LMFDB - Embedded newform 1155.2.l.e.1121.9

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			1121.9
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88704 q^{2} +(1.57144 - 0.728399i) q^{3} +1.56093 q^{4} -1.00000i q^{5} +(-2.96538 + 1.37452i) q^{6} +1.00000i q^{7} +0.828540 q^{8} +(1.93887 - 2.28928i) q^{9} +O(q^{10})$	\(q-1.88704 q^{2} +(1.57144 - 0.728399i) q^{3} +1.56093 q^{4} -1.00000i q^{5} +(-2.96538 + 1.37452i) q^{6} +1.00000i q^{7} +0.828540 q^{8} +(1.93887 - 2.28928i) q^{9} +1.88704i q^{10} +(-0.471887 + 3.28288i) q^{11} +(2.45292 - 1.13698i) q^{12} +4.81609i q^{13} -1.88704i q^{14} +(-0.728399 - 1.57144i) q^{15} -4.68535 q^{16} -6.59628 q^{17} +(-3.65873 + 4.31996i) q^{18} +3.38911i q^{19} -1.56093i q^{20} +(0.728399 + 1.57144i) q^{21} +(0.890472 - 6.19494i) q^{22} +4.14617i q^{23} +(1.30200 - 0.603508i) q^{24} -1.00000 q^{25} -9.08818i q^{26} +(1.37932 - 5.00974i) q^{27} +1.56093i q^{28} -8.19160 q^{29} +(1.37452 + 2.96538i) q^{30} -7.59366 q^{31} +7.18439 q^{32} +(1.64971 + 5.50259i) q^{33} +12.4475 q^{34} +1.00000 q^{35} +(3.02644 - 3.57341i) q^{36} -1.20065 q^{37} -6.39539i q^{38} +(3.50804 + 7.56822i) q^{39} -0.828540i q^{40} -0.331296 q^{41} +(-1.37452 - 2.96538i) q^{42} -6.55160i q^{43} +(-0.736584 + 5.12436i) q^{44} +(-2.28928 - 1.93887i) q^{45} -7.82401i q^{46} +7.08376i q^{47} +(-7.36277 + 3.41281i) q^{48} -1.00000 q^{49} +1.88704 q^{50} +(-10.3657 + 4.80473i) q^{51} +7.51760i q^{52} -1.29776i q^{53} +(-2.60283 + 9.45359i) q^{54} +(3.28288 + 0.471887i) q^{55} +0.828540i q^{56} +(2.46862 + 5.32579i) q^{57} +15.4579 q^{58} +13.1893i q^{59} +(-1.13698 - 2.45292i) q^{60} +1.41421i q^{61} +14.3296 q^{62} +(2.28928 + 1.93887i) q^{63} -4.18654 q^{64} +4.81609 q^{65} +(-3.11307 - 10.3836i) q^{66} -12.6154 q^{67} -10.2964 q^{68} +(3.02007 + 6.51548i) q^{69} -1.88704 q^{70} -5.43492i q^{71} +(1.60643 - 1.89676i) q^{72} -8.50372i q^{73} +2.26568 q^{74} +(-1.57144 + 0.728399i) q^{75} +5.29017i q^{76} +(-3.28288 - 0.471887i) q^{77} +(-6.61982 - 14.2816i) q^{78} -8.53441i q^{79} +4.68535i q^{80} +(-1.48157 - 8.87721i) q^{81} +0.625170 q^{82} +13.3014 q^{83} +(1.13698 + 2.45292i) q^{84} +6.59628i q^{85} +12.3632i q^{86} +(-12.8726 + 5.96675i) q^{87} +(-0.390977 + 2.72000i) q^{88} -1.23222i q^{89} +(4.31996 + 3.65873i) q^{90} -4.81609 q^{91} +6.47190i q^{92} +(-11.9330 + 5.53121i) q^{93} -13.3674i q^{94} +3.38911 q^{95} +(11.2899 - 5.23310i) q^{96} +18.3387 q^{97} +1.88704 q^{98} +(6.60050 + 7.44536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.88704			−1.33434			−0.667171	−	0.744905i	$-0.732495\pi$
$2$	−1.88704			−1.33434			−0.667171	+	0.744905i	$0.732495\pi$
$3$	1.57144	−	0.728399i	0.907273	−	0.420541i
$3$	1.57144	−	0.728399i	0.907273	−	0.420541i
$4$	1.56093			0.780466
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.96538	+	1.37452i	−1.21061	+	0.561146i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.828540			0.292933
$9$	1.93887	−	2.28928i	0.646290	−	0.763092i
$10$			1.88704i			0.596735i
$11$	−0.471887	+	3.28288i	−0.142279	+	0.989827i
$11$	−0.471887	+	3.28288i	−0.142279	+	0.989827i
$12$	2.45292	−	1.13698i	0.708096	−	0.328218i
$13$			4.81609i			1.33574i	0.744276	+	0.667872i	$0.232795\pi$
$13$			4.81609i			1.33574i	−0.744276	+	0.667872i	$0.767205\pi$
$14$		−	1.88704i		−	0.504334i
$15$	−0.728399	−	1.57144i	−0.188072	−	0.405745i
$16$	−4.68535			−1.17134
$17$	−6.59628			−1.59983			−0.799917	−	0.600111i	$-0.795123\pi$
$17$	−6.59628			−1.59983			−0.799917	+	0.600111i	$0.795123\pi$
$18$	−3.65873	+	4.31996i	−0.862371	+	1.01823i
$19$			3.38911i			0.777515i	0.921340	+	0.388757i	$0.127096\pi$
$19$			3.38911i			0.777515i	−0.921340	+	0.388757i	$0.872904\pi$
$20$		−	1.56093i		−	0.349035i
$21$	0.728399	+	1.57144i	0.158950	+	0.342917i
$22$	0.890472	−	6.19494i	0.189849	−	1.32077i
$23$			4.14617i			0.864537i	0.901745	+	0.432269i	$0.142287\pi$
$23$			4.14617i			0.864537i	−0.901745	+	0.432269i	$0.857713\pi$
$24$	1.30200	−	0.603508i	0.265770	−	0.123190i
$25$	−1.00000			−0.200000
$26$		−	9.08818i		−	1.78234i
$27$	1.37932	−	5.00974i	0.265450	−	0.964125i
$28$			1.56093i			0.294988i
$29$	−8.19160			−1.52114			−0.760571	−	0.649255i	$-0.775081\pi$
$29$	−8.19160			−1.52114			−0.760571	+	0.649255i	$0.775081\pi$
$30$	1.37452	+	2.96538i	0.250952	+	0.541402i
$31$	−7.59366			−1.36386			−0.681931	−	0.731417i	$-0.738859\pi$
$31$	−7.59366			−1.36386			−0.681931	+	0.731417i	$0.738859\pi$
$32$	7.18439			1.27003
$33$	1.64971	+	5.50259i	0.287177	+	0.957878i
$34$	12.4475			2.13472
$35$	1.00000			0.169031
$36$	3.02644	−	3.57341i	0.504407	−	0.595568i
$37$	−1.20065			−0.197386			−0.0986930	−	0.995118i	$-0.531466\pi$
$37$	−1.20065			−0.197386			−0.0986930	+	0.995118i	$0.531466\pi$
$38$		−	6.39539i		−	1.03747i
$39$	3.50804	+	7.56822i	0.561736	+	1.21188i
$40$		−	0.828540i		−	0.131004i
$41$	−0.331296			−0.0517398			−0.0258699	−	0.999665i	$-0.508236\pi$
$41$	−0.331296			−0.0517398			−0.0258699	+	0.999665i	$0.508236\pi$
$42$	−1.37452	−	2.96538i	−0.212093	−	0.457568i
$43$		−	6.55160i		−	0.999110i	−0.866282	−	0.499555i	$-0.833497\pi$
$43$		−	6.55160i		−	0.999110i	0.866282	−	0.499555i	$-0.166503\pi$
$44$	−0.736584	+	5.12436i	−0.111044	+	0.772526i
$45$	−2.28928	−	1.93887i	−0.341265	−	0.289030i
$46$		−	7.82401i		−	1.15359i
$47$			7.08376i			1.03327i	0.856205	+	0.516637i	$0.172816\pi$
$47$			7.08376i			1.03327i	−0.856205	+	0.516637i	$0.827184\pi$
$48$	−7.36277	+	3.41281i	−1.06272	+	0.492597i
$49$	−1.00000			−0.142857
$50$	1.88704			0.266868
$51$	−10.3657	+	4.80473i	−1.45149	+	0.672796i
$52$			7.51760i			1.04250i
$53$		−	1.29776i		−	0.178261i	−0.996020	−	0.0891306i	$-0.971591\pi$
$53$		−	1.29776i		−	0.178261i	0.996020	−	0.0891306i	$-0.0284089\pi$
$54$	−2.60283	+	9.45359i	−0.354200	+	1.28647i
$55$	3.28288	+	0.471887i	0.442664	+	0.0636293i
$56$			0.828540i			0.110718i
$57$	2.46862	+	5.32579i	0.326977	+	0.705418i
$58$	15.4579			2.02972
$59$			13.1893i			1.71711i	0.512725	+	0.858553i	$0.328636\pi$
$59$			13.1893i			1.71711i	−0.512725	+	0.858553i	$0.671364\pi$
$60$	−1.13698	−	2.45292i	−0.146784	−	0.316670i
$61$			1.41421i			0.181071i	0.995893	+	0.0905353i	$0.0288578\pi$
$61$			1.41421i			0.181071i	−0.995893	+	0.0905353i	$0.971142\pi$
$62$	14.3296			1.81986
$63$	2.28928	+	1.93887i	0.288422	+	0.244275i
$64$	−4.18654			−0.523318
$65$	4.81609			0.597363
$66$	−3.11307	−	10.3836i	−0.383192	−	1.27814i
$67$	−12.6154			−1.54122			−0.770609	−	0.637308i	$-0.780048\pi$
$67$	−12.6154			−1.54122			−0.770609	+	0.637308i	$0.780048\pi$
$68$	−10.2964			−1.24862
$69$	3.02007	+	6.51548i	0.363574	+	0.784371i
$70$	−1.88704			−0.225545
$71$		−	5.43492i		−	0.645006i	−0.946568	−	0.322503i	$-0.895476\pi$
$71$		−	5.43492i		−	0.645006i	0.946568	−	0.322503i	$-0.104524\pi$
$72$	1.60643	−	1.89676i	0.189320	−	0.223535i
$73$		−	8.50372i		−	0.995285i	−0.867382	−	0.497642i	$-0.834199\pi$
$73$		−	8.50372i		−	0.995285i	0.867382	−	0.497642i	$-0.165801\pi$
$74$	2.26568			0.263380
$75$	−1.57144	+	0.728399i	−0.181455	+	0.0841083i
$76$			5.29017i			0.606824i
$77$	−3.28288	−	0.471887i	−0.374119	−	0.0537765i
$78$	−6.61982	−	14.2816i	−0.749547	−	1.61707i
$79$		−	8.53441i		−	0.960196i	−0.877215	−	0.480098i	$-0.840601\pi$
$79$		−	8.53441i		−	0.960196i	0.877215	−	0.480098i	$-0.159399\pi$
$80$			4.68535i			0.523839i
