LMFDB - Embedded newform 1155.2.l.f.1121.18

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			1121.18
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.371904 q^{2} +(-0.305927 + 1.70482i) q^{3} -1.86169 q^{4} +1.00000i q^{5} +(0.113775 - 0.634029i) q^{6} +1.00000i q^{7} +1.43618 q^{8} +(-2.81282 - 1.04310i) q^{9} +O(q^{10})$	\(q-0.371904 q^{2} +(-0.305927 + 1.70482i) q^{3} -1.86169 q^{4} +1.00000i q^{5} +(0.113775 - 0.634029i) q^{6} +1.00000i q^{7} +1.43618 q^{8} +(-2.81282 - 1.04310i) q^{9} -0.371904i q^{10} +(1.93655 + 2.69254i) q^{11} +(0.569541 - 3.17384i) q^{12} +6.33935i q^{13} -0.371904i q^{14} +(-1.70482 - 0.305927i) q^{15} +3.18926 q^{16} -1.53825 q^{17} +(1.04610 + 0.387933i) q^{18} +1.59870i q^{19} -1.86169i q^{20} +(-1.70482 - 0.305927i) q^{21} +(-0.720209 - 1.00137i) q^{22} +0.203060i q^{23} +(-0.439365 + 2.44842i) q^{24} -1.00000 q^{25} -2.35763i q^{26} +(2.63882 - 4.47623i) q^{27} -1.86169i q^{28} +2.40776 q^{29} +(0.634029 + 0.113775i) q^{30} -5.91934 q^{31} -4.05845 q^{32} +(-5.18274 + 2.47774i) q^{33} +0.572081 q^{34} -1.00000 q^{35} +(5.23659 + 1.94193i) q^{36} +8.80308 q^{37} -0.594564i q^{38} +(-10.8074 - 1.93938i) q^{39} +1.43618i q^{40} -9.29098 q^{41} +(0.634029 + 0.113775i) q^{42} +9.25080i q^{43} +(-3.60524 - 5.01267i) q^{44} +(1.04310 - 2.81282i) q^{45} -0.0755188i q^{46} -4.56524i q^{47} +(-0.975680 + 5.43710i) q^{48} -1.00000 q^{49} +0.371904 q^{50} +(0.470593 - 2.62244i) q^{51} -11.8019i q^{52} +2.51051i q^{53} +(-0.981386 + 1.66473i) q^{54} +(-2.69254 + 1.93655i) q^{55} +1.43618i q^{56} +(-2.72550 - 0.489087i) q^{57} -0.895455 q^{58} -4.95625i q^{59} +(3.17384 + 0.569541i) q^{60} -8.69894i q^{61} +2.20143 q^{62} +(1.04310 - 2.81282i) q^{63} -4.86916 q^{64} -6.33935 q^{65} +(1.92748 - 0.921481i) q^{66} -4.79152 q^{67} +2.86374 q^{68} +(-0.346181 - 0.0621216i) q^{69} +0.371904 q^{70} -13.9800i q^{71} +(-4.03970 - 1.49808i) q^{72} -7.53140i q^{73} -3.27390 q^{74} +(0.305927 - 1.70482i) q^{75} -2.97629i q^{76} +(-2.69254 + 1.93655i) q^{77} +(4.01933 + 0.721262i) q^{78} +6.74980i q^{79} +3.18926i q^{80} +(6.82388 + 5.86810i) q^{81} +3.45535 q^{82} -5.23364 q^{83} +(3.17384 + 0.569541i) q^{84} -1.53825i q^{85} -3.44041i q^{86} +(-0.736599 + 4.10480i) q^{87} +(2.78122 + 3.86697i) q^{88} -10.6093i q^{89} +(-0.387933 + 1.04610i) q^{90} -6.33935 q^{91} -0.378034i q^{92} +(1.81089 - 10.0914i) q^{93} +1.69783i q^{94} -1.59870 q^{95} +(1.24159 - 6.91892i) q^{96} +4.65451 q^{97} +0.371904 q^{98} +(-2.63856 - 9.59364i) 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} + 28 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} - 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} + 56 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 + 28 * 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 - 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 + 56 * 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 $

$2$	−0.371904			−0.262976			−0.131488	−	0.991318i	$-0.541975\pi$
$2$	−0.371904			−0.262976			−0.131488	+	0.991318i	$0.541975\pi$
$3$	−0.305927	+	1.70482i	−0.176627	+	0.984278i
$3$	−0.305927	+	1.70482i	−0.176627	+	0.984278i
$4$	−1.86169			−0.930844
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.113775	−	0.634029i	0.0464486	−	0.258841i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.43618			0.507765
$9$	−2.81282	−	1.04310i	−0.937606	−	0.347700i
$10$		−	0.371904i		−	0.117606i
$11$	1.93655	+	2.69254i	0.583891	+	0.811832i
$11$	1.93655	+	2.69254i	0.583891	+	0.811832i
$12$	0.569541	−	3.17384i	0.164412	−	0.916209i
$13$			6.33935i			1.75822i	0.476620	+	0.879109i	$0.341862\pi$
$13$			6.33935i			1.75822i	−0.476620	+	0.879109i	$0.658138\pi$
$14$		−	0.371904i		−	0.0993955i
$15$	−1.70482	−	0.305927i	−0.440182	−	0.0789900i
$16$	3.18926			0.797314
$17$	−1.53825			−0.373081			−0.186540	−	0.982447i	$-0.559727\pi$
$17$	−1.53825			−0.373081			−0.186540	+	0.982447i	$0.559727\pi$
$18$	1.04610	+	0.387933i	0.246568	+	0.0914367i
$19$			1.59870i			0.366768i	0.983041	+	0.183384i	$0.0587051\pi$
$19$			1.59870i			0.366768i	−0.983041	+	0.183384i	$0.941295\pi$
$20$		−	1.86169i		−	0.416286i
$21$	−1.70482	−	0.305927i	−0.372022	−	0.0667588i
$22$	−0.720209	−	1.00137i	−0.153549	−	0.213492i
$23$			0.203060i			0.0423410i	0.999776	+	0.0211705i	$0.00673928\pi$
$23$			0.203060i			0.0423410i	−0.999776	+	0.0211705i	$0.993261\pi$
$24$	−0.439365	+	2.44842i	−0.0896851	+	0.499782i
$25$	−1.00000			−0.200000
$26$		−	2.35763i		−	0.462369i
$27$	2.63882	−	4.47623i	0.507840	−	0.861451i
$28$		−	1.86169i		−	0.351826i
$29$	2.40776			0.447110			0.223555	−	0.974691i	$-0.428234\pi$
$29$	2.40776			0.447110			0.223555	+	0.974691i	$0.428234\pi$
$30$	0.634029	+	0.113775i	0.115757	+	0.0207725i
$31$	−5.91934			−1.06315			−0.531573	−	0.847013i	$-0.678399\pi$
$31$	−5.91934			−1.06315			−0.531573	+	0.847013i	$0.678399\pi$
$32$	−4.05845			−0.717439
$33$	−5.18274	+	2.47774i	−0.902199	+	0.431319i
$34$	0.572081			0.0981112
$35$	−1.00000			−0.169031
$36$	5.23659	+	1.94193i	0.872764	+	0.323655i
$37$	8.80308			1.44722			0.723609	−	0.690210i	$-0.242482\pi$
$37$	8.80308			1.44722			0.723609	+	0.690210i	$0.242482\pi$
$38$		−	0.594564i		−	0.0964510i
$39$	−10.8074	−	1.93938i	−1.73058	−	0.310549i
$40$			1.43618i			0.227079i
$41$	−9.29098			−1.45101			−0.725503	−	0.688219i	$-0.758393\pi$
$41$	−9.29098			−1.45101			−0.725503	+	0.688219i	$0.758393\pi$
$42$	0.634029	+	0.113775i	0.0978328	+	0.0175559i
$43$			9.25080i			1.41073i	0.708842	+	0.705367i	$0.249218\pi$
$43$			9.25080i			1.41073i	−0.708842	+	0.705367i	$0.750782\pi$
$44$	−3.60524	−	5.01267i	−0.543511	−	0.755689i
$45$	1.04310	−	2.81282i	0.155496	−	0.419310i
$46$		−	0.0755188i		−	0.0111346i
$47$		−	4.56524i		−	0.665908i	−0.942943	−	0.332954i	$-0.891955\pi$
$47$		−	4.56524i		−	0.665908i	0.942943	−	0.332954i	$-0.108045\pi$
$48$	−0.975680	+	5.43710i	−0.140827	+	0.784778i
$49$	−1.00000			−0.142857
$50$	0.371904			0.0525951
$51$	0.470593	−	2.62244i	0.0658962	−	0.367215i
$52$		−	11.8019i		−	1.63663i
$53$			2.51051i			0.344845i	0.985023	+	0.172423i	$0.0551594\pi$
$53$			2.51051i			0.344845i	−0.985023	+	0.172423i	$0.944841\pi$
$54$	−0.981386	+	1.66473i	−0.133550	+	0.226541i
$55$	−2.69254	+	1.93655i	−0.363062	+	0.261124i
$56$			1.43618i			0.191917i
$57$	−2.72550	−	0.489087i	−0.361001	−	0.0647811i
$58$	−0.895455			−0.117579
$59$		−	4.95625i		−	0.645249i	−0.946527	−	0.322624i	$-0.895435\pi$
$59$		−	4.95625i		−	0.645249i	0.946527	−	0.322624i	$-0.104565\pi$
$60$	3.17384	+	0.569541i	0.409741	+	0.0735274i
$61$		−	8.69894i		−	1.11378i	−0.830585	−	0.556892i	$-0.811994\pi$
$61$		−	8.69894i		−	1.11378i	0.830585	−	0.556892i	$-0.188006\pi$
$62$	2.20143			0.279582
$63$	1.04310	−	2.81282i	0.131418	−	0.354382i
$64$	−4.86916			−0.608645
$65$	−6.33935			−0.786299
$66$	1.92748	−	0.921481i	0.237257	−	0.113426i
$67$	−4.79152			−0.585378			−0.292689	−	0.956208i	$-0.594550\pi$
$67$	−4.79152			−0.585378			−0.292689	+	0.956208i	$0.594550\pi$
$68$	2.86374			0.347280
$69$	−0.346181	−	0.0621216i	−0.0416753	−	0.00747856i
$70$	0.371904			0.0444510
$71$		−	13.9800i		−	1.65912i	−0.558417	−	0.829560i	$-0.688591\pi$
$71$		−	13.9800i		−	1.65912i	0.558417	−	0.829560i	$-0.311409\pi$
$72$	−4.03970	−	1.49808i	−0.476083	−	0.176550i
$73$		−	7.53140i		−	0.881484i	−0.897634	−	0.440742i	$-0.854715\pi$
$73$		−	7.53140i		−	0.881484i	0.897634	−	0.440742i	$-0.145285\pi$
$74$	−3.27390			−0.380583
