LMFDB - Embedded newform 1155.2.l.f.1121.19

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			1121.19
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.261999 q^{2} +(-0.733531 - 1.56905i) q^{3} -1.93136 q^{4} +1.00000i q^{5} +(0.192184 + 0.411090i) q^{6} +1.00000i q^{7} +1.03001 q^{8} +(-1.92386 + 2.30190i) q^{9} +O(q^{10})$	\(q-0.261999 q^{2} +(-0.733531 - 1.56905i) q^{3} -1.93136 q^{4} +1.00000i q^{5} +(0.192184 + 0.411090i) q^{6} +1.00000i q^{7} +1.03001 q^{8} +(-1.92386 + 2.30190i) q^{9} -0.261999i q^{10} +(-3.25104 + 0.656295i) q^{11} +(1.41671 + 3.03040i) q^{12} -3.73185i q^{13} -0.261999i q^{14} +(1.56905 - 0.733531i) q^{15} +3.59285 q^{16} -1.46566 q^{17} +(0.504050 - 0.603095i) q^{18} +5.82779i q^{19} -1.93136i q^{20} +(1.56905 - 0.733531i) q^{21} +(0.851768 - 0.171948i) q^{22} -2.98817i q^{23} +(-0.755544 - 1.61614i) q^{24} -1.00000 q^{25} +0.977738i q^{26} +(5.02302 + 1.33013i) q^{27} -1.93136i q^{28} +4.36772 q^{29} +(-0.411090 + 0.192184i) q^{30} +5.20497 q^{31} -3.00134 q^{32} +(3.41450 + 4.61965i) q^{33} +0.384002 q^{34} -1.00000 q^{35} +(3.71567 - 4.44579i) q^{36} +2.14447 q^{37} -1.52687i q^{38} +(-5.85547 + 2.73742i) q^{39} +1.03001i q^{40} +3.91153 q^{41} +(-0.411090 + 0.192184i) q^{42} +1.80264i q^{43} +(6.27892 - 1.26754i) q^{44} +(-2.30190 - 1.92386i) q^{45} +0.782895i q^{46} -8.56489i q^{47} +(-2.63547 - 5.63738i) q^{48} -1.00000 q^{49} +0.261999 q^{50} +(1.07511 + 2.29971i) q^{51} +7.20752i q^{52} -14.0920i q^{53} +(-1.31602 - 0.348493i) q^{54} +(-0.656295 - 3.25104i) q^{55} +1.03001i q^{56} +(9.14411 - 4.27486i) q^{57} -1.14434 q^{58} -4.17129i q^{59} +(-3.03040 + 1.41671i) q^{60} +0.658282i q^{61} -1.36369 q^{62} +(-2.30190 - 1.92386i) q^{63} -6.39936 q^{64} +3.73185 q^{65} +(-0.894595 - 1.21034i) q^{66} +12.4934 q^{67} +2.83072 q^{68} +(-4.68859 + 2.19191i) q^{69} +0.261999 q^{70} +0.170048i q^{71} +(-1.98160 + 2.37098i) q^{72} +7.57123i q^{73} -0.561848 q^{74} +(0.733531 + 1.56905i) q^{75} -11.2555i q^{76} +(-0.656295 - 3.25104i) q^{77} +(1.53412 - 0.717201i) q^{78} -12.2638i q^{79} +3.59285i q^{80} +(-1.59749 - 8.85709i) q^{81} -1.02482 q^{82} -5.56653 q^{83} +(-3.03040 + 1.41671i) q^{84} -1.46566i q^{85} -0.472289i q^{86} +(-3.20386 - 6.85320i) q^{87} +(-3.34861 + 0.675990i) q^{88} -7.47519i q^{89} +(0.603095 + 0.504050i) q^{90} +3.73185 q^{91} +5.77121i q^{92} +(-3.81801 - 8.16688i) q^{93} +2.24399i q^{94} -5.82779 q^{95} +(2.20158 + 4.70927i) q^{96} +9.21194 q^{97} +0.261999 q^{98} +(4.74384 - 8.74620i) 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 $

$2$	−0.261999			−0.185261			−0.0926305	−	0.995701i	$-0.529528\pi$
$2$	−0.261999			−0.185261			−0.0926305	+	0.995701i	$0.529528\pi$
$3$	−0.733531	−	1.56905i	−0.423504	−	0.905894i
$3$	−0.733531	−	1.56905i	−0.423504	−	0.905894i
$4$	−1.93136			−0.965678
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.192184	+	0.411090i	0.0784588	+	0.167827i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.03001			0.364163
$9$	−1.92386	+	2.30190i	−0.641288	+	0.767300i
$10$		−	0.261999i		−	0.0828512i
$11$	−3.25104	+	0.656295i	−0.980226	+	0.197880i
$11$	−3.25104	+	0.656295i	−0.980226	+	0.197880i
$12$	1.41671	+	3.03040i	0.408969	+	0.874802i
$13$		−	3.73185i		−	1.03503i	−0.855675	−	0.517514i	$-0.826858\pi$
$13$		−	3.73185i		−	1.03503i	0.855675	−	0.517514i	$-0.173142\pi$
$14$		−	0.261999i		−	0.0700221i
$15$	1.56905	−	0.733531i	0.405128	−	0.189397i
$16$	3.59285			0.898213
$17$	−1.46566			−0.355476			−0.177738	−	0.984078i	$-0.556878\pi$
$17$	−1.46566			−0.355476			−0.177738	+	0.984078i	$0.556878\pi$
$18$	0.504050	−	0.603095i	0.118806	−	0.142151i
$19$			5.82779i			1.33699i	0.743719	+	0.668493i	$0.233060\pi$
$19$			5.82779i			1.33699i	−0.743719	+	0.668493i	$0.766940\pi$
$20$		−	1.93136i		−	0.431865i
$21$	1.56905	−	0.733531i	0.342396	−	0.160070i
$22$	0.851768	−	0.171948i	0.181598	−	0.0366595i
$23$		−	2.98817i		−	0.623076i	−0.950234	−	0.311538i	$-0.899156\pi$
$23$		−	2.98817i		−	0.623076i	0.950234	−	0.311538i	$-0.100844\pi$
$24$	−0.755544	−	1.61614i	−0.154225	−	0.329893i
$25$	−1.00000			−0.200000
$26$			0.977738i			0.191750i
$27$	5.02302	+	1.33013i	0.966681	+	0.255984i
$28$		−	1.93136i		−	0.364992i
$29$	4.36772			0.811066			0.405533	−	0.914080i	$-0.367086\pi$
$29$	4.36772			0.811066			0.405533	+	0.914080i	$0.367086\pi$
$30$	−0.411090	+	0.192184i	−0.0750544	+	0.0350879i
$31$	5.20497			0.934840			0.467420	−	0.884035i	$-0.345184\pi$
$31$	5.20497			0.934840			0.467420	+	0.884035i	$0.345184\pi$
$32$	−3.00134			−0.530567
$33$	3.41450	+	4.61965i	0.594389	+	0.804178i
$34$	0.384002			0.0658558
$35$	−1.00000			−0.169031
$36$	3.71567	−	4.44579i	0.619278	−	0.740965i
$37$	2.14447			0.352549			0.176274	−	0.984341i	$-0.443595\pi$
$37$	2.14447			0.352549			0.176274	+	0.984341i	$0.443595\pi$
$38$		−	1.52687i		−	0.247691i
$39$	−5.85547	+	2.73742i	−0.937625	+	0.438339i
$40$			1.03001i			0.162859i
$41$	3.91153			0.610879			0.305440	−	0.952211i	$-0.401197\pi$
$41$	3.91153			0.610879			0.305440	+	0.952211i	$0.401197\pi$
$42$	−0.411090	+	0.192184i	−0.0634326	+	0.0296546i
$43$			1.80264i			0.274900i	0.990509	+	0.137450i	$0.0438906\pi$
$43$			1.80264i			0.274900i	−0.990509	+	0.137450i	$0.956109\pi$
$44$	6.27892	−	1.26754i	0.946583	−	0.191089i
$45$	−2.30190	−	1.92386i	−0.343147	−	0.286793i
$46$			0.782895i			0.115432i
$47$		−	8.56489i		−	1.24932i	−0.780898	−	0.624659i	$-0.785238\pi$
$47$		−	8.56489i		−	1.24932i	0.780898	−	0.624659i	$-0.214762\pi$
$48$	−2.63547	−	5.63738i	−0.380397	−	0.813686i
$49$	−1.00000			−0.142857
$50$	0.261999			0.0370522
$51$	1.07511	+	2.29971i	0.150546	+	0.322023i
$52$			7.20752i			0.999504i
$53$		−	14.0920i		−	1.93568i	−0.251560	−	0.967842i	$-0.580944\pi$
$53$		−	14.0920i		−	1.93568i	0.251560	−	0.967842i	$-0.419056\pi$
$54$	−1.31602	−	0.348493i	−0.179088	−	0.0474238i
$55$	−0.656295	−	3.25104i	−0.0884948	−	0.438370i
$56$			1.03001i			0.137641i
$57$	9.14411	−	4.27486i	1.21117	−	0.566219i
$58$	−1.14434			−0.150259
$59$		−	4.17129i		−	0.543055i	−0.962431	−	0.271528i	$-0.912471\pi$
$59$		−	4.17129i		−	0.543055i	0.962431	−	0.271528i	$-0.0875288\pi$
$60$	−3.03040	+	1.41671i	−0.391223	+	0.182897i
$61$			0.658282i			0.0842844i	0.999112	+	0.0421422i	$0.0134182\pi$
$61$			0.658282i			0.0842844i	−0.999112	+	0.0421422i	$0.986582\pi$
$62$	−1.36369			−0.173189
$63$	−2.30190	−	1.92386i	−0.290012	−	0.242384i
$64$	−6.39936			−0.799920
$65$	3.73185			0.462878
$66$	−0.894595	−	1.21034i	−0.110117	−	0.148983i
$67$	12.4934			1.52631			0.763154	−	0.646217i	$-0.223650\pi$
$67$	12.4934			1.52631			0.763154	+	0.646217i	$0.223650\pi$
$68$	2.83072			0.343275
$69$	−4.68859	+	2.19191i	−0.564440	+	0.263875i
$70$	0.261999			0.0313148
$71$			0.170048i			0.0201810i	0.999949	+	0.0100905i	$0.00321196\pi$
$71$			0.170048i			0.0201810i	−0.999949	+	0.0100905i	$0.996788\pi$
$72$	−1.98160	+	2.37098i	−0.233534	+	0.279423i
$73$			7.57123i			0.886146i	0.896486	+	0.443073i	$0.146112\pi$
$73$			7.57123i			0.886146i	−0.896486	+	0.443073i	$0.853888\pi$
$74$	−0.561848			−0.0653135
$75$	0.733531	+	1.56905i	0.0847009	+	0.181179i
$76$		−	11.2555i		−	1.29110i
$77$	−0.656295	−	3.25104i	−0.0747918	−	0.370491i
$78$	1.53412	−	0.717201i	0.173705	−	0.0812070i
$79$		−	12.2638i		−	1.37978i	−0.723914	−	0.689890i	$-0.757659\pi$
$79$		−	12.2638i		−	1.37978i	0.723914	−	0.689890i	$-0.242341\pi$