$81$	−1.48157	−	8.87721i	−0.164619	−	0.986357i
$82$	0.625170			0.0690385
$83$	13.3014			1.46001			0.730007	−	0.683440i	$-0.239517\pi$
$83$	13.3014			1.46001			0.730007	+	0.683440i	$0.239517\pi$
$84$	1.13698	+	2.45292i	0.124055	+	0.267635i
$85$			6.59628i			0.715467i
$86$			12.3632i			1.33315i
$87$	−12.8726	+	5.96675i	−1.38009	+	0.639703i
$88$	−0.390977	+	2.72000i	−0.0416783	+	0.289953i
$89$		−	1.23222i		−	0.130615i	−0.997865	−	0.0653075i	$-0.979197\pi$
$89$		−	1.23222i		−	0.130615i	0.997865	−	0.0653075i	$-0.0208028\pi$
$90$	4.31996	+	3.65873i	0.455364	+	0.385664i
$91$	−4.81609			−0.504864
$92$			6.47190i			0.674742i
$93$	−11.9330	+	5.53121i	−1.23739	+	0.573560i
$94$		−	13.3674i		−	1.37874i
$95$	3.38911			0.347715
$96$	11.2899	−	5.23310i	1.15227	−	0.534101i
$97$	18.3387			1.86201			0.931006	−	0.365003i	$-0.118932\pi$
$97$	18.3387			1.86201			0.931006	+	0.365003i	$0.118932\pi$
$98$	1.88704			0.190620
$99$	6.60050	+	7.44536i	0.663375	+	0.748287i
$100$	−1.56093			−0.156093
$101$	−17.3141			−1.72281			−0.861407	−	0.507916i	$-0.830416\pi$
$101$	−17.3141			−1.72281			−0.861407	+	0.507916i	$0.830416\pi$
$102$	19.5605	−	9.06673i	1.93678	−	0.897740i
$103$	7.54916			0.743841			0.371920	−	0.928265i	$-0.378699\pi$
$103$	7.54916			0.743841			0.371920	+	0.928265i	$0.378699\pi$
$104$			3.99032i			0.391284i
$105$	1.57144	−	0.728399i	0.153357	−	0.0710845i
$106$			2.44893i			0.237861i
$107$	10.7755			1.04171			0.520855	−	0.853645i	$-0.325613\pi$
$107$	10.7755			1.04171			0.520855	+	0.853645i	$0.325613\pi$
$108$	2.15302	−	7.81986i	0.207174	−	0.752467i
$109$		−	1.57800i		−	0.151145i	−0.997140	−	0.0755726i	$-0.975922\pi$
$109$		−	1.57800i		−	0.151145i	0.997140	−	0.0755726i	$-0.0240785\pi$
$110$	−6.19494	−	0.890472i	−0.590665	−	0.0849031i
$111$	−1.88676	+	0.874554i	−0.179083	+	0.0830090i
$112$		−	4.68535i		−	0.442724i
$113$			17.1721i			1.61541i	0.589584	+	0.807707i	$0.299292\pi$
$113$			17.1721i			1.61541i	−0.589584	+	0.807707i	$0.700708\pi$
$114$	−4.65840	−	10.0500i	−0.436299	−	0.941269i
$115$	4.14617			0.386633
$116$	−12.7865			−1.18720
$117$	11.0254	+	9.33778i	1.01930	+	0.863278i
$118$		−	24.8889i		−	2.29120i
$119$		−	6.59628i		−	0.604680i
$120$	−0.603508	−	1.30200i	−0.0550925	−	0.118856i
$121$	−10.5546	−	3.09830i	−0.959513	−	0.281664i
$122$		−	2.66867i		−	0.241610i
$123$	−0.520613	+	0.241316i	−0.0469421	+	0.0217587i
$124$	−11.8532			−1.06445
$125$			1.00000i			0.0894427i
$126$	−4.31996	−	3.65873i	−0.384853	−	0.325946i
$127$			6.89191i			0.611558i	0.952102	+	0.305779i	$0.0989170\pi$
$127$			6.89191i			0.611558i	−0.952102	+	0.305779i	$0.901083\pi$
$128$	−6.46859			−0.571748
$129$	−4.77218	−	10.2955i	−0.420167	−	0.906466i
$130$	−9.08818			−0.797086
$131$	7.32535			0.640019			0.320009	−	0.947414i	$-0.396314\pi$
$131$	7.32535			0.640019			0.320009	+	0.947414i	$0.396314\pi$
$132$	2.57508	+	8.58917i	0.224132	+	0.747591i
$133$	−3.38911			−0.293873
$134$	23.8058			2.05651
$135$	−5.00974	−	1.37932i	−0.431170	−	0.118713i
$136$	−5.46528			−0.468644
$137$			10.8763i			0.929222i	0.885515	+	0.464611i	$0.153806\pi$
$137$			10.8763i			0.929222i	−0.885515	+	0.464611i	$0.846194\pi$
$138$	−5.69900	−	12.2950i	−0.485131	−	1.04662i
$139$			12.0609i			1.02300i	0.859285	+	0.511498i	$0.170909\pi$
$139$			12.0609i			1.02300i	−0.859285	+	0.511498i	$0.829091\pi$
$140$	1.56093			0.131923
$141$	5.15981	+	11.1317i	0.434534	+	0.937461i
$142$			10.2559i			0.860658i
$143$	−15.8107	−	2.27265i	−1.32215	−	0.190049i
$144$	−9.08429	+	10.7261i	−0.757024	+	0.893839i
$145$			8.19160i			0.680275i
$146$			16.0469i			1.32805i
$147$	−1.57144	+	0.728399i	−0.129610	+	0.0600774i
$148$	−1.87414			−0.154053
$149$	−14.7746			−1.21038			−0.605189	−	0.796082i	$-0.706903\pi$
$149$	−14.7746			−1.21038			−0.605189	+	0.796082i	$0.706903\pi$
$150$	2.96538	−	1.37452i	0.242122	−	0.112229i
$151$			17.2699i			1.40541i	0.711484	+	0.702703i	$0.248024\pi$
$151$			17.2699i			1.40541i	−0.711484	+	0.702703i	$0.751976\pi$
$152$			2.80801i			0.227760i
$153$	−12.7893	+	15.1007i	−1.03396	+	1.22082i
$154$	6.19494	+	0.890472i	0.499203	+	0.0717563i
$155$			7.59366i			0.609937i
$156$	5.47581	+	11.8135i	0.438416	+	0.945835i
$157$	8.20632			0.654936			0.327468	−	0.944862i	$-0.393805\pi$
$157$	8.20632			0.654936			0.327468	+	0.944862i	$0.393805\pi$
$158$			16.1048i			1.28123i
$159$	−0.945288	−	2.03936i	−0.0749662	−	0.161732i
$160$		−	7.18439i		−	0.567976i
$161$	−4.14617			−0.326764
$162$	2.79579	+	16.7517i	0.219658	+	1.31614i
$163$	3.02205			0.236705			0.118353	−	0.992972i	$-0.462239\pi$
$163$	3.02205			0.236705			0.118353	+	0.992972i	$0.462239\pi$
$164$	−0.517131			−0.0403811
$165$	5.50259	−	1.64971i	0.428376	−	0.128429i
$166$	−25.1002			−1.94816
$167$	4.24922			0.328814			0.164407	−	0.986393i	$-0.447429\pi$
$167$	4.24922			0.328814			0.164407	+	0.986393i	$0.447429\pi$
$168$	0.603508	+	1.30200i	0.0465616	+	0.100452i
$169$	−10.1948			−0.784212
$170$		−	12.4475i		−	0.954678i
$171$	7.75860	+	6.57104i	0.593315	+	0.502500i
$172$		−	10.2266i		−	0.779772i
$173$	13.0991			0.995904			0.497952	−	0.867204i	$-0.334086\pi$
$173$	13.0991			0.995904			0.497952	+	0.867204i	$0.334086\pi$
$174$	24.2912	−	11.2595i	1.84151	−	0.853582i
$175$		−	1.00000i		−	0.0755929i
$176$	2.21096	−	15.3815i	0.166657	−	1.15942i
$177$	9.60710	+	20.7263i	0.722114	+	1.55788i
$178$			2.32525i			0.174285i
$179$		−	2.54943i		−	0.190553i	−0.995451	−	0.0952766i	$-0.969626\pi$
$179$		−	2.54943i		−	0.190553i	0.995451	−	0.0952766i	$-0.0303735\pi$
$180$	−3.57341	−	3.02644i	−0.266346	−	0.225578i
$181$	−22.7396			−1.69022			−0.845111	−	0.534591i	$-0.820466\pi$
$181$	−22.7396			−1.69022			−0.845111	+	0.534591i	$0.820466\pi$
$182$	9.08818			0.673660
$183$	1.03011	+	2.22234i	0.0761477	+	0.164280i
$184$			3.43527i			0.253251i
$185$			1.20065i			0.0882737i
$186$	22.5181	−	10.4376i	1.65111	−	0.765325i
$187$	3.11270	−	21.6548i	0.227623	−	1.58356i
$188$			11.0573i			0.806435i
$189$	5.00974	+	1.37932i	0.364405	+	0.100331i
$190$	−6.39539			−0.463971
$191$		−	14.3775i		−	1.04032i	−0.854068	−	0.520161i	$-0.825872\pi$
$191$		−	14.3775i		−	1.04032i	0.854068	−	0.520161i	$-0.174128\pi$
$192$	−6.57891	+	3.04947i	−0.474792	+	0.220077i
$193$			4.94027i			0.355608i	0.984066	+	0.177804i	$0.0568993\pi$
$193$			4.94027i			0.355608i	−0.984066	+	0.177804i	$0.943101\pi$
$194$	−34.6059			−2.48456
$195$	7.56822	−	3.50804i	0.541971	−	0.251216i
$196$	−1.56093			−0.111495
$197$	17.5393			1.24962			0.624810	−	0.780777i	$-0.285176\pi$
$197$	17.5393			1.24962			0.624810	+	0.780777i	$0.285176\pi$
$198$	−12.4554	−	14.0497i	−0.885169	−	0.998470i
$199$	4.87616			0.345662			0.172831	−	0.984951i	$-0.444709\pi$
$199$	4.87616			0.345662			0.172831	+	0.984951i	$0.444709\pi$
$200$	−0.828540			−0.0585866
$201$	−19.8244	+	9.18906i	−1.39831	+	0.648146i
$202$	32.6724			2.29882
$203$		−	8.19160i		−	0.574937i
$204$	−16.1801	+	7.49985i	−1.13284	+	0.525095i
$205$			0.331296i			0.0231387i
$206$	−14.2456			−0.992537
$207$	9.49174	+	8.03889i	0.659721	+	0.558741i
$208$		−	22.5651i		−	1.56461i
$209$	−11.1260	−	1.59928i	−0.769605	−	0.110624i
$210$	−2.96538	+	1.37452i	−0.204631	+	0.0948509i
$211$			3.19746i			0.220122i	0.993925	+	0.110061i	$0.0351046\pi$
$211$			3.19746i			0.220122i	−0.993925	+	0.110061i	$0.964895\pi$
$212$		−	2.02572i		−	0.139127i