$75$	0.305927	−	1.70482i	0.0353254	−	0.196856i
$76$		−	2.97629i		−	0.341403i
$77$	−2.69254	+	1.93655i	−0.306844	+	0.220690i
$78$	4.01933	+	0.721262i	0.455099	+	0.0816669i
$79$			6.74980i			0.759412i	0.925107	+	0.379706i	$0.123975\pi$
$79$			6.74980i			0.759412i	−0.925107	+	0.379706i	$0.876025\pi$
$80$			3.18926i			0.356570i
$81$	6.82388	+	5.86810i	0.758209	+	0.652012i
$82$	3.45535			0.381580
$83$	−5.23364			−0.574466			−0.287233	−	0.957861i	$-0.592735\pi$
$83$	−5.23364			−0.574466			−0.287233	+	0.957861i	$0.592735\pi$
$84$	3.17384	+	0.569541i	0.346294	+	0.0621420i
$85$		−	1.53825i		−	0.166847i
$86$		−	3.44041i		−	0.370989i
$87$	−0.736599	+	4.10480i	−0.0789717	+	0.440080i
$88$	2.78122	+	3.86697i	0.296479	+	0.412220i
$89$		−	10.6093i		−	1.12458i	−0.826940	−	0.562290i	$-0.809921\pi$
$89$		−	10.6093i		−	1.12458i	0.826940	−	0.562290i	$-0.190079\pi$
$90$	−0.387933	+	1.04610i	−0.0408918	+	0.110268i
$91$	−6.33935			−0.664544
$92$		−	0.378034i		−	0.0394128i
$93$	1.81089	−	10.0914i	0.187780	−	1.04643i
$94$			1.69783i			0.175118i
$95$	−1.59870			−0.164023
$96$	1.24159	−	6.91892i	0.126719	−	0.706160i
$97$	4.65451			0.472594			0.236297	−	0.971681i	$-0.424066\pi$
$97$	4.65451			0.472594			0.236297	+	0.971681i	$0.424066\pi$
$98$	0.371904			0.0375680
$99$	−2.63856	−	9.59364i	−0.265185	−	0.964198i
$100$	1.86169			0.186169
$101$	−8.78821			−0.874459			−0.437230	−	0.899350i	$-0.644040\pi$
$101$	−8.78821			−0.874459			−0.437230	+	0.899350i	$0.644040\pi$
$102$	−0.175015	+	0.975295i	−0.0173291	+	0.0965686i
$103$	−15.7440			−1.55130			−0.775650	−	0.631163i	$-0.782578\pi$
$103$	−15.7440			−1.55130			−0.775650	+	0.631163i	$0.782578\pi$
$104$			9.10442i			0.892762i
$105$	0.305927	−	1.70482i	0.0298554	−	0.166373i
$106$		−	0.933668i		−	0.0906859i
$107$	12.6492			1.22285			0.611424	−	0.791303i	$-0.290597\pi$
$107$	12.6492			1.22285			0.611424	+	0.791303i	$0.290597\pi$
$108$	−4.91265	+	8.33335i	−0.472720	+	0.801877i
$109$			17.1008i			1.63796i	0.573824	+	0.818979i	$0.305459\pi$
$109$			17.1008i			1.63796i	−0.573824	+	0.818979i	$0.694541\pi$
$110$	1.00137	−	0.720209i	0.0954766	−	0.0686692i
$111$	−2.69310	+	15.0077i	−0.255618	+	1.42446i
$112$			3.18926i			0.301356i
$113$		−	12.8670i		−	1.21042i	−0.796064	−	0.605212i	$-0.793088\pi$
$113$		−	12.8670i		−	1.21042i	0.796064	−	0.605212i	$-0.206912\pi$
$114$	1.01362	+	0.181893i	0.0949346	+	0.0170359i
$115$	−0.203060			−0.0189354
$116$	−4.48250			−0.416189
$117$	6.61258	−	17.8314i	0.611333	−	1.64852i
$118$			1.84325i			0.169685i
$119$		−	1.53825i		−	0.141011i
$120$	−2.44842	−	0.439365i	−0.223509	−	0.0401084i
$121$	−3.49958	+	10.4285i	−0.318143	+	0.948043i
$122$			3.23517i			0.292898i
$123$	2.84236	−	15.8394i	0.256287	−	1.42819i
$124$	11.0200			0.989623
$125$		−	1.00000i		−	0.0894427i
$126$	−0.387933	+	1.04610i	−0.0345598	+	0.0931938i
$127$		−	7.56541i		−	0.671322i	−0.941983	−	0.335661i	$-0.891040\pi$
$127$		−	7.56541i		−	0.671322i	0.941983	−	0.335661i	$-0.108960\pi$
$128$	9.92776			0.877498
$129$	−15.7709	−	2.83007i	−1.38855	−	0.249174i
$130$	2.35763			0.206778
$131$	3.22550			0.281814			0.140907	−	0.990023i	$-0.454998\pi$
$131$	3.22550			0.281814			0.140907	+	0.990023i	$0.454998\pi$
$132$	9.64865	−	4.61278i	0.839807	−	0.401491i
$133$	−1.59870			−0.138625
$134$	1.78199			0.153940
$135$	4.47623	+	2.63882i	0.385253	+	0.227113i
$136$	−2.20920			−0.189437
$137$			10.2827i			0.878513i	0.898362	+	0.439257i	$0.144758\pi$
$137$			10.2827i			0.878513i	−0.898362	+	0.439257i	$0.855242\pi$
$138$	0.128746	+	0.0231033i	0.0109596	+	0.00196668i
$139$			12.4124i			1.05281i	0.850234	+	0.526405i	$0.176460\pi$
$139$			12.4124i			1.05281i	−0.850234	+	0.526405i	$0.823540\pi$
$140$	1.86169			0.157341
$141$	7.78290	+	1.39663i	0.655439	+	0.117617i
$142$			5.19921i			0.436308i
$143$	−17.0690	+	12.2764i	−1.42738	+	1.02661i
$144$	−8.97079	−	3.32672i	−0.747566	−	0.277226i
$145$			2.40776i			0.199954i
$146$			2.80096i			0.231809i
$147$	0.305927	−	1.70482i	0.0252324	−	0.140611i
$148$	−16.3886			−1.34713
$149$	6.29104			0.515382			0.257691	−	0.966227i	$-0.417038\pi$
$149$	6.29104			0.515382			0.257691	+	0.966227i	$0.417038\pi$
$150$	−0.113775	+	0.634029i	−0.00928973	+	0.0517682i
$151$			23.7041i			1.92901i	0.264064	+	0.964505i	$0.414937\pi$
$151$			23.7041i			1.92901i	−0.264064	+	0.964505i	$0.585063\pi$
$152$			2.29602i			0.186232i
$153$	4.32682	+	1.60455i	0.349803	+	0.129720i
$154$	1.00137	−	0.720209i	0.0806925	−	0.0580361i
$155$		−	5.91934i		−	0.475453i
$156$	20.1201	+	3.61052i	1.61090	+	0.289073i
$157$	−2.92790			−0.233672			−0.116836	−	0.993151i	$-0.537275\pi$
$157$	−2.92790			−0.233672			−0.116836	+	0.993151i	$0.537275\pi$
$158$		−	2.51028i		−	0.199707i
$159$	−4.27997	−	0.768033i	−0.339423	−	0.0609090i
$160$		−	4.05845i		−	0.320849i
$161$	−0.203060			−0.0160034
$162$	−2.53783	−	2.18237i	−0.199391	−	0.171463i
$163$	18.3622			1.43824			0.719118	−	0.694888i	$-0.244546\pi$
$163$	18.3622			1.43824			0.719118	+	0.694888i	$0.244546\pi$
$164$	17.2969			1.35066
$165$	−2.47774	−	5.18274i	−0.192892	−	0.403476i
$166$	1.94641			0.151071
$167$	−1.73416			−0.134193			−0.0670965	−	0.997746i	$-0.521374\pi$
$167$	−1.73416			−0.134193			−0.0670965	+	0.997746i	$0.521374\pi$
$168$	−2.44842	−	0.439365i	−0.188900	−	0.0338978i
$169$	−27.1873			−2.09133
$170$			0.572081i			0.0438766i
$171$	1.66761	−	4.49686i	0.127525	−	0.343883i
$172$		−	17.2221i		−	1.31317i
$173$	25.6736			1.95193			0.975965	−	0.217927i	$-0.0699293\pi$
$173$	25.6736			1.95193			0.975965	+	0.217927i	$0.0699293\pi$
$174$	0.273944	−	1.52659i	0.0207676	−	0.115730i
$175$		−	1.00000i		−	0.0755929i
$176$	6.17614	+	8.58721i	0.465544	+	0.647285i
$177$	8.44951	+	1.51625i	0.635104	+	0.113968i
$178$			3.94562i			0.295737i
$179$			21.9913i			1.64370i	0.569701	+	0.821852i	$0.307059\pi$
$179$			21.9913i			1.64370i	−0.569701	+	0.821852i	$0.692941\pi$
$180$	−1.94193	+	5.23659i	−0.144743	+	0.390312i
$181$	−7.58218			−0.563579			−0.281790	−	0.959476i	$-0.590928\pi$
$181$	−7.58218			−0.563579			−0.281790	+	0.959476i	$0.590928\pi$
$182$	2.35763			0.174759
$183$	14.8301	+	2.66124i	1.09627	+	0.196725i
$184$			0.291630i			0.0214993i
$185$			8.80308i			0.647215i
$186$	−0.673476	+	3.75304i	−0.0493817	+	0.275186i
$187$	−2.97889	−	4.14181i	−0.217838	−	0.302879i
$188$			8.49904i			0.619857i
$189$	4.47623	+	2.63882i	0.325598	+	0.191946i
$190$	0.594564			0.0431342
$191$			1.00862i			0.0729811i	0.999334	+	0.0364906i	$0.0116179\pi$
$191$			1.00862i			0.0729811i	−0.999334	+	0.0364906i	$0.988382\pi$
$192$	1.48961	−	8.30103i	0.107503	−	0.599076i
$193$		−	0.243010i		−	0.0174922i	−0.999962	−	0.00874611i	$-0.997216\pi$
$193$		−	0.243010i		−	0.0174922i	0.999962	−	0.00874611i	$-0.00278401\pi$
$194$	−1.73103			−0.124281
$195$	1.93938	−	10.8074i	0.138882	−	0.773937i
$196$	1.86169			0.132978
$197$	7.49743			0.534170			0.267085	−	0.963673i	$-0.413940\pi$
$197$	7.49743			0.534170			0.267085	+	0.963673i	$0.413940\pi$
$198$	0.981289	+	3.56791i	0.0697372	+	0.253561i
$199$	−12.6548			−0.897077			−0.448538	−	0.893764i	$-0.648055\pi$
$199$	−12.6548			−0.897077			−0.448538	+	0.893764i	$0.648055\pi$
$200$	−1.43618			−0.101553
$201$	1.46586	−	8.16868i	0.103394	−	0.576174i
$202$	3.26837			0.229962
$203$			2.40776i			0.168992i
$204$	−0.876097	+	4.88216i	−0.0613390	+	0.341820i
$205$		−	9.29098i		−	0.648910i
$206$	5.85525			0.407954
$207$	0.211812	−	0.571171i	0.0147220	−	0.0396991i
$208$			20.2178i			1.40185i