$80$			3.59285i			0.401693i
$81$	−1.59749	−	8.85709i	−0.177499	−	0.984121i
$82$	−1.02482			−0.113172
$83$	−5.56653			−0.611006			−0.305503	−	0.952191i	$-0.598825\pi$
$83$	−5.56653			−0.611006			−0.305503	+	0.952191i	$0.598825\pi$
$84$	−3.03040	+	1.41671i	−0.330644	+	0.154576i
$85$		−	1.46566i		−	0.158974i
$86$		−	0.472289i		−	0.0509282i
$87$	−3.20386	−	6.85320i	−0.343490	−	0.734740i
$88$	−3.34861	+	0.675990i	−0.356963	+	0.0720608i
$89$		−	7.47519i		−	0.792369i	−0.918171	−	0.396184i	$-0.870334\pi$
$89$		−	7.47519i		−	0.792369i	0.918171	−	0.396184i	$-0.129666\pi$
$90$	0.603095	+	0.504050i	0.0635718	+	0.0531315i
$91$	3.73185			0.391204
$92$			5.77121i			0.601691i
$93$	−3.81801	−	8.16688i	−0.395909	−	0.846866i
$94$			2.24399i			0.231450i
$95$	−5.82779			−0.597918
$96$	2.20158	+	4.70927i	0.224698	+	0.480638i
$97$	9.21194			0.935331			0.467666	−	0.883905i	$-0.345095\pi$
$97$	9.21194			0.935331			0.467666	+	0.883905i	$0.345095\pi$
$98$	0.261999			0.0264658
$99$	4.74384	−	8.74620i	0.476774	−	0.879026i
$100$	1.93136			0.193136
$101$	−12.9444			−1.28802			−0.644009	−	0.765018i	$-0.722730\pi$
$101$	−12.9444			−1.28802			−0.644009	+	0.765018i	$0.722730\pi$
$102$	−0.281677	−	0.602520i	−0.0278902	−	0.0596584i
$103$	12.3301			1.21492			0.607462	−	0.794349i	$-0.292188\pi$
$103$	12.3301			1.21492			0.607462	+	0.794349i	$0.292188\pi$
$104$		−	3.84384i		−	0.376919i
$105$	0.733531	+	1.56905i	0.0715853	+	0.153124i
$106$			3.69208i			0.358607i
$107$	13.5664			1.31151			0.655755	−	0.754974i	$-0.272351\pi$
$107$	13.5664			1.31151			0.655755	+	0.754974i	$0.272351\pi$
$108$	−9.70125	−	2.56896i	−0.933503	−	0.247198i
$109$		−	12.3347i		−	1.18145i	−0.806872	−	0.590727i	$-0.798841\pi$
$109$		−	12.3347i		−	1.18145i	0.806872	−	0.590727i	$-0.201159\pi$
$110$	0.171948	+	0.851768i	0.0163946	+	0.0812129i
$111$	−1.57303	−	3.36479i	−0.149306	−	0.319372i
$112$			3.59285i			0.339493i
$113$			1.93983i			0.182484i	0.995829	+	0.0912420i	$0.0290837\pi$
$113$			1.93983i			0.182484i	−0.995829	+	0.0912420i	$0.970916\pi$
$114$	−2.39574	+	1.12001i	−0.224382	+	0.104898i
$115$	2.98817			0.278648
$116$	−8.43563			−0.783229
$117$	8.59034	+	7.17956i	0.794177	+	0.663751i
$118$			1.09287i			0.100607i
$119$		−	1.46566i		−	0.134357i
$120$	1.61614	−	0.755544i	0.147533	−	0.0689714i
$121$	10.1386	−	4.26729i	0.921687	−	0.387935i
$122$		−	0.172469i		−	0.0156146i
$123$	−2.86923	−	6.13741i	−0.258710	−	0.553392i
$124$	−10.0527			−0.902755
$125$		−	1.00000i		−	0.0894427i
$126$	0.603095	+	0.504050i	0.0537279	+	0.0449043i
$127$			14.5879i			1.29447i	0.762291	+	0.647235i	$0.224075\pi$
$127$			14.5879i			1.29447i	−0.762291	+	0.647235i	$0.775925\pi$
$128$	7.67931			0.678761
$129$	2.82844	−	1.32229i	0.249030	−	0.116421i
$130$	−0.977738			−0.0857533
$131$	14.2678			1.24658			0.623291	−	0.781990i	$-0.285795\pi$
$131$	14.2678			1.24658			0.623291	+	0.781990i	$0.285795\pi$
$132$	−6.59462	−	8.92219i	−0.573988	−	0.776577i
$133$	−5.82779			−0.505333
$134$	−3.27324			−0.282765
$135$	−1.33013	+	5.02302i	−0.114480	+	0.432313i
$136$	−1.50965			−0.129451
$137$			0.845410i			0.0722283i	0.999348	+	0.0361141i	$0.0114980\pi$
$137$			0.845410i			0.0722283i	−0.999348	+	0.0361141i	$0.988502\pi$
$138$	1.22840	−	0.574278i	0.104569	−	0.0488858i
$139$			9.92982i			0.842236i	0.907006	+	0.421118i	$0.138362\pi$
$139$			9.92982i			0.842236i	−0.907006	+	0.421118i	$0.861638\pi$
$140$	1.93136			0.163229
$141$	−13.4388	+	6.28261i	−1.13175	+	0.529092i
$142$		−	0.0445523i		−	0.00373875i
$143$	2.44919	+	12.1324i	0.204812	+	1.01456i
$144$	−6.91216	+	8.27039i	−0.576013	+	0.689199i
$145$			4.36772i			0.362720i
$146$		−	1.98365i		−	0.164168i
$147$	0.733531	+	1.56905i	0.0605006	+	0.129413i
$148$	−4.14174			−0.340449
$149$	−8.54552			−0.700076			−0.350038	−	0.936736i	$-0.613831\pi$
$149$	−8.54552			−0.700076			−0.350038	+	0.936736i	$0.613831\pi$
$150$	−0.192184	−	0.411090i	−0.0156918	−	0.0335654i
$151$			21.9474i			1.78605i	0.450005	+	0.893026i	$0.351422\pi$
$151$			21.9474i			1.78605i	−0.450005	+	0.893026i	$0.648578\pi$
$152$			6.00268i			0.486881i
$153$	2.81974	−	3.37381i	0.227962	−	0.272757i
$154$	0.171948	+	0.851768i	0.0138560	+	0.0686375i
$155$			5.20497i			0.418073i
$156$	11.3090	−	5.28694i	0.905445	−	0.423294i
$157$	22.2463			1.77545			0.887723	−	0.460378i	$-0.152286\pi$
$157$	22.2463			1.77545			0.887723	+	0.460378i	$0.152286\pi$
$158$			3.21308i			0.255619i
$159$	−22.1111	+	10.3369i	−1.75352	+	0.819770i
$160$		−	3.00134i		−	0.237277i
$161$	2.98817			0.235500
$162$	0.418541	+	2.32054i	0.0328837	+	0.182319i
$163$	10.9420			0.857044			0.428522	−	0.903531i	$-0.359034\pi$
$163$	10.9420			0.857044			0.428522	+	0.903531i	$0.359034\pi$
$164$	−7.55457			−0.589913
$165$	−4.61965	+	3.41450i	−0.359639	+	0.265819i
$166$	1.45842			0.113196
$167$	−16.8281			−1.30220			−0.651098	−	0.758994i	$-0.725691\pi$
$167$	−16.8281			−1.30220			−0.651098	+	0.758994i	$0.725691\pi$
$168$	1.61614	−	0.755544i	0.124688	−	0.0582915i
$169$	−0.926667			−0.0712821
$170$			0.384002i			0.0294516i
$171$	−13.4150	−	11.2119i	−1.02587	−	0.857393i
$172$		−	3.48154i		−	0.265465i
$173$	−2.97685			−0.226326			−0.113163	−	0.993576i	$-0.536098\pi$
$173$	−2.97685			−0.226326			−0.113163	+	0.993576i	$0.536098\pi$
$174$	0.839407	+	1.79553i	0.0636353	+	0.136119i
$175$		−	1.00000i		−	0.0755929i
$176$	−11.6805	+	2.35797i	−0.880452	+	0.177739i
$177$	−6.54498	+	3.05977i	−0.491950	+	0.229986i
$178$			1.95849i			0.146795i
$179$			12.0737i			0.902429i	0.892416	+	0.451214i	$0.149009\pi$
$179$			12.0737i			0.902429i	−0.892416	+	0.451214i	$0.850991\pi$
$180$	4.44579	+	3.71567i	0.331370	+	0.276950i
$181$	−11.4976			−0.854612			−0.427306	−	0.904107i	$-0.640537\pi$
$181$	−11.4976			−0.854612			−0.427306	+	0.904107i	$0.640537\pi$
$182$	−0.977738			−0.0724748
$183$	1.03288	−	0.482870i	0.0763527	−	0.0356948i
$184$		−	3.07784i		−	0.226901i
$185$			2.14447i			0.157665i
$186$	1.00031	+	2.13971i	0.0733465	+	0.156891i
$187$	4.76494	−	0.961908i	0.348447	−	0.0703417i
$188$			16.5419i			1.20644i
$189$	−1.33013	+	5.02302i	−0.0967528	+	0.365371i
$190$	1.52687			0.110771
$191$			12.1472i			0.878937i	0.898258	+	0.439468i	$0.144833\pi$
$191$			12.1472i			0.878937i	−0.898258	+	0.439468i	$0.855167\pi$
$192$	4.69413	+	10.0409i	0.338770	+	0.724643i
$193$		−	11.7086i		−	0.842806i	−0.906874	−	0.421403i	$-0.861538\pi$
$193$		−	11.7086i		−	0.842806i	0.906874	−	0.421403i	$-0.138462\pi$
$194$	−2.41352			−0.173280
$195$	−2.73742	−	5.85547i	−0.196031	−	0.419319i
$196$	1.93136			0.137954
$197$	25.4302			1.81182			0.905912	−	0.423465i	$-0.139186\pi$
$197$	25.4302			1.81182			0.905912	+	0.423465i	$0.139186\pi$
$198$	−1.24288	+	2.29149i	−0.0883275	+	0.162849i
$199$	−6.31202			−0.447447			−0.223724	−	0.974653i	$-0.571821\pi$
$199$	−6.31202			−0.447447			−0.223724	+	0.974653i	$0.571821\pi$
$200$	−1.03001			−0.0728327
$201$	−9.16427	−	19.6028i	−0.646398	−	1.38267i
$202$	3.39142			0.238619
$203$			4.36772i			0.306554i
$204$	−2.07642	−	4.44156i	−0.145379	−	0.310971i
$205$			3.91153i			0.273193i
$206$	−3.23048			−0.225078
$207$	6.87846	+	5.74882i	0.478086	+	0.399571i
$208$		−	13.4080i		−	0.929675i
$209$	−3.82475	−	18.9464i	−0.264563	−	1.31055i
$210$	−0.192184	−	0.411090i	−0.0132620	−	0.0283679i
$211$			5.98246i			0.411849i	0.978568	+	0.205925i	$0.0660202\pi$
$211$			5.98246i			0.411849i	−0.978568	+	0.205925i	$0.933980\pi$