$213$	−3.95879	−	8.54067i	−0.271252	−	0.585197i
$214$	−20.3339			−1.39000
$215$	−6.55160			−0.446816
$216$	1.14282	−	4.15077i	0.0777590	−	0.282424i
$217$		−	7.59366i		−	0.515491i
$218$			2.97776i			0.201679i
$219$	−6.19410	−	13.3631i	−0.418559	−	0.902995i
$220$	5.12436	+	0.736584i	0.345484	+	0.0496605i
$221$		−	31.7683i		−	2.13697i
$222$	3.56039	−	1.65032i	0.238958	−	0.110762i
$223$	20.2335			1.35493			0.677467	−	0.735554i	$-0.263078\pi$
$223$	20.2335			1.35493			0.677467	+	0.735554i	$0.263078\pi$
$224$			7.18439i			0.480027i
$225$	−1.93887	+	2.28928i	−0.129258	+	0.152618i
$226$		−	32.4045i		−	2.15551i
$227$	−1.32772			−0.0881237			−0.0440619	−	0.999029i	$-0.514030\pi$
$227$	−1.32772			−0.0881237			−0.0440619	+	0.999029i	$0.514030\pi$
$228$	3.85335	+	8.31320i	0.255195	+	0.550555i
$229$	24.4769			1.61748			0.808739	−	0.588168i	$-0.200151\pi$
$229$	24.4769			1.61748			0.808739	+	0.588168i	$0.200151\pi$
$230$	−7.82401			−0.515900
$231$	−5.50259	+	1.64971i	−0.362044	+	0.108543i
$232$	−6.78706			−0.445592
$233$	7.24397			0.474568			0.237284	−	0.971440i	$-0.423743\pi$
$233$	7.24397			0.474568			0.237284	+	0.971440i	$0.423743\pi$
$234$	−20.8053	−	17.6208i	−1.36009	−	1.15191i
$235$	7.08376			0.462094
$236$			20.5877i			1.34014i
$237$	−6.21646	−	13.4113i	−0.403802	−	0.871160i
$238$			12.4475i			0.806850i
$239$	4.13420			0.267419			0.133710	−	0.991021i	$-0.457311\pi$
$239$	4.13420			0.267419			0.133710	+	0.991021i	$0.457311\pi$
$240$	3.41281	+	7.36277i	0.220296	+	0.475265i
$241$		−	12.8900i		−	0.830315i	−0.909749	−	0.415158i	$-0.863726\pi$
$241$		−	12.8900i		−	0.830315i	0.909749	−	0.415158i	$-0.136274\pi$
$242$	19.9171	+	5.84663i	1.28032	+	0.375836i
$243$	−8.79436	−	12.8709i	−0.564159	−	0.825666i
$244$			2.20748i			0.141319i
$245$			1.00000i			0.0638877i
$246$	0.982419	−	0.455373i	0.0626368	−	0.0290335i
$247$	−16.3223			−1.03856
$248$	−6.29165			−0.399520
$249$	20.9023	−	9.68869i	1.32463	−	0.613996i
$250$		−	1.88704i		−	0.119347i
$251$			2.73625i			0.172710i	0.996264	+	0.0863552i	$0.0275220\pi$
$251$			2.73625i			0.172710i	−0.996264	+	0.0863552i	$0.972478\pi$
$252$	3.57341	+	3.02644i	0.225103	+	0.190648i
$253$	−13.6114	−	1.95653i	−0.855742	−	0.123006i
$254$		−	13.0053i		−	0.816028i
$255$	4.80473	+	10.3657i	0.300884	+	0.649124i
$256$	20.5796			1.28622
$257$		−	18.1483i		−	1.13206i	−0.824385	−	0.566029i	$-0.808479\pi$
$257$		−	18.1483i		−	1.13206i	0.824385	−	0.566029i	$-0.191521\pi$
$258$	9.00532	+	19.4280i	0.560646	+	1.20953i
$259$		−	1.20065i		−	0.0746049i
$260$	7.51760			0.466222
$261$	−15.8824	+	18.7528i	−0.983098	+	1.16077i
$262$	−13.8232			−0.854003
$263$	0.209670			0.0129288			0.00646441	−	0.999979i	$-0.497942\pi$
$263$	0.209670			0.0129288			0.00646441	+	0.999979i	$0.497942\pi$
$264$	1.36685	+	4.55911i	0.0841236	+	0.280594i
$265$	−1.29776			−0.0797208
$266$	6.39539			0.392127
$267$	−0.897548	−	1.93636i	−0.0549291	−	0.118504i
$268$	−19.6918			−1.20287
$269$		−	19.0343i		−	1.16054i	−0.814424	−	0.580271i	$-0.802947\pi$
$269$		−	19.0343i		−	1.16054i	0.814424	−	0.580271i	$-0.197053\pi$
$270$	9.45359	+	2.60283i	0.575327	+	0.158403i
$271$			3.07086i			0.186542i	0.995641	+	0.0932708i	$0.0297322\pi$
$271$			3.07086i			0.186542i	−0.995641	+	0.0932708i	$0.970268\pi$
$272$	30.9059			1.87395
$273$	−7.56822	+	3.50804i	−0.458049	+	0.212316i
$274$		−	20.5240i		−	1.23990i
$275$	0.471887	−	3.28288i	0.0284559	−	0.197965i
$276$	4.71412	+	10.1702i	0.283757	+	0.612175i
$277$			17.8382i			1.07179i	0.844284	+	0.535897i	$0.180026\pi$
$277$			17.8382i			1.07179i	−0.844284	+	0.535897i	$0.819974\pi$
$278$		−	22.7595i		−	1.36502i
$279$	−14.7231	+	17.3840i	−0.881449	+	1.04075i
$280$	0.828540			0.0495147
$281$	24.7501			1.47647			0.738233	−	0.674546i	$-0.235661\pi$
$281$	24.7501			1.47647			0.738233	+	0.674546i	$0.235661\pi$
$282$	−9.73678	−	21.0061i	−0.579817	−	1.25089i
$283$		−	5.29389i		−	0.314689i	−0.987544	−	0.157345i	$-0.949707\pi$
$283$		−	5.29389i		−	0.314689i	0.987544	−	0.157345i	$-0.0502933\pi$
$284$		−	8.48354i		−	0.503405i
$285$	5.32579	−	2.46862i	0.315473	−	0.146229i
$286$	29.8354	+	4.28859i	1.76421	+	0.253590i
$287$		−	0.331296i		−	0.0195558i
$288$	13.9296	−	16.4470i	0.820809	−	0.969152i
$289$	26.5110			1.55947
$290$		−	15.4579i		−	0.907719i
$291$	28.8182	−	13.3579i	1.68935	−	0.783054i
$292$		−	13.2737i		−	0.776786i
$293$	1.00950			0.0589757			0.0294879	−	0.999565i	$-0.490612\pi$
$293$	1.00950			0.0589757			0.0294879	+	0.999565i	$0.490612\pi$
$294$	2.96538	−	1.37452i	0.172945	−	0.0801637i
$295$	13.1893			0.767913
$296$	−0.994788			−0.0578209
$297$	15.7955	+	6.89217i	0.916548	+	0.399924i
$298$	27.8802			1.61506
$299$	−19.9684			−1.15480
$300$	−2.45292	+	1.13698i	−0.141619	+	0.0656437i
$301$	6.55160			0.377628
$302$		−	32.5891i		−	1.87529i
$303$	−27.2081	+	12.6115i	−1.56306	+	0.724515i
$304$		−	15.8792i		−	0.910733i
$305$	1.41421			0.0809772
$306$	24.1340	−	28.4957i	1.37965	−	1.62899i
$307$		−	20.5059i		−	1.17033i	−0.810914	−	0.585165i	$-0.801030\pi$
$307$		−	20.5059i		−	1.17033i	0.810914	−	0.585165i	$-0.198970\pi$
$308$	−5.12436	−	0.736584i	−0.291987	−	0.0419708i
$309$	11.8631	−	5.49880i	0.674867	−	0.312816i
$310$		−	14.3296i		−	0.813864i
$311$			4.56242i			0.258711i	0.991598	+	0.129356i	$0.0412909\pi$
$311$			4.56242i			0.258711i	−0.991598	+	0.129356i	$0.958709\pi$
$312$	2.90655	+	6.27057i	0.164551	+	0.355001i
$313$	−18.7483			−1.05971			−0.529857	−	0.848087i	$-0.677755\pi$
$313$	−18.7483			−1.05971			−0.529857	+	0.848087i	$0.677755\pi$
$314$	−15.4857			−0.873908
$315$	1.93887	−	2.28928i	0.109243	−	0.128986i
$316$		−	13.3216i		−	0.749401i
$317$			0.535056i			0.0300518i	0.999887	+	0.0150259i	$0.00478307\pi$
$317$			0.535056i			0.0300518i	−0.999887	+	0.0150259i	$0.995217\pi$
$318$	1.78380	+	3.84836i	0.100031	+	0.215805i
$319$	3.86551	−	26.8921i	0.216427	−	1.50567i
$320$			4.18654i			0.234035i
$321$	16.9331	−	7.84889i	0.945116	−	0.438082i
$322$	7.82401			0.436015
$323$		−	22.3555i		−	1.24389i
$324$	−2.31263	−	13.8567i	−0.128480	−	0.769818i
$325$		−	4.81609i		−	0.267149i
$326$	−5.70274			−0.315846
$327$	−1.14942	−	2.47974i	−0.0635628	−	0.137130i
$328$	−0.274492			−0.0151563
$329$	−7.08376			−0.390541
$330$	−10.3836	+	3.11307i	−0.571600	+	0.171369i
$331$	−28.0830			−1.54358			−0.771791	−	0.635877i	$-0.780639\pi$
$331$	−28.0830			−1.54358			−0.771791	+	0.635877i	$0.780639\pi$
$332$	20.7625			1.13949
$333$	−2.32791	+	2.74862i	−0.127569	+	0.150624i
$334$	−8.01846			−0.438750
$335$			12.6154i			0.689254i
$336$	−3.41281	−	7.36277i	−0.186184	−	0.401672i
$337$			24.4783i			1.33342i	0.745318	+	0.666709i	$0.232298\pi$
$337$			24.4783i			1.33342i	−0.745318	+	0.666709i	$0.767702\pi$
$338$	19.2379			1.04641
$339$	12.5081	+	26.9850i	0.679349	+	1.46562i
$340$			10.2964i			0.558398i
$341$	3.58335	−	24.9291i	0.194049	−	1.34999i
$342$	−14.6408	−	12.3998i	−0.791685	−	0.670506i
$343$		−	1.00000i		−	0.0539949i
$344$		−	5.42826i		−	0.292672i
$345$	6.51548	−	3.02007i	0.350782	−	0.162595i
$346$	−24.7185			−1.32888
$347$	−7.24327			−0.388839			−0.194420	−	0.980918i	$-0.562282\pi$
$347$	−7.24327			−0.388839			−0.194420	+	0.980918i	$0.562282\pi$
$348$	−20.0933	+	9.31370i	−1.07711	+	0.499266i
$349$		−	2.97055i		−	0.159010i	−0.996834	−	0.0795051i	$-0.974666\pi$
$349$		−	2.97055i		−	0.159010i	0.996834	−	0.0795051i	$-0.0253340\pi$