$209$	−4.30458	+	3.09596i	−0.297754	+	0.214152i
$210$	−0.113775	+	0.634029i	−0.00785125	+	0.0437521i
$211$			9.69087i			0.667147i	0.942724	+	0.333574i	$0.108255\pi$
$211$			9.69087i			0.667147i	−0.942724	+	0.333574i	$0.891745\pi$
$212$		−	4.67378i		−	0.320997i
$213$	23.8334	+	4.27686i	1.63304	+	0.293046i
$214$	−4.70430			−0.321579
$215$	−9.25080			−0.630900
$216$	3.78980	−	6.42866i	0.257864	−	0.437415i
$217$		−	5.91934i		−	0.401831i
$218$		−	6.35985i		−	0.430743i
$219$	12.8397	+	2.30406i	0.867625	+	0.155694i
$220$	5.01267	−	3.60524i	0.337954	−	0.243065i
$221$		−	9.75151i		−	0.655957i
$222$	1.00157	−	5.58141i	0.0672213	−	0.374600i
$223$	5.07601			0.339915			0.169957	−	0.985451i	$-0.445637\pi$
$223$	5.07601			0.339915			0.169957	+	0.985451i	$0.445637\pi$
$224$		−	4.05845i		−	0.271167i
$225$	2.81282	+	1.04310i	0.187521	+	0.0695401i
$226$			4.78528i			0.318312i
$227$	0.646823			0.0429312			0.0214656	−	0.999770i	$-0.493167\pi$
$227$	0.646823			0.0429312			0.0214656	+	0.999770i	$0.493167\pi$
$228$	5.07403	+	0.910526i	0.336036	+	0.0603011i
$229$	−8.00704			−0.529120			−0.264560	−	0.964369i	$-0.585227\pi$
$229$	−8.00704			−0.529120			−0.264560	+	0.964369i	$0.585227\pi$
$230$	0.0755188			0.00497956
$231$	−2.47774	−	5.18274i	−0.163023	−	0.340999i
$232$	3.45797			0.227027
$233$	−26.2432			−1.71925			−0.859624	−	0.510928i	$-0.829302\pi$
$233$	−26.2432			−1.71925			−0.859624	+	0.510928i	$0.829302\pi$
$234$	−2.45924	+	6.63158i	−0.160766	+	0.433520i
$235$	4.56524			0.297803
$236$			9.22699i			0.600626i
$237$	−11.5072	−	2.06495i	−0.747472	−	0.134133i
$238$			0.572081i			0.0370825i
$239$	19.9990			1.29363			0.646814	−	0.762648i	$-0.276101\pi$
$239$	19.9990			1.29363			0.646814	+	0.762648i	$0.276101\pi$
$240$	−5.43710	−	0.975680i	−0.350964	−	0.0629799i
$241$			1.76865i			0.113929i	0.998376	+	0.0569644i	$0.0181421\pi$
$241$			1.76865i			0.113929i	−0.998376	+	0.0569644i	$0.981858\pi$
$242$	1.30151	−	3.87839i	0.0836640	−	0.249312i
$243$	−12.0917	+	9.83827i	−0.775681	+	0.631125i
$244$			16.1947i			1.03676i
$245$		−	1.00000i		−	0.0638877i
$246$	−1.05709	+	5.89075i	−0.0673973	+	0.375580i
$247$	−10.1347			−0.644858
$248$	−8.50122			−0.539828
$249$	1.60111	−	8.92240i	0.101466	−	0.565434i
$250$			0.371904i			0.0235213i
$251$			14.2322i			0.898329i	0.893449	+	0.449164i	$0.148278\pi$
$251$			14.2322i			0.898329i	−0.893449	+	0.449164i	$0.851722\pi$
$252$	−1.94193	+	5.23659i	−0.122330	+	0.329874i
$253$	−0.546748	+	0.393235i	−0.0343738	+	0.0247225i
$254$			2.81361i			0.176541i
$255$	2.62244	+	0.470593i	0.164224	+	0.0294697i
$256$	6.04615			0.377884
$257$		−	5.10855i		−	0.318663i	−0.987225	−	0.159331i	$-0.949066\pi$
$257$		−	5.10855i		−	0.318663i	0.987225	−	0.159331i	$-0.0509338\pi$
$258$	5.86528	+	1.05251i	0.365156	+	0.0655267i
$259$			8.80308i			0.546997i
$260$	11.8019			0.731922
$261$	−6.77259	−	2.51154i	−0.419213	−	0.155460i
$262$	−1.19958			−0.0741101
$263$	11.9064			0.734183			0.367091	−	0.930185i	$-0.380354\pi$
$263$	11.9064			0.734183			0.367091	+	0.930185i	$0.380354\pi$
$264$	−7.44333	+	3.55847i	−0.458105	+	0.219009i
$265$	−2.51051			−0.154219
$266$	0.594564			0.0364550
$267$	18.0869	+	3.24566i	1.10690	+	0.198631i
$268$	8.92032			0.544895
$269$			12.4435i			0.758693i	0.925255	+	0.379346i	$0.123851\pi$
$269$			12.4435i			0.758693i	−0.925255	+	0.379346i	$0.876149\pi$
$270$	−1.66473	−	0.981386i	−0.101312	−	0.0597252i
$271$		−	2.26964i		−	0.137871i	−0.997621	−	0.0689353i	$-0.978040\pi$
$271$		−	2.26964i		−	0.137871i	0.997621	−	0.0689353i	$-0.0219602\pi$
$272$	−4.90588			−0.297462
$273$	1.93938	−	10.8074i	0.117377	−	0.654096i
$274$		−	3.82419i		−	0.231028i
$275$	−1.93655	−	2.69254i	−0.116778	−	0.162366i
$276$	0.644480	+	0.115651i	0.0387932	+	0.00696137i
$277$		−	13.8816i		−	0.834062i	−0.908892	−	0.417031i	$-0.863071\pi$
$277$		−	13.8816i		−	0.834062i	0.908892	−	0.417031i	$-0.136929\pi$
$278$		−	4.61624i		−	0.276863i
$279$	16.6500	+	6.17447i	0.996812	+	0.369656i
$280$	−1.43618			−0.0858280
$281$	−10.4563			−0.623773			−0.311887	−	0.950119i	$-0.600961\pi$
$281$	−10.4563			−0.623773			−0.311887	+	0.950119i	$0.600961\pi$
$282$	−2.89449	−	0.519412i	−0.172364	−	0.0309305i
$283$			1.31367i			0.0780893i	0.999237	+	0.0390446i	$0.0124315\pi$
$283$			1.31367i			0.0780893i	−0.999237	+	0.0390446i	$0.987569\pi$
$284$			26.0264i			1.54438i
$285$	0.489087	−	2.72550i	0.0289710	−	0.161445i
$286$	6.34801	−	4.56565i	0.375366	−	0.269973i
$287$		−	9.29098i		−	0.548429i
$288$	11.4157	+	4.23337i	0.672675	+	0.249454i
$289$	−14.6338			−0.860811
$290$		−	0.895455i		−	0.0525829i
$291$	−1.42394	+	7.93510i	−0.0834730	+	0.465164i
$292$			14.0211i			0.820524i
$293$	−20.7289			−1.21099			−0.605497	−	0.795848i	$-0.707026\pi$
$293$	−20.7289			−1.21099			−0.605497	+	0.795848i	$0.707026\pi$
$294$	−0.113775	+	0.634029i	−0.00663552	+	0.0369773i
$295$	4.95625			0.288564
$296$	12.6428			0.734847
$297$	17.1626	−	1.56330i	0.995877	−	0.0907121i
$298$	−2.33966			−0.135533
$299$	−1.28727			−0.0744446
$300$	−0.569541	+	3.17384i	−0.0328824	+	0.183242i
$301$	−9.25080			−0.533207
$302$		−	8.81564i		−	0.507283i
$303$	2.68855	−	14.9823i	0.154453	−	0.860711i
$304$			5.09867i			0.292429i
$305$	8.69894			0.498100
$306$	−1.60916	−	0.596739i	−0.0919896	−	0.0341133i
$307$			16.8466i			0.961484i	0.876862	+	0.480742i	$0.159633\pi$
$307$			16.8466i			0.961484i	−0.876862	+	0.480742i	$0.840367\pi$
$308$	5.01267	−	3.60524i	0.285624	−	0.205428i
$309$	4.81651	−	26.8406i	0.274002	−	1.52691i
$310$			2.20143i			0.125033i
$311$		−	8.35105i		−	0.473544i	−0.971565	−	0.236772i	$-0.923910\pi$
$311$		−	8.35105i		−	0.473544i	0.971565	−	0.236772i	$-0.0760895\pi$
$312$	−15.5214	−	2.78529i	−0.878726	−	0.157686i
$313$	11.5707			0.654013			0.327007	−	0.945022i	$-0.393960\pi$
$313$	11.5707			0.654013			0.327007	+	0.945022i	$0.393960\pi$
$314$	1.08890			0.0614500
$315$	2.81282	+	1.04310i	0.158484	+	0.0587721i
$316$		−	12.5660i		−	0.706894i
$317$		−	22.4733i		−	1.26223i	−0.775690	−	0.631114i	$-0.782598\pi$
$317$		−	22.4733i		−	1.26223i	0.775690	−	0.631114i	$-0.217402\pi$
$318$	1.59174	+	0.285634i	0.0892601	+	0.0160176i
$319$	4.66274	+	6.48300i	0.261063	+	0.362978i
$320$		−	4.86916i		−	0.272194i
$321$	−3.86974	+	21.5647i	−0.215988	+	1.20362i
$322$	0.0755188			0.00420850
$323$		−	2.45921i		−	0.136834i
$324$	−12.7039	−	10.9246i	−0.705774	−	0.606921i
$325$		−	6.33935i		−	0.351644i
$326$	−6.82896			−0.378221
$327$	−29.1537	−	5.23159i	−1.61221	−	0.289308i
$328$	−13.3435			−0.736771
$329$	4.56524			0.251690
$330$	0.921481	+	1.92748i	0.0507258	+	0.106104i
$331$	6.39749			0.351638			0.175819	−	0.984423i	$-0.443743\pi$
$331$	6.39749			0.351638			0.175819	+	0.984423i	$0.443743\pi$
$332$	9.74339			0.534738
$333$	−24.7615	−	9.18250i	−1.35692	−	0.503198i
$334$	0.644939			0.0352895
$335$		−	4.79152i		−	0.261789i
$336$	−5.43710	−	0.975680i	−0.296618	−	0.0532277i
$337$		−	5.59994i		−	0.305048i	−0.988300	−	0.152524i	$-0.951260\pi$
$337$		−	5.59994i		−	0.305048i	0.988300	−	0.152524i	$-0.0487402\pi$
$338$	10.1111			0.549970
$339$	21.9359	+	3.93636i	1.19139	+	0.213794i
$340$			2.86374i			0.155308i
$341$	−11.4631	−	15.9381i	−0.620761	−	0.863096i
$342$	−0.620190	+	1.67240i	−0.0335360	+	0.0904330i
$343$		−	1.00000i		−	0.0539949i
$344$			13.2858i			0.716322i
$345$	0.0621216	−	0.346181i	0.00334451	−	0.0186377i
$346$	−9.54812			−0.513310
$347$	9.01492			0.483946			0.241973	−	0.970283i	$-0.422205\pi$
$347$	9.01492			0.483946			0.241973	+	0.970283i	$0.422205\pi$