$212$			27.2167i			1.86925i
$213$	0.266815	−	0.124735i	0.0182818	−	0.00854673i
$214$	−3.55437			−0.242971
$215$	−1.80264			−0.122939
$216$	5.17376	+	1.37005i	0.352030	+	0.0932200i
$217$			5.20497i			0.353336i
$218$			3.23168i			0.218877i
$219$	11.8797	−	5.55374i	0.802754	−	0.375287i
$220$	1.26754	+	6.27892i	0.0854575	+	0.423325i
$221$			5.46963i			0.367927i
$222$	0.412133	+	0.881570i	0.0276605	+	0.0591671i
$223$	11.2250			0.751683			0.375841	−	0.926684i	$-0.377354\pi$
$223$	11.2250			0.751683			0.375841	+	0.926684i	$0.377354\pi$
$224$		−	3.00134i		−	0.200536i
$225$	1.92386	−	2.30190i	0.128258	−	0.153460i
$226$		−	0.508233i		−	0.0338072i
$227$	−14.9073			−0.989429			−0.494714	−	0.869056i	$-0.664727\pi$
$227$	−14.9073			−0.989429			−0.494714	+	0.869056i	$0.664727\pi$
$228$	−17.6605	+	8.25629i	−1.16960	+	0.546786i
$229$	7.35651			0.486132			0.243066	−	0.970010i	$-0.421847\pi$
$229$	7.35651			0.486132			0.243066	+	0.970010i	$0.421847\pi$
$230$	−0.782895			−0.0516226
$231$	−4.61965	+	3.41450i	−0.303951	+	0.224658i
$232$	4.49880			0.295361
$233$	12.0439			0.789022			0.394511	−	0.918891i	$-0.370914\pi$
$233$	12.0439			0.789022			0.394511	+	0.918891i	$0.370914\pi$
$234$	−2.25066	−	1.88103i	−0.147130	−	0.122967i
$235$	8.56489			0.558712
$236$			8.05624i			0.524417i
$237$	−19.2425	+	8.99584i	−1.24993	+	0.584343i
$238$			0.384002i			0.0248911i
$239$	25.3603			1.64042			0.820211	−	0.572061i	$-0.193856\pi$
$239$	25.3603			1.64042			0.820211	+	0.572061i	$0.193856\pi$
$240$	5.63738	−	2.63547i	0.363891	−	0.170119i
$241$		−	25.4501i		−	1.63938i	−0.572806	−	0.819691i	$-0.694145\pi$
$241$		−	25.4501i		−	1.63938i	0.572806	−	0.819691i	$-0.305855\pi$
$242$	−2.65629	+	1.11802i	−0.170753	+	0.0718692i
$243$	−12.7254	+	9.00351i	−0.816338	+	0.577575i
$244$		−	1.27138i		−	0.0813916i
$245$		−	1.00000i		−	0.0638877i
$246$	0.751735	+	1.60799i	0.0479289	+	0.102522i
$247$	21.7484			1.38382
$248$	5.36117			0.340435
$249$	4.08322	+	8.73419i	0.258764	+	0.553507i
$250$			0.261999i			0.0165702i
$251$			7.10973i			0.448762i	0.974501	+	0.224381i	$0.0720360\pi$
$251$			7.10973i			0.448762i	−0.974501	+	0.224381i	$0.927964\pi$
$252$	4.44579	+	3.71567i	0.280059	+	0.234065i
$253$	1.96112	+	9.71465i	0.123294	+	0.610755i
$254$		−	3.82202i		−	0.239815i
$255$	−2.29971	+	1.07511i	−0.144013	+	0.0673260i
$256$	10.7867			0.674172
$257$			8.31224i			0.518503i	0.965810	+	0.259252i	$0.0834759\pi$
$257$			8.31224i			0.518503i	−0.965810	+	0.259252i	$0.916524\pi$
$258$	−0.741047	+	0.346439i	−0.0461356	+	0.0215683i
$259$			2.14447i			0.133251i
$260$	−7.20752			−0.446992
$261$	−8.40291	+	10.0541i	−0.520127	+	0.622331i
$262$	−3.73814			−0.230943
$263$	6.41353			0.395475			0.197738	−	0.980255i	$-0.436641\pi$
$263$	6.41353			0.395475			0.197738	+	0.980255i	$0.436641\pi$
$264$	3.51697	+	4.75828i	0.216455	+	0.292852i
$265$	14.0920			0.865664
$266$	1.52687			0.0936185
$267$	−11.7290	+	5.48329i	−0.717802	+	0.335572i
$268$	−24.1291			−1.47392
$269$		−	14.8966i		−	0.908261i	−0.890935	−	0.454130i	$-0.849950\pi$
$269$		−	14.8966i		−	0.908261i	0.890935	−	0.454130i	$-0.150050\pi$
$270$	0.348493	−	1.31602i	0.0212086	−	0.0800907i
$271$			0.321699i			0.0195418i	0.999952	+	0.00977092i	$0.00311023\pi$
$271$			0.321699i			0.0195418i	−0.999952	+	0.00977092i	$0.996890\pi$
$272$	−5.26592			−0.319293
$273$	−2.73742	−	5.85547i	−0.165676	−	0.354389i
$274$		−	0.221496i		−	0.0133811i
$275$	3.25104	−	0.656295i	0.196045	−	0.0395761i
$276$	9.05535	−	4.23336i	0.545068	−	0.254819i
$277$		−	30.0634i		−	1.80633i	−0.429291	−	0.903166i	$-0.641236\pi$
$277$		−	30.0634i		−	1.80633i	0.429291	−	0.903166i	$-0.358764\pi$
$278$		−	2.60160i		−	0.156033i
$279$	−10.0137	+	11.9813i	−0.599502	+	0.717303i
$280$	−1.03001			−0.0615549
$281$	16.0581			0.957945			0.478972	−	0.877830i	$-0.341009\pi$
$281$	16.0581			0.957945			0.478972	+	0.877830i	$0.341009\pi$
$282$	3.52094	−	1.64604i	0.209669	−	0.0980200i
$283$		−	0.0998452i		−	0.00593518i	−0.999996	−	0.00296759i	$-0.999055\pi$
$283$		−	0.0998452i		−	0.00593518i	0.999996	−	0.00296759i	$-0.000944614\pi$
$284$		−	0.328423i		−	0.0194883i
$285$	4.27486	+	9.14411i	0.253221	+	0.541651i
$286$	−0.641684	−	3.17867i	−0.0379436	−	0.187959i
$287$			3.91153i			0.230891i
$288$	5.77417	−	6.90879i	0.340246	−	0.407104i
$289$	−14.8518			−0.873637
$290$		−	1.14434i		−	0.0671978i
$291$	−6.75725	−	14.4540i	−0.396117	−	0.847311i
$292$		−	14.6228i		−	0.855732i
$293$	−31.7610			−1.85550			−0.927749	−	0.373205i	$-0.878259\pi$
$293$	−31.7610			−1.85550			−0.927749	+	0.373205i	$0.878259\pi$
$294$	−0.192184	−	0.411090i	−0.0112084	−	0.0239753i
$295$	4.17129			0.242862
$296$	2.20882			0.128385
$297$	−17.2030	−	1.02773i	−0.998220	−	0.0596350i
$298$	2.23891			0.129697
$299$	−11.1514			−0.644900
$300$	−1.41671	−	3.03040i	−0.0817938	−	0.174960i
$301$	−1.80264			−0.103902
$302$		−	5.75018i		−	0.330886i
$303$	9.49514	+	20.3105i	0.545481	+	1.16681i
$304$			20.9384i			1.20090i
$305$	−0.658282			−0.0376931
$306$	−0.738767	+	0.883934i	−0.0422325	+	0.0505312i
$307$			0.737113i			0.0420693i	0.999779	+	0.0210346i	$0.00669603\pi$
$307$			0.737113i			0.0420693i	−0.999779	+	0.0210346i	$0.993304\pi$
$308$	1.26754	+	6.27892i	0.0722248	+	0.357775i
$309$	−9.04454	−	19.3467i	−0.514526	−	1.10059i
$310$		−	1.36369i		−	0.0774526i
$311$		−	3.52144i		−	0.199683i	−0.995003	−	0.0998414i	$-0.968166\pi$
$311$		−	3.52144i		−	0.199683i	0.995003	−	0.0998414i	$-0.0318335\pi$
$312$	−6.03119	+	2.81957i	−0.341449	+	0.159627i
$313$	3.59040			0.202942			0.101471	−	0.994839i	$-0.467645\pi$
$313$	3.59040			0.202942			0.101471	+	0.994839i	$0.467645\pi$
$314$	−5.82849			−0.328921
$315$	1.92386	−	2.30190i	0.108397	−	0.129697i
$316$			23.6857i			1.33242i
$317$		−	27.2836i		−	1.53240i	−0.642603	−	0.766199i	$-0.722146\pi$
$317$		−	27.2836i		−	1.53240i	0.642603	−	0.766199i	$-0.277854\pi$
$318$	5.79307	−	2.70826i	0.324859	−	0.151871i
$319$	−14.1997	+	2.86652i	−0.795028	+	0.160494i
$320$		−	6.39936i		−	0.357735i
$321$	−9.95135	−	21.2864i	−0.555430	−	1.18809i
$322$	−0.782895			−0.0436290
$323$		−	8.54158i		−	0.475266i
$324$	3.08533	+	17.1062i	0.171407	+	0.950344i
$325$			3.73185i			0.207006i
$326$	−2.86679			−0.158777
$327$	−19.3539	+	9.04791i	−1.07027	+	0.500351i
$328$	4.02892			0.222460
$329$	8.56489			0.472198
$330$	1.21034	−	0.894595i	0.0666271	−	0.0492458i
$331$	−35.6863			−1.96150			−0.980749	−	0.195272i	$-0.937441\pi$
$331$	−35.6863			−1.96150			−0.980749	+	0.195272i	$0.937441\pi$
$332$	10.7510			0.590035
$333$	−4.12567	+	4.93636i	−0.226085	+	0.270511i
$334$	4.40893			0.241246
$335$			12.4934i			0.682586i
$336$	5.63738	−	2.63547i	0.307544	−	0.143777i
$337$			30.3005i			1.65058i	0.564712	+	0.825288i	$0.308987\pi$
$337$			30.3005i			1.65058i	−0.564712	+	0.825288i	$0.691013\pi$
$338$	0.242786			0.0132058
$339$	3.04370	−	1.42293i	0.165311	−	0.0772828i
$340$			2.83072i			0.153517i
$341$	−16.9216	+	3.41600i	−0.916355	+	0.184987i
$342$	3.51471	+	2.93749i	0.190054	+	0.158841i
$343$		−	1.00000i		−	0.0539949i
$344$			1.85674i			0.100108i
$345$	−2.19191	−	4.68859i	−0.118009	−	0.252425i
$346$	0.779931			0.0419294
$347$	9.03778			0.485174			0.242587	−	0.970130i	$-0.422004\pi$
$347$	9.03778			0.485174			0.242587	+	0.970130i	$0.422004\pi$
$348$	6.18780	+	13.2360i	0.331701	+	0.709522i
$349$		−	27.4859i		−	1.47129i	−0.677369	−	0.735644i	$-0.736880\pi$