$350$			1.88704i			0.100867i
$351$	24.1274	+	6.64292i	1.28782	+	0.354573i
$352$	−3.39022	+	23.5855i	−0.180699	+	1.25711i
$353$		−	5.03630i		−	0.268055i	−0.990978	−	0.134028i	$-0.957209\pi$
$353$		−	5.03630i		−	0.268055i	0.990978	−	0.134028i	$-0.0427911\pi$
$354$	−18.1290	−	39.1114i	−0.963547	−	2.07875i
$355$	−5.43492			−0.288456
$356$		−	1.92341i		−	0.101941i
$357$	−4.80473	−	10.3657i	−0.254293	−	0.548610i
$358$			4.81088i			0.254263i
$359$	23.2996			1.22970			0.614852	−	0.788643i	$-0.289216\pi$
$359$	23.2996			1.22970			0.614852	+	0.788643i	$0.289216\pi$
$360$	−1.89676	−	1.60643i	−0.0999678	−	0.0846663i
$361$	7.51395			0.395471
$362$	42.9106			2.25533
$363$	−18.8428	+	2.81919i	−0.988992	+	0.147969i
$364$	−7.51760			−0.394029
$365$	−8.50372			−0.445105
$366$	−1.94386	−	4.19366i	−0.101607	−	0.219206i
$367$	7.22034			0.376899			0.188449	−	0.982083i	$-0.439654\pi$
$367$	7.22034			0.376899			0.188449	+	0.982083i	$0.439654\pi$
$368$		−	19.4263i		−	1.01267i
$369$	−0.642340	+	0.758428i	−0.0334389	+	0.0394822i
$370$		−	2.26568i		−	0.117787i
$371$	1.29776			0.0673764
$372$	−18.6266	+	8.63385i	−0.965745	+	0.447644i
$373$			16.5566i			0.857267i	0.903478	+	0.428633i	$0.141005\pi$
$373$			16.5566i			0.857267i	−0.903478	+	0.428633i	$0.858995\pi$
$374$	−5.87380	+	40.8636i	−0.303727	+	2.11301i
$375$	0.728399	+	1.57144i	0.0376144	+	0.0811490i
$376$			5.86918i			0.302680i
$377$		−	39.4515i		−	2.03186i
$378$	−9.45359	−	2.60283i	−0.486240	−	0.133875i
$379$	−7.35634			−0.377870			−0.188935	−	0.981990i	$-0.560504\pi$
$379$	−7.35634			−0.377870			−0.188935	+	0.981990i	$0.560504\pi$
$380$	5.29017			0.271380
$381$	5.02006	+	10.8303i	0.257186	+	0.554851i
$382$			27.1310i			1.38814i
$383$			4.20119i			0.214671i	0.994223	+	0.107335i	$0.0342318\pi$
$383$			4.20119i			0.214671i	−0.994223	+	0.107335i	$0.965768\pi$
$384$	−10.1650	+	4.71172i	−0.518732	+	0.240444i
$385$	−0.471887	+	3.28288i	−0.0240496	+	0.167311i
$386$		−	9.32249i		−	0.474502i
$387$	−14.9984	−	12.7027i	−0.762413	−	0.645715i
$388$	28.6255			1.45324
$389$			32.7572i			1.66085i	0.557127	+	0.830427i	$0.311904\pi$
$389$			32.7572i			1.66085i	−0.557127	+	0.830427i	$0.688096\pi$
$390$	−14.2816	+	6.61982i	−0.723175	+	0.335208i
$391$		−	27.3493i		−	1.38312i
$392$	−0.828540			−0.0418476
$393$	11.5114	−	5.33578i	0.580672	−	0.269154i
$394$	−33.0973			−1.66742
$395$	−8.53441			−0.429413
$396$	10.3029	+	11.6217i	0.517742	+	0.584013i
$397$	−30.2037			−1.51588			−0.757940	−	0.652325i	$-0.773794\pi$
$397$	−30.2037			−1.51588			−0.757940	+	0.652325i	$0.773794\pi$
$398$	−9.20153			−0.461231
$399$	−5.32579	+	2.46862i	−0.266623	+	0.123586i
$400$	4.68535			0.234268
$401$			27.3517i			1.36588i	0.730476	+	0.682939i	$0.239298\pi$
$401$			27.3517i			1.36588i	−0.730476	+	0.682939i	$0.760702\pi$
$402$	37.4095	−	17.3402i	1.86582	−	0.864848i
$403$		−	36.5718i		−	1.82177i
$404$	−27.0261			−1.34460
$405$	−8.87721	+	1.48157i	−0.441112	+	0.0736199i
$406$			15.4579i			0.767162i
$407$	0.566572	−	3.94160i	0.0280840	−	0.195378i
$408$	−8.58838	+	3.98091i	−0.425188	+	0.197084i
$409$		−	29.4695i		−	1.45717i	−0.684954	−	0.728586i	$-0.740178\pi$
$409$		−	29.4695i		−	1.45717i	0.684954	−	0.728586i	$-0.259822\pi$
$410$		−	0.625170i		−	0.0308749i
$411$	7.92226	+	17.0914i	0.390776	+	0.843058i
$412$	11.7837			0.580543
$413$	−13.1893			−0.649005
$414$	−17.9113	−	15.1697i	−0.880293	−	0.745552i
$415$		−	13.3014i		−	0.652938i
$416$			34.6007i			1.69644i
$417$	8.78517	+	18.9531i	0.430212	+	0.928136i
$418$	20.9953	+	3.01790i	1.02691	+	0.147611i
$419$		−	26.7445i		−	1.30655i	−0.757119	−	0.653277i	$-0.773394\pi$
$419$		−	26.7445i		−	1.30655i	0.757119	−	0.653277i	$-0.226606\pi$
$420$	2.45292	−	1.13698i	0.119690	−	0.0554790i
$421$	−26.2827			−1.28094			−0.640471	−	0.767983i	$-0.721261\pi$
$421$	−26.2827			−1.28094			−0.640471	+	0.767983i	$0.721261\pi$
$422$		−	6.03374i		−	0.293718i
$423$	16.2167	+	13.7345i	0.788483	+	0.667794i
$424$		−	1.07525i		−	0.0522186i
$425$	6.59628			0.319967
$426$	7.47041	+	16.1166i	0.361942	+	0.780852i
$427$	−1.41421			−0.0684382
$428$	16.8199			0.813019
$429$	−26.5010	+	7.94513i	−1.27948	+	0.383595i
$430$	12.3632			0.596205
$431$	−25.5386			−1.23015			−0.615075	−	0.788468i	$-0.710874\pi$
$431$	−25.5386			−1.23015			−0.615075	+	0.788468i	$0.710874\pi$
$432$	−6.46259	+	23.4724i	−0.310931	+	1.12932i
$433$	17.9211			0.861235			0.430617	−	0.902535i	$-0.358296\pi$
$433$	17.9211			0.861235			0.430617	+	0.902535i	$0.358296\pi$
$434$			14.3296i			0.687841i
$435$	5.96675	+	12.8726i	0.286084	+	0.617195i
$436$		−	2.46316i		−	0.117964i
$437$	−14.0518			−0.672190
$438$	11.6885	+	25.2168i	0.558500	+	1.20490i
$439$			40.4391i			1.93005i	0.262155	+	0.965026i	$0.415567\pi$
$439$			40.4391i			1.93005i	−0.262155	+	0.965026i	$0.584433\pi$
$440$	2.72000	+	0.390977i	0.129671	+	0.0186391i
$441$	−1.93887	+	2.28928i	−0.0923271	+	0.109013i
$442$			59.9482i			2.85144i
$443$		−	16.0411i		−	0.762136i	−0.924547	−	0.381068i	$-0.875556\pi$
$443$		−	16.0411i		−	0.762136i	0.924547	−	0.381068i	$-0.124444\pi$
$444$	−2.94510	+	1.36512i	−0.139768	+	0.0647857i
$445$	−1.23222			−0.0584128
$446$	−38.1814			−1.80794
$447$	−23.2174	+	10.7618i	−1.09814	+	0.509014i
$448$		−	4.18654i		−	0.197795i
$449$		−	15.8914i		−	0.749963i	−0.927032	−	0.374981i	$-0.877649\pi$
$449$		−	15.8914i		−	0.749963i	0.927032	−	0.374981i	$-0.122351\pi$
$450$	3.65873	−	4.31996i	0.172474	−	0.203645i
$451$	0.156334	−	1.08761i	0.00736150	−	0.0512134i
$452$			26.8045i			1.26078i
$453$	12.5794	+	27.1387i	0.591031	+	1.27509i
$454$	2.50546			0.117587
$455$			4.81609i			0.225782i
$456$	2.04535	+	4.41263i	0.0957824	+	0.206640i
$457$		−	14.7199i		−	0.688570i	−0.938865	−	0.344285i	$-0.888121\pi$
$457$		−	14.7199i		−	0.688570i	0.938865	−	0.344285i	$-0.111879\pi$
$458$	−46.1889			−2.15827
$459$	−9.09836	+	33.0457i	−0.424675	+	1.54244i
$460$	6.47190			0.301754
$461$	9.59090			0.446693			0.223346	−	0.974739i	$-0.428302\pi$
$461$	9.59090			0.446693			0.223346	+	0.974739i	$0.428302\pi$
$462$	10.3836	−	3.11307i	0.483090	−	0.144833i
$463$	−21.1432			−0.982607			−0.491304	−	0.870988i	$-0.663479\pi$
$463$	−21.1432			−0.982607			−0.491304	+	0.870988i	$0.663479\pi$
$464$	38.3805			1.78177
$465$	5.53121	+	11.9330i	0.256504	+	0.553380i
$466$	−13.6697			−0.633236
$467$		−	28.6347i		−	1.32505i	−0.749038	−	0.662527i	$-0.769484\pi$
$467$		−	28.6347i		−	1.32505i	0.749038	−	0.662527i	$-0.230516\pi$
$468$	17.2099	+	14.5756i	0.795526	+	0.673759i
$469$		−	12.6154i		−	0.582526i
$470$	−13.3674			−0.616591
$471$	12.8958	−	5.97748i	0.594206	−	0.275428i
$472$			10.9279i			0.502997i
$473$	21.5082	+	3.09162i	0.988946	+	0.142153i
$474$	11.7307	+	25.3078i	0.538810	+	1.16243i
$475$		−	3.38911i		−	0.155503i
$476$		−	10.2964i		−	0.471933i
$477$	−2.97093	−	2.51619i	−0.136030	−	0.115208i
$478$	−7.80141			−0.356828
$479$	−12.1373			−0.554565			−0.277283	−	0.960788i	$-0.589434\pi$
$479$	−12.1373			−0.554565			−0.277283	+	0.960788i	$0.589434\pi$
$480$	−5.23310	−	11.2899i	−0.238857	−	0.515309i
$481$		−	5.78245i		−	0.263657i
$482$			24.3239i			1.10792i
$483$	−6.51548	+	3.02007i	−0.296465	+	0.137418i
$484$	−16.4751	−	4.83624i	−0.748868	−	0.219829i
$485$		−	18.3387i		−	0.832717i
$486$	16.5953	+	24.2879i	0.752780	+	1.10172i