$348$	1.37132	−	7.64185i	0.0735103	−	0.409646i
$349$		−	32.7560i		−	1.75339i	−0.481049	−	0.876694i	$-0.659744\pi$
$349$		−	32.7560i		−	1.75339i	0.481049	−	0.876694i	$-0.340256\pi$
$350$			0.371904i			0.0198791i
$351$	28.3764	+	16.7284i	1.51462	+	0.892894i
$352$	−7.85937	−	10.9276i	−0.418906	−	0.582440i
$353$			13.5928i			0.723474i	0.932280	+	0.361737i	$0.117816\pi$
$353$			13.5928i			0.723474i	−0.932280	+	0.361737i	$0.882184\pi$
$354$	−3.14241	−	0.563900i	−0.167017	−	0.0299709i
$355$	13.9800			0.741981
$356$			19.7511i			1.04681i
$357$	2.62244	+	0.470593i	0.138794	+	0.0249064i
$358$		−	8.17863i		−	0.432254i
$359$	8.99779			0.474885			0.237443	−	0.971402i	$-0.423691\pi$
$359$	8.99779			0.474885			0.237443	+	0.971402i	$0.423691\pi$
$360$	1.49808	−	4.03970i	0.0789556	−	0.212911i
$361$	16.4441			0.865482
$362$	2.81984			0.148208
$363$	−16.7080	−	9.15650i	−0.876945	−	0.480592i
$364$	11.8019			0.618587
$365$	7.53140			0.394212
$366$	−5.51538	−	0.989726i	−0.288293	−	0.0517338i
$367$	15.5503			0.811718			0.405859	−	0.913936i	$-0.366972\pi$
$367$	15.5503			0.811718			0.405859	+	0.913936i	$0.366972\pi$
$368$			0.647610i			0.0337590i
$369$	26.1338	+	9.69143i	1.36047	+	0.504515i
$370$		−	3.27390i		−	0.170202i
$371$	−2.51051			−0.130339
$372$	−3.37131	+	18.7871i	−0.174794	+	0.974064i
$373$			36.2158i			1.87518i	0.347741	+	0.937591i	$0.386949\pi$
$373$			36.2158i			1.87518i	−0.347741	+	0.937591i	$0.613051\pi$
$374$	1.10786	+	1.54035i	0.0572862	+	0.0796498i
$375$	1.70482	+	0.305927i	0.0880365	+	0.0157980i
$376$		−	6.55649i		−	0.338125i
$377$			15.2636i			0.786117i
$378$	−1.66473	−	0.981386i	−0.0856244	−	0.0504770i
$379$	18.1582			0.932725			0.466362	−	0.884594i	$-0.345564\pi$
$379$	18.1582			0.932725			0.466362	+	0.884594i	$0.345564\pi$
$380$	2.97629			0.152680
$381$	12.8977	+	2.31446i	0.660767	+	0.118574i
$382$		−	0.375109i		−	0.0191923i
$383$			13.9481i			0.712715i	0.934350	+	0.356358i	$0.115981\pi$
$383$			13.9481i			0.712715i	−0.934350	+	0.356358i	$0.884019\pi$
$384$	−3.03717	+	16.9250i	−0.154990	+	0.863702i
$385$	−1.93655	−	2.69254i	−0.0986955	−	0.137225i
$386$			0.0903762i			0.00460003i
$387$	9.64952	−	26.0208i	0.490513	−	1.32271i
$388$	−8.66525			−0.439911
$389$		−	14.4405i		−	0.732164i	−0.930583	−	0.366082i	$-0.880699\pi$
$389$		−	14.4405i		−	0.732164i	0.930583	−	0.366082i	$-0.119301\pi$
$390$	−0.721262	+	4.01933i	−0.0365225	+	0.203527i
$391$		−	0.312357i		−	0.0157966i
$392$	−1.43618			−0.0725379
$393$	−0.986769	+	5.49890i	−0.0497759	+	0.277383i
$394$	−2.78832			−0.140474
$395$	−6.74980			−0.339619
$396$	4.91217	+	17.8604i	0.246846	+	0.897517i
$397$	17.5759			0.882107			0.441053	−	0.897481i	$-0.354605\pi$
$397$	17.5759			0.882107			0.441053	+	0.897481i	$0.354605\pi$
$398$	4.70638			0.235909
$399$	0.489087	−	2.72550i	0.0244850	−	0.136446i
$400$	−3.18926			−0.159463
$401$		−	31.0189i		−	1.54901i	−0.632567	−	0.774506i	$-0.717999\pi$
$401$		−	31.0189i		−	1.54901i	0.632567	−	0.774506i	$-0.282001\pi$
$402$	−0.545158	+	3.03796i	−0.0271900	+	0.151520i
$403$		−	37.5248i		−	1.86924i
$404$	16.3609			0.813985
$405$	−5.86810	+	6.82388i	−0.291588	+	0.339081i
$406$		−	0.895455i		−	0.0444407i
$407$	17.0476	+	23.7027i	0.845017	+	1.17490i
$408$	0.675854	−	3.76629i	0.0334598	−	0.186459i
$409$			30.3748i			1.50194i	0.660338	+	0.750968i	$0.270413\pi$
$409$			30.3748i			1.50194i	−0.660338	+	0.750968i	$0.729587\pi$
$410$			3.45535i			0.170648i
$411$	−17.5302	−	3.14577i	−0.864701	−	0.155169i
$412$	29.3104			1.44402
$413$	4.95625			0.243881
$414$	−0.0787737	+	0.212421i	−0.00387152	+	0.0104399i
$415$		−	5.23364i		−	0.256909i
$416$		−	25.7279i		−	1.26142i
$417$	−21.1610	−	3.79730i	−1.03626	−	0.185955i
$418$	1.60089	−	1.15140i	0.0783020	−	0.0563168i
$419$			16.3474i			0.798625i	0.916815	+	0.399312i	$0.130751\pi$
$419$			16.3474i			0.798625i	−0.916815	+	0.399312i	$0.869249\pi$
$420$	−0.569541	+	3.17384i	−0.0277907	+	0.154868i
$421$	−9.55578			−0.465720			−0.232860	−	0.972510i	$-0.574808\pi$
$421$	−9.55578			−0.465720			−0.232860	+	0.972510i	$0.574808\pi$
$422$		−	3.60407i		−	0.175444i
$423$	−4.76200	+	12.8412i	−0.231537	+	0.624359i
$424$			3.60553i			0.175100i
$425$	1.53825			0.0746161
$426$	−8.86372	−	1.59058i	−0.429449	−	0.0770639i
$427$	8.69894			0.420971
$428$	−23.5489			−1.13828
$429$	−15.7072	−	32.8552i	−0.758353	−	1.58626i
$430$	3.44041			0.165911
$431$	−18.0682			−0.870313			−0.435157	−	0.900355i	$-0.643307\pi$
$431$	−18.0682			−0.870313			−0.435157	+	0.900355i	$0.643307\pi$
$432$	8.41586	−	14.2758i	0.404908	−	0.686847i
$433$	11.2323			0.539788			0.269894	−	0.962890i	$-0.413011\pi$
$433$	11.2323			0.539788			0.269894	+	0.962890i	$0.413011\pi$
$434$			2.20143i			0.105672i
$435$	−4.10480	−	0.736599i	−0.196810	−	0.0353172i
$436$		−	31.8363i		−	1.52468i
$437$	−0.324633			−0.0155293
$438$	−4.77513	−	0.856889i	−0.228164	−	0.0409437i
$439$			2.77440i			0.132415i	0.997806	+	0.0662074i	$0.0210899\pi$
$439$			2.77440i			0.132415i	−0.997806	+	0.0662074i	$0.978910\pi$
$440$	−3.86697	+	2.78122i	−0.184350	+	0.132590i
$441$	2.81282	+	1.04310i	0.133944	+	0.0496715i
$442$			3.62662i			0.172501i
$443$		−	3.07378i		−	0.146040i	−0.997330	−	0.0730199i	$-0.976736\pi$
$443$		−	3.07378i		−	0.146040i	0.997330	−	0.0730199i	$-0.0232637\pi$
$444$	5.01371	−	27.9396i	0.237940	−	1.32595i
$445$	10.6093			0.502927
$446$	−1.88779			−0.0893893
$447$	−1.92460	+	10.7251i	−0.0910304	+	0.507279i
$448$		−	4.86916i		−	0.230046i
$449$			13.8064i			0.651565i	0.945445	+	0.325782i	$0.105628\pi$
$449$			13.8064i			0.651565i	−0.945445	+	0.325782i	$0.894372\pi$
$450$	−1.04610	−	0.387933i	−0.0493135	−	0.0182873i
$451$	−17.9924	−	25.0164i	−0.847229	−	1.17797i
$452$			23.9543i			1.12672i
$453$	−40.4112	−	7.25172i	−1.89868	−	0.340716i
$454$	−0.240556			−0.0112899
$455$		−	6.33935i		−	0.297193i
$456$	−3.91430	−	0.702415i	−0.183304	−	0.0328936i
$457$		−	25.5388i		−	1.19466i	−0.801997	−	0.597328i	$-0.796229\pi$
$457$		−	25.5388i		−	1.19466i	0.801997	−	0.597328i	$-0.203771\pi$
$458$	2.97785			0.139146
$459$	−4.05916	+	6.88557i	−0.189465	+	0.321391i
$460$	0.378034			0.0176259
$461$	−41.6262			−1.93872			−0.969362	−	0.245637i	$-0.921003\pi$
$461$	−41.6262			−1.93872			−0.969362	+	0.245637i	$0.921003\pi$
$462$	0.921481	+	1.92748i	0.0428712	+	0.0896746i
$463$	−4.40831			−0.204871			−0.102436	−	0.994740i	$-0.532664\pi$
$463$	−4.40831			−0.204871			−0.102436	+	0.994740i	$0.532664\pi$
$464$	7.67896			0.356487
$465$	10.0914	+	1.81089i	0.467978	+	0.0839779i
$466$	9.75993			0.452120
$467$			27.8584i			1.28913i	0.764547	+	0.644567i	$0.222963\pi$
$467$			27.8584i			1.28913i	−0.764547	+	0.644567i	$0.777037\pi$
$468$	−12.3106	+	33.1965i	−0.569056	+	1.53451i
$469$		−	4.79152i		−	0.221252i
$470$	−1.69783			−0.0783150
$471$	0.895724	−	4.99154i	0.0412728	−	0.229998i
$472$		−	7.11805i		−	0.327635i
$473$	−24.9082	+	17.9146i	−1.14528	+	0.823715i
$474$	4.27957	+	0.767962i	0.196567	+	0.0352737i
$475$		−	1.59870i		−	0.0733535i
$476$			2.86374i			0.131259i
$477$	2.61871	−	7.06160i	0.119903	−	0.323329i
$478$	−7.43771			−0.340193
$479$	30.0801			1.37440			0.687199	−	0.726470i	$-0.258840\pi$
$479$	30.0801			1.37440			0.687199	+	0.726470i	$0.258840\pi$
$480$	6.91892	+	1.24159i	0.315804	+	0.0566706i
$481$			55.8058i			2.54453i
$482$		−	0.657768i		−	0.0299605i
$483$	0.0621216	−	0.346181i	0.00282663	−	0.0157518i
$484$	6.51512	−	19.4145i	0.296142	−	0.882480i
$485$			4.65451i			0.211351i