$349$		−	27.4859i		−	1.47129i	0.677369	−	0.735644i	$-0.263120\pi$
$350$			0.261999i			0.0140044i
$351$	4.96385	−	18.7451i	0.264950	−	1.00054i
$352$	9.75749	−	1.96977i	0.520076	−	0.104989i
$353$		−	0.616761i		−	0.0328269i	−0.999865	−	0.0164134i	$-0.994775\pi$
$353$		−	0.616761i		−	0.0328269i	0.999865	−	0.0164134i	$-0.00522480\pi$
$354$	1.71477	−	0.801655i	0.0911392	−	0.0426075i
$355$	−0.170048			−0.00902521
$356$			14.4373i			0.765173i
$357$	−2.29971	+	1.07511i	−0.121713	+	0.0569009i
$358$		−	3.16328i		−	0.167185i
$359$	4.46738			0.235779			0.117890	−	0.993027i	$-0.462387\pi$
$359$	4.46738			0.235779			0.117890	+	0.993027i	$0.462387\pi$
$360$	−2.37098	−	1.98160i	−0.124962	−	0.104439i
$361$	−14.9631			−0.787531
$362$	3.01236			0.158326
$363$	−14.1325	−	12.7778i	−0.741766	−	0.670658i
$364$	−7.20752			−0.377777
$365$	−7.57123			−0.396296
$366$	−0.270613	+	0.126511i	−0.0141452	+	0.00661285i
$367$	−21.6584			−1.13056			−0.565279	−	0.824900i	$-0.691232\pi$
$367$	−21.6584			−1.13056			−0.565279	+	0.824900i	$0.691232\pi$
$368$		−	10.7360i		−	0.559655i
$369$	−7.52526	+	9.00397i	−0.391749	+	0.468728i
$370$		−	0.561848i		−	0.0292091i
$371$	14.0920			0.731620
$372$	7.37393	+	15.7732i	0.382321	+	0.817800i
$373$			19.7570i			1.02298i	0.859289	+	0.511490i	$0.170906\pi$
$373$			19.7570i			1.02298i	−0.859289	+	0.511490i	$0.829094\pi$
$374$	−1.24841	+	0.252019i	−0.0645536	+	0.0130316i
$375$	−1.56905	+	0.733531i	−0.0810256	+	0.0378794i
$376$		−	8.82192i		−	0.454956i
$377$		−	16.2997i		−	0.839476i
$378$	0.348493	−	1.31602i	0.0179245	−	0.0676890i
$379$	23.1902			1.19120			0.595601	−	0.803281i	$-0.296914\pi$
$379$	23.1902			1.19120			0.595601	+	0.803281i	$0.296914\pi$
$380$	11.2555			0.577397
$381$	22.8893	−	10.7007i	1.17265	−	0.548214i
$382$		−	3.18254i		−	0.162833i
$383$			15.3472i			0.784206i	0.919921	+	0.392103i	$0.128252\pi$
$383$			15.3472i			0.784206i	−0.919921	+	0.392103i	$0.871748\pi$
$384$	−5.63301	−	12.0492i	−0.287458	−	0.614886i
$385$	3.25104	−	0.656295i	0.165688	−	0.0334479i
$386$			3.06764i			0.156139i
$387$	−4.14950	−	3.46803i	−0.210931	−	0.176290i
$388$	−17.7915			−0.903229
$389$		−	30.6736i		−	1.55521i	−0.628752	−	0.777606i	$-0.716434\pi$
$389$		−	30.6736i		−	1.55521i	0.628752	−	0.777606i	$-0.283566\pi$
$390$	0.717201	+	1.53412i	0.0363169	+	0.0776834i
$391$			4.37965i			0.221488i
$392$	−1.03001			−0.0520233
$393$	−10.4659	−	22.3869i	−0.527933	−	1.12927i
$394$	−6.66267			−0.335660
$395$	12.2638			0.617056
$396$	−9.16204	+	16.8920i	−0.460410	+	0.848856i
$397$	4.43589			0.222631			0.111315	−	0.993785i	$-0.464494\pi$
$397$	4.43589			0.222631			0.111315	+	0.993785i	$0.464494\pi$
$398$	1.65374			0.0828945
$399$	4.27486	+	9.14411i	0.214011	+	0.457778i
$400$	−3.59285			−0.179643
$401$			26.8464i			1.34065i	0.742069	+	0.670323i	$0.233845\pi$
$401$			26.8464i			1.34065i	−0.742069	+	0.670323i	$0.766155\pi$
$402$	2.40103	+	5.13590i	0.119752	+	0.256155i
$403$		−	19.4241i		−	0.967585i
$404$	25.0003			1.24381
$405$	8.85709	−	1.59749i	0.440112	−	0.0793801i
$406$		−	1.14434i		−	0.0567925i
$407$	−6.97176	+	1.40740i	−0.345577	+	0.0697624i
$408$	1.10737	+	2.36872i	0.0548232	+	0.117269i
$409$			24.3310i			1.20309i	0.798840	+	0.601544i	$0.205448\pi$
$409$			24.3310i			1.20309i	−0.798840	+	0.601544i	$0.794552\pi$
$410$		−	1.02482i		−	0.0506121i
$411$	1.32649	−	0.620135i	0.0654312	−	0.0305890i
$412$	−23.8139			−1.17323
$413$	4.17129			0.205256
$414$	−1.80215	−	1.50618i	−0.0885707	−	0.0740249i
$415$		−	5.56653i		−	0.273250i
$416$			11.2005i			0.549152i
$417$	15.5804	−	7.28383i	0.762977	−	0.356691i
$418$	1.00208	+	4.96392i	0.0490132	+	0.242793i
$419$		−	12.3078i		−	0.601277i	−0.953738	−	0.300639i	$-0.902800\pi$
$419$		−	12.3078i		−	0.601277i	0.953738	−	0.300639i	$-0.0971998\pi$
$420$	−1.41671	−	3.03040i	−0.0691284	−	0.147869i
$421$	−23.4814			−1.14441			−0.572207	−	0.820109i	$-0.693913\pi$
$421$	−23.4814			−1.14441			−0.572207	+	0.820109i	$0.693913\pi$
$422$		−	1.56740i		−	0.0762996i
$423$	19.7155	+	16.4777i	0.958602	+	0.801172i
$424$		−	14.5149i		−	0.704905i
$425$	1.46566			0.0710952
$426$	−0.0699050	+	0.0326805i	−0.00338691	+	0.00158338i
$427$	−0.658282			−0.0318565
$428$	−26.2015			−1.26650
$429$	17.2398	−	12.7424i	0.832346	−	0.615209i
$430$	0.472289			0.0227758
$431$	−9.82457			−0.473233			−0.236617	−	0.971603i	$-0.576039\pi$
$431$	−9.82457			−0.473233			−0.236617	+	0.971603i	$0.576039\pi$
$432$	18.0470	+	4.77897i	0.868286	+	0.229928i
$433$	−26.0392			−1.25136			−0.625682	−	0.780078i	$-0.715179\pi$
$433$	−26.0392			−1.25136			−0.625682	+	0.780078i	$0.715179\pi$
$434$		−	1.36369i		−	0.0654594i
$435$	6.85320	−	3.20386i	0.328586	−	0.153613i
$436$			23.8228i			1.14090i
$437$	17.4144			0.833043
$438$	−3.11246	+	1.45507i	−0.148719	+	0.0695260i
$439$		−	25.0142i		−	1.19386i	−0.802293	−	0.596931i	$-0.796387\pi$
$439$		−	25.0142i		−	1.19386i	0.802293	−	0.596931i	$-0.203613\pi$
$440$	−0.675990	−	3.34861i	−0.0322266	−	0.159638i
$441$	1.92386	−	2.30190i	0.0916126	−	0.109614i
$442$		−	1.43304i		−	0.0681626i
$443$			4.88064i			0.231886i	0.993256	+	0.115943i	$0.0369890\pi$
$443$			4.88064i			0.231886i	−0.993256	+	0.115943i	$0.963011\pi$
$444$	3.03809	+	6.49861i	0.144181	+	0.308410i
$445$	7.47519			0.354358
$446$	−2.94094			−0.139257
$447$	6.26840	+	13.4084i	0.296485	+	0.634195i
$448$		−	6.39936i		−	0.302341i
$449$		−	8.94667i		−	0.422219i	−0.977462	−	0.211110i	$-0.932292\pi$
$449$		−	8.94667i		−	0.422219i	0.977462	−	0.211110i	$-0.0677077\pi$
$450$	−0.504050	+	0.603095i	−0.0237611	+	0.0284302i
$451$	−12.7166	+	2.56712i	−0.598800	+	0.120881i
$452$		−	3.74651i		−	0.176221i
$453$	34.4366	−	16.0991i	1.61797	−	0.756401i
$454$	3.90568			0.183303
$455$			3.73185i			0.174952i
$456$	9.41853	−	4.40315i	0.441063	−	0.206196i
$457$			13.5517i			0.633923i	0.948438	+	0.316961i	$0.102663\pi$
$457$			13.5517i			0.633923i	−0.948438	+	0.316961i	$0.897337\pi$
$458$	−1.92740			−0.0900613
$459$	−7.36206	−	1.94953i	−0.343632	−	0.0909961i
$460$	−5.77121			−0.269084
$461$	−25.3295			−1.17971			−0.589857	−	0.807508i	$-0.700816\pi$
$461$	−25.3295			−1.17971			−0.589857	+	0.807508i	$0.700816\pi$
$462$	1.21034	−	0.894595i	0.0563102	−	0.0416203i
$463$	8.24000			0.382945			0.191473	−	0.981498i	$-0.438674\pi$
$463$	8.24000			0.382945			0.191473	+	0.981498i	$0.438674\pi$
$464$	15.6926			0.728510
$465$	8.16688	−	3.81801i	0.378730	−	0.177056i
$466$	−3.15548			−0.146175
$467$			3.69287i			0.170886i	0.996343	+	0.0854428i	$0.0272305\pi$
$467$			3.69287i			0.170886i	−0.996343	+	0.0854428i	$0.972770\pi$
$468$	−16.5910	−	13.8663i	−0.766919	−	0.640970i
$469$			12.4934i			0.576890i
$470$	−2.24399			−0.103507
$471$	−16.3183	−	34.9056i	−0.751909	−	1.60837i
$472$		−	4.29647i		−	0.197761i
$473$	−1.18306	−	5.86046i	−0.0543973	−	0.269464i
$474$	5.04151	−	2.35690i	0.231564	−	0.108256i
$475$		−	5.82779i		−	0.267397i
$476$			2.83072i			0.129746i
$477$	32.4384	+	27.1111i	1.48525	+	1.24133i
$478$	−6.64436			−0.303906
$479$	−11.9052			−0.543965			−0.271982	−	0.962302i	$-0.587679\pi$
$479$	−11.9052			−0.543965			−0.271982	+	0.962302i	$0.587679\pi$
$480$	−4.70927	+	2.20158i	−0.214948	+	0.100488i
$481$		−	8.00283i		−	0.364897i
$482$			6.66788i			0.303714i
$483$	−2.19191	−	4.68859i	−0.0997355	−	0.213338i
$484$	−19.5812	+	8.24165i	−0.890053	+	0.374620i
$485$			9.21194i			0.418293i
$486$	3.33405	−	2.35891i	0.151235	−	0.107002i