$487$	−30.6300			−1.38798			−0.693990	−	0.719985i	$-0.744149\pi$
$487$	−30.6300			−1.38798			−0.693990	+	0.719985i	$0.744149\pi$
$488$			1.17173i			0.0530415i
$489$	4.74898	−	2.20126i	0.214756	−	0.0995444i
$490$		−	1.88704i		−	0.0852479i
$491$	−23.0703			−1.04115			−0.520573	−	0.853817i	$-0.674282\pi$
$491$	−23.0703			−1.04115			−0.520573	+	0.853817i	$0.674282\pi$
$492$	−0.812642	+	0.376678i	−0.0366367	+	0.0169819i
$493$	54.0341			2.43357
$494$	30.8008			1.38579
$495$	7.44536	−	6.60050i	0.334644	−	0.296670i
$496$	35.5790			1.59754
$497$	5.43492			0.243789
$498$	−39.4436	+	18.2830i	−1.76751	+	0.819280i
$499$	17.7806			0.795969			0.397985	−	0.917392i	$-0.369710\pi$
$499$	17.7806			0.795969			0.397985	+	0.917392i	$0.369710\pi$
$500$			1.56093i			0.0698070i
$501$	6.67741	−	3.09513i	0.298324	−	0.138280i
$502$		−	5.16342i		−	0.230455i
$503$	8.03647			0.358329			0.179164	−	0.983819i	$-0.442661\pi$
$503$	8.03647			0.358329			0.179164	+	0.983819i	$0.442661\pi$
$504$	1.89676	+	1.60643i	0.0844882	+	0.0715561i
$505$			17.3141i			0.770466i
$506$	25.6853	+	3.69205i	1.14185	+	0.164132i
$507$	−16.0205	+	7.42585i	−0.711495	+	0.329794i
$508$			10.7578i			0.477301i
$509$			35.0407i			1.55315i	0.630023	+	0.776576i	$0.283045\pi$
$509$			35.0407i			1.55315i	−0.630023	+	0.776576i	$0.716955\pi$
$510$	−9.06673	−	19.5605i	−0.401481	−	0.866153i
$511$	8.50372			0.376182
$512$	−25.8974			−1.14451
$513$	16.9785	+	4.67465i	0.749621	+	0.206391i
$514$			34.2466i			1.51055i
$515$		−	7.54916i		−	0.332656i
$516$	−7.44905	−	16.0705i	−0.327926	−	0.707466i
$517$	−23.2552	−	3.34274i	−1.02276	−	0.147013i
$518$			2.26568i			0.0995484i
$519$	20.5845	−	9.54136i	0.903557	−	0.418819i
$520$	3.99032			0.174987
$521$			11.8477i			0.519056i	0.965736	+	0.259528i	$0.0835669\pi$
$521$			11.8477i			0.519056i	−0.965736	+	0.259528i	$0.916433\pi$
$522$	29.9708	−	35.3874i	1.31179	−	1.54886i
$523$			15.1192i			0.661115i	0.943786	+	0.330558i	$0.107237\pi$
$523$			15.1192i			0.661115i	−0.943786	+	0.330558i	$0.892763\pi$
$524$	11.4344			0.499513
$525$	−0.728399	−	1.57144i	−0.0317899	−	0.0685834i
$526$	−0.395657			−0.0172514
$527$	50.0899			2.18195
$528$	−7.72945	−	25.7816i	−0.336381	−	1.12200i
$529$	5.80924			0.252576
$530$	2.44893			0.106375
$531$	30.1940	+	25.5724i	1.31031	+	1.10975i
$532$	−5.29017			−0.229358
$533$		−	1.59555i		−	0.0691111i
$534$	1.69371	+	3.65400i	0.0732941	+	0.158124i
$535$		−	10.7755i		−	0.465867i
$536$	−10.4524			−0.451474
$537$	−1.85700	−	4.00628i	−0.0801355	−	0.172884i
$538$			35.9185i			1.54856i
$539$	0.471887	−	3.28288i	0.0203256	−	0.141404i
$540$	−7.81986	−	2.15302i	−0.336513	−	0.0926512i
$541$			14.7251i			0.633081i	0.948579	+	0.316540i	$0.102521\pi$
$541$			14.7251i			0.633081i	−0.948579	+	0.316540i	$0.897479\pi$
$542$		−	5.79485i		−	0.248910i
$543$	−35.7340	+	16.5635i	−1.53349	+	0.710808i
$544$	−47.3903			−2.03184
$545$	−1.57800			−0.0675942
$546$	14.2816	−	6.61982i	0.611194	−	0.283302i
$547$		−	0.167747i		−	0.00717234i	−0.999994	−	0.00358617i	$-0.998858\pi$
$547$		−	0.167747i		−	0.00717234i	0.999994	−	0.00358617i	$-0.00114152\pi$
$548$			16.9771i			0.725226i
$549$	3.23751	+	2.74196i	0.138173	+	0.117024i
$550$	−0.890472	+	6.19494i	−0.0379698	+	0.264153i
$551$		−	27.7622i		−	1.18271i
$552$	2.50225	+	5.39833i	0.106503	+	0.229768i
$553$	8.53441			0.362920
$554$		−	33.6614i		−	1.43014i
$555$	0.874554	+	1.88676i	0.0371228	+	0.0800884i
$556$			18.8263i			0.798413i
$557$	−36.4274			−1.54348			−0.771739	−	0.635940i	$-0.780613\pi$
$557$	−36.4274			−1.54348			−0.771739	+	0.635940i	$0.780613\pi$
$558$	27.7831	−	32.8043i	1.17615	−	1.38872i
$559$	31.5531			1.33456
$560$	−4.68535			−0.197992
$561$	−10.8819	−	36.2966i	−0.459435	−	1.53244i
$562$	−46.7044			−1.97011
$563$	14.0561			0.592394			0.296197	−	0.955127i	$-0.404282\pi$
$563$	14.0561			0.592394			0.296197	+	0.955127i	$0.404282\pi$
$564$	8.05411	+	17.3759i	0.339139	+	0.731657i
$565$	17.1721			0.722435
$566$			9.98980i			0.419903i
$567$	8.87721	−	1.48157i	0.372808	−	0.0622202i
$568$		−	4.50305i		−	0.188944i
$569$	−39.7142			−1.66491			−0.832453	−	0.554096i	$-0.813064\pi$
$569$	−39.7142			−1.66491			−0.832453	+	0.554096i	$0.813064\pi$
$570$	−10.0500	+	4.65840i	−0.420948	+	0.195119i
$571$			14.2732i			0.597315i	0.954360	+	0.298657i	$0.0965387\pi$
$571$			14.2732i			0.597315i	−0.954360	+	0.298657i	$0.903461\pi$
$572$	−24.6794	−	3.54746i	−1.03190	−	0.148327i
$573$	−10.4726	−	22.5935i	−0.437498	−	0.943856i
$574$			0.625170i			0.0260941i
$575$		−	4.14617i		−	0.172907i
$576$	−8.11716	+	9.58415i	−0.338215	+	0.399340i
$577$	−9.06939			−0.377564			−0.188782	−	0.982019i	$-0.560454\pi$
$577$	−9.06939			−0.377564			−0.188782	+	0.982019i	$0.560454\pi$
$578$	−50.0273			−2.08086
$579$	3.59849	+	7.76335i	0.149548	+	0.322634i
$580$			12.7865i			0.530932i
$581$			13.3014i			0.551833i
$582$	−54.3812	+	25.2069i	−2.25417	+	1.04486i
$583$	4.26040	+	0.612397i	0.176448	+	0.0253629i
$584$		−	7.04567i		−	0.291552i
$585$	9.33778	−	11.0254i	0.386070	−	0.455843i
$586$	−1.90497			−0.0786938
$587$			32.6316i			1.34685i	0.739256	+	0.673425i	$0.235177\pi$
$587$			32.6316i			1.34685i	−0.739256	+	0.673425i	$0.764823\pi$
$588$	−2.45292	+	1.13698i	−0.101157	+	0.0468883i
$589$		−	25.7357i		−	1.06042i
$590$	−24.8889			−1.02466
$591$	27.5619	−	12.7756i	1.13375	−	0.525517i
$592$	5.62548			0.231206
$593$	29.5381			1.21298			0.606492	−	0.795090i	$-0.292576\pi$
$593$	29.5381			1.21298			0.606492	+	0.795090i	$0.292576\pi$
$594$	−29.8068	−	13.0058i	−1.22299	−	0.533635i
$595$	−6.59628			−0.270421
$596$	−23.0621			−0.944659
$597$	7.66262	−	3.55179i	0.313610	−	0.145365i
$598$	37.6812			1.54090
$599$			0.400987i			0.0163839i	0.999966	+	0.00819193i	$0.00260760\pi$
$599$			0.400987i			0.0163839i	−0.999966	+	0.00819193i	$0.997392\pi$
$600$	−1.30200	+	0.603508i	−0.0531541	+	0.0246381i
$601$			47.0976i			1.92115i	0.278017	+	0.960576i	$0.410323\pi$
$601$			47.0976i			1.92115i	−0.278017	+	0.960576i	$0.589677\pi$
$602$	−12.3632			−0.503885
$603$	−24.4596	+	28.8802i	−0.996074	+	1.17609i
$604$			26.9572i			1.09687i
$605$	−3.09830	+	10.5546i	−0.125964	+	0.429107i
$606$	51.3428	−	23.7985i	2.08566	−	0.966750i
$607$			0.531467i			0.0215716i	0.999942	+	0.0107858i	$0.00343329\pi$
$607$			0.531467i			0.0215716i	−0.999942	+	0.0107858i	$0.996567\pi$
$608$			24.3487i			0.987469i
$609$	−5.96675	−	12.8726i	−0.241785	−	0.521625i
$610$	−2.66867			−0.108051
$611$	−34.1161			−1.38019
$612$	−19.9633	+	23.5712i	−0.806968	+	0.952809i
$613$			17.6834i			0.714227i	0.934061	+	0.357113i	$0.116239\pi$
$613$			17.6834i			0.714227i	−0.934061	+	0.357113i	$0.883761\pi$
$614$			38.6954i			1.56162i
$615$	0.241316	+	0.520613i	0.00973079	+	0.0209931i
$616$	−2.72000	−	0.390977i	−0.109592	−	0.0157529i
$617$			7.18204i			0.289138i	0.989495	+	0.144569i	$0.0461796\pi$
$617$			7.18204i			0.289138i	−0.989495	+	0.144569i	$0.953820\pi$
$618$	−22.3861	+	10.3765i	−0.900503	+	0.417403i
$619$	13.7657			0.553290			0.276645	−	0.960972i	$-0.410777\pi$
$619$	13.7657			0.553290			0.276645	+	0.960972i	$0.410777\pi$
$620$			11.8532i			0.476035i
$621$	20.7713	+	5.71889i	0.833522	+	0.229491i
$622$		−	8.60949i		−	0.345209i
$623$	1.23222			0.0493679
$624$	−16.4364	−	35.4598i	−0.657983	−	1.41953i
$625$	1.00000			0.0400000
$626$	35.3788			1.41402
$627$	−18.6489	+	5.59103i	−0.744764	+	0.223284i