$486$	4.49694	−	3.65889i	0.203985	−	0.165971i
$487$	−24.3910			−1.10526			−0.552631	−	0.833426i	$-0.686376\pi$
$487$	−24.3910			−1.10526			−0.552631	+	0.833426i	$0.686376\pi$
$488$		−	12.4932i		−	0.565541i
$489$	−5.61749	+	31.3042i	−0.254032	+	1.41562i
$490$			0.371904i			0.0168009i
$491$	−41.2737			−1.86266			−0.931328	−	0.364180i	$-0.881349\pi$
$491$	−41.2737			−1.86266			−0.931328	+	0.364180i	$0.881349\pi$
$492$	−5.29159	+	29.4881i	−0.238563	+	1.32943i
$493$	−3.70374			−0.166808
$494$	3.76915			0.169582
$495$	9.59364	−	2.63856i	0.431202	−	0.118594i
$496$	−18.8783			−0.847661
$497$	13.9800			0.627089
$498$	−0.595459	+	3.31828i	−0.0266832	+	0.148695i
$499$	−21.3700			−0.956653			−0.478326	−	0.878182i	$-0.658756\pi$
$499$	−21.3700			−0.956653			−0.478326	+	0.878182i	$0.658756\pi$
$500$			1.86169i			0.0832572i
$501$	0.530525	−	2.95642i	0.0237021	−	0.132083i
$502$		−	5.29301i		−	0.236239i
$503$	42.6898			1.90345			0.951723	−	0.306959i	$-0.0993114\pi$
$503$	42.6898			1.90345			0.951723	+	0.306959i	$0.0993114\pi$
$504$	1.49808	−	4.03970i	0.0667297	−	0.179943i
$505$		−	8.78821i		−	0.391070i
$506$	0.203338	−	0.146246i	0.00903946	−	0.00650141i
$507$	8.31734	−	46.3495i	0.369386	−	2.05845i
$508$			14.0844i			0.624896i
$509$		−	0.749245i		−	0.0332097i	−0.999862	−	0.0166049i	$-0.994714\pi$
$509$		−	0.749245i		−	0.0332097i	0.999862	−	0.0166049i	$-0.00528573\pi$
$510$	−0.975295	−	0.175015i	−0.0431868	−	0.00774980i
$511$	7.53140			0.333170
$512$	−22.1041			−0.976872
$513$	7.15616	+	4.21868i	0.315952	+	0.186259i
$514$			1.89989i			0.0838005i
$515$		−	15.7440i		−	0.693763i
$516$	29.3606	+	5.26871i	1.29253	+	0.231942i
$517$	12.2921	−	8.84079i	0.540606	−	0.388818i
$518$		−	3.27390i		−	0.143847i
$519$	−7.85426	+	43.7689i	−0.344764	+	1.92124i
$520$	−9.10442			−0.399255
$521$		−	20.2905i		−	0.888943i	−0.895793	−	0.444472i	$-0.853391\pi$
$521$		−	20.2905i		−	0.888943i	0.895793	−	0.444472i	$-0.146609\pi$
$522$	2.51875	+	0.934050i	0.110243	+	0.0408823i
$523$		−	25.4809i		−	1.11420i	−0.830445	−	0.557100i	$-0.811914\pi$
$523$		−	25.4809i		−	1.11420i	0.830445	−	0.557100i	$-0.188086\pi$
$524$	−6.00488			−0.262324
$525$	1.70482	+	0.305927i	0.0744044	+	0.0133518i
$526$	−4.42805			−0.193072
$527$	9.10544			0.396639
$528$	−16.5291	+	7.90214i	−0.719336	+	0.343897i
$529$	22.9588			0.998207
$530$	0.933668			0.0405560
$531$	−5.16987	+	13.9410i	−0.224353	+	0.604989i
$532$	2.97629			0.129038
$533$		−	58.8987i		−	2.55119i
$534$	−6.72658	−	1.20707i	−0.291087	−	0.0522352i
$535$			12.6492i			0.546874i
$536$	−6.88147			−0.297234
$537$	−37.4911	−	6.72772i	−1.61786	−	0.290323i
$538$		−	4.62778i		−	0.199518i
$539$	−1.93655	−	2.69254i	−0.0834129	−	0.115976i
$540$	−8.33335	−	4.91265i	−0.358610	−	0.211407i
$541$			18.0972i			0.778061i	0.921225	+	0.389030i	$0.127190\pi$
$541$			18.0972i			0.778061i	−0.921225	+	0.389030i	$0.872810\pi$
$542$			0.844086i			0.0362566i
$543$	2.31959	−	12.9262i	0.0995433	−	0.554718i
$544$	6.24291			0.267663
$545$	−17.1008			−0.732517
$546$	−0.721262	+	4.01933i	−0.0308672	+	0.172011i
$547$			5.52070i			0.236048i	0.993011	+	0.118024i	$0.0376560\pi$
$547$			5.52070i			0.236048i	−0.993011	+	0.118024i	$0.962344\pi$
$548$		−	19.1432i		−	0.817758i
$549$	−9.07387	+	24.4685i	−0.387263	+	1.04429i
$550$	0.720209	+	1.00137i	0.0307098	+	0.0426984i
$551$			3.84929i			0.163985i
$552$	−0.497177	−	0.0892176i	−0.0211612	−	0.00379735i
$553$	−6.74980			−0.287031
$554$			5.16261i			0.219338i
$555$	−15.0077	−	2.69310i	−0.637040	−	0.114316i
$556$		−	23.1081i		−	0.980002i
$557$	−24.4054			−1.03409			−0.517044	−	0.855959i	$-0.672968\pi$
$557$	−24.4054			−1.03409			−0.517044	+	0.855959i	$0.672968\pi$
$558$	−6.19221	−	2.29631i	−0.262137	−	0.0972106i
$559$	−58.6441			−2.48038
$560$	−3.18926			−0.134771
$561$	7.97236	−	3.81138i	0.336593	−	0.160917i
$562$	3.88875			0.164037
$563$	−26.4077			−1.11295			−0.556476	−	0.830864i	$-0.687847\pi$
$563$	−26.4077			−1.11295			−0.556476	+	0.830864i	$0.687847\pi$
$564$	−14.4893	−	2.60009i	−0.610111	−	0.109483i
$565$	12.8670			0.541318
$566$		−	0.488557i		−	0.0205356i
$567$	−5.86810	+	6.82388i	−0.246437	+	0.286576i
$568$		−	20.0777i		−	0.842443i
$569$	−23.5575			−0.987581			−0.493791	−	0.869581i	$-0.664389\pi$
$569$	−23.5575			−0.987581			−0.493791	+	0.869581i	$0.664389\pi$
$570$	−0.181893	+	1.01362i	−0.00761867	+	0.0424560i
$571$			25.5412i			1.06887i	0.845211	+	0.534433i	$0.179475\pi$
$571$			25.5412i			1.06887i	−0.845211	+	0.534433i	$0.820525\pi$
$572$	31.7771	−	22.8549i	1.32867	−	0.955611i
$573$	−1.71951	−	0.308564i	−0.0718337	−	0.0128904i
$574$			3.45535i			0.144224i
$575$		−	0.203060i		−	0.00846819i
$576$	13.6961	+	5.07902i	0.570669	+	0.211626i
$577$	−22.9697			−0.956241			−0.478120	−	0.878294i	$-0.658682\pi$
$577$	−22.9697			−0.956241			−0.478120	+	0.878294i	$0.658682\pi$
$578$	5.44236			0.226372
$579$	0.414288	+	0.0743433i	0.0172172	+	0.00308960i
$580$		−	4.48250i		−	0.186126i
$581$		−	5.23364i		−	0.217128i
$582$	0.529569	−	2.95110i	0.0219514	−	0.122327i
$583$	−6.75966	+	4.86172i	−0.279956	+	0.201352i
$584$		−	10.8164i		−	0.447587i
$585$	17.8314	+	6.61258i	0.737239	+	0.273397i
$586$	7.70915			0.318462
$587$			45.7897i			1.88994i	0.327151	+	0.944972i	$0.393911\pi$
$587$			45.7897i			1.88994i	−0.327151	+	0.944972i	$0.606089\pi$
$588$	−0.569541	+	3.17384i	−0.0234875	+	0.130887i
$589$		−	9.46327i		−	0.389927i
$590$	−1.84325			−0.0758854
$591$	−2.29367	+	12.7818i	−0.0943489	+	0.525772i
$592$	28.0753			1.15389
$593$	−12.5248			−0.514331			−0.257165	−	0.966367i	$-0.582788\pi$
$593$	−12.5248			−0.514331			−0.257165	+	0.966367i	$0.582788\pi$
$594$	−6.38285	+	0.581399i	−0.261892	+	0.0238551i
$595$	1.53825			0.0630621
$596$	−11.7119			−0.479740
$597$	3.87145	−	21.5742i	0.158448	−	0.882973i
$598$	0.478740			0.0195771
$599$		−	44.4200i		−	1.81495i	−0.420102	−	0.907477i	$-0.638006\pi$
$599$		−	44.4200i		−	1.81495i	0.420102	−	0.907477i	$-0.361994\pi$
$600$	0.439365	−	2.44842i	0.0179370	−	0.0999564i
$601$		−	26.9805i		−	1.10056i	−0.834981	−	0.550278i	$-0.814522\pi$
$601$		−	26.9805i		−	1.10056i	0.834981	−	0.550278i	$-0.185478\pi$
$602$	3.44041			0.140221
$603$	13.4777	+	4.99804i	0.548853	+	0.203536i
$604$		−	44.1296i		−	1.79561i
$605$	−10.4285	−	3.49958i	−0.423978	−	0.142278i
$606$	−0.999883	+	5.57198i	−0.0406175	+	0.226346i
$607$			23.1897i			0.941243i	0.882335	+	0.470621i	$0.155970\pi$
$607$			23.1897i			0.941243i	−0.882335	+	0.470621i	$0.844030\pi$
$608$		−	6.48825i		−	0.263133i
$609$	−4.10480	−	0.736599i	−0.166335	−	0.0298485i
$610$	−3.23517			−0.130988
$611$	28.9406			1.17081
$612$	−8.05518	−	2.98717i	−0.325612	−	0.120749i
$613$			47.7921i			1.93030i	0.261691	+	0.965152i	$0.415720\pi$
$613$			47.7921i			1.93030i	−0.261691	+	0.965152i	$0.584280\pi$
$614$		−	6.26530i		−	0.252847i
$615$	15.8394	+	2.84236i	0.638708	+	0.114615i
$616$	−3.86697	+	2.78122i	−0.155805	+	0.112059i
$617$		−	24.4639i		−	0.984880i	−0.870346	−	0.492440i	$-0.836105\pi$
$617$		−	24.4639i		−	0.984880i	0.870346	−	0.492440i	$-0.163895\pi$
$618$	−1.79128	+	9.98214i	−0.0720558	+	0.401541i
$619$	30.7284			1.23508			0.617539	−	0.786540i	$-0.288130\pi$
$619$	30.7284			1.23508			0.617539	+	0.786540i	$0.288130\pi$
$620$			11.0200i			0.442573i
$621$	0.908944	+	0.535838i	0.0364747	+	0.0215024i
$622$			3.10579i			0.124531i
$623$	10.6093			0.425051
$624$	−34.4677	−	6.18517i	−1.37981	−	0.247605i
$625$	1.00000			0.0400000
$626$	−4.30318			−0.171990
