LMFDB - Embedded newform 1155.2.l.f.1121.8

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			1121.8
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78181 q^{2} +(-1.68629 + 0.395519i) q^{3} +1.17485 q^{4} -1.00000i q^{5} +(3.00464 - 0.704739i) q^{6} -1.00000i q^{7} +1.47026 q^{8} +(2.68713 - 1.33392i) q^{9} +O(q^{10})$	\(q-1.78181 q^{2} +(-1.68629 + 0.395519i) q^{3} +1.17485 q^{4} -1.00000i q^{5} +(3.00464 - 0.704739i) q^{6} -1.00000i q^{7} +1.47026 q^{8} +(2.68713 - 1.33392i) q^{9} +1.78181i q^{10} +(1.85876 - 2.74682i) q^{11} +(-1.98113 + 0.464674i) q^{12} -5.68767i q^{13} +1.78181i q^{14} +(0.395519 + 1.68629i) q^{15} -4.96943 q^{16} +2.05164 q^{17} +(-4.78796 + 2.37679i) q^{18} -4.08963i q^{19} -1.17485i q^{20} +(0.395519 + 1.68629i) q^{21} +(-3.31195 + 4.89432i) q^{22} +5.58256i q^{23} +(-2.47929 + 0.581517i) q^{24} -1.00000 q^{25} +10.1343i q^{26} +(-4.00368 + 3.31218i) q^{27} -1.17485i q^{28} +6.60729 q^{29} +(-0.704739 - 3.00464i) q^{30} +8.58989 q^{31} +5.91405 q^{32} +(-2.04798 + 5.36710i) q^{33} -3.65564 q^{34} -1.00000 q^{35} +(3.15697 - 1.56715i) q^{36} -9.54021 q^{37} +7.28694i q^{38} +(2.24958 + 9.59104i) q^{39} -1.47026i q^{40} +4.92313 q^{41} +(-0.704739 - 3.00464i) q^{42} -1.16189i q^{43} +(2.18376 - 3.22710i) q^{44} +(-1.33392 - 2.68713i) q^{45} -9.94706i q^{46} -1.41613i q^{47} +(8.37988 - 1.96550i) q^{48} -1.00000 q^{49} +1.78181 q^{50} +(-3.45966 + 0.811463i) q^{51} -6.68214i q^{52} +4.49877i q^{53} +(7.13381 - 5.90167i) q^{54} +(-2.74682 - 1.85876i) q^{55} -1.47026i q^{56} +(1.61752 + 6.89629i) q^{57} -11.7729 q^{58} +3.29555i q^{59} +(0.464674 + 1.98113i) q^{60} -2.93235i q^{61} -15.3056 q^{62} +(-1.33392 - 2.68713i) q^{63} -0.598859 q^{64} -5.68767 q^{65} +(3.64911 - 9.56316i) q^{66} -10.6260 q^{67} +2.41037 q^{68} +(-2.20801 - 9.41380i) q^{69} +1.78181 q^{70} -7.13813i q^{71} +(3.95079 - 1.96121i) q^{72} -10.7737i q^{73} +16.9988 q^{74} +(1.68629 - 0.395519i) q^{75} -4.80469i q^{76} +(-2.74682 - 1.85876i) q^{77} +(-4.00832 - 17.0894i) q^{78} +8.84368i q^{79} +4.96943i q^{80} +(5.44134 - 7.16881i) q^{81} -8.77209 q^{82} +4.64901 q^{83} +(0.464674 + 1.98113i) q^{84} -2.05164i q^{85} +2.07027i q^{86} +(-11.1418 + 2.61331i) q^{87} +(2.73286 - 4.03855i) q^{88} -0.807374i q^{89} +(2.37679 + 4.78796i) q^{90} -5.68767 q^{91} +6.55866i q^{92} +(-14.4850 + 3.39746i) q^{93} +2.52328i q^{94} -4.08963 q^{95} +(-9.97279 + 2.33912i) q^{96} +7.68700 q^{97} +1.78181 q^{98} +(1.33069 - 9.86049i) 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 $

$2$	−1.78181			−1.25993			−0.629965	−	0.776623i	$-0.716931\pi$
$2$	−1.78181			−1.25993			−0.629965	+	0.776623i	$0.716931\pi$
$3$	−1.68629	+	0.395519i	−0.973578	+	0.228353i
$3$	−1.68629	+	0.395519i	−0.973578	+	0.228353i
$4$	1.17485			0.587424
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	3.00464	−	0.704739i	1.22664	−	0.287709i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.47026			0.519817
$9$	2.68713	−	1.33392i	0.895710	−	0.444639i
$10$			1.78181i			0.563458i
$11$	1.85876	−	2.74682i	0.560436	−	0.828198i
$11$	1.85876	−	2.74682i	0.560436	−	0.828198i
$12$	−1.98113	+	0.464674i	−0.571903	+	0.134140i
$13$		−	5.68767i		−	1.57747i	−0.614730	−	0.788737i	$-0.710735\pi$
$13$		−	5.68767i		−	1.57747i	0.614730	−	0.788737i	$-0.289265\pi$
$14$			1.78181i			0.476209i
$15$	0.395519	+	1.68629i	0.102122	+	0.435398i
$16$	−4.96943			−1.24236
$17$	2.05164			0.497597			0.248798	−	0.968555i	$-0.419964\pi$
$17$	2.05164			0.497597			0.248798	+	0.968555i	$0.419964\pi$
$18$	−4.78796	+	2.37679i	−1.12853	+	0.560214i
$19$		−	4.08963i		−	0.938225i	−0.883138	−	0.469113i	$-0.844574\pi$
$19$		−	4.08963i		−	0.938225i	0.883138	−	0.469113i	$-0.155426\pi$
$20$		−	1.17485i		−	0.262704i
$21$	0.395519	+	1.68629i	0.0863092	+	0.367978i
$22$	−3.31195	+	4.89432i	−0.706110	+	1.04347i
$23$			5.58256i			1.16404i	0.813173	+	0.582022i	$0.197738\pi$
$23$			5.58256i			1.16404i	−0.813173	+	0.582022i	$0.802262\pi$
$24$	−2.47929	+	0.581517i	−0.506083	+	0.118702i
$25$	−1.00000			−0.200000
$26$			10.1343i			1.98751i
$27$	−4.00368	+	3.31218i	−0.770509	+	0.637429i
$28$		−	1.17485i		−	0.222025i
$29$	6.60729			1.22694			0.613471	−	0.789717i	$-0.289773\pi$
$29$	6.60729			1.22694			0.613471	+	0.789717i	$0.289773\pi$
$30$	−0.704739	−	3.00464i	−0.128667	−	0.548570i
$31$	8.58989			1.54279			0.771395	−	0.636357i	$-0.219559\pi$
$31$	8.58989			1.54279			0.771395	+	0.636357i	$0.219559\pi$
$32$	5.91405			1.04547
$33$	−2.04798	+	5.36710i	−0.356507	+	0.934293i
$34$	−3.65564			−0.626937
$35$	−1.00000			−0.169031
$36$	3.15697	−	1.56715i	0.526162	−	0.261191i
$37$	−9.54021			−1.56840			−0.784200	−	0.620508i	$-0.786927\pi$
$37$	−9.54021			−1.56840			−0.784200	+	0.620508i	$0.786927\pi$
$38$			7.28694i			1.18210i
$39$	2.24958	+	9.59104i	0.360221	+	1.53580i
$40$		−	1.47026i		−	0.232469i
$41$	4.92313			0.768864			0.384432	−	0.923153i	$-0.374397\pi$
$41$	4.92313			0.768864			0.384432	+	0.923153i	$0.374397\pi$
$42$	−0.704739	−	3.00464i	−0.108744	−	0.463627i
$43$		−	1.16189i		−	0.177187i	−0.996068	−	0.0885935i	$-0.971763\pi$
$43$		−	1.16189i		−	0.177187i	0.996068	−	0.0885935i	$-0.0282372\pi$
$44$	2.18376	−	3.22710i	0.329213	−	0.486503i
$45$	−1.33392	−	2.68713i	−0.198848	−	0.400574i
$46$		−	9.94706i		−	1.46661i
$47$		−	1.41613i		−	0.206564i	−0.994652	−	0.103282i	$-0.967066\pi$
$47$		−	1.41613i		−	0.206564i	0.994652	−	0.103282i	$-0.0329344\pi$
$48$	8.37988	−	1.96550i	1.20953	−	0.283696i
$49$	−1.00000			−0.142857
$50$	1.78181			0.251986
$51$	−3.45966	+	0.811463i	−0.484449	+	0.113628i
$52$		−	6.68214i		−	0.926647i
$53$			4.49877i			0.617953i	0.951070	+	0.308976i	$0.0999864\pi$
$53$			4.49877i			0.617953i	−0.951070	+	0.308976i	$0.900014\pi$
$54$	7.13381	−	5.90167i	0.970788	−	0.803115i
$55$	−2.74682	−	1.85876i	−0.370381	−	0.250635i
$56$		−	1.47026i		−	0.196472i
$57$	1.61752	+	6.89629i	0.214246	+	0.913436i
$58$	−11.7729			−1.54586
$59$			3.29555i			0.429044i	0.976719	+	0.214522i	$0.0688194\pi$
$59$			3.29555i			0.429044i	−0.976719	+	0.214522i	$0.931181\pi$
$60$	0.464674	+	1.98113i	0.0599892	+	0.255763i
$61$		−	2.93235i		−	0.375449i	−0.982222	−	0.187724i	$-0.939889\pi$
$61$		−	2.93235i		−	0.375449i	0.982222	−	0.187724i	$-0.0601111\pi$
$62$	−15.3056			−1.94381
$63$	−1.33392	−	2.68713i	−0.168058	−	0.338547i
$64$	−0.598859			−0.0748574
$65$	−5.68767			−0.705468
$66$	3.64911	−	9.56316i	0.449174	−	1.17714i
$67$	−10.6260			−1.29817			−0.649085	−	0.760716i	$-0.724848\pi$
$67$	−10.6260			−1.29817			−0.649085	+	0.760716i	$0.724848\pi$
$68$	2.41037			0.292300
$69$	−2.20801	−	9.41380i	−0.265813	−	1.13329i
$70$	1.78181			0.212967
$71$		−	7.13813i		−	0.847140i	−0.905863	−	0.423570i	$-0.860777\pi$
$71$		−	7.13813i		−	0.847140i	0.905863	−	0.423570i	$-0.139223\pi$
$72$	3.95079	−	1.96121i	0.465605	−	0.231131i
$73$		−	10.7737i		−	1.26097i	−0.776203	−	0.630483i	$-0.782857\pi$
$73$		−	10.7737i		−	1.26097i	0.776203	−	0.630483i	$-0.217143\pi$
$74$	16.9988			1.97608
$75$	1.68629	−	0.395519i	0.194716	−	0.0456706i
$76$		−	4.80469i		−	0.551136i
$77$	−2.74682	−	1.85876i	−0.313029	−	0.211825i
$78$	−4.00832	−	17.0894i	−0.453853	−	1.93500i
$79$			8.84368i			0.994992i	0.867466	+	0.497496i	$0.165747\pi$
$79$			8.84368i			0.994992i	−0.867466	+	0.497496i	$0.834253\pi$
$80$			4.96943i			0.555599i