$628$	12.8095			0.511155
$629$	7.91984			0.315785
$630$	−3.65873	+	4.31996i	−0.145767	+	0.172111i
$631$	20.4440			0.813861			0.406931	−	0.913459i	$-0.366599\pi$
$631$	20.4440			0.813861			0.406931	+	0.913459i	$0.366599\pi$
$632$		−	7.07110i		−	0.281273i
$633$	2.32902	+	5.02462i	0.0925704	+	0.199711i
$634$		−	1.00967i		−	0.0400993i
$635$	6.89191			0.273497
$636$	−1.47553	−	3.18330i	−0.0585086	−	0.126226i
$637$		−	4.81609i		−	0.190821i
$638$	−7.29438	+	50.7465i	−0.288787	+	2.00907i
$639$	−12.4420	−	10.5376i	−0.492199	−	0.416861i
$640$			6.46859i			0.255694i
$641$			37.8085i			1.49335i	0.665192	+	0.746673i	$0.268350\pi$
$641$			37.8085i			1.49335i	−0.665192	+	0.746673i	$0.731650\pi$
$642$	−31.9536	+	14.8112i	−1.26111	+	0.584551i
$643$	−21.6376			−0.853303			−0.426651	−	0.904416i	$-0.640307\pi$
$643$	−21.6376			−0.853303			−0.426651	+	0.904416i	$0.640307\pi$
$644$	−6.47190			−0.255028
$645$	−10.2955	+	4.77218i	−0.405384	+	0.187905i
$646$			42.1858i			1.65978i
$647$			4.17226i			0.164029i	0.996631	+	0.0820143i	$0.0261353\pi$
$647$			4.17226i			0.164029i	−0.996631	+	0.0820143i	$0.973865\pi$
$648$	−1.22754	−	7.35513i	−0.0482224	−	0.288937i
$649$	−43.2991	−	6.22388i	−1.69964	−	0.244309i
$650$			9.08818i			0.356468i
$651$	−5.53121	−	11.9330i	−0.216785	−	0.467691i
$652$	4.71722			0.184740
$653$		−	1.96831i		−	0.0770259i	−0.999258	−	0.0385130i	$-0.987738\pi$
$653$		−	1.96831i		−	0.0770259i	0.999258	−	0.0385130i	$-0.0122621\pi$
$654$	2.16900	+	4.67938i	0.0848145	+	0.182978i
$655$		−	7.32535i		−	0.286225i
$656$	1.55224			0.0606048
$657$	−19.4674	−	16.4876i	−0.759494	−	0.643242i
$658$	13.3674			0.521114
$659$	−0.540513			−0.0210554			−0.0105277	−	0.999945i	$-0.503351\pi$
$659$	−0.540513			−0.0210554			−0.0105277	+	0.999945i	$0.503351\pi$
$660$	8.58917	−	2.57508i	0.334333	−	0.100235i
$661$	42.4926			1.65277			0.826386	−	0.563104i	$-0.190393\pi$
$661$	42.4926			1.65277			0.826386	+	0.563104i	$0.190393\pi$
$662$	52.9938			2.05966
$663$	−23.1400	−	49.9221i	−0.898684	−	1.93881i
$664$	11.0207			0.427686
$665$			3.38911i			0.131424i
$666$	4.39286	−	5.18677i	0.170220	−	0.200983i
$667$		−	33.9638i		−	1.31508i
$668$	6.63274			0.256628
$669$	31.7957	−	14.7380i	1.22929	−	0.569806i
$670$		−	23.8058i		−	0.919700i
$671$	−4.64267	−	0.667346i	−0.179228	−	0.0257626i
$672$	5.23310	+	11.2899i	0.201871	+	0.435516i
$673$			5.98655i			0.230764i	0.993321	+	0.115382i	$0.0368093\pi$
$673$			5.98655i			0.230764i	−0.993321	+	0.115382i	$0.963191\pi$
$674$		−	46.1916i		−	1.77923i
$675$	−1.37932	+	5.00974i	−0.0530899	+	0.192825i
$676$	−15.9133			−0.612051
$677$	9.39905			0.361235			0.180617	−	0.983553i	$-0.442190\pi$
$677$	9.39905			0.361235			0.180617	+	0.983553i	$0.442190\pi$
$678$	−23.6034	−	50.9218i	−0.906483	−	1.95564i
$679$			18.3387i			0.703775i
$680$			5.46528i			0.209584i
$681$	−2.08643	+	0.967109i	−0.0799523	+	0.0370597i
$682$	−6.76194	+	47.0423i	−0.258928	+	1.80134i
$683$		−	22.3592i		−	0.855551i	−0.903885	−	0.427775i	$-0.859297\pi$
$683$		−	22.3592i		−	0.855551i	0.903885	−	0.427775i	$-0.140703\pi$
$684$	12.1107	+	10.2569i	0.463062	+	0.392184i
$685$	10.8763			0.415561
$686$			1.88704i			0.0720476i
$687$	38.4640	−	17.8289i	1.46749	−	0.680216i
$688$			30.6966i			1.17030i
$689$	6.25014			0.238111
$690$	−12.2950	+	5.69900i	−0.468062	+	0.216957i
$691$	5.86952			0.223287			0.111644	−	0.993748i	$-0.464389\pi$
$691$	5.86952			0.223287			0.111644	+	0.993748i	$0.464389\pi$
$692$	20.4468			0.777270
$693$	−7.44536	+	6.60050i	−0.282826	+	0.250732i
$694$	13.6684			0.518844
$695$	12.0609			0.457497
$696$	−10.6655	+	4.94369i	−0.404274	+	0.187390i
$697$	2.18532			0.0827750
$698$			5.60556i			0.212174i
$699$	11.3835	−	5.27650i	0.430563	−	0.199576i
$700$		−	1.56093i		−	0.0589977i
$701$	−23.3115			−0.880462			−0.440231	−	0.897885i	$-0.645103\pi$
$701$	−23.3115			−0.880462			−0.440231	+	0.897885i	$0.645103\pi$
$702$	−45.5294	−	12.5355i	−1.71840	−	0.473121i
$703$		−	4.06914i		−	0.153470i
$704$	1.97558	−	13.7439i	0.0744573	−	0.517994i
$705$	11.1317	−	5.15981i	0.419245	−	0.194330i
$706$			9.50371i			0.357677i
$707$		−	17.3141i		−	0.651162i
$708$	14.9960	+	32.3524i	0.563586	+	1.21588i
$709$	2.66583			0.100117			0.0500586	−	0.998746i	$-0.484059\pi$
$709$	2.66583			0.100117			0.0500586	+	0.998746i	$0.484059\pi$
$710$	10.2559			0.384898
$711$	−19.5376	−	16.5471i	−0.732718	−	0.620565i
$712$		−	1.02094i		−	0.0382615i
$713$		−	31.4846i		−	1.17911i
$714$	9.06673	+	19.5605i	0.339314	+	0.732033i
$715$	−2.27265	+	15.8107i	−0.0849924	+	0.591286i
$716$		−	3.97948i		−	0.148720i
$717$	6.49666	−	3.01135i	0.242622	−	0.112461i
$718$	−43.9673			−1.64084
$719$			13.1804i			0.491548i	0.969327	+	0.245774i	$0.0790421\pi$
$719$			13.1804i			0.491548i	−0.969327	+	0.245774i	$0.920958\pi$
$720$	10.7261	+	9.08429i	0.399737	+	0.338552i
$721$			7.54916i			0.281145i
$722$	−14.1792			−0.527693
$723$	−9.38904	−	20.2558i	−0.349182	−	0.753323i
$724$	−35.4950			−1.31916
$725$	8.19160			0.304228
$726$	35.5572	−	5.31993i	1.31965	−	0.197441i
$727$	−29.4440			−1.09202			−0.546008	−	0.837780i	$-0.683853\pi$
$727$	−29.4440			−1.09202			−0.546008	+	0.837780i	$0.683853\pi$
$728$	−3.99032			−0.147891
$729$	−23.1950	−	13.8200i	−0.859073	−	0.511853i
$730$	16.0469			0.593922
$731$			43.2162i			1.59841i
$732$	1.60793	+	3.46893i	0.0594307	+	0.128215i
$733$			24.3710i			0.900162i	0.892988	+	0.450081i	$0.148605\pi$
$733$			24.3710i			0.900162i	−0.892988	+	0.450081i	$0.851395\pi$
$734$	−13.6251			−0.502911
$735$	0.728399	+	1.57144i	0.0268674	+	0.0579636i
$736$			29.7877i			1.09799i
$737$	5.95305	−	41.4149i	0.219284	−	1.52554i
$738$	1.21212	−	1.43119i	0.0446189	−	0.0526827i
$739$		−	27.0306i		−	0.994337i	−0.867654	−	0.497169i	$-0.834373\pi$
$739$		−	27.0306i		−	0.994337i	0.867654	−	0.497169i	$-0.165627\pi$
$740$			1.87414i			0.0688946i
$741$	−25.6495	+	11.8891i	−0.942258	+	0.436758i
$742$	−2.44893			−0.0899031
$743$	−5.47168			−0.200737			−0.100368	−	0.994950i	$-0.532002\pi$
$743$	−5.47168			−0.200737			−0.100368	+	0.994950i	$0.532002\pi$
$744$	−9.88697	+	4.58283i	−0.362474	+	0.168015i
$745$			14.7746i			0.541298i
$746$		−	31.2430i		−	1.14389i
$747$	25.7896	−	30.4505i	0.943591	−	1.11412i
$748$	4.85872	−	33.8017i	0.177652	−	1.23591i
$749$			10.7755i			0.393729i
$750$	−1.37452	−	2.96538i	−0.0501904	−	0.108280i
$751$	−22.6620			−0.826946			−0.413473	−	0.910516i	$-0.635684\pi$
$751$	−22.6620			−0.826946			−0.413473	+	0.910516i	$0.635684\pi$
$752$		−	33.1900i		−	1.21031i
$753$	1.99308	+	4.29986i	0.0726319	+	0.156696i
$754$			74.4467i			2.71119i
$755$	17.2699			0.628516
$756$	7.81986	+	2.15302i	0.284406	+	0.0783046i
$757$	−8.42299			−0.306139			−0.153069	−	0.988215i	$-0.548916\pi$
$757$	−8.42299			−0.306139			−0.153069	+	0.988215i	$0.548916\pi$
$758$	13.8817			0.504207
$759$	−22.8147	+	6.83997i	−0.828121	+	0.248275i
$760$	2.80801			0.101857
$761$	−24.2476			−0.878973			−0.439487	−	0.898249i	$-0.644840\pi$
$761$	−24.2476			−0.878973			−0.439487	+	0.898249i	$0.644840\pi$
$762$	−9.47308	−	20.4372i	−0.343173	−	0.740360i
$763$	1.57800			0.0571275
$764$		−	22.4423i		−	0.811936i
$765$	15.1007	+	12.7893i	0.545967	+	0.462399i
$766$		−	7.92782i		−	0.286444i
$767$	−63.5211			−2.29361
$768$	32.3397	−	14.9902i	1.16696	−	0.540911i