$627$	−3.96117	−	8.28566i	−0.158194	−	0.330898i
$628$	5.45084			0.217512
$629$	−13.5413			−0.539929
$630$	−1.04610	−	0.387933i	−0.0416775	−	0.0154556i
$631$	−19.2442			−0.766100			−0.383050	−	0.923728i	$-0.625126\pi$
$631$	−19.2442			−0.766100			−0.383050	+	0.923728i	$0.625126\pi$
$632$			9.69391i			0.385603i
$633$	−16.5212	−	2.96470i	−0.656658	−	0.117836i
$634$			8.35792i			0.331935i
$635$	7.56541			0.300224
$636$	7.96796	+	1.42984i	0.315950	+	0.0566967i
$637$		−	6.33935i		−	0.251174i
$638$	−1.73409	−	2.41105i	−0.0686533	−	0.0954545i
$639$	−14.5825	+	39.3232i	−0.576877	+	1.55560i
$640$			9.92776i			0.392429i
$641$			3.88055i			0.153273i	0.997059	+	0.0766363i	$0.0244180\pi$
$641$			3.88055i			0.153273i	−0.997059	+	0.0766363i	$0.975582\pi$
$642$	1.43917	−	8.01998i	0.0567996	−	0.316523i
$643$	26.2625			1.03569			0.517846	−	0.855474i	$-0.326734\pi$
$643$	26.2625			1.03569			0.517846	+	0.855474i	$0.326734\pi$
$644$	0.378034			0.0148966
$645$	2.83007	−	15.7709i	0.111434	−	0.620980i
$646$			0.914588i			0.0359840i
$647$			38.4122i			1.51014i	0.655645	+	0.755069i	$0.272397\pi$
$647$			38.4122i			1.51014i	−0.655645	+	0.755069i	$0.727603\pi$
$648$	9.80030	+	8.42763i	0.384992	+	0.331069i
$649$	13.3449	−	9.59801i	0.523834	−	0.376755i
$650$			2.35763i			0.0924738i
$651$	10.0914	+	1.81089i	0.395514	+	0.0709743i
$652$	−34.1846			−1.33877
$653$			27.7633i			1.08646i	0.839583	+	0.543231i	$0.182799\pi$
$653$			27.7633i			1.08646i	−0.839583	+	0.543231i	$0.817201\pi$
$654$	10.8424	+	1.94565i	0.423971	+	0.0760809i
$655$			3.22550i			0.126031i
$656$	−29.6313			−1.15691
$657$	−7.85601	+	21.1845i	−0.306492	+	0.826484i
$658$	−1.69783			−0.0661883
$659$	−6.15183			−0.239641			−0.119821	−	0.992796i	$-0.538232\pi$
$659$	−6.15183			−0.239641			−0.119821	+	0.992796i	$0.538232\pi$
$660$	4.61278	+	9.64865i	0.179552	+	0.375573i
$661$	−29.3755			−1.14258			−0.571288	−	0.820750i	$-0.693556\pi$
$661$	−29.3755			−1.14258			−0.571288	+	0.820750i	$0.693556\pi$
$662$	−2.37925			−0.0924723
$663$	16.6246	+	2.98325i	0.645644	+	0.115860i
$664$	−7.51642			−0.291694
$665$		−	1.59870i		−	0.0619950i
$666$	9.20888	+	3.41501i	0.356837	+	0.132329i
$667$			0.488920i			0.0189311i
$668$	3.22845			0.124913
$669$	−1.55289	+	8.65368i	−0.0600381	+	0.334570i
$670$			1.78199i			0.0688441i
$671$	23.4223	−	16.8459i	0.904206	−	0.650328i
$672$	6.91892	+	1.24159i	0.266903	+	0.0478954i
$673$		−	11.4574i		−	0.441649i	−0.975314	−	0.220825i	$-0.929125\pi$
$673$		−	11.4574i		−	0.441649i	0.975314	−	0.220825i	$-0.0708749\pi$
$674$			2.08264i			0.0802203i
$675$	−2.63882	+	4.47623i	−0.101568	+	0.172290i
$676$	50.6143			1.94670
$677$	−21.2360			−0.816167			−0.408083	−	0.912945i	$-0.633803\pi$
$677$	−21.2360			−0.816167			−0.408083	+	0.912945i	$0.633803\pi$
$678$	−8.15804	−	1.46395i	−0.313308	−	0.0562225i
$679$			4.65451i			0.178624i
$680$		−	2.20920i		−	0.0847189i
$681$	−0.197881	+	1.10272i	−0.00758281	+	0.0422562i
$682$	4.26317	+	5.92744i	0.163245	+	0.226973i
$683$		−	31.3440i		−	1.19934i	−0.800246	−	0.599672i	$-0.795298\pi$
$683$		−	31.3440i		−	1.19934i	0.800246	−	0.599672i	$-0.204702\pi$
$684$	−3.10457	+	8.37175i	−0.118706	+	0.320102i
$685$	−10.2827			−0.392883
$686$			0.371904i			0.0141994i
$687$	2.44957	−	13.6506i	0.0934570	−	0.520801i
$688$			29.5032i			1.12480i
$689$	−15.9150			−0.606313
$690$	−0.0231033	+	0.128746i	−0.000879526	+	0.00490127i
$691$	−16.5068			−0.627948			−0.313974	−	0.949432i	$-0.601661\pi$
$691$	−16.5068			−0.627948			−0.313974	+	0.949432i	$0.601661\pi$
$692$	−47.7963			−1.81694
$693$	9.59364	−	2.63856i	0.364432	−	0.100230i
$694$	−3.35268			−0.127266
$695$	−12.4124			−0.470831
$696$	−1.05789	+	5.89521i	−0.0400991	+	0.223457i
$697$	14.2919			0.541343
$698$			12.1821i			0.461098i
$699$	8.02850	−	44.7399i	0.303666	−	1.69222i
$700$			1.86169i			0.0703652i
$701$	−3.17079			−0.119759			−0.0598794	−	0.998206i	$-0.519072\pi$
$701$	−3.17079			−0.119759			−0.0598794	+	0.998206i	$0.519072\pi$
$702$	−10.5533	−	6.22134i	−0.398308	−	0.234810i
$703$			14.0735i			0.530793i
$704$	−9.42935	−	13.1104i	−0.355382	−	0.494118i
$705$	−1.39663	+	7.78290i	−0.0526001	+	0.293121i
$706$		−	5.05523i		−	0.190256i
$707$		−	8.78821i		−	0.330515i
$708$	−15.7304	−	2.82279i	−0.591183	−	0.106087i
$709$	−29.1988			−1.09658			−0.548292	−	0.836287i	$-0.684722\pi$
$709$	−29.1988			−1.09658			−0.548292	+	0.836287i	$0.684722\pi$
$710$	−5.19921			−0.195123
$711$	7.04072	−	18.9860i	0.264048	−	0.712029i
$712$		−	15.2368i		−	0.571022i
$713$		−	1.20198i		−	0.0450146i
$714$	−0.975295	−	0.175015i	−0.0364995	−	0.00654978i
$715$	−12.2764	−	17.0690i	−0.459113	−	0.638343i
$716$		−	40.9408i		−	1.53003i
$717$	−6.11824	+	34.0947i	−0.228490	+	1.27329i
$718$	−3.34631			−0.124883
$719$			29.4854i			1.09962i	0.835290	+	0.549810i	$0.185300\pi$
$719$			29.4854i			1.09962i	−0.835290	+	0.549810i	$0.814700\pi$
$720$	3.32672	−	8.97079i	0.123979	−	0.334322i
$721$		−	15.7440i		−	0.586337i
$722$	−6.11564			−0.227601
$723$	−3.01523	−	0.541078i	−0.112138	−	0.0201229i
$724$	14.1157			0.524604
$725$	−2.40776			−0.0894220
$726$	6.21378	+	3.40534i	0.230615	+	0.126384i
$727$	−33.5853			−1.24561			−0.622804	−	0.782378i	$-0.714007\pi$
$727$	−33.5853			−1.24561			−0.622804	+	0.782378i	$0.714007\pi$
$728$	−9.10442			−0.337432
$729$	−13.0733	−	23.6239i	−0.484196	−	0.874959i
$730$	−2.80096			−0.103668
$731$		−	14.2301i		−	0.526318i
$732$	−27.6090	−	4.95440i	−1.02046	−	0.183120i
$733$		−	22.5054i		−	0.831256i	−0.909535	−	0.415628i	$-0.863562\pi$
$733$		−	22.5054i		−	0.831256i	0.909535	−	0.415628i	$-0.136438\pi$
$734$	−5.78321			−0.213462
$735$	1.70482	+	0.305927i	0.0628832	+	0.0112843i
$736$		−	0.824109i		−	0.0303771i
$737$	−9.27900	−	12.9014i	−0.341797	−	0.475228i
$738$	−9.71927	−	3.60428i	−0.357771	−	0.132675i
$739$			22.4659i			0.826420i	0.910636	+	0.413210i	$0.135592\pi$
$739$			22.4659i			0.826420i	−0.910636	+	0.413210i	$0.864408\pi$
$740$		−	16.3886i		−	0.602456i
$741$	3.10049	−	17.2779i	0.113899	−	0.634719i
$742$	0.933668			0.0342760
$743$	25.1035			0.920960			0.460480	−	0.887670i	$-0.347677\pi$
$743$	25.1035			0.920960			0.460480	+	0.887670i	$0.347677\pi$
$744$	2.60075	−	14.4930i	0.0953483	−	0.531341i
$745$			6.29104i			0.230486i
$746$		−	13.4688i		−	0.493127i
$747$	14.7213	+	5.45921i	0.538623	+	0.199742i
$748$	5.54577	+	7.71075i	0.202773	+	0.281933i
$749$			12.6492i			0.462193i
$750$	−0.634029	−	0.113775i	−0.0231515	−	0.00415449i
$751$	27.4254			1.00077			0.500384	−	0.865804i	$-0.333192\pi$
$751$	27.4254			1.00077			0.500384	+	0.865804i	$0.333192\pi$
$752$		−	14.5597i		−	0.530938i
$753$	−24.2633	−	4.35402i	−0.884205	−	0.158669i
$754$		−	5.67660i		−	0.206730i
$755$	−23.7041			−0.862680
$756$	−8.33335	−	4.91265i	−0.303081	−	0.178671i
$757$	47.4060			1.72300			0.861500	−	0.507758i	$-0.169526\pi$
$757$	47.4060			1.72300			0.861500	+	0.507758i	$0.169526\pi$
$758$	−6.75311			−0.245284
$759$	−0.503130	−	1.05241i	−0.0182625	−	0.0382000i
$760$	−2.29602			−0.0832854
$761$	37.1364			1.34620			0.673098	−	0.739554i	$-0.264963\pi$
$761$	37.1364			1.34620			0.673098	+	0.739554i	$0.264963\pi$
$762$	−4.79669	−	0.860758i	−0.173766	−	0.0311820i
$763$	−17.1008			−0.619090
$764$		−	1.87773i		−	0.0679340i
$765$	−1.60455	+	4.32682i	−0.0580127	+	0.156436i
$766$		−	5.18736i		−	0.187427i
$767$	31.4194			1.13449
$768$	−1.84968	+	10.3076i	−0.0667446	+	0.371943i
$769$		−	9.71184i		−	0.350218i	−0.984549	−	0.175109i	$-0.943972\pi$