$487$	17.9877			0.815103			0.407551	−	0.913182i	$-0.366383\pi$
$487$	17.9877			0.815103			0.407551	+	0.913182i	$0.366383\pi$
$488$			0.678037i			0.0306933i
$489$	−8.02630	−	17.1686i	−0.362962	−	0.776391i
$490$			0.261999i			0.0118359i
$491$	14.7055			0.663651			0.331826	−	0.943341i	$-0.392335\pi$
$491$	14.7055			0.663651			0.331826	+	0.943341i	$0.392335\pi$
$492$	5.54151	+	11.8535i	0.249831	+	0.534398i
$493$	−6.40162			−0.288314
$494$	−5.69805			−0.256367
$495$	8.74620	+	4.74384i	0.393112	+	0.213220i
$496$	18.7007			0.839686
$497$	−0.170048			−0.00762769
$498$	−1.06980	−	2.28834i	−0.0479388	−	0.102543i
$499$	18.1829			0.813979			0.406990	−	0.913433i	$-0.366579\pi$
$499$	18.1829			0.813979			0.406990	+	0.913433i	$0.366579\pi$
$500$			1.93136i			0.0863729i
$501$	12.3439	+	26.4042i	0.551485	+	1.17965i
$502$		−	1.86274i		−	0.0831381i
$503$	−32.3127			−1.44075			−0.720376	−	0.693583i	$-0.756031\pi$
$503$	−32.3127			−1.44075			−0.720376	+	0.693583i	$0.756031\pi$
$504$	−2.37098	−	1.98160i	−0.105612	−	0.0882674i
$505$		−	12.9444i		−	0.576019i
$506$	−0.513810	−	2.54522i	−0.0228416	−	0.113149i
$507$	0.679739	+	1.45399i	0.0301883	+	0.0645740i
$508$		−	28.1745i		−	1.25004i
$509$		−	39.7166i		−	1.76041i	−0.474595	−	0.880205i	$-0.657405\pi$
$509$		−	39.7166i		−	1.76041i	0.474595	−	0.880205i	$-0.342595\pi$
$510$	0.602520	−	0.281677i	0.0266800	−	0.0124729i
$511$	−7.57123			−0.334932
$512$	−18.1847			−0.803659
$513$	−7.75172	+	29.2731i	−0.342247	+	1.29244i
$514$		−	2.17779i		−	0.0960584i
$515$			12.3301i			0.543331i
$516$	−5.46272	+	2.55382i	−0.240483	+	0.112426i
$517$	5.62109	+	27.8448i	0.247215	+	1.22461i
$518$		−	0.561848i		−	0.0246862i
$519$	2.18361	+	4.67085i	0.0958501	+	0.205027i
$520$	3.84384			0.168563
$521$		−	25.0560i		−	1.09772i	−0.835913	−	0.548862i	$-0.815061\pi$
$521$		−	25.0560i		−	1.09772i	0.835913	−	0.548862i	$-0.184939\pi$
$522$	2.20155	−	2.63415i	0.0963592	−	0.115294i
$523$			4.37339i			0.191235i	0.995418	+	0.0956176i	$0.0304826\pi$
$523$			4.37339i			0.191235i	−0.995418	+	0.0956176i	$0.969517\pi$
$524$	−27.5562			−1.20380
$525$	−1.56905	+	0.733531i	−0.0684792	+	0.0320139i
$526$	−1.68034			−0.0732661
$527$	−7.62874			−0.332313
$528$	12.2678	+	16.5977i	0.533888	+	0.722323i
$529$	14.0709			0.611777
$530$	−3.69208			−0.160374
$531$	9.60189	+	8.02499i	0.416686	+	0.348255i
$532$	11.2555			0.487989
$533$		−	14.5972i		−	0.632277i
$534$	3.07298	−	1.43661i	0.132981	−	0.0621683i
$535$			13.5664i			0.586525i
$536$	12.8683			0.555825
$537$	18.9443	−	8.85641i	0.817505	−	0.382183i
$538$			3.90288i			0.168265i
$539$	3.25104	−	0.656295i	0.140032	−	0.0282686i
$540$	2.56896	−	9.70125i	0.110550	−	0.417475i
$541$		−	2.30608i		−	0.0991461i	−0.998771	−	0.0495730i	$-0.984214\pi$
$541$		−	2.30608i		−	0.0991461i	0.998771	−	0.0495730i	$-0.0157861\pi$
$542$		−	0.0842848i		−	0.00362034i
$543$	8.43387	+	18.0404i	0.361932	+	0.774188i
$544$	4.39896			0.188604
$545$	12.3347			0.528362
$546$	0.717201	+	1.53412i	0.0306934	+	0.0656545i
$547$		−	19.9628i		−	0.853549i	−0.904358	−	0.426775i	$-0.859650\pi$
$547$		−	19.9628i		−	0.853549i	0.904358	−	0.426775i	$-0.140350\pi$
$548$		−	1.63279i		−	0.0697493i
$549$	−1.51530	−	1.26644i	−0.0646714	−	0.0540506i
$550$	−0.851768	+	0.171948i	−0.0363195	+	0.00733190i
$551$			25.4542i			1.08438i
$552$	−4.82930	+	2.25769i	−0.205549	+	0.0960937i
$553$	12.2638			0.521508
$554$			7.87656i			0.334643i
$555$	3.36479	−	1.57303i	0.142827	−	0.0667716i
$556$		−	19.1780i		−	0.813329i
$557$	11.8290			0.501212			0.250606	−	0.968089i	$-0.419370\pi$
$557$	11.8290			0.501212			0.250606	+	0.968089i	$0.419370\pi$
$558$	2.62356	−	3.13909i	0.111064	−	0.132888i
$559$	6.72717			0.284529
$560$	−3.59285			−0.151826
$561$	−5.00452	−	6.77086i	−0.211291	−	0.285866i
$562$	−4.20719			−0.177470
$563$	35.8081			1.50913			0.754565	−	0.656225i	$-0.227848\pi$
$563$	35.8081			1.50913			0.754565	+	0.656225i	$0.227848\pi$
$564$	25.9551	−	12.1340i	1.09291	−	0.510932i
$565$	−1.93983			−0.0816093
$566$			0.0261593i			0.00109956i
$567$	8.85709	−	1.59749i	0.371963	−	0.0670884i
$568$			0.175151i			0.00734918i
$569$	46.8842			1.96549			0.982744	−	0.184971i	$-0.0592192\pi$
$569$	46.8842			1.96549			0.982744	+	0.184971i	$0.0592192\pi$
$570$	−1.12001	−	2.39574i	−0.0469120	−	0.100347i
$571$		−	18.3657i		−	0.768580i	−0.923212	−	0.384290i	$-0.874446\pi$
$571$		−	18.3657i		−	0.768580i	0.923212	−	0.384290i	$-0.125554\pi$
$572$	−4.73026	−	23.4320i	−0.197782	−	0.979740i
$573$	19.0595	−	8.91031i	0.796224	−	0.372234i
$574$		−	1.02482i		−	0.0427750i
$575$			2.98817i			0.124615i
$576$	12.3115	−	14.7307i	0.512979	−	0.613779i
$577$	22.7377			0.946582			0.473291	−	0.880906i	$-0.343066\pi$
$577$	22.7377			0.946582			0.473291	+	0.880906i	$0.343066\pi$
$578$	3.89116			0.161851
$579$	−18.3715	+	8.58864i	−0.763493	+	0.356932i
$580$		−	8.43563i		−	0.350271i
$581$		−	5.56653i		−	0.230938i
$582$	1.77039	+	3.78694i	0.0733850	+	0.156974i
$583$	9.24850	+	45.8136i	0.383034	+	1.89741i
$584$			7.79844i			0.322702i
$585$	−7.17956	+	8.59034i	−0.296838	+	0.355167i
$586$	8.32134			0.343751
$587$		−	21.6213i		−	0.892406i	−0.894932	−	0.446203i	$-0.852776\pi$
$587$		−	21.6213i		−	0.892406i	0.894932	−	0.446203i	$-0.147224\pi$
$588$	−1.41671	−	3.03040i	−0.0584242	−	0.124972i
$589$			30.3335i			1.24987i
$590$	−1.09287			−0.0449928
$591$	−18.6538	−	39.9013i	−0.767316	−	1.64132i
$592$	7.70476			0.316664
$593$	−12.0584			−0.495181			−0.247590	−	0.968865i	$-0.579639\pi$
$593$	−12.0584			−0.495181			−0.247590	+	0.968865i	$0.579639\pi$
$594$	4.50717	+	0.269264i	0.184931	+	0.0110480i
$595$	1.46566			0.0600864
$596$	16.5044			0.676048
$597$	4.63006	+	9.90390i	0.189496	+	0.405340i
$598$	2.92164			0.119475
$599$			5.90003i			0.241069i	0.992709	+	0.120534i	$0.0384608\pi$
$599$			5.90003i			0.241069i	−0.992709	+	0.120534i	$0.961539\pi$
$600$	0.755544	+	1.61614i	0.0308450	+	0.0659787i
$601$			21.6955i			0.884978i	0.896774	+	0.442489i	$0.145904\pi$
$601$			21.6955i			0.884978i	−0.896774	+	0.442489i	$0.854096\pi$
$602$	0.472289			0.0192491
$603$	−24.0355	+	28.7585i	−0.978803	+	1.17114i
$604$		−	42.3882i		−	1.72475i
$605$	4.26729	+	10.1386i	0.173490	+	0.412191i
$606$	−2.48771	−	5.32132i	−0.101056	−	0.216164i
$607$		−	33.6016i		−	1.36385i	−0.731424	−	0.681923i	$-0.761144\pi$
$607$		−	33.6016i		−	1.36385i	0.731424	−	0.681923i	$-0.238856\pi$
$608$		−	17.4912i		−	0.709361i
$609$	6.85320	−	3.20386i	0.277706	−	0.129827i
$610$	0.172469			0.00698306
$611$	−31.9628			−1.29308
$612$	−5.44592	+	6.51604i	−0.220138	+	0.263395i
$613$		−	39.9271i		−	1.61264i	−0.591480	−	0.806320i	$-0.701456\pi$
$613$		−	39.9271i		−	1.61264i	0.591480	−	0.806320i	$-0.298544\pi$
$614$		−	0.193123i		−	0.00779379i
$615$	6.13741	−	2.86923i	0.247484	−	0.115699i
$616$	−0.675990	−	3.34861i	−0.0272364	−	0.134919i
$617$		−	12.8556i		−	0.517546i	−0.965938	−	0.258773i	$-0.916682\pi$
$617$		−	12.8556i		−	0.517546i	0.965938	−	0.258773i	$-0.0833181\pi$
$618$	2.36966	+	5.06880i	0.0953216	+	0.203897i
$619$	−39.7691			−1.59845			−0.799227	−	0.601029i	$-0.794758\pi$
$619$	−39.7691			−1.59845			−0.799227	+	0.601029i	$0.794758\pi$
$620$		−	10.0527i		−	0.403724i
$621$	3.97465	−	15.0096i	0.159497	−	0.602315i
$622$			0.922613i			0.0369934i
$623$	7.47519			0.299487
$624$	−21.0378	+	9.83516i	−0.842187	+	0.393722i
$625$	1.00000			0.0400000
$626$	−0.940681			−0.0375972