$81$	5.44134	−	7.16881i	0.604593	−	0.796535i
$82$	−8.77209			−0.968715
$83$	4.64901			0.510296			0.255148	−	0.966902i	$-0.417876\pi$
$83$	4.64901			0.510296			0.255148	+	0.966902i	$0.417876\pi$
$84$	0.464674	+	1.98113i	0.0507001	+	0.216159i
$85$		−	2.05164i		−	0.222532i
$86$			2.07027i			0.223243i
$87$	−11.1418	+	2.61331i	−1.19452	+	0.280176i
$88$	2.73286	−	4.03855i	0.291324	−	0.430511i
$89$		−	0.807374i		−	0.0855814i	−0.999084	−	0.0427907i	$-0.986375\pi$
$89$		−	0.807374i		−	0.0855814i	0.999084	−	0.0427907i	$-0.0136249\pi$
$90$	2.37679	+	4.78796i	0.250535	+	0.504695i
$91$	−5.68767			−0.596229
$92$			6.55866i			0.683787i
$93$	−14.4850	+	3.39746i	−1.50203	+	0.352300i
$94$			2.52328i			0.260256i
$95$	−4.08963			−0.419587
$96$	−9.97279	+	2.33912i	−1.01784	+	0.238735i
$97$	7.68700			0.780497			0.390248	−	0.920710i	$-0.372389\pi$
$97$	7.68700			0.780497			0.390248	+	0.920710i	$0.372389\pi$
$98$	1.78181			0.179990
$99$	1.33069	−	9.86049i	0.133739	−	0.991017i
$100$	−1.17485			−0.117485
$101$	5.48973			0.546249			0.273124	−	0.961979i	$-0.411943\pi$
$101$	5.48973			0.546249			0.273124	+	0.961979i	$0.411943\pi$
$102$	6.16446	−	1.44587i	0.610372	−	0.143163i
$103$	14.9039			1.46853			0.734264	−	0.678864i	$-0.237527\pi$
$103$	14.9039			1.46853			0.734264	+	0.678864i	$0.237527\pi$
$104$		−	8.36237i		−	0.819998i
$105$	1.68629	−	0.395519i	0.164565	−	0.0385987i
$106$		−	8.01595i		−	0.778578i
$107$	−18.9261			−1.82965			−0.914826	−	0.403847i	$-0.867673\pi$
$107$	−18.9261			−1.82965			−0.914826	+	0.403847i	$0.867673\pi$
$108$	−4.70372	+	3.89130i	−0.452616	+	0.374441i
$109$		−	16.5564i		−	1.58582i	−0.609341	−	0.792909i	$-0.708566\pi$
$109$		−	16.5564i		−	1.58582i	0.609341	−	0.792909i	$-0.291434\pi$
$110$	4.89432	+	3.31195i	0.466655	+	0.315782i
$111$	16.0875	−	3.77333i	1.52696	−	0.358149i
$112$			4.96943i			0.469567i
$113$		−	17.3754i		−	1.63454i	−0.576254	−	0.817271i	$-0.695486\pi$
$113$		−	17.3754i		−	1.63454i	0.576254	−	0.817271i	$-0.304514\pi$
$114$	−2.88212	−	12.2879i	−0.269935	−	1.15087i
$115$	5.58256			0.520576
$116$	7.76256			0.720736
$117$	−7.58687	−	15.2835i	−0.701406	−	1.41296i
$118$		−	5.87204i		−	0.540565i
$119$		−	2.05164i		−	0.188074i
$120$	0.581517	+	2.47929i	0.0530850	+	0.226327i
$121$	−4.09006	−	10.2113i	−0.371823	−	0.928303i
$122$			5.22489i			0.473039i
$123$	−8.30181	+	1.94719i	−0.748549	+	0.175572i
$124$	10.0918			0.906272
$125$			1.00000i			0.0894427i
$126$	2.37679	+	4.78796i	0.211741	+	0.426545i
$127$			1.23383i			0.109484i	0.998501	+	0.0547422i	$0.0174337\pi$
$127$			1.23383i			0.109484i	−0.998501	+	0.0547422i	$0.982566\pi$
$128$	−10.7610			−0.951151
$129$	0.459550	+	1.95928i	0.0404611	+	0.172505i
$130$	10.1343			0.888841
$131$	−8.62710			−0.753753			−0.376876	−	0.926264i	$-0.623002\pi$
$131$	−8.62710			−0.753753			−0.376876	+	0.926264i	$0.623002\pi$
$132$	−2.40606	+	6.30553i	−0.209421	+	0.548826i
$133$	−4.08963			−0.354616
$134$	18.9335			1.63560
$135$	3.31218	+	4.00368i	0.285067	+	0.344582i
$136$	3.01646			0.258659
$137$		−	2.54814i		−	0.217703i	−0.994058	−	0.108851i	$-0.965283\pi$
$137$		−	2.54814i		−	0.217703i	0.994058	−	0.108851i	$-0.0347172\pi$
$138$	3.93425	+	16.7736i	0.334905	+	1.42786i
$139$			13.7428i			1.16565i	0.812598	+	0.582824i	$0.198052\pi$
$139$			13.7428i			1.16565i	−0.812598	+	0.582824i	$0.801948\pi$
$140$	−1.17485			−0.0992928
$141$	0.560106	+	2.38800i	0.0471695	+	0.201106i
$142$			12.7188i			1.06734i
$143$	−15.6230	−	10.5720i	−1.30646	−	0.884073i
$144$	−13.3535	+	6.62880i	−1.11279	+	0.552400i
$145$		−	6.60729i		−	0.548705i
$146$			19.1967i			1.58873i
$147$	1.68629	−	0.395519i	0.139083	−	0.0326218i
$148$	−11.2083			−0.921316
$149$	−13.6206			−1.11585			−0.557923	−	0.829892i	$-0.688402\pi$
$149$	−13.6206			−1.11585			−0.557923	+	0.829892i	$0.688402\pi$
$150$	−3.00464	+	0.704739i	−0.245328	+	0.0575417i
$151$			6.04754i			0.492142i	0.969252	+	0.246071i	$0.0791396\pi$
$151$			6.04754i			0.492142i	−0.969252	+	0.246071i	$0.920860\pi$
$152$		−	6.01283i		−	0.487705i
$153$	5.51303	−	2.73672i	0.445702	−	0.221251i
$154$	4.89432	+	3.31195i	0.394395	+	0.266884i
$155$		−	8.58989i		−	0.689957i
$156$	2.64291	+	11.2680i	0.211602	+	0.902163i
$157$	−9.27732			−0.740411			−0.370206	−	0.928950i	$-0.620713\pi$
$157$	−9.27732			−0.740411			−0.370206	+	0.928950i	$0.620713\pi$
$158$		−	15.7578i		−	1.25362i
$159$	−1.77935	−	7.58621i	−0.141111	−	0.601626i
$160$		−	5.91405i		−	0.467547i
$161$	5.58256			0.439967
$162$	−9.69543	+	12.7735i	−0.761745	+	1.00358i
$163$	15.2211			1.19221			0.596104	−	0.802907i	$-0.296715\pi$
$163$	15.2211			1.19221			0.596104	+	0.802907i	$0.296715\pi$
$164$	5.78393			0.451649
$165$	5.36710	+	2.04798i	0.417828	+	0.159435i
$166$	−8.28366			−0.642937
$167$	23.7210			1.83559			0.917794	−	0.397057i	$-0.129969\pi$
$167$	23.7210			1.83559			0.917794	+	0.397057i	$0.129969\pi$
$168$	0.581517	+	2.47929i	0.0448650	+	0.191281i
$169$	−19.3495			−1.48843
$170$			3.65564i			0.280375i
$171$	−5.45522	−	10.9894i	−0.417171	−	0.840378i
$172$		−	1.36505i		−	0.104084i
$173$	7.98486			0.607078			0.303539	−	0.952819i	$-0.401832\pi$
$173$	7.98486			0.607078			0.303539	+	0.952819i	$0.401832\pi$
$174$	19.8526	−	4.65642i	1.50502	−	0.353002i
$175$			1.00000i			0.0755929i
$176$	−9.23695	+	13.6501i	−0.696261	+	1.02892i
$177$	−1.30345	−	5.55724i	−0.0979734	−	0.417708i
$178$			1.43859i			0.107827i
$179$			4.27426i			0.319473i	0.987160	+	0.159737i	$0.0510645\pi$
$179$			4.27426i			0.319473i	−0.987160	+	0.159737i	$0.948935\pi$
$180$	−1.56715	−	3.15697i	−0.116808	−	0.235307i
$181$	−9.72903			−0.723153			−0.361576	−	0.932342i	$-0.617761\pi$
$181$	−9.72903			−0.723153			−0.361576	+	0.932342i	$0.617761\pi$
$182$	10.1343			0.751207
$183$	1.15980	+	4.94478i	0.0857347	+	0.365529i
$184$			8.20784i			0.605090i
$185$			9.54021i			0.701410i
$186$	25.8096	−	6.05363i	1.89245	−	0.443874i
$187$	3.81350	−	5.63550i	0.278871	−	0.412108i
$188$		−	1.66374i		−	0.121341i
$189$	3.31218	+	4.00368i	0.240925	+	0.291225i
$190$	7.28694			0.528650
$191$		−	7.86420i		−	0.569033i	−0.958671	−	0.284517i	$-0.908167\pi$
$191$		−	7.86420i		−	0.569033i	0.958671	−	0.284517i	$-0.0918331\pi$
$192$	1.00985	−	0.236860i	0.0728796	−	0.0170939i
$193$		−	0.744532i		−	0.0535926i	−0.999641	−	0.0267963i	$-0.991469\pi$
$193$		−	0.744532i		−	0.0535926i	0.999641	−	0.0267963i	$-0.00853054\pi$
$194$	−13.6968			−0.983372
$195$	9.59104	−	2.24958i	0.686829	−	0.161096i
$196$	−1.17485			−0.0839177
$197$	−1.17142			−0.0834603			−0.0417301	−	0.999129i	$-0.513287\pi$
$197$	−1.17142			−0.0834603			−0.0417301	+	0.999129i	$0.513287\pi$
$198$	−2.37103	+	17.5695i	−0.168502	+	1.24861i
$199$	−18.2367			−1.29277			−0.646384	−	0.763012i	$-0.723720\pi$
$199$	−18.2367			−1.29277			−0.646384	+	0.763012i	$0.723720\pi$
$200$	−1.47026			−0.103963
$201$	17.9184	−	4.20277i	1.26387	−	0.296441i
$202$	−9.78166			−0.688235
$203$		−	6.60729i		−	0.463741i
$204$	−4.06457	+	0.953346i	−0.284577	+	0.0667476i
$205$		−	4.92313i		−	0.343846i
$206$	−26.5560			−1.85024
$207$	7.44667	+	15.0011i	0.517579	+	1.04265i
$208$			28.2644i			1.95979i
$209$	−11.2335	−	7.60162i	−0.777036	−	0.525815i
$210$	−3.00464	+	0.704739i	−0.207340	+	0.0486316i
$211$		−	1.41804i		−	0.0976217i	−0.998808	−	0.0488108i	$-0.984457\pi$
$211$		−	1.41804i		−	0.0976217i	0.998808	−	0.0488108i	$-0.0155431\pi$