$769$		−	9.71184i		−	0.350218i	0.984549	−	0.175109i	$-0.0560278\pi$
$770$	0.720209	+	1.00137i	0.0259545	+	0.0360868i
$771$	8.70915	+	1.56284i	0.313652	+	0.0562844i
$772$			0.452408i			0.0162825i
$773$			47.6414i			1.71354i	0.515697	+	0.856771i	$0.327533\pi$
$773$			47.6414i			1.71354i	−0.515697	+	0.856771i	$0.672467\pi$
$774$	−3.58869	+	9.67724i	−0.128993	+	0.347841i
$775$	5.91934			0.212629
$776$	6.68470			0.239967
$777$	−15.0077	−	2.69310i	−0.538397	−	0.0966145i
$778$			5.37049i			0.192541i
$779$		−	14.8535i		−	0.532182i
$780$	−3.61052	+	20.1201i	−0.129277	+	0.720414i
$781$	37.6417	−	27.0729i	1.34693	−	0.968745i
$782$			0.116167i			0.00415412i
$783$	6.35364	−	10.7777i	0.227060	−	0.385163i
$784$	−3.18926			−0.113902
$785$		−	2.92790i		−	0.104501i
$786$	0.366983	−	2.04506i	0.0130899	−	0.0729449i
$787$			1.17455i			0.0418682i	0.999781	+	0.0209341i	$0.00666402\pi$
$787$			1.17455i			0.0418682i	−0.999781	+	0.0209341i	$0.993336\pi$
$788$	−13.9579			−0.497229
$789$	−3.64250	+	20.2983i	−0.129677	+	0.722640i
$790$	2.51028			0.0893117
$791$	12.8670			0.457497
$792$	−3.78943	−	13.7782i	−0.134652	−	0.489586i
$793$	55.1456			1.95828
$794$	−6.53653			−0.231973
$795$	0.768033	−	4.27997i	0.0272393	−	0.151795i
$796$	23.5593			0.835038
$797$			11.5674i			0.409738i	0.978789	+	0.204869i	$0.0656768\pi$
$797$			11.5674i			0.409738i	−0.978789	+	0.204869i	$0.934323\pi$
$798$	−0.181893	+	1.01362i	−0.00643895	+	0.0358819i
$799$			7.02248i			0.248437i
$800$	4.05845			0.143488
$801$	−11.0665	+	29.8419i	−0.391017	+	1.05441i
$802$			11.5361i			0.407352i
$803$	20.2786	−	14.5849i	0.715617	−	0.514690i
$804$	−2.72897	+	15.2075i	−0.0962433	+	0.536328i
$805$		−	0.203060i		−	0.00715693i
$806$			13.9556i			0.491565i
$807$	−21.2139	−	3.80680i	−0.746764	−	0.134006i
$808$	−12.6214			−0.444020
$809$	41.3606			1.45416			0.727081	−	0.686552i	$-0.240877\pi$
$809$	41.3606			1.45416			0.727081	+	0.686552i	$0.240877\pi$
$810$	2.18237	−	2.53783i	0.0766807	−	0.0891702i
$811$			26.1194i			0.917176i	0.888649	+	0.458588i	$0.151645\pi$
$811$			26.1194i			0.917176i	−0.888649	+	0.458588i	$0.848355\pi$
$812$		−	4.48250i		−	0.157305i
$813$	3.86932	+	0.694343i	0.135703	+	0.0243517i
$814$	−6.34006	−	8.81512i	−0.222219	−	0.308970i
$815$			18.3622i			0.643199i
$816$	1.50084	−	8.36363i	0.0525399	−	0.292786i
$817$	−14.7893			−0.517412
$818$		−	11.2965i		−	0.394973i
$819$	17.8314	+	6.61258i	0.623080	+	0.231062i
$820$			17.2969i			0.604034i
$821$	−44.8397			−1.56492			−0.782458	−	0.622703i	$-0.786034\pi$
$821$	−44.8397			−1.56492			−0.782458	+	0.622703i	$0.786034\pi$
$822$	6.51955	+	1.16992i	0.227395	+	0.0408057i
$823$	−0.897833			−0.0312965			−0.0156482	−	0.999878i	$-0.504981\pi$
$823$	−0.897833			−0.0312965			−0.0156482	+	0.999878i	$0.504981\pi$
$824$	−22.6111			−0.787696
$825$	5.18274	−	2.47774i	0.180440	−	0.0862638i
$826$	−1.84325			−0.0641348
$827$	51.8437			1.80278			0.901391	−	0.433006i	$-0.142547\pi$
$827$	51.8437			1.80278			0.901391	+	0.433006i	$0.142547\pi$
$828$	−0.394328	+	1.06334i	−0.0137038	+	0.0369537i
$829$	53.2057			1.84791			0.923955	−	0.382502i	$-0.124938\pi$
$829$	53.2057			1.84791			0.923955	+	0.382502i	$0.124938\pi$
$830$			1.94641i			0.0675608i
$831$	23.6656	+	4.24675i	0.820949	+	0.147318i
$832$		−	30.8673i		−	1.07013i
$833$	1.53825			0.0532972
$834$	7.86985	+	1.41223i	0.272511	+	0.0489016i
$835$		−	1.73416i		−	0.0600129i
$836$	8.01378	−	5.76371i	0.277162	−	0.199342i
$837$	−15.6201	+	26.4964i	−0.539908	+	0.915848i
$838$		−	6.07967i		−	0.210019i
$839$		−	51.8079i		−	1.78861i	−0.447459	−	0.894304i	$-0.647671\pi$
$839$		−	51.8079i		−	1.78861i	0.447459	−	0.894304i	$-0.352329\pi$
$840$	0.439365	−	2.44842i	0.0151595	−	0.0844786i
$841$	−23.2027			−0.800093
$842$	3.55383			0.122473
$843$	3.19888	−	17.8262i	0.110175	−	0.613966i
$844$		−	18.0414i		−	0.621010i
$845$		−	27.1873i		−	0.935272i
$846$	1.77101	−	4.77568i	0.0608885	−	0.164191i
$847$	−10.4285	−	3.49958i	−0.358326	−	0.120247i
$848$			8.00666i			0.274950i
$849$	−2.23956	−	0.401886i	−0.0768616	−	0.0137927i
$850$	−0.572081			−0.0196222
$851$			1.78755i			0.0612766i
$852$	−44.3703	−	7.96218i	−1.52010	−	0.272780i
$853$		−	36.8473i		−	1.26163i	−0.775934	−	0.630814i	$-0.782721\pi$
$853$		−	36.8473i		−	1.26163i	0.775934	−	0.630814i	$-0.217279\pi$
$854$	−3.23517			−0.110705
$855$	4.49686	+	1.66761i	0.153789	+	0.0570310i
$856$	18.1665			0.620919
$857$	13.7230			0.468770			0.234385	−	0.972144i	$-0.424692\pi$
$857$	13.7230			0.468770			0.234385	+	0.972144i	$0.424692\pi$
$858$	5.84159	+	12.2190i	0.199428	+	0.417149i
$859$	38.0731			1.29904			0.649519	−	0.760345i	$-0.274970\pi$
$859$	38.0731			1.29904			0.649519	+	0.760345i	$0.274970\pi$
$860$	17.2221			0.587269
$861$	15.8394	+	2.84236i	0.539807	+	0.0968674i
$862$	6.71962			0.228871
$863$			53.4696i			1.82012i	0.414471	+	0.910062i	$0.363966\pi$
$863$			53.4696i			1.82012i	−0.414471	+	0.910062i	$0.636034\pi$
$864$	−10.7095	+	18.1666i	−0.364345	+	0.618039i
$865$			25.6736i			0.872930i
$866$	−4.17732			−0.141951
$867$	4.47687	−	24.9480i	0.152043	−	0.847277i
$868$			11.0200i			0.374042i
$869$	−18.1741	+	13.0713i	−0.616515	+	0.443414i
$870$	1.52659	+	0.273944i	0.0517562	+	0.00928757i
$871$		−	30.3751i		−	1.02922i
$872$			24.5597i			0.831698i
$873$	−13.0923	−	4.85513i	−0.443107	−	0.164321i
$874$	0.120732			0.00408383
$875$	1.00000			0.0338062
$876$	−23.9035	−	4.28944i	−0.807623	−	0.144927i
$877$			14.8686i			0.502077i	0.967977	+	0.251039i	$0.0807721\pi$
$877$			14.8686i			0.502077i	−0.967977	+	0.251039i	$0.919228\pi$
$878$		−	1.03181i		−	0.0348219i
$879$	6.34153	−	35.3390i	0.213894	−	1.19195i
$880$	−8.58721	+	6.17614i	−0.289475	+	0.208198i
$881$			17.2158i			0.580016i	0.957024	+	0.290008i	$0.0936579\pi$
$881$			17.2158i			0.580016i	−0.957024	+	0.290008i	$0.906342\pi$
$882$	−1.04610	−	0.387933i	−0.0352239	−	0.0130624i
$883$	26.6571			0.897083			0.448542	−	0.893762i	$-0.351944\pi$
$883$	26.6571			0.897083			0.448542	+	0.893762i	$0.351944\pi$
$884$			18.1543i			0.610594i
$885$	−1.51625	+	8.44951i	−0.0509682	+	0.284027i
$886$			1.14315i			0.0384049i
$887$	−39.5870			−1.32920			−0.664600	−	0.747199i	$-0.731398\pi$
$887$	−39.5870			−1.32920			−0.664600	+	0.747199i	$0.731398\pi$
$888$	−3.86777	+	21.5537i	−0.129794	+	0.723293i
$889$	7.56541			0.253736
$890$	−3.94562			−0.132258
$891$	−2.58536	+	29.7374i	−0.0866130	+	0.996242i
$892$	−9.44994			−0.316407
$893$	7.29846			0.244234
$894$	0.715766	−	3.98870i	0.0239388	−	0.133402i
$895$	−21.9913			−0.735087
$896$			9.92776i			0.331663i
$897$	0.393810	−	2.19456i	0.0131489	−	0.0732742i
$898$		−	5.13466i		−	0.171346i
$899$	−14.2524			−0.475343
$900$	−5.23659	−	1.94193i	−0.174553	−	0.0647309i
$901$		−	3.86179i		−	0.128655i
$902$	6.69144	+	9.30368i	0.222801	+	0.309779i
$903$	2.83007	−	15.7709i	0.0941789	−	0.524824i
$904$		−	18.4793i		−	0.614611i
$905$		−	7.58218i		−	0.252040i
$906$	15.0291	+	2.69694i	0.499307	+	0.0895999i
$907$	17.3815			0.577143			0.288572	−	0.957458i	$-0.406820\pi$
$907$	17.3815			0.577143			0.288572	+	0.957458i	$0.406820\pi$
$908$	−1.20418			−0.0399622
$909$	24.7196	+	9.16699i	0.819898	+	0.304050i
$910$			2.35763i			0.0781546i
$911$			38.1794i			1.26494i	0.774585	+	0.632470i	$0.217959\pi$
$911$			38.1794i			1.26494i	−0.774585	+	0.632470i	$0.782041\pi$
$912$	−8.69231	−	1.55982i	−0.287831	−	0.0516509i
$913$	−10.1352	−	14.0918i	−0.335425	−	0.466370i
$914$			9.49800i			0.314166i