$627$	−26.9223	+	19.8990i	−1.07517	+	0.794689i
$628$	−42.9655			−1.71451
$629$	−3.14307			−0.125322
$630$	−0.504050	+	0.603095i	−0.0200818	+	0.0240279i
$631$	30.3630			1.20873			0.604366	−	0.796707i	$-0.293426\pi$
$631$	30.3630			1.20873			0.604366	+	0.796707i	$0.293426\pi$
$632$		−	12.6318i		−	0.502465i
$633$	9.38680	−	4.38832i	0.373092	−	0.174420i
$634$			7.14826i			0.283894i
$635$	−14.5879			−0.578904
$636$	42.7044	−	19.9643i	1.69334	−	0.791635i
$637$			3.73185i			0.147861i
$638$	3.72029	−	0.751023i	0.147288	−	0.0297333i
$639$	−0.391434	−	0.327149i	−0.0154849	−	0.0129418i
$640$			7.67931i			0.303551i
$641$			41.1978i			1.62722i	0.581413	+	0.813609i	$0.302500\pi$
$641$			41.1978i			1.62722i	−0.581413	+	0.813609i	$0.697500\pi$
$642$	2.60724	+	5.57699i	0.102899	+	0.220106i
$643$	−11.1661			−0.440349			−0.220174	−	0.975461i	$-0.570663\pi$
$643$	−11.1661			−0.440349			−0.220174	+	0.975461i	$0.570663\pi$
$644$	−5.77121			−0.227418
$645$	1.32229	+	2.82844i	0.0520652	+	0.111370i
$646$			2.23788i			0.0880483i
$647$		−	16.4203i		−	0.645547i	−0.946476	−	0.322773i	$-0.895385\pi$
$647$		−	16.4203i		−	0.645547i	0.946476	−	0.322773i	$-0.104615\pi$
$648$	−1.64543	−	9.12289i	−0.0646388	−	0.358381i
$649$	2.73759	+	13.5610i	0.107460	+	0.532317i
$650$		−	0.977738i		−	0.0383500i
$651$	8.16688	−	3.81801i	0.320085	−	0.149640i
$652$	−21.1329			−0.827629
$653$			3.38622i			0.132513i	0.997803	+	0.0662565i	$0.0211056\pi$
$653$			3.38622i			0.132513i	−0.997803	+	0.0662565i	$0.978894\pi$
$654$	5.07069	−	2.37054i	0.198279	−	0.0926954i
$655$			14.2678i			0.557488i
$656$	14.0536			0.548700
$657$	−17.4282	−	14.5660i	−0.679940	−	0.568275i
$658$	−2.24399			−0.0874798
$659$	3.13982			0.122310			0.0611550	−	0.998128i	$-0.480522\pi$
$659$	3.13982			0.122310			0.0611550	+	0.998128i	$0.480522\pi$
$660$	8.92219	−	6.59462i	0.347296	−	0.256695i
$661$	29.2989			1.13960			0.569798	−	0.821785i	$-0.307021\pi$
$661$	29.2989			1.13960			0.569798	+	0.821785i	$0.307021\pi$
$662$	9.34977			0.363389
$663$	8.58215	−	4.01215i	0.333303	−	0.155819i
$664$	−5.73358			−0.222506
$665$		−	5.82779i		−	0.225992i
$666$	1.08092	−	1.29332i	0.0418848	−	0.0501150i
$667$		−	13.0515i		−	0.505355i
$668$	32.5010			1.25750
$669$	−8.23390	−	17.6127i	−0.318341	−	0.680945i
$670$		−	3.27324i		−	0.126456i
$671$	−0.432027	−	2.14010i	−0.0166782	−	0.0826177i
$672$	−4.70927	+	2.20158i	−0.181664	+	0.0849277i
$673$		−	6.67799i		−	0.257418i	−0.991682	−	0.128709i	$-0.958917\pi$
$673$		−	6.67799i		−	0.257418i	0.991682	−	0.128709i	$-0.0410832\pi$
$674$		−	7.93870i		−	0.305787i
$675$	−5.02302	−	1.33013i	−0.193336	−	0.0511968i
$676$	1.78973			0.0688356
$677$	43.0833			1.65583			0.827913	−	0.560857i	$-0.189528\pi$
$677$	43.0833			1.65583			0.827913	+	0.560857i	$0.189528\pi$
$678$	−0.797445	+	0.372805i	−0.0306257	+	0.0143175i
$679$			9.21194i			0.353522i
$680$		−	1.50965i		−	0.0578924i
$681$	10.9349	+	23.3903i	0.419028	+	0.896318i
$682$	4.43343	−	0.894986i	0.169765	−	0.0342708i
$683$			11.6623i			0.446247i	0.974790	+	0.223123i	$0.0716253\pi$
$683$			11.6623i			0.446247i	−0.974790	+	0.223123i	$0.928375\pi$
$684$	25.9091	+	21.6541i	0.990660	+	0.827966i
$685$	−0.845410			−0.0323015
$686$			0.261999i			0.0100032i
$687$	−5.39623	−	11.5428i	−0.205879	−	0.440384i
$688$			6.47662i			0.246919i
$689$	−52.5891			−2.00349
$690$	0.574278	+	1.22840i	0.0218624	+	0.0467646i
$691$	−8.66772			−0.329736			−0.164868	−	0.986316i	$-0.552720\pi$
$691$	−8.66772			−0.329736			−0.164868	+	0.986316i	$0.552720\pi$
$692$	5.74937			0.218558
$693$	8.74620	+	4.74384i	0.332241	+	0.180204i
$694$	−2.36789			−0.0898837
$695$	−9.92982			−0.376659
$696$	−3.30001	−	7.05886i	−0.125086	−	0.267565i
$697$	−5.73300			−0.217153
$698$			7.20127i			0.272572i
$699$	−8.83457	−	18.8975i	−0.334154	−	0.714770i
$700$			1.93136i			0.0729984i
$701$	38.8333			1.46671			0.733357	−	0.679844i	$-0.237952\pi$
$701$	38.8333			1.46671			0.733357	+	0.679844i	$0.237952\pi$
$702$	−1.30052	+	4.91120i	−0.0490850	+	0.185361i
$703$			12.4975i			0.471352i
$704$	20.8046	−	4.19987i	0.784102	−	0.158288i
$705$	−6.28261	−	13.4388i	−0.236617	−	0.506134i
$706$			0.161591i			0.00608154i
$707$		−	12.9444i		−	0.486825i
$708$	12.6407	−	5.90950i	0.475066	−	0.222093i
$709$	2.67995			0.100648			0.0503238	−	0.998733i	$-0.483975\pi$
$709$	2.67995			0.100648			0.0503238	+	0.998733i	$0.483975\pi$
$710$	0.0445523			0.00167202
$711$	28.2299	+	23.5938i	1.05871	+	0.884836i
$712$		−	7.69952i		−	0.288552i
$713$		−	15.5533i		−	0.582476i
$714$	0.602520	−	0.281677i	0.0225487	−	0.0105415i
$715$	−12.1324	+	2.44919i	−0.453726	+	0.0915946i
$716$		−	23.3186i		−	0.871456i
$717$	−18.6026	−	39.7917i	−0.694726	−	1.48605i
$718$	−1.17045			−0.0436807
$719$			17.4319i			0.650099i	0.945697	+	0.325049i	$0.105381\pi$
$719$			17.4319i			0.650099i	−0.945697	+	0.325049i	$0.894619\pi$
$720$	−8.27039	−	6.91216i	−0.308219	−	0.257601i
$721$			12.3301i			0.459198i
$722$	3.92031			0.145899
$723$	−39.9325	+	18.6684i	−1.48511	+	0.694286i
$724$	22.2060			0.825281
$725$	−4.36772			−0.162213
$726$	3.70271	+	3.34775i	0.137420	+	0.124247i
$727$	−9.79534			−0.363289			−0.181645	−	0.983364i	$-0.558142\pi$
$727$	−9.79534			−0.363289			−0.181645	+	0.983364i	$0.558142\pi$
$728$	3.84384			0.142462
$729$	23.4615	+	13.3626i	0.868944	+	0.494910i
$730$	1.98365			0.0734183
$731$		−	2.64206i		−	0.0977203i
$732$	−1.99486	+	0.932595i	−0.0737322	+	0.0344697i
$733$		−	31.1919i		−	1.15210i	−0.817415	−	0.576050i	$-0.804593\pi$
$733$		−	31.1919i		−	1.15210i	0.817415	−	0.576050i	$-0.195407\pi$
$734$	5.67446			0.209448
$735$	−1.56905	+	0.733531i	−0.0578754	+	0.0270567i
$736$			8.96851i			0.330583i
$737$	−40.6165	+	8.19933i	−1.49613	+	0.302026i
$738$	1.97161	−	2.35903i	0.0725759	−	0.0868369i
$739$			7.56995i			0.278465i	0.990260	+	0.139233i	$0.0444636\pi$
$739$			7.56995i			0.278465i	−0.990260	+	0.139233i	$0.955536\pi$
$740$		−	4.14174i		−	0.152253i
$741$	−15.9531	−	34.1244i	−0.586053	−	1.25359i
$742$	−3.69208			−0.135541
$743$	23.6898			0.869094			0.434547	−	0.900649i	$-0.356909\pi$
$743$	23.6898			0.869094			0.434547	+	0.900649i	$0.356909\pi$
$744$	−3.93258	−	8.41197i	−0.144176	−	0.308398i
$745$		−	8.54552i		−	0.313083i
$746$		−	5.17632i		−	0.189518i
$747$	10.7092	−	12.8136i	0.391831	−	0.468825i
$748$	−9.20279	+	1.85779i	−0.336487	+	0.0679274i
$749$			13.5664i			0.495704i
$750$	0.411090	−	0.192184i	0.0150109	−	0.00701757i
$751$	−4.14137			−0.151121			−0.0755604	−	0.997141i	$-0.524075\pi$
$751$	−4.14137			−0.151121			−0.0755604	+	0.997141i	$0.524075\pi$
$752$		−	30.7724i		−	1.12215i
$753$	11.1556	−	5.21521i	0.406531	−	0.190053i
$754$			4.27049i			0.155522i
$755$	−21.9474			−0.798747
$756$	2.56896	−	9.70125i	0.0934321	−	0.352831i
$757$	−36.5281			−1.32763			−0.663817	−	0.747895i	$-0.731065\pi$
$757$	−36.5281			−1.32763			−0.663817	+	0.747895i	$0.731065\pi$
$758$	−6.07580			−0.220683
$759$	13.8043	−	10.2031i	0.501064	−	0.370349i
$760$	−6.00268			−0.217740
$761$	24.8144			0.899523			0.449762	−	0.893149i	$-0.351509\pi$
$761$	24.8144			0.899523			0.449762	+	0.893149i	$0.351509\pi$
$762$	−5.99695	+	2.80357i	−0.217247	+	0.101563i
$763$	12.3347			0.446547
$764$		−	23.4605i		−	0.848770i
$765$	3.37381	+	2.81974i	0.121980	+	0.101948i
$766$		−	4.02095i		−	0.145283i
$767$	−15.5666			−0.562077
$768$	−7.91242	−	16.9250i	−0.285515	−	0.610728i
$769$		−	18.6353i		−	0.672007i	−0.941861	−	0.336004i	$-0.890925\pi$