$212$			5.28537i			0.363000i
$213$	2.82326	+	12.0369i	0.193447	+	0.824757i
$214$	33.7227			2.30523
$215$	−1.16189			−0.0792404
$216$	−5.88647	+	4.86977i	−0.400524	+	0.331346i
$217$		−	8.58989i		−	0.583120i
$218$			29.5004i			1.99802i
$219$	4.26120	+	18.1676i	0.287945	+	1.22765i
$220$	−3.22710	−	2.18376i	−0.217571	−	0.147229i
$221$		−	11.6691i		−	0.784946i
$222$	−28.6649	+	6.72336i	−1.92386	+	0.451242i
$223$	11.7292			0.785446			0.392723	−	0.919657i	$-0.371533\pi$
$223$	11.7292			0.785446			0.392723	+	0.919657i	$0.371533\pi$
$224$		−	5.91405i		−	0.395149i
$225$	−2.68713	+	1.33392i	−0.179142	+	0.0889277i
$226$			30.9597i			2.05941i
$227$	−26.5374			−1.76135			−0.880674	−	0.473722i	$-0.842910\pi$
$227$	−26.5374			−1.76135			−0.880674	+	0.473722i	$0.842910\pi$
$228$	1.90035	+	8.10209i	0.125853	+	0.536574i
$229$	−4.75255			−0.314057			−0.157029	−	0.987594i	$-0.550191\pi$
$229$	−4.75255			−0.314057			−0.157029	+	0.987594i	$0.550191\pi$
$230$	−9.94706			−0.655890
$231$	5.36710	+	2.04798i	0.353129	+	0.134747i
$232$	9.71446			0.637786
$233$	7.01788			0.459757			0.229878	−	0.973219i	$-0.426167\pi$
$233$	7.01788			0.459757			0.229878	+	0.973219i	$0.426167\pi$
$234$	13.5184	+	27.2323i	0.883723	+	1.78023i
$235$	−1.41613			−0.0923782
$236$			3.87177i			0.252031i
$237$	−3.49784	−	14.9130i	−0.227209	−	0.968702i
$238$			3.65564i			0.236960i
$239$	5.65364			0.365704			0.182852	−	0.983140i	$-0.441467\pi$
$239$	5.65364			0.365704			0.182852	+	0.983140i	$0.441467\pi$
$240$	−1.96550	−	8.37988i	−0.126873	−	0.540919i
$241$		−	5.41450i		−	0.348779i	−0.984677	−	0.174389i	$-0.944205\pi$
$241$		−	5.41450i		−	0.348779i	0.984677	−	0.174389i	$-0.0557952\pi$
$242$	7.28771	+	18.1947i	0.468472	+	1.16960i
$243$	−6.34026	+	14.2408i	−0.406728	+	0.913549i
$244$		−	3.44506i		−	0.220548i
$245$			1.00000i			0.0638877i
$246$	14.7923	−	3.46952i	0.943120	−	0.221209i
$247$	−23.2604			−1.48003
$248$	12.6294			0.801968
$249$	−7.83957	+	1.83877i	−0.496813	+	0.116527i
$250$		−	1.78181i		−	0.112692i
$251$			19.0694i			1.20365i	0.798628	+	0.601825i	$0.205560\pi$
$251$			19.0694i			1.20365i	−0.798628	+	0.601825i	$0.794440\pi$
$252$	−1.56715	−	3.15697i	−0.0987211	−	0.198870i
$253$	15.3343	+	10.3766i	0.964059	+	0.652372i
$254$		−	2.19845i		−	0.137943i
$255$	0.811463	+	3.45966i	0.0508158	+	0.216652i
$256$	20.3719			1.27324
$257$			30.1757i			1.88231i	0.337977	+	0.941154i	$0.390257\pi$
$257$			30.1757i			1.88231i	−0.337977	+	0.941154i	$0.609743\pi$
$258$	−0.818831	−	3.49107i	−0.0509782	−	0.217345i
$259$			9.54021i			0.592800i
$260$	−6.68214			−0.414409
$261$	17.7546	−	8.81357i	1.09898	−	0.545546i
$262$	15.3718			0.949676
$263$	16.1667			0.996884			0.498442	−	0.866923i	$-0.333906\pi$
$263$	16.1667			0.996884			0.498442	+	0.866923i	$0.333906\pi$
$264$	−3.01107	+	7.89106i	−0.185318	+	0.485661i
$265$	4.49877			0.276357
$266$	7.28694			0.446791
$267$	0.319331	+	1.36146i	0.0195428	+	0.0833202i
$268$	−12.4839			−0.762576
$269$		−	31.6490i		−	1.92967i	−0.262848	−	0.964837i	$-0.584662\pi$
$269$		−	31.6490i		−	1.92967i	0.262848	−	0.964837i	$-0.415338\pi$
$270$	−5.90167	−	7.13381i	−0.359164	−	0.434150i
$271$		−	2.86169i		−	0.173835i	−0.996216	−	0.0869176i	$-0.972298\pi$
$271$		−	2.86169i		−	0.173835i	0.996216	−	0.0869176i	$-0.0277017\pi$
$272$	−10.1955			−0.618193
$273$	9.59104	−	2.24958i	0.580476	−	0.136151i
$274$			4.54031i			0.274290i
$275$	−1.85876	+	2.74682i	−0.112087	+	0.165640i
$276$	−2.59407	−	11.0598i	−0.156145	−	0.665721i
$277$			20.2613i			1.21739i	0.793406	+	0.608693i	$0.208306\pi$
$277$			20.2613i			1.21739i	−0.793406	+	0.608693i	$0.791694\pi$
$278$		−	24.4871i		−	1.46864i
$279$	23.0822	−	11.4582i	1.38189	−	0.685984i
$280$	−1.47026			−0.0878651
$281$	−1.07941			−0.0643923			−0.0321962	−	0.999482i	$-0.510250\pi$
$281$	−1.07941			−0.0643923			−0.0321962	+	0.999482i	$0.510250\pi$
$282$	−0.998003	−	4.25497i	−0.0594302	−	0.253380i
$283$		−	15.4562i		−	0.918773i	−0.888236	−	0.459386i	$-0.848069\pi$
$283$		−	15.4562i		−	0.918773i	0.888236	−	0.459386i	$-0.151931\pi$
$284$		−	8.38621i		−	0.497630i
$285$	6.89629	−	1.61752i	0.408501	−	0.0958139i
$286$	27.8372	+	18.8373i	1.64605	+	1.11387i
$287$		−	4.92313i		−	0.290603i
$288$	15.8918	−	7.88885i	0.936435	−	0.464855i
$289$	−12.7908			−0.752398
$290$			11.7729i			0.691331i
$291$	−12.9625	+	3.04035i	−0.759875	+	0.178229i
$292$		−	12.6575i		−	0.740722i
$293$	−1.35129			−0.0789435			−0.0394717	−	0.999221i	$-0.512568\pi$
$293$	−1.35129			−0.0789435			−0.0394717	+	0.999221i	$0.512568\pi$
$294$	−3.00464	+	0.704739i	−0.175234	+	0.0411012i
$295$	3.29555			0.191874
$296$	−14.0266			−0.815281
$297$	1.65609	+	17.1539i	0.0960959	+	0.995372i
$298$	24.2694			1.40589
$299$	31.7517			1.83625
$300$	1.98113	−	0.464674i	0.114381	−	0.0268280i
$301$	−1.16189			−0.0669704
$302$		−	10.7756i		−	0.620064i
$303$	−9.25727	+	2.17129i	−0.531816	+	0.124737i
$304$			20.3231i			1.16561i
$305$	−2.93235			−0.167906
$306$	−9.82318	+	4.87632i	−0.561554	+	0.278760i
$307$		−	22.6141i		−	1.29065i	−0.763906	−	0.645327i	$-0.776721\pi$
$307$		−	22.6141i		−	1.29065i	0.763906	−	0.645327i	$-0.223279\pi$
$308$	−3.22710	−	2.18376i	−0.183881	−	0.124431i
$309$	−25.1323	+	5.89479i	−1.42973	+	0.335343i
$310$			15.3056i			0.869297i
$311$			13.2364i			0.750567i	0.926910	+	0.375283i	$0.122455\pi$
$311$			13.2364i			0.750567i	−0.926910	+	0.375283i	$0.877545\pi$
$312$	3.30747	+	14.1014i	0.187249	+	0.798332i
$313$	−6.10492			−0.345070			−0.172535	−	0.985003i	$-0.555196\pi$
$313$	−6.10492			−0.345070			−0.172535	+	0.985003i	$0.555196\pi$
$314$	16.5304			0.932866
$315$	−2.68713	+	1.33392i	−0.151403	+	0.0751577i
$316$			10.3900i			0.584482i
$317$		−	3.02957i		−	0.170158i	−0.996374	−	0.0850788i	$-0.972886\pi$
$317$		−	3.02957i		−	0.170158i	0.996374	−	0.0850788i	$-0.0271142\pi$
$318$	3.17046	+	13.5172i	0.177790	+	0.758006i
$319$	12.2813	−	18.1490i	0.687623	−	1.01615i
$320$			0.598859i			0.0334772i
$321$	31.9148	−	7.48562i	1.78131	−	0.417806i
$322$	−9.94706			−0.554328
$323$		−	8.39046i		−	0.466858i
$324$	6.39274	−	8.42227i	0.355152	−	0.467904i
$325$			5.68767i			0.315495i
$326$	−27.1211			−1.50210
$327$	6.54837	+	27.9189i	0.362126	+	1.54392i
$328$	7.23830			0.399668
$329$	−1.41613			−0.0780739
$330$	−9.56316	−	3.64911i	−0.526435	−	0.200877i
$331$	8.84518			0.486175			0.243088	−	0.970004i	$-0.421840\pi$
$331$	8.84518			0.486175			0.243088	+	0.970004i	$0.421840\pi$
$332$	5.46188			0.299760
$333$	−25.6358	+	12.7258i	−1.40483	+	0.697372i
$334$	−42.2664			−2.31271
$335$			10.6260i			0.580559i
$336$	−1.96550	−	8.37988i	−0.107227	−	0.457160i
$337$			16.1100i			0.877566i	0.898593	+	0.438783i	$0.144590\pi$
$337$			16.1100i			0.877566i	−0.898593	+	0.438783i	$0.855410\pi$
$338$	34.4772			1.87531
$339$	6.87230	+	29.2999i	0.373252	+	1.59135i
$340$		−	2.41037i		−	0.130721i
$341$	15.9665	−	23.5949i	0.864635	−	1.27774i
$342$	9.72017	+	19.5810i	0.525607	+	1.05882i
$343$			1.00000i			0.0539949i
$344$		−	1.70829i		−	0.0921048i
$345$	−9.41380	+	2.20801i	−0.506822	+	0.118875i
$346$	−14.2275			−0.764876
$347$	−12.4875			−0.670365			−0.335183	−	0.942153i	$-0.608798\pi$
$347$	−12.4875			−0.670365			−0.335183	+	0.942153i	$0.608798\pi$
$348$	−13.0899	+	3.07024i	−0.701693	+	0.164582i
$349$		−	17.9786i		−	0.962371i	−0.876619	−	0.481185i	$-0.840206\pi$
