} +15.5613 q^{83} +(-1.59892 - 0.124838i) q^{84} -2.59640i q^{85} +13.1550i q^{86} +(-0.492027 + 6.30187i) q^{87} +(2.98919 + 5.30975i) q^{88} +1.96852i q^{89} +(0.796462 - 5.06944i) q^{90} +2.91265 q^{91} +5.07150i q^{92} +(0.110411 - 1.41413i) q^{93} +14.2597i q^{94} -8.54218 q^{95} +(-0.656436 + 8.40760i) q^{96} +1.84185 q^{97} +1.71054 q^{98} +(-3.47624 - 9.32286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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