$769$		−	18.6353i		−	0.672007i	0.941861	−	0.336004i	$-0.109075\pi$
$770$	−0.851768	+	0.171948i	−0.0306956	+	0.00619659i
$771$	13.0424	−	6.09728i	0.469709	−	0.219588i
$772$			22.6135i			0.813879i
$773$		−	33.0820i		−	1.18988i	−0.803772	−	0.594938i	$-0.797177\pi$
$773$		−	33.0820i		−	1.18988i	0.803772	−	0.594938i	$-0.202823\pi$
$774$	1.08716	+	0.908619i	0.0390772	+	0.0326597i
$775$	−5.20497			−0.186968
$776$	9.48839			0.340613
$777$	3.36479	−	1.57303i	0.120711	−	0.0564323i
$778$			8.03643i			0.288120i
$779$			22.7956i			0.816737i
$780$	5.28694	+	11.3090i	0.189303	+	0.404927i
$781$	−0.111602	−	0.552833i	−0.00399342	−	0.0197819i
$782$		−	1.14746i		−	0.0410331i
$783$	21.9392	+	5.80965i	0.784042	+	0.207620i
$784$	−3.59285			−0.128316
$785$			22.2463i			0.794004i
$786$	2.74204	+	5.86534i	0.0978054	+	0.209210i
$787$			25.0117i			0.891570i	0.895140	+	0.445785i	$0.147075\pi$
$787$			25.0117i			0.891570i	−0.895140	+	0.445785i	$0.852925\pi$
$788$	−49.1147			−1.74964
$789$	−4.70452	−	10.0632i	−0.167486	−	0.358259i
$790$	−3.21308			−0.114316
$791$	−1.93983			−0.0689725
$792$	4.88620	−	9.00867i	0.173624	−	0.320109i
$793$	2.45661			0.0872366
$794$	−1.16220			−0.0412448
$795$	−10.3369	−	22.1111i	−0.366612	−	0.784200i
$796$	12.1908			0.432090
$797$			5.68891i			0.201511i	0.994911	+	0.100756i	$0.0321261\pi$
$797$			5.68891i			0.201511i	−0.994911	+	0.100756i	$0.967874\pi$
$798$	−1.12001	−	2.39574i	−0.0396478	−	0.0848084i
$799$			12.5533i			0.444102i
$800$	3.00134			0.106113
$801$	17.2071	+	14.3813i	0.607985	+	0.508137i
$802$		−	7.03372i		−	0.248369i
$803$	−4.96896	−	24.6144i	−0.175351	−	0.868623i
$804$	17.6995	+	37.8599i	0.624213	+	1.33522i
$805$			2.98817i			0.105319i
$806$			5.08910i			0.179256i
$807$	−23.3736	+	10.9271i	−0.822788	+	0.384652i
$808$	−13.3329			−0.469049
$809$	−23.5609			−0.828358			−0.414179	−	0.910195i	$-0.635931\pi$
$809$	−23.5609			−0.828358			−0.414179	+	0.910195i	$0.635931\pi$
$810$	−2.32054	+	0.418541i	−0.0815356	+	0.0147060i
$811$			14.6501i			0.514433i	0.966354	+	0.257217i	$0.0828054\pi$
$811$			14.6501i			0.514433i	−0.966354	+	0.257217i	$0.917195\pi$
$812$		−	8.43563i		−	0.296033i
$813$	0.504764	−	0.235977i	0.0177028	−	0.00827606i
$814$	1.82659	−	0.368738i	0.0640220	−	0.0129243i
$815$			10.9420i			0.383282i
$816$	3.86271	+	8.26251i	0.135222	+	0.289246i
$817$	−10.5054			−0.367537
$818$		−	6.37467i		−	0.222885i
$819$	−7.17956	+	8.59034i	−0.250874	+	0.300171i
$820$		−	7.55457i		−	0.263817i
$821$	−39.7646			−1.38779			−0.693897	−	0.720074i	$-0.744108\pi$
$821$	−39.7646			−1.38779			−0.693897	+	0.720074i	$0.744108\pi$
$822$	−0.347540	+	0.162474i	−0.0121218	+	0.00566695i
$823$	26.1953			0.913110			0.456555	−	0.889695i	$-0.349083\pi$
$823$	26.1953			0.913110			0.456555	+	0.889695i	$0.349083\pi$
$824$	12.7002			0.442431
$825$	−3.41450	−	4.61965i	−0.118878	−	0.160836i
$826$	−1.09287			−0.0380258
$827$	−23.0319			−0.800896			−0.400448	−	0.916319i	$-0.631146\pi$
$827$	−23.0319			−0.800896			−0.400448	+	0.916319i	$0.631146\pi$
$828$	−13.2848	−	11.1030i	−0.461677	−	0.385857i
$829$	−16.8971			−0.586860			−0.293430	−	0.955981i	$-0.594797\pi$
$829$	−16.8971			−0.586860			−0.293430	+	0.955981i	$0.594797\pi$
$830$			1.45842i			0.0506226i
$831$	−47.1711	+	22.0524i	−1.63635	+	0.764990i
$832$			23.8814i			0.827939i
$833$	1.46566			0.0507823
$834$	−4.08205	+	1.90835i	−0.141350	+	0.0660809i
$835$		−	16.8281i		−	0.582359i
$836$	7.38695	+	36.5922i	0.255483	+	1.26557i
$837$	26.1447	+	6.92330i	0.903692	+	0.239304i
$838$			3.22464i			0.111393i
$839$			46.2466i			1.59661i	0.602254	+	0.798305i	$0.294270\pi$
$839$			46.2466i			1.59661i	−0.602254	+	0.798305i	$0.705730\pi$
$840$	0.755544	+	1.61614i	0.0260688	+	0.0557622i
$841$	−9.92299			−0.342172
$842$	6.15210			0.212015
$843$	−11.7791	−	25.1960i	−0.405694	−	0.867796i
$844$		−	11.5543i		−	0.397714i
$845$		−	0.926667i		−	0.0318783i
$846$	−5.16544	−	4.31713i	−0.177591	−	0.148426i
$847$	4.26729	+	10.1386i	0.146626	+	0.348365i
$848$		−	50.6304i		−	1.73866i
$849$	−0.156662	+	0.0732395i	−0.00537664	+	0.00251357i
$850$	−0.384002			−0.0131712
$851$		−	6.40803i		−	0.219664i
$852$	−0.515314	+	0.240909i	−0.0176544	+	0.00825340i
$853$			28.4536i			0.974232i	0.873337	+	0.487116i	$0.161951\pi$
$853$			28.4536i			0.974232i	−0.873337	+	0.487116i	$0.838049\pi$
$854$	0.172469			0.00590176
$855$	11.2119	−	13.4150i	0.383438	−	0.458783i
$856$	13.9735			0.477604
$857$	−31.5736			−1.07853			−0.539267	−	0.842135i	$-0.681299\pi$
$857$	−31.5736			−1.07853			−0.539267	+	0.842135i	$0.681299\pi$
$858$	−4.51681	+	3.33849i	−0.154201	+	0.113974i
$859$	−18.0451			−0.615692			−0.307846	−	0.951436i	$-0.599608\pi$
$859$	−18.0451			−0.615692			−0.307846	+	0.951436i	$0.599608\pi$
$860$	3.48154			0.118720
$861$	6.13741	−	2.86923i	0.209162	−	0.0977832i
$862$	2.57402			0.0876716
$863$			35.8600i			1.22069i	0.792136	+	0.610345i	$0.208969\pi$
$863$			35.8600i			1.22069i	−0.792136	+	0.610345i	$0.791031\pi$
$864$	−15.0758	−	3.99218i	−0.512889	−	0.135817i
$865$		−	2.97685i		−	0.101216i
$866$	6.82223			0.231829
$867$	10.8943	+	23.3033i	0.369989	+	0.791423i
$868$		−	10.0527i		−	0.341209i
$869$	8.04864	+	39.8700i	0.273031	+	1.35250i
$870$	−1.79553	+	0.839407i	−0.0608741	+	0.0284586i
$871$		−	46.6233i		−	1.57977i
$872$		−	12.7049i		−	0.430242i
$873$	−17.7225	+	21.2050i	−0.599817	+	0.717680i
$874$	−4.56254			−0.154330
$875$	1.00000			0.0338062
$876$	−22.9439	+	10.7262i	−0.775202	+	0.362406i
$877$		−	38.2876i		−	1.29288i	−0.762964	−	0.646441i	$-0.776257\pi$
$877$		−	38.2876i		−	1.29288i	0.762964	−	0.646441i	$-0.223743\pi$
$878$			6.55368i			0.221176i
$879$	23.2977	+	49.8347i	0.785811	+	1.68088i
$880$	−2.35797	−	11.6805i	−0.0794872	−	0.393750i
$881$			24.5281i			0.826371i	0.910647	+	0.413186i	$0.135584\pi$
$881$			24.5281i			0.826371i	−0.910647	+	0.413186i	$0.864416\pi$
$882$	−0.504050	+	0.603095i	−0.0169722	+	0.0203073i
$883$	16.4928			0.555025			0.277513	−	0.960722i	$-0.410490\pi$
$883$	16.4928			0.555025			0.277513	+	0.960722i	$0.410490\pi$
$884$		−	10.5638i		−	0.355299i
$885$	−3.05977	−	6.54498i	−0.102853	−	0.220007i
$886$		−	1.27872i		−	0.0429595i
$887$	0.448856			0.0150711			0.00753556	−	0.999972i	$-0.497601\pi$
$887$	0.448856			0.0150711			0.00753556	+	0.999972i	$0.497601\pi$
$888$	−1.62024	−	3.46577i	−0.0543717	−	0.116303i
$889$	−14.5879			−0.489264
$890$	−1.95849			−0.0656487
$891$	11.0064	+	27.7463i	0.368728	+	0.929537i
$892$	−21.6795			−0.725884
$893$	49.9143			1.67032
$894$	−1.64231	−	3.51298i	−0.0549271	−	0.117491i
$895$	−12.0737			−0.403578
$896$			7.67931i			0.256548i
$897$	8.17988	+	17.4971i	0.273118	+	0.584211i
$898$			2.34401i			0.0782208i
$899$	22.7339			0.758217
$900$	−3.71567	+	4.44579i	−0.123856	+	0.148193i
$901$			20.6541i			0.688089i
$902$	3.33172	−	0.672582i	0.110934	−	0.0223945i
$903$	1.32229	+	2.82844i	0.0440031	+	0.0941246i
$904$			1.99805i			0.0664540i
$905$		−	11.4976i		−	0.382194i
$906$	−9.02234	+	4.21794i	−0.299747	+	0.140132i
$907$	−40.2752			−1.33732			−0.668658	−	0.743570i	$-0.733131\pi$
$907$	−40.2752			−1.33732			−0.668658	+	0.743570i	$0.733131\pi$
$908$	28.7912			0.955470
$909$	24.9033	−	29.7968i	0.825991	−	0.988297i
$910$		−	0.977738i		−	0.0324117i
$911$			24.5628i			0.813801i	0.913472	+	0.406901i	$0.133390\pi$
$911$			24.5628i			0.813801i	−0.913472	+	0.406901i	$0.866610\pi$