$349$		−	17.9786i		−	0.962371i	0.876619	−	0.481185i	$-0.159794\pi$
$350$		−	1.78181i		−	0.0952418i
$351$	18.8386	+	22.7716i	1.00553	+	1.21546i
$352$	10.9928	−	16.2448i	0.585917	−	0.865853i
$353$			22.9618i			1.22213i	0.791579	+	0.611067i	$0.209259\pi$
$353$			22.9618i			1.22213i	−0.791579	+	0.611067i	$0.790741\pi$
$354$	2.32250	+	9.90195i	0.123440	+	0.526283i
$355$	−7.13813			−0.378852
$356$		−	0.948541i		−	0.0502726i
$357$	0.811463	+	3.45966i	0.0429472	+	0.183105i
$358$		−	7.61592i		−	0.402514i
$359$	−30.5048			−1.60998			−0.804990	−	0.593289i	$-0.797829\pi$
$359$	−30.5048			−1.60998			−0.804990	+	0.593289i	$0.797829\pi$
$360$	−1.96121	−	3.95079i	−0.103365	−	0.208225i
$361$	2.27494			0.119734
$362$	17.3353			0.911122
$363$	10.9358	+	15.6016i	0.573980	+	0.818869i
$364$	−6.68214			−0.350240
$365$	−10.7737			−0.563922
$366$	−2.06654	−	8.81066i	−0.108020	−	0.460541i
$367$	−16.8825			−0.881258			−0.440629	−	0.897689i	$-0.645245\pi$
$367$	−16.8825			−0.881258			−0.440629	+	0.897689i	$0.645245\pi$
$368$		−	27.7421i		−	1.44616i
$369$	13.2291	−	6.56704i	0.688679	−	0.341867i
$370$		−	16.9988i		−	0.883728i
$371$	4.49877			0.233564
$372$	−17.0177	+	3.99150i	−0.882327	+	0.206950i
$373$		−	32.0794i		−	1.66101i	−0.557012	−	0.830504i	$-0.688052\pi$
$373$		−	32.0794i		−	1.66101i	0.557012	−	0.830504i	$-0.311948\pi$
$374$	−6.79494	+	10.0414i	−0.351358	+	0.519228i
$375$	−0.395519	−	1.68629i	−0.0204245	−	0.0870795i
$376$		−	2.08209i		−	0.107375i
$377$		−	37.5801i		−	1.93547i
$378$	−5.90167	−	7.13381i	−0.303549	−	0.366923i
$379$	−23.3299			−1.19838			−0.599189	−	0.800608i	$-0.704510\pi$
$379$	−23.3299			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$380$	−4.80469			−0.246476
$381$	−0.488001	−	2.08059i	−0.0250011	−	0.106592i
$382$			14.0125i			0.716942i
$383$		−	16.7968i		−	0.858275i	−0.903239	−	0.429138i	$-0.858818\pi$
$383$		−	16.7968i		−	0.858275i	0.903239	−	0.429138i	$-0.141182\pi$
$384$	18.1462	−	4.25619i	0.926020	−	0.217198i
$385$	−1.85876	+	2.74682i	−0.0947309	+	0.139991i
$386$			1.32661i			0.0675229i
$387$	−1.54987	−	3.12216i	−0.0787842	−	0.158708i
$388$	9.03106			0.458483
$389$		−	4.27192i		−	0.216595i	−0.994119	−	0.108298i	$-0.965460\pi$
$389$		−	4.27192i		−	0.216595i	0.994119	−	0.108298i	$-0.0345399\pi$
$390$	−17.0894	+	4.00832i	−0.865356	+	0.202969i
$391$			11.4534i			0.579224i
$392$	−1.47026			−0.0742596
$393$	14.5478	−	3.41218i	0.733838	−	0.172122i
$394$	2.08725			0.105154
$395$	8.84368			0.444974
$396$	1.56336	−	11.5846i	0.0785616	−	0.582147i
$397$	−24.7743			−1.24338			−0.621692	−	0.783262i	$-0.713555\pi$
$397$	−24.7743			−1.24338			−0.621692	+	0.783262i	$0.713555\pi$
$398$	32.4944			1.62880
$399$	6.89629	−	1.61752i	0.345246	−	0.0809775i
$400$	4.96943			0.248471
$401$			24.8914i			1.24302i	0.783408	+	0.621508i	$0.213480\pi$
$401$			24.8914i			1.24302i	−0.783408	+	0.621508i	$0.786520\pi$
$402$	−31.9273	+	7.48854i	−1.59239	+	0.373495i
$403$		−	48.8564i		−	2.43371i
$404$	6.44960			0.320880
$405$	−7.16881	−	5.44134i	−0.356221	−	0.270382i
$406$			11.7729i			0.584281i
$407$	−17.7329	+	26.2052i	−0.878988	+	1.29895i
$408$	−5.08661	+	1.19307i	−0.251825	+	0.0590655i
$409$		−	13.7994i		−	0.682335i	−0.940002	−	0.341168i	$-0.889178\pi$
$409$		−	13.7994i		−	0.682335i	0.940002	−	0.341168i	$-0.110822\pi$
$410$			8.77209i			0.433222i
$411$	1.00784	+	4.29690i	0.0497130	+	0.211951i
$412$	17.5099			0.862649
$413$	3.29555			0.162163
$414$	−13.2685	−	26.7290i	−0.652113	−	1.31366i
$415$		−	4.64901i		−	0.228211i
$416$		−	33.6371i		−	1.64920i
$417$	−5.43553	−	23.1743i	−0.266179	−	1.13485i
$418$	20.0159	+	13.5446i	0.979011	+	0.662490i
$419$			40.2176i			1.96476i	0.186894	+	0.982380i	$0.440158\pi$
$419$			40.2176i			1.96476i	−0.186894	+	0.982380i	$0.559842\pi$
$420$	1.98113	−	0.464674i	0.0966693	−	0.0226738i
$421$	−38.8337			−1.89264			−0.946318	−	0.323236i	$-0.895229\pi$
$421$	−38.8337			−1.89264			−0.946318	+	0.323236i	$0.895229\pi$
$422$			2.52667i			0.122996i
$423$	−1.88900	−	3.80533i	−0.0918464	−	0.185021i
$424$			6.61437i			0.321222i
$425$	−2.05164			−0.0995193
$426$	−5.03052	−	21.4475i	−0.243729	−	1.03914i
$427$	−2.93235			−0.141906
$428$	−22.2353			−1.07478
$429$	30.5263	+	11.6482i	1.47382	+	0.562381i
$430$	2.07027			0.0998374
$431$	−7.04274			−0.339237			−0.169618	−	0.985510i	$-0.554254\pi$
$431$	−7.04274			−0.339237			−0.169618	+	0.985510i	$0.554254\pi$
$432$	19.8960	−	16.4596i	0.957248	−	0.791914i
$433$	−1.66757			−0.0801385			−0.0400692	−	0.999197i	$-0.512758\pi$
$433$	−1.66757			−0.0801385			−0.0400692	+	0.999197i	$0.512758\pi$
$434$			15.3056i			0.734690i
$435$	2.61331	+	11.1418i	0.125298	+	0.534208i
$436$		−	19.4513i		−	0.931547i
$437$	22.8306			1.09214
$438$	−7.59265	−	32.3712i	−0.362791	−	1.54675i
$439$			13.6258i			0.650322i	0.945659	+	0.325161i	$0.105418\pi$
$439$			13.6258i			0.650322i	−0.945659	+	0.325161i	$0.894582\pi$
$440$	−4.03855	−	2.73286i	−0.192530	−	0.130284i
$441$	−2.68713	+	1.33392i	−0.127959	+	0.0635198i
$442$			20.7921i			0.988977i
$443$			22.7363i			1.08023i	0.841590	+	0.540117i	$0.181620\pi$
$443$			22.7363i			1.08023i	−0.841590	+	0.540117i	$0.818380\pi$
$444$	18.9004	−	4.43309i	0.896974	−	0.210385i
$445$	−0.807374			−0.0382732
$446$	−20.8992			−0.989608
$447$	22.9683	−	5.38722i	1.08636	−	0.254807i
$448$			0.598859i			0.0282934i
$449$		−	28.2401i		−	1.33273i	−0.745625	−	0.666366i	$-0.767849\pi$
$449$		−	28.2401i		−	1.33273i	0.745625	−	0.666366i	$-0.232151\pi$
$450$	4.78796	−	2.37679i	0.225706	−	0.112043i
$451$	9.15089	−	13.5230i	0.430899	−	0.636771i
$452$		−	20.4135i		−	0.960169i
$453$	−2.39191	−	10.1979i	−0.112382	−	0.479138i
$454$	47.2846			2.21918
$455$			5.68767i			0.266642i
$456$	2.37819	+	10.1394i	0.111369	+	0.474819i
$457$		−	30.1221i		−	1.40905i	−0.709679	−	0.704525i	$-0.751160\pi$
$457$		−	30.1221i		−	1.40905i	0.709679	−	0.704525i	$-0.248840\pi$
$458$	8.46814			0.395690
$459$	−8.21413	+	6.79540i	−0.383403	+	0.317182i
$460$	6.55866			0.305799
$461$	9.65723			0.449782			0.224891	−	0.974384i	$-0.427797\pi$
$461$	9.65723			0.449782			0.224891	+	0.974384i	$0.427797\pi$
$462$	−9.56316	−	3.64911i	−0.444918	−	0.169772i
$463$	5.37135			0.249628			0.124814	−	0.992180i	$-0.460167\pi$
$463$	5.37135			0.249628			0.124814	+	0.992180i	$0.460167\pi$
$464$	−32.8344			−1.52430
$465$	3.39746	+	14.4850i	0.157554	+	0.671727i
$466$	−12.5045			−0.579261
$467$		−	5.96560i		−	0.276055i	−0.990428	−	0.138028i	$-0.955924\pi$
$467$		−	5.96560i		−	0.276055i	0.990428	−	0.138028i	$-0.0440762\pi$
$468$	−8.91342	−	17.9558i	−0.412023	−	0.830007i
$469$			10.6260i			0.490662i
$470$	2.52328			0.116390
$471$	15.6442	−	3.66935i	0.720848	−	0.169075i
$472$			4.84533i			0.223024i
$473$	−3.19151	−	2.15967i	−0.146746	−	0.0993019i
$474$	6.23249	+	26.5721i	0.286268	+	1.22050i
$475$			4.08963i			0.187645i
$476$		−	2.41037i		−	0.110479i
$477$	6.00098	+	12.0888i	0.274766	+	0.553507i
$478$	−10.0737			−0.460761
$479$	7.21212			0.329530			0.164765	−	0.986333i	$-0.447313\pi$
$479$	7.21212			0.329530			0.164765	+	0.986333i	$0.447313\pi$
$480$	2.33912	+	9.97279i	0.106766	+	0.455193i
$481$			54.2615i			2.47411i
$482$			9.64762i			0.439437i
$483$	−9.41380	+	2.20801i	−0.428343	+	0.100468i
$484$	−4.80520	−	11.9968i	−0.218418	−	0.545308i
$485$		−	7.68700i		−	0.349049i
$486$	11.2971	−	25.3745i	0.512448	−	1.15101i