$769$			43.5795i			1.57152i	0.618533	+	0.785759i	$0.287727\pi$
$769$			43.5795i			1.57152i	−0.618533	+	0.785759i	$0.712273\pi$
$770$	0.890472	−	6.19494i	0.0320904	−	0.223250i
$771$	−13.2192	−	28.5190i	−0.476077	−	1.02709i
$772$			7.71142i			0.277540i
$773$		−	46.1628i		−	1.66036i	−0.557496	−	0.830180i	$-0.688238\pi$
$773$		−	46.1628i		−	1.66036i	0.557496	−	0.830180i	$-0.311762\pi$
$774$	28.3027	+	23.9706i	1.01732	+	0.861604i
$775$	7.59366			0.272772
$776$	15.1943			0.545445
$777$	−0.874554	−	1.88676i	−0.0313745	−	0.0676870i
$778$		−	61.8142i		−	2.21615i
$779$		−	1.12280i		−	0.0402284i
$780$	11.8135	−	5.47581i	0.422990	−	0.196065i
$781$	17.8422	+	2.56467i	0.638444	+	0.0917711i
$782$			51.6094i			1.84555i
$783$	−11.2988	+	41.0378i	−0.403786	+	1.46657i
$784$	4.68535			0.167334
$785$		−	8.20632i		−	0.292896i
$786$	−21.7225	+	10.0688i	−0.774814	+	0.359144i
$787$			6.84529i			0.244008i	0.992530	+	0.122004i	$0.0389321\pi$
$787$			6.84529i			0.244008i	−0.992530	+	0.122004i	$0.961068\pi$
$788$	27.3776			0.975286
$789$	0.329485	−	0.152724i	0.0117300	−	0.00543710i
$790$	16.1048			0.572983
$791$	−17.1721			−0.610569
$792$	5.46878	+	6.16878i	0.194324	+	0.219198i
$793$	−6.81095			−0.241864
$794$	56.9956			2.02270
$795$	−2.03936	+	0.945288i	−0.0723286	+	0.0335259i
$796$	7.61136			0.269778
$797$			17.8254i			0.631408i	0.948858	+	0.315704i	$0.102241\pi$
$797$			17.8254i			0.631408i	−0.948858	+	0.315704i	$0.897759\pi$
$798$	10.0500	−	4.65840i	0.355766	−	0.164906i
$799$		−	46.7265i		−	1.65307i
$800$	−7.18439			−0.254006
$801$	−2.82089	−	2.38911i	−0.0996713	−	0.0844152i
$802$		−	51.6138i		−	1.82255i
$803$	27.9167	+	4.01280i	0.985159	+	0.141609i
$804$	−30.9446	+	14.3435i	−1.09133	+	0.505856i
$805$			4.14617i			0.146133i
$806$			69.0125i			2.43086i
$807$	−13.8646	−	29.9113i	−0.488056	−	1.05293i
$808$	−14.3454			−0.504669
$809$	−41.0970			−1.44489			−0.722446	−	0.691427i	$-0.756982\pi$
$809$	−41.0970			−1.44489			−0.722446	+	0.691427i	$0.756982\pi$
$810$	16.7517	−	2.79579i	0.588594	−	0.0982341i
$811$		−	51.7331i		−	1.81659i	−0.418327	−	0.908297i	$-0.637383\pi$
$811$		−	51.7331i		−	1.81659i	0.418327	−	0.908297i	$-0.362617\pi$
$812$		−	12.7865i		−	0.448719i
$813$	2.23681	+	4.82569i	0.0784485	+	0.169244i
$814$	−1.06915	+	7.43797i	−0.0374736	+	0.260701i
$815$		−	3.02205i		−	0.105858i
$816$	48.5669	−	22.5119i	1.70018	−	0.788072i
$817$	22.2041			0.776823
$818$			55.6102i			1.94437i
$819$	−9.33778	+	11.0254i	−0.326288	+	0.385258i
$820$			0.517131i			0.0180590i
$821$	7.83061			0.273290			0.136645	−	0.990620i	$-0.456368\pi$
$821$	7.83061			0.273290			0.136645	+	0.990620i	$0.456368\pi$
$822$	−14.9496	−	32.2523i	−0.521429	−	1.12493i
$823$	−26.8224			−0.934970			−0.467485	−	0.884001i	$-0.654840\pi$
$823$	−26.8224			−0.934970			−0.467485	+	0.884001i	$0.654840\pi$
$824$	6.25478			0.217896
$825$	−1.64971	−	5.50259i	−0.0574354	−	0.191576i
$826$	24.8889			0.865994
$827$	−36.7635			−1.27839			−0.639197	−	0.769043i	$-0.720733\pi$
$827$	−36.7635			−1.27839			−0.639197	+	0.769043i	$0.720733\pi$
$828$	14.8160	+	12.5482i	0.514890	+	0.436079i
$829$	−10.4722			−0.363713			−0.181857	−	0.983325i	$-0.558211\pi$
$829$	−10.4722			−0.363713			−0.181857	+	0.983325i	$0.558211\pi$
$830$			25.1002i			0.871242i
$831$	12.9933	+	28.0317i	0.450733	+	0.972409i
$832$		−	20.1628i		−	0.699018i
$833$	6.59628			0.228548
$834$	−16.5780	−	35.7653i	−0.574049	−	1.23845i
$835$		−	4.24922i		−	0.147050i
$836$	−17.3670	−	2.49636i	−0.600650	−	0.0863385i
$837$	−10.4741	+	38.0422i	−0.362036	+	1.31493i
$838$			50.4680i			1.74339i
$839$		−	48.6042i		−	1.67800i	−0.544128	−	0.839002i	$-0.683140\pi$
$839$		−	48.6042i		−	1.67800i	0.544128	−	0.839002i	$-0.316860\pi$
$840$	1.30200	−	0.603508i	0.0449234	−	0.0208230i
$841$	38.1022			1.31387
$842$	49.5966			1.70921
$843$	38.8933	−	18.0279i	1.33956	−	0.620915i
$844$			4.99101i			0.171798i
$845$			10.1948i			0.350710i
$846$	−30.6016	−	25.9176i	−1.05210	−	0.891065i
$847$	3.09830	−	10.5546i	0.106459	−	0.362662i
$848$			6.08047i			0.208804i
$849$	−3.85607	−	8.31905i	−0.132340	−	0.285509i
$850$	−12.4475			−0.426945
$851$		−	4.97811i		−	0.170648i
$852$	−6.17940	−	13.3314i	−0.211703	−	0.456726i
$853$			50.8769i			1.74199i	0.491290	+	0.870996i	$0.336525\pi$
$853$			50.8769i			1.74199i	−0.491290	+	0.870996i	$0.663475\pi$
$854$	2.66867			0.0913199
$855$	6.57104	−	7.75860i	0.224725	−	0.265339i
$856$	8.92796			0.305151
$857$	−8.22530			−0.280971			−0.140486	−	0.990083i	$-0.544866\pi$
$857$	−8.22530			−0.280971			−0.140486	+	0.990083i	$0.544866\pi$
$858$	50.0085	−	14.9928i	1.70726	−	0.511846i
$859$	0.256020			0.00873528			0.00436764	−	0.999990i	$-0.498610\pi$
$859$	0.256020			0.00873528			0.00436764	+	0.999990i	$0.498610\pi$
$860$	−10.2266			−0.348725
$861$	−0.241316	−	0.520613i	−0.00822402	−	0.0177424i
$862$	48.1924			1.64144
$863$			20.9475i			0.713062i	0.934284	+	0.356531i	$0.116041\pi$
$863$			20.9475i			0.713062i	−0.934284	+	0.356531i	$0.883959\pi$
$864$	9.90955	−	35.9919i	0.337130	−	1.22447i
$865$		−	13.0991i		−	0.445382i
$866$	−33.8180			−1.14918
$867$	41.6605	−	19.3106i	1.41486	−	0.655821i
$868$		−	11.8532i		−	0.402323i
$869$	28.0175	+	4.02728i	0.950428	+	0.136616i
$870$	−11.2595	−	24.2912i	−0.381733	−	0.823549i
$871$		−	60.7570i		−	2.05867i
$872$		−	1.30744i		−	0.0442754i
$873$	35.5563	−	41.9823i	1.20340	−	1.42089i
$874$	26.5164			0.896931
$875$	−1.00000			−0.0338062
$876$	−9.66857	−	20.8589i	−0.326671	−	0.704757i
$877$			27.0100i			0.912061i	0.889964	+	0.456031i	$0.150729\pi$
$877$			27.0100i			0.912061i	−0.889964	+	0.456031i	$0.849271\pi$
$878$		−	76.3103i		−	2.57535i
$879$	1.58638	−	0.735320i	0.0535071	−	0.0248017i
$880$	−15.3815	−	2.21096i	−0.518509	−	0.0745314i
$881$		−	27.4389i		−	0.924439i	−0.886766	−	0.462220i	$-0.847053\pi$
$881$		−	27.4389i		−	0.924439i	0.886766	−	0.462220i	$-0.152947\pi$
$882$	3.65873	−	4.31996i	0.123196	−	0.145461i
$883$	27.3964			0.921963			0.460981	−	0.887410i	$-0.347497\pi$
$883$	27.3964			0.921963			0.460981	+	0.887410i	$0.347497\pi$
$884$		−	49.5882i		−	1.66783i
$885$	20.7263	−	9.60710i	0.696707	−	0.322939i
$886$			30.2703i			1.01695i
$887$	25.4305			0.853874			0.426937	−	0.904281i	$-0.359593\pi$
$887$	25.4305			0.853874			0.426937	+	0.904281i	$0.359593\pi$
$888$	−1.56325	+	0.724603i	−0.0524593	+	0.0243161i
$889$	−6.89191			−0.231147
$890$	2.32525			0.0779427
$891$	29.8420	−	0.674783i	0.999744	−	0.0226061i
$892$	31.5831			1.05748
$893$	−24.0076			−0.803385
$894$	43.8122	−	20.3079i	1.46530	−	0.679199i
$895$	−2.54943			−0.0852180
$896$		−	6.46859i		−	0.216100i
$897$	−31.3792	+	14.5449i	−1.04772	+	0.485641i
$898$			29.9878i			1.00071i
$899$	62.2042			2.07463
$900$	−3.02644	+	3.57341i	−0.100881	+	0.119114i
$901$			8.56040i			0.285188i
$902$	−0.295010	+	2.05236i	−0.00982275	+	0.0683361i
$903$	10.2955	−	4.77218i	0.342612	−	0.158808i
$904$			14.2278i			0.473208i
$905$			22.7396i			0.755890i
$906$	−23.7378	−	51.2119i	−0.788637	−	1.70140i
$907$	−35.4494			−1.17708			−0.588539	−	0.808469i	$-0.700297\pi$
$907$	−35.4494			−1.17708			−0.588539	+	0.808469i	$0.700297\pi$
$908$	−2.07248			−0.0687776
$909$	−33.5697	+	39.6367i	−1.11344	+	1.31467i
$910$		−	9.08818i		−	0.301270i
$911$			18.9387i			0.627467i	0.949511	+	0.313733i	$0.101580\pi$
$911$			18.9387i			0.627467i	−0.949511	+	0.313733i	$0.898420\pi$