$912$	32.8535	−	15.3590i	1.08789	−	0.508586i
$913$	18.0970	−	3.65328i	0.598924	−	0.120906i
$914$		−	3.55053i		−	0.117441i
$915$	0.482870	+	1.03288i	0.0159632	+	0.0341460i
$916$	−14.2081			−0.469447
$917$			14.2678i			0.471164i
$918$	1.92885	+	0.510773i	0.0636615	+	0.0168580i
$919$		−	50.9250i		−	1.67986i	−0.542694	−	0.839930i	$-0.682596\pi$
$919$		−	50.9250i		−	1.67986i	0.542694	−	0.839930i	$-0.317404\pi$
$920$	3.07784			0.101473
$921$	1.15657	−	0.540696i	0.0381103	−	0.0178165i
$922$	6.63630			0.218555
$923$	0.634593			0.0208879
$924$	8.92219	−	6.59462i	0.293519	−	0.216947i
$925$	−2.14447			−0.0705097
$926$	−2.15887			−0.0709448
$927$	−23.7215	+	28.3828i	−0.779117	+	0.932212i
$928$	−13.1090			−0.430325
$929$			44.4977i			1.45992i	0.683489	+	0.729961i	$0.260462\pi$
$929$			44.4977i			1.45992i	−0.683489	+	0.729961i	$0.739538\pi$
$930$	−2.13971	+	1.00031i	−0.0701639	+	0.0328015i
$931$		−	5.82779i		−	0.190998i
$932$	−23.2611			−0.761941
$933$	−5.52534	+	2.58309i	−0.180891	+	0.0845665i
$934$		−	0.967526i		−	0.0316584i
$935$	0.961908	+	4.76494i	0.0314578	+	0.155830i
$936$	8.84813	+	7.39502i	0.289210	+	0.241714i
$937$			7.56866i			0.247257i	0.992329	+	0.123629i	$0.0394532\pi$
$937$			7.56866i			0.247257i	−0.992329	+	0.123629i	$0.960547\pi$
$938$		−	3.27324i		−	0.106875i
$939$	−2.63367	−	5.63354i	−0.0859467	−	0.183844i
$940$	−16.5419			−0.539536
$941$	−45.0874			−1.46981			−0.734903	−	0.678172i	$-0.762772\pi$
$941$	−45.0874			−1.46981			−0.734903	+	0.678172i	$0.762772\pi$
$942$	4.27538	+	9.14522i	0.139299	+	0.297967i
$943$		−	11.6883i		−	0.380624i
$944$		−	14.9868i		−	0.487779i
$945$	−5.02302	−	1.33013i	−0.163399	−	0.0432692i
$946$	0.309961	+	1.53543i	0.0100777	+	0.0499212i
$947$		−	52.9315i		−	1.72004i	−0.510258	−	0.860022i	$-0.670450\pi$
$947$		−	52.9315i		−	1.72004i	0.510258	−	0.860022i	$-0.329550\pi$
$948$	37.1641	−	17.3742i	1.20703	−	0.564287i
$949$	28.2547			0.917185
$950$			1.52687i			0.0495383i
$951$	−42.8094	+	20.0134i	−1.38819	+	0.648978i
$952$		−	1.50965i		−	0.0489280i
$953$	−16.0907			−0.521229			−0.260615	−	0.965443i	$-0.583925\pi$
$953$	−16.0907			−0.521229			−0.260615	+	0.965443i	$0.583925\pi$
$954$	−8.49880	−	7.10306i	−0.275159	−	0.229970i
$955$	−12.1472			−0.393073
$956$	−48.9798			−1.58412
$957$	14.9136	+	20.1774i	0.482088	+	0.652241i
$958$	3.11916			0.100775
$959$	−0.845410			−0.0272997
$960$	−10.0409	+	4.69413i	−0.324070	+	0.151502i
$961$	−3.90829			−0.126074
$962$			2.09673i			0.0676013i
$963$	−26.0998	+	31.2284i	−0.841055	+	1.00632i
$964$			49.1531i			1.58312i
$965$	11.7086			0.376914
$966$	0.574278	+	1.22840i	0.0184771	+	0.0395233i
$967$			13.5562i			0.435937i	0.975956	+	0.217968i	$0.0699429\pi$
$967$			13.5562i			0.435937i	−0.975956	+	0.217968i	$0.930057\pi$
$968$	10.4428	−	4.39535i	0.335645	−	0.141272i
$969$	−13.4022	+	6.26551i	−0.430541	+	0.201277i
$970$		−	2.41352i		−	0.0774933i
$971$			5.48644i			0.176068i	0.996117	+	0.0880342i	$0.0280585\pi$
$971$			5.48644i			0.176068i	−0.996117	+	0.0880342i	$0.971942\pi$
$972$	24.5774	−	17.3890i	0.788320	−	0.557752i
$973$	−9.92982			−0.318335
$974$	−4.71276			−0.151007
$975$	5.85547	−	2.73742i	0.187525	−	0.0876677i
$976$			2.36511i			0.0757053i
$977$			2.26639i			0.0725084i	0.999343	+	0.0362542i	$0.0115426\pi$
$977$			2.26639i			0.0725084i	−0.999343	+	0.0362542i	$0.988457\pi$
$978$	2.10288	+	4.49815i	0.0672426	+	0.143835i
$979$	4.90593	+	24.3022i	0.156794	+	0.776701i
$980$			1.93136i			0.0616949i
$981$	28.3933	+	23.7303i	0.906529	+	0.757652i
$982$	−3.85283			−0.122949
$983$		−	2.01372i		−	0.0642276i	−0.999484	−	0.0321138i	$-0.989776\pi$
$983$		−	2.01372i		−	0.0642276i	0.999484	−	0.0321138i	$-0.0102239\pi$
$984$	−2.95534	−	6.32159i	−0.0942127	−	0.201525i
$985$			25.4302i			0.810273i
$986$	1.67721			0.0534134
$987$	−6.28261	−	13.4388i	−0.199978	−	0.427761i
$988$	−42.0039			−1.33632
$989$	5.38658			0.171283
$990$	−2.29149	−	1.24288i	−0.0728284	−	0.0395013i
$991$	−12.5453			−0.398516			−0.199258	−	0.979947i	$-0.563853\pi$
$991$	−12.5453			−0.398516			−0.199258	+	0.979947i	$0.563853\pi$
$992$	−15.6219			−0.495996
$993$	26.1770	+	55.9938i	0.830703	+	1.77691i
$994$	0.0445523			0.00141311
$995$		−	6.31202i		−	0.200105i
$996$	−7.88616	−	16.8688i	−0.249882	−	0.534509i
$997$		−	6.80756i		−	0.215598i	−0.994173	−	0.107799i	$-0.965620\pi$
$997$		−	6.80756i		−	0.215598i	0.994173	−	0.107799i	$-0.0343802\pi$
$998$	−4.76390			−0.150799
$999$	10.7717	+	2.85243i	0.340802	+	0.0902468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.19	yes	40
3.2	odd	2		1155.2.l.e.1121.22	yes	40
11.10	odd	2		1155.2.l.e.1121.21	✓	40
33.32	even	2	inner	1155.2.l.f.1121.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.21	✓	40	11.10	odd	2
1155.2.l.e.1121.22	yes	40	3.2	odd	2
1155.2.l.f.1121.19	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.20	yes	40	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.261999 q^{2} +(-0.733531 - 1.56905i) q^{3} -1.93136 q^{4} +1.00000i q^{5} +(0.192184 + 0.411090i) q^{6} +1.00000i q^{7} +1.03001 q^{8} +(-1.92386 + 2.30190i) q^{9} +O(q^{10})\)	\(q-0.261999 q^{2} +(-0.733531 - 1.56905i) q^{3} -1.93136 q^{4} +1.00000i q^{5} +(0.192184 + 0.411090i) q^{6} +1.00000i q^{7} +1.03001 q^{8} +(-1.92386 + 2.30190i) q^{9} -0.261999i q^{10} +(-3.25104 + 0.656295i) q^{11} +(1.41671 + 3.03040i) q^{12} -3.73185i q^{13} -0.261999i q^{14} +(1.56905 - 0.733531i) q^{15} +3.59285 q^{16} -1.46566 q^{17} +(0.504050 - 0.603095i) q^{18} +5.82779i q^{19} -1.93136i q^{20} +(1.56905 - 0.733531i) q^{21} +(0.851768 - 0.171948i) q^{22} -2.98817i q^{23} +(-0.755544 - 1.61614i) q^{24} -1.00000 q^{25} +0.977738i q^{26} +(5.02302 + 1.33013i) q^{27} -1.93136i q^{28} +4.36772 q^{29} +(-0.411090 + 0.192184i) q^{30} +5.20497 q^{31} -3.00134 q^{32} +(3.41450 + 4.61965i) q^{33} +0.384002 q^{34} -1.00000 q^{35} +(3.71567 - 4.44579i) q^{36} +2.14447 q^{37} -1.52687i q^{38} +(-5.85547 + 2.73742i) q^{39} +1.03001i q^{40} +3.91153 q^{41} +(-0.411090 + 0.192184i) q^{42} +1.80264i q^{43} +(6.27892 - 1.26754i) q^{44} +(-2.30190 - 1.92386i) q^{45} +0.782895i q^{46} -8.56489i q^{47} +(-2.63547 - 5.63738i) q^{48} -1.00000 q^{49} +0.261999 q^{50} +(1.07511 + 2.29971i) q^{51} +7.20752i q^{52} -14.0920i q^{53} +(-1.31602 - 0.348493i) q^{54} +(-0.656295 - 3.25104i) q^{55} +1.03001i q^{56} +(9.14411 - 4.27486i) q^{57} -1.14434 q^{58} -4.17129i q^{59} +(-3.03040 + 1.41671i) q^{60} +0.658282i q^{61} -1.36369 q^{62} +(-2.30190 - 1.92386i) q^{63} -6.39936 q^{64} +3.73185 q^{65} +(-0.894595 - 1.21034i) q^{66} +12.4934 q^{67} +2.83072 q^{68} +(-4.68859 + 2.19191i) q^{69} +0.261999 q^{70} +0.170048i q^{71} +(-1.98160 + 2.37098i) q^{72} +7.57123i q^{73} -0.561848 q^{74} +(0.733531 + 1.56905i) q^{75} -11.2555i q^{76} +(-0.656295 - 3.25104i) q^{77} +(1.53412 - 0.717201i) q^{78} -12.2638i q^{79} +3.59285i q^{80} +(-1.59749 - 8.85709i) q^{81} -1.02482 q^{82} -5.56653 q^{83} +(-3.03040 + 1.41671i) q^{84} -1.46566i q^{85} -0.472289i q^{86} +(-3.20386 - 6.85320i) q^{87} +(-3.34861 + 0.675990i) q^{88} -7.47519i q^{89} +(0.603095 + 0.504050i) q^{90} +3.73185 q^{91} +5.77121i q^{92} +(-3.81801 - 8.16688i) q^{93} +2.24399i q^{94} -5.82779 q^{95} +(2.20158 + 4.70927i) q^{96} +9.21194 q^{97} +0.261999 q^{98} +(4.74384 - 8.74620i) 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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