$487$	−1.55800			−0.0705999			−0.0352999	−	0.999377i	$-0.511239\pi$
$487$	−1.55800			−0.0705999			−0.0352999	+	0.999377i	$0.511239\pi$
$488$		−	4.31133i		−	0.195165i
$489$	−25.6671	+	6.02023i	−1.16071	+	0.272244i
$490$		−	1.78181i		−	0.0804940i
$491$	24.2789			1.09569			0.547847	−	0.836579i	$-0.315448\pi$
$491$	24.2789			1.09569			0.547847	+	0.836579i	$0.315448\pi$
$492$	−9.75337	+	2.28765i	−0.439716	+	0.103135i
$493$	13.5558			0.610522
$494$	41.4457			1.86473
$495$	−9.86049	−	1.33069i	−0.443196	−	0.0598099i
$496$	−42.6868			−1.91670
$497$	−7.13813			−0.320189
$498$	13.9686	−	3.27634i	0.625949	−	0.146816i
$499$	33.7752			1.51199			0.755994	−	0.654579i	$-0.227154\pi$
$499$	33.7752			1.51199			0.755994	+	0.654579i	$0.227154\pi$
$500$			1.17485i			0.0525408i
$501$	−40.0005	+	9.38211i	−1.78709	+	0.419162i
$502$		−	33.9781i		−	1.51652i
$503$	−35.8208			−1.59717			−0.798585	−	0.601881i	$-0.794418\pi$
$503$	−35.8208			−1.59717			−0.798585	+	0.601881i	$0.794418\pi$
$504$	−1.96121	−	3.95079i	−0.0873592	−	0.175982i
$505$		−	5.48973i		−	0.244290i
$506$	−27.3228	−	18.4892i	−1.21465	−	0.821943i
$507$	32.6289	−	7.65311i	1.44910	−	0.339886i
$508$			1.44956i			0.0643138i
$509$		−	17.4524i		−	0.773565i	−0.922171	−	0.386783i	$-0.873586\pi$
$509$		−	17.4524i		−	0.773565i	0.922171	−	0.386783i	$-0.126414\pi$
$510$	−1.44587	−	6.16446i	−0.0640243	−	0.272967i
$511$	−10.7737			−0.476601
$512$	−14.7767			−0.653044
$513$	13.5456	+	16.3736i	0.598052	+	0.722911i
$514$		−	53.7674i		−	2.37158i
$515$		−	14.9039i		−	0.656746i
$516$	0.539902	+	2.30186i	0.0237678	+	0.101334i
$517$	−3.88986	−	2.63224i	−0.171076	−	0.115766i
$518$		−	16.9988i		−	0.746886i
$519$	−13.4648	+	3.15816i	−0.591038	+	0.138628i
$520$	−8.36237			−0.366714
$521$		−	27.1302i		−	1.18860i	−0.804245	−	0.594298i	$-0.797430\pi$
$521$		−	27.1302i		−	1.18860i	0.804245	−	0.594298i	$-0.202570\pi$
$522$	−31.6354	+	15.7041i	−1.38464	+	0.687350i
$523$			11.0793i			0.484462i	0.970219	+	0.242231i	$0.0778792\pi$
$523$			11.0793i			0.484462i	−0.970219	+	0.242231i	$0.922121\pi$
$524$	−10.1355			−0.442773
$525$	−0.395519	−	1.68629i	−0.0172618	−	0.0735956i
$526$	−28.8061			−1.25600
$527$	17.6234			0.767687
$528$	10.1773	−	26.6714i	0.442909	−	1.16073i
$529$	−8.16497			−0.354999
$530$	−8.01595			−0.348190
$531$	4.39599	+	8.85557i	0.190770	+	0.384299i
$532$	−4.80469			−0.208310
$533$		−	28.0011i		−	1.21286i
$534$	−0.568988	−	2.42587i	−0.0246225	−	0.104978i
$535$			18.9261i			0.818246i
$536$	−15.6230			−0.674810
$537$	−1.69055	−	7.20763i	−0.0729526	−	0.311032i
$538$			56.3925i			2.43126i
$539$	−1.85876	+	2.74682i	−0.0800623	+	0.118314i
$540$	3.89130	+	4.70372i	0.167455	+	0.202416i
$541$		−	6.72960i		−	0.289328i	−0.989481	−	0.144664i	$-0.953790\pi$
$541$		−	6.72960i		−	0.289328i	0.989481	−	0.144664i	$-0.0462102\pi$
$542$			5.09898i			0.219020i
$543$	16.4059	−	3.84801i	0.704046	−	0.165134i
$544$	12.1335			0.520220
$545$	−16.5564			−0.709199
$546$	−17.0894	+	4.00832i	−0.731359	+	0.171540i
$547$			45.9170i			1.96327i	0.190774	+	0.981634i	$0.438900\pi$
$547$			45.9170i			1.96327i	−0.190774	+	0.981634i	$0.561100\pi$
$548$		−	2.99368i		−	0.127884i
$549$	−3.91151	−	7.87960i	−0.166939	−	0.336293i
$550$	3.31195	−	4.89432i	0.141222	−	0.208694i
$551$		−	27.0214i		−	1.15115i
$552$	−3.24635	−	13.8408i	−0.138174	−	0.589102i
$553$	8.84368			0.376071
$554$		−	36.1019i		−	1.53382i
$555$	−3.77333	−	16.0875i	−0.160169	−	0.682878i
$556$			16.1457i			0.684730i
$557$	10.8660			0.460405			0.230203	−	0.973143i	$-0.426061\pi$
$557$	10.8660			0.460405			0.230203	+	0.973143i	$0.426061\pi$
$558$	−41.1280	+	20.4163i	−1.74109	+	0.864292i
$559$	−6.60846			−0.279508
$560$	4.96943			0.209997
$561$	−4.20172	+	11.0114i	−0.177397	+	0.464901i
$562$	1.92331			0.0811298
$563$	17.6558			0.744104			0.372052	−	0.928212i	$-0.378654\pi$
$563$	17.6558			0.744104			0.372052	+	0.928212i	$0.378654\pi$
$564$	0.658040	+	2.80554i	0.0277085	+	0.118135i
$565$	−17.3754			−0.730989
$566$			27.5399i			1.15759i
$567$	−7.16881	−	5.44134i	−0.301062	−	0.228515i
$568$		−	10.4949i		−	0.440357i
$569$	−8.10914			−0.339953			−0.169976	−	0.985448i	$-0.554369\pi$
$569$	−8.10914			−0.339953			−0.169976	+	0.985448i	$0.554369\pi$
$570$	−12.2879	+	2.88212i	−0.514683	+	0.120719i
$571$		−	13.2401i		−	0.554083i	−0.960858	−	0.277041i	$-0.910646\pi$
$571$		−	13.2401i		−	0.554083i	0.960858	−	0.277041i	$-0.0893539\pi$
$572$	−18.3547	−	12.4205i	−0.767447	−	0.519326i
$573$	3.11044	+	13.2613i	0.129940	+	0.553999i
$574$			8.77209i			0.366140i
$575$		−	5.58256i		−	0.232809i
$576$	−1.60921	+	0.798828i	−0.0670505	+	0.0332845i
$577$	42.4776			1.76836			0.884182	−	0.467142i	$-0.154716\pi$
$577$	42.4776			1.76836			0.884182	+	0.467142i	$0.154716\pi$
$578$	22.7907			0.947969
$579$	0.294476	+	1.25549i	0.0122380	+	0.0521766i
$580$		−	7.76256i		−	0.322323i
$581$		−	4.64901i		−	0.192874i
$582$	23.0967	−	5.41733i	0.957389	−	0.224556i
$583$	12.3573	+	8.36210i	0.511787	+	0.346323i
$584$		−	15.8402i		−	0.655472i
$585$	−15.2835	+	7.58687i	−0.631895	+	0.313678i
$586$	2.40775			0.0994633
$587$		−	25.7335i		−	1.06213i	−0.847330	−	0.531067i	$-0.821791\pi$
$587$		−	25.7335i		−	1.06213i	0.847330	−	0.531067i	$-0.178209\pi$
$588$	1.98113	−	0.464674i	0.0817005	−	0.0191628i
$589$		−	35.1295i		−	1.44748i
$590$	−5.87204			−0.241748
$591$	1.97535	−	0.463319i	0.0812551	−	0.0190584i
$592$	47.4094			1.94851
$593$	−2.30135			−0.0945052			−0.0472526	−	0.998883i	$-0.515047\pi$
$593$	−2.30135			−0.0945052			−0.0472526	+	0.998883i	$0.515047\pi$
$594$	−2.95083	−	30.5651i	−0.121074	−	1.25410i
$595$	−2.05164			−0.0841092
$596$	−16.0022			−0.655475
$597$	30.7524	−	7.21297i	1.25861	−	0.295207i
$598$	−56.5756			−2.31355
$599$			41.8048i			1.70810i	0.520193	+	0.854049i	$0.325860\pi$
$599$			41.8048i			1.70810i	−0.520193	+	0.854049i	$0.674140\pi$
$600$	2.47929	−	0.581517i	0.101217	−	0.0237403i
$601$			6.17906i			0.252049i	0.992027	+	0.126025i	$0.0402218\pi$
$601$			6.17906i			0.252049i	−0.992027	+	0.126025i	$0.959778\pi$
$602$	2.07027			0.0843780
$603$	−28.5534	+	14.1742i	−1.16278	+	0.577216i
$604$			7.10494i			0.289096i
$605$	−10.2113	+	4.09006i	−0.415150	+	0.166284i
$606$	16.4947	−	3.86883i	0.670051	−	0.157160i
$607$		−	32.4677i		−	1.31782i	−0.752220	−	0.658912i	$-0.771017\pi$
$607$		−	32.4677i		−	1.31782i	0.752220	−	0.658912i	$-0.228983\pi$
$608$		−	24.1863i		−	0.980883i
$609$	2.61331	+	11.1418i	0.105896	+	0.451488i
$610$	5.22489			0.211549
$611$	−8.05448			−0.325849
$612$	6.47697	−	3.21523i	0.261816	−	0.129968i
$613$		−	18.6584i		−	0.753605i	−0.926294	−	0.376802i	$-0.877024\pi$
$613$		−	18.6584i		−	0.753605i	0.926294	−	0.376802i	$-0.122976\pi$
$614$			40.2940i			1.62613i
$615$	1.94719	+	8.30181i	0.0785183	+	0.334761i
$616$	−4.03855	−	2.73286i	−0.162718	−	0.110110i
$617$			1.42959i			0.0575532i	0.999586	+	0.0287766i	$0.00916114\pi$
$617$			1.42959i			0.0575532i	−0.999586	+	0.0287766i	$0.990839\pi$
$618$	44.7810	−	10.5034i	1.80136	−	0.422508i
$619$	−23.7870			−0.956079			−0.478040	−	0.878338i	$-0.658652\pi$
$619$	−23.7870			−0.956079			−0.478040	+	0.878338i	$0.658652\pi$
$620$		−	10.0918i		−	0.405297i
$621$	−18.4904	−	22.3508i	−0.741995	−	0.896907i
$622$		−	23.5847i		−	0.945662i
$623$	−0.807374			−0.0323467
$624$	−11.1791	−	47.6620i	−0.447523	−	1.90801i