$915$	−2.66124	+	14.8301i	−0.0879779	+	0.490268i
$916$	14.9066			0.492528
$917$			3.22550i			0.106516i
$918$	1.50962	−	2.56077i	0.0498248	−	0.0845180i
$919$		−	13.9298i		−	0.459500i	−0.973250	−	0.229750i	$-0.926209\pi$
$919$		−	13.9298i		−	0.459500i	0.973250	−	0.229750i	$-0.0737909\pi$
$920$	−0.291630			−0.00961476
$921$	−28.7203	−	5.15382i	−0.946368	−	0.169824i
$922$	15.4809			0.509837
$923$	88.6241			2.91710
$924$	4.61278	+	9.64865i	0.151749	+	0.317417i
$925$	−8.80308			−0.289444
$926$	1.63947			0.0538762
$927$	44.2849	+	16.4226i	1.45451	+	0.539388i
$928$	−9.77177			−0.320774
$929$		−	9.88547i		−	0.324332i	−0.986764	−	0.162166i	$-0.948152\pi$
$929$		−	9.88547i		−	0.324332i	0.986764	−	0.162166i	$-0.0518479\pi$
$930$	−3.75304	−	0.673476i	−0.123067	−	0.0220842i
$931$		−	1.59870i		−	0.0523954i
$932$	48.8566			1.60035
$933$	14.2370	+	2.55481i	0.466099	+	0.0836408i
$934$		−	10.3607i		−	0.339011i
$935$	4.14181	−	2.97889i	0.135452	−	0.0974202i
$936$	9.49683	−	25.6091i	0.310414	−	0.837059i
$937$			8.40012i			0.274420i	0.990542	+	0.137210i	$0.0438135\pi$
$937$			8.40012i			0.274420i	−0.990542	+	0.137210i	$0.956186\pi$
$938$			1.78199i			0.0581839i
$939$	−3.53978	+	19.7259i	−0.115516	+	0.643731i
$940$	−8.49904			−0.277208
$941$	53.2510			1.73593			0.867966	−	0.496623i	$-0.165427\pi$
$941$	53.2510			1.73593			0.867966	+	0.496623i	$0.165427\pi$
$942$	−0.333123	+	1.85637i	−0.0108537	+	0.0604839i
$943$		−	1.88663i		−	0.0614370i
$944$		−	15.8068i		−	0.514466i
$945$	−2.63882	+	4.47623i	−0.0858407	+	0.145612i
$946$	9.26345	−	6.66251i	0.301181	−	0.216617i
$947$			23.2044i			0.754041i	0.926205	+	0.377020i	$0.123051\pi$
$947$			23.2044i			0.754041i	−0.926205	+	0.377020i	$0.876949\pi$
$948$	21.4228	+	3.84429i	0.695780	+	0.124857i
$949$	47.7442			1.54984
$950$			0.594564i			0.0192902i
$951$	38.3130	+	6.87520i	1.24238	+	0.222944i
$952$		−	2.20920i		−	0.0716006i
$953$	41.8804			1.35664			0.678320	−	0.734766i	$-0.262708\pi$
$953$	41.8804			1.35664			0.678320	+	0.734766i	$0.262708\pi$
$954$	−0.973910	+	2.62624i	−0.0315315	+	0.0850276i
$955$	−1.00862			−0.0326381
$956$	−37.2319			−1.20417
$957$	−12.4788	+	5.96580i	−0.403382	+	0.192847i
$958$	−11.1869			−0.361433
$959$	−10.2827			−0.332047
$960$	8.30103	+	1.48961i	0.267915	+	0.0480769i
$961$	4.03864			0.130279
$962$		−	20.7544i		−	0.669148i
$963$	−35.5800	−	13.1944i	−1.14655	−	0.425184i
$964$		−	3.29267i		−	0.106050i
$965$	0.243010			0.00782276
$966$	−0.0231033	+	0.128746i	−0.000743335	+	0.00414233i
$967$			39.2470i			1.26210i	0.775743	+	0.631049i	$0.217376\pi$
$967$			39.2470i			1.26210i	−0.775743	+	0.631049i	$0.782624\pi$
$968$	−5.02601	+	14.9771i	−0.161542	+	0.481383i
$969$	4.19250	+	0.752338i	0.134683	+	0.0241686i
$970$		−	1.73103i		−	0.0555801i
$971$			7.58590i			0.243443i	0.992564	+	0.121721i	$0.0388415\pi$
$971$			7.58590i			0.243443i	−0.992564	+	0.121721i	$0.961159\pi$
$972$	22.5109	−	18.3158i	0.722038	−	0.587479i
$973$	−12.4124			−0.397925
$974$	9.07111			0.290657
$975$	10.8074	+	1.93938i	0.346115	+	0.0621098i
$976$		−	27.7431i		−	0.888036i
$977$		−	2.59895i		−	0.0831479i	−0.999135	−	0.0415740i	$-0.986763\pi$
$977$		−	2.59895i		−	0.0831479i	0.999135	−	0.0415740i	$-0.0132372\pi$
$978$	2.08916	−	11.6421i	0.0668041	−	0.372275i
$979$	28.5659	−	20.5453i	0.912970	−	0.656631i
$980$			1.86169i			0.0594694i
$981$	17.8378	−	48.1014i	0.569518	−	1.53576i
$982$	15.3499			0.489834
$983$			19.5881i			0.624763i	0.949957	+	0.312381i	$0.101127\pi$
$983$			19.5881i			0.624763i	−0.949957	+	0.312381i	$0.898873\pi$
$984$	4.08213	−	22.7482i	0.130134	−	0.725187i
$985$			7.49743i			0.238888i
$986$	1.37743			0.0438665
$987$	−1.39663	+	7.78290i	−0.0444552	+	0.247733i
$988$	18.8677			0.600262
$989$	−1.87847			−0.0597318
$990$	−3.56791	+	0.981289i	−0.113396	+	0.0311874i
$991$	−59.8952			−1.90263			−0.951317	−	0.308216i	$-0.900268\pi$
$991$	−59.8952			−1.90263			−0.951317	+	0.308216i	$0.900268\pi$
$992$	24.0234			0.762742
$993$	−1.95717	+	10.9066i	−0.0621088	+	0.346109i
$994$	−5.19921			−0.164909
$995$		−	12.6548i		−	0.401185i
$996$	−2.98077	+	16.6107i	−0.0944493	+	0.526331i
$997$		−	14.3915i		−	0.455784i	−0.973686	−	0.227892i	$-0.926817\pi$
$997$		−	14.3915i		−	0.455784i	0.973686	−	0.227892i	$-0.0731833\pi$
$998$	7.94758			0.251576
$999$	23.2297	−	39.4046i	0.734956	−	1.24671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.18	yes	40
3.2	odd	2		1155.2.l.e.1121.23	✓	40
11.10	odd	2		1155.2.l.e.1121.24	yes	40
33.32	even	2	inner	1155.2.l.f.1121.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.23	✓	40	3.2	odd	2
1155.2.l.e.1121.24	yes	40	11.10	odd	2
1155.2.l.f.1121.17	yes	40	33.32	even	2	inner
1155.2.l.f.1121.18	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-0.371904 q^{2} +(-0.305927 + 1.70482i) q^{3} -1.86169 q^{4} +1.00000i q^{5} +(0.113775 - 0.634029i) q^{6} +1.00000i q^{7} +1.43618 q^{8} +(-2.81282 - 1.04310i) q^{9} +O(q^{10})\)	\(q-0.371904 q^{2} +(-0.305927 + 1.70482i) q^{3} -1.86169 q^{4} +1.00000i q^{5} +(0.113775 - 0.634029i) q^{6} +1.00000i q^{7} +1.43618 q^{8} +(-2.81282 - 1.04310i) q^{9} -0.371904i q^{10} +(1.93655 + 2.69254i) q^{11} +(0.569541 - 3.17384i) q^{12} +6.33935i q^{13} -0.371904i q^{14} +(-1.70482 - 0.305927i) q^{15} +3.18926 q^{16} -1.53825 q^{17} +(1.04610 + 0.387933i) q^{18} +1.59870i q^{19} -1.86169i q^{20} +(-1.70482 - 0.305927i) q^{21} +(-0.720209 - 1.00137i) q^{22} +0.203060i q^{23} +(-0.439365 + 2.44842i) q^{24} -1.00000 q^{25} -2.35763i q^{26} +(2.63882 - 4.47623i) q^{27} -1.86169i q^{28} +2.40776 q^{29} +(0.634029 + 0.113775i) q^{30} -5.91934 q^{31} -4.05845 q^{32} +(-5.18274 + 2.47774i) q^{33} +0.572081 q^{34} -1.00000 q^{35} +(5.23659 + 1.94193i) q^{36} +8.80308 q^{37} -0.594564i q^{38} +(-10.8074 - 1.93938i) q^{39} +1.43618i q^{40} -9.29098 q^{41} +(0.634029 + 0.113775i) q^{42} +9.25080i q^{43} +(-3.60524 - 5.01267i) q^{44} +(1.04310 - 2.81282i) q^{45} -0.0755188i q^{46} -4.56524i q^{47} +(-0.975680 + 5.43710i) q^{48} -1.00000 q^{49} +0.371904 q^{50} +(0.470593 - 2.62244i) q^{51} -11.8019i q^{52} +2.51051i q^{53} +(-0.981386 + 1.66473i) q^{54} +(-2.69254 + 1.93655i) q^{55} +1.43618i q^{56} +(-2.72550 - 0.489087i) q^{57} -0.895455 q^{58} -4.95625i q^{59} +(3.17384 + 0.569541i) q^{60} -8.69894i q^{61} +2.20143 q^{62} +(1.04310 - 2.81282i) q^{63} -4.86916 q^{64} -6.33935 q^{65} +(1.92748 - 0.921481i) q^{66} -4.79152 q^{67} +2.86374 q^{68} +(-0.346181 - 0.0621216i) q^{69} +0.371904 q^{70} -13.9800i q^{71} +(-4.03970 - 1.49808i) q^{72} -7.53140i q^{73} -3.27390 q^{74} +(0.305927 - 1.70482i) q^{75} -2.97629i q^{76} +(-2.69254 + 1.93655i) q^{77} +(4.01933 + 0.721262i) q^{78} +6.74980i q^{79} +3.18926i q^{80} +(6.82388 + 5.86810i) q^{81} +3.45535 q^{82} -5.23364 q^{83} +(3.17384 + 0.569541i) q^{84} -1.53825i q^{85} -3.44041i q^{86} +(-0.736599 + 4.10480i) q^{87} +(2.78122 + 3.86697i) q^{88} -10.6093i q^{89} +(-0.387933 + 1.04610i) q^{90} -6.33935 q^{91} -0.378034i q^{92} +(1.81089 - 10.0914i) q^{93} +1.69783i q^{94} -1.59870 q^{95} +(1.24159 - 6.91892i) q^{96} +4.65451 q^{97} +0.371904 q^{98} +(-2.63856 - 9.59364i) 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	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 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 + 28 * 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 - 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 + 56 * q^99

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