$912$	−11.5664	−	24.9532i	−0.383001	−	0.826284i
$913$	−6.27674	+	43.6668i	−0.207730	+	1.44516i
$914$			27.7772i			0.918787i
$915$	2.22234	−	1.03011i	0.0734685	−	0.0340543i
$916$	38.2067			1.26239
$917$			7.32535i			0.241904i
$918$	17.1690	−	62.3586i	0.566662	−	2.05814i
$919$			52.8522i			1.74343i	0.490010	+	0.871717i	$0.336993\pi$
$919$			52.8522i			1.74343i	−0.490010	+	0.871717i	$0.663007\pi$
$920$	3.43527			0.113257
$921$	−14.9364	−	32.2238i	−0.492173	−	1.06181i
$922$	−18.0984			−0.596041
$923$	26.1751			0.861563
$924$	−8.58917	+	2.57508i	−0.282563	+	0.0847139i
$925$	1.20065			0.0394772
$926$	39.8981			1.31113
$927$	14.6368	−	17.2821i	0.480737	−	0.567619i
$928$	−58.8516			−1.93190
$929$		−	1.06166i		−	0.0348319i	−0.999848	−	0.0174160i	$-0.994456\pi$
$929$		−	1.06166i		−	0.0348319i	0.999848	−	0.0174160i	$-0.00554395\pi$
$930$	−10.4376	−	22.5181i	−0.342264	−	0.738397i
$931$		−	3.38911i		−	0.111074i
$932$	11.3073			0.370384
$933$	3.32327	+	7.16959i	0.108799	+	0.234722i
$934$			54.0348i			1.76807i
$935$	−21.6548	−	3.11270i	−0.708189	−	0.101796i
$936$	9.13496	+	7.73672i	0.298585	+	0.252883i
$937$		−	34.1861i		−	1.11681i	−0.829568	−	0.558406i	$-0.811413\pi$
$937$		−	34.1861i		−	1.11681i	0.829568	−	0.558406i	$-0.188587\pi$
$938$			23.8058i			0.777288i
$939$	−29.4618	+	13.6562i	−0.961451	+	0.445654i
$940$	11.0573			0.360649
$941$	−13.3160			−0.434088			−0.217044	−	0.976162i	$-0.569642\pi$
$941$	−13.3160			−0.434088			−0.217044	+	0.976162i	$0.569642\pi$
$942$	−24.3349	+	11.2798i	−0.792873	+	0.367514i
$943$		−	1.37361i		−	0.0447309i
$944$		−	61.7967i		−	2.01131i
$945$	1.37932	−	5.00974i	0.0448692	−	0.162967i
$946$	−40.5868	−	5.83402i	−1.31959	−	0.189680i
$947$			51.6096i			1.67709i	0.544834	+	0.838544i	$0.316593\pi$
$947$			51.6096i			1.67709i	−0.544834	+	0.838544i	$0.683407\pi$
$948$	−9.70347	−	20.9342i	−0.315154	−	0.679911i
$949$	40.9547			1.32945
$950$			6.39539i			0.207494i
$951$	0.389735	+	0.840811i	0.0126380	+	0.0272652i
$952$		−	5.46528i		−	0.177131i
$953$	−5.87208			−0.190215			−0.0951077	−	0.995467i	$-0.530320\pi$
$953$	−5.87208			−0.190215			−0.0951077	+	0.995467i	$0.530320\pi$
$954$	5.60628	+	4.74816i	0.181510	+	0.153727i
$955$	−14.3775			−0.465246
$956$	6.45320			0.208712
$957$	−13.5137	−	45.0750i	−0.436836	−	1.45707i
$958$	22.9035			0.739979
$959$	−10.8763			−0.351213
$960$	3.04947	+	6.57891i	0.0984213	+	0.212334i
$961$	26.6636			0.860117
$962$			10.9117i			0.351809i
$963$	20.8924	−	24.6682i	0.673247	−	0.794921i
$964$		−	20.1204i		−	0.648033i
$965$	4.94027			0.159033
$966$	12.2950	−	5.69900i	0.395585	−	0.183362i
$967$		−	28.7927i		−	0.925911i	−0.886382	−	0.462956i	$-0.846789\pi$
$967$		−	28.7927i		−	0.925911i	0.886382	−	0.462956i	$-0.153211\pi$
$968$	−8.74494	−	2.56707i	−0.281073	−	0.0825086i
$969$	−16.2837	−	35.1304i	−0.523109	−	1.12855i
$970$			34.6059i			1.11113i
$971$		−	12.5992i		−	0.404327i	−0.979352	−	0.202164i	$-0.935203\pi$
$971$		−	12.5992i		−	0.404327i	0.979352	−	0.202164i	$-0.0647973\pi$
$972$	−13.7274	−	20.0906i	−0.440307	−	0.644405i
$973$	−12.0609			−0.386656
$974$	57.8002			1.85204
$975$	−3.50804	−	7.56822i	−0.112347	−	0.242377i
$976$		−	6.62606i		−	0.212095i
$977$			46.9448i			1.50190i	0.660360	+	0.750949i	$0.270404\pi$
$977$			46.9448i			1.50190i	−0.660360	+	0.750949i	$0.729596\pi$
$978$	−8.96153	+	4.15387i	−0.286558	+	0.132826i
$979$	4.04524	+	0.581469i	0.129286	+	0.0185838i
$980$			1.56093i			0.0498622i
$981$	−3.61248	−	3.05954i	−0.115338	−	0.0976836i
$982$	43.5346			1.38924
$983$		−	22.4243i		−	0.715223i	−0.933871	−	0.357611i	$-0.883591\pi$
$983$		−	22.4243i		−	0.715223i	0.933871	−	0.357611i	$-0.116409\pi$
$984$	−0.431349	+	0.199940i	−0.0137509	+	0.00637385i
$985$		−	17.5393i		−	0.558847i
$986$	−101.965			−3.24722
$987$	−11.1317	+	5.15981i	−0.354327	+	0.164239i
$988$	−25.4779			−0.810561
$989$	27.1641			0.863768
$990$	−14.0497	+	12.4554i	−0.446529	+	0.395859i
$991$	−10.4851			−0.333070			−0.166535	−	0.986036i	$-0.553258\pi$
$991$	−10.4851			−0.333070			−0.166535	+	0.986036i	$0.553258\pi$
$992$	−54.5558			−1.73215
$993$	−44.1309	+	20.4556i	−1.40045	+	0.649140i
$994$	−10.2559			−0.325298
$995$		−	4.87616i		−	0.154585i
$996$	32.6271	−	15.1234i	1.03383	−	0.479203i
$997$			25.6354i			0.811880i	0.913900	+	0.405940i	$0.133056\pi$
$997$			25.6354i			0.811880i	−0.913900	+	0.405940i	$0.866944\pi$
$998$	−33.5528			−1.06209
$999$	−1.65608	+	6.01495i	−0.0523960	+	0.190305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.9	✓	40
3.2	odd	2		1155.2.l.f.1121.32	yes	40
11.10	odd	2		1155.2.l.f.1121.31	yes	40
33.32	even	2	inner	1155.2.l.e.1121.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.9	✓	40	1.1	even	1	trivial
1155.2.l.e.1121.10	yes	40	33.32	even	2	inner
1155.2.l.f.1121.31	yes	40	11.10	odd	2
1155.2.l.f.1121.32	yes	40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.88704 q^{2} +(1.57144 - 0.728399i) q^{3} +1.56093 q^{4} -1.00000i q^{5} +(-2.96538 + 1.37452i) q^{6} +1.00000i q^{7} +0.828540 q^{8} +(1.93887 - 2.28928i) q^{9} +O(q^{10})\)	\(q-1.88704 q^{2} +(1.57144 - 0.728399i) q^{3} +1.56093 q^{4} -1.00000i q^{5} +(-2.96538 + 1.37452i) q^{6} +1.00000i q^{7} +0.828540 q^{8} +(1.93887 - 2.28928i) q^{9} +1.88704i q^{10} +(-0.471887 + 3.28288i) q^{11} +(2.45292 - 1.13698i) q^{12} +4.81609i q^{13} -1.88704i q^{14} +(-0.728399 - 1.57144i) q^{15} -4.68535 q^{16} -6.59628 q^{17} +(-3.65873 + 4.31996i) q^{18} +3.38911i q^{19} -1.56093i q^{20} +(0.728399 + 1.57144i) q^{21} +(0.890472 - 6.19494i) q^{22} +4.14617i q^{23} +(1.30200 - 0.603508i) q^{24} -1.00000 q^{25} -9.08818i q^{26} +(1.37932 - 5.00974i) q^{27} +1.56093i q^{28} -8.19160 q^{29} +(1.37452 + 2.96538i) q^{30} -7.59366 q^{31} +7.18439 q^{32} +(1.64971 + 5.50259i) q^{33} +12.4475 q^{34} +1.00000 q^{35} +(3.02644 - 3.57341i) q^{36} -1.20065 q^{37} -6.39539i q^{38} +(3.50804 + 7.56822i) q^{39} -0.828540i q^{40} -0.331296 q^{41} +(-1.37452 - 2.96538i) q^{42} -6.55160i q^{43} +(-0.736584 + 5.12436i) q^{44} +(-2.28928 - 1.93887i) q^{45} -7.82401i q^{46} +7.08376i q^{47} +(-7.36277 + 3.41281i) q^{48} -1.00000 q^{49} +1.88704 q^{50} +(-10.3657 + 4.80473i) q^{51} +7.51760i q^{52} -1.29776i q^{53} +(-2.60283 + 9.45359i) q^{54} +(3.28288 + 0.471887i) q^{55} +0.828540i q^{56} +(2.46862 + 5.32579i) q^{57} +15.4579 q^{58} +13.1893i q^{59} +(-1.13698 - 2.45292i) q^{60} +1.41421i q^{61} +14.3296 q^{62} +(2.28928 + 1.93887i) q^{63} -4.18654 q^{64} +4.81609 q^{65} +(-3.11307 - 10.3836i) q^{66} -12.6154 q^{67} -10.2964 q^{68} +(3.02007 + 6.51548i) q^{69} -1.88704 q^{70} -5.43492i q^{71} +(1.60643 - 1.89676i) q^{72} -8.50372i q^{73} +2.26568 q^{74} +(-1.57144 + 0.728399i) q^{75} +5.29017i q^{76} +(-3.28288 - 0.471887i) q^{77} +(-6.61982 - 14.2816i) q^{78} -8.53441i q^{79} +4.68535i q^{80} +(-1.48157 - 8.87721i) q^{81} +0.625170 q^{82} +13.3014 q^{83} +(1.13698 + 2.45292i) q^{84} +6.59628i q^{85} +12.3632i q^{86} +(-12.8726 + 5.96675i) q^{87} +(-0.390977 + 2.72000i) q^{88} -1.23222i q^{89} +(4.31996 + 3.65873i) q^{90} -4.81609 q^{91} +6.47190i q^{92} +(-11.9330 + 5.53121i) q^{93} -13.3674i q^{94} +3.38911 q^{95} +(11.2899 - 5.23310i) q^{96} +18.3387 q^{97} +1.88704 q^{98} +(6.60050 + 7.44536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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