$625$	1.00000			0.0400000
$626$	10.8778			0.434765
$627$	21.9495	+	8.37546i	0.876577	+	0.334484i
$628$	−10.8994			−0.434935
$629$	−19.5731			−0.780431
$630$	4.78796	−	2.37679i	0.190757	−	0.0946934i
$631$	−21.1356			−0.841396			−0.420698	−	0.907201i	$-0.638215\pi$
$631$	−21.1356			−0.841396			−0.420698	+	0.907201i	$0.638215\pi$
$632$			13.0025i			0.517213i
$633$	0.560860	+	2.39122i	0.0222922	+	0.0950423i
$634$			5.39812i			0.214387i
$635$	1.23383			0.0489629
$636$	−2.09046	−	8.91265i	−0.0828922	−	0.353409i
$637$			5.68767i			0.225354i
$638$	−21.8830	+	32.3382i	−0.866356	+	1.28028i
$639$	−9.52166	−	19.1811i	−0.376671	−	0.758791i
$640$			10.7610i			0.425368i
$641$			27.5292i			1.08734i	0.839300	+	0.543669i	$0.182965\pi$
$641$			27.5292i			1.08734i	−0.839300	+	0.543669i	$0.817035\pi$
$642$	−56.8661	+	13.3379i	−2.24433	+	0.526407i
$643$	45.1942			1.78229			0.891143	−	0.453723i	$-0.149904\pi$
$643$	45.1942			1.78229			0.891143	+	0.453723i	$0.149904\pi$
$644$	6.55866			0.258447
$645$	1.95928	−	0.459550i	0.0771468	−	0.0180948i
$646$			14.9502i			0.588208i
$647$		−	39.2600i		−	1.54347i	−0.635945	−	0.771734i	$-0.719389\pi$
$647$		−	39.2600i		−	1.54347i	0.635945	−	0.771734i	$-0.280611\pi$
$648$	8.00020	−	10.5400i	0.314278	−	0.414052i
$649$	9.05229	+	6.12562i	0.355333	+	0.240452i
$650$		−	10.1343i		−	0.397502i
$651$	3.39746	+	14.4850i	0.133157	+	0.567713i
$652$	17.8825			0.700332
$653$			49.7480i			1.94679i	0.229134	+	0.973395i	$0.426411\pi$
$653$			49.7480i			1.94679i	−0.229134	+	0.973395i	$0.573589\pi$
$654$	−11.6680	−	49.7461i	−0.456253	−	1.94523i
$655$			8.62710i			0.337089i
$656$	−24.4651			−0.955203
$657$	−14.3712	−	28.9504i	−0.560675	−	1.12946i
$658$	2.52328			0.0983676
$659$	−5.85425			−0.228049			−0.114025	−	0.993478i	$-0.536374\pi$
$659$	−5.85425			−0.228049			−0.114025	+	0.993478i	$0.536374\pi$
$660$	6.30553	+	2.40606i	0.245442	+	0.0936558i
$661$	9.53643			0.370924			0.185462	−	0.982651i	$-0.440622\pi$
$661$	9.53643			0.370924			0.185462	+	0.982651i	$0.440622\pi$
$662$	−15.7604			−0.612547
$663$	4.61533	+	19.6774i	0.179245	+	0.764207i
$664$	6.83528			0.265260
$665$			4.08963i			0.158589i
$666$	45.6781	−	22.6750i	1.76999	−	0.878640i
$667$			36.8856i			1.42822i
$668$	27.8686			1.07827
$669$	−19.7788	+	4.63912i	−0.764694	+	0.179359i
$670$		−	18.9335i		−	0.731464i
$671$	−8.05464	−	5.45052i	−0.310946	−	0.210415i
$672$	2.33912	+	9.97279i	0.0902334	+	0.384709i
$673$		−	23.3409i		−	0.899725i	−0.893098	−	0.449862i	$-0.851473\pi$
$673$		−	23.3409i		−	0.899725i	0.893098	−	0.449862i	$-0.148527\pi$
$674$		−	28.7049i		−	1.10567i
$675$	4.00368	−	3.31218i	0.154102	−	0.127486i
$676$	−22.7328			−0.874338
$677$	4.05783			0.155955			0.0779775	−	0.996955i	$-0.475154\pi$
$677$	4.05783			0.155955			0.0779775	+	0.996955i	$0.475154\pi$
$678$	−12.2451	−	52.2069i	−0.470272	−	2.00500i
$679$		−	7.68700i		−	0.295000i
$680$		−	3.01646i		−	0.115676i
$681$	44.7497	−	10.4960i	1.71481	−	0.402209i
$682$	−28.4493	+	42.0416i	−1.08938	+	1.60986i
$683$			4.78539i			0.183108i	0.995800	+	0.0915539i	$0.0291834\pi$
$683$			4.78539i			0.183108i	−0.995800	+	0.0915539i	$0.970817\pi$
$684$	−6.40906	−	12.9108i	−0.245056	−	0.493658i
$685$	−2.54814			−0.0973596
$686$		−	1.78181i		−	0.0680298i
$687$	8.01416	−	1.87972i	0.305759	−	0.0717158i
$688$			5.77394i			0.220129i
$689$	25.5875			0.974805
$690$	16.7736	−	3.93425i	0.638560	−	0.149774i
$691$	29.3632			1.11703			0.558515	−	0.829494i	$-0.311371\pi$
$691$	29.3632			1.11703			0.558515	+	0.829494i	$0.311371\pi$
$692$	9.38100			0.356612
$693$	−9.86049	−	1.33069i	−0.374569	−	0.0505486i
$694$	22.2504			0.844613
$695$	13.7428			0.521294
$696$	−16.3814	+	3.84225i	−0.620934	+	0.145640i
$697$	10.1005			0.382584
$698$			32.0344i			1.21252i
$699$	−11.8342	+	2.77570i	−0.447609	+	0.104987i
$700$			1.17485i			0.0444051i
$701$	7.87676			0.297501			0.148750	−	0.988875i	$-0.452475\pi$
$701$	7.87676			0.297501			0.148750	+	0.988875i	$0.452475\pi$
$702$	−33.5667	−	40.5747i	−1.26689	−	1.53139i
$703$			39.0159i			1.47151i
$704$	−1.11313	+	1.64496i	−0.0419528	+	0.0619967i
$705$	2.38800	−	0.560106i	0.0899375	−	0.0210948i
$706$		−	40.9136i		−	1.53980i
$707$		−	5.48973i		−	0.206463i
$708$	−1.53136	−	6.52892i	−0.0575519	−	0.245372i
$709$	30.5053			1.14565			0.572826	−	0.819677i	$-0.305847\pi$
$709$	30.5053			1.14565			0.572826	+	0.819677i	$0.305847\pi$
$710$	12.7188			0.477327
$711$	11.7967	+	23.7641i	0.442412	+	0.891224i
$712$		−	1.18705i		−	0.0444867i
$713$			47.9536i			1.79588i
$714$	−1.44587	−	6.16446i	−0.0541105	−	0.230699i
$715$	−10.5720	+	15.6230i	−0.395370	+	0.584267i
$716$			5.02161i			0.187666i
$717$	−9.53367	+	2.23612i	−0.356041	+	0.0835095i
$718$	54.3537			2.02846
$719$		−	4.86628i		−	0.181482i	−0.995875	−	0.0907408i	$-0.971077\pi$
$719$		−	4.86628i		−	0.181482i	0.995875	−	0.0907408i	$-0.0289235\pi$
$720$	6.62880	+	13.3535i	0.247041	+	0.497656i
$721$		−	14.9039i		−	0.555052i
$722$	−4.05351			−0.150856
$723$	2.14154	+	9.13041i	0.0796446	+	0.339564i
$724$	−11.4301			−0.424797
$725$	−6.60729			−0.245389
$726$	−19.4855	−	27.7990i	−0.723175	−	1.03172i
$727$	−15.6398			−0.580047			−0.290023	−	0.957020i	$-0.593663\pi$
$727$	−15.6398			−0.580047			−0.290023	+	0.957020i	$0.593663\pi$
$728$	−8.36237			−0.309930
$729$	5.05898	−	26.5218i	0.187370	−	0.982289i
$730$	19.1967			0.710502
$731$		−	2.38379i		−	0.0881676i
$732$	1.36259	+	5.80937i	0.0503626	+	0.214720i
$733$		−	28.1397i		−	1.03936i	−0.854359	−	0.519682i	$-0.826050\pi$
$733$		−	28.1397i		−	1.03936i	0.854359	−	0.519682i	$-0.173950\pi$
$734$	30.0814			1.11032
$735$	−0.395519	−	1.68629i	−0.0145889	−	0.0621996i
$736$			33.0155i			1.21697i
$737$	−19.7511	+	29.1877i	−0.727541	+	1.07514i
$738$	−23.5717	+	11.7012i	−0.867687	+	0.430728i
$739$			28.9368i			1.06446i	0.846601	+	0.532228i	$0.178645\pi$
$739$			28.9368i			1.06446i	−0.846601	+	0.532228i	$0.821355\pi$
$740$			11.2083i			0.412025i
$741$	39.2238	−	9.19994i	1.44092	−	0.337968i
$742$	−8.01595			−0.294275
$743$	−33.1616			−1.21658			−0.608290	−	0.793715i	$-0.708144\pi$
$743$	−33.1616			−1.21658			−0.608290	+	0.793715i	$0.708144\pi$
$744$	−21.2968	+	4.99517i	−0.780779	+	0.183132i
$745$			13.6206i			0.499022i
$746$			57.1594i			2.09275i
$747$	12.4925	−	6.20139i	0.457077	−	0.226897i
$748$	4.48029	−	6.62085i	0.163815	−	0.242082i
$749$			18.9261i			0.691544i
$750$	0.704739	+	3.00464i	0.0257334	+	0.109714i
$751$	−34.8209			−1.27063			−0.635316	−	0.772252i	$-0.719130\pi$
$751$	−34.8209			−1.27063			−0.635316	+	0.772252i	$0.719130\pi$
$752$			7.03736i			0.256626i
$753$	−7.54231	−	32.1565i	−0.274857	−	1.17185i
$754$			66.9605i			2.43856i
$755$	6.04754			0.220092
$756$	3.89130	+	4.70372i	0.141525	+	0.171073i
$757$	36.6110			1.33065			0.665325	−	0.746554i	$-0.268293\pi$
$757$	36.6110			1.33065			0.665325	+	0.746554i	$0.268293\pi$
$758$	41.5695			1.50987
$759$	−29.9622	−	11.4329i	−1.08756	−	0.414990i
$760$	−6.01283			−0.218108
$761$	42.2181			1.53041			0.765203	−	0.643790i	$-0.222639\pi$
$761$	42.2181			1.53041			0.765203	+	0.643790i	$0.222639\pi$
$762$	0.869526	+	3.70721i	0.0314996	+	0.134298i
$763$	−16.5564			−0.599383
$764$		−	9.23924i		−	0.334264i
$765$	−2.73672	−	5.51303i	−0.0989463	−	0.199324i
$766$			29.9287i			1.08137i
$767$	18.7440			0.676806
$768$	−34.3528	+	8.05745i	−1.23960	+	0.290748i
$769$			41.4528i			1.49483i	0.664359	+	0.747414i	$0.268705\pi$
$769$			41.4528i			1.49483i	−0.664359	+	0.747414i	$0.731295\pi$
$770$	3.31195	−	4.89432i	0.119354	−	0.176379i
$771$	−11.9351	−	50.8849i	−0.429830	−	1.83258i
$772$		−	0.874711i		−	0.0314816i
$773$		−	11.7231i		−	0.421652i	−0.977524	−	0.210826i	$-0.932385\pi$
$773$		−	11.7231i		−	0.421652i	0.977524	−	0.210826i	$-0.0676154\pi$
$774$	2.76157	+	5.56309i	0.0992626	+	0.199961i
$775$	−8.58989			−0.308558
$776$	11.3019			0.405715
$777$	−3.77333	−	16.0875i	−0.135367	−	0.577137i
$778$			7.61176i			0.272895i
$779$		−	20.1338i		−	0.721367i
$780$	11.2680	−	2.64291i	0.403460	−	0.0946314i
$781$	−19.6072	−	13.2680i	−0.701599	−	0.474767i
$782$		−	20.4078i		−	0.729782i
$783$	−26.4535	+	21.8845i	−0.945371	+	0.782088i
$784$	4.96943			0.177480
$785$			9.27732i			0.331122i
$786$	−25.9214	+	6.07985i	−0.924584	+	0.216861i
$787$		−	49.1778i		−	1.75300i	−0.481403	−	0.876499i	$-0.659873\pi$
$787$		−	49.1778i		−	1.75300i	0.481403	−	0.876499i	$-0.340127\pi$
$788$	−1.37624			−0.0490266
$789$	−27.2618	+	6.39425i	−0.970545	+	0.227641i
$790$	−15.7578			−0.560636
$791$	−17.3754			−0.617799
$792$	1.95646	−	14.4975i	0.0695198	−	0.515147i
$793$	−16.6782			−0.592261
$794$	44.1430			1.56658
$795$	−7.58621	+	1.77935i	−0.269055	+	0.0631069i
$796$	−21.4254			−0.759403
$797$			6.69641i			0.237199i	0.992942	+	0.118600i	$0.0378405\pi$
$797$			6.69641i			0.237199i	−0.992942	+	0.118600i	$0.962160\pi$
$798$	−12.2879	+	2.88212i	−0.434986	+	0.102026i
$799$		−	2.90540i		−	0.102786i
$800$	−5.91405			−0.209093
$801$	−1.07697	−	2.16952i	−0.0380528	−	0.0766562i
$802$		−	44.3517i		−	1.56611i
$803$	−29.5935	−	20.0257i	−1.04433	−	0.706691i
$804$	21.0515	−	4.93762i	0.742428	−	0.174136i
$805$		−	5.58256i		−	0.196759i
$806$			87.0529i			3.06631i
$807$	12.5178	+	53.3693i	0.440647	+	1.87869i
$808$	8.07136			0.283949
$809$	−43.5440			−1.53093			−0.765463	−	0.643480i	$-0.777490\pi$
$809$	−43.5440			−1.53093			−0.765463	+	0.643480i	$0.777490\pi$
$810$	12.7735	+	9.69543i	0.448814	+	0.340663i
$811$			15.7699i			0.553757i	0.960905	+	0.276879i	$0.0893000\pi$
$811$			15.7699i			0.553757i	−0.960905	+	0.276879i	$0.910700\pi$
$812$		−	7.76256i		−	0.272412i
$813$	1.13185	+	4.82563i	0.0396957	+	0.169242i
$814$	31.5967	−	46.6928i	1.10746	−	1.63658i
$815$		−	15.2211i		−	0.533172i
$816$	17.1925	−	4.03251i	0.601859	−	0.141166i
$817$	−4.75171			−0.166241
$818$			24.5879i			0.859695i
$819$	−15.2835	+	7.58687i	−0.534049	+	0.265107i
$820$		−	5.78393i		−	0.201984i
$821$	−1.35089			−0.0471463			−0.0235732	−	0.999722i	$-0.507504\pi$
$821$	−1.35089			−0.0471463			−0.0235732	+	0.999722i	$0.507504\pi$
$822$	−1.79578	−	7.65627i	−0.0626349	−	0.267043i
$823$	−10.5161			−0.366569			−0.183284	−	0.983060i	$-0.558673\pi$
$823$	−10.5161			−0.366569			−0.183284	+	0.983060i	$0.558673\pi$
$824$	21.9127			0.763366
$825$	2.04798	−	5.36710i	0.0713014	−	0.186859i
$826$	−5.87204			−0.204315
$827$	48.5995			1.68997			0.844985	−	0.534790i	$-0.179609\pi$
$827$	48.5995			1.68997			0.844985	+	0.534790i	$0.179609\pi$
$828$	8.74870	+	17.6240i	0.304038	+	0.612475i
$829$	10.9448			0.380129			0.190064	−	0.981772i	$-0.439130\pi$
$829$	10.9448			0.380129			0.190064	+	0.981772i	$0.439130\pi$
$830$			8.28366i			0.287530i
$831$	−8.01374	−	34.1665i	−0.277994	−	1.18522i
$832$			3.40611i			0.118086i
$833$	−2.05164			−0.0710852
$834$	9.68509	+	41.2922i	0.335367	+	1.42983i
$835$		−	23.7210i		−	0.820900i
$836$	−13.1976	−	8.93075i	−0.456450	−	0.308876i
$837$	−34.3912	+	28.4512i	−1.18873	+	0.983418i
$838$		−	71.6602i		−	2.47546i
$839$			4.12409i			0.142379i	0.997463	+	0.0711897i	$0.0226796\pi$
$839$			4.12409i			0.142379i	−0.997463	+	0.0711897i	$0.977320\pi$
$840$	2.47929	−	0.581517i	0.0855436	−	0.0200642i
$841$	14.6563			0.505388
$842$	69.1942			2.38459
$843$	1.82020	−	0.426927i	0.0626910	−	0.0147042i
$844$		−	1.66598i		−	0.0573453i
$845$			19.3495i			0.665645i
$846$	3.36584	+	6.78037i	0.115720	+	0.233114i
$847$	−10.2113	+	4.09006i	−0.350866	+	0.140536i
$848$		−	22.3563i		−	0.767718i
$849$	6.11320	+	26.0635i	0.209804	+	0.894498i
$850$	3.65564			0.125387
$851$		−	53.2588i		−	1.82569i
$852$	3.31690	+	14.1416i	0.113635	+	0.484482i
$853$		−	1.79425i		−	0.0614339i	−0.999528	−	0.0307170i	$-0.990221\pi$
$853$		−	1.79425i		−	0.0614339i	0.999528	−	0.0307170i	$-0.00977905\pi$
$854$	5.22489			0.178792
$855$	−10.9894	+	5.45522i	−0.375828	+	0.186565i
$856$	−27.8263			−0.951084
$857$	23.6109			0.806532			0.403266	−	0.915083i	$-0.367875\pi$
$857$	23.6109			0.806532			0.403266	+	0.915083i	$0.367875\pi$
$858$	−54.3921	−	20.7549i	−1.85691	−	0.708560i
$859$	46.2827			1.57915			0.789573	−	0.613657i	$-0.210302\pi$
$859$	46.2827			1.57915			0.789573	+	0.613657i	$0.210302\pi$
$860$	−1.36505			−0.0465477
$861$	1.94719	+	8.30181i	0.0663601	+	0.282925i
$862$	12.5488			0.427415
$863$			27.4490i			0.934373i	0.884159	+	0.467187i	$0.154732\pi$
$863$			27.4490i			0.934373i	−0.884159	+	0.467187i	$0.845268\pi$
$864$	−23.6780	+	19.5884i	−0.805542	+	0.666410i
$865$		−	7.98486i		−	0.271493i
$866$	2.97130			0.100969
$867$	21.5689	−	5.05898i	0.732518	−	0.171812i
$868$		−	10.0918i		−	0.342539i
$869$	24.2920	+	16.4382i	0.824050	+	0.557629i
$870$	−4.65642	−	19.8526i	−0.157867	−	0.673065i
$871$			60.4370i			2.04783i
$872$		−	24.3423i		−	0.824335i
$873$	20.6560	−	10.2538i	0.699099	−	0.347039i
$874$	−40.6798			−1.37601
$875$	1.00000			0.0338062
$876$	5.00626	+	21.3441i	0.169146	+	0.721151i
$877$		−	33.4212i		−	1.12855i	−0.825586	−	0.564276i	$-0.809155\pi$
$877$		−	33.4212i		−	1.12855i	0.825586	−	0.564276i	$-0.190845\pi$
$878$		−	24.2785i		−	0.819360i
$879$	2.27867	−	0.534462i	0.0768577	−	0.0180270i
$880$	13.6501	+	9.23695i	0.460146	+	0.311378i
$881$			13.9557i			0.470178i	0.971974	+	0.235089i	$0.0755382\pi$
$881$			13.9557i			0.470178i	−0.971974	+	0.235089i	$0.924462\pi$
$882$	4.78796	−	2.37679i	0.161219	−	0.0800305i
$883$	−40.8787			−1.37568			−0.687839	−	0.725863i	$-0.741441\pi$
$883$	−40.8787			−1.37568			−0.687839	+	0.725863i	$0.741441\pi$
$884$		−	13.7094i		−	0.461096i
$885$	−5.55724	+	1.30345i	−0.186805	+	0.0438150i
$886$		−	40.5118i		−	1.36102i
$887$	48.6792			1.63449			0.817243	−	0.576293i	$-0.195501\pi$
$887$	48.6792			1.63449			0.817243	+	0.576293i	$0.195501\pi$
$888$	23.6529	−	5.54779i	0.793740	−	0.186172i
$889$	1.23383			0.0413812
$890$	1.43859			0.0482215
$891$	−9.57734	−	28.2714i	−0.320853	−	0.947129i
$892$	13.7800			0.461390
$893$	−5.79145			−0.193804
$894$	−40.9252	+	9.59900i	−1.36874	+	0.321039i
$895$	4.27426			0.142873
$896$			10.7610i			0.359501i
$897$	−53.5425	+	12.5584i	−1.78773	+	0.419313i
$898$			50.3184i			1.67915i
$899$	56.7559			1.89291
$900$	−3.15697	+	1.56715i	−0.105232	+	0.0522383i
$901$			9.22986i			0.307491i
$902$	−16.3052	+	24.0954i	−0.542902	+	0.802287i
$903$	1.95928	−	0.459550i	0.0652009	−	0.0152929i
$904$		−	25.5465i		−	0.849662i
$905$			9.72903i			0.323404i
$906$	4.26194	+	18.1707i	0.141593	+	0.603681i
$907$	45.5925			1.51388			0.756938	−	0.653487i	$-0.226695\pi$
$907$	45.5925			1.51388			0.756938	+	0.653487i	$0.226695\pi$
$908$	−31.1774			−1.03466
$909$	14.7516	−	7.32284i	0.489281	−	0.242883i
$910$		−	10.1343i		−	0.335950i
$911$			38.6330i			1.27997i	0.768388	+	0.639984i	$0.221059\pi$
$911$			38.6330i			1.27997i	−0.768388	+	0.639984i	$0.778941\pi$
$912$	−8.03817	−	34.2706i	−0.266170	−	1.13481i
$913$	8.64138	−	12.7700i	0.285988	−	0.422626i
$914$			53.6718i			1.77530i
$915$	4.94478	−	1.15980i	0.163469	−	0.0383417i
$916$	−5.58352			−0.184485
$917$			8.62710i			0.284892i
$918$	14.6360	−	12.1081i	0.483061	−	0.399627i
$919$			49.8765i			1.64527i	0.568566	+	0.822637i	$0.307498\pi$
$919$			49.8765i			1.64527i	−0.568566	+	0.822637i	$0.692502\pi$
$920$	8.20784			0.270604
$921$	8.94429	+	38.1339i	0.294725	+	1.25655i
$922$	−17.2074			−0.566694
$923$	−40.5993			−1.33634
$924$	6.30553	+	2.40606i	0.207437	+	0.0791536i
$925$	9.54021			0.313680
$926$	−9.57072			−0.314513
$927$	40.0488	−	19.8806i	1.31538	−	0.652965i
$928$	39.0758			1.28273
$929$			24.7841i			0.813140i	0.913620	+	0.406570i	$0.133275\pi$
$929$			24.7841i			0.813140i	−0.913620	+	0.406570i	$0.866725\pi$
$930$	−6.05363	−	25.8096i	−0.198506	−	0.846329i
$931$			4.08963i			0.134032i
$932$	8.24495			0.270072
$933$	−5.23524	−	22.3204i	−0.171394	−	0.730736i
$934$			10.6296i			0.347810i
$935$	−5.63550	−	3.81350i	−0.184300	−	0.124715i
$936$	−11.1547	−	22.4708i	−0.364603	−	0.734480i
$937$		−	10.8352i		−	0.353972i	−0.984213	−	0.176986i	$-0.943365\pi$
$937$		−	10.8352i		−	0.353972i	0.984213	−	0.176986i	$-0.0566347\pi$
$938$		−	18.9335i		−	0.618200i
$939$	10.2946	−	2.41461i	0.335953	−	0.0787978i
$940$	−1.66374			−0.0542652
$941$	−15.8011			−0.515101			−0.257551	−	0.966265i	$-0.582915\pi$
$941$	−15.8011			−0.515101			−0.257551	+	0.966265i	$0.582915\pi$
$942$	−27.8751	+	6.53809i	−0.908219	+	0.213023i
$943$			27.4837i			0.894991i
$944$		−	16.3770i		−	0.533026i
$945$	4.00368	−	3.31218i	0.130240	−	0.107745i
$946$	5.68667	+	3.84813i	0.184890	+	0.125113i
$947$			25.6919i			0.834873i	0.908706	+	0.417437i	$0.137071\pi$
$947$			25.6919i			0.834873i	−0.908706	+	0.417437i	$0.862929\pi$
$948$	−4.10943	−	17.5205i	−0.133468	−	0.569039i
$949$	−61.2772			−1.98914
$950$		−	7.28694i		−	0.236420i
$951$	1.19825	+	5.10873i	0.0388560	+	0.165662i
$952$		−	3.01646i		−	0.0977639i
$953$	−24.3263			−0.788007			−0.394004	−	0.919109i	$-0.628910\pi$
$953$	−24.3263			−0.788007			−0.394004	+	0.919109i	$0.628910\pi$
$954$	−10.6926	−	21.5399i	−0.346186	−	0.697380i
$955$	−7.86420			−0.254479
$956$	6.64217			0.214823
$957$	−13.5316	+	35.4620i	−0.437414	+	1.14632i
$958$	−12.8506			−0.415185
$959$	−2.54814			−0.0822839
$960$	−0.236860	−	1.00985i	−0.00764462	−	0.0325927i
$961$	42.7862			1.38020
$962$		−	96.6837i		−	3.11721i
$963$	−50.8568	+	25.2458i	−1.63884	+	0.813534i
$964$		−	6.36122i		−	0.204881i
$965$	−0.744532			−0.0239673
$966$	16.7736	−	3.93425i	0.539682	−	0.126582i
$967$			58.6009i			1.88448i	0.334940	+	0.942239i	$0.391284\pi$
$967$			58.6009i			1.88448i	−0.334940	+	0.942239i	$0.608716\pi$
$968$	−6.01347	−	15.0134i	−0.193280	−	0.482548i
$969$	3.31858	+	14.1487i	0.106608	+	0.454522i
$970$			13.6968i			0.439777i
$971$			20.9457i			0.672179i	0.941830	+	0.336089i	$0.109104\pi$
$971$			20.9457i			0.672179i	−0.941830	+	0.336089i	$0.890896\pi$
$972$	−7.44884	+	16.7308i	−0.238922	+	0.536641i
$973$	13.7428			0.440574
$974$	2.77607			0.0889509
$975$	−2.24958	−	9.59104i	−0.0720442	−	0.307159i
$976$			14.5721i			0.466441i
$977$			1.66886i			0.0533917i	0.999644	+	0.0266958i	$0.00849856\pi$
$977$			1.66886i			0.0533917i	−0.999644	+	0.0266958i	$0.991501\pi$
$978$	45.7340	−	10.7269i	1.46241	−	0.343009i
$979$	−2.21771	−	1.50071i	−0.0708784	−	0.0479629i
$980$			1.17485i			0.0375291i
$981$	−22.0849	−	44.4892i	−0.705116	−	1.42043i
$982$	−43.2605			−1.38050
$983$			35.9735i			1.14738i	0.819074	+	0.573688i	$0.194488\pi$
$983$			35.9735i			1.14738i	−0.819074	+	0.573688i	$0.805512\pi$
$984$	−12.2059	+	2.86288i	−0.389109	+	0.0912654i
$985$			1.17142i			0.0373246i
$986$	−24.1539			−0.769216
$987$	2.38800	−	0.560106i	0.0760110	−	0.0178284i
$988$	−27.3275			−0.869403
$989$	6.48633			0.206253
$990$	17.5695	+	2.37103i	0.558396	+	0.0753564i
$991$	46.6480			1.48182			0.740912	−	0.671602i	$-0.234394\pi$
$991$	46.6480			1.48182			0.740912	+	0.671602i	$0.234394\pi$
$992$	50.8010			1.61293
$993$	−14.9155	+	3.49844i	−0.473330	+	0.111019i
$994$	12.7188			0.403415
$995$			18.2367i			0.578144i
$996$	−9.21031	+	2.16028i	−0.291840	+	0.0684510i
$997$			30.3678i			0.961757i	0.876787	+	0.480878i	$0.159682\pi$
$997$			30.3678i			0.961757i	−0.876787	+	0.480878i	$0.840318\pi$
$998$	−60.1811			−1.90500
$999$	38.1960	−	31.5988i	1.20847	−	0.999743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.8	yes	40
3.2	odd	2		1155.2.l.e.1121.33	✓	40
11.10	odd	2		1155.2.l.e.1121.34	yes	40
33.32	even	2	inner	1155.2.l.f.1121.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.33	✓	40	3.2	odd	2
1155.2.l.e.1121.34	yes	40	11.10	odd	2
1155.2.l.f.1121.7	yes	40	33.32	even	2	inner
1155.2.l.f.1121.8	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)

\(f(q)\)	\(=\)	\(q-1.78181 q^{2} +(-1.68629 + 0.395519i) q^{3} +1.17485 q^{4} -1.00000i q^{5} +(3.00464 - 0.704739i) q^{6} -1.00000i q^{7} +1.47026 q^{8} +(2.68713 - 1.33392i) q^{9} +O(q^{10})\)	\(q-1.78181 q^{2} +(-1.68629 + 0.395519i) q^{3} +1.17485 q^{4} -1.00000i q^{5} +(3.00464 - 0.704739i) q^{6} -1.00000i q^{7} +1.47026 q^{8} +(2.68713 - 1.33392i) q^{9} +1.78181i q^{10} +(1.85876 - 2.74682i) q^{11} +(-1.98113 + 0.464674i) q^{12} -5.68767i q^{13} +1.78181i q^{14} +(0.395519 + 1.68629i) q^{15} -4.96943 q^{16} +2.05164 q^{17} +(-4.78796 + 2.37679i) q^{18} -4.08963i q^{19} -1.17485i q^{20} +(0.395519 + 1.68629i) q^{21} +(-3.31195 + 4.89432i) q^{22} +5.58256i q^{23} +(-2.47929 + 0.581517i) q^{24} -1.00000 q^{25} +10.1343i q^{26} +(-4.00368 + 3.31218i) q^{27} -1.17485i q^{28} +6.60729 q^{29} +(-0.704739 - 3.00464i) q^{30} +8.58989 q^{31} +5.91405 q^{32} +(-2.04798 + 5.36710i) q^{33} -3.65564 q^{34} -1.00000 q^{35} +(3.15697 - 1.56715i) q^{36} -9.54021 q^{37} +7.28694i q^{38} +(2.24958 + 9.59104i) q^{39} -1.47026i q^{40} +4.92313 q^{41} +(-0.704739 - 3.00464i) q^{42} -1.16189i q^{43} +(2.18376 - 3.22710i) q^{44} +(-1.33392 - 2.68713i) q^{45} -9.94706i q^{46} -1.41613i q^{47} +(8.37988 - 1.96550i) q^{48} -1.00000 q^{49} +1.78181 q^{50} +(-3.45966 + 0.811463i) q^{51} -6.68214i q^{52} +4.49877i q^{53} +(7.13381 - 5.90167i) q^{54} +(-2.74682 - 1.85876i) q^{55} -1.47026i q^{56} +(1.61752 + 6.89629i) q^{57} -11.7729 q^{58} +3.29555i q^{59} +(0.464674 + 1.98113i) q^{60} -2.93235i q^{61} -15.3056 q^{62} +(-1.33392 - 2.68713i) q^{63} -0.598859 q^{64} -5.68767 q^{65} +(3.64911 - 9.56316i) q^{66} -10.6260 q^{67} +2.41037 q^{68} +(-2.20801 - 9.41380i) q^{69} +1.78181 q^{70} -7.13813i q^{71} +(3.95079 - 1.96121i) q^{72} -10.7737i q^{73} +16.9988 q^{74} +(1.68629 - 0.395519i) q^{75} -4.80469i q^{76} +(-2.74682 - 1.85876i) q^{77} +(-4.00832 - 17.0894i) q^{78} +8.84368i q^{79} +4.96943i q^{80} +(5.44134 - 7.16881i) q^{81} -8.77209 q^{82} +4.64901 q^{83} +(0.464674 + 1.98113i) q^{84} -2.05164i q^{85} +2.07027i q^{86} +(-11.1418 + 2.61331i) q^{87} +(2.73286 - 4.03855i) q^{88} -0.807374i q^{89} +(2.37679 + 4.78796i) q^{90} -5.68767 q^{91} +6.55866i q^{92} +(-14.4850 + 3.39746i) q^{93} +2.52328i q^{94} -4.08963 q^{95} +(-9.97279 + 2.33912i) q^{96} +7.68700 q^{97} +1.78181 q^{98} +(1.33069 - 9.86049i